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 /* ---------------------------------------------------------------------- * Project: CMSIS DSP Library * Title: arm_conv_f32.c * Description: Convolution of floating-point sequences * * \$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 */ /** @defgroup Conv Convolution Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector. Convolution is similar to correlation and is frequently used in filtering and data analysis. The CMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types. The library also provides fast versions of the Q15 and Q31 functions. @par Algorithm Let a[n] and b[n] be sequences of length srcALen and srcBLen samples respectively. Then the convolution
c[n] = a[n] * b[n]
@par is defined as \image html ConvolutionEquation.gif @par Note that c[n] is of length srcALen + srcBLen - 1 and is defined over the interval n=0, 1, 2, ..., srcALen + srcBLen - 2. pSrcA points to the first input vector of length srcALen and pSrcB points to the second input vector of length srcBLen. The output result is written to pDst and the calling function must allocate srcALen+srcBLen-1 words for the result. @par Conceptually, when two signals a[n] and b[n] are convolved, the signal b[n] slides over a[n]. For each offset \c n, the overlapping portions of a[n] and b[n] are multiplied and summed together. @par Note that convolution is a commutative operation:
a[n] * b[n] = b[n] * a[n].
@par This means that switching the A and B arguments to the convolution functions has no effect. @par Fixed-Point Behavior Convolution 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. @par Fast Versions 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 the input signals should be scaled down to avoid intermediate overflows. @par Opt Versions 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 */ /** @addtogroup Conv @{ */ /** @brief Convolution 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 srcALen+srcBLen-1. @return none */ void arm_conv_f32( const float32_t * pSrcA, uint32_t srcALen, const float32_t * pSrcB, uint32_t srcBLen, float32_t * pDst) { #if (1) //#if !defined(ARM_MATH_CM0_FAMILY) const float32_t *pIn1; /* InputA pointer */ const float32_t *pIn2; /* InputB pointer */ float32_t *pOut = pDst; /* Output pointer */ const float32_t *px; /* Intermediate inputA pointer */ const float32_t *py; /* Intermediate inputB pointer */ const float32_t *pSrc1, *pSrc2; /* Intermediate pointers */ float32_t sum; /* Accumulators */ uint32_t blockSize1, blockSize2, blockSize3; /* Loop counters */ uint32_t j, k, count, blkCnt; /* Loop counters */ #if defined (ARM_MATH_LOOPUNROLL) || defined(ARM_MATH_NEON) float32_t acc0, acc1, acc2, acc3; /* Accumulators */ float32_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */ #endif /* 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; } 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; } /* conv(x,y) at n = x[n] * y + x[n-1] * y + x[n-2] * y + ...+ x[n-N+1] * y[N -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 * y * sum = x * y + x * y * .... * sum = x * y[srcBlen - 1] + x * y[srcBlen - 2] +...+ x[srcBLen - 1] * y */ /* 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 */ py = pIn2; /* ------------------------ * Stage1 process * ----------------------*/ #if defined(ARM_MATH_NEON) float32x4_t vec1; float32x4_t vec2; float32x4_t res = vdupq_n_f32(0) ; float32x2_t accum = vdup_n_f32(0); #endif /* #if defined(ARM_MATH_NEON) */ /* The first stage starts here */ while (blockSize1 > 0U) { /* Accumulator is made zero for every iteration */ sum = 0.0f; #if defined (ARM_MATH_LOOPUNROLL) || defined(ARM_MATH_NEON) /* Loop unrolling: Compute 4 outputs at a time */ k = count >> 2U; #if defined(ARM_MATH_NEON) res = vdupq_n_f32(0) ; accum = vdup_n_f32(0); /* Compute 4 MACs simultaneously. */ k = count >> 2U; /* First part of the processing. Compute 4 MACs at a time. ** a second loop below computes MACs for the remaining 1 to 3 samples. */ while (k > 0U) { vec1 = vld1q_f32(px); vec2 = vld1q_f32(py-3); vec2 = vrev64q_f32(vec2); vec2 = vcombine_f32(vget_high_f32(vec2), vget_low_f32(vec2)); res = vmlaq_f32(res,vec1, vec2); /* Increment pointers */ px += 4; py -= 4; /* Decrement the loop counter */ k--; } accum = vpadd_f32(vget_low_f32(res), vget_high_f32(res)); sum += accum + accum; /* If the count is not a multiple of 4, compute any remaining MACs here. ** No loop unrolling is used. */ k = count & 3; #else while (k > 0U) { /* x * y[srcBLen - 1] */ sum += *px++ * *py--; /* x * y[srcBLen - 2] */ sum += *px++ * *py--; /* x * y[srcBLen - 3] */ sum += *px++ * *py--; /* x * y[srcBLen - 4] */ sum += *px++ * *py--; /* Decrement loop counter */ k--; } /* Loop unrolling: Compute remaining outputs */ k = count % 0x4U; #endif /* #if defined(ARM_MATH_NEON) */ #else /* Initialize k with number of samples */ k = count; #endif /* #if defined (ARM_MATH_LOOPUNROLL) || defined(ARM_MATH_NEON) */ while (k > 0U) { /* Perform the multiply-accumulate */ sum += *px++ * *py--; /* Decrement 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 */ py = pIn2 + count; px = pIn1; /* Increment MAC count */ count++; /* Decrement loop counter */ blockSize1--; } /* -------------------------- * Initializations of stage2 * ------------------------*/ /* sum = x * y[srcBLen-1] + x * y[srcBLen-2] +...+ x[srcBLen-1] * y * sum = x * y[srcBLen-1] + x * y[srcBLen-2] +...+ x[srcBLen] * y * .... * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y */ /* Working pointer of inputA */ px = pIn1; /* Working pointer of inputB */ pSrc2 = pIn2 + (srcBLen - 1U); py = pSrc2; /* 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) { #if defined(ARM_MATH_NEON) float32x4_t c; float32x4_t x1v; float32x4_t x2v; uint32x4_t x1v_u; uint32x4_t x2v_u; uint32x4_t x_u; float32x4_t x; float32x4_t res = vdupq_n_f32(0) ; #endif /* #if defined(ARM_MATH_NEON) */ #if defined (ARM_MATH_LOOPUNROLL) || defined(ARM_MATH_NEON) /* Loop unrolling: Compute 4 outputs at a time */ blkCnt = blockSize2 >> 2U; while (blkCnt > 0U) { /* Set all accumulators to zero */ acc0 = 0.0f; acc1 = 0.0f; acc2 = 0.0f; acc3 = 0.0f; /* Apply loop unrolling and compute 4 MACs simultaneously. */ k = srcBLen >> 2U; #if defined(ARM_MATH_NEON) res = vdupq_n_f32(0) ; x1v = vld1q_f32(px); x2v = vld1q_f32(px+4); do { c = vld1q_f32(py-3); px += 4; x = x1v; res = vmlaq_n_f32(res,x,c); x = vextq_f32(x1v,x2v,1); res = vmlaq_n_f32(res,x,c); x = vextq_f32(x1v,x2v,2); res = vmlaq_n_f32(res,x,c); x = vextq_f32(x1v,x2v,3); res = vmlaq_n_f32(res,x,c); py -= 4; x1v = x2v ; x2v = vld1q_f32(px+4); } while (--k); /* If the srcBLen is not a multiple of 4, compute any remaining MACs here. ** No loop unrolling is used. */ k = srcBLen & 0x3; x1v = vld1q_f32(px); px += 4; while (k > 0U) { /* Read y[srcBLen - 5] sample */ c0 = *(py--); res = vmlaq_n_f32(res,x1v,c0); /* Reuse the present samples for the next MAC */ x1v = x1v; x1v = x1v; x1v = x1v; x1v = *(px++); /* Decrement the loop counter */ k--; } acc0 = res; acc1 = res; acc2 = res; acc3 = res; #else /* read x, x, x samples */ x0 = *px++; x1 = *px++; x2 = *px++; /* 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[srcBLen - 1] sample */ c0 = *py--; /* Read x sample */ x3 = *(px); /* Perform the multiply-accumulate */ /* acc0 += x * y[srcBLen - 1] */ acc0 += x0 * c0; /* acc1 += x * y[srcBLen - 1] */ acc1 += x1 * c0; /* acc2 += x * y[srcBLen - 1] */ acc2 += x2 * c0; /* acc3 += x * y[srcBLen - 1] */ acc3 += x3 * c0; /* Read y[srcBLen - 2] sample */ c0 = *py--; /* Read x sample */ x0 = *(px + 1U); /* Perform the multiply-accumulate */ /* acc0 += x * y[srcBLen - 2] */ acc0 += x1 * c0; /* acc1 += x * y[srcBLen - 2] */ acc1 += x2 * c0; /* acc2 += x * y[srcBLen - 2] */ acc2 += x3 * c0; /* acc3 += x * y[srcBLen - 2] */ acc3 += x0 * c0; /* Read y[srcBLen - 3] sample */ c0 = *py--; /* Read x sample */ x1 = *(px + 2U); /* Perform the multiply-accumulate */ /* acc0 += x * y[srcBLen - 3] */ acc0 += x2 * c0; /* acc1 += x * y[srcBLen - 2] */ acc1 += x3 * c0; /* acc2 += x * y[srcBLen - 2] */ acc2 += x0 * c0; /* acc3 += x * y[srcBLen - 2] */ acc3 += x1 * c0; /* Read y[srcBLen - 4] sample */ c0 = *py--; /* Read x sample */ x2 = *(px + 3U); px += 4U; /* Perform the multiply-accumulate */ /* acc0 += x * y[srcBLen - 4] */ acc0 += x3 * c0; /* acc1 += x * y[srcBLen - 4] */ acc1 += x0 * c0; /* acc2 += x * y[srcBLen - 4] */ acc2 += x1 * c0; /* acc3 += x * y[srcBLen - 4] */ 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[srcBLen - 5] sample */ c0 = *py--; /* Read x sample */ x3 = *px++; /* Perform the multiply-accumulate */ /* acc0 += x * y[srcBLen - 5] */ acc0 += x0 * c0; /* acc1 += x * y[srcBLen - 5] */ acc1 += x1 * c0; /* acc2 += x * y[srcBLen - 5] */ acc2 += x2 * c0; /* acc3 += x * y[srcBLen - 5] */ acc3 += x3 * c0; /* Reuse the present samples for the next MAC */ x0 = x1; x1 = x2; x2 = x3; /* Decrement the loop counter */ k--; } #endif /* #if defined(ARM_MATH_NEON) */ /* Store the result in the accumulator in the destination buffer. */ *pOut++ = acc0; *pOut++ = acc1; *pOut++ = acc2; *pOut++ = acc3; /* Increment the pointer pIn1 index, count by 4 */ count += 4U; /* Update the inputA and inputB pointers for next MAC calculation */ px = pIn1 + count; py = pSrc2; /* 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; #else /* Initialize blkCnt with number of samples */ blkCnt = blockSize2; #endif /* #if defined (ARM_MATH_LOOPUNROLL) || defined (ARM_MATH_NEON)*/ while (blkCnt > 0U) { /* Accumulator is made zero for every iteration */ sum = 0.0f; #if defined(ARM_MATH_NEON) || defined (ARM_MATH_LOOPUNROLL) /* Loop unrolling: Compute 4 outputs at a time */ k = srcBLen >> 2U; #if defined (ARM_MATH_NEON) float32x4_t res = vdupq_n_f32(0) ; float32x4_t x = vdupq_n_f32(0) ; float32x4_t y = vdupq_n_f32(0) ; float32x2_t accum = vdup_n_f32(0) ; /* First part of the processing. Compute 4 MACs at a time. ** a second loop below computes MACs for the remaining 1 to 3 samples. */ while (k > 0U) { x = vld1q_f32(px); y = vld1q_f32(py-3); y = vrev64q_f32(y); y = vcombine_f32(vget_high_f32(y), vget_low_f32(y)); res = vmlaq_f32(res,x,y); px += 4 ; py -= 4 ; /* Decrement the loop counter */ k--; } accum = vpadd_f32(vget_low_f32(res), vget_high_f32(res)); sum += accum + accum; /* If the srcBLen is not a multiple of 4, compute any remaining MACs here. ** No loop unrolling is used. */ k = srcBLen & 0x3U; #else while (k > 0U) { /* Perform the multiply-accumulate */ sum += *px++ * *py--; sum += *px++ * *py--; sum += *px++ * *py--; sum += *px++ * *py--; /* Decrement loop counter */ k--; } /* Loop unrolling: Compute remaining outputs */ k = srcBLen % 0x4U; #endif /* if defined (ARM_MATH_NEON) */ #else /* Initialize blkCnt with number of samples */ k = srcBLen; #endif /* #if defined(ARM_MATH_NEON) || defined (ARM_MATH_LOOPUNROLL) */ 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; /* 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--; } } 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; /* srcBLen number of MACS should be performed */ 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; /* 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 * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y * .... * 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; #if defined (ARM_MATH_LOOPUNROLL) || defined(ARM_MATH_NEON) /* Loop unrolling: Compute 4 outputs at a time */ k = blockSize3 >> 2U; #if defined(ARM_MATH_NEON) float32x4_t res = vdupq_n_f32(0) ; float32x4_t x = vdupq_n_f32(0) ; float32x4_t y = vdupq_n_f32(0) ; float32x2_t accum = vdup_n_f32(0) ; while (k > 0U) { x = vld1q_f32(px); y = vld1q_f32(py-3); y = vrev64q_f32(y); y = vcombine_f32(vget_high_f32(y), vget_low_f32(y)); res = vmlaq_f32(res,x,y); px += 4 ; py -= 4 ; /* Decrement the loop counter */ k--; } accum = vpadd_f32(vget_low_f32(res), vget_high_f32(res)); sum += accum + accum; #else while (k > 0U) { /* Perform the multiply-accumulate */ /* 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 loop counter */ k--; } #endif /* #if defined (ARM_MATH_NEON) */ /* Loop unrolling: Compute remaining outputs */ k = blockSize3 % 0x4U; #else /* Initialize blkCnt with number of samples */ k = blockSize3; #endif /* #if defined (ARM_MATH_NEON) || defined (ARM_MATH_LOOPUNROLL)*/ while (k > 0U) { /* Perform the multiply-accumulate */ /* sum += x[srcALen-1] * y[srcBLen-1] */ sum += *px++ * *py--; /* Decrement 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 /* alternate version for CM0_FAMILY */ const float32_t *pIn1 = pSrcA; /* InputA pointer */ const 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 /* #if !defined(ARM_MATH_CM0_FAMILY) */ } /** @} end of Conv group */