arm_correlate_q31.c

/* ----------------------------------------------------------------------    
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
*    
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*    
* Project: 	    CMSIS DSP Library    
* Title:		arm_correlate_q31.c    
*    
* Description:	Correlation of Q31 sequences.  
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Redistribution and use in source and binary forms, with or without 
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the 
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @ingroup groupFilters    
 */

/**    
 * @addtogroup Corr    
 * @{    
 */

/**    
 * @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 location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.    
 * @return none.    
 *    
 * @details    
 * <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.    
 * There is no saturation on intermediate additions.    
 * Thus, if the accumulator overflows it wraps around and distorts the result.    
 * The input signals should be scaled down to avoid intermediate overflows.    
 * Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a    
 * maximum of min(srcALen, srcBLen) number of additions is carried internally.    
 * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.    
 *    
 * \par    
 * See <code>arm_correlate_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.    
 */

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

#ifndef ARM_MATH_CM0_FAMILY

  /* Run the below code for Cortex-M4 and Cortex-M3 */

  q31_t *pIn1;                                   /* inputA pointer               */
  q31_t *pIn2;                                   /* inputB pointer               */
  q31_t *pOut = pDst;                            /* output pointer               */
  q31_t *px;                                     /* Intermediate inputA pointer  */
  q31_t *py;                                     /* Intermediate inputB pointer  */
  q31_t *pSrc1;                                  /* Intermediate pointers        */
  q63_t sum, acc0, acc1, acc2;                   /* Accumulators                  */
  q31_t x0, x1, x2, c0;                          /* temporary variables for holding input and coefficient values */
  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */
  int32_t inc = 1;                               /* Destination address modifier */


  /* The algorithm implementation is based on the lengths of the inputs. */
  /* srcB is always made to slide across srcA. */
  /* So srcBLen is always considered as shorter or equal to srcALen */
  /* But CORR(x, y) is reverse of CORR(y, x) */
  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
  /* and the destination pointer modifier, inc is set to -1 */
  /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
  /* But to improve the performance,    
   * we include zeroes in the output instead of zero padding either of the the inputs*/
  /* If srcALen > srcBLen,    
   * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
  /* If srcALen < srcBLen,    
   * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
  if(srcALen >= srcBLen)
  {
    /* Initialization of inputA pointer */
    pIn1 = (pSrcA);

    /* Initialization of inputB pointer */
    pIn2 = (pSrcB);

    /* Number of output samples is calculated */
    outBlockSize = (2u * srcALen) - 1u;

    /* When srcALen > srcBLen, zero padding is done to srcB    
     * to make their lengths equal.    
     * Instead, (outBlockSize - (srcALen + srcBLen - 1))    
     * number of output samples are made zero */
    j = outBlockSize - (srcALen + (srcBLen - 1u));

    /* Updating the pointer position to non zero value */
    pOut += j;

  }
  else
  {
    /* Initialization of inputA pointer */
    pIn1 = (pSrcB);

    /* Initialization of inputB pointer */
    pIn2 = (pSrcA);

    /* srcBLen is always considered as shorter or equal to srcALen */
    j = srcBLen;
    srcBLen = srcALen;
    srcALen = j;

    /* CORR(x, y) = Reverse order(CORR(y, x)) */
    /* Hence set the destination pointer to point to the last output sample */
    pOut = pDst + ((srcALen + srcBLen) - 2u);

    /* Destination address modifier is set to -1 */
    inc = -1;

  }

  /* The function is internally    
   * divided into three parts according to the number of multiplications that has to be    
   * taken place between inputA samples and inputB samples. In the first part of the    
   * algorithm, the multiplications increase by one for every iteration.    
   * In the second part of the algorithm, srcBLen number of multiplications are done.    
   * In the third part of the algorithm, the multiplications decrease by one    
   * for every iteration.*/
  /* The algorithm is implemented in three stages.    
   * The loop counters of each stage is initiated here. */
  blockSize1 = srcBLen - 1u;
  blockSize2 = srcALen - (srcBLen - 1u);
  blockSize3 = blockSize1;

  /* --------------------------    
   * Initializations of stage1    
   * -------------------------*/

  /* sum = x[0] * y[srcBlen - 1]    
   * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]    
   * ....    
   * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]    
   */

  /* In this stage the MAC operations are increased by 1 for every iteration.    
     The count variable holds the number of MAC operations performed */
  count = 1u;

  /* Working pointer of inputA */
  px = pIn1;

  /* Working pointer of inputB */
  pSrc1 = pIn2 + (srcBLen - 1u);
  py = pSrc1;

  /* ------------------------    
   * Stage1 process    
   * ----------------------*/

  /* The first stage starts here */
  while(blockSize1 > 0u)
  {
    /* Accumulator is made zero for every iteration */
    sum = 0;

    /* Apply loop unrolling and compute 4 MACs simultaneously. */
    k = count >> 2;

    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
    while(k > 0u)
    {
      /* x[0] * y[srcBLen - 4] */
      sum += (q63_t) * px++ * (*py++);
      /* x[1] * y[srcBLen - 3] */
      sum += (q63_t) * px++ * (*py++);
      /* x[2] * y[srcBLen - 2] */
      sum += (q63_t) * px++ * (*py++);
      /* x[3] * y[srcBLen - 1] */
      sum += (q63_t) * px++ * (*py++);

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

    /* If the count is not a multiple of 4, compute any remaining MACs here.    
     ** No loop unrolling is used. */
    k = count % 0x4u;

    while(k > 0u)
    {
      /* Perform the multiply-accumulates */
      /* x[0] * y[srcBLen - 1] */
      sum += (q63_t) * px++ * (*py++);

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut = (q31_t) (sum >> 31);
    /* Destination pointer is updated according to the address modifier, inc */
    pOut += inc;

    /* Update the inputA and inputB pointers for next MAC calculation */
    py = pSrc1 - count;
    px = pIn1;

    /* Increment the MAC count */
    count++;

    /* Decrement the loop counter */
    blockSize1--;
  }

  /* --------------------------    
   * Initializations of stage2    
   * ------------------------*/

  /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]    
   * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]    
   * ....    
   * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
   */

  /* Working pointer of inputA */
  px = pIn1;

  /* Working pointer of inputB */
  py = pIn2;

  /* count is index by which the pointer pIn1 to be incremented */
  count = 0u;

  /* -------------------    
   * Stage2 process    
   * ------------------*/

  /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.    
   * So, to loop unroll over blockSize2,    
   * srcBLen should be greater than or equal to 4 */
  if(srcBLen >= 4u)
  {
    /* Loop unroll by 3 */
    blkCnt = blockSize2 / 3;

    while(blkCnt > 0u)
    {
      /* Set all accumulators to zero */
      acc0 = 0;
      acc1 = 0;
      acc2 = 0;

      /* read x[0], x[1] samples */
      x0 = *(px++);
      x1 = *(px++);

      /* Apply loop unrolling and compute 3 MACs simultaneously. */
      k = srcBLen / 3;

      /* First part of the processing with loop unrolling.  Compute 3 MACs at a time.        
       ** a second loop below computes MACs for the remaining 1 to 2 samples. */
      do
      {
        /* Read y[0] sample */
        c0 = *(py);

        /* Read x[2] sample */
        x2 = *(px);

        /* Perform the multiply-accumulate */
        /* acc0 +=  x[0] * y[0] */
        acc0 += ((q63_t) x0 * c0);
        /* acc1 +=  x[1] * y[0] */
        acc1 += ((q63_t) x1 * c0);
        /* acc2 +=  x[2] * y[0] */
        acc2 += ((q63_t) x2 * c0);

        /* Read y[1] sample */
        c0 = *(py + 1u);

        /* Read x[3] sample */
        x0 = *(px + 1u);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[1] * y[1] */
        acc0 += ((q63_t) x1 * c0);
        /* acc1 +=  x[2] * y[1] */
        acc1 += ((q63_t) x2 * c0);
        /* acc2 +=  x[3] * y[1] */
        acc2 += ((q63_t) x0 * c0);

        /* Read y[2] sample */
        c0 = *(py + 2u);

        /* Read x[4] sample */
        x1 = *(px + 2u);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[2] * y[2] */
        acc0 += ((q63_t) x2 * c0);
        /* acc1 +=  x[3] * y[2] */
        acc1 += ((q63_t) x0 * c0);
        /* acc2 +=  x[4] * y[2] */
        acc2 += ((q63_t) x1 * c0);

        /* update scratch pointers */
        px += 3u;
        py += 3u;

      } while(--k);

      /* If the srcBLen is not a multiple of 3, compute any remaining MACs here.        
       ** No loop unrolling is used. */
      k = srcBLen - (3 * (srcBLen / 3));

      while(k > 0u)
      {
        /* Read y[4] sample */
        c0 = *(py++);

        /* Read x[7] sample */
        x2 = *(px++);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[4] * y[4] */
        acc0 += ((q63_t) x0 * c0);
        /* acc1 +=  x[5] * y[4] */
        acc1 += ((q63_t) x1 * c0);
        /* acc2 +=  x[6] * y[4] */
        acc2 += ((q63_t) x2 * c0);

        /* Reuse the present samples for the next MAC */
        x0 = x1;
        x1 = x2;

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

      /* Store the result in the accumulator in the destination buffer. */
      *pOut = (q31_t) (acc0 >> 31);
      /* Destination pointer is updated according to the address modifier, inc */
      pOut += inc;

      *pOut = (q31_t) (acc1 >> 31);
      pOut += inc;

      *pOut = (q31_t) (acc2 >> 31);
      pOut += inc;

      /* Increment the pointer pIn1 index, count by 3 */
      count += 3u;

      /* Update the inputA and inputB pointers for next MAC calculation */
      px = pIn1 + count;
      py = pIn2;


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

    /* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.        
     ** No loop unrolling is used. */
    blkCnt = blockSize2 - 3 * (blockSize2 / 3);

    while(blkCnt > 0u)
    {
      /* Accumulator is made zero for every iteration */
      sum = 0;

      /* Apply loop unrolling and compute 4 MACs simultaneously. */
      k = srcBLen >> 2u;

      /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
       ** a second loop below computes MACs for the remaining 1 to 3 samples. */
      while(k > 0u)
      {
        /* Perform the multiply-accumulates */
        sum += (q63_t) * px++ * (*py++);
        sum += (q63_t) * px++ * (*py++);
        sum += (q63_t) * px++ * (*py++);
        sum += (q63_t) * px++ * (*py++);

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

      /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.    
       ** No loop unrolling is used. */
      k = srcBLen % 0x4u;

      while(k > 0u)
      {
        /* Perform the multiply-accumulate */
        sum += (q63_t) * px++ * (*py++);

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

      /* Store the result in the accumulator in the destination buffer. */
      *pOut = (q31_t) (sum >> 31);
      /* Destination pointer is updated according to the address modifier, inc */
      pOut += inc;

      /* Increment the MAC count */
      count++;

      /* Update the inputA and inputB pointers for next MAC calculation */
      px = pIn1 + count;
      py = pIn2;

      /* Decrement the loop counter */
      blkCnt--;
    }
  }
  else
  {
    /* If the srcBLen is not a multiple of 4,    
     * the blockSize2 loop cannot be unrolled by 4 */
    blkCnt = blockSize2;

    while(blkCnt > 0u)
    {
      /* Accumulator is made zero for every iteration */
      sum = 0;

      /* Loop over srcBLen */
      k = srcBLen;

      while(k > 0u)
      {
        /* Perform the multiply-accumulate */
        sum += (q63_t) * px++ * (*py++);

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

      /* Store the result in the accumulator in the destination buffer. */
      *pOut = (q31_t) (sum >> 31);
      /* Destination pointer is updated according to the address modifier, inc */
      pOut += inc;

      /* Increment the MAC count */
      count++;

      /* Update the inputA and inputB pointers for next MAC calculation */
      px = pIn1 + count;
      py = pIn2;

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

  /* --------------------------    
   * Initializations of stage3    
   * -------------------------*/

  /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
   * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]    
   * ....    
   * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]    
   * sum +=  x[srcALen-1] * y[0]    
   */

  /* In this stage the MAC operations are decreased by 1 for every iteration.    
     The count variable holds the number of MAC operations performed */
  count = srcBLen - 1u;

  /* Working pointer of inputA */
  pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
  px = pSrc1;

  /* Working pointer of inputB */
  py = pIn2;

  /* -------------------    
   * Stage3 process    
   * ------------------*/

  while(blockSize3 > 0u)
  {
    /* Accumulator is made zero for every iteration */
    sum = 0;

    /* Apply loop unrolling and compute 4 MACs simultaneously. */
    k = count >> 2u;

    /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.    
     ** a second loop below computes MACs for the remaining 1 to 3 samples. */
    while(k > 0u)
    {
      /* Perform the multiply-accumulates */
      /* sum += x[srcALen - srcBLen + 4] * y[3] */
      sum += (q63_t) * px++ * (*py++);
      /* sum += x[srcALen - srcBLen + 3] * y[2] */
      sum += (q63_t) * px++ * (*py++);
      /* sum += x[srcALen - srcBLen + 2] * y[1] */
      sum += (q63_t) * px++ * (*py++);
      /* sum += x[srcALen - srcBLen + 1] * y[0] */
      sum += (q63_t) * px++ * (*py++);

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

    /* If the count is not a multiple of 4, compute any remaining MACs here.    
     ** No loop unrolling is used. */
    k = count % 0x4u;

    while(k > 0u)
    {
      /* Perform the multiply-accumulates */
      sum += (q63_t) * px++ * (*py++);

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut = (q31_t) (sum >> 31);
    /* Destination pointer is updated according to the address modifier, inc */
    pOut += inc;

    /* Update the inputA and inputB pointers for next MAC calculation */
    px = ++pSrc1;
    py = pIn2;

    /* Decrement the MAC count */
    count--;

    /* Decrement the loop counter */
    blockSize3--;
  }

#else

  /* Run the below code for Cortex-M0 */

  q31_t *pIn1 = pSrcA;                           /* inputA pointer               */
  q31_t *pIn2 = pSrcB + (srcBLen - 1u);          /* inputB pointer               */
  q63_t sum;                                     /* Accumulators                  */
  uint32_t i = 0u, j;                            /* loop counters */
  uint32_t inv = 0u;                             /* Reverse order flag */
  uint32_t tot = 0u;                             /* Length */

  /* The algorithm implementation is based on the lengths of the inputs. */
  /* srcB is always made to slide across srcA. */
  /* So srcBLen is always considered as shorter or equal to srcALen */
  /* But CORR(x, y) is reverse of CORR(y, x) */
  /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
  /* and a varaible, inv is set to 1 */
  /* If lengths are not equal then zero pad has to be done to  make the two    
   * inputs of same length. But to improve the performance, we include zeroes    
   * in the output instead of zero padding either of the the inputs*/
  /* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the    
   * starting of the output buffer */
  /* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the   
   * ending of the output buffer */
  /* Once the zero padding is done the remaining of the output is calcualted   
   * using correlation but with the shorter signal time shifted. */

  /* Calculate the length of the remaining sequence */
  tot = ((srcALen + srcBLen) - 2u);

  if(srcALen > srcBLen)
  {
    /* Calculating the number of zeros to be padded to the output */
    j = srcALen - srcBLen;

    /* Initialise the pointer after zero padding */
    pDst += j;
  }

  else if(srcALen < srcBLen)
  {
    /* Initialization to inputB pointer */
    pIn1 = pSrcB;

    /* Initialization to the end of inputA pointer */
    pIn2 = pSrcA + (srcALen - 1u);

    /* Initialisation of the pointer after zero padding */
    pDst = pDst + tot;

    /* Swapping the lengths */
    j = srcALen;
    srcALen = srcBLen;
    srcBLen = j;

    /* Setting the reverse flag */
    inv = 1;

  }

  /* Loop to calculate correlation for output length number of times */
  for (i = 0u; i <= tot; i++)
  {
    /* Initialize sum with zero to carry on MAC operations */
    sum = 0;

    /* Loop to perform MAC operations according to correlation equation */
    for (j = 0u; j <= i; j++)
    {
      /* Check the array limitations */
      if((((i - j) < srcBLen) && (j < srcALen)))
      {
        /* z[i] += x[i-j] * y[j] */
        sum += ((q63_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
      }
    }
    /* Store the output in the destination buffer */
    if(inv == 1)
      *pDst-- = (q31_t) (sum >> 31u);
    else
      *pDst++ = (q31_t) (sum >> 31u);
  }

#endif /*   #ifndef ARM_MATH_CM0_FAMILY */

}

/**    
 * @} end of Corr group    
 */