math/2020/03/11/SinCosPi

[utterances-bot]

A design and implementation of sincospi in binary32

Walks through constructing faithfully rounded $\sin\left(\pi x\right)$ and $\cos\left(\pi x\right)$.

http://marc-b-reynolds.github.io/math/2020/03/11/SinCosPi.html

[VinInn]

Really nice implementation. Pretty fast once vectorized...

unfortunately compilers refuse to vectorize

dst[q  ] = c;
dst[q^1] = s;

so I had to change it in

 dst[0] = q==0 ? s :c;
 dst[1] = q==0 ? c :s;

see https://godbolt.org/z/e6fdfvTM1

I think there is no real way to convince the compiler that q can only be 0 or 1...

[VinInn]

btw I'm under the impression that

c=fpminimax(cos(pi*x), [|0,2,4,6|], [|24...|], [0;1/4], floating, absolute);

corresponding to

f32_cospi_6_k[] = { 0x1p0, -0x1.3bd3ap2, 0x1.03b132p2, -0x1.4ea1aep0};

produces a better approximation that "relative"

[Marc-B-Reynolds]

@VinInn Thanks for your feedback. Yeah the return the result is not ideal. And you are also correct that optimizing for abs error does produce better cosine coefficients.