Exactness is not "advertized" on the main page or as a "design principle" but it is there !
Geogram uses "arithmetic expansions", arrays of floating point numbers that can represent numbers with arbitrary precision while being reasonably performant (it is the same thing used by Jonathan Shewchuk in his predicates). In addition, besides predicates, Geogram can use arithmetic expansions to represent intermediary results of computation (I'm currently developing boolean operations that extensively make use of this feature).