-- !!! test quot/rem/div/mod functions on Ints and Integers
--
main
  = putStr
       (-- w/ Ints and Integers
        show (unzipWith div ints_list)
        ++ "\n"
        ++ show (unzipWith div integers_list)
        ++ "\n"
        ++ show (unzipWith rem ints_list)
        ++ "\n"
        ++ show (unzipWith rem integers_list)
        ++ "\n"
        ++ show (unzipWith quot ints_list)
        ++ "\n"
        ++ show (unzipWith quot integers_list)
        ++ "\n"
        ++ show (unzipWith mod ints_list)
        ++ "\n"
        ++ show (unzipWith mod integers_list)
        ++ "\n"
        ++ show (unzipWith law1 ints_list)
        ++ "\n"
        ++ show (unzipWith law1 integers_list)
        ++ "\n"
        ++ show (unzipWith law2 ints_list)
        ++ "\n"
        ++ show (unzipWith law2 integers_list)
        ++ "\n"
        )
  where
    ints_list :: [(Int, Int)]
    integers_list :: [(Integer, Integer)]

    ints_list = [
        (0, 4),
        (0, -8),
        (7, 3),
        (13, 4),
        (13, -4),
        (-13, 4),
        (-13, -4),
        (12345678, 10000),
        (12345678, -10000),
        (-12345678, 10000),
        (-12345678, -10000),
        (123456,10000),
        (1234567,20000),
        (12345678,-10000),
        (123456789,10000),
        (1234567890,-10000),
        (-12345,10000),
        (-123456789,-10000)
        ]

    integers_list = [
        (0, 4),
        (0, -8),
        (7, 3),
        (13, 4),
        (13, -4),
        (-13, 4),
        (-13, -4),
        (12345678, 10000),
        (12345678, -10000),
        (-12345678, 10000),
        (-12345678, -10000),
        (123456,10000),
        (1234567,20000),
        (12345678,-10000),
        (123456789,10000),
        (1234567890,-10000),
        (-12345,10000),
        (-123456789,-10000),
        (12345678900,500000000),
        (1234000000000000000000005678900,5001111111111111000000)
        ]

unzipWith :: (a -> b -> c) -> [(a,b)] -> [c]
unzipWith f []         = []
unzipWith f ((x,y):zs) = f x y : unzipWith f zs

law1, law2 :: Integral a => a -> a -> Bool

law1 x y = (x `quot` y)*y + (x `rem` y) == x
law2 x y = (x `div`  y)*y + (x `mod` y) == x
