Lambert W Function (hp-42s)

[lyuka]

(10-05-2020 03:20 PM)Albert Chan Wrote:  This is not as accurate when |x| is huge, but for guess, it does not matter.

BTW, In my function of the eW(x) for real x written in C, the following code is used for the guess.

Code:


#include <math.h>
r = 1.0 / M_E;
y = x < 7.9488901779546342
        ? r + sqrt((r + r) * (x + r)) + 0.3 * (x + r)
        : 1.1 * x / log(0.5 * x) - 1.0; /* Initial value */

[attachment=8779]
This guess y is accurate within +/- 0.09 for -1/e < x < 1E128, and it may reduce one or two itteration for the Newton-Raphson method, however, it may not so useful as it requires extra condition branch and one log() calculation.