/* ----------------------------------------------------------------------    
* Copyright (C) 2010 ARM Limited. All rights reserved.    
*    
* $Date: 14/06/07 1:57a $Revision: 	V1.1.0  
*    
* Project: 	    CMSIS DSP Library    
* Title:		arm_std_q31.c    
*    
* Description:	Standard deviation of an array of Q31 type.    
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Version 1.1.0 2012/02/15 
*    Updated with more optimizations, bug fixes and minor API changes.  
*   
* Version 1.0.10 2011/7/15  
*    Big Endian support added and Merged M0 and M3/M4 Source code.   
*    
* Version 1.0.3 2010/11/29   
*    Re-organized the CMSIS folders and updated documentation.    
*     
* Version 1.0.2 2010/11/11    
*    Documentation updated.     
*    
* Version 1.0.1 2010/10/05     
*    Production release and review comments incorporated.    
*    
* Version 1.0.0 2010/09/20     
*    Production release and review comments incorporated.    
* -------------------------------------------------------------------- */

#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, 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_std_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult)
{
  q63_t sum = 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 */
  q63_t sumOfSquares = 0;                        /* Accumulator */

#ifndef ARM_MATH_CM0

  /* 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++;
    sum += in;
    sumOfSquares += ((q63_t) (in) * (in));
    in = *pSrc++;
    sum += in;
    sumOfSquares += ((q63_t) (in) * (in));
    in = *pSrc++;
    sum += in;
    sumOfSquares += ((q63_t) (in) * (in));
    in = *pSrc++;
    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++;
    sum += in;
    sumOfSquares += ((q63_t) (in) * (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. */
  sumOfSquares = (sumOfSquares >> 31);
  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);

#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 += ((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. */
  t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
  sumOfSquares = (sumOfSquares >> 31);
  meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);

#endif /* #ifndef ARM_MATH_CM0 */

  /* 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 standard deviation and then store the result to the destination */
  arm_sqrt_q31(meanOfSquares - squareOfMean, pResult);

}

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