Non-decimal radices/Convert: Difference between revisions

<lang haskell>Prelude> Numeric.showIntAtBase 16 Char.intToDigit 42 ""

"2a"

Prelude> fst $ head $ Numeric.readInt 16 Char.isHexDigit Char.digitToInt "2a"

42</lang>

It's actually more useful to represent digits internally as numbers instead of characters, because then one can define operations that work directly on this representation.

So conversion to and from digits represented as 0-9 and a-z is done in an additional step.

<lang haskell>import Data.List

import Data.Char

toBase :: Int -> Int -> [Int]

toBase b v = toBase' [] v where

toBase' a 0 = a

toBase' a v = toBase' (r:a) q where (q,r) = v `divMod` b

fromBase :: Int -> [Int] -> Int

fromBase b ds = foldl' (\n k -> n * b + k) 0 ds

toAlphaDigits :: [Int] -> String

toAlphaDigits = map convert where

convert n | n < 10 = chr (n + ord '0')

| otherwise = chr (n + ord 'a' - 10)

fromAlphaDigits :: String -> [Int]

fromAlphaDigits = map convert where

convert c | isDigit c = ord c - ord '0'

| isUpper c = ord c - ord 'A' + 10

| isLower c = ord c - ord 'a' + 10</lang>

Example:

<lang haskell>*Main> toAlphaDigits $ toBase 16 $ 42

"2a"

*Main> fromBase 16 $ fromAlphaDigits $ "2a"

42</lang>

Or, allow for digit variants like upper case vs lower case Hexadecimal, we can express our conversion function(s) in terms of a more general '''inBaseDigits''' function which, given an ordered list of digits as its first argument, returns an Int -> String unfold function. (The base is the length of the digit list).

If we want to assume a default character set, then a general '''toBase''' (Int -> Int -> String) can be also be derived from '''inBaseDigits'''.

inBaseDigits :: [Char] -> Int -> String

fe</pre>