Our previous record announcements, up to 42 * 10^8 digits of pi and 1/pi are

available through ftp://pi.super-computing.org/.

20th October 2005 Dear folks, Our latest record which was announced already at press release time of 6-th of December, 2002 was as the followings; Declared record: 1,030,700,000,000 hexadecimal digits 1,241,100,000,000 decimal digits Two independent hexadecimal calculation based on two different algorithms generated more than 1,030,775,430,000 hexadecimal digits of pi and comparison of two generated sequences matched completely. Computed hexadecimal digits of pi were radix converted into base 10, generating more than 1,241,177,300,000 decimal digits of pi and generated decimal digits of pi were radix converted again into base 16. Radix converted hexadecimal digits of pi were compared with original hexadecimal digits of pi. There were no difference up to 1,241,100,000,000 decimal digits. Then we are declaring 1,030,700,000,000 hexadecimal digits and 1,241,100,000,000 decimal digits as the new world records. Details of computed results are available on the following URL's. http://www.super-computing.org/pi-hexa_current.html (hexadecimal) http://www.super-computing.org/pi-decimal_current.html (decimal) Summary of computation: (1) 64 nodes of HITACHI SR8000/MPP (144 nodes, 14.4GFlops/node, 16GB/node, node to node data transmission speed: 1.6GB/sec one-way and 3.2GB/sec both- way) at Information Technology Center, University of Tokyo were used. (2) Project completion date and time : 15:06 JST, 24-th of November 2002 (3) Formulae used for the computations; Main computation : formula discovered by Mr. K. Takano in 1982. pi = 48 arc tan(1/49) +128 arc tan(1/57) - 20 arc tan (1/239) + 48 arc tan(1/110443) Verification computation : formula discovered by F.C.M. Stoemer in 1896. pi = 176 arc tan(1/57) + 28 arc tan(1/239) - 48 arc tan(1/682) + 96 arc tan(1/12943) N.B. Both formulae are not so efficient in the total computation timing point of view. We hoped the usage of the formula discovered by Japanese and correctness checking efficiency. (4) Flow of computation and elapsed times for each computation (a) Hexadecimal pi computation based on the Takano's arc tangent relation for pi : 400 hours 0 minutes (b) Hexadecimal pi computation based on the Stoemer's arc tangent relation for pi : 157 hours 4 minutes (c) Radix conversion from hexadecimal pi to decimal pi : 23 hours 20 minutes (d) Radix conversion form decimal pi to hexadecimal pi : 21 hours 32 minutes Total elapsed time : 601 hours 56 minutes Total elapsed time includes elapsed time for data transfer of 400 TB between main memory and auxiliary disk storage. (5) Programs : FORTRAN(major part) + C(minor part). Roughly 79,200 lines of source code including comments. (6) Reason why we computed with base 16 then radix converted to base 10 For shorten total computing time and checking the effectiveness of DRM (Divide and Rationalize Method.) Key algorithms or methods for hexadecimal digits of pi computation and radix conversion between base 10 and base 16 are the same. We call them as DRM. DRM is applicable not only to efficient high precision computation of polynomials with rational coefficient and radix conversion but also to the efficient high precision computation of continued fraction. If we compute 206,100,000,000 decimal digits of pi with similar machine of HITACHI SR8000 by using the same method, estimated computing time will be 38 hours (main computation : 25 hours, verification computation : 10 hours, radix conversions from base 10 to base 16 and from base 16 to base 10 : 3 hours.) Reference of DRM. Yasunori USHIRO, Yasumasa KANADA and Daisuke TAKAHASHI, IPSJ, Vol. 41, No. 6, pp. 1811-1819, 2000. (7) It took more than four years for completing the project with total of 10 main people and 2 supporters. University of Tokyo (a) Yasumasa KANADA : Information Technology Center, Computer Centre Division (b) Hisayasu KURODA : Information Technology Center, Computer Centre Division (c) Makoto KUDOH : Graduate School of Information Science and Technology, Department of Computer Science, 2nd year Hitachi Ltd. (a) Yasunori USHIRO : Senior Engineer, High Performance Computing Business Department, Enterprise Server Division, Hitachi, Ltd. (b) Nobuhiro IOKI : Senior Engineer, Language Processor Department, Software Division, Hitachi, Ltd. (c) Shinichi TANAKA : Engineer, Language Processor Department, Software Division, Hitachi, Ltd. (d) Hiroki KAWAMURA : Application Software Development Department, Hitachi Software Engineering Co., Ltd. (e) Fujio FUJITA : Chief Engineer, 1st Operating System Department, Software Division, Hitachi, Ltd. (f) Hajime SHINOHARA :Senior Engineer, Science Information Systems Department, Government & Public Corporation Information Systems Division, Hitachi, Ltd. (g) Hiroki HASEBE : Engineer, Science Information Systems Department, Government & Public Corporation Information Systems Division, Hitachi, Ltd. Supporter at Hitachi Ltd. (a) Tokuro ANZAKI : Chief Engineer, Software Division, Hitachi, Ltd. (b) Yaoko NAKAGAWA : Chief Engineer, Server Development Operation, Enterprise Server Division, Hitachi, Ltd. Yasumasa KANADA Information Technology Center, Computer Centre Division, University of Tokyo (Old Computer Centre, University of Tokyo) Bunkyo-ku Yayoi 2-11-16 Tokyo 113-8658 Japan Fax : +81-3-3814-7231 (office, G3 & Super G3) E-mail: yasumasa.kanada at klab.cc.u-tokyo.ac.jp