module ComplexNumbersTests open FsUnit.Xunit open Xunit open System open ComplexNumbers [] let ``Real part of a purely real number`` () = real (create 1.0 0.0) |> should equal 1.0 [] let ``Real part of a purely imaginary number`` () = real (create 0.0 1.0) |> should equal 0.0 [] let ``Real part of a number with real and imaginary part`` () = real (create 1.0 2.0) |> should equal 1.0 [] let ``Imaginary part of a purely real number`` () = imaginary (create 1.0 0.0) |> should equal 0.0 [] let ``Imaginary part of a purely imaginary number`` () = imaginary (create 0.0 1.0) |> should equal 1.0 [] let ``Imaginary part of a number with real and imaginary part`` () = imaginary (create 1.0 2.0) |> should equal 2.0 [] let ``Imaginary unit`` () = let sut = mul (create 0.0 1.0) (create 0.0 1.0) real sut |> should (equalWithin 0.01) -1.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Add purely real numbers`` () = let sut = add (create 1.0 0.0) (create 2.0 0.0) real sut |> should (equalWithin 0.01) 3.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Add purely imaginary numbers`` () = let sut = add (create 0.0 1.0) (create 0.0 2.0) real sut |> should (equalWithin 0.01) 0.0 imaginary sut |> should (equalWithin 0.01) 3.0 [] let ``Add numbers with real and imaginary part`` () = let sut = add (create 1.0 2.0) (create 3.0 4.0) real sut |> should (equalWithin 0.01) 4.0 imaginary sut |> should (equalWithin 0.01) 6.0 [] let ``Subtract purely real numbers`` () = let sut = sub (create 1.0 0.0) (create 2.0 0.0) real sut |> should (equalWithin 0.01) -1.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Subtract purely imaginary numbers`` () = let sut = sub (create 0.0 1.0) (create 0.0 2.0) real sut |> should (equalWithin 0.01) 0.0 imaginary sut |> should (equalWithin 0.01) -1.0 [] let ``Subtract numbers with real and imaginary part`` () = let sut = sub (create 1.0 2.0) (create 3.0 4.0) real sut |> should (equalWithin 0.01) -2.0 imaginary sut |> should (equalWithin 0.01) -2.0 [] let ``Multiply purely real numbers`` () = let sut = mul (create 1.0 0.0) (create 2.0 0.0) real sut |> should (equalWithin 0.01) 2.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Multiply purely imaginary numbers`` () = let sut = mul (create 0.0 1.0) (create 0.0 2.0) real sut |> should (equalWithin 0.01) -2.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Multiply numbers with real and imaginary part`` () = let sut = mul (create 1.0 2.0) (create 3.0 4.0) real sut |> should (equalWithin 0.01) -5.0 imaginary sut |> should (equalWithin 0.01) 10.0 [] let ``Divide purely real numbers`` () = let sut = div (create 1.0 0.0) (create 2.0 0.0) real sut |> should (equalWithin 0.01) 0.5 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Divide purely imaginary numbers`` () = let sut = div (create 0.0 1.0) (create 0.0 2.0) real sut |> should (equalWithin 0.01) 0.5 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Divide numbers with real and imaginary part`` () = let sut = div (create 1.0 2.0) (create 3.0 4.0) real sut |> should (equalWithin 0.01) 0.44 imaginary sut |> should (equalWithin 0.01) 0.08 [] let ``Absolute value of a positive purely real number`` () = abs (create 5.0 0.0) |> should equal 5.0 [] let ``Absolute value of a negative purely real number`` () = abs (create -5.0 0.0) |> should equal 5.0 [] let ``Absolute value of a purely imaginary number with positive imaginary part`` () = abs (create 0.0 5.0) |> should equal 5.0 [] let ``Absolute value of a purely imaginary number with negative imaginary part`` () = abs (create 0.0 -5.0) |> should equal 5.0 [] let ``Absolute value of a number with real and imaginary part`` () = abs (create 3.0 4.0) |> should equal 5.0 [] let ``Conjugate a purely real number`` () = let sut = conjugate (create 5.0 0.0) real sut |> should (equalWithin 0.01) 5.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Conjugate a purely imaginary number`` () = let sut = conjugate (create 0.0 5.0) real sut |> should (equalWithin 0.01) 0.0 imaginary sut |> should (equalWithin 0.01) -5.0 [] let ``Conjugate a number with real and imaginary part`` () = let sut = conjugate (create 1.0 1.0) real sut |> should (equalWithin 0.01) 1.0 imaginary sut |> should (equalWithin 0.01) -1.0 [] let ``Euler's identity/formula`` () = let sut = exp (create 0.0 (Math.PI)) real sut |> should (equalWithin 0.01) -1.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Exponential of 0`` () = let sut = exp (create 0.0 0.0) real sut |> should (equalWithin 0.01) 1.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Exponential of a purely real number`` () = let sut = exp (create 1.0 0.0) real sut |> should (equalWithin 0.01) (Math.E) imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Exponential of a number with real and imaginary part`` () = let sut = exp (create (Math.Log(2.0)) (Math.PI)) real sut |> should (equalWithin 0.01) -2.0 imaginary sut |> should (equalWithin 0.01) 0.0 [] let ``Exponential resulting in a number with real and imaginary part`` () = let sut = exp (create (Math.Log(2.0)/2.0) (Math.PI/4.0)) real sut |> should (equalWithin 0.01) 1.0 imaginary sut |> should (equalWithin 0.01) 1.0