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Re: Re: Re: Sum problem

  • To: mathgroup at
  • Subject: [mg65380] Re: [mg65359] Re: Re: Sum problem
  • From: "Virgilio, Vincent - SSD" <Vincent.Virgilio at>
  • Date: Wed, 29 Mar 2006 06:34:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at
  • Thread-index: AcZSV5iiO4faU99JQ4286aMOeYcC0gAN1PRA

Wow, the memory footprint of the first code is about 100x less than the
second ( ~ 2MB vs 200MB ).

Vince Virgilio

-----Original Message-----
From: Maxim [mailto:m.r at] 
To: mathgroup at
Subject: [mg65380] [mg65359] Re: Re: Sum problem

On Mon, 27 Mar 2006 12:09:40 +0000 (UTC), Virgilio, Vincent - SSD
<Vincent.Virgilio at> wrote:

> Hello,
> Does this "tail recursion" work (instead of "plain recursion") because

> doSumAux is never a subexpression of itself?  Rather, stack is saved 
> by changing the last function argument "acc"?
> It looks like an example in the documentation for "Trace" in the 
> Mathematica Book.  The example shows nested sublists in an expression 
> chain.  The example Traced a recursive function that was a 
> subexpression of itself, typical of simple recursion.  A nearby 
> example showed a /flat/ expression chain for a Trace of a recursive 
> function that was /not/ a subexpression of itself, like your tail
> Thanks,
> Vince Virgilio

Yes, or we could say that the recursive call should be the last
statement to be evaluated. Then at that point Mathematica needn't save
the state of the caller function, so it works similar to what is known
as "reduction"  
in Scheme (although what is in fact happening is term rewriting, that
is, certain parts of the expression are being replaced and the
evaluation sequence is restarted). Compare:

doSum[L_, acc_] := If[L =!= {}, doSum[Rest@ L, acc + First@ L], acc]
Block[{$IterationLimit = Infinity}, doSum[Range[10^4], 0]];

doSum[L_] := If[L =!= {}, doSum[Rest@ L] + First@ L, 0]
Block[{$RecursionLimit = Infinity}, doSum[Range[10^4]]]; MaxMemoryUsed[]

In the second case each sublist will have to be kept on the stack during
the evaluation of the recursive calls.

Maxim Rytin
m.r at

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