I gave an invited lecture and hands-on tutorial, “Verificarlo: Debugging and optimising floating-point calculations”, at the Argonne Training Program on Extreme-Scale Computing (ATPESC 2026), in the Track 4b: Mixed Precision Computing session (Thursday, July 30, 2026, Q Center, St. Charles, IL).

📊 Slides — the tutorial part runs in Google Colab.

Content

The talk covers how numerical variability arises in scientific software, and what the Verificarlo toolchain gives you to measure and act on it:

  • Why floating point bites: Ariane 5, the Vancouver Stock Exchange index, the Pentium FDIV bug — rounding, overflow, and cancellation as engineering risks, amplified by long-lived codes and hardware/software updates.
  • Measuring error without a ground truth: Monte Carlo Arithmetic and stochastic rounding turn “do I trust this result?” into an observable number of significant digits (illustrated on an ill-conditioned 2×2 Cramer system, and on Muller’s sequence, which converges to the wrong limit at every finite precision).
  • Verificarlo: a clang/flang-based compiler that replaces floating-point operations with generic calls, so several numerical models can be selected at runtime from a single compilation.
  • VPREC: dynamic reduced-precision emulation (3–15× overhead), and its use to find mixed-precision configurations — cutting time, memory footprint, and MPI communication volume on the YALES2 combustion solver.
  • Fuzzy and PRISM: stochastic arithmetic for Python, libm, and PyTorch. PRISM’s vectorized stochastic rounding is ~50× faster than the state of the art, making SR tractable on CPU for models like FastSurfer and WavLM.
  • Localizing instabilities: VeriTracer and PyTracer, and case studies where the instability was traced to max-pooling index selection (FastSurfer) or to a significant numerical change introduced in fMRIPrep LTS 20.2.5.

Takeaways

Numerical error is measurable, more precision is not a silver bullet, and the same instrumentation answers three different questions: is it right? (stochastic rounding), how little precision do I need? (VPREC), and where does it break? (VeriTracer, PyTracer).