Big Numbers: Input And Output
June 14, 2011
We continue our series on implementing a big number library by writing the functions that translate between strings and big numbers. You may recall that we cheated in the first big number exercise by using the native big numbers of Scheme to provide input and output. In today’s exercise we overcome that cheating by writing our own functions.
The two functions that convert between strings and big numbers both take an optional argument that represents the radix in which the strings are represented, which can range from 2 to 36 inclusive; if no radix is given, it defaults to 10. The functions are similar to the digits and undigits functions of the Standard Prelude.
Your task is to write the two functions that convert between big numbers and strings. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
My Haskell solution (see http://bonsaicode.wordpress.com/2011/06/14/programming-praxis-big-numbers-input-and-output/ for a version with comments):
readBase :: (Num a, Enum a) => a -> String -> a readBase b ('-':xs) = - readBase b xs readBase b xs = foldl (\a x -> b * a + val x) 0 xs where val d = maybe (error "unrecognized digit") id . lookup d $ zip (['0'..'9'] ++ ['A'..'Z'] ++ ['a'..'z']) [0..] showBase :: Integral a => a -> a -> String showBase b n = if n < 0 then '-' : showBase b (abs n) else map (digit . snd) $ m : reverse ms where ((_:ms), (m:_)) = span ((> 0) . fst) $ iterate (flip divMod b . fst) (n, 0) digit d = maybe undefined id . lookup d . zip [0..] $ ['0'..'9'] ++ ['A'..'Z'] ++ ['a'..'z']