Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912897011023872 |
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| author | Xie, Peichen |
| author_facet | Xie, Peichen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing Xie, Peichen Numerical Analysis Software Engineering 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. |
| title | Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing |
| topic | Numerical Analysis Software Engineering |
| url | https://arxiv.org/abs/2602.10605 |