| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_correlate_fast_q31.c |
| * Description: Fast Q31 Correlation |
| * |
| * $Date: 18. March 2019 |
| * $Revision: V1.6.0 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2019 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 |
| */ |
| |
| /** |
| @addtogroup Corr |
| @{ |
| */ |
| |
| /** |
| @brief Correlation of Q31 sequences (fast version). |
| @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 |
| |
| @par Scaling and Overflow Behavior |
| This function is optimized for speed at the expense of fixed-point precision and overflow protection. |
| The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format. |
| These intermediate results are accumulated in a 32-bit register in 2.30 format. |
| Finally, the accumulator is saturated and converted to a 1.31 result. |
| @par |
| The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result. |
| In order to avoid overflows completely the input signals must be scaled down. |
| The input signals should be scaled down to avoid intermediate overflows. |
| Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a |
| maximum of min(srcALen, srcBLen) number of additions is carried internally. |
| |
| @remark |
| Refer to \ref arm_correlate_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision. |
| */ |
| |
| void arm_correlate_fast_q31( |
| const q31_t * pSrcA, |
| uint32_t srcALen, |
| const q31_t * pSrcB, |
| uint32_t srcBLen, |
| q31_t * pDst) |
| { |
| const q31_t *pIn1; /* InputA pointer */ |
| const q31_t *pIn2; /* InputB pointer */ |
| q31_t *pOut = pDst; /* Output pointer */ |
| const q31_t *px; /* Intermediate inputA pointer */ |
| const q31_t *py; /* Intermediate inputB pointer */ |
| const q31_t *pSrc1; /* Intermediate pointers */ |
| q31_t sum, acc0, acc1, acc2, acc3; /* Accumulators */ |
| q31_t x0, x1, x2, x3, c0; /* Temporary variables for holding input and coefficient values */ |
| uint32_t blockSize1, blockSize2, blockSize3; /* Loop counters */ |
| uint32_t j, k, count, blkCnt; /* Loop counters */ |
| uint32_t outBlockSize; |
| 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 */ |
| 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 is 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; |
| |
| } |
| 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 stages according to the number of multiplications that has to be |
| * taken place between inputA samples and inputB samples. In the first stage of the |
| * algorithm, the multiplications increase by one for every iteration. |
| * In the second stage of the algorithm, srcBLen number of multiplications are done. |
| * In the third stage 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; |
| |
| /* 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 = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* x[1] * y[srcBLen - 3] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* x[2] * y[srcBLen - 2] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* x[3] * y[srcBLen - 1] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* If the count is not a multiple of 4, compute any remaining MACs here. |
| ** No loop unrolling is used. */ |
| k = count % 0x4U; |
| |
| while (k > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| /* x[0] * y[srcBLen - 1] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut = sum << 1; |
| /* Destination pointer is updated according to the address modifier, inc */ |
| pOut += inc; |
| |
| /* Update the inputA and inputB pointers for next MAC calculation */ |
| py = pSrc1 - count; |
| px = pIn1; |
| |
| /* Increment MAC count */ |
| count++; |
| |
| /* Decrement 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 */ |
| if (srcBLen >= 4U) |
| { |
| /* Loop unroll over blockSize2, by 4 */ |
| blkCnt = blockSize2 >> 2U; |
| |
| while (blkCnt > 0U) |
| { |
| /* Set all accumulators to zero */ |
| acc0 = 0; |
| acc1 = 0; |
| acc2 = 0; |
| acc3 = 0; |
| |
| /* 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 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32); |
| /* acc1 += x[1] * y[0] */ |
| acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32); |
| /* acc2 += x[2] * y[0] */ |
| acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32); |
| /* acc3 += x[3] * y[0] */ |
| acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32); |
| |
| |
| /* Read y[1] sample */ |
| c0 = *py++; |
| /* Read x[4] sample */ |
| x0 = *px++; |
| |
| /* Perform the multiply-accumulate */ |
| /* acc0 += x[1] * y[1] */ |
| acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32); |
| /* acc1 += x[2] * y[1] */ |
| acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32); |
| /* acc2 += x[3] * y[1] */ |
| acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32); |
| /* acc3 += x[4] * y[1] */ |
| acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32); |
| |
| |
| /* Read y[2] sample */ |
| c0 = *py++; |
| /* Read x[5] sample */ |
| x1 = *px++; |
| |
| /* Perform the multiply-accumulates */ |
| /* acc0 += x[2] * y[2] */ |
| acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32); |
| /* acc1 += x[3] * y[2] */ |
| acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32); |
| /* acc2 += x[4] * y[2] */ |
| acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32); |
| /* acc3 += x[5] * y[2] */ |
| acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32); |
| |
| |
| /* Read y[3] sample */ |
| c0 = *py++; |
| /* Read x[6] sample */ |
| x2 = *px++; |
| |
| /* Perform the multiply-accumulates */ |
| /* acc0 += x[3] * y[3] */ |
| acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32); |
| /* acc1 += x[4] * y[3] */ |
| acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32); |
| /* acc2 += x[5] * y[3] */ |
| acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32); |
| /* acc3 += x[6] * y[3] */ |
| acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32); |
| |
| |
| } 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 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32); |
| /* acc1 += x[5] * y[4] */ |
| acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32); |
| /* acc2 += x[6] * y[4] */ |
| acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32); |
| /* acc3 += x[7] * y[4] */ |
| acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32); |
| |
| /* Reuse the present samples for the next MAC */ |
| x0 = x1; |
| x1 = x2; |
| x2 = x3; |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut = (q31_t) (acc0 << 1); |
| /* Destination pointer is updated according to the address modifier, inc */ |
| pOut += inc; |
| |
| *pOut = (q31_t) (acc1 << 1); |
| pOut += inc; |
| |
| *pOut = (q31_t) (acc2 << 1); |
| pOut += inc; |
| |
| *pOut = (q31_t) (acc3 << 1); |
| 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 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; |
| |
| /* 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 = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement 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 = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut = sum << 1; |
| /* Destination pointer is updated according to the address modifier, inc */ |
| pOut += inc; |
| |
| /* Increment MAC count */ |
| count++; |
| |
| /* Update the inputA and inputB pointers for next MAC calculation */ |
| px = pIn1 + count; |
| py = pIn2; |
| |
| /* Decrement loop counter */ |
| blkCnt--; |
| } |
| } |
| 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; |
| |
| /* srcBLen number of MACS should be performed */ |
| k = srcBLen; |
| |
| while (k > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut = sum << 1; |
| /* Destination pointer is updated according to the address modifier, inc */ |
| pOut += inc; |
| |
| /* Increment MAC count */ |
| count++; |
| |
| /* Update the inputA and inputB pointers for next MAC calculation */ |
| px = pIn1 + count; |
| py = pIn2; |
| |
| /* Decrement loop counter */ |
| blkCnt--; |
| } |
| } |
| |
| |
| /* -------------------------- |
| * Initializations of stage3 |
| * -------------------------*/ |
| |
| /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1] |
| * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1] |
| * .... |
| * sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1] |
| * sum += x[srcALen-1] * y[0] |
| */ |
| |
| /* In this stage the MAC operations are decreased by 1 for every iteration. |
| The count variable holds the number of MAC operations performed */ |
| count = srcBLen - 1U; |
| |
| /* Working pointer of inputA */ |
| pSrc1 = ((pIn1 + srcALen) - srcBLen) + 1U; |
| px = pSrc1; |
| |
| /* Working pointer of inputB */ |
| py = pIn2; |
| |
| /* ------------------- |
| * Stage3 process |
| * ------------------*/ |
| |
| while (blockSize3 > 0U) |
| { |
| /* Accumulator is made zero for every iteration */ |
| sum = 0; |
| |
| /* Apply loop unrolling and compute 4 MACs simultaneously. */ |
| k = count >> 2U; |
| |
| /* First part of the processing with loop unrolling. Compute 4 MACs at a time. |
| ** a second loop below computes MACs for the remaining 1 to 3 samples. */ |
| while (k > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| /* sum += x[srcALen - srcBLen + 4] * y[3] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* sum += x[srcALen - srcBLen + 3] * y[2] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* sum += x[srcALen - srcBLen + 2] * y[1] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* sum += x[srcALen - srcBLen + 1] * y[0] */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* If the count is not a multiple of 4, compute any remaining MACs here. |
| ** No loop unrolling is used. */ |
| k = count % 0x4U; |
| |
| while (k > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| sum = (q31_t) ((((q63_t) sum << 32) + |
| ((q63_t) *px++ * (*py++))) >> 32); |
| |
| /* Decrement loop counter */ |
| k--; |
| } |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut = sum << 1; |
| /* Destination pointer is updated according to the address modifier, inc */ |
| pOut += inc; |
| |
| /* Update the inputA and inputB pointers for next MAC calculation */ |
| px = ++pSrc1; |
| py = pIn2; |
| |
| /* Decrement MAC count */ |
| count--; |
| |
| /* Decrement loop counter */ |
| blockSize3--; |
| } |
| |
| } |
| |
| /** |
| @} end of Corr group |
| */ |
