CGO 2023
Sat 25 February - Wed 1 March 2023 Montreal, Canada
Mon 27 Feb 2023 15:40 - 16:06 at Montreal 1-2-3 - Session 3 -- Potpourri Chair(s): Bernhard Egger

This paper proposes fast polynomial evaluation methods for correctly rounded elementary functions generated using our RLibm approach. The resulting functions produce correct results for all inputs with multiple representations and rounding modes. Given an oracle, the RLibm approach approximates the correctly rounded result rather than the real value of an elementary function. A key observation is that there is an interval of real values around the correctly rounded result such that any real value in it rounds to the correct result. This interval is the maximum freedom available to RLibm’s polynomial generation procedure. Subsequently, the problem of generating correctly rounded elementary functions using these intervals can be structured as a linear programming problem. Our prior work on the RLibm approach uses Horner’s method for polynomial evaluation.

This paper explores polynomial evaluation techniques such as Knuth’s coefficient adaptation procedure, parallel execution of operations using Estrin’s procedure, and the use of fused multiply-add operations in the context of the RLibm approach. If we take the polynomial generated by the RLibm approach and subsequently perform polynomial evaluation optimizations, it results in incorrect results due to rounding errors during polynomial evaluation. Hence, we propose to integrate the fast polynomial evaluation procedure in the RLibm’s polynomial generation process. Our new polynomial evaluation procedure that combines parallel execution with fused multiply-add operations outperforms the Horner’s method used by RLibm’s correctly rounded functions. We show the resulting polynomials for 32-bit float are not only correct but also faster than prior functions in RLibm by 24%

Mon 27 Feb

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

15:40 - 17:00
Session 3 -- PotpourriMain Conference at Montreal 1-2-3
Chair(s): Bernhard Egger Seoul National University
15:40
26m
Talk
Fast Polynomial Evaluation for Correctly Rounded Elementary Functions using the RLIBM Approach
Main Conference
Mridul Aanjaneya Rutgers University, Santosh Nagarakatte Rutgers University
DOI
16:06
26m
Talk
A Game-Based Framework to Compare Program Classifiers and Evaders
Main Conference
Thaís Regina Damásio Federal University of Minas Gerais, Michael Canesche Federal University of Minas Gerais, Vinícius Pacheco Federal University of Minas Gerais, Marcus Botacin Texas A&M University, Anderson Faustino da Silva State University of Maringá, Fernando Magno Quintão Pereira Federal University of Minas Gerais
DOI
16:33
26m
Talk
WARDen: Specializing Cache Coherence for High-Level Parallel Languages
Main Conference
Michael Wilkins Northwestern University, Sam Westrick Carnegie Mellon University, Vijay Kandiah Northwestern University, Alex Bernat Northwestern University, Brian Suchy Northwestern University, Enrico Armenio Deiana Northwestern University, Simone Campanoni Northwestern University, Umut A. Acar Carnegie Mellon University, Peter Dinda Northwestern University, Nikos Hardavellas Northwestern University
DOI