Software for calculating π
From Wikipedia, the free encyclopedia
Over the years, several programs have been written for calculating π to many digits on personal computers.
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[edit] General-purpose
Most computer algebra systems can calculate π and other common mathematical constants to any desired precision.
Functions for calculating π are also included in many general software libraries for arbitrary-precision arithmetic, for instance MPFR.
[edit] Special-purpose
Programs designed for the specific purpose of calculating π may have better performance than general-purpose mathematical software. They typically implement checkpointing and efficient disk swapping to facilitate extremely long-running and memory-expensive computations.
- PiFast, by Xavier Gourdon was the fastest program for Microsoft Windows in 2003. According to its author, it can compute one million digits in 3.5 seconds on a 2.4 GHz Pentium 4.[1] PiFast can also compute other irrational numbers like e and √2. It can also work at lesser efficiency with very little memory (down to a few tens of megabytes to compute well over a billion (109) digits). This closed source freeware tool is a popular benchmark in the overclocking community. PiFast 4.4 is available from Stu's Pi Page. PiFast 4.3 is available from Gourdon's page.
- The Windows program QuickPi v4.00a by Steve Pagliarulo is faster than PiFast for small runs of digits. Version 4.00a is available on Stu's Pi Page below. QuickPi is less efficient than PiFast 4.4 for runs of approximately 160,000,000 digits or more. QuickPi can also compute other irrational numbers like e and √2. The software may be obtained from the author through the Pi-Hacks Yahoo! forum.
[edit] Most digits calculated on a home computer
The most digits calculated on a home PC is by Shigeru Kondo on his Xeon 3.6Ghz, 12GB RAM, HDD 2x300GB (RAID0) using Windows 2003 server x64. Kondo calculated 51,600,000,000 digits (48.06-gigs) starting 26 November 2005 in 48 days, 14 hours, 23 mins, 17.81 secs using Pagliarulo's QuickPi v4.00. Stu's Pi Page (below) is compiling a listing of large digit runs (over 1-gig or 1,073,741,824).
Latest record for digits on a supercomputer is 1,241,100,000,000 digits as of November 2002 by Yasumasa Kanada's lab at The University of Tokyo.
[edit] External and related links
- Conclusive comparison of many implementations and algorithms for calculating Pi
- Stu's Pi page - List of fastest Pi programs on the planet
- An open source FFT
- An open source FFT for pi
- Shigeru Kondou's Pi page - in English, digits avail. to 10b
- Pi-Hacks 'Yahoo! Groups' Discussion Forum
- Computing billions of π digits using GMP
- A fast package for Debian GNU/Linux
- A pi calculation applet
