acos

Inverse circular cosine.

SYNOPSIS:

double x, y, acos();
y = acos(x);

DESCRIPTION:

Returns radian angle between 0 and pi whose cosine is x.
Analytically, acos(x) = pi/2 - asin(x). However if |x| is near 1, there is cancellation error in subtracting asin(x) from pi/2. Hence if x < -0.5,   acos(x) = pi - 2.0 * asin(sqrt((1+x)/2)); or if x > +0.5, acos(x) = 2.0 * asin(sqrt((1-x)/2)).

ACCURACY:
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC       -1, 1       50000       3.3e-17     8.2e-18
    IEEE      -1, 1       10^6        2.2e-16     6.5e-17

ERROR MESSAGES:
message      condition      value returned
domain        |x| > 1           NAN