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

• URL: http://arxiv.org/abs/2602.10605v1
• Date: Wed, 11 Feb 2026 07:54:04 GMT
• Title: Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing
• Authors: Peichen Xie,
• Abstract summary: When implementing custom mixed-precision functions, it is critical to verify their numerical accuracy.<n>Traditional approaches typically compare the custom implementation against a reference using a single error metric.<n>This paper introduces textitDual-Delta Testing, a systematic methodology that evaluates two error distributions against a high-precision oracle.
• Score: 0.7106986689736828
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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