Thursday 09 October 2025
A team of researchers has made significant strides in verifying the correctness of floating-point optimizations in scientific computing programs. In a new paper, they’ve developed a framework that can prove the accuracy of these optimizations, which is crucial for ensuring the reliability and reproducibility of complex scientific simulations.
Floating-point operations are ubiquitous in scientific computing, where they’re used to perform calculations involving extremely large or small numbers. However, due to the nature of floating-point arithmetic, even tiny rounding errors can accumulate and wreak havoc on simulation results. To mitigate this issue, compiler optimizations like FMA (fused multiply-add) are employed to speed up computations while maintaining accuracy.
The problem is that these optimizations can be tricky to verify, as they involve complex interactions between multiple components, including the compiler, the CPU, and the memory hierarchy. Traditional verification methods often struggle to keep pace with the complexity of modern computing systems, making it difficult to ensure the correctness of optimized code.
To address this challenge, the researchers have developed a novel framework that combines formal verification techniques with the LLVM compiler infrastructure. Their approach involves translating scientific programs into a verified intermediate representation, which can then be analyzed and optimized using formal methods.
The key innovation is the use of interaction trees, a data structure that allows the researchers to represent complex program behaviors in a concise and tractable manner. This enables them to define refinement relations between different program versions, including both original code and optimized variants.
Using this framework, the team has successfully verified the correctness of FMA optimizations for a basic arithmetic expression involving multiplication and addition. Their proof establishes that the optimized code is equivalent to the original code within a certain tolerance, ensuring that any discrepancies are due to rounding errors rather than bugs in the optimization process.
The implications of this work are significant. By providing a rigorous verification framework for floating-point optimizations, scientists can now have greater confidence in the accuracy and reproducibility of their simulations. This is particularly important in fields like climate modeling, where small changes in simulation inputs or parameters can have significant effects on model outcomes.
While there’s still much work to be done to fully realize the benefits of this framework, the researchers’ achievement represents a major milestone in the quest for trustworthy scientific computing. As the complexity of simulations continues to increase, the need for robust verification methods will only grow more pressing. With their innovative approach, the team is helping pave the way for a new era of accurate and reliable scientific discovery.
Cite this article: “Verifying Floating-Point Optimizations in Scientific Computing”, The Science Archive, 2025.
Formal Verification, Floating-Point Arithmetic, Compiler Optimizations, Fma, Llvm, Intermediate Representation, Interaction Trees, Refinement Relations, Scientific Computing, Reproducibility
