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Re: predicting cycle sizes of 2r+1 mod p on (0..p-1)

Subject: Re: predicting cycle sizes of 2r+1 mod p on 0..p-1
From: Phil Carmody
Date: 30 Jul 2005 15:08:43 +0300
Newsgroups: sci.math
"Alex" <alex@xxxxxxxxxxxxx> writes:

> Hello,
> 
> Phil Carmody wrote:
> > "Alex" <alex@xxxxxxxxxxxxx> writes:
> > > Current sieving by software is looking for factors for the
> > > remaining 9 k values for n < 50,000,000 and p is approaching
> > > the limit of the software siever at 2^50.
> >
> > The only reason I claimed that the limit of my sieve (NbeGon)
> > was p=2^52 was that my C implementation was portable across
> > all platforms and that many (all but x86) don't have floating
> > point precision greater than that. Paul's sieve, written in
> > x86 asm, and NbeGon run on x86 do not have such a 2^52 limit.
> > (Having a 2^63 one instead.)
> 
> This is proth_sieve by Paul Jobling and Mikael Klasson. From what
> I've read the cmov version (x86 assembly for Athlons) has a limit
> of 2^50. That's what SoB is using at the moment.

I can imagine a P4/SSE2 version might have that limitation, but
there's no need for an Athlon version to, particularly if you're
using assembly language routines. That's what the 80-bit FPU is 
designed for. 

> Thanks for the tip on floating point, it had never even crossed
> my mind, although I would guess you're using FFT multiplcation and
> getting the modulus operation for free.

Nope, only use FFTs for bignums. Not a bignum in sight here.
 
> My siever will never be quick but it's a good learning experience.

You can't beat learning by doing.

Phil
-- 
If a religion is defined to be a system of ideas that contains unprovable
statements, then Godel taught us that mathematics is not only a religion, it
is the only religion that can prove itself to be one. -- John Barrow

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