Optimise floating point is_finite (2x) and is_infinite (1.6x).

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
6284190
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));
}
```

Author: huonw

src/libcore/num/f32.rs

@@ -161,6 +161,14 @@ impl f32 {
         self != self
     }
 
+    // FIXME(#50145): `abs` is publicly unavailable in libcore due to
+    // concerns about portability, so this implementation is for
+    // private use internally.
+    #[inline]
+    fn abs_private(self) -> f32 {
+        f32::from_bits(self.to_bits() & 0x7fff_ffff)
+    }
+
     /// Returns `true` if this value is positive infinity or negative infinity and
     /// false otherwise.
     ///
@@ -181,7 +189,7 @@ impl f32 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn is_infinite(self) -> bool {
-        self == INFINITY || self == NEG_INFINITY
+        self.abs_private() == INFINITY
     }
 
     /// Returns `true` if this number is neither infinite nor `NaN`.
@@ -203,7 +211,9 @@ impl f32 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn is_finite(self) -> bool {
-        !(self.is_nan() || self.is_infinite())
+        // There's no need to handle NaN separately: if self is NaN,
+        // the comparison is not true, exactly as desired.
+        self.abs_private() < INFINITY
     }
 
     /// Returns `true` if the number is neither zero, infinite,

src/libcore/num/f64.rs

@@ -161,6 +161,14 @@ impl f64 {
         self != self
     }
 
+    // FIXME(#50145): `abs` is publicly unavailable in libcore due to
+    // concerns about portability, so this implementation is for
+    // private use internally.
+    #[inline]
+    fn abs_private(self) -> f64 {
+        f64::from_bits(self.to_bits() & 0x7fff_ffff_ffff_ffff)
+    }
+
     /// Returns `true` if this value is positive infinity or negative infinity and
     /// false otherwise.
     ///
@@ -181,7 +189,7 @@ impl f64 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn is_infinite(self) -> bool {
-        self == INFINITY || self == NEG_INFINITY
+        self.abs_private() == INFINITY
     }
 
     /// Returns `true` if this number is neither infinite nor `NaN`.
@@ -203,7 +211,9 @@ impl f64 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn is_finite(self) -> bool {
-        !(self.is_nan() || self.is_infinite())
+        // There's no need to handle NaN separately: if self is NaN,
+        // the comparison is not true, exactly as desired.
+        self.abs_private() < INFINITY
     }
 
     /// Returns `true` if the number is neither zero, infinite,