1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
4 * $Date: 17. January 2013
7 * Project: CMSIS DSP Library
10 * Description: Variance of an array of Q15 type.
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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48 * @addtogroup variance
53 * @brief Variance of the elements of a Q15 vector.
54 * @param[in] *pSrc points to the input vector
55 * @param[in] blockSize length of the input vector
56 * @param[out] *pResult variance value returned here
60 * <b>Scaling and Overflow Behavior:</b>
63 * The function is implemented using a 64-bit internal accumulator.
64 * The input is represented in 1.15 format.
65 * Intermediate multiplication yields a 2.30 format, and this
66 * result is added without saturation to a 64-bit accumulator in 34.30 format.
67 * With 33 guard bits in the accumulator, there is no risk of overflow, and the
68 * full precision of the intermediate multiplication is preserved.
69 * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
70 * 15 bits, and then saturated to yield a result in 1.15 format.
80 q31_t sum = 0; /* Accumulator */
81 q31_t meanOfSquares, squareOfMean; /* Mean of square and square of mean */
82 q15_t mean; /* mean */
83 uint32_t blkCnt; /* loop counter */
84 q15_t t; /* Temporary variable */
85 q63_t sumOfSquares = 0; /* Accumulator */
87 #ifndef ARM_MATH_CM0_FAMILY
89 /* Run the below code for Cortex-M4 and Cortex-M3 */
91 q31_t in; /* Input variable */
92 q15_t in1; /* Temporary variable */
95 blkCnt = blockSize >> 2u;
97 /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
98 ** a second loop below computes the remaining 1 to 3 samples. */
101 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
102 /* Compute Sum of squares of the input samples
103 * and then store the result in a temporary variable, sum. */
104 in = *__SIMD32(pSrc)++;
105 sum += ((in << 16) >> 16);
107 sumOfSquares = __SMLALD(in, in, sumOfSquares);
108 in = *__SIMD32(pSrc)++;
109 sum += ((in << 16) >> 16);
111 sumOfSquares = __SMLALD(in, in, sumOfSquares);
113 /* Decrement the loop counter */
117 /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
118 ** No loop unrolling is used. */
119 blkCnt = blockSize % 0x4u;
123 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
124 /* Compute Sum of squares of the input samples
125 * and then store the result in a temporary variable, sum. */
128 sumOfSquares = __SMLALD(in1, in1, sumOfSquares);
130 /* Decrement the loop counter */
134 /* Compute Mean of squares of the input samples
135 * and then store the result in a temporary variable, meanOfSquares. */
136 t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
137 sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
139 meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
143 /* Run the below code for Cortex-M0 */
145 q15_t in; /* Temporary variable */
146 /* Loop over blockSize number of values */
151 /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
152 /* Compute Sum of squares of the input samples
153 * and then store the result in a temporary variable, sumOfSquares. */
155 sumOfSquares += (in * in);
157 /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
158 /* Compute sum of all input values and then store the result in a temporary variable, sum. */
161 /* Decrement the loop counter */
165 /* Compute Mean of squares of the input samples
166 * and then store the result in a temporary variable, meanOfSquares. */
167 t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
168 sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
169 meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
171 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
173 /* Compute mean of all input values */
174 t = (q15_t) ((1.0f / (float32_t) (blockSize * (blockSize - 1u))) * 32768);
175 mean = __SSAT(sum, 16u);
177 /* Compute square of mean */
178 squareOfMean = ((q31_t) mean * mean) >> 15;
179 squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
181 /* Compute variance and then store the result to the destination */
182 *pResult = (meanOfSquares - squareOfMean);
187 * @} end of variance group