# A Double Precision Puzzle with the Gaussian

Mar 20, 2013 · 1 minute read · CommentsSome library computes $$e^{-\frac{x^2}{2}}$$ the following way:

xsq = fint(x * 1.6) / 1.6;

del = (x - xsq) * (x + xsq);

result = exp(-xsq * xsq * 0.5) * exp(-del * 0.5);

where fint(z) computes the floor of z.

Basically, x*x is rewritten as xsq*xsq+del. I have seen that trick once before, but I just can’t figure out where and why (except that it is probably related to high accuracy issues).

The answer is in the next post.