Organizing Committee
 David Bailey
University of California, Davis  Neil Burgess
Arm, UK  Jack Dongarra
University of Tennessee  Alyson Fox
Lawrence Livermore National Laboratory  Jeffrey Hittinger
Lawrence Livermore National Laboratory  Cindy RubioGonzález
University of California Davis
Abstract
From its introduction in the 1980s, the IEEE754 standard for floatingpoint arithmetic has ably served a wide range of scientists and engineers. Even today, the vast majority of numerical computations employ either IEEE single or IEEE double, typically one or the other exclusively in a single application. However, recent developments have exhibited the need for a broader range of precision levels, and a varying level of precision within a single application. There are clear performance advantages to a variable precision framework: faster processing, better cache utilization, lower memory usage, and lower longterm data storage. But effective usage of variable precision requires a more sophisticated mathematical framework, together with corresponding software tools and diagnostic facilities.
At the low end, the explosive rise of graphics, artificial intelligence, and machine learning has underscored the utility of reduced precision levels. Accordingly, an IEEE 16bit "half" precision standard has been specified, with five exponent bits and ten mantissa bits. Many in the machine learning community are using the "bfloat16" format, which has eight exponent bits and seven mantissa bits. Hardware such as NVIDIA's tensor core units can take advantage of these formats to significantly increase processing rates.
At the same time, researchers in the highperformance computing (HPC) field, in a drive to achieve exascale computing, are considering mixedprecision, such as in iterative refinement calculations where initial iterations are performed using half or singleprecision. Along this line, recognizing that for many simulations much of the data stored in a IEEE 64bit double precision variable has low information content, researchers are exploring the use of lossy floating point compression, not only for I/O, but also for storing solution state variables.
Exascale computing has also exposed the need for even greater precision than IEEE 64bit double in some cases, because greatly magnified numerical sensitivities often mean that one can no longer be certain that results are numerically reliable. One remedy is to use IEEE 128bit quad precision in selected portions of the computation, which is now available via software in some compilers, notably the gfortran compiler. As a single example, researchers at Stanford have had remarkable success in using quad precision in multiscale linear programming applications in biology.
There has also been a rise in the usage of very high precision (hundreds or even thousands of digits). For example, numerous new results have been discovered by computing mathematical expressions to very high precision, and then using integer relation algorithms such as the "PSLQ" algorithm to recognize these numerical values in terms of simple mathematical formulas. Among the results that have been discovered in this fashion are new formulas connecting mathematical constants and the elucidation of polynomials connected to the Poisson potential function of mathematical physics (the latter requiring up to 64,000digit precision). Such computations are most efficiently performed using a dynamically varying level of precision, doing as much computation as possible with standard precision and only invoking very high precision when necessary.
In summary, although the IEEE 754 floatingpoint standard has served the mathematical, scientific and engineering world very well for over 30 years, we now are seeing rapidly growing demand for reduced precision (machine learning, neural nets, graphics, etc.), a growing need for mixed 3264bit precision, and also a need for greater than 64bit, all typically varying within a given application. To the extent that IEEE754 fails to adequately meet new demands such as these, researchers are considering completely different alternatives, for which a flexible precision level is a fundamental feature of the design, and are exploring new mathematical and software frameworks to better understand and utilize such facilities.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Khalid Ahmad
University of Utah

H. Metin Aktulga
Michigan State University

Marco Alvarez
University of Rhode Island

Hartwig Anzt
Karlsruhe Institute of Technology

David Bailey
University of California, Davis

Mark Bell
Independent

Brian Borchers
New Mexico Institute of Mining and Technology

Tilman Dannert
Max Planck Computing and Data Facility

Florent de Dinechin
University of Lyon, INSA

Jack Dongarra
University of Tennessee

Massimiliano Fasi
The University of Manchester

Alyson Fox
Lawrence Livermore National Laboratory

Roberto Garrappa
University of Bari

Ganesh Gopalakrishnan
University of Utah

Hidehiko Hasegawa
University of Tsukuba

Behnam Hashemi
Shiraz University of Technology

Nick Higham
University of Manchester

Jeffrey Hittinger
Lawrence Livermore National Laboratory

Ihor Holod
Max Planck Computing and Data Facility

Roman Iakymchuk
Sorbonne

Fabienne JEZEQUEL
Sorbonne Université

Vasileios Kalantzis
IBM Research

Ignacio Laguna
Lawerence Livermore National Laboratory

Michael Lam
James Madison University

Sven Leyffer
Argonne National Laboratory

Xiaoye Li
Lawrence Berkeley National Laboratory

Neil Lindquist
University of Tennessee

Peter Lindstrom
Lawrence Livermore National Laboratory

Jennifer Loe
Sandia National Laboratories

Piotr Luszczek
University of Tennessee

Oana Marin
Argonne National Laboratory

Krystal Maughan
University of Vermont

Maurice Maurer
Max Planck Institute for Plasma Physics

Harshitha Menon
Lawrence Livermore National Laboratory

Agnieszka Miedlar
University of Kansas

Mantas Mikaitis
The University of Manchester

Pratik Nayak
Karlsruhe Institute of Technology

Daniel OseiKuffuor
LLNL

Emmanuel deGraft Johnson OwusuAnsah
Kwame Nkrumah University of Science and Technology

Marina Popolizio
Politecnico di Bari

Nathalie Revol
Inria

Jason Riedy
Georgia Institute of Technology

Cindy RubioGonzález
University of California Davis

David Sanders
National University of Mexico

Saul Schleimer
University of Warwick

Nikolay Shilov
Innopolis University

SUDHIR SINGH
National Institute of Technology, Trichy India

Barry Smith
Argonne National Laboratory

Katarzyna Swirydowicz
National Renewable Energy Lab

STEPHEN THOMAS
National Renewable Energy Laboratory

Nicholas Timmons
University of Cambridge

Stanimire Tomov
University of Tennessee

Yaohung Tsai
University of Tennessee, Knoxville

Wim vanroose
U. Antwerpen

Homer Walker
Worcester Polytechnic Institute

Carol Woodward
Lawrence Livermore National Laboratory

hotaka yagi
Tokyo University of Science

Ichitaro Yamazaki
Sandia National Labs

Ulrike Yang
Lawrence Livermore National Laboratory

Kazutomo Yoshii
Argonne National Laboratory

Paul Zimmermann
INRIA

Edoardo Zoni
Lawrence Berkeley National Laboratory