content: Compute the digits of "e" using continued fractions.
  Original program due to Dale Thurston, Aug 2001
  
  > module Main where
  > import System.Environment (getArgs)
  
  > type ContFrac = [Integer]
  
  Compute the decimal representation of e progressively.
  
  A continued fraction expansion for e is
  
  [2,1,2,1,1,4,1,1,6,1,...]
  
  > eContFrac :: ContFrac
  > eContFrac = 2:aux 2 where aux n = 1:n:1:aux (n+2)
  
  We need a general function that applies an arbitrary linear fractional
  transformation to a legal continued fraction, represented as a list of
  positive integers.  The complicated guard is to see if we can output a
  digit regardless of what the input is; i.e., to see if the interval
  [1,infinity) is mapped into [k,k+1) for some k.
  
  > -- ratTrans (a,b,c,d) x: compute (a + bx)/(c+dx) as a continued fraction 
  > ratTrans :: (Integer,Integer,Integer,Integer) -> ContFrac -> ContFrac
  > -- Output a digit if we can
  > ratTrans (a,b,c,d) xs |
  >   ((signum c == signum d) || (abs c < abs d)) && -- No pole in range
  >   (c+d)*q <= a+b && (c+d)*q + (c+d) > a+b       -- Next digit is determined
  >      = q:ratTrans (c,d,a-q*c,b-q*d) xs
  >   where q = b `div` d
  > ratTrans (a,b,c,d) (x:xs) = ratTrans (b,a+x*b,d,c+x*d) xs
  
  Finally, we convert a continued fraction to digits by repeatedly multiplying by 10.
  
  > toDigits :: ContFrac -> [Integer]
  > toDigits (x:xs) = x:toDigits (ratTrans (10,0,0,1) xs)
  
  > e :: [Integer]
  > e = toDigits eContFrac
  
  > main = do
  >	[digits] <- getArgs
  >	print (take (read digits) e)
  
  
  