From 7cdd676d002e33015b496f609538a9e86d77c543 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Thu, 8 Aug 2019 11:18:38 +0200 Subject: AArch64 port This commit adds a back-end for the AArch64 architecture, namely ARMv8 in 64-bit mode. --- aarch64/CombineOpproof.v | 161 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 161 insertions(+) create mode 100644 aarch64/CombineOpproof.v (limited to 'aarch64/CombineOpproof.v') diff --git a/aarch64/CombineOpproof.v b/aarch64/CombineOpproof.v new file mode 100644 index 00000000..7d13b964 --- /dev/null +++ b/aarch64/CombineOpproof.v @@ -0,0 +1,161 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and 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. *) +(* *) +(* *********************************************************************) + +Require Import FunInd. +Require Import Coqlib. +Require Import AST Integers Values Memory. +Require Import Op Registers RTL. +Require Import 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. +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. +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_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. +- (* indexed - addimml *) + UseGetSound. simpl. rewrite <- H0. rewrite Val.addl_assoc. 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. + (* addimm - addimm *) + - UseGetSound. FuncInv. simpl. + rewrite <- H0. rewrite Val.add_assoc. auto. + (* andimm - andimm *) + - UseGetSound; simpl. + generalize (Int.eq_spec p m0); rewrite H7; intros. + rewrite <- H0. rewrite Val.and_assoc. simpl. fold p. rewrite H1. auto. + - 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. + (* addlimm - addlimm *) + - UseGetSound. FuncInv. simpl. + rewrite <- H0. rewrite Val.addl_assoc. auto. + (* andlimm - andlimm *) + - UseGetSound; simpl. + generalize (Int64.eq_spec p m0); rewrite H7; intros. + rewrite <- H0. rewrite Val.andl_assoc. simpl. fold p. rewrite H1. auto. + - UseGetSound; simpl. + rewrite <- H0. rewrite Val.andl_assoc. auto. + (* orlimm - orlimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.orl_assoc. auto. + (* xorlimm - xorlimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.xorl_assoc. auto. + (* cmp *) + - simpl. decEq; decEq. eapply combine_cond_sound; eauto. +Qed. + +End COMBINE. -- cgit