Section Fprop_relative_FLX.
Variable prec : Z.
Variable Hp : Z.lt 0 prec.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
Proof with auto with typeclass_instances.
intros x Hx.
destruct (mag beta x) as (ex, He).
specialize (He Hx).
apply relative_error with (ex - 1)%Z...
intros k _.
apply relative_error_FLX_aux.
apply He.
Qed.
Proof with auto with typeclass_instances.
intros x.
apply relative_error_lt_conversion...
apply bpow_gt_0.
now apply relative_error_FLX.
Qed.

Theorem relative_error_FLX_round :
forall x,
(x <> 0)%R ->
(Rabs (round beta (FLX_exp prec) rnd x - x) < bpow (-prec + 1) * Rabs (round beta (FLX_exp prec) rnd x))%R.