Fast evaluation of the real valued parts of the principal and secondary branches of the Lambert W function using the method of Toshio Fukushima to either 24 or 50 bits of accuracy.

This method works by splitting the domain of the function into subdomains, and on each subdomain it uses a rational function evaluated on a simple transformation of the input to describe the function.
It is implemented in code as conditional switches on the input value followed by either a square root (and possibly a division) or a logarithm and then a series of multiplications and additions by fixed constants and finished with a division.

The functions with 50 bits of accuracy use higher degree polynomials in the rational functions, and thus more of the multiplications and additions by constants.

#![no_std] compatible.

Compute the value of the Omega constant with the principal branch of the Lambert W function to 50 bits of accuracy:

use lambert_w::lambert_w0;

let Ω = lambert_w0(1.0);

assert_abs_diff_eq!(Ω, 0.5671432904097838);

or to only 24 bits of accuracy, but with faster execution time:

use lambert_w::sp_lambert_w0;

let Ω = sp_lambert_w0(1.0);

assert_abs_diff_eq!(Ω, 0.5671432904097838, epsilon = 1e-7);

Evaluate the secondary branch of the Lambert W function at -ln(2)/2 to 50 and 24 bits of accuracy:

use lambert_w::{lambert_wm1, sp_lambert_wm1};

let z = -f64::ln(2.0) / 2.0;

let mln4_50b = lambert_wm1(z);
let mln4_24b = sp_lambert_wm1(z);


assert_abs_diff_eq!(mln4_50b, -f64::ln(4.0));
assert_abs_diff_eq!(mln4_24b, -f64::ln(4.0), epsilon = 1e-9);

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.