I believe that this is a copy/paste error; this example was using f32,
but it's the docs for f64.

This renames and stabilizes unsafe floating point to integer casts, which are
intended to be the substitute for the currently unsound `as` behavior, once that
changes to safe-but-slower saturating casts.

As discussed in https://github.com/rust-lang/rust/issues/10184

Currently, casting a floating point number to an integer with `as` is Undefined Behavior if the value is out of range. `-Z saturating-float-casts` fixes this soundness hole by making `as` “saturate” to the maximum or minimum value of the integer type (or zero for `NaN`), but has measurable negative performance impact in some benchmarks. There is some consensus in that thread for enabling saturation by default anyway, but provide an `unsafe fn` alternative for users who know through some other mean that their values are in range.

Use the same API as for integers.

Fixes #57492.

These can both rely on IEEE754 semantics to be made faster, by folding
away the sign with an abs (left private for now), and then comparing
to infinity, letting the NaN semantics of a direct float comparison
handle NaN input properly.

The `abs` bit-fiddling is simple (a single and), and so these new
forms compile down to a few instructions, without branches, e.g. for
f32:

```asm
is_infinite:
        andps   xmm0, xmmword ptr [rip + .LCPI2_0] ; 0x7FFF_FFFF
        ucomiss xmm0, dword ptr [rip + .LCPI2_1]   ; 0x7F80_0000
        setae   al
        ret

is_finite:
        andps   xmm0, xmmword ptr [rip + .LCPI1_0] ; 0x7FFF_FFFF
        movss   xmm1, dword ptr [rip + .LCPI1_1]   ; 0x7F80_0000
        ucomiss xmm1, xmm0
        seta    al
        ret
```

When used in loops/repeatedly, they get even better: the memory
operations (loading the mask 0x7FFFFFFF for abs, and infinity
0x7F80_0000) are likely to be hoisted out of the individual calls, to
be shared, and the `seta`/`setae` are likely to be collapsed into
conditional jumps or moves (or similar).

The old `is_infinite` did two comparisons, and the old `is_finite` did
three (with a branch), and both of them had to check the flags after
every one of those comparison. These functions have had that old
implementation since they were added in
https://github.com/rust-lang/rust/commit/6284190ef9918e05cb9147a2a81100ddcb06fea8
7 years ago.

Benchmark (`abs` is the new form, `std` is the old):

```
test f32_is_finite_abs            ... bench:          55 ns/iter (+/- 10)
test f32_is_finite_std            ... bench:         118 ns/iter (+/- 5)

test f32_is_infinite_abs          ... bench:          53 ns/iter (+/- 1)
test f32_is_infinite_std          ... bench:          84 ns/iter (+/- 6)

test f64_is_finite_abs            ... bench:          52 ns/iter (+/- 12)
test f64_is_finite_std            ... bench:         128 ns/iter (+/- 25)

test f64_is_infinite_abs          ... bench:          54 ns/iter (+/- 5)
test f64_is_infinite_std          ... bench:          93 ns/iter (+/- 23)
```

```rust
 #![feature(test)]
extern crate test;

use std::{f32, f64};
use test::Bencher;

const VALUES_F32: &[f32] = &[0.910, 0.135, 0.735, -0.874, 0.518, 0.150, -0.527, -0.418, 0.449, -0.158, -0.064, -0.144, -0.948, -0.103, 0.225, -0.104, -0.795, 0.435, 0.860, 0.027, 0.625, -0.848, -0.454, 0.359, -0.930, 0.067, 0.642, 0.976, -0.682, -0.035, 0.750, 0.005, -0.825, 0.731, -0.850, -0.740, -0.118, -0.972, 0.888, -0.958, 0.086, 0.237, -0.580, 0.488, 0.028, -0.552, 0.302, 0.058, -0.229, -0.166, -0.248, -0.430, 0.789, -0.122, 0.120, -0.934, -0.911, -0.976, 0.882, -0.410, 0.311, -0.611, -0.758, 0.786, -0.711, 0.378, 0.803, -0.068, 0.932, 0.483, 0.085, 0.247, -0.128, -0.839, -0.737, -0.605, 0.637, -0.230, -0.502, 0.231, -0.694, -0.400, -0.441, 0.142, 0.174, 0.681, -0.763, -0.608, 0.848, -0.550, 0.883, -0.212, 0.876, 0.186, -0.909, 0.401, -0.533, -0.961, 0.539, -0.298, -0.448, 0.223, -0.307, -0.594, 0.629, -0.534, 0.959, 0.349, -0.926, -0.523, -0.895, -0.157, -0.074, -0.060, 0.513, -0.647, -0.649, 0.428, 0.401, 0.391, 0.426, 0.700, 0.880, -0.101, 0.862, 0.493, 0.819, -0.597];

 #[bench]
fn f32_is_infinite_std(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F32).iter().any(|x| x.is_infinite()));
}
 #[bench]
fn f32_is_infinite_abs(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F32).iter().any(|x| x.abs()== f32::INFINITY));
}
 #[bench]
fn f32_is_finite_std(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F32).iter().all(|x| x.is_finite()));
}
 #[bench]
fn f32_is_finite_abs(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F32).iter().all(|x| x.abs() < f32::INFINITY));
}

const VALUES_F64: &[f64] = &[0.910, 0.135, 0.735, -0.874, 0.518, 0.150, -0.527, -0.418, 0.449, -0.158, -0.064, -0.144, -0.948, -0.103, 0.225, -0.104, -0.795, 0.435, 0.860, 0.027, 0.625, -0.848, -0.454, 0.359, -0.930, 0.067, 0.642, 0.976, -0.682, -0.035, 0.750, 0.005, -0.825, 0.731, -0.850, -0.740, -0.118, -0.972, 0.888, -0.958, 0.086, 0.237, -0.580, 0.488, 0.028, -0.552, 0.302, 0.058, -0.229, -0.166, -0.248, -0.430, 0.789, -0.122, 0.120, -0.934, -0.911, -0.976, 0.882, -0.410, 0.311, -0.611, -0.758, 0.786, -0.711, 0.378, 0.803, -0.068, 0.932, 0.483, 0.085, 0.247, -0.128, -0.839, -0.737, -0.605, 0.637, -0.230, -0.502, 0.231, -0.694, -0.400, -0.441, 0.142, 0.174, 0.681, -0.763, -0.608, 0.848, -0.550, 0.883, -0.212, 0.876, 0.186, -0.909, 0.401, -0.533, -0.961, 0.539, -0.298, -0.448, 0.223, -0.307, -0.594, 0.629, -0.534, 0.959, 0.349, -0.926, -0.523, -0.895, -0.157, -0.074, -0.060, 0.513, -0.647, -0.649, 0.428, 0.401, 0.391, 0.426, 0.700, 0.880, -0.101, 0.862, 0.493, 0.819, -0.597];

 #[bench]
fn f64_is_infinite_std(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F64).iter().any(|x| x.is_infinite()));
}
 #[bench]
fn f64_is_infinite_abs(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F64).iter().any(|x| x.abs() == f64::INFINITY));
}
 #[bench]
fn f64_is_finite_std(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F64).iter().all(|x| x.is_finite()));
}
 #[bench]
fn f64_is_finite_abs(b: &mut Bencher) {
    b.iter(|| test::black_box(VALUES_F64).iter().all(|x| x.abs() < f64::INFINITY));
}
```

Following up to #49896 and #50629. Fixes #32110.

E0689 is weird.

Affected methods are `abs`, `signum`, and `powi`.
CC https://github.com/rust-lang/rust/issues/32110#issuecomment-379503183

… previously in the unstable core::num::Float trait.

Per https://github.com/rust-lang/rust/issues/32110#issuecomment-379503183,
the `abs`, `signum`, and `powi` methods are *not* included for now
since they rely on LLVM intrinsics and we haven’t determined yet whether
those instrinsics lower to calls to libm functions on any platform.

The current `f32|f64.to_degrees` implementation uses a division to calculate 180/π, which causes a loss of precision. Using a constant is still not perfect (implementing a maximally-precise algorithm would come with a high performance cost), but improves precision with a minimal change.

Swapping the conditions generates more efficient x86 assembly. See
https://github.com/rust-lang/rust/pull/46926#issuecomment-354567412.