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)
arm_std_q31(const q31_t * pSrc,uint32_t blockSize,q31_t * pResult)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
arm_std_q31(const q31_t * pSrc,uint32_t blockSize,q31_t * pResult)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 */
160
