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Emulating round-to-nearest ties-to-zero "augmented" floating-point operations using round-to-nearest ties-to-even arithmetic

Sylvie Boldo 1 Christoph Q. Lauter 2 Jean-Michel Muller 3, 4 
1 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
Inria Saclay - Ile de France, LMF - Laboratoire Méthodes Formelles
3 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The 2019 version of the IEEE 754 Standard for Floating-Point Arithmetic recommends that new “augmented” operations should be provided for the binary formats. These operations use a new “rounding direction”: round to nearest ties-to-zero. We show how they can be implemented using the currently available operations, using round-to-nearest ties-to-even with a partial formal proof of correctness.
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https://hal.archives-ouvertes.fr/hal-02137968
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Submitted on : Friday, March 13, 2020 - 10:42:45 AM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM

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Sylvie Boldo, Christoph Q. Lauter, Jean-Michel Muller. Emulating round-to-nearest ties-to-zero "augmented" floating-point operations using round-to-nearest ties-to-even arithmetic. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2021, 70 (7), pp.1046 - 1058. ⟨10.1109/TC.2020.3002702⟩. ⟨hal-02137968v4⟩

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