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1 /* ----------------------------------------------------------------------
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2 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.
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3 *
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4 * $Date: 19. March 2015
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5 * $Revision: V.1.4.5
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6 *
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7 * Project: CMSIS DSP Library
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8 * Title: arm_var_q31.c
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9 *
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10 * Description: Variance of an array of Q31 type.
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11 *
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12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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13 *
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14 * Redistribution and use in source and binary forms, with or without
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15 * modification, are permitted provided that the following conditions
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16 * are met:
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17 * - Redistributions of source code must retain the above copyright
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18 * notice, this list of conditions and the following disclaimer.
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19 * - Redistributions in binary form must reproduce the above copyright
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20 * notice, this list of conditions and the following disclaimer in
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21 * the documentation and/or other materials provided with the
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22 * distribution.
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23 * - Neither the name of ARM LIMITED nor the names of its contributors
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24 * may be used to endorse or promote products derived from this
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25 * software without specific prior written permission.
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26 *
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27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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38 * POSSIBILITY OF SUCH DAMAGE.
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39 * -------------------------------------------------------------------- */
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40
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41 #include "arm_math.h"
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42
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43 /**
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44 * @ingroup groupStats
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45 */
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46
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47 /**
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48 * @addtogroup variance
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49 * @{
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50 */
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51
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52 /**
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53 * @brief Variance of the elements of a Q31 vector.
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54 * @param[in] *pSrc points to the input vector
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55 * @param[in] blockSize length of the input vector
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56 * @param[out] *pResult variance value returned here
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57 * @return none.
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58 *
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59 * @details
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60 * <b>Scaling and Overflow Behavior:</b>
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61 *
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62 *\par
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63 * The function is implemented using an internal 64-bit accumulator.
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64 * The input is represented in 1.31 format, which is then downshifted by 8 bits
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65 * which yields 1.23, and intermediate multiplication yields a 2.46 format.
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66 * The accumulator maintains full precision of the intermediate multiplication results,
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67 * but provides only a 16 guard bits.
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68 * There is no saturation on intermediate additions.
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69 * If the accumulator overflows it wraps around and distorts the result.
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70 * In order to avoid overflows completely the input signal must be scaled down by
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71 * log2(blockSize)-8 bits, as a total of blockSize additions are performed internally.
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72 * After division, internal variables should be Q18.46
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73 * Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value.
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74 *
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75 */
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76
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77
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78 void arm_var_q31(
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79 q31_t * pSrc,
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80 uint32_t blockSize,
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81 q31_t * pResult)
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82 {
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83 q63_t sum = 0; /* Accumulator */
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84 q63_t meanOfSquares, squareOfMean; /* square of mean and mean of square */
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85 q31_t in; /* input value */
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86 uint32_t blkCnt; /* loop counter */
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87 q63_t sumOfSquares = 0; /* Accumulator */
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88
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89 if(blockSize == 1)
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90 {
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91 *pResult = 0;
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92 return;
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93 }
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94
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95 #ifndef ARM_MATH_CM0_FAMILY
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96
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97 /* Run the below code for Cortex-M4 and Cortex-M3 */
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98
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99 /*loop Unrolling */
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100 blkCnt = blockSize >> 2u;
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101
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102 /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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103 ** a second loop below computes the remaining 1 to 3 samples. */
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104 while(blkCnt > 0u)
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105 {
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106 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
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107 /* Compute Sum of squares of the input samples
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108 * and then store the result in a temporary variable, sum. */
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109 in = *pSrc++ >> 8;
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110 sum += in;
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111 sumOfSquares += ((q63_t) (in) * (in));
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112 in = *pSrc++ >> 8;
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113 sum += in;
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114 sumOfSquares += ((q63_t) (in) * (in));
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115 in = *pSrc++ >> 8;
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116 sum += in;
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117 sumOfSquares += ((q63_t) (in) * (in));
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118 in = *pSrc++ >> 8;
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119 sum += in;
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120 sumOfSquares += ((q63_t) (in) * (in));
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121
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122 /* Decrement the loop counter */
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123 blkCnt--;
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124 }
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125
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126 /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
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127 ** No loop unrolling is used. */
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128 blkCnt = blockSize % 0x4u;
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129
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130 while(blkCnt > 0u)
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131 {
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132 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
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133 /* Compute Sum of squares of the input samples
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134 * and then store the result in a temporary variable, sum. */
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135 in = *pSrc++ >> 8;
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136 sum += in;
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137 sumOfSquares += ((q63_t) (in) * (in));
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138
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139 /* Decrement the loop counter */
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140 blkCnt--;
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141 }
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142
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143 /* Compute Mean of squares of the input samples
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144 * and then store the result in a temporary variable, meanOfSquares. */
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145 meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1);
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146
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147 #else
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148
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149 /* Run the below code for Cortex-M0 */
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150
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151 /* Loop over blockSize number of values */
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152 blkCnt = blockSize;
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153
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154 while(blkCnt > 0u)
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155 {
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156 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
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157 /* Compute Sum of squares of the input samples
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158 * and then store the result in a temporary variable, sumOfSquares. */
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159 in = *pSrc++ >> 8;
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160 sumOfSquares += ((q63_t) (in) * (in));
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161
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162 /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
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163 /* Compute sum of all input values and then store the result in a temporary variable, sum. */
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164 sum += in;
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165
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166 /* Decrement the loop counter */
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167 blkCnt--;
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168 }
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169
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170 /* Compute Mean of squares of the input samples
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171 * and then store the result in a temporary variable, meanOfSquares. */
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172 meanOfSquares = sumOfSquares / (q63_t)(blockSize - 1);
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173
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174 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
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175
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176 /* Compute square of mean */
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177 squareOfMean = sum * sum / (q63_t)(blockSize * (blockSize - 1u));
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178
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179
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180 /* Compute standard deviation and then store the result to the destination */
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181 *pResult = (meanOfSquares - squareOfMean) >> 15;
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182
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183 }
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184
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185 /**
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186 * @} end of variance group
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187 */
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