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648 lines
20 KiB
C
648 lines
20 KiB
C
/* ----------------------------------------------------------------------------
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* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
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*
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* $Date: 19. March 2015
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* $Revision: V.1.4.5
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*
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* Project: CMSIS DSP Library
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* Title: arm_conv_f32.c
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*
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* Description: Convolution of floating-point sequences.
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* - Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* - Neither the name of ARM LIMITED nor the names of its contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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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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* @defgroup Conv Convolution
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*
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* Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector.
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* Convolution is similar to correlation and is frequently used in filtering and data analysis.
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* The CMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types.
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* The library also provides fast versions of the Q15 and Q31 functions on Cortex-M4 and Cortex-M3.
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*
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* \par Algorithm
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* Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively.
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* Then the convolution
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*
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* <pre>
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* c[n] = a[n] * b[n]
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* </pre>
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*
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* \par
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* is defined as
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* \image html ConvolutionEquation.gif
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* \par
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* Note that <code>c[n]</code> is of length <code>srcALen + srcBLen - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., srcALen + srcBLen - 2</code>.
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* <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and
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* <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>.
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* The output result is written to <code>pDst</code> and the calling function must allocate <code>srcALen+srcBLen-1</code> words for the result.
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*
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* \par
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* Conceptually, when two signals <code>a[n]</code> and <code>b[n]</code> are convolved,
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* the signal <code>b[n]</code> slides over <code>a[n]</code>.
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* For each offset \c n, the overlapping portions of a[n] and b[n] are multiplied and summed together.
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*
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* \par
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* Note that convolution is a commutative operation:
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*
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* <pre>
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* a[n] * b[n] = b[n] * a[n].
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* </pre>
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*
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* \par
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* This means that switching the A and B arguments to the convolution functions has no effect.
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*
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* <b>Fixed-Point Behavior</b>
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*
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* \par
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* Convolution requires summing up a large number of intermediate products.
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* As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation.
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* Refer to the function specific documentation below for further details of the particular algorithm used.
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*
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*
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* <b>Fast Versions</b>
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*
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* \par
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* Fast versions are supported for Q31 and Q15. Cycles for Fast versions are less compared to Q31 and Q15 of conv and the design requires
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* the input signals should be scaled down to avoid intermediate overflows.
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*
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*
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* <b>Opt Versions</b>
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*
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* \par
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* Opt versions are supported for Q15 and Q7. Design uses internal scratch buffer for getting good optimisation.
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* These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions
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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 floating-point 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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void arm_conv_f32(
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float32_t * pSrcA,
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uint32_t srcALen,
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float32_t * pSrcB,
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uint32_t srcBLen,
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float32_t * pDst)
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{
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#ifndef ARM_MATH_CM0_FAMILY
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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float32_t *pIn1; /* inputA pointer */
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float32_t *pIn2; /* inputB pointer */
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float32_t *pOut = pDst; /* output pointer */
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float32_t *px; /* Intermediate inputA pointer */
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float32_t *py; /* Intermediate inputB pointer */
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float32_t *pSrc1, *pSrc2; /* Intermediate pointers */
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float32_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
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float32_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
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uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3; /* loop counters */
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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 = 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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}
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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 = 0.0f;
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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 += *px++ * *py--;
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/* x[1] * y[srcBLen - 2] */
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sum += *px++ * *py--;
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/* x[2] * y[srcBLen - 3] */
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sum += *px++ * *py--;
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/* x[3] * y[srcBLen - 4] */
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sum += *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 += *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++ = sum;
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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 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 = 0.0f;
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acc1 = 0.0f;
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acc2 = 0.0f;
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acc3 = 0.0f;
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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[srcBLen - 1] 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[srcBLen - 1] */
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acc0 += x0 * c0;
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/* acc1 += x[1] * y[srcBLen - 1] */
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acc1 += x1 * c0;
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/* acc2 += x[2] * y[srcBLen - 1] */
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acc2 += x2 * c0;
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/* acc3 += x[3] * y[srcBLen - 1] */
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acc3 += x3 * c0;
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/* Read y[srcBLen - 2] sample */
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c0 = *(py--);
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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 += x1 * c0;
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/* acc1 += x[2] * y[srcBLen - 2] */
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acc1 += x2 * c0;
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/* acc2 += x[3] * y[srcBLen - 2] */
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acc2 += x3 * c0;
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/* acc3 += x[4] * y[srcBLen - 2] */
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acc3 += x0 * c0;
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/* Read y[srcBLen - 3] sample */
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c0 = *(py--);
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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 += x2 * c0;
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/* acc1 += x[3] * y[srcBLen - 2] */
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acc1 += x3 * c0;
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/* acc2 += x[4] * y[srcBLen - 2] */
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acc2 += x0 * c0;
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/* acc3 += x[5] * y[srcBLen - 2] */
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acc3 += x1 * c0;
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/* Read y[srcBLen - 4] sample */
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c0 = *(py--);
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/* Read x[6] sample */
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x2 = *(px + 3u);
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px += 4u;
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/* Perform the multiply-accumulates */
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/* acc0 += x[3] * y[srcBLen - 4] */
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acc0 += x3 * c0;
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/* acc1 += x[4] * y[srcBLen - 4] */
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acc1 += x0 * c0;
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/* acc2 += x[5] * y[srcBLen - 4] */
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acc2 += x1 * c0;
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/* acc3 += x[6] * y[srcBLen - 4] */
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acc3 += x2 * c0;
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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[srcBLen - 5] 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[srcBLen - 5] */
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acc0 += x0 * c0;
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/* acc1 += x[5] * y[srcBLen - 5] */
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acc1 += x1 * c0;
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/* acc2 += x[6] * y[srcBLen - 5] */
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acc2 += x2 * c0;
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/* acc3 += x[7] * y[srcBLen - 5] */
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acc3 += x3 * 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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x2 = x3;
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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++ = acc0;
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*pOut++ = acc1;
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*pOut++ = acc2;
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*pOut++ = acc3;
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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 = 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 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 = 0.0f;
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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 += *px++ * *py--;
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sum += *px++ * *py--;
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sum += *px++ * *py--;
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sum += *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 += *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++ = sum;
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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 = 0.0f;
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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 */
|
|
sum += *px++ * *py--;
|
|
|
|
/* Decrement the loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut++ = sum;
|
|
|
|
/* Increment the MAC count */
|
|
count++;
|
|
|
|
/* Update the inputA and inputB pointers for next MAC calculation */
|
|
px = pIn1 + count;
|
|
py = pSrc2;
|
|
|
|
/* Decrement the loop counter */
|
|
blkCnt--;
|
|
}
|
|
}
|
|
|
|
|
|
/* --------------------------
|
|
* Initializations of stage3
|
|
* -------------------------*/
|
|
|
|
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
|
|
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
|
|
* ....
|
|
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
|
|
* sum += x[srcALen-1] * y[srcBLen-1]
|
|
*/
|
|
|
|
/* In this stage the MAC operations are decreased by 1 for every iteration.
|
|
The blockSize3 variable holds the number of MAC operations performed */
|
|
|
|
/* Working pointer of inputA */
|
|
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
|
|
px = pSrc1;
|
|
|
|
/* Working pointer of inputB */
|
|
pSrc2 = pIn2 + (srcBLen - 1u);
|
|
py = pSrc2;
|
|
|
|
/* -------------------
|
|
* Stage3 process
|
|
* ------------------*/
|
|
|
|
while(blockSize3 > 0u)
|
|
{
|
|
/* Accumulator is made zero for every iteration */
|
|
sum = 0.0f;
|
|
|
|
/* Apply loop unrolling and compute 4 MACs simultaneously. */
|
|
k = blockSize3 >> 2u;
|
|
|
|
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
|
|
** a second loop below computes MACs for the remaining 1 to 3 samples. */
|
|
while(k > 0u)
|
|
{
|
|
/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
|
|
sum += *px++ * *py--;
|
|
|
|
/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
|
|
sum += *px++ * *py--;
|
|
|
|
/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
|
|
sum += *px++ * *py--;
|
|
|
|
/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
|
|
sum += *px++ * *py--;
|
|
|
|
/* Decrement the loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
|
|
** No loop unrolling is used. */
|
|
k = blockSize3 % 0x4u;
|
|
|
|
while(k > 0u)
|
|
{
|
|
/* Perform the multiply-accumulates */
|
|
/* sum += x[srcALen-1] * y[srcBLen-1] */
|
|
sum += *px++ * *py--;
|
|
|
|
/* Decrement the loop counter */
|
|
k--;
|
|
}
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut++ = sum;
|
|
|
|
/* Update the inputA and inputB pointers for next MAC calculation */
|
|
px = ++pSrc1;
|
|
py = pSrc2;
|
|
|
|
/* Decrement the loop counter */
|
|
blockSize3--;
|
|
}
|
|
|
|
#else
|
|
|
|
/* Run the below code for Cortex-M0 */
|
|
|
|
float32_t *pIn1 = pSrcA; /* inputA pointer */
|
|
float32_t *pIn2 = pSrcB; /* inputB pointer */
|
|
float32_t sum; /* Accumulator */
|
|
uint32_t i, j; /* loop counters */
|
|
|
|
/* Loop to calculate convolution for output length number of times */
|
|
for (i = 0u; i < ((srcALen + srcBLen) - 1u); i++)
|
|
{
|
|
/* Initialize sum with zero to carry out MAC operations */
|
|
sum = 0.0f;
|
|
|
|
/* Loop to perform MAC operations according to convolution 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 += pIn1[j] * pIn2[i - j];
|
|
}
|
|
}
|
|
/* Store the output in the destination buffer */
|
|
pDst[i] = sum;
|
|
}
|
|
|
|
#endif /* #ifndef ARM_MATH_CM0_FAMILY */
|
|
|
|
}
|
|
|
|
/**
|
|
* @} end of Conv group
|
|
*/
|