Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:C3L-A

Session:

Number:433

Fast Multiprecision Algorithm like Quad-Double Arithmetic

Naoya Yamanaka,  Shin'ichi Oishi,  

pp.433-436

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.433

PDF download (280.7KB)

Summary:
A quad-double number is an unevaluated sum of four double precision numbers, capable of representing at least 212 bits of significand. Hida et. al. have developed the well-known software for quad-double arithmetic called “QD”. Similarly to their algorithms, in this paper, fast multiprecision algorithms are proposed. The proposed algorithms in this paper are designed to achieve the results as if computed in almost 4-fold working precision. Numerical results are presented showing the performance of the proposed multiprecision algorithms.

References:

[1] The GNU MPFR Library: http://www.mpfr.org/

[2] exflib - extend precision floating-point arithmetic library: http://www-an.acs.i.kyoto-u.ac.jp/˜fujiwara/exflib/

[3] D. H. Bailey, Y. Hida, X. S. Li and B. Thompson. “ARPREC: an arbitrary precision computational package”, Lawrence Berkeley National Laboratory. Berkeley. CA94720. 2002.

[4] D. H. Bailey. “A fortran-90 double-double library”, Available at http://www.nersc.gov/˜dhbailey/mpdist/mpdist.html

[5] Y. Hida, X. S. Li and D. H. Bailey. “Quad-Double Arithmetic: Algorithms, Implementation, and Application” October 30, 2000 Report LBL-46996.

[6] S.M. Rump, T. Ogita, and S. Oishi: “Accurate floating-point summation part I: Faithful rounding”. SIAM J. Sci. Comput., 31(1):189-224, 2008.

[7] S.M. Rump, T. Ogita, and S. Oishi: “Accurate floating-point summation part II: Sign, K-fold faithful and rounding to nearest”. Siam J. Sci. Comput., 31(2):1269-1302, 2008.

[8] D. E. Knuth: The Art of Computer Programming: Seminumerical Algorithms, vol. 2, Addison-Wesley, Reading, Massachusetts, 1969.

[9] T. J. Dekker: A floating-point technique for extending the available precision, Numer. Math., 18 (1971), pp. 224-242.