public void DigammaUnnormalValueTest()
{
MultiPrecision <Pow2.N8>[] nans = new MultiPrecision <Pow2.N8>[] {
MultiPrecision <Pow2.N8> .NaN,
0
- 1,
-2,
MultiPrecision <Pow2.N8> .NegativeInfinity
};
foreach (MultiPrecision <Pow2.N8> v in nans)
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Digamma(v);
Assert.IsTrue(y.IsNaN);
}
MultiPrecision <Pow2.N8>[] infs = new MultiPrecision <Pow2.N8>[] {
MultiPrecision <Pow2.N8> .PositiveInfinity,
};
foreach (MultiPrecision <Pow2.N8> v in infs)
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Digamma(v);
Assert.AreEqual(MultiPrecision <Pow2.N8> .PositiveInfinity, y);
}
}
public void DigammaTest()
{
for (int i = 0; i < 200; i++)
{
MultiPrecision <Pow2.N4> x = i;
MultiPrecision <Pow2.N4> y_expected = MultiPrecision <Pow2.N4> .HarmonicNumber(i) - MultiPrecision <Pow2.N4> .EulerGamma;
MultiPrecision <Pow2.N4> y_actual = MultiPrecision <Pow2.N4> .Digamma(x + 1);
Console.WriteLine(x);
Console.WriteLine(y_expected);
Console.WriteLine(y_actual);
Assert.IsTrue(MultiPrecision <Pow2.N4> .NearlyEqualBits(y_expected, y_actual, 1));
}
for (int i = 0; i < 200; i++)
{
MultiPrecision <Pow2.N8> x = i;
MultiPrecision <Pow2.N8> y_expected = MultiPrecision <Pow2.N8> .HarmonicNumber(i) - MultiPrecision <Pow2.N8> .EulerGamma;
MultiPrecision <Pow2.N8> y_actual = MultiPrecision <Pow2.N8> .Digamma(x + 1);
Console.WriteLine(x);
Console.WriteLine(y_expected);
Console.WriteLine(y_actual);
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(y_expected, y_actual, 1));
}
for (int i = 0; i < 200; i++)
{
MultiPrecision <Pow2.N16> x = i;
MultiPrecision <Pow2.N16> y_expected = MultiPrecision <Pow2.N16> .HarmonicNumber(i) - MultiPrecision <Pow2.N16> .EulerGamma;
MultiPrecision <Pow2.N16> y_actual = MultiPrecision <Pow2.N16> .Digamma(x + 1);
Console.WriteLine(x);
Console.WriteLine(y_expected);
Console.WriteLine(y_actual);
Assert.IsTrue(MultiPrecision <Pow2.N16> .NearlyEqualBits(y_expected, y_actual, 1));
}
for (int i = 0; i < 200; i++)
{
MultiPrecision <Pow2.N32> x = i;
MultiPrecision <Pow2.N32> y_expected = MultiPrecision <Pow2.N32> .HarmonicNumber(i) - MultiPrecision <Pow2.N32> .EulerGamma;
MultiPrecision <Pow2.N32> y_actual = MultiPrecision <Pow2.N32> .Digamma(x + 1);
Console.WriteLine(x);
Console.WriteLine(y_expected);
Console.WriteLine(y_actual);
Assert.IsTrue(MultiPrecision <Pow2.N32> .NearlyEqualBits(y_expected, y_actual, 1));
}
}
public void DigammaP75Test()
{
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
"-1.085860879786472169626886" +
"762817180693170075039333" +
"136450680334967211140389" +
"543644318440519631609944" +
"278149561847054877986358" +
"470142416985643391459506" +
"548485910863320540994877" +
"082382755815236352795801",
MultiPrecision <Pow2.N8> .Digamma(0.75),
2
));
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .Digamma(0.75);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .Digamma(0.75);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .Digamma(0.75);
MultiPrecision <Pow2.N64> y64 = MultiPrecision <Pow2.N64> .Digamma(0.75);
MultiPrecision <Pow2.N128> y128 = MultiPrecision <Pow2.N128> .Digamma(0.75);
MultiPrecision <Pow2.N256> y256 = MultiPrecision <Pow2.N256> .Digamma(0.75);
Console.WriteLine(y8);
Console.WriteLine(y8.ToHexcode());
Console.WriteLine(y16);
Console.WriteLine(y16.ToHexcode());
Console.WriteLine(y32);
Console.WriteLine(y32.ToHexcode());
Console.WriteLine(y64);
Console.WriteLine(y64.ToHexcode());
Console.WriteLine(y128);
Console.WriteLine(y128.ToHexcode());
Console.WriteLine(y256);
Console.WriteLine(y256.ToHexcode());
}
public void DigammaMP25Test()
{
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEqualBits(
"2.9141391202135278303731132" +
"3718281930682992496066686" +
"3549319665032788859610456" +
"3556815594803683900557218" +
"5043815294512201364152985" +
"7583014356608540493451514" +
"0891366794590051229176172" +
"4418476364720419880472602",
MultiPrecision <Pow2.N8> .Digamma(-0.25),
2
));
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .Digamma(-0.25);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .Digamma(-0.25);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .Digamma(-0.25);
MultiPrecision <Pow2.N64> y64 = MultiPrecision <Pow2.N64> .Digamma(-0.25);
MultiPrecision <Pow2.N128> y128 = MultiPrecision <Pow2.N128> .Digamma(-0.25);
MultiPrecision <Pow2.N256> y256 = MultiPrecision <Pow2.N256> .Digamma(-0.25);
Console.WriteLine(y8);
Console.WriteLine(y8.ToHexcode());
Console.WriteLine(y16);
Console.WriteLine(y16.ToHexcode());
Console.WriteLine(y32);
Console.WriteLine(y32.ToHexcode());
Console.WriteLine(y64);
Console.WriteLine(y64.ToHexcode());
Console.WriteLine(y128);
Console.WriteLine(y128.ToHexcode());
Console.WriteLine(y256);
Console.WriteLine(y256.ToHexcode());
}
public void DigammaZeropointTest()
{
const string zeropoint =
"1.4616321449683623412626595423257213284681962040064463512959884085987864403538018102430749927337255927" +
"5055679336553305334161736577846698582917716838164502465254261879204438438197833355977396197607471943" +
"1934937175414059451930109963724166527772172791673250880463960076932978144901475185803414306536810631" +
"0107060169497854579337655771161136468526538644077372589890682262958196750529119944311972207258664056" +
"4820749522728080666492780264672546913947612363653574355170333094944302512419288581347767763803726821";
Assert.IsTrue(MultiPrecision <Pow2.N8> .Digamma(zeropoint).Exponent < -256);
MultiPrecision <Pow2.N8> y8 = MultiPrecision <Pow2.N8> .Digamma(zeropoint);
MultiPrecision <Pow2.N16> y16 = MultiPrecision <Pow2.N16> .Digamma(zeropoint);
MultiPrecision <Pow2.N32> y32 = MultiPrecision <Pow2.N32> .Digamma(zeropoint);
Console.WriteLine(y8);
Console.WriteLine(y8.ToHexcode());
Console.WriteLine(y16);
Console.WriteLine(y16.ToHexcode());
Console.WriteLine(y32);
Console.WriteLine(y32.ToHexcode());
}
public void DigammaApproxBorderTest()
{
{
List <MultiPrecision <Pow2.N4> > ys = new();
foreach (MultiPrecision <Pow2.N4> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N4>) 16, 4))
{
MultiPrecision <Pow2.N4> y = MultiPrecision <Pow2.N4> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N8> > ys = new();
foreach (MultiPrecision <Pow2.N8> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N8>) 32, 4))
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N16> > ys = new();
foreach (MultiPrecision <Pow2.N16> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N16>) 60, 4))
{
MultiPrecision <Pow2.N16> y = MultiPrecision <Pow2.N16> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N32> > ys = new();
foreach (MultiPrecision <Pow2.N32> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N32>) 116, 4))
{
MultiPrecision <Pow2.N32> y = MultiPrecision <Pow2.N32> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N64> > ys = new();
foreach (MultiPrecision <Pow2.N64> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N64>) 228, 4))
{
MultiPrecision <Pow2.N64> y = MultiPrecision <Pow2.N64> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N128> > ys = new();
foreach (MultiPrecision <Pow2.N128> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N128>) 456, 4))
{
MultiPrecision <Pow2.N128> y = MultiPrecision <Pow2.N128> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
{
List <MultiPrecision <Pow2.N256> > ys = new();
foreach (MultiPrecision <Pow2.N256> x in TestTool.EnumerateNeighbor((MultiPrecision <Pow2.N256>) 908, 4))
{
MultiPrecision <Pow2.N256> y = MultiPrecision <Pow2.N256> .Digamma(x);
Console.WriteLine(x);
Console.WriteLine(x.ToHexcode());
Console.WriteLine(y);
Console.WriteLine(y.ToHexcode());
Console.Write("\n");
ys.Add(y);
}
TestTool.NearlyNeighbors(ys, 14);
TestTool.SmoothnessSatisfied(ys, 1);
TestTool.MonotonicitySatisfied(ys);
}
}
