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diff --git a/ia32/SelectLongproof.v b/ia32/SelectLongproof.v deleted file mode 100644 index a3d2bb19..00000000 --- a/ia32/SelectLongproof.v +++ /dev/null @@ -1,557 +0,0 @@ -(* *********************************************************************) -(* *) -(* 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. *) -(* *) -(* *********************************************************************) - -(** Correctness of instruction selection for 64-bit integer operations *) - -Require Import String Coqlib Maps Integers Floats Errors. -Require Archi. -Require Import AST Values Memory Globalenvs Events. -Require Import Cminor Op CminorSel. -Require Import SelectOp SelectOpproof SplitLong SplitLongproof. -Require Import SelectLong. - -Open Local Scope cminorsel_scope. -Open Local Scope string_scope. - -(** * Correctness of the instruction selection functions for 64-bit operators *) - -Section CMCONSTR. - -Variable prog: program. -Variable hf: helper_functions. -Hypothesis HELPERS: helper_functions_declared prog hf. -Let ge := Genv.globalenv prog. -Variable sp: val. -Variable e: env. -Variable m: mem. - -Definition unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop := - forall le a x, - eval_expr ge sp e m le a x -> - exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef (sem x) v. - -Definition binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> val) : Prop := - forall le a x b y, - eval_expr ge sp e m le a x -> - eval_expr ge sp e m le b y -> - exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. - -Definition partial_unary_constructor_sound (cstr: expr -> expr) (sem: val -> option val) : Prop := - forall le a x y, - eval_expr ge sp e m le a x -> - sem x = Some y -> - exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef y v. - -Definition partial_binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> option val) : Prop := - forall le a x b y z, - eval_expr ge sp e m le a x -> - eval_expr ge sp e m le b y -> - sem x y = Some z -> - exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef z v. - -Theorem eval_longconst: - forall le n, eval_expr ge sp e m le (longconst n) (Vlong n). -Proof. - unfold longconst; intros; destruct Archi.splitlong. - apply SplitLongproof.eval_longconst. - EvalOp. -Qed. - -Lemma is_longconst_sound: - forall v a n le, - is_longconst a = Some n -> eval_expr ge sp e m le a v -> v = Vlong n. -Proof with (try discriminate). - intros. unfold is_longconst in *. destruct Archi.splitlong. - eapply SplitLongproof.is_longconst_sound; eauto. - assert (a = Eop (Olongconst n) Enil). - { destruct a... destruct o... destruct e0... congruence. } - subst a. InvEval. auto. -Qed. - -Theorem eval_intoflong: unary_constructor_sound intoflong Val.loword. -Proof. - unfold intoflong; destruct Archi.splitlong. apply SplitLongproof.eval_intoflong. - red; intros. destruct (is_longconst a) as [n|] eqn:C. -- TrivialExists. simpl. erewrite (is_longconst_sound x) by eauto. auto. -- TrivialExists. -Qed. - -Theorem eval_longofintu: unary_constructor_sound longofintu Val.longofintu. -Proof. - unfold longofintu; destruct Archi.splitlong. apply SplitLongproof.eval_longofintu. - red; intros. destruct (is_intconst a) as [n|] eqn:C. -- econstructor; split. apply eval_longconst. - exploit is_intconst_sound; eauto. intros; subst x. auto. -- TrivialExists. -Qed. - -Theorem eval_longofint: unary_constructor_sound longofint Val.longofint. -Proof. - unfold longofint; destruct Archi.splitlong. apply SplitLongproof.eval_longofint. - red; intros. destruct (is_intconst a) as [n|] eqn:C. -- econstructor; split. apply eval_longconst. - exploit is_intconst_sound; eauto. intros; subst x. auto. -- TrivialExists. -Qed. - -Theorem eval_notl: unary_constructor_sound notl Val.notl. -Proof. - unfold notl; destruct Archi.splitlong. apply SplitLongproof.eval_notl. - red; intros. destruct (notl_match a). -- InvEval. econstructor; split. apply eval_longconst. auto. -- InvEval. subst. exists v1; split; auto. destruct v1; simpl; auto. rewrite Int64.not_involutive; auto. -- TrivialExists. -Qed. - -Theorem eval_andlimm: forall n, unary_constructor_sound (andlimm n) (fun v => Val.andl v (Vlong n)). -Proof. - unfold andlimm; intros; red; intros. - predSpec Int64.eq Int64.eq_spec n Int64.zero. - exists (Vlong Int64.zero); split. apply eval_longconst. - subst. destruct x; simpl; auto. rewrite Int64.and_zero; auto. - predSpec Int64.eq Int64.eq_spec n Int64.mone. - exists x; split. assumption. - subst. destruct x; simpl; auto. rewrite Int64.and_mone; auto. - destruct (andlimm_match a); InvEval; subst. -- econstructor; split. apply eval_longconst. simpl. rewrite Int64.and_commut; auto. -- TrivialExists. simpl. rewrite Val.andl_assoc. rewrite Int64.and_commut; auto. -- TrivialExists. -Qed. - -Theorem eval_andl: binary_constructor_sound andl Val.andl. -Proof. - unfold andl; destruct Archi.splitlong. apply SplitLongproof.eval_andl. - red; intros. destruct (andl_match a b). -- InvEval. rewrite Val.andl_commut. apply eval_andlimm; auto. -- InvEval. apply eval_andlimm; auto. -- TrivialExists. -Qed. - -Theorem eval_orlimm: forall n, unary_constructor_sound (orlimm n) (fun v => Val.orl v (Vlong n)). -Proof. - unfold orlimm; intros; red; intros. - predSpec Int64.eq Int64.eq_spec n Int64.zero. - exists x; split; auto. subst. destruct x; simpl; auto. rewrite Int64.or_zero; auto. - predSpec Int64.eq Int64.eq_spec n Int64.mone. - econstructor; split. apply eval_longconst. subst. destruct x; simpl; auto. rewrite Int64.or_mone; auto. - destruct (orlimm_match a); InvEval; subst. -- econstructor; split. apply eval_longconst. simpl. rewrite Int64.or_commut; auto. -- TrivialExists. simpl. rewrite Val.orl_assoc. rewrite Int64.or_commut; auto. -- TrivialExists. -Qed. - -Theorem eval_orl: binary_constructor_sound orl Val.orl. -Proof. - unfold orl; destruct Archi.splitlong. apply SplitLongproof.eval_orl. - red; intros. - assert (DEFAULT: exists v, eval_expr ge sp e m le (Eop Oorl (a:::b:::Enil)) v /\ Val.lessdef (Val.orl x y) v) by TrivialExists. - assert (ROR: forall v n1 n2, - Int.add n1 n2 = Int64.iwordsize' -> - Val.lessdef (Val.orl (Val.shll v (Vint n1)) (Val.shrlu v (Vint n2))) - (Val.rorl v (Vint n2))). - { intros. destruct v; simpl; auto. - destruct (Int.ltu n1 Int64.iwordsize') eqn:N1; auto. - destruct (Int.ltu n2 Int64.iwordsize') eqn:N2; auto. - simpl. rewrite <- Int64.or_ror'; auto. } - destruct (orl_match a b). -- InvEval. rewrite Val.orl_commut. apply eval_orlimm; auto. -- InvEval. apply eval_orlimm; auto. -- predSpec Int.eq Int.eq_spec (Int.add n1 n2) Int64.iwordsize'; auto. - destruct (same_expr_pure t1 t2) eqn:?; auto. - InvEval. exploit eval_same_expr; eauto. intros [EQ1 EQ2]; subst. - exists (Val.rorl v0 (Vint n2)); split. EvalOp. apply ROR; auto. -- predSpec Int.eq Int.eq_spec (Int.add n1 n2) Int64.iwordsize'; auto. - destruct (same_expr_pure t1 t2) eqn:?; auto. - InvEval. exploit eval_same_expr; eauto. intros [EQ1 EQ2]; subst. - exists (Val.rorl v1 (Vint n2)); split. EvalOp. rewrite Val.orl_commut. apply ROR; auto. -- apply DEFAULT. -Qed. - -Theorem eval_xorlimm: forall n, unary_constructor_sound (xorlimm n) (fun v => Val.xorl v (Vlong n)). -Proof. - unfold xorlimm; intros; red; intros. - predSpec Int64.eq Int64.eq_spec n Int64.zero. - exists x; split; auto. subst. destruct x; simpl; auto. rewrite Int64.xor_zero; auto. - predSpec Int64.eq Int64.eq_spec n Int64.mone. - replace (Val.xorl x (Vlong n)) with (Val.notl x). apply eval_notl; auto. - subst n. destruct x; simpl; auto. - destruct (xorlimm_match a); InvEval; subst. -- econstructor; split. apply eval_longconst. simpl. rewrite Int64.xor_commut; auto. -- TrivialExists. simpl. rewrite Val.xorl_assoc. rewrite Int64.xor_commut; auto. -- TrivialExists. simpl. destruct v1; simpl; auto. unfold Int64.not. - rewrite Int64.xor_assoc. apply f_equal. apply f_equal. apply f_equal. - apply Int64.xor_commut. -- TrivialExists. -Qed. - -Theorem eval_xorl: binary_constructor_sound xorl Val.xorl. -Proof. - unfold xorl; destruct Archi.splitlong. apply SplitLongproof.eval_xorl. - red; intros. destruct (xorl_match a b). -- InvEval. rewrite Val.xorl_commut. apply eval_xorlimm; auto. -- InvEval. apply eval_xorlimm; auto. -- TrivialExists. -Qed. - -Theorem eval_shllimm: forall n, unary_constructor_sound (fun e => shllimm e n) (fun v => Val.shll v (Vint n)). -Proof. - intros; unfold shllimm. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shllimm; auto. - red; intros. - predSpec Int.eq Int.eq_spec n Int.zero. - exists x; split; auto. subst n; destruct x; simpl; auto. - destruct (Int.ltu Int.zero Int64.iwordsize'); auto. - change (Int64.shl' i Int.zero) with (Int64.shl i Int64.zero). rewrite Int64.shl_zero; auto. - destruct (Int.ltu n Int64.iwordsize') eqn:LT; simpl. - assert (DEFAULT: exists v, eval_expr ge sp e m le (Eop (Oshllimm n) (a:::Enil)) v - /\ Val.lessdef (Val.shll x (Vint n)) v) by TrivialExists. - destruct (shllimm_match a); InvEval. -- TrivialExists. simpl; rewrite LT; auto. -- destruct (Int.ltu (Int.add n n1) Int64.iwordsize') eqn:LT'; auto. - subst. econstructor; split. EvalOp. simpl; eauto. - destruct v1; simpl; auto. rewrite LT'. - destruct (Int.ltu n1 Int64.iwordsize') eqn:LT1; auto. - simpl; rewrite LT. rewrite Int.add_commut, Int64.shl'_shl'; auto. rewrite Int.add_commut; auto. -- destruct (shift_is_scale n); auto. - TrivialExists. simpl. subst x. destruct v1; simpl; auto. - rewrite LT. rewrite ! Int64.repr_unsigned. rewrite Int64.shl'_one_two_p. - rewrite ! Int64.shl'_mul_two_p. rewrite Int64.mul_add_distr_l. auto. - destruct Archi.ptr64; reflexivity. -- destruct (shift_is_scale n); auto. - TrivialExists. simpl. destruct x; simpl; auto. - rewrite LT. rewrite ! Int64.repr_unsigned. rewrite Int64.shl'_one_two_p. - rewrite ! Int64.shl'_mul_two_p. rewrite Int64.add_zero. auto. -- TrivialExists. constructor; eauto. constructor. EvalOp. simpl; eauto. constructor. auto. -Qed. - -Theorem eval_shrluimm: forall n, unary_constructor_sound (fun e => shrluimm e n) (fun v => Val.shrlu v (Vint n)). -Proof. - intros; unfold shrluimm. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shrluimm; auto. - red; intros. - predSpec Int.eq Int.eq_spec n Int.zero. - exists x; split; auto. subst n; destruct x; simpl; auto. - destruct (Int.ltu Int.zero Int64.iwordsize'); auto. - change (Int64.shru' i Int.zero) with (Int64.shru i Int64.zero). rewrite Int64.shru_zero; auto. - destruct (Int.ltu n Int64.iwordsize') eqn:LT; simpl. - assert (DEFAULT: exists v, eval_expr ge sp e m le (Eop (Oshrluimm n) (a:::Enil)) v - /\ Val.lessdef (Val.shrlu x (Vint n)) v) by TrivialExists. - destruct (shrluimm_match a); InvEval. -- TrivialExists. simpl; rewrite LT; auto. -- destruct (Int.ltu (Int.add n n1) Int64.iwordsize') eqn:LT'; auto. - subst. econstructor; split. EvalOp. simpl; eauto. - destruct v1; simpl; auto. rewrite LT'. - destruct (Int.ltu n1 Int64.iwordsize') eqn:LT1; auto. - simpl; rewrite LT. rewrite Int.add_commut, Int64.shru'_shru'; auto. rewrite Int.add_commut; auto. -- apply DEFAULT. -- TrivialExists. constructor; eauto. constructor. EvalOp. simpl; eauto. constructor. auto. -Qed. - -Theorem eval_shrlimm: forall n, unary_constructor_sound (fun e => shrlimm e n) (fun v => Val.shrl v (Vint n)). -Proof. - intros; unfold shrlimm. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shrlimm; auto. - red; intros. - predSpec Int.eq Int.eq_spec n Int.zero. - exists x; split; auto. subst n; destruct x; simpl; auto. - destruct (Int.ltu Int.zero Int64.iwordsize'); auto. - change (Int64.shr' i Int.zero) with (Int64.shr i Int64.zero). rewrite Int64.shr_zero; auto. - destruct (Int.ltu n Int64.iwordsize') eqn:LT; simpl. - assert (DEFAULT: exists v, eval_expr ge sp e m le (Eop (Oshrlimm n) (a:::Enil)) v - /\ Val.lessdef (Val.shrl x (Vint n)) v) by TrivialExists. - destruct (shrlimm_match a); InvEval. -- TrivialExists. simpl; rewrite LT; auto. -- destruct (Int.ltu (Int.add n n1) Int64.iwordsize') eqn:LT'; auto. - subst. econstructor; split. EvalOp. simpl; eauto. - destruct v1; simpl; auto. rewrite LT'. - destruct (Int.ltu n1 Int64.iwordsize') eqn:LT1; auto. - simpl; rewrite LT. rewrite Int.add_commut, Int64.shr'_shr'; auto. rewrite Int.add_commut; auto. -- apply DEFAULT. -- TrivialExists. constructor; eauto. constructor. EvalOp. simpl; eauto. constructor. auto. -Qed. - -Theorem eval_shll: binary_constructor_sound shll Val.shll. -Proof. - unfold shll. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shll; auto. - red; intros. destruct (is_intconst b) as [n2|] eqn:C. -- exploit is_intconst_sound; eauto. intros EQ; subst y. apply eval_shllimm; auto. -- TrivialExists. -Qed. - -Theorem eval_shrlu: binary_constructor_sound shrlu Val.shrlu. -Proof. - unfold shrlu. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shrlu; auto. - red; intros. destruct (is_intconst b) as [n2|] eqn:C. -- exploit is_intconst_sound; eauto. intros EQ; subst y. apply eval_shrluimm; auto. -- TrivialExists. -Qed. - -Theorem eval_shrl: binary_constructor_sound shrl Val.shrl. -Proof. - unfold shrl. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_shrl; auto. - red; intros. destruct (is_intconst b) as [n2|] eqn:C. -- exploit is_intconst_sound; eauto. intros EQ; subst y. apply eval_shrlimm; auto. -- TrivialExists. -Qed. - -Theorem eval_negl: unary_constructor_sound negl Val.negl. -Proof. - unfold negl. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_negl; auto. - red; intros. destruct (is_longconst a) as [n|] eqn:C. -- exploit is_longconst_sound; eauto. intros EQ; subst x. - econstructor; split. apply eval_longconst. auto. -- TrivialExists. -Qed. - -Theorem eval_addlimm: forall n, unary_constructor_sound (addlimm n) (fun v => Val.addl v (Vlong n)). -Proof. - unfold addlimm; intros; red; intros. - predSpec Int64.eq Int64.eq_spec n Int64.zero. - subst. exists x; split; auto. - destruct x; simpl; auto. - rewrite Int64.add_zero; auto. - destruct Archi.ptr64; auto. rewrite Ptrofs.add_zero; auto. - destruct (addlimm_match a); InvEval. -- econstructor; split. apply eval_longconst. rewrite Int64.add_commut; auto. -- inv H. simpl in H6. TrivialExists. simpl. - erewrite eval_offset_addressing_total_64 by eauto. rewrite Int64.repr_signed; auto. -- TrivialExists. simpl. rewrite Int64.repr_signed; auto. -Qed. - -Theorem eval_addl: binary_constructor_sound addl Val.addl. -Proof. - assert (A: forall x y, Int64.repr (x + y) = Int64.add (Int64.repr x) (Int64.repr y)). - { intros; apply Int64.eqm_samerepr; auto with ints. } - assert (B: forall id ofs n, Archi.ptr64 = true -> - Genv.symbol_address ge id (Ptrofs.add ofs (Ptrofs.repr n)) = - Val.addl (Genv.symbol_address ge id ofs) (Vlong (Int64.repr n))). - { intros. replace (Ptrofs.repr n) with (Ptrofs.of_int64 (Int64.repr n)) by auto with ptrofs. - apply Genv.shift_symbol_address_64; auto. } - unfold addl. destruct Archi.splitlong eqn:SL. - apply SplitLongproof.eval_addl. apply Archi.splitlong_ptr32; auto. - red; intros; destruct (addl_match a b); InvEval. -- rewrite Val.addl_commut. apply eval_addlimm; auto. -- apply eval_addlimm; auto. -- subst. TrivialExists. simpl. rewrite A, Val.addl_permut_4. auto. -- subst. TrivialExists. simpl. rewrite A, Val.addl_assoc. decEq; decEq. rewrite Val.addl_permut. auto. -- subst. TrivialExists. simpl. rewrite A, Val.addl_permut_4. rewrite <- Val.addl_permut. rewrite <- Val.addl_assoc. auto. -- subst. TrivialExists. simpl. rewrite Val.addl_commut; auto. -- subst. TrivialExists. -- subst. TrivialExists. simpl. rewrite ! Val.addl_assoc. rewrite (Val.addl_commut y). auto. -- subst. TrivialExists. simpl. rewrite ! Val.addl_assoc. auto. -- TrivialExists. simpl. destruct x; destruct y; simpl; auto. - rewrite Int64.add_zero; auto. - destruct Archi.ptr64 eqn:SF; simpl; auto. rewrite SF. rewrite Ptrofs.add_assoc, Ptrofs.add_zero. auto. - destruct Archi.ptr64 eqn:SF; simpl; auto. rewrite SF. rewrite Ptrofs.add_assoc, Ptrofs.add_zero. auto. -Qed. - -Theorem eval_subl: binary_constructor_sound subl Val.subl. -Proof. - unfold subl. destruct Archi.splitlong eqn:SL. - apply SplitLongproof.eval_subl. apply Archi.splitlong_ptr32; auto. - red; intros; destruct (subl_match a b); InvEval. -- rewrite Val.subl_addl_opp. apply eval_addlimm; auto. -- subst. rewrite Val.subl_addl_l. rewrite Val.subl_addl_r. - rewrite Val.addl_assoc. simpl. rewrite Int64.add_commut. rewrite <- Int64.sub_add_opp. - replace (Int64.repr (n1 - n2)) with (Int64.sub (Int64.repr n1) (Int64.repr n2)). - apply eval_addlimm; EvalOp. - apply Int64.eqm_samerepr; auto with ints. -- subst. rewrite Val.subl_addl_l. apply eval_addlimm; EvalOp. -- subst. rewrite Val.subl_addl_r. - replace (Int64.repr (-n2)) with (Int64.neg (Int64.repr n2)). - apply eval_addlimm; EvalOp. - apply Int64.eqm_samerepr; auto with ints. -- TrivialExists. -Qed. - -Theorem eval_mullimm_base: forall n, unary_constructor_sound (mullimm_base n) (fun v => Val.mull v (Vlong n)). -Proof. - intros; unfold mullimm_base. red; intros. - generalize (Int64.one_bits'_decomp n); intros D. - destruct (Int64.one_bits' n) as [ | i [ | j [ | ? ? ]]] eqn:B. -- TrivialExists. -- replace (Val.mull x (Vlong n)) with (Val.shll x (Vint i)). - apply eval_shllimm; auto. - simpl in D. rewrite D, Int64.add_zero. destruct x; simpl; auto. - rewrite (Int64.one_bits'_range n) by (rewrite B; auto with coqlib). - rewrite Int64.shl'_mul; auto. -- set (le' := x :: le). - assert (A0: eval_expr ge sp e m le' (Eletvar O) x) by (constructor; reflexivity). - exploit (eval_shllimm i). eexact A0. intros (v1 & A1 & B1). - exploit (eval_shllimm j). eexact A0. intros (v2 & A2 & B2). - exploit (eval_addl). eexact A1. eexact A2. intros (v3 & A3 & B3). - exists v3; split. econstructor; eauto. - rewrite D. simpl. rewrite Int64.add_zero. destruct x; auto. - simpl in *. - rewrite (Int64.one_bits'_range n) in B1 by (rewrite B; auto with coqlib). - rewrite (Int64.one_bits'_range n) in B2 by (rewrite B; auto with coqlib). - inv B1; inv B2. simpl in B3; inv B3. - rewrite Int64.mul_add_distr_r. rewrite <- ! Int64.shl'_mul. auto. -- TrivialExists. -Qed. - -Theorem eval_mullimm: forall n, unary_constructor_sound (mullimm n) (fun v => Val.mull v (Vlong n)). -Proof. - unfold mullimm. intros; red; intros. - destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_mullimm; eauto. - predSpec Int64.eq Int64.eq_spec n Int64.zero. - exists (Vlong Int64.zero); split. apply eval_longconst. - destruct x; simpl; auto. subst n; rewrite Int64.mul_zero; auto. - predSpec Int64.eq Int64.eq_spec n Int64.one. - exists x; split; auto. - destruct x; simpl; auto. subst n; rewrite Int64.mul_one; auto. - destruct (mullimm_match a); InvEval. -- econstructor; split. apply eval_longconst. rewrite Int64.mul_commut; auto. -- exploit (eval_mullimm_base n); eauto. intros (v2 & A2 & B2). - exploit (eval_addlimm (Int64.mul n (Int64.repr n2))). eexact A2. intros (v3 & A3 & B3). - exists v3; split; auto. subst x. - destruct v1; simpl; auto. - simpl in B2; inv B2. simpl in B3; inv B3. rewrite Int64.mul_add_distr_l. - rewrite (Int64.mul_commut n). auto. - destruct Archi.ptr64; auto. -- apply eval_mullimm_base; auto. -Qed. - -Theorem eval_mull: binary_constructor_sound mull Val.mull. -Proof. - unfold mull. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_mull; auto. - red; intros; destruct (mull_match a b); InvEval. -- rewrite Val.mull_commut. apply eval_mullimm; auto. -- apply eval_mullimm; auto. -- TrivialExists. -Qed. - -Theorem eval_mullhu: - forall n, unary_constructor_sound (fun a => mullhu a n) (fun v => Val.mullhu v (Vlong n)). -Proof. - unfold mullhu; intros. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_mullhu; auto. - red; intros. TrivialExists. constructor. eauto. constructor. apply eval_longconst. constructor. auto. -Qed. - -Theorem eval_mullhs: - forall n, unary_constructor_sound (fun a => mullhs a n) (fun v => Val.mullhs v (Vlong n)). -Proof. - unfold mullhs; intros. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_mullhs; auto. - red; intros. TrivialExists. constructor. eauto. constructor. apply eval_longconst. constructor. auto. -Qed. - -Theorem eval_shrxlimm: - forall le a n x z, - eval_expr ge sp e m le a x -> - Val.shrxl x (Vint n) = Some z -> - exists v, eval_expr ge sp e m le (shrxlimm a n) v /\ Val.lessdef z v. -Proof. - unfold shrxlimm; intros. destruct Archi.splitlong eqn:SL. -+ eapply SplitLongproof.eval_shrxlimm; eauto. apply Archi.splitlong_ptr32; auto. -+ predSpec Int.eq Int.eq_spec n Int.zero. -- subst n. destruct x; simpl in H0; inv H0. econstructor; split; eauto. - change (Int.ltu Int.zero (Int.repr 63)) with true. simpl. rewrite Int64.shrx'_zero; auto. -- TrivialExists. -Qed. - -Theorem eval_divls_base: partial_binary_constructor_sound divls_base Val.divls. -Proof. - unfold divls_base; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_divls_base; eauto. - TrivialExists. -Qed. - -Theorem eval_modls_base: partial_binary_constructor_sound modls_base Val.modls. -Proof. - unfold modls_base; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_modls_base; eauto. - TrivialExists. -Qed. - -Theorem eval_divlu_base: partial_binary_constructor_sound divlu_base Val.divlu. -Proof. - unfold divlu_base; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_divlu_base; eauto. - TrivialExists. -Qed. - -Theorem eval_modlu_base: partial_binary_constructor_sound modlu_base Val.modlu. -Proof. - unfold modlu_base; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_modlu_base; eauto. - TrivialExists. -Qed. - -Theorem eval_cmplu: - forall c le a x b y v, - eval_expr ge sp e m le a x -> - eval_expr ge sp e m le b y -> - Val.cmplu (Mem.valid_pointer m) c x y = Some v -> - eval_expr ge sp e m le (cmplu c a b) v. -Proof. - unfold cmplu; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_cmplu; eauto. apply Archi.splitlong_ptr32; auto. - unfold Val.cmplu in H1. - destruct (Val.cmplu_bool (Mem.valid_pointer m) c x y) as [vb|] eqn:C; simpl in H1; inv H1. - destruct (is_longconst a) as [n1|] eqn:LC1; destruct (is_longconst b) as [n2|] eqn:LC2; - try (assert (x = Vlong n1) by (eapply is_longconst_sound; eauto)); - try (assert (y = Vlong n2) by (eapply is_longconst_sound; eauto)); - subst. -- simpl in C; inv C. EvalOp. destruct (Int64.cmpu c n1 n2); reflexivity. -- EvalOp. simpl. rewrite Val.swap_cmplu_bool. rewrite C; auto. -- EvalOp. simpl; rewrite C; auto. -- EvalOp. simpl; rewrite C; auto. -Qed. - -Theorem eval_cmpl: - forall c le a x b y v, - eval_expr ge sp e m le a x -> - eval_expr ge sp e m le b y -> - Val.cmpl c x y = Some v -> - eval_expr ge sp e m le (cmpl c a b) v. -Proof. - unfold cmpl; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_cmpl; eauto. - unfold Val.cmpl in H1. - destruct (Val.cmpl_bool c x y) as [vb|] eqn:C; simpl in H1; inv H1. - destruct (is_longconst a) as [n1|] eqn:LC1; destruct (is_longconst b) as [n2|] eqn:LC2; - try (assert (x = Vlong n1) by (eapply is_longconst_sound; eauto)); - try (assert (y = Vlong n2) by (eapply is_longconst_sound; eauto)); - subst. -- simpl in C; inv C. EvalOp. destruct (Int64.cmp c n1 n2); reflexivity. -- EvalOp. simpl. rewrite Val.swap_cmpl_bool. rewrite C; auto. -- EvalOp. simpl; rewrite C; auto. -- EvalOp. simpl; rewrite C; auto. -Qed. - -Theorem eval_longoffloat: partial_unary_constructor_sound longoffloat Val.longoffloat. -Proof. - unfold longoffloat; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_longoffloat; eauto. - TrivialExists. -Qed. - -Theorem eval_floatoflong: partial_unary_constructor_sound floatoflong Val.floatoflong. -Proof. - unfold floatoflong; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_floatoflong; eauto. - TrivialExists. -Qed. - -Theorem eval_longofsingle: partial_unary_constructor_sound longofsingle Val.longofsingle. -Proof. - unfold longofsingle; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_longofsingle; eauto. - TrivialExists. -Qed. - -Theorem eval_singleoflong: partial_unary_constructor_sound singleoflong Val.singleoflong. -Proof. - unfold singleoflong; red; intros. destruct Archi.splitlong eqn:SL. - eapply SplitLongproof.eval_singleoflong; eauto. - TrivialExists. -Qed. - -End CMCONSTR. |