148 lines
4.8 KiB
C
148 lines
4.8 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_var_q31.c
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* Description: Variance of an array of Q31 type
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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 groupStats
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*/
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/**
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@addtogroup variance
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@{
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*/
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/**
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@brief Variance of the elements of a Q31 vector.
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@param[in] pSrc points to the input vector
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@param[in] blockSize number of samples in input vector
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@param[out] pResult variance value returned here
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@return none
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@par Scaling and Overflow Behavior
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The function is implemented using an internal 64-bit accumulator.
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The input is represented in 1.31 format, which is then downshifted by 8 bits
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which yields 1.23, and intermediate multiplication yields a 2.46 format.
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The accumulator maintains full precision of the intermediate multiplication results,
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but provides only a 16 guard bits.
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There is no saturation on intermediate additions.
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If the accumulator overflows it wraps around and distorts the result.
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In order to avoid overflows completely the input signal must be scaled down by
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log2(blockSize)-8 bits, as a total of blockSize additions are performed internally.
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After division, internal variables should be Q18.46
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Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value.
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*/
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void arm_var_q31(
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const q31_t * pSrc,
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uint32_t blockSize,
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q31_t * pResult)
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{
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uint32_t blkCnt; /* Loop counter */
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q63_t sum = 0; /* Temporary result storage */
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q63_t meanOfSquares, squareOfMean; /* Square of mean and mean of square */
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q63_t sumOfSquares = 0; /* Sum of squares */
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q31_t in; /* Temporary variable to store input value */
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if (blockSize <= 1U)
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{
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*pResult = 0;
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return;
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}
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#if defined (ARM_MATH_LOOPUNROLL)
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/* Loop unrolling: Compute 4 outputs at a time */
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blkCnt = blockSize >> 2U;
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while (blkCnt > 0U)
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{
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/* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */
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/* C = A[0] + A[1] + ... + A[blockSize-1] */
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in = *pSrc++ >> 8U;
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/* Compute sum of squares and store result in a temporary variable, sumOfSquares. */
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sumOfSquares += ((q63_t) (in) * (in));
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/* Compute sum and store result in a temporary variable, sum. */
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sum += in;
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in = *pSrc++ >> 8U;
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sumOfSquares += ((q63_t) (in) * (in));
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sum += in;
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in = *pSrc++ >> 8U;
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sumOfSquares += ((q63_t) (in) * (in));
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sum += in;
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in = *pSrc++ >> 8U;
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sumOfSquares += ((q63_t) (in) * (in));
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sum += in;
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/* Decrement loop counter */
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blkCnt--;
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}
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/* Loop unrolling: Compute remaining outputs */
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blkCnt = blockSize % 0x4U;
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#else
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/* Initialize blkCnt with number of samples */
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blkCnt = blockSize;
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#endif /* #if defined (ARM_MATH_LOOPUNROLL) */
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while (blkCnt > 0U)
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{
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/* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */
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/* C = A[0] + A[1] + ... + A[blockSize-1] */
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in = *pSrc++ >> 8U;
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/* Compute sum of squares and store result in a temporary variable, sumOfSquares. */
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sumOfSquares += ((q63_t) (in) * (in));
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/* Compute sum and store result in a temporary variable, sum. */
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sum += in;
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/* Decrement loop counter */
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blkCnt--;
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}
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/* Compute Mean of squares and store result in a temporary variable, meanOfSquares. */
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meanOfSquares = (sumOfSquares / (q63_t)(blockSize - 1U));
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/* Compute square of mean */
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squareOfMean = ( sum * sum / (q63_t)(blockSize * (blockSize - 1U)));
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/* Compute variance and store result in destination */
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*pResult = (meanOfSquares - squareOfMean) >> 15U;
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}
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/**
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@} end of variance group
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*/
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