text: /* ----------------------------------------------------------------------
   * Copyright (C) 2010-2011 ARM Limited. All rights reserved.
   *
   * $Date:        15. July 2011
   * $Revision: 	V1.0.10
   *
   * Project: 	    CMSIS DSP Library
   * Title:	     arm_math.h
   *
   * Description:	 Public header file for CMSIS DSP Library
   *
   * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
   *
   * Version 1.0.10 2011/7/15
   *    Big Endian support added and Merged M0 and M3/M4 Source code.
   *
   * Version 1.0.3 2010/11/29
   *    Re-organized the CMSIS folders and updated documentation.
   *
   * Version 1.0.2 2010/11/11
   *    Documentation updated.
   *
   * Version 1.0.1 2010/10/05
   *    Production release and review comments incorporated.
   *
   * Version 1.0.0 2010/09/20
   *    Production release and review comments incorporated.
   * -------------------------------------------------------------------- */
  
  /**
     \mainpage CMSIS DSP Software Library
     *
     * <b>Introduction</b>
     *
     * This user manual describes the CMSIS DSP software library,
     * a suite of common signal processing functions for use on Cortex-M processor based devices.
     *
     * The library is divided into a number of modules each covering a specific category:
     * - Basic math functions
     * - Fast math functions
     * - Complex math functions
     * - Filters
     * - Matrix functions
     * - Transforms
     * - Motor control functions
     * - Statistical functions
     * - Support functions
     * - Interpolation functions
     *
     * The library has separate functions for operating on 8-bit integers, 16-bit integers,
     * 32-bit integer and 32-bit floating-point values.
     *
     * <b>Processor Support</b>
     *
     * The library is completely written in C and is fully CMSIS compliant.
     * High performance is achieved through maximum use of Cortex-M4 intrinsics.
     *
     * The supplied library source code also builds and runs on the Cortex-M3 and Cortex-M0 processor,
     * with the DSP intrinsics being emulated through software.
     *
     *
     * <b>Toolchain Support</b>
     *
     * The library has been developed and tested with MDK-ARM version 4.21.
     * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
     *
     * <b>Using the Library</b>
     *
     * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
     * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
     * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
     * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
     * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
     * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
     * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
     * - arm_cortexM0l_math.lib (Little endian on Cortex-M0)
     * - arm_cortexM0b_math.lib (Big endian on Cortex-M3)
     *
     * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
     * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
     * public header file <code>arm_math.h</code> for Cortex-M4/M3/M0 with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
     * Define the appropriate pre processor MACRO ARM_MATH_CM4 or  ARM_MATH_CM3 or
     * ARM_MATH_CM0 depending on the target processor in the application.
     *
     * <b>Examples</b>
     *
     * The library ships with a number of examples which demonstrate how to use the library functions.
     *
     * <b>Building the Library</b>
     *
     * The library installer contains project files to re build libraries on MDK Tool chain in the <code>CMSIS\\DSP_Lib\\Source\\ARM</code> folder.
     * - arm_cortexM0b_math.uvproj
     * - arm_cortexM0l_math.uvproj
     * - arm_cortexM3b_math.uvproj
     * - arm_cortexM3l_math.uvproj
     * - arm_cortexM4b_math.uvproj
     * - arm_cortexM4l_math.uvproj
     * - arm_cortexM4bf_math.uvproj
     * - arm_cortexM4lf_math.uvproj
     *
     * Each library project have differant pre-processor macros.
     *
     * <b>ARM_MATH_CMx:</b>
     * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
     * and ARM_MATH_CM0 for building library on cortex-M0 target.
     *
     * <b>ARM_MATH_BIG_ENDIAN:</b>
     * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
     *
     * <b>ARM_MATH_MATRIX_CHECK:</b>
     * Define macro for checking on the input and output sizes of matrices
     *
     * <b>ARM_MATH_ROUNDING:</b>
     * Define macro for rounding on support functions
     *
     * <b>__FPU_PRESENT:</b>
     * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
     *
     *
     * The project can be built by opening the appropriate project in MDK-ARM 4.21 chain and defining the optional pre processor MACROs detailed above.
     *
     * <b>Copyright Notice</b>
     *
     * Copyright (C) 2010 ARM Limited. All rights reserved.
     */
  
  
  /**
   * @defgroup groupMath Basic Math Functions
   */
  
  /**
   * @defgroup groupFastMath Fast Math Functions
   * This set of functions provides a fast approximation to sine, cosine, and square root.
   * As compared to most of the other functions in the CMSIS math library, the fast math functions
   * operate on individual values and not arrays.
   * There are separate functions for Q15, Q31, and floating-point data.
   *
   */
  
  /**
   * @defgroup groupCmplxMath Complex Math Functions
   * This set of functions operates on complex data vectors.
   * The data in the complex arrays is stored in an interleaved fashion
   * (real, imag, real, imag, ...).
   * In the API functions, the number of samples in a complex array refers
   * to the number of complex values; the array contains twice this number of
   * real values.
   */
  
  /**
   * @defgroup groupFilters Filtering Functions
   */
  
  /**
   * @defgroup groupMatrix Matrix Functions
   *
   * This set of functions provides basic matrix math operations.
   * The functions operate on matrix data structures.  For example,
   * the type
   * definition for the floating-point matrix structure is shown
   * below:
   * <pre>
   *     typedef struct
   *     {
   *       uint16_t numRows;     // number of rows of the matrix.
   *       uint16_t numCols;     // number of columns of the matrix.
   *       float32_t *pData;     // points to the data of the matrix.
   *     } arm_matrix_instance_f32;
   * </pre>
   * There are similar definitions for Q15 and Q31 data types.
   *
   * The structure specifies the size of the matrix and then points to
   * an array of data.  The array is of size <code>numRows X numCols</code>
   * and the values are arranged in row order.  That is, the
   * matrix element (i, j) is stored at:
   * <pre>
   *     pData[i*numCols + j]
   * </pre>
   *
   * \par Init Functions
   * There is an associated initialization function for each type of matrix
   * data structure.
   * The initialization function sets the values of the internal structure fields.
   * Refer to the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
   * and <code>arm_mat_init_q15()</code> for floating-point, Q31 and Q15 types,  respectively.
   *
   * \par
   * Use of the initialization function is optional. However, if initialization function is used
   * then the instance structure cannot be placed into a const data section.
   * To place the instance structure in a const data
   * section, manually initialize the data structure.  For example:
   * <pre>
   * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
   * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
   * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
   * </pre>
   * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
   * specifies the number of columns, and <code>pData</code> points to the
   * data array.
   *
   * \par Size Checking
   * By default all of the matrix functions perform size checking on the input and
   * output matrices.  For example, the matrix addition function verifies that the
   * two input matrices and the output matrix all have the same number of rows and
   * columns.  If the size check fails the functions return:
   * <pre>
   *     ARM_MATH_SIZE_MISMATCH
   * </pre>
   * Otherwise the functions return
   * <pre>
   *     ARM_MATH_SUCCESS
   * </pre>
   * There is some overhead associated with this matrix size checking.
   * The matrix size checking is enabled via the \#define
   * <pre>
   *     ARM_MATH_MATRIX_CHECK
   * </pre>
   * within the library project settings.  By default this macro is defined
   * and size checking is enabled.  By changing the project settings and
   * undefining this macro size checking is eliminated and the functions
   * run a bit faster.  With size checking disabled the functions always
   * return <code>ARM_MATH_SUCCESS</code>.
   */
  
  /**
   * @defgroup groupTransforms Transform Functions
   */
  
  /**
   * @defgroup groupController Controller Functions
   */
  
  /**
   * @defgroup groupStats Statistics Functions
   */
  /**
   * @defgroup groupSupport Support Functions
   */
  
  /**
   * @defgroup groupInterpolation Interpolation Functions
   * These functions perform 1- and 2-dimensional interpolation of data.
   * Linear interpolation is used for 1-dimensional data and
   * bilinear interpolation is used for 2-dimensional data.
   */
  
  /**
   * @defgroup groupExamples Examples
   */
  #ifndef _ARM_MATH_H
  #define _ARM_MATH_H
  
  #define __CMSIS_GENERIC              /* disable NVIC and Systick functions */
  
  #if defined (ARM_MATH_CM4)
  #include "core_cm4.h"
  #elif defined (ARM_MATH_CM3)
  #include "core_cm3.h"
  #elif defined (ARM_MATH_CM0)
  #include "core_cm0.h"
  #else
  #include "ARMCM4.h"
  #warning "Define either ARM_MATH_CM4 OR ARM_MATH_CM3...By Default building on ARM_MATH_CM4....."
  #endif
  
  #undef  __CMSIS_GENERIC              /* enable NVIC and Systick functions */
  #include "string.h"
  #include "math.h"
  #ifdef	__cplusplus
  extern "C"
  {
  #endif
  
  
      /**
       * @brief Macros required for reciprocal calculation in Normalized LMS
       */
  
  #define DELTA_Q31 			(0x100)
  #define DELTA_Q15 			0x5
  #define INDEX_MASK 			0x0000003F
  #define PI					3.14159265358979f
  
      /**
       * @brief Macros required for SINE and COSINE Fast math approximations
       */
  
  #define TABLE_SIZE			256
  #define TABLE_SPACING_Q31	0x800000
  #define TABLE_SPACING_Q15	0x80
  
      /**
       * @brief Macros required for SINE and COSINE Controller functions
       */
      /* 1.31(q31) Fixed value of 2/360 */
      /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
  #define INPUT_SPACING			0xB60B61
  
  
      /**
       * @brief Error status returned by some functions in the library.
       */
  
      typedef enum
      {
          ARM_MATH_SUCCESS = 0,              /**< No error */
          ARM_MATH_ARGUMENT_ERROR = -1,      /**< One or more arguments are incorrect */
          ARM_MATH_LENGTH_ERROR = -2,        /**< Length of data buffer is incorrect */
          ARM_MATH_SIZE_MISMATCH = -3,       /**< Size of matrices is not compatible with the operation. */
          ARM_MATH_NANINF = -4,              /**< Not-a-number (NaN) or infinity is generated */
          ARM_MATH_SINGULAR = -5,            /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
          ARM_MATH_TEST_FAILURE = -6         /**< Test Failed  */
      }
                              arm_status;
  
      /**
       * @brief 8-bit fractional data type in 1.7 format.
       */
      typedef int8_t q7_t;
  
      /**
       * @brief 16-bit fractional data type in 1.15 format.
       */
      typedef int16_t q15_t;
  
      /**
       * @brief 32-bit fractional data type in 1.31 format.
       */
      typedef int32_t q31_t;
  
      /**
       * @brief 64-bit fractional data type in 1.63 format.
       */
      typedef int64_t q63_t;
  
      /**
       * @brief 32-bit floating-point type definition.
       */
      typedef float float32_t;
  
      /**
       * @brief 64-bit floating-point type definition.
       */
      typedef double float64_t;
  
      /**
       * @brief definition to read/write two 16 bit values.
       */
  #define __SIMD32(addr)  (*(int32_t **) & (addr))
  
  #if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)
      /**
       * @brief definition to pack two 16 bit values.
       */
  #define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
                                           (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
  
  #endif
  
  
      /**
      * @brief definition to pack four 8 bit values.
      */
  #ifndef ARM_MATH_BIG_ENDIAN
  
  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) |	\
                                  (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) |	\
  							    (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) |	\
  							    (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
  #else
  
  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) |	\
                                  (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) |	\
  							    (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) |	\
  							    (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
  
  #endif
  
  
      /**
       * @brief Clips Q63 to Q31 values.
       */
      __STATIC_INLINE q31_t clip_q63_to_q31(
          q63_t x)
      {
          return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
                 ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
      }
  
      /**
       * @brief Clips Q63 to Q15 values.
       */
      __STATIC_INLINE q15_t clip_q63_to_q15(
          q63_t x)
      {
          return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
                 ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
      }
  
      /**
       * @brief Clips Q31 to Q7 values.
       */
      __STATIC_INLINE q7_t clip_q31_to_q7(
          q31_t x)
      {
          return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
                 ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
      }
  
      /**
       * @brief Clips Q31 to Q15 values.
       */
      __STATIC_INLINE q15_t clip_q31_to_q15(
          q31_t x)
      {
          return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
                 ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
      }
  
      /**
       * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
       */
  
      __STATIC_INLINE q63_t mult32x64(
          q63_t x,
          q31_t y)
      {
          return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
                  (((q63_t) (x >> 32) * y)));
      }
  
  
  #if defined (ARM_MATH_CM0) && defined ( __CC_ARM   )
  #define __CLZ __clz
  #endif
  
  #if defined (ARM_MATH_CM0) && defined ( __TASKING__ )
      /* No need to redefine __CLZ */
  #endif
  
  #if defined (ARM_MATH_CM0) && ((defined (__ICCARM__)) ||(defined (__GNUC__)) )
  
      __STATIC_INLINE  uint32_t __CLZ(q31_t data);
  
  
      __STATIC_INLINE uint32_t __CLZ(q31_t data)
      {
          uint32_t count = 0;
          uint32_t mask = 0x80000000;
  
          while((data & mask) ==  0)
          {
              count += 1u;
              mask = mask >> 1u;
          }
  
          return(count);
  
      }
  
  #endif
  
      /**
       * @brief Function to Calculates 1/in(reciprocal) value of Q31 Data type.
       */
  
      __STATIC_INLINE uint32_t arm_recip_q31(
          q31_t in,
          q31_t * dst,
          q31_t * pRecipTable)
      {
  
          uint32_t out, tempVal;
          uint32_t index, i;
          uint32_t signBits;
  
          if(in > 0)
          {
              signBits = __CLZ(in) - 1;
          }
          else
          {
              signBits = __CLZ(-in) - 1;
          }
  
          /* Convert input sample to 1.31 format */
          in = in << signBits;
  
          /* calculation of index for initial approximated Val */
          index = (uint32_t) (in >> 24u);
          index = (index & INDEX_MASK);
  
          /* 1.31 with exp 1 */
          out = pRecipTable[index];
  
          /* calculation of reciprocal value */
          /* running approximation for two iterations */
          for (i = 0u; i < 2u; i++)
          {
              tempVal = (q31_t) (((q63_t) in * out) >> 31u);
              tempVal = 0x7FFFFFFF - tempVal;
              /*      1.31 with exp 1 */
              //out = (q31_t) (((q63_t) out * tempVal) >> 30u);
              out = (q31_t) clip_q63_to_q31(((q63_t) out * tempVal) >> 30u);
          }
  
          /* write output */
          *dst = out;
  
          /* return num of signbits of out = 1/in value */
          return (signBits + 1u);
  
      }
  
      /**
       * @brief Function to Calculates 1/in(reciprocal) value of Q15 Data type.
       */
      __STATIC_INLINE uint32_t arm_recip_q15(
          q15_t in,
          q15_t * dst,
          q15_t * pRecipTable)
      {
  
          uint32_t out = 0, tempVal = 0;
          uint32_t index = 0, i = 0;
          uint32_t signBits = 0;
  
          if(in > 0)
          {
              signBits = __CLZ(in) - 17;
          }
          else
          {
              signBits = __CLZ(-in) - 17;
          }
  
          /* Convert input sample to 1.15 format */
          in = in << signBits;
  
          /* calculation of index for initial approximated Val */
          index = in >> 8;
          index = (index & INDEX_MASK);
  
          /*      1.15 with exp 1  */
          out = pRecipTable[index];
  
          /* calculation of reciprocal value */
          /* running approximation for two iterations */
          for (i = 0; i < 2; i++)
          {
              tempVal = (q15_t) (((q31_t) in * out) >> 15);
              tempVal = 0x7FFF - tempVal;
              /*      1.15 with exp 1 */
              out = (q15_t) (((q31_t) out * tempVal) >> 14);
          }
  
          /* write output */
          *dst = out;
  
          /* return num of signbits of out = 1/in value */
          return (signBits + 1);
  
      }
  
  
      /*
       * @brief C custom defined intrinisic function for only M0 processors
       */
  #if defined(ARM_MATH_CM0)
  
      __STATIC_INLINE q31_t __SSAT(
          q31_t x,
          uint32_t y)
      {
          int32_t posMax, negMin;
          uint32_t i;
  
          posMax = 1;
          for (i = 0; i < (y - 1); i++)
          {
              posMax = posMax * 2;
          }
  
          if(x > 0)
          {
              posMax = (posMax - 1);
  
              if(x > posMax)
              {
                  x = posMax;
              }
          }
          else
          {
              negMin = -posMax;
  
              if(x < negMin)
              {
                  x = negMin;
              }
          }
          return (x);
  
  
      }
  
  #endif /* end of ARM_MATH_CM0 */
  
  
  
      /*
       * @brief C custom defined intrinsic function for M3 and M0 processors
       */
  #if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0)
  
      /*
       * @brief C custom defined QADD8 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QADD8(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q7_t r, s, t, u;
  
          r = (char) x;
          s = (char) y;
  
          r = __SSAT((q31_t) (r + s), 8);
          s = __SSAT(((q31_t) (((x << 16) >> 24) + ((y << 16) >> 24))), 8);
          t = __SSAT(((q31_t) (((x << 8) >> 24) + ((y << 8) >> 24))), 8);
          u = __SSAT(((q31_t) ((x >> 24) + (y >> 24))), 8);
  
          sum = (((q31_t) u << 24) & 0xFF000000) | (((q31_t) t << 16) & 0x00FF0000) |
                (((q31_t) s << 8) & 0x0000FF00) | (r & 0x000000FF);
  
          return sum;
  
      }
  
      /*
       * @brief C custom defined QSUB8 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QSUB8(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s, t, u;
  
          r = (char) x;
          s = (char) y;
  
          r = __SSAT((r - s), 8);
          s = __SSAT(((q31_t) (((x << 16) >> 24) - ((y << 16) >> 24))), 8) << 8;
          t = __SSAT(((q31_t) (((x << 8) >> 24) - ((y << 8) >> 24))), 8) << 16;
          u = __SSAT(((q31_t) ((x >> 24) - (y >> 24))), 8) << 24;
  
          sum =
              (u & 0xFF000000) | (t & 0x00FF0000) | (s & 0x0000FF00) | (r & 0x000000FF);
  
          return sum;
      }
  
      /*
       * @brief C custom defined QADD16 for M3 and M0 processors
       */
  
      /*
       * @brief C custom defined QADD16 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QADD16(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = __SSAT(r + s, 16);
          s = __SSAT(((q31_t) ((x >> 16) + (y >> 16))), 16) << 16;
  
          sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return sum;
  
      }
  
      /*
       * @brief C custom defined SHADD16 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SHADD16(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = ((r >> 1) + (s >> 1));
          s = ((q31_t) ((x >> 17) + (y >> 17))) << 16;
  
          sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return sum;
  
      }
  
      /*
       * @brief C custom defined QSUB16 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QSUB16(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = __SSAT(r - s, 16);
          s = __SSAT(((q31_t) ((x >> 16) - (y >> 16))), 16) << 16;
  
          sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return sum;
      }
  
      /*
       * @brief C custom defined SHSUB16 for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SHSUB16(
          q31_t x,
          q31_t y)
      {
  
          q31_t diff;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = ((r >> 1) - (s >> 1));
          s = (((x >> 17) - (y >> 17)) << 16);
  
          diff = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return diff;
      }
  
      /*
       * @brief C custom defined QASX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QASX(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum = 0;
  
          sum = ((sum + clip_q31_to_q15((q31_t) ((short) (x >> 16) + (short) y))) << 16) +
                clip_q31_to_q15((q31_t) ((short) x - (short) (y >> 16)));
  
          return sum;
      }
  
      /*
       * @brief C custom defined SHASX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SHASX(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = ((r >> 1) - (y >> 17));
          s = (((x >> 17) + (s >> 1)) << 16);
  
          sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return sum;
      }
  
  
      /*
       * @brief C custom defined QSAX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QSAX(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum = 0;
  
          sum = ((sum + clip_q31_to_q15((q31_t) ((short) (x >> 16) - (short) y))) << 16) +
                clip_q31_to_q15((q31_t) ((short) x + (short) (y >> 16)));
  
          return sum;
      }
  
      /*
       * @brief C custom defined SHSAX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SHSAX(
          q31_t x,
          q31_t y)
      {
  
          q31_t sum;
          q31_t r, s;
  
          r = (short) x;
          s = (short) y;
  
          r = ((r >> 1) + (y >> 17));
          s = (((x >> 17) - (s >> 1)) << 16);
  
          sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
  
          return sum;
      }
  
      /*
       * @brief C custom defined SMUSDX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMUSDX(
          q31_t x,
          q31_t y)
      {
  
          return ((q31_t)(((short) x * (short) (y >> 16)) -
                          ((short) (x >> 16) * (short) y)));
      }
  
      /*
       * @brief C custom defined SMUADX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMUADX(
          q31_t x,
          q31_t y)
      {
  
          return ((q31_t)(((short) x * (short) (y >> 16)) +
                          ((short) (x >> 16) * (short) y)));
      }
  
      /*
       * @brief C custom defined QADD for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QADD(
          q31_t x,
          q31_t y)
      {
          return clip_q63_to_q31((q63_t) x + y);
      }
  
      /*
       * @brief C custom defined QSUB for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __QSUB(
          q31_t x,
          q31_t y)
      {
          return clip_q63_to_q31((q63_t) x - y);
      }
  
      /*
       * @brief C custom defined SMLAD for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMLAD(
          q31_t x,
          q31_t y,
          q31_t sum)
      {
  
          return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
                  ((short) x * (short) y));
      }
  
      /*
       * @brief C custom defined SMLADX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMLADX(
          q31_t x,
          q31_t y,
          q31_t sum)
      {
  
          return (sum + ((short) (x >> 16) * (short) (y)) +
                  ((short) x * (short) (y >> 16)));
      }
  
      /*
       * @brief C custom defined SMLSDX for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMLSDX(
          q31_t x,
          q31_t y,
          q31_t sum)
      {
  
          return (sum - ((short) (x >> 16) * (short) (y)) +
                  ((short) x * (short) (y >> 16)));
      }
  
      /*
       * @brief C custom defined SMLALD for M3 and M0 processors
       */
      __STATIC_INLINE q63_t __SMLALD(
          q31_t x,
          q31_t y,
          q63_t sum)
      {
  
          return (sum + ((short) (x >> 16) * (short) (y >> 16)) +
                  ((short) x * (short) y));
      }
  
      /*
       * @brief C custom defined SMLALDX for M3 and M0 processors
       */
      __STATIC_INLINE q63_t __SMLALDX(
          q31_t x,
          q31_t y,
          q63_t sum)
      {
  
          return (sum + ((short) (x >> 16) * (short) y)) +
                 ((short) x * (short) (y >> 16));
      }
  
      /*
       * @brief C custom defined SMUAD for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMUAD(
          q31_t x,
          q31_t y)
      {
  
          return (((x >> 16) * (y >> 16)) +
                  (((x << 16) >> 16) * ((y << 16) >> 16)));
      }
  
      /*
       * @brief C custom defined SMUSD for M3 and M0 processors
       */
      __STATIC_INLINE q31_t __SMUSD(
          q31_t x,
          q31_t y)
      {
  
          return (-((x >> 16) * (y >> 16)) +
                  (((x << 16) >> 16) * ((y << 16) >> 16)));
      }
  
  
  
  
  #endif /* (ARM_MATH_CM3) || defined (ARM_MATH_CM0) */
  
  
      /**
       * @brief Instance structure for the Q7 FIR filter.
       */
      typedef struct
      {
          uint16_t numTaps;        /**< number of filter coefficients in the filter. */
          q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
      } arm_fir_instance_q7;
  
      /**
       * @brief Instance structure for the Q15 FIR filter.
       */
      typedef struct
      {
          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
          q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
      } arm_fir_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 FIR filter.
       */
      typedef struct
      {
          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
          q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
      } arm_fir_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point FIR filter.
       */
      typedef struct
      {
          uint16_t numTaps;     /**< number of filter coefficients in the filter. */
          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
      } arm_fir_instance_f32;
  
  
      /**
       * @brief Processing function for the Q7 FIR filter.
       * @param[in] *S points to an instance of the Q7 FIR filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_q7(
          const arm_fir_instance_q7 * S,
          q7_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the Q7 FIR filter.
       * @param[in,out] *S points to an instance of the Q7 FIR structure.
       * @param[in] numTaps  Number of filter coefficients in the filter.
       * @param[in] *pCoeffs points to the filter coefficients.
       * @param[in] *pState points to the state buffer.
       * @param[in] blockSize number of samples that are processed.
       * @return none
       */
      void arm_fir_init_q7(
          arm_fir_instance_q7 * S,
          uint16_t numTaps,
          q7_t * pCoeffs,
          q7_t * pState,
          uint32_t blockSize);
  
  
      /**
       * @brief Processing function for the Q15 FIR filter.
       * @param[in] *S points to an instance of the Q15 FIR structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_q15(
          const arm_fir_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
       * @param[in] *S points to an instance of the Q15 FIR filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_fast_q15(
          const arm_fir_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q15 FIR filter.
       * @param[in,out] *S points to an instance of the Q15 FIR filter structure.
       * @param[in] numTaps  Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
       * @param[in] *pCoeffs points to the filter coefficients.
       * @param[in] *pState points to the state buffer.
       * @param[in] blockSize number of samples that are processed at a time.
       * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
       * <code>numTaps</code> is not a supported value.
       */
  
      arm_status arm_fir_init_q15(
          arm_fir_instance_q15 * S,
          uint16_t numTaps,
          q15_t * pCoeffs,
          q15_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q31 FIR filter.
       * @param[in] *S points to an instance of the Q31 FIR filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_q31(
          const arm_fir_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
       * @param[in] *S points to an instance of the Q31 FIR structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_fast_q31(
          const arm_fir_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q31 FIR filter.
       * @param[in,out] *S points to an instance of the Q31 FIR structure.
       * @param[in] 	numTaps  Number of filter coefficients in the filter.
       * @param[in] 	*pCoeffs points to the filter coefficients.
       * @param[in] 	*pState points to the state buffer.
       * @param[in] 	blockSize number of samples that are processed at a time.
       * @return 		none.
       */
      void arm_fir_init_q31(
          arm_fir_instance_q31 * S,
          uint16_t numTaps,
          q31_t * pCoeffs,
          q31_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the floating-point FIR filter.
       * @param[in] *S points to an instance of the floating-point FIR structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_f32(
          const arm_fir_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the floating-point FIR filter.
       * @param[in,out] *S points to an instance of the floating-point FIR filter structure.
       * @param[in] 	numTaps  Number of filter coefficients in the filter.
       * @param[in] 	*pCoeffs points to the filter coefficients.
       * @param[in] 	*pState points to the state buffer.
       * @param[in] 	blockSize number of samples that are processed at a time.
       * @return    	none.
       */
      void arm_fir_init_f32(
          arm_fir_instance_f32 * S,
          uint16_t numTaps,
          float32_t * pCoeffs,
          float32_t * pState,
          uint32_t blockSize);
  
  
      /**
       * @brief Instance structure for the Q15 Biquad cascade filter.
       */
      typedef struct
      {
          int8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
          q15_t *pState;            /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
          q15_t *pCoeffs;           /**< Points to the array of coefficients.  The array is of length 5*numStages. */
          int8_t postShift;         /**< Additional shift, in bits, applied to each output sample. */
  
      } arm_biquad_casd_df1_inst_q15;
  
  
      /**
       * @brief Instance structure for the Q31 Biquad cascade filter.
       */
      typedef struct
      {
          uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
          q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
          q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
          uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
  
      } arm_biquad_casd_df1_inst_q31;
  
      /**
       * @brief Instance structure for the floating-point Biquad cascade filter.
       */
      typedef struct
      {
          uint32_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
          float32_t *pState;          /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
          float32_t *pCoeffs;         /**< Points to the array of coefficients.  The array is of length 5*numStages. */
  
  
      } arm_biquad_casd_df1_inst_f32;
  
  
  
      /**
       * @brief Processing function for the Q15 Biquad cascade filter.
       * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
       * @param[in]  *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in]  blockSize number of samples to process.
       * @return     none.
       */
  
      void arm_biquad_cascade_df1_q15(
          const arm_biquad_casd_df1_inst_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q15 Biquad cascade filter.
       * @param[in,out] *S           points to an instance of the Q15 Biquad cascade structure.
       * @param[in]     numStages    number of 2nd order stages in the filter.
       * @param[in]     *pCoeffs     points to the filter coefficients.
       * @param[in]     *pState      points to the state buffer.
       * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
       * @return        none
       */
  
      void arm_biquad_cascade_df1_init_q15(
          arm_biquad_casd_df1_inst_q15 * S,
          uint8_t numStages,
          q15_t * pCoeffs,
          q15_t * pState,
          int8_t postShift);
  
  
      /**
       * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
       * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
       * @param[in]  *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in]  blockSize number of samples to process.
       * @return     none.
       */
  
      void arm_biquad_cascade_df1_fast_q15(
          const arm_biquad_casd_df1_inst_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief Processing function for the Q31 Biquad cascade filter
       * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
       * @param[in]  *pSrc      points to the block of input data.
       * @param[out] *pDst      points to the block of output data.
       * @param[in]  blockSize  number of samples to process.
       * @return     none.
       */
  
      void arm_biquad_cascade_df1_q31(
          const arm_biquad_casd_df1_inst_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
       * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
       * @param[in]  *pSrc      points to the block of input data.
       * @param[out] *pDst      points to the block of output data.
       * @param[in]  blockSize  number of samples to process.
       * @return     none.
       */
  
      void arm_biquad_cascade_df1_fast_q31(
          const arm_biquad_casd_df1_inst_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q31 Biquad cascade filter.
       * @param[in,out] *S           points to an instance of the Q31 Biquad cascade structure.
       * @param[in]     numStages      number of 2nd order stages in the filter.
       * @param[in]     *pCoeffs     points to the filter coefficients.
       * @param[in]     *pState      points to the state buffer.
       * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
       * @return        none
       */
  
      void arm_biquad_cascade_df1_init_q31(
          arm_biquad_casd_df1_inst_q31 * S,
          uint8_t numStages,
          q31_t * pCoeffs,
          q31_t * pState,
          int8_t postShift);
  
      /**
       * @brief Processing function for the floating-point Biquad cascade filter.
       * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.
       * @param[in]  *pSrc      points to the block of input data.
       * @param[out] *pDst      points to the block of output data.
       * @param[in]  blockSize  number of samples to process.
       * @return     none.
       */
  
      void arm_biquad_cascade_df1_f32(
          const arm_biquad_casd_df1_inst_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the floating-point Biquad cascade filter.
       * @param[in,out] *S           points to an instance of the floating-point Biquad cascade structure.
       * @param[in]     numStages    number of 2nd order stages in the filter.
       * @param[in]     *pCoeffs     points to the filter coefficients.
       * @param[in]     *pState      points to the state buffer.
       * @return        none
       */
  
      void arm_biquad_cascade_df1_init_f32(
          arm_biquad_casd_df1_inst_f32 * S,
          uint8_t numStages,
          float32_t * pCoeffs,
          float32_t * pState);
  
  
      /**
       * @brief Instance structure for the floating-point matrix structure.
       */
  
      typedef struct
      {
          uint16_t numRows;     /**< number of rows of the matrix.     */
          uint16_t numCols;     /**< number of columns of the matrix.  */
          float32_t *pData;     /**< points to the data of the matrix. */
      } arm_matrix_instance_f32;
  
      /**
       * @brief Instance structure for the Q15 matrix structure.
       */
  
      typedef struct
      {
          uint16_t numRows;     /**< number of rows of the matrix.     */
          uint16_t numCols;     /**< number of columns of the matrix.  */
          q15_t *pData;         /**< points to the data of the matrix. */
  
      } arm_matrix_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 matrix structure.
       */
  
      typedef struct
      {
          uint16_t numRows;     /**< number of rows of the matrix.     */
          uint16_t numCols;     /**< number of columns of the matrix.  */
          q31_t *pData;         /**< points to the data of the matrix. */
  
      } arm_matrix_instance_q31;
  
  
  
      /**
       * @brief Floating-point matrix addition.
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_add_f32(
          const arm_matrix_instance_f32 * pSrcA,
          const arm_matrix_instance_f32 * pSrcB,
          arm_matrix_instance_f32 * pDst);
  
      /**
       * @brief Q15 matrix addition.
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_add_q15(
          const arm_matrix_instance_q15 * pSrcA,
          const arm_matrix_instance_q15 * pSrcB,
          arm_matrix_instance_q15 * pDst);
  
      /**
       * @brief Q31 matrix addition.
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_add_q31(
          const arm_matrix_instance_q31 * pSrcA,
          const arm_matrix_instance_q31 * pSrcB,
          arm_matrix_instance_q31 * pDst);
  
  
      /**
       * @brief Floating-point matrix transpose.
       * @param[in]  *pSrc points to the input matrix
       * @param[out] *pDst points to the output matrix
       * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
       * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_trans_f32(
          const arm_matrix_instance_f32 * pSrc,
          arm_matrix_instance_f32 * pDst);
  
  
      /**
       * @brief Q15 matrix transpose.
       * @param[in]  *pSrc points to the input matrix
       * @param[out] *pDst points to the output matrix
       * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
       * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_trans_q15(
          const arm_matrix_instance_q15 * pSrc,
          arm_matrix_instance_q15 * pDst);
  
      /**
       * @brief Q31 matrix transpose.
       * @param[in]  *pSrc points to the input matrix
       * @param[out] *pDst points to the output matrix
       * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
       * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_trans_q31(
          const arm_matrix_instance_q31 * pSrc,
          arm_matrix_instance_q31 * pDst);
  
  
      /**
       * @brief Floating-point matrix multiplication
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_mult_f32(
          const arm_matrix_instance_f32 * pSrcA,
          const arm_matrix_instance_f32 * pSrcB,
          arm_matrix_instance_f32 * pDst);
  
      /**
       * @brief Q15 matrix multiplication
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_mult_q15(
          const arm_matrix_instance_q15 * pSrcA,
          const arm_matrix_instance_q15 * pSrcB,
          arm_matrix_instance_q15 * pDst,
          q15_t * pState);
  
      /**
       * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
       * @param[in]       *pSrcA  points to the first input matrix structure
       * @param[in]       *pSrcB  points to the second input matrix structure
       * @param[out]      *pDst   points to output matrix structure
       * @param[in]		  *pState points to the array for storing intermediate results
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_mult_fast_q15(
          const arm_matrix_instance_q15 * pSrcA,
          const arm_matrix_instance_q15 * pSrcB,
          arm_matrix_instance_q15 * pDst,
          q15_t * pState);
  
      /**
       * @brief Q31 matrix multiplication
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_mult_q31(
          const arm_matrix_instance_q31 * pSrcA,
          const arm_matrix_instance_q31 * pSrcB,
          arm_matrix_instance_q31 * pDst);
  
      /**
       * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_mult_fast_q31(
          const arm_matrix_instance_q31 * pSrcA,
          const arm_matrix_instance_q31 * pSrcB,
          arm_matrix_instance_q31 * pDst);
  
  
      /**
       * @brief Floating-point matrix subtraction
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_sub_f32(
          const arm_matrix_instance_f32 * pSrcA,
          const arm_matrix_instance_f32 * pSrcB,
          arm_matrix_instance_f32 * pDst);
  
      /**
       * @brief Q15 matrix subtraction
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_sub_q15(
          const arm_matrix_instance_q15 * pSrcA,
          const arm_matrix_instance_q15 * pSrcB,
          arm_matrix_instance_q15 * pDst);
  
      /**
       * @brief Q31 matrix subtraction
       * @param[in]       *pSrcA points to the first input matrix structure
       * @param[in]       *pSrcB points to the second input matrix structure
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_sub_q31(
          const arm_matrix_instance_q31 * pSrcA,
          const arm_matrix_instance_q31 * pSrcB,
          arm_matrix_instance_q31 * pDst);
  
      /**
       * @brief Floating-point matrix scaling.
       * @param[in]  *pSrc points to the input matrix
       * @param[in]  scale scale factor
       * @param[out] *pDst points to the output matrix
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_scale_f32(
          const arm_matrix_instance_f32 * pSrc,
          float32_t scale,
          arm_matrix_instance_f32 * pDst);
  
      /**
       * @brief Q15 matrix scaling.
       * @param[in]       *pSrc points to input matrix
       * @param[in]       scaleFract fractional portion of the scale factor
       * @param[in]       shift number of bits to shift the result by
       * @param[out]      *pDst points to output matrix
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_scale_q15(
          const arm_matrix_instance_q15 * pSrc,
          q15_t scaleFract,
          int32_t shift,
          arm_matrix_instance_q15 * pDst);
  
      /**
       * @brief Q31 matrix scaling.
       * @param[in]       *pSrc points to input matrix
       * @param[in]       scaleFract fractional portion of the scale factor
       * @param[in]       shift number of bits to shift the result by
       * @param[out]      *pDst points to output matrix structure
       * @return     The function returns either
       * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
       */
  
      arm_status arm_mat_scale_q31(
          const arm_matrix_instance_q31 * pSrc,
          q31_t scaleFract,
          int32_t shift,
          arm_matrix_instance_q31 * pDst);
  
  
      /**
       * @brief  Q31 matrix initialization.
       * @param[in,out] *S             points to an instance of the floating-point matrix structure.
       * @param[in]     nRows          number of rows in the matrix.
       * @param[in]     nColumns       number of columns in the matrix.
       * @param[in]     *pData	       points to the matrix data array.
       * @return        none
       */
  
      void arm_mat_init_q31(
          arm_matrix_instance_q31 * S,
          uint16_t nRows,
          uint16_t nColumns,
          q31_t   *pData);
  
      /**
       * @brief  Q15 matrix initialization.
       * @param[in,out] *S             points to an instance of the floating-point matrix structure.
       * @param[in]     nRows          number of rows in the matrix.
       * @param[in]     nColumns       number of columns in the matrix.
       * @param[in]     *pData	       points to the matrix data array.
       * @return        none
       */
  
      void arm_mat_init_q15(
          arm_matrix_instance_q15 * S,
          uint16_t nRows,
          uint16_t nColumns,
          q15_t    *pData);
  
      /**
       * @brief  Floating-point matrix initialization.
       * @param[in,out] *S             points to an instance of the floating-point matrix structure.
       * @param[in]     nRows          number of rows in the matrix.
       * @param[in]     nColumns       number of columns in the matrix.
       * @param[in]     *pData	       points to the matrix data array.
       * @return        none
       */
  
      void arm_mat_init_f32(
          arm_matrix_instance_f32 * S,
          uint16_t nRows,
          uint16_t nColumns,
          float32_t   *pData);
  
  
  
      /**
       * @brief Instance structure for the Q15 PID Control.
       */
      typedef struct
      {
          q15_t A0; 	 /**< The derived gain, A0 = Kp + Ki + Kd . */
  #ifdef ARM_MATH_CM0
          q15_t A1;
          q15_t A2;
  #else
          q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
  #endif
          q15_t state[3];       /**< The state array of length 3. */
          q15_t Kp;           /**< The proportional gain. */
          q15_t Ki;           /**< The integral gain. */
          q15_t Kd;           /**< The derivative gain. */
      } arm_pid_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 PID Control.
       */
      typedef struct
      {
          q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
          q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
          q31_t A2;            /**< The derived gain, A2 = Kd . */
          q31_t state[3];      /**< The state array of length 3. */
          q31_t Kp;            /**< The proportional gain. */
          q31_t Ki;            /**< The integral gain. */
          q31_t Kd;            /**< The derivative gain. */
  
      } arm_pid_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point PID Control.
       */
      typedef struct
      {
          float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
          float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
          float32_t A2;          /**< The derived gain, A2 = Kd . */
          float32_t state[3];    /**< The state array of length 3. */
          float32_t Kp;               /**< The proportional gain. */
          float32_t Ki;               /**< The integral gain. */
          float32_t Kd;               /**< The derivative gain. */
      } arm_pid_instance_f32;
  
  
  
      /**
       * @brief  Initialization function for the floating-point PID Control.
       * @param[in,out] *S      points to an instance of the PID structure.
       * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
       * @return none.
       */
      void arm_pid_init_f32(
          arm_pid_instance_f32 * S,
          int32_t resetStateFlag);
  
      /**
       * @brief  Reset function for the floating-point PID Control.
       * @param[in,out] *S is an instance of the floating-point PID Control structure
       * @return none
       */
      void arm_pid_reset_f32(
          arm_pid_instance_f32 * S);
  
  
      /**
       * @brief  Initialization function for the Q31 PID Control.
       * @param[in,out] *S points to an instance of the Q15 PID structure.
       * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
       * @return none.
       */
      void arm_pid_init_q31(
          arm_pid_instance_q31 * S,
          int32_t resetStateFlag);
  
  
      /**
       * @brief  Reset function for the Q31 PID Control.
       * @param[in,out] *S points to an instance of the Q31 PID Control structure
       * @return none
       */
  
      void arm_pid_reset_q31(
          arm_pid_instance_q31 * S);
  
      /**
       * @brief  Initialization function for the Q15 PID Control.
       * @param[in,out] *S points to an instance of the Q15 PID structure.
       * @param[in] resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
       * @return none.
       */
      void arm_pid_init_q15(
          arm_pid_instance_q15 * S,
          int32_t resetStateFlag);
  
      /**
       * @brief  Reset function for the Q15 PID Control.
       * @param[in,out] *S points to an instance of the q15 PID Control structure
       * @return none
       */
      void arm_pid_reset_q15(
          arm_pid_instance_q15 * S);
  
  
      /**
       * @brief Instance structure for the floating-point Linear Interpolate function.
       */
      typedef struct
      {
          uint32_t nValues;           /**< nValues */
          float32_t x1;               /**< x1 */
          float32_t xSpacing;         /**< xSpacing */
          float32_t *pYData;          /**< pointer to the table of Y values */
      } arm_linear_interp_instance_f32;
  
      /**
       * @brief Instance structure for the floating-point bilinear interpolation function.
       */
  
      typedef struct
      {
          uint16_t numRows;	/**< number of rows in the data table. */
          uint16_t numCols;	/**< number of columns in the data table. */
          float32_t *pData;	/**< points to the data table. */
      } arm_bilinear_interp_instance_f32;
  
      /**
      * @brief Instance structure for the Q31 bilinear interpolation function.
      */
  
      typedef struct
      {
          uint16_t numRows;	/**< number of rows in the data table. */
          uint16_t numCols;	/**< number of columns in the data table. */
          q31_t *pData;	/**< points to the data table. */
      } arm_bilinear_interp_instance_q31;
  
      /**
      * @brief Instance structure for the Q15 bilinear interpolation function.
      */
  
      typedef struct
      {
          uint16_t numRows;	/**< number of rows in the data table. */
          uint16_t numCols;	/**< number of columns in the data table. */
          q15_t *pData;	/**< points to the data table. */
      } arm_bilinear_interp_instance_q15;
  
      /**
      * @brief Instance structure for the Q15 bilinear interpolation function.
      */
  
      typedef struct
      {
          uint16_t numRows; 	/**< number of rows in the data table. */
          uint16_t numCols;	/**< number of columns in the data table. */
          q7_t *pData;		/**< points to the data table. */
      } arm_bilinear_interp_instance_q7;
  
  
      /**
       * @brief Q7 vector multiplication.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst  points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_mult_q7(
          q7_t * pSrcA,
          q7_t * pSrcB,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q15 vector multiplication.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst  points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_mult_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q31 vector multiplication.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_mult_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Floating-point vector multiplication.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_mult_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          float32_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief Instance structure for the Q15 CFFT/CIFFT function.
       */
  
      typedef struct
      {
          uint16_t  fftLen;                /**< length of the FFT. */
          uint8_t   ifftFlag;              /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
          uint8_t   bitReverseFlag;        /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
          q15_t     *pTwiddle;             /**< points to the twiddle factor table. */
          uint16_t  *pBitRevTable;         /**< points to the bit reversal table. */
          uint16_t  twidCoefModifier;      /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          uint16_t  bitRevFactor;          /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
      } arm_cfft_radix4_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 CFFT/CIFFT function.
       */
  
      typedef struct
      {
          uint16_t    fftLen;              /**< length of the FFT. */
          uint8_t     ifftFlag;            /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
          uint8_t     bitReverseFlag;      /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
          q31_t       *pTwiddle;           /**< points to the twiddle factor table. */
          uint16_t    *pBitRevTable;       /**< points to the bit reversal table. */
          uint16_t    twidCoefModifier;    /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          uint16_t    bitRevFactor;        /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
      } arm_cfft_radix4_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point CFFT/CIFFT function.
       */
  
      typedef struct
      {
          uint16_t     fftLen;               /**< length of the FFT. */
          uint8_t      ifftFlag;             /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
          uint8_t      bitReverseFlag;       /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
          float32_t    *pTwiddle;            /**< points to the twiddle factor table. */
          uint16_t     *pBitRevTable;        /**< points to the bit reversal table. */
          uint16_t     twidCoefModifier;     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          uint16_t     bitRevFactor;         /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
          float32_t    onebyfftLen;          /**< value of 1/fftLen. */
      } arm_cfft_radix4_instance_f32;
  
      /**
       * @brief Processing function for the Q15 CFFT/CIFFT.
       * @param[in]      *S    points to an instance of the Q15 CFFT/CIFFT structure.
       * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
       * @return none.
       */
  
      void arm_cfft_radix4_q15(
          const arm_cfft_radix4_instance_q15 * S,
          q15_t * pSrc);
  
      /**
       * @brief Initialization function for the Q15 CFFT/CIFFT.
       * @param[in,out] *S             points to an instance of the Q15 CFFT/CIFFT structure.
       * @param[in]     fftLen         length of the FFT.
       * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
       * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
       */
  
      arm_status arm_cfft_radix4_init_q15(
          arm_cfft_radix4_instance_q15 * S,
          uint16_t fftLen,
          uint8_t ifftFlag,
          uint8_t bitReverseFlag);
  
      /**
       * @brief Processing function for the Q31 CFFT/CIFFT.
       * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.
       * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
       * @return none.
       */
  
      void arm_cfft_radix4_q31(
          const arm_cfft_radix4_instance_q31 * S,
          q31_t * pSrc);
  
      /**
       * @brief  Initialization function for the Q31 CFFT/CIFFT.
       * @param[in,out] *S             points to an instance of the Q31 CFFT/CIFFT structure.
       * @param[in]     fftLen         length of the FFT.
       * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
       * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return        arm_status     function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
       */
  
      arm_status arm_cfft_radix4_init_q31(
          arm_cfft_radix4_instance_q31 * S,
          uint16_t fftLen,
          uint8_t ifftFlag,
          uint8_t bitReverseFlag);
  
      /**
       * @brief Processing function for the floating-point CFFT/CIFFT.
       * @param[in]      *S    points to an instance of the floating-point CFFT/CIFFT structure.
       * @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
       * @return none.
       */
  
      void arm_cfft_radix4_f32(
          const arm_cfft_radix4_instance_f32 * S,
          float32_t * pSrc);
  
      /**
       * @brief  Initialization function for the floating-point CFFT/CIFFT.
       * @param[in,out] *S             points to an instance of the floating-point CFFT/CIFFT structure.
       * @param[in]     fftLen         length of the FFT.
       * @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
       * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
       */
  
      arm_status arm_cfft_radix4_init_f32(
          arm_cfft_radix4_instance_f32 * S,
          uint16_t fftLen,
          uint8_t ifftFlag,
          uint8_t bitReverseFlag);
  
  
  
      /*----------------------------------------------------------------------
       *		Internal functions prototypes FFT function
       ----------------------------------------------------------------------*/
  
      /**
       * @brief  Core function for the floating-point CFFT butterfly process.
       * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef           points to the twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @return none.
       */
  
      void arm_radix4_butterfly_f32(
          float32_t * pSrc,
          uint16_t fftLen,
          float32_t * pCoef,
          uint16_t twidCoefModifier);
  
      /**
       * @brief  Core function for the floating-point CIFFT butterfly process.
       * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef           points to twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @param[in]      onebyfftLen      value of 1/fftLen.
       * @return none.
       */
  
      void arm_radix4_butterfly_inverse_f32(
          float32_t * pSrc,
          uint16_t fftLen,
          float32_t * pCoef,
          uint16_t twidCoefModifier,
          float32_t onebyfftLen);
  
      /**
       * @brief  In-place bit reversal function.
       * @param[in, out] *pSrc        points to the in-place buffer of floating-point data type.
       * @param[in]      fftSize      length of the FFT.
       * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
       * @param[in]      *pBitRevTab  points to the bit reversal table.
       * @return none.
       */
  
      void arm_bitreversal_f32(
          float32_t *pSrc,
          uint16_t fftSize,
          uint16_t bitRevFactor,
          uint16_t *pBitRevTab);
  
      /**
       * @brief  Core function for the Q31 CFFT butterfly process.
       * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef           points to twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @return none.
       */
  
      void arm_radix4_butterfly_q31(
          q31_t *pSrc,
          uint32_t fftLen,
          q31_t *pCoef,
          uint32_t twidCoefModifier);
  
      /**
       * @brief  Core function for the Q31 CIFFT butterfly process.
       * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef           points to twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @return none.
       */
  
      void arm_radix4_butterfly_inverse_q31(
          q31_t * pSrc,
          uint32_t fftLen,
          q31_t * pCoef,
          uint32_t twidCoefModifier);
  
      /**
       * @brief  In-place bit reversal function.
       * @param[in, out] *pSrc        points to the in-place buffer of Q31 data type.
       * @param[in]      fftLen       length of the FFT.
       * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
       * @param[in]      *pBitRevTab  points to bit reversal table.
       * @return none.
       */
  
      void arm_bitreversal_q31(
          q31_t * pSrc,
          uint32_t fftLen,
          uint16_t bitRevFactor,
          uint16_t *pBitRevTab);
  
      /**
       * @brief  Core function for the Q15 CFFT butterfly process.
       * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef16         points to twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @return none.
       */
  
      void arm_radix4_butterfly_q15(
          q15_t *pSrc16,
          uint32_t fftLen,
          q15_t *pCoef16,
          uint32_t twidCoefModifier);
  
      /**
       * @brief  Core function for the Q15 CIFFT butterfly process.
       * @param[in, out] *pSrc16          points to the in-place buffer of Q15 data type.
       * @param[in]      fftLen           length of the FFT.
       * @param[in]      *pCoef16         points to twiddle coefficient buffer.
       * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
       * @return none.
       */
  
      void arm_radix4_butterfly_inverse_q15(
          q15_t *pSrc16,
          uint32_t fftLen,
          q15_t *pCoef16,
          uint32_t twidCoefModifier);
  
      /**
       * @brief  In-place bit reversal function.
       * @param[in, out] *pSrc        points to the in-place buffer of Q15 data type.
       * @param[in]      fftLen       length of the FFT.
       * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
       * @param[in]      *pBitRevTab  points to bit reversal table.
       * @return none.
       */
  
      void arm_bitreversal_q15(
          q15_t * pSrc,
          uint32_t fftLen,
          uint16_t bitRevFactor,
          uint16_t *pBitRevTab);
  
      /**
       * @brief Instance structure for the Q15 RFFT/RIFFT function.
       */
  
      typedef struct
      {
          uint32_t fftLenReal;                      /**< length of the real FFT. */
          uint32_t fftLenBy2;                       /**< length of the complex FFT. */
          uint8_t  ifftFlagR;                       /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
          uint8_t  bitReverseFlagR;                 /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
          uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          q15_t    *pTwiddleAReal;                  /**< points to the real twiddle factor table. */
          q15_t    *pTwiddleBReal;                  /**< points to the imag twiddle factor table. */
          arm_cfft_radix4_instance_q15 *pCfft;	  /**< points to the complex FFT instance. */
      } arm_rfft_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 RFFT/RIFFT function.
       */
  
      typedef struct
      {
          uint32_t fftLenReal;                        /**< length of the real FFT. */
          uint32_t fftLenBy2;                         /**< length of the complex FFT. */
          uint8_t  ifftFlagR;                         /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
          uint8_t  bitReverseFlagR;                   /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
          uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          q31_t    *pTwiddleAReal;                    /**< points to the real twiddle factor table. */
          q31_t    *pTwiddleBReal;                    /**< points to the imag twiddle factor table. */
          arm_cfft_radix4_instance_q31 *pCfft;        /**< points to the complex FFT instance. */
      } arm_rfft_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point RFFT/RIFFT function.
       */
  
      typedef struct
      {
          uint32_t  fftLenReal;                       /**< length of the real FFT. */
          uint16_t  fftLenBy2;                        /**< length of the complex FFT. */
          uint8_t   ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
          uint8_t   bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
          uint32_t  twidCoefRModifier;                /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
          float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
          float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
          arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
      } arm_rfft_instance_f32;
  
      /**
       * @brief Processing function for the Q15 RFFT/RIFFT.
       * @param[in]  *S    points to an instance of the Q15 RFFT/RIFFT structure.
       * @param[in]  *pSrc points to the input buffer.
       * @param[out] *pDst points to the output buffer.
       * @return none.
       */
  
      void arm_rfft_q15(
          const arm_rfft_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst);
  
      /**
       * @brief  Initialization function for the Q15 RFFT/RIFFT.
       * @param[in, out] *S             points to an instance of the Q15 RFFT/RIFFT structure.
       * @param[in]      *S_CFFT        points to an instance of the Q15 CFFT/CIFFT structure.
       * @param[in]      fftLenReal     length of the FFT.
       * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
       * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
       */
  
      arm_status arm_rfft_init_q15(
          arm_rfft_instance_q15 * S,
          arm_cfft_radix4_instance_q15 * S_CFFT,
          uint32_t fftLenReal,
          uint32_t ifftFlagR,
          uint32_t bitReverseFlag);
  
      /**
       * @brief Processing function for the Q31 RFFT/RIFFT.
       * @param[in]  *S    points to an instance of the Q31 RFFT/RIFFT structure.
       * @param[in]  *pSrc points to the input buffer.
       * @param[out] *pDst points to the output buffer.
       * @return none.
       */
  
      void arm_rfft_q31(
          const arm_rfft_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst);
  
      /**
       * @brief  Initialization function for the Q31 RFFT/RIFFT.
       * @param[in, out] *S             points to an instance of the Q31 RFFT/RIFFT structure.
       * @param[in, out] *S_CFFT        points to an instance of the Q31 CFFT/CIFFT structure.
       * @param[in]      fftLenReal     length of the FFT.
       * @param[in]      ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
       * @param[in]      bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
       */
  
      arm_status arm_rfft_init_q31(
          arm_rfft_instance_q31 * S,
          arm_cfft_radix4_instance_q31 * S_CFFT,
          uint32_t fftLenReal,
          uint32_t ifftFlagR,
          uint32_t bitReverseFlag);
  
      /**
       * @brief  Initialization function for the floating-point RFFT/RIFFT.
       * @param[in,out] *S             points to an instance of the floating-point RFFT/RIFFT structure.
       * @param[in,out] *S_CFFT        points to an instance of the floating-point CFFT/CIFFT structure.
       * @param[in]     fftLenReal     length of the FFT.
       * @param[in]     ifftFlagR      flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
       * @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
       * @return		The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
       */
  
      arm_status arm_rfft_init_f32(
          arm_rfft_instance_f32 * S,
          arm_cfft_radix4_instance_f32 * S_CFFT,
          uint32_t fftLenReal,
          uint32_t ifftFlagR,
          uint32_t bitReverseFlag);
  
      /**
       * @brief Processing function for the floating-point RFFT/RIFFT.
       * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure.
       * @param[in]  *pSrc points to the input buffer.
       * @param[out] *pDst points to the output buffer.
       * @return none.
       */
  
      void arm_rfft_f32(
          const arm_rfft_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst);
  
      /**
       * @brief Instance structure for the floating-point DCT4/IDCT4 function.
       */
  
      typedef struct
      {
          uint16_t N;                         /**< length of the DCT4. */
          uint16_t Nby2;                      /**< half of the length of the DCT4. */
          float32_t normalize;                /**< normalizing factor. */
          float32_t *pTwiddle;                /**< points to the twiddle factor table. */
          float32_t *pCosFactor;              /**< points to the cosFactor table. */
          arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
          arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
      } arm_dct4_instance_f32;
  
      /**
       * @brief  Initialization function for the floating-point DCT4/IDCT4.
       * @param[in,out] *S         points to an instance of floating-point DCT4/IDCT4 structure.
       * @param[in]     *S_RFFT    points to an instance of floating-point RFFT/RIFFT structure.
       * @param[in]     *S_CFFT    points to an instance of floating-point CFFT/CIFFT structure.
       * @param[in]     N          length of the DCT4.
       * @param[in]     Nby2       half of the length of the DCT4.
       * @param[in]     normalize  normalizing factor.
       * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
       */
  
      arm_status arm_dct4_init_f32(
          arm_dct4_instance_f32 * S,
          arm_rfft_instance_f32 * S_RFFT,
          arm_cfft_radix4_instance_f32 * S_CFFT,
          uint16_t N,
          uint16_t Nby2,
          float32_t normalize);
  
      /**
       * @brief Processing function for the floating-point DCT4/IDCT4.
       * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
       * @param[in]       *pState        points to state buffer.
       * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
       * @return none.
       */
  
      void arm_dct4_f32(
          const arm_dct4_instance_f32 * S,
          float32_t * pState,
          float32_t * pInlineBuffer);
  
      /**
       * @brief Instance structure for the Q31 DCT4/IDCT4 function.
       */
  
      typedef struct
      {
          uint16_t N;                         /**< length of the DCT4. */
          uint16_t Nby2;                      /**< half of the length of the DCT4. */
          q31_t normalize;                    /**< normalizing factor. */
          q31_t *pTwiddle;                    /**< points to the twiddle factor table. */
          q31_t *pCosFactor;                  /**< points to the cosFactor table. */
          arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
          arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
      } arm_dct4_instance_q31;
  
      /**
       * @brief  Initialization function for the Q31 DCT4/IDCT4.
       * @param[in,out] *S         points to an instance of Q31 DCT4/IDCT4 structure.
       * @param[in]     *S_RFFT    points to an instance of Q31 RFFT/RIFFT structure
       * @param[in]     *S_CFFT    points to an instance of Q31 CFFT/CIFFT structure
       * @param[in]     N          length of the DCT4.
       * @param[in]     Nby2       half of the length of the DCT4.
       * @param[in]     normalize  normalizing factor.
       * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
       */
  
      arm_status arm_dct4_init_q31(
          arm_dct4_instance_q31 * S,
          arm_rfft_instance_q31 * S_RFFT,
          arm_cfft_radix4_instance_q31 * S_CFFT,
          uint16_t N,
          uint16_t Nby2,
          q31_t normalize);
  
      /**
       * @brief Processing function for the Q31 DCT4/IDCT4.
       * @param[in]       *S             points to an instance of the Q31 DCT4 structure.
       * @param[in]       *pState        points to state buffer.
       * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
       * @return none.
       */
  
      void arm_dct4_q31(
          const arm_dct4_instance_q31 * S,
          q31_t * pState,
          q31_t * pInlineBuffer);
  
      /**
       * @brief Instance structure for the Q15 DCT4/IDCT4 function.
       */
  
      typedef struct
      {
          uint16_t N;                         /**< length of the DCT4. */
          uint16_t Nby2;                      /**< half of the length of the DCT4. */
          q15_t normalize;                    /**< normalizing factor. */
          q15_t *pTwiddle;                    /**< points to the twiddle factor table. */
          q15_t *pCosFactor;                  /**< points to the cosFactor table. */
          arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
          arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
      } arm_dct4_instance_q15;
  
      /**
       * @brief  Initialization function for the Q15 DCT4/IDCT4.
       * @param[in,out] *S         points to an instance of Q15 DCT4/IDCT4 structure.
       * @param[in]     *S_RFFT    points to an instance of Q15 RFFT/RIFFT structure.
       * @param[in]     *S_CFFT    points to an instance of Q15 CFFT/CIFFT structure.
       * @param[in]     N          length of the DCT4.
       * @param[in]     Nby2       half of the length of the DCT4.
       * @param[in]     normalize  normalizing factor.
       * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
       */
  
      arm_status arm_dct4_init_q15(
          arm_dct4_instance_q15 * S,
          arm_rfft_instance_q15 * S_RFFT,
          arm_cfft_radix4_instance_q15 * S_CFFT,
          uint16_t N,
          uint16_t Nby2,
          q15_t normalize);
  
      /**
       * @brief Processing function for the Q15 DCT4/IDCT4.
       * @param[in]       *S             points to an instance of the Q15 DCT4 structure.
       * @param[in]       *pState        points to state buffer.
       * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
       * @return none.
       */
  
      void arm_dct4_q15(
          const arm_dct4_instance_q15 * S,
          q15_t * pState,
          q15_t * pInlineBuffer);
  
      /**
       * @brief Floating-point vector addition.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_add_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q7 vector addition.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_add_q7(
          q7_t * pSrcA,
          q7_t * pSrcB,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q15 vector addition.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_add_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q31 vector addition.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_add_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Floating-point vector subtraction.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_sub_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q7 vector subtraction.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_sub_q7(
          q7_t * pSrcA,
          q7_t * pSrcB,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q15 vector subtraction.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_sub_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q31 vector subtraction.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_sub_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Multiplies a floating-point vector by a scalar.
       * @param[in]       *pSrc points to the input vector
       * @param[in]       scale scale factor to be applied
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_scale_f32(
          float32_t * pSrc,
          float32_t scale,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Multiplies a Q7 vector by a scalar.
       * @param[in]       *pSrc points to the input vector
       * @param[in]       scaleFract fractional portion of the scale value
       * @param[in]       shift number of bits to shift the result by
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_scale_q7(
          q7_t * pSrc,
          q7_t scaleFract,
          int8_t shift,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Multiplies a Q15 vector by a scalar.
       * @param[in]       *pSrc points to the input vector
       * @param[in]       scaleFract fractional portion of the scale value
       * @param[in]       shift number of bits to shift the result by
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_scale_q15(
          q15_t * pSrc,
          q15_t scaleFract,
          int8_t shift,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Multiplies a Q31 vector by a scalar.
       * @param[in]       *pSrc points to the input vector
       * @param[in]       scaleFract fractional portion of the scale value
       * @param[in]       shift number of bits to shift the result by
       * @param[out]      *pDst points to the output vector
       * @param[in]       blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_scale_q31(
          q31_t * pSrc,
          q31_t scaleFract,
          int8_t shift,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q7 vector absolute value.
       * @param[in]       *pSrc points to the input buffer
       * @param[out]      *pDst points to the output buffer
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_abs_q7(
          q7_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Floating-point vector absolute value.
       * @param[in]       *pSrc points to the input buffer
       * @param[out]      *pDst points to the output buffer
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_abs_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q15 vector absolute value.
       * @param[in]       *pSrc points to the input buffer
       * @param[out]      *pDst points to the output buffer
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_abs_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Q31 vector absolute value.
       * @param[in]       *pSrc points to the input buffer
       * @param[out]      *pDst points to the output buffer
       * @param[in]       blockSize number of samples in each vector
       * @return none.
       */
  
      void arm_abs_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Dot product of floating-point vectors.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[in]       blockSize number of samples in each vector
       * @param[out]      *result output result returned here
       * @return none.
       */
  
      void arm_dot_prod_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          uint32_t blockSize,
          float32_t * result);
  
      /**
       * @brief Dot product of Q7 vectors.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[in]       blockSize number of samples in each vector
       * @param[out]      *result output result returned here
       * @return none.
       */
  
      void arm_dot_prod_q7(
          q7_t * pSrcA,
          q7_t * pSrcB,
          uint32_t blockSize,
          q31_t * result);
  
      /**
       * @brief Dot product of Q15 vectors.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[in]       blockSize number of samples in each vector
       * @param[out]      *result output result returned here
       * @return none.
       */
  
      void arm_dot_prod_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          uint32_t blockSize,
          q63_t * result);
  
      /**
       * @brief Dot product of Q31 vectors.
       * @param[in]       *pSrcA points to the first input vector
       * @param[in]       *pSrcB points to the second input vector
       * @param[in]       blockSize number of samples in each vector
       * @param[out]      *result output result returned here
       * @return none.
       */
  
      void arm_dot_prod_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          uint32_t blockSize,
          q63_t * result);
  
      /**
       * @brief  Shifts the elements of a Q7 vector a specified number of bits.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_shift_q7(
          q7_t * pSrc,
          int8_t shiftBits,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Shifts the elements of a Q15 vector a specified number of bits.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_shift_q15(
          q15_t * pSrc,
          int8_t shiftBits,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Shifts the elements of a Q31 vector a specified number of bits.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_shift_q31(
          q31_t * pSrc,
          int8_t shiftBits,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Adds a constant offset to a floating-point vector.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  offset is the offset to be added
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_offset_f32(
          float32_t * pSrc,
          float32_t offset,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Adds a constant offset to a Q7 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  offset is the offset to be added
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_offset_q7(
          q7_t * pSrc,
          q7_t offset,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Adds a constant offset to a Q15 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  offset is the offset to be added
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_offset_q15(
          q15_t * pSrc,
          q15_t offset,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Adds a constant offset to a Q31 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[in]  offset is the offset to be added
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_offset_q31(
          q31_t * pSrc,
          q31_t offset,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Negates the elements of a floating-point vector.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_negate_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Negates the elements of a Q7 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_negate_q7(
          q7_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Negates the elements of a Q15 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_negate_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Negates the elements of a Q31 vector.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  blockSize number of samples in the vector
       * @return none.
       */
  
      void arm_negate_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
      /**
       * @brief  Copies the elements of a floating-point vector.
       * @param[in]  *pSrc input pointer
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_copy_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Copies the elements of a Q7 vector.
       * @param[in]  *pSrc input pointer
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_copy_q7(
          q7_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Copies the elements of a Q15 vector.
       * @param[in]  *pSrc input pointer
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_copy_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Copies the elements of a Q31 vector.
       * @param[in]  *pSrc input pointer
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_copy_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
      /**
       * @brief  Fills a constant value into a floating-point vector.
       * @param[in]  value input value to be filled
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_fill_f32(
          float32_t value,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Fills a constant value into a Q7 vector.
       * @param[in]  value input value to be filled
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_fill_q7(
          q7_t value,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Fills a constant value into a Q15 vector.
       * @param[in]  value input value to be filled
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_fill_q15(
          q15_t value,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Fills a constant value into a Q31 vector.
       * @param[in]  value input value to be filled
       * @param[out]  *pDst output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_fill_q31(
          q31_t value,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Convolution of floating-point sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_f32(
          float32_t * pSrcA,
          uint32_t srcALen,
          float32_t * pSrcB,
          uint32_t srcBLen,
          float32_t * pDst);
  
      /**
       * @brief Convolution of Q15 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst);
  
      /**
       * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_fast_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst);
  
      /**
       * @brief Convolution of Q31 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst);
  
      /**
       * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_fast_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst);
  
      /**
       * @brief Convolution of Q7 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
       * @return none.
       */
  
      void arm_conv_q7(
          q7_t * pSrcA,
          uint32_t srcALen,
          q7_t * pSrcB,
          uint32_t srcBLen,
          q7_t * pDst);
  
      /**
       * @brief Partial convolution of floating-point sequences.
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_f32(
          float32_t * pSrcA,
          uint32_t srcALen,
          float32_t * pSrcB,
          uint32_t srcBLen,
          float32_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
      /**
       * @brief Partial convolution of Q15 sequences.
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
      /**
       * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_fast_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
      /**
       * @brief Partial convolution of Q31 sequences.
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
  
      /**
       * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_fast_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
      /**
       * @brief Partial convolution of Q7 sequences.
       * @param[in]       *pSrcA points to the first input sequence.
       * @param[in]       srcALen length of the first input sequence.
       * @param[in]       *pSrcB points to the second input sequence.
       * @param[in]       srcBLen length of the second input sequence.
       * @param[out]      *pDst points to the block of output data
       * @param[in]       firstIndex is the first output sample to start with.
       * @param[in]       numPoints is the number of output points to be computed.
       * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
       */
  
      arm_status arm_conv_partial_q7(
          q7_t * pSrcA,
          uint32_t srcALen,
          q7_t * pSrcB,
          uint32_t srcBLen,
          q7_t * pDst,
          uint32_t firstIndex,
          uint32_t numPoints);
  
  
      /**
       * @brief Instance structure for the Q15 FIR decimator.
       */
  
      typedef struct
      {
          uint8_t M;                      /**< decimation factor. */
          uint16_t numTaps;               /**< number of coefficients in the filter. */
          q15_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
          q15_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
      } arm_fir_decimate_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 FIR decimator.
       */
  
      typedef struct
      {
          uint8_t M;                  /**< decimation factor. */
          uint16_t numTaps;           /**< number of coefficients in the filter. */
          q31_t *pCoeffs;              /**< points to the coefficient array. The array is of length numTaps.*/
          q31_t *pState;               /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
  
      } arm_fir_decimate_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point FIR decimator.
       */
  
      typedef struct
      {
          uint8_t M;                          /**< decimation factor. */
          uint16_t numTaps;                   /**< number of coefficients in the filter. */
          float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
          float32_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
  
      } arm_fir_decimate_instance_f32;
  
  
  
      /**
       * @brief Processing function for the floating-point FIR decimator.
       * @param[in] *S points to an instance of the floating-point FIR decimator structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data
       * @param[in] blockSize number of input samples to process per call.
       * @return none
       */
  
      void arm_fir_decimate_f32(
          const arm_fir_decimate_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the floating-point FIR decimator.
       * @param[in,out] *S points to an instance of the floating-point FIR decimator structure.
       * @param[in] numTaps  number of coefficients in the filter.
       * @param[in] M  decimation factor.
       * @param[in] *pCoeffs points to the filter coefficients.
       * @param[in] *pState points to the state buffer.
       * @param[in] blockSize number of input samples to process per call.
       * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * <code>blockSize</code> is not a multiple of <code>M</code>.
       */
  
      arm_status arm_fir_decimate_init_f32(
          arm_fir_decimate_instance_f32 * S,
          uint16_t numTaps,
          uint8_t M,
          float32_t * pCoeffs,
          float32_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q15 FIR decimator.
       * @param[in] *S points to an instance of the Q15 FIR decimator structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data
       * @param[in] blockSize number of input samples to process per call.
       * @return none
       */
  
      void arm_fir_decimate_q15(
          const arm_fir_decimate_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
       * @param[in] *S points to an instance of the Q15 FIR decimator structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data
       * @param[in] blockSize number of input samples to process per call.
       * @return none
       */
  
      void arm_fir_decimate_fast_q15(
          const arm_fir_decimate_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
  
  
      /**
       * @brief  Initialization function for the Q15 FIR decimator.
       * @param[in,out] *S points to an instance of the Q15 FIR decimator structure.
       * @param[in] numTaps  number of coefficients in the filter.
       * @param[in] M  decimation factor.
       * @param[in] *pCoeffs points to the filter coefficients.
       * @param[in] *pState points to the state buffer.
       * @param[in] blockSize number of input samples to process per call.
       * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * <code>blockSize</code> is not a multiple of <code>M</code>.
       */
  
      arm_status arm_fir_decimate_init_q15(
          arm_fir_decimate_instance_q15 * S,
          uint16_t numTaps,
          uint8_t M,
          q15_t * pCoeffs,
          q15_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q31 FIR decimator.
       * @param[in] *S points to an instance of the Q31 FIR decimator structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data
       * @param[in] blockSize number of input samples to process per call.
       * @return none
       */
  
      void arm_fir_decimate_q31(
          const arm_fir_decimate_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
       * @param[in] *S points to an instance of the Q31 FIR decimator structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data
       * @param[in] blockSize number of input samples to process per call.
       * @return none
       */
  
      void arm_fir_decimate_fast_q31(
          arm_fir_decimate_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the Q31 FIR decimator.
       * @param[in,out] *S points to an instance of the Q31 FIR decimator structure.
       * @param[in] numTaps  number of coefficients in the filter.
       * @param[in] M  decimation factor.
       * @param[in] *pCoeffs points to the filter coefficients.
       * @param[in] *pState points to the state buffer.
       * @param[in] blockSize number of input samples to process per call.
       * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * <code>blockSize</code> is not a multiple of <code>M</code>.
       */
  
      arm_status arm_fir_decimate_init_q31(
          arm_fir_decimate_instance_q31 * S,
          uint16_t numTaps,
          uint8_t M,
          q31_t * pCoeffs,
          q31_t * pState,
          uint32_t blockSize);
  
  
  
      /**
       * @brief Instance structure for the Q15 FIR interpolator.
       */
  
      typedef struct
      {
          uint8_t L;                      /**< upsample factor. */
          uint16_t phaseLength;           /**< length of each polyphase filter component. */
          q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
          q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
      } arm_fir_interpolate_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 FIR interpolator.
       */
  
      typedef struct
      {
          uint8_t L;                      /**< upsample factor. */
          uint16_t phaseLength;           /**< length of each polyphase filter component. */
          q31_t *pCoeffs;                  /**< points to the coefficient array. The array is of length L*phaseLength. */
          q31_t *pState;                   /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
      } arm_fir_interpolate_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point FIR interpolator.
       */
  
      typedef struct
      {
          uint8_t L;                     /**< upsample factor. */
          uint16_t phaseLength;          /**< length of each polyphase filter component. */
          float32_t *pCoeffs;             /**< points to the coefficient array. The array is of length L*phaseLength. */
          float32_t *pState;              /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
      } arm_fir_interpolate_instance_f32;
  
  
      /**
       * @brief Processing function for the Q15 FIR interpolator.
       * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
       * @param[in] *pSrc     points to the block of input data.
       * @param[out] *pDst    points to the block of output data.
       * @param[in] blockSize number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_interpolate_q15(
          const arm_fir_interpolate_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the Q15 FIR interpolator.
       * @param[in,out] *S        points to an instance of the Q15 FIR interpolator structure.
       * @param[in]     L         upsample factor.
       * @param[in]     numTaps   number of filter coefficients in the filter.
       * @param[in]     *pCoeffs  points to the filter coefficient buffer.
       * @param[in]     *pState   points to the state buffer.
       * @param[in]     blockSize number of input samples to process per call.
       * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
       */
  
      arm_status arm_fir_interpolate_init_q15(
          arm_fir_interpolate_instance_q15 * S,
          uint8_t L,
          uint16_t numTaps,
          q15_t * pCoeffs,
          q15_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q31 FIR interpolator.
       * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
       * @param[in] *pSrc     points to the block of input data.
       * @param[out] *pDst    points to the block of output data.
       * @param[in] blockSize number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_interpolate_q31(
          const arm_fir_interpolate_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q31 FIR interpolator.
       * @param[in,out] *S        points to an instance of the Q31 FIR interpolator structure.
       * @param[in]     L         upsample factor.
       * @param[in]     numTaps   number of filter coefficients in the filter.
       * @param[in]     *pCoeffs  points to the filter coefficient buffer.
       * @param[in]     *pState   points to the state buffer.
       * @param[in]     blockSize number of input samples to process per call.
       * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
       */
  
      arm_status arm_fir_interpolate_init_q31(
          arm_fir_interpolate_instance_q31 * S,
          uint8_t L,
          uint16_t numTaps,
          q31_t * pCoeffs,
          q31_t * pState,
          uint32_t blockSize);
  
  
      /**
       * @brief Processing function for the floating-point FIR interpolator.
       * @param[in] *S        points to an instance of the floating-point FIR interpolator structure.
       * @param[in] *pSrc     points to the block of input data.
       * @param[out] *pDst    points to the block of output data.
       * @param[in] blockSize number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_interpolate_f32(
          const arm_fir_interpolate_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the floating-point FIR interpolator.
       * @param[in,out] *S        points to an instance of the floating-point FIR interpolator structure.
       * @param[in]     L         upsample factor.
       * @param[in]     numTaps   number of filter coefficients in the filter.
       * @param[in]     *pCoeffs  points to the filter coefficient buffer.
       * @param[in]     *pState   points to the state buffer.
       * @param[in]     blockSize number of input samples to process per call.
       * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
       * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
       */
  
      arm_status arm_fir_interpolate_init_f32(
          arm_fir_interpolate_instance_f32 * S,
          uint8_t L,
          uint16_t numTaps,
          float32_t * pCoeffs,
          float32_t * pState,
          uint32_t blockSize);
  
      /**
       * @brief Instance structure for the high precision Q31 Biquad cascade filter.
       */
  
      typedef struct
      {
          uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
          q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
          q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
          uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
  
      } arm_biquad_cas_df1_32x64_ins_q31;
  
  
      /**
       * @param[in]  *S        points to an instance of the high precision Q31 Biquad cascade filter structure.
       * @param[in]  *pSrc     points to the block of input data.
       * @param[out] *pDst     points to the block of output data
       * @param[in]  blockSize number of samples to process.
       * @return none.
       */
  
      void arm_biquad_cas_df1_32x64_q31(
          const arm_biquad_cas_df1_32x64_ins_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @param[in,out] *S           points to an instance of the high precision Q31 Biquad cascade filter structure.
       * @param[in]     numStages    number of 2nd order stages in the filter.
       * @param[in]     *pCoeffs     points to the filter coefficients.
       * @param[in]     *pState      points to the state buffer.
       * @param[in]     postShift    shift to be applied to the output. Varies according to the coefficients format
       * @return        none
       */
  
      void arm_biquad_cas_df1_32x64_init_q31(
          arm_biquad_cas_df1_32x64_ins_q31 * S,
          uint8_t numStages,
          q31_t * pCoeffs,
          q63_t * pState,
          uint8_t postShift);
  
  
  
      /**
       * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
       */
  
      typedef struct
      {
          uint8_t   numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
          float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
          float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
      } arm_biquad_cascade_df2T_instance_f32;
  
  
      /**
       * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
       * @param[in]  *S        points to an instance of the filter data structure.
       * @param[in]  *pSrc     points to the block of input data.
       * @param[out] *pDst     points to the block of output data
       * @param[in]  blockSize number of samples to process.
       * @return none.
       */
  
      void arm_biquad_cascade_df2T_f32(
          const arm_biquad_cascade_df2T_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
       * @param[in,out] *S           points to an instance of the filter data structure.
       * @param[in]     numStages    number of 2nd order stages in the filter.
       * @param[in]     *pCoeffs     points to the filter coefficients.
       * @param[in]     *pState      points to the state buffer.
       * @return        none
       */
  
      void arm_biquad_cascade_df2T_init_f32(
          arm_biquad_cascade_df2T_instance_f32 * S,
          uint8_t numStages,
          float32_t * pCoeffs,
          float32_t * pState);
  
  
  
      /**
       * @brief Instance structure for the Q15 FIR lattice filter.
       */
  
      typedef struct
      {
          uint16_t numStages;                          /**< number of filter stages. */
          q15_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
          q15_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
      } arm_fir_lattice_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 FIR lattice filter.
       */
  
      typedef struct
      {
          uint16_t numStages;                          /**< number of filter stages. */
          q31_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
          q31_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
      } arm_fir_lattice_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point FIR lattice filter.
       */
  
      typedef struct
      {
          uint16_t numStages;                  /**< number of filter stages. */
          float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
          float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
      } arm_fir_lattice_instance_f32;
  
      /**
       * @brief Initialization function for the Q15 FIR lattice filter.
       * @param[in] *S points to an instance of the Q15 FIR lattice structure.
       * @param[in] numStages  number of filter stages.
       * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
       * @param[in] *pState points to the state buffer.  The array is of length numStages.
       * @return none.
       */
  
      void arm_fir_lattice_init_q15(
          arm_fir_lattice_instance_q15 * S,
          uint16_t numStages,
          q15_t * pCoeffs,
          q15_t * pState);
  
  
      /**
       * @brief Processing function for the Q15 FIR lattice filter.
       * @param[in] *S points to an instance of the Q15 FIR lattice structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
      void arm_fir_lattice_q15(
          const arm_fir_lattice_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for the Q31 FIR lattice filter.
       * @param[in] *S points to an instance of the Q31 FIR lattice structure.
       * @param[in] numStages  number of filter stages.
       * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
       * @param[in] *pState points to the state buffer.   The array is of length numStages.
       * @return none.
       */
  
      void arm_fir_lattice_init_q31(
          arm_fir_lattice_instance_q31 * S,
          uint16_t numStages,
          q31_t * pCoeffs,
          q31_t * pState);
  
  
      /**
       * @brief Processing function for the Q31 FIR lattice filter.
       * @param[in]  *S        points to an instance of the Q31 FIR lattice structure.
       * @param[in]  *pSrc     points to the block of input data.
       * @param[out] *pDst     points to the block of output data
       * @param[in]  blockSize number of samples to process.
       * @return none.
       */
  
      void arm_fir_lattice_q31(
          const arm_fir_lattice_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for the floating-point FIR lattice filter.
       * @param[in] *S points to an instance of the floating-point FIR lattice structure.
       * @param[in] numStages  number of filter stages.
       * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
       * @param[in] *pState points to the state buffer.  The array is of length numStages.
       * @return none.
       */
  
      void arm_fir_lattice_init_f32(
          arm_fir_lattice_instance_f32 * S,
          uint16_t numStages,
          float32_t * pCoeffs,
          float32_t * pState);
  
      /**
       * @brief Processing function for the floating-point FIR lattice filter.
       * @param[in]  *S        points to an instance of the floating-point FIR lattice structure.
       * @param[in]  *pSrc     points to the block of input data.
       * @param[out] *pDst     points to the block of output data
       * @param[in]  blockSize number of samples to process.
       * @return none.
       */
  
      void arm_fir_lattice_f32(
          const arm_fir_lattice_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Instance structure for the Q15 IIR lattice filter.
       */
      typedef struct
      {
          uint16_t numStages;                         /**< number of stages in the filter. */
          q15_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
          q15_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
          q15_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
      } arm_iir_lattice_instance_q15;
  
      /**
       * @brief Instance structure for the Q31 IIR lattice filter.
       */
      typedef struct
      {
          uint16_t numStages;                         /**< number of stages in the filter. */
          q31_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
          q31_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
          q31_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
      } arm_iir_lattice_instance_q31;
  
      /**
       * @brief Instance structure for the floating-point IIR lattice filter.
       */
      typedef struct
      {
          uint16_t numStages;                         /**< number of stages in the filter. */
          float32_t *pState;                          /**< points to the state variable array. The array is of length numStages+blockSize. */
          float32_t *pkCoeffs;                        /**< points to the reflection coefficient array. The array is of length numStages. */
          float32_t *pvCoeffs;                        /**< points to the ladder coefficient array. The array is of length numStages+1. */
      } arm_iir_lattice_instance_f32;
  
      /**
       * @brief Processing function for the floating-point IIR lattice filter.
       * @param[in] *S points to an instance of the floating-point IIR lattice structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_iir_lattice_f32(
          const arm_iir_lattice_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for the floating-point IIR lattice filter.
       * @param[in] *S points to an instance of the floating-point IIR lattice structure.
       * @param[in] numStages number of stages in the filter.
       * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
       * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
       * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize-1.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_iir_lattice_init_f32(
          arm_iir_lattice_instance_f32 * S,
          uint16_t numStages,
          float32_t *pkCoeffs,
          float32_t *pvCoeffs,
          float32_t *pState,
          uint32_t blockSize);
  
  
      /**
       * @brief Processing function for the Q31 IIR lattice filter.
       * @param[in] *S points to an instance of the Q31 IIR lattice structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_iir_lattice_q31(
          const arm_iir_lattice_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief Initialization function for the Q31 IIR lattice filter.
       * @param[in] *S points to an instance of the Q31 IIR lattice structure.
       * @param[in] numStages number of stages in the filter.
       * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
       * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
       * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_iir_lattice_init_q31(
          arm_iir_lattice_instance_q31 * S,
          uint16_t numStages,
          q31_t *pkCoeffs,
          q31_t *pvCoeffs,
          q31_t *pState,
          uint32_t blockSize);
  
  
      /**
       * @brief Processing function for the Q15 IIR lattice filter.
       * @param[in] *S points to an instance of the Q15 IIR lattice structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[out] *pDst points to the block of output data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_iir_lattice_q15(
          const arm_iir_lattice_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief Initialization function for the Q15 IIR lattice filter.
       * @param[in] *S points to an instance of the fixed-point Q15 IIR lattice structure.
       * @param[in] numStages  number of stages in the filter.
       * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.
       * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.
       * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.
       * @param[in] blockSize number of samples to process per call.
       * @return none.
       */
  
      void arm_iir_lattice_init_q15(
          arm_iir_lattice_instance_q15 * S,
          uint16_t numStages,
          q15_t *pkCoeffs,
          q15_t *pvCoeffs,
          q15_t *pState,
          uint32_t blockSize);
  
      /**
       * @brief Instance structure for the floating-point LMS filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;    /**< number of coefficients in the filter. */
          float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
          float32_t mu;        /**< step size that controls filter coefficient updates. */
      } arm_lms_instance_f32;
  
      /**
       * @brief Processing function for floating-point LMS filter.
       * @param[in]  *S points to an instance of the floating-point LMS filter structure.
       * @param[in]  *pSrc points to the block of input data.
       * @param[in]  *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in]  blockSize number of samples to process.
       * @return     none.
       */
  
      void arm_lms_f32(
          const arm_lms_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pRef,
          float32_t * pOut,
          float32_t * pErr,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for floating-point LMS filter.
       * @param[in] *S points to an instance of the floating-point LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to the coefficient buffer.
       * @param[in] *pState points to state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_init_f32(
          arm_lms_instance_f32 * S,
          uint16_t numTaps,
          float32_t * pCoeffs,
          float32_t * pState,
          float32_t mu,
          uint32_t blockSize);
  
      /**
       * @brief Instance structure for the Q15 LMS filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;    /**< number of coefficients in the filter. */
          q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
          q15_t mu;            /**< step size that controls filter coefficient updates. */
          uint32_t postShift;  /**< bit shift applied to coefficients. */
      } arm_lms_instance_q15;
  
  
      /**
       * @brief Initialization function for the Q15 LMS filter.
       * @param[in] *S points to an instance of the Q15 LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to the coefficient buffer.
       * @param[in] *pState points to the state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @param[in] postShift bit shift applied to coefficients.
       * @return    none.
       */
  
      void arm_lms_init_q15(
          arm_lms_instance_q15 * S,
          uint16_t numTaps,
          q15_t * pCoeffs,
          q15_t * pState,
          q15_t mu,
          uint32_t blockSize,
          uint32_t postShift);
  
      /**
       * @brief Processing function for Q15 LMS filter.
       * @param[in] *S points to an instance of the Q15 LMS filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[in] *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_q15(
          const arm_lms_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pRef,
          q15_t * pOut,
          q15_t * pErr,
          uint32_t blockSize);
  
  
      /**
       * @brief Instance structure for the Q31 LMS filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;    /**< number of coefficients in the filter. */
          q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
          q31_t mu;            /**< step size that controls filter coefficient updates. */
          uint32_t postShift;  /**< bit shift applied to coefficients. */
  
      } arm_lms_instance_q31;
  
      /**
       * @brief Processing function for Q31 LMS filter.
       * @param[in]  *S points to an instance of the Q15 LMS filter structure.
       * @param[in]  *pSrc points to the block of input data.
       * @param[in]  *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in]  blockSize number of samples to process.
       * @return     none.
       */
  
      void arm_lms_q31(
          const arm_lms_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pRef,
          q31_t * pOut,
          q31_t * pErr,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for Q31 LMS filter.
       * @param[in] *S points to an instance of the Q31 LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to coefficient buffer.
       * @param[in] *pState points to state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @param[in] postShift bit shift applied to coefficients.
       * @return none.
       */
  
      void arm_lms_init_q31(
          arm_lms_instance_q31 * S,
          uint16_t numTaps,
          q31_t *pCoeffs,
          q31_t *pState,
          q31_t mu,
          uint32_t blockSize,
          uint32_t postShift);
  
      /**
       * @brief Instance structure for the floating-point normalized LMS filter.
       */
  
      typedef struct
      {
          uint16_t  numTaps;    /**< number of coefficients in the filter. */
          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
          float32_t mu;        /**< step size that control filter coefficient updates. */
          float32_t energy;    /**< saves previous frame energy. */
          float32_t x0;        /**< saves previous input sample. */
      } arm_lms_norm_instance_f32;
  
      /**
       * @brief Processing function for floating-point normalized LMS filter.
       * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[in] *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_norm_f32(
          arm_lms_norm_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pRef,
          float32_t * pOut,
          float32_t * pErr,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for floating-point normalized LMS filter.
       * @param[in] *S points to an instance of the floating-point LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to coefficient buffer.
       * @param[in] *pState points to state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_norm_init_f32(
          arm_lms_norm_instance_f32 * S,
          uint16_t numTaps,
          float32_t * pCoeffs,
          float32_t * pState,
          float32_t mu,
          uint32_t blockSize);
  
  
      /**
       * @brief Instance structure for the Q31 normalized LMS filter.
       */
      typedef struct
      {
          uint16_t numTaps;     /**< number of coefficients in the filter. */
          q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
          q31_t mu;             /**< step size that controls filter coefficient updates. */
          uint8_t postShift;    /**< bit shift applied to coefficients. */
          q31_t *recipTable;    /**< points to the reciprocal initial value table. */
          q31_t energy;         /**< saves previous frame energy. */
          q31_t x0;             /**< saves previous input sample. */
      } arm_lms_norm_instance_q31;
  
      /**
       * @brief Processing function for Q31 normalized LMS filter.
       * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[in] *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_norm_q31(
          arm_lms_norm_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pRef,
          q31_t * pOut,
          q31_t * pErr,
          uint32_t blockSize);
  
      /**
       * @brief Initialization function for Q31 normalized LMS filter.
       * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to coefficient buffer.
       * @param[in] *pState points to state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @param[in] postShift bit shift applied to coefficients.
       * @return none.
       */
  
      void arm_lms_norm_init_q31(
          arm_lms_norm_instance_q31 * S,
          uint16_t numTaps,
          q31_t * pCoeffs,
          q31_t * pState,
          q31_t mu,
          uint32_t blockSize,
          uint8_t postShift);
  
      /**
       * @brief Instance structure for the Q15 normalized LMS filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;    /**< Number of coefficients in the filter. */
          q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
          q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
          q15_t mu;            /**< step size that controls filter coefficient updates. */
          uint8_t postShift;   /**< bit shift applied to coefficients. */
          q15_t *recipTable;   /**< Points to the reciprocal initial value table. */
          q15_t energy;        /**< saves previous frame energy. */
          q15_t x0;            /**< saves previous input sample. */
      } arm_lms_norm_instance_q15;
  
      /**
       * @brief Processing function for Q15 normalized LMS filter.
       * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
       * @param[in] *pSrc points to the block of input data.
       * @param[in] *pRef points to the block of reference data.
       * @param[out] *pOut points to the block of output data.
       * @param[out] *pErr points to the block of error data.
       * @param[in] blockSize number of samples to process.
       * @return none.
       */
  
      void arm_lms_norm_q15(
          arm_lms_norm_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pRef,
          q15_t * pOut,
          q15_t * pErr,
          uint32_t blockSize);
  
  
      /**
       * @brief Initialization function for Q15 normalized LMS filter.
       * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
       * @param[in] numTaps  number of filter coefficients.
       * @param[in] *pCoeffs points to coefficient buffer.
       * @param[in] *pState points to state buffer.
       * @param[in] mu step size that controls filter coefficient updates.
       * @param[in] blockSize number of samples to process.
       * @param[in] postShift bit shift applied to coefficients.
       * @return none.
       */
  
      void arm_lms_norm_init_q15(
          arm_lms_norm_instance_q15 * S,
          uint16_t numTaps,
          q15_t * pCoeffs,
          q15_t * pState,
          q15_t mu,
          uint32_t blockSize,
          uint8_t postShift);
  
      /**
       * @brief Correlation of floating-point sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_f32(
          float32_t * pSrcA,
          uint32_t srcALen,
          float32_t * pSrcB,
          uint32_t srcBLen,
          float32_t * pDst);
  
      /**
       * @brief Correlation of Q15 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst);
  
      /**
       * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_fast_q15(
          q15_t * pSrcA,
          uint32_t srcALen,
          q15_t * pSrcB,
          uint32_t srcBLen,
          q15_t * pDst);
  
      /**
       * @brief Correlation of Q31 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst);
  
      /**
       * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_fast_q31(
          q31_t * pSrcA,
          uint32_t srcALen,
          q31_t * pSrcB,
          uint32_t srcBLen,
          q31_t * pDst);
  
      /**
       * @brief Correlation of Q7 sequences.
       * @param[in] *pSrcA points to the first input sequence.
       * @param[in] srcALen length of the first input sequence.
       * @param[in] *pSrcB points to the second input sequence.
       * @param[in] srcBLen length of the second input sequence.
       * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
       * @return none.
       */
  
      void arm_correlate_q7(
          q7_t * pSrcA,
          uint32_t srcALen,
          q7_t * pSrcB,
          uint32_t srcBLen,
          q7_t * pDst);
  
      /**
       * @brief Instance structure for the floating-point sparse FIR filter.
       */
      typedef struct
      {
          uint16_t numTaps;             /**< number of coefficients in the filter. */
          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
          float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
          float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
      } arm_fir_sparse_instance_f32;
  
      /**
       * @brief Instance structure for the Q31 sparse FIR filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;             /**< number of coefficients in the filter. */
          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
          q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
          q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
      } arm_fir_sparse_instance_q31;
  
      /**
       * @brief Instance structure for the Q15 sparse FIR filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;             /**< number of coefficients in the filter. */
          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
          q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
          q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
      } arm_fir_sparse_instance_q15;
  
      /**
       * @brief Instance structure for the Q7 sparse FIR filter.
       */
  
      typedef struct
      {
          uint16_t numTaps;             /**< number of coefficients in the filter. */
          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
          q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
          q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
      } arm_fir_sparse_instance_q7;
  
      /**
       * @brief Processing function for the floating-point sparse FIR filter.
       * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.
       * @param[in]  *pSrc       points to the block of input data.
       * @param[out] *pDst       points to the block of output data
       * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
       * @param[in]  blockSize   number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_sparse_f32(
          arm_fir_sparse_instance_f32 * S,
          float32_t * pSrc,
          float32_t * pDst,
          float32_t * pScratchIn,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the floating-point sparse FIR filter.
       * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.
       * @param[in]     numTaps    number of nonzero coefficients in the filter.
       * @param[in]     *pCoeffs   points to the array of filter coefficients.
       * @param[in]     *pState    points to the state buffer.
       * @param[in]     *pTapDelay points to the array of offset times.
       * @param[in]     maxDelay   maximum offset time supported.
       * @param[in]     blockSize  number of samples that will be processed per block.
       * @return none
       */
  
      void arm_fir_sparse_init_f32(
          arm_fir_sparse_instance_f32 * S,
          uint16_t numTaps,
          float32_t * pCoeffs,
          float32_t * pState,
          int32_t * pTapDelay,
          uint16_t maxDelay,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q31 sparse FIR filter.
       * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.
       * @param[in]  *pSrc       points to the block of input data.
       * @param[out] *pDst       points to the block of output data
       * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
       * @param[in]  blockSize   number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_sparse_q31(
          arm_fir_sparse_instance_q31 * S,
          q31_t * pSrc,
          q31_t * pDst,
          q31_t * pScratchIn,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q31 sparse FIR filter.
       * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.
       * @param[in]     numTaps    number of nonzero coefficients in the filter.
       * @param[in]     *pCoeffs   points to the array of filter coefficients.
       * @param[in]     *pState    points to the state buffer.
       * @param[in]     *pTapDelay points to the array of offset times.
       * @param[in]     maxDelay   maximum offset time supported.
       * @param[in]     blockSize  number of samples that will be processed per block.
       * @return none
       */
  
      void arm_fir_sparse_init_q31(
          arm_fir_sparse_instance_q31 * S,
          uint16_t numTaps,
          q31_t * pCoeffs,
          q31_t * pState,
          int32_t * pTapDelay,
          uint16_t maxDelay,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q15 sparse FIR filter.
       * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.
       * @param[in]  *pSrc        points to the block of input data.
       * @param[out] *pDst        points to the block of output data
       * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
       * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
       * @param[in]  blockSize    number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_sparse_q15(
          arm_fir_sparse_instance_q15 * S,
          q15_t * pSrc,
          q15_t * pDst,
          q15_t * pScratchIn,
          q31_t * pScratchOut,
          uint32_t blockSize);
  
  
      /**
       * @brief  Initialization function for the Q15 sparse FIR filter.
       * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.
       * @param[in]     numTaps    number of nonzero coefficients in the filter.
       * @param[in]     *pCoeffs   points to the array of filter coefficients.
       * @param[in]     *pState    points to the state buffer.
       * @param[in]     *pTapDelay points to the array of offset times.
       * @param[in]     maxDelay   maximum offset time supported.
       * @param[in]     blockSize  number of samples that will be processed per block.
       * @return none
       */
  
      void arm_fir_sparse_init_q15(
          arm_fir_sparse_instance_q15 * S,
          uint16_t numTaps,
          q15_t * pCoeffs,
          q15_t * pState,
          int32_t * pTapDelay,
          uint16_t maxDelay,
          uint32_t blockSize);
  
      /**
       * @brief Processing function for the Q7 sparse FIR filter.
       * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.
       * @param[in]  *pSrc        points to the block of input data.
       * @param[out] *pDst        points to the block of output data
       * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
       * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
       * @param[in]  blockSize    number of input samples to process per call.
       * @return none.
       */
  
      void arm_fir_sparse_q7(
          arm_fir_sparse_instance_q7 * S,
          q7_t * pSrc,
          q7_t * pDst,
          q7_t * pScratchIn,
          q31_t * pScratchOut,
          uint32_t blockSize);
  
      /**
       * @brief  Initialization function for the Q7 sparse FIR filter.
       * @param[in,out] *S         points to an instance of the Q7 sparse FIR structure.
       * @param[in]     numTaps    number of nonzero coefficients in the filter.
       * @param[in]     *pCoeffs   points to the array of filter coefficients.
       * @param[in]     *pState    points to the state buffer.
       * @param[in]     *pTapDelay points to the array of offset times.
       * @param[in]     maxDelay   maximum offset time supported.
       * @param[in]     blockSize  number of samples that will be processed per block.
       * @return none
       */
  
      void arm_fir_sparse_init_q7(
          arm_fir_sparse_instance_q7 * S,
          uint16_t numTaps,
          q7_t * pCoeffs,
          q7_t * pState,
          int32_t *pTapDelay,
          uint16_t maxDelay,
          uint32_t blockSize);
  
  
      /*
       * @brief  Floating-point sin_cos function.
       * @param[in]  theta    input value in degrees
       * @param[out] *pSinVal points to the processed sine output.
       * @param[out] *pCosVal points to the processed cos output.
       * @return none.
       */
  
      void arm_sin_cos_f32(
          float32_t theta,
          float32_t *pSinVal,
          float32_t *pCcosVal);
  
      /*
       * @brief  Q31 sin_cos function.
       * @param[in]  theta    scaled input value in degrees
       * @param[out] *pSinVal points to the processed sine output.
       * @param[out] *pCosVal points to the processed cosine output.
       * @return none.
       */
  
      void arm_sin_cos_q31(
          q31_t theta,
          q31_t *pSinVal,
          q31_t *pCosVal);
  
  
      /**
       * @brief  Floating-point complex conjugate.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_conj_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q31 complex conjugate.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_conj_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q15 complex conjugate.
       * @param[in]  *pSrc points to the input vector
       * @param[out]  *pDst points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_conj_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t numSamples);
  
  
  
      /**
       * @brief  Floating-point complex magnitude squared
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_squared_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q31 complex magnitude squared
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_squared_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q15 complex magnitude squared
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_squared_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t numSamples);
  
  
      /**
        * @ingroup groupController
        */
  
      /**
       * @defgroup PID PID Motor Control
       *
       * A Proportional Integral Derivative (PID) controller is a generic feedback control
       * loop mechanism widely used in industrial control systems.
       * A PID controller is the most commonly used type of feedback controller.
       *
       * This set of functions implements (PID) controllers
       * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
       * of data and each call to the function returns a single processed value.
       * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
       * is the input sample value. The functions return the output value.
       *
       * \par Algorithm:
       * <pre>
       *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
       *    A0 = Kp + Ki + Kd
       *    A1 = (-Kp ) - (2 * Kd )
       *    A2 = Kd  </pre>
       *
       * \par
       * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
       *
       * \par
       * \image html PID.gif "Proportional Integral Derivative Controller"
       *
       * \par
       * The PID controller calculates an "error" value as the difference between
       * the measured output and the reference input.
       * The controller attempts to minimize the error by adjusting the process control inputs.
       * The proportional value determines the reaction to the current error,
       * the integral value determines the reaction based on the sum of recent errors,
       * and the derivative value determines the reaction based on the rate at which the error has been changing.
       *
       * \par Instance Structure
       * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
       * A separate instance structure must be defined for each PID Controller.
       * There are separate instance structure declarations for each of the 3 supported data types.
       *
       * \par Reset Functions
       * There is also an associated reset function for each data type which clears the state array.
       *
       * \par Initialization Functions
       * There is also an associated initialization function for each data type.
       * The initialization function performs the following operations:
       * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
       * - Zeros out the values in the state buffer.
       *
       * \par
       * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
       *
       * \par Fixed-Point Behavior
       * Care must be taken when using the fixed-point versions of the PID Controller functions.
       * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
       * Refer to the function specific documentation below for usage guidelines.
       */
  
      /**
       * @addtogroup PID
       * @{
       */
  
      /**
       * @brief  Process function for the floating-point PID Control.
       * @param[in,out] *S is an instance of the floating-point PID Control structure
       * @param[in] in input sample to process
       * @return out processed output sample.
       */
  
  
      __STATIC_INLINE float32_t arm_pid_f32(
          arm_pid_instance_f32 * S,
          float32_t in)
      {
          float32_t out;
  
          /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
          out = (S->A0 * in) +
                (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
  
          /* Update state */
          S->state[1] = S->state[0];
          S->state[0] = in;
          S->state[2] = out;
  
          /* return to application */
          return (out);
  
      }
  
      /**
       * @brief  Process function for the Q31 PID Control.
       * @param[in,out] *S points to an instance of the Q31 PID Control structure
       * @param[in] in input sample to process
       * @return out processed output sample.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using an internal 64-bit accumulator.
       * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
       * Thus, if the accumulator result overflows it wraps around rather than clip.
       * In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
       * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
       */
  
      __STATIC_INLINE q31_t arm_pid_q31(
          arm_pid_instance_q31 * S,
          q31_t in)
      {
          q63_t acc;
          q31_t out;
  
          /* acc = A0 * x[n]  */
          acc = (q63_t) S->A0 * in;
  
          /* acc += A1 * x[n-1] */
          acc += (q63_t) S->A1 * S->state[0];
  
          /* acc += A2 * x[n-2]  */
          acc += (q63_t) S->A2 * S->state[1];
  
          /* convert output to 1.31 format to add y[n-1] */
          out = (q31_t) (acc >> 31u);
  
          /* out += y[n-1] */
          out += S->state[2];
  
          /* Update state */
          S->state[1] = S->state[0];
          S->state[0] = in;
          S->state[2] = out;
  
          /* return to application */
          return (out);
  
      }
  
      /**
       * @brief  Process function for the Q15 PID Control.
       * @param[in,out] *S points to an instance of the Q15 PID Control structure
       * @param[in] in input sample to process
       * @return out processed output sample.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using a 64-bit internal accumulator.
       * Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
       * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
       * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
       * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
       * Lastly, the accumulator is saturated to yield a result in 1.15 format.
       */
  
      __STATIC_INLINE q15_t arm_pid_q15(
          arm_pid_instance_q15 * S,
          q15_t in)
      {
          q63_t acc;
          q15_t out;
  
          /* Implementation of PID controller */
  
  #ifdef ARM_MATH_CM0
  
          /* acc = A0 * x[n]  */
          acc = ((q31_t) S->A0 )* in ;
  
  #else
  
          /* acc = A0 * x[n]  */
          acc = (q31_t) __SMUAD(S->A0, in);
  
  #endif
  
  #ifdef ARM_MATH_CM0
  
          /* acc += A1 * x[n-1] + A2 * x[n-2]  */
          acc += (q31_t) S->A1  *  S->state[0] ;
          acc += (q31_t) S->A2  *  S->state[1] ;
  
  #else
  
          /* acc += A1 * x[n-1] + A2 * x[n-2]  */
          acc = __SMLALD(S->A1, (q31_t)__SIMD32(S->state), acc);
  
  #endif
  
          /* acc += y[n-1] */
          acc += (q31_t) S->state[2] << 15;
  
          /* saturate the output */
          out = (q15_t) (__SSAT((acc >> 15), 16));
  
          /* Update state */
          S->state[1] = S->state[0];
          S->state[0] = in;
          S->state[2] = out;
  
          /* return to application */
          return (out);
  
      }
  
      /**
       * @} end of PID group
       */
  
  
      /**
       * @brief Floating-point matrix inverse.
       * @param[in]  *src points to the instance of the input floating-point matrix structure.
       * @param[out] *dst points to the instance of the output floating-point matrix structure.
       * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
       * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
       */
  
      arm_status arm_mat_inverse_f32(
          const arm_matrix_instance_f32 * src,
          arm_matrix_instance_f32 * dst);
  
  
  
      /**
       * @ingroup groupController
       */
  
  
      /**
       * @defgroup clarke Vector Clarke Transform
       * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
       * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
       * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
       * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
       * \image html clarke.gif Stator current space vector and its components in (a,b).
       * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
       * can be calculated using only <code>Ia</code> and <code>Ib</code>.
       *
       * The function operates on a single sample of data and each call to the function returns the processed output.
       * The library provides separate functions for Q31 and floating-point data types.
       * \par Algorithm
       * \image html clarkeFormula.gif
       * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
       * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
       * \par Fixed-Point Behavior
       * Care must be taken when using the Q31 version of the Clarke transform.
       * In particular, the overflow and saturation behavior of the accumulator used must be considered.
       * Refer to the function specific documentation below for usage guidelines.
       */
  
      /**
       * @addtogroup clarke
       * @{
       */
  
      /**
       *
       * @brief  Floating-point Clarke transform
       * @param[in]       Ia       input three-phase coordinate <code>a</code>
       * @param[in]       Ib       input three-phase coordinate <code>b</code>
       * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
       * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
       * @return none.
       */
  
      __STATIC_INLINE void arm_clarke_f32(
          float32_t Ia,
          float32_t Ib,
          float32_t * pIalpha,
          float32_t * pIbeta)
      {
          /* Calculate pIalpha using the equation, pIalpha = Ia */
          *pIalpha = Ia;
  
          /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
          *pIbeta = ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
  
      }
  
      /**
       * @brief  Clarke transform for Q31 version
       * @param[in]       Ia       input three-phase coordinate <code>a</code>
       * @param[in]       Ib       input three-phase coordinate <code>b</code>
       * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
       * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
       * @return none.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using an internal 32-bit accumulator.
       * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
       * There is saturation on the addition, hence there is no risk of overflow.
       */
  
      __STATIC_INLINE void arm_clarke_q31(
          q31_t Ia,
          q31_t Ib,
          q31_t * pIalpha,
          q31_t * pIbeta)
      {
          q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
  
          /* Calculating pIalpha from Ia by equation pIalpha = Ia */
          *pIalpha = Ia;
  
          /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
          product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
  
          /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
          product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
  
          /* pIbeta is calculated by adding the intermediate products */
          *pIbeta = __QADD(product1, product2);
      }
  
      /**
       * @} end of clarke group
       */
  
      /**
       * @brief  Converts the elements of the Q7 vector to Q31 vector.
       * @param[in]  *pSrc     input pointer
       * @param[out]  *pDst    output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_q7_to_q31(
          q7_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
  
  
  
      /**
       * @ingroup groupController
       */
  
      /**
       * @defgroup inv_clarke Vector Inverse Clarke Transform
       * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
       *
       * The function operates on a single sample of data and each call to the function returns the processed output.
       * The library provides separate functions for Q31 and floating-point data types.
       * \par Algorithm
       * \image html clarkeInvFormula.gif
       * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
       * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
       * \par Fixed-Point Behavior
       * Care must be taken when using the Q31 version of the Clarke transform.
       * In particular, the overflow and saturation behavior of the accumulator used must be considered.
       * Refer to the function specific documentation below for usage guidelines.
       */
  
      /**
       * @addtogroup inv_clarke
       * @{
       */
  
      /**
      * @brief  Floating-point Inverse Clarke transform
      * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
      * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
      * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
      * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
      * @return none.
      */
  
  
      __STATIC_INLINE void arm_inv_clarke_f32(
          float32_t Ialpha,
          float32_t Ibeta,
          float32_t * pIa,
          float32_t * pIb)
      {
          /* Calculating pIa from Ialpha by equation pIa = Ialpha */
          *pIa = Ialpha;
  
          /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
          *pIb = -0.5 * Ialpha + (float32_t) 0.8660254039 *Ibeta;
  
      }
  
      /**
       * @brief  Inverse Clarke transform for Q31 version
       * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
       * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
       * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
       * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
       * @return none.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using an internal 32-bit accumulator.
       * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
       * There is saturation on the subtraction, hence there is no risk of overflow.
       */
  
      __STATIC_INLINE void arm_inv_clarke_q31(
          q31_t Ialpha,
          q31_t Ibeta,
          q31_t * pIa,
          q31_t * pIb)
      {
          q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
  
          /* Calculating pIa from Ialpha by equation pIa = Ialpha */
          *pIa = Ialpha;
  
          /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
          product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
  
          /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
          product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
  
          /* pIb is calculated by subtracting the products */
          *pIb = __QSUB(product2, product1);
  
      }
  
      /**
       * @} end of inv_clarke group
       */
  
      /**
       * @brief  Converts the elements of the Q7 vector to Q15 vector.
       * @param[in]  *pSrc     input pointer
       * @param[out] *pDst     output pointer
       * @param[in]  blockSize number of samples to process
       * @return none.
       */
      void arm_q7_to_q15(
          q7_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
  
  
      /**
       * @ingroup groupController
       */
  
      /**
       * @defgroup park Vector Park Transform
       *
       * Forward Park transform converts the input two-coordinate vector to flux and torque components.
       * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
       * from the stationary to the moving reference frame and control the spatial relationship between
       * the stator vector current and rotor flux vector.
       * If we consider the d axis aligned with the rotor flux, the diagram below shows the
       * current vector and the relationship from the two reference frames:
       * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
       *
       * The function operates on a single sample of data and each call to the function returns the processed output.
       * The library provides separate functions for Q31 and floating-point data types.
       * \par Algorithm
       * \image html parkFormula.gif
       * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
       * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
       * cosine and sine values of theta (rotor flux position).
       * \par Fixed-Point Behavior
       * Care must be taken when using the Q31 version of the Park transform.
       * In particular, the overflow and saturation behavior of the accumulator used must be considered.
       * Refer to the function specific documentation below for usage guidelines.
       */
  
      /**
       * @addtogroup park
       * @{
       */
  
      /**
       * @brief Floating-point Park transform
       * @param[in]       Ialpha input two-phase vector coordinate alpha
       * @param[in]       Ibeta  input two-phase vector coordinate beta
       * @param[out]      *pId   points to output	rotor reference frame d
       * @param[out]      *pIq   points to output	rotor reference frame q
       * @param[in]       sinVal sine value of rotation angle theta
       * @param[in]       cosVal cosine value of rotation angle theta
       * @return none.
       *
       * The function implements the forward Park transform.
       *
       */
  
      __STATIC_INLINE void arm_park_f32(
          float32_t Ialpha,
          float32_t Ibeta,
          float32_t * pId,
          float32_t * pIq,
          float32_t sinVal,
          float32_t cosVal)
      {
          /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
          *pId = Ialpha * cosVal + Ibeta * sinVal;
  
          /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
          *pIq = -Ialpha * sinVal + Ibeta * cosVal;
  
      }
  
      /**
       * @brief  Park transform for Q31 version
       * @param[in]       Ialpha input two-phase vector coordinate alpha
       * @param[in]       Ibeta  input two-phase vector coordinate beta
       * @param[out]      *pId   points to output rotor reference frame d
       * @param[out]      *pIq   points to output rotor reference frame q
       * @param[in]       sinVal sine value of rotation angle theta
       * @param[in]       cosVal cosine value of rotation angle theta
       * @return none.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using an internal 32-bit accumulator.
       * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
       * There is saturation on the addition and subtraction, hence there is no risk of overflow.
       */
  
  
      __STATIC_INLINE void arm_park_q31(
          q31_t Ialpha,
          q31_t Ibeta,
          q31_t * pId,
          q31_t * pIq,
          q31_t sinVal,
          q31_t cosVal)
      {
          q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
          q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
  
          /* Intermediate product is calculated by (Ialpha * cosVal) */
          product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
  
          /* Intermediate product is calculated by (Ibeta * sinVal) */
          product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
  
  
          /* Intermediate product is calculated by (Ialpha * sinVal) */
          product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
  
          /* Intermediate product is calculated by (Ibeta * cosVal) */
          product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
  
          /* Calculate pId by adding the two intermediate products 1 and 2 */
          *pId = __QADD(product1, product2);
  
          /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
          *pIq = __QSUB(product4, product3);
      }
  
      /**
       * @} end of park group
       */
  
      /**
       * @brief  Converts the elements of the Q7 vector to floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q7_to_float(
          q7_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @ingroup groupController
       */
  
      /**
       * @defgroup inv_park Vector Inverse Park transform
       * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
       *
       * The function operates on a single sample of data and each call to the function returns the processed output.
       * The library provides separate functions for Q31 and floating-point data types.
       * \par Algorithm
       * \image html parkInvFormula.gif
       * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
       * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
       * cosine and sine values of theta (rotor flux position).
       * \par Fixed-Point Behavior
       * Care must be taken when using the Q31 version of the Park transform.
       * In particular, the overflow and saturation behavior of the accumulator used must be considered.
       * Refer to the function specific documentation below for usage guidelines.
       */
  
      /**
       * @addtogroup inv_park
       * @{
       */
  
      /**
      * @brief  Floating-point Inverse Park transform
      * @param[in]       Id        input coordinate of rotor reference frame d
      * @param[in]       Iq        input coordinate of rotor reference frame q
      * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
      * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
      * @param[in]       sinVal    sine value of rotation angle theta
      * @param[in]       cosVal    cosine value of rotation angle theta
      * @return none.
      */
  
      __STATIC_INLINE void arm_inv_park_f32(
          float32_t Id,
          float32_t Iq,
          float32_t * pIalpha,
          float32_t * pIbeta,
          float32_t sinVal,
          float32_t cosVal)
      {
          /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
          *pIalpha = Id * cosVal - Iq * sinVal;
  
          /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
          *pIbeta = Id * sinVal + Iq * cosVal;
  
      }
  
  
      /**
       * @brief  Inverse Park transform for	Q31 version
       * @param[in]       Id        input coordinate of rotor reference frame d
       * @param[in]       Iq        input coordinate of rotor reference frame q
       * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
       * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
       * @param[in]       sinVal    sine value of rotation angle theta
       * @param[in]       cosVal    cosine value of rotation angle theta
       * @return none.
       *
       * <b>Scaling and Overflow Behavior:</b>
       * \par
       * The function is implemented using an internal 32-bit accumulator.
       * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
       * There is saturation on the addition, hence there is no risk of overflow.
       */
  
  
      __STATIC_INLINE void arm_inv_park_q31(
          q31_t Id,
          q31_t Iq,
          q31_t * pIalpha,
          q31_t * pIbeta,
          q31_t sinVal,
          q31_t cosVal)
      {
          q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
          q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
  
          /* Intermediate product is calculated by (Id * cosVal) */
          product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
  
          /* Intermediate product is calculated by (Iq * sinVal) */
          product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
  
  
          /* Intermediate product is calculated by (Id * sinVal) */
          product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
  
          /* Intermediate product is calculated by (Iq * cosVal) */
          product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
  
          /* Calculate pIalpha by using the two intermediate products 1 and 2 */
          *pIalpha = __QSUB(product1, product2);
  
          /* Calculate pIbeta by using the two intermediate products 3 and 4 */
          *pIbeta = __QADD(product4, product3);
  
      }
  
      /**
       * @} end of Inverse park group
       */
  
  
      /**
       * @brief  Converts the elements of the Q31 vector to floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q31_to_float(
          q31_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
      /**
       * @ingroup groupInterpolation
       */
  
      /**
       * @defgroup LinearInterpolate Linear Interpolation
       *
       * Linear interpolation is a method of curve fitting using linear polynomials.
       * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
       *
       * \par
       * \image html LinearInterp.gif "Linear interpolation"
       *
       * \par
       * A  Linear Interpolate function calculates an output value(y), for the input(x)
       * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
       *
       * \par Algorithm:
       * <pre>
       *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
       *       where x0, x1 are nearest values of input x
       *             y0, y1 are nearest values to output y
       * </pre>
       *
       * \par
       * This set of functions implements Linear interpolation process
       * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
       * sample of data and each call to the function returns a single processed value.
       * <code>S</code> points to an instance of the Linear Interpolate function data structure.
       * <code>x</code> is the input sample value. The functions returns the output value.
       *
       * \par
       * if x is outside of the table boundary, Linear interpolation returns first value of the table
       * if x is below input range and returns last value of table if x is above range.
       */
  
      /**
       * @addtogroup LinearInterpolate
       * @{
       */
  
      /**
       * @brief  Process function for the floating-point Linear Interpolation Function.
       * @param[in,out] *S is an instance of the floating-point Linear Interpolation structure
       * @param[in] x input sample to process
       * @return y processed output sample.
       *
       */
  
      __STATIC_INLINE float32_t arm_linear_interp_f32(
          arm_linear_interp_instance_f32 * S,
          float32_t x)
      {
  
          float32_t y;
          float32_t x0, x1;						/* Nearest input values */
          float32_t y0, y1;	  					/* Nearest output values */
          float32_t xSpacing = S->xSpacing;		/* spacing between input values */
          int32_t i;  							/* Index variable */
          float32_t *pYData = S->pYData;	    /* pointer to output table */
  
          /* Calculation of index */
          i =   (x - S->x1) / xSpacing;
  
          if(i < 0)
          {
              /* Iniatilize output for below specified range as least output value of table */
              y = pYData[0];
          }
          else if(i >= S->nValues)
          {
              /* Iniatilize output for above specified range as last output value of table */
              y = pYData[S->nValues-1];
          }
          else
          {
              /* Calculation of nearest input values */
              x0 = S->x1 + i * xSpacing;
              x1 = S->x1 + (i +1) * xSpacing;
  
              /* Read of nearest output values */
              y0 = pYData[i];
              y1 = pYData[i + 1];
  
              /* Calculation of output */
              y = y0 + (x - x0) * ((y1 - y0)/(x1-x0));
  
          }
  
          /* returns output value */
          return (y);
      }
  
      /**
      *
      * @brief  Process function for the Q31 Linear Interpolation Function.
      * @param[in] *pYData  pointer to Q31 Linear Interpolation table
      * @param[in] x input sample to process
      * @param[in] nValues number of table values
      * @return y processed output sample.
      *
      * \par
      * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
      * This function can support maximum of table size 2^12.
      *
      */
  
  
      __STATIC_INLINE q31_t arm_linear_interp_q31(q31_t *pYData,
              q31_t x, uint32_t nValues)
      {
          q31_t y;                                   /* output */
          q31_t y0, y1;                                /* Nearest output values */
          q31_t fract;                                 /* fractional part */
          int32_t index;                              /* Index to read nearest output values */
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          index = ((x & 0xFFF00000) >> 20);
  
          if(index >= (nValues - 1))
          {
              return(pYData[nValues - 1]);
          }
          else if(index < 0)
          {
              return(pYData[0]);
          }
          else
          {
  
              /* 20 bits for the fractional part */
              /* shift left by 11 to keep fract in 1.31 format */
              fract = (x & 0x000FFFFF) << 11;
  
              /* Read two nearest output values from the index in 1.31(q31) format */
              y0 = pYData[index];
              y1 = pYData[index + 1u];
  
              /* Calculation of y0 * (1-fract) and y is in 2.30 format */
              y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
  
              /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
              y += ((q31_t) (((q63_t) y1 * fract) >> 32));
  
              /* Convert y to 1.31 format */
              return (y << 1u);
  
          }
  
      }
  
      /**
       *
       * @brief  Process function for the Q15 Linear Interpolation Function.
       * @param[in] *pYData  pointer to Q15 Linear Interpolation table
       * @param[in] x input sample to process
       * @param[in] nValues number of table values
       * @return y processed output sample.
       *
       * \par
       * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
       * This function can support maximum of table size 2^12.
       *
       */
  
  
      __STATIC_INLINE q15_t arm_linear_interp_q15(q15_t *pYData, q31_t x, uint32_t nValues)
      {
          q63_t y;                                   /* output */
          q15_t y0, y1;                              /* Nearest output values */
          q31_t fract;                               /* fractional part */
          int32_t index;                            /* Index to read nearest output values */
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          index = ((x & 0xFFF00000) >> 20u);
  
          if(index >= (nValues - 1))
          {
              return(pYData[nValues - 1]);
          }
          else if(index < 0)
          {
              return(pYData[0]);
          }
          else
          {
              /* 20 bits for the fractional part */
              /* fract is in 12.20 format */
              fract = (x & 0x000FFFFF);
  
              /* Read two nearest output values from the index */
              y0 = pYData[index];
              y1 = pYData[index + 1u];
  
              /* Calculation of y0 * (1-fract) and y is in 13.35 format */
              y = ((q63_t) y0 * (0xFFFFF - fract));
  
              /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
              y += ((q63_t) y1 * (fract));
  
              /* convert y to 1.15 format */
              return (y >> 20);
          }
  
  
      }
  
      /**
       *
       * @brief  Process function for the Q7 Linear Interpolation Function.
       * @param[in] *pYData  pointer to Q7 Linear Interpolation table
       * @param[in] x input sample to process
       * @param[in] nValues number of table values
       * @return y processed output sample.
       *
       * \par
       * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
       * This function can support maximum of table size 2^12.
       */
  
  
      __STATIC_INLINE q7_t arm_linear_interp_q7(q7_t *pYData, q31_t x,  uint32_t nValues)
      {
          q31_t y;                                   /* output */
          q7_t y0, y1;                                 /* Nearest output values */
          q31_t fract;                                 /* fractional part */
          int32_t index;                              /* Index to read nearest output values */
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          index = ((x & 0xFFF00000) >> 20u);
  
  
          if(index >= (nValues - 1))
          {
              return(pYData[nValues - 1]);
          }
          else if(index < 0)
          {
              return(pYData[0]);
          }
          else
          {
  
              /* 20 bits for the fractional part */
              /* fract is in 12.20 format */
              fract = (x & 0x000FFFFF);
  
              /* Read two nearest output values from the index and are in 1.7(q7) format */
              y0 = pYData[index];
              y1 = pYData[index + 1u];
  
              /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
              y = ((y0 * (0xFFFFF - fract)));
  
              /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
              y += (y1 * fract);
  
              /* convert y to 1.7(q7) format */
              return (y >> 20u);
  
          }
  
      }
      /**
       * @} end of LinearInterpolate group
       */
  
      /**
       * @brief  Fast approximation to the trigonometric sine function for floating-point data.
       * @param[in] x input value in radians.
       * @return  sin(x).
       */
  
      float32_t arm_sin_f32(
          float32_t x);
  
      /**
       * @brief  Fast approximation to the trigonometric sine function for Q31 data.
       * @param[in] x Scaled input value in radians.
       * @return  sin(x).
       */
  
      q31_t arm_sin_q31(
          q31_t x);
  
      /**
       * @brief  Fast approximation to the trigonometric sine function for Q15 data.
       * @param[in] x Scaled input value in radians.
       * @return  sin(x).
       */
  
      q15_t arm_sin_q15(
          q15_t x);
  
      /**
       * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
       * @param[in] x input value in radians.
       * @return  cos(x).
       */
  
      float32_t arm_cos_f32(
          float32_t x);
  
      /**
       * @brief Fast approximation to the trigonometric cosine function for Q31 data.
       * @param[in] x Scaled input value in radians.
       * @return  cos(x).
       */
  
      q31_t arm_cos_q31(
          q31_t x);
  
      /**
       * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
       * @param[in] x Scaled input value in radians.
       * @return  cos(x).
       */
  
      q15_t arm_cos_q15(
          q15_t x);
  
  
      /**
       * @ingroup groupFastMath
       */
  
  
      /**
       * @defgroup SQRT Square Root
       *
       * Computes the square root of a number.
       * There are separate functions for Q15, Q31, and floating-point data types.
       * The square root function is computed using the Newton-Raphson algorithm.
       * This is an iterative algorithm of the form:
       * <pre>
       *      x1 = x0 - f(x0)/f'(x0)
       * </pre>
       * where <code>x1</code> is the current estimate,
       * <code>x0</code> is the previous estimate and
       * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
       * For the square root function, the algorithm reduces to:
       * <pre>
       *     x0 = in/2                         [initial guess]
       *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
       * </pre>
       */
  
  
      /**
       * @addtogroup SQRT
       * @{
       */
  
      /**
       * @brief  Floating-point square root function.
       * @param[in]  in     input value.
       * @param[out] *pOut  square root of input value.
       * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
       * <code>in</code> is negative value and returns zero output for negative values.
       */
  
      __STATIC_INLINE arm_status  arm_sqrt_f32(
          float32_t in, float32_t *pOut)
      {
          if(in > 0)
          {
  
  //    #if __FPU_USED
  #if (__FPU_USED == 1) && defined ( __CC_ARM   )
              *pOut = __sqrtf(in);
  #elif (__FPU_USED == 1) && defined ( __TMS_740 )
              *pOut = __builtin_sqrtf(in);
  #else
              *pOut = sqrtf(in);
  #endif
  
              return (ARM_MATH_SUCCESS);
          }
          else
          {
              *pOut = 0.0f;
              return (ARM_MATH_ARGUMENT_ERROR);
          }
  
      }
  
  
      /**
       * @brief Q31 square root function.
       * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
       * @param[out]  *pOut square root of input value.
       * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
       * <code>in</code> is negative value and returns zero output for negative values.
       */
      arm_status arm_sqrt_q31(
          q31_t in, q31_t *pOut);
  
      /**
       * @brief  Q15 square root function.
       * @param[in]   in     input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
       * @param[out]  *pOut  square root of input value.
       * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
       * <code>in</code> is negative value and returns zero output for negative values.
       */
      arm_status arm_sqrt_q15(
          q15_t in, q15_t *pOut);
  
      /**
       * @} end of SQRT group
       */
  
  
  
  
  
  
      /**
       * @brief floating-point Circular write function.
       */
  
      __STATIC_INLINE void arm_circularWrite_f32(
          int32_t * circBuffer,
          int32_t L,
          uint16_t * writeOffset,
          int32_t bufferInc,
          const int32_t * src,
          int32_t srcInc,
          uint32_t blockSize)
      {
          uint32_t i = 0u;
          int32_t wOffset;
  
          /* Copy the value of Index pointer that points
           * to the current location where the input samples to be copied */
          wOffset = *writeOffset;
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the input sample to the circular buffer */
              circBuffer[wOffset] = *src;
  
              /* Update the input pointer */
              src += srcInc;
  
              /* Circularly update wOffset.  Watch out for positive and negative value */
              wOffset += bufferInc;
              if(wOffset >= L)
                  wOffset -= L;
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *writeOffset = wOffset;
      }
  
  
  
      /**
       * @brief floating-point Circular Read function.
       */
      __STATIC_INLINE void arm_circularRead_f32(
          int32_t * circBuffer,
          int32_t L,
          int32_t * readOffset,
          int32_t bufferInc,
          int32_t * dst,
          int32_t * dst_base,
          int32_t dst_length,
          int32_t dstInc,
          uint32_t blockSize)
      {
          uint32_t i = 0u;
          int32_t rOffset, dst_end;
  
          /* Copy the value of Index pointer that points
           * to the current location from where the input samples to be read */
          rOffset = *readOffset;
          dst_end = (int32_t) (dst_base + dst_length);
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the sample from the circular buffer to the destination buffer */
              *dst = circBuffer[rOffset];
  
              /* Update the input pointer */
              dst += dstInc;
  
              if(dst == (int32_t *) dst_end)
              {
                  dst = dst_base;
              }
  
              /* Circularly update rOffset.  Watch out for positive and negative value  */
              rOffset += bufferInc;
  
              if(rOffset >= L)
              {
                  rOffset -= L;
              }
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *readOffset = rOffset;
      }
  
      /**
       * @brief Q15 Circular write function.
       */
  
      __STATIC_INLINE void arm_circularWrite_q15(
          q15_t * circBuffer,
          int32_t L,
          uint16_t * writeOffset,
          int32_t bufferInc,
          const q15_t * src,
          int32_t srcInc,
          uint32_t blockSize)
      {
          uint32_t i = 0u;
          int32_t wOffset;
  
          /* Copy the value of Index pointer that points
           * to the current location where the input samples to be copied */
          wOffset = *writeOffset;
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the input sample to the circular buffer */
              circBuffer[wOffset] = *src;
  
              /* Update the input pointer */
              src += srcInc;
  
              /* Circularly update wOffset.  Watch out for positive and negative value */
              wOffset += bufferInc;
              if(wOffset >= L)
                  wOffset -= L;
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *writeOffset = wOffset;
      }
  
  
  
      /**
       * @brief Q15 Circular Read function.
       */
      __STATIC_INLINE void arm_circularRead_q15(
          q15_t * circBuffer,
          int32_t L,
          int32_t * readOffset,
          int32_t bufferInc,
          q15_t * dst,
          q15_t * dst_base,
          int32_t dst_length,
          int32_t dstInc,
          uint32_t blockSize)
      {
          uint32_t i = 0;
          int32_t rOffset, dst_end;
  
          /* Copy the value of Index pointer that points
           * to the current location from where the input samples to be read */
          rOffset = *readOffset;
  
          dst_end = (int32_t) (dst_base + dst_length);
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the sample from the circular buffer to the destination buffer */
              *dst = circBuffer[rOffset];
  
              /* Update the input pointer */
              dst += dstInc;
  
              if(dst == (q15_t *) dst_end)
              {
                  dst = dst_base;
              }
  
              /* Circularly update wOffset.  Watch out for positive and negative value */
              rOffset += bufferInc;
  
              if(rOffset >= L)
              {
                  rOffset -= L;
              }
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *readOffset = rOffset;
      }
  
  
      /**
       * @brief Q7 Circular write function.
       */
  
      __STATIC_INLINE void arm_circularWrite_q7(
          q7_t * circBuffer,
          int32_t L,
          uint16_t * writeOffset,
          int32_t bufferInc,
          const q7_t * src,
          int32_t srcInc,
          uint32_t blockSize)
      {
          uint32_t i = 0u;
          int32_t wOffset;
  
          /* Copy the value of Index pointer that points
           * to the current location where the input samples to be copied */
          wOffset = *writeOffset;
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the input sample to the circular buffer */
              circBuffer[wOffset] = *src;
  
              /* Update the input pointer */
              src += srcInc;
  
              /* Circularly update wOffset.  Watch out for positive and negative value */
              wOffset += bufferInc;
              if(wOffset >= L)
                  wOffset -= L;
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *writeOffset = wOffset;
      }
  
  
  
      /**
       * @brief Q7 Circular Read function.
       */
      __STATIC_INLINE void arm_circularRead_q7(
          q7_t * circBuffer,
          int32_t L,
          int32_t * readOffset,
          int32_t bufferInc,
          q7_t * dst,
          q7_t * dst_base,
          int32_t dst_length,
          int32_t dstInc,
          uint32_t blockSize)
      {
          uint32_t i = 0;
          int32_t rOffset, dst_end;
  
          /* Copy the value of Index pointer that points
           * to the current location from where the input samples to be read */
          rOffset = *readOffset;
  
          dst_end = (int32_t) (dst_base + dst_length);
  
          /* Loop over the blockSize */
          i = blockSize;
  
          while(i > 0u)
          {
              /* copy the sample from the circular buffer to the destination buffer */
              *dst = circBuffer[rOffset];
  
              /* Update the input pointer */
              dst += dstInc;
  
              if(dst == (q7_t *) dst_end)
              {
                  dst = dst_base;
              }
  
              /* Circularly update rOffset.  Watch out for positive and negative value */
              rOffset += bufferInc;
  
              if(rOffset >= L)
              {
                  rOffset -= L;
              }
  
              /* Decrement the loop counter */
              i--;
          }
  
          /* Update the index pointer */
          *readOffset = rOffset;
      }
  
  
      /**
       * @brief  Sum of the squares of the elements of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_power_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q63_t * pResult);
  
      /**
       * @brief  Sum of the squares of the elements of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_power_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult);
  
      /**
       * @brief  Sum of the squares of the elements of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_power_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q63_t * pResult);
  
      /**
       * @brief  Sum of the squares of the elements of a Q7 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_power_q7(
          q7_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult);
  
      /**
       * @brief  Mean value of a Q7 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_mean_q7(
          q7_t * pSrc,
          uint32_t blockSize,
          q7_t * pResult);
  
      /**
       * @brief  Mean value of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
      void arm_mean_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q15_t * pResult);
  
      /**
       * @brief  Mean value of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
      void arm_mean_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult);
  
      /**
       * @brief  Mean value of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
      void arm_mean_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult);
  
      /**
       * @brief  Variance of the elements of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_var_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult);
  
      /**
       * @brief  Variance of the elements of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_var_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q63_t * pResult);
  
      /**
       * @brief  Variance of the elements of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_var_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult);
  
      /**
       * @brief  Root Mean Square of the elements of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_rms_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult);
  
      /**
       * @brief  Root Mean Square of the elements of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_rms_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult);
  
      /**
       * @brief  Root Mean Square of the elements of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_rms_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q15_t * pResult);
  
      /**
       * @brief  Standard deviation of the elements of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_std_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult);
  
      /**
       * @brief  Standard deviation of the elements of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_std_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult);
  
      /**
       * @brief  Standard deviation of the elements of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output value.
       * @return none.
       */
  
      void arm_std_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q15_t * pResult);
  
      /**
       * @brief  Floating-point complex magnitude
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_f32(
          float32_t * pSrc,
          float32_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q31 complex magnitude
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_q31(
          q31_t * pSrc,
          q31_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q15 complex magnitude
       * @param[in]  *pSrc points to the complex input vector
       * @param[out]  *pDst points to the real output vector
       * @param[in]  numSamples number of complex samples in the input vector
       * @return none.
       */
  
      void arm_cmplx_mag_q15(
          q15_t * pSrc,
          q15_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q15 complex dot product
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[in]  numSamples number of complex samples in each vector
       * @param[out]  *realResult real part of the result returned here
       * @param[out]  *imagResult imaginary part of the result returned here
       * @return none.
       */
  
      void arm_cmplx_dot_prod_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          uint32_t numSamples,
          q31_t * realResult,
          q31_t * imagResult);
  
      /**
       * @brief  Q31 complex dot product
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[in]  numSamples number of complex samples in each vector
       * @param[out]  *realResult real part of the result returned here
       * @param[out]  *imagResult imaginary part of the result returned here
       * @return none.
       */
  
      void arm_cmplx_dot_prod_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          uint32_t numSamples,
          q63_t * realResult,
          q63_t * imagResult);
  
      /**
       * @brief  Floating-point complex dot product
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[in]  numSamples number of complex samples in each vector
       * @param[out]  *realResult real part of the result returned here
       * @param[out]  *imagResult imaginary part of the result returned here
       * @return none.
       */
  
      void arm_cmplx_dot_prod_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          uint32_t numSamples,
          float32_t * realResult,
          float32_t * imagResult);
  
      /**
       * @brief  Q15 complex-by-real multiplication
       * @param[in]  *pSrcCmplx points to the complex input vector
       * @param[in]  *pSrcReal points to the real input vector
       * @param[out]  *pCmplxDst points to the complex output vector
       * @param[in]  numSamples number of samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_real_q15(
          q15_t * pSrcCmplx,
          q15_t * pSrcReal,
          q15_t * pCmplxDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q31 complex-by-real multiplication
       * @param[in]  *pSrcCmplx points to the complex input vector
       * @param[in]  *pSrcReal points to the real input vector
       * @param[out]  *pCmplxDst points to the complex output vector
       * @param[in]  numSamples number of samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_real_q31(
          q31_t * pSrcCmplx,
          q31_t * pSrcReal,
          q31_t * pCmplxDst,
          uint32_t numSamples);
  
      /**
       * @brief  Floating-point complex-by-real multiplication
       * @param[in]  *pSrcCmplx points to the complex input vector
       * @param[in]  *pSrcReal points to the real input vector
       * @param[out]  *pCmplxDst points to the complex output vector
       * @param[in]  numSamples number of samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_real_f32(
          float32_t * pSrcCmplx,
          float32_t * pSrcReal,
          float32_t * pCmplxDst,
          uint32_t numSamples);
  
      /**
       * @brief  Minimum value of a Q7 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *result is output pointer
       * @param[in]  index is the array index of the minimum value in the input buffer.
       * @return none.
       */
  
      void arm_min_q7(
          q7_t * pSrc,
          uint32_t blockSize,
          q7_t * result,
          uint32_t * index);
  
      /**
       * @brief  Minimum value of a Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output pointer
       * @param[in]  *pIndex is the array index of the minimum value in the input buffer.
       * @return none.
       */
  
      void arm_min_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q15_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief  Minimum value of a Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output pointer
       * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
       * @return none.
       */
      void arm_min_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief  Minimum value of a floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[in]  blockSize is the number of samples to process
       * @param[out]  *pResult is output pointer
       * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
       * @return none.
       */
  
      void arm_min_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief Maximum value of a Q7 vector.
       * @param[in]       *pSrc points to the input buffer
       * @param[in]       blockSize length of the input vector
       * @param[out]      *pResult maximum value returned here
       * @param[out]      *pIndex index of maximum value returned here
       * @return none.
       */
  
      void arm_max_q7(
          q7_t * pSrc,
          uint32_t blockSize,
          q7_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief Maximum value of a Q15 vector.
       * @param[in]       *pSrc points to the input buffer
       * @param[in]       blockSize length of the input vector
       * @param[out]      *pResult maximum value returned here
       * @param[out]      *pIndex index of maximum value returned here
       * @return none.
       */
  
      void arm_max_q15(
          q15_t * pSrc,
          uint32_t blockSize,
          q15_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief Maximum value of a Q31 vector.
       * @param[in]       *pSrc points to the input buffer
       * @param[in]       blockSize length of the input vector
       * @param[out]      *pResult maximum value returned here
       * @param[out]      *pIndex index of maximum value returned here
       * @return none.
       */
  
      void arm_max_q31(
          q31_t * pSrc,
          uint32_t blockSize,
          q31_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief Maximum value of a floating-point vector.
       * @param[in]       *pSrc points to the input buffer
       * @param[in]       blockSize length of the input vector
       * @param[out]      *pResult maximum value returned here
       * @param[out]      *pIndex index of maximum value returned here
       * @return none.
       */
  
      void arm_max_f32(
          float32_t * pSrc,
          uint32_t blockSize,
          float32_t * pResult,
          uint32_t * pIndex);
  
      /**
       * @brief  Q15 complex-by-complex multiplication
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[out]  *pDst  points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_cmplx_q15(
          q15_t * pSrcA,
          q15_t * pSrcB,
          q15_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Q31 complex-by-complex multiplication
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[out]  *pDst  points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_cmplx_q31(
          q31_t * pSrcA,
          q31_t * pSrcB,
          q31_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief  Floating-point complex-by-complex multiplication
       * @param[in]  *pSrcA points to the first input vector
       * @param[in]  *pSrcB points to the second input vector
       * @param[out]  *pDst  points to the output vector
       * @param[in]  numSamples number of complex samples in each vector
       * @return none.
       */
  
      void arm_cmplx_mult_cmplx_f32(
          float32_t * pSrcA,
          float32_t * pSrcB,
          float32_t * pDst,
          uint32_t numSamples);
  
      /**
       * @brief Converts the elements of the floating-point vector to Q31 vector.
       * @param[in]       *pSrc points to the floating-point input vector
       * @param[out]      *pDst points to the Q31 output vector
       * @param[in]       blockSize length of the input vector
       * @return none.
       */
      void arm_float_to_q31(
          float32_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Converts the elements of the floating-point vector to Q15 vector.
       * @param[in]       *pSrc points to the floating-point input vector
       * @param[out]      *pDst points to the Q15 output vector
       * @param[in]       blockSize length of the input vector
       * @return          none
       */
      void arm_float_to_q15(
          float32_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief Converts the elements of the floating-point vector to Q7 vector.
       * @param[in]       *pSrc points to the floating-point input vector
       * @param[out]      *pDst points to the Q7 output vector
       * @param[in]       blockSize length of the input vector
       * @return          none
       */
      void arm_float_to_q7(
          float32_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Converts the elements of the Q31 vector to Q15 vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q31_to_q15(
          q31_t * pSrc,
          q15_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Converts the elements of the Q31 vector to Q7 vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q31_to_q7(
          q31_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
      /**
       * @brief  Converts the elements of the Q15 vector to floating-point vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q15_to_float(
          q15_t * pSrc,
          float32_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Converts the elements of the Q15 vector to Q31 vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q15_to_q31(
          q15_t * pSrc,
          q31_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @brief  Converts the elements of the Q15 vector to Q7 vector.
       * @param[in]  *pSrc is input pointer
       * @param[out]  *pDst is output pointer
       * @param[in]  blockSize is the number of samples to process
       * @return none.
       */
      void arm_q15_to_q7(
          q15_t * pSrc,
          q7_t * pDst,
          uint32_t blockSize);
  
  
      /**
       * @ingroup groupInterpolation
       */
  
      /**
       * @defgroup BilinearInterpolate Bilinear Interpolation
       *
       * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
       * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
       * determines values between the grid points.
       * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
       * Bilinear interpolation is often used in image processing to rescale images.
       * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
       *
       * <b>Algorithm</b>
       * \par
       * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
       * For floating-point, the instance structure is defined as:
       * <pre>
       *   typedef struct
       *   {
       *     uint16_t numRows;
       *     uint16_t numCols;
       *     float32_t *pData;
       * } arm_bilinear_interp_instance_f32;
       * </pre>
       *
       * \par
       * where <code>numRows</code> specifies the number of rows in the table;
       * <code>numCols</code> specifies the number of columns in the table;
       * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
       * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
       * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
       *
       * \par
       * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
       * <pre>
       *     XF = floor(x)
       *     YF = floor(y)
       * </pre>
       * \par
       * The interpolated output point is computed as:
       * <pre>
       *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
       *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
       *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
       *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
       * </pre>
       * Note that the coordinates (x, y) contain integer and fractional components.
       * The integer components specify which portion of the table to use while the
       * fractional components control the interpolation processor.
       *
       * \par
       * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
       */
  
      /**
       * @addtogroup BilinearInterpolate
       * @{
       */
  
      /**
      *
      * @brief  Floating-point bilinear interpolation.
      * @param[in,out] *S points to an instance of the interpolation structure.
      * @param[in] X interpolation coordinate.
      * @param[in] Y interpolation coordinate.
      * @return out interpolated value.
      */
  
  
      __STATIC_INLINE float32_t arm_bilinear_interp_f32(
          const arm_bilinear_interp_instance_f32 * S,
          float32_t X,
          float32_t Y)
      {
          float32_t out;
          float32_t f00, f01, f10, f11;
          float32_t *pData = S->pData;
          int32_t xIndex, yIndex, index;
          float32_t xdiff, ydiff;
          float32_t b1, b2, b3, b4;
  
          xIndex = (int32_t) X;
          yIndex = (int32_t) Y;
  
          /* Care taken for table outside boundary */
          /* Returns zero output when values are outside table boundary */
          if(xIndex < 0 || xIndex > (S->numRows-1) || yIndex < 0  || yIndex > ( S->numCols-1))
          {
              return(0);
          }
  
          /* Calculation of index for two nearest points in X-direction */
          index = (xIndex - 1) + (yIndex-1) *  S->numCols ;
  
  
          /* Read two nearest points in X-direction */
          f00 = pData[index];
          f01 = pData[index + 1];
  
          /* Calculation of index for two nearest points in Y-direction */
          index = (xIndex-1) + (yIndex) * S->numCols;
  
  
          /* Read two nearest points in Y-direction */
          f10 = pData[index];
          f11 = pData[index + 1];
  
          /* Calculation of intermediate values */
          b1 = f00;
          b2 = f01 - f00;
          b3 = f10 - f00;
          b4 = f00 - f01 - f10 + f11;
  
          /* Calculation of fractional part in X */
          xdiff = X - xIndex;
  
          /* Calculation of fractional part in Y */
          ydiff = Y - yIndex;
  
          /* Calculation of bi-linear interpolated output */
          out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
  
          /* return to application */
          return (out);
  
      }
  
      /**
      *
      * @brief  Q31 bilinear interpolation.
      * @param[in,out] *S points to an instance of the interpolation structure.
      * @param[in] X interpolation coordinate in 12.20 format.
      * @param[in] Y interpolation coordinate in 12.20 format.
      * @return out interpolated value.
      */
  
      __STATIC_INLINE q31_t arm_bilinear_interp_q31(
          arm_bilinear_interp_instance_q31 * S,
          q31_t X,
          q31_t Y)
      {
          q31_t out;                                   /* Temporary output */
          q31_t acc = 0;                               /* output */
          q31_t xfract, yfract;                        /* X, Y fractional parts */
          q31_t x1, x2, y1, y2;                        /* Nearest output values */
          int32_t rI, cI;                             /* Row and column indices */
          q31_t *pYData = S->pData;                    /* pointer to output table values */
          uint32_t nCols = S->numCols;                 /* num of rows */
  
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          rI = ((X & 0xFFF00000) >> 20u);
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          cI = ((Y & 0xFFF00000) >> 20u);
  
          /* Care taken for table outside boundary */
          /* Returns zero output when values are outside table boundary */
          if(rI < 0 || rI > (S->numRows-1) || cI < 0  || cI > ( S->numCols-1))
          {
              return(0);
          }
  
          /* 20 bits for the fractional part */
          /* shift left xfract by 11 to keep 1.31 format */
          xfract = (X & 0x000FFFFF) << 11u;
  
          /* Read two nearest output values from the index */
          x1 = pYData[(rI) + nCols * (cI)];
          x2 = pYData[(rI) + nCols * (cI) + 1u];
  
          /* 20 bits for the fractional part */
          /* shift left yfract by 11 to keep 1.31 format */
          yfract = (Y & 0x000FFFFF) << 11u;
  
          /* Read two nearest output values from the index */
          y1 = pYData[(rI) + nCols * (cI + 1)];
          y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
  
          /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
          out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32));
          acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
  
          /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
          out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
          acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
  
          /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
          out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
          acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
  
          /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
          out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
          acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
  
          /* Convert acc to 1.31(q31) format */
          return (acc << 2u);
  
      }
  
      /**
      * @brief  Q15 bilinear interpolation.
      * @param[in,out] *S points to an instance of the interpolation structure.
      * @param[in] X interpolation coordinate in 12.20 format.
      * @param[in] Y interpolation coordinate in 12.20 format.
      * @return out interpolated value.
      */
  
      __STATIC_INLINE q15_t arm_bilinear_interp_q15(
          arm_bilinear_interp_instance_q15 * S,
          q31_t X,
          q31_t Y)
      {
          q63_t acc = 0;                               /* output */
          q31_t out;                                   /* Temporary output */
          q15_t x1, x2, y1, y2;                        /* Nearest output values */
          q31_t xfract, yfract;                        /* X, Y fractional parts */
          int32_t rI, cI;                             /* Row and column indices */
          q15_t *pYData = S->pData;                    /* pointer to output table values */
          uint32_t nCols = S->numCols;                 /* num of rows */
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          rI = ((X & 0xFFF00000) >> 20);
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          cI = ((Y & 0xFFF00000) >> 20);
  
          /* Care taken for table outside boundary */
          /* Returns zero output when values are outside table boundary */
          if(rI < 0 || rI > (S->numRows-1) || cI < 0  || cI > ( S->numCols-1))
          {
              return(0);
          }
  
          /* 20 bits for the fractional part */
          /* xfract should be in 12.20 format */
          xfract = (X & 0x000FFFFF);
  
          /* Read two nearest output values from the index */
          x1 = pYData[(rI) + nCols * (cI)];
          x2 = pYData[(rI) + nCols * (cI) + 1u];
  
  
          /* 20 bits for the fractional part */
          /* yfract should be in 12.20 format */
          yfract = (Y & 0x000FFFFF);
  
          /* Read two nearest output values from the index */
          y1 = pYData[(rI) + nCols * (cI + 1)];
          y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
  
          /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
  
          /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
          /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
          out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
          acc = ((q63_t) out * (0xFFFFF - yfract));
  
          /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
          out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
          acc += ((q63_t) out * (xfract));
  
          /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
          out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
          acc += ((q63_t) out * (yfract));
  
          /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
          out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
          acc += ((q63_t) out * (yfract));
  
          /* acc is in 13.51 format and down shift acc by 36 times */
          /* Convert out to 1.15 format */
          return (acc >> 36);
  
      }
  
      /**
      * @brief  Q7 bilinear interpolation.
      * @param[in,out] *S points to an instance of the interpolation structure.
      * @param[in] X interpolation coordinate in 12.20 format.
      * @param[in] Y interpolation coordinate in 12.20 format.
      * @return out interpolated value.
      */
  
      __STATIC_INLINE q7_t arm_bilinear_interp_q7(
          arm_bilinear_interp_instance_q7 * S,
          q31_t X,
          q31_t Y)
      {
          q63_t acc = 0;                               /* output */
          q31_t out;                                   /* Temporary output */
          q31_t xfract, yfract;                        /* X, Y fractional parts */
          q7_t x1, x2, y1, y2;                         /* Nearest output values */
          int32_t rI, cI;                             /* Row and column indices */
          q7_t *pYData = S->pData;                     /* pointer to output table values */
          uint32_t nCols = S->numCols;                 /* num of rows */
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          rI = ((X & 0xFFF00000) >> 20);
  
          /* Input is in 12.20 format */
          /* 12 bits for the table index */
          /* Index value calculation */
          cI = ((Y & 0xFFF00000) >> 20);
  
          /* Care taken for table outside boundary */
          /* Returns zero output when values are outside table boundary */
          if(rI < 0 || rI > (S->numRows-1) || cI < 0  || cI > ( S->numCols-1))
          {
              return(0);
          }
  
          /* 20 bits for the fractional part */
          /* xfract should be in 12.20 format */
          xfract = (X & 0x000FFFFF);
  
          /* Read two nearest output values from the index */
          x1 = pYData[(rI) + nCols * (cI)];
          x2 = pYData[(rI) + nCols * (cI) + 1u];
  
  
          /* 20 bits for the fractional part */
          /* yfract should be in 12.20 format */
          yfract = (Y & 0x000FFFFF);
  
          /* Read two nearest output values from the index */
          y1 = pYData[(rI) + nCols * (cI + 1)];
          y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
  
          /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
          out = ((x1 * (0xFFFFF - xfract)));
          acc = (((q63_t) out * (0xFFFFF - yfract)));
  
          /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
          out = ((x2 * (0xFFFFF - yfract)));
          acc += (((q63_t) out * (xfract)));
  
          /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
          out = ((y1 * (0xFFFFF - xfract)));
          acc += (((q63_t) out * (yfract)));
  
          /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
          out = ((y2 * (yfract)));
          acc += (((q63_t) out * (xfract)));
  
          /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
          return (acc >> 40);
  
      }
  
      /**
       * @} end of BilinearInterpolate group
       */
  
  
  
  
  
  
  #ifdef	__cplusplus
  }
  #endif
  
  
  #endif /* _ARM_MATH_H */
  
  
  /**
   *
   * End of file.
   */
  