/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_conv_q31.c
* Description: Convolution of Q31 sequences
*
* $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
* @{
*/
/**
* @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)
{
#if defined (ARM_MATH_DSP)
/* 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; /* Accumulator */
q31_t x0, x1, x2, 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 by 3 */
blkCnt = blockSize2 / 3;
while (blkCnt > 0U)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
/* read x[0], x[1], x[2] 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[srcBLen - 1] sample */
c0 = *(py);
/* Read x[3] sample */
x2 = *(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);
/* Read y[srcBLen - 2] sample */
c0 = *(py - 1U);
/* Read x[4] sample */
x0 = *(px + 1U);
/* 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) x0 * c0);
/* Read y[srcBLen - 3] sample */
c0 = *(py - 2U);
/* Read x[5] sample */
x1 = *(px + 2U);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[srcBLen - 3] */
acc0 += ((q63_t) x2 * c0);
/* acc1 += x[3] * y[srcBLen - 2] */
acc1 += ((q63_t) x0 * c0);
/* acc2 += x[4] * y[srcBLen - 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[srcBLen - 5] sample */
c0 = *(py--);
/* Read x[7] sample */
x2 = *(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);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
/* 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);
/* Increment the pointer pIn1 index, count by 3 */
count += 3U;
/* 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 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);
/* 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 /* #if defined (ARM_MATH_DSP) */
}
/**
* @} end of Conv group
*/