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 the
polynomial approximation has for an input, which is larger than the
freedom with prior approaches (i.e., minimax
approaches). Hence, the 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.
Participants
Collaborators
Transition to Practice
Blog posts
Code
Talks
Publications

Fast Polynomial Evaluation for Correctly Rounded Elementary
Functions using the RLIBM
Approach. [preprint]
Mridul Aanjaneya and Santosh Nagarakatte
Proceedings of the IEEE/ACM International
Symposium on Code Generation and Optimization (CGO2023), Montreal, Canada,
Feb 25 March 1st, 2023.
Acceptance rate: 39% (20 out of 51 submissions)

Progressive Polynomial Approximations for Fast Correctly Rounded
Math Libraries
[preprint]
Mridul Aanjaneya, Jay P. Lim, and Santosh
Nagarakatte
Proceedings of the 2022 ACM SIGPLAN Conference
on Programming Langauge Design and Implementation (PLDI2022), San
Diego, USA, June, 2022.
Acceptance rate: 21% (68 out of 326 submissions)

One Polynomial Approximation to Produce Correctly Rounded Results
of an Elementary Function for Multiple Representations and Rounding
Modes
[preprint]
Jay Lim and Santosh Nagarakatte
Proceedings of the 49th ACM SIGPLAN Symposium on Principles
of Programming Languages (POPL2022), Philadelphia, USA, January 1622, 2022.
Acceptance rate: 23% (65 out of 286 submissions)
ACM SIGPLAN POPL 2022 Distinguished Paper Award

RLIBMPROG: Progressive Polynomial Approximations for Fast
Correctly Rounded Math Libraries
[pdf]
Mridul Aanjaneya and Jay P Lim and Santosh Nagarakatte
Department of Computer
Science, Rutgers University, Technical Report DCSTR758,
November 2021

Novel Polynomial Approximation Methods for Generating
Correctly Rounded Elementary Functions
[pdf]
Jay P Lim's PhD dissertation supervised
by Santosh Nagarakatte
Department of Computer
Science, Rutgers University
October 2021
2022 ACM SIGPLAN John C Reynolds Outstanding Dissertation
Award

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:
 Intel Corporation Research Gift, $62,000, "A Case for Correctly Rounded Math Libraries with the RLIBM
Approach",
2022.
 NSF CORE ProgramSHF,
$499,979, "Techniques
for Generating Correctly Rounded Math Libraries", 2021.
 NSF CORE ProgramSHF,
$500,000, "Formalisms,
Implementations, and Verification Procedures for Alternatives to
Floating Point", 20192022.
Last modified: Mon May 15 15:46 EST 2022
