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'''Bellard's formula''', as used by [[PiHex]], the now-completed [[distributed computing]] project, is used to calculate the ''n''th digit of [[Pi|π]] in [[base 2]]. It is a faster version (about 43% faster<ref>[http://oldweb.cecm.sfu.ca/projects/pihex/credits.html PiHex Credits<!-- Bot generated title -->]</ref>) of the [[Bailey–Borwein–Plouffe formula]]. | |||
Bellard's formula was discovered by [[Fabrice Bellard]] in 1997. | |||
== Formula == | |||
: <math> | |||
\begin{align} | |||
\pi = \frac1{2^6} \sum_{n=0}^\infty \frac{(-1)^n}{2^{10n}} \, \left(-\frac{2^5}{4n+1} \right. & {} - \frac1{4n+3} + \frac{2^8}{10n+1} - \frac{2^6}{10n+3} \left. {} - \frac{2^2}{10n+5} - \frac{2^2}{10n+7} + \frac1{10n+9} \right) | |||
\end{align} | |||
</math> | |||
==Notes== | |||
<references/> | |||
==External links== | |||
*[http://bellard.org/pi/ Fabrice Bellard's PI page] | |||
*[http://oldweb.cecm.sfu.ca/projects/pihex/ PiHex web site] | |||
*[http://denistn.mine.nu/pdf2html.php?url=http://oldweb.cecm.sfu.ca/projects/pihex/p123.pdf David Bailey, Peter Borwein, and Simon Plouffe's BBP formula (''On the rapid computation of various polylogarithmic constants'') (PDF)] | |||
[[Category:Distributed computing projects]] | |||
[[Category:Pi algorithms]] | |||
[[Category:Pi]] | |||
Revision as of 17:07, 24 December 2013
Bellard's formula, as used by PiHex, the now-completed distributed computing project, is used to calculate the nth digit of π in base 2. It is a faster version (about 43% faster[1]) of the Bailey–Borwein–Plouffe formula.
Bellard's formula was discovered by Fabrice Bellard in 1997.