/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 19. March 2015
* $Revision: V.1.4.5
*
* Project: CMSIS DSP Library
* Title: arm_var_q31.c
*
* Description: Variance of an array of Q31 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* - Neither the name of ARM LIMITED nor the names of its contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup variance
* @{
*/
/**
* @brief Variance 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 variance 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_var_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 == 1)
{
*pResult = 0;
return;
}
#ifndef ARM_MATH_CM0_FAMILY
/* 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++ >> 8;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8;
sum += in;
sumOfSquares += ((q63_t) (in) * (in));
in = *pSrc++ >> 8;
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++ >> 8;
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 - 1);
#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++ >> 8;
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 - 1);
#endif /* #ifndef ARM_MATH_CM0_FAMILY */
/* Compute square of mean */
squareOfMean = sum * sum / (q63_t)(blockSize * (blockSize - 1u));
/* Compute standard deviation and then store the result to the destination */
*pResult = (meanOfSquares - squareOfMean) >> 15;
}
/**
* @} end of variance group
*/