# [Maxima] compilation speeds

Bill Wood william.wood3
Thu Nov 16 09:38:35 CST 2006

```On Thu, 2006-11-16 at 06:58 -0600, Barton Willis wrote:
. . .
> Compiling a Maxima function does remove tail-recursion. (Maybe CL
> isn't required to do this, but GCL does.) Removing tail-recursion
> allows a recursively defined function to handle larger data:

By "removing tail-recursion" you mean transforming tail-recursion into
iteration?

> (%i1) sumlist(l) := if l = [] then 0 else first(l) + sumlist(rest(l))\$
> (%i2) p : makelist((-1)^k,k,1,1000)\$
> (%i3) sumlist(p);
> Error in PROGN [or a callee]: Bind stack overflow.

But, this function isn't tail-recursive, that is, the recursive call to
sumlist is not what is known as a tail call, since further work (the
addition) is done on the result returned by the recursive call.

A tail-recursive version of sumlist would look more like

sumlist( l, a ) := if l = [] then a else sumlist( rest(l), a + first(l)

with line (%i3) changed to "sumlist( p, 0 )"

(please forgive any syntactic errors; I haven't studied the maxima
programming language syntax yet, so I'm winging it).
>
> Let's compile and re-try:
>
> (%i4) compile(sumlist)\$
> (%i5) sumlist(p);
> (%o5) 0
>
> So even when the Maxima translator isn't able to speed things up, sometimes
> there is an advantage to compiling Maxima code.

This apparently depends critically on which Common Lisp your maxima was
built with, since I can't duplicate your error with your data; I'm using
cmucl.

-- Bill Wood

```