A Mathematics-Guided Approach to Floating-Point Error Detection

• URL: http://arxiv.org/abs/2510.10081v1
• Date: Sat, 11 Oct 2025 07:38:14 GMT
• Title: A Mathematics-Guided Approach to Floating-Point Error Detection
• Abstract summary: Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications.<n>We propose a novel method, named MGDE, to detect error-inducing inputs based on mathematical guidance.<n>By employing the Newton-Raphson method, which exhibits quadratic convergence properties, we achieve highly effective and efficient results.
• Score: 9.800281082826567
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop methods for identifying these error-inducing inputs. Although existing approaches have achieved some success, they still suffer from two major limitations: (1) High computational cost: The evaluation of error magnitude for candidate inputs relies on high-precision programs, which are prohibitively time-consuming. (2) Limited long-range convergence capability: Current methods exhibit inefficiency in search, making the process akin to finding a needle in a haystack. To address these two limitations, we propose a novel method, named MGDE, to detect error-inducing inputs based on mathematical guidance. By employing the Newton-Raphson method, which exhibits quadratic convergence properties, we achieve highly effective and efficient results. Since the goal of identifying error-inducing inputs is to uncover the underlying bugs, we use the number of bugs detected in floating-point programs as the primary evaluation metric in our experiments. As FPCC represents the most effective state-of-the-art approach to date, we use it as the baseline for comparison. The dataset of FPCC consists of 88 single-input floating-point programs. FPCC is able to detect 48 bugs across 29 programs, whereas our method successfully identifies 89 bugs across 44 programs. Moreover, FPCC takes 6.4096 times as long as our proposed method. We also deploy our method to multi-input programs, identifying a total of nine bugs with an average detection time of 0.6443 seconds per program. In contrast, FPCC fails to detect any bugs while requiring an average computation time of 100 seconds per program.

Related papers

• FPScan: An Automated Constraint-Based Analyzer for Floating-Point Anomaly Detection [0.0]
  FPScan is a novel tool to formally define and detect catastrophic cancellation and absorption in floating-point programs.<n>Our approach starts with a custom static analyzer based on abstract interpretation to infer the order of magnitude of all program variables.<n>Off-the-shelf SMT solver is used to determine whether the program exhibits any of these critical numerical pitfalls.
  arXiv  Detail & Related papers  (2026-09-07T13:41:01Z)
• Computing Floating-Point Errors by Injecting Perturbations [10.580959733598519]
  Floating-point programs form the foundation of modern science and engineering.<n> floating-point errors widely exist, but only a subset of inputs may trigger significant errors in floating-point programs.<n>We propose PI-detector to computing floating-point errors effectively and efficiently.
  arXiv  Detail & Related papers  (2025-07-11T10:19:14Z)
• Specification-Guided Repair of Arithmetic Errors in Dafny Programs using LLMs [79.74676890436174]
  We present an APR tool for Dafny that uses formal specifications as oracles for fault localization and repair.<n>We localize faults through a series of steps, which include using Hoare logic to determine the state of each statement within the program.<n>Our tool achieves 89.6% fault localization coverage and GPT-4o mini yields the highest repair success rate of 74.18%.
  arXiv  Detail & Related papers  (2025-07-04T15:36:12Z)
• Low-overhead error detection with spacetime codes [1.3689968346415426]
  We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities.<n>We show our algorithm can efficiently find checks in universal circuits, but the space of valid checks diminishes exponentially with the non-Cliffordness of the circuit.
  arXiv  Detail & Related papers  (2025-04-22T09:20:25Z)
• NumScout: Unveiling Numerical Defects in Smart Contracts using LLM-Pruning Symbolic Execution [31.708329829466567]
  We identify five new types of numerical defects through the analysis of 1,199 audit reports.<n>We propose NumScout, a symbolic execution-based tool designed to detect these five defects.<n>We run NumScout on 6,617 real-world contracts and evaluate its performance based on manually labeled results.
  arXiv  Detail & Related papers  (2025-03-13T04:46:53Z)
• An Efficient Outlier Detection Algorithm for Data Streaming [51.56874851156008]
  Traditional outlier detection methods, such as the Local Outlier Factor (LOF) algorithm, struggle with real-time data.<n>We propose a novel approach to enhance the efficiency of LOF algorithms for online anomaly detection, named the Efficient Incremental LOF (EILOF) algorithm.<n>The EILOF algorithm not only significantly reduces computational costs, but also systematically improves detection accuracy when the number of additional points increases.
  arXiv  Detail & Related papers  (2025-01-02T05:12:43Z)
• DELA: A Novel Approach for Detecting Errors Induced by Large Atomic Condition Numbers [10.580959733598519]
  Most numerical errors stem from large condition numbers in atomic operations, which then propagate and accumulate.<n>Our approach is based on the observation that most numerical errors stem from large condition numbers in atomic operations.<n> DELA injects small perturbations into the results of individual atomic operations within the program and compares the outcomes of the original program with the perturbed version to detect errors.
  arXiv  Detail & Related papers  (2024-12-30T08:56:46Z)
• Efficient Simulation of Leakage Errors in Quantum Error Correcting Codes Using Tensor Network Methods [0.196629787330046]
  We present a computationally efficient simulation methodology for studying leakage errors in quantum error correcting codes (QECCs)<n>Our approach enables the simulation of various leakage processes, including thermal noise and coherent errors, without approximations.<n>By leveraging the small amount of entanglement generated during the error correction process, we are able to study large systems, up to a few hundred qudits, over many code cycles.
  arXiv  Detail & Related papers  (2023-08-16T07:36:33Z)
• Fault-Aware Neural Code Rankers [64.41888054066861]
  We propose fault-aware neural code rankers that can predict the correctness of a sampled program without executing it. Our fault-aware rankers can significantly increase the pass@1 accuracy of various code generation models.
  arXiv  Detail & Related papers  (2022-06-04T22:01:05Z)
• Fast and Accurate Error Simulation for CNNs against Soft Errors [64.54260986994163]
  We present a framework for the reliability analysis of Conal Neural Networks (CNNs) via an error simulation engine. These error models are defined based on the corruption patterns of the output of the CNN operators induced by faults. We show that our methodology achieves about 99% accuracy of the fault effects w.r.t. SASSIFI, and a speedup ranging from 44x up to 63x w.r.t.FI, that only implements a limited set of error models.
  arXiv  Detail & Related papers  (2022-06-04T19:45:02Z)
• Real-Time Anomaly Detection in Edge Streams [49.26098240310257]
  We propose MIDAS, which focuses on detecting microcluster anomalies, or suddenly arriving groups of suspiciously similar edges. We further propose MIDAS-F, to solve the problem by which anomalies are incorporated into the algorithm's internal states. Experiments show that MIDAS-F has significantly higher accuracy than MIDAS.
  arXiv  Detail & Related papers  (2020-09-17T17:59:27Z)
• Bayesian Optimization with Missing Inputs [53.476096769837724]
  We develop a new acquisition function based on the well-known Upper Confidence Bound (UCB) acquisition function. We conduct comprehensive experiments on both synthetic and real-world applications to show the usefulness of our method.
  arXiv  Detail & Related papers  (2020-06-19T03:56:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.