MPFR Algorithms

Algorithms used in MPFR are described in the algorithms.tex file, available from the doc directory of the MPFR Git repository. You can also directly view a version in PDF online (however, it may not always be up-to-date).

The main paper on MPFR, which can be used to properly cite MPFR in a scientific publication, is the following one.

Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Paul Zimmermann. MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding. ACM Transactions on Mathematical Software, 33(2), June 2007.

Other papers on MPFR include:

Emmanuel Jeandel. Évaluation rapide de fonctions hypergéométriques. Technical report RT-0242, INRIA, July 2000.
Vincent Lefèvre. The Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library). In Proceedings of the 6th Conference on Real Numbers and Computers, pages 135–145, Dagstuhl, Germany, November 2004.
Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Paul Zimmermann. MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding. Research report RR-5753, INRIA, November 2005. Note: This is an earlier version of the main paper cited above.
Y.-F. S. Pétermann and Jean-Luc Rémy. Arbitrary Precision Error Analysis for computing ζ(s) with the Cohen-Olivier algorithm: Complete description of the real case and preliminary report on the general case. Research report RR-5852, INRIA, February 2006.
Vincent Lefèvre and Paul Zimmermann. Optimized binary64 and binary128 arithmetic with GNU MPFR. In Proceedings of the 24th IEEE Symposium on Computer Arithmetic (ARITH 24), London, United Kingdom, July 2017.
Vincent Lefèvre. Correctly rounded arbitrary-precision floating-point summation. IEEE Transactions on Computers, 2017 (version on HAL, and an earlier, shorter version).