Reply To: Floating Point Rounding

One more thing, IEEE 754-2008, actually defines 5 rounding modes for single and doubel precission floating point number to integer conversions: tieEven (nearest), towardsZero (chop), Positive (to +infinity), Negative (to -infinity), Away (away from zero). So, that would require 3 bits. And if same 3 bits would be used in other ops (like adds and multiplications), maybe the remaining 11 combinations can be used for something constructive, like some combinations meaning random/stochastic rounding, or up-and-down-and-near for vector operations (which would be useful for interval arithmetic A LOT).