Abstract
In a recent work [6], Borwein and Borwein derived a class of algorithms based on the theory of elliptic integrals that yield very rapidly convergent approximations to elementary constants. The author has implemented Borweins’ quartically convergent algorithm for 1/π, using a prime modulus transform multi-precision technique, to compute over 29,360,000 digits of the decimal expansion of π. The result was checked by using a different algorithm, also due to the Borweins, that converges quadratically to π. These computations were performed as a system test of the Cray-2 operated by the Numerical Aerodynamical Simulation (NAS) Program at NASA Ames Research Center. The calculations were made possible by the very large memory of the Cray-2.
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© 2000 Springer Science+Business Media New York
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Bailey, D.H. (2000). The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_60
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DOI: https://doi.org/10.1007/978-1-4757-3240-5_60
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3242-9
Online ISBN: 978-1-4757-3240-5
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