public void DoubleDoubleSqrt()
{
foreach (DoubleDouble x in DoubleDoubleTest.GetRandomDoubleDoubles(1.0E-4, 1.0E4, 16))
{
DoubleDouble y = DoubleDouble.Sqrt(x);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(y * y, x));
}
}
public void DoubleDoubleLogExp()
{
foreach (DoubleDouble x in DoubleDoubleTest.GetRandomDoubleDoubles(1.0E-2, 1.0E6, 16))
{
DoubleDouble xLog = DoubleDouble.Log(x);
DoubleDouble xLogExp = DoubleDouble.Exp(xLog);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(xLogExp, x));
}
}
public void DoubleDoubleErrorFunctionComplementiarity()
{
foreach (DoubleDouble x in DoubleDoubleTest.GetRandomDoubleDoubles(1.0E-2, 1.0E2, 8))
{
DoubleDouble xErf = AdvancedDoubleDoubleMath.Erf(x);
DoubleDouble xErfc = AdvancedDoubleDoubleMath.Erfc(x);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(xErf + xErfc, DoubleDouble.One));
}
}
public void DoubleDoubleLogGammaRecurrence()
{
foreach (DoubleDouble x in DoubleDoubleTest.GetRandomDoubleDoubles(1.0, 1.0E4, 8))
{
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(
DoubleDouble.Log(x) + AdvancedDoubleDoubleMath.LogGamma(x),
AdvancedDoubleDoubleMath.LogGamma(x + DoubleDouble.One)
));
}
}
public void DoubleDoubleLogExpSpecialValues()
{
Assert.IsTrue(DoubleDouble.IsNaN(DoubleDouble.Log(DoubleDouble.NaN)));
Assert.IsTrue(DoubleDouble.Log(DoubleDouble.Zero) == DoubleDouble.NegativeInfinity);
Assert.IsTrue(DoubleDouble.Log(DoubleDouble.One) == DoubleDouble.Zero);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Log(DoubleDouble.E), DoubleDouble.One));
Assert.IsTrue(DoubleDouble.Log(DoubleDouble.PositiveInfinity) == DoubleDouble.PositiveInfinity);
Assert.IsTrue(DoubleDouble.Exp(DoubleDouble.Zero) == DoubleDouble.One);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Exp(DoubleDouble.One), DoubleDouble.E));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Exp(-DoubleDouble.One), DoubleDouble.One / DoubleDouble.E));
}
public void DoubleDoubleTrigIdentities()
{
Random rng = new Random(1);
for (int i = 0; i < 16; i++)
{
DoubleDouble x = (2.0 * DoubleDouble.Pi) * (1.0 - 2.0 * DoubleDouble.GetRandomValue(rng));
DoubleDouble s = DoubleDouble.Sin(x);
DoubleDouble c = DoubleDouble.Cos(x);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(s * s + c * c, DoubleDouble.One));
DoubleDouble s2 = DoubleDouble.Sin(2.0 * x);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(s2, 2.0 * s * c));
}
}
public void DoubleDoubleErrorFunctionAgreement()
{
foreach (DoubleDouble x in DoubleDoubleTest.GetRandomDoubleDoubles(1.0E-2, 1.0E2, 8))
{
DoubleDouble xErf = AdvancedDoubleDoubleMath.Erf(x);
double xErfAsDouble = (double)xErf;
double xAsDouble = (double)x;
double xAsDoubleErf = AdvancedMath.Erf(xAsDouble);
Assert.IsTrue(TestUtilities.IsNearlyEqual(xErfAsDouble, xAsDoubleErf));
DoubleDouble xErfc = AdvancedDoubleDoubleMath.Erfc(x);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(xErf + xErfc, DoubleDouble.One));
}
}
public void DoubleDoubleTrigSpecialCases()
{
Assert.IsTrue(DoubleDouble.Sin(0.0) == DoubleDouble.Zero);
Assert.IsTrue(DoubleDouble.Cos(0.0) == DoubleDouble.One);
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Sin(DoubleDouble.Pi / 6), DoubleDouble.One / 2));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Cos(DoubleDouble.Pi / 6), DoubleDouble.Sqrt(3) / 2));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Cos(DoubleDouble.Pi / 5), (1 + DoubleDouble.Sqrt(5)) / 4));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Sin(DoubleDouble.Pi / 4), DoubleDouble.One / DoubleDouble.Sqrt(2)));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Cos(DoubleDouble.Pi / 4), DoubleDouble.One / DoubleDouble.Sqrt(2)));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Cos(DoubleDouble.Pi / 3), DoubleDouble.One / 2));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Sin(DoubleDouble.Pi / 3), DoubleDouble.Sqrt(3) / 2));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Sin(DoubleDouble.Pi / 2), DoubleDouble.One));
Assert.IsTrue(DoubleDoubleTest.IsNearlyEqual(DoubleDouble.Cos(DoubleDouble.Pi), -DoubleDouble.One));
// Not testing zeros because of need to distingish very small values
}