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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 ...
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.
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.
The arithmetic–geometric mean of two numbers, a 0 and b 0, is found by calculating the limit of the sequences + = +, + =, which both converge to the same limit. If = and = then the limit is () where () is the complete elliptic integral of the first kind
Newton steps and time bsearch steps and time 2-root of 123^13 5 in 0.000124 s 45 in 0.000358 s 3-root of 123^13 4 in 0.000081 s 30 in 0.000198 s 15-root of 123^13 1 in 0.000053 s 6 in 0.000077 s 37-root of 123^13 185 in 0.003073 s 2 in 0.000072 s 68-root of 123^13 0 in 0.000040 s 1 in 0.000046 s 111-root of 123^13 0 in 0.000029 s 0 in 0.000030 s 150-root of 123^13 0 in 0.000028 s 0 in 0.000029 ...
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:
Finds a formula that allows the nth hexadecimal digit of pi to be calculated without calculating the preceding digits. 28 August 1995 Yasumasa Kanada and Daisuke Takahashi: HITAC S-3800/480 (dual CPU) [36] [37] 56.74 hours? 4,294,960,000: 11 October 1995 Yasumasa Kanada and Daisuke Takahashi: HITAC S-3800/480 (dual CPU) [38] [37] 116.63 hours ...
Super PI by Kanada Laboratory [101] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.9 is available from Super PI 1.9 page.