sci.math #139994 (18 + 1065 more) [1]
From: xpolakis@prometheus.hol.gr (Antreas P. Hatzipolakis)
Newsgroups: sci.math
[1] Pi to 6+ billions places (was: Pi to a million places)
Date: Sat, 01 Jun 1996 00:04:28 +0200
Organization: Hellas On Line
Lines: 89
Message-ID:
NNTP-Posting-Host: cronos.hol.gr
On Wed, 29 May 1996, wrote:
>Hi.
>Can someone tell me how many places pi has been calculated to,
>and/or the publication details of a book with, say, the first million or so?
>Many thanks for any help on this.
>Neil
From: ftp://www.cc.u-tokyo.ac.jp/
File : README.our_latest_record
----------------------------------------------------------------------------
Dear folks,
Our latest record was established as the followings;
Declared record:
6,442,450,000 decimal digits
Two independent calculation based on two different algorithms generated
6,442,450,944 (=3*2^31) decimal digits of pi and comparison of two generated
sequences matched 6,442,450,938 decimal digits, e.g., 6 decimal digits
difference. Then we are declaring 6,442,450,000 decimal digits as the
new world record.
Main program run:
Job start : 19th September 1995 20:54
Job end : 24th September 1995 17:32
Elapsed time : 116:38:12
Vector CPU : 112:36:06
Main memory : 1856.75 MB
ES memory : 32764 MB
Algorithm : Borwein's 4-th order convergent algorithm
Verification program run:
Job start : 06th October 1995 09:58
Job end : 11th October 1995 21:38
Elapsed time : 131:40:24
Vector CPU : 135:45:52
Main memory : 1792.75 MB
ES memory : 32328 MB
Algorithm : Gauss-Legendre algorithm
======================= From here =========================
4,000,000,000-th digits of pi and 1/pi:
pi : 94375 34306 22684 47216
1/pi: 71480 70425 69013 58924
^
4,000,000,000-th
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
================= to there, to be updated later ===========
Frequency distribution for pi-3 up to 6,000,000,000 decimal places:
'0' : 599963005; '1' : 600033260; '2' : 599999169; '3' : 600000243
'4' : 599957439; '5' : 600017176; '6' : 600016588; '7' : 600009044
'8' : 599987038; '9' : 600017038; Chi square = 9.00
Frequency distribution for 1/pi up to 6,000,000,000 decimal places:
'0' : 599978305; '1' : 600024329; '2' : 600007880; '3' : 600006529
'4' : 599976720; '5' : 599986534; '6' : 600012285; '7' : 600023761
'8' : 599975659; '9' : 600007998; Chi square = 5.44
======================= From here =========================
4,294,960,000-th digits of pi and 1/pi;
pi : 55675 13149 35865 45528
1/pi: 96350 29339 14953 51156
^
4,294,960,000-th
(First digit '3' for pi or '0' for 1/pi is not included in the above count.)
================= to there, to be updated later ===========
Programs were written by Mr. Daisuke TAKAHASHI, a member of Kanada Lab.
CPU used was HITAC S-3800/480 at the Computer Centre, University of Tokyo.
Two CPU were definitely used through single job parallel processing for
total of four 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
----------------------------------------------------------------------------
Antreas
End of article 139994 (of 140056) -- what next? [npq]
Contents in each directory are as follows:
pi 4,200,000,000 digits of pi with packed binary format
pi10m 10,000,000 digits of pi with text format
pi10m-compressed same as the above, but they are compressed with compress
pi10m-gzipped same as the above, but they are compressed with GNU gzip
pi200m 200,000,000 digits of pi with text format
pi200m-compressed same as the above, but they are compressed with compress
1_over_pi 4,200,000,000 digits of 1/pi with packed binary format
1_over_pi10m 10,000,000 digits of 1/pi with text format
1_over_pi10m-compressed
same as the above, but they are compressed with compress
1_over_pi10m-gzipped
same as the above, but they are compressed with GNU gzip
1_over_pi200m 200,000,000 digits of 1/pi with text format
1_over_pi200m-compressed
same as the above, but they are compressed with compress
exec_windows English version of super_pi for MS-Windows
exec_windows_jp Japanese version of super_pi for MS-windows
README this file
Dear folks,
Our latest record was established as the followings;
Declared record:
3,221,220,000 decimal digits
Two independent calculation based on two different algorithms generated
3,221,225,472 (=3*2^30) decimal digits of pi and comparison of two generated
sequences matched 3,221,225,466 decimal digits, e.g., 6 decimal digits
difference. Then we are declaring 3,221,220,000 decimal digits as the
new world record.
Main program run:
Job start : 16th June 1995 22:41
Job end : 18th June 1995 11:33
Elapsed time : 36:52:28
Vector CPU : 44:30:50
Main memory : 1888.5 MB
ES memory : 26608 MB
Algorithm : Borwein's 4-th order convergent algorithm
Verification program run:
Job start : 24th June 1995 01:13
Job end : 26th June 1995 06:56
Elapsed time : 53:43:46
Vector CPU : 48:28:43
Main memory : 1891.25 MB
ES memory : 26612 MB
Disk storage : 164 MB * 5 = 820 MB
Algorithm : Gauss-Legendre algorithm
3,000,000,000-th digits of pi and 1/pi:
pi : 37608 19468 51598 04548
1/pi: 43270 91443 13660 42701
^
3,000,000,000-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 3,000,000,000 decimal places:
'0' : 299999143; '1' : 299995932; '2' : 299989126; '3' : 299992290
'4' : 300002257; '5' : 299979016; '6' : 300025447; '7' : 299975510
'8' : 300016550; '9' : 300024729; Chi square = 9.24
Frequency distribution for 1/pi up to 3,000,000,000 decimal places:
'0' : 300009029; '1' : 300002431; '2' : 299992729; '3' : 299998519
'4' : 299970883; '5' : 299980175; '6' : 300010123; '7' : 300025696
'8' : 300008447; '9' : 300001968; Chi square = 7.40
3,221,220,000-th digits of pi and 1/pi;
pi : 34929 13958 77673 90319
1/pi: 21355 75330 20722 29175
^
3,221,220,000-th
(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 member of Kanada Lab.
CPU used was HITAC S-3800/480 at the Computer Centre, University of Tokyo.
Two CPU were definitely used through single job parallel processing for
both program 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
Dear folks,
Our latest record was established as the followings;
Declared record:
4,294,960,000 decimal digits
Two independent calculation based on two different algorithms generated
4,294,967,296 (=2^32) decimal digits of pi and comparison of two generated
sequences matched 4,294,967,286 decimal digits, e.g., 10 decimal digits
difference. Then we are declaring 4,294,960,000 decimal digits as the
new world record.
Main program run:
Job start (1-st) : 28th July 1995 22:59
Job end (1-st) : 31st July 1995 07:42
Elapsed time (1-st) : 56:44:24
Vector CPU (1-st) : 67:33:04
Job start (2-nd) : 04th Aug. 1995 20:38
Job end (2-nd) : 07st Aug. 1995 05:35
Elapsed time (2-nd) : 56:57:11
Vector CPU (2-nd) : 66:15:37
Main memory : 1792.75 MB
ES memory : 25120 MB
Disk storage : 2 GB * 2 = 4 GB (as for the intermediate data storage)
Algorithm : Borwein's 4-th order convergent algorithm
Verification program run:
Job start (1-st) : 11th Aug. 1995 21:31
Job end (1-st) : 14st Aug. 1995 15:54
Elapsed time (1-st) : 66:23:29
Vector CPU (1-st) : 77:14:59
Job start (2-nd) : 25th Aug. 1995 23:12
Job end (2-nd) : 28st Aug. 1995 15:09
Elapsed time (2-nd) : 63:57:22
Vector CPU (2-nd) : 75:10:29
Main memory : 1792.75 MB
ES memory : 26152 MB
Disk storage : 2 GB * 3 = 6 GB (as for the intermediate data storage)
Algorithm : Gauss-Legendre algorithm
4,000,000,000-th digits of pi and 1/pi:
pi : 94375 34306 22684 47216
1/pi: 71480 70425 69013 58924
^
4,000,000,000-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 4,000,000,000 decimal places:
'0' : 400001233; '1' : 400002285; '2' : 399965405; '3' : 399984469
'4' : 400006936; '5' : 399989052; '6' : 400033035; '7' : 399996122
'8' : 400004741; '9' : 400016722; Chi square = 7.55
Frequency distribution for 1/pi up to 4,000,000,000 decimal places:
'0' : 400003502; '1' : 400016211; '2' : 400002106; '3' : 399991609
'4' : 399987516; '5' : 399972897; '6' : 400003565; '7' : 400018249
'8' : 399999949; '9' : 400004396; Chi square = 4.01
4,294,960,000-th digits of pi and 1/pi;
pi : 55675 13149 35865 45528
1/pi: 96350 29339 14953 51156
^
4,294,960,000-th
(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 member of Kanada Lab.
CPU used was HITAC S-3800/480 at the Computer Centre, University of Tokyo.
Two CPU were definitely used through single job parallel processing for
total of four 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