ACP: More float constants

[joshuarayton]

Proposal

Implement more float constants, namely: sqrt(5), 1/sqrt(5), ln(3)

Problem statement

The need for using floating point representations of the numerical constants.

Motivating examples or use cases

Constant time generation of Fibonacci numbers

#![feature(f128)]
#![feature(more_float_constants)]

use std::f128::consts::PHI;

const FRAC_1_SQRT_5: f128 =
    0.447213595499957939281834733746255247088123671922305144854179_f128;

fn fib(n: i32) -> u64 {
    return (FRAC_1_SQRT_5 * PHI.powi(n)).round() as u64
}

pub fn main() {
    for n in 1..94 {
        println!("{}", fib(n));
    }
}

Generates all Fibonacci numbers that fit in u64

Solution sketch

In core/src/num/f32.rs:

pub mod consts {
    // ...

    // sqrt(5)
    pub const SQRT_5: f32 = 2.236067977499789696409173668731276235_f32;

    // 1/sqrt(5)
    pub const FRAC_1_SQRT_5: f32 = 0.447213595499957939281834733746255247_f32;

    // ln(3)
    pub const LN_3: f32 = 1.098612288668109691395245236922525704_f32;

    // ...
}

Basically the same in f64.rs, f16.rs, f128.rs

Alternatives

Links and related work

rust-lang/rust#146934
rust-lang/rust#146939
rust-lang/rust#103883
rust-lang/rust#125253
rust-lang/rust#116909
#383
#119

[kennytm]

#119 ($\phi, \gamma, \frac1{\sqrt\pi}, \sqrt3, \frac1{\sqrt3}$) was accepted because they are part of C++20's list of constants

#383 ($\frac1{\sqrt{2\pi}}$) was accepted because it indeed appears in many formula e.g. the normal distribution, error function, Fourier transform, Black-Scholes model etc.

What is the reason we want $\sqrt5, \frac1{\sqrt5}, \ln 3$ in the standard library? IMO calculating Fibonacci number using $F_n = \left\lfloor \frac{\phi^n}{\sqrt5} \right\rceil$ is not one ($F_{2n} = F_n(2F_{n-1}+F_n)$ is perhaps more efficient), and this does not explain $\sqrt5, \ln 3$ either.

[joshuarayton]

What is the reason we want $\sqrt{5}$ , $\frac{1}{\sqrt{5}}$, $\ln 3$ in the standard library? IMO calculating Fibonacci number using $F_n = ⌊ \frac{\phi^n}{\sqrt{5}} ⌉$ is not one ( $F_{2n} = F_n(2F_{n-1} + F_n)$ ) is perhaps more efficient), and this does not explain $\sqrt{5}$ , $\ln 3$ either.

$\sqrt{5}$ was proposed in a comment on the issue (rust-lang/rust#103883 (comment))

I agree with this, it is useful in geometry and trigonometry. When working with the golden ratio, the sqrt(5) is often useful by itself too. It's also used with Diophantine approximations. At least 8 others seemed to agree with this comment.

$\frac{1}{\sqrt{5}}$ was proposed by me in the pull request. This is so division by the sqrt(5) can be done by reciprocal multiplication at full floating point precision.

$\ln 3$ was originally proposed in the original issue (rust-lang/rust#103883) for additional constants.

I no longer think it's needed. Searching GitHub for rust projects that contain the beginning of the decimal expansion didn't give results. It's not even a constant on Wikipedia's list of mathematical constants and it doesn't have it's own Wikipedia page unlike sqrt(5).