arm_correlate_f32.c
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CLexer
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r16 | /* ---------------------------------------------------------------------------- | ||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 29. November 2010 | ||||
* $Revision: V1.0.3 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_correlate_f32.c | ||||
* | ||||
* Description: Correlation for floating-point sequences. | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3 | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated | ||||
* | ||||
* Version 0.0.7 2010/06/10 | ||||
* Misra-C changes done | ||||
* | ||||
* -------------------------------------------------------------------------- */ | ||||
#include "arm_math.h" | ||||
/** | ||||
* @ingroup groupFilters | ||||
*/ | ||||
/** | ||||
* @defgroup Corr Correlation | ||||
* | ||||
* Correlation is a mathematical operation that is similar to convolution. | ||||
* As with convolution, correlation uses two signals to produce a third signal. | ||||
* The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution. | ||||
* Correlation is commonly used to measure the similarity between two signals. | ||||
* It has applications in pattern recognition, cryptanalysis, and searching. | ||||
* The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types. | ||||
* Fast versions of the Q15 and Q31 functions are also provided. | ||||
* | ||||
* \par Algorithm | ||||
* Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively. | ||||
* The convolution of the two signals is denoted by | ||||
* <pre> | ||||
* c[n] = a[n] * b[n] | ||||
* </pre> | ||||
* In correlation, one of the signals is flipped in time | ||||
* <pre> | ||||
* c[n] = a[n] * b[-n] | ||||
* </pre> | ||||
* | ||||
* \par | ||||
* and this is mathematically defined as | ||||
* \image html CorrelateEquation.gif | ||||
* \par | ||||
* The <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>. | ||||
* The result <code>c[n]</code> is of length <code>2 * max(srcALen, srcBLen) - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2)</code>. | ||||
* The output result is written to <code>pDst</code> and the calling function must allocate <code>2 * max(srcALen, srcBLen) - 1</code> words for the result. | ||||
* | ||||
* <b>Fixed-Point Behavior</b> | ||||
* \par | ||||
* Correlation requires summing up a large number of intermediate products. | ||||
* As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation. | ||||
* Refer to the function specific documentation below for further details of the particular algorithm used. | ||||
*/ | ||||
/** | ||||
* @addtogroup Corr | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* @brief Correlation of floating-point sequences | ||||
* @param[in] *pSrcA points to the first input sequence. | ||||
* @param[in] srcALen length of the first input sequence. | ||||
* @param[in] *pSrcB points to the second input sequence. | ||||
* @param[in] srcBLen length of the second input sequence. | ||||
* @param[out] *pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1. | ||||
* @return none. | ||||
*/ | ||||
void arm_correlate_f32( | ||||
float32_t * pSrcA, | ||||
uint32_t srcALen, | ||||
float32_t * pSrcB, | ||||
uint32_t srcBLen, | ||||
float32_t * pDst) | ||||
{ | ||||
float32_t *pIn1; /* inputA pointer */ | ||||
float32_t *pIn2; /* inputB pointer */ | ||||
float32_t *pOut = pDst; /* output pointer */ | ||||
float32_t *px; /* Intermediate inputA pointer */ | ||||
float32_t *py; /* Intermediate inputB pointer */ | ||||
float32_t *pSrc1; /* Intermediate pointers */ | ||||
float32_t sum, acc0, acc1, acc2, acc3; /* Accumulators */ | ||||
float32_t x0, x1, x2, x3, c0; /* temporary variables for holding input and coefficient values */ | ||||
uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3; /* loop counters */ | ||||
int32_t inc = 1; /* Destination address modifier */ | ||||
/* 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 the destination pointer modifier, inc is set to -1 */ | ||||
/* If srcALen > srcBLen, zero pad has to be done to srcB 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 */ | ||||
if(srcALen >= srcBLen) | ||||
{ | ||||
/* Initialization of inputA pointer */ | ||||
pIn1 = pSrcA; | ||||
/* Initialization of inputB pointer */ | ||||
pIn2 = pSrcB; | ||||
/* Number of output samples is calculated */ | ||||
outBlockSize = (2u * srcALen) - 1u; | ||||
/* When srcALen > srcBLen, zero padding has to be done to srcB | ||||
* to make their lengths equal. | ||||
* Instead, (outBlockSize - (srcALen + srcBLen - 1)) | ||||
* number of output samples are made zero */ | ||||
j = outBlockSize - (srcALen + (srcBLen - 1u)); | ||||
while(j > 0u) | ||||
{ | ||||
/* Zero is stored in the destination buffer */ | ||||
*pOut++ = 0.0f; | ||||
/* Decrement the loop counter */ | ||||
j--; | ||||
} | ||||
} | ||||
else | ||||
{ | ||||
/* Initialization of inputA pointer */ | ||||
pIn1 = pSrcB; | ||||
/* Initialization of inputB pointer */ | ||||
pIn2 = pSrcA; | ||||
/* srcBLen is always considered as shorter or equal to srcALen */ | ||||
j = srcBLen; | ||||
srcBLen = srcALen; | ||||
srcALen = j; | ||||
/* CORR(x, y) = Reverse order(CORR(y, x)) */ | ||||
/* Hence set the destination pointer to point to the last output sample */ | ||||
pOut = pDst + ((srcALen + srcBLen) - 2u); | ||||
/* Destination address modifier is set to -1 */ | ||||
inc = -1; | ||||
} | ||||
/* The function is internally | ||||
* divided into three parts according to the number of multiplications that has to be | ||||
* taken place between inputA samples and inputB samples. In the first part of the | ||||
* algorithm, the multiplications increase by one for every iteration. | ||||
* In the second part of the algorithm, srcBLen number of multiplications are done. | ||||
* In the third part of the algorithm, the multiplications decrease by one | ||||
* for every iteration.*/ | ||||
/* The algorithm is implemented in three stages. | ||||
* The loop counters of each stage is initiated here. */ | ||||
blockSize1 = srcBLen - 1u; | ||||
blockSize2 = srcALen - (srcBLen - 1u); | ||||
blockSize3 = blockSize1; | ||||
/* -------------------------- | ||||
* Initializations of stage1 | ||||
* -------------------------*/ | ||||
/* sum = x[0] * y[srcBlen - 1] | ||||
* sum = x[0] * y[srcBlen-2] + x[1] * y[srcBlen - 1] | ||||
* .... | ||||
* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1] | ||||
*/ | ||||
/* In this stage the MAC operations are increased by 1 for every iteration. | ||||
The count variable holds the number of MAC operations performed */ | ||||
count = 1u; | ||||
/* Working pointer of inputA */ | ||||
px = pIn1; | ||||
/* Working pointer of inputB */ | ||||
pSrc1 = pIn2 + (srcBLen - 1u); | ||||
py = pSrc1; | ||||
/* ------------------------ | ||||
* Stage1 process | ||||
* ----------------------*/ | ||||
/* The first stage starts here */ | ||||
while(blockSize1 > 0u) | ||||
{ | ||||
/* Accumulator is made zero for every iteration */ | ||||
sum = 0.0f; | ||||
/* 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) | ||||
{ | ||||
/* x[0] * y[srcBLen - 4] */ | ||||
sum += *px++ * *py++; | ||||
/* x[1] * y[srcBLen - 3] */ | ||||
sum += *px++ * *py++; | ||||
/* x[2] * y[srcBLen - 2] */ | ||||
sum += *px++ * *py++; | ||||
/* x[3] * y[srcBLen - 1] */ | ||||
sum += *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-accumulate */ | ||||
/* x[0] * y[srcBLen - 1] */ | ||||
sum += *px++ * *py++; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut = sum; | ||||
/* Destination pointer is updated according to the address modifier, inc */ | ||||
pOut += inc; | ||||
/* Update the inputA and inputB pointers for next MAC calculation */ | ||||
py = pSrc1 - count; | ||||
px = pIn1; | ||||
/* Increment the MAC count */ | ||||
count++; | ||||
/* Decrement the loop counter */ | ||||
blockSize1--; | ||||
} | ||||
/* -------------------------- | ||||
* Initializations of stage2 | ||||
* ------------------------*/ | ||||
/* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1] | ||||
* sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1] | ||||
* .... | ||||
* sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1] | ||||
*/ | ||||
/* Working pointer of inputA */ | ||||
px = pIn1; | ||||
/* Working pointer of inputB */ | ||||
py = pIn2; | ||||
/* count is index by which the pointer pIn1 to be incremented */ | ||||
count = 1u; | ||||
/* ------------------- | ||||
* Stage2 process | ||||
* ------------------*/ | ||||
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed. | ||||
* So, to loop unroll over blockSize2, | ||||
* srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */ | ||||
if(srcBLen >= 4u) | ||||
{ | ||||
/* Loop unroll over blockSize2, by 4 */ | ||||
blkCnt = blockSize2 >> 2u; | ||||
while(blkCnt > 0u) | ||||
{ | ||||
/* Set all accumulators to zero */ | ||||
acc0 = 0.0f; | ||||
acc1 = 0.0f; | ||||
acc2 = 0.0f; | ||||
acc3 = 0.0f; | ||||
/* read x[0], x[1], x[2] samples */ | ||||
x0 = *(px++); | ||||
x1 = *(px++); | ||||
x2 = *(px++); | ||||
/* Apply loop unrolling and compute 4 MACs simultaneously. */ | ||||
k = srcBLen >> 2u; | ||||
/* First part of the processing with loop unrolling. Compute 4 MACs at a time. | ||||
** a second loop below computes MACs for the remaining 1 to 3 samples. */ | ||||
do | ||||
{ | ||||
/* Read y[0] sample */ | ||||
c0 = *(py++); | ||||
/* Read x[3] sample */ | ||||
x3 = *(px++); | ||||
/* Perform the multiply-accumulate */ | ||||
/* acc0 += x[0] * y[0] */ | ||||
acc0 += x0 * c0; | ||||
/* acc1 += x[1] * y[0] */ | ||||
acc1 += x1 * c0; | ||||
/* acc2 += x[2] * y[0] */ | ||||
acc2 += x2 * c0; | ||||
/* acc3 += x[3] * y[0] */ | ||||
acc3 += x3 * c0; | ||||
/* Read y[1] sample */ | ||||
c0 = *(py++); | ||||
/* Read x[4] sample */ | ||||
x0 = *(px++); | ||||
/* Perform the multiply-accumulate */ | ||||
/* acc0 += x[1] * y[1] */ | ||||
acc0 += x1 * c0; | ||||
/* acc1 += x[2] * y[1] */ | ||||
acc1 += x2 * c0; | ||||
/* acc2 += x[3] * y[1] */ | ||||
acc2 += x3 * c0; | ||||
/* acc3 += x[4] * y[1] */ | ||||
acc3 += x0 * c0; | ||||
/* Read y[2] sample */ | ||||
c0 = *(py++); | ||||
/* Read x[5] sample */ | ||||
x1 = *(px++); | ||||
/* Perform the multiply-accumulates */ | ||||
/* acc0 += x[2] * y[2] */ | ||||
acc0 += x2 * c0; | ||||
/* acc1 += x[3] * y[2] */ | ||||
acc1 += x3 * c0; | ||||
/* acc2 += x[4] * y[2] */ | ||||
acc2 += x0 * c0; | ||||
/* acc3 += x[5] * y[2] */ | ||||
acc3 += x1 * c0; | ||||
/* Read y[3] sample */ | ||||
c0 = *(py++); | ||||
/* Read x[6] sample */ | ||||
x2 = *(px++); | ||||
/* Perform the multiply-accumulates */ | ||||
/* acc0 += x[3] * y[3] */ | ||||
acc0 += x3 * c0; | ||||
/* acc1 += x[4] * y[3] */ | ||||
acc1 += x0 * c0; | ||||
/* acc2 += x[5] * y[3] */ | ||||
acc2 += x1 * c0; | ||||
/* acc3 += x[6] * y[3] */ | ||||
acc3 += x2 * c0; | ||||
} while(--k); | ||||
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here. | ||||
** No loop unrolling is used. */ | ||||
k = srcBLen % 0x4u; | ||||
while(k > 0u) | ||||
{ | ||||
/* Read y[4] sample */ | ||||
c0 = *(py++); | ||||
/* Read x[7] sample */ | ||||
x3 = *(px++); | ||||
/* Perform the multiply-accumulates */ | ||||
/* acc0 += x[4] * y[4] */ | ||||
acc0 += x0 * c0; | ||||
/* acc1 += x[5] * y[4] */ | ||||
acc1 += x1 * c0; | ||||
/* acc2 += x[6] * y[4] */ | ||||
acc2 += x2 * c0; | ||||
/* acc3 += x[7] * y[4] */ | ||||
acc3 += x3 * c0; | ||||
/* Reuse the present samples for the next MAC */ | ||||
x0 = x1; | ||||
x1 = x2; | ||||
x2 = x3; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut = acc0; | ||||
/* Destination pointer is updated according to the address modifier, inc */ | ||||
pOut += inc; | ||||
*pOut = acc1; | ||||
pOut += inc; | ||||
*pOut = acc2; | ||||
pOut += inc; | ||||
*pOut = acc3; | ||||
pOut += inc; | ||||
/* Update the inputA and inputB pointers for next MAC calculation */ | ||||
px = pIn1 + (count * 4u); | ||||
py = pIn2; | ||||
/* Increment the pointer pIn1 index, count by 1 */ | ||||
count++; | ||||
/* Decrement the loop counter */ | ||||
blkCnt--; | ||||
} | ||||
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here. | ||||
** No loop unrolling is used. */ | ||||
blkCnt = blockSize2 % 0x4u; | ||||
while(blkCnt > 0u) | ||||
{ | ||||
/* Accumulator is made zero for every iteration */ | ||||
sum = 0.0f; | ||||
/* Apply loop unrolling and compute 4 MACs simultaneously. */ | ||||
k = srcBLen >> 2u; | ||||
/* First part of the processing with loop unrolling. Compute 4 MACs at a time. | ||||
** a second loop below computes MACs for the remaining 1 to 3 samples. */ | ||||
while(k > 0u) | ||||
{ | ||||
/* Perform the multiply-accumulates */ | ||||
sum += *px++ * *py++; | ||||
sum += *px++ * *py++; | ||||
sum += *px++ * *py++; | ||||
sum += *px++ * *py++; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here. | ||||
** No loop unrolling is used. */ | ||||
k = srcBLen % 0x4u; | ||||
while(k > 0u) | ||||
{ | ||||
/* Perform the multiply-accumulate */ | ||||
sum += *px++ * *py++; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut = sum; | ||||
/* Destination pointer is updated according to the address modifier, inc */ | ||||
pOut += inc; | ||||
/* Update the inputA and inputB pointers for next MAC calculation */ | ||||
px = pIn1 + count; | ||||
py = pIn2; | ||||
/* Increment the pointer pIn1 index, count by 1 */ | ||||
count++; | ||||
/* Decrement the loop counter */ | ||||
blkCnt--; | ||||
} | ||||
} | ||||
else | ||||
{ | ||||
/* If the srcBLen is not a multiple of 4, | ||||
* the blockSize2 loop cannot be unrolled by 4 */ | ||||
blkCnt = blockSize2; | ||||
while(blkCnt > 0u) | ||||
{ | ||||
/* Accumulator is made zero for every iteration */ | ||||
sum = 0.0f; | ||||
/* Loop over srcBLen */ | ||||
k = srcBLen; | ||||
while(k > 0u) | ||||
{ | ||||
/* Perform the multiply-accumulate */ | ||||
sum += *px++ * *py++; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut = sum; | ||||
/* Destination pointer is updated according to the address modifier, inc */ | ||||
pOut += inc; | ||||
/* Update the inputA and inputB pointers for next MAC calculation */ | ||||
px = pIn1 + count; | ||||
py = pIn2; | ||||
/* Increment the pointer pIn1 index, count by 1 */ | ||||
count++; | ||||
/* Decrement the 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 = 0.0f; | ||||
/* Apply loop unrolling and compute 4 MACs simultaneously. */ | ||||
k = count >> 2u; | ||||
/* First part of the processing with loop unrolling. Compute 4 MACs at a time. | ||||
** a second loop below computes MACs for the remaining 1 to 3 samples. */ | ||||
while(k > 0u) | ||||
{ | ||||
/* Perform the multiply-accumulates */ | ||||
/* sum += x[srcALen - srcBLen + 4] * y[3] */ | ||||
sum += *px++ * *py++; | ||||
/* sum += x[srcALen - srcBLen + 3] * y[2] */ | ||||
sum += *px++ * *py++; | ||||
/* sum += x[srcALen - srcBLen + 2] * y[1] */ | ||||
sum += *px++ * *py++; | ||||
/* sum += x[srcALen - srcBLen + 1] * y[0] */ | ||||
sum += *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 += *px++ * *py++; | ||||
/* Decrement the loop counter */ | ||||
k--; | ||||
} | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut = sum; | ||||
/* 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--; | ||||
} | ||||
} | ||||
/** | ||||
* @} end of Corr group | ||||
*/ | ||||