
TL;DR
This paper introduces a method for fast arithmetic using twofold approximations to automatically verify floating-point accuracy, enabling on-the-fly error tracking during computations.
Contribution
It proposes a novel approach for real-time accuracy verification in floating-point computations based on twofold arithmetic, with implementation in C++ for Intel AVX.
Findings
Effective on-the-fly error detection
Implementation available in C++ for Intel AVX
Potential for improved computational reliability
Abstract
Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1971]) over twofold approximations , such that is standard result and assesses inaccuracy . We propose on-fly tracking , detecting if appears too high. We believe permanent tracking is worth its cost. C++ test code for Intel AVX available via web.
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Taxonomy
TopicsNumerical Methods and Algorithms · Digital Filter Design and Implementation · Polynomial and algebraic computation
