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/* ----------------------------------------------------------------------

 * Project:      CMSIS DSP Library

 * Title:        arm_var_q15.c

 * Description:  Variance of an array of Q15 type

 *

 * $Date:        27. January 2017

 * $Revision:    V.1.5.1

 *

 * Target Processor: Cortex-M cores

 * -------------------------------------------------------------------- */

/*

 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.

 *

 * SPDX-License-Identifier: Apache-2.0

 *

 * Licensed under the Apache License, Version 2.0 (the License); you may

 * not use this file except in compliance with the License.

 * You may obtain a copy of the License at

 *

 * www.apache.org/licenses/LICENSE-2.0

 *

 * Unless required by applicable law or agreed to in writing, software

 * distributed under the License is distributed on an AS IS BASIS, WITHOUT

 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

 * See the License for the specific language governing permissions and

 * limitations under the License.

 */

#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 */

#if defined (ARM_MATH_DSP)

  q31_t in;                                      /* input value */

  q15_t in1;                                     /* input value */

#else

  q15_t in;                                      /* input value */

#endif

  if (blockSize == 1U)

  {

    *pResult = 0;

    return;

  }

#if defined (ARM_MATH_DSP)

  /* 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. */

  *pResult = (meanOfSquares - squareOfMean) >> 15U;

#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. */

  *pResult = (meanOfSquares - squareOfMean) >> 15;

#endif /* #if defined (ARM_MATH_DSP) */

}

/**

 * @} end of variance group

 */