/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_mat_mult_fast_q15.c
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* Description: Q15 matrix multiplication (fast variant)
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*
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* $Date: 18. March 2019
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* $Revision: V1.6.0
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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/**
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@ingroup groupMatrix
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*/
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/**
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@addtogroup MatrixMult
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@{
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*/
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/**
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@brief Q15 matrix multiplication (fast variant).
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@param[in] pSrcA points to the first input matrix structure
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@param[in] pSrcB points to the second input matrix structure
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@param[out] pDst points to output matrix structure
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@param[in] pState points to the array for storing intermediate results
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@return execution status
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- \ref ARM_MATH_SUCCESS : Operation successful
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- \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
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@par Scaling and Overflow Behavior
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The difference between the function \ref arm_mat_mult_q15() and this fast variant is that
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the fast variant use a 32-bit rather than a 64-bit accumulator.
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The result of each 1.15 x 1.15 multiplication is truncated to
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2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30
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format. Finally, the accumulator is saturated and converted to a 1.15 result.
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@par
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The fast version has the same overflow behavior as the standard version but provides
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less precision since it discards the low 16 bits of each multiplication result.
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In order to avoid overflows completely the input signals must be scaled down.
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Scale down one of the input matrices by log2(numColsA) bits to avoid overflows,
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as a total of numColsA additions are computed internally for each output element.
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@remark
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Refer to \ref arm_mat_mult_q15() for a slower implementation of this function
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which uses 64-bit accumulation to provide higher precision.
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*/
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arm_status arm_mat_mult_fast_q15(
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const arm_matrix_instance_q15 * pSrcA,
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const arm_matrix_instance_q15 * pSrcB,
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arm_matrix_instance_q15 * pDst,
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q15_t * pState)
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{
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q31_t sum; /* Accumulator */
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q15_t *pSrcBT = pState; /* Input data matrix pointer for transpose */
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q15_t *pInA = pSrcA->pData; /* Input data matrix pointer A of Q15 type */
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q15_t *pInB = pSrcB->pData; /* Input data matrix pointer B of Q15 type */
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q15_t *px; /* Temporary output data matrix pointer */
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uint16_t numRowsA = pSrcA->numRows; /* Number of rows of input matrix A */
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uint16_t numColsB = pSrcB->numCols; /* Number of columns of input matrix B */
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uint16_t numColsA = pSrcA->numCols; /* Number of columns of input matrix A */
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uint16_t numRowsB = pSrcB->numRows; /* Number of rows of input matrix A */
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uint32_t col, i = 0U, row = numRowsB, colCnt; /* Loop counters */
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arm_status status; /* Status of matrix multiplication */
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#if defined (ARM_MATH_DSP)
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q31_t in; /* Temporary variable to hold the input value */
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q31_t inA1, inB1, inA2, inB2;
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q31_t sum2, sum3, sum4;
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q15_t *pInA2, *pInB2, *px2;
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uint32_t j = 0;
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#else
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q15_t in; /* Temporary variable to hold the input value */
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q15_t inA1, inB1, inA2, inB2;
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#endif /* #if defined (ARM_MATH_DSP) */
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#ifdef ARM_MATH_MATRIX_CHECK
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/* Check for matrix mismatch condition */
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if ((pSrcA->numCols != pSrcB->numRows) ||
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(pSrcA->numRows != pDst->numRows) ||
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(pSrcB->numCols != pDst->numCols) )
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{
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/* Set status as ARM_MATH_SIZE_MISMATCH */
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status = ARM_MATH_SIZE_MISMATCH;
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}
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else
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#endif /* #ifdef ARM_MATH_MATRIX_CHECK */
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{
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/* Matrix transpose */
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do
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{
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/* The pointer px is set to starting address of column being processed */
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px = pSrcBT + i;
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/* Apply loop unrolling and exchange columns with row elements */
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col = numColsB >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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while (col > 0U)
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{
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#if defined (ARM_MATH_DSP)
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/* Read two elements from row */
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in = read_q15x2_ia ((q15_t **) &pInB);
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/* Unpack and store one element in destination */
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#ifndef ARM_MATH_BIG_ENDIAN
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*px = (q15_t) in;
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#else
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*px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
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#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
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/* Update pointer px to point to next row of transposed matrix */
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px += numRowsB;
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/* Unpack and store second element in destination */
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#ifndef ARM_MATH_BIG_ENDIAN
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*px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
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#else
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*px = (q15_t) in;
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#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
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/* Update pointer px to point to next row of transposed matrix */
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px += numRowsB;
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in = read_q15x2_ia ((q15_t **) &pInB);
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#ifndef ARM_MATH_BIG_ENDIAN
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*px = (q15_t) in;
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#else
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*px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
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#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
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px += numRowsB;
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#ifndef ARM_MATH_BIG_ENDIAN
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*px = (q15_t) ((in & (q31_t) 0xffff0000) >> 16);
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#else
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*px = (q15_t) in;
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#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
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px += numRowsB;
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#else /* #if defined (ARM_MATH_DSP) */
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/* Read one element from row */
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in = *pInB++;
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/* Store one element in destination */
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*px = in;
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/* Update pointer px to point to next row of transposed matrix */
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px += numRowsB;
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in = *pInB++;
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*px = in;
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px += numRowsB;
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in = *pInB++;
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*px = in;
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px += numRowsB;
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in = *pInB++;
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*px = in;
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px += numRowsB;
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#endif /* #if defined (ARM_MATH_DSP) */
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/* Decrement column loop counter */
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col--;
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}
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/* If the columns of pSrcB 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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col = numColsB % 0x4U;
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while (col > 0U)
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{
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/* Read and store input element in destination */
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*px = *pInB++;
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/* Update pointer px to point to next row of transposed matrix */
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px += numRowsB;
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/* Decrement column loop counter */
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col--;
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}
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i++;
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/* Decrement row loop counter */
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row--;
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} while (row > 0U);
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/* Reset variables for usage in following multiplication process */
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row = numRowsA;
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i = 0U;
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px = pDst->pData;
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#if defined (ARM_MATH_DSP)
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/* Process two rows from matrix A at a time and output two rows at a time */
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row = row >> 1U;
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px2 = px + numColsB;
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#endif
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/* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
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/* row loop */
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while (row > 0U)
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{
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/* For every row wise process, column loop counter is to be initiated */
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col = numColsB;
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/* For every row wise process, pIn2 pointer is set to starting address of transposed pSrcB data */
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pInB = pSrcBT;
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#if defined (ARM_MATH_DSP)
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/* Process two (transposed) columns from matrix B at a time */
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col = col >> 1U;
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j = 0;
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#endif
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/* column loop */
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while (col > 0U)
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{
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/* Set variable sum, that acts as accumulator, to zero */
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sum = 0;
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/* Initiate pointer pInA to point to starting address of column being processed */
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pInA = pSrcA->pData + i;
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#if defined (ARM_MATH_DSP)
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sum2 = 0;
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sum3 = 0;
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sum4 = 0;
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pInB = pSrcBT + j;
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pInA2 = pInA + numColsA;
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pInB2 = pInB + numRowsB;
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/* Read in two elements at once - alows dual MAC instruction */
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colCnt = numColsA >> 1U;
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#else
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colCnt = numColsA >> 2U;
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#endif
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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/* c(m,n) = a(1,1) * b(1,1) + a(1,2) * b(2,1) + .... + a(m,p) * b(p,n) */
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#if defined (ARM_MATH_DSP)
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/* read real and imag values from pSrcA and pSrcB buffer */
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inA1 = read_q15x2_ia ((q15_t **) &pInA);
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inB1 = read_q15x2_ia ((q15_t **) &pInB);
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inA2 = read_q15x2_ia ((q15_t **) &pInA2);
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inB2 = read_q15x2_ia ((q15_t **) &pInB2);
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/* Multiply and Accumlates */
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sum = __SMLAD(inA1, inB1, sum);
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sum2 = __SMLAD(inA1, inB2, sum2);
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sum3 = __SMLAD(inA2, inB1, sum3);
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sum4 = __SMLAD(inA2, inB2, sum4);
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#else
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/* read real and imag values from pSrcA and pSrcB buffer */
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inA1 = *pInA++;
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inB1 = *pInB++;
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/* Multiply and Accumlates */
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sum += inA1 * inB1;
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inA2 = *pInA++;
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inB2 = *pInB++;
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sum += inA2 * inB2;
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inA1 = *pInA++;
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inB1 = *pInB++;
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sum += inA1 * inB1;
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inA2 = *pInA++;
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inB2 = *pInB++;
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sum += inA2 * inB2;
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#endif /* #if defined (ARM_MATH_DSP) */
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/* Decrement loop counter */
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colCnt--;
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}
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/* process odd column samples */
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#if defined (ARM_MATH_DSP)
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if (numColsA & 1U) {
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inA1 = *pInA++;
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inB1 = *pInB++;
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inA2 = *pInA2++;
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inB2 = *pInB2++;
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sum += inA1 * inB1;
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sum2 += inA1 * inB2;
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sum3 += inA2 * inB1;
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sum4 += inA2 * inB2;
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}
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#else
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colCnt = numColsA % 0x4U;
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while (colCnt > 0U)
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{
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/* c(m,n) = a(1,1) * b(1,1) + a(1,2) * b(2,1) + .... + a(m,p) * b(p,n) */
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sum += (q31_t) *pInA++ * *pInB++;
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/* Decrement loop counter */
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colCnt--;
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}
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#endif /* #if defined (ARM_MATH_DSP) */
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/* Saturate and store result in destination buffer */
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*px++ = (q15_t) (sum >> 15);
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#if defined (ARM_MATH_DSP)
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*px++ = (q15_t) (sum2 >> 15);
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*px2++ = (q15_t) (sum3 >> 15);
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*px2++ = (q15_t) (sum4 >> 15);
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j += numRowsB * 2;
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#endif
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/* Decrement column loop counter */
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col--;
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}
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i = i + numColsA;
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#if defined (ARM_MATH_DSP)
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i = i + numColsA;
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px = px2 + (numColsB & 1U);
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px2 = px + numColsB;
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#endif
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/* Decrement row loop counter */
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row--;
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}
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/* Compute any remaining odd row/column below */
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#if defined (ARM_MATH_DSP)
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/* Compute remaining output column */
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if (numColsB & 1U) {
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/* Avoid redundant computation of last element */
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row = numRowsA & (~0x1);
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/* Point to remaining unfilled column in output matrix */
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px = pDst->pData + numColsB-1;
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pInA = pSrcA->pData;
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/* row loop */
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while (row > 0)
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{
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/* point to last column in matrix B */
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pInB = pSrcBT + numRowsB * (numColsB-1);
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/* Set variable sum, that acts as accumulator, to zero */
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sum = 0;
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/* Compute 4 columns at once */
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colCnt = numColsA >> 2U;
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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inA1 = read_q15x2_ia ((q15_t **) &pInA);
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inA2 = read_q15x2_ia ((q15_t **) &pInA);
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inB1 = read_q15x2_ia ((q15_t **) &pInB);
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inB2 = read_q15x2_ia ((q15_t **) &pInB);
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sum = __SMLAD(inA1, inB1, sum);
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sum = __SMLAD(inA2, inB2, sum);
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/* Decrement loop counter */
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colCnt--;
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}
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colCnt = numColsA & 3U;
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while (colCnt > 0U) {
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sum += (q31_t) (*pInA++) * (*pInB++);
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colCnt--;
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}
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/* Store result in destination buffer */
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*px = (q15_t) (sum >> 15);
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px += numColsB;
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/* Decrement row loop counter */
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row--;
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}
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}
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/* Compute remaining output row */
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if (numRowsA & 1U) {
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/* point to last row in output matrix */
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px = pDst->pData + (numColsB) * (numRowsA-1);
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pInB = pSrcBT;
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col = numColsB;
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i = 0U;
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/* col loop */
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while (col > 0)
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{
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/* point to last row in matrix A */
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pInA = pSrcA->pData + (numRowsA-1) * numColsA;
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/* Set variable sum, that acts as accumulator, to zero */
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sum = 0;
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/* Compute 4 columns at once */
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colCnt = numColsA >> 2U;
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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inA1 = read_q15x2_ia ((q15_t **) &pInA);
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inA2 = read_q15x2_ia ((q15_t **) &pInA);
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inB1 = read_q15x2_ia ((q15_t **) &pInB);
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inB2 = read_q15x2_ia ((q15_t **) &pInB);
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sum = __SMLAD(inA1, inB1, sum);
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sum = __SMLAD(inA2, inB2, sum);
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/* Decrement loop counter */
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colCnt--;
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}
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colCnt = numColsA % 4U;
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while (colCnt > 0U) {
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sum += (q31_t) (*pInA++) * (*pInB++);
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colCnt--;
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}
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/* Store result in destination buffer */
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*px++ = (q15_t) (sum >> 15);
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/* Decrement column loop counter */
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col--;
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}
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}
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#endif /* #if defined (ARM_MATH_DSP) */
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/* Set status as ARM_MATH_SUCCESS */
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status = ARM_MATH_SUCCESS;
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}
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/* Return to application */
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return (status);
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}
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/**
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@} end of MatrixMult group
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*/
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