RISC-V port and assorted changes

This commits adds code generation for the RISC-V architecture, both in 32- and 64-bit modes.

The generated code was lightly tested using the simulator and cross-binutils from https://riscv.org/software-tools/

This port required the following additional changes:

- Integers: More properties about shrx

- SelectOp: now provides smart constructors for mulhs and mulhu

- SelectDiv, 32-bit integer division and modulus: implement constant propagation, use the new smart constructors mulhs and mulhu.

- Runtime library: if no asm implementation is provided, run the reference C implementation through CompCert.  Since CompCert rejects the definitions of names of special functions such as __i64_shl, the reference implementation now uses "i64_" names, e.g. "i64_shl", and a renaming "i64_ -> __i64_" is performed over the generated assembly file, before assembling and building the runtime library.

- test/: add SIMU make variable to run tests through a simulator

- test/regression/alignas.c: make sure _Alignas and _Alignof are not #define'd by C headers

commit da14495c01cf4f66a928c2feff5c53f09bde837f
Author: Xavier Leroy <xavier.leroy@inria.fr>
Date:   Thu Apr 13 17:36:10 2017 +0200

    RISC-V port, continued

    Now working on Asmgen.

commit 36f36eb3a5abfbb8805960443d087b6a83e86005
Author: Xavier Leroy <xavier.leroy@inria.fr>
Date:   Wed Apr 12 17:26:39 2017 +0200

    RISC-V port, first steps

    This port is based on Prashanth Mundkur's experimental RV32 port and brings it up to date with CompCert, and adds 64-bit support (RV64).  Work in progress.

1 files changed, 915 insertions, 0 deletions

diff --git a/riscV/SelectOpproof.v b/riscV/SelectOpproof.v
new file mode 100644
index 00000000..b9652b34
--- /dev/null
+++ b/riscV/SelectOpproof.v
@@ -0,0 +1,915 @@
+(* *********************************************************************)
+(*                                                                     *)
+(*              The Compcert verified compiler                         *)
+(*                                                                     *)
+(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
+(*           Prashanth Mundkur, SRI International                      *)
+(*                                                                     *)
+(*  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.     *)
+(*                                                                     *)
+(*  The contributions by Prashanth Mundkur are reused and adapted      *)
+(*  under the terms of a Contributor License Agreement between         *)
+(*  SRI International and INRIA.                                       *)
+(*                                                                     *)
+(* *********************************************************************)
+
+(** Correctness of instruction selection for operators *)
+
+Require Import Coqlib.
+Require Import Maps.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Values.
+Require Import Memory.
+Require Import Globalenvs.
+Require Import Cminor.
+Require Import Op.
+Require Import CminorSel.
+Require Import SelectOp.
+
+Local Open Scope cminorsel_scope.
+
+(** * Useful lemmas and tactics *)
+
+(** The following are trivial lemmas and custom tactics that help
+  perform backward (inversion) and forward reasoning over the evaluation
+  of operator applications. *)
+
+Ltac EvalOp := eapply eval_Eop; eauto with evalexpr.
+
+Ltac InvEval1 :=
+  match goal with
+  | [ H: (eval_expr _ _ _ _ _ (Eop _ Enil) _) |- _ ] =>
+      inv H; InvEval1
+  | [ H: (eval_expr _ _ _ _ _ (Eop _ (_ ::: Enil)) _) |- _ ] =>
+      inv H; InvEval1
+  | [ H: (eval_expr _ _ _ _ _ (Eop _ (_ ::: _ ::: Enil)) _) |- _ ] =>
+      inv H; InvEval1
+  | [ H: (eval_exprlist _ _ _ _ _ Enil _) |- _ ] =>
+      inv H; InvEval1
+  | [ H: (eval_exprlist _ _ _ _ _ (_ ::: _) _) |- _ ] =>
+      inv H; InvEval1
+  | _ =>
+      idtac
+  end.
+
+Ltac InvEval2 :=
+  match goal with
+  | [ H: (eval_operation _ _ _ nil _ = Some _) |- _ ] =>
+      simpl in H; inv H
+  | [ H: (eval_operation _ _ _ (_ :: nil) _ = Some _) |- _ ] =>
+      simpl in H; FuncInv
+  | [ H: (eval_operation _ _ _ (_ :: _ :: nil) _ = Some _) |- _ ] =>
+      simpl in H; FuncInv
+  | [ H: (eval_operation _ _ _ (_ :: _ :: _ :: nil) _ = Some _) |- _ ] =>
+      simpl in H; FuncInv
+  | _ =>
+      idtac
+  end.
+
+Ltac InvEval := InvEval1; InvEval2; InvEval2.
+
+Ltac TrivialExists :=
+  match goal with
+  | [ |- exists v, _ /\ Val.lessdef ?a v ] => exists a; split; [EvalOp | auto]
+  end.
+
+(** * Correctness of the smart constructors *)
+
+Section CMCONSTR.
+
+Variable ge: genv.
+Variable sp: val.
+Variable e: env.
+Variable m: mem.
+
+(** We now show that the code generated by "smart constructor" functions
+  such as [Selection.notint] behaves as expected.  Continuing the
+  [notint] example, we show that if the expression [e]
+  evaluates to some integer value [Vint n], then [Selection.notint e]
+  evaluates to a value [Vint (Int.not n)] which is indeed the integer
+  negation of the value of [e].
+
+  All proofs follow a common pattern:
+- Reasoning by case over the result of the classification functions
+  (such as [add_match] for integer addition), gathering additional
+  information on the shape of the argument expressions in the non-default
+  cases.
+- Inversion of the evaluations of the arguments, exploiting the additional
+  information thus gathered.
+- Equational reasoning over the arithmetic operations performed,
+  using the lemmas from the [Int] and [Float] modules.
+- Construction of an evaluation derivation for the expression returned
+  by the smart constructor.
+*)
+
+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.
+
+Theorem eval_addrsymbol:
+  forall le id ofs,
+  exists v, eval_expr ge sp e m le (addrsymbol id ofs) v /\ Val.lessdef (Genv.symbol_address ge id ofs) v.
+Proof.
+  intros. unfold addrsymbol. econstructor; split.
+  EvalOp. simpl; eauto.
+  auto.
+Qed.
+
+Theorem eval_addrstack:
+  forall le ofs,
+  exists v, eval_expr ge sp e m le (addrstack ofs) v /\ Val.lessdef (Val.offset_ptr sp ofs) v.
+Proof.
+  intros. unfold addrstack. econstructor; split.
+  EvalOp. simpl; eauto.
+  auto.
+Qed.
+
+Theorem eval_addimm:
+  forall n, unary_constructor_sound (addimm n) (fun x => Val.add x (Vint n)).
+Proof.
+  red; unfold addimm; intros until x.
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  - subst n. intros. exists x; split; auto.
+    destruct x; simpl; auto.
+    rewrite Int.add_zero; auto.
+    destruct Archi.ptr64; auto. rewrite Ptrofs.add_zero; auto. 
+  - case (addimm_match a); intros; InvEval; simpl.
+    + TrivialExists; simpl. rewrite Int.add_commut. auto.
+    + econstructor; split. EvalOp. simpl; eauto. 
+      unfold Genv.symbol_address. destruct (Genv.find_symbol ge s); simpl; auto.
+      destruct Archi.ptr64; auto. rewrite Ptrofs.add_commut; auto.
+    + econstructor; split. EvalOp. simpl; eauto. 
+      destruct sp; simpl; auto. destruct Archi.ptr64; auto. 
+      rewrite Ptrofs.add_assoc. rewrite (Ptrofs.add_commut m0). auto.
+    + TrivialExists; simpl. subst x. rewrite Val.add_assoc. rewrite Int.add_commut. auto.
+    + TrivialExists.
+Qed.
+
+Theorem eval_add: binary_constructor_sound add Val.add.
+Proof.
+  red; intros until y.
+  unfold add; case (add_match a b); intros; InvEval.
+  - rewrite Val.add_commut. apply eval_addimm; auto.
+  - apply eval_addimm; auto.
+  - subst.
+    replace (Val.add (Val.add v1 (Vint n1)) (Val.add v0 (Vint n2)))
+       with (Val.add (Val.add v1 v0) (Val.add (Vint n1) (Vint n2))).
+    apply eval_addimm. EvalOp.
+    repeat rewrite Val.add_assoc. decEq. apply Val.add_permut.
+  - subst. econstructor; split.
+    EvalOp. constructor. EvalOp. simpl; eauto. constructor. eauto. constructor. simpl; eauto.
+    rewrite Val.add_commut. destruct sp; simpl; auto.
+    destruct v1; simpl; auto.
+    destruct Archi.ptr64 eqn:SF; auto. 
+    apply Val.lessdef_same. f_equal. rewrite ! Ptrofs.add_assoc. f_equal. 
+    rewrite (Ptrofs.add_commut (Ptrofs.of_int n1)), Ptrofs.add_assoc. f_equal. auto with ptrofs.
+    destruct Archi.ptr64 eqn:SF; auto.
+  - subst. econstructor; split.
+    EvalOp. constructor. EvalOp. simpl; eauto. constructor. eauto. constructor. simpl; eauto.
+    destruct sp; simpl; auto.
+    destruct v1; simpl; auto.
+    destruct Archi.ptr64 eqn:SF; auto. 
+    apply Val.lessdef_same. f_equal. rewrite ! Ptrofs.add_assoc. f_equal. f_equal.
+    rewrite Ptrofs.add_commut. auto with ptrofs.
+    destruct Archi.ptr64 eqn:SF; auto.
+  - subst.
+    replace (Val.add (Val.add v1 (Vint n1)) y)
+       with (Val.add (Val.add v1 y) (Vint n1)).
+    apply eval_addimm. EvalOp.
+    repeat rewrite Val.add_assoc. decEq. apply Val.add_commut.
+  - subst.
+    replace (Val.add x (Val.add v1 (Vint n2)))
+       with (Val.add (Val.add x v1) (Vint n2)).
+    apply eval_addimm. EvalOp.
+    repeat rewrite Val.add_assoc. reflexivity.
+  - TrivialExists.
+Qed.
+
+Theorem eval_sub: binary_constructor_sound sub Val.sub.
+Proof.
+  red; intros until y.
+  unfold sub; case (sub_match a b); intros; InvEval.
+  - rewrite Val.sub_add_opp. apply eval_addimm; auto.
+  - subst. rewrite Val.sub_add_l. rewrite Val.sub_add_r.
+    rewrite Val.add_assoc. simpl. rewrite Int.add_commut. rewrite <- Int.sub_add_opp.
+    apply eval_addimm; EvalOp.
+  - subst. rewrite Val.sub_add_l. apply eval_addimm; EvalOp.
+  - subst. rewrite Val.sub_add_r. apply eval_addimm; EvalOp.
+  - TrivialExists.
+Qed.
+
+Theorem eval_negint: unary_constructor_sound negint (fun v => Val.sub Vzero v).
+Proof.
+  red; intros until x. unfold negint. case (negint_match a); intros; InvEval.
+  TrivialExists.
+  TrivialExists.
+Qed.
+
+Theorem eval_shlimm:
+  forall n, unary_constructor_sound (fun a => shlimm a n)
+                                    (fun x => Val.shl x (Vint n)).
+Proof.
+  red; intros until x.  unfold shlimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shl_zero; auto.
+
+  destruct (Int.ltu n Int.iwordsize) eqn:LT; simpl.
+  destruct (shlimm_match a); intros; InvEval.
+  - exists (Vint (Int.shl n1 n)); split. EvalOp.
+    simpl. rewrite LT. auto.
+  - destruct (Int.ltu (Int.add n n1) Int.iwordsize) eqn:?.
+    + exists (Val.shl v1 (Vint (Int.add n n1))); split. EvalOp.
+      subst. destruct v1; simpl; auto.
+      rewrite Heqb.
+      destruct (Int.ltu n1 Int.iwordsize) eqn:?; simpl; auto.
+      destruct (Int.ltu n Int.iwordsize) eqn:?; simpl; auto.
+      rewrite Int.add_commut. rewrite Int.shl_shl; auto. rewrite Int.add_commut; auto.
+    + subst. TrivialExists. econstructor. EvalOp. simpl; eauto. constructor.
+      simpl. auto.
+  - TrivialExists.
+  - intros; TrivialExists. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor.
+    auto.
+Qed.
+
+Theorem eval_shruimm:
+  forall n, unary_constructor_sound (fun a => shruimm a n)
+                                    (fun x => Val.shru x (Vint n)).
+Proof.
+  red; intros until x. unfold shruimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shru_zero; auto.
+
+  destruct (Int.ltu n Int.iwordsize) eqn:LT; simpl.
+  destruct (shruimm_match a); intros; InvEval.
+  - exists (Vint (Int.shru n1 n)); split. EvalOp.
+    simpl. rewrite LT; auto.
+  - destruct (Int.ltu (Int.add n n1) Int.iwordsize) eqn:?.
+    exists (Val.shru v1 (Vint (Int.add n n1))); split. EvalOp.
+    subst. destruct v1; simpl; auto.
+    rewrite Heqb.
+    destruct (Int.ltu n1 Int.iwordsize) eqn:?; simpl; auto.
+    rewrite LT. rewrite Int.add_commut. rewrite Int.shru_shru; auto. rewrite Int.add_commut; auto.
+    subst. TrivialExists. econstructor. EvalOp. simpl; eauto. constructor.
+    simpl. auto.
+  - TrivialExists.
+  - intros; TrivialExists. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor.
+    auto.
+Qed.
+
+Theorem eval_shrimm:
+  forall n, unary_constructor_sound (fun a => shrimm a n)
+                                    (fun x => Val.shr x (Vint n)).
+Proof.
+  red; intros until x. unfold shrimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shr_zero; auto.
+
+  destruct (Int.ltu n Int.iwordsize) eqn:LT; simpl.
+  destruct (shrimm_match a); intros; InvEval.
+  - exists (Vint (Int.shr n1 n)); split. EvalOp.
+    simpl. rewrite LT; auto.
+  - destruct (Int.ltu (Int.add n n1) Int.iwordsize) eqn:?.
+    exists (Val.shr v1 (Vint (Int.add n n1))); split. EvalOp.
+    subst. destruct v1; simpl; auto.
+    rewrite Heqb.
+    destruct (Int.ltu n1 Int.iwordsize) eqn:?; simpl; auto.
+    rewrite LT.
+    rewrite Int.add_commut. rewrite Int.shr_shr; auto. rewrite Int.add_commut; auto.
+    subst. TrivialExists. econstructor. EvalOp. simpl; eauto. constructor.
+    simpl. auto.
+  - TrivialExists.
+  - intros; TrivialExists. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor.
+    auto.
+Qed.
+
+Lemma eval_mulimm_base:
+  forall n, unary_constructor_sound (mulimm_base n) (fun x => Val.mul x (Vint n)).
+Proof.
+  intros; red; intros; unfold mulimm_base.
+
+  assert (DFL: exists v, eval_expr ge sp e m le (Eop Omul (Eop (Ointconst n) Enil ::: a ::: Enil)) v /\ Val.lessdef (Val.mul x (Vint n)) v).
+  TrivialExists. econstructor. EvalOp. simpl; eauto. econstructor. eauto. constructor.
+  rewrite Val.mul_commut. auto.
+
+  generalize (Int.one_bits_decomp n).
+  generalize (Int.one_bits_range n).
+  destruct (Int.one_bits n).
+  - intros. auto.
+  - destruct l.
+    + intros. rewrite H1. simpl.
+      rewrite Int.add_zero.
+      replace (Vint (Int.shl Int.one i)) with (Val.shl Vone (Vint i)). rewrite Val.shl_mul.
+      apply eval_shlimm. auto. simpl. rewrite H0; auto with coqlib.
+    + destruct l.
+      intros. rewrite H1. simpl.
+      exploit (eval_shlimm i (x :: le) (Eletvar 0) x). constructor; auto. intros [v1 [A1 B1]].
+      exploit (eval_shlimm i0 (x :: le) (Eletvar 0) x). constructor; auto. intros [v2 [A2 B2]].
+      exploit (eval_add (x :: le)). eexact A1. eexact A2. intros [v [A B]].
+      exists v; split. econstructor; eauto.
+      rewrite Int.add_zero.
+      replace (Vint (Int.add (Int.shl Int.one i) (Int.shl Int.one i0)))
+         with (Val.add (Val.shl Vone (Vint i)) (Val.shl Vone (Vint i0))).
+      rewrite Val.mul_add_distr_r.
+      repeat rewrite Val.shl_mul. eapply Val.lessdef_trans. 2: eauto. apply Val.add_lessdef; auto.
+      simpl. repeat rewrite H0; auto with coqlib.
+      intros. auto.
+Qed.
+
+Theorem eval_mulimm:
+  forall n, unary_constructor_sound (mulimm n) (fun x => Val.mul x (Vint n)).
+Proof.
+  intros; red; intros until x; unfold mulimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros. exists (Vint Int.zero); split. EvalOp.
+  destruct x; simpl; auto. subst n. rewrite Int.mul_zero. auto.
+
+  predSpec Int.eq Int.eq_spec n Int.one.
+  intros. exists x; split; auto.
+  destruct x; simpl; auto. subst n. rewrite Int.mul_one. auto.
+
+  case (mulimm_match a); intros; InvEval.
+  - TrivialExists. simpl. rewrite Int.mul_commut; auto.
+  - subst. rewrite Val.mul_add_distr_l.
+    exploit eval_mulimm_base; eauto. instantiate (1 := n). intros [v' [A1 B1]].
+    exploit (eval_addimm (Int.mul n n2) le (mulimm_base n t2) v'). auto. intros [v'' [A2 B2]].
+    exists v''; split; auto. eapply Val.lessdef_trans. eapply Val.add_lessdef; eauto.
+    rewrite Val.mul_commut; auto.
+  - apply eval_mulimm_base; auto.
+Qed.
+
+Theorem eval_mul: binary_constructor_sound mul Val.mul.
+Proof.
+  red; intros until y.
+  unfold mul; case (mul_match a b); intros; InvEval.
+  rewrite Val.mul_commut. apply eval_mulimm. auto.
+  apply eval_mulimm. auto.
+  TrivialExists.
+Qed.
+
+Theorem eval_mulhs: binary_constructor_sound mulhs Val.mulhs.
+Proof.
+  red; intros. unfold mulhs; destruct Archi.ptr64 eqn:SF.
+- econstructor; split.
+  EvalOp. constructor. EvalOp. constructor. EvalOp. constructor. EvalOp. simpl; eauto. 
+  constructor. EvalOp. simpl; eauto. constructor. 
+  simpl; eauto. constructor. simpl; eauto. constructor. simpl; eauto.
+  destruct x; simpl; auto. destruct y; simpl; auto.
+  change (Int.ltu (Int.repr 32) Int64.iwordsize') with true; simpl.
+  apply Val.lessdef_same. f_equal. 
+  transitivity (Int.repr (Z.shiftr (Int.signed i * Int.signed i0) 32)).
+  unfold Int.mulhs; f_equal. rewrite Int.Zshiftr_div_two_p by omega. reflexivity.
+  apply Int.same_bits_eq; intros n N.
+  change Int.zwordsize with 32 in *.
+  assert (N1: 0 <= n < 64) by omega.
+  rewrite Int64.bits_loword by auto.
+  rewrite Int64.bits_shr' by auto.
+  change (Int.unsigned (Int.repr 32)) with 32. change Int64.zwordsize with 64.
+  rewrite zlt_true by omega.
+  rewrite Int.testbit_repr by auto. 
+  unfold Int64.mul. rewrite Int64.testbit_repr by (change Int64.zwordsize with 64; omega).
+  transitivity (Z.testbit (Int.signed i * Int.signed i0) (n + 32)).
+  rewrite Z.shiftr_spec by omega. auto.
+  apply Int64.same_bits_eqm. apply Int64.eqm_mult; apply Int64.eqm_unsigned_repr. 
+  change Int64.zwordsize with 64; omega.
+- TrivialExists.
+Qed.
+
+Theorem eval_mulhu: binary_constructor_sound mulhu Val.mulhu.
+Proof.
+  red; intros. unfold mulhu; destruct Archi.ptr64 eqn:SF.
+- econstructor; split.
+  EvalOp. constructor. EvalOp. constructor. EvalOp. constructor. EvalOp. simpl; eauto. 
+  constructor. EvalOp. simpl; eauto. constructor. 
+  simpl; eauto. constructor. simpl; eauto. constructor. simpl; eauto.
+  destruct x; simpl; auto. destruct y; simpl; auto.
+  change (Int.ltu (Int.repr 32) Int64.iwordsize') with true; simpl.
+  apply Val.lessdef_same. f_equal. 
+  transitivity (Int.repr (Z.shiftr (Int.unsigned i * Int.unsigned i0) 32)).
+  unfold Int.mulhu; f_equal. rewrite Int.Zshiftr_div_two_p by omega. reflexivity.
+  apply Int.same_bits_eq; intros n N.
+  change Int.zwordsize with 32 in *.
+  assert (N1: 0 <= n < 64) by omega.
+  rewrite Int64.bits_loword by auto.
+  rewrite Int64.bits_shru' by auto.
+  change (Int.unsigned (Int.repr 32)) with 32. change Int64.zwordsize with 64.
+  rewrite zlt_true by omega.
+  rewrite Int.testbit_repr by auto. 
+  unfold Int64.mul. rewrite Int64.testbit_repr by (change Int64.zwordsize with 64; omega).
+  transitivity (Z.testbit (Int.unsigned i * Int.unsigned i0) (n + 32)).
+  rewrite Z.shiftr_spec by omega. auto.
+  apply Int64.same_bits_eqm. apply Int64.eqm_mult; apply Int64.eqm_unsigned_repr. 
+  change Int64.zwordsize with 64; omega.
+- TrivialExists.
+Qed.
+
+Theorem eval_andimm:
+  forall n, unary_constructor_sound (andimm n) (fun x => Val.and x (Vint n)).
+Proof.
+  intros; red; intros until x. unfold andimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros. exists (Vint Int.zero); split. EvalOp.
+  destruct x; simpl; auto. subst n. rewrite Int.and_zero. auto.
+
+  predSpec Int.eq Int.eq_spec n Int.mone.
+  intros. exists x; split; auto.
+  subst. destruct x; simpl; auto. rewrite Int.and_mone; auto.
+
+  case (andimm_match a); intros.
+  - InvEval. TrivialExists. simpl. rewrite Int.and_commut; auto.
+  - InvEval. subst. rewrite Val.and_assoc. simpl. rewrite Int.and_commut. TrivialExists.
+  - TrivialExists.
+Qed.
+
+Theorem eval_and: binary_constructor_sound and Val.and.
+Proof.
+  red; intros until y; unfold and; case (and_match a b); intros; InvEval.
+  - rewrite Val.and_commut. apply eval_andimm; auto.
+  - apply eval_andimm; auto.
+  - TrivialExists.
+Qed.
+
+Theorem eval_orimm:
+  forall n, unary_constructor_sound (orimm n) (fun x => Val.or x (Vint n)).
+Proof.
+  intros; red; intros until x. unfold orimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros. subst. exists x; split; auto.
+  destruct x; simpl; auto. rewrite Int.or_zero; auto.
+
+  predSpec Int.eq Int.eq_spec n Int.mone.
+  intros. exists (Vint Int.mone); split. EvalOp.
+  destruct x; simpl; auto. subst n. rewrite Int.or_mone. auto.
+
+  destruct (orimm_match a); intros; InvEval.
+  - TrivialExists. simpl. rewrite Int.or_commut; auto.
+  - subst. rewrite Val.or_assoc. simpl. rewrite Int.or_commut. TrivialExists.
+  - TrivialExists.
+Qed.
+
+Theorem eval_or: binary_constructor_sound or Val.or.
+Proof.
+  red; intros until y; unfold or; case (or_match a b); intros; InvEval.
+  - rewrite Val.or_commut. apply eval_orimm; auto.
+  - apply eval_orimm; auto.
+  - TrivialExists.
+Qed.
+
+Theorem eval_xorimm:
+  forall n, unary_constructor_sound (xorimm n) (fun x => Val.xor x (Vint n)).
+Proof.
+  intros; red; intros until x. unfold xorimm.
+
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  intros. exists x; split. auto.
+  destruct x; simpl; auto. subst n. rewrite Int.xor_zero. auto.
+
+  intros. destruct (xorimm_match a); intros; InvEval.
+  - TrivialExists. simpl. rewrite Int.xor_commut; auto.
+  - subst. rewrite Val.xor_assoc. simpl. rewrite Int.xor_commut. 
+    predSpec Int.eq Int.eq_spec (Int.xor n2 n) Int.zero.
+    + exists v1; split; auto. destruct v1; simpl; auto. rewrite H0, Int.xor_zero; auto.  
+    + TrivialExists.
+  - TrivialExists.
+Qed.
+
+Theorem eval_xor: binary_constructor_sound xor Val.xor.
+Proof.
+  red; intros until y; unfold xor; case (xor_match a b); intros; InvEval.
+  - rewrite Val.xor_commut. apply eval_xorimm; auto.
+  - apply eval_xorimm; auto.
+  - TrivialExists.
+Qed.
+
+Theorem eval_notint: unary_constructor_sound notint Val.notint.
+Proof.
+  unfold notint; red; intros. rewrite Val.not_xor. apply eval_xorimm; auto.
+Qed.
+
+Theorem eval_divs_base:
+  forall le a b x y z,
+    eval_expr ge sp e m le a x ->
+    eval_expr ge sp e m le b y ->
+    Val.divs x y = Some z ->
+    exists v, eval_expr ge sp e m le (divs_base a b) v /\ Val.lessdef z v.
+Proof.
+  intros. unfold divs_base. exists z; split. EvalOp. auto.
+Qed.
+
+Theorem eval_mods_base:
+  forall le a b x y z,
+    eval_expr ge sp e m le a x ->
+    eval_expr ge sp e m le b y ->
+    Val.mods x y = Some z ->
+    exists v, eval_expr ge sp e m le (mods_base a b) v /\ Val.lessdef z v.
+Proof.
+  intros. unfold mods_base. exists z; split. EvalOp. auto.
+Qed.
+
+Theorem eval_divu_base:
+  forall le a b x y z,
+    eval_expr ge sp e m le a x ->
+    eval_expr ge sp e m le b y ->
+    Val.divu x y = Some z ->
+    exists v, eval_expr ge sp e m le (divu_base a b) v /\ Val.lessdef z v.
+Proof.
+  intros. unfold divu_base. exists z; split. EvalOp. auto.
+Qed.
+
+Theorem eval_modu_base:
+  forall le a b x y z,
+    eval_expr ge sp e m le a x ->
+    eval_expr ge sp e m le b y ->
+    Val.modu x y = Some z ->
+    exists v, eval_expr ge sp e m le (modu_base a b) v /\ Val.lessdef z v.
+Proof.
+  intros. unfold modu_base. exists z; split. EvalOp. auto.
+Qed.
+
+Theorem eval_shrximm:
+  forall le a n x z,
+    eval_expr ge sp e m le a x ->
+    Val.shrx x (Vint n) = Some z ->
+    exists v, eval_expr ge sp e m le (shrximm a n) v /\ Val.lessdef z v.
+Proof.
+  intros. unfold shrximm.
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  subst n. exists x; split; auto.
+  destruct x; simpl in H0; try discriminate.
+  destruct (Int.ltu Int.zero (Int.repr 31)); inv H0.
+  replace (Int.shrx i Int.zero) with i. auto.
+  unfold Int.shrx, Int.divs. rewrite Int.shl_zero.
+  change (Int.signed Int.one) with 1. rewrite Z.quot_1_r. rewrite Int.repr_signed; auto.
+  econstructor; split. EvalOp. auto.
+(*
+  intros. destruct x; simpl in H0; try discriminate. 
+  destruct (Int.ltu n (Int.repr 31)) eqn:LTU; inv H0.
+  unfold shrximm.
+  predSpec Int.eq Int.eq_spec n Int.zero.
+  - subst n. exists (Vint i); split; auto.
+    unfold Int.shrx, Int.divs. rewrite Z.quot_1_r. rewrite Int.repr_signed. auto.
+  - assert (NZ: Int.unsigned n <> 0).
+    { intro EQ; elim H0. rewrite <- (Int.repr_unsigned n). rewrite EQ; auto. }
+    assert (LT: 0 <= Int.unsigned n < 31) by (apply Int.ltu_inv in LTU; assumption).
+    assert (LTU2: Int.ltu (Int.sub Int.iwordsize n) Int.iwordsize = true).
+    { unfold Int.ltu; apply zlt_true.
+      unfold Int.sub. change (Int.unsigned Int.iwordsize) with 32. 
+      rewrite Int.unsigned_repr. omega. 
+      assert (32 < Int.max_unsigned) by reflexivity. omega. }
+    assert (X: eval_expr ge sp e m le
+               (Eop (Oshrimm (Int.repr (Int.zwordsize - 1))) (a ::: Enil))
+               (Vint (Int.shr i (Int.repr (Int.zwordsize - 1))))).
+    { EvalOp. }
+    assert (Y: eval_expr ge sp e m le (shrximm_inner a n)
+               (Vint (Int.shru (Int.shr i (Int.repr (Int.zwordsize - 1))) (Int.sub Int.iwordsize n)))).
+    { EvalOp. simpl. rewrite LTU2. auto. }
+    TrivialExists. 
+    constructor. EvalOp. simpl; eauto. constructor. 
+    simpl. unfold Int.ltu; rewrite zlt_true. rewrite Int.shrx_shr_2 by auto. reflexivity. 
+    change (Int.unsigned Int.iwordsize) with 32; omega.
+*)
+Qed.
+
+Theorem eval_shl: binary_constructor_sound shl Val.shl.
+Proof.
+  red; intros until y; unfold shl; case (shl_match b); intros.
+  InvEval. apply eval_shlimm; auto.
+  TrivialExists.
+Qed.
+
+Theorem eval_shr: binary_constructor_sound shr Val.shr.
+Proof.
+  red; intros until y; unfold shr; case (shr_match b); intros.
+  InvEval. apply eval_shrimm; auto.
+  TrivialExists.
+Qed.
+
+Theorem eval_shru: binary_constructor_sound shru Val.shru.
+Proof.
+  red; intros until y; unfold shru; case (shru_match b); intros.
+  InvEval. apply eval_shruimm; auto.
+  TrivialExists.
+Qed.
+
+Theorem eval_negf: unary_constructor_sound negf Val.negf.
+Proof.
+  red; intros. TrivialExists.
+Qed.
+
+Theorem eval_absf: unary_constructor_sound absf Val.absf.
+Proof.
+  red; intros. TrivialExists.
+Qed.
+
+Theorem eval_addf: binary_constructor_sound addf Val.addf.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Theorem eval_subf: binary_constructor_sound subf Val.subf.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Theorem eval_mulf: binary_constructor_sound mulf Val.mulf.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Theorem eval_negfs: unary_constructor_sound negfs Val.negfs.
+Proof.
+  red; intros. TrivialExists.
+Qed.
+
+Theorem eval_absfs: unary_constructor_sound absfs Val.absfs.
+Proof.
+  red; intros. TrivialExists.
+Qed.
+
+Theorem eval_addfs: binary_constructor_sound addfs Val.addfs.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Theorem eval_subfs: binary_constructor_sound subfs Val.subfs.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Theorem eval_mulfs: binary_constructor_sound mulfs Val.mulfs.
+Proof.
+  red; intros; TrivialExists.
+Qed.
+
+Section COMP_IMM.
+
+Variable default: comparison -> int -> condition.
+Variable intsem: comparison -> int -> int -> bool.
+Variable sem: comparison -> val -> val -> val.
+
+Hypothesis sem_int: forall c x y, sem c (Vint x) (Vint y) = Val.of_bool (intsem c x y).
+Hypothesis sem_undef: forall c v, sem c Vundef v = Vundef.
+Hypothesis sem_eq: forall x y, sem Ceq (Vint x) (Vint y) = Val.of_bool (Int.eq x y).
+Hypothesis sem_ne: forall x y, sem Cne (Vint x) (Vint y) = Val.of_bool (negb (Int.eq x y)).
+Hypothesis sem_default: forall c v n, sem c v (Vint n) = Val.of_optbool (eval_condition (default c n) (v :: nil) m).
+
+Lemma eval_compimm:
+  forall le c a n2 x,
+  eval_expr ge sp e m le a x ->
+  exists v, eval_expr ge sp e m le (compimm default intsem c a n2) v
+         /\ Val.lessdef (sem c x (Vint n2)) v.
+Proof.
+  intros until x.
+  unfold compimm; case (compimm_match c a); intros.
+(* constant *)
+  - InvEval. rewrite sem_int. TrivialExists. simpl. destruct (intsem c0 n1 n2); auto.
+(* eq cmp *)
+  - InvEval. inv H. simpl in H5. inv H5.
+    destruct (Int.eq_dec n2 Int.zero).
+    + subst n2. TrivialExists.
+      simpl. rewrite eval_negate_condition.
+      destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_eq; auto.
+      rewrite sem_undef; auto.
+    + destruct (Int.eq_dec n2 Int.one). subst n2. TrivialExists.
+      simpl. destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_eq; auto.
+      rewrite sem_undef; auto.
+      exists (Vint Int.zero); split. EvalOp.
+      destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; rewrite sem_eq; rewrite Int.eq_false; auto.
+      rewrite sem_undef; auto.
+(* ne cmp *)
+  - InvEval. inv H. simpl in H5. inv H5.
+    destruct (Int.eq_dec n2 Int.zero).
+    + subst n2. TrivialExists.
+      simpl. destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_ne; auto.
+      rewrite sem_undef; auto.
+    + destruct (Int.eq_dec n2 Int.one). subst n2. TrivialExists.
+      simpl. rewrite eval_negate_condition. destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_ne; auto.
+      rewrite sem_undef; auto.
+      exists (Vint Int.one); split. EvalOp.
+      destruct (eval_condition c0 vl m); simpl.
+      unfold Vtrue, Vfalse. destruct b; rewrite sem_ne; rewrite Int.eq_false; auto.
+      rewrite sem_undef; auto.
+(* default *)
+  - TrivialExists. simpl. rewrite sem_default. auto.
+Qed.
+
+Hypothesis sem_swap:
+  forall c x y, sem (swap_comparison c) x y = sem c y x.
+
+Lemma eval_compimm_swap:
+  forall le c a n2 x,
+  eval_expr ge sp e m le a x ->
+  exists v, eval_expr ge sp e m le (compimm default intsem (swap_comparison c) a n2) v
+         /\ Val.lessdef (sem c (Vint n2) x) v.
+Proof.
+  intros. rewrite <- sem_swap. eapply eval_compimm; eauto.
+Qed.
+
+End COMP_IMM.
+
+Theorem eval_comp:
+  forall c, binary_constructor_sound (comp c) (Val.cmp c).
+Proof.
+  intros; red; intros until y. unfold comp; case (comp_match a b); intros; InvEval.
+  eapply eval_compimm_swap; eauto.
+  intros. unfold Val.cmp. rewrite Val.swap_cmp_bool; auto.
+  eapply eval_compimm; eauto.
+  TrivialExists.
+Qed.
+
+Theorem eval_compu:
+  forall c, binary_constructor_sound (compu c) (Val.cmpu (Mem.valid_pointer m) c).
+Proof.
+  intros; red; intros until y. unfold compu; case (compu_match a b); intros; InvEval.
+  eapply eval_compimm_swap; eauto.
+  intros. unfold Val.cmpu. rewrite Val.swap_cmpu_bool; auto.
+  eapply eval_compimm; eauto.
+  TrivialExists.
+Qed.
+
+Theorem eval_compf:
+  forall c, binary_constructor_sound (compf c) (Val.cmpf c).
+Proof.
+  intros; red; intros. unfold compf. TrivialExists.
+Qed.
+
+Theorem eval_compfs:
+  forall c, binary_constructor_sound (compfs c) (Val.cmpfs c).
+Proof.
+  intros; red; intros. unfold compfs. TrivialExists.
+Qed.
+
+Theorem eval_cast8signed: unary_constructor_sound cast8signed (Val.sign_ext 8).
+Proof.
+  red; intros until x. unfold cast8signed. case (cast8signed_match a); intros; InvEval.
+  TrivialExists.
+  TrivialExists.
+Qed.
+
+Theorem eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8).
+Proof.
+  red; intros until x. unfold cast8unsigned.
+  rewrite Val.zero_ext_and. apply eval_andimm. compute; auto.
+Qed.
+
+Theorem eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16).
+Proof.
+  red; intros until x. unfold cast16signed. case (cast16signed_match a); intros; InvEval.
+  TrivialExists.
+  TrivialExists.
+Qed.
+
+Theorem eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16).
+Proof.
+  red; intros until x. unfold cast8unsigned.
+  rewrite Val.zero_ext_and. apply eval_andimm. compute; auto.
+Qed.
+
+Theorem eval_intoffloat:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.intoffloat x = Some y ->
+  exists v, eval_expr ge sp e m le (intoffloat a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold intoffloat. TrivialExists.
+Qed.
+
+Theorem eval_intuoffloat:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.intuoffloat x = Some y ->
+  exists v, eval_expr ge sp e m le (intuoffloat a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold intuoffloat. TrivialExists.
+Qed.
+
+Theorem eval_floatofintu:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.floatofintu x = Some y ->
+  exists v, eval_expr ge sp e m le (floatofintu a) v /\ Val.lessdef y v.
+Proof.
+  intros until y; unfold floatofintu. case (floatofintu_match a); intros.
+  InvEval. simpl in H0. TrivialExists.
+  TrivialExists.
+Qed.
+
+Theorem eval_floatofint:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.floatofint x = Some y ->
+  exists v, eval_expr ge sp e m le (floatofint a) v /\ Val.lessdef y v.
+Proof.
+  intros until y; unfold floatofint. case (floatofint_match a); intros.
+  InvEval. simpl in H0. TrivialExists.
+  TrivialExists.
+Qed.
+
+Theorem eval_intofsingle:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.intofsingle x = Some y ->
+  exists v, eval_expr ge sp e m le (intofsingle a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold intofsingle. TrivialExists.
+Qed.
+
+Theorem eval_singleofint:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.singleofint x = Some y ->
+  exists v, eval_expr ge sp e m le (singleofint a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold singleofint; TrivialExists.
+Qed.
+
+Theorem eval_intuofsingle:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.intuofsingle x = Some y ->
+  exists v, eval_expr ge sp e m le (intuofsingle a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold intuofsingle. TrivialExists.
+Qed.
+
+Theorem eval_singleofintu:
+  forall le a x y,
+  eval_expr ge sp e m le a x ->
+  Val.singleofintu x = Some y ->
+  exists v, eval_expr ge sp e m le (singleofintu a) v /\ Val.lessdef y v.
+Proof.
+  intros; unfold intuofsingle. TrivialExists.
+Qed.
+
+Theorem eval_singleoffloat: unary_constructor_sound singleoffloat Val.singleoffloat.
+Proof.
+  red; intros. unfold singleoffloat. TrivialExists.
+Qed.
+
+Theorem eval_floatofsingle: unary_constructor_sound floatofsingle Val.floatofsingle.
+Proof.
+  red; intros. unfold floatofsingle. TrivialExists.
+Qed.
+
+Theorem eval_addressing:
+  forall le chunk a v b ofs,
+  eval_expr ge sp e m le a v ->
+  v = Vptr b ofs ->
+  match addressing chunk a with (mode, args) =>
+    exists vl,
+    eval_exprlist ge sp e m le args vl /\
+    eval_addressing ge sp mode vl = Some v
+  end.
+Proof.
+  intros until v. unfold addressing; case (addressing_match a); intros; InvEval.
+  - exists (@nil val);  split. eauto with evalexpr. simpl. auto.
+  - destruct (Archi.pic_code tt).
+  + exists (Vptr b ofs0 :: nil); split.
+    constructor. EvalOp. simpl. congruence. constructor. simpl. rewrite Ptrofs.add_zero. congruence.
+  + exists (@nil val); split. constructor. simpl; auto.
+  - exists (v1 :: nil); split. eauto with evalexpr. simpl.
+    destruct v1; simpl in H; try discriminate. destruct Archi.ptr64 eqn:SF; inv H. 
+    simpl. auto.
+  - exists (v1 :: nil); split. eauto with evalexpr. simpl.
+    destruct v1; simpl in H; try discriminate. destruct Archi.ptr64 eqn:SF; inv H. 
+    simpl. auto.
+  - exists (v :: nil);  split. eauto with evalexpr. subst. simpl. rewrite Ptrofs.add_zero; auto.
+Qed.
+
+Theorem eval_builtin_arg:
+  forall a v,
+  eval_expr ge sp e m nil a v ->
+  CminorSel.eval_builtin_arg ge sp e m (builtin_arg a) v.
+Proof.
+  intros until v. unfold builtin_arg; case (builtin_arg_match a); intros; InvEval.
+- constructor.
+- constructor.
+- constructor.
+- simpl in H5. inv H5. constructor.
+- subst v. constructor; auto.
+- inv H. InvEval. simpl in H6; inv H6. constructor; auto.
+- constructor; auto.
+Qed.
+
+End CMCONSTR.