lambert_w

Fast evaluation 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 uses a piecewise minimax rational approximation of the function.

Examples

Evaluate the principal branch of the Lambert W function to 50 bits of accuracy:

use lambert_w::accurate::lambert_w_0;
use core::f64::consts::PI;
use approx::assert_abs_diff_eq;

let w = lambert_w_0(PI)?;

assert_abs_diff_eq!(w, 1.0736581947961492);

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

use lambert_w::fast::lambert_w_0;
use core::f64::consts::PI;
use approx::assert_abs_diff_eq;

let w = lambert_w_0(PI)?;

assert_abs_diff_eq!(w, 1.0736581947961492, epsilon = 1e-7);

Speed-accuracy trade-off

The 50-bit accurate versions in the accurate module are more accurate, but slightly slower, than the 24-bit accurate versions in the fast module. fast::lambert_w_0 is around 15% faster than accurate::lambert_w_0 and fast::lambert_w_m1 is around 41% faster than accurate::lambert_w_m1.