/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_conv_q15.c
* Description: Convolution of Q15 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 Q15 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 a 64-bit internal accumulator.
* Both inputs are in 1.15 format and multiplications yield a 2.30 result.
* The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
* This approach provides 33 guard bits and there is no risk of overflow.
* The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.
*
* \par
* Refer to <code>arm_conv_fast_q15()</code> for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.
*
* \par
* Refer the function <code>arm_conv_opt_q15()</code> for a faster implementation of this function using scratch buffers.
*
*/
void arm_conv_q15(
q15_t * pSrcA,
uint32_t srcALen,
q15_t * pSrcB,
uint32_t srcBLen,
q15_t * pDst)
{
#if (defined(ARM_MATH_CM7) || defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE)
/* Run the below code for Cortex-M4 and Cortex-M3 */
q15_t *pIn1; /* inputA pointer */
q15_t *pIn2; /* inputB pointer */
q15_t *pOut = pDst; /* output pointer */
q63_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q15_t *px; /* Intermediate inputA pointer */
q15_t *py; /* Intermediate inputB pointer */
q15_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt; /* 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);
/* --------------------------
* 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
* ----------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations less than 4 */
/* Second part of this stage computes the MAC operations greater than or equal to 4 */
/* The first part of the stage starts here */
while ((count < 4U) && (blockSize1 > 0U))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over number of MAC operations between
* inputA samples and inputB samples */
k = count;
while (k > 0U)
{
/* Perform the multiply-accumulates */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* 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--;
}
/* The second part of the stage starts here */
/* The internal loop, over count, is unrolled by 4 */
/* To, read the last two inputB samples using SIMD:
* y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
py = py - 1;
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)
{
/* Perform the multiply-accumulates */
/* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1U;
/* 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 = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + (count - 1U);
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 the 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)
{
py = py - 1U;
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1] samples */
x0 = *__SIMD32(px);
/* read x[1], x[2] samples */
x1 = _SIMD32_OFFSET(px+1);
px+= 2U;
/* 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 the last two inputB samples using SIMD:
* y[srcBLen - 1] and y[srcBLen - 2] */
c0 = *__SIMD32(py)--;
/* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
acc0 = __SMLALDX(x0, c0, acc0);
/* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
acc1 = __SMLALDX(x1, c0, acc1);
/* Read x[2], x[3] */
x2 = *__SIMD32(px);
/* Read x[3], x[4] */
x3 = _SIMD32_OFFSET(px+1);
/* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
acc2 = __SMLALDX(x2, c0, acc2);
/* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
acc3 = __SMLALDX(x3, c0, acc3);
/* Read y[srcBLen - 3] and y[srcBLen - 4] */
c0 = *__SIMD32(py)--;
/* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
acc0 = __SMLALDX(x2, c0, acc0);
/* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
acc1 = __SMLALDX(x3, c0, acc1);
/* Read x[4], x[5] */
x0 = _SIMD32_OFFSET(px+2);
/* Read x[5], x[6] */
x1 = _SIMD32_OFFSET(px+3);
px += 4U;
/* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
acc2 = __SMLALDX(x0, c0, acc2);
/* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
acc3 = __SMLALDX(x1, c0, acc3);
} while (--k);
/* For the next MAC operations, SIMD is not used
* So, the 16 bit pointer if inputB, py is updated */
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4U;
if (k == 1U)
{
/* Read y[srcBLen - 5] */
c0 = *(py+1);
#ifdef ARM_MATH_BIG_ENDIAN
c0 = c0 << 16U;
#else
c0 = c0 & 0x0000FFFF;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[7] */
x3 = *__SIMD32(px);
px++;
/* Perform the multiply-accumulates */
acc0 = __SMLALD(x0, c0, acc0);
acc1 = __SMLALD(x1, c0, acc1);
acc2 = __SMLALDX(x1, c0, acc2);
acc3 = __SMLALDX(x3, c0, acc3);
}
if (k == 2U)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = _SIMD32_OFFSET(py);
/* Read x[7], x[8] */
x3 = *__SIMD32(px);
/* Read x[9] */
x2 = _SIMD32_OFFSET(px+1);
px += 2U;
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x0, c0, acc0);
acc1 = __SMLALDX(x1, c0, acc1);
acc2 = __SMLALDX(x3, c0, acc2);
acc3 = __SMLALDX(x2, c0, acc3);
}
if (k == 3U)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = _SIMD32_OFFSET(py);
/* Read x[7], x[8] */
x3 = *__SIMD32(px);
/* Read x[9] */
x2 = _SIMD32_OFFSET(px+1);
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x0, c0, acc0);
acc1 = __SMLALDX(x1, c0, acc1);
acc2 = __SMLALDX(x3, c0, acc2);
acc3 = __SMLALDX(x2, c0, acc3);
c0 = *(py-1);
#ifdef ARM_MATH_BIG_ENDIAN
c0 = c0 << 16U;
#else
c0 = c0 & 0x0000FFFF;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[10] */
x3 = _SIMD32_OFFSET(px+2);
px += 3U;
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x1, c0, acc0);
acc1 = __SMLALD(x2, c0, acc1);
acc2 = __SMLALDX(x2, c0, acc2);
acc3 = __SMLALDX(x3, c0, acc3);
}
/* Store the results in the accumulators in the destination buffer. */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
#else
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* 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) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_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-accumulates */
sum += (q63_t) ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
/* Increment the pointer pIn1 index, count by 1 */
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) ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
/* 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 */
blockSize3 = srcBLen - 1U;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1U);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1U);
pIn2 = pSrc2 - 1U;
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations greater than 4 */
/* Second part of this stage computes the MAC operations less than or equal to 4 */
/* The first part of the stage starts here */
j = blockSize3 >> 2U;
while ((j > 0U) && (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)
{
/* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied
* with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied
* with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1U;
/* 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)
{
/* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the loop counter */
blockSize3--;
j--;
}
/* The second part of the stage starts here */
/* SIMD is not used for the next MAC operations,
* so pointer py is updated to read only one sample at a time */
py = py + 1U;
while (blockSize3 > 0U)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3;
while (k > 0U)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* 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 */
q15_t *pIn1 = pSrcA; /* input pointer */
q15_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 += (q31_t) pIn1[j] * (pIn2[i - j]);
}
}
/* Store the output in the destination buffer */
pDst[i] = (q15_t) __SSAT((sum >> 15U), 16U);
}
#endif /* #if (defined(ARM_MATH_CM7) || defined(ARM_MATH_CM4) || defined(ARM_MATH_CM3)) && !defined(UNALIGNED_SUPPORT_DISABLE) */
}
/**
* @} end of Conv group
*/