Add the constants in std::f32::consts and std::f64::consts as associated constants to the f32 and f64 types (e.g. f32::PI).

Motivation

Currently mathematical constants such as π live in std::{f32, f64}::consts. This is difficult to type and read if written out in full everywhere. Consider

assert_eq!(std::f32::consts::FRAC_PI_4.sin(), std::f32::consts::FRAC_1_SQRT_2);

assert_eq!(f32::FRAC_PI_4.sin(), f32::FRAC_1_SQRT_2);

While it is possible to use std::f32::consts as f32c; or similar, it could be cumbersome to do that in every file in a project which uses mathematical constants heavily.

Also new users of Rust might expect mathematical constants to be there. Currently NAN, INFINITY, etc. are associated constants, and it might be confusing for f32::NAN to exist, but not f32::PI.

Guide-level explanation

When writing code which uses mathematical constants, the associated constants in f32 and f64 can be used. For example, the function f(x) = (π/e)^x can be written as:

fn f(x: f32) -> f32 {
	(f32::PI / f32::E).powf(x)
}

Reference-level explanation

The following constants will be added with their values taken from the respective constants in std::f32::consts and std::f64::consts.

f32::{PI, TAU, FRAC_PI_2, FRAC_PI_3, FRAC_PI_4, FRAC_PI_6, FRAC_PI_8, FRAC_1_PI, FRAC_2_PI, FRAC_2_SQRT_PI, SQRT_2, FRAC_1_SQRT_2, E, LOG2_E, LOG2_10, LOG10_E, LOG10_2, LN_2, LN_10}
f64::{PI, TAU, FRAC_PI_2, FRAC_PI_3, FRAC_PI_4, FRAC_PI_6, FRAC_PI_8, FRAC_1_PI, FRAC_2_PI, FRAC_2_SQRT_PI, SQRT_2, FRAC_1_SQRT_2, E, LOG2_E, LOG2_10, LOG10_E, LOG10_2, LN_2, LN_10}

Drawbacks

Currently it is not possible to use associated constants, so in order to use mathematical constants, it will still be necessary to refer to them by their paths in std.

Even if use-ing associated constants does become possible in a future version of Rust, it will likely never be possible or a good idea to do use f32::*; whereas use std::f32::consts::*; is perhaps more reasonable (although, it's worth mentioning that more mathematical constants could be added in future versions of Rust, so using * is probably not a good idea in general).

This proposal would add many more items to the f32 and f64 types, which might not be desirable.

Rationale and alternatives

The mathematical constants in std could be (planned to be) deprecated. The drawback as mentioned above is that f32::PI, etc. are not use-able. The benefit is that there would be a clear "preferred" path for mathematical constants.
We could create a trait similar to num::traits::FloatConst which houses these constants. The benefits are that the constants can be used in a generic context and we wouldn't be crowding the f32 and f64 types. The downside would be that adding a new constant would be a breaking change for any user types implementing the trait (unless it was made externally unimplementable via the usual "hack" of a pub trait in a private module).
Creating a type for each constant, e.g. struct Pi; then implementing From<f32>, From<f64> for them (and perhaps also Add<f32>, etc.). The benefits are that these could be used in generic contexts, wouldn't be crowding the f32/f64 types, and non-std types could add From<T> implementations for the constants. The downsides are that f32::from(Pi) (which you might end up needing to use in a lot of cases to get type inference to work) is a bit less "ergonomic" than f32::PI, the names would need to change from CONSTANT_CASE to TypeCase, and it might be less intuitive (especially for beginners) that mathematical constants are structs and not constants.

Prior art

The crates half and fixed have these as associated constants on their types.
RFC 2700 originally proposed to do this, but since it was "met with mild resistance", it was decided that it would be left for a later RFC since the focus of 2700 was on adding integral associated constants (e.g. u32::MAX).

Unresolved questions

Future possibilities

In the future, especially if associated constants become use-able, we could deprecate std::{f32, f64}::consts.

assoc_math_consts