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This does not compute the nth decimal digit of π (i.e., in base 10). [3] But another formula discovered by Plouffe in 2022 allows extracting the nth digit of π in decimal. [4] BBP and BBP-inspired algorithms have been used in projects such as PiHex [5] for calculating many digits of π using distributed computing. The existence of this ...
One important application is verifying computations of all digits of pi performed by other means. Rather than having to compute all of the digits twice by two separate algorithms to ensure that a computation is correct, the final digits of a very long all-digits computation can be verified by the much faster Bellard's formula. [3] Formula:
Simon Plouffe (born June 11, 1956) is a French Canadian mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the nth binary digit of π, in 1995. [1] [2] [3] His other 2022 formula allows extracting the nth digit of π in decimal. [4] He was born in Saint-Jovite, Quebec.
A variant of the spigot approach uses an algorithm which can be used to compute a single arbitrary digit of the transcendental without computing the preceding digits: an example is the Bailey–Borwein–Plouffe formula, a digit extraction algorithm for π which produces base 16 digits. The inevitable truncation of the underlying infinite ...
The Gauss–Legendre algorithm is an algorithm to compute the digits of π.It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π.
Gauss–Legendre algorithm: computes the digits of pi; Chudnovsky algorithm: a fast method for calculating the digits of π; Bailey–Borwein–Plouffe formula: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π; Division algorithms: for computing quotient and/or remainder of two numbers Long division; Restoring ...
While the PiHex project calculated the least significant digits of π ever attempted at the time in any base, the second place is held by Peter Trueb who computed some 22+ trillion digits in 2016 and third place by houkouonchi who derived the 13.3 trillionth digit in base 10.
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