Accurate Normal Distribution for the HP67/97

[Albert Chan]

Above 1 Exp method, if done on the computer, is almost as fast as direct method.
In other words, the extra precision almost without cost.

PHP Code:

double pdf(double z)            // 1 Exp method
{
    double x = (float) z;       // clear low bits
    double y = x - z;           // y = -h
    double y2 = y * y;
    z = 0.3989422804014327 * exp(-0.5 * x * x);
    x *= y;                     // correction 1
    y = 0.5 * (x+y) * (x-y);    // correction 2
    x += y + (1./3) * x*(y-y2); // correction 3
    return z + x * z;
} 


Updated: fix typo in constant 1/√(2 Pi)