Gigaflops rate greatly exceeds trend predicted 2 1/2 years ago

GP2 · 2003-10-19, 20:42

At the by-now rather obsolete page
http://mersenne.org/ips/stats.html
a graph show a linear progression in Gigaflops for the GIMPS project.

The regression formula given is:
y = 1.2658 x - 57.418

Where y is the rate in Gigaflops
and x is the number of days since Nov 23 1997.

The graph shows the plot from Nov 23 1997 to Mar 9 2001 (1202 days).

If we extrapolate the regression line to Oct 19 2003 (2155 days), we get a prediction of 2670 Gigaflops.

In fact, though, the Primenet server is currently reporting 7698 Gigaflops, exceeding the prediction by almost a factor of 3.

I wonder what can explain this? I don't think SSE2 code for Pentium 4s or the arrival of large teams like Team_Prime_Rib, alone, can explain a factor of 3.

It would be interesting to see what happened to the graph after Nov 14 2001 when M39 was discovered.

PageFault · 2003-10-20, 01:23

It is mainly SSE2 and also the fact that modern cpu's have gotten very fast. Late 2000 I bought my first GHz cpu. Now I couldn't be bothered to run prime95 on it. My 2.4C @ 3.0 does the work of six 1.1 tbirds.

Team Prime Rib has about 600 GHz of power active now. This will increase as our woes with curtisc have resulted in a call for reinforcements - one of the benefits of being with a large group.

GP2 · 2003-10-20, 02:05

I don't think that "modern CPUs getting very fast" can explain a radical difference in the trends from 1997-2001 versus 2001-2003. Moore's law hasn't suddenly accelerated over the past 2 1/2 years. Then again Moore's law would predict exponential growth, so why does the data from 1997 to 2001 show only a straight-line trend?

SSE2 can't explain it. The speed gain in version 23 is "only" 30-40%, not a factor of 3.

A team like Team_Prime_Rib, despite its number one position, probably contributes less than (wild guess) 10% of the overall crunching power. So that wouldn't explain it either.

mephisto · 2003-10-20, 04:16

Team Prime Rib has contributed 3.7% of the total GIMPS work (sum CPU-years LL and factoring).

Accumulative contributions:
top 1 - 3.7%
top 10 - 12.5%
top 100 - 28%
top 1000 - 60%
top 10000 - 94%

(Data from a few weeks back.)

So user contributions is an exponential distribution as well, it's not just a 'top few' doing everything.

I won't attempt to guess at reasons for the increase, other than noting that exponential functions start out pretty much linear.

nucleon · 2003-10-20, 08:32

It'll be interesting to see how the graph goes after the $100k prize is claimed :)

-- Craig

mephisto · 2003-10-20, 12:36

True enough - as motivation factors go, it is hard to beat $100K :)

garo · 2003-10-20, 17:28

While v23 is only 30-40% better v21 was more than twice as fast as v20. In that respect v23 is about 3 times as fast - if not more - on a P4 than the version out in early 2001 was.

markhl · 2003-10-20, 20:04

I see several factors:

1 CPUs and FSBs are getting faster; Moore's Law is exponential.
2 George continues to optimize for the latest chips.
3 Worldwide, more people now have PCs at home.
4 People who have a PC are more likely to own more than 1 PC.
5 A higher fraction of PC owners choose to run DC projects e.g. GIMPS.
6 DC projects are likely to speed up when the economy improves: more companies have more PCs to borg, and there are more employees to borg them!
7 A DC project enjoys a burst after publicity for that project: UD, Seti@Home, and others have seen that.
...

Some of these trends may saturate, so that you have a sigmoidal curve instead of an exponential:

8 Moore noted that speed will grow more slowly.
9 PC ownership will tend to saturate at some % of population.
10 Some PC owners will stop buying the latest and greatest because what they have meets their needs.
...

QuintLeo · 2003-10-22, 21:07

I suspect an additional factor may have been the completion of RC5-64 - when one of the largest (by participant count) DC projects ends, that leaves a LOT of folks (like me) looking for something new to do....

PageFault · 2003-10-23, 02:09

This is partly correct. Where I am, there are at least a dozen teams ... TPR grew out of the fallout of a stats debacle on another project, the last straw on the part of bad management. Within four months trial factoring crown was ours ... Of course this only applies to dc fanatics ... projects like seti get most of their power from casual users and with gimps there are only two teams to speak of ...

Quote:

Originally posted by QuintLeo
I suspect an additional factor may have been the completion of RC5-64 - when one of the largest (by participant count) DC projects ends, that leaves a LOT of folks (like me) looking for something new to do....

GP2 · 2003-11-14, 19:16

Now that I have a bunch of old summary.txt files, we can take another look:

LL-testing P90 years/day (7 day average)

We see that the data follows one straight-line trend until late 2001, then it follows another straight-line trend with a much steeper slope.

For good measure, we can also look at:

Trial factoring P90 years/day (7 day average)

Here the data follows a consistent straight-line trend, with no inflection in 2001.

2003-10-19, 20:42	#1
GP2 Sep 2003 5×11×47 Posts	Gigaflops rate greatly exceeds trend predicted 2 1/2 years ago At the by-now rather obsolete page http://mersenne.org/ips/stats.html a graph show a linear progression in Gigaflops for the GIMPS project. The regression formula given is: y = 1.2658 x - 57.418 Where y is the rate in Gigaflops and x is the number of days since Nov 23 1997. The graph shows the plot from Nov 23 1997 to Mar 9 2001 (1202 days). If we extrapolate the regression line to Oct 19 2003 (2155 days), we get a prediction of 2670 Gigaflops. In fact, though, the Primenet server is currently reporting 7698 Gigaflops, exceeding the prediction by almost a factor of 3. I wonder what can explain this? I don't think SSE2 code for Pentium 4s or the arrival of large teams like Team_Prime_Rib, alone, can explain a factor of 3. It would be interesting to see what happened to the graph after Nov 14 2001 when M39 was discovered.

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2003-10-20, 01:23	#2
PageFault Aug 2002 Dawn of the Dead 5·47 Posts	It is mainly SSE2 and also the fact that modern cpu's have gotten very fast. Late 2000 I bought my first GHz cpu. Now I couldn't be bothered to run prime95 on it. My 2.4C @ 3.0 does the work of six 1.1 tbirds. Team Prime Rib has about 600 GHz of power active now. This will increase as our woes with curtisc have resulted in a call for reinforcements - one of the benefits of being with a large group.

2003-10-20, 02:05	#3
GP2 Sep 2003 5×11×47 Posts	I don't think that "modern CPUs getting very fast" can explain a radical difference in the trends from 1997-2001 versus 2001-2003. Moore's law hasn't suddenly accelerated over the past 2 1/2 years. Then again Moore's law would predict exponential growth, so why does the data from 1997 to 2001 show only a straight-line trend? SSE2 can't explain it. The speed gain in version 23 is "only" 30-40%, not a factor of 3. A team like Team_Prime_Rib, despite its number one position, probably contributes less than (wild guess) 10% of the overall crunching power. So that wouldn't explain it either.

2003-10-20, 04:16	#4
mephisto Feb 2003 Norway 2³×7 Posts	Team Prime Rib has contributed 3.7% of the total GIMPS work (sum CPU-years LL and factoring). Accumulative contributions: top 1 - 3.7% top 10 - 12.5% top 100 - 28% top 1000 - 60% top 10000 - 94% (Data from a few weeks back.) So user contributions is an exponential distribution as well, it's not just a 'top few' doing everything. I won't attempt to guess at reasons for the increase, other than noting that exponential functions start out pretty much linear.

2003-10-20, 08:32	#5
nucleon Mar 2003 Melbourne 1003₈ Posts	It'll be interesting to see how the graph goes after the $100k prize is claimed :) -- Craig

2003-10-20, 12:36	#6
mephisto Feb 2003 Norway 2³×7 Posts	True enough - as motivation factors go, it is hard to beat $100K :)

2003-10-20, 17:28	#7
garo Aug 2002 Termonfeckin, IE 101011001100₂ Posts	While v23 is only 30-40% better v21 was more than twice as fast as v20. In that respect v23 is about 3 times as fast - if not more - on a P4 than the version out in early 2001 was.

2003-10-20, 20:04	#8
markhl Apr 2003 California 2²×23 Posts	I see several factors: 1 CPUs and FSBs are getting faster; Moore's Law is exponential. 2 George continues to optimize for the latest chips. 3 Worldwide, more people now have PCs at home. 4 People who have a PC are more likely to own more than 1 PC. 5 A higher fraction of PC owners choose to run DC projects e.g. GIMPS. 6 DC projects are likely to speed up when the economy improves: more companies have more PCs to borg, and there are more employees to borg them! 7 A DC project enjoys a burst after publicity for that project: UD, Seti@Home, and others have seen that. ... Some of these trends may saturate, so that you have a sigmoidal curve instead of an exponential: 8 Moore noted that speed will grow more slowly. 9 PC ownership will tend to saturate at some % of population. 10 Some PC owners will stop buying the latest and greatest because what they have meets their needs. ...

2003-10-22, 21:07	#9
QuintLeo Oct 2002 Lost in the hills of Iowa 2⁶×7 Posts	I suspect an additional factor may have been the completion of RC5-64 - when one of the largest (by participant count) DC projects ends, that leaves a LOT of folks (like me) looking for something new to do....

2003-11-14, 19:16	#11
GP2 Sep 2003 5×11×47 Posts	Now that I have a bunch of old summary.txt files, we can take another look: LL-testing P90 years/day (7 day average) We see that the data follows one straight-line trend until late 2001, then it follows another straight-line trend with a much steeper slope. For good measure, we can also look at: Trial factoring P90 years/day (7 day average) Here the data follows a consistent straight-line trend, with no inflection in 2001.