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).