This code will find "the last 20 elements of the Fibonacci series backwards" Of course it will never actually work. Runs for about 5 seconds on my machine and then complains it's out of memory.

endfibs.hs

{- 
 - Fast doubling Fibonacci algorithm
 - Copyright (c) 2011 Nayuki Minase
 - 
 - http://nayuki.eigenstate.org/page/fast-fibonacci-algorithms
 -}


-- fibonacci n = F(n)
fibonacci :: Integer -> Integer
fibonacci n | n >= 0 = a where (a, _) = fib n

-- Internal function: fib n = (F(n), F(n+1))
fib :: Integer -> (Integer, Integer)
fib 0 = (0, 1)
fib n =
	let (a, b) = fib (div n 2)
            c = a * (2 * b - a)
            d = b * b + a * a
	in if mod n 2 == 0
		then (c, d)
		else (d, c + d)
		
		
{- Should get farther with a faster algo -}

fibs = map fibonacci [1..]

lastN n xs = let m = length xs in drop (m-n) xs

end = lastN 20 fibs

result = reverse end