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A Multiple-Precision Division Algorithm
Author(s):
David
M.
Smith.
Journal:
Math. Comp.
65
(1996),
157-163.
MSC (1991):
Primary 65-04, 65D15
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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:
- 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.
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Additional Information:
David
M.
Smith
Affiliation:
Department of Mathematics, Loyola Marymount University, Los Angeles, California 90045
Email:
dsmith@lmumail.lmu.edu
DOI:
10.1090/S0025-5718-96-00688-6
PII:
S 0025-5718(96)00688-6
Received by editor(s):
June 17, 1994
Received by editor(s) in revised form:
February 12, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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