Implements the Lambert W-function (inverse of f(W) = we^w) of z, useful in solving for we^w = z.

w_lambert.c

// w_lambert.c Lambert W-function
// c99

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double W(double z) {
	double EPSILON = 0.000000000000001;
	double w = 0, ew, wN = z;
	// approximate w_j+1
	while (fabs(w - wN) > EPSILON) {
		w = wN;
		ew = exp(w);
		wN = w - (w*ew - z) / (ew + w*ew);
	}
	return wN;
}

int main(int argc, char **argv) {
	double n = 0;
	if (argc > 0)
		sscanf(argv[1], "%lf", &n);
	printf("W(%lf) = %lf\n", n, W(n));
}