CORE-MATH References

Bibliographic references

• the current N3096 draft of the next C standard has reserved names cr_exp, cr_log, cr_sin for correctly rounded functions (cf 7.33.8, item 4, page 457).
• Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision, Vincenzo Innocente and Paul Zimmermann, 2021.
• High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations, Jay P. Lim and Santosh Nagarakatte, PLDI'21, 2021. More references about the RLibm project are available here.
• One Polynomial Approximation to Produce Correctly Rounded Results of an Elementary Function for Multiple Representations and Rounding Modes, Jay P. Lim and Santosh Nagarakatte, POPL 2022.
• RLibm-Prog: Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries, Mridul Aanjaneya, Jay P. Lim and Santosh Nagarakatte, Rutgers Department of Computer Science Technical Report DCS-TR-758, 2021.
• MLFS - Mathematical Library for Flight Software, European Space Agency, 2018.
• An efficient rounding boundary test for pow(x,y) in double precision, Christoph Lauter and Vincent Lefèvre, IEEE Transactions on Computers, vol. 58, nb. 2, pages 197-207, 2009. [HAL version]
• Algorithms for Calculating Correctly Rounded Exponential Function in Double-Precision Arithmetic, Alexander Godunov, IEEE Transactions on Computers, vol. 69, no. 9, 2020, pages 1388-1400 (+ appendix of 10 pages)
• A High Throughput Polynomial and Rational Function Approximations Evaluator, Nicolas Brisebarre, George Constantinides, Miloš Ercegovac, Silviu-Ioan Filip, Matei Istoan, Jean-Michel Muller, 2018.
• Test of Mathematical Functions of the Standard C Library, Vincent Lefèvre.
• CR-LIBM: A library of correctly rounded elementary functions in double-precision, Catherine Daramy-Loirat, David Defour Florent de Dinechin, Matthieu Gallet, Nicolas Gast, Christoph Lauter and Jean-Michel Muller, 2006.
• High-level algorithms for correctly-rounded reciprocal square roots, Carlos F. Borges, Claude-Pierre Jeannerod, Jean-Michel Muller, Proceedings of the 29th IEEE Symposium on Computer Arithmetic (ARITH 2022), 2022.
• IA-64 and Elementary Functions, Peter Markstein, Hewlett-Packard Professional Books, 2000
• Tight Interval Inclusions with Compensated Algorithms, Stef Graillat and Fabienne Jézéquel, IEEE Transactions in Computers, volume 69, issue 12, pages 1774-1783, 2020.
• Note on FastTwoSum with Directed Roundings, Paul Zimmermann, preprint, 3 pages, 2022
• Tight and rigorous error bounds for basic building blocks of double-word arithmetic, Mioara Maria Joldes, Jean-Michel Muller, Valentina Popescu, ACM Transactions on Mathematical Software, Vol. 44, No. 2, 2017.
• Formalization of double-word arithmetic, and comments on "Tight and rigorous error bounds for basic building blocks of double-word arithmetic", J.-M. Muller and Laurence Rideau, ACM Transactions on Mathematical Software, Vol. 48 No 1, DOI 10.1145/3484514, March 2022.
• Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?, George Paul and M. Wayne Wilson, ACM Transactions on Mathematical Software, vol. 2, nb. 2, pages 132-142, 1976.
• Non-official copy of MathLib's library (MathLib was designed by IBM)
• On the Robustness of the 2Sum and Fast2Sum Algorithms, Sylvie Boldo, Stef Graillat, Jean-Michel Muller, ACM Transactions on Mathematical Software, vol. 44, no. 1
• Algorithms for triple-word arithmetic, Nicolas Fabiano, Jean-Michel Muller and Joris Picot, IEEE Transactions on Computers, 2019, 68 (11), pages 1573-1583.
• Useful applications of correctly-rounded operators of the form ab + cd + e, Tom Hubrecht, Claude-Pierre Jeannerod, Jean-Michel Muller, 2024

Articles citing CORE-MATH

• The CORE-MATH Project, Alexei Sibidanov, Paul Zimmermann, Stéphane Glondu, Proceedings of the 29th IEEE Symposium on Computer Arithmetic (ARITH 2022), 2022.
• Correctly rounded power function in double precision, talk given by Tom Hubrecht at FPTalks 2022, 2022.
• Towards a correctly-rounded and fast power function in binary64 arithmetic, Tom Hubrecht, Claude-Pierre Jeannerod and Paul Zimmermann, extended version of an article published in the Proceedings of Arith 2023, 2023.
• Correctly-rounded evaluation of a function: why, how, and at what cost?, Nicolas Brisebarre, Guillaume Hanrot, Jean-Michel Muller, Paul Zimmermann, 2024
• Implementation and Synthesis of Math Library Functions, Ian Briggs, Yash Lad and Pavel Panchekha, Proceedings of the ACM on Programming Languages, Volume 8, Issue POPL, Article No 32, pages 942–969, 2024.
• Accurate complex Jacobi rotations, by Vedran Novaković, Journal of Computational and Applied Mathematics, volume 450, 2024.
• Arithmetical enhancements of the Kogbetliantz method for the SVD of order two, by Vedran Novaković, preprint, 2024.

Software references

• Integrate CORE-MATH implementations into openlibm #260