ARITH 2026: Program

Keynotes

Mixed-precision Computing: High Accuracy With Low Precision

Erin Carson

Associate Professor in the Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

Mixed-precision algorithms have launched an era in which efficiency and accuracy are no longer mutually exclusive. Rather than rely entirely on high-precision formats like double (64-bit) precision, mixed-precision algorithms apply lower precisions such as single (32-bit) or half (16-bit) precision whenever possible, reserving higher precision only for critical steps. Doing so can drastically reduce memory requirements, improve performance, and lessen energy consumption on modern computer hardware without sacrificing accuracy or stability. In this talk, we discuss the challenges of using low/mixed precision, and present five cases, common in scientific applications, where using mixed precision makes sense.

The Table Maker's Dilemma and Correctly-Rounded Functions: A Quick Review of 25 Years of Work

Jean-Michel Muller

CNRS Emeritus, Laboratoire LIP, Author of the books "Elementary Functions, algorithms and implementation" and lead-author of the "Handbook of floating-point arithmetic".

I will argue that providing a core set of correctly rounded elementary functions can greatly benefit many domains of numerical computing. I will also review some of the problems the community has addressed over the years to achieve this, such as solving part of the Table Maker's Dilemma and designing algorithms that build special polynomial approximations or compute tight, certified bounds on approximation and evaluation errors.

Symposium at a glance

All talks take place at room 010 in building 52 (see campus plan).

Time (UTC+2)	Sunday June 28th, 2026	Monday June 29th, 2026	Tuesday June 30th, 2026	Wednesday July 1st, 2026
8:30 to 9:00		Registration
9:00 to 9:30		Welcome Location: 52.010	Session 4: Hardware Arithmetic Chair: Bogdan Pasca Location: 52.010 Area-Efficient LUT-Based Multipliers for AMD Versal FPGAs Zetao Miao, Xander Pottier, Jonas Bertels, Wouter Legiest and Ingrid Verbauwhede 🏆 (Nominated as Best Paper) LUT-Oriented Boolean Decomposition for Efficient Arithmetic on FPGAs and ASICs Danila Gorodecky and Leonel Sousa Approximating Floating-Point Addition Using The Geometric Mean Theodor Lindberg and Oscar Gustafsson 🏆 (Nominated as Best Paper) Enhancing Digit-Recurrence Floating-Point HUB Division (Invited talk from Recent Journal Contributions) Julio Villalba-Moreno	Session 7: Hardware for Multiply-Accumulate, Dot Products and Matrix Multiplication Chair: Reto Zimmermann Location: 52.010 TensorGauge: A Pre-silicon End-to-end Framework for Quantifying Numerical Effects of Tensor Core Microarchitecture in GEMM Wei Liu, Yi Yu, Qianliang Liu, Xiaoyou Song, Mingyuan Ma, Yuhan Wang, Haonan Sun, Yumin Hou and Hu He Vectorized Fused Dot Product Thomas Ferrere, Jeremy Zolnai-Lucas, Tai Li and Adedotun Adeyemo Efficacy of Pipelining to Reduce Energy of Floating-Point Adders and Multipliers Per Larsson-Edefors and Erik Börjeson Automating High-Efficiency Compressor Trees in Vivado (Invited talk from Recent Journal Contributions) Thomas Preußer, Shikha Soni, Fan Zhang and Michaela Blott
9:30 to 11:00		Session 1: Software with Basic Arithmetic Operations Chair: Guillaume Melquiond Location: 52.010 Odd but Error-Free FastTwoSum Sehyeok Park, Jay Lim and Santosh Nagarakatte 64-bit integer division for the JavaScript platform Sébastien Doeraene and Tobias Schlatter Extended-Precision FMA under Parameterized Double-Word Overlap: Tight Error Bounds and Examples Claude-Pierre Jeannerod, Mioara Joldes, Nicolas Louvet and Jean-Michel Muller.
11:00 to 11:30		Break
11:30 to 12:30		1st Keynote Talk: Mixed-precision Computing: High Accuracy With Low Precision by Erin Carson Chair: Anastasia Volkova Location: 52.010	2nd Keynote Talk: The Table Maker's Dilemma and Correctly-Rounded Functions: A Quick Review of 25 Years of Work by Jean-Michel Muller Chair: Peter Tang Location: 52.010	Session 8: Quantum Algorithms for Elementary Functions Chair: Jean-Michel Muller Location: 52.010 The table maker's quantum search Benjamin Morrison, Stefanos Kourtis Quantum Algorithms for Exponentiation in a Group Xavier Bonnetain, Pierrick Gaudry and Medhi Kermaoui
12:30 to 14:00		Lunch Location: 52.010	Lunch (Location: 52.010)/ Steering Committee meeting (Location: 46.307)	Closing Session (Location: 52.010)
12:30 to 14:00		Lunch Location: 52.010		Lunch Location: 52.010
14:00 to 15:30		Session 2: Formats and Arithmetic for Machine Learning Chair: Tue Ly Location: 52.010 Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning Andrew Fitzgibbon, Christoph M. Wintersteiger and Jeffrey Sarnoff 🏆 (Nominated as Best Paper) FMA Is (Almost) All You Need: sharing FMA resources for linear and non-linear Function Acceleration in Attention-based Networks Arpan Suravi Prasad, Andrea Belano, Davide Rossi, Francesco Conti and Luca Benini A Word-Level Multi-Precision Systolic Array Architecture for Accelerating Deep Neural Networks Xinjun Zhou, Fen Ge, Hui Chen and Weiqiang Liu A Hardware-Efficient Training-oriented Quadratic Approximation Softmax for Transformers Zehao Cheng, Weichao Yi, Hui Chen, Chenggang Yan, Bi Wu, Ke Chen and Weiqiang Liu	Session 5: Elementary Functions Chair: Santosh Nagarakatte Location: 52.010 The GNU libc atanh is Correctly Rounded Paul Zimmermann Correctly Rounded Vector Implementation of the Exponential Function in binary64 Arithmetic Nicolas Brisebarre, Tom Hubrecht, Christoph Lauter, Jean-Michel Muller and Kristalys Ruiz-Rohena Computing hard-to-round Cases of sin, cos, tan in Double Precision Vincent Lefèvre, Tue Ly and Paul Zimmermann 🏆 (Nominated as Best Paper)	Social Event Hiking in UNESCO Biosphere Reserve Rhön Details see Social Program

15:30 to 16:00			Break
16:00 to 16:30		Break	Session 6: Crypto / Finite Fields Chair: Vassil Dimitrov Location: 52.010 Explicit Correction Probabilities for Montgomery Multiplication via Arithmetic Analysis Daichi Aoki and Tsuyoshi Takagi Exploration of High-Speed Modulo 2ⁿ-1 Adders Konstantinos Vasilas, Theofanis Vergos, Polykarpos Vergos and Haridimos Vergos RNS Base Extension through Operand Scaling on FPGA for Large Integers Emilie Debelle, Arnaud Tisserand and Karim Bigou
16:30 to 17:30		Session 3: Verification Chair: Mioara Joldes Location: 52.010 Verifying Code That Uses Error-Free Transformations Tom Hubrecht and Guillaume Melquiond A Conflict-Aware Learning Approach to SCA Verification for MAC Architectures Jan Kleinekathöfer, Lennart Weingarten, Kamalika Datta and Rolf Drechsler
17:30 to 19:00		In Memoriam Session for Alberto Nannarelli Demo Session (see below) Chair: Anastasia Volkova, Theo Drane Location: 52.009
18:30 to 19:30			City Tour Meeting Point: Tourist-Info Fulda
19:30 to 22:00	Welcome Reception Location: Wiesenmühle Fulda		Banquet Location: FLORA Klostercafé, Frauenberg Fulda

Demo Session

The Demo Session will focus on recent trends of tools in computer arithmetic.
Organization and charing is done by Anastasia Volkova and Theo Drane.
The following presentations will be given at the demo session on Monday afternoon:

Golden Models for Numerical Datapath, Artem Yadrov and Pavel Panchekha (University of Utah, USA)
APyTypes - Like NumPy but with fully configurable data types, Oscar Gustafsson and Theodor Lindberg (Linköping University, Sweden)
Sollya, Christoph Lauter (University of Texas at El Paso, USA)
Gappa, Guillaume Melquiond (Inria, France)
Can you really build hardware with MLIR and CIRCT?, Sam Coward (University College London, UK)
Printing Mathematical Intent onto Silicon with Emeraude-MLIR, HAriCo, and OpenROAD, Louis Ledoux (INSA Lyon, France)
Eggroll: Guiding E-graph exploration with Reinforcement Learning, Andy Wanna (Georgia Tech, USA), Stefan Abi-Karam (Georgia Tech, USA), Theo Drane (AMD, USA), Cong “Callie” Hao (Georgia Tech, USA)
Papercuts: Leveraging Formal Verification for Hardware Improvement (on the subject of HW HLS), Ethan Miller (Georgia Tech, USA), Andy Wanna (Georgia Tech, USA), Theo Drane (AMD, USA), Cong “Callie” Hao (Georgia Tech, USA)
Advances in Data Path Verification in VC Formal, Sai Karthik Madabhushi (Synopsys, USA)

Keynotes

Mixed-precision Computing: High Accuracy With Low Precision

The Table Maker's Dilemma and Correctly-Rounded Functions: A Quick Review of 25 Years of Work

Symposium at a glance

Time (UTC+2)

Sunday June 28th, 2026

Monday June 29th, 2026

Tuesday June 30th, 2026

Wednesday July 1st, 2026

Demo Session