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by Philosopher on February 5th, 2007

Philosopher

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How do computers calculate the next digit in the sequence of Pi?

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  • by canadianhelper on February 5th, 2007

    canadianhelper

    http://en.wikipedia.org/wiki/Software_for_calculating_%CF%80

    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 November 26, 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.

    If you can do programing here are some opensource files you can look at:
    http://momonga.t.u-tokyo.ac.jp/~ooura/pi_fft.html

    Better tasting Pie:

    Comments

    • But what is their system? do they follow a formula to get the next digit? Do they measure the circumference and diameter and work it out from there? How?

      Farino

      by Farino on February 5th, 2007

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