20th September 1999

Two independent calculations based on two different algorithms generated 206,158,430,208 (=3*2^36) decimal digits of pi and comparison of two generated sequences matched up to 206,158,430,163 decimal digits, e.g., 45 decimal digits difference. Then we are declaring 206,158,430,000 decimal digits as the new world record.

(More details soon at http://pi2.cc.u-tokyo.ac.jp/index.html)

Declared record: 206,158,430,000 decimal digits

Yasumasa KANADA and Daisuke TAKAHASHI

Optimized main program run:
Job start : 18th September 1999 19:00:52 (JST)
Job end : 20th September 1999 08:21:56 (JST)
Elapsed time : 37:21:04
Main memory : 865 GB (= 6.758 GB * 128)
Algorithm : Gauss-Legendre algorithm (Brent-Salamin)

Optimized verification program run:
Job start : 26th June 1999 01:22:50 (JST)
Job end : 27th June 1999 23:30:40 (JST)
Elapsed time : 46:07:10
Main memory : 817 GB (= 6.383 GB * 128)
Algorithm : Borweins' 4-th order convergent algorithm
(Run the algorithm.)
The 19th iterate actually agrees with Pi to more than 750 billion digits.

206,158,430,000-th digits of pi and 1/pi;

pi : 22144 96687 55157 30964
1/pi: 96680 12734 08711 53514

(First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Notes. Programs consisted of two sets of routines, e.g. calculation routines and message passing routines. Calculation routines were written by Dr. Daisuke TAKAHASHI, a Research Associate at our Centre and rather speed sensitive message passing routines were written by myself. Calculation routines used were more optimized than these used for the 51.5 billion record establishment. For establishing this new record, high speed message passing routines were seriously used for both of programs, e.g. main program and verification program.

Machine used: HITACHI SR8000 at the Information Technology Center, Computer Centre Division, University of Tokyo. with 128 Processors, using the full total CPU, e.g. 128PE's (theoretical peak processing speed for the single PE is eight Billion floating operations per second. One Trillion floating point operations per second for all PE's), were definitely used as single job and parallel processing for both of programs run.

Yasumasa KANADA Information Technology Center, Computer Centre Division, University of Tokyo
(Old Computer Centre, University of Tokyo)

E-mail: kanada@pi.cc.u-tokyo.ac.jp