RLibm: Rutgers Architecture and Programming Languages Lab's Correctly Rounded Libm
The RLibm project is building a collection of correctly rounded
elementary functions for multiple representations ( e.g.,
32bit float, posits, bfloat16, tensorfloat32) for multiple rounding
modes. This project makes a case for approximating the correctly
rounded result of an elementary function rather than the real value of
an elementary function. When 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 our
approach for polynomial approximation has for an input, which is
larger than the freedom with prior approaches (i.e., minimax
approaches). Hence, our RLibm approach has more margin to generate
correct, yet, efficient polynomials.
Using these intervals, we structure the problem of generating
polynomial approximations that produce correctly rounded results for
all inputs as a linear programming problem. We have developed
correctly rounded implementations of elementary functions for multiple
representations: 32bit floating point, 32bit posits, 16bit posits,
bfloat16, and tensorfloat32.
Developers
Collaborators
Code
Talks
Publications

RLIBMALL: A Novel Polynomial Approximation Method to Produce
Correctly Rounded Results for Multiple Representations and
Rounding Modes
[pdf]
Jay P Lim and Santosh Nagarakatte
Department of Computer
Science, Rutgers University, Technical Report DCSTR757,
August 2021

High Performance Correctly Rounded Math Libraries for 32bit
Floating Point
Representations
[preprint]
Jay P Lim and Santosh Nagarakatte
Proceedings of the 2021 ACM SIGPLAN
Conference on Programming Language Design and Implementation
(PLDI2021), June 2025, 2021.
Acceptance rate: 27% (87 out of 320 submissions)
ACM SIGPLAN PLDI 2021 Distinguished Paper Award
 RLIBM32: High Performance Correctly Rounded Math Libraries
for 32bit Floating Point
Representations [pdf]
Jay P Lim and Santosh Nagarakatte Department of Computer
Science, Rutgers University, Technical Report DCSTR754,
April 2021 Extended version of our PLDI 2021 paper.

An Approach to Generate Correctly Rounded Math Libraries for New Floating Point Variants
[preprint]
Jay P Lim, Mridul Aanjaneya, John Gustafson, and Santosh Nagarakatte
Proceedings of the 2021 ACM SIGPLAN Symposium on Principles
of Programming Languages (POPL2021), Jan 1722, 2021.
Acceptance Rate: 23% (61 out of 258 submissions).
 A Novel Approach to Generate Correctly Rounded Math
Libraries for New Floating Point
Representations [pdf]
Jay P Lim, Mridul Aanjaneya, John Gustafson, and Santosh
Nagarakatte
Department of Computer Science, Rutgers University, Technical
Report DCSTR753, July 2020
Funding:
 NSF CORE ProgramSHF, PI,
$499,979, "Techniques
for Generating Correctly Rounded Math Libraries", 2021.
 NSF CORE ProgramSHF, PI,
$500,000, "Formalisms,
Implementations, and Verification Procedures for Alternatives to
Floating Point", 20192022.
Last modified: Mon August 15 16:00 EST 2021
