602 lines
19 KiB
C
602 lines
19 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_correlate_fast_q31.c
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* Description: Fast Q31 Correlation
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*
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* $Date: 18. March 2019
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* $Revision: V1.6.0
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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) 2010-2019 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 Corr
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@{
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*/
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/**
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@brief Correlation of Q31 sequences (fast version).
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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 2 * max(srcALen, srcBLen) - 1.
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@return none
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@par Scaling and Overflow Behavior
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This function is optimized for speed at the expense of fixed-point precision and overflow protection.
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The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.
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These intermediate results are accumulated in a 32-bit register in 2.30 format.
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Finally, the accumulator is saturated and converted to a 1.31 result.
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@par
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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.
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In order to avoid overflows completely the input signals must be scaled down.
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The input signals should be scaled down to avoid intermediate overflows.
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Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a
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maximum of min(srcALen, srcBLen) number of additions is carried internally.
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@remark
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Refer to \ref arm_correlate_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.
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*/
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void arm_correlate_fast_q31(
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const q31_t * pSrcA,
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uint32_t srcALen,
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const 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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const q31_t *pIn1; /* InputA pointer */
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const q31_t *pIn2; /* InputB pointer */
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q31_t *pOut = pDst; /* Output pointer */
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const q31_t *px; /* Intermediate inputA pointer */
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const q31_t *py; /* Intermediate inputB pointer */
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const q31_t *pSrc1; /* Intermediate pointers */
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q31_t sum, acc0, acc1, acc2, acc3; /* Accumulators */
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q31_t x0, x1, x2, x3, c0; /* Temporary variables for holding input and coefficient values */
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uint32_t blockSize1, blockSize2, blockSize3; /* Loop counters */
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uint32_t j, k, count, blkCnt; /* Loop counters */
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uint32_t outBlockSize;
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int32_t inc = 1; /* Destination address modifier */
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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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/* Number of output samples is calculated */
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outBlockSize = (2U * srcALen) - 1U;
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/* When srcALen > srcBLen, zero padding is done to srcB
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* to make their lengths equal.
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* Instead, (outBlockSize - (srcALen + srcBLen - 1))
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* number of output samples are made zero */
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j = outBlockSize - (srcALen + (srcBLen - 1U));
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/* Updating the pointer position to non zero value */
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pOut += j;
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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 = pSrcB;
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/* Initialization of inputB pointer */
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pIn2 = 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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/* CORR(x, y) = Reverse order(CORR(y, x)) */
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/* Hence set the destination pointer to point to the last output sample */
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pOut = pDst + ((srcALen + srcBLen) - 2U);
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/* Destination address modifier is set to -1 */
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inc = -1;
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}
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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[srcBlen - 1]
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* sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]
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* ....
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* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]
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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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pSrc1 = pIn2 + (srcBLen - 1U);
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py = pSrc1;
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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 - 4] */
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* x[1] * y[srcBLen - 3] */
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* x[2] * y[srcBLen - 2] */
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* x[3] * y[srcBLen - 1] */
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* Decrement 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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/* x[0] * y[srcBLen - 1] */
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* Decrement 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 = sum << 1;
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/* Destination pointer is updated according to the address modifier, inc */
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pOut += inc;
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/* Update the inputA and inputB pointers for next MAC calculation */
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py = pSrc1 - count;
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px = pIn1;
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/* Increment MAC count */
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count++;
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/* Decrement 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[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]
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* sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]
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* ....
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* sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
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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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py = pIn2;
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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 over blockSize2, by 4 */
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blkCnt = blockSize2 >> 2U;
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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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acc3 = 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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x2 = *px++;
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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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do
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{
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/* Read y[0] sample */
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c0 = *py++;
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/* Read x[3] sample */
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x3 = *px++;
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/* Perform the multiply-accumulate */
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/* acc0 += x[0] * y[0] */
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acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
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/* acc1 += x[1] * y[0] */
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acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
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/* acc2 += x[2] * y[0] */
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acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
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/* acc3 += x[3] * y[0] */
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acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
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/* Read y[1] sample */
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c0 = *py++;
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/* Read x[4] sample */
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x0 = *px++;
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/* Perform the multiply-accumulate */
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/* acc0 += x[1] * y[1] */
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acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
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/* acc1 += x[2] * y[1] */
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acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
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/* acc2 += x[3] * y[1] */
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acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
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/* acc3 += x[4] * y[1] */
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acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
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/* Read y[2] sample */
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c0 = *py++;
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/* Read x[5] sample */
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x1 = *px++;
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/* Perform the multiply-accumulates */
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/* acc0 += x[2] * y[2] */
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acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
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/* acc1 += x[3] * y[2] */
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acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
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/* acc2 += x[4] * y[2] */
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acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
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/* acc3 += x[5] * y[2] */
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acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
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/* Read y[3] sample */
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c0 = *py++;
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/* Read x[6] sample */
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x2 = *px++;
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/* Perform the multiply-accumulates */
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/* acc0 += x[3] * y[3] */
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acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
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/* acc1 += x[4] * y[3] */
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acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
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/* acc2 += x[5] * y[3] */
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acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
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/* acc3 += x[6] * y[3] */
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acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
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} while (--k);
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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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/* Read y[4] sample */
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c0 = *py++;
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/* Read x[7] sample */
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x3 = *px++;
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/* Perform the multiply-accumulates */
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/* acc0 += x[4] * y[4] */
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acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
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/* acc1 += x[5] * y[4] */
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acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
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/* acc2 += x[6] * y[4] */
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acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
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/* acc3 += x[7] * y[4] */
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acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
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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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x2 = x3;
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/* Decrement 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) (acc0 << 1);
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/* Destination pointer is updated according to the address modifier, inc */
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pOut += inc;
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*pOut = (q31_t) (acc1 << 1);
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pOut += inc;
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*pOut = (q31_t) (acc2 << 1);
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pOut += inc;
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*pOut = (q31_t) (acc3 << 1);
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pOut += inc;
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/* Increment the pointer pIn1 index, count by 4 */
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count += 4U;
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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 = pIn2;
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/* Decrement loop counter */
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blkCnt--;
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}
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/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
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** No loop unrolling is used. */
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blkCnt = blockSize2 % 0x4U;
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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 = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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sum = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* Decrement 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 = (q31_t) ((((q63_t) sum << 32) +
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((q63_t) *px++ * (*py++))) >> 32);
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/* Decrement 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 = sum << 1;
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/* Destination pointer is updated according to the address modifier, inc */
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pOut += inc;
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/* Increment 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 = pIn2;
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/* Decrement 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 = (q31_t) ((((q63_t) sum << 32) +
|
|
((q63_t) *px++ * (*py++))) >> 32);
|
|
|
|
/* Decrement loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut = sum << 1;
|
|
/* Destination pointer is updated according to the address modifier, inc */
|
|
pOut += inc;
|
|
|
|
/* Increment MAC count */
|
|
count++;
|
|
|
|
/* Update the inputA and inputB pointers for next MAC calculation */
|
|
px = pIn1 + count;
|
|
py = pIn2;
|
|
|
|
/* Decrement loop counter */
|
|
blkCnt--;
|
|
}
|
|
}
|
|
|
|
|
|
/* --------------------------
|
|
* Initializations of stage3
|
|
* -------------------------*/
|
|
|
|
/* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
|
|
* sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
|
|
* ....
|
|
* sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1]
|
|
* sum += x[srcALen-1] * y[0]
|
|
*/
|
|
|
|
/* In this stage the MAC operations are decreased by 1 for every iteration.
|
|
The count variable holds the number of MAC operations performed */
|
|
count = srcBLen - 1U;
|
|
|
|
/* Working pointer of inputA */
|
|
pSrc1 = ((pIn1 + srcALen) - srcBLen) + 1U;
|
|
px = pSrc1;
|
|
|
|
/* Working pointer of inputB */
|
|
py = pIn2;
|
|
|
|
/* -------------------
|
|
* Stage3 process
|
|
* ------------------*/
|
|
|
|
while (blockSize3 > 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-accumulate */
|
|
/* sum += x[srcALen - srcBLen + 4] * y[3] */
|
|
sum = (q31_t) ((((q63_t) sum << 32) +
|
|
((q63_t) *px++ * (*py++))) >> 32);
|
|
|
|
/* sum += x[srcALen - srcBLen + 3] * y[2] */
|
|
sum = (q31_t) ((((q63_t) sum << 32) +
|
|
((q63_t) *px++ * (*py++))) >> 32);
|
|
|
|
/* sum += x[srcALen - srcBLen + 2] * y[1] */
|
|
sum = (q31_t) ((((q63_t) sum << 32) +
|
|
((q63_t) *px++ * (*py++))) >> 32);
|
|
|
|
/* sum += x[srcALen - srcBLen + 1] * y[0] */
|
|
sum = (q31_t) ((((q63_t) sum << 32) +
|
|
((q63_t) *px++ * (*py++))) >> 32);
|
|
|
|
/* Decrement 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 loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut = sum << 1;
|
|
/* Destination pointer is updated according to the address modifier, inc */
|
|
pOut += inc;
|
|
|
|
/* Update the inputA and inputB pointers for next MAC calculation */
|
|
px = ++pSrc1;
|
|
py = pIn2;
|
|
|
|
/* Decrement MAC count */
|
|
count--;
|
|
|
|
/* Decrement loop counter */
|
|
blockSize3--;
|
|
}
|
|
|
|
}
|
|
|
|
/**
|
|
@} end of Corr group
|
|
*/
|