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  1. /* ----------------------------------------------------------------------
  2.  * Project:      CMSIS DSP Library
  3.  * Title:        arm_var_q31.c
  4.  * Description:  Variance of an array of Q31 type
  5.  *
  6.  * $Date:        27. January 2017
  7.  * $Revision:    V.1.5.1
  8.  *
  9.  * Target Processor: Cortex-M cores
  10.  * -------------------------------------------------------------------- */
  11. /*
  12.  * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
  13.  *
  14.  * SPDX-License-Identifier: Apache-2.0
  15.  *
  16.  * Licensed under the Apache License, Version 2.0 (the License); you may
  17.  * not use this file except in compliance with the License.
  18.  * You may obtain a copy of the License at
  19.  *
  20.  * www.apache.org/licenses/LICENSE-2.0
  21.  *
  22.  * Unless required by applicable law or agreed to in writing, software
  23.  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
  24.  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  25.  * See the License for the specific language governing permissions and
  26.  * limitations under the License.
  27.  */
  28.  
  29. #include "arm_math.h"
  30.  
  31. /**
  32.  * @ingroup groupStats
  33.  */
  34.  
  35. /**
  36.  * @addtogroup variance
  37.  * @{
  38.  */
  39.  
  40. /**
  41.  * @brief Variance of the elements of a Q31 vector.
  42.  * @param[in]       *pSrc points to the input vector
  43.  * @param[in]       blockSize length of the input vector
  44.  * @param[out]      *pResult variance value returned here
  45.  * @return none.
  46.  * @details
  47.  * <b>Scaling and Overflow Behavior:</b>
  48.  *
  49.  *\par
  50.  * The function is implemented using an internal 64-bit accumulator.
  51.  * The input is represented in 1.31 format, which is then downshifted by 8 bits
  52.  * which yields 1.23, and intermediate multiplication yields a 2.46 format.
  53.  * The accumulator maintains full precision of the intermediate multiplication results,
  54.  * but provides only a 16 guard bits.
  55.  * There is no saturation on intermediate additions.
  56.  * If the accumulator overflows it wraps around and distorts the result.
  57.  * In order to avoid overflows completely the input signal must be scaled down by
  58.  * log2(blockSize)-8 bits, as a total of blockSize additions are performed internally.
  59.  * After division, internal variables should be Q18.46
  60.  * Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value.
  61.  *
  62.  */
  63.  
  64. void arm_var_q31(
  65.   q31_t * pSrc,
  66.   uint32_t blockSize,
  67.   q31_t * pResult)
  68. {
  69.   q63_t sum = 0;                                 /* Accumulator */
  70.   q63_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
  71.   q31_t in;                                      /* input value */
  72.   uint32_t blkCnt;                               /* loop counter */
  73.   q63_t sumOfSquares = 0;                        /* Accumulator */
  74.  
  75.   if (blockSize == 1U)
  76.   {
  77.     *pResult = 0;
  78.     return;
  79.   }
  80.  
  81. #if defined (ARM_MATH_DSP)
  82.   /* Run the below code for Cortex-M4 and Cortex-M3 */
  83.  
  84.   /*loop Unrolling */
  85.   blkCnt = blockSize >> 2U;
  86.  
  87.   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
  88.    ** a second loop below computes the remaining 1 to 3 samples. */
  89.   while (blkCnt > 0U)
  90.   {
  91.     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
  92.     /* Compute Sum of squares of the input samples
  93.      * and then store the result in a temporary variable, sum. */
  94.     in = *pSrc++ >> 8U;
  95.     sum += in;
  96.     sumOfSquares += ((q63_t) (in) * (in));
  97.     in = *pSrc++ >> 8U;
  98.     sum += in;
  99.     sumOfSquares += ((q63_t) (in) * (in));
  100.     in = *pSrc++ >> 8U;
  101.     sum += in;
  102.     sumOfSquares += ((q63_t) (in) * (in));
  103.     in = *pSrc++ >> 8U;
  104.     sum += in;
  105.     sumOfSquares += ((q63_t) (in) * (in));
  106.  
  107.     /* Decrement the loop counter */
  108.     blkCnt--;
  109.   }
  110.  
  111.   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
  112.    ** No loop unrolling is used. */
  113.   blkCnt = blockSize % 0x4U;
  114.  
  115.   while (blkCnt > 0U)
  116.   {
  117.     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
  118.     /* Compute Sum of squares of the input samples
  119.      * and then store the result in a temporary variable, sum. */
  120.     in = *pSrc++ >> 8U;
  121.     sum += in;
  122.     sumOfSquares += ((q63_t) (in) * (in));
  123.  
  124.     /* Decrement the loop counter */
  125.     blkCnt--;
  126.   }
  127.  
  128.   /* Compute Mean of squares of the input samples
  129.    * and then store the result in a temporary variable, meanOfSquares. */
  130.   meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1U);
  131.  
  132. #else
  133.   /* Run the below code for Cortex-M0 */
  134.  
  135.   /* Loop over blockSize number of values */
  136.   blkCnt = blockSize;
  137.  
  138.   while (blkCnt > 0U)
  139.   {
  140.     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
  141.     /* Compute Sum of squares of the input samples
  142.      * and then store the result in a temporary variable, sumOfSquares. */
  143.     in = *pSrc++ >> 8U;
  144.     sumOfSquares += ((q63_t) (in) * (in));
  145.  
  146.     /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
  147.     /* Compute sum of all input values and then store the result in a temporary variable, sum. */
  148.     sum += in;
  149.  
  150.     /* Decrement the loop counter */
  151.     blkCnt--;
  152.   }
  153.  
  154.   /* Compute Mean of squares of the input samples
  155.    * and then store the result in a temporary variable, meanOfSquares. */
  156.   meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1U);
  157.  
  158. #endif /* #if defined (ARM_MATH_DSP) */
  159.  
  160.   /* Compute square of mean */
  161.   squareOfMean = sum * sum / (q63_t)(blockSize * (blockSize - 1U));
  162.  
  163.   /* Compute standard deviation and then store the result to the destination */
  164.   *pResult = (meanOfSquares - squareOfMean) >> 15U;
  165. }
  166.  
  167. /**
  168.  * @} end of variance group
  169.  */
  170.