On Sat, Apr 03, 2010 at 11:18:45PM +0400, Stanislav Maslovski wrote:
> Well, I can do that too in this Maxima, but for some reason only
> gradually. That is, if try it in one step, it fails:
>
> (%i1) pi[n]:=if n = 2 then 1 elseif primep(n) then pi[n-1]+1 else
> pi[n-1]$
>
> (%i2) pi[5000];
>
> Maxima encountered a Lisp error:
>
> Error in PROGN [or a callee]: Bind stack overflow.
>
> Automatically continuing.
> To enable the Lisp debugger set *debugger-hook* to nil.
>
> Now, if I restart Maxima and do this, it works:
>
> (%i1) pi[n]:=if n = 2 then 1 elseif primep(n) then pi[n-1]+1 else pi[n-1]$
>
> (%i2) for n: 100 thru 5000 step 100 do print(pi[n]);
> 25
> 46
> 62
> ...
> 646
> 654
> 669
I thought a little bit more about it and I think I understand now
what is going on. Basically, in a recursive function like that, the
pi[n]s are not evaluated (and therefore their values are not stored
anywhere for reuse) until stack is filled with nested calls for
pi[500], pi[499], ... pi[1]. The fact that pi[] is an array function
does not prevent this from happening. Right?
--
Stanislav