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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 ...
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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.
Using the P function mentioned above, the simplest known formula for π is for s = 1, but m > 1. Many now-discovered formulae are known for b as an exponent of 2 or 3 and m as an exponent of 2 or it some other factor-rich value, but where several of the terms of sequence A are zero. The discovery of these formulae involves a computer search for ...
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 .
The π-calculus belongs to the family of process calculi, mathematical formalisms for describing and analyzing properties of concurrent computation.In fact, the π-calculus, like the λ-calculus, is so minimal that it does not contain primitives such as numbers, booleans, data structures, variables, functions, or even the usual control flow statements (such as if-then-else, while).
i ← ProcessNo for ℓ from 0 to N − 1 exclusive level[i] ← ℓ last_to_enter[ℓ] ← i while last_to_enter[ℓ] = i and there exists k ≠ i, such that level[k] ≥ ℓ wait. To release the lock upon exiting the critical section, process i sets level[i] to −1. That this algorithm achieves mutual exclusion can be proven as follows.
The algorithm uses a message called probe(i,j,k) to transfer a message from controller of process P j to controller of process P k. It specifies a message started by process P i to find whether a deadlock has occurred or not. Every process P j maintains a boolean array dependent which contains the information about the processes that depend on ...