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

From: [at]} <Wojtek>
Date: Fri, 11 May 2012 15:00:20 -0400

----boundary-LibPST-iamunique-600221024_-_-
Content-type: text/plain

Robert:

  since you are interested in theory... I have a book on my desk with a
title "A (literally!) by Petkovsek at al, with a foreword by Knuth.
The book is printed on excellent paper. The covers are thick and stiff.
So it must be a very important book. It is loaded with sums of binomial
coefficients that say nothing to me. Knuth's foreword is raving about
the content for a reason that I do not understand.

The book has something to do with computers because it is devoted to
algorithms that are evaluating those binomial sums.

If you are going to visit Rochester in any point in the future then the
book is yours. I would have sent it your way if only I could figure out a
cheap way of shipping the book.

I confess I have no idea how or when this book fell into my possession. I
think that in your hands it would be put to some good use.

Thank you,

Wojtek


> 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-600221024_-_---

Received on Fri May 11 2012 - 21:00:20 UTC