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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.
To calculate 16 n−k mod (8k + 1) quickly and efficiently, the modular exponentiation algorithm is done at the same loop level, not nested. When its running 16x product becomes greater than one, the modulus is taken, just as for the running total in each sum. Now to complete the calculation, this must be applied to each of the four sums in turn.
ISBN 978-0-13-153271-7. This book has been updated by Jim Davies at the Oxford University Computing Laboratory and the new edition is available for download as a PDF file at the Using CSP website. Roscoe, A. W. (1997). The Theory and Practice of Concurrency. Prentice Hall. ISBN 978-0-13-674409-2. Some links relating to this book are available here.
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Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
C. A. R. Hoare: Communicating Sequential Processes, Prentice Hall, ISBN 0-13-153289-8. This book has been updated by Jim Davies at the Oxford University Computing Laboratory and the new edition is available for download as a PDF file at the Using CSP website. Robin Milner: A Calculus of Communicating Systems, Springer Verlag, ISBN 0-387-10235-3.