ellie

Incomplete elliptic integral of the second kind.

SYNOPSIS:

double phi, m, y, ellie();
y = ellie(phi, m);

DESCRIPTION:

Approximates the integral:

                phi
                 -
                | |
                |                  2
E(phi_\m) =    |    sqrt(1 - m sin t) dt
                |
              | |
               -
                0

of amplitude phi and modulus m, using the arithmetic - geometric mean algorithm.

ACCURACY:

Tested at random arguments with phi in [-10, 10] and m in [0, 1].
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC        0,2         2000       1.9e-16     3.4e-17
    IEEE     -10,10      150000       3.3e-15     1.4e-16