public void EllipticNomeAgreement()
{
foreach (double k in TestUtilities.GenerateRealValues(1.0E-2, 1.0, 4))
{
double K = AdvancedMath.EllipticK(k);
double k1 = Math.Sqrt((1.0 - k) * (1.0 + k));
double K1 = AdvancedMath.EllipticK(k1);
double q = AdvancedMath.EllipticNome(k);
// For k << 1, this test fails if formulated as q = e^{\pi K' / K}.
// Problem is that computation of k' looses some digits to cancellation,
// then K' is near singularity so error is amplified, then
// exp function amplifies error some more. Investigation indicates
// that q agrees with Mathematica to nearly all digits, so problem
// isn't in nome function. Run test in log space and don't let k get
// extremely small.
Assert.IsTrue(TestUtilities.IsNearlyEqual(
Math.Log(q),
-Math.PI * K1 / K
));
}
}
