public void EllipticKUnnormalValueTest()
{
MultiPrecision <Pow2.N8> inf = MultiPrecision <Pow2.N8> .EllipticK(1);
Assert.AreEqual(MultiPrecision <Pow2.N8> .PositiveInfinity, inf);
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> .EllipticK(v);
Assert.IsTrue(y.IsNaN);
}
}
public void EllipticKTest()
{
double[] expecteds =
{
1.5707963267948966192,
1.5708922137626348384,
1.5711800327950414382,
1.5716602590854044625,
1.5723336873167065823,
1.5732014357326469747,
1.5742649518971571344,
1.5755260202037926323,
1.5769867712158131421,
1.5786496929386844702,
1.5805176441495632799,
1.5825938699335270894,
1.5848820196044282199,
1.5873861672199078079,
1.5901108349360414470,
1.5930610194881743919,
1.5962422221317835101,
1.5996604824319273643,
1.6033224163535283547,
1.6072352591792112210,
1.6114069138689479181,
1.6158460055790900447,
1.6205619431809133463,
1.6255649887647804235,
1.6308663362907171768,
1.6364782007562008756,
1.6424139195055974161,
1.6486880676135124582,
1.6553165896497853013,
1.6623169505942065935,
1.6697083092365505436,
1.6775117181011207095,
1.6857503548125960429,
1.6944497909214828361,
1.7036383055993221024,
1.7133472533849584282,
1.7236114974339794600,
1.7344699226581490085,
1.7459660469667769180,
1.7581487538531659485,
1.7710731762515814444,
1.7848017705587752735,
1.7994056318875859810,
1.8149661183461979700,
1.8315768754231192499,
1.8493463844468008136,
1.8684012062736826855,
1.8888901602273695618,
1.9109897807518291966,
1.9349115498481339540,
1.9609116453188370344,
1.9893043310480998110,
2.0204807505101105943,
2.0549359644344846108,
2.0933089821785136758,
2.1364440658135019426,
2.1854884692782236869,
2.2420560837698999062,
2.3085186232456553532,
2.3885657507906773322,
2.4884004914010351610,
2.6196934131113362507,
2.8087438358654412952,
3.1398110351826142968,
};
for (int i = 0; i < 64; i++)
{
decimal k = i / 64m;
double expected = expecteds[i];
MultiPrecision <Pow2.N4> y4 = MultiPrecision <Pow2.N4> .EllipticK(k);
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .EllipticK(k);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .EllipticK(k);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .EllipticK(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));
}
}
public void EllipticKNearOneTest()
{
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> .EllipticK(k);
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .EllipticK(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> .EllipticK(k);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .EllipticK(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> .EllipticK(k);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .EllipticK(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> .EllipticK(k);
MultiPrecision <Pow2.N64> y64 = MultiPrecision <Pow2.N64> .EllipticK(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));
}
}
}