module Exercise01 where

import Test.QuickCheck ((==>),  Property )

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

{-H1.1b)-}
-- helper function that does the actual math
countDivs :: Integer -> Integer -> Integer
countDivs n i
    | n `mod` 2 == 0    = countDivs (n `div` 2) (i + 1)
    | otherwise         = i

mySnd :: Integer -> Integer
mySnd n = countDivs (n + 1) 0

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

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

{-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"

{- BACKUP
strIf :: Bool -> String -> String
strIf b str = if b then str else ""

threeDigitNumberToEo :: Integer -> String
threeDigitNumberToEo n =    strIf (div100 > 1) (digitToEo div100)
                        ++  strIf nBEH "cent"
                        ++  strIf (sndDigit > 0 && nBEH) " "
                        ++  strIf (sndDigit > 1) (digitToEo sndDigit)
                        ++  strIf (sndDigit >= 1) "dek"
                        ++  strIf (mod10gZ && n `div` 10 > 0) " "
                        ++  strIf mod10gZ (digitToEo mod10)
                        where
                            nBEH = n >= 100
                            sndDigit = (n `mod` 100) `div` 10
                            mod10 = n `mod` 10
                            div100 = n `div` 100
                            mod10gZ = mod10 > 0

milPrefix :: Integer -> String
milPrefix 10 = "dek"
milPrefix n = digitToEo n

threeDigitPartToEo :: Integer -> Integer -> String
threeDigitPartToEo 0 p = ""
threeDigitPartToEo n p =    threeDigitNumberToEo n
                        ++  " "
                        ++  (if p < 2 then "m" else milPrefix ((p `div` 2) + 1))
                        ++  (if even p then "iliono" else "iliardo")
                        ++  strIf (n > 1) "j"

recNumberToEo :: Integer -> Integer -> String
recNumberToEo n p = strIf div1000GZ (recNumberToEo div1000 (p + 1))
                ++  strIf (div1000GZ && mod1000 > 0) " "
                ++  threeDigitPartToEo mod1000 p
                where
                    div1000 = n `div` 1000
                    div1000GZ = div1000 > 0
                    mod1000 = n `mod` 1000

numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n =      recNumberToEo (n `div` 1000000) 0
                ++  strIf (n > 1000000 && modMil > 0) " "
                ++  strIf (div1000 > 1) (threeDigitNumberToEo div1000 ++ " ")
                ++  strIf nGT "mil"
                ++  strIf (mod1000 > 0 && nGT) " "
                ++  threeDigitNumberToEo mod1000
                where
                    modMil = n `mod` 1000000
                    nGT = modMil >= 1000
                    div1000 = modMil `div` 1000
                    mod1000 = modMil `mod` 1000
BACKUP -}

{-WETT-}
strIf :: Bool -> String -> String
strIf b str = if b then str else ""

threeDigitNumberToEo :: Integer -> String
threeDigitNumberToEo n =    strIf (div100 > 1) (digitToEo div100)
                        ++  strIf nBEH "cent"
                        ++  strIf (sndDigit > 0 && nBEH) " "
                        ++  strIf (sndDigit > 1) (digitToEo sndDigit)
                        ++  strIf (sndDigit >= 1) "dek"
                        ++  strIf (mod10gZ && n `div` 10 > 0) " "
                        ++  strIf mod10gZ (digitToEo mod10)
                        where
                            nBEH = n >= 100
                            sndDigit = (n `mod` 100) `div` 10
                            mod10 = n `mod` 10
                            div100 = n `div` 100
                            mod10gZ = mod10 > 0

milPrefix :: Integer -> String
milPrefix 10 = "dek"
milPrefix n = digitToEo n

threeDigitPartToEo :: Integer -> Integer -> String
threeDigitPartToEo 0 p = ""
threeDigitPartToEo n p =    threeDigitNumberToEo n
                        ++  " "
                        ++  (if p < 2 then "m" else milPrefix ((p `div` 2) + 1))
                        ++  (if even p then "iliono" else "iliardo")
                        ++  strIf (n > 1) "j"

recNumberToEo :: Integer -> Integer -> String
recNumberToEo n p = strIf div1000GZ (recNumberToEo div1000 (p + 1))
                ++  strIf (div1000GZ && mod1000 > 0) " "
                ++  threeDigitPartToEo mod1000 p
                where
                    div1000 = n `div` 1000
                    div1000GZ = div1000 > 0
                    mod1000 = n `mod` 1000

numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n =      recNumberToEo (n `div` 1000000) 0
                ++  strIf (n > 1000000 && modMil > 0) " "
                ++  strIf (div1000 > 1) (threeDigitNumberToEo div1000 ++ " ")
                ++  strIf nGT "mil"
                ++  strIf (mod1000 > 0 && nGT) " "
                ++  threeDigitNumberToEo mod1000
                where
                    modMil = n `mod` 1000000
                    nGT = modMil >= 1000
                    div1000 = modMil `div` 1000
                    mod1000 = modMil `mod` 1000

{-TTEW-}