text: /* ----------------------------------------------------------------------   
  * Copyright (C) 2010 ARM Limited. All rights reserved.   
  *   
  * $Date:        18. Oct 2011  
  * $Revision: 	V1.0.11  
  *   
  * Project: 	    CMSIS DSP Library   
  * Title:		arm_conv_q31.c   
  *   
  * Description:	Convolution of Q31 sequences. 
  *   
  * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  *
  * Version 1.0.11 2011/10/18 
  *    Bug Fix in conv, correlation, partial convolution. 
  *  
  * 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   
  *   
  * Version 0.0.7  2010/06/10    
  *    Misra-C changes done   
  *   
  * -------------------------------------------------------------------- */
  
  #include "arm_math.h"
  
  /**   
   * @ingroup groupFilters   
   */
  
  /**   
   * @addtogroup Conv   
   * @{   
   */
  
  /**   
   * @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 location where the output result is written.  Length 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 the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,   
   * as maximum of min(srcALen, srcBLen) number of additions are 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_conv_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.   
   */
  
  void arm_conv_q31(
    q31_t * pSrcA,
    uint32_t srcALen,
    q31_t * pSrcB,
    uint32_t srcBLen,
    q31_t * pDst)
  {
  
  
  #ifndef ARM_MATH_CM0
  
    /* 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, *pSrc2;                          /* Intermediate pointers */
    q63_t sum;                                     /* Accumulator */
    q63_t acc0, acc1, acc2, acc3;                  /* Accumulator */
    q31_t x0, x1, x2, x3, c0;                      /* Temporary variables to hold state and coefficient values */
    uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counter */
  
    /* 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 */
    if(srcALen >= srcBLen)
    {
      /* Initialization of inputA pointer */
      pIn1 = pSrcA;
  
      /* Initialization of inputB pointer */
      pIn2 = pSrcB;
    }
    else
    {
      /* Initialization of inputA pointer */
      pIn1 = (q31_t *) pSrcB;
  
      /* Initialization of inputB pointer */
      pIn2 = (q31_t *) pSrcA;
  
      /* srcBLen is always considered as shorter or equal to srcALen */
      j = srcBLen;
      srcBLen = srcALen;
      srcALen = j;
    }
  
    /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
    /* The function is internally   
     * divided into three stages according to the number of multiplications that has to be   
     * taken place between inputA samples and inputB samples. In the first stage of the   
     * algorithm, the multiplications increase by one for every iteration.   
     * In the second stage of the algorithm, srcBLen number of multiplications are done.   
     * In the third stage 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[0]   
     * sum = x[0] * y[1] + x[1] * y[0]   
     * ....   
     * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]   
     */
  
    /* 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 */
    py = pIn2;
  
  
    /* ------------------------   
     * 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 >> 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 - 1] */
        sum += (q63_t) * px++ * (*py--);
        /* x[1] * y[srcBLen - 2] */
        sum += (q63_t) * px++ * (*py--);
        /* x[2] * y[srcBLen - 3] */
        sum += (q63_t) * px++ * (*py--);
        /* x[3] * y[srcBLen - 4] */
        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-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);
  
      /* Update the inputA and inputB pointers for next MAC calculation */
      py = pIn2 + count;
      px = pIn1;
  
      /* Increment the MAC count */
      count++;
  
      /* Decrement the loop counter */
      blockSize1--;
    }
  
    /* --------------------------   
     * Initializations of stage2   
     * ------------------------*/
  
    /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]   
     * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]   
     * ....   
     * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]   
     */
  
    /* Working pointer of inputA */
    px = pIn1;
  
    /* Working pointer of inputB */
    pSrc2 = pIn2 + (srcBLen - 1u);
    py = pSrc2;
  
    /* 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 over blockSize2, by 4 */
      blkCnt = blockSize2 >> 2u;
  
      while(blkCnt > 0u)
      {
        /* Set all accumulators to zero */
        acc0 = 0;
        acc1 = 0;
        acc2 = 0;
        acc3 = 0;
  
        /* 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[srcBLen - 1] sample */
          c0 = *(py--);
  
          /* Read x[3] sample */
          x3 = *(px++);
  
          /* Perform the multiply-accumulates */
          /* acc0 +=  x[0] * y[srcBLen - 1] */
          acc0 += ((q63_t) x0 * c0);
          /* acc1 +=  x[1] * y[srcBLen - 1] */
          acc1 += ((q63_t) x1 * c0);
          /* acc2 +=  x[2] * y[srcBLen - 1] */
          acc2 += ((q63_t) x2 * c0);
          /* acc3 +=  x[3] * y[srcBLen - 1] */
          acc3 += ((q63_t) x3 * c0);
  
          /* Read y[srcBLen - 2] sample */
          c0 = *(py--);
  
          /* Read x[4] sample */
          x0 = *(px++);
  
          /* Perform the multiply-accumulate */
          /* acc0 +=  x[1] * y[srcBLen - 2] */
          acc0 += ((q63_t) x1 * c0);
          /* acc1 +=  x[2] * y[srcBLen - 2] */
          acc1 += ((q63_t) x2 * c0);
          /* acc2 +=  x[3] * y[srcBLen - 2] */
          acc2 += ((q63_t) x3 * c0);
          /* acc3 +=  x[4] * y[srcBLen - 2] */
          acc3 += ((q63_t) x0 * c0);
  
          /* Read y[srcBLen - 3] sample */
          c0 = *(py--);
  
          /* Read x[5] sample */
          x1 = *(px++);
  
          /* Perform the multiply-accumulates */
          /* acc0 +=  x[2] * y[srcBLen - 3] */
          acc0 += ((q63_t) x2 * c0);
          /* acc1 +=  x[3] * y[srcBLen - 2] */
          acc1 += ((q63_t) x3 * c0);
          /* acc2 +=  x[4] * y[srcBLen - 2] */
          acc2 += ((q63_t) x0 * c0);
          /* acc3 +=  x[5] * y[srcBLen - 2] */
          acc3 += ((q63_t) x1 * c0);
  
          /* Read y[srcBLen - 4] sample */
          c0 = *(py--);
  
          /* Read x[6] sample */
          x2 = *(px++);
  
          /* Perform the multiply-accumulates */
          /* acc0 +=  x[3] * y[srcBLen - 4] */
          acc0 += ((q63_t) x3 * c0);
          /* acc1 +=  x[4] * y[srcBLen - 4] */
          acc1 += ((q63_t) x0 * c0);
          /* acc2 +=  x[5] * y[srcBLen - 4] */
          acc2 += ((q63_t) x1 * c0);
          /* acc3 +=  x[6] * y[srcBLen - 4] */
          acc3 += ((q63_t) 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[srcBLen - 5] sample */
          c0 = *(py--);
  
          /* Read x[7] sample */
          x3 = *(px++);
  
          /* Perform the multiply-accumulates */
          /* acc0 +=  x[4] * y[srcBLen - 5] */
          acc0 += ((q63_t) x0 * c0);
          /* acc1 +=  x[5] * y[srcBLen - 5] */
          acc1 += ((q63_t) x1 * c0);
          /* acc2 +=  x[6] * y[srcBLen - 5] */
          acc2 += ((q63_t) x2 * c0);
          /* acc3 +=  x[7] * y[srcBLen - 5] */
          acc3 += ((q63_t) x3 * c0);
  
          /* Reuse the present samples for the next MAC */
          x0 = x1;
          x1 = x2;
          x2 = x3;
  
          /* Decrement the loop counter */
          k--;
        }
  
        /* Store the results in the accumulators in the destination buffer. */
        *pOut++ = (q31_t) (acc0 >> 31);
        *pOut++ = (q31_t) (acc1 >> 31);
        *pOut++ = (q31_t) (acc2 >> 31);
        *pOut++ = (q31_t) (acc3 >> 31);
  
        /* Increment the pointer pIn1 index, count by 4 */
        count += 4u;
  
        /* Update the inputA and inputB pointers for next MAC calculation */
        px = pIn1 + count;
        py = pSrc2;
  
        /* 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;
  
        /* 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);
  
        /* Increment the MAC count */
        count++;
  
        /* Update the inputA and inputB pointers for next MAC calculation */
        px = pIn1 + count;
        py = pSrc2;
  
        /* 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;
  
        /* srcBLen number of MACS should be performed */
        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);
  
        /* Increment the MAC count */
        count++;
  
        /* Update the inputA and inputB pointers for next MAC calculation */
        px = pIn1 + count;
        py = pSrc2;
  
        /* Decrement the loop counter */
        blkCnt--;
      }
    }
  
  
    /* --------------------------   
     * Initializations of stage3   
     * -------------------------*/
  
    /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]   
     * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]   
     * ....   
     * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]   
     * sum +=  x[srcALen-1] * y[srcBLen-1]   
     */
  
    /* In this stage the MAC operations are decreased by 1 for every iteration.   
       The blockSize3 variable holds the number of MAC operations performed */
  
    /* Working pointer of inputA */
    pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
    px = pSrc1;
  
    /* Working pointer of inputB */
    pSrc2 = pIn2 + (srcBLen - 1u);
    py = pSrc2;
  
    /* -------------------   
     * Stage3 process   
     * ------------------*/
  
    while(blockSize3 > 0u)
    {
      /* Accumulator is made zero for every iteration */
      sum = 0;
  
      /* Apply loop unrolling and compute 4 MACs simultaneously. */
      k = blockSize3 >> 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)
      {
        /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
        sum += (q63_t) * px++ * (*py--);
        /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
        sum += (q63_t) * px++ * (*py--);
        /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
        sum += (q63_t) * px++ * (*py--);
        /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
        sum += (q63_t) * px++ * (*py--);
  
        /* Decrement the loop counter */
        k--;
      }
  
      /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.   
       ** No loop unrolling is used. */
      k = blockSize3 % 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);
  
      /* Update the inputA and inputB pointers for next MAC calculation */
      px = ++pSrc1;
      py = pSrc2;
  
      /* Decrement the loop counter */
      blockSize3--;
    }
  
  #else
  
    /* Run the below code for Cortex-M0 */
  
    q31_t *pIn1 = pSrcA;                           /* input pointer */
    q31_t *pIn2 = pSrcB;                           /* coefficient pointer */
    q63_t sum;                                     /* Accumulator */
    uint32_t i, j;                                 /* loop counter */
  
    /* Loop to calculate output of convolution for output length number of times */
    for (i = 0; i < (srcALen + srcBLen - 1); i++)
    {
      /* Initialize sum with zero to carry on MAC operations */
      sum = 0;
  
      /* Loop to perform MAC operations according to convolution equation */
      for (j = 0; 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[i - j]));
        }
      }
  
      /* Store the output in the destination buffer */
      pDst[i] = (q31_t) (sum >> 31u);
    }
  
  #endif /*     #ifndef ARM_MATH_CM0 */
  
  }
  
  /**   
   * @} end of Conv group   
   */
  