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-/* ----------------------------------------------------------------------
- * Project: CMSIS DSP Library
- * Title: arm_correlate_f32.c
- * Description: Correlation of floating-point sequences
- *
- * $Date: 27. January 2017
- * $Revision: V.1.5.1
- *
- * Target Processor: Cortex-M cores
- * -------------------------------------------------------------------- */
-/*
- * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
- *
- * SPDX-License-Identifier: Apache-2.0
- *
- * Licensed under the Apache License, Version 2.0 (the License); you may
- * not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an AS IS BASIS, WITHOUT
- * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-#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>Note</b>
- * \par
- * The <code>pDst</code> should be initialized to all zeros before being used.
- *
- * <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.
- *
- *
- * <b>Fast Versions</b>
- *
- * \par
- * Fast versions are supported for Q31 and Q15. Cycles for Fast versions are less compared to Q31 and Q15 of correlate and the design requires
- * the input signals should be scaled down to avoid intermediate overflows.
- *
- *
- * <b>Opt Versions</b>
- *
- * \par
- * Opt versions are supported for Q15 and Q7. Design uses internal scratch buffer for getting good optimisation.
- * These versions are optimised in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions of correlate
- */
-
-/**
- * @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)
-{
-
-
-#if defined (ARM_MATH_DSP)
-
- /* Run the below code for Cortex-M4 and Cortex-M3 */
-
- 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 assume 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));
-
- /* Updating the pointer position to non zero value */
- pOut += j;
-
- //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 = 0U;
-
- /* -------------------
- * 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;
-
- /* Increment the pointer pIn1 index, count by 4 */
- count += 4U;
-
- /* Update the inputA and inputB pointers for next MAC calculation */
- px = pIn1 + count;
- py = pIn2;
-
- /* 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;
-
- /* Increment the pointer pIn1 index, count by 1 */
- count++;
-
- /* Update the inputA and inputB pointers for next MAC calculation */
- px = pIn1 + count;
- py = pIn2;
-
- /* 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;
-
- /* Increment the pointer pIn1 index, count by 1 */
- count++;
-
- /* Update the inputA and inputB pointers for next MAC calculation */
- px = pIn1 + count;
- py = pIn2;
-
- /* 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--;
- }
-
-#else
-
- /* Run the below code for Cortex-M0 */
-
- float32_t *pIn1 = pSrcA; /* inputA pointer */
- float32_t *pIn2 = pSrcB + (srcBLen - 1U); /* inputB pointer */
- float32_t sum; /* Accumulator */
- 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 assume 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 convolution 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 convolution for output length number of times */
- for (i = 0U; i <= tot; i++)
- {
- /* Initialize sum with zero to carry on 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[-((int32_t) i - j)];
- }
- }
- /* Store the output in the destination buffer */
- if (inv == 1)
- *pDst-- = sum;
- else
- *pDst++ = sum;
- }
-
-#endif /* #if defined (ARM_MATH_DSP) */
-
-}
-
-/**
- * @} end of Corr group
- */