/* ----------------------------------------------------------------------
|
* 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
|
*/
|
