CORE-MATH 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.
• 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.
• 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.
• 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.