mul(avx_simd_complex_float<T> lhs, avx_simd_complex_float<T> rhs) {
//lhs = [x1.real, x1.img, x2.real, x2.img, ...]
//rhs = [y1.real, y1.img, y2.real, y2.img, ...]
//ymm1 = [y1.real, y1.real, y2.real, y2.real, ...]
__m256 ymm1 = _mm256_moveldup_ps(rhs.value);
//ymm2 = [x1.img, x1.real, x2.img, x2.real]
__m256 ymm2 = _mm256_permute_ps(lhs.value, 0b10110001);
//ymm3 = [y1.imag, y1.imag, y2.imag, y2.imag]
__m256 ymm3 = _mm256_movehdup_ps(rhs.value);
//ymm4 = ymm2 * ymm3
__m256 ymm4 = _mm256_mul_ps(ymm2, ymm3);
//result = [(lhs * ymm1) -+ ymm4];
#ifdef __FMA__
return _mm256_fmaddsub_ps(lhs.value, ymm1, ymm4);
#elif defined(__FMA4__)
return _mm256_maddsub_ps(lhs.value, ymm1, ymm4);
#else
__m256 tmp = _mm256_mul_ps(lhs.value, ymm1);
return _mm256_addsub_ps(tmp, ymm4);
#endif
}
/****************************************************************
* This technique for efficient SIMD complex-complex multiplication was found at
* https://software.intel.com/file/1000
*****************************************************************/
inline __m256 avx_multiply_float_complex_(const __m256& vecA, const __m256& vecB) {
__m256 vec1 = _mm256_moveldup_ps(vecB);
__m256 vec2 = _mm256_movehdup_ps(vecB);
vec1 = _mm256_mul_ps(vecA,vec1);
vec2 = _mm256_mul_ps(vecA,vec2);
vec2 = _mm256_permute_ps(vec2,0xB1);
return _mm256_addsub_ps(vec1,vec2);
}
div(avx_simd_complex_float<T> lhs, avx_simd_complex_float<T> rhs) {
//lhs = [x1.real, x1.img, x2.real, x2.img ...]
//rhs = [y1.real, y1.img, y2.real, y2.img ...]
//ymm0 = [y1.real, y1.real, y2.real, y2.real, ...]
__m256 ymm0 = _mm256_moveldup_ps(rhs.value);
//ymm1 = [y1.imag, y1.imag, y2.imag, y2.imag]
__m256 ymm1 = _mm256_movehdup_ps(rhs.value);
//ymm2 = [x1.img, x1.real, x2.img, x2.real]
__m256 ymm2 = _mm256_permute_ps(lhs.value, 0b10110001);
//ymm4 = [x.img * y.img, x.real * y.img]
__m256 ymm4 = _mm256_mul_ps(ymm2, ymm1);
//ymm5 = subadd((lhs * ymm0), ymm4)
#ifdef __FMA__
__m256 ymm5 = _mm256_fmsubadd_ps(lhs.value, ymm0, ymm4);
#else
__m256 t1 = _mm256_mul_ps(lhs.value, ymm0);
__m256 t2 = _mm256_sub_ps(_mm256_set1_ps(0.0), ymm4);
__m256 ymm5 = _mm256_addsub_ps(t1, t2);
#endif
//ymm3 = [y.imag^2, y.imag^2]
__m256 ymm3 = _mm256_mul_ps(ymm1, ymm1);
//ymm0 = (ymm0 * ymm0 + ymm3)
#ifdef __FMA__
ymm0 = _mm256_fmadd_ps(ymm0, ymm0, ymm3);
#else
__m256 t3 = _mm256_mul_ps(ymm0, ymm0);
ymm0 = _mm256_add_ps(t3, ymm3);
#endif
//result = ymm5 / ymm0
return _mm256_div_ps(ymm5, ymm0);
}
// PRE: all vectors aligned,
// imag_c = [i1,i1,...,i4,i4]
// vec = [v1r,v1i,...,v4r,v4i]
// component-wise multiplication
// POST: returns [-i1*v1i,i1*v1r,...,-i4*v4i,i4*v4r]
inline __m256 avx_multiply_float_imag_(const __m256& imag_c, const __m256& vec) {
static const __m256 zero = _mm256_setzero_ps();
__m256 vec1 = _mm256_mul_ps(imag_c,vec);
vec1 = _mm256_permute_ps(vec1,0xB1);
return _mm256_addsub_ps(zero,vec1);
}