[libc-commits] [PATCH] D133400: [libc][math] Implement asinf function correctly rounded for all rounding modes.

[Tue Ly via Phabricator via libc-commits]

lntue added a comment.

In D133400#3774132 <https://reviews.llvm.org/D133400#3774132>, @orex wrote:

> Good job, Tue!
>
> I have an optional suggestion. You can use formula
> `asin(x)=1/2*acos(1-2*x^2)`
> and, of course,
> `acos(x)=pi/2-asin(x)`
> for cases where `|x|>=0.5` Probably it can be much faster than `sqrt`.

Thanks @orex for the suggestion!  Unfortunately the formula `asin(x) = pi/4 - 1/2 * asin(1 - 2*x^2)` only works
well when `|1 - 2*x^2| <= 0.5`, i.e. `0.5 <= |x| <= sqrt(3)/2`.

For `sqrt(3)/2 < |x| <= 1`, we still need some sort of range reduction involving square root.

Nonetheless, I've tried adding another branch for `0.5 <= |x| <= sqrt(3)/2` using the formula
`asin(x) = pi/4 - 1/2 * asin(1 - 2*x^2)` and it actually makes both the throughput and the latency
slightly worse than 2 branches.


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