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Commit ec480f3a by Guillaume Melquiond

### Added definition of opposite rounding.

parent 7fbe3efd
 ... ... @@ -552,6 +552,46 @@ Qed. End Fcore_generic_rounding_pos. Section Zrounding_opp. Variable rnd : Zrounding. Definition Zrnd_opp x := Zopp (Zrnd rnd (-x)). Lemma Zrnd_opp_le : forall x y, (x <= y)%R -> (Zrnd_opp x <= Zrnd_opp y)%Z. Proof. intros x y Hxy. unfold Zrnd_opp. generalize (Zrnd_monotone rnd _ _ (Ropp_le_contravar _ _ Hxy)). omega. Qed. Lemma Zrnd_opp_Z2R : forall n, Zrnd_opp (Z2R n) = n. Proof. intros n. unfold Zrnd_opp. rewrite <- opp_Z2R, Zrnd_Z2R. apply Zopp_involutive. Qed. Definition Zrounding_opp := mkZrounding Zrnd_opp Zrnd_opp_le Zrnd_opp_Z2R. Theorem rounding_opp : forall x, rounding rnd (- x) = Ropp (rounding Zrounding_opp x). Proof. intros x. unfold rounding. rewrite opp_F2R, canonic_exponent_opp, scaled_mantissa_opp. apply (f_equal (fun m => F2R (Float beta m _))). apply sym_eq. exact (Zopp_involutive _). Qed. End Zrounding_opp. Definition ZrndDN := mkZrounding Zfloor Zfloor_le Zfloor_Z2R. Definition ZrndUP := mkZrounding Zceil Zceil_le Zceil_Z2R. ... ...
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