Fwd: Re: GMP 3.1.1
- The following is from a discussion with the GMP guys:
Phil Carmody <fatphil@...> writes:
> Most of the ideas in the tasks file for perfsqr are what I had
> in mind, as most are simple. For reference - if you have 64
> bits to wave around then 2^24-1 is obsoleted by 2^60-1
> 24: 3 5 7 13 17 241
> 60: 3 5 7 11 13 31 41 61 151 331 1321
> However, as these remainders are probably totally memoryFor a typical RISC 64bit architecture, we were agreed that one probably can't get much more efficient than (it requires some cooperative barrel-shifter/extract/insert opcodes).
> bound, it's possible to run several such reductions in
> On a 64 bit systems for example,
> 36: 3 5 7 13 19 37 73 109
> 40: 3 5 11 17 31 41 61681
> which is a better yield than 60 and anything else.
However, we're also agreed that the 2^24-1 scheme can be implemented _blazingly_ fast on any pentium class x86, and gives you everything that my earlier 2^12-1 gives you and a mod 17 decision to boot!
If you see it in GMP in the near future, you'll know where it came from. However, feel free to implement at will on your own (and submit to the GMP guys too of course!) and not wait for me to get off my [SNIP] [SNIP] :-) . Hmmm, I guess I could charge my laptop batteries overnight...
Bonsoir mes amis,
Mathematics should not have to involve martyrdom;
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