FreeRTOS/Demo/CORTEX_M0+_Atmel_SAMD20_XPlained/RTOSDemo/src/ASF/thirdparty/CMSIS/Include/arm_math.h

/* ----------------------------------------------------------------------
 * Copyright (C) 2010-2011 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"
    #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 ( __TASKING__ )
/* No need to redefine __CLZ */
#endif

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

  __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;           /**< nValues */
    float32_t x1;               /**< x1 */
    float32_t xSpacing;         /**< xSpacing */
    float32_t *pYData;          /**< pointer to the table of Y values */
  } arm_linear_interp_instance_f32;

  /**
   * @brief Instance structure for the floating-point bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;	/**< number of rows in the data table. */
    uint16_t numCols;	/**< number of columns in the data table. */
    float32_t *pData;	/**< points to the data table. */
  } arm_bilinear_interp_instance_f32;

   /**
   * @brief Instance structure for the Q31 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;	/**< number of rows in the data table. */
    uint16_t numCols;	/**< number of columns in the data table. */
    q31_t *pData;	/**< points to the data table. */
  } arm_bilinear_interp_instance_q31;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;	/**< number of rows in the data table. */
    uint16_t numCols;	/**< number of columns in the data table. */
    q15_t *pData;	/**< points to the data table. */
  } arm_bilinear_interp_instance_q15;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows; 	/**< number of rows in the data table. */
    uint16_t numCols;	/**< number of columns in the data table. */
    q7_t *pData;		/**< points to the data table. */
  } arm_bilinear_interp_instance_q7;


  /**
   * @brief Q7 vector multiplication.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst  points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @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.
   */