Speaker: Prof. Santosh Nagarkatte, Associate Professor, Rutgers University
Abstract: 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 or
equal to 32-bits.
Speaker bio:
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 Top
Picks papers of computer architecture conferences in 2010 and 2013. He
received the NSF CAREER Award in 2015, ACM SIGPLAN PLDI 2015
Distinguished Paper Award, ACM SIGSOFT ICSE 2016 Distinguished Paper
Award, and 2018 Communications of the ACM Research Highlights paper
for his research on LLVM compiler verification. His PhD student David
Menendez's dissertation on LLVM verification was awarded the 2018 ACM
SIGPLAN John C Reynolds Outstanding Dissertation Award. His papers on
correctly rounded elementary functions have been recognized with the
ACM SIGPLAN PLDI 2021 Distinguished Paper Award and the ACM SIGPLAN
POPL 2022 Distinguished Paper Award. His PhD student Jay Lim's
dissertation on correctly rounded elementary functions was awarded the
2022 ACM SIGPLAN John C Reynolds Outstanding Dissertation Award.