/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_conv_q31.c
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* Description: Convolution of Q31 sequences
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*
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* $Date: 27. January 2017
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* $Revision: V.1.5.1
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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/**
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* @ingroup groupFilters
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*/
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/**
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* @addtogroup Conv
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* @{
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*/
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/**
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* @brief Convolution of Q31 sequences.
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* @param[in] *pSrcA points to the first input sequence.
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* @param[in] srcALen length of the first input sequence.
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* @param[in] *pSrcB points to the second input sequence.
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* @param[in] srcBLen length of the second input sequence.
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* @param[out] *pDst points to the location where the output result is written. Length srcALen+srcBLen-1.
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* @return none.
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*
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* @details
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* <b>Scaling and Overflow Behavior:</b>
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*
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* \par
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* The function is implemented using an internal 64-bit accumulator.
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* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
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* There is no saturation on intermediate additions.
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* Thus, if the accumulator overflows it wraps around and distorts the result.
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* The input signals should be scaled down to avoid intermediate overflows.
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* Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,
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* as maximum of min(srcALen, srcBLen) number of additions are carried internally.
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* The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
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*
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* \par
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* See <code>arm_conv_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.
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*/
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void arm_conv_q31(
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q31_t * pSrcA,
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uint32_t srcALen,
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q31_t * pSrcB,
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uint32_t srcBLen,
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q31_t * pDst)
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{
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#if defined (ARM_MATH_DSP)
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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q31_t *pIn1; /* inputA pointer */
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q31_t *pIn2; /* inputB pointer */
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q31_t *pOut = pDst; /* output pointer */
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q31_t *px; /* Intermediate inputA pointer */
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q31_t *py; /* Intermediate inputB pointer */
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q31_t *pSrc1, *pSrc2; /* Intermediate pointers */
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q63_t sum; /* Accumulator */
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q63_t acc0, acc1, acc2; /* Accumulator */
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q31_t x0, x1, x2, c0; /* Temporary variables to hold state and coefficient values */
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uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3; /* loop counter */
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/* The algorithm implementation is based on the lengths of the inputs. */
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/* srcB is always made to slide across srcA. */
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/* So srcBLen is always considered as shorter or equal to srcALen */
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if (srcALen >= srcBLen)
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{
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/* Initialization of inputA pointer */
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pIn1 = pSrcA;
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/* Initialization of inputB pointer */
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pIn2 = pSrcB;
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}
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else
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{
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/* Initialization of inputA pointer */
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pIn1 = (q31_t *) pSrcB;
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/* Initialization of inputB pointer */
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pIn2 = (q31_t *) pSrcA;
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/* srcBLen is always considered as shorter or equal to srcALen */
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j = srcBLen;
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srcBLen = srcALen;
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srcALen = j;
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}
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/* 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] */
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/* The function is internally
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* divided into three stages according to the number of multiplications that has to be
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* taken place between inputA samples and inputB samples. In the first stage of the
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* algorithm, the multiplications increase by one for every iteration.
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* In the second stage of the algorithm, srcBLen number of multiplications are done.
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* In the third stage of the algorithm, the multiplications decrease by one
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* for every iteration. */
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/* The algorithm is implemented in three stages.
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The loop counters of each stage is initiated here. */
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blockSize1 = srcBLen - 1U;
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blockSize2 = srcALen - (srcBLen - 1U);
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blockSize3 = blockSize1;
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/* --------------------------
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* Initializations of stage1
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* -------------------------*/
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/* sum = x[0] * y[0]
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* sum = x[0] * y[1] + x[1] * y[0]
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* ....
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* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
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*/
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/* In this stage the MAC operations are increased by 1 for every iteration.
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The count variable holds the number of MAC operations performed */
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count = 1U;
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/* Working pointer of inputA */
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px = pIn1;
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/* Working pointer of inputB */
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py = pIn2;
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/* ------------------------
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* Stage1 process
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* ----------------------*/
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/* The first stage starts here */
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while (blockSize1 > 0U)
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{
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/* Accumulator is made zero for every iteration */
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sum = 0;
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/* Apply loop unrolling and compute 4 MACs simultaneously. */
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k = count >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
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** a second loop below computes MACs for the remaining 1 to 3 samples. */
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while (k > 0U)
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{
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/* x[0] * y[srcBLen - 1] */
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sum += (q63_t) * px++ * (*py--);
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/* x[1] * y[srcBLen - 2] */
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sum += (q63_t) * px++ * (*py--);
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/* x[2] * y[srcBLen - 3] */
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sum += (q63_t) * px++ * (*py--);
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/* x[3] * y[srcBLen - 4] */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* If the count is not a multiple of 4, compute any remaining MACs here.
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** No loop unrolling is used. */
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k = count % 0x4U;
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while (k > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = (q31_t) (sum >> 31);
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/* Update the inputA and inputB pointers for next MAC calculation */
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py = pIn2 + count;
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px = pIn1;
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/* Increment the MAC count */
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count++;
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/* Decrement the loop counter */
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blockSize1--;
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}
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/* --------------------------
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* Initializations of stage2
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* ------------------------*/
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/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
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* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
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* ....
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* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
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*/
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/* Working pointer of inputA */
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px = pIn1;
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/* Working pointer of inputB */
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pSrc2 = pIn2 + (srcBLen - 1U);
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py = pSrc2;
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/* count is index by which the pointer pIn1 to be incremented */
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count = 0U;
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/* -------------------
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* Stage2 process
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* ------------------*/
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/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
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* So, to loop unroll over blockSize2,
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* srcBLen should be greater than or equal to 4 */
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if (srcBLen >= 4U)
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{
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/* Loop unroll by 3 */
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blkCnt = blockSize2 / 3;
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while (blkCnt > 0U)
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{
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/* Set all accumulators to zero */
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acc0 = 0;
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acc1 = 0;
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acc2 = 0;
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/* read x[0], x[1], x[2] samples */
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x0 = *(px++);
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x1 = *(px++);
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/* Apply loop unrolling and compute 3 MACs simultaneously. */
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k = srcBLen / 3;
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/* First part of the processing with loop unrolling. Compute 3 MACs at a time.
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** a second loop below computes MACs for the remaining 1 to 2 samples. */
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do
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{
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/* Read y[srcBLen - 1] sample */
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c0 = *(py);
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/* Read x[3] sample */
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x2 = *(px);
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/* Perform the multiply-accumulates */
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/* acc0 += x[0] * y[srcBLen - 1] */
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acc0 += ((q63_t) x0 * c0);
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/* acc1 += x[1] * y[srcBLen - 1] */
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acc1 += ((q63_t) x1 * c0);
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/* acc2 += x[2] * y[srcBLen - 1] */
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acc2 += ((q63_t) x2 * c0);
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/* Read y[srcBLen - 2] sample */
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c0 = *(py - 1U);
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/* Read x[4] sample */
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x0 = *(px + 1U);
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/* Perform the multiply-accumulate */
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/* acc0 += x[1] * y[srcBLen - 2] */
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acc0 += ((q63_t) x1 * c0);
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/* acc1 += x[2] * y[srcBLen - 2] */
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acc1 += ((q63_t) x2 * c0);
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/* acc2 += x[3] * y[srcBLen - 2] */
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acc2 += ((q63_t) x0 * c0);
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/* Read y[srcBLen - 3] sample */
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c0 = *(py - 2U);
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/* Read x[5] sample */
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x1 = *(px + 2U);
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/* Perform the multiply-accumulates */
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/* acc0 += x[2] * y[srcBLen - 3] */
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acc0 += ((q63_t) x2 * c0);
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/* acc1 += x[3] * y[srcBLen - 2] */
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acc1 += ((q63_t) x0 * c0);
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/* acc2 += x[4] * y[srcBLen - 2] */
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acc2 += ((q63_t) x1 * c0);
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/* update scratch pointers */
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px += 3U;
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py -= 3U;
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} while (--k);
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/* If the srcBLen is not a multiple of 3, compute any remaining MACs here.
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** No loop unrolling is used. */
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k = srcBLen - (3 * (srcBLen / 3));
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while (k > 0U)
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{
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/* Read y[srcBLen - 5] sample */
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c0 = *(py--);
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/* Read x[7] sample */
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x2 = *(px++);
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/* Perform the multiply-accumulates */
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/* acc0 += x[4] * y[srcBLen - 5] */
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acc0 += ((q63_t) x0 * c0);
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/* acc1 += x[5] * y[srcBLen - 5] */
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acc1 += ((q63_t) x1 * c0);
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/* acc2 += x[6] * y[srcBLen - 5] */
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acc2 += ((q63_t) x2 * c0);
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/* Reuse the present samples for the next MAC */
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x0 = x1;
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x1 = x2;
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/* Decrement the loop counter */
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k--;
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}
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/* Store the results in the accumulators in the destination buffer. */
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*pOut++ = (q31_t) (acc0 >> 31);
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*pOut++ = (q31_t) (acc1 >> 31);
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*pOut++ = (q31_t) (acc2 >> 31);
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/* Increment the pointer pIn1 index, count by 3 */
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count += 3U;
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/* Update the inputA and inputB pointers for next MAC calculation */
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px = pIn1 + count;
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py = pSrc2;
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/* Decrement the loop counter */
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blkCnt--;
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}
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/* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.
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** No loop unrolling is used. */
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blkCnt = blockSize2 - 3 * (blockSize2 / 3);
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while (blkCnt > 0U)
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{
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/* Accumulator is made zero for every iteration */
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sum = 0;
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/* Apply loop unrolling and compute 4 MACs simultaneously. */
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k = srcBLen >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
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** a second loop below computes MACs for the remaining 1 to 3 samples. */
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while (k > 0U)
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{
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/* Perform the multiply-accumulates */
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sum += (q63_t) * px++ * (*py--);
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sum += (q63_t) * px++ * (*py--);
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sum += (q63_t) * px++ * (*py--);
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
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** No loop unrolling is used. */
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k = srcBLen % 0x4U;
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while (k > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = (q31_t) (sum >> 31);
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/* Increment the MAC count */
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count++;
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/* Update the inputA and inputB pointers for next MAC calculation */
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px = pIn1 + count;
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py = pSrc2;
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/* Decrement the loop counter */
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blkCnt--;
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}
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}
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else
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{
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/* If the srcBLen is not a multiple of 4,
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* the blockSize2 loop cannot be unrolled by 4 */
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blkCnt = blockSize2;
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while (blkCnt > 0U)
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{
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/* Accumulator is made zero for every iteration */
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sum = 0;
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/* srcBLen number of MACS should be performed */
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k = srcBLen;
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while (k > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = (q31_t) (sum >> 31);
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/* Increment the MAC count */
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count++;
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/* Update the inputA and inputB pointers for next MAC calculation */
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px = pIn1 + count;
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py = pSrc2;
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/* Decrement the loop counter */
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blkCnt--;
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}
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}
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/* --------------------------
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* Initializations of stage3
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* -------------------------*/
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/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
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* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
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* ....
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* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
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* sum += x[srcALen-1] * y[srcBLen-1]
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*/
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/* In this stage the MAC operations are decreased by 1 for every iteration.
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The blockSize3 variable holds the number of MAC operations performed */
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/* Working pointer of inputA */
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pSrc1 = (pIn1 + srcALen) - (srcBLen - 1U);
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px = pSrc1;
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/* Working pointer of inputB */
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pSrc2 = pIn2 + (srcBLen - 1U);
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py = pSrc2;
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/* -------------------
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* Stage3 process
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* ------------------*/
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while (blockSize3 > 0U)
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{
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/* Accumulator is made zero for every iteration */
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sum = 0;
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/* Apply loop unrolling and compute 4 MACs simultaneously. */
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k = blockSize3 >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
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** a second loop below computes MACs for the remaining 1 to 3 samples. */
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while (k > 0U)
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{
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/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
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sum += (q63_t) * px++ * (*py--);
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/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
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sum += (q63_t) * px++ * (*py--);
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/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
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sum += (q63_t) * px++ * (*py--);
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/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
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** No loop unrolling is used. */
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k = blockSize3 % 0x4U;
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while (k > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (q63_t) * px++ * (*py--);
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/* Decrement the loop counter */
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k--;
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}
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = (q31_t) (sum >> 31);
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/* Update the inputA and inputB pointers for next MAC calculation */
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px = ++pSrc1;
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py = pSrc2;
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/* Decrement the loop counter */
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blockSize3--;
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}
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#else
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/* Run the below code for Cortex-M0 */
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q31_t *pIn1 = pSrcA; /* input pointer */
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q31_t *pIn2 = pSrcB; /* coefficient pointer */
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q63_t sum; /* Accumulator */
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uint32_t i, j; /* loop counter */
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/* Loop to calculate output of convolution for output length number of times */
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for (i = 0; i < (srcALen + srcBLen - 1); i++)
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{
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/* Initialize sum with zero to carry on MAC operations */
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sum = 0;
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/* Loop to perform MAC operations according to convolution equation */
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for (j = 0; j <= i; j++)
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{
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/* Check the array limitations */
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if (((i - j) < srcBLen) && (j < srcALen))
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{
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/* z[i] += x[i-j] * y[j] */
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sum += ((q63_t) pIn1[j] * (pIn2[i - j]));
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}
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}
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/* Store the output in the destination buffer */
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pDst[i] = (q31_t) (sum >> 31U);
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}
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#endif /* #if defined (ARM_MATH_DSP) */
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}
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/**
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* @} end of Conv group
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*/
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