From a0d054f85a15e334818b95475f16de1e85941756 Mon Sep 17 00:00:00 2001
From: Robofish <1683502971@qq.com>
Date: Sun, 6 Jul 2025 20:06:33 +0800
Subject: [PATCH] =?UTF-8?q?=E6=8D=A2=E7=94=B5=E8=84=91?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 CtrBoard-H7_ALL.ioc                         |   12 +-
 MDK-ARM/CtrBoard-H7_ALL.uvoptx              |   10 +
 MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.axf |  Bin 2495444 -> 2495908 bytes
 MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.hex | 9386 ++++++++++---------
 Middlewares/ST/ARM/DSP/Inc/arm_math.h       | 8970 ++++++++++++++++++
 Middlewares/Third_Party/ARM/DSP/LICENSE.txt |  201 +
 User/component/cmd.c                        |   15 +-
 User/component/cmd.h                        |    4 +
 User/module/chassis.c                       |    4 +-
 User/module/chassis.h                       |   51 +-
 User/module/config.c                        |   67 +-
 11 files changed, 13969 insertions(+), 4751 deletions(-)
 create mode 100644 Middlewares/ST/ARM/DSP/Inc/arm_math.h
 create mode 100644 Middlewares/Third_Party/ARM/DSP/LICENSE.txt

diff --git a/CtrBoard-H7_ALL.ioc b/CtrBoard-H7_ALL.ioc
index c5af9d2..94f93b1 100644
--- a/CtrBoard-H7_ALL.ioc
+++ b/CtrBoard-H7_ALL.ioc
@@ -433,11 +433,13 @@ Mcu.Pin61=VP_OCTOSPI2_VS_quad
 Mcu.Pin62=VP_SYS_VS_tim23
 Mcu.Pin63=VP_USB_DEVICE_VS_USB_DEVICE_CDC_HS
 Mcu.Pin64=VP_MEMORYMAP_VS_MEMORYMAP
+Mcu.Pin65=VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.4.0_1.4.0
 Mcu.Pin7=PC0
 Mcu.Pin8=PC1
 Mcu.Pin9=PC2_C
-Mcu.PinsNb=65
-Mcu.ThirdPartyNb=0
+Mcu.PinsNb=66
+Mcu.ThirdParty0=STMicroelectronics.X-CUBE-ALGOBUILD.1.4.0
+Mcu.ThirdPartyNb=1
 Mcu.UserConstants=
 Mcu.UserName=STM32H723VGTx
 MxCube.Version=6.14.1
@@ -846,6 +848,10 @@ SPI2.Direction=SPI_DIRECTION_2LINES
 SPI2.IPParameters=VirtualType,Mode,Direction,CalculateBaudRate,DataSize,BaudRatePrescaler,CLKPolarity,CLKPhase
 SPI2.Mode=SPI_MODE_MASTER
 SPI2.VirtualType=VM_MASTER
+STMicroelectronics.X-CUBE-ALGOBUILD.1.4.0.DSPOoLibraryJjLibrary_Checked=true
+STMicroelectronics.X-CUBE-ALGOBUILD.1.4.0.IPParameters=LibraryCcDSPOoLibraryJjDSPOoLibrary
+STMicroelectronics.X-CUBE-ALGOBUILD.1.4.0.LibraryCcDSPOoLibraryJjDSPOoLibrary=true
+STMicroelectronics.X-CUBE-ALGOBUILD.1.4.0_SwParameter=LibraryCcDSPOoLibraryJjDSPOoLibrary\:true;
 TIM1.Channel-PWM\ Generation1\ CH1=TIM_CHANNEL_1
 TIM1.Channel-PWM\ Generation3\ CH3=TIM_CHANNEL_3
 TIM1.IPParameters=Channel-PWM Generation3 CH3,Channel-PWM Generation1 CH1,Period,Pulse-PWM Generation1 CH1,Pulse-PWM Generation3 CH3,Prescaler
@@ -908,6 +914,8 @@ VP_MEMORYMAP_VS_MEMORYMAP.Mode=CurAppReg
 VP_MEMORYMAP_VS_MEMORYMAP.Signal=MEMORYMAP_VS_MEMORYMAP
 VP_OCTOSPI2_VS_quad.Mode=quad_mode
 VP_OCTOSPI2_VS_quad.Signal=OCTOSPI2_VS_quad
+VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.4.0_1.4.0.Mode=DSPOoLibraryJjLibrary
+VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.4.0_1.4.0.Signal=STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.4.0_1.4.0
 VP_SYS_VS_tim23.Mode=TIM23
 VP_SYS_VS_tim23.Signal=SYS_VS_tim23
 VP_USB_DEVICE_VS_USB_DEVICE_CDC_HS.Mode=CDC_HS
diff --git a/MDK-ARM/CtrBoard-H7_ALL.uvoptx b/MDK-ARM/CtrBoard-H7_ALL.uvoptx
index 63408c8..873fd37 100644
--- a/MDK-ARM/CtrBoard-H7_ALL.uvoptx
+++ b/MDK-ARM/CtrBoard-H7_ALL.uvoptx
@@ -175,6 +175,16 @@
           <WinNumber>1</WinNumber>
           <ItemText>n100_cali</ItemText>
         </Ww>
+        <Ww>
+          <count>4</count>
+          <WinNumber>1</WinNumber>
+          <ItemText>n100</ItemText>
+        </Ww>
+        <Ww>
+          <count>5</count>
+          <WinNumber>1</WinNumber>
+          <ItemText>cmd</ItemText>
+        </Ww>
       </WatchWindow1>
       <Tracepoint>
         <THDelay>0</THDelay>
diff --git a/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.axf b/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.axf
index 2c2a4f6c007e6c375ab65f16525834db145f97d9..d5d255f1139c2bb0357d927d6654e200b48a774b 100644
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diff --git a/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.hex b/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.hex
index 11a9d71..cb5c9d4 100644
--- a/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.hex
+++ b/MDK-ARM/CtrBoard-H7_ALL/CtrBoard-H7_ALL.hex
@@ -1,29 +1,29 @@
 :020000040800F2
-:10000000700C012019050008C1D70008F1C60008CE
-:10001000E9D50008893300081D110108000000001F
+:10000000700C012019050008EDD700081DC7000875
+:1000100015D60008893300084911010800000000C6
 :10002000000000000000000000000000590400086B
-:10003000094A000800000000B50400085BE1000860
+:10003000354A000800000000B504000887E1000808
 :1000400037050008370500083705000837050008A0
 :100050003705000837050008370500083705000890
-:100060003705000837050008370500087143000808
-:100070007D4300088943000895430008A143000818
-:10008000AD430008B943000837050008BD4A000821
-:10009000D54A0008C94A0008E14A000837050008A7
+:100060003705000837050008370500089D430008DC
+:10007000A9430008B5430008C1430008CD43000868
+:10008000D9430008E543000837050008E94A00089D
+:10009000014B0008F54A00080D4B00083705000821
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diff --git a/Middlewares/ST/ARM/DSP/Inc/arm_math.h b/Middlewares/ST/ARM/DSP/Inc/arm_math.h
new file mode 100644
index 0000000..8daa218
--- /dev/null
+++ b/Middlewares/ST/ARM/DSP/Inc/arm_math.h
@@ -0,0 +1,8970 @@
+/******************************************************************************
+ * @file     arm_math.h
+ * @brief    Public header file for CMSIS DSP Library
+ * @version  V1.7.0
+ * @date     18. March 2019
+ ******************************************************************************/
+/*
+ * Copyright (c) 2010-2019 Arm Limited or its affiliates. All rights reserved.
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ *
+ * Licensed under the Apache License, Version 2.0 (the License); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an AS IS BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+   \mainpage CMSIS DSP Software Library
+   *
+   * Introduction
+   * ------------
+   *
+   * This user manual describes the CMSIS DSP software library,
+   * a suite of common signal processing functions for use on Cortex-M and Cortex-A processor 
+   * based devices.
+   *
+   * The library is divided into a number of functions each covering a specific category:
+   * - Basic math functions
+   * - Fast math functions
+   * - Complex math functions
+   * - Filtering functions
+   * - Matrix functions
+   * - Transform functions
+   * - Motor control functions
+   * - Statistical functions
+   * - Support functions
+   * - Interpolation functions
+   * - Support Vector Machine functions (SVM)
+   * - Bayes classifier functions
+   * - Distance functions
+   *
+   * The library has generally separate functions for operating on 8-bit integers, 16-bit integers,
+   * 32-bit integer and 32-bit floating-point values.
+   *
+   * Using the Library
+   * ------------
+   *
+   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
+   *
+   * Here is the list of pre-built libraries :
+   * - arm_cortexM7lfdp_math.lib (Cortex-M7, Little endian, Double Precision Floating Point Unit)
+   * - arm_cortexM7bfdp_math.lib (Cortex-M7, Big endian, Double Precision Floating Point Unit)
+   * - arm_cortexM7lfsp_math.lib (Cortex-M7, Little endian, Single Precision Floating Point Unit)
+   * - arm_cortexM7bfsp_math.lib (Cortex-M7, Big endian and Single Precision Floating Point Unit on)
+   * - arm_cortexM7l_math.lib (Cortex-M7, Little endian)
+   * - arm_cortexM7b_math.lib (Cortex-M7, Big endian)
+   * - arm_cortexM4lf_math.lib (Cortex-M4, Little endian, Floating Point Unit)
+   * - arm_cortexM4bf_math.lib (Cortex-M4, Big endian, Floating Point Unit)
+   * - arm_cortexM4l_math.lib (Cortex-M4, Little endian)
+   * - arm_cortexM4b_math.lib (Cortex-M4, Big endian)
+   * - arm_cortexM3l_math.lib (Cortex-M3, Little endian)
+   * - arm_cortexM3b_math.lib (Cortex-M3, Big endian)
+   * - arm_cortexM0l_math.lib (Cortex-M0 / Cortex-M0+, Little endian)
+   * - arm_cortexM0b_math.lib (Cortex-M0 / Cortex-M0+, Big endian)
+   * - arm_ARMv8MBLl_math.lib (Armv8-M Baseline, Little endian)
+   * - arm_ARMv8MMLl_math.lib (Armv8-M Mainline, Little endian)
+   * - arm_ARMv8MMLlfsp_math.lib (Armv8-M Mainline, Little endian, Single Precision Floating Point Unit)
+   * - arm_ARMv8MMLld_math.lib (Armv8-M Mainline, Little endian, DSP instructions)
+   * - arm_ARMv8MMLldfsp_math.lib (Armv8-M Mainline, Little endian, DSP instructions, Single Precision Floating Point Unit)
+   *
+   * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
+   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
+   * public header file <code> arm_math.h</code> for Cortex-M cores with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
+   *
+   *
+   * Examples
+   * --------
+   *
+   * The library ships with a number of examples which demonstrate how to use the library functions.
+   *
+   * Toolchain Support
+   * ------------
+   *
+   * The library is now tested on Fast Models building with cmake.
+   * Core M0, M7, A5 are tested.
+   * 
+   * 
+   *
+   * Building the Library
+   * ------------
+   *
+   * The library installer contains a project file to rebuild libraries on MDK toolchain in the <code>CMSIS\\DSP\\Projects\\ARM</code> folder.
+   * - arm_cortexM_math.uvprojx
+   *
+   *
+   * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional preprocessor macros detailed above.
+   *
+   * There is also a work in progress cmake build. The README file is giving more details.
+   *
+   * Preprocessor Macros
+   * ------------
+   *
+   * Each library project have different preprocessor macros.
+   *
+   * - ARM_MATH_BIG_ENDIAN:
+   *
+   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
+   *
+   * - ARM_MATH_MATRIX_CHECK:
+   *
+   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
+   *
+   * - ARM_MATH_ROUNDING:
+   *
+   * Define macro ARM_MATH_ROUNDING for rounding on support functions
+   *
+   * - ARM_MATH_LOOPUNROLL:
+   *
+   * Define macro ARM_MATH_LOOPUNROLL to enable manual loop unrolling in DSP functions
+   *
+   * - ARM_MATH_NEON:
+   *
+   * Define macro ARM_MATH_NEON to enable Neon versions of the DSP functions.
+   * It is not enabled by default when Neon is available because performances are 
+   * dependent on the compiler and target architecture.
+   *
+   * - ARM_MATH_NEON_EXPERIMENTAL:
+   *
+   * Define macro ARM_MATH_NEON_EXPERIMENTAL to enable experimental Neon versions of 
+   * of some DSP functions. Experimental Neon versions currently do not have better
+   * performances than the scalar versions.
+   *
+   * - ARM_MATH_HELIUM:
+   *
+   * It implies the flags ARM_MATH_MVEF and ARM_MATH_MVEI and ARM_MATH_FLOAT16.
+   *
+   * - ARM_MATH_MVEF:
+   *
+   * Select Helium versions of the f32 algorithms.
+   * It implies ARM_MATH_FLOAT16 and ARM_MATH_MVEI.
+   *
+   * - ARM_MATH_MVEI:
+   *
+   * Select Helium versions of the int and fixed point algorithms.
+   *
+   * - ARM_MATH_FLOAT16:
+   *
+   * Float16 implementations of some algorithms (Requires MVE extension).
+   *
+   * <hr>
+   * CMSIS-DSP in ARM::CMSIS Pack
+   * -----------------------------
+   *
+   * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
+   * |File/Folder                      |Content                                                                 |
+   * |---------------------------------|------------------------------------------------------------------------|
+   * |\b CMSIS\\Documentation\\DSP     | This documentation                                                     |
+   * |\b CMSIS\\DSP\\DSP_Lib_TestSuite | DSP_Lib test suite                                                     |
+   * |\b CMSIS\\DSP\\Examples          | Example projects demonstrating the usage of the library functions      |
+   * |\b CMSIS\\DSP\\Include           | DSP_Lib include files                                                  |
+   * |\b CMSIS\\DSP\\Lib               | DSP_Lib binaries                                                       |
+   * |\b CMSIS\\DSP\\Projects          | Projects to rebuild DSP_Lib binaries                                   |
+   * |\b CMSIS\\DSP\\Source            | DSP_Lib source files                                                   |
+   *
+   * <hr>
+   * Revision History of CMSIS-DSP
+   * ------------
+   * Please refer to \ref ChangeLog_pg.
+   */
+
+
+/**
+ * @defgroup groupMath Basic Math Functions
+ */
+
+/**
+ * @defgroup groupFastMath Fast Math Functions
+ * This set of functions provides a fast approximation to sine, cosine, and square root.
+ * As compared to most of the other functions in the CMSIS math library, the fast math functions
+ * operate on individual values and not arrays.
+ * There are separate functions for Q15, Q31, and floating-point data.
+ *
+ */
+
+/**
+ * @defgroup groupCmplxMath Complex Math Functions
+ * This set of functions operates on complex data vectors.
+ * The data in the complex arrays is stored in an interleaved fashion
+ * (real, imag, real, imag, ...).
+ * In the API functions, the number of samples in a complex array refers
+ * to the number of complex values; the array contains twice this number of
+ * real values.
+ */
+
+/**
+ * @defgroup groupFilters Filtering Functions
+ */
+
+/**
+ * @defgroup groupMatrix Matrix Functions
+ *
+ * This set of functions provides basic matrix math operations.
+ * The functions operate on matrix data structures.  For example,
+ * the type
+ * definition for the floating-point matrix structure is shown
+ * below:
+ * <pre>
+ *     typedef struct
+ *     {
+ *       uint16_t numRows;     // number of rows of the matrix.
+ *       uint16_t numCols;     // number of columns of the matrix.
+ *       float32_t *pData;     // points to the data of the matrix.
+ *     } arm_matrix_instance_f32;
+ * </pre>
+ * There are similar definitions for Q15 and Q31 data types.
+ *
+ * The structure specifies the size of the matrix and then points to
+ * an array of data.  The array is of size <code>numRows X numCols</code>
+ * and the values are arranged in row order.  That is, the
+ * matrix element (i, j) is stored at:
+ * <pre>
+ *     pData[i*numCols + j]
+ * </pre>
+ *
+ * \par Init Functions
+ * There is an associated initialization function for each type of matrix
+ * data structure.
+ * The initialization function sets the values of the internal structure fields.
+ * Refer to \ref arm_mat_init_f32(), \ref arm_mat_init_q31() and \ref arm_mat_init_q15()
+ * for floating-point, Q31 and Q15 types,  respectively.
+ *
+ * \par
+ * Use of the initialization function is optional. However, if initialization function is used
+ * then the instance structure cannot be placed into a const data section.
+ * To place the instance structure in a const data
+ * section, manually initialize the data structure.  For example:
+ * <pre>
+ * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
+ * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
+ * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
+ * </pre>
+ * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
+ * specifies the number of columns, and <code>pData</code> points to the
+ * data array.
+ *
+ * \par Size Checking
+ * By default all of the matrix functions perform size checking on the input and
+ * output matrices. For example, the matrix addition function verifies that the
+ * two input matrices and the output matrix all have the same number of rows and
+ * columns. If the size check fails the functions return:
+ * <pre>
+ *     ARM_MATH_SIZE_MISMATCH
+ * </pre>
+ * Otherwise the functions return
+ * <pre>
+ *     ARM_MATH_SUCCESS
+ * </pre>
+ * There is some overhead associated with this matrix size checking.
+ * The matrix size checking is enabled via the \#define
+ * <pre>
+ *     ARM_MATH_MATRIX_CHECK
+ * </pre>
+ * within the library project settings.  By default this macro is defined
+ * and size checking is enabled. By changing the project settings and
+ * undefining this macro size checking is eliminated and the functions
+ * run a bit faster. With size checking disabled the functions always
+ * return <code>ARM_MATH_SUCCESS</code>.
+ */
+
+/**
+ * @defgroup groupTransforms Transform Functions
+ */
+
+/**
+ * @defgroup groupController Controller Functions
+ */
+
+/**
+ * @defgroup groupStats Statistics Functions
+ */
+
+/**
+ * @defgroup groupSupport Support Functions
+ */
+
+/**
+ * @defgroup groupInterpolation Interpolation Functions
+ * These functions perform 1- and 2-dimensional interpolation of data.
+ * Linear interpolation is used for 1-dimensional data and
+ * bilinear interpolation is used for 2-dimensional data.
+ */
+
+/**
+ * @defgroup groupExamples Examples
+ */
+
+/**
+ * @defgroup groupSVM SVM Functions
+ * This set of functions is implementing SVM classification on 2 classes.
+ * The training must be done from scikit-learn. The parameters can be easily
+ * generated from the scikit-learn object. Some examples are given in
+ * DSP/Testing/PatternGeneration/SVM.py
+ *
+ * If more than 2 classes are needed, the functions in this folder 
+ * will have to be used, as building blocks, to do multi-class classification.
+ *
+ * No multi-class classification is provided in this SVM folder.
+ * 
+ */
+
+
+/**
+ * @defgroup groupBayes Bayesian estimators
+ *
+ * Implement the naive gaussian Bayes estimator.
+ * The training must be done from scikit-learn.
+ *
+ * The parameters can be easily
+ * generated from the scikit-learn object. Some examples are given in
+ * DSP/Testing/PatternGeneration/Bayes.py
+ */
+
+/**
+ * @defgroup groupDistance Distance functions
+ *
+ * Distance functions for use with clustering algorithms.
+ * There are distance functions for float vectors and boolean vectors.
+ *
+ */
+
+
+#ifndef _ARM_MATH_H
+#define _ARM_MATH_H
+
+#ifdef   __cplusplus
+extern "C"
+{
+#endif
+
+/* Compiler specific diagnostic adjustment */
+#if   defined ( __CC_ARM )
+
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+
+#elif defined ( __GNUC__ )
+  #pragma GCC diagnostic push
+  #pragma GCC diagnostic ignored "-Wsign-conversion"
+  #pragma GCC diagnostic ignored "-Wconversion"
+  #pragma GCC diagnostic ignored "-Wunused-parameter"
+
+#elif defined ( __ICCARM__ )
+
+#elif defined ( __TI_ARM__ )
+
+#elif defined ( __CSMC__ )
+
+#elif defined ( __TASKING__ )
+
+#elif defined ( _MSC_VER )
+
+#else
+  #error Unknown compiler
+#endif
+
+
+/* Included for instrinsics definitions */
+#if defined (_MSC_VER ) 
+#include <stdint.h>
+#define __STATIC_FORCEINLINE static __forceinline
+#define __STATIC_INLINE static __inline
+#define __ALIGNED(x) __declspec(align(x))
+
+#elif defined (__GNUC_PYTHON__)
+#include <stdint.h>
+#define  __ALIGNED(x) __attribute__((aligned(x)))
+#define __STATIC_FORCEINLINE static __attribute__((inline))
+#define __STATIC_INLINE static __attribute__((inline))
+#pragma GCC diagnostic ignored "-Wunused-function"
+#pragma GCC diagnostic ignored "-Wattributes"
+
+#else
+#include "cmsis_compiler.h"
+#endif
+
+
+
+#include <string.h>
+#include <math.h>
+#include <float.h>
+#include <limits.h>
+
+
+#define F64_MAX   ((float64_t)DBL_MAX)
+#define F32_MAX   ((float32_t)FLT_MAX)
+
+#if defined(ARM_MATH_FLOAT16)
+#define F16_MAX   ((float16_t)FLT_MAX)
+#endif
+
+#define F64_MIN   (-DBL_MAX)
+#define F32_MIN   (-FLT_MAX)
+
+#if defined(ARM_MATH_FLOAT16)
+#define F16_MIN   (-(float16_t)FLT_MAX)
+#endif
+
+#define F64_ABSMAX   ((float64_t)DBL_MAX)
+#define F32_ABSMAX   ((float32_t)FLT_MAX)
+
+#if defined(ARM_MATH_FLOAT16)
+#define F16_ABSMAX   ((float16_t)FLT_MAX)
+#endif
+
+#define F64_ABSMIN   ((float64_t)0.0)
+#define F32_ABSMIN   ((float32_t)0.0)
+
+#if defined(ARM_MATH_FLOAT16)
+#define F16_ABSMIN   ((float16_t)0.0)
+#endif
+
+#define Q31_MAX   ((q31_t)(0x7FFFFFFFL))
+#define Q15_MAX   ((q15_t)(0x7FFF))
+#define Q7_MAX    ((q7_t)(0x7F))
+#define Q31_MIN   ((q31_t)(0x80000000L))
+#define Q15_MIN   ((q15_t)(0x8000))
+#define Q7_MIN    ((q7_t)(0x80))
+
+#define Q31_ABSMAX   ((q31_t)(0x7FFFFFFFL))
+#define Q15_ABSMAX   ((q15_t)(0x7FFF))
+#define Q7_ABSMAX    ((q7_t)(0x7F))
+#define Q31_ABSMIN   ((q31_t)0)
+#define Q15_ABSMIN   ((q15_t)0)
+#define Q7_ABSMIN    ((q7_t)0)
+
+/* evaluate ARM DSP feature */
+#if (defined (__ARM_FEATURE_DSP) && (__ARM_FEATURE_DSP == 1))
+  #define ARM_MATH_DSP                   1
+#endif
+
+#if defined(ARM_MATH_NEON)
+#include <arm_neon.h>
+#endif
+
+#if defined (ARM_MATH_HELIUM)
+  #define ARM_MATH_MVEF
+  #define ARM_MATH_FLOAT16
+#endif
+
+#if defined (ARM_MATH_MVEF)
+  #define ARM_MATH_MVEI
+  #define ARM_MATH_FLOAT16
+#endif
+
+#if defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI)
+#include <arm_mve.h>
+#endif
+
+
+  /**
+   * @brief Macros required for reciprocal calculation in Normalized LMS
+   */
+
+#define DELTA_Q31          ((q31_t)(0x100))
+#define DELTA_Q15          ((q15_t)0x5)
+#define INDEX_MASK         0x0000003F
+#ifndef PI
+  #define PI               3.14159265358979f
+#endif
+
+  /**
+   * @brief Macros required for SINE and COSINE Fast math approximations
+   */
+
+#define FAST_MATH_TABLE_SIZE  512
+#define FAST_MATH_Q31_SHIFT   (32 - 10)
+#define FAST_MATH_Q15_SHIFT   (16 - 10)
+#define CONTROLLER_Q31_SHIFT  (32 - 9)
+#define TABLE_SPACING_Q31     0x400000
+#define TABLE_SPACING_Q15     0x80
+
+  /**
+   * @brief Macros required for SINE and COSINE Controller functions
+   */
+  /* 1.31(q31) Fixed value of 2/360 */
+  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
+#define INPUT_SPACING         0xB60B61
+
+  /**
+   * @brief Macros for complex numbers
+   */
+
+  /* Dimension C vector space */
+  #define CMPLX_DIM 2
+
+  /**
+   * @brief Error status returned by some functions in the library.
+   */
+
+  typedef enum
+  {
+    ARM_MATH_SUCCESS        =  0,        /**< No error */
+    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
+    ARM_MATH_LENGTH_ERROR   = -2,        /**< Length of data buffer is incorrect */
+    ARM_MATH_SIZE_MISMATCH  = -3,        /**< Size of matrices is not compatible with the operation */
+    ARM_MATH_NANINF         = -4,        /**< Not-a-number (NaN) or infinity is generated */
+    ARM_MATH_SINGULAR       = -5,        /**< Input matrix is singular and cannot be inverted */
+    ARM_MATH_TEST_FAILURE   = -6         /**< Test Failed */
+  } arm_status;
+
+  /**
+   * @brief 8-bit fractional data type in 1.7 format.
+   */
+  typedef int8_t q7_t;
+
+  /**
+   * @brief 16-bit fractional data type in 1.15 format.
+   */
+  typedef int16_t q15_t;
+
+  /**
+   * @brief 32-bit fractional data type in 1.31 format.
+   */
+  typedef int32_t q31_t;
+
+  /**
+   * @brief 64-bit fractional data type in 1.63 format.
+   */
+  typedef int64_t q63_t;
+
+  /**
+   * @brief 32-bit floating-point type definition.
+   */
+  typedef float float32_t;
+
+  /**
+   * @brief 64-bit floating-point type definition.
+   */
+  typedef double float64_t;
+
+  /**
+   * @brief vector types
+   */
+#if defined(ARM_MATH_NEON) || defined (ARM_MATH_MVEI)
+  /**
+   * @brief 64-bit fractional 128-bit vector data type in 1.63 format
+   */
+  typedef int64x2_t q63x2_t;
+
+  /**
+   * @brief 32-bit fractional 128-bit vector data type in 1.31 format.
+   */
+  typedef int32x4_t q31x4_t;
+
+  /**
+   * @brief 16-bit fractional 128-bit vector data type with 16-bit alignement in 1.15 format.
+   */
+  typedef __ALIGNED(2) int16x8_t q15x8_t;
+
+ /**
+   * @brief 8-bit fractional 128-bit vector data type with 8-bit alignement in 1.7 format.
+   */
+  typedef __ALIGNED(1) int8x16_t q7x16_t;
+
+    /**
+   * @brief 32-bit fractional 128-bit vector pair data type in 1.31 format.
+   */
+  typedef int32x4x2_t q31x4x2_t;
+
+  /**
+   * @brief 32-bit fractional 128-bit vector quadruplet data type in 1.31 format.
+   */
+  typedef int32x4x4_t q31x4x4_t;
+
+  /**
+   * @brief 16-bit fractional 128-bit vector pair data type in 1.15 format.
+   */
+  typedef int16x8x2_t q15x8x2_t;
+
+  /**
+   * @brief 16-bit fractional 128-bit vector quadruplet data type in 1.15 format.
+   */
+  typedef int16x8x4_t q15x8x4_t;
+
+  /**
+   * @brief 8-bit fractional 128-bit vector pair data type in 1.7 format.
+   */
+  typedef int8x16x2_t q7x16x2_t;
+
+  /**
+   * @brief 8-bit fractional 128-bit vector quadruplet data type in 1.7 format.
+   */
+   typedef int8x16x4_t q7x16x4_t;
+
+  /**
+   * @brief 32-bit fractional data type in 9.23 format.
+   */
+  typedef int32_t q23_t;
+
+  /**
+   * @brief 32-bit fractional 128-bit vector data type in 9.23 format.
+   */
+  typedef int32x4_t q23x4_t;
+
+  /**
+   * @brief 64-bit status 128-bit vector data type.
+   */
+  typedef int64x2_t status64x2_t;
+
+  /**
+   * @brief 32-bit status 128-bit vector data type.
+   */
+  typedef int32x4_t status32x4_t;
+
+  /**
+   * @brief 16-bit status 128-bit vector data type.
+   */
+  typedef int16x8_t status16x8_t;
+
+  /**
+   * @brief 8-bit status 128-bit vector data type.
+   */
+  typedef int8x16_t status8x16_t;
+
+
+#endif
+
+#if defined(ARM_MATH_NEON) || defined(ARM_MATH_MVEF) /* floating point vector*/
+  /**
+   * @brief 32-bit floating-point 128-bit vector type
+   */
+  typedef float32x4_t f32x4_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit floating-point 128-bit vector data type
+   */
+  typedef __ALIGNED(2) float16x8_t f16x8_t;
+#endif
+
+  /**
+   * @brief 32-bit floating-point 128-bit vector pair data type
+   */
+  typedef float32x4x2_t f32x4x2_t;
+
+  /**
+   * @brief 32-bit floating-point 128-bit vector quadruplet data type
+   */
+  typedef float32x4x4_t f32x4x4_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit floating-point 128-bit vector pair data type
+   */
+  typedef float16x8x2_t f16x8x2_t;
+
+  /**
+   * @brief 16-bit floating-point 128-bit vector quadruplet data type
+   */
+  typedef float16x8x4_t f16x8x4_t;
+#endif
+
+  /**
+   * @brief 32-bit ubiquitous 128-bit vector data type
+   */
+  typedef union _any32x4_t
+  {
+      float32x4_t     f;
+      int32x4_t       i;
+  } any32x4_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit ubiquitous 128-bit vector data type
+   */
+  typedef union _any16x8_t
+  {
+      float16x8_t     f;
+      int16x8_t       i;
+  } any16x8_t;
+#endif
+
+#endif
+
+#if defined(ARM_MATH_NEON)
+  /**
+   * @brief 32-bit fractional 64-bit vector data type in 1.31 format.
+   */
+  typedef int32x2_t  q31x2_t;
+
+  /**
+   * @brief 16-bit fractional 64-bit vector data type in 1.15 format.
+   */
+  typedef  __ALIGNED(2) int16x4_t q15x4_t;
+
+  /**
+   * @brief 8-bit fractional 64-bit vector data type in 1.7 format.
+   */
+  typedef  __ALIGNED(1) int8x8_t q7x8_t;
+
+  /**
+   * @brief 32-bit float 64-bit vector data type.
+   */
+  typedef float32x2_t  f32x2_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit float 64-bit vector data type.
+   */
+  typedef  __ALIGNED(2) float16x4_t f16x4_t;
+#endif 
+
+  /**
+   * @brief 32-bit floating-point 128-bit vector triplet data type
+   */
+  typedef float32x4x3_t f32x4x3_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit floating-point 128-bit vector triplet data type
+   */
+  typedef float16x8x3_t f16x8x3_t;
+#endif
+
+  /**
+   * @brief 32-bit fractional 128-bit vector triplet data type in 1.31 format
+   */
+  typedef int32x4x3_t q31x4x3_t;
+
+  /**
+   * @brief 16-bit fractional 128-bit vector triplet data type in 1.15 format
+   */
+  typedef int16x8x3_t q15x8x3_t;
+
+  /**
+   * @brief 8-bit fractional 128-bit vector triplet data type in 1.7 format
+   */
+  typedef int8x16x3_t q7x16x3_t;
+
+  /**
+   * @brief 32-bit floating-point 64-bit vector pair data type
+   */
+  typedef float32x2x2_t f32x2x2_t;
+
+  /**
+   * @brief 32-bit floating-point 64-bit vector triplet data type
+   */
+  typedef float32x2x3_t f32x2x3_t;
+
+  /**
+   * @brief 32-bit floating-point 64-bit vector quadruplet data type
+   */
+  typedef float32x2x4_t f32x2x4_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit floating-point 64-bit vector pair data type
+   */
+  typedef float16x4x2_t f16x4x2_t;
+
+  /**
+   * @brief 16-bit floating-point 64-bit vector triplet data type
+   */
+  typedef float16x4x3_t f16x4x3_t;
+
+  /**
+   * @brief 16-bit floating-point 64-bit vector quadruplet data type
+   */
+  typedef float16x4x4_t f16x4x4_t;
+#endif 
+
+  /**
+   * @brief 32-bit fractional 64-bit vector pair data type in 1.31 format
+   */
+  typedef int32x2x2_t q31x2x2_t;
+
+  /**
+   * @brief 32-bit fractional 64-bit vector triplet data type in 1.31 format
+   */
+  typedef int32x2x3_t q31x2x3_t;
+
+  /**
+   * @brief 32-bit fractional 64-bit vector quadruplet data type in 1.31 format
+   */
+  typedef int32x4x3_t q31x2x4_t;
+
+  /**
+   * @brief 16-bit fractional 64-bit vector pair data type in 1.15 format
+   */
+  typedef int16x4x2_t q15x4x2_t;
+
+  /**
+   * @brief 16-bit fractional 64-bit vector triplet data type in 1.15 format
+   */
+  typedef int16x4x2_t q15x4x3_t;
+
+  /**
+   * @brief 16-bit fractional 64-bit vector quadruplet data type in 1.15 format
+   */
+  typedef int16x4x3_t q15x4x4_t;
+
+  /**
+   * @brief 8-bit fractional 64-bit vector pair data type in 1.7 format
+   */
+  typedef int8x8x2_t q7x8x2_t;
+
+  /**
+   * @brief 8-bit fractional 64-bit vector triplet data type in 1.7 format
+   */
+  typedef int8x8x3_t q7x8x3_t;
+
+  /**
+   * @brief 8-bit fractional 64-bit vector quadruplet data type in 1.7 format
+   */
+  typedef int8x8x4_t q7x8x4_t;
+
+  /**
+   * @brief 32-bit ubiquitous 64-bit vector data type
+   */
+  typedef union _any32x2_t
+  {
+      float32x2_t     f;
+      int32x2_t       i;
+  } any32x2_t;
+
+#if defined(ARM_MATH_FLOAT16)
+  /**
+   * @brief 16-bit ubiquitous 64-bit vector data type
+   */
+  typedef union _any16x4_t
+  {
+      float16x4_t     f;
+      int16x4_t       i;
+  } any16x4_t;
+#endif 
+
+  /**
+   * @brief 32-bit status 64-bit vector data type.
+   */
+  typedef int32x4_t status32x2_t;
+
+  /**
+   * @brief 16-bit status 64-bit vector data type.
+   */
+  typedef int16x8_t status16x4_t;
+
+  /**
+   * @brief 8-bit status 64-bit vector data type.
+   */
+  typedef int8x16_t status8x8_t;
+
+#endif
+
+
+
+/**
+  @brief definition to read/write two 16 bit values.
+  @deprecated
+ */
+#if   defined ( __CC_ARM )
+  #define __SIMD32_TYPE int32_t __packed
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __GNUC__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __ICCARM__ )
+  #define __SIMD32_TYPE int32_t __packed
+#elif defined ( __TI_ARM__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __CSMC__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __TASKING__ )
+  #define __SIMD32_TYPE __un(aligned) int32_t
+#elif defined(_MSC_VER )
+  #define __SIMD32_TYPE int32_t
+#else
+  #error Unknown compiler
+#endif
+
+#define __SIMD32(addr)        (*(__SIMD32_TYPE **) & (addr))
+#define __SIMD32_CONST(addr)  ( (__SIMD32_TYPE * )   (addr))
+#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE * )   (addr))
+#define __SIMD64(addr)        (*(      int64_t **) & (addr))
+
+#define STEP(x) (x) <= 0 ? 0 : 1
+#define SQ(x) ((x) * (x))
+
+/* SIMD replacement */
+
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2 (
+  q15_t * pQ15)
+{
+  q31_t val;
+
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (&val, pQ15, 4);
+#else
+  val = (pQ15[1] << 16) | (pQ15[0] & 0x0FFFF) ;
+#endif
+
+  return (val);
+}
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer and increment pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2_ia (
+  q15_t ** pQ15)
+{
+  q31_t val;
+
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (&val, *pQ15, 4);
+#else
+  val = ((*pQ15)[1] << 16) | ((*pQ15)[0] & 0x0FFFF);
+#endif
+
+ *pQ15 += 2;
+ return (val);
+}
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer and decrement pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2_da (
+  q15_t ** pQ15)
+{
+  q31_t val;
+
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (&val, *pQ15, 4);
+#else
+  val = ((*pQ15)[1] << 16) | ((*pQ15)[0] & 0x0FFFF);
+#endif
+
+  *pQ15 -= 2;
+  return (val);
+}
+
+/**
+  @brief         Write 2 Q15 to Q15 pointer and increment pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q15x2_ia (
+  q15_t ** pQ15,
+  q31_t    value)
+{
+  q31_t val = value;
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (*pQ15, &val, 4);
+#else
+  (*pQ15)[0] = (val & 0x0FFFF);
+  (*pQ15)[1] = (val >> 16) & 0x0FFFF;
+#endif
+
+ *pQ15 += 2;
+}
+
+/**
+  @brief         Write 2 Q15 to Q15 pointer.
+  @param[in]     pQ15      points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q15x2 (
+  q15_t * pQ15,
+  q31_t   value)
+{
+  q31_t val = value;
+
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (pQ15, &val, 4);
+#else
+  pQ15[0] = val & 0x0FFFF;
+  pQ15[1] = val >> 16;
+#endif
+}
+
+
+/**
+  @brief         Read 4 Q7 from Q7 pointer and increment pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q7x4_ia (
+  q7_t ** pQ7)
+{
+  q31_t val;
+
+
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (&val, *pQ7, 4);
+#else
+  val =(((*pQ7)[3] & 0x0FF) << 24)  | (((*pQ7)[2] & 0x0FF) << 16)  | (((*pQ7)[1] & 0x0FF) << 8)  | ((*pQ7)[0] & 0x0FF);
+#endif 
+
+  *pQ7 += 4;
+
+  return (val);
+}
+
+/**
+  @brief         Read 4 Q7 from Q7 pointer and decrement pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q7x4_da (
+  q7_t ** pQ7)
+{
+  q31_t val;
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (&val, *pQ7, 4);
+#else
+  val = ((((*pQ7)[3]) & 0x0FF) << 24) | ((((*pQ7)[2]) & 0x0FF) << 16)   | ((((*pQ7)[1]) & 0x0FF) << 8)  | ((*pQ7)[0] & 0x0FF);
+#endif 
+  *pQ7 -= 4;
+
+  return (val);
+}
+
+/**
+  @brief         Write 4 Q7 to Q7 pointer and increment pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q7x4_ia (
+  q7_t ** pQ7,
+  q31_t   value)
+{
+  q31_t val = value;
+#ifdef __ARM_FEATURE_UNALIGNED
+  memcpy (*pQ7, &val, 4);
+#else
+  (*pQ7)[0] = val & 0x0FF;
+  (*pQ7)[1] = (val >> 8) & 0x0FF;
+  (*pQ7)[2] = (val >> 16) & 0x0FF;
+  (*pQ7)[3] = (val >> 24) & 0x0FF;
+
+#endif
+  *pQ7 += 4;
+}
+
+/*
+
+Normally those kind of definitions are in a compiler file
+in Core or Core_A.
+
+But for MSVC compiler it is a bit special. The goal is very specific
+to CMSIS-DSP and only to allow the use of this library from other
+systems like Python or Matlab.
+
+MSVC is not going to be used to cross-compile to ARM. So, having a MSVC
+compiler file in Core or Core_A would not make sense.
+
+*/
+#if defined ( _MSC_VER ) || defined(__GNUC_PYTHON__)
+    __STATIC_FORCEINLINE uint8_t __CLZ(uint32_t data)
+    {
+      if (data == 0U) { return 32U; }
+
+      uint32_t count = 0U;
+      uint32_t mask = 0x80000000U;
+
+      while ((data & mask) == 0U)
+      {
+        count += 1U;
+        mask = mask >> 1U;
+      }
+      return count;
+    }
+
+  __STATIC_FORCEINLINE int32_t __SSAT(int32_t val, uint32_t sat)
+  {
+    if ((sat >= 1U) && (sat <= 32U))
+    {
+      const int32_t max = (int32_t)((1U << (sat - 1U)) - 1U);
+      const int32_t min = -1 - max ;
+      if (val > max)
+      {
+        return max;
+      }
+      else if (val < min)
+      {
+        return min;
+      }
+    }
+    return val;
+  }
+
+  __STATIC_FORCEINLINE uint32_t __USAT(int32_t val, uint32_t sat)
+  {
+    if (sat <= 31U)
+    {
+      const uint32_t max = ((1U << sat) - 1U);
+      if (val > (int32_t)max)
+      {
+        return max;
+      }
+      else if (val < 0)
+      {
+        return 0U;
+      }
+    }
+    return (uint32_t)val;
+  }
+#endif
+
+#ifndef ARM_MATH_DSP
+  /**
+   * @brief definition to pack two 16 bit values.
+   */
+  #define __PKHBT(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) <<    0) & (int32_t)0x0000FFFF) | \
+                                      (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
+  #define __PKHTB(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) <<    0) & (int32_t)0xFFFF0000) | \
+                                      (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )
+#endif
+
+   /**
+   * @brief definition to pack four 8 bit values.
+   */
+#ifndef ARM_MATH_BIG_ENDIAN
+  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) | \
+                                  (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) | \
+                                  (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \
+                                  (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
+#else
+  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) | \
+                                  (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) | \
+                                  (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \
+                                  (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
+#endif
+
+
+  /**
+   * @brief Clips Q63 to Q31 values.
+   */
+  __STATIC_FORCEINLINE q31_t clip_q63_to_q31(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
+  }
+
+  /**
+   * @brief Clips Q63 to Q15 values.
+   */
+  __STATIC_FORCEINLINE q15_t clip_q63_to_q15(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
+  }
+
+  /**
+   * @brief Clips Q31 to Q7 values.
+   */
+  __STATIC_FORCEINLINE q7_t clip_q31_to_q7(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
+      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
+  }
+
+  /**
+   * @brief Clips Q31 to Q15 values.
+   */
+  __STATIC_FORCEINLINE q15_t clip_q31_to_q15(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
+  }
+
+  /**
+   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
+   */
+  __STATIC_FORCEINLINE q63_t mult32x64(
+  q63_t x,
+  q31_t y)
+  {
+    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
+            (((q63_t) (x >> 32)                * y)      )  );
+  }
+
+  /**
+   * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
+   */
+  __STATIC_FORCEINLINE uint32_t arm_recip_q31(
+        q31_t in,
+        q31_t * dst,
+  const q31_t * pRecipTable)
+  {
+    q31_t out;
+    uint32_t tempVal;
+    uint32_t index, i;
+    uint32_t signBits;
+
+    if (in > 0)
+    {
+      signBits = ((uint32_t) (__CLZ( in) - 1));
+    }
+    else
+    {
+      signBits = ((uint32_t) (__CLZ(-in) - 1));
+    }
+
+    /* Convert input sample to 1.31 format */
+    in = (in << signBits);
+
+    /* calculation of index for initial approximated Val */
+    index = (uint32_t)(in >> 24);
+    index = (index & INDEX_MASK);
+
+    /* 1.31 with exp 1 */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0U; i < 2U; i++)
+    {
+      tempVal = (uint32_t) (((q63_t) in * out) >> 31);
+      tempVal = 0x7FFFFFFFu - tempVal;
+      /*      1.31 with exp 1 */
+      /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */
+      out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30);
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1U);
+  }
+
+
+  /**
+   * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
+   */
+  __STATIC_FORCEINLINE uint32_t arm_recip_q15(
+        q15_t in,
+        q15_t * dst,
+  const q15_t * pRecipTable)
+  {
+    q15_t out = 0;
+    uint32_t tempVal = 0;
+    uint32_t index = 0, i = 0;
+    uint32_t signBits = 0;
+
+    if (in > 0)
+    {
+      signBits = ((uint32_t)(__CLZ( in) - 17));
+    }
+    else
+    {
+      signBits = ((uint32_t)(__CLZ(-in) - 17));
+    }
+
+    /* Convert input sample to 1.15 format */
+    in = (in << signBits);
+
+    /* calculation of index for initial approximated Val */
+    index = (uint32_t)(in >>  8);
+    index = (index & INDEX_MASK);
+
+    /*      1.15 with exp 1  */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0U; i < 2U; i++)
+    {
+      tempVal = (uint32_t) (((q31_t) in * out) >> 15);
+      tempVal = 0x7FFFu - tempVal;
+      /*      1.15 with exp 1 */
+      out = (q15_t) (((q31_t) out * tempVal) >> 14);
+      /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1);
+  }
+
+/**
+ * @brief Integer exponentiation
+ * @param[in]    x           value
+ * @param[in]    nb          integer exponent >= 1
+ * @return x^nb
+ *
+ */
+__STATIC_INLINE float32_t arm_exponent_f32(float32_t x, int32_t nb)
+{
+    float32_t r = x;
+    nb --;
+    while(nb > 0)
+    {
+        r = r * x;
+        nb--;
+    }
+    return(r);
+}
+
+/**
+ * @brief  64-bit to 32-bit unsigned normalization
+ * @param[in]  in           is input unsigned long long value
+ * @param[out] normalized   is the 32-bit normalized value
+ * @param[out] norm         is norm scale
+ */
+__STATIC_INLINE  void arm_norm_64_to_32u(uint64_t in, int32_t * normalized, int32_t *norm)
+{
+    int32_t     n1;
+    int32_t     hi = (int32_t) (in >> 32);
+    int32_t     lo = (int32_t) ((in << 32) >> 32);
+
+    n1 = __CLZ(hi) - 32;
+    if (!n1)
+    {
+        /*
+         * input fits in 32-bit
+         */
+        n1 = __CLZ(lo);
+        if (!n1)
+        {
+            /*
+             * MSB set, need to scale down by 1
+             */
+            *norm = -1;
+            *normalized = (((uint32_t) lo) >> 1);
+        } else
+        {
+            if (n1 == 32)
+            {
+                /*
+                 * input is zero
+                 */
+                *norm = 0;
+                *normalized = 0;
+            } else
+            {
+                /*
+                 * 32-bit normalization
+                 */
+                *norm = n1 - 1;
+                *normalized = lo << *norm;
+            }
+        }
+    } else
+    {
+        /*
+         * input fits in 64-bit
+         */
+        n1 = 1 - n1;
+        *norm = -n1;
+        /*
+         * 64 bit normalization
+         */
+        *normalized = (((uint32_t) lo) >> n1) | (hi << (32 - n1));
+    }
+}
+
+__STATIC_INLINE q31_t arm_div_q63_to_q31(q63_t num, q31_t den)
+{
+    q31_t   result;
+    uint64_t   absNum;
+    int32_t   normalized;
+    int32_t   norm;
+
+    /*
+     * if sum fits in 32bits
+     * avoid costly 64-bit division
+     */
+    absNum = num > 0 ? num : -num;
+    arm_norm_64_to_32u(absNum, &normalized, &norm);
+    if (norm > 0)
+        /*
+         * 32-bit division
+         */
+        result = (q31_t) num / den;
+    else
+        /*
+         * 64-bit division
+         */
+        result = (q31_t) (num / den);
+
+    return result;
+}
+
+
+/*
+ * @brief C custom defined intrinsic functions
+ */
+#if !defined (ARM_MATH_DSP)
+
+  /*
+   * @brief C custom defined QADD8
+   */
+  __STATIC_FORCEINLINE uint32_t __QADD8(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s, t, u;
+
+    r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
+    s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
+    t = __SSAT(((((q31_t)x <<  8) >> 24) + (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
+    u = __SSAT(((((q31_t)x      ) >> 24) + (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
+
+    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB8
+   */
+  __STATIC_FORCEINLINE uint32_t __QSUB8(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s, t, u;
+
+    r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
+    s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
+    t = __SSAT(((((q31_t)x <<  8) >> 24) - (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
+    u = __SSAT(((((q31_t)x      ) >> 24) - (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
+
+    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QADD16
+   */
+  __STATIC_FORCEINLINE uint32_t __QADD16(
+  uint32_t x,
+  uint32_t y)
+  {
+/*  q31_t r,     s;  without initialisation 'arm_offset_q15 test' fails  but 'intrinsic' tests pass! for armCC */
+    q31_t r = 0, s = 0;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHADD16
+   */
+  __STATIC_FORCEINLINE uint32_t __SHADD16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB16
+   */
+  __STATIC_FORCEINLINE uint32_t __QSUB16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHSUB16
+   */
+  __STATIC_FORCEINLINE uint32_t __SHSUB16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QASX
+   */
+  __STATIC_FORCEINLINE uint32_t __QASX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHASX
+   */
+  __STATIC_FORCEINLINE uint32_t __SHASX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSAX
+   */
+  __STATIC_FORCEINLINE uint32_t __QSAX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHSAX
+   */
+  __STATIC_FORCEINLINE uint32_t __SHSAX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SMUSDX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUSDX(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
+  }
+
+  /*
+   * @brief C custom defined SMUADX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUADX(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined QADD
+   */
+  __STATIC_FORCEINLINE int32_t __QADD(
+  int32_t x,
+  int32_t y)
+  {
+    return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y)));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB
+   */
+  __STATIC_FORCEINLINE int32_t __QSUB(
+  int32_t x,
+  int32_t y)
+  {
+    return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y)));
+  }
+
+
+  /*
+   * @brief C custom defined SMLAD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLAD(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLADX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLADX(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLSDX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLSDX(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLALD
+   */
+  __STATIC_FORCEINLINE uint64_t __SMLALD(
+  uint32_t x,
+  uint32_t y,
+  uint64_t sum)
+  {
+/*  return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */
+    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ( ((q63_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLALDX
+   */
+  __STATIC_FORCEINLINE uint64_t __SMLALDX(
+  uint32_t x,
+  uint32_t y,
+  uint64_t sum)
+  {
+/*  return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */
+    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q63_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMUAD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUAD(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMUSD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUSD(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined SXTB16
+   */
+  __STATIC_FORCEINLINE uint32_t __SXTB16(
+  uint32_t x)
+  {
+    return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) |
+                       ((((q31_t)x <<  8) >>  8) & (q31_t)0xFFFF0000)  ));
+  }
+
+  /*
+   * @brief C custom defined SMMLA
+   */
+  __STATIC_FORCEINLINE int32_t __SMMLA(
+  int32_t x,
+  int32_t y,
+  int32_t sum)
+  {
+    return (sum + (int32_t) (((int64_t) x * y) >> 32));
+  }
+
+#endif /* !defined (ARM_MATH_DSP) */
+
+
+  /**
+   * @brief Instance structure for the Q7 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;        /**< number of filter coefficients in the filter. */
+          q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q7;
+
+  /**
+   * @brief Instance structure for the Q15 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+          q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+          q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of filter coefficients in the filter. */
+          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_f32;
+
+  /**
+   * @brief Processing function for the Q7 FIR filter.
+   * @param[in]  S          points to an instance of the Q7 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q7(
+  const arm_fir_instance_q7 * S,
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q7 FIR filter.
+   * @param[in,out] S          points to an instance of the Q7 FIR structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed.
+   */
+  void arm_fir_init_q7(
+        arm_fir_instance_q7 * S,
+        uint16_t numTaps,
+  const q7_t * pCoeffs,
+        q7_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q15 FIR filter.
+   * @param[in]  S          points to an instance of the Q15 FIR structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q15 FIR filter (fast version).
+   * @param[in]  S          points to an instance of the Q15 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_fast_q15(
+  const arm_fir_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 FIR filter.
+   * @param[in,out] S          points to an instance of the Q15 FIR filter structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   * @return     The function returns either
+   * <code>ARM_MATH_SUCCESS</code> if initialization was successful or
+   * <code>ARM_MATH_ARGUMENT_ERROR</code> if <code>numTaps</code> is not a supported value.
+   */
+  arm_status arm_fir_init_q15(
+        arm_fir_instance_q15 * S,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR filter.
+   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q31(
+  const arm_fir_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q31 FIR filter (fast version).
+   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_fast_q31(
+  const arm_fir_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 FIR filter.
+   * @param[in,out] S          points to an instance of the Q31 FIR structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   */
+  void arm_fir_init_q31(
+        arm_fir_instance_q31 * S,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the floating-point FIR filter.
+   * @param[in]  S          points to an instance of the floating-point FIR structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_f32(
+  const arm_fir_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point FIR filter.
+   * @param[in,out] S          points to an instance of the floating-point FIR filter structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   */
+  void arm_fir_init_f32(
+        arm_fir_instance_f32 * S,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the Q15 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          int8_t numStages;        /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q15_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q15_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+          int8_t postShift;        /**< Additional shift, in bits, applied to each output sample. */
+  } arm_biquad_casd_df1_inst_q15;
+
+  /**
+   * @brief Instance structure for the Q31 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+          uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
+  } arm_biquad_casd_df1_inst_q31;
+
+  /**
+   * @brief Instance structure for the floating-point Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;       /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const float32_t *pCoeffs;      /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_casd_df1_inst_f32;
+
+#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
+  /**
+   * @brief Instance structure for the modified Biquad coefs required by vectorized code.
+   */
+  typedef struct
+  {
+      float32_t coeffs[8][4]; /**< Points to the array of modified coefficients.  The array is of length 32. There is one per stage */
+  } arm_biquad_mod_coef_f32;
+#endif 
+
+  /**
+   * @brief Processing function for the Q15 Biquad cascade filter.
+   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cascade_df1_init_q15(
+        arm_biquad_casd_df1_inst_q15 * S,
+        uint8_t numStages,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        int8_t postShift);
+
+  /**
+   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_fast_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 Biquad cascade filter
+   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_fast_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cascade_df1_init_q31(
+        arm_biquad_casd_df1_inst_q31 * S,
+        uint8_t numStages,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        int8_t postShift);
+
+  /**
+   * @brief Processing function for the floating-point Biquad cascade filter.
+   * @param[in]  S          points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_f32(
+  const arm_biquad_casd_df1_inst_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pCoeffsMod points to the modified filter coefficients (only MVE version).
+   * @param[in]     pState     points to the state buffer.
+   */
+#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
+  void arm_biquad_cascade_df1_mve_init_f32(
+      arm_biquad_casd_df1_inst_f32 * S,
+      uint8_t numStages,
+      const float32_t * pCoeffs, 
+      arm_biquad_mod_coef_f32 * pCoeffsMod, 
+      float32_t * pState);
+#endif
+  
+  void arm_biquad_cascade_df1_init_f32(
+        arm_biquad_casd_df1_inst_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief         Compute the logical bitwise AND of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_and_u16(
+    const uint16_t * pSrcA,
+    const uint16_t * pSrcB,
+          uint16_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise AND of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_and_u32(
+    const uint32_t * pSrcA,
+    const uint32_t * pSrcB,
+          uint32_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise AND of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_and_u8(
+    const uint8_t * pSrcA,
+    const uint8_t * pSrcB,
+          uint8_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise OR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_or_u16(
+    const uint16_t * pSrcA,
+    const uint16_t * pSrcB,
+          uint16_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise OR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_or_u32(
+    const uint32_t * pSrcA,
+    const uint32_t * pSrcB,
+          uint32_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise OR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_or_u8(
+    const uint8_t * pSrcA,
+    const uint8_t * pSrcB,
+          uint8_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise NOT of a fixed-point vector.
+   * @param[in]     pSrc       points to input vector 
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_not_u16(
+    const uint16_t * pSrc,
+          uint16_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise NOT of a fixed-point vector.
+   * @param[in]     pSrc       points to input vector 
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_not_u32(
+    const uint32_t * pSrc,
+          uint32_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise NOT of a fixed-point vector.
+   * @param[in]     pSrc       points to input vector 
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_not_u8(
+    const uint8_t * pSrc,
+          uint8_t * pDst,
+          uint32_t blockSize);
+
+/**
+   * @brief         Compute the logical bitwise XOR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_xor_u16(
+    const uint16_t * pSrcA,
+    const uint16_t * pSrcB,
+          uint16_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise XOR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_xor_u32(
+    const uint32_t * pSrcA,
+    const uint32_t * pSrcB,
+          uint32_t * pDst,
+          uint32_t blockSize);
+
+  /**
+   * @brief         Compute the logical bitwise XOR of two fixed-point vectors.
+   * @param[in]     pSrcA      points to input vector A
+   * @param[in]     pSrcB      points to input vector B
+   * @param[out]    pDst       points to output vector
+   * @param[in]     blockSize  number of samples in each vector
+   * @return        none
+   */
+  void arm_xor_u8(
+    const uint8_t * pSrcA,
+    const uint8_t * pSrcB,
+          uint8_t * pDst,
+    uint32_t blockSize);
+
+  /**
+   * @brief Struct for specifying sorting algorithm
+   */
+  typedef enum
+  {
+    ARM_SORT_BITONIC   = 0,
+             /**< Bitonic sort   */
+    ARM_SORT_BUBBLE    = 1,
+             /**< Bubble sort    */
+    ARM_SORT_HEAP      = 2,
+             /**< Heap sort      */
+    ARM_SORT_INSERTION = 3,
+             /**< Insertion sort */
+    ARM_SORT_QUICK     = 4,
+             /**< Quick sort     */
+    ARM_SORT_SELECTION = 5
+             /**< Selection sort */
+  } arm_sort_alg;
+
+  /**
+   * @brief Struct for specifying sorting algorithm
+   */
+  typedef enum
+  {
+    ARM_SORT_DESCENDING = 0,
+             /**< Descending order (9 to 0) */
+    ARM_SORT_ASCENDING = 1
+             /**< Ascending order (0 to 9) */
+  } arm_sort_dir;
+
+  /**
+   * @brief Instance structure for the sorting algorithms.
+   */
+  typedef struct            
+  {
+    arm_sort_alg alg;        /**< Sorting algorithm selected */
+    arm_sort_dir dir;        /**< Sorting order (direction)  */
+  } arm_sort_instance_f32;  
+
+  /**
+   * @param[in]  S          points to an instance of the sorting structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_sort_f32(
+    const arm_sort_instance_f32 * S, 
+          float32_t * pSrc, 
+          float32_t * pDst, 
+          uint32_t blockSize);
+
+  /**
+   * @param[in,out]  S            points to an instance of the sorting structure.
+   * @param[in]      alg          Selected algorithm.
+   * @param[in]      dir          Sorting order.
+   */
+  void arm_sort_init_f32(
+    arm_sort_instance_f32 * S, 
+    arm_sort_alg alg, 
+    arm_sort_dir dir); 
+
+  /**
+   * @brief Instance structure for the sorting algorithms.
+   */
+  typedef struct            
+  {
+    arm_sort_dir dir;        /**< Sorting order (direction)  */
+    float32_t * buffer;      /**< Working buffer */
+  } arm_merge_sort_instance_f32;  
+
+  /**
+   * @param[in]      S          points to an instance of the sorting structure.
+   * @param[in,out]  pSrc       points to the block of input data.
+   * @param[out]     pDst       points to the block of output data
+   * @param[in]      blockSize  number of samples to process.
+   */
+  void arm_merge_sort_f32(
+    const arm_merge_sort_instance_f32 * S,
+          float32_t *pSrc,
+          float32_t *pDst,
+          uint32_t blockSize);
+
+  /**
+   * @param[in,out]  S            points to an instance of the sorting structure.
+   * @param[in]      dir          Sorting order.
+   * @param[in]      buffer       Working buffer.
+   */
+  void arm_merge_sort_init_f32(
+    arm_merge_sort_instance_f32 * S,
+    arm_sort_dir dir,
+    float32_t * buffer);
+
+  /**
+   * @brief Struct for specifying cubic spline type
+   */
+  typedef enum
+  {
+    ARM_SPLINE_NATURAL = 0,           /**< Natural spline */
+    ARM_SPLINE_PARABOLIC_RUNOUT = 1   /**< Parabolic runout spline */
+  } arm_spline_type;
+
+  /**
+   * @brief Instance structure for the floating-point cubic spline interpolation.
+   */
+  typedef struct
+  {
+    arm_spline_type type;      /**< Type (boundary conditions) */
+    const float32_t * x;       /**< x values */
+    const float32_t * y;       /**< y values */
+    uint32_t n_x;              /**< Number of known data points */
+    float32_t * coeffs;        /**< Coefficients buffer (b,c, and d) */
+  } arm_spline_instance_f32;
+
+  /**
+   * @brief Processing function for the floating-point cubic spline interpolation.
+   * @param[in]  S          points to an instance of the floating-point spline structure.
+   * @param[in]  xq         points to the x values ot the interpolated data points.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples of output data.
+   */
+  void arm_spline_f32(
+        arm_spline_instance_f32 * S, 
+  const float32_t * xq,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Initialization function for the floating-point cubic spline interpolation.
+   * @param[in,out] S        points to an instance of the floating-point spline structure.
+   * @param[in]     type     type of cubic spline interpolation (boundary conditions)
+   * @param[in]     x        points to the x values of the known data points.
+   * @param[in]     y        points to the y values of the known data points.
+   * @param[in]     n        number of known data points.
+   * @param[in]     coeffs   coefficients array for b, c, and d
+   * @param[in]     tempBuffer   buffer array for internal computations
+   */
+  void arm_spline_init_f32(
+          arm_spline_instance_f32 * S,
+          arm_spline_type type,
+    const float32_t * x,
+    const float32_t * y,
+          uint32_t n, 
+          float32_t * coeffs,
+          float32_t * tempBuffer);
+
+  /**
+   * @brief Instance structure for the floating-point matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    float32_t *pData;     /**< points to the data of the matrix. */
+  } arm_matrix_instance_f32;
+ 
+ /**
+   * @brief Instance structure for the floating-point matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    float64_t *pData;     /**< points to the data of the matrix. */
+  } arm_matrix_instance_f64;
+
+  /**
+   * @brief Instance structure for the Q15 matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q15_t *pData;         /**< points to the data of the matrix. */
+  } arm_matrix_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q31_t *pData;         /**< points to the data of the matrix. */
+  } arm_matrix_instance_q31;
+
+  /**
+   * @brief Floating-point matrix addition.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix addition.
+   * @param[in]   pSrcA  points to the first input matrix structure
+   * @param[in]   pSrcB  points to the second input matrix structure
+   * @param[out]  pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix addition.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point, complex, matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15, complex,  matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pScratch);
+
+  /**
+   * @brief Q31, complex, matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_f32(
+  const arm_matrix_instance_f32 * pSrc,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_q15(
+  const arm_matrix_instance_q15 * pSrc,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_q31(
+  const arm_matrix_instance_q31 * pSrc,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix multiplication
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix multiplication
+   * @param[in]  pSrcA   points to the first input matrix structure
+   * @param[in]  pSrcB   points to the second input matrix structure
+   * @param[out] pDst    points to output matrix structure
+   * @param[in]  pState  points to the array for storing intermediate results
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pState);
+
+  /**
+   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA   points to the first input matrix structure
+   * @param[in]  pSrcB   points to the second input matrix structure
+   * @param[out] pDst    points to output matrix structure
+   * @param[in]  pState  points to the array for storing intermediate results
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_fast_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pState);
+
+  /**
+   * @brief Q31 matrix multiplication
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_fast_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix scaling.
+   * @param[in]  pSrc   points to the input matrix
+   * @param[in]  scale  scale factor
+   * @param[out] pDst   points to the output matrix
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_f32(
+  const arm_matrix_instance_f32 * pSrc,
+        float32_t scale,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix scaling.
+   * @param[in]  pSrc        points to input matrix
+   * @param[in]  scaleFract  fractional portion of the scale factor
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to output matrix
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_q15(
+  const arm_matrix_instance_q15 * pSrc,
+        q15_t scaleFract,
+        int32_t shift,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix scaling.
+   * @param[in]  pSrc        points to input matrix
+   * @param[in]  scaleFract  fractional portion of the scale factor
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_q31(
+  const arm_matrix_instance_q31 * pSrc,
+        q31_t scaleFract,
+        int32_t shift,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief  Q31 matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_q31(
+        arm_matrix_instance_q31 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        q31_t * pData);
+
+  /**
+   * @brief  Q15 matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_q15(
+        arm_matrix_instance_q15 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        q15_t * pData);
+
+  /**
+   * @brief  Floating-point matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_f32(
+        arm_matrix_instance_f32 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        float32_t * pData);
+
+
+  /**
+   * @brief Instance structure for the Q15 PID Control.
+   */
+  typedef struct
+  {
+          q15_t A0;           /**< The derived gain, A0 = Kp + Ki + Kd . */
+#if !defined (ARM_MATH_DSP)
+          q15_t A1;
+          q15_t A2;
+#else
+          q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
+#endif
+          q15_t state[3];     /**< The state array of length 3. */
+          q15_t Kp;           /**< The proportional gain. */
+          q15_t Ki;           /**< The integral gain. */
+          q15_t Kd;           /**< The derivative gain. */
+  } arm_pid_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 PID Control.
+   */
+  typedef struct
+  {
+          q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
+          q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
+          q31_t A2;            /**< The derived gain, A2 = Kd . */
+          q31_t state[3];      /**< The state array of length 3. */
+          q31_t Kp;            /**< The proportional gain. */
+          q31_t Ki;            /**< The integral gain. */
+          q31_t Kd;            /**< The derivative gain. */
+  } arm_pid_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point PID Control.
+   */
+  typedef struct
+  {
+          float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
+          float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
+          float32_t A2;          /**< The derived gain, A2 = Kd . */
+          float32_t state[3];    /**< The state array of length 3. */
+          float32_t Kp;          /**< The proportional gain. */
+          float32_t Ki;          /**< The integral gain. */
+          float32_t Kd;          /**< The derivative gain. */
+  } arm_pid_instance_f32;
+
+
+
+  /**
+   * @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.
+   */
+  void arm_pid_init_f32(
+        arm_pid_instance_f32 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the floating-point PID Control.
+   * @param[in,out] S  is an instance of the floating-point PID Control structure
+   */
+  void arm_pid_reset_f32(
+        arm_pid_instance_f32 * S);
+
+
+  /**
+   * @brief  Initialization function for the Q31 PID Control.
+   * @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.
+   */
+  void arm_pid_init_q31(
+        arm_pid_instance_q31 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the Q31 PID Control.
+   * @param[in,out] S   points to an instance of the Q31 PID Control structure
+   */
+
+  void arm_pid_reset_q31(
+        arm_pid_instance_q31 * S);
+
+
+  /**
+   * @brief  Initialization function for the Q15 PID Control.
+   * @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.
+   */
+  void arm_pid_init_q15(
+        arm_pid_instance_q15 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the Q15 PID Control.
+   * @param[in,out] S  points to an instance of the q15 PID Control structure
+   */
+  void arm_pid_reset_q15(
+        arm_pid_instance_q15 * S);
+
+
+  /**
+   * @brief Instance structure for the floating-point Linear Interpolate function.
+   */
+  typedef struct
+  {
+          uint32_t nValues;           /**< nValues */
+          float32_t x1;               /**< x1 */
+          float32_t xSpacing;         /**< xSpacing */
+          float32_t *pYData;          /**< pointer to the table of Y values */
+  } arm_linear_interp_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          float32_t *pData;   /**< points to the data table. */
+  } arm_bilinear_interp_instance_f32;
+
+   /**
+   * @brief Instance structure for the Q31 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q31_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q31;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q15_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q15;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q7_t *pData;        /**< points to the data table. */
+  } arm_bilinear_interp_instance_q7;
+
+
+  /**
+   * @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
+   */
+  void arm_mult_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_mult_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_mult_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_mult_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q15_t *pTwiddle;                 /**< points to the Sin twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q15;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_q15(
+        arm_cfft_radix2_instance_q15 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_q15(
+  const arm_cfft_radix2_instance_q15 * S,
+        q15_t * pSrc);
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q15;
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_q15(
+        arm_cfft_radix4_instance_q15 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix4_q15(
+  const arm_cfft_radix4_instance_q15 * S,
+        q15_t * pSrc);
+
+  /**
+   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q31_t *pTwiddle;                 /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q31;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_q31(
+        arm_cfft_radix2_instance_q31 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_q31(
+  const arm_cfft_radix2_instance_q31 * S,
+        q31_t * pSrc);
+
+  /**
+   * @brief Instance structure for the Q31 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q31;
+
+/* Deprecated */
+  void arm_cfft_radix4_q31(
+  const arm_cfft_radix4_instance_q31 * S,
+        q31_t * pSrc);
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_q31(
+        arm_cfft_radix4_instance_q31 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+          uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+          float32_t onebyfftLen;             /**< value of 1/fftLen. */
+  } arm_cfft_radix2_instance_f32;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_f32(
+        arm_cfft_radix2_instance_f32 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_f32(
+  const arm_cfft_radix2_instance_f32 * S,
+        float32_t * pSrc);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+          uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+          float32_t onebyfftLen;             /**< value of 1/fftLen. */
+  } arm_cfft_radix4_instance_f32;
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_f32(
+        arm_cfft_radix4_instance_f32 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix4_f32(
+  const arm_cfft_radix4_instance_f32 * S,
+        float32_t * pSrc);
+
+  /**
+   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+#if defined(ARM_MATH_MVEI)
+   const uint32_t *rearranged_twiddle_tab_stride1_arr;        /**< Per stage reordered twiddle pointer (offset 1) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride2_arr;        /**< Per stage reordered twiddle pointer (offset 2) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride3_arr;        /**< Per stage reordered twiddle pointer (offset 3) */                                                       \
+   const q15_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */                                                                   \
+   const q15_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */                                                                   \
+   const q15_t *rearranged_twiddle_stride3;
+#endif
+  } arm_cfft_instance_q15;
+
+arm_status arm_cfft_init_q15(
+  arm_cfft_instance_q15 * S,
+  uint16_t fftLen);
+
+void arm_cfft_q15(
+    const arm_cfft_instance_q15 * S,
+          q15_t * p1,
+          uint8_t ifftFlag,
+          uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+#if defined(ARM_MATH_MVEI)
+   const uint32_t *rearranged_twiddle_tab_stride1_arr;        /**< Per stage reordered twiddle pointer (offset 1) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride2_arr;        /**< Per stage reordered twiddle pointer (offset 2) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride3_arr;        /**< Per stage reordered twiddle pointer (offset 3) */                                                       \
+   const q31_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */                                                                   \
+   const q31_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */                                                                   \
+   const q31_t *rearranged_twiddle_stride3;
+#endif
+  } arm_cfft_instance_q31;
+
+arm_status arm_cfft_init_q31(
+  arm_cfft_instance_q31 * S,
+  uint16_t fftLen);
+
+void arm_cfft_q31(
+    const arm_cfft_instance_q31 * S,
+          q31_t * p1,
+          uint8_t ifftFlag,
+          uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
+   const uint32_t *rearranged_twiddle_tab_stride1_arr;        /**< Per stage reordered twiddle pointer (offset 1) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride2_arr;        /**< Per stage reordered twiddle pointer (offset 2) */                                                       \
+   const uint32_t *rearranged_twiddle_tab_stride3_arr;        /**< Per stage reordered twiddle pointer (offset 3) */                                                       \
+   const float32_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */                                                                   \
+   const float32_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */                                                                   \
+   const float32_t *rearranged_twiddle_stride3;
+#endif
+  } arm_cfft_instance_f32;
+
+
+  arm_status arm_cfft_init_f32(
+  arm_cfft_instance_f32 * S,
+  uint16_t fftLen);
+
+  void arm_cfft_f32(
+  const arm_cfft_instance_f32 * S,
+        float32_t * p1,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+
+  /**
+   * @brief Instance structure for the Double Precision Floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const float64_t *pTwiddle;         /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+  } arm_cfft_instance_f64;
+
+  void arm_cfft_f64(
+  const arm_cfft_instance_f64 * S,
+        float64_t * p1,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the Q15 RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                      /**< length of the real FFT. */
+          uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
+    const q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
+#if defined(ARM_MATH_MVEI)
+    arm_cfft_instance_q15 cfftInst;
+#else
+    const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
+#endif
+  } arm_rfft_instance_q15;
+
+  arm_status arm_rfft_init_q15(
+        arm_rfft_instance_q15 * S,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_q15(
+  const arm_rfft_instance_q15 * S,
+        q15_t * pSrc,
+        q15_t * pDst);
+
+  /**
+   * @brief Instance structure for the Q31 RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                        /**< length of the real FFT. */
+          uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
+    const q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
+#if defined(ARM_MATH_MVEI)
+    arm_cfft_instance_q31 cfftInst;
+#else
+    const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
+#endif
+  } arm_rfft_instance_q31;
+
+  arm_status arm_rfft_init_q31(
+        arm_rfft_instance_q31 * S,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_q31(
+  const arm_rfft_instance_q31 * S,
+        q31_t * pSrc,
+        q31_t * pDst);
+
+  /**
+   * @brief Instance structure for the floating-point RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                        /**< length of the real FFT. */
+          uint16_t fftLenBy2;                         /**< length of the complex FFT. */
+          uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
+    const float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
+          arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
+  } arm_rfft_instance_f32;
+
+  arm_status arm_rfft_init_f32(
+        arm_rfft_instance_f32 * S,
+        arm_cfft_radix4_instance_f32 * S_CFFT,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_f32(
+  const arm_rfft_instance_f32 * S,
+        float32_t * pSrc,
+        float32_t * pDst);
+
+  /**
+   * @brief Instance structure for the Double Precision Floating-point RFFT/RIFFT function.
+   */
+typedef struct
+  {
+          arm_cfft_instance_f64 Sint;      /**< Internal CFFT structure. */
+          uint16_t fftLenRFFT;             /**< length of the real sequence */
+    const float64_t * pTwiddleRFFT;        /**< Twiddle factors real stage  */
+  } arm_rfft_fast_instance_f64 ;
+
+arm_status arm_rfft_fast_init_f64 (
+         arm_rfft_fast_instance_f64 * S,
+         uint16_t fftLen);
+
+
+void arm_rfft_fast_f64(
+    arm_rfft_fast_instance_f64 * S,
+    float64_t * p, float64_t * pOut,
+    uint8_t ifftFlag);
+
+
+  /**
+   * @brief Instance structure for the floating-point RFFT/RIFFT function.
+   */
+typedef struct
+  {
+          arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
+          uint16_t fftLenRFFT;             /**< length of the real sequence */
+    const float32_t * pTwiddleRFFT;        /**< Twiddle factors real stage  */
+  } arm_rfft_fast_instance_f32 ;
+
+arm_status arm_rfft_fast_init_f32 (
+         arm_rfft_fast_instance_f32 * S,
+         uint16_t fftLen);
+
+
+  void arm_rfft_fast_f32(
+        const arm_rfft_fast_instance_f32 * S,
+        float32_t * p, float32_t * pOut,
+        uint8_t ifftFlag);
+
+  /**
+   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          float32_t normalize;                 /**< normalizing factor. */
+    const float32_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const float32_t *pCosFactor;               /**< points to the cosFactor table. */
+          arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_f32;
+
+
+  /**
+   * @brief  Initialization function for the floating-point DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of floating-point DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of floating-point RFFT/RIFFT structure.
+   * @param[in]     S_CFFT     points to an instance of floating-point CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_f32(
+        arm_dct4_instance_f32 * S,
+        arm_rfft_instance_f32 * S_RFFT,
+        arm_cfft_radix4_instance_f32 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        float32_t normalize);
+
+
+  /**
+   * @brief Processing function for the floating-point DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the floating-point DCT4/IDCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_f32(
+  const arm_dct4_instance_f32 * S,
+        float32_t * pState,
+        float32_t * pInlineBuffer);
+
+
+  /**
+   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          q31_t normalize;                     /**< normalizing factor. */
+    const q31_t *pTwiddle;                     /**< points to the twiddle factor table. */
+    const q31_t *pCosFactor;                   /**< points to the cosFactor table. */
+          arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q31;
+
+
+  /**
+   * @brief  Initialization function for the Q31 DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of Q31 DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of Q31 RFFT/RIFFT structure
+   * @param[in]     S_CFFT     points to an instance of Q31 CFFT/CIFFT structure
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_q31(
+        arm_dct4_instance_q31 * S,
+        arm_rfft_instance_q31 * S_RFFT,
+        arm_cfft_radix4_instance_q31 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        q31_t normalize);
+
+
+  /**
+   * @brief Processing function for the Q31 DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the Q31 DCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_q31(
+  const arm_dct4_instance_q31 * S,
+        q31_t * pState,
+        q31_t * pInlineBuffer);
+
+
+  /**
+   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          q15_t normalize;                     /**< normalizing factor. */
+    const q15_t *pTwiddle;                     /**< points to the twiddle factor table. */
+    const q15_t *pCosFactor;                   /**< points to the cosFactor table. */
+          arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q15;
+
+
+  /**
+   * @brief  Initialization function for the Q15 DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of Q15 DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of Q15 RFFT/RIFFT structure.
+   * @param[in]     S_CFFT     points to an instance of Q15 CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_q15(
+        arm_dct4_instance_q15 * S,
+        arm_rfft_instance_q15 * S_RFFT,
+        arm_cfft_radix4_instance_q15 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        q15_t normalize);
+
+
+  /**
+   * @brief Processing function for the Q15 DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the Q15 DCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_q15(
+  const arm_dct4_instance_q15 * S,
+        q15_t * pState,
+        q15_t * pInlineBuffer);
+
+
+  /**
+   * @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
+   */
+  void arm_add_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_add_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_add_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_add_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_sub_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_sub_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_sub_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_sub_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_scale_f32(
+  const float32_t * pSrc,
+        float32_t scale,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_scale_q7(
+  const q7_t * pSrc,
+        q7_t scaleFract,
+        int8_t shift,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_scale_q15(
+  const q15_t * pSrc,
+        q15_t scaleFract,
+        int8_t shift,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_scale_q31(
+  const q31_t * pSrc,
+        q31_t scaleFract,
+        int8_t shift,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_abs_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_abs_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_abs_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_abs_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_dot_prod_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        uint32_t blockSize,
+        float32_t * result);
+
+
+  /**
+   * @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
+   */
+  void arm_dot_prod_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        uint32_t blockSize,
+        q31_t * result);
+
+
+  /**
+   * @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
+   */
+  void arm_dot_prod_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        uint32_t blockSize,
+        q63_t * result);
+
+
+  /**
+   * @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
+   */
+  void arm_dot_prod_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        uint32_t blockSize,
+        q63_t * result);
+
+
+  /**
+   * @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
+   */
+  void arm_shift_q7(
+  const q7_t * pSrc,
+        int8_t shiftBits,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_shift_q15(
+  const q15_t * pSrc,
+        int8_t shiftBits,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_shift_q31(
+  const q31_t * pSrc,
+        int8_t shiftBits,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_offset_f32(
+  const float32_t * pSrc,
+        float32_t offset,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_offset_q7(
+  const q7_t * pSrc,
+        q7_t offset,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_offset_q15(
+  const q15_t * pSrc,
+        q15_t offset,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_offset_q31(
+  const q31_t * pSrc,
+        q31_t offset,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_negate_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_negate_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_negate_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @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
+   */
+  void arm_negate_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a floating-point vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q7 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q15 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q31 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a floating-point vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_f32(
+        float32_t value,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q7 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q7(
+        q7_t value,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q15 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q15(
+        q15_t value,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q31 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q31(
+        q31_t value,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Convolution of floating-point sequences.
+ * @param[in]  pSrcA    points to the first input sequence.
+ * @param[in]  srcALen  length of the first input sequence.
+ * @param[in]  pSrcB    points to the second input sequence.
+ * @param[in]  srcBLen  length of the second input sequence.
+ * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
+ */
+  void arm_conv_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
+   */
+  void arm_conv_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+/**
+ * @brief Convolution of Q15 sequences.
+ * @param[in]  pSrcA    points to the first input sequence.
+ * @param[in]  srcALen  length of the first input sequence.
+ * @param[in]  pSrcB    points to the second input sequence.
+ * @param[in]  srcBLen  length of the second input sequence.
+ * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
+ */
+  void arm_conv_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
+   */
+  void arm_conv_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Convolution of Q31 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+    /**
+   * @brief Convolution of Q7 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   */
+  void arm_conv_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Convolution of Q7 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst);
+
+
+  /**
+   * @brief Partial convolution of floating-point sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q7 sequences
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+/**
+   * @brief Partial convolution of Q7 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR decimator.
+   */
+  typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const q15_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
+          q15_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR decimator.
+   */
+  typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const q31_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
+          q31_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_q31;
+
+/**
+  @brief Instance structure for floating-point FIR decimator.
+ */
+typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const float32_t *pCoeffs;         /**< points to the coefficient array. The array is of length numTaps.*/
+          float32_t *pState;          /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_f32;
+
+
+/**
+  @brief         Processing function for floating-point FIR decimator.
+  @param[in]     S         points to an instance of the floating-point FIR decimator structure
+  @param[in]     pSrc      points to the block of input data
+  @param[out]    pDst      points to the block of output data
+  @param[in]     blockSize number of samples to process
+ */
+void arm_fir_decimate_f32(
+  const arm_fir_decimate_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+  @brief         Initialization function for the floating-point FIR decimator.
+  @param[in,out] S          points to an instance of the floating-point FIR decimator structure
+  @param[in]     numTaps    number of coefficients in the filter
+  @param[in]     M          decimation factor
+  @param[in]     pCoeffs    points to the filter coefficients
+  @param[in]     pState     points to the state buffer
+  @param[in]     blockSize  number of input samples to process per call
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS      : Operation successful
+                   - \ref ARM_MATH_LENGTH_ERROR : <code>blockSize</code> is not a multiple of <code>M</code>
+ */
+arm_status arm_fir_decimate_init_f32(
+        arm_fir_decimate_instance_f32 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator.
+   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_fast_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR decimator.
+   * @param[in,out] S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]     numTaps    number of coefficients in the filter.
+   * @param[in]     M          decimation factor.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * <code>blockSize</code> is not a multiple of <code>M</code>.
+   */
+  arm_status arm_fir_decimate_init_q15(
+        arm_fir_decimate_instance_q15 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator.
+   * @param[in]  S     points to an instance of the Q31 FIR decimator structure.
+   * @param[in]  pSrc  points to the block of input data.
+   * @param[out] pDst  points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   */
+  void arm_fir_decimate_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q31 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_fast_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 FIR decimator.
+   * @param[in,out] S          points to an instance of the Q31 FIR decimator structure.
+   * @param[in]     numTaps    number of coefficients in the filter.
+   * @param[in]     M          decimation factor.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * <code>blockSize</code> is not a multiple of <code>M</code>.
+   */
+  arm_status arm_fir_decimate_init_q31(
+        arm_fir_decimate_instance_q31 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                      /**< upsample factor. */
+        uint16_t phaseLength;           /**< length of each polyphase filter component. */
+  const q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
+        q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                      /**< upsample factor. */
+        uint16_t phaseLength;           /**< length of each polyphase filter component. */
+  const q31_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
+        q31_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                     /**< upsample factor. */
+        uint16_t phaseLength;          /**< length of each polyphase filter component. */
+  const float32_t *pCoeffs;            /**< points to the coefficient array. The array is of length L*phaseLength. */
+        float32_t *pState;             /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
+  } arm_fir_interpolate_instance_f32;
+
+
+  /**
+   * @brief Processing function for the Q15 FIR interpolator.
+   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_q15(
+  const arm_fir_interpolate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR interpolator.
+   * @param[in,out] S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_q15(
+        arm_fir_interpolate_instance_q15 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR interpolator.
+   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_q31(
+  const arm_fir_interpolate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 FIR interpolator.
+   * @param[in,out] S          points to an instance of the Q31 FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_q31(
+        arm_fir_interpolate_instance_q31 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point FIR interpolator.
+   * @param[in]  S          points to an instance of the floating-point FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_f32(
+  const arm_fir_interpolate_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point FIR interpolator.
+   * @param[in,out] S          points to an instance of the floating-point FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_f32(
+        arm_fir_interpolate_instance_f32 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the high precision Q31 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
+          uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
+  } arm_biquad_cas_df1_32x64_ins_q31;
+
+
+  /**
+   * @param[in]  S          points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cas_df1_32x64_q31(
+  const arm_biquad_cas_df1_32x64_ins_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @param[in,out] S          points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cas_df1_32x64_init_q31(
+        arm_biquad_cas_df1_32x64_ins_q31 * S,
+        uint8_t numStages,
+  const q31_t * pCoeffs,
+        q63_t * pState,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
+    const float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_df2T_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 4*numStages. */
+    const float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_stereo_df2T_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float64_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
+    const float64_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_df2T_instance_f64;
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df2T_f32(
+  const arm_biquad_cascade_df2T_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_stereo_df2T_f32(
+  const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df2T_f64(
+  const arm_biquad_cascade_df2T_instance_f64 * S,
+  const float64_t * pSrc,
+        float64_t * pDst,
+        uint32_t blockSize);
+
+
+#if defined(ARM_MATH_NEON) 
+void arm_biquad_cascade_df2T_compute_coefs_f32(
+  arm_biquad_cascade_df2T_instance_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs);
+#endif
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_df2T_init_f32(
+        arm_biquad_cascade_df2T_instance_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_stereo_df2T_init_f32(
+        arm_biquad_cascade_stereo_df2T_instance_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_df2T_init_f64(
+        arm_biquad_cascade_df2T_instance_f64 * S,
+        uint8_t numStages,
+        const float64_t * pCoeffs,
+        float64_t * pState);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          q15_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
+    const q15_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          q31_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
+    const q31_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
+    const float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_f32;
+
+
+  /**
+   * @brief Initialization function for the Q15 FIR lattice filter.
+   * @param[in] S          points to an instance of the Q15 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages.
+   */
+  void arm_fir_lattice_init_q15(
+        arm_fir_lattice_instance_q15 * S,
+        uint16_t numStages,
+  const q15_t * pCoeffs,
+        q15_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR lattice filter.
+   * @param[in]  S          points to an instance of the Q15 FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_q15(
+  const arm_fir_lattice_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the Q31 FIR lattice filter.
+   * @param[in] S          points to an instance of the Q31 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+   * @param[in] pState     points to the state buffer.   The array is of length numStages.
+   */
+  void arm_fir_lattice_init_q31(
+        arm_fir_lattice_instance_q31 * S,
+        uint16_t numStages,
+  const q31_t * pCoeffs,
+        q31_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR lattice filter.
+   * @param[in]  S          points to an instance of the Q31 FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_q31(
+  const arm_fir_lattice_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Initialization function for the floating-point FIR lattice filter.
+ * @param[in] S          points to an instance of the floating-point FIR lattice structure.
+ * @param[in] numStages  number of filter stages.
+ * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+ * @param[in] pState     points to the state buffer.  The array is of length numStages.
+ */
+  void arm_fir_lattice_init_f32(
+        arm_fir_lattice_instance_f32 * S,
+        uint16_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief Processing function for the floating-point FIR lattice filter.
+   * @param[in]  S          points to an instance of the floating-point FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_f32(
+  const arm_fir_lattice_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          q15_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
+          q15_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
+          q15_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          q31_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
+          q31_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
+          q31_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          float32_t *pState;                   /**< points to the state variable array. The array is of length numStages+blockSize. */
+          float32_t *pkCoeffs;                 /**< points to the reflection coefficient array. The array is of length numStages. */
+          float32_t *pvCoeffs;                 /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_f32;
+
+
+  /**
+   * @brief Processing function for the floating-point IIR lattice filter.
+   * @param[in]  S          points to an instance of the floating-point IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_f32(
+  const arm_iir_lattice_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the floating-point IIR lattice filter.
+   * @param[in] S          points to an instance of the floating-point IIR lattice structure.
+   * @param[in] numStages  number of stages in the filter.
+   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize-1.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_init_f32(
+        arm_iir_lattice_instance_f32 * S,
+        uint16_t numStages,
+        float32_t * pkCoeffs,
+        float32_t * pvCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 IIR lattice filter.
+   * @param[in]  S          points to an instance of the Q31 IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_q31(
+  const arm_iir_lattice_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the Q31 IIR lattice filter.
+   * @param[in] S          points to an instance of the Q31 IIR lattice structure.
+   * @param[in] numStages  number of stages in the filter.
+   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_init_q31(
+        arm_iir_lattice_instance_q31 * S,
+        uint16_t numStages,
+        q31_t * pkCoeffs,
+        q31_t * pvCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 IIR lattice filter.
+   * @param[in]  S          points to an instance of the Q15 IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_q15(
+  const arm_iir_lattice_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Initialization function for the Q15 IIR lattice filter.
+ * @param[in] S          points to an instance of the fixed-point Q15 IIR lattice structure.
+ * @param[in] numStages  number of stages in the filter.
+ * @param[in] pkCoeffs   points to reflection coefficient buffer.  The array is of length numStages.
+ * @param[in] pvCoeffs   points to ladder coefficient buffer.  The array is of length numStages+1.
+ * @param[in] pState     points to state buffer.  The array is of length numStages+blockSize.
+ * @param[in] blockSize  number of samples to process per call.
+ */
+  void arm_iir_lattice_init_q15(
+        arm_iir_lattice_instance_q15 * S,
+        uint16_t numStages,
+        q15_t * pkCoeffs,
+        q15_t * pvCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the floating-point LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
+          float32_t mu;        /**< step size that controls filter coefficient updates. */
+  } arm_lms_instance_f32;
+
+
+  /**
+   * @brief Processing function for floating-point LMS filter.
+   * @param[in]  S          points to an instance of the floating-point LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_f32(
+  const arm_lms_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pRef,
+        float32_t * pOut,
+        float32_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for floating-point LMS filter.
+   * @param[in] S          points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to the coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_lms_init_f32(
+        arm_lms_instance_f32 * S,
+        uint16_t numTaps,
+        float32_t * pCoeffs,
+        float32_t * pState,
+        float32_t mu,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+          q15_t mu;            /**< step size that controls filter coefficient updates. */
+          uint32_t postShift;  /**< bit shift applied to coefficients. */
+  } arm_lms_instance_q15;
+
+
+  /**
+   * @brief Initialization function for the Q15 LMS filter.
+   * @param[in] S          points to an instance of the Q15 LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to the coefficient buffer.
+   * @param[in] pState     points to the state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_init_q15(
+        arm_lms_instance_q15 * S,
+        uint16_t numTaps,
+        q15_t * pCoeffs,
+        q15_t * pState,
+        q15_t mu,
+        uint32_t blockSize,
+        uint32_t postShift);
+
+
+  /**
+   * @brief Processing function for Q15 LMS filter.
+   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_q15(
+  const arm_lms_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pRef,
+        q15_t * pOut,
+        q15_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+          q31_t mu;            /**< step size that controls filter coefficient updates. */
+          uint32_t postShift;  /**< bit shift applied to coefficients. */
+  } arm_lms_instance_q31;
+
+
+  /**
+   * @brief Processing function for Q31 LMS filter.
+   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_q31(
+  const arm_lms_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pRef,
+        q31_t * pOut,
+        q31_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q31 LMS filter.
+   * @param[in] S          points to an instance of the Q31 LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_init_q31(
+        arm_lms_instance_q31 * S,
+        uint16_t numTaps,
+        q31_t * pCoeffs,
+        q31_t * pState,
+        q31_t mu,
+        uint32_t blockSize,
+        uint32_t postShift);
+
+
+  /**
+   * @brief Instance structure for the floating-point normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of coefficients in the filter. */
+          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+          float32_t mu;         /**< step size that control filter coefficient updates. */
+          float32_t energy;     /**< saves previous frame energy. */
+          float32_t x0;         /**< saves previous input sample. */
+  } arm_lms_norm_instance_f32;
+
+
+  /**
+   * @brief Processing function for floating-point normalized LMS filter.
+   * @param[in]  S          points to an instance of the floating-point normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_f32(
+        arm_lms_norm_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pRef,
+        float32_t * pOut,
+        float32_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for floating-point normalized LMS filter.
+   * @param[in] S          points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_lms_norm_init_f32(
+        arm_lms_norm_instance_f32 * S,
+        uint16_t numTaps,
+        float32_t * pCoeffs,
+        float32_t * pState,
+        float32_t mu,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of coefficients in the filter. */
+          q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+          q31_t mu;             /**< step size that controls filter coefficient updates. */
+          uint8_t postShift;    /**< bit shift applied to coefficients. */
+    const q31_t *recipTable;    /**< points to the reciprocal initial value table. */
+          q31_t energy;         /**< saves previous frame energy. */
+          q31_t x0;             /**< saves previous input sample. */
+  } arm_lms_norm_instance_q31;
+
+
+  /**
+   * @brief Processing function for Q31 normalized LMS filter.
+   * @param[in]  S          points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_q31(
+        arm_lms_norm_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pRef,
+        q31_t * pOut,
+        q31_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q31 normalized LMS filter.
+   * @param[in] S          points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_norm_init_q31(
+        arm_lms_norm_instance_q31 * S,
+        uint16_t numTaps,
+        q31_t * pCoeffs,
+        q31_t * pState,
+        q31_t mu,
+        uint32_t blockSize,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Instance structure for the Q15 normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< Number of coefficients in the filter. */
+          q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+          q15_t mu;             /**< step size that controls filter coefficient updates. */
+          uint8_t postShift;    /**< bit shift applied to coefficients. */
+    const q15_t *recipTable;    /**< Points to the reciprocal initial value table. */
+          q15_t energy;         /**< saves previous frame energy. */
+          q15_t x0;             /**< saves previous input sample. */
+  } arm_lms_norm_instance_q15;
+
+
+  /**
+   * @brief Processing function for Q15 normalized LMS filter.
+   * @param[in]  S          points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_q15(
+        arm_lms_norm_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pRef,
+        q15_t * pOut,
+        q15_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q15 normalized LMS filter.
+   * @param[in] S          points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_norm_init_q15(
+        arm_lms_norm_instance_q15 * S,
+        uint16_t numTaps,
+        q15_t * pCoeffs,
+        q15_t * pState,
+        q15_t mu,
+        uint32_t blockSize,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Correlation of floating-point sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst);
+
+
+/**
+ @brief Correlation of Q15 sequences
+ @param[in]  pSrcA     points to the first input sequence
+ @param[in]  srcALen   length of the first input sequence
+ @param[in]  pSrcB     points to the second input sequence
+ @param[in]  srcBLen   length of the second input sequence
+ @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+*/
+void arm_correlate_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch);
+
+
+/**
+  @brief Correlation of Q15 sequences.
+  @param[in]  pSrcA    points to the first input sequence
+  @param[in]  srcALen  length of the first input sequence
+  @param[in]  pSrcB    points to the second input sequence
+  @param[in]  srcBLen  length of the second input sequence
+  @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ */
+  void arm_correlate_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+/**
+  @brief         Correlation of Q15 sequences (fast version).
+  @param[in]     pSrcA      points to the first input sequence
+  @param[in]     srcALen    length of the first input sequence
+  @param[in]     pSrcB      points to the second input sequence
+  @param[in]     srcBLen    length of the second input sequence
+  @param[out]    pDst       points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.
+  @return        none
+ */
+void arm_correlate_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+/**
+  @brief Correlation of Q15 sequences (fast version).
+  @param[in]  pSrcA     points to the first input sequence.
+  @param[in]  srcALen   length of the first input sequence.
+  @param[in]  pSrcB     points to the second input sequence.
+  @param[in]  srcBLen   length of the second input sequence.
+  @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+  @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+ */
+void arm_correlate_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch);
+
+
+  /**
+   * @brief Correlation of Q31 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+/**
+  @brief Correlation of Q31 sequences (fast version).
+  @param[in]  pSrcA    points to the first input sequence
+  @param[in]  srcALen  length of the first input sequence
+  @param[in]  pSrcB    points to the second input sequence
+  @param[in]  srcBLen  length of the second input sequence
+  @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ */
+void arm_correlate_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+ /**
+   * @brief Correlation of Q7 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   */
+  void arm_correlate_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Correlation of Q7 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst);
+
+
+  /**
+   * @brief Instance structure for the floating-point sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_f32;
+
+  /**
+   * @brief Instance structure for the Q31 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q31;
+
+  /**
+   * @brief Instance structure for the Q15 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q7 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q7;
+
+
+  /**
+   * @brief Processing function for the floating-point sparse FIR filter.
+   * @param[in]  S           points to an instance of the floating-point sparse FIR structure.
+   * @param[in]  pSrc        points to the block of input data.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   */
+  void arm_fir_sparse_f32(
+        arm_fir_sparse_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        float32_t * pScratchIn,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point sparse FIR filter.
+   * @param[in,out] S          points to an instance of the floating-point sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_f32(
+        arm_fir_sparse_instance_f32 * S,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 sparse FIR filter.
+   * @param[in]  S           points to an instance of the Q31 sparse FIR structure.
+   * @param[in]  pSrc        points to the block of input data.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   */
+  void arm_fir_sparse_q31(
+        arm_fir_sparse_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        q31_t * pScratchIn,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q31 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q31(
+        arm_fir_sparse_instance_q31 * S,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 sparse FIR filter.
+   * @param[in]  S            points to an instance of the Q15 sparse FIR structure.
+   * @param[in]  pSrc         points to the block of input data.
+   * @param[out] pDst         points to the block of output data
+   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
+   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   */
+  void arm_fir_sparse_q15(
+        arm_fir_sparse_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        q15_t * pScratchIn,
+        q31_t * pScratchOut,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q15 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q15(
+        arm_fir_sparse_instance_q15 * S,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q7 sparse FIR filter.
+   * @param[in]  S            points to an instance of the Q7 sparse FIR structure.
+   * @param[in]  pSrc         points to the block of input data.
+   * @param[out] pDst         points to the block of output data
+   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
+   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   */
+  void arm_fir_sparse_q7(
+        arm_fir_sparse_instance_q7 * S,
+  const q7_t * pSrc,
+        q7_t * pDst,
+        q7_t * pScratchIn,
+        q31_t * pScratchOut,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q7 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q7 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q7(
+        arm_fir_sparse_instance_q7 * S,
+        uint16_t numTaps,
+  const q7_t * pCoeffs,
+        q7_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Floating-point sin_cos function.
+   * @param[in]  theta   input value in degrees
+   * @param[out] pSinVal  points to the processed sine output.
+   * @param[out] pCosVal  points to the processed cos output.
+   */
+  void arm_sin_cos_f32(
+        float32_t theta,
+        float32_t * pSinVal,
+        float32_t * pCosVal);
+
+
+  /**
+   * @brief  Q31 sin_cos function.
+   * @param[in]  theta    scaled input value in degrees
+   * @param[out] pSinVal  points to the processed sine output.
+   * @param[out] pCosVal  points to the processed cosine output.
+   */
+  void arm_sin_cos_q31(
+        q31_t theta,
+        q31_t * pSinVal,
+        q31_t * pCosVal);
+
+
+  /**
+   * @brief  Floating-point complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mag_squared_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 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
+   */
+  void arm_cmplx_mag_squared_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 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
+   */
+  void arm_cmplx_mag_squared_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+ /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup PID PID Motor Control
+   *
+   * A Proportional Integral Derivative (PID) controller is a generic feedback control
+   * loop mechanism widely used in industrial control systems.
+   * A PID controller is the most commonly used type of feedback controller.
+   *
+   * This set of functions implements (PID) controllers
+   * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
+   * of data and each call to the function returns a single processed value.
+   * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
+   * is the input sample value. The functions return the output value.
+   *
+   * \par Algorithm:
+   * <pre>
+   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
+   *    A0 = Kp + Ki + Kd
+   *    A1 = (-Kp ) - (2 * Kd )
+   *    A2 = Kd
+   * </pre>
+   *
+   * \par
+   * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
+   *
+   * \par
+   * \image html PID.gif "Proportional Integral Derivative Controller"
+   *
+   * \par
+   * The PID controller calculates an "error" value as the difference between
+   * the measured output and the reference input.
+   * The controller attempts to minimize the error by adjusting the process control inputs.
+   * The proportional value determines the reaction to the current error,
+   * the integral value determines the reaction based on the sum of recent errors,
+   * and the derivative value determines the reaction based on the rate at which the error has been changing.
+   *
+   * \par Instance Structure
+   * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
+   * A separate instance structure must be defined for each PID Controller.
+   * There are separate instance structure declarations for each of the 3 supported data types.
+   *
+   * \par Reset Functions
+   * There is also an associated reset function for each data type which clears the state array.
+   *
+   * \par Initialization Functions
+   * There is also an associated initialization function for each data type.
+   * The initialization function performs the following operations:
+   * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
+   * - Zeros out the values in the state buffer.
+   *
+   * \par
+   * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
+   *
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the fixed-point versions of the PID Controller functions.
+   * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup PID
+   * @{
+   */
+
+  /**
+   * @brief         Process function for the floating-point PID Control.
+   * @param[in,out] S   is an instance of the floating-point PID Control structure
+   * @param[in]     in  input sample to process
+   * @return        processed output sample.
+   */
+  __STATIC_FORCEINLINE float32_t arm_pid_f32(
+  arm_pid_instance_f32 * S,
+  float32_t in)
+  {
+    float32_t out;
+
+    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
+    out = (S->A0 * in) +
+      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+
+  }
+
+/**
+  @brief         Process function for the Q31 PID Control.
+  @param[in,out] S  points to an instance of the Q31 PID Control structure
+  @param[in]     in  input sample to process
+  @return        processed output sample.
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 64-bit accumulator.
+         The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
+         Thus, if the accumulator result overflows it wraps around rather than clip.
+         In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
+         After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
+ */
+__STATIC_FORCEINLINE q31_t arm_pid_q31(
+  arm_pid_instance_q31 * S,
+  q31_t in)
+  {
+    q63_t acc;
+    q31_t out;
+
+    /* acc = A0 * x[n]  */
+    acc = (q63_t) S->A0 * in;
+
+    /* acc += A1 * x[n-1] */
+    acc += (q63_t) S->A1 * S->state[0];
+
+    /* acc += A2 * x[n-2]  */
+    acc += (q63_t) S->A2 * S->state[1];
+
+    /* convert output to 1.31 format to add y[n-1] */
+    out = (q31_t) (acc >> 31U);
+
+    /* out += y[n-1] */
+    out += S->state[2];
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+  }
+
+
+/**
+  @brief         Process function for the Q15 PID Control.
+  @param[in,out] S   points to an instance of the Q15 PID Control structure
+  @param[in]     in  input sample to process
+  @return        processed output sample.
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using a 64-bit internal accumulator.
+         Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
+         The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
+         There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
+         After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
+         Lastly, the accumulator is saturated to yield a result in 1.15 format.
+ */
+__STATIC_FORCEINLINE q15_t arm_pid_q15(
+  arm_pid_instance_q15 * S,
+  q15_t in)
+  {
+    q63_t acc;
+    q15_t out;
+
+#if defined (ARM_MATH_DSP)
+    /* Implementation of PID controller */
+
+    /* acc = A0 * x[n]  */
+    acc = (q31_t) __SMUAD((uint32_t)S->A0, (uint32_t)in);
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc = (q63_t)__SMLALD((uint32_t)S->A1, (uint32_t)read_q15x2 (S->state), (uint64_t)acc);
+#else
+    /* acc = A0 * x[n]  */
+    acc = ((q31_t) S->A0) * in;
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc += (q31_t) S->A1 * S->state[0];
+    acc += (q31_t) S->A2 * S->state[1];
+#endif
+
+    /* acc += y[n-1] */
+    acc += (q31_t) S->state[2] << 15;
+
+    /* saturate the output */
+    out = (q15_t) (__SSAT((q31_t)(acc >> 15), 16));
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+  }
+
+  /**
+   * @} end of PID group
+   */
+
+
+  /**
+   * @brief Floating-point matrix inverse.
+   * @param[in]  src   points to the instance of the input floating-point matrix structure.
+   * @param[out] dst   points to the instance of the output floating-point matrix structure.
+   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
+   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
+   */
+  arm_status arm_mat_inverse_f32(
+  const arm_matrix_instance_f32 * src,
+  arm_matrix_instance_f32 * dst);
+
+
+  /**
+   * @brief Floating-point matrix inverse.
+   * @param[in]  src   points to the instance of the input floating-point matrix structure.
+   * @param[out] dst   points to the instance of the output floating-point matrix structure.
+   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
+   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
+   */
+  arm_status arm_mat_inverse_f64(
+  const arm_matrix_instance_f64 * src,
+  arm_matrix_instance_f64 * dst);
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup clarke Vector Clarke Transform
+   * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
+   * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
+   * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
+   * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
+   * \image html clarke.gif Stator current space vector and its components in (a,b).
+   * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
+   * can be calculated using only <code>Ia</code> and <code>Ib</code>.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeFormula.gif
+   * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
+   * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup clarke
+   * @{
+   */
+
+  /**
+   *
+   * @brief  Floating-point Clarke transform
+   * @param[in]  Ia       input three-phase coordinate <code>a</code>
+   * @param[in]  Ib       input three-phase coordinate <code>b</code>
+   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+   * @return        none
+   */
+  __STATIC_FORCEINLINE void arm_clarke_f32(
+  float32_t Ia,
+  float32_t Ib,
+  float32_t * pIalpha,
+  float32_t * pIbeta)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
+    *pIbeta = ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
+  }
+
+
+/**
+  @brief  Clarke transform for Q31 version
+  @param[in]  Ia       input three-phase coordinate <code>a</code>
+  @param[in]  Ib       input three-phase coordinate <code>b</code>
+  @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+  @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_clarke_q31(
+  q31_t Ia,
+  q31_t Ib,
+  q31_t * pIalpha,
+  q31_t * pIbeta)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
+
+    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
+    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
+
+    /* pIbeta is calculated by adding the intermediate products */
+    *pIbeta = __QADD(product1, product2);
+  }
+
+  /**
+   * @} end of clarke group
+   */
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_clarke Vector Inverse Clarke Transform
+   * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeInvFormula.gif
+   * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
+   * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_clarke
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Clarke transform
+   * @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
+   * @param[in]  Ibeta   input two-phase orthogonal vector axis beta
+   * @param[out] pIa     points to output three-phase coordinate <code>a</code>
+   * @param[out] pIb     points to output three-phase coordinate <code>b</code>
+   * @return     none
+   */
+  __STATIC_FORCEINLINE void arm_inv_clarke_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pIa,
+  float32_t * pIb)
+  {
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
+    *pIb = -0.5f * Ialpha + 0.8660254039f * Ibeta;
+  }
+
+
+/**
+  @brief  Inverse Clarke transform for Q31 version
+  @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
+  @param[in]  Ibeta   input two-phase orthogonal vector axis beta
+  @param[out] pIa     points to output three-phase coordinate <code>a</code>
+  @param[out] pIb     points to output three-phase coordinate <code>b</code>
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the subtraction, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_inv_clarke_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pIa,
+  q31_t * pIb)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
+
+    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
+
+    /* pIb is calculated by subtracting the products */
+    *pIb = __QSUB(product2, product1);
+  }
+
+  /**
+   * @} end of inv_clarke group
+   */
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup park Vector Park Transform
+   *
+   * Forward Park transform converts the input two-coordinate vector to flux and torque components.
+   * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
+   * from the stationary to the moving reference frame and control the spatial relationship between
+   * the stator vector current and rotor flux vector.
+   * If we consider the d axis aligned with the rotor flux, the diagram below shows the
+   * current vector and the relationship from the two reference frames:
+   * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkFormula.gif
+   * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
+   * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup park
+   * @{
+   */
+
+  /**
+   * @brief Floating-point Park transform
+   * @param[in]  Ialpha  input two-phase vector coordinate alpha
+   * @param[in]  Ibeta   input two-phase vector coordinate beta
+   * @param[out] pId     points to output   rotor reference frame d
+   * @param[out] pIq     points to output   rotor reference frame q
+   * @param[in]  sinVal  sine value of rotation angle theta
+   * @param[in]  cosVal  cosine value of rotation angle theta
+   * @return     none
+   *
+   * The function implements the forward Park transform.
+   *
+   */
+  __STATIC_FORCEINLINE void arm_park_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pId,
+  float32_t * pIq,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
+    *pId = Ialpha * cosVal + Ibeta * sinVal;
+
+    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
+    *pIq = -Ialpha * sinVal + Ibeta * cosVal;
+  }
+
+
+/**
+  @brief  Park transform for Q31 version
+  @param[in]  Ialpha  input two-phase vector coordinate alpha
+  @param[in]  Ibeta   input two-phase vector coordinate beta
+  @param[out] pId     points to output rotor reference frame d
+  @param[out] pIq     points to output rotor reference frame q
+  @param[in]  sinVal  sine value of rotation angle theta
+  @param[in]  cosVal  cosine value of rotation angle theta
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition and subtraction, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_park_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pId,
+  q31_t * pIq,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Ialpha * cosVal) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * sinVal) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Ialpha * sinVal) */
+    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * cosVal) */
+    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
+
+    /* Calculate pId by adding the two intermediate products 1 and 2 */
+    *pId = __QADD(product1, product2);
+
+    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
+    *pIq = __QSUB(product4, product3);
+  }
+
+  /**
+   * @} end of park group
+   */
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_park Vector Inverse Park transform
+   * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkInvFormula.gif
+   * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
+   * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_park
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Park transform
+   * @param[in]  Id       input coordinate of rotor reference frame d
+   * @param[in]  Iq       input coordinate of rotor reference frame q
+   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+   * @param[in]  sinVal   sine value of rotation angle theta
+   * @param[in]  cosVal   cosine value of rotation angle theta
+   * @return     none
+   */
+  __STATIC_FORCEINLINE void arm_inv_park_f32(
+  float32_t Id,
+  float32_t Iq,
+  float32_t * pIalpha,
+  float32_t * pIbeta,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
+    *pIalpha = Id * cosVal - Iq * sinVal;
+
+    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
+    *pIbeta = Id * sinVal + Iq * cosVal;
+  }
+
+
+/**
+  @brief  Inverse Park transform for   Q31 version
+  @param[in]  Id       input coordinate of rotor reference frame d
+  @param[in]  Iq       input coordinate of rotor reference frame q
+  @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+  @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+  @param[in]  sinVal   sine value of rotation angle theta
+  @param[in]  cosVal   cosine value of rotation angle theta
+  @return     none
+
+  @par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_inv_park_q31(
+  q31_t Id,
+  q31_t Iq,
+  q31_t * pIalpha,
+  q31_t * pIbeta,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Id * cosVal) */
+    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * sinVal) */
+    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Id * sinVal) */
+    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * cosVal) */
+    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
+
+    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
+    *pIalpha = __QSUB(product1, product2);
+
+    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
+    *pIbeta = __QADD(product4, product3);
+  }
+
+  /**
+   * @} end of Inverse park group
+   */
+
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup LinearInterpolate Linear Interpolation
+   *
+   * Linear interpolation is a method of curve fitting using linear polynomials.
+   * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
+   *
+   * \par
+   * \image html LinearInterp.gif "Linear interpolation"
+   *
+   * \par
+   * A  Linear Interpolate function calculates an output value(y), for the input(x)
+   * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
+   *
+   * \par Algorithm:
+   * <pre>
+   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
+   *       where x0, x1 are nearest values of input x
+   *             y0, y1 are nearest values to output y
+   * </pre>
+   *
+   * \par
+   * This set of functions implements Linear interpolation process
+   * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
+   * sample of data and each call to the function returns a single processed value.
+   * <code>S</code> points to an instance of the Linear Interpolate function data structure.
+   * <code>x</code> is the input sample value. The functions returns the output value.
+   *
+   * \par
+   * if x is outside of the table boundary, Linear interpolation returns first value of the table
+   * if x is below input range and returns last value of table if x is above range.
+   */
+
+  /**
+   * @addtogroup LinearInterpolate
+   * @{
+   */
+
+  /**
+   * @brief  Process function for the floating-point Linear Interpolation Function.
+   * @param[in,out] S  is an instance of the floating-point Linear Interpolation structure
+   * @param[in]     x  input sample to process
+   * @return y processed output sample.
+   *
+   */
+  __STATIC_FORCEINLINE float32_t arm_linear_interp_f32(
+  arm_linear_interp_instance_f32 * S,
+  float32_t x)
+  {
+    float32_t y;
+    float32_t x0, x1;                            /* Nearest input values */
+    float32_t y0, y1;                            /* Nearest output values */
+    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
+    int32_t i;                                   /* Index variable */
+    float32_t *pYData = S->pYData;               /* pointer to output table */
+
+    /* Calculation of index */
+    i = (int32_t) ((x - S->x1) / xSpacing);
+
+    if (i < 0)
+    {
+      /* Iniatilize output for below specified range as least output value of table */
+      y = pYData[0];
+    }
+    else if ((uint32_t)i >= (S->nValues - 1))
+    {
+      /* Iniatilize output for above specified range as last output value of table */
+      y = pYData[S->nValues - 1];
+    }
+    else
+    {
+      /* Calculation of nearest input values */
+      x0 = S->x1 +  i      * xSpacing;
+      x1 = S->x1 + (i + 1) * xSpacing;
+
+      /* Read of nearest output values */
+      y0 = pYData[i];
+      y1 = pYData[i + 1];
+
+      /* Calculation of output */
+      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));
+
+    }
+
+    /* returns output value */
+    return (y);
+  }
+
+
+   /**
+   *
+   * @brief  Process function for the Q31 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q31 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   *
+   */
+  __STATIC_FORCEINLINE q31_t arm_linear_interp_q31(
+  q31_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q31_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & (q31_t)0xFFF00000) >> 20);
+
+    if (index >= (int32_t)(nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if (index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* shift left by 11 to keep fract in 1.31 format */
+      fract = (x & 0x000FFFFF) << 11;
+
+      /* Read two nearest output values from the index in 1.31(q31) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
+      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
+
+      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
+      y += ((q31_t) (((q63_t) y1 * fract) >> 32));
+
+      /* Convert y to 1.31 format */
+      return (y << 1U);
+    }
+  }
+
+
+  /**
+   *
+   * @brief  Process function for the Q15 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q15 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   *
+   */
+  __STATIC_FORCEINLINE q15_t arm_linear_interp_q15(
+  q15_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q63_t y;                                     /* output */
+    q15_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & (int32_t)0xFFF00000) >> 20);
+
+    if (index >= (int32_t)(nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if (index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
+      y = ((q63_t) y0 * (0xFFFFF - fract));
+
+      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
+      y += ((q63_t) y1 * (fract));
+
+      /* convert y to 1.15 format */
+      return (q15_t) (y >> 20);
+    }
+  }
+
+
+  /**
+   *
+   * @brief  Process function for the Q7 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q7 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   */
+  __STATIC_FORCEINLINE q7_t arm_linear_interp_q7(
+  q7_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q7_t y0, y1;                                 /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    uint32_t index;                              /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    if (x < 0)
+    {
+      return (pYData[0]);
+    }
+    index = (x >> 20) & 0xfff;
+
+    if (index >= (nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index and are in 1.7(q7) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
+      y = ((y0 * (0xFFFFF - fract)));
+
+      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
+      y += (y1 * fract);
+
+      /* convert y to 1.7(q7) format */
+      return (q7_t) (y >> 20);
+     }
+  }
+
+  /**
+   * @} end of LinearInterpolate group
+   */
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for floating-point data.
+   * @param[in] x  input value in radians.
+   * @return  sin(x).
+   */
+  float32_t arm_sin_f32(
+  float32_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q31 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  sin(x).
+   */
+  q31_t arm_sin_q31(
+  q31_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q15 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  sin(x).
+   */
+  q15_t arm_sin_q15(
+  q15_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
+   * @param[in] x  input value in radians.
+   * @return  cos(x).
+   */
+  float32_t arm_cos_f32(
+  float32_t x);
+
+
+  /**
+   * @brief Fast approximation to the trigonometric cosine function for Q31 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  cos(x).
+   */
+  q31_t arm_cos_q31(
+  q31_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  cos(x).
+   */
+  q15_t arm_cos_q15(
+  q15_t x);
+
+
+/**
+  @brief         Floating-point vector of log values.
+  @param[in]     pSrc       points to the input vector
+  @param[out]    pDst       points to the output vector
+  @param[in]     blockSize  number of samples in each vector
+  @return        none
+ */
+  void arm_vlog_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+/**
+  @brief         Floating-point vector of exp values.
+  @param[in]     pSrc       points to the input vector
+  @param[out]    pDst       points to the output vector
+  @param[in]     blockSize  number of samples in each vector
+  @return        none
+ */
+  void arm_vexp_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @ingroup groupFastMath
+   */
+
+
+  /**
+   * @defgroup SQRT Square Root
+   *
+   * Computes the square root of a number.
+   * There are separate functions for Q15, Q31, and floating-point data types.
+   * The square root function is computed using the Newton-Raphson algorithm.
+   * This is an iterative algorithm of the form:
+   * <pre>
+   *      x1 = x0 - f(x0)/f'(x0)
+   * </pre>
+   * where <code>x1</code> is the current estimate,
+   * <code>x0</code> is the previous estimate, and
+   * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
+   * For the square root function, the algorithm reduces to:
+   * <pre>
+   *     x0 = in/2                         [initial guess]
+   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
+   * </pre>
+   */
+
+
+  /**
+   * @addtogroup SQRT
+   * @{
+   */
+
+/**
+  @brief         Floating-point square root function.
+  @param[in]     in    input value
+  @param[out]    pOut  square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+__STATIC_FORCEINLINE arm_status arm_sqrt_f32(
+  float32_t in,
+  float32_t * pOut)
+  {
+    if (in >= 0.0f)
+    {
+#if defined ( __CC_ARM )
+  #if defined __TARGET_FPU_VFP
+      *pOut = __sqrtf(in);
+  #else
+      *pOut = sqrtf(in);
+  #endif
+
+#elif defined ( __ICCARM__ )
+  #if defined __ARMVFP__
+      __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in));
+  #else
+      *pOut = sqrtf(in);
+  #endif
+
+#else
+      *pOut = sqrtf(in);
+#endif
+
+      return (ARM_MATH_SUCCESS);
+    }
+    else
+    {
+      *pOut = 0.0f;
+      return (ARM_MATH_ARGUMENT_ERROR);
+    }
+  }
+
+
+/**
+  @brief         Q31 square root function.
+  @param[in]     in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF
+  @param[out]    pOut  points to square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+arm_status arm_sqrt_q31(
+  q31_t in,
+  q31_t * pOut);
+
+
+/**
+  @brief         Q15 square root function.
+  @param[in]     in    input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF
+  @param[out]    pOut  points to square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+arm_status arm_sqrt_q15(
+  q15_t in,
+  q15_t * pOut);
+
+  /**
+   * @brief  Vector Floating-point square root function.
+   * @param[in]  pIn   input vector.
+   * @param[out] pOut  vector of square roots of input elements.
+   * @param[in]  len   length of input vector.
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
+   * <code>in</code> is negative value and returns zero output for negative values.
+   */
+  void arm_vsqrt_f32(
+  float32_t * pIn,
+  float32_t * pOut,
+  uint16_t len);
+
+  void arm_vsqrt_q31(
+  q31_t * pIn,
+  q31_t * pOut,
+  uint16_t len);
+
+  void arm_vsqrt_q15(
+  q15_t * pIn,
+  q15_t * pOut,
+  uint16_t len);
+
+  /**
+   * @} end of SQRT group
+   */
+
+
+  /**
+   * @brief floating-point Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const int32_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+
+  /**
+   * @brief floating-point Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  int32_t * dst,
+  int32_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t rOffset;
+    int32_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value  */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief Q15 Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q15_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+  /**
+   * @brief Q15 Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q15_t * dst,
+  q15_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset;
+    q15_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief Q7 Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q7_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+  /**
+   * @brief Q7 Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q7_t * dst,
+  q7_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset;
+    q7_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q63_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q63_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Floating-point complex magnitude
+   * @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
+   */
+  void arm_cmplx_mag_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 complex magnitude
+   * @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
+   */
+  void arm_cmplx_mag_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex magnitude
+   * @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
+   */
+  void arm_cmplx_mag_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        uint32_t numSamples,
+        q31_t * realResult,
+        q31_t * imagResult);
+
+
+  /**
+   * @brief  Q31 complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        uint32_t numSamples,
+        q63_t * realResult,
+        q63_t * imagResult);
+
+
+  /**
+   * @brief  Floating-point complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        uint32_t numSamples,
+        float32_t * realResult,
+        float32_t * imagResult);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_real_q15(
+  const q15_t * pSrcCmplx,
+  const q15_t * pSrcReal,
+        q15_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_real_q31(
+  const q31_t * pSrcCmplx,
+  const q31_t * pSrcReal,
+        q31_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_real_f32(
+  const float32_t * pSrcCmplx,
+  const float32_t * pSrcReal,
+        float32_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Minimum value of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] result     is output pointer
+   * @param[in]  index      is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * result,
+        uint32_t * index);
+
+
+  /**
+   * @brief  Minimum value of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[in]  pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult,
+        uint32_t * pIndex);
+
+
+  /**
+   * @brief  Minimum value of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult,
+        uint32_t * pIndex);
+
+
+  /**
+   * @brief  Minimum value of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q7 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q15 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q31 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a floating-point vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult,
+        uint32_t * pIndex);
+
+  /**
+    @brief         Maximum value of a floating-point vector.
+    @param[in]     pSrc       points to the input vector
+    @param[in]     blockSize  number of samples in input vector
+    @param[out]    pResult    maximum value returned here
+    @return        none
+   */
+  void arm_max_no_idx_f32(
+      const float32_t *pSrc,
+      uint32_t   blockSize,
+      float32_t *pResult);
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_cmplx_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_cmplx_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @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
+   */
+  void arm_cmplx_mult_cmplx_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q31 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q31 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q31(
+  const float32_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q15 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q15 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q15(
+  const float32_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q7 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q7 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q7(
+  const float32_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_float(
+  const q31_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_q15(
+  const q31_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_q7(
+  const q31_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_float(
+  const q15_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_q31(
+  const q15_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_q7(
+  const q15_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q7_to_float(
+  const q7_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q31 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_q7_to_q31(
+  const q7_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q15 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_q7_to_q15(
+  const q7_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+/**
+ * @brief Struct for specifying SVM Kernel
+ */
+typedef enum
+{
+    ARM_ML_KERNEL_LINEAR = 0,
+             /**< Linear kernel */
+    ARM_ML_KERNEL_POLYNOMIAL = 1,
+             /**< Polynomial kernel */
+    ARM_ML_KERNEL_RBF = 2,
+             /**< Radial Basis Function kernel */
+    ARM_ML_KERNEL_SIGMOID = 3
+             /**< Sigmoid kernel */
+} arm_ml_kernel_type;
+
+
+/**
+ * @brief Instance structure for linear SVM prediction function.
+ */
+typedef struct
+{
+  uint32_t        nbOfSupportVectors;     /**< Number of support vectors */
+  uint32_t        vectorDimension;        /**< Dimension of vector space */
+  float32_t       intercept;              /**< Intercept */
+  const float32_t *dualCoefficients;      /**< Dual coefficients */
+  const float32_t *supportVectors;        /**< Support vectors */
+  const int32_t   *classes;               /**< The two SVM classes */
+} arm_svm_linear_instance_f32;
+
+
+/**
+ * @brief Instance structure for polynomial SVM prediction function.
+ */
+typedef struct
+{
+  uint32_t        nbOfSupportVectors;     /**< Number of support vectors */
+  uint32_t        vectorDimension;        /**< Dimension of vector space */
+  float32_t       intercept;              /**< Intercept */
+  const float32_t *dualCoefficients;      /**< Dual coefficients */
+  const float32_t *supportVectors;        /**< Support vectors */
+  const int32_t   *classes;               /**< The two SVM classes */
+  int32_t         degree;                 /**< Polynomial degree */
+  float32_t       coef0;                  /**< Polynomial constant */
+  float32_t       gamma;                  /**< Gamma factor */
+} arm_svm_polynomial_instance_f32;
+
+/**
+ * @brief Instance structure for rbf SVM prediction function.
+ */
+typedef struct
+{
+  uint32_t        nbOfSupportVectors;     /**< Number of support vectors */
+  uint32_t        vectorDimension;        /**< Dimension of vector space */
+  float32_t       intercept;              /**< Intercept */
+  const float32_t *dualCoefficients;      /**< Dual coefficients */
+  const float32_t *supportVectors;        /**< Support vectors */
+  const int32_t   *classes;               /**< The two SVM classes */
+  float32_t       gamma;                  /**< Gamma factor */
+} arm_svm_rbf_instance_f32;
+
+/**
+ * @brief Instance structure for sigmoid SVM prediction function.
+ */
+typedef struct
+{
+  uint32_t        nbOfSupportVectors;     /**< Number of support vectors */
+  uint32_t        vectorDimension;        /**< Dimension of vector space */
+  float32_t       intercept;              /**< Intercept */
+  const float32_t *dualCoefficients;      /**< Dual coefficients */
+  const float32_t *supportVectors;        /**< Support vectors */
+  const int32_t   *classes;               /**< The two SVM classes */
+  float32_t       coef0;                  /**< Independant constant */
+  float32_t       gamma;                  /**< Gamma factor */
+} arm_svm_sigmoid_instance_f32;
+
+/**
+ * @brief        SVM linear instance init function
+ * @param[in]    S                      Parameters for SVM functions
+ * @param[in]    nbOfSupportVectors     Number of support vectors
+ * @param[in]    vectorDimension        Dimension of vector space
+ * @param[in]    intercept              Intercept
+ * @param[in]    dualCoefficients       Array of dual coefficients
+ * @param[in]    supportVectors         Array of support vectors
+ * @param[in]    classes                Array of 2 classes ID
+ * @return none.
+ *
+ */
+
+
+void arm_svm_linear_init_f32(arm_svm_linear_instance_f32 *S, 
+  uint32_t nbOfSupportVectors,
+  uint32_t vectorDimension,
+  float32_t intercept,
+  const float32_t *dualCoefficients,
+  const float32_t *supportVectors,
+  const int32_t  *classes);
+
+/**
+ * @brief SVM linear prediction
+ * @param[in]    S          Pointer to an instance of the linear SVM structure.
+ * @param[in]    in         Pointer to input vector
+ * @param[out]   pResult    Decision value
+ * @return none.
+ *
+ */
+  
+void arm_svm_linear_predict_f32(const arm_svm_linear_instance_f32 *S, 
+   const float32_t * in, 
+   int32_t * pResult);
+
+
+/**
+ * @brief        SVM polynomial instance init function
+ * @param[in]    S                      points to an instance of the polynomial SVM structure.
+ * @param[in]    nbOfSupportVectors     Number of support vectors
+ * @param[in]    vectorDimension        Dimension of vector space
+ * @param[in]    intercept              Intercept
+ * @param[in]    dualCoefficients       Array of dual coefficients
+ * @param[in]    supportVectors         Array of support vectors
+ * @param[in]    classes                Array of 2 classes ID
+ * @param[in]    degree                 Polynomial degree
+ * @param[in]    coef0                  coeff0 (scikit-learn terminology)
+ * @param[in]    gamma                  gamma (scikit-learn terminology)
+ * @return none.
+ *
+ */
+
+
+void arm_svm_polynomial_init_f32(arm_svm_polynomial_instance_f32 *S, 
+  uint32_t nbOfSupportVectors,
+  uint32_t vectorDimension,
+  float32_t intercept,
+  const float32_t *dualCoefficients,
+  const float32_t *supportVectors,
+  const int32_t   *classes,
+  int32_t      degree,
+  float32_t coef0,
+  float32_t gamma
+  );
+
+/**
+ * @brief SVM polynomial prediction
+ * @param[in]    S          Pointer to an instance of the polynomial SVM structure.
+ * @param[in]    in         Pointer to input vector
+ * @param[out]   pResult    Decision value
+ * @return none.
+ *
+ */
+void arm_svm_polynomial_predict_f32(const arm_svm_polynomial_instance_f32 *S, 
+   const float32_t * in, 
+   int32_t * pResult);
+
+
+/**
+ * @brief        SVM radial basis function instance init function
+ * @param[in]    S                      points to an instance of the polynomial SVM structure.
+ * @param[in]    nbOfSupportVectors     Number of support vectors
+ * @param[in]    vectorDimension        Dimension of vector space
+ * @param[in]    intercept              Intercept
+ * @param[in]    dualCoefficients       Array of dual coefficients
+ * @param[in]    supportVectors         Array of support vectors
+ * @param[in]    classes                Array of 2 classes ID
+ * @param[in]    gamma                  gamma (scikit-learn terminology)
+ * @return none.
+ *
+ */
+
+void arm_svm_rbf_init_f32(arm_svm_rbf_instance_f32 *S, 
+  uint32_t nbOfSupportVectors,
+  uint32_t vectorDimension,
+  float32_t intercept,
+  const float32_t *dualCoefficients,
+  const float32_t *supportVectors,
+  const int32_t   *classes,
+  float32_t gamma
+  );
+
+/**
+ * @brief SVM rbf prediction
+ * @param[in]    S         Pointer to an instance of the rbf SVM structure.
+ * @param[in]    in        Pointer to input vector
+ * @param[out]   pResult   decision value
+ * @return none.
+ *
+ */
+void arm_svm_rbf_predict_f32(const arm_svm_rbf_instance_f32 *S, 
+   const float32_t * in, 
+   int32_t * pResult);
+
+/**
+ * @brief        SVM sigmoid instance init function
+ * @param[in]    S                      points to an instance of the rbf SVM structure.
+ * @param[in]    nbOfSupportVectors     Number of support vectors
+ * @param[in]    vectorDimension        Dimension of vector space
+ * @param[in]    intercept              Intercept
+ * @param[in]    dualCoefficients       Array of dual coefficients
+ * @param[in]    supportVectors         Array of support vectors
+ * @param[in]    classes                Array of 2 classes ID
+ * @param[in]    coef0                  coeff0 (scikit-learn terminology)
+ * @param[in]    gamma                  gamma (scikit-learn terminology)
+ * @return none.
+ *
+ */
+
+void arm_svm_sigmoid_init_f32(arm_svm_sigmoid_instance_f32 *S, 
+  uint32_t nbOfSupportVectors,
+  uint32_t vectorDimension,
+  float32_t intercept,
+  const float32_t *dualCoefficients,
+  const float32_t *supportVectors,
+  const int32_t   *classes,
+  float32_t coef0,
+  float32_t gamma
+  );
+
+/**
+ * @brief SVM sigmoid prediction
+ * @param[in]    S        Pointer to an instance of the rbf SVM structure.
+ * @param[in]    in       Pointer to input vector
+ * @param[out]   pResult  Decision value
+ * @return none.
+ *
+ */
+void arm_svm_sigmoid_predict_f32(const arm_svm_sigmoid_instance_f32 *S, 
+   const float32_t * in, 
+   int32_t * pResult);
+
+
+
+/**
+ * @brief Instance structure for Naive Gaussian Bayesian estimator.
+ */
+typedef struct
+{
+  uint32_t vectorDimension;  /**< Dimension of vector space */
+  uint32_t numberOfClasses;  /**< Number of different classes  */
+  const float32_t *theta;          /**< Mean values for the Gaussians */
+  const float32_t *sigma;          /**< Variances for the Gaussians */
+  const float32_t *classPriors;    /**< Class prior probabilities */
+  float32_t epsilon;         /**< Additive value to variances */
+} arm_gaussian_naive_bayes_instance_f32;
+
+/**
+ * @brief Naive Gaussian Bayesian Estimator
+ *
+ * @param[in]  S         points to a naive bayes instance structure
+ * @param[in]  in        points to the elements of the input vector.
+ * @param[in]  pBuffer   points to a buffer of length numberOfClasses
+ * @return The predicted class
+ *
+ */
+
+
+uint32_t arm_gaussian_naive_bayes_predict_f32(const arm_gaussian_naive_bayes_instance_f32 *S, 
+   const float32_t * in, 
+   float32_t *pBuffer);
+
+/**
+ * @brief Computation of the LogSumExp
+ *
+ * In probabilistic computations, the dynamic of the probability values can be very
+ * wide because they come from gaussian functions.
+ * To avoid underflow and overflow issues, the values are represented by their log.
+ * In this representation, multiplying the original exp values is easy : their logs are added.
+ * But adding the original exp values is requiring some special handling and it is the
+ * goal of the LogSumExp function.
+ *
+ * If the values are x1...xn, the function is computing:
+ *
+ * ln(exp(x1) + ... + exp(xn)) and the computation is done in such a way that
+ * rounding issues are minimised.
+ *
+ * The max xm of the values is extracted and the function is computing:
+ * xm + ln(exp(x1 - xm) + ... + exp(xn - xm))
+ *
+ * @param[in]  *in         Pointer to an array of input values.
+ * @param[in]  blockSize   Number of samples in the input array.
+ * @return LogSumExp
+ *
+ */
+
+
+float32_t arm_logsumexp_f32(const float32_t *in, uint32_t blockSize);
+
+/**
+ * @brief Dot product with log arithmetic
+ *
+ * Vectors are containing the log of the samples
+ *
+ * @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[in]       pTmpBuffer temporary buffer of length blockSize
+ * @return The log of the dot product .
+ *
+ */
+
+
+float32_t arm_logsumexp_dot_prod_f32(const float32_t * pSrcA,
+  const float32_t * pSrcB,
+  uint32_t blockSize,
+  float32_t *pTmpBuffer);
+
+/**
+ * @brief Entropy
+ *
+ * @param[in]  pSrcA        Array of input values.
+ * @param[in]  blockSize    Number of samples in the input array.
+ * @return     Entropy      -Sum(p ln p)
+ *
+ */
+
+
+float32_t arm_entropy_f32(const float32_t * pSrcA,uint32_t blockSize);
+
+
+/**
+ * @brief Entropy
+ *
+ * @param[in]  pSrcA        Array of input values.
+ * @param[in]  blockSize    Number of samples in the input array.
+ * @return     Entropy      -Sum(p ln p)
+ *
+ */
+
+
+float64_t arm_entropy_f64(const float64_t * pSrcA, uint32_t blockSize);
+
+
+/**
+ * @brief Kullback-Leibler
+ *
+ * @param[in]  pSrcA         Pointer to an array of input values for probability distribution A.
+ * @param[in]  pSrcB         Pointer to an array of input values for probability distribution B.
+ * @param[in]  blockSize     Number of samples in the input array.
+ * @return Kullback-Leibler  Divergence D(A || B)
+ *
+ */
+float32_t arm_kullback_leibler_f32(const float32_t * pSrcA
+  ,const float32_t * pSrcB
+  ,uint32_t blockSize);
+
+
+/**
+ * @brief Kullback-Leibler
+ *
+ * @param[in]  pSrcA         Pointer to an array of input values for probability distribution A.
+ * @param[in]  pSrcB         Pointer to an array of input values for probability distribution B.
+ * @param[in]  blockSize     Number of samples in the input array.
+ * @return Kullback-Leibler  Divergence D(A || B)
+ *
+ */
+float64_t arm_kullback_leibler_f64(const float64_t * pSrcA, 
+                const float64_t * pSrcB, 
+                uint32_t blockSize);
+
+
+/**
+ * @brief Weighted sum
+ *
+ *
+ * @param[in]    *in           Array of input values.
+ * @param[in]    *weigths      Weights
+ * @param[in]    blockSize     Number of samples in the input array.
+ * @return Weighted sum
+ *
+ */
+float32_t arm_weighted_sum_f32(const float32_t *in
+  , const float32_t *weigths
+  , uint32_t blockSize);
+
+
+/**
+ * @brief Barycenter
+ *
+ *
+ * @param[in]    in         List of vectors
+ * @param[in]    weights    Weights of the vectors
+ * @param[out]   out        Barycenter
+ * @param[in]    nbVectors  Number of vectors
+ * @param[in]    vecDim     Dimension of space (vector dimension)
+ * @return       None
+ *
+ */
+void arm_barycenter_f32(const float32_t *in
+  , const float32_t *weights
+  , float32_t *out
+  , uint32_t nbVectors
+  , uint32_t vecDim);
+
+/**
+ * @brief        Euclidean distance between two vectors
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+
+float32_t arm_euclidean_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+/**
+ * @brief        Bray-Curtis distance between two vectors
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+float32_t arm_braycurtis_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+/**
+ * @brief        Canberra distance between two vectors
+ *
+ * This function may divide by zero when samples pA[i] and pB[i] are both zero.
+ * The result of the computation will be correct. So the division per zero may be
+ * ignored.
+ *
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+float32_t arm_canberra_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+
+/**
+ * @brief        Chebyshev distance between two vectors
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+float32_t arm_chebyshev_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+
+/**
+ * @brief        Cityblock (Manhattan) distance between two vectors
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+float32_t arm_cityblock_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+/**
+ * @brief        Correlation distance between two vectors
+ *
+ * The input vectors are modified in place !
+ *
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+float32_t arm_correlation_distance_f32(float32_t *pA,float32_t *pB, uint32_t blockSize);
+
+/**
+ * @brief        Cosine distance between two vectors
+ *
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+
+float32_t arm_cosine_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize);
+
+/**
+ * @brief        Jensen-Shannon distance between two vectors
+ *
+ * This function is assuming that elements of second vector are > 0
+ * and 0 only when the corresponding element of first vector is 0.
+ * Otherwise the result of the computation does not make sense
+ * and for speed reasons, the cases returning NaN or Infinity are not
+ * managed.
+ *
+ * When the function is computing x log (x / y) with x 0 and y 0,
+ * it will compute the right value (0) but a division per zero will occur
+ * and shoudl be ignored in client code.
+ *
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+
+float32_t arm_jensenshannon_distance_f32(const float32_t *pA,const float32_t *pB,uint32_t blockSize);
+
+/**
+ * @brief        Minkowski distance between two vectors
+ *
+ * @param[in]    pA         First vector
+ * @param[in]    pB         Second vector
+ * @param[in]    n          Norm order (>= 2)
+ * @param[in]    blockSize  vector length
+ * @return distance
+ *
+ */
+
+
+
+float32_t arm_minkowski_distance_f32(const float32_t *pA,const float32_t *pB, int32_t order, uint32_t blockSize);
+
+/**
+ * @brief        Dice distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    order           Distance order
+ * @param[in]    blockSize       Number of samples
+ * @return distance
+ *
+ */
+
+
+float32_t arm_dice_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Hamming distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_hamming_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Jaccard distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_jaccard_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Kulsinski distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_kulsinski_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Roger Stanimoto distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_rogerstanimoto_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Russell-Rao distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_russellrao_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Sokal-Michener distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_sokalmichener_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Sokal-Sneath distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_sokalsneath_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+/**
+ * @brief        Yule distance between two vectors
+ *
+ * @param[in]    pA              First vector of packed booleans
+ * @param[in]    pB              Second vector of packed booleans
+ * @param[in]    numberOfBools   Number of booleans
+ * @return distance
+ *
+ */
+
+float32_t arm_yule_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools);
+
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup BilinearInterpolate Bilinear Interpolation
+   *
+   * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
+   * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
+   * determines values between the grid points.
+   * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
+   * Bilinear interpolation is often used in image processing to rescale images.
+   * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
+   *
+   * <b>Algorithm</b>
+   * \par
+   * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
+   * For floating-point, the instance structure is defined as:
+   * <pre>
+   *   typedef struct
+   *   {
+   *     uint16_t numRows;
+   *     uint16_t numCols;
+   *     float32_t *pData;
+   * } arm_bilinear_interp_instance_f32;
+   * </pre>
+   *
+   * \par
+   * where <code>numRows</code> specifies the number of rows in the table;
+   * <code>numCols</code> specifies the number of columns in the table;
+   * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
+   * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
+   * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
+   *
+   * \par
+   * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
+   * <pre>
+   *     XF = floor(x)
+   *     YF = floor(y)
+   * </pre>
+   * \par
+   * The interpolated output point is computed as:
+   * <pre>
+   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
+   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
+   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
+   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
+   * </pre>
+   * Note that the coordinates (x, y) contain integer and fractional components.
+   * The integer components specify which portion of the table to use while the
+   * fractional components control the interpolation processor.
+   *
+   * \par
+   * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
+   */
+
+
+  /**
+   * @addtogroup BilinearInterpolate
+   * @{
+   */
+
+  /**
+  * @brief  Floating-point bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate.
+  * @param[in]     Y  interpolation coordinate.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE float32_t arm_bilinear_interp_f32(
+  const arm_bilinear_interp_instance_f32 * S,
+  float32_t X,
+  float32_t Y)
+  {
+    float32_t out;
+    float32_t f00, f01, f10, f11;
+    float32_t *pData = S->pData;
+    int32_t xIndex, yIndex, index;
+    float32_t xdiff, ydiff;
+    float32_t b1, b2, b3, b4;
+
+    xIndex = (int32_t) X;
+    yIndex = (int32_t) Y;
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (xIndex < 0 || xIndex > (S->numCols - 2) || yIndex < 0 || yIndex > (S->numRows - 2))
+    {
+      return (0);
+    }
+
+    /* Calculation of index for two nearest points in X-direction */
+    index = (xIndex ) + (yIndex ) * S->numCols;
+
+
+    /* Read two nearest points in X-direction */
+    f00 = pData[index];
+    f01 = pData[index + 1];
+
+    /* Calculation of index for two nearest points in Y-direction */
+    index = (xIndex ) + (yIndex+1) * S->numCols;
+
+
+    /* Read two nearest points in Y-direction */
+    f10 = pData[index];
+    f11 = pData[index + 1];
+
+    /* Calculation of intermediate values */
+    b1 = f00;
+    b2 = f01 - f00;
+    b3 = f10 - f00;
+    b4 = f00 - f01 - f10 + f11;
+
+    /* Calculation of fractional part in X */
+    xdiff = X - xIndex;
+
+    /* Calculation of fractional part in Y */
+    ydiff = Y - yIndex;
+
+    /* Calculation of bi-linear interpolated output */
+    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
+
+    /* return to application */
+    return (out);
+  }
+
+
+  /**
+  * @brief  Q31 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q31_t arm_bilinear_interp_q31(
+  arm_bilinear_interp_instance_q31 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q31_t out;                                   /* Temporary output */
+    q31_t acc = 0;                               /* output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q31_t x1, x2, y1, y2;                        /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q31_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* shift left xfract by 11 to keep 1.31 format */
+    xfract = (X & 0x000FFFFF) << 11U;
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[(rI) + (int32_t)nCols * (cI)    ];
+    x2 = pYData[(rI) + (int32_t)nCols * (cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* shift left yfract by 11 to keep 1.31 format */
+    yfract = (Y & 0x000FFFFF) << 11U;
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[(rI) + (int32_t)nCols * (cI + 1)    ];
+    y2 = pYData[(rI) + (int32_t)nCols * (cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
+    out = ((q31_t) (((q63_t) x1  * (0x7FFFFFFF - xfract)) >> 32));
+    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
+
+    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
+
+    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* Convert acc to 1.31(q31) format */
+    return ((q31_t)(acc << 2));
+  }
+
+
+  /**
+  * @brief  Q15 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q15_t arm_bilinear_interp_q15(
+  arm_bilinear_interp_instance_q15 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q15_t x1, x2, y1, y2;                        /* Nearest output values */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    int32_t rI, cI;                              /* Row and column indices */
+    q15_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
+    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
+    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
+
+    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
+    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
+    out = (q31_t) (((q63_t) x1 * (0x0FFFFF - xfract)) >> 4U);
+    acc = ((q63_t) out * (0x0FFFFF - yfract));
+
+    /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) x2 * (0x0FFFFF - yfract)) >> 4U);
+    acc += ((q63_t) out * (xfract));
+
+    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y1 * (0x0FFFFF - xfract)) >> 4U);
+    acc += ((q63_t) out * (yfract));
+
+    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4U);
+    acc += ((q63_t) out * (yfract));
+
+    /* acc is in 13.51 format and down shift acc by 36 times */
+    /* Convert out to 1.15 format */
+    return ((q15_t)(acc >> 36));
+  }
+
+
+  /**
+  * @brief  Q7 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q7_t arm_bilinear_interp_q7(
+  arm_bilinear_interp_instance_q7 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q7_t x1, x2, y1, y2;                         /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q7_t *pYData = S->pData;                     /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & (q31_t)0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
+    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & (q31_t)0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
+    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
+    out = ((x1 * (0xFFFFF - xfract)));
+    acc = (((q63_t) out * (0xFFFFF - yfract)));
+
+    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
+    out = ((x2 * (0xFFFFF - yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y1 * (0xFFFFF - xfract)));
+    acc += (((q63_t) out * (yfract)));
+
+    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y2 * (yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
+    return ((q7_t)(acc >> 40));
+  }
+
+  /**
+   * @} end of BilinearInterpolate group
+   */
+
+
+/* SMMLAR */
+#define multAcc_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)
+
+/* SMMLSR */
+#define multSub_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)
+
+/* SMMULR */
+#define mult_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)
+
+/* SMMLA */
+#define multAcc_32x32_keep32(a, x, y) \
+    a += (q31_t) (((q63_t) x * y) >> 32)
+
+/* SMMLS */
+#define multSub_32x32_keep32(a, x, y) \
+    a -= (q31_t) (((q63_t) x * y) >> 32)
+
+/* SMMUL */
+#define mult_32x32_keep32(a, x, y) \
+    a = (q31_t) (((q63_t) x * y ) >> 32)
+
+
+#if   defined ( __CC_ARM )
+  /* Enter low optimization region - place directly above function definition */
+  #if defined( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_ENTER \
+       _Pragma ("push")         \
+       _Pragma ("O1")
+  #else
+    #define LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_EXIT \
+       _Pragma ("pop")
+  #else
+    #define LOW_OPTIMIZATION_EXIT
+  #endif
+
+  /* Enter low optimization region - place directly above function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined (__ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __GNUC__ )
+  #define LOW_OPTIMIZATION_ENTER \
+       __attribute__(( optimize("-O1") ))
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __ICCARM__ )
+  /* Enter low optimization region - place directly above function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_ENTER \
+       _Pragma ("optimize=low")
+  #else
+    #define LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define LOW_OPTIMIZATION_EXIT
+
+  /* Enter low optimization region - place directly above function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
+       _Pragma ("optimize=low")
+  #else
+    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __TI_ARM__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __CSMC__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __TASKING__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+       
+#elif defined ( _MSC_VER ) || defined(__GNUC_PYTHON__)
+      #define LOW_OPTIMIZATION_ENTER
+      #define LOW_OPTIMIZATION_EXIT
+      #define IAR_ONLY_LOW_OPTIMIZATION_ENTER 
+      #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+#endif
+
+
+
+/* Compiler specific diagnostic adjustment */
+#if   defined ( __CC_ARM )
+
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+
+#elif defined ( __GNUC__ )
+#pragma GCC diagnostic pop
+
+#elif defined ( __ICCARM__ )
+
+#elif defined ( __TI_ARM__ )
+
+#elif defined ( __CSMC__ )
+
+#elif defined ( __TASKING__ )
+
+#elif defined ( _MSC_VER )
+
+#else
+  #error Unknown compiler
+#endif
+
+#ifdef   __cplusplus
+}
+#endif
+
+
+#endif /* _ARM_MATH_H */
+
+/**
+ *
+ * End of file.
+ */
diff --git a/Middlewares/Third_Party/ARM/DSP/LICENSE.txt b/Middlewares/Third_Party/ARM/DSP/LICENSE.txt
new file mode 100644
index 0000000..c0ee812
--- /dev/null
+++ b/Middlewares/Third_Party/ARM/DSP/LICENSE.txt
@@ -0,0 +1,201 @@
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diff --git a/User/component/cmd.c b/User/component/cmd.c
index 161af6e..e1931ad 100644
--- a/User/component/cmd.c
+++ b/User/component/cmd.c
@@ -19,36 +19,39 @@ static void CMD_RcLogic(const CMD_RC_t *rc, CMD_t *cmd, float dt_sec) {
   switch (rc->sw_l) {
       /* 左拨杆相应行为选择和解析 */
     case CMD_SW_UP:
-      cmd->chassis.mode = CHASSIS_MODE_RELAX;
       switch (rc->sw_r) {
       /* 右拨杆相应行为选择和解析*/ 
       case CMD_SW_UP:
+        cmd->chassis.mode = CHASSIS_MODE_RELAX;
         cmd->chassis.action = CHASSIS_ACTION_NONE;
         break;
       case CMD_SW_MID:
+        cmd->chassis.mode = CHASSIS_MODE_DAMP;
         cmd->chassis.action = CHASSIS_ACTION_NONE;
         break;
       case CMD_SW_DOWN:
+        cmd->chassis.mode = CHASSIS_MODE_DAMP;
         cmd->chassis.action = CHASSIS_ACTION_NONE;
         break;
       case CMD_SW_ERR:
+        cmd->chassis.mode = CHASSIS_MODE_RELAX;
         cmd->chassis.action = CHASSIS_ACTION_NONE;
         break;
       }
       break;
 
     case CMD_SW_MID:
-      cmd->chassis.mode = CHASSIS_MODE_DAMP;
+      cmd->chassis.mode = CHASSIS_MODE_JUMP;
       switch (rc->sw_r) {
       /* 右拨杆相应行为选择和解析*/ 
       case CMD_SW_UP:
-        cmd->chassis.action = CHASSIS_ACTION_NONE;
+        cmd->chassis.action = CHASSIS_ACTION_STAND;
         break;
       case CMD_SW_MID:
-        cmd->chassis.action = CHASSIS_ACTION_NONE;
+        cmd->chassis.action = CHASSIS_ACTION_WAIT_JUMP;
         break;
       case CMD_SW_DOWN:
-        cmd->chassis.action = CHASSIS_ACTION_NONE;
+        cmd->chassis.action = CHASSIS_ACTION_JUMP;
         break;
       case CMD_SW_ERR:
         cmd->chassis.action = CHASSIS_ACTION_NONE;
@@ -67,7 +70,7 @@ static void CMD_RcLogic(const CMD_RC_t *rc, CMD_t *cmd, float dt_sec) {
         cmd->chassis.action = CHASSIS_ACTION_STAND;
         break;
       case CMD_SW_DOWN:
-        cmd->chassis.action = CHASSIS_ACTION_TROT;
+        cmd->chassis.action = CHASSIS_ACTION_SLOW_TROT;
         break;
       case CMD_SW_ERR:
         cmd->chassis.action = CHASSIS_ACTION_NONE;
diff --git a/User/component/cmd.h b/User/component/cmd.h
index db2b331..8e4e0bc 100644
--- a/User/component/cmd.h
+++ b/User/component/cmd.h
@@ -20,6 +20,7 @@ typedef enum {
   CHASSIS_MODE_BREAK, /* 刹车模式，电机闭环控制保持静止。用于机器人停止状态 */
   CHASSIS_MODE_POSITION, /* 位置模式，电机闭环控制保持在指定位置 */
   CHASSIS_MODE_FOLLOW, /* 通过闭环控制使车头方向跟随遥控器 */
+  CHASSIS_MODE_JUMP, /*跳跃模式*/
 } CMD_ChassisMode_t;
 
 typedef enum {
@@ -27,6 +28,9 @@ typedef enum {
   CHASSIS_ACTION_STAND, /* 站立动作 */
   CHASSIS_ACTION_WALK, /* 行走动作 */
   CHASSIS_ACTION_TROT, /* 小跑动作 */
+  CHASSIS_ACTION_SLOW_TROT,
+  CHASSIS_ACTION_WAIT_JUMP,
+  
   CHASSIS_ACTION_JUMP, /* 跳跃动作 */
   CHASSIS_ACTION_RUN,
   CHASSIS_ACTION_NUM,
diff --git a/User/module/chassis.c b/User/module/chassis.c
index fd2fbcc..b093ac4 100644
--- a/User/module/chassis.c
+++ b/User/module/chassis.c
@@ -44,8 +44,8 @@ static Kinematics_JointCMD_t position_mode = {
     .T = 0.0f, /* 零力矩 */
     .W = 0.0f, /* 零速度 */
     .Pos = 0.0f, /* 零位置 */
-    .K_P = 1.2f, /* 刚度系数 */
-    .K_W = 0.05f, /* 速度系数 */
+    .K_P = 2.2f, /* 刚度系数 */
+    .K_W = 0.08f, /* 速度系数 */
 };
 
 // static uint8_t chassis_mode_states = 0;
diff --git a/User/module/chassis.h b/User/module/chassis.h
index f1034a8..6490c29 100644
--- a/User/module/chassis.h
+++ b/User/module/chassis.h
@@ -41,18 +41,18 @@ typedef enum {
 typedef union {
   float id[GO_MOTOR_NUM];
   struct{
-    float lf_hip;   /* 左前腿髋关节长度，单位：米 */
-    float lf_thigh; /* 左前腿大腿长度，单位：米 */
-    float lf_calf;  /* 左前腿小腿长度，单位：米 */
-    float rf_hip;   /* 右前腿髋关节长度，单位：米 */
-    float rf_thigh; /* 右前腿大腿长度，单位：米 */
-    float rf_calf;  /* 右前腿小腿长度，单位：米 */
-    float lr_hip;   /* 左后腿髋关节长度，单位：米 */
-    float lr_thigh; /* 左后腿大腿长度，单位：米 */
-    float lr_calf;  /* 左后腿小腿长度，单位：米 */
-    float rr_hip;   /* 右后腿髋关节长度，单位：米 */
-    float rr_thigh; /* 右后腿大腿长度，单位：米 */
-    float rr_calf;  /* 右后腿小腿长度，单位：米 */
+    float lf_hip;
+    float lf_thigh;
+    float lf_calf;
+    float rf_hip;
+    float rf_thigh;
+    float rf_calf;
+    float lr_hip;
+    float lr_thigh;
+    float lr_calf;
+    float rr_hip;
+    float rr_thigh;
+    float rr_calf;
   } named;
 } joint_params;
 
@@ -61,6 +61,20 @@ typedef struct {
   float y;
   float z;
 } joint_pos;
+
+typedef struct {
+  float x;
+  float y;
+  float z;
+} foot_pos;
+
+typedef struct {
+  foot_pos lf;
+  foot_pos rf;
+  foot_pos lr;
+  foot_pos rr;
+} foots_pos;
+
 typedef struct {
   joint_params min;
   joint_params max;
@@ -80,8 +94,6 @@ typedef union {
 typedef struct{
   joint_params zero_point; /* 零点角度，单位：弧度 */
 
-  // joint_params length;     /* 关节长度，单位：米 */
- 
   joint_params ratio;      /* 关节减速比 */
   joint_limits limit; /* 关节的最小和最大角度，单位：弧度 */
   
@@ -99,6 +111,7 @@ typedef struct {
 
   KPID_Params_t torque_pid_param; /* 力矩矩控制PID的参数 */
   KPID_Params_t blance_pid_param; /* 平衡PID的参数 */
+
   /* 低通滤波器截止频率 */
   struct {
     float in;  /* 输入 */
@@ -113,11 +126,11 @@ typedef struct {
  */
 typedef struct {
   uint32_t lask_wakeup;
+
   float dt;
   float time;
 
   const Chassis_Params_t *param; /* 底盘的参数，用Chassis_Init设定 */
-
   GO_ChassisFeedback_t feedback; /* 底盘反馈信息 */
   GO_ChassisCMD_t output;
   float height; /* 底盘高度，单位：米 */
@@ -143,14 +156,18 @@ typedef struct {
     }end_pos;  
   } leg_pos; /* 四条腿的关节位置，单位：米 */
 
+  struct {
+    foots_pos *leg;
+  } foots; /* 四条腿的足端位置*/
+
   /* 模块通用 */
   CMD_ChassisMode_t mode; /* 底盘模式 */
   
   CMD_ChassisAction_t action; /* 底盘模式 */
 
-  AHRS_Eulr_t eulr_imu; /* 欧拉角，单位：弧度 */
+  AHRS_Eulr_t eulr_imu; /* IMU获取的欧拉角 */
 
-  AHRS_Eulr_t delta_eulr; /* 欧拉角变化量，单位：弧度 */
+  AHRS_Eulr_t delta_eulr; /* 欧拉角变化量 */
 
   AHRS_Eulr_t eulr_setpoint; /* 期望的欧拉角，单位：弧度 */
   
diff --git a/User/module/config.c b/User/module/config.c
index 7440eb2..fca5dea 100644
--- a/User/module/config.c
+++ b/User/module/config.c
@@ -11,15 +11,17 @@
 
 #define CONFIG_BASE_ADDRESS (ADDR_FLASH_SECTOR_11)
 
-#define JOINT_CALF_OFFSET (2.7321f * 12.66)
+#define JOINT_CALF_OFFSET (2.7321f * 12.66f)
 
 Config_t param_default = {
-    
+
     .uart = {
         .left_leg = BSP_UART_LEFT_LEG,
         .right_leg = BSP_UART_RIGHT_LEG,
     },
+
     .chassis_imu_type = IMU_WHEELREC_N100,
+
     .cali = {
         .bmi088 = {
             .gyro_offset = {0.0f, 0.0f, 0.0f},
@@ -30,25 +32,25 @@ Config_t param_default = {
         .type = CHASSIS_TYPE_QUADRUPED,
 
         .torque_pid_param = {
-            .k = 5.0f, /* 控制器增益 */
-            .p = 20.0f, /* 比例项增益 */
-            .i = 1.0f, /* 积分项增益 */
-            .d = 0.0f, /* 微分项增益 */
-            .i_limit = 100.0f, /* 积分项上限 */
-            .out_limit = 100.0f, /* 输出绝对值限制 */
-            .d_cutoff_freq = -1.0f, /* D项低通截止频率 */
-            .range = -1.0f, /* 计算循环误差时使用，大于0时启用 */
+            .k = 5.0f,
+            .p = 20.0f,
+            .i = 1.0f,
+            .d = 0.0f,
+            .i_limit = 100.0f,
+            .out_limit = 100.0f,
+            .d_cutoff_freq = -1.0f,
+            .range = -1.0f,
         },
 
         .blance_pid_param = {
-            .k = 1.00f, /* 控制器增益 */
-            .p = 0.08f, /* 比例项增益 */
-            .i = 0.08f, /* 积分项增益 */
-            .d = 0.0f, /* 微分项增益 */
-            .i_limit = 0.05f, /* 积分项上限 */
-            .out_limit = 0.1f, /* 输出绝对值限制 */
-            .d_cutoff_freq = -1.0f, /* D项低通截止频率 */
-            .range = -1.0f, /* 计算循环误差时使用，大于0时启用 */
+            .k = 1.00f,
+            .p = 0.08f,
+            .i = 0.08f,
+            .d = 0.0f,
+            .i_limit = 0.05f,
+            .out_limit = 0.1f,
+            .d_cutoff_freq = -1.0f,
+            .range = -1.0f,
         },
         
         .low_pass_cutoff_freq = {
@@ -57,11 +59,13 @@ Config_t param_default = {
         },
 
         .mech_param = {
+            
             .length = {
                 .hip = 0.0861f,
                 .thigh = 0.20f,
                 .calf = 0.20f, 
             },
+
             .limit = {
                 .max = {
                     .named = {
@@ -79,6 +83,7 @@ Config_t param_default = {
                         .rr_calf = -1.2f,  /* 右后腿小腿最大角度，单位：弧度 */
                     }
                 },
+
                 .min = {
                     .named = {
                         .lf_hip = -0.50f,   /* 左前腿髋关节最大角度，单位：弧度 */
@@ -97,29 +102,26 @@ Config_t param_default = {
                 }
             },
 
-
             .zero_point = {
                 .named = {
                     .lf_hip = 0.02f,   /* 左前腿髋关节零点角度，单位：弧度 */
-                    .lf_thigh = -3.17f, /* 左前腿大腿零点角度，单位：弧度 */
-                    .lf_calf = 0.72f - JOINT_CALF_OFFSET,  /* 左前腿小腿零点角度，单位：弧度 */
+                    .lf_thigh = -4.90f, /* 左前腿大腿零点角度，单位：弧度 */
+                    .lf_calf = 0.9f - JOINT_CALF_OFFSET,  /* 左前腿小腿零点角度，单位：弧度 */
 
-                    .rf_hip = 5.37f,   /* 右前腿髋关节零点角度，单位：弧度 */
-                    .rf_thigh = 9.38f, /* 右前腿大腿零点角度，单位：弧度 */
-                    .rf_calf = 4.96f + JOINT_CALF_OFFSET,  /* 右前腿小腿零点角度，单位：弧度 */
+                    .rf_hip = 5.27f,   /* 右前腿髋关节零点角度，单位：弧度 */
+                    .rf_thigh = 9.443f, /* 右前腿大腿零点角度，单位：弧度 */
+                    .rf_calf = 6.02777243f + JOINT_CALF_OFFSET,  /* 右前腿小腿零点角度，单位：弧度 */
 
                     .lr_hip = 4.5f,   /* 左后腿髋关节零点角度，单位：弧度 */
                     .lr_thigh = -3.2f, /* 左后腿大腿零点角度，单位：弧度 */
-                    .lr_calf = 1.73f - JOINT_CALF_OFFSET,  /* 左后腿小腿零点角度，单位：弧度 */
+                    .lr_calf = 1.22f - JOINT_CALF_OFFSET,  /* 左后腿小腿零点角度，单位：弧度 */
 
-                    .rr_hip = 2.7f,   /* 右后腿髋关节零点角度，单位：弧度 */
-                    .rr_thigh = 10.58f, /* 右后腿大腿零点角度，单位：弧度 */
-                    .rr_calf = 3.58f + JOINT_CALF_OFFSET,  /* 右后腿小腿零点角度，单位：弧度 */
+                    .rr_hip = 2.55f,   /* 右后腿髋关节零点角度，单位：弧度 */
+                    .rr_thigh = 10.45f, /* 右后腿大腿零点角度，单位：弧度 */
+                    .rr_calf = 3.48f + JOINT_CALF_OFFSET,  /* 右后腿小腿零点角度，单位：弧度 */
                 }
             },
 
-
-
             .sign = {
                 .leg = {
                     [0] = { .hip = 1, .thigh = 1, .calf = -1 }, /* 左前腿 */
@@ -128,6 +130,7 @@ Config_t param_default = {
                     [3] = { .hip = 1, .thigh = -1, .calf = 1 },   /* 右后腿 */
                 }
             },
+
             .ratio = {
                 .named = {
                     .lf_hip = 6.33f,   /* 左前腿髋关节减速比 */
@@ -144,15 +147,13 @@ Config_t param_default = {
                     .rr_calf = 12.66f, /* 右后腿小腿减速比 */
                 }
             },
+
             .leg_offset = {
                 .x = 0.19625f, /* 腿偏移X轴，单位：米 */
                 .y = 0.0825f, /* 腿偏移Y轴，单位：米 */
                 .z = 0.0f, /* 腿偏移Z轴，单位：米 */
             }
-
         },
-
-
     },
 }; /* param_default */