public void ComplexArcTrigInversion()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 32))
{
Complex asin = ComplexMath.Asin(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(asin), z));
Complex acos = ComplexMath.Acos(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(acos), z));
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(asin, acos, Math.PI / 2.0));
}
}
public void ComplexArcTrigReflection()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-3, 1.0E3, 32))
{
Complex asin = ComplexMath.Asin(z);
Complex masin = ComplexMath.Asin(-z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(masin, -asin));
Complex acos = ComplexMath.Acos(z);
Complex macos = ComplexMath.Acos(-z);
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(acos, macos, Math.PI));
}
}
public void ComplexArcTrigSpecialValues()
{
Assert.IsTrue(ComplexMath.Asin(Complex.Zero) == Complex.Zero);
Assert.IsTrue(ComplexMath.Asin(Complex.One) == Math.PI / 2.0);
Assert.IsTrue(ComplexMath.Asin(-Complex.One) == -Math.PI / 2.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Asin(Complex.I), Complex.I * Math.Log(1.0 + Math.Sqrt(2.0))));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Asin(-Complex.I), -Complex.I * Math.Log(1.0 + Math.Sqrt(2.0))));
Assert.IsTrue(ComplexMath.Acos(Complex.Zero) == Math.PI / 2.0);
Assert.IsTrue(ComplexMath.Acos(Complex.One) == Complex.Zero);
Assert.IsTrue(ComplexMath.Acos(-Complex.One) == Math.PI);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Acos(Complex.I), Math.PI / 2.0 - Complex.I * Math.Log(1.0 + Math.Sqrt(2.0))));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Acos(-Complex.I), Math.PI / 2.0 + Complex.I * Math.Log(1.0 + Math.Sqrt(2.0))));
}
public void ComplexAsinRealAgreement()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 8))
{
Complex z = ComplexMath.Asin(x);
if (x <= 1.0)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(z, Math.Asin(x)));
}
else
{
double im = Math.Log(x + Math.Sqrt((x - 1.0) * (x + 1.0)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(z, new Complex(Math.PI / 2.0, im)));
}
}
}
public void ComplexArcTrigExtremeValues()
{
double logMax = Math.Log(Double.MaxValue);
Assert.IsTrue(TestUtilities.IsNearlyEqual(
ComplexMath.Asin(Double.MaxValue),
new Complex(Math.PI / 2.0, Math.Log(2.0) + logMax)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
ComplexMath.Asin(Double.MaxValue * Complex.I),
new Complex(0.0, Math.Log(2.0) + logMax)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
ComplexMath.Asin(new Complex(Double.MaxValue, Double.MaxValue)),
new Complex(Math.PI / 4.0, 1.5 * Math.Log(2.0) + logMax)
));
}