Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



A Multiple-Precision Division Algorithm

Author: David M. Smith
Journal: Math. Comp. 65 (1996), 157-163
MSC (1991): Primary 65-04, 65D15
MathSciNet review: 1325874
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The classical algorithm for multiple-precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.

References [Enhancements On Off] (What's this?)

  • 1 D.H. Bailey, Algorithm 719: Multiprecision translation and execution of FORTRAN programs, ACM Trans. Math. Software 19 (1993), 288--319.
  • 2 R.P. Brent, A Fortran multiple-precision arithmetic package, ACM Trans. Math. Software 4 (1978), 57--70.
  • 3 D.E. Knuth, The art of computer programming, Vol. 2: Seminumerical algorithms, Addison-Wesley, Reading, MA, 1981, MR 83i:68003.
  • 4 E.V. Krishnamurthy and S.K. Nandi, On the normalization requirement of divisor in divide-and-correct methods, Comm. ACM 10 (1967), 809--813.
  • 5 C.J. Mifsud, A multiple-precision division algorithm, Comm. ACM 13 (1970), 666--668.
  • 6 D.A. Pope and M.L. Stein, Multiple precision arithmetic, Comm. ACM 3 (1960), 652--654, MR 22:7277.
  • 7 D.M. Smith, Algorithm 693: A Fortran package for floating-point multiple-precision arithmetic, ACM Trans. Math. Software 17 (1991), 273--283.
  • 8 M.L. Stein, Divide-and-correct methods for multiple precision division, Comm. ACM 7 (1964), 472--474.
  • 9 S. Wolfram, Mathematica: A system for doing mathematics by computer, Addison-Wesley, Redwood City, CA, 1991.

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 65-04, 65D15

Retrieve articles in all journals with MSC (1991): 65-04, 65D15

Additional Information

David M. Smith

Received by editor(s): June 17, 1994
Received by editor(s) in revised form: February 12, 1995
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society