[BLACKBOX] Unsigned Integer Arithmetic (Was Trap while compiling SYSTEM.GET)

From: [at]} <Robert>
Date: Fri, 11 May 2012 16:41:50 +0100

----boundary-LibPST-iamunique-1311361447_-_-
Content-type: text/plain

A little history ...

I have always had a (hobby) interest in number theory, and originally wrote
a base 2^16 arbitrary precision integer arithmetic package in Motorola 68000
assembler.

This was then translated into Modula II using 32 bit Cardinals - much easier
than assembler !

Then I began using Oberon/L (the previous name of Component Pascal) and had to
switch to using base 2^15 and 32 bit INTEGERs with the Most Significant Bit
'wasted' as CP does not support Cardinals. Still, with bigger, faster, machines,
not that big a problem.


Very common number theory functions are to evaluated:
(1) a * b MOD m
and to use BOTH
(2) a MOD m & a DIV m.

CP cannot do (1) with numbers bigger than about 2^31, and (2) requires two
divides where, at assembler level, one will suffice. Using an arbitrary
precision package for (1) when the numbers may be only about 50 bits is
overkill, and the inefficiency of (2) is also nice to avoid.

These reasons motivated the Modules I attach with this email.


Having written these modules it was then easy to reimplement my arbitrary
precision integer package to use base 2^32 using my 32-bit "Cardinal" and 64 bit
"LongCard" types.

By far the most involved routine was to implement

   a * b MOD m

for 64-bit a, b, & m. It involves 128-bit intermediate values.


I am not an Intel assembler expert by any means, and would welcome constructive
criticism of the routines.


The only imported Module is LibFmtrs, which is simply a(n extensive) wrapper
around TextMappers.Formatter. It is only used for ASCII output, so is not
essential to the main purpose of this library.


As far as speed is concerned I have done some experiments with very confusing
results. The speeds of algorithms can vary significantly depending on CPU (Intel
or AMD) and operating system, but no rational pattern emerged.


Regards

Robert



On 10/05/2012 18:03, Oleg N. Cher wrote:
> Dear Robert,
>
> Can we see source of this Modules? Thank you.
>
> Robert wrote:
>
>> I have written a couple of Modules to do unsigned integer arithmetic (32 & 64
>> bit - and some 128 bit!).
>>
>> PS - I know this design is not type safe as the compiler allows signed &
>> unsigned quantities to be mixed, but hey, its not a perfect world!

>
> Oh yes.
>
>

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----boundary-LibPST-iamunique-1311361447_-_---
Received on Fri May 11 2012 - 17:41:50 UTC

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