Santosh Nagarakatte
Rutgers University
A Case for Correctly Rounded Math Libraries
This talk will provide an overview of the RLIBM project where we are building a collection of correctly rounded elementary functions for multiple representations and rounding modes. Historically, polynomial approximations for elementary functions have been designed by approximating the real value. In contrast, we make a case for approximating the correctly rounded result of an elementary function rather than the real value of an elementary function in the RLIBM project. Once we approximate the correctly rounded result, there is an interval of real values around the correctly rounded result such that producing a real value in this interval rounds to the correct result. This interval is the freedom that the polynomial approximation has for an input, which is larger than the ones with the mini-max approach. Using these intervals, we structure the problem of generating polynomial approximations that produce correctly rounded results for all inputs as a linear programming problem. The results from the RLIBM project makes a strong case for mandating correctly rounded results at least for any representation that has fewer than orequal to 32-bits.
References
- RLIBM with a focus on An Approach to Generate Correctly Rounded Math Libraries for New Floating Point Variants by Jay P. Lim, Mridul Aanjaneya, John Gustafson, Santosh Nagarakatte
- High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations by Jay P. Lim, Santosh Nagarakatte
- One Polynomial Approximation to Produce Correctly Rounded Results of an Elementary Function for Multiple Representations and Rounding Modes by Jay P. Lim, Santosh Nagarakatte
- Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries by by Mridul Aanjaneya, Jay P. Lim, Santosh Nagarakatte
Santosh Nagarakatte is an Associate Professor at Rutgers University. He obtained his PhD from the University of Pennsylvania in 2012. His research interests are in Hardware-Software Interfaces spanning Programming Languages, Compilers, Software Engineering, and Computer Architecture. His papers have been selected as IEEE MICRO TopPicks papers of computer architecture conferences in 2010 and 2013. Hereceived the NSF CAREER Award in 2015, ACM SIGPLAN PLDI 2015 Distinguished Paper Award, ACM SIGSOFT ICSE 2016 Distinguished PaperAward, and 2018 Communications of the ACM Research Highlights paperfor his research on LLVM compiler verification.
His PhD student David Menendez's dissertation on LLVM verification was awarded the 2018 ACMSIGPLAN John C Reynolds Outstanding Dissertation Award. His papers oncorrectly rounded elementary functions have been recognized with the ACM SIGPLAN PLDI 2021 Distinguished Paper Award and the ACM SIGPLANPOPL 2022 Distinguished Paper Award. His PhD student Jay Lim'sdissertation on correctly rounded elementary functions was awarded the 2022 ACM SIGPLAN John C Reynolds Outstanding Dissertation Award.
- Google Scholar: https://scholar.google.com/citations?hl=en&user=J7H4N_4AAAAJ