mersenneforum.org optimal memory settings for the P-1 stage
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 2007-05-27, 13:20 #12 axn     Jun 2003 112518 Posts I can see how my post could be misunderstood that way. However the point I was trying to make was that you cannot analyze the "efficiency" of P-1 without considering the LL cost. Supposing that the LL cost was more than 1200 hrs. In that case, Prime95 would've chosen Combo Z, despite the fact that the "efficiency ratio" indicated Combo X.
 2007-05-28, 04:37 #13 cheesehead     "Richard B. Woods" Aug 2002 Wisconsin USA 22·3·599 Posts Subconscious sez: P-1 run time is proportional to not only the B1/B2 bounds (as in my example), but also FFT transform time (for mod 2p-1, same as used in L-L), of course! Sorry for my confusion, but I've never written this all down at once. I need to consult the source code, but I think this may be O($t$) for typical auto-chosen B1/B2. So that "Expected Cost" column should be more like: 0.990$t$ + 1.0 * O($t$) 0.987$t$ + 1.5 * O($t$) 0.985$t$ + 1.6 * O($t$) ... which, I guess, is what I meant about the implied multiplication. Last fiddled with by cheesehead on 2007-05-28 at 05:01
2007-05-28, 05:20   #14
crash893

Sep 2002

23×37 Posts

Quote:
 Originally Posted by cheesehead Do you think something's wrong with that? (Other than the real percentages being much lower than 50%/60%/65% -- maybe substitute 1.0%/1.2%/1.3% ) If so, what numbers would you think were "normal"? Increasing memory does not increase the chance of factor-finding in _linear proportion_. (-- to be continued in a few minutes --)

actually thats what im looking for

1gig = 1.0% chance
1.5 gig =1.1% chance
2 gig = 1.5% chance

some sort of graph like that

2007-05-28, 08:49   #15
axn

Jun 2003

17×281 Posts

Quote:
 Originally Posted by cheesehead Subconscious sez: P-1 run time is proportional to not only the B1/B2 bounds (as in my example), but also FFT transform time (for mod 2p-1, same as used in L-L), of course!
True, but irrelevant. In your example, the time for the various P-1 options have already been given.

Quote:
 Originally Posted by cheesehead So that "Expected Cost" column should be more like: 0.990$t$ + 1.0 * O($t$) 0.987$t$ + 1.5 * O($t$) 0.985$t$ + 1.6 * O($t$) ... which, I guess, is what I meant about the implied multiplication.
I think you are confusing yourself. In that table, I was using the numbers you had provided (like 10hrs, 15hrs, 16hrs).

Let's cut to the chase. Do you understand why Prime95 cannot choose the optimal B1/B2 values /just/ by the ratio (chance of finding a factor)/(P-1 cost)?

2007-05-28, 11:47   #16

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·599 Posts

Quote:
 Originally Posted by crash893 actually thats what im looking for 1gig = 1.0% chance 1.5 gig =1.1% chance 2 gig = 1.5% chance some sort of graph like that
It would be:

exponent xxxxxxxx @ 1gig = 1.0% chance
exponent xxxxxxxx @ 1.5 gig =1.1% chance
exponent xxxxxxxx @ 2 gig = 1.5% chance

exponent yyyyyyyy @ 1gig = 0.9% chance
exponent yyyyyyyy @ 1.5 gig =1.0% chance
exponent yyyyyyyy @ 2 gig = 1.4% chance

exponent zzzzzzzz @ 1gig = 0.8% chance
exponent zzzzzzzz @ 1.5 gig =0.9% chance
exponent zzzzzzzz @ 2 gig = 1.3% chance

One could plot a separate curve for each exponent on one x-y graph with axes of Available Memory and chance of finding a factor. (Actually, there'd have to be a separate multi-exponent graph for each CPU type.)

2007-05-28, 12:08   #17

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·599 Posts

Quote:
 Originally Posted by axn1 I think you are confusing yourself.
I'm temporarily having trouble concentrating in general, for medical reasons.

Quote:
 In your example, the time for the various P-1 options have already been given. < snip > In that table, I was using the numbers you had provided (like 10hrs, 15hrs, 16hrs).
But that's what was wrong previously -- the (10hrs, 15hrs, 16hrs) were wrong.

It gave the incorrect impression that P-1 run time was not dependent on exponent size or B1/B2 size. What I had meant in my original example was that for a particular, but unstated (which was confusing to the reader!!), example-only exponent and the given B1/B2, those were particular-(unstated)-exponent-example-only run times for illustrative purposes.

What I meant last post was that the P-1 run times should have been 1.0 * O($t$), 1.5 * O($t$), 1.6 * O($t$) instead of (10hrs, 15hrs, 16hrs). Or maybe it would've been clearer to write:

0.010 * O($t$)
0.015 * O($t$)
0.016 * O($t$)

since some (I, at least) may tend to think of O($t$) as being close to 1 * $t$ in magnitude.

Of course, what I really should have done was to present a rewritten example.

Quote:
 Do you understand why Prime95 cannot choose the optimal B1/B2 values /just/ by the ratio (chance of finding a factor)/(P-1 cost)?
Is that question still valid, in light of this correction to the P-1 cost?

Last fiddled with by cheesehead on 2007-05-28 at 12:46

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