k1c -> kvx changes

1 files changed, 176 insertions, 0 deletions

diff --git a/kvx/CombineOpproof.v b/kvx/CombineOpproof.v
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+(* *************************************************************)
+(*                                                             *)
+(*             The Compcert verified compiler                  *)
+(*                                                             *)
+(*           Sylvain Boulmé     Grenoble-INP, VERIMAG          *)
+(*           Xavier Leroy       INRIA Paris-Rocquencourt       *)
+(*           David Monniaux     CNRS, VERIMAG                  *)
+(*           Cyril Six          Kalray                         *)
+(*                                                             *)
+(*  Copyright Kalray. Copyright VERIMAG. 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 AST.
+Require Import Integers.
+Require Import Values.
+Require Import Memory.
+Require Import Op.
+Require Import Registers.
+Require Import 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 - addimm *)
+  UseGetSound. simpl. rewrite <- H0. destruct v; auto. simpl; rewrite H7; simpl.
+  rewrite Ptrofs.add_assoc. auto.
+- (* indexed - addimml *)
+  UseGetSound. simpl. rewrite <- H0. destruct v; auto. simpl; rewrite H7; simpl.
+  rewrite Ptrofs.add_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.