public void LogIntegrateTest()
{
(MultiPrecision <Pow2.N4> actual, _) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .Log, 1, 2);
MultiPrecision <Pow2.N4> expected = 2 * MultiPrecision <Pow2.N4> .Log(2) - 1;
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 1));
}
public void LogDiffTest()
{
(MultiPrecision <Pow2.N4> actual, MultiPrecision <Pow2.N4> error) = MultiPrecisionUtil.FiniteDifference <Pow2.N4>(MultiPrecision <Pow2.N4> .Log, 1);
MultiPrecision <Pow2.N4> expected = 1;
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 16));
}
public void ZeroIntegrateTest()
{
(MultiPrecision <Pow2.N4> actual, _) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .Cube, -1, 1);
MultiPrecision <Pow2.N4> expected = 0;
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 1));
}
public void PolyIntegrateTest()
{
(MultiPrecision <Pow2.N4> actual, _) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .Square, 0, 1);
MultiPrecision <Pow2.N4> expected = MultiPrecision <Pow2.N4> .One / 3;
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 1));
}
public void SinIntegrateTest()
{
(MultiPrecision <Pow2.N4> actual, _) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .SinPI, 0, 1);
MultiPrecision <Pow2.N4> expected = 2 / MultiPrecision <Pow2.N4> .PI;
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 1));
}
public void ExpIntegrateTest()
{
(MultiPrecision <Pow2.N4> actual, _) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .Exp, 1, 2);
MultiPrecision <Pow2.N4> expected = MultiPrecision <Pow2.N4> .E * (MultiPrecision <Pow2.N4> .E - 1);
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(expected, actual, 1));
}
static void Main(string[] args)
{
//MultiPrecisionUtil.RichardsonExtrapolation<Pow2.N4>.R(5);
//MultiPrecisionUtil.RichardsonExtrapolation<Pow2.N4> extrapolation = new();
//
//extrapolation.Append(1 / 2m);
//extrapolation.Append(17 / 64m);
//extrapolation.Append(197 / 1024m);
(var value, var error) = MultiPrecisionUtil.RombergIntegrate <Pow2.N4>(MultiPrecision <Pow2.N4> .Log, 1, 2);
Console.WriteLine("END");
Console.Read();
}
public void NewtonRaphsonRootFindingTest()
{
MultiPrecision <Pow2.N8> f(MultiPrecision <Pow2.N8> x)
{
return(x * x * x - 2);
}
MultiPrecision <Pow2.N8> df(MultiPrecision <Pow2.N8> x)
{
return(3 * x * x);
}
MultiPrecision <Pow2.N8> y = MultiPrecisionUtil.NewtonRaphsonRootFinding <Pow2.N8>(2, f, df);
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(y, MultiPrecision <Pow2.N8> .Cbrt(2), 1));
}
public void HalleyRootFindingTest()
{
MultiPrecision <Pow2.N8> f(MultiPrecision <Pow2.N8> x)
{
return(x * x * x - 2);
}
(MultiPrecision <Pow2.N8> d1, MultiPrecision <Pow2.N8> d2) df(MultiPrecision <Pow2.N8> x)
{
return(3 * x * x, 6 * x);
}
MultiPrecision <Pow2.N8> y = MultiPrecisionUtil.HalleyRootFinding <Pow2.N8>(2, f, df);
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(y, MultiPrecision <Pow2.N8> .Cbrt(2), 1));
}
private static MultiPrecision <N> InverseErfcRootFinding(MultiPrecision <N> x)
{
MultiPrecision <N> s = 2 / Sqrt(PI);
MultiPrecision <N> z0;
if (Length <= 4)
{
const double a = 0.147;
MultiPrecision <Pow2.N4> xl4 = x.Convert <Pow2.N4>();
MultiPrecision <Pow2.N4> lg = MultiPrecision <Pow2.N4> .Log((2 - xl4) *xl4);
MultiPrecision <Pow2.N4> lga = 2 / (MultiPrecision <Pow2.N4> .PI * a) + lg / 2;
z0 = MultiPrecision <Pow2.N4> .Sqrt(MultiPrecision <Pow2.N4> .Sqrt(lga *lga - lg / a) - lga).Convert <N>();
}
else
{
z0 = MultiPrecision <Pow2.N4> .InverseErfcRootFinding(x.Convert <Pow2.N4>()).Convert <N>();
}
MultiPrecision <N> erfc(MultiPrecision <N> z)
{
return(Erfc(z) - x);
};
(MultiPrecision <N>, MultiPrecision <N>) derfc(MultiPrecision <N> z)
{
MultiPrecision <N> d1 = -Exp(-z * z) * s;
MultiPrecision <N> d2 = -2 * z * d1;
return(d1, d2);
};
MultiPrecision <N> y = MultiPrecisionUtil.HalleyRootFinding(z0, erfc, derfc, break_overshoot: true);
return(y);
}
