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This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in category "Pi algorithms"
In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus. The π -calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation.
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.
The modification to the algorithm does not affect the way the controller responds to process disturbances. Basing proportional action on PV eliminates the instant and possibly very large change in output caused by a sudden change to the setpoint. Depending on the process and tuning this may be beneficial to the response to a setpoint step.
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems.Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes.
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 ...
Such algorithms are particularly important in modern π computations because most of the computer's time is devoted to multiplication. [121] They include the Karatsuba algorithm , Toom–Cook multiplication , and Fourier transform-based methods .
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 .