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

Speaker

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".

Speaker

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 Juliy 1st, 2026
8:30 to 9:00   Registration    
9:00 to 9:30   Welcome
Location: 52.010 		Session 4: Hardware Arithmetic (Chair: TBA)
Location: 52.010
  • Area-Efficient LUT-Based Multipliers for AMD Versal FPGAs
    Zetao Miao, Xander Pottier, Jonas Bertels, Wouter Legiest and Ingrid Verbauwhede
  • 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
  • Enhancing Digit-Recurrence Floating-Point HUB Division
    (Invited talk from Recent Journal Contributions)
    Julio Villalba
Session 7: Hardware for Multiply-Accumulate, Dot Products and Matrix Multiplication (Chair: TBA)
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: TBA)
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
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
Location: 52.010 		Session 8: Quantum Algorithms for Elementary Functions (Chair: TBA)
Location: 52.010
  • The table maker's quantum search
    Stefanos Kourtis
  • Quantum Algorithms for Exponentiation in a Group
    Xavier Bonnetain, Pierrick Gaudry and Medhi Kermaoui
12:30 to 2:00   Lunch
Location: 52.010		 Lunch / Steering Committee meeting
Location: TBA		 Lunch
Location: 52.010
14:00 to 15:30   Session 2: Formats and Arithmetic for Machine Learning (Chair:TBA)
Location: 52.010
  • Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning
    Andrew Fitzgibbon, Christoph M. Wintersteiger and Jeffrey Sarnoff
  • 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: TBA)
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
Social Event

Hiking in Rhön

Details tba
15:30 to 16:00 Break
16:00 to 16:30   Break Session 6: Crypto / Finite Fields (Chair: TBA)
Location: 52.010
  • Explicit Correction Probabilities for Montgomery Multiplication via Arithmetic Analysis
    Daichi Aoki and Tsuyoshi Takagi
  • Exploration of High-Speed Modulo $2^n-1$ 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: TBA)
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   Demo Session
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