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