```{-# LANGUAGE Rank2Types #-}
--------------------------------------------------------------------------------
-- |
-- Module      :  Numeric.Lens
-- Copyright   :  (C) 2012-13 Edward Kmett
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
-------------------------------------------------------------------------------
module Numeric.Lens (base, integral) where

import Control.Lens
import Data.Char (chr, ord, isAsciiLower, isAsciiUpper, isDigit)
import Data.Maybe (fromMaybe)

-- \$setup

-- | This 'Prism' extracts can be used to model the fact that every 'Integral'
-- type is a subset of 'Integer'.
--
-- Embedding through the 'Prism' only succeeds if the 'Integer' would pass
-- through unmodified when re-extracted.
integral :: (Integral a, Integral b) => Prism Integer Integer a b
integral = prism toInteger \$ \ i -> let a = fromInteger i in
if toInteger a == i
then Right a
else Left i

-- | A prism that shows and reads integers in base-2 through base-36
--
-- >>> "100" ^? base 16
-- Just 256
--
-- >>> 1767707668033969 ^. re (base 36)
-- "helloworld"
base :: Integral a => a -> Prism' String a
base b
| b < 2 || b > 36 = error ("base: Invalid base " ++ show (toInteger b))
| otherwise       = prism intShow intRead
where
intShow n = showSigned' (showIntAtBase (toInteger b) intToDigit') (toInteger n) ""

[(n,"")] -> Right n
_ -> Left s
{-# INLINE base #-}

-- | Like 'Data.Char.intToDigit', but handles up to base-36
intToDigit' :: Int -> Char
intToDigit' i
| i >= 0  && i < 10 = chr (ord '0' + i)
| i >= 10 && i < 36 = chr (ord 'a' + i - 10)
| otherwise = error ("intToDigit': Invalid int " ++ show i)

-- | Like 'Data.Char.digitToInt', but handles up to base-36
digitToInt' :: Char -> Int
digitToInt' c = fromMaybe (error ("digitToInt': Invalid digit " ++ show c))
(digitToIntMay c)

-- | A safe variant of 'digitToInt''
digitToIntMay :: Char -> Maybe Int
digitToIntMay c
| isDigit c      = Just (ord c - ord '0')
| isAsciiLower c = Just (ord c - ord 'a' + 10)
| isAsciiUpper c = Just (ord c - ord 'A' + 10)
| otherwise = Nothing

-- | Select digits that fall into the given base
isDigit' :: Integral a => a -> Char -> Bool
isDigit' b c = case digitToIntMay c of
Just i | fromIntegral i < b -> True
_ -> False

-- | A simpler variant of 'Numeric.showSigned' that only prepends a dash and