asin

Inverse circular sine.

SYNOPSIS:

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

DESCRIPTION:

Returns the radian angle between -pi/2 and +pi/2 whose sine is x.

A rational function of the form x + x**3 P(x**2)/Q(x**2) is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is transformed by the identity:

    asin(x) = pi/2 - 2 asin(sqrt((1-x)/2)).

ACCURACY:
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC      -1, 1        40000       2.6e-17     7.1e-18
    IEEE     -1, 1        10^6        1.9e-16     5.4e-17

ERROR MESSAGES:

message       condition      value returned
   domain        |x| > 1           NAN