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This article is about twofold arithmetic [1, 2]. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function í µí±¦ 0 + í µí±¦ 1 ≈ f(í µí±¥ 0 + í µí±¥ 1) is nearly 2x-precise so can assess accuracy of standard one. Performance allows assessing on-fly: twofold… (More)

Here I propose C and C++ interfaces and experimental implementation for twofolds arithmetic I introduce in [1] for tracking floating-point inaccuracy. Testing shows, plain C enables high-performance computing with twofolds. C++ interface enables coding as easily as ordinary floating-point numbers. My goal is convincing you to try twofolds; I think assuring… (More)

- Evgeny Latkin
- 2014

Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1]) over twofold approximations í µí± § ≈ í µí± § 0 + í µí± § 1 , such that í µí± § 0 is standard result and í µí± § 1 assesses inaccuracy ∆í µí± § 0 = í µí± § − í µí± § 0. We propose on-fly tracking í µí± § 1 , detecting if ∆í µí± § 0… (More)

Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of exact real with value + error pair of floating-point numbers. Normally, value + error sum is more accurate than value alone, so error can estimate deviation between value and its exact target. Fast summation… (More)

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