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