Software for calculating π: Difference between revisions

Revision as of 00:07, 13 September 2008

Revision as of 08:15, 17 October 2008

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{{Mergeto|#REDIRECT [[Computing π|date=September 2008}}]]

Over the years, several programs have been written for calculating [[pi]] (π) to [[arbitrary-precision arithmetic|many digits]] on [[personal computer]]s.

==General-purpose==

Most [[computer algebra system]]s can calculate π and other common [[mathematical constant]]s to any desired precision.

Functions for calculating π are also included in many general [[Library (computing)|libraries]] for [[arbitrary-precision arithmetic]], for instance [[MPFR]].

==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 [[paging|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]].<ref>[http://numbers.computation.free.fr/Constants/PiProgram/timings.html PiFast timings<!-- Bot generated title -->]</ref> PiFast can also compute other irrational numbers like ''[[e (mathematical constant)|e]]'' and [[square root of 2|√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 tool is a popular benchmark in the [[overclocking]] community. PiFast 4.4 is available from [http://home.istar.ca/~lyster/pi.html Stu's Pi page]. PiFast 4.3 is available from Gourdon's page.

* '''QuickPi''' by Steve Pagliarulo for Windows is faster than PiFast for runs of under 400,000,000 digits. Version 4.5 is available on Stu's Pi Page below. Like PiFast, QuickPi can also compute other irrational numbers like ''e'', √2, and √3. The software may be obtained from the Pi-Hacks Yahoo! forum, or from [http://home.istar.ca/~lyster/pi.html Stu's Pi page].

==See also==

* [[Pi]]

* [[Computing π]]

* [[Super PI]]

==References==

<references />

==External links==

*[http://myownlittleworld.com/miscellaneous/computers/pilargetable.html Conclusive comparison of many implementations and algorithms for calculating Pi]

*[http://myownlittleworld.com/miscellaneous/computers/otherpiprograms.html Comparison of different pi programs (part 2 of previous link)]

*[http://home.istar.ca/~lyster/pi.html Stu's Pi page] - List of fastest Pi programs on the planet for the PC

*[http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html An open source FFT]

*[http://momonga.t.u-tokyo.ac.jp/~ooura/pi_fft.html An open source FFT for pi]

*[http://ja0hxv.calico.jp/pai/estart.html Shigeru Kondou's Pi page - in English, digits avail. to 70b]

*[http://groups.yahoo.com/group/pi-hacks/ Pi-Hacks 'Yahoo! Groups' Discussion Forum]

*[http://gmplib.org/pi-with-gmp.html Computing billions of π digits using GMP]

*[http://packages.debian.org/stable/math/pi A fast package for Debian GNU/Linux]

*[http://www.apfloat.org/apfloat_java/applet/pi.html A pi calculation applet]

[[Category:Pi software]]