DSP/Source/FilteringFunctions/arm_conv_fast_q31.c

/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_conv_fast_q31.c
 * Description:  Fast Q31 Convolution
 *
 * $Date:        27. January 2017
 * $Revision:    V.1.5.1
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"

/**
 * @ingroup groupFilters
 */

/**
 * @addtogroup Conv
 * @{
 */

/**
 * @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
 * This function is optimized for speed at the expense of fixed-point precision and overflow protection.
 * The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.
 * These intermediate results are accumulated in a 32-bit register in 2.30 format.
 * Finally, the accumulator is saturated and converted to a 1.31 result.
 *
 * \par
 * The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result.
 * In order to avoid overflows completely the input signals must be scaled down.
 * 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.
 *
 * \par
 * See <code>arm_conv_q31()</code> for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.
 */

void arm_conv_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst)
{
  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 */
  q31_t sum, 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 = pSrcB;

    /* Initialization of inputB pointer */
    pIn2 = 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 = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* x[1] * y[srcBLen - 2] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* x[2] * y[srcBLen - 3] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* x[3] * y[srcBLen - 4] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* 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 = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut++ = sum << 1;

    /* 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 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);

        /* acc1 +=  x[1] * y[srcBLen - 1] */
        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);

        /* acc2 +=  x[2] * y[srcBLen - 1] */
        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);

        /* acc3 +=  x[3] * y[srcBLen - 1] */
        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);

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

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

        /* Perform the multiply-accumulate */
        /* acc0 +=  x[1] * y[srcBLen - 2] */
        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
        /* acc1 +=  x[2] * y[srcBLen - 2] */
        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
        /* acc2 +=  x[3] * y[srcBLen - 2] */
        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
        /* acc3 +=  x[4] * y[srcBLen - 2] */
        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);

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

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

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[2] * y[srcBLen - 3] */
        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
        /* acc1 +=  x[3] * y[srcBLen - 3] */
        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
        /* acc2 +=  x[4] * y[srcBLen - 3] */
        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
        /* acc3 +=  x[5] * y[srcBLen - 3] */
        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);

        /* Read y[srcBLen - 4] sample */
        c0 = *(py--);

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

        /* Perform the multiply-accumulates */
        /* acc0 +=  x[3] * y[srcBLen - 4] */
        acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
        /* acc1 +=  x[4] * y[srcBLen - 4] */
        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
        /* acc2 +=  x[5] * y[srcBLen - 4] */
        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
        /* acc3 +=  x[6] * y[srcBLen - 4] */
        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);


      } 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 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
        /* acc1 +=  x[5] * y[srcBLen - 5] */
        acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
        /* acc2 +=  x[6] * y[srcBLen - 5] */
        acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
        /* acc3 +=  x[7] * y[srcBLen - 5] */
        acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);

        /* 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 << 1);
      *pOut++ = (q31_t) (acc1 << 1);
      *pOut++ = (q31_t) (acc2 << 1);
      *pOut++ = (q31_t) (acc3 << 1);

      /* 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 = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);
        sum = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);
        sum = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);
        sum = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);

        /* 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 = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);

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

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = sum << 1;

      /* 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 = (q31_t) ((((q63_t) sum << 32) +
                        ((q63_t) * px++ * (*py--))) >> 32);

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

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = sum << 1;

      /* 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 = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
      sum = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

      /* 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 = (q31_t) ((((q63_t) sum << 32) +
                      ((q63_t) * px++ * (*py--))) >> 32);

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

    /* Store the result in the accumulator in the destination buffer. */
    *pOut++ = sum << 1;

    /* Update the inputA and inputB pointers for next MAC calculation */
    px = ++pSrc1;
    py = pSrc2;

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

}

/**
 * @} end of Conv group
 */