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/* ----------------------------------------------------------------------    
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* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
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*    
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* $Date:        19. March 2015
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* $Revision:    V.1.4.5  
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*    
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* Project:          CMSIS DSP Library    
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* Title:                arm_var_q31.c    
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*    
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* Description:  Variance of an array of Q31 type.    
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*    
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*  
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*   - Redistributions of source code must retain the above copyright
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*     notice, this list of conditions and the following disclaimer.
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*   - Redistributions in binary form must reproduce the above copyright
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*     notice, this list of conditions and the following disclaimer in
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*     the documentation and/or other materials provided with the
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*     distribution.
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*   - Neither the name of ARM LIMITED nor the names of its contributors
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*     may be used to endorse or promote products derived from this
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*     software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.  
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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 length of the input vector        
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 * @param[out]      *pResult variance value returned here        
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 * @return none.        
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 *        
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 * @details        
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 * <b>Scaling and Overflow Behavior:</b>        
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 *        
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 *\par        
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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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 */
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void arm_var_q31(
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  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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  q63_t sum = 0;                                 /* Accumulator */
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  q63_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
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  q31_t in;                                      /* input value */
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  uint32_t blkCnt;                               /* loop counter */
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  q63_t sumOfSquares = 0;                        /* Accumulator */
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        if(blockSize == 1)
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        {
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                *pResult = 0;
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                return;
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        }
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#ifndef ARM_MATH_CM0_FAMILY
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  /* Run the below code for Cortex-M4 and Cortex-M3 */
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  /*loop Unrolling */
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  blkCnt = blockSize >> 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(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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    /* Compute Sum of squares of the input samples    
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     * and then store the result in a temporary variable, sum. */
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    in = *pSrc++ >> 8;
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    sum += in;
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    sumOfSquares += ((q63_t) (in) * (in));
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    in = *pSrc++ >> 8;
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    sum += in;
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    sumOfSquares += ((q63_t) (in) * (in));
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    in = *pSrc++ >> 8;
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    sum += in;
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    sumOfSquares += ((q63_t) (in) * (in));
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    in = *pSrc++ >> 8;
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    sum += in;
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    sumOfSquares += ((q63_t) (in) * (in));
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    /* Decrement the loop counter */
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    blkCnt--;
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  }
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  /* If the blockSize 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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  blkCnt = blockSize % 0x4u;
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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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    /* Compute Sum of squares of the input samples    
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     * and then store the result in a temporary variable, sum. */
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    in = *pSrc++ >> 8;
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    sum += in;
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    sumOfSquares += ((q63_t) (in) * (in));
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    /* Decrement the loop counter */
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    blkCnt--;
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  }
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  /* Compute Mean of squares of the input samples    
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   * and then store the result in a temporary variable, meanOfSquares. */
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  meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1);
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#else
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  /* Run the below code for Cortex-M0 */
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  /* Loop over blockSize number of values */
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  blkCnt = blockSize;
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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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    /* Compute Sum of squares of the input samples    
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     * and then store the result in a temporary variable, sumOfSquares. */
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    in = *pSrc++ >> 8;
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    sumOfSquares += ((q63_t) (in) * (in));
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    /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
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    /* Compute sum of all input values and then store the result in a temporary variable, sum. */
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    sum += in;
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    /* Decrement the loop counter */
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    blkCnt--;
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  }
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  /* Compute Mean of squares of the input samples    
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   * and then store the result in a temporary variable, meanOfSquares. */
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  meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1);
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#endif /* #ifndef ARM_MATH_CM0_FAMILY */
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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 standard deviation and then store the result to the destination */
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  *pResult = (meanOfSquares - squareOfMean) >> 15;
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}
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/**        
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 * @} end of variance group        
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 */