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Forum: Math 2019-04-28, 02:43
Replies: 1
Views: 400
Posted By __HRB__
Sieving Question

What advanced knowledge do we have about the factors of the following numbers?

P = (k*2^m)^(2^n)+1

where k is an odd 32-bit number, and m ~ n.

The idea is to use Proth's theorem for a...
Forum: Lounge 2010-11-03, 16:15
Replies: 959
Views: 46,511
Posted By __HRB__
Naglfar - I am Vengeance

http://www.youtube.com/watch?v=eQcLWjHnBp0

To quote a comment:

"I pity the f***** that cuts me off in traffic while blasting this song on my car stereo."

Lyrics:

Humanity what have you...
Forum: Software 2010-09-28, 19:00
Replies: 15
Views: 1,277
Posted By __HRB__
The argument is that one will efficiently load...

The argument is that one will efficiently load stride-X-separated cachelines from L2 to L1 if you use cachelines as your data type. If loading a cacheline takes 4 cycles, then if your code partially...
Forum: Software 2010-09-28, 00:26
Replies: 15
Views: 1,277
Posted By __HRB__
It also makes sense for FFTs: a split-radix...

It also makes sense for FFTs: a split-radix butterfly has 16 additions and 8 multiplies, which (IIRC) can be done in 48 instructions including branching code. Then you loop over one FFT of length N/2...
Forum: Software 2010-09-27, 21:43
Replies: 15
Views: 1,277
Posted By __HRB__
I don't think that's a good way to approach the...

I don't think that's a good way to approach the problem, as SSE-stuff is designed to 'stream' data through the processor. IMO it is much easier to achieve peak performance by using only a few...
Forum: Software 2010-09-27, 20:43
Replies: 15
Views: 1,277
Posted By __HRB__
Using assembly is the only way to actually be...

Using assembly is the only way to actually be limited by hardware bottlenecks. In http://www.mersenneforum.org/showthread.php?t=13176 for example the compiled code runs at ~66% of the theoretical...
Forum: Lounge 2010-09-27, 12:48
Replies: 51
Views: 2,083
Posted By __HRB__
We should redefine something to make it easier...

We should redefine something to make it easier for you to do arithmetic using your fingers and thumbs? Tsk, tsk.

How about we change it to a 2^-16th of a day? Or better, use something that can me...
Forum: Lounge 2010-09-26, 21:03
Replies: 3,897
Views: 231,859
Posted By __HRB__
What happens when editors don't pay attention?

http://laughterizer.weebly.com/1/post/2010/09/unintentional-porn.html
Forum: Lounge 2010-09-22, 18:06
Replies: 959
Views: 46,511
Posted By __HRB__
You used to go to hip joints and now you need new...

You used to go to hip joints and now you need new hip joints?
Forum: Lounge 2010-08-21, 20:24
Replies: 1,577
Views: 75,290
Posted By __HRB__
In the mean time you can get LASIK (e.g. here...

In the mean time you can get LASIK (e.g. here (http://www.lasikvisioninstitute.us.com/lasikvision/unique/113422.php)) for $1299 per eye. Also, a years supply of Acuvue Oasis contact lenses is roughly...
Forum: Software 2010-08-09, 11:13
Replies: 188
Views: 15,521
Posted By __HRB__
I think you will find these helpful: The...

I think you will find these helpful:

The microarchitecture of Intel, AMD and VIA CPUs: An optimization guide for assembly programmers and compiler makers
...
Forum: Software 2010-08-09, 01:44
Replies: 188
Views: 15,521
Posted By __HRB__
Aim for: ~3 instructions/clock for Core2 ...

Aim for:

~3 instructions/clock for Core2
~2.7 instructions/clock for Athlon II.
Forum: Software 2010-08-08, 23:16
Replies: 188
Views: 15,521
Posted By __HRB__
See:...

See: http://www.mersenneforum.org/showthread.php?t=13176
Performance for a split radix real FFT, i.e ~4/3*n*log2(n) adds and 2/3*n*log2(n) multiplies, on CPUs is limited by the throughput of the...
Forum: Software 2010-08-08, 22:41
Replies: 188
Views: 15,521
Posted By __HRB__
The problem is that if you are not using SSE2 you...

The problem is that if you are not using SSE2 you immediately suffer a 100% penalty, because 128-bit registers can simply do twice as much as 64-bit registers. Your best bet is to use 2^96==-1 (mod...
Forum: Hardware 2010-08-06, 06:30
Replies: 18
Views: 1,125
Posted By __HRB__
At most AVX will speed up the search by 100%, but...

At most AVX will speed up the search by 100%, but since it will take a while until a significant portion of users owns a processor that supports these new extensions...

Considering that a $200...
Forum: Lounge 2010-07-12, 12:52
Replies: 267
Views: 21,735
Posted By __HRB__
Not the best, but memorable...

http://amaroklive.com/blog/archives/452-Geek-Mobile.html
Forum: Conjectures 'R Us 2010-07-12, 01:59
Replies: 90
Sticky: Come join us!
Views: 27,022
Posted By __HRB__
Hm, it appears that I forgot to mention that it...

Hm, it appears that I forgot to mention that it would only work for generalized Fermats!



Really? The idea would be to search for very large primes, for instance among the numbers that have...
Forum: Conjectures 'R Us 2010-07-11, 23:18
Replies: 90
Sticky: Come join us!
Views: 27,022
Posted By __HRB__
Faster special case algorithm?

If we use Proth's theorem to search for primes of the form (k*2^n)^(2^m)+1 with k<2^n, and if (k*2^n)^2+m<2^m, we could do the required negacyclic convolution with Schoenhage-Strassen in base k*2^n....
Forum: Lounge 2010-06-16, 01:14
Replies: 46
Views: 1,299
Posted By __HRB__
It is easier to be wise for others than for...

It is easier to be wise for others than for oneself.
-- La Rochefoucauld

A lot of people think they are generous because they give away free advice.
-- La Retourcouche
Forum: Lounge 2010-06-16, 01:06
Replies: 46
Views: 1,299
Posted By __HRB__
d) bush.

d) bush.
Forum: Lounge 2010-06-13, 15:42
Replies: 959
Views: 46,511
Posted By __HRB__
Eric Petersen's side project

Haven't listened to this in a while. My favorites:

Dragonlord - Rapture: http://www.youtube.com/watch?v=BXkXY9BDtVc
Dragonlord - Unholy Void: http://www.youtube.com/watch?v=ZNssp1UVIII
Forum: Math 2010-06-12, 20:09
Replies: 1
Views: 400
Posted By __HRB__
After some fudging I managed to find: ...

After some fudging I managed to find:

Mod(127316999246511176001337524256693, 162259276829213363391578010288127) + Mod(100755747211248383624389262455139, 162259276829213363391578010288127)*IWhich...
Forum: Math 2010-06-12, 17:03
Replies: 1
Views: 400
Posted By __HRB__
pari-gp and trigonometry in Galois fields

Is there a straightforward way to compute roots modulo p^2 with pari-gp?

Specifically, if p=2^107-1, then 4th roots of unity are free, 8th roots are computationally cheap (i.e. +/-2^53 +/- i*2^53,...
Forum: Lounge 2010-06-08, 16:45
Replies: 3,897
Views: 231,859
Posted By __HRB__
You read Bruce Schneier's blog. :-)

You read Bruce Schneier's blog. :-)
Forum: Software 2010-06-04, 12:55
Replies: 188
Views: 15,521
Posted By __HRB__
Hm...formatting came out wrong...it should read ...

Hm...formatting came out wrong...it should read
"1050640^4096+1", "2^13", "(mod 1050640^4096+1)" and "k*2^n+/-1"

Also, if we're doing stuff (mod k*2^n+/-1), then we can also use ...
Showing results 1 to 25 of 720

 
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