Is mine bigger than yours?

[tqft]

Now crunching
n=3146863

(the hardrive does sound a bit that way when spinning up)

k=24737

the stats page hasn't quite updated yet.

Given all the people with bigger/faster machines, I doubt mine will be biggest for long.

ps: I cannot find a definition of cEMs. Have read the FAQ's and googled for it. Thought I saw one somewhere sometime but for the life of me cannot find it. Am I blind/stupid (please don't agree too much).

[montrd]

I found an explaination from mad-ness on the ARS Technica forums:

cEMs explained (http://arstechnica.infopop.net/OpenTopic/page?a=tpc&s=50009562&f=122097561&m=9880930935&r=8500979355#8500979355)

[MAD-ness]

The referenced answer in the Ars forum was 'stolen' from a thread here on the official forum where Louie stepped up and answered, in detail, my questions about what exactly 'cEMs' were.


Re: Need help with explanations please

quote:Originally posted by MAD-ness


1) what exactly are cEMs? If I remember correctly from somewhere (perhaps the SoB page or the FAQ before it was pulled) cEMs stands for "Corrected Exponent Mod.' I always sort of wondered what mod was an abbreviation for. Having just dug through the Sierpinski math pages my guess would be that it stands for "modulo." Would it be possible for someone to explain in some detail (and hopefully simultaneously and/or seperately) exactly what an exponent mod is?




Well, I'm sure no one else is going to step up and field this one... so here goes.

"cEMs are the pronouncable acronym for corrected Exponentiation Modulus's. To understand the origin of this unit, you have to understand a little about the origin of SB. Historically, the first versions of SB (v0.1 - v0.90) used GMP as an underlying math lib. Anyone involved with SB back in April 2002 might remember the first month or so where we simply used EMs. An EM was equal to one pass through the squaring (exponentiation) and modulus loop in the original GMP versions of SB. When we had vital systems of SB working, we went back and decided to redefine the work measurement. This is because the speed of the EM is not constant or linear with respect to the input size. The larger the number under test becomes, the longer a single EM takes. For GMP, the steps supposedly grow as O(n ln n) the input length of the numbers. However, we found that the FFT multiplication routines in GMP were dominated by many sub-routines which ran in O(n^2) time. Therefore, we added a correction factor and redefined EMs as cEMs. Specifically, the forumula to calculate cEMs for an entire test is:

cEMs = n^2 / 1 billion.

cEMs were great. They worked really well.

Now, fast forward half a year later. George Woltman appoaches the SB team. He offers his math routines from PRP which are highly superior to GMP's more general routines. We integrate PRPs routines but don't immediately change units. However, the unit should probably change for several reasons. For one, PRP techincally doesn't even do a modulus operation anymore... making it a little inappropriate for the unit itself to refer to modulus'. [For those interested, the modulus is done "for free" as a side-effect of the discrete weighted transforms used to square numbers.] Also, the routine is not O(n^2)... it's closer to O(n ln ln ln n). So to make things even more confusing, it turns out the PRP routines are not only faster, they also "slow down slower" as the size of their inputs increases. This means that cEMs artifically inflate slightly as test sizes increase.

Currently, Dave has isolated specific test points in the database which we are using to create a new unit the doesn't skew over time. Unless something changes, cEMs will eventually be replaced by Flops (Floating-Point Operations). Once an appropriate correction factor is decided on, Flops will replace cEMs. EMs made sense for a month. cEMs made sense for a couple more months. And now, Flops make sense going forward so we'll change as soon as possible... making this entire question on the FAQ only a depreciated curiosity. "

-Louie

The thread in question can be found here:

http://www.free-dc.org/forum/showthread.php?s=&threadid=2361

[Lagardo]

Originally posted by tqft
Now crunching
n=3146863
...


This brings to mind the question: who got 3141592 for the various k? ;)

[tqft]

Great info on cEMs people.

Also the other links in thsi and another thread I posted have started down the road to understanding.

Now I am starting to understand the method behind the brute grunt needed and why the "key space" is so large.

[Cmarc]

I could be wrong but I believe the formula is acutaly n^3/10E9 for current n values around 3,000,000 this would amount to 27*10E18/10E9 or 27GcEM which is about what we see.
Cheers,
Marc

[Lagardo]

Originally posted by tqft

Given all the people with bigger/faster machines, I doubt mine will be biggest for long.


You got that right: I'm noddling on n=3150857

[smh]

On average, every 3 minutes a complete test is returned, this means that every 3 minutes a new test will be assigned. And since tests are assigned by increasing N's, everytime you get a new exponents it will be the largest out there for a short while.

[tqft]

Andy Warhol - I was promised 15 minutes of fame and looks I only got 3 min:D

My (home) machine appears to like being awake - it must sleep hard currently at 50 cEM/s, seems to cruise at about half that when I am not using it (and yes I basically just use it for surfing and SoB). Though that will change soon I expect - mgt seem to be sharpening their axes.

[dmbrubac]

everytime you get a new exponents it will be the largest out there for a short while.

But on a K by K basis right? So you only have the highest exponent if your client is working on the K that is fursthest along. Since there are still 12 K's, 15 minutes of fame is more like 36.

Now you owe Andy