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Arb: a C library for ball arithmetic

Published: 28 January 2014 Publication History
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References

[1]
A. Enge. MPFRCX: a library for univariate polynomials over arbitrary precision real or complex numbers, 2012. http://www.multiprecision.org/index.php?prog=mpfrcx.
[2]
L. Fousse, G. Hanrot, V. Lef`evre, P. Pélissier, and P. Zimmermann. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Transactions on Mathematical Software, 33(2):13:1--13:15, June 2007. http://mpfr.org.
[3]
W. B. Hart. Fast Library for Number Theory: An Introduction. In Proceedings of the Third international congress conference on Mathematical software, ICMS'10, pages 88--91, Berlin, Heidelberg, 2010. Springer-Verlag. http://flintlib.org.
[4]
W. B. Hart and A. Novocin. Practical divide-and-conquer algorithms for polynomial arithmetic. In Computer Algebra in Scientific Computing, pages 200--214. Springer, 2011.
[5]
F. Johansson et al. mpmath: a Python library for arbitrary-precision floating-point arithmetic, version 0.17, 2011. http://mpmath.org.
[6]
Xian-Jin Li. The positivity of a sequence of numbers and the Riemann Hypothesis. Journal of Number Theory, 65(2):325--333, 1997.
[7]
N. Müller. The iRRAM: Exact arithmetic in C++. In Computability and Complexity in Analysis, pages 222--252. Springer, 2001. http://irram.uni-trier.de.
[8]
N. Revol and F. Rouillier. Motivations for an arbitrary precision interval arithmetic library and the MPFI library. Reliable Computing, 11(4):275--290, 2005. http://perso.ens-lyon.fr/nathalie.revol/software.html.
[9]
M. Sofroniou and G. Spaletta. Precise numerical computation. Journal of Logic and Algebraic Programming, 64(1):113--134, 2005.
[10]
The PARI Group, Bordeaux. PARI/GP, version 2.5.3, 2012. http://pari.math.u-bordeaux.fr.
[11]
J. van der Hoeven. Making fast multiplication of polynomials numerically stable. Technical Report 2008-02, Université Paris-Sud, Orsay, France, 2008.
[12]
J. van der Hoeven. Ball arithmetic. Technical report, HAL, 2009. http://hal.archives-ouvertes.fr/hal-00432152/fr/.
[13]
J. van der Hoeven, G. Lecerf, B. Mourrain, P. Trébuchet, J. Berthomieu, D. N. Diatta, and A. Mantzaflaris. Mathemagix: the quest of modularity and efficiency for symbolic and certified numeric computation? ACM Communications in Computer Algebra, 45(3/4):186--188, January 2012. http://mathemagix.org.

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cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 47, Issue 3/4
September/December 2013
116 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/2576802
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 January 2014
Published in SIGSAM-CCA Volume 47, Issue 3/4

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