Journal
IEEE TRANSACTIONS ON COMPUTERS
Volume 70, Issue 7, Pages 1046-1058Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TC.2020.3002702
Keywords
Standards; Hardware; Floating-point arithmetic; Computer science; Lips; Error analysis; Transforms; Floating-point arithmetic; numerical reproducibility; rounding error analysis; error-free transforms; rounding mode; formal proof
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The 2019 version of the IEEE 754 Standard recommends new augmented operations for binary formats, utilizing a new rounding direction: round-to-nearest ties-to-zero. These operations can be implemented using currently available operations, with a partial formal proof of correctness using round-to-nearest ties-to-even.
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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