[Feature Request] `arm_cmplx_dot_prod_real_*` — optimized real × complex dot product

[xerpi]

Summary

Add a function to compute a dot product between a real input vector and complex coefficient vector, returning a complex result. This is useful for FIR filtering with complex taps and real input (e.g., frequency-translating FIR filters on real data), or filtering complex input with real taps.

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Current API gap

CMSIS-DSP currently provides:

Function	Operation	Input types	Output
arm_dot_prod_*	Real dot product	real × real	real
arm_cmplx_dot_prod_*	Complex dot product	complex × complex	complex
arm_cmplx_mult_real_*	Element-wise multiply	complex × real	complex

However, there is no function for real × complex → complex in dot-product form.

Proposed API

Following the existing naming and prototype conventions:

void arm_cmplx_dot_prod_real_f16(const float16_t *pSrcReal,
    const float16_t *pSrcCmplx,
    uint32_t numSamples,
    float16_t *realResult,
    float16_t *imagResult);

void arm_cmplx_dot_prod_real_f32(const float32_t *pSrcReal,
    const float32_t *pSrcCmplx,
    uint32_t numSamples,
    float32_t *realResult,
    float32_t *imagResult);

void arm_cmplx_dot_prod_real_q15(const q15_t *pSrcReal,
    const q15_t *pSrcCmplx,
    uint32_t numSamples,
    q31_t *realResult,
    q31_t *imagResult);

void arm_cmplx_dot_prod_real_q31(const q31_t *pSrcReal,
    const q31_t *pSrcCmplx,
    uint32_t numSamples,
    q63_t *realResult,
    q63_t *imagResult);`

Semantics:

$$ (\text{realResult}, \text{imagResult}) = \sum_{n=0}^{N-1} x[n] \cdot (h_r[n] + j h_i[n]) $$

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Implementation notes

• Could internally reuse the complex-by-real multiplication kernels (arm_cmplx_mult_real_*) with accumulation.

Example use case

Frequency-translating FIR filter:

// x: real input, h: complex bandpass taps
arm_cmplx_dot_prod_real_f32(x, h, numTaps, &accReal, &accImag);

This avoids manually separating real/imag taps or converting x[n] to complex.