Large Computations

(Last updated: March 7, 2011)

 

 

By Alexander J. Yee

 

Below is a listing of all the large computations that have been performed on "Nagisa", my dual-processor gaming computer/workstation.

The program that was used in all computations here is y-cruncher.

Computations:

Date Completed:	Constant:	Decimal Digits:	Purpose/Comments:
September 17, 2010	Zeta(3) - Apery's Constant	100,000,000,000	World Record Size Computation
July 8, 2010	Golden Ratio	1,000,000,000,000	World Record Size Computation
April 3, 2010	Pi	250,000,000,000	Test for v0.5.3.
March 28, 2010	Pi	100,000,000,000	Burn-In after motherboard RMA.
April 16, 2009	Catalan's Constant	31,026,000,000	World Record Size Computation
March 13, 2009	Euler-Mascheroni Constant	29,844,489,545	World Record Size Computation
February 28, 2009	Log(10)	31,026,000,000	World Record Size Computation
February 15, 2009	Zeta(3) - Apery's Constant	31,026,000,000	World Record Size Computation
February 4, 2009	Log(2)	31,026,000,000	World Record Size Computation
February 3, 2009	Pi	31,026,000,000	Test run for 31 billion digit arithmetic.
January 31, 2009	Catalan's Constant	15,510,000,000	World Record Size Computation
January 21, 2009	Zeta(3) - Apery's Constant	15,510,000,000	World Record Size Computation
January 18, 2009	Euler-Mascheroni Constant	14,922,244,771	World Record Size Computation
January 7, 2009	Log(2)	15,500,000,000	World Record Size Computation

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Zeta(3) - Apery's Constant - 100,000,001,000 digits

(World Record: September 17, 2010)

 

This computation improves the previous verified record of 31,026,000,000 digits by Raymond Chan and myself.

 

The purpose of this computation was to test if any bugs were introduced into the other constants since the February 2009 computation.

There had been a lot of changes to the program since February 2009. So it became necessary to re-test some of the less commonly used features.

 

Neither the computation nor the verification was done in a single contiguous run.

• The computation crashed in the base conversion step. This was due to a bug that was introduced into the program while it was being ported to Linux.
  This bug is only in the Windows version. Since the Linux port was done after the current public release of the Windows versions, the current public Windows version does not have this issue.
  
  
• The verification was run on a separate (and less powerful) computer at low priority using spare CPU cycles. Therefore it took significantly longer.
  
  Furthermore, it was interrupted twice:
  • The first interrupt was about 30% through the series. It was caused by a hard drive CRC error. Goes to show how unreliable hardware can be...
  • The second interrupt was about 70% through the series. It was caused by a crash in Remote Desktop which somehow resulted in a Blue Screen of Death.

Decimal Digits Computed:	1,000,000,001,000	Computation 148 hours (6.2 days) - Not a continuous computation. Start : 10:14 PM (CST) September  1, 2010 Finish:  2:23 AM (CST) September  8, 2010
Hexadecimal Digits Computed:	83,048,203,203	Verification 366 hours (15.25 days) - Not a continuous computation. Start : 10:30 AM (CST) September  2, 2010 Finish:  7:11 AM (CST) September 17, 2010
Algorithm for Computation:	Amdeberhan-Zeilberger Formula 2
Algorithm for Verification:	Amdeberhan-Zeilberger Formula 1
Computers Involved:	Computation: "Nagisa" 2 x Intel Xeon X5482 Harpertown @ 3.2 GHz 64 GB (16 x 4 GB) DDR2 FB-DIMM @ 800 MHz 8 x 2 TB Hitachi Deskstar 7200 RPM
	Verification: "Ushio" Intel Core i7 920 @ 2.67 GHz (overclock 3.5 GHz) 12 GB (6 x 2 GB) DDR3 @ 1066 MHz (overclock 1333 MHz) 4 x 1 TB Seagate 7200 RPM

Golden Ratio - 1,000,000,000,000 digits

(World Record: July 8, 2010)

 

This computation improves the previous verified record of 100,000,000,000 digits by Shigeru Kondo and Steve Pagliarulo.

This computation also verifies the previous unverified record of 300,647,710,720 digits by Yuliyan Anastasov and Steve Pagliarulo.

 

Decimal Digits Computed:	1,000,000,000,000	Computation 114 hours (4.7 days) Start :  9:30 AM (PST) June 27, 2010 Finish:  2:06 AM (PST) July  2, 2010
Hexadecimal Digits Computed:	830,482,023,722	Verification ~7 days - Not a continuous computation. Start : 10:30 AM (PST) July  2, 2010 Finish:  7:18 AM (PST) July  9, 2010
Algorithm for Computation:	Newton's Method of sqrt(5)
Algorithm for Verification:	Newton's Method of sqrt(125)

 

Catalan's Constant - 31,026,000,000 digits

(World Record: April 16, 2009)

 

This computation improves the previous record of 15,510,000,000 digits by Raymond Chan and myself.

This is also the first "very long" computation that was completed without any interrupts, on this computer.

 

Decimal Digits Computed:	31,026,000,000	Computation 178 hours (7.4 days) Start :  8:30 AM (CST) March 31, 2009
Hexadecimal Digits Computed:	25,766,535,268	Verification 221 hours (9.2 days) Finish: 11:16 PM (CST) April 16, 2009
Algorithm for Computation:	Lupas Formula
Algorithm for Verification:	Ramanujan's Formula

Euler-Mascheroni Constant - 29,844,489,545 digits

(World Record: March 13, 2009)

 

This computation improves the previous record of 14,922,244,771 digits by Raymond Chan and myself.

Note that this computation was supposed to be a compute and verify done in one contiguous run starting from February 17, 2009 and ending sometime around March 7 - 9.

However, a power outage occurred roughly 9 hours after the computation run had finished (and 9 hours into the verification). The backup battery surprisingly failed to handle the load.

The timing was very fortunate in that, had it been 9 hours earlier, it would have ruined the computation.
After taking a few days to test some new code, compute Log(10), and do some gaming, the verification was restarted on March 2, 2009.

 

Decimal Digits Computed:	29,844,489,545	Computation 205 hours (8.5 days) Start : 10:30 PM (CST) February 17, 2009 Finish:  9:20 AM (CST) February 26, 2009
Hexadecimal Digits Computed:	24,785,312,074	Verification 269 hours (11.2 days) Start : 12:26 AM (CST) March  2, 2009 Finish:  5:04 AM (CST) March 13, 2009
Algorithm for Computation:	Brent-McMillan with Refinement (n = 233)
Algorithm for Verification:	Brent-McMillan (alone) (n = 234)

Log(10) - 31,026,000,000 digits

(World Record: March 13, 2009)

 

This computation verifies the previous record of 10,000,000,000 digits by S. Kondo and S. Pagliarulo.

 

Decimal Digits Computed:	31,026,000,000	Computation and Verification: 40 hours (1.7 days) Start :  4:55 AM (CST) February 27, 2009 Finish:  9:20 PM (CST) February 28, 2009
Hexadecimal Digits Computed:	25,766,535,268
Algorithm for Computation:	Machin-like Formula
Algorithm for Verification:	Machin-like Formula

Zeta(3) - Apery's Constant - 31,026,000,000 digits

(World Record: March 13, 2009)

 

This computation improves the previous record of 15,510,000,000 digits by Raymond Chan and myself.

Note that this computation was supposed to be a compute and verify done in one contiguous run starting from February 11, 2009 and ending 4 days later.

Since Zeta(3) is a relatively fast constant to compute, we decided to use this 31 billion digit run as a part of a multi-tasking test on the computer. (So that it's no big deal if we crashed the computer.)

The computation was given 60 GB of ram and set to low priority to make it a background program. This left 4 GB of ram for everything else - which is just enough to run Crysis on 64-bit Vista... Then throughout the computation, we played games (mainly Crysis), watched Anime, did backups, defragmented, etc... Hence why the computation was slower than the verification.

 

Of all the things we did, nothing really destabilized the computer. Crysis did cause the computer to stall a few times from pagefile thrashing due to its memory leaks, but it never killed the computer.

After the computation had finished (and the verification had just started), we decided to test whether the computer could go into standby in the middle of a computation. The test failed - it turned off the monitors but it didn't power down - nor did it wake back up. (We have yet to resolve this issue.)
The computer was rebooted and the verification run was restarted a few hours later. (Hence why the timings below don't add up.)

In the future we'll try a hibernate test. It'll be interesting to see how long it takes to hibernate 64 GB of ram in the middle of a computation.

 

Decimal Digits Computed:	31,026,000,000	Computation 45 hours (1.9 days) Start : 11:00 PM (CST) February 11, 2009	No Screenie Available
Hexadecimal Digits Computed:	25,766,535,268	Verification 44 hours (1.8 days) Finish: 11:59 PM (CST) February 15, 2009
Algorithm for Computation:	Amdeberhan-Zeilberger Formula 2
Algorithm for Verification:	Amdeberhan-Zeilberger Formula 1

Log(2) - 31,026,000,000 digits

(World Record: March 13, 2009)

 

This computation improves the previous record of 15,500,000,000 digits by Raymond Chan and myself.

 

Decimal Digits Computed:	31,026,000,000	Computation: 24 hours (1 day) Start :  4:00 AM (CST) February  3, 2009
Hexadecimal Digits Computed:	25,766,535,268	Verification: 16 hours (0.67 days) Finish:  9:35 PM (CST) February  4, 2009
Algorithm for Computation:	Machin-like Formula
Algorithm for Verification:	Machin-like Formula

Pi - 31,026,000,000 digits

 

No size record here - obviously... The purpose of this computation was to test y-cruncher's ability to handle 31 billion digit arithmetic.

This might be a new speed record for a non-supercomputer though...

 

Decimal Digits Computed:	31,026,000,000	Computation: 9 hours, 8 minutes Start :  5:30 AM (CST) February  2, 2009	No Screenie Available
Hexadecimal Digits Computed:	25,766,535,268	Verification: 13 hours, 17 minutes Finish:  3:56 AM (CST) February  3, 2009
Algorithm for Computation:	Chudnovsky Formula
Algorithm for Verification:	Ramanujan's Fomula

Catalan's Constant - 15,510,000,000 digits

(World Record: January 31, 2009)

 

This computation verifies the previous record of 10,000,000,000 digits by S. Kondo and S. Pagliarulo.

Finally!!! After a hard drive failure during verification and a long day of swapfile salvaging, I have FINALLY verified my 15.5 billion digits of Catalan's Constant!!!

 

Decimal Digits Computed:	15,510,000,000	Computation 88 hours, 13 minutes Start :  4:30 PM (CST) January 21, 2009 Finish: ~9:30 AM (CST) January 25, 2009
Hexadecimal Digits Computed:	12,880,776,188	Verification ~100 hours of actual run-time Start : ~9:30 AM (CST) January 25, 2009 Finish:  5:40 AM (CST) January 31, 2009
Algorithm for Computation:	Lupas Formula
Algorithm for Verification:	Ramanujan's Formula

Zeta(3) - Apery's Constant - 15,510,000,000 digits

(World Record: January 21, 2009)

 

This computation verifies the previous record of 10,000,000,000 digits by S. Kondo and S. Pagliarulo.

 

Decimal Digits Computed:	15,510,000,000	Computation 20 hours, 18 minutes Start :  7:00 PM (CST) January 19, 2009
Hexadecimal Digits Computed:	12,880,776,188	Verification 21 hours, 1 minute Finish:  1:42 PM (CST) January 21, 2009
Algorithm for Computation:	Amdeberhan-Zeilberger Formula 2
Algorithm for Verification:	Amdeberhan-Zeilberger Formula 1

Euler-Mascheroni Constant - 14,922,244,771 digits

(World Record: January 20, 2009)

 

This computation verifies the previous record of 10,000,000,000 digits by S. Kondo and S. Pagliarulo.

 

Decimal Digits Computed:	14,922,244,771	Computation ~96 hours of actual run-time Start :  3:30 PM (CST) January  7, 2009 Finish: 12:00 AM (CST) January 13, 2009
Hexadecimal Digits Computed:	12,392,656,036	Verification 133 hours, 41 minutes Start :  2:30 AM (CST) January 13, 2009 Finish:  4:16 PM (CST) January 18, 2009
Algorithm for Computation:	Brent-McMillan with Refinement (n = 232)
Algorithm for Verification:	Brent-McMillan (alone) (n = 233)

Log(2) - 15,500,000,000 digits

(World Record: January 20, 2009)

 

This computation verifies the previous record of 10,000,000,000 digits by S. Kondo and S. Pagliarulo.

 

Decimal Digits Computed:	15,500,000,000	Computation: 12 hours, 34 minutes Start :  5:00 PM (CST) January  6, 2009
Hexadecimal Digits Computed:	12,872,471,368	Verification: 8 hours, 20 minutes Finish:  1:40 PM (CST) January  7, 2009
Algorithm for Computation:	Machin-like Formula
Algorithm for Verification:	Machin-like Formula

 

Questions or Comments

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