Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries
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 JunDisplayed time zone: Pacific Time (US & Canada) change
13:30 - 14:50 | |||
13:30 20mTalk | Choosing Mathematical Function Implementations for Speed and Accuracy PLDI DOI | ||
13:50 20mTalk | 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 20mTalk | 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 20mTalk | Karp: A Language for NP Reductions PLDI Chenhao Zhang Northwestern University, Jason D. Hartline Northwestern University, Christos Dimoulas PLT @ Northwestern University DOI |
Fri 17 JunDisplayed time zone: Pacific Time (US & Canada) change
01:30 - 02:50 | |||
01:30 20mTalk | Choosing Mathematical Function Implementations for Speed and Accuracy PLDI DOI | ||
01:50 20mTalk | 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 20mTalk | 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 20mTalk | Karp: A Language for NP Reductions PLDI Chenhao Zhang Northwestern University, Jason D. Hartline Northwestern University, Christos Dimoulas PLT @ Northwestern University DOI |