Thinking Fast and Correct: Automated Rewriting of Numerical Code through Compiler Augmentation

Floating-point numbers are finite-precision approximations to real numbers and are ubiquitous in computer applications in nearly every field. Selecting the right floating-point representation that balances performance and numerical accuracy is a difficult task – one that has become even more critical as hardware trends toward high-performance, low-precision operations. Although the common wisdom around changing floating-point precision implies that accuracy and performance are inversely correlated, more advanced techniques can often circumvent this tradeoff. Applying complex numerical optimizations to real-world code, however, is an arduous engineering task that requires expertise in numerical analysis and performance engineering, and application-specific numerical context. While there is a plethora of existing tools that partially automate this process, they are limited in the scope of optimization techniques or still require substantial human intervention. We present Poseidon, a modular and extensible framework that fully automates floating-point optimizations for real-world applications within a production compiler. Our key insight is that a small surrogate profile often reveals sufficient numerical context to drive effective rewrites. Poseidon operates as a two-phase compiler: the first compilation instruments the program to capture numerical context; the second compilation consumes profiled data, generates and evaluates candidate rewrites, and solves for optimal performance/accuracy tradeoffs. Poseidon’s interoperability with standard compiler analyses and optimizations grants it analysis and optimization advantages unavailable to existing source- and binary-level approaches. On multiple large-scale applications, Poseidon leads to outsized benefits in performance without substantially changing accuracy, and outsized accuracy benefits without diminishing performance. On a quaternion differentiator, Poseidon enables a 1.46× speedup with a relative error of 10−7. On DOE’s LULESH hydrodynamics application, Poseidon improves program accuracy to exactly match a 512-bit simulation run without substantially reducing performance.