Add rsqrt method to Float trait

[cuviper]

From @davll on November 9, 2017 8:48

rsqrt is a widely used math function in game development, and is faster than combining the two functions: recip(sqrt(x)) thanks to x86 SSE instructions RSQRTSS, RSQRTPS, RSQRTSD, and RSQRTPD. Should we consider add rsqrt to Float trait?

• x86/x86_64 SSE: _mm_rsqrt_ps (note that RSQRT instruction is approximate, less accurate than SQRT)
• ARM Neon VRSQRTE
• PowerPC Altivec: vec_rsqrte

Copied from original issue: rust-num/num#343

[cuviper]

This should probably be proposed for the standard library first. So far we don't have any arch-specific code -- I'd rather just have num's impl Float for f64 forward to an optimized/intrinsic call in std.

[cuviper]

From @clarcharr on November 10, 2017 1:8

I agree; it makes sense to offer this in libstd.

[cuviper]

From @davll on November 10, 2017 3:10

Reasonable, I'll propose it in rust-lang/rust.
I'll keep the issue open as reminder.

[clarfonthey]

This appears to have been in libstd originally, then later removed. I don't think that anyone actually opened an issue for it, because I can't find it.

[cuviper]

rust-lang/rust#23549 added:

#[deprecated(since = "1.0.0", reason = "use self.sqrt().recip() instead")]

and then rust-lang/rust#24636 removed it. Neither PR mentioned rsqrt specifically.

If you propose it back to std, make sure to point out the possibility of intrinsics doing better than sqrt().recip(). However, you should also make sure that LLVM isn't already optimizing it to one op. It might not be able to do that because of the difference in precision, but it's worth checking.

[upsuper]

Looks like LLVM wouldn't optimize it automatically. Also it's probably worth following progress on fast math support in rust-lang/rust#21690, since LLVM may generate rsqrt when the corresponding code uses fdiv fast intrinsic, see https://github.com/llvm-mirror/llvm/blob/5e8f334dfad1ec4b8bcaae385d1c2598e18a03af/test/CodeGen/X86/sqrt-fastmath.ll#L245-L279

[andrewhickman]

This should probably be added to the Real trait at the same time