Rounding Semantics

This umbrella contains rounding functions and their semantic laws: directed modes, nearest choices, order properties, round-to-odd, round-away, and double rounding. It is independent of concrete IEEE bit encodings; a format supplies the representable grid and a rounding policy selects a point on that grid.

References

• IEEE, IEEE Standard for Floating-Point Arithmetic, IEEE 754-2019, Sections 4 and 7.
• D. Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic," ACM Computing Surveys 23(1), 1991, doi:10.1145/103162.103163.