Hi, FWIW, there is a translation of some of the Numerical Recipes code into
Lisp, available at the CMU website (I can send a link if anyone wants). It
covers the special functions, random number generators, FFT-related stuff,
and a few odds and ends out of interpolation. BTW, this is not an official
translation! Anyway, it may be of some help.
Dave Holmgren
> -----Original Message-----
> From: James Amundson [SMTP:amundson at fnal]
> Sent: Monday, February 04, 2002 12:19 PM
> To: Richard Fateman
> Cc: Raymond Toy; Tuukka Toivonen; Maxima List; Gerard Jungman
> Subject: Re: [Maxima] Gaussian RNG?, numerics in general...
>
> Sigh. I had really hoped to postpone this conversation until I felt we
> had fixed a few more underpinnings of Maxima (like the packages!), but
> the topic has suddenly heated up. Before I go on to agree with Richard
> and to make a concrete proposal, let me say this:
>
> Some (if not much, or even all) of the numerical code in Maxima is in
> really bad shape. Only after Ray Toy started fixing up the bessel code
> did I notice that the Maxima test suite has been dutifully verifying
> that
> jn(3,4) = 0.1320342093678868 ;
> j0(1) = 0.7651977429270344 ;
> bessel(2,3) = 0.1289432631185581-5.717744444379852e-08*%i;
> even though only the first six digits or so of each expression is
> correct. Yes, Maxima always gets the same answer to 16 or so digits, but
> most of the digits are wrong. bessel(2,3) should be real, but we've been
> verifying that it gets the wrong imaginary part to sixteen digits!
>
> Writing reliable numerical software is a hard job. I think it is
> completely unreasonable to think we can go about improving the numerical
> part of Maxima one function at a time. Ray's work is fine as a stopgap
> measure, but we need to think about a real long-term solution.
>
> On Mon, 2002-02-04 at 11:42, Richard Fateman wrote:
> > If someone has a program in C or Fortran which takes as input
> > a few integers and/or floats and returns, after some substantial
> > computation, a float, an integers, or an array of these, then it should
> > be possible to link this to maxima easily via foreign function
> > calls, and not ever worry about lisp's speed.
>
> Yes, absolutely. I'm worried about maintenance even more than speed. If
> bugs are identified and fixed in the original C/Fortran/whatever code,
> we want to be able to take advantage of them immediately.
>
> For me, the biggest issue is the foreign function interfaces in the
> various Lisps on various platforms. Unfortunately, I don't know anything
> about it! I hope someone on the list can enlighten me as to some of the
> issues.
>
> > For a random number generator you might even produce an array
> > of a whole bunch of these from one call.
> >
> > An idea which really capitalizes on the fact that we are
> > using lisp and maxima as open source is that we can patch in
> > any old stuff from a "subset domain". Thus any numerical
> > code should be simple. Octave, a Matlab clone, could be
> > swallowed whole, I think.
>
> Interesting. Actually, I had a different idea for combining Maxima and
> Octave, but I think we differ primarily in details. Maybe we can have
> that conversation later...
>
> > For example, over the weekend I tried out (successfully) loading
> > gmp 3.0 (gnu multiple precision) into a lisp. Interestingly, I
> > did NOT need the source for gmp. I loaded a dll. All i needed
> > was the documentation for the entry points.
> >
> >
> > Other features which come free from other peoples' lisp libraries
> > include network socket code, html generation.
> >
> > The major hassle in my view in doing this is that other peoples' code
> > may not work on all relevant platforms, or may be subject to random
> > fluctuations. E.g. incompatible changes in interfaces, legal status,
> > etc.
>
> These are all things to worry about. I propose we use the GNU Scientific
> Library (GSL) to replace {X} in Maxima, where the set {X} includes at
> least special functions and random number generators. GSL has the
> following features:
> - For most of what it does, it is the best such code I know of.
> - It is actively maintained.
> - It is documented.
> - It has been ported to a large number of platforms.
> - Its license is completely compatible with ours.
> A number of smart people have done a *large* amount of work on GSL. We
> should take advantage of it.
>
> --Jim
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