lpc-field

arm_math.h (233229B)

---

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