diff options
Diffstat (limited to 'mppa_k1c/SelectLongproof.v')
| -rw-r--r-- | mppa_k1c/SelectLongproof.v | 104 |
1 files changed, 104 insertions, 0 deletions
diff --git a/mppa_k1c/SelectLongproof.v b/mppa_k1c/SelectLongproof.v index 51b989d6..3fab35b3 100644 --- a/mppa_k1c/SelectLongproof.v +++ b/mppa_k1c/SelectLongproof.v @@ -390,6 +390,15 @@ Proof. - TrivialExists. Qed. +Lemma int64_eq_commut: forall x y : int64, + (Int64.eq x y) = (Int64.eq y x). +Proof. + intros. + predSpec Int64.eq Int64.eq_spec x y; + predSpec Int64.eq Int64.eq_spec y x; + congruence. +Qed. + Theorem eval_andl: binary_constructor_sound andl Val.andl. Proof. unfold andl; destruct Archi.splitlong. apply SplitLongproof.eval_andl. @@ -398,6 +407,25 @@ Proof. - InvEval. apply eval_andlimm; auto. - (*andn*) InvEval. TrivialExists. simpl. congruence. - (*andn reverse*) InvEval. rewrite Val.andl_commut. TrivialExists; simpl. congruence. + (* +- (* selectl *) + InvEval. + predSpec Int64.eq Int64.eq_spec zero1 Int64.zero; simpl; TrivialExists. + + constructor. econstructor; constructor. + constructor; try constructor; try constructor; try eassumption. + + simpl in *. f_equal. inv H6. + unfold selectl. + simpl. + destruct v3; simpl; trivial. + rewrite int64_eq_commut. + destruct (Int64.eq i Int64.zero); simpl. + * replace (Int64.repr (Int.signed (Int.neg Int.zero))) with Int64.zero by Int64.bit_solve. + destruct y; simpl; trivial. + * replace (Int64.repr (Int.signed (Int.neg Int.one))) with Int64.mone by Int64.bit_solve. + destruct y; simpl; trivial. + rewrite Int64.and_commut. rewrite Int64.and_mone. reflexivity. + + constructor. econstructor. constructor. econstructor. constructor. econstructor. constructor. eassumption. constructor. simpl. f_equal. constructor. simpl. f_equal. constructor. simpl. f_equal. constructor. eassumption. constructor. + + simpl in *. congruence. *) - TrivialExists. Qed. @@ -414,6 +442,7 @@ Proof. - TrivialExists. Qed. + Theorem eval_orl: binary_constructor_sound orl Val.orl. Proof. unfold orl; destruct Archi.splitlong. apply SplitLongproof.eval_orl. @@ -423,6 +452,81 @@ Proof. - InvEval. apply eval_orlimm; auto. - (*orn*) InvEval. TrivialExists; simpl; congruence. - (*orn reversed*) InvEval. rewrite Val.orl_commut. TrivialExists; simpl; congruence. + - (* selectl *) + destruct (same_expr_pure y0 y1) eqn:PURE; simpl; try TrivialExists. + predSpec Int64.eq Int64.eq_spec zero0 Int64.zero; simpl; try TrivialExists. + predSpec Int64.eq Int64.eq_spec zero1 Int64.zero; simpl; [ | TrivialExists]. + inv H. + inv H0. + inv H6. + inv H3. + inv H2. + inv H7. + inv H4. + inv H3. + inv H6. + inv H4. + inv H3. + inv H14. + inv H13. + inv H6. + inv H4. + inv H13. + inv H14. + inv H9. + inv H11. + inv H13. + inv H3. + inv H6. + inv H7. + inv H3. + inv H14. + inv H17. + simpl in *. + inv H8. + inv H5. + inv H10. + inv H12. + inv H15. + inv H16. + inv H11. + inv H13. + unfold same_expr_pure in PURE. + destruct y0; try congruence. + destruct y1; try congruence. + destruct (ident_eq i i0); try congruence; clear PURE. + rewrite <- e0 in *; clear e0. + inv H6. + inv H7. + rename v10 into vtest. + replace v11 with vtest in * by congruence. + TrivialExists. + simpl. + f_equal. + rewrite eval_selectl_to2. + unfold eval_selectl2. + destruct vtest; simpl; trivial. + rewrite Val.andl_commut. + destruct v4; simpl; trivial. + rewrite Val.andl_commut. + rewrite Val.orl_commut. + destruct v9; simpl; trivial. + rewrite int64_eq_commut. + destruct (Int64.eq Int64.zero i1); simpl. + + + replace (Int64.repr (Int.signed (Int.neg Int.one))) with Int64.mone by Int64.bit_solve. + replace (Int64.repr (Int.signed (Int.neg Int.zero))) with Int64.zero by Int64.bit_solve. + rewrite Int64.and_mone. + rewrite Int64.and_zero. + rewrite Int64.or_commut. + rewrite Int64.or_zero. + reflexivity. + + replace (Int64.repr (Int.signed (Int.neg Int.one))) with Int64.mone by Int64.bit_solve. + replace (Int64.repr (Int.signed (Int.neg Int.zero))) with Int64.zero by Int64.bit_solve. + rewrite Int64.and_mone. + rewrite Int64.and_zero. + rewrite Int64.or_zero. + reflexivity. - TrivialExists. Qed. |