module Main where
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 1A: BINARY RECURSION
f n | n <  2 = 1
    | n >= 2 = f (n-1) + f (n-2)
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f n))
-- Function main is the entry point of the program
main = f_print 46

module Main where
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 2A-1: INFINITE LIST
-- This example is based on the one-liner from The Gentle Introduction to Haskell
f = 1 : 1 : zipWith (+) f (tail f)
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f!!n))
-- Function main is the entry point of the program
main = f_print 160000

module Main where
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 2B: SIMPLE RECURSION
f n = l 1 1 n where
      l a b c = if c<2 then a else l (a+b) a (c-1)
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f n))
-- Function main is the entry point of the program
main = f_print 160000

Haskell does not support non-recursive loops.
Rewriting this algorithm in recursion produces ALGORITHM 2B.

module Main where
import List(transpose)
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 3A: MATRIX EQUATION
f n = head (head (mp [[1,1],[1,0]] n))
-- Function mm performs matrix multiplication.
-- I don't know the original author of this one-liner.
mm a b  = [[sum$zipWith (*) row col | col <- transpose a] | row <-b]
-- Function mp raises a matrix m into nth power (for n>0)
mp m n | n <= 1 = m
       | otherwise = if (mod n 2)==1 then mm (mm a a) m else mm a a
		             where a = mp m (div n 2)
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f n))
-- Function main is the entry point of the program
main = f_print 1000000

module Main where
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 3B: FAST RECURSION
f n = fst (l n) where
   l n |  n<2 = (1,1)
       | n==2 = (2,1)
       |  n>2 = if (rem n 2)==1 then ( k1*(k1+k2)+k1*k2    ,  k1*k1+k2*k2    )
                                else ((l1+l2)*(l1+l2)+l1*l1, (l1+l2)*l1+l1*l2)
       where (k1,k2) = l (div (n-1) 2)
             (l1,l2) = l ((div n 2)-1)
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f n))
-- Function main is the entry point of the program
main = f_print 500000

module Main where
-- Function f returns the n'th Fibonacci number
-- It uses ALGORITHM 3C: BINET'S FORMULA
f n = round((phi**(x+1)-(1-phi)**(x+1))/(sqrt 5))
	  where phi = (1+sqrt 5)/2
	        x = (fromInteger n)::Float
-- Function f_print  prints the n'th Fibonacci number
f_print n = print(show n ++ "th Fibonacci number is " ++ show (f n))
-- Function main is the entry point of the program
main = f_print 30