Dear folks,
Our latest record was established as the followings;
Declared record:
51,539,600,000 decimal digits
Two independent calculation based on two different algorithms generated
51,539,607,552 (=3*2^34) decimal digits of pi and comparison of two generated
sequences matched 51,539,607,510 decimal digits, e.g., 42 decimal digits
difference. Then we are declaring 51,539,600,000 decimal digits as the
new world record.
Main program run:
Job start : 6th June 1997 22:29:06
Job end : 8th June 1997 03:32:17
Elapsed time : 29:03:11
Main memory : 212 GB
Algorithm : Borwein's 4-th order convergent algorithm
Optimized main program run:
Job start : 1st Augst 1997 23:04:15
Job end : 3rd Augst 1997 00:18:47
Elapsed time : 25:14:32
Main memory : 212 GB
Algorithm : Borwein's 4-th order convergent algorithm
Optimized verification program run:
Job start : 4th July 1997 22:11:42
Job end : 6th July 1997 11:19:58
Elapsed time : 37:08:16
Main memory : 188 GB
Algorithm : Gauss-Legendre algorithm
50,000,000,000-th digits of pi and 1/pi:
pi : 85133 98712 75109 30042
1/pi: 91191 08624 25640 78042
^
50,000,000,000-th
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
Frequency distribution for pi-3 up to 50,000,000,000 decimal places:
'0' : 5000012647; '1' : 4999986263; '2' : 5000020237; '3' : 4999914405
'4' : 5000023598; '5' : 4999991499; '6' : 4999928368; '7' : 5000014860
'8' : 5000117637; '9' : 4999990486; Chi square = 5.60
Frequency distribution for 1/pi up to 50,000,000,000 decimal places:
'0' : 4999969955; '1' : 5000113699; '2' : 4999987893; '3' : 5000040906
'4' : 4999985863; '5' : 4999977583; '6' : 4999990916; '7' : 4999985552
'8' : 4999881183; '9' : 5000066450; Chi square = 7.04
51,539,600,000-th digits of pi and 1/pi;
pi : 70532 46569 86142 12904
1/pi: 60081 50624 62192 72973
^
51,539,600,000-th
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
Some of interesting digits sequences;
0123456789 : from 17,387,594,880-th of pi
0123456789 : from 26,852,899,245-th of pi
0123456789 : from 30,243,957,439-th of pi
0123456789 : from 34,549,153,953-th of pi
0123456789 : from 41,952,536,161-th of pi
0123456789 : from 43,289,964,000-th of pi
9876543210 : from 21,981,157,633-th of pi
9876543210 : from 29,832,636,867-th of pi
9876543210 : from 39,232,573,648-th of pi
9876543210 : from 42,140,457,481-th of pi
9876543210 : from 43,065,796,214-th of pi
09876543210 : from 42,321,758,803-th of pi
27182818284 : from 45,111,908,393-th of pi
0123456789 : from 6,214,876,462-th of 1/pi
01234567890 : from 50,494,465,695-th of 1/pi
9876543210 : from 15,603,388,145-th of 1/pi
9876543210 : from 51,507,034,812-th of 1/pi
999999999999 : from 12,479,021,132-th of 1/pi
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
Programs were written by Mr. Daisuke TAKAHASHI, a Research Associate at
our Computer Centre. Message passing routines were written by myself and
used for the optimized calculations. CPU used was HITACHI SR2201 at the
Computer Centre, University of Tokyo. 1024 PE's were definitely used
through single job parallel processing for total of two programs run.
Yasumasa KANADA
Computer Centre, University of Tokyo
Bunkyo-ku Yayoi 2-11-16
Tokyo 113 Japan
Fax : +81-3-3814-7231 (office)
E-mail: kanada@pi.cc.u-tokyo.ac.jp