{-# LANGUAGE UnicodeSyntax #-}

-- |
-- Module      :  Math.Dozenal
-- Copyright   :  (C) 2014 Siddhanathan Shanmugam
-- License     :  LGPL (see LICENSE)
-- Maintainer  :  siddhanathan@gmail.com
-- Portability :  very
--
-- Dozenal (Duodecimal) number system, promoting the use of base 12.
--
-- The dozenal number system is superior to the decimal number system
-- which is widely in use today.
--
-- For information on why you should bother, see
-- <http://io9.com/5977095/why-we-should-switch-to-a-base-12-counting-system>
--
-- Example usage:
--
-- @ 
--   module Main where
--   import Math.Dozenal
--   main = print $ (Dozenal "4")^2
-- @
--
--

module Math.Dozenal ( decimalToDozenal
               , dozenalToDecimal
               , Dozenal(..)
               ) where


import Numeric (showIntAtBase, readInt)
import Data.Char (intToDigit, digitToInt)
import Data.Maybe (listToMaybe, fromJust)

-- | Dozenal numbers need to be represented as strings since they contain more
-- than 9 digits
newtype Dozenal = Dozenal { number ∷ String } deriving (Show, Eq)

dozenalBase ∷ Int
dozenalBase = 12

dozenalCharacters ∷ String
dozenalCharacters = "0123456789ab"

changeConvention ∷ String → String
changeConvention = map changeCharacters
                   where changeCharacters 'X' = 'a'
                         changeCharacters 'E' = 'b'
                         changeCharacters 'a' = 'X'
                         changeCharacters 'b' = 'E'
                         changeCharacters  x  =  x

-- | Convert a decimal int to a dozenal string
decimalToDozenal ∷ Int → Dozenal
decimalToDozenal decimal = Dozenal
                         $ changeConvention
                         $ showIntAtBase dozenalBase intToDigit decimal ""

-- | Convert a dozenal string to a decimal integer if base conversions allow it
dozenalToDecimal ∷ String → Maybe Int
dozenalToDecimal = fmap fst
                 . listToMaybe
                 . readInt dozenalBase (`elem` dozenalCharacters) digitToInt
                 . changeConvention

operand = fromJust . dozenalToDecimal

instance Num Dozenal where
   Dozenal a + Dozenal b = decimalToDozenal $ operand a + operand b
   Dozenal a ★ Dozenal b = decimalToDozenal $ operand a ★ operand b
   Dozenal a - Dozenal b = decimalToDozenal $ operand a - operand b
   abs    (Dozenal a)    = decimalToDozenal $ operand a
   signum (Dozenal a)    = decimalToDozenal $ signum $ operand a
   fromInteger i         = fromInteger i