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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.
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 ...
The variable turn is set arbitrarily to a number between 0 and n−1 at the start of the algorithm. The flags variable for each process is set to WAITING whenever it intends to enter the critical section. flags takes either IDLE or WAITING or ACTIVE. Initially the flags variable for each process is initialized to IDLE.
$ mpicc example.c && mpiexec -n 4 ./a.out We have 4 processes. Process 1 reporting for duty. Process 2 reporting for duty. Process 3 reporting for duty. Here, mpiexec is a command used to execute the example program with 4 processes, each of which is an independent instance of the program at run time and assigned ranks (i.e. numeric IDs) 0, 1 ...
The programming control structures on which autoparallelization places the most focus are loops, because, in general, most of the execution time of a program takes place inside some form of loop. There are two main approaches to parallelization of loops: pipelined multi-threading and cyclic multi-threading. [ 3 ]
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 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).
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 .