Thu 16 Jun 2022 14:10 - 14:30 at Toucan - Numbers Chair(s): Chandrakana Nandi
Fri 17 Jun 2022 02:10 - 02:30 at Toucan - Numbers

This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has the nice property that the first few lower degree terms produce correctly rounded results for specific representations of smaller bitwidths, which we call progressive performance. To generate such progressive polynomial approximations, we approximate the correctly rounded result and formulate the computation of correctly rounded polynomial approximations as a linear program inspired by the RLIBM project. In contrast to RLIBM, we avoid storing large lookup tables for the polynomial coefficients. We observe that the problem of computing polynomial approximations to elementary functions is a linear programming problem in low dimensions, i.e., with a small number of unknowns. We design a fast randomized algorithm for efficiently computing polynomial approximations with progressive performance. Our method produces polynomial approximations that are faster than the RLIBM project and other mainstream libraries while also having progressive performance.

Thu 16 Jun

Displayed time zone: Pacific Time (US & Canada) change

13:30 - 14:50
NumbersPLDI at Toucan +12h
Chair(s): Chandrakana Nandi Certora, inc.
13:30
20m
Talk
Choosing Mathematical Function Implementations for Speed and Accuracy
PLDI
Ian Briggs University of Utah, Pavel Panchekha University of Utah
DOI
13:50
20m
Talk
Guaranteed bounds for posterior inference in universal probabilistic programming
PLDI
Raven Beutner CISPA Helmholtz Center for Information Security, Germany, C.-H. Luke Ong University of Oxford, Fabian Zaiser University of Oxford
DOI Pre-print
14:10
20m
Talk
Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries
PLDI
Mridul Aanjaneya Rutgers University, Jay P. Lim Yale University, Santosh Nagarakatte Rutgers University
Link to publication DOI Pre-print
14:30
20m
Talk
Karp: A Language for NP Reductions
PLDI
Chenhao Zhang Northwestern University, Jason D. Hartline Northwestern University, Christos Dimoulas PLT @ Northwestern University
DOI

Fri 17 Jun

Displayed time zone: Pacific Time (US & Canada) change

01:30 - 02:50
NumbersPLDI at Toucan
01:30
20m
Talk
Choosing Mathematical Function Implementations for Speed and Accuracy
PLDI
Ian Briggs University of Utah, Pavel Panchekha University of Utah
DOI
01:50
20m
Talk
Guaranteed bounds for posterior inference in universal probabilistic programming
PLDI
Raven Beutner CISPA Helmholtz Center for Information Security, Germany, C.-H. Luke Ong University of Oxford, Fabian Zaiser University of Oxford
DOI Pre-print
02:10
20m
Talk
Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries
PLDI
Mridul Aanjaneya Rutgers University, Jay P. Lim Yale University, Santosh Nagarakatte Rutgers University
Link to publication DOI Pre-print
02:30
20m
Talk
Karp: A Language for NP Reductions
PLDI
Chenhao Zhang Northwestern University, Jason D. Hartline Northwestern University, Christos Dimoulas PLT @ Northwestern University
DOI