module Exercise01 where

import Test.QuickCheck
import GHC.Float

{-H1.1a)-}
myPair :: Integer -> Integer -> Integer
myPair x y = 2^y * (2*x + 1) - 1

{-H1.1b)-}
mySnd :: Integer -> Integer
mySnd z
    | z `mod` 2 == 0    = 0
    | otherwise         = 1 + mySnd (z `div` 2)

{-H1.1c)-}
myFst :: Integer -> Integer
myFst z = (((z + 1) `div` (2^mySnd z)) - 1) `div` 2

{-H1.1d)-}
prop_myPair :: Integer -> Integer -> Integer -> Property
prop_myPair p x y = (p > 0 && x > 0 && y > 0) ==> p == myPair x y

{-H2-}
digitToEo :: Integer -> String
digitToEo 0 = "nul"
digitToEo 1 = "unu"
digitToEo 2 = "du"
digitToEo 3 = "tri"
digitToEo 4 = "kvar"
digitToEo 5 = "kvin"
digitToEo 6 = "ses"
digitToEo 7 = "sep"
digitToEo 8 = "ok"
digitToEo 9 = "nau"

{-WETT-}
numberToEo :: Integer -> String
numberToEo x
    | log == 0 = digitToEo x
    | log >= 3 = chooseMiddle log3 (x `div` 10^(log3*3)) ++ if logMLower > 0 then " " ++ numberToEo logMLower else ""
    | otherwise = (if logUpper > 1 then digitToEo logUpper else "") ++ chooseMinor log ++ if logLower > 0 then " " ++ numberToEo logLower else ""
    where
        log = toInteger $integerLogBase 10 x
        log3 = log `div` 3
        logUpper = x `div` 10^log
        logLower = x `mod` 10^log
        logMLower = x `mod` 10^(log3*3)
        digitToEoM 1 = " m"
        digitToEoM 10 = " dek"
        digitToEoM x = " " ++ digitToEo x
        chooseMiddle 1 logMUpper = if logMUpper > 1 then numberToEo logMUpper ++ " mil" else "mil"
        chooseMiddle log3 logMUpper = numberToEo logMUpper ++ digitToEoM (log3 `div` 2) ++ (if even log3 then "iliono" else "iliardo") ++ if logMUpper > 1 then "j" else ""
        chooseMinor 2 = "cent"
        chooseMinor 1 = "dek"
{-TTEW-}