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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.
Download as PDF; Printable version; In other projects ... This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in ...
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 .
A spigot algorithm is an algorithm for computing the value of a transcendental number (such as π or e) that generates the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds. Spigot algorithms also aim to minimize the amount of intermediate storage required.
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 ...
The more properties can be preserved, the more expressive the target of the encoding is said to be. For process calculi, the celebrated results are that the synchronous π-calculus is more expressive than its asynchronous variant, has the same expressive power as the higher-order π-calculus, [5] but is less than the ambient calculus. [citation ...
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Widely used in many programs, e.g. it is used in Excel 2003 and later versions for the Excel function RAND [8] and it was the default generator in the language Python up to version 2.2. [9] Rule 30: 1983 S. Wolfram [10] Based on cellular automata. Inversive congruential generator (ICG) 1986 J. Eichenauer and J. Lehn [11] Blum Blum Shub: 1986