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Reduced Floating-Point Precision Implicit Monte Carlo

Simon Butson, Mathew Cleveland, Alex Long, Todd Palmer

TL;DR

The paper tackles the challenge of performing thermally driven radiative transfer with reduced-precision arithmetic by developing a portfolio of arithmetic manipulations and scaling strategies to preserve accuracy in the Implicit Monte Carlo method. The approach combines alternative summation algorithms, stable evaluation of near-canceling expressions via $\mathrm{expm1}$, and rearrangements of operation order, alongside distance and multiple energy scaling to keep quantities within representable ranges; it also leverages random-walk diffusion acceleration for optically thick regimes. Demonstrations on Su Olson, Marshak Wave, and Crooked Pipe show that half-precision IMC can closely reproduce double-precision benchmarks when these techniques are employed, with careful choices like energy scaling factors ($S$) and expm1 usage affecting wavefront propagation. The results indicate substantial performance gains and broadened applicability of reduced-precision IMC, offering pathways to faster, energy-efficient simulations on architectures lacking high-precision support and potential extensions to other scientific computations. The work provides practical, extensible methods for maintaining accuracy in reduced-precision radiative transfer simulations and highlights trade-offs between accuracy, memory, and run-time for various techniques.

Abstract

This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the categories of arithmetic manipulations and scaling methods are evaluated for their ability to improve the accuracy of reduced-precision computations. The results for half- and double-precision implementations of various thermal radiation benchmark problems are compared.

Reduced Floating-Point Precision Implicit Monte Carlo

TL;DR

The paper tackles the challenge of performing thermally driven radiative transfer with reduced-precision arithmetic by developing a portfolio of arithmetic manipulations and scaling strategies to preserve accuracy in the Implicit Monte Carlo method. The approach combines alternative summation algorithms, stable evaluation of near-canceling expressions via , and rearrangements of operation order, alongside distance and multiple energy scaling to keep quantities within representable ranges; it also leverages random-walk diffusion acceleration for optically thick regimes. Demonstrations on Su Olson, Marshak Wave, and Crooked Pipe show that half-precision IMC can closely reproduce double-precision benchmarks when these techniques are employed, with careful choices like energy scaling factors () and expm1 usage affecting wavefront propagation. The results indicate substantial performance gains and broadened applicability of reduced-precision IMC, offering pathways to faster, energy-efficient simulations on architectures lacking high-precision support and potential extensions to other scientific computations. The work provides practical, extensible methods for maintaining accuracy in reduced-precision radiative transfer simulations and highlights trade-offs between accuracy, memory, and run-time for various techniques.

Abstract

This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the categories of arithmetic manipulations and scaling methods are evaluated for their ability to improve the accuracy of reduced-precision computations. The results for half- and double-precision implementations of various thermal radiation benchmark problems are compared.
Paper Structure (22 sections, 32 equations, 9 figures, 6 tables, 2 algorithms)

This paper contains 22 sections, 32 equations, 9 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Thermal Radiation Transport & The Implicit Monte Carlo Method
  3. Implicit Monte Carlo Algorithm
  4. Floating-Point Numbers
  5. Arithmetic Techniques
  6. Summation Algorithms
  7. Naive Summation
  8. Pairwise Summation
  9. Kahan Summation
  10. Accurate Evaluation of $\left(1-\exp{(x)}\right)$
  11. Rearranging the Order of Operations
  12. Scaling Methods
  13. Distance Scaling
  14. Multiple Energy Scaling
  15. Algorithmic Complexity
  16. ...and 7 more sections

Figures (9)

  • Figure 1: Su-Olson Problem Double-Precision Radiation Energy Density
  • Figure 2: Su-Olson Problem Half-Precision Radiation Energy Density
  • Figure 3: Su-Olson Problem Double-Precision Material Energy Density
  • Figure 4: Su-Olson Problem Half-Precision Material Energy Density
  • Figure 5: Marshak Wave Double-Precision at Time $t = 2.00$ Shakes
  • ...and 4 more figures