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This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in category "Pi algorithms" The following 17 pages are in this category, out of 17 total.
The search procedure consists of choosing a range of parameter values for s, b, and m, evaluating the sums out to many digits, and then using an integer relation-finding algorithm (typically Helaman Ferguson's PSLQ algorithm) to find a sequence A that adds up those intermediate sums to a well-known constant or perhaps to zero.
Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of /. This and other algorithms can be found in the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity .
Machin-like formulas for π can be constructed by finding a set of integers , =, where all the prime factorisations of + , taken together, use a number of distinct primes , and then using either linear algebra or the LLL basis-reduction algorithm to construct linear combinations of arctangents of . For example, in the Størmer formula ...
Spigot algorithms can be contrasted with algorithms that store and process complete numbers to produce successively more accurate approximations to the desired transcendental. Interest in spigot algorithms was spurred in the early days of computational mathematics by extreme constraints on memory, and such an algorithm for calculating the ...
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 . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...
The Wiring IDE includes a C/C++ library called "Wiring", which makes common input/output operations much easier. Wiring programs are written in C++. A minimal program requires only two functions: setup(): a function run once at the start of a program which can be used to define initial environment settings.
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.