I take it that the extra case always fails but forces the arguments to be evaluated? Nice trick. Thanks! --wgm --- oleg@pobox.com wrote:
I added two lines to your code:
iterate2 f x n | seq f $ seq x $ seq n $ False = undefined iterate2 f x n = --- as before
rk4Next f h (x, y) | seq f $ seq h $ seq x $ seq y $ False = undefined rk4Next f h (x, y) = -- as before
I also increased ten times the number of steps for the last iteration, to make the example more illustrative. putStr (show (rk4 stiff 0 1 (exp (-1)) 1000000))
The rest of the code is unchanged. The program now runs on GHCi
*Foo> main Begin (1.0000000000000007,-6.503275017254139) (0.9999999999999062,-6.497717470015538) (1.000000000007918,-6.497716616653335)
on on hugs
Begin (1.0,-6.50327501725414) (0.999999999999906,-6.49771747001554) (1.00000000000792,-6.49771661665334)
with the default stack size for both interpreters. It seems the code does run in constant space now.
The added lines are meant to turn the relevant functions from lazy to strict. When you see something like '(n-1)' and 'y + a1/6', it is a red flag. These are exactly the kinds of expressions that lead to memory exhaustion. Perhaps it is because the size of an unevaluated thunk for (n-1) is so much bigger than the size of the evaluated thunk. It seems that arithmetic expressions are the best candidates for some opportunistic evaluation...
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