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 $Δz_0=z-z_0$. 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.