Is it possible to have GCC inline vectorized trig functions?

Question

Cosine and sine are computed with Horner's method and a Chebyshev polynomial, e.g. a0 + x(a1 + x(a2 + ...))). The fused-multiply add instructions this generates form a dependency chain, meaning we can only execute one every clock cycle.

This is a waste, so in a code where many trig functions are called, such as the following, we would ideally evaluate two trig functions at the same time, and interleave the instructions of Horner's method.

However, gcc 15.2.0 generates calls to glibc's vectorized trig implementations, rather than inlining it ( https://godbolt.org/z/sWfMfW93b ), even with -flto, which inhibits the interleaving of instructions. How can I get gcc to produce the assembly I want?

#include <math.h>

#define LANES 4

void twiddle(double * restrict x_r, double * restrict x_i, int m, int n)
{
    double angles[LANES];
    for (int k = 0; k < m; k++) {
        for (int j = 0; j < n; j += LANES) {
            double base = -2.0 * M_PI / (m * n) * k * j;
            #pragma omp simd
            for (int j2 = 0; j2 < LANES; j2++) {
                angles[j2] = base * j2;
            }
            #pragma omp simd
            for (int j2 = 0; j2 < LANES; j2++) {
                double tmp_r = cos(angles[j2]) * x_r[k * n + (j + j2)] - 
                               sin(angles[j2]) * x_i[k * n + (j + j2)];
                double tmp_i = cos(angles[j2]) * x_i[k * n + (j + j2)] + 
                               sin(angles[j2]) * x_r[k * n + (j + j2)];
                x_r[k * n + (j + j2)] = tmp_r;
                x_i[k * n + (j + j2)] = tmp_i;
            }
        }

    }
}

Generated hot-loop:

.L4:
  vxorpd %xmm5, %xmm5, %xmm5
  vcvtsi2sdl %ebx, %xmm5, %xmm0
  vmulsd -120(%rbp), %xmm0, %xmm0
  vmovddup %xmm0, %xmm0
  vandpd .LC1(%rip), %xmm0, %xmm1
  vmulpd .LC2(%rip), %xmm0, %xmm0
  vmovdqa %xmm1, -80(%rbp)
  vmovapd %xmm0, -64(%rbp)
  vmovapd -80(%rbp), %ymm0
  call _ZGVdN4v_sin
  vmovapd %ymm0, -112(%rbp)
  vmovapd -80(%rbp), %ymm0
  call _ZGVdN4v_cos
  vmovupd (%r15,%rbx,8), %ymm1
  vmovapd -112(%rbp), %ymm4
  vmovapd %ymm0, %ymm3
  vmovupd (%r14,%rbx,8), %ymm0
  vmulpd %ymm3, %ymm1, %ymm2
  vmulpd %ymm4, %ymm1, %ymm1
  vfmadd231pd %ymm0, %ymm4, %ymm2
  vfmsub132pd %ymm3, %ymm1, %ymm0
  vmovupd %ymm2, (%r15,%rbx,8)
  vmovupd %ymm0, (%r14,%rbx,8)
  addq $4, %rbx
  cmpq %rbx, %r12
  jne .L4

Answer 1

1. You cannot make GCC inline its own sin/cos
2. You need to write something on your own or use C source level libraries like SLEEF

Example of self written code: https://godbolt.org/z/Ysc8KxWeY