Item: 768 by jurjen at cwi.nl
Author: [Jurjen NE Bos]
  Subj: Modulo computations on 48SX
  Keyw: Number theory
  Date: Tue Sep 18 1990 16:46 
 Lines: 45

This article is meant for factorization and number theory freaks.
I wrote a machine code program that does modulo multiplication for
binaries.  The program is equivalent to the RPL
\<< ROT ROT * SWAP DUP2 / * - \>>,
except that the latter program only works if the intermediate product is
smaller than 2^64.
This machine code version does not have this problem.

Usage:
enter #a #b #m MULMOD to get (#a*#b) MOD #m
All arguments must be binaries.
#a must be < #m to make sure that the result is < #m.
#b and #m are unrestricted.
All arguments are checked, so that you don't have to be afraid for
mistakes.  You'll get a nice "Too Few Arguments" or "Bad Argument Type"
if applicable.

Remark: it is only tested on a version D.
If you have another version, you're probably safe.  To be sure, check
out memory location 53F8D.  It should contain 174E773DF1C4143 for the
program to work.

A nice example of the use of MULMOD is the "Random imitator".
The random generator uses internally a seed of 15 digits, and can be
imitated using the program:
\<< #2851130928467d R #1000000000000000 MULMOD DUP 'R' STO B->R 1E15 /
\>>
Seed the random generator by replacing
      .xxxxxxxxxxxxEyy RDZ
by
      #xxxxxxxxxxxxyy1 'R' STO
You can also produce the reverse of the random sequence replacing
the factor 2851130928467 by 953992389123803.
Have fun!
--
|                 | "Never imagine yourself not to be otherwise than what |
| Jurjen N.E. Bos | it might appear to others that what you were or might |
|                 | have been was not otherwise than what you had been    |
|  jurjen@cwi.nl  | would have appeared to them to be otherwise."         |