| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_var_q31.c |
| * Description: Variance of an array of Q31 type |
| * |
| * $Date: 18. March 2019 |
| * $Revision: V1.6.0 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved. |
| * |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the License); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #include "arm_math.h" |
| |
| /** |
| @ingroup groupStats |
| */ |
| |
| /** |
| @addtogroup variance |
| @{ |
| */ |
| |
| /** |
| @brief Variance of the elements of a Q31 vector. |
| @param[in] pSrc points to the input vector |
| @param[in] blockSize number of samples in input vector |
| @param[out] pResult variance value returned here |
| @return none |
| |
| @par Scaling and Overflow Behavior |
| The function is implemented using an internal 64-bit accumulator. |
| The input is represented in 1.31 format, which is then downshifted by 8 bits |
| which yields 1.23, and intermediate multiplication yields a 2.46 format. |
| The accumulator maintains full precision of the intermediate multiplication results, |
| but provides only a 16 guard bits. |
| There is no saturation on intermediate additions. |
| If the accumulator overflows it wraps around and distorts the result. |
| In order to avoid overflows completely the input signal must be scaled down by |
| log2(blockSize)-8 bits, as a total of blockSize additions are performed internally. |
| After division, internal variables should be Q18.46 |
| Finally, the 18.46 accumulator is right shifted by 15 bits to yield a 1.31 format value. |
| */ |
| |
| void arm_var_q31( |
| const q31_t * pSrc, |
| uint32_t blockSize, |
| q31_t * pResult) |
| { |
| uint32_t blkCnt; /* Loop counter */ |
| q63_t sum = 0; /* Temporary result storage */ |
| q63_t meanOfSquares, squareOfMean; /* Square of mean and mean of square */ |
| q63_t sumOfSquares = 0; /* Sum of squares */ |
| q31_t in; /* Temporary variable to store input value */ |
| |
| if (blockSize <= 1U) |
| { |
| *pResult = 0; |
| return; |
| } |
| |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Loop unrolling: Compute 4 outputs at a time */ |
| blkCnt = blockSize >> 2U; |
| |
| while (blkCnt > 0U) |
| { |
| /* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */ |
| /* C = A[0] + A[1] + ... + A[blockSize-1] */ |
| |
| in = *pSrc++ >> 8U; |
| /* Compute sum of squares and store result in a temporary variable, sumOfSquares. */ |
| sumOfSquares += ((q63_t) (in) * (in)); |
| /* Compute sum and store result in a temporary variable, sum. */ |
| sum += in; |
| |
| in = *pSrc++ >> 8U; |
| sumOfSquares += ((q63_t) (in) * (in)); |
| sum += in; |
| |
| in = *pSrc++ >> 8U; |
| sumOfSquares += ((q63_t) (in) * (in)); |
| sum += in; |
| |
| in = *pSrc++ >> 8U; |
| sumOfSquares += ((q63_t) (in) * (in)); |
| sum += in; |
| |
| /* Decrement loop counter */ |
| blkCnt--; |
| } |
| |
| /* Loop unrolling: Compute remaining outputs */ |
| blkCnt = blockSize % 0x4U; |
| |
| #else |
| |
| /* Initialize blkCnt with number of samples */ |
| blkCnt = blockSize; |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| while (blkCnt > 0U) |
| { |
| /* C = A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1] */ |
| /* C = A[0] + A[1] + ... + A[blockSize-1] */ |
| |
| in = *pSrc++ >> 8U; |
| /* Compute sum of squares and store result in a temporary variable, sumOfSquares. */ |
| sumOfSquares += ((q63_t) (in) * (in)); |
| /* Compute sum and store result in a temporary variable, sum. */ |
| sum += in; |
| |
| /* Decrement loop counter */ |
| blkCnt--; |
| } |
| |
| /* Compute Mean of squares and store result in a temporary variable, meanOfSquares. */ |
| meanOfSquares = (sumOfSquares / (q63_t)(blockSize - 1U)); |
| |
| /* Compute square of mean */ |
| squareOfMean = ( sum * sum / (q63_t)(blockSize * (blockSize - 1U))); |
| |
| /* Compute variance and store result in destination */ |
| *pResult = (meanOfSquares - squareOfMean) >> 15U; |
| } |
| |
| /** |
| @} end of variance group |
| */ |