public void ComplexSqrtExtremeValues()
{
// Max values
double sqrtMaxValue = Math.Sqrt(Double.MaxValue);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sqrt(Double.MaxValue), sqrtMaxValue, TestUtilities.RelativeTarget));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sqrt(-Double.MaxValue), sqrtMaxValue * Complex.I, TestUtilities.RelativeTarget));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
ComplexMath.Sqrt(Double.MaxValue + Double.MaxValue * Complex.I),
Math.Sqrt(Math.Sqrt(2.0)) * sqrtMaxValue * (Math.Cos(Math.PI / 8.0) + Math.Sin(Math.PI / 8.0) * Complex.I),
TestUtilities.RelativeTarget));
// One component infinite
Assert.IsTrue(ComplexMath.Sqrt(Double.PositiveInfinity) == new Complex(Double.PositiveInfinity, 0.0));
Assert.IsTrue(ComplexMath.Sqrt(Double.NegativeInfinity) == new Complex(0.0, Double.PositiveInfinity));
// Both components infinite
Complex ppInfinity = new Complex(Double.PositiveInfinity, Double.PositiveInfinity);
Complex pnInfinity = new Complex(Double.PositiveInfinity, Double.NegativeInfinity);
Complex nnInfinity = new Complex(Double.NegativeInfinity, Double.NegativeInfinity);
Complex npInfinity = new Complex(Double.NegativeInfinity, Double.PositiveInfinity);
Assert.IsTrue(ComplexMath.Sqrt(ppInfinity) == ppInfinity);
Assert.IsTrue(ComplexMath.Sqrt(pnInfinity) == pnInfinity);
Assert.IsTrue(ComplexMath.Sqrt(nnInfinity) == pnInfinity);
Assert.IsTrue(ComplexMath.Sqrt(npInfinity) == ppInfinity);
// NaNs
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.NaN, 0.0))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(0.0, Double.NaN))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.NaN, Double.MaxValue))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.MaxValue, Double.NaN))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.NaN, Double.PositiveInfinity))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.PositiveInfinity, Double.NaN))));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sqrt(new Complex(Double.NaN, Double.NaN))));
}
public void ComplexIDefinition()
{
Assert.IsTrue(ComplexMath.Sqrt(-1.0) == Complex.I);
}
