I Failx0r at teh Haskell!!11 :-/

Posted on July 13, 2012

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UPDATE: 2012/07/13

It wasn’t a Haskell idiosyncrasy or my lack of Haskell skills after all (of which I have extremely little.) It was just a bug.  My Haskell program had the wrong Fibonacci upper bound set at 40,000,000 instead of 4,000,000.

uber_bound	= 40000000  -- OOOPS!!!! It should be 4M, not 40M.

Thanks StackOverflow. Many pair of eyes >> mine own. I leave the rest of the original post (including the bug) as it were.

SPOILER ALERT:  2012/07/12 – Please don’t look at this if you are trying to solve Project Euler’s problem #2 on your own w/o looking at the answer.

I’ve already completed problem #2 of Project Euler (computing the sum of all even Fibonacci(n) numbers less than or equal to 4 million) – I’m using these problems to practice my C/Ada bread-n-butter skills, to revisit my Common Lisp and to learn Haskell. My typical approach (and current goal) is to do a C implementation first (brute-force if necessary) to compute the right result. Then I refine the program (step-wise refinement, nested functions, recursion, etc) into Ada, Lisp and Haskell (the later being my target of learning.)

When I’m trying to re-implement my solution in Haskell, I’m running into a problem. In classical fashion, it is calculating the wrong answer. However, I think my Haskell implementation resembles my Common Lisp one (which does produce the correct result.)

The algorithm only computes the Fibonacci number for n where n % 3 == 0. This is because we need to sum only the even-valued Fibonacci numbers F(n) <= 4M, and

((n % 3) == 0) \leftrightarrow ((F(n) % 2) == 0)

Here is the Haskell implementation:

-- Created on 2012-07-12

-- Each new term in the Fibonacci sequence is generated by adding
-- the previous two terms. By starting with 1 and 2, the first 10
-- terms will be:
--
-- 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
--
-- By considering the terms in the Fibonacci sequence whose values
-- do not exceed four million, find the sum of the even-valued terms.
--
-- SOLUTION (in C):
--    1. computer the fibs(n) by brute force, starting from n=0
--       0 1 1 2 3 5 8 13 21 34 55 89 144...
--    2. Then, notice the following:
--       (n % 3 = 0 ) -> ( fibs(n) % 2 == 0 )
--    3. By computing the fibs of only those numbers multiple of 3
--       (including 0), we reduce the number of calculations by 1/3

-- EXPECTED VALUE : 4613732

uber_bound	= 40000000  -- Upper bound (exclusive) for fibonacci values
expected	= 4613732   -- the correct answer

-- The implementation amenable for tail-recursion optimization
fibonacci :: Int -> Int
fibonacci n = __fibs (abs n) 0 1
  where
    -- The auxiliary, tail-recursive fibs function
    __fibs    :: Int -> Int -> Int -> Int
    __fibs 0 f1 f2 = f1 -- the stopping case
    __fibs n f1 f2 = __fibs (n - 1) f2 (f1 + f2)

-- NOT working. It computes 19544084 when it should compute 4613732
find_solution :: Int
find_solution = sum_fibs 0
  where
    sum_fibs :: Int -> Int
    sum_fibs n =
      if fibs > uber_bound
        then
          0 -- stopping condition
        else
          -- remember, (n % 3 == 0) <--> (fib(n) % 2 == 0)
          -- so, seek the next even fibs by looking at the
          -- the next n = n@pre + 3
          fibs + sum_fibs (n + 3)
      where
        fibs = fibonacci n

actual = find_solution

problem_2 = (expected == actual)

The thing is printing 19544084 when the correct answer is 4613732. My Common Lisp solution (which does work) is below.

I thought my Haskell implementation would resemble it, but I’m missing something.

(set `expected 4613732)  ;; the correct answer

;; very inefficient recursive implementation
(defun crappy_fibonacci (x)
  (cond
    ((<= x 0) 0)
    ((= x 1) 1)
    (t
       (+ (fibonacci (- x 1)) (fibonacci (- x 2)) )
    )
  );; end cond
) ;; end naive_fibonacci

;; tail-recursive fibonacci
(defun fibonacci (n)
  (labels
    ( ;; define an auxiliary fibs for tail recursion optimization
      (__fibs (n f1 f2)
        (if (<= n 0)
          f1 ;; the stopping condition
          (__fibs
            (- n 1) ;; decrement to ensure a stopping condition
            f2
            (+ f1 f2))))
    ) ;; end tail_rec_fibs auxiliary
   (__fibs n 0 1)
  );; end labels
) ;; end fibonacci

(defun sum_fibs(seed)
  (let*
    ((f (fibonacci seed)))
    (if (> f 4000000)
      0
    ;; else
      (+ f (sum_fibs (+ 3 seed)))
    );; end if
  );; end of let
);; end of sum-fibs

(defun solution () (sum_fibs 0))

(defun problem_2 ()
  (let
    (
     (actual (solution))
    )
    (format t "expected:~d actual:~d" expected actual)
    (= expected actual)
  )
) ;; end of problem_2 defun

What on Earth am I doing wrong?

Granted that I’m using a Neanderthal approach to learning Haskell (I’m currently just re-implementing my Lisp on Haskell as opposed to learning idiomatic Haskell, the coding/problem solving approach that goes with the language.)

I’ve put my question on StackOverflow. Hopefully I’ll get an answer 🙂 In the meantime, however…

Indeed, I haz teh dumb

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