acosh

Inverse hyperbolic cosine.

SYNOPSIS:

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

DESCRIPTION:

Returns the inverse hyperbolic cosine of an argument.

If 1 <= x < 1.5, a rational approximation:

sqrt(z) * P(z)/Q(z)

where z = x-1, is used. Otherwise:

        acosh(x) = log(x + sqrt((x-1)(x+1)).

ACCURACY:

                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC       1,3         30000       4.2e-17     1.1e-17
    IEEE      1,3         30000       4.6e-16     8.7e-17

ERROR MESSAGES:

message     condition      value returned
domain       |x| < 1            NAN