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Diffstat (limited to 'verilog/CombineOpproof.v')
| -rw-r--r-- | verilog/CombineOpproof.v | 180 |
1 files changed, 180 insertions, 0 deletions
diff --git a/verilog/CombineOpproof.v b/verilog/CombineOpproof.v new file mode 100644 index 00000000..69abbf61 --- /dev/null +++ b/verilog/CombineOpproof.v @@ -0,0 +1,180 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Recognition of combined operations, addressing modes and conditions + during the [CSE] phase. *) + +Require Import FunInd. +Require Import Coqlib. +Require Import Integers Values Memory. +Require Import Op RTL CSEdomain. +Require Import CombineOp. + +Section COMBINE. + +Variable ge: genv. +Variable sp: val. +Variable m: mem. +Variable get: valnum -> option rhs. +Variable valu: valnum -> val. +Hypothesis get_sound: forall v rhs, get v = Some rhs -> rhs_eval_to valu ge sp m rhs (valu v). + +Lemma get_op_sound: + forall v op vl, get v = Some (Op op vl) -> eval_operation ge sp op (map valu vl) m = Some (valu v). +Proof. + intros. exploit get_sound; eauto. intros REV; inv REV; auto. +Qed. + +Ltac UseGetSound := + match goal with + | [ H: get _ = Some _ |- _ ] => + let x := fresh "EQ" in (generalize (get_op_sound _ _ _ H); intros x; simpl in x; FuncInv) + end. + +Lemma combine_compimm_ne_0_sound: + forall x cond args, + combine_compimm_ne_0 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Cne (valu x) (Vint Int.zero) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Cne (valu x) (Vint Int.zero). +Proof. + intros until args. functional induction (combine_compimm_ne_0 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. + (* of and *) + UseGetSound. rewrite <- H. + destruct v; simpl; auto. +Qed. + +Lemma combine_compimm_eq_0_sound: + forall x cond args, + combine_compimm_eq_0 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Ceq (valu x) (Vint Int.zero) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Ceq (valu x) (Vint Int.zero). +Proof. + intros until args. functional induction (combine_compimm_eq_0 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + rewrite eval_negate_condition. + destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. + (* of and *) + UseGetSound. rewrite <- H. destruct v; auto. +Qed. + +Lemma combine_compimm_eq_1_sound: + forall x cond args, + combine_compimm_eq_1 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Ceq (valu x) (Vint Int.one) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Ceq (valu x) (Vint Int.one). +Proof. + intros until args. functional induction (combine_compimm_eq_1 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Lemma combine_compimm_ne_1_sound: + forall x cond args, + combine_compimm_ne_1 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Cne (valu x) (Vint Int.one) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Cne (valu x) (Vint Int.one). +Proof. + intros until args. functional induction (combine_compimm_ne_1 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + rewrite eval_negate_condition. + destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Theorem combine_cond_sound: + forall cond args cond' args', + combine_cond get cond args = Some(cond', args') -> + eval_condition cond' (map valu args') m = eval_condition cond (map valu args) m. +Proof. + intros. functional inversion H; subst. + (* compimm ne zero *) + simpl; eapply combine_compimm_ne_0_sound; eauto. + (* compimm ne one *) + simpl; eapply combine_compimm_ne_1_sound; eauto. + (* compimm eq zero *) + simpl; eapply combine_compimm_eq_0_sound; eauto. + (* compimm eq one *) + simpl; eapply combine_compimm_eq_1_sound; eauto. + (* compuimm ne zero *) + simpl; eapply combine_compimm_ne_0_sound; eauto. + (* compuimm ne one *) + simpl; eapply combine_compimm_ne_1_sound; eauto. + (* compuimm eq zero *) + simpl; eapply combine_compimm_eq_0_sound; eauto. + (* compuimm eq one *) + simpl; eapply combine_compimm_eq_1_sound; eauto. +Qed. + +Theorem combine_addr_32_sound: + forall addr args addr' args', + combine_addr_32 get addr args = Some(addr', args') -> + eval_addressing32 ge sp addr' (map valu args') = eval_addressing32 ge sp addr (map valu args). +Proof. + intros. functional inversion H; subst. + (* indexed - lea *) + UseGetSound. simpl. unfold offset_addressing in H7. destruct (addressing_valid (offset_addressing_total a n)); inv H7. + eapply eval_offset_addressing_total_32; eauto. +Qed. + +Theorem combine_addr_64_sound: + forall addr args addr' args', + combine_addr_64 get addr args = Some(addr', args') -> + eval_addressing64 ge sp addr' (map valu args') = eval_addressing64 ge sp addr (map valu args). +Proof. + intros. functional inversion H; subst. + (* indexed - leal *) + UseGetSound. simpl. unfold offset_addressing in H7. destruct (addressing_valid (offset_addressing_total a n)); inv H7. + eapply eval_offset_addressing_total_64; eauto. +Qed. + +Theorem combine_addr_sound: + forall addr args addr' args', + combine_addr get addr args = Some(addr', args') -> + eval_addressing ge sp addr' (map valu args') = eval_addressing ge sp addr (map valu args). +Proof. + unfold combine_addr, eval_addressing; intros; destruct Archi.ptr64. + apply combine_addr_64_sound; auto. + apply combine_addr_32_sound; auto. +Qed. + +Theorem combine_op_sound: + forall op args op' args', + combine_op get op args = Some(op', args') -> + eval_operation ge sp op' (map valu args') m = eval_operation ge sp op (map valu args) m. +Proof. + intros. functional inversion H; subst. +(* lea-lea *) + simpl. eapply combine_addr_32_sound; eauto. +(* leal-leal *) + simpl. eapply combine_addr_64_sound; eauto. +(* andimm - andimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.and_assoc. auto. +(* orimm - orimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.or_assoc. auto. +(* xorimm - xorimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.xor_assoc. auto. +(* andimm - andimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.andl_assoc. auto. +(* orimm - orimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.orl_assoc. auto. +(* xorimm - xorimm *) + UseGetSound; simpl. rewrite <- H0. rewrite Val.xorl_assoc. auto. +(* cmp *) + simpl. decEq; decEq. eapply combine_cond_sound; eauto. +Qed. + +End COMBINE. |