A New Tapered Precision Machine Number Format

• Date: 6. 11. 2025
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Laslo Hunhold

IEEE 754 floating-point arithmetic has dominated computing for decades, but the necessary shift towards low-precision computing has exposed its limitations, both in machine learning and, with mixed-precision methods, in computational mathematics. New number formats such as OFP8, bfloat16, and posits have been proposed, but they are primarily tailored for AI workloads and small dynamic ranges, not general-purpose computation. In mixed-precision contexts, reducing precision typically entails a significant reduction in representable dynamic range, necessitating specialised approaches. This talk presents takum, a new number format that maintains a constant, general-purpose dynamic range even at extremely low precisions, so reducing precision affects only accuracy. I will present results showing that takums outperform IEEE 754 floats, improve over posits for general-purpose use, and offer new arithmetic properties and promising avenues for hardware implementation.