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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
*
* $Date: 17. January 2013
* $Revision: V1.4.1
*
* 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
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* 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, and intermediate multiplication
* yields a 2.62 format.
* The accumulator maintains full precision of the intermediate multiplication results,
* but provides only a single guard bit.
* 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) bits, as a total of blockSize additions are performed internally.
* Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.
*
*/
void arm_var_q31(
q31_t * pSrc,
uint32_t blockSize,
q63_t * pResult)
{
q63_t sum = 0, sumSquare = 0; /* Accumulator */
q31_t meanOfSquares, squareOfMean; /* square of mean and mean of square */
q31_t mean; /* mean */
q31_t in; /* input value */
q31_t t; /* Temporary variable */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0_FAMILY
/* Run the below code for Cortex-M4 and Cortex-M3 */
q63_t sumSquare1 = 0; /* Accumulator */
q31_t in1, in2, in3, in4; /* Temporary input variables */
/*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. */
/* read input samples from source buffer */
in1 = pSrc[0];
in2 = pSrc[1];
/* calculate sum of inputs */
sum += in1;
/* calculate sum of squares */
sumSquare += ((q63_t) (in1) * (in1));
in3 = pSrc[2];
sum += in2;
sumSquare1 += ((q63_t) (in2) * (in2));
in4 = pSrc[3];
sum += in3;
sumSquare += ((q63_t) (in3) * (in3));
sum += in4;
sumSquare1 += ((q63_t) (in4) * (in4));
/* update input pointer to process next samples */
pSrc += 4u;
/* Decrement the loop counter */
blkCnt--;
}
/* add two accumulators */
sumSquare = sumSquare + sumSquare1;
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0_FAMILY */
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++;
sumSquare += ((q63_t) (in) * (in));
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
sumSquare = (sumSquare >> 31);
meanOfSquares = (q31_t) ((sumSquare * t) >> 30);
/* Compute mean of all input values */
t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
mean = (q31_t) (sum);
/* Compute square of mean */
squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
/* Compute variance and then store the result to the destination */
*pResult = (q63_t) meanOfSquares - squareOfMean;
}
/**
* @} end of variance group
*/
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