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Diffstat (limited to 'ia32/CombineOpproof.v')
| -rw-r--r-- | ia32/CombineOpproof.v | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/ia32/CombineOpproof.v b/ia32/CombineOpproof.v new file mode 100644 index 0000000..c6d2509 --- /dev/null +++ b/ia32/CombineOpproof.v @@ -0,0 +1,130 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* *) +(* 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 Coqlib. +Require Import AST. +Require Import Integers. +Require Import Values. +Require Import Memory. +Require Import Op. +Require Import Registers. +Require Import RTL. +Require Import CombineOp. +Require Import CSE. + +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 -> equation_holds valu ge sp m v rhs. + +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 *) + exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. + (* of and *) + exploit get_sound; eauto. unfold equation_holds; simpl. + destruct args; try discriminate. destruct args; try discriminate. simpl. + intros EQ; inv EQ. destruct (valu 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 *) + exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + rewrite eval_negate_condition. + destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. + (* of and *) + exploit get_sound; eauto. unfold equation_holds; simpl. + destruct args; try discriminate. destruct args; try discriminate. simpl. + intros EQ; inv EQ. destruct (valu v); simpl; 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 eq zero *) + simpl; eapply combine_compimm_eq_0_sound; eauto. + (* compuimm ne zero *) + simpl; eapply combine_compimm_ne_0_sound; eauto. + (* compuimm eq zero *) + simpl; eapply combine_compimm_eq_0_sound; 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. + intros. functional inversion H; subst. + exploit get_sound; eauto. unfold equation_holds; simpl; intro EQ. + assert (forall vl, + eval_addressing ge sp (SelectOp.offset_addressing a n) vl = + option_map (fun v => Val.add v (Vint n)) (eval_addressing ge sp a vl)). + intros. destruct a; simpl; repeat (destruct vl; auto); simpl. + rewrite Val.add_assoc. auto. + repeat rewrite Val.add_assoc. auto. + rewrite Val.add_assoc. auto. + repeat rewrite Val.add_assoc. auto. + unfold symbol_address. destruct (Globalenvs.Genv.find_symbol ge i); auto. + unfold symbol_address. destruct (Globalenvs.Genv.find_symbol ge i); auto. + repeat rewrite <- (Val.add_commut v). rewrite Val.add_assoc. auto. + unfold symbol_address. destruct (Globalenvs.Genv.find_symbol ge i0); auto. + repeat rewrite <- (Val.add_commut (Val.mul v (Vint i))). rewrite Val.add_assoc. auto. + rewrite Val.add_assoc; auto. + rewrite H0. rewrite EQ. 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. +(* andimm *) + exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. + rewrite <- H1. rewrite Val.and_assoc. auto. +(* orimm *) + exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. + rewrite <- H1. rewrite Val.or_assoc. auto. +(* xorimm *) + exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. + rewrite <- H1. rewrite Val.xor_assoc. auto. +(* lea *) + simpl. eapply combine_addr_sound; eauto. +(* cmp *) + simpl. decEq; decEq. eapply combine_cond_sound; eauto. +Qed. + +End COMBINE. |