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ellie
Incomplete elliptic integral of the second kind.SYNOPSIS:
double phi, m, y, ellie();
y = ellie(phi, m);
DESCRIPTION:
Approximates the integral:
phi
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| 2
E(phi_\m) = | sqrt(1 - m sin t) dt
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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