P-1 formula (help wanted)

[Prime95]

Originally Posted by R.D. Silverman

This is poorly posed.

Dubslow's response is essentially correct. This isn't an interesting mathematics optimization problem, rather a mundane programming optimization problem. I'm looking for a fast function that quickly, but not necessarily super accurately, simulates prime95's existing P-1 bounds generator over a range of values that the typical prime95 user encounters.

I forget all the details, but I received a bug report that accurately generating these optimal bounds on hundreds of assignments was causing problems at startup (sending expected completion dates to the server). This seemed like a potential quick and dirty fix.

[cheesehead]

I like the idea of saving:

1) a time estimate (not actual ETA, which would get mixed up if worktodo lines are rearranged/removed/added) and

2) (except for "Pminus1" where B1/B2 are specified) algorithmic B1/B2 bounds ^*

for each P-1 assignment in the worktodo line for that individual assignment

The first time these are calculated the long way, store them in the worktodo line. Then just read them out after that, unless something forces re-calculation of bounds/time.

Computing fresh ETAs each time, based on the stored time estimates, would be trivial.

This way, only the new assignments that have been added since the preceding request for ETAs would need to go through the full optimization algorithm to produce the ETA listing.

- - -

^* If a particular worktodo line's assignment had not yet actually started, there wouldn't exist any save file with the bounds in it.

[R.D. Silverman]

Originally Posted by Dubslow

I think you missed what he's getting at. Prime95 already has an excellent bounds optimizer, which optimizes for maximum success for lowest running time*

This is TOTAL nonsense. To achieve what you suggest, just run for ZERO
time.

[R.D. Silverman]

Originally Posted by Prime95

Dubslow's response is essentially correct. This isn't an interesting mathematics optimization problem, rather a mundane programming optimization problem. I'm looking for a fast function that quickly, but not necessarily super accurately, simulates prime95's existing P-1 bounds generator over a range of values that the typical prime95 user encounters.

No, Dubslow's response was total nonsense. (max prob of success for
minimal time)


And the question that you ask now is different from what was asked originally.


The true question should be how to optimize the "existing P-1 bounds generator over a range of values that the typical prime95 user encounters."

and that question IS a mathematical one.

As for a fast function, just use table lookup combined with some
simple interpolation.

[ckdo]

Originally Posted by Dubslow

I have 29 P-1 assignments currently, and it took 7 seconds to run (yes I did time it).

I have a quad with 5620 P-1 assignments. Bounds calculation took 63:29.93 (yes, I actually did time that too).

Problem: Assignments finish faster than bounds can be calculated, and submitting a result triggers bounds calculation.

If I had set the machine to automatically communicate with PrimeNet, it would (a) never finish communicating and (b) permanently use half a core for nothing useful - it has enough work such that it will not request more and little enough that it won't unreserve anything.

[Dubslow]

Originally Posted by R.D. Silverman

The true question should be how to optimize the "existing P-1 bounds generator over a range of values that the typical prime95 user encounters."

False. He is only looking to mimic it, for significantly less run time.

Originally Posted by R.D. Silverman

As for a fast function, just use table lookup combined with some
simple interpolation.

True. (And has already been suggested.)

Originally Posted by ckdo

I have a quad with 5620 P-1 assignments. Bounds calculation took 63:29.93 (yes, I actually did time that too).

Problem: Assignments finish faster than bounds can be calculated, and submitting a result triggers bounds calculation.

If I had set the machine to automatically communicate with PrimeNet, it would (a) never finish communicating and (b) permanently use half a core for nothing useful - it has enough work such that it will not request more and little enough that it won't unreserve anything.

Dear god that's a lot of assignments.

[Mr. P-1]

Originally Posted by R.D. Silverman

No, Dubslow's response was total nonsense. (max prob of success for minimal time)

You are correct. A more precise statement of the optimisation problem which the client tries to solve is:

Input Available Memory, number of bits Trial Factored, number of LL's already completed. Output optimal B1,B2, where the quantity to be optimised (minimised) is the expected running time to clear the exponent, either by finding a factor, or by completing two matching LL tests.

Assumptions: No further factorisation (either TF or some other method) will be attempted after P-1 but before the final LL. The LL will be done on the same machine as the P-1

As I have remarked on many occasions, for people doing P-1 work specifically (as opposed to people P-1ing exponents they are going to LL), these assumptions aren't valid. Additionally, for these people, the quantity the client tries to optimise is, well, non-optimal. Instead of trying to minimise the expected time to clear an exponent, it should be trying to maximise the expected time saving per unit time expended by me, where "expected time saving" means the difference between the expected time the average machine will take to clear the assignment if I don't do the P-1 first and if I do.

[axn]

Ok. Very crude first attempt. Assumes "tests saved" is two. For "tests saved" = 1, you can halve the output, I guess. Error is roughly within +/-10% ( for about 95% of the cases). Only calibrated within 25m < p < 75m. No idea how good it will be outside this range.

EDIT:- Produces rubbish values way outside the calibration range