Twofold fast arithmetic

Abstract

Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1971]) over twofold approximations $z\approx z_0+z_1$, such that $z_0$ is standard result and $z_1$ assesses inaccuracy $\Delta z_0=z-z_0$. We propose on-fly tracking $z_1$, detecting if $\Delta z_0$ appears too high. We believe permanent tracking is worth its cost. C++ test code for Intel AVX available via web.

arXiv commentC++ experimental code and test results available via Web: https://sites.google.com/site/yevgenylatkin/

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