proposition: Theorem relative_error_ex : forall x, (bpow emin <= Rabs x)%R -> exists eps, (Rabs eps < bpow (-p + 1))%R /\ round beta fexp rnd x = (x * (1 + eps))%R.
proof: Proof. Proof with auto with typeclass_instances. intros x Hx. apply relative_error_lt_conversion... apply bpow_gt_0. intros _. now apply relative_error. Qed.
imports: Coq(ZArith Reals Psatz) Core