public void GammaBorderTest()
{
MultiPrecision <Pow2.N8>[] borders = new MultiPrecision <Pow2.N8>[] { 0.5, 1 };
foreach (MultiPrecision <Pow2.N8> b in borders)
{
List <MultiPrecision <Pow2.N8> > ys = new();
foreach (MultiPrecision <Pow2.N8> x in TestTool.EnumerateNeighbor(b))
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Gamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
TestTool.Tolerance(Approx.Gamma((double)x), y, ignore_sign: true);
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 2);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
Console.Write("\n");
}
}
public void GammaApproxTest()
{
Assert.AreEqual(1, Approx.Gamma(1), 1e-10);
Assert.AreEqual(1, Approx.Gamma(2), 1e-10);
Assert.AreEqual(2, Approx.Gamma(3), 1e-10);
Assert.AreEqual(6, Approx.Gamma(4), 1e-10);
Assert.AreEqual(24, Approx.Gamma(5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI) * 4 / 3, Approx.Gamma(-1.5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI) * -2, Approx.Gamma(-0.5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI), Approx.Gamma(0.5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI) / 2, Approx.Gamma(1.5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI) * 3 / 4, Approx.Gamma(2.5), 1e-10);
Assert.AreEqual(Math.Sqrt(Math.PI) * 15 / 8, Approx.Gamma(3.5), 1e-10);
}
public void GammaTest()
{
for (int i = -200; i < 200; i++)
{
if (i <= 0 && i % 4 == 0)
{
continue;
}
MultiPrecision <Pow2.N8> x = MultiPrecision <Pow2.N8> .Ldexp(MultiPrecision <Pow2.N8> .One, -2) * i;
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Gamma(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(Approx.Gamma((double)x), y, rateerr: 1e-10, ignore_sign: true);
}
Assert.IsTrue(1 == MultiPrecision <Pow2.N8> .Gamma(1));
Assert.IsTrue(1 == MultiPrecision <Pow2.N8> .Gamma(2));
Assert.IsTrue(2 == MultiPrecision <Pow2.N8> .Gamma(3));
Assert.IsTrue(6 == MultiPrecision <Pow2.N8> .Gamma(4));
Assert.IsTrue(24 == MultiPrecision <Pow2.N8> .Gamma(5));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI) * 4 / 3,
MultiPrecision <Pow2.N8> .Gamma(-1.5),
2
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI) * -2,
MultiPrecision <Pow2.N8> .Gamma(-0.5),
2
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI),
MultiPrecision <Pow2.N8> .Gamma(0.5),
2
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI) / 2,
MultiPrecision <Pow2.N8> .Gamma(1.5),
2
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI) * 3 / 4,
MultiPrecision <Pow2.N8> .Gamma(2.5),
2
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .Sqrt(MultiPrecision <Pow2.N8> .PI) * 15 / 8,
MultiPrecision <Pow2.N8> .Gamma(3.5),
2
));
}