This Article 
 Bibliographic References 
 Add to: 
A New Range-Reduction Algorithm
March 2005 (vol. 54 no. 3)
pp. 331-339
Range-reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double-precision range.

[1] M. Daumas, C. Mazenc, X. Merrheim, and J.M. Muller, “Modular Range-Reduction: A New Algorithm for Fast and Accurate Computation of the Elementary Functions,” J. Universal Computer Science, vol. 1, no. 3, pp. 162-175, Mar. 1995.
[2] M. Hata, “Legendre Type Polynomials and Rationality Measures,” J. reine angew. Math., vol. 407, pp. 99-125, 1990.
[3] M. Hata, “Rational Approximations to $\pi$ and Some Other Numbers,” Acta Arithmetica, vol. 63, no. 4, pp. 335-349, 1993.
[4] W. Kahan, Minimizing q*m-n, wkahan/ at the beginning of the file “nearpi.c,” 1983.
[5] A. Ya Khintchine, “Einige Sätze über Kettenbrüche, mit Anwendungen auf die Theorie der diophantischen Approximationen,” Math. Ann., vol. 92, pp. 115-125, 1924.
[6] A. Ya Khintchine, Continued Fractions. Chicago, London: Univ. of Chicago Press, 1964.
[7] D. Knuth, The Art of Computer Programming, vol. 2. Reading, Mass.: Addison Wesley, 1973.
[8] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences. Pure and Applied Mathematics. New York-London-Sydney: Wiley-Interscience (John Wiley & Sons), 1974.
[9] J.-M. Muller, Elementary Functions, Algorithms and Implementation. Boston: Birkhäuser, 1997.
[10] K.C. Ng, “Argument Reduction for Huge Arguments: Good to the Last Bit,” technical report, SunPro, 1992. http://www.validlab. comarg. pdf.
[11] M. Payne and R. Hanek, “Radian Reduction for Trigonometric Functions,” SIGNUM Newsletter, vol. 18, pp. 19-24, 1983.
[12] R.A. Smith, “A Continued-Fraction Analysis of Trigonometric Argument Reduction,” IEEE Trans. Computers, vol. 44, no. 11, pp. 1348-1351, Nov. 1995.

Index Terms:
Range-reduction, elementary function evaluation, floating-point arithmetic.
Nicolas Brisebarre, David Defour, Peter Kornerup, Jean-Michel Muller, Nathalie Revol, "A New Range-Reduction Algorithm," IEEE Transactions on Computers, vol. 54, no. 3, pp. 331-339, March 2005, doi:10.1109/TC.2005.36
Usage of this product signifies your acceptance of the Terms of Use.