CMSIS_5/CMSIS/DSP/Source/StatisticsFunctions/arm_std_q15.c

/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date:        19. March 2015
* $Revision:    V.1.4.5
*
* Project:      CMSIS DSP Library
* Title:        arm_std_q15.c
*
* Description:  Standard deviation of an array of Q15 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
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*     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
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupStats
 */

/**
 * @addtogroup STD
 * @{
 */

/**
 * @brief Standard deviation of the elements of a Q15 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 a 64-bit internal accumulator.
 * The input is represented in 1.15 format.
 * Intermediate multiplication yields a 2.30 format, and this
 * result is added without saturation to a 64-bit accumulator in 34.30 format.
 * With 33 guard bits in the accumulator, there is no risk of overflow, and the
 * full precision of the intermediate multiplication is preserved.
 * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
 * 15 bits, and then saturated to yield a result in 1.15 format.
 */

void arm_std_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult)
{
  q31_t sum = 0;                                 /* Accumulator */
  q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
  uint32_t blkCnt;                               /* loop counter */
  q63_t sumOfSquares = 0;                        /* Accumulator */
#ifndef ARM_MATH_CM0_FAMILY
  q31_t in;                                      /* input value */
  q15_t in1;                                     /* input value */
#else
  q15_t in;                                      /* input value */
#endif

  if(blockSize == 1u)
  {
    *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 = *__SIMD32(pSrc)++;
    sum += ((in << 16u) >> 16u);
    sum +=  (in >> 16u);
    sumOfSquares = __SMLALD(in, in, sumOfSquares);
    in = *__SIMD32(pSrc)++;
    sum += ((in << 16u) >> 16u);
    sum +=  (in >> 16u);
    sumOfSquares = __SMLALD(in, in, sumOfSquares);

    /* 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. */
    in1 = *pSrc++;
    sumOfSquares = __SMLALD(in1, in1, sumOfSquares);
    sum += in1;

    /* Decrement the loop counter */
    blkCnt--;
  }

  /* Compute Mean of squares of the input samples
   * and then store the result in a temporary variable, meanOfSquares. */
  meanOfSquares = (q31_t)(sumOfSquares / (q63_t)(blockSize - 1u));

  /* Compute square of mean */
  squareOfMean = (q31_t)((q63_t)sum * sum / (q63_t)(blockSize * (blockSize - 1u)));

  /* mean of the squares minus the square of the mean. */
  /* Compute standard deviation and store the result to the destination */
  arm_sqrt_q15(__SSAT((meanOfSquares - squareOfMean) >> 15u, 16u), pResult);

#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++;
    sumOfSquares += (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 = (q31_t)(sumOfSquares / (q63_t)(blockSize - 1u));

  /* Compute square of mean */
  squareOfMean = (q31_t)((q63_t)sum * sum / (q63_t)(blockSize * (blockSize - 1u)));

  /* mean of the squares minus the square of the mean. */
  /* Compute standard deviation and store the result to the destination */
  arm_sqrt_q15(__SSAT((meanOfSquares - squareOfMean) >> 15u, 16u), pResult);

#endif /* #ifndef ARM_MATH_CM0_FAMILY */
}

/**
 * @} end of STD group
 */