Section round_dir.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
Variable choice : Z -> location -> Z.
Hypothesis inbetween_int_valid :
forall x m l,
inbetween_int m x l ->
rnd x = choice m l.

Theorem round_any_correct :
forall x m e l,
inbetween_float beta m e x l ->
(e = cexp beta fexp x \/ (l = loc_Exact /\ format x)) ->
round beta fexp rnd x = F2R (Float beta (choice m l) e).