In trying to learn Haskell, I have implemented a pi calculation in order to understand functions and recursion properly.

Using the Leibniz Formula for calculating pi, I came up with the following, which prints pi to the tolerance of the given parameter, and the number of recursive function calls in order to get that value:

reverseSign :: (Fractional a, Ord a) => a -> a 
reverseSign num = ((if num > 0
                        then -1
                        else 1) * (abs(num) + 2))

piCalc :: (Fractional a, Integral b, Ord a) => a -> (a, b)
piCalc tolerance = piCalc' 1 0.0 tolerance 0

piCalc' :: (Ord a, Fractional a, Integral b) => a -> a -> a -> b -> (a, b)
piCalc' denom prevPi tolerance count = if abs(newPi - prevPi) < tolerance
                                        then (newPi, count)
                                        else piCalc' (reverseSign denom) newPi tolerance (count + 1)
                                        where newPi = prevPi + (4 / denom)

So when I run this in GHCI, it seems to work as expected:

*Main> piCalc 0.001
(3.1420924036835256,2000)

But if I set my tolerance too fine, this happens:

*Main> piCalc 0.0000001
(3.1415927035898146,*** Exception: stack overflow

This seems wholly counter-intuitive to me; the actual calculation works fine, but just trying to print how many recursive calls fails??

Why is this so?

haskell ghci
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