20th September 1999
Adding Info. 4th October 1999
Dear folks,
Our latest record was established as the followings;
Declared record:
206,158,430,000 decimal digits
Two independent calculation 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.
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
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 : Borwein's 4-th order convergent algorithm
200,000,000,000-th digits of pi and 1/pi:
pi : 90828 20114 56238 31042
1/pi: 79556 96122 88268 33356
^
200,000,000,000-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 200,000,000,000 decimal places:
'0' : 20000030841; '1' : 19999914711; '2' : 20000136978; '3' : 20000069393
'4' : 19999921691; '5' : 19999917053; '6' : 19999881515; '7' : 19999967594
'8' : 20000291044; '9' : 19999869180; Chi square = 8.09
Frequency distribution for 1/pi up to 200,000,000,000 decimal places:
'0' : 19999945794; '1' : 20000122770; '2' : 20000060451; '3' : 20000182235
'4' : 19999876817; '5' : 19999977273; '6' : 19999911742; '7' : 20000001035
'8' : 19999927489; '9' : 19999994394; Chi square = 4.18
206,158,430,000-th digits of pi and 1/pi;
pi : 22144 96687 55157 30964
1/pi: 96680 12734 08711 53514
^
206,158,430,000-th
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
Some of interesting digits sequences;
01234567891 : from 26,852,899,245-th of pi
01234567891 : from 41,952,536,161-th of pi
01234567891 : from 99,972,955,571-th of pi
01234567891 : from 102,081,851,717-th of pi
01234567891 : from 171,257,652,369-th of pi
01234567890 : from 53,217,681,704-th of pi
01234567890 : from 148,425,641,592-th of pi
432109876543 : from 149,589,314,822-th of pi
543210987654 : from 197,954,994,289-th of pi
98765432109 : from 123,040,860,473-th of pi
98765432109 : from 133,601,569,485-th of pi
98765432109 : from 150,339,161,883-th of pi
98765432109 : from 183,859,550,237-th of pi
09876543210 : from 42,321,758,803-th of pi
09876543210 : from 57,402,068,394-th of pi
09876543210 : from 83,358,197,954-th of pi
10987654321 : from 89,634,825,550-th of pi
10987654321 : from 137,803,268,208-th of pi
10987654321 : from 152,752,201,245-th of pi
27182818284 : from 45,111,908,393-th of pi
01234567891 : from 173,036,790,762-th of 1/pi
01234567891 : from 199,571,086,462-th of 1/pi
01234567890 : from 50,494,465,695-th of 1/pi
01234567890 : from 66,787,942,929-th of 1/pi
01234567890 : from 132,217,072,915-th of 1/pi
234567890123 : from 100,850,401,743-th of 1/pi
5678901234567 : from 189,727,479,303-th of 1/pi
09876543210 : from 125,310,799,184-th of 1/pi
09876543210 : from 129,469,449,048-th of 1/pi
09876543210 : from 168,614,433,523-th of 1/pi
10987654321 : from 8,728,557,724-th of 1/pi
10987654321 : from 40,852,015,448-th of 1/pi
10987654321 : from 149,835,855,053-th of 1/pi
654321098765 : from 53,699,510,337-th of 1/pi
27182818284 : from 66,625,560,317-th of 1/pi
27182818284 : from 181,276,557,577-th of 1/pi
31415926535 : from 91,912,325,844-th of 1/pi
31415926535 : from 115,040,878,310-th of 1/pi
3333333333333 : from 55,172,085,586-th of 1/pi
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
Programs are 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. CPU used was HITACHI SR8000 at the Information Technology Center,
Computer Centre Division (old Computer Centre,) University of Tokyo.
Full of the 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)
Bunkyo-ku Yayoi 2-11-16
Tokyo 113-8658 Japan
Fax : +81-3-3814-7231 (office, G3 & Super G3)
E-mail: kanada@pi.cc.u-tokyo.ac.jp