/* ----------------------------------------------------------------------
 * Copyright (C) 2010 ARM Limited. All rights reserved.
 *
 * $Date:        15. July 2011
 * $Revision: 	V1.0.10
 *
 * Project: 	    CMSIS DSP Library
 * Title:	     arm_math.h
 *
 * Description:	 Public header file for CMSIS DSP Library
 *
 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
 *
 * Version 1.0.10 2011/7/15
 *    Big Endian support added and Merged M0 and M3/M4 Source code.
 *
 * Version 1.0.3 2010/11/29
 *    Re-organized the CMSIS folders and updated documentation.
 *
 * Version 1.0.2 2010/11/11
 *    Documentation updated.
 *
 * Version 1.0.1 2010/10/05
 *    Production release and review comments incorporated.
 *
 * Version 1.0.0 2010/09/20
 *    Production release and review comments incorporated.
 * -------------------------------------------------------------------- */

/**
   \mainpage CMSIS DSP Software Library
   *
   * <b>Introduction</b>
   *
   * This user manual describes the CMSIS DSP software library,
   * a suite of common signal processing functions for use on Cortex-M processor based devices.
   *
   * The library is divided into a number of modules each covering a specific category:
   * - Basic math functions
   * - Fast math functions
   * - Complex math functions
   * - Filters
   * - Matrix functions
   * - Transforms
   * - Motor control functions
   * - Statistical functions
   * - Support functions
   * - Interpolation functions
   *
   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
   * 32-bit integer and 32-bit floating-point values.
   *
   * <b>Processor Support</b>
   *
   * The library is completely written in C and is fully CMSIS compliant.
   * High performance is achieved through maximum use of Cortex-M4 intrinsics.
   *
   * The supplied library source code also builds and runs on the Cortex-M3 and Cortex-M0 processor,
   * with the DSP intrinsics being emulated through software.
   *
   *
   * <b>Toolchain Support</b>
   *
   * The library has been developed and tested with MDK-ARM version 4.21.
   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
   *
   * <b>Using the Library</b>
   *
   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
   * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
   * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
   * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
   * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
   * - arm_cortexM0l_math.lib (Little endian on Cortex-M0)
   * - arm_cortexM0b_math.lib (Big endian on Cortex-M3)
   *
   * 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-M4/M3/M0 with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
   * Define the appropriate pre processor MACRO ARM_MATH_CM4 or  ARM_MATH_CM3 or
   * ARM_MATH_CM0 depending on the target processor in the application.
   *
   * <b>Examples</b>
   *
   * The library ships with a number of examples which demonstrate how to use the library functions.
   *
   * <b>Building the Library</b>
   *
   * The library installer contains project files to re build libraries on MDK Tool chain in the <code>CMSIS\DSP_Lib\Source\ARM</code> folder.
   * - arm_cortexM0b_math.uvproj
   * - arm_cortexM0l_math.uvproj
   * - arm_cortexM3b_math.uvproj
   * - arm_cortexM3l_math.uvproj
   * - arm_cortexM4b_math.uvproj
   * - arm_cortexM4l_math.uvproj
   * - arm_cortexM4bf_math.uvproj
   * - arm_cortexM4lf_math.uvproj
   *
   * Each library project have differant pre-processor macros.
   *
   * <b>ARM_MATH_CMx:</b>
   * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
   * and ARM_MATH_CM0 for building library on cortex-M0 target.
   *
   * <b>ARM_MATH_BIG_ENDIAN:</b>
   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
   *
   * <b>ARM_MATH_MATRIX_CHECK:</b>
   * Define macro for checking on the input and output sizes of matrices
   *
   * <b>ARM_MATH_ROUNDING:</b>
   * Define macro for rounding on support functions
   *
   * <b>__FPU_PRESENT:</b>
   * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
   *
   *
   * The project can be built by opening the appropriate project in MDK-ARM 4.21 chain and defining the optional pre processor MACROs detailed above.
   *
   * <b>Copyright Notice</b>
   *
   * Copyright (C) 2010 ARM Limited. All rights reserved.
   */


/**
 * @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 the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
 * and <code>arm_mat_init_q15()</code> 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
 */
#ifndef _ARM_MATH_H
#define _ARM_MATH_H

#define __CMSIS_GENERIC              /* disable NVIC and Systick functions */

#if defined (ARM_MATH_CM4)
#include "core_cm4.h"
#elif defined (ARM_MATH_CM3)
#include "core_cm3.h"
#elif defined (ARM_MATH_CM0)
#include "core_cm0.h"
#else
#include "ARMCM4.h"
#warning "Define either ARM_MATH_CM4 OR ARM_MATH_CM3...By Default building on ARM_MATH_CM4....."
#endif

#undef  __CMSIS_GENERIC              /* enable NVIC and Systick functions */
//#include "string.h"
__intrinsic void __DSB(void);
#include "math.h"
#ifdef	__cplusplus
extern "C"
{
#endif


    /**
     * @brief Macros required for reciprocal calculation in Normalized LMS
     */

#define DELTA_Q31 			(0x100)
#define DELTA_Q15 			0x5
#define INDEX_MASK 			0x0000003F
#define PI					3.14159265358979f

    /**
     * @brief Macros required for SINE and COSINE Fast math approximations
     */

#define TABLE_SIZE			256
#define TABLE_SPACING_Q31	0x800000
#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 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,            /**< Generated by matrix inversion if the 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 definition to read/write two 16 bit values.
     */
#define __SIMD32(addr)  (*(int32_t **) & (addr))

#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)
    /**
     * @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)  )

#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 __INLINE 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 __INLINE 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 __INLINE 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 __INLINE 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 __INLINE q63_t mult32x64(
        q63_t x,
        q31_t y)
    {
        return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
                (((q63_t) (x >> 32) * y)));
    }


#if defined (ARM_MATH_CM0) && defined ( __CC_ARM   )
#define __CLZ __clz
#endif

#if defined (ARM_MATH_CM0) && ((defined (__ICCARM__)) ||(defined (__GNUC__)) || defined (__TASKING__) )

    static __INLINE  uint32_t __CLZ(q31_t data);


    static __INLINE uint32_t __CLZ(q31_t data)
    {
        uint32_t count = 0;
        uint32_t mask = 0x80000000;

        while((data & mask) ==  0)
        {
            count += 1u;
            mask = mask >> 1u;
        }

        return(count);

    }

#endif

    /**
     * @brief Function to Calculates 1/in(reciprocal) value of Q31 Data type.
     */

    static __INLINE uint32_t arm_recip_q31(
        q31_t in,
        q31_t *dst,
        q31_t *pRecipTable)
    {

        uint32_t out, tempVal;
        uint32_t index, i;
        uint32_t signBits;

        if(in > 0)
        {
            signBits = __CLZ(in) - 1;
        }
        else
        {
            signBits = __CLZ(-in) - 1;
        }

        /* Convert input sample to 1.31 format */
        in = in << signBits;

        /* calculation of index for initial approximated Val */
        index = (uint32_t) (in >> 24u);
        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 = (q31_t) (((q63_t) in * out) >> 31u);
            tempVal = 0x7FFFFFFF - tempVal;
            /*      1.31 with exp 1 */
            //out = (q31_t) (((q63_t) out * tempVal) >> 30u);
            out = (q31_t) clip_q63_to_q31(((q63_t) out * tempVal) >> 30u);
        }

        /* 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 __INLINE uint32_t arm_recip_q15(
        q15_t in,
        q15_t *dst,
        q15_t *pRecipTable)
    {

        uint32_t out = 0, tempVal = 0;
        uint32_t index = 0, i = 0;
        uint32_t signBits = 0;

        if(in > 0)
        {
            signBits = __CLZ(in) - 17;
        }
        else
        {
            signBits = __CLZ(-in) - 17;
        }

        /* Convert input sample to 1.15 format */
        in = in << signBits;

        /* calculation of index for initial approximated Val */
        index = 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 = 0; i < 2; i++)
        {
            tempVal = (q15_t) (((q31_t) in * out) >> 15);
            tempVal = 0x7FFF - tempVal;
            /*      1.15 with exp 1 */
            out = (q15_t) (((q31_t) out * tempVal) >> 14);
        }

        /* write output */
        *dst = out;

        /* return num of signbits of out = 1/in value */
        return (signBits + 1);

    }


    /*
     * @brief C custom defined intrinisic function for only M0 processors
     */
#if defined(ARM_MATH_CM0)

    static __INLINE q31_t __SSAT(
        q31_t x,
        uint32_t y)
    {
        int32_t posMax, negMin;
        uint32_t i;

        posMax = 1;
        for (i = 0; i < (y - 1); i++)
        {
            posMax = posMax * 2;
        }

        if(x > 0)
        {
            posMax = (posMax - 1);

            if(x > posMax)
            {
                x = posMax;
            }
        }
        else
        {
            negMin = -posMax;

            if(x < negMin)
            {
                x = negMin;
            }
        }
        return (x);


    }

#endif /* end of ARM_MATH_CM0 */



    /*
     * @brief C custom defined intrinsic function for M3 and M0 processors
     */
#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)

    /*
     * @brief C custom defined QADD8 for M3 and M0 processors
     */
    static __INLINE q31_t __QADD8(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q7_t r, s, t, u;

        r = (char) x;
        s = (char) y;

        r = __SSAT((q31_t) (r + s), 8);
        s = __SSAT(((q31_t) (((x << 16) >> 24) + ((y << 16) >> 24))), 8);
        t = __SSAT(((q31_t) (((x << 8) >> 24) + ((y << 8) >> 24))), 8);
        u = __SSAT(((q31_t) ((x >> 24) + (y >> 24))), 8);

        sum = (((q31_t) u << 24) & 0xFF000000) | (((q31_t) t << 16) & 0x00FF0000) |
              (((q31_t) s << 8) & 0x0000FF00) | (r & 0x000000FF);

        return sum;

    }

    /*
     * @brief C custom defined QSUB8 for M3 and M0 processors
     */
    static __INLINE q31_t __QSUB8(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s, t, u;

        r = (char) x;
        s = (char) y;

        r = __SSAT((r - s), 8);
        s = __SSAT(((q31_t) (((x << 16) >> 24) - ((y << 16) >> 24))), 8) << 8;
        t = __SSAT(((q31_t) (((x << 8) >> 24) - ((y << 8) >> 24))), 8) << 16;
        u = __SSAT(((q31_t) ((x >> 24) - (y >> 24))), 8) << 24;

        sum =
            (u & 0xFF000000) | (t & 0x00FF0000) | (s & 0x0000FF00) | (r & 0x000000FF);

        return sum;
    }

    /*
     * @brief C custom defined QADD16 for M3 and M0 processors
     */

    /*
     * @brief C custom defined QADD16 for M3 and M0 processors
     */
    static __INLINE q31_t __QADD16(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = __SSAT(r + s, 16);
        s = __SSAT(((q31_t) ((x >> 16) + (y >> 16))), 16) << 16;

        sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return sum;

    }

    /*
     * @brief C custom defined SHADD16 for M3 and M0 processors
     */
    static __INLINE q31_t __SHADD16(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = ((r >> 1) + (s >> 1));
        s = ((q31_t) ((x >> 17) + (y >> 17))) << 16;

        sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return sum;

    }

    /*
     * @brief C custom defined QSUB16 for M3 and M0 processors
     */
    static __INLINE q31_t __QSUB16(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = __SSAT(r - s, 16);
        s = __SSAT(((q31_t) ((x >> 16) - (y >> 16))), 16) << 16;

        sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return sum;
    }

    /*
     * @brief C custom defined SHSUB16 for M3 and M0 processors
     */
    static __INLINE q31_t __SHSUB16(
        q31_t x,
        q31_t y)
    {

        q31_t diff;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = ((r >> 1) - (s >> 1));
        s = (((x >> 17) - (y >> 17)) << 16);

        diff = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return diff;
    }

    /*
     * @brief C custom defined QASX for M3 and M0 processors
     */
    static __INLINE q31_t __QASX(
        q31_t x,
        q31_t y)
    {

        q31_t sum = 0;

        sum = ((sum + clip_q31_to_q15((q31_t) ((short) (x >> 16) + (short) y))) << 16) +
              clip_q31_to_q15((q31_t) ((short) x - (short) (y >> 16)));

        return sum;
    }

    /*
     * @brief C custom defined SHASX for M3 and M0 processors
     */
    static __INLINE q31_t __SHASX(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = ((r >> 1) - (y >> 17));
        s = (((x >> 17) + (s >> 1)) << 16);

        sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return sum;
    }


    /*
     * @brief C custom defined QSAX for M3 and M0 processors
     */
    static __INLINE q31_t __QSAX(
        q31_t x,
        q31_t y)
    {

        q31_t sum = 0;

        sum = ((sum + clip_q31_to_q15((q31_t) ((short) (x >> 16) - (short) y))) << 16) +
              clip_q31_to_q15((q31_t) ((short) x + (short) (y >> 16)));

        return sum;
    }

    /*
     * @brief C custom defined SHSAX for M3 and M0 processors
     */
    static __INLINE q31_t __SHSAX(
        q31_t x,
        q31_t y)
    {

        q31_t sum;
        q31_t r, s;

        r = (short) x;
        s = (short) y;

        r = ((r >> 1) + (y >> 17));
        s = (((x >> 17) - (s >> 1)) << 16);

        sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

        return sum;
    }

    /*
     * @brief C custom defined SMUSDX for M3 and M0 processors
     */
    static __INLINE q31_t __SMUSDX(
        q31_t x,
        q31_t y)
    {

        return ((q31_t)(((short) x * (short) (y >> 16)) -
                        ((short) (x >> 16) * (short) y)));
    }

    /*
     * @brief C custom defined SMUADX for M3 and M0 processors
     */
    static __INLINE q31_t __SMUADX(
        q31_t x,
        q31_t y)
    {

        return ((q31_t)(((short) x * (short) (y >> 16)) +
                        ((short) (x >> 16) * (short) y)));
    }

    /*
     * @brief C custom defined QADD for M3 and M0 processors
     */
    static __INLINE q31_t __QADD(
        q31_t x,
        q31_t y)
    {
        return clip_q63_to_q31((q63_t) x + y);
    }

    /*
     * @brief C custom defined QSUB for M3 and M0 processors
     */
    static __INLINE q31_t __QSUB(
        q31_t x,
        q31_t y)
    {
        return clip_q63_to_q31((q63_t) x - y);
    }

    /*
     * @brief C custom defined SMLAD for M3 and M0 processors
     */
    static __INLINE q31_t __SMLAD(
        q31_t x,
        q31_t y,
        q31_t sum)
    {

        return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
                ((short) x * (short) y));
    }

    /*
     * @brief C custom defined SMLADX for M3 and M0 processors
     */
    static __INLINE q31_t __SMLADX(
        q31_t x,
        q31_t y,
        q31_t sum)
    {

        return (sum + ((short) (x >> 16) * (short) (y)) +
                ((short) x * (short) (y >> 16)));
    }

    /*
     * @brief C custom defined SMLSDX for M3 and M0 processors
     */
    static __INLINE q31_t __SMLSDX(
        q31_t x,
        q31_t y,
        q31_t sum)
    {

        return (sum - ((short) (x >> 16) * (short) (y)) +
                ((short) x * (short) (y >> 16)));
    }

    /*
     * @brief C custom defined SMLALD for M3 and M0 processors
     */
    static __INLINE q63_t __SMLALD(
        q31_t x,
        q31_t y,
        q63_t sum)
    {

        return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
                ((short) x * (short) y));
    }

    /*
     * @brief C custom defined SMLALDX for M3 and M0 processors
     */
    static __INLINE q63_t __SMLALDX(
        q31_t x,
        q31_t y,
        q63_t sum)
    {

        return (sum + ((short) (x >> 16) * (short) y)) +
               ((short) x * (short) (y >> 16));
    }

    /*
     * @brief C custom defined SMUAD for M3 and M0 processors
     */
    static __INLINE q31_t __SMUAD(
        q31_t x,
        q31_t y)
    {

        return (((x >> 16) * (y >> 16)) +
                (((x << 16) >> 16) * ((y << 16) >> 16)));
    }

    /*
     * @brief C custom defined SMUSD for M3 and M0 processors
     */
    static __INLINE q31_t __SMUSD(
        q31_t x,
        q31_t y)
    {

        return (-((x >> 16) * (y >> 16)) +
                (((x << 16) >> 16) * ((y << 16) >> 16)));
    }




#endif /* (ARM_MATH_CM3) || defined (ARM_MATH_CM0) */


    /**
     * @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. */
        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. */
        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. */
        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. */
        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.
     * @return none.
     */
    void arm_fir_q7(
        const arm_fir_instance_q7 *S,
        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.
     * @return none
     */
    void arm_fir_init_q7(
        arm_fir_instance_q7 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */
    void arm_fir_q15(
        const arm_fir_instance_q15 *S,
        q15_t *pSrc,
        q15_t *pDst,
        uint32_t blockSize);

    /**
     * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
     * @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.
     * @return none.
     */
    void arm_fir_fast_q15(
        const arm_fir_instance_q15 *S,
        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 ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
     * <code>numTaps</code> is not a supported value.
     */

    arm_status arm_fir_init_q15(
        arm_fir_instance_q15 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */
    void arm_fir_q31(
        const arm_fir_instance_q31 *S,
        q31_t *pSrc,
        q31_t *pDst,
        uint32_t blockSize);

    /**
     * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
     * @param[in] *S points to an instance of the Q31 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.
     * @return none.
     */
    void arm_fir_fast_q31(
        const arm_fir_instance_q31 *S,
        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.
     * @return 		none.
     */
    void arm_fir_init_q31(
        arm_fir_instance_q31 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */
    void arm_fir_f32(
        const arm_fir_instance_f32 *S,
        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.
     * @return    	none.
     */
    void arm_fir_init_f32(
        arm_fir_instance_f32 *S,
        uint16_t numTaps,
        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. */
        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. */
        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. */
        float32_t *pCoeffs;         /**< Points to the array of coefficients.  The array is of length 5*numStages. */


    } arm_biquad_casd_df1_inst_f32;



    /**
     * @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.
     * @return     none.
     */

    void arm_biquad_cascade_df1_q15(
        const arm_biquad_casd_df1_inst_q15 *S,
        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
     * @return        none
     */

    void arm_biquad_cascade_df1_init_q15(
        arm_biquad_casd_df1_inst_q15 *S,
        uint8_t numStages,
        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.
     * @return     none.
     */

    void arm_biquad_cascade_df1_fast_q15(
        const arm_biquad_casd_df1_inst_q15 *S,
        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.
     * @return     none.
     */

    void arm_biquad_cascade_df1_q31(
        const arm_biquad_casd_df1_inst_q31 *S,
        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.
     * @return     none.
     */

    void arm_biquad_cascade_df1_fast_q31(
        const arm_biquad_casd_df1_inst_q31 *S,
        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
     * @return        none
     */

    void arm_biquad_cascade_df1_init_q31(
        arm_biquad_casd_df1_inst_q31 *S,
        uint8_t numStages,
        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.
     * @return     none.
     */

    void arm_biquad_cascade_df1_f32(
        const arm_biquad_casd_df1_inst_f32 *S,
        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]     *pState      points to the state buffer.
     * @return        none
     */

    void arm_biquad_cascade_df1_init_f32(
        arm_biquad_casd_df1_inst_f32 *S,
        uint8_t numStages,
        float32_t *pCoeffs,
        float32_t *pState);


    /**
     * @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 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 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
     * @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.
     * @return        none
     */

    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.
     * @return        none
     */

    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.
     * @return        none
     */

    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 . */
#ifdef ARM_MATH_CM0
        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.
     * @return none.
     */
    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
     * @return none
     */
    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.
     * @return none.
     */
    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
     * @return none
     */

    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.
     * @return none.
     */
    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
     * @return none
     */
    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;
        float32_t x1;
        float32_t 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
     * @return none.
     */

    void arm_mult_q7(
        q7_t *pSrcA,
        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
     * @return none.
     */

    void arm_mult_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_mult_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_mult_f32(
        float32_t *pSrcA,
        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. */
        q15_t     *pTwiddle;             /**< points to the twiddle factor table. */
        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;

    /**
     * @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. */
        q31_t       *pTwiddle;           /**< points to the twiddle factor table. */
        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;

    /**
     * @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. */
        float32_t    *pTwiddle;            /**< points to the twiddle factor table. */
        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;

    /**
     * @brief Processing function for the Q15 CFFT/CIFFT.
     * @param[in]      *S    points to an instance of the Q15 CFFT/CIFFT structure.
     * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
     * @return none.
     */

    void arm_cfft_radix4_q15(
        const arm_cfft_radix4_instance_q15 *S,
        q15_t *pSrc);

    /**
     * @brief Initialization function for the Q15 CFFT/CIFFT.
     * @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.
     * @param[in]     fftLen         length of the FFT.
     * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
     * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
     */

    arm_status arm_cfft_radix4_init_q15(
        arm_cfft_radix4_instance_q15 *S,
        uint16_t fftLen,
        uint8_t ifftFlag,
        uint8_t bitReverseFlag);

    /**
     * @brief Processing function for the Q31 CFFT/CIFFT.
     * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.
     * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
     * @return none.
     */

    void arm_cfft_radix4_q31(
        const arm_cfft_radix4_instance_q31 *S,
        q31_t *pSrc);

    /**
     * @brief  Initialization function for the Q31 CFFT/CIFFT.
     * @param[in,out] *S             points to an instance of the Q31 CFFT/CIFFT structure.
     * @param[in]     fftLen         length of the FFT.
     * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
     * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
     */

    arm_status arm_cfft_radix4_init_q31(
        arm_cfft_radix4_instance_q31 *S,
        uint16_t fftLen,
        uint8_t ifftFlag,
        uint8_t bitReverseFlag);

    /**
     * @brief Processing function for the floating-point CFFT/CIFFT.
     * @param[in]      *S    points to an instance of the floating-point CFFT/CIFFT structure.
     * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
     * @return none.
     */

    void arm_cfft_radix4_f32(
        const arm_cfft_radix4_instance_f32 *S,
        float32_t *pSrc);

    /**
     * @brief  Initialization function for the floating-point CFFT/CIFFT.
     * @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.
     * @param[in]     fftLen         length of the FFT.
     * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
     * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
     */

    arm_status arm_cfft_radix4_init_f32(
        arm_cfft_radix4_instance_f32 *S,
        uint16_t fftLen,
        uint8_t ifftFlag,
        uint8_t bitReverseFlag);



    /*----------------------------------------------------------------------
     *		Internal functions prototypes FFT function
     ----------------------------------------------------------------------*/

    /**
     * @brief  Core function for the floating-point CFFT butterfly process.
     * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef           points to the twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @return none.
     */

    void arm_radix4_butterfly_f32(
        float32_t *pSrc,
        uint16_t fftLen,
        float32_t *pCoef,
        uint16_t twidCoefModifier);

    /**
     * @brief  Core function for the floating-point CIFFT butterfly process.
     * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef           points to twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @param[in]      onebyfftLen      value of 1/fftLen.
     * @return none.
     */

    void arm_radix4_butterfly_inverse_f32(
        float32_t *pSrc,
        uint16_t fftLen,
        float32_t *pCoef,
        uint16_t twidCoefModifier,
        float32_t onebyfftLen);

    /**
     * @brief  In-place bit reversal function.
     * @param[in, out] *pSrc        points to the in-place buffer of floating-point data type.
     * @param[in]      fftSize      length of the FFT.
     * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
     * @param[in]      *pBitRevTab  points to the bit reversal table.
     * @return none.
     */

    void arm_bitreversal_f32(
        float32_t *pSrc,
        uint16_t fftSize,
        uint16_t bitRevFactor,
        uint16_t *pBitRevTab);

    /**
     * @brief  Core function for the Q31 CFFT butterfly process.
     * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef           points to twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @return none.
     */

    void arm_radix4_butterfly_q31(
        q31_t *pSrc,
        uint32_t fftLen,
        q31_t *pCoef,
        uint32_t twidCoefModifier);

    /**
     * @brief  Core function for the Q31 CIFFT butterfly process.
     * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef           points to twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @return none.
     */

    void arm_radix4_butterfly_inverse_q31(
        q31_t *pSrc,
        uint32_t fftLen,
        q31_t *pCoef,
        uint32_t twidCoefModifier);

    /**
     * @brief  In-place bit reversal function.
     * @param[in, out] *pSrc        points to the in-place buffer of Q31 data type.
     * @param[in]      fftLen       length of the FFT.
     * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
     * @param[in]      *pBitRevTab  points to bit reversal table.
     * @return none.
     */

    void arm_bitreversal_q31(
        q31_t *pSrc,
        uint32_t fftLen,
        uint16_t bitRevFactor,
        uint16_t *pBitRevTab);

    /**
     * @brief  Core function for the Q15 CFFT butterfly process.
     * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef16         points to twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @return none.
     */

    void arm_radix4_butterfly_q15(
        q15_t *pSrc16,
        uint32_t fftLen,
        q15_t *pCoef16,
        uint32_t twidCoefModifier);

    /**
     * @brief  Core function for the Q15 CIFFT butterfly process.
     * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
     * @param[in]      fftLen           length of the FFT.
     * @param[in]      *pCoef16         points to twiddle coefficient buffer.
     * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
     * @return none.
     */

    void arm_radix4_butterfly_inverse_q15(
        q15_t *pSrc16,
        uint32_t fftLen,
        q15_t *pCoef16,
        uint32_t twidCoefModifier);

    /**
     * @brief  In-place bit reversal function.
     * @param[in, out] *pSrc        points to the in-place buffer of Q15 data type.
     * @param[in]      fftLen       length of the FFT.
     * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
     * @param[in]      *pBitRevTab  points to bit reversal table.
     * @return none.
     */

    void arm_bitreversal_q15(
        q15_t *pSrc,
        uint32_t fftLen,
        uint16_t bitRevFactor,
        uint16_t *pBitRevTab);

    /**
     * @brief Instance structure for the Q15 RFFT/RIFFT function.
     */

    typedef struct
    {
        uint32_t fftLenReal;                      /**< length of the real FFT. */
        uint32_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. */
        q15_t    *pTwiddleAReal;                  /**< points to the real twiddle factor table. */
        q15_t    *pTwiddleBReal;                  /**< points to the imag twiddle factor table. */
        arm_cfft_radix4_instance_q15 *pCfft;	  /**< points to the complex FFT instance. */
    } arm_rfft_instance_q15;

    /**
     * @brief Instance structure for the Q31 RFFT/RIFFT function.
     */

    typedef struct
    {
        uint32_t fftLenReal;                        /**< length of the real FFT. */
        uint32_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. */
        q31_t    *pTwiddleAReal;                    /**< points to the real twiddle factor table. */
        q31_t    *pTwiddleBReal;                    /**< points to the imag twiddle factor table. */
        arm_cfft_radix4_instance_q31 *pCfft;        /**< points to the complex FFT instance. */
    } arm_rfft_instance_q31;

    /**
     * @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. */
        float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
        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;

    /**
     * @brief Processing function for the Q15 RFFT/RIFFT.
     * @param[in]  *S    points to an instance of the Q15 RFFT/RIFFT structure.
     * @param[in]  *pSrc points to the input buffer.
     * @param[out] *pDst points to the output buffer.
     * @return none.
     */

    void arm_rfft_q15(
        const arm_rfft_instance_q15 *S,
        q15_t *pSrc,
        q15_t *pDst);

    /**
     * @brief  Initialization function for the Q15 RFFT/RIFFT.
     * @param[in, out] *S             points to an instance of the Q15 RFFT/RIFFT structure.
     * @param[in]      *S_CFFT        points to an instance of the Q15 CFFT/CIFFT structure.
     * @param[in]      fftLenReal     length of the FFT.
     * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
     * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
     */

    arm_status arm_rfft_init_q15(
        arm_rfft_instance_q15 *S,
        arm_cfft_radix4_instance_q15 *S_CFFT,
        uint32_t fftLenReal,
        uint32_t ifftFlagR,
        uint32_t bitReverseFlag);

    /**
     * @brief Processing function for the Q31 RFFT/RIFFT.
     * @param[in]  *S    points to an instance of the Q31 RFFT/RIFFT structure.
     * @param[in]  *pSrc points to the input buffer.
     * @param[out] *pDst points to the output buffer.
     * @return none.
     */

    void arm_rfft_q31(
        const arm_rfft_instance_q31 *S,
        q31_t *pSrc,
        q31_t *pDst);

    /**
     * @brief  Initialization function for the Q31 RFFT/RIFFT.
     * @param[in, out] *S             points to an instance of the Q31 RFFT/RIFFT structure.
     * @param[in, out] *S_CFFT        points to an instance of the Q31 CFFT/CIFFT structure.
     * @param[in]      fftLenReal     length of the FFT.
     * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
     * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
     */

    arm_status arm_rfft_init_q31(
        arm_rfft_instance_q31 *S,
        arm_cfft_radix4_instance_q31 *S_CFFT,
        uint32_t fftLenReal,
        uint32_t ifftFlagR,
        uint32_t bitReverseFlag);

    /**
     * @brief  Initialization function for the floating-point RFFT/RIFFT.
     * @param[in,out] *S             points to an instance of the floating-point RFFT/RIFFT structure.
     * @param[in,out] *S_CFFT        points to an instance of the floating-point CFFT/CIFFT structure.
     * @param[in]     fftLenReal     length of the FFT.
     * @param[in]     ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
     * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
     * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
     */

    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);

    /**
     * @brief Processing function for the floating-point RFFT/RIFFT.
     * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure.
     * @param[in]  *pSrc points to the input buffer.
     * @param[out] *pDst points to the output buffer.
     * @return none.
     */

    void arm_rfft_f32(
        const arm_rfft_instance_f32 *S,
        float32_t *pSrc,
        float32_t *pDst);

    /**
     * @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. */
        float32_t *pTwiddle;                /**< points to the twiddle factor table. */
        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.
     * @return none.
     */

    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. */
        q31_t *pTwiddle;                    /**< points to the twiddle factor table. */
        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.
     * @return none.
     */

    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. */
        q15_t *pTwiddle;                    /**< points to the twiddle factor table. */
        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.
     * @return none.
     */

    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
     * @return none.
     */

    void arm_add_f32(
        float32_t *pSrcA,
        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
     * @return none.
     */

    void arm_add_q7(
        q7_t *pSrcA,
        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
     * @return none.
     */

    void arm_add_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_add_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_sub_f32(
        float32_t *pSrcA,
        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
     * @return none.
     */

    void arm_sub_q7(
        q7_t *pSrcA,
        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
     * @return none.
     */

    void arm_sub_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_sub_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_scale_f32(
        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
     * @return none.
     */

    void arm_scale_q7(
        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
     * @return none.
     */

    void arm_scale_q15(
        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
     * @return none.
     */

    void arm_scale_q31(
        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
     * @return none.
     */

    void arm_abs_q7(
        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
     * @return none.
     */

    void arm_abs_f32(
        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
     * @return none.
     */

    void arm_abs_q15(
        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
     * @return none.
     */

    void arm_abs_q31(
        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
     * @return none.
     */

    void arm_dot_prod_f32(
        float32_t *pSrcA,
        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
     * @return none.
     */

    void arm_dot_prod_q7(
        q7_t *pSrcA,
        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
     * @return none.
     */

    void arm_dot_prod_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_dot_prod_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_shift_q7(
        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
     * @return none.
     */

    void arm_shift_q15(
        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
     * @return none.
     */

    void arm_shift_q31(
        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
     * @return none.
     */

    void arm_offset_f32(
        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
     * @return none.
     */

    void arm_offset_q7(
        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
     * @return none.
     */

    void arm_offset_q15(
        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
     * @return none.
     */

    void arm_offset_q31(
        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
     * @return none.
     */

    void arm_negate_f32(
        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
     * @return none.
     */

    void arm_negate_q7(
        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
     * @return none.
     */

    void arm_negate_q15(
        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
     * @return none.
     */

    void arm_negate_q31(
        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
     * @return none.
     */
    void arm_copy_f32(
        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
     * @return none.
     */
    void arm_copy_q7(
        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
     * @return none.
     */
    void arm_copy_q15(
        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
     * @return none.
     */
    void arm_copy_q31(
        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
     * @return none.
     */
    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
     * @return none.
     */
    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
     * @return none.
     */
    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
     * @return none.
     */
    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.
     * @return none.
     */

    void arm_conv_f32(
        float32_t *pSrcA,
        uint32_t srcALen,
        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 location where the output result is written.  Length srcALen+srcBLen-1.
     * @return none.
     */

    void arm_conv_q15(
        q15_t *pSrcA,
        uint32_t srcALen,
        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.
     * @return none.
     */

    void arm_conv_fast_q15(
        q15_t *pSrcA,
        uint32_t srcALen,
        q15_t *pSrcB,
        uint32_t srcBLen,
        q15_t *pDst);

    /**
     * @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.
     * @return none.
     */

    void arm_conv_q31(
        q31_t *pSrcA,
        uint32_t srcALen,
        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.
     * @return none.
     */

    void arm_conv_fast_q31(
        q31_t *pSrcA,
        uint32_t srcALen,
        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.
     * @return none.
     */

    void arm_conv_q7(
        q7_t *pSrcA,
        uint32_t srcALen,
        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(
        float32_t *pSrcA,
        uint32_t srcALen,
        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.
     * @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(
        q15_t *pSrcA,
        uint32_t srcALen,
        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(
        q15_t *pSrcA,
        uint32_t srcALen,
        q15_t *pSrcB,
        uint32_t srcBLen,
        q15_t *pDst,
        uint32_t firstIndex,
        uint32_t numPoints);

    /**
     * @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(
        q31_t *pSrcA,
        uint32_t srcALen,
        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(
        q31_t *pSrcA,
        uint32_t srcALen,
        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.
     * @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(
        q7_t *pSrcA,
        uint32_t srcALen,
        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. */
        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. */
        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 the floating-point FIR decimator.
     */

    typedef struct
    {
        uint8_t M;                          /**< decimation factor. */
        uint16_t numTaps;                   /**< number of coefficients in the filter. */
        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 the 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 input samples to process per call.
     * @return none
     */

    void arm_fir_decimate_f32(
        const arm_fir_decimate_instance_f32 *S,
        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    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_f32(
        arm_fir_decimate_instance_f32 *S,
        uint16_t numTaps,
        uint8_t M,
        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.
     * @return none
     */

    void arm_fir_decimate_q15(
        const arm_fir_decimate_instance_q15 *S,
        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.
     * @return none
     */

    void arm_fir_decimate_fast_q15(
        const arm_fir_decimate_instance_q15 *S,
        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,
        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.
     * @return none
     */

    void arm_fir_decimate_q31(
        const arm_fir_decimate_instance_q31 *S,
        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.
     * @return none
     */

    void arm_fir_decimate_fast_q31(
        arm_fir_decimate_instance_q31 *S,
        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,
        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. */
        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. */
        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. */
        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.
     * @return none.
     */

    void arm_fir_interpolate_q15(
        const arm_fir_interpolate_instance_q15 *S,
        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,
        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.
     * @return none.
     */

    void arm_fir_interpolate_q31(
        const arm_fir_interpolate_instance_q31 *S,
        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,
        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.
     * @return none.
     */

    void arm_fir_interpolate_f32(
        const arm_fir_interpolate_instance_f32 *S,
        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,
        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. */
        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.
     * @return none.
     */

    void arm_biquad_cas_df1_32x64_q31(
        const arm_biquad_cas_df1_32x64_ins_q31 *S,
        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
     * @return        none
     */

    void arm_biquad_cas_df1_32x64_init_q31(
        arm_biquad_cas_df1_32x64_ins_q31 *S,
        uint8_t numStages,
        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. */
        float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
    } arm_biquad_cascade_df2T_instance_f32;


    /**
     * @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.
     * @return none.
     */

    void arm_biquad_cascade_df2T_f32(
        const arm_biquad_cascade_df2T_instance_f32 *S,
        float32_t *pSrc,
        float32_t *pDst,
        uint32_t blockSize);


    /**
     * @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.
     * @return        none
     */

    void arm_biquad_cascade_df2T_init_f32(
        arm_biquad_cascade_df2T_instance_f32 *S,
        uint8_t numStages,
        float32_t *pCoeffs,
        float32_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. */
        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. */
        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. */
        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.
     * @return none.
     */

    void arm_fir_lattice_init_q15(
        arm_fir_lattice_instance_q15 *S,
        uint16_t numStages,
        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.
     * @return none.
     */
    void arm_fir_lattice_q15(
        const arm_fir_lattice_instance_q15 *S,
        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.
     * @return none.
     */

    void arm_fir_lattice_init_q31(
        arm_fir_lattice_instance_q31 *S,
        uint16_t numStages,
        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.
     * @return none.
     */

    void arm_fir_lattice_q31(
        const arm_fir_lattice_instance_q31 *S,
        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.
     * @return none.
     */

    void arm_fir_lattice_init_f32(
        arm_fir_lattice_instance_f32 *S,
        uint16_t numStages,
        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.
     * @return none.
     */

    void arm_fir_lattice_f32(
        const arm_fir_lattice_instance_f32 *S,
        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.
     * @return none.
     */

    void arm_iir_lattice_f32(
        const arm_iir_lattice_instance_f32 *S,
        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.
     * @return none.
     */

    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.
     * @return none.
     */

    void arm_iir_lattice_q31(
        const arm_iir_lattice_instance_q31 *S,
        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.
     * @return none.
     */

    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.
     * @return none.
     */

    void arm_iir_lattice_q15(
        const arm_iir_lattice_instance_q15 *S,
        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.
     * @return none.
     */

    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.
     * @return     none.
     */

    void arm_lms_f32(
        const arm_lms_instance_f32 *S,
        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.
     * @return none.
     */

    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.
     * @return    none.
     */

    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.
     * @return none.
     */

    void arm_lms_q15(
        const arm_lms_instance_q15 *S,
        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.
     * @return     none.
     */

    void arm_lms_q31(
        const arm_lms_instance_q31 *S,
        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.
     * @return none.
     */

    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.
     * @return none.
     */

    void arm_lms_norm_f32(
        arm_lms_norm_instance_f32 *S,
        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.
     * @return none.
     */

    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. */
        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.
     * @return none.
     */

    void arm_lms_norm_q31(
        arm_lms_norm_instance_q31 *S,
        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.
     * @return none.
     */

    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. */
        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.
     * @return none.
     */

    void arm_lms_norm_q15(
        arm_lms_norm_instance_q15 *S,
        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.
     * @return none.
     */

    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.
     * @return none.
     */

    void arm_correlate_f32(
        float32_t *pSrcA,
        uint32_t srcALen,
        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.
     * @return none.
     */

    void arm_correlate_q15(
        q15_t *pSrcA,
        uint32_t srcALen,
        q15_t *pSrcB,
        uint32_t srcBLen,
        q15_t *pDst);

    /**
     * @brief Correlation 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 2 * max(srcALen, srcBLen) - 1.
     * @return none.
     */

    void arm_correlate_fast_q15(
        q15_t *pSrcA,
        uint32_t srcALen,
        q15_t *pSrcB,
        uint32_t srcBLen,
        q15_t *pDst);

    /**
     * @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.
     * @return none.
     */

    void arm_correlate_q31(
        q31_t *pSrcA,
        uint32_t srcALen,
        q31_t *pSrcB,
        uint32_t srcBLen,
        q31_t *pDst);

    /**
     * @brief Correlation 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 2 * max(srcALen, srcBLen) - 1.
     * @return none.
     */

    void arm_correlate_fast_q31(
        q31_t *pSrcA,
        uint32_t srcALen,
        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.
     * @return none.
     */

    void arm_correlate_q7(
        q7_t *pSrcA,
        uint32_t srcALen,
        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. */
        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. */
        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. */
        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. */
        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.
     * @return none.
     */

    void arm_fir_sparse_f32(
        arm_fir_sparse_instance_f32 *S,
        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.
     * @return none
     */

    void arm_fir_sparse_init_f32(
        arm_fir_sparse_instance_f32 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */

    void arm_fir_sparse_q31(
        arm_fir_sparse_instance_q31 *S,
        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.
     * @return none
     */

    void arm_fir_sparse_init_q31(
        arm_fir_sparse_instance_q31 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */

    void arm_fir_sparse_q15(
        arm_fir_sparse_instance_q15 *S,
        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.
     * @return none
     */

    void arm_fir_sparse_init_q15(
        arm_fir_sparse_instance_q15 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */

    void arm_fir_sparse_q7(
        arm_fir_sparse_instance_q7 *S,
        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.
     * @return none
     */

    void arm_fir_sparse_init_q7(
        arm_fir_sparse_instance_q7 *S,
        uint16_t numTaps,
        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.
     * @return none.
     */

    void arm_sin_cos_f32(
        float32_t theta,
        float32_t *pSinVal,
        float32_t *pCcosVal);

    /*
     * @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.
     * @return none.
     */

    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
     * @return none.
     */

    void arm_cmplx_conj_f32(
        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
     * @return none.
     */

    void arm_cmplx_conj_q31(
        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
     * @return none.
     */

    void arm_cmplx_conj_q15(
        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
     * @return none.
     */

    void arm_cmplx_mag_squared_f32(
        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
     * @return none.
     */

    void arm_cmplx_mag_squared_q31(
        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
     * @return none.
     */

    void arm_cmplx_mag_squared_q15(
        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 out processed output sample.
     */


    static __INLINE 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 out processed output sample.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE 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 out processed output sample.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE q15_t arm_pid_q15(
        arm_pid_instance_q15 *S,
        q15_t in)
    {
        q63_t acc;
        q15_t out;

        /* Implementation of PID controller */

#ifdef ARM_MATH_CM0

        /* acc = A0 * x[n]  */
        acc = ((q31_t) S->A0 ) * in ;

#else

        /* acc = A0 * x[n]  */
        acc = (q31_t) __SMUAD(S->A0, in);

#endif

#ifdef ARM_MATH_CM0

        /* 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] ;

#else

        /* acc += A1 * x[n-1] + A2 * x[n-2]  */
        acc = __SMLALD(S->A1, (q31_t)__SIMD32(S->state), acc);

#endif

        /* acc += y[n-1] */
        acc += (q31_t) S->state[2] << 15;

        /* saturate the output */
        out = (q15_t) (__SSAT((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);



    /**
     * @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 __INLINE 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.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE 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
     */

    /**
     * @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
     * @return none.
     */
    void arm_q7_to_q31(
        q7_t *pSrc,
        q31_t *pDst,
        uint32_t blockSize);




    /**
     * @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 __INLINE 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 = -0.5 * Ialpha + (float32_t) 0.8660254039 * 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.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE 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
     */

    /**
     * @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
     * @return none.
     */
    void arm_q7_to_q15(
        q7_t *pSrc,
        q15_t *pDst,
        uint32_t blockSize);



    /**
     * @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 __INLINE 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.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE 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
     */

    /**
     * @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
     * @return none.
     */
    void arm_q7_to_float(
        q7_t *pSrc,
        float32_t *pDst,
        uint32_t blockSize);


    /**
     * @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 __INLINE 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.
     *
     * <b>Scaling and Overflow Behavior:</b>
     * \par
     * 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 __INLINE 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
     */


    /**
     * @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
     * @return none.
     */
    void arm_q31_to_float(
        q31_t *pSrc,
        float32_t *pDst,
        uint32_t blockSize);

    /**
     * @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 __INLINE 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(i >= S->nValues)
        {
            /* 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 __INLINE 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 & 0xFFF00000) >> 20);

        if(index >= (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 + 1u];

            /* 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 __INLINE 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 & 0xFFF00000) >> 20u);

        if(index >= (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 + 1u];

            /* 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 (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 __INLINE 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 */
        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 & 0xFFF00000) >> 20u);


        if(index >= (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 and are in 1.7(q7) format */
            y0 = pYData[index];
            y1 = pYData[index + 1u];

            /* 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 (y >> 20u);

        }

    }
    /**
     * @} 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);


    /**
     * @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 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.
     */

    static __INLINE arm_status  arm_sqrt_f32(
        float32_t in, float32_t *pOut)
    {
        if(in > 0)
        {

            //	#if __FPU_USED
#if (__FPU_USED == 1) && defined ( __CC_ARM   )
            *pOut = __sqrtf(in);
#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 square root of input value.
     * @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.
     */
    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  square root of input value.
     * @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.
     */
    arm_status arm_sqrt_q15(
        q15_t in, q15_t *pOut);

    /**
     * @} end of SQRT group
     */






    /**
     * @brief floating-point Circular write function.
     */

    static __INLINE 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 = wOffset;
    }



    /**
     * @brief floating-point Circular Read function.
     */
    static __INLINE 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, 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 = (int32_t) (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 == (int32_t *) 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 __INLINE 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 = wOffset;
    }



    /**
     * @brief Q15 Circular Read function.
     */
    static __INLINE 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, 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 = (int32_t) (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 == (q15_t *) 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 __INLINE 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 = wOffset;
    }



    /**
     * @brief Q7 Circular Read function.
     */
    static __INLINE 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, 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 = (int32_t) (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 == (q7_t *) 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.
     * @return none.
     */

    void arm_power_q31(
        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.
     * @return none.
     */

    void arm_power_f32(
        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.
     * @return none.
     */

    void arm_power_q15(
        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.
     * @return none.
     */

    void arm_power_q7(
        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.
     * @return none.
     */

    void arm_mean_q7(
        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.
     * @return none.
     */
    void arm_mean_q15(
        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.
     * @return none.
     */
    void arm_mean_q31(
        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.
     * @return none.
     */
    void arm_mean_f32(
        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.
     * @return none.
     */

    void arm_var_f32(
        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.
     * @return none.
     */

    void arm_var_q31(
        q31_t *pSrc,
        uint32_t blockSize,
        q63_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.
     * @return none.
     */

    void arm_var_q15(
        q15_t *pSrc,
        uint32_t blockSize,
        q31_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.
     * @return none.
     */

    void arm_rms_f32(
        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.
     * @return none.
     */

    void arm_rms_q31(
        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.
     * @return none.
     */

    void arm_rms_q15(
        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.
     * @return none.
     */

    void arm_std_f32(
        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.
     * @return none.
     */

    void arm_std_q31(
        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.
     * @return none.
     */

    void arm_std_q15(
        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
     * @return none.
     */

    void arm_cmplx_mag_f32(
        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
     * @return none.
     */

    void arm_cmplx_mag_q31(
        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
     * @return none.
     */

    void arm_cmplx_mag_q15(
        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
     * @return none.
     */

    void arm_cmplx_dot_prod_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_cmplx_dot_prod_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_cmplx_dot_prod_f32(
        float32_t *pSrcA,
        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
     * @return none.
     */

    void arm_cmplx_mult_real_q15(
        q15_t *pSrcCmplx,
        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
     * @return none.
     */

    void arm_cmplx_mult_real_q31(
        q31_t *pSrcCmplx,
        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
     * @return none.
     */

    void arm_cmplx_mult_real_f32(
        float32_t *pSrcCmplx,
        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.
     * @return none.
     */

    void arm_min_q7(
        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.
     * @return none.
     */

    void arm_min_q15(
        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.
     * @return none.
     */
    void arm_min_q31(
        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.
     * @return none.
     */

    void arm_min_f32(
        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
     * @return none.
     */

    void arm_max_q7(
        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
     * @return none.
     */

    void arm_max_q15(
        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
     * @return none.
     */

    void arm_max_q31(
        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
     * @return none.
     */

    void arm_max_f32(
        float32_t *pSrc,
        uint32_t blockSize,
        float32_t *pResult,
        uint32_t *pIndex);

    /**
     * @brief  Q15 complex-by-complex multiplication
     * @param[in]  *pSrcA points to the first input vector
     * @param[in]  *pSrcB points to the second input vector
     * @param[out]  *pDst  points to the output vector
     * @param[in]  numSamples number of complex samples in each vector
     * @return none.
     */

    void arm_cmplx_mult_cmplx_q15(
        q15_t *pSrcA,
        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
     * @return none.
     */

    void arm_cmplx_mult_cmplx_q31(
        q31_t *pSrcA,
        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
     * @return none.
     */

    void arm_cmplx_mult_cmplx_f32(
        float32_t *pSrcA,
        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
     * @return none.
     */
    void arm_float_to_q31(
        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
     * @return          none
     */
    void arm_float_to_q15(
        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
     * @return          none
     */
    void arm_float_to_q7(
        float32_t *pSrc,
        q7_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
     * @return none.
     */
    void arm_q31_to_q15(
        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
     * @return none.
     */
    void arm_q31_to_q7(
        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
     * @return none.
     */
    void arm_q15_to_float(
        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
     * @return none.
     */
    void arm_q15_to_q31(
        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
     * @return none.
     */
    void arm_q15_to_q7(
        q15_t *pSrc,
        q7_t *pDst,
        uint32_t blockSize);


    /**
     * @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 __INLINE 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->numRows - 1) || yIndex < 0  || yIndex > ( S->numCols - 1))
        {
            return(0);
        }

        /* Calculation of index for two nearest points in X-direction */
        index = (xIndex - 1) + (yIndex - 1) *  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 - 1) + (yIndex) * 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 __INLINE 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 & 0xFFF00000) >> 20u);

        /* Input is in 12.20 format */
        /* 12 bits for the table index */
        /* Index value calculation */
        cI = ((Y & 0xFFF00000) >> 20u);

        /* Care taken for table outside boundary */
        /* Returns zero output when values are outside table boundary */
        if(rI < 0 || rI > (S->numRows - 1) || cI < 0  || cI > ( S->numCols - 1))
        {
            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) + nCols * (cI)];
        x2 = pYData[(rI) + nCols * (cI) + 1u];

        /* 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) + nCols * (cI + 1)];
        y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

        /* 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 (acc << 2u);

    }

    /**
    * @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 __INLINE 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 & 0xFFF00000) >> 20);

        /* Input is in 12.20 format */
        /* 12 bits for the table index */
        /* Index value calculation */
        cI = ((Y & 0xFFF00000) >> 20);

        /* Care taken for table outside boundary */
        /* Returns zero output when values are outside table boundary */
        if(rI < 0 || rI > (S->numRows - 1) || cI < 0  || cI > ( S->numCols - 1))
        {
            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[(rI) + nCols * (cI)];
        x2 = pYData[(rI) + nCols * (cI) + 1u];


        /* 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[(rI) + nCols * (cI + 1)];
        y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

        /* 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 * (0xFFFFF - xfract)) >> 4u);
        acc = ((q63_t) out * (0xFFFFF - yfract));

        /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
        out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
        acc += ((q63_t) out * (xfract));

        /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
        out = (q31_t) (((q63_t) y1 * (0xFFFFF - 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 (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 __INLINE 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 & 0xFFF00000) >> 20);

        /* Input is in 12.20 format */
        /* 12 bits for the table index */
        /* Index value calculation */
        cI = ((Y & 0xFFF00000) >> 20);

        /* Care taken for table outside boundary */
        /* Returns zero output when values are outside table boundary */
        if(rI < 0 || rI > (S->numRows - 1) || cI < 0  || cI > ( S->numCols - 1))
        {
            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[(rI) + nCols * (cI)];
        x2 = pYData[(rI) + nCols * (cI) + 1u];


        /* 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[(rI) + nCols * (cI + 1)];
        y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

        /* 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 (acc >> 40);

    }

    /**
     * @} end of BilinearInterpolate group
     */






#ifdef	__cplusplus
}
#endif


#endif /* _ARM_MATH_H */


/**
 *
 * End of file.
 */
