CAN版本，后续更新

.clang-format

@@ -0,0 +1,280 @@
+---
+# 语言: None, Cpp, Java, JavaScript, ObjC, Proto, TableGen, TextProto
+Language:        Cpp
+# BasedOnStyle:  LLVM
+# 访问说明符(public、private等)的偏移
+AccessModifierOffset: -4
+# 开括号(开圆括号、开尖括号、开方括号)后的对齐: Align, DontAlign, AlwaysBreak(总是在开括号后换行)
+AlignAfterOpenBracket: Align
+# 对齐数组列
+AlignArrayOfStructures: None
+# 对齐连续宏定义
+AlignConsecutiveMacros: true
+# 连续赋值时，对齐所有等号
+AlignConsecutiveAssignments: true
+# 对齐连续位字段
+AlignConsecutiveBitFields: true
+# 连续声明时，对齐所有声明的变量名
+AlignConsecutiveDeclarations: true
+# 左对齐逃脱换行(使用反斜杠换行)的反斜杠
+AlignEscapedNewlines: Right
+# 水平对齐二元和三元表达式的操作数
+AllowAllArgumentsOnNextLine: true
+AllowAllConstructorInitializersOnNextLine: true
+AlwaysBreakAfterDefinitionReturnType: None
+AlignOperands:   Align
+# 对齐连续的尾随的注释
+AlignTrailingComments: true
+# 允许函数声明的所有参数在放在下一行
+AllowAllParametersOfDeclarationOnNextLine: true
+# 允许短的枚举放在同一行
+AllowShortEnumsOnASingleLine: true
+# 允许短的块放在同一行
+AllowShortBlocksOnASingleLine: Never
+# 允许短的case标签放在同一行
+AllowShortCaseLabelsOnASingleLine: false
+# 允许短的函数放在同一行
+AllowShortFunctionsOnASingleLine: All
+# 允许短的匿名函数放在同一行
+AllowShortLambdasOnASingleLine: All
+# 允许短的if语句保持在同一行
+AllowShortIfStatementsOnASingleLine: Never
+# 允许短的循环保持在同一行
+AllowShortLoopsOnASingleLine: false
+# 总是在返回类型后换行
+AlwaysBreakAfterReturnType: None
+# 总是在多行string字面量前换行
+AlwaysBreakBeforeMultilineStrings: false
+# 总是在template声明后换行
+AlwaysBreakTemplateDeclarations: MultiLine
+AttributeMacros:
+  - __capability
+# false表示函数实参要么都在同一行，要么都各自一行
+BinPackArguments: true
+# false表示所有形参要么都在同一行，要么都各自一行
+BinPackParameters: true
+# 大括号换行，只有当BreakBeforeBraces设置为Custom时才有效
+BraceWrapping:
+  AfterCaseLabel:  false
+  AfterClass:      false
+  AfterControlStatement: Never
+  AfterEnum:       false
+  AfterFunction:   false
+  AfterNamespace:  false
+  AfterObjCDeclaration: false
+  AfterStruct:     false
+  AfterUnion:      false
+  AfterExternBlock: false
+  BeforeCatch:     false
+  BeforeElse:      false
+  BeforeLambdaBody: false
+  BeforeWhile:     false
+  IndentBraces:    false
+  SplitEmptyFunction: true
+  SplitEmptyRecord: true
+  SplitEmptyNamespace: true
+# 在二元运算符前换行
+BreakBeforeBinaryOperators: None
+# 在concept前换行
+BreakBeforeConceptDeclarations: true
+# 在大括号前换行: Attach(始终将大括号附加到周围的上下文)
+BreakBeforeBraces: Allman
+BreakBeforeInheritanceComma: false
+# 继承列表样式
+BreakInheritanceList: AfterComma
+# 在三元运算符前换行
+BreakBeforeTernaryOperators: true
+# 构造函数初始值设定项换行样式
+BreakConstructorInitializers: BeforeComma
+# 在java字段的注释后换行
+BreakAfterJavaFieldAnnotations: false
+# 每行字符的限制，0表示没有限制
+ColumnLimit:     0
+# 描述具有特殊意义的注释的正则表达式，它不应该被分割为多行或以其它方式改变
+CommentPragmas:  '^ IWYU pragma:'
+# 在新行上声明每个命名空间
+CompactNamespaces: false
+# 构造函数的初始化列表的缩进宽度
+ConstructorInitializerIndentWidth: 4
+# 延续的行的缩进宽度
+ContinuationIndentWidth: 4
+# 去除C++11的列表初始化的大括号{后和}前的空格
+Cpp11BracedListStyle: true
+# 继承最常用的换行方式
+DeriveLineEnding: true
+# 继承最常用的指针和引用的对齐方式
+DerivePointerAlignment: false
+# 关闭格式化
+DisableFormat:   false
+# 删除访问修饰符后的所有空行
+EmptyLineAfterAccessModifier: Never
+# 仅当访问修饰符开始一个新的逻辑块时才添加空行
+EmptyLineBeforeAccessModifier: LogicalBlock
+# 自动检测函数的调用和定义是否被格式为每行一个参数(Experimental)
+ExperimentalAutoDetectBinPacking: false
+# 自动补充namespace注释
+FixNamespaceComments: true
+# 需要被解读为foreach循环而不是函数调用的宏
+ForEachMacros:
+  - foreach
+  - Q_FOREACH
+  - BOOST_FOREACH
+IfMacros:
+  - KJ_IF_MAYBE
+# 多个#include块合并在一起并排序为一个
+IncludeBlocks:   Merge
+# 可以定义负数优先级从而保证某些#include永远在最前面
+IncludeCategories:
+  - Regex:           '^"(llvm|llvm-c|clang|clang-c)/'
+    Priority:        2
+    SortPriority:    0
+    CaseSensitive:   false
+  - Regex:           '^(<|"(gtest|gmock|isl|json)/)'
+    Priority:        3
+    SortPriority:    0
+    CaseSensitive:   false
+  - Regex:           '.*'
+    Priority:        1
+    SortPriority:    0
+    CaseSensitive:   false
+IncludeIsMainRegex: '(Test)?$'
+IncludeIsMainSourceRegex: ''
+# 缩进访问修饰符
+IndentAccessModifiers: false
+# 缩进case标签
+IndentCaseLabels: false
+# case 标签后面的块使用与 case 标签相同的缩进级别
+IndentCaseBlocks: false
+# 缩进goto标签。
+IndentGotoLabels: false
+# 缩进预处理器指令
+IndentPPDirectives: None
+# 向后兼容缩进外部块
+IndentExternBlock: AfterExternBlock
+# 缩进模板中的requires子句
+IndentRequires:  false
+# 缩进宽度
+IndentWidth:     4
+# 函数返回类型换行时，缩进函数声明或函数定义的函数名
+IndentWrappedFunctionNames: false
+# 插入尾随逗号
+InsertTrailingCommas: None
+# 保留JavaScript字符串引号
+JavaScriptQuotes: Leave
+# 包装 JavaScript 导入/导出语句
+JavaScriptWrapImports: true
+# 保留在块开始处的空行
+KeepEmptyLinesAtTheStartOfBlocks: true
+# 相对于 lambda 签名对齐 lambda 主体
+LambdaBodyIndentation: Signature
+# 开始一个块的宏的正则表达式
+MacroBlockBegin: ''
+# 结束一个块的宏的正则表达式
+MacroBlockEnd:   ''
+# 连续空行的最大数量
+MaxEmptyLinesToKeep: 1
+# 命名空间的缩进
+NamespaceIndentation: None
+ObjCBinPackProtocolList: Auto
+# 使用ObjC块时缩进宽度
+ObjCBlockIndentWidth: 4
+ObjCBreakBeforeNestedBlockParam: true
+# 在ObjC的@property后添加一个空格
+ObjCSpaceAfterProperty: false
+# 在ObjC的protocol列表前添加一个空格
+ObjCSpaceBeforeProtocolList: true
+PenaltyBreakAssignment: 2
+PenaltyBreakBeforeFirstCallParameter: 19
+PenaltyBreakComment: 300
+PenaltyBreakFirstLessLess: 120
+PenaltyBreakString: 1000
+PenaltyBreakTemplateDeclaration: 10
+PenaltyExcessCharacter: 1000000
+PenaltyReturnTypeOnItsOwnLine: 60
+PenaltyIndentedWhitespace: 0
+# 指针的对齐: Left, Right, Middle
+PointerAlignment: Right
+# 缩进预处理器语句的列数
+PPIndentWidth:   -1
+# 引用的对齐
+ReferenceAlignment: Pointer
+# 允许重新排版注释
+ReflowComments:  true
+# 短命名空间跨越的最大展开行数
+ShortNamespaceLines: 1
+# 允许排序#include
+SortIncludes:    true
+# java静态导入放在非静态导入之前
+SortJavaStaticImport: Before
+# 对using声明排序
+SortUsingDeclarations: true
+# 在C风格类型转换后添加空格
+SpaceAfterCStyleCast: false
+# 在!后添加空格
+SpaceAfterLogicalNot: false
+# 在Template关键字后添加空格
+SpaceAfterTemplateKeyword: true
+# 在赋值运算符之前添加空格
+SpaceBeforeAssignmentOperators: true
+# 不在case冒号之前添加空格
+SpaceBeforeCaseColon: false
+# 不在C++11大括号列表之前添加空格
+SpaceBeforeCpp11BracedList: false
+# 在构造函数初始化器冒号之前添加空格
+SpaceBeforeCtorInitializerColon: true
+# 在继承冒号前添加空格
+SpaceBeforeInheritanceColon: true
+# 开圆括号之前添加一个空格: Never, ControlStatements, Always
+SpaceBeforeParens: ControlStatements
+# 不要确保指针限定符周围有空格，而是使用 PointerAlignment
+SpaceAroundPointerQualifiers: Default
+# 在基于范围的for循环冒号之前添加空格
+SpaceBeforeRangeBasedForLoopColon: true
+# {}中间不添加空格
+SpaceInEmptyBlock: false
+# 在空的圆括号中添加空格
+SpaceInEmptyParentheses: false
+# 在尾随的评论前添加的空格数(只适用于//)
+SpacesBeforeTrailingComments: 1
+# 在尖括号的<后和>前添加空格
+SpacesInAngles:  Never
+# 不在if/for/switch/while条件周围插入空格
+SpacesInConditionalStatement: false
+# 在容器(ObjC和JavaScript的数组和字典等)字面量中添加空格
+SpacesInContainerLiterals: true
+# 在C风格类型转换的括号中添加空格
+SpacesInCStyleCastParentheses: false
+# 行注释开头允许有多少个空格。要禁用最大值，请将其设置为-1，除此之外，最大值优先于最小值
+SpacesInLineCommentPrefix:
+  Minimum:         1
+  Maximum:         -1
+# 在圆括号的(后和)前添加空格
+SpacesInParentheses: false
+# 在方括号的[后和]前添加空格，lamda表达式和未指明大小的数组的声明不受影响
+SpacesInSquareBrackets: false
+# 不在[前添加空格
+SpaceBeforeSquareBrackets: false
+# 位域:每边都添加空格
+BitFieldColonSpacing: Both
+# 标准
+Standard:        Latest
+# 在语句前面被忽略的宏定义，就好像它们是一个属性一样
+StatementAttributeLikeMacros:
+  - Q_EMIT
+# 应该被解释为完整语句的宏定义
+StatementMacros:
+  - Q_UNUSED
+  - QT_REQUIRE_VERSION
+# tab宽度
+TabWidth:        4
+# 使用\n换行
+UseCRLF:         false
+# 使用tab字符：ForIndentation——仅将制表符用于缩进
+UseTab:          Never
+# 对空格敏感的宏定义
+WhitespaceSensitiveMacros:
+  - STRINGIZE
+  - PP_STRINGIZE
+  - BOOST_PP_STRINGIZE
+  - NS_SWIFT_NAME
+  - CF_SWIFT_NAME

.gitignore

@@ -0,0 +1,16 @@
+# Mac
+.DS_Store
+*/.DS_Store
+
+# vscode 
+.vscode
+.vscode/
+
+# idea
+.idea
+.idea/
+
+.cache
+Project/GCC/build
+compile_commands.json
+**/Thumbs.db

CMakeLists.txt

@@ -0,0 +1,171 @@
+cmake_minimum_required(VERSION 3.20)
+
+
+# 项目设置
+project(armfly_bootloader)
+enable_language(C CXX ASM)
+message("Build type: " ${CMAKE_BUILD_TYPE})
+
+# 编译脚本设置
+set(CMAKE_C_STANDARD 11)
+set(CMAKE_C_STANDARD_REQUIRED ON)
+set(CMAKE_C_EXTENSIONS ON)
+set(CMAKE_CXX_STANDARD 20)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_CXX_EXTENSIONS ON)
+
+#添加的部分，关闭警告
+add_definitions(-w)
+
+# MCU 参数设置
+set(MCU_PARAMS
+        -mthumb
+        -mcpu=cortex-m4
+        -mfpu=fpv5-d16
+        -mfloat-abi=hard
+        )
+
+# C 源文件
+set(C_SRCS
+    ${CMAKE_CURRENT_SOURCE_DIR}/Project/main.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Project/stm32f4xx_it.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Project/system_stm32f4xx.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/app/bootloader/bootloader.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/app/global/var.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/app/iap/iap.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/app/queue/queue.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/can/can.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/dwt/dwt.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/led/led.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Project/GCC/startup_stm32f40xx.s
+    ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/src/misc.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/src/stm32f4xx_can.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/src/stm32f4xx_flash.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/src/stm32f4xx_rcc.c
+    ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/src/stm32f4xx_gpio.c
+)
+
+# C .h文件
+set(INC_C_DIRS
+        ${CMAKE_CURRENT_SOURCE_DIR}/Project
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/led
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/dwt
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/bsp/can
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/app/bootloader
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/app/iap
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/app/global
+        ${CMAKE_CURRENT_SOURCE_DIR}/User/app/queue
+        ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/CMSIS/Include
+        ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/CMSIS/Device/ST/STM32F4xx/Include
+        ${CMAKE_CURRENT_SOURCE_DIR}/Libraries/STM32F4xx_StdPeriph_Driver/inc
+        )
+
+set(INC_CXX_DIRS)
+set(INC_ASM_DIRS)
+
+# 链接定义
+set(C_SYMB
+        "DEBUG"
+        "STM32F40_41xxx"
+        "USE_STDPERIPH_DRIVER"
+        )
+set(CXX_SYMB)
+set(ASM_SYMB)
+
+# 链接静态库或者文件夹
+set(LINK_DIRS)
+set(LINK_LIBS)
+
+# 链接脚本
+set(LINK_SRC
+        ${CMAKE_CURRENT_SOURCE_DIR}/Project/GCC/STM32F417IG_FLASH.ld
+        )
+
+# 编译器参数
+set(compiler_OPTS)
+
+# 链接脚本参数
+set(LINK_OPTS)
+
+
+link_directories(${CMAKE_PROJECT_NAME} ${LINK_DIRS})
+add_executable(${CMAKE_PROJECT_NAME})
+target_sources(${CMAKE_PROJECT_NAME} PUBLIC ${C_SRCS})
+
+# 添加 include 路径
+target_include_directories(${CMAKE_PROJECT_NAME} PRIVATE
+        $<$<COMPILE_LANGUAGE:C>: ${INC_C_DIRS}>
+        $<$<COMPILE_LANGUAGE:CXX>: ${INC_CXX_DIRS}>
+        $<$<COMPILE_LANGUAGE:ASM>: ${INC_ASM_DIRS}>
+        )
+
+# 添加 链接 文件
+target_compile_definitions(${CMAKE_PROJECT_NAME} PRIVATE
+        $<$<COMPILE_LANGUAGE:C>: ${C_SYMB}>
+        $<$<COMPILE_LANGUAGE:CXX>: ${CXX_SYMB}>
+        $<$<COMPILE_LANGUAGE:ASM>: ${ASM_SYMB}>
+
+        $<$<CONFIG:Debug>:DEBUG>
+        $<$<CONFIG:Release>: >
+        )
+
+target_link_libraries(${CMAKE_PROJECT_NAME} ${LINK_LIBS})
+
+# 编译器参数
+target_compile_options(${CMAKE_PROJECT_NAME} PRIVATE
+        ${MCU_PARAMS}
+        ${compiler_OPTS}
+        -Wall
+        -Wextra
+        -Wpedantic
+        $<$<COMPILE_LANGUAGE:C>: >
+        $<$<COMPILE_LANGUAGE:CXX>:
+
+        # 去除编译警告
+        -Wno-unused-parameter
+        -Wno-unused-variable
+        -Wno-pointer-sign
+        -Wno-unused-but-set-variable
+        # -Wno-volatile
+        # -Wold-style-cast
+        # -Wuseless-cast
+        # -Wsuggest-override
+        >
+        $<$<COMPILE_LANGUAGE:ASM>:-x assembler-with-cpp -MMD -MP>
+        $<$<CONFIG:Debug>:-Og -g3 -ggdb>
+        $<$<CONFIG:Release>:-Og -g0>
+        )
+
+# 链接参数
+target_link_options(${CMAKE_PROJECT_NAME} PRIVATE
+        -T${LINK_SRC}
+        ${MCU_PARAMS}
+        ${LINK_OPTS}
+        -Wl,-Map=${CMAKE_PROJECT_NAME}.map
+#        -u _printf_float
+        --specs=nosys.specs
+        -Wl,--start-group
+        -lc
+        -lm
+        -lstdc++
+        -lsupc++
+        -Wl,--end-group
+        # Allow good software remapping across address space (with proper GCC section making)
+        -Wl,-z,max-page-size=8
+        -Wl,--print-memory-usage
+        )
+
+# post-build
+add_custom_command(TARGET ${CMAKE_PROJECT_NAME} POST_BUILD
+        COMMAND ${CMAKE_SIZE} $<TARGET_FILE:${CMAKE_PROJECT_NAME}>
+        )
+
+# 生成 hex 文件
+add_custom_command(TARGET ${CMAKE_PROJECT_NAME} POST_BUILD
+        COMMAND ${CMAKE_OBJCOPY} -O ihex $<TARGET_FILE:${CMAKE_PROJECT_NAME}> ${CMAKE_PROJECT_NAME}.hex
+        )
+
+# 生成 bin 文件
+add_custom_command(TARGET ${CMAKE_PROJECT_NAME} POST_BUILD
+        COMMAND ${CMAKE_OBJCOPY} -O binary $<TARGET_FILE:${CMAKE_PROJECT_NAME}> ${CMAKE_PROJECT_NAME}.bin
+        )

CMakePresets.json

@@ -0,0 +1,61 @@
+{
+    "version": 3,
+    "configurePresets": [
+        {
+            "name": "default",
+            "hidden": true,
+            "generator": "Ninja",
+            "binaryDir": "${sourceDir}/Project/GCC/build/${presetName}",
+            "toolchainFile": "${sourceDir}/Project/GCC/cmake/gcc-arm-none-eabi.cmake",
+            "cacheVariables": {
+                "CMAKE_EXPORT_COMPILE_COMMANDS": "ON"
+            }
+        },
+        {
+            "name": "Debug",
+            "inherits": "default",
+            "cacheVariables": {
+                "CMAKE_BUILD_TYPE": "Debug"
+            }
+        },
+        {
+            "name": "RelWithDebInfo",
+            "inherits": "default",
+            "cacheVariables": {
+                "CMAKE_BUILD_TYPE": "RelWithDebInfo"
+            }
+        },
+        {
+            "name": "Release",
+            "inherits": "default",
+            "cacheVariables": {
+                "CMAKE_BUILD_TYPE": "Release"
+            }
+        },
+        {
+            "name": "MinSizeRel",
+            "inherits": "default",
+            "cacheVariables": {
+                "CMAKE_BUILD_TYPE": "MinSizeRel"
+            }
+        }
+    ],
+    "buildPresets": [
+        {
+            "name": "Debug",
+            "configurePreset": "Debug"
+        },
+        {
+            "name": "RelWithDebInfo",
+            "configurePreset": "RelWithDebInfo"
+        },
+        {
+            "name": "Release",
+            "configurePreset": "Release"
+        },
+        {
+            "name": "MinSizeRel",
+            "configurePreset": "MinSizeRel"
+        }
+    ]
+}

Doc/说明.md

@@ -0,0 +1,8 @@
+# STM32 固件库学习
+
+1. Build 目录为编译文件夹
+2. Doc 为文档说明目录
+3. Libraries 为固件库存储目录
+4. MiddleWare 为中间件存储目录
+5. Project 为项目启动文件所在目录
+6. User 应用层以及板极固件所在目录

Libraries/CMSIS/CMSIS_END_USER_LICENCE_AGREEMENT.rtf

@@ -0,0 +1,793 @@
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+{\f2\fbidi \fmodern\fcharset0\fprq1{\*\panose 02070309020205020404}Courier New;}{\f3\fbidi \froman\fcharset2\fprq2{\*\panose 05050102010706020507}Symbol;}{\f10\fbidi \fnil\fcharset2\fprq2{\*\panose 05000000000000000000}Wingdings;}
+{\f14\fbidi \froman\fcharset136\fprq2{\*\panose 02020500000000000000}PMingLiU{\*\falt \'b7\'73\'b2\'d3\'a9\'fa\'c5\'e9};}{\f34\fbidi \froman\fcharset0\fprq2{\*\panose 02040503050406030204}Cambria Math;}
+{\f37\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}{\f38\fbidi \fswiss\fcharset0\fprq2{\*\panose 020b0604030504040204}Tahoma;}{\f39\fbidi \fmodern\fcharset0\fprq1{\*\panose 020b0609020204030204}Consolas;}
+{\f40\fbidi \froman\fcharset136\fprq2{\*\panose 02020500000000000000}@PMingLiU;}{\flomajor\f31500\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
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+{\fbiminor\f31507\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f41\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\f42\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
+{\f44\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\f45\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\f46\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\f47\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
+{\f48\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\f49\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\f51\fbidi \fswiss\fcharset238\fprq2 Arial CE;}{\f52\fbidi \fswiss\fcharset204\fprq2 Arial Cyr;}
+{\f54\fbidi \fswiss\fcharset161\fprq2 Arial Greek;}{\f55\fbidi \fswiss\fcharset162\fprq2 Arial Tur;}{\f56\fbidi \fswiss\fcharset177\fprq2 Arial (Hebrew);}{\f57\fbidi \fswiss\fcharset178\fprq2 Arial (Arabic);}
+{\f58\fbidi \fswiss\fcharset186\fprq2 Arial Baltic;}{\f59\fbidi \fswiss\fcharset163\fprq2 Arial (Vietnamese);}{\f61\fbidi \fmodern\fcharset238\fprq1 Courier New CE;}{\f62\fbidi \fmodern\fcharset204\fprq1 Courier New Cyr;}
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+{\f68\fbidi \fmodern\fcharset186\fprq1 Courier New Baltic;}{\f69\fbidi \fmodern\fcharset163\fprq1 Courier New (Vietnamese);}{\f183\fbidi \froman\fcharset0\fprq2 PMingLiU Western{\*\falt \'b7\'73\'b2\'d3\'a9\'fa\'c5\'e9};}
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+{\f388\fbidi \froman\fcharset186\fprq2 Cambria Math Baltic;}{\f389\fbidi \froman\fcharset163\fprq2 Cambria Math (Vietnamese);}{\f411\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}{\f412\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}
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+\fs22\lang2057\langfe1033\loch\af37\hich\af37\dbch\af37\cgrid\langnp2057\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1198806 \chftnsepc 
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+\fs22\lang2057\langfe1033\loch\af37\hich\af37\dbch\af37\cgrid\langnp2057\langfenp1033 {\rtlch\fcs1 \af1 \ltrch\fcs0 \fs18\loch\af1\hich\af1\dbch\af1\insrsid11754636 \hich\af1\dbch\af1\loch\f1 1 June 2014\cell }\pard \ltrpar\qc \li0\ri0\sa200\sl276\slmult1
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+\fs18\loch\af1\hich\af1\dbch\af1\insrsid11754636 \hich\af1\dbch\af1\loch\f1 PAGE}}{\fldrslt {\rtlch\fcs1 \af1 \ltrch\fcs0 \fs18\lang1024\langfe1024\loch\af1\hich\af1\dbch\af1\noproof\insrsid9508363 \hich\af1\dbch\af1\loch\f1 4}}}\sectd \ltrsect
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+\cltxlrtb\clftsWidth3\clwWidth4513\clshdrawnil \cellx4405\clvertalt\clbrdrt\brdrtbl \clbrdrl\brdrtbl \clbrdrb\brdrtbl \clbrdrr\brdrtbl \cltxlrtb\clftsWidth3\clwWidth4513\clshdrawnil \cellx8918\row }\pard \ltrpar\ql \li0\ri0\sa200\sl276\slmult1
+\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11754636 
+\par }}{\*\pnseclvl1\pnucrm\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl2\pnucltr\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang {\pntxta )}}
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+\pnlcltr\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}\pard\plain \ltrpar\qj \li0\ri0\sa240\widctlpar
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+\fs22\lang2057\langfe1033\loch\af37\hich\af37\dbch\af37\cgrid\langnp2057\langfenp1033 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 END USER LICENCE AGREEMENT FOR THE }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CORTEX MICROCONTROLLER SOFTWARE INTERFACE STANDARD (CMSIS) DELIVERABLES }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+\par THIS END USER LICENCE AGREEMENT ("LICENCE") IS A LEGAL AGREEMENT BETWEEN YOU (EITHER A }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid5861575 
+SINGLE INDIVIDUAL, OR SINGLE LEGAL ENTITY) AND ARM LIMITED ("ARM") FOR THE USE OF THE CMSIS }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 DELIVERABLES}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid5861575 . ARM IS ONLY WILLING TO LICENSE THE }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid5861575 TO YOU ON CONDITION THAT YOU ACCEPT ALL OF THE}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  TERMS IN THIS LICENCE. BY CLICKING "I AGREE", OR BY INSTALLING OR OTHERWISE USING OR COPYING THE }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+YOU INDICATE THAT YOU AGREE TO BE BOUND BY ALL THE TERMS OF THIS LICENCE. IF YOU DO NOT AGREE TO THE TERMS OF THIS LICENCE, ARM IS UNWILLING TO LICENSE YOU TO USE }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 OF }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 THE }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  AND YOU MAY NOT INSTALL, USE OR COPY THE }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 .
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'93
+CMSIS Deliverables\'94 means the following components: (i) CMSIS-CORE; (ii) CMSIS-DRIVER; (iii) CMSIS-DSP; (iv) CMSIS-PACK; (v) CMSIS-RTOS API; and (vi) CMSIS-SVD . 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\tx0\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'93CMSIS-CORE
+\'94 means the specification defining the application programming interface, naming and coding conventions for the Cortex-M processor cores.
+\par \'94}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid488451 \hich\af1\dbch\af37\loch\f1 CMSIS-DRIVER}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'94}{\rtlch\fcs1 \af0 \ltrch\fcs0 
+\insrsid11754636 \hich\af37\dbch\af37\loch\f37  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid488451 \hich\af1\dbch\af37\loch\f1 means the specification defining }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\hich\af1\dbch\af37\loch\f1 a generic}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid488451 \hich\af1\dbch\af37\loch\f1  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 p}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid488451 \hich\af1\dbch\af37\loch\f1 eripheral }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 d}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\insrsid11754636\charrsid488451 \hich\af1\dbch\af37\loch\f1 river application programming interface, naming and coding conventions}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11754636 .
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  \'93CMSIS-DSP\'94
+ means the digital signal process (DSP) library specification defining the application programming interface of a DSP library implementation}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15023647 .}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\tx0\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'93}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13240697 \hich\af1\dbch\af37\loch\f1 CMSIS-PACK}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'94}{\rtlch\fcs1 \af0 \ltrch\fcs0 
+\insrsid11754636\charrsid13240697 \hich\af37\dbch\af37\loch\f37  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13240697 \hich\af1\dbch\af37\loch\f1 means the specification defining a software pack file format}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 , verification utility, }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13240697 \hich\af1\dbch\af37\loch\f1 and the associated XML schema file}{\rtlch\fcs1 
+\af0 \ltrch\fcs0 \insrsid11754636\charrsid13240697 .}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11754636 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \'93CMSIS-RTOS API\'94 means the
+ real-time operating system (RTOS) specification defining a generic application programming interface layer for a RTOS system}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15023647 .}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1 
+Notwithstanding the foregoing, }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4730869 \hich\af1\dbch\af37\loch\f1 the CMSIS D}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4730869 \hich\af1\dbch\af37\loch\f1  shall not}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1  include}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 :}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1  (i) the implementation of other published specification
+\hich\af1\dbch\af37\loch\f1 s }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 referenced }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1 in th}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 e}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 CMSIS Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 \hich\af1\dbch\af37\loch\f1 
+; (ii) any enabling technologies that may be necessary to make or use any product or portion thereof that }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4283548 \hich\af1\dbch\af37\loch\f1 complies with the }{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4283548 \hich\af1\dbch\af37\loch\f1 , but are not themselves expressly set forth in the }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 CMSIS Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4283548 \hich\af1\dbch\af37\loch\f1  (e.\hich\af1\dbch\af37\loch\f1 
+g. compiler front ends, code generators, back ends, libraries or other compiler, assembler or linker technologies; validation or debug software or hardware; applications, operating system or driver software; RISC architecture; processor microarchitecture)
+\hich\af1\dbch\af37\loch\f1 ;\hich\af1\dbch\af37\loch\f1  (iii) maskworks and physical layouts of integrated circuit designs; or (iv) RTL or other high}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid4029239 
+\hich\af1\dbch\af37\loch\f1  level representations of integrated circuit designs.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  \'93CMSIS-SVD\'94 }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid9306407 means }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 the specification defining the System View Description (SVD), verification utility, }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf17\lang1033\langfe2057\langnp1033\langfenp2057\insrsid11754636\charrsid9306407 and associated XML}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf17\lang1033\langfe2057\langnp1033\langfenp2057\insrsid11754636  schema}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\cf17\lang1033\langfe2057\langnp1033\langfenp2057\insrsid11754636\charrsid9306407  files. }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid9306407 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  \'93Separate Files\'94 means the components in }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid10227990 the CMSIS reference implementation identified}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+ in the Schedule that demonstrate the usage of the CMSIS-CORE, CMSIS-DRIVER, CMSIS-DSP, CMSIS-PACK and CMSIS-RTOS API, }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid3618484  for microprocessors 
+or device specific software applications that are for use with microprocessors.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 1. LICENCE GRANTS.
+\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 1.1}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES 
+\par 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 ARM hereby grants to you, subject to the terms and conditions of this Licence, a non-exclusive, non-transferable }{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid1317547 licence, to use and copy the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS D}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 for the purpose of: }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar
+\tx426\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 (i) subject to clause 1.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 2}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 , developing, having developed, manufacturing, having manufactured, offering to sell, selling, supplying or otherwise distributing products that comply with the }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS D}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 ; and 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid1317547 (ii) distributing and having distributed (directly or through your customers and authorised distributors) the CMSIS-D}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid1317547  unmodified, with the products}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135  you have developed under }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 Clause 1.1 (i) }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 provided you preserve any copyright notices which are included with the CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  D}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid6756135 . 
+\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 1.2}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  CONDITIONS ON REDISTRIBUTION}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 .}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 
+\cbpat8 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 \hich\af1\dbch\af37\loch\f1 
+If you distribute (directly or through your customers and authorised distributors) the products you have created pursuant to Clauses 1.1}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1  
+}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 \hich\af1\dbch\af37\loch\f1 (i) you agree: (a) not to use ARM\hich\f1 \rquote \loch\f1 s name\hich\af1\dbch\af37\loch\f1 
+, logo or trademarks to market any or all of the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid1928237 products created under Clause 1.1 (i); }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 \hich\af1\dbch\af37\loch\f1 (b) }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1 to }{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 \hich\af1\dbch\af37\loch\f1 pr}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1 e}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 \hich\af1\dbch\af37\loch\f1 serve any copyright notices included in the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 
+\hich\af1\dbch\af37\loch\f1 CMSIS D}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 eliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 
+\hich\af1\dbch\af37\loch\f1 ; and (c) to ensure your customers and authorised distributors comply with this Clause 1.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1 2}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid1928237 .}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1     }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 2. RESTRICTIONS ON USE OF THE}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+ CMSIS DELIVERABLES}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 .
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 
+\cbpat8 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 PERMITTED USERS: The }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+CMSIS Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 shall be used only by you (either a single individual, or single legal entity) your employees, or by your }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 on-site }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+bona fide sub-contractors for whose acts and omissions you hereby agree to be responsible to ARM}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  for}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  to the same extent as }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 you are for }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 your employees, and provided always that such sub-contractors}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 :}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  (i) are contractually obligated to use the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+CMSIS Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 only for your benefit}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+;}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  and (i}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 i}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 ) agree to assign all their work product and any rights they create therein in the supply of such work to you.
+\par COPYRIGHT AND RESERVATION OF RIGHTS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid14488502 : The }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid14488502 
+ are owned by ARM or its licensors and are protected by copyright and other intellectual property laws and international treaties. The }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid14488502  are licensed not sold. Except as expressly licensed herein, you acquire no right, title or interest in the }{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid14488502 
+ or any intellectual property therein. In no event shall the licences granted herein be construed as granting you, expressly or by implication, estoppels or otherwise, a licence to use any ARM technology except the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid14488502 .}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 3}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . SUPPORT.
+\par ARM is not obligated to support the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables but}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  may do so entirely at ARM's discretion. 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 4}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 NO }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 WARRANT}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 Y.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+\par YOU AGREE THAT THE }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS DELIVERABLES ARE}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+ LICENSED "AS IS", AND THAT ARM EXPRESSLY DISCLAIMS ALL REPRESENTATIONS, WARRANTIES, CONDITIONS OR OTHER TERMS, EXPRESS, IMPLIED OR STATUTORY, INCLUDING WITHOUT LIMITATION THE IMPLIED WARR
+ANTIES OF NON-INFRINGEMENT, SATISFACTORY QUALITY, AND FITNESS FOR A PARTICULAR PURPOSE.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  THE CMSIS DELIVERABLES MAY CONTAIN ERRORS.  }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 5}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . LIMITATION OF LIABILITY.
+\par THE MAXIMUM LIABILITY OF ARM TO YOU IN AGGREGATE FOR ALL CLAIMS MADE AGAINST ARM IN CONTRACT}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 ,}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  TORT OR OTHERWISE UNDER OR IN CONNECTION WITH THE SUBJECT MATTER OF THIS LICENCE SHALL NOT EXCEED }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 THE GREATER OF (I) }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+THE TOTAL OF SUMS PAID BY YOU TO ARM (IF ANY) FOR THIS LICENCE}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  AND (II) US$10.00}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 .}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636   THE LIMITATIONS, EXCLUSIONS AND DISCLAIMERS IN THIS LICEN
+CE SHALL APPLY TO THE MAXIMUM EXTENT ALLOWED BY APPLICABLE LAW.
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1 6
+}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid13830602 \hich\af1\dbch\af37\loch\f1 . THIRD PARTY RIGHTS.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13830602 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid13830602 \hich\af1\dbch\af37\loch\f1 
+The Separate Files are delivered subject to and your use is governed by their own separate licence agreements. This Licence does not apply to such Separate Files and the\hich\af1\dbch\af37\loch\f1 \hich\f1 y are not included in the term \'93}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636 \hich\af1\dbch\af37\loch\f1 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\lang1024\langfe1024\noproof\insrsid11754636\charrsid13830602 
+\loch\af1\dbch\af37\hich\f1 \'94\loch\f1 \hich\f1  under this Licence. You agree to comply with all terms and conditions imposed on you in respect of such Separate Files including those identified in the Schedule (\'93\loch\f1 \hich\f1 Third Party Terms
+\'94\loch\f1 ).  
+\par \hich\af1\dbch\af37\loch\f1 ARM HEREBY DISCLA\hich\af1\dbch\af37\loch\f1 \hich\f1 
+IMS ANY AND ALL WARRANTIES EXPRESS OR IMPLIED FROM ANY THIRD PARTIES REGARDING ANY SEPARATE FILES, ANY THIRD PARTY MATERIALS INCLUDED IN THE SOFTWARE, ANY THIRD PARTY MATERIALS FROM WHICH THE SOFTWARE IS DERIVED (COLLECTIVELY \'93\loch\f1 \hich\f1 
+OTHER CODE\'94\loch\f1 ), AND THE USE OF\hich\af1\dbch\af37\loch\f1  \hich\af1\dbch\af37\loch\f1 
+ANY OR ALL THE OTHER CODE IN CONNECTION WITH THE SOFTWARE, INCLUDING (WITHOUT LIMITATION) ANY WARRANTIES OF SATISFACTORY QUALITY OR FITNESS FOR A PARTICULAR PURPOSE.
+\par \hich\af1\dbch\af37\loch\f1 NO THIRD PARTY LICENSORS OF OTHER CODE SHALL HAVE ANY LIABILITY FOR ANY DIRECT, INDIRECT, \hich\af1\dbch\af37\loch\f1 
+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING WITHOUT LIMITATION LOST PROFITS), HOWEVER CAUSED AND WHETHER MADE UNDER CONTRACT, TORT OR OTHER LEGAL THEORY, ARISING IN ANY WAY OUT OF THE USE OR DISTRIBUTION OF THE OTHER CODE OR THE EX
+\hich\af1\dbch\af37\loch\f1 E\hich\af1\dbch\af37\loch\f1 RCISE OF ANY RIGHTS GRANTED UNDER EITHER OR BOTH THIS LICENCE AND THE LEGAL TERMS APPLICABLE TO ANY SEPARATE FILES, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 7}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . U.S. GOVERNMENT END USERS.
+\par US Government Restrictions: Use, duplication, reproduction, release, modification, disclosure or transfer of this commercial product and accompanying documentation is restricted in accordance with the terms of this Licence.
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 8}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . TERM AND TERMINATION.
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 8.1 }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+This Licence shall remain in force until terminated }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 in accordance with the terms of Clause 8.2 or Clause 8.3 below}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par 8.2 }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+Without prejudice to any of its other rights if you are in breach of any of the terms and conditions of this Licence then ARM may terminate this Licence immediately upon giving written notice to you}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid7630822 .  You may terminate this Licence at any time. }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1 
+8.3 This Licence shall immediately terminate and shall be unavailable to you if you or any party affiliated to you asserts any patents against ARM, ARM affiliates, third parties who have a valid licence fro\hich\af1\dbch\af37\loch\f1 
+m ARM for the CMSIS Deliverables, or any customers or distributors of any of them based upon a claim that your (or your affiliate) patent is Necessary to implement the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\hich\af1\dbch\af37\loch\f1 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1 . In this Licence}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\hich\af1\dbch\af37\loch\f1 :}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1  (i) "affiliate" means any entity controlling, contr\hich\af1\dbch\af37\loch\f1 
+olled by or under common control with a party (in fact or in law, via voting securities, management control or otherwise) and "affiliated" shall be construed accordingly; (ii) "assert" means to allege infringement in legal or administrative proceedings, o
+\hich\af1\dbch\af37\loch\f1 r\hich\af1\dbch\af37\loch\f1  proceedings before any other competent trade, arbitral or international authority; }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 and }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1 \hich\f1 (iii) \'93\loch\f1 \hich\f1 Necessary\'94\loch\f1 
+ means with respect to any claims of any patent, those claims which, without the appropriate permission of the patent owner, will be infringed when imp\hich\af1\dbch\af37\loch\f1 lementing the CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1 
+because no alternative, commercially reasonable, non-infringing way of implementing the CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  Deliverables }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\insrsid11754636\charrsid7106724 \hich\af1\dbch\af37\loch\f1 is known.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid5900444 \hich\af1\dbch\af37\loch\f1  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 8.4 }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid7630822 Upon termination of this Licence,}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636  you shall stop }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 
+using the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 
+ and destroy all copies of the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396  in your possession. The provisions of clauses 5, 6, 7, 8 and 9 shall survive termination of this Licence.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636   
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 9}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 . GENERAL.
+\par This Licence is governed by English Law. Except where ARM agrees otherwise in a written contract signed by you and ARM, this is the only agreement between you and ARM relating to the }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 CMSIS Deliverables}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15280636 
+ and it may only be modified by written agreement between you and ARM. Except as expressly agreed in writing, this Licence may not be modified by purchase orders, ad
+vertising or other representation by any person. If any clause or sentence in this Licence is held by a court of law to be illegal or unenforceable the remaining provisions of this Licence shall not be affected thereby. The failure by ARM to enforce any o
+f the provisions of this Licence, unless waived in writing, shall not constitute a waiver of ARM's rights to enforce such provision or any other provision of this Licence in the future.}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636   This Licence may not be assigned without the prior written consent of ARM.
+\par }\pard \ltrpar\qc \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 \page SCHEDULE
+\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \cbpat8 {
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 Separate Files
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 The }{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 package }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 also }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 includes the components}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636  contained in the following directories}{\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 :}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 
+\par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\insrsid11754636 \hich\af1\dbch\af0\loch\f1 (a)\tab}}\pard \ltrpar
+\qj \fi-360\li720\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\ls16\adjustright\rin0\lin720\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 ./}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 /}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 
+\hich\af1\dbch\af37\loch\f1 DSP_Lib}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  -  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636\charrsid15098396 
+DSP Library sources and examples}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 ; 
+\par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\insrsid11754636 \hich\af1\dbch\af0\loch\f1 (b)\tab}}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 ./}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 /}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 
+\hich\af1\dbch\af37\loch\f1 Include}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  - Header files; 
+\par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\insrsid11754636 \hich\af1\dbch\af0\loch\f1 (c)\tab}}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 ./}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 /}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 
+\hich\af1\dbch\af37\loch\f1 Lib}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  - }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 
+DSP Library build for various toolchains}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 ; 
+\par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\insrsid11754636 \hich\af1\dbch\af0\loch\f1 (d)\tab}}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 ./}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 CMSIS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 /}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 
+\hich\af1\dbch\af37\loch\f1 RTOS}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  - }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid7090778 \hich\af1\dbch\af37\loch\f1 
+Header file template for CMSIS-RTOS implementation}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 ; and 
+\par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\insrsid11754636 \hich\af1\dbch\af0\loch\f1 (e)\tab}}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\cf1\lang2057\langfe2057\langfenp2057\insrsid11754636 .}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 /Device - T}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid14488502 \hich\af1\dbch\af37\loch\f1 emplate files and implementations for Cortex-M class processors}{
+\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 . 
+\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par \hich\af1\dbch\af37\loch\f1 All of the above components (a\hich\f1 \endash \loch\f1  e) are licensed to you under the terms of the BSD licence, which is incorp\hich\af1\dbch\af37\loch\f1 orated within or alongside the above components.  
+\par }\pard \ltrpar\qj \li284\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin284\itap0\pararsid11754636 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1   }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 
+\f1\fs18\insrsid11754636\charrsid13975144 \hich\af1\dbch\af37\loch\f1 (f)}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1    }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13975144 
+\hich\af1\dbch\af37\loch\f1 ./CMSIS/Driver \hich\f1 \endash \loch\f1  CMSIS-Driver header files}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid13975144 \hich\af1\dbch\af37\loch\f1   (g)}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1  }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11754636 
+\hich\af37\dbch\af37\loch\f37  }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 ./CMSIS/Pack \hich\f1 \endash \loch\f1  Example Device Family Pack}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11754636\charrsid13975144 
+
+\par }\pard\plain \ltrpar\s32\ql \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \rtlch\fcs1 \af0\afs21\alang1025 \ltrch\fcs0 \f39\fs21\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\rtlch\fcs1 
+\af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par The above components (f \endash  g) are licensed to you under the terms of the zlib licence, which is incorporated within or alongside the above components.
+\par 
+\par }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid14488502        }{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636 
+\par 
+\par 
+\par }\pard\plain \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11754636 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
+\fs22\lang2057\langfe1033\loch\af37\hich\af37\dbch\af37\cgrid\langnp2057\langfenp1033 {\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid2958685 \hich\af1\dbch\af37\loch\f1 ARM contract reference LEC-PRE-00489}{\rtlch\fcs1 \af1\afs18 
+\ltrch\fcs0 \f1\fs18\insrsid11754636 \hich\af1\dbch\af37\loch\f1 - v3.0}{\rtlch\fcs1 \af1\afs18 \ltrch\fcs0 \f1\fs18\insrsid11754636\charrsid2958685 
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Libraries/CMSIS/DSP_Lib/Examples/arm_class_marks_example/ARM/arm_class_marks_example_f32.c

@@ -0,0 +1,211 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_class_marks_example_f32.c
+*
+* Description:   Example code to calculate Minimum, Maximum
+*                Mean, std and variance of marks obtained in a class
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup ClassMarks Class Marks Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use the Maximum, Minimum, Mean, Standard Deviation, Variance
+ * and Matrix functions to calculate statistical values of marks obtained in a class.
+ *
+ * \note This example also demonstrates the usage of static initialization.
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testMarks_f32 points to the marks scored by 20 students in 4 subjects
+ * \li \c max_marks     Maximum of all marks
+ * \li \c min_marks     Minimum of all marks
+ * \li \c mean          Mean of all marks
+ * \li \c var           Variance of the marks
+ * \li \c std           Standard deviation of the marks
+ * \li \c numStudents   Total number of students in the class
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_mat_init_f32()
+ * - arm_mat_mult_f32()
+ * - arm_max_f32()
+ * - arm_min_f32()
+ * - arm_mean_f32()
+ * - arm_std_f32()
+ * - arm_var_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_class_marks_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_class_marks_example_f32.c
+  */
+#include "arm_math.h"
+
+#define USE_STATIC_INIT
+
+ /* ----------------------------------------------------------------------
+** Global defines
+** ------------------------------------------------------------------- */
+
+#define TEST_LENGTH_SAMPLES   (20*4)
+
+/* ----------------------------------------------------------------------
+** List of Marks scored by 20 students for 4 subjects
+** ------------------------------------------------------------------- */
+const float32_t testMarks_f32[TEST_LENGTH_SAMPLES] =
+{
+  42.000000,  37.000000,  81.000000,  28.000000,
+  83.000000,  72.000000,  36.000000,  38.000000,
+  32.000000,  51.000000,  63.000000,  64.000000,
+  97.000000,  82.000000,  95.000000,  90.000000,
+  66.000000,  51.000000,  54.000000,  42.000000,
+  67.000000,  56.000000,  45.000000,  57.000000,
+  67.000000,  69.000000,  35.000000,  52.000000,
+  29.000000,  81.000000,  58.000000,  47.000000,
+  38.000000,  76.000000, 100.000000,  29.000000,
+  33.000000,  47.000000,  29.000000,  50.000000,
+  34.000000,  41.000000,  61.000000,  46.000000,
+  52.000000,  50.000000,  48.000000,  36.000000,
+  47.000000,  55.000000,  44.000000,  40.000000,
+ 100.000000,  94.000000,  84.000000,  37.000000,
+  32.000000,  71.000000,  47.000000,  77.000000,
+  31.000000,  50.000000,  49.000000,  35.000000,
+  63.000000,  67.000000,  40.000000,  31.000000,
+  29.000000,  68.000000,  61.000000,  38.000000,
+  31.000000,  28.000000,  28.000000,  76.000000,
+  55.000000,  33.000000,  29.000000,  39.000000
+};
+
+
+/* ----------------------------------------------------------------------
+* Number of subjects X 1
+* ------------------------------------------------------------------- */
+const float32_t testUnity_f32[4] =
+{
+  1.000,  1.000,   1.000,  1.000
+};
+
+
+/* ----------------------------------------------------------------------
+** f32 Output buffer
+** ------------------------------------------------------------------- */
+static float32_t testOutput[TEST_LENGTH_SAMPLES];
+
+
+/* ------------------------------------------------------------------
+* Global defines
+*------------------------------------------------------------------- */
+#define   NUMSTUDENTS  20
+#define     NUMSUBJECTS  4
+
+/* ------------------------------------------------------------------
+* Global variables
+*------------------------------------------------------------------- */
+
+ uint32_t    numStudents = 20;
+ uint32_t    numSubjects = 4;
+float32_t    max_marks, min_marks, mean, std, var;
+ uint32_t    student_num;
+
+/* ----------------------------------------------------------------------------------
+* Main f32 test function.  It returns maximum marks secured and student number
+* ------------------------------------------------------------------------------- */
+
+int32_t main()
+{
+
+#ifndef  USE_STATIC_INIT
+
+  arm_matrix_instance_f32 srcA;
+  arm_matrix_instance_f32 srcB;
+  arm_matrix_instance_f32 dstC;
+
+  /* Input and output matrices initializations */
+  arm_mat_init_f32(&srcA, numStudents, numSubjects, (float32_t *)testMarks_f32);
+  arm_mat_init_f32(&srcB, numSubjects, 1, (float32_t *)testUnity_f32);
+  arm_mat_init_f32(&dstC, numStudents, 1, testOutput);
+
+#else
+
+  /* Static Initializations of Input and output matrix sizes and array */
+  arm_matrix_instance_f32 srcA = {NUMSTUDENTS, NUMSUBJECTS, (float32_t *)testMarks_f32};
+  arm_matrix_instance_f32 srcB = {NUMSUBJECTS, 1, (float32_t *)testUnity_f32};
+  arm_matrix_instance_f32 dstC = {NUMSTUDENTS, 1, testOutput};
+
+#endif
+
+
+  /* ----------------------------------------------------------------------
+  *Call the Matrix multiplication process function
+  * ------------------------------------------------------------------- */
+  arm_mat_mult_f32(&srcA, &srcB, &dstC);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Max function to calculate max marks among numStudents
+  ** ------------------------------------------------------------------- */
+  arm_max_f32(testOutput, numStudents, &max_marks, &student_num);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Min function to calculate min marks among numStudents
+  ** ------------------------------------------------------------------- */
+  arm_min_f32(testOutput, numStudents, &min_marks, &student_num);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Mean function to calculate mean
+  ** ------------------------------------------------------------------- */
+  arm_mean_f32(testOutput, numStudents, &mean);
+
+  /* ----------------------------------------------------------------------
+  ** Call the std function to calculate standard deviation
+  ** ------------------------------------------------------------------- */
+  arm_std_f32(testOutput, numStudents, &std);
+
+  /* ----------------------------------------------------------------------
+  ** Call the var function to calculate variance
+  ** ------------------------------------------------------------------- */
+  arm_var_f32(testOutput, numStudents, &var);
+
+  while(1);                             /* main function does not return */
+}

Libraries/CMSIS/DSP_Lib/Examples/arm_class_marks_example/GCC/arm_class_marks_example_f32.c

@@ -0,0 +1,211 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_class_marks_example_f32.c
+*
+* Description:   Example code to calculate Minimum, Maximum
+*                Mean, std and variance of marks obtained in a class
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup ClassMarks Class Marks Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use the Maximum, Minimum, Mean, Standard Deviation, Variance
+ * and Matrix functions to calculate statistical values of marks obtained in a class.
+ *
+ * \note This example also demonstrates the usage of static initialization.
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testMarks_f32 points to the marks scored by 20 students in 4 subjects
+ * \li \c max_marks     Maximum of all marks
+ * \li \c min_marks     Minimum of all marks
+ * \li \c mean          Mean of all marks
+ * \li \c var           Variance of the marks
+ * \li \c std           Standard deviation of the marks
+ * \li \c numStudents   Total number of students in the class
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_mat_init_f32()
+ * - arm_mat_mult_f32()
+ * - arm_max_f32()
+ * - arm_min_f32()
+ * - arm_mean_f32()
+ * - arm_std_f32()
+ * - arm_var_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_class_marks_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_class_marks_example_f32.c
+  */
+#include "arm_math.h"
+
+#define USE_STATIC_INIT
+
+ /* ----------------------------------------------------------------------
+** Global defines
+** ------------------------------------------------------------------- */
+
+#define TEST_LENGTH_SAMPLES   (20*4)
+
+/* ----------------------------------------------------------------------
+** List of Marks scored by 20 students for 4 subjects
+** ------------------------------------------------------------------- */
+const float32_t testMarks_f32[TEST_LENGTH_SAMPLES] =
+{
+  42.000000,  37.000000,  81.000000,  28.000000,
+  83.000000,  72.000000,  36.000000,  38.000000,
+  32.000000,  51.000000,  63.000000,  64.000000,
+  97.000000,  82.000000,  95.000000,  90.000000,
+  66.000000,  51.000000,  54.000000,  42.000000,
+  67.000000,  56.000000,  45.000000,  57.000000,
+  67.000000,  69.000000,  35.000000,  52.000000,
+  29.000000,  81.000000,  58.000000,  47.000000,
+  38.000000,  76.000000, 100.000000,  29.000000,
+  33.000000,  47.000000,  29.000000,  50.000000,
+  34.000000,  41.000000,  61.000000,  46.000000,
+  52.000000,  50.000000,  48.000000,  36.000000,
+  47.000000,  55.000000,  44.000000,  40.000000,
+ 100.000000,  94.000000,  84.000000,  37.000000,
+  32.000000,  71.000000,  47.000000,  77.000000,
+  31.000000,  50.000000,  49.000000,  35.000000,
+  63.000000,  67.000000,  40.000000,  31.000000,
+  29.000000,  68.000000,  61.000000,  38.000000,
+  31.000000,  28.000000,  28.000000,  76.000000,
+  55.000000,  33.000000,  29.000000,  39.000000
+};
+
+
+/* ----------------------------------------------------------------------
+* Number of subjects X 1
+* ------------------------------------------------------------------- */
+const float32_t testUnity_f32[4] =
+{
+  1.000,  1.000,   1.000,  1.000
+};
+
+
+/* ----------------------------------------------------------------------
+** f32 Output buffer
+** ------------------------------------------------------------------- */
+static float32_t testOutput[TEST_LENGTH_SAMPLES];
+
+
+/* ------------------------------------------------------------------
+* Global defines
+*------------------------------------------------------------------- */
+#define   NUMSTUDENTS  20
+#define     NUMSUBJECTS  4
+
+/* ------------------------------------------------------------------
+* Global variables
+*------------------------------------------------------------------- */
+
+ uint32_t    numStudents = 20;
+ uint32_t    numSubjects = 4;
+float32_t    max_marks, min_marks, mean, std, var;
+ uint32_t    student_num;
+
+/* ----------------------------------------------------------------------------------
+* Main f32 test function.  It returns maximum marks secured and student number
+* ------------------------------------------------------------------------------- */
+
+int32_t main()
+{
+
+#ifndef  USE_STATIC_INIT
+
+  arm_matrix_instance_f32 srcA;
+  arm_matrix_instance_f32 srcB;
+  arm_matrix_instance_f32 dstC;
+
+  /* Input and output matrices initializations */
+  arm_mat_init_f32(&srcA, numStudents, numSubjects, (float32_t *)testMarks_f32);
+  arm_mat_init_f32(&srcB, numSubjects, 1, (float32_t *)testUnity_f32);
+  arm_mat_init_f32(&dstC, numStudents, 1, testOutput);
+
+#else
+
+  /* Static Initializations of Input and output matrix sizes and array */
+  arm_matrix_instance_f32 srcA = {NUMSTUDENTS, NUMSUBJECTS, (float32_t *)testMarks_f32};
+  arm_matrix_instance_f32 srcB = {NUMSUBJECTS, 1, (float32_t *)testUnity_f32};
+  arm_matrix_instance_f32 dstC = {NUMSTUDENTS, 1, testOutput};
+
+#endif
+
+
+  /* ----------------------------------------------------------------------
+  *Call the Matrix multiplication process function
+  * ------------------------------------------------------------------- */
+  arm_mat_mult_f32(&srcA, &srcB, &dstC);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Max function to calculate max marks among numStudents
+  ** ------------------------------------------------------------------- */
+  arm_max_f32(testOutput, numStudents, &max_marks, &student_num);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Min function to calculate min marks among numStudents
+  ** ------------------------------------------------------------------- */
+  arm_min_f32(testOutput, numStudents, &min_marks, &student_num);
+
+  /* ----------------------------------------------------------------------
+  ** Call the Mean function to calculate mean
+  ** ------------------------------------------------------------------- */
+  arm_mean_f32(testOutput, numStudents, &mean);
+
+  /* ----------------------------------------------------------------------
+  ** Call the std function to calculate standard deviation
+  ** ------------------------------------------------------------------- */
+  arm_std_f32(testOutput, numStudents, &std);
+
+  /* ----------------------------------------------------------------------
+  ** Call the var function to calculate variance
+  ** ------------------------------------------------------------------- */
+  arm_var_f32(testOutput, numStudents, &var);
+
+  while(1);                             /* main function does not return */
+}

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/ARM/arm_convolution_example_f32.c

@@ -0,0 +1,247 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_convolution_example_f32.c
+*
+* Description:   Example code demonstrating Convolution of two input signals using fft.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup ConvolutionExample Convolution Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex
+ * Multiplication, and Support Functions.
+ *
+ * \par Algorithm:
+ * \par
+ * The convolution theorem states that convolution in the time domain corresponds to
+ * multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of
+ * two signals is equal to the product of their individual Fourier transforms.
+ * The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT).
+ * \par
+ * Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively,
+ * are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code>
+ * and is a power of 4 as FFT implementation is radix-4.
+ * The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input
+ * signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of
+ * the multiplied result.
+ * \par
+ * This is denoted by the following equations:
+ * <pre> A[k] = FFT(a[n],N)
+ * B[k] = FFT(b[n],N)
+ * conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre>
+ * where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code>
+ * and <code>b[n]</code> respectively.
+ * The length of the convolved signal is <code>(n1+n2-1)</code>.
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html Convolution.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInputA_f32 points to the first input sequence
+ * \li \c srcALen length of the first input sequence
+ * \li \c testInputB_f32 points to the second input sequence
+ * \li \c srcBLen length of the second input sequence
+ * \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code>
+ * \li \c AxB points to the output array where the product of individual FFTs of inputs is stored.
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_fill_f32()
+ * - arm_copy_f32()
+ * - arm_cfft_radix4_init_f32()
+ * - arm_cfft_radix4_f32()
+ * - arm_cmplx_mult_cmplx_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_convolution_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_convolution_example_f32.c
+  */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE   128
+#define DELTA           (0.000001f)
+#define SNR_THRESHOLD   90
+
+/* ----------------------------------------------------------------------
+* Declare I/O buffers
+* ------------------------------------------------------------------- */
+float32_t Ak[MAX_BLOCKSIZE];        /* Input A */
+float32_t Bk[MAX_BLOCKSIZE];        /* Input B */
+float32_t AxB[MAX_BLOCKSIZE * 2];   /* Output */
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point Convolution example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+float32_t testInputA_f32[64] =
+{
+  -0.808920,   1.357369,   1.180861,  -0.504544,   1.762637,  -0.703285,
+   1.696966,   0.620571,  -0.151093,  -0.100235,  -0.872382,  -0.403579,
+  -0.860749,  -0.382648,  -1.052338,   0.128113,  -0.646269,   1.093377,
+  -2.209198,   0.471706,   0.408901,   1.266242,   0.598252,   1.176827,
+  -0.203421,   0.213596,  -0.851964,  -0.466958,   0.021841,  -0.698938,
+  -0.604107,   0.461778,  -0.318219,   0.942520,   0.577585,   0.417619,
+   0.614665,   0.563679,  -1.295073,  -0.764437,   0.952194,  -0.859222,
+  -0.618554,  -2.268542,  -1.210592,   1.655853,  -2.627219,  -0.994249,
+  -1.374704,   0.343799,   0.025619,   1.227481,  -0.708031,   0.069355,
+  -1.845228,  -1.570886,   1.010668,  -1.802084,   1.630088,   1.286090,
+  -0.161050,  -0.940794,   0.367961,   0.291907
+
+};
+
+float32_t testInputB_f32[64] =
+{
+   0.933724,   0.046881,   1.316470,   0.438345,   0.332682,   2.094885,
+   0.512081,   0.035546,   0.050894,  -2.320371,   0.168711,  -1.830493,
+  -0.444834,  -1.003242,  -0.531494,  -1.365600,  -0.155420,  -0.757692,
+  -0.431880,  -0.380021,   0.096243,  -0.695835,   0.558850,  -1.648962,
+   0.020369,  -0.363630,   0.887146,   0.845503,  -0.252864,  -0.330397,
+   1.269131,  -1.109295,  -1.027876,   0.135940,   0.116721,  -0.293399,
+  -1.349799,   0.166078,  -0.802201,   0.369367,  -0.964568,  -2.266011,
+   0.465178,   0.651222,  -0.325426,   0.320245,  -0.784178,  -0.579456,
+   0.093374,   0.604778,  -0.048225,   0.376297,  -0.394412,   0.578182,
+  -1.218141,  -1.387326,   0.692462,  -0.631297,   0.153137,  -0.638952,
+  0.635474,   -0.970468,   1.334057,  -0.111370
+};
+
+const float testRefOutput_f32[127] =
+{
+   -0.818943,    1.229484,  -0.533664,    1.016604,   0.341875,  -1.963656,
+    5.171476,    3.478033,   7.616361,    6.648384,   0.479069,   1.792012,
+   -1.295591,   -7.447818,   0.315830,  -10.657445,  -2.483469,  -6.524236,
+   -7.380591,   -3.739005,  -8.388957,    0.184147,  -1.554888,   3.786508,
+   -1.684421,    5.400610,  -1.578126,    7.403361,   8.315999,   2.080267,
+   11.077776,    2.749673,   7.138962,    2.748762,   0.660363,   0.981552,
+    1.442275,    0.552721,  -2.576892,    4.703989,   0.989156,   8.759344,
+   -0.564825,   -3.994680,   0.954710,   -5.014144,   6.592329,   1.599488,
+  -13.979146,   -0.391891,  -4.453369,   -2.311242,  -2.948764,   1.761415,
+   -0.138322,   10.433007,  -2.309103,    4.297153,   8.535523,   3.209462,
+    8.695819,    5.569919,   2.514304,    5.582029,   2.060199,   0.642280,
+    7.024616,    1.686615,  -6.481756,    1.343084,  -3.526451,   1.099073,
+   -2.965764,   -0.173723,  -4.111484,    6.528384,  -6.965658,   1.726291,
+    1.535172,   11.023435,   2.338401,   -4.690188,   1.298210,   3.943885,
+    8.407885,    5.168365,   0.684131,    1.559181,   1.859998,   2.852417,
+    8.574070,   -6.369078,   6.023458,   11.837963,  -6.027632,   4.469678,
+   -6.799093,   -2.674048,   6.250367,   -6.809971,  -3.459360,   9.112410,
+   -2.711621,   -1.336678,   1.564249,   -1.564297,  -1.296760,   8.904013,
+   -3.230109,    6.878013,  -7.819823,    3.369909,  -1.657410,  -2.007358,
+   -4.112825,    1.370685,  -3.420525,   -6.276605,   3.244873,  -3.352638,
+    1.545372,    0.902211,   0.197489,   -1.408732,   0.523390,   0.348440, 0
+};
+
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+uint32_t srcALen = 64;   /* Length of Input A */
+uint32_t srcBLen = 64;   /* Length of Input B */
+uint32_t outLen;         /* Length of convolution output */
+float32_t snr;           /* output SNR */
+
+int32_t main(void)
+{
+  arm_status status;                           /* Status of the example */
+  arm_cfft_radix4_instance_f32 cfft_instance;  /* CFFT Structure instance */
+
+  /* CFFT Structure instance pointer */
+  arm_cfft_radix4_instance_f32 *cfft_instance_ptr =
+      (arm_cfft_radix4_instance_f32*) &cfft_instance;
+
+  /* output length of convolution */
+  outLen = srcALen + srcBLen - 1;
+
+  /* Initialise the fft input buffers with all zeros */
+  arm_fill_f32(0.0,  Ak, MAX_BLOCKSIZE);
+  arm_fill_f32(0.0,  Bk, MAX_BLOCKSIZE);
+
+  /* Copy the input values to the fft input buffers */
+  arm_copy_f32(testInputA_f32,  Ak, MAX_BLOCKSIZE/2);
+  arm_copy_f32(testInputB_f32,  Bk, MAX_BLOCKSIZE/2);
+
+  /* Initialize the CFFT function to compute 64 point fft */
+  status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1);
+
+  /* Transform input a[n] from time domain to frequency domain A[k] */
+  arm_cfft_radix4_f32(cfft_instance_ptr, Ak);
+  /* Transform input b[n] from time domain to frequency domain B[k] */
+  arm_cfft_radix4_f32(cfft_instance_ptr, Bk);
+
+  /* Complex Multiplication of the two input buffers in frequency domain */
+  arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2);
+
+  /* Initialize the CIFFT function to compute 64 point ifft */
+  status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1);
+
+  /* Transform the multiplication output from frequency domain to time domain,
+     that gives the convolved output  */
+  arm_cfft_radix4_f32(cfft_instance_ptr, AxB);
+
+  /* SNR Calculation */
+  snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1);
+
+  /* Compare the SNR with threshold to test whether the
+     computed output is matched with the reference output values. */
+  if( snr > SNR_THRESHOLD)
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/GCC/arm_convolution_example_f32.c

@@ -0,0 +1,247 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_convolution_example_f32.c
+*
+* Description:   Example code demonstrating Convolution of two input signals using fft.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup ConvolutionExample Convolution Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex
+ * Multiplication, and Support Functions.
+ *
+ * \par Algorithm:
+ * \par
+ * The convolution theorem states that convolution in the time domain corresponds to
+ * multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of
+ * two signals is equal to the product of their individual Fourier transforms.
+ * The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT).
+ * \par
+ * Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively,
+ * are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code>
+ * and is a power of 4 as FFT implementation is radix-4.
+ * The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input
+ * signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of
+ * the multiplied result.
+ * \par
+ * This is denoted by the following equations:
+ * <pre> A[k] = FFT(a[n],N)
+ * B[k] = FFT(b[n],N)
+ * conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre>
+ * where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code>
+ * and <code>b[n]</code> respectively.
+ * The length of the convolved signal is <code>(n1+n2-1)</code>.
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html Convolution.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInputA_f32 points to the first input sequence
+ * \li \c srcALen length of the first input sequence
+ * \li \c testInputB_f32 points to the second input sequence
+ * \li \c srcBLen length of the second input sequence
+ * \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code>
+ * \li \c AxB points to the output array where the product of individual FFTs of inputs is stored.
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_fill_f32()
+ * - arm_copy_f32()
+ * - arm_cfft_radix4_init_f32()
+ * - arm_cfft_radix4_f32()
+ * - arm_cmplx_mult_cmplx_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_convolution_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_convolution_example_f32.c
+  */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE   128
+#define DELTA           (0.000001f)
+#define SNR_THRESHOLD   90
+
+/* ----------------------------------------------------------------------
+* Declare I/O buffers
+* ------------------------------------------------------------------- */
+float32_t Ak[MAX_BLOCKSIZE];        /* Input A */
+float32_t Bk[MAX_BLOCKSIZE];        /* Input B */
+float32_t AxB[MAX_BLOCKSIZE * 2];   /* Output */
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point Convolution example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+float32_t testInputA_f32[64] =
+{
+  -0.808920,   1.357369,   1.180861,  -0.504544,   1.762637,  -0.703285,
+   1.696966,   0.620571,  -0.151093,  -0.100235,  -0.872382,  -0.403579,
+  -0.860749,  -0.382648,  -1.052338,   0.128113,  -0.646269,   1.093377,
+  -2.209198,   0.471706,   0.408901,   1.266242,   0.598252,   1.176827,
+  -0.203421,   0.213596,  -0.851964,  -0.466958,   0.021841,  -0.698938,
+  -0.604107,   0.461778,  -0.318219,   0.942520,   0.577585,   0.417619,
+   0.614665,   0.563679,  -1.295073,  -0.764437,   0.952194,  -0.859222,
+  -0.618554,  -2.268542,  -1.210592,   1.655853,  -2.627219,  -0.994249,
+  -1.374704,   0.343799,   0.025619,   1.227481,  -0.708031,   0.069355,
+  -1.845228,  -1.570886,   1.010668,  -1.802084,   1.630088,   1.286090,
+  -0.161050,  -0.940794,   0.367961,   0.291907
+
+};
+
+float32_t testInputB_f32[64] =
+{
+   0.933724,   0.046881,   1.316470,   0.438345,   0.332682,   2.094885,
+   0.512081,   0.035546,   0.050894,  -2.320371,   0.168711,  -1.830493,
+  -0.444834,  -1.003242,  -0.531494,  -1.365600,  -0.155420,  -0.757692,
+  -0.431880,  -0.380021,   0.096243,  -0.695835,   0.558850,  -1.648962,
+   0.020369,  -0.363630,   0.887146,   0.845503,  -0.252864,  -0.330397,
+   1.269131,  -1.109295,  -1.027876,   0.135940,   0.116721,  -0.293399,
+  -1.349799,   0.166078,  -0.802201,   0.369367,  -0.964568,  -2.266011,
+   0.465178,   0.651222,  -0.325426,   0.320245,  -0.784178,  -0.579456,
+   0.093374,   0.604778,  -0.048225,   0.376297,  -0.394412,   0.578182,
+  -1.218141,  -1.387326,   0.692462,  -0.631297,   0.153137,  -0.638952,
+  0.635474,   -0.970468,   1.334057,  -0.111370
+};
+
+const float testRefOutput_f32[127] =
+{
+   -0.818943,    1.229484,  -0.533664,    1.016604,   0.341875,  -1.963656,
+    5.171476,    3.478033,   7.616361,    6.648384,   0.479069,   1.792012,
+   -1.295591,   -7.447818,   0.315830,  -10.657445,  -2.483469,  -6.524236,
+   -7.380591,   -3.739005,  -8.388957,    0.184147,  -1.554888,   3.786508,
+   -1.684421,    5.400610,  -1.578126,    7.403361,   8.315999,   2.080267,
+   11.077776,    2.749673,   7.138962,    2.748762,   0.660363,   0.981552,
+    1.442275,    0.552721,  -2.576892,    4.703989,   0.989156,   8.759344,
+   -0.564825,   -3.994680,   0.954710,   -5.014144,   6.592329,   1.599488,
+  -13.979146,   -0.391891,  -4.453369,   -2.311242,  -2.948764,   1.761415,
+   -0.138322,   10.433007,  -2.309103,    4.297153,   8.535523,   3.209462,
+    8.695819,    5.569919,   2.514304,    5.582029,   2.060199,   0.642280,
+    7.024616,    1.686615,  -6.481756,    1.343084,  -3.526451,   1.099073,
+   -2.965764,   -0.173723,  -4.111484,    6.528384,  -6.965658,   1.726291,
+    1.535172,   11.023435,   2.338401,   -4.690188,   1.298210,   3.943885,
+    8.407885,    5.168365,   0.684131,    1.559181,   1.859998,   2.852417,
+    8.574070,   -6.369078,   6.023458,   11.837963,  -6.027632,   4.469678,
+   -6.799093,   -2.674048,   6.250367,   -6.809971,  -3.459360,   9.112410,
+   -2.711621,   -1.336678,   1.564249,   -1.564297,  -1.296760,   8.904013,
+   -3.230109,    6.878013,  -7.819823,    3.369909,  -1.657410,  -2.007358,
+   -4.112825,    1.370685,  -3.420525,   -6.276605,   3.244873,  -3.352638,
+    1.545372,    0.902211,   0.197489,   -1.408732,   0.523390,   0.348440, 0
+};
+
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+uint32_t srcALen = 64;   /* Length of Input A */
+uint32_t srcBLen = 64;   /* Length of Input B */
+uint32_t outLen;         /* Length of convolution output */
+float32_t snr;           /* output SNR */
+
+int32_t main(void)
+{
+  arm_status status;                           /* Status of the example */
+  arm_cfft_radix4_instance_f32 cfft_instance;  /* CFFT Structure instance */
+
+  /* CFFT Structure instance pointer */
+  arm_cfft_radix4_instance_f32 *cfft_instance_ptr =
+      (arm_cfft_radix4_instance_f32*) &cfft_instance;
+
+  /* output length of convolution */
+  outLen = srcALen + srcBLen - 1;
+
+  /* Initialise the fft input buffers with all zeros */
+  arm_fill_f32(0.0,  Ak, MAX_BLOCKSIZE);
+  arm_fill_f32(0.0,  Bk, MAX_BLOCKSIZE);
+
+  /* Copy the input values to the fft input buffers */
+  arm_copy_f32(testInputA_f32,  Ak, MAX_BLOCKSIZE/2);
+  arm_copy_f32(testInputB_f32,  Bk, MAX_BLOCKSIZE/2);
+
+  /* Initialize the CFFT function to compute 64 point fft */
+  status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1);
+
+  /* Transform input a[n] from time domain to frequency domain A[k] */
+  arm_cfft_radix4_f32(cfft_instance_ptr, Ak);
+  /* Transform input b[n] from time domain to frequency domain B[k] */
+  arm_cfft_radix4_f32(cfft_instance_ptr, Bk);
+
+  /* Complex Multiplication of the two input buffers in frequency domain */
+  arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2);
+
+  /* Initialize the CIFFT function to compute 64 point ifft */
+  status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1);
+
+  /* Transform the multiplication output from frequency domain to time domain,
+     that gives the convolved output  */
+  arm_cfft_radix4_f32(cfft_instance_ptr, AxB);
+
+  /* SNR Calculation */
+  snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1);
+
+  /* Compare the SNR with threshold to test whether the
+     computed output is matched with the reference output values. */
+  if( snr > SNR_THRESHOLD)
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/GCC/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_convolution_example/GCC/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_dotproduct_example/ARM/arm_dotproduct_example_f32.c

@@ -0,0 +1,178 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_dotproduct_example_f32.c
+*
+* Description:   Example code computing dot product of two vectors.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup DotproductExample Dot Product Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use of the Multiply and Add functions to perform the dot product.
+ * The dot product of two vectors is obtained by multiplying corresponding elements
+ * and summing the products.
+
+ * \par Algorithm:
+ * \par
+ * The two input vectors \c A and \c B with length \c n, are multiplied element-by-element
+ * and then added to obtain dot product.
+ * \par
+ * This is denoted by the following equation:
+ *         <pre>  dotProduct = A[0] * B[0] + A[1] * B[1] + ... + A[n-1] * B[n-1]</pre>
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html dotProduct.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c srcA_buf_f32 points to first input vector
+ * \li \c srcB_buf_f32 points to second input vector
+ * \li \c testOutput   stores dot product of the two input vectors.
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_mult_f32()
+ * - arm_add_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_dotproduct_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_dotproduct_example_f32.c
+  */
+
+#include <math.h>
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE     32
+#define DELTA           (0.000001f)
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point Dot Product example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+/* ----------------------------------------------------------------------
+** Test input data of srcA for blockSize 32
+** ------------------------------------------------------------------- */
+float32_t srcA_buf_f32[MAX_BLOCKSIZE] =
+{
+  -0.4325648115282207,  -1.6655843782380970,  0.1253323064748307,
+   0.2876764203585489,  -1.1464713506814637,  1.1909154656429988,
+   1.1891642016521031,  -0.0376332765933176,  0.3272923614086541,
+   0.1746391428209245,  -0.1867085776814394,  0.7257905482933027,
+  -0.5883165430141887,   2.1831858181971011, -0.1363958830865957,
+   0.1139313135208096,   1.0667682113591888,  0.0592814605236053,
+  -0.0956484054836690,  -0.8323494636500225,  0.2944108163926404,
+  -1.3361818579378040,   0.7143245518189522,  1.6235620644462707,
+  -0.6917757017022868,   0.8579966728282626,  1.2540014216025324,
+  -1.5937295764474768,  -1.4409644319010200,  0.5711476236581780,
+  -0.3998855777153632,   0.6899973754643451
+};
+
+/* ----------------------------------------------------------------------
+** Test input data of srcB for blockSize 32
+** ------------------------------------------------------------------- */
+float32_t srcB_buf_f32[MAX_BLOCKSIZE] =
+{
+   1.7491401329284098,  0.1325982188803279,   0.3252281811989881,
+  -0.7938091410349637,  0.3149236145048914,  -0.5272704888029532,
+   0.9322666565031119,  1.1646643544607362,  -2.0456694357357357,
+  -0.6443728590041911,  1.7410657940825480,   0.4867684246821860,
+   1.0488288293660140,  1.4885752747099299,   1.2705014969484090,
+  -1.8561241921210170,  2.1343209047321410,  1.4358467535865909,
+  -0.9173023332875400, -1.1060770780029008,   0.8105708062681296,
+   0.6985430696369063, -0.4015827425012831,   1.2687512030669628,
+  -0.7836083053674872,  0.2132664971465569,   0.7878984786088954,
+   0.8966819356782295, -0.1869172943544062,   1.0131816724341454,
+   0.2484350696132857,  0.0596083377937976
+};
+
+/* Reference dot product output */
+float32_t  refDotProdOut = 5.9273644806352142;
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+float32_t multOutput[MAX_BLOCKSIZE];  /* Intermediate output */
+float32_t testOutput;  /* Final ouput */
+
+arm_status status;   /* Status of the example */
+
+int32_t main(void)
+{
+  uint32_t i;       /* Loop counter */
+  float32_t diff;     /* Difference between reference and test outputs */
+
+  /* Multiplication of two input buffers */
+  arm_mult_f32(srcA_buf_f32, srcB_buf_f32, multOutput, MAX_BLOCKSIZE);
+
+  /* Accumulate the multiplication output values to
+     get the dot product of the two inputs */
+  for(i=0; i< MAX_BLOCKSIZE; i++)
+  {
+    arm_add_f32(&testOutput, &multOutput[i], &testOutput, 1);
+  }
+
+  /* absolute value of difference between ref and test */
+  diff = fabsf(refDotProdOut - testOutput);
+
+  /* Comparison of dot product value with reference */
+  if(diff > DELTA)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  if( status == ARM_MATH_TEST_FAILURE)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_dotproduct_example/GCC/arm_dotproduct_example_f32.c

@@ -0,0 +1,178 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_dotproduct_example_f32.c
+*
+* Description:   Example code computing dot product of two vectors.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup DotproductExample Dot Product Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use of the Multiply and Add functions to perform the dot product.
+ * The dot product of two vectors is obtained by multiplying corresponding elements
+ * and summing the products.
+
+ * \par Algorithm:
+ * \par
+ * The two input vectors \c A and \c B with length \c n, are multiplied element-by-element
+ * and then added to obtain dot product.
+ * \par
+ * This is denoted by the following equation:
+ *         <pre>  dotProduct = A[0] * B[0] + A[1] * B[1] + ... + A[n-1] * B[n-1]</pre>
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html dotProduct.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c srcA_buf_f32 points to first input vector
+ * \li \c srcB_buf_f32 points to second input vector
+ * \li \c testOutput   stores dot product of the two input vectors.
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_mult_f32()
+ * - arm_add_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_dotproduct_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_dotproduct_example_f32.c
+  */
+
+#include <math.h>
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE     32
+#define DELTA           (0.000001f)
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point Dot Product example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+/* ----------------------------------------------------------------------
+** Test input data of srcA for blockSize 32
+** ------------------------------------------------------------------- */
+float32_t srcA_buf_f32[MAX_BLOCKSIZE] =
+{
+  -0.4325648115282207,  -1.6655843782380970,  0.1253323064748307,
+   0.2876764203585489,  -1.1464713506814637,  1.1909154656429988,
+   1.1891642016521031,  -0.0376332765933176,  0.3272923614086541,
+   0.1746391428209245,  -0.1867085776814394,  0.7257905482933027,
+  -0.5883165430141887,   2.1831858181971011, -0.1363958830865957,
+   0.1139313135208096,   1.0667682113591888,  0.0592814605236053,
+  -0.0956484054836690,  -0.8323494636500225,  0.2944108163926404,
+  -1.3361818579378040,   0.7143245518189522,  1.6235620644462707,
+  -0.6917757017022868,   0.8579966728282626,  1.2540014216025324,
+  -1.5937295764474768,  -1.4409644319010200,  0.5711476236581780,
+  -0.3998855777153632,   0.6899973754643451
+};
+
+/* ----------------------------------------------------------------------
+** Test input data of srcB for blockSize 32
+** ------------------------------------------------------------------- */
+float32_t srcB_buf_f32[MAX_BLOCKSIZE] =
+{
+   1.7491401329284098,  0.1325982188803279,   0.3252281811989881,
+  -0.7938091410349637,  0.3149236145048914,  -0.5272704888029532,
+   0.9322666565031119,  1.1646643544607362,  -2.0456694357357357,
+  -0.6443728590041911,  1.7410657940825480,   0.4867684246821860,
+   1.0488288293660140,  1.4885752747099299,   1.2705014969484090,
+  -1.8561241921210170,  2.1343209047321410,  1.4358467535865909,
+  -0.9173023332875400, -1.1060770780029008,   0.8105708062681296,
+   0.6985430696369063, -0.4015827425012831,   1.2687512030669628,
+  -0.7836083053674872,  0.2132664971465569,   0.7878984786088954,
+   0.8966819356782295, -0.1869172943544062,   1.0131816724341454,
+   0.2484350696132857,  0.0596083377937976
+};
+
+/* Reference dot product output */
+float32_t  refDotProdOut = 5.9273644806352142;
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+float32_t multOutput[MAX_BLOCKSIZE];  /* Intermediate output */
+float32_t testOutput;  /* Final ouput */
+
+arm_status status;   /* Status of the example */
+
+int32_t main(void)
+{
+  uint32_t i;       /* Loop counter */
+  float32_t diff;     /* Difference between reference and test outputs */
+
+  /* Multiplication of two input buffers */
+  arm_mult_f32(srcA_buf_f32, srcB_buf_f32, multOutput, MAX_BLOCKSIZE);
+
+  /* Accumulate the multiplication output values to
+     get the dot product of the two inputs */
+  for(i=0; i< MAX_BLOCKSIZE; i++)
+  {
+    arm_add_f32(&testOutput, &multOutput[i], &testOutput, 1);
+  }
+
+  /* absolute value of difference between ref and test */
+  diff = fabsf(refDotProdOut - testOutput);
+
+  /* Comparison of dot product value with reference */
+  if(diff > DELTA)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  if( status == ARM_MATH_TEST_FAILURE)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_fft_bin_example/ARM/arm_fft_bin_data.c

@@ -0,0 +1,308 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_fft_bin_data.c
+*   
+* Description:	 Data file used for example code
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+ * -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+Test Input signal contains 10KHz signal + Uniformly distributed white noise
+** ------------------------------------------------------------------- */
+
+float32_t testInput_f32_10khz[2048] = 
+{   
+-0.865129623056441, 	0.000000000000000, 	-2.655020678073846, 	0.000000000000000, 	0.600664612949661, 	0.000000000000000, 	0.080378093886515, 	0.000000000000000, 	
+-2.899160484012034, 	0.000000000000000, 	2.563004262857762, 	0.000000000000000, 	3.078328403304206, 	0.000000000000000, 	0.105906778385130, 	0.000000000000000, 	
+0.048366940168201, 	0.000000000000000, 	-0.145696461188734, 	0.000000000000000, 	-0.023417155362879, 	0.000000000000000, 	2.127729174988954, 	0.000000000000000, 	
+-1.176633086028377, 	0.000000000000000, 	3.690223557991855, 	0.000000000000000, 	-0.622791766173194, 	0.000000000000000, 	0.722837373872203, 	0.000000000000000, 	
+2.739754205367484, 	0.000000000000000, 	-0.062610410524552, 	0.000000000000000, 	-0.891296810967338, 	0.000000000000000, 	-1.845872258871811, 	0.000000000000000, 	
+1.195039415434387, 	0.000000000000000, 	-2.177388969045026, 	0.000000000000000, 	1.078649103637905, 	0.000000000000000, 	2.570976050490193, 	0.000000000000000, 	
+-1.383551403404574, 	0.000000000000000, 	2.392141424058873, 	0.000000000000000, 	2.858002843205065, 	0.000000000000000, 	-3.682433899725536, 	0.000000000000000, 	
+-3.488146646451150, 	0.000000000000000, 	1.323468578888120, 	0.000000000000000, 	-0.099771155430726, 	0.000000000000000, 	1.561168082500454, 	0.000000000000000, 	
+1.025026795103179, 	0.000000000000000, 	0.928841900171200, 	0.000000000000000, 	2.930499509864950, 	0.000000000000000, 	2.013349089766430, 	0.000000000000000, 	
+2.381676148486737, 	0.000000000000000, 	-3.081062307950236, 	0.000000000000000, 	-0.389579115537544, 	0.000000000000000, 	0.181540149166620, 	0.000000000000000, 	
+-2.601953341353208, 	0.000000000000000, 	0.333435137783218, 	0.000000000000000, 	-2.812945856162965, 	0.000000000000000, 	2.649109640172910, 	0.000000000000000, 	
+-1.003963025744654, 	0.000000000000000, 	1.552460768755035, 	0.000000000000000, 	0.088641345335247, 	0.000000000000000, 	-2.519951327113426, 	0.000000000000000, 	
+-4.341348988610527, 	0.000000000000000, 	0.557772429359965, 	0.000000000000000, 	-1.671267412948494, 	0.000000000000000, 	0.733951350960387, 	0.000000000000000, 	
+0.409263788034864, 	0.000000000000000, 	3.566033071952806, 	0.000000000000000, 	1.882565173848352, 	0.000000000000000, 	-1.106017073793287, 	0.000000000000000, 	
+0.154456720778718, 	0.000000000000000, 	-2.513205795512153, 	0.000000000000000, 	0.310978660939421, 	0.000000000000000, 	0.579706500111723, 	0.000000000000000, 	
+0.000086383683251, 	0.000000000000000, 	-1.311866980897721, 	0.000000000000000, 	1.840007477574986, 	0.000000000000000, 	-3.253005768451345, 	0.000000000000000, 	
+1.462584328739432, 	0.000000000000000, 	1.610103610851738, 	0.000000000000000, 	0.761914676858907, 	0.000000000000000, 	0.974541361089834, 	0.000000000000000, 	
+0.686845845885983, 	0.000000000000000, 	1.849153122025191, 	0.000000000000000, 	0.787800410401453, 	0.000000000000000, 	-1.187438909666279, 	0.000000000000000, 	
+-0.754937911044720, 	0.000000000000000, 	0.084373858395232, 	0.000000000000000, 	-2.600269011710521, 	0.000000000000000, 	-0.962982842142644, 	0.000000000000000, 	
+-0.369328108540868, 	0.000000000000000, 	0.810791418361879, 	0.000000000000000, 	3.587016488699641, 	0.000000000000000, 	-0.520776145083723, 	0.000000000000000, 	
+0.640249919627884, 	0.000000000000000, 	1.103122489464969, 	0.000000000000000, 	2.231779881455556, 	0.000000000000000, 	-1.308035392685241, 	0.000000000000000, 	
+0.424070304330106, 	0.000000000000000, 	-0.200383932651189, 	0.000000000000000, 	-2.365526783356541, 	0.000000000000000, 	-0.989114757436628, 	0.000000000000000, 	
+2.770807688959777, 	0.000000000000000, 	-0.444172737462307, 	0.000000000000000, 	0.079760979374078, 	0.000000000000000, 	-0.005199118412183, 	0.000000000000000, 	
+-0.664712668309527, 	0.000000000000000, 	-0.624171857561896, 	0.000000000000000, 	0.537306979007338, 	0.000000000000000, 	-2.575955675497642, 	0.000000000000000, 	
+1.562363235756780, 	0.000000000000000, 	1.814069369848895, 	0.000000000000000, 	-1.293428583392509, 	0.000000000000000, 	-1.026188449495686, 	0.000000000000000, 	
+-2.981771815588717, 	0.000000000000000, 	-4.223468103075124, 	0.000000000000000, 	2.672674782004045, 	0.000000000000000, 	-0.856096801117735, 	0.000000000000000, 	
+0.048517345512563, 	0.000000000000000, 	-0.026860721136222, 	0.000000000000000, 	0.392932277758187, 	0.000000000000000, 	-1.331740855093099, 	0.000000000000000, 	
+-1.894292129477081, 	0.000000000000000, 	-1.425006468460681, 	0.000000000000000, 	-2.721772427617057, 	0.000000000000000, 	-1.616831100216806, 	0.000000000000000, 	
+3.551177651488947, 	0.000000000000000, 	-0.069685667896087, 	0.000000000000000, 	-3.134634907409102, 	0.000000000000000, 	-0.263627598944639, 	0.000000000000000, 	
+-1.650469945991350, 	0.000000000000000, 	-2.203580339374399, 	0.000000000000000, 	-0.872203246123242, 	0.000000000000000, 	1.230782812607287, 	0.000000000000000, 	
+0.257288860093291, 	0.000000000000000, 	1.989083106173137, 	0.000000000000000, 	-1.985638729453261, 	0.000000000000000, 	-1.416185105842892, 	0.000000000000000, 	
+-1.131097688325772, 	0.000000000000000, 	-2.245130805416057, 	0.000000000000000, 	-1.938873996219074, 	0.000000000000000, 	2.043608361562645, 	0.000000000000000, 	
+-0.583727989880841, 	0.000000000000000, 	-1.785266378212929, 	0.000000000000000, 	1.961457586224753, 	0.000000000000000, 	1.139400099963223, 	0.000000000000000, 	
+-1.979519343363991, 	0.000000000000000, 	2.003023322818429, 	0.000000000000000, 	0.229004069076829, 	0.000000000000000, 	3.452808862193135, 	0.000000000000000, 	
+2.882273808365857, 	0.000000000000000, 	-1.549450501844438, 	0.000000000000000, 	-3.283872089931876, 	0.000000000000000, 	-0.327025884099064, 	0.000000000000000, 	
+-0.054979977136430, 	0.000000000000000, 	-1.192280531479012, 	0.000000000000000, 	0.645539328365578, 	0.000000000000000, 	2.300832863404618, 	0.000000000000000, 	
+-1.092951789535240, 	0.000000000000000, 	-1.017368249363773, 	0.000000000000000, 	-0.142673056169787, 	0.000000000000000, 	0.831073544881250, 	0.000000000000000, 	
+-2.314612531587064, 	0.000000000000000, 	-2.221456299106321, 	0.000000000000000, 	0.460261143885226, 	0.000000000000000, 	0.050585301888595, 	0.000000000000000, 	
+0.364373329183988, 	0.000000000000000, 	-1.685956552069538, 	0.000000000000000, 	0.050664512351055, 	0.000000000000000, 	-0.193355783902718, 	0.000000000000000, 	
+-0.158660446046828, 	0.000000000000000, 	2.394156453841953, 	0.000000000000000, 	-1.562965718554525, 	0.000000000000000, 	-2.199750600869900, 	0.000000000000000, 	
+1.544984022381773, 	0.000000000000000, 	-1.988307216807315, 	0.000000000000000, 	-0.628240722541046, 	0.000000000000000, 	-1.436235771505429, 	0.000000000000000, 	
+1.677013691147313, 	0.000000000000000, 	1.600741781678228, 	0.000000000000000, 	-0.757380959134706, 	0.000000000000000, 	-4.784797439515566, 	0.000000000000000, 	
+0.265121462834569, 	0.000000000000000, 	3.862029485934378, 	0.000000000000000, 	2.386823577249430, 	0.000000000000000, 	-3.655779745436893, 	0.000000000000000, 	
+-0.763541621368016, 	0.000000000000000, 	-1.182140388432962, 	0.000000000000000, 	-1.349106114858063, 	0.000000000000000, 	-2.287533624396759, 	0.000000000000000, 	
+-0.028603745188423, 	0.000000000000000, 	-1.353580755934427, 	0.000000000000000, 	0.461602380352937, 	0.000000000000000, 	-0.059599055078928, 	0.000000000000000, 	
+-0.929946734342228, 	0.000000000000000, 	0.065773089295561, 	0.000000000000000, 	1.106565863102982, 	0.000000000000000, 	4.719295086373593, 	0.000000000000000, 	
+-2.108377703544395, 	0.000000000000000, 	-2.226393620240159, 	0.000000000000000, 	1.375668397437521, 	0.000000000000000, 	-0.960772428525443, 	0.000000000000000, 	
+-2.156313465390571, 	0.000000000000000, 	1.126060012375311, 	0.000000000000000, 	2.756485137030720, 	0.000000000000000, 	0.739639690862600, 	0.000000000000000, 	
+3.914769510295006, 	0.000000000000000, 	1.685232785586675, 	0.000000000000000, 	4.079058040970612, 	0.000000000000000, 	-1.174598301660513, 	0.000000000000000, 	
+-2.885776587275580, 	0.000000000000000, 	-0.241073635188767, 	0.000000000000000, 	3.080489872502403, 	0.000000000000000, 	-2.051244183999421, 	0.000000000000000, 	
+0.664330486845139, 	0.000000000000000, 	-1.697798999370016, 	0.000000000000000, 	1.452369423649782, 	0.000000000000000, 	-1.523532831019280, 	0.000000000000000, 	
+0.171981186587481, 	0.000000000000000, 	-4.685274721583927, 	0.000000000000000, 	-1.336175835319380, 	0.000000000000000, 	1.419070770428945, 	0.000000000000000, 	
+-0.035791601713475, 	0.000000000000000, 	2.291937971632081, 	0.000000000000000, 	-1.962559313450293, 	0.000000000000000, 	-4.831595589339301, 	0.000000000000000, 	
+-1.857055284000925, 	0.000000000000000, 	2.606271522635512, 	0.000000000000000, 	-0.576447978738030, 	0.000000000000000, 	0.082299166967720, 	0.000000000000000, 	
+1.888399453494614, 	0.000000000000000, 	-3.564705298046079, 	0.000000000000000, 	-0.939357831083889, 	0.000000000000000, 	-1.903578203697778, 	0.000000000000000, 	
+-2.642492215447250, 	0.000000000000000, 	-0.182990405251017, 	0.000000000000000, 	3.742026478011174, 	0.000000000000000, 	0.104295803798333, 	0.000000000000000, 	
+1.848678195370347, 	0.000000000000000, 	-1.887384346896369, 	0.000000000000000, 	0.365048973046045, 	0.000000000000000, 	-0.889638010354219, 	0.000000000000000, 	
+1.173877118428863, 	0.000000000000000, 	-1.178562827540109, 	0.000000000000000, 	0.610271645685184, 	0.000000000000000, 	1.831284815697871, 	0.000000000000000, 	
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+0.582643134746494, 	0.000000000000000, 	2.321256382353331, 	0.000000000000000, 	-0.238118642223180, 	0.000000000000000, 	-2.890287868054370, 	0.000000000000000, 	
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+3.120583443719949, 	0.000000000000000, 	-0.863945271701041, 	0.000000000000000, 	0.906848893874630, 	0.000000000000000, 	-1.434124930222570, 	0.000000000000000, 	
+0.754659384848783, 	0.000000000000000, 	-5.224154442713778, 	0.000000000000000, 	2.330229744098967, 	0.000000000000000, 	1.113946320164698, 	0.000000000000000, 	
+0.523324920322840, 	0.000000000000000, 	1.750740911548348, 	0.000000000000000, 	-0.899333972913577, 	0.000000000000000, 	0.228705845203506, 	0.000000000000000, 	
+-1.934782624767648, 	0.000000000000000, 	-3.508386237231303, 	0.000000000000000, 	-2.107108523073510, 	0.000000000000000, 	0.380587645474815, 	0.000000000000000, 	
+-0.476200877183279, 	0.000000000000000, 	-2.172086712642198, 	0.000000000000000, 	1.795372535780299, 	0.000000000000000, 	-2.100318983391055, 	0.000000000000000, 	
+-0.022571122461405, 	0.000000000000000, 	0.674514020010955, 	0.000000000000000, 	-0.148872569390857, 	0.000000000000000, 	0.298175890592737, 	0.000000000000000, 	
+-1.134244492493590, 	0.000000000000000, 	-3.146848422289455, 	0.000000000000000, 	-1.357950199087602, 	0.000000000000000, 	0.667362732020878, 	0.000000000000000, 	
+-3.119397998316724, 	0.000000000000000, 	-1.189341126297637, 	0.000000000000000, 	-1.532744386856668, 	0.000000000000000, 	-1.672972484202534, 	0.000000000000000, 	
+-2.042283373871558, 	0.000000000000000, 	-1.479481547595924, 	0.000000000000000, 	-0.002668662875396, 	0.000000000000000, 	0.262737760129546, 	0.000000000000000, 	
+2.734456080621830, 	0.000000000000000, 	-0.671945925075102, 	0.000000000000000, 	-3.735078262179111, 	0.000000000000000, 	-0.161705013319883, 	0.000000000000000, 	
+0.748963512361001, 	0.000000000000000, 	1.128046374367600, 	0.000000000000000, 	0.649651335592966, 	0.000000000000000, 	1.880020215025867, 	0.000000000000000, 	
+-1.095632293842306, 	0.000000000000000, 	1.197764876160487, 	0.000000000000000, 	0.323646656252985, 	0.000000000000000, 	-1.655502751114502, 	0.000000000000000, 	
+3.666399062961496, 	0.000000000000000, 	-0.334060899735197, 	0.000000000000000, 	-2.119056978738397, 	0.000000000000000, 	3.721375117275012, 	0.000000000000000, 	
+0.044874186872307, 	0.000000000000000, 	-2.733053897593234, 	0.000000000000000, 	1.590700278891042, 	0.000000000000000, 	3.215711772781902, 	0.000000000000000, 	
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+
+
+};
+

Libraries/CMSIS/DSP_Lib/Examples/arm_fft_bin_example/ARM/arm_fft_bin_example_f32.c

@@ -0,0 +1,158 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:	     arm_fft_bin_example_f32.c
+*
+* Description:   Example code demonstrating calculation of Max energy bin of
+*                frequency domain of input signal.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup FrequencyBin Frequency Bin Example
+ *
+ * \par Description
+ * \par
+ * Demonstrates the calculation of the maximum energy bin in the frequency
+ * domain of the input signal with the use of Complex FFT, Complex
+ * Magnitude, and Maximum functions.
+ *
+ * \par Algorithm:
+ * \par
+ * The input test signal contains a 10 kHz signal with uniformly distributed white noise.
+ * Calculating the FFT of the input signal will give us the maximum energy of the
+ * bin corresponding to the input frequency of 10 kHz.
+ *
+ * \par Block Diagram:
+ * \image html FFTBin.gif "Block Diagram"
+ * \par
+ * The figure below shows the time domain signal of 10 kHz signal with
+ * uniformly distributed white noise, and the next figure shows the input
+ * in the frequency domain. The bin with maximum energy corresponds to 10 kHz signal.
+ * \par
+ * \image html FFTBinInput.gif "Input signal in Time domain"
+ * \image html FFTBinOutput.gif "Input signal in Frequency domain"
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32_10khz points to the input data
+ * \li \c testOutput points to the output data
+ * \li \c fftSize length of FFT
+ * \li \c ifftFlag flag for the selection of CFFT/CIFFT
+ * \li \c doBitReverse Flag for selection of normal order or bit reversed order
+ * \li \c refIndex reference index value at which maximum energy of bin ocuurs
+ * \li \c testIndex calculated index value at which maximum energy of bin ocuurs
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_cfft_f32()
+ * - arm_cmplx_mag_f32()
+ * - arm_max_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_fft_bin_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_fft_bin_example_f32.c
+  */
+
+
+#include "arm_math.h"
+#include "arm_const_structs.h"
+
+#define TEST_LENGTH_SAMPLES 2048
+
+/* -------------------------------------------------------------------
+* External Input and Output buffer Declarations for FFT Bin Example
+* ------------------------------------------------------------------- */
+extern float32_t testInput_f32_10khz[TEST_LENGTH_SAMPLES];
+static float32_t testOutput[TEST_LENGTH_SAMPLES/2];
+
+/* ------------------------------------------------------------------
+* Global variables for FFT Bin Example
+* ------------------------------------------------------------------- */
+uint32_t fftSize = 1024;
+uint32_t ifftFlag = 0;
+uint32_t doBitReverse = 1;
+
+/* Reference index at which max energy of bin ocuurs */
+uint32_t refIndex = 213, testIndex = 0;
+
+/* ----------------------------------------------------------------------
+* Max magnitude FFT Bin test
+* ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+
+  arm_status status;
+  float32_t maxValue;
+
+  status = ARM_MATH_SUCCESS;
+
+  /* Process the data through the CFFT/CIFFT module */
+  arm_cfft_f32(&arm_cfft_sR_f32_len1024, testInput_f32_10khz, ifftFlag, doBitReverse);
+
+  /* Process the data through the Complex Magnitude Module for
+  calculating the magnitude at each bin */
+  arm_cmplx_mag_f32(testInput_f32_10khz, testOutput, fftSize);
+
+  /* Calculates maxValue and returns corresponding BIN value */
+  arm_max_f32(testOutput, fftSize, &maxValue, &testIndex);
+
+  if(testIndex !=  refIndex)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signals fail the PASS check.
+  ** This denotes a test failure
+  ** ------------------------------------------------------------------- */
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_fft_bin_example/GCC/arm_fft_bin_data.c

@@ -0,0 +1,308 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_fft_bin_data.c
+*   
+* Description:	 Data file used for example code
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+ * -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+Test Input signal contains 10KHz signal + Uniformly distributed white noise
+** ------------------------------------------------------------------- */
+
+float32_t testInput_f32_10khz[2048] = 
+{   
+-0.865129623056441, 	0.000000000000000, 	-2.655020678073846, 	0.000000000000000, 	0.600664612949661, 	0.000000000000000, 	0.080378093886515, 	0.000000000000000, 	
+-2.899160484012034, 	0.000000000000000, 	2.563004262857762, 	0.000000000000000, 	3.078328403304206, 	0.000000000000000, 	0.105906778385130, 	0.000000000000000, 	
+0.048366940168201, 	0.000000000000000, 	-0.145696461188734, 	0.000000000000000, 	-0.023417155362879, 	0.000000000000000, 	2.127729174988954, 	0.000000000000000, 	
+-1.176633086028377, 	0.000000000000000, 	3.690223557991855, 	0.000000000000000, 	-0.622791766173194, 	0.000000000000000, 	0.722837373872203, 	0.000000000000000, 	
+2.739754205367484, 	0.000000000000000, 	-0.062610410524552, 	0.000000000000000, 	-0.891296810967338, 	0.000000000000000, 	-1.845872258871811, 	0.000000000000000, 	
+1.195039415434387, 	0.000000000000000, 	-2.177388969045026, 	0.000000000000000, 	1.078649103637905, 	0.000000000000000, 	2.570976050490193, 	0.000000000000000, 	
+-1.383551403404574, 	0.000000000000000, 	2.392141424058873, 	0.000000000000000, 	2.858002843205065, 	0.000000000000000, 	-3.682433899725536, 	0.000000000000000, 	
+-3.488146646451150, 	0.000000000000000, 	1.323468578888120, 	0.000000000000000, 	-0.099771155430726, 	0.000000000000000, 	1.561168082500454, 	0.000000000000000, 	
+1.025026795103179, 	0.000000000000000, 	0.928841900171200, 	0.000000000000000, 	2.930499509864950, 	0.000000000000000, 	2.013349089766430, 	0.000000000000000, 	
+2.381676148486737, 	0.000000000000000, 	-3.081062307950236, 	0.000000000000000, 	-0.389579115537544, 	0.000000000000000, 	0.181540149166620, 	0.000000000000000, 	
+-2.601953341353208, 	0.000000000000000, 	0.333435137783218, 	0.000000000000000, 	-2.812945856162965, 	0.000000000000000, 	2.649109640172910, 	0.000000000000000, 	
+-1.003963025744654, 	0.000000000000000, 	1.552460768755035, 	0.000000000000000, 	0.088641345335247, 	0.000000000000000, 	-2.519951327113426, 	0.000000000000000, 	
+-4.341348988610527, 	0.000000000000000, 	0.557772429359965, 	0.000000000000000, 	-1.671267412948494, 	0.000000000000000, 	0.733951350960387, 	0.000000000000000, 	
+0.409263788034864, 	0.000000000000000, 	3.566033071952806, 	0.000000000000000, 	1.882565173848352, 	0.000000000000000, 	-1.106017073793287, 	0.000000000000000, 	
+0.154456720778718, 	0.000000000000000, 	-2.513205795512153, 	0.000000000000000, 	0.310978660939421, 	0.000000000000000, 	0.579706500111723, 	0.000000000000000, 	
+0.000086383683251, 	0.000000000000000, 	-1.311866980897721, 	0.000000000000000, 	1.840007477574986, 	0.000000000000000, 	-3.253005768451345, 	0.000000000000000, 	
+1.462584328739432, 	0.000000000000000, 	1.610103610851738, 	0.000000000000000, 	0.761914676858907, 	0.000000000000000, 	0.974541361089834, 	0.000000000000000, 	
+0.686845845885983, 	0.000000000000000, 	1.849153122025191, 	0.000000000000000, 	0.787800410401453, 	0.000000000000000, 	-1.187438909666279, 	0.000000000000000, 	
+-0.754937911044720, 	0.000000000000000, 	0.084373858395232, 	0.000000000000000, 	-2.600269011710521, 	0.000000000000000, 	-0.962982842142644, 	0.000000000000000, 	
+-0.369328108540868, 	0.000000000000000, 	0.810791418361879, 	0.000000000000000, 	3.587016488699641, 	0.000000000000000, 	-0.520776145083723, 	0.000000000000000, 	
+0.640249919627884, 	0.000000000000000, 	1.103122489464969, 	0.000000000000000, 	2.231779881455556, 	0.000000000000000, 	-1.308035392685241, 	0.000000000000000, 	
+0.424070304330106, 	0.000000000000000, 	-0.200383932651189, 	0.000000000000000, 	-2.365526783356541, 	0.000000000000000, 	-0.989114757436628, 	0.000000000000000, 	
+2.770807688959777, 	0.000000000000000, 	-0.444172737462307, 	0.000000000000000, 	0.079760979374078, 	0.000000000000000, 	-0.005199118412183, 	0.000000000000000, 	
+-0.664712668309527, 	0.000000000000000, 	-0.624171857561896, 	0.000000000000000, 	0.537306979007338, 	0.000000000000000, 	-2.575955675497642, 	0.000000000000000, 	
+1.562363235756780, 	0.000000000000000, 	1.814069369848895, 	0.000000000000000, 	-1.293428583392509, 	0.000000000000000, 	-1.026188449495686, 	0.000000000000000, 	
+-2.981771815588717, 	0.000000000000000, 	-4.223468103075124, 	0.000000000000000, 	2.672674782004045, 	0.000000000000000, 	-0.856096801117735, 	0.000000000000000, 	
+0.048517345512563, 	0.000000000000000, 	-0.026860721136222, 	0.000000000000000, 	0.392932277758187, 	0.000000000000000, 	-1.331740855093099, 	0.000000000000000, 	
+-1.894292129477081, 	0.000000000000000, 	-1.425006468460681, 	0.000000000000000, 	-2.721772427617057, 	0.000000000000000, 	-1.616831100216806, 	0.000000000000000, 	
+3.551177651488947, 	0.000000000000000, 	-0.069685667896087, 	0.000000000000000, 	-3.134634907409102, 	0.000000000000000, 	-0.263627598944639, 	0.000000000000000, 	
+-1.650469945991350, 	0.000000000000000, 	-2.203580339374399, 	0.000000000000000, 	-0.872203246123242, 	0.000000000000000, 	1.230782812607287, 	0.000000000000000, 	
+0.257288860093291, 	0.000000000000000, 	1.989083106173137, 	0.000000000000000, 	-1.985638729453261, 	0.000000000000000, 	-1.416185105842892, 	0.000000000000000, 	
+-1.131097688325772, 	0.000000000000000, 	-2.245130805416057, 	0.000000000000000, 	-1.938873996219074, 	0.000000000000000, 	2.043608361562645, 	0.000000000000000, 	
+-0.583727989880841, 	0.000000000000000, 	-1.785266378212929, 	0.000000000000000, 	1.961457586224753, 	0.000000000000000, 	1.139400099963223, 	0.000000000000000, 	
+-1.979519343363991, 	0.000000000000000, 	2.003023322818429, 	0.000000000000000, 	0.229004069076829, 	0.000000000000000, 	3.452808862193135, 	0.000000000000000, 	
+2.882273808365857, 	0.000000000000000, 	-1.549450501844438, 	0.000000000000000, 	-3.283872089931876, 	0.000000000000000, 	-0.327025884099064, 	0.000000000000000, 	
+-0.054979977136430, 	0.000000000000000, 	-1.192280531479012, 	0.000000000000000, 	0.645539328365578, 	0.000000000000000, 	2.300832863404618, 	0.000000000000000, 	
+-1.092951789535240, 	0.000000000000000, 	-1.017368249363773, 	0.000000000000000, 	-0.142673056169787, 	0.000000000000000, 	0.831073544881250, 	0.000000000000000, 	
+-2.314612531587064, 	0.000000000000000, 	-2.221456299106321, 	0.000000000000000, 	0.460261143885226, 	0.000000000000000, 	0.050585301888595, 	0.000000000000000, 	
+0.364373329183988, 	0.000000000000000, 	-1.685956552069538, 	0.000000000000000, 	0.050664512351055, 	0.000000000000000, 	-0.193355783902718, 	0.000000000000000, 	
+-0.158660446046828, 	0.000000000000000, 	2.394156453841953, 	0.000000000000000, 	-1.562965718554525, 	0.000000000000000, 	-2.199750600869900, 	0.000000000000000, 	
+1.544984022381773, 	0.000000000000000, 	-1.988307216807315, 	0.000000000000000, 	-0.628240722541046, 	0.000000000000000, 	-1.436235771505429, 	0.000000000000000, 	
+1.677013691147313, 	0.000000000000000, 	1.600741781678228, 	0.000000000000000, 	-0.757380959134706, 	0.000000000000000, 	-4.784797439515566, 	0.000000000000000, 	
+0.265121462834569, 	0.000000000000000, 	3.862029485934378, 	0.000000000000000, 	2.386823577249430, 	0.000000000000000, 	-3.655779745436893, 	0.000000000000000, 	
+-0.763541621368016, 	0.000000000000000, 	-1.182140388432962, 	0.000000000000000, 	-1.349106114858063, 	0.000000000000000, 	-2.287533624396759, 	0.000000000000000, 	
+-0.028603745188423, 	0.000000000000000, 	-1.353580755934427, 	0.000000000000000, 	0.461602380352937, 	0.000000000000000, 	-0.059599055078928, 	0.000000000000000, 	
+-0.929946734342228, 	0.000000000000000, 	0.065773089295561, 	0.000000000000000, 	1.106565863102982, 	0.000000000000000, 	4.719295086373593, 	0.000000000000000, 	
+-2.108377703544395, 	0.000000000000000, 	-2.226393620240159, 	0.000000000000000, 	1.375668397437521, 	0.000000000000000, 	-0.960772428525443, 	0.000000000000000, 	
+-2.156313465390571, 	0.000000000000000, 	1.126060012375311, 	0.000000000000000, 	2.756485137030720, 	0.000000000000000, 	0.739639690862600, 	0.000000000000000, 	
+3.914769510295006, 	0.000000000000000, 	1.685232785586675, 	0.000000000000000, 	4.079058040970612, 	0.000000000000000, 	-1.174598301660513, 	0.000000000000000, 	
+-2.885776587275580, 	0.000000000000000, 	-0.241073635188767, 	0.000000000000000, 	3.080489872502403, 	0.000000000000000, 	-2.051244183999421, 	0.000000000000000, 	
+0.664330486845139, 	0.000000000000000, 	-1.697798999370016, 	0.000000000000000, 	1.452369423649782, 	0.000000000000000, 	-1.523532831019280, 	0.000000000000000, 	
+0.171981186587481, 	0.000000000000000, 	-4.685274721583927, 	0.000000000000000, 	-1.336175835319380, 	0.000000000000000, 	1.419070770428945, 	0.000000000000000, 	
+-0.035791601713475, 	0.000000000000000, 	2.291937971632081, 	0.000000000000000, 	-1.962559313450293, 	0.000000000000000, 	-4.831595589339301, 	0.000000000000000, 	
+-1.857055284000925, 	0.000000000000000, 	2.606271522635512, 	0.000000000000000, 	-0.576447978738030, 	0.000000000000000, 	0.082299166967720, 	0.000000000000000, 	
+1.888399453494614, 	0.000000000000000, 	-3.564705298046079, 	0.000000000000000, 	-0.939357831083889, 	0.000000000000000, 	-1.903578203697778, 	0.000000000000000, 	
+-2.642492215447250, 	0.000000000000000, 	-0.182990405251017, 	0.000000000000000, 	3.742026478011174, 	0.000000000000000, 	0.104295803798333, 	0.000000000000000, 	
+1.848678195370347, 	0.000000000000000, 	-1.887384346896369, 	0.000000000000000, 	0.365048973046045, 	0.000000000000000, 	-0.889638010354219, 	0.000000000000000, 	
+1.173877118428863, 	0.000000000000000, 	-1.178562827540109, 	0.000000000000000, 	0.610271645685184, 	0.000000000000000, 	1.831284815697871, 	0.000000000000000, 	
+0.449575390102283, 	0.000000000000000, 	1.597171905253443, 	0.000000000000000, 	3.918574971904773, 	0.000000000000000, 	0.868104027970404, 	0.000000000000000, 	
+0.582643134746494, 	0.000000000000000, 	2.321256382353331, 	0.000000000000000, 	-0.238118642223180, 	0.000000000000000, 	-2.890287868054370, 	0.000000000000000, 	
+0.970995414625622, 	0.000000000000000, 	0.666137930891283, 	0.000000000000000, 	-0.202435718709502, 	0.000000000000000, 	2.057930200518194, 	0.000000000000000, 	
+3.120583443719949, 	0.000000000000000, 	-0.863945271701041, 	0.000000000000000, 	0.906848893874630, 	0.000000000000000, 	-1.434124930222570, 	0.000000000000000, 	
+0.754659384848783, 	0.000000000000000, 	-5.224154442713778, 	0.000000000000000, 	2.330229744098967, 	0.000000000000000, 	1.113946320164698, 	0.000000000000000, 	
+0.523324920322840, 	0.000000000000000, 	1.750740911548348, 	0.000000000000000, 	-0.899333972913577, 	0.000000000000000, 	0.228705845203506, 	0.000000000000000, 	
+-1.934782624767648, 	0.000000000000000, 	-3.508386237231303, 	0.000000000000000, 	-2.107108523073510, 	0.000000000000000, 	0.380587645474815, 	0.000000000000000, 	
+-0.476200877183279, 	0.000000000000000, 	-2.172086712642198, 	0.000000000000000, 	1.795372535780299, 	0.000000000000000, 	-2.100318983391055, 	0.000000000000000, 	
+-0.022571122461405, 	0.000000000000000, 	0.674514020010955, 	0.000000000000000, 	-0.148872569390857, 	0.000000000000000, 	0.298175890592737, 	0.000000000000000, 	
+-1.134244492493590, 	0.000000000000000, 	-3.146848422289455, 	0.000000000000000, 	-1.357950199087602, 	0.000000000000000, 	0.667362732020878, 	0.000000000000000, 	
+-3.119397998316724, 	0.000000000000000, 	-1.189341126297637, 	0.000000000000000, 	-1.532744386856668, 	0.000000000000000, 	-1.672972484202534, 	0.000000000000000, 	
+-2.042283373871558, 	0.000000000000000, 	-1.479481547595924, 	0.000000000000000, 	-0.002668662875396, 	0.000000000000000, 	0.262737760129546, 	0.000000000000000, 	
+2.734456080621830, 	0.000000000000000, 	-0.671945925075102, 	0.000000000000000, 	-3.735078262179111, 	0.000000000000000, 	-0.161705013319883, 	0.000000000000000, 	
+0.748963512361001, 	0.000000000000000, 	1.128046374367600, 	0.000000000000000, 	0.649651335592966, 	0.000000000000000, 	1.880020215025867, 	0.000000000000000, 	
+-1.095632293842306, 	0.000000000000000, 	1.197764876160487, 	0.000000000000000, 	0.323646656252985, 	0.000000000000000, 	-1.655502751114502, 	0.000000000000000, 	
+3.666399062961496, 	0.000000000000000, 	-0.334060899735197, 	0.000000000000000, 	-2.119056978738397, 	0.000000000000000, 	3.721375117275012, 	0.000000000000000, 	
+0.044874186872307, 	0.000000000000000, 	-2.733053897593234, 	0.000000000000000, 	1.590700278891042, 	0.000000000000000, 	3.215711772781902, 	0.000000000000000, 	
+-1.792085012843801, 	0.000000000000000, 	-0.405797188885475, 	0.000000000000000, 	-0.628080020080892, 	0.000000000000000, 	-1.831815840843960, 	0.000000000000000, 	
+2.973656862522834, 	0.000000000000000, 	-0.212032655138417, 	0.000000000000000, 	0.372437389437234, 	0.000000000000000, 	-1.614030579023492, 	0.000000000000000, 	
+-0.704900996358698, 	0.000000000000000, 	1.123700273452105, 	0.000000000000000, 	-0.136371848130819, 	0.000000000000000, 	3.020284357635585, 	0.000000000000000, 	
+-0.550211350877649, 	0.000000000000000, 	5.101256236381711, 	0.000000000000000, 	3.367051512192333, 	0.000000000000000, 	-4.385131946669234, 	0.000000000000000, 	
+-3.967303337694391, 	0.000000000000000, 	-0.965894936640022, 	0.000000000000000, 	0.328366945264681, 	0.000000000000000, 	0.199041562924914, 	0.000000000000000, 	
+1.067681999025495, 	0.000000000000000, 	-1.939516091697170, 	0.000000000000000, 	-1.092980954328824, 	0.000000000000000, 	0.273786079368066, 	0.000000000000000, 	
+-0.040928322190265, 	0.000000000000000, 	-0.118368078577437, 	0.000000000000000, 	1.766589628899997, 	0.000000000000000, 	1.738321311635393, 	0.000000000000000, 	
+-2.895012794321649, 	0.000000000000000, 	1.213521771395142, 	0.000000000000000, 	0.922971726633985, 	0.000000000000000, 	1.091516563636489, 	0.000000000000000, 	
+3.226378465469620, 	0.000000000000000, 	1.149169778666974, 	0.000000000000000, 	-1.695986327709386, 	0.000000000000000, 	-0.974803077355813, 	0.000000000000000, 	
+-4.898035507513607, 	0.000000000000000, 	1.622719302889447, 	0.000000000000000, 	0.583891313586579, 	0.000000000000000, 	-1.677182424094957, 	0.000000000000000, 	
+-1.915633132814685, 	0.000000000000000, 	-1.980150370851616, 	0.000000000000000, 	0.604538269404190, 	0.000000000000000, 	0.939862406149365, 	0.000000000000000, 	
+-1.266939874246416, 	0.000000000000000, 	-1.494771249200063, 	0.000000000000000, 	0.278042784093988, 	0.000000000000000, 	0.326627416008916, 	0.000000000000000, 	
+-1.914530157643303, 	0.000000000000000, 	1.908947721862196, 	0.000000000000000, 	0.531819285694044, 	0.000000000000000, 	3.056856632319658, 	0.000000000000000, 	
+-0.389241827774643, 	0.000000000000000, 	-2.418606606780420, 	0.000000000000000, 	0.915299238878703, 	0.000000000000000, 	-0.098774174295283, 	0.000000000000000, 	
+-0.906199428444304, 	0.000000000000000, 	0.316716451217743, 	0.000000000000000, 	-4.367700643578311, 	0.000000000000000, 	1.491687997515293, 	0.000000000000000, 	
+-1.962381126288365, 	0.000000000000000, 	-0.700829196527045, 	0.000000000000000, 	3.028958963615630, 	0.000000000000000, 	-2.313461067462598, 	0.000000000000000, 	
+-1.431933239886712, 	0.000000000000000, 	-0.831153039725342, 	0.000000000000000, 	3.939495598250743, 	0.000000000000000, 	0.342974753984771, 	0.000000000000000, 	
+-2.768330763002974, 	0.000000000000000, 	-2.744010370019008, 	0.000000000000000, 	3.821352685212561, 	0.000000000000000, 	4.551065271455856, 	0.000000000000000, 	
+3.270136437041298, 	0.000000000000000, 	-3.188028411950982, 	0.000000000000000, 	-0.777075012417436, 	0.000000000000000, 	0.097110650265216, 	0.000000000000000, 	
+1.221216137608812, 	0.000000000000000, 	-1.325824244541822, 	0.000000000000000, 	-2.655296734084113, 	0.000000000000000, 	-1.074792144885704, 	0.000000000000000, 	
+2.770401584439407, 	0.000000000000000, 	5.240270645610543, 	0.000000000000000, 	0.108576672208892, 	0.000000000000000, 	-1.209394350650142, 	0.000000000000000, 	
+1.403344353838785, 	0.000000000000000, 	-0.299032904177277, 	0.000000000000000, 	4.074959450638227, 	0.000000000000000, 	1.718727473952107, 	0.000000000000000, 	
+-3.061349227080806, 	0.000000000000000, 	-1.158596888541269, 	0.000000000000000, 	3.381858904662625, 	0.000000000000000, 	0.957339964054052, 	0.000000000000000, 	
+0.179900074904899, 	0.000000000000000, 	-3.909641902506081, 	0.000000000000000, 	0.805717289408649, 	0.000000000000000, 	2.047413793928261, 	0.000000000000000, 	
+-1.273580225826614, 	0.000000000000000, 	-2.681359186869971, 	0.000000000000000, 	-0.721241345822093, 	0.000000000000000, 	-1.613090681569475, 	0.000000000000000, 	
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+-2.097831202853255, 	0.000000000000000, 	2.711952282071310, 	0.000000000000000, 	1.498539238246888, 	0.000000000000000, 	1.317457282535915, 	0.000000000000000, 	
+-0.302765938349717, 	0.000000000000000, 	-0.044623707947201, 	0.000000000000000, 	2.337405215062395, 	0.000000000000000, 	-3.980689173859100, 	0.000000000000000, 	
+
+
+};
+

Libraries/CMSIS/DSP_Lib/Examples/arm_fft_bin_example/GCC/arm_fft_bin_example_f32.c

@@ -0,0 +1,158 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:	     arm_fft_bin_example_f32.c
+*
+* Description:   Example code demonstrating calculation of Max energy bin of
+*                frequency domain of input signal.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup FrequencyBin Frequency Bin Example
+ *
+ * \par Description
+ * \par
+ * Demonstrates the calculation of the maximum energy bin in the frequency
+ * domain of the input signal with the use of Complex FFT, Complex
+ * Magnitude, and Maximum functions.
+ *
+ * \par Algorithm:
+ * \par
+ * The input test signal contains a 10 kHz signal with uniformly distributed white noise.
+ * Calculating the FFT of the input signal will give us the maximum energy of the
+ * bin corresponding to the input frequency of 10 kHz.
+ *
+ * \par Block Diagram:
+ * \image html FFTBin.gif "Block Diagram"
+ * \par
+ * The figure below shows the time domain signal of 10 kHz signal with
+ * uniformly distributed white noise, and the next figure shows the input
+ * in the frequency domain. The bin with maximum energy corresponds to 10 kHz signal.
+ * \par
+ * \image html FFTBinInput.gif "Input signal in Time domain"
+ * \image html FFTBinOutput.gif "Input signal in Frequency domain"
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32_10khz points to the input data
+ * \li \c testOutput points to the output data
+ * \li \c fftSize length of FFT
+ * \li \c ifftFlag flag for the selection of CFFT/CIFFT
+ * \li \c doBitReverse Flag for selection of normal order or bit reversed order
+ * \li \c refIndex reference index value at which maximum energy of bin ocuurs
+ * \li \c testIndex calculated index value at which maximum energy of bin ocuurs
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_cfft_f32()
+ * - arm_cmplx_mag_f32()
+ * - arm_max_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_fft_bin_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_fft_bin_example_f32.c
+  */
+
+
+#include "arm_math.h"
+#include "arm_const_structs.h"
+
+#define TEST_LENGTH_SAMPLES 2048
+
+/* -------------------------------------------------------------------
+* External Input and Output buffer Declarations for FFT Bin Example
+* ------------------------------------------------------------------- */
+extern float32_t testInput_f32_10khz[TEST_LENGTH_SAMPLES];
+static float32_t testOutput[TEST_LENGTH_SAMPLES/2];
+
+/* ------------------------------------------------------------------
+* Global variables for FFT Bin Example
+* ------------------------------------------------------------------- */
+uint32_t fftSize = 1024;
+uint32_t ifftFlag = 0;
+uint32_t doBitReverse = 1;
+
+/* Reference index at which max energy of bin ocuurs */
+uint32_t refIndex = 213, testIndex = 0;
+
+/* ----------------------------------------------------------------------
+* Max magnitude FFT Bin test
+* ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+
+  arm_status status;
+  float32_t maxValue;
+
+  status = ARM_MATH_SUCCESS;
+
+  /* Process the data through the CFFT/CIFFT module */
+  arm_cfft_f32(&arm_cfft_sR_f32_len1024, testInput_f32_10khz, ifftFlag, doBitReverse);
+
+  /* Process the data through the Complex Magnitude Module for
+  calculating the magnitude at each bin */
+  arm_cmplx_mag_f32(testInput_f32_10khz, testOutput, fftSize);
+
+  /* Calculates maxValue and returns corresponding BIN value */
+  arm_max_f32(testOutput, fftSize, &maxValue, &testIndex);
+
+  if(testIndex !=  refIndex)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signals fail the PASS check.
+  ** This denotes a test failure
+  ** ------------------------------------------------------------------- */
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_fir_example/ARM/arm_fir_data.c

@@ -0,0 +1,134 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_fir_data.c
+*   
+* Description:	 Data file used for example code
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+ * -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+** Test input signal contains 1000Hz + 15000 Hz
+** ------------------------------------------------------------------- */
+
+float32_t testInput_f32_1kHz_15kHz[320] =
+{
++0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
+-0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
++0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
++0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
++0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
++0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
+-0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
+-0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
++0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
++0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
+-0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
++0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+-0.8660254038f, -0.4619397663f, -1.3194792169f, -1.1827865776f, -0.5000000000f, -1.1827865776f, -1.3194792169f, -0.4619397663f, 
+-0.8660254038f, -1.2552931065f, -0.3535533906f, -0.4174197128f, -1.0000000000f, -0.1913417162f, +0.0947343455f, -0.5924659585f, 
+-0.0000000000f, +0.5924659585f, -0.0947343455f, +0.1913417162f, +1.0000000000f, +0.4174197128f, +0.3535533906f, +1.2552931065f, 
++0.8660254038f, +0.4619397663f, +1.3194792169f, +1.1827865776f, +0.5000000000f, +1.1827865776f, +1.3194792169f, +0.4619397663f, 
++0.8660254038f, +1.2552931065f, +0.3535533906f, +0.4174197128f, +1.0000000000f, +0.1913417162f, -0.0947343455f, +0.5924659585f, 
++0.0000000000f, -0.5924659585f, +0.0947343455f, -0.1913417162f, -1.0000000000f, -0.4174197128f, -0.3535533906f, -1.2552931065f, 
+};
+
+float32_t refOutput[320] = 
+{
++0.0000000000f, -0.0010797829f, -0.0007681386f, -0.0001982932f, +0.0000644313f, +0.0020854271f, +0.0036891871f, +0.0015855941f, 
+-0.0026280805f, -0.0075907658f, -0.0119390538f, -0.0086665968f, +0.0088981202f, +0.0430539279f, +0.0974468742f, +0.1740405600f, 
++0.2681416601f, +0.3747720089f, +0.4893362230f, +0.6024154672f, +0.7058740791f, +0.7968348987f, +0.8715901940f, +0.9277881093f, 
++0.9682182661f, +0.9934674267f, +1.0012052245f, +0.9925859371f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, -0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, +0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, -0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, +0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, -0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, +0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, +0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, +0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, +0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, -0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f, 
++0.7085021596f, +0.6100062330f, +0.5012752767f, +0.3834386057f, +0.2592435399f, +0.1309866321f, +0.0000000000f, -0.1309866321f, 
+-0.2592435399f, -0.3834386057f, -0.5012752767f, -0.6100062330f, -0.7085021596f, -0.7952493046f, -0.8679010068f, -0.9257026822f, 
+-0.9681538347f, -0.9936657199f, -1.0019733630f, -0.9936657199f, -0.9681538347f, -0.9257026822f, -0.8679010068f, -0.7952493046f, 
+-0.7085021596f, -0.6100062330f, -0.5012752767f, -0.3834386057f, -0.2592435399f, -0.1309866321f, +0.0000000000f, +0.1309866321f, 
++0.2592435399f, +0.3834386057f, +0.5012752767f, +0.6100062330f, +0.7085021596f, +0.7952493046f, +0.8679010068f, +0.9257026822f, 
++0.9681538347f, +0.9936657199f, +1.0019733630f, +0.9936657199f, +0.9681538347f, +0.9257026822f, +0.8679010068f, +0.7952493046f 
+};
+

Libraries/CMSIS/DSP_Lib/Examples/arm_fir_example/ARM/arm_fir_example_f32.c

@@ -0,0 +1,233 @@
+/* ----------------------------------------------------------------------
+ * Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+ *
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+ * Title:        arm_fir_example_f32.c
+ *
+ * Description:  Example code demonstrating how an FIR filter can be used
+ *               as a low pass filter.
+ *
+ * Target Processor: Cortex-M4/Cortex-M3
+ *
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup FIRLPF FIR Lowpass Filter Example
+ *
+ * \par Description:
+ * \par
+ * Removes high frequency signal components from the input using an FIR lowpass filter.
+ * The example demonstrates how to configure an FIR filter and then pass data through
+ * it in a block-by-block fashion.
+ * \image html FIRLPF_signalflow.gif
+ *
+ * \par Algorithm:
+ * \par
+ * The input signal is a sum of two sine waves:  1 kHz and 15 kHz.
+ * This is processed by an FIR lowpass filter with cutoff frequency 6 kHz.
+ * The lowpass filter eliminates the 15 kHz signal leaving only the 1 kHz sine wave at the output.
+ * \par
+ * The lowpass filter was designed using MATLAB with a sample rate of 48 kHz and
+ * a length of 29 points.
+ * The MATLAB code to generate the filter coefficients is shown below:
+ * <pre>
+ *     h = fir1(28, 6/24);
+ * </pre>
+ * The first argument is the "order" of the filter and is always one less than the desired length.
+ * The second argument is the normalized cutoff frequency.  This is in the range 0 (DC) to 1.0 (Nyquist).
+ * A 6 kHz cutoff with a Nyquist frequency of 24 kHz lies at a normalized frequency of 6/24 = 0.25.
+ * The CMSIS FIR filter function requires the coefficients to be in time reversed order.
+ * <pre>
+ *     fliplr(h)
+ * </pre>
+ * The resulting filter coefficients and are shown below.
+ * Note that the filter is symmetric (a property of linear phase FIR filters)
+ * and the point of symmetry is sample 14.  Thus the filter will have a delay of
+ * 14 samples for all frequencies.
+ * \par
+ * \image html FIRLPF_coeffs.gif
+ * \par
+ * The frequency response of the filter is shown next.
+ * The passband gain of the filter is 1.0 and it reaches 0.5 at the cutoff frequency 6 kHz.
+ * \par
+ * \image html FIRLPF_response.gif
+ * \par
+ * The input signal is shown below.
+ * The left hand side shows the signal in the time domain while the right hand side is a frequency domain representation.
+ * The two sine wave components can be clearly seen.
+ * \par
+ * \image html FIRLPF_input.gif
+ * \par
+ * The output of the filter is shown below.  The 15 kHz component has been eliminated.
+ * \par
+ * \image html FIRLPF_output.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32_1kHz_15kHz points to the input data
+ * \li \c refOutput points to the reference output data
+ * \li \c testOutput points to the test output data
+ * \li \c firStateF32 points to state buffer
+ * \li \c firCoeffs32 points to coefficient buffer
+ * \li \c blockSize number of samples processed at a time
+ * \li \c numBlocks number of frames
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_fir_init_f32()
+ * - arm_fir_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_fir_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_fir_example_f32.c
+ */
+
+/* ----------------------------------------------------------------------
+** Include Files
+** ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+/* ----------------------------------------------------------------------
+** Macro Defines
+** ------------------------------------------------------------------- */
+
+#define TEST_LENGTH_SAMPLES  320
+#define SNR_THRESHOLD_F32    140.0f
+#define BLOCK_SIZE            32
+#define NUM_TAPS              29
+
+/* -------------------------------------------------------------------
+ * The input signal and reference output (computed with MATLAB)
+ * are defined externally in arm_fir_lpf_data.c.
+ * ------------------------------------------------------------------- */
+
+extern float32_t testInput_f32_1kHz_15kHz[TEST_LENGTH_SAMPLES];
+extern float32_t refOutput[TEST_LENGTH_SAMPLES];
+
+/* -------------------------------------------------------------------
+ * Declare Test output buffer
+ * ------------------------------------------------------------------- */
+
+static float32_t testOutput[TEST_LENGTH_SAMPLES];
+
+/* -------------------------------------------------------------------
+ * Declare State buffer of size (numTaps + blockSize - 1)
+ * ------------------------------------------------------------------- */
+
+static float32_t firStateF32[BLOCK_SIZE + NUM_TAPS - 1];
+
+/* ----------------------------------------------------------------------
+** FIR Coefficients buffer generated using fir1() MATLAB function.
+** fir1(28, 6/24)
+** ------------------------------------------------------------------- */
+
+const float32_t firCoeffs32[NUM_TAPS] = {
+  -0.0018225230f, -0.0015879294f, +0.0000000000f, +0.0036977508f, +0.0080754303f, +0.0085302217f, -0.0000000000f, -0.0173976984f,
+  -0.0341458607f, -0.0333591565f, +0.0000000000f, +0.0676308395f, +0.1522061835f, +0.2229246956f, +0.2504960933f, +0.2229246956f,
+  +0.1522061835f, +0.0676308395f, +0.0000000000f, -0.0333591565f, -0.0341458607f, -0.0173976984f, -0.0000000000f, +0.0085302217f,
+  +0.0080754303f, +0.0036977508f, +0.0000000000f, -0.0015879294f, -0.0018225230f
+};
+
+/* ------------------------------------------------------------------
+ * Global variables for FIR LPF Example
+ * ------------------------------------------------------------------- */
+
+uint32_t blockSize = BLOCK_SIZE;
+uint32_t numBlocks = TEST_LENGTH_SAMPLES/BLOCK_SIZE;
+
+float32_t  snr;
+
+/* ----------------------------------------------------------------------
+ * FIR LPF Example
+ * ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+  uint32_t i;
+  arm_fir_instance_f32 S;
+  arm_status status;
+  float32_t  *inputF32, *outputF32;
+
+  /* Initialize input and output buffer pointers */
+  inputF32 = &testInput_f32_1kHz_15kHz[0];
+  outputF32 = &testOutput[0];
+
+  /* Call FIR init function to initialize the instance structure. */
+  arm_fir_init_f32(&S, NUM_TAPS, (float32_t *)&firCoeffs32[0], &firStateF32[0], blockSize);
+
+  /* ----------------------------------------------------------------------
+  ** Call the FIR process function for every blockSize samples
+  ** ------------------------------------------------------------------- */
+
+  for(i=0; i < numBlocks; i++)
+  {
+    arm_fir_f32(&S, inputF32 + (i * blockSize), outputF32 + (i * blockSize), blockSize);
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Compare the generated output against the reference output computed
+  ** in MATLAB.
+  ** ------------------------------------------------------------------- */
+
+  snr = arm_snr_f32(&refOutput[0], &testOutput[0], TEST_LENGTH_SAMPLES);
+
+  if (snr < SNR_THRESHOLD_F32)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+  else
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signal does not match the reference output.
+  ** ------------------------------------------------------------------- */
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+/** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_fir_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_fir_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_graphic_equalizer_example/ARM/arm_graphic_equalizer_data.c

@@ -0,0 +1,134 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_graphic_equalizer_data.c
+*   
+* Description:	 Data file used for example code
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+ * -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+float32_t testRefOutput_f32[320] = {
+
+0.000000000000000000,	0.001898396760225296,	0.004215449094772339,	0.007432077080011368,	0.010948467999696732,	0.015026375651359558,	0.019191544502973557,	0.023574527353048325,	
+0.027919445186853409,	0.032277785241603851,	0.036551639437675476,	0.040732793509960175,	0.044799156486988068,	0.048710610717535019,	0.052476800978183746,	0.056059073656797409,	
+0.059482168406248093,	0.062726479023694992,	0.065821025520563126,	0.068763464689254761,	0.071577839553356171,	0.074270240962505341,	0.076856281608343124,	0.079344697296619415,	
+0.081745062023401260,	0.084067162126302719,	0.086318407207727432,	0.088509257882833481,	0.090647127479314804,	0.092742368578910828,	0.094802625477313995,	0.096837285906076431,	
+0.098853722214698792,	0.100859899073839190,	0.102862443774938580,	0.104867763817310330,	0.106881409883499150,	0.108908228576183320,	0.110952425748109820,	0.113017357885837550,	
+0.115105822682380680,	0.117219865322113040,	0.119361080229282380,	0.121530555188655850,	0.123729091137647630,	0.125957202166318890,	0.128215309232473370,	0.130503740161657330,	
+0.132822841405868530,	0.135173004120588300,	0.137554679065942760,	0.139968376606702800,	0.142414685338735580,	0.144894234836101530,	0.147407654672861100,	0.149955596774816510,	
+0.152538605034351350,	0.155157200992107390,	0.157811731100082400,	0.160502441227436070,	0.163229387253522870,	0.165992442518472670,	0.168791320174932480,	0.171625509858131410,	
+0.174494370818138120,	0.177397061139345170,	0.180332608520984650,	0.183299910277128220,	0.186297744512557980,	0.189324837177991870,	0.192379791289567950,	0.195461250841617580,	
+0.198567759245634080,	0.201697919517755510,	0.204850304871797560,	0.208023533225059510,	0.211216274648904800,	0.214427210390567780,	0.217655111104249950,	0.220898788422346120,	
+0.224157124757766720,	0.227429077029228210,	0.230713658034801480,	0.234009962528944020,	0.237317133694887160,	0.240634419023990630,	0.243961080908775330,	0.247296508401632310,	
+0.250640105456113820,	0.253991369158029560,	0.257349837571382520,	0.260715119540691380,	0.264086868613958360,	0.267464816570281980,	0.270848698914051060,	0.274238351732492450,	
+0.277633611112833020,	0.281034380197525020,	0.284440591931343080,	0.287852220237255100,	0.291269283741712570,	0.294691801071166990,	0.298119872808456420,	0.301553562283515930,	
+0.304993014782667160,	0.308438356965780260,	0.311889752745628360,	0.315347377210855480,	0.318811416625976560,	0.322282072156667710,	0.325759567320346830,	0.329244095832109450,	
+0.332735907286405560,	0.336235217750072480,	0.339742250740528110,	0.343257248401641850,	0.346780419349670410,	0.350311983376741410,	0.353852160274982450,	0.357401121407747270,	
+0.360959105193614960,	0.364526227116584780,	0.368102725595235820,	0.371688675135374070,	0.375284302979707720,	0.378889638930559160,	0.382504884153604510,	0.386130042374134060,	
+0.389765247702598570,	0.393410529941320420,	0.397065933793783190,	0.400731507688760760,	0.404407206922769550,	0.408093083649873730,	0.411789052188396450,	0.415495119988918300,	
+0.419211201369762420,	0.422937240451574330,	0.426673140376806260,	0.430418811738491060,	0.434174135327339170,	0.437938995659351350,	0.441713258624076840,	0.445496778935194020,	
+0.449289388954639430,	0.453090950846672060,	0.456901267170906070,	0.460720170289278030,	0.464547459036111830,	0.468382950872182850,	0.472226426005363460,	0.476077698171138760,	
+0.479936532676219940,	0.483802750706672670,	0.487676106393337250,	0.491556398570537570,	0.495443399995565410,	0.499336875975131990,	0.503236617892980580,	0.507142387330532070,	
+0.511053957045078280,	0.514971107244491580,	0.518893606960773470,	0.522821225225925450,	0.526753749698400500,	0.530690938234329220,	0.534632585942745210,	0.538578454405069350,	
+0.542528338730335240,	0.546481993049383160,	0.550439231097698210,	0.554399792104959490,	0.558363504707813260,	0.562330115586519240,	0.566299438476562500,	0.570271246135234830,	
+0.574245333671569820,	0.578221492469310760,	0.582199502736330030,	0.586179181933403020,	0.590160276740789410,	0.594142623245716090,	0.598125983029603960,	0.602110169827938080,	
+0.606094967573881150,	0.610080175101757050,	0.614065583795309070,	0.618050977587699890,	0.622036151587963100,	0.626020893454551700,	0.630004994571208950,	0.633988231420516970,	
+0.637970402836799620,	0.641951277852058410,	0.645930647850036620,	0.649908289313316350,	0.653883971273899080,	0.657857488840818410,	0.661828581243753430,	0.665797054767608640,	
+0.669762641191482540,	0.673725124448537830,	0.677684243768453600,	0.681639779359102250,	0.685591462999582290,	0.689539063721895220,	0.693482317030429840,	0.697420965880155560,	
+0.701354760676622390,	0.705283410847187040,	0.709206689149141310,	0.713124278932809830,	0.717035952955484390,	0.720941375941038130,	0.724840316921472550,	0.728732451796531680,	
+0.732617516070604320,	0.736495196819305420,	0.740365199744701390,	0.744227230548858640,	0.748080968856811520,	0.751926124095916750,	0.755762357264757160,	0.759589381515979770,	
+0.763406842947006230,	0.767214450985193250,	0.771011855453252790,	0.774798732250928880,	0.778574761003255840,	0.782339565455913540,	0.786092851310968400,	0.789834223687648770,	
+0.793563373386859890,	0.797279909253120420,	0.800983514636754990,	0.804673787206411360,	0.808350402861833570,	0.812012966722249980,	0.815661124885082240,	0.819294504821300510,	
+0.822912722826004030,	0.826515413820743560,	0.830102190375328060,	0.833672653883695600,	0.837226435542106630,	0.840763118118047710,	0.844282336533069610,	0.847783654928207400,	
+0.851266715675592420,	0.854731071740388870,	0.858176350593566890,	0.861602116376161580,	0.865007970482110980,	0.868393491953611370,	0.871758259832859040,	0.875101849436759950,	
+0.878423850983381270,	0.881723806262016300,	0.885001312941312790,	0.888255912810564040,	0.891487173736095430,	0.894694659858942030,	0.897877920418977740,	0.901036512106657030,	
+0.904169965535402300,	0.907277844846248630,	0.910359673202037810,	0.913415014743804930,	0.916443370282649990,	0.919444311410188670,	0.922417331486940380,	0.925361987203359600,	
+0.928277771919965740,	0.931164238601922990,	0.934020876884460450,	0.936847217381000520,	0.939642757177352910,	0.942407000809907910,	0.945139460265636440,	0.947839632630348210,	
+0.950507018715143200,	0.953141096979379650,	0.955741371959447860,	0.958307322114706040,	0.960838429629802700,	0.963334184139966960,	0.965794049203395840,	0.968217510730028150,	
+0.970604017376899720,	0.972953058779239650,	0.975264083594083790,	0.977536566555500030,	0.979769956320524220,	0.981963708996772770,	0.984117280691862110,	0.986230112612247470,	
+0.988301653414964680,	0.990331344306468960,	0.992318630218505860,	0.994262944906950000,	0.996163722127676010,	0.998020399361848830,	0.999832402914762500,	1.001599155366420700,	
+1.003320086747407900,	1.004994612187147100,	1.006622135639190700,	1.008202098309993700,	1.009733878076076500,	1.011216927319765100,	1.012650609016418500,	1.014034371823072400,	
+1.015367589890956900,	1.016649682074785200,	1.017880033701658200,	1.019058048725128200,	1.020183108747005500,	1.021254621446132700,	1.022271949797868700,	1.023234523832798000,	
+
+};
+/* ----------------------------------------------------------------------
+** Test input - logarithmic chirp signal
+** ------------------------------------------------------------------- */
+
+float32_t testInput_f32[320] =
+  {
+    0.000000000000000061,	0.002622410992047861,	0.005253663973466970,	0.007893770384930297,	0.010542741395035495,	0.013200587895525877,	0.015867320496454066,	0.018542949521290073,	
+0.021227485001971542,	0.023920936673895138,	0.026623313970853074,	0.029334626019908643,	0.032054881636210709,	0.034784089317753723,	0.037522257240071598,	0.040269393250875855,	
+0.043025504864628375,	0.045790599257054837,	0.048564683259595690,	0.051347763353792118,	0.054139845665610427,	0.056940935959702531,	0.059751039633601337,	0.062570161711849828,	
+0.065398306840066575,	0.068235479278943648,	0.071081682898178900,	0.073936921170339814,	0.076801197164660218,	0.079674513540768196,	0.082556872542344922,	0.085448275990715375,	
+0.088348725278367082,	0.091258221362398390,	0.094176764757897533,	0.097104355531246703,	0.100040993293358240,	0.102986677192832010,	0.105941405909045980,	0.108905177645166230,	
+0.111877990121087980,	0.114859840566297130,	0.117850725712659680,	0.120850641787131110,	0.123859584504392860,	0.126877549059407400,	0.129904530119898690,	0.132940521818751430,	
+0.135985517746334080,	0.139039510942737950,	0.142102493889940090,	0.145174458503884160,	0.148255396126476810,	0.151345297517508140,	0.154444152846483080,	0.157551951684374300,	
+0.160668682995289720,	0.163794335128054890,	0.166928895807713030,	0.170072352126936720,	0.173224690537355760,	0.176385896840798810,	0.179555956180445340,	0.182734853031894270,	
+0.185922571194139130,	0.189119093780459800,	0.192324403209221870,	0.195538481194587030,	0.198761308737133020,	0.201992866114384050,	0.205233132871247170,	0.208482087810360570,	
+0.211739708982344370,	0.215005973675965020,	0.218280858408200220,	0.221564338914212730,	0.224856390137231970,	0.228156986218334190,	0.231466100486134670,	0.234783705446379690,	
+0.238109772771442410,	0.241444273289723230,	0.244787176974952890,	0.248138452935395580,	0.251498069402956710,	0.254865993722190930,	0.258242192339209860,	0.261626630790492030,	
+0.265019273691591620,	0.268420084725748410,	0.271829026632395280,	0.275246061195565440,	0.278671149232197430,	0.282104250580339830,	0.285545324087251580,	0.288994327597401960,	
+0.292451217940364990,	0.295915950918612280,	0.299388481295203350,	0.302868762781368150,	0.306356748023990040,	0.309852388592980640,	0.313355634968552230,	0.316866436528383590,	
+0.320384741534681720,	0.323910497121136620,	0.327443649279772870,	0.330984142847692230,	0.334531921493712690,	0.338086927704900790,	0.341649102772995210,	0.345218386780727190,	
+0.348794718588032520,	0.352378035818156910,	0.355968274843654950,	0.359565370772282730,	0.363169257432780890,	0.366779867360555120,	0.370397131783246010,	0.374020980606193880,	
+0.377651342397795690,	0.381288144374756830,	0.384931312387234990,	0.388580770903877330,	0.392236442996751310,	0.395898250326170650,	0.399566113125414350,	0.403239950185338420,	
+0.406919678838884410,	0.410605214945482130,	0.414296472875345100,	0.417993365493664670,	0.421695804144698540,	0.425403698635752780,	0.429116957221065130,	0.432835486585582130,	
+0.436559191828633180,	0.440287976447505720,	0.444021742320914510,	0.447760389692375140,	0.451503817153472210,	0.455251921627031540,	0.459004598350192470,	0.462761740857380200,	
+0.466523240963184150,	0.470288988745136360,	0.474058872526396560,	0.477832778858340690,	0.481610592503056990,	0.485392196415748600,	0.489177471727042850,	0.492966297725213780,	
+0.496758551838309250,	0.500554109616195060,	0.504352844712508190,	0.508154628866524960,	0.511959331884944910,	0.515766821623591440,	0.519576963969030530,	0.523389622820107150,	
+0.527204660069405030,	0.531021935584629400,	0.534841307189911630,	0.538662630647041900,	0.542485759636628150,	0.546310545739186690,	0.550136838416161340,	0.553964484990880020,	
+0.557793330629441700,	0.561623218321546380,	0.565453988861259300,	0.569285480827721570,	0.573117530565801950,	0.576949972166696630,	0.580782637448476910,	0.584615355936589420,	
+0.588447954844309340,	0.592280259053150400,	0.596112091093235260,	0.599943271123626440,	0.603773616912622660,	0.607602943818024150,	0.611431064767369080,	0.615257790238142090,	
+0.619082928237961740,	0.622906284284749700,	0.626727661386881850,	0.630546860023327600,	0.634363678123782030,	0.638177911048790960,	0.641989351569874020,	0.645797789849653410,	
+0.649603013421986450,	0.653404807172108140,	0.657202953316791350,	0.660997231384523490,	0.664787418195706640,	0.668573287842887610,	0.672354611671016960,	0.676131158257749170,	
+0.679902693393781730,	0.683668980063242500,	0.687429778424128110,	0.691184845788802130,	0.694933936604551380,	0.698676802434213370,	0.702413191936877570,	0.706142850848662460,	
+0.709865521963579990,	0.713580945114492330,	0.717288857154159800,	0.720988991936399870,	0.724681080297347790,	0.728364850036839040,	0.732040025899910680,	0.735706329558433620,	
+0.739363479592880620,	0.743011191474238440,	0.746649177546067850,	0.750277147006723990,	0.753894805891742180,	0.757501857056394940,	0.761098000158428880,	0.764682931640995540,	
+0.768256344715771980,	0.771817929346292900,	0.775367372231492210,	0.778904356789468790,	0.782428563141483460,	0.785939668096195860,	0.789437345134148760,	0.792921264392515420,	
+0.796391092650110770,	0.799846493312681210,	0.803287126398485760,	0.806712648524170680,	0.810122712890953390,	0.813516969271127150,	0.816895063994893090,	0.820256639937531280,	
+0.823601336506926020,	0.826928789631450890,	0.830238631748229430,	0.833530491791779850,	0.836803995183058700,	0.840058763818912760,	0.843294416061954100,	0.846510566730867220,	
+0.849706827091166740,	0.852882804846411770,	0.856038104129895340,	0.859172325496819990,	0.862285065916973510,	0.865375918767918860,	0.868444473828712590,	0.871490317274166260,	
+0.874513031669661770,	0.877512195966544280,	0.880487385498096800,	0.883438171976119850,	0.886364123488128100,	0.889264804495180530,	0.892139775830360640,	0.894988594697921020,	
+0.897810814673113080,	0.900605985702712770,	0.903373654106265470,	0.906113362578062300,	0.908824650189867690,	0.911507052394417540,	0.914160101029702910,	0.916783324324059180,	
+0.919376246902079860,	0.921938389791372770,	0.924469270430179120,	0.926968402675872660,	0.929435296814361430,	0.931869459570409790,	0.934270394118903560,	0.936637600097074200,	
+0.938970573617708970,	0.941268807283364040,	0.943531790201601380,	0.945759008001275100,	0.947949942849885320,	0.950104073472023970,	0.952220875168933280,	0.954299819839202090,	
+0.956340376000621160,	0.958342008813221960,	0.960304180103520260,	0.962226348389994210,	0.964107968909812760,	0.965948493646846980,	0.967747371360983650,	0.969504047618768740,	
+0.971217964825405680,	0.972888562258134030,	0.974515276101013520,	0.976097539481141750,	0.977634782506330400,	0.979126432304266880,	0.980571913063189360,	0.981970646074102120,	
+0.983322049774557390,	0.984625539794035220,	0.985880529000944810,	0.987086427551279730,	0.988242642938953360,	0.989348580047844540,	0.990403641205582440,	0.991407226239099710,	
+0.992358732531984260,	0.993257555083659870,	0.994103086570423680,	0.994894717408374870,	0.995631835818261310,	0.996313827892278070,	0.996940077662846650,	0.997509967173408010,	
+
+  };

Libraries/CMSIS/DSP_Lib/Examples/arm_graphic_equalizer_example/ARM/arm_graphic_equalizer_example_q31.c

@@ -0,0 +1,411 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_graphic_equalizer_example_q31.c
+*
+* Description:   Example showing an audio graphic equalizer constructed
+*                out of Biquad filters.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup GEQ5Band Graphic Audio Equalizer Example
+ *
+ * \par Description:
+ * \par
+ * This example demonstrates how a 5-band graphic equalizer can be constructed
+ * using the Biquad cascade functions.
+ * A graphic equalizer is used in audio applications to vary the tonal quality
+ * of the audio.
+ *
+ * \par Block Diagram:
+ * \par
+ * The design is based on a cascade of 5 filter sections.
+ * \image html GEQ_signalflow.gif
+ * Each filter section is 4th order and consists of a cascade of two Biquads.
+ * Each filter has a nominal gain of 0 dB (1.0 in linear units) and
+ * boosts or cuts signals within a specific frequency range.
+ * The edge frequencies between the 5 bands are 100, 500, 2000, and 6000 Hz.
+ * Each band has an adjustable boost or cut in the range of +/- 9 dB.
+ * For example, the band that extends from 500 to 2000 Hz has the response shown below:
+ * \par
+ * \image html GEQ_bandresponse.gif
+ * \par
+ * With 1 dB steps, each filter has a total of 19 different settings.
+ * The filter coefficients for all possible 19 settings were precomputed
+ * in MATLAB and stored in a table.  With 5 different tables, there are
+ * a total of 5 x 19 = 95 different 4th order filters.
+ * All 95 responses are shown below:
+ * \par
+ * \image html GEQ_allbandresponse.gif
+ * \par
+ * Each 4th order filter has 10 coefficents for a grand total of 950 different filter
+ * coefficients that must be tabulated. The input and output data is in Q31 format.
+ * For better noise performance, the two low frequency bands are implemented using the high
+ * precision 32x64-bit Biquad filters. The remaining 3 high frequency bands use standard
+ * 32x32-bit Biquad filters. The input signal used in the example is a logarithmic chirp.
+ * \par
+ * \image html GEQ_inputchirp.gif
+ * \par
+ * The array <code>bandGains</code> specifies the gain in dB to apply in each band.
+ * For example, if <code>bandGains={0, -3, 6, 4, -6};</code> then the output signal will be:
+ * \par
+ * \image html GEQ_outputchirp.gif
+ * \par
+ * \note The output chirp signal follows the gain or boost of each band.
+ * \par
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32 points to the input data
+ * \li \c testRefOutput_f32 points to the reference output data
+ * \li \c testOutput points to the test output data
+ * \li \c inputQ31 temporary input buffer
+ * \li \c outputQ31 temporary output buffer
+ * \li \c biquadStateBand1Q31 points to state buffer for band1
+ * \li \c biquadStateBand2Q31 points to state buffer for band2
+ * \li \c biquadStateBand3Q31 points to state buffer for band3
+ * \li \c biquadStateBand4Q31 points to state buffer for band4
+ * \li \c biquadStateBand5Q31 points to state buffer for band5
+ * \li \c coeffTable points to coefficient buffer for all bands
+ * \li \c gainDB gain buffer which has gains applied for all the bands
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_biquad_cas_df1_32x64_init_q31()
+ * - arm_biquad_cas_df1_32x64_q31()
+ * - arm_biquad_cascade_df1_init_q31()
+ * - arm_biquad_cascade_df1_q31()
+ * - arm_scale_q31()
+ * - arm_scale_f32()
+ * - arm_float_to_q31()
+ * - arm_q31_to_float()
+ *
+ * <b> Refer  </b>
+ * \link arm_graphic_equalizer_example_q31.c \endlink
+ *
+ */
+
+
+/** \example arm_graphic_equalizer_example_q31.c
+ */
+
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+/* Length of the overall data in the test */
+#define TESTLENGTH 320
+
+/* Block size for the underlying processing */
+#define BLOCKSIZE 32
+
+/* Total number of blocks to run */
+#define NUMBLOCKS (TESTLENGTH/BLOCKSIZE)
+
+/* Number of 2nd order Biquad stages per filter */
+#define NUMSTAGES 2
+
+#define SNR_THRESHOLD_F32  98
+
+/* -------------------------------------------------------------------
+ * External Declarations for Input and Output buffers
+ * ------------------------------------------------------------------- */
+
+extern float32_t testInput_f32[TESTLENGTH];
+static float32_t testOutput[TESTLENGTH];
+
+extern float32_t testRefOutput_f32[TESTLENGTH];
+
+/* ----------------------------------------------------------------------
+** Q31 state buffers for Band1, Band2, Band3, Band4, Band5
+** ------------------------------------------------------------------- */
+
+static q63_t biquadStateBand1Q31[4 * 2];
+static q63_t biquadStateBand2Q31[4 * 2];
+static q31_t biquadStateBand3Q31[4 * 2];
+static q31_t biquadStateBand4Q31[4 * 2];
+static q31_t biquadStateBand5Q31[4 * 2];
+
+/* ----------------------------------------------------------------------
+** Q31 input and output buffers
+** ------------------------------------------------------------------- */
+
+q31_t inputQ31[BLOCKSIZE];
+q31_t outputQ31[BLOCKSIZE];
+
+/* ----------------------------------------------------------------------
+** Entire coefficient table.  There are 10 coefficients per 4th order Biquad
+** cascade filter.  The first 10 coefficients correspond to the -9 dB gain
+** setting of band 1; the next 10 coefficient correspond to the -8 dB gain
+** setting of band 1; and so on.  There are 10*19=190 coefficients in total
+** for band 1 (gains = -9, -8, -7, ..., 9).  After this come the 190 coefficients
+** for band 2.
+**
+** The coefficients are in Q29 format and require a postShift of 2.
+** ------------------------------------------------------------------- */
+
+const q31_t coeffTable[950] = {
+
+  /* Band 1, -9 dB gain */
+  535576962, -1071153923, 535576962, 1073741824, -536870912, 535576962, -1063501998, 527979313, 1060865294, -524146981,
+  /* Band 1, -8 dB gain */
+  535723226, -1071446451, 535723226, 1073741824, -536870912, 535723226, -1063568947, 527903217, 1061230578, -524503778,
+  535868593, -1071737186, 535868593, 1073741824, -536870912, 535868593, -1063627467, 527819780, 1061585502, -524850686,
+  536013181, -1072026363, 536013181, 1073741824, -536870912, 536013181, -1063677598, 527728935, 1061930361, -525187972,
+  536157109, -1072314217, 536157109, 1073741824, -536870912, 536157109, -1063719372, 527630607, 1062265438, -525515897,
+  536300492, -1072600983, 536300492, 1073741824, -536870912, 536300492, -1063752815, 527524720, 1062591011, -525834716,
+  536443447, -1072886894, 536443447, 1073741824, -536870912, 536443447, -1063777945, 527411186, 1062907350, -526144676,
+  536586091, -1073172183, 536586091, 1073741824, -536870912, 536586091, -1063794775, 527289917, 1063214717, -526446017,
+  536728541, -1073457082, 536728541, 1073741824, -536870912, 536728541, -1063803308, 527160815, 1063513366, -526738975,
+  536870912, -1073741824, 536870912, 1073741824, -536870912, 536870912, -1063803543, 527023777, 1063803543, -527023777,
+  537013321, -1074026642, 537013321, 1073741824, -536870912, 537013321, -1063795470, 526878696, 1064085490, -527300648,
+  537155884, -1074311768, 537155884, 1073741824, -536870912, 537155884, -1063779073, 526725455, 1064359439, -527569803,
+  537298718, -1074597435, 537298718, 1073741824, -536870912, 537298718, -1063754328, 526563934, 1064625617, -527831454,
+  537441939, -1074883878, 537441939, 1073741824, -536870912, 537441939, -1063721205, 526394005, 1064884245, -528085806,
+  537585666, -1075171331, 537585666, 1073741824, -536870912, 537585666, -1063679666, 526215534, 1065135536, -528333059,
+  537730015, -1075460030, 537730015, 1073741824, -536870912, 537730015, -1063629666, 526028380, 1065379699, -528573409,
+  537875106, -1075750212, 537875106, 1073741824, -536870912, 537875106, -1063571152, 525832396, 1065616936, -528807045,
+  538021057, -1076042114, 538021057, 1073741824, -536870912, 538021057, -1063504065, 525627429, 1065847444, -529034151,
+  538167989, -1076335977, 538167989, 1073741824, -536870912, 538167989, -1063428338, 525413317, 1066071412, -529254907,
+
+  /* Band 2, -9 dB gain */
+  531784976, -1055497692, 523873415, 1066213307, -529420241, 531784976, -1040357886, 509828014, 1028908252, -494627367,
+  /* Band 2, -8 dB gain */
+  532357636, -1056601982, 524400080, 1066115844, -529326645, 532357636, -1040623406, 509562600, 1030462237, -496062122,
+  532927392, -1057707729, 524931110, 1066024274, -529239070, 532927392, -1040848253, 509262081, 1031969246, -497457090,
+  533494678, -1058816094, 525467240, 1065939047, -529157961, 533494678, -1041032161, 508925950, 1033429976, -498812573,
+  534059929, -1059928204, 526009170, 1065860582, -529083734, 534059929, -1041174868, 508553717, 1034845124, -500128887,
+  534623580, -1061045148, 526557561, 1065789260, -529016764, 534623580, -1041276126, 508144920, 1036215393, -501406373,
+  535186068, -1062167969, 527113032, 1065725420, -528957385, 535186068, -1041335703, 507699125, 1037541500, -502645399,
+  535747827, -1063297666, 527676151, 1065669351, -528905879, 535747827, -1041353386, 507215934, 1038824183, -503846368,
+  536309295, -1064435183, 528247436, 1065621289, -528862476, 536309295, -1041328990, 506694984, 1040064203, -505009724,
+  536870912, -1065581413, 528827349, 1065581413, -528827349, 536870912, -1041262354, 506135953, 1041262354, -506135953,
+  537433117, -1066737194, 529416295, 1065549847, -528800610, 537433117, -1041153346, 505538564, 1042419457, -507225588,
+  537996352, -1067903307, 530014622, 1065526651, -528782316, 537996352, -1041001864, 504902578, 1043536370, -508279208,
+  538561061, -1069080480, 530622620, 1065511830, -528772462, 538561061, -1040807833, 504227800, 1044613981, -509297437,
+  539127690, -1070269387, 531240527, 1065505333, -528770987, 539127690, -1040571205, 503514074, 1045653211, -510280946,
+  539696690, -1071470656, 531868525, 1065507054, -528777778, 539696690, -1040291951, 502761277, 1046655011, -511230450,
+  540268512, -1072684867, 532506750, 1065516837, -528792672, 540268512, -1039970063, 501969320, 1047620358, -512146700,
+  540843613, -1073912567, 533155297, 1065534483, -528815459, 540843613, -1039605542, 501138139, 1048550251, -513030484,
+  541422451, -1075154268, 533814224, 1065559750, -528845892, 541422451, -1039198394, 500267687, 1049445708, -513882621,
+  542005489, -1076410460, 534483561, 1065592362, -528883686, 542005489, -1038748624, 499357932, 1050307760, -514703956,
+  518903861, -1001986830, 486725277, 1037235801, -502367695, 518903861, -945834422, 446371043, 902366163, -400700571,
+  520899989, -1005630916, 488289126, 1036926846, -502147311, 520899989, -946490935, 445581846, 907921945, -404936158,
+  522893209, -1009290002, 489869792, 1036650484, -501961419, 522893209, -947006359, 444685310, 913306106, -409075225,
+  524884763, -1012968199, 491470256, 1036407567, -501810737, 524884763, -947377809, 443679533, 918521018, -413116221,
+  526875910, -1016669649, 493093518, 1036198712, -501695739, 526875910, -947602324, 442562672, 923569247, -417057897,
+  528867927, -1020398503, 494742575, 1036024293, -501616651, 528867927, -947676875, 441332970, 928453558, -420899319,
+  530862111, -1024158905, 496420407, 1035884447, -501573457, 530862111, -947598385, 439988777, 933176909, -424639872,
+  532859778, -1027954970, 498129955, 1035779077, -501565907, 532859778, -947363742, 438528571, 937742446, -428279254,
+  534862260, -1031790763, 499874098, 1035707863, -501593525, 534862260, -946969823, 436950987, 942153486, -431817474,
+  536870912, -1035670279, 501655630, 1035670279, -501655630, 536870912, -946413508, 435254839, 946413508, -435254839,
+  538887107, -1039597419, 503477238, 1035665609, -501751354, 538887107, -945691703, 433439146, 950526127, -438591937,
+  540912240, -1043575967, 505341475, 1035692963, -501879659, 540912240, -944801359, 431503152, 954495080, -441829621,
+  542947726, -1047609569, 507250741, 1035751307, -502039364, 542947726, -943739490, 429446349, 958324201, -444968987,
+  544995000, -1051701717, 509207261, 1035839473, -502229165, 544995000, -942503190, 427268492, 962017400, -448011351,
+  547055523, -1055855728, 511213065, 1035956193, -502447657, 547055523, -941089647, 424969617, 965578640, -450958226,
+  549130774, -1060074734, 513269973, 1036100110, -502693359, 549130774, -939496155, 422550049, 969011913, -453811298,
+  551222259, -1064361672, 515379585, 1036269804, -502964731, 551222259, -937720119, 420010407, 972321228, -456572401,
+  553331507, -1068719280, 517543273, 1036463810, -503260192, 553331507, -935759057, 417351601, 975510582, -459243495,
+  555460072, -1073150100, 519762181, 1036680633, -503578144, 555460072, -933610600, 414574832, 978583948, -461826644,
+  494084017, -851422604, 404056273, 930151631, -423619864, 494084017, -673714108, 339502486, 561843007, -265801750,
+  498713542, -859177141, 406587077, 929211656, -423786402, 498713542, -673274906, 338185129, 573719128, -272222942,
+  503369016, -867012190, 409148384, 928362985, -424054784, 503369016, -672533059, 336693984, 585290277, -278599028,
+  508052536, -874935599, 411746438, 927604291, -424422151, 508052536, -671478538, 335026905, 596558312, -284920289,
+  512766286, -882955583, 414387826, 926933782, -424885216, 512766286, -670100998, 333182045, 607525792, -291177811,
+  517512534, -891080712, 417079474, 926349262, -425440318, 517512534, -668389789, 331157902, 618195914, -297363485,
+  522293635, -899319903, 419828635, 925848177, -426083491, 522293635, -666333963, 328953368, 628572440, -303470012,
+  527112032, -907682405, 422642886, 925427679, -426810526, 527112032, -663922286, 326567785, 638659631, -309490882,
+  531970251, -916177781, 425530105, 925084675, -427617023, 531970251, -661143261, 324000998, 648462180, -315420352,
+  536870912, -924815881, 428498454, 924815881, -428498454, 536870912, -657985147, 321253420, 657985147, -321253420,
+  541816719, -933606817, 431556352, 924617870, -429450209, 541816719, -654435997, 318326093, 667233900, -326985786,
+  546810467, -942560921, 434712438, 924487114, -430467639, 546810467, -650483688, 315220754, 676214053, -332613816,
+  551855042, -951688708, 437975532, 924420027, -431546101, 551855042, -646115970, 311939896, 684931422, -338134495,
+  556953421, -961000826, 441354588, 924413001, -432680993, 556953421, -641320513, 308486839, 693391970, -343545389,
+  562108672, -970508005, 444858642, 924462435, -433867780, 562108672, -636084967, 304865786, 701601770, -348844597,
+  567323959, -980220994, 448496743, 924564764, -435102022, 567323959, -630397020, 301081886, 709566963, -354030710,
+  572602539, -990150500, 452277894, 924716482, -436379394, 572602539, -624244471, 297141281, 717293726, -359102767,
+  577947763, -1000307125, 456210977, 924914158, -437695705, 577947763, -617615296, 293051155, 724788245, -364060214,
+  583363084, -1010701292, 460304674, 925154455, -439046908, 583363084, -610497723, 288819761, 732056685, -368902865,
+  387379495, -506912469, 196933274, 840112184, -347208270, 387379495, 506912469, 196933274, -840112184, -347208270,
+  401658082, -532275898, 207149427, 833765363, -343175316, 401658082, 532275898, 207149427, -833765363, -343175316,
+  416472483, -558722695, 217902617, 827270154, -339107319, 416472483, 558722695, 217902617, -827270154, -339107319,
+  431841949, -586290861, 229212798, 820624988, -335007540, 431841949, 586290861, 229212798, -820624988, -335007540,
+  447786335, -615019650, 241100489, 813828443, -330879528, 447786335, 615019650, 241100489, -813828443, -330879528,
+  464326111, -644949597, 253586805, 806879270, -326727141, 464326111, 644949597, 253586805, -806879270, -326727141,
+  481482377, -676122557, 266693475, 799776409, -322554559, 481482377, 676122557, 266693475, -799776409, -322554559,
+  499276882, -708581728, 280442865, 792519013, -318366296, 499276882, 708581728, 280442865, -792519013, -318366296,
+  517732032, -742371685, 294857996, 785106465, -314167221, 517732032, 742371685, 294857996, -785106465, -314167221,
+  536870912, -777538408, 309962566, 777538408, -309962566, 536870912, 777538408, 309962566, -777538408, -309962566,
+  556717294, -814129313, 325780968, 769814766, -305757943, 556717294, 814129313, 325780968, -769814766, -305757943,
+  577295658, -852193284, 342338310, 761935777, -301559360, 577295658, 852193284, 342338310, -761935777, -301559360,
+  598631206, -891780698, 359660433, 753902014, -297373230, 598631206, 891780698, 359660433, -753902014, -297373230,
+  620749877, -932943463, 377773927, 745714425, -293206383, 620749877, 932943463, 377773927, -745714425, -293206383,
+  643678365, -975735041, 396706151, 737374355, -289066077, 643678365, 975735041, 396706151, -737374355, -289066077,
+  667444134, -1020210487, 416485252, 728883588, -284960004, 667444134, 1020210487, 416485252, -728883588, -284960004,
+  692075438, -1066426476, 437140179, 720244375, -280896294, 692075438, 1066426476, 437140179, -720244375, -280896294,
+  717601336, -1114441339, 458700704, 711459472, -276883515, 717601336, 1114441339, 458700704, -711459472, -276883515,
+  744051710, -1164315096, 481197437, 702532174, -272930673, 744051710, 1164315096, 481197437, -702532174, -272930673
+
+};
+
+/* ----------------------------------------------------------------------
+** Desired gains, in dB, per band
+** ------------------------------------------------------------------- */
+
+int gainDB[5] = {0, -3, 6, 4, -6};
+
+float32_t snr;
+
+
+/* ----------------------------------------------------------------------
+ * Graphic equalizer Example
+ * ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+  float32_t  *inputF32, *outputF32;
+  arm_biquad_cas_df1_32x64_ins_q31 S1;
+  arm_biquad_cas_df1_32x64_ins_q31 S2;
+  arm_biquad_casd_df1_inst_q31 S3;
+  arm_biquad_casd_df1_inst_q31 S4;
+  arm_biquad_casd_df1_inst_q31 S5;
+  int i;
+  int32_t status;
+
+  inputF32 = &testInput_f32[0];
+  outputF32 = &testOutput[0];
+
+  /* Initialize the state and coefficient buffers for all Biquad sections */
+
+  arm_biquad_cas_df1_32x64_init_q31(&S1, NUMSTAGES,
+            (q31_t *) &coeffTable[190*0 + 10*(gainDB[0] + 9)],
+            &biquadStateBand1Q31[0], 2);
+
+  arm_biquad_cas_df1_32x64_init_q31(&S2, NUMSTAGES,
+            (q31_t *) &coeffTable[190*1 + 10*(gainDB[1] + 9)],
+            &biquadStateBand2Q31[0], 2);
+
+  arm_biquad_cascade_df1_init_q31(&S3, NUMSTAGES,
+          (q31_t *) &coeffTable[190*2 + 10*(gainDB[2] + 9)],
+          &biquadStateBand3Q31[0], 2);
+
+  arm_biquad_cascade_df1_init_q31(&S4, NUMSTAGES,
+          (q31_t *) &coeffTable[190*3 + 10*(gainDB[3] + 9)],
+          &biquadStateBand4Q31[0], 2);
+
+  arm_biquad_cascade_df1_init_q31(&S5, NUMSTAGES,
+          (q31_t *) &coeffTable[190*4 + 10*(gainDB[4] + 9)],
+          &biquadStateBand5Q31[0], 2);
+
+
+  /* Call the process functions and needs to change filter coefficients
+     for varying the gain of each band */
+
+  for(i=0; i < NUMBLOCKS; i++)
+  {
+
+    /* ----------------------------------------------------------------------
+    ** Convert block of input data from float to Q31
+    ** ------------------------------------------------------------------- */
+
+    arm_float_to_q31(inputF32 + (i*BLOCKSIZE), inputQ31, BLOCKSIZE);
+
+    /* ----------------------------------------------------------------------
+    ** Scale down by 1/8.  This provides additional headroom so that the
+    ** graphic EQ can apply gain.
+    ** ------------------------------------------------------------------- */
+
+    arm_scale_q31(inputQ31, 0x7FFFFFFF, -3, inputQ31, BLOCKSIZE);
+
+    /* ----------------------------------------------------------------------
+    ** Call the Q31 Biquad Cascade DF1 32x64 process function for band1, band2
+    ** ------------------------------------------------------------------- */
+
+    arm_biquad_cas_df1_32x64_q31(&S1, inputQ31, outputQ31, BLOCKSIZE);
+    arm_biquad_cas_df1_32x64_q31(&S2, outputQ31, outputQ31, BLOCKSIZE);
+
+    /* ----------------------------------------------------------------------
+    ** Call the Q31 Biquad Cascade DF1 process function for band3, band4, band5
+    ** ------------------------------------------------------------------- */
+
+    arm_biquad_cascade_df1_q31(&S3, outputQ31, outputQ31, BLOCKSIZE);
+    arm_biquad_cascade_df1_q31(&S4, outputQ31, outputQ31, BLOCKSIZE);
+    arm_biquad_cascade_df1_q31(&S5, outputQ31, outputQ31, BLOCKSIZE);
+
+    /* ----------------------------------------------------------------------
+    ** Convert Q31 result back to float
+    ** ------------------------------------------------------------------- */
+
+    arm_q31_to_float(outputQ31, outputF32 + (i * BLOCKSIZE), BLOCKSIZE);
+
+    /* ----------------------------------------------------------------------
+    ** Scale back up
+    ** ------------------------------------------------------------------- */
+
+    arm_scale_f32(outputF32 + (i * BLOCKSIZE), 8.0f, outputF32 + (i * BLOCKSIZE), BLOCKSIZE);
+  };
+
+  snr = arm_snr_f32(testRefOutput_f32, testOutput, TESTLENGTH);
+
+  if (snr < SNR_THRESHOLD_F32)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+  else
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signal does not match the reference output.
+  ** ------------------------------------------------------------------- */
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+/** \endlink */
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_graphic_equalizer_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_graphic_equalizer_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_linear_interp_example/ARM/arm_linear_interp_data.c

@@ -0,0 +1,23616 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_linear_interp_data.c
+*   
+* Description:	 Data file used for example.  Generation method described
+*               below
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+ * -------------------------------------------------------------------- */
+ 
+/* ---------------------------------------------------------------------- 
+* Table generated from following MATLAB Command
+* x = -pi: 0.00005 : (2*pi - 0.00005);
+* y = sin(x);
+* where pi value is 3.141592653589793
+* --------------------------------------------------------------------*/
+
+float arm_linear_interep_table[188495] =  {
+
+
+-0.000000000000000122,	-0.000049999999979173,	-0.000099999999833667,	-0.000149999999437717,	-0.000199999998666767,	-0.000249999997395817,	-0.000299999995500311,	-0.000349999992854362,	
+-0.000399999989333412,	-0.000449999984812462,	-0.000499999979166956,	-0.000549999972271007,	-0.000599999964000057,	-0.000649999954229107,	-0.000699999942833602,	-0.000749999929687653,	
+-0.000799999914666704,	-0.000849999897645755,	-0.000899999878500250,	-0.000949999857104302,	-0.000999999833333354,	-0.001049999807062851,	-0.001099999778166904,	-0.001149999746520957,	
+-0.001199999712000011,	-0.001249999674479510,	-0.001299999633833566,	-0.001349999589937622,	-0.001399999542666680,	-0.001449999491896183,	-0.001499999437500243,	-0.001549999379354304,	
+-0.001599999317333367,	-0.001649999251312876,	-0.001699999181166942,	-0.001749999106771011,	-0.001799999028000082,	-0.001849998944729599,	-0.001899998856833675,	-0.001949998764187754,	
+-0.001999998666666836,	-0.002049998564146365,	-0.002099998456500453,	-0.002149998343604546,	-0.002199998225334087,	-0.002249998101563188,	-0.002299997972167294,	-0.002349997837021405,	
+-0.002399997696000966,	-0.002449997548980088,	-0.002499997395834216,	-0.002549997236438351,	-0.002599997070667937,	-0.002649996898397086,	-0.002699996719501243,	-0.002749996533855408,	
+-0.002799996341335026,	-0.002849996141814208,	-0.002899995935168401,	-0.002949995721272604,	-0.002999995500002261,	-0.003049995271231486,	-0.003099995034835722,	-0.003149994790690415,	
+-0.003199994538669677,	-0.003249994278648952,	-0.003299994010503243,	-0.003349993734107991,	-0.003399993449337312,	-0.003449993156066649,	-0.003499992854171003,	-0.003549992543525819,	
+-0.003599992224005209,	-0.003649991895484619,	-0.003699991557839049,	-0.003749991210943944,	-0.003799990854673418,	-0.003849990488902914,	-0.003899990113507434,	-0.003949989728362423,	
+-0.003999989333341993,	-0.004049988928321590,	-0.004099988513176658,	-0.004149988087781312,	-0.004199987652010995,	-0.004249987205740709,	-0.004299986748845899,	-0.004349986281200678,	
+-0.004399985802680492,	-0.004449985313160341,	-0.004499984812515671,	-0.004549984300620594,	-0.004599983777350557,	-0.004649983242580561,	-0.004699982696186050,	-0.004749982138041138,	
+-0.004799981568021272,	-0.004849980986001451,	-0.004899980391857122,	-0.004949979785462398,	-0.004999979166692725,	-0.005049978535423547,	-0.005099977891528979,	-0.005149977234884466,	
+-0.005199976565365011,	-0.005249975882846058,	-0.005299975187201721,	-0.005349974478307446,	-0.005399973756038235,	-0.005449973020269535,	-0.005499972270875456,	-0.005549971507731448,	
+-0.005599970730712511,	-0.005649969939694091,	-0.005699969134550302,	-0.005749968315156590,	-0.005799967481387958,	-0.005849966633119851,	-0.005899965770226383,	-0.005949964892583000,	
+-0.005999964000064706,	-0.006049963092546945,	-0.006099962169903833,	-0.006149961232010816,	-0.006199960278743339,	-0.006249959309975518,	-0.006299958325582797,	-0.006349957325440182,	
+-0.006399956309423117,	-0.006449955277405718,	-0.006499954229263430,	-0.006549953164871257,	-0.006599952084104644,	-0.006649950986837708,	-0.006699949872945895,	-0.006749948742304206,	
+-0.006799947594788089,	-0.006849946430271660,	-0.006899945248630365,	-0.006949944049739206,	-0.006999942833473632,	-0.007049941599707755,	-0.007099940348317025,	-0.007149939079176889,	
+-0.007199937792161461,	-0.007249936487146187,	-0.007299935164006074,	-0.007349933822616566,	-0.007399932462851779,	-0.007449931084587162,	-0.007499929687697716,	-0.007549928272058891,	
+-0.007599926837544801,	-0.007649925384030893,	-0.007699923911392173,	-0.007749922419504085,	-0.007799920908240749,	-0.007849919377477610,	-0.007899917827089672,	-0.007949916256952384,	
+-0.007999914666939863,	-0.008049913056927554,	-0.008099911426790906,	-0.008149909776404035,	-0.008199908105642390,	-0.008249906414380975,	-0.008299904702495238,	-0.008349902969859295,	
+-0.008399901216348595,	-0.008449899441838141,	-0.008499897646203384,	-0.008549895829318437,	-0.008599893991058752,	-0.008649892131299332,	-0.008699890249915625,	-0.008749888346781748,	
+-0.008799886421773151,	-0.008849884474764837,	-0.008899882505632256,	-0.008949880514249525,	-0.008999878500492093,	-0.009049876464234965,	-0.009099874405353590,	-0.009149872323722084,	
+-0.009199870219215898,	-0.009249868091710479,	-0.009299865941079948,	-0.009349863767199750,	-0.009399861569944894,	-0.009449859349190827,	-0.009499857104811669,	-0.009549854836682867,	
+-0.009599852544679429,	-0.009649850228676803,	-0.009699847888549109,	-0.009749845524171793,	-0.009799843135419864,	-0.009849840722168771,	-0.009899838284292632,	-0.009949835821666898,	
+-0.009999833334166574,	-0.010049830821667110,	-0.010099828284042626,	-0.010149825721168572,	-0.010199823132920397,	-0.010249820519172219,	-0.010299817879799491,	-0.010349815214677217,	
+-0.010399812523680850,	-0.010449809806684508,	-0.010499807063563642,	-0.010549804294193258,	-0.010599801498448806,	-0.010649798676204407,	-0.010699795827335511,	-0.010749792951717126,	
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+};
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_linear_interp_example/ARM/arm_linear_interp_example_f32.c

@@ -0,0 +1,204 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_linear_interp_example_f32.c
+*
+* Description:   Example code demonstrating usage of sin function
+*                and uses linear interpolation to get higher precision
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup LinearInterpExample Linear Interpolate Example
+ *
+ * <b> CMSIS DSP Software Library -- Linear Interpolate Example  </b>
+ *
+ * <b> Description </b>
+ * This example demonstrates usage of linear interpolate modules and fast math modules.
+ * Method 1 uses fast math sine function to calculate sine values using cubic interpolation and method 2 uses
+ * linear interpolation function and results are compared to reference output.
+ * Example shows linear interpolation function can be used to get higher precision compared to fast math sin calculation.
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html linearInterpExampleMethod1.gif "Method 1: Sine caluclation using fast math"
+ * \par
+ * \image html linearInterpExampleMethod2.gif "Method 2: Sine caluclation using interpolation function"
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInputSin_f32         points to the input values for sine calculation
+ * \li \c testRefSinOutput32_f32   points to the reference values caculated from sin() matlab function
+ * \li \c testOutput               points to output buffer calculation from cubic interpolation
+ * \li \c testLinIntOutput         points to output buffer calculation from linear interpolation
+ * \li \c snr1                     Signal to noise ratio for reference and cubic interpolation output
+ * \li \c snr2                     Signal to noise ratio for reference and linear interpolation output
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_sin_f32()
+ * - arm_linear_interp_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_linear_interp_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_linear_interp_example_f32.c
+  */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+#define SNR_THRESHOLD           90
+#define TEST_LENGTH_SAMPLES     10
+#define XSPACING               (0.00005f)
+
+/* ----------------------------------------------------------------------
+* Test input data for F32 SIN function
+* Generated by the MATLAB rand() function
+* randn('state', 0)
+* xi = (((1/4.18318581819710)* randn(blockSize, 1) * 2* pi));
+* --------------------------------------------------------------------*/
+float32_t testInputSin_f32[TEST_LENGTH_SAMPLES] =
+{
+   -0.649716504673081170, -2.501723745497831200,
+    0.188250329003310100,  0.432092748487532540,
+   -1.722010988459680800,  1.788766476323060600,
+    1.786136060975809500, -0.056525543169408797,
+    0.491596272728153760,  0.262309671126153390
+};
+
+/*------------------------------------------------------------------------------
+*  Reference out of SIN F32 function for Block Size = 10
+*  Calculated from sin(testInputSin_f32)
+*------------------------------------------------------------------------------*/
+float32_t testRefSinOutput32_f32[TEST_LENGTH_SAMPLES] =
+{
+   -0.604960695383043530, -0.597090287967934840,
+    0.187140422442966500,  0.418772124875992690,
+   -0.988588831792106880,  0.976338412038794010,
+    0.976903856413481100, -0.056495446835214236,
+    0.472033731854734240,  0.259311907228582830
+};
+
+/*------------------------------------------------------------------------------
+*  Method 1: Test out Buffer Calculated from Cubic Interpolation
+*------------------------------------------------------------------------------*/
+float32_t testOutput[TEST_LENGTH_SAMPLES];
+
+/*------------------------------------------------------------------------------
+*  Method 2: Test out buffer Calculated from Linear Interpolation
+*------------------------------------------------------------------------------*/
+float32_t testLinIntOutput[TEST_LENGTH_SAMPLES];
+
+/*------------------------------------------------------------------------------
+*  External table used for linear interpolation
+*------------------------------------------------------------------------------*/
+extern float arm_linear_interep_table[188495];
+
+/* ----------------------------------------------------------------------
+* Global Variables for caluclating SNR's for Method1 & Method 2
+* ------------------------------------------------------------------- */
+float32_t snr1;
+float32_t snr2;
+
+/* ----------------------------------------------------------------------------
+* Calculation of Sine values from Cubic Interpolation and Linear interpolation
+* ---------------------------------------------------------------------------- */
+int32_t main(void)
+{
+  uint32_t i;
+  arm_status status;
+
+  arm_linear_interp_instance_f32 S = {188495, -3.141592653589793238, XSPACING, &arm_linear_interep_table[0]};
+
+  /*------------------------------------------------------------------------------
+  *  Method 1: Test out Calculated from Cubic Interpolation
+  *------------------------------------------------------------------------------*/
+  for(i=0; i< TEST_LENGTH_SAMPLES; i++)
+  {
+    testOutput[i] = arm_sin_f32(testInputSin_f32[i]);
+  }
+
+  /*------------------------------------------------------------------------------
+  *  Method 2: Test out Calculated from Cubic Interpolation and Linear interpolation
+  *------------------------------------------------------------------------------*/
+
+  for(i=0; i< TEST_LENGTH_SAMPLES; i++)
+  {
+      testLinIntOutput[i] = arm_linear_interp_f32(&S, testInputSin_f32[i]);
+  }
+
+  /*------------------------------------------------------------------------------
+  *            SNR calculation for method 1
+  *------------------------------------------------------------------------------*/
+  snr1 = arm_snr_f32(testRefSinOutput32_f32, testOutput, 2);
+
+  /*------------------------------------------------------------------------------
+  *            SNR calculation for method 2
+  *------------------------------------------------------------------------------*/
+  snr2 = arm_snr_f32(testRefSinOutput32_f32, testLinIntOutput, 2);
+
+  /*------------------------------------------------------------------------------
+  *            Initialise status depending on SNR calculations
+  *------------------------------------------------------------------------------*/
+  if( snr2 > snr1)
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+  else
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signals fail the PASS check.
+  ** This denotes a test failure
+  ** ------------------------------------------------------------------- */
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_linear_interp_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_linear_interp_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_matrix_example/ARM/arm_matrix_example_f32.c

@@ -0,0 +1,233 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_matrix_example_f32.c
+*
+* Description:   Example code demonstrating least square fit to data
+*                using matrix functions
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup MatrixExample Matrix Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use of Matrix Transpose, Matrix Muliplication, and Matrix Inverse
+ * functions to apply least squares fitting to input data. Least squares fitting is
+ * the procedure for finding the best-fitting curve that minimizes the sum of the
+ * squares of the offsets (least square error) from a given set of data.
+ *
+ * \par Algorithm:
+ * \par
+ * The linear combination of parameters considered is as follows:
+ * \par
+ * <code>A * X = B</code>, where \c X is the unknown value and can be estimated
+ * from \c A & \c B.
+ * \par
+ * The least squares estimate \c X is given by the following equation:
+ * \par
+ * <code>X = Inverse(A<sup>T</sup> * A) *  A<sup>T</sup> * B</code>
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html matrixExample.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c A_f32 input matrix in the linear combination equation
+ * \li \c B_f32 output matrix in the linear combination equation
+ * \li \c X_f32 unknown matrix estimated using \c A_f32 & \c B_f32 matrices
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_mat_init_f32()
+ * - arm_mat_trans_f32()
+ * - arm_mat_mult_f32()
+ * - arm_mat_inverse_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_matrix_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_matrix_example_f32.c
+  */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+#define SNR_THRESHOLD   90
+
+/* --------------------------------------------------------------------------------
+* Test input data(Cycles) taken from FIR Q15 module for differant cases of blockSize
+* and tapSize
+* --------------------------------------------------------------------------------- */
+
+const float32_t B_f32[4] =
+{
+  782.0, 7577.0, 470.0, 4505.0
+};
+
+/* --------------------------------------------------------------------------------
+* Formula to fit is  C1 + C2 * numTaps + C3 * blockSize + C4 * numTaps * blockSize
+* -------------------------------------------------------------------------------- */
+
+const float32_t A_f32[16] =
+{
+  /* Const,   numTaps,   blockSize,   numTaps*blockSize */
+  1.0,     32.0,      4.0,     128.0,
+  1.0,     32.0,     64.0,    2048.0,
+  1.0,     16.0,      4.0,      64.0,
+  1.0,     16.0,     64.0,    1024.0,
+};
+
+
+/* ----------------------------------------------------------------------
+* Temporary buffers  for storing intermediate values
+* ------------------------------------------------------------------- */
+/* Transpose of A Buffer */
+float32_t AT_f32[16];
+/* (Transpose of A * A) Buffer */
+float32_t ATMA_f32[16];
+/* Inverse(Transpose of A * A)  Buffer */
+float32_t ATMAI_f32[16];
+/* Test Output Buffer */
+float32_t X_f32[4];
+
+/* ----------------------------------------------------------------------
+* Reference ouput buffer C1, C2, C3 and C4 taken from MATLAB
+* ------------------------------------------------------------------- */
+const float32_t xRef_f32[4] = {73.0, 8.0, 21.25, 2.875};
+
+float32_t snr;
+
+
+/* ----------------------------------------------------------------------
+* Max magnitude FFT Bin test
+* ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+
+  arm_matrix_instance_f32 A;      /* Matrix A Instance */
+  arm_matrix_instance_f32 AT;     /* Matrix AT(A transpose) instance */
+  arm_matrix_instance_f32 ATMA;   /* Matrix ATMA( AT multiply with A) instance */
+  arm_matrix_instance_f32 ATMAI;  /* Matrix ATMAI(Inverse of ATMA) instance */
+  arm_matrix_instance_f32 B;      /* Matrix B instance */
+  arm_matrix_instance_f32 X;      /* Matrix X(Unknown Matrix) instance */
+
+  uint32_t srcRows, srcColumns;  /* Temporary variables */
+  arm_status status;
+
+  /* Initialise A Matrix Instance with numRows, numCols and data array(A_f32) */
+  srcRows = 4;
+  srcColumns = 4;
+  arm_mat_init_f32(&A, srcRows, srcColumns, (float32_t *)A_f32);
+
+  /* Initialise Matrix Instance AT with numRows, numCols and data array(AT_f32) */
+  srcRows = 4;
+  srcColumns = 4;
+  arm_mat_init_f32(&AT, srcRows, srcColumns, AT_f32);
+
+  /* calculation of A transpose */
+  status = arm_mat_trans_f32(&A, &AT);
+
+
+  /* Initialise ATMA Matrix Instance with numRows, numCols and data array(ATMA_f32) */
+  srcRows = 4;
+  srcColumns = 4;
+  arm_mat_init_f32(&ATMA, srcRows, srcColumns, ATMA_f32);
+
+  /* calculation of AT Multiply with A */
+  status = arm_mat_mult_f32(&AT, &A, &ATMA);
+
+  /* Initialise ATMAI Matrix Instance with numRows, numCols and data array(ATMAI_f32) */
+  srcRows = 4;
+  srcColumns = 4;
+  arm_mat_init_f32(&ATMAI, srcRows, srcColumns, ATMAI_f32);
+
+  /* calculation of Inverse((Transpose(A) * A) */
+  status = arm_mat_inverse_f32(&ATMA, &ATMAI);
+
+  /* calculation of (Inverse((Transpose(A) * A)) *  Transpose(A)) */
+  status = arm_mat_mult_f32(&ATMAI, &AT, &ATMA);
+
+  /* Initialise B Matrix Instance with numRows, numCols and data array(B_f32) */
+  srcRows = 4;
+  srcColumns = 1;
+  arm_mat_init_f32(&B, srcRows, srcColumns, (float32_t *)B_f32);
+
+  /* Initialise X Matrix Instance with numRows, numCols and data array(X_f32) */
+  srcRows = 4;
+  srcColumns = 1;
+  arm_mat_init_f32(&X, srcRows, srcColumns, X_f32);
+
+  /* calculation ((Inverse((Transpose(A) * A)) *  Transpose(A)) * B) */
+  status = arm_mat_mult_f32(&ATMA, &B, &X);
+
+  /* Comparison of reference with test output */
+  snr = arm_snr_f32((float32_t *)xRef_f32, X_f32, 4);
+
+  /*------------------------------------------------------------------------------
+  *            Initialise status depending on SNR calculations
+  *------------------------------------------------------------------------------*/
+  if( snr > SNR_THRESHOLD)
+  {
+    status = ARM_MATH_SUCCESS;
+  }
+  else
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+
+  /* ----------------------------------------------------------------------
+  ** Loop here if the signals fail the PASS check.
+  ** This denotes a test failure
+  ** ------------------------------------------------------------------- */
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_matrix_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_matrix_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_signal_converge_example/ARM/arm_signal_converge_data.c

@@ -0,0 +1,269 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*   
+* Project: 	    CMSIS DSP Library   
+* Title:	     	arm_signal_converge_data.c
+*   
+* Description:	 Test input data for Floating point LMS Norm FIR filter
+*   
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+** Test input data for Floating point LMS Norm FIR filter
+** Generated by the MATLAB randn() function
+** ------------------------------------------------------------------- */
+
+float32_t testInput_f32[1536] = 
+{   
+-0.432565,	-1.665584,	0.125332,	0.287676,	-1.146471,	1.190915,	1.189164,	-0.037633,	
+0.327292,	0.174639,	-0.186709,	0.725791,	-0.588317,	2.183186,	-0.136396,	0.113931,	
+1.066768,	0.059281,	-0.095648,	-0.832349,	0.294411,	-1.336182,	0.714325,	1.623562,	
+-0.691776,	0.857997,	1.254001,	-1.593730,	-1.440964,	0.571148,	-0.399886,	0.689997,	
+0.815622,	0.711908,	1.290250,	0.668601,	1.190838,	-1.202457,	-0.019790,	-0.156717,	
+-1.604086,	0.257304,	-1.056473,	1.415141,	-0.805090,	0.528743,	0.219321,	-0.921902,	
+-2.170674,	-0.059188,	-1.010634,	0.614463,	0.507741,	1.692430,	0.591283,	-0.643595,	
+0.380337,	-1.009116,	-0.019511,	-0.048221,	0.000043,	-0.317859,	1.095004,	-1.873990,	
+0.428183,	0.895638,	0.730957,	0.577857,	0.040314,	0.677089,	0.568900,	-0.255645,	
+-0.377469,	-0.295887,	-1.475135,	-0.234004,	0.118445,	0.314809,	1.443508,	-0.350975,	
+0.623234,	0.799049,	0.940890,	-0.992092,	0.212035,	0.237882,	-1.007763,	-0.742045,	
+1.082295,	-0.131500,	0.389880,	0.087987,	-0.635465,	-0.559573,	0.443653,	-0.949904,	
+0.781182,	0.568961,	-0.821714,	-0.265607,	-1.187777,	-2.202321,	0.986337,	-0.518635,	
+0.327368,	0.234057,	0.021466,	-1.003944,	-0.947146,	-0.374429,	-1.185886,	-1.055903,	
+1.472480,	0.055744,	-1.217317,	-0.041227,	-1.128344,	-1.349278,	-0.261102,	0.953465,	
+0.128644,	0.656468,	-1.167819,	-0.460605,	-0.262440,	-1.213152,	-1.319437,	0.931218,	
+0.011245,	-0.645146,	0.805729,	0.231626,	-0.989760,	1.339586,	0.289502,	1.478917,	
+1.138028,	-0.684139,	-1.291936,	-0.072926,	-0.330599,	-0.843628,	0.497770,	1.488490,	
+-0.546476,	-0.846758,	-0.246337,	0.663024,	-0.854197,	-1.201315,	-0.119869,	-0.065294,	
+0.485296,	-0.595491,	-0.149668,	-0.434752,	-0.079330,	1.535152,	-0.606483,	-1.347363,	
+0.469383,	-0.903567,	0.035880,	-0.627531,	0.535398,	0.552884,	-0.203690,	-2.054325,	
+0.132561,	1.592941,	1.018412,	-1.580402,	-0.078662,	-0.681657,	-1.024553,	-1.234353,	
+0.288807,	-0.429303,	0.055801,	-0.367874,	-0.464973,	0.370961,	0.728283,	2.112160,	
+-1.357298,	-1.022610,	1.037834,	-0.389800,	-1.381266,	0.315543,	1.553243,	0.707894,	
+1.957385,	0.504542,	1.864529,	-0.339812,	-1.139779,	-0.211123,	1.190245,	-1.116209,	
+0.635274,	-0.601412,	0.551185,	-1.099840,	0.085991,	-2.004563,	-0.493088,	0.462048,	
+-0.321005,	1.236556,	-0.631280,	-2.325211,	-1.231637,	1.055648,	-0.113224,	0.379224,	
+0.944200,	-2.120427,	-0.644679,	-0.704302,	-1.018137,	-0.182082,	1.521013,	-0.038439,	
+1.227448,	-0.696205,	0.007524,	-0.782893,	0.586939,	-0.251207,	0.480136,	0.668155,	
+-0.078321,	0.889173,	2.309287,	0.524639,	-0.011787,	0.913141,	0.055941,	-1.107070,	
+0.485498,	-0.005005,	-0.276218,	1.276452,	1.863401,	-0.522559,	0.103424,	-0.807649,	
+0.680439,	-2.364590,	0.990115,	0.218899,	0.261662,	1.213444,	-0.274667,	-0.133134,	
+-1.270500,	-1.663606,	-0.703554,	0.280880,	-0.541209,	-1.333531,	1.072686,	-0.712085,	
+-0.011286,	-0.000817,	-0.249436,	0.396575,	-0.264013,	-1.664011,	-1.028975,	0.243095,	
+-1.256590,	-0.347183,	-0.941372,	-1.174560,	-1.021142,	-0.401667,	0.173666,	-0.116118,	
+1.064119,	-0.245386,	-1.517539,	0.009734,	0.071373,	0.316536,	0.499826,	1.278084,	
+-0.547816,	0.260808,	-0.013177,	-0.580264,	2.136308,	-0.257617,	-1.409528,	1.770101,	
+0.325546,	-1.119040,	0.620350,	1.269782,	-0.896043,	0.135175,	-0.139040,	-1.163395,	
+1.183720,	-0.015430,	0.536219,	-0.716429,	-0.655559,	0.314363,	0.106814,	1.848216,	
+-0.275106,	2.212554,	1.508526,	-1.945079,	-1.680543,	-0.573534,	-0.185817,	0.008934,	
+0.836950,	-0.722271,	-0.721490,	-0.201181,	-0.020464,	0.278890,	1.058295,	0.621673,	
+-1.750615,	0.697348,	0.811486,	0.636345,	1.310080,	0.327098,	-0.672993,	-0.149327,	
+-2.449018,	0.473286,	0.116946,	-0.591104,	-0.654708,	-1.080662,	-0.047731,	0.379345,	
+-0.330361,	-0.499898,	-0.035979,	-0.174760,	-0.957265,	1.292548,	0.440910,	1.280941,	
+-0.497730,	-1.118717,	0.807650,	0.041200,	-0.756209,	-0.089129,	-2.008850,	1.083918,	
+-0.981191,	-0.688489,	1.339479,	-0.909243,	-0.412858,	-0.506163,	1.619748,	0.080901,	
+-1.081056,	-1.124518,	1.735676,	1.937459,	1.635068,	-1.255940,	-0.213538,	-0.198932,	
+0.307499,	-0.572325,	-0.977648,	-0.446809,	1.082092,	2.372648,	0.229288,	-0.266623,	
+0.701672,	-0.487590,	1.862480,	1.106851,	-1.227566,	-0.669885,	1.340929,	0.388083,	
+0.393059,	-1.707334,	0.227859,	0.685633,	-0.636790,	-1.002606,	-0.185621,	-1.054033,	
+-0.071539,	0.279198,	1.373275,	0.179841,	-0.542017,	1.634191,	0.825215,	0.230761,	
+0.671634,	-0.508078,	0.856352,	0.268503,	0.624975,	-1.047338,	1.535670,	0.434426,	
+-1.917136,	0.469940,	1.274351,	0.638542,	1.380782,	1.319843,	-0.909429,	-2.305605,	
+1.788730,	0.390798,	0.020324,	-0.405977,	-1.534895,	0.221373,	-1.374479,	-0.839286,	
+-0.208643,	0.755913,	0.375734,	-1.345413,	1.481876,	0.032736,	1.870453,	-1.208991,	
+-0.782632,	-0.767299,	-0.107200,	-0.977057,	-0.963988,	-2.379172,	-0.838188,	0.257346,	
+-0.183834,	-0.167615,	-0.116989,	0.168488,	-0.501206,	-0.705076,	0.508165,	-0.420922,	
+0.229133,	-0.959497,	-0.146043,	0.744538,	-0.890496,	0.139062,	-0.236144,	-0.075459,	
+-0.358572,	-2.077635,	-0.143546,	1.393341,	0.651804,	-0.377134,	-0.661443,	0.248958,	
+-0.383516,	-0.528480,	0.055388,	1.253769,	-2.520004,	0.584856,	-1.008064,	0.944285,	
+-2.423957,	-0.223831,	0.058070,	-0.424614,	-0.202918,	-1.513077,	-1.126352,	-0.815002,	
+0.366614,	-0.586107,	1.537409,	0.140072,	-1.862767,	-0.454193,	-0.652074,	0.103318,	
+-0.220632,	-0.279043,	-0.733662,	-0.064534,	-1.444004,	0.612340,	-1.323503,	-0.661577,	
+-0.146115,	0.248085,	-0.076633,	1.738170,	1.621972,	0.626436,	0.091814,	-0.807607,	
+-0.461337,	-1.405969,	-0.374530,	-0.470911,	1.751296,	0.753225,	0.064989,	-0.292764,	
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+0.863327,	-0.642411,	0.660010,	1.294116,	0.314579,	0.859573,	0.128670,	0.016568,	
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+0.175088,	0.229433,	-1.240889,	0.700004,	0.426877,	1.454803,	-0.510186,	-0.006657,	
+-0.525496,	0.717698,	1.088374,	0.500552,	2.771790,	-0.160309,	0.429489,	-1.966817,	
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+-1.833687,	1.827363,	0.654075,	-1.544769,	-0.375109,	0.207688,	-0.765615,	-0.106355,	
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+0.741336,	0.811980,	-0.142808,	-0.099858,	-0.800131,	0.493249,	1.237574,	1.295951,	
+-0.278196,	0.217127,	0.630728,	-0.548549,	0.229632,	0.355311,	0.521284,	-0.615971,	
+1.345803,	0.974922,	-2.377934,	-1.092319,	-0.325710,	-2.012228,	1.567660,	0.233337,	
+0.646420,	-1.129412,	0.197038,	1.696870,	0.726034,	0.792526,	0.603357,	-0.058405,	
+-1.108666,	2.144229,	-1.352821,	0.457021,	0.391175,	2.073013,	-0.323318,	1.468132,	
+-0.502399,	0.209593,	0.754800,	-0.948189,	0.613157,	1.760503,	0.088762,	2.595570,	
+-0.675470,	2.786804,	-0.016827,	0.271651,	-0.914102,	-1.951371,	-0.317418,	0.588333,	
+0.828996,	-1.674851,	-1.922293,	-0.436662,	0.044974,	2.416609,	-0.309892,	0.187583,	
+0.947699,	-0.525703,	-1.115605,	-1.592320,	1.174844,	0.485144,	1.645480,	-0.454233,	
+1.008768,	2.049403,	0.602020,	0.017860,	-1.610426,	1.238752,	0.683587,	-0.780716,	
+0.530979,	2.134498,	0.354361,	0.231700,	1.287980,	-0.013488,	-1.333345,	-0.556343,	
+0.755597,	-0.911854,	1.371684,	0.245580,	0.118845,	0.384690,	-0.070152,	-0.578309,	
+0.469308,	1.299687,	1.634798,	-0.702809,	0.807253,	-1.027451,	1.294496,	0.014930,	
+0.218705,	1.713188,	-2.078805,	0.112917,	-1.086491,	-1.558311,	0.637406,	-0.404576,	
+-0.403325,	0.084076,	-0.435349,	-0.562623,	0.878062,	-0.814650,	-0.258363,	0.493299,	
+-0.802694,	-0.008329,	0.627571,	0.154382,	2.580735,	-1.306246,	1.023526,	0.777795,	
+-0.833884,	-0.586663,	0.065664,	-0.012342,	-0.076987,	-1.558587,	1.702607,	-0.468984,	
+0.094619,	0.287071,	0.919354,	0.510136,	0.245440,	-1.400519,	0.969571,	1.593698,	
+-1.437917,	-1.534230,	-0.074710,	0.081459,	-0.843240,	-0.564640,	-0.028207,	-1.243702,	
+0.733039,	0.059580,	0.149144,	1.595857,	-0.777250,	1.550277,	1.055002,	-0.166654,	
+0.314484,	1.419571,	0.327348,	0.475653,	0.398754,	-0.072770,	1.314784,	0.978279,	
+1.722114,	-0.412302,	0.565133,	0.739851,	0.220138,	1.312807,	0.629152,	-1.107987,	
+-0.447001,	-0.725993,	0.354045,	-0.506772,	-2.103747,	-0.664684,	1.450110,	-0.329805,	
+2.701872,	-1.634939,	-0.536325,	0.547223,	1.492603,	-0.455243,	-0.496416,	1.235260,	
+0.040926,	0.748467,	1.230764,	0.304903,	1.077771,	0.765151,	-1.319580,	-0.509191,	
+0.555116,	-1.957625,	-0.760453,	-2.443886,	-0.659366,	-0.114779,	0.300079,	-0.583996,	
+-3.073745,	1.551042,	-0.407369,	1.428095,	-1.353242,	0.903970,	0.541671,	-0.465020
+};
+
+
+
+/* ----------------------------------------------------------------------
+** Coefficients for 32-tap filter for Floating point LMS FIR filter
+*  FIR high pass filter with cutoff freq 9.6kHz (transition 9.6KHz to 11.52KHz) 
+** ------------------------------------------------------------------- */  
+float32_t lmsNormCoeff_f32[32] = {
+-0.004240,	0.002301,	0.008860,	-0.000000,	-0.019782,	-0.010543,	0.032881,	0.034736,	
+-0.037374,	-0.069586,	0.022397,	0.102169,	0.014185,	-0.115908,	-0.061648,	0.101018,	
+0.101018,	-0.061648,	-0.115908,	0.014185,	0.102169,	0.022397,	-0.069586,	-0.037374,	
+0.034736,	0.032881,	-0.010543,	-0.019782,	-0.000000,	0.008860,	0.002301,	-0.004240	
+
+};
+
+/* ----------------------------------------------------------------------
+** Coefficients for 32-tap filter for Floating point FIR filter
+*  FIR low pass filter with cutoff freq 24Hz (transition 24Hz to 240Hz) 
+** ------------------------------------------------------------------- */  
+const float32_t FIRCoeff_f32[32] = {
+0.004502,	0.005074,	0.006707,	0.009356,	0.012933,	0.017303,	0.022298,	0.027717,	
+0.033338,	0.038930,	0.044258,	0.049098,	0.053243,	0.056519,	0.058784,	0.059941,	
+0.059941,	0.058784,	0.056519,	0.053243,	0.049098,	0.044258,	0.038930,	0.033338,	
+0.027717,	0.022298,	0.017303,	0.012933,	0.009356,	0.006707,	0.005074,	0.004502
+
+};
+

Libraries/CMSIS/DSP_Lib/Examples/arm_signal_converge_example/ARM/arm_signal_converge_example_f32.c

@@ -0,0 +1,259 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_signal_converge_example_f32.c
+*
+* Description:   Example code demonstrating convergence of an adaptive
+*                filter.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+ * -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup SignalConvergence Signal Convergence Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the ability of an adaptive filter to "learn" the transfer function of
+ * a FIR lowpass filter using the Normalized LMS Filter, Finite Impulse
+ * Response (FIR) Filter, and Basic Math Functions.
+ *
+ * \par Algorithm:
+ * \par
+ * The figure below illustrates the signal flow in this example. Uniformly distributed white
+ * noise is passed through an FIR lowpass filter. The output of the FIR filter serves as the
+ * reference input of the adaptive filter (normalized LMS filter). The white noise is input
+ * to the adaptive filter. The adaptive filter learns the transfer function of the FIR filter.
+ * The filter outputs two signals: (1) the output of the internal adaptive FIR filter, and
+ * (2) the error signal which is the difference between the adaptive filter and the reference
+ * output of the FIR filter. Over time as the adaptive filter learns the transfer function
+ * of the FIR filter, the first output approaches the reference output of the FIR filter,
+ * and the error signal approaches zero.
+ * \par
+ * The adaptive filter converges properly even if the input signal has a large dynamic
+ * range (i.e., varies from small to large values). The coefficients of the adaptive filter
+ * are initially zero, and then converge over 1536 samples. The internal function test_signal_converge()
+ * implements the stopping condition. The function checks if all of the values of the error signal have a
+ * magnitude below a threshold DELTA.
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html SignalFlow.gif
+ *
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32 points to the input data
+ * \li \c firStateF32 points to FIR state buffer
+ * \li \c lmsStateF32 points to Normalised Least mean square FIR filter state buffer
+ * \li \c FIRCoeff_f32 points to coefficient buffer
+ * \li \c lmsNormCoeff_f32 points to Normalised Least mean square FIR filter coefficient buffer
+ * \li \c wire1, wir2, wire3 temporary buffers
+ * \li \c errOutput, err_signal temporary error buffers
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_lms_norm_init_f32()
+ * - arm_fir_init_f32()
+ * - arm_fir_f32()
+ * - arm_lms_norm_f32()
+ * - arm_scale_f32()
+ * - arm_abs_f32()
+ * - arm_sub_f32()
+ * - arm_min_f32()
+ * - arm_copy_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_signal_converge_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_signal_converge_example_f32.c
+  */
+
+#include "arm_math.h"
+#include "math_helper.h"
+
+/* ----------------------------------------------------------------------
+** Global defines for the simulation
+* ------------------------------------------------------------------- */
+
+#define TEST_LENGTH_SAMPLES 1536
+#define NUMTAPS               32
+#define BLOCKSIZE             32
+#define DELTA_ERROR         0.000001f
+#define DELTA_COEFF         0.0001f
+#define MU                  0.5f
+
+#define NUMFRAMES (TEST_LENGTH_SAMPLES / BLOCKSIZE)
+
+/* ----------------------------------------------------------------------
+* Declare FIR state buffers and structure
+* ------------------------------------------------------------------- */
+
+float32_t firStateF32[NUMTAPS + BLOCKSIZE];
+arm_fir_instance_f32 LPF_instance;
+
+/* ----------------------------------------------------------------------
+* Declare LMSNorm state buffers and structure
+* ------------------------------------------------------------------- */
+
+float32_t lmsStateF32[NUMTAPS + BLOCKSIZE];
+float32_t errOutput[TEST_LENGTH_SAMPLES];
+arm_lms_norm_instance_f32 lmsNorm_instance;
+
+
+/* ----------------------------------------------------------------------
+* Function Declarations for Signal Convergence Example
+* ------------------------------------------------------------------- */
+
+arm_status test_signal_converge_example( void );
+
+
+/* ----------------------------------------------------------------------
+* Internal functions
+* ------------------------------------------------------------------- */
+arm_status test_signal_converge(float32_t* err_signal,
+                        uint32_t blockSize);
+
+void getinput(float32_t* input,
+     uint32_t fr_cnt,
+          uint32_t blockSize);
+
+/* ----------------------------------------------------------------------
+* External Declarations for FIR F32 module Test
+* ------------------------------------------------------------------- */
+extern float32_t testInput_f32[TEST_LENGTH_SAMPLES];
+extern float32_t lmsNormCoeff_f32[32];
+extern const float32_t FIRCoeff_f32[32];
+extern arm_lms_norm_instance_f32 lmsNorm_instance;
+
+/* ----------------------------------------------------------------------
+* Declare I/O buffers
+* ------------------------------------------------------------------- */
+
+float32_t wire1[BLOCKSIZE];
+float32_t wire2[BLOCKSIZE];
+float32_t wire3[BLOCKSIZE];
+float32_t err_signal[BLOCKSIZE];
+
+/* ----------------------------------------------------------------------
+* Signal converge test
+* ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+  uint32_t i;
+  arm_status status;
+  uint32_t index;
+  float32_t minValue;
+
+  /* Initialize the LMSNorm data structure */
+  arm_lms_norm_init_f32(&lmsNorm_instance, NUMTAPS, lmsNormCoeff_f32, lmsStateF32, MU, BLOCKSIZE);
+
+  /* Initialize the FIR data structure */
+  arm_fir_init_f32(&LPF_instance, NUMTAPS, (float32_t *)FIRCoeff_f32, firStateF32, BLOCKSIZE);
+
+  /* ----------------------------------------------------------------------
+  * Loop over the frames of data and execute each of the processing
+  * functions in the system.
+  * ------------------------------------------------------------------- */
+
+  for(i=0; i < NUMFRAMES; i++)
+  {
+    /* Read the input data - uniformly distributed random noise - into wire1 */
+    arm_copy_f32(testInput_f32 + (i * BLOCKSIZE), wire1, BLOCKSIZE);
+
+    /* Execute the FIR processing function.  Input wire1 and output wire2 */
+    arm_fir_f32(&LPF_instance, wire1, wire2, BLOCKSIZE);
+
+    /* Execute the LMS Norm processing function*/
+
+    arm_lms_norm_f32(&lmsNorm_instance, /* LMSNorm instance */
+         wire1,                         /* Input signal */
+         wire2,                         /* Reference Signal */
+         wire3,                         /* Converged Signal */
+         err_signal,                    /* Error Signal, this will become small as the signal converges */
+         BLOCKSIZE);                    /* BlockSize */
+
+    /* apply overall gain */
+    arm_scale_f32(wire3, 5, wire3, BLOCKSIZE);   /* in-place buffer */
+  }
+
+  status = ARM_MATH_SUCCESS;
+
+  /* -------------------------------------------------------------------------------
+  * Test whether the error signal has reached towards 0.
+  * ----------------------------------------------------------------------------- */
+
+  arm_abs_f32(err_signal, err_signal, BLOCKSIZE);
+  arm_min_f32(err_signal, BLOCKSIZE, &minValue, &index);
+
+  if (minValue > DELTA_ERROR)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  /* ----------------------------------------------------------------------
+  * Test whether the filter coefficients have converged.
+  * ------------------------------------------------------------------- */
+
+  arm_sub_f32((float32_t *)FIRCoeff_f32, lmsNormCoeff_f32, lmsNormCoeff_f32, NUMTAPS);
+
+  arm_abs_f32(lmsNormCoeff_f32, lmsNormCoeff_f32, NUMTAPS);
+  arm_min_f32(lmsNormCoeff_f32, NUMTAPS, &minValue, &index);
+
+  if (minValue > DELTA_COEFF)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  /* ----------------------------------------------------------------------
+  * Loop here if the signals did not pass the convergence check.
+  * This denotes a test failure
+  * ------------------------------------------------------------------- */
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_signal_converge_example/ARM/math_helper.c

@@ -0,0 +1,458 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0    
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.c
+*
+* Description:	Definition of all helper functions required.  
+*  
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+/* ----------------------------------------------------------------------
+*		Include standard header files  
+* -------------------------------------------------------------------- */
+#include<math.h>
+
+/* ----------------------------------------------------------------------
+*		Include project header files  
+* -------------------------------------------------------------------- */
+#include "math_helper.h"
+
+/** 
+ * @brief  Caluclation of SNR
+ * @param  float* 	Pointer to the reference buffer
+ * @param  float*	Pointer to the test buffer
+ * @param  uint32_t	total number of samples
+ * @return float	SNR
+ * The function Caluclates signal to noise ratio for the reference output 
+ * and test output 
+ */
+
+float arm_snr_f32(float *pRef, float *pTest, uint32_t buffSize)
+{
+  float EnergySignal = 0.0, EnergyError = 0.0;
+  uint32_t i;
+  float SNR;
+  int temp;
+  int *test;
+
+  for (i = 0; i < buffSize; i++)
+    {
+ 	  /* Checking for a NAN value in pRef array */
+	  test =   (int *)(&pRef[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+
+	  /* Checking for a NAN value in pTest array */
+	  test =   (int *)(&pTest[i]);
+      temp =  *test;
+
+	  if(temp == 0x7FC00000)
+	  {
+	  		return(0);
+	  }
+      EnergySignal += pRef[i] * pRef[i];
+      EnergyError += (pRef[i] - pTest[i]) * (pRef[i] - pTest[i]); 
+    }
+
+	/* Checking for a NAN value in EnergyError */
+	test =   (int *)(&EnergyError);
+    temp =  *test;
+
+    if(temp == 0x7FC00000)
+    {
+  		return(0);
+    }
+	
+
+  SNR = 10 * log10 (EnergySignal / EnergyError);
+
+  return (SNR);
+
+}
+
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q15_t* 	    Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q15 (q15_t * input_buf, uint32_t blockSize,
+                            uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed in q12.20 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point(q12.20) values 
+ */
+
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1048576.0f corresponds to pow(2, 20) */
+      pOut[i] = (q31_t) (pIn[i] * 1048576.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 1.0)
+        {
+          pOut[i] = 0x000FFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q15_t* 	Pointer to Ref buffer
+ * @param  q15_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}	
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Compare MATLAB Reference Output and ARM Test output
+ * @param  q31_t* 	Pointer to Ref buffer
+ * @param  q31_t* 	Pointer to Test buffer
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none 
+ */
+
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t * pOut, uint32_t numSamples)
+{
+  uint32_t i; 
+  int32_t diff, diffCrnt = 0;
+  uint32_t maxDiff = 0;
+
+  for (i = 0; i < numSamples; i++)
+  {
+  	diff = pIn[i] - pOut[i];
+  	diffCrnt = (diff > 0) ? diff : -diff;
+
+	if(diffCrnt > maxDiff)
+	{
+		maxDiff = diffCrnt;
+	}
+  }
+
+  return(maxDiff);
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q31 (q31_t * input_buf, 
+								 uint32_t blockSize,
+                                 uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+/** 
+ * @brief  Provide guard bits for Input buffer
+ * @param  q31_t* 	Pointer to input buffer
+ * @param  uint32_t 	blockSize
+ * @param  uint32_t 	guard_bits
+ * @return none
+ * The function Provides the guard bits for the buffer 
+ * to avoid overflow 
+ */
+
+void arm_provide_guard_bits_q7 (q7_t * input_buf, 
+								uint32_t blockSize,
+                                uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < blockSize; i++)
+    {
+      input_buf[i] = input_buf[i] >> guard_bits;
+    }
+}
+
+
+
+/** 
+ * @brief  Caluclates number of guard bits 
+ * @param  uint32_t 	number of additions
+ * @return none
+ * The function Caluclates the number of guard bits  
+ * depending on the numtaps 
+ */
+
+uint32_t arm_calc_guard_bits (uint32_t num_adds)
+{
+  uint32_t i = 1, j = 0;
+
+  if (num_adds == 1)
+    {
+      return (0);
+    }
+
+  while (i < num_adds)
+    {
+      i = i * 2;
+      j++;
+    }
+
+  return (j);
+}
+
+/** 
+ * @brief  Converts Q15 to floating-point
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ */
+
+void arm_apply_guard_bits (float32_t * pIn, 
+						   uint32_t numSamples, 
+						   uint32_t guard_bits)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      pIn[i] = pIn[i] * arm_calc_2pow(guard_bits);
+    }
+}
+
+/** 
+ * @brief  Calculates pow(2, numShifts)
+ * @param  uint32_t 	number of shifts
+ * @return pow(2, numShifts)
+ */
+uint32_t arm_calc_2pow(uint32_t numShifts)
+{
+
+  uint32_t i, val = 1;
+
+  for (i = 0; i < numShifts; i++)
+    {
+      val = val * 2;
+    }	
+
+  return(val);
+}
+
+
+
+/** 
+ * @brief  Converts float to fixed q14 
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q14 (float *pIn, q15_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 16384.0f corresponds to pow(2, 14) */
+      pOut[i] = (q15_t) (pIn[i] * 16384.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFF;
+        }
+
+    }
+
+}
+
+ 
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q30 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 1073741824.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 2.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Converts float to fixed q30 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q29 (float *pIn, q31_t * pOut, 
+					   uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	  /* 1073741824.0f corresponds to pow(2, 30) */
+      pOut[i] = (q31_t) (pIn[i] * 536870912.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 4.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+
+/** 
+ * @brief  Converts float to fixed q28 format
+ * @param  uint32_t 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_float_to_q28 (float *pIn, q31_t * pOut, 
+                       uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+	/* 268435456.0f corresponds to pow(2, 28) */
+      pOut[i] = (q31_t) (pIn[i] * 268435456.0f);
+
+      pOut[i] += pIn[i] > 0 ? 0.5 : -0.5;
+
+      if (pIn[i] == (float) 8.0)
+        {
+          pOut[i] = 0x7FFFFFFF;
+        }
+    }
+}
+
+/** 
+ * @brief  Clip the float values to +/- 1 
+ * @param  pIn 	input buffer
+ * @param  numSamples 	number of samples in the buffer
+ * @return none
+ * The function converts floating point values to fixed point values 
+ */
+
+void arm_clip_f32 (float *pIn, uint32_t numSamples)
+{
+  uint32_t i;
+
+  for (i = 0; i < numSamples; i++)
+    {
+      if(pIn[i] > 1.0f)
+	  {
+	    pIn[i] = 1.0;
+	  }
+	  else if( pIn[i] < -1.0f)
+	  {
+	    pIn[i] = -1.0;
+	  }
+	       
+    }
+}
+
+
+
+

Libraries/CMSIS/DSP_Lib/Examples/arm_signal_converge_example/ARM/math_helper.h

@@ -0,0 +1,63 @@
+/* ----------------------------------------------------------------------   
+* Copyright (C) 2010-2013 ARM Limited. All rights reserved.   
+*   
+* $Date:        17. January 2013  
+* $Revision: 	V1.4.0   
+*  
+* Project: 	    CMSIS DSP Library 
+*
+* Title:	    math_helper.h
+* 
+* Description:	Prototypes of all helper functions required.  
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+
+#ifndef MATH_HELPER_H
+#define MATH_HELPER_H
+
+float arm_snr_f32(float *pRef, float *pTest,  uint32_t buffSize);  
+void arm_float_to_q12_20(float *pIn, q31_t * pOut, uint32_t numSamples);
+void arm_provide_guard_bits_q15(q15_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_provide_guard_bits_q31(q31_t *input_buf, uint32_t blockSize, uint32_t guard_bits);
+void arm_float_to_q14(float *pIn, q15_t *pOut, uint32_t numSamples);
+void arm_float_to_q29(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q28(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_float_to_q30(float *pIn, q31_t *pOut, uint32_t numSamples);
+void arm_clip_f32(float *pIn, uint32_t numSamples);
+uint32_t arm_calc_guard_bits(uint32_t num_adds);
+void arm_apply_guard_bits (float32_t * pIn, uint32_t numSamples, uint32_t guard_bits);
+uint32_t arm_compare_fixed_q15(q15_t *pIn, q15_t * pOut, uint32_t numSamples);
+uint32_t arm_compare_fixed_q31(q31_t *pIn, q31_t *pOut, uint32_t numSamples);
+uint32_t arm_calc_2pow(uint32_t guard_bits);
+#endif
+

Libraries/CMSIS/DSP_Lib/Examples/arm_sin_cos_example/ARM/arm_sin_cos_example_f32.c

@@ -0,0 +1,161 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         12. March 2014
+* $Revision:     V1.4.3
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_sin_cos_example_f32.c
+*
+* Description:   Example code demonstrating sin and cos calculation of input signal.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup SinCosExample SineCosine Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the Pythagorean trignometric identity with the use of Cosine, Sine, Vector
+ * Multiplication, and Vector Addition functions.
+ *
+ * \par Algorithm:
+ * \par
+ * Mathematically, the Pythagorean trignometric identity is defined by the following equation:
+ *  <pre>sin(x) * sin(x) + cos(x) * cos(x) = 1</pre>
+ * where \c x is the angle in radians.
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html sinCos.gif
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32 array of input angle in radians
+ * \li \c testOutput stores sum of the squares of sine and cosine values of input angle
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_cos_f32()
+ * - arm_sin_f32()
+ * - arm_mult_f32()
+ * - arm_add_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_sin_cos_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_sin_cos_example_f32.c
+  */
+
+#include <math.h>
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE   32
+#define DELTA           (0.0001f)
+
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point sin_cos example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+
+const float32_t testInput_f32[MAX_BLOCKSIZE] =
+{
+  -1.244916875853235400,  -4.793533929171324800,   0.360705030233248850,   0.827929644170887320,  -3.299532218312426900,   3.427441903227623800,   3.422401784294607700,  -0.108308165334010680,
+   0.941943896490312180,   0.502609575000365850,  -0.537345278736373500,   2.088817392965764500,  -1.693168684143455700,   6.283185307179590700,  -0.392545884746175080,   0.327893095115825040,
+   3.070147440456292300,   0.170611405884662230,  -0.275275082396073010,  -2.395492805446796300,   0.847311163536506600,  -3.845517018083148800,   2.055818378415868300,   4.672594161978930800,
+  -1.990923030266425800,   2.469305197656249500,   3.609002606064021000,  -4.586736582331667500,  -4.147080139136136300,   1.643756718868359500,  -1.150866392366494800,   1.985805026477433800
+
+
+};
+
+const float32_t testRefOutput_f32 = 1.000000000;
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+uint32_t blockSize = 32;
+float32_t  testOutput;
+float32_t  cosOutput;
+float32_t  sinOutput;
+float32_t  cosSquareOutput;
+float32_t  sinSquareOutput;
+
+/* ----------------------------------------------------------------------
+* Max magnitude FFT Bin test
+* ------------------------------------------------------------------- */
+
+arm_status status;
+
+int32_t main(void)
+{
+  float32_t diff;
+  uint32_t i;
+
+  for(i=0; i< blockSize; i++)
+  {
+    cosOutput = arm_cos_f32(testInput_f32[i]);
+    sinOutput = arm_sin_f32(testInput_f32[i]);
+
+    arm_mult_f32(&cosOutput, &cosOutput, &cosSquareOutput, 1);
+    arm_mult_f32(&sinOutput, &sinOutput, &sinSquareOutput, 1);
+
+    arm_add_f32(&cosSquareOutput, &sinSquareOutput, &testOutput, 1);
+
+    /* absolute value of difference between ref and test */
+    diff = fabsf(testRefOutput_f32 - testOutput);
+
+    /* Comparison of sin_cos value with reference */
+    if(diff > DELTA)
+    {
+       status = ARM_MATH_TEST_FAILURE;
+    }
+
+    if( status == ARM_MATH_TEST_FAILURE)
+    {
+       while(1);
+    }
+
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Examples/arm_variance_example/ARM/arm_variance_example_f32.c

@@ -0,0 +1,204 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
+*
+* $Date:         17. January 2013
+* $Revision:     V1.4.0
+*
+* Project:       CMSIS DSP Library
+* Title:         arm_variance_example_f32.c
+*
+* Description:   Example code demonstrating variance calculation of input sequence.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+/**
+ * @ingroup groupExamples
+ */
+
+/**
+ * @defgroup VarianceExample Variance Example
+ *
+ * \par Description:
+ * \par
+ * Demonstrates the use of Basic Math and Support Functions to calculate the variance of an
+ * input sequence with N samples. Uniformly distributed white noise is taken as input.
+ *
+ * \par Algorithm:
+ * \par
+ * The variance of a sequence is the mean of the squared deviation of the sequence from its mean.
+ * \par
+ * This is denoted by the following equation:
+ * <pre> variance = ((x[0] - x') * (x[0] - x') + (x[1] - x') * (x[1] - x') + ... + * (x[n-1] - x') * (x[n-1] - x')) / (N-1)</pre>
+ * where, <code>x[n]</code> is the input sequence, <code>N</code> is the number of input samples, and
+ * <code>x'</code> is the mean value of the input sequence, <code>x[n]</code>.
+ * \par
+ * The mean value <code>x'</code> is defined as:
+ * <pre> x' = (x[0] + x[1] + ... + x[n-1]) / N</pre>
+ *
+ * \par Block Diagram:
+ * \par
+ * \image html Variance.gif
+ *
+ *
+ * \par Variables Description:
+ * \par
+ * \li \c testInput_f32 points to the input data
+ * \li \c wire1, \c wir2, \c wire3 temporary buffers
+ * \li \c blockSize number of samples processed at a time
+ * \li \c refVarianceOut reference variance value
+ *
+ * \par CMSIS DSP Software Library Functions Used:
+ * \par
+ * - arm_dot_prod_f32()
+ * - arm_mult_f32()
+ * - arm_sub_f32()
+ * - arm_fill_f32()
+ * - arm_copy_f32()
+ *
+ * <b> Refer  </b>
+ * \link arm_variance_example_f32.c \endlink
+ *
+ */
+
+
+/** \example arm_variance_example_f32.c
+  */
+#include <math.h>
+#include "arm_math.h"
+
+/* ----------------------------------------------------------------------
+* Defines each of the tests performed
+* ------------------------------------------------------------------- */
+#define MAX_BLOCKSIZE   32
+#define DELTA           (0.000001f)
+
+
+/* ----------------------------------------------------------------------
+* Declare I/O buffers
+* ------------------------------------------------------------------- */
+float32_t wire1[MAX_BLOCKSIZE];
+float32_t wire2[MAX_BLOCKSIZE];
+float32_t wire3[MAX_BLOCKSIZE];
+
+/* ----------------------------------------------------------------------
+* Test input data for Floating point Variance example for 32-blockSize
+* Generated by the MATLAB randn() function
+* ------------------------------------------------------------------- */
+
+float32_t testInput_f32[32] =
+{
+  -0.432564811528221,  -1.665584378238097,   0.125332306474831,   0.287676420358549,
+  -1.146471350681464,   1.190915465642999,   1.189164201652103,  -0.037633276593318,
+   0.327292361408654,   0.174639142820925,  -0.186708577681439,   0.725790548293303,
+  -0.588316543014189,   2.183185818197101,  -0.136395883086596,   0.113931313520810,
+   1.066768211359189,   0.059281460523605,  -0.095648405483669,  -0.832349463650022,
+   0.294410816392640,  -1.336181857937804,   0.714324551818952,   1.623562064446271,
+  -0.691775701702287,   0.857996672828263,   1.254001421602532,  -1.593729576447477,
+  -1.440964431901020,   0.571147623658178,  -0.399885577715363,   0.689997375464345
+
+};
+
+/* ----------------------------------------------------------------------
+* Declare Global variables
+* ------------------------------------------------------------------- */
+uint32_t blockSize = 32;
+float32_t  refVarianceOut = 0.903941793931839;
+
+/* ----------------------------------------------------------------------
+* Variance calculation test
+* ------------------------------------------------------------------- */
+
+int32_t main(void)
+{
+  arm_status status;
+  float32_t mean, oneByBlockSize;
+  float32_t variance;
+  float32_t diff;
+
+  status = ARM_MATH_SUCCESS;
+
+  /* Calculation of mean value of input */
+
+  /* x' = 1/blockSize * (x(0)* 1 + x(1) * 1 + ... + x(n-1) * 1) */
+
+  /* Fill wire1 buffer with 1.0 value */
+  arm_fill_f32(1.0,  wire1, blockSize);
+
+  /* Calculate the dot product of wire1 and wire2 */
+  /* (x(0)* 1 + x(1) * 1 + ...+ x(n-1) * 1) */
+  arm_dot_prod_f32(testInput_f32, wire1, blockSize, &mean);
+
+  /* Calculation of 1/blockSize */
+  oneByBlockSize = 1.0 / (blockSize);
+
+  /* 1/blockSize * (x(0)* 1 + x(1) * 1 + ... + x(n-1) * 1)  */
+  arm_mult_f32(&mean, &oneByBlockSize, &mean, 1);
+
+
+  /* Calculation of variance value of input */
+
+  /* (1/blockSize) * (x(0) - x') * (x(0) - x') + (x(1) - x') * (x(1) - x') + ... + (x(n-1) - x') * (x(n-1) - x') */
+
+  /* Fill wire2 with mean value x' */
+  arm_fill_f32(mean,  wire2, blockSize);
+
+  /* wire3 contains (x-x') */
+  arm_sub_f32(testInput_f32, wire2, wire3, blockSize);
+
+  /* wire2 contains (x-x') */
+  arm_copy_f32(wire3, wire2, blockSize);
+
+  /* (x(0) - x') * (x(0) - x') + (x(1) - x') * (x(1) - x') + ... + (x(n-1) - x') * (x(n-1) - x') */
+  arm_dot_prod_f32(wire2, wire3, blockSize, &variance);
+
+    /* Calculation of 1/blockSize */
+  oneByBlockSize = 1.0 / (blockSize - 1);
+
+  /* Calculation of variance */
+  arm_mult_f32(&variance, &oneByBlockSize, &variance, 1);
+
+  /* absolute value of difference between ref and test */
+  diff = fabsf(refVarianceOut - variance);
+
+  /* Comparison of variance value with reference */
+  if(diff > DELTA)
+  {
+    status = ARM_MATH_TEST_FAILURE;
+  }
+
+  if( status != ARM_MATH_SUCCESS)
+  {
+    while(1);
+  }
+
+  while(1);                             /* main function does not return */
+}
+
+ /** \endlink */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_f32.c

@@ -0,0 +1,165 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_abs_f32.c    
+*    
+* Description:	Vector absolute value.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include <math.h>
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup BasicAbs Vector Absolute Value        
+ *        
+ * Computes the absolute value of a vector on an element-by-element basis.        
+ *        
+ * <pre>        
+ *     pDst[n] = abs(pSrc[n]),   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * The functions support in-place computation allowing the source and
+ * destination pointers to reference the same memory buffer.
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.
+ */
+
+/**        
+ * @addtogroup BasicAbs        
+ * @{        
+ */
+
+/**        
+ * @brief Floating-point vector absolute value.        
+ * @param[in]       *pSrc points to the input buffer        
+ * @param[out]      *pDst points to the output buffer        
+ * @param[in]       blockSize number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_abs_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;                  /* temporary variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Calculate absolute and then store the results in the destination buffer. */
+    /* read sample from source */
+    in1 = *pSrc;
+    in2 = *(pSrc + 1);
+    in3 = *(pSrc + 2);
+
+    /* find absolute value */
+    in1 = fabsf(in1);
+
+    /* read sample from source */
+    in4 = *(pSrc + 3);
+
+    /* find absolute value */
+    in2 = fabsf(in2);
+
+    /* read sample from source */
+    *pDst = in1;
+
+    /* find absolute value */
+    in3 = fabsf(in3);
+
+    /* find absolute value */
+    in4 = fabsf(in4);
+
+    /* store result to destination */
+    *(pDst + 1) = in2;
+
+    /* store result to destination */
+    *(pDst + 2) = in3;
+
+    /* store result to destination */
+    *(pDst + 3) = in4;
+
+
+    /* Update source pointer to process next sampels */
+    pSrc += 4u;
+
+    /* Update destination pointer to process next sampels */
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /*   #ifndef ARM_MATH_CM0_FAMILY   */
+
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Calculate absolute and then store the results in the destination buffer. */
+    *pDst++ = fabsf(*pSrc++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of BasicAbs group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q15.c

@@ -0,0 +1,179 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_abs_q15.c    
+*    
+* Description:	Q15 vector absolute value.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicAbs    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 vector absolute value.    
+ * @param[in]       *pSrc points to the input buffer    
+ * @param[out]      *pDst points to the output buffer    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF.    
+ */
+
+void arm_abs_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+  __SIMD32_TYPE *simd;
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t in1;                                     /* Input value1 */
+  q15_t in2;                                     /* Input value2 */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  simd = __SIMD32_CONST(pDst);
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Read two inputs */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+
+
+    /* Store the Absolute result in the destination buffer by packing the two values, in a single cycle */
+#ifndef  ARM_MATH_BIG_ENDIAN
+    *simd++ =
+      __PKHBT(((in1 > 0) ? in1 : (q15_t)__QSUB16(0, in1)),
+              ((in2 > 0) ? in2 : (q15_t)__QSUB16(0, in2)), 16);
+
+#else
+
+
+    *simd++ =
+      __PKHBT(((in2 > 0) ? in2 : (q15_t)__QSUB16(0, in2)),
+              ((in1 > 0) ? in1 : (q15_t)__QSUB16(0, in1)), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+    *simd++ =
+      __PKHBT(((in1 > 0) ? in1 : (q15_t)__QSUB16(0, in1)),
+              ((in2 > 0) ? in2 : (q15_t)__QSUB16(0, in2)), 16);
+
+#else
+
+
+    *simd++ =
+      __PKHBT(((in2 > 0) ? in2 : (q15_t)__QSUB16(0, in2)),
+              ((in1 > 0) ? in1 : (q15_t)__QSUB16(0, in1)), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+  pDst = (q15_t *)simd;
+	
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Read the input */
+    in1 = *pSrc++;
+
+    /* Calculate absolute value of input and then store the result in the destination buffer. */
+    *pDst++ = (in1 > 0) ? in1 : (q15_t)__QSUB16(0, in1);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q15_t in;                                      /* Temporary input variable */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Read the input */
+    in = *pSrc++;
+
+    /* Calculate absolute value of input and then store the result in the destination buffer. */
+    *pDst++ = (in > 0) ? in : ((in == (q15_t) 0x8000) ? 0x7fff : -in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of BasicAbs group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q31.c

@@ -0,0 +1,130 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_abs_q31.c    
+*    
+* Description:	Q31 vector absolute value.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicAbs    
+ * @{    
+ */
+
+
+/**    
+ * @brief Q31 vector absolute value.    
+ * @param[in]       *pSrc points to the input buffer    
+ * @param[out]      *pDst points to the output buffer    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF.    
+ */
+
+void arm_abs_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in;                                      /* Input value */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Calculate absolute of input (if -1 then saturated to 0x7fffffff) and then store the results in the destination buffer. */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    *pDst++ = (in1 > 0) ? in1 : (q31_t)__QSUB(0, in1);
+    *pDst++ = (in2 > 0) ? in2 : (q31_t)__QSUB(0, in2);
+    *pDst++ = (in3 > 0) ? in3 : (q31_t)__QSUB(0, in3);
+    *pDst++ = (in4 > 0) ? in4 : (q31_t)__QSUB(0, in4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /*   #ifndef ARM_MATH_CM0_FAMILY   */
+
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Calculate absolute value of the input (if -1 then saturated to 0x7fffffff) and then store the results in the destination buffer. */
+    in = *pSrc++;
+    *pDst++ = (in > 0) ? in : ((in == INT32_MIN) ? INT32_MAX : -in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+}
+
+/**    
+ * @} end of BasicAbs group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_abs_q7.c

@@ -0,0 +1,157 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_abs_q7.c    
+*    
+* Description:	Q7 vector absolute value.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @addtogroup BasicAbs        
+ * @{        
+ */
+
+/**        
+ * @brief Q7 vector absolute value.        
+ * @param[in]       *pSrc points to the input buffer        
+ * @param[out]      *pDst points to the output buffer        
+ * @param[in]       blockSize number of samples in each vector        
+ * @return none.        
+ *    
+ * \par Conditions for optimum performance    
+ *  Input and output buffers should be aligned by 32-bit    
+ *    
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * The Q7 value -1 (0x80) will be saturated to the maximum allowable positive value 0x7F.        
+ */
+
+void arm_abs_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q7_t in;                                       /* Input value1 */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;                      /* temporary input variables */
+  q31_t out1, out2, out3, out4;                  /* temporary output variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Read inputs */
+    in1 = (q31_t) * pSrc;
+    in2 = (q31_t) * (pSrc + 1);
+    in3 = (q31_t) * (pSrc + 2);
+
+    /* find absolute value */
+    out1 = (in1 > 0) ? in1 : (q31_t)__QSUB8(0, in1);
+
+    /* read input */
+    in4 = (q31_t) * (pSrc + 3);
+
+    /* find absolute value */
+    out2 = (in2 > 0) ? in2 : (q31_t)__QSUB8(0, in2);
+
+    /* store result to destination */
+    *pDst = (q7_t) out1;
+
+    /* find absolute value */
+    out3 = (in3 > 0) ? in3 : (q31_t)__QSUB8(0, in3);
+
+    /* find absolute value */
+    out4 = (in4 > 0) ? in4 : (q31_t)__QSUB8(0, in4);
+
+    /* store result to destination */
+    *(pDst + 1) = (q7_t) out2;
+
+    /* store result to destination */
+    *(pDst + 2) = (q7_t) out3;
+
+    /* store result to destination */
+    *(pDst + 3) = (q7_t) out4;
+
+    /* update pointers to process next samples */
+    pSrc += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = blockSize;
+
+#endif //      #define ARM_MATH_CM0_FAMILY
+
+  while(blkCnt > 0u)
+  {
+    /* C = |A| */
+    /* Read the input */
+    in = *pSrc++;
+
+    /* Store the Absolute result in the destination buffer */
+    *pDst++ = (in > 0) ? in : ((in == (q7_t) 0x80) ? 0x7f : -in);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of BasicAbs group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_f32.c

@@ -0,0 +1,150 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_add_f32.c    
+*    
+* Description:	Floating-point vector addition.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup BasicAdd Vector Addition        
+ *        
+ * Element-by-element addition of two vectors.        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrcA[n] + pSrcB[n],   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup BasicAdd        
+ * @{        
+ */
+
+/**        
+ * @brief Floating-point vector addition.        
+ * @param[in]       *pSrcA points to the first input vector        
+ * @param[in]       *pSrcB points to the second input vector        
+ * @param[out]      *pDst points to the output vector        
+ * @param[in]       blockSize number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_add_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inA1, inA2, inA3, inA4;              /* temporary input variabels */
+  float32_t inB1, inB2, inB3, inB4;              /* temporary input variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+
+    /* read four inputs from sourceA and four inputs from sourceB */
+    inA1 = *pSrcA;
+    inB1 = *pSrcB;
+    inA2 = *(pSrcA + 1);
+    inB2 = *(pSrcB + 1);
+    inA3 = *(pSrcA + 2);
+    inB3 = *(pSrcB + 2);
+    inA4 = *(pSrcA + 3);
+    inB4 = *(pSrcB + 3);
+
+    /* C = A + B */
+    /* add and store result to destination */
+    *pDst = inA1 + inB1;
+    *(pDst + 1) = inA2 + inB2;
+    *(pDst + 2) = inA3 + inB3;
+    *(pDst + 3) = inA4 + inB4;
+
+    /* update pointers to process next samples */
+    pSrcA += 4u;
+    pSrcB += 4u;
+    pDst += 4u;
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (*pSrcA++) + (*pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of BasicAdd group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q15.c

@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_add_q15.c    
+*    
+* Description:	Q15 vector addition    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicAdd    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 vector addition.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_add_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inB1, inB2;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    inA1 = *__SIMD32(pSrcA)++;
+    inA2 = *__SIMD32(pSrcA)++;
+    inB1 = *__SIMD32(pSrcB)++;
+    inB2 = *__SIMD32(pSrcB)++;
+
+    *__SIMD32(pDst)++ = __QADD16(inA1, inB1);
+    *__SIMD32(pDst)++ = __QADD16(inA2, inB2);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (q15_t) __QADD16(*pSrcA++, *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (q15_t) __SSAT(((q31_t) * pSrcA++ + *pSrcB++), 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+}
+
+/**    
+ * @} end of BasicAdd group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q31.c

@@ -0,0 +1,148 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_add_q31.c    
+*    
+* Description:	Q31 vector addition.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicAdd    
+ * @{    
+ */
+
+
+/**    
+ * @brief Q31 vector addition.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated.    
+ */
+
+void arm_add_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inA3, inA4;
+  q31_t inB1, inB2, inB3, inB4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    inA1 = *pSrcA++;
+    inA2 = *pSrcA++;
+    inB1 = *pSrcB++;
+    inB2 = *pSrcB++;
+
+    inA3 = *pSrcA++;
+    inA4 = *pSrcA++;
+    inB3 = *pSrcB++;
+    inB4 = *pSrcB++;
+
+    *pDst++ = __QADD(inA1, inB1);
+    *pDst++ = __QADD(inA2, inB2);
+    *pDst++ = __QADD(inA3, inB3);
+    *pDst++ = __QADD(inA4, inB4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = __QADD(*pSrcA++, *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrcA++ + *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of BasicAdd group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_add_q7.c

@@ -0,0 +1,134 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_add_q7.c    
+*    
+* Description:	Q7 vector addition.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicAdd    
+ * @{    
+ */
+
+/**    
+ * @brief Q7 vector addition.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated.    
+ */
+
+void arm_add_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *__SIMD32(pDst)++ = __QADD8(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (q7_t) __SSAT(*pSrcA++ + *pSrcB++, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + B */
+    /* Add and then store the results in the destination buffer. */
+    *pDst++ = (q7_t) __SSAT((q15_t) * pSrcA++ + *pSrcB++, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+}
+
+/**    
+ * @} end of BasicAdd group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_f32.c

@@ -0,0 +1,135 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_dot_prod_f32.c    
+*    
+* Description:	Floating-point dot product.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath
+ */
+
+/**
+ * @defgroup dot_prod Vector Dot Product
+ *
+ * Computes the dot product of two vectors.
+ * The vectors are multiplied element-by-element and then summed.
+ *
+ * <pre>
+ *     sum = pSrcA[0]*pSrcB[0] + pSrcA[1]*pSrcB[1] + ... + pSrcA[blockSize-1]*pSrcB[blockSize-1]
+ * </pre>     
+ *
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.    
+ */
+
+/**    
+ * @addtogroup dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief Dot product of floating-point vectors.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @param[out]      *result output result returned here    
+ * @return none.    
+ */
+
+
+void arm_dot_prod_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  uint32_t blockSize,
+  float32_t * result)
+{
+  float32_t sum = 0.0f;                          /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the result in a temporary buffer */
+    sum += (*pSrcA++) * (*pSrcB++);
+    sum += (*pSrcA++) * (*pSrcB++);
+    sum += (*pSrcA++) * (*pSrcB++);
+    sum += (*pSrcA++) * (*pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the result in a temporary buffer. */
+    sum += (*pSrcA++) * (*pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+  /* Store the result back in the destination buffer */
+  *result = sum;
+}
+
+/**    
+ * @} end of dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q15.c

@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_dot_prod_q15.c    
+*    
+* Description:	Q15 dot product.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief Dot product of Q15 vectors.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @param[out]      *result output result returned here    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The intermediate multiplications are in 1.15 x 1.15 = 2.30 format and these    
+ * results are added to a 64-bit accumulator in 34.30 format.    
+ * Nonsaturating additions are used and given that there are 33 guard bits in the accumulator    
+ * there is no risk of overflow.    
+ * The return result is in 34.30 format.    
+ */
+
+void arm_dot_prod_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  uint32_t blockSize,
+  q63_t * result)
+{
+  q63_t sum = 0;                                 /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the result in a temporary buffer. */
+    sum = __SMLALD(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++, sum);
+    sum = __SMLALD(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the results in a temporary buffer. */
+    sum = __SMLALD(*pSrcA++, *pSrcB++, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the results in a temporary buffer. */
+    sum += (q63_t) ((q31_t) * pSrcA++ * *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  /* Store the result in the destination buffer in 34.30 format */
+  *result = sum;
+
+}
+
+/**    
+ * @} end of dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q31.c

@@ -0,0 +1,143 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_dot_prod_q31.c    
+*    
+* Description:	Q31 dot product.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief Dot product of Q31 vectors.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @param[out]      *result output result returned here    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The intermediate multiplications are in 1.31 x 1.31 = 2.62 format and these    
+ * are truncated to 2.48 format by discarding the lower 14 bits.    
+ * The 2.48 result is then added without saturation to a 64-bit accumulator in 16.48 format.    
+ * There are 15 guard bits in the accumulator and there is no risk of overflow as long as    
+ * the length of the vectors is less than 2^16 elements.    
+ * The return result is in 16.48 format.    
+ */
+
+void arm_dot_prod_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  uint32_t blockSize,
+  q63_t * result)
+{
+  q63_t sum = 0;                                 /* Temporary result storage */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inA3, inA4;
+  q31_t inB1, inB2, inB3, inB4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the result in a temporary buffer. */
+    inA1 = *pSrcA++;
+    inA2 = *pSrcA++;
+    inA3 = *pSrcA++;
+    inA4 = *pSrcA++;
+    inB1 = *pSrcB++;
+    inB2 = *pSrcB++;
+    inB3 = *pSrcB++;
+    inB4 = *pSrcB++;
+
+    sum += ((q63_t) inA1 * inB1) >> 14u;
+    sum += ((q63_t) inA2 * inB2) >> 14u;
+    sum += ((q63_t) inA3 * inB3) >> 14u;
+    sum += ((q63_t) inA4 * inB4) >> 14u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Calculate dot product and then store the result in a temporary buffer. */
+    sum += ((q63_t) * pSrcA++ * *pSrcB++) >> 14u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* Store the result in the destination buffer in 16.48 format */
+  *result = sum;
+}
+
+/**    
+ * @} end of dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_dot_prod_q7.c

@@ -0,0 +1,159 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_dot_prod_q7.c    
+*    
+* Description:	Q7 dot product.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief Dot product of Q7 vectors.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @param[out]      *result output result returned here    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The intermediate multiplications are in 1.7 x 1.7 = 2.14 format and these    
+ * results are added to an accumulator in 18.14 format.    
+ * Nonsaturating additions are used and there is no danger of wrap around as long as    
+ * the vectors are less than 2^18 elements long.    
+ * The return result is in 18.14 format.    
+ */
+
+void arm_dot_prod_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  uint32_t blockSize,
+  q31_t * result)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+  q31_t sum = 0;                                 /* Temporary variables to store output */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t input1, input2;                          /* Temporary variables to store input */
+  q31_t inA1, inA2, inB1, inB2;                  /* Temporary variables to store input */
+
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* read 4 samples at a time from sourceA */
+    input1 = *__SIMD32(pSrcA)++;
+    /* read 4 samples at a time from sourceB */
+    input2 = *__SIMD32(pSrcB)++;
+
+    /* extract two q7_t samples to q15_t samples */
+    inA1 = __SXTB16(__ROR(input1, 8));
+    /* extract reminaing two samples */
+    inA2 = __SXTB16(input1);
+    /* extract two q7_t samples to q15_t samples */
+    inB1 = __SXTB16(__ROR(input2, 8));
+    /* extract reminaing two samples */
+    inB2 = __SXTB16(input2);
+
+    /* multiply and accumulate two samples at a time */
+    sum = __SMLAD(inA1, inB1, sum);
+    sum = __SMLAD(inA2, inB2, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Dot product and then store the results in a temporary buffer. */
+    sum = __SMLAD(*pSrcA++, *pSrcB++, sum);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A[0]* B[0] + A[1]* B[1] + A[2]* B[2] + .....+ A[blockSize-1]* B[blockSize-1] */
+    /* Dot product and then store the results in a temporary buffer. */
+    sum += (q31_t) ((q15_t) * pSrcA++ * *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  /* Store the result in the destination buffer in 18.14 format */
+  *result = sum;
+}
+
+/**    
+ * @} end of dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_f32.c

@@ -0,0 +1,174 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mult_f32.c    
+*    
+* Description:	Floating-point vector multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup BasicMult Vector Multiplication        
+ *        
+ * Element-by-element multiplication of two vectors.        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrcA[n] * pSrcB[n],   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup BasicMult        
+ * @{        
+ */
+
+/**        
+ * @brief Floating-point vector multiplication.        
+ * @param[in]       *pSrcA points to the first input vector        
+ * @param[in]       *pSrcB points to the second input vector        
+ * @param[out]      *pDst points to the output vector        
+ * @param[in]       blockSize number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_mult_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counters */
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inA1, inA2, inA3, inA4;              /* temporary input variables */
+  float32_t inB1, inB2, inB3, inB4;              /* temporary input variables */
+  float32_t out1, out2, out3, out4;              /* temporary output variables */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and store the results in output buffer */
+    /* read sample from sourceA */
+    inA1 = *pSrcA;
+    /* read sample from sourceB */
+    inB1 = *pSrcB;
+    /* read sample from sourceA */
+    inA2 = *(pSrcA + 1);
+    /* read sample from sourceB */
+    inB2 = *(pSrcB + 1);
+
+    /* out = sourceA * sourceB */
+    out1 = inA1 * inB1;
+
+    /* read sample from sourceA */
+    inA3 = *(pSrcA + 2);
+    /* read sample from sourceB */
+    inB3 = *(pSrcB + 2);
+
+    /* out = sourceA * sourceB */
+    out2 = inA2 * inB2;
+
+    /* read sample from sourceA */
+    inA4 = *(pSrcA + 3);
+
+    /* store result to destination buffer */
+    *pDst = out1;
+
+    /* read sample from sourceB */
+    inB4 = *(pSrcB + 3);
+
+    /* out = sourceA * sourceB */
+    out3 = inA3 * inB3;
+
+    /* store result to destination buffer */
+    *(pDst + 1) = out2;
+
+    /* out = sourceA * sourceB */
+    out4 = inA4 * inB4;
+    /* store result to destination buffer */
+    *(pDst + 2) = out3;
+    /* store result to destination buffer */
+    *(pDst + 3) = out4;
+
+
+    /* update pointers to process next samples */
+    pSrcA += 4u;
+    pSrcB += 4u;
+    pDst += 4u;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and store the results in output buffer */
+    *pDst++ = (*pSrcA++) * (*pSrcB++);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of BasicMult group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q15.c

@@ -0,0 +1,154 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mult_q15.c    
+*    
+* Description:	Q15 vector multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief           Q15 vector multiplication    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_mult_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inB1, inB2;                  /* temporary input variables */
+  q15_t out1, out2, out3, out4;                  /* temporary output variables */
+  q31_t mul1, mul2, mul3, mul4;                  /* temporary variables */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* read two samples at a time from sourceA */
+    inA1 = *__SIMD32(pSrcA)++;
+    /* read two samples at a time from sourceB */
+    inB1 = *__SIMD32(pSrcB)++;
+    /* read two samples at a time from sourceA */
+    inA2 = *__SIMD32(pSrcA)++;
+    /* read two samples at a time from sourceB */
+    inB2 = *__SIMD32(pSrcB)++;
+
+    /* multiply mul = sourceA * sourceB */
+    mul1 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16));
+    mul2 = (q31_t) ((q15_t) inA1 * (q15_t) inB1);
+    mul3 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB2 >> 16));
+    mul4 = (q31_t) ((q15_t) inA2 * (q15_t) inB2);
+
+    /* saturate result to 16 bit */
+    out1 = (q15_t) __SSAT(mul1 >> 15, 16);
+    out2 = (q15_t) __SSAT(mul2 >> 15, 16);
+    out3 = (q15_t) __SSAT(mul3 >> 15, 16);
+    out4 = (q15_t) __SSAT(mul4 >> 15, 16);
+
+    /* store the result */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    *__SIMD32(pDst)++ = __PKHBT(out2, out1, 16);
+    *__SIMD32(pDst)++ = __PKHBT(out4, out3, 16);
+
+#else
+
+    *__SIMD32(pDst)++ = __PKHBT(out2, out1, 16);
+    *__SIMD32(pDst)++ = __PKHBT(out4, out3, 16);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and store the result in the destination buffer */
+    *pDst++ = (q15_t) __SSAT((((q31_t) (*pSrcA++) * (*pSrcB++)) >> 15), 16);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q31.c

@@ -0,0 +1,160 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mult_q31.c    
+*    
+* Description:	Q31 vector multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicMult    
+ * @{    
+ */
+
+/**    
+ * @brief Q31 vector multiplication.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated.    
+ */
+
+void arm_mult_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inA3, inA4;                  /* temporary input variables */
+  q31_t inB1, inB2, inB3, inB4;                  /* temporary input variables */
+  q31_t out1, out2, out3, out4;                  /* temporary output variables */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and then store the results in the destination buffer. */
+    inA1 = *pSrcA++;
+    inA2 = *pSrcA++;
+    inA3 = *pSrcA++;
+    inA4 = *pSrcA++;
+    inB1 = *pSrcB++;
+    inB2 = *pSrcB++;
+    inB3 = *pSrcB++;
+    inB4 = *pSrcB++;
+
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB2) >> 32;
+    out3 = ((q63_t) inA3 * inB3) >> 32;
+    out4 = ((q63_t) inA4 * inB4) >> 32;
+
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+    out3 = __SSAT(out3, 31);
+    out4 = __SSAT(out4, 31);
+
+    *pDst++ = out1 << 1u;
+    *pDst++ = out2 << 1u;
+    *pDst++ = out3 << 1u;
+    *pDst++ = out4 << 1u;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+  
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and then store the results in the destination buffer. */
+    inA1 = *pSrcA++;
+    inB1 = *pSrcB++;
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out1 = __SSAT(out1, 31);
+    *pDst++ = out1 << 1u;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and then store the results in the destination buffer. */
+    *pDst++ =
+      (q31_t) clip_q63_to_q31(((q63_t) (*pSrcA++) * (*pSrcB++)) >> 31);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+  
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+}
+
+/**    
+ * @} end of BasicMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_mult_q7.c

@@ -0,0 +1,127 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_mult_q7.c    
+*    
+* Description:	Q7 vector multiplication.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicMult    
+ * @{    
+ */
+
+/**    
+ * @brief           Q7 vector multiplication    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated.    
+ */
+
+void arm_mult_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q7_t out1, out2, out3, out4;                   /* Temporary variables to store the product */
+
+  /* loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and store the results in temporary variables */
+    out1 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8);
+    out2 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8);
+    out3 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8);
+    out4 = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8);
+
+    /* Store the results of 4 inputs in the destination buffer in single cycle by packing */
+    *__SIMD32(pDst)++ = __PACKq7(out1, out2, out3, out4);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * B */
+    /* Multiply the inputs and store the result in the destination buffer */
+    *pDst++ = (q7_t) __SSAT((((q15_t) (*pSrcA++) * (*pSrcB++)) >> 7), 8);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of BasicMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_f32.c

@@ -0,0 +1,146 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_negate_f32.c    
+*    
+* Description:	Negates floating-point vectors.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup negate Vector Negate        
+ *        
+ * Negates the elements of a vector.        
+ *        
+ * <pre>        
+ *     pDst[n] = -pSrc[n],   0 <= n < blockSize.        
+ * </pre>        
+ *
+ * The functions support in-place computation allowing the source and
+ * destination pointers to reference the same memory buffer.
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.
+ */
+
+/**        
+ * @addtogroup negate        
+ * @{        
+ */
+
+/**        
+ * @brief  Negates the elements of a floating-point vector.        
+ * @param[in]  *pSrc points to the input vector        
+ * @param[out]  *pDst points to the output vector        
+ * @param[in]  blockSize number of samples in the vector        
+ * @return none.        
+ */
+
+void arm_negate_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;                  /* temporary variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* read inputs from source */
+    in1 = *pSrc;
+    in2 = *(pSrc + 1);
+    in3 = *(pSrc + 2);
+    in4 = *(pSrc + 3);
+
+    /* negate the input */
+    in1 = -in1;
+    in2 = -in2;
+    in3 = -in3;
+    in4 = -in4;
+
+    /* store the result to destination */
+    *pDst = in1;
+    *(pDst + 1) = in2;
+    *(pDst + 2) = in3;
+    *(pDst + 3) = in4;
+
+    /* update pointers to process next samples */
+    pSrc += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Negate and then store the results in the destination buffer. */
+    *pDst++ = -*pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of negate group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q15.c

@@ -0,0 +1,142 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_negate_q15.c    
+*    
+* Description:	Negates Q15 vectors.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @addtogroup negate        
+ * @{        
+ */
+
+/**        
+ * @brief  Negates the elements of a Q15 vector.        
+ * @param[in]  *pSrc points to the input vector        
+ * @param[out]  *pDst points to the output vector        
+ * @param[in]  blockSize number of samples in the vector        
+ * @return none.        
+ *    
+ * \par Conditions for optimum performance    
+ *  Input and output buffers should be aligned by 32-bit    
+ *    
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF.        
+ */
+
+void arm_negate_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q15_t in;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in1, in2;                                /* Temporary variables */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Read two inputs at a time */
+    in1 = _SIMD32_OFFSET(pSrc);
+    in2 = _SIMD32_OFFSET(pSrc + 2);
+
+    /* negate two samples at a time */
+    in1 = __QSUB16(0, in1);
+
+    /* negate two samples at a time */
+    in2 = __QSUB16(0, in2);
+
+    /* store the result to destination 2 samples at a time */
+    _SIMD32_OFFSET(pDst) = in1;
+    /* store the result to destination 2 samples at a time */
+    _SIMD32_OFFSET(pDst + 2) = in2;
+
+
+    /* update pointers to process next samples */
+    pSrc += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Negate and then store the result in the destination buffer. */
+    in = *pSrc++;
+    *pDst++ = (in == (q15_t) 0x8000) ? 0x7fff : -in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of negate group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q31.c

@@ -0,0 +1,129 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_negate_q31.c    
+*    
+* Description:	Negates Q31 vectors.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup negate    
+ * @{    
+ */
+
+/**    
+ * @brief  Negates the elements of a Q31 vector.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF.    
+ */
+
+void arm_negate_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  q31_t in;                                      /* Temporary variable */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Negate and then store the results in the destination buffer. */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    *pDst++ = __QSUB(0, in1);
+    *pDst++ = __QSUB(0, in2);
+    *pDst++ = __QSUB(0, in3);
+    *pDst++ = __QSUB(0, in4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Negate and then store the result in the destination buffer. */
+    in = *pSrc++;
+    *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of negate group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_negate_q7.c

@@ -0,0 +1,125 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_negate_q7.c    
+*    
+* Description:	Negates Q7 vectors.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup negate    
+ * @{    
+ */
+
+/**    
+ * @brief  Negates the elements of a Q7 vector.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q7 value -1 (0x80) will be saturated to the maximum allowable positive value 0x7F.    
+ */
+
+void arm_negate_q7(
+  q7_t * pSrc,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q7_t in;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t input;                                   /* Input values1-4 */
+  q31_t zero = 0x00000000;
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Read four inputs */
+    input = *__SIMD32(pSrc)++;
+
+    /* Store the Negated results in the destination buffer in a single cycle by packing the results */
+    *__SIMD32(pDst)++ = __QSUB8(zero, input);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = -A */
+    /* Negate and then store the results in the destination buffer. */ \
+      in = *pSrc++;
+    *pDst++ = (in == (q7_t) 0x80) ? 0x7f : -in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**    
+ * @} end of negate group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_f32.c

@@ -0,0 +1,165 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_offset_f32.c    
+*    
+* Description:	Floating-point vector offset.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup offset Vector Offset        
+ *        
+ * Adds a constant offset to each element of a vector.        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrc[n] + offset,   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * The functions support in-place computation allowing the source and
+ * destination pointers to reference the same memory buffer.
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.
+ */
+
+/**        
+ * @addtogroup offset        
+ * @{        
+ */
+
+/**        
+ * @brief  Adds a constant offset to a floating-point vector.        
+ * @param[in]  *pSrc points to the input vector        
+ * @param[in]  offset is the offset to be added        
+ * @param[out]  *pDst points to the output vector        
+ * @param[in]  blockSize number of samples in the vector        
+ * @return none.        
+ */
+
+
+void arm_offset_f32(
+  float32_t * pSrc,
+  float32_t offset,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination buffer. */
+    /* read samples from source */
+    in1 = *pSrc;
+    in2 = *(pSrc + 1);
+
+    /* add offset to input */
+    in1 = in1 + offset;
+
+    /* read samples from source */
+    in3 = *(pSrc + 2);
+
+    /* add offset to input */
+    in2 = in2 + offset;
+
+    /* read samples from source */
+    in4 = *(pSrc + 3);
+
+    /* add offset to input */
+    in3 = in3 + offset;
+
+    /* store result to destination */
+    *pDst = in1;
+
+    /* add offset to input */
+    in4 = in4 + offset;
+
+    /* store result to destination */
+    *(pDst + 1) = in2;
+
+    /* store result to destination */
+    *(pDst + 2) = in3;
+
+    /* store result to destination */
+    *(pDst + 3) = in4;
+
+    /* update pointers to process next samples */
+    pSrc += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the result in the destination buffer. */
+    *pDst++ = (*pSrc++) + offset;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of offset group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q15.c

@@ -0,0 +1,136 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_offset_q15.c    
+*    
+* Description:	Q15 vector offset.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup offset    
+ * @{    
+ */
+
+/**    
+ * @brief  Adds a constant offset to a Q15 vector.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[in]  offset is the offset to be added    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] are saturated.    
+ */
+
+void arm_offset_q15(
+  q15_t * pSrc,
+  q15_t offset,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t offset_packed;                           /* Offset packed to 32 bit */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Offset is packed to 32 bit in order to use SIMD32 for addition */
+  offset_packed = __PKHBT(offset, offset, 16);
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination buffer, 2 samples at a time. */
+    *__SIMD32(pDst)++ = __QADD16(*__SIMD32(pSrc)++, offset_packed);
+    *__SIMD32(pDst)++ = __QADD16(*__SIMD32(pSrc)++, offset_packed);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination buffer. */
+    *pDst++ = (q15_t) __QADD16(*pSrc++, offset);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination buffer. */
+    *pDst++ = (q15_t) __SSAT(((q31_t) * pSrc++ + offset), 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of offset group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q31.c

@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_offset_q31.c    
+*    
+* Description:	Q31 vector offset.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup offset    
+ * @{    
+ */
+
+/**    
+ * @brief  Adds a constant offset to a Q31 vector.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[in]  offset is the offset to be added    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] are saturated.    
+ */
+
+void arm_offset_q31(
+  q31_t * pSrc,
+  q31_t offset,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t in1, in2, in3, in4;
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination buffer. */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    *pDst++ = __QADD(in1, offset);
+    *pDst++ = __QADD(in2, offset);
+    *pDst++ = __QADD(in3, offset);
+    *pDst++ = __QADD(in4, offset);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the result in the destination buffer. */
+    *pDst++ = __QADD(*pSrc++, offset);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the result in the destination buffer. */
+    *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrc++ + offset);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of offset group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_offset_q7.c

@@ -0,0 +1,135 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_offset_q7.c    
+*    
+* Description:	Q7 vector offset.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup offset    
+ * @{    
+ */
+
+/**    
+ * @brief  Adds a constant offset to a Q7 vector.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[in]  offset is the offset to be added    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q7 range [0x80 0x7F] are saturated.    
+ */
+
+void arm_offset_q7(
+  q7_t * pSrc,
+  q7_t offset,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t offset_packed;                           /* Offset packed to 32 bit */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Offset is packed to 32 bit in order to use SIMD32 for addition */
+  offset_packed = __PACKq7(offset, offset, offset, offset);
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the results in the destination bufferfor 4 samples at a time. */
+    *__SIMD32(pDst)++ = __QADD8(*__SIMD32(pSrc)++, offset_packed);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the result in the destination buffer. */
+    *pDst++ = (q7_t) __SSAT(*pSrc++ + offset, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A + offset */
+    /* Add offset and then store the result in the destination buffer. */
+    *pDst++ = (q7_t) __SSAT((q15_t) * pSrc++ + offset, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of offset group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_f32.c

@@ -0,0 +1,169 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_scale_f32.c    
+*    
+* Description:	Multiplies a floating-point vector by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup scale Vector Scale        
+ *        
+ * Multiply a vector by a scalar value.  For floating-point data, the algorithm used is:        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrc[n] * scale,   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * In the fixed-point Q7, Q15, and Q31 functions, <code>scale</code> is represented by        
+ * a fractional multiplication <code>scaleFract</code> and an arithmetic shift <code>shift</code>.        
+ * The shift allows the gain of the scaling operation to exceed 1.0.        
+ * The algorithm used with fixed-point data is:        
+ *        
+ * <pre>        
+ *     pDst[n] = (pSrc[n] * scaleFract) << shift,   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * The overall scale factor applied to the fixed-point data is        
+ * <pre>        
+ *     scale = scaleFract * 2^shift.        
+ * </pre>        
+ *
+ * The functions support in-place computation allowing the source and destination
+ * pointers to reference the same memory buffer.
+ */
+
+/**        
+ * @addtogroup scale        
+ * @{        
+ */
+
+/**        
+ * @brief Multiplies a floating-point vector by a scalar.        
+ * @param[in]       *pSrc points to the input vector        
+ * @param[in]       scale scale factor to be applied        
+ * @param[out]      *pDst points to the output vector        
+ * @param[in]       blockSize number of samples in the vector        
+ * @return none.        
+ */
+
+
+void arm_scale_f32(
+  float32_t * pSrc,
+  float32_t scale,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t in1, in2, in3, in4;                  /* temporary variabels */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the results in the destination buffer. */
+    /* read input samples from source */
+    in1 = *pSrc;
+    in2 = *(pSrc + 1);
+
+    /* multiply with scaling factor */
+    in1 = in1 * scale;
+
+    /* read input sample from source */
+    in3 = *(pSrc + 2);
+
+    /* multiply with scaling factor */
+    in2 = in2 * scale;
+
+    /* read input sample from source */
+    in4 = *(pSrc + 3);
+
+    /* multiply with scaling factor */
+    in3 = in3 * scale;
+    in4 = in4 * scale;
+    /* store the result to destination */
+    *pDst = in1;
+    *(pDst + 1) = in2;
+    *(pDst + 2) = in3;
+    *(pDst + 3) = in4;
+
+    /* update pointers to process next samples */
+    pSrc += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the result in the destination buffer. */
+    *pDst++ = (*pSrc++) * scale;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of scale group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q15.c

@@ -0,0 +1,162 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_scale_q15.c    
+*    
+* Description:	Multiplies a Q15 vector by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup scale    
+ * @{    
+ */
+
+/**    
+ * @brief Multiplies a Q15 vector by a scalar.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       scaleFract fractional portion of the scale value    
+ * @param[in]       shift number of bits to shift the result by    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The input data <code>*pSrc</code> and <code>scaleFract</code> are in 1.15 format.    
+ * These are multiplied to yield a 2.30 intermediate result and this is shifted with saturation to 1.15 format.    
+ */
+
+
+void arm_scale_q15(
+  q15_t * pSrc,
+  q15_t scaleFract,
+  int8_t shift,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  int8_t kShift = 15 - shift;                    /* shift to apply after scaling */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q15_t in1, in2, in3, in4;
+  q31_t inA1, inA2;                              /* Temporary variables */
+  q31_t out1, out2, out3, out4;
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Reading 2 inputs from memory */
+    inA1 = *__SIMD32(pSrc)++;
+    inA2 = *__SIMD32(pSrc)++;
+
+    /* C = A * scale */
+    /* Scale the inputs and then store the 2 results in the destination buffer        
+     * in single cycle by packing the outputs */
+    out1 = (q31_t) ((q15_t) (inA1 >> 16) * scaleFract);
+    out2 = (q31_t) ((q15_t) inA1 * scaleFract);
+    out3 = (q31_t) ((q15_t) (inA2 >> 16) * scaleFract);
+    out4 = (q31_t) ((q15_t) inA2 * scaleFract);
+
+    /* apply shifting */
+    out1 = out1 >> kShift;
+    out2 = out2 >> kShift;
+    out3 = out3 >> kShift;
+    out4 = out4 >> kShift;
+
+    /* saturate the output */
+    in1 = (q15_t) (__SSAT(out1, 16));
+    in2 = (q15_t) (__SSAT(out2, 16));
+    in3 = (q15_t) (__SSAT(out3, 16));
+    in4 = (q15_t) (__SSAT(out4, 16));
+
+    /* store the result to destination */
+    *__SIMD32(pDst)++ = __PKHBT(in2, in1, 16);
+    *__SIMD32(pDst)++ = __PKHBT(in4, in3, 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the result in the destination buffer. */
+    *pDst++ = (q15_t) (__SSAT(((*pSrc++) * scaleFract) >> kShift, 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the result in the destination buffer. */
+    *pDst++ = (q15_t) (__SSAT(((q31_t) * pSrc++ * scaleFract) >> kShift, 16));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of scale group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q31.c

@@ -0,0 +1,239 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_scale_q31.c    
+*    
+* Description:	Multiplies a Q31 vector by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**       
+ * @ingroup groupMath       
+ */
+
+/**       
+ * @addtogroup scale       
+ * @{       
+ */
+
+/**       
+ * @brief Multiplies a Q31 vector by a scalar.       
+ * @param[in]       *pSrc points to the input vector       
+ * @param[in]       scaleFract fractional portion of the scale value       
+ * @param[in]       shift number of bits to shift the result by       
+ * @param[out]      *pDst points to the output vector       
+ * @param[in]       blockSize number of samples in the vector       
+ * @return none.       
+ *       
+ * <b>Scaling and Overflow Behavior:</b>       
+ * \par       
+ * The input data <code>*pSrc</code> and <code>scaleFract</code> are in 1.31 format.       
+ * These are multiplied to yield a 2.62 intermediate result and this is shifted with saturation to 1.31 format.       
+ */
+
+void arm_scale_q31(
+  q31_t * pSrc,
+  q31_t scaleFract,
+  int8_t shift,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  int8_t kShift = shift + 1;                     /* Shift to apply after scaling */
+  int8_t sign = (kShift & 0x80);
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in, out;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q31_t in1, in2, in3, in4;                      /* temporary input variables */
+  q31_t out1, out2, out3, out4;                  /* temporary output variabels */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  if(sign == 0u)
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* read four inputs from source */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      in3 = *(pSrc + 2);
+      in4 = *(pSrc + 3);
+
+      /* multiply input with scaler value */
+      in1 = ((q63_t) in1 * scaleFract) >> 32;
+      in2 = ((q63_t) in2 * scaleFract) >> 32;
+      in3 = ((q63_t) in3 * scaleFract) >> 32;
+      in4 = ((q63_t) in4 * scaleFract) >> 32;
+
+      /* apply shifting */
+      out1 = in1 << kShift;
+      out2 = in2 << kShift;
+
+      /* saturate the results. */
+      if(in1 != (out1 >> kShift))
+        out1 = 0x7FFFFFFF ^ (in1 >> 31);
+
+      if(in2 != (out2 >> kShift))
+        out2 = 0x7FFFFFFF ^ (in2 >> 31);
+
+      out3 = in3 << kShift;
+      out4 = in4 << kShift;
+
+      *pDst = out1;
+      *(pDst + 1) = out2;
+
+      if(in3 != (out3 >> kShift))
+        out3 = 0x7FFFFFFF ^ (in3 >> 31);
+
+      if(in4 != (out4 >> kShift))
+        out4 = 0x7FFFFFFF ^ (in4 >> 31);
+
+      /* Store result destination */
+      *(pDst + 2) = out3;
+      *(pDst + 3) = out4;
+
+      /* Update pointers to process next sampels */
+      pSrc += 4u;
+      pDst += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+  }
+  else
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* read four inputs from source */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      in3 = *(pSrc + 2);
+      in4 = *(pSrc + 3);
+
+      /* multiply input with scaler value */
+      in1 = ((q63_t) in1 * scaleFract) >> 32;
+      in2 = ((q63_t) in2 * scaleFract) >> 32;
+      in3 = ((q63_t) in3 * scaleFract) >> 32;
+      in4 = ((q63_t) in4 * scaleFract) >> 32;
+
+      /* apply shifting */
+      out1 = in1 >> -kShift;
+      out2 = in2 >> -kShift;
+
+      out3 = in3 >> -kShift;
+      out4 = in4 >> -kShift;
+
+      /* Store result destination */
+      *pDst = out1;
+      *(pDst + 1) = out2;
+
+      *(pDst + 2) = out3;
+      *(pDst + 3) = out4;
+
+      /* Update pointers to process next sampels */
+      pSrc += 4u;
+      pDst += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.       
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  if(sign == 0)
+  {
+	  while(blkCnt > 0u)
+	  {
+		/* C = A * scale */
+		/* Scale the input and then store the result in the destination buffer. */
+		in = *pSrc++;
+		in = ((q63_t) in * scaleFract) >> 32;
+
+		out = in << kShift;
+		
+		if(in != (out >> kShift))
+			out = 0x7FFFFFFF ^ (in >> 31);
+
+		*pDst++ = out;
+
+		/* Decrement the loop counter */
+		blkCnt--;
+	  }
+  }
+  else
+  {
+	  while(blkCnt > 0u)
+	  {
+		/* C = A * scale */
+		/* Scale the input and then store the result in the destination buffer. */
+		in = *pSrc++;
+		in = ((q63_t) in * scaleFract) >> 32;
+
+		out = in >> -kShift;
+
+		*pDst++ = out;
+
+		/* Decrement the loop counter */
+		blkCnt--;
+	  }
+  
+  }
+}
+
+/**       
+ * @} end of scale group       
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_scale_q7.c

@@ -0,0 +1,149 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_scale_q7.c    
+*    
+* Description:	Multiplies a Q7 vector by a scalar.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup scale    
+ * @{    
+ */
+
+/**    
+ * @brief Multiplies a Q7 vector by a scalar.    
+ * @param[in]       *pSrc points to the input vector    
+ * @param[in]       scaleFract fractional portion of the scale value    
+ * @param[in]       shift number of bits to shift the result by    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The input data <code>*pSrc</code> and <code>scaleFract</code> are in 1.7 format.    
+ * These are multiplied to yield a 2.14 intermediate result and this is shifted with saturation to 1.7 format.    
+ */
+
+void arm_scale_q7(
+  q7_t * pSrc,
+  q7_t scaleFract,
+  int8_t shift,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  int8_t kShift = 7 - shift;                     /* shift to apply after scaling */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q7_t in1, in2, in3, in4, out1, out2, out3, out4;      /* Temporary variables to store input & output */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* Reading 4 inputs from memory */
+    in1 = *pSrc++;
+    in2 = *pSrc++;
+    in3 = *pSrc++;
+    in4 = *pSrc++;
+
+    /* C = A * scale */
+    /* Scale the inputs and then store the results in the temporary variables. */
+    out1 = (q7_t) (__SSAT(((in1) * scaleFract) >> kShift, 8));
+    out2 = (q7_t) (__SSAT(((in2) * scaleFract) >> kShift, 8));
+    out3 = (q7_t) (__SSAT(((in3) * scaleFract) >> kShift, 8));
+    out4 = (q7_t) (__SSAT(((in4) * scaleFract) >> kShift, 8));
+
+    /* Packing the individual outputs into 32bit and storing in    
+     * destination buffer in single write */
+    *__SIMD32(pDst)++ = __PACKq7(out1, out2, out3, out4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the result in the destination buffer. */
+    *pDst++ = (q7_t) (__SSAT(((*pSrc++) * scaleFract) >> kShift, 8));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A * scale */
+    /* Scale the input and then store the result in the destination buffer. */
+    *pDst++ = (q7_t) (__SSAT((((q15_t) * pSrc++ * scaleFract) >> kShift), 8));
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of scale group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q15.c

@@ -0,0 +1,248 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_shift_q15.c    
+*    
+* Description:	Shifts the elements of a Q15 vector by a specified number of bits.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup shift    
+ * @{    
+ */
+
+/**    
+ * @brief  Shifts the elements of a Q15 vector a specified number of bits.    
+ * @param[in]  *pSrc points to the input vector    
+ * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.    
+ * @param[out]  *pDst points to the output vector    
+ * @param[in]  blockSize number of samples in the vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_shift_q15(
+  q15_t * pSrc,
+  int8_t shiftBits,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  uint8_t sign;                                  /* Sign of shiftBits */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  q15_t in1, in2;                                /* Temporary variables */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Getting the sign of shiftBits */
+  sign = (shiftBits & 0x80);
+
+  /* If the shift value is positive then do right shift else left shift */
+  if(sign == 0u)
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* Read 2 inputs */
+      in1 = *pSrc++;
+      in2 = *pSrc++;
+      /* C = A << shiftBits */
+      /* Shift the inputs and then store the results in the destination buffer. */
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pDst)++ = __PKHBT(__SSAT((in1 << shiftBits), 16),
+                                  __SSAT((in2 << shiftBits), 16), 16);
+
+#else
+
+      *__SIMD32(pDst)++ = __PKHBT(__SSAT((in2 << shiftBits), 16),
+                                  __SSAT((in1 << shiftBits), 16), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      in1 = *pSrc++;
+      in2 = *pSrc++;
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pDst)++ = __PKHBT(__SSAT((in1 << shiftBits), 16),
+                                  __SSAT((in2 << shiftBits), 16), 16);
+
+#else
+
+      *__SIMD32(pDst)++ = __PKHBT(__SSAT((in2 << shiftBits), 16),
+                                  __SSAT((in1 << shiftBits), 16), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A << shiftBits */
+      /* Shift and then store the results in the destination buffer. */
+      *pDst++ = __SSAT((*pSrc++ << shiftBits), 16);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* Read 2 inputs */
+      in1 = *pSrc++;
+      in2 = *pSrc++;
+
+      /* C = A >> shiftBits */
+      /* Shift the inputs and then store the results in the destination buffer. */
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pDst)++ = __PKHBT((in1 >> -shiftBits),
+                                  (in2 >> -shiftBits), 16);
+
+#else
+
+      *__SIMD32(pDst)++ = __PKHBT((in2 >> -shiftBits),
+                                  (in1 >> -shiftBits), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      in1 = *pSrc++;
+      in2 = *pSrc++;
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+      *__SIMD32(pDst)++ = __PKHBT((in1 >> -shiftBits),
+                                  (in2 >> -shiftBits), 16);
+
+#else
+
+      *__SIMD32(pDst)++ = __PKHBT((in2 >> -shiftBits),
+                                  (in1 >> -shiftBits), 16);
+
+#endif /* #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A >> shiftBits */
+      /* Shift the inputs and then store the results in the destination buffer. */
+      *pDst++ = (*pSrc++ >> -shiftBits);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Getting the sign of shiftBits */
+  sign = (shiftBits & 0x80);
+
+  /* If the shift value is positive then do right shift else left shift */
+  if(sign == 0u)
+  {
+    /* Initialize blkCnt with number of samples */
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A << shiftBits */
+      /* Shift and then store the results in the destination buffer. */
+      *pDst++ = __SSAT(((q31_t) * pSrc++ << shiftBits), 16);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* Initialize blkCnt with number of samples */
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A >> shiftBits */
+      /* Shift the inputs and then store the results in the destination buffer. */
+      *pDst++ = (*pSrc++ >> -shiftBits);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of shift group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q31.c

@@ -0,0 +1,203 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_shift_q31.c    
+*    
+* Description:	Shifts the elements of a Q31 vector by a specified number of bits.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+/**        
+ * @defgroup shift Vector Shift        
+ *        
+ * Shifts the elements of a fixed-point vector by a specified number of bits.        
+ * There are separate functions for Q7, Q15, and Q31 data types.        
+ * The underlying algorithm used is:        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrc[n] << shift,   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * If <code>shift</code> is positive then the elements of the vector are shifted to the left.        
+ * If <code>shift</code> is negative then the elements of the vector are shifted to the right.        
+ *
+ * The functions support in-place computation allowing the source and destination
+ * pointers to reference the same memory buffer.
+ */
+
+/**        
+ * @addtogroup shift        
+ * @{        
+ */
+
+/**        
+ * @brief  Shifts the elements of a Q31 vector a specified number of bits.        
+ * @param[in]  *pSrc points to the input vector        
+ * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.        
+ * @param[out]  *pDst points to the output vector        
+ * @param[in]  blockSize number of samples in the vector        
+ * @return none.        
+ *        
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated.        
+ */
+
+void arm_shift_q31(
+  q31_t * pSrc,
+  int8_t shiftBits,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  uint8_t sign = (shiftBits & 0x80);             /* Sign of shiftBits */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  q31_t in1, in2, in3, in4;                      /* Temporary input variables */
+  q31_t out1, out2, out3, out4;                  /* Temporary output variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+
+  if(sign == 0u)
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C = A  << shiftBits */
+      /* Shift the input and then store the results in the destination buffer. */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      out1 = in1 << shiftBits;
+      in3 = *(pSrc + 2);
+      out2 = in2 << shiftBits;
+      in4 = *(pSrc + 3);
+      if(in1 != (out1 >> shiftBits))
+        out1 = 0x7FFFFFFF ^ (in1 >> 31);
+
+      if(in2 != (out2 >> shiftBits))
+        out2 = 0x7FFFFFFF ^ (in2 >> 31);
+
+      *pDst = out1;
+      out3 = in3 << shiftBits;
+      *(pDst + 1) = out2;
+      out4 = in4 << shiftBits;
+
+      if(in3 != (out3 >> shiftBits))
+        out3 = 0x7FFFFFFF ^ (in3 >> 31);
+
+      if(in4 != (out4 >> shiftBits))
+        out4 = 0x7FFFFFFF ^ (in4 >> 31);
+
+      *(pDst + 2) = out3;
+      *(pDst + 3) = out4;
+
+      /* Update destination pointer to process next sampels */
+      pSrc += 4u;
+      pDst += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C = A >>  shiftBits */
+      /* Shift the input and then store the results in the destination buffer. */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      in3 = *(pSrc + 2);
+      in4 = *(pSrc + 3);
+
+      *pDst = (in1 >> -shiftBits);
+      *(pDst + 1) = (in2 >> -shiftBits);
+      *(pDst + 2) = (in3 >> -shiftBits);
+      *(pDst + 3) = (in4 >> -shiftBits);
+
+
+      pSrc += 4u;
+      pDst += 4u;
+
+      blkCnt--;
+    }
+
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+  while(blkCnt > 0u)
+  {
+    /* C = A (>> or <<) shiftBits */
+    /* Shift the input and then store the result in the destination buffer. */
+    *pDst++ = (sign == 0u) ? clip_q63_to_q31((q63_t) * pSrc++ << shiftBits) :
+      (*pSrc++ >> -shiftBits);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+
+}
+
+/**        
+ * @} end of shift group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_shift_q7.c

@@ -0,0 +1,220 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_shift_q7.c    
+*    
+* Description:	Processing function for the Q7 Shifting    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @addtogroup shift        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Shifts the elements of a Q7 vector a specified number of bits.        
+ * @param[in]  *pSrc points to the input vector        
+ * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.        
+ * @param[out]  *pDst points to the output vector        
+ * @param[in]  blockSize number of samples in the vector        
+ * @return none.        
+ *    
+ * \par Conditions for optimum performance    
+ *  Input and output buffers should be aligned by 32-bit    
+ *    
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * Results outside of the allowable Q7 range [0x8 0x7F] will be saturated.        
+ */
+
+void arm_shift_q7(
+  q7_t * pSrc,
+  int8_t shiftBits,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  uint8_t sign;                                  /* Sign of shiftBits */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q7_t in1;                                      /* Input value1 */
+  q7_t in2;                                      /* Input value2 */
+  q7_t in3;                                      /* Input value3 */
+  q7_t in4;                                      /* Input value4 */
+
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* Getting the sign of shiftBits */
+  sign = (shiftBits & 0x80);
+
+  /* If the shift value is positive then do right shift else left shift */
+  if(sign == 0u)
+  {
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C = A << shiftBits */
+      /* Read 4 inputs */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      in3 = *(pSrc + 2);
+      in4 = *(pSrc + 3);
+
+      /* Store the Shifted result in the destination buffer in single cycle by packing the outputs */
+      *__SIMD32(pDst)++ = __PACKq7(__SSAT((in1 << shiftBits), 8),
+                                   __SSAT((in2 << shiftBits), 8),
+                                   __SSAT((in3 << shiftBits), 8),
+                                   __SSAT((in4 << shiftBits), 8));
+      /* Update source pointer to process next sampels */
+      pSrc += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+     ** No loop unrolling is used. */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A << shiftBits */
+      /* Shift the input and then store the result in the destination buffer. */
+      *pDst++ = (q7_t) __SSAT((*pSrc++ << shiftBits), 8);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    shiftBits = -shiftBits;
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(blkCnt > 0u)
+    {
+      /* C = A >> shiftBits */
+      /* Read 4 inputs */
+      in1 = *pSrc;
+      in2 = *(pSrc + 1);
+      in3 = *(pSrc + 2);
+      in4 = *(pSrc + 3);
+
+      /* Store the Shifted result in the destination buffer in single cycle by packing the outputs */
+      *__SIMD32(pDst)++ = __PACKq7((in1 >> shiftBits), (in2 >> shiftBits),
+                                   (in3 >> shiftBits), (in4 >> shiftBits));
+
+
+      pSrc += 4u;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+     ** No loop unrolling is used. */
+    blkCnt = blockSize % 0x4u;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A >> shiftBits */
+      /* Shift the input and then store the result in the destination buffer. */
+      in1 = *pSrc++;
+      *pDst++ = (in1 >> shiftBits);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Getting the sign of shiftBits */
+  sign = (shiftBits & 0x80);
+
+  /* If the shift value is positive then do right shift else left shift */
+  if(sign == 0u)
+  {
+    /* Initialize blkCnt with number of samples */
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A << shiftBits */
+      /* Shift the input and then store the result in the destination buffer. */
+      *pDst++ = (q7_t) __SSAT(((q15_t) * pSrc++ << shiftBits), 8);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+  else
+  {
+    /* Initialize blkCnt with number of samples */
+    blkCnt = blockSize;
+
+    while(blkCnt > 0u)
+    {
+      /* C = A >> shiftBits */
+      /* Shift the input and then store the result in the destination buffer. */
+      *pDst++ = (*pSrc++ >> -shiftBits);
+
+      /* Decrement the loop counter */
+      blkCnt--;
+    }
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+}
+
+/**        
+ * @} end of shift group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_f32.c

@@ -0,0 +1,150 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sub_f32.c    
+*    
+* Description:	Floating-point vector subtraction.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupMath        
+ */
+
+/**        
+ * @defgroup BasicSub Vector Subtraction        
+ *        
+ * Element-by-element subtraction of two vectors.        
+ *        
+ * <pre>        
+ *     pDst[n] = pSrcA[n] - pSrcB[n],   0 <= n < blockSize.        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q7, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup BasicSub        
+ * @{        
+ */
+
+
+/**        
+ * @brief Floating-point vector subtraction.        
+ * @param[in]       *pSrcA points to the first input vector        
+ * @param[in]       *pSrcB points to the second input vector        
+ * @param[out]      *pDst points to the output vector        
+ * @param[in]       blockSize number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_sub_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inA1, inA2, inA3, inA4;              /* temporary variables */
+  float32_t inB1, inB2, inB3, inB4;              /* temporary variables */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the results in the destination buffer. */
+    /* Read 4 input samples from sourceA and sourceB */
+    inA1 = *pSrcA;
+    inB1 = *pSrcB;
+    inA2 = *(pSrcA + 1);
+    inB2 = *(pSrcB + 1);
+    inA3 = *(pSrcA + 2);
+    inB3 = *(pSrcB + 2);
+    inA4 = *(pSrcA + 3);
+    inB4 = *(pSrcB + 3);
+
+    /* dst = srcA - srcB */
+    /* subtract and store the result */
+    *pDst = inA1 - inB1;
+    *(pDst + 1) = inA2 - inB2;
+    *(pDst + 2) = inA3 - inB3;
+    *(pDst + 3) = inA4 - inB4;
+
+
+    /* Update pointers to process next sampels */
+    pSrcA += 4u;
+    pSrcB += 4u;
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the results in the destination buffer. */
+    *pDst++ = (*pSrcA++) - (*pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of BasicSub group        
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q15.c

@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sub_q15.c    
+*    
+* Description:	Q15 vector subtraction.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicSub    
+ * @{    
+ */
+
+/**    
+ * @brief Q15 vector subtraction.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_sub_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2;
+  q31_t inB1, inB2;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the results in the destination buffer two samples at a time. */
+    inA1 = *__SIMD32(pSrcA)++;
+    inA2 = *__SIMD32(pSrcA)++;
+    inB1 = *__SIMD32(pSrcB)++;
+    inB2 = *__SIMD32(pSrcB)++;
+
+    *__SIMD32(pDst)++ = __QSUB16(inA1, inB1);
+    *__SIMD32(pDst)++ = __QSUB16(inA2, inB2);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = (q15_t) __QSUB16(*pSrcA++, *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = (q15_t) __SSAT(((q31_t) * pSrcA++ - *pSrcB++), 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+}
+
+/**    
+ * @} end of BasicSub group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q31.c

@@ -0,0 +1,146 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sub_q31.c    
+*    
+* Description:	Q31 vector subtraction.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicSub    
+ * @{    
+ */
+
+/**    
+ * @brief Q31 vector subtraction.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range [0x80000000 0x7FFFFFFF] will be saturated.    
+ */
+
+void arm_sub_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inA1, inA2, inA3, inA4;
+  q31_t inB1, inB2, inB3, inB4;
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the results in the destination buffer. */
+    inA1 = *pSrcA++;
+    inA2 = *pSrcA++;
+    inB1 = *pSrcB++;
+    inB2 = *pSrcB++;
+
+    inA3 = *pSrcA++;
+    inA4 = *pSrcA++;
+    inB3 = *pSrcB++;
+    inB4 = *pSrcB++;
+
+    *pDst++ = __QSUB(inA1, inB1);
+    *pDst++ = __QSUB(inA2, inB2);
+    *pDst++ = __QSUB(inA3, inB3);
+    *pDst++ = __QSUB(inA4, inB4);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = __QSUB(*pSrcA++, *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = (q31_t) clip_q63_to_q31((q63_t) * pSrcA++ - *pSrcB++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of BasicSub group    
+ */

Libraries/CMSIS/DSP_Lib/Source/BasicMathFunctions/arm_sub_q7.c

@@ -0,0 +1,131 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_sub_q7.c    
+*    
+* Description:	Q7 vector subtraction.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupMath    
+ */
+
+/**    
+ * @addtogroup BasicSub    
+ * @{    
+ */
+
+/**    
+ * @brief Q7 vector subtraction.    
+ * @param[in]       *pSrcA points to the first input vector    
+ * @param[in]       *pSrcB points to the second input vector    
+ * @param[out]      *pDst points to the output vector    
+ * @param[in]       blockSize number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q7 range [0x80 0x7F] will be saturated.    
+ */
+
+void arm_sub_q7(
+  q7_t * pSrcA,
+  q7_t * pSrcB,
+  q7_t * pDst,
+  uint32_t blockSize)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+/* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /*loop Unrolling */
+  blkCnt = blockSize >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the results in the destination buffer 4 samples at a time. */
+    *__SIMD32(pDst)++ = __QSUB8(*__SIMD32(pSrcA)++, *__SIMD32(pSrcB)++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = blockSize % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = __SSAT(*pSrcA++ - *pSrcB++, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initialize blkCnt with number of samples */
+  blkCnt = blockSize;
+
+  while(blkCnt > 0u)
+  {
+    /* C = A - B */
+    /* Subtract and then store the result in the destination buffer. */
+    *pDst++ = (q7_t) __SSAT((q15_t) * pSrcA++ - *pSrcB++, 8);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+
+}
+
+/**    
+ * @} end of BasicSub group    
+ */

Libraries/CMSIS/DSP_Lib/Source/CommonTables/arm_common_tables.c

@@ -0,0 +1,27251 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        31. July 2014 
+* $Revision: 	V1.4.4  
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_common_tables.c    
+*    
+* Description:	This file has common tables like fft twiddle factors, Bitreverse, reciprocal etc which are used across different functions    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**    
+ * @ingroup groupTransforms    
+ */
+
+/**    
+ * @addtogroup CFFT_CIFFT Complex FFT Tables  
+ * @{    
+ */
+
+/**    
+* \par    
+* Pseudo code for Generation of Bit reversal Table is    
+* \par    
+* <pre>for(l=1;l <= N/4;l++)    
+* {    
+*   for(i=0;i<logN2;i++)    
+*   {     
+*     a[i]=l&(1<<i);    
+*   }    
+*   for(j=0; j<logN2; j++)    
+*   {    
+*     if (a[j]!=0)    
+*     y[l]+=(1<<((logN2-1)-j));    
+*   }    
+*   y[l] = y[l] >> 1;    
+*  } </pre>    
+* \par    
+* where N = 4096	logN2 = 12   
+* \par    
+* N is the maximum FFT Size supported    
+*/
+
+/*    
+* @brief  Table for bit reversal process    
+*/
+const uint16_t armBitRevTable[1024] = {
+   0x400, 0x200, 0x600, 0x100, 0x500, 0x300, 0x700, 0x80, 0x480, 0x280, 
+   0x680, 0x180, 0x580, 0x380, 0x780, 0x40, 0x440, 0x240, 0x640, 0x140, 
+   0x540, 0x340, 0x740, 0xc0, 0x4c0, 0x2c0, 0x6c0, 0x1c0, 0x5c0, 0x3c0, 
+   0x7c0, 0x20, 0x420, 0x220, 0x620, 0x120, 0x520, 0x320, 0x720, 0xa0, 
+   0x4a0, 0x2a0, 0x6a0, 0x1a0, 0x5a0, 0x3a0, 0x7a0, 0x60, 0x460, 0x260, 
+   0x660, 0x160, 0x560, 0x360, 0x760, 0xe0, 0x4e0, 0x2e0, 0x6e0, 0x1e0, 
+   0x5e0, 0x3e0, 0x7e0, 0x10, 0x410, 0x210, 0x610, 0x110, 0x510, 0x310, 
+   0x710, 0x90, 0x490, 0x290, 0x690, 0x190, 0x590, 0x390, 0x790, 0x50, 
+   0x450, 0x250, 0x650, 0x150, 0x550, 0x350, 0x750, 0xd0, 0x4d0, 0x2d0, 
+   0x6d0, 0x1d0, 0x5d0, 0x3d0, 0x7d0, 0x30, 0x430, 0x230, 0x630, 0x130, 
+   0x530, 0x330, 0x730, 0xb0, 0x4b0, 0x2b0, 0x6b0, 0x1b0, 0x5b0, 0x3b0, 
+   0x7b0, 0x70, 0x470, 0x270, 0x670, 0x170, 0x570, 0x370, 0x770, 0xf0, 
+   0x4f0, 0x2f0, 0x6f0, 0x1f0, 0x5f0, 0x3f0, 0x7f0, 0x8, 0x408, 0x208, 
+   0x608, 0x108, 0x508, 0x308, 0x708, 0x88, 0x488, 0x288, 0x688, 0x188, 
+   0x588, 0x388, 0x788, 0x48, 0x448, 0x248, 0x648, 0x148, 0x548, 0x348, 
+   0x748, 0xc8, 0x4c8, 0x2c8, 0x6c8, 0x1c8, 0x5c8, 0x3c8, 0x7c8, 0x28, 
+   0x428, 0x228, 0x628, 0x128, 0x528, 0x328, 0x728, 0xa8, 0x4a8, 0x2a8, 
+   0x6a8, 0x1a8, 0x5a8, 0x3a8, 0x7a8, 0x68, 0x468, 0x268, 0x668, 0x168, 
+   0x568, 0x368, 0x768, 0xe8, 0x4e8, 0x2e8, 0x6e8, 0x1e8, 0x5e8, 0x3e8, 
+   0x7e8, 0x18, 0x418, 0x218, 0x618, 0x118, 0x518, 0x318, 0x718, 0x98, 
+   0x498, 0x298, 0x698, 0x198, 0x598, 0x398, 0x798, 0x58, 0x458, 0x258, 
+   0x658, 0x158, 0x558, 0x358, 0x758, 0xd8, 0x4d8, 0x2d8, 0x6d8, 0x1d8, 
+   0x5d8, 0x3d8, 0x7d8, 0x38, 0x438, 0x238, 0x638, 0x138, 0x538, 0x338, 
+   0x738, 0xb8, 0x4b8, 0x2b8, 0x6b8, 0x1b8, 0x5b8, 0x3b8, 0x7b8, 0x78, 
+   0x478, 0x278, 0x678, 0x178, 0x578, 0x378, 0x778, 0xf8, 0x4f8, 0x2f8, 
+   0x6f8, 0x1f8, 0x5f8, 0x3f8, 0x7f8, 0x4, 0x404, 0x204, 0x604, 0x104, 
+   0x504, 0x304, 0x704, 0x84, 0x484, 0x284, 0x684, 0x184, 0x584, 0x384, 
+   0x784, 0x44, 0x444, 0x244, 0x644, 0x144, 0x544, 0x344, 0x744, 0xc4, 
+   0x4c4, 0x2c4, 0x6c4, 0x1c4, 0x5c4, 0x3c4, 0x7c4, 0x24, 0x424, 0x224, 
+   0x624, 0x124, 0x524, 0x324, 0x724, 0xa4, 0x4a4, 0x2a4, 0x6a4, 0x1a4, 
+   0x5a4, 0x3a4, 0x7a4, 0x64, 0x464, 0x264, 0x664, 0x164, 0x564, 0x364, 
+   0x764, 0xe4, 0x4e4, 0x2e4, 0x6e4, 0x1e4, 0x5e4, 0x3e4, 0x7e4, 0x14, 
+   0x414, 0x214, 0x614, 0x114, 0x514, 0x314, 0x714, 0x94, 0x494, 0x294, 
+   0x694, 0x194, 0x594, 0x394, 0x794, 0x54, 0x454, 0x254, 0x654, 0x154, 
+   0x554, 0x354, 0x754, 0xd4, 0x4d4, 0x2d4, 0x6d4, 0x1d4, 0x5d4, 0x3d4, 
+   0x7d4, 0x34, 0x434, 0x234, 0x634, 0x134, 0x534, 0x334, 0x734, 0xb4, 
+   0x4b4, 0x2b4, 0x6b4, 0x1b4, 0x5b4, 0x3b4, 0x7b4, 0x74, 0x474, 0x274, 
+   0x674, 0x174, 0x574, 0x374, 0x774, 0xf4, 0x4f4, 0x2f4, 0x6f4, 0x1f4, 
+   0x5f4, 0x3f4, 0x7f4, 0xc, 0x40c, 0x20c, 0x60c, 0x10c, 0x50c, 0x30c, 
+   0x70c, 0x8c, 0x48c, 0x28c, 0x68c, 0x18c, 0x58c, 0x38c, 0x78c, 0x4c, 
+   0x44c, 0x24c, 0x64c, 0x14c, 0x54c, 0x34c, 0x74c, 0xcc, 0x4cc, 0x2cc, 
+   0x6cc, 0x1cc, 0x5cc, 0x3cc, 0x7cc, 0x2c, 0x42c, 0x22c, 0x62c, 0x12c, 
+   0x52c, 0x32c, 0x72c, 0xac, 0x4ac, 0x2ac, 0x6ac, 0x1ac, 0x5ac, 0x3ac, 
+   0x7ac, 0x6c, 0x46c, 0x26c, 0x66c, 0x16c, 0x56c, 0x36c, 0x76c, 0xec, 
+   0x4ec, 0x2ec, 0x6ec, 0x1ec, 0x5ec, 0x3ec, 0x7ec, 0x1c, 0x41c, 0x21c, 
+   0x61c, 0x11c, 0x51c, 0x31c, 0x71c, 0x9c, 0x49c, 0x29c, 0x69c, 0x19c, 
+   0x59c, 0x39c, 0x79c, 0x5c, 0x45c, 0x25c, 0x65c, 0x15c, 0x55c, 0x35c, 
+   0x75c, 0xdc, 0x4dc, 0x2dc, 0x6dc, 0x1dc, 0x5dc, 0x3dc, 0x7dc, 0x3c, 
+   0x43c, 0x23c, 0x63c, 0x13c, 0x53c, 0x33c, 0x73c, 0xbc, 0x4bc, 0x2bc, 
+   0x6bc, 0x1bc, 0x5bc, 0x3bc, 0x7bc, 0x7c, 0x47c, 0x27c, 0x67c, 0x17c, 
+   0x57c, 0x37c, 0x77c, 0xfc, 0x4fc, 0x2fc, 0x6fc, 0x1fc, 0x5fc, 0x3fc, 
+   0x7fc, 0x2, 0x402, 0x202, 0x602, 0x102, 0x502, 0x302, 0x702, 0x82, 
+   0x482, 0x282, 0x682, 0x182, 0x582, 0x382, 0x782, 0x42, 0x442, 0x242, 
+   0x642, 0x142, 0x542, 0x342, 0x742, 0xc2, 0x4c2, 0x2c2, 0x6c2, 0x1c2, 
+   0x5c2, 0x3c2, 0x7c2, 0x22, 0x422, 0x222, 0x622, 0x122, 0x522, 0x322, 
+   0x722, 0xa2, 0x4a2, 0x2a2, 0x6a2, 0x1a2, 0x5a2, 0x3a2, 0x7a2, 0x62, 
+   0x462, 0x262, 0x662, 0x162, 0x562, 0x362, 0x762, 0xe2, 0x4e2, 0x2e2, 
+   0x6e2, 0x1e2, 0x5e2, 0x3e2, 0x7e2, 0x12, 0x412, 0x212, 0x612, 0x112, 
+   0x512, 0x312, 0x712, 0x92, 0x492, 0x292, 0x692, 0x192, 0x592, 0x392, 
+   0x792, 0x52, 0x452, 0x252, 0x652, 0x152, 0x552, 0x352, 0x752, 0xd2, 
+   0x4d2, 0x2d2, 0x6d2, 0x1d2, 0x5d2, 0x3d2, 0x7d2, 0x32, 0x432, 0x232, 
+   0x632, 0x132, 0x532, 0x332, 0x732, 0xb2, 0x4b2, 0x2b2, 0x6b2, 0x1b2, 
+   0x5b2, 0x3b2, 0x7b2, 0x72, 0x472, 0x272, 0x672, 0x172, 0x572, 0x372, 
+   0x772, 0xf2, 0x4f2, 0x2f2, 0x6f2, 0x1f2, 0x5f2, 0x3f2, 0x7f2, 0xa, 
+   0x40a, 0x20a, 0x60a, 0x10a, 0x50a, 0x30a, 0x70a, 0x8a, 0x48a, 0x28a, 
+   0x68a, 0x18a, 0x58a, 0x38a, 0x78a, 0x4a, 0x44a, 0x24a, 0x64a, 0x14a, 
+   0x54a, 0x34a, 0x74a, 0xca, 0x4ca, 0x2ca, 0x6ca, 0x1ca, 0x5ca, 0x3ca, 
+   0x7ca, 0x2a, 0x42a, 0x22a, 0x62a, 0x12a, 0x52a, 0x32a, 0x72a, 0xaa, 
+   0x4aa, 0x2aa, 0x6aa, 0x1aa, 0x5aa, 0x3aa, 0x7aa, 0x6a, 0x46a, 0x26a, 
+   0x66a, 0x16a, 0x56a, 0x36a, 0x76a, 0xea, 0x4ea, 0x2ea, 0x6ea, 0x1ea, 
+   0x5ea, 0x3ea, 0x7ea, 0x1a, 0x41a, 0x21a, 0x61a, 0x11a, 0x51a, 0x31a, 
+   0x71a, 0x9a, 0x49a, 0x29a, 0x69a, 0x19a, 0x59a, 0x39a, 0x79a, 0x5a, 
+   0x45a, 0x25a, 0x65a, 0x15a, 0x55a, 0x35a, 0x75a, 0xda, 0x4da, 0x2da, 
+   0x6da, 0x1da, 0x5da, 0x3da, 0x7da, 0x3a, 0x43a, 0x23a, 0x63a, 0x13a, 
+   0x53a, 0x33a, 0x73a, 0xba, 0x4ba, 0x2ba, 0x6ba, 0x1ba, 0x5ba, 0x3ba, 
+   0x7ba, 0x7a, 0x47a, 0x27a, 0x67a, 0x17a, 0x57a, 0x37a, 0x77a, 0xfa, 
+   0x4fa, 0x2fa, 0x6fa, 0x1fa, 0x5fa, 0x3fa, 0x7fa, 0x6, 0x406, 0x206, 
+   0x606, 0x106, 0x506, 0x306, 0x706, 0x86, 0x486, 0x286, 0x686, 0x186, 
+   0x586, 0x386, 0x786, 0x46, 0x446, 0x246, 0x646, 0x146, 0x546, 0x346, 
+   0x746, 0xc6, 0x4c6, 0x2c6, 0x6c6, 0x1c6, 0x5c6, 0x3c6, 0x7c6, 0x26, 
+   0x426, 0x226, 0x626, 0x126, 0x526, 0x326, 0x726, 0xa6, 0x4a6, 0x2a6, 
+   0x6a6, 0x1a6, 0x5a6, 0x3a6, 0x7a6, 0x66, 0x466, 0x266, 0x666, 0x166, 
+   0x566, 0x366, 0x766, 0xe6, 0x4e6, 0x2e6, 0x6e6, 0x1e6, 0x5e6, 0x3e6, 
+   0x7e6, 0x16, 0x416, 0x216, 0x616, 0x116, 0x516, 0x316, 0x716, 0x96, 
+   0x496, 0x296, 0x696, 0x196, 0x596, 0x396, 0x796, 0x56, 0x456, 0x256, 
+   0x656, 0x156, 0x556, 0x356, 0x756, 0xd6, 0x4d6, 0x2d6, 0x6d6, 0x1d6, 
+   0x5d6, 0x3d6, 0x7d6, 0x36, 0x436, 0x236, 0x636, 0x136, 0x536, 0x336, 
+   0x736, 0xb6, 0x4b6, 0x2b6, 0x6b6, 0x1b6, 0x5b6, 0x3b6, 0x7b6, 0x76, 
+   0x476, 0x276, 0x676, 0x176, 0x576, 0x376, 0x776, 0xf6, 0x4f6, 0x2f6, 
+   0x6f6, 0x1f6, 0x5f6, 0x3f6, 0x7f6, 0xe, 0x40e, 0x20e, 0x60e, 0x10e, 
+   0x50e, 0x30e, 0x70e, 0x8e, 0x48e, 0x28e, 0x68e, 0x18e, 0x58e, 0x38e, 
+   0x78e, 0x4e, 0x44e, 0x24e, 0x64e, 0x14e, 0x54e, 0x34e, 0x74e, 0xce, 
+   0x4ce, 0x2ce, 0x6ce, 0x1ce, 0x5ce, 0x3ce, 0x7ce, 0x2e, 0x42e, 0x22e, 
+   0x62e, 0x12e, 0x52e, 0x32e, 0x72e, 0xae, 0x4ae, 0x2ae, 0x6ae, 0x1ae, 
+   0x5ae, 0x3ae, 0x7ae, 0x6e, 0x46e, 0x26e, 0x66e, 0x16e, 0x56e, 0x36e, 
+   0x76e, 0xee, 0x4ee, 0x2ee, 0x6ee, 0x1ee, 0x5ee, 0x3ee, 0x7ee, 0x1e, 
+   0x41e, 0x21e, 0x61e, 0x11e, 0x51e, 0x31e, 0x71e, 0x9e, 0x49e, 0x29e, 
+   0x69e, 0x19e, 0x59e, 0x39e, 0x79e, 0x5e, 0x45e, 0x25e, 0x65e, 0x15e, 
+   0x55e, 0x35e, 0x75e, 0xde, 0x4de, 0x2de, 0x6de, 0x1de, 0x5de, 0x3de, 
+   0x7de, 0x3e, 0x43e, 0x23e, 0x63e, 0x13e, 0x53e, 0x33e, 0x73e, 0xbe, 
+   0x4be, 0x2be, 0x6be, 0x1be, 0x5be, 0x3be, 0x7be, 0x7e, 0x47e, 0x27e, 
+   0x67e, 0x17e, 0x57e, 0x37e, 0x77e, 0xfe, 0x4fe, 0x2fe, 0x6fe, 0x1fe, 
+   0x5fe, 0x3fe, 0x7fe, 0x1 
+};
+
+
+/*    
+* @brief  Floating-point Twiddle factors Table Generation    
+*/
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 16	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_16[32] = {
+    1.000000000f,  0.000000000f,
+    0.923879533f,  0.382683432f,
+    0.707106781f,  0.707106781f,
+    0.382683432f,  0.923879533f,
+    0.000000000f,  1.000000000f,
+   -0.382683432f,  0.923879533f,
+   -0.707106781f,  0.707106781f,
+   -0.923879533f,  0.382683432f,
+   -1.000000000f,  0.000000000f,
+   -0.923879533f, -0.382683432f,
+   -0.707106781f, -0.707106781f,
+   -0.382683432f, -0.923879533f,
+   -0.000000000f, -1.000000000f,
+    0.382683432f, -0.923879533f,
+    0.707106781f, -0.707106781f,
+    0.923879533f, -0.382683432f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 32	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_32[64] = {
+    1.000000000f,  0.000000000f,
+    0.980785280f,  0.195090322f,
+    0.923879533f,  0.382683432f,
+    0.831469612f,  0.555570233f,
+    0.707106781f,  0.707106781f,
+    0.555570233f,  0.831469612f,
+    0.382683432f,  0.923879533f,
+    0.195090322f,  0.980785280f,
+    0.000000000f,  1.000000000f,
+   -0.195090322f,  0.980785280f,
+   -0.382683432f,  0.923879533f,
+   -0.555570233f,  0.831469612f,
+   -0.707106781f,  0.707106781f,
+   -0.831469612f,  0.555570233f,
+   -0.923879533f,  0.382683432f,
+   -0.980785280f,  0.195090322f,
+   -1.000000000f,  0.000000000f,
+   -0.980785280f, -0.195090322f,
+   -0.923879533f, -0.382683432f,
+   -0.831469612f, -0.555570233f,
+   -0.707106781f, -0.707106781f,
+   -0.555570233f, -0.831469612f,
+   -0.382683432f, -0.923879533f,
+   -0.195090322f, -0.980785280f,
+   -0.000000000f, -1.000000000f,
+    0.195090322f, -0.980785280f,
+    0.382683432f, -0.923879533f,
+    0.555570233f, -0.831469612f,
+    0.707106781f, -0.707106781f,
+    0.831469612f, -0.555570233f,
+    0.923879533f, -0.382683432f,
+    0.980785280f, -0.195090322f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 64	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_64[128] = {
+    1.000000000f,  0.000000000f,
+    0.995184727f,  0.098017140f,
+    0.980785280f,  0.195090322f,
+    0.956940336f,  0.290284677f,
+    0.923879533f,  0.382683432f,
+    0.881921264f,  0.471396737f,
+    0.831469612f,  0.555570233f,
+    0.773010453f,  0.634393284f,
+    0.707106781f,  0.707106781f,
+    0.634393284f,  0.773010453f,
+    0.555570233f,  0.831469612f,
+    0.471396737f,  0.881921264f,
+    0.382683432f,  0.923879533f,
+    0.290284677f,  0.956940336f,
+    0.195090322f,  0.980785280f,
+    0.098017140f,  0.995184727f,
+    0.000000000f,  1.000000000f,
+   -0.098017140f,  0.995184727f,
+   -0.195090322f,  0.980785280f,
+   -0.290284677f,  0.956940336f,
+   -0.382683432f,  0.923879533f,
+   -0.471396737f,  0.881921264f,
+   -0.555570233f,  0.831469612f,
+   -0.634393284f,  0.773010453f,
+   -0.707106781f,  0.707106781f,
+   -0.773010453f,  0.634393284f,
+   -0.831469612f,  0.555570233f,
+   -0.881921264f,  0.471396737f,
+   -0.923879533f,  0.382683432f,
+   -0.956940336f,  0.290284677f,
+   -0.980785280f,  0.195090322f,
+   -0.995184727f,  0.098017140f,
+   -1.000000000f,  0.000000000f,
+   -0.995184727f, -0.098017140f,
+   -0.980785280f, -0.195090322f,
+   -0.956940336f, -0.290284677f,
+   -0.923879533f, -0.382683432f,
+   -0.881921264f, -0.471396737f,
+   -0.831469612f, -0.555570233f,
+   -0.773010453f, -0.634393284f,
+   -0.707106781f, -0.707106781f,
+   -0.634393284f, -0.773010453f,
+   -0.555570233f, -0.831469612f,
+   -0.471396737f, -0.881921264f,
+   -0.382683432f, -0.923879533f,
+   -0.290284677f, -0.956940336f,
+   -0.195090322f, -0.980785280f,
+   -0.098017140f, -0.995184727f,
+   -0.000000000f, -1.000000000f,
+    0.098017140f, -0.995184727f,
+    0.195090322f, -0.980785280f,
+    0.290284677f, -0.956940336f,
+    0.382683432f, -0.923879533f,
+    0.471396737f, -0.881921264f,
+    0.555570233f, -0.831469612f,
+    0.634393284f, -0.773010453f,
+    0.707106781f, -0.707106781f,
+    0.773010453f, -0.634393284f,
+    0.831469612f, -0.555570233f,
+    0.881921264f, -0.471396737f,
+    0.923879533f, -0.382683432f,
+    0.956940336f, -0.290284677f,
+    0.980785280f, -0.195090322f,
+    0.995184727f, -0.098017140f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 128	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+
+const float32_t twiddleCoef_128[256] = {
+    1.000000000f	,	0.000000000f	,
+    0.998795456f	,	0.049067674f	,
+    0.995184727f	,	0.098017140f	,
+    0.989176510f	,	0.146730474f	,
+    0.980785280f	,	0.195090322f	,
+    0.970031253f	,	0.242980180f	,
+    0.956940336f	,	0.290284677f	,
+    0.941544065f	,	0.336889853f	,
+    0.923879533f	,	0.382683432f	,
+    0.903989293f	,	0.427555093f	,
+    0.881921264f	,	0.471396737f	,
+    0.857728610f	,	0.514102744f	,
+    0.831469612f	,	0.555570233f	,
+    0.803207531f	,	0.595699304f	,
+    0.773010453f	,	0.634393284f	,
+    0.740951125f	,	0.671558955f	,
+    0.707106781f	,	0.707106781f	,
+    0.671558955f	,	0.740951125f	,
+    0.634393284f	,	0.773010453f	,
+    0.595699304f	,	0.803207531f	,
+    0.555570233f	,	0.831469612f	,
+    0.514102744f	,	0.857728610f	,
+    0.471396737f	,	0.881921264f	,
+    0.427555093f	,	0.903989293f	,
+    0.382683432f	,	0.923879533f	,
+    0.336889853f	,	0.941544065f	,
+    0.290284677f	,	0.956940336f	,
+    0.242980180f	,	0.970031253f	,
+    0.195090322f	,	0.980785280f	,
+    0.146730474f	,	0.989176510f	,
+    0.098017140f	,	0.995184727f	,
+    0.049067674f	,	0.998795456f	,
+    0.000000000f	,	1.000000000f	,
+    -0.049067674f	,	0.998795456f	,
+    -0.098017140f	,	0.995184727f	,
+    -0.146730474f	,	0.989176510f	,
+    -0.195090322f	,	0.980785280f	,
+    -0.242980180f	,	0.970031253f	,
+    -0.290284677f	,	0.956940336f	,
+    -0.336889853f	,	0.941544065f	,
+    -0.382683432f	,	0.923879533f	,
+    -0.427555093f	,	0.903989293f	,
+    -0.471396737f	,	0.881921264f	,
+    -0.514102744f	,	0.857728610f	,
+    -0.555570233f	,	0.831469612f	,
+    -0.595699304f	,	0.803207531f	,
+    -0.634393284f	,	0.773010453f	,
+    -0.671558955f	,	0.740951125f	,
+    -0.707106781f	,	0.707106781f	,
+    -0.740951125f	,	0.671558955f	,
+    -0.773010453f	,	0.634393284f	,
+    -0.803207531f	,	0.595699304f	,
+    -0.831469612f	,	0.555570233f	,
+    -0.857728610f	,	0.514102744f	,
+    -0.881921264f	,	0.471396737f	,
+    -0.903989293f	,	0.427555093f	,
+    -0.923879533f	,	0.382683432f	,
+    -0.941544065f	,	0.336889853f	,
+    -0.956940336f	,	0.290284677f	,
+    -0.970031253f	,	0.242980180f	,
+    -0.980785280f	,	0.195090322f	,
+    -0.989176510f	,	0.146730474f	,
+    -0.995184727f	,	0.098017140f	,
+    -0.998795456f	,	0.049067674f	,
+    -1.000000000f	,	0.000000000f	,
+    -0.998795456f	,	-0.049067674f	,
+    -0.995184727f	,	-0.098017140f	,
+    -0.989176510f	,	-0.146730474f	,
+    -0.980785280f	,	-0.195090322f	,
+    -0.970031253f	,	-0.242980180f	,
+    -0.956940336f	,	-0.290284677f	,
+    -0.941544065f	,	-0.336889853f	,
+    -0.923879533f	,	-0.382683432f	,
+    -0.903989293f	,	-0.427555093f	,
+    -0.881921264f	,	-0.471396737f	,
+    -0.857728610f	,	-0.514102744f	,
+    -0.831469612f	,	-0.555570233f	,
+    -0.803207531f	,	-0.595699304f	,
+    -0.773010453f	,	-0.634393284f	,
+    -0.740951125f	,	-0.671558955f	,
+    -0.707106781f	,	-0.707106781f	,
+    -0.671558955f	,	-0.740951125f	,
+    -0.634393284f	,	-0.773010453f	,
+    -0.595699304f	,	-0.803207531f	,
+    -0.555570233f	,	-0.831469612f	,
+    -0.514102744f	,	-0.857728610f	,
+    -0.471396737f	,	-0.881921264f	,
+    -0.427555093f	,	-0.903989293f	,
+    -0.382683432f	,	-0.923879533f	,
+    -0.336889853f	,	-0.941544065f	,
+    -0.290284677f	,	-0.956940336f	,
+    -0.242980180f	,	-0.970031253f	,
+    -0.195090322f	,	-0.980785280f	,
+    -0.146730474f	,	-0.989176510f	,
+    -0.098017140f	,	-0.995184727f	,
+    -0.049067674f	,	-0.998795456f	,
+    -0.000000000f	,	-1.000000000f	,
+    0.049067674f	,	-0.998795456f	,
+    0.098017140f	,	-0.995184727f	,
+    0.146730474f	,	-0.989176510f	,
+    0.195090322f	,	-0.980785280f	,
+    0.242980180f	,	-0.970031253f	,
+    0.290284677f	,	-0.956940336f	,
+    0.336889853f	,	-0.941544065f	,
+    0.382683432f	,	-0.923879533f	,
+    0.427555093f	,	-0.903989293f	,
+    0.471396737f	,	-0.881921264f	,
+    0.514102744f	,	-0.857728610f	,
+    0.555570233f	,	-0.831469612f	,
+    0.595699304f	,	-0.803207531f	,
+    0.634393284f	,	-0.773010453f	,
+    0.671558955f	,	-0.740951125f	,
+    0.707106781f	,	-0.707106781f	,
+    0.740951125f	,	-0.671558955f	,
+    0.773010453f	,	-0.634393284f	,
+    0.803207531f	,	-0.595699304f	,
+    0.831469612f	,	-0.555570233f	,
+    0.857728610f	,	-0.514102744f	,
+    0.881921264f	,	-0.471396737f	,
+    0.903989293f	,	-0.427555093f	,
+    0.923879533f	,	-0.382683432f	,
+    0.941544065f	,	-0.336889853f	,
+    0.956940336f	,	-0.290284677f	,
+    0.970031253f	,	-0.242980180f	,
+    0.980785280f	,	-0.195090322f	,
+    0.989176510f	,	-0.146730474f	,
+    0.995184727f	,	-0.098017140f	,
+    0.998795456f	,	-0.049067674f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 256	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_256[512] = {
+    1.000000000f,  0.000000000f,
+    0.999698819f,  0.024541229f,
+    0.998795456f,  0.049067674f,
+    0.997290457f,  0.073564564f,
+    0.995184727f,  0.098017140f,
+    0.992479535f,  0.122410675f,
+    0.989176510f,  0.146730474f,
+    0.985277642f,  0.170961889f,
+    0.980785280f,  0.195090322f,
+    0.975702130f,  0.219101240f,
+    0.970031253f,  0.242980180f,
+    0.963776066f,  0.266712757f,
+    0.956940336f,  0.290284677f,
+    0.949528181f,  0.313681740f,
+    0.941544065f,  0.336889853f,
+    0.932992799f,  0.359895037f,
+    0.923879533f,  0.382683432f,
+    0.914209756f,  0.405241314f,
+    0.903989293f,  0.427555093f,
+    0.893224301f,  0.449611330f,
+    0.881921264f,  0.471396737f,
+    0.870086991f,  0.492898192f,
+    0.857728610f,  0.514102744f,
+    0.844853565f,  0.534997620f,
+    0.831469612f,  0.555570233f,
+    0.817584813f,  0.575808191f,
+    0.803207531f,  0.595699304f,
+    0.788346428f,  0.615231591f,
+    0.773010453f,  0.634393284f,
+    0.757208847f,  0.653172843f,
+    0.740951125f,  0.671558955f,
+    0.724247083f,  0.689540545f,
+    0.707106781f,  0.707106781f,
+    0.689540545f,  0.724247083f,
+    0.671558955f,  0.740951125f,
+    0.653172843f,  0.757208847f,
+    0.634393284f,  0.773010453f,
+    0.615231591f,  0.788346428f,
+    0.595699304f,  0.803207531f,
+    0.575808191f,  0.817584813f,
+    0.555570233f,  0.831469612f,
+    0.534997620f,  0.844853565f,
+    0.514102744f,  0.857728610f,
+    0.492898192f,  0.870086991f,
+    0.471396737f,  0.881921264f,
+    0.449611330f,  0.893224301f,
+    0.427555093f,  0.903989293f,
+    0.405241314f,  0.914209756f,
+    0.382683432f,  0.923879533f,
+    0.359895037f,  0.932992799f,
+    0.336889853f,  0.941544065f,
+    0.313681740f,  0.949528181f,
+    0.290284677f,  0.956940336f,
+    0.266712757f,  0.963776066f,
+    0.242980180f,  0.970031253f,
+    0.219101240f,  0.975702130f,
+    0.195090322f,  0.980785280f,
+    0.170961889f,  0.985277642f,
+    0.146730474f,  0.989176510f,
+    0.122410675f,  0.992479535f,
+    0.098017140f,  0.995184727f,
+    0.073564564f,  0.997290457f,
+    0.049067674f,  0.998795456f,
+    0.024541229f,  0.999698819f,
+    0.000000000f,  1.000000000f,
+   -0.024541229f,  0.999698819f,
+   -0.049067674f,  0.998795456f,
+   -0.073564564f,  0.997290457f,
+   -0.098017140f,  0.995184727f,
+   -0.122410675f,  0.992479535f,
+   -0.146730474f,  0.989176510f,
+   -0.170961889f,  0.985277642f,
+   -0.195090322f,  0.980785280f,
+   -0.219101240f,  0.975702130f,
+   -0.242980180f,  0.970031253f,
+   -0.266712757f,  0.963776066f,
+   -0.290284677f,  0.956940336f,
+   -0.313681740f,  0.949528181f,
+   -0.336889853f,  0.941544065f,
+   -0.359895037f,  0.932992799f,
+   -0.382683432f,  0.923879533f,
+   -0.405241314f,  0.914209756f,
+   -0.427555093f,  0.903989293f,
+   -0.449611330f,  0.893224301f,
+   -0.471396737f,  0.881921264f,
+   -0.492898192f,  0.870086991f,
+   -0.514102744f,  0.857728610f,
+   -0.534997620f,  0.844853565f,
+   -0.555570233f,  0.831469612f,
+   -0.575808191f,  0.817584813f,
+   -0.595699304f,  0.803207531f,
+   -0.615231591f,  0.788346428f,
+   -0.634393284f,  0.773010453f,
+   -0.653172843f,  0.757208847f,
+   -0.671558955f,  0.740951125f,
+   -0.689540545f,  0.724247083f,
+   -0.707106781f,  0.707106781f,
+   -0.724247083f,  0.689540545f,
+   -0.740951125f,  0.671558955f,
+   -0.757208847f,  0.653172843f,
+   -0.773010453f,  0.634393284f,
+   -0.788346428f,  0.615231591f,
+   -0.803207531f,  0.595699304f,
+   -0.817584813f,  0.575808191f,
+   -0.831469612f,  0.555570233f,
+   -0.844853565f,  0.534997620f,
+   -0.857728610f,  0.514102744f,
+   -0.870086991f,  0.492898192f,
+   -0.881921264f,  0.471396737f,
+   -0.893224301f,  0.449611330f,
+   -0.903989293f,  0.427555093f,
+   -0.914209756f,  0.405241314f,
+   -0.923879533f,  0.382683432f,
+   -0.932992799f,  0.359895037f,
+   -0.941544065f,  0.336889853f,
+   -0.949528181f,  0.313681740f,
+   -0.956940336f,  0.290284677f,
+   -0.963776066f,  0.266712757f,
+   -0.970031253f,  0.242980180f,
+   -0.975702130f,  0.219101240f,
+   -0.980785280f,  0.195090322f,
+   -0.985277642f,  0.170961889f,
+   -0.989176510f,  0.146730474f,
+   -0.992479535f,  0.122410675f,
+   -0.995184727f,  0.098017140f,
+   -0.997290457f,  0.073564564f,
+   -0.998795456f,  0.049067674f,
+   -0.999698819f,  0.024541229f,
+   -1.000000000f,  0.000000000f,
+   -0.999698819f, -0.024541229f,
+   -0.998795456f, -0.049067674f,
+   -0.997290457f, -0.073564564f,
+   -0.995184727f, -0.098017140f,
+   -0.992479535f, -0.122410675f,
+   -0.989176510f, -0.146730474f,
+   -0.985277642f, -0.170961889f,
+   -0.980785280f, -0.195090322f,
+   -0.975702130f, -0.219101240f,
+   -0.970031253f, -0.242980180f,
+   -0.963776066f, -0.266712757f,
+   -0.956940336f, -0.290284677f,
+   -0.949528181f, -0.313681740f,
+   -0.941544065f, -0.336889853f,
+   -0.932992799f, -0.359895037f,
+   -0.923879533f, -0.382683432f,
+   -0.914209756f, -0.405241314f,
+   -0.903989293f, -0.427555093f,
+   -0.893224301f, -0.449611330f,
+   -0.881921264f, -0.471396737f,
+   -0.870086991f, -0.492898192f,
+   -0.857728610f, -0.514102744f,
+   -0.844853565f, -0.534997620f,
+   -0.831469612f, -0.555570233f,
+   -0.817584813f, -0.575808191f,
+   -0.803207531f, -0.595699304f,
+   -0.788346428f, -0.615231591f,
+   -0.773010453f, -0.634393284f,
+   -0.757208847f, -0.653172843f,
+   -0.740951125f, -0.671558955f,
+   -0.724247083f, -0.689540545f,
+   -0.707106781f, -0.707106781f,
+   -0.689540545f, -0.724247083f,
+   -0.671558955f, -0.740951125f,
+   -0.653172843f, -0.757208847f,
+   -0.634393284f, -0.773010453f,
+   -0.615231591f, -0.788346428f,
+   -0.595699304f, -0.803207531f,
+   -0.575808191f, -0.817584813f,
+   -0.555570233f, -0.831469612f,
+   -0.534997620f, -0.844853565f,
+   -0.514102744f, -0.857728610f,
+   -0.492898192f, -0.870086991f,
+   -0.471396737f, -0.881921264f,
+   -0.449611330f, -0.893224301f,
+   -0.427555093f, -0.903989293f,
+   -0.405241314f, -0.914209756f,
+   -0.382683432f, -0.923879533f,
+   -0.359895037f, -0.932992799f,
+   -0.336889853f, -0.941544065f,
+   -0.313681740f, -0.949528181f,
+   -0.290284677f, -0.956940336f,
+   -0.266712757f, -0.963776066f,
+   -0.242980180f, -0.970031253f,
+   -0.219101240f, -0.975702130f,
+   -0.195090322f, -0.980785280f,
+   -0.170961889f, -0.985277642f,
+   -0.146730474f, -0.989176510f,
+   -0.122410675f, -0.992479535f,
+   -0.098017140f, -0.995184727f,
+   -0.073564564f, -0.997290457f,
+   -0.049067674f, -0.998795456f,
+   -0.024541229f, -0.999698819f,
+   -0.000000000f, -1.000000000f,
+    0.024541229f, -0.999698819f,
+    0.049067674f, -0.998795456f,
+    0.073564564f, -0.997290457f,
+    0.098017140f, -0.995184727f,
+    0.122410675f, -0.992479535f,
+    0.146730474f, -0.989176510f,
+    0.170961889f, -0.985277642f,
+    0.195090322f, -0.980785280f,
+    0.219101240f, -0.975702130f,
+    0.242980180f, -0.970031253f,
+    0.266712757f, -0.963776066f,
+    0.290284677f, -0.956940336f,
+    0.313681740f, -0.949528181f,
+    0.336889853f, -0.941544065f,
+    0.359895037f, -0.932992799f,
+    0.382683432f, -0.923879533f,
+    0.405241314f, -0.914209756f,
+    0.427555093f, -0.903989293f,
+    0.449611330f, -0.893224301f,
+    0.471396737f, -0.881921264f,
+    0.492898192f, -0.870086991f,
+    0.514102744f, -0.857728610f,
+    0.534997620f, -0.844853565f,
+    0.555570233f, -0.831469612f,
+    0.575808191f, -0.817584813f,
+    0.595699304f, -0.803207531f,
+    0.615231591f, -0.788346428f,
+    0.634393284f, -0.773010453f,
+    0.653172843f, -0.757208847f,
+    0.671558955f, -0.740951125f,
+    0.689540545f, -0.724247083f,
+    0.707106781f, -0.707106781f,
+    0.724247083f, -0.689540545f,
+    0.740951125f, -0.671558955f,
+    0.757208847f, -0.653172843f,
+    0.773010453f, -0.634393284f,
+    0.788346428f, -0.615231591f,
+    0.803207531f, -0.595699304f,
+    0.817584813f, -0.575808191f,
+    0.831469612f, -0.555570233f,
+    0.844853565f, -0.534997620f,
+    0.857728610f, -0.514102744f,
+    0.870086991f, -0.492898192f,
+    0.881921264f, -0.471396737f,
+    0.893224301f, -0.449611330f,
+    0.903989293f, -0.427555093f,
+    0.914209756f, -0.405241314f,
+    0.923879533f, -0.382683432f,
+    0.932992799f, -0.359895037f,
+    0.941544065f, -0.336889853f,
+    0.949528181f, -0.313681740f,
+    0.956940336f, -0.290284677f,
+    0.963776066f, -0.266712757f,
+    0.970031253f, -0.242980180f,
+    0.975702130f, -0.219101240f,
+    0.980785280f, -0.195090322f,
+    0.985277642f, -0.170961889f,
+    0.989176510f, -0.146730474f,
+    0.992479535f, -0.122410675f,
+    0.995184727f, -0.098017140f,
+    0.997290457f, -0.073564564f,
+    0.998795456f, -0.049067674f,
+    0.999698819f, -0.024541229f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 512	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_512[1024] = {
+    1.000000000f,  0.000000000f,
+    0.999924702f,  0.012271538f,
+    0.999698819f,  0.024541229f,
+    0.999322385f,  0.036807223f,
+    0.998795456f,  0.049067674f,
+    0.998118113f,  0.061320736f,
+    0.997290457f,  0.073564564f,
+    0.996312612f,  0.085797312f,
+    0.995184727f,  0.098017140f,
+    0.993906970f,  0.110222207f,
+    0.992479535f,  0.122410675f,
+    0.990902635f,  0.134580709f,
+    0.989176510f,  0.146730474f,
+    0.987301418f,  0.158858143f,
+    0.985277642f,  0.170961889f,
+    0.983105487f,  0.183039888f,
+    0.980785280f,  0.195090322f,
+    0.978317371f,  0.207111376f,
+    0.975702130f,  0.219101240f,
+    0.972939952f,  0.231058108f,
+    0.970031253f,  0.242980180f,
+    0.966976471f,  0.254865660f,
+    0.963776066f,  0.266712757f,
+    0.960430519f,  0.278519689f,
+    0.956940336f,  0.290284677f,
+    0.953306040f,  0.302005949f,
+    0.949528181f,  0.313681740f,
+    0.945607325f,  0.325310292f,
+    0.941544065f,  0.336889853f,
+    0.937339012f,  0.348418680f,
+    0.932992799f,  0.359895037f,
+    0.928506080f,  0.371317194f,
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+    0.336889853f, -0.941544065f,
+    0.348418680f, -0.937339012f,
+    0.359895037f, -0.932992799f,
+    0.371317194f, -0.928506080f,
+    0.382683432f, -0.923879533f,
+    0.393992040f, -0.919113852f,
+    0.405241314f, -0.914209756f,
+    0.416429560f, -0.909167983f,
+    0.427555093f, -0.903989293f,
+    0.438616239f, -0.898674466f,
+    0.449611330f, -0.893224301f,
+    0.460538711f, -0.887639620f,
+    0.471396737f, -0.881921264f,
+    0.482183772f, -0.876070094f,
+    0.492898192f, -0.870086991f,
+    0.503538384f, -0.863972856f,
+    0.514102744f, -0.857728610f,
+    0.524589683f, -0.851355193f,
+    0.534997620f, -0.844853565f,
+    0.545324988f, -0.838224706f,
+    0.555570233f, -0.831469612f,
+    0.565731811f, -0.824589303f,
+    0.575808191f, -0.817584813f,
+    0.585797857f, -0.810457198f,
+    0.595699304f, -0.803207531f,
+    0.605511041f, -0.795836905f,
+    0.615231591f, -0.788346428f,
+    0.624859488f, -0.780737229f,
+    0.634393284f, -0.773010453f,
+    0.643831543f, -0.765167266f,
+    0.653172843f, -0.757208847f,
+    0.662415778f, -0.749136395f,
+    0.671558955f, -0.740951125f,
+    0.680600998f, -0.732654272f,
+    0.689540545f, -0.724247083f,
+    0.698376249f, -0.715730825f,
+    0.707106781f, -0.707106781f,
+    0.715730825f, -0.698376249f,
+    0.724247083f, -0.689540545f,
+    0.732654272f, -0.680600998f,
+    0.740951125f, -0.671558955f,
+    0.749136395f, -0.662415778f,
+    0.757208847f, -0.653172843f,
+    0.765167266f, -0.643831543f,
+    0.773010453f, -0.634393284f,
+    0.780737229f, -0.624859488f,
+    0.788346428f, -0.615231591f,
+    0.795836905f, -0.605511041f,
+    0.803207531f, -0.595699304f,
+    0.810457198f, -0.585797857f,
+    0.817584813f, -0.575808191f,
+    0.824589303f, -0.565731811f,
+    0.831469612f, -0.555570233f,
+    0.838224706f, -0.545324988f,
+    0.844853565f, -0.534997620f,
+    0.851355193f, -0.524589683f,
+    0.857728610f, -0.514102744f,
+    0.863972856f, -0.503538384f,
+    0.870086991f, -0.492898192f,
+    0.876070094f, -0.482183772f,
+    0.881921264f, -0.471396737f,
+    0.887639620f, -0.460538711f,
+    0.893224301f, -0.449611330f,
+    0.898674466f, -0.438616239f,
+    0.903989293f, -0.427555093f,
+    0.909167983f, -0.416429560f,
+    0.914209756f, -0.405241314f,
+    0.919113852f, -0.393992040f,
+    0.923879533f, -0.382683432f,
+    0.928506080f, -0.371317194f,
+    0.932992799f, -0.359895037f,
+    0.937339012f, -0.348418680f,
+    0.941544065f, -0.336889853f,
+    0.945607325f, -0.325310292f,
+    0.949528181f, -0.313681740f,
+    0.953306040f, -0.302005949f,
+    0.956940336f, -0.290284677f,
+    0.960430519f, -0.278519689f,
+    0.963776066f, -0.266712757f,
+    0.966976471f, -0.254865660f,
+    0.970031253f, -0.242980180f,
+    0.972939952f, -0.231058108f,
+    0.975702130f, -0.219101240f,
+    0.978317371f, -0.207111376f,
+    0.980785280f, -0.195090322f,
+    0.983105487f, -0.183039888f,
+    0.985277642f, -0.170961889f,
+    0.987301418f, -0.158858143f,
+    0.989176510f, -0.146730474f,
+    0.990902635f, -0.134580709f,
+    0.992479535f, -0.122410675f,
+    0.993906970f, -0.110222207f,
+    0.995184727f, -0.098017140f,
+    0.996312612f, -0.085797312f,
+    0.997290457f, -0.073564564f,
+    0.998118113f, -0.061320736f,
+    0.998795456f, -0.049067674f,
+    0.999322385f, -0.036807223f,
+    0.999698819f, -0.024541229f,
+    0.999924702f, -0.012271538f
+};
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 1024	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_1024[2048] = {
+1.000000000f	,	0.000000000f	,
+0.999981175f	,	0.006135885f	,
+0.999924702f	,	0.012271538f	,
+0.999830582f	,	0.018406730f	,
+0.999698819f	,	0.024541229f	,
+0.999529418f	,	0.030674803f	,
+0.999322385f	,	0.036807223f	,
+0.999077728f	,	0.042938257f	,
+0.998795456f	,	0.049067674f	,
+0.998475581f	,	0.055195244f	,
+0.998118113f	,	0.061320736f	,
+0.997723067f	,	0.067443920f	,
+0.997290457f	,	0.073564564f	,
+0.996820299f	,	0.079682438f	,
+0.996312612f	,	0.085797312f	,
+0.995767414f	,	0.091908956f	,
+0.995184727f	,	0.098017140f	,
+0.994564571f	,	0.104121634f	,
+0.993906970f	,	0.110222207f	,
+0.993211949f	,	0.116318631f	,
+0.992479535f	,	0.122410675f	,
+0.991709754f	,	0.128498111f	,
+0.990902635f	,	0.134580709f	,
+0.990058210f	,	0.140658239f	,
+0.989176510f	,	0.146730474f	,
+0.988257568f	,	0.152797185f	,
+0.987301418f	,	0.158858143f	,
+0.986308097f	,	0.164913120f	,
+0.985277642f	,	0.170961889f	,
+0.984210092f	,	0.177004220f	,
+0.983105487f	,	0.183039888f	,
+0.981963869f	,	0.189068664f	,
+0.980785280f	,	0.195090322f	,
+0.979569766f	,	0.201104635f	,
+0.978317371f	,	0.207111376f	,
+0.977028143f	,	0.213110320f	,
+0.975702130f	,	0.219101240f	,
+0.974339383f	,	0.225083911f	,
+0.972939952f	,	0.231058108f	,
+0.971503891f	,	0.237023606f	,
+0.970031253f	,	0.242980180f	,
+0.968522094f	,	0.248927606f	,
+0.966976471f	,	0.254865660f	,
+0.965394442f	,	0.260794118f	,
+0.963776066f	,	0.266712757f	,
+0.962121404f	,	0.272621355f	,
+0.960430519f	,	0.278519689f	,
+0.958703475f	,	0.284407537f	,
+0.956940336f	,	0.290284677f	,
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+0.947585591f	,	0.319502031f	,
+0.945607325f	,	0.325310292f	,
+0.943593458f	,	0.331106306f	,
+0.941544065f	,	0.336889853f	,
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+0.761202385f	,	0.648514401f	,
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+0.732654272f	,	0.680600998f	,
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+0.720002508f	,	0.693971461f	,
+0.715730825f	,	0.698376249f	,
+0.711432196f	,	0.702754744f	,
+0.707106781f	,	0.707106781f	,
+0.702754744f	,	0.711432196f	,
+0.698376249f	,	0.715730825f	,
+0.693971461f	,	0.720002508f	,
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+0.979569766f	,	-0.201104635f	,
+0.980785280f	,	-0.195090322f	,
+0.981963869f	,	-0.189068664f	,
+0.983105487f	,	-0.183039888f	,
+0.984210092f	,	-0.177004220f	,
+0.985277642f	,	-0.170961889f	,
+0.986308097f	,	-0.164913120f	,
+0.987301418f	,	-0.158858143f	,
+0.988257568f	,	-0.152797185f	,
+0.989176510f	,	-0.146730474f	,
+0.990058210f	,	-0.140658239f	,
+0.990902635f	,	-0.134580709f	,
+0.991709754f	,	-0.128498111f	,
+0.992479535f	,	-0.122410675f	,
+0.993211949f	,	-0.116318631f	,
+0.993906970f	,	-0.110222207f	,
+0.994564571f	,	-0.104121634f	,
+0.995184727f	,	-0.098017140f	,
+0.995767414f	,	-0.091908956f	,
+0.996312612f	,	-0.085797312f	,
+0.996820299f	,	-0.079682438f	,
+0.997290457f	,	-0.073564564f	,
+0.997723067f	,	-0.067443920f	,
+0.998118113f	,	-0.061320736f	,
+0.998475581f	,	-0.055195244f	,
+0.998795456f	,	-0.049067674f	,
+0.999077728f	,	-0.042938257f	,
+0.999322385f	,	-0.036807223f	,
+0.999529418f	,	-0.030674803f	,
+0.999698819f	,	-0.024541229f	,
+0.999830582f	,	-0.018406730f	,
+0.999924702f	,	-0.012271538f	,
+0.999981175f	,	-0.006135885f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 2048	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_2048[4096] = {
+    1.000000000f,  0.000000000f,
+    0.999995294f,  0.003067957f,
+    0.999981175f,  0.006135885f,
+    0.999957645f,  0.009203755f,
+    0.999924702f,  0.012271538f,
+    0.999882347f,  0.015339206f,
+    0.999830582f,  0.018406730f,
+    0.999769405f,  0.021474080f,
+    0.999698819f,  0.024541229f,
+    0.999618822f,  0.027608146f,
+    0.999529418f,  0.030674803f,
+    0.999430605f,  0.033741172f,
+    0.999322385f,  0.036807223f,
+    0.999204759f,  0.039872928f,
+    0.999077728f,  0.042938257f,
+    0.998941293f,  0.046003182f,
+    0.998795456f,  0.049067674f,
+    0.998640218f,  0.052131705f,
+    0.998475581f,  0.055195244f,
+    0.998301545f,  0.058258265f,
+    0.998118113f,  0.061320736f,
+    0.997925286f,  0.064382631f,
+    0.997723067f,  0.067443920f,
+    0.997511456f,  0.070504573f,
+    0.997290457f,  0.073564564f,
+    0.997060070f,  0.076623861f,
+    0.996820299f,  0.079682438f,
+    0.996571146f,  0.082740265f,
+    0.996312612f,  0.085797312f,
+    0.996044701f,  0.088853553f,
+    0.995767414f,  0.091908956f,
+    0.995480755f,  0.094963495f,
+    0.995184727f,  0.098017140f,
+    0.994879331f,  0.101069863f,
+    0.994564571f,  0.104121634f,
+    0.994240449f,  0.107172425f,
+    0.993906970f,  0.110222207f,
+    0.993564136f,  0.113270952f,
+    0.993211949f,  0.116318631f,
+    0.992850414f,  0.119365215f,
+    0.992479535f,  0.122410675f,
+    0.992099313f,  0.125454983f,
+    0.991709754f,  0.128498111f,
+    0.991310860f,  0.131540029f,
+    0.990902635f,  0.134580709f,
+    0.990485084f,  0.137620122f,
+    0.990058210f,  0.140658239f,
+    0.989622017f,  0.143695033f,
+    0.989176510f,  0.146730474f,
+    0.988721692f,  0.149764535f,
+    0.988257568f,  0.152797185f,
+    0.987784142f,  0.155828398f,
+    0.987301418f,  0.158858143f,
+    0.986809402f,  0.161886394f,
+    0.986308097f,  0.164913120f,
+    0.985797509f,  0.167938295f,
+    0.985277642f,  0.170961889f,
+    0.984748502f,  0.173983873f,
+    0.984210092f,  0.177004220f,
+    0.983662419f,  0.180022901f,
+    0.983105487f,  0.183039888f,
+    0.982539302f,  0.186055152f,
+    0.981963869f,  0.189068664f,
+    0.981379193f,  0.192080397f,
+    0.980785280f,  0.195090322f,
+    0.980182136f,  0.198098411f,
+    0.979569766f,  0.201104635f,
+    0.978948175f,  0.204108966f,
+    0.978317371f,  0.207111376f,
+    0.977677358f,  0.210111837f,
+    0.977028143f,  0.213110320f,
+    0.976369731f,  0.216106797f,
+    0.975702130f,  0.219101240f,
+    0.975025345f,  0.222093621f,
+    0.974339383f,  0.225083911f,
+    0.973644250f,  0.228072083f,
+    0.972939952f,  0.231058108f,
+    0.972226497f,  0.234041959f,
+    0.971503891f,  0.237023606f,
+    0.970772141f,  0.240003022f,
+    0.970031253f,  0.242980180f,
+    0.969281235f,  0.245955050f,
+    0.968522094f,  0.248927606f,
+    0.967753837f,  0.251897818f,
+    0.966976471f,  0.254865660f,
+    0.966190003f,  0.257831102f,
+    0.965394442f,  0.260794118f,
+    0.964589793f,  0.263754679f,
+    0.963776066f,  0.266712757f,
+    0.962953267f,  0.269668326f,
+    0.962121404f,  0.272621355f,
+    0.961280486f,  0.275571819f,
+    0.960430519f,  0.278519689f,
+    0.959571513f,  0.281464938f,
+    0.958703475f,  0.284407537f,
+    0.957826413f,  0.287347460f,
+    0.956940336f,  0.290284677f,
+    0.956045251f,  0.293219163f,
+    0.955141168f,  0.296150888f,
+    0.954228095f,  0.299079826f,
+    0.953306040f,  0.302005949f,
+    0.952375013f,  0.304929230f,
+    0.951435021f,  0.307849640f,
+    0.950486074f,  0.310767153f,
+    0.949528181f,  0.313681740f,
+    0.948561350f,  0.316593376f,
+    0.947585591f,  0.319502031f,
+    0.946600913f,  0.322407679f,
+    0.945607325f,  0.325310292f,
+    0.944604837f,  0.328209844f,
+    0.943593458f,  0.331106306f,
+    0.942573198f,  0.333999651f,
+    0.941544065f,  0.336889853f,
+    0.940506071f,  0.339776884f,
+    0.939459224f,  0.342660717f,
+    0.938403534f,  0.345541325f,
+    0.937339012f,  0.348418680f,
+    0.936265667f,  0.351292756f,
+    0.935183510f,  0.354163525f,
+    0.934092550f,  0.357030961f,
+    0.932992799f,  0.359895037f,
+    0.931884266f,  0.362755724f,
+    0.930766961f,  0.365612998f,
+    0.929640896f,  0.368466830f,
+    0.928506080f,  0.371317194f,
+    0.927362526f,  0.374164063f,
+    0.926210242f,  0.377007410f,
+    0.925049241f,  0.379847209f,
+    0.923879533f,  0.382683432f,
+    0.922701128f,  0.385516054f,
+    0.921514039f,  0.388345047f,
+    0.920318277f,  0.391170384f,
+    0.919113852f,  0.393992040f,
+    0.917900776f,  0.396809987f,
+    0.916679060f,  0.399624200f,
+    0.915448716f,  0.402434651f,
+    0.914209756f,  0.405241314f,
+    0.912962190f,  0.408044163f,
+    0.911706032f,  0.410843171f,
+    0.910441292f,  0.413638312f,
+    0.909167983f,  0.416429560f,
+    0.907886116f,  0.419216888f,
+    0.906595705f,  0.422000271f,
+    0.905296759f,  0.424779681f,
+    0.903989293f,  0.427555093f,
+    0.902673318f,  0.430326481f,
+    0.901348847f,  0.433093819f,
+    0.900015892f,  0.435857080f,
+    0.898674466f,  0.438616239f,
+    0.897324581f,  0.441371269f,
+    0.895966250f,  0.444122145f,
+    0.894599486f,  0.446868840f,
+    0.893224301f,  0.449611330f,
+    0.891840709f,  0.452349587f,
+    0.890448723f,  0.455083587f,
+    0.889048356f,  0.457813304f,
+    0.887639620f,  0.460538711f,
+    0.886222530f,  0.463259784f,
+    0.884797098f,  0.465976496f,
+    0.883363339f,  0.468688822f,
+    0.881921264f,  0.471396737f,
+    0.880470889f,  0.474100215f,
+    0.879012226f,  0.476799230f,
+    0.877545290f,  0.479493758f,
+    0.876070094f,  0.482183772f,
+    0.874586652f,  0.484869248f,
+    0.873094978f,  0.487550160f,
+    0.871595087f,  0.490226483f,
+    0.870086991f,  0.492898192f,
+    0.868570706f,  0.495565262f,
+    0.867046246f,  0.498227667f,
+    0.865513624f,  0.500885383f,
+    0.863972856f,  0.503538384f,
+    0.862423956f,  0.506186645f,
+    0.860866939f,  0.508830143f,
+    0.859301818f,  0.511468850f,
+    0.857728610f,  0.514102744f,
+    0.856147328f,  0.516731799f,
+    0.854557988f,  0.519355990f,
+    0.852960605f,  0.521975293f,
+    0.851355193f,  0.524589683f,
+    0.849741768f,  0.527199135f,
+    0.848120345f,  0.529803625f,
+    0.846490939f,  0.532403128f,
+    0.844853565f,  0.534997620f,
+    0.843208240f,  0.537587076f,
+    0.841554977f,  0.540171473f,
+    0.839893794f,  0.542750785f,
+    0.838224706f,  0.545324988f,
+    0.836547727f,  0.547894059f,
+    0.834862875f,  0.550457973f,
+    0.833170165f,  0.553016706f,
+    0.831469612f,  0.555570233f,
+    0.829761234f,  0.558118531f,
+    0.828045045f,  0.560661576f,
+    0.826321063f,  0.563199344f,
+    0.824589303f,  0.565731811f,
+    0.822849781f,  0.568258953f,
+    0.821102515f,  0.570780746f,
+    0.819347520f,  0.573297167f,
+    0.817584813f,  0.575808191f,
+    0.815814411f,  0.578313796f,
+    0.814036330f,  0.580813958f,
+    0.812250587f,  0.583308653f,
+    0.810457198f,  0.585797857f,
+    0.808656182f,  0.588281548f,
+    0.806847554f,  0.590759702f,
+    0.805031331f,  0.593232295f,
+    0.803207531f,  0.595699304f,
+    0.801376172f,  0.598160707f,
+    0.799537269f,  0.600616479f,
+    0.797690841f,  0.603066599f,
+    0.795836905f,  0.605511041f,
+    0.793975478f,  0.607949785f,
+    0.792106577f,  0.610382806f,
+    0.790230221f,  0.612810082f,
+    0.788346428f,  0.615231591f,
+    0.786455214f,  0.617647308f,
+    0.784556597f,  0.620057212f,
+    0.782650596f,  0.622461279f,
+    0.780737229f,  0.624859488f,
+    0.778816512f,  0.627251815f,
+    0.776888466f,  0.629638239f,
+    0.774953107f,  0.632018736f,
+    0.773010453f,  0.634393284f,
+    0.771060524f,  0.636761861f,
+    0.769103338f,  0.639124445f,
+    0.767138912f,  0.641481013f,
+    0.765167266f,  0.643831543f,
+    0.763188417f,  0.646176013f,
+    0.761202385f,  0.648514401f,
+    0.759209189f,  0.650846685f,
+    0.757208847f,  0.653172843f,
+    0.755201377f,  0.655492853f,
+    0.753186799f,  0.657806693f,
+    0.751165132f,  0.660114342f,
+    0.749136395f,  0.662415778f,
+    0.747100606f,  0.664710978f,
+    0.745057785f,  0.666999922f,
+    0.743007952f,  0.669282588f,
+    0.740951125f,  0.671558955f,
+    0.738887324f,  0.673829000f,
+    0.736816569f,  0.676092704f,
+    0.734738878f,  0.678350043f,
+    0.732654272f,  0.680600998f,
+    0.730562769f,  0.682845546f,
+    0.728464390f,  0.685083668f,
+    0.726359155f,  0.687315341f,
+    0.724247083f,  0.689540545f,
+    0.722128194f,  0.691759258f,
+    0.720002508f,  0.693971461f,
+    0.717870045f,  0.696177131f,
+    0.715730825f,  0.698376249f,
+    0.713584869f,  0.700568794f,
+    0.711432196f,  0.702754744f,
+    0.709272826f,  0.704934080f,
+    0.707106781f,  0.707106781f,
+    0.704934080f,  0.709272826f,
+    0.702754744f,  0.711432196f,
+    0.700568794f,  0.713584869f,
+    0.698376249f,  0.715730825f,
+    0.696177131f,  0.717870045f,
+    0.693971461f,  0.720002508f,
+    0.691759258f,  0.722128194f,
+    0.689540545f,  0.724247083f,
+    0.687315341f,  0.726359155f,
+    0.685083668f,  0.728464390f,
+    0.682845546f,  0.730562769f,
+    0.680600998f,  0.732654272f,
+    0.678350043f,  0.734738878f,
+    0.676092704f,  0.736816569f,
+    0.673829000f,  0.738887324f,
+    0.671558955f,  0.740951125f,
+    0.669282588f,  0.743007952f,
+    0.666999922f,  0.745057785f,
+    0.664710978f,  0.747100606f,
+    0.662415778f,  0.749136395f,
+    0.660114342f,  0.751165132f,
+    0.657806693f,  0.753186799f,
+    0.655492853f,  0.755201377f,
+    0.653172843f,  0.757208847f,
+    0.650846685f,  0.759209189f,
+    0.648514401f,  0.761202385f,
+    0.646176013f,  0.763188417f,
+    0.643831543f,  0.765167266f,
+    0.641481013f,  0.767138912f,
+    0.639124445f,  0.769103338f,
+    0.636761861f,  0.771060524f,
+    0.634393284f,  0.773010453f,
+    0.632018736f,  0.774953107f,
+    0.629638239f,  0.776888466f,
+    0.627251815f,  0.778816512f,
+    0.624859488f,  0.780737229f,
+    0.622461279f,  0.782650596f,
+    0.620057212f,  0.784556597f,
+    0.617647308f,  0.786455214f,
+    0.615231591f,  0.788346428f,
+    0.612810082f,  0.790230221f,
+    0.610382806f,  0.792106577f,
+    0.607949785f,  0.793975478f,
+    0.605511041f,  0.795836905f,
+    0.603066599f,  0.797690841f,
+    0.600616479f,  0.799537269f,
+    0.598160707f,  0.801376172f,
+    0.595699304f,  0.803207531f,
+    0.593232295f,  0.805031331f,
+    0.590759702f,  0.806847554f,
+    0.588281548f,  0.808656182f,
+    0.585797857f,  0.810457198f,
+    0.583308653f,  0.812250587f,
+    0.580813958f,  0.814036330f,
+    0.578313796f,  0.815814411f,
+    0.575808191f,  0.817584813f,
+    0.573297167f,  0.819347520f,
+    0.570780746f,  0.821102515f,
+    0.568258953f,  0.822849781f,
+    0.565731811f,  0.824589303f,
+    0.563199344f,  0.826321063f,
+    0.560661576f,  0.828045045f,
+    0.558118531f,  0.829761234f,
+    0.555570233f,  0.831469612f,
+    0.553016706f,  0.833170165f,
+    0.550457973f,  0.834862875f,
+    0.547894059f,  0.836547727f,
+    0.545324988f,  0.838224706f,
+    0.542750785f,  0.839893794f,
+    0.540171473f,  0.841554977f,
+    0.537587076f,  0.843208240f,
+    0.534997620f,  0.844853565f,
+    0.532403128f,  0.846490939f,
+    0.529803625f,  0.848120345f,
+    0.527199135f,  0.849741768f,
+    0.524589683f,  0.851355193f,
+    0.521975293f,  0.852960605f,
+    0.519355990f,  0.854557988f,
+    0.516731799f,  0.856147328f,
+    0.514102744f,  0.857728610f,
+    0.511468850f,  0.859301818f,
+    0.508830143f,  0.860866939f,
+    0.506186645f,  0.862423956f,
+    0.503538384f,  0.863972856f,
+    0.500885383f,  0.865513624f,
+    0.498227667f,  0.867046246f,
+    0.495565262f,  0.868570706f,
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+    0.843208240f, -0.537587076f,
+    0.844853565f, -0.534997620f,
+    0.846490939f, -0.532403128f,
+    0.848120345f, -0.529803625f,
+    0.849741768f, -0.527199135f,
+    0.851355193f, -0.524589683f,
+    0.852960605f, -0.521975293f,
+    0.854557988f, -0.519355990f,
+    0.856147328f, -0.516731799f,
+    0.857728610f, -0.514102744f,
+    0.859301818f, -0.511468850f,
+    0.860866939f, -0.508830143f,
+    0.862423956f, -0.506186645f,
+    0.863972856f, -0.503538384f,
+    0.865513624f, -0.500885383f,
+    0.867046246f, -0.498227667f,
+    0.868570706f, -0.495565262f,
+    0.870086991f, -0.492898192f,
+    0.871595087f, -0.490226483f,
+    0.873094978f, -0.487550160f,
+    0.874586652f, -0.484869248f,
+    0.876070094f, -0.482183772f,
+    0.877545290f, -0.479493758f,
+    0.879012226f, -0.476799230f,
+    0.880470889f, -0.474100215f,
+    0.881921264f, -0.471396737f,
+    0.883363339f, -0.468688822f,
+    0.884797098f, -0.465976496f,
+    0.886222530f, -0.463259784f,
+    0.887639620f, -0.460538711f,
+    0.889048356f, -0.457813304f,
+    0.890448723f, -0.455083587f,
+    0.891840709f, -0.452349587f,
+    0.893224301f, -0.449611330f,
+    0.894599486f, -0.446868840f,
+    0.895966250f, -0.444122145f,
+    0.897324581f, -0.441371269f,
+    0.898674466f, -0.438616239f,
+    0.900015892f, -0.435857080f,
+    0.901348847f, -0.433093819f,
+    0.902673318f, -0.430326481f,
+    0.903989293f, -0.427555093f,
+    0.905296759f, -0.424779681f,
+    0.906595705f, -0.422000271f,
+    0.907886116f, -0.419216888f,
+    0.909167983f, -0.416429560f,
+    0.910441292f, -0.413638312f,
+    0.911706032f, -0.410843171f,
+    0.912962190f, -0.408044163f,
+    0.914209756f, -0.405241314f,
+    0.915448716f, -0.402434651f,
+    0.916679060f, -0.399624200f,
+    0.917900776f, -0.396809987f,
+    0.919113852f, -0.393992040f,
+    0.920318277f, -0.391170384f,
+    0.921514039f, -0.388345047f,
+    0.922701128f, -0.385516054f,
+    0.923879533f, -0.382683432f,
+    0.925049241f, -0.379847209f,
+    0.926210242f, -0.377007410f,
+    0.927362526f, -0.374164063f,
+    0.928506080f, -0.371317194f,
+    0.929640896f, -0.368466830f,
+    0.930766961f, -0.365612998f,
+    0.931884266f, -0.362755724f,
+    0.932992799f, -0.359895037f,
+    0.934092550f, -0.357030961f,
+    0.935183510f, -0.354163525f,
+    0.936265667f, -0.351292756f,
+    0.937339012f, -0.348418680f,
+    0.938403534f, -0.345541325f,
+    0.939459224f, -0.342660717f,
+    0.940506071f, -0.339776884f,
+    0.941544065f, -0.336889853f,
+    0.942573198f, -0.333999651f,
+    0.943593458f, -0.331106306f,
+    0.944604837f, -0.328209844f,
+    0.945607325f, -0.325310292f,
+    0.946600913f, -0.322407679f,
+    0.947585591f, -0.319502031f,
+    0.948561350f, -0.316593376f,
+    0.949528181f, -0.313681740f,
+    0.950486074f, -0.310767153f,
+    0.951435021f, -0.307849640f,
+    0.952375013f, -0.304929230f,
+    0.953306040f, -0.302005949f,
+    0.954228095f, -0.299079826f,
+    0.955141168f, -0.296150888f,
+    0.956045251f, -0.293219163f,
+    0.956940336f, -0.290284677f,
+    0.957826413f, -0.287347460f,
+    0.958703475f, -0.284407537f,
+    0.959571513f, -0.281464938f,
+    0.960430519f, -0.278519689f,
+    0.961280486f, -0.275571819f,
+    0.962121404f, -0.272621355f,
+    0.962953267f, -0.269668326f,
+    0.963776066f, -0.266712757f,
+    0.964589793f, -0.263754679f,
+    0.965394442f, -0.260794118f,
+    0.966190003f, -0.257831102f,
+    0.966976471f, -0.254865660f,
+    0.967753837f, -0.251897818f,
+    0.968522094f, -0.248927606f,
+    0.969281235f, -0.245955050f,
+    0.970031253f, -0.242980180f,
+    0.970772141f, -0.240003022f,
+    0.971503891f, -0.237023606f,
+    0.972226497f, -0.234041959f,
+    0.972939952f, -0.231058108f,
+    0.973644250f, -0.228072083f,
+    0.974339383f, -0.225083911f,
+    0.975025345f, -0.222093621f,
+    0.975702130f, -0.219101240f,
+    0.976369731f, -0.216106797f,
+    0.977028143f, -0.213110320f,
+    0.977677358f, -0.210111837f,
+    0.978317371f, -0.207111376f,
+    0.978948175f, -0.204108966f,
+    0.979569766f, -0.201104635f,
+    0.980182136f, -0.198098411f,
+    0.980785280f, -0.195090322f,
+    0.981379193f, -0.192080397f,
+    0.981963869f, -0.189068664f,
+    0.982539302f, -0.186055152f,
+    0.983105487f, -0.183039888f,
+    0.983662419f, -0.180022901f,
+    0.984210092f, -0.177004220f,
+    0.984748502f, -0.173983873f,
+    0.985277642f, -0.170961889f,
+    0.985797509f, -0.167938295f,
+    0.986308097f, -0.164913120f,
+    0.986809402f, -0.161886394f,
+    0.987301418f, -0.158858143f,
+    0.987784142f, -0.155828398f,
+    0.988257568f, -0.152797185f,
+    0.988721692f, -0.149764535f,
+    0.989176510f, -0.146730474f,
+    0.989622017f, -0.143695033f,
+    0.990058210f, -0.140658239f,
+    0.990485084f, -0.137620122f,
+    0.990902635f, -0.134580709f,
+    0.991310860f, -0.131540029f,
+    0.991709754f, -0.128498111f,
+    0.992099313f, -0.125454983f,
+    0.992479535f, -0.122410675f,
+    0.992850414f, -0.119365215f,
+    0.993211949f, -0.116318631f,
+    0.993564136f, -0.113270952f,
+    0.993906970f, -0.110222207f,
+    0.994240449f, -0.107172425f,
+    0.994564571f, -0.104121634f,
+    0.994879331f, -0.101069863f,
+    0.995184727f, -0.098017140f,
+    0.995480755f, -0.094963495f,
+    0.995767414f, -0.091908956f,
+    0.996044701f, -0.088853553f,
+    0.996312612f, -0.085797312f,
+    0.996571146f, -0.082740265f,
+    0.996820299f, -0.079682438f,
+    0.997060070f, -0.076623861f,
+    0.997290457f, -0.073564564f,
+    0.997511456f, -0.070504573f,
+    0.997723067f, -0.067443920f,
+    0.997925286f, -0.064382631f,
+    0.998118113f, -0.061320736f,
+    0.998301545f, -0.058258265f,
+    0.998475581f, -0.055195244f,
+    0.998640218f, -0.052131705f,
+    0.998795456f, -0.049067674f,
+    0.998941293f, -0.046003182f,
+    0.999077728f, -0.042938257f,
+    0.999204759f, -0.039872928f,
+    0.999322385f, -0.036807223f,
+    0.999430605f, -0.033741172f,
+    0.999529418f, -0.030674803f,
+    0.999618822f, -0.027608146f,
+    0.999698819f, -0.024541229f,
+    0.999769405f, -0.021474080f,
+    0.999830582f, -0.018406730f,
+    0.999882347f, -0.015339206f,
+    0.999924702f, -0.012271538f,
+    0.999957645f, -0.009203755f,
+    0.999981175f, -0.006135885f,
+    0.999995294f, -0.003067957f
+};
+
+/**    
+* \par    
+* Example code for Floating-point Twiddle factors Generation:    
+* \par    
+* <pre>for(i = 0; i< N/; i++)    
+* {    
+*	twiddleCoef[2*i]= cos(i * 2*PI/(float)N);    
+*	twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 4096	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are in interleaved fashion    
+*     
+*/
+const float32_t twiddleCoef_4096[8192] = {
+    1.000000000f,  0.000000000f,
+    0.999998823f,  0.001533980f,
+    0.999995294f,  0.003067957f,
+    0.999989411f,  0.004601926f,
+    0.999981175f,  0.006135885f,
+    0.999970586f,  0.007669829f,
+    0.999957645f,  0.009203755f,
+    0.999942350f,  0.010737659f,
+    0.999924702f,  0.012271538f,
+    0.999904701f,  0.013805389f,
+    0.999882347f,  0.015339206f,
+    0.999857641f,  0.016872988f,
+    0.999830582f,  0.018406730f,
+    0.999801170f,  0.019940429f,
+    0.999769405f,  0.021474080f,
+    0.999735288f,  0.023007681f,
+    0.999698819f,  0.024541229f,
+    0.999659997f,  0.026074718f,
+    0.999618822f,  0.027608146f,
+    0.999575296f,  0.029141509f,
+    0.999529418f,  0.030674803f,
+    0.999481187f,  0.032208025f,
+    0.999430605f,  0.033741172f,
+    0.999377670f,  0.035274239f,
+    0.999322385f,  0.036807223f,
+    0.999264747f,  0.038340120f,
+    0.999204759f,  0.039872928f,
+    0.999142419f,  0.041405641f,
+    0.999077728f,  0.042938257f,
+    0.999010686f,  0.044470772f,
+    0.998941293f,  0.046003182f,
+    0.998869550f,  0.047535484f,
+    0.998795456f,  0.049067674f,
+    0.998719012f,  0.050599749f,
+    0.998640218f,  0.052131705f,
+    0.998559074f,  0.053663538f,
+    0.998475581f,  0.055195244f,
+    0.998389737f,  0.056726821f,
+    0.998301545f,  0.058258265f,
+    0.998211003f,  0.059789571f,
+    0.998118113f,  0.061320736f,
+    0.998022874f,  0.062851758f,
+    0.997925286f,  0.064382631f,
+    0.997825350f,  0.065913353f,
+    0.997723067f,  0.067443920f,
+    0.997618435f,  0.068974328f,
+    0.997511456f,  0.070504573f,
+    0.997402130f,  0.072034653f,
+    0.997290457f,  0.073564564f,
+    0.997176437f,  0.075094301f,
+    0.997060070f,  0.076623861f,
+    0.996941358f,  0.078153242f,
+    0.996820299f,  0.079682438f,
+    0.996696895f,  0.081211447f,
+    0.996571146f,  0.082740265f,
+    0.996443051f,  0.084268888f,
+    0.996312612f,  0.085797312f,
+    0.996179829f,  0.087325535f,
+    0.996044701f,  0.088853553f,
+    0.995907229f,  0.090381361f,
+    0.995767414f,  0.091908956f,
+    0.995625256f,  0.093436336f,
+    0.995480755f,  0.094963495f,
+    0.995333912f,  0.096490431f,
+    0.995184727f,  0.098017140f,
+    0.995033199f,  0.099543619f,
+    0.994879331f,  0.101069863f,
+    0.994723121f,  0.102595869f,
+    0.994564571f,  0.104121634f,
+    0.994403680f,  0.105647154f,
+    0.994240449f,  0.107172425f,
+    0.994074879f,  0.108697444f,
+    0.993906970f,  0.110222207f,
+    0.993736722f,  0.111746711f,
+    0.993564136f,  0.113270952f,
+    0.993389211f,  0.114794927f,
+    0.993211949f,  0.116318631f,
+    0.993032350f,  0.117842062f,
+    0.992850414f,  0.119365215f,
+    0.992666142f,  0.120888087f,
+    0.992479535f,  0.122410675f,
+    0.992290591f,  0.123932975f,
+    0.992099313f,  0.125454983f,
+    0.991905700f,  0.126976696f,
+    0.991709754f,  0.128498111f,
+    0.991511473f,  0.130019223f,
+    0.991310860f,  0.131540029f,
+    0.991107914f,  0.133060525f,
+    0.990902635f,  0.134580709f,
+    0.990695025f,  0.136100575f,
+    0.990485084f,  0.137620122f,
+    0.990272812f,  0.139139344f,
+    0.990058210f,  0.140658239f,
+    0.989841278f,  0.142176804f,
+    0.989622017f,  0.143695033f,
+    0.989400428f,  0.145212925f,
+    0.989176510f,  0.146730474f,
+    0.988950265f,  0.148247679f,
+    0.988721692f,  0.149764535f,
+    0.988490793f,  0.151281038f,
+    0.988257568f,  0.152797185f,
+    0.988022017f,  0.154312973f,
+    0.987784142f,  0.155828398f,
+    0.987543942f,  0.157343456f,
+    0.987301418f,  0.158858143f,
+    0.987056571f,  0.160372457f,
+    0.986809402f,  0.161886394f,
+    0.986559910f,  0.163399949f,
+    0.986308097f,  0.164913120f,
+    0.986053963f,  0.166425904f,
+    0.985797509f,  0.167938295f,
+    0.985538735f,  0.169450291f,
+    0.985277642f,  0.170961889f,
+    0.985014231f,  0.172473084f,
+    0.984748502f,  0.173983873f,
+    0.984480455f,  0.175494253f,
+    0.984210092f,  0.177004220f,
+    0.983937413f,  0.178513771f,
+    0.983662419f,  0.180022901f,
+    0.983385110f,  0.181531608f,
+    0.983105487f,  0.183039888f,
+    0.982823551f,  0.184547737f,
+    0.982539302f,  0.186055152f,
+    0.982252741f,  0.187562129f,
+    0.981963869f,  0.189068664f,
+    0.981672686f,  0.190574755f,
+    0.981379193f,  0.192080397f,
+    0.981083391f,  0.193585587f,
+    0.980785280f,  0.195090322f,
+    0.980484862f,  0.196594598f,
+    0.980182136f,  0.198098411f,
+    0.979877104f,  0.199601758f,
+    0.979569766f,  0.201104635f,
+    0.979260123f,  0.202607039f,
+    0.978948175f,  0.204108966f,
+    0.978633924f,  0.205610413f,
+    0.978317371f,  0.207111376f,
+    0.977998515f,  0.208611852f,
+    0.977677358f,  0.210111837f,
+    0.977353900f,  0.211611327f,
+    0.977028143f,  0.213110320f,
+    0.976700086f,  0.214608811f,
+    0.976369731f,  0.216106797f,
+    0.976037079f,  0.217604275f,
+    0.975702130f,  0.219101240f,
+    0.975364885f,  0.220597690f,
+    0.975025345f,  0.222093621f,
+    0.974683511f,  0.223589029f,
+    0.974339383f,  0.225083911f,
+    0.973992962f,  0.226578264f,
+    0.973644250f,  0.228072083f,
+    0.973293246f,  0.229565366f,
+    0.972939952f,  0.231058108f,
+    0.972584369f,  0.232550307f,
+    0.972226497f,  0.234041959f,
+    0.971866337f,  0.235533059f,
+    0.971503891f,  0.237023606f,
+    0.971139158f,  0.238513595f,
+    0.970772141f,  0.240003022f,
+    0.970402839f,  0.241491885f,
+    0.970031253f,  0.242980180f,
+    0.969657385f,  0.244467903f,
+    0.969281235f,  0.245955050f,
+    0.968902805f,  0.247441619f,
+    0.968522094f,  0.248927606f,
+    0.968139105f,  0.250413007f,
+    0.967753837f,  0.251897818f,
+    0.967366292f,  0.253382037f,
+    0.966976471f,  0.254865660f,
+    0.966584374f,  0.256348682f,
+    0.966190003f,  0.257831102f,
+    0.965793359f,  0.259312915f,
+    0.965394442f,  0.260794118f,
+    0.964993253f,  0.262274707f,
+    0.964589793f,  0.263754679f,
+    0.964184064f,  0.265234030f,
+    0.963776066f,  0.266712757f,
+    0.963365800f,  0.268190857f,
+    0.962953267f,  0.269668326f,
+    0.962538468f,  0.271145160f,
+    0.962121404f,  0.272621355f,
+    0.961702077f,  0.274096910f,
+    0.961280486f,  0.275571819f,
+    0.960856633f,  0.277046080f,
+    0.960430519f,  0.278519689f,
+    0.960002146f,  0.279992643f,
+    0.959571513f,  0.281464938f,
+    0.959138622f,  0.282936570f,
+    0.958703475f,  0.284407537f,
+    0.958266071f,  0.285877835f,
+    0.957826413f,  0.287347460f,
+    0.957384501f,  0.288816408f,
+    0.956940336f,  0.290284677f,
+    0.956493919f,  0.291752263f,
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+    0.991905700f, -0.126976696f,
+    0.992099313f, -0.125454983f,
+    0.992290591f, -0.123932975f,
+    0.992479535f, -0.122410675f,
+    0.992666142f, -0.120888087f,
+    0.992850414f, -0.119365215f,
+    0.993032350f, -0.117842062f,
+    0.993211949f, -0.116318631f,
+    0.993389211f, -0.114794927f,
+    0.993564136f, -0.113270952f,
+    0.993736722f, -0.111746711f,
+    0.993906970f, -0.110222207f,
+    0.994074879f, -0.108697444f,
+    0.994240449f, -0.107172425f,
+    0.994403680f, -0.105647154f,
+    0.994564571f, -0.104121634f,
+    0.994723121f, -0.102595869f,
+    0.994879331f, -0.101069863f,
+    0.995033199f, -0.099543619f,
+    0.995184727f, -0.098017140f,
+    0.995333912f, -0.096490431f,
+    0.995480755f, -0.094963495f,
+    0.995625256f, -0.093436336f,
+    0.995767414f, -0.091908956f,
+    0.995907229f, -0.090381361f,
+    0.996044701f, -0.088853553f,
+    0.996179829f, -0.087325535f,
+    0.996312612f, -0.085797312f,
+    0.996443051f, -0.084268888f,
+    0.996571146f, -0.082740265f,
+    0.996696895f, -0.081211447f,
+    0.996820299f, -0.079682438f,
+    0.996941358f, -0.078153242f,
+    0.997060070f, -0.076623861f,
+    0.997176437f, -0.075094301f,
+    0.997290457f, -0.073564564f,
+    0.997402130f, -0.072034653f,
+    0.997511456f, -0.070504573f,
+    0.997618435f, -0.068974328f,
+    0.997723067f, -0.067443920f,
+    0.997825350f, -0.065913353f,
+    0.997925286f, -0.064382631f,
+    0.998022874f, -0.062851758f,
+    0.998118113f, -0.061320736f,
+    0.998211003f, -0.059789571f,
+    0.998301545f, -0.058258265f,
+    0.998389737f, -0.056726821f,
+    0.998475581f, -0.055195244f,
+    0.998559074f, -0.053663538f,
+    0.998640218f, -0.052131705f,
+    0.998719012f, -0.050599749f,
+    0.998795456f, -0.049067674f,
+    0.998869550f, -0.047535484f,
+    0.998941293f, -0.046003182f,
+    0.999010686f, -0.044470772f,
+    0.999077728f, -0.042938257f,
+    0.999142419f, -0.041405641f,
+    0.999204759f, -0.039872928f,
+    0.999264747f, -0.038340120f,
+    0.999322385f, -0.036807223f,
+    0.999377670f, -0.035274239f,
+    0.999430605f, -0.033741172f,
+    0.999481187f, -0.032208025f,
+    0.999529418f, -0.030674803f,
+    0.999575296f, -0.029141509f,
+    0.999618822f, -0.027608146f,
+    0.999659997f, -0.026074718f,
+    0.999698819f, -0.024541229f,
+    0.999735288f, -0.023007681f,
+    0.999769405f, -0.021474080f,
+    0.999801170f, -0.019940429f,
+    0.999830582f, -0.018406730f,
+    0.999857641f, -0.016872988f,
+    0.999882347f, -0.015339206f,
+    0.999904701f, -0.013805389f,
+    0.999924702f, -0.012271538f,
+    0.999942350f, -0.010737659f,
+    0.999957645f, -0.009203755f,
+    0.999970586f, -0.007669829f,
+    0.999981175f, -0.006135885f,
+    0.999989411f, -0.004601926f,
+    0.999995294f, -0.003067957f,
+    0.999998823f, -0.001533980f
+};
+
+/*    
+* @brief  Q31 Twiddle factors Table    
+*/
+
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 16	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_16_q31[24] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7641AF3C, 0x30FBC54D,
+    0x5A82799A, 0x5A82799A,
+    0x30FBC54D, 0x7641AF3C,
+    0x00000000, 0x7FFFFFFF,
+    0xCF043AB2, 0x7641AF3C,
+    0xA57D8666, 0x5A82799A,
+    0x89BE50C3, 0x30FBC54D,
+    0x80000000, 0x00000000,
+    0x89BE50C3, 0xCF043AB2,
+    0xA57D8666, 0xA57D8666,
+    0xCF043AB2, 0x89BE50C3
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 32	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_32_q31[48] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7641AF3C, 0x30FBC54D,
+    0x6A6D98A4, 0x471CECE6,
+    0x5A82799A, 0x5A82799A,
+    0x471CECE6, 0x6A6D98A4,
+    0x30FBC54D, 0x7641AF3C,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x00000000, 0x7FFFFFFF,
+    0xE70747C3, 0x7D8A5F3F,
+    0xCF043AB2, 0x7641AF3C,
+    0xB8E31319, 0x6A6D98A4,
+    0xA57D8666, 0x5A82799A,
+    0x9592675B, 0x471CECE6,
+    0x89BE50C3, 0x30FBC54D,
+    0x8275A0C0, 0x18F8B83C,
+    0x80000000, 0x00000000,
+    0x8275A0C0, 0xE70747C3,
+    0x89BE50C3, 0xCF043AB2,
+    0x9592675B, 0xB8E31319,
+    0xA57D8666, 0xA57D8666,
+    0xB8E31319, 0x9592675B,
+    0xCF043AB2, 0x89BE50C3,
+    0xE70747C3, 0x8275A0C0
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 64	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_64_q31[96] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7F62368F, 0x0C8BD35E,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7A7D055B, 0x25280C5D,
+    0x7641AF3C, 0x30FBC54D,
+    0x70E2CBC6, 0x3C56BA70,
+    0x6A6D98A4, 0x471CECE6,
+    0x62F201AC, 0x5133CC94,
+    0x5A82799A, 0x5A82799A,
+    0x5133CC94, 0x62F201AC,
+    0x471CECE6, 0x6A6D98A4,
+    0x3C56BA70, 0x70E2CBC6,
+    0x30FBC54D, 0x7641AF3C,
+    0x25280C5D, 0x7A7D055B,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x0C8BD35E, 0x7F62368F,
+    0x00000000, 0x7FFFFFFF,
+    0xF3742CA1, 0x7F62368F,
+    0xE70747C3, 0x7D8A5F3F,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xCF043AB2, 0x7641AF3C,
+    0xC3A9458F, 0x70E2CBC6,
+    0xB8E31319, 0x6A6D98A4,
+    0xAECC336B, 0x62F201AC,
+    0xA57D8666, 0x5A82799A,
+    0x9D0DFE53, 0x5133CC94,
+    0x9592675B, 0x471CECE6,
+    0x8F1D343A, 0x3C56BA70,
+    0x89BE50C3, 0x30FBC54D,
+    0x8582FAA4, 0x25280C5D,
+    0x8275A0C0, 0x18F8B83C,
+    0x809DC970, 0x0C8BD35E,
+    0x80000000, 0x00000000,
+    0x809DC970, 0xF3742CA1,
+    0x8275A0C0, 0xE70747C3,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x89BE50C3, 0xCF043AB2,
+    0x8F1D343A, 0xC3A9458F,
+    0x9592675B, 0xB8E31319,
+    0x9D0DFE53, 0xAECC336B,
+    0xA57D8666, 0xA57D8666,
+    0xAECC336B, 0x9D0DFE53,
+    0xB8E31319, 0x9592675B,
+    0xC3A9458F, 0x8F1D343A,
+    0xCF043AB2, 0x89BE50C3,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xE70747C3, 0x8275A0C0,
+    0xF3742CA1, 0x809DC970
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 128	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_128_q31[192] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7FD8878D, 0x0647D97C,
+    0x7F62368F, 0x0C8BD35E,
+    0x7E9D55FC, 0x12C8106E,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7A7D055B, 0x25280C5D,
+    0x78848413, 0x2B1F34EB,
+    0x7641AF3C, 0x30FBC54D,
+    0x73B5EBD0, 0x36BA2013,
+    0x70E2CBC6, 0x3C56BA70,
+    0x6DCA0D14, 0x41CE1E64,
+    0x6A6D98A4, 0x471CECE6,
+    0x66CF811F, 0x4C3FDFF3,
+    0x62F201AC, 0x5133CC94,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5A82799A, 0x5A82799A,
+    0x55F5A4D2, 0x5ED77C89,
+    0x5133CC94, 0x62F201AC,
+    0x4C3FDFF3, 0x66CF811F,
+    0x471CECE6, 0x6A6D98A4,
+    0x41CE1E64, 0x6DCA0D14,
+    0x3C56BA70, 0x70E2CBC6,
+    0x36BA2013, 0x73B5EBD0,
+    0x30FBC54D, 0x7641AF3C,
+    0x2B1F34EB, 0x78848413,
+    0x25280C5D, 0x7A7D055B,
+    0x1F19F97B, 0x7C29FBEE,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x12C8106E, 0x7E9D55FC,
+    0x0C8BD35E, 0x7F62368F,
+    0x0647D97C, 0x7FD8878D,
+    0x00000000, 0x7FFFFFFF,
+    0xF9B82683, 0x7FD8878D,
+    0xF3742CA1, 0x7F62368F,
+    0xED37EF91, 0x7E9D55FC,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE0E60684, 0x7C29FBEE,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xD4E0CB14, 0x78848413,
+    0xCF043AB2, 0x7641AF3C,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC3A9458F, 0x70E2CBC6,
+    0xBE31E19B, 0x6DCA0D14,
+    0xB8E31319, 0x6A6D98A4,
+    0xB3C0200C, 0x66CF811F,
+    0xAECC336B, 0x62F201AC,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA57D8666, 0x5A82799A,
+    0xA1288376, 0x55F5A4D2,
+    0x9D0DFE53, 0x5133CC94,
+    0x99307EE0, 0x4C3FDFF3,
+    0x9592675B, 0x471CECE6,
+    0x9235F2EB, 0x41CE1E64,
+    0x8F1D343A, 0x3C56BA70,
+    0x8C4A142F, 0x36BA2013,
+    0x89BE50C3, 0x30FBC54D,
+    0x877B7BEC, 0x2B1F34EB,
+    0x8582FAA4, 0x25280C5D,
+    0x83D60411, 0x1F19F97B,
+    0x8275A0C0, 0x18F8B83C,
+    0x8162AA03, 0x12C8106E,
+    0x809DC970, 0x0C8BD35E,
+    0x80277872, 0x0647D97C,
+    0x80000000, 0x00000000,
+    0x80277872, 0xF9B82683,
+    0x809DC970, 0xF3742CA1,
+    0x8162AA03, 0xED37EF91,
+    0x8275A0C0, 0xE70747C3,
+    0x83D60411, 0xE0E60684,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x877B7BEC, 0xD4E0CB14,
+    0x89BE50C3, 0xCF043AB2,
+    0x8C4A142F, 0xC945DFEC,
+    0x8F1D343A, 0xC3A9458F,
+    0x9235F2EB, 0xBE31E19B,
+    0x9592675B, 0xB8E31319,
+    0x99307EE0, 0xB3C0200C,
+    0x9D0DFE53, 0xAECC336B,
+    0xA1288376, 0xAA0A5B2D,
+    0xA57D8666, 0xA57D8666,
+    0xAA0A5B2D, 0xA1288376,
+    0xAECC336B, 0x9D0DFE53,
+    0xB3C0200C, 0x99307EE0,
+    0xB8E31319, 0x9592675B,
+    0xBE31E19B, 0x9235F2EB,
+    0xC3A9458F, 0x8F1D343A,
+    0xC945DFEC, 0x8C4A142F,
+    0xCF043AB2, 0x89BE50C3,
+    0xD4E0CB14, 0x877B7BEC,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xE0E60684, 0x83D60411,
+    0xE70747C3, 0x8275A0C0,
+    0xED37EF91, 0x8162AA03,
+    0xF3742CA1, 0x809DC970,
+    0xF9B82683, 0x80277872
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 256	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_256_q31[384] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7FF62182, 0x03242ABF,
+    0x7FD8878D, 0x0647D97C,
+    0x7FA736B4, 0x096A9049,
+    0x7F62368F, 0x0C8BD35E,
+    0x7F0991C3, 0x0FAB272B,
+    0x7E9D55FC, 0x12C8106E,
+    0x7E1D93E9, 0x15E21444,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7CE3CEB1, 0x1C0B826A,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7B5D039D, 0x2223A4C5,
+    0x7A7D055B, 0x25280C5D,
+    0x798A23B1, 0x2826B928,
+    0x78848413, 0x2B1F34EB,
+    0x776C4EDB, 0x2E110A62,
+    0x7641AF3C, 0x30FBC54D,
+    0x7504D345, 0x33DEF287,
+    0x73B5EBD0, 0x36BA2013,
+    0x72552C84, 0x398CDD32,
+    0x70E2CBC6, 0x3C56BA70,
+    0x6F5F02B1, 0x3F1749B7,
+    0x6DCA0D14, 0x41CE1E64,
+    0x6C242960, 0x447ACD50,
+    0x6A6D98A4, 0x471CECE6,
+    0x68A69E81, 0x49B41533,
+    0x66CF811F, 0x4C3FDFF3,
+    0x64E88926, 0x4EBFE8A4,
+    0x62F201AC, 0x5133CC94,
+    0x60EC3830, 0x539B2AEF,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5CB420DF, 0x5842DD54,
+    0x5A82799A, 0x5A82799A,
+    0x5842DD54, 0x5CB420DF,
+    0x55F5A4D2, 0x5ED77C89,
+    0x539B2AEF, 0x60EC3830,
+    0x5133CC94, 0x62F201AC,
+    0x4EBFE8A4, 0x64E88926,
+    0x4C3FDFF3, 0x66CF811F,
+    0x49B41533, 0x68A69E81,
+    0x471CECE6, 0x6A6D98A4,
+    0x447ACD50, 0x6C242960,
+    0x41CE1E64, 0x6DCA0D14,
+    0x3F1749B7, 0x6F5F02B1,
+    0x3C56BA70, 0x70E2CBC6,
+    0x398CDD32, 0x72552C84,
+    0x36BA2013, 0x73B5EBD0,
+    0x33DEF287, 0x7504D345,
+    0x30FBC54D, 0x7641AF3C,
+    0x2E110A62, 0x776C4EDB,
+    0x2B1F34EB, 0x78848413,
+    0x2826B928, 0x798A23B1,
+    0x25280C5D, 0x7A7D055B,
+    0x2223A4C5, 0x7B5D039D,
+    0x1F19F97B, 0x7C29FBEE,
+    0x1C0B826A, 0x7CE3CEB1,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x15E21444, 0x7E1D93E9,
+    0x12C8106E, 0x7E9D55FC,
+    0x0FAB272B, 0x7F0991C3,
+    0x0C8BD35E, 0x7F62368F,
+    0x096A9049, 0x7FA736B4,
+    0x0647D97C, 0x7FD8878D,
+    0x03242ABF, 0x7FF62182,
+    0x00000000, 0x7FFFFFFF,
+    0xFCDBD541, 0x7FF62182,
+    0xF9B82683, 0x7FD8878D,
+    0xF6956FB6, 0x7FA736B4,
+    0xF3742CA1, 0x7F62368F,
+    0xF054D8D4, 0x7F0991C3,
+    0xED37EF91, 0x7E9D55FC,
+    0xEA1DEBBB, 0x7E1D93E9,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE3F47D95, 0x7CE3CEB1,
+    0xE0E60684, 0x7C29FBEE,
+    0xDDDC5B3A, 0x7B5D039D,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xD7D946D7, 0x798A23B1,
+    0xD4E0CB14, 0x78848413,
+    0xD1EEF59E, 0x776C4EDB,
+    0xCF043AB2, 0x7641AF3C,
+    0xCC210D78, 0x7504D345,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC67322CD, 0x72552C84,
+    0xC3A9458F, 0x70E2CBC6,
+    0xC0E8B648, 0x6F5F02B1,
+    0xBE31E19B, 0x6DCA0D14,
+    0xBB8532AF, 0x6C242960,
+    0xB8E31319, 0x6A6D98A4,
+    0xB64BEACC, 0x68A69E81,
+    0xB3C0200C, 0x66CF811F,
+    0xB140175B, 0x64E88926,
+    0xAECC336B, 0x62F201AC,
+    0xAC64D510, 0x60EC3830,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA7BD22AB, 0x5CB420DF,
+    0xA57D8666, 0x5A82799A,
+    0xA34BDF20, 0x5842DD54,
+    0xA1288376, 0x55F5A4D2,
+    0x9F13C7D0, 0x539B2AEF,
+    0x9D0DFE53, 0x5133CC94,
+    0x9B1776D9, 0x4EBFE8A4,
+    0x99307EE0, 0x4C3FDFF3,
+    0x9759617E, 0x49B41533,
+    0x9592675B, 0x471CECE6,
+    0x93DBD69F, 0x447ACD50,
+    0x9235F2EB, 0x41CE1E64,
+    0x90A0FD4E, 0x3F1749B7,
+    0x8F1D343A, 0x3C56BA70,
+    0x8DAAD37B, 0x398CDD32,
+    0x8C4A142F, 0x36BA2013,
+    0x8AFB2CBA, 0x33DEF287,
+    0x89BE50C3, 0x30FBC54D,
+    0x8893B124, 0x2E110A62,
+    0x877B7BEC, 0x2B1F34EB,
+    0x8675DC4E, 0x2826B928,
+    0x8582FAA4, 0x25280C5D,
+    0x84A2FC62, 0x2223A4C5,
+    0x83D60411, 0x1F19F97B,
+    0x831C314E, 0x1C0B826A,
+    0x8275A0C0, 0x18F8B83C,
+    0x81E26C16, 0x15E21444,
+    0x8162AA03, 0x12C8106E,
+    0x80F66E3C, 0x0FAB272B,
+    0x809DC970, 0x0C8BD35E,
+    0x8058C94C, 0x096A9049,
+    0x80277872, 0x0647D97C,
+    0x8009DE7D, 0x03242ABF,
+    0x80000000, 0x00000000,
+    0x8009DE7D, 0xFCDBD541,
+    0x80277872, 0xF9B82683,
+    0x8058C94C, 0xF6956FB6,
+    0x809DC970, 0xF3742CA1,
+    0x80F66E3C, 0xF054D8D4,
+    0x8162AA03, 0xED37EF91,
+    0x81E26C16, 0xEA1DEBBB,
+    0x8275A0C0, 0xE70747C3,
+    0x831C314E, 0xE3F47D95,
+    0x83D60411, 0xE0E60684,
+    0x84A2FC62, 0xDDDC5B3A,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x8675DC4E, 0xD7D946D7,
+    0x877B7BEC, 0xD4E0CB14,
+    0x8893B124, 0xD1EEF59E,
+    0x89BE50C3, 0xCF043AB2,
+    0x8AFB2CBA, 0xCC210D78,
+    0x8C4A142F, 0xC945DFEC,
+    0x8DAAD37B, 0xC67322CD,
+    0x8F1D343A, 0xC3A9458F,
+    0x90A0FD4E, 0xC0E8B648,
+    0x9235F2EB, 0xBE31E19B,
+    0x93DBD69F, 0xBB8532AF,
+    0x9592675B, 0xB8E31319,
+    0x9759617E, 0xB64BEACC,
+    0x99307EE0, 0xB3C0200C,
+    0x9B1776D9, 0xB140175B,
+    0x9D0DFE53, 0xAECC336B,
+    0x9F13C7D0, 0xAC64D510,
+    0xA1288376, 0xAA0A5B2D,
+    0xA34BDF20, 0xA7BD22AB,
+    0xA57D8666, 0xA57D8666,
+    0xA7BD22AB, 0xA34BDF20,
+    0xAA0A5B2D, 0xA1288376,
+    0xAC64D510, 0x9F13C7D0,
+    0xAECC336B, 0x9D0DFE53,
+    0xB140175B, 0x9B1776D9,
+    0xB3C0200C, 0x99307EE0,
+    0xB64BEACC, 0x9759617E,
+    0xB8E31319, 0x9592675B,
+    0xBB8532AF, 0x93DBD69F,
+    0xBE31E19B, 0x9235F2EB,
+    0xC0E8B648, 0x90A0FD4E,
+    0xC3A9458F, 0x8F1D343A,
+    0xC67322CD, 0x8DAAD37B,
+    0xC945DFEC, 0x8C4A142F,
+    0xCC210D78, 0x8AFB2CBA,
+    0xCF043AB2, 0x89BE50C3,
+    0xD1EEF59E, 0x8893B124,
+    0xD4E0CB14, 0x877B7BEC,
+    0xD7D946D7, 0x8675DC4E,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xDDDC5B3A, 0x84A2FC62,
+    0xE0E60684, 0x83D60411,
+    0xE3F47D95, 0x831C314E,
+    0xE70747C3, 0x8275A0C0,
+    0xEA1DEBBB, 0x81E26C16,
+    0xED37EF91, 0x8162AA03,
+    0xF054D8D4, 0x80F66E3C,
+    0xF3742CA1, 0x809DC970,
+    0xF6956FB6, 0x8058C94C,
+    0xF9B82683, 0x80277872,
+    0xFCDBD541, 0x8009DE7D
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 512	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_512_q31[768] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7FFD885A, 0x01921D1F,
+    0x7FF62182, 0x03242ABF,
+    0x7FE9CBC0, 0x04B6195D,
+    0x7FD8878D, 0x0647D97C,
+    0x7FC25596, 0x07D95B9E,
+    0x7FA736B4, 0x096A9049,
+    0x7F872BF3, 0x0AFB6805,
+    0x7F62368F, 0x0C8BD35E,
+    0x7F3857F5, 0x0E1BC2E3,
+    0x7F0991C3, 0x0FAB272B,
+    0x7ED5E5C6, 0x1139F0CE,
+    0x7E9D55FC, 0x12C8106E,
+    0x7E5FE493, 0x145576B1,
+    0x7E1D93E9, 0x15E21444,
+    0x7DD6668E, 0x176DD9DE,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7D3980EC, 0x1A82A025,
+    0x7CE3CEB1, 0x1C0B826A,
+    0x7C894BDD, 0x1D934FE5,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7BC5E28F, 0x209F701C,
+    0x7B5D039D, 0x2223A4C5,
+    0x7AEF6323, 0x23A6887E,
+    0x7A7D055B, 0x25280C5D,
+    0x7A05EEAD, 0x26A82185,
+    0x798A23B1, 0x2826B928,
+    0x7909A92C, 0x29A3C484,
+    0x78848413, 0x2B1F34EB,
+    0x77FAB988, 0x2C98FBBA,
+    0x776C4EDB, 0x2E110A62,
+    0x76D94988, 0x2F875262,
+    0x7641AF3C, 0x30FBC54D,
+    0x75A585CF, 0x326E54C7,
+    0x7504D345, 0x33DEF287,
+    0x745F9DD1, 0x354D9056,
+    0x73B5EBD0, 0x36BA2013,
+    0x7307C3D0, 0x382493B0,
+    0x72552C84, 0x398CDD32,
+    0x719E2CD2, 0x3AF2EEB7,
+    0x70E2CBC6, 0x3C56BA70,
+    0x70231099, 0x3DB832A5,
+    0x6F5F02B1, 0x3F1749B7,
+    0x6E96A99C, 0x4073F21D,
+    0x6DCA0D14, 0x41CE1E64,
+    0x6CF934FB, 0x4325C135,
+    0x6C242960, 0x447ACD50,
+    0x6B4AF278, 0x45CD358F,
+    0x6A6D98A4, 0x471CECE6,
+    0x698C246C, 0x4869E664,
+    0x68A69E81, 0x49B41533,
+    0x67BD0FBC, 0x4AFB6C97,
+    0x66CF811F, 0x4C3FDFF3,
+    0x65DDFBD3, 0x4D8162C4,
+    0x64E88926, 0x4EBFE8A4,
+    0x63EF328F, 0x4FFB654D,
+    0x62F201AC, 0x5133CC94,
+    0x61F1003E, 0x5269126E,
+    0x60EC3830, 0x539B2AEF,
+    0x5FE3B38D, 0x54CA0A4A,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5DC79D7C, 0x571DEEF9,
+    0x5CB420DF, 0x5842DD54,
+    0x5B9D1153, 0x59646497,
+    0x5A82799A, 0x5A82799A,
+    0x59646497, 0x5B9D1153,
+    0x5842DD54, 0x5CB420DF,
+    0x571DEEF9, 0x5DC79D7C,
+    0x55F5A4D2, 0x5ED77C89,
+    0x54CA0A4A, 0x5FE3B38D,
+    0x539B2AEF, 0x60EC3830,
+    0x5269126E, 0x61F1003E,
+    0x5133CC94, 0x62F201AC,
+    0x4FFB654D, 0x63EF328F,
+    0x4EBFE8A4, 0x64E88926,
+    0x4D8162C4, 0x65DDFBD3,
+    0x4C3FDFF3, 0x66CF811F,
+    0x4AFB6C97, 0x67BD0FBC,
+    0x49B41533, 0x68A69E81,
+    0x4869E664, 0x698C246C,
+    0x471CECE6, 0x6A6D98A4,
+    0x45CD358F, 0x6B4AF278,
+    0x447ACD50, 0x6C242960,
+    0x4325C135, 0x6CF934FB,
+    0x41CE1E64, 0x6DCA0D14,
+    0x4073F21D, 0x6E96A99C,
+    0x3F1749B7, 0x6F5F02B1,
+    0x3DB832A5, 0x70231099,
+    0x3C56BA70, 0x70E2CBC6,
+    0x3AF2EEB7, 0x719E2CD2,
+    0x398CDD32, 0x72552C84,
+    0x382493B0, 0x7307C3D0,
+    0x36BA2013, 0x73B5EBD0,
+    0x354D9056, 0x745F9DD1,
+    0x33DEF287, 0x7504D345,
+    0x326E54C7, 0x75A585CF,
+    0x30FBC54D, 0x7641AF3C,
+    0x2F875262, 0x76D94988,
+    0x2E110A62, 0x776C4EDB,
+    0x2C98FBBA, 0x77FAB988,
+    0x2B1F34EB, 0x78848413,
+    0x29A3C484, 0x7909A92C,
+    0x2826B928, 0x798A23B1,
+    0x26A82185, 0x7A05EEAD,
+    0x25280C5D, 0x7A7D055B,
+    0x23A6887E, 0x7AEF6323,
+    0x2223A4C5, 0x7B5D039D,
+    0x209F701C, 0x7BC5E28F,
+    0x1F19F97B, 0x7C29FBEE,
+    0x1D934FE5, 0x7C894BDD,
+    0x1C0B826A, 0x7CE3CEB1,
+    0x1A82A025, 0x7D3980EC,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x176DD9DE, 0x7DD6668E,
+    0x15E21444, 0x7E1D93E9,
+    0x145576B1, 0x7E5FE493,
+    0x12C8106E, 0x7E9D55FC,
+    0x1139F0CE, 0x7ED5E5C6,
+    0x0FAB272B, 0x7F0991C3,
+    0x0E1BC2E3, 0x7F3857F5,
+    0x0C8BD35E, 0x7F62368F,
+    0x0AFB6805, 0x7F872BF3,
+    0x096A9049, 0x7FA736B4,
+    0x07D95B9E, 0x7FC25596,
+    0x0647D97C, 0x7FD8878D,
+    0x04B6195D, 0x7FE9CBC0,
+    0x03242ABF, 0x7FF62182,
+    0x01921D1F, 0x7FFD885A,
+    0x00000000, 0x7FFFFFFF,
+    0xFE6DE2E0, 0x7FFD885A,
+    0xFCDBD541, 0x7FF62182,
+    0xFB49E6A2, 0x7FE9CBC0,
+    0xF9B82683, 0x7FD8878D,
+    0xF826A461, 0x7FC25596,
+    0xF6956FB6, 0x7FA736B4,
+    0xF50497FA, 0x7F872BF3,
+    0xF3742CA1, 0x7F62368F,
+    0xF1E43D1C, 0x7F3857F5,
+    0xF054D8D4, 0x7F0991C3,
+    0xEEC60F31, 0x7ED5E5C6,
+    0xED37EF91, 0x7E9D55FC,
+    0xEBAA894E, 0x7E5FE493,
+    0xEA1DEBBB, 0x7E1D93E9,
+    0xE8922621, 0x7DD6668E,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE57D5FDA, 0x7D3980EC,
+    0xE3F47D95, 0x7CE3CEB1,
+    0xE26CB01A, 0x7C894BDD,
+    0xE0E60684, 0x7C29FBEE,
+    0xDF608FE3, 0x7BC5E28F,
+    0xDDDC5B3A, 0x7B5D039D,
+    0xDC597781, 0x7AEF6323,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xD957DE7A, 0x7A05EEAD,
+    0xD7D946D7, 0x798A23B1,
+    0xD65C3B7B, 0x7909A92C,
+    0xD4E0CB14, 0x78848413,
+    0xD3670445, 0x77FAB988,
+    0xD1EEF59E, 0x776C4EDB,
+    0xD078AD9D, 0x76D94988,
+    0xCF043AB2, 0x7641AF3C,
+    0xCD91AB38, 0x75A585CF,
+    0xCC210D78, 0x7504D345,
+    0xCAB26FA9, 0x745F9DD1,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC7DB6C50, 0x7307C3D0,
+    0xC67322CD, 0x72552C84,
+    0xC50D1148, 0x719E2CD2,
+    0xC3A9458F, 0x70E2CBC6,
+    0xC247CD5A, 0x70231099,
+    0xC0E8B648, 0x6F5F02B1,
+    0xBF8C0DE2, 0x6E96A99C,
+    0xBE31E19B, 0x6DCA0D14,
+    0xBCDA3ECA, 0x6CF934FB,
+    0xBB8532AF, 0x6C242960,
+    0xBA32CA70, 0x6B4AF278,
+    0xB8E31319, 0x6A6D98A4,
+    0xB796199B, 0x698C246C,
+    0xB64BEACC, 0x68A69E81,
+    0xB5049368, 0x67BD0FBC,
+    0xB3C0200C, 0x66CF811F,
+    0xB27E9D3B, 0x65DDFBD3,
+    0xB140175B, 0x64E88926,
+    0xB0049AB2, 0x63EF328F,
+    0xAECC336B, 0x62F201AC,
+    0xAD96ED91, 0x61F1003E,
+    0xAC64D510, 0x60EC3830,
+    0xAB35F5B5, 0x5FE3B38D,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA8E21106, 0x5DC79D7C,
+    0xA7BD22AB, 0x5CB420DF,
+    0xA69B9B68, 0x5B9D1153,
+    0xA57D8666, 0x5A82799A,
+    0xA462EEAC, 0x59646497,
+    0xA34BDF20, 0x5842DD54,
+    0xA2386283, 0x571DEEF9,
+    0xA1288376, 0x55F5A4D2,
+    0xA01C4C72, 0x54CA0A4A,
+    0x9F13C7D0, 0x539B2AEF,
+    0x9E0EFFC1, 0x5269126E,
+    0x9D0DFE53, 0x5133CC94,
+    0x9C10CD70, 0x4FFB654D,
+    0x9B1776D9, 0x4EBFE8A4,
+    0x9A22042C, 0x4D8162C4,
+    0x99307EE0, 0x4C3FDFF3,
+    0x9842F043, 0x4AFB6C97,
+    0x9759617E, 0x49B41533,
+    0x9673DB94, 0x4869E664,
+    0x9592675B, 0x471CECE6,
+    0x94B50D87, 0x45CD358F,
+    0x93DBD69F, 0x447ACD50,
+    0x9306CB04, 0x4325C135,
+    0x9235F2EB, 0x41CE1E64,
+    0x91695663, 0x4073F21D,
+    0x90A0FD4E, 0x3F1749B7,
+    0x8FDCEF66, 0x3DB832A5,
+    0x8F1D343A, 0x3C56BA70,
+    0x8E61D32D, 0x3AF2EEB7,
+    0x8DAAD37B, 0x398CDD32,
+    0x8CF83C30, 0x382493B0,
+    0x8C4A142F, 0x36BA2013,
+    0x8BA0622F, 0x354D9056,
+    0x8AFB2CBA, 0x33DEF287,
+    0x8A5A7A30, 0x326E54C7,
+    0x89BE50C3, 0x30FBC54D,
+    0x8926B677, 0x2F875262,
+    0x8893B124, 0x2E110A62,
+    0x88054677, 0x2C98FBBA,
+    0x877B7BEC, 0x2B1F34EB,
+    0x86F656D3, 0x29A3C484,
+    0x8675DC4E, 0x2826B928,
+    0x85FA1152, 0x26A82185,
+    0x8582FAA4, 0x25280C5D,
+    0x85109CDC, 0x23A6887E,
+    0x84A2FC62, 0x2223A4C5,
+    0x843A1D70, 0x209F701C,
+    0x83D60411, 0x1F19F97B,
+    0x8376B422, 0x1D934FE5,
+    0x831C314E, 0x1C0B826A,
+    0x82C67F13, 0x1A82A025,
+    0x8275A0C0, 0x18F8B83C,
+    0x82299971, 0x176DD9DE,
+    0x81E26C16, 0x15E21444,
+    0x81A01B6C, 0x145576B1,
+    0x8162AA03, 0x12C8106E,
+    0x812A1A39, 0x1139F0CE,
+    0x80F66E3C, 0x0FAB272B,
+    0x80C7A80A, 0x0E1BC2E3,
+    0x809DC970, 0x0C8BD35E,
+    0x8078D40D, 0x0AFB6805,
+    0x8058C94C, 0x096A9049,
+    0x803DAA69, 0x07D95B9E,
+    0x80277872, 0x0647D97C,
+    0x80163440, 0x04B6195D,
+    0x8009DE7D, 0x03242ABF,
+    0x800277A5, 0x01921D1F,
+    0x80000000, 0x00000000,
+    0x800277A5, 0xFE6DE2E0,
+    0x8009DE7D, 0xFCDBD541,
+    0x80163440, 0xFB49E6A2,
+    0x80277872, 0xF9B82683,
+    0x803DAA69, 0xF826A461,
+    0x8058C94C, 0xF6956FB6,
+    0x8078D40D, 0xF50497FA,
+    0x809DC970, 0xF3742CA1,
+    0x80C7A80A, 0xF1E43D1C,
+    0x80F66E3C, 0xF054D8D4,
+    0x812A1A39, 0xEEC60F31,
+    0x8162AA03, 0xED37EF91,
+    0x81A01B6C, 0xEBAA894E,
+    0x81E26C16, 0xEA1DEBBB,
+    0x82299971, 0xE8922621,
+    0x8275A0C0, 0xE70747C3,
+    0x82C67F13, 0xE57D5FDA,
+    0x831C314E, 0xE3F47D95,
+    0x8376B422, 0xE26CB01A,
+    0x83D60411, 0xE0E60684,
+    0x843A1D70, 0xDF608FE3,
+    0x84A2FC62, 0xDDDC5B3A,
+    0x85109CDC, 0xDC597781,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x85FA1152, 0xD957DE7A,
+    0x8675DC4E, 0xD7D946D7,
+    0x86F656D3, 0xD65C3B7B,
+    0x877B7BEC, 0xD4E0CB14,
+    0x88054677, 0xD3670445,
+    0x8893B124, 0xD1EEF59E,
+    0x8926B677, 0xD078AD9D,
+    0x89BE50C3, 0xCF043AB2,
+    0x8A5A7A30, 0xCD91AB38,
+    0x8AFB2CBA, 0xCC210D78,
+    0x8BA0622F, 0xCAB26FA9,
+    0x8C4A142F, 0xC945DFEC,
+    0x8CF83C30, 0xC7DB6C50,
+    0x8DAAD37B, 0xC67322CD,
+    0x8E61D32D, 0xC50D1148,
+    0x8F1D343A, 0xC3A9458F,
+    0x8FDCEF66, 0xC247CD5A,
+    0x90A0FD4E, 0xC0E8B648,
+    0x91695663, 0xBF8C0DE2,
+    0x9235F2EB, 0xBE31E19B,
+    0x9306CB04, 0xBCDA3ECA,
+    0x93DBD69F, 0xBB8532AF,
+    0x94B50D87, 0xBA32CA70,
+    0x9592675B, 0xB8E31319,
+    0x9673DB94, 0xB796199B,
+    0x9759617E, 0xB64BEACC,
+    0x9842F043, 0xB5049368,
+    0x99307EE0, 0xB3C0200C,
+    0x9A22042C, 0xB27E9D3B,
+    0x9B1776D9, 0xB140175B,
+    0x9C10CD70, 0xB0049AB2,
+    0x9D0DFE53, 0xAECC336B,
+    0x9E0EFFC1, 0xAD96ED91,
+    0x9F13C7D0, 0xAC64D510,
+    0xA01C4C72, 0xAB35F5B5,
+    0xA1288376, 0xAA0A5B2D,
+    0xA2386283, 0xA8E21106,
+    0xA34BDF20, 0xA7BD22AB,
+    0xA462EEAC, 0xA69B9B68,
+    0xA57D8666, 0xA57D8666,
+    0xA69B9B68, 0xA462EEAC,
+    0xA7BD22AB, 0xA34BDF20,
+    0xA8E21106, 0xA2386283,
+    0xAA0A5B2D, 0xA1288376,
+    0xAB35F5B5, 0xA01C4C72,
+    0xAC64D510, 0x9F13C7D0,
+    0xAD96ED91, 0x9E0EFFC1,
+    0xAECC336B, 0x9D0DFE53,
+    0xB0049AB2, 0x9C10CD70,
+    0xB140175B, 0x9B1776D9,
+    0xB27E9D3B, 0x9A22042C,
+    0xB3C0200C, 0x99307EE0,
+    0xB5049368, 0x9842F043,
+    0xB64BEACC, 0x9759617E,
+    0xB796199B, 0x9673DB94,
+    0xB8E31319, 0x9592675B,
+    0xBA32CA70, 0x94B50D87,
+    0xBB8532AF, 0x93DBD69F,
+    0xBCDA3ECA, 0x9306CB04,
+    0xBE31E19B, 0x9235F2EB,
+    0xBF8C0DE2, 0x91695663,
+    0xC0E8B648, 0x90A0FD4E,
+    0xC247CD5A, 0x8FDCEF66,
+    0xC3A9458F, 0x8F1D343A,
+    0xC50D1148, 0x8E61D32D,
+    0xC67322CD, 0x8DAAD37B,
+    0xC7DB6C50, 0x8CF83C30,
+    0xC945DFEC, 0x8C4A142F,
+    0xCAB26FA9, 0x8BA0622F,
+    0xCC210D78, 0x8AFB2CBA,
+    0xCD91AB38, 0x8A5A7A30,
+    0xCF043AB2, 0x89BE50C3,
+    0xD078AD9D, 0x8926B677,
+    0xD1EEF59E, 0x8893B124,
+    0xD3670445, 0x88054677,
+    0xD4E0CB14, 0x877B7BEC,
+    0xD65C3B7B, 0x86F656D3,
+    0xD7D946D7, 0x8675DC4E,
+    0xD957DE7A, 0x85FA1152,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xDC597781, 0x85109CDC,
+    0xDDDC5B3A, 0x84A2FC62,
+    0xDF608FE3, 0x843A1D70,
+    0xE0E60684, 0x83D60411,
+    0xE26CB01A, 0x8376B422,
+    0xE3F47D95, 0x831C314E,
+    0xE57D5FDA, 0x82C67F13,
+    0xE70747C3, 0x8275A0C0,
+    0xE8922621, 0x82299971,
+    0xEA1DEBBB, 0x81E26C16,
+    0xEBAA894E, 0x81A01B6C,
+    0xED37EF91, 0x8162AA03,
+    0xEEC60F31, 0x812A1A39,
+    0xF054D8D4, 0x80F66E3C,
+    0xF1E43D1C, 0x80C7A80A,
+    0xF3742CA1, 0x809DC970,
+    0xF50497FA, 0x8078D40D,
+    0xF6956FB6, 0x8058C94C,
+    0xF826A461, 0x803DAA69,
+    0xF9B82683, 0x80277872,
+    0xFB49E6A2, 0x80163440,
+    0xFCDBD541, 0x8009DE7D,
+    0xFE6DE2E0, 0x800277A5
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 1024	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_1024_q31[1536] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7FFF6216, 0x00C90F88,
+    0x7FFD885A, 0x01921D1F,
+    0x7FFA72D1, 0x025B26D7,
+    0x7FF62182, 0x03242ABF,
+    0x7FF09477, 0x03ED26E6,
+    0x7FE9CBC0, 0x04B6195D,
+    0x7FE1C76B, 0x057F0034,
+    0x7FD8878D, 0x0647D97C,
+    0x7FCE0C3E, 0x0710A344,
+    0x7FC25596, 0x07D95B9E,
+    0x7FB563B2, 0x08A2009A,
+    0x7FA736B4, 0x096A9049,
+    0x7F97CEBC, 0x0A3308BC,
+    0x7F872BF3, 0x0AFB6805,
+    0x7F754E7F, 0x0BC3AC35,
+    0x7F62368F, 0x0C8BD35E,
+    0x7F4DE450, 0x0D53DB92,
+    0x7F3857F5, 0x0E1BC2E3,
+    0x7F2191B4, 0x0EE38765,
+    0x7F0991C3, 0x0FAB272B,
+    0x7EF0585F, 0x1072A047,
+    0x7ED5E5C6, 0x1139F0CE,
+    0x7EBA3A39, 0x120116D4,
+    0x7E9D55FC, 0x12C8106E,
+    0x7E7F3956, 0x138EDBB0,
+    0x7E5FE493, 0x145576B1,
+    0x7E3F57FE, 0x151BDF85,
+    0x7E1D93E9, 0x15E21444,
+    0x7DFA98A7, 0x16A81305,
+    0x7DD6668E, 0x176DD9DE,
+    0x7DB0FDF7, 0x183366E8,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7D628AC5, 0x19BDCBF2,
+    0x7D3980EC, 0x1A82A025,
+    0x7D0F4218, 0x1B4732EF,
+    0x7CE3CEB1, 0x1C0B826A,
+    0x7CB72724, 0x1CCF8CB3,
+    0x7C894BDD, 0x1D934FE5,
+    0x7C5A3D4F, 0x1E56CA1E,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7BF88830, 0x1FDCDC1A,
+    0x7BC5E28F, 0x209F701C,
+    0x7B920B89, 0x2161B39F,
+    0x7B5D039D, 0x2223A4C5,
+    0x7B26CB4F, 0x22E541AE,
+    0x7AEF6323, 0x23A6887E,
+    0x7AB6CBA3, 0x24677757,
+    0x7A7D055B, 0x25280C5D,
+    0x7A4210D8, 0x25E845B5,
+    0x7A05EEAD, 0x26A82185,
+    0x79C89F6D, 0x27679DF4,
+    0x798A23B1, 0x2826B928,
+    0x794A7C11, 0x28E5714A,
+    0x7909A92C, 0x29A3C484,
+    0x78C7ABA1, 0x2A61B101,
+    0x78848413, 0x2B1F34EB,
+    0x78403328, 0x2BDC4E6F,
+    0x77FAB988, 0x2C98FBBA,
+    0x77B417DF, 0x2D553AFB,
+    0x776C4EDB, 0x2E110A62,
+    0x77235F2D, 0x2ECC681E,
+    0x76D94988, 0x2F875262,
+    0x768E0EA5, 0x3041C760,
+    0x7641AF3C, 0x30FBC54D,
+    0x75F42C0A, 0x31B54A5D,
+    0x75A585CF, 0x326E54C7,
+    0x7555BD4B, 0x3326E2C2,
+    0x7504D345, 0x33DEF287,
+    0x74B2C883, 0x3496824F,
+    0x745F9DD1, 0x354D9056,
+    0x740B53FA, 0x36041AD9,
+    0x73B5EBD0, 0x36BA2013,
+    0x735F6626, 0x376F9E46,
+    0x7307C3D0, 0x382493B0,
+    0x72AF05A6, 0x38D8FE93,
+    0x72552C84, 0x398CDD32,
+    0x71FA3948, 0x3A402DD1,
+    0x719E2CD2, 0x3AF2EEB7,
+    0x71410804, 0x3BA51E29,
+    0x70E2CBC6, 0x3C56BA70,
+    0x708378FE, 0x3D07C1D5,
+    0x70231099, 0x3DB832A5,
+    0x6FC19385, 0x3E680B2C,
+    0x6F5F02B1, 0x3F1749B7,
+    0x6EFB5F12, 0x3FC5EC97,
+    0x6E96A99C, 0x4073F21D,
+    0x6E30E349, 0x4121589A,
+    0x6DCA0D14, 0x41CE1E64,
+    0x6D6227FA, 0x427A41D0,
+    0x6CF934FB, 0x4325C135,
+    0x6C8F351C, 0x43D09AEC,
+    0x6C242960, 0x447ACD50,
+    0x6BB812D0, 0x452456BC,
+    0x6B4AF278, 0x45CD358F,
+    0x6ADCC964, 0x46756827,
+    0x6A6D98A4, 0x471CECE6,
+    0x69FD614A, 0x47C3C22E,
+    0x698C246C, 0x4869E664,
+    0x6919E320, 0x490F57EE,
+    0x68A69E81, 0x49B41533,
+    0x683257AA, 0x4A581C9D,
+    0x67BD0FBC, 0x4AFB6C97,
+    0x6746C7D7, 0x4B9E038F,
+    0x66CF811F, 0x4C3FDFF3,
+    0x66573CBB, 0x4CE10034,
+    0x65DDFBD3, 0x4D8162C4,
+    0x6563BF92, 0x4E210617,
+    0x64E88926, 0x4EBFE8A4,
+    0x646C59BF, 0x4F5E08E3,
+    0x63EF328F, 0x4FFB654D,
+    0x637114CC, 0x5097FC5E,
+    0x62F201AC, 0x5133CC94,
+    0x6271FA69, 0x51CED46E,
+    0x61F1003E, 0x5269126E,
+    0x616F146B, 0x53028517,
+    0x60EC3830, 0x539B2AEF,
+    0x60686CCE, 0x5433027D,
+    0x5FE3B38D, 0x54CA0A4A,
+    0x5F5E0DB3, 0x556040E2,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5E50015D, 0x568A34A9,
+    0x5DC79D7C, 0x571DEEF9,
+    0x5D3E5236, 0x57B0D256,
+    0x5CB420DF, 0x5842DD54,
+    0x5C290ACC, 0x58D40E8C,
+    0x5B9D1153, 0x59646497,
+    0x5B1035CF, 0x59F3DE12,
+    0x5A82799A, 0x5A82799A,
+    0x59F3DE12, 0x5B1035CF,
+    0x59646497, 0x5B9D1153,
+    0x58D40E8C, 0x5C290ACC,
+    0x5842DD54, 0x5CB420DF,
+    0x57B0D256, 0x5D3E5236,
+    0x571DEEF9, 0x5DC79D7C,
+    0x568A34A9, 0x5E50015D,
+    0x55F5A4D2, 0x5ED77C89,
+    0x556040E2, 0x5F5E0DB3,
+    0x54CA0A4A, 0x5FE3B38D,
+    0x5433027D, 0x60686CCE,
+    0x539B2AEF, 0x60EC3830,
+    0x53028517, 0x616F146B,
+    0x5269126E, 0x61F1003E,
+    0x51CED46E, 0x6271FA69,
+    0x5133CC94, 0x62F201AC,
+    0x5097FC5E, 0x637114CC,
+    0x4FFB654D, 0x63EF328F,
+    0x4F5E08E3, 0x646C59BF,
+    0x4EBFE8A4, 0x64E88926,
+    0x4E210617, 0x6563BF92,
+    0x4D8162C4, 0x65DDFBD3,
+    0x4CE10034, 0x66573CBB,
+    0x4C3FDFF3, 0x66CF811F,
+    0x4B9E038F, 0x6746C7D7,
+    0x4AFB6C97, 0x67BD0FBC,
+    0x4A581C9D, 0x683257AA,
+    0x49B41533, 0x68A69E81,
+    0x490F57EE, 0x6919E320,
+    0x4869E664, 0x698C246C,
+    0x47C3C22E, 0x69FD614A,
+    0x471CECE6, 0x6A6D98A4,
+    0x46756827, 0x6ADCC964,
+    0x45CD358F, 0x6B4AF278,
+    0x452456BC, 0x6BB812D0,
+    0x447ACD50, 0x6C242960,
+    0x43D09AEC, 0x6C8F351C,
+    0x4325C135, 0x6CF934FB,
+    0x427A41D0, 0x6D6227FA,
+    0x41CE1E64, 0x6DCA0D14,
+    0x4121589A, 0x6E30E349,
+    0x4073F21D, 0x6E96A99C,
+    0x3FC5EC97, 0x6EFB5F12,
+    0x3F1749B7, 0x6F5F02B1,
+    0x3E680B2C, 0x6FC19385,
+    0x3DB832A5, 0x70231099,
+    0x3D07C1D5, 0x708378FE,
+    0x3C56BA70, 0x70E2CBC6,
+    0x3BA51E29, 0x71410804,
+    0x3AF2EEB7, 0x719E2CD2,
+    0x3A402DD1, 0x71FA3948,
+    0x398CDD32, 0x72552C84,
+    0x38D8FE93, 0x72AF05A6,
+    0x382493B0, 0x7307C3D0,
+    0x376F9E46, 0x735F6626,
+    0x36BA2013, 0x73B5EBD0,
+    0x36041AD9, 0x740B53FA,
+    0x354D9056, 0x745F9DD1,
+    0x3496824F, 0x74B2C883,
+    0x33DEF287, 0x7504D345,
+    0x3326E2C2, 0x7555BD4B,
+    0x326E54C7, 0x75A585CF,
+    0x31B54A5D, 0x75F42C0A,
+    0x30FBC54D, 0x7641AF3C,
+    0x3041C760, 0x768E0EA5,
+    0x2F875262, 0x76D94988,
+    0x2ECC681E, 0x77235F2D,
+    0x2E110A62, 0x776C4EDB,
+    0x2D553AFB, 0x77B417DF,
+    0x2C98FBBA, 0x77FAB988,
+    0x2BDC4E6F, 0x78403328,
+    0x2B1F34EB, 0x78848413,
+    0x2A61B101, 0x78C7ABA1,
+    0x29A3C484, 0x7909A92C,
+    0x28E5714A, 0x794A7C11,
+    0x2826B928, 0x798A23B1,
+    0x27679DF4, 0x79C89F6D,
+    0x26A82185, 0x7A05EEAD,
+    0x25E845B5, 0x7A4210D8,
+    0x25280C5D, 0x7A7D055B,
+    0x24677757, 0x7AB6CBA3,
+    0x23A6887E, 0x7AEF6323,
+    0x22E541AE, 0x7B26CB4F,
+    0x2223A4C5, 0x7B5D039D,
+    0x2161B39F, 0x7B920B89,
+    0x209F701C, 0x7BC5E28F,
+    0x1FDCDC1A, 0x7BF88830,
+    0x1F19F97B, 0x7C29FBEE,
+    0x1E56CA1E, 0x7C5A3D4F,
+    0x1D934FE5, 0x7C894BDD,
+    0x1CCF8CB3, 0x7CB72724,
+    0x1C0B826A, 0x7CE3CEB1,
+    0x1B4732EF, 0x7D0F4218,
+    0x1A82A025, 0x7D3980EC,
+    0x19BDCBF2, 0x7D628AC5,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x183366E8, 0x7DB0FDF7,
+    0x176DD9DE, 0x7DD6668E,
+    0x16A81305, 0x7DFA98A7,
+    0x15E21444, 0x7E1D93E9,
+    0x151BDF85, 0x7E3F57FE,
+    0x145576B1, 0x7E5FE493,
+    0x138EDBB0, 0x7E7F3956,
+    0x12C8106E, 0x7E9D55FC,
+    0x120116D4, 0x7EBA3A39,
+    0x1139F0CE, 0x7ED5E5C6,
+    0x1072A047, 0x7EF0585F,
+    0x0FAB272B, 0x7F0991C3,
+    0x0EE38765, 0x7F2191B4,
+    0x0E1BC2E3, 0x7F3857F5,
+    0x0D53DB92, 0x7F4DE450,
+    0x0C8BD35E, 0x7F62368F,
+    0x0BC3AC35, 0x7F754E7F,
+    0x0AFB6805, 0x7F872BF3,
+    0x0A3308BC, 0x7F97CEBC,
+    0x096A9049, 0x7FA736B4,
+    0x08A2009A, 0x7FB563B2,
+    0x07D95B9E, 0x7FC25596,
+    0x0710A344, 0x7FCE0C3E,
+    0x0647D97C, 0x7FD8878D,
+    0x057F0034, 0x7FE1C76B,
+    0x04B6195D, 0x7FE9CBC0,
+    0x03ED26E6, 0x7FF09477,
+    0x03242ABF, 0x7FF62182,
+    0x025B26D7, 0x7FFA72D1,
+    0x01921D1F, 0x7FFD885A,
+    0x00C90F88, 0x7FFF6216,
+    0x00000000, 0x7FFFFFFF,
+    0xFF36F078, 0x7FFF6216,
+    0xFE6DE2E0, 0x7FFD885A,
+    0xFDA4D928, 0x7FFA72D1,
+    0xFCDBD541, 0x7FF62182,
+    0xFC12D919, 0x7FF09477,
+    0xFB49E6A2, 0x7FE9CBC0,
+    0xFA80FFCB, 0x7FE1C76B,
+    0xF9B82683, 0x7FD8878D,
+    0xF8EF5CBB, 0x7FCE0C3E,
+    0xF826A461, 0x7FC25596,
+    0xF75DFF65, 0x7FB563B2,
+    0xF6956FB6, 0x7FA736B4,
+    0xF5CCF743, 0x7F97CEBC,
+    0xF50497FA, 0x7F872BF3,
+    0xF43C53CA, 0x7F754E7F,
+    0xF3742CA1, 0x7F62368F,
+    0xF2AC246D, 0x7F4DE450,
+    0xF1E43D1C, 0x7F3857F5,
+    0xF11C789A, 0x7F2191B4,
+    0xF054D8D4, 0x7F0991C3,
+    0xEF8D5FB8, 0x7EF0585F,
+    0xEEC60F31, 0x7ED5E5C6,
+    0xEDFEE92B, 0x7EBA3A39,
+    0xED37EF91, 0x7E9D55FC,
+    0xEC71244F, 0x7E7F3956,
+    0xEBAA894E, 0x7E5FE493,
+    0xEAE4207A, 0x7E3F57FE,
+    0xEA1DEBBB, 0x7E1D93E9,
+    0xE957ECFB, 0x7DFA98A7,
+    0xE8922621, 0x7DD6668E,
+    0xE7CC9917, 0x7DB0FDF7,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE642340D, 0x7D628AC5,
+    0xE57D5FDA, 0x7D3980EC,
+    0xE4B8CD10, 0x7D0F4218,
+    0xE3F47D95, 0x7CE3CEB1,
+    0xE330734C, 0x7CB72724,
+    0xE26CB01A, 0x7C894BDD,
+    0xE1A935E1, 0x7C5A3D4F,
+    0xE0E60684, 0x7C29FBEE,
+    0xE02323E5, 0x7BF88830,
+    0xDF608FE3, 0x7BC5E28F,
+    0xDE9E4C60, 0x7B920B89,
+    0xDDDC5B3A, 0x7B5D039D,
+    0xDD1ABE51, 0x7B26CB4F,
+    0xDC597781, 0x7AEF6323,
+    0xDB9888A8, 0x7AB6CBA3,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xDA17BA4A, 0x7A4210D8,
+    0xD957DE7A, 0x7A05EEAD,
+    0xD898620C, 0x79C89F6D,
+    0xD7D946D7, 0x798A23B1,
+    0xD71A8EB5, 0x794A7C11,
+    0xD65C3B7B, 0x7909A92C,
+    0xD59E4EFE, 0x78C7ABA1,
+    0xD4E0CB14, 0x78848413,
+    0xD423B190, 0x78403328,
+    0xD3670445, 0x77FAB988,
+    0xD2AAC504, 0x77B417DF,
+    0xD1EEF59E, 0x776C4EDB,
+    0xD13397E1, 0x77235F2D,
+    0xD078AD9D, 0x76D94988,
+    0xCFBE389F, 0x768E0EA5,
+    0xCF043AB2, 0x7641AF3C,
+    0xCE4AB5A2, 0x75F42C0A,
+    0xCD91AB38, 0x75A585CF,
+    0xCCD91D3D, 0x7555BD4B,
+    0xCC210D78, 0x7504D345,
+    0xCB697DB0, 0x74B2C883,
+    0xCAB26FA9, 0x745F9DD1,
+    0xC9FBE527, 0x740B53FA,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC89061BA, 0x735F6626,
+    0xC7DB6C50, 0x7307C3D0,
+    0xC727016C, 0x72AF05A6,
+    0xC67322CD, 0x72552C84,
+    0xC5BFD22E, 0x71FA3948,
+    0xC50D1148, 0x719E2CD2,
+    0xC45AE1D7, 0x71410804,
+    0xC3A9458F, 0x70E2CBC6,
+    0xC2F83E2A, 0x708378FE,
+    0xC247CD5A, 0x70231099,
+    0xC197F4D3, 0x6FC19385,
+    0xC0E8B648, 0x6F5F02B1,
+    0xC03A1368, 0x6EFB5F12,
+    0xBF8C0DE2, 0x6E96A99C,
+    0xBEDEA765, 0x6E30E349,
+    0xBE31E19B, 0x6DCA0D14,
+    0xBD85BE2F, 0x6D6227FA,
+    0xBCDA3ECA, 0x6CF934FB,
+    0xBC2F6513, 0x6C8F351C,
+    0xBB8532AF, 0x6C242960,
+    0xBADBA943, 0x6BB812D0,
+    0xBA32CA70, 0x6B4AF278,
+    0xB98A97D8, 0x6ADCC964,
+    0xB8E31319, 0x6A6D98A4,
+    0xB83C3DD1, 0x69FD614A,
+    0xB796199B, 0x698C246C,
+    0xB6F0A811, 0x6919E320,
+    0xB64BEACC, 0x68A69E81,
+    0xB5A7E362, 0x683257AA,
+    0xB5049368, 0x67BD0FBC,
+    0xB461FC70, 0x6746C7D7,
+    0xB3C0200C, 0x66CF811F,
+    0xB31EFFCB, 0x66573CBB,
+    0xB27E9D3B, 0x65DDFBD3,
+    0xB1DEF9E8, 0x6563BF92,
+    0xB140175B, 0x64E88926,
+    0xB0A1F71C, 0x646C59BF,
+    0xB0049AB2, 0x63EF328F,
+    0xAF6803A1, 0x637114CC,
+    0xAECC336B, 0x62F201AC,
+    0xAE312B91, 0x6271FA69,
+    0xAD96ED91, 0x61F1003E,
+    0xACFD7AE8, 0x616F146B,
+    0xAC64D510, 0x60EC3830,
+    0xABCCFD82, 0x60686CCE,
+    0xAB35F5B5, 0x5FE3B38D,
+    0xAA9FBF1D, 0x5F5E0DB3,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA975CB56, 0x5E50015D,
+    0xA8E21106, 0x5DC79D7C,
+    0xA84F2DA9, 0x5D3E5236,
+    0xA7BD22AB, 0x5CB420DF,
+    0xA72BF173, 0x5C290ACC,
+    0xA69B9B68, 0x5B9D1153,
+    0xA60C21ED, 0x5B1035CF,
+    0xA57D8666, 0x5A82799A,
+    0xA4EFCA31, 0x59F3DE12,
+    0xA462EEAC, 0x59646497,
+    0xA3D6F533, 0x58D40E8C,
+    0xA34BDF20, 0x5842DD54,
+    0xA2C1ADC9, 0x57B0D256,
+    0xA2386283, 0x571DEEF9,
+    0xA1AFFEA2, 0x568A34A9,
+    0xA1288376, 0x55F5A4D2,
+    0xA0A1F24C, 0x556040E2,
+    0xA01C4C72, 0x54CA0A4A,
+    0x9F979331, 0x5433027D,
+    0x9F13C7D0, 0x539B2AEF,
+    0x9E90EB94, 0x53028517,
+    0x9E0EFFC1, 0x5269126E,
+    0x9D8E0596, 0x51CED46E,
+    0x9D0DFE53, 0x5133CC94,
+    0x9C8EEB33, 0x5097FC5E,
+    0x9C10CD70, 0x4FFB654D,
+    0x9B93A640, 0x4F5E08E3,
+    0x9B1776D9, 0x4EBFE8A4,
+    0x9A9C406D, 0x4E210617,
+    0x9A22042C, 0x4D8162C4,
+    0x99A8C344, 0x4CE10034,
+    0x99307EE0, 0x4C3FDFF3,
+    0x98B93828, 0x4B9E038F,
+    0x9842F043, 0x4AFB6C97,
+    0x97CDA855, 0x4A581C9D,
+    0x9759617E, 0x49B41533,
+    0x96E61CDF, 0x490F57EE,
+    0x9673DB94, 0x4869E664,
+    0x96029EB5, 0x47C3C22E,
+    0x9592675B, 0x471CECE6,
+    0x9523369B, 0x46756827,
+    0x94B50D87, 0x45CD358F,
+    0x9447ED2F, 0x452456BC,
+    0x93DBD69F, 0x447ACD50,
+    0x9370CAE4, 0x43D09AEC,
+    0x9306CB04, 0x4325C135,
+    0x929DD805, 0x427A41D0,
+    0x9235F2EB, 0x41CE1E64,
+    0x91CF1CB6, 0x4121589A,
+    0x91695663, 0x4073F21D,
+    0x9104A0ED, 0x3FC5EC97,
+    0x90A0FD4E, 0x3F1749B7,
+    0x903E6C7A, 0x3E680B2C,
+    0x8FDCEF66, 0x3DB832A5,
+    0x8F7C8701, 0x3D07C1D5,
+    0x8F1D343A, 0x3C56BA70,
+    0x8EBEF7FB, 0x3BA51E29,
+    0x8E61D32D, 0x3AF2EEB7,
+    0x8E05C6B7, 0x3A402DD1,
+    0x8DAAD37B, 0x398CDD32,
+    0x8D50FA59, 0x38D8FE93,
+    0x8CF83C30, 0x382493B0,
+    0x8CA099D9, 0x376F9E46,
+    0x8C4A142F, 0x36BA2013,
+    0x8BF4AC05, 0x36041AD9,
+    0x8BA0622F, 0x354D9056,
+    0x8B4D377C, 0x3496824F,
+    0x8AFB2CBA, 0x33DEF287,
+    0x8AAA42B4, 0x3326E2C2,
+    0x8A5A7A30, 0x326E54C7,
+    0x8A0BD3F5, 0x31B54A5D,
+    0x89BE50C3, 0x30FBC54D,
+    0x8971F15A, 0x3041C760,
+    0x8926B677, 0x2F875262,
+    0x88DCA0D3, 0x2ECC681E,
+    0x8893B124, 0x2E110A62,
+    0x884BE820, 0x2D553AFB,
+    0x88054677, 0x2C98FBBA,
+    0x87BFCCD7, 0x2BDC4E6F,
+    0x877B7BEC, 0x2B1F34EB,
+    0x8738545E, 0x2A61B101,
+    0x86F656D3, 0x29A3C484,
+    0x86B583EE, 0x28E5714A,
+    0x8675DC4E, 0x2826B928,
+    0x86376092, 0x27679DF4,
+    0x85FA1152, 0x26A82185,
+    0x85BDEF27, 0x25E845B5,
+    0x8582FAA4, 0x25280C5D,
+    0x8549345C, 0x24677757,
+    0x85109CDC, 0x23A6887E,
+    0x84D934B0, 0x22E541AE,
+    0x84A2FC62, 0x2223A4C5,
+    0x846DF476, 0x2161B39F,
+    0x843A1D70, 0x209F701C,
+    0x840777CF, 0x1FDCDC1A,
+    0x83D60411, 0x1F19F97B,
+    0x83A5C2B0, 0x1E56CA1E,
+    0x8376B422, 0x1D934FE5,
+    0x8348D8DB, 0x1CCF8CB3,
+    0x831C314E, 0x1C0B826A,
+    0x82F0BDE8, 0x1B4732EF,
+    0x82C67F13, 0x1A82A025,
+    0x829D753A, 0x19BDCBF2,
+    0x8275A0C0, 0x18F8B83C,
+    0x824F0208, 0x183366E8,
+    0x82299971, 0x176DD9DE,
+    0x82056758, 0x16A81305,
+    0x81E26C16, 0x15E21444,
+    0x81C0A801, 0x151BDF85,
+    0x81A01B6C, 0x145576B1,
+    0x8180C6A9, 0x138EDBB0,
+    0x8162AA03, 0x12C8106E,
+    0x8145C5C6, 0x120116D4,
+    0x812A1A39, 0x1139F0CE,
+    0x810FA7A0, 0x1072A047,
+    0x80F66E3C, 0x0FAB272B,
+    0x80DE6E4C, 0x0EE38765,
+    0x80C7A80A, 0x0E1BC2E3,
+    0x80B21BAF, 0x0D53DB92,
+    0x809DC970, 0x0C8BD35E,
+    0x808AB180, 0x0BC3AC35,
+    0x8078D40D, 0x0AFB6805,
+    0x80683143, 0x0A3308BC,
+    0x8058C94C, 0x096A9049,
+    0x804A9C4D, 0x08A2009A,
+    0x803DAA69, 0x07D95B9E,
+    0x8031F3C1, 0x0710A344,
+    0x80277872, 0x0647D97C,
+    0x801E3894, 0x057F0034,
+    0x80163440, 0x04B6195D,
+    0x800F6B88, 0x03ED26E6,
+    0x8009DE7D, 0x03242ABF,
+    0x80058D2E, 0x025B26D7,
+    0x800277A5, 0x01921D1F,
+    0x80009DE9, 0x00C90F88,
+    0x80000000, 0x00000000,
+    0x80009DE9, 0xFF36F078,
+    0x800277A5, 0xFE6DE2E0,
+    0x80058D2E, 0xFDA4D928,
+    0x8009DE7D, 0xFCDBD541,
+    0x800F6B88, 0xFC12D919,
+    0x80163440, 0xFB49E6A2,
+    0x801E3894, 0xFA80FFCB,
+    0x80277872, 0xF9B82683,
+    0x8031F3C1, 0xF8EF5CBB,
+    0x803DAA69, 0xF826A461,
+    0x804A9C4D, 0xF75DFF65,
+    0x8058C94C, 0xF6956FB6,
+    0x80683143, 0xF5CCF743,
+    0x8078D40D, 0xF50497FA,
+    0x808AB180, 0xF43C53CA,
+    0x809DC970, 0xF3742CA1,
+    0x80B21BAF, 0xF2AC246D,
+    0x80C7A80A, 0xF1E43D1C,
+    0x80DE6E4C, 0xF11C789A,
+    0x80F66E3C, 0xF054D8D4,
+    0x810FA7A0, 0xEF8D5FB8,
+    0x812A1A39, 0xEEC60F31,
+    0x8145C5C6, 0xEDFEE92B,
+    0x8162AA03, 0xED37EF91,
+    0x8180C6A9, 0xEC71244F,
+    0x81A01B6C, 0xEBAA894E,
+    0x81C0A801, 0xEAE4207A,
+    0x81E26C16, 0xEA1DEBBB,
+    0x82056758, 0xE957ECFB,
+    0x82299971, 0xE8922621,
+    0x824F0208, 0xE7CC9917,
+    0x8275A0C0, 0xE70747C3,
+    0x829D753A, 0xE642340D,
+    0x82C67F13, 0xE57D5FDA,
+    0x82F0BDE8, 0xE4B8CD10,
+    0x831C314E, 0xE3F47D95,
+    0x8348D8DB, 0xE330734C,
+    0x8376B422, 0xE26CB01A,
+    0x83A5C2B0, 0xE1A935E1,
+    0x83D60411, 0xE0E60684,
+    0x840777CF, 0xE02323E5,
+    0x843A1D70, 0xDF608FE3,
+    0x846DF476, 0xDE9E4C60,
+    0x84A2FC62, 0xDDDC5B3A,
+    0x84D934B0, 0xDD1ABE51,
+    0x85109CDC, 0xDC597781,
+    0x8549345C, 0xDB9888A8,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x85BDEF27, 0xDA17BA4A,
+    0x85FA1152, 0xD957DE7A,
+    0x86376092, 0xD898620C,
+    0x8675DC4E, 0xD7D946D7,
+    0x86B583EE, 0xD71A8EB5,
+    0x86F656D3, 0xD65C3B7B,
+    0x8738545E, 0xD59E4EFE,
+    0x877B7BEC, 0xD4E0CB14,
+    0x87BFCCD7, 0xD423B190,
+    0x88054677, 0xD3670445,
+    0x884BE820, 0xD2AAC504,
+    0x8893B124, 0xD1EEF59E,
+    0x88DCA0D3, 0xD13397E1,
+    0x8926B677, 0xD078AD9D,
+    0x8971F15A, 0xCFBE389F,
+    0x89BE50C3, 0xCF043AB2,
+    0x8A0BD3F5, 0xCE4AB5A2,
+    0x8A5A7A30, 0xCD91AB38,
+    0x8AAA42B4, 0xCCD91D3D,
+    0x8AFB2CBA, 0xCC210D78,
+    0x8B4D377C, 0xCB697DB0,
+    0x8BA0622F, 0xCAB26FA9,
+    0x8BF4AC05, 0xC9FBE527,
+    0x8C4A142F, 0xC945DFEC,
+    0x8CA099D9, 0xC89061BA,
+    0x8CF83C30, 0xC7DB6C50,
+    0x8D50FA59, 0xC727016C,
+    0x8DAAD37B, 0xC67322CD,
+    0x8E05C6B7, 0xC5BFD22E,
+    0x8E61D32D, 0xC50D1148,
+    0x8EBEF7FB, 0xC45AE1D7,
+    0x8F1D343A, 0xC3A9458F,
+    0x8F7C8701, 0xC2F83E2A,
+    0x8FDCEF66, 0xC247CD5A,
+    0x903E6C7A, 0xC197F4D3,
+    0x90A0FD4E, 0xC0E8B648,
+    0x9104A0ED, 0xC03A1368,
+    0x91695663, 0xBF8C0DE2,
+    0x91CF1CB6, 0xBEDEA765,
+    0x9235F2EB, 0xBE31E19B,
+    0x929DD805, 0xBD85BE2F,
+    0x9306CB04, 0xBCDA3ECA,
+    0x9370CAE4, 0xBC2F6513,
+    0x93DBD69F, 0xBB8532AF,
+    0x9447ED2F, 0xBADBA943,
+    0x94B50D87, 0xBA32CA70,
+    0x9523369B, 0xB98A97D8,
+    0x9592675B, 0xB8E31319,
+    0x96029EB5, 0xB83C3DD1,
+    0x9673DB94, 0xB796199B,
+    0x96E61CDF, 0xB6F0A811,
+    0x9759617E, 0xB64BEACC,
+    0x97CDA855, 0xB5A7E362,
+    0x9842F043, 0xB5049368,
+    0x98B93828, 0xB461FC70,
+    0x99307EE0, 0xB3C0200C,
+    0x99A8C344, 0xB31EFFCB,
+    0x9A22042C, 0xB27E9D3B,
+    0x9A9C406D, 0xB1DEF9E8,
+    0x9B1776D9, 0xB140175B,
+    0x9B93A640, 0xB0A1F71C,
+    0x9C10CD70, 0xB0049AB2,
+    0x9C8EEB33, 0xAF6803A1,
+    0x9D0DFE53, 0xAECC336B,
+    0x9D8E0596, 0xAE312B91,
+    0x9E0EFFC1, 0xAD96ED91,
+    0x9E90EB94, 0xACFD7AE8,
+    0x9F13C7D0, 0xAC64D510,
+    0x9F979331, 0xABCCFD82,
+    0xA01C4C72, 0xAB35F5B5,
+    0xA0A1F24C, 0xAA9FBF1D,
+    0xA1288376, 0xAA0A5B2D,
+    0xA1AFFEA2, 0xA975CB56,
+    0xA2386283, 0xA8E21106,
+    0xA2C1ADC9, 0xA84F2DA9,
+    0xA34BDF20, 0xA7BD22AB,
+    0xA3D6F533, 0xA72BF173,
+    0xA462EEAC, 0xA69B9B68,
+    0xA4EFCA31, 0xA60C21ED,
+    0xA57D8666, 0xA57D8666,
+    0xA60C21ED, 0xA4EFCA31,
+    0xA69B9B68, 0xA462EEAC,
+    0xA72BF173, 0xA3D6F533,
+    0xA7BD22AB, 0xA34BDF20,
+    0xA84F2DA9, 0xA2C1ADC9,
+    0xA8E21106, 0xA2386283,
+    0xA975CB56, 0xA1AFFEA2,
+    0xAA0A5B2D, 0xA1288376,
+    0xAA9FBF1D, 0xA0A1F24C,
+    0xAB35F5B5, 0xA01C4C72,
+    0xABCCFD82, 0x9F979331,
+    0xAC64D510, 0x9F13C7D0,
+    0xACFD7AE8, 0x9E90EB94,
+    0xAD96ED91, 0x9E0EFFC1,
+    0xAE312B91, 0x9D8E0596,
+    0xAECC336B, 0x9D0DFE53,
+    0xAF6803A1, 0x9C8EEB33,
+    0xB0049AB2, 0x9C10CD70,
+    0xB0A1F71C, 0x9B93A640,
+    0xB140175B, 0x9B1776D9,
+    0xB1DEF9E8, 0x9A9C406D,
+    0xB27E9D3B, 0x9A22042C,
+    0xB31EFFCB, 0x99A8C344,
+    0xB3C0200C, 0x99307EE0,
+    0xB461FC70, 0x98B93828,
+    0xB5049368, 0x9842F043,
+    0xB5A7E362, 0x97CDA855,
+    0xB64BEACC, 0x9759617E,
+    0xB6F0A811, 0x96E61CDF,
+    0xB796199B, 0x9673DB94,
+    0xB83C3DD1, 0x96029EB5,
+    0xB8E31319, 0x9592675B,
+    0xB98A97D8, 0x9523369B,
+    0xBA32CA70, 0x94B50D87,
+    0xBADBA943, 0x9447ED2F,
+    0xBB8532AF, 0x93DBD69F,
+    0xBC2F6513, 0x9370CAE4,
+    0xBCDA3ECA, 0x9306CB04,
+    0xBD85BE2F, 0x929DD805,
+    0xBE31E19B, 0x9235F2EB,
+    0xBEDEA765, 0x91CF1CB6,
+    0xBF8C0DE2, 0x91695663,
+    0xC03A1368, 0x9104A0ED,
+    0xC0E8B648, 0x90A0FD4E,
+    0xC197F4D3, 0x903E6C7A,
+    0xC247CD5A, 0x8FDCEF66,
+    0xC2F83E2A, 0x8F7C8701,
+    0xC3A9458F, 0x8F1D343A,
+    0xC45AE1D7, 0x8EBEF7FB,
+    0xC50D1148, 0x8E61D32D,
+    0xC5BFD22E, 0x8E05C6B7,
+    0xC67322CD, 0x8DAAD37B,
+    0xC727016C, 0x8D50FA59,
+    0xC7DB6C50, 0x8CF83C30,
+    0xC89061BA, 0x8CA099D9,
+    0xC945DFEC, 0x8C4A142F,
+    0xC9FBE527, 0x8BF4AC05,
+    0xCAB26FA9, 0x8BA0622F,
+    0xCB697DB0, 0x8B4D377C,
+    0xCC210D78, 0x8AFB2CBA,
+    0xCCD91D3D, 0x8AAA42B4,
+    0xCD91AB38, 0x8A5A7A30,
+    0xCE4AB5A2, 0x8A0BD3F5,
+    0xCF043AB2, 0x89BE50C3,
+    0xCFBE389F, 0x8971F15A,
+    0xD078AD9D, 0x8926B677,
+    0xD13397E1, 0x88DCA0D3,
+    0xD1EEF59E, 0x8893B124,
+    0xD2AAC504, 0x884BE820,
+    0xD3670445, 0x88054677,
+    0xD423B190, 0x87BFCCD7,
+    0xD4E0CB14, 0x877B7BEC,
+    0xD59E4EFE, 0x8738545E,
+    0xD65C3B7B, 0x86F656D3,
+    0xD71A8EB5, 0x86B583EE,
+    0xD7D946D7, 0x8675DC4E,
+    0xD898620C, 0x86376092,
+    0xD957DE7A, 0x85FA1152,
+    0xDA17BA4A, 0x85BDEF27,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xDB9888A8, 0x8549345C,
+    0xDC597781, 0x85109CDC,
+    0xDD1ABE51, 0x84D934B0,
+    0xDDDC5B3A, 0x84A2FC62,
+    0xDE9E4C60, 0x846DF476,
+    0xDF608FE3, 0x843A1D70,
+    0xE02323E5, 0x840777CF,
+    0xE0E60684, 0x83D60411,
+    0xE1A935E1, 0x83A5C2B0,
+    0xE26CB01A, 0x8376B422,
+    0xE330734C, 0x8348D8DB,
+    0xE3F47D95, 0x831C314E,
+    0xE4B8CD10, 0x82F0BDE8,
+    0xE57D5FDA, 0x82C67F13,
+    0xE642340D, 0x829D753A,
+    0xE70747C3, 0x8275A0C0,
+    0xE7CC9917, 0x824F0208,
+    0xE8922621, 0x82299971,
+    0xE957ECFB, 0x82056758,
+    0xEA1DEBBB, 0x81E26C16,
+    0xEAE4207A, 0x81C0A801,
+    0xEBAA894E, 0x81A01B6C,
+    0xEC71244F, 0x8180C6A9,
+    0xED37EF91, 0x8162AA03,
+    0xEDFEE92B, 0x8145C5C6,
+    0xEEC60F31, 0x812A1A39,
+    0xEF8D5FB8, 0x810FA7A0,
+    0xF054D8D4, 0x80F66E3C,
+    0xF11C789A, 0x80DE6E4C,
+    0xF1E43D1C, 0x80C7A80A,
+    0xF2AC246D, 0x80B21BAF,
+    0xF3742CA1, 0x809DC970,
+    0xF43C53CA, 0x808AB180,
+    0xF50497FA, 0x8078D40D,
+    0xF5CCF743, 0x80683143,
+    0xF6956FB6, 0x8058C94C,
+    0xF75DFF65, 0x804A9C4D,
+    0xF826A461, 0x803DAA69,
+    0xF8EF5CBB, 0x8031F3C1,
+    0xF9B82683, 0x80277872,
+    0xFA80FFCB, 0x801E3894,
+    0xFB49E6A2, 0x80163440,
+    0xFC12D919, 0x800F6B88,
+    0xFCDBD541, 0x8009DE7D,
+    0xFDA4D928, 0x80058D2E,
+    0xFE6DE2E0, 0x800277A5,
+    0xFF36F078, 0x80009DE9
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 2048	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_2048_q31[3072] = {
+    0x7FFFFFFF, 0x00000000,
+    0x7FFFD885, 0x006487E3,
+    0x7FFF6216, 0x00C90F88,
+    0x7FFE9CB2, 0x012D96B0,
+    0x7FFD885A, 0x01921D1F,
+    0x7FFC250F, 0x01F6A296,
+    0x7FFA72D1, 0x025B26D7,
+    0x7FF871A1, 0x02BFA9A4,
+    0x7FF62182, 0x03242ABF,
+    0x7FF38273, 0x0388A9E9,
+    0x7FF09477, 0x03ED26E6,
+    0x7FED5790, 0x0451A176,
+    0x7FE9CBC0, 0x04B6195D,
+    0x7FE5F108, 0x051A8E5C,
+    0x7FE1C76B, 0x057F0034,
+    0x7FDD4EEC, 0x05E36EA9,
+    0x7FD8878D, 0x0647D97C,
+    0x7FD37152, 0x06AC406F,
+    0x7FCE0C3E, 0x0710A344,
+    0x7FC85853, 0x077501BE,
+    0x7FC25596, 0x07D95B9E,
+    0x7FBC040A, 0x083DB0A7,
+    0x7FB563B2, 0x08A2009A,
+    0x7FAE7494, 0x09064B3A,
+    0x7FA736B4, 0x096A9049,
+    0x7F9FAA15, 0x09CECF89,
+    0x7F97CEBC, 0x0A3308BC,
+    0x7F8FA4AF, 0x0A973BA5,
+    0x7F872BF3, 0x0AFB6805,
+    0x7F7E648B, 0x0B5F8D9F,
+    0x7F754E7F, 0x0BC3AC35,
+    0x7F6BE9D4, 0x0C27C389,
+    0x7F62368F, 0x0C8BD35E,
+    0x7F5834B6, 0x0CEFDB75,
+    0x7F4DE450, 0x0D53DB92,
+    0x7F434563, 0x0DB7D376,
+    0x7F3857F5, 0x0E1BC2E3,
+    0x7F2D1C0E, 0x0E7FA99D,
+    0x7F2191B4, 0x0EE38765,
+    0x7F15B8EE, 0x0F475BFE,
+    0x7F0991C3, 0x0FAB272B,
+    0x7EFD1C3C, 0x100EE8AD,
+    0x7EF0585F, 0x1072A047,
+    0x7EE34635, 0x10D64DBC,
+    0x7ED5E5C6, 0x1139F0CE,
+    0x7EC8371A, 0x119D8940,
+    0x7EBA3A39, 0x120116D4,
+    0x7EABEF2C, 0x1264994E,
+    0x7E9D55FC, 0x12C8106E,
+    0x7E8E6EB1, 0x132B7BF9,
+    0x7E7F3956, 0x138EDBB0,
+    0x7E6FB5F3, 0x13F22F57,
+    0x7E5FE493, 0x145576B1,
+    0x7E4FC53E, 0x14B8B17F,
+    0x7E3F57FE, 0x151BDF85,
+    0x7E2E9CDF, 0x157F0086,
+    0x7E1D93E9, 0x15E21444,
+    0x7E0C3D29, 0x16451A83,
+    0x7DFA98A7, 0x16A81305,
+    0x7DE8A670, 0x170AFD8D,
+    0x7DD6668E, 0x176DD9DE,
+    0x7DC3D90D, 0x17D0A7BB,
+    0x7DB0FDF7, 0x183366E8,
+    0x7D9DD55A, 0x18961727,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7D769BB5, 0x195B49E9,
+    0x7D628AC5, 0x19BDCBF2,
+    0x7D4E2C7E, 0x1A203E1B,
+    0x7D3980EC, 0x1A82A025,
+    0x7D24881A, 0x1AE4F1D6,
+    0x7D0F4218, 0x1B4732EF,
+    0x7CF9AEF0, 0x1BA96334,
+    0x7CE3CEB1, 0x1C0B826A,
+    0x7CCDA168, 0x1C6D9053,
+    0x7CB72724, 0x1CCF8CB3,
+    0x7CA05FF1, 0x1D31774D,
+    0x7C894BDD, 0x1D934FE5,
+    0x7C71EAF8, 0x1DF5163F,
+    0x7C5A3D4F, 0x1E56CA1E,
+    0x7C4242F2, 0x1EB86B46,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7C116853, 0x1F7B7480,
+    0x7BF88830, 0x1FDCDC1A,
+    0x7BDF5B94, 0x203E300D,
+    0x7BC5E28F, 0x209F701C,
+    0x7BAC1D31, 0x21009C0B,
+    0x7B920B89, 0x2161B39F,
+    0x7B77ADA8, 0x21C2B69C,
+    0x7B5D039D, 0x2223A4C5,
+    0x7B420D7A, 0x22847DDF,
+    0x7B26CB4F, 0x22E541AE,
+    0x7B0B3D2C, 0x2345EFF7,
+    0x7AEF6323, 0x23A6887E,
+    0x7AD33D45, 0x24070B07,
+    0x7AB6CBA3, 0x24677757,
+    0x7A9A0E4F, 0x24C7CD32,
+    0x7A7D055B, 0x25280C5D,
+    0x7A5FB0D8, 0x2588349D,
+    0x7A4210D8, 0x25E845B5,
+    0x7A24256E, 0x26483F6C,
+    0x7A05EEAD, 0x26A82185,
+    0x79E76CA6, 0x2707EBC6,
+    0x79C89F6D, 0x27679DF4,
+    0x79A98715, 0x27C737D2,
+    0x798A23B1, 0x2826B928,
+    0x796A7554, 0x288621B9,
+    0x794A7C11, 0x28E5714A,
+    0x792A37FE, 0x2944A7A2,
+    0x7909A92C, 0x29A3C484,
+    0x78E8CFB1, 0x2A02C7B8,
+    0x78C7ABA1, 0x2A61B101,
+    0x78A63D10, 0x2AC08025,
+    0x78848413, 0x2B1F34EB,
+    0x786280BF, 0x2B7DCF17,
+    0x78403328, 0x2BDC4E6F,
+    0x781D9B64, 0x2C3AB2B9,
+    0x77FAB988, 0x2C98FBBA,
+    0x77D78DAA, 0x2CF72939,
+    0x77B417DF, 0x2D553AFB,
+    0x7790583D, 0x2DB330C7,
+    0x776C4EDB, 0x2E110A62,
+    0x7747FBCE, 0x2E6EC792,
+    0x77235F2D, 0x2ECC681E,
+    0x76FE790E, 0x2F29EBCC,
+    0x76D94988, 0x2F875262,
+    0x76B3D0B3, 0x2FE49BA6,
+    0x768E0EA5, 0x3041C760,
+    0x76680376, 0x309ED555,
+    0x7641AF3C, 0x30FBC54D,
+    0x761B1211, 0x3158970D,
+    0x75F42C0A, 0x31B54A5D,
+    0x75CCFD42, 0x3211DF03,
+    0x75A585CF, 0x326E54C7,
+    0x757DC5CA, 0x32CAAB6F,
+    0x7555BD4B, 0x3326E2C2,
+    0x752D6C6C, 0x3382FA88,
+    0x7504D345, 0x33DEF287,
+    0x74DBF1EF, 0x343ACA87,
+    0x74B2C883, 0x3496824F,
+    0x7489571B, 0x34F219A7,
+    0x745F9DD1, 0x354D9056,
+    0x74359CBD, 0x35A8E624,
+    0x740B53FA, 0x36041AD9,
+    0x73E0C3A3, 0x365F2E3B,
+    0x73B5EBD0, 0x36BA2013,
+    0x738ACC9E, 0x3714F02A,
+    0x735F6626, 0x376F9E46,
+    0x7333B883, 0x37CA2A30,
+    0x7307C3D0, 0x382493B0,
+    0x72DB8828, 0x387EDA8E,
+    0x72AF05A6, 0x38D8FE93,
+    0x72823C66, 0x3932FF87,
+    0x72552C84, 0x398CDD32,
+    0x7227D61C, 0x39E6975D,
+    0x71FA3948, 0x3A402DD1,
+    0x71CC5626, 0x3A99A057,
+    0x719E2CD2, 0x3AF2EEB7,
+    0x716FBD68, 0x3B4C18BA,
+    0x71410804, 0x3BA51E29,
+    0x71120CC5, 0x3BFDFECD,
+    0x70E2CBC6, 0x3C56BA70,
+    0x70B34524, 0x3CAF50DA,
+    0x708378FE, 0x3D07C1D5,
+    0x70536771, 0x3D600D2B,
+    0x70231099, 0x3DB832A5,
+    0x6FF27496, 0x3E10320D,
+    0x6FC19385, 0x3E680B2C,
+    0x6F906D84, 0x3EBFBDCC,
+    0x6F5F02B1, 0x3F1749B7,
+    0x6F2D532C, 0x3F6EAEB8,
+    0x6EFB5F12, 0x3FC5EC97,
+    0x6EC92682, 0x401D0320,
+    0x6E96A99C, 0x4073F21D,
+    0x6E63E87F, 0x40CAB957,
+    0x6E30E349, 0x4121589A,
+    0x6DFD9A1B, 0x4177CFB0,
+    0x6DCA0D14, 0x41CE1E64,
+    0x6D963C54, 0x42244480,
+    0x6D6227FA, 0x427A41D0,
+    0x6D2DD027, 0x42D0161E,
+    0x6CF934FB, 0x4325C135,
+    0x6CC45697, 0x437B42E1,
+    0x6C8F351C, 0x43D09AEC,
+    0x6C59D0A9, 0x4425C923,
+    0x6C242960, 0x447ACD50,
+    0x6BEE3F62, 0x44CFA73F,
+    0x6BB812D0, 0x452456BC,
+    0x6B81A3CD, 0x4578DB93,
+    0x6B4AF278, 0x45CD358F,
+    0x6B13FEF5, 0x4621647C,
+    0x6ADCC964, 0x46756827,
+    0x6AA551E8, 0x46C9405C,
+    0x6A6D98A4, 0x471CECE6,
+    0x6A359DB9, 0x47706D93,
+    0x69FD614A, 0x47C3C22E,
+    0x69C4E37A, 0x4816EA85,
+    0x698C246C, 0x4869E664,
+    0x69532442, 0x48BCB598,
+    0x6919E320, 0x490F57EE,
+    0x68E06129, 0x4961CD32,
+    0x68A69E81, 0x49B41533,
+    0x686C9B4B, 0x4A062FBD,
+    0x683257AA, 0x4A581C9D,
+    0x67F7D3C4, 0x4AA9DBA1,
+    0x67BD0FBC, 0x4AFB6C97,
+    0x67820BB6, 0x4B4CCF4D,
+    0x6746C7D7, 0x4B9E038F,
+    0x670B4443, 0x4BEF092D,
+    0x66CF811F, 0x4C3FDFF3,
+    0x66937E90, 0x4C9087B1,
+    0x66573CBB, 0x4CE10034,
+    0x661ABBC5, 0x4D31494B,
+    0x65DDFBD3, 0x4D8162C4,
+    0x65A0FD0B, 0x4DD14C6E,
+    0x6563BF92, 0x4E210617,
+    0x6526438E, 0x4E708F8F,
+    0x64E88926, 0x4EBFE8A4,
+    0x64AA907F, 0x4F0F1126,
+    0x646C59BF, 0x4F5E08E3,
+    0x642DE50D, 0x4FACCFAB,
+    0x63EF328F, 0x4FFB654D,
+    0x63B0426D, 0x5049C999,
+    0x637114CC, 0x5097FC5E,
+    0x6331A9D4, 0x50E5FD6C,
+    0x62F201AC, 0x5133CC94,
+    0x62B21C7B, 0x518169A4,
+    0x6271FA69, 0x51CED46E,
+    0x62319B9D, 0x521C0CC1,
+    0x61F1003E, 0x5269126E,
+    0x61B02876, 0x52B5E545,
+    0x616F146B, 0x53028517,
+    0x612DC446, 0x534EF1B5,
+    0x60EC3830, 0x539B2AEF,
+    0x60AA704F, 0x53E73097,
+    0x60686CCE, 0x5433027D,
+    0x60262DD5, 0x547EA073,
+    0x5FE3B38D, 0x54CA0A4A,
+    0x5FA0FE1E, 0x55153FD4,
+    0x5F5E0DB3, 0x556040E2,
+    0x5F1AE273, 0x55AB0D46,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5E93DC1F, 0x56400757,
+    0x5E50015D, 0x568A34A9,
+    0x5E0BEC6E, 0x56D42C99,
+    0x5DC79D7C, 0x571DEEF9,
+    0x5D8314B0, 0x57677B9D,
+    0x5D3E5236, 0x57B0D256,
+    0x5CF95638, 0x57F9F2F7,
+    0x5CB420DF, 0x5842DD54,
+    0x5C6EB258, 0x588B913F,
+    0x5C290ACC, 0x58D40E8C,
+    0x5BE32A67, 0x591C550E,
+    0x5B9D1153, 0x59646497,
+    0x5B56BFBD, 0x59AC3CFD,
+    0x5B1035CF, 0x59F3DE12,
+    0x5AC973B4, 0x5A3B47AA,
+    0x5A82799A, 0x5A82799A,
+    0x5A3B47AA, 0x5AC973B4,
+    0x59F3DE12, 0x5B1035CF,
+    0x59AC3CFD, 0x5B56BFBD,
+    0x59646497, 0x5B9D1153,
+    0x591C550E, 0x5BE32A67,
+    0x58D40E8C, 0x5C290ACC,
+    0x588B913F, 0x5C6EB258,
+    0x5842DD54, 0x5CB420DF,
+    0x57F9F2F7, 0x5CF95638,
+    0x57B0D256, 0x5D3E5236,
+    0x57677B9D, 0x5D8314B0,
+    0x571DEEF9, 0x5DC79D7C,
+    0x56D42C99, 0x5E0BEC6E,
+    0x568A34A9, 0x5E50015D,
+    0x56400757, 0x5E93DC1F,
+    0x55F5A4D2, 0x5ED77C89,
+    0x55AB0D46, 0x5F1AE273,
+    0x556040E2, 0x5F5E0DB3,
+    0x55153FD4, 0x5FA0FE1E,
+    0x54CA0A4A, 0x5FE3B38D,
+    0x547EA073, 0x60262DD5,
+    0x5433027D, 0x60686CCE,
+    0x53E73097, 0x60AA704F,
+    0x539B2AEF, 0x60EC3830,
+    0x534EF1B5, 0x612DC446,
+    0x53028517, 0x616F146B,
+    0x52B5E545, 0x61B02876,
+    0x5269126E, 0x61F1003E,
+    0x521C0CC1, 0x62319B9D,
+    0x51CED46E, 0x6271FA69,
+    0x518169A4, 0x62B21C7B,
+    0x5133CC94, 0x62F201AC,
+    0x50E5FD6C, 0x6331A9D4,
+    0x5097FC5E, 0x637114CC,
+    0x5049C999, 0x63B0426D,
+    0x4FFB654D, 0x63EF328F,
+    0x4FACCFAB, 0x642DE50D,
+    0x4F5E08E3, 0x646C59BF,
+    0x4F0F1126, 0x64AA907F,
+    0x4EBFE8A4, 0x64E88926,
+    0x4E708F8F, 0x6526438E,
+    0x4E210617, 0x6563BF92,
+    0x4DD14C6E, 0x65A0FD0B,
+    0x4D8162C4, 0x65DDFBD3,
+    0x4D31494B, 0x661ABBC5,
+    0x4CE10034, 0x66573CBB,
+    0x4C9087B1, 0x66937E90,
+    0x4C3FDFF3, 0x66CF811F,
+    0x4BEF092D, 0x670B4443,
+    0x4B9E038F, 0x6746C7D7,
+    0x4B4CCF4D, 0x67820BB6,
+    0x4AFB6C97, 0x67BD0FBC,
+    0x4AA9DBA1, 0x67F7D3C4,
+    0x4A581C9D, 0x683257AA,
+    0x4A062FBD, 0x686C9B4B,
+    0x49B41533, 0x68A69E81,
+    0x4961CD32, 0x68E06129,
+    0x490F57EE, 0x6919E320,
+    0x48BCB598, 0x69532442,
+    0x4869E664, 0x698C246C,
+    0x4816EA85, 0x69C4E37A,
+    0x47C3C22E, 0x69FD614A,
+    0x47706D93, 0x6A359DB9,
+    0x471CECE6, 0x6A6D98A4,
+    0x46C9405C, 0x6AA551E8,
+    0x46756827, 0x6ADCC964,
+    0x4621647C, 0x6B13FEF5,
+    0x45CD358F, 0x6B4AF278,
+    0x4578DB93, 0x6B81A3CD,
+    0x452456BC, 0x6BB812D0,
+    0x44CFA73F, 0x6BEE3F62,
+    0x447ACD50, 0x6C242960,
+    0x4425C923, 0x6C59D0A9,
+    0x43D09AEC, 0x6C8F351C,
+    0x437B42E1, 0x6CC45697,
+    0x4325C135, 0x6CF934FB,
+    0x42D0161E, 0x6D2DD027,
+    0x427A41D0, 0x6D6227FA,
+    0x42244480, 0x6D963C54,
+    0x41CE1E64, 0x6DCA0D14,
+    0x4177CFB0, 0x6DFD9A1B,
+    0x4121589A, 0x6E30E349,
+    0x40CAB957, 0x6E63E87F,
+    0x4073F21D, 0x6E96A99C,
+    0x401D0320, 0x6EC92682,
+    0x3FC5EC97, 0x6EFB5F12,
+    0x3F6EAEB8, 0x6F2D532C,
+    0x3F1749B7, 0x6F5F02B1,
+    0x3EBFBDCC, 0x6F906D84,
+    0x3E680B2C, 0x6FC19385,
+    0x3E10320D, 0x6FF27496,
+    0x3DB832A5, 0x70231099,
+    0x3D600D2B, 0x70536771,
+    0x3D07C1D5, 0x708378FE,
+    0x3CAF50DA, 0x70B34524,
+    0x3C56BA70, 0x70E2CBC6,
+    0x3BFDFECD, 0x71120CC5,
+    0x3BA51E29, 0x71410804,
+    0x3B4C18BA, 0x716FBD68,
+    0x3AF2EEB7, 0x719E2CD2,
+    0x3A99A057, 0x71CC5626,
+    0x3A402DD1, 0x71FA3948,
+    0x39E6975D, 0x7227D61C,
+    0x398CDD32, 0x72552C84,
+    0x3932FF87, 0x72823C66,
+    0x38D8FE93, 0x72AF05A6,
+    0x387EDA8E, 0x72DB8828,
+    0x382493B0, 0x7307C3D0,
+    0x37CA2A30, 0x7333B883,
+    0x376F9E46, 0x735F6626,
+    0x3714F02A, 0x738ACC9E,
+    0x36BA2013, 0x73B5EBD0,
+    0x365F2E3B, 0x73E0C3A3,
+    0x36041AD9, 0x740B53FA,
+    0x35A8E624, 0x74359CBD,
+    0x354D9056, 0x745F9DD1,
+    0x34F219A7, 0x7489571B,
+    0x3496824F, 0x74B2C883,
+    0x343ACA87, 0x74DBF1EF,
+    0x33DEF287, 0x7504D345,
+    0x3382FA88, 0x752D6C6C,
+    0x3326E2C2, 0x7555BD4B,
+    0x32CAAB6F, 0x757DC5CA,
+    0x326E54C7, 0x75A585CF,
+    0x3211DF03, 0x75CCFD42,
+    0x31B54A5D, 0x75F42C0A,
+    0x3158970D, 0x761B1211,
+    0x30FBC54D, 0x7641AF3C,
+    0x309ED555, 0x76680376,
+    0x3041C760, 0x768E0EA5,
+    0x2FE49BA6, 0x76B3D0B3,
+    0x2F875262, 0x76D94988,
+    0x2F29EBCC, 0x76FE790E,
+    0x2ECC681E, 0x77235F2D,
+    0x2E6EC792, 0x7747FBCE,
+    0x2E110A62, 0x776C4EDB,
+    0x2DB330C7, 0x7790583D,
+    0x2D553AFB, 0x77B417DF,
+    0x2CF72939, 0x77D78DAA,
+    0x2C98FBBA, 0x77FAB988,
+    0x2C3AB2B9, 0x781D9B64,
+    0x2BDC4E6F, 0x78403328,
+    0x2B7DCF17, 0x786280BF,
+    0x2B1F34EB, 0x78848413,
+    0x2AC08025, 0x78A63D10,
+    0x2A61B101, 0x78C7ABA1,
+    0x2A02C7B8, 0x78E8CFB1,
+    0x29A3C484, 0x7909A92C,
+    0x2944A7A2, 0x792A37FE,
+    0x28E5714A, 0x794A7C11,
+    0x288621B9, 0x796A7554,
+    0x2826B928, 0x798A23B1,
+    0x27C737D2, 0x79A98715,
+    0x27679DF4, 0x79C89F6D,
+    0x2707EBC6, 0x79E76CA6,
+    0x26A82185, 0x7A05EEAD,
+    0x26483F6C, 0x7A24256E,
+    0x25E845B5, 0x7A4210D8,
+    0x2588349D, 0x7A5FB0D8,
+    0x25280C5D, 0x7A7D055B,
+    0x24C7CD32, 0x7A9A0E4F,
+    0x24677757, 0x7AB6CBA3,
+    0x24070B07, 0x7AD33D45,
+    0x23A6887E, 0x7AEF6323,
+    0x2345EFF7, 0x7B0B3D2C,
+    0x22E541AE, 0x7B26CB4F,
+    0x22847DDF, 0x7B420D7A,
+    0x2223A4C5, 0x7B5D039D,
+    0x21C2B69C, 0x7B77ADA8,
+    0x2161B39F, 0x7B920B89,
+    0x21009C0B, 0x7BAC1D31,
+    0x209F701C, 0x7BC5E28F,
+    0x203E300D, 0x7BDF5B94,
+    0x1FDCDC1A, 0x7BF88830,
+    0x1F7B7480, 0x7C116853,
+    0x1F19F97B, 0x7C29FBEE,
+    0x1EB86B46, 0x7C4242F2,
+    0x1E56CA1E, 0x7C5A3D4F,
+    0x1DF5163F, 0x7C71EAF8,
+    0x1D934FE5, 0x7C894BDD,
+    0x1D31774D, 0x7CA05FF1,
+    0x1CCF8CB3, 0x7CB72724,
+    0x1C6D9053, 0x7CCDA168,
+    0x1C0B826A, 0x7CE3CEB1,
+    0x1BA96334, 0x7CF9AEF0,
+    0x1B4732EF, 0x7D0F4218,
+    0x1AE4F1D6, 0x7D24881A,
+    0x1A82A025, 0x7D3980EC,
+    0x1A203E1B, 0x7D4E2C7E,
+    0x19BDCBF2, 0x7D628AC5,
+    0x195B49E9, 0x7D769BB5,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x18961727, 0x7D9DD55A,
+    0x183366E8, 0x7DB0FDF7,
+    0x17D0A7BB, 0x7DC3D90D,
+    0x176DD9DE, 0x7DD6668E,
+    0x170AFD8D, 0x7DE8A670,
+    0x16A81305, 0x7DFA98A7,
+    0x16451A83, 0x7E0C3D29,
+    0x15E21444, 0x7E1D93E9,
+    0x157F0086, 0x7E2E9CDF,
+    0x151BDF85, 0x7E3F57FE,
+    0x14B8B17F, 0x7E4FC53E,
+    0x145576B1, 0x7E5FE493,
+    0x13F22F57, 0x7E6FB5F3,
+    0x138EDBB0, 0x7E7F3956,
+    0x132B7BF9, 0x7E8E6EB1,
+    0x12C8106E, 0x7E9D55FC,
+    0x1264994E, 0x7EABEF2C,
+    0x120116D4, 0x7EBA3A39,
+    0x119D8940, 0x7EC8371A,
+    0x1139F0CE, 0x7ED5E5C6,
+    0x10D64DBC, 0x7EE34635,
+    0x1072A047, 0x7EF0585F,
+    0x100EE8AD, 0x7EFD1C3C,
+    0x0FAB272B, 0x7F0991C3,
+    0x0F475BFE, 0x7F15B8EE,
+    0x0EE38765, 0x7F2191B4,
+    0x0E7FA99D, 0x7F2D1C0E,
+    0x0E1BC2E3, 0x7F3857F5,
+    0x0DB7D376, 0x7F434563,
+    0x0D53DB92, 0x7F4DE450,
+    0x0CEFDB75, 0x7F5834B6,
+    0x0C8BD35E, 0x7F62368F,
+    0x0C27C389, 0x7F6BE9D4,
+    0x0BC3AC35, 0x7F754E7F,
+    0x0B5F8D9F, 0x7F7E648B,
+    0x0AFB6805, 0x7F872BF3,
+    0x0A973BA5, 0x7F8FA4AF,
+    0x0A3308BC, 0x7F97CEBC,
+    0x09CECF89, 0x7F9FAA15,
+    0x096A9049, 0x7FA736B4,
+    0x09064B3A, 0x7FAE7494,
+    0x08A2009A, 0x7FB563B2,
+    0x083DB0A7, 0x7FBC040A,
+    0x07D95B9E, 0x7FC25596,
+    0x077501BE, 0x7FC85853,
+    0x0710A344, 0x7FCE0C3E,
+    0x06AC406F, 0x7FD37152,
+    0x0647D97C, 0x7FD8878D,
+    0x05E36EA9, 0x7FDD4EEC,
+    0x057F0034, 0x7FE1C76B,
+    0x051A8E5C, 0x7FE5F108,
+    0x04B6195D, 0x7FE9CBC0,
+    0x0451A176, 0x7FED5790,
+    0x03ED26E6, 0x7FF09477,
+    0x0388A9E9, 0x7FF38273,
+    0x03242ABF, 0x7FF62182,
+    0x02BFA9A4, 0x7FF871A1,
+    0x025B26D7, 0x7FFA72D1,
+    0x01F6A296, 0x7FFC250F,
+    0x01921D1F, 0x7FFD885A,
+    0x012D96B0, 0x7FFE9CB2,
+    0x00C90F88, 0x7FFF6216,
+    0x006487E3, 0x7FFFD885,
+    0x00000000, 0x7FFFFFFF,
+    0xFF9B781D, 0x7FFFD885,
+    0xFF36F078, 0x7FFF6216,
+    0xFED2694F, 0x7FFE9CB2,
+    0xFE6DE2E0, 0x7FFD885A,
+    0xFE095D69, 0x7FFC250F,
+    0xFDA4D928, 0x7FFA72D1,
+    0xFD40565B, 0x7FF871A1,
+    0xFCDBD541, 0x7FF62182,
+    0xFC775616, 0x7FF38273,
+    0xFC12D919, 0x7FF09477,
+    0xFBAE5E89, 0x7FED5790,
+    0xFB49E6A2, 0x7FE9CBC0,
+    0xFAE571A4, 0x7FE5F108,
+    0xFA80FFCB, 0x7FE1C76B,
+    0xFA1C9156, 0x7FDD4EEC,
+    0xF9B82683, 0x7FD8878D,
+    0xF953BF90, 0x7FD37152,
+    0xF8EF5CBB, 0x7FCE0C3E,
+    0xF88AFE41, 0x7FC85853,
+    0xF826A461, 0x7FC25596,
+    0xF7C24F58, 0x7FBC040A,
+    0xF75DFF65, 0x7FB563B2,
+    0xF6F9B4C5, 0x7FAE7494,
+    0xF6956FB6, 0x7FA736B4,
+    0xF6313076, 0x7F9FAA15,
+    0xF5CCF743, 0x7F97CEBC,
+    0xF568C45A, 0x7F8FA4AF,
+    0xF50497FA, 0x7F872BF3,
+    0xF4A07260, 0x7F7E648B,
+    0xF43C53CA, 0x7F754E7F,
+    0xF3D83C76, 0x7F6BE9D4,
+    0xF3742CA1, 0x7F62368F,
+    0xF310248A, 0x7F5834B6,
+    0xF2AC246D, 0x7F4DE450,
+    0xF2482C89, 0x7F434563,
+    0xF1E43D1C, 0x7F3857F5,
+    0xF1805662, 0x7F2D1C0E,
+    0xF11C789A, 0x7F2191B4,
+    0xF0B8A401, 0x7F15B8EE,
+    0xF054D8D4, 0x7F0991C3,
+    0xEFF11752, 0x7EFD1C3C,
+    0xEF8D5FB8, 0x7EF0585F,
+    0xEF29B243, 0x7EE34635,
+    0xEEC60F31, 0x7ED5E5C6,
+    0xEE6276BF, 0x7EC8371A,
+    0xEDFEE92B, 0x7EBA3A39,
+    0xED9B66B2, 0x7EABEF2C,
+    0xED37EF91, 0x7E9D55FC,
+    0xECD48406, 0x7E8E6EB1,
+    0xEC71244F, 0x7E7F3956,
+    0xEC0DD0A8, 0x7E6FB5F3,
+    0xEBAA894E, 0x7E5FE493,
+    0xEB474E80, 0x7E4FC53E,
+    0xEAE4207A, 0x7E3F57FE,
+    0xEA80FF79, 0x7E2E9CDF,
+    0xEA1DEBBB, 0x7E1D93E9,
+    0xE9BAE57C, 0x7E0C3D29,
+    0xE957ECFB, 0x7DFA98A7,
+    0xE8F50273, 0x7DE8A670,
+    0xE8922621, 0x7DD6668E,
+    0xE82F5844, 0x7DC3D90D,
+    0xE7CC9917, 0x7DB0FDF7,
+    0xE769E8D8, 0x7D9DD55A,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE6A4B616, 0x7D769BB5,
+    0xE642340D, 0x7D628AC5,
+    0xE5DFC1E4, 0x7D4E2C7E,
+    0xE57D5FDA, 0x7D3980EC,
+    0xE51B0E2A, 0x7D24881A,
+    0xE4B8CD10, 0x7D0F4218,
+    0xE4569CCB, 0x7CF9AEF0,
+    0xE3F47D95, 0x7CE3CEB1,
+    0xE3926FAC, 0x7CCDA168,
+    0xE330734C, 0x7CB72724,
+    0xE2CE88B2, 0x7CA05FF1,
+    0xE26CB01A, 0x7C894BDD,
+    0xE20AE9C1, 0x7C71EAF8,
+    0xE1A935E1, 0x7C5A3D4F,
+    0xE14794B9, 0x7C4242F2,
+    0xE0E60684, 0x7C29FBEE,
+    0xE0848B7F, 0x7C116853,
+    0xE02323E5, 0x7BF88830,
+    0xDFC1CFF2, 0x7BDF5B94,
+    0xDF608FE3, 0x7BC5E28F,
+    0xDEFF63F4, 0x7BAC1D31,
+    0xDE9E4C60, 0x7B920B89,
+    0xDE3D4963, 0x7B77ADA8,
+    0xDDDC5B3A, 0x7B5D039D,
+    0xDD7B8220, 0x7B420D7A,
+    0xDD1ABE51, 0x7B26CB4F,
+    0xDCBA1008, 0x7B0B3D2C,
+    0xDC597781, 0x7AEF6323,
+    0xDBF8F4F8, 0x7AD33D45,
+    0xDB9888A8, 0x7AB6CBA3,
+    0xDB3832CD, 0x7A9A0E4F,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xDA77CB62, 0x7A5FB0D8,
+    0xDA17BA4A, 0x7A4210D8,
+    0xD9B7C093, 0x7A24256E,
+    0xD957DE7A, 0x7A05EEAD,
+    0xD8F81439, 0x79E76CA6,
+    0xD898620C, 0x79C89F6D,
+    0xD838C82D, 0x79A98715,
+    0xD7D946D7, 0x798A23B1,
+    0xD779DE46, 0x796A7554,
+    0xD71A8EB5, 0x794A7C11,
+    0xD6BB585D, 0x792A37FE,
+    0xD65C3B7B, 0x7909A92C,
+    0xD5FD3847, 0x78E8CFB1,
+    0xD59E4EFE, 0x78C7ABA1,
+    0xD53F7FDA, 0x78A63D10,
+    0xD4E0CB14, 0x78848413,
+    0xD48230E8, 0x786280BF,
+    0xD423B190, 0x78403328,
+    0xD3C54D46, 0x781D9B64,
+    0xD3670445, 0x77FAB988,
+    0xD308D6C6, 0x77D78DAA,
+    0xD2AAC504, 0x77B417DF,
+    0xD24CCF38, 0x7790583D,
+    0xD1EEF59E, 0x776C4EDB,
+    0xD191386D, 0x7747FBCE,
+    0xD13397E1, 0x77235F2D,
+    0xD0D61433, 0x76FE790E,
+    0xD078AD9D, 0x76D94988,
+    0xD01B6459, 0x76B3D0B3,
+    0xCFBE389F, 0x768E0EA5,
+    0xCF612AAA, 0x76680376,
+    0xCF043AB2, 0x7641AF3C,
+    0xCEA768F2, 0x761B1211,
+    0xCE4AB5A2, 0x75F42C0A,
+    0xCDEE20FC, 0x75CCFD42,
+    0xCD91AB38, 0x75A585CF,
+    0xCD355490, 0x757DC5CA,
+    0xCCD91D3D, 0x7555BD4B,
+    0xCC7D0577, 0x752D6C6C,
+    0xCC210D78, 0x7504D345,
+    0xCBC53578, 0x74DBF1EF,
+    0xCB697DB0, 0x74B2C883,
+    0xCB0DE658, 0x7489571B,
+    0xCAB26FA9, 0x745F9DD1,
+    0xCA5719DB, 0x74359CBD,
+    0xC9FBE527, 0x740B53FA,
+    0xC9A0D1C4, 0x73E0C3A3,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC8EB0FD6, 0x738ACC9E,
+    0xC89061BA, 0x735F6626,
+    0xC835D5D0, 0x7333B883,
+    0xC7DB6C50, 0x7307C3D0,
+    0xC7812571, 0x72DB8828,
+    0xC727016C, 0x72AF05A6,
+    0xC6CD0079, 0x72823C66,
+    0xC67322CD, 0x72552C84,
+    0xC61968A2, 0x7227D61C,
+    0xC5BFD22E, 0x71FA3948,
+    0xC5665FA8, 0x71CC5626,
+    0xC50D1148, 0x719E2CD2,
+    0xC4B3E746, 0x716FBD68,
+    0xC45AE1D7, 0x71410804,
+    0xC4020132, 0x71120CC5,
+    0xC3A9458F, 0x70E2CBC6,
+    0xC350AF25, 0x70B34524,
+    0xC2F83E2A, 0x708378FE,
+    0xC29FF2D4, 0x70536771,
+    0xC247CD5A, 0x70231099,
+    0xC1EFCDF2, 0x6FF27496,
+    0xC197F4D3, 0x6FC19385,
+    0xC1404233, 0x6F906D84,
+    0xC0E8B648, 0x6F5F02B1,
+    0xC0915147, 0x6F2D532C,
+    0xC03A1368, 0x6EFB5F12,
+    0xBFE2FCDF, 0x6EC92682,
+    0xBF8C0DE2, 0x6E96A99C,
+    0xBF3546A8, 0x6E63E87F,
+    0xBEDEA765, 0x6E30E349,
+    0xBE88304F, 0x6DFD9A1B,
+    0xBE31E19B, 0x6DCA0D14,
+    0xBDDBBB7F, 0x6D963C54,
+    0xBD85BE2F, 0x6D6227FA,
+    0xBD2FE9E1, 0x6D2DD027,
+    0xBCDA3ECA, 0x6CF934FB,
+    0xBC84BD1E, 0x6CC45697,
+    0xBC2F6513, 0x6C8F351C,
+    0xBBDA36DC, 0x6C59D0A9,
+    0xBB8532AF, 0x6C242960,
+    0xBB3058C0, 0x6BEE3F62,
+    0xBADBA943, 0x6BB812D0,
+    0xBA87246C, 0x6B81A3CD,
+    0xBA32CA70, 0x6B4AF278,
+    0xB9DE9B83, 0x6B13FEF5,
+    0xB98A97D8, 0x6ADCC964,
+    0xB936BFA3, 0x6AA551E8,
+    0xB8E31319, 0x6A6D98A4,
+    0xB88F926C, 0x6A359DB9,
+    0xB83C3DD1, 0x69FD614A,
+    0xB7E9157A, 0x69C4E37A,
+    0xB796199B, 0x698C246C,
+    0xB7434A67, 0x69532442,
+    0xB6F0A811, 0x6919E320,
+    0xB69E32CD, 0x68E06129,
+    0xB64BEACC, 0x68A69E81,
+    0xB5F9D042, 0x686C9B4B,
+    0xB5A7E362, 0x683257AA,
+    0xB556245E, 0x67F7D3C4,
+    0xB5049368, 0x67BD0FBC,
+    0xB4B330B2, 0x67820BB6,
+    0xB461FC70, 0x6746C7D7,
+    0xB410F6D2, 0x670B4443,
+    0xB3C0200C, 0x66CF811F,
+    0xB36F784E, 0x66937E90,
+    0xB31EFFCB, 0x66573CBB,
+    0xB2CEB6B5, 0x661ABBC5,
+    0xB27E9D3B, 0x65DDFBD3,
+    0xB22EB392, 0x65A0FD0B,
+    0xB1DEF9E8, 0x6563BF92,
+    0xB18F7070, 0x6526438E,
+    0xB140175B, 0x64E88926,
+    0xB0F0EEDA, 0x64AA907F,
+    0xB0A1F71C, 0x646C59BF,
+    0xB0533055, 0x642DE50D,
+    0xB0049AB2, 0x63EF328F,
+    0xAFB63667, 0x63B0426D,
+    0xAF6803A1, 0x637114CC,
+    0xAF1A0293, 0x6331A9D4,
+    0xAECC336B, 0x62F201AC,
+    0xAE7E965B, 0x62B21C7B,
+    0xAE312B91, 0x6271FA69,
+    0xADE3F33E, 0x62319B9D,
+    0xAD96ED91, 0x61F1003E,
+    0xAD4A1ABA, 0x61B02876,
+    0xACFD7AE8, 0x616F146B,
+    0xACB10E4A, 0x612DC446,
+    0xAC64D510, 0x60EC3830,
+    0xAC18CF68, 0x60AA704F,
+    0xABCCFD82, 0x60686CCE,
+    0xAB815F8C, 0x60262DD5,
+    0xAB35F5B5, 0x5FE3B38D,
+    0xAAEAC02B, 0x5FA0FE1E,
+    0xAA9FBF1D, 0x5F5E0DB3,
+    0xAA54F2B9, 0x5F1AE273,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA9BFF8A8, 0x5E93DC1F,
+    0xA975CB56, 0x5E50015D,
+    0xA92BD366, 0x5E0BEC6E,
+    0xA8E21106, 0x5DC79D7C,
+    0xA8988463, 0x5D8314B0,
+    0xA84F2DA9, 0x5D3E5236,
+    0xA8060D08, 0x5CF95638,
+    0xA7BD22AB, 0x5CB420DF,
+    0xA7746EC0, 0x5C6EB258,
+    0xA72BF173, 0x5C290ACC,
+    0xA6E3AAF2, 0x5BE32A67,
+    0xA69B9B68, 0x5B9D1153,
+    0xA653C302, 0x5B56BFBD,
+    0xA60C21ED, 0x5B1035CF,
+    0xA5C4B855, 0x5AC973B4,
+    0xA57D8666, 0x5A82799A,
+    0xA5368C4B, 0x5A3B47AA,
+    0xA4EFCA31, 0x59F3DE12,
+    0xA4A94042, 0x59AC3CFD,
+    0xA462EEAC, 0x59646497,
+    0xA41CD598, 0x591C550E,
+    0xA3D6F533, 0x58D40E8C,
+    0xA3914DA7, 0x588B913F,
+    0xA34BDF20, 0x5842DD54,
+    0xA306A9C7, 0x57F9F2F7,
+    0xA2C1ADC9, 0x57B0D256,
+    0xA27CEB4F, 0x57677B9D,
+    0xA2386283, 0x571DEEF9,
+    0xA1F41391, 0x56D42C99,
+    0xA1AFFEA2, 0x568A34A9,
+    0xA16C23E1, 0x56400757,
+    0xA1288376, 0x55F5A4D2,
+    0xA0E51D8C, 0x55AB0D46,
+    0xA0A1F24C, 0x556040E2,
+    0xA05F01E1, 0x55153FD4,
+    0xA01C4C72, 0x54CA0A4A,
+    0x9FD9D22A, 0x547EA073,
+    0x9F979331, 0x5433027D,
+    0x9F558FB0, 0x53E73097,
+    0x9F13C7D0, 0x539B2AEF,
+    0x9ED23BB9, 0x534EF1B5,
+    0x9E90EB94, 0x53028517,
+    0x9E4FD789, 0x52B5E545,
+    0x9E0EFFC1, 0x5269126E,
+    0x9DCE6462, 0x521C0CC1,
+    0x9D8E0596, 0x51CED46E,
+    0x9D4DE384, 0x518169A4,
+    0x9D0DFE53, 0x5133CC94,
+    0x9CCE562B, 0x50E5FD6C,
+    0x9C8EEB33, 0x5097FC5E,
+    0x9C4FBD92, 0x5049C999,
+    0x9C10CD70, 0x4FFB654D,
+    0x9BD21AF2, 0x4FACCFAB,
+    0x9B93A640, 0x4F5E08E3,
+    0x9B556F80, 0x4F0F1126,
+    0x9B1776D9, 0x4EBFE8A4,
+    0x9AD9BC71, 0x4E708F8F,
+    0x9A9C406D, 0x4E210617,
+    0x9A5F02F5, 0x4DD14C6E,
+    0x9A22042C, 0x4D8162C4,
+    0x99E5443A, 0x4D31494B,
+    0x99A8C344, 0x4CE10034,
+    0x996C816F, 0x4C9087B1,
+    0x99307EE0, 0x4C3FDFF3,
+    0x98F4BBBC, 0x4BEF092D,
+    0x98B93828, 0x4B9E038F,
+    0x987DF449, 0x4B4CCF4D,
+    0x9842F043, 0x4AFB6C97,
+    0x98082C3B, 0x4AA9DBA1,
+    0x97CDA855, 0x4A581C9D,
+    0x979364B5, 0x4A062FBD,
+    0x9759617E, 0x49B41533,
+    0x971F9ED6, 0x4961CD32,
+    0x96E61CDF, 0x490F57EE,
+    0x96ACDBBD, 0x48BCB598,
+    0x9673DB94, 0x4869E664,
+    0x963B1C85, 0x4816EA85,
+    0x96029EB5, 0x47C3C22E,
+    0x95CA6246, 0x47706D93,
+    0x9592675B, 0x471CECE6,
+    0x955AAE17, 0x46C9405C,
+    0x9523369B, 0x46756827,
+    0x94EC010B, 0x4621647C,
+    0x94B50D87, 0x45CD358F,
+    0x947E5C32, 0x4578DB93,
+    0x9447ED2F, 0x452456BC,
+    0x9411C09D, 0x44CFA73F,
+    0x93DBD69F, 0x447ACD50,
+    0x93A62F56, 0x4425C923,
+    0x9370CAE4, 0x43D09AEC,
+    0x933BA968, 0x437B42E1,
+    0x9306CB04, 0x4325C135,
+    0x92D22FD8, 0x42D0161E,
+    0x929DD805, 0x427A41D0,
+    0x9269C3AC, 0x42244480,
+    0x9235F2EB, 0x41CE1E64,
+    0x920265E4, 0x4177CFB0,
+    0x91CF1CB6, 0x4121589A,
+    0x919C1780, 0x40CAB957,
+    0x91695663, 0x4073F21D,
+    0x9136D97D, 0x401D0320,
+    0x9104A0ED, 0x3FC5EC97,
+    0x90D2ACD3, 0x3F6EAEB8,
+    0x90A0FD4E, 0x3F1749B7,
+    0x906F927B, 0x3EBFBDCC,
+    0x903E6C7A, 0x3E680B2C,
+    0x900D8B69, 0x3E10320D,
+    0x8FDCEF66, 0x3DB832A5,
+    0x8FAC988E, 0x3D600D2B,
+    0x8F7C8701, 0x3D07C1D5,
+    0x8F4CBADB, 0x3CAF50DA,
+    0x8F1D343A, 0x3C56BA70,
+    0x8EEDF33B, 0x3BFDFECD,
+    0x8EBEF7FB, 0x3BA51E29,
+    0x8E904298, 0x3B4C18BA,
+    0x8E61D32D, 0x3AF2EEB7,
+    0x8E33A9D9, 0x3A99A057,
+    0x8E05C6B7, 0x3A402DD1,
+    0x8DD829E4, 0x39E6975D,
+    0x8DAAD37B, 0x398CDD32,
+    0x8D7DC399, 0x3932FF87,
+    0x8D50FA59, 0x38D8FE93,
+    0x8D2477D8, 0x387EDA8E,
+    0x8CF83C30, 0x382493B0,
+    0x8CCC477D, 0x37CA2A30,
+    0x8CA099D9, 0x376F9E46,
+    0x8C753361, 0x3714F02A,
+    0x8C4A142F, 0x36BA2013,
+    0x8C1F3C5C, 0x365F2E3B,
+    0x8BF4AC05, 0x36041AD9,
+    0x8BCA6342, 0x35A8E624,
+    0x8BA0622F, 0x354D9056,
+    0x8B76A8E4, 0x34F219A7,
+    0x8B4D377C, 0x3496824F,
+    0x8B240E10, 0x343ACA87,
+    0x8AFB2CBA, 0x33DEF287,
+    0x8AD29393, 0x3382FA88,
+    0x8AAA42B4, 0x3326E2C2,
+    0x8A823A35, 0x32CAAB6F,
+    0x8A5A7A30, 0x326E54C7,
+    0x8A3302BD, 0x3211DF03,
+    0x8A0BD3F5, 0x31B54A5D,
+    0x89E4EDEE, 0x3158970D,
+    0x89BE50C3, 0x30FBC54D,
+    0x8997FC89, 0x309ED555,
+    0x8971F15A, 0x3041C760,
+    0x894C2F4C, 0x2FE49BA6,
+    0x8926B677, 0x2F875262,
+    0x890186F1, 0x2F29EBCC,
+    0x88DCA0D3, 0x2ECC681E,
+    0x88B80431, 0x2E6EC792,
+    0x8893B124, 0x2E110A62,
+    0x886FA7C2, 0x2DB330C7,
+    0x884BE820, 0x2D553AFB,
+    0x88287255, 0x2CF72939,
+    0x88054677, 0x2C98FBBA,
+    0x87E2649B, 0x2C3AB2B9,
+    0x87BFCCD7, 0x2BDC4E6F,
+    0x879D7F40, 0x2B7DCF17,
+    0x877B7BEC, 0x2B1F34EB,
+    0x8759C2EF, 0x2AC08025,
+    0x8738545E, 0x2A61B101,
+    0x8717304E, 0x2A02C7B8,
+    0x86F656D3, 0x29A3C484,
+    0x86D5C802, 0x2944A7A2,
+    0x86B583EE, 0x28E5714A,
+    0x86958AAB, 0x288621B9,
+    0x8675DC4E, 0x2826B928,
+    0x865678EA, 0x27C737D2,
+    0x86376092, 0x27679DF4,
+    0x86189359, 0x2707EBC6,
+    0x85FA1152, 0x26A82185,
+    0x85DBDA91, 0x26483F6C,
+    0x85BDEF27, 0x25E845B5,
+    0x85A04F28, 0x2588349D,
+    0x8582FAA4, 0x25280C5D,
+    0x8565F1B0, 0x24C7CD32,
+    0x8549345C, 0x24677757,
+    0x852CC2BA, 0x24070B07,
+    0x85109CDC, 0x23A6887E,
+    0x84F4C2D3, 0x2345EFF7,
+    0x84D934B0, 0x22E541AE,
+    0x84BDF285, 0x22847DDF,
+    0x84A2FC62, 0x2223A4C5,
+    0x84885257, 0x21C2B69C,
+    0x846DF476, 0x2161B39F,
+    0x8453E2CE, 0x21009C0B,
+    0x843A1D70, 0x209F701C,
+    0x8420A46B, 0x203E300D,
+    0x840777CF, 0x1FDCDC1A,
+    0x83EE97AC, 0x1F7B7480,
+    0x83D60411, 0x1F19F97B,
+    0x83BDBD0D, 0x1EB86B46,
+    0x83A5C2B0, 0x1E56CA1E,
+    0x838E1507, 0x1DF5163F,
+    0x8376B422, 0x1D934FE5,
+    0x835FA00E, 0x1D31774D,
+    0x8348D8DB, 0x1CCF8CB3,
+    0x83325E97, 0x1C6D9053,
+    0x831C314E, 0x1C0B826A,
+    0x8306510F, 0x1BA96334,
+    0x82F0BDE8, 0x1B4732EF,
+    0x82DB77E5, 0x1AE4F1D6,
+    0x82C67F13, 0x1A82A025,
+    0x82B1D381, 0x1A203E1B,
+    0x829D753A, 0x19BDCBF2,
+    0x8289644A, 0x195B49E9,
+    0x8275A0C0, 0x18F8B83C,
+    0x82622AA5, 0x18961727,
+    0x824F0208, 0x183366E8,
+    0x823C26F2, 0x17D0A7BB,
+    0x82299971, 0x176DD9DE,
+    0x8217598F, 0x170AFD8D,
+    0x82056758, 0x16A81305,
+    0x81F3C2D7, 0x16451A83,
+    0x81E26C16, 0x15E21444,
+    0x81D16320, 0x157F0086,
+    0x81C0A801, 0x151BDF85,
+    0x81B03AC1, 0x14B8B17F,
+    0x81A01B6C, 0x145576B1,
+    0x81904A0C, 0x13F22F57,
+    0x8180C6A9, 0x138EDBB0,
+    0x8171914E, 0x132B7BF9,
+    0x8162AA03, 0x12C8106E,
+    0x815410D3, 0x1264994E,
+    0x8145C5C6, 0x120116D4,
+    0x8137C8E6, 0x119D8940,
+    0x812A1A39, 0x1139F0CE,
+    0x811CB9CA, 0x10D64DBC,
+    0x810FA7A0, 0x1072A047,
+    0x8102E3C3, 0x100EE8AD,
+    0x80F66E3C, 0x0FAB272B,
+    0x80EA4712, 0x0F475BFE,
+    0x80DE6E4C, 0x0EE38765,
+    0x80D2E3F1, 0x0E7FA99D,
+    0x80C7A80A, 0x0E1BC2E3,
+    0x80BCBA9C, 0x0DB7D376,
+    0x80B21BAF, 0x0D53DB92,
+    0x80A7CB49, 0x0CEFDB75,
+    0x809DC970, 0x0C8BD35E,
+    0x8094162B, 0x0C27C389,
+    0x808AB180, 0x0BC3AC35,
+    0x80819B74, 0x0B5F8D9F,
+    0x8078D40D, 0x0AFB6805,
+    0x80705B50, 0x0A973BA5,
+    0x80683143, 0x0A3308BC,
+    0x806055EA, 0x09CECF89,
+    0x8058C94C, 0x096A9049,
+    0x80518B6B, 0x09064B3A,
+    0x804A9C4D, 0x08A2009A,
+    0x8043FBF6, 0x083DB0A7,
+    0x803DAA69, 0x07D95B9E,
+    0x8037A7AC, 0x077501BE,
+    0x8031F3C1, 0x0710A344,
+    0x802C8EAD, 0x06AC406F,
+    0x80277872, 0x0647D97C,
+    0x8022B113, 0x05E36EA9,
+    0x801E3894, 0x057F0034,
+    0x801A0EF7, 0x051A8E5C,
+    0x80163440, 0x04B6195D,
+    0x8012A86F, 0x0451A176,
+    0x800F6B88, 0x03ED26E6,
+    0x800C7D8C, 0x0388A9E9,
+    0x8009DE7D, 0x03242ABF,
+    0x80078E5E, 0x02BFA9A4,
+    0x80058D2E, 0x025B26D7,
+    0x8003DAF0, 0x01F6A296,
+    0x800277A5, 0x01921D1F,
+    0x8001634D, 0x012D96B0,
+    0x80009DE9, 0x00C90F88,
+    0x8000277A, 0x006487E3,
+    0x80000000, 0x00000000,
+    0x8000277A, 0xFF9B781D,
+    0x80009DE9, 0xFF36F078,
+    0x8001634D, 0xFED2694F,
+    0x800277A5, 0xFE6DE2E0,
+    0x8003DAF0, 0xFE095D69,
+    0x80058D2E, 0xFDA4D928,
+    0x80078E5E, 0xFD40565B,
+    0x8009DE7D, 0xFCDBD541,
+    0x800C7D8C, 0xFC775616,
+    0x800F6B88, 0xFC12D919,
+    0x8012A86F, 0xFBAE5E89,
+    0x80163440, 0xFB49E6A2,
+    0x801A0EF7, 0xFAE571A4,
+    0x801E3894, 0xFA80FFCB,
+    0x8022B113, 0xFA1C9156,
+    0x80277872, 0xF9B82683,
+    0x802C8EAD, 0xF953BF90,
+    0x8031F3C1, 0xF8EF5CBB,
+    0x8037A7AC, 0xF88AFE41,
+    0x803DAA69, 0xF826A461,
+    0x8043FBF6, 0xF7C24F58,
+    0x804A9C4D, 0xF75DFF65,
+    0x80518B6B, 0xF6F9B4C5,
+    0x8058C94C, 0xF6956FB6,
+    0x806055EA, 0xF6313076,
+    0x80683143, 0xF5CCF743,
+    0x80705B50, 0xF568C45A,
+    0x8078D40D, 0xF50497FA,
+    0x80819B74, 0xF4A07260,
+    0x808AB180, 0xF43C53CA,
+    0x8094162B, 0xF3D83C76,
+    0x809DC970, 0xF3742CA1,
+    0x80A7CB49, 0xF310248A,
+    0x80B21BAF, 0xF2AC246D,
+    0x80BCBA9C, 0xF2482C89,
+    0x80C7A80A, 0xF1E43D1C,
+    0x80D2E3F1, 0xF1805662,
+    0x80DE6E4C, 0xF11C789A,
+    0x80EA4712, 0xF0B8A401,
+    0x80F66E3C, 0xF054D8D4,
+    0x8102E3C3, 0xEFF11752,
+    0x810FA7A0, 0xEF8D5FB8,
+    0x811CB9CA, 0xEF29B243,
+    0x812A1A39, 0xEEC60F31,
+    0x8137C8E6, 0xEE6276BF,
+    0x8145C5C6, 0xEDFEE92B,
+    0x815410D3, 0xED9B66B2,
+    0x8162AA03, 0xED37EF91,
+    0x8171914E, 0xECD48406,
+    0x8180C6A9, 0xEC71244F,
+    0x81904A0C, 0xEC0DD0A8,
+    0x81A01B6C, 0xEBAA894E,
+    0x81B03AC1, 0xEB474E80,
+    0x81C0A801, 0xEAE4207A,
+    0x81D16320, 0xEA80FF79,
+    0x81E26C16, 0xEA1DEBBB,
+    0x81F3C2D7, 0xE9BAE57C,
+    0x82056758, 0xE957ECFB,
+    0x8217598F, 0xE8F50273,
+    0x82299971, 0xE8922621,
+    0x823C26F2, 0xE82F5844,
+    0x824F0208, 0xE7CC9917,
+    0x82622AA5, 0xE769E8D8,
+    0x8275A0C0, 0xE70747C3,
+    0x8289644A, 0xE6A4B616,
+    0x829D753A, 0xE642340D,
+    0x82B1D381, 0xE5DFC1E4,
+    0x82C67F13, 0xE57D5FDA,
+    0x82DB77E5, 0xE51B0E2A,
+    0x82F0BDE8, 0xE4B8CD10,
+    0x8306510F, 0xE4569CCB,
+    0x831C314E, 0xE3F47D95,
+    0x83325E97, 0xE3926FAC,
+    0x8348D8DB, 0xE330734C,
+    0x835FA00E, 0xE2CE88B2,
+    0x8376B422, 0xE26CB01A,
+    0x838E1507, 0xE20AE9C1,
+    0x83A5C2B0, 0xE1A935E1,
+    0x83BDBD0D, 0xE14794B9,
+    0x83D60411, 0xE0E60684,
+    0x83EE97AC, 0xE0848B7F,
+    0x840777CF, 0xE02323E5,
+    0x8420A46B, 0xDFC1CFF2,
+    0x843A1D70, 0xDF608FE3,
+    0x8453E2CE, 0xDEFF63F4,
+    0x846DF476, 0xDE9E4C60,
+    0x84885257, 0xDE3D4963,
+    0x84A2FC62, 0xDDDC5B3A,
+    0x84BDF285, 0xDD7B8220,
+    0x84D934B0, 0xDD1ABE51,
+    0x84F4C2D3, 0xDCBA1008,
+    0x85109CDC, 0xDC597781,
+    0x852CC2BA, 0xDBF8F4F8,
+    0x8549345C, 0xDB9888A8,
+    0x8565F1B0, 0xDB3832CD,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x85A04F28, 0xDA77CB62,
+    0x85BDEF27, 0xDA17BA4A,
+    0x85DBDA91, 0xD9B7C093,
+    0x85FA1152, 0xD957DE7A,
+    0x86189359, 0xD8F81439,
+    0x86376092, 0xD898620C,
+    0x865678EA, 0xD838C82D,
+    0x8675DC4E, 0xD7D946D7,
+    0x86958AAB, 0xD779DE46,
+    0x86B583EE, 0xD71A8EB5,
+    0x86D5C802, 0xD6BB585D,
+    0x86F656D3, 0xD65C3B7B,
+    0x8717304E, 0xD5FD3847,
+    0x8738545E, 0xD59E4EFE,
+    0x8759C2EF, 0xD53F7FDA,
+    0x877B7BEC, 0xD4E0CB14,
+    0x879D7F40, 0xD48230E8,
+    0x87BFCCD7, 0xD423B190,
+    0x87E2649B, 0xD3C54D46,
+    0x88054677, 0xD3670445,
+    0x88287255, 0xD308D6C6,
+    0x884BE820, 0xD2AAC504,
+    0x886FA7C2, 0xD24CCF38,
+    0x8893B124, 0xD1EEF59E,
+    0x88B80431, 0xD191386D,
+    0x88DCA0D3, 0xD13397E1,
+    0x890186F1, 0xD0D61433,
+    0x8926B677, 0xD078AD9D,
+    0x894C2F4C, 0xD01B6459,
+    0x8971F15A, 0xCFBE389F,
+    0x8997FC89, 0xCF612AAA,
+    0x89BE50C3, 0xCF043AB2,
+    0x89E4EDEE, 0xCEA768F2,
+    0x8A0BD3F5, 0xCE4AB5A2,
+    0x8A3302BD, 0xCDEE20FC,
+    0x8A5A7A30, 0xCD91AB38,
+    0x8A823A35, 0xCD355490,
+    0x8AAA42B4, 0xCCD91D3D,
+    0x8AD29393, 0xCC7D0577,
+    0x8AFB2CBA, 0xCC210D78,
+    0x8B240E10, 0xCBC53578,
+    0x8B4D377C, 0xCB697DB0,
+    0x8B76A8E4, 0xCB0DE658,
+    0x8BA0622F, 0xCAB26FA9,
+    0x8BCA6342, 0xCA5719DB,
+    0x8BF4AC05, 0xC9FBE527,
+    0x8C1F3C5C, 0xC9A0D1C4,
+    0x8C4A142F, 0xC945DFEC,
+    0x8C753361, 0xC8EB0FD6,
+    0x8CA099D9, 0xC89061BA,
+    0x8CCC477D, 0xC835D5D0,
+    0x8CF83C30, 0xC7DB6C50,
+    0x8D2477D8, 0xC7812571,
+    0x8D50FA59, 0xC727016C,
+    0x8D7DC399, 0xC6CD0079,
+    0x8DAAD37B, 0xC67322CD,
+    0x8DD829E4, 0xC61968A2,
+    0x8E05C6B7, 0xC5BFD22E,
+    0x8E33A9D9, 0xC5665FA8,
+    0x8E61D32D, 0xC50D1148,
+    0x8E904298, 0xC4B3E746,
+    0x8EBEF7FB, 0xC45AE1D7,
+    0x8EEDF33B, 0xC4020132,
+    0x8F1D343A, 0xC3A9458F,
+    0x8F4CBADB, 0xC350AF25,
+    0x8F7C8701, 0xC2F83E2A,
+    0x8FAC988E, 0xC29FF2D4,
+    0x8FDCEF66, 0xC247CD5A,
+    0x900D8B69, 0xC1EFCDF2,
+    0x903E6C7A, 0xC197F4D3,
+    0x906F927B, 0xC1404233,
+    0x90A0FD4E, 0xC0E8B648,
+    0x90D2ACD3, 0xC0915147,
+    0x9104A0ED, 0xC03A1368,
+    0x9136D97D, 0xBFE2FCDF,
+    0x91695663, 0xBF8C0DE2,
+    0x919C1780, 0xBF3546A8,
+    0x91CF1CB6, 0xBEDEA765,
+    0x920265E4, 0xBE88304F,
+    0x9235F2EB, 0xBE31E19B,
+    0x9269C3AC, 0xBDDBBB7F,
+    0x929DD805, 0xBD85BE2F,
+    0x92D22FD8, 0xBD2FE9E1,
+    0x9306CB04, 0xBCDA3ECA,
+    0x933BA968, 0xBC84BD1E,
+    0x9370CAE4, 0xBC2F6513,
+    0x93A62F56, 0xBBDA36DC,
+    0x93DBD69F, 0xBB8532AF,
+    0x9411C09D, 0xBB3058C0,
+    0x9447ED2F, 0xBADBA943,
+    0x947E5C32, 0xBA87246C,
+    0x94B50D87, 0xBA32CA70,
+    0x94EC010B, 0xB9DE9B83,
+    0x9523369B, 0xB98A97D8,
+    0x955AAE17, 0xB936BFA3,
+    0x9592675B, 0xB8E31319,
+    0x95CA6246, 0xB88F926C,
+    0x96029EB5, 0xB83C3DD1,
+    0x963B1C85, 0xB7E9157A,
+    0x9673DB94, 0xB796199B,
+    0x96ACDBBD, 0xB7434A67,
+    0x96E61CDF, 0xB6F0A811,
+    0x971F9ED6, 0xB69E32CD,
+    0x9759617E, 0xB64BEACC,
+    0x979364B5, 0xB5F9D042,
+    0x97CDA855, 0xB5A7E362,
+    0x98082C3B, 0xB556245E,
+    0x9842F043, 0xB5049368,
+    0x987DF449, 0xB4B330B2,
+    0x98B93828, 0xB461FC70,
+    0x98F4BBBC, 0xB410F6D2,
+    0x99307EE0, 0xB3C0200C,
+    0x996C816F, 0xB36F784E,
+    0x99A8C344, 0xB31EFFCB,
+    0x99E5443A, 0xB2CEB6B5,
+    0x9A22042C, 0xB27E9D3B,
+    0x9A5F02F5, 0xB22EB392,
+    0x9A9C406D, 0xB1DEF9E8,
+    0x9AD9BC71, 0xB18F7070,
+    0x9B1776D9, 0xB140175B,
+    0x9B556F80, 0xB0F0EEDA,
+    0x9B93A640, 0xB0A1F71C,
+    0x9BD21AF2, 0xB0533055,
+    0x9C10CD70, 0xB0049AB2,
+    0x9C4FBD92, 0xAFB63667,
+    0x9C8EEB33, 0xAF6803A1,
+    0x9CCE562B, 0xAF1A0293,
+    0x9D0DFE53, 0xAECC336B,
+    0x9D4DE384, 0xAE7E965B,
+    0x9D8E0596, 0xAE312B91,
+    0x9DCE6462, 0xADE3F33E,
+    0x9E0EFFC1, 0xAD96ED91,
+    0x9E4FD789, 0xAD4A1ABA,
+    0x9E90EB94, 0xACFD7AE8,
+    0x9ED23BB9, 0xACB10E4A,
+    0x9F13C7D0, 0xAC64D510,
+    0x9F558FB0, 0xAC18CF68,
+    0x9F979331, 0xABCCFD82,
+    0x9FD9D22A, 0xAB815F8C,
+    0xA01C4C72, 0xAB35F5B5,
+    0xA05F01E1, 0xAAEAC02B,
+    0xA0A1F24C, 0xAA9FBF1D,
+    0xA0E51D8C, 0xAA54F2B9,
+    0xA1288376, 0xAA0A5B2D,
+    0xA16C23E1, 0xA9BFF8A8,
+    0xA1AFFEA2, 0xA975CB56,
+    0xA1F41391, 0xA92BD366,
+    0xA2386283, 0xA8E21106,
+    0xA27CEB4F, 0xA8988463,
+    0xA2C1ADC9, 0xA84F2DA9,
+    0xA306A9C7, 0xA8060D08,
+    0xA34BDF20, 0xA7BD22AB,
+    0xA3914DA7, 0xA7746EC0,
+    0xA3D6F533, 0xA72BF173,
+    0xA41CD598, 0xA6E3AAF2,
+    0xA462EEAC, 0xA69B9B68,
+    0xA4A94042, 0xA653C302,
+    0xA4EFCA31, 0xA60C21ED,
+    0xA5368C4B, 0xA5C4B855,
+    0xA57D8666, 0xA57D8666,
+    0xA5C4B855, 0xA5368C4B,
+    0xA60C21ED, 0xA4EFCA31,
+    0xA653C302, 0xA4A94042,
+    0xA69B9B68, 0xA462EEAC,
+    0xA6E3AAF2, 0xA41CD598,
+    0xA72BF173, 0xA3D6F533,
+    0xA7746EC0, 0xA3914DA7,
+    0xA7BD22AB, 0xA34BDF20,
+    0xA8060D08, 0xA306A9C7,
+    0xA84F2DA9, 0xA2C1ADC9,
+    0xA8988463, 0xA27CEB4F,
+    0xA8E21106, 0xA2386283,
+    0xA92BD366, 0xA1F41391,
+    0xA975CB56, 0xA1AFFEA2,
+    0xA9BFF8A8, 0xA16C23E1,
+    0xAA0A5B2D, 0xA1288376,
+    0xAA54F2B9, 0xA0E51D8C,
+    0xAA9FBF1D, 0xA0A1F24C,
+    0xAAEAC02B, 0xA05F01E1,
+    0xAB35F5B5, 0xA01C4C72,
+    0xAB815F8C, 0x9FD9D22A,
+    0xABCCFD82, 0x9F979331,
+    0xAC18CF68, 0x9F558FB0,
+    0xAC64D510, 0x9F13C7D0,
+    0xACB10E4A, 0x9ED23BB9,
+    0xACFD7AE8, 0x9E90EB94,
+    0xAD4A1ABA, 0x9E4FD789,
+    0xAD96ED91, 0x9E0EFFC1,
+    0xADE3F33E, 0x9DCE6462,
+    0xAE312B91, 0x9D8E0596,
+    0xAE7E965B, 0x9D4DE384,
+    0xAECC336B, 0x9D0DFE53,
+    0xAF1A0293, 0x9CCE562B,
+    0xAF6803A1, 0x9C8EEB33,
+    0xAFB63667, 0x9C4FBD92,
+    0xB0049AB2, 0x9C10CD70,
+    0xB0533055, 0x9BD21AF2,
+    0xB0A1F71C, 0x9B93A640,
+    0xB0F0EEDA, 0x9B556F80,
+    0xB140175B, 0x9B1776D9,
+    0xB18F7070, 0x9AD9BC71,
+    0xB1DEF9E8, 0x9A9C406D,
+    0xB22EB392, 0x9A5F02F5,
+    0xB27E9D3B, 0x9A22042C,
+    0xB2CEB6B5, 0x99E5443A,
+    0xB31EFFCB, 0x99A8C344,
+    0xB36F784E, 0x996C816F,
+    0xB3C0200C, 0x99307EE0,
+    0xB410F6D2, 0x98F4BBBC,
+    0xB461FC70, 0x98B93828,
+    0xB4B330B2, 0x987DF449,
+    0xB5049368, 0x9842F043,
+    0xB556245E, 0x98082C3B,
+    0xB5A7E362, 0x97CDA855,
+    0xB5F9D042, 0x979364B5,
+    0xB64BEACC, 0x9759617E,
+    0xB69E32CD, 0x971F9ED6,
+    0xB6F0A811, 0x96E61CDF,
+    0xB7434A67, 0x96ACDBBD,
+    0xB796199B, 0x9673DB94,
+    0xB7E9157A, 0x963B1C85,
+    0xB83C3DD1, 0x96029EB5,
+    0xB88F926C, 0x95CA6246,
+    0xB8E31319, 0x9592675B,
+    0xB936BFA3, 0x955AAE17,
+    0xB98A97D8, 0x9523369B,
+    0xB9DE9B83, 0x94EC010B,
+    0xBA32CA70, 0x94B50D87,
+    0xBA87246C, 0x947E5C32,
+    0xBADBA943, 0x9447ED2F,
+    0xBB3058C0, 0x9411C09D,
+    0xBB8532AF, 0x93DBD69F,
+    0xBBDA36DC, 0x93A62F56,
+    0xBC2F6513, 0x9370CAE4,
+    0xBC84BD1E, 0x933BA968,
+    0xBCDA3ECA, 0x9306CB04,
+    0xBD2FE9E1, 0x92D22FD8,
+    0xBD85BE2F, 0x929DD805,
+    0xBDDBBB7F, 0x9269C3AC,
+    0xBE31E19B, 0x9235F2EB,
+    0xBE88304F, 0x920265E4,
+    0xBEDEA765, 0x91CF1CB6,
+    0xBF3546A8, 0x919C1780,
+    0xBF8C0DE2, 0x91695663,
+    0xBFE2FCDF, 0x9136D97D,
+    0xC03A1368, 0x9104A0ED,
+    0xC0915147, 0x90D2ACD3,
+    0xC0E8B648, 0x90A0FD4E,
+    0xC1404233, 0x906F927B,
+    0xC197F4D3, 0x903E6C7A,
+    0xC1EFCDF2, 0x900D8B69,
+    0xC247CD5A, 0x8FDCEF66,
+    0xC29FF2D4, 0x8FAC988E,
+    0xC2F83E2A, 0x8F7C8701,
+    0xC350AF25, 0x8F4CBADB,
+    0xC3A9458F, 0x8F1D343A,
+    0xC4020132, 0x8EEDF33B,
+    0xC45AE1D7, 0x8EBEF7FB,
+    0xC4B3E746, 0x8E904298,
+    0xC50D1148, 0x8E61D32D,
+    0xC5665FA8, 0x8E33A9D9,
+    0xC5BFD22E, 0x8E05C6B7,
+    0xC61968A2, 0x8DD829E4,
+    0xC67322CD, 0x8DAAD37B,
+    0xC6CD0079, 0x8D7DC399,
+    0xC727016C, 0x8D50FA59,
+    0xC7812571, 0x8D2477D8,
+    0xC7DB6C50, 0x8CF83C30,
+    0xC835D5D0, 0x8CCC477D,
+    0xC89061BA, 0x8CA099D9,
+    0xC8EB0FD6, 0x8C753361,
+    0xC945DFEC, 0x8C4A142F,
+    0xC9A0D1C4, 0x8C1F3C5C,
+    0xC9FBE527, 0x8BF4AC05,
+    0xCA5719DB, 0x8BCA6342,
+    0xCAB26FA9, 0x8BA0622F,
+    0xCB0DE658, 0x8B76A8E4,
+    0xCB697DB0, 0x8B4D377C,
+    0xCBC53578, 0x8B240E10,
+    0xCC210D78, 0x8AFB2CBA,
+    0xCC7D0577, 0x8AD29393,
+    0xCCD91D3D, 0x8AAA42B4,
+    0xCD355490, 0x8A823A35,
+    0xCD91AB38, 0x8A5A7A30,
+    0xCDEE20FC, 0x8A3302BD,
+    0xCE4AB5A2, 0x8A0BD3F5,
+    0xCEA768F2, 0x89E4EDEE,
+    0xCF043AB2, 0x89BE50C3,
+    0xCF612AAA, 0x8997FC89,
+    0xCFBE389F, 0x8971F15A,
+    0xD01B6459, 0x894C2F4C,
+    0xD078AD9D, 0x8926B677,
+    0xD0D61433, 0x890186F1,
+    0xD13397E1, 0x88DCA0D3,
+    0xD191386D, 0x88B80431,
+    0xD1EEF59E, 0x8893B124,
+    0xD24CCF38, 0x886FA7C2,
+    0xD2AAC504, 0x884BE820,
+    0xD308D6C6, 0x88287255,
+    0xD3670445, 0x88054677,
+    0xD3C54D46, 0x87E2649B,
+    0xD423B190, 0x87BFCCD7,
+    0xD48230E8, 0x879D7F40,
+    0xD4E0CB14, 0x877B7BEC,
+    0xD53F7FDA, 0x8759C2EF,
+    0xD59E4EFE, 0x8738545E,
+    0xD5FD3847, 0x8717304E,
+    0xD65C3B7B, 0x86F656D3,
+    0xD6BB585D, 0x86D5C802,
+    0xD71A8EB5, 0x86B583EE,
+    0xD779DE46, 0x86958AAB,
+    0xD7D946D7, 0x8675DC4E,
+    0xD838C82D, 0x865678EA,
+    0xD898620C, 0x86376092,
+    0xD8F81439, 0x86189359,
+    0xD957DE7A, 0x85FA1152,
+    0xD9B7C093, 0x85DBDA91,
+    0xDA17BA4A, 0x85BDEF27,
+    0xDA77CB62, 0x85A04F28,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xDB3832CD, 0x8565F1B0,
+    0xDB9888A8, 0x8549345C,
+    0xDBF8F4F8, 0x852CC2BA,
+    0xDC597781, 0x85109CDC,
+    0xDCBA1008, 0x84F4C2D3,
+    0xDD1ABE51, 0x84D934B0,
+    0xDD7B8220, 0x84BDF285,
+    0xDDDC5B3A, 0x84A2FC62,
+    0xDE3D4963, 0x84885257,
+    0xDE9E4C60, 0x846DF476,
+    0xDEFF63F4, 0x8453E2CE,
+    0xDF608FE3, 0x843A1D70,
+    0xDFC1CFF2, 0x8420A46B,
+    0xE02323E5, 0x840777CF,
+    0xE0848B7F, 0x83EE97AC,
+    0xE0E60684, 0x83D60411,
+    0xE14794B9, 0x83BDBD0D,
+    0xE1A935E1, 0x83A5C2B0,
+    0xE20AE9C1, 0x838E1507,
+    0xE26CB01A, 0x8376B422,
+    0xE2CE88B2, 0x835FA00E,
+    0xE330734C, 0x8348D8DB,
+    0xE3926FAC, 0x83325E97,
+    0xE3F47D95, 0x831C314E,
+    0xE4569CCB, 0x8306510F,
+    0xE4B8CD10, 0x82F0BDE8,
+    0xE51B0E2A, 0x82DB77E5,
+    0xE57D5FDA, 0x82C67F13,
+    0xE5DFC1E4, 0x82B1D381,
+    0xE642340D, 0x829D753A,
+    0xE6A4B616, 0x8289644A,
+    0xE70747C3, 0x8275A0C0,
+    0xE769E8D8, 0x82622AA5,
+    0xE7CC9917, 0x824F0208,
+    0xE82F5844, 0x823C26F2,
+    0xE8922621, 0x82299971,
+    0xE8F50273, 0x8217598F,
+    0xE957ECFB, 0x82056758,
+    0xE9BAE57C, 0x81F3C2D7,
+    0xEA1DEBBB, 0x81E26C16,
+    0xEA80FF79, 0x81D16320,
+    0xEAE4207A, 0x81C0A801,
+    0xEB474E80, 0x81B03AC1,
+    0xEBAA894E, 0x81A01B6C,
+    0xEC0DD0A8, 0x81904A0C,
+    0xEC71244F, 0x8180C6A9,
+    0xECD48406, 0x8171914E,
+    0xED37EF91, 0x8162AA03,
+    0xED9B66B2, 0x815410D3,
+    0xEDFEE92B, 0x8145C5C6,
+    0xEE6276BF, 0x8137C8E6,
+    0xEEC60F31, 0x812A1A39,
+    0xEF29B243, 0x811CB9CA,
+    0xEF8D5FB8, 0x810FA7A0,
+    0xEFF11752, 0x8102E3C3,
+    0xF054D8D4, 0x80F66E3C,
+    0xF0B8A401, 0x80EA4712,
+    0xF11C789A, 0x80DE6E4C,
+    0xF1805662, 0x80D2E3F1,
+    0xF1E43D1C, 0x80C7A80A,
+    0xF2482C89, 0x80BCBA9C,
+    0xF2AC246D, 0x80B21BAF,
+    0xF310248A, 0x80A7CB49,
+    0xF3742CA1, 0x809DC970,
+    0xF3D83C76, 0x8094162B,
+    0xF43C53CA, 0x808AB180,
+    0xF4A07260, 0x80819B74,
+    0xF50497FA, 0x8078D40D,
+    0xF568C45A, 0x80705B50,
+    0xF5CCF743, 0x80683143,
+    0xF6313076, 0x806055EA,
+    0xF6956FB6, 0x8058C94C,
+    0xF6F9B4C5, 0x80518B6B,
+    0xF75DFF65, 0x804A9C4D,
+    0xF7C24F58, 0x8043FBF6,
+    0xF826A461, 0x803DAA69,
+    0xF88AFE41, 0x8037A7AC,
+    0xF8EF5CBB, 0x8031F3C1,
+    0xF953BF90, 0x802C8EAD,
+    0xF9B82683, 0x80277872,
+    0xFA1C9156, 0x8022B113,
+    0xFA80FFCB, 0x801E3894,
+    0xFAE571A4, 0x801A0EF7,
+    0xFB49E6A2, 0x80163440,
+    0xFBAE5E89, 0x8012A86F,
+    0xFC12D919, 0x800F6B88,
+    0xFC775616, 0x800C7D8C,
+    0xFCDBD541, 0x8009DE7D,
+    0xFD40565B, 0x80078E5E,
+    0xFDA4D928, 0x80058D2E,
+    0xFE095D69, 0x8003DAF0,
+    0xFE6DE2E0, 0x800277A5,
+    0xFED2694F, 0x8001634D,
+    0xFF36F078, 0x80009DE9,
+    0xFF9B781D, 0x8000277A
+};
+
+/**    
+* \par   
+* Example code for Q31 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 4096	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to Q31(Fixed point 1.31):    
+*	round(twiddleCoefQ31(i) * pow(2, 31))    
+*    
+*/
+const q31_t twiddleCoef_4096_q31[6144] = 
+{
+    0x7FFFFFFF, 0x00000000,
+    0x7FFFF621, 0x003243F5,
+    0x7FFFD885, 0x006487E3,
+    0x7FFFA72C, 0x0096CBC1,
+    0x7FFF6216, 0x00C90F88,
+    0x7FFF0942, 0x00FB532F,
+    0x7FFE9CB2, 0x012D96B0,
+    0x7FFE1C64, 0x015FDA03,
+    0x7FFD885A, 0x01921D1F,
+    0x7FFCE093, 0x01C45FFE,
+    0x7FFC250F, 0x01F6A296,
+    0x7FFB55CE, 0x0228E4E1,
+    0x7FFA72D1, 0x025B26D7,
+    0x7FF97C17, 0x028D6870,
+    0x7FF871A1, 0x02BFA9A4,
+    0x7FF7536F, 0x02F1EA6B,
+    0x7FF62182, 0x03242ABF,
+    0x7FF4DBD8, 0x03566A96,
+    0x7FF38273, 0x0388A9E9,
+    0x7FF21553, 0x03BAE8B1,
+    0x7FF09477, 0x03ED26E6,
+    0x7FEEFFE1, 0x041F647F,
+    0x7FED5790, 0x0451A176,
+    0x7FEB9B85, 0x0483DDC3,
+    0x7FE9CBC0, 0x04B6195D,
+    0x7FE7E840, 0x04E8543D,
+    0x7FE5F108, 0x051A8E5C,
+    0x7FE3E616, 0x054CC7B0,
+    0x7FE1C76B, 0x057F0034,
+    0x7FDF9508, 0x05B137DF,
+    0x7FDD4EEC, 0x05E36EA9,
+    0x7FDAF518, 0x0615A48A,
+    0x7FD8878D, 0x0647D97C,
+    0x7FD6064B, 0x067A0D75,
+    0x7FD37152, 0x06AC406F,
+    0x7FD0C8A3, 0x06DE7261,
+    0x7FCE0C3E, 0x0710A344,
+    0x7FCB3C23, 0x0742D310,
+    0x7FC85853, 0x077501BE,
+    0x7FC560CF, 0x07A72F45,
+    0x7FC25596, 0x07D95B9E,
+    0x7FBF36A9, 0x080B86C1,
+    0x7FBC040A, 0x083DB0A7,
+    0x7FB8BDB7, 0x086FD947,
+    0x7FB563B2, 0x08A2009A,
+    0x7FB1F5FC, 0x08D42698,
+    0x7FAE7494, 0x09064B3A,
+    0x7FAADF7C, 0x09386E77,
+    0x7FA736B4, 0x096A9049,
+    0x7FA37A3C, 0x099CB0A7,
+    0x7F9FAA15, 0x09CECF89,
+    0x7F9BC63F, 0x0A00ECE8,
+    0x7F97CEBC, 0x0A3308BC,
+    0x7F93C38C, 0x0A6522FE,
+    0x7F8FA4AF, 0x0A973BA5,
+    0x7F8B7226, 0x0AC952AA,
+    0x7F872BF3, 0x0AFB6805,
+    0x7F82D214, 0x0B2D7BAE,
+    0x7F7E648B, 0x0B5F8D9F,
+    0x7F79E35A, 0x0B919DCE,
+    0x7F754E7F, 0x0BC3AC35,
+    0x7F70A5FD, 0x0BF5B8CB,
+    0x7F6BE9D4, 0x0C27C389,
+    0x7F671A04, 0x0C59CC67,
+    0x7F62368F, 0x0C8BD35E,
+    0x7F5D3F75, 0x0CBDD865,
+    0x7F5834B6, 0x0CEFDB75,
+    0x7F531654, 0x0D21DC87,
+    0x7F4DE450, 0x0D53DB92,
+    0x7F489EAA, 0x0D85D88F,
+    0x7F434563, 0x0DB7D376,
+    0x7F3DD87C, 0x0DE9CC3F,
+    0x7F3857F5, 0x0E1BC2E3,
+    0x7F32C3D0, 0x0E4DB75B,
+    0x7F2D1C0E, 0x0E7FA99D,
+    0x7F2760AF, 0x0EB199A3,
+    0x7F2191B4, 0x0EE38765,
+    0x7F1BAF1E, 0x0F1572DC,
+    0x7F15B8EE, 0x0F475BFE,
+    0x7F0FAF24, 0x0F7942C6,
+    0x7F0991C3, 0x0FAB272B,
+    0x7F0360CB, 0x0FDD0925,
+    0x7EFD1C3C, 0x100EE8AD,
+    0x7EF6C418, 0x1040C5BB,
+    0x7EF0585F, 0x1072A047,
+    0x7EE9D913, 0x10A4784A,
+    0x7EE34635, 0x10D64DBC,
+    0x7EDC9FC6, 0x11082096,
+    0x7ED5E5C6, 0x1139F0CE,
+    0x7ECF1837, 0x116BBE5F,
+    0x7EC8371A, 0x119D8940,
+    0x7EC1426F, 0x11CF516A,
+    0x7EBA3A39, 0x120116D4,
+    0x7EB31E77, 0x1232D978,
+    0x7EABEF2C, 0x1264994E,
+    0x7EA4AC58, 0x1296564D,
+    0x7E9D55FC, 0x12C8106E,
+    0x7E95EC19, 0x12F9C7AA,
+    0x7E8E6EB1, 0x132B7BF9,
+    0x7E86DDC5, 0x135D2D53,
+    0x7E7F3956, 0x138EDBB0,
+    0x7E778165, 0x13C0870A,
+    0x7E6FB5F3, 0x13F22F57,
+    0x7E67D702, 0x1423D492,
+    0x7E5FE493, 0x145576B1,
+    0x7E57DEA6, 0x148715AD,
+    0x7E4FC53E, 0x14B8B17F,
+    0x7E47985B, 0x14EA4A1F,
+    0x7E3F57FE, 0x151BDF85,
+    0x7E37042A, 0x154D71AA,
+    0x7E2E9CDF, 0x157F0086,
+    0x7E26221E, 0x15B08C11,
+    0x7E1D93E9, 0x15E21444,
+    0x7E14F242, 0x16139917,
+    0x7E0C3D29, 0x16451A83,
+    0x7E03749F, 0x1676987F,
+    0x7DFA98A7, 0x16A81305,
+    0x7DF1A942, 0x16D98A0C,
+    0x7DE8A670, 0x170AFD8D,
+    0x7DDF9034, 0x173C6D80,
+    0x7DD6668E, 0x176DD9DE,
+    0x7DCD2981, 0x179F429F,
+    0x7DC3D90D, 0x17D0A7BB,
+    0x7DBA7534, 0x1802092C,
+    0x7DB0FDF7, 0x183366E8,
+    0x7DA77359, 0x1864C0E9,
+    0x7D9DD55A, 0x18961727,
+    0x7D9423FB, 0x18C7699B,
+    0x7D8A5F3F, 0x18F8B83C,
+    0x7D808727, 0x192A0303,
+    0x7D769BB5, 0x195B49E9,
+    0x7D6C9CE9, 0x198C8CE6,
+    0x7D628AC5, 0x19BDCBF2,
+    0x7D58654C, 0x19EF0706,
+    0x7D4E2C7E, 0x1A203E1B,
+    0x7D43E05E, 0x1A517127,
+    0x7D3980EC, 0x1A82A025,
+    0x7D2F0E2A, 0x1AB3CB0C,
+    0x7D24881A, 0x1AE4F1D6,
+    0x7D19EEBE, 0x1B161479,
+    0x7D0F4218, 0x1B4732EF,
+    0x7D048228, 0x1B784D30,
+    0x7CF9AEF0, 0x1BA96334,
+    0x7CEEC873, 0x1BDA74F5,
+    0x7CE3CEB1, 0x1C0B826A,
+    0x7CD8C1AD, 0x1C3C8B8C,
+    0x7CCDA168, 0x1C6D9053,
+    0x7CC26DE5, 0x1C9E90B8,
+    0x7CB72724, 0x1CCF8CB3,
+    0x7CABCD27, 0x1D00843C,
+    0x7CA05FF1, 0x1D31774D,
+    0x7C94DF82, 0x1D6265DD,
+    0x7C894BDD, 0x1D934FE5,
+    0x7C7DA504, 0x1DC4355D,
+    0x7C71EAF8, 0x1DF5163F,
+    0x7C661DBB, 0x1E25F281,
+    0x7C5A3D4F, 0x1E56CA1E,
+    0x7C4E49B6, 0x1E879D0C,
+    0x7C4242F2, 0x1EB86B46,
+    0x7C362904, 0x1EE934C2,
+    0x7C29FBEE, 0x1F19F97B,
+    0x7C1DBBB2, 0x1F4AB967,
+    0x7C116853, 0x1F7B7480,
+    0x7C0501D1, 0x1FAC2ABF,
+    0x7BF88830, 0x1FDCDC1A,
+    0x7BEBFB70, 0x200D888C,
+    0x7BDF5B94, 0x203E300D,
+    0x7BD2A89E, 0x206ED295,
+    0x7BC5E28F, 0x209F701C,
+    0x7BB9096A, 0x20D0089B,
+    0x7BAC1D31, 0x21009C0B,
+    0x7B9F1DE5, 0x21312A65,
+    0x7B920B89, 0x2161B39F,
+    0x7B84E61E, 0x219237B4,
+    0x7B77ADA8, 0x21C2B69C,
+    0x7B6A6227, 0x21F3304E,
+    0x7B5D039D, 0x2223A4C5,
+    0x7B4F920E, 0x225413F8,
+    0x7B420D7A, 0x22847DDF,
+    0x7B3475E4, 0x22B4E274,
+    0x7B26CB4F, 0x22E541AE,
+    0x7B190DBB, 0x23159B87,
+    0x7B0B3D2C, 0x2345EFF7,
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+    0x7AD33D45, 0x24070B07,
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+    0x7AB6CBA3, 0x24677757,
+    0x7AA8766E, 0x2497A517,
+    0x7A9A0E4F, 0x24C7CD32,
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+    0x7A151377, 0x26783370,
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+    0x79D80F6F, 0x2737C7E3,
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+    0x7999DEC3, 0x27F6FB92,
+    0x798A23B1, 0x2826B928,
+    0x797A55E0, 0x2856708C,
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+    0x795A820E, 0x28B5CCA5,
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+    0x792A37FE, 0x2944A7A2,
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+    0x7909A92C, 0x29A3C484,
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+    0x719E2CD2, 0x3AF2EEB7,
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+    0x71120CC5, 0x3BFDFECD,
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+    0x703B44AC, 0x3D8C24A7,
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+    0x6A1987B0, 0x479A1D66,
+    0x69FD614A, 0x47C3C22E,
+    0x69E12A8C, 0x47ED5BE6,
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+    0x696FAC78, 0x48935397,
+    0x69532442, 0x48BCB598,
+    0x69368BCE, 0x48E60C62,
+    0x6919E320, 0x490F57EE,
+    0x68FD2A3D, 0x49389836,
+    0x68E06129, 0x4961CD32,
+    0x68C387E9, 0x498AF6DE,
+    0x68A69E81, 0x49B41533,
+    0x6889A4F5, 0x49DD282A,
+    0x686C9B4B, 0x4A062FBD,
+    0x684F8186, 0x4A2F2BE5,
+    0x683257AA, 0x4A581C9D,
+    0x68151DBE, 0x4A8101DE,
+    0x67F7D3C4, 0x4AA9DBA1,
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+    0x67BD0FBC, 0x4AFB6C97,
+    0x679F95B7, 0x4B2423BD,
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+    0x676471C0, 0x4B756F3F,
+    0x6746C7D7, 0x4B9E038F,
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+    0x670B4443, 0x4BEF092D,
+    0x66ED6AA1, 0x4C177A6E,
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+    0x66B187C3, 0x4C6839B6,
+    0x66937E90, 0x4C9087B1,
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+    0x66573CBB, 0x4CE10034,
+    0x66390422, 0x4D092AB0,
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+    0x65FC63A9, 0x4D595BFE,
+    0x65DDFBD3, 0x4D8162C4,
+    0x65BF8447, 0x4DA95D96,
+    0x65A0FD0B, 0x4DD14C6E,
+    0x65826622, 0x4DF92F45,
+    0x6563BF92, 0x4E210617,
+    0x6545095F, 0x4E48D0DC,
+    0x6526438E, 0x4E708F8F,
+    0x65076E24, 0x4E984229,
+    0x64E88926, 0x4EBFE8A4,
+    0x64C99498, 0x4EE782FA,
+    0x64AA907F, 0x4F0F1126,
+    0x648B7CDF, 0x4F369320,
+    0x646C59BF, 0x4F5E08E3,
+    0x644D2722, 0x4F857268,
+    0x642DE50D, 0x4FACCFAB,
+    0x640E9385, 0x4FD420A3,
+    0x63EF328F, 0x4FFB654D,
+    0x63CFC230, 0x50229DA0,
+    0x63B0426D, 0x5049C999,
+    0x6390B34A, 0x5070E92F,
+    0x637114CC, 0x5097FC5E,
+    0x635166F8, 0x50BF031F,
+    0x6331A9D4, 0x50E5FD6C,
+    0x6311DD63, 0x510CEB40,
+    0x62F201AC, 0x5133CC94,
+    0x62D216B2, 0x515AA162,
+    0x62B21C7B, 0x518169A4,
+    0x6292130C, 0x51A82555,
+    0x6271FA69, 0x51CED46E,
+    0x6251D297, 0x51F576E9,
+    0x62319B9D, 0x521C0CC1,
+    0x6211557D, 0x524295EF,
+    0x61F1003E, 0x5269126E,
+    0x61D09BE5, 0x528F8237,
+    0x61B02876, 0x52B5E545,
+    0x618FA5F6, 0x52DC3B92,
+    0x616F146B, 0x53028517,
+    0x614E73D9, 0x5328C1D0,
+    0x612DC446, 0x534EF1B5,
+    0x610D05B7, 0x537514C1,
+    0x60EC3830, 0x539B2AEF,
+    0x60CB5BB6, 0x53C13438,
+    0x60AA704F, 0x53E73097,
+    0x60897600, 0x540D2005,
+    0x60686CCE, 0x5433027D,
+    0x604754BE, 0x5458D7F9,
+    0x60262DD5, 0x547EA073,
+    0x6004F818, 0x54A45BE5,
+    0x5FE3B38D, 0x54CA0A4A,
+    0x5FC26038, 0x54EFAB9C,
+    0x5FA0FE1E, 0x55153FD4,
+    0x5F7F8D46, 0x553AC6ED,
+    0x5F5E0DB3, 0x556040E2,
+    0x5F3C7F6B, 0x5585ADAC,
+    0x5F1AE273, 0x55AB0D46,
+    0x5EF936D1, 0x55D05FAA,
+    0x5ED77C89, 0x55F5A4D2,
+    0x5EB5B3A1, 0x561ADCB8,
+    0x5E93DC1F, 0x56400757,
+    0x5E71F606, 0x566524AA,
+    0x5E50015D, 0x568A34A9,
+    0x5E2DFE28, 0x56AF3750,
+    0x5E0BEC6E, 0x56D42C99,
+    0x5DE9CC32, 0x56F9147E,
+    0x5DC79D7C, 0x571DEEF9,
+    0x5DA5604E, 0x5742BC05,
+    0x5D8314B0, 0x57677B9D,
+    0x5D60BAA6, 0x578C2DB9,
+    0x5D3E5236, 0x57B0D256,
+    0x5D1BDB65, 0x57D5696C,
+    0x5CF95638, 0x57F9F2F7,
+    0x5CD6C2B4, 0x581E6EF1,
+    0x5CB420DF, 0x5842DD54,
+    0x5C9170BF, 0x58673E1B,
+    0x5C6EB258, 0x588B913F,
+    0x5C4BE5B0, 0x58AFD6BC,
+    0x5C290ACC, 0x58D40E8C,
+    0x5C0621B2, 0x58F838A9,
+    0x5BE32A67, 0x591C550E,
+    0x5BC024F0, 0x594063B4,
+    0x5B9D1153, 0x59646497,
+    0x5B79EF96, 0x598857B1,
+    0x5B56BFBD, 0x59AC3CFD,
+    0x5B3381CE, 0x59D01474,
+    0x5B1035CF, 0x59F3DE12,
+    0x5AECDBC4, 0x5A1799D0,
+    0x5AC973B4, 0x5A3B47AA,
+    0x5AA5FDA4, 0x5A5EE79A,
+    0x5A82799A, 0x5A82799A,
+    0x5A5EE79A, 0x5AA5FDA4,
+    0x5A3B47AA, 0x5AC973B4,
+    0x5A1799D0, 0x5AECDBC4,
+    0x59F3DE12, 0x5B1035CF,
+    0x59D01474, 0x5B3381CE,
+    0x59AC3CFD, 0x5B56BFBD,
+    0x598857B1, 0x5B79EF96,
+    0x59646497, 0x5B9D1153,
+    0x594063B4, 0x5BC024F0,
+    0x591C550E, 0x5BE32A67,
+    0x58F838A9, 0x5C0621B2,
+    0x58D40E8C, 0x5C290ACC,
+    0x58AFD6BC, 0x5C4BE5B0,
+    0x588B913F, 0x5C6EB258,
+    0x58673E1B, 0x5C9170BF,
+    0x5842DD54, 0x5CB420DF,
+    0x581E6EF1, 0x5CD6C2B4,
+    0x57F9F2F7, 0x5CF95638,
+    0x57D5696C, 0x5D1BDB65,
+    0x57B0D256, 0x5D3E5236,
+    0x578C2DB9, 0x5D60BAA6,
+    0x57677B9D, 0x5D8314B0,
+    0x5742BC05, 0x5DA5604E,
+    0x571DEEF9, 0x5DC79D7C,
+    0x56F9147E, 0x5DE9CC32,
+    0x56D42C99, 0x5E0BEC6E,
+    0x56AF3750, 0x5E2DFE28,
+    0x568A34A9, 0x5E50015D,
+    0x566524AA, 0x5E71F606,
+    0x56400757, 0x5E93DC1F,
+    0x561ADCB8, 0x5EB5B3A1,
+    0x55F5A4D2, 0x5ED77C89,
+    0x55D05FAA, 0x5EF936D1,
+    0x55AB0D46, 0x5F1AE273,
+    0x5585ADAC, 0x5F3C7F6B,
+    0x556040E2, 0x5F5E0DB3,
+    0x553AC6ED, 0x5F7F8D46,
+    0x55153FD4, 0x5FA0FE1E,
+    0x54EFAB9C, 0x5FC26038,
+    0x54CA0A4A, 0x5FE3B38D,
+    0x54A45BE5, 0x6004F818,
+    0x547EA073, 0x60262DD5,
+    0x5458D7F9, 0x604754BE,
+    0x5433027D, 0x60686CCE,
+    0x540D2005, 0x60897600,
+    0x53E73097, 0x60AA704F,
+    0x53C13438, 0x60CB5BB6,
+    0x539B2AEF, 0x60EC3830,
+    0x537514C1, 0x610D05B7,
+    0x534EF1B5, 0x612DC446,
+    0x5328C1D0, 0x614E73D9,
+    0x53028517, 0x616F146B,
+    0x52DC3B92, 0x618FA5F6,
+    0x52B5E545, 0x61B02876,
+    0x528F8237, 0x61D09BE5,
+    0x5269126E, 0x61F1003E,
+    0x524295EF, 0x6211557D,
+    0x521C0CC1, 0x62319B9D,
+    0x51F576E9, 0x6251D297,
+    0x51CED46E, 0x6271FA69,
+    0x51A82555, 0x6292130C,
+    0x518169A4, 0x62B21C7B,
+    0x515AA162, 0x62D216B2,
+    0x5133CC94, 0x62F201AC,
+    0x510CEB40, 0x6311DD63,
+    0x50E5FD6C, 0x6331A9D4,
+    0x50BF031F, 0x635166F8,
+    0x5097FC5E, 0x637114CC,
+    0x5070E92F, 0x6390B34A,
+    0x5049C999, 0x63B0426D,
+    0x50229DA0, 0x63CFC230,
+    0x4FFB654D, 0x63EF328F,
+    0x4FD420A3, 0x640E9385,
+    0x4FACCFAB, 0x642DE50D,
+    0x4F857268, 0x644D2722,
+    0x4F5E08E3, 0x646C59BF,
+    0x4F369320, 0x648B7CDF,
+    0x4F0F1126, 0x64AA907F,
+    0x4EE782FA, 0x64C99498,
+    0x4EBFE8A4, 0x64E88926,
+    0x4E984229, 0x65076E24,
+    0x4E708F8F, 0x6526438E,
+    0x4E48D0DC, 0x6545095F,
+    0x4E210617, 0x6563BF92,
+    0x4DF92F45, 0x65826622,
+    0x4DD14C6E, 0x65A0FD0B,
+    0x4DA95D96, 0x65BF8447,
+    0x4D8162C4, 0x65DDFBD3,
+    0x4D595BFE, 0x65FC63A9,
+    0x4D31494B, 0x661ABBC5,
+    0x4D092AB0, 0x66390422,
+    0x4CE10034, 0x66573CBB,
+    0x4CB8C9DD, 0x6675658C,
+    0x4C9087B1, 0x66937E90,
+    0x4C6839B6, 0x66B187C3,
+    0x4C3FDFF3, 0x66CF811F,
+    0x4C177A6E, 0x66ED6AA1,
+    0x4BEF092D, 0x670B4443,
+    0x4BC68C36, 0x67290E02,
+    0x4B9E038F, 0x6746C7D7,
+    0x4B756F3F, 0x676471C0,
+    0x4B4CCF4D, 0x67820BB6,
+    0x4B2423BD, 0x679F95B7,
+    0x4AFB6C97, 0x67BD0FBC,
+    0x4AD2A9E1, 0x67DA79C2,
+    0x4AA9DBA1, 0x67F7D3C4,
+    0x4A8101DE, 0x68151DBE,
+    0x4A581C9D, 0x683257AA,
+    0x4A2F2BE5, 0x684F8186,
+    0x4A062FBD, 0x686C9B4B,
+    0x49DD282A, 0x6889A4F5,
+    0x49B41533, 0x68A69E81,
+    0x498AF6DE, 0x68C387E9,
+    0x4961CD32, 0x68E06129,
+    0x49389836, 0x68FD2A3D,
+    0x490F57EE, 0x6919E320,
+    0x48E60C62, 0x69368BCE,
+    0x48BCB598, 0x69532442,
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+    0x4869E664, 0x698C246C,
+    0x48406E07, 0x69A88C18,
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+    0x47C3C22E, 0x69FD614A,
+    0x479A1D66, 0x6A1987B0,
+    0x47706D93, 0x6A359DB9,
+    0x4746B2BC, 0x6A51A361,
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+    0x46F31C1A, 0x6A897D7D,
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+    0x464B6BBD, 0x6AF86C6C,
+    0x4621647C, 0x6B13FEF5,
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+    0x45A30DF0, 0x6B66536A,
+    0x4578DB93, 0x6B81A3CD,
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+    0x43A5F41E, 0x6CA9CE3A,
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+    0x4325C135, 0x6CF934FB,
+    0x42FAF0D4, 0x6D138AFA,
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+    0x4177CFB0, 0x6DFD9A1B,
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+    0x40F60DFB, 0x6E4A6E65,
+    0x40CAB957, 0x6E63E87F,
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+    0x4073F21D, 0x6E96A99C,
+    0x40487F93, 0x6EAFF098,
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+    0x3F9A528F, 0x6F1461AF,
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+    0x3EEB889C, 0x6F77C0B3,
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+    0x3D600D2B, 0x70536771,
+    0x3D33EC39, 0x706B78E3,
+    0x3D07C1D5, 0x708378FE,
+    0x3CDB8E09, 0x709B67C0,
+    0x3CAF50DA, 0x70B34524,
+    0x3C830A4F, 0x70CB1127,
+    0x3C56BA70, 0x70E2CBC6,
+    0x3C2A6142, 0x70FA74FB,
+    0x3BFDFECD, 0x71120CC5,
+    0x3BD19317, 0x7129931E,
+    0x3BA51E29, 0x71410804,
+    0x3B78A007, 0x71586B73,
+    0x3B4C18BA, 0x716FBD68,
+    0x3B1F8847, 0x7186FDDE,
+    0x3AF2EEB7, 0x719E2CD2,
+    0x3AC64C0F, 0x71B54A40,
+    0x3A99A057, 0x71CC5626,
+    0x3A6CEB95, 0x71E3507F,
+    0x3A402DD1, 0x71FA3948,
+    0x3A136712, 0x7211107D,
+    0x39E6975D, 0x7227D61C,
+    0x39B9BEBB, 0x723E8A1F,
+    0x398CDD32, 0x72552C84,
+    0x395FF2C9, 0x726BBD48,
+    0x3932FF87, 0x72823C66,
+    0x39060372, 0x7298A9DC,
+    0x38D8FE93, 0x72AF05A6,
+    0x38ABF0EF, 0x72C54FC0,
+    0x387EDA8E, 0x72DB8828,
+    0x3851BB76, 0x72F1AED8,
+    0x382493B0, 0x7307C3D0,
+    0x37F76340, 0x731DC709,
+    0x37CA2A30, 0x7333B883,
+    0x379CE884, 0x73499838,
+    0x376F9E46, 0x735F6626,
+    0x37424B7A, 0x73752249,
+    0x3714F02A, 0x738ACC9E,
+    0x36E78C5A, 0x73A06522,
+    0x36BA2013, 0x73B5EBD0,
+    0x368CAB5C, 0x73CB60A7,
+    0x365F2E3B, 0x73E0C3A3,
+    0x3631A8B7, 0x73F614C0,
+    0x36041AD9, 0x740B53FA,
+    0x35D684A5, 0x74208150,
+    0x35A8E624, 0x74359CBD,
+    0x357B3F5D, 0x744AA63E,
+    0x354D9056, 0x745F9DD1,
+    0x351FD917, 0x74748371,
+    0x34F219A7, 0x7489571B,
+    0x34C4520D, 0x749E18CD,
+    0x3496824F, 0x74B2C883,
+    0x3468AA76, 0x74C7663A,
+    0x343ACA87, 0x74DBF1EF,
+    0x340CE28A, 0x74F06B9E,
+    0x33DEF287, 0x7504D345,
+    0x33B0FA84, 0x751928E0,
+    0x3382FA88, 0x752D6C6C,
+    0x3354F29A, 0x75419DE6,
+    0x3326E2C2, 0x7555BD4B,
+    0x32F8CB07, 0x7569CA98,
+    0x32CAAB6F, 0x757DC5CA,
+    0x329C8402, 0x7591AEDD,
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+    0x32401DC5, 0x75B94A9C,
+    0x3211DF03, 0x75CCFD42,
+    0x31E39889, 0x75E09DBD,
+    0x31B54A5D, 0x75F42C0A,
+    0x3186F487, 0x7607A827,
+    0x3158970D, 0x761B1211,
+    0x312A31F8, 0x762E69C3,
+    0x30FBC54D, 0x7641AF3C,
+    0x30CD5114, 0x7654E279,
+    0x309ED555, 0x76680376,
+    0x30705217, 0x767B1230,
+    0x3041C760, 0x768E0EA5,
+    0x30133538, 0x76A0F8D2,
+    0x2FE49BA6, 0x76B3D0B3,
+    0x2FB5FAB2, 0x76C69646,
+    0x2F875262, 0x76D94988,
+    0x2F58A2BD, 0x76EBEA77,
+    0x2F29EBCC, 0x76FE790E,
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+    0x2E9D9B70, 0x7735B6AE,
+    0x2E6EC792, 0x7747FBCE,
+    0x2E3FEC8B, 0x775A2E88,
+    0x2E110A62, 0x776C4EDB,
+    0x2DE2211E, 0x777E5CC3,
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+    0x2D843963, 0x77A24148,
+    0x2D553AFB, 0x77B417DF,
+    0x2D263595, 0x77C5DC01,
+    0x2CF72939, 0x77D78DAA,
+    0x2CC815ED, 0x77E92CD8,
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+    0x2C69DAA6, 0x780C33B8,
+    0x2C3AB2B9, 0x781D9B64,
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+    0x2BDC4E6F, 0x78403328,
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+    0x2B7DCF17, 0x786280BF,
+    0x2B4E8558, 0x78738BB3,
+    0x2B1F34EB, 0x78848413,
+    0x2AEFDDD8, 0x789569DE,
+    0x2AC08025, 0x78A63D10,
+    0x2A911BDB, 0x78B6FDA8,
+    0x2A61B101, 0x78C7ABA1,
+    0x2A323F9D, 0x78D846FB,
+    0x2A02C7B8, 0x78E8CFB1,
+    0x29D34958, 0x78F945C3,
+    0x29A3C484, 0x7909A92C,
+    0x29743945, 0x7919F9EB,
+    0x2944A7A2, 0x792A37FE,
+    0x29150FA1, 0x793A6360,
+    0x28E5714A, 0x794A7C11,
+    0x28B5CCA5, 0x795A820E,
+    0x288621B9, 0x796A7554,
+    0x2856708C, 0x797A55E0,
+    0x2826B928, 0x798A23B1,
+    0x27F6FB92, 0x7999DEC3,
+    0x27C737D2, 0x79A98715,
+    0x27976DF1, 0x79B91CA4,
+    0x27679DF4, 0x79C89F6D,
+    0x2737C7E3, 0x79D80F6F,
+    0x2707EBC6, 0x79E76CA6,
+    0x26D809A5, 0x79F6B711,
+    0x26A82185, 0x7A05EEAD,
+    0x26783370, 0x7A151377,
+    0x26483F6C, 0x7A24256E,
+    0x26184581, 0x7A33248F,
+    0x25E845B5, 0x7A4210D8,
+    0x25B84012, 0x7A50EA46,
+    0x2588349D, 0x7A5FB0D8,
+    0x2558235E, 0x7A6E648A,
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+    0x24F7EFA1, 0x7A8B9348,
+    0x24C7CD32, 0x7A9A0E4F,
+    0x2497A517, 0x7AA8766E,
+    0x24677757, 0x7AB6CBA3,
+    0x243743FA, 0x7AC50DEB,
+    0x24070B07, 0x7AD33D45,
+    0x23D6CC86, 0x7AE159AE,
+    0x23A6887E, 0x7AEF6323,
+    0x23763EF7, 0x7AFD59A3,
+    0x2345EFF7, 0x7B0B3D2C,
+    0x23159B87, 0x7B190DBB,
+    0x22E541AE, 0x7B26CB4F,
+    0x22B4E274, 0x7B3475E4,
+    0x22847DDF, 0x7B420D7A,
+    0x225413F8, 0x7B4F920E,
+    0x2223A4C5, 0x7B5D039D,
+    0x21F3304E, 0x7B6A6227,
+    0x21C2B69C, 0x7B77ADA8,
+    0x219237B4, 0x7B84E61E,
+    0x2161B39F, 0x7B920B89,
+    0x21312A65, 0x7B9F1DE5,
+    0x21009C0B, 0x7BAC1D31,
+    0x20D0089B, 0x7BB9096A,
+    0x209F701C, 0x7BC5E28F,
+    0x206ED295, 0x7BD2A89E,
+    0x203E300D, 0x7BDF5B94,
+    0x200D888C, 0x7BEBFB70,
+    0x1FDCDC1A, 0x7BF88830,
+    0x1FAC2ABF, 0x7C0501D1,
+    0x1F7B7480, 0x7C116853,
+    0x1F4AB967, 0x7C1DBBB2,
+    0x1F19F97B, 0x7C29FBEE,
+    0x1EE934C2, 0x7C362904,
+    0x1EB86B46, 0x7C4242F2,
+    0x1E879D0C, 0x7C4E49B6,
+    0x1E56CA1E, 0x7C5A3D4F,
+    0x1E25F281, 0x7C661DBB,
+    0x1DF5163F, 0x7C71EAF8,
+    0x1DC4355D, 0x7C7DA504,
+    0x1D934FE5, 0x7C894BDD,
+    0x1D6265DD, 0x7C94DF82,
+    0x1D31774D, 0x7CA05FF1,
+    0x1D00843C, 0x7CABCD27,
+    0x1CCF8CB3, 0x7CB72724,
+    0x1C9E90B8, 0x7CC26DE5,
+    0x1C6D9053, 0x7CCDA168,
+    0x1C3C8B8C, 0x7CD8C1AD,
+    0x1C0B826A, 0x7CE3CEB1,
+    0x1BDA74F5, 0x7CEEC873,
+    0x1BA96334, 0x7CF9AEF0,
+    0x1B784D30, 0x7D048228,
+    0x1B4732EF, 0x7D0F4218,
+    0x1B161479, 0x7D19EEBE,
+    0x1AE4F1D6, 0x7D24881A,
+    0x1AB3CB0C, 0x7D2F0E2A,
+    0x1A82A025, 0x7D3980EC,
+    0x1A517127, 0x7D43E05E,
+    0x1A203E1B, 0x7D4E2C7E,
+    0x19EF0706, 0x7D58654C,
+    0x19BDCBF2, 0x7D628AC5,
+    0x198C8CE6, 0x7D6C9CE9,
+    0x195B49E9, 0x7D769BB5,
+    0x192A0303, 0x7D808727,
+    0x18F8B83C, 0x7D8A5F3F,
+    0x18C7699B, 0x7D9423FB,
+    0x18961727, 0x7D9DD55A,
+    0x1864C0E9, 0x7DA77359,
+    0x183366E8, 0x7DB0FDF7,
+    0x1802092C, 0x7DBA7534,
+    0x17D0A7BB, 0x7DC3D90D,
+    0x179F429F, 0x7DCD2981,
+    0x176DD9DE, 0x7DD6668E,
+    0x173C6D80, 0x7DDF9034,
+    0x170AFD8D, 0x7DE8A670,
+    0x16D98A0C, 0x7DF1A942,
+    0x16A81305, 0x7DFA98A7,
+    0x1676987F, 0x7E03749F,
+    0x16451A83, 0x7E0C3D29,
+    0x16139917, 0x7E14F242,
+    0x15E21444, 0x7E1D93E9,
+    0x15B08C11, 0x7E26221E,
+    0x157F0086, 0x7E2E9CDF,
+    0x154D71AA, 0x7E37042A,
+    0x151BDF85, 0x7E3F57FE,
+    0x14EA4A1F, 0x7E47985B,
+    0x14B8B17F, 0x7E4FC53E,
+    0x148715AD, 0x7E57DEA6,
+    0x145576B1, 0x7E5FE493,
+    0x1423D492, 0x7E67D702,
+    0x13F22F57, 0x7E6FB5F3,
+    0x13C0870A, 0x7E778165,
+    0x138EDBB0, 0x7E7F3956,
+    0x135D2D53, 0x7E86DDC5,
+    0x132B7BF9, 0x7E8E6EB1,
+    0x12F9C7AA, 0x7E95EC19,
+    0x12C8106E, 0x7E9D55FC,
+    0x1296564D, 0x7EA4AC58,
+    0x1264994E, 0x7EABEF2C,
+    0x1232D978, 0x7EB31E77,
+    0x120116D4, 0x7EBA3A39,
+    0x11CF516A, 0x7EC1426F,
+    0x119D8940, 0x7EC8371A,
+    0x116BBE5F, 0x7ECF1837,
+    0x1139F0CE, 0x7ED5E5C6,
+    0x11082096, 0x7EDC9FC6,
+    0x10D64DBC, 0x7EE34635,
+    0x10A4784A, 0x7EE9D913,
+    0x1072A047, 0x7EF0585F,
+    0x1040C5BB, 0x7EF6C418,
+    0x100EE8AD, 0x7EFD1C3C,
+    0x0FDD0925, 0x7F0360CB,
+    0x0FAB272B, 0x7F0991C3,
+    0x0F7942C6, 0x7F0FAF24,
+    0x0F475BFE, 0x7F15B8EE,
+    0x0F1572DC, 0x7F1BAF1E,
+    0x0EE38765, 0x7F2191B4,
+    0x0EB199A3, 0x7F2760AF,
+    0x0E7FA99D, 0x7F2D1C0E,
+    0x0E4DB75B, 0x7F32C3D0,
+    0x0E1BC2E3, 0x7F3857F5,
+    0x0DE9CC3F, 0x7F3DD87C,
+    0x0DB7D376, 0x7F434563,
+    0x0D85D88F, 0x7F489EAA,
+    0x0D53DB92, 0x7F4DE450,
+    0x0D21DC87, 0x7F531654,
+    0x0CEFDB75, 0x7F5834B6,
+    0x0CBDD865, 0x7F5D3F75,
+    0x0C8BD35E, 0x7F62368F,
+    0x0C59CC67, 0x7F671A04,
+    0x0C27C389, 0x7F6BE9D4,
+    0x0BF5B8CB, 0x7F70A5FD,
+    0x0BC3AC35, 0x7F754E7F,
+    0x0B919DCE, 0x7F79E35A,
+    0x0B5F8D9F, 0x7F7E648B,
+    0x0B2D7BAE, 0x7F82D214,
+    0x0AFB6805, 0x7F872BF3,
+    0x0AC952AA, 0x7F8B7226,
+    0x0A973BA5, 0x7F8FA4AF,
+    0x0A6522FE, 0x7F93C38C,
+    0x0A3308BC, 0x7F97CEBC,
+    0x0A00ECE8, 0x7F9BC63F,
+    0x09CECF89, 0x7F9FAA15,
+    0x099CB0A7, 0x7FA37A3C,
+    0x096A9049, 0x7FA736B4,
+    0x09386E77, 0x7FAADF7C,
+    0x09064B3A, 0x7FAE7494,
+    0x08D42698, 0x7FB1F5FC,
+    0x08A2009A, 0x7FB563B2,
+    0x086FD947, 0x7FB8BDB7,
+    0x083DB0A7, 0x7FBC040A,
+    0x080B86C1, 0x7FBF36A9,
+    0x07D95B9E, 0x7FC25596,
+    0x07A72F45, 0x7FC560CF,
+    0x077501BE, 0x7FC85853,
+    0x0742D310, 0x7FCB3C23,
+    0x0710A344, 0x7FCE0C3E,
+    0x06DE7261, 0x7FD0C8A3,
+    0x06AC406F, 0x7FD37152,
+    0x067A0D75, 0x7FD6064B,
+    0x0647D97C, 0x7FD8878D,
+    0x0615A48A, 0x7FDAF518,
+    0x05E36EA9, 0x7FDD4EEC,
+    0x05B137DF, 0x7FDF9508,
+    0x057F0034, 0x7FE1C76B,
+    0x054CC7B0, 0x7FE3E616,
+    0x051A8E5C, 0x7FE5F108,
+    0x04E8543D, 0x7FE7E840,
+    0x04B6195D, 0x7FE9CBC0,
+    0x0483DDC3, 0x7FEB9B85,
+    0x0451A176, 0x7FED5790,
+    0x041F647F, 0x7FEEFFE1,
+    0x03ED26E6, 0x7FF09477,
+    0x03BAE8B1, 0x7FF21553,
+    0x0388A9E9, 0x7FF38273,
+    0x03566A96, 0x7FF4DBD8,
+    0x03242ABF, 0x7FF62182,
+    0x02F1EA6B, 0x7FF7536F,
+    0x02BFA9A4, 0x7FF871A1,
+    0x028D6870, 0x7FF97C17,
+    0x025B26D7, 0x7FFA72D1,
+    0x0228E4E1, 0x7FFB55CE,
+    0x01F6A296, 0x7FFC250F,
+    0x01C45FFE, 0x7FFCE093,
+    0x01921D1F, 0x7FFD885A,
+    0x015FDA03, 0x7FFE1C64,
+    0x012D96B0, 0x7FFE9CB2,
+    0x00FB532F, 0x7FFF0942,
+    0x00C90F88, 0x7FFF6216,
+    0x0096CBC1, 0x7FFFA72C,
+    0x006487E3, 0x7FFFD885,
+    0x003243F5, 0x7FFFF621,
+    0x00000000, 0x7FFFFFFF,
+    0xFFCDBC0A, 0x7FFFF621,
+    0xFF9B781D, 0x7FFFD885,
+    0xFF69343E, 0x7FFFA72C,
+    0xFF36F078, 0x7FFF6216,
+    0xFF04ACD0, 0x7FFF0942,
+    0xFED2694F, 0x7FFE9CB2,
+    0xFEA025FC, 0x7FFE1C64,
+    0xFE6DE2E0, 0x7FFD885A,
+    0xFE3BA001, 0x7FFCE093,
+    0xFE095D69, 0x7FFC250F,
+    0xFDD71B1E, 0x7FFB55CE,
+    0xFDA4D928, 0x7FFA72D1,
+    0xFD72978F, 0x7FF97C17,
+    0xFD40565B, 0x7FF871A1,
+    0xFD0E1594, 0x7FF7536F,
+    0xFCDBD541, 0x7FF62182,
+    0xFCA99569, 0x7FF4DBD8,
+    0xFC775616, 0x7FF38273,
+    0xFC45174E, 0x7FF21553,
+    0xFC12D919, 0x7FF09477,
+    0xFBE09B80, 0x7FEEFFE1,
+    0xFBAE5E89, 0x7FED5790,
+    0xFB7C223C, 0x7FEB9B85,
+    0xFB49E6A2, 0x7FE9CBC0,
+    0xFB17ABC2, 0x7FE7E840,
+    0xFAE571A4, 0x7FE5F108,
+    0xFAB3384F, 0x7FE3E616,
+    0xFA80FFCB, 0x7FE1C76B,
+    0xFA4EC820, 0x7FDF9508,
+    0xFA1C9156, 0x7FDD4EEC,
+    0xF9EA5B75, 0x7FDAF518,
+    0xF9B82683, 0x7FD8878D,
+    0xF985F28A, 0x7FD6064B,
+    0xF953BF90, 0x7FD37152,
+    0xF9218D9E, 0x7FD0C8A3,
+    0xF8EF5CBB, 0x7FCE0C3E,
+    0xF8BD2CEF, 0x7FCB3C23,
+    0xF88AFE41, 0x7FC85853,
+    0xF858D0BA, 0x7FC560CF,
+    0xF826A461, 0x7FC25596,
+    0xF7F4793E, 0x7FBF36A9,
+    0xF7C24F58, 0x7FBC040A,
+    0xF79026B8, 0x7FB8BDB7,
+    0xF75DFF65, 0x7FB563B2,
+    0xF72BD967, 0x7FB1F5FC,
+    0xF6F9B4C5, 0x7FAE7494,
+    0xF6C79188, 0x7FAADF7C,
+    0xF6956FB6, 0x7FA736B4,
+    0xF6634F58, 0x7FA37A3C,
+    0xF6313076, 0x7F9FAA15,
+    0xF5FF1317, 0x7F9BC63F,
+    0xF5CCF743, 0x7F97CEBC,
+    0xF59ADD01, 0x7F93C38C,
+    0xF568C45A, 0x7F8FA4AF,
+    0xF536AD55, 0x7F8B7226,
+    0xF50497FA, 0x7F872BF3,
+    0xF4D28451, 0x7F82D214,
+    0xF4A07260, 0x7F7E648B,
+    0xF46E6231, 0x7F79E35A,
+    0xF43C53CA, 0x7F754E7F,
+    0xF40A4734, 0x7F70A5FD,
+    0xF3D83C76, 0x7F6BE9D4,
+    0xF3A63398, 0x7F671A04,
+    0xF3742CA1, 0x7F62368F,
+    0xF342279A, 0x7F5D3F75,
+    0xF310248A, 0x7F5834B6,
+    0xF2DE2378, 0x7F531654,
+    0xF2AC246D, 0x7F4DE450,
+    0xF27A2770, 0x7F489EAA,
+    0xF2482C89, 0x7F434563,
+    0xF21633C0, 0x7F3DD87C,
+    0xF1E43D1C, 0x7F3857F5,
+    0xF1B248A5, 0x7F32C3D0,
+    0xF1805662, 0x7F2D1C0E,
+    0xF14E665C, 0x7F2760AF,
+    0xF11C789A, 0x7F2191B4,
+    0xF0EA8D23, 0x7F1BAF1E,
+    0xF0B8A401, 0x7F15B8EE,
+    0xF086BD39, 0x7F0FAF24,
+    0xF054D8D4, 0x7F0991C3,
+    0xF022F6DA, 0x7F0360CB,
+    0xEFF11752, 0x7EFD1C3C,
+    0xEFBF3A44, 0x7EF6C418,
+    0xEF8D5FB8, 0x7EF0585F,
+    0xEF5B87B5, 0x7EE9D913,
+    0xEF29B243, 0x7EE34635,
+    0xEEF7DF6A, 0x7EDC9FC6,
+    0xEEC60F31, 0x7ED5E5C6,
+    0xEE9441A0, 0x7ECF1837,
+    0xEE6276BF, 0x7EC8371A,
+    0xEE30AE95, 0x7EC1426F,
+    0xEDFEE92B, 0x7EBA3A39,
+    0xEDCD2687, 0x7EB31E77,
+    0xED9B66B2, 0x7EABEF2C,
+    0xED69A9B2, 0x7EA4AC58,
+    0xED37EF91, 0x7E9D55FC,
+    0xED063855, 0x7E95EC19,
+    0xECD48406, 0x7E8E6EB1,
+    0xECA2D2AC, 0x7E86DDC5,
+    0xEC71244F, 0x7E7F3956,
+    0xEC3F78F5, 0x7E778165,
+    0xEC0DD0A8, 0x7E6FB5F3,
+    0xEBDC2B6D, 0x7E67D702,
+    0xEBAA894E, 0x7E5FE493,
+    0xEB78EA52, 0x7E57DEA6,
+    0xEB474E80, 0x7E4FC53E,
+    0xEB15B5E0, 0x7E47985B,
+    0xEAE4207A, 0x7E3F57FE,
+    0xEAB28E55, 0x7E37042A,
+    0xEA80FF79, 0x7E2E9CDF,
+    0xEA4F73EE, 0x7E26221E,
+    0xEA1DEBBB, 0x7E1D93E9,
+    0xE9EC66E8, 0x7E14F242,
+    0xE9BAE57C, 0x7E0C3D29,
+    0xE9896780, 0x7E03749F,
+    0xE957ECFB, 0x7DFA98A7,
+    0xE92675F4, 0x7DF1A942,
+    0xE8F50273, 0x7DE8A670,
+    0xE8C3927F, 0x7DDF9034,
+    0xE8922621, 0x7DD6668E,
+    0xE860BD60, 0x7DCD2981,
+    0xE82F5844, 0x7DC3D90D,
+    0xE7FDF6D3, 0x7DBA7534,
+    0xE7CC9917, 0x7DB0FDF7,
+    0xE79B3F16, 0x7DA77359,
+    0xE769E8D8, 0x7D9DD55A,
+    0xE7389664, 0x7D9423FB,
+    0xE70747C3, 0x7D8A5F3F,
+    0xE6D5FCFC, 0x7D808727,
+    0xE6A4B616, 0x7D769BB5,
+    0xE6737319, 0x7D6C9CE9,
+    0xE642340D, 0x7D628AC5,
+    0xE610F8F9, 0x7D58654C,
+    0xE5DFC1E4, 0x7D4E2C7E,
+    0xE5AE8ED8, 0x7D43E05E,
+    0xE57D5FDA, 0x7D3980EC,
+    0xE54C34F3, 0x7D2F0E2A,
+    0xE51B0E2A, 0x7D24881A,
+    0xE4E9EB86, 0x7D19EEBE,
+    0xE4B8CD10, 0x7D0F4218,
+    0xE487B2CF, 0x7D048228,
+    0xE4569CCB, 0x7CF9AEF0,
+    0xE4258B0A, 0x7CEEC873,
+    0xE3F47D95, 0x7CE3CEB1,
+    0xE3C37473, 0x7CD8C1AD,
+    0xE3926FAC, 0x7CCDA168,
+    0xE3616F47, 0x7CC26DE5,
+    0xE330734C, 0x7CB72724,
+    0xE2FF7BC3, 0x7CABCD27,
+    0xE2CE88B2, 0x7CA05FF1,
+    0xE29D9A22, 0x7C94DF82,
+    0xE26CB01A, 0x7C894BDD,
+    0xE23BCAA2, 0x7C7DA504,
+    0xE20AE9C1, 0x7C71EAF8,
+    0xE1DA0D7E, 0x7C661DBB,
+    0xE1A935E1, 0x7C5A3D4F,
+    0xE17862F3, 0x7C4E49B6,
+    0xE14794B9, 0x7C4242F2,
+    0xE116CB3D, 0x7C362904,
+    0xE0E60684, 0x7C29FBEE,
+    0xE0B54698, 0x7C1DBBB2,
+    0xE0848B7F, 0x7C116853,
+    0xE053D541, 0x7C0501D1,
+    0xE02323E5, 0x7BF88830,
+    0xDFF27773, 0x7BEBFB70,
+    0xDFC1CFF2, 0x7BDF5B94,
+    0xDF912D6A, 0x7BD2A89E,
+    0xDF608FE3, 0x7BC5E28F,
+    0xDF2FF764, 0x7BB9096A,
+    0xDEFF63F4, 0x7BAC1D31,
+    0xDECED59B, 0x7B9F1DE5,
+    0xDE9E4C60, 0x7B920B89,
+    0xDE6DC84B, 0x7B84E61E,
+    0xDE3D4963, 0x7B77ADA8,
+    0xDE0CCFB1, 0x7B6A6227,
+    0xDDDC5B3A, 0x7B5D039D,
+    0xDDABEC07, 0x7B4F920E,
+    0xDD7B8220, 0x7B420D7A,
+    0xDD4B1D8B, 0x7B3475E4,
+    0xDD1ABE51, 0x7B26CB4F,
+    0xDCEA6478, 0x7B190DBB,
+    0xDCBA1008, 0x7B0B3D2C,
+    0xDC89C108, 0x7AFD59A3,
+    0xDC597781, 0x7AEF6323,
+    0xDC293379, 0x7AE159AE,
+    0xDBF8F4F8, 0x7AD33D45,
+    0xDBC8BC05, 0x7AC50DEB,
+    0xDB9888A8, 0x7AB6CBA3,
+    0xDB685AE8, 0x7AA8766E,
+    0xDB3832CD, 0x7A9A0E4F,
+    0xDB08105E, 0x7A8B9348,
+    0xDAD7F3A2, 0x7A7D055B,
+    0xDAA7DCA1, 0x7A6E648A,
+    0xDA77CB62, 0x7A5FB0D8,
+    0xDA47BFED, 0x7A50EA46,
+    0xDA17BA4A, 0x7A4210D8,
+    0xD9E7BA7E, 0x7A33248F,
+    0xD9B7C093, 0x7A24256E,
+    0xD987CC8F, 0x7A151377,
+    0xD957DE7A, 0x7A05EEAD,
+    0xD927F65B, 0x79F6B711,
+    0xD8F81439, 0x79E76CA6,
+    0xD8C8381C, 0x79D80F6F,
+    0xD898620C, 0x79C89F6D,
+    0xD868920F, 0x79B91CA4,
+    0xD838C82D, 0x79A98715,
+    0xD809046D, 0x7999DEC3,
+    0xD7D946D7, 0x798A23B1,
+    0xD7A98F73, 0x797A55E0,
+    0xD779DE46, 0x796A7554,
+    0xD74A335A, 0x795A820E,
+    0xD71A8EB5, 0x794A7C11,
+    0xD6EAF05E, 0x793A6360,
+    0xD6BB585D, 0x792A37FE,
+    0xD68BC6BA, 0x7919F9EB,
+    0xD65C3B7B, 0x7909A92C,
+    0xD62CB6A7, 0x78F945C3,
+    0xD5FD3847, 0x78E8CFB1,
+    0xD5CDC062, 0x78D846FB,
+    0xD59E4EFE, 0x78C7ABA1,
+    0xD56EE424, 0x78B6FDA8,
+    0xD53F7FDA, 0x78A63D10,
+    0xD5102227, 0x789569DE,
+    0xD4E0CB14, 0x78848413,
+    0xD4B17AA7, 0x78738BB3,
+    0xD48230E8, 0x786280BF,
+    0xD452EDDE, 0x7851633B,
+    0xD423B190, 0x78403328,
+    0xD3F47C06, 0x782EF08B,
+    0xD3C54D46, 0x781D9B64,
+    0xD3962559, 0x780C33B8,
+    0xD3670445, 0x77FAB988,
+    0xD337EA12, 0x77E92CD8,
+    0xD308D6C6, 0x77D78DAA,
+    0xD2D9CA6A, 0x77C5DC01,
+    0xD2AAC504, 0x77B417DF,
+    0xD27BC69C, 0x77A24148,
+    0xD24CCF38, 0x7790583D,
+    0xD21DDEE1, 0x777E5CC3,
+    0xD1EEF59E, 0x776C4EDB,
+    0xD1C01374, 0x775A2E88,
+    0xD191386D, 0x7747FBCE,
+    0xD162648F, 0x7735B6AE,
+    0xD13397E1, 0x77235F2D,
+    0xD104D26B, 0x7710F54B,
+    0xD0D61433, 0x76FE790E,
+    0xD0A75D42, 0x76EBEA77,
+    0xD078AD9D, 0x76D94988,
+    0xD04A054D, 0x76C69646,
+    0xD01B6459, 0x76B3D0B3,
+    0xCFECCAC7, 0x76A0F8D2,
+    0xCFBE389F, 0x768E0EA5,
+    0xCF8FADE8, 0x767B1230,
+    0xCF612AAA, 0x76680376,
+    0xCF32AEEB, 0x7654E279,
+    0xCF043AB2, 0x7641AF3C,
+    0xCED5CE08, 0x762E69C3,
+    0xCEA768F2, 0x761B1211,
+    0xCE790B78, 0x7607A827,
+    0xCE4AB5A2, 0x75F42C0A,
+    0xCE1C6776, 0x75E09DBD,
+    0xCDEE20FC, 0x75CCFD42,
+    0xCDBFE23A, 0x75B94A9C,
+    0xCD91AB38, 0x75A585CF,
+    0xCD637BFD, 0x7591AEDD,
+    0xCD355490, 0x757DC5CA,
+    0xCD0734F8, 0x7569CA98,
+    0xCCD91D3D, 0x7555BD4B,
+    0xCCAB0D65, 0x75419DE6,
+    0xCC7D0577, 0x752D6C6C,
+    0xCC4F057B, 0x751928E0,
+    0xCC210D78, 0x7504D345,
+    0xCBF31D75, 0x74F06B9E,
+    0xCBC53578, 0x74DBF1EF,
+    0xCB975589, 0x74C7663A,
+    0xCB697DB0, 0x74B2C883,
+    0xCB3BADF2, 0x749E18CD,
+    0xCB0DE658, 0x7489571B,
+    0xCAE026E8, 0x74748371,
+    0xCAB26FA9, 0x745F9DD1,
+    0xCA84C0A2, 0x744AA63E,
+    0xCA5719DB, 0x74359CBD,
+    0xCA297B5A, 0x74208150,
+    0xC9FBE527, 0x740B53FA,
+    0xC9CE5748, 0x73F614C0,
+    0xC9A0D1C4, 0x73E0C3A3,
+    0xC97354A3, 0x73CB60A7,
+    0xC945DFEC, 0x73B5EBD0,
+    0xC91873A5, 0x73A06522,
+    0xC8EB0FD6, 0x738ACC9E,
+    0xC8BDB485, 0x73752249,
+    0xC89061BA, 0x735F6626,
+    0xC863177B, 0x73499838,
+    0xC835D5D0, 0x7333B883,
+    0xC8089CBF, 0x731DC709,
+    0xC7DB6C50, 0x7307C3D0,
+    0xC7AE4489, 0x72F1AED8,
+    0xC7812571, 0x72DB8828,
+    0xC7540F10, 0x72C54FC0,
+    0xC727016C, 0x72AF05A6,
+    0xC6F9FC8D, 0x7298A9DC,
+    0xC6CD0079, 0x72823C66,
+    0xC6A00D36, 0x726BBD48,
+    0xC67322CD, 0x72552C84,
+    0xC6464144, 0x723E8A1F,
+    0xC61968A2, 0x7227D61C,
+    0xC5EC98ED, 0x7211107D,
+    0xC5BFD22E, 0x71FA3948,
+    0xC593146A, 0x71E3507F,
+    0xC5665FA8, 0x71CC5626,
+    0xC539B3F0, 0x71B54A40,
+    0xC50D1148, 0x719E2CD2,
+    0xC4E077B8, 0x7186FDDE,
+    0xC4B3E746, 0x716FBD68,
+    0xC4875FF8, 0x71586B73,
+    0xC45AE1D7, 0x71410804,
+    0xC42E6CE8, 0x7129931E,
+    0xC4020132, 0x71120CC5,
+    0xC3D59EBD, 0x70FA74FB,
+    0xC3A9458F, 0x70E2CBC6,
+    0xC37CF5B0, 0x70CB1127,
+    0xC350AF25, 0x70B34524,
+    0xC32471F6, 0x709B67C0,
+    0xC2F83E2A, 0x708378FE,
+    0xC2CC13C7, 0x706B78E3,
+    0xC29FF2D4, 0x70536771,
+    0xC273DB58, 0x703B44AC,
+    0xC247CD5A, 0x70231099,
+    0xC21BC8E0, 0x700ACB3B,
+    0xC1EFCDF2, 0x6FF27496,
+    0xC1C3DC96, 0x6FDA0CAD,
+    0xC197F4D3, 0x6FC19385,
+    0xC16C16B0, 0x6FA90920,
+    0xC1404233, 0x6F906D84,
+    0xC1147763, 0x6F77C0B3,
+    0xC0E8B648, 0x6F5F02B1,
+    0xC0BCFEE7, 0x6F463383,
+    0xC0915147, 0x6F2D532C,
+    0xC065AD70, 0x6F1461AF,
+    0xC03A1368, 0x6EFB5F12,
+    0xC00E8335, 0x6EE24B57,
+    0xBFE2FCDF, 0x6EC92682,
+    0xBFB7806C, 0x6EAFF098,
+    0xBF8C0DE2, 0x6E96A99C,
+    0xBF60A54A, 0x6E7D5193,
+    0xBF3546A8, 0x6E63E87F,
+    0xBF09F204, 0x6E4A6E65,
+    0xBEDEA765, 0x6E30E349,
+    0xBEB366D1, 0x6E17472F,
+    0xBE88304F, 0x6DFD9A1B,
+    0xBE5D03E5, 0x6DE3DC11,
+    0xBE31E19B, 0x6DCA0D14,
+    0xBE06C977, 0x6DB02D29,
+    0xBDDBBB7F, 0x6D963C54,
+    0xBDB0B7BA, 0x6D7C3A98,
+    0xBD85BE2F, 0x6D6227FA,
+    0xBD5ACEE5, 0x6D48047E,
+    0xBD2FE9E1, 0x6D2DD027,
+    0xBD050F2C, 0x6D138AFA,
+    0xBCDA3ECA, 0x6CF934FB,
+    0xBCAF78C3, 0x6CDECE2E,
+    0xBC84BD1E, 0x6CC45697,
+    0xBC5A0BE1, 0x6CA9CE3A,
+    0xBC2F6513, 0x6C8F351C,
+    0xBC04C8BA, 0x6C748B3F,
+    0xBBDA36DC, 0x6C59D0A9,
+    0xBBAFAF81, 0x6C3F055D,
+    0xBB8532AF, 0x6C242960,
+    0xBB5AC06C, 0x6C093CB6,
+    0xBB3058C0, 0x6BEE3F62,
+    0xBB05FBB0, 0x6BD3316A,
+    0xBADBA943, 0x6BB812D0,
+    0xBAB1617F, 0x6B9CE39B,
+    0xBA87246C, 0x6B81A3CD,
+    0xBA5CF210, 0x6B66536A,
+    0xBA32CA70, 0x6B4AF278,
+    0xBA08AD94, 0x6B2F80FA,
+    0xB9DE9B83, 0x6B13FEF5,
+    0xB9B49442, 0x6AF86C6C,
+    0xB98A97D8, 0x6ADCC964,
+    0xB960A64B, 0x6AC115E1,
+    0xB936BFA3, 0x6AA551E8,
+    0xB90CE3E6, 0x6A897D7D,
+    0xB8E31319, 0x6A6D98A4,
+    0xB8B94D44, 0x6A51A361,
+    0xB88F926C, 0x6A359DB9,
+    0xB865E299, 0x6A1987B0,
+    0xB83C3DD1, 0x69FD614A,
+    0xB812A419, 0x69E12A8C,
+    0xB7E9157A, 0x69C4E37A,
+    0xB7BF91F8, 0x69A88C18,
+    0xB796199B, 0x698C246C,
+    0xB76CAC68, 0x696FAC78,
+    0xB7434A67, 0x69532442,
+    0xB719F39D, 0x69368BCE,
+    0xB6F0A811, 0x6919E320,
+    0xB6C767CA, 0x68FD2A3D,
+    0xB69E32CD, 0x68E06129,
+    0xB6750921, 0x68C387E9,
+    0xB64BEACC, 0x68A69E81,
+    0xB622D7D5, 0x6889A4F5,
+    0xB5F9D042, 0x686C9B4B,
+    0xB5D0D41A, 0x684F8186,
+    0xB5A7E362, 0x683257AA,
+    0xB57EFE21, 0x68151DBE,
+    0xB556245E, 0x67F7D3C4,
+    0xB52D561E, 0x67DA79C2,
+    0xB5049368, 0x67BD0FBC,
+    0xB4DBDC42, 0x679F95B7,
+    0xB4B330B2, 0x67820BB6,
+    0xB48A90C0, 0x676471C0,
+    0xB461FC70, 0x6746C7D7,
+    0xB43973C9, 0x67290E02,
+    0xB410F6D2, 0x670B4443,
+    0xB3E88591, 0x66ED6AA1,
+    0xB3C0200C, 0x66CF811F,
+    0xB397C649, 0x66B187C3,
+    0xB36F784E, 0x66937E90,
+    0xB3473622, 0x6675658C,
+    0xB31EFFCB, 0x66573CBB,
+    0xB2F6D54F, 0x66390422,
+    0xB2CEB6B5, 0x661ABBC5,
+    0xB2A6A401, 0x65FC63A9,
+    0xB27E9D3B, 0x65DDFBD3,
+    0xB256A26A, 0x65BF8447,
+    0xB22EB392, 0x65A0FD0B,
+    0xB206D0BA, 0x65826622,
+    0xB1DEF9E8, 0x6563BF92,
+    0xB1B72F23, 0x6545095F,
+    0xB18F7070, 0x6526438E,
+    0xB167BDD6, 0x65076E24,
+    0xB140175B, 0x64E88926,
+    0xB1187D05, 0x64C99498,
+    0xB0F0EEDA, 0x64AA907F,
+    0xB0C96CDF, 0x648B7CDF,
+    0xB0A1F71C, 0x646C59BF,
+    0xB07A8D97, 0x644D2722,
+    0xB0533055, 0x642DE50D,
+    0xB02BDF5C, 0x640E9385,
+    0xB0049AB2, 0x63EF328F,
+    0xAFDD625F, 0x63CFC230,
+    0xAFB63667, 0x63B0426D,
+    0xAF8F16D0, 0x6390B34A,
+    0xAF6803A1, 0x637114CC,
+    0xAF40FCE0, 0x635166F8,
+    0xAF1A0293, 0x6331A9D4,
+    0xAEF314BF, 0x6311DD63,
+    0xAECC336B, 0x62F201AC,
+    0xAEA55E9D, 0x62D216B2,
+    0xAE7E965B, 0x62B21C7B,
+    0xAE57DAAA, 0x6292130C,
+    0xAE312B91, 0x6271FA69,
+    0xAE0A8916, 0x6251D297,
+    0xADE3F33E, 0x62319B9D,
+    0xADBD6A10, 0x6211557D,
+    0xAD96ED91, 0x61F1003E,
+    0xAD707DC8, 0x61D09BE5,
+    0xAD4A1ABA, 0x61B02876,
+    0xAD23C46D, 0x618FA5F6,
+    0xACFD7AE8, 0x616F146B,
+    0xACD73E30, 0x614E73D9,
+    0xACB10E4A, 0x612DC446,
+    0xAC8AEB3E, 0x610D05B7,
+    0xAC64D510, 0x60EC3830,
+    0xAC3ECBC7, 0x60CB5BB6,
+    0xAC18CF68, 0x60AA704F,
+    0xABF2DFFA, 0x60897600,
+    0xABCCFD82, 0x60686CCE,
+    0xABA72806, 0x604754BE,
+    0xAB815F8C, 0x60262DD5,
+    0xAB5BA41A, 0x6004F818,
+    0xAB35F5B5, 0x5FE3B38D,
+    0xAB105464, 0x5FC26038,
+    0xAAEAC02B, 0x5FA0FE1E,
+    0xAAC53912, 0x5F7F8D46,
+    0xAA9FBF1D, 0x5F5E0DB3,
+    0xAA7A5253, 0x5F3C7F6B,
+    0xAA54F2B9, 0x5F1AE273,
+    0xAA2FA055, 0x5EF936D1,
+    0xAA0A5B2D, 0x5ED77C89,
+    0xA9E52347, 0x5EB5B3A1,
+    0xA9BFF8A8, 0x5E93DC1F,
+    0xA99ADB56, 0x5E71F606,
+    0xA975CB56, 0x5E50015D,
+    0xA950C8AF, 0x5E2DFE28,
+    0xA92BD366, 0x5E0BEC6E,
+    0xA906EB81, 0x5DE9CC32,
+    0xA8E21106, 0x5DC79D7C,
+    0xA8BD43FA, 0x5DA5604E,
+    0xA8988463, 0x5D8314B0,
+    0xA873D246, 0x5D60BAA6,
+    0xA84F2DA9, 0x5D3E5236,
+    0xA82A9693, 0x5D1BDB65,
+    0xA8060D08, 0x5CF95638,
+    0xA7E1910E, 0x5CD6C2B4,
+    0xA7BD22AB, 0x5CB420DF,
+    0xA798C1E4, 0x5C9170BF,
+    0xA7746EC0, 0x5C6EB258,
+    0xA7502943, 0x5C4BE5B0,
+    0xA72BF173, 0x5C290ACC,
+    0xA707C756, 0x5C0621B2,
+    0xA6E3AAF2, 0x5BE32A67,
+    0xA6BF9C4B, 0x5BC024F0,
+    0xA69B9B68, 0x5B9D1153,
+    0xA677A84E, 0x5B79EF96,
+    0xA653C302, 0x5B56BFBD,
+    0xA62FEB8B, 0x5B3381CE,
+    0xA60C21ED, 0x5B1035CF,
+    0xA5E8662F, 0x5AECDBC4,
+    0xA5C4B855, 0x5AC973B4,
+    0xA5A11865, 0x5AA5FDA4,
+    0xA57D8666, 0x5A82799A,
+    0xA55A025B, 0x5A5EE79A,
+    0xA5368C4B, 0x5A3B47AA,
+    0xA513243B, 0x5A1799D0,
+    0xA4EFCA31, 0x59F3DE12,
+    0xA4CC7E31, 0x59D01474,
+    0xA4A94042, 0x59AC3CFD,
+    0xA4861069, 0x598857B1,
+    0xA462EEAC, 0x59646497,
+    0xA43FDB0F, 0x594063B4,
+    0xA41CD598, 0x591C550E,
+    0xA3F9DE4D, 0x58F838A9,
+    0xA3D6F533, 0x58D40E8C,
+    0xA3B41A4F, 0x58AFD6BC,
+    0xA3914DA7, 0x588B913F,
+    0xA36E8F40, 0x58673E1B,
+    0xA34BDF20, 0x5842DD54,
+    0xA3293D4B, 0x581E6EF1,
+    0xA306A9C7, 0x57F9F2F7,
+    0xA2E4249A, 0x57D5696C,
+    0xA2C1ADC9, 0x57B0D256,
+    0xA29F4559, 0x578C2DB9,
+    0xA27CEB4F, 0x57677B9D,
+    0xA25A9FB1, 0x5742BC05,
+    0xA2386283, 0x571DEEF9,
+    0xA21633CD, 0x56F9147E,
+    0xA1F41391, 0x56D42C99,
+    0xA1D201D7, 0x56AF3750,
+    0xA1AFFEA2, 0x568A34A9,
+    0xA18E09F9, 0x566524AA,
+    0xA16C23E1, 0x56400757,
+    0xA14A4C5E, 0x561ADCB8,
+    0xA1288376, 0x55F5A4D2,
+    0xA106C92E, 0x55D05FAA,
+    0xA0E51D8C, 0x55AB0D46,
+    0xA0C38094, 0x5585ADAC,
+    0xA0A1F24C, 0x556040E2,
+    0xA08072BA, 0x553AC6ED,
+    0xA05F01E1, 0x55153FD4,
+    0xA03D9FC7, 0x54EFAB9C,
+    0xA01C4C72, 0x54CA0A4A,
+    0x9FFB07E7, 0x54A45BE5,
+    0x9FD9D22A, 0x547EA073,
+    0x9FB8AB41, 0x5458D7F9,
+    0x9F979331, 0x5433027D,
+    0x9F7689FF, 0x540D2005,
+    0x9F558FB0, 0x53E73097,
+    0x9F34A449, 0x53C13438,
+    0x9F13C7D0, 0x539B2AEF,
+    0x9EF2FA48, 0x537514C1,
+    0x9ED23BB9, 0x534EF1B5,
+    0x9EB18C26, 0x5328C1D0,
+    0x9E90EB94, 0x53028517,
+    0x9E705A09, 0x52DC3B92,
+    0x9E4FD789, 0x52B5E545,
+    0x9E2F641A, 0x528F8237,
+    0x9E0EFFC1, 0x5269126E,
+    0x9DEEAA82, 0x524295EF,
+    0x9DCE6462, 0x521C0CC1,
+    0x9DAE2D68, 0x51F576E9,
+    0x9D8E0596, 0x51CED46E,
+    0x9D6DECF4, 0x51A82555,
+    0x9D4DE384, 0x518169A4,
+    0x9D2DE94D, 0x515AA162,
+    0x9D0DFE53, 0x5133CC94,
+    0x9CEE229C, 0x510CEB40,
+    0x9CCE562B, 0x50E5FD6C,
+    0x9CAE9907, 0x50BF031F,
+    0x9C8EEB33, 0x5097FC5E,
+    0x9C6F4CB5, 0x5070E92F,
+    0x9C4FBD92, 0x5049C999,
+    0x9C303DCF, 0x50229DA0,
+    0x9C10CD70, 0x4FFB654D,
+    0x9BF16C7A, 0x4FD420A3,
+    0x9BD21AF2, 0x4FACCFAB,
+    0x9BB2D8DD, 0x4F857268,
+    0x9B93A640, 0x4F5E08E3,
+    0x9B748320, 0x4F369320,
+    0x9B556F80, 0x4F0F1126,
+    0x9B366B67, 0x4EE782FA,
+    0x9B1776D9, 0x4EBFE8A4,
+    0x9AF891DB, 0x4E984229,
+    0x9AD9BC71, 0x4E708F8F,
+    0x9ABAF6A0, 0x4E48D0DC,
+    0x9A9C406D, 0x4E210617,
+    0x9A7D99DD, 0x4DF92F45,
+    0x9A5F02F5, 0x4DD14C6E,
+    0x9A407BB8, 0x4DA95D96,
+    0x9A22042C, 0x4D8162C4,
+    0x9A039C56, 0x4D595BFE,
+    0x99E5443A, 0x4D31494B,
+    0x99C6FBDE, 0x4D092AB0,
+    0x99A8C344, 0x4CE10034,
+    0x998A9A73, 0x4CB8C9DD,
+    0x996C816F, 0x4C9087B1,
+    0x994E783C, 0x4C6839B6,
+    0x99307EE0, 0x4C3FDFF3,
+    0x9912955E, 0x4C177A6E,
+    0x98F4BBBC, 0x4BEF092D,
+    0x98D6F1FE, 0x4BC68C36,
+    0x98B93828, 0x4B9E038F,
+    0x989B8E3F, 0x4B756F3F,
+    0x987DF449, 0x4B4CCF4D,
+    0x98606A48, 0x4B2423BD,
+    0x9842F043, 0x4AFB6C97,
+    0x9825863D, 0x4AD2A9E1,
+    0x98082C3B, 0x4AA9DBA1,
+    0x97EAE241, 0x4A8101DE,
+    0x97CDA855, 0x4A581C9D,
+    0x97B07E7A, 0x4A2F2BE5,
+    0x979364B5, 0x4A062FBD,
+    0x97765B0A, 0x49DD282A,
+    0x9759617E, 0x49B41533,
+    0x973C7816, 0x498AF6DE,
+    0x971F9ED6, 0x4961CD32,
+    0x9702D5C2, 0x49389836,
+    0x96E61CDF, 0x490F57EE,
+    0x96C97431, 0x48E60C62,
+    0x96ACDBBD, 0x48BCB598,
+    0x96905387, 0x48935397,
+    0x9673DB94, 0x4869E664,
+    0x965773E7, 0x48406E07,
+    0x963B1C85, 0x4816EA85,
+    0x961ED573, 0x47ED5BE6,
+    0x96029EB5, 0x47C3C22E,
+    0x95E6784F, 0x479A1D66,
+    0x95CA6246, 0x47706D93,
+    0x95AE5C9E, 0x4746B2BC,
+    0x9592675B, 0x471CECE6,
+    0x95768282, 0x46F31C1A,
+    0x955AAE17, 0x46C9405C,
+    0x953EEA1E, 0x469F59B4,
+    0x9523369B, 0x46756827,
+    0x95079393, 0x464B6BBD,
+    0x94EC010B, 0x4621647C,
+    0x94D07F05, 0x45F7526B,
+    0x94B50D87, 0x45CD358F,
+    0x9499AC95, 0x45A30DF0,
+    0x947E5C32, 0x4578DB93,
+    0x94631C64, 0x454E9E80,
+    0x9447ED2F, 0x452456BC,
+    0x942CCE95, 0x44FA044F,
+    0x9411C09D, 0x44CFA73F,
+    0x93F6C34A, 0x44A53F93,
+    0x93DBD69F, 0x447ACD50,
+    0x93C0FAA2, 0x4450507E,
+    0x93A62F56, 0x4425C923,
+    0x938B74C0, 0x43FB3745,
+    0x9370CAE4, 0x43D09AEC,
+    0x935631C5, 0x43A5F41E,
+    0x933BA968, 0x437B42E1,
+    0x932131D1, 0x4350873C,
+    0x9306CB04, 0x4325C135,
+    0x92EC7505, 0x42FAF0D4,
+    0x92D22FD8, 0x42D0161E,
+    0x92B7FB82, 0x42A5311A,
+    0x929DD805, 0x427A41D0,
+    0x9283C567, 0x424F4845,
+    0x9269C3AC, 0x42244480,
+    0x924FD2D6, 0x41F93688,
+    0x9235F2EB, 0x41CE1E64,
+    0x921C23EE, 0x41A2FC1A,
+    0x920265E4, 0x4177CFB0,
+    0x91E8B8D0, 0x414C992E,
+    0x91CF1CB6, 0x4121589A,
+    0x91B5919A, 0x40F60DFB,
+    0x919C1780, 0x40CAB957,
+    0x9182AE6C, 0x409F5AB6,
+    0x91695663, 0x4073F21D,
+    0x91500F67, 0x40487F93,
+    0x9136D97D, 0x401D0320,
+    0x911DB4A8, 0x3FF17CCA,
+    0x9104A0ED, 0x3FC5EC97,
+    0x90EB9E50, 0x3F9A528F,
+    0x90D2ACD3, 0x3F6EAEB8,
+    0x90B9CC7C, 0x3F430118,
+    0x90A0FD4E, 0x3F1749B7,
+    0x90883F4C, 0x3EEB889C,
+    0x906F927B, 0x3EBFBDCC,
+    0x9056F6DF, 0x3E93E94F,
+    0x903E6C7A, 0x3E680B2C,
+    0x9025F352, 0x3E3C2369,
+    0x900D8B69, 0x3E10320D,
+    0x8FF534C4, 0x3DE4371F,
+    0x8FDCEF66, 0x3DB832A5,
+    0x8FC4BB53, 0x3D8C24A7,
+    0x8FAC988E, 0x3D600D2B,
+    0x8F94871D, 0x3D33EC39,
+    0x8F7C8701, 0x3D07C1D5,
+    0x8F64983F, 0x3CDB8E09,
+    0x8F4CBADB, 0x3CAF50DA,
+    0x8F34EED8, 0x3C830A4F,
+    0x8F1D343A, 0x3C56BA70,
+    0x8F058B04, 0x3C2A6142,
+    0x8EEDF33B, 0x3BFDFECD,
+    0x8ED66CE1, 0x3BD19317,
+    0x8EBEF7FB, 0x3BA51E29,
+    0x8EA7948C, 0x3B78A007,
+    0x8E904298, 0x3B4C18BA,
+    0x8E790222, 0x3B1F8847,
+    0x8E61D32D, 0x3AF2EEB7,
+    0x8E4AB5BF, 0x3AC64C0F,
+    0x8E33A9D9, 0x3A99A057,
+    0x8E1CAF80, 0x3A6CEB95,
+    0x8E05C6B7, 0x3A402DD1,
+    0x8DEEEF82, 0x3A136712,
+    0x8DD829E4, 0x39E6975D,
+    0x8DC175E0, 0x39B9BEBB,
+    0x8DAAD37B, 0x398CDD32,
+    0x8D9442B7, 0x395FF2C9,
+    0x8D7DC399, 0x3932FF87,
+    0x8D675623, 0x39060372,
+    0x8D50FA59, 0x38D8FE93,
+    0x8D3AB03F, 0x38ABF0EF,
+    0x8D2477D8, 0x387EDA8E,
+    0x8D0E5127, 0x3851BB76,
+    0x8CF83C30, 0x382493B0,
+    0x8CE238F6, 0x37F76340,
+    0x8CCC477D, 0x37CA2A30,
+    0x8CB667C7, 0x379CE884,
+    0x8CA099D9, 0x376F9E46,
+    0x8C8ADDB6, 0x37424B7A,
+    0x8C753361, 0x3714F02A,
+    0x8C5F9ADD, 0x36E78C5A,
+    0x8C4A142F, 0x36BA2013,
+    0x8C349F58, 0x368CAB5C,
+    0x8C1F3C5C, 0x365F2E3B,
+    0x8C09EB40, 0x3631A8B7,
+    0x8BF4AC05, 0x36041AD9,
+    0x8BDF7EAF, 0x35D684A5,
+    0x8BCA6342, 0x35A8E624,
+    0x8BB559C1, 0x357B3F5D,
+    0x8BA0622F, 0x354D9056,
+    0x8B8B7C8F, 0x351FD917,
+    0x8B76A8E4, 0x34F219A7,
+    0x8B61E732, 0x34C4520D,
+    0x8B4D377C, 0x3496824F,
+    0x8B3899C5, 0x3468AA76,
+    0x8B240E10, 0x343ACA87,
+    0x8B0F9461, 0x340CE28A,
+    0x8AFB2CBA, 0x33DEF287,
+    0x8AE6D71F, 0x33B0FA84,
+    0x8AD29393, 0x3382FA88,
+    0x8ABE6219, 0x3354F29A,
+    0x8AAA42B4, 0x3326E2C2,
+    0x8A963567, 0x32F8CB07,
+    0x8A823A35, 0x32CAAB6F,
+    0x8A6E5122, 0x329C8402,
+    0x8A5A7A30, 0x326E54C7,
+    0x8A46B563, 0x32401DC5,
+    0x8A3302BD, 0x3211DF03,
+    0x8A1F6242, 0x31E39889,
+    0x8A0BD3F5, 0x31B54A5D,
+    0x89F857D8, 0x3186F487,
+    0x89E4EDEE, 0x3158970D,
+    0x89D1963C, 0x312A31F8,
+    0x89BE50C3, 0x30FBC54D,
+    0x89AB1D86, 0x30CD5114,
+    0x8997FC89, 0x309ED555,
+    0x8984EDCF, 0x30705217,
+    0x8971F15A, 0x3041C760,
+    0x895F072D, 0x30133538,
+    0x894C2F4C, 0x2FE49BA6,
+    0x893969B9, 0x2FB5FAB2,
+    0x8926B677, 0x2F875262,
+    0x89141589, 0x2F58A2BD,
+    0x890186F1, 0x2F29EBCC,
+    0x88EF0AB4, 0x2EFB2D94,
+    0x88DCA0D3, 0x2ECC681E,
+    0x88CA4951, 0x2E9D9B70,
+    0x88B80431, 0x2E6EC792,
+    0x88A5D177, 0x2E3FEC8B,
+    0x8893B124, 0x2E110A62,
+    0x8881A33C, 0x2DE2211E,
+    0x886FA7C2, 0x2DB330C7,
+    0x885DBEB7, 0x2D843963,
+    0x884BE820, 0x2D553AFB,
+    0x883A23FE, 0x2D263595,
+    0x88287255, 0x2CF72939,
+    0x8816D327, 0x2CC815ED,
+    0x88054677, 0x2C98FBBA,
+    0x87F3CC47, 0x2C69DAA6,
+    0x87E2649B, 0x2C3AB2B9,
+    0x87D10F75, 0x2C0B83F9,
+    0x87BFCCD7, 0x2BDC4E6F,
+    0x87AE9CC5, 0x2BAD1221,
+    0x879D7F40, 0x2B7DCF17,
+    0x878C744C, 0x2B4E8558,
+    0x877B7BEC, 0x2B1F34EB,
+    0x876A9621, 0x2AEFDDD8,
+    0x8759C2EF, 0x2AC08025,
+    0x87490257, 0x2A911BDB,
+    0x8738545E, 0x2A61B101,
+    0x8727B904, 0x2A323F9D,
+    0x8717304E, 0x2A02C7B8,
+    0x8706BA3C, 0x29D34958,
+    0x86F656D3, 0x29A3C484,
+    0x86E60614, 0x29743945,
+    0x86D5C802, 0x2944A7A2,
+    0x86C59C9F, 0x29150FA1,
+    0x86B583EE, 0x28E5714A,
+    0x86A57DF1, 0x28B5CCA5,
+    0x86958AAB, 0x288621B9,
+    0x8685AA1F, 0x2856708C,
+    0x8675DC4E, 0x2826B928,
+    0x8666213C, 0x27F6FB92,
+    0x865678EA, 0x27C737D2,
+    0x8646E35B, 0x27976DF1,
+    0x86376092, 0x27679DF4,
+    0x8627F090, 0x2737C7E3,
+    0x86189359, 0x2707EBC6,
+    0x860948EE, 0x26D809A5,
+    0x85FA1152, 0x26A82185,
+    0x85EAEC88, 0x26783370,
+    0x85DBDA91, 0x26483F6C,
+    0x85CCDB70, 0x26184581,
+    0x85BDEF27, 0x25E845B5,
+    0x85AF15B9, 0x25B84012,
+    0x85A04F28, 0x2588349D,
+    0x85919B75, 0x2558235E,
+    0x8582FAA4, 0x25280C5D,
+    0x85746CB7, 0x24F7EFA1,
+    0x8565F1B0, 0x24C7CD32,
+    0x85578991, 0x2497A517,
+    0x8549345C, 0x24677757,
+    0x853AF214, 0x243743FA,
+    0x852CC2BA, 0x24070B07,
+    0x851EA652, 0x23D6CC86,
+    0x85109CDC, 0x23A6887E,
+    0x8502A65C, 0x23763EF7,
+    0x84F4C2D3, 0x2345EFF7,
+    0x84E6F244, 0x23159B87,
+    0x84D934B0, 0x22E541AE,
+    0x84CB8A1B, 0x22B4E274,
+    0x84BDF285, 0x22847DDF,
+    0x84B06DF1, 0x225413F8,
+    0x84A2FC62, 0x2223A4C5,
+    0x84959DD9, 0x21F3304E,
+    0x84885257, 0x21C2B69C,
+    0x847B19E1, 0x219237B4,
+    0x846DF476, 0x2161B39F,
+    0x8460E21A, 0x21312A65,
+    0x8453E2CE, 0x21009C0B,
+    0x8446F695, 0x20D0089B,
+    0x843A1D70, 0x209F701C,
+    0x842D5761, 0x206ED295,
+    0x8420A46B, 0x203E300D,
+    0x8414048F, 0x200D888C,
+    0x840777CF, 0x1FDCDC1A,
+    0x83FAFE2E, 0x1FAC2ABF,
+    0x83EE97AC, 0x1F7B7480,
+    0x83E2444D, 0x1F4AB967,
+    0x83D60411, 0x1F19F97B,
+    0x83C9D6FB, 0x1EE934C2,
+    0x83BDBD0D, 0x1EB86B46,
+    0x83B1B649, 0x1E879D0C,
+    0x83A5C2B0, 0x1E56CA1E,
+    0x8399E244, 0x1E25F281,
+    0x838E1507, 0x1DF5163F,
+    0x83825AFB, 0x1DC4355D,
+    0x8376B422, 0x1D934FE5,
+    0x836B207D, 0x1D6265DD,
+    0x835FA00E, 0x1D31774D,
+    0x835432D8, 0x1D00843C,
+    0x8348D8DB, 0x1CCF8CB3,
+    0x833D921A, 0x1C9E90B8,
+    0x83325E97, 0x1C6D9053,
+    0x83273E52, 0x1C3C8B8C,
+    0x831C314E, 0x1C0B826A,
+    0x8311378C, 0x1BDA74F5,
+    0x8306510F, 0x1BA96334,
+    0x82FB7DD8, 0x1B784D30,
+    0x82F0BDE8, 0x1B4732EF,
+    0x82E61141, 0x1B161479,
+    0x82DB77E5, 0x1AE4F1D6,
+    0x82D0F1D5, 0x1AB3CB0C,
+    0x82C67F13, 0x1A82A025,
+    0x82BC1FA1, 0x1A517127,
+    0x82B1D381, 0x1A203E1B,
+    0x82A79AB3, 0x19EF0706,
+    0x829D753A, 0x19BDCBF2,
+    0x82936316, 0x198C8CE6,
+    0x8289644A, 0x195B49E9,
+    0x827F78D8, 0x192A0303,
+    0x8275A0C0, 0x18F8B83C,
+    0x826BDC04, 0x18C7699B,
+    0x82622AA5, 0x18961727,
+    0x82588CA6, 0x1864C0E9,
+    0x824F0208, 0x183366E8,
+    0x82458ACB, 0x1802092C,
+    0x823C26F2, 0x17D0A7BB,
+    0x8232D67E, 0x179F429F,
+    0x82299971, 0x176DD9DE,
+    0x82206FCB, 0x173C6D80,
+    0x8217598F, 0x170AFD8D,
+    0x820E56BE, 0x16D98A0C,
+    0x82056758, 0x16A81305,
+    0x81FC8B60, 0x1676987F,
+    0x81F3C2D7, 0x16451A83,
+    0x81EB0DBD, 0x16139917,
+    0x81E26C16, 0x15E21444,
+    0x81D9DDE1, 0x15B08C11,
+    0x81D16320, 0x157F0086,
+    0x81C8FBD5, 0x154D71AA,
+    0x81C0A801, 0x151BDF85,
+    0x81B867A4, 0x14EA4A1F,
+    0x81B03AC1, 0x14B8B17F,
+    0x81A82159, 0x148715AD,
+    0x81A01B6C, 0x145576B1,
+    0x819828FD, 0x1423D492,
+    0x81904A0C, 0x13F22F57,
+    0x81887E9A, 0x13C0870A,
+    0x8180C6A9, 0x138EDBB0,
+    0x8179223A, 0x135D2D53,
+    0x8171914E, 0x132B7BF9,
+    0x816A13E6, 0x12F9C7AA,
+    0x8162AA03, 0x12C8106E,
+    0x815B53A8, 0x1296564D,
+    0x815410D3, 0x1264994E,
+    0x814CE188, 0x1232D978,
+    0x8145C5C6, 0x120116D4,
+    0x813EBD90, 0x11CF516A,
+    0x8137C8E6, 0x119D8940,
+    0x8130E7C8, 0x116BBE5F,
+    0x812A1A39, 0x1139F0CE,
+    0x81236039, 0x11082096,
+    0x811CB9CA, 0x10D64DBC,
+    0x811626EC, 0x10A4784A,
+    0x810FA7A0, 0x1072A047,
+    0x81093BE8, 0x1040C5BB,
+    0x8102E3C3, 0x100EE8AD,
+    0x80FC9F35, 0x0FDD0925,
+    0x80F66E3C, 0x0FAB272B,
+    0x80F050DB, 0x0F7942C6,
+    0x80EA4712, 0x0F475BFE,
+    0x80E450E2, 0x0F1572DC,
+    0x80DE6E4C, 0x0EE38765,
+    0x80D89F51, 0x0EB199A3,
+    0x80D2E3F1, 0x0E7FA99D,
+    0x80CD3C2F, 0x0E4DB75B,
+    0x80C7A80A, 0x0E1BC2E3,
+    0x80C22783, 0x0DE9CC3F,
+    0x80BCBA9C, 0x0DB7D376,
+    0x80B76155, 0x0D85D88F,
+    0x80B21BAF, 0x0D53DB92,
+    0x80ACE9AB, 0x0D21DC87,
+    0x80A7CB49, 0x0CEFDB75,
+    0x80A2C08B, 0x0CBDD865,
+    0x809DC970, 0x0C8BD35E,
+    0x8098E5FB, 0x0C59CC67,
+    0x8094162B, 0x0C27C389,
+    0x808F5A02, 0x0BF5B8CB,
+    0x808AB180, 0x0BC3AC35,
+    0x80861CA5, 0x0B919DCE,
+    0x80819B74, 0x0B5F8D9F,
+    0x807D2DEB, 0x0B2D7BAE,
+    0x8078D40D, 0x0AFB6805,
+    0x80748DD9, 0x0AC952AA,
+    0x80705B50, 0x0A973BA5,
+    0x806C3C73, 0x0A6522FE,
+    0x80683143, 0x0A3308BC,
+    0x806439C0, 0x0A00ECE8,
+    0x806055EA, 0x09CECF89,
+    0x805C85C3, 0x099CB0A7,
+    0x8058C94C, 0x096A9049,
+    0x80552083, 0x09386E77,
+    0x80518B6B, 0x09064B3A,
+    0x804E0A03, 0x08D42698,
+    0x804A9C4D, 0x08A2009A,
+    0x80474248, 0x086FD947,
+    0x8043FBF6, 0x083DB0A7,
+    0x8040C956, 0x080B86C1,
+    0x803DAA69, 0x07D95B9E,
+    0x803A9F31, 0x07A72F45,
+    0x8037A7AC, 0x077501BE,
+    0x8034C3DC, 0x0742D310,
+    0x8031F3C1, 0x0710A344,
+    0x802F375C, 0x06DE7261,
+    0x802C8EAD, 0x06AC406F,
+    0x8029F9B4, 0x067A0D75,
+    0x80277872, 0x0647D97C,
+    0x80250AE7, 0x0615A48A,
+    0x8022B113, 0x05E36EA9,
+    0x80206AF8, 0x05B137DF,
+    0x801E3894, 0x057F0034,
+    0x801C19E9, 0x054CC7B0,
+    0x801A0EF7, 0x051A8E5C,
+    0x801817BF, 0x04E8543D,
+    0x80163440, 0x04B6195D,
+    0x8014647A, 0x0483DDC3,
+    0x8012A86F, 0x0451A176,
+    0x8011001E, 0x041F647F,
+    0x800F6B88, 0x03ED26E6,
+    0x800DEAAC, 0x03BAE8B1,
+    0x800C7D8C, 0x0388A9E9,
+    0x800B2427, 0x03566A96,
+    0x8009DE7D, 0x03242ABF,
+    0x8008AC90, 0x02F1EA6B,
+    0x80078E5E, 0x02BFA9A4,
+    0x800683E8, 0x028D6870,
+    0x80058D2E, 0x025B26D7,
+    0x8004AA31, 0x0228E4E1,
+    0x8003DAF0, 0x01F6A296,
+    0x80031F6C, 0x01C45FFE,
+    0x800277A5, 0x01921D1F,
+    0x8001E39B, 0x015FDA03,
+    0x8001634D, 0x012D96B0,
+    0x8000F6BD, 0x00FB532F,
+    0x80009DE9, 0x00C90F88,
+    0x800058D3, 0x0096CBC1,
+    0x8000277A, 0x006487E3,
+    0x800009DE, 0x003243F5,
+    0x80000000, 0x00000000,
+    0x800009DE, 0xFFCDBC0A,
+    0x8000277A, 0xFF9B781D,
+    0x800058D3, 0xFF69343E,
+    0x80009DE9, 0xFF36F078,
+    0x8000F6BD, 0xFF04ACD0,
+    0x8001634D, 0xFED2694F,
+    0x8001E39B, 0xFEA025FC,
+    0x800277A5, 0xFE6DE2E0,
+    0x80031F6C, 0xFE3BA001,
+    0x8003DAF0, 0xFE095D69,
+    0x8004AA31, 0xFDD71B1E,
+    0x80058D2E, 0xFDA4D928,
+    0x800683E8, 0xFD72978F,
+    0x80078E5E, 0xFD40565B,
+    0x8008AC90, 0xFD0E1594,
+    0x8009DE7D, 0xFCDBD541,
+    0x800B2427, 0xFCA99569,
+    0x800C7D8C, 0xFC775616,
+    0x800DEAAC, 0xFC45174E,
+    0x800F6B88, 0xFC12D919,
+    0x8011001E, 0xFBE09B80,
+    0x8012A86F, 0xFBAE5E89,
+    0x8014647A, 0xFB7C223C,
+    0x80163440, 0xFB49E6A2,
+    0x801817BF, 0xFB17ABC2,
+    0x801A0EF7, 0xFAE571A4,
+    0x801C19E9, 0xFAB3384F,
+    0x801E3894, 0xFA80FFCB,
+    0x80206AF8, 0xFA4EC820,
+    0x8022B113, 0xFA1C9156,
+    0x80250AE7, 0xF9EA5B75,
+    0x80277872, 0xF9B82683,
+    0x8029F9B4, 0xF985F28A,
+    0x802C8EAD, 0xF953BF90,
+    0x802F375C, 0xF9218D9E,
+    0x8031F3C1, 0xF8EF5CBB,
+    0x8034C3DC, 0xF8BD2CEF,
+    0x8037A7AC, 0xF88AFE41,
+    0x803A9F31, 0xF858D0BA,
+    0x803DAA69, 0xF826A461,
+    0x8040C956, 0xF7F4793E,
+    0x8043FBF6, 0xF7C24F58,
+    0x80474248, 0xF79026B8,
+    0x804A9C4D, 0xF75DFF65,
+    0x804E0A03, 0xF72BD967,
+    0x80518B6B, 0xF6F9B4C5,
+    0x80552083, 0xF6C79188,
+    0x8058C94C, 0xF6956FB6,
+    0x805C85C3, 0xF6634F58,
+    0x806055EA, 0xF6313076,
+    0x806439C0, 0xF5FF1317,
+    0x80683143, 0xF5CCF743,
+    0x806C3C73, 0xF59ADD01,
+    0x80705B50, 0xF568C45A,
+    0x80748DD9, 0xF536AD55,
+    0x8078D40D, 0xF50497FA,
+    0x807D2DEB, 0xF4D28451,
+    0x80819B74, 0xF4A07260,
+    0x80861CA5, 0xF46E6231,
+    0x808AB180, 0xF43C53CA,
+    0x808F5A02, 0xF40A4734,
+    0x8094162B, 0xF3D83C76,
+    0x8098E5FB, 0xF3A63398,
+    0x809DC970, 0xF3742CA1,
+    0x80A2C08B, 0xF342279A,
+    0x80A7CB49, 0xF310248A,
+    0x80ACE9AB, 0xF2DE2378,
+    0x80B21BAF, 0xF2AC246D,
+    0x80B76155, 0xF27A2770,
+    0x80BCBA9C, 0xF2482C89,
+    0x80C22783, 0xF21633C0,
+    0x80C7A80A, 0xF1E43D1C,
+    0x80CD3C2F, 0xF1B248A5,
+    0x80D2E3F1, 0xF1805662,
+    0x80D89F51, 0xF14E665C,
+    0x80DE6E4C, 0xF11C789A,
+    0x80E450E2, 0xF0EA8D23,
+    0x80EA4712, 0xF0B8A401,
+    0x80F050DB, 0xF086BD39,
+    0x80F66E3C, 0xF054D8D4,
+    0x80FC9F35, 0xF022F6DA,
+    0x8102E3C3, 0xEFF11752,
+    0x81093BE8, 0xEFBF3A44,
+    0x810FA7A0, 0xEF8D5FB8,
+    0x811626EC, 0xEF5B87B5,
+    0x811CB9CA, 0xEF29B243,
+    0x81236039, 0xEEF7DF6A,
+    0x812A1A39, 0xEEC60F31,
+    0x8130E7C8, 0xEE9441A0,
+    0x8137C8E6, 0xEE6276BF,
+    0x813EBD90, 0xEE30AE95,
+    0x8145C5C6, 0xEDFEE92B,
+    0x814CE188, 0xEDCD2687,
+    0x815410D3, 0xED9B66B2,
+    0x815B53A8, 0xED69A9B2,
+    0x8162AA03, 0xED37EF91,
+    0x816A13E6, 0xED063855,
+    0x8171914E, 0xECD48406,
+    0x8179223A, 0xECA2D2AC,
+    0x8180C6A9, 0xEC71244F,
+    0x81887E9A, 0xEC3F78F5,
+    0x81904A0C, 0xEC0DD0A8,
+    0x819828FD, 0xEBDC2B6D,
+    0x81A01B6C, 0xEBAA894E,
+    0x81A82159, 0xEB78EA52,
+    0x81B03AC1, 0xEB474E80,
+    0x81B867A4, 0xEB15B5E0,
+    0x81C0A801, 0xEAE4207A,
+    0x81C8FBD5, 0xEAB28E55,
+    0x81D16320, 0xEA80FF79,
+    0x81D9DDE1, 0xEA4F73EE,
+    0x81E26C16, 0xEA1DEBBB,
+    0x81EB0DBD, 0xE9EC66E8,
+    0x81F3C2D7, 0xE9BAE57C,
+    0x81FC8B60, 0xE9896780,
+    0x82056758, 0xE957ECFB,
+    0x820E56BE, 0xE92675F4,
+    0x8217598F, 0xE8F50273,
+    0x82206FCB, 0xE8C3927F,
+    0x82299971, 0xE8922621,
+    0x8232D67E, 0xE860BD60,
+    0x823C26F2, 0xE82F5844,
+    0x82458ACB, 0xE7FDF6D3,
+    0x824F0208, 0xE7CC9917,
+    0x82588CA6, 0xE79B3F16,
+    0x82622AA5, 0xE769E8D8,
+    0x826BDC04, 0xE7389664,
+    0x8275A0C0, 0xE70747C3,
+    0x827F78D8, 0xE6D5FCFC,
+    0x8289644A, 0xE6A4B616,
+    0x82936316, 0xE6737319,
+    0x829D753A, 0xE642340D,
+    0x82A79AB3, 0xE610F8F9,
+    0x82B1D381, 0xE5DFC1E4,
+    0x82BC1FA1, 0xE5AE8ED8,
+    0x82C67F13, 0xE57D5FDA,
+    0x82D0F1D5, 0xE54C34F3,
+    0x82DB77E5, 0xE51B0E2A,
+    0x82E61141, 0xE4E9EB86,
+    0x82F0BDE8, 0xE4B8CD10,
+    0x82FB7DD8, 0xE487B2CF,
+    0x8306510F, 0xE4569CCB,
+    0x8311378C, 0xE4258B0A,
+    0x831C314E, 0xE3F47D95,
+    0x83273E52, 0xE3C37473,
+    0x83325E97, 0xE3926FAC,
+    0x833D921A, 0xE3616F47,
+    0x8348D8DB, 0xE330734C,
+    0x835432D8, 0xE2FF7BC3,
+    0x835FA00E, 0xE2CE88B2,
+    0x836B207D, 0xE29D9A22,
+    0x8376B422, 0xE26CB01A,
+    0x83825AFB, 0xE23BCAA2,
+    0x838E1507, 0xE20AE9C1,
+    0x8399E244, 0xE1DA0D7E,
+    0x83A5C2B0, 0xE1A935E1,
+    0x83B1B649, 0xE17862F3,
+    0x83BDBD0D, 0xE14794B9,
+    0x83C9D6FB, 0xE116CB3D,
+    0x83D60411, 0xE0E60684,
+    0x83E2444D, 0xE0B54698,
+    0x83EE97AC, 0xE0848B7F,
+    0x83FAFE2E, 0xE053D541,
+    0x840777CF, 0xE02323E5,
+    0x8414048F, 0xDFF27773,
+    0x8420A46B, 0xDFC1CFF2,
+    0x842D5761, 0xDF912D6A,
+    0x843A1D70, 0xDF608FE3,
+    0x8446F695, 0xDF2FF764,
+    0x8453E2CE, 0xDEFF63F4,
+    0x8460E21A, 0xDECED59B,
+    0x846DF476, 0xDE9E4C60,
+    0x847B19E1, 0xDE6DC84B,
+    0x84885257, 0xDE3D4963,
+    0x84959DD9, 0xDE0CCFB1,
+    0x84A2FC62, 0xDDDC5B3A,
+    0x84B06DF1, 0xDDABEC07,
+    0x84BDF285, 0xDD7B8220,
+    0x84CB8A1B, 0xDD4B1D8B,
+    0x84D934B0, 0xDD1ABE51,
+    0x84E6F244, 0xDCEA6478,
+    0x84F4C2D3, 0xDCBA1008,
+    0x8502A65C, 0xDC89C108,
+    0x85109CDC, 0xDC597781,
+    0x851EA652, 0xDC293379,
+    0x852CC2BA, 0xDBF8F4F8,
+    0x853AF214, 0xDBC8BC05,
+    0x8549345C, 0xDB9888A8,
+    0x85578991, 0xDB685AE8,
+    0x8565F1B0, 0xDB3832CD,
+    0x85746CB7, 0xDB08105E,
+    0x8582FAA4, 0xDAD7F3A2,
+    0x85919B75, 0xDAA7DCA1,
+    0x85A04F28, 0xDA77CB62,
+    0x85AF15B9, 0xDA47BFED,
+    0x85BDEF27, 0xDA17BA4A,
+    0x85CCDB70, 0xD9E7BA7E,
+    0x85DBDA91, 0xD9B7C093,
+    0x85EAEC88, 0xD987CC8F,
+    0x85FA1152, 0xD957DE7A,
+    0x860948EE, 0xD927F65B,
+    0x86189359, 0xD8F81439,
+    0x8627F090, 0xD8C8381C,
+    0x86376092, 0xD898620C,
+    0x8646E35B, 0xD868920F,
+    0x865678EA, 0xD838C82D,
+    0x8666213C, 0xD809046D,
+    0x8675DC4E, 0xD7D946D7,
+    0x8685AA1F, 0xD7A98F73,
+    0x86958AAB, 0xD779DE46,
+    0x86A57DF1, 0xD74A335A,
+    0x86B583EE, 0xD71A8EB5,
+    0x86C59C9F, 0xD6EAF05E,
+    0x86D5C802, 0xD6BB585D,
+    0x86E60614, 0xD68BC6BA,
+    0x86F656D3, 0xD65C3B7B,
+    0x8706BA3C, 0xD62CB6A7,
+    0x8717304E, 0xD5FD3847,
+    0x8727B904, 0xD5CDC062,
+    0x8738545E, 0xD59E4EFE,
+    0x87490257, 0xD56EE424,
+    0x8759C2EF, 0xD53F7FDA,
+    0x876A9621, 0xD5102227,
+    0x877B7BEC, 0xD4E0CB14,
+    0x878C744C, 0xD4B17AA7,
+    0x879D7F40, 0xD48230E8,
+    0x87AE9CC5, 0xD452EDDE,
+    0x87BFCCD7, 0xD423B190,
+    0x87D10F75, 0xD3F47C06,
+    0x87E2649B, 0xD3C54D46,
+    0x87F3CC47, 0xD3962559,
+    0x88054677, 0xD3670445,
+    0x8816D327, 0xD337EA12,
+    0x88287255, 0xD308D6C6,
+    0x883A23FE, 0xD2D9CA6A,
+    0x884BE820, 0xD2AAC504,
+    0x885DBEB7, 0xD27BC69C,
+    0x886FA7C2, 0xD24CCF38,
+    0x8881A33C, 0xD21DDEE1,
+    0x8893B124, 0xD1EEF59E,
+    0x88A5D177, 0xD1C01374,
+    0x88B80431, 0xD191386D,
+    0x88CA4951, 0xD162648F,
+    0x88DCA0D3, 0xD13397E1,
+    0x88EF0AB4, 0xD104D26B,
+    0x890186F1, 0xD0D61433,
+    0x89141589, 0xD0A75D42,
+    0x8926B677, 0xD078AD9D,
+    0x893969B9, 0xD04A054D,
+    0x894C2F4C, 0xD01B6459,
+    0x895F072D, 0xCFECCAC7,
+    0x8971F15A, 0xCFBE389F,
+    0x8984EDCF, 0xCF8FADE8,
+    0x8997FC89, 0xCF612AAA,
+    0x89AB1D86, 0xCF32AEEB,
+    0x89BE50C3, 0xCF043AB2,
+    0x89D1963C, 0xCED5CE08,
+    0x89E4EDEE, 0xCEA768F2,
+    0x89F857D8, 0xCE790B78,
+    0x8A0BD3F5, 0xCE4AB5A2,
+    0x8A1F6242, 0xCE1C6776,
+    0x8A3302BD, 0xCDEE20FC,
+    0x8A46B563, 0xCDBFE23A,
+    0x8A5A7A30, 0xCD91AB38,
+    0x8A6E5122, 0xCD637BFD,
+    0x8A823A35, 0xCD355490,
+    0x8A963567, 0xCD0734F8,
+    0x8AAA42B4, 0xCCD91D3D,
+    0x8ABE6219, 0xCCAB0D65,
+    0x8AD29393, 0xCC7D0577,
+    0x8AE6D71F, 0xCC4F057B,
+    0x8AFB2CBA, 0xCC210D78,
+    0x8B0F9461, 0xCBF31D75,
+    0x8B240E10, 0xCBC53578,
+    0x8B3899C5, 0xCB975589,
+    0x8B4D377C, 0xCB697DB0,
+    0x8B61E732, 0xCB3BADF2,
+    0x8B76A8E4, 0xCB0DE658,
+    0x8B8B7C8F, 0xCAE026E8,
+    0x8BA0622F, 0xCAB26FA9,
+    0x8BB559C1, 0xCA84C0A2,
+    0x8BCA6342, 0xCA5719DB,
+    0x8BDF7EAF, 0xCA297B5A,
+    0x8BF4AC05, 0xC9FBE527,
+    0x8C09EB40, 0xC9CE5748,
+    0x8C1F3C5C, 0xC9A0D1C4,
+    0x8C349F58, 0xC97354A3,
+    0x8C4A142F, 0xC945DFEC,
+    0x8C5F9ADD, 0xC91873A5,
+    0x8C753361, 0xC8EB0FD6,
+    0x8C8ADDB6, 0xC8BDB485,
+    0x8CA099D9, 0xC89061BA,
+    0x8CB667C7, 0xC863177B,
+    0x8CCC477D, 0xC835D5D0,
+    0x8CE238F6, 0xC8089CBF,
+    0x8CF83C30, 0xC7DB6C50,
+    0x8D0E5127, 0xC7AE4489,
+    0x8D2477D8, 0xC7812571,
+    0x8D3AB03F, 0xC7540F10,
+    0x8D50FA59, 0xC727016C,
+    0x8D675623, 0xC6F9FC8D,
+    0x8D7DC399, 0xC6CD0079,
+    0x8D9442B7, 0xC6A00D36,
+    0x8DAAD37B, 0xC67322CD,
+    0x8DC175E0, 0xC6464144,
+    0x8DD829E4, 0xC61968A2,
+    0x8DEEEF82, 0xC5EC98ED,
+    0x8E05C6B7, 0xC5BFD22E,
+    0x8E1CAF80, 0xC593146A,
+    0x8E33A9D9, 0xC5665FA8,
+    0x8E4AB5BF, 0xC539B3F0,
+    0x8E61D32D, 0xC50D1148,
+    0x8E790222, 0xC4E077B8,
+    0x8E904298, 0xC4B3E746,
+    0x8EA7948C, 0xC4875FF8,
+    0x8EBEF7FB, 0xC45AE1D7,
+    0x8ED66CE1, 0xC42E6CE8,
+    0x8EEDF33B, 0xC4020132,
+    0x8F058B04, 0xC3D59EBD,
+    0x8F1D343A, 0xC3A9458F,
+    0x8F34EED8, 0xC37CF5B0,
+    0x8F4CBADB, 0xC350AF25,
+    0x8F64983F, 0xC32471F6,
+    0x8F7C8701, 0xC2F83E2A,
+    0x8F94871D, 0xC2CC13C7,
+    0x8FAC988E, 0xC29FF2D4,
+    0x8FC4BB53, 0xC273DB58,
+    0x8FDCEF66, 0xC247CD5A,
+    0x8FF534C4, 0xC21BC8E0,
+    0x900D8B69, 0xC1EFCDF2,
+    0x9025F352, 0xC1C3DC96,
+    0x903E6C7A, 0xC197F4D3,
+    0x9056F6DF, 0xC16C16B0,
+    0x906F927B, 0xC1404233,
+    0x90883F4C, 0xC1147763,
+    0x90A0FD4E, 0xC0E8B648,
+    0x90B9CC7C, 0xC0BCFEE7,
+    0x90D2ACD3, 0xC0915147,
+    0x90EB9E50, 0xC065AD70,
+    0x9104A0ED, 0xC03A1368,
+    0x911DB4A8, 0xC00E8335,
+    0x9136D97D, 0xBFE2FCDF,
+    0x91500F67, 0xBFB7806C,
+    0x91695663, 0xBF8C0DE2,
+    0x9182AE6C, 0xBF60A54A,
+    0x919C1780, 0xBF3546A8,
+    0x91B5919A, 0xBF09F204,
+    0x91CF1CB6, 0xBEDEA765,
+    0x91E8B8D0, 0xBEB366D1,
+    0x920265E4, 0xBE88304F,
+    0x921C23EE, 0xBE5D03E5,
+    0x9235F2EB, 0xBE31E19B,
+    0x924FD2D6, 0xBE06C977,
+    0x9269C3AC, 0xBDDBBB7F,
+    0x9283C567, 0xBDB0B7BA,
+    0x929DD805, 0xBD85BE2F,
+    0x92B7FB82, 0xBD5ACEE5,
+    0x92D22FD8, 0xBD2FE9E1,
+    0x92EC7505, 0xBD050F2C,
+    0x9306CB04, 0xBCDA3ECA,
+    0x932131D1, 0xBCAF78C3,
+    0x933BA968, 0xBC84BD1E,
+    0x935631C5, 0xBC5A0BE1,
+    0x9370CAE4, 0xBC2F6513,
+    0x938B74C0, 0xBC04C8BA,
+    0x93A62F56, 0xBBDA36DC,
+    0x93C0FAA2, 0xBBAFAF81,
+    0x93DBD69F, 0xBB8532AF,
+    0x93F6C34A, 0xBB5AC06C,
+    0x9411C09D, 0xBB3058C0,
+    0x942CCE95, 0xBB05FBB0,
+    0x9447ED2F, 0xBADBA943,
+    0x94631C64, 0xBAB1617F,
+    0x947E5C32, 0xBA87246C,
+    0x9499AC95, 0xBA5CF210,
+    0x94B50D87, 0xBA32CA70,
+    0x94D07F05, 0xBA08AD94,
+    0x94EC010B, 0xB9DE9B83,
+    0x95079393, 0xB9B49442,
+    0x9523369B, 0xB98A97D8,
+    0x953EEA1E, 0xB960A64B,
+    0x955AAE17, 0xB936BFA3,
+    0x95768282, 0xB90CE3E6,
+    0x9592675B, 0xB8E31319,
+    0x95AE5C9E, 0xB8B94D44,
+    0x95CA6246, 0xB88F926C,
+    0x95E6784F, 0xB865E299,
+    0x96029EB5, 0xB83C3DD1,
+    0x961ED573, 0xB812A419,
+    0x963B1C85, 0xB7E9157A,
+    0x965773E7, 0xB7BF91F8,
+    0x9673DB94, 0xB796199B,
+    0x96905387, 0xB76CAC68,
+    0x96ACDBBD, 0xB7434A67,
+    0x96C97431, 0xB719F39D,
+    0x96E61CDF, 0xB6F0A811,
+    0x9702D5C2, 0xB6C767CA,
+    0x971F9ED6, 0xB69E32CD,
+    0x973C7816, 0xB6750921,
+    0x9759617E, 0xB64BEACC,
+    0x97765B0A, 0xB622D7D5,
+    0x979364B5, 0xB5F9D042,
+    0x97B07E7A, 0xB5D0D41A,
+    0x97CDA855, 0xB5A7E362,
+    0x97EAE241, 0xB57EFE21,
+    0x98082C3B, 0xB556245E,
+    0x9825863D, 0xB52D561E,
+    0x9842F043, 0xB5049368,
+    0x98606A48, 0xB4DBDC42,
+    0x987DF449, 0xB4B330B2,
+    0x989B8E3F, 0xB48A90C0,
+    0x98B93828, 0xB461FC70,
+    0x98D6F1FE, 0xB43973C9,
+    0x98F4BBBC, 0xB410F6D2,
+    0x9912955E, 0xB3E88591,
+    0x99307EE0, 0xB3C0200C,
+    0x994E783C, 0xB397C649,
+    0x996C816F, 0xB36F784E,
+    0x998A9A73, 0xB3473622,
+    0x99A8C344, 0xB31EFFCB,
+    0x99C6FBDE, 0xB2F6D54F,
+    0x99E5443A, 0xB2CEB6B5,
+    0x9A039C56, 0xB2A6A401,
+    0x9A22042C, 0xB27E9D3B,
+    0x9A407BB8, 0xB256A26A,
+    0x9A5F02F5, 0xB22EB392,
+    0x9A7D99DD, 0xB206D0BA,
+    0x9A9C406D, 0xB1DEF9E8,
+    0x9ABAF6A0, 0xB1B72F23,
+    0x9AD9BC71, 0xB18F7070,
+    0x9AF891DB, 0xB167BDD6,
+    0x9B1776D9, 0xB140175B,
+    0x9B366B67, 0xB1187D05,
+    0x9B556F80, 0xB0F0EEDA,
+    0x9B748320, 0xB0C96CDF,
+    0x9B93A640, 0xB0A1F71C,
+    0x9BB2D8DD, 0xB07A8D97,
+    0x9BD21AF2, 0xB0533055,
+    0x9BF16C7A, 0xB02BDF5C,
+    0x9C10CD70, 0xB0049AB2,
+    0x9C303DCF, 0xAFDD625F,
+    0x9C4FBD92, 0xAFB63667,
+    0x9C6F4CB5, 0xAF8F16D0,
+    0x9C8EEB33, 0xAF6803A1,
+    0x9CAE9907, 0xAF40FCE0,
+    0x9CCE562B, 0xAF1A0293,
+    0x9CEE229C, 0xAEF314BF,
+    0x9D0DFE53, 0xAECC336B,
+    0x9D2DE94D, 0xAEA55E9D,
+    0x9D4DE384, 0xAE7E965B,
+    0x9D6DECF4, 0xAE57DAAA,
+    0x9D8E0596, 0xAE312B91,
+    0x9DAE2D68, 0xAE0A8916,
+    0x9DCE6462, 0xADE3F33E,
+    0x9DEEAA82, 0xADBD6A10,
+    0x9E0EFFC1, 0xAD96ED91,
+    0x9E2F641A, 0xAD707DC8,
+    0x9E4FD789, 0xAD4A1ABA,
+    0x9E705A09, 0xAD23C46D,
+    0x9E90EB94, 0xACFD7AE8,
+    0x9EB18C26, 0xACD73E30,
+    0x9ED23BB9, 0xACB10E4A,
+    0x9EF2FA48, 0xAC8AEB3E,
+    0x9F13C7D0, 0xAC64D510,
+    0x9F34A449, 0xAC3ECBC7,
+    0x9F558FB0, 0xAC18CF68,
+    0x9F7689FF, 0xABF2DFFA,
+    0x9F979331, 0xABCCFD82,
+    0x9FB8AB41, 0xABA72806,
+    0x9FD9D22A, 0xAB815F8C,
+    0x9FFB07E7, 0xAB5BA41A,
+    0xA01C4C72, 0xAB35F5B5,
+    0xA03D9FC7, 0xAB105464,
+    0xA05F01E1, 0xAAEAC02B,
+    0xA08072BA, 0xAAC53912,
+    0xA0A1F24C, 0xAA9FBF1D,
+    0xA0C38094, 0xAA7A5253,
+    0xA0E51D8C, 0xAA54F2B9,
+    0xA106C92E, 0xAA2FA055,
+    0xA1288376, 0xAA0A5B2D,
+    0xA14A4C5E, 0xA9E52347,
+    0xA16C23E1, 0xA9BFF8A8,
+    0xA18E09F9, 0xA99ADB56,
+    0xA1AFFEA2, 0xA975CB56,
+    0xA1D201D7, 0xA950C8AF,
+    0xA1F41391, 0xA92BD366,
+    0xA21633CD, 0xA906EB81,
+    0xA2386283, 0xA8E21106,
+    0xA25A9FB1, 0xA8BD43FA,
+    0xA27CEB4F, 0xA8988463,
+    0xA29F4559, 0xA873D246,
+    0xA2C1ADC9, 0xA84F2DA9,
+    0xA2E4249A, 0xA82A9693,
+    0xA306A9C7, 0xA8060D08,
+    0xA3293D4B, 0xA7E1910E,
+    0xA34BDF20, 0xA7BD22AB,
+    0xA36E8F40, 0xA798C1E4,
+    0xA3914DA7, 0xA7746EC0,
+    0xA3B41A4F, 0xA7502943,
+    0xA3D6F533, 0xA72BF173,
+    0xA3F9DE4D, 0xA707C756,
+    0xA41CD598, 0xA6E3AAF2,
+    0xA43FDB0F, 0xA6BF9C4B,
+    0xA462EEAC, 0xA69B9B68,
+    0xA4861069, 0xA677A84E,
+    0xA4A94042, 0xA653C302,
+    0xA4CC7E31, 0xA62FEB8B,
+    0xA4EFCA31, 0xA60C21ED,
+    0xA513243B, 0xA5E8662F,
+    0xA5368C4B, 0xA5C4B855,
+    0xA55A025B, 0xA5A11865,
+    0xA57D8666, 0xA57D8666,
+    0xA5A11865, 0xA55A025B,
+    0xA5C4B855, 0xA5368C4B,
+    0xA5E8662F, 0xA513243B,
+    0xA60C21ED, 0xA4EFCA31,
+    0xA62FEB8B, 0xA4CC7E31,
+    0xA653C302, 0xA4A94042,
+    0xA677A84E, 0xA4861069,
+    0xA69B9B68, 0xA462EEAC,
+    0xA6BF9C4B, 0xA43FDB0F,
+    0xA6E3AAF2, 0xA41CD598,
+    0xA707C756, 0xA3F9DE4D,
+    0xA72BF173, 0xA3D6F533,
+    0xA7502943, 0xA3B41A4F,
+    0xA7746EC0, 0xA3914DA7,
+    0xA798C1E4, 0xA36E8F40,
+    0xA7BD22AB, 0xA34BDF20,
+    0xA7E1910E, 0xA3293D4B,
+    0xA8060D08, 0xA306A9C7,
+    0xA82A9693, 0xA2E4249A,
+    0xA84F2DA9, 0xA2C1ADC9,
+    0xA873D246, 0xA29F4559,
+    0xA8988463, 0xA27CEB4F,
+    0xA8BD43FA, 0xA25A9FB1,
+    0xA8E21106, 0xA2386283,
+    0xA906EB81, 0xA21633CD,
+    0xA92BD366, 0xA1F41391,
+    0xA950C8AF, 0xA1D201D7,
+    0xA975CB56, 0xA1AFFEA2,
+    0xA99ADB56, 0xA18E09F9,
+    0xA9BFF8A8, 0xA16C23E1,
+    0xA9E52347, 0xA14A4C5E,
+    0xAA0A5B2D, 0xA1288376,
+    0xAA2FA055, 0xA106C92E,
+    0xAA54F2B9, 0xA0E51D8C,
+    0xAA7A5253, 0xA0C38094,
+    0xAA9FBF1D, 0xA0A1F24C,
+    0xAAC53912, 0xA08072BA,
+    0xAAEAC02B, 0xA05F01E1,
+    0xAB105464, 0xA03D9FC7,
+    0xAB35F5B5, 0xA01C4C72,
+    0xAB5BA41A, 0x9FFB07E7,
+    0xAB815F8C, 0x9FD9D22A,
+    0xABA72806, 0x9FB8AB41,
+    0xABCCFD82, 0x9F979331,
+    0xABF2DFFA, 0x9F7689FF,
+    0xAC18CF68, 0x9F558FB0,
+    0xAC3ECBC7, 0x9F34A449,
+    0xAC64D510, 0x9F13C7D0,
+    0xAC8AEB3E, 0x9EF2FA48,
+    0xACB10E4A, 0x9ED23BB9,
+    0xACD73E30, 0x9EB18C26,
+    0xACFD7AE8, 0x9E90EB94,
+    0xAD23C46D, 0x9E705A09,
+    0xAD4A1ABA, 0x9E4FD789,
+    0xAD707DC8, 0x9E2F641A,
+    0xAD96ED91, 0x9E0EFFC1,
+    0xADBD6A10, 0x9DEEAA82,
+    0xADE3F33E, 0x9DCE6462,
+    0xAE0A8916, 0x9DAE2D68,
+    0xAE312B91, 0x9D8E0596,
+    0xAE57DAAA, 0x9D6DECF4,
+    0xAE7E965B, 0x9D4DE384,
+    0xAEA55E9D, 0x9D2DE94D,
+    0xAECC336B, 0x9D0DFE53,
+    0xAEF314BF, 0x9CEE229C,
+    0xAF1A0293, 0x9CCE562B,
+    0xAF40FCE0, 0x9CAE9907,
+    0xAF6803A1, 0x9C8EEB33,
+    0xAF8F16D0, 0x9C6F4CB5,
+    0xAFB63667, 0x9C4FBD92,
+    0xAFDD625F, 0x9C303DCF,
+    0xB0049AB2, 0x9C10CD70,
+    0xB02BDF5C, 0x9BF16C7A,
+    0xB0533055, 0x9BD21AF2,
+    0xB07A8D97, 0x9BB2D8DD,
+    0xB0A1F71C, 0x9B93A640,
+    0xB0C96CDF, 0x9B748320,
+    0xB0F0EEDA, 0x9B556F80,
+    0xB1187D05, 0x9B366B67,
+    0xB140175B, 0x9B1776D9,
+    0xB167BDD6, 0x9AF891DB,
+    0xB18F7070, 0x9AD9BC71,
+    0xB1B72F23, 0x9ABAF6A0,
+    0xB1DEF9E8, 0x9A9C406D,
+    0xB206D0BA, 0x9A7D99DD,
+    0xB22EB392, 0x9A5F02F5,
+    0xB256A26A, 0x9A407BB8,
+    0xB27E9D3B, 0x9A22042C,
+    0xB2A6A401, 0x9A039C56,
+    0xB2CEB6B5, 0x99E5443A,
+    0xB2F6D54F, 0x99C6FBDE,
+    0xB31EFFCB, 0x99A8C344,
+    0xB3473622, 0x998A9A73,
+    0xB36F784E, 0x996C816F,
+    0xB397C649, 0x994E783C,
+    0xB3C0200C, 0x99307EE0,
+    0xB3E88591, 0x9912955E,
+    0xB410F6D2, 0x98F4BBBC,
+    0xB43973C9, 0x98D6F1FE,
+    0xB461FC70, 0x98B93828,
+    0xB48A90C0, 0x989B8E3F,
+    0xB4B330B2, 0x987DF449,
+    0xB4DBDC42, 0x98606A48,
+    0xB5049368, 0x9842F043,
+    0xB52D561E, 0x9825863D,
+    0xB556245E, 0x98082C3B,
+    0xB57EFE21, 0x97EAE241,
+    0xB5A7E362, 0x97CDA855,
+    0xB5D0D41A, 0x97B07E7A,
+    0xB5F9D042, 0x979364B5,
+    0xB622D7D5, 0x97765B0A,
+    0xB64BEACC, 0x9759617E,
+    0xB6750921, 0x973C7816,
+    0xB69E32CD, 0x971F9ED6,
+    0xB6C767CA, 0x9702D5C2,
+    0xB6F0A811, 0x96E61CDF,
+    0xB719F39D, 0x96C97431,
+    0xB7434A67, 0x96ACDBBD,
+    0xB76CAC68, 0x96905387,
+    0xB796199B, 0x9673DB94,
+    0xB7BF91F8, 0x965773E7,
+    0xB7E9157A, 0x963B1C85,
+    0xB812A419, 0x961ED573,
+    0xB83C3DD1, 0x96029EB5,
+    0xB865E299, 0x95E6784F,
+    0xB88F926C, 0x95CA6246,
+    0xB8B94D44, 0x95AE5C9E,
+    0xB8E31319, 0x9592675B,
+    0xB90CE3E6, 0x95768282,
+    0xB936BFA3, 0x955AAE17,
+    0xB960A64B, 0x953EEA1E,
+    0xB98A97D8, 0x9523369B,
+    0xB9B49442, 0x95079393,
+    0xB9DE9B83, 0x94EC010B,
+    0xBA08AD94, 0x94D07F05,
+    0xBA32CA70, 0x94B50D87,
+    0xBA5CF210, 0x9499AC95,
+    0xBA87246C, 0x947E5C32,
+    0xBAB1617F, 0x94631C64,
+    0xBADBA943, 0x9447ED2F,
+    0xBB05FBB0, 0x942CCE95,
+    0xBB3058C0, 0x9411C09D,
+    0xBB5AC06C, 0x93F6C34A,
+    0xBB8532AF, 0x93DBD69F,
+    0xBBAFAF81, 0x93C0FAA2,
+    0xBBDA36DC, 0x93A62F56,
+    0xBC04C8BA, 0x938B74C0,
+    0xBC2F6513, 0x9370CAE4,
+    0xBC5A0BE1, 0x935631C5,
+    0xBC84BD1E, 0x933BA968,
+    0xBCAF78C3, 0x932131D1,
+    0xBCDA3ECA, 0x9306CB04,
+    0xBD050F2C, 0x92EC7505,
+    0xBD2FE9E1, 0x92D22FD8,
+    0xBD5ACEE5, 0x92B7FB82,
+    0xBD85BE2F, 0x929DD805,
+    0xBDB0B7BA, 0x9283C567,
+    0xBDDBBB7F, 0x9269C3AC,
+    0xBE06C977, 0x924FD2D6,
+    0xBE31E19B, 0x9235F2EB,
+    0xBE5D03E5, 0x921C23EE,
+    0xBE88304F, 0x920265E4,
+    0xBEB366D1, 0x91E8B8D0,
+    0xBEDEA765, 0x91CF1CB6,
+    0xBF09F204, 0x91B5919A,
+    0xBF3546A8, 0x919C1780,
+    0xBF60A54A, 0x9182AE6C,
+    0xBF8C0DE2, 0x91695663,
+    0xBFB7806C, 0x91500F67,
+    0xBFE2FCDF, 0x9136D97D,
+    0xC00E8335, 0x911DB4A8,
+    0xC03A1368, 0x9104A0ED,
+    0xC065AD70, 0x90EB9E50,
+    0xC0915147, 0x90D2ACD3,
+    0xC0BCFEE7, 0x90B9CC7C,
+    0xC0E8B648, 0x90A0FD4E,
+    0xC1147763, 0x90883F4C,
+    0xC1404233, 0x906F927B,
+    0xC16C16B0, 0x9056F6DF,
+    0xC197F4D3, 0x903E6C7A,
+    0xC1C3DC96, 0x9025F352,
+    0xC1EFCDF2, 0x900D8B69,
+    0xC21BC8E0, 0x8FF534C4,
+    0xC247CD5A, 0x8FDCEF66,
+    0xC273DB58, 0x8FC4BB53,
+    0xC29FF2D4, 0x8FAC988E,
+    0xC2CC13C7, 0x8F94871D,
+    0xC2F83E2A, 0x8F7C8701,
+    0xC32471F6, 0x8F64983F,
+    0xC350AF25, 0x8F4CBADB,
+    0xC37CF5B0, 0x8F34EED8,
+    0xC3A9458F, 0x8F1D343A,
+    0xC3D59EBD, 0x8F058B04,
+    0xC4020132, 0x8EEDF33B,
+    0xC42E6CE8, 0x8ED66CE1,
+    0xC45AE1D7, 0x8EBEF7FB,
+    0xC4875FF8, 0x8EA7948C,
+    0xC4B3E746, 0x8E904298,
+    0xC4E077B8, 0x8E790222,
+    0xC50D1148, 0x8E61D32D,
+    0xC539B3F0, 0x8E4AB5BF,
+    0xC5665FA8, 0x8E33A9D9,
+    0xC593146A, 0x8E1CAF80,
+    0xC5BFD22E, 0x8E05C6B7,
+    0xC5EC98ED, 0x8DEEEF82,
+    0xC61968A2, 0x8DD829E4,
+    0xC6464144, 0x8DC175E0,
+    0xC67322CD, 0x8DAAD37B,
+    0xC6A00D36, 0x8D9442B7,
+    0xC6CD0079, 0x8D7DC399,
+    0xC6F9FC8D, 0x8D675623,
+    0xC727016C, 0x8D50FA59,
+    0xC7540F10, 0x8D3AB03F,
+    0xC7812571, 0x8D2477D8,
+    0xC7AE4489, 0x8D0E5127,
+    0xC7DB6C50, 0x8CF83C30,
+    0xC8089CBF, 0x8CE238F6,
+    0xC835D5D0, 0x8CCC477D,
+    0xC863177B, 0x8CB667C7,
+    0xC89061BA, 0x8CA099D9,
+    0xC8BDB485, 0x8C8ADDB6,
+    0xC8EB0FD6, 0x8C753361,
+    0xC91873A5, 0x8C5F9ADD,
+    0xC945DFEC, 0x8C4A142F,
+    0xC97354A3, 0x8C349F58,
+    0xC9A0D1C4, 0x8C1F3C5C,
+    0xC9CE5748, 0x8C09EB40,
+    0xC9FBE527, 0x8BF4AC05,
+    0xCA297B5A, 0x8BDF7EAF,
+    0xCA5719DB, 0x8BCA6342,
+    0xCA84C0A2, 0x8BB559C1,
+    0xCAB26FA9, 0x8BA0622F,
+    0xCAE026E8, 0x8B8B7C8F,
+    0xCB0DE658, 0x8B76A8E4,
+    0xCB3BADF2, 0x8B61E732,
+    0xCB697DB0, 0x8B4D377C,
+    0xCB975589, 0x8B3899C5,
+    0xCBC53578, 0x8B240E10,
+    0xCBF31D75, 0x8B0F9461,
+    0xCC210D78, 0x8AFB2CBA,
+    0xCC4F057B, 0x8AE6D71F,
+    0xCC7D0577, 0x8AD29393,
+    0xCCAB0D65, 0x8ABE6219,
+    0xCCD91D3D, 0x8AAA42B4,
+    0xCD0734F8, 0x8A963567,
+    0xCD355490, 0x8A823A35,
+    0xCD637BFD, 0x8A6E5122,
+    0xCD91AB38, 0x8A5A7A30,
+    0xCDBFE23A, 0x8A46B563,
+    0xCDEE20FC, 0x8A3302BD,
+    0xCE1C6776, 0x8A1F6242,
+    0xCE4AB5A2, 0x8A0BD3F5,
+    0xCE790B78, 0x89F857D8,
+    0xCEA768F2, 0x89E4EDEE,
+    0xCED5CE08, 0x89D1963C,
+    0xCF043AB2, 0x89BE50C3,
+    0xCF32AEEB, 0x89AB1D86,
+    0xCF612AAA, 0x8997FC89,
+    0xCF8FADE8, 0x8984EDCF,
+    0xCFBE389F, 0x8971F15A,
+    0xCFECCAC7, 0x895F072D,
+    0xD01B6459, 0x894C2F4C,
+    0xD04A054D, 0x893969B9,
+    0xD078AD9D, 0x8926B677,
+    0xD0A75D42, 0x89141589,
+    0xD0D61433, 0x890186F1,
+    0xD104D26B, 0x88EF0AB4,
+    0xD13397E1, 0x88DCA0D3,
+    0xD162648F, 0x88CA4951,
+    0xD191386D, 0x88B80431,
+    0xD1C01374, 0x88A5D177,
+    0xD1EEF59E, 0x8893B124,
+    0xD21DDEE1, 0x8881A33C,
+    0xD24CCF38, 0x886FA7C2,
+    0xD27BC69C, 0x885DBEB7,
+    0xD2AAC504, 0x884BE820,
+    0xD2D9CA6A, 0x883A23FE,
+    0xD308D6C6, 0x88287255,
+    0xD337EA12, 0x8816D327,
+    0xD3670445, 0x88054677,
+    0xD3962559, 0x87F3CC47,
+    0xD3C54D46, 0x87E2649B,
+    0xD3F47C06, 0x87D10F75,
+    0xD423B190, 0x87BFCCD7,
+    0xD452EDDE, 0x87AE9CC5,
+    0xD48230E8, 0x879D7F40,
+    0xD4B17AA7, 0x878C744C,
+    0xD4E0CB14, 0x877B7BEC,
+    0xD5102227, 0x876A9621,
+    0xD53F7FDA, 0x8759C2EF,
+    0xD56EE424, 0x87490257,
+    0xD59E4EFE, 0x8738545E,
+    0xD5CDC062, 0x8727B904,
+    0xD5FD3847, 0x8717304E,
+    0xD62CB6A7, 0x8706BA3C,
+    0xD65C3B7B, 0x86F656D3,
+    0xD68BC6BA, 0x86E60614,
+    0xD6BB585D, 0x86D5C802,
+    0xD6EAF05E, 0x86C59C9F,
+    0xD71A8EB5, 0x86B583EE,
+    0xD74A335A, 0x86A57DF1,
+    0xD779DE46, 0x86958AAB,
+    0xD7A98F73, 0x8685AA1F,
+    0xD7D946D7, 0x8675DC4E,
+    0xD809046D, 0x8666213C,
+    0xD838C82D, 0x865678EA,
+    0xD868920F, 0x8646E35B,
+    0xD898620C, 0x86376092,
+    0xD8C8381C, 0x8627F090,
+    0xD8F81439, 0x86189359,
+    0xD927F65B, 0x860948EE,
+    0xD957DE7A, 0x85FA1152,
+    0xD987CC8F, 0x85EAEC88,
+    0xD9B7C093, 0x85DBDA91,
+    0xD9E7BA7E, 0x85CCDB70,
+    0xDA17BA4A, 0x85BDEF27,
+    0xDA47BFED, 0x85AF15B9,
+    0xDA77CB62, 0x85A04F28,
+    0xDAA7DCA1, 0x85919B75,
+    0xDAD7F3A2, 0x8582FAA4,
+    0xDB08105E, 0x85746CB7,
+    0xDB3832CD, 0x8565F1B0,
+    0xDB685AE8, 0x85578991,
+    0xDB9888A8, 0x8549345C,
+    0xDBC8BC05, 0x853AF214,
+    0xDBF8F4F8, 0x852CC2BA,
+    0xDC293379, 0x851EA652,
+    0xDC597781, 0x85109CDC,
+    0xDC89C108, 0x8502A65C,
+    0xDCBA1008, 0x84F4C2D3,
+    0xDCEA6478, 0x84E6F244,
+    0xDD1ABE51, 0x84D934B0,
+    0xDD4B1D8B, 0x84CB8A1B,
+    0xDD7B8220, 0x84BDF285,
+    0xDDABEC07, 0x84B06DF1,
+    0xDDDC5B3A, 0x84A2FC62,
+    0xDE0CCFB1, 0x84959DD9,
+    0xDE3D4963, 0x84885257,
+    0xDE6DC84B, 0x847B19E1,
+    0xDE9E4C60, 0x846DF476,
+    0xDECED59B, 0x8460E21A,
+    0xDEFF63F4, 0x8453E2CE,
+    0xDF2FF764, 0x8446F695,
+    0xDF608FE3, 0x843A1D70,
+    0xDF912D6A, 0x842D5761,
+    0xDFC1CFF2, 0x8420A46B,
+    0xDFF27773, 0x8414048F,
+    0xE02323E5, 0x840777CF,
+    0xE053D541, 0x83FAFE2E,
+    0xE0848B7F, 0x83EE97AC,
+    0xE0B54698, 0x83E2444D,
+    0xE0E60684, 0x83D60411,
+    0xE116CB3D, 0x83C9D6FB,
+    0xE14794B9, 0x83BDBD0D,
+    0xE17862F3, 0x83B1B649,
+    0xE1A935E1, 0x83A5C2B0,
+    0xE1DA0D7E, 0x8399E244,
+    0xE20AE9C1, 0x838E1507,
+    0xE23BCAA2, 0x83825AFB,
+    0xE26CB01A, 0x8376B422,
+    0xE29D9A22, 0x836B207D,
+    0xE2CE88B2, 0x835FA00E,
+    0xE2FF7BC3, 0x835432D8,
+    0xE330734C, 0x8348D8DB,
+    0xE3616F47, 0x833D921A,
+    0xE3926FAC, 0x83325E97,
+    0xE3C37473, 0x83273E52,
+    0xE3F47D95, 0x831C314E,
+    0xE4258B0A, 0x8311378C,
+    0xE4569CCB, 0x8306510F,
+    0xE487B2CF, 0x82FB7DD8,
+    0xE4B8CD10, 0x82F0BDE8,
+    0xE4E9EB86, 0x82E61141,
+    0xE51B0E2A, 0x82DB77E5,
+    0xE54C34F3, 0x82D0F1D5,
+    0xE57D5FDA, 0x82C67F13,
+    0xE5AE8ED8, 0x82BC1FA1,
+    0xE5DFC1E4, 0x82B1D381,
+    0xE610F8F9, 0x82A79AB3,
+    0xE642340D, 0x829D753A,
+    0xE6737319, 0x82936316,
+    0xE6A4B616, 0x8289644A,
+    0xE6D5FCFC, 0x827F78D8,
+    0xE70747C3, 0x8275A0C0,
+    0xE7389664, 0x826BDC04,
+    0xE769E8D8, 0x82622AA5,
+    0xE79B3F16, 0x82588CA6,
+    0xE7CC9917, 0x824F0208,
+    0xE7FDF6D3, 0x82458ACB,
+    0xE82F5844, 0x823C26F2,
+    0xE860BD60, 0x8232D67E,
+    0xE8922621, 0x82299971,
+    0xE8C3927F, 0x82206FCB,
+    0xE8F50273, 0x8217598F,
+    0xE92675F4, 0x820E56BE,
+    0xE957ECFB, 0x82056758,
+    0xE9896780, 0x81FC8B60,
+    0xE9BAE57C, 0x81F3C2D7,
+    0xE9EC66E8, 0x81EB0DBD,
+    0xEA1DEBBB, 0x81E26C16,
+    0xEA4F73EE, 0x81D9DDE1,
+    0xEA80FF79, 0x81D16320,
+    0xEAB28E55, 0x81C8FBD5,
+    0xEAE4207A, 0x81C0A801,
+    0xEB15B5E0, 0x81B867A4,
+    0xEB474E80, 0x81B03AC1,
+    0xEB78EA52, 0x81A82159,
+    0xEBAA894E, 0x81A01B6C,
+    0xEBDC2B6D, 0x819828FD,
+    0xEC0DD0A8, 0x81904A0C,
+    0xEC3F78F5, 0x81887E9A,
+    0xEC71244F, 0x8180C6A9,
+    0xECA2D2AC, 0x8179223A,
+    0xECD48406, 0x8171914E,
+    0xED063855, 0x816A13E6,
+    0xED37EF91, 0x8162AA03,
+    0xED69A9B2, 0x815B53A8,
+    0xED9B66B2, 0x815410D3,
+    0xEDCD2687, 0x814CE188,
+    0xEDFEE92B, 0x8145C5C6,
+    0xEE30AE95, 0x813EBD90,
+    0xEE6276BF, 0x8137C8E6,
+    0xEE9441A0, 0x8130E7C8,
+    0xEEC60F31, 0x812A1A39,
+    0xEEF7DF6A, 0x81236039,
+    0xEF29B243, 0x811CB9CA,
+    0xEF5B87B5, 0x811626EC,
+    0xEF8D5FB8, 0x810FA7A0,
+    0xEFBF3A44, 0x81093BE8,
+    0xEFF11752, 0x8102E3C3,
+    0xF022F6DA, 0x80FC9F35,
+    0xF054D8D4, 0x80F66E3C,
+    0xF086BD39, 0x80F050DB,
+    0xF0B8A401, 0x80EA4712,
+    0xF0EA8D23, 0x80E450E2,
+    0xF11C789A, 0x80DE6E4C,
+    0xF14E665C, 0x80D89F51,
+    0xF1805662, 0x80D2E3F1,
+    0xF1B248A5, 0x80CD3C2F,
+    0xF1E43D1C, 0x80C7A80A,
+    0xF21633C0, 0x80C22783,
+    0xF2482C89, 0x80BCBA9C,
+    0xF27A2770, 0x80B76155,
+    0xF2AC246D, 0x80B21BAF,
+    0xF2DE2378, 0x80ACE9AB,
+    0xF310248A, 0x80A7CB49,
+    0xF342279A, 0x80A2C08B,
+    0xF3742CA1, 0x809DC970,
+    0xF3A63398, 0x8098E5FB,
+    0xF3D83C76, 0x8094162B,
+    0xF40A4734, 0x808F5A02,
+    0xF43C53CA, 0x808AB180,
+    0xF46E6231, 0x80861CA5,
+    0xF4A07260, 0x80819B74,
+    0xF4D28451, 0x807D2DEB,
+    0xF50497FA, 0x8078D40D,
+    0xF536AD55, 0x80748DD9,
+    0xF568C45A, 0x80705B50,
+    0xF59ADD01, 0x806C3C73,
+    0xF5CCF743, 0x80683143,
+    0xF5FF1317, 0x806439C0,
+    0xF6313076, 0x806055EA,
+    0xF6634F58, 0x805C85C3,
+    0xF6956FB6, 0x8058C94C,
+    0xF6C79188, 0x80552083,
+    0xF6F9B4C5, 0x80518B6B,
+    0xF72BD967, 0x804E0A03,
+    0xF75DFF65, 0x804A9C4D,
+    0xF79026B8, 0x80474248,
+    0xF7C24F58, 0x8043FBF6,
+    0xF7F4793E, 0x8040C956,
+    0xF826A461, 0x803DAA69,
+    0xF858D0BA, 0x803A9F31,
+    0xF88AFE41, 0x8037A7AC,
+    0xF8BD2CEF, 0x8034C3DC,
+    0xF8EF5CBB, 0x8031F3C1,
+    0xF9218D9E, 0x802F375C,
+    0xF953BF90, 0x802C8EAD,
+    0xF985F28A, 0x8029F9B4,
+    0xF9B82683, 0x80277872,
+    0xF9EA5B75, 0x80250AE7,
+    0xFA1C9156, 0x8022B113,
+    0xFA4EC820, 0x80206AF8,
+    0xFA80FFCB, 0x801E3894,
+    0xFAB3384F, 0x801C19E9,
+    0xFAE571A4, 0x801A0EF7,
+    0xFB17ABC2, 0x801817BF,
+    0xFB49E6A2, 0x80163440,
+    0xFB7C223C, 0x8014647A,
+    0xFBAE5E89, 0x8012A86F,
+    0xFBE09B80, 0x8011001E,
+    0xFC12D919, 0x800F6B88,
+    0xFC45174E, 0x800DEAAC,
+    0xFC775616, 0x800C7D8C,
+    0xFCA99569, 0x800B2427,
+    0xFCDBD541, 0x8009DE7D,
+    0xFD0E1594, 0x8008AC90,
+    0xFD40565B, 0x80078E5E,
+    0xFD72978F, 0x800683E8,
+    0xFDA4D928, 0x80058D2E,
+    0xFDD71B1E, 0x8004AA31,
+    0xFE095D69, 0x8003DAF0,
+    0xFE3BA001, 0x80031F6C,
+    0xFE6DE2E0, 0x800277A5,
+    0xFEA025FC, 0x8001E39B,
+    0xFED2694F, 0x8001634D,
+    0xFF04ACD0, 0x8000F6BD,
+    0xFF36F078, 0x80009DE9,
+    0xFF69343E, 0x800058D3,
+    0xFF9B781D, 0x8000277A,
+    0xFFCDBC0A, 0x800009DE
+};
+
+
+
+/*    
+* @brief  q15 Twiddle factors Table    
+*/
+
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 16	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_16_q15[24] = {
+    0x7FFF, 0x0000,
+    0x7641, 0x30FB,
+    0x5A82, 0x5A82,
+    0x30FB, 0x7641,
+    0x0000, 0x7FFF,
+    0xCF04, 0x7641,
+    0xA57D, 0x5A82,
+    0x89BE, 0x30FB,
+    0x8000, 0x0000,
+    0x89BE, 0xCF04,
+    0xA57D, 0xA57D,
+    0xCF04, 0x89BE
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 32	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_32_q15[48] = {
+    0x7FFF, 0x0000,
+    0x7D8A, 0x18F8,
+    0x7641, 0x30FB,
+    0x6A6D, 0x471C,
+    0x5A82, 0x5A82,
+    0x471C, 0x6A6D,
+    0x30FB, 0x7641,
+    0x18F8, 0x7D8A,
+    0x0000, 0x7FFF,
+    0xE707, 0x7D8A,
+    0xCF04, 0x7641,
+    0xB8E3, 0x6A6D,
+    0xA57D, 0x5A82,
+    0x9592, 0x471C,
+    0x89BE, 0x30FB,
+    0x8275, 0x18F8,
+    0x8000, 0x0000,
+    0x8275, 0xE707,
+    0x89BE, 0xCF04,
+    0x9592, 0xB8E3,
+    0xA57D, 0xA57D,
+    0xB8E3, 0x9592,
+    0xCF04, 0x89BE,
+    0xE707, 0x8275
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 64	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_64_q15[96] = {
+    0x7FFF, 0x0000,
+    0x7F62, 0x0C8B,
+    0x7D8A, 0x18F8,
+    0x7A7D, 0x2528,
+    0x7641, 0x30FB,
+    0x70E2, 0x3C56,
+    0x6A6D, 0x471C,
+    0x62F2, 0x5133,
+    0x5A82, 0x5A82,
+    0x5133, 0x62F2,
+    0x471C, 0x6A6D,
+    0x3C56, 0x70E2,
+    0x30FB, 0x7641,
+    0x2528, 0x7A7D,
+    0x18F8, 0x7D8A,
+    0x0C8B, 0x7F62,
+    0x0000, 0x7FFF,
+    0xF374, 0x7F62,
+    0xE707, 0x7D8A,
+    0xDAD7, 0x7A7D,
+    0xCF04, 0x7641,
+    0xC3A9, 0x70E2,
+    0xB8E3, 0x6A6D,
+    0xAECC, 0x62F2,
+    0xA57D, 0x5A82,
+    0x9D0D, 0x5133,
+    0x9592, 0x471C,
+    0x8F1D, 0x3C56,
+    0x89BE, 0x30FB,
+    0x8582, 0x2528,
+    0x8275, 0x18F8,
+    0x809D, 0x0C8B,
+    0x8000, 0x0000,
+    0x809D, 0xF374,
+    0x8275, 0xE707,
+    0x8582, 0xDAD7,
+    0x89BE, 0xCF04,
+    0x8F1D, 0xC3A9,
+    0x9592, 0xB8E3,
+    0x9D0D, 0xAECC,
+    0xA57D, 0xA57D,
+    0xAECC, 0x9D0D,
+    0xB8E3, 0x9592,
+    0xC3A9, 0x8F1D,
+    0xCF04, 0x89BE,
+    0xDAD7, 0x8582,
+    0xE707, 0x8275,
+    0xF374, 0x809D
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 128	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_128_q15[192] = {
+    0x7FFF, 0x0000,
+    0x7FD8, 0x0647,
+    0x7F62, 0x0C8B,
+    0x7E9D, 0x12C8,
+    0x7D8A, 0x18F8,
+    0x7C29, 0x1F19,
+    0x7A7D, 0x2528,
+    0x7884, 0x2B1F,
+    0x7641, 0x30FB,
+    0x73B5, 0x36BA,
+    0x70E2, 0x3C56,
+    0x6DCA, 0x41CE,
+    0x6A6D, 0x471C,
+    0x66CF, 0x4C3F,
+    0x62F2, 0x5133,
+    0x5ED7, 0x55F5,
+    0x5A82, 0x5A82,
+    0x55F5, 0x5ED7,
+    0x5133, 0x62F2,
+    0x4C3F, 0x66CF,
+    0x471C, 0x6A6D,
+    0x41CE, 0x6DCA,
+    0x3C56, 0x70E2,
+    0x36BA, 0x73B5,
+    0x30FB, 0x7641,
+    0x2B1F, 0x7884,
+    0x2528, 0x7A7D,
+    0x1F19, 0x7C29,
+    0x18F8, 0x7D8A,
+    0x12C8, 0x7E9D,
+    0x0C8B, 0x7F62,
+    0x0647, 0x7FD8,
+    0x0000, 0x7FFF,
+    0xF9B8, 0x7FD8,
+    0xF374, 0x7F62,
+    0xED37, 0x7E9D,
+    0xE707, 0x7D8A,
+    0xE0E6, 0x7C29,
+    0xDAD7, 0x7A7D,
+    0xD4E0, 0x7884,
+    0xCF04, 0x7641,
+    0xC945, 0x73B5,
+    0xC3A9, 0x70E2,
+    0xBE31, 0x6DCA,
+    0xB8E3, 0x6A6D,
+    0xB3C0, 0x66CF,
+    0xAECC, 0x62F2,
+    0xAA0A, 0x5ED7,
+    0xA57D, 0x5A82,
+    0xA128, 0x55F5,
+    0x9D0D, 0x5133,
+    0x9930, 0x4C3F,
+    0x9592, 0x471C,
+    0x9235, 0x41CE,
+    0x8F1D, 0x3C56,
+    0x8C4A, 0x36BA,
+    0x89BE, 0x30FB,
+    0x877B, 0x2B1F,
+    0x8582, 0x2528,
+    0x83D6, 0x1F19,
+    0x8275, 0x18F8,
+    0x8162, 0x12C8,
+    0x809D, 0x0C8B,
+    0x8027, 0x0647,
+    0x8000, 0x0000,
+    0x8027, 0xF9B8,
+    0x809D, 0xF374,
+    0x8162, 0xED37,
+    0x8275, 0xE707,
+    0x83D6, 0xE0E6,
+    0x8582, 0xDAD7,
+    0x877B, 0xD4E0,
+    0x89BE, 0xCF04,
+    0x8C4A, 0xC945,
+    0x8F1D, 0xC3A9,
+    0x9235, 0xBE31,
+    0x9592, 0xB8E3,
+    0x9930, 0xB3C0,
+    0x9D0D, 0xAECC,
+    0xA128, 0xAA0A,
+    0xA57D, 0xA57D,
+    0xAA0A, 0xA128,
+    0xAECC, 0x9D0D,
+    0xB3C0, 0x9930,
+    0xB8E3, 0x9592,
+    0xBE31, 0x9235,
+    0xC3A9, 0x8F1D,
+    0xC945, 0x8C4A,
+    0xCF04, 0x89BE,
+    0xD4E0, 0x877B,
+    0xDAD7, 0x8582,
+    0xE0E6, 0x83D6,
+    0xE707, 0x8275,
+    0xED37, 0x8162,
+    0xF374, 0x809D,
+    0xF9B8, 0x8027
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 256	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_256_q15[384] = {
+    0x7FFF, 0x0000,
+    0x7FF6, 0x0324,
+    0x7FD8, 0x0647,
+    0x7FA7, 0x096A,
+    0x7F62, 0x0C8B,
+    0x7F09, 0x0FAB,
+    0x7E9D, 0x12C8,
+    0x7E1D, 0x15E2,
+    0x7D8A, 0x18F8,
+    0x7CE3, 0x1C0B,
+    0x7C29, 0x1F19,
+    0x7B5D, 0x2223,
+    0x7A7D, 0x2528,
+    0x798A, 0x2826,
+    0x7884, 0x2B1F,
+    0x776C, 0x2E11,
+    0x7641, 0x30FB,
+    0x7504, 0x33DE,
+    0x73B5, 0x36BA,
+    0x7255, 0x398C,
+    0x70E2, 0x3C56,
+    0x6F5F, 0x3F17,
+    0x6DCA, 0x41CE,
+    0x6C24, 0x447A,
+    0x6A6D, 0x471C,
+    0x68A6, 0x49B4,
+    0x66CF, 0x4C3F,
+    0x64E8, 0x4EBF,
+    0x62F2, 0x5133,
+    0x60EC, 0x539B,
+    0x5ED7, 0x55F5,
+    0x5CB4, 0x5842,
+    0x5A82, 0x5A82,
+    0x5842, 0x5CB4,
+    0x55F5, 0x5ED7,
+    0x539B, 0x60EC,
+    0x5133, 0x62F2,
+    0x4EBF, 0x64E8,
+    0x4C3F, 0x66CF,
+    0x49B4, 0x68A6,
+    0x471C, 0x6A6D,
+    0x447A, 0x6C24,
+    0x41CE, 0x6DCA,
+    0x3F17, 0x6F5F,
+    0x3C56, 0x70E2,
+    0x398C, 0x7255,
+    0x36BA, 0x73B5,
+    0x33DE, 0x7504,
+    0x30FB, 0x7641,
+    0x2E11, 0x776C,
+    0x2B1F, 0x7884,
+    0x2826, 0x798A,
+    0x2528, 0x7A7D,
+    0x2223, 0x7B5D,
+    0x1F19, 0x7C29,
+    0x1C0B, 0x7CE3,
+    0x18F8, 0x7D8A,
+    0x15E2, 0x7E1D,
+    0x12C8, 0x7E9D,
+    0x0FAB, 0x7F09,
+    0x0C8B, 0x7F62,
+    0x096A, 0x7FA7,
+    0x0647, 0x7FD8,
+    0x0324, 0x7FF6,
+    0x0000, 0x7FFF,
+    0xFCDB, 0x7FF6,
+    0xF9B8, 0x7FD8,
+    0xF695, 0x7FA7,
+    0xF374, 0x7F62,
+    0xF054, 0x7F09,
+    0xED37, 0x7E9D,
+    0xEA1D, 0x7E1D,
+    0xE707, 0x7D8A,
+    0xE3F4, 0x7CE3,
+    0xE0E6, 0x7C29,
+    0xDDDC, 0x7B5D,
+    0xDAD7, 0x7A7D,
+    0xD7D9, 0x798A,
+    0xD4E0, 0x7884,
+    0xD1EE, 0x776C,
+    0xCF04, 0x7641,
+    0xCC21, 0x7504,
+    0xC945, 0x73B5,
+    0xC673, 0x7255,
+    0xC3A9, 0x70E2,
+    0xC0E8, 0x6F5F,
+    0xBE31, 0x6DCA,
+    0xBB85, 0x6C24,
+    0xB8E3, 0x6A6D,
+    0xB64B, 0x68A6,
+    0xB3C0, 0x66CF,
+    0xB140, 0x64E8,
+    0xAECC, 0x62F2,
+    0xAC64, 0x60EC,
+    0xAA0A, 0x5ED7,
+    0xA7BD, 0x5CB4,
+    0xA57D, 0x5A82,
+    0xA34B, 0x5842,
+    0xA128, 0x55F5,
+    0x9F13, 0x539B,
+    0x9D0D, 0x5133,
+    0x9B17, 0x4EBF,
+    0x9930, 0x4C3F,
+    0x9759, 0x49B4,
+    0x9592, 0x471C,
+    0x93DB, 0x447A,
+    0x9235, 0x41CE,
+    0x90A0, 0x3F17,
+    0x8F1D, 0x3C56,
+    0x8DAA, 0x398C,
+    0x8C4A, 0x36BA,
+    0x8AFB, 0x33DE,
+    0x89BE, 0x30FB,
+    0x8893, 0x2E11,
+    0x877B, 0x2B1F,
+    0x8675, 0x2826,
+    0x8582, 0x2528,
+    0x84A2, 0x2223,
+    0x83D6, 0x1F19,
+    0x831C, 0x1C0B,
+    0x8275, 0x18F8,
+    0x81E2, 0x15E2,
+    0x8162, 0x12C8,
+    0x80F6, 0x0FAB,
+    0x809D, 0x0C8B,
+    0x8058, 0x096A,
+    0x8027, 0x0647,
+    0x8009, 0x0324,
+    0x8000, 0x0000,
+    0x8009, 0xFCDB,
+    0x8027, 0xF9B8,
+    0x8058, 0xF695,
+    0x809D, 0xF374,
+    0x80F6, 0xF054,
+    0x8162, 0xED37,
+    0x81E2, 0xEA1D,
+    0x8275, 0xE707,
+    0x831C, 0xE3F4,
+    0x83D6, 0xE0E6,
+    0x84A2, 0xDDDC,
+    0x8582, 0xDAD7,
+    0x8675, 0xD7D9,
+    0x877B, 0xD4E0,
+    0x8893, 0xD1EE,
+    0x89BE, 0xCF04,
+    0x8AFB, 0xCC21,
+    0x8C4A, 0xC945,
+    0x8DAA, 0xC673,
+    0x8F1D, 0xC3A9,
+    0x90A0, 0xC0E8,
+    0x9235, 0xBE31,
+    0x93DB, 0xBB85,
+    0x9592, 0xB8E3,
+    0x9759, 0xB64B,
+    0x9930, 0xB3C0,
+    0x9B17, 0xB140,
+    0x9D0D, 0xAECC,
+    0x9F13, 0xAC64,
+    0xA128, 0xAA0A,
+    0xA34B, 0xA7BD,
+    0xA57D, 0xA57D,
+    0xA7BD, 0xA34B,
+    0xAA0A, 0xA128,
+    0xAC64, 0x9F13,
+    0xAECC, 0x9D0D,
+    0xB140, 0x9B17,
+    0xB3C0, 0x9930,
+    0xB64B, 0x9759,
+    0xB8E3, 0x9592,
+    0xBB85, 0x93DB,
+    0xBE31, 0x9235,
+    0xC0E8, 0x90A0,
+    0xC3A9, 0x8F1D,
+    0xC673, 0x8DAA,
+    0xC945, 0x8C4A,
+    0xCC21, 0x8AFB,
+    0xCF04, 0x89BE,
+    0xD1EE, 0x8893,
+    0xD4E0, 0x877B,
+    0xD7D9, 0x8675,
+    0xDAD7, 0x8582,
+    0xDDDC, 0x84A2,
+    0xE0E6, 0x83D6,
+    0xE3F4, 0x831C,
+    0xE707, 0x8275,
+    0xEA1D, 0x81E2,
+    0xED37, 0x8162,
+    0xF054, 0x80F6,
+    0xF374, 0x809D,
+    0xF695, 0x8058,
+    0xF9B8, 0x8027,
+    0xFCDB, 0x8009
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 512	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_512_q15[768] = {
+    0x7FFF, 0x0000,
+    0x7FFD, 0x0192,
+    0x7FF6, 0x0324,
+    0x7FE9, 0x04B6,
+    0x7FD8, 0x0647,
+    0x7FC2, 0x07D9,
+    0x7FA7, 0x096A,
+    0x7F87, 0x0AFB,
+    0x7F62, 0x0C8B,
+    0x7F38, 0x0E1B,
+    0x7F09, 0x0FAB,
+    0x7ED5, 0x1139,
+    0x7E9D, 0x12C8,
+    0x7E5F, 0x1455,
+    0x7E1D, 0x15E2,
+    0x7DD6, 0x176D,
+    0x7D8A, 0x18F8,
+    0x7D39, 0x1A82,
+    0x7CE3, 0x1C0B,
+    0x7C89, 0x1D93,
+    0x7C29, 0x1F19,
+    0x7BC5, 0x209F,
+    0x7B5D, 0x2223,
+    0x7AEF, 0x23A6,
+    0x7A7D, 0x2528,
+    0x7A05, 0x26A8,
+    0x798A, 0x2826,
+    0x7909, 0x29A3,
+    0x7884, 0x2B1F,
+    0x77FA, 0x2C98,
+    0x776C, 0x2E11,
+    0x76D9, 0x2F87,
+    0x7641, 0x30FB,
+    0x75A5, 0x326E,
+    0x7504, 0x33DE,
+    0x745F, 0x354D,
+    0x73B5, 0x36BA,
+    0x7307, 0x3824,
+    0x7255, 0x398C,
+    0x719E, 0x3AF2,
+    0x70E2, 0x3C56,
+    0x7023, 0x3DB8,
+    0x6F5F, 0x3F17,
+    0x6E96, 0x4073,
+    0x6DCA, 0x41CE,
+    0x6CF9, 0x4325,
+    0x6C24, 0x447A,
+    0x6B4A, 0x45CD,
+    0x6A6D, 0x471C,
+    0x698C, 0x4869,
+    0x68A6, 0x49B4,
+    0x67BD, 0x4AFB,
+    0x66CF, 0x4C3F,
+    0x65DD, 0x4D81,
+    0x64E8, 0x4EBF,
+    0x63EF, 0x4FFB,
+    0x62F2, 0x5133,
+    0x61F1, 0x5269,
+    0x60EC, 0x539B,
+    0x5FE3, 0x54CA,
+    0x5ED7, 0x55F5,
+    0x5DC7, 0x571D,
+    0x5CB4, 0x5842,
+    0x5B9D, 0x5964,
+    0x5A82, 0x5A82,
+    0x5964, 0x5B9D,
+    0x5842, 0x5CB4,
+    0x571D, 0x5DC7,
+    0x55F5, 0x5ED7,
+    0x54CA, 0x5FE3,
+    0x539B, 0x60EC,
+    0x5269, 0x61F1,
+    0x5133, 0x62F2,
+    0x4FFB, 0x63EF,
+    0x4EBF, 0x64E8,
+    0x4D81, 0x65DD,
+    0x4C3F, 0x66CF,
+    0x4AFB, 0x67BD,
+    0x49B4, 0x68A6,
+    0x4869, 0x698C,
+    0x471C, 0x6A6D,
+    0x45CD, 0x6B4A,
+    0x447A, 0x6C24,
+    0x4325, 0x6CF9,
+    0x41CE, 0x6DCA,
+    0x4073, 0x6E96,
+    0x3F17, 0x6F5F,
+    0x3DB8, 0x7023,
+    0x3C56, 0x70E2,
+    0x3AF2, 0x719E,
+    0x398C, 0x7255,
+    0x3824, 0x7307,
+    0x36BA, 0x73B5,
+    0x354D, 0x745F,
+    0x33DE, 0x7504,
+    0x326E, 0x75A5,
+    0x30FB, 0x7641,
+    0x2F87, 0x76D9,
+    0x2E11, 0x776C,
+    0x2C98, 0x77FA,
+    0x2B1F, 0x7884,
+    0x29A3, 0x7909,
+    0x2826, 0x798A,
+    0x26A8, 0x7A05,
+    0x2528, 0x7A7D,
+    0x23A6, 0x7AEF,
+    0x2223, 0x7B5D,
+    0x209F, 0x7BC5,
+    0x1F19, 0x7C29,
+    0x1D93, 0x7C89,
+    0x1C0B, 0x7CE3,
+    0x1A82, 0x7D39,
+    0x18F8, 0x7D8A,
+    0x176D, 0x7DD6,
+    0x15E2, 0x7E1D,
+    0x1455, 0x7E5F,
+    0x12C8, 0x7E9D,
+    0x1139, 0x7ED5,
+    0x0FAB, 0x7F09,
+    0x0E1B, 0x7F38,
+    0x0C8B, 0x7F62,
+    0x0AFB, 0x7F87,
+    0x096A, 0x7FA7,
+    0x07D9, 0x7FC2,
+    0x0647, 0x7FD8,
+    0x04B6, 0x7FE9,
+    0x0324, 0x7FF6,
+    0x0192, 0x7FFD,
+    0x0000, 0x7FFF,
+    0xFE6D, 0x7FFD,
+    0xFCDB, 0x7FF6,
+    0xFB49, 0x7FE9,
+    0xF9B8, 0x7FD8,
+    0xF826, 0x7FC2,
+    0xF695, 0x7FA7,
+    0xF504, 0x7F87,
+    0xF374, 0x7F62,
+    0xF1E4, 0x7F38,
+    0xF054, 0x7F09,
+    0xEEC6, 0x7ED5,
+    0xED37, 0x7E9D,
+    0xEBAA, 0x7E5F,
+    0xEA1D, 0x7E1D,
+    0xE892, 0x7DD6,
+    0xE707, 0x7D8A,
+    0xE57D, 0x7D39,
+    0xE3F4, 0x7CE3,
+    0xE26C, 0x7C89,
+    0xE0E6, 0x7C29,
+    0xDF60, 0x7BC5,
+    0xDDDC, 0x7B5D,
+    0xDC59, 0x7AEF,
+    0xDAD7, 0x7A7D,
+    0xD957, 0x7A05,
+    0xD7D9, 0x798A,
+    0xD65C, 0x7909,
+    0xD4E0, 0x7884,
+    0xD367, 0x77FA,
+    0xD1EE, 0x776C,
+    0xD078, 0x76D9,
+    0xCF04, 0x7641,
+    0xCD91, 0x75A5,
+    0xCC21, 0x7504,
+    0xCAB2, 0x745F,
+    0xC945, 0x73B5,
+    0xC7DB, 0x7307,
+    0xC673, 0x7255,
+    0xC50D, 0x719E,
+    0xC3A9, 0x70E2,
+    0xC247, 0x7023,
+    0xC0E8, 0x6F5F,
+    0xBF8C, 0x6E96,
+    0xBE31, 0x6DCA,
+    0xBCDA, 0x6CF9,
+    0xBB85, 0x6C24,
+    0xBA32, 0x6B4A,
+    0xB8E3, 0x6A6D,
+    0xB796, 0x698C,
+    0xB64B, 0x68A6,
+    0xB504, 0x67BD,
+    0xB3C0, 0x66CF,
+    0xB27E, 0x65DD,
+    0xB140, 0x64E8,
+    0xB004, 0x63EF,
+    0xAECC, 0x62F2,
+    0xAD96, 0x61F1,
+    0xAC64, 0x60EC,
+    0xAB35, 0x5FE3,
+    0xAA0A, 0x5ED7,
+    0xA8E2, 0x5DC7,
+    0xA7BD, 0x5CB4,
+    0xA69B, 0x5B9D,
+    0xA57D, 0x5A82,
+    0xA462, 0x5964,
+    0xA34B, 0x5842,
+    0xA238, 0x571D,
+    0xA128, 0x55F5,
+    0xA01C, 0x54CA,
+    0x9F13, 0x539B,
+    0x9E0E, 0x5269,
+    0x9D0D, 0x5133,
+    0x9C10, 0x4FFB,
+    0x9B17, 0x4EBF,
+    0x9A22, 0x4D81,
+    0x9930, 0x4C3F,
+    0x9842, 0x4AFB,
+    0x9759, 0x49B4,
+    0x9673, 0x4869,
+    0x9592, 0x471C,
+    0x94B5, 0x45CD,
+    0x93DB, 0x447A,
+    0x9306, 0x4325,
+    0x9235, 0x41CE,
+    0x9169, 0x4073,
+    0x90A0, 0x3F17,
+    0x8FDC, 0x3DB8,
+    0x8F1D, 0x3C56,
+    0x8E61, 0x3AF2,
+    0x8DAA, 0x398C,
+    0x8CF8, 0x3824,
+    0x8C4A, 0x36BA,
+    0x8BA0, 0x354D,
+    0x8AFB, 0x33DE,
+    0x8A5A, 0x326E,
+    0x89BE, 0x30FB,
+    0x8926, 0x2F87,
+    0x8893, 0x2E11,
+    0x8805, 0x2C98,
+    0x877B, 0x2B1F,
+    0x86F6, 0x29A3,
+    0x8675, 0x2826,
+    0x85FA, 0x26A8,
+    0x8582, 0x2528,
+    0x8510, 0x23A6,
+    0x84A2, 0x2223,
+    0x843A, 0x209F,
+    0x83D6, 0x1F19,
+    0x8376, 0x1D93,
+    0x831C, 0x1C0B,
+    0x82C6, 0x1A82,
+    0x8275, 0x18F8,
+    0x8229, 0x176D,
+    0x81E2, 0x15E2,
+    0x81A0, 0x1455,
+    0x8162, 0x12C8,
+    0x812A, 0x1139,
+    0x80F6, 0x0FAB,
+    0x80C7, 0x0E1B,
+    0x809D, 0x0C8B,
+    0x8078, 0x0AFB,
+    0x8058, 0x096A,
+    0x803D, 0x07D9,
+    0x8027, 0x0647,
+    0x8016, 0x04B6,
+    0x8009, 0x0324,
+    0x8002, 0x0192,
+    0x8000, 0x0000,
+    0x8002, 0xFE6D,
+    0x8009, 0xFCDB,
+    0x8016, 0xFB49,
+    0x8027, 0xF9B8,
+    0x803D, 0xF826,
+    0x8058, 0xF695,
+    0x8078, 0xF504,
+    0x809D, 0xF374,
+    0x80C7, 0xF1E4,
+    0x80F6, 0xF054,
+    0x812A, 0xEEC6,
+    0x8162, 0xED37,
+    0x81A0, 0xEBAA,
+    0x81E2, 0xEA1D,
+    0x8229, 0xE892,
+    0x8275, 0xE707,
+    0x82C6, 0xE57D,
+    0x831C, 0xE3F4,
+    0x8376, 0xE26C,
+    0x83D6, 0xE0E6,
+    0x843A, 0xDF60,
+    0x84A2, 0xDDDC,
+    0x8510, 0xDC59,
+    0x8582, 0xDAD7,
+    0x85FA, 0xD957,
+    0x8675, 0xD7D9,
+    0x86F6, 0xD65C,
+    0x877B, 0xD4E0,
+    0x8805, 0xD367,
+    0x8893, 0xD1EE,
+    0x8926, 0xD078,
+    0x89BE, 0xCF04,
+    0x8A5A, 0xCD91,
+    0x8AFB, 0xCC21,
+    0x8BA0, 0xCAB2,
+    0x8C4A, 0xC945,
+    0x8CF8, 0xC7DB,
+    0x8DAA, 0xC673,
+    0x8E61, 0xC50D,
+    0x8F1D, 0xC3A9,
+    0x8FDC, 0xC247,
+    0x90A0, 0xC0E8,
+    0x9169, 0xBF8C,
+    0x9235, 0xBE31,
+    0x9306, 0xBCDA,
+    0x93DB, 0xBB85,
+    0x94B5, 0xBA32,
+    0x9592, 0xB8E3,
+    0x9673, 0xB796,
+    0x9759, 0xB64B,
+    0x9842, 0xB504,
+    0x9930, 0xB3C0,
+    0x9A22, 0xB27E,
+    0x9B17, 0xB140,
+    0x9C10, 0xB004,
+    0x9D0D, 0xAECC,
+    0x9E0E, 0xAD96,
+    0x9F13, 0xAC64,
+    0xA01C, 0xAB35,
+    0xA128, 0xAA0A,
+    0xA238, 0xA8E2,
+    0xA34B, 0xA7BD,
+    0xA462, 0xA69B,
+    0xA57D, 0xA57D,
+    0xA69B, 0xA462,
+    0xA7BD, 0xA34B,
+    0xA8E2, 0xA238,
+    0xAA0A, 0xA128,
+    0xAB35, 0xA01C,
+    0xAC64, 0x9F13,
+    0xAD96, 0x9E0E,
+    0xAECC, 0x9D0D,
+    0xB004, 0x9C10,
+    0xB140, 0x9B17,
+    0xB27E, 0x9A22,
+    0xB3C0, 0x9930,
+    0xB504, 0x9842,
+    0xB64B, 0x9759,
+    0xB796, 0x9673,
+    0xB8E3, 0x9592,
+    0xBA32, 0x94B5,
+    0xBB85, 0x93DB,
+    0xBCDA, 0x9306,
+    0xBE31, 0x9235,
+    0xBF8C, 0x9169,
+    0xC0E8, 0x90A0,
+    0xC247, 0x8FDC,
+    0xC3A9, 0x8F1D,
+    0xC50D, 0x8E61,
+    0xC673, 0x8DAA,
+    0xC7DB, 0x8CF8,
+    0xC945, 0x8C4A,
+    0xCAB2, 0x8BA0,
+    0xCC21, 0x8AFB,
+    0xCD91, 0x8A5A,
+    0xCF04, 0x89BE,
+    0xD078, 0x8926,
+    0xD1EE, 0x8893,
+    0xD367, 0x8805,
+    0xD4E0, 0x877B,
+    0xD65C, 0x86F6,
+    0xD7D9, 0x8675,
+    0xD957, 0x85FA,
+    0xDAD7, 0x8582,
+    0xDC59, 0x8510,
+    0xDDDC, 0x84A2,
+    0xDF60, 0x843A,
+    0xE0E6, 0x83D6,
+    0xE26C, 0x8376,
+    0xE3F4, 0x831C,
+    0xE57D, 0x82C6,
+    0xE707, 0x8275,
+    0xE892, 0x8229,
+    0xEA1D, 0x81E2,
+    0xEBAA, 0x81A0,
+    0xED37, 0x8162,
+    0xEEC6, 0x812A,
+    0xF054, 0x80F6,
+    0xF1E4, 0x80C7,
+    0xF374, 0x809D,
+    0xF504, 0x8078,
+    0xF695, 0x8058,
+    0xF826, 0x803D,
+    0xF9B8, 0x8027,
+    0xFB49, 0x8016,
+    0xFCDB, 0x8009,
+    0xFE6D, 0x8002
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 1024	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_1024_q15[1536] = {
+    0x7FFF, 0x0000,
+    0x7FFF, 0x00C9,
+    0x7FFD, 0x0192,
+    0x7FFA, 0x025B,
+    0x7FF6, 0x0324,
+    0x7FF0, 0x03ED,
+    0x7FE9, 0x04B6,
+    0x7FE1, 0x057F,
+    0x7FD8, 0x0647,
+    0x7FCE, 0x0710,
+    0x7FC2, 0x07D9,
+    0x7FB5, 0x08A2,
+    0x7FA7, 0x096A,
+    0x7F97, 0x0A33,
+    0x7F87, 0x0AFB,
+    0x7F75, 0x0BC3,
+    0x7F62, 0x0C8B,
+    0x7F4D, 0x0D53,
+    0x7F38, 0x0E1B,
+    0x7F21, 0x0EE3,
+    0x7F09, 0x0FAB,
+    0x7EF0, 0x1072,
+    0x7ED5, 0x1139,
+    0x7EBA, 0x1201,
+    0x7E9D, 0x12C8,
+    0x7E7F, 0x138E,
+    0x7E5F, 0x1455,
+    0x7E3F, 0x151B,
+    0x7E1D, 0x15E2,
+    0x7DFA, 0x16A8,
+    0x7DD6, 0x176D,
+    0x7DB0, 0x1833,
+    0x7D8A, 0x18F8,
+    0x7D62, 0x19BD,
+    0x7D39, 0x1A82,
+    0x7D0F, 0x1B47,
+    0x7CE3, 0x1C0B,
+    0x7CB7, 0x1CCF,
+    0x7C89, 0x1D93,
+    0x7C5A, 0x1E56,
+    0x7C29, 0x1F19,
+    0x7BF8, 0x1FDC,
+    0x7BC5, 0x209F,
+    0x7B92, 0x2161,
+    0x7B5D, 0x2223,
+    0x7B26, 0x22E5,
+    0x7AEF, 0x23A6,
+    0x7AB6, 0x2467,
+    0x7A7D, 0x2528,
+    0x7A42, 0x25E8,
+    0x7A05, 0x26A8,
+    0x79C8, 0x2767,
+    0x798A, 0x2826,
+    0x794A, 0x28E5,
+    0x7909, 0x29A3,
+    0x78C7, 0x2A61,
+    0x7884, 0x2B1F,
+    0x7840, 0x2BDC,
+    0x77FA, 0x2C98,
+    0x77B4, 0x2D55,
+    0x776C, 0x2E11,
+    0x7723, 0x2ECC,
+    0x76D9, 0x2F87,
+    0x768E, 0x3041,
+    0x7641, 0x30FB,
+    0x75F4, 0x31B5,
+    0x75A5, 0x326E,
+    0x7555, 0x3326,
+    0x7504, 0x33DE,
+    0x74B2, 0x3496,
+    0x745F, 0x354D,
+    0x740B, 0x3604,
+    0x73B5, 0x36BA,
+    0x735F, 0x376F,
+    0x7307, 0x3824,
+    0x72AF, 0x38D8,
+    0x7255, 0x398C,
+    0x71FA, 0x3A40,
+    0x719E, 0x3AF2,
+    0x7141, 0x3BA5,
+    0x70E2, 0x3C56,
+    0x7083, 0x3D07,
+    0x7023, 0x3DB8,
+    0x6FC1, 0x3E68,
+    0x6F5F, 0x3F17,
+    0x6EFB, 0x3FC5,
+    0x6E96, 0x4073,
+    0x6E30, 0x4121,
+    0x6DCA, 0x41CE,
+    0x6D62, 0x427A,
+    0x6CF9, 0x4325,
+    0x6C8F, 0x43D0,
+    0x6C24, 0x447A,
+    0x6BB8, 0x4524,
+    0x6B4A, 0x45CD,
+    0x6ADC, 0x4675,
+    0x6A6D, 0x471C,
+    0x69FD, 0x47C3,
+    0x698C, 0x4869,
+    0x6919, 0x490F,
+    0x68A6, 0x49B4,
+    0x6832, 0x4A58,
+    0x67BD, 0x4AFB,
+    0x6746, 0x4B9E,
+    0x66CF, 0x4C3F,
+    0x6657, 0x4CE1,
+    0x65DD, 0x4D81,
+    0x6563, 0x4E21,
+    0x64E8, 0x4EBF,
+    0x646C, 0x4F5E,
+    0x63EF, 0x4FFB,
+    0x6371, 0x5097,
+    0x62F2, 0x5133,
+    0x6271, 0x51CE,
+    0x61F1, 0x5269,
+    0x616F, 0x5302,
+    0x60EC, 0x539B,
+    0x6068, 0x5433,
+    0x5FE3, 0x54CA,
+    0x5F5E, 0x5560,
+    0x5ED7, 0x55F5,
+    0x5E50, 0x568A,
+    0x5DC7, 0x571D,
+    0x5D3E, 0x57B0,
+    0x5CB4, 0x5842,
+    0x5C29, 0x58D4,
+    0x5B9D, 0x5964,
+    0x5B10, 0x59F3,
+    0x5A82, 0x5A82,
+    0x59F3, 0x5B10,
+    0x5964, 0x5B9D,
+    0x58D4, 0x5C29,
+    0x5842, 0x5CB4,
+    0x57B0, 0x5D3E,
+    0x571D, 0x5DC7,
+    0x568A, 0x5E50,
+    0x55F5, 0x5ED7,
+    0x5560, 0x5F5E,
+    0x54CA, 0x5FE3,
+    0x5433, 0x6068,
+    0x539B, 0x60EC,
+    0x5302, 0x616F,
+    0x5269, 0x61F1,
+    0x51CE, 0x6271,
+    0x5133, 0x62F2,
+    0x5097, 0x6371,
+    0x4FFB, 0x63EF,
+    0x4F5E, 0x646C,
+    0x4EBF, 0x64E8,
+    0x4E21, 0x6563,
+    0x4D81, 0x65DD,
+    0x4CE1, 0x6657,
+    0x4C3F, 0x66CF,
+    0x4B9E, 0x6746,
+    0x4AFB, 0x67BD,
+    0x4A58, 0x6832,
+    0x49B4, 0x68A6,
+    0x490F, 0x6919,
+    0x4869, 0x698C,
+    0x47C3, 0x69FD,
+    0x471C, 0x6A6D,
+    0x4675, 0x6ADC,
+    0x45CD, 0x6B4A,
+    0x4524, 0x6BB8,
+    0x447A, 0x6C24,
+    0x43D0, 0x6C8F,
+    0x4325, 0x6CF9,
+    0x427A, 0x6D62,
+    0x41CE, 0x6DCA,
+    0x4121, 0x6E30,
+    0x4073, 0x6E96,
+    0x3FC5, 0x6EFB,
+    0x3F17, 0x6F5F,
+    0x3E68, 0x6FC1,
+    0x3DB8, 0x7023,
+    0x3D07, 0x7083,
+    0x3C56, 0x70E2,
+    0x3BA5, 0x7141,
+    0x3AF2, 0x719E,
+    0x3A40, 0x71FA,
+    0x398C, 0x7255,
+    0x38D8, 0x72AF,
+    0x3824, 0x7307,
+    0x376F, 0x735F,
+    0x36BA, 0x73B5,
+    0x3604, 0x740B,
+    0x354D, 0x745F,
+    0x3496, 0x74B2,
+    0x33DE, 0x7504,
+    0x3326, 0x7555,
+    0x326E, 0x75A5,
+    0x31B5, 0x75F4,
+    0x30FB, 0x7641,
+    0x3041, 0x768E,
+    0x2F87, 0x76D9,
+    0x2ECC, 0x7723,
+    0x2E11, 0x776C,
+    0x2D55, 0x77B4,
+    0x2C98, 0x77FA,
+    0x2BDC, 0x7840,
+    0x2B1F, 0x7884,
+    0x2A61, 0x78C7,
+    0x29A3, 0x7909,
+    0x28E5, 0x794A,
+    0x2826, 0x798A,
+    0x2767, 0x79C8,
+    0x26A8, 0x7A05,
+    0x25E8, 0x7A42,
+    0x2528, 0x7A7D,
+    0x2467, 0x7AB6,
+    0x23A6, 0x7AEF,
+    0x22E5, 0x7B26,
+    0x2223, 0x7B5D,
+    0x2161, 0x7B92,
+    0x209F, 0x7BC5,
+    0x1FDC, 0x7BF8,
+    0x1F19, 0x7C29,
+    0x1E56, 0x7C5A,
+    0x1D93, 0x7C89,
+    0x1CCF, 0x7CB7,
+    0x1C0B, 0x7CE3,
+    0x1B47, 0x7D0F,
+    0x1A82, 0x7D39,
+    0x19BD, 0x7D62,
+    0x18F8, 0x7D8A,
+    0x1833, 0x7DB0,
+    0x176D, 0x7DD6,
+    0x16A8, 0x7DFA,
+    0x15E2, 0x7E1D,
+    0x151B, 0x7E3F,
+    0x1455, 0x7E5F,
+    0x138E, 0x7E7F,
+    0x12C8, 0x7E9D,
+    0x1201, 0x7EBA,
+    0x1139, 0x7ED5,
+    0x1072, 0x7EF0,
+    0x0FAB, 0x7F09,
+    0x0EE3, 0x7F21,
+    0x0E1B, 0x7F38,
+    0x0D53, 0x7F4D,
+    0x0C8B, 0x7F62,
+    0x0BC3, 0x7F75,
+    0x0AFB, 0x7F87,
+    0x0A33, 0x7F97,
+    0x096A, 0x7FA7,
+    0x08A2, 0x7FB5,
+    0x07D9, 0x7FC2,
+    0x0710, 0x7FCE,
+    0x0647, 0x7FD8,
+    0x057F, 0x7FE1,
+    0x04B6, 0x7FE9,
+    0x03ED, 0x7FF0,
+    0x0324, 0x7FF6,
+    0x025B, 0x7FFA,
+    0x0192, 0x7FFD,
+    0x00C9, 0x7FFF,
+    0x0000, 0x7FFF,
+    0xFF36, 0x7FFF,
+    0xFE6D, 0x7FFD,
+    0xFDA4, 0x7FFA,
+    0xFCDB, 0x7FF6,
+    0xFC12, 0x7FF0,
+    0xFB49, 0x7FE9,
+    0xFA80, 0x7FE1,
+    0xF9B8, 0x7FD8,
+    0xF8EF, 0x7FCE,
+    0xF826, 0x7FC2,
+    0xF75D, 0x7FB5,
+    0xF695, 0x7FA7,
+    0xF5CC, 0x7F97,
+    0xF504, 0x7F87,
+    0xF43C, 0x7F75,
+    0xF374, 0x7F62,
+    0xF2AC, 0x7F4D,
+    0xF1E4, 0x7F38,
+    0xF11C, 0x7F21,
+    0xF054, 0x7F09,
+    0xEF8D, 0x7EF0,
+    0xEEC6, 0x7ED5,
+    0xEDFE, 0x7EBA,
+    0xED37, 0x7E9D,
+    0xEC71, 0x7E7F,
+    0xEBAA, 0x7E5F,
+    0xEAE4, 0x7E3F,
+    0xEA1D, 0x7E1D,
+    0xE957, 0x7DFA,
+    0xE892, 0x7DD6,
+    0xE7CC, 0x7DB0,
+    0xE707, 0x7D8A,
+    0xE642, 0x7D62,
+    0xE57D, 0x7D39,
+    0xE4B8, 0x7D0F,
+    0xE3F4, 0x7CE3,
+    0xE330, 0x7CB7,
+    0xE26C, 0x7C89,
+    0xE1A9, 0x7C5A,
+    0xE0E6, 0x7C29,
+    0xE023, 0x7BF8,
+    0xDF60, 0x7BC5,
+    0xDE9E, 0x7B92,
+    0xDDDC, 0x7B5D,
+    0xDD1A, 0x7B26,
+    0xDC59, 0x7AEF,
+    0xDB98, 0x7AB6,
+    0xDAD7, 0x7A7D,
+    0xDA17, 0x7A42,
+    0xD957, 0x7A05,
+    0xD898, 0x79C8,
+    0xD7D9, 0x798A,
+    0xD71A, 0x794A,
+    0xD65C, 0x7909,
+    0xD59E, 0x78C7,
+    0xD4E0, 0x7884,
+    0xD423, 0x7840,
+    0xD367, 0x77FA,
+    0xD2AA, 0x77B4,
+    0xD1EE, 0x776C,
+    0xD133, 0x7723,
+    0xD078, 0x76D9,
+    0xCFBE, 0x768E,
+    0xCF04, 0x7641,
+    0xCE4A, 0x75F4,
+    0xCD91, 0x75A5,
+    0xCCD9, 0x7555,
+    0xCC21, 0x7504,
+    0xCB69, 0x74B2,
+    0xCAB2, 0x745F,
+    0xC9FB, 0x740B,
+    0xC945, 0x73B5,
+    0xC890, 0x735F,
+    0xC7DB, 0x7307,
+    0xC727, 0x72AF,
+    0xC673, 0x7255,
+    0xC5BF, 0x71FA,
+    0xC50D, 0x719E,
+    0xC45A, 0x7141,
+    0xC3A9, 0x70E2,
+    0xC2F8, 0x7083,
+    0xC247, 0x7023,
+    0xC197, 0x6FC1,
+    0xC0E8, 0x6F5F,
+    0xC03A, 0x6EFB,
+    0xBF8C, 0x6E96,
+    0xBEDE, 0x6E30,
+    0xBE31, 0x6DCA,
+    0xBD85, 0x6D62,
+    0xBCDA, 0x6CF9,
+    0xBC2F, 0x6C8F,
+    0xBB85, 0x6C24,
+    0xBADB, 0x6BB8,
+    0xBA32, 0x6B4A,
+    0xB98A, 0x6ADC,
+    0xB8E3, 0x6A6D,
+    0xB83C, 0x69FD,
+    0xB796, 0x698C,
+    0xB6F0, 0x6919,
+    0xB64B, 0x68A6,
+    0xB5A7, 0x6832,
+    0xB504, 0x67BD,
+    0xB461, 0x6746,
+    0xB3C0, 0x66CF,
+    0xB31E, 0x6657,
+    0xB27E, 0x65DD,
+    0xB1DE, 0x6563,
+    0xB140, 0x64E8,
+    0xB0A1, 0x646C,
+    0xB004, 0x63EF,
+    0xAF68, 0x6371,
+    0xAECC, 0x62F2,
+    0xAE31, 0x6271,
+    0xAD96, 0x61F1,
+    0xACFD, 0x616F,
+    0xAC64, 0x60EC,
+    0xABCC, 0x6068,
+    0xAB35, 0x5FE3,
+    0xAA9F, 0x5F5E,
+    0xAA0A, 0x5ED7,
+    0xA975, 0x5E50,
+    0xA8E2, 0x5DC7,
+    0xA84F, 0x5D3E,
+    0xA7BD, 0x5CB4,
+    0xA72B, 0x5C29,
+    0xA69B, 0x5B9D,
+    0xA60C, 0x5B10,
+    0xA57D, 0x5A82,
+    0xA4EF, 0x59F3,
+    0xA462, 0x5964,
+    0xA3D6, 0x58D4,
+    0xA34B, 0x5842,
+    0xA2C1, 0x57B0,
+    0xA238, 0x571D,
+    0xA1AF, 0x568A,
+    0xA128, 0x55F5,
+    0xA0A1, 0x5560,
+    0xA01C, 0x54CA,
+    0x9F97, 0x5433,
+    0x9F13, 0x539B,
+    0x9E90, 0x5302,
+    0x9E0E, 0x5269,
+    0x9D8E, 0x51CE,
+    0x9D0D, 0x5133,
+    0x9C8E, 0x5097,
+    0x9C10, 0x4FFB,
+    0x9B93, 0x4F5E,
+    0x9B17, 0x4EBF,
+    0x9A9C, 0x4E21,
+    0x9A22, 0x4D81,
+    0x99A8, 0x4CE1,
+    0x9930, 0x4C3F,
+    0x98B9, 0x4B9E,
+    0x9842, 0x4AFB,
+    0x97CD, 0x4A58,
+    0x9759, 0x49B4,
+    0x96E6, 0x490F,
+    0x9673, 0x4869,
+    0x9602, 0x47C3,
+    0x9592, 0x471C,
+    0x9523, 0x4675,
+    0x94B5, 0x45CD,
+    0x9447, 0x4524,
+    0x93DB, 0x447A,
+    0x9370, 0x43D0,
+    0x9306, 0x4325,
+    0x929D, 0x427A,
+    0x9235, 0x41CE,
+    0x91CF, 0x4121,
+    0x9169, 0x4073,
+    0x9104, 0x3FC5,
+    0x90A0, 0x3F17,
+    0x903E, 0x3E68,
+    0x8FDC, 0x3DB8,
+    0x8F7C, 0x3D07,
+    0x8F1D, 0x3C56,
+    0x8EBE, 0x3BA5,
+    0x8E61, 0x3AF2,
+    0x8E05, 0x3A40,
+    0x8DAA, 0x398C,
+    0x8D50, 0x38D8,
+    0x8CF8, 0x3824,
+    0x8CA0, 0x376F,
+    0x8C4A, 0x36BA,
+    0x8BF4, 0x3604,
+    0x8BA0, 0x354D,
+    0x8B4D, 0x3496,
+    0x8AFB, 0x33DE,
+    0x8AAA, 0x3326,
+    0x8A5A, 0x326E,
+    0x8A0B, 0x31B5,
+    0x89BE, 0x30FB,
+    0x8971, 0x3041,
+    0x8926, 0x2F87,
+    0x88DC, 0x2ECC,
+    0x8893, 0x2E11,
+    0x884B, 0x2D55,
+    0x8805, 0x2C98,
+    0x87BF, 0x2BDC,
+    0x877B, 0x2B1F,
+    0x8738, 0x2A61,
+    0x86F6, 0x29A3,
+    0x86B5, 0x28E5,
+    0x8675, 0x2826,
+    0x8637, 0x2767,
+    0x85FA, 0x26A8,
+    0x85BD, 0x25E8,
+    0x8582, 0x2528,
+    0x8549, 0x2467,
+    0x8510, 0x23A6,
+    0x84D9, 0x22E5,
+    0x84A2, 0x2223,
+    0x846D, 0x2161,
+    0x843A, 0x209F,
+    0x8407, 0x1FDC,
+    0x83D6, 0x1F19,
+    0x83A5, 0x1E56,
+    0x8376, 0x1D93,
+    0x8348, 0x1CCF,
+    0x831C, 0x1C0B,
+    0x82F0, 0x1B47,
+    0x82C6, 0x1A82,
+    0x829D, 0x19BD,
+    0x8275, 0x18F8,
+    0x824F, 0x1833,
+    0x8229, 0x176D,
+    0x8205, 0x16A8,
+    0x81E2, 0x15E2,
+    0x81C0, 0x151B,
+    0x81A0, 0x1455,
+    0x8180, 0x138E,
+    0x8162, 0x12C8,
+    0x8145, 0x1201,
+    0x812A, 0x1139,
+    0x810F, 0x1072,
+    0x80F6, 0x0FAB,
+    0x80DE, 0x0EE3,
+    0x80C7, 0x0E1B,
+    0x80B2, 0x0D53,
+    0x809D, 0x0C8B,
+    0x808A, 0x0BC3,
+    0x8078, 0x0AFB,
+    0x8068, 0x0A33,
+    0x8058, 0x096A,
+    0x804A, 0x08A2,
+    0x803D, 0x07D9,
+    0x8031, 0x0710,
+    0x8027, 0x0647,
+    0x801E, 0x057F,
+    0x8016, 0x04B6,
+    0x800F, 0x03ED,
+    0x8009, 0x0324,
+    0x8005, 0x025B,
+    0x8002, 0x0192,
+    0x8000, 0x00C9,
+    0x8000, 0x0000,
+    0x8000, 0xFF36,
+    0x8002, 0xFE6D,
+    0x8005, 0xFDA4,
+    0x8009, 0xFCDB,
+    0x800F, 0xFC12,
+    0x8016, 0xFB49,
+    0x801E, 0xFA80,
+    0x8027, 0xF9B8,
+    0x8031, 0xF8EF,
+    0x803D, 0xF826,
+    0x804A, 0xF75D,
+    0x8058, 0xF695,
+    0x8068, 0xF5CC,
+    0x8078, 0xF504,
+    0x808A, 0xF43C,
+    0x809D, 0xF374,
+    0x80B2, 0xF2AC,
+    0x80C7, 0xF1E4,
+    0x80DE, 0xF11C,
+    0x80F6, 0xF054,
+    0x810F, 0xEF8D,
+    0x812A, 0xEEC6,
+    0x8145, 0xEDFE,
+    0x8162, 0xED37,
+    0x8180, 0xEC71,
+    0x81A0, 0xEBAA,
+    0x81C0, 0xEAE4,
+    0x81E2, 0xEA1D,
+    0x8205, 0xE957,
+    0x8229, 0xE892,
+    0x824F, 0xE7CC,
+    0x8275, 0xE707,
+    0x829D, 0xE642,
+    0x82C6, 0xE57D,
+    0x82F0, 0xE4B8,
+    0x831C, 0xE3F4,
+    0x8348, 0xE330,
+    0x8376, 0xE26C,
+    0x83A5, 0xE1A9,
+    0x83D6, 0xE0E6,
+    0x8407, 0xE023,
+    0x843A, 0xDF60,
+    0x846D, 0xDE9E,
+    0x84A2, 0xDDDC,
+    0x84D9, 0xDD1A,
+    0x8510, 0xDC59,
+    0x8549, 0xDB98,
+    0x8582, 0xDAD7,
+    0x85BD, 0xDA17,
+    0x85FA, 0xD957,
+    0x8637, 0xD898,
+    0x8675, 0xD7D9,
+    0x86B5, 0xD71A,
+    0x86F6, 0xD65C,
+    0x8738, 0xD59E,
+    0x877B, 0xD4E0,
+    0x87BF, 0xD423,
+    0x8805, 0xD367,
+    0x884B, 0xD2AA,
+    0x8893, 0xD1EE,
+    0x88DC, 0xD133,
+    0x8926, 0xD078,
+    0x8971, 0xCFBE,
+    0x89BE, 0xCF04,
+    0x8A0B, 0xCE4A,
+    0x8A5A, 0xCD91,
+    0x8AAA, 0xCCD9,
+    0x8AFB, 0xCC21,
+    0x8B4D, 0xCB69,
+    0x8BA0, 0xCAB2,
+    0x8BF4, 0xC9FB,
+    0x8C4A, 0xC945,
+    0x8CA0, 0xC890,
+    0x8CF8, 0xC7DB,
+    0x8D50, 0xC727,
+    0x8DAA, 0xC673,
+    0x8E05, 0xC5BF,
+    0x8E61, 0xC50D,
+    0x8EBE, 0xC45A,
+    0x8F1D, 0xC3A9,
+    0x8F7C, 0xC2F8,
+    0x8FDC, 0xC247,
+    0x903E, 0xC197,
+    0x90A0, 0xC0E8,
+    0x9104, 0xC03A,
+    0x9169, 0xBF8C,
+    0x91CF, 0xBEDE,
+    0x9235, 0xBE31,
+    0x929D, 0xBD85,
+    0x9306, 0xBCDA,
+    0x9370, 0xBC2F,
+    0x93DB, 0xBB85,
+    0x9447, 0xBADB,
+    0x94B5, 0xBA32,
+    0x9523, 0xB98A,
+    0x9592, 0xB8E3,
+    0x9602, 0xB83C,
+    0x9673, 0xB796,
+    0x96E6, 0xB6F0,
+    0x9759, 0xB64B,
+    0x97CD, 0xB5A7,
+    0x9842, 0xB504,
+    0x98B9, 0xB461,
+    0x9930, 0xB3C0,
+    0x99A8, 0xB31E,
+    0x9A22, 0xB27E,
+    0x9A9C, 0xB1DE,
+    0x9B17, 0xB140,
+    0x9B93, 0xB0A1,
+    0x9C10, 0xB004,
+    0x9C8E, 0xAF68,
+    0x9D0D, 0xAECC,
+    0x9D8E, 0xAE31,
+    0x9E0E, 0xAD96,
+    0x9E90, 0xACFD,
+    0x9F13, 0xAC64,
+    0x9F97, 0xABCC,
+    0xA01C, 0xAB35,
+    0xA0A1, 0xAA9F,
+    0xA128, 0xAA0A,
+    0xA1AF, 0xA975,
+    0xA238, 0xA8E2,
+    0xA2C1, 0xA84F,
+    0xA34B, 0xA7BD,
+    0xA3D6, 0xA72B,
+    0xA462, 0xA69B,
+    0xA4EF, 0xA60C,
+    0xA57D, 0xA57D,
+    0xA60C, 0xA4EF,
+    0xA69B, 0xA462,
+    0xA72B, 0xA3D6,
+    0xA7BD, 0xA34B,
+    0xA84F, 0xA2C1,
+    0xA8E2, 0xA238,
+    0xA975, 0xA1AF,
+    0xAA0A, 0xA128,
+    0xAA9F, 0xA0A1,
+    0xAB35, 0xA01C,
+    0xABCC, 0x9F97,
+    0xAC64, 0x9F13,
+    0xACFD, 0x9E90,
+    0xAD96, 0x9E0E,
+    0xAE31, 0x9D8E,
+    0xAECC, 0x9D0D,
+    0xAF68, 0x9C8E,
+    0xB004, 0x9C10,
+    0xB0A1, 0x9B93,
+    0xB140, 0x9B17,
+    0xB1DE, 0x9A9C,
+    0xB27E, 0x9A22,
+    0xB31E, 0x99A8,
+    0xB3C0, 0x9930,
+    0xB461, 0x98B9,
+    0xB504, 0x9842,
+    0xB5A7, 0x97CD,
+    0xB64B, 0x9759,
+    0xB6F0, 0x96E6,
+    0xB796, 0x9673,
+    0xB83C, 0x9602,
+    0xB8E3, 0x9592,
+    0xB98A, 0x9523,
+    0xBA32, 0x94B5,
+    0xBADB, 0x9447,
+    0xBB85, 0x93DB,
+    0xBC2F, 0x9370,
+    0xBCDA, 0x9306,
+    0xBD85, 0x929D,
+    0xBE31, 0x9235,
+    0xBEDE, 0x91CF,
+    0xBF8C, 0x9169,
+    0xC03A, 0x9104,
+    0xC0E8, 0x90A0,
+    0xC197, 0x903E,
+    0xC247, 0x8FDC,
+    0xC2F8, 0x8F7C,
+    0xC3A9, 0x8F1D,
+    0xC45A, 0x8EBE,
+    0xC50D, 0x8E61,
+    0xC5BF, 0x8E05,
+    0xC673, 0x8DAA,
+    0xC727, 0x8D50,
+    0xC7DB, 0x8CF8,
+    0xC890, 0x8CA0,
+    0xC945, 0x8C4A,
+    0xC9FB, 0x8BF4,
+    0xCAB2, 0x8BA0,
+    0xCB69, 0x8B4D,
+    0xCC21, 0x8AFB,
+    0xCCD9, 0x8AAA,
+    0xCD91, 0x8A5A,
+    0xCE4A, 0x8A0B,
+    0xCF04, 0x89BE,
+    0xCFBE, 0x8971,
+    0xD078, 0x8926,
+    0xD133, 0x88DC,
+    0xD1EE, 0x8893,
+    0xD2AA, 0x884B,
+    0xD367, 0x8805,
+    0xD423, 0x87BF,
+    0xD4E0, 0x877B,
+    0xD59E, 0x8738,
+    0xD65C, 0x86F6,
+    0xD71A, 0x86B5,
+    0xD7D9, 0x8675,
+    0xD898, 0x8637,
+    0xD957, 0x85FA,
+    0xDA17, 0x85BD,
+    0xDAD7, 0x8582,
+    0xDB98, 0x8549,
+    0xDC59, 0x8510,
+    0xDD1A, 0x84D9,
+    0xDDDC, 0x84A2,
+    0xDE9E, 0x846D,
+    0xDF60, 0x843A,
+    0xE023, 0x8407,
+    0xE0E6, 0x83D6,
+    0xE1A9, 0x83A5,
+    0xE26C, 0x8376,
+    0xE330, 0x8348,
+    0xE3F4, 0x831C,
+    0xE4B8, 0x82F0,
+    0xE57D, 0x82C6,
+    0xE642, 0x829D,
+    0xE707, 0x8275,
+    0xE7CC, 0x824F,
+    0xE892, 0x8229,
+    0xE957, 0x8205,
+    0xEA1D, 0x81E2,
+    0xEAE4, 0x81C0,
+    0xEBAA, 0x81A0,
+    0xEC71, 0x8180,
+    0xED37, 0x8162,
+    0xEDFE, 0x8145,
+    0xEEC6, 0x812A,
+    0xEF8D, 0x810F,
+    0xF054, 0x80F6,
+    0xF11C, 0x80DE,
+    0xF1E4, 0x80C7,
+    0xF2AC, 0x80B2,
+    0xF374, 0x809D,
+    0xF43C, 0x808A,
+    0xF504, 0x8078,
+    0xF5CC, 0x8068,
+    0xF695, 0x8058,
+    0xF75D, 0x804A,
+    0xF826, 0x803D,
+    0xF8EF, 0x8031,
+    0xF9B8, 0x8027,
+    0xFA80, 0x801E,
+    0xFB49, 0x8016,
+    0xFC12, 0x800F,
+    0xFCDB, 0x8009,
+    0xFDA4, 0x8005,
+    0xFE6D, 0x8002,
+    0xFF36, 0x8000
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 2048	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_2048_q15[3072] = {
+    0x7FFF, 0x0000,
+    0x7FFF, 0x0064,
+    0x7FFF, 0x00C9,
+    0x7FFE, 0x012D,
+    0x7FFD, 0x0192,
+    0x7FFC, 0x01F6,
+    0x7FFA, 0x025B,
+    0x7FF8, 0x02BF,
+    0x7FF6, 0x0324,
+    0x7FF3, 0x0388,
+    0x7FF0, 0x03ED,
+    0x7FED, 0x0451,
+    0x7FE9, 0x04B6,
+    0x7FE5, 0x051A,
+    0x7FE1, 0x057F,
+    0x7FDD, 0x05E3,
+    0x7FD8, 0x0647,
+    0x7FD3, 0x06AC,
+    0x7FCE, 0x0710,
+    0x7FC8, 0x0775,
+    0x7FC2, 0x07D9,
+    0x7FBC, 0x083D,
+    0x7FB5, 0x08A2,
+    0x7FAE, 0x0906,
+    0x7FA7, 0x096A,
+    0x7F9F, 0x09CE,
+    0x7F97, 0x0A33,
+    0x7F8F, 0x0A97,
+    0x7F87, 0x0AFB,
+    0x7F7E, 0x0B5F,
+    0x7F75, 0x0BC3,
+    0x7F6B, 0x0C27,
+    0x7F62, 0x0C8B,
+    0x7F58, 0x0CEF,
+    0x7F4D, 0x0D53,
+    0x7F43, 0x0DB7,
+    0x7F38, 0x0E1B,
+    0x7F2D, 0x0E7F,
+    0x7F21, 0x0EE3,
+    0x7F15, 0x0F47,
+    0x7F09, 0x0FAB,
+    0x7EFD, 0x100E,
+    0x7EF0, 0x1072,
+    0x7EE3, 0x10D6,
+    0x7ED5, 0x1139,
+    0x7EC8, 0x119D,
+    0x7EBA, 0x1201,
+    0x7EAB, 0x1264,
+    0x7E9D, 0x12C8,
+    0x7E8E, 0x132B,
+    0x7E7F, 0x138E,
+    0x7E6F, 0x13F2,
+    0x7E5F, 0x1455,
+    0x7E4F, 0x14B8,
+    0x7E3F, 0x151B,
+    0x7E2E, 0x157F,
+    0x7E1D, 0x15E2,
+    0x7E0C, 0x1645,
+    0x7DFA, 0x16A8,
+    0x7DE8, 0x170A,
+    0x7DD6, 0x176D,
+    0x7DC3, 0x17D0,
+    0x7DB0, 0x1833,
+    0x7D9D, 0x1896,
+    0x7D8A, 0x18F8,
+    0x7D76, 0x195B,
+    0x7D62, 0x19BD,
+    0x7D4E, 0x1A20,
+    0x7D39, 0x1A82,
+    0x7D24, 0x1AE4,
+    0x7D0F, 0x1B47,
+    0x7CF9, 0x1BA9,
+    0x7CE3, 0x1C0B,
+    0x7CCD, 0x1C6D,
+    0x7CB7, 0x1CCF,
+    0x7CA0, 0x1D31,
+    0x7C89, 0x1D93,
+    0x7C71, 0x1DF5,
+    0x7C5A, 0x1E56,
+    0x7C42, 0x1EB8,
+    0x7C29, 0x1F19,
+    0x7C11, 0x1F7B,
+    0x7BF8, 0x1FDC,
+    0x7BDF, 0x203E,
+    0x7BC5, 0x209F,
+    0x7BAC, 0x2100,
+    0x7B92, 0x2161,
+    0x7B77, 0x21C2,
+    0x7B5D, 0x2223,
+    0x7B42, 0x2284,
+    0x7B26, 0x22E5,
+    0x7B0B, 0x2345,
+    0x7AEF, 0x23A6,
+    0x7AD3, 0x2407,
+    0x7AB6, 0x2467,
+    0x7A9A, 0x24C7,
+    0x7A7D, 0x2528,
+    0x7A5F, 0x2588,
+    0x7A42, 0x25E8,
+    0x7A24, 0x2648,
+    0x7A05, 0x26A8,
+    0x79E7, 0x2707,
+    0x79C8, 0x2767,
+    0x79A9, 0x27C7,
+    0x798A, 0x2826,
+    0x796A, 0x2886,
+    0x794A, 0x28E5,
+    0x792A, 0x2944,
+    0x7909, 0x29A3,
+    0x78E8, 0x2A02,
+    0x78C7, 0x2A61,
+    0x78A6, 0x2AC0,
+    0x7884, 0x2B1F,
+    0x7862, 0x2B7D,
+    0x7840, 0x2BDC,
+    0x781D, 0x2C3A,
+    0x77FA, 0x2C98,
+    0x77D7, 0x2CF7,
+    0x77B4, 0x2D55,
+    0x7790, 0x2DB3,
+    0x776C, 0x2E11,
+    0x7747, 0x2E6E,
+    0x7723, 0x2ECC,
+    0x76FE, 0x2F29,
+    0x76D9, 0x2F87,
+    0x76B3, 0x2FE4,
+    0x768E, 0x3041,
+    0x7668, 0x309E,
+    0x7641, 0x30FB,
+    0x761B, 0x3158,
+    0x75F4, 0x31B5,
+    0x75CC, 0x3211,
+    0x75A5, 0x326E,
+    0x757D, 0x32CA,
+    0x7555, 0x3326,
+    0x752D, 0x3382,
+    0x7504, 0x33DE,
+    0x74DB, 0x343A,
+    0x74B2, 0x3496,
+    0x7489, 0x34F2,
+    0x745F, 0x354D,
+    0x7435, 0x35A8,
+    0x740B, 0x3604,
+    0x73E0, 0x365F,
+    0x73B5, 0x36BA,
+    0x738A, 0x3714,
+    0x735F, 0x376F,
+    0x7333, 0x37CA,
+    0x7307, 0x3824,
+    0x72DB, 0x387E,
+    0x72AF, 0x38D8,
+    0x7282, 0x3932,
+    0x7255, 0x398C,
+    0x7227, 0x39E6,
+    0x71FA, 0x3A40,
+    0x71CC, 0x3A99,
+    0x719E, 0x3AF2,
+    0x716F, 0x3B4C,
+    0x7141, 0x3BA5,
+    0x7112, 0x3BFD,
+    0x70E2, 0x3C56,
+    0x70B3, 0x3CAF,
+    0x7083, 0x3D07,
+    0x7053, 0x3D60,
+    0x7023, 0x3DB8,
+    0x6FF2, 0x3E10,
+    0x6FC1, 0x3E68,
+    0x6F90, 0x3EBF,
+    0x6F5F, 0x3F17,
+    0x6F2D, 0x3F6E,
+    0x6EFB, 0x3FC5,
+    0x6EC9, 0x401D,
+    0x6E96, 0x4073,
+    0x6E63, 0x40CA,
+    0x6E30, 0x4121,
+    0x6DFD, 0x4177,
+    0x6DCA, 0x41CE,
+    0x6D96, 0x4224,
+    0x6D62, 0x427A,
+    0x6D2D, 0x42D0,
+    0x6CF9, 0x4325,
+    0x6CC4, 0x437B,
+    0x6C8F, 0x43D0,
+    0x6C59, 0x4425,
+    0x6C24, 0x447A,
+    0x6BEE, 0x44CF,
+    0x6BB8, 0x4524,
+    0x6B81, 0x4578,
+    0x6B4A, 0x45CD,
+    0x6B13, 0x4621,
+    0x6ADC, 0x4675,
+    0x6AA5, 0x46C9,
+    0x6A6D, 0x471C,
+    0x6A35, 0x4770,
+    0x69FD, 0x47C3,
+    0x69C4, 0x4816,
+    0x698C, 0x4869,
+    0x6953, 0x48BC,
+    0x6919, 0x490F,
+    0x68E0, 0x4961,
+    0x68A6, 0x49B4,
+    0x686C, 0x4A06,
+    0x6832, 0x4A58,
+    0x67F7, 0x4AA9,
+    0x67BD, 0x4AFB,
+    0x6782, 0x4B4C,
+    0x6746, 0x4B9E,
+    0x670B, 0x4BEF,
+    0x66CF, 0x4C3F,
+    0x6693, 0x4C90,
+    0x6657, 0x4CE1,
+    0x661A, 0x4D31,
+    0x65DD, 0x4D81,
+    0x65A0, 0x4DD1,
+    0x6563, 0x4E21,
+    0x6526, 0x4E70,
+    0x64E8, 0x4EBF,
+    0x64AA, 0x4F0F,
+    0x646C, 0x4F5E,
+    0x642D, 0x4FAC,
+    0x63EF, 0x4FFB,
+    0x63B0, 0x5049,
+    0x6371, 0x5097,
+    0x6331, 0x50E5,
+    0x62F2, 0x5133,
+    0x62B2, 0x5181,
+    0x6271, 0x51CE,
+    0x6231, 0x521C,
+    0x61F1, 0x5269,
+    0x61B0, 0x52B5,
+    0x616F, 0x5302,
+    0x612D, 0x534E,
+    0x60EC, 0x539B,
+    0x60AA, 0x53E7,
+    0x6068, 0x5433,
+    0x6026, 0x547E,
+    0x5FE3, 0x54CA,
+    0x5FA0, 0x5515,
+    0x5F5E, 0x5560,
+    0x5F1A, 0x55AB,
+    0x5ED7, 0x55F5,
+    0x5E93, 0x5640,
+    0x5E50, 0x568A,
+    0x5E0B, 0x56D4,
+    0x5DC7, 0x571D,
+    0x5D83, 0x5767,
+    0x5D3E, 0x57B0,
+    0x5CF9, 0x57F9,
+    0x5CB4, 0x5842,
+    0x5C6E, 0x588B,
+    0x5C29, 0x58D4,
+    0x5BE3, 0x591C,
+    0x5B9D, 0x5964,
+    0x5B56, 0x59AC,
+    0x5B10, 0x59F3,
+    0x5AC9, 0x5A3B,
+    0x5A82, 0x5A82,
+    0x5A3B, 0x5AC9,
+    0x59F3, 0x5B10,
+    0x59AC, 0x5B56,
+    0x5964, 0x5B9D,
+    0x591C, 0x5BE3,
+    0x58D4, 0x5C29,
+    0x588B, 0x5C6E,
+    0x5842, 0x5CB4,
+    0x57F9, 0x5CF9,
+    0x57B0, 0x5D3E,
+    0x5767, 0x5D83,
+    0x571D, 0x5DC7,
+    0x56D4, 0x5E0B,
+    0x568A, 0x5E50,
+    0x5640, 0x5E93,
+    0x55F5, 0x5ED7,
+    0x55AB, 0x5F1A,
+    0x5560, 0x5F5E,
+    0x5515, 0x5FA0,
+    0x54CA, 0x5FE3,
+    0x547E, 0x6026,
+    0x5433, 0x6068,
+    0x53E7, 0x60AA,
+    0x539B, 0x60EC,
+    0x534E, 0x612D,
+    0x5302, 0x616F,
+    0x52B5, 0x61B0,
+    0x5269, 0x61F1,
+    0x521C, 0x6231,
+    0x51CE, 0x6271,
+    0x5181, 0x62B2,
+    0x5133, 0x62F2,
+    0x50E5, 0x6331,
+    0x5097, 0x6371,
+    0x5049, 0x63B0,
+    0x4FFB, 0x63EF,
+    0x4FAC, 0x642D,
+    0x4F5E, 0x646C,
+    0x4F0F, 0x64AA,
+    0x4EBF, 0x64E8,
+    0x4E70, 0x6526,
+    0x4E21, 0x6563,
+    0x4DD1, 0x65A0,
+    0x4D81, 0x65DD,
+    0x4D31, 0x661A,
+    0x4CE1, 0x6657,
+    0x4C90, 0x6693,
+    0x4C3F, 0x66CF,
+    0x4BEF, 0x670B,
+    0x4B9E, 0x6746,
+    0x4B4C, 0x6782,
+    0x4AFB, 0x67BD,
+    0x4AA9, 0x67F7,
+    0x4A58, 0x6832,
+    0x4A06, 0x686C,
+    0x49B4, 0x68A6,
+    0x4961, 0x68E0,
+    0x490F, 0x6919,
+    0x48BC, 0x6953,
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+    0x42D0, 0x6D2D,
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+    0x4177, 0x6DFD,
+    0x4121, 0x6E30,
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+    0x4073, 0x6E96,
+    0x401D, 0x6EC9,
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+    0x3F17, 0x6F5F,
+    0x3EBF, 0x6F90,
+    0x3E68, 0x6FC1,
+    0x3E10, 0x6FF2,
+    0x3DB8, 0x7023,
+    0x3D60, 0x7053,
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+    0x3CAF, 0x70B3,
+    0x3C56, 0x70E2,
+    0x3BFD, 0x7112,
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+    0x3B4C, 0x716F,
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+    0x39E6, 0x7227,
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+    0x387E, 0x72DB,
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+    0x365F, 0x73E0,
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+    0x354D, 0x745F,
+    0x34F2, 0x7489,
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+    0x343A, 0x74DB,
+    0x33DE, 0x7504,
+    0x3382, 0x752D,
+    0x3326, 0x7555,
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+    0x326E, 0x75A5,
+    0x3211, 0x75CC,
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+    0x3041, 0x768E,
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+    0x2F29, 0x76FE,
+    0x2ECC, 0x7723,
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+    0x2E11, 0x776C,
+    0x2DB3, 0x7790,
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+    0x2C98, 0x77FA,
+    0x2C3A, 0x781D,
+    0x2BDC, 0x7840,
+    0x2B7D, 0x7862,
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+    0x2528, 0x7A7D,
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+    0x919C, 0x40CA,
+    0x9169, 0x4073,
+    0x9136, 0x401D,
+    0x9104, 0x3FC5,
+    0x90D2, 0x3F6E,
+    0x90A0, 0x3F17,
+    0x906F, 0x3EBF,
+    0x903E, 0x3E68,
+    0x900D, 0x3E10,
+    0x8FDC, 0x3DB8,
+    0x8FAC, 0x3D60,
+    0x8F7C, 0x3D07,
+    0x8F4C, 0x3CAF,
+    0x8F1D, 0x3C56,
+    0x8EED, 0x3BFD,
+    0x8EBE, 0x3BA5,
+    0x8E90, 0x3B4C,
+    0x8E61, 0x3AF2,
+    0x8E33, 0x3A99,
+    0x8E05, 0x3A40,
+    0x8DD8, 0x39E6,
+    0x8DAA, 0x398C,
+    0x8D7D, 0x3932,
+    0x8D50, 0x38D8,
+    0x8D24, 0x387E,
+    0x8CF8, 0x3824,
+    0x8CCC, 0x37CA,
+    0x8CA0, 0x376F,
+    0x8C75, 0x3714,
+    0x8C4A, 0x36BA,
+    0x8C1F, 0x365F,
+    0x8BF4, 0x3604,
+    0x8BCA, 0x35A8,
+    0x8BA0, 0x354D,
+    0x8B76, 0x34F2,
+    0x8B4D, 0x3496,
+    0x8B24, 0x343A,
+    0x8AFB, 0x33DE,
+    0x8AD2, 0x3382,
+    0x8AAA, 0x3326,
+    0x8A82, 0x32CA,
+    0x8A5A, 0x326E,
+    0x8A33, 0x3211,
+    0x8A0B, 0x31B5,
+    0x89E4, 0x3158,
+    0x89BE, 0x30FB,
+    0x8997, 0x309E,
+    0x8971, 0x3041,
+    0x894C, 0x2FE4,
+    0x8926, 0x2F87,
+    0x8901, 0x2F29,
+    0x88DC, 0x2ECC,
+    0x88B8, 0x2E6E,
+    0x8893, 0x2E11,
+    0x886F, 0x2DB3,
+    0x884B, 0x2D55,
+    0x8828, 0x2CF7,
+    0x8805, 0x2C98,
+    0x87E2, 0x2C3A,
+    0x87BF, 0x2BDC,
+    0x879D, 0x2B7D,
+    0x877B, 0x2B1F,
+    0x8759, 0x2AC0,
+    0x8738, 0x2A61,
+    0x8717, 0x2A02,
+    0x86F6, 0x29A3,
+    0x86D5, 0x2944,
+    0x86B5, 0x28E5,
+    0x8695, 0x2886,
+    0x8675, 0x2826,
+    0x8656, 0x27C7,
+    0x8637, 0x2767,
+    0x8618, 0x2707,
+    0x85FA, 0x26A8,
+    0x85DB, 0x2648,
+    0x85BD, 0x25E8,
+    0x85A0, 0x2588,
+    0x8582, 0x2528,
+    0x8565, 0x24C7,
+    0x8549, 0x2467,
+    0x852C, 0x2407,
+    0x8510, 0x23A6,
+    0x84F4, 0x2345,
+    0x84D9, 0x22E5,
+    0x84BD, 0x2284,
+    0x84A2, 0x2223,
+    0x8488, 0x21C2,
+    0x846D, 0x2161,
+    0x8453, 0x2100,
+    0x843A, 0x209F,
+    0x8420, 0x203E,
+    0x8407, 0x1FDC,
+    0x83EE, 0x1F7B,
+    0x83D6, 0x1F19,
+    0x83BD, 0x1EB8,
+    0x83A5, 0x1E56,
+    0x838E, 0x1DF5,
+    0x8376, 0x1D93,
+    0x835F, 0x1D31,
+    0x8348, 0x1CCF,
+    0x8332, 0x1C6D,
+    0x831C, 0x1C0B,
+    0x8306, 0x1BA9,
+    0x82F0, 0x1B47,
+    0x82DB, 0x1AE4,
+    0x82C6, 0x1A82,
+    0x82B1, 0x1A20,
+    0x829D, 0x19BD,
+    0x8289, 0x195B,
+    0x8275, 0x18F8,
+    0x8262, 0x1896,
+    0x824F, 0x1833,
+    0x823C, 0x17D0,
+    0x8229, 0x176D,
+    0x8217, 0x170A,
+    0x8205, 0x16A8,
+    0x81F3, 0x1645,
+    0x81E2, 0x15E2,
+    0x81D1, 0x157F,
+    0x81C0, 0x151B,
+    0x81B0, 0x14B8,
+    0x81A0, 0x1455,
+    0x8190, 0x13F2,
+    0x8180, 0x138E,
+    0x8171, 0x132B,
+    0x8162, 0x12C8,
+    0x8154, 0x1264,
+    0x8145, 0x1201,
+    0x8137, 0x119D,
+    0x812A, 0x1139,
+    0x811C, 0x10D6,
+    0x810F, 0x1072,
+    0x8102, 0x100E,
+    0x80F6, 0x0FAB,
+    0x80EA, 0x0F47,
+    0x80DE, 0x0EE3,
+    0x80D2, 0x0E7F,
+    0x80C7, 0x0E1B,
+    0x80BC, 0x0DB7,
+    0x80B2, 0x0D53,
+    0x80A7, 0x0CEF,
+    0x809D, 0x0C8B,
+    0x8094, 0x0C27,
+    0x808A, 0x0BC3,
+    0x8081, 0x0B5F,
+    0x8078, 0x0AFB,
+    0x8070, 0x0A97,
+    0x8068, 0x0A33,
+    0x8060, 0x09CE,
+    0x8058, 0x096A,
+    0x8051, 0x0906,
+    0x804A, 0x08A2,
+    0x8043, 0x083D,
+    0x803D, 0x07D9,
+    0x8037, 0x0775,
+    0x8031, 0x0710,
+    0x802C, 0x06AC,
+    0x8027, 0x0647,
+    0x8022, 0x05E3,
+    0x801E, 0x057F,
+    0x801A, 0x051A,
+    0x8016, 0x04B6,
+    0x8012, 0x0451,
+    0x800F, 0x03ED,
+    0x800C, 0x0388,
+    0x8009, 0x0324,
+    0x8007, 0x02BF,
+    0x8005, 0x025B,
+    0x8003, 0x01F6,
+    0x8002, 0x0192,
+    0x8001, 0x012D,
+    0x8000, 0x00C9,
+    0x8000, 0x0064,
+    0x8000, 0x0000,
+    0x8000, 0xFF9B,
+    0x8000, 0xFF36,
+    0x8001, 0xFED2,
+    0x8002, 0xFE6D,
+    0x8003, 0xFE09,
+    0x8005, 0xFDA4,
+    0x8007, 0xFD40,
+    0x8009, 0xFCDB,
+    0x800C, 0xFC77,
+    0x800F, 0xFC12,
+    0x8012, 0xFBAE,
+    0x8016, 0xFB49,
+    0x801A, 0xFAE5,
+    0x801E, 0xFA80,
+    0x8022, 0xFA1C,
+    0x8027, 0xF9B8,
+    0x802C, 0xF953,
+    0x8031, 0xF8EF,
+    0x8037, 0xF88A,
+    0x803D, 0xF826,
+    0x8043, 0xF7C2,
+    0x804A, 0xF75D,
+    0x8051, 0xF6F9,
+    0x8058, 0xF695,
+    0x8060, 0xF631,
+    0x8068, 0xF5CC,
+    0x8070, 0xF568,
+    0x8078, 0xF504,
+    0x8081, 0xF4A0,
+    0x808A, 0xF43C,
+    0x8094, 0xF3D8,
+    0x809D, 0xF374,
+    0x80A7, 0xF310,
+    0x80B2, 0xF2AC,
+    0x80BC, 0xF248,
+    0x80C7, 0xF1E4,
+    0x80D2, 0xF180,
+    0x80DE, 0xF11C,
+    0x80EA, 0xF0B8,
+    0x80F6, 0xF054,
+    0x8102, 0xEFF1,
+    0x810F, 0xEF8D,
+    0x811C, 0xEF29,
+    0x812A, 0xEEC6,
+    0x8137, 0xEE62,
+    0x8145, 0xEDFE,
+    0x8154, 0xED9B,
+    0x8162, 0xED37,
+    0x8171, 0xECD4,
+    0x8180, 0xEC71,
+    0x8190, 0xEC0D,
+    0x81A0, 0xEBAA,
+    0x81B0, 0xEB47,
+    0x81C0, 0xEAE4,
+    0x81D1, 0xEA80,
+    0x81E2, 0xEA1D,
+    0x81F3, 0xE9BA,
+    0x8205, 0xE957,
+    0x8217, 0xE8F5,
+    0x8229, 0xE892,
+    0x823C, 0xE82F,
+    0x824F, 0xE7CC,
+    0x8262, 0xE769,
+    0x8275, 0xE707,
+    0x8289, 0xE6A4,
+    0x829D, 0xE642,
+    0x82B1, 0xE5DF,
+    0x82C6, 0xE57D,
+    0x82DB, 0xE51B,
+    0x82F0, 0xE4B8,
+    0x8306, 0xE456,
+    0x831C, 0xE3F4,
+    0x8332, 0xE392,
+    0x8348, 0xE330,
+    0x835F, 0xE2CE,
+    0x8376, 0xE26C,
+    0x838E, 0xE20A,
+    0x83A5, 0xE1A9,
+    0x83BD, 0xE147,
+    0x83D6, 0xE0E6,
+    0x83EE, 0xE084,
+    0x8407, 0xE023,
+    0x8420, 0xDFC1,
+    0x843A, 0xDF60,
+    0x8453, 0xDEFF,
+    0x846D, 0xDE9E,
+    0x8488, 0xDE3D,
+    0x84A2, 0xDDDC,
+    0x84BD, 0xDD7B,
+    0x84D9, 0xDD1A,
+    0x84F4, 0xDCBA,
+    0x8510, 0xDC59,
+    0x852C, 0xDBF8,
+    0x8549, 0xDB98,
+    0x8565, 0xDB38,
+    0x8582, 0xDAD7,
+    0x85A0, 0xDA77,
+    0x85BD, 0xDA17,
+    0x85DB, 0xD9B7,
+    0x85FA, 0xD957,
+    0x8618, 0xD8F8,
+    0x8637, 0xD898,
+    0x8656, 0xD838,
+    0x8675, 0xD7D9,
+    0x8695, 0xD779,
+    0x86B5, 0xD71A,
+    0x86D5, 0xD6BB,
+    0x86F6, 0xD65C,
+    0x8717, 0xD5FD,
+    0x8738, 0xD59E,
+    0x8759, 0xD53F,
+    0x877B, 0xD4E0,
+    0x879D, 0xD482,
+    0x87BF, 0xD423,
+    0x87E2, 0xD3C5,
+    0x8805, 0xD367,
+    0x8828, 0xD308,
+    0x884B, 0xD2AA,
+    0x886F, 0xD24C,
+    0x8893, 0xD1EE,
+    0x88B8, 0xD191,
+    0x88DC, 0xD133,
+    0x8901, 0xD0D6,
+    0x8926, 0xD078,
+    0x894C, 0xD01B,
+    0x8971, 0xCFBE,
+    0x8997, 0xCF61,
+    0x89BE, 0xCF04,
+    0x89E4, 0xCEA7,
+    0x8A0B, 0xCE4A,
+    0x8A33, 0xCDEE,
+    0x8A5A, 0xCD91,
+    0x8A82, 0xCD35,
+    0x8AAA, 0xCCD9,
+    0x8AD2, 0xCC7D,
+    0x8AFB, 0xCC21,
+    0x8B24, 0xCBC5,
+    0x8B4D, 0xCB69,
+    0x8B76, 0xCB0D,
+    0x8BA0, 0xCAB2,
+    0x8BCA, 0xCA57,
+    0x8BF4, 0xC9FB,
+    0x8C1F, 0xC9A0,
+    0x8C4A, 0xC945,
+    0x8C75, 0xC8EB,
+    0x8CA0, 0xC890,
+    0x8CCC, 0xC835,
+    0x8CF8, 0xC7DB,
+    0x8D24, 0xC781,
+    0x8D50, 0xC727,
+    0x8D7D, 0xC6CD,
+    0x8DAA, 0xC673,
+    0x8DD8, 0xC619,
+    0x8E05, 0xC5BF,
+    0x8E33, 0xC566,
+    0x8E61, 0xC50D,
+    0x8E90, 0xC4B3,
+    0x8EBE, 0xC45A,
+    0x8EED, 0xC402,
+    0x8F1D, 0xC3A9,
+    0x8F4C, 0xC350,
+    0x8F7C, 0xC2F8,
+    0x8FAC, 0xC29F,
+    0x8FDC, 0xC247,
+    0x900D, 0xC1EF,
+    0x903E, 0xC197,
+    0x906F, 0xC140,
+    0x90A0, 0xC0E8,
+    0x90D2, 0xC091,
+    0x9104, 0xC03A,
+    0x9136, 0xBFE2,
+    0x9169, 0xBF8C,
+    0x919C, 0xBF35,
+    0x91CF, 0xBEDE,
+    0x9202, 0xBE88,
+    0x9235, 0xBE31,
+    0x9269, 0xBDDB,
+    0x929D, 0xBD85,
+    0x92D2, 0xBD2F,
+    0x9306, 0xBCDA,
+    0x933B, 0xBC84,
+    0x9370, 0xBC2F,
+    0x93A6, 0xBBDA,
+    0x93DB, 0xBB85,
+    0x9411, 0xBB30,
+    0x9447, 0xBADB,
+    0x947E, 0xBA87,
+    0x94B5, 0xBA32,
+    0x94EC, 0xB9DE,
+    0x9523, 0xB98A,
+    0x955A, 0xB936,
+    0x9592, 0xB8E3,
+    0x95CA, 0xB88F,
+    0x9602, 0xB83C,
+    0x963B, 0xB7E9,
+    0x9673, 0xB796,
+    0x96AC, 0xB743,
+    0x96E6, 0xB6F0,
+    0x971F, 0xB69E,
+    0x9759, 0xB64B,
+    0x9793, 0xB5F9,
+    0x97CD, 0xB5A7,
+    0x9808, 0xB556,
+    0x9842, 0xB504,
+    0x987D, 0xB4B3,
+    0x98B9, 0xB461,
+    0x98F4, 0xB410,
+    0x9930, 0xB3C0,
+    0x996C, 0xB36F,
+    0x99A8, 0xB31E,
+    0x99E5, 0xB2CE,
+    0x9A22, 0xB27E,
+    0x9A5F, 0xB22E,
+    0x9A9C, 0xB1DE,
+    0x9AD9, 0xB18F,
+    0x9B17, 0xB140,
+    0x9B55, 0xB0F0,
+    0x9B93, 0xB0A1,
+    0x9BD2, 0xB053,
+    0x9C10, 0xB004,
+    0x9C4F, 0xAFB6,
+    0x9C8E, 0xAF68,
+    0x9CCE, 0xAF1A,
+    0x9D0D, 0xAECC,
+    0x9D4D, 0xAE7E,
+    0x9D8E, 0xAE31,
+    0x9DCE, 0xADE3,
+    0x9E0E, 0xAD96,
+    0x9E4F, 0xAD4A,
+    0x9E90, 0xACFD,
+    0x9ED2, 0xACB1,
+    0x9F13, 0xAC64,
+    0x9F55, 0xAC18,
+    0x9F97, 0xABCC,
+    0x9FD9, 0xAB81,
+    0xA01C, 0xAB35,
+    0xA05F, 0xAAEA,
+    0xA0A1, 0xAA9F,
+    0xA0E5, 0xAA54,
+    0xA128, 0xAA0A,
+    0xA16C, 0xA9BF,
+    0xA1AF, 0xA975,
+    0xA1F4, 0xA92B,
+    0xA238, 0xA8E2,
+    0xA27C, 0xA898,
+    0xA2C1, 0xA84F,
+    0xA306, 0xA806,
+    0xA34B, 0xA7BD,
+    0xA391, 0xA774,
+    0xA3D6, 0xA72B,
+    0xA41C, 0xA6E3,
+    0xA462, 0xA69B,
+    0xA4A9, 0xA653,
+    0xA4EF, 0xA60C,
+    0xA536, 0xA5C4,
+    0xA57D, 0xA57D,
+    0xA5C4, 0xA536,
+    0xA60C, 0xA4EF,
+    0xA653, 0xA4A9,
+    0xA69B, 0xA462,
+    0xA6E3, 0xA41C,
+    0xA72B, 0xA3D6,
+    0xA774, 0xA391,
+    0xA7BD, 0xA34B,
+    0xA806, 0xA306,
+    0xA84F, 0xA2C1,
+    0xA898, 0xA27C,
+    0xA8E2, 0xA238,
+    0xA92B, 0xA1F4,
+    0xA975, 0xA1AF,
+    0xA9BF, 0xA16C,
+    0xAA0A, 0xA128,
+    0xAA54, 0xA0E5,
+    0xAA9F, 0xA0A1,
+    0xAAEA, 0xA05F,
+    0xAB35, 0xA01C,
+    0xAB81, 0x9FD9,
+    0xABCC, 0x9F97,
+    0xAC18, 0x9F55,
+    0xAC64, 0x9F13,
+    0xACB1, 0x9ED2,
+    0xACFD, 0x9E90,
+    0xAD4A, 0x9E4F,
+    0xAD96, 0x9E0E,
+    0xADE3, 0x9DCE,
+    0xAE31, 0x9D8E,
+    0xAE7E, 0x9D4D,
+    0xAECC, 0x9D0D,
+    0xAF1A, 0x9CCE,
+    0xAF68, 0x9C8E,
+    0xAFB6, 0x9C4F,
+    0xB004, 0x9C10,
+    0xB053, 0x9BD2,
+    0xB0A1, 0x9B93,
+    0xB0F0, 0x9B55,
+    0xB140, 0x9B17,
+    0xB18F, 0x9AD9,
+    0xB1DE, 0x9A9C,
+    0xB22E, 0x9A5F,
+    0xB27E, 0x9A22,
+    0xB2CE, 0x99E5,
+    0xB31E, 0x99A8,
+    0xB36F, 0x996C,
+    0xB3C0, 0x9930,
+    0xB410, 0x98F4,
+    0xB461, 0x98B9,
+    0xB4B3, 0x987D,
+    0xB504, 0x9842,
+    0xB556, 0x9808,
+    0xB5A7, 0x97CD,
+    0xB5F9, 0x9793,
+    0xB64B, 0x9759,
+    0xB69E, 0x971F,
+    0xB6F0, 0x96E6,
+    0xB743, 0x96AC,
+    0xB796, 0x9673,
+    0xB7E9, 0x963B,
+    0xB83C, 0x9602,
+    0xB88F, 0x95CA,
+    0xB8E3, 0x9592,
+    0xB936, 0x955A,
+    0xB98A, 0x9523,
+    0xB9DE, 0x94EC,
+    0xBA32, 0x94B5,
+    0xBA87, 0x947E,
+    0xBADB, 0x9447,
+    0xBB30, 0x9411,
+    0xBB85, 0x93DB,
+    0xBBDA, 0x93A6,
+    0xBC2F, 0x9370,
+    0xBC84, 0x933B,
+    0xBCDA, 0x9306,
+    0xBD2F, 0x92D2,
+    0xBD85, 0x929D,
+    0xBDDB, 0x9269,
+    0xBE31, 0x9235,
+    0xBE88, 0x9202,
+    0xBEDE, 0x91CF,
+    0xBF35, 0x919C,
+    0xBF8C, 0x9169,
+    0xBFE2, 0x9136,
+    0xC03A, 0x9104,
+    0xC091, 0x90D2,
+    0xC0E8, 0x90A0,
+    0xC140, 0x906F,
+    0xC197, 0x903E,
+    0xC1EF, 0x900D,
+    0xC247, 0x8FDC,
+    0xC29F, 0x8FAC,
+    0xC2F8, 0x8F7C,
+    0xC350, 0x8F4C,
+    0xC3A9, 0x8F1D,
+    0xC402, 0x8EED,
+    0xC45A, 0x8EBE,
+    0xC4B3, 0x8E90,
+    0xC50D, 0x8E61,
+    0xC566, 0x8E33,
+    0xC5BF, 0x8E05,
+    0xC619, 0x8DD8,
+    0xC673, 0x8DAA,
+    0xC6CD, 0x8D7D,
+    0xC727, 0x8D50,
+    0xC781, 0x8D24,
+    0xC7DB, 0x8CF8,
+    0xC835, 0x8CCC,
+    0xC890, 0x8CA0,
+    0xC8EB, 0x8C75,
+    0xC945, 0x8C4A,
+    0xC9A0, 0x8C1F,
+    0xC9FB, 0x8BF4,
+    0xCA57, 0x8BCA,
+    0xCAB2, 0x8BA0,
+    0xCB0D, 0x8B76,
+    0xCB69, 0x8B4D,
+    0xCBC5, 0x8B24,
+    0xCC21, 0x8AFB,
+    0xCC7D, 0x8AD2,
+    0xCCD9, 0x8AAA,
+    0xCD35, 0x8A82,
+    0xCD91, 0x8A5A,
+    0xCDEE, 0x8A33,
+    0xCE4A, 0x8A0B,
+    0xCEA7, 0x89E4,
+    0xCF04, 0x89BE,
+    0xCF61, 0x8997,
+    0xCFBE, 0x8971,
+    0xD01B, 0x894C,
+    0xD078, 0x8926,
+    0xD0D6, 0x8901,
+    0xD133, 0x88DC,
+    0xD191, 0x88B8,
+    0xD1EE, 0x8893,
+    0xD24C, 0x886F,
+    0xD2AA, 0x884B,
+    0xD308, 0x8828,
+    0xD367, 0x8805,
+    0xD3C5, 0x87E2,
+    0xD423, 0x87BF,
+    0xD482, 0x879D,
+    0xD4E0, 0x877B,
+    0xD53F, 0x8759,
+    0xD59E, 0x8738,
+    0xD5FD, 0x8717,
+    0xD65C, 0x86F6,
+    0xD6BB, 0x86D5,
+    0xD71A, 0x86B5,
+    0xD779, 0x8695,
+    0xD7D9, 0x8675,
+    0xD838, 0x8656,
+    0xD898, 0x8637,
+    0xD8F8, 0x8618,
+    0xD957, 0x85FA,
+    0xD9B7, 0x85DB,
+    0xDA17, 0x85BD,
+    0xDA77, 0x85A0,
+    0xDAD7, 0x8582,
+    0xDB38, 0x8565,
+    0xDB98, 0x8549,
+    0xDBF8, 0x852C,
+    0xDC59, 0x8510,
+    0xDCBA, 0x84F4,
+    0xDD1A, 0x84D9,
+    0xDD7B, 0x84BD,
+    0xDDDC, 0x84A2,
+    0xDE3D, 0x8488,
+    0xDE9E, 0x846D,
+    0xDEFF, 0x8453,
+    0xDF60, 0x843A,
+    0xDFC1, 0x8420,
+    0xE023, 0x8407,
+    0xE084, 0x83EE,
+    0xE0E6, 0x83D6,
+    0xE147, 0x83BD,
+    0xE1A9, 0x83A5,
+    0xE20A, 0x838E,
+    0xE26C, 0x8376,
+    0xE2CE, 0x835F,
+    0xE330, 0x8348,
+    0xE392, 0x8332,
+    0xE3F4, 0x831C,
+    0xE456, 0x8306,
+    0xE4B8, 0x82F0,
+    0xE51B, 0x82DB,
+    0xE57D, 0x82C6,
+    0xE5DF, 0x82B1,
+    0xE642, 0x829D,
+    0xE6A4, 0x8289,
+    0xE707, 0x8275,
+    0xE769, 0x8262,
+    0xE7CC, 0x824F,
+    0xE82F, 0x823C,
+    0xE892, 0x8229,
+    0xE8F5, 0x8217,
+    0xE957, 0x8205,
+    0xE9BA, 0x81F3,
+    0xEA1D, 0x81E2,
+    0xEA80, 0x81D1,
+    0xEAE4, 0x81C0,
+    0xEB47, 0x81B0,
+    0xEBAA, 0x81A0,
+    0xEC0D, 0x8190,
+    0xEC71, 0x8180,
+    0xECD4, 0x8171,
+    0xED37, 0x8162,
+    0xED9B, 0x8154,
+    0xEDFE, 0x8145,
+    0xEE62, 0x8137,
+    0xEEC6, 0x812A,
+    0xEF29, 0x811C,
+    0xEF8D, 0x810F,
+    0xEFF1, 0x8102,
+    0xF054, 0x80F6,
+    0xF0B8, 0x80EA,
+    0xF11C, 0x80DE,
+    0xF180, 0x80D2,
+    0xF1E4, 0x80C7,
+    0xF248, 0x80BC,
+    0xF2AC, 0x80B2,
+    0xF310, 0x80A7,
+    0xF374, 0x809D,
+    0xF3D8, 0x8094,
+    0xF43C, 0x808A,
+    0xF4A0, 0x8081,
+    0xF504, 0x8078,
+    0xF568, 0x8070,
+    0xF5CC, 0x8068,
+    0xF631, 0x8060,
+    0xF695, 0x8058,
+    0xF6F9, 0x8051,
+    0xF75D, 0x804A,
+    0xF7C2, 0x8043,
+    0xF826, 0x803D,
+    0xF88A, 0x8037,
+    0xF8EF, 0x8031,
+    0xF953, 0x802C,
+    0xF9B8, 0x8027,
+    0xFA1C, 0x8022,
+    0xFA80, 0x801E,
+    0xFAE5, 0x801A,
+    0xFB49, 0x8016,
+    0xFBAE, 0x8012,
+    0xFC12, 0x800F,
+    0xFC77, 0x800C,
+    0xFCDB, 0x8009,
+    0xFD40, 0x8007,
+    0xFDA4, 0x8005,
+    0xFE09, 0x8003,
+    0xFE6D, 0x8002,
+    0xFED2, 0x8001,
+    0xFF36, 0x8000,
+    0xFF9B, 0x8000
+};
+
+/**    
+* \par   
+* Example code for q15 Twiddle factors Generation::    
+* \par    
+* <pre>for(i = 0; i< 3N/4; i++)    
+* {    
+*    twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);    
+*    twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);    
+* } </pre>    
+* \par    
+* where N = 4096	and PI = 3.14159265358979    
+* \par    
+* Cos and Sin values are interleaved fashion    
+* \par    
+* Convert Floating point to q15(Fixed point 1.15):    
+*	round(twiddleCoefq15(i) * pow(2, 15))    
+*    
+*/
+const q15_t twiddleCoef_4096_q15[6144] = 
+{
+    0x7FFF, 0x0000,
+    0x7FFF, 0x0032,
+    0x7FFF, 0x0064,
+    0x7FFF, 0x0096,
+    0x7FFF, 0x00C9,
+    0x7FFF, 0x00FB,
+    0x7FFE, 0x012D,
+    0x7FFE, 0x015F,
+    0x7FFD, 0x0192,
+    0x7FFC, 0x01C4,
+    0x7FFC, 0x01F6,
+    0x7FFB, 0x0228,
+    0x7FFA, 0x025B,
+    0x7FF9, 0x028D,
+    0x7FF8, 0x02BF,
+    0x7FF7, 0x02F1,
+    0x7FF6, 0x0324,
+    0x7FF4, 0x0356,
+    0x7FF3, 0x0388,
+    0x7FF2, 0x03BA,
+    0x7FF0, 0x03ED,
+    0x7FEE, 0x041F,
+    0x7FED, 0x0451,
+    0x7FEB, 0x0483,
+    0x7FE9, 0x04B6,
+    0x7FE7, 0x04E8,
+    0x7FE5, 0x051A,
+    0x7FE3, 0x054C,
+    0x7FE1, 0x057F,
+    0x7FDF, 0x05B1,
+    0x7FDD, 0x05E3,
+    0x7FDA, 0x0615,
+    0x7FD8, 0x0647,
+    0x7FD6, 0x067A,
+    0x7FD3, 0x06AC,
+    0x7FD0, 0x06DE,
+    0x7FCE, 0x0710,
+    0x7FCB, 0x0742,
+    0x7FC8, 0x0775,
+    0x7FC5, 0x07A7,
+    0x7FC2, 0x07D9,
+    0x7FBF, 0x080B,
+    0x7FBC, 0x083D,
+    0x7FB8, 0x086F,
+    0x7FB5, 0x08A2,
+    0x7FB1, 0x08D4,
+    0x7FAE, 0x0906,
+    0x7FAA, 0x0938,
+    0x7FA7, 0x096A,
+    0x7FA3, 0x099C,
+    0x7F9F, 0x09CE,
+    0x7F9B, 0x0A00,
+    0x7F97, 0x0A33,
+    0x7F93, 0x0A65,
+    0x7F8F, 0x0A97,
+    0x7F8B, 0x0AC9,
+    0x7F87, 0x0AFB,
+    0x7F82, 0x0B2D,
+    0x7F7E, 0x0B5F,
+    0x7F79, 0x0B91,
+    0x7F75, 0x0BC3,
+    0x7F70, 0x0BF5,
+    0x7F6B, 0x0C27,
+    0x7F67, 0x0C59,
+    0x7F62, 0x0C8B,
+    0x7F5D, 0x0CBD,
+    0x7F58, 0x0CEF,
+    0x7F53, 0x0D21,
+    0x7F4D, 0x0D53,
+    0x7F48, 0x0D85,
+    0x7F43, 0x0DB7,
+    0x7F3D, 0x0DE9,
+    0x7F38, 0x0E1B,
+    0x7F32, 0x0E4D,
+    0x7F2D, 0x0E7F,
+    0x7F27, 0x0EB1,
+    0x7F21, 0x0EE3,
+    0x7F1B, 0x0F15,
+    0x7F15, 0x0F47,
+    0x7F0F, 0x0F79,
+    0x7F09, 0x0FAB,
+    0x7F03, 0x0FDD,
+    0x7EFD, 0x100E,
+    0x7EF6, 0x1040,
+    0x7EF0, 0x1072,
+    0x7EE9, 0x10A4,
+    0x7EE3, 0x10D6,
+    0x7EDC, 0x1108,
+    0x7ED5, 0x1139,
+    0x7ECF, 0x116B,
+    0x7EC8, 0x119D,
+    0x7EC1, 0x11CF,
+    0x7EBA, 0x1201,
+    0x7EB3, 0x1232,
+    0x7EAB, 0x1264,
+    0x7EA4, 0x1296,
+    0x7E9D, 0x12C8,
+    0x7E95, 0x12F9,
+    0x7E8E, 0x132B,
+    0x7E86, 0x135D,
+    0x7E7F, 0x138E,
+    0x7E77, 0x13C0,
+    0x7E6F, 0x13F2,
+    0x7E67, 0x1423,
+    0x7E5F, 0x1455,
+    0x7E57, 0x1487,
+    0x7E4F, 0x14B8,
+    0x7E47, 0x14EA,
+    0x7E3F, 0x151B,
+    0x7E37, 0x154D,
+    0x7E2E, 0x157F,
+    0x7E26, 0x15B0,
+    0x7E1D, 0x15E2,
+    0x7E14, 0x1613,
+    0x7E0C, 0x1645,
+    0x7E03, 0x1676,
+    0x7DFA, 0x16A8,
+    0x7DF1, 0x16D9,
+    0x7DE8, 0x170A,
+    0x7DDF, 0x173C,
+    0x7DD6, 0x176D,
+    0x7DCD, 0x179F,
+    0x7DC3, 0x17D0,
+    0x7DBA, 0x1802,
+    0x7DB0, 0x1833,
+    0x7DA7, 0x1864,
+    0x7D9D, 0x1896,
+    0x7D94, 0x18C7,
+    0x7D8A, 0x18F8,
+    0x7D80, 0x192A,
+    0x7D76, 0x195B,
+    0x7D6C, 0x198C,
+    0x7D62, 0x19BD,
+    0x7D58, 0x19EF,
+    0x7D4E, 0x1A20,
+    0x7D43, 0x1A51,
+    0x7D39, 0x1A82,
+    0x7D2F, 0x1AB3,
+    0x7D24, 0x1AE4,
+    0x7D19, 0x1B16,
+    0x7D0F, 0x1B47,
+    0x7D04, 0x1B78,
+    0x7CF9, 0x1BA9,
+    0x7CEE, 0x1BDA,
+    0x7CE3, 0x1C0B,
+    0x7CD8, 0x1C3C,
+    0x7CCD, 0x1C6D,
+    0x7CC2, 0x1C9E,
+    0x7CB7, 0x1CCF,
+    0x7CAB, 0x1D00,
+    0x7CA0, 0x1D31,
+    0x7C94, 0x1D62,
+    0x7C89, 0x1D93,
+    0x7C7D, 0x1DC4,
+    0x7C71, 0x1DF5,
+    0x7C66, 0x1E25,
+    0x7C5A, 0x1E56,
+    0x7C4E, 0x1E87,
+    0x7C42, 0x1EB8,
+    0x7C36, 0x1EE9,
+    0x7C29, 0x1F19,
+    0x7C1D, 0x1F4A,
+    0x7C11, 0x1F7B,
+    0x7C05, 0x1FAC,
+    0x7BF8, 0x1FDC,
+    0x7BEB, 0x200D,
+    0x7BDF, 0x203E,
+    0x7BD2, 0x206E,
+    0x7BC5, 0x209F,
+    0x7BB9, 0x20D0,
+    0x7BAC, 0x2100,
+    0x7B9F, 0x2131,
+    0x7B92, 0x2161,
+    0x7B84, 0x2192,
+    0x7B77, 0x21C2,
+    0x7B6A, 0x21F3,
+    0x7B5D, 0x2223,
+    0x7B4F, 0x2254,
+    0x7B42, 0x2284,
+    0x7B34, 0x22B4,
+    0x7B26, 0x22E5,
+    0x7B19, 0x2315,
+    0x7B0B, 0x2345,
+    0x7AFD, 0x2376,
+    0x7AEF, 0x23A6,
+    0x7AE1, 0x23D6,
+    0x7AD3, 0x2407,
+    0x7AC5, 0x2437,
+    0x7AB6, 0x2467,
+    0x7AA8, 0x2497,
+    0x7A9A, 0x24C7,
+    0x7A8B, 0x24F7,
+    0x7A7D, 0x2528,
+    0x7A6E, 0x2558,
+    0x7A5F, 0x2588,
+    0x7A50, 0x25B8,
+    0x7A42, 0x25E8,
+    0x7A33, 0x2618,
+    0x7A24, 0x2648,
+    0x7A15, 0x2678,
+    0x7A05, 0x26A8,
+    0x79F6, 0x26D8,
+    0x79E7, 0x2707,
+    0x79D8, 0x2737,
+    0x79C8, 0x2767,
+    0x79B9, 0x2797,
+    0x79A9, 0x27C7,
+    0x7999, 0x27F6,
+    0x798A, 0x2826,
+    0x797A, 0x2856,
+    0x796A, 0x2886,
+    0x795A, 0x28B5,
+    0x794A, 0x28E5,
+    0x793A, 0x2915,
+    0x792A, 0x2944,
+    0x7919, 0x2974,
+    0x7909, 0x29A3,
+    0x78F9, 0x29D3,
+    0x78E8, 0x2A02,
+    0x78D8, 0x2A32,
+    0x78C7, 0x2A61,
+    0x78B6, 0x2A91,
+    0x78A6, 0x2AC0,
+    0x7895, 0x2AEF,
+    0x7884, 0x2B1F,
+    0x7873, 0x2B4E,
+    0x7862, 0x2B7D,
+    0x7851, 0x2BAD,
+    0x7840, 0x2BDC,
+    0x782E, 0x2C0B,
+    0x781D, 0x2C3A,
+    0x780C, 0x2C69,
+    0x77FA, 0x2C98,
+    0x77E9, 0x2CC8,
+    0x77D7, 0x2CF7,
+    0x77C5, 0x2D26,
+    0x77B4, 0x2D55,
+    0x77A2, 0x2D84,
+    0x7790, 0x2DB3,
+    0x777E, 0x2DE2,
+    0x776C, 0x2E11,
+    0x775A, 0x2E3F,
+    0x7747, 0x2E6E,
+    0x7735, 0x2E9D,
+    0x7723, 0x2ECC,
+    0x7710, 0x2EFB,
+    0x76FE, 0x2F29,
+    0x76EB, 0x2F58,
+    0x76D9, 0x2F87,
+    0x76C6, 0x2FB5,
+    0x76B3, 0x2FE4,
+    0x76A0, 0x3013,
+    0x768E, 0x3041,
+    0x767B, 0x3070,
+    0x7668, 0x309E,
+    0x7654, 0x30CD,
+    0x7641, 0x30FB,
+    0x762E, 0x312A,
+    0x761B, 0x3158,
+    0x7607, 0x3186,
+    0x75F4, 0x31B5,
+    0x75E0, 0x31E3,
+    0x75CC, 0x3211,
+    0x75B9, 0x3240,
+    0x75A5, 0x326E,
+    0x7591, 0x329C,
+    0x757D, 0x32CA,
+    0x7569, 0x32F8,
+    0x7555, 0x3326,
+    0x7541, 0x3354,
+    0x752D, 0x3382,
+    0x7519, 0x33B0,
+    0x7504, 0x33DE,
+    0x74F0, 0x340C,
+    0x74DB, 0x343A,
+    0x74C7, 0x3468,
+    0x74B2, 0x3496,
+    0x749E, 0x34C4,
+    0x7489, 0x34F2,
+    0x7474, 0x351F,
+    0x745F, 0x354D,
+    0x744A, 0x357B,
+    0x7435, 0x35A8,
+    0x7420, 0x35D6,
+    0x740B, 0x3604,
+    0x73F6, 0x3631,
+    0x73E0, 0x365F,
+    0x73CB, 0x368C,
+    0x73B5, 0x36BA,
+    0x73A0, 0x36E7,
+    0x738A, 0x3714,
+    0x7375, 0x3742,
+    0x735F, 0x376F,
+    0x7349, 0x379C,
+    0x7333, 0x37CA,
+    0x731D, 0x37F7,
+    0x7307, 0x3824,
+    0x72F1, 0x3851,
+    0x72DB, 0x387E,
+    0x72C5, 0x38AB,
+    0x72AF, 0x38D8,
+    0x7298, 0x3906,
+    0x7282, 0x3932,
+    0x726B, 0x395F,
+    0x7255, 0x398C,
+    0x723E, 0x39B9,
+    0x7227, 0x39E6,
+    0x7211, 0x3A13,
+    0x71FA, 0x3A40,
+    0x71E3, 0x3A6C,
+    0x71CC, 0x3A99,
+    0x71B5, 0x3AC6,
+    0x719E, 0x3AF2,
+    0x7186, 0x3B1F,
+    0x716F, 0x3B4C,
+    0x7158, 0x3B78,
+    0x7141, 0x3BA5,
+    0x7129, 0x3BD1,
+    0x7112, 0x3BFD,
+    0x70FA, 0x3C2A,
+    0x70E2, 0x3C56,
+    0x70CB, 0x3C83,
+    0x70B3, 0x3CAF,
+    0x709B, 0x3CDB,
+    0x7083, 0x3D07,
+    0x706B, 0x3D33,
+    0x7053, 0x3D60,
+    0x703B, 0x3D8C,
+    0x7023, 0x3DB8,
+    0x700A, 0x3DE4,
+    0x6FF2, 0x3E10,
+    0x6FDA, 0x3E3C,
+    0x6FC1, 0x3E68,
+    0x6FA9, 0x3E93,
+    0x6F90, 0x3EBF,
+    0x6F77, 0x3EEB,
+    0x6F5F, 0x3F17,
+    0x6F46, 0x3F43,
+    0x6F2D, 0x3F6E,
+    0x6F14, 0x3F9A,
+    0x6EFB, 0x3FC5,
+    0x6EE2, 0x3FF1,
+    0x6EC9, 0x401D,
+    0x6EAF, 0x4048,
+    0x6E96, 0x4073,
+    0x6E7D, 0x409F,
+    0x6E63, 0x40CA,
+    0x6E4A, 0x40F6,
+    0x6E30, 0x4121,
+    0x6E17, 0x414C,
+    0x6DFD, 0x4177,
+    0x6DE3, 0x41A2,
+    0x6DCA, 0x41CE,
+    0x6DB0, 0x41F9,
+    0x6D96, 0x4224,
+    0x6D7C, 0x424F,
+    0x6D62, 0x427A,
+    0x6D48, 0x42A5,
+    0x6D2D, 0x42D0,
+    0x6D13, 0x42FA,
+    0x6CF9, 0x4325,
+    0x6CDE, 0x4350,
+    0x6CC4, 0x437B,
+    0x6CA9, 0x43A5,
+    0x6C8F, 0x43D0,
+    0x6C74, 0x43FB,
+    0x6C59, 0x4425,
+    0x6C3F, 0x4450,
+    0x6C24, 0x447A,
+    0x6C09, 0x44A5,
+    0x6BEE, 0x44CF,
+    0x6BD3, 0x44FA,
+    0x6BB8, 0x4524,
+    0x6B9C, 0x454E,
+    0x6B81, 0x4578,
+    0x6B66, 0x45A3,
+    0x6B4A, 0x45CD,
+    0x6B2F, 0x45F7,
+    0x6B13, 0x4621,
+    0x6AF8, 0x464B,
+    0x6ADC, 0x4675,
+    0x6AC1, 0x469F,
+    0x6AA5, 0x46C9,
+    0x6A89, 0x46F3,
+    0x6A6D, 0x471C,
+    0x6A51, 0x4746,
+    0x6A35, 0x4770,
+    0x6A19, 0x479A,
+    0x69FD, 0x47C3,
+    0x69E1, 0x47ED,
+    0x69C4, 0x4816,
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+    0x138E, 0x7E7F,
+    0x135D, 0x7E86,
+    0x132B, 0x7E8E,
+    0x12F9, 0x7E95,
+    0x12C8, 0x7E9D,
+    0x1296, 0x7EA4,
+    0x1264, 0x7EAB,
+    0x1232, 0x7EB3,
+    0x1201, 0x7EBA,
+    0x11CF, 0x7EC1,
+    0x119D, 0x7EC8,
+    0x116B, 0x7ECF,
+    0x1139, 0x7ED5,
+    0x1108, 0x7EDC,
+    0x10D6, 0x7EE3,
+    0x10A4, 0x7EE9,
+    0x1072, 0x7EF0,
+    0x1040, 0x7EF6,
+    0x100E, 0x7EFD,
+    0x0FDD, 0x7F03,
+    0x0FAB, 0x7F09,
+    0x0F79, 0x7F0F,
+    0x0F47, 0x7F15,
+    0x0F15, 0x7F1B,
+    0x0EE3, 0x7F21,
+    0x0EB1, 0x7F27,
+    0x0E7F, 0x7F2D,
+    0x0E4D, 0x7F32,
+    0x0E1B, 0x7F38,
+    0x0DE9, 0x7F3D,
+    0x0DB7, 0x7F43,
+    0x0D85, 0x7F48,
+    0x0D53, 0x7F4D,
+    0x0D21, 0x7F53,
+    0x0CEF, 0x7F58,
+    0x0CBD, 0x7F5D,
+    0x0C8B, 0x7F62,
+    0x0C59, 0x7F67,
+    0x0C27, 0x7F6B,
+    0x0BF5, 0x7F70,
+    0x0BC3, 0x7F75,
+    0x0B91, 0x7F79,
+    0x0B5F, 0x7F7E,
+    0x0B2D, 0x7F82,
+    0x0AFB, 0x7F87,
+    0x0AC9, 0x7F8B,
+    0x0A97, 0x7F8F,
+    0x0A65, 0x7F93,
+    0x0A33, 0x7F97,
+    0x0A00, 0x7F9B,
+    0x09CE, 0x7F9F,
+    0x099C, 0x7FA3,
+    0x096A, 0x7FA7,
+    0x0938, 0x7FAA,
+    0x0906, 0x7FAE,
+    0x08D4, 0x7FB1,
+    0x08A2, 0x7FB5,
+    0x086F, 0x7FB8,
+    0x083D, 0x7FBC,
+    0x080B, 0x7FBF,
+    0x07D9, 0x7FC2,
+    0x07A7, 0x7FC5,
+    0x0775, 0x7FC8,
+    0x0742, 0x7FCB,
+    0x0710, 0x7FCE,
+    0x06DE, 0x7FD0,
+    0x06AC, 0x7FD3,
+    0x067A, 0x7FD6,
+    0x0647, 0x7FD8,
+    0x0615, 0x7FDA,
+    0x05E3, 0x7FDD,
+    0x05B1, 0x7FDF,
+    0x057F, 0x7FE1,
+    0x054C, 0x7FE3,
+    0x051A, 0x7FE5,
+    0x04E8, 0x7FE7,
+    0x04B6, 0x7FE9,
+    0x0483, 0x7FEB,
+    0x0451, 0x7FED,
+    0x041F, 0x7FEE,
+    0x03ED, 0x7FF0,
+    0x03BA, 0x7FF2,
+    0x0388, 0x7FF3,
+    0x0356, 0x7FF4,
+    0x0324, 0x7FF6,
+    0x02F1, 0x7FF7,
+    0x02BF, 0x7FF8,
+    0x028D, 0x7FF9,
+    0x025B, 0x7FFA,
+    0x0228, 0x7FFB,
+    0x01F6, 0x7FFC,
+    0x01C4, 0x7FFC,
+    0x0192, 0x7FFD,
+    0x015F, 0x7FFE,
+    0x012D, 0x7FFE,
+    0x00FB, 0x7FFF,
+    0x00C9, 0x7FFF,
+    0x0096, 0x7FFF,
+    0x0064, 0x7FFF,
+    0x0032, 0x7FFF,
+    0x0000, 0x7FFF,
+    0xFFCD, 0x7FFF,
+    0xFF9B, 0x7FFF,
+    0xFF69, 0x7FFF,
+    0xFF36, 0x7FFF,
+    0xFF04, 0x7FFF,
+    0xFED2, 0x7FFE,
+    0xFEA0, 0x7FFE,
+    0xFE6D, 0x7FFD,
+    0xFE3B, 0x7FFC,
+    0xFE09, 0x7FFC,
+    0xFDD7, 0x7FFB,
+    0xFDA4, 0x7FFA,
+    0xFD72, 0x7FF9,
+    0xFD40, 0x7FF8,
+    0xFD0E, 0x7FF7,
+    0xFCDB, 0x7FF6,
+    0xFCA9, 0x7FF4,
+    0xFC77, 0x7FF3,
+    0xFC45, 0x7FF2,
+    0xFC12, 0x7FF0,
+    0xFBE0, 0x7FEE,
+    0xFBAE, 0x7FED,
+    0xFB7C, 0x7FEB,
+    0xFB49, 0x7FE9,
+    0xFB17, 0x7FE7,
+    0xFAE5, 0x7FE5,
+    0xFAB3, 0x7FE3,
+    0xFA80, 0x7FE1,
+    0xFA4E, 0x7FDF,
+    0xFA1C, 0x7FDD,
+    0xF9EA, 0x7FDA,
+    0xF9B8, 0x7FD8,
+    0xF985, 0x7FD6,
+    0xF953, 0x7FD3,
+    0xF921, 0x7FD0,
+    0xF8EF, 0x7FCE,
+    0xF8BD, 0x7FCB,
+    0xF88A, 0x7FC8,
+    0xF858, 0x7FC5,
+    0xF826, 0x7FC2,
+    0xF7F4, 0x7FBF,
+    0xF7C2, 0x7FBC,
+    0xF790, 0x7FB8,
+    0xF75D, 0x7FB5,
+    0xF72B, 0x7FB1,
+    0xF6F9, 0x7FAE,
+    0xF6C7, 0x7FAA,
+    0xF695, 0x7FA7,
+    0xF663, 0x7FA3,
+    0xF631, 0x7F9F,
+    0xF5FF, 0x7F9B,
+    0xF5CC, 0x7F97,
+    0xF59A, 0x7F93,
+    0xF568, 0x7F8F,
+    0xF536, 0x7F8B,
+    0xF504, 0x7F87,
+    0xF4D2, 0x7F82,
+    0xF4A0, 0x7F7E,
+    0xF46E, 0x7F79,
+    0xF43C, 0x7F75,
+    0xF40A, 0x7F70,
+    0xF3D8, 0x7F6B,
+    0xF3A6, 0x7F67,
+    0xF374, 0x7F62,
+    0xF342, 0x7F5D,
+    0xF310, 0x7F58,
+    0xF2DE, 0x7F53,
+    0xF2AC, 0x7F4D,
+    0xF27A, 0x7F48,
+    0xF248, 0x7F43,
+    0xF216, 0x7F3D,
+    0xF1E4, 0x7F38,
+    0xF1B2, 0x7F32,
+    0xF180, 0x7F2D,
+    0xF14E, 0x7F27,
+    0xF11C, 0x7F21,
+    0xF0EA, 0x7F1B,
+    0xF0B8, 0x7F15,
+    0xF086, 0x7F0F,
+    0xF054, 0x7F09,
+    0xF022, 0x7F03,
+    0xEFF1, 0x7EFD,
+    0xEFBF, 0x7EF6,
+    0xEF8D, 0x7EF0,
+    0xEF5B, 0x7EE9,
+    0xEF29, 0x7EE3,
+    0xEEF7, 0x7EDC,
+    0xEEC6, 0x7ED5,
+    0xEE94, 0x7ECF,
+    0xEE62, 0x7EC8,
+    0xEE30, 0x7EC1,
+    0xEDFE, 0x7EBA,
+    0xEDCD, 0x7EB3,
+    0xED9B, 0x7EAB,
+    0xED69, 0x7EA4,
+    0xED37, 0x7E9D,
+    0xED06, 0x7E95,
+    0xECD4, 0x7E8E,
+    0xECA2, 0x7E86,
+    0xEC71, 0x7E7F,
+    0xEC3F, 0x7E77,
+    0xEC0D, 0x7E6F,
+    0xEBDC, 0x7E67,
+    0xEBAA, 0x7E5F,
+    0xEB78, 0x7E57,
+    0xEB47, 0x7E4F,
+    0xEB15, 0x7E47,
+    0xEAE4, 0x7E3F,
+    0xEAB2, 0x7E37,
+    0xEA80, 0x7E2E,
+    0xEA4F, 0x7E26,
+    0xEA1D, 0x7E1D,
+    0xE9EC, 0x7E14,
+    0xE9BA, 0x7E0C,
+    0xE989, 0x7E03,
+    0xE957, 0x7DFA,
+    0xE926, 0x7DF1,
+    0xE8F5, 0x7DE8,
+    0xE8C3, 0x7DDF,
+    0xE892, 0x7DD6,
+    0xE860, 0x7DCD,
+    0xE82F, 0x7DC3,
+    0xE7FD, 0x7DBA,
+    0xE7CC, 0x7DB0,
+    0xE79B, 0x7DA7,
+    0xE769, 0x7D9D,
+    0xE738, 0x7D94,
+    0xE707, 0x7D8A,
+    0xE6D5, 0x7D80,
+    0xE6A4, 0x7D76,
+    0xE673, 0x7D6C,
+    0xE642, 0x7D62,
+    0xE610, 0x7D58,
+    0xE5DF, 0x7D4E,
+    0xE5AE, 0x7D43,
+    0xE57D, 0x7D39,
+    0xE54C, 0x7D2F,
+    0xE51B, 0x7D24,
+    0xE4E9, 0x7D19,
+    0xE4B8, 0x7D0F,
+    0xE487, 0x7D04,
+    0xE456, 0x7CF9,
+    0xE425, 0x7CEE,
+    0xE3F4, 0x7CE3,
+    0xE3C3, 0x7CD8,
+    0xE392, 0x7CCD,
+    0xE361, 0x7CC2,
+    0xE330, 0x7CB7,
+    0xE2FF, 0x7CAB,
+    0xE2CE, 0x7CA0,
+    0xE29D, 0x7C94,
+    0xE26C, 0x7C89,
+    0xE23B, 0x7C7D,
+    0xE20A, 0x7C71,
+    0xE1DA, 0x7C66,
+    0xE1A9, 0x7C5A,
+    0xE178, 0x7C4E,
+    0xE147, 0x7C42,
+    0xE116, 0x7C36,
+    0xE0E6, 0x7C29,
+    0xE0B5, 0x7C1D,
+    0xE084, 0x7C11,
+    0xE053, 0x7C05,
+    0xE023, 0x7BF8,
+    0xDFF2, 0x7BEB,
+    0xDFC1, 0x7BDF,
+    0xDF91, 0x7BD2,
+    0xDF60, 0x7BC5,
+    0xDF2F, 0x7BB9,
+    0xDEFF, 0x7BAC,
+    0xDECE, 0x7B9F,
+    0xDE9E, 0x7B92,
+    0xDE6D, 0x7B84,
+    0xDE3D, 0x7B77,
+    0xDE0C, 0x7B6A,
+    0xDDDC, 0x7B5D,
+    0xDDAB, 0x7B4F,
+    0xDD7B, 0x7B42,
+    0xDD4B, 0x7B34,
+    0xDD1A, 0x7B26,
+    0xDCEA, 0x7B19,
+    0xDCBA, 0x7B0B,
+    0xDC89, 0x7AFD,
+    0xDC59, 0x7AEF,
+    0xDC29, 0x7AE1,
+    0xDBF8, 0x7AD3,
+    0xDBC8, 0x7AC5,
+    0xDB98, 0x7AB6,
+    0xDB68, 0x7AA8,
+    0xDB38, 0x7A9A,
+    0xDB08, 0x7A8B,
+    0xDAD7, 0x7A7D,
+    0xDAA7, 0x7A6E,
+    0xDA77, 0x7A5F,
+    0xDA47, 0x7A50,
+    0xDA17, 0x7A42,
+    0xD9E7, 0x7A33,
+    0xD9B7, 0x7A24,
+    0xD987, 0x7A15,
+    0xD957, 0x7A05,
+    0xD927, 0x79F6,
+    0xD8F8, 0x79E7,
+    0xD8C8, 0x79D8,
+    0xD898, 0x79C8,
+    0xD868, 0x79B9,
+    0xD838, 0x79A9,
+    0xD809, 0x7999,
+    0xD7D9, 0x798A,
+    0xD7A9, 0x797A,
+    0xD779, 0x796A,
+    0xD74A, 0x795A,
+    0xD71A, 0x794A,
+    0xD6EA, 0x793A,
+    0xD6BB, 0x792A,
+    0xD68B, 0x7919,
+    0xD65C, 0x7909,
+    0xD62C, 0x78F9,
+    0xD5FD, 0x78E8,
+    0xD5CD, 0x78D8,
+    0xD59E, 0x78C7,
+    0xD56E, 0x78B6,
+    0xD53F, 0x78A6,
+    0xD510, 0x7895,
+    0xD4E0, 0x7884,
+    0xD4B1, 0x7873,
+    0xD482, 0x7862,
+    0xD452, 0x7851,
+    0xD423, 0x7840,
+    0xD3F4, 0x782E,
+    0xD3C5, 0x781D,
+    0xD396, 0x780C,
+    0xD367, 0x77FA,
+    0xD337, 0x77E9,
+    0xD308, 0x77D7,
+    0xD2D9, 0x77C5,
+    0xD2AA, 0x77B4,
+    0xD27B, 0x77A2,
+    0xD24C, 0x7790,
+    0xD21D, 0x777E,
+    0xD1EE, 0x776C,
+    0xD1C0, 0x775A,
+    0xD191, 0x7747,
+    0xD162, 0x7735,
+    0xD133, 0x7723,
+    0xD104, 0x7710,
+    0xD0D6, 0x76FE,
+    0xD0A7, 0x76EB,
+    0xD078, 0x76D9,
+    0xD04A, 0x76C6,
+    0xD01B, 0x76B3,
+    0xCFEC, 0x76A0,
+    0xCFBE, 0x768E,
+    0xCF8F, 0x767B,
+    0xCF61, 0x7668,
+    0xCF32, 0x7654,
+    0xCF04, 0x7641,
+    0xCED5, 0x762E,
+    0xCEA7, 0x761B,
+    0xCE79, 0x7607,
+    0xCE4A, 0x75F4,
+    0xCE1C, 0x75E0,
+    0xCDEE, 0x75CC,
+    0xCDBF, 0x75B9,
+    0xCD91, 0x75A5,
+    0xCD63, 0x7591,
+    0xCD35, 0x757D,
+    0xCD07, 0x7569,
+    0xCCD9, 0x7555,
+    0xCCAB, 0x7541,
+    0xCC7D, 0x752D,
+    0xCC4F, 0x7519,
+    0xCC21, 0x7504,
+    0xCBF3, 0x74F0,
+    0xCBC5, 0x74DB,
+    0xCB97, 0x74C7,
+    0xCB69, 0x74B2,
+    0xCB3B, 0x749E,
+    0xCB0D, 0x7489,
+    0xCAE0, 0x7474,
+    0xCAB2, 0x745F,
+    0xCA84, 0x744A,
+    0xCA57, 0x7435,
+    0xCA29, 0x7420,
+    0xC9FB, 0x740B,
+    0xC9CE, 0x73F6,
+    0xC9A0, 0x73E0,
+    0xC973, 0x73CB,
+    0xC945, 0x73B5,
+    0xC918, 0x73A0,
+    0xC8EB, 0x738A,
+    0xC8BD, 0x7375,
+    0xC890, 0x735F,
+    0xC863, 0x7349,
+    0xC835, 0x7333,
+    0xC808, 0x731D,
+    0xC7DB, 0x7307,
+    0xC7AE, 0x72F1,
+    0xC781, 0x72DB,
+    0xC754, 0x72C5,
+    0xC727, 0x72AF,
+    0xC6F9, 0x7298,
+    0xC6CD, 0x7282,
+    0xC6A0, 0x726B,
+    0xC673, 0x7255,
+    0xC646, 0x723E,
+    0xC619, 0x7227,
+    0xC5EC, 0x7211,
+    0xC5BF, 0x71FA,
+    0xC593, 0x71E3,
+    0xC566, 0x71CC,
+    0xC539, 0x71B5,
+    0xC50D, 0x719E,
+    0xC4E0, 0x7186,
+    0xC4B3, 0x716F,
+    0xC487, 0x7158,
+    0xC45A, 0x7141,
+    0xC42E, 0x7129,
+    0xC402, 0x7112,
+    0xC3D5, 0x70FA,
+    0xC3A9, 0x70E2,
+    0xC37C, 0x70CB,
+    0xC350, 0x70B3,
+    0xC324, 0x709B,
+    0xC2F8, 0x7083,
+    0xC2CC, 0x706B,
+    0xC29F, 0x7053,
+    0xC273, 0x703B,
+    0xC247, 0x7023,
+    0xC21B, 0x700A,
+    0xC1EF, 0x6FF2,
+    0xC1C3, 0x6FDA,
+    0xC197, 0x6FC1,
+    0xC16C, 0x6FA9,
+    0xC140, 0x6F90,
+    0xC114, 0x6F77,
+    0xC0E8, 0x6F5F,
+    0xC0BC, 0x6F46,
+    0xC091, 0x6F2D,
+    0xC065, 0x6F14,
+    0xC03A, 0x6EFB,
+    0xC00E, 0x6EE2,
+    0xBFE2, 0x6EC9,
+    0xBFB7, 0x6EAF,
+    0xBF8C, 0x6E96,
+    0xBF60, 0x6E7D,
+    0xBF35, 0x6E63,
+    0xBF09, 0x6E4A,
+    0xBEDE, 0x6E30,
+    0xBEB3, 0x6E17,
+    0xBE88, 0x6DFD,
+    0xBE5D, 0x6DE3,
+    0xBE31, 0x6DCA,
+    0xBE06, 0x6DB0,
+    0xBDDB, 0x6D96,
+    0xBDB0, 0x6D7C,
+    0xBD85, 0x6D62,
+    0xBD5A, 0x6D48,
+    0xBD2F, 0x6D2D,
+    0xBD05, 0x6D13,
+    0xBCDA, 0x6CF9,
+    0xBCAF, 0x6CDE,
+    0xBC84, 0x6CC4,
+    0xBC5A, 0x6CA9,
+    0xBC2F, 0x6C8F,
+    0xBC04, 0x6C74,
+    0xBBDA, 0x6C59,
+    0xBBAF, 0x6C3F,
+    0xBB85, 0x6C24,
+    0xBB5A, 0x6C09,
+    0xBB30, 0x6BEE,
+    0xBB05, 0x6BD3,
+    0xBADB, 0x6BB8,
+    0xBAB1, 0x6B9C,
+    0xBA87, 0x6B81,
+    0xBA5C, 0x6B66,
+    0xBA32, 0x6B4A,
+    0xBA08, 0x6B2F,
+    0xB9DE, 0x6B13,
+    0xB9B4, 0x6AF8,
+    0xB98A, 0x6ADC,
+    0xB960, 0x6AC1,
+    0xB936, 0x6AA5,
+    0xB90C, 0x6A89,
+    0xB8E3, 0x6A6D,
+    0xB8B9, 0x6A51,
+    0xB88F, 0x6A35,
+    0xB865, 0x6A19,
+    0xB83C, 0x69FD,
+    0xB812, 0x69E1,
+    0xB7E9, 0x69C4,
+    0xB7BF, 0x69A8,
+    0xB796, 0x698C,
+    0xB76C, 0x696F,
+    0xB743, 0x6953,
+    0xB719, 0x6936,
+    0xB6F0, 0x6919,
+    0xB6C7, 0x68FD,
+    0xB69E, 0x68E0,
+    0xB675, 0x68C3,
+    0xB64B, 0x68A6,
+    0xB622, 0x6889,
+    0xB5F9, 0x686C,
+    0xB5D0, 0x684F,
+    0xB5A7, 0x6832,
+    0xB57E, 0x6815,
+    0xB556, 0x67F7,
+    0xB52D, 0x67DA,
+    0xB504, 0x67BD,
+    0xB4DB, 0x679F,
+    0xB4B3, 0x6782,
+    0xB48A, 0x6764,
+    0xB461, 0x6746,
+    0xB439, 0x6729,
+    0xB410, 0x670B,
+    0xB3E8, 0x66ED,
+    0xB3C0, 0x66CF,
+    0xB397, 0x66B1,
+    0xB36F, 0x6693,
+    0xB347, 0x6675,
+    0xB31E, 0x6657,
+    0xB2F6, 0x6639,
+    0xB2CE, 0x661A,
+    0xB2A6, 0x65FC,
+    0xB27E, 0x65DD,
+    0xB256, 0x65BF,
+    0xB22E, 0x65A0,
+    0xB206, 0x6582,
+    0xB1DE, 0x6563,
+    0xB1B7, 0x6545,
+    0xB18F, 0x6526,
+    0xB167, 0x6507,
+    0xB140, 0x64E8,
+    0xB118, 0x64C9,
+    0xB0F0, 0x64AA,
+    0xB0C9, 0x648B,
+    0xB0A1, 0x646C,
+    0xB07A, 0x644D,
+    0xB053, 0x642D,
+    0xB02B, 0x640E,
+    0xB004, 0x63EF,
+    0xAFDD, 0x63CF,
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+    0x8047, 0x086F,
+    0x8043, 0x083D,
+    0x8040, 0x080B,
+    0x803D, 0x07D9,
+    0x803A, 0x07A7,
+    0x8037, 0x0775,
+    0x8034, 0x0742,
+    0x8031, 0x0710,
+    0x802F, 0x06DE,
+    0x802C, 0x06AC,
+    0x8029, 0x067A,
+    0x8027, 0x0647,
+    0x8025, 0x0615,
+    0x8022, 0x05E3,
+    0x8020, 0x05B1,
+    0x801E, 0x057F,
+    0x801C, 0x054C,
+    0x801A, 0x051A,
+    0x8018, 0x04E8,
+    0x8016, 0x04B6,
+    0x8014, 0x0483,
+    0x8012, 0x0451,
+    0x8011, 0x041F,
+    0x800F, 0x03ED,
+    0x800D, 0x03BA,
+    0x800C, 0x0388,
+    0x800B, 0x0356,
+    0x8009, 0x0324,
+    0x8008, 0x02F1,
+    0x8007, 0x02BF,
+    0x8006, 0x028D,
+    0x8005, 0x025B,
+    0x8004, 0x0228,
+    0x8003, 0x01F6,
+    0x8003, 0x01C4,
+    0x8002, 0x0192,
+    0x8001, 0x015F,
+    0x8001, 0x012D,
+    0x8000, 0x00FB,
+    0x8000, 0x00C9,
+    0x8000, 0x0096,
+    0x8000, 0x0064,
+    0x8000, 0x0032,
+    0x8000, 0x0000,
+    0x8000, 0xFFCD,
+    0x8000, 0xFF9B,
+    0x8000, 0xFF69,
+    0x8000, 0xFF36,
+    0x8000, 0xFF04,
+    0x8001, 0xFED2,
+    0x8001, 0xFEA0,
+    0x8002, 0xFE6D,
+    0x8003, 0xFE3B,
+    0x8003, 0xFE09,
+    0x8004, 0xFDD7,
+    0x8005, 0xFDA4,
+    0x8006, 0xFD72,
+    0x8007, 0xFD40,
+    0x8008, 0xFD0E,
+    0x8009, 0xFCDB,
+    0x800B, 0xFCA9,
+    0x800C, 0xFC77,
+    0x800D, 0xFC45,
+    0x800F, 0xFC12,
+    0x8011, 0xFBE0,
+    0x8012, 0xFBAE,
+    0x8014, 0xFB7C,
+    0x8016, 0xFB49,
+    0x8018, 0xFB17,
+    0x801A, 0xFAE5,
+    0x801C, 0xFAB3,
+    0x801E, 0xFA80,
+    0x8020, 0xFA4E,
+    0x8022, 0xFA1C,
+    0x8025, 0xF9EA,
+    0x8027, 0xF9B8,
+    0x8029, 0xF985,
+    0x802C, 0xF953,
+    0x802F, 0xF921,
+    0x8031, 0xF8EF,
+    0x8034, 0xF8BD,
+    0x8037, 0xF88A,
+    0x803A, 0xF858,
+    0x803D, 0xF826,
+    0x8040, 0xF7F4,
+    0x8043, 0xF7C2,
+    0x8047, 0xF790,
+    0x804A, 0xF75D,
+    0x804E, 0xF72B,
+    0x8051, 0xF6F9,
+    0x8055, 0xF6C7,
+    0x8058, 0xF695,
+    0x805C, 0xF663,
+    0x8060, 0xF631,
+    0x8064, 0xF5FF,
+    0x8068, 0xF5CC,
+    0x806C, 0xF59A,
+    0x8070, 0xF568,
+    0x8074, 0xF536,
+    0x8078, 0xF504,
+    0x807D, 0xF4D2,
+    0x8081, 0xF4A0,
+    0x8086, 0xF46E,
+    0x808A, 0xF43C,
+    0x808F, 0xF40A,
+    0x8094, 0xF3D8,
+    0x8098, 0xF3A6,
+    0x809D, 0xF374,
+    0x80A2, 0xF342,
+    0x80A7, 0xF310,
+    0x80AC, 0xF2DE,
+    0x80B2, 0xF2AC,
+    0x80B7, 0xF27A,
+    0x80BC, 0xF248,
+    0x80C2, 0xF216,
+    0x80C7, 0xF1E4,
+    0x80CD, 0xF1B2,
+    0x80D2, 0xF180,
+    0x80D8, 0xF14E,
+    0x80DE, 0xF11C,
+    0x80E4, 0xF0EA,
+    0x80EA, 0xF0B8,
+    0x80F0, 0xF086,
+    0x80F6, 0xF054,
+    0x80FC, 0xF022,
+    0x8102, 0xEFF1,
+    0x8109, 0xEFBF,
+    0x810F, 0xEF8D,
+    0x8116, 0xEF5B,
+    0x811C, 0xEF29,
+    0x8123, 0xEEF7,
+    0x812A, 0xEEC6,
+    0x8130, 0xEE94,
+    0x8137, 0xEE62,
+    0x813E, 0xEE30,
+    0x8145, 0xEDFE,
+    0x814C, 0xEDCD,
+    0x8154, 0xED9B,
+    0x815B, 0xED69,
+    0x8162, 0xED37,
+    0x816A, 0xED06,
+    0x8171, 0xECD4,
+    0x8179, 0xECA2,
+    0x8180, 0xEC71,
+    0x8188, 0xEC3F,
+    0x8190, 0xEC0D,
+    0x8198, 0xEBDC,
+    0x81A0, 0xEBAA,
+    0x81A8, 0xEB78,
+    0x81B0, 0xEB47,
+    0x81B8, 0xEB15,
+    0x81C0, 0xEAE4,
+    0x81C8, 0xEAB2,
+    0x81D1, 0xEA80,
+    0x81D9, 0xEA4F,
+    0x81E2, 0xEA1D,
+    0x81EB, 0xE9EC,
+    0x81F3, 0xE9BA,
+    0x81FC, 0xE989,
+    0x8205, 0xE957,
+    0x820E, 0xE926,
+    0x8217, 0xE8F5,
+    0x8220, 0xE8C3,
+    0x8229, 0xE892,
+    0x8232, 0xE860,
+    0x823C, 0xE82F,
+    0x8245, 0xE7FD,
+    0x824F, 0xE7CC,
+    0x8258, 0xE79B,
+    0x8262, 0xE769,
+    0x826B, 0xE738,
+    0x8275, 0xE707,
+    0x827F, 0xE6D5,
+    0x8289, 0xE6A4,
+    0x8293, 0xE673,
+    0x829D, 0xE642,
+    0x82A7, 0xE610,
+    0x82B1, 0xE5DF,
+    0x82BC, 0xE5AE,
+    0x82C6, 0xE57D,
+    0x82D0, 0xE54C,
+    0x82DB, 0xE51B,
+    0x82E6, 0xE4E9,
+    0x82F0, 0xE4B8,
+    0x82FB, 0xE487,
+    0x8306, 0xE456,
+    0x8311, 0xE425,
+    0x831C, 0xE3F4,
+    0x8327, 0xE3C3,
+    0x8332, 0xE392,
+    0x833D, 0xE361,
+    0x8348, 0xE330,
+    0x8354, 0xE2FF,
+    0x835F, 0xE2CE,
+    0x836B, 0xE29D,
+    0x8376, 0xE26C,
+    0x8382, 0xE23B,
+    0x838E, 0xE20A,
+    0x8399, 0xE1DA,
+    0x83A5, 0xE1A9,
+    0x83B1, 0xE178,
+    0x83BD, 0xE147,
+    0x83C9, 0xE116,
+    0x83D6, 0xE0E6,
+    0x83E2, 0xE0B5,
+    0x83EE, 0xE084,
+    0x83FA, 0xE053,
+    0x8407, 0xE023,
+    0x8414, 0xDFF2,
+    0x8420, 0xDFC1,
+    0x842D, 0xDF91,
+    0x843A, 0xDF60,
+    0x8446, 0xDF2F,
+    0x8453, 0xDEFF,
+    0x8460, 0xDECE,
+    0x846D, 0xDE9E,
+    0x847B, 0xDE6D,
+    0x8488, 0xDE3D,
+    0x8495, 0xDE0C,
+    0x84A2, 0xDDDC,
+    0x84B0, 0xDDAB,
+    0x84BD, 0xDD7B,
+    0x84CB, 0xDD4B,
+    0x84D9, 0xDD1A,
+    0x84E6, 0xDCEA,
+    0x84F4, 0xDCBA,
+    0x8502, 0xDC89,
+    0x8510, 0xDC59,
+    0x851E, 0xDC29,
+    0x852C, 0xDBF8,
+    0x853A, 0xDBC8,
+    0x8549, 0xDB98,
+    0x8557, 0xDB68,
+    0x8565, 0xDB38,
+    0x8574, 0xDB08,
+    0x8582, 0xDAD7,
+    0x8591, 0xDAA7,
+    0x85A0, 0xDA77,
+    0x85AF, 0xDA47,
+    0x85BD, 0xDA17,
+    0x85CC, 0xD9E7,
+    0x85DB, 0xD9B7,
+    0x85EA, 0xD987,
+    0x85FA, 0xD957,
+    0x8609, 0xD927,
+    0x8618, 0xD8F8,
+    0x8627, 0xD8C8,
+    0x8637, 0xD898,
+    0x8646, 0xD868,
+    0x8656, 0xD838,
+    0x8666, 0xD809,
+    0x8675, 0xD7D9,
+    0x8685, 0xD7A9,
+    0x8695, 0xD779,
+    0x86A5, 0xD74A,
+    0x86B5, 0xD71A,
+    0x86C5, 0xD6EA,
+    0x86D5, 0xD6BB,
+    0x86E6, 0xD68B,
+    0x86F6, 0xD65C,
+    0x8706, 0xD62C,
+    0x8717, 0xD5FD,
+    0x8727, 0xD5CD,
+    0x8738, 0xD59E,
+    0x8749, 0xD56E,
+    0x8759, 0xD53F,
+    0x876A, 0xD510,
+    0x877B, 0xD4E0,
+    0x878C, 0xD4B1,
+    0x879D, 0xD482,
+    0x87AE, 0xD452,
+    0x87BF, 0xD423,
+    0x87D1, 0xD3F4,
+    0x87E2, 0xD3C5,
+    0x87F3, 0xD396,
+    0x8805, 0xD367,
+    0x8816, 0xD337,
+    0x8828, 0xD308,
+    0x883A, 0xD2D9,
+    0x884B, 0xD2AA,
+    0x885D, 0xD27B,
+    0x886F, 0xD24C,
+    0x8881, 0xD21D,
+    0x8893, 0xD1EE,
+    0x88A5, 0xD1C0,
+    0x88B8, 0xD191,
+    0x88CA, 0xD162,
+    0x88DC, 0xD133,
+    0x88EF, 0xD104,
+    0x8901, 0xD0D6,
+    0x8914, 0xD0A7,
+    0x8926, 0xD078,
+    0x8939, 0xD04A,
+    0x894C, 0xD01B,
+    0x895F, 0xCFEC,
+    0x8971, 0xCFBE,
+    0x8984, 0xCF8F,
+    0x8997, 0xCF61,
+    0x89AB, 0xCF32,
+    0x89BE, 0xCF04,
+    0x89D1, 0xCED5,
+    0x89E4, 0xCEA7,
+    0x89F8, 0xCE79,
+    0x8A0B, 0xCE4A,
+    0x8A1F, 0xCE1C,
+    0x8A33, 0xCDEE,
+    0x8A46, 0xCDBF,
+    0x8A5A, 0xCD91,
+    0x8A6E, 0xCD63,
+    0x8A82, 0xCD35,
+    0x8A96, 0xCD07,
+    0x8AAA, 0xCCD9,
+    0x8ABE, 0xCCAB,
+    0x8AD2, 0xCC7D,
+    0x8AE6, 0xCC4F,
+    0x8AFB, 0xCC21,
+    0x8B0F, 0xCBF3,
+    0x8B24, 0xCBC5,
+    0x8B38, 0xCB97,
+    0x8B4D, 0xCB69,
+    0x8B61, 0xCB3B,
+    0x8B76, 0xCB0D,
+    0x8B8B, 0xCAE0,
+    0x8BA0, 0xCAB2,
+    0x8BB5, 0xCA84,
+    0x8BCA, 0xCA57,
+    0x8BDF, 0xCA29,
+    0x8BF4, 0xC9FB,
+    0x8C09, 0xC9CE,
+    0x8C1F, 0xC9A0,
+    0x8C34, 0xC973,
+    0x8C4A, 0xC945,
+    0x8C5F, 0xC918,
+    0x8C75, 0xC8EB,
+    0x8C8A, 0xC8BD,
+    0x8CA0, 0xC890,
+    0x8CB6, 0xC863,
+    0x8CCC, 0xC835,
+    0x8CE2, 0xC808,
+    0x8CF8, 0xC7DB,
+    0x8D0E, 0xC7AE,
+    0x8D24, 0xC781,
+    0x8D3A, 0xC754,
+    0x8D50, 0xC727,
+    0x8D67, 0xC6F9,
+    0x8D7D, 0xC6CD,
+    0x8D94, 0xC6A0,
+    0x8DAA, 0xC673,
+    0x8DC1, 0xC646,
+    0x8DD8, 0xC619,
+    0x8DEE, 0xC5EC,
+    0x8E05, 0xC5BF,
+    0x8E1C, 0xC593,
+    0x8E33, 0xC566,
+    0x8E4A, 0xC539,
+    0x8E61, 0xC50D,
+    0x8E79, 0xC4E0,
+    0x8E90, 0xC4B3,
+    0x8EA7, 0xC487,
+    0x8EBE, 0xC45A,
+    0x8ED6, 0xC42E,
+    0x8EED, 0xC402,
+    0x8F05, 0xC3D5,
+    0x8F1D, 0xC3A9,
+    0x8F34, 0xC37C,
+    0x8F4C, 0xC350,
+    0x8F64, 0xC324,
+    0x8F7C, 0xC2F8,
+    0x8F94, 0xC2CC,
+    0x8FAC, 0xC29F,
+    0x8FC4, 0xC273,
+    0x8FDC, 0xC247,
+    0x8FF5, 0xC21B,
+    0x900D, 0xC1EF,
+    0x9025, 0xC1C3,
+    0x903E, 0xC197,
+    0x9056, 0xC16C,
+    0x906F, 0xC140,
+    0x9088, 0xC114,
+    0x90A0, 0xC0E8,
+    0x90B9, 0xC0BC,
+    0x90D2, 0xC091,
+    0x90EB, 0xC065,
+    0x9104, 0xC03A,
+    0x911D, 0xC00E,
+    0x9136, 0xBFE2,
+    0x9150, 0xBFB7,
+    0x9169, 0xBF8C,
+    0x9182, 0xBF60,
+    0x919C, 0xBF35,
+    0x91B5, 0xBF09,
+    0x91CF, 0xBEDE,
+    0x91E8, 0xBEB3,
+    0x9202, 0xBE88,
+    0x921C, 0xBE5D,
+    0x9235, 0xBE31,
+    0x924F, 0xBE06,
+    0x9269, 0xBDDB,
+    0x9283, 0xBDB0,
+    0x929D, 0xBD85,
+    0x92B7, 0xBD5A,
+    0x92D2, 0xBD2F,
+    0x92EC, 0xBD05,
+    0x9306, 0xBCDA,
+    0x9321, 0xBCAF,
+    0x933B, 0xBC84,
+    0x9356, 0xBC5A,
+    0x9370, 0xBC2F,
+    0x938B, 0xBC04,
+    0x93A6, 0xBBDA,
+    0x93C0, 0xBBAF,
+    0x93DB, 0xBB85,
+    0x93F6, 0xBB5A,
+    0x9411, 0xBB30,
+    0x942C, 0xBB05,
+    0x9447, 0xBADB,
+    0x9463, 0xBAB1,
+    0x947E, 0xBA87,
+    0x9499, 0xBA5C,
+    0x94B5, 0xBA32,
+    0x94D0, 0xBA08,
+    0x94EC, 0xB9DE,
+    0x9507, 0xB9B4,
+    0x9523, 0xB98A,
+    0x953E, 0xB960,
+    0x955A, 0xB936,
+    0x9576, 0xB90C,
+    0x9592, 0xB8E3,
+    0x95AE, 0xB8B9,
+    0x95CA, 0xB88F,
+    0x95E6, 0xB865,
+    0x9602, 0xB83C,
+    0x961E, 0xB812,
+    0x963B, 0xB7E9,
+    0x9657, 0xB7BF,
+    0x9673, 0xB796,
+    0x9690, 0xB76C,
+    0x96AC, 0xB743,
+    0x96C9, 0xB719,
+    0x96E6, 0xB6F0,
+    0x9702, 0xB6C7,
+    0x971F, 0xB69E,
+    0x973C, 0xB675,
+    0x9759, 0xB64B,
+    0x9776, 0xB622,
+    0x9793, 0xB5F9,
+    0x97B0, 0xB5D0,
+    0x97CD, 0xB5A7,
+    0x97EA, 0xB57E,
+    0x9808, 0xB556,
+    0x9825, 0xB52D,
+    0x9842, 0xB504,
+    0x9860, 0xB4DB,
+    0x987D, 0xB4B3,
+    0x989B, 0xB48A,
+    0x98B9, 0xB461,
+    0x98D6, 0xB439,
+    0x98F4, 0xB410,
+    0x9912, 0xB3E8,
+    0x9930, 0xB3C0,
+    0x994E, 0xB397,
+    0x996C, 0xB36F,
+    0x998A, 0xB347,
+    0x99A8, 0xB31E,
+    0x99C6, 0xB2F6,
+    0x99E5, 0xB2CE,
+    0x9A03, 0xB2A6,
+    0x9A22, 0xB27E,
+    0x9A40, 0xB256,
+    0x9A5F, 0xB22E,
+    0x9A7D, 0xB206,
+    0x9A9C, 0xB1DE,
+    0x9ABA, 0xB1B7,
+    0x9AD9, 0xB18F,
+    0x9AF8, 0xB167,
+    0x9B17, 0xB140,
+    0x9B36, 0xB118,
+    0x9B55, 0xB0F0,
+    0x9B74, 0xB0C9,
+    0x9B93, 0xB0A1,
+    0x9BB2, 0xB07A,
+    0x9BD2, 0xB053,
+    0x9BF1, 0xB02B,
+    0x9C10, 0xB004,
+    0x9C30, 0xAFDD,
+    0x9C4F, 0xAFB6,
+    0x9C6F, 0xAF8F,
+    0x9C8E, 0xAF68,
+    0x9CAE, 0xAF40,
+    0x9CCE, 0xAF1A,
+    0x9CEE, 0xAEF3,
+    0x9D0D, 0xAECC,
+    0x9D2D, 0xAEA5,
+    0x9D4D, 0xAE7E,
+    0x9D6D, 0xAE57,
+    0x9D8E, 0xAE31,
+    0x9DAE, 0xAE0A,
+    0x9DCE, 0xADE3,
+    0x9DEE, 0xADBD,
+    0x9E0E, 0xAD96,
+    0x9E2F, 0xAD70,
+    0x9E4F, 0xAD4A,
+    0x9E70, 0xAD23,
+    0x9E90, 0xACFD,
+    0x9EB1, 0xACD7,
+    0x9ED2, 0xACB1,
+    0x9EF2, 0xAC8A,
+    0x9F13, 0xAC64,
+    0x9F34, 0xAC3E,
+    0x9F55, 0xAC18,
+    0x9F76, 0xABF2,
+    0x9F97, 0xABCC,
+    0x9FB8, 0xABA7,
+    0x9FD9, 0xAB81,
+    0x9FFB, 0xAB5B,
+    0xA01C, 0xAB35,
+    0xA03D, 0xAB10,
+    0xA05F, 0xAAEA,
+    0xA080, 0xAAC5,
+    0xA0A1, 0xAA9F,
+    0xA0C3, 0xAA7A,
+    0xA0E5, 0xAA54,
+    0xA106, 0xAA2F,
+    0xA128, 0xAA0A,
+    0xA14A, 0xA9E5,
+    0xA16C, 0xA9BF,
+    0xA18E, 0xA99A,
+    0xA1AF, 0xA975,
+    0xA1D2, 0xA950,
+    0xA1F4, 0xA92B,
+    0xA216, 0xA906,
+    0xA238, 0xA8E2,
+    0xA25A, 0xA8BD,
+    0xA27C, 0xA898,
+    0xA29F, 0xA873,
+    0xA2C1, 0xA84F,
+    0xA2E4, 0xA82A,
+    0xA306, 0xA806,
+    0xA329, 0xA7E1,
+    0xA34B, 0xA7BD,
+    0xA36E, 0xA798,
+    0xA391, 0xA774,
+    0xA3B4, 0xA750,
+    0xA3D6, 0xA72B,
+    0xA3F9, 0xA707,
+    0xA41C, 0xA6E3,
+    0xA43F, 0xA6BF,
+    0xA462, 0xA69B,
+    0xA486, 0xA677,
+    0xA4A9, 0xA653,
+    0xA4CC, 0xA62F,
+    0xA4EF, 0xA60C,
+    0xA513, 0xA5E8,
+    0xA536, 0xA5C4,
+    0xA55A, 0xA5A1,
+    0xA57D, 0xA57D,
+    0xA5A1, 0xA55A,
+    0xA5C4, 0xA536,
+    0xA5E8, 0xA513,
+    0xA60C, 0xA4EF,
+    0xA62F, 0xA4CC,
+    0xA653, 0xA4A9,
+    0xA677, 0xA486,
+    0xA69B, 0xA462,
+    0xA6BF, 0xA43F,
+    0xA6E3, 0xA41C,
+    0xA707, 0xA3F9,
+    0xA72B, 0xA3D6,
+    0xA750, 0xA3B4,
+    0xA774, 0xA391,
+    0xA798, 0xA36E,
+    0xA7BD, 0xA34B,
+    0xA7E1, 0xA329,
+    0xA806, 0xA306,
+    0xA82A, 0xA2E4,
+    0xA84F, 0xA2C1,
+    0xA873, 0xA29F,
+    0xA898, 0xA27C,
+    0xA8BD, 0xA25A,
+    0xA8E2, 0xA238,
+    0xA906, 0xA216,
+    0xA92B, 0xA1F4,
+    0xA950, 0xA1D2,
+    0xA975, 0xA1AF,
+    0xA99A, 0xA18E,
+    0xA9BF, 0xA16C,
+    0xA9E5, 0xA14A,
+    0xAA0A, 0xA128,
+    0xAA2F, 0xA106,
+    0xAA54, 0xA0E5,
+    0xAA7A, 0xA0C3,
+    0xAA9F, 0xA0A1,
+    0xAAC5, 0xA080,
+    0xAAEA, 0xA05F,
+    0xAB10, 0xA03D,
+    0xAB35, 0xA01C,
+    0xAB5B, 0x9FFB,
+    0xAB81, 0x9FD9,
+    0xABA7, 0x9FB8,
+    0xABCC, 0x9F97,
+    0xABF2, 0x9F76,
+    0xAC18, 0x9F55,
+    0xAC3E, 0x9F34,
+    0xAC64, 0x9F13,
+    0xAC8A, 0x9EF2,
+    0xACB1, 0x9ED2,
+    0xACD7, 0x9EB1,
+    0xACFD, 0x9E90,
+    0xAD23, 0x9E70,
+    0xAD4A, 0x9E4F,
+    0xAD70, 0x9E2F,
+    0xAD96, 0x9E0E,
+    0xADBD, 0x9DEE,
+    0xADE3, 0x9DCE,
+    0xAE0A, 0x9DAE,
+    0xAE31, 0x9D8E,
+    0xAE57, 0x9D6D,
+    0xAE7E, 0x9D4D,
+    0xAEA5, 0x9D2D,
+    0xAECC, 0x9D0D,
+    0xAEF3, 0x9CEE,
+    0xAF1A, 0x9CCE,
+    0xAF40, 0x9CAE,
+    0xAF68, 0x9C8E,
+    0xAF8F, 0x9C6F,
+    0xAFB6, 0x9C4F,
+    0xAFDD, 0x9C30,
+    0xB004, 0x9C10,
+    0xB02B, 0x9BF1,
+    0xB053, 0x9BD2,
+    0xB07A, 0x9BB2,
+    0xB0A1, 0x9B93,
+    0xB0C9, 0x9B74,
+    0xB0F0, 0x9B55,
+    0xB118, 0x9B36,
+    0xB140, 0x9B17,
+    0xB167, 0x9AF8,
+    0xB18F, 0x9AD9,
+    0xB1B7, 0x9ABA,
+    0xB1DE, 0x9A9C,
+    0xB206, 0x9A7D,
+    0xB22E, 0x9A5F,
+    0xB256, 0x9A40,
+    0xB27E, 0x9A22,
+    0xB2A6, 0x9A03,
+    0xB2CE, 0x99E5,
+    0xB2F6, 0x99C6,
+    0xB31E, 0x99A8,
+    0xB347, 0x998A,
+    0xB36F, 0x996C,
+    0xB397, 0x994E,
+    0xB3C0, 0x9930,
+    0xB3E8, 0x9912,
+    0xB410, 0x98F4,
+    0xB439, 0x98D6,
+    0xB461, 0x98B9,
+    0xB48A, 0x989B,
+    0xB4B3, 0x987D,
+    0xB4DB, 0x9860,
+    0xB504, 0x9842,
+    0xB52D, 0x9825,
+    0xB556, 0x9808,
+    0xB57E, 0x97EA,
+    0xB5A7, 0x97CD,
+    0xB5D0, 0x97B0,
+    0xB5F9, 0x9793,
+    0xB622, 0x9776,
+    0xB64B, 0x9759,
+    0xB675, 0x973C,
+    0xB69E, 0x971F,
+    0xB6C7, 0x9702,
+    0xB6F0, 0x96E6,
+    0xB719, 0x96C9,
+    0xB743, 0x96AC,
+    0xB76C, 0x9690,
+    0xB796, 0x9673,
+    0xB7BF, 0x9657,
+    0xB7E9, 0x963B,
+    0xB812, 0x961E,
+    0xB83C, 0x9602,
+    0xB865, 0x95E6,
+    0xB88F, 0x95CA,
+    0xB8B9, 0x95AE,
+    0xB8E3, 0x9592,
+    0xB90C, 0x9576,
+    0xB936, 0x955A,
+    0xB960, 0x953E,
+    0xB98A, 0x9523,
+    0xB9B4, 0x9507,
+    0xB9DE, 0x94EC,
+    0xBA08, 0x94D0,
+    0xBA32, 0x94B5,
+    0xBA5C, 0x9499,
+    0xBA87, 0x947E,
+    0xBAB1, 0x9463,
+    0xBADB, 0x9447,
+    0xBB05, 0x942C,
+    0xBB30, 0x9411,
+    0xBB5A, 0x93F6,
+    0xBB85, 0x93DB,
+    0xBBAF, 0x93C0,
+    0xBBDA, 0x93A6,
+    0xBC04, 0x938B,
+    0xBC2F, 0x9370,
+    0xBC5A, 0x9356,
+    0xBC84, 0x933B,
+    0xBCAF, 0x9321,
+    0xBCDA, 0x9306,
+    0xBD05, 0x92EC,
+    0xBD2F, 0x92D2,
+    0xBD5A, 0x92B7,
+    0xBD85, 0x929D,
+    0xBDB0, 0x9283,
+    0xBDDB, 0x9269,
+    0xBE06, 0x924F,
+    0xBE31, 0x9235,
+    0xBE5D, 0x921C,
+    0xBE88, 0x9202,
+    0xBEB3, 0x91E8,
+    0xBEDE, 0x91CF,
+    0xBF09, 0x91B5,
+    0xBF35, 0x919C,
+    0xBF60, 0x9182,
+    0xBF8C, 0x9169,
+    0xBFB7, 0x9150,
+    0xBFE2, 0x9136,
+    0xC00E, 0x911D,
+    0xC03A, 0x9104,
+    0xC065, 0x90EB,
+    0xC091, 0x90D2,
+    0xC0BC, 0x90B9,
+    0xC0E8, 0x90A0,
+    0xC114, 0x9088,
+    0xC140, 0x906F,
+    0xC16C, 0x9056,
+    0xC197, 0x903E,
+    0xC1C3, 0x9025,
+    0xC1EF, 0x900D,
+    0xC21B, 0x8FF5,
+    0xC247, 0x8FDC,
+    0xC273, 0x8FC4,
+    0xC29F, 0x8FAC,
+    0xC2CC, 0x8F94,
+    0xC2F8, 0x8F7C,
+    0xC324, 0x8F64,
+    0xC350, 0x8F4C,
+    0xC37C, 0x8F34,
+    0xC3A9, 0x8F1D,
+    0xC3D5, 0x8F05,
+    0xC402, 0x8EED,
+    0xC42E, 0x8ED6,
+    0xC45A, 0x8EBE,
+    0xC487, 0x8EA7,
+    0xC4B3, 0x8E90,
+    0xC4E0, 0x8E79,
+    0xC50D, 0x8E61,
+    0xC539, 0x8E4A,
+    0xC566, 0x8E33,
+    0xC593, 0x8E1C,
+    0xC5BF, 0x8E05,
+    0xC5EC, 0x8DEE,
+    0xC619, 0x8DD8,
+    0xC646, 0x8DC1,
+    0xC673, 0x8DAA,
+    0xC6A0, 0x8D94,
+    0xC6CD, 0x8D7D,
+    0xC6F9, 0x8D67,
+    0xC727, 0x8D50,
+    0xC754, 0x8D3A,
+    0xC781, 0x8D24,
+    0xC7AE, 0x8D0E,
+    0xC7DB, 0x8CF8,
+    0xC808, 0x8CE2,
+    0xC835, 0x8CCC,
+    0xC863, 0x8CB6,
+    0xC890, 0x8CA0,
+    0xC8BD, 0x8C8A,
+    0xC8EB, 0x8C75,
+    0xC918, 0x8C5F,
+    0xC945, 0x8C4A,
+    0xC973, 0x8C34,
+    0xC9A0, 0x8C1F,
+    0xC9CE, 0x8C09,
+    0xC9FB, 0x8BF4,
+    0xCA29, 0x8BDF,
+    0xCA57, 0x8BCA,
+    0xCA84, 0x8BB5,
+    0xCAB2, 0x8BA0,
+    0xCAE0, 0x8B8B,
+    0xCB0D, 0x8B76,
+    0xCB3B, 0x8B61,
+    0xCB69, 0x8B4D,
+    0xCB97, 0x8B38,
+    0xCBC5, 0x8B24,
+    0xCBF3, 0x8B0F,
+    0xCC21, 0x8AFB,
+    0xCC4F, 0x8AE6,
+    0xCC7D, 0x8AD2,
+    0xCCAB, 0x8ABE,
+    0xCCD9, 0x8AAA,
+    0xCD07, 0x8A96,
+    0xCD35, 0x8A82,
+    0xCD63, 0x8A6E,
+    0xCD91, 0x8A5A,
+    0xCDBF, 0x8A46,
+    0xCDEE, 0x8A33,
+    0xCE1C, 0x8A1F,
+    0xCE4A, 0x8A0B,
+    0xCE79, 0x89F8,
+    0xCEA7, 0x89E4,
+    0xCED5, 0x89D1,
+    0xCF04, 0x89BE,
+    0xCF32, 0x89AB,
+    0xCF61, 0x8997,
+    0xCF8F, 0x8984,
+    0xCFBE, 0x8971,
+    0xCFEC, 0x895F,
+    0xD01B, 0x894C,
+    0xD04A, 0x8939,
+    0xD078, 0x8926,
+    0xD0A7, 0x8914,
+    0xD0D6, 0x8901,
+    0xD104, 0x88EF,
+    0xD133, 0x88DC,
+    0xD162, 0x88CA,
+    0xD191, 0x88B8,
+    0xD1C0, 0x88A5,
+    0xD1EE, 0x8893,
+    0xD21D, 0x8881,
+    0xD24C, 0x886F,
+    0xD27B, 0x885D,
+    0xD2AA, 0x884B,
+    0xD2D9, 0x883A,
+    0xD308, 0x8828,
+    0xD337, 0x8816,
+    0xD367, 0x8805,
+    0xD396, 0x87F3,
+    0xD3C5, 0x87E2,
+    0xD3F4, 0x87D1,
+    0xD423, 0x87BF,
+    0xD452, 0x87AE,
+    0xD482, 0x879D,
+    0xD4B1, 0x878C,
+    0xD4E0, 0x877B,
+    0xD510, 0x876A,
+    0xD53F, 0x8759,
+    0xD56E, 0x8749,
+    0xD59E, 0x8738,
+    0xD5CD, 0x8727,
+    0xD5FD, 0x8717,
+    0xD62C, 0x8706,
+    0xD65C, 0x86F6,
+    0xD68B, 0x86E6,
+    0xD6BB, 0x86D5,
+    0xD6EA, 0x86C5,
+    0xD71A, 0x86B5,
+    0xD74A, 0x86A5,
+    0xD779, 0x8695,
+    0xD7A9, 0x8685,
+    0xD7D9, 0x8675,
+    0xD809, 0x8666,
+    0xD838, 0x8656,
+    0xD868, 0x8646,
+    0xD898, 0x8637,
+    0xD8C8, 0x8627,
+    0xD8F8, 0x8618,
+    0xD927, 0x8609,
+    0xD957, 0x85FA,
+    0xD987, 0x85EA,
+    0xD9B7, 0x85DB,
+    0xD9E7, 0x85CC,
+    0xDA17, 0x85BD,
+    0xDA47, 0x85AF,
+    0xDA77, 0x85A0,
+    0xDAA7, 0x8591,
+    0xDAD7, 0x8582,
+    0xDB08, 0x8574,
+    0xDB38, 0x8565,
+    0xDB68, 0x8557,
+    0xDB98, 0x8549,
+    0xDBC8, 0x853A,
+    0xDBF8, 0x852C,
+    0xDC29, 0x851E,
+    0xDC59, 0x8510,
+    0xDC89, 0x8502,
+    0xDCBA, 0x84F4,
+    0xDCEA, 0x84E6,
+    0xDD1A, 0x84D9,
+    0xDD4B, 0x84CB,
+    0xDD7B, 0x84BD,
+    0xDDAB, 0x84B0,
+    0xDDDC, 0x84A2,
+    0xDE0C, 0x8495,
+    0xDE3D, 0x8488,
+    0xDE6D, 0x847B,
+    0xDE9E, 0x846D,
+    0xDECE, 0x8460,
+    0xDEFF, 0x8453,
+    0xDF2F, 0x8446,
+    0xDF60, 0x843A,
+    0xDF91, 0x842D,
+    0xDFC1, 0x8420,
+    0xDFF2, 0x8414,
+    0xE023, 0x8407,
+    0xE053, 0x83FA,
+    0xE084, 0x83EE,
+    0xE0B5, 0x83E2,
+    0xE0E6, 0x83D6,
+    0xE116, 0x83C9,
+    0xE147, 0x83BD,
+    0xE178, 0x83B1,
+    0xE1A9, 0x83A5,
+    0xE1DA, 0x8399,
+    0xE20A, 0x838E,
+    0xE23B, 0x8382,
+    0xE26C, 0x8376,
+    0xE29D, 0x836B,
+    0xE2CE, 0x835F,
+    0xE2FF, 0x8354,
+    0xE330, 0x8348,
+    0xE361, 0x833D,
+    0xE392, 0x8332,
+    0xE3C3, 0x8327,
+    0xE3F4, 0x831C,
+    0xE425, 0x8311,
+    0xE456, 0x8306,
+    0xE487, 0x82FB,
+    0xE4B8, 0x82F0,
+    0xE4E9, 0x82E6,
+    0xE51B, 0x82DB,
+    0xE54C, 0x82D0,
+    0xE57D, 0x82C6,
+    0xE5AE, 0x82BC,
+    0xE5DF, 0x82B1,
+    0xE610, 0x82A7,
+    0xE642, 0x829D,
+    0xE673, 0x8293,
+    0xE6A4, 0x8289,
+    0xE6D5, 0x827F,
+    0xE707, 0x8275,
+    0xE738, 0x826B,
+    0xE769, 0x8262,
+    0xE79B, 0x8258,
+    0xE7CC, 0x824F,
+    0xE7FD, 0x8245,
+    0xE82F, 0x823C,
+    0xE860, 0x8232,
+    0xE892, 0x8229,
+    0xE8C3, 0x8220,
+    0xE8F5, 0x8217,
+    0xE926, 0x820E,
+    0xE957, 0x8205,
+    0xE989, 0x81FC,
+    0xE9BA, 0x81F3,
+    0xE9EC, 0x81EB,
+    0xEA1D, 0x81E2,
+    0xEA4F, 0x81D9,
+    0xEA80, 0x81D1,
+    0xEAB2, 0x81C8,
+    0xEAE4, 0x81C0,
+    0xEB15, 0x81B8,
+    0xEB47, 0x81B0,
+    0xEB78, 0x81A8,
+    0xEBAA, 0x81A0,
+    0xEBDC, 0x8198,
+    0xEC0D, 0x8190,
+    0xEC3F, 0x8188,
+    0xEC71, 0x8180,
+    0xECA2, 0x8179,
+    0xECD4, 0x8171,
+    0xED06, 0x816A,
+    0xED37, 0x8162,
+    0xED69, 0x815B,
+    0xED9B, 0x8154,
+    0xEDCD, 0x814C,
+    0xEDFE, 0x8145,
+    0xEE30, 0x813E,
+    0xEE62, 0x8137,
+    0xEE94, 0x8130,
+    0xEEC6, 0x812A,
+    0xEEF7, 0x8123,
+    0xEF29, 0x811C,
+    0xEF5B, 0x8116,
+    0xEF8D, 0x810F,
+    0xEFBF, 0x8109,
+    0xEFF1, 0x8102,
+    0xF022, 0x80FC,
+    0xF054, 0x80F6,
+    0xF086, 0x80F0,
+    0xF0B8, 0x80EA,
+    0xF0EA, 0x80E4,
+    0xF11C, 0x80DE,
+    0xF14E, 0x80D8,
+    0xF180, 0x80D2,
+    0xF1B2, 0x80CD,
+    0xF1E4, 0x80C7,
+    0xF216, 0x80C2,
+    0xF248, 0x80BC,
+    0xF27A, 0x80B7,
+    0xF2AC, 0x80B2,
+    0xF2DE, 0x80AC,
+    0xF310, 0x80A7,
+    0xF342, 0x80A2,
+    0xF374, 0x809D,
+    0xF3A6, 0x8098,
+    0xF3D8, 0x8094,
+    0xF40A, 0x808F,
+    0xF43C, 0x808A,
+    0xF46E, 0x8086,
+    0xF4A0, 0x8081,
+    0xF4D2, 0x807D,
+    0xF504, 0x8078,
+    0xF536, 0x8074,
+    0xF568, 0x8070,
+    0xF59A, 0x806C,
+    0xF5CC, 0x8068,
+    0xF5FF, 0x8064,
+    0xF631, 0x8060,
+    0xF663, 0x805C,
+    0xF695, 0x8058,
+    0xF6C7, 0x8055,
+    0xF6F9, 0x8051,
+    0xF72B, 0x804E,
+    0xF75D, 0x804A,
+    0xF790, 0x8047,
+    0xF7C2, 0x8043,
+    0xF7F4, 0x8040,
+    0xF826, 0x803D,
+    0xF858, 0x803A,
+    0xF88A, 0x8037,
+    0xF8BD, 0x8034,
+    0xF8EF, 0x8031,
+    0xF921, 0x802F,
+    0xF953, 0x802C,
+    0xF985, 0x8029,
+    0xF9B8, 0x8027,
+    0xF9EA, 0x8025,
+    0xFA1C, 0x8022,
+    0xFA4E, 0x8020,
+    0xFA80, 0x801E,
+    0xFAB3, 0x801C,
+    0xFAE5, 0x801A,
+    0xFB17, 0x8018,
+    0xFB49, 0x8016,
+    0xFB7C, 0x8014,
+    0xFBAE, 0x8012,
+    0xFBE0, 0x8011,
+    0xFC12, 0x800F,
+    0xFC45, 0x800D,
+    0xFC77, 0x800C,
+    0xFCA9, 0x800B,
+    0xFCDB, 0x8009,
+    0xFD0E, 0x8008,
+    0xFD40, 0x8007,
+    0xFD72, 0x8006,
+    0xFDA4, 0x8005,
+    0xFDD7, 0x8004,
+    0xFE09, 0x8003,
+    0xFE3B, 0x8003,
+    0xFE6D, 0x8002,
+    0xFEA0, 0x8001,
+    0xFED2, 0x8001,
+    0xFF04, 0x8000,
+    0xFF36, 0x8000,
+    0xFF69, 0x8000,
+    0xFF9B, 0x8000,
+    0xFFCD, 0x8000
+};
+
+
+/**    
+* @} end of CFFT_CIFFT group    
+*/
+
+/*    
+* @brief  Q15 table for reciprocal    
+*/
+const q15_t ALIGN4 armRecipTableQ15[64] = {
+ 0x7F03, 0x7D13, 0x7B31, 0x795E, 0x7798, 0x75E0,
+ 0x7434, 0x7294, 0x70FF, 0x6F76, 0x6DF6, 0x6C82,
+ 0x6B16, 0x69B5, 0x685C, 0x670C, 0x65C4, 0x6484,
+ 0x634C, 0x621C, 0x60F3, 0x5FD0, 0x5EB5, 0x5DA0,
+ 0x5C91, 0x5B88, 0x5A85, 0x5988, 0x5890, 0x579E,
+ 0x56B0, 0x55C8, 0x54E4, 0x5405, 0x532B, 0x5255,
+ 0x5183, 0x50B6, 0x4FEC, 0x4F26, 0x4E64, 0x4DA6,
+ 0x4CEC, 0x4C34, 0x4B81, 0x4AD0, 0x4A23, 0x4978,
+ 0x48D1, 0x482D, 0x478C, 0x46ED, 0x4651, 0x45B8,
+ 0x4521, 0x448D, 0x43FC, 0x436C, 0x42DF, 0x4255,
+ 0x41CC, 0x4146, 0x40C2, 0x4040
+};
+
+/*    
+* @brief  Q31 table for reciprocal    
+*/
+const q31_t armRecipTableQ31[64] = {
+  0x7F03F03F, 0x7D137420, 0x7B31E739, 0x795E9F94, 0x7798FD29, 0x75E06928,
+  0x7434554D, 0x72943B4B, 0x70FF9C40, 0x6F760031, 0x6DF6F593, 0x6C8210E3,
+  0x6B16EC3A, 0x69B526F6, 0x685C655F, 0x670C505D, 0x65C4952D, 0x6484E519,
+  0x634CF53E, 0x621C7E4F, 0x60F33C61, 0x5FD0EEB3, 0x5EB55785, 0x5DA03BEB,
+  0x5C9163A1, 0x5B8898E6, 0x5A85A85A, 0x598860DF, 0x58909373, 0x579E1318,
+  0x56B0B4B8, 0x55C84F0B, 0x54E4BA80, 0x5405D124, 0x532B6E8F, 0x52556FD0,
+  0x5183B35A, 0x50B618F3, 0x4FEC81A2, 0x4F26CFA2, 0x4E64E64E, 0x4DA6AA1D,
+  0x4CEC008B, 0x4C34D010, 0x4B810016, 0x4AD078EF, 0x4A2323C4, 0x4978EA96,
+  0x48D1B827, 0x482D77FE, 0x478C1657, 0x46ED801D, 0x4651A2E5, 0x45B86CE2,
+  0x4521CCE1, 0x448DB244, 0x43FC0CFA, 0x436CCD78, 0x42DFE4B4, 0x42554426,
+  0x41CCDDB6, 0x4146A3C6, 0x40C28923, 0x40408102
+};
+
+const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE__16_TABLE_LENGTH] = 
+{
+   //8x2, size 20
+   8,64, 24,72, 16,64, 40,80, 32,64, 56,88, 48,72, 88,104, 72,96, 104,112
+};
+
+const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE__32_TABLE_LENGTH] = 
+{
+   //8x4, size 48
+   8,64, 16,128, 24,192, 32,64, 40,72, 48,136, 56,200, 64,128, 72,80, 88,208,
+   80,144, 96,192, 104,208, 112,152, 120,216, 136,192, 144,160, 168,208,
+   152,224, 176,208, 184,232, 216,240, 200,224, 232,240
+};
+
+const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE__64_TABLE_LENGTH] = 
+{   
+   //radix 8, size 56
+   8,64, 16,128, 24,192, 32,256, 40,320, 48,384, 56,448, 80,136, 88,200, 
+   96,264, 104,328, 112,392, 120,456, 152,208, 160,272, 168,336, 176,400, 
+   184,464, 224,280, 232,344, 240,408, 248,472, 296,352, 304,416, 312,480, 
+   368,424, 376,488, 440,496
+};
+
+const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH] = 
+{
+   //8x2, size 208
+   8,512, 16,64, 24,576, 32,128, 40,640, 48,192, 56,704, 64,256, 72,768, 
+   80,320, 88,832, 96,384, 104,896, 112,448, 120,960, 128,512, 136,520, 
+   144,768, 152,584, 160,520, 168,648, 176,200, 184,712, 192,264, 200,776, 
+   208,328, 216,840, 224,392, 232,904, 240,456, 248,968, 264,528, 272,320, 
+   280,592, 288,768, 296,656, 304,328, 312,720, 328,784, 344,848, 352,400, 
+   360,912, 368,464, 376,976, 384,576, 392,536, 400,832, 408,600, 416,584, 
+   424,664, 432,840, 440,728, 448,592, 456,792, 464,848, 472,856, 480,600, 
+   488,920, 496,856, 504,984, 520,544, 528,576, 536,608, 552,672, 560,608, 
+   568,736, 576,768, 584,800, 592,832, 600,864, 608,800, 616,928, 624,864, 
+   632,992, 648,672, 656,896, 664,928, 688,904, 696,744, 704,896, 712,808, 
+   720,912, 728,872, 736,928, 744,936, 752,920, 760,1000, 776,800, 784,832, 
+   792,864, 808,904, 816,864, 824,920, 840,864, 856,880, 872,944, 888,1008, 
+   904,928, 912,960, 920,992, 944,968, 952,1000, 968,992, 984,1008
+};
+
+const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH] = 
+{
+   //8x4, size 440
+   8,512, 16,1024, 24,1536, 32,64, 40,576, 48,1088, 56,1600, 64,128, 72,640, 
+   80,1152, 88,1664, 96,192, 104,704, 112,1216, 120,1728, 128,256, 136,768, 
+   144,1280, 152,1792, 160,320, 168,832, 176,1344, 184,1856, 192,384, 
+   200,896, 208,1408, 216,1920, 224,448, 232,960, 240,1472, 248,1984, 
+   256,512, 264,520, 272,1032, 280,1544, 288,640, 296,584, 304,1096, 312,1608, 
+   320,768, 328,648, 336,1160, 344,1672, 352,896, 360,712, 368,1224, 376,1736, 
+   384,520, 392,776, 400,1288, 408,1800, 416,648, 424,840, 432,1352, 440,1864, 
+   448,776, 456,904, 464,1416, 472,1928, 480,904, 488,968, 496,1480, 504,1992, 
+   520,528, 512,1024, 528,1040, 536,1552, 544,1152, 552,592, 560,1104, 
+   568,1616, 576,1280, 584,656, 592,1168, 600,1680, 608,1408, 616,720, 
+   624,1232, 632,1744, 640,1032, 648,784, 656,1296, 664,1808, 672,1160, 
+   680,848, 688,1360, 696,1872, 704,1288, 712,912, 720,1424, 728,1936, 
+   736,1416, 744,976, 752,1488, 760,2000, 768,1536, 776,1552, 784,1048, 
+   792,1560, 800,1664, 808,1680, 816,1112, 824,1624, 832,1792, 840,1808, 
+   848,1176, 856,1688, 864,1920, 872,1936, 880,1240, 888,1752, 896,1544, 
+   904,1560, 912,1304, 920,1816, 928,1672, 936,1688, 944,1368, 952,1880, 
+   960,1800, 968,1816, 976,1432, 984,1944, 992,1928, 1000,1944, 1008,1496, 
+   1016,2008, 1032,1152, 1040,1056, 1048,1568, 1064,1408, 1072,1120, 
+   1080,1632, 1088,1536, 1096,1160, 1104,1184, 1112,1696, 1120,1552, 
+   1128,1416, 1136,1248, 1144,1760, 1160,1664, 1168,1312, 1176,1824, 
+   1184,1544, 1192,1920, 1200,1376, 1208,1888, 1216,1568, 1224,1672, 
+   1232,1440, 1240,1952, 1248,1560, 1256,1928, 1264,1504, 1272,2016, 
+   1288,1312, 1296,1408, 1304,1576, 1320,1424, 1328,1416, 1336,1640, 
+   1344,1792, 1352,1824, 1360,1920, 1368,1704, 1376,1800, 1384,1432, 
+   1392,1928, 1400,1768, 1416,1680, 1432,1832, 1440,1576, 1448,1936, 
+   1456,1832, 1464,1896, 1472,1808, 1480,1688, 1488,1936, 1496,1960, 
+   1504,1816, 1512,1944, 1520,1944, 1528,2024, 1560,1584, 1592,1648, 
+   1600,1792, 1608,1920, 1616,1800, 1624,1712, 1632,1808, 1640,1936, 
+   1648,1816, 1656,1776, 1672,1696, 1688,1840, 1704,1952, 1712,1928, 
+   1720,1904, 1728,1824, 1736,1952, 1744,1832, 1752,1968, 1760,1840, 
+   1768,1960, 1776,1944, 1784,2032, 1864,1872, 1848,1944, 1872,1888, 
+   1880,1904, 1888,1984, 1896,2000, 1912,2032, 1904,2016, 1976,2032,
+   1960,1968, 2008,2032, 1992,2016, 2024,2032
+};
+
+const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH] = 
+{
+   //radix 8, size 448
+   8,512, 16,1024, 24,1536, 32,2048, 40,2560, 48,3072, 56,3584, 72,576, 
+   80,1088, 88,1600, 96,2112, 104,2624, 112,3136, 120,3648, 136,640, 144,1152, 
+   152,1664, 160,2176, 168,2688, 176,3200, 184,3712, 200,704, 208,1216, 
+   216,1728, 224,2240, 232,2752, 240,3264, 248,3776, 264,768, 272,1280, 
+   280,1792, 288,2304, 296,2816, 304,3328, 312,3840, 328,832, 336,1344, 
+   344,1856, 352,2368, 360,2880, 368,3392, 376,3904, 392,896, 400,1408, 
+   408,1920, 416,2432, 424,2944, 432,3456, 440,3968, 456,960, 464,1472, 
+   472,1984, 480,2496, 488,3008, 496,3520, 504,4032, 528,1032, 536,1544, 
+   544,2056, 552,2568, 560,3080, 568,3592, 592,1096, 600,1608, 608,2120, 
+   616,2632, 624,3144, 632,3656, 656,1160, 664,1672, 672,2184, 680,2696, 
+   688,3208, 696,3720, 720,1224, 728,1736, 736,2248, 744,2760, 752,3272, 
+   760,3784, 784,1288, 792,1800, 800,2312, 808,2824, 816,3336, 824,3848, 
+   848,1352, 856,1864, 864,2376, 872,2888, 880,3400, 888,3912, 912,1416, 
+   920,1928, 928,2440, 936,2952, 944,3464, 952,3976, 976,1480, 984,1992, 
+   992,2504, 1000,3016, 1008,3528, 1016,4040, 1048,1552, 1056,2064, 1064,2576, 
+   1072,3088, 1080,3600, 1112,1616, 1120,2128, 1128,2640, 1136,3152, 
+   1144,3664, 1176,1680, 1184,2192, 1192,2704, 1200,3216, 1208,3728, 
+   1240,1744, 1248,2256, 1256,2768, 1264,3280, 1272,3792, 1304,1808, 
+   1312,2320, 1320,2832, 1328,3344, 1336,3856, 1368,1872, 1376,2384, 
+   1384,2896, 1392,3408, 1400,3920, 1432,1936, 1440,2448, 1448,2960, 
+   1456,3472, 1464,3984, 1496,2000, 1504,2512, 1512,3024, 1520,3536, 
+   1528,4048, 1568,2072, 1576,2584, 1584,3096, 1592,3608, 1632,2136, 
+   1640,2648, 1648,3160, 1656,3672, 1696,2200, 1704,2712, 1712,3224, 
+   1720,3736, 1760,2264, 1768,2776, 1776,3288, 1784,3800, 1824,2328, 
+   1832,2840, 1840,3352, 1848,3864, 1888,2392, 1896,2904, 1904,3416, 
+   1912,3928, 1952,2456, 1960,2968, 1968,3480, 1976,3992, 2016,2520, 
+   2024,3032, 2032,3544, 2040,4056, 2088,2592, 2096,3104, 2104,3616, 
+   2152,2656, 2160,3168, 2168,3680, 2216,2720, 2224,3232, 2232,3744, 
+   2280,2784, 2288,3296, 2296,3808, 2344,2848, 2352,3360, 2360,3872, 
+   2408,2912, 2416,3424, 2424,3936, 2472,2976, 2480,3488, 2488,4000, 
+   2536,3040, 2544,3552, 2552,4064, 2608,3112, 2616,3624, 2672,3176, 
+   2680,3688, 2736,3240, 2744,3752, 2800,3304, 2808,3816, 2864,3368, 
+   2872,3880, 2928,3432, 2936,3944, 2992,3496, 3000,4008, 3056,3560, 
+   3064,4072, 3128,3632, 3192,3696, 3256,3760, 3320,3824, 3384,3888, 
+   3448,3952, 3512,4016, 3576,4080
+};
+
+const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE1024_TABLE_LENGTH] = 
+{
+   //8x2, size 1800
+   8,4096, 16,512, 24,4608, 32,1024, 40,5120, 48,1536, 56,5632, 64,2048, 
+   72,6144, 80,2560, 88,6656, 96,3072, 104,7168, 112,3584, 120,7680, 128,2048, 
+   136,4160, 144,576, 152,4672, 160,1088, 168,5184, 176,1600, 184,5696, 
+   192,2112, 200,6208, 208,2624, 216,6720, 224,3136, 232,7232, 240,3648, 
+   248,7744, 256,2048, 264,4224, 272,640, 280,4736, 288,1152, 296,5248, 
+   304,1664, 312,5760, 320,2176, 328,6272, 336,2688, 344,6784, 352,3200, 
+   360,7296, 368,3712, 376,7808, 384,2112, 392,4288, 400,704, 408,4800, 
+   416,1216, 424,5312, 432,1728, 440,5824, 448,2240, 456,6336, 464,2752, 
+   472,6848, 480,3264, 488,7360, 496,3776, 504,7872, 512,2048, 520,4352, 
+   528,768, 536,4864, 544,1280, 552,5376, 560,1792, 568,5888, 576,2304, 
+   584,6400, 592,2816, 600,6912, 608,3328, 616,7424, 624,3840, 632,7936, 
+   640,2176, 648,4416, 656,832, 664,4928, 672,1344, 680,5440, 688,1856, 
+   696,5952, 704,2368, 712,6464, 720,2880, 728,6976, 736,3392, 744,7488, 
+   752,3904, 760,8000, 768,2112, 776,4480, 784,896, 792,4992, 800,1408, 
+   808,5504, 816,1920, 824,6016, 832,2432, 840,6528, 848,2944, 856,7040, 
+   864,3456, 872,7552, 880,3968, 888,8064, 896,2240, 904,4544, 912,960, 
+   920,5056, 928,1472, 936,5568, 944,1984, 952,6080, 960,2496, 968,6592, 
+   976,3008, 984,7104, 992,3520, 1000,7616, 1008,4032, 1016,8128, 1024,4096, 
+   1032,4104, 1040,4352, 1048,4616, 1056,4104, 1064,5128, 1072,1544, 
+   1080,5640, 1088,2056, 1096,6152, 1104,2568, 1112,6664, 1120,3080, 
+   1128,7176, 1136,3592, 1144,7688, 1152,6144, 1160,4168, 1168,6400, 
+   1176,4680, 1184,6152, 1192,5192, 1200,1608, 1208,5704, 1216,2120, 
+   1224,6216, 1232,2632, 1240,6728, 1248,3144, 1256,7240, 1264,3656, 
+   1272,7752, 1280,4160, 1288,4232, 1296,4416, 1304,4744, 1312,4168, 
+   1320,5256, 1328,1672, 1336,5768, 1344,2184, 1352,6280, 1360,2696, 
+   1368,6792, 1376,3208, 1384,7304, 1392,3720, 1400,7816, 1408,6208, 
+   1416,4296, 1424,6464, 1432,4808, 1440,6216, 1448,5320, 1456,1736, 
+   1464,5832, 1472,2248, 1480,6344, 1488,2760, 1496,6856, 1504,3272, 
+   1512,7368, 1520,3784, 1528,7880, 1536,4224, 1544,4360, 1552,4480, 
+   1560,4872, 1568,4232, 1576,5384, 1584,1800, 1592,5896, 1600,2312, 
+   1608,6408, 1616,2824, 1624,6920, 1632,3336, 1640,7432, 1648,3848, 
+   1656,7944, 1664,6272, 1672,4424, 1680,6528, 1688,4936, 1696,6280, 
+   1704,5448, 1712,1864, 1720,5960, 1728,2376, 1736,6472, 1744,2888, 
+   1752,6984, 1760,3400, 1768,7496, 1776,3912, 1784,8008, 1792,4288, 
+   1800,4488, 1808,4544, 1816,5000, 1824,4296, 1832,5512, 1840,1928, 
+   1848,6024, 1856,2440, 1864,6536, 1872,2952, 1880,7048, 1888,3464, 
+   1896,7560, 1904,3976, 1912,8072, 1920,6336, 1928,4552, 1936,6592, 
+   1944,5064, 1952,6344, 1960,5576, 1968,1992, 1976,6088, 1984,2504, 
+   1992,6600, 2000,3016, 2008,7112, 2016,3528, 2024,7624, 2032,4040, 
+   2040,8136, 2056,4112, 2064,2112, 2072,4624, 2080,4352, 2088,5136, 
+   2096,4480, 2104,5648, 2120,6160, 2128,2576, 2136,6672, 2144,3088, 
+   2152,7184, 2160,3600, 2168,7696, 2176,2560, 2184,4176, 2192,2816, 
+   2200,4688, 2208,2568, 2216,5200, 2224,2824, 2232,5712, 2240,2576, 
+   2248,6224, 2256,2640, 2264,6736, 2272,3152, 2280,7248, 2288,3664, 
+   2296,7760, 2312,4240, 2320,2432, 2328,4752, 2336,6400, 2344,5264, 
+   2352,6528, 2360,5776, 2368,2816, 2376,6288, 2384,2704, 2392,6800, 
+   2400,3216, 2408,7312, 2416,3728, 2424,7824, 2432,2624, 2440,4304, 
+   2448,2880, 2456,4816, 2464,2632, 2472,5328, 2480,2888, 2488,5840, 
+   2496,2640, 2504,6352, 2512,2768, 2520,6864, 2528,3280, 2536,7376, 
+   2544,3792, 2552,7888, 2568,4368, 2584,4880, 2592,4416, 2600,5392, 
+   2608,4544, 2616,5904, 2632,6416, 2640,2832, 2648,6928, 2656,3344, 
+   2664,7440, 2672,3856, 2680,7952, 2696,4432, 2704,2944, 2712,4944, 
+   2720,4432, 2728,5456, 2736,2952, 2744,5968, 2752,2944, 2760,6480, 
+   2768,2896, 2776,6992, 2784,3408, 2792,7504, 2800,3920, 2808,8016, 
+   2824,4496, 2840,5008, 2848,6464, 2856,5520, 2864,6592, 2872,6032, 
+   2888,6544, 2896,2960, 2904,7056, 2912,3472, 2920,7568, 2928,3984, 
+   2936,8080, 2952,4560, 2960,3008, 2968,5072, 2976,6480, 2984,5584, 
+   2992,3016, 3000,6096, 3016,6608, 3032,7120, 3040,3536, 3048,7632, 
+   3056,4048, 3064,8144, 3072,4608, 3080,4120, 3088,4864, 3096,4632, 
+   3104,4616, 3112,5144, 3120,4872, 3128,5656, 3136,4624, 3144,6168, 
+   3152,4880, 3160,6680, 3168,4632, 3176,7192, 3184,3608, 3192,7704, 
+   3200,6656, 3208,4184, 3216,6912, 3224,4696, 3232,6664, 3240,5208, 
+   3248,6920, 3256,5720, 3264,6672, 3272,6232, 3280,6928, 3288,6744, 
+   3296,6680, 3304,7256, 3312,3672, 3320,7768, 3328,4672, 3336,4248, 
+   3344,4928, 3352,4760, 3360,4680, 3368,5272, 3376,4936, 3384,5784, 
+   3392,4688, 3400,6296, 3408,4944, 3416,6808, 3424,4696, 3432,7320, 
+   3440,3736, 3448,7832, 3456,6720, 3464,4312, 3472,6976, 3480,4824, 
+   3488,6728, 3496,5336, 3504,6984, 3512,5848, 3520,6736, 3528,6360, 
+   3536,6992, 3544,6872, 3552,6744, 3560,7384, 3568,3800, 3576,7896, 
+   3584,4736, 3592,4376, 3600,4992, 3608,4888, 3616,4744, 3624,5400, 
+   3632,5000, 3640,5912, 3648,4752, 3656,6424, 3664,5008, 3672,6936, 
+   3680,4760, 3688,7448, 3696,3864, 3704,7960, 3712,6784, 3720,4440, 
+   3728,7040, 3736,4952, 3744,6792, 3752,5464, 3760,7048, 3768,5976, 
+   3776,6800, 3784,6488, 3792,7056, 3800,7000, 3808,6808, 3816,7512, 
+   3824,3928, 3832,8024, 3840,4800, 3848,4504, 3856,5056, 3864,5016, 
+   3872,4808, 3880,5528, 3888,5064, 3896,6040, 3904,4816, 3912,6552, 
+   3920,5072, 3928,7064, 3936,4824, 3944,7576, 3952,3992, 3960,8088, 
+   3968,6848, 3976,4568, 3984,7104, 3992,5080, 4000,6856, 4008,5592, 
+   4016,7112, 4024,6104, 4032,6864, 4040,6616, 4048,7120, 4056,7128, 
+   4064,6872, 4072,7640, 4080,7128, 4088,8152, 4104,4128, 4112,4160, 
+   4120,4640, 4136,5152, 4144,4232, 4152,5664, 4160,4352, 4168,6176, 
+   4176,4416, 4184,6688, 4192,4616, 4200,7200, 4208,4744, 4216,7712, 
+   4224,4608, 4232,4616, 4240,4672, 4248,4704, 4256,4640, 4264,5216, 
+   4272,4704, 4280,5728, 4288,4864, 4296,6240, 4304,4928, 4312,6752, 
+   4320,4632, 4328,7264, 4336,4760, 4344,7776, 4360,4640, 4368,4416, 
+   4376,4768, 4384,6152, 4392,5280, 4400,6280, 4408,5792, 4424,6304, 
+   4440,6816, 4448,6664, 4456,7328, 4464,6792, 4472,7840, 4480,4624, 
+   4488,4632, 4496,4688, 4504,4832, 4512,6168, 4520,5344, 4528,6296, 
+   4536,5856, 4544,4880, 4552,6368, 4560,4944, 4568,6880, 4576,6680, 
+   4584,7392, 4592,6808, 4600,7904, 4608,6144, 4616,6152, 4624,6208, 
+   4632,4896, 4640,6176, 4648,5408, 4656,6240, 4664,5920, 4672,6400, 
+   4680,6432, 4688,6464, 4696,6944, 4704,6432, 4712,7456, 4720,4808, 
+   4728,7968, 4736,6656, 4744,6664, 4752,6720, 4760,4960, 4768,6688, 
+   4776,5472, 4784,6752, 4792,5984, 4800,6912, 4808,6496, 4816,6976, 
+   4824,7008, 4832,6944, 4840,7520, 4848,7008, 4856,8032, 4864,6160, 
+   4872,6168, 4880,6224, 4888,5024, 4896,6216, 4904,5536, 4912,6344, 
+   4920,6048, 4928,6416, 4936,6560, 4944,6480, 4952,7072, 4960,6728, 
+   4968,7584, 4976,6856, 4984,8096, 4992,6672, 5000,6680, 5008,6736, 
+   5016,5088, 5024,6232, 5032,5600, 5040,6360, 5048,6112, 5056,6928, 
+   5064,6624, 5072,6992, 5080,7136, 5088,6744, 5096,7648, 5104,6872, 
+   5112,8160, 5128,5152, 5136,5376, 5144,5408, 5168,5384, 5176,5672, 
+   5184,5376, 5192,6184, 5200,5392, 5208,6696, 5216,5408, 5224,7208, 
+   5232,5400, 5240,7720, 5248,7168, 5256,7200, 5264,7424, 5272,7456, 
+   5280,7176, 5288,7208, 5296,7432, 5304,5736, 5312,7184, 5320,6248, 
+   5328,7440, 5336,6760, 5344,7192, 5352,7272, 5360,7448, 5368,7784, 
+   5384,5408, 5392,5440, 5400,5472, 5408,6184, 5416,7208, 5424,5448, 
+   5432,5800, 5448,6312, 5464,6824, 5472,6696, 5480,7336, 5488,6824, 
+   5496,7848, 5504,7232, 5512,7264, 5520,7488, 5528,7520, 5536,7240, 
+   5544,7272, 5552,7496, 5560,5864, 5568,7248, 5576,6376, 5584,7504, 
+   5592,6888, 5600,7256, 5608,7400, 5616,7512, 5624,7912, 5632,7168, 
+   5640,7176, 5648,7232, 5656,7240, 5664,7200, 5672,7208, 5680,7264, 
+   5688,5928, 5696,7424, 5704,6440, 5712,7488, 5720,6952, 5728,7456, 
+   5736,7464, 5744,7520, 5752,7976, 5760,7296, 5768,7328, 5776,7552, 
+   5784,7584, 5792,7304, 5800,7336, 5808,7560, 5816,5992, 5824,7312, 
+   5832,6504, 5840,7568, 5848,7016, 5856,7320, 5864,7528, 5872,7576, 
+   5880,8040, 5888,7184, 5896,7192, 5904,7248, 5912,7256, 5920,6248, 
+   5928,7272, 5936,6376, 5944,6056, 5952,7440, 5960,6568, 5968,7504, 
+   5976,7080, 5984,6760, 5992,7592, 6000,6888, 6008,8104, 6016,7360, 
+   6024,7392, 6032,7616, 6040,7648, 6048,7368, 6056,7400, 6064,7624, 
+   6072,6120, 6080,7376, 6088,6632, 6096,7632, 6104,7144, 6112,7384, 
+   6120,7656, 6128,7640, 6136,8168, 6168,6240, 6192,6216, 6200,7264, 
+   6232,6704, 6248,7216, 6256,6680, 6264,7728, 6272,6656, 6280,6664, 
+   6288,6912, 6296,6496, 6304,6688, 6312,6696, 6320,6944, 6328,7520, 
+   6336,6672, 6344,6680, 6352,6928, 6360,6768, 6368,6704, 6376,7280, 
+   6384,6744, 6392,7792, 6408,6432, 6424,6752, 6440,7432, 6448,6536, 
+   6456,7560, 6472,6944, 6488,6832, 6496,6920, 6504,7344, 6512,7048, 
+   6520,7856, 6528,6720, 6536,6728, 6544,6976, 6552,7008, 6560,6752, 
+   6568,7448, 6576,7008, 6584,7576, 6592,6736, 6600,6744, 6608,6992, 
+   6616,6896, 6624,6936, 6632,7408, 6640,7064, 6648,7920, 6712,7280, 
+   6744,6960, 6760,7472, 6768,6936, 6776,7984, 6800,6848, 6808,6856, 
+   6832,6880, 6840,6888, 6848,7040, 6856,7048, 6864,7104, 6872,7024, 
+   6880,7072, 6888,7536, 6896,7136, 6904,8048, 6952,7496, 6968,7624, 
+   6984,7008, 7000,7088, 7016,7600, 7024,7112, 7032,8112, 7056,7104, 
+   7064,7112, 7080,7512, 7088,7136, 7096,7640, 7128,7152, 7144,7664, 
+   7160,8176, 7176,7200, 7192,7216, 7224,7272, 7240,7264, 7256,7280, 
+   7288,7736, 7296,7680, 7304,7712, 7312,7936, 7320,7968, 7328,7688, 
+   7336,7720, 7344,7944, 7352,7976, 7360,7696, 7368,7728, 7376,7952, 
+   7384,7984, 7392,7704, 7400,7736, 7408,7960, 7416,7800, 7432,7456, 
+   7448,7472, 7480,7592, 7496,7520, 7512,7536, 7528,7976, 7544,7864, 
+   7552,7744, 7560,7776, 7568,8000, 7576,8032, 7584,7752, 7592,7784, 
+   7600,8008, 7608,8040, 7616,7760, 7624,7792, 7632,8016, 7640,8048, 
+   7648,7768, 7656,7800, 7664,8024, 7672,7928, 7688,7712, 7704,7728, 
+   7752,7776, 7768,7792, 7800,7992, 7816,7840, 7824,8064, 7832,8096, 
+   7856,8072, 7864,8104, 7872,8064, 7880,8072, 7888,8080, 7896,8112, 
+   7904,8096, 7912,8104, 7920,8088, 7928,8056, 7944,7968, 7960,7984, 
+   8008,8032, 8024,8048, 8056,8120, 8072,8096, 8080,8128, 8088,8160, 
+   8112,8136, 8120,8168, 8136,8160, 8152,8176
+};
+
+const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE2048_TABLE_LENGTH] = 
+{
+   //8x2, size 3808
+   8,4096, 16,8192, 24,12288, 32,512, 40,4608, 48,8704, 56,12800, 64,1024, 
+   72,5120, 80,9216, 88,13312, 96,1536, 104,5632, 112,9728, 120,13824, 
+   128,2048, 136,6144, 144,10240, 152,14336, 160,2560, 168,6656, 176,10752, 
+   184,14848, 192,3072, 200,7168, 208,11264, 216,15360, 224,3584, 232,7680, 
+   240,11776, 248,15872, 256,1024, 264,4160, 272,8256, 280,12352, 288,576, 
+   296,4672, 304,8768, 312,12864, 320,1088, 328,5184, 336,9280, 344,13376, 
+   352,1600, 360,5696, 368,9792, 376,13888, 384,2112, 392,6208, 400,10304, 
+   408,14400, 416,2624, 424,6720, 432,10816, 440,14912, 448,3136, 456,7232, 
+   464,11328, 472,15424, 480,3648, 488,7744, 496,11840, 504,15936, 512,2048, 
+   520,4224, 528,8320, 536,12416, 544,640, 552,4736, 560,8832, 568,12928, 
+   576,1152, 584,5248, 592,9344, 600,13440, 608,1664, 616,5760, 624,9856, 
+   632,13952, 640,2176, 648,6272, 656,10368, 664,14464, 672,2688, 680,6784, 
+   688,10880, 696,14976, 704,3200, 712,7296, 720,11392, 728,15488, 736,3712, 
+   744,7808, 752,11904, 760,16000, 768,3072, 776,4288, 784,8384, 792,12480, 
+   800,3200, 808,4800, 816,8896, 824,12992, 832,1216, 840,5312, 848,9408, 
+   856,13504, 864,1728, 872,5824, 880,9920, 888,14016, 896,2240, 904,6336, 
+   912,10432, 920,14528, 928,2752, 936,6848, 944,10944, 952,15040, 960,3264, 
+   968,7360, 976,11456, 984,15552, 992,3776, 1000,7872, 1008,11968, 1016,16064, 
+   1032,4352, 1040,8448, 1048,12544, 1056,3072, 1064,4864, 1072,8960, 
+   1080,13056, 1088,1280, 1096,5376, 1104,9472, 1112,13568, 1120,1792, 
+   1128,5888, 1136,9984, 1144,14080, 1152,2304, 1160,6400, 1168,10496, 
+   1176,14592, 1184,2816, 1192,6912, 1200,11008, 1208,15104, 1216,3328, 
+   1224,7424, 1232,11520, 1240,15616, 1248,3840, 1256,7936, 1264,12032, 
+   1272,16128, 1288,4416, 1296,8512, 1304,12608, 1312,3328, 1320,4928, 
+   1328,9024, 1336,13120, 1352,5440, 1360,9536, 1368,13632, 1376,1856, 
+   1384,5952, 1392,10048, 1400,14144, 1408,2368, 1416,6464, 1424,10560, 
+   1432,14656, 1440,2880, 1448,6976, 1456,11072, 1464,15168, 1472,3392, 
+   1480,7488, 1488,11584, 1496,15680, 1504,3904, 1512,8000, 1520,12096, 
+   1528,16192, 1536,2112, 1544,4480, 1552,8576, 1560,12672, 1568,2240, 
+   1576,4992, 1584,9088, 1592,13184, 1600,2368, 1608,5504, 1616,9600, 
+   1624,13696, 1632,1920, 1640,6016, 1648,10112, 1656,14208, 1664,2432, 
+   1672,6528, 1680,10624, 1688,14720, 1696,2944, 1704,7040, 1712,11136, 
+   1720,15232, 1728,3456, 1736,7552, 1744,11648, 1752,15744, 1760,3968, 
+   1768,8064, 1776,12160, 1784,16256, 1792,3136, 1800,4544, 1808,8640, 
+   1816,12736, 1824,3264, 1832,5056, 1840,9152, 1848,13248, 1856,3392, 
+   1864,5568, 1872,9664, 1880,13760, 1888,1984, 1896,6080, 1904,10176, 
+   1912,14272, 1920,2496, 1928,6592, 1936,10688, 1944,14784, 1952,3008, 
+   1960,7104, 1968,11200, 1976,15296, 1984,3520, 1992,7616, 2000,11712, 
+   2008,15808, 2016,4032, 2024,8128, 2032,12224, 2040,16320, 2048,4096, 
+   2056,4104, 2064,8200, 2072,12296, 2080,4224, 2088,4616, 2096,8712, 
+   2104,12808, 2112,4352, 2120,5128, 2128,9224, 2136,13320, 2144,4480, 
+   2152,5640, 2160,9736, 2168,13832, 2176,4104, 2184,6152, 2192,10248, 
+   2200,14344, 2208,2568, 2216,6664, 2224,10760, 2232,14856, 2240,3080, 
+   2248,7176, 2256,11272, 2264,15368, 2272,3592, 2280,7688, 2288,11784, 
+   2296,15880, 2304,5120, 2312,4168, 2320,8264, 2328,12360, 2336,5248, 
+   2344,4680, 2352,8776, 2360,12872, 2368,5376, 2376,5192, 2384,9288, 
+   2392,13384, 2400,5504, 2408,5704, 2416,9800, 2424,13896, 2432,5128, 
+   2440,6216, 2448,10312, 2456,14408, 2464,2632, 2472,6728, 2480,10824, 
+   2488,14920, 2496,3144, 2504,7240, 2512,11336, 2520,15432, 2528,3656, 
+   2536,7752, 2544,11848, 2552,15944, 2560,6144, 2568,4232, 2576,8328, 
+   2584,12424, 2592,6272, 2600,4744, 2608,8840, 2616,12936, 2624,6400, 
+   2632,5256, 2640,9352, 2648,13448, 2656,6528, 2664,5768, 2672,9864, 
+   2680,13960, 2688,6152, 2696,6280, 2704,10376, 2712,14472, 2720,6280, 
+   2728,6792, 2736,10888, 2744,14984, 2752,3208, 2760,7304, 2768,11400, 
+   2776,15496, 2784,3720, 2792,7816, 2800,11912, 2808,16008, 2816,7168, 
+   2824,4296, 2832,8392, 2840,12488, 2848,7296, 2856,4808, 2864,8904, 
+   2872,13000, 2880,7424, 2888,5320, 2896,9416, 2904,13512, 2912,7552, 
+   2920,5832, 2928,9928, 2936,14024, 2944,7176, 2952,6344, 2960,10440, 
+   2968,14536, 2976,7304, 2984,6856, 2992,10952, 3000,15048, 3008,3272, 
+   3016,7368, 3024,11464, 3032,15560, 3040,3784, 3048,7880, 3056,11976, 
+   3064,16072, 3072,4160, 3080,4360, 3088,8456, 3096,12552, 3104,4288, 
+   3112,4872, 3120,8968, 3128,13064, 3136,4416, 3144,5384, 3152,9480, 
+   3160,13576, 3168,4544, 3176,5896, 3184,9992, 3192,14088, 3200,4168, 
+   3208,6408, 3216,10504, 3224,14600, 3232,4296, 3240,6920, 3248,11016, 
+   3256,15112, 3264,3336, 3272,7432, 3280,11528, 3288,15624, 3296,3848, 
+   3304,7944, 3312,12040, 3320,16136, 3328,5184, 3336,4424, 3344,8520, 
+   3352,12616, 3360,5312, 3368,4936, 3376,9032, 3384,13128, 3392,5440, 
+   3400,5448, 3408,9544, 3416,13640, 3424,5568, 3432,5960, 3440,10056, 
+   3448,14152, 3456,5192, 3464,6472, 3472,10568, 3480,14664, 3488,5320, 
+   3496,6984, 3504,11080, 3512,15176, 3520,5448, 3528,7496, 3536,11592, 
+   3544,15688, 3552,3912, 3560,8008, 3568,12104, 3576,16200, 3584,6208, 
+   3592,4488, 3600,8584, 3608,12680, 3616,6336, 3624,5000, 3632,9096, 
+   3640,13192, 3648,6464, 3656,5512, 3664,9608, 3672,13704, 3680,6592, 
+   3688,6024, 3696,10120, 3704,14216, 3712,6216, 3720,6536, 3728,10632, 
+   3736,14728, 3744,6344, 3752,7048, 3760,11144, 3768,15240, 3776,6472, 
+   3784,7560, 3792,11656, 3800,15752, 3808,3976, 3816,8072, 3824,12168, 
+   3832,16264, 3840,7232, 3848,4552, 3856,8648, 3864,12744, 3872,7360, 
+   3880,5064, 3888,9160, 3896,13256, 3904,7488, 3912,5576, 3920,9672, 
+   3928,13768, 3936,7616, 3944,6088, 3952,10184, 3960,14280, 3968,7240, 
+   3976,6600, 3984,10696, 3992,14792, 4000,7368, 4008,7112, 4016,11208, 
+   4024,15304, 4032,7496, 4040,7624, 4048,11720, 4056,15816, 4064,7624, 
+   4072,8136, 4080,12232, 4088,16328, 4096,8192, 4104,4112, 4112,8208, 
+   4120,12304, 4128,8320, 4136,4624, 4144,8720, 4152,12816, 4160,8448, 
+   4168,5136, 4176,9232, 4184,13328, 4192,8576, 4200,5648, 4208,9744, 
+   4216,13840, 4224,8200, 4232,6160, 4240,10256, 4248,14352, 4256,8328, 
+   4264,6672, 4272,10768, 4280,14864, 4288,8456, 4296,7184, 4304,11280, 
+   4312,15376, 4320,8584, 4328,7696, 4336,11792, 4344,15888, 4352,9216, 
+   4360,9232, 4368,8272, 4376,12368, 4384,9344, 4392,4688, 4400,8784, 
+   4408,12880, 4416,9472, 4424,5200, 4432,9296, 4440,13392, 4448,9600, 
+   4456,5712, 4464,9808, 4472,13904, 4480,9224, 4488,6224, 4496,10320, 
+   4504,14416, 4512,9352, 4520,6736, 4528,10832, 4536,14928, 4544,9480, 
+   4552,7248, 4560,11344, 4568,15440, 4576,9608, 4584,7760, 4592,11856, 
+   4600,15952, 4608,10240, 4616,10256, 4624,8336, 4632,12432, 4640,10368, 
+   4648,4752, 4656,8848, 4664,12944, 4672,10496, 4680,5264, 4688,9360, 
+   4696,13456, 4704,10624, 4712,5776, 4720,9872, 4728,13968, 4736,10248, 
+   4744,6288, 4752,10384, 4760,14480, 4768,10376, 4776,6800, 4784,10896, 
+   4792,14992, 4800,10504, 4808,7312, 4816,11408, 4824,15504, 4832,10632, 
+   4840,7824, 4848,11920, 4856,16016, 4864,11264, 4872,11280, 4880,8400, 
+   4888,12496, 4896,11392, 4904,11408, 4912,8912, 4920,13008, 4928,11520, 
+   4936,5328, 4944,9424, 4952,13520, 4960,11648, 4968,5840, 4976,9936, 
+   4984,14032, 4992,11272, 5000,6352, 5008,10448, 5016,14544, 5024,11400, 
+   5032,6864, 5040,10960, 5048,15056, 5056,11528, 5064,7376, 5072,11472, 
+   5080,15568, 5088,11656, 5096,7888, 5104,11984, 5112,16080, 5120,8256, 
+   5128,8272, 5136,8464, 5144,12560, 5152,8384, 5160,8400, 5168,8976, 
+   5176,13072, 5184,8512, 5192,5392, 5200,9488, 5208,13584, 5216,8640, 
+   5224,5904, 5232,10000, 5240,14096, 5248,8264, 5256,6416, 5264,10512, 
+   5272,14608, 5280,8392, 5288,6928, 5296,11024, 5304,15120, 5312,8520, 
+   5320,7440, 5328,11536, 5336,15632, 5344,8648, 5352,7952, 5360,12048, 
+   5368,16144, 5376,9280, 5384,9296, 5392,8528, 5400,12624, 5408,9408, 
+   5416,9424, 5424,9040, 5432,13136, 5440,9536, 5448,5456, 5456,9552, 
+   5464,13648, 5472,9664, 5480,5968, 5488,10064, 5496,14160, 5504,9288, 
+   5512,6480, 5520,10576, 5528,14672, 5536,9416, 5544,6992, 5552,11088, 
+   5560,15184, 5568,9544, 5576,7504, 5584,11600, 5592,15696, 5600,9672, 
+   5608,8016, 5616,12112, 5624,16208, 5632,10304, 5640,10320, 5648,8592, 
+   5656,12688, 5664,10432, 5672,10448, 5680,9104, 5688,13200, 5696,10560, 
+   5704,10576, 5712,9616, 5720,13712, 5728,10688, 5736,6032, 5744,10128, 
+   5752,14224, 5760,10312, 5768,6544, 5776,10640, 5784,14736, 5792,10440, 
+   5800,7056, 5808,11152, 5816,15248, 5824,10568, 5832,7568, 5840,11664, 
+   5848,15760, 5856,10696, 5864,8080, 5872,12176, 5880,16272, 5888,11328, 
+   5896,11344, 5904,8656, 5912,12752, 5920,11456, 5928,11472, 5936,9168, 
+   5944,13264, 5952,11584, 5960,11600, 5968,9680, 5976,13776, 5984,11712, 
+   5992,6096, 6000,10192, 6008,14288, 6016,11336, 6024,6608, 6032,10704, 
+   6040,14800, 6048,11464, 6056,7120, 6064,11216, 6072,15312, 6080,11592, 
+   6088,7632, 6096,11728, 6104,15824, 6112,11720, 6120,8144, 6128,12240, 
+   6136,16336, 6144,12288, 6152,12304, 6160,8216, 6168,12312, 6176,12416, 
+   6184,12432, 6192,8728, 6200,12824, 6208,12544, 6216,12560, 6224,9240, 
+   6232,13336, 6240,12672, 6248,12688, 6256,9752, 6264,13848, 6272,12296, 
+   6280,12312, 6288,10264, 6296,14360, 6304,12424, 6312,6680, 6320,10776, 
+   6328,14872, 6336,12552, 6344,7192, 6352,11288, 6360,15384, 6368,12680, 
+   6376,7704, 6384,11800, 6392,15896, 6400,13312, 6408,13328, 6416,8280, 
+   6424,12376, 6432,13440, 6440,13456, 6448,8792, 6456,12888, 6464,13568, 
+   6472,13584, 6480,9304, 6488,13400, 6496,13696, 6504,13712, 6512,9816, 
+   6520,13912, 6528,13320, 6536,13336, 6544,10328, 6552,14424, 6560,13448, 
+   6568,6744, 6576,10840, 6584,14936, 6592,13576, 6600,7256, 6608,11352, 
+   6616,15448, 6624,13704, 6632,7768, 6640,11864, 6648,15960, 6656,14336, 
+   6664,14352, 6672,8344, 6680,12440, 6688,14464, 6696,14480, 6704,8856, 
+   6712,12952, 6720,14592, 6728,14608, 6736,9368, 6744,13464, 6752,14720, 
+   6760,14736, 6768,9880, 6776,13976, 6784,14344, 6792,14360, 6800,10392, 
+   6808,14488, 6816,14472, 6824,14488, 6832,10904, 6840,15000, 6848,14600, 
+   6856,7320, 6864,11416, 6872,15512, 6880,14728, 6888,7832, 6896,11928, 
+   6904,16024, 6912,15360, 6920,15376, 6928,8408, 6936,12504, 6944,15488, 
+   6952,15504, 6960,8920, 6968,13016, 6976,15616, 6984,15632, 6992,9432, 
+   7000,13528, 7008,15744, 7016,15760, 7024,9944, 7032,14040, 7040,15368, 
+   7048,15384, 7056,10456, 7064,14552, 7072,15496, 7080,15512, 7088,10968, 
+   7096,15064, 7104,15624, 7112,7384, 7120,11480, 7128,15576, 7136,15752, 
+   7144,7896, 7152,11992, 7160,16088, 7168,12352, 7176,12368, 7184,8472, 
+   7192,12568, 7200,12480, 7208,12496, 7216,8984, 7224,13080, 7232,12608, 
+   7240,12624, 7248,9496, 7256,13592, 7264,12736, 7272,12752, 7280,10008, 
+   7288,14104, 7296,12360, 7304,12376, 7312,10520, 7320,14616, 7328,12488, 
+   7336,12504, 7344,11032, 7352,15128, 7360,12616, 7368,7448, 7376,11544, 
+   7384,15640, 7392,12744, 7400,7960, 7408,12056, 7416,16152, 7424,13376, 
+   7432,13392, 7440,8536, 7448,12632, 7456,13504, 7464,13520, 7472,9048, 
+   7480,13144, 7488,13632, 7496,13648, 7504,9560, 7512,13656, 7520,13760, 
+   7528,13776, 7536,10072, 7544,14168, 7552,13384, 7560,13400, 7568,10584, 
+   7576,14680, 7584,13512, 7592,13528, 7600,11096, 7608,15192, 7616,13640, 
+   7624,13656, 7632,11608, 7640,15704, 7648,13768, 7656,8024, 7664,12120, 
+   7672,16216, 7680,14400, 7688,14416, 7696,8600, 7704,12696, 7712,14528, 
+   7720,14544, 7728,9112, 7736,13208, 7744,14656, 7752,14672, 7760,9624, 
+   7768,13720, 7776,14784, 7784,14800, 7792,10136, 7800,14232, 7808,14408, 
+   7816,14424, 7824,10648, 7832,14744, 7840,14536, 7848,14552, 7856,11160, 
+   7864,15256, 7872,14664, 7880,14680, 7888,11672, 7896,15768, 7904,14792, 
+   7912,8088, 7920,12184, 7928,16280, 7936,15424, 7944,15440, 7952,8664, 
+   7960,12760, 7968,15552, 7976,15568, 7984,9176, 7992,13272, 8000,15680, 
+   8008,15696, 8016,9688, 8024,13784, 8032,15808, 8040,15824, 8048,10200, 
+   8056,14296, 8064,15432, 8072,15448, 8080,10712, 8088,14808, 8096,15560, 
+   8104,15576, 8112,11224, 8120,15320, 8128,15688, 8136,15704, 8144,11736, 
+   8152,15832, 8160,15816, 8168,15832, 8176,12248, 8184,16344, 8200,8320, 
+   8208,8224, 8216,12320, 8232,10368, 8240,8736, 8248,12832, 8256,8448, 
+   8264,8384, 8272,9248, 8280,13344, 8288,9232, 8296,10432, 8304,9760, 
+   8312,13856, 8328,12416, 8336,10272, 8344,14368, 8352,12296, 8360,14464, 
+   8368,10784, 8376,14880, 8384,8456, 8392,12480, 8400,11296, 8408,15392, 
+   8416,12552, 8424,14528, 8432,11808, 8440,15904, 8448,9216, 8456,8576, 
+   8464,9232, 8472,12384, 8480,9248, 8488,10624, 8496,8800, 8504,12896, 
+   8512,9472, 8520,8640, 8528,9312, 8536,13408, 8544,9296, 8552,10688, 
+   8560,9824, 8568,13920, 8576,9224, 8584,12672, 8592,10336, 8600,14432, 
+   8608,13320, 8616,14720, 8624,10848, 8632,14944, 8640,9480, 8648,12736, 
+   8656,11360, 8664,15456, 8672,13576, 8680,14784, 8688,11872, 8696,15968, 
+   8704,12288, 8712,12416, 8720,12296, 8728,12448, 8736,12304, 8744,10376, 
+   8752,8864, 8760,12960, 8768,12352, 8776,12480, 8784,9376, 8792,13472, 
+   8800,12368, 8808,10440, 8816,9888, 8824,13984, 8832,12320, 8840,12424, 
+   8848,10400, 8856,14496, 8864,12312, 8872,14472, 8880,10912, 8888,15008, 
+   8896,12384, 8904,12488, 8912,11424, 8920,15520, 8928,12568, 8936,14536, 
+   8944,11936, 8952,16032, 8960,12544, 8968,12672, 8976,12552, 8984,12512, 
+   8992,12560, 9000,10632, 9008,12568, 9016,13024, 9024,12608, 9032,12736, 
+   9040,9440, 9048,13536, 9056,12624, 9064,10696, 9072,9952, 9080,14048, 
+   9088,9240, 9096,12680, 9104,10464, 9112,14560, 9120,13336, 9128,14728, 
+   9136,10976, 9144,15072, 9152,9496, 9160,12744, 9168,11488, 9176,15584, 
+   9184,13592, 9192,14792, 9200,12000, 9208,16096, 9224,9344, 9232,9248, 
+   9240,12576, 9256,11392, 9264,12560, 9272,13088, 9280,9472, 9288,9408, 
+   9296,9504, 9304,13600, 9312,9488, 9320,11456, 9328,10016, 9336,14112, 
+   9352,13440, 9360,10528, 9368,14624, 9376,12360, 9384,15488, 9392,11040, 
+   9400,15136, 9408,9480, 9416,13504, 9424,11552, 9432,15648, 9440,12616, 
+   9448,15552, 9456,12064, 9464,16160, 9480,9600, 9488,9504, 9496,12640, 
+   9512,11648, 9520,12624, 9528,13152, 9544,9664, 9552,9568, 9560,13664, 
+   9576,11712, 9584,10080, 9592,14176, 9608,13696, 9616,10592, 9624,14688, 
+   9632,13384, 9640,15744, 9648,11104, 9656,15200, 9672,13760, 9680,11616, 
+   9688,15712, 9696,13640, 9704,15808, 9712,12128, 9720,16224, 9728,13312, 
+   9736,13440, 9744,13320, 9752,12704, 9760,13328, 9768,11400, 9776,13336, 
+   9784,13216, 9792,13376, 9800,13504, 9808,13384, 9816,13728, 9824,13392, 
+   9832,11464, 9840,10144, 9848,14240, 9856,13344, 9864,13448, 9872,10656, 
+   9880,14752, 9888,12376, 9896,15496, 9904,11168, 9912,15264, 9920,13408, 
+   9928,13512, 9936,11680, 9944,15776, 9952,12632, 9960,15560, 9968,12192, 
+   9976,16288, 9984,13568, 9992,13696, 10000,13576, 10008,12768, 10016,13584, 
+   10024,11656, 10032,13592, 10040,13280, 10048,13632, 10056,13760, 
+   10064,13640, 10072,13792, 10080,13648, 10088,11720, 10096,10208, 
+   10104,14304, 10112,13600, 10120,13704, 10128,10720, 10136,14816, 
+   10144,13400, 10152,15752, 10160,11232, 10168,15328, 10176,13664, 
+   10184,13768, 10192,11744, 10200,15840, 10208,13656, 10216,15816, 
+   10224,12256, 10232,16352, 10248,10272, 10256,10368, 10264,12328, 
+   10280,10384, 10288,10376, 10296,12840, 10304,11264, 10312,11296, 
+   10320,11392, 10328,13352, 10336,11272, 10344,10448, 10352,11400, 
+   10360,13864, 10376,12432, 10392,14376, 10400,12328, 10408,14480, 
+   10416,10792, 10424,14888, 10432,11280, 10440,12496, 10448,11304, 
+   10456,15400, 10464,11288, 10472,14544, 10480,11816, 10488,15912, 
+   10496,11264, 10504,11272, 10512,11280, 10520,12392, 10528,11296, 
+   10536,10640, 10544,12496, 10552,12904, 10560,11328, 10568,11360, 
+   10576,11456, 10584,13416, 10592,11336, 10600,10704, 10608,11464, 
+   10616,13928, 10624,11392, 10632,12688, 10640,11304, 10648,14440, 
+   10656,13352, 10664,14736, 10672,10856, 10680,14952, 10688,11344, 
+   10696,12752, 10704,11368, 10712,15464, 10720,11352, 10728,14800, 
+   10736,11880, 10744,15976, 10752,14336, 10760,14368, 10768,14464, 
+   10776,12456, 10784,14344, 10792,14376, 10800,14472, 10808,12968, 
+   10816,15360, 10824,15392, 10832,15488, 10840,13480, 10848,15368, 
+   10856,15400, 10864,15496, 10872,13992, 10880,14352, 10888,12440, 
+   10896,14480, 10904,14504, 10912,14360, 10920,14488, 10928,14488, 
+   10936,15016, 10944,15376, 10952,12504, 10960,11432, 10968,15528, 
+   10976,15384, 10984,14552, 10992,11944, 11000,16040, 11008,14400, 
+   11016,14432, 11024,14528, 11032,12520, 11040,14408, 11048,14440, 
+   11056,14536, 11064,13032, 11072,15424, 11080,15456, 11088,15552, 
+   11096,13544, 11104,15432, 11112,15464, 11120,15560, 11128,14056, 
+   11136,14416, 11144,12696, 11152,14544, 11160,14568, 11168,14424, 
+   11176,14744, 11184,14552, 11192,15080, 11200,15440, 11208,12760, 
+   11216,11496, 11224,15592, 11232,15448, 11240,14808, 11248,12008, 
+   11256,16104, 11272,11296, 11280,11392, 11288,12584, 11304,11408, 
+   11312,12688, 11320,13096, 11328,11520, 11336,11552, 11344,11648, 
+   11352,13608, 11360,11528, 11368,11472, 11376,11656, 11384,14120, 
+   11400,13456, 11416,14632, 11424,12392, 11432,15504, 11440,14440, 
+   11448,15144, 11456,11536, 11464,13520, 11472,11560, 11480,15656, 
+   11488,11544, 11496,15568, 11504,12072, 11512,16168, 11528,11552, 
+   11536,11648, 11544,12648, 11560,11664, 11568,12752, 11576,13160, 
+   11592,11616, 11600,11712, 11608,13672, 11624,11728, 11632,11720, 
+   11640,14184, 11656,13712, 11672,14696, 11680,13416, 11688,15760, 
+   11696,15464, 11704,15208, 11720,13776, 11736,15720, 11744,13672, 
+   11752,15824, 11760,12136, 11768,16232, 11776,14592, 11784,14624, 
+   11792,14720, 11800,12712, 11808,14600, 11816,14632, 11824,14728, 
+   11832,13224, 11840,15616, 11848,15648, 11856,15744, 11864,13736, 
+   11872,15624, 11880,15656, 11888,15752, 11896,14248, 11904,14608, 
+   11912,13464, 11920,14736, 11928,14760, 11936,14616, 11944,15512, 
+   11952,14744, 11960,15272, 11968,15632, 11976,13528, 11984,15760, 
+   11992,15784, 12000,15640, 12008,15576, 12016,12200, 12024,16296, 
+   12032,14656, 12040,14688, 12048,14784, 12056,12776, 12064,14664, 
+   12072,14696, 12080,14792, 12088,13288, 12096,15680, 12104,15712, 
+   12112,15808, 12120,13800, 12128,15688, 12136,15720, 12144,15816, 
+   12152,14312, 12160,14672, 12168,13720, 12176,14800, 12184,14824, 
+   12192,14680, 12200,15768, 12208,14808, 12216,15336, 12224,15696, 
+   12232,13784, 12240,15824, 12248,15848, 12256,15704, 12264,15832, 
+   12272,15832, 12280,16360, 12312,12336, 12344,12848, 12352,12544, 
+   12360,12552, 12368,12560, 12376,13360, 12384,12576, 12392,12584, 
+   12400,13336, 12408,13872, 12424,12448, 12440,14384, 12456,14496, 
+   12464,14472, 12472,14896, 12480,12672, 12488,12512, 12496,12688, 
+   12504,15408, 12512,12680, 12520,14560, 12528,14728, 12536,15920, 
+   12544,13312, 12552,13320, 12560,13328, 12568,13336, 12576,13344, 
+   12584,13352, 12592,13360, 12600,12912, 12608,13568, 12616,13576, 
+   12624,13584, 12632,13424, 12640,13600, 12648,13608, 12656,13400, 
+   12664,13936, 12672,13440, 12680,12704, 12688,13456, 12696,14448, 
+   12704,13448, 12712,14752, 12720,15496, 12728,14960, 12736,13696, 
+   12744,12768, 12752,13712, 12760,15472, 12768,13704, 12776,14816, 
+   12784,15752, 12792,15984, 12800,14336, 12808,14464, 12816,14344, 
+   12824,14472, 12832,14352, 12840,14480, 12848,14360, 12856,12976, 
+   12864,14400, 12872,14528, 12880,14408, 12888,13488, 12896,14416, 
+   12904,14544, 12912,14424, 12920,14000, 12928,14368, 12936,14496, 
+   12944,14376, 12952,14512, 12960,14384, 12968,14504, 12976,14488, 
+   12984,15024, 12992,14432, 13000,14560, 13008,14440, 13016,15536, 
+   13024,14448, 13032,14568, 13040,14744, 13048,16048, 13056,14592, 
+   13064,14720, 13072,14600, 13080,14728, 13088,14608, 13096,14736, 
+   13104,14616, 13112,14744, 13120,14656, 13128,14784, 13136,14664, 
+   13144,13552, 13152,14672, 13160,14800, 13168,14680, 13176,14064, 
+   13184,14624, 13192,14752, 13200,14632, 13208,14576, 13216,13464, 
+   13224,14760, 13232,15512, 13240,15088, 13248,14688, 13256,14816, 
+   13264,14696, 13272,15600, 13280,13720, 13288,14824, 13296,15768, 
+   13304,16112, 13336,13360, 13368,14616, 13376,13568, 13384,13576, 
+   13392,13584, 13400,13616, 13408,13600, 13416,13608, 13424,13592, 
+   13432,14128, 13448,13472, 13464,14640, 13480,15520, 13488,14536, 
+   13496,15152, 13504,13696, 13512,13536, 13520,13712, 13528,15664, 
+   13536,13704, 13544,15584, 13552,14792, 13560,16176, 13592,13616, 
+   13624,14680, 13656,13680, 13688,14192, 13704,13728, 13720,14704, 
+   13736,15776, 13744,15560, 13752,15216, 13768,13792, 13784,15728, 
+   13800,15840, 13808,15816, 13816,16240, 13824,15360, 13832,15488, 
+   13840,15368, 13848,15496, 13856,15376, 13864,15504, 13872,15384, 
+   13880,15512, 13888,15424, 13896,15552, 13904,15432, 13912,15560, 
+   13920,15440, 13928,15568, 13936,15448, 13944,14256, 13952,15392, 
+   13960,15520, 13968,15400, 13976,14768, 13984,15408, 13992,15528, 
+   14000,14552, 14008,15280, 14016,15456, 14024,15584, 14032,15464, 
+   14040,15792, 14048,15472, 14056,15592, 14064,14808, 14072,16304, 
+   14080,15616, 14088,15744, 14096,15624, 14104,15752, 14112,15632, 
+   14120,15760, 14128,15640, 14136,15768, 14144,15680, 14152,15808, 
+   14160,15688, 14168,15816, 14176,15696, 14184,15824, 14192,15704, 
+   14200,14320, 14208,15648, 14216,15776, 14224,15656, 14232,14832, 
+   14240,15664, 14248,15784, 14256,15576, 14264,15344, 14272,15712, 
+   14280,15840, 14288,15720, 14296,15856, 14304,15728, 14312,15848, 
+   14320,15832, 14328,16368, 14392,14488, 14400,14592, 14408,14600, 
+   14416,14608, 14424,14616, 14432,14624, 14440,14632, 14448,14640, 
+   14456,15512, 14504,14512, 14520,14904, 14528,14720, 14536,14728, 
+   14544,14736, 14552,15416, 14560,14752, 14568,14576, 14584,15928,
+   14576,14760, 14592,15360, 14600,15368, 14608,15376, 14616,15384, 
+   14624,15392, 14632,15400, 14640,15408, 14648,15416, 14656,15616, 
+   14664,15624, 14672,15632, 14680,15640, 14688,15648, 14696,15656, 
+   14704,15664, 14712,15576, 14720,15488, 14728,15496, 14736,15504, 
+   14744,15512, 14752,15520, 14760,14768, 14776,14968, 14768,15528, 
+   14784,15744, 14792,15752, 14800,15760, 14808,15480, 14816,15776, 
+   14824,14832, 14840,15992, 14832,15784, 14856,14864, 14864,14880, 
+   14872,14896, 14880,14976, 14888,14992, 14896,15008, 14904,15024, 
+   14912,15104, 14920,15120, 14928,15136, 14936,15152, 14944,15232, 
+   14952,15248, 14960,15264, 14968,15280, 14984,15008, 15000,15024, 
+   15016,15024, 15040,15112, 15048,15128, 15056,15144, 15064,15544, 
+   15072,15240, 15080,15256, 15088,15272, 15096,16056, 15104,15872, 
+   15112,15888, 15120,15904, 15128,15920, 15136,16000, 15144,16016, 
+   15152,16032, 15160,16048, 15168,16128, 15176,16144, 15184,16160, 
+   15192,16176, 15200,16256, 15208,16272, 15216,16288, 15224,16304, 
+   15232,15880, 15240,15896, 15248,15912, 15256,15928, 15264,16008, 
+   15272,16024, 15280,16040, 15288,16056, 15296,16136, 15304,16152, 
+   15312,16168, 15320,15608, 15328,16264, 15336,16280, 15344,16296, 
+   15352,16120, 15416,15512, 15424,15616, 15432,15624, 15440,15632, 
+   15448,15640, 15456,15648, 15464,15656, 15472,15664, 15480,15768, 
+   15528,15536, 15544,16048, 15552,15744, 15560,15752, 15568,15760, 
+   15576,15672, 15584,15776, 15592,15600, 15600,15784, 15608,16184, 
+   15672,15768, 15736,15832, 15784,15792, 15800,16304, 15848,15856, 
+   15880,16000, 15864,16248, 15888,16000, 15896,16008, 15904,16000, 
+   15912,16016, 15920,16008, 15928,16024, 15936,16128, 15944,16160, 
+   15952,16256, 15960,16288, 15968,16136, 15976,16168, 15984,16264, 
+   15992,16296, 16008,16032, 16024,16040, 16064,16144, 16040,16048, 
+   16072,16176, 16080,16272, 16088,16304, 16096,16152, 16104,16184, 
+   16112,16280, 16136,16256, 16120,16312, 16144,16256, 16152,16264, 
+   16160,16256, 16168,16272, 16176,16264, 16184,16280, 16200,16208, 
+   16208,16224, 16216,16240, 16224,16320, 16232,16336, 16240,16352, 
+   16248,16368, 16264,16288, 16280,16296, 16296,16304, 16344,16368,
+   16328,16352, 16360,16368
+};
+
+const uint16_t armBitRevIndexTable4096[ARMBITREVINDEXTABLE4096_TABLE_LENGTH] = 
+{
+   //radix 8, size 4032
+   8,4096, 16,8192, 24,12288, 32,16384, 40,20480, 48,24576, 56,28672, 64,512, 
+   72,4608, 80,8704, 88,12800, 96,16896, 104,20992, 112,25088, 120,29184, 
+   128,1024, 136,5120, 144,9216, 152,13312, 160,17408, 168,21504, 176,25600, 
+   184,29696, 192,1536, 200,5632, 208,9728, 216,13824, 224,17920, 232,22016, 
+   240,26112, 248,30208, 256,2048, 264,6144, 272,10240, 280,14336, 288,18432, 
+   296,22528, 304,26624, 312,30720, 320,2560, 328,6656, 336,10752, 344,14848, 
+   352,18944, 360,23040, 368,27136, 376,31232, 384,3072, 392,7168, 400,11264, 
+   408,15360, 416,19456, 424,23552, 432,27648, 440,31744, 448,3584, 456,7680, 
+   464,11776, 472,15872, 480,19968, 488,24064, 496,28160, 504,32256, 520,4160, 
+   528,8256, 536,12352, 544,16448, 552,20544, 560,24640, 568,28736, 584,4672, 
+   592,8768, 600,12864, 608,16960, 616,21056, 624,25152, 632,29248, 640,1088, 
+   648,5184, 656,9280, 664,13376, 672,17472, 680,21568, 688,25664, 696,29760, 
+   704,1600, 712,5696, 720,9792, 728,13888, 736,17984, 744,22080, 752,26176, 
+   760,30272, 768,2112, 776,6208, 784,10304, 792,14400, 800,18496, 808,22592, 
+   816,26688, 824,30784, 832,2624, 840,6720, 848,10816, 856,14912, 864,19008, 
+   872,23104, 880,27200, 888,31296, 896,3136, 904,7232, 912,11328, 920,15424, 
+   928,19520, 936,23616, 944,27712, 952,31808, 960,3648, 968,7744, 976,11840, 
+   984,15936, 992,20032, 1000,24128, 1008,28224, 1016,32320, 1032,4224, 
+   1040,8320, 1048,12416, 1056,16512, 1064,20608, 1072,24704, 1080,28800, 
+   1096,4736, 1104,8832, 1112,12928, 1120,17024, 1128,21120, 1136,25216, 
+   1144,29312, 1160,5248, 1168,9344, 1176,13440, 1184,17536, 1192,21632, 
+   1200,25728, 1208,29824, 1216,1664, 1224,5760, 1232,9856, 1240,13952, 
+   1248,18048, 1256,22144, 1264,26240, 1272,30336, 1280,2176, 1288,6272, 
+   1296,10368, 1304,14464, 1312,18560, 1320,22656, 1328,26752, 1336,30848, 
+   1344,2688, 1352,6784, 1360,10880, 1368,14976, 1376,19072, 1384,23168, 
+   1392,27264, 1400,31360, 1408,3200, 1416,7296, 1424,11392, 1432,15488, 
+   1440,19584, 1448,23680, 1456,27776, 1464,31872, 1472,3712, 1480,7808, 
+   1488,11904, 1496,16000, 1504,20096, 1512,24192, 1520,28288, 1528,32384, 
+   1544,4288, 1552,8384, 1560,12480, 1568,16576, 1576,20672, 1584,24768, 
+   1592,28864, 1608,4800, 1616,8896, 1624,12992, 1632,17088, 1640,21184, 
+   1648,25280, 1656,29376, 1672,5312, 1680,9408, 1688,13504, 1696,17600, 
+   1704,21696, 1712,25792, 1720,29888, 1736,5824, 1744,9920, 1752,14016, 
+   1760,18112, 1768,22208, 1776,26304, 1784,30400, 1792,2240, 1800,6336, 
+   1808,10432, 1816,14528, 1824,18624, 1832,22720, 1840,26816, 1848,30912, 
+   1856,2752, 1864,6848, 1872,10944, 1880,15040, 1888,19136, 1896,23232, 
+   1904,27328, 1912,31424, 1920,3264, 1928,7360, 1936,11456, 1944,15552, 
+   1952,19648, 1960,23744, 1968,27840, 1976,31936, 1984,3776, 1992,7872, 
+   2000,11968, 2008,16064, 2016,20160, 2024,24256, 2032,28352, 2040,32448, 
+   2056,4352, 2064,8448, 2072,12544, 2080,16640, 2088,20736, 2096,24832, 
+   2104,28928, 2120,4864, 2128,8960, 2136,13056, 2144,17152, 2152,21248, 
+   2160,25344, 2168,29440, 2184,5376, 2192,9472, 2200,13568, 2208,17664, 
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+   15464,21400, 15472,25496, 15480,29592, 15520,17816, 15528,21912, 
+   15536,26008, 15544,30104, 15584,18328, 15592,22424, 15600,26520, 
+   15608,30616, 15648,18840, 15656,22936, 15664,27032, 15672,31128, 
+   15712,19352, 15720,23448, 15728,27544, 15736,31640, 15776,19864, 
+   15784,23960, 15792,28056, 15800,32152, 15832,16280, 15840,20376, 
+   15848,24472, 15856,28568, 15864,32664, 15904,16856, 15912,20952, 
+   15920,25048, 15928,29144, 15968,17368, 15976,21464, 15984,25560, 
+   15992,29656, 16032,17880, 16040,21976, 16048,26072, 16056,30168, 
+   16096,18392, 16104,22488, 16112,26584, 16120,30680, 16160,18904, 
+   16168,23000, 16176,27096, 16184,31192, 16224,19416, 16232,23512, 
+   16240,27608, 16248,31704, 16288,19928, 16296,24024, 16304,28120, 
+   16312,32216, 16352,20440, 16360,24536, 16368,28632, 16376,32728, 
+   16424,20512, 16432,24608, 16440,28704, 16480,16928, 16488,21024, 
+   16496,25120, 16504,29216, 16544,17440, 16552,21536, 16560,25632, 
+   16568,29728, 16608,17952, 16616,22048, 16624,26144, 16632,30240, 
+   16672,18464, 16680,22560, 16688,26656, 16696,30752, 16736,18976, 
+   16744,23072, 16752,27168, 16760,31264, 16800,19488, 16808,23584, 
+   16816,27680, 16824,31776, 16864,20000, 16872,24096, 16880,28192, 
+   16888,32288, 16936,20576, 16944,24672, 16952,28768, 17000,21088, 
+   17008,25184, 17016,29280, 17056,17504, 17064,21600, 17072,25696, 
+   17080,29792, 17120,18016, 17128,22112, 17136,26208, 17144,30304, 
+   17184,18528, 17192,22624, 17200,26720, 17208,30816, 17248,19040, 
+   17256,23136, 17264,27232, 17272,31328, 17312,19552, 17320,23648, 
+   17328,27744, 17336,31840, 17376,20064, 17384,24160, 17392,28256, 
+   17400,32352, 17448,20640, 17456,24736, 17464,28832, 17512,21152, 
+   17520,25248, 17528,29344, 17576,21664, 17584,25760, 17592,29856, 
+   17632,18080, 17640,22176, 17648,26272, 17656,30368, 17696,18592, 
+   17704,22688, 17712,26784, 17720,30880, 17760,19104, 17768,23200, 
+   17776,27296, 17784,31392, 17824,19616, 17832,23712, 17840,27808, 
+   17848,31904, 17888,20128, 17896,24224, 17904,28320, 17912,32416, 
+   17960,20704, 17968,24800, 17976,28896, 18024,21216, 18032,25312, 
+   18040,29408, 18088,21728, 18096,25824, 18104,29920, 18152,22240, 
+   18160,26336, 18168,30432, 18208,18656, 18216,22752, 18224,26848, 
+   18232,30944, 18272,19168, 18280,23264, 18288,27360, 18296,31456, 
+   18336,19680, 18344,23776, 18352,27872, 18360,31968, 18400,20192, 
+   18408,24288, 18416,28384, 18424,32480, 18472,20768, 18480,24864, 
+   18488,28960, 18536,21280, 18544,25376, 18552,29472, 18600,21792, 
+   18608,25888, 18616,29984, 18664,22304, 18672,26400, 18680,30496, 
+   18728,22816, 18736,26912, 18744,31008, 18784,19232, 18792,23328, 
+   18800,27424, 18808,31520, 18848,19744, 18856,23840, 18864,27936, 
+   18872,32032, 18912,20256, 18920,24352, 18928,28448, 18936,32544, 
+   18984,20832, 18992,24928, 19000,29024, 19048,21344, 19056,25440, 
+   19064,29536, 19112,21856, 19120,25952, 19128,30048, 19176,22368, 
+   19184,26464, 19192,30560, 19240,22880, 19248,26976, 19256,31072, 
+   19304,23392, 19312,27488, 19320,31584, 19360,19808, 19368,23904, 
+   19376,28000, 19384,32096, 19424,20320, 19432,24416, 19440,28512, 
+   19448,32608, 19496,20896, 19504,24992, 19512,29088, 19560,21408, 
+   19568,25504, 19576,29600, 19624,21920, 19632,26016, 19640,30112, 
+   19688,22432, 19696,26528, 19704,30624, 19752,22944, 19760,27040, 
+   19768,31136, 19816,23456, 19824,27552, 19832,31648, 19880,23968, 
+   19888,28064, 19896,32160, 19936,20384, 19944,24480, 19952,28576, 
+   19960,32672, 20008,20960, 20016,25056, 20024,29152, 20072,21472, 
+   20080,25568, 20088,29664, 20136,21984, 20144,26080, 20152,30176, 
+   20200,22496, 20208,26592, 20216,30688, 20264,23008, 20272,27104, 
+   20280,31200, 20328,23520, 20336,27616, 20344,31712, 20392,24032, 
+   20400,28128, 20408,32224, 20456,24544, 20464,28640, 20472,32736, 
+   20528,24616, 20536,28712, 20584,21032, 20592,25128, 20600,29224, 
+   20648,21544, 20656,25640, 20664,29736, 20712,22056, 20720,26152, 
+   20728,30248, 20776,22568, 20784,26664, 20792,30760, 20840,23080, 
+   20848,27176, 20856,31272, 20904,23592, 20912,27688, 20920,31784, 
+   20968,24104, 20976,28200, 20984,32296, 21040,24680, 21048,28776, 
+   21104,25192, 21112,29288, 21160,21608, 21168,25704, 21176,29800, 
+   21224,22120, 21232,26216, 21240,30312, 21288,22632, 21296,26728, 
+   21304,30824, 21352,23144, 21360,27240, 21368,31336, 21416,23656, 
+   21424,27752, 21432,31848, 21480,24168, 21488,28264, 21496,32360, 
+   21552,24744, 21560,28840, 21616,25256, 21624,29352, 21680,25768, 
+   21688,29864, 21736,22184, 21744,26280, 21752,30376, 21800,22696, 
+   21808,26792, 21816,30888, 21864,23208, 21872,27304, 21880,31400, 
+   21928,23720, 21936,27816, 21944,31912, 21992,24232, 22000,28328, 
+   22008,32424, 22064,24808, 22072,28904, 22128,25320, 22136,29416, 
+   22192,25832, 22200,29928, 22256,26344, 22264,30440, 22312,22760, 
+   22320,26856, 22328,30952, 22376,23272, 22384,27368, 22392,31464, 
+   22440,23784, 22448,27880, 22456,31976, 22504,24296, 22512,28392, 
+   22520,32488, 22576,24872, 22584,28968, 22640,25384, 22648,29480, 
+   22704,25896, 22712,29992, 22768,26408, 22776,30504, 22832,26920, 
+   22840,31016, 22888,23336, 22896,27432, 22904,31528, 22952,23848, 
+   22960,27944, 22968,32040, 23016,24360, 23024,28456, 23032,32552, 
+   23088,24936, 23096,29032, 23152,25448, 23160,29544, 23216,25960, 
+   23224,30056, 23280,26472, 23288,30568, 23344,26984, 23352,31080, 
+   23408,27496, 23416,31592, 23464,23912, 23472,28008, 23480,32104, 
+   23528,24424, 23536,28520, 23544,32616, 23600,25000, 23608,29096, 
+   23664,25512, 23672,29608, 23728,26024, 23736,30120, 23792,26536, 
+   23800,30632, 23856,27048, 23864,31144, 23920,27560, 23928,31656, 
+   23984,28072, 23992,32168, 24040,24488, 24048,28584, 24056,32680, 
+   24112,25064, 24120,29160, 24176,25576, 24184,29672, 24240,26088, 
+   24248,30184, 24304,26600, 24312,30696, 24368,27112, 24376,31208, 
+   24432,27624, 24440,31720, 24496,28136, 24504,32232, 24560,28648, 
+   24568,32744, 24632,28720, 24688,25136, 24696,29232, 24752,25648, 
+   24760,29744, 24816,26160, 24824,30256, 24880,26672, 24888,30768, 
+   24944,27184, 24952,31280, 25008,27696, 25016,31792, 25072,28208, 
+   25080,32304, 25144,28784, 25208,29296, 25264,25712, 25272,29808, 
+   25328,26224, 25336,30320, 25392,26736, 25400,30832, 25456,27248, 
+   25464,31344, 25520,27760, 25528,31856, 25584,28272, 25592,32368, 
+   25656,28848, 25720,29360, 25784,29872, 25840,26288, 25848,30384, 
+   25904,26800, 25912,30896, 25968,27312, 25976,31408, 26032,27824, 
+   26040,31920, 26096,28336, 26104,32432, 26168,28912, 26232,29424, 
+   26296,29936, 26360,30448, 26416,26864, 26424,30960, 26480,27376, 
+   26488,31472, 26544,27888, 26552,31984, 26608,28400, 26616,32496, 
+   26680,28976, 26744,29488, 26808,30000, 26872,30512, 26936,31024, 
+   26992,27440, 27000,31536, 27056,27952, 27064,32048, 27120,28464, 
+   27128,32560, 27192,29040, 27256,29552, 27320,30064, 27384,30576, 
+   27448,31088, 27512,31600, 27568,28016, 27576,32112, 27632,28528, 
+   27640,32624, 27704,29104, 27768,29616, 27832,30128, 27896,30640, 
+   27960,31152, 28024,31664, 28088,32176, 28144,28592, 28152,32688, 
+   28216,29168, 28280,29680, 28344,30192, 28408,30704, 28472,31216, 
+   28536,31728, 28600,32240, 28664,32752, 28792,29240, 28856,29752, 
+   28920,30264, 28984,30776, 29048,31288, 29112,31800, 29176,32312, 
+   29368,29816, 29432,30328, 29496,30840, 29560,31352, 29624,31864, 
+   29688,32376, 29944,30392, 30008,30904, 30072,31416, 30136,31928, 
+   30200,32440, 30520,30968, 30584,31480, 30648,31992, 30712,32504, 
+   31096,31544, 31160,32056, 31224,32568, 31672,32120, 31736,32632, 
+   32248,32696
+};
+
+
+const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH] = 
+{
+   //radix 4, size 12
+   8,64, 16,32, 24,96, 40,80, 56,112, 88,104
+};
+
+const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH] = 
+{
+   //4x2, size 24
+   8,128, 16,64, 24,192, 40,160, 48,96, 56,224, 72,144,
+   88,208, 104,176, 120,240, 152,200, 184,232
+};
+
+const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH] = 
+{   
+   //radix 4, size 56
+   8,256, 16,128, 24,384, 32,64, 40,320, 48,192, 56,448, 72,288, 80,160, 88,416, 104,352,
+   112,224, 120,480, 136,272, 152,400, 168,336, 176,208, 184,464, 200,304, 216,432,
+   232,368, 248,496, 280,392, 296,328, 312,456, 344,424, 376,488, 440,472
+};
+
+const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH] = 
+{
+   //4x2, size 112
+   8,512, 16,256, 24,768, 32,128, 40,640, 48,384, 56,896, 72,576, 80,320, 88,832, 96,192,
+   104,704, 112,448, 120,960, 136,544, 144,288, 152,800, 168,672, 176,416, 184,928, 200,608,
+   208,352, 216,864, 232,736, 240,480, 248,992, 264,528, 280,784, 296,656, 304,400, 312,912,
+   328,592, 344,848, 360,720, 368,464, 376,976, 392,560, 408,816, 424,688, 440,944, 456,624,
+   472,880, 488,752, 504,1008, 536,776, 552,648, 568,904, 600,840, 616,712, 632,968,
+   664,808, 696,936, 728,872, 760,1000, 824,920, 888,984
+};
+
+const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH] = 
+{
+   //radix 4, size 240
+   8,1024, 16,512, 24,1536, 32,256, 40,1280, 48,768, 56,1792, 64,128, 72,1152, 80,640,
+   88,1664, 96,384, 104,1408, 112,896, 120,1920, 136,1088, 144,576, 152,1600, 160,320,
+   168,1344, 176,832, 184,1856, 200,1216, 208,704, 216,1728, 224,448, 232,1472, 240,960,
+   248,1984, 264,1056, 272,544, 280,1568, 296,1312, 304,800, 312,1824, 328,1184, 336,672,
+   344,1696, 352,416, 360,1440, 368,928, 376,1952, 392,1120, 400,608, 408,1632, 424,1376,
+   432,864, 440,1888, 456,1248, 464,736, 472,1760, 488,1504, 496,992, 504,2016, 520,1040,
+   536,1552, 552,1296, 560,784, 568,1808, 584,1168, 592,656, 600,1680, 616,1424, 624,912,
+   632,1936, 648,1104, 664,1616, 680,1360, 688,848, 696,1872, 712,1232, 728,1744, 744,1488,
+   752,976, 760,2000, 776,1072, 792,1584, 808,1328, 824,1840, 840,1200, 856,1712, 872,1456,
+   880,944, 888,1968, 904,1136, 920,1648, 936,1392, 952,1904, 968,1264, 984,1776, 1000,1520,
+   1016,2032, 1048,1544, 1064,1288, 1080,1800, 1096,1160, 1112,1672, 1128,1416, 1144,1928,
+   1176,1608, 1192,1352, 1208,1864, 1240,1736, 1256,1480, 1272,1992, 1304,1576, 1336,1832,
+   1368,1704, 1384,1448, 1400,1960, 1432,1640, 1464,1896, 1496,1768, 1528,2024, 1592,1816,
+   1624,1688, 1656,1944, 1720,1880, 1784,2008, 1912,1976
+};
+
+const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH] = 
+{
+   //4x2, size 480
+   8,2048, 16,1024, 24,3072, 32,512, 40,2560, 48,1536, 56,3584, 64,256, 72,2304, 80,1280,
+   88,3328, 96,768, 104,2816, 112,1792, 120,3840, 136,2176, 144,1152, 152,3200, 160,640,
+   168,2688, 176,1664, 184,3712, 192,384, 200,2432, 208,1408, 216,3456, 224,896, 232,2944,
+   240,1920, 248,3968, 264,2112, 272,1088, 280,3136, 288,576, 296,2624, 304,1600, 312,3648,
+   328,2368, 336,1344, 344,3392, 352,832, 360,2880, 368,1856, 376,3904, 392,2240, 400,1216,
+   408,3264, 416,704, 424,2752, 432,1728, 440,3776, 456,2496, 464,1472, 472,3520, 480,960,
+   488,3008, 496,1984, 504,4032, 520,2080, 528,1056, 536,3104, 552,2592, 560,1568, 568,3616,
+   584,2336, 592,1312, 600,3360, 608,800, 616,2848, 624,1824, 632,3872, 648,2208, 656,1184,
+   664,3232, 680,2720, 688,1696, 696,3744, 712,2464, 720,1440, 728,3488, 736,928, 744,2976,
+   752,1952, 760,4000, 776,2144, 784,1120, 792,3168, 808,2656, 816,1632, 824,3680, 840,2400,
+   848,1376, 856,3424, 872,2912, 880,1888, 888,3936, 904,2272, 912,1248, 920,3296, 936,2784,
+   944,1760, 952,3808, 968,2528, 976,1504, 984,3552, 1000,3040, 1008,2016, 1016,4064,
+   1032,2064, 1048,3088, 1064,2576, 1072,1552, 1080,3600, 1096,2320, 1104,1296, 1112,3344,
+   1128,2832, 1136,1808, 1144,3856, 1160,2192, 1176,3216, 1192,2704, 1200,1680, 1208,3728,
+   1224,2448, 1232,1424, 1240,3472, 1256,2960, 1264,1936, 1272,3984, 1288,2128, 1304,3152,
+   1320,2640, 1328,1616, 1336,3664, 1352,2384, 1368,3408, 1384,2896, 1392,1872, 1400,3920,
+   1416,2256, 1432,3280, 1448,2768, 1456,1744, 1464,3792, 1480,2512, 1496,3536, 1512,3024,
+   1520,2000, 1528,4048, 1544,2096, 1560,3120, 1576,2608, 1592,3632, 1608,2352, 1624,3376,
+   1640,2864, 1648,1840, 1656,3888, 1672,2224, 1688,3248, 1704,2736, 1720,3760, 1736,2480,
+   1752,3504, 1768,2992, 1776,1968, 1784,4016, 1800,2160, 1816,3184, 1832,2672, 1848,3696,
+   1864,2416, 1880,3440, 1896,2928, 1912,3952, 1928,2288, 1944,3312, 1960,2800, 1976,3824,
+   1992,2544, 2008,3568, 2024,3056, 2040,4080, 2072,3080, 2088,2568, 2104,3592, 2120,2312,
+   2136,3336, 2152,2824, 2168,3848, 2200,3208, 2216,2696, 2232,3720, 2248,2440, 2264,3464,
+   2280,2952, 2296,3976, 2328,3144, 2344,2632, 2360,3656, 2392,3400, 2408,2888, 2424,3912,
+   2456,3272, 2472,2760, 2488,3784, 2520,3528, 2536,3016, 2552,4040, 2584,3112, 2616,3624,
+   2648,3368, 2664,2856, 2680,3880, 2712,3240, 2744,3752, 2776,3496, 2792,2984, 2808,4008,
+   2840,3176, 2872,3688, 2904,3432, 2936,3944, 2968,3304, 3000,3816, 3032,3560, 3064,4072,
+   3128,3608, 3160,3352, 3192,3864, 3256,3736, 3288,3480, 3320,3992, 3384,3672, 3448,3928,
+   3512,3800, 3576,4056, 3704,3896, 3832,4024
+};
+
+const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH] = 
+{
+    //radix 4, size 992
+    8,4096, 16,2048, 24,6144, 32,1024, 40,5120, 48,3072, 56,7168, 64,512, 72,4608, 
+    80,2560, 88,6656, 96,1536, 104,5632, 112,3584, 120,7680, 128,256, 136,4352, 
+    144,2304, 152,6400, 160,1280, 168,5376, 176,3328, 184,7424, 192,768, 200,4864, 
+    208,2816, 216,6912, 224,1792, 232,5888, 240,3840, 248,7936, 264,4224, 272,2176, 
+    280,6272, 288,1152, 296,5248, 304,3200, 312,7296, 320,640, 328,4736, 336,2688, 
+    344,6784, 352,1664, 360,5760, 368,3712, 376,7808, 392,4480, 400,2432, 408,6528, 
+    416,1408, 424,5504, 432,3456, 440,7552, 448,896, 456,4992, 464,2944, 472,7040, 
+    480,1920, 488,6016, 496,3968, 504,8064, 520,4160, 528,2112, 536,6208, 544,1088, 
+    552,5184, 560,3136, 568,7232, 584,4672, 592,2624, 600,6720, 608,1600, 616,5696, 
+    624,3648, 632,7744, 648,4416, 656,2368, 664,6464, 672,1344, 680,5440, 688,3392, 
+    696,7488, 704,832, 712,4928, 720,2880, 728,6976, 736,1856, 744,5952, 752,3904, 
+    760,8000, 776,4288, 784,2240, 792,6336, 800,1216, 808,5312, 816,3264, 824,7360, 
+    840,4800, 848,2752, 856,6848, 864,1728, 872,5824, 880,3776, 888,7872, 904,4544, 
+    912,2496, 920,6592, 928,1472, 936,5568, 944,3520, 952,7616, 968,5056, 976,3008, 
+    984,7104, 992,1984, 1000,6080, 1008,4032, 1016,8128, 1032,4128, 1040,2080, 
+    1048,6176, 1064,5152, 1072,3104, 1080,7200, 1096,4640, 1104,2592, 1112,6688, 
+    1120,1568, 1128,5664, 1136,3616, 1144,7712, 1160,4384, 1168,2336, 1176,6432, 
+    1184,1312, 1192,5408, 1200,3360, 1208,7456, 1224,4896, 1232,2848, 1240,6944, 
+    1248,1824, 1256,5920, 1264,3872, 1272,7968, 1288,4256, 1296,2208, 1304,6304, 
+    1320,5280, 1328,3232, 1336,7328, 1352,4768, 1360,2720, 1368,6816, 1376,1696, 
+    1384,5792, 1392,3744, 1400,7840, 1416,4512, 1424,2464, 1432,6560, 1448,5536, 
+    1456,3488, 1464,7584, 1480,5024, 1488,2976, 1496,7072, 1504,1952, 1512,6048, 
+    1520,4000, 1528,8096, 1544,4192, 1552,2144, 1560,6240, 1576,5216, 1584,3168, 
+    1592,7264, 1608,4704, 1616,2656, 1624,6752, 1640,5728, 1648,3680, 1656,7776, 
+    1672,4448, 1680,2400, 1688,6496, 1704,5472, 1712,3424, 1720,7520, 1736,4960, 
+    1744,2912, 1752,7008, 1760,1888, 1768,5984, 1776,3936, 1784,8032, 1800,4320, 
+    1808,2272, 1816,6368, 1832,5344, 1840,3296, 1848,7392, 1864,4832, 1872,2784, 
+    1880,6880, 1896,5856, 1904,3808, 1912,7904, 1928,4576, 1936,2528, 1944,6624, 
+    1960,5600, 1968,3552, 1976,7648, 1992,5088, 2000,3040, 2008,7136, 2024,6112, 
+    2032,4064, 2040,8160, 2056,4112, 2072,6160, 2088,5136, 2096,3088, 2104,7184, 
+    2120,4624, 2128,2576, 2136,6672, 2152,5648, 2160,3600, 2168,7696, 2184,4368, 
+    2192,2320, 2200,6416, 2216,5392, 2224,3344, 2232,7440, 2248,4880, 2256,2832, 
+    2264,6928, 2280,5904, 2288,3856, 2296,7952, 2312,4240, 2328,6288, 2344,5264, 
+    2352,3216, 2360,7312, 2376,4752, 2384,2704, 2392,6800, 2408,5776, 2416,3728, 
+    2424,7824, 2440,4496, 2456,6544, 2472,5520, 2480,3472, 2488,7568, 2504,5008, 
+    2512,2960, 2520,7056, 2536,6032, 2544,3984, 2552,8080, 2568,4176, 2584,6224, 
+    2600,5200, 2608,3152, 2616,7248, 2632,4688, 2648,6736, 2664,5712, 2672,3664, 
+    2680,7760, 2696,4432, 2712,6480, 2728,5456, 2736,3408, 2744,7504, 2760,4944, 
+    2768,2896, 2776,6992, 2792,5968, 2800,3920, 2808,8016, 2824,4304, 2840,6352, 
+    2856,5328, 2864,3280, 2872,7376, 2888,4816, 2904,6864, 2920,5840, 2928,3792, 
+    2936,7888, 2952,4560, 2968,6608, 2984,5584, 2992,3536, 3000,7632, 3016,5072, 
+    3032,7120, 3048,6096, 3056,4048, 3064,8144, 3080,4144, 3096,6192, 3112,5168, 
+    3128,7216, 3144,4656, 3160,6704, 3176,5680, 3184,3632, 3192,7728, 3208,4400, 
+    3224,6448, 3240,5424, 3248,3376, 3256,7472, 3272,4912, 3288,6960, 3304,5936, 
+    3312,3888, 3320,7984, 3336,4272, 3352,6320, 3368,5296, 3384,7344, 3400,4784, 
+    3416,6832, 3432,5808, 3440,3760, 3448,7856, 3464,4528, 3480,6576, 3496,5552, 
+    3512,7600, 3528,5040, 3544,7088, 3560,6064, 3568,4016, 3576,8112, 3592,4208, 
+    3608,6256, 3624,5232, 3640,7280, 3656,4720, 3672,6768, 3688,5744, 3704,7792, 
+    3720,4464, 3736,6512, 3752,5488, 3768,7536, 3784,4976, 3800,7024, 3816,6000, 
+    3824,3952, 3832,8048, 3848,4336, 3864,6384, 3880,5360, 3896,7408, 3912,4848, 
+    3928,6896, 3944,5872, 3960,7920, 3976,4592, 3992,6640, 4008,5616, 4024,7664, 
+    4040,5104, 4056,7152, 4072,6128, 4088,8176, 4120,6152, 4136,5128, 4152,7176, 
+    4168,4616, 4184,6664, 4200,5640, 4216,7688, 4232,4360, 4248,6408, 4264,5384, 
+    4280,7432, 4296,4872, 4312,6920, 4328,5896, 4344,7944, 4376,6280, 4392,5256, 
+    4408,7304, 4424,4744, 4440,6792, 4456,5768, 4472,7816, 4504,6536, 4520,5512, 
+    4536,7560, 4552,5000, 4568,7048, 4584,6024, 4600,8072, 4632,6216, 4648,5192, 
+    4664,7240, 4696,6728, 4712,5704, 4728,7752, 4760,6472, 4776,5448, 4792,7496, 
+    4808,4936, 4824,6984, 4840,5960, 4856,8008, 4888,6344, 4904,5320, 4920,7368, 
+    4952,6856, 4968,5832, 4984,7880, 5016,6600, 5032,5576, 5048,7624, 5080,7112, 
+    5096,6088, 5112,8136, 5144,6184, 5176,7208, 5208,6696, 5224,5672, 5240,7720, 
+    5272,6440, 5288,5416, 5304,7464, 5336,6952, 5352,5928, 5368,7976, 5400,6312, 
+    5432,7336, 5464,6824, 5480,5800, 5496,7848, 5528,6568, 5560,7592, 5592,7080, 
+    5608,6056, 5624,8104, 5656,6248, 5688,7272, 5720,6760, 5752,7784, 5784,6504, 
+    5816,7528, 5848,7016, 5864,5992, 5880,8040, 5912,6376, 5944,7400, 5976,6888, 
+    6008,7912, 6040,6632, 6072,7656, 6104,7144, 6136,8168, 6200,7192, 6232,6680, 
+    6264,7704, 6296,6424, 6328,7448, 6360,6936, 6392,7960, 6456,7320, 6488,6808, 
+    6520,7832, 6584,7576, 6616,7064, 6648,8088, 6712,7256, 6776,7768, 6840,7512, 
+    6872,7000, 6904,8024, 6968,7384, 7032,7896, 7096,7640, 7160,8152, 7288,7736, 
+    7352,7480, 7416,7992, 7544,7864, 7672,8120, 7928,8056 
+};
+
+const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH] = 
+{
+    //4x2, size 1984
+    8,8192, 16,4096, 24,12288, 32,2048, 40,10240, 48,6144, 56,14336, 64,1024, 
+    72,9216, 80,5120, 88,13312, 96,3072, 104,11264, 112,7168, 120,15360, 128,512, 
+    136,8704, 144,4608, 152,12800, 160,2560, 168,10752, 176,6656, 184,14848, 
+    192,1536, 200,9728, 208,5632, 216,13824, 224,3584, 232,11776, 240,7680, 
+    248,15872, 264,8448, 272,4352, 280,12544, 288,2304, 296,10496, 304,6400, 
+    312,14592, 320,1280, 328,9472, 336,5376, 344,13568, 352,3328, 360,11520, 
+    368,7424, 376,15616, 384,768, 392,8960, 400,4864, 408,13056, 416,2816, 
+    424,11008, 432,6912, 440,15104, 448,1792, 456,9984, 464,5888, 472,14080, 
+    480,3840, 488,12032, 496,7936, 504,16128, 520,8320, 528,4224, 536,12416, 
+    544,2176, 552,10368, 560,6272, 568,14464, 576,1152, 584,9344, 592,5248, 
+    600,13440, 608,3200, 616,11392, 624,7296, 632,15488, 648,8832, 656,4736, 
+    664,12928, 672,2688, 680,10880, 688,6784, 696,14976, 704,1664, 712,9856, 
+    720,5760, 728,13952, 736,3712, 744,11904, 752,7808, 760,16000, 776,8576, 
+    784,4480, 792,12672, 800,2432, 808,10624, 816,6528, 824,14720, 832,1408, 
+    840,9600, 848,5504, 856,13696, 864,3456, 872,11648, 880,7552, 888,15744, 
+    904,9088, 912,4992, 920,13184, 928,2944, 936,11136, 944,7040, 952,15232, 
+    960,1920, 968,10112, 976,6016, 984,14208, 992,3968, 1000,12160, 1008,8064, 
+    1016,16256, 1032,8256, 1040,4160, 1048,12352, 1056,2112, 1064,10304, 1072,6208, 
+    1080,14400, 1096,9280, 1104,5184, 1112,13376, 1120,3136, 1128,11328, 1136,7232, 
+    1144,15424, 1160,8768, 1168,4672, 1176,12864, 1184,2624, 1192,10816, 1200,6720, 
+    1208,14912, 1216,1600, 1224,9792, 1232,5696, 1240,13888, 1248,3648, 1256,11840, 
+    1264,7744, 1272,15936, 1288,8512, 1296,4416, 1304,12608, 1312,2368, 1320,10560, 
+    1328,6464, 1336,14656, 1352,9536, 1360,5440, 1368,13632, 1376,3392, 1384,11584, 
+    1392,7488, 1400,15680, 1416,9024, 1424,4928, 1432,13120, 1440,2880, 1448,11072, 
+    1456,6976, 1464,15168, 1472,1856, 1480,10048, 1488,5952, 1496,14144, 1504,3904, 
+    1512,12096, 1520,8000, 1528,16192, 1544,8384, 1552,4288, 1560,12480, 1568,2240, 
+    1576,10432, 1584,6336, 1592,14528, 1608,9408, 1616,5312, 1624,13504, 1632,3264, 
+    1640,11456, 1648,7360, 1656,15552, 1672,8896, 1680,4800, 1688,12992, 1696,2752, 
+    1704,10944, 1712,6848, 1720,15040, 1736,9920, 1744,5824, 1752,14016, 1760,3776, 
+    1768,11968, 1776,7872, 1784,16064, 1800,8640, 1808,4544, 1816,12736, 1824,2496, 
+    1832,10688, 1840,6592, 1848,14784, 1864,9664, 1872,5568, 1880,13760, 1888,3520, 
+    1896,11712, 1904,7616, 1912,15808, 1928,9152, 1936,5056, 1944,13248, 1952,3008, 
+    1960,11200, 1968,7104, 1976,15296, 1992,10176, 2000,6080, 2008,14272, 2016,4032, 
+    2024,12224, 2032,8128, 2040,16320, 2056,8224, 2064,4128, 2072,12320, 2088,10272, 
+    2096,6176, 2104,14368, 2120,9248, 2128,5152, 2136,13344, 2144,3104, 2152,11296, 
+    2160,7200, 2168,15392, 2184,8736, 2192,4640, 2200,12832, 2208,2592, 2216,10784, 
+    2224,6688, 2232,14880, 2248,9760, 2256,5664, 2264,13856, 2272,3616, 2280,11808, 
+    2288,7712, 2296,15904, 2312,8480, 2320,4384, 2328,12576, 2344,10528, 2352,6432, 
+    2360,14624, 2376,9504, 2384,5408, 2392,13600, 2400,3360, 2408,11552, 2416,7456, 
+    2424,15648, 2440,8992, 2448,4896, 2456,13088, 2464,2848, 2472,11040, 2480,6944, 
+    2488,15136, 2504,10016, 2512,5920, 2520,14112, 2528,3872, 2536,12064, 2544,7968, 
+    2552,16160, 2568,8352, 2576,4256, 2584,12448, 2600,10400, 2608,6304, 2616,14496, 
+    2632,9376, 2640,5280, 2648,13472, 2656,3232, 2664,11424, 2672,7328, 2680,15520, 
+    2696,8864, 2704,4768, 2712,12960, 2728,10912, 2736,6816, 2744,15008, 2760,9888, 
+    2768,5792, 2776,13984, 2784,3744, 2792,11936, 2800,7840, 2808,16032, 2824,8608, 
+    2832,4512, 2840,12704, 2856,10656, 2864,6560, 2872,14752, 2888,9632, 2896,5536, 
+    2904,13728, 2912,3488, 2920,11680, 2928,7584, 2936,15776, 2952,9120, 2960,5024, 
+    2968,13216, 2984,11168, 2992,7072, 3000,15264, 3016,10144, 3024,6048, 
+    3032,14240, 3040,4000, 3048,12192, 3056,8096, 3064,16288, 3080,8288, 3088,4192, 
+    3096,12384, 3112,10336, 3120,6240, 3128,14432, 3144,9312, 3152,5216, 3160,13408, 
+    3176,11360, 3184,7264, 3192,15456, 3208,8800, 3216,4704, 3224,12896, 3240,10848, 
+    3248,6752, 3256,14944, 3272,9824, 3280,5728, 3288,13920, 3296,3680, 3304,11872, 
+    3312,7776, 3320,15968, 3336,8544, 3344,4448, 3352,12640, 3368,10592, 3376,6496, 
+    3384,14688, 3400,9568, 3408,5472, 3416,13664, 3432,11616, 3440,7520, 3448,15712, 
+    3464,9056, 3472,4960, 3480,13152, 3496,11104, 3504,7008, 3512,15200, 3528,10080, 
+    3536,5984, 3544,14176, 3552,3936, 3560,12128, 3568,8032, 3576,16224, 3592,8416, 
+    3600,4320, 3608,12512, 3624,10464, 3632,6368, 3640,14560, 3656,9440, 3664,5344, 
+    3672,13536, 3688,11488, 3696,7392, 3704,15584, 3720,8928, 3728,4832, 3736,13024, 
+    3752,10976, 3760,6880, 3768,15072, 3784,9952, 3792,5856, 3800,14048, 3816,12000, 
+    3824,7904, 3832,16096, 3848,8672, 3856,4576, 3864,12768, 3880,10720, 3888,6624, 
+    3896,14816, 3912,9696, 3920,5600, 3928,13792, 3944,11744, 3952,7648, 3960,15840, 
+    3976,9184, 3984,5088, 3992,13280, 4008,11232, 4016,7136, 4024,15328, 4040,10208, 
+    4048,6112, 4056,14304, 4072,12256, 4080,8160, 4088,16352, 4104,8208, 4120,12304, 
+    4136,10256, 4144,6160, 4152,14352, 4168,9232, 4176,5136, 4184,13328, 4200,11280, 
+    4208,7184, 4216,15376, 4232,8720, 4240,4624, 4248,12816, 4264,10768, 4272,6672, 
+    4280,14864, 4296,9744, 4304,5648, 4312,13840, 4328,11792, 4336,7696, 4344,15888, 
+    4360,8464, 4376,12560, 4392,10512, 4400,6416, 4408,14608, 4424,9488, 4432,5392, 
+    4440,13584, 4456,11536, 4464,7440, 4472,15632, 4488,8976, 4496,4880, 4504,13072, 
+    4520,11024, 4528,6928, 4536,15120, 4552,10000, 4560,5904, 4568,14096, 
+    4584,12048, 4592,7952, 4600,16144, 4616,8336, 4632,12432, 4648,10384, 4656,6288, 
+    4664,14480, 4680,9360, 4688,5264, 4696,13456, 4712,11408, 4720,7312, 4728,15504, 
+    4744,8848, 4760,12944, 4776,10896, 4784,6800, 4792,14992, 4808,9872, 4816,5776, 
+    4824,13968, 4840,11920, 4848,7824, 4856,16016, 4872,8592, 4888,12688, 
+    4904,10640, 4912,6544, 4920,14736, 4936,9616, 4944,5520, 4952,13712, 4968,11664, 
+    4976,7568, 4984,15760, 5000,9104, 5016,13200, 5032,11152, 5040,7056, 5048,15248, 
+    5064,10128, 5072,6032, 5080,14224, 5096,12176, 5104,8080, 5112,16272, 5128,8272, 
+    5144,12368, 5160,10320, 5168,6224, 5176,14416, 5192,9296, 5208,13392, 
+    5224,11344, 5232,7248, 5240,15440, 5256,8784, 5272,12880, 5288,10832, 5296,6736, 
+    5304,14928, 5320,9808, 5328,5712, 5336,13904, 5352,11856, 5360,7760, 5368,15952, 
+    5384,8528, 5400,12624, 5416,10576, 5424,6480, 5432,14672, 5448,9552, 5464,13648, 
+    5480,11600, 5488,7504, 5496,15696, 5512,9040, 5528,13136, 5544,11088, 5552,6992, 
+    5560,15184, 5576,10064, 5584,5968, 5592,14160, 5608,12112, 5616,8016, 
+    5624,16208, 5640,8400, 5656,12496, 5672,10448, 5680,6352, 5688,14544, 5704,9424, 
+    5720,13520, 5736,11472, 5744,7376, 5752,15568, 5768,8912, 5784,13008, 
+    5800,10960, 5808,6864, 5816,15056, 5832,9936, 5848,14032, 5864,11984, 5872,7888, 
+    5880,16080, 5896,8656, 5912,12752, 5928,10704, 5936,6608, 5944,14800, 5960,9680, 
+    5976,13776, 5992,11728, 6000,7632, 6008,15824, 6024,9168, 6040,13264, 
+    6056,11216, 6064,7120, 6072,15312, 6088,10192, 6104,14288, 6120,12240, 
+    6128,8144, 6136,16336, 6152,8240, 6168,12336, 6184,10288, 6200,14384, 6216,9264, 
+    6232,13360, 6248,11312, 6256,7216, 6264,15408, 6280,8752, 6296,12848, 
+    6312,10800, 6320,6704, 6328,14896, 6344,9776, 6360,13872, 6376,11824, 6384,7728, 
+    6392,15920, 6408,8496, 6424,12592, 6440,10544, 6456,14640, 6472,9520, 
+    6488,13616, 6504,11568, 6512,7472, 6520,15664, 6536,9008, 6552,13104, 
+    6568,11056, 6576,6960, 6584,15152, 6600,10032, 6616,14128, 6632,12080, 
+    6640,7984, 6648,16176, 6664,8368, 6680,12464, 6696,10416, 6712,14512, 6728,9392, 
+    6744,13488, 6760,11440, 6768,7344, 6776,15536, 6792,8880, 6808,12976, 
+    6824,10928, 6840,15024, 6856,9904, 6872,14000, 6888,11952, 6896,7856, 
+    6904,16048, 6920,8624, 6936,12720, 6952,10672, 6968,14768, 6984,9648, 
+    7000,13744, 7016,11696, 7024,7600, 7032,15792, 7048,9136, 7064,13232, 
+    7080,11184, 7096,15280, 7112,10160, 7128,14256, 7144,12208, 7152,8112, 
+    7160,16304, 7176,8304, 7192,12400, 7208,10352, 7224,14448, 7240,9328, 
+    7256,13424, 7272,11376, 7288,15472, 7304,8816, 7320,12912, 7336,10864, 
+    7352,14960, 7368,9840, 7384,13936, 7400,11888, 7408,7792, 7416,15984, 7432,8560, 
+    7448,12656, 7464,10608, 7480,14704, 7496,9584, 7512,13680, 7528,11632, 
+    7544,15728, 7560,9072, 7576,13168, 7592,11120, 7608,15216, 7624,10096, 
+    7640,14192, 7656,12144, 7664,8048, 7672,16240, 7688,8432, 7704,12528, 
+    7720,10480, 7736,14576, 7752,9456, 7768,13552, 7784,11504, 7800,15600, 
+    7816,8944, 7832,13040, 7848,10992, 7864,15088, 7880,9968, 7896,14064, 
+    7912,12016, 7928,16112, 7944,8688, 7960,12784, 7976,10736, 7992,14832, 
+    8008,9712, 8024,13808, 8040,11760, 8056,15856, 8072,9200, 8088,13296, 
+    8104,11248, 8120,15344, 8136,10224, 8152,14320, 8168,12272, 8184,16368, 
+    8216,12296, 8232,10248, 8248,14344, 8264,9224, 8280,13320, 8296,11272, 
+    8312,15368, 8328,8712, 8344,12808, 8360,10760, 8376,14856, 8392,9736, 
+    8408,13832, 8424,11784, 8440,15880, 8472,12552, 8488,10504, 8504,14600, 
+    8520,9480, 8536,13576, 8552,11528, 8568,15624, 8584,8968, 8600,13064, 
+    8616,11016, 8632,15112, 8648,9992, 8664,14088, 8680,12040, 8696,16136, 
+    8728,12424, 8744,10376, 8760,14472, 8776,9352, 8792,13448, 8808,11400, 
+    8824,15496, 8856,12936, 8872,10888, 8888,14984, 8904,9864, 8920,13960, 
+    8936,11912, 8952,16008, 8984,12680, 9000,10632, 9016,14728, 9032,9608, 
+    9048,13704, 9064,11656, 9080,15752, 9112,13192, 9128,11144, 9144,15240, 
+    9160,10120, 9176,14216, 9192,12168, 9208,16264, 9240,12360, 9256,10312, 
+    9272,14408, 9304,13384, 9320,11336, 9336,15432, 9368,12872, 9384,10824, 
+    9400,14920, 9416,9800, 9432,13896, 9448,11848, 9464,15944, 9496,12616, 
+    9512,10568, 9528,14664, 9560,13640, 9576,11592, 9592,15688, 9624,13128, 
+    9640,11080, 9656,15176, 9672,10056, 9688,14152, 9704,12104, 9720,16200, 
+    9752,12488, 9768,10440, 9784,14536, 9816,13512, 9832,11464, 9848,15560, 
+    9880,13000, 9896,10952, 9912,15048, 9944,14024, 9960,11976, 9976,16072, 
+    10008,12744, 10024,10696, 10040,14792, 10072,13768, 10088,11720, 10104,15816, 
+    10136,13256, 10152,11208, 10168,15304, 10200,14280, 10216,12232, 10232,16328, 
+    10264,12328, 10296,14376, 10328,13352, 10344,11304, 10360,15400, 10392,12840, 
+    10408,10792, 10424,14888, 10456,13864, 10472,11816, 10488,15912, 10520,12584, 
+    10552,14632, 10584,13608, 10600,11560, 10616,15656, 10648,13096, 10664,11048, 
+    10680,15144, 10712,14120, 10728,12072, 10744,16168, 10776,12456, 10808,14504, 
+    10840,13480, 10856,11432, 10872,15528, 10904,12968, 10936,15016, 10968,13992, 
+    10984,11944, 11000,16040, 11032,12712, 11064,14760, 11096,13736, 11112,11688, 
+    11128,15784, 11160,13224, 11192,15272, 11224,14248, 11240,12200, 11256,16296, 
+    11288,12392, 11320,14440, 11352,13416, 11384,15464, 11416,12904, 11448,14952, 
+    11480,13928, 11496,11880, 11512,15976, 11544,12648, 11576,14696, 11608,13672, 
+    11640,15720, 11672,13160, 11704,15208, 11736,14184, 11752,12136, 11768,16232, 
+    11800,12520, 11832,14568, 11864,13544, 11896,15592, 11928,13032, 11960,15080, 
+    11992,14056, 12024,16104, 12056,12776, 12088,14824, 12120,13800, 12152,15848, 
+    12184,13288, 12216,15336, 12248,14312, 12280,16360, 12344,14360, 12376,13336, 
+    12408,15384, 12440,12824, 12472,14872, 12504,13848, 12536,15896, 12600,14616, 
+    12632,13592, 12664,15640, 12696,13080, 12728,15128, 12760,14104, 12792,16152, 
+    12856,14488, 12888,13464, 12920,15512, 12984,15000, 13016,13976, 13048,16024, 
+    13112,14744, 13144,13720, 13176,15768, 13240,15256, 13272,14232, 13304,16280, 
+    13368,14424, 13432,15448, 13496,14936, 13528,13912, 13560,15960, 13624,14680, 
+    13688,15704, 13752,15192, 13784,14168, 13816,16216, 13880,14552, 13944,15576, 
+    14008,15064, 14072,16088, 14136,14808, 14200,15832, 14264,15320, 14328,16344, 
+    14456,15416, 14520,14904, 14584,15928, 14712,15672, 14776,15160, 14840,16184, 
+    14968,15544, 15096,16056, 15224,15800, 15352,16312, 15608,15992, 15864,16248 
+};
+
+const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH] = 
+{
+    //radix 4, size 4032
+    8,16384, 16,8192, 24,24576, 32,4096, 40,20480, 48,12288, 56,28672, 64,2048, 
+    72,18432, 80,10240, 88,26624, 96,6144, 104,22528, 112,14336, 120,30720, 
+    128,1024, 136,17408, 144,9216, 152,25600, 160,5120, 168,21504, 176,13312, 
+    184,29696, 192,3072, 200,19456, 208,11264, 216,27648, 224,7168, 232,23552, 
+    240,15360, 248,31744, 256,512, 264,16896, 272,8704, 280,25088, 288,4608, 
+    296,20992, 304,12800, 312,29184, 320,2560, 328,18944, 336,10752, 344,27136, 
+    352,6656, 360,23040, 368,14848, 376,31232, 384,1536, 392,17920, 400,9728, 
+    408,26112, 416,5632, 424,22016, 432,13824, 440,30208, 448,3584, 456,19968, 
+    464,11776, 472,28160, 480,7680, 488,24064, 496,15872, 504,32256, 520,16640, 
+    528,8448, 536,24832, 544,4352, 552,20736, 560,12544, 568,28928, 576,2304, 
+    584,18688, 592,10496, 600,26880, 608,6400, 616,22784, 624,14592, 632,30976, 
+    640,1280, 648,17664, 656,9472, 664,25856, 672,5376, 680,21760, 688,13568, 
+    696,29952, 704,3328, 712,19712, 720,11520, 728,27904, 736,7424, 744,23808, 
+    752,15616, 760,32000, 776,17152, 784,8960, 792,25344, 800,4864, 808,21248, 
+    816,13056, 824,29440, 832,2816, 840,19200, 848,11008, 856,27392, 864,6912, 
+    872,23296, 880,15104, 888,31488, 896,1792, 904,18176, 912,9984, 920,26368, 
+    928,5888, 936,22272, 944,14080, 952,30464, 960,3840, 968,20224, 976,12032, 
+    984,28416, 992,7936, 1000,24320, 1008,16128, 1016,32512, 1032,16512, 1040,8320, 
+    1048,24704, 1056,4224, 1064,20608, 1072,12416, 1080,28800, 1088,2176, 
+    1096,18560, 1104,10368, 1112,26752, 1120,6272, 1128,22656, 1136,14464, 
+    1144,30848, 1160,17536, 1168,9344, 1176,25728, 1184,5248, 1192,21632, 
+    1200,13440, 1208,29824, 1216,3200, 1224,19584, 1232,11392, 1240,27776, 
+    1248,7296, 1256,23680, 1264,15488, 1272,31872, 1288,17024, 1296,8832, 
+    1304,25216, 1312,4736, 1320,21120, 1328,12928, 1336,29312, 1344,2688, 
+    1352,19072, 1360,10880, 1368,27264, 1376,6784, 1384,23168, 1392,14976, 
+    1400,31360, 1408,1664, 1416,18048, 1424,9856, 1432,26240, 1440,5760, 1448,22144, 
+    1456,13952, 1464,30336, 1472,3712, 1480,20096, 1488,11904, 1496,28288, 
+    1504,7808, 1512,24192, 1520,16000, 1528,32384, 1544,16768, 1552,8576, 
+    1560,24960, 1568,4480, 1576,20864, 1584,12672, 1592,29056, 1600,2432, 
+    1608,18816, 1616,10624, 1624,27008, 1632,6528, 1640,22912, 1648,14720, 
+    1656,31104, 1672,17792, 1680,9600, 1688,25984, 1696,5504, 1704,21888, 
+    1712,13696, 1720,30080, 1728,3456, 1736,19840, 1744,11648, 1752,28032, 
+    1760,7552, 1768,23936, 1776,15744, 1784,32128, 1800,17280, 1808,9088, 
+    1816,25472, 1824,4992, 1832,21376, 1840,13184, 1848,29568, 1856,2944, 
+    1864,19328, 1872,11136, 1880,27520, 1888,7040, 1896,23424, 1904,15232, 
+    1912,31616, 1928,18304, 1936,10112, 1944,26496, 1952,6016, 1960,22400, 
+    1968,14208, 1976,30592, 1984,3968, 1992,20352, 2000,12160, 2008,28544, 
+    2016,8064, 2024,24448, 2032,16256, 2040,32640, 2056,16448, 2064,8256, 
+    2072,24640, 2080,4160, 2088,20544, 2096,12352, 2104,28736, 2120,18496, 
+    2128,10304, 2136,26688, 2144,6208, 2152,22592, 2160,14400, 2168,30784, 
+    2184,17472, 2192,9280, 2200,25664, 2208,5184, 2216,21568, 2224,13376, 
+    2232,29760, 2240,3136, 2248,19520, 2256,11328, 2264,27712, 2272,7232, 
+    2280,23616, 2288,15424, 2296,31808, 2312,16960, 2320,8768, 2328,25152, 
+    2336,4672, 2344,21056, 2352,12864, 2360,29248, 2368,2624, 2376,19008, 
+    2384,10816, 2392,27200, 2400,6720, 2408,23104, 2416,14912, 2424,31296, 
+    2440,17984, 2448,9792, 2456,26176, 2464,5696, 2472,22080, 2480,13888, 
+    2488,30272, 2496,3648, 2504,20032, 2512,11840, 2520,28224, 2528,7744, 
+    2536,24128, 2544,15936, 2552,32320, 2568,16704, 2576,8512, 2584,24896, 
+    2592,4416, 2600,20800, 2608,12608, 2616,28992, 2632,18752, 2640,10560, 
+    2648,26944, 2656,6464, 2664,22848, 2672,14656, 2680,31040, 2696,17728, 
+    2704,9536, 2712,25920, 2720,5440, 2728,21824, 2736,13632, 2744,30016, 2752,3392, 
+    2760,19776, 2768,11584, 2776,27968, 2784,7488, 2792,23872, 2800,15680, 
+    2808,32064, 2824,17216, 2832,9024, 2840,25408, 2848,4928, 2856,21312, 
+    2864,13120, 2872,29504, 2888,19264, 2896,11072, 2904,27456, 2912,6976, 
+    2920,23360, 2928,15168, 2936,31552, 2952,18240, 2960,10048, 2968,26432, 
+    2976,5952, 2984,22336, 2992,14144, 3000,30528, 3008,3904, 3016,20288, 
+    3024,12096, 3032,28480, 3040,8000, 3048,24384, 3056,16192, 3064,32576, 
+    3080,16576, 3088,8384, 3096,24768, 3104,4288, 3112,20672, 3120,12480, 
+    3128,28864, 3144,18624, 3152,10432, 3160,26816, 3168,6336, 3176,22720, 
+    3184,14528, 3192,30912, 3208,17600, 3216,9408, 3224,25792, 3232,5312, 
+    3240,21696, 3248,13504, 3256,29888, 3272,19648, 3280,11456, 3288,27840, 
+    3296,7360, 3304,23744, 3312,15552, 3320,31936, 3336,17088, 3344,8896, 
+    3352,25280, 3360,4800, 3368,21184, 3376,12992, 3384,29376, 3400,19136, 
+    3408,10944, 3416,27328, 3424,6848, 3432,23232, 3440,15040, 3448,31424, 
+    3464,18112, 3472,9920, 3480,26304, 3488,5824, 3496,22208, 3504,14016, 
+    3512,30400, 3520,3776, 3528,20160, 3536,11968, 3544,28352, 3552,7872, 
+    3560,24256, 3568,16064, 3576,32448, 3592,16832, 3600,8640, 3608,25024, 
+    3616,4544, 3624,20928, 3632,12736, 3640,29120, 3656,18880, 3664,10688, 
+    3672,27072, 3680,6592, 3688,22976, 3696,14784, 3704,31168, 3720,17856, 
+    3728,9664, 3736,26048, 3744,5568, 3752,21952, 3760,13760, 3768,30144, 
+    3784,19904, 3792,11712, 3800,28096, 3808,7616, 3816,24000, 3824,15808, 
+    3832,32192, 3848,17344, 3856,9152, 3864,25536, 3872,5056, 3880,21440, 
+    3888,13248, 3896,29632, 3912,19392, 3920,11200, 3928,27584, 3936,7104, 
+    3944,23488, 3952,15296, 3960,31680, 3976,18368, 3984,10176, 3992,26560, 
+    4000,6080, 4008,22464, 4016,14272, 4024,30656, 4040,20416, 4048,12224, 
+    4056,28608, 4064,8128, 4072,24512, 4080,16320, 4088,32704, 4104,16416, 
+    4112,8224, 4120,24608, 4136,20512, 4144,12320, 4152,28704, 4168,18464, 
+    4176,10272, 4184,26656, 4192,6176, 4200,22560, 4208,14368, 4216,30752, 
+    4232,17440, 4240,9248, 4248,25632, 4256,5152, 4264,21536, 4272,13344, 
+    4280,29728, 4296,19488, 4304,11296, 4312,27680, 4320,7200, 4328,23584, 
+    4336,15392, 4344,31776, 4360,16928, 4368,8736, 4376,25120, 4384,4640, 
+    4392,21024, 4400,12832, 4408,29216, 4424,18976, 4432,10784, 4440,27168, 
+    4448,6688, 4456,23072, 4464,14880, 4472,31264, 4488,17952, 4496,9760, 
+    4504,26144, 4512,5664, 4520,22048, 4528,13856, 4536,30240, 4552,20000, 
+    4560,11808, 4568,28192, 4576,7712, 4584,24096, 4592,15904, 4600,32288, 
+    4616,16672, 4624,8480, 4632,24864, 4648,20768, 4656,12576, 4664,28960, 
+    4680,18720, 4688,10528, 4696,26912, 4704,6432, 4712,22816, 4720,14624, 
+    4728,31008, 4744,17696, 4752,9504, 4760,25888, 4768,5408, 4776,21792, 
+    4784,13600, 4792,29984, 4808,19744, 4816,11552, 4824,27936, 4832,7456, 
+    4840,23840, 4848,15648, 4856,32032, 4872,17184, 4880,8992, 4888,25376, 
+    4904,21280, 4912,13088, 4920,29472, 4936,19232, 4944,11040, 4952,27424, 
+    4960,6944, 4968,23328, 4976,15136, 4984,31520, 5000,18208, 5008,10016, 
+    5016,26400, 5024,5920, 5032,22304, 5040,14112, 5048,30496, 5064,20256, 
+    5072,12064, 5080,28448, 5088,7968, 5096,24352, 5104,16160, 5112,32544, 
+    5128,16544, 5136,8352, 5144,24736, 5160,20640, 5168,12448, 5176,28832, 
+    5192,18592, 5200,10400, 5208,26784, 5216,6304, 5224,22688, 5232,14496, 
+    5240,30880, 5256,17568, 5264,9376, 5272,25760, 5288,21664, 5296,13472, 
+    5304,29856, 5320,19616, 5328,11424, 5336,27808, 5344,7328, 5352,23712, 
+    5360,15520, 5368,31904, 5384,17056, 5392,8864, 5400,25248, 5416,21152, 
+    5424,12960, 5432,29344, 5448,19104, 5456,10912, 5464,27296, 5472,6816, 
+    5480,23200, 5488,15008, 5496,31392, 5512,18080, 5520,9888, 5528,26272, 
+    5536,5792, 5544,22176, 5552,13984, 5560,30368, 5576,20128, 5584,11936, 
+    5592,28320, 5600,7840, 5608,24224, 5616,16032, 5624,32416, 5640,16800, 
+    5648,8608, 5656,24992, 5672,20896, 5680,12704, 5688,29088, 5704,18848, 
+    5712,10656, 5720,27040, 5728,6560, 5736,22944, 5744,14752, 5752,31136, 
+    5768,17824, 5776,9632, 5784,26016, 5800,21920, 5808,13728, 5816,30112, 
+    5832,19872, 5840,11680, 5848,28064, 5856,7584, 5864,23968, 5872,15776, 
+    5880,32160, 5896,17312, 5904,9120, 5912,25504, 5928,21408, 5936,13216, 
+    5944,29600, 5960,19360, 5968,11168, 5976,27552, 5984,7072, 5992,23456, 
+    6000,15264, 6008,31648, 6024,18336, 6032,10144, 6040,26528, 6056,22432, 
+    6064,14240, 6072,30624, 6088,20384, 6096,12192, 6104,28576, 6112,8096, 
+    6120,24480, 6128,16288, 6136,32672, 6152,16480, 6160,8288, 6168,24672, 
+    6184,20576, 6192,12384, 6200,28768, 6216,18528, 6224,10336, 6232,26720, 
+    6248,22624, 6256,14432, 6264,30816, 6280,17504, 6288,9312, 6296,25696, 
+    6312,21600, 6320,13408, 6328,29792, 6344,19552, 6352,11360, 6360,27744, 
+    6368,7264, 6376,23648, 6384,15456, 6392,31840, 6408,16992, 6416,8800, 
+    6424,25184, 6440,21088, 6448,12896, 6456,29280, 6472,19040, 6480,10848, 
+    6488,27232, 6496,6752, 6504,23136, 6512,14944, 6520,31328, 6536,18016, 
+    6544,9824, 6552,26208, 6568,22112, 6576,13920, 6584,30304, 6600,20064, 
+    6608,11872, 6616,28256, 6624,7776, 6632,24160, 6640,15968, 6648,32352, 
+    6664,16736, 6672,8544, 6680,24928, 6696,20832, 6704,12640, 6712,29024, 
+    6728,18784, 6736,10592, 6744,26976, 6760,22880, 6768,14688, 6776,31072, 
+    6792,17760, 6800,9568, 6808,25952, 6824,21856, 6832,13664, 6840,30048, 
+    6856,19808, 6864,11616, 6872,28000, 6880,7520, 6888,23904, 6896,15712, 
+    6904,32096, 6920,17248, 6928,9056, 6936,25440, 6952,21344, 6960,13152, 
+    6968,29536, 6984,19296, 6992,11104, 7000,27488, 7016,23392, 7024,15200, 
+    7032,31584, 7048,18272, 7056,10080, 7064,26464, 7080,22368, 7088,14176, 
+    7096,30560, 7112,20320, 7120,12128, 7128,28512, 7136,8032, 7144,24416, 
+    7152,16224, 7160,32608, 7176,16608, 7184,8416, 7192,24800, 7208,20704, 
+    7216,12512, 7224,28896, 7240,18656, 7248,10464, 7256,26848, 7272,22752, 
+    7280,14560, 7288,30944, 7304,17632, 7312,9440, 7320,25824, 7336,21728, 
+    7344,13536, 7352,29920, 7368,19680, 7376,11488, 7384,27872, 7400,23776, 
+    7408,15584, 7416,31968, 7432,17120, 7440,8928, 7448,25312, 7464,21216, 
+    7472,13024, 7480,29408, 7496,19168, 7504,10976, 7512,27360, 7528,23264, 
+    7536,15072, 7544,31456, 7560,18144, 7568,9952, 7576,26336, 7592,22240, 
+    7600,14048, 7608,30432, 7624,20192, 7632,12000, 7640,28384, 7648,7904, 
+    7656,24288, 7664,16096, 7672,32480, 7688,16864, 7696,8672, 7704,25056, 
+    7720,20960, 7728,12768, 7736,29152, 7752,18912, 7760,10720, 7768,27104, 
+    7784,23008, 7792,14816, 7800,31200, 7816,17888, 7824,9696, 7832,26080, 
+    7848,21984, 7856,13792, 7864,30176, 7880,19936, 7888,11744, 7896,28128, 
+    7912,24032, 7920,15840, 7928,32224, 7944,17376, 7952,9184, 7960,25568, 
+    7976,21472, 7984,13280, 7992,29664, 8008,19424, 8016,11232, 8024,27616, 
+    8040,23520, 8048,15328, 8056,31712, 8072,18400, 8080,10208, 8088,26592, 
+    8104,22496, 8112,14304, 8120,30688, 8136,20448, 8144,12256, 8152,28640, 
+    8168,24544, 8176,16352, 8184,32736, 8200,16400, 8216,24592, 8232,20496, 
+    8240,12304, 8248,28688, 8264,18448, 8272,10256, 8280,26640, 8296,22544, 
+    8304,14352, 8312,30736, 8328,17424, 8336,9232, 8344,25616, 8360,21520, 
+    8368,13328, 8376,29712, 8392,19472, 8400,11280, 8408,27664, 8424,23568, 
+    8432,15376, 8440,31760, 8456,16912, 8464,8720, 8472,25104, 8488,21008, 
+    8496,12816, 8504,29200, 8520,18960, 8528,10768, 8536,27152, 8552,23056, 
+    8560,14864, 8568,31248, 8584,17936, 8592,9744, 8600,26128, 8616,22032, 
+    8624,13840, 8632,30224, 8648,19984, 8656,11792, 8664,28176, 8680,24080, 
+    8688,15888, 8696,32272, 8712,16656, 8728,24848, 8744,20752, 8752,12560, 
+    8760,28944, 8776,18704, 8784,10512, 8792,26896, 8808,22800, 8816,14608, 
+    8824,30992, 8840,17680, 8848,9488, 8856,25872, 8872,21776, 8880,13584, 
+    8888,29968, 8904,19728, 8912,11536, 8920,27920, 8936,23824, 8944,15632, 
+    8952,32016, 8968,17168, 8984,25360, 9000,21264, 9008,13072, 9016,29456, 
+    9032,19216, 9040,11024, 9048,27408, 9064,23312, 9072,15120, 9080,31504, 
+    9096,18192, 9104,10000, 9112,26384, 9128,22288, 9136,14096, 9144,30480, 
+    9160,20240, 9168,12048, 9176,28432, 9192,24336, 9200,16144, 9208,32528, 
+    9224,16528, 9240,24720, 9256,20624, 9264,12432, 9272,28816, 9288,18576, 
+    9296,10384, 9304,26768, 9320,22672, 9328,14480, 9336,30864, 9352,17552, 
+    9368,25744, 9384,21648, 9392,13456, 9400,29840, 9416,19600, 9424,11408, 
+    9432,27792, 9448,23696, 9456,15504, 9464,31888, 9480,17040, 9496,25232, 
+    9512,21136, 9520,12944, 9528,29328, 9544,19088, 9552,10896, 9560,27280, 
+    9576,23184, 9584,14992, 9592,31376, 9608,18064, 9616,9872, 9624,26256, 
+    9640,22160, 9648,13968, 9656,30352, 9672,20112, 9680,11920, 9688,28304, 
+    9704,24208, 9712,16016, 9720,32400, 9736,16784, 9752,24976, 9768,20880, 
+    9776,12688, 9784,29072, 9800,18832, 9808,10640, 9816,27024, 9832,22928, 
+    9840,14736, 9848,31120, 9864,17808, 9880,26000, 9896,21904, 9904,13712, 
+    9912,30096, 9928,19856, 9936,11664, 9944,28048, 9960,23952, 9968,15760, 
+    9976,32144, 9992,17296, 10008,25488, 10024,21392, 10032,13200, 10040,29584, 
+    10056,19344, 10064,11152, 10072,27536, 10088,23440, 10096,15248, 10104,31632, 
+    10120,18320, 10136,26512, 10152,22416, 10160,14224, 10168,30608, 10184,20368, 
+    10192,12176, 10200,28560, 10216,24464, 10224,16272, 10232,32656, 10248,16464, 
+    10264,24656, 10280,20560, 10288,12368, 10296,28752, 10312,18512, 10328,26704, 
+    10344,22608, 10352,14416, 10360,30800, 10376,17488, 10392,25680, 10408,21584, 
+    10416,13392, 10424,29776, 10440,19536, 10448,11344, 10456,27728, 10472,23632, 
+    10480,15440, 10488,31824, 10504,16976, 10520,25168, 10536,21072, 10544,12880, 
+    10552,29264, 10568,19024, 10576,10832, 10584,27216, 10600,23120, 10608,14928, 
+    10616,31312, 10632,18000, 10648,26192, 10664,22096, 10672,13904, 10680,30288, 
+    10696,20048, 10704,11856, 10712,28240, 10728,24144, 10736,15952, 10744,32336, 
+    10760,16720, 10776,24912, 10792,20816, 10800,12624, 10808,29008, 10824,18768, 
+    10840,26960, 10856,22864, 10864,14672, 10872,31056, 10888,17744, 10904,25936, 
+    10920,21840, 10928,13648, 10936,30032, 10952,19792, 10960,11600, 10968,27984, 
+    10984,23888, 10992,15696, 11000,32080, 11016,17232, 11032,25424, 11048,21328, 
+    11056,13136, 11064,29520, 11080,19280, 11096,27472, 11112,23376, 11120,15184, 
+    11128,31568, 11144,18256, 11160,26448, 11176,22352, 11184,14160, 11192,30544, 
+    11208,20304, 11216,12112, 11224,28496, 11240,24400, 11248,16208, 11256,32592, 
+    11272,16592, 11288,24784, 11304,20688, 11312,12496, 11320,28880, 11336,18640, 
+    11352,26832, 11368,22736, 11376,14544, 11384,30928, 11400,17616, 11416,25808, 
+    11432,21712, 11440,13520, 11448,29904, 11464,19664, 11480,27856, 11496,23760, 
+    11504,15568, 11512,31952, 11528,17104, 11544,25296, 11560,21200, 11568,13008, 
+    11576,29392, 11592,19152, 11608,27344, 11624,23248, 11632,15056, 11640,31440, 
+    11656,18128, 11672,26320, 11688,22224, 11696,14032, 11704,30416, 11720,20176, 
+    11728,11984, 11736,28368, 11752,24272, 11760,16080, 11768,32464, 11784,16848, 
+    11800,25040, 11816,20944, 11824,12752, 11832,29136, 11848,18896, 11864,27088, 
+    11880,22992, 11888,14800, 11896,31184, 11912,17872, 11928,26064, 11944,21968, 
+    11952,13776, 11960,30160, 11976,19920, 11992,28112, 12008,24016, 12016,15824, 
+    12024,32208, 12040,17360, 12056,25552, 12072,21456, 12080,13264, 12088,29648, 
+    12104,19408, 12120,27600, 12136,23504, 12144,15312, 12152,31696, 12168,18384, 
+    12184,26576, 12200,22480, 12208,14288, 12216,30672, 12232,20432, 12248,28624, 
+    12264,24528, 12272,16336, 12280,32720, 12296,16432, 12312,24624, 12328,20528, 
+    12344,28720, 12360,18480, 12376,26672, 12392,22576, 12400,14384, 12408,30768, 
+    12424,17456, 12440,25648, 12456,21552, 12464,13360, 12472,29744, 12488,19504, 
+    12504,27696, 12520,23600, 12528,15408, 12536,31792, 12552,16944, 12568,25136, 
+    12584,21040, 12592,12848, 12600,29232, 12616,18992, 12632,27184, 12648,23088, 
+    12656,14896, 12664,31280, 12680,17968, 12696,26160, 12712,22064, 12720,13872, 
+    12728,30256, 12744,20016, 12760,28208, 12776,24112, 12784,15920, 12792,32304, 
+    12808,16688, 12824,24880, 12840,20784, 12856,28976, 12872,18736, 12888,26928, 
+    12904,22832, 12912,14640, 12920,31024, 12936,17712, 12952,25904, 12968,21808, 
+    12976,13616, 12984,30000, 13000,19760, 13016,27952, 13032,23856, 13040,15664, 
+    13048,32048, 13064,17200, 13080,25392, 13096,21296, 13112,29488, 13128,19248, 
+    13144,27440, 13160,23344, 13168,15152, 13176,31536, 13192,18224, 13208,26416, 
+    13224,22320, 13232,14128, 13240,30512, 13256,20272, 13272,28464, 13288,24368, 
+    13296,16176, 13304,32560, 13320,16560, 13336,24752, 13352,20656, 13368,28848, 
+    13384,18608, 13400,26800, 13416,22704, 13424,14512, 13432,30896, 13448,17584, 
+    13464,25776, 13480,21680, 13496,29872, 13512,19632, 13528,27824, 13544,23728, 
+    13552,15536, 13560,31920, 13576,17072, 13592,25264, 13608,21168, 13624,29360, 
+    13640,19120, 13656,27312, 13672,23216, 13680,15024, 13688,31408, 13704,18096, 
+    13720,26288, 13736,22192, 13744,14000, 13752,30384, 13768,20144, 13784,28336, 
+    13800,24240, 13808,16048, 13816,32432, 13832,16816, 13848,25008, 13864,20912, 
+    13880,29104, 13896,18864, 13912,27056, 13928,22960, 13936,14768, 13944,31152, 
+    13960,17840, 13976,26032, 13992,21936, 14008,30128, 14024,19888, 14040,28080, 
+    14056,23984, 14064,15792, 14072,32176, 14088,17328, 14104,25520, 14120,21424, 
+    14136,29616, 14152,19376, 14168,27568, 14184,23472, 14192,15280, 14200,31664, 
+    14216,18352, 14232,26544, 14248,22448, 14264,30640, 14280,20400, 14296,28592, 
+    14312,24496, 14320,16304, 14328,32688, 14344,16496, 14360,24688, 14376,20592, 
+    14392,28784, 14408,18544, 14424,26736, 14440,22640, 14456,30832, 14472,17520, 
+    14488,25712, 14504,21616, 14520,29808, 14536,19568, 14552,27760, 14568,23664, 
+    14576,15472, 14584,31856, 14600,17008, 14616,25200, 14632,21104, 14648,29296, 
+    14664,19056, 14680,27248, 14696,23152, 14704,14960, 14712,31344, 14728,18032, 
+    14744,26224, 14760,22128, 14776,30320, 14792,20080, 14808,28272, 14824,24176, 
+    14832,15984, 14840,32368, 14856,16752, 14872,24944, 14888,20848, 14904,29040, 
+    14920,18800, 14936,26992, 14952,22896, 14968,31088, 14984,17776, 15000,25968, 
+    15016,21872, 15032,30064, 15048,19824, 15064,28016, 15080,23920, 15088,15728, 
+    15096,32112, 15112,17264, 15128,25456, 15144,21360, 15160,29552, 15176,19312, 
+    15192,27504, 15208,23408, 15224,31600, 15240,18288, 15256,26480, 15272,22384, 
+    15288,30576, 15304,20336, 15320,28528, 15336,24432, 15344,16240, 15352,32624, 
+    15368,16624, 15384,24816, 15400,20720, 15416,28912, 15432,18672, 15448,26864, 
+    15464,22768, 15480,30960, 15496,17648, 15512,25840, 15528,21744, 15544,29936, 
+    15560,19696, 15576,27888, 15592,23792, 15608,31984, 15624,17136, 15640,25328, 
+    15656,21232, 15672,29424, 15688,19184, 15704,27376, 15720,23280, 15736,31472, 
+    15752,18160, 15768,26352, 15784,22256, 15800,30448, 15816,20208, 15832,28400, 
+    15848,24304, 15856,16112, 15864,32496, 15880,16880, 15896,25072, 15912,20976, 
+    15928,29168, 15944,18928, 15960,27120, 15976,23024, 15992,31216, 16008,17904, 
+    16024,26096, 16040,22000, 16056,30192, 16072,19952, 16088,28144, 16104,24048, 
+    16120,32240, 16136,17392, 16152,25584, 16168,21488, 16184,29680, 16200,19440, 
+    16216,27632, 16232,23536, 16248,31728, 16264,18416, 16280,26608, 16296,22512, 
+    16312,30704, 16328,20464, 16344,28656, 16360,24560, 16376,32752, 16408,24584, 
+    16424,20488, 16440,28680, 16456,18440, 16472,26632, 16488,22536, 16504,30728, 
+    16520,17416, 16536,25608, 16552,21512, 16568,29704, 16584,19464, 16600,27656, 
+    16616,23560, 16632,31752, 16648,16904, 16664,25096, 16680,21000, 16696,29192, 
+    16712,18952, 16728,27144, 16744,23048, 16760,31240, 16776,17928, 16792,26120, 
+    16808,22024, 16824,30216, 16840,19976, 16856,28168, 16872,24072, 16888,32264, 
+    16920,24840, 16936,20744, 16952,28936, 16968,18696, 16984,26888, 17000,22792, 
+    17016,30984, 17032,17672, 17048,25864, 17064,21768, 17080,29960, 17096,19720, 
+    17112,27912, 17128,23816, 17144,32008, 17176,25352, 17192,21256, 17208,29448, 
+    17224,19208, 17240,27400, 17256,23304, 17272,31496, 17288,18184, 17304,26376, 
+    17320,22280, 17336,30472, 17352,20232, 17368,28424, 17384,24328, 17400,32520, 
+    17432,24712, 17448,20616, 17464,28808, 17480,18568, 17496,26760, 17512,22664, 
+    17528,30856, 17560,25736, 17576,21640, 17592,29832, 17608,19592, 17624,27784, 
+    17640,23688, 17656,31880, 17688,25224, 17704,21128, 17720,29320, 17736,19080, 
+    17752,27272, 17768,23176, 17784,31368, 17800,18056, 17816,26248, 17832,22152, 
+    17848,30344, 17864,20104, 17880,28296, 17896,24200, 17912,32392, 17944,24968, 
+    17960,20872, 17976,29064, 17992,18824, 18008,27016, 18024,22920, 18040,31112, 
+    18072,25992, 18088,21896, 18104,30088, 18120,19848, 18136,28040, 18152,23944, 
+    18168,32136, 18200,25480, 18216,21384, 18232,29576, 18248,19336, 18264,27528, 
+    18280,23432, 18296,31624, 18328,26504, 18344,22408, 18360,30600, 18376,20360, 
+    18392,28552, 18408,24456, 18424,32648, 18456,24648, 18472,20552, 18488,28744, 
+    18520,26696, 18536,22600, 18552,30792, 18584,25672, 18600,21576, 18616,29768, 
+    18632,19528, 18648,27720, 18664,23624, 18680,31816, 18712,25160, 18728,21064, 
+    18744,29256, 18760,19016, 18776,27208, 18792,23112, 18808,31304, 18840,26184, 
+    18856,22088, 18872,30280, 18888,20040, 18904,28232, 18920,24136, 18936,32328, 
+    18968,24904, 18984,20808, 19000,29000, 19032,26952, 19048,22856, 19064,31048, 
+    19096,25928, 19112,21832, 19128,30024, 19144,19784, 19160,27976, 19176,23880, 
+    19192,32072, 19224,25416, 19240,21320, 19256,29512, 19288,27464, 19304,23368, 
+    19320,31560, 19352,26440, 19368,22344, 19384,30536, 19400,20296, 19416,28488, 
+    19432,24392, 19448,32584, 19480,24776, 19496,20680, 19512,28872, 19544,26824, 
+    19560,22728, 19576,30920, 19608,25800, 19624,21704, 19640,29896, 19672,27848, 
+    19688,23752, 19704,31944, 19736,25288, 19752,21192, 19768,29384, 19800,27336, 
+    19816,23240, 19832,31432, 19864,26312, 19880,22216, 19896,30408, 19912,20168, 
+    19928,28360, 19944,24264, 19960,32456, 19992,25032, 20008,20936, 20024,29128, 
+    20056,27080, 20072,22984, 20088,31176, 20120,26056, 20136,21960, 20152,30152, 
+    20184,28104, 20200,24008, 20216,32200, 20248,25544, 20264,21448, 20280,29640, 
+    20312,27592, 20328,23496, 20344,31688, 20376,26568, 20392,22472, 20408,30664, 
+    20440,28616, 20456,24520, 20472,32712, 20504,24616, 20536,28712, 20568,26664, 
+    20584,22568, 20600,30760, 20632,25640, 20648,21544, 20664,29736, 20696,27688, 
+    20712,23592, 20728,31784, 20760,25128, 20776,21032, 20792,29224, 20824,27176, 
+    20840,23080, 20856,31272, 20888,26152, 20904,22056, 20920,30248, 20952,28200, 
+    20968,24104, 20984,32296, 21016,24872, 21048,28968, 21080,26920, 21096,22824, 
+    21112,31016, 21144,25896, 21160,21800, 21176,29992, 21208,27944, 21224,23848, 
+    21240,32040, 21272,25384, 21304,29480, 21336,27432, 21352,23336, 21368,31528, 
+    21400,26408, 21416,22312, 21432,30504, 21464,28456, 21480,24360, 21496,32552, 
+    21528,24744, 21560,28840, 21592,26792, 21608,22696, 21624,30888, 21656,25768, 
+    21688,29864, 21720,27816, 21736,23720, 21752,31912, 21784,25256, 21816,29352, 
+    21848,27304, 21864,23208, 21880,31400, 21912,26280, 21928,22184, 21944,30376, 
+    21976,28328, 21992,24232, 22008,32424, 22040,25000, 22072,29096, 22104,27048, 
+    22120,22952, 22136,31144, 22168,26024, 22200,30120, 22232,28072, 22248,23976, 
+    22264,32168, 22296,25512, 22328,29608, 22360,27560, 22376,23464, 22392,31656, 
+    22424,26536, 22456,30632, 22488,28584, 22504,24488, 22520,32680, 22552,24680, 
+    22584,28776, 22616,26728, 22648,30824, 22680,25704, 22712,29800, 22744,27752, 
+    22760,23656, 22776,31848, 22808,25192, 22840,29288, 22872,27240, 22888,23144, 
+    22904,31336, 22936,26216, 22968,30312, 23000,28264, 23016,24168, 23032,32360, 
+    23064,24936, 23096,29032, 23128,26984, 23160,31080, 23192,25960, 23224,30056, 
+    23256,28008, 23272,23912, 23288,32104, 23320,25448, 23352,29544, 23384,27496, 
+    23416,31592, 23448,26472, 23480,30568, 23512,28520, 23528,24424, 23544,32616, 
+    23576,24808, 23608,28904, 23640,26856, 23672,30952, 23704,25832, 23736,29928, 
+    23768,27880, 23800,31976, 23832,25320, 23864,29416, 23896,27368, 23928,31464, 
+    23960,26344, 23992,30440, 24024,28392, 24040,24296, 24056,32488, 24088,25064, 
+    24120,29160, 24152,27112, 24184,31208, 24216,26088, 24248,30184, 24280,28136, 
+    24312,32232, 24344,25576, 24376,29672, 24408,27624, 24440,31720, 24472,26600, 
+    24504,30696, 24536,28648, 24568,32744, 24632,28696, 24664,26648, 24696,30744, 
+    24728,25624, 24760,29720, 24792,27672, 24824,31768, 24856,25112, 24888,29208, 
+    24920,27160, 24952,31256, 24984,26136, 25016,30232, 25048,28184, 25080,32280, 
+    25144,28952, 25176,26904, 25208,31000, 25240,25880, 25272,29976, 25304,27928, 
+    25336,32024, 25400,29464, 25432,27416, 25464,31512, 25496,26392, 25528,30488, 
+    25560,28440, 25592,32536, 25656,28824, 25688,26776, 25720,30872, 25784,29848, 
+    25816,27800, 25848,31896, 25912,29336, 25944,27288, 25976,31384, 26008,26264, 
+    26040,30360, 26072,28312, 26104,32408, 26168,29080, 26200,27032, 26232,31128, 
+    26296,30104, 26328,28056, 26360,32152, 26424,29592, 26456,27544, 26488,31640, 
+    26552,30616, 26584,28568, 26616,32664, 26680,28760, 26744,30808, 26808,29784, 
+    26840,27736, 26872,31832, 26936,29272, 26968,27224, 27000,31320, 27064,30296, 
+    27096,28248, 27128,32344, 27192,29016, 27256,31064, 27320,30040, 27352,27992, 
+    27384,32088, 27448,29528, 27512,31576, 27576,30552, 27608,28504, 27640,32600, 
+    27704,28888, 27768,30936, 27832,29912, 27896,31960, 27960,29400, 28024,31448, 
+    28088,30424, 28120,28376, 28152,32472, 28216,29144, 28280,31192, 28344,30168, 
+    28408,32216, 28472,29656, 28536,31704, 28600,30680, 28664,32728, 28792,30776, 
+    28856,29752, 28920,31800, 28984,29240, 29048,31288, 29112,30264, 29176,32312, 
+    29304,31032, 29368,30008, 29432,32056, 29560,31544, 29624,30520, 29688,32568, 
+    29816,30904, 29944,31928, 30072,31416, 30136,30392, 30200,32440, 30328,31160, 
+    30456,32184, 30584,31672, 30712,32696, 30968,31864, 31096,31352, 31224,32376, 
+    31480,32120, 31736,32632, 32248,32504 
+};
+
+/**    
+* \par    
+* Example code for Floating-point RFFT Twiddle factors Generation:    
+* \par    
+* <pre>TW = exp(2*pi*i*[0:L/2-1]/L - pi/2*i).' </pre>    
+* \par    
+* Real and Imag values are in interleaved fashion    
+*/
+const float32_t twiddleCoef_rfft_32[32] = {
+0.0f			,	1.0f			,
+0.195090322f	,	0.98078528f 	,
+0.382683432f	,	0.923879533f	,
+0.555570233f	,	0.831469612f	,
+0.707106781f	,	0.707106781f	,
+0.831469612f	,	0.555570233f	,
+0.923879533f	,	0.382683432f    ,	
+0.98078528f		,	0.195090322f	,
+1.0f			,	0.0f			,
+0.98078528f		,	-0.195090322f	,
+0.923879533f	,	-0.382683432f	,
+0.831469612f	,	-0.555570233f	,
+0.707106781f	,	-0.707106781f	,
+0.555570233f	,	-0.831469612f	,
+0.382683432f	,	-0.923879533f	,
+0.195090322f	,	-0.98078528f	
+};
+
+const float32_t twiddleCoef_rfft_64[64] = {
+0.0f,	1.0f,
+0.098017140329561f,	0.995184726672197f,
+0.195090322016128f,	0.98078528040323f,
+0.290284677254462f,	0.956940335732209f,
+0.38268343236509f,	0.923879532511287f,
+0.471396736825998f,	0.881921264348355f,
+0.555570233019602f,	0.831469612302545f,
+0.634393284163645f,	0.773010453362737f,
+0.707106781186547f,	0.707106781186548f,
+0.773010453362737f,	0.634393284163645f,
+0.831469612302545f,	0.555570233019602f,
+0.881921264348355f,	0.471396736825998f,
+0.923879532511287f,	0.38268343236509f,
+0.956940335732209f,	0.290284677254462f,
+0.98078528040323f,	0.195090322016128f,
+0.995184726672197f,	0.098017140329561f,
+1.0f,	0.0f,
+0.995184726672197f,	-0.098017140329561f,
+0.98078528040323f,	-0.195090322016128f,
+0.956940335732209f,	-0.290284677254462f,
+0.923879532511287f,	-0.38268343236509f,
+0.881921264348355f,	-0.471396736825998f,
+0.831469612302545f,	-0.555570233019602f,
+0.773010453362737f,	-0.634393284163645f,
+0.707106781186548f,	-0.707106781186547f,
+0.634393284163645f,	-0.773010453362737f,
+0.555570233019602f,	-0.831469612302545f,
+0.471396736825998f,	-0.881921264348355f,
+0.38268343236509f,	-0.923879532511287f,
+0.290284677254462f,	-0.956940335732209f,
+0.195090322016129f,	-0.98078528040323f,
+0.098017140329561f,	-0.995184726672197f
+};
+
+const float32_t twiddleCoef_rfft_128[128] = {
+    0.000000000f,  1.000000000f,
+    0.049067674f,  0.998795456f,
+    0.098017140f,  0.995184727f,
+    0.146730474f,  0.989176510f,
+    0.195090322f,  0.980785280f,
+    0.242980180f,  0.970031253f,
+    0.290284677f,  0.956940336f,
+    0.336889853f,  0.941544065f,
+    0.382683432f,  0.923879533f,
+    0.427555093f,  0.903989293f,
+    0.471396737f,  0.881921264f,
+    0.514102744f,  0.857728610f,
+    0.555570233f,  0.831469612f,
+    0.595699304f,  0.803207531f,
+    0.634393284f,  0.773010453f,
+    0.671558955f,  0.740951125f,
+    0.707106781f,  0.707106781f,
+    0.740951125f,  0.671558955f,
+    0.773010453f,  0.634393284f,
+    0.803207531f,  0.595699304f,
+    0.831469612f,  0.555570233f,
+    0.857728610f,  0.514102744f,
+    0.881921264f,  0.471396737f,
+    0.903989293f,  0.427555093f,
+    0.923879533f,  0.382683432f,
+    0.941544065f,  0.336889853f,
+    0.956940336f,  0.290284677f,
+    0.970031253f,  0.242980180f,
+    0.980785280f,  0.195090322f,
+    0.989176510f,  0.146730474f,
+    0.995184727f,  0.098017140f,
+    0.998795456f,  0.049067674f,
+    1.000000000f,  0.000000000f,
+    0.998795456f, -0.049067674f,
+    0.995184727f, -0.098017140f,
+    0.989176510f, -0.146730474f,
+    0.980785280f, -0.195090322f,
+    0.970031253f, -0.242980180f,
+    0.956940336f, -0.290284677f,
+    0.941544065f, -0.336889853f,
+    0.923879533f, -0.382683432f,
+    0.903989293f, -0.427555093f,
+    0.881921264f, -0.471396737f,
+    0.857728610f, -0.514102744f,
+    0.831469612f, -0.555570233f,
+    0.803207531f, -0.595699304f,
+    0.773010453f, -0.634393284f,
+    0.740951125f, -0.671558955f,
+    0.707106781f, -0.707106781f,
+    0.671558955f, -0.740951125f,
+    0.634393284f, -0.773010453f,
+    0.595699304f, -0.803207531f,
+    0.555570233f, -0.831469612f,
+    0.514102744f, -0.857728610f,
+    0.471396737f, -0.881921264f,
+    0.427555093f, -0.903989293f,
+    0.382683432f, -0.923879533f,
+    0.336889853f, -0.941544065f,
+    0.290284677f, -0.956940336f,
+    0.242980180f, -0.970031253f,
+    0.195090322f, -0.980785280f,
+    0.146730474f, -0.989176510f,
+    0.098017140f, -0.995184727f,
+    0.049067674f, -0.998795456f
+};
+
+const float32_t twiddleCoef_rfft_256[256] = {
+    0.000000000f,  1.000000000f,
+    0.024541229f,  0.999698819f,
+    0.049067674f,  0.998795456f,
+    0.073564564f,  0.997290457f,
+    0.098017140f,  0.995184727f,
+    0.122410675f,  0.992479535f,
+    0.146730474f,  0.989176510f,
+    0.170961889f,  0.985277642f,
+    0.195090322f,  0.980785280f,
+    0.219101240f,  0.975702130f,
+    0.242980180f,  0.970031253f,
+    0.266712757f,  0.963776066f,
+    0.290284677f,  0.956940336f,
+    0.313681740f,  0.949528181f,
+    0.336889853f,  0.941544065f,
+    0.359895037f,  0.932992799f,
+    0.382683432f,  0.923879533f,
+    0.405241314f,  0.914209756f,
+    0.427555093f,  0.903989293f,
+    0.449611330f,  0.893224301f,
+    0.471396737f,  0.881921264f,
+    0.492898192f,  0.870086991f,
+    0.514102744f,  0.857728610f,
+    0.534997620f,  0.844853565f,
+    0.555570233f,  0.831469612f,
+    0.575808191f,  0.817584813f,
+    0.595699304f,  0.803207531f,
+    0.615231591f,  0.788346428f,
+    0.634393284f,  0.773010453f,
+    0.653172843f,  0.757208847f,
+    0.671558955f,  0.740951125f,
+    0.689540545f,  0.724247083f,
+    0.707106781f,  0.707106781f,
+    0.724247083f,  0.689540545f,
+    0.740951125f,  0.671558955f,
+    0.757208847f,  0.653172843f,
+    0.773010453f,  0.634393284f,
+    0.788346428f,  0.615231591f,
+    0.803207531f,  0.595699304f,
+    0.817584813f,  0.575808191f,
+    0.831469612f,  0.555570233f,
+    0.844853565f,  0.534997620f,
+    0.857728610f,  0.514102744f,
+    0.870086991f,  0.492898192f,
+    0.881921264f,  0.471396737f,
+    0.893224301f,  0.449611330f,
+    0.903989293f,  0.427555093f,
+    0.914209756f,  0.405241314f,
+    0.923879533f,  0.382683432f,
+    0.932992799f,  0.359895037f,
+    0.941544065f,  0.336889853f,
+    0.949528181f,  0.313681740f,
+    0.956940336f,  0.290284677f,
+    0.963776066f,  0.266712757f,
+    0.970031253f,  0.242980180f,
+    0.975702130f,  0.219101240f,
+    0.980785280f,  0.195090322f,
+    0.985277642f,  0.170961889f,
+    0.989176510f,  0.146730474f,
+    0.992479535f,  0.122410675f,
+    0.995184727f,  0.098017140f,
+    0.997290457f,  0.073564564f,
+    0.998795456f,  0.049067674f,
+    0.999698819f,  0.024541229f,
+    1.000000000f,  0.000000000f,
+    0.999698819f, -0.024541229f,
+    0.998795456f, -0.049067674f,
+    0.997290457f, -0.073564564f,
+    0.995184727f, -0.098017140f,
+    0.992479535f, -0.122410675f,
+    0.989176510f, -0.146730474f,
+    0.985277642f, -0.170961889f,
+    0.980785280f, -0.195090322f,
+    0.975702130f, -0.219101240f,
+    0.970031253f, -0.242980180f,
+    0.963776066f, -0.266712757f,
+    0.956940336f, -0.290284677f,
+    0.949528181f, -0.313681740f,
+    0.941544065f, -0.336889853f,
+    0.932992799f, -0.359895037f,
+    0.923879533f, -0.382683432f,
+    0.914209756f, -0.405241314f,
+    0.903989293f, -0.427555093f,
+    0.893224301f, -0.449611330f,
+    0.881921264f, -0.471396737f,
+    0.870086991f, -0.492898192f,
+    0.857728610f, -0.514102744f,
+    0.844853565f, -0.534997620f,
+    0.831469612f, -0.555570233f,
+    0.817584813f, -0.575808191f,
+    0.803207531f, -0.595699304f,
+    0.788346428f, -0.615231591f,
+    0.773010453f, -0.634393284f,
+    0.757208847f, -0.653172843f,
+    0.740951125f, -0.671558955f,
+    0.724247083f, -0.689540545f,
+    0.707106781f, -0.707106781f,
+    0.689540545f, -0.724247083f,
+    0.671558955f, -0.740951125f,
+    0.653172843f, -0.757208847f,
+    0.634393284f, -0.773010453f,
+    0.615231591f, -0.788346428f,
+    0.595699304f, -0.803207531f,
+    0.575808191f, -0.817584813f,
+    0.555570233f, -0.831469612f,
+    0.534997620f, -0.844853565f,
+    0.514102744f, -0.857728610f,
+    0.492898192f, -0.870086991f,
+    0.471396737f, -0.881921264f,
+    0.449611330f, -0.893224301f,
+    0.427555093f, -0.903989293f,
+    0.405241314f, -0.914209756f,
+    0.382683432f, -0.923879533f,
+    0.359895037f, -0.932992799f,
+    0.336889853f, -0.941544065f,
+    0.313681740f, -0.949528181f,
+    0.290284677f, -0.956940336f,
+    0.266712757f, -0.963776066f,
+    0.242980180f, -0.970031253f,
+    0.219101240f, -0.975702130f,
+    0.195090322f, -0.980785280f,
+    0.170961889f, -0.985277642f,
+    0.146730474f, -0.989176510f,
+    0.122410675f, -0.992479535f,
+    0.098017140f, -0.995184727f,
+    0.073564564f, -0.997290457f,
+    0.049067674f, -0.998795456f,
+    0.024541229f, -0.999698819f
+};
+
+const float32_t twiddleCoef_rfft_512[512] = {
+    0.000000000f,  1.000000000f,
+    0.012271538f,  0.999924702f,
+    0.024541229f,  0.999698819f,
+    0.036807223f,  0.999322385f,
+    0.049067674f,  0.998795456f,
+    0.061320736f,  0.998118113f,
+    0.073564564f,  0.997290457f,
+    0.085797312f,  0.996312612f,
+    0.098017140f,  0.995184727f,
+    0.110222207f,  0.993906970f,
+    0.122410675f,  0.992479535f,
+    0.134580709f,  0.990902635f,
+    0.146730474f,  0.989176510f,
+    0.158858143f,  0.987301418f,
+    0.170961889f,  0.985277642f,
+    0.183039888f,  0.983105487f,
+    0.195090322f,  0.980785280f,
+    0.207111376f,  0.978317371f,
+    0.219101240f,  0.975702130f,
+    0.231058108f,  0.972939952f,
+    0.242980180f,  0.970031253f,
+    0.254865660f,  0.966976471f,
+    0.266712757f,  0.963776066f,
+    0.278519689f,  0.960430519f,
+    0.290284677f,  0.956940336f,
+    0.302005949f,  0.953306040f,
+    0.313681740f,  0.949528181f,
+    0.325310292f,  0.945607325f,
+    0.336889853f,  0.941544065f,
+    0.348418680f,  0.937339012f,
+    0.359895037f,  0.932992799f,
+    0.371317194f,  0.928506080f,
+    0.382683432f,  0.923879533f,
+    0.393992040f,  0.919113852f,
+    0.405241314f,  0.914209756f,
+    0.416429560f,  0.909167983f,
+    0.427555093f,  0.903989293f,
+    0.438616239f,  0.898674466f,
+    0.449611330f,  0.893224301f,
+    0.460538711f,  0.887639620f,
+    0.471396737f,  0.881921264f,
+    0.482183772f,  0.876070094f,
+    0.492898192f,  0.870086991f,
+    0.503538384f,  0.863972856f,
+    0.514102744f,  0.857728610f,
+    0.524589683f,  0.851355193f,
+    0.534997620f,  0.844853565f,
+    0.545324988f,  0.838224706f,
+    0.555570233f,  0.831469612f,
+    0.565731811f,  0.824589303f,
+    0.575808191f,  0.817584813f,
+    0.585797857f,  0.810457198f,
+    0.595699304f,  0.803207531f,
+    0.605511041f,  0.795836905f,
+    0.615231591f,  0.788346428f,
+    0.624859488f,  0.780737229f,
+    0.634393284f,  0.773010453f,
+    0.643831543f,  0.765167266f,
+    0.653172843f,  0.757208847f,
+    0.662415778f,  0.749136395f,
+    0.671558955f,  0.740951125f,
+    0.680600998f,  0.732654272f,
+    0.689540545f,  0.724247083f,
+    0.698376249f,  0.715730825f,
+    0.707106781f,  0.707106781f,
+    0.715730825f,  0.698376249f,
+    0.724247083f,  0.689540545f,
+    0.732654272f,  0.680600998f,
+    0.740951125f,  0.671558955f,
+    0.749136395f,  0.662415778f,
+    0.757208847f,  0.653172843f,
+    0.765167266f,  0.643831543f,
+    0.773010453f,  0.634393284f,
+    0.780737229f,  0.624859488f,
+    0.788346428f,  0.615231591f,
+    0.795836905f,  0.605511041f,
+    0.803207531f,  0.595699304f,
+    0.810457198f,  0.585797857f,
+    0.817584813f,  0.575808191f,
+    0.824589303f,  0.565731811f,
+    0.831469612f,  0.555570233f,
+    0.838224706f,  0.545324988f,
+    0.844853565f,  0.534997620f,
+    0.851355193f,  0.524589683f,
+    0.857728610f,  0.514102744f,
+    0.863972856f,  0.503538384f,
+    0.870086991f,  0.492898192f,
+    0.876070094f,  0.482183772f,
+    0.881921264f,  0.471396737f,
+    0.887639620f,  0.460538711f,
+    0.893224301f,  0.449611330f,
+    0.898674466f,  0.438616239f,
+    0.903989293f,  0.427555093f,
+    0.909167983f,  0.416429560f,
+    0.914209756f,  0.405241314f,
+    0.919113852f,  0.393992040f,
+    0.923879533f,  0.382683432f,
+    0.928506080f,  0.371317194f,
+    0.932992799f,  0.359895037f,
+    0.937339012f,  0.348418680f,
+    0.941544065f,  0.336889853f,
+    0.945607325f,  0.325310292f,
+    0.949528181f,  0.313681740f,
+    0.953306040f,  0.302005949f,
+    0.956940336f,  0.290284677f,
+    0.960430519f,  0.278519689f,
+    0.963776066f,  0.266712757f,
+    0.966976471f,  0.254865660f,
+    0.970031253f,  0.242980180f,
+    0.972939952f,  0.231058108f,
+    0.975702130f,  0.219101240f,
+    0.978317371f,  0.207111376f,
+    0.980785280f,  0.195090322f,
+    0.983105487f,  0.183039888f,
+    0.985277642f,  0.170961889f,
+    0.987301418f,  0.158858143f,
+    0.989176510f,  0.146730474f,
+    0.990902635f,  0.134580709f,
+    0.992479535f,  0.122410675f,
+    0.993906970f,  0.110222207f,
+    0.995184727f,  0.098017140f,
+    0.996312612f,  0.085797312f,
+    0.997290457f,  0.073564564f,
+    0.998118113f,  0.061320736f,
+    0.998795456f,  0.049067674f,
+    0.999322385f,  0.036807223f,
+    0.999698819f,  0.024541229f,
+    0.999924702f,  0.012271538f,
+    1.000000000f,  0.000000000f,
+    0.999924702f, -0.012271538f,
+    0.999698819f, -0.024541229f,
+    0.999322385f, -0.036807223f,
+    0.998795456f, -0.049067674f,
+    0.998118113f, -0.061320736f,
+    0.997290457f, -0.073564564f,
+    0.996312612f, -0.085797312f,
+    0.995184727f, -0.098017140f,
+    0.993906970f, -0.110222207f,
+    0.992479535f, -0.122410675f,
+    0.990902635f, -0.134580709f,
+    0.989176510f, -0.146730474f,
+    0.987301418f, -0.158858143f,
+    0.985277642f, -0.170961889f,
+    0.983105487f, -0.183039888f,
+    0.980785280f, -0.195090322f,
+    0.978317371f, -0.207111376f,
+    0.975702130f, -0.219101240f,
+    0.972939952f, -0.231058108f,
+    0.970031253f, -0.242980180f,
+    0.966976471f, -0.254865660f,
+    0.963776066f, -0.266712757f,
+    0.960430519f, -0.278519689f,
+    0.956940336f, -0.290284677f,
+    0.953306040f, -0.302005949f,
+    0.949528181f, -0.313681740f,
+    0.945607325f, -0.325310292f,
+    0.941544065f, -0.336889853f,
+    0.937339012f, -0.348418680f,
+    0.932992799f, -0.359895037f,
+    0.928506080f, -0.371317194f,
+    0.923879533f, -0.382683432f,
+    0.919113852f, -0.393992040f,
+    0.914209756f, -0.405241314f,
+    0.909167983f, -0.416429560f,
+    0.903989293f, -0.427555093f,
+    0.898674466f, -0.438616239f,
+    0.893224301f, -0.449611330f,
+    0.887639620f, -0.460538711f,
+    0.881921264f, -0.471396737f,
+    0.876070094f, -0.482183772f,
+    0.870086991f, -0.492898192f,
+    0.863972856f, -0.503538384f,
+    0.857728610f, -0.514102744f,
+    0.851355193f, -0.524589683f,
+    0.844853565f, -0.534997620f,
+    0.838224706f, -0.545324988f,
+    0.831469612f, -0.555570233f,
+    0.824589303f, -0.565731811f,
+    0.817584813f, -0.575808191f,
+    0.810457198f, -0.585797857f,
+    0.803207531f, -0.595699304f,
+    0.795836905f, -0.605511041f,
+    0.788346428f, -0.615231591f,
+    0.780737229f, -0.624859488f,
+    0.773010453f, -0.634393284f,
+    0.765167266f, -0.643831543f,
+    0.757208847f, -0.653172843f,
+    0.749136395f, -0.662415778f,
+    0.740951125f, -0.671558955f,
+    0.732654272f, -0.680600998f,
+    0.724247083f, -0.689540545f,
+    0.715730825f, -0.698376249f,
+    0.707106781f, -0.707106781f,
+    0.698376249f, -0.715730825f,
+    0.689540545f, -0.724247083f,
+    0.680600998f, -0.732654272f,
+    0.671558955f, -0.740951125f,
+    0.662415778f, -0.749136395f,
+    0.653172843f, -0.757208847f,
+    0.643831543f, -0.765167266f,
+    0.634393284f, -0.773010453f,
+    0.624859488f, -0.780737229f,
+    0.615231591f, -0.788346428f,
+    0.605511041f, -0.795836905f,
+    0.595699304f, -0.803207531f,
+    0.585797857f, -0.810457198f,
+    0.575808191f, -0.817584813f,
+    0.565731811f, -0.824589303f,
+    0.555570233f, -0.831469612f,
+    0.545324988f, -0.838224706f,
+    0.534997620f, -0.844853565f,
+    0.524589683f, -0.851355193f,
+    0.514102744f, -0.857728610f,
+    0.503538384f, -0.863972856f,
+    0.492898192f, -0.870086991f,
+    0.482183772f, -0.876070094f,
+    0.471396737f, -0.881921264f,
+    0.460538711f, -0.887639620f,
+    0.449611330f, -0.893224301f,
+    0.438616239f, -0.898674466f,
+    0.427555093f, -0.903989293f,
+    0.416429560f, -0.909167983f,
+    0.405241314f, -0.914209756f,
+    0.393992040f, -0.919113852f,
+    0.382683432f, -0.923879533f,
+    0.371317194f, -0.928506080f,
+    0.359895037f, -0.932992799f,
+    0.348418680f, -0.937339012f,
+    0.336889853f, -0.941544065f,
+    0.325310292f, -0.945607325f,
+    0.313681740f, -0.949528181f,
+    0.302005949f, -0.953306040f,
+    0.290284677f, -0.956940336f,
+    0.278519689f, -0.960430519f,
+    0.266712757f, -0.963776066f,
+    0.254865660f, -0.966976471f,
+    0.242980180f, -0.970031253f,
+    0.231058108f, -0.972939952f,
+    0.219101240f, -0.975702130f,
+    0.207111376f, -0.978317371f,
+    0.195090322f, -0.980785280f,
+    0.183039888f, -0.983105487f,
+    0.170961889f, -0.985277642f,
+    0.158858143f, -0.987301418f,
+    0.146730474f, -0.989176510f,
+    0.134580709f, -0.990902635f,
+    0.122410675f, -0.992479535f,
+    0.110222207f, -0.993906970f,
+    0.098017140f, -0.995184727f,
+    0.085797312f, -0.996312612f,
+    0.073564564f, -0.997290457f,
+    0.061320736f, -0.998118113f,
+    0.049067674f, -0.998795456f,
+    0.036807223f, -0.999322385f,
+    0.024541229f, -0.999698819f,
+    0.012271538f, -0.999924702f
+};
+
+const float32_t twiddleCoef_rfft_1024[1024] = {
+    0.000000000f,  1.000000000f,
+    0.006135885f,  0.999981175f,
+    0.012271538f,  0.999924702f,
+    0.018406730f,  0.999830582f,
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+    0.648514401f, -0.761202385f,
+    0.643831543f, -0.765167266f,
+    0.639124445f, -0.769103338f,
+    0.634393284f, -0.773010453f,
+    0.629638239f, -0.776888466f,
+    0.624859488f, -0.780737229f,
+    0.620057212f, -0.784556597f,
+    0.615231591f, -0.788346428f,
+    0.610382806f, -0.792106577f,
+    0.605511041f, -0.795836905f,
+    0.600616479f, -0.799537269f,
+    0.595699304f, -0.803207531f,
+    0.590759702f, -0.806847554f,
+    0.585797857f, -0.810457198f,
+    0.580813958f, -0.814036330f,
+    0.575808191f, -0.817584813f,
+    0.570780746f, -0.821102515f,
+    0.565731811f, -0.824589303f,
+    0.560661576f, -0.828045045f,
+    0.555570233f, -0.831469612f,
+    0.550457973f, -0.834862875f,
+    0.545324988f, -0.838224706f,
+    0.540171473f, -0.841554977f,
+    0.534997620f, -0.844853565f,
+    0.529803625f, -0.848120345f,
+    0.524589683f, -0.851355193f,
+    0.519355990f, -0.854557988f,
+    0.514102744f, -0.857728610f,
+    0.508830143f, -0.860866939f,
+    0.503538384f, -0.863972856f,
+    0.498227667f, -0.867046246f,
+    0.492898192f, -0.870086991f,
+    0.487550160f, -0.873094978f,
+    0.482183772f, -0.876070094f,
+    0.476799230f, -0.879012226f,
+    0.471396737f, -0.881921264f,
+    0.465976496f, -0.884797098f,
+    0.460538711f, -0.887639620f,
+    0.455083587f, -0.890448723f,
+    0.449611330f, -0.893224301f,
+    0.444122145f, -0.895966250f,
+    0.438616239f, -0.898674466f,
+    0.433093819f, -0.901348847f,
+    0.427555093f, -0.903989293f,
+    0.422000271f, -0.906595705f,
+    0.416429560f, -0.909167983f,
+    0.410843171f, -0.911706032f,
+    0.405241314f, -0.914209756f,
+    0.399624200f, -0.916679060f,
+    0.393992040f, -0.919113852f,
+    0.388345047f, -0.921514039f,
+    0.382683432f, -0.923879533f,
+    0.377007410f, -0.926210242f,
+    0.371317194f, -0.928506080f,
+    0.365612998f, -0.930766961f,
+    0.359895037f, -0.932992799f,
+    0.354163525f, -0.935183510f,
+    0.348418680f, -0.937339012f,
+    0.342660717f, -0.939459224f,
+    0.336889853f, -0.941544065f,
+    0.331106306f, -0.943593458f,
+    0.325310292f, -0.945607325f,
+    0.319502031f, -0.947585591f,
+    0.313681740f, -0.949528181f,
+    0.307849640f, -0.951435021f,
+    0.302005949f, -0.953306040f,
+    0.296150888f, -0.955141168f,
+    0.290284677f, -0.956940336f,
+    0.284407537f, -0.958703475f,
+    0.278519689f, -0.960430519f,
+    0.272621355f, -0.962121404f,
+    0.266712757f, -0.963776066f,
+    0.260794118f, -0.965394442f,
+    0.254865660f, -0.966976471f,
+    0.248927606f, -0.968522094f,
+    0.242980180f, -0.970031253f,
+    0.237023606f, -0.971503891f,
+    0.231058108f, -0.972939952f,
+    0.225083911f, -0.974339383f,
+    0.219101240f, -0.975702130f,
+    0.213110320f, -0.977028143f,
+    0.207111376f, -0.978317371f,
+    0.201104635f, -0.979569766f,
+    0.195090322f, -0.980785280f,
+    0.189068664f, -0.981963869f,
+    0.183039888f, -0.983105487f,
+    0.177004220f, -0.984210092f,
+    0.170961889f, -0.985277642f,
+    0.164913120f, -0.986308097f,
+    0.158858143f, -0.987301418f,
+    0.152797185f, -0.988257568f,
+    0.146730474f, -0.989176510f,
+    0.140658239f, -0.990058210f,
+    0.134580709f, -0.990902635f,
+    0.128498111f, -0.991709754f,
+    0.122410675f, -0.992479535f,
+    0.116318631f, -0.993211949f,
+    0.110222207f, -0.993906970f,
+    0.104121634f, -0.994564571f,
+    0.098017140f, -0.995184727f,
+    0.091908956f, -0.995767414f,
+    0.085797312f, -0.996312612f,
+    0.079682438f, -0.996820299f,
+    0.073564564f, -0.997290457f,
+    0.067443920f, -0.997723067f,
+    0.061320736f, -0.998118113f,
+    0.055195244f, -0.998475581f,
+    0.049067674f, -0.998795456f,
+    0.042938257f, -0.999077728f,
+    0.036807223f, -0.999322385f,
+    0.030674803f, -0.999529418f,
+    0.024541229f, -0.999698819f,
+    0.018406730f, -0.999830582f,
+    0.012271538f, -0.999924702f,
+    0.006135885f, -0.999981175f
+};
+
+const float32_t twiddleCoef_rfft_2048[2048] = {
+    0.000000000f,  1.000000000f,
+    0.003067957f,  0.999995294f,
+    0.006135885f,  0.999981175f,
+    0.009203755f,  0.999957645f,
+    0.012271538f,  0.999924702f,
+    0.015339206f,  0.999882347f,
+    0.018406730f,  0.999830582f,
+    0.021474080f,  0.999769405f,
+    0.024541229f,  0.999698819f,
+    0.027608146f,  0.999618822f,
+    0.030674803f,  0.999529418f,
+    0.033741172f,  0.999430605f,
+    0.036807223f,  0.999322385f,
+    0.039872928f,  0.999204759f,
+    0.042938257f,  0.999077728f,
+    0.046003182f,  0.998941293f,
+    0.049067674f,  0.998795456f,
+    0.052131705f,  0.998640218f,
+    0.055195244f,  0.998475581f,
+    0.058258265f,  0.998301545f,
+    0.061320736f,  0.998118113f,
+    0.064382631f,  0.997925286f,
+    0.067443920f,  0.997723067f,
+    0.070504573f,  0.997511456f,
+    0.073564564f,  0.997290457f,
+    0.076623861f,  0.997060070f,
+    0.079682438f,  0.996820299f,
+    0.082740265f,  0.996571146f,
+    0.085797312f,  0.996312612f,
+    0.088853553f,  0.996044701f,
+    0.091908956f,  0.995767414f,
+    0.094963495f,  0.995480755f,
+    0.098017140f,  0.995184727f,
+    0.101069863f,  0.994879331f,
+    0.104121634f,  0.994564571f,
+    0.107172425f,  0.994240449f,
+    0.110222207f,  0.993906970f,
+    0.113270952f,  0.993564136f,
+    0.116318631f,  0.993211949f,
+    0.119365215f,  0.992850414f,
+    0.122410675f,  0.992479535f,
+    0.125454983f,  0.992099313f,
+    0.128498111f,  0.991709754f,
+    0.131540029f,  0.991310860f,
+    0.134580709f,  0.990902635f,
+    0.137620122f,  0.990485084f,
+    0.140658239f,  0.990058210f,
+    0.143695033f,  0.989622017f,
+    0.146730474f,  0.989176510f,
+    0.149764535f,  0.988721692f,
+    0.152797185f,  0.988257568f,
+    0.155828398f,  0.987784142f,
+    0.158858143f,  0.987301418f,
+    0.161886394f,  0.986809402f,
+    0.164913120f,  0.986308097f,
+    0.167938295f,  0.985797509f,
+    0.170961889f,  0.985277642f,
+    0.173983873f,  0.984748502f,
+    0.177004220f,  0.984210092f,
+    0.180022901f,  0.983662419f,
+    0.183039888f,  0.983105487f,
+    0.186055152f,  0.982539302f,
+    0.189068664f,  0.981963869f,
+    0.192080397f,  0.981379193f,
+    0.195090322f,  0.980785280f,
+    0.198098411f,  0.980182136f,
+    0.201104635f,  0.979569766f,
+    0.204108966f,  0.978948175f,
+    0.207111376f,  0.978317371f,
+    0.210111837f,  0.977677358f,
+    0.213110320f,  0.977028143f,
+    0.216106797f,  0.976369731f,
+    0.219101240f,  0.975702130f,
+    0.222093621f,  0.975025345f,
+    0.225083911f,  0.974339383f,
+    0.228072083f,  0.973644250f,
+    0.231058108f,  0.972939952f,
+    0.234041959f,  0.972226497f,
+    0.237023606f,  0.971503891f,
+    0.240003022f,  0.970772141f,
+    0.242980180f,  0.970031253f,
+    0.245955050f,  0.969281235f,
+    0.248927606f,  0.968522094f,
+    0.251897818f,  0.967753837f,
+    0.254865660f,  0.966976471f,
+    0.257831102f,  0.966190003f,
+    0.260794118f,  0.965394442f,
+    0.263754679f,  0.964589793f,
+    0.266712757f,  0.963776066f,
+    0.269668326f,  0.962953267f,
+    0.272621355f,  0.962121404f,
+    0.275571819f,  0.961280486f,
+    0.278519689f,  0.960430519f,
+    0.281464938f,  0.959571513f,
+    0.284407537f,  0.958703475f,
+    0.287347460f,  0.957826413f,
+    0.290284677f,  0.956940336f,
+    0.293219163f,  0.956045251f,
+    0.296150888f,  0.955141168f,
+    0.299079826f,  0.954228095f,
+    0.302005949f,  0.953306040f,
+    0.304929230f,  0.952375013f,
+    0.307849640f,  0.951435021f,
+    0.310767153f,  0.950486074f,
+    0.313681740f,  0.949528181f,
+    0.316593376f,  0.948561350f,
+    0.319502031f,  0.947585591f,
+    0.322407679f,  0.946600913f,
+    0.325310292f,  0.945607325f,
+    0.328209844f,  0.944604837f,
+    0.331106306f,  0.943593458f,
+    0.333999651f,  0.942573198f,
+    0.336889853f,  0.941544065f,
+    0.339776884f,  0.940506071f,
+    0.342660717f,  0.939459224f,
+    0.345541325f,  0.938403534f,
+    0.348418680f,  0.937339012f,
+    0.351292756f,  0.936265667f,
+    0.354163525f,  0.935183510f,
+    0.357030961f,  0.934092550f,
+    0.359895037f,  0.932992799f,
+    0.362755724f,  0.931884266f,
+    0.365612998f,  0.930766961f,
+    0.368466830f,  0.929640896f,
+    0.371317194f,  0.928506080f,
+    0.374164063f,  0.927362526f,
+    0.377007410f,  0.926210242f,
+    0.379847209f,  0.925049241f,
+    0.382683432f,  0.923879533f,
+    0.385516054f,  0.922701128f,
+    0.388345047f,  0.921514039f,
+    0.391170384f,  0.920318277f,
+    0.393992040f,  0.919113852f,
+    0.396809987f,  0.917900776f,
+    0.399624200f,  0.916679060f,
+    0.402434651f,  0.915448716f,
+    0.405241314f,  0.914209756f,
+    0.408044163f,  0.912962190f,
+    0.410843171f,  0.911706032f,
+    0.413638312f,  0.910441292f,
+    0.416429560f,  0.909167983f,
+    0.419216888f,  0.907886116f,
+    0.422000271f,  0.906595705f,
+    0.424779681f,  0.905296759f,
+    0.427555093f,  0.903989293f,
+    0.430326481f,  0.902673318f,
+    0.433093819f,  0.901348847f,
+    0.435857080f,  0.900015892f,
+    0.438616239f,  0.898674466f,
+    0.441371269f,  0.897324581f,
+    0.444122145f,  0.895966250f,
+    0.446868840f,  0.894599486f,
+    0.449611330f,  0.893224301f,
+    0.452349587f,  0.891840709f,
+    0.455083587f,  0.890448723f,
+    0.457813304f,  0.889048356f,
+    0.460538711f,  0.887639620f,
+    0.463259784f,  0.886222530f,
+    0.465976496f,  0.884797098f,
+    0.468688822f,  0.883363339f,
+    0.471396737f,  0.881921264f,
+    0.474100215f,  0.880470889f,
+    0.476799230f,  0.879012226f,
+    0.479493758f,  0.877545290f,
+    0.482183772f,  0.876070094f,
+    0.484869248f,  0.874586652f,
+    0.487550160f,  0.873094978f,
+    0.490226483f,  0.871595087f,
+    0.492898192f,  0.870086991f,
+    0.495565262f,  0.868570706f,
+    0.498227667f,  0.867046246f,
+    0.500885383f,  0.865513624f,
+    0.503538384f,  0.863972856f,
+    0.506186645f,  0.862423956f,
+    0.508830143f,  0.860866939f,
+    0.511468850f,  0.859301818f,
+    0.514102744f,  0.857728610f,
+    0.516731799f,  0.856147328f,
+    0.519355990f,  0.854557988f,
+    0.521975293f,  0.852960605f,
+    0.524589683f,  0.851355193f,
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+    0.529803625f,  0.848120345f,
+    0.532403128f,  0.846490939f,
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+    0.537587076f,  0.843208240f,
+    0.540171473f,  0.841554977f,
+    0.542750785f,  0.839893794f,
+    0.545324988f,  0.838224706f,
+    0.547894059f,  0.836547727f,
+    0.550457973f,  0.834862875f,
+    0.553016706f,  0.833170165f,
+    0.555570233f,  0.831469612f,
+    0.558118531f,  0.829761234f,
+    0.560661576f,  0.828045045f,
+    0.563199344f,  0.826321063f,
+    0.565731811f,  0.824589303f,
+    0.568258953f,  0.822849781f,
+    0.570780746f,  0.821102515f,
+    0.573297167f,  0.819347520f,
+    0.575808191f,  0.817584813f,
+    0.578313796f,  0.815814411f,
+    0.580813958f,  0.814036330f,
+    0.583308653f,  0.812250587f,
+    0.585797857f,  0.810457198f,
+    0.588281548f,  0.808656182f,
+    0.590759702f,  0.806847554f,
+    0.593232295f,  0.805031331f,
+    0.595699304f,  0.803207531f,
+    0.598160707f,  0.801376172f,
+    0.600616479f,  0.799537269f,
+    0.603066599f,  0.797690841f,
+    0.605511041f,  0.795836905f,
+    0.607949785f,  0.793975478f,
+    0.610382806f,  0.792106577f,
+    0.612810082f,  0.790230221f,
+    0.615231591f,  0.788346428f,
+    0.617647308f,  0.786455214f,
+    0.620057212f,  0.784556597f,
+    0.622461279f,  0.782650596f,
+    0.624859488f,  0.780737229f,
+    0.627251815f,  0.778816512f,
+    0.629638239f,  0.776888466f,
+    0.632018736f,  0.774953107f,
+    0.634393284f,  0.773010453f,
+    0.636761861f,  0.771060524f,
+    0.639124445f,  0.769103338f,
+    0.641481013f,  0.767138912f,
+    0.643831543f,  0.765167266f,
+    0.646176013f,  0.763188417f,
+    0.648514401f,  0.761202385f,
+    0.650846685f,  0.759209189f,
+    0.653172843f,  0.757208847f,
+    0.655492853f,  0.755201377f,
+    0.657806693f,  0.753186799f,
+    0.660114342f,  0.751165132f,
+    0.662415778f,  0.749136395f,
+    0.664710978f,  0.747100606f,
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+    0.669282588f,  0.743007952f,
+    0.671558955f,  0.740951125f,
+    0.673829000f,  0.738887324f,
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+    0.678350043f,  0.734738878f,
+    0.680600998f,  0.732654272f,
+    0.682845546f,  0.730562769f,
+    0.685083668f,  0.728464390f,
+    0.687315341f,  0.726359155f,
+    0.689540545f,  0.724247083f,
+    0.691759258f,  0.722128194f,
+    0.693971461f,  0.720002508f,
+    0.696177131f,  0.717870045f,
+    0.698376249f,  0.715730825f,
+    0.700568794f,  0.713584869f,
+    0.702754744f,  0.711432196f,
+    0.704934080f,  0.709272826f,
+    0.707106781f,  0.707106781f,
+    0.709272826f,  0.704934080f,
+    0.711432196f,  0.702754744f,
+    0.713584869f,  0.700568794f,
+    0.715730825f,  0.698376249f,
+    0.717870045f,  0.696177131f,
+    0.720002508f,  0.693971461f,
+    0.722128194f,  0.691759258f,
+    0.724247083f,  0.689540545f,
+    0.726359155f,  0.687315341f,
+    0.728464390f,  0.685083668f,
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+    0.740951125f,  0.671558955f,
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+    0.101069863f, -0.994879331f,
+    0.098017140f, -0.995184727f,
+    0.094963495f, -0.995480755f,
+    0.091908956f, -0.995767414f,
+    0.088853553f, -0.996044701f,
+    0.085797312f, -0.996312612f,
+    0.082740265f, -0.996571146f,
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+    0.067443920f, -0.997723067f,
+    0.064382631f, -0.997925286f,
+    0.061320736f, -0.998118113f,
+    0.058258265f, -0.998301545f,
+    0.055195244f, -0.998475581f,
+    0.052131705f, -0.998640218f,
+    0.049067674f, -0.998795456f,
+    0.046003182f, -0.998941293f,
+    0.042938257f, -0.999077728f,
+    0.039872928f, -0.999204759f,
+    0.036807223f, -0.999322385f,
+    0.033741172f, -0.999430605f,
+    0.030674803f, -0.999529418f,
+    0.027608146f, -0.999618822f,
+    0.024541229f, -0.999698819f,
+    0.021474080f, -0.999769405f,
+    0.018406730f, -0.999830582f,
+    0.015339206f, -0.999882347f,
+    0.012271538f, -0.999924702f,
+    0.009203755f, -0.999957645f,
+    0.006135885f, -0.999981175f,
+    0.003067957f, -0.999995294f
+};
+
+const float32_t twiddleCoef_rfft_4096[4096] = {
+    0.000000000f,  1.000000000f,
+    0.001533980f,  0.999998823f,
+    0.003067957f,  0.999995294f,
+    0.004601926f,  0.999989411f,
+    0.006135885f,  0.999981175f,
+    0.007669829f,  0.999970586f,
+    0.009203755f,  0.999957645f,
+    0.010737659f,  0.999942350f,
+    0.012271538f,  0.999924702f,
+    0.013805389f,  0.999904701f,
+    0.015339206f,  0.999882347f,
+    0.016872988f,  0.999857641f,
+    0.018406730f,  0.999830582f,
+    0.019940429f,  0.999801170f,
+    0.021474080f,  0.999769405f,
+    0.023007681f,  0.999735288f,
+    0.024541229f,  0.999698819f,
+    0.026074718f,  0.999659997f,
+    0.027608146f,  0.999618822f,
+    0.029141509f,  0.999575296f,
+    0.030674803f,  0.999529418f,
+    0.032208025f,  0.999481187f,
+    0.033741172f,  0.999430605f,
+    0.035274239f,  0.999377670f,
+    0.036807223f,  0.999322385f,
+    0.038340120f,  0.999264747f,
+    0.039872928f,  0.999204759f,
+    0.041405641f,  0.999142419f,
+    0.042938257f,  0.999077728f,
+    0.044470772f,  0.999010686f,
+    0.046003182f,  0.998941293f,
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+    0.091908956f, -0.995767414f,
+    0.090381361f, -0.995907229f,
+    0.088853553f, -0.996044701f,
+    0.087325535f, -0.996179829f,
+    0.085797312f, -0.996312612f,
+    0.084268888f, -0.996443051f,
+    0.082740265f, -0.996571146f,
+    0.081211447f, -0.996696895f,
+    0.079682438f, -0.996820299f,
+    0.078153242f, -0.996941358f,
+    0.076623861f, -0.997060070f,
+    0.075094301f, -0.997176437f,
+    0.073564564f, -0.997290457f,
+    0.072034653f, -0.997402130f,
+    0.070504573f, -0.997511456f,
+    0.068974328f, -0.997618435f,
+    0.067443920f, -0.997723067f,
+    0.065913353f, -0.997825350f,
+    0.064382631f, -0.997925286f,
+    0.062851758f, -0.998022874f,
+    0.061320736f, -0.998118113f,
+    0.059789571f, -0.998211003f,
+    0.058258265f, -0.998301545f,
+    0.056726821f, -0.998389737f,
+    0.055195244f, -0.998475581f,
+    0.053663538f, -0.998559074f,
+    0.052131705f, -0.998640218f,
+    0.050599749f, -0.998719012f,
+    0.049067674f, -0.998795456f,
+    0.047535484f, -0.998869550f,
+    0.046003182f, -0.998941293f,
+    0.044470772f, -0.999010686f,
+    0.042938257f, -0.999077728f,
+    0.041405641f, -0.999142419f,
+    0.039872928f, -0.999204759f,
+    0.038340120f, -0.999264747f,
+    0.036807223f, -0.999322385f,
+    0.035274239f, -0.999377670f,
+    0.033741172f, -0.999430605f,
+    0.032208025f, -0.999481187f,
+    0.030674803f, -0.999529418f,
+    0.029141509f, -0.999575296f,
+    0.027608146f, -0.999618822f,
+    0.026074718f, -0.999659997f,
+    0.024541229f, -0.999698819f,
+    0.023007681f, -0.999735288f,
+    0.021474080f, -0.999769405f,
+    0.019940429f, -0.999801170f,
+    0.018406730f, -0.999830582f,
+    0.016872988f, -0.999857641f,
+    0.015339206f, -0.999882347f,
+    0.013805389f, -0.999904701f,
+    0.012271538f, -0.999924702f,
+    0.010737659f, -0.999942350f,
+    0.009203755f, -0.999957645f,
+    0.007669829f, -0.999970586f,
+    0.006135885f, -0.999981175f,
+    0.004601926f, -0.999989411f,
+    0.003067957f, -0.999995294f,
+    0.001533980f, -0.999998823f
+};
+
+
+/**   
+ * \par    
+ * Example code for the generation of the floating-point sine table:
+ * <pre>
+ * tableSize = 512;    
+ * for(n = 0; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n]=sin(2*pi*n/tableSize);    
+ * }</pre>    
+ * \par    
+ * where pi value is  3.14159265358979    
+ */
+
+const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = {
+   0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
+   0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
+   0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
+   0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
+   0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
+   0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
+   0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
+   0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
+   0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
+   0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
+   0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
+   0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
+   0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
+   0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
+   0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
+   0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
+   0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
+   0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
+   0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
+   0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
+   0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
+   0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
+   0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
+   0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
+   0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
+   0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
+   0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
+   0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
+   0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
+   0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
+   0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
+   0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
+   0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
+   0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
+   0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
+   0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
+   0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
+   0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
+   0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
+   0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
+   0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
+   0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
+   0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
+   -0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
+   -0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
+   -0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f, 
+   -0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f, 
+   -0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f, 
+   -0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f, 
+   -0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f, 
+   -0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f, 
+   -0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f, 
+   -0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f, 
+   -0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f, 
+   -0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f, 
+   -0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f, 
+   -0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f, 
+   -0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f, 
+   -0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f, 
+   -0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f, 
+   -0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f, 
+   -0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f, 
+   -0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f, 
+   -0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f, 
+   -0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f, 
+   -0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f, 
+   -0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f, 
+   -0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f, 
+   -0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f, 
+   -0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f, 
+   -0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f, 
+   -0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f, 
+   -0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f, 
+   -0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f, 
+   -0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f, 
+   -0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f, 
+   -0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f, 
+   -0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f, 
+   -0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f, 
+   -0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f, 
+   -0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f, 
+   -0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f, 
+   -0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f, 
+   -0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f, 
+   -0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f, 
+   -0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f, 
+   -0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f, 
+   -0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f, 
+   -0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f, 
+   -0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f, 
+   -0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f, 
+   -0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f, 
+   -0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f, 
+   -0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
+};
+
+/**   
+ * \par    
+ * Table values are in Q31 (1.31 fixed-point format) and generation is done in 
+ * three steps.  First,  generate sin values in floating point:    
+ * <pre>
+ * tableSize = 512;      
+ * for(n = 0; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n]= sin(2*pi*n/tableSize);    
+ * } </pre>    
+ * where pi value is  3.14159265358979    
+ * \par    
+ * Second, convert floating-point to Q31 (Fixed point):
+ *	(sinTable[i] * pow(2, 31))    
+ * \par    
+ * Finally, round to the nearest integer value:
+ * 	sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
+ */
+const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1] = {
+   0x00000000, 0x01921D20, 0x03242ABF, 0x04B6195D, 0x0647D97C, 0x07D95B9E, 
+   0x096A9049, 0x0AFB6805, 0x0C8BD35E, 0x0E1BC2E4, 0x0FAB272B, 0x1139F0CF, 
+   0x12C8106F, 0x145576B1, 0x15E21445, 0x176DD9DE, 0x18F8B83C, 0x1A82A026, 
+   0x1C0B826A, 0x1D934FE5, 0x1F19F97B, 0x209F701C, 0x2223A4C5, 0x23A6887F, 
+   0x25280C5E, 0x26A82186, 0x2826B928, 0x29A3C485, 0x2B1F34EB, 0x2C98FBBA, 
+   0x2E110A62, 0x2F875262, 0x30FBC54D, 0x326E54C7, 0x33DEF287, 0x354D9057, 
+   0x36BA2014, 0x382493B0, 0x398CDD32, 0x3AF2EEB7, 0x3C56BA70, 0x3DB832A6, 
+   0x3F1749B8, 0x4073F21D, 0x41CE1E65, 0x4325C135, 0x447ACD50, 0x45CD358F, 
+   0x471CECE7, 0x4869E665, 0x49B41533, 0x4AFB6C98, 0x4C3FDFF4, 0x4D8162C4, 
+   0x4EBFE8A5, 0x4FFB654D, 0x5133CC94, 0x5269126E, 0x539B2AF0, 0x54CA0A4B, 
+   0x55F5A4D2, 0x571DEEFA, 0x5842DD54, 0x59646498, 0x5A82799A, 0x5B9D1154, 
+   0x5CB420E0, 0x5DC79D7C, 0x5ED77C8A, 0x5FE3B38D, 0x60EC3830, 0x61F1003F, 
+   0x62F201AC, 0x63EF3290, 0x64E88926, 0x65DDFBD3, 0x66CF8120, 0x67BD0FBD, 
+   0x68A69E81, 0x698C246C, 0x6A6D98A4, 0x6B4AF279, 0x6C242960, 0x6CF934FC, 
+   0x6DCA0D14, 0x6E96A99D, 0x6F5F02B2, 0x7023109A, 0x70E2CBC6, 0x719E2CD2, 
+   0x72552C85, 0x7307C3D0, 0x73B5EBD1, 0x745F9DD1, 0x7504D345, 0x75A585CF, 
+   0x7641AF3D, 0x76D94989, 0x776C4EDB, 0x77FAB989, 0x78848414, 0x7909A92D, 
+   0x798A23B1, 0x7A05EEAD, 0x7A7D055B, 0x7AEF6323, 0x7B5D039E, 0x7BC5E290, 
+   0x7C29FBEE, 0x7C894BDE, 0x7CE3CEB2, 0x7D3980EC, 0x7D8A5F40, 0x7DD6668F, 
+   0x7E1D93EA, 0x7E5FE493, 0x7E9D55FC, 0x7ED5E5C6, 0x7F0991C4, 0x7F3857F6, 
+   0x7F62368F, 0x7F872BF3, 0x7FA736B4, 0x7FC25596, 0x7FD8878E, 0x7FE9CBC0, 
+   0x7FF62182, 0x7FFD885A, 0x7FFFFFFF, 0x7FFD885A, 0x7FF62182, 0x7FE9CBC0, 
+   0x7FD8878E, 0x7FC25596, 0x7FA736B4, 0x7F872BF3, 0x7F62368F, 0x7F3857F6, 
+   0x7F0991C4, 0x7ED5E5C6, 0x7E9D55FC, 0x7E5FE493, 0x7E1D93EA, 0x7DD6668F, 
+   0x7D8A5F40, 0x7D3980EC, 0x7CE3CEB2, 0x7C894BDE, 0x7C29FBEE, 0x7BC5E290, 
+   0x7B5D039E, 0x7AEF6323, 0x7A7D055B, 0x7A05EEAD, 0x798A23B1, 0x7909A92D, 
+   0x78848414, 0x77FAB989, 0x776C4EDB, 0x76D94989, 0x7641AF3D, 0x75A585CF, 
+   0x7504D345, 0x745F9DD1, 0x73B5EBD1, 0x7307C3D0, 0x72552C85, 0x719E2CD2, 
+   0x70E2CBC6, 0x7023109A, 0x6F5F02B2, 0x6E96A99D, 0x6DCA0D14, 0x6CF934FC, 
+   0x6C242960, 0x6B4AF279, 0x6A6D98A4, 0x698C246C, 0x68A69E81, 0x67BD0FBD, 
+   0x66CF8120, 0x65DDFBD3, 0x64E88926, 0x63EF3290, 0x62F201AC, 0x61F1003F, 
+   0x60EC3830, 0x5FE3B38D, 0x5ED77C8A, 0x5DC79D7C, 0x5CB420E0, 0x5B9D1154, 
+   0x5A82799A, 0x59646498, 0x5842DD54, 0x571DEEFA, 0x55F5A4D2, 0x54CA0A4B, 
+   0x539B2AF0, 0x5269126E, 0x5133CC94, 0x4FFB654D, 0x4EBFE8A5, 0x4D8162C4, 
+   0x4C3FDFF4, 0x4AFB6C98, 0x49B41533, 0x4869E665, 0x471CECE7, 0x45CD358F, 
+   0x447ACD50, 0x4325C135, 0x41CE1E65, 0x4073F21D, 0x3F1749B8, 0x3DB832A6, 
+   0x3C56BA70, 0x3AF2EEB7, 0x398CDD32, 0x382493B0, 0x36BA2014, 0x354D9057, 
+   0x33DEF287, 0x326E54C7, 0x30FBC54D, 0x2F875262, 0x2E110A62, 0x2C98FBBA, 
+   0x2B1F34EB, 0x29A3C485, 0x2826B928, 0x26A82186, 0x25280C5E, 0x23A6887F, 
+   0x2223A4C5, 0x209F701C, 0x1F19F97B, 0x1D934FE5, 0x1C0B826A, 0x1A82A026, 
+   0x18F8B83C, 0x176DD9DE, 0x15E21445, 0x145576B1, 0x12C8106F, 0x1139F0CF, 
+   0x0FAB272B, 0x0E1BC2E4, 0x0C8BD35E, 0x0AFB6805, 0x096A9049, 0x07D95B9E, 
+   0x0647D97C, 0x04B6195D, 0x03242ABF, 0x01921D20, 0x00000000, 0xFE6DE2E0, 
+   0xFCDBD541, 0xFB49E6A3, 0xF9B82684, 0xF826A462, 0xF6956FB7, 0xF50497FB, 
+   0xF3742CA2, 0xF1E43D1C, 0xF054D8D5, 0xEEC60F31, 0xED37EF91, 0xEBAA894F, 
+   0xEA1DEBBB, 0xE8922622, 0xE70747C4, 0xE57D5FDA, 0xE3F47D96, 0xE26CB01B, 
+   0xE0E60685, 0xDF608FE4, 0xDDDC5B3B, 0xDC597781, 0xDAD7F3A2, 0xD957DE7A, 
+   0xD7D946D8, 0xD65C3B7B, 0xD4E0CB15, 0xD3670446, 0xD1EEF59E, 0xD078AD9E, 
+   0xCF043AB3, 0xCD91AB39, 0xCC210D79, 0xCAB26FA9, 0xC945DFEC, 0xC7DB6C50, 
+   0xC67322CE, 0xC50D1149, 0xC3A94590, 0xC247CD5A, 0xC0E8B648, 0xBF8C0DE3, 
+   0xBE31E19B, 0xBCDA3ECB, 0xBB8532B0, 0xBA32CA71, 0xB8E31319, 0xB796199B, 
+   0xB64BEACD, 0xB5049368, 0xB3C0200C, 0xB27E9D3C, 0xB140175B, 0xB0049AB3, 
+   0xAECC336C, 0xAD96ED92, 0xAC64D510, 0xAB35F5B5, 0xAA0A5B2E, 0xA8E21106, 
+   0xA7BD22AC, 0xA69B9B68, 0xA57D8666, 0xA462EEAC, 0xA34BDF20, 0xA2386284, 
+   0xA1288376, 0xA01C4C73, 0x9F13C7D0, 0x9E0EFFC1, 0x9D0DFE54, 0x9C10CD70, 
+   0x9B1776DA, 0x9A22042D, 0x99307EE0, 0x9842F043, 0x9759617F, 0x9673DB94, 
+   0x9592675C, 0x94B50D87, 0x93DBD6A0, 0x9306CB04, 0x9235F2EC, 0x91695663, 
+   0x90A0FD4E, 0x8FDCEF66, 0x8F1D343A, 0x8E61D32E, 0x8DAAD37B, 0x8CF83C30, 
+   0x8C4A142F, 0x8BA0622F, 0x8AFB2CBB, 0x8A5A7A31, 0x89BE50C3, 0x8926B677, 
+   0x8893B125, 0x88054677, 0x877B7BEC, 0x86F656D3, 0x8675DC4F, 0x85FA1153, 
+   0x8582FAA5, 0x85109CDD, 0x84A2FC62, 0x843A1D70, 0x83D60412, 0x8376B422, 
+   0x831C314E, 0x82C67F14, 0x8275A0C0, 0x82299971, 0x81E26C16, 0x81A01B6D, 
+   0x8162AA04, 0x812A1A3A, 0x80F66E3C, 0x80C7A80A, 0x809DC971, 0x8078D40D, 
+   0x8058C94C, 0x803DAA6A, 0x80277872, 0x80163440, 0x8009DE7E, 0x800277A6, 
+   0x80000000, 0x800277A6, 0x8009DE7E, 0x80163440, 0x80277872, 0x803DAA6A, 
+   0x8058C94C, 0x8078D40D, 0x809DC971, 0x80C7A80A, 0x80F66E3C, 0x812A1A3A, 
+   0x8162AA04, 0x81A01B6D, 0x81E26C16, 0x82299971, 0x8275A0C0, 0x82C67F14, 
+   0x831C314E, 0x8376B422, 0x83D60412, 0x843A1D70, 0x84A2FC62, 0x85109CDD, 
+   0x8582FAA5, 0x85FA1153, 0x8675DC4F, 0x86F656D3, 0x877B7BEC, 0x88054677, 
+   0x8893B125, 0x8926B677, 0x89BE50C3, 0x8A5A7A31, 0x8AFB2CBB, 0x8BA0622F, 
+   0x8C4A142F, 0x8CF83C30, 0x8DAAD37B, 0x8E61D32E, 0x8F1D343A, 0x8FDCEF66, 
+   0x90A0FD4E, 0x91695663, 0x9235F2EC, 0x9306CB04, 0x93DBD6A0, 0x94B50D87, 
+   0x9592675C, 0x9673DB94, 0x9759617F, 0x9842F043, 0x99307EE0, 0x9A22042D, 
+   0x9B1776DA, 0x9C10CD70, 0x9D0DFE54, 0x9E0EFFC1, 0x9F13C7D0, 0xA01C4C73, 
+   0xA1288376, 0xA2386284, 0xA34BDF20, 0xA462EEAC, 0xA57D8666, 0xA69B9B68, 
+   0xA7BD22AC, 0xA8E21106, 0xAA0A5B2E, 0xAB35F5B5, 0xAC64D510, 0xAD96ED92, 
+   0xAECC336C, 0xB0049AB3, 0xB140175B, 0xB27E9D3C, 0xB3C0200C, 0xB5049368, 
+   0xB64BEACD, 0xB796199B, 0xB8E31319, 0xBA32CA71, 0xBB8532B0, 0xBCDA3ECB, 
+   0xBE31E19B, 0xBF8C0DE3, 0xC0E8B648, 0xC247CD5A, 0xC3A94590, 0xC50D1149, 
+   0xC67322CE, 0xC7DB6C50, 0xC945DFEC, 0xCAB26FA9, 0xCC210D79, 0xCD91AB39, 
+   0xCF043AB3, 0xD078AD9E, 0xD1EEF59E, 0xD3670446, 0xD4E0CB15, 0xD65C3B7B, 
+   0xD7D946D8, 0xD957DE7A, 0xDAD7F3A2, 0xDC597781, 0xDDDC5B3B, 0xDF608FE4, 
+   0xE0E60685, 0xE26CB01B, 0xE3F47D96, 0xE57D5FDA, 0xE70747C4, 0xE8922622, 
+   0xEA1DEBBB, 0xEBAA894F, 0xED37EF91, 0xEEC60F31, 0xF054D8D5, 0xF1E43D1C, 
+   0xF3742CA2, 0xF50497FB, 0xF6956FB7, 0xF826A462, 0xF9B82684, 0xFB49E6A3, 
+   0xFCDBD541, 0xFE6DE2E0, 0x00000000 
+};
+
+/**   
+ * \par    
+ * Table values are in Q15 (1.15 fixed-point format) and generation is done in 
+ * three steps.  First,  generate sin values in floating point:    
+ * <pre>
+ * tableSize = 512;      
+ * for(n = 0; n < (tableSize + 1); n++)    
+ * {    
+ *	sinTable[n]= sin(2*pi*n/tableSize);    
+ * } </pre>    
+ * where pi value is  3.14159265358979    
+ * \par    
+ * Second, convert floating-point to Q15 (Fixed point):
+ *	(sinTable[i] * pow(2, 15))    
+ * \par    
+ * Finally, round to the nearest integer value:
+ * 	sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
+ */
+const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1] = {
+   0x0000, 0x0192, 0x0324, 0x04B6, 0x0648, 0x07D9, 0x096B, 0x0AFB, 0x0C8C, 0x0E1C, 0x0FAB, 0x113A, 0x12C8,
+   0x1455, 0x15E2, 0x176E, 0x18F9, 0x1A83, 0x1C0C, 0x1D93, 0x1F1A, 0x209F, 0x2224, 0x23A7, 0x2528, 0x26A8,
+   0x2827, 0x29A4, 0x2B1F, 0x2C99, 0x2E11, 0x2F87, 0x30FC, 0x326E, 0x33DF, 0x354E, 0x36BA, 0x3825, 0x398D,
+   0x3AF3, 0x3C57, 0x3DB8, 0x3F17, 0x4074, 0x41CE, 0x4326, 0x447B, 0x45CD, 0x471D, 0x486A, 0x49B4, 0x4AFB,
+   0x4C40, 0x4D81, 0x4EC0, 0x4FFB, 0x5134, 0x5269, 0x539B, 0x54CA, 0x55F6, 0x571E, 0x5843, 0x5964, 0x5A82,
+   0x5B9D, 0x5CB4, 0x5DC8, 0x5ED7, 0x5FE4, 0x60EC, 0x61F1, 0x62F2, 0x63EF, 0x64E9, 0x65DE, 0x66D0, 0x67BD,
+   0x68A7, 0x698C, 0x6A6E, 0x6B4B, 0x6C24, 0x6CF9, 0x6DCA, 0x6E97, 0x6F5F, 0x7023, 0x70E3, 0x719E, 0x7255,
+   0x7308, 0x73B6, 0x7460, 0x7505, 0x75A6, 0x7642, 0x76D9, 0x776C, 0x77FB, 0x7885, 0x790A, 0x798A, 0x7A06,
+   0x7A7D, 0x7AEF, 0x7B5D, 0x7BC6, 0x7C2A, 0x7C89, 0x7CE4, 0x7D3A, 0x7D8A, 0x7DD6, 0x7E1E, 0x7E60, 0x7E9D,
+   0x7ED6, 0x7F0A, 0x7F38, 0x7F62, 0x7F87, 0x7FA7, 0x7FC2, 0x7FD9, 0x7FEA, 0x7FF6, 0x7FFE, 0x7FFF, 0x7FFE,
+   0x7FF6, 0x7FEA, 0x7FD9, 0x7FC2, 0x7FA7, 0x7F87, 0x7F62, 0x7F38, 0x7F0A, 0x7ED6, 0x7E9D, 0x7E60, 0x7E1E,
+   0x7DD6, 0x7D8A, 0x7D3A, 0x7CE4, 0x7C89, 0x7C2A, 0x7BC6, 0x7B5D, 0x7AEF, 0x7A7D, 0x7A06, 0x798A, 0x790A,
+   0x7885, 0x77FB, 0x776C, 0x76D9, 0x7642, 0x75A6, 0x7505, 0x7460, 0x73B6, 0x7308, 0x7255, 0x719E, 0x70E3,
+   0x7023, 0x6F5F, 0x6E97, 0x6DCA, 0x6CF9, 0x6C24, 0x6B4B, 0x6A6E, 0x698C, 0x68A7, 0x67BD, 0x66D0, 0x65DE,
+   0x64E9, 0x63EF, 0x62F2, 0x61F1, 0x60EC, 0x5FE4, 0x5ED7, 0x5DC8, 0x5CB4, 0x5B9D, 0x5A82, 0x5964, 0x5843,
+   0x571E, 0x55F6, 0x54CA, 0x539B, 0x5269, 0x5134, 0x4FFB, 0x4EC0, 0x4D81, 0x4C40, 0x4AFB, 0x49B4, 0x486A,
+   0x471D, 0x45CD, 0x447B, 0x4326, 0x41CE, 0x4074, 0x3F17, 0x3DB8, 0x3C57, 0x3AF3, 0x398D, 0x3825, 0x36BA,
+   0x354E, 0x33DF, 0x326E, 0x30FC, 0x2F87, 0x2E11, 0x2C99, 0x2B1F, 0x29A4, 0x2827, 0x26A8, 0x2528, 0x23A7,
+   0x2224, 0x209F, 0x1F1A, 0x1D93, 0x1C0C, 0x1A83, 0x18F9, 0x176E, 0x15E2, 0x1455, 0x12C8, 0x113A, 0x0FAB,
+   0x0E1C, 0x0C8C, 0x0AFB, 0x096B, 0x07D9, 0x0648, 0x04B6, 0x0324, 0x0192, 0x0000, 0xFE6E, 0xFCDC, 0xFB4A,
+   0xF9B8, 0xF827, 0xF695, 0xF505, 0xF374, 0xF1E4, 0xF055, 0xEEC6, 0xED38, 0xEBAB, 0xEA1E, 0xE892, 0xE707,
+   0xE57D, 0xE3F4, 0xE26D, 0xE0E6, 0xDF61, 0xDDDC, 0xDC59, 0xDAD8, 0xD958, 0xD7D9, 0xD65C, 0xD4E1, 0xD367,
+   0xD1EF, 0xD079, 0xCF04, 0xCD92, 0xCC21, 0xCAB2, 0xC946, 0xC7DB, 0xC673, 0xC50D, 0xC3A9, 0xC248, 0xC0E9,
+   0xBF8C, 0xBE32, 0xBCDA, 0xBB85, 0xBA33, 0xB8E3, 0xB796, 0xB64C, 0xB505, 0xB3C0, 0xB27F, 0xB140, 0xB005,
+   0xAECC, 0xAD97, 0xAC65, 0xAB36, 0xAA0A, 0xA8E2, 0xA7BD, 0xA69C, 0xA57E, 0xA463, 0xA34C, 0xA238, 0xA129,
+   0xA01C, 0x9F14, 0x9E0F, 0x9D0E, 0x9C11, 0x9B17, 0x9A22, 0x9930, 0x9843, 0x9759, 0x9674, 0x9592, 0x94B5,
+   0x93DC, 0x9307, 0x9236, 0x9169, 0x90A1, 0x8FDD, 0x8F1D, 0x8E62, 0x8DAB, 0x8CF8, 0x8C4A, 0x8BA0, 0x8AFB,
+   0x8A5A, 0x89BE, 0x8927, 0x8894, 0x8805, 0x877B, 0x86F6, 0x8676, 0x85FA, 0x8583, 0x8511, 0x84A3, 0x843A,
+   0x83D6, 0x8377, 0x831C, 0x82C6, 0x8276, 0x822A, 0x81E2, 0x81A0, 0x8163, 0x812A, 0x80F6, 0x80C8, 0x809E,
+   0x8079, 0x8059, 0x803E, 0x8027, 0x8016, 0x800A, 0x8002, 0x8000, 0x8002, 0x800A, 0x8016, 0x8027, 0x803E,
+   0x8059, 0x8079, 0x809E, 0x80C8, 0x80F6, 0x812A, 0x8163, 0x81A0, 0x81E2, 0x822A, 0x8276, 0x82C6, 0x831C,
+   0x8377, 0x83D6, 0x843A, 0x84A3, 0x8511, 0x8583, 0x85FA, 0x8676, 0x86F6, 0x877B, 0x8805, 0x8894, 0x8927,
+   0x89BE, 0x8A5A, 0x8AFB, 0x8BA0, 0x8C4A, 0x8CF8, 0x8DAB, 0x8E62, 0x8F1D, 0x8FDD, 0x90A1, 0x9169, 0x9236,
+   0x9307, 0x93DC, 0x94B5, 0x9592, 0x9674, 0x9759, 0x9843, 0x9930, 0x9A22, 0x9B17, 0x9C11, 0x9D0E, 0x9E0F,
+   0x9F14, 0xA01C, 0xA129, 0xA238, 0xA34C, 0xA463, 0xA57E, 0xA69C, 0xA7BD, 0xA8E2, 0xAA0A, 0xAB36, 0xAC65,
+   0xAD97, 0xAECC, 0xB005, 0xB140, 0xB27F, 0xB3C0, 0xB505, 0xB64C, 0xB796, 0xB8E3, 0xBA33, 0xBB85, 0xBCDA,
+   0xBE32, 0xBF8C, 0xC0E9, 0xC248, 0xC3A9, 0xC50D, 0xC673, 0xC7DB, 0xC946, 0xCAB2, 0xCC21, 0xCD92, 0xCF04,
+   0xD079, 0xD1EF, 0xD367, 0xD4E1, 0xD65C, 0xD7D9, 0xD958, 0xDAD8, 0xDC59, 0xDDDC, 0xDF61, 0xE0E6, 0xE26D,
+   0xE3F4, 0xE57D, 0xE707, 0xE892, 0xEA1E, 0xEBAB, 0xED38, 0xEEC6, 0xF055, 0xF1E4, 0xF374, 0xF505, 0xF695,
+   0xF827, 0xF9B8, 0xFB4A, 0xFCDC, 0xFE6E, 0x0000
+};

Libraries/CMSIS/DSP_Lib/Source/CommonTables/arm_const_structs.c

@@ -0,0 +1,156 @@
+/* ---------------------------------------------------------------------- 
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved. 
+* 
+* $Date:        31. July 2014 
+* $Revision: 	V1.4.4
+* 
+* Project: 	    CMSIS DSP Library 
+* Title:	    arm_const_structs.c 
+* 
+* Description:	This file has constant structs that are initialized for
+*              user convenience.  For example, some can be given as 
+*              arguments to the arm_cfft_f32() function.
+* 
+* Target Processor: Cortex-M4/Cortex-M3
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_const_structs.h"
+
+//Floating-point structs
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len16 = {
+	16, twiddleCoef_16, armBitRevIndexTable16, ARMBITREVINDEXTABLE__16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len32 = {
+	32, twiddleCoef_32, armBitRevIndexTable32, ARMBITREVINDEXTABLE__32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len64 = {
+	64, twiddleCoef_64, armBitRevIndexTable64, ARMBITREVINDEXTABLE__64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len128 = {
+	128, twiddleCoef_128, armBitRevIndexTable128, ARMBITREVINDEXTABLE_128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len256 = {
+	256, twiddleCoef_256, armBitRevIndexTable256, ARMBITREVINDEXTABLE_256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len512 = {
+	512, twiddleCoef_512, armBitRevIndexTable512, ARMBITREVINDEXTABLE_512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024 = {
+	1024, twiddleCoef_1024, armBitRevIndexTable1024, ARMBITREVINDEXTABLE1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048 = {
+	2048, twiddleCoef_2048, armBitRevIndexTable2048, ARMBITREVINDEXTABLE2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096 = {
+	4096, twiddleCoef_4096, armBitRevIndexTable4096, ARMBITREVINDEXTABLE4096_TABLE_LENGTH
+};
+
+//Fixed-point structs
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len16 = {
+	16, twiddleCoef_16_q31, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len32 = {
+	32, twiddleCoef_32_q31, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len64 = {
+	64, twiddleCoef_64_q31, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len128 = {
+	128, twiddleCoef_128_q31, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len256 = {
+	256, twiddleCoef_256_q31, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len512 = {
+	512, twiddleCoef_512_q31, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024 = {
+	1024, twiddleCoef_1024_q31, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048 = {
+	2048, twiddleCoef_2048_q31, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096 = {
+	4096, twiddleCoef_4096_q31, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH
+};
+
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len16 = {
+	16, twiddleCoef_16_q15, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len32 = {
+	32, twiddleCoef_32_q15, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len64 = {
+	64, twiddleCoef_64_q15, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len128 = {
+	128, twiddleCoef_128_q15, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len256 = {
+	256, twiddleCoef_256_q15, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len512 = {
+	512, twiddleCoef_512_q15, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024 = {
+	1024, twiddleCoef_1024_q15, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048 = {
+	2048, twiddleCoef_2048_q15, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096 = {
+	4096, twiddleCoef_4096_q15, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH
+};

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c

@@ -0,0 +1,182 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_conj_f32.c    
+*    
+* Description:	Floating-point complex conjugate.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup cmplx_conj Complex Conjugate        
+ *        
+ * Conjugates the elements of a complex data vector.        
+ *       
+ * The <code>pSrc</code> points to the source data and        
+ * <code>pDst</code> points to the where the result should be written.        
+ * <code>numSamples</code> specifies the number of complex samples        
+ * and the data in each array is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * Each array has a total of <code>2*numSamples</code> values.        
+ * The underlying algorithm is used:        
+ *        
+ * <pre>        
+ * for(n=0; n<numSamples; n++) {        
+ *     pDst[(2*n)+0)] = pSrc[(2*n)+0];     // real part        
+ *     pDst[(2*n)+1)] = -pSrc[(2*n)+1];    // imag part        
+ * }        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup cmplx_conj        
+ * @{        
+ */
+
+/**        
+ * @brief  Floating-point complex conjugate.        
+ * @param  *pSrc points to the input vector        
+ * @param  *pDst points to the output vector        
+ * @param  numSamples number of complex samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_conj_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inR1, inR2, inR3, inR4;
+  float32_t inI1, inI2, inI3, inI4;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* read real input samples */
+    inR1 = pSrc[0];
+    /* store real samples to destination */
+    pDst[0] = inR1;
+    inR2 = pSrc[2];
+    pDst[2] = inR2;
+    inR3 = pSrc[4];
+    pDst[4] = inR3;
+    inR4 = pSrc[6];
+    pDst[6] = inR4;
+
+    /* read imaginary input samples */
+    inI1 = pSrc[1];
+    inI2 = pSrc[3];
+
+    /* conjugate input */
+    inI1 = -inI1;
+
+    /* read imaginary input samples */
+    inI3 = pSrc[5];
+
+    /* conjugate input */
+    inI2 = -inI2;
+
+    /* read imaginary input samples */
+    inI4 = pSrc[7];
+
+    /* conjugate input */
+    inI3 = -inI3;
+
+    /* store imaginary samples to destination */
+    pDst[1] = inI1;
+    pDst[3] = inI2;
+
+    /* conjugate input */
+    inI4 = -inI4;
+
+    /* store imaginary samples to destination */
+    pDst[5] = inI3;
+
+    /* increment source pointer by 8 to process next sampels */
+    pSrc += 8u;
+
+    /* store imaginary sample to destination */
+    pDst[7] = inI4;
+
+    /* increment destination pointer by 8 to store next samples */
+    pDst += 8u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* realOut + j (imagOut) = realIn + j (-1) imagIn */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    *pDst++ = -*pSrc++;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_conj group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c

@@ -0,0 +1,161 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_conj_q15.c    
+*    
+* Description:	Q15 complex conjugate.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_conj    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex conjugate.    
+ * @param  *pSrc points to the input vector    
+ * @param  *pDst points to the output vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF.    
+ */
+
+void arm_cmplx_conj_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t zero = 0;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    in1 = __QASX(zero, in1);
+    in2 = __QASX(zero, in2);
+    in3 = __QASX(zero, in3);
+    in4 = __QASX(zero, in4);
+
+#else
+
+    in1 = __QSAX(zero, in1);
+    in2 = __QSAX(zero, in2);
+    in3 = __QSAX(zero, in3);
+    in4 = __QSAX(zero, in4);
+
+#endif //       #ifndef ARM_MATH_BIG_ENDIAN
+
+    in1 = ((uint32_t) in1 >> 16) | ((uint32_t) in1 << 16);
+    in2 = ((uint32_t) in2 >> 16) | ((uint32_t) in2 << 16);
+    in3 = ((uint32_t) in3 >> 16) | ((uint32_t) in3 << 16);
+    in4 = ((uint32_t) in4 >> 16) | ((uint32_t) in4 << 16);
+
+    *__SIMD32(pDst)++ = in1;
+    *__SIMD32(pDst)++ = in2;
+    *__SIMD32(pDst)++ = in3;
+    *__SIMD32(pDst)++ = in4;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    *pDst++ = __SSAT(-*pSrc++, 16);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  q15_t in;
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut + j (imagOut) = realIn+ j (-1) imagIn */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    *pDst++ = *pSrc++;
+    in = *pSrc++;
+    *pDst++ = (in == (q15_t) 0x8000) ? 0x7fff : -in;
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of cmplx_conj group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c

@@ -0,0 +1,180 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_conj_q31.c    
+*    
+* Description:	Q31 complex conjugate.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.    
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @addtogroup cmplx_conj        
+ * @{        
+ */
+
+/**        
+ * @brief  Q31 complex conjugate.        
+ * @param  *pSrc points to the input vector        
+ * @param  *pDst points to the output vector        
+ * @param  numSamples number of complex samples in each vector        
+ * @return none.        
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function uses saturating arithmetic.        
+ * The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF.        
+ */
+
+void arm_cmplx_conj_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in;                                      /* Input value */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t inR1, inR2, inR3, inR4;                  /* Temporary real variables */
+  q31_t inI1, inI2, inI3, inI4;                  /* Temporary imaginary variables */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* Saturated to 0x7fffffff if the input is -1(0x80000000) */
+    /* read real input sample */
+    inR1 = pSrc[0];
+    /* store real input sample */
+    pDst[0] = inR1;
+
+    /* read imaginary input sample */
+    inI1 = pSrc[1];
+
+    /* read real input sample */
+    inR2 = pSrc[2];
+    /* store real input sample */
+    pDst[2] = inR2;
+
+    /* read imaginary input sample */
+    inI2 = pSrc[3];
+
+    /* negate imaginary input sample */
+    inI1 = __QSUB(0, inI1);
+
+    /* read real input sample */
+    inR3 = pSrc[4];
+    /* store real input sample */
+    pDst[4] = inR3;
+
+    /* read imaginary input sample */
+    inI3 = pSrc[5];
+
+    /* negate imaginary input sample */
+    inI2 = __QSUB(0, inI2);
+
+    /* read real input sample */
+    inR4 = pSrc[6];
+    /* store real input sample */
+    pDst[6] = inR4;
+
+    /* negate imaginary input sample */
+    inI3 = __QSUB(0, inI3);
+
+    /* store imaginary input sample */
+    inI4 = pSrc[7];
+
+    /* store imaginary input samples */
+    pDst[1] = inI1;
+
+    /* negate imaginary input sample */
+    inI4 = __QSUB(0, inI4);
+
+    /* store imaginary input samples */
+    pDst[3] = inI2;
+
+    /* increment source pointer by 8 to proecess next samples */
+    pSrc += 8u;
+
+    /* store imaginary input samples */
+    pDst[5] = inI3;
+    pDst[7] = inI4;
+
+    /* increment destination pointer by 8 to process next samples */
+    pDst += 8u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0]+jC[1] = A[0]+ j (-1) A[1] */
+    /* Calculate Complex Conjugate and then store the results in the destination buffer. */
+    /* Saturated to 0x7fffffff if the input is -1(0x80000000) */
+    *pDst++ = *pSrc++;
+    in = *pSrc++;
+    *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_conj group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c

@@ -0,0 +1,203 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_f32.c    
+*    
+* Description:	Floating-point complex dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.    
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @defgroup cmplx_dot_prod Complex Dot Product    
+ *    
+ * Computes the dot product of two complex vectors.    
+ * The vectors are multiplied element-by-element and then summed.    
+ *   
+ * The <code>pSrcA</code> points to the first complex input vector and    
+ * <code>pSrcB</code> points to the second complex input vector.    
+ * <code>numSamples</code> specifies the number of complex samples    
+ * and the data in each array is stored in an interleaved fashion    
+ * (real, imag, real, imag, ...).    
+ * Each array has a total of <code>2*numSamples</code> values.    
+ *    
+ * The underlying algorithm is used:    
+ * <pre>    
+ * realResult=0;    
+ * imagResult=0;    
+ * for(n=0; n<numSamples; n++) {    
+ *     realResult += pSrcA[(2*n)+0]*pSrcB[(2*n)+0] - pSrcA[(2*n)+1]*pSrcB[(2*n)+1];    
+ *     imagResult += pSrcA[(2*n)+0]*pSrcB[(2*n)+1] + pSrcA[(2*n)+1]*pSrcB[(2*n)+0];    
+ * }    
+ * </pre>    
+ *    
+ * There are separate functions for floating-point, Q15, and Q31 data types.    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Floating-point complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ */
+
+void arm_cmplx_dot_prod_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  uint32_t numSamples,
+  float32_t * realResult,
+  float32_t * imagResult)
+{
+  float32_t real_sum = 0.0f, imag_sum = 0.0f;    /* Temporary result storage */
+  float32_t a0,b0,c0,d0;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+    
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++; 
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+    
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++; 
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples & 0x3u;
+
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+
+      /* Decrement the loop counter */
+      numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  /* Store the real and imaginary results in the destination buffers */
+  *realResult = real_sum;
+  *imagResult = imag_sum;
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c

@@ -0,0 +1,189 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_q15.c    
+*    
+* Description:	Processing function for the Q15 Complex Dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The intermediate 1.15 by 1.15 multiplications are performed with full precision and yield a 2.30 result.    
+ * These are accumulated in a 64-bit accumulator with 34.30 precision.    
+ * As a final step, the accumulators are converted to 8.24 format.    
+ * The return results <code>realResult</code> and <code>imagResult</code> are in 8.24 format.    
+ */
+
+void arm_cmplx_dot_prod_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  uint32_t numSamples,
+  q31_t * realResult,
+  q31_t * imagResult)
+{
+  q63_t real_sum = 0, imag_sum = 0;              /* Temporary result storage */
+  q15_t a0,b0,c0,d0;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += (q31_t)a0 * c0;
+      imag_sum += (q31_t)a0 * d0;
+      real_sum -= (q31_t)b0 * d0;
+      imag_sum += (q31_t)b0 * c0;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += (q31_t)a0 * c0;
+      imag_sum += (q31_t)a0 * d0;
+      real_sum -= (q31_t)b0 * d0;
+      imag_sum += (q31_t)b0 * c0;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += (q31_t)a0 * c0;
+      imag_sum += (q31_t)a0 * d0;
+      real_sum -= (q31_t)b0 * d0;
+      imag_sum += (q31_t)b0 * c0;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += (q31_t)a0 * c0;
+      imag_sum += (q31_t)a0 * d0;
+      real_sum -= (q31_t)b0 * d0;
+      imag_sum += (q31_t)b0 * c0;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += (q31_t)a0 * c0;
+      imag_sum += (q31_t)a0 * d0;
+      real_sum -= (q31_t)b0 * d0;
+      imag_sum += (q31_t)b0 * c0;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += a0 * c0;
+      imag_sum += a0 * d0;
+      real_sum -= b0 * d0;
+      imag_sum += b0 * c0;
+
+
+      /* Decrement the loop counter */
+      numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  /* Store the real and imaginary results in 8.24 format  */
+  /* Convert real data in 34.30 to 8.24 by 6 right shifts */
+  *realResult = (q31_t) (real_sum >> 6);
+  /* Convert imaginary data in 34.30 to 8.24 by 6 right shifts */
+  *imagResult = (q31_t) (imag_sum >> 6);
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c

@@ -0,0 +1,187 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_dot_prod_q31.c    
+*    
+* Description:	Q31 complex dot product    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_dot_prod    
+ * @{    
+ */
+
+/**    
+ * @brief  Q31 complex dot product    
+ * @param  *pSrcA points to the first input vector    
+ * @param  *pSrcB points to the second input vector    
+ * @param  numSamples number of complex samples in each vector    
+ * @param  *realResult real part of the result returned here    
+ * @param  *imagResult imaginary part of the result returned here    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function is implemented using an internal 64-bit accumulator.    
+ * The intermediate 1.31 by 1.31 multiplications are performed with 64-bit precision and then shifted to 16.48 format.    
+ * The internal real and imaginary accumulators are in 16.48 format and provide 15 guard bits.    
+ * Additions are nonsaturating and no overflow will occur as long as <code>numSamples</code> is less than 32768.    
+ * The return results <code>realResult</code> and <code>imagResult</code> are in 16.48 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_dot_prod_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  uint32_t numSamples,
+  q63_t * realResult,
+  q63_t * imagResult)
+{
+  q63_t real_sum = 0, imag_sum = 0;              /* Temporary result storage */
+  q31_t a0,b0,c0,d0;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+      
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+  /* If the numSamples  is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+
+      /* Decrement the loop counter */
+      blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+      a0 = *pSrcA++;
+      b0 = *pSrcA++;
+      c0 = *pSrcB++;
+      d0 = *pSrcB++;  
+  
+      real_sum += ((q63_t)a0 * c0) >> 14;
+      imag_sum += ((q63_t)a0 * d0) >> 14;
+      real_sum -= ((q63_t)b0 * d0) >> 14;
+      imag_sum += ((q63_t)b0 * c0) >> 14;
+
+      /* Decrement the loop counter */
+      numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  /* Store the real and imaginary results in 16.48 format  */
+  *realResult = real_sum;
+  *imagResult = imag_sum;
+}
+
+/**    
+ * @} end of cmplx_dot_prod group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c

@@ -0,0 +1,165 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_f32.c    
+*    
+* Description:	Floating-point complex magnitude.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @defgroup cmplx_mag Complex Magnitude    
+ *    
+ * Computes the magnitude of the elements of a complex data vector.    
+ *   
+ * The <code>pSrc</code> points to the source data and    
+ * <code>pDst</code> points to the where the result should be written.    
+ * <code>numSamples</code> specifies the number of complex samples    
+ * in the input array and the data is stored in an interleaved fashion    
+ * (real, imag, real, imag, ...).    
+ * The input array has a total of <code>2*numSamples</code> values;    
+ * the output array has a total of <code>numSamples</code> values.    
+ * The underlying algorithm is used:    
+ *    
+ * <pre>    
+ * for(n=0; n<numSamples; n++) {    
+ *     pDst[n] = sqrt(pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2);    
+ * }    
+ * </pre>    
+ *    
+ * There are separate functions for floating-point, Q15, and Q31 data types.    
+ */
+
+/**    
+ * @addtogroup cmplx_mag    
+ * @{    
+ */
+/**    
+ * @brief Floating-point complex magnitude.    
+ * @param[in]       *pSrc points to complex input buffer    
+ * @param[out]      *pDst points to real output buffer    
+ * @param[in]       numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ */
+
+
+void arm_cmplx_mag_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t realIn, imagIn;                      /* Temporary variables to hold input values */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* out = sqrt((real * real) + (imag * imag)) */
+    realIn = *pSrc++;
+    imagIn = *pSrc++;
+    /* store the result in the destination buffer. */
+    arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of cmplx_mag group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c

@@ -0,0 +1,153 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_q15.c    
+*    
+* Description:	Q15 complex magnitude.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q15 complex magnitude    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 2.14 format.    
+ */
+
+void arm_cmplx_mag_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t acc2, acc3;
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+    acc0 = __SMUAD(in1, in1);
+    acc1 = __SMUAD(in2, in2);
+    acc2 = __SMUAD(in3, in3);
+    acc3 = __SMUAD(in4, in4);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) ((acc0) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc1) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc2) >> 17), pDst++);
+    arm_sqrt_q15((q15_t) ((acc3) >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    acc0 = __SMUAD(in1, in1);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t real, imag;                              /* Temporary variables to hold input values */
+
+  while(numSamples > 0u)
+  {
+    /* out = sqrt(real * real + imag * imag) */
+    real = *pSrc++;
+    imag = *pSrc++;
+
+    acc0 = (real * real);
+    acc1 = (imag * imag);
+
+    /* store the result in 2.14 format in the destination buffer. */
+    arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of cmplx_mag group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c

@@ -0,0 +1,185 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_q31.c    
+*    
+* Description:	Q31 complex magnitude    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @addtogroup cmplx_mag        
+ * @{        
+ */
+
+/**        
+ * @brief  Q31 complex magnitude        
+ * @param  *pSrc points to the complex input vector        
+ * @param  *pDst points to the real output vector        
+ * @param  numSamples number of complex samples in the input vector        
+ * @return none.        
+ *        
+ * <b>Scaling and Overflow Behavior:</b>        
+ * \par        
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 2.30 format.        
+ * Input down scaling is not required.        
+ */
+
+void arm_cmplx_mag_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t real, imag;                              /* Temporary variables to hold input values */
+  q31_t acc0, acc1;                              /* Accumulators */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  q31_t real1, real2, imag1, imag2;              /* Temporary variables to hold input values */
+  q31_t out1, out2, out3, out4;                  /* Accumulators */
+  q63_t mul1, mul2, mul3, mul4;                  /* Temporary variables */
+
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* read complex input from source buffer */
+    real1 = pSrc[0];
+    imag1 = pSrc[1];
+    real2 = pSrc[2];
+    imag2 = pSrc[3];
+
+    /* calculate power of input values */
+    mul1 = (q63_t) real1 *real1;
+    mul2 = (q63_t) imag1 *imag1;
+    mul3 = (q63_t) real2 *real2;
+    mul4 = (q63_t) imag2 *imag2;
+
+    /* get the result to 3.29 format */
+    out1 = (q31_t) (mul1 >> 33);
+    out2 = (q31_t) (mul2 >> 33);
+    out3 = (q31_t) (mul3 >> 33);
+    out4 = (q31_t) (mul4 >> 33);
+
+    /* add real and imaginary accumulators */
+    out1 = out1 + out2;
+    out3 = out3 + out4;
+
+    /* read complex input from source buffer */
+    real1 = pSrc[4];
+    imag1 = pSrc[5];
+    real2 = pSrc[6];
+    imag2 = pSrc[7];
+
+    /* calculate square root */
+    arm_sqrt_q31(out1, &pDst[0]);
+
+    /* calculate power of input values */
+    mul1 = (q63_t) real1 *real1;
+
+    /* calculate square root */
+    arm_sqrt_q31(out3, &pDst[1]);
+
+    /* calculate power of input values */
+    mul2 = (q63_t) imag1 *imag1;
+    mul3 = (q63_t) real2 *real2;
+    mul4 = (q63_t) imag2 *imag2;
+
+    /* get the result to 3.29 format */
+    out1 = (q31_t) (mul1 >> 33);
+    out2 = (q31_t) (mul2 >> 33);
+    out3 = (q31_t) (mul3 >> 33);
+    out4 = (q31_t) (mul4 >> 33);
+
+    /* add real and imaginary accumulators */
+    out1 = out1 + out2;
+    out3 = out3 + out4;
+
+    /* calculate square root */
+    arm_sqrt_q31(out1, &pDst[2]);
+
+    /* increment destination by 8 to process next samples */
+    pSrc += 8u;
+
+    /* calculate square root */
+    arm_sqrt_q31(out3, &pDst[3]);
+
+    /* increment destination by 4 to process next samples */
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 2.30 format in the destination buffer. */
+    arm_sqrt_q31(acc0 + acc1, pDst++);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_mag group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c

@@ -0,0 +1,215 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_f32.c    
+*    
+* Description:	Floating-point complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ---------------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup cmplx_mag_squared Complex Magnitude Squared        
+ *        
+ * Computes the magnitude squared of the elements of a complex data vector.        
+ *       
+ * The <code>pSrc</code> points to the source data and        
+ * <code>pDst</code> points to the where the result should be written.        
+ * <code>numSamples</code> specifies the number of complex samples        
+ * in the input array and the data is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The input array has a total of <code>2*numSamples</code> values;        
+ * the output array has a total of <code>numSamples</code> values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * <pre>        
+ * for(n=0; n<numSamples; n++) {        
+ *     pDst[n] = pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2;        
+ * }        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup cmplx_mag_squared        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex magnitude squared        
+ * @param[in]  *pSrc points to the complex input vector        
+ * @param[out]  *pDst points to the real output vector        
+ * @param[in]  numSamples number of complex samples in the input vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mag_squared_f32(
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t real, imag;                          /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counter */
+
+#ifndef ARM_MATH_CM0_FAMILY
+  float32_t real1, real2, real3, real4;          /* Temporary variables to hold real values */
+  float32_t imag1, imag2, imag3, imag4;          /* Temporary variables to hold imaginary values */
+  float32_t mul1, mul2, mul3, mul4;              /* Temporary variables */
+  float32_t mul5, mul6, mul7, mul8;              /* Temporary variables */
+  float32_t out1, out2, out3, out4;              /* Temporary variables to hold output values */
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    /* read real input sample from source buffer */
+    real1 = pSrc[0];
+    /* read imaginary input sample from source buffer */
+    imag1 = pSrc[1];
+
+    /* calculate power of real value */
+    mul1 = real1 * real1;
+
+    /* read real input sample from source buffer */
+    real2 = pSrc[2];
+
+    /* calculate power of imaginary value */
+    mul2 = imag1 * imag1;
+
+    /* read imaginary input sample from source buffer */
+    imag2 = pSrc[3];
+
+    /* calculate power of real value */
+    mul3 = real2 * real2;
+
+    /* read real input sample from source buffer */
+    real3 = pSrc[4];
+
+    /* calculate power of imaginary value */
+    mul4 = imag2 * imag2;
+
+    /* read imaginary input sample from source buffer */
+    imag3 = pSrc[5];
+
+    /* calculate power of real value */
+    mul5 = real3 * real3;
+    /* calculate power of imaginary value */
+    mul6 = imag3 * imag3;
+
+    /* read real input sample from source buffer */
+    real4 = pSrc[6];
+
+    /* accumulate real and imaginary powers */
+    out1 = mul1 + mul2;
+
+    /* read imaginary input sample from source buffer */
+    imag4 = pSrc[7];
+
+    /* accumulate real and imaginary powers */
+    out2 = mul3 + mul4;
+
+    /* calculate power of real value */
+    mul7 = real4 * real4;
+    /* calculate power of imaginary value */
+    mul8 = imag4 * imag4;
+
+    /* store output to destination */
+    pDst[0] = out1;
+
+    /* accumulate real and imaginary powers */
+    out3 = mul5 + mul6;
+
+    /* store output to destination */
+    pDst[1] = out2;
+
+    /* accumulate real and imaginary powers */
+    out4 = mul7 + mul8;
+
+    /* store output to destination */
+    pDst[2] = out3;
+
+    /* increment destination pointer by 8 to process next samples */
+    pSrc += 8u;
+
+    /* store output to destination */
+    pDst[3] = out4;
+
+    /* increment destination pointer by 4 to process next samples */
+    pDst += 4u;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+
+    /* out = (real * real) + (imag * imag) */
+    /* store the result in the destination buffer. */
+    *pDst++ = (real * real) + (imag * imag);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of cmplx_mag_squared group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c

@@ -0,0 +1,148 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_q15.c    
+*    
+* Description:	Q15 complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag_squared    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex magnitude squared    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.    
+ */
+
+void arm_cmplx_mag_squared_q15(
+  q15_t * pSrc,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+  q31_t in1, in2, in3, in4;
+  q31_t acc2, acc3;
+
+  /*loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    in2 = *__SIMD32(pSrc)++;
+    in3 = *__SIMD32(pSrc)++;
+    in4 = *__SIMD32(pSrc)++;
+
+    acc0 = __SMUAD(in1, in1);
+    acc1 = __SMUAD(in2, in2);
+    acc2 = __SMUAD(in3, in3);
+    acc3 = __SMUAD(in4, in4);
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (acc0 >> 17);
+    *pDst++ = (q15_t) (acc1 >> 17);
+    *pDst++ = (q15_t) (acc2 >> 17);
+    *pDst++ = (q15_t) (acc3 >> 17);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    in1 = *__SIMD32(pSrc)++;
+    acc0 = __SMUAD(in1, in1);
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (acc0 >> 17);
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  q15_t real, imag;                              /* Temporary variables to store real and imaginary values */
+
+  while(numSamples > 0u)
+  {
+    /* out = ((real * real) + (imag * imag)) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (real * real);
+    acc1 = (imag * imag);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of cmplx_mag_squared group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c

@@ -0,0 +1,161 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:		arm_cmplx_mag_squared_q31.c    
+*    
+* Description:	Q31 complex magnitude squared.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* ---------------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup cmplx_mag_squared    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex magnitude squared    
+ * @param  *pSrc points to the complex input vector    
+ * @param  *pDst points to the real output vector    
+ * @param  numSamples number of complex samples in the input vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_mag_squared_q31(
+  q31_t * pSrc,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t real, imag;                              /* Temporary variables to store real and imaginary values */
+  q31_t acc0, acc1;                              /* Accumulators */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counter */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[0] = (A[0] * A[0] + A[1] * A[1]) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* out = ((real * real) + (imag * imag)) */
+    real = *pSrc++;
+    imag = *pSrc++;
+    acc0 = (q31_t) (((q63_t) real * real) >> 33);
+    acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
+    /* store the result in 3.29 format in the destination buffer. */
+    *pDst++ = acc0 + acc1;
+
+    /* Decrement the loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of cmplx_mag_squared group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c

@@ -0,0 +1,207 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_f32.c    
+*    
+* Description:	Floating-point complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup CmplxByCmplxMult Complex-by-Complex Multiplication        
+ *        
+ * Multiplies a complex vector by another complex vector and generates a complex result.        
+ * The data in the complex arrays is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The parameter <code>numSamples</code> represents the number of complex        
+ * samples processed.  The complex arrays have a total of <code>2*numSamples</code>        
+ * real values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * <pre>        
+ * for(n=0; n<numSamples; n++) {        
+ *     pDst[(2*n)+0] = pSrcA[(2*n)+0] * pSrcB[(2*n)+0] - pSrcA[(2*n)+1] * pSrcB[(2*n)+1];        
+ *     pDst[(2*n)+1] = pSrcA[(2*n)+0] * pSrcB[(2*n)+1] + pSrcA[(2*n)+1] * pSrcB[(2*n)+0];        
+ * }        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup CmplxByCmplxMult        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex-by-complex multiplication        
+ * @param[in]  *pSrcA points to the first input vector        
+ * @param[in]  *pSrcB points to the second input vector        
+ * @param[out]  *pDst  points to the output vector        
+ * @param[in]  numSamples number of complex samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mult_cmplx_f32(
+  float32_t * pSrcA,
+  float32_t * pSrcB,
+  float32_t * pDst,
+  uint32_t numSamples)
+{
+  float32_t a1, b1, c1, d1;                      /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t a2, b2, c2, d2;                      /* Temporary variables to store real and imaginary values */
+  float32_t acc1, acc2, acc3, acc4;
+
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a1 = *pSrcA;                /* A[2 * i] */
+    c1 = *pSrcB;                /* B[2 * i] */
+
+    b1 = *(pSrcA + 1);          /* A[2 * i + 1] */
+    acc1 = a1 * c1;             /* acc1 = A[2 * i] * B[2 * i] */
+
+    a2 = *(pSrcA + 2);          /* A[2 * i + 2] */
+    acc2 = (b1 * c1);           /* acc2 = A[2 * i + 1] * B[2 * i] */
+
+    d1 = *(pSrcB + 1);          /* B[2 * i + 1] */
+    c2 = *(pSrcB + 2);          /* B[2 * i + 2] */
+    acc1 -= b1 * d1;            /* acc1 =      A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1] */
+
+    d2 = *(pSrcB + 3);          /* B[2 * i + 3] */
+    acc3 = a2 * c2;             /* acc3 =       A[2 * i + 2] * B[2 * i + 2] */
+
+    b2 = *(pSrcA + 3);          /* A[2 * i + 3] */
+    acc2 += (a1 * d1);          /* acc2 =      A[2 * i + 1] * B[2 * i] + A[2 * i] * B[2 * i + 1] */
+
+    a1 = *(pSrcA + 4);          /* A[2 * i + 4] */
+    acc4 = (a2 * d2);           /* acc4 =   A[2 * i + 2] * B[2 * i + 3] */
+
+    c1 = *(pSrcB + 4);          /* B[2 * i + 4] */
+    acc3 -= (b2 * d2);          /* acc3 =       A[2 * i + 2] * B[2 * i + 2] - A[2 * i + 3] * B[2 * i + 3] */
+    *pDst = acc1;               /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1] */
+
+    b1 = *(pSrcA + 5);          /* A[2 * i + 5] */
+    acc4 += b2 * c2;            /* acc4 =   A[2 * i + 2] * B[2 * i + 3] + A[2 * i + 3] * B[2 * i + 2] */
+
+    *(pDst + 1) = acc2;         /* C[2 * i + 1] = A[2 * i + 1] * B[2 * i] + A[2 * i] * B[2 * i + 1]  */
+    acc1 = (a1 * c1);
+
+    d1 = *(pSrcB + 5);
+    acc2 = (b1 * c1);
+
+    *(pDst + 2) = acc3;
+    *(pDst + 3) = acc4;
+
+    a2 = *(pSrcA + 6);
+    acc1 -= (b1 * d1);
+
+    c2 = *(pSrcB + 6);
+    acc2 += (a1 * d1);
+
+    b2 = *(pSrcA + 7);
+    acc3 = (a2 * c2);
+
+    d2 = *(pSrcB + 7);
+    acc4 = (b2 * c2);
+
+    *(pDst + 4) = acc1;
+    pSrcA += 8u;
+
+    acc3 -= (b2 * d2);
+    acc4 += (a2 * d2);
+
+    *(pDst + 5) = acc2;
+    pSrcB += 8u;
+
+    *(pDst + 6) = acc3;
+    *(pDst + 7) = acc4;
+
+    pDst += 8u;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a1 = *pSrcA++;
+    b1 = *pSrcA++;
+    c1 = *pSrcB++;
+    d1 = *pSrcB++;
+
+    /* store the result in the destination buffer. */
+    *pDst++ = (a1 * c1) - (b1 * d1);
+    *pDst++ = (a1 * d1) + (b1 * c1);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of CmplxByCmplxMult group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c

@@ -0,0 +1,193 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_q15.c    
+*    
+* Description:	Q15 complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByCmplxMult    
+ * @{    
+ */
+
+/**    
+ * @brief  Q15 complex-by-complex multiplication    
+ * @param[in]  *pSrcA points to the first input vector    
+ * @param[in]  *pSrcB points to the second input vector    
+ * @param[out]  *pDst  points to the output vector    
+ * @param[in]  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.    
+ */
+
+void arm_cmplx_mult_cmplx_q15(
+  q15_t * pSrcA,
+  q15_t * pSrcB,
+  q15_t * pDst,
+  uint32_t numSamples)
+{
+  q15_t a, b, c, d;                              /* Temporary variables to store real and imaginary values */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
+    /* store the result in 3.13 format in the destination buffer. */
+    *pDst++ =
+      (q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
+
+    /* Decrement the blockSize loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of CmplxByCmplxMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c

@@ -0,0 +1,326 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_cmplx_q31.c    
+*    
+* Description:	Q31 complex-by-complex multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByCmplxMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex-by-complex multiplication    
+ * @param[in]  *pSrcA points to the first input vector    
+ * @param[in]  *pSrcB points to the second input vector    
+ * @param[out]  *pDst  points to the output vector    
+ * @param[in]  numSamples number of complex samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format.    
+ * Input down scaling is not required.    
+ */
+
+void arm_cmplx_mult_cmplx_q31(
+  q31_t * pSrcA,
+  q31_t * pSrcB,
+  q31_t * pDst,
+  uint32_t numSamples)
+{
+  q31_t a, b, c, d;                              /* Temporary variables to store real and imaginary values */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t mul1, mul2, mul3, mul4;
+  q31_t out1, out2;
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 1u;
+
+  /* First part of the processing with loop unrolling.  Compute 2 outputs at a time.     
+   ** a second loop below computes the remaining 1 sample. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+  /* If the blockSize is not a multiple of 2, compute any remaining output samples here.     
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x2u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1].  */
+    /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i].  */
+    a = *pSrcA++;
+    b = *pSrcA++;
+    c = *pSrcB++;
+    d = *pSrcB++;
+
+    mul1 = (q31_t) (((q63_t) a * c) >> 32);
+    mul2 = (q31_t) (((q63_t) b * d) >> 32);
+    mul3 = (q31_t) (((q63_t) a * d) >> 32);
+    mul4 = (q31_t) (((q63_t) b * c) >> 32);
+
+    mul1 = (mul1 >> 1);
+    mul2 = (mul2 >> 1);
+    mul3 = (mul3 >> 1);
+    mul4 = (mul4 >> 1);
+
+    out1 = mul1 - mul2;
+    out2 = mul3 + mul4;
+
+    /* store the real result in 3.29 format in the destination buffer. */
+    *pDst++ = out1;
+    /* store the imag result in 3.29 format in the destination buffer. */
+    *pDst++ = out2;
+
+    /* Decrement the blockSize loop counter */
+    blkCnt--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of CmplxByCmplxMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c

@@ -0,0 +1,225 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_f32.c    
+*    
+* Description:	Floating-point complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**        
+ * @ingroup groupCmplxMath        
+ */
+
+/**        
+ * @defgroup CmplxByRealMult Complex-by-Real Multiplication        
+ *        
+ * Multiplies a complex vector by a real vector and generates a complex result.        
+ * The data in the complex arrays is stored in an interleaved fashion        
+ * (real, imag, real, imag, ...).        
+ * The parameter <code>numSamples</code> represents the number of complex        
+ * samples processed.  The complex arrays have a total of <code>2*numSamples</code>        
+ * real values while the real array has a total of <code>numSamples</code>        
+ * real values.        
+ *        
+ * The underlying algorithm is used:        
+ *        
+ * <pre>        
+ * for(n=0; n<numSamples; n++) {        
+ *     pCmplxDst[(2*n)+0] = pSrcCmplx[(2*n)+0] * pSrcReal[n];        
+ *     pCmplxDst[(2*n)+1] = pSrcCmplx[(2*n)+1] * pSrcReal[n];        
+ * }        
+ * </pre>        
+ *        
+ * There are separate functions for floating-point, Q15, and Q31 data types.        
+ */
+
+/**        
+ * @addtogroup CmplxByRealMult        
+ * @{        
+ */
+
+
+/**        
+ * @brief  Floating-point complex-by-real multiplication        
+ * @param[in]  *pSrcCmplx points to the complex input vector        
+ * @param[in]  *pSrcReal points to the real input vector        
+ * @param[out]  *pCmplxDst points to the complex output vector        
+ * @param[in]  numSamples number of samples in each vector        
+ * @return none.        
+ */
+
+void arm_cmplx_mult_real_f32(
+  float32_t * pSrcCmplx,
+  float32_t * pSrcReal,
+  float32_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  float32_t in;                                  /* Temporary variable to store input value */
+  uint32_t blkCnt;                               /* loop counters */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  float32_t inA1, inA2, inA3, inA4;              /* Temporary variables to hold input data */
+  float32_t inA5, inA6, inA7, inA8;              /* Temporary variables to hold input data */
+  float32_t inB1, inB2, inB3, inB4;              /* Temporary variables to hold input data */
+  float32_t out1, out2, out3, out4;              /* Temporary variables to hold output data */
+  float32_t out5, out6, out7, out8;              /* Temporary variables to hold output data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.        
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read input from complex input buffer */
+    inA1 = pSrcCmplx[0];
+    inA2 = pSrcCmplx[1];
+    /* read input from real input buffer */
+    inB1 = pSrcReal[0];
+
+    /* read input from complex input buffer */
+    inA3 = pSrcCmplx[2];
+
+    /* multiply complex buffer real input with real buffer input */
+    out1 = inA1 * inB1;
+
+    /* read input from complex input buffer */
+    inA4 = pSrcCmplx[3];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out2 = inA2 * inB1;
+
+    /* read input from real input buffer */
+    inB2 = pSrcReal[1];
+    /* read input from complex input buffer */
+    inA5 = pSrcCmplx[4];
+
+    /* multiply complex buffer real input with real buffer input */
+    out3 = inA3 * inB2;
+
+    /* read input from complex input buffer */
+    inA6 = pSrcCmplx[5];
+    /* read input from real input buffer */
+    inB3 = pSrcReal[2];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out4 = inA4 * inB2;
+
+    /* read input from complex input buffer */
+    inA7 = pSrcCmplx[6];
+
+    /* multiply complex buffer real input with real buffer input */
+    out5 = inA5 * inB3;
+
+    /* read input from complex input buffer */
+    inA8 = pSrcCmplx[7];
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out6 = inA6 * inB3;
+
+    /* read input from real input buffer */
+    inB4 = pSrcReal[3];
+
+    /* store result to destination bufer */
+    pCmplxDst[0] = out1;
+
+    /* multiply complex buffer real input with real buffer input */
+    out7 = inA7 * inB4;
+
+    /* store result to destination bufer */
+    pCmplxDst[1] = out2;
+
+    /* multiply complex buffer imaginary input with real buffer input */
+    out8 = inA8 * inB4;
+
+    /* store result to destination bufer */
+    pCmplxDst[2] = out3;
+    pCmplxDst[3] = out4;
+    pCmplxDst[4] = out5;
+
+    /* incremnet complex input buffer by 8 to process next samples */
+    pSrcCmplx += 8u;
+
+    /* store result to destination bufer */
+    pCmplxDst[5] = out6;
+
+    /* increment real input buffer by 4 to process next samples */
+    pSrcReal += 4u;
+
+    /* store result to destination bufer */
+    pCmplxDst[6] = out7;
+    pCmplxDst[7] = out8;
+
+    /* increment destination buffer by 8 to process next sampels */
+    pCmplxDst += 8u;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.        
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+  blkCnt = numSamples;
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ = (*pSrcCmplx++) * (in);
+    *pCmplxDst++ = (*pSrcCmplx++) * (in);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+}
+
+/**        
+ * @} end of CmplxByRealMult group        
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c

@@ -0,0 +1,203 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_q15.c    
+*    
+* Description:	Q15 complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE. 
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByRealMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q15 complex-by-real multiplication    
+ * @param[in]  *pSrcCmplx points to the complex input vector    
+ * @param[in]  *pSrcReal points to the real input vector    
+ * @param[out]  *pCmplxDst points to the complex output vector    
+ * @param[in]  numSamples number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.    
+ */
+
+void arm_cmplx_mult_real_q15(
+  q15_t * pSrcCmplx,
+  q15_t * pSrcReal,
+  q15_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  q15_t in;                                      /* Temporary variable to store input value */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t inA1, inA2;                              /* Temporary variables to hold input data */
+  q31_t inB1;                                    /* Temporary variables to hold input data */
+  q15_t out1, out2, out3, out4;                  /* Temporary variables to hold output data */
+  q31_t mul1, mul2, mul3, mul4;                  /* Temporary variables to hold intermediate data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read complex number both real and imaginary from complex input buffer */
+    inA1 = *__SIMD32(pSrcCmplx)++;
+    /* read two real values at a time from real input buffer */
+    inB1 = *__SIMD32(pSrcReal)++;
+    /* read complex number both real and imaginary from complex input buffer */
+    inA2 = *__SIMD32(pSrcCmplx)++;
+
+    /* multiply complex number with real numbers */
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1));
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1));
+    mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16));
+
+#else
+
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16));
+    mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1);
+    mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    /* saturate the result */
+    out1 = (q15_t) __SSAT(mul1 >> 15u, 16);
+    out2 = (q15_t) __SSAT(mul2 >> 15u, 16);
+    out3 = (q15_t) __SSAT(mul3 >> 15u, 16);
+    out4 = (q15_t) __SSAT(mul4 >> 15u, 16);
+
+    /* pack real and imaginary outputs and store them to destination */
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out1, out2, 16);
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out3, out4, 16);
+
+    inA1 = *__SIMD32(pSrcCmplx)++;
+    inB1 = *__SIMD32(pSrcReal)++;
+    inA2 = *__SIMD32(pSrcCmplx)++;
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+    mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1));
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1));
+    mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16));
+
+#else
+
+    mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16));
+    mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16));
+    mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1);
+    mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1);
+
+#endif //      #ifndef ARM_MATH_BIG_ENDIAN
+
+    out1 = (q15_t) __SSAT(mul1 >> 15u, 16);
+    out2 = (q15_t) __SSAT(mul2 >> 15u, 16);
+    out3 = (q15_t) __SSAT(mul3 >> 15u, 16);
+    out4 = (q15_t) __SSAT(mul4 >> 15u, 16);
+
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out1, out2, 16);
+    *__SIMD32(pCmplxDst)++ = __PKHBT(out3, out4, 16);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut = realA * realB.            */
+    /* imagOut = imagA * realB.                */
+    in = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+    *pCmplxDst++ =
+      (q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
+
+    /* Decrement the numSamples loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of CmplxByRealMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c

@@ -0,0 +1,223 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_cmplx_mult_real_q31.c    
+*    
+* Description:	Q31 complex by real multiplication    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @ingroup groupCmplxMath    
+ */
+
+/**    
+ * @addtogroup CmplxByRealMult    
+ * @{    
+ */
+
+
+/**    
+ * @brief  Q31 complex-by-real multiplication    
+ * @param[in]  *pSrcCmplx points to the complex input vector    
+ * @param[in]  *pSrcReal points to the real input vector    
+ * @param[out]  *pCmplxDst points to the complex output vector    
+ * @param[in]  numSamples number of samples in each vector    
+ * @return none.    
+ *    
+ * <b>Scaling and Overflow Behavior:</b>    
+ * \par    
+ * The function uses saturating arithmetic.    
+ * Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] will be saturated.    
+ */
+
+void arm_cmplx_mult_real_q31(
+  q31_t * pSrcCmplx,
+  q31_t * pSrcReal,
+  q31_t * pCmplxDst,
+  uint32_t numSamples)
+{
+  q31_t inA1;                                    /* Temporary variable to store input value */
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  uint32_t blkCnt;                               /* loop counters */
+  q31_t inA2, inA3, inA4;                        /* Temporary variables to hold input data */
+  q31_t inB1, inB2;                              /* Temporary variabels to hold input data */
+  q31_t out1, out2, out3, out4;                  /* Temporary variables to hold output data */
+
+  /* loop Unrolling */
+  blkCnt = numSamples >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+    inB2 = *pSrcReal++;
+    /* read imaginary input from complex input buffer */
+    inA3 = *pSrcCmplx++;
+    inA4 = *pSrcCmplx++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+    out3 = ((q63_t) inA3 * inB2) >> 32;
+    out4 = ((q63_t) inA4 * inB2) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+    out3 = __SSAT(out3, 31);
+    out4 = __SSAT(out4, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+    out3 = out3 << 1;
+    out4 = out4 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+    *pCmplxDst++ = out3;
+    *pCmplxDst++ = out4;
+
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+    inB2 = *pSrcReal++;
+    /* read imaginary input from complex input buffer */
+    inA3 = *pSrcCmplx++;
+    inA4 = *pSrcCmplx++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+    out3 = ((q63_t) inA3 * inB2) >> 32;
+    out4 = ((q63_t) inA4 * inB2) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+    out3 = __SSAT(out3, 31);
+    out4 = __SSAT(out4, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+    out3 = out3 << 1;
+    out4 = out4 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+    *pCmplxDst++ = out3;
+    *pCmplxDst++ = out4;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+  /* If the numSamples is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  blkCnt = numSamples % 0x4u;
+
+  while(blkCnt > 0u)
+  {
+    /* C[2 * i] = A[2 * i] * B[i].            */
+    /* C[2 * i + 1] = A[2 * i + 1] * B[i].        */
+    /* read real input from complex input buffer */
+    inA1 = *pSrcCmplx++;
+    inA2 = *pSrcCmplx++;
+    /* read input from real input bufer */
+    inB1 = *pSrcReal++;
+
+    /* multiply complex input with real input */
+    out1 = ((q63_t) inA1 * inB1) >> 32;
+    out2 = ((q63_t) inA2 * inB1) >> 32;
+
+    /* sature the result */
+    out1 = __SSAT(out1, 31);
+    out2 = __SSAT(out2, 31);
+
+    /* get result in 1.31 format */
+    out1 = out1 << 1;
+    out2 = out2 << 1;
+
+    /* store the result to destination buffer */
+    *pCmplxDst++ = out1;
+    *pCmplxDst++ = out2;
+
+    /* Decrement the numSamples loop counter */
+    blkCnt--;
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  while(numSamples > 0u)
+  {
+    /* realOut = realA * realB.            */
+    /* imagReal = imagA * realB.               */
+    inA1 = *pSrcReal++;
+    /* store the result in the destination buffer. */
+    *pCmplxDst++ =
+      (q31_t) clip_q63_to_q31(((q63_t) * pSrcCmplx++ * inA1) >> 31);
+    *pCmplxDst++ =
+      (q31_t) clip_q63_to_q31(((q63_t) * pSrcCmplx++ * inA1) >> 31);
+
+    /* Decrement the numSamples loop counter */
+    numSamples--;
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of CmplxByRealMult group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_f32.c

@@ -0,0 +1,87 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_f32.c    
+*    
+* Description:	Floating-point PID Control initialization function    
+*				   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.   
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the floating-point PID Control.   
+ * @param[in,out] *S points to an instance of the PID structure.   
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state & 1 = reset the state.   
+ * @return none.   
+ * \par Description:   
+ * \par    
+ * The <code>resetStateFlag</code> specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: <code>A0</code>, <code>A1</code> <code>A2</code>    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_f32(
+  arm_pid_instance_f32 * S,
+  int32_t resetStateFlag)
+{
+
+  /* Derived coefficient A0 */
+  S->A0 = S->Kp + S->Ki + S->Kd;
+
+  /* Derived coefficient A1 */
+  S->A1 = (-S->Kp) - ((float32_t) 2.0 * S->Kd);
+
+  /* Derived coefficient A2 */
+  S->A2 = S->Kd;
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(float32_t));
+  }
+
+}
+
+/**    
+ * @} end of PID group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q15.c

@@ -0,0 +1,122 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_q15.c    
+*    
+* Description:	Q15 PID Control initialization function    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @details    
+ * @param[in,out] *S points to an instance of the Q15 PID structure.    
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.    
+ * @return none.    
+ * \par Description:   
+ * \par    
+ * The <code>resetStateFlag</code> specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: <code>A0</code>, <code>A1</code> <code>A2</code>    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_q15(
+  arm_pid_instance_q15 * S,
+  int32_t resetStateFlag)
+{
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Derived coefficient A0 */
+  S->A0 = __QADD16(__QADD16(S->Kp, S->Ki), S->Kd);
+
+  /* Derived coefficients and pack into A1 */
+
+#ifndef  ARM_MATH_BIG_ENDIAN
+
+  S->A1 = __PKHBT(-__QADD16(__QADD16(S->Kd, S->Kd), S->Kp), S->Kd, 16);
+
+#else
+
+  S->A1 = __PKHBT(S->Kd, -__QADD16(__QADD16(S->Kd, S->Kd), S->Kp), 16);
+
+#endif /*      #ifndef  ARM_MATH_BIG_ENDIAN    */
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q15_t));
+  }
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t temp;                                    /*to store the sum */
+
+  /* Derived coefficient A0 */
+  temp = S->Kp + S->Ki + S->Kd;
+  S->A0 = (q15_t) __SSAT(temp, 16);
+
+  /* Derived coefficients and pack into A1 */
+  temp = -(S->Kd + S->Kd + S->Kp);
+  S->A1 = (q15_t) __SSAT(temp, 16);
+  S->A2 = S->Kd;
+
+
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q15_t));
+  }
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+}
+
+/**    
+ * @} end of PID group    
+ */

Libraries/CMSIS/DSP_Lib/Source/ControllerFunctions/arm_pid_init_q31.c

@@ -0,0 +1,107 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
+*    
+* $Date:        12. March 2014
+* $Revision: 	V1.4.4
+*    
+* Project: 	    CMSIS DSP Library    
+* Title:	    arm_pid_init_q31.c    
+*    
+* Description:	Q31 PID Control initialization function     
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Redistribution and use in source and binary forms, with or without 
+* modification, are permitted provided that the following conditions
+* are met:
+*   - Redistributions of source code must retain the above copyright
+*     notice, this list of conditions and the following disclaimer.
+*   - Redistributions in binary form must reproduce the above copyright
+*     notice, this list of conditions and the following disclaimer in
+*     the documentation and/or other materials provided with the 
+*     distribution.
+*   - Neither the name of ARM LIMITED nor the names of its contributors
+*     may be used to endorse or promote products derived from this
+*     software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.  
+* ------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+ /**    
+ * @addtogroup PID    
+ * @{    
+ */
+
+/**    
+ * @brief  Initialization function for the Q31 PID Control.   
+ * @param[in,out] *S points to an instance of the Q31 PID structure.   
+ * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.   
+ * @return none.    
+ * \par Description:   
+ * \par    
+ * The <code>resetStateFlag</code> specifies whether to set state to zero or not. \n   
+ * The function computes the structure fields: <code>A0</code>, <code>A1</code> <code>A2</code>    
+ * using the proportional gain( \c Kp), integral gain( \c Ki) and derivative gain( \c Kd)    
+ * also sets the state variables to all zeros.    
+ */
+
+void arm_pid_init_q31(
+  arm_pid_instance_q31 * S,
+  int32_t resetStateFlag)
+{
+
+#ifndef ARM_MATH_CM0_FAMILY
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Derived coefficient A0 */
+  S->A0 = __QADD(__QADD(S->Kp, S->Ki), S->Kd);
+
+  /* Derived coefficient A1 */
+  S->A1 = -__QADD(__QADD(S->Kd, S->Kd), S->Kp);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  q31_t temp;
+
+  /* Derived coefficient A0 */
+  temp = clip_q63_to_q31((q63_t) S->Kp + S->Ki);
+  S->A0 = clip_q63_to_q31((q63_t) temp + S->Kd);
+
+  /* Derived coefficient A1 */
+  temp = clip_q63_to_q31((q63_t) S->Kd + S->Kd);
+  S->A1 = -clip_q63_to_q31((q63_t) temp + S->Kp);
+
+#endif /* #ifndef ARM_MATH_CM0_FAMILY */
+
+  /* Derived coefficient A2 */
+  S->A2 = S->Kd;
+
+  /* Check whether state needs reset or not */
+  if(resetStateFlag)
+  {
+    /* Clear the state buffer.  The size will be always 3 samples */
+    memset(S->state, 0, 3u * sizeof(q31_t));
+  }
+
+}
+
+/**    
+ * @} end of PID group    
+ */