pigweed / third_party / github / STMicroelectronics / cmsis_core / refs/heads/cm4 / . / DSP / Source / StatisticsFunctions / arm_std_q31.c

/* ---------------------------------------------------------------------- | |

* Project: CMSIS DSP Library | |

* Title: arm_std_q31.c | |

* Description: Standard deviation of the elements of a Q31 vector | |

* | |

* $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 STD | |

@{ | |

*/ | |

/** | |

@brief Standard deviation 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 standard deviation 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_std_q31( | |

const q31_t * pSrc, | |

uint32_t blockSize, | |

q31_t * pResult) | |

{ | |

uint32_t blkCnt; /* Loop counter */ | |

q63_t sum = 0; /* Accumulator */ | |

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 standard deviation and store result in destination */ | |

arm_sqrt_q31((meanOfSquares - squareOfMean) >> 15U, pResult); | |

} | |

/** | |

@} end of STD group | |

*/ |