1  /* ----------------------------------------------------------------------
  2   * Project:      CMSIS DSP Library
  3   * Title:        arm_std_q31.c
  4   * Description:  Standard deviation of the elements of a Q31 vector
  5   *
  6   * $Date:        23 April 2021
  7   * $Revision:    V1.9.0
  8   *
  9   * Target Processor: Cortex-M and Cortex-A cores
 10   * -------------------------------------------------------------------- */
 11  /*
 12   * Copyright (C) 2010-2021 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 "dsp/statistics_functions.h"
 30  
 31  /**
 32    @ingroup groupStats
 33   */
 34  
 35  /**
 36    @addtogroup STD
 37    @{
 38   */
 39  
 40  /**
 41    @brief         Standard deviation of the elements of a Q31 vector.
 42    @param[in]     pSrc       points to the input vector.
 43    @param[in]     blockSize  number of samples in input vector.
 44    @param[out]    pResult    standard deviation value returned here.
 45    @return        none
 46  
 47    @par           Scaling and Overflow Behavior
 48                     The function is implemented using an internal 64-bit accumulator.
 49                     The input is represented in 1.31 format, which is then downshifted by 8 bits
 50                     which yields 1.23, and intermediate multiplication yields a 2.46 format.
 51                     The accumulator maintains full precision of the intermediate multiplication results,
 52                     but provides only a 16 guard bits.
 53                     There is no saturation on intermediate additions.
 54                     If the accumulator overflows it wraps around and distorts the result.
 55                     In order to avoid overflows completely the input signal must be scaled down by
 56                     log2(blockSize)-8 bits, as a total of blockSize additions are performed internally.
 57                     After division, internal variables should be Q18.46
 58                     Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value.
 59   */
 60  #if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE)
 61  void arm_std_q31(
 62    const q31_t * pSrc,
 63          uint32_t blockSize,
 64          q31_t * pResult)
 65  {
 66      q31_t var=0;
 67  
 68      arm_var_q31(pSrc, blockSize, &var);
 69      arm_sqrt_q31(var, pResult);
 70  }
 71  #else
 72  void arm_std_q31(
 73    const q31_t * pSrc,
 74          uint32_t blockSize,
 75          q31_t * pResult)
 76  {
 77          uint32_t blkCnt;                               /* Loop counter */
 78          q63_t sum = 0;                                 /* Accumulator */
 79          q63_t meanOfSquares, squareOfMean;             /* Square of mean and mean of square */
 80          q63_t sumOfSquares = 0;                        /* Sum of squares */
 81          q31_t in;                                      /* Temporary variable to store input value */
 82  
 83    if (blockSize <= 1U)
 84    {
 85      *pResult = 0;
 86      return;
 87    }
 88  
 89  #if defined (ARM_MATH_LOOPUNROLL)
 90  
 91    /* Loop unrolling: Compute 4 outputs at a time */
 92    blkCnt = blockSize >> 2U;
 93  
 94    while (blkCnt > 0U)
 95    {
 96      /* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */
 97      /* C = A[0] + A[1] + ... + A[blockSize-1] */
 98  
 99      in = *pSrc++ >> 8U;
100      /* Compute sum of squares and store result in a temporary variable, sumOfSquares. */
101      sumOfSquares += ((q63_t) (in) * (in));
102      /* Compute sum and store result in a temporary variable, sum. */
103      sum += in;
104  
105      in = *pSrc++ >> 8U;
106      sumOfSquares += ((q63_t) (in) * (in));
107      sum += in;
108  
109      in = *pSrc++ >> 8U;
110      sumOfSquares += ((q63_t) (in) * (in));
111      sum += in;
112  
113      in = *pSrc++ >> 8U;
114      sumOfSquares += ((q63_t) (in) * (in));
115      sum += in;
116  
117      /* Decrement loop counter */
118      blkCnt--;
119    }
120  
121    /* Loop unrolling: Compute remaining outputs */
122    blkCnt = blockSize % 0x4U;
123  
124  #else
125  
126    /* Initialize blkCnt with number of samples */
127    blkCnt = blockSize;
128  
129  #endif /* #if defined (ARM_MATH_LOOPUNROLL) */
130  
131    while (blkCnt > 0U)
132    {
133      /* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */
134      /* C = A[0] + A[1] + ... + A[blockSize-1] */
135  
136      in = *pSrc++ >> 8U;
137      /* Compute sum of squares and store result in a temporary variable, sumOfSquares. */
138      sumOfSquares += ((q63_t) (in) * (in));
139      /* Compute sum and store result in a temporary variable, sum. */
140      sum += in;
141  
142      /* Decrement loop counter */
143      blkCnt--;
144    }
145  
146    /* Compute Mean of squares and store result in a temporary variable, meanOfSquares. */
147    meanOfSquares = (sumOfSquares / (q63_t)(blockSize - 1U));
148  
149    /* Compute square of mean */
150    squareOfMean = ( sum * sum / (q63_t)(blockSize * (blockSize - 1U)));
151  
152    /* Compute standard deviation and store result in destination */
153    arm_sqrt_q31((meanOfSquares - squareOfMean) >> 15U, pResult);
154  }
155  #endif /* defined(ARM_MATH_MVEI) */
156  
157  /**
158    @} end of STD group
159   */