> From:  Dean Swan at MITEL on 11/01/99 01:07 PM
>
> Before anybody gets too far along on this, I'd like to encourage
> folks to look
> at a few references for work already done in the area of multiple
> precision
> arithmetic:
>
>      1) "Multiple-Precision Arithmetic in C", Kaliski, Burton S., Jr., Dr.
> Dobb's Journal, August 1992
>      2) "The Z80180 and Big-number Arithmetic", Kaliski, Burton
> S., Jr., Dr.
> Dobb's Journal, September 1993
>      3) "Arbirtrary Precision Floating Point Arithmetic",
> Moteller, Frederick
> C., Dr. Dobb's Journal, September 1993
>      3) "Using the Multiple Precision Library", Rogers, John, Dr. Dobb's
> Journal, January 1995
>      4) "Basic Arithmetic with Inifinite Integers", Hamilton,
> Jeffery W., Dr.
> Dobb's Journal January 1995
>      5) Chapter 20, Section 20.6 "Arithmetic at Arbitrary
> Precision", Numerical
> Recipes in C, (c) 1988-1992 Cambridge University Press.
>
> http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf/c20-6.pdf
>

Thanx!

> The first two of these references were written by the Cheif
> Scientist (at the
> time, I don't know if he still is) at RSA Laboratories, with cryptographic
> applications in mind, and he has some interesting things to say about
> performance.
>
> The _Numerical_Recipes_In_C_  (sorry about the _ underscores for
> those of you
> reading your mail with Celeste), shows a neat trick to do fast multiple
> precision multiplies using the FFT.  Since Squeak already has a
> pretty good
> implementation of the FFT, this may be worth looking at.

I'm not sure, because I have found big differences between the result plots
of slow and fast computation of FFT in squeak (recently tested) and one -
missing sign - error in the code (didn't have the time to follow this path
further). Try it! One additional reason could be different float precision?!

> It may
> offer a very
> efficient way to do LargeInteger multiplies, without new primitives.
>
> A web search on 'multiple or arbitrary precision arithmetic' also
> will yeild
> lots of references (of varying quality, as usual).  Because of
> it's uses in
> cryptography, amongst other things, a lot of work has been done
> in the area of
> multiple precision arithmetic since the original implementation of the
> LargeInteger classes in Squeak.

Sure, but my first wish was just to make LargeInterger computation say at
least twice as fast as before without the claim to become an expert at the
edge of the newest methods before...

> Also, just my opinion, but if people feel compelled to implement
> primitives for
> this stuff, I would definitely like to see them implemented in
> Smalltalk, as
> plug-ins.  I think Squeak already has too many primitives (all in
> the name of
> performance, to be sure), and they just move the whole system
> further away from
> one of Dan Ingalls' original design premises, that Smalltalk be a
> system that
> could be completely understood by a single person.

That's a very important point! The didactic point of view to give every
interested guy the chance to understand _some_ principles of large integer
arithmetics. This gives much credit to the dual approach of doing it in
Smalltalk _and_ as Plugin.

> I would love
> to see some
> effort put into simplifying Squeak, without eliminating functionality, of
> course.  Especially since my ideal target environment is the
> Casio E-105.  (BTW,
> I am making some progress on my Cursor/Sensor changes for the
> E-105.  I'll post
> an update in the near future).
>
>
>
>                               -Dean Swan
>
>                               dean_swan at mitel.com
>
>
>
>