arm_correlate_f32.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_f32.c    
*    
* Description:	 Correlation of floating-point 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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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.  
* -------------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @ingroup groupFilters    
 */

/**    
 * @defgroup Corr Correlation    
 *    
 * Correlation is a mathematical operation that is similar to convolution.    
 * As with convolution, correlation uses two signals to produce a third signal.    
 * The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution.    
 * Correlation is commonly used to measure the similarity between two signals.    
 * It has applications in pattern recognition, cryptanalysis, and searching.    
 * The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types.    
 * Fast versions of the Q15 and Q31 functions are also provided.    
 *    
 * \par Algorithm    
 * Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively.    
 * The convolution of the two signals is denoted by    
 * <pre>    
 *                   c[n] = a[n] * b[n]    
 * </pre>    
 * In correlation, one of the signals is flipped in time    
 * <pre>    
 *                   c[n] = a[n] * b[-n]    
 * </pre>    
 *    
 * \par    
 * and this is mathematically defined as    
 * \image html CorrelateEquation.gif    
 * \par    
 * The <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>.    
 * The result <code>c[n]</code> is of length <code>2 * max(srcALen, srcBLen) - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2)</code>.    
 * The output result is written to <code>pDst</code> and the calling function must allocate <code>2 * max(srcALen, srcBLen) - 1</code> words for the result.    
 *    
 * <b>Note</b>   
 * \par  
 * The <code>pDst</code> should be initialized to all zeros before being used.  
 *  
 * <b>Fixed-Point Behavior</b>    
 * \par    
 * Correlation requires summing up a large number of intermediate products.    
 * As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation.    
 * Refer to the function specific documentation below for further details of the particular algorithm used.    
 *
 *
 * <b>Fast Versions</b>
 *
 * \par 
 * Fast versions are supported for Q31 and Q15.  Cycles for Fast versions are less compared to Q31 and Q15 of correlate and the design requires
 * the input signals should be scaled down to avoid intermediate overflows.   
 *
 *
 * <b>Opt Versions</b>
 *
 * \par 
 * Opt versions are supported for Q15 and Q7.  Design uses internal scratch buffer for getting good optimisation.
 * These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions of correlate 
 */

/**    
 * @addtogroup Corr    
 * @{    
 */
/**    
 * @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 location where the output result is written.  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)
{


#ifndef ARM_MATH_CM0_FAMILY

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

  float32_t *pIn1;                               /* inputA pointer */
  float32_t *pIn2;                               /* inputB pointer */
  float32_t *pOut = pDst;                        /* output pointer */
  float32_t *px;                                 /* Intermediate inputA pointer */
  float32_t *py;                                 /* Intermediate inputB pointer */
  float32_t *pSrc1;                              /* Intermediate pointers */
  float32_t sum, acc0, acc1, acc2, acc3;         /* Accumulators */
  float32_t x0, x1, x2, x3, c0;                  /* temporary variables for holding input and coefficient values */
  uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counters */
  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 assume 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 has to be 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;

    //while(j > 0u)   
    //{   
    //  /* Zero is stored in the destination buffer */   
    //  *pOut++ = 0.0f;   

    //  /* Decrement the loop counter */   
    //  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 = 0.0f;

    /* 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)
    {
      /* x[0] * y[srcBLen - 4] */
      sum += *px++ * *py++;
      /* x[1] * y[srcBLen - 3] */
      sum += *px++ * *py++;
      /* x[2] * y[srcBLen - 2] */
      sum += *px++ * *py++;
      /* x[3] * y[srcBLen - 1] */
      sum += *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-accumulate */
      /* x[0] * y[srcBLen - 1] */
      sum += *px++ * *py++;

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut = sum;
    /* 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, to loop unroll the srcBLen loop */
  if(srcBLen >= 4u)
  {
    /* Loop unroll over blockSize2, by 4 */
    blkCnt = blockSize2 >> 2u;

    while(blkCnt > 0u)
    {
      /* Set all accumulators to zero */
      acc0 = 0.0f;
      acc1 = 0.0f;
      acc2 = 0.0f;
      acc3 = 0.0f;

      /* read x[0], x[1], x[2] samples */
      x0 = *(px++);
      x1 = *(px++);
      x2 = *(px++);

      /* 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. */
      do
      {
        /* Read y[0] sample */
        c0 = *(py++);

        /* Read x[3] sample */
        x3 = *(px++);

        /* Perform the multiply-accumulate */
        /* acc0 +=  x[0] * y[0] */
        acc0 += x0 * c0;
        /* acc1 +=  x[1] * y[0] */
        acc1 += x1 * c0;
        /* acc2 +=  x[2] * y[0] */
        acc2 += x2 * c0;
        /* acc3 +=  x[3] * y[0] */
        acc3 += x3 * c0;

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

        /* Read x[4] sample */
        x0 = *(px++);

        /* Perform the multiply-accumulate */
        /* acc0 +=  x[1] * y[1] */
        acc0 += x1 * c0;
        /* acc1 +=  x[2] * y[1] */
        acc1 += x2 * c0;
        /* acc2 +=  x[3] * y[1] */
        acc2 += x3 * c0;
        /* acc3 +=  x[4] * y[1] */
        acc3 += x0 * c0;

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

        /* Read x[5] sample */
        x1 = *(px++);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[2] * y[2] */
        acc0 += x2 * c0;
        /* acc1 +=  x[3] * y[2] */
        acc1 += x3 * c0;
        /* acc2 +=  x[4] * y[2] */
        acc2 += x0 * c0;
        /* acc3 +=  x[5] * y[2] */
        acc3 += x1 * c0;

        /* Read y[3] sample */
        c0 = *(py++);

        /* Read x[6] sample */
        x2 = *(px++);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[3] * y[3] */
        acc0 += x3 * c0;
        /* acc1 +=  x[4] * y[3] */
        acc1 += x0 * c0;
        /* acc2 +=  x[5] * y[3] */
        acc2 += x1 * c0;
        /* acc3 +=  x[6] * y[3] */
        acc3 += x2 * c0;


      } while(--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)
      {
        /* Read y[4] sample */
        c0 = *(py++);

        /* Read x[7] sample */
        x3 = *(px++);

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[4] * y[4] */
        acc0 += x0 * c0;
        /* acc1 +=  x[5] * y[4] */
        acc1 += x1 * c0;
        /* acc2 +=  x[6] * y[4] */
        acc2 += x2 * c0;
        /* acc3 +=  x[7] * y[4] */
        acc3 += x3 * c0;

        /* Reuse the present samples for the next MAC */
        x0 = x1;
        x1 = x2;
        x2 = x3;

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

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

      *pOut = acc1;
      pOut += inc;

      *pOut = acc2;
      pOut += inc;

      *pOut = acc3;
      pOut += inc;

      /* Increment the pointer pIn1 index, count by 4 */
      count += 4u;

      /* 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 4, compute any remaining output samples here.    
     ** No loop unrolling is used. */
    blkCnt = blockSize2 % 0x4u;

    while(blkCnt > 0u)
    {
      /* Accumulator is made zero for every iteration */
      sum = 0.0f;

      /* 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 += *px++ * *py++;
        sum += *px++ * *py++;
        sum += *px++ * *py++;
        sum += *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 += *px++ * *py++;

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

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

      /* Increment the pointer pIn1 index, count by 1 */
      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 = 0.0f;

      /* Loop over srcBLen */
      k = srcBLen;

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

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

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

      /* Increment the pointer pIn1 index, count by 1 */
      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 = 0.0f;

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

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut = sum;
    /* 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 */

  float32_t *pIn1 = pSrcA;                       /* inputA pointer */
  float32_t *pIn2 = pSrcB + (srcBLen - 1u);      /* inputB pointer */
  float32_t sum;                                 /* Accumulator */
  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 assume 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 convolution 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 convolution for output length number of times */
  for (i = 0u; i <= tot; i++)
  {
    /* Initialize sum with zero to carry on MAC operations */
    sum = 0.0f;

    /* Loop to perform MAC operations according to convolution 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 += pIn1[j] * pIn2[-((int32_t) i - j)];
      }
    }
    /* Store the output in the destination buffer */
    if(inv == 1)
      *pDst-- = sum;
    else
      *pDst++ = sum;
  }

#endif /*   #ifndef ARM_MATH_CM0_FAMILY */

}

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