/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 16/10/14 6:01p $Revision:  V.1.4.5
*
* Project:      CMSIS DSP Library
* Title:        arm_var_q15.c
*
* Description:  Variance 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
* 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
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupStats
 */

/**
 * @addtogroup variance
 * @{
 */

/**
 * @brief Variance 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 variance 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_var_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

    /* Run the below code for Cortex-M4 and Cortex-M3 */

    q31_t in;                                      /* input value */
    q15_t in1;                                     /* input value */

    if(blockSize == 1)
    {
        *pResult = 0;
        return;
    }

    /*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 << 16) >> 16);
        sum += (in >> 16);
        sumOfSquares = __SMLALD(in, in, sumOfSquares);
        in = *__SIMD32(pSrc)++;
        sum += ((in << 16) >> 16);
        sum += (in >> 16);
        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 - 1));

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

    /* mean of the squares minus the square of the mean. */
    *pResult = (meanOfSquares - squareOfMean) >> 15;

#else

    /* Run the below code for Cortex-M0 */
    q15_t in;                                      /* input value */

    if(blockSize == 1)
    {
        *pResult = 0;
        return;
    }

    /* 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 - 1));

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

    /* mean of the squares minus the square of the mean. */
    *pResult = (meanOfSquares - squareOfMean) >> 15;

#endif /* #ifndef ARM_MATH_CM0_FAMILY */

}

/**
 * @} end of variance group
 */
