public void EllipticEUnnormalValueTest()
{
MultiPrecision <Pow2.N8>[] nans = new MultiPrecision <Pow2.N8>[] {
-1,
2,
MultiPrecision <Pow2.N8> .PositiveInfinity,
MultiPrecision <Pow2.N8> .NegativeInfinity,
MultiPrecision <Pow2.N8> .NaN
};
foreach (MultiPrecision <Pow2.N8> v in nans)
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .EllipticE(v);
Assert.IsTrue(y.IsNaN);
}
}
public void EllipticENearOneTest()
{
const int exponent = -32;
{
MultiPrecision <Pow2.N4>[] ks =
{
MultiPrecision <Pow2.N4> .BitDecrement(1),
MultiPrecision <Pow2.N4> .BitDecrement(1 - MultiPrecision <Pow2.N4> .Ldexp(1,exponent)),
1 - MultiPrecision <Pow2.N4> .Ldexp(1, exponent),
MultiPrecision <Pow2.N4> .BitIncrement(1 - MultiPrecision <Pow2.N4> .Ldexp(1,exponent)),
};
foreach (var k in ks)
{
MultiPrecision <Pow2.N4> y4 = MultiPrecision <Pow2.N4> .EllipticE(k);
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .EllipticE(k.Convert <Pow2.N8>());
Console.WriteLine(k.ToHexcode());
Console.WriteLine(y4);
Console.WriteLine(y4.ToHexcode());
Console.WriteLine(y8.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(y4, y8.Convert <Pow2.N4>(), 32));
}
}
{
MultiPrecision <Pow2.N8>[] ks =
{
MultiPrecision <Pow2.N8> .BitDecrement(1),
MultiPrecision <Pow2.N8> .BitDecrement(1 - MultiPrecision <Pow2.N8> .Ldexp(1,exponent)),
1 - MultiPrecision <Pow2.N8> .Ldexp(1, exponent),
MultiPrecision <Pow2.N8> .BitIncrement(1 - MultiPrecision <Pow2.N8> .Ldexp(1,exponent)),
};
foreach (var k in ks)
{
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .EllipticE(k);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .EllipticE(k.Convert <Pow2.N16>());
Console.WriteLine(k.ToHexcode());
Console.WriteLine(y8);
Console.WriteLine(y8.ToHexcode());
Console.WriteLine(y16.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(y8, y16.Convert <Pow2.N8>(), 64));
}
}
{
MultiPrecision <Pow2.N16>[] ks =
{
MultiPrecision <Pow2.N16> .BitDecrement(1),
MultiPrecision <Pow2.N16> .BitDecrement(1 - MultiPrecision <Pow2.N16> .Ldexp(1,exponent)),
1 - MultiPrecision <Pow2.N16> .Ldexp(1, exponent),
MultiPrecision <Pow2.N16> .BitIncrement(1 - MultiPrecision <Pow2.N16> .Ldexp(1,exponent)),
};
foreach (var k in ks)
{
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .EllipticE(k);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .EllipticE(k.Convert <Pow2.N32>());
Console.WriteLine(k.ToHexcode());
Console.WriteLine(y16);
Console.WriteLine(y16.ToHexcode());
Console.WriteLine(y32.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N16> .NearlyEqualBits(y16, y32.Convert <Pow2.N16>(), 128));
}
}
{
MultiPrecision <Pow2.N32>[] ks =
{
MultiPrecision <Pow2.N32> .BitDecrement(1),
MultiPrecision <Pow2.N32> .BitDecrement(1 - MultiPrecision <Pow2.N32> .Ldexp(1,exponent)),
1 - MultiPrecision <Pow2.N32> .Ldexp(1, exponent),
MultiPrecision <Pow2.N32> .BitIncrement(1 - MultiPrecision <Pow2.N32> .Ldexp(1,exponent)),
};
foreach (var k in ks)
{
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .EllipticE(k);
MultiPrecision <Pow2.N64> y64 = MultiPrecision <Pow2.N64> .EllipticE(k.Convert <Pow2.N64>());
Console.WriteLine(k.ToHexcode());
Console.WriteLine(y32);
Console.WriteLine(y32.ToHexcode());
Console.WriteLine(y64.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N32> .NearlyEqualBits(y32, y64.Convert <Pow2.N32>(), 256));
}
}
}
public void EllipticETest()
{
double[] expecteds =
{
1.5707963267948966192,
1.5704127613492695165,
1.5692612206533624497,
1.5673391612665478615,
1.5646423092625568944,
1.5611646068271051886,
1.5568981352002313413,
1.5518330115106139179,
1.5459572561054650350,
1.5392566258222057728,
1.5317144071889349200,
1.5233111616582831849,
1.5140244125021051094,
1.5038282596752396589,
1.4926929044313435533,
1.4805840591964266491,
1.4674622093394271555,
1.4532816807130160277,
1.4379894480673063924,
1.4215235911932390135,
1.4038112620302649031,
1.3847659565934378968,
1.3642837714465253786,
1.3422381292201173264,
1.3184721079946209974,
1.2927868476159125057,
1.2649231666855462759,
1.2345305754464217204,
1.2011106307369146978,
1.1639009595942138950,
1.1215931702323738421,
1.0714005291435245968,
1.0000000000000000000
};
for (int i = 0; i <= 32; i++)
{
decimal k = i / 32m;
double expected = expecteds[i];
MultiPrecision <Pow2.N4> y4 = MultiPrecision <Pow2.N4> .EllipticE(k);
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .EllipticE(k);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .EllipticE(k);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .EllipticE(k);
Console.WriteLine(k);
Console.WriteLine(y4);
Console.WriteLine(y4.ToHexcode());
Console.WriteLine(y8.ToHexcode());
Console.WriteLine(y16.ToHexcode());
Console.WriteLine(y32.ToHexcode());
Assert.AreEqual(expected, (double)y4, expected * 1e-15);
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(y4, y8.Convert <Pow2.N4>(), 1));
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(y8, y16.Convert <Pow2.N8>(), 1));
Assert.IsTrue(MultiPrecision <Pow2.N16> .NearlyEqualBits(y16, y32.Convert <Pow2.N16>(), 1));
}
}
