Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing

TL;DR

This paper introduces Dual-Delta Testing, a systematic method for evaluating the numerical accuracy of mixed-precision computations by comparing two error distributions against a high-precision baseline, providing deeper insights than traditional single-error metrics.

Contribution

The paper presents a novel Dual-Delta Testing methodology, including mathematical framework and algorithms, for more rigorous accuracy assessment of mixed-precision implementations.

Findings

Dual-Delta Testing effectively distinguishes inherent precision errors from implementation artifacts.

The methodology provides statistically robust comparisons of numerical accuracy.

Practical examples demonstrate improved evaluation of custom mixed-precision functions.

Abstract

Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or quantized inference paths -- it is critical to verify their numerical accuracy. Traditional approaches typically compare the custom implementation against a reference using a single error metric. However, this single-delta approach provides limited insight into whether the observed errors are inherent to the precision level or specific to the implementation. This paper introduces \textit{Dual-Delta Testing}, a systematic methodology that evaluates two error distributions against a high-precision oracle, enabling rigorous comparison between a custom implementation and a baseline reference. We present the mathematical framework, algorithmic formulation, statistical analysis techniques, and practical examples demonstrating the methodology's effectiveness in evaluating numerical accuracy.