Pi Formulas, Algorithms and Computations (2009)
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Pi Formulas, Algorithms and Computations
Pi Computation
(Dec 31 2009)
2700 billion decimal digits of Pi computed with a desktop computer.
Formulas and Algorithms
(Jan 20 1997)
A new and faster formula to
compute the n'th binary digit of Pi. The article (Jan 20 1997) in html or in PDF
pi_bin.pdf
(revised edition, Feb 2007). A systematic way to find similar formulas is presented here.
(Jan 10 1997)
Simon Plouffe has
found an algorithm to compute the n'th digit of Pi in any base in
O(n^3log(n)^3) with little memory. We give here an improvement of his algorithm
to get a speed of O(n^2). The postscript file of the
alpha version
of the article: pi_n2.ps
, the html
version, and the corresponding implementation in C: pi.c
.
(Feb 27 1997) A faster implementation which
uses the Gosper formula : pi1.c .
(Feb 4 1997)
While testing some numerical relations with the PSLQ
algorithm
, I found this exotic formula for Pi:
with
(Aug 2003)Boris Gourevitch and Jesus Guillera show how to demonstrate similar formulas.
Related information
- Numbers, constants and computation, by Xavier Gourdon and Pascal Sebah
- The Pi entry in Wolfram MathWorld.
- Jörg Arndt's home page .
- Favorite Mathematical Constants from Steven Finch.
- L'univers de Pi, by Boris Gourevitch.
- Simon Plouffe's home page .
- A French book about Pi: Le fascinant nombre Pi , Jean-Paul Delahaye, Editions Belin / Pour La Science, Paris, 1997, ISSN 0224-5159 ISBN 2-9029-1825-9.
- A German book about Pi by Jörg Arndt: Pi - Algorithmen, Computer, Arithmetik, Springer-Verlag Heidelberg, ISBN 3-540-63419-3. English translation to come.
Fabrice Bellard - http://bellard.org/
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