Main.hs

-- There was a lot of discussion about various ways of computing
-- Bernouilli numbers (whatever they are) on haskell-cafe in March 2003
-- Here's one of the programs.

-- It's not a very good test, I suspect, because it manipulates big integers,
-- and so probably spends most of its time in GMP.  

import Data.Ratio
import System.Environment

-- powers = [[r^n | r<-[2..]] | n<-1..]
-- type signature required for compilers lacking the monomorphism restriction
powers :: [[Integer]]
powers = [2..] : map (zipWith (*) (head powers)) powers

-- powers = [[(-1)^r * r^n | r<-[2..]] | n<-1..]
-- type signature required for compilers lacking the monomorphism restriction
neg_powers :: [[Integer]]
neg_powers = 
  map (zipWith (\n x -> if n then x else -x) (iterate not True)) powers

pascal:: [[Integer]]
pascal = [1,2,1] : map (\line -> zipWith (+) (line++[0]) (0:line)) pascal

bernoulli 0 = 1
bernoulli 1 = -(1%2)	
bernoulli n | odd n = 0
bernoulli n = 
   (-1)%2 
     + sum [ fromIntegral ((sum $ zipWith (*) powers (tail $ tail combs)) - 
                            fromIntegral k) %
             fromIntegral (k+1)
     | (k,combs)<- zip [2..n] pascal]
  where powers = (neg_powers!!(n-1))

main = do
 [arg] <- getArgs
 let n = (read arg)::Int
 putStr $ "Bernoulli of " ++ (show n) ++ " is "
 print (bernoulli n)