Inverse Error Function in C

Question

Is it possible to calculate the inverse error function in C?

I can find erf(x) in <math.h> which calculates the error function, but I can't find anything to do the inverse.

Answer 1

Quick & dirty, tolerance under +-6e-3. Work based on "A handy approximation for the error function and its inverse" by Sergei Winitzki.

C/C++ CODE:

float myErfInv2(float x){
   float tt1, tt2, lnx, sgn;
   sgn = (x < 0) ? -1.0f : 1.0f;

   x = (1 - x)*(1 + x);        // x = 1 - x*x;
   lnx = logf(x);

   tt1 = 2/(PI*0.147) + 0.5f * lnx;
   tt2 = 1/(0.147) * lnx;

   return(sgn*sqrtf(-tt1 + sqrtf(tt1*tt1 - tt2)));
}

MATLAB sanity check:

clear all,  close all, clc 

x = linspace(-1, 1,10000);
% x = 1 - logspace(-8,-15,1000);

a = 0.15449436008930206298828125;
% a = 0.147;

u = log(1-x.^2);  
u1 = 2/(pi*a) + u/2;    u2 = u/a;
y = sign(x).*sqrt(-u1+sqrt(u1.^2 - u2)); 

f = erfinv(x); axis equal

figure(1);
plot(x, [y; f]); legend('Approx. erf(x)', 'erf(x)')

figure(2);
e = f-y;
plot(x, e);

MATLAB Plots: