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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.
Super PI finishing a calculation of 1,048,576, or 2 20 digits of pi. Super PI is a computer program that calculates pi to a specified number of digits after the decimal point—up to a maximum of 32 million. It uses Gauss–Legendre algorithm and is a Windows port of the program used by Yasumasa Kanada in 1995 to compute pi to 2 32 digits.
Liu Hui's method of calculating the area of a circle. Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei.Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter ...
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.
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In practical implementations such as y-cruncher, there is a relatively large constant overhead per term plus a time proportional to / , and a point of diminishing returns appears beyond three or four arctangent terms in the sum; this is why the supercomputer calculation above used only a four-term version.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
The version presented below is also known as the Gauss–Euler, Brent–Salamin (or Salamin–Brent) algorithm; [1] it was independently discovered in 1975 by Richard Brent and Eugene Salamin. It was used to compute the first 206,158,430,000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm.