Perft(14) Weekly Status Reports for 2015

[sje]

Perft(14) Weekly Status 2015-10-18

Symbolic has produced more than 21,900,000 perft(7) results so far, about 22.72% of the 96,400,068 needed.

Day count: 438
Estimated remaining day count: 1,490
Estimated total day count: 1,928

Average throughput: 50,000 results/day
Effective frequency: 64.71 GHz

Work units not yet started (724): 230-963

Sum of perft()s: 508,867,849,150,614,276
Sum of products: 2,448,700,896,737,212,462

[sje]

Perft(14) Weekly Status 2015-10-25

Symbolic has produced more than 22,500,000 perft(7) results so far, about 23.34% of the 96,400,068 needed.

Day count: 445
Estimated remaining day count: 1,462
Estimated total day count: 1,907

Average throughput: 50,562 results/day
Effective frequency: 66.71 GHz

Work units not yet started (728): 236-963

Sum of perft()s: 520,707,787,871,746,459
Sum of products: 2,565,137,696,173,103,674

[sje]

Perft(14) Weekly Status 2015-11-01

Symbolic has produced more than 23,300,000 perft(7) results so far, about 24.17% of the 96,400,068 needed.

Day count: 452
Estimated remaining day count: 1,418
Estimated total day count: 1,870

Average throughput: 51,549 results/day
Effective frequency: 70.46 GHz

Work units not yet started (720): 244-963

Sum of perft()s: 537,672,272,657,811,173
Sum of products: 2,751,561,859,634,729,399

[sje]

Perft(14) Weekly Status 2015-11-08

Symbolic has produced more than 24,000,000 perft(7) results so far, about 24.90% of the 96,400,068 needed.

Day count: 459
Estimated remaining day count: 1,385
Estimated total day count: 1,844

Average throughput: 52,288 results/day
Effective frequency: 73.73 GHz

Work units not yet started (712): 252-963

Sum of perft()s: 553,978,528,084,422,410
Sum of products: 2,924,250,666,703,176,523

[sje]

Projection estimations

Current projection estimations are based on a first order approximation of a calculation rate determined by the number of work units processed divided by the number of days since the project started. This rate is called the cumulative rate.

The above is not very accurate in that it does not account for speed improvements in the perft() algorithm or for machinery improvements and additions. The recent perft(7) result rate is about 100,000 per day, close to twice the cumulative rate. This, the recent rate, will be improved even further in a week or so with the addition of 40+ GiB memory to be distributed among the machines. Although the weekly progress reports will continue to use the cumulative rate, based on the recent rate I expect that the project will conclude in mid 2017, less than two years from now.

However, the final perft(14) result will need verification. This would be true even if someone else produces a result before I do, as was the case with perft(12) and perft(13). At present, only 400 of the 984 100,000 position work units have second party results, and these were produced using 64 bit signatures, not the 128 bit signatures used by Symbolic and Oscar. Further, given the amount of elapsed calculation time combined with the total silicon area in use, the prospect of errors caused by cosmic rays cannot be discarded. There might be some good luck on this point, as the processing was done at an altitude of only some 80 meters above sea level and so has about as much atmospheric shielding as possible.

[petero2]

However, the final perft(14) result will need verification. This would be true even if someone else produces a result before I do, as was the case with perft(12) and perft(13).

I computed perft 14 back in 2013. If your computation matches my number, it would be a strong hint that the number is correct. If your computation does not match my number, I think a third independent computation would be needed, since the algorithm I use (from Paul Byrne) does not compute any sub results, such as the 400 perft 12 results after 2 ply.

[sje]

Perft(14) Weekly Status 2015-11-15

Symbolic has produced more than 24,800,000 perft(7) results so far, about 25.73% of the 96,400,068 needed.

Day count: 466
Estimated remaining day count: 1,345
Estimated total day count: 1,811

Average throughput: 53,219 results/day
Effective frequency: 78.46 GHz

Work units not yet started (704): 260-963

Sum of perft()s: 573,774,121,095,631,029
Sum of products: 3,158,598,046,491,025,334

[sje]

However, the final perft(14) result will need verification. This would be true even if someone else produces a result before I do, as was the case with perft(12) and perft(13).

I computed perft 14 back in 2013. If your computation matches my number, it would be a strong hint that the number is correct. If your computation does not match my number, I think a third independent computation would be needed, since the algorithm I use (from Paul Byrne) does not compute any sub results, such as the 400 perft 12 results after 2 ply.

Yes, I saw your post and I commented upon it. Up until now, I was not sure if you meant it as a actual exact result or as a refined estimate, as were other posts in that thread. This was because there was no mention of the algorithm in use, signature bit length, the machinery, any past calculations, or -- most importantly -- partial results.

For each of my high level results, I've posted as proofs the 20 ply one subtotals and the 400 ply two subtotals. I believe that these are the minimum needed to establish authenticity. For perft(14), I will go further and provide the subtotal sets from ply one to ply seven. Indeed, I've been posting on Dropbox and Google Drive all of the ply seven subtotals as they are calculated. I want others to be able to attack my calculations without having to re-calculate the entire perft() grand total.

[petero2]

However, the final perft(14) result will need verification. This would be true even if someone else produces a result before I do, as was the case with perft(12) and perft(13).

I computed perft 14 back in 2013. If your computation matches my number, it would be a strong hint that the number is correct. If your computation does not match my number, I think a third independent computation would be needed, since the algorithm I use (from Paul Byrne) does not compute any sub results, such as the 400 perft 12 results after 2 ply.

Yes, I saw your post and I commented upon it. Up until now, I was not sure if you meant it as a actual exact result or as a refined estimate, as were other posts in that thread. This was because there was no mention of the algorithm in use, signature bit length, the machinery, any past calculations, or -- most importantly -- partial results.

That was an exact calculation, not an estimate. I did describe the algorithm I used, but in a different thread.

Regarding partial results, the only partial results computed by this algorithm is the number of unique positions after N plies, which I reported here. That post also contains information about some past results, where the algorithm had correctly computed perft 11, 12 and 13.

The used algorithm is a deliberate trade-off that made it possible to compute perft 14 in a couple of months instead of in several years. Paul Byrne made the same trade-off when he computed perft 13, and there was some discussion of the trade-off here.

[sje]

It's possible that I missed some of your posts on perft(14) if they appeared in a thread with perft(13) in its title.

I have serious doubts about the reliability of 64 bit signatures over extended calculation times. I've given examples of 64 bit false positives and have shown how the number of required signature bits is roughly proportional to log2(N) where N is the probe count. Others have posted on how their chess engines have had 64 bit false positives and how such are handled in a search.

A second area of doubt comes from the possibility of undetected I/O disk errors where an application could beat on disk more in a single month than what is their total lifetime projected use. While undetected hard drive I/O errors are uncommon with modern hardware, they are common enough that I've seen a couple of them.