Convolution

void riscv_conv_f32(const float32_t *pSrcA, uint32_t srcALen, const float32_t *pSrcB, uint32_t srcBLen, float32_t *pDst)
void riscv_conv_fast_opt_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst, q15_t *pScratch1, q15_t *pScratch2)
void riscv_conv_fast_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)
void riscv_conv_fast_q31(const q31_t *pSrcA, uint32_t srcALen, const q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)
void riscv_conv_opt_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst, q15_t *pScratch1, q15_t *pScratch2)
void riscv_conv_opt_q7(const q7_t *pSrcA, uint32_t srcALen, const q7_t *pSrcB, uint32_t srcBLen, q7_t *pDst, q15_t *pScratch1, q15_t *pScratch2)
void riscv_conv_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)
void riscv_conv_q31(const q31_t *pSrcA, uint32_t srcALen, const q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)
void riscv_conv_q7(const q7_t *pSrcA, uint32_t srcALen, const q7_t *pSrcB, uint32_t srcBLen, q7_t *pDst)
group Conv

Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector. Convolution is similar to correlation and is frequently used in filtering and data analysis. The NMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types. The library also provides fast versions of the Q15 and Q31 functions.

Algorithm

Let a[n] and b[n] be sequences of length srcALen and srcBLen samples respectively. Then the convolution

is defined as ../../../_images/ConvolutionEquation.png

Note that c[n] is of length srcALen + srcBLen - 1 and is defined over the interval n=0, 1, 2, ..., srcALen + srcBLen - 2. pSrcA points to the first input vector of length srcALen and pSrcB points to the second input vector of length srcBLen. The output result is written to pDst and the calling function must allocate srcALen+srcBLen-1 words for the result.

Conceptually, when two signals a[n] and b[n] are convolved, the signal b[n] slides over a[n]. For each offset n, the overlapping portions of a[n] and b[n] are multiplied and summed together.

Note that convolution is a commutative operation:

This means that switching the A and B arguments to the convolution functions has no effect.

Fixed-Point Behavior

Convolution requires summing up a large number of intermediate products. As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation. Refer to the function specific documentation below for further details of the particular algorithm used.

Fast Versions

Fast versions are supported for Q31 and Q15. Cycles for Fast versions are less compared to Q31 and Q15 of conv and the design requires the input signals should be scaled down to avoid intermediate overflows.

Opt Versions

Opt versions are supported for Q15 and Q7. Design uses internal scratch buffer for getting good optimisation. These versions are optimised in cycles and consumes more memory (Scratch memory) compared to Q15 and Q7 versions

Functions

void riscv_conv_f32(const float32_t *pSrcA, uint32_t srcALen, const float32_t *pSrcB, uint32_t srcBLen, float32_t *pDst)

Convolution of floating-point sequences.

Return

none

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

void riscv_conv_fast_opt_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst, q15_t *pScratch1, q15_t *pScratch2)

Convolution of Q15 sequences (fast version).

Convolution of Q15 sequences (fast version) for RISC-V Core with DSP enabled.

Return

none

Scaling and Overflow Behavior

This fast version uses a 32-bit accumulator with 2.30 format. The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit. There is no saturation on intermediate additions. Thus, if the accumulator overflows it wraps around and distorts the result. The input signals should be scaled down to avoid intermediate overflows. Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows, as maximum of min(srcALen, srcBLen) number of additions are carried internally. The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.

Remark

Refer to riscv_conv_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1

  • [in] pScratch1: points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2

  • [in] pScratch2: points to scratch buffer of size min(srcALen, srcBLen

void riscv_conv_fast_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)

Convolution of Q15 sequences (fast version).

Convolution of Q15 sequences (fast version) for RISC-V Core with DSP enabled.

Return

none

Scaling and Overflow Behavior

This fast version uses a 32-bit accumulator with 2.30 format. The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit. There is no saturation on intermediate additions. Thus, if the accumulator overflows it wraps around and distorts the result. The input signals should be scaled down to avoid intermediate overflows. Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows, as maximum of min(srcALen, srcBLen) number of additions are carried internally. The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.

Remark

Refer to riscv_conv_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1

void riscv_conv_fast_q31(const q31_t *pSrcA, uint32_t srcALen, const q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)

Convolution of Q31 sequences (fast version).

Convolution of Q31 sequences (fast version) for RISC-V Core with DSP enabled.

Return

none

Scaling and Overflow Behavior

This function is optimized for speed at the expense of fixed-point precision and overflow protection. The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30 format. Finally, the accumulator is saturated and converted to a 1.31 result.

The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result. In order to avoid overflows completely the input signals must be scaled down. Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows, as maximum of min(srcALen, srcBLen) number of additions are carried internally.

Remark

Refer to riscv_conv_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.

Parameters
  • [in] pSrcA: points to the first input sequence.

  • [in] srcALen: length of the first input sequence.

  • [in] pSrcB: points to the second input sequence.

  • [in] srcBLen: length of the second input sequence.

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

void riscv_conv_opt_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst, q15_t *pScratch1, q15_t *pScratch2)

Convolution of Q15 sequences.

Return

none

Scaling and Overflow Behavior

The function is implemented using a 64-bit internal accumulator. Both inputs are in 1.15 format and multiplications yield a 2.30 result. The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. This approach provides 33 guard bits and there is no risk of overflow. The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.

Remark

Refer to riscv_conv_fast_q15() for a faster but less precise version of this function.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

  • [in] pScratch1: points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.

  • [in] pScratch2: points to scratch buffer of size min(srcALen, srcBLen).

void riscv_conv_opt_q7(const q7_t *pSrcA, uint32_t srcALen, const q7_t *pSrcB, uint32_t srcBLen, q7_t *pDst, q15_t *pScratch1, q15_t *pScratch2)

Convolution of Q7 sequences.

Return

none

Scaling and Overflow Behavior

The function is implemented using a 32-bit internal accumulator. Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result. The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format. This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072. The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and then saturated to 1.7 format.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

  • [in] pScratch1: points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.

  • [in] pScratch2: points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).

void riscv_conv_q15(const q15_t *pSrcA, uint32_t srcALen, const q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)

Convolution of Q15 sequences.

Return

none

Scaling and Overflow Behavior

The function is implemented using a 64-bit internal accumulator. Both inputs are in 1.15 format and multiplications yield a 2.30 result. The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. This approach provides 33 guard bits and there is no risk of overflow. The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.

Remark

Refer to riscv_conv_fast_q15() for a faster but less precise version of this function.

Remark

Refer to riscv_conv_opt_q15() for a faster implementation of this function using scratch buffers.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

void riscv_conv_q31(const q31_t *pSrcA, uint32_t srcALen, const q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)

Convolution of Q31 sequences.

Return

none

Scaling and Overflow Behavior

The function is implemented using an internal 64-bit accumulator. The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. There is no saturation on intermediate additions. Thus, if the accumulator overflows it wraps around and distorts the result. The input signals should be scaled down to avoid intermediate overflows. Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows, as maximum of min(srcALen, srcBLen) number of additions are carried internally. The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.

Remark

Refer to riscv_conv_fast_q31() for a faster but less precise implementation of this function.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.

void riscv_conv_q7(const q7_t *pSrcA, uint32_t srcALen, const q7_t *pSrcB, uint32_t srcBLen, q7_t *pDst)

Convolution of Q7 sequences.

Return

none

Scaling and Overflow Behavior

The function is implemented using a 32-bit internal accumulator. Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result. The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format. This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072. The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and then saturated to 1.7 format.

Remark

Refer to riscv_conv_opt_q7() for a faster implementation of this function.

Parameters
  • [in] pSrcA: points to the first input sequence

  • [in] srcALen: length of the first input sequence

  • [in] pSrcB: points to the second input sequence

  • [in] srcBLen: length of the second input sequence

  • [out] pDst: points to the location where the output result is written. Length srcALen+srcBLen-1.