Multiple precision arithmetic

Mr Felscher has asked me to post this for him, and I can't see any

reason why not. I would ask that e-mail replies be directed to him,

or perhaps posted. (He is able to read comp.lang.apl, but evidently

not able to post.)

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Subject: Long Arithmetic in APL

Background: It obviously is tempting to use APL for algorithms transforming

matrices into their various normal forms. Everything works well over

fields GF(p). Working over integers, already intermeadiary results

easily surpass APL's precise 15 digits. Working over rationals is

quite hopeless since the need to form common denominators leads to

large numbers very fast.

Question: Has anyone implemented a well working integer multiple precision

arithmetic for APL ?

I did, some time ago, write a multiple precision arithmetic (MPA)

_within_ APL , but this, understandably, will work fairly slow.

And of course, it isn't vectorial in the way APL's basic operations

are, so that using it will require additional lines in a program.

A much better solution would be an AP (auxiliary processor)

written in assembler and containing the MPA functions. That then

could be associated with help of shared variables . [The hardware

I am using are PS2's with either the 286 or the 386 processor, plus

coprocessor; the particular APL is IBM's APL2-PC. ]

Walter Felscher / Math. Institut / Univ. Tuebingen