Clang and Eigen's alternatives to complex multiplication SIMD

Mon, 11 Mar 2024 20:00:00 +0800

Clang isn’t much better than MSVC for complex number multiplication, while Eigen is equivalent to GCC but uses slightly different instructions.

Complex Number Multiplication Is Probably Not Common Enough

I think I might have bashed MSVC too much on the last post; trying to vectorise our simple 4-element complex number multiplication using clang with AVX instructions delivers similarly poor results:

#include <complex>

void cmul(
 const std::complex<float>* __restrict__ x,
 const std::complex<float>* __restrict__ y,
 std::complex<float>* __restrict__ z
){
 for (int i = 0; i < 4; ++i)
 z[i] = x[i] * y[i];
}

void mul(
 const float* __restrict__ x,
 const float* __restrict__ y,
 float* __restrict__ z
){
 for (int i = 0; i < 8; ++i)
 z[i] = x[i] * y[i];
}

cmul(std::complex<float> const*, std::complex<float> const*, std::complex<float>*): # @cmul(std::complex<float> const*, std::complex<float> const*, std::complex<float>*)
 vmovsd xmm0, qword ptr [rdi] # xmm0 = mem[0],zero
 vmovsd xmm1, qword ptr [rsi] # xmm1 = mem[0],zero
 vbroadcastss xmm2, xmm0
 vmovshdup xmm0, xmm0 # xmm0 = xmm0[1,1,3,3]
 vshufps xmm3, xmm1, xmm1, 225 # xmm3 = xmm1[1,0,2,3]
 vmulps xmm0, xmm3, xmm0
 vfmaddsub231ps xmm0, xmm1, xmm2 # xmm0 = (xmm1 * xmm2) +/- xmm0
 vmovlps qword ptr [rdx], xmm0
 vmovsd xmm0, qword ptr [rdi + 8] # xmm0 = mem[0],zero
 vmovsd xmm1, qword ptr [rsi + 8] # xmm1 = mem[0],zero
 vbroadcastss xmm2, xmm0
 vmovshdup xmm0, xmm0 # xmm0 = xmm0[1,1,3,3]
 vshufps xmm3, xmm1, xmm1, 225 # xmm3 = xmm1[1,0,2,3]
 vmulps xmm0, xmm3, xmm0
 vfmaddsub231ps xmm0, xmm1, xmm2 # xmm0 = (xmm1 * xmm2) +/- xmm0
 vmovlps qword ptr [rdx + 8], xmm0
 vmovsd xmm0, qword ptr [rdi + 16] # xmm0 = mem[0],zero
 vmovsd xmm1, qword ptr [rsi + 16] # xmm1 = mem[0],zero
 vbroadcastss xmm2, xmm0
 vmovshdup xmm0, xmm0 # xmm0 = xmm0[1,1,3,3]
 vshufps xmm3, xmm1, xmm1, 225 # xmm3 = xmm1[1,0,2,3]
 vmulps xmm0, xmm3, xmm0
 vfmaddsub231ps xmm0, xmm1, xmm2 # xmm0 = (xmm1 * xmm2) +/- xmm0
 vmovlps qword ptr [rdx + 16], xmm0
 vmovsd xmm0, qword ptr [rdi + 24] # xmm0 = mem[0],zero
 vmovsd xmm1, qword ptr [rsi + 24] # xmm1 = mem[0],zero
 vbroadcastss xmm2, xmm0
 vmovshdup xmm0, xmm0 # xmm0 = xmm0[1,1,3,3]
 vshufps xmm3, xmm1, xmm1, 225 # xmm3 = xmm1[1,0,2,3]
 vmulps xmm0, xmm3, xmm0
 vfmaddsub231ps xmm0, xmm1, xmm2 # xmm0 = (xmm1 * xmm2) +/- xmm0
 vmovlps qword ptr [rdx + 24], xmm0
 ret
mul(float const*, float const*, float*): # @mul(float const*, float const*, float*)
 vmovups ymm0, ymmword ptr [rsi]
 vmulps ymm0, ymm0, ymmword ptr [rdi]
 vmovups ymmword ptr [rdx], ymm0
 vzeroupper
 ret

Compiled with clang 18.1.0, with -O3 -ffast-math -march=x86-64-v3, this still refuses to vectorise the cmul function correctly, only using the xmm registers. I included the normal real-valued float multiplication to check that clang is indeed able to vectorise that. Note that you still need the __restrict__ keywords for the vectorisation to work. Using -ffast-math doesn’t seem to do anything for us in the real float vectorisation, but it does make the complex-valued vectorisation less verbose.

Clang on icyveins7's blog

Clang and Eigen's alternatives to complex multiplication SIMD

Complex Number Multiplication Is Probably Not Common Enough