how is the throughput calculated?
 

Does anyone know how the GIMPS throughput is calculated?

I'm asking this because the numbers don't seem to add up. It appears that the actual throughput is much higher than the figure listed on the PrimeNet page.

Here is an example:

It is reported that a 3.2 GHz Pentium 4 processor (with 512 kb L2 cache) can peak at 12 GFLOPs, but most benchmarks put it at around 6 GFLOPs, so I'll go with the latter figure. According to the [url=http://mersenne.org/bench.htm]benchmarks page[/url], each iteration takes 0.0764 seconds for exponents that are between 39.5M and 49.1M (most exponents that are being tested right now are in this range). Therefore, a 40M exponent should take about 35 days on a Pentium 4, assuming that the test is run continuously. Since the PrimeNet server is synchronized every half month, we can mathematically expect a 3.2 GHz processor to clear 0.4 exponents during this half-month period. GIMPS' current throughput of 30 TFLOPs would be equivalent to 6,000 of those processors. This would mean that about 2,400 exponents are cleared (by Lucas-Lehmer testing) every half month. However, the actual number of exponents that are cleared by Lucas-Lehmer testing are much higher, often exceeding 10,000. This leads me to think that GIMPs' actual throughput is much higher than 30 TFLOPS. While there is no perfect correlation between the iteration time and the processor speed (there are many other factors that determine a processor's performance), something just seems wrong here.

I've noticed another thing. The PrimeNet page only lists processors up to the Pentium 4. The newer chips, such as the Xeon and Core 2 processors, are not included. Is it possible that GIMPS is not recognizing some of the newer processors, or even mistaking them for older ones? PrimeNet lists 98 "unspecified" processors, but I'm pretty sure that there are way more than 98 people that are using newer processors than the Pentium 4.

According to my observations, Primenet suggests that
30 Tflops clears about ten tests per hour, which amounts
to 3600 tests in 15 days.
BTW the synchronization is performed monthly (on the 15th of
the month), not every half month.
This goes a long way towards accounting for your "discrepancy".

David

[quote=ixfd64;133627]
It is reported that a 3.2 GHz Pentium 4 processor (with 512 kb L2 cache) can peak at 12 GFLOPs, but most benchmarks put it at around 6 GFLOPs, so I'll go with the latter figure.[/quote]

If the actual performance when doing an LLtest was 4 GFLOPs,
this would account for the remainder of your "discrepancy".

Does not the throughput also measure double checks, TF, and P-1?

If you use the formulas from these threads with the new FFT sizes cutoffs:

[url]http://www.mersenneforum.org/showthread.php?t=10235[/url]

[url]http://www.mersenneforum.org/showthread.php?t=3337[/url]

and remember from status page we can calculate 1 P90yr = 1,040,057 GFLOP (not GFLOP/s).

[U]29.69M to 34.56M (1792K):[/U] p90yr=exp*1.113*5.5/31536000
so 1 LL-iteration = exp*1.113*5.5*1040057 / ( 31536000 * exp) = 0.201887 GFLOP (not GFLOP/s)

[U]34.56M to 39.50M (2048K):[/U] p90=exp*1.226*5.5/31536000
1 LL-iteration = exp*1.226*5.5/ ( 31536000 * exp) = 0.222384 GFLOP

[U]39.50M to 49.10M (2560K):[/U] p90=exp*1.640*5.5/31536000
1 LL-iteration = exp*1.640*5.5/ ( 31536000 * exp) = 0.297480 GFLOP

[U]49.10M to 58.52M (3072K):[/U] p90=exp*1.990*5.5/31536000
1 LL-iteration = exp*1.990*5.5/ ( 31536000 * exp) = 0.360966 GFLOP

So if you test your average iteration time on exponents in each range you can see how many GFLOP/s that is, and I got fairly same number from the different FFT ranges.

From 2048K range for example my average iteration on my P4 Prescott 3.4 Ghz was 57.7ms so I got 0.222384 GFLOP / 0.0577s = 3.85 GFLOP/s. From 3 different FFT range I got 3.70-3.95 GFLOP/s so nowhere near 6 GFLOPs. On my Athlon XP 2200+ 1.8Ghz I got 1.23-1.25 GFLOP/s.

[QUOTE=ixfd64;133627]It is reported that a 3.2 GHz Pentium 4 processor (with 512 kb L2 cache) can peak at 12 GFLOPs.[/QUOTE]

The theoretical maximum throughput for a single core of Pentium 4 is one add and one multiply per clock cycle. So a 3.2GHz CPU has a 6.4 GFLOPs theoretical max.