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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.
exp4j is a small Java library for evaluation of mathematical expressions. [1] It implements Dijkstra's Shunting-yard algorithm to translate expressions from infix notation to Reverse Polish notation and calculates the result using a simple Stack algorithm.
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 .
Programming involves activities such as analysis, developing understanding, generating algorithms, verification of requirements of algorithms including their correctness and resources consumption, and implementation (commonly referred to as coding [1] [2]) of algorithms in a target programming language.
Super PI by Kanada Laboratory [101] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.9 is available from Super PI 1.9 page.
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.
As a simple example, in the C programming language, this is a typical macro that is not a parameterized macro, i.e., a parameterless macro: #define PI 3.14159 This causes PI to always be replaced with 3.14159 wherever it occurs. An example of a parameterized macro, on the other hand, is this: #define pred(x) ((x)-1)