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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Efficient multiple-precision evaluation of elementary functions
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by David M. Smith PDF
Math. Comp. 52 (1989), 131-134 Request permission

Abstract:

Let $M(t)$ denote the time required to multiply two t-digit numbers using base b arithmetic. Methods are presented for computing the elementary functions in $O({t^{1/3}}M(t))$ time.
References
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  • Richard P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976), no. 2, 242–251. MR 395314, DOI 10.1145/321941.321944
  • R. P. Brent, "A Fortran multiple-precision arithmetic package," ACM Trans. Math. Software, v. 4, 1978, pp. 57-70.
  • Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
  • Michael S. Paterson and Larry J. Stockmeyer, On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM J. Comput. 2 (1973), 60–66. MR 314238, DOI 10.1137/0202007
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 52 (1989), 131-134
  • MSC: Primary 65D15; Secondary 26-04
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0971406-0
  • MathSciNet review: 971406