arm_math.h

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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date:        12. March 2014
* $Revision:    V1.4.4
*
* Project:          CMSIS DSP Library
* Title:            arm_math.h
*
* Description:  Public header file for CMSIS DSP Library
*
* Target Processor: Cortex-M7/Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
 * -------------------------------------------------------------------- */

#ifndef _ARM_MATH_H
#define _ARM_MATH_H

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

#if defined(ARM_MATH_CM7)
  #include "core_cm7.h"
#elif 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"
#define ARM_MATH_CM0_FAMILY
  #elif defined (ARM_MATH_CM0PLUS)
#include "core_cm0plus.h"
  #define ARM_MATH_CM0_FAMILY
#else
  #error "Define according the used Cortex core ARM_MATH_CM7, ARM_MATH_CM4, ARM_MATH_CM3, ARM_MATH_CM0PLUS or ARM_MATH_CM0"
#endif

#undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
#include "string.h"
#include "math.h"
#ifdef  __cplusplus
extern "C"
{
#endif


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

#define FAST_MATH_TABLE_SIZE  512
#define FAST_MATH_Q31_SHIFT   (32 - 10)
#define FAST_MATH_Q15_SHIFT   (16 - 10)
#define CONTROLLER_Q31_SHIFT  (32 - 9)
#define TABLE_SIZE  256
#define TABLE_SPACING_Q31          0x400000
#define TABLE_SPACING_Q15          0x80

  /* 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

#ifndef UNALIGNED_SUPPORT_DISABLE
    #define ALIGN4
#else
  #if defined  (__GNUC__)
    #define ALIGN4 __attribute__((aligned(4)))
  #else
    #define ALIGN4 __align(4)
  #endif
#endif  /*      #ifndef UNALIGNED_SUPPORT_DISABLE       */

  typedef enum
  {
    ARM_MATH_SUCCESS = 0,                
    ARM_MATH_ARGUMENT_ERROR = -1,        
    ARM_MATH_LENGTH_ERROR = -2,          
    ARM_MATH_SIZE_MISMATCH = -3,         
    ARM_MATH_NANINF = -4,                
    ARM_MATH_SINGULAR = -5,              
    ARM_MATH_TEST_FAILURE = -6           
  } arm_status;

  typedef int8_t q7_t;

  typedef int16_t q15_t;

  typedef int32_t q31_t;

  typedef int64_t q63_t;

  typedef float float32_t;

  typedef double float64_t;

#if defined __CC_ARM
#define __SIMD32_TYPE int32_t __packed
#define CMSIS_UNUSED __attribute__((unused))
#elif defined __ICCARM__
#define CMSIS_UNUSED
#define __SIMD32_TYPE int32_t __packed
#elif defined __GNUC__
#define __SIMD32_TYPE int32_t
#define CMSIS_UNUSED __attribute__((unused))
#elif defined __CSMC__                  /* Cosmic */
#define CMSIS_UNUSED
#define __SIMD32_TYPE int32_t
#else
#error Unknown compiler
#endif

#define __SIMD32(addr)  (*(__SIMD32_TYPE **) & (addr))
#define __SIMD32_CONST(addr)  ((__SIMD32_TYPE *)(addr))

#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE *)  (addr))

#define __SIMD64(addr)  (*(int64_t **) & (addr))

#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)

#define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
                                         (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
#define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
                                         (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )

#endif


#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


  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;
  }

  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);
  }

  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;
  }

  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;
  }

  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_FAMILY) && defined ( __CC_ARM   )
#define __CLZ __clz
#endif

#if defined (ARM_MATH_CM0_FAMILY) && ((defined (__ICCARM__)) ||(defined (__GNUC__)) || defined (__TASKING__) )

  static __INLINE uint32_t __CLZ(
  q31_t data);


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

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

    return (count);

  }

#endif

  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);

  }

  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_FAMILY)

  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_FAMILY */



  /*
   * @brief C custom defined intrinsic function for M3 and M0 processors
   */
#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)

  /*
   * @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 = (q7_t) x;
    s = (q7_t) 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 = (q7_t) x;
    s = (q7_t) 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 = (q15_t) x;
    s = (q15_t) 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 = (q15_t) x;
    s = (q15_t) 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 = (q15_t) x;
    s = (q15_t) 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 = (q15_t) x;
    s = (q15_t) 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) ((q15_t) (x >> 16) + (q15_t) y))) << 16) +
      clip_q31_to_q15((q31_t) ((q15_t) x - (q15_t) (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 = (q15_t) x;
    s = (q15_t) 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) ((q15_t) (x >> 16) - (q15_t) y))) << 16) +
      clip_q31_to_q15((q31_t) ((q15_t) x + (q15_t) (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 = (q15_t) x;
    s = (q15_t) 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) (((q15_t) x * (q15_t) (y >> 16)) -
                     ((q15_t) (x >> 16) * (q15_t) 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) (((q15_t) x * (q15_t) (y >> 16)) +
                     ((q15_t) (x >> 16) * (q15_t) 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 + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
            ((q15_t) x * (q15_t) 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 + ((q15_t) (x >> 16) * (q15_t) (y)) +
            ((q15_t) x * (q15_t) (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 - ((q15_t) (x >> 16) * (q15_t) (y)) +
            ((q15_t) x * (q15_t) (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 + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
            ((q15_t) x * (q15_t) 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 + ((q15_t) (x >> 16) * (q15_t) y)) +
      ((q15_t) x * (q15_t) (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)));
  }


  /*
   * @brief C custom defined SXTB16 for M3 and M0 processors
   */
  static __INLINE q31_t __SXTB16(
  q31_t x)
  {

    return ((((x << 24) >> 24) & 0x0000FFFF) |
            (((x << 8) >> 8) & 0xFFFF0000));
  }


#endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY) */


  typedef struct
  {
    uint16_t numTaps;        
    q7_t *pState;            
    q7_t *pCoeffs;           
  } arm_fir_instance_q7;

  typedef struct
  {
    uint16_t numTaps;         
    q15_t *pState;            
    q15_t *pCoeffs;           
  } arm_fir_instance_q15;

  typedef struct
  {
    uint16_t numTaps;         
    q31_t *pState;            
    q31_t *pCoeffs;           
  } arm_fir_instance_q31;

  typedef struct
  {
    uint16_t numTaps;     
    float32_t *pState;    
    float32_t *pCoeffs;   
  } arm_fir_instance_f32;


  void arm_fir_q7(
  const arm_fir_instance_q7 * S,
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  void arm_fir_init_q7(
  arm_fir_instance_q7 * S,
  uint16_t numTaps,
  q7_t * pCoeffs,
  q7_t * pState,
  uint32_t blockSize);


  void arm_fir_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_fir_fast_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  arm_status arm_fir_init_q15(
  arm_fir_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  void arm_fir_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_fir_fast_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_fir_init_q31(
  arm_fir_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);

  void arm_fir_f32(
  const arm_fir_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_fir_init_f32(
  arm_fir_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  typedef struct
  {
    int8_t numStages;         
    q15_t *pState;            
    q15_t *pCoeffs;           
    int8_t postShift;         
  } arm_biquad_casd_df1_inst_q15;


  typedef struct
  {
    uint32_t numStages;      
    q31_t *pState;           
    q31_t *pCoeffs;          
    uint8_t postShift;       
  } arm_biquad_casd_df1_inst_q31;

  typedef struct
  {
    uint32_t numStages;         
    float32_t *pState;          
    float32_t *pCoeffs;         
  } arm_biquad_casd_df1_inst_f32;



  void arm_biquad_cascade_df1_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  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);


  void arm_biquad_cascade_df1_fast_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  void arm_biquad_cascade_df1_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_biquad_cascade_df1_fast_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  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);

  void arm_biquad_cascade_df1_f32(
  const arm_biquad_casd_df1_inst_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

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


  typedef struct
  {
    uint16_t numRows;     
    uint16_t numCols;     
    float32_t *pData;     
  } arm_matrix_instance_f32;


  typedef struct
  {
    uint16_t numRows;     
    uint16_t numCols;     
    float64_t *pData;     
  } arm_matrix_instance_f64;

  typedef struct
  {
    uint16_t numRows;     
    uint16_t numCols;     
    q15_t *pData;         
  } arm_matrix_instance_q15;

  typedef struct
  {
    uint16_t numRows;     
    uint16_t numCols;     
    q31_t *pData;         
  } arm_matrix_instance_q31;



  arm_status arm_mat_add_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  arm_status arm_mat_add_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);

  arm_status arm_mat_add_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  arm_status arm_mat_cmplx_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  arm_status arm_mat_cmplx_mult_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pScratch);

  arm_status arm_mat_cmplx_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  arm_status arm_mat_trans_f32(
  const arm_matrix_instance_f32 * pSrc,
  arm_matrix_instance_f32 * pDst);


  arm_status arm_mat_trans_q15(
  const arm_matrix_instance_q15 * pSrc,
  arm_matrix_instance_q15 * pDst);

  arm_status arm_mat_trans_q31(
  const arm_matrix_instance_q31 * pSrc,
  arm_matrix_instance_q31 * pDst);


  arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  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);

  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);

  arm_status arm_mat_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  arm_status arm_mat_mult_fast_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  arm_status arm_mat_sub_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  arm_status arm_mat_sub_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);

  arm_status arm_mat_sub_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  arm_status arm_mat_scale_f32(
  const arm_matrix_instance_f32 * pSrc,
  float32_t scale,
  arm_matrix_instance_f32 * pDst);

  arm_status arm_mat_scale_q15(
  const arm_matrix_instance_q15 * pSrc,
  q15_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q15 * pDst);

  arm_status arm_mat_scale_q31(
  const arm_matrix_instance_q31 * pSrc,
  q31_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q31 * pDst);


  void arm_mat_init_q31(
  arm_matrix_instance_q31 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q31_t * pData);

  void arm_mat_init_q15(
  arm_matrix_instance_q15 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q15_t * pData);

  void arm_mat_init_f32(
  arm_matrix_instance_f32 * S,
  uint16_t nRows,
  uint16_t nColumns,
  float32_t * pData);



  typedef struct
  {
    q15_t A0;    
#ifdef ARM_MATH_CM0_FAMILY
    q15_t A1;
    q15_t A2;
#else
    q31_t A1;           
#endif
    q15_t state[3];       
    q15_t Kp;           
    q15_t Ki;           
    q15_t Kd;           
  } arm_pid_instance_q15;

  typedef struct
  {
    q31_t A0;            
    q31_t A1;            
    q31_t A2;            
    q31_t state[3];      
    q31_t Kp;            
    q31_t Ki;            
    q31_t Kd;            
  } arm_pid_instance_q31;

  typedef struct
  {
    float32_t A0;          
    float32_t A1;          
    float32_t A2;          
    float32_t state[3];    
    float32_t Kp;               
    float32_t Ki;               
    float32_t Kd;               
  } arm_pid_instance_f32;



  void arm_pid_init_f32(
  arm_pid_instance_f32 * S,
  int32_t resetStateFlag);

  void arm_pid_reset_f32(
  arm_pid_instance_f32 * S);


  void arm_pid_init_q31(
  arm_pid_instance_q31 * S,
  int32_t resetStateFlag);


  void arm_pid_reset_q31(
  arm_pid_instance_q31 * S);

  void arm_pid_init_q15(
  arm_pid_instance_q15 * S,
  int32_t resetStateFlag);

  void arm_pid_reset_q15(
  arm_pid_instance_q15 * S);


  typedef struct
  {
    uint32_t nValues;           
    float32_t x1;               
    float32_t xSpacing;         
    float32_t *pYData;          
  } arm_linear_interp_instance_f32;

  typedef struct
  {
    uint16_t numRows;   
    uint16_t numCols;   
    float32_t *pData;   
  } arm_bilinear_interp_instance_f32;

  typedef struct
  {
    uint16_t numRows;   
    uint16_t numCols;   
    q31_t *pData;       
  } arm_bilinear_interp_instance_q31;

  typedef struct
  {
    uint16_t numRows;   
    uint16_t numCols;   
    q15_t *pData;       
  } arm_bilinear_interp_instance_q15;

  typedef struct
  {
    uint16_t numRows;   
    uint16_t numCols;   
    q7_t *pData;                
  } arm_bilinear_interp_instance_q7;


  void arm_mult_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_mult_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_mult_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_mult_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);






  typedef struct
  {
    uint16_t fftLen;                 
    uint8_t ifftFlag;                
    uint8_t bitReverseFlag;          
    q15_t *pTwiddle;                     
    uint16_t *pBitRevTable;          
    uint16_t twidCoefModifier;       
    uint16_t bitRevFactor;           
  } arm_cfft_radix2_instance_q15;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q15(
  arm_cfft_radix2_instance_q15 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q15(
  const arm_cfft_radix2_instance_q15 * S,
  q15_t * pSrc);



  typedef struct
  {
    uint16_t fftLen;                 
    uint8_t ifftFlag;                
    uint8_t bitReverseFlag;          
    q15_t *pTwiddle;                 
    uint16_t *pBitRevTable;          
    uint16_t twidCoefModifier;       
    uint16_t bitRevFactor;           
  } arm_cfft_radix4_instance_q15;

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

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

  typedef struct
  {
    uint16_t fftLen;                 
    uint8_t ifftFlag;                
    uint8_t bitReverseFlag;          
    q31_t *pTwiddle;                     
    uint16_t *pBitRevTable;          
    uint16_t twidCoefModifier;       
    uint16_t bitRevFactor;           
  } arm_cfft_radix2_instance_q31;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q31(
  arm_cfft_radix2_instance_q31 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q31(
  const arm_cfft_radix2_instance_q31 * S,
  q31_t * pSrc);

  typedef struct
  {
    uint16_t fftLen;                 
    uint8_t ifftFlag;                
    uint8_t bitReverseFlag;          
    q31_t *pTwiddle;                 
    uint16_t *pBitRevTable;          
    uint16_t twidCoefModifier;       
    uint16_t bitRevFactor;           
  } arm_cfft_radix4_instance_q31;

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

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

  typedef struct
  {
    uint16_t fftLen;                   
    uint8_t ifftFlag;                  
    uint8_t bitReverseFlag;            
    float32_t *pTwiddle;               
    uint16_t *pBitRevTable;            
    uint16_t twidCoefModifier;         
    uint16_t bitRevFactor;             
    float32_t onebyfftLen;                 
  } arm_cfft_radix2_instance_f32;

/* Deprecated */
  arm_status arm_cfft_radix2_init_f32(
  arm_cfft_radix2_instance_f32 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_f32(
  const arm_cfft_radix2_instance_f32 * S,
  float32_t * pSrc);

  typedef struct
  {
    uint16_t fftLen;                   
    uint8_t ifftFlag;                  
    uint8_t bitReverseFlag;            
    float32_t *pTwiddle;               
    uint16_t *pBitRevTable;            
    uint16_t twidCoefModifier;         
    uint16_t bitRevFactor;             
    float32_t onebyfftLen;                 
  } arm_cfft_radix4_instance_f32;

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

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

  typedef struct
  {
    uint16_t fftLen;                   
    const q15_t *pTwiddle;             
    const uint16_t *pBitRevTable;      
    uint16_t bitRevLength;             
  } arm_cfft_instance_q15;

void arm_cfft_q15( 
    const arm_cfft_instance_q15 * S, 
    q15_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);  

  typedef struct
  {
    uint16_t fftLen;                   
    const q31_t *pTwiddle;             
    const uint16_t *pBitRevTable;      
    uint16_t bitRevLength;             
  } arm_cfft_instance_q31;

void arm_cfft_q31( 
    const arm_cfft_instance_q31 * S, 
    q31_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);  
  
  typedef struct
  {
    uint16_t fftLen;                   
    const float32_t *pTwiddle;         
    const uint16_t *pBitRevTable;      
    uint16_t bitRevLength;             
  } arm_cfft_instance_f32;

  void arm_cfft_f32(
  const arm_cfft_instance_f32 * S,
  float32_t * p1,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

  typedef struct
  {
    uint32_t fftLenReal;                      
    uint8_t ifftFlagR;                        
    uint8_t bitReverseFlagR;                  
    uint32_t twidCoefRModifier;               
    q15_t *pTwiddleAReal;                     
    q15_t *pTwiddleBReal;                     
    const arm_cfft_instance_q15 *pCfft;       
  } arm_rfft_instance_q15;

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

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

  typedef struct
  {
    uint32_t fftLenReal;                        
    uint8_t ifftFlagR;                          
    uint8_t bitReverseFlagR;                    
    uint32_t twidCoefRModifier;                 
    q31_t *pTwiddleAReal;                       
    q31_t *pTwiddleBReal;                       
    const arm_cfft_instance_q31 *pCfft;         
  } arm_rfft_instance_q31;

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

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

  typedef struct
  {
    uint32_t fftLenReal;                        
    uint16_t fftLenBy2;                         
    uint8_t ifftFlagR;                          
    uint8_t bitReverseFlagR;                    
    uint32_t twidCoefRModifier;                     
    float32_t *pTwiddleAReal;                   
    float32_t *pTwiddleBReal;                   
    arm_cfft_radix4_instance_f32 *pCfft;        
  } arm_rfft_instance_f32;

  arm_status arm_rfft_init_f32(
  arm_rfft_instance_f32 * S,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

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

typedef struct
  {
    arm_cfft_instance_f32 Sint;      
    uint16_t fftLenRFFT;                        
        float32_t * pTwiddleRFFT;                                       
  } arm_rfft_fast_instance_f32 ;

arm_status arm_rfft_fast_init_f32 (
        arm_rfft_fast_instance_f32 * S,
        uint16_t fftLen);

void arm_rfft_fast_f32(
  arm_rfft_fast_instance_f32 * S,
  float32_t * p, float32_t * pOut,
  uint8_t ifftFlag);

  typedef struct
  {
    uint16_t N;                         
    uint16_t Nby2;                      
    float32_t normalize;                
    float32_t *pTwiddle;                
    float32_t *pCosFactor;              
    arm_rfft_instance_f32 *pRfft;        
    arm_cfft_radix4_instance_f32 *pCfft; 
  } arm_dct4_instance_f32;

  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);

  void arm_dct4_f32(
  const arm_dct4_instance_f32 * S,
  float32_t * pState,
  float32_t * pInlineBuffer);

  typedef struct
  {
    uint16_t N;                         
    uint16_t Nby2;                      
    q31_t normalize;                    
    q31_t *pTwiddle;                    
    q31_t *pCosFactor;                  
    arm_rfft_instance_q31 *pRfft;        
    arm_cfft_radix4_instance_q31 *pCfft; 
  } arm_dct4_instance_q31;

  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);

  void arm_dct4_q31(
  const arm_dct4_instance_q31 * S,
  q31_t * pState,
  q31_t * pInlineBuffer);

  typedef struct
  {
    uint16_t N;                         
    uint16_t Nby2;                      
    q15_t normalize;                    
    q15_t *pTwiddle;                    
    q15_t *pCosFactor;                  
    arm_rfft_instance_q15 *pRfft;        
    arm_cfft_radix4_instance_q15 *pCfft; 
  } arm_dct4_instance_q15;

  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);

  void arm_dct4_q15(
  const arm_dct4_instance_q15 * S,
  q15_t * pState,
  q15_t * pInlineBuffer);

  void arm_add_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_add_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_add_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_add_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_sub_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_sub_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_sub_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_sub_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_scale_f32(
  float32_t * pSrc,
  float32_t scale,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_scale_q7(
  q7_t * pSrc,
  q7_t scaleFract,
  int8_t shift,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_scale_q15(
  q15_t * pSrc,
  q15_t scaleFract,
  int8_t shift,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_scale_q31(
  q31_t * pSrc,
  q31_t scaleFract,
  int8_t shift,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_abs_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_abs_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_abs_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_abs_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_dot_prod_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  uint32_t blockSize,
  float32_t * result);

  void arm_dot_prod_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  uint32_t blockSize,
  q31_t * result);

  void arm_dot_prod_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);

  void arm_dot_prod_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);

  void arm_shift_q7(
  q7_t * pSrc,
  int8_t shiftBits,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_shift_q15(
  q15_t * pSrc,
  int8_t shiftBits,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_shift_q31(
  q31_t * pSrc,
  int8_t shiftBits,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_offset_f32(
  float32_t * pSrc,
  float32_t offset,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_offset_q7(
  q7_t * pSrc,
  q7_t offset,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_offset_q15(
  q15_t * pSrc,
  q15_t offset,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_offset_q31(
  q31_t * pSrc,
  q31_t offset,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_negate_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_negate_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_negate_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_negate_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);
  void arm_copy_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_copy_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_copy_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_copy_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);
  void arm_fill_f32(
  float32_t value,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_fill_q7(
  q7_t value,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_fill_q15(
  q15_t value,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_fill_q31(
  q31_t value,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_conv_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst);


  void arm_conv_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);


  void arm_conv_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst);

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

  void arm_conv_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);



  void arm_conv_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);

  void arm_conv_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);


  void arm_conv_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);



  void arm_conv_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst);


  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);

  arm_status arm_conv_partial_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


  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);

  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);


  arm_status arm_conv_partial_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


  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);


  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);


  arm_status arm_conv_partial_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


  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);



  typedef struct
  {
    uint8_t M;                      
    uint16_t numTaps;               
    q15_t *pCoeffs;                  
    q15_t *pState;                   
  } arm_fir_decimate_instance_q15;

  typedef struct
  {
    uint8_t M;                  
    uint16_t numTaps;           
    q31_t *pCoeffs;              
    q31_t *pState;               
  } arm_fir_decimate_instance_q31;

  typedef struct
  {
    uint8_t M;                          
    uint16_t numTaps;                   
    float32_t *pCoeffs;                  
    float32_t *pState;                   
  } arm_fir_decimate_instance_f32;



  void arm_fir_decimate_f32(
  const arm_fir_decimate_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  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);

  void arm_fir_decimate_q15(
  const arm_fir_decimate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_fir_decimate_fast_q15(
  const arm_fir_decimate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);



  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);

  void arm_fir_decimate_q31(
  const arm_fir_decimate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_fir_decimate_fast_q31(
  arm_fir_decimate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  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);



  typedef struct
  {
    uint8_t L;                      
    uint16_t phaseLength;           
    q15_t *pCoeffs;                 
    q15_t *pState;                  
  } arm_fir_interpolate_instance_q15;

  typedef struct
  {
    uint8_t L;                      
    uint16_t phaseLength;           
    q31_t *pCoeffs;                  
    q31_t *pState;                   
  } arm_fir_interpolate_instance_q31;

  typedef struct
  {
    uint8_t L;                     
    uint16_t phaseLength;          
    float32_t *pCoeffs;             
    float32_t *pState;              
  } arm_fir_interpolate_instance_f32;


  void arm_fir_interpolate_q15(
  const arm_fir_interpolate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  arm_status arm_fir_interpolate_init_q15(
  arm_fir_interpolate_instance_q15 * S,
  uint8_t L,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  void arm_fir_interpolate_q31(
  const arm_fir_interpolate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  arm_status arm_fir_interpolate_init_q31(
  arm_fir_interpolate_instance_q31 * S,
  uint8_t L,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  void arm_fir_interpolate_f32(
  const arm_fir_interpolate_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  arm_status arm_fir_interpolate_init_f32(
  arm_fir_interpolate_instance_f32 * S,
  uint8_t L,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);

  typedef struct
  {
    uint8_t numStages;       
    q63_t *pState;           
    q31_t *pCoeffs;          
    uint8_t postShift;       
  } arm_biquad_cas_df1_32x64_ins_q31;


  void arm_biquad_cas_df1_32x64_q31(
  const arm_biquad_cas_df1_32x64_ins_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  void arm_biquad_cas_df1_32x64_init_q31(
  arm_biquad_cas_df1_32x64_ins_q31 * S,
  uint8_t numStages,
  q31_t * pCoeffs,
  q63_t * pState,
  uint8_t postShift);



  typedef struct
  {
    uint8_t numStages;         
    float32_t *pState;         
    float32_t *pCoeffs;        
  } arm_biquad_cascade_df2T_instance_f32;



  typedef struct
  {
    uint8_t numStages;         
    float32_t *pState;         
    float32_t *pCoeffs;        
  } arm_biquad_cascade_stereo_df2T_instance_f32;



  typedef struct
  {
    uint8_t numStages;         
    float64_t *pState;         
    float64_t *pCoeffs;        
  } arm_biquad_cascade_df2T_instance_f64;


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


  void arm_biquad_cascade_stereo_df2T_f32(
  const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_biquad_cascade_df2T_f64(
  const arm_biquad_cascade_df2T_instance_f64 * S,
  float64_t * pSrc,
  float64_t * pDst,
  uint32_t blockSize);


  void arm_biquad_cascade_df2T_init_f32(
  arm_biquad_cascade_df2T_instance_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  void arm_biquad_cascade_stereo_df2T_init_f32(
  arm_biquad_cascade_stereo_df2T_instance_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  void arm_biquad_cascade_df2T_init_f64(
  arm_biquad_cascade_df2T_instance_f64 * S,
  uint8_t numStages,
  float64_t * pCoeffs,
  float64_t * pState);



  typedef struct
  {
    uint16_t numStages;                          
    q15_t *pState;                               
    q15_t *pCoeffs;                              
  } arm_fir_lattice_instance_q15;

  typedef struct
  {
    uint16_t numStages;                          
    q31_t *pState;                               
    q31_t *pCoeffs;                              
  } arm_fir_lattice_instance_q31;

  typedef struct
  {
    uint16_t numStages;                  
    float32_t *pState;                   
    float32_t *pCoeffs;                  
  } arm_fir_lattice_instance_f32;

  void arm_fir_lattice_init_q15(
  arm_fir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pCoeffs,
  q15_t * pState);


  void arm_fir_lattice_q15(
  const arm_fir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_fir_lattice_init_q31(
  arm_fir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pCoeffs,
  q31_t * pState);


  void arm_fir_lattice_q31(
  const arm_fir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_fir_lattice_init_f32(
  arm_fir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);

  void arm_fir_lattice_f32(
  const arm_fir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  typedef struct
  {
    uint16_t numStages;                         
    q15_t *pState;                              
    q15_t *pkCoeffs;                            
    q15_t *pvCoeffs;                            
  } arm_iir_lattice_instance_q15;

  typedef struct
  {
    uint16_t numStages;                         
    q31_t *pState;                              
    q31_t *pkCoeffs;                            
    q31_t *pvCoeffs;                            
  } arm_iir_lattice_instance_q31;

  typedef struct
  {
    uint16_t numStages;                         
    float32_t *pState;                          
    float32_t *pkCoeffs;                        
    float32_t *pvCoeffs;                        
  } arm_iir_lattice_instance_f32;

  void arm_iir_lattice_f32(
  const arm_iir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  void arm_iir_lattice_init_f32(
  arm_iir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pkCoeffs,
  float32_t * pvCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  void arm_iir_lattice_q31(
  const arm_iir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  void arm_iir_lattice_init_q31(
  arm_iir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pkCoeffs,
  q31_t * pvCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  void arm_iir_lattice_q15(
  const arm_iir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  void arm_iir_lattice_init_q15(
  arm_iir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pkCoeffs,
  q15_t * pvCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  typedef struct
  {
    uint16_t numTaps;    
    float32_t *pState;   
    float32_t *pCoeffs;  
    float32_t mu;        
  } arm_lms_instance_f32;

  void arm_lms_f32(
  const arm_lms_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  void arm_lms_init_f32(
  arm_lms_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);

  typedef struct
  {
    uint16_t numTaps;    
    q15_t *pState;       
    q15_t *pCoeffs;      
    q15_t mu;            
    uint32_t postShift;  
  } arm_lms_instance_q15;


  void arm_lms_init_q15(
  arm_lms_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  void arm_lms_q15(
  const arm_lms_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  typedef struct
  {
    uint16_t numTaps;    
    q31_t *pState;       
    q31_t *pCoeffs;      
    q31_t mu;            
    uint32_t postShift;  
  } arm_lms_instance_q31;

  void arm_lms_q31(
  const arm_lms_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  void arm_lms_init_q31(
  arm_lms_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  typedef struct
  {
    uint16_t numTaps;     
    float32_t *pState;    
    float32_t *pCoeffs;   
    float32_t mu;        
    float32_t energy;    
    float32_t x0;        
  } arm_lms_norm_instance_f32;

  void arm_lms_norm_f32(
  arm_lms_norm_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  void arm_lms_norm_init_f32(
  arm_lms_norm_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);


  typedef struct
  {
    uint16_t numTaps;     
    q31_t *pState;        
    q31_t *pCoeffs;       
    q31_t mu;             
    uint8_t postShift;    
    q31_t *recipTable;    
    q31_t energy;         
    q31_t x0;             
  } arm_lms_norm_instance_q31;

  void arm_lms_norm_q31(
  arm_lms_norm_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  void arm_lms_norm_init_q31(
  arm_lms_norm_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  typedef struct
  {
    uint16_t numTaps;    
    q15_t *pState;        
    q15_t *pCoeffs;       
    q15_t mu;            
    uint8_t postShift;   
    q15_t *recipTable;   
    q15_t energy;        
    q15_t x0;            
  } arm_lms_norm_instance_q15;

  void arm_lms_norm_q15(
  arm_lms_norm_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  void arm_lms_norm_init_q15(
  arm_lms_norm_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  void arm_correlate_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst);


  void arm_correlate_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);


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

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



  void arm_correlate_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);

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

  void arm_correlate_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);



  void arm_correlate_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);


  void arm_correlate_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst);


  typedef struct
  {
    uint16_t numTaps;             
    uint16_t stateIndex;          
    float32_t *pState;            
    float32_t *pCoeffs;           
    uint16_t maxDelay;            
    int32_t *pTapDelay;           
  } arm_fir_sparse_instance_f32;

  typedef struct
  {
    uint16_t numTaps;             
    uint16_t stateIndex;          
    q31_t *pState;                
    q31_t *pCoeffs;               
    uint16_t maxDelay;            
    int32_t *pTapDelay;           
  } arm_fir_sparse_instance_q31;

  typedef struct
  {
    uint16_t numTaps;             
    uint16_t stateIndex;          
    q15_t *pState;                
    q15_t *pCoeffs;               
    uint16_t maxDelay;            
    int32_t *pTapDelay;           
  } arm_fir_sparse_instance_q15;

  typedef struct
  {
    uint16_t numTaps;             
    uint16_t stateIndex;          
    q7_t *pState;                 
    q7_t *pCoeffs;                
    uint16_t maxDelay;            
    int32_t *pTapDelay;           
  } arm_fir_sparse_instance_q7;

  void arm_fir_sparse_f32(
  arm_fir_sparse_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  float32_t * pScratchIn,
  uint32_t blockSize);

  void arm_fir_sparse_init_f32(
  arm_fir_sparse_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  void arm_fir_sparse_q31(
  arm_fir_sparse_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  q31_t * pScratchIn,
  uint32_t blockSize);

  void arm_fir_sparse_init_q31(
  arm_fir_sparse_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  void arm_fir_sparse_q15(
  arm_fir_sparse_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  q15_t * pScratchIn,
  q31_t * pScratchOut,
  uint32_t blockSize);


  void arm_fir_sparse_init_q15(
  arm_fir_sparse_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  void arm_fir_sparse_q7(
  arm_fir_sparse_instance_q7 * S,
  q7_t * pSrc,
  q7_t * pDst,
  q7_t * pScratchIn,
  q31_t * pScratchOut,
  uint32_t blockSize);

  void arm_fir_sparse_init_q7(
  arm_fir_sparse_instance_q7 * S,
  uint16_t numTaps,
  q7_t * pCoeffs,
  q7_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);


  /*
   * @brief  Floating-point sin_cos function.
   * @param[in]  theta    input value in degrees
   * @param[out] *pSinVal points to the processed sine output.
   * @param[out] *pCosVal points to the processed cos output.
   * @return none.
   */

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

  /*
   * @brief  Q31 sin_cos function.
   * @param[in]  theta    scaled input value in degrees
   * @param[out] *pSinVal points to the processed sine output.
   * @param[out] *pCosVal points to the processed cosine output.
   * @return none.
   */

  void arm_sin_cos_q31(
  q31_t theta,
  q31_t * pSinVal,
  q31_t * pCosVal);


  void arm_cmplx_conj_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_conj_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_conj_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);



  void arm_cmplx_mag_squared_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mag_squared_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mag_squared_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);


  static __INLINE float32_t arm_pid_f32(
  arm_pid_instance_f32 * S,
  float32_t in)
  {
    float32_t out;

    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
    out = (S->A0 * in) +
      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  static __INLINE q31_t arm_pid_q31(
  arm_pid_instance_q31 * S,
  q31_t in)
  {
    q63_t acc;
    q31_t out;

    /* acc = A0 * x[n]  */
    acc = (q63_t) S->A0 * in;

    /* acc += A1 * x[n-1] */
    acc += (q63_t) S->A1 * S->state[0];

    /* acc += A2 * x[n-2]  */
    acc += (q63_t) S->A2 * S->state[1];

    /* convert output to 1.31 format to add y[n-1] */
    out = (q31_t) (acc >> 31u);

    /* out += y[n-1] */
    out += S->state[2];

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  static __INLINE q15_t arm_pid_q15(
  arm_pid_instance_q15 * S,
  q15_t in)
  {
    q63_t acc;
    q15_t out;

#ifndef ARM_MATH_CM0_FAMILY
    __SIMD32_TYPE *vstate;

    /* Implementation of PID controller */

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

    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
    vstate = __SIMD32_CONST(S->state);
    acc = __SMLALD(S->A1, (q31_t) *vstate, acc);

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

    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
    acc += (q31_t) S->A1 * S->state[0];
    acc += (q31_t) S->A2 * S->state[1];

#endif

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

    /* saturate the output */
    out = (q15_t) (__SSAT((acc >> 15), 16));

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  arm_status arm_mat_inverse_f32(
  const arm_matrix_instance_f32 * src,
  arm_matrix_instance_f32 * dst);


  arm_status arm_mat_inverse_f64(
  const arm_matrix_instance_f64 * src,
  arm_matrix_instance_f64 * dst);



  static __INLINE void arm_clarke_f32(
  float32_t Ia,
  float32_t Ib,
  float32_t * pIalpha,
  float32_t * pIbeta)
  {
    /* Calculate pIalpha using the equation, pIalpha = Ia */
    *pIalpha = Ia;

    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
    *pIbeta =
      ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);

  }

  static __INLINE void arm_clarke_q31(
  q31_t Ia,
  q31_t Ib,
  q31_t * pIalpha,
  q31_t * pIbeta)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */

    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
    *pIalpha = Ia;

    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);

    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);

    /* pIbeta is calculated by adding the intermediate products */
    *pIbeta = __QADD(product1, product2);
  }

  void arm_q7_to_q31(
  q7_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);




  static __INLINE void arm_inv_clarke_f32(
  float32_t Ialpha,
  float32_t Ibeta,
  float32_t * pIa,
  float32_t * pIb)
  {
    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
    *pIa = Ialpha;

    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
    *pIb = -0.5 * Ialpha + (float32_t) 0.8660254039 *Ibeta;

  }

  static __INLINE void arm_inv_clarke_q31(
  q31_t Ialpha,
  q31_t Ibeta,
  q31_t * pIa,
  q31_t * pIb)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */

    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
    *pIa = Ialpha;

    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);

    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);

    /* pIb is calculated by subtracting the products */
    *pIb = __QSUB(product2, product1);

  }

  void arm_q7_to_q15(
  q7_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);



  static __INLINE void arm_park_f32(
  float32_t Ialpha,
  float32_t Ibeta,
  float32_t * pId,
  float32_t * pIq,
  float32_t sinVal,
  float32_t cosVal)
  {
    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
    *pId = Ialpha * cosVal + Ibeta * sinVal;

    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
    *pIq = -Ialpha * sinVal + Ibeta * cosVal;

  }

  static __INLINE void arm_park_q31(
  q31_t Ialpha,
  q31_t Ibeta,
  q31_t * pId,
  q31_t * pIq,
  q31_t sinVal,
  q31_t cosVal)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */

    /* Intermediate product is calculated by (Ialpha * cosVal) */
    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);

    /* Intermediate product is calculated by (Ibeta * sinVal) */
    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);


    /* Intermediate product is calculated by (Ialpha * sinVal) */
    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);

    /* Intermediate product is calculated by (Ibeta * cosVal) */
    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);

    /* Calculate pId by adding the two intermediate products 1 and 2 */
    *pId = __QADD(product1, product2);

    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
    *pIq = __QSUB(product4, product3);
  }

  void arm_q7_to_float(
  q7_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  static __INLINE void arm_inv_park_f32(
  float32_t Id,
  float32_t Iq,
  float32_t * pIalpha,
  float32_t * pIbeta,
  float32_t sinVal,
  float32_t cosVal)
  {
    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
    *pIalpha = Id * cosVal - Iq * sinVal;

    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
    *pIbeta = Id * sinVal + Iq * cosVal;

  }


  static __INLINE void arm_inv_park_q31(
  q31_t Id,
  q31_t Iq,
  q31_t * pIalpha,
  q31_t * pIbeta,
  q31_t sinVal,
  q31_t cosVal)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */

    /* Intermediate product is calculated by (Id * cosVal) */
    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);

    /* Intermediate product is calculated by (Iq * sinVal) */
    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);


    /* Intermediate product is calculated by (Id * sinVal) */
    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);

    /* Intermediate product is calculated by (Iq * cosVal) */
    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);

    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
    *pIalpha = __QSUB(product1, product2);

    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
    *pIbeta = __QADD(product4, product3);

  }

  void arm_q31_to_float(
  q31_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  static __INLINE float32_t arm_linear_interp_f32(
  arm_linear_interp_instance_f32 * S,
  float32_t x)
  {

    float32_t y;
    float32_t x0, x1;                            /* Nearest input values */
    float32_t y0, y1;                            /* Nearest output values */
    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
    int32_t i;                                   /* Index variable */
    float32_t *pYData = S->pYData;               /* pointer to output table */

    /* Calculation of index */
    i = (int32_t) ((x - S->x1) / xSpacing);

    if(i < 0)
    {
      /* Iniatilize output for below specified range as least output value of table */
      y = pYData[0];
    }
    else if((uint32_t)i >= S->nValues)
    {
      /* Iniatilize output for above specified range as last output value of table */
      y = pYData[S->nValues - 1];
    }
    else
    {
      /* Calculation of nearest input values */
      x0 = S->x1 + i * xSpacing;
      x1 = S->x1 + (i + 1) * xSpacing;

      /* Read of nearest output values */
      y0 = pYData[i];
      y1 = pYData[i + 1];

      /* Calculation of output */
      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));

    }

    /* returns output value */
    return (y);
  }

  static __INLINE q31_t arm_linear_interp_q31(
  q31_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q31_t y;                                     /* output */
    q31_t y0, y1;                                /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    int32_t index;                               /* Index to read nearest output values */

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

    if(index >= (int32_t)(nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else if(index < 0)
    {
      return (pYData[0]);
    }
    else
    {

      /* 20 bits for the fractional part */
      /* shift left by 11 to keep fract in 1.31 format */
      fract = (x & 0x000FFFFF) << 11;

      /* Read two nearest output values from the index in 1.31(q31) format */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));

      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
      y += ((q31_t) (((q63_t) y1 * fract) >> 32));

      /* Convert y to 1.31 format */
      return (y << 1u);

    }

  }

  static __INLINE q15_t arm_linear_interp_q15(
  q15_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q63_t y;                                     /* output */
    q15_t y0, y1;                                /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    int32_t index;                               /* Index to read nearest output values */

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

    if(index >= (int32_t)(nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else if(index < 0)
    {
      return (pYData[0]);
    }
    else
    {
      /* 20 bits for the fractional part */
      /* fract is in 12.20 format */
      fract = (x & 0x000FFFFF);

      /* Read two nearest output values from the index */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
      y = ((q63_t) y0 * (0xFFFFF - fract));

      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
      y += ((q63_t) y1 * (fract));

      /* convert y to 1.15 format */
      return (y >> 20);
    }


  }

  static __INLINE q7_t arm_linear_interp_q7(
  q7_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q31_t y;                                     /* output */
    q7_t y0, y1;                                 /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    uint32_t index;                              /* Index to read nearest output values */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    if (x < 0)
    {
      return (pYData[0]);
    }
    index = (x >> 20) & 0xfff;


    if(index >= (nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else
    {

      /* 20 bits for the fractional part */
      /* fract is in 12.20 format */
      fract = (x & 0x000FFFFF);

      /* Read two nearest output values from the index and are in 1.7(q7) format */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
      y = ((y0 * (0xFFFFF - fract)));

      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
      y += (y1 * fract);

      /* convert y to 1.7(q7) format */
      return (y >> 20u);

    }

  }
  float32_t arm_sin_f32(
  float32_t x);

  q31_t arm_sin_q31(
  q31_t x);

  q15_t arm_sin_q15(
  q15_t x);

  float32_t arm_cos_f32(
  float32_t x);

  q31_t arm_cos_q31(
  q31_t x);

  q15_t arm_cos_q15(
  q15_t x);


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

//      #if __FPU_USED
#if (__FPU_USED == 1) && defined ( __CC_ARM   )
      *pOut = __sqrtf(in);
#else
      *pOut = sqrtf(in);
#endif

      return (ARM_MATH_SUCCESS);
    }
    else
    {
      *pOut = 0.0f;
      return (ARM_MATH_ARGUMENT_ERROR);
    }

  }


  arm_status arm_sqrt_q31(
  q31_t in,
  q31_t * pOut);

  arm_status arm_sqrt_q15(
  q15_t in,
  q15_t * pOut);

  static __INLINE void arm_circularWrite_f32(
  int32_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const int32_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  static __INLINE void arm_circularRead_f32(
  int32_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  int32_t * dst,
  int32_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;
    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (int32_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update rOffset.  Watch out for positive and negative value  */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }

  static __INLINE void arm_circularWrite_q15(
  q15_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const q15_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  static __INLINE void arm_circularRead_q15(
  q15_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  q15_t * dst,
  q15_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;

    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (q15_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update wOffset.  Watch out for positive and negative value */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }


  static __INLINE void arm_circularWrite_q7(
  q7_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const q7_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  static __INLINE void arm_circularRead_q7(
  q7_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  q7_t * dst,
  q7_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;

    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (q7_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update rOffset.  Watch out for positive and negative value */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }


  void arm_power_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q63_t * pResult);

  void arm_power_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  void arm_power_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q63_t * pResult);

  void arm_power_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  void arm_mean_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * pResult);

  void arm_mean_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  void arm_mean_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  void arm_mean_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  void arm_var_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  void arm_var_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  void arm_var_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  void arm_rms_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  void arm_rms_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  void arm_rms_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  void arm_std_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  void arm_std_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  void arm_std_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  void arm_cmplx_mag_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mag_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mag_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_dot_prod_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  uint32_t numSamples,
  q31_t * realResult,
  q31_t * imagResult);

  void arm_cmplx_dot_prod_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  uint32_t numSamples,
  q63_t * realResult,
  q63_t * imagResult);

  void arm_cmplx_dot_prod_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  uint32_t numSamples,
  float32_t * realResult,
  float32_t * imagResult);

  void arm_cmplx_mult_real_q15(
  q15_t * pSrcCmplx,
  q15_t * pSrcReal,
  q15_t * pCmplxDst,
  uint32_t numSamples);

  void arm_cmplx_mult_real_q31(
  q31_t * pSrcCmplx,
  q31_t * pSrcReal,
  q31_t * pCmplxDst,
  uint32_t numSamples);

  void arm_cmplx_mult_real_f32(
  float32_t * pSrcCmplx,
  float32_t * pSrcReal,
  float32_t * pCmplxDst,
  uint32_t numSamples);

  void arm_min_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * result,
  uint32_t * index);

  void arm_min_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult,
  uint32_t * pIndex);

  void arm_min_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult,
  uint32_t * pIndex);

  void arm_min_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult,
  uint32_t * pIndex);

  void arm_max_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * pResult,
  uint32_t * pIndex);

  void arm_max_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult,
  uint32_t * pIndex);

  void arm_max_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult,
  uint32_t * pIndex);

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

  void arm_cmplx_mult_cmplx_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mult_cmplx_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t numSamples);

  void arm_cmplx_mult_cmplx_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t numSamples);

  void arm_float_to_q31(
  float32_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  void arm_float_to_q15(
  float32_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_float_to_q7(
  float32_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  void arm_q31_to_q15(
  q31_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  void arm_q31_to_q7(
  q31_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  void arm_q15_to_float(
  q15_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  void arm_q15_to_q31(
  q15_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  void arm_q15_to_q7(
  q15_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  static __INLINE float32_t arm_bilinear_interp_f32(
  const arm_bilinear_interp_instance_f32 * S,
  float32_t X,
  float32_t Y)
  {
    float32_t out;
    float32_t f00, f01, f10, f11;
    float32_t *pData = S->pData;
    int32_t xIndex, yIndex, index;
    float32_t xdiff, ydiff;
    float32_t b1, b2, b3, b4;

    xIndex = (int32_t) X;
    yIndex = (int32_t) Y;

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0
       || yIndex > (S->numCols - 1))
    {
      return (0);
    }

    /* Calculation of index for two nearest points in X-direction */
    index = (xIndex - 1) + (yIndex - 1) * S->numCols;


    /* Read two nearest points in X-direction */
    f00 = pData[index];
    f01 = pData[index + 1];

    /* Calculation of index for two nearest points in Y-direction */
    index = (xIndex - 1) + (yIndex) * S->numCols;


    /* Read two nearest points in Y-direction */
    f10 = pData[index];
    f11 = pData[index + 1];

    /* Calculation of intermediate values */
    b1 = f00;
    b2 = f01 - f00;
    b3 = f10 - f00;
    b4 = f00 - f01 - f10 + f11;

    /* Calculation of fractional part in X */
    xdiff = X - xIndex;

    /* Calculation of fractional part in Y */
    ydiff = Y - yIndex;

    /* Calculation of bi-linear interpolated output */
    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;

    /* return to application */
    return (out);

  }

  static __INLINE q31_t arm_bilinear_interp_q31(
  arm_bilinear_interp_instance_q31 * S,
  q31_t X,
  q31_t Y)
  {
    q31_t out;                                   /* Temporary output */
    q31_t acc = 0;                               /* output */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    q31_t x1, x2, y1, y2;                        /* Nearest output values */
    int32_t rI, cI;                              /* Row and column indices */
    q31_t *pYData = S->pData;                    /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */


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

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

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* shift left xfract by 11 to keep 1.31 format */
    xfract = (X & 0x000FFFFF) << 11u;

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];

    /* 20 bits for the fractional part */
    /* shift left yfract by 11 to keep 1.31 format */
    yfract = (Y & 0x000FFFFF) << 11u;

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
    out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32));
    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));

    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));

    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));

    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));

    /* Convert acc to 1.31(q31) format */
    return (acc << 2u);

  }

  static __INLINE q15_t arm_bilinear_interp_q15(
  arm_bilinear_interp_instance_q15 * S,
  q31_t X,
  q31_t Y)
  {
    q63_t acc = 0;                               /* output */
    q31_t out;                                   /* Temporary output */
    q15_t x1, x2, y1, y2;                        /* Nearest output values */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    int32_t rI, cI;                              /* Row and column indices */
    q15_t *pYData = S->pData;                    /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */

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

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

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* xfract should be in 12.20 format */
    xfract = (X & 0x000FFFFF);

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];


    /* 20 bits for the fractional part */
    /* yfract should be in 12.20 format */
    yfract = (Y & 0x000FFFFF);

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */

    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
    out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
    acc = ((q63_t) out * (0xFFFFF - yfract));

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

    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
    out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
    acc += ((q63_t) out * (yfract));

    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
    acc += ((q63_t) out * (yfract));

    /* acc is in 13.51 format and down shift acc by 36 times */
    /* Convert out to 1.15 format */
    return (acc >> 36);

  }

  static __INLINE q7_t arm_bilinear_interp_q7(
  arm_bilinear_interp_instance_q7 * S,
  q31_t X,
  q31_t Y)
  {
    q63_t acc = 0;                               /* output */
    q31_t out;                                   /* Temporary output */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    q7_t x1, x2, y1, y2;                         /* Nearest output values */
    int32_t rI, cI;                              /* Row and column indices */
    q7_t *pYData = S->pData;                     /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */

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

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

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* xfract should be in 12.20 format */
    xfract = (X & 0x000FFFFF);

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];


    /* 20 bits for the fractional part */
    /* yfract should be in 12.20 format */
    yfract = (Y & 0x000FFFFF);

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
    out = ((x1 * (0xFFFFF - xfract)));
    acc = (((q63_t) out * (0xFFFFF - yfract)));

    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
    out = ((x2 * (0xFFFFF - yfract)));
    acc += (((q63_t) out * (xfract)));

    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
    out = ((y1 * (0xFFFFF - xfract)));
    acc += (((q63_t) out * (yfract)));

    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
    out = ((y2 * (yfract)));
    acc += (((q63_t) out * (xfract)));

    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
    return (acc >> 40);

  }

//SMMLAR
#define multAcc_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)

//SMMLSR
#define multSub_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)

//SMMULR
#define mult_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)

//SMMLA
#define multAcc_32x32_keep32(a, x, y) \
    a += (q31_t) (((q63_t) x * y) >> 32)

//SMMLS
#define multSub_32x32_keep32(a, x, y) \
    a -= (q31_t) (((q63_t) x * y) >> 32)

//SMMUL
#define mult_32x32_keep32(a, x, y) \
    a = (q31_t) (((q63_t) x * y ) >> 32)


#if defined ( __CC_ARM ) //Keil

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_ENTER \
         _Pragma ("push")         \
         _Pragma ("O1")
    #else
      #define LOW_OPTIMIZATION_ENTER 
    #endif

//Exit low optimization region - place directly after end of function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_EXIT \
         _Pragma ("pop")
    #else
      #define LOW_OPTIMIZATION_EXIT  
    #endif

//Enter low optimization region - place directly above function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER

//Exit low optimization region - place directly after end of function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__ICCARM__) //IAR

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_ENTER \
         _Pragma ("optimize=low")
    #else
      #define LOW_OPTIMIZATION_ENTER   
    #endif

//Exit low optimization region - place directly after end of function definition
  #define LOW_OPTIMIZATION_EXIT

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
         _Pragma ("optimize=low")
    #else
      #define IAR_ONLY_LOW_OPTIMIZATION_ENTER   
    #endif

//Exit low optimization region - place directly after end of function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__GNUC__)

  #define LOW_OPTIMIZATION_ENTER __attribute__(( optimize("-O1") ))

  #define LOW_OPTIMIZATION_EXIT

  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER

  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__CSMC__)         // Cosmic

#define LOW_OPTIMIZATION_ENTER
#define LOW_OPTIMIZATION_EXIT
#define IAR_ONLY_LOW_OPTIMIZATION_ENTER
#define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#endif


#ifdef  __cplusplus
}
#endif


#endif /* _ARM_MATH_H */