654 lines
20 KiB
C
654 lines
20 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_correlate_q31.c
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* Description: Correlation 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 Corr
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* @{
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*/
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/**
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* @brief Correlation 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 2 * max(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 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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* 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_correlate_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_correlate_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; /* Intermediate pointers */
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q63_t sum, acc0, acc1, acc2; /* Accumulators */
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q31_t x0, x1, x2, c0; /* temporary variables for holding input and coefficient values */
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uint32_t j, k = 0U, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3; /* loop counter */
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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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/* But CORR(x, y) is reverse of CORR(y, x) */
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/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
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/* and the destination pointer modifier, inc is set to -1 */
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/* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
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/* But to improve the performance,
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* we include zeroes in the output instead of zero padding either of the the inputs*/
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/* If srcALen > srcBLen,
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* (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
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/* If srcALen < srcBLen,
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* (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
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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 parts 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 part of the
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* algorithm, the multiplications increase by one for every iteration.
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* In the second part of the algorithm, srcBLen number of multiplications are done.
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* In the third part 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 >> 2;
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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 += (q63_t) * px++ * (*py++);
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/* x[1] * y[srcBLen - 3] */
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sum += (q63_t) * px++ * (*py++);
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/* x[2] * y[srcBLen - 2] */
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sum += (q63_t) * px++ * (*py++);
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/* x[3] * y[srcBLen - 1] */
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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-accumulates */
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/* x[0] * y[srcBLen - 1] */
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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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/* 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 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[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 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] 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[0] sample */
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c0 = *(py);
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/* Read x[2] sample */
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x2 = *(px);
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/* Perform the multiply-accumulate */
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/* acc0 += x[0] * y[0] */
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acc0 += ((q63_t) x0 * c0);
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/* acc1 += x[1] * y[0] */
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acc1 += ((q63_t) x1 * c0);
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/* acc2 += x[2] * y[0] */
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acc2 += ((q63_t) x2 * c0);
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/* Read y[1] sample */
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c0 = *(py + 1U);
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/* Read x[3] sample */
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x0 = *(px + 1U);
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/* Perform the multiply-accumulates */
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/* acc0 += x[1] * y[1] */
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acc0 += ((q63_t) x1 * c0);
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/* acc1 += x[2] * y[1] */
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acc1 += ((q63_t) x2 * c0);
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/* acc2 += x[3] * y[1] */
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acc2 += ((q63_t) x0 * c0);
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/* Read y[2] sample */
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c0 = *(py + 2U);
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/* Read x[4] sample */
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x1 = *(px + 2U);
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/* Perform the multiply-accumulates */
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/* acc0 += x[2] * y[2] */
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acc0 += ((q63_t) x2 * c0);
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/* acc1 += x[3] * y[2] */
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acc1 += ((q63_t) x0 * c0);
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/* acc2 += x[4] * y[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[4] 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[4] */
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acc0 += ((q63_t) x0 * c0);
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/* acc1 += x[5] * y[4] */
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acc1 += ((q63_t) x1 * c0);
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/* acc2 += x[6] * y[4] */
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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 result in the accumulator in the destination buffer. */
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*pOut = (q31_t) (acc0 >> 31);
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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 >> 31);
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pOut += inc;
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*pOut = (q31_t) (acc2 >> 31);
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pOut += inc;
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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 = pIn2;
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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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/* Destination pointer is updated according to the address modifier, inc */
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pOut += inc;
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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 = pIn2;
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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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/* Loop over srcBLen */
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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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/* Destination pointer is updated according to the address modifier, inc */
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pOut += inc;
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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 = pIn2;
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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[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
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* sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
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* ....
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* sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1]
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* sum += x[srcALen-1] * y[0]
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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 count variable holds the number of MAC operations performed */
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count = srcBLen - 1U;
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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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py = pIn2;
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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 = count >> 2U;
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/* 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 += x[srcALen - srcBLen + 4] * y[3] */
|
|
sum += (q63_t) * px++ * (*py++);
|
|
/* sum += x[srcALen - srcBLen + 3] * y[2] */
|
|
sum += (q63_t) * px++ * (*py++);
|
|
/* sum += x[srcALen - srcBLen + 2] * y[1] */
|
|
sum += (q63_t) * px++ * (*py++);
|
|
/* sum += x[srcALen - srcBLen + 1] * y[0] */
|
|
sum += (q63_t) * px++ * (*py++);
|
|
|
|
/* Decrement the loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* If the count is not a multiple of 4, compute any remaining MACs here.
|
|
** No loop unrolling is used. */
|
|
k = count % 0x4U;
|
|
|
|
while (k > 0U)
|
|
{
|
|
/* Perform the multiply-accumulates */
|
|
sum += (q63_t) * px++ * (*py++);
|
|
|
|
/* Decrement the loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut = (q31_t) (sum >> 31);
|
|
/* 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 the MAC count */
|
|
count--;
|
|
|
|
/* Decrement the loop counter */
|
|
blockSize3--;
|
|
}
|
|
|
|
#else
|
|
|
|
/* Run the below code for Cortex-M0 */
|
|
|
|
q31_t *pIn1 = pSrcA; /* inputA pointer */
|
|
q31_t *pIn2 = pSrcB + (srcBLen - 1U); /* inputB pointer */
|
|
q63_t sum; /* Accumulators */
|
|
uint32_t i = 0U, j; /* loop counters */
|
|
uint32_t inv = 0U; /* Reverse order flag */
|
|
uint32_t tot = 0U; /* Length */
|
|
|
|
/* 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 */
|
|
/* But CORR(x, y) is reverse of CORR(y, x) */
|
|
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
|
|
/* and a varaible, inv is set to 1 */
|
|
/* If lengths are not equal then zero pad has to be done to make the two
|
|
* inputs of same length. But to improve the performance, we include zeroes
|
|
* in the output instead of zero padding either of the the inputs*/
|
|
/* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the
|
|
* starting of the output buffer */
|
|
/* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the
|
|
* ending of the output buffer */
|
|
/* Once the zero padding is done the remaining of the output is calcualted
|
|
* using correlation but with the shorter signal time shifted. */
|
|
|
|
/* Calculate the length of the remaining sequence */
|
|
tot = ((srcALen + srcBLen) - 2U);
|
|
|
|
if (srcALen > srcBLen)
|
|
{
|
|
/* Calculating the number of zeros to be padded to the output */
|
|
j = srcALen - srcBLen;
|
|
|
|
/* Initialise the pointer after zero padding */
|
|
pDst += j;
|
|
}
|
|
|
|
else if (srcALen < srcBLen)
|
|
{
|
|
/* Initialization to inputB pointer */
|
|
pIn1 = pSrcB;
|
|
|
|
/* Initialization to the end of inputA pointer */
|
|
pIn2 = pSrcA + (srcALen - 1U);
|
|
|
|
/* Initialisation of the pointer after zero padding */
|
|
pDst = pDst + tot;
|
|
|
|
/* Swapping the lengths */
|
|
j = srcALen;
|
|
srcALen = srcBLen;
|
|
srcBLen = j;
|
|
|
|
/* Setting the reverse flag */
|
|
inv = 1;
|
|
|
|
}
|
|
|
|
/* Loop to calculate correlation for output length number of times */
|
|
for (i = 0U; i <= tot; i++)
|
|
{
|
|
/* Initialize sum with zero to carry on MAC operations */
|
|
sum = 0;
|
|
|
|
/* Loop to perform MAC operations according to correlation equation */
|
|
for (j = 0U; j <= i; j++)
|
|
{
|
|
/* Check the array limitations */
|
|
if ((((i - j) < srcBLen) && (j < srcALen)))
|
|
{
|
|
/* z[i] += x[i-j] * y[j] */
|
|
sum += ((q63_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
|
|
}
|
|
}
|
|
/* Store the output in the destination buffer */
|
|
if (inv == 1)
|
|
*pDst-- = (q31_t) (sum >> 31U);
|
|
else
|
|
*pDst++ = (q31_t) (sum >> 31U);
|
|
}
|
|
|
|
#endif /* #if defined (ARM_MATH_DSP) */
|
|
|
|
}
|
|
|
|
/**
|
|
* @} end of Corr group
|
|
*/
|