Abstract
We produce more elementary algorithms than those of Brent and Salamin for, respectively, evaluating e x and π. Although the Gauss arithmetic-geometric process still plays a central role, the elliptic function theory is now unnecessary.
Supported in part by NSF Grant MGS 7802171.
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Reference
R. Brent, “Fast multiple evaluation of elementary functions,” J. Assoc. Comput. Mach., v. 23, 1976, pp. 242–251.
R. Brent, Multiple-Precision Zero-Finding Methods and the Complexity of Elementary Function Evaluation (J. F. Traub, ed.), Academic Press, New York, 1975, pp. 151–176.
E. Salamin, “Computation of zt using the arithmetic-geometric mean,” Math. Comp., v. 30, 1976, pp. 565–570.
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© 1985 Springer Science+Business Media New York
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Newman, D.J. (1985). A Simplified Version of the Fast Algorithms of Brent and Salamin. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2736-4_57
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DOI: https://doi.org/10.1007/978-1-4757-2736-4_57
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2738-8
Online ISBN: 978-1-4757-2736-4
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