Forum: Hardware
2009-09-07, 21:15
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Replies: 142
Views: 14,488
Exactly, it's 8 SP : 1 DP : 1 SF for the G200...
Exactly, it's 8 SP : 1 DP : 1 SF for the G200 Nvidia cards. The ATI isn't a constant 5x at all.. it's variable based on operation type since it's software, but also it's not IEEE either so sometimes...
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Forum: Hardware
2009-09-07, 18:31
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Replies: 142
Views: 14,488
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Forum: Math
2009-08-28, 17:18
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Replies: 6
Views: 662
Kevin, wow, thanks very much. This is not an...
Kevin, wow, thanks very much. This is not an answer I expected... my amateur gut feeling was leading me in a very wrong direction.
Thanks for the fast and expert answer. Now I have yet a new...
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Forum: Math
2009-08-28, 06:06
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Replies: 6
Views: 662
Number and identity of n-th roots of 1 mod p
How can you count (and/or compute) the solutions for the relationship
a^n ==1 mod p
where p is prime, n is fixed?
Obviously for some n, the answer is easy. If n=2, this is the square root,...
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Forum: Math
2009-08-26, 03:05
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Replies: 3
Views: 616
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Forum: Math
2009-08-25, 07:32
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Replies: 3
Views: 616
Breaking a prime p into a^2 + 3* b^2
I'm playing with cubic reciprocity (http://en.wikipedia.org/wiki/Cubic_reciprocity) formulas.
From that link, it states "A theorem of Fermat states that every prime p ≡ 1 (mod 3) is the sum of a...
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Forum: Math
2009-08-24, 23:26
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Replies: 8
Views: 2,056
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Forum: Math
2009-08-24, 23:22
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Replies: 8
Views: 2,056
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Forum: Math
2009-08-24, 20:34
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Replies: 8
Views: 2,056
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Forum: Math
2009-08-24, 20:06
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Replies: 8
Views: 2,056
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Forum: Math
2009-08-24, 17:56
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Replies: 8
Views: 2,056
P95 trial division strategy
I'm experimenting with my own GPU Mersenne trial division tool.. it's got its own fun challenges.
The classic way to test for divisibility of 2^p -1 by q is to compute
2^p mod q and look for a...
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Forum: Math
2009-08-22, 07:12
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Replies: 5
Views: 731
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Forum: Math
2009-08-21, 17:12
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Replies: 5
Views: 731
Mersenne trial division candidate counts
Another thread mentioned the nice benchmark page (http://mersenne-aries.sili.net/throughput.php?cpu=Intel%28R%29+Atom%28TM%29+CPU+330+%40+1.60GHz%7C512%7C0&mhz=1600) listing hardware speeds for FFT...
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Forum: Math
2009-08-20, 22:06
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Replies: 25
Views: 1,317
Now that is a nearly ideal link to start...
Now that is a nearly ideal link to start exploring. I'm not sure why I didn't find it when I was searching myself.
I agree.. there's a lot of discussion there! And maybe a decent algorithm or two,...
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Forum: Math
2009-08-20, 22:02
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Replies: 25
Views: 1,317
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Forum: Math
2009-08-20, 21:41
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Replies: 25
Views: 1,317
Thanks for the quick reply!
This is useful,...
Thanks for the quick reply!
This is useful, since it provides a clear general algorithm for evaluating the answer.
The annoying part is that for large p, computing x^(large) mod p is...
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Forum: Math
2009-08-20, 21:18
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Replies: 25
Views: 1,317
Residue identification algorithm
I'm trying to understand the identification of residues of x^n mod p, where p is an odd prime.
For the residues of x^2 mod p, there are exactly (p+1)/2 residues. You can compute whether a specific...
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Forum: Math
2009-08-17, 17:41
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Replies: 5
Views: 1,499
A followup question on Montgomery reduction.
...
A followup question on Montgomery reduction.
Using a radix R=2^s is most common of course.
But the Montgomery method only works with N that are coprime to R..
so for the R=2^s case, N must be...
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Forum: Math
2009-08-17, 04:43
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Replies: 5
Views: 1,499
Thanks for the verification!
But that...
Thanks for the verification!
But that laddering code is awkward. It doesn't match the 9.3.1 code, it unwraps one extra pass for the high bit, which makes it uselessly compute a full and...
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Forum: Math
2009-08-17, 00:34
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Replies: 5
Views: 1,499
Montgomery method in Prime Numbers: ACP
I love the book Prime Numbers: a Computational Perspective. (http://www.amazon.com/Prime-Numbers-Computational-Richard-Crandall/dp/0387252827)
But I'm going wild trying to get Montgomery reduction...
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Forum: Lounge
2009-07-28, 03:44
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Replies: 20
Views: 1,194
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Forum: Lounge
2009-07-28, 03:41
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Replies: 20
Views: 1,194
He seemed quite happy to get some notes I sent...
He seemed quite happy to get some notes I sent him a few years back. Anyone mailing him went through some effort, so he's usually interested.
His astounding encyclopediac knowledge was proved yet...
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Forum: Programming
2009-07-26, 00:06
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Replies: 10
Views: 2,559
Alex, wow, excellent.. I would never have found...
Alex, wow, excellent.. I would never have found that. This is also a lot to digest! Thanks.
Knuth was so correct when he wrote that there was a rich and mysterious theory behind efficient addition...
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Forum: Programming
2009-07-25, 14:57
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Replies: 10
Views: 2,559
Googling for Montgomery PRAC doesn't turn up...
Googling for Montgomery PRAC doesn't turn up anything.
Is this the idea of precomputing a table of 1 x^2 x^3 x^4 x^5 x^6 x^7
(or up to some 2^m -1) and then taking big steps of m bits at once and...
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Forum: Programming
2009-07-25, 14:53
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Replies: 10
Views: 2,559
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