module Addition where

import Test.Hspec
import Test.QuickCheck

dividedBy :: Integral a => a -> a -> (a, a)
dividedBy num denom = go num denom 0
    where go n d count
            | n < d = (count, n)
            | otherwise =  go (n - d) d (count + 1)

multiplyBy :: (Ord a, Eq a, Num a) => a -> a -> a
multiplyBy a b
    | a == 0 || b == 0 = 0
    | a > 0 && b > 0   = multiplyBy' a b
    | a < 0 && b < 0   = multiplyBy' (-a) (-b)
    | a < 0 && b > 0   = -(multiplyBy' (-a) b)
    | a > 0 && b < 0   = -(multiplyBy' a (-b))
    where  multiplyBy' c 1 = c
           multiplyBy' c d = c + (multiplyBy c (d - 1))

main :: IO ()
main = hspec $ do
    describe "Addition" $ do
        it "15 divided by 3 is 5" $ do
            dividedBy 15 3 `shouldBe` (5, 0)
        it "22 divided by 5 is 4 remainder 2" $ do
            dividedBy 22 5 `shouldBe` (4, 2)
        it "x + 1 is always greater than x" $ do
            property $ \x -> x + 1 > (x :: Int)
    describe "Multiplication" $ do
        it "15 multiplied by 3 is 45" $ do
            multiplyBy 15 3 `shouldBe` 45
        it "22 multiplied by 5 is 110" $ do
            multiplyBy 22 5 `shouldBe` 110