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POPL 2021
Sun 17 - Fri 22 January 2021 Online
Wed 20 Jan 2021 18:50 - 19:00 at POPL-A - Program Analysis

Given the importance of floating-point (FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded math libraries. Further, the use of existing FP libraries for these new representations can produce incorrect results. This paper proposes a novel approach for generating polynomial approximations that can be used to implement correctly rounded math libraries. Existing methods generate polynomials that approximate the real value of an elementary function f(x) and produce wrong results due to approximation errors and rounding errors in the implementation. In contrast, our approach generates polynomials that approximate the correctly rounded value of f(x) (i.e., the value of f(x) rounded to the target representation). It provides more margin to identify efficient polynomials that produce correctly rounded results for all inputs. We frame the problem of generating efficient polynomials that produce correctly rounded results as a linear programming problem. Using our approach, we have developed correctly rounded, yet faster, implementations of elementary functions for multiple target representations.

Wed 20 Jan

Displayed time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change

18:30 - 19:30
Program AnalysisPOPL at POPL-A
18:30
10m
Talk
Verifying Correct Usage of Context-Free API Protocols
POPL
Kostas Ferles UT Austin, Jon Stephens University of Texas at Austin, Isil Dillig University of Texas at Austin
Link to publication DOI
18:40
10m
Talk
Data Flow Refinement Type Inference
POPL
Zvonimir Pavlinovic Google, USA, Yusen Su New York University, University of Waterloo, Thomas Wies New York University, USA
Link to publication DOI
18:50
10m
Talk
An Approach to Generate Correctly Rounded Math Libraries for New Floating Point Variants
POPL
Jay P. Lim Rutgers University, USA, Mridul Aanjaneya Rutgers University, John Gustafson National University of Singapore, Santosh Nagarakatte Rutgers University, USA
Link to publication DOI
19:00
10m
Talk
An Abstract Interpretation for SPMD Divergence on Reducible Control Flow GraphsDistinguished Paper
POPL
Julian Rosemann Saarland University, Saarland Informatics Campus, Simon Moll NEC Deutschland, Sebastian Hack Saarland University, Germany
Link to publication DOI
19:10
10m
Talk
Relatively Complete Verification of Probabilistic Programs
POPL
Kevin Batz RWTH Aachen University, Benjamin Lucien Kaminski RWTH Aachen University, Germany, Joost-Pieter Katoen RWTH Aachen University, Christoph Matheja ETH Zurich
Link to publication DOI
19:20
10m
Talk
A Practical Mode System for Recursive Definitions
POPL
Alban Reynaud ENS Lyon, Gabriel Scherer INRIA Saclay, Jeremy Yallop University of Cambridge
Link to publication DOI Pre-print