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/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_std_q31.c
* Description: Standard deviation of an array of Q31 type.
*
* $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 groupStats
*/
/**
* @addtogroup STD
* @{
*/
/**
* @brief Standard deviation of the elements of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult standard deviation value returned here
* @return none.
* @details
* <b>Scaling and Overflow Behavior:</b>
*
*\par
* The function is implemented using an internal 64-bit accumulator.
* The input is represented in 1.31 format, which is then downshifted by 8 bits
* which yields 1.23, and intermediate multiplication yields a 2.46 format.
* The accumulator maintains full precision of the intermediate multiplication results,
* but provides only a 16 guard bits.
* There is no saturation on intermediate additions.
* If the accumulator overflows it wraps around and distorts the result.
* In order to avoid overflows completely the input signal must be scaled down by
* log2(blockSize)-8 bits, as a total of blockSize additions are performed internally.
* After division, internal variables should be Q18.46
* Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value.
*
*/
void arm_std_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q63_t sum = 0; /* Accumulator */
q63_t meanOfSquares, squareOfMean; /* square of mean and mean of square */
q31_t in; /* input value */
uint32_t blkCnt; /* loop counter */
q63_t sumOfSquares = 0; /* Accumulator */
if (blockSize == 1U)
{
*pResult = 0;
return;
}
#if defined (ARM_MATH_DSP)
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2U;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while (blkCnt > 0U)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++ >> 8U;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8U;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8U;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8U;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4U;
while (blkCnt > 0U)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++ >> 8U;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1U);
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while (blkCnt > 0U)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++ >> 8U;
sumOfSquares += ((q63_t) (in) * (in));
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1U);
#endif /* #if defined (ARM_MATH_DSP) */
/* Compute square of mean */
squareOfMean = sum * sum / (q63_t)(blockSize * (blockSize - 1U));
/* Compute standard deviation and then store the result to the destination */
arm_sqrt_q31((meanOfSquares - squareOfMean) >> 15U, pResult);
}
/**
* @} end of STD group
*/
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