asinh

Inverse hyperbolic sine.

SYNOPSIS:

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

DESCRIPTION:

Returns the inverse hyperbolic sine of an argument.

If |x| < 0.5, the function is approximated by a rational form x + x**3 P(x)/Q(x).
Otherwise, asinh(x) = log(x + sqrt(1 + x*x)).

ACCURACY:
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC      -3,3         75000       4.6e-17     1.1e-17
    IEEE     -1,1         30000       3.7e-16     7.8e-17
    IEEE      1,3         30000       2.5e-16     6.7e-17