Twofold fast arithmetic

Evgeny Latkin

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arXiv · 1401.6235

Twofold fast arithmetic

Evgeny Latkin

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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 $Δz_0=z-z_0$. We propose on-fly tracking $z_1$, detecting if $Δz_0$ appears too high. We believe permanent tracking is worth its cost. C++ test code for Intel AVX available via web.

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Evgeny Latkin. 2014-07-10. Twofold fast arithmetic. https://arxiv.org/abs/1401.6235

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