Complex Dot Product

Collaboration diagram for Complex Dot Product:

Functions
void	tpt_cmplx_dot_prod_f32 (f32_t *__restrict aRealResult, f32_t *__restrict aImagResult, const f32_t *__restrict aInDataA, const f32_t *__restrict aInDataB, uint32_t aCount)
	Floating-point complex dot product. More...
void	tpt_cmplx_dot_prod_q15 (q33_30_t *__restrict aRealResult, q33_30_t *__restrict aImagResult, const q15_t *__restrict aInDataA, const q15_t *__restrict aInDataB, uint32_t aCount)
	Q15 complex dot product. More...
void	tpt_cmplx_dot_prod_q31 (q15_48_t *__restrict aRealResult, q15_48_t *__restrict aImagResult, const q31_t *__restrict aInDataA, const q31_t *__restrict aInDataB, uint32_t aCount)
	Q31 complex dot product. More...

Detailed Description

Computes the dot product of two complex vectors. The vectors are multiplied element-by-element and then summed.

The aInDataA points to the first complex input vector and aInDataB points to the second complex input vector. aCount specifies the number of complex samples and the data in each array is stored in an interleaved fashion (real, imag, real, imag, ...). Each array has a total of 2 * aCount values.

The underlying algorithm is used:

    aRealResult = 0;
    aImagResult = 0;
    for (n = 0; n < aCount; n++)
    {
      aRealResult += aInDataA[2 * n + 0] * aInDataB[2 * n + 0]

aInDataA[2 * n + 1] * aInDataB[2 * n + 1];
      aImagResult += aInDataA[2 * n + 0] * aInDataB[2 * n + 1]
                   + aInDataA[2 * n + 1] * aInDataB[2 * n + 0];
    }
  

  There are separate functions for floating-point, Q15, and Q31 data types. 

Function Documentation

tpt_cmplx_dot_prod_f32()

void tpt_cmplx_dot_prod_f32	(	f32_t *__restrict	aRealResult,
		f32_t *__restrict	aImagResult,
		const f32_t *__restrict	aInDataA,
		const f32_t *__restrict	aInDataB,
		uint32_t	aCount
	)

Floating-point complex dot product.

Parameters

[out]	aRealResult	real part of the result returned here
[out]	aImagResult	imaginary part of the result returned here
[in]	aInDataA	points to the first input vector.
[in]	aInDataB	points to the second input vector.
[in]	aCount	number of samples in each vector

Returns

none

tpt_cmplx_dot_prod_q15()

void tpt_cmplx_dot_prod_q15	(	q33_30_t *__restrict	aRealResult,
		q33_30_t *__restrict	aImagResult,
		const q15_t *__restrict	aInDataA,
		const q15_t *__restrict	aInDataB,
		uint32_t	aCount
	)

Q15 complex dot product.

Parameters

[out]	aRealResult	real part of the result returned here
[out]	aImagResult	imaginary part of the result returned here
[in]	aInDataA	points to the first input vector.
[in]	aInDataB	points to the second input vector.
[in]	aCount	number of samples in each vector

Returns

none

Scaling and Overflow Behavior

The function is implemented using an internal 64-bit accumulator. The intermediate 1.15 by 1.15 multiplications are performed with full precision and yield a 2.30 result. These are accumulated in a 32-bit accumulator with 8.24 precision. The return results aRealResult and aImagResult are in Q24 format.

tpt_cmplx_dot_prod_q31()

void tpt_cmplx_dot_prod_q31	(	q15_48_t *__restrict	aRealResult,
		q15_48_t *__restrict	aImagResult,
		const q31_t *__restrict	aInDataA,
		const q31_t *__restrict	aInDataB,
		uint32_t	aCount
	)

Q31 complex dot product.

Parameters

[out]	aRealResult	real part of the result returned here
[out]	aImagResult	imaginary part of the result returned here
[in]	aInDataA	points to the first input vector.
[in]	aInDataB	points to the second input vector.
[in]	aCount	number of samples in each vector

Returns

none

Scaling and Overflow Behavior

The function is implemented using an internal 64-bit accumulator. The intermediate 1.31 by 1.31 multiplications are performed with 64-bit precision and then shifted to 16.48 format. The internal real and imaginary accumulators are in 16.48 format and provide 15 guard bits. Additions are nonsaturating and no overflow will occur as long as aCount is less than 32768. The return results aRealResult and aImagResult are in 16.48 format. Input down scaling is not required.