How do you make this Haskell power function tail recursive?

Question

How would I make this Haskell power function tail recursive?

turboPower a 0 = 1
turboPower a b
    | even b = turboPower (a*a) (b `div` 2)
    | otherwise = a * turboPower a (b-1)

You don't need `>` in front of code. Just indent it by four spaces. — Marcelo Cantos, Apr 30 '10 at 01:26
By the way, you should probably use `quot` instead of `div`. Also, note that the usual `(^)` is also based on a fast exponentiation algorithm. — dfeuer, Jan 28 '15 at 02:13

Daniel Martin · Accepted Answer · 2010-05-08T18:49:58.470

10

turboPower a b = turboPower' 1 a b
  where
    turboPower' x a 0 = x
    turboPower' x a b
        | x `seq` a `seq` b `seq` False = undefined
        | even b = turboPower' x (a*a) (b `div` 2)
        | otherwise = turboPower' (x*a) a (b-1)

Basically, what you want to do is move the multiplication that you're doing in the "otherwise" step (since that's what keeps this from being tail-recursive initially) to another parameter.

Edited to add a line making all three parameters strictly evaluated, instead of lazy, since this is one of those well-known situations where laziness can hurt us.

edited May 08 '10 at 18:49

answered Apr 30 '10 at 01:26

Daniel Martin

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It looks like you'll want to make the tail recursive version strict in the accumulator argument. Otherwise, your turboPower will probably cause memory exhaustion when the result of the computation is demanded. – Jason Dagit May 07 '10 at 21:58
Good point - and I also want to make it strict in `a` too. Done. – Daniel Martin May 08 '10 at 18:51

How do you make this Haskell power function tail recursive?

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