pr3-sose2026-fork/haskell/06-complex/complex.hs

{-# OPTIONS_GHC -Wno-unrecognised-pragmas #-}

{-# HLINT ignore "Use void" #-}
import Test.HUnit

data Complex a = Complex a a deriving (Eq)

instance (Show a, Num a, Eq a, Ord a) => Show (Complex a) where
  show (Complex re im)
    | re == 0 && im == 0 = "0"
    | re == 0 && im == 1 = "i"
    | re == 0 && im == -1 = "-i"
    | re == 0 = show im ++ "i"
    | im == 0 = show re
    | im == 1 = show re ++ "+i"
    | im == -1 = show re ++ "-i"
    | im > 0 = show re ++ "+" ++ show im ++ "i"
    | otherwise = show re ++ show im ++ "i"

instance (Num a, Floating a, Eq a) => Num (Complex a) where
  (Complex re1 im1) + (Complex re2 im2) = Complex (re1 + re2) (im1 + im2)
  (Complex re1 im1) - (Complex re2 im2) = Complex (re1 - re2) (im1 - im2)
  (Complex re1 im1) * (Complex re2 im2) = Complex (re1 * re2 - im1 * im2) (re1 * im2 + im1 * re2)

  abs (Complex re im) = Complex (sqrt (re * re + im * im)) 0
  signum (Complex re im)
    | re == 0 && im == 0 = Complex 0 0
    | otherwise = let mag = sqrt (re * re + im * im) in Complex (re / mag) (im / mag)

  fromInteger n = Complex (fromInteger n) 0
  negate (Complex re im) = Complex (negate re) (negate im)

instance (Fractional a, Floating a, Eq a) => Fractional (Complex a) where
  fromRational r = Complex (fromRational r) 0
  recip (Complex re im) =
    let denom = re * re + im * im
     in Complex (re / denom) (negate im / denom)

  (Complex re1 im1) / (Complex re2 im2) =
    let denom = re2 * re2 + im2 * im2
     in Complex ((re1 * re2 + im1 * im2) / denom) ((im1 * re2 - re1 * im2) / denom)

conj :: (Num a) => Complex a -> Complex a
conj (Complex re im) = Complex re (negate im)

-- Imaginary unit
i :: (Num a) => Complex a
i = Complex 0 1

tests :: Test
tests =
  TestList
    [ Test.HUnit.TestCase (assertEqual "Show 1+2i" "1+2i" (show $ Complex 1 2)),
      Test.HUnit.TestCase (assertEqual "Show 1" "1" (show $ Complex 1 0)),
      Test.HUnit.TestCase (assertEqual "Show i" "i" (show i)),
      Test.HUnit.TestCase (assertEqual "Show 5i" "5i" (show $ Complex 0 5)),
      Test.HUnit.TestCase (assertEqual "Show 0" "0" (show $ Complex 0 0)),
      Test.HUnit.TestCase (assertEqual "Compare Equal" True (Complex 2 3 == Complex 2 3)),
      Test.HUnit.TestCase (assertEqual "Compare Real Not Equal" False (Complex 1 3 == Complex 2 3)),
      Test.HUnit.TestCase
        (assertEqual "Compare Imag Not Equal" False (Complex 2 4 == Complex 2 3)),
      Test.HUnit.TestCase
        (assertEqual "Compare Not Equal" False (Complex 2 3 /= Complex 2 3)),
      Test.HUnit.TestCase
        ( assertEqual
            "Addition 1"
            (Complex 6.0 8.0)
            (Complex 2.0 3.0 + Complex 4.0 5.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Addition 2"
            (Complex 2.0 3.0)
            (Complex 0.0 3.0 + Complex 2.0 0.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Subtraction 1"
            (Complex 4.0 (-4.0))
            (Complex 7.0 2.0 - Complex 3.0 6.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Subtraction 2"
            (Complex 4.0 2.0)
            (Complex 5.0 4.0 - Complex 1.0 2.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Negation"
            (Complex (-7.0) (-2.0))
            (negate (Complex 7.0 2.0))
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Multiplication 1"
            (Complex (-5.0) 10.0)
            (Complex 1.0 2.0 * Complex 3.0 4.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Multiplication 2"
            (Complex 5.0 1.0)
            (Complex 2.0 3.0 * Complex 1.0 (-1.0))
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Multiplication 3"
            (Complex 11.0 (-10.0))
            (Complex 4.0 1.0 * Complex 2.0 (-3.0))
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Multiplication 4"
            (Complex 5.0 12.0)
            (Complex 3.0 2.0 * Complex 3.0 2.0)
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Magnitude 1"
            (Complex 5.0 0.0)
            (abs (Complex 3.0 4.0))
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Magnitude 2"
            (Complex (sqrt 2.0) 0.0)
            (abs (Complex 1.0 (-1.0)))
        ),
      Test.HUnit.TestCase
        ( assertEqual
            "Magnitude 3"
            (Complex 5.0 0.0)
            (abs (Complex 0.0 5.0))
        ),
      TestCase (assertEqual "Conjugate of 3+4i" (Complex 3 (-4)) (conj (Complex 3 4))),
      TestCase (assertEqual "Conjugate of 5-i" (Complex 5 1) (conj (Complex 5 (-1)))),
      TestCase (assertEqual "Conjugate of -2+3i" (Complex (-2) (-3)) (conj (Complex (-2) 3)))
    ]

main :: IO ()
main = runTestTT tests >> return ()