Added volatile_read_global and volatile_store_global builtins.

Finished updating IA32 and ARM ports.


git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@1792 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e

4 files changed, 400 insertions, 835 deletions

diff --git a/ia32/ConstpropOp.v b/ia32/ConstpropOp.v
deleted file mode 100644
index 3d07a4d..0000000
--- a/ia32/ConstpropOp.v
+++ /dev/null
@@ -1,805 +0,0 @@
-(* *********************************************************************)
-(*                                                                     *)
-(*              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.     *)
-(*                                                                     *)
-(* *********************************************************************)
-
-(** Static analysis and strength reduction for operators 
-  and conditions.  This is the machine-dependent part of [Constprop]. *)
-
-Require Import Coqlib.
-Require Import AST.
-Require Import Integers.
-Require Import Floats.
-Require Import Values.
-Require Import Op.
-Require Import Registers.
-
-(** * Static analysis *)
-
-(** To each pseudo-register at each program point, the static analysis 
-  associates a compile-time approximation taken from the following set. *)
-
-Inductive approx : Type :=
-  | Novalue: approx      (** No value possible, code is unreachable. *)
-  | Unknown: approx      (** All values are possible,
-                             no compile-time information is available. *)
-  | I: int -> approx     (** A known integer value. *)
-  | F: float -> approx   (** A known floating-point value. *)
-  | G: ident -> int -> approx
-                         (** The value is the address of the given global
-                             symbol plus the given integer offset. *)
-  | S: int -> approx.    (** The value is the stack pointer plus the offset. *)
-
-(** We now define the abstract interpretations of conditions and operators
-  over this set of approximations.  For instance, the abstract interpretation
-  of the operator [Oaddf] applied to two expressions [a] and [b] is
-  [F(Float.add f g)] if [a] and [b] have static approximations [Vfloat f]
-  and [Vfloat g] respectively, and [Unknown] otherwise.
-
-  The static approximations are defined by large pattern-matchings over
-  the approximations of the results.  We write these matchings in the
-  indirect style described in file [SelectOp] to avoid excessive
-  duplication of cases in proofs. *)
-
-(** Original definition:
-<<
-Nondetfunction eval_static_condition (cond: condition) (vl: list approx) :=
-  match cond, vl with
-  | Ccomp c, I n1 :: I n2 :: nil => Some(Int.cmp c n1 n2)
-  | Ccompu c, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 n2)
-  | Ccompimm c n, I n1 :: nil => Some(Int.cmp c n1 n)
-  | Ccompuimm c n, I n1 :: nil => Some(Int.cmpu c n1 n)
-  | Ccompf c, F n1 :: F n2 :: nil => Some(Float.cmp c n1 n2)
-  | Cnotcompf c, F n1 :: F n2 :: nil => Some(negb(Float.cmp c n1 n2))
-  | Cmaskzero n, I n1 :: nil => Some(Int.eq (Int.and n1 n) Int.zero)
-  | Cmasknotzero n, I n1::nil => Some(negb(Int.eq (Int.and n1 n) Int.zero))
-  | _, _ => None
-  end.
->>
-*)
-
-Inductive eval_static_condition_cases: forall (cond: condition) (vl: list approx), Type :=
-  | eval_static_condition_case1: forall c n1 n2, eval_static_condition_cases (Ccomp c) (I n1 :: I n2 :: nil)
-  | eval_static_condition_case2: forall c n1 n2, eval_static_condition_cases (Ccompu c) (I n1 :: I n2 :: nil)
-  | eval_static_condition_case3: forall c n n1, eval_static_condition_cases (Ccompimm c n) (I n1 :: nil)
-  | eval_static_condition_case4: forall c n n1, eval_static_condition_cases (Ccompuimm c n) (I n1 :: nil)
-  | eval_static_condition_case5: forall c n1 n2, eval_static_condition_cases (Ccompf c) (F n1 :: F n2 :: nil)
-  | eval_static_condition_case6: forall c n1 n2, eval_static_condition_cases (Cnotcompf c) (F n1 :: F n2 :: nil)
-  | eval_static_condition_case7: forall n n1, eval_static_condition_cases (Cmaskzero n) (I n1 :: nil)
-  | eval_static_condition_case8: forall n n1, eval_static_condition_cases (Cmasknotzero n) (I n1::nil)
-  | eval_static_condition_default: forall (cond: condition) (vl: list approx), eval_static_condition_cases cond vl.
-
-Definition eval_static_condition_match (cond: condition) (vl: list approx) :=
-  match cond as zz1, vl as zz2 return eval_static_condition_cases zz1 zz2 with
-  | Ccomp c, I n1 :: I n2 :: nil => eval_static_condition_case1 c n1 n2
-  | Ccompu c, I n1 :: I n2 :: nil => eval_static_condition_case2 c n1 n2
-  | Ccompimm c n, I n1 :: nil => eval_static_condition_case3 c n n1
-  | Ccompuimm c n, I n1 :: nil => eval_static_condition_case4 c n n1
-  | Ccompf c, F n1 :: F n2 :: nil => eval_static_condition_case5 c n1 n2
-  | Cnotcompf c, F n1 :: F n2 :: nil => eval_static_condition_case6 c n1 n2
-  | Cmaskzero n, I n1 :: nil => eval_static_condition_case7 n n1
-  | Cmasknotzero n, I n1::nil => eval_static_condition_case8 n n1
-  | cond, vl => eval_static_condition_default cond vl
-  end.
-
-Definition eval_static_condition (cond: condition) (vl: list approx) :=
-  match eval_static_condition_match cond vl with
-  | eval_static_condition_case1 c n1 n2 => (* Ccomp c, I n1 :: I n2 :: nil *) 
-      Some(Int.cmp c n1 n2)
-  | eval_static_condition_case2 c n1 n2 => (* Ccompu c, I n1 :: I n2 :: nil *) 
-      Some(Int.cmpu c n1 n2)
-  | eval_static_condition_case3 c n n1 => (* Ccompimm c n, I n1 :: nil *) 
-      Some(Int.cmp c n1 n)
-  | eval_static_condition_case4 c n n1 => (* Ccompuimm c n, I n1 :: nil *) 
-      Some(Int.cmpu c n1 n)
-  | eval_static_condition_case5 c n1 n2 => (* Ccompf c, F n1 :: F n2 :: nil *) 
-      Some(Float.cmp c n1 n2)
-  | eval_static_condition_case6 c n1 n2 => (* Cnotcompf c, F n1 :: F n2 :: nil *) 
-      Some(negb(Float.cmp c n1 n2))
-  | eval_static_condition_case7 n n1 => (* Cmaskzero n, I n1 :: nil *) 
-      Some(Int.eq (Int.and n1 n) Int.zero)
-  | eval_static_condition_case8 n n1 => (* Cmasknotzero n, I n1::nil *) 
-      Some(negb(Int.eq (Int.and n1 n) Int.zero))
-  | eval_static_condition_default cond vl =>
-      None
-  end.
-
-
-Definition eval_static_condition_val (cond: condition) (vl: list approx) :=
-  match eval_static_condition cond vl with
-  | None => Unknown
-  | Some b => I(if b then Int.one else Int.zero)
-  end.
-
-Definition eval_static_intoffloat (f: float) :=
-  match Float.intoffloat f with Some x => I x | None => Unknown end.
-
-(** Original definition:
-<<
-Nondetfunction eval_static_addressing (addr: addressing) (vl: list approx) :=
-  match addr, vl with
-  | Aindexed n, I n1::nil => I (Int.add n1 n)
-  | Aindexed n, G id ofs::nil => G id (Int.add ofs n)
-  | Aindexed n, S ofs::nil => S (Int.add ofs n)
-  | Aindexed2 n, I n1::I n2::nil => I (Int.add (Int.add n1 n2) n)
-  | Aindexed2 n, G id ofs::I n2::nil => G id (Int.add (Int.add ofs n2) n)
-  | Aindexed2 n, I n1::G id ofs::nil => G id (Int.add (Int.add ofs n1) n)
-  | Aindexed2 n, S ofs::I n2::nil => S (Int.add (Int.add ofs n2) n)
-  | Aindexed2 n, I n1::S ofs::nil => S (Int.add (Int.add ofs n1) n)
-  | Ascaled sc n, I n1::nil => I (Int.add (Int.mul n1 sc) n)
-  | Aindexed2scaled sc n, I n1::I n2::nil => I (Int.add n1 (Int.add (Int.mul n2 sc) n))
-  | Aindexed2scaled sc n, G id ofs::I n2::nil => G id (Int.add ofs (Int.add (Int.mul n2 sc) n))
-  | Aindexed2scaled sc n, S ofs::I n2::nil => S (Int.add ofs (Int.add (Int.mul n2 sc) n))
-  | Aglobal id ofs, nil => G id ofs
-  | Abased id ofs, I n1::nil => G id (Int.add ofs n1)
-  | Abasedscaled sc id ofs, I n1::nil => G id (Int.add ofs (Int.mul sc n1))
-  | Ainstack ofs, nil => S ofs
-  | _, _ => Unknown
-  end.
->>
-*)
-
-Inductive eval_static_addressing_cases: forall (addr: addressing) (vl: list approx), Type :=
-  | eval_static_addressing_case1: forall n n1, eval_static_addressing_cases (Aindexed n) (I n1::nil)
-  | eval_static_addressing_case2: forall n id ofs, eval_static_addressing_cases (Aindexed n) (G id ofs::nil)
-  | eval_static_addressing_case3: forall n ofs, eval_static_addressing_cases (Aindexed n) (S ofs::nil)
-  | eval_static_addressing_case4: forall n n1 n2, eval_static_addressing_cases (Aindexed2 n) (I n1::I n2::nil)
-  | eval_static_addressing_case5: forall n id ofs n2, eval_static_addressing_cases (Aindexed2 n) (G id ofs::I n2::nil)
-  | eval_static_addressing_case6: forall n n1 id ofs, eval_static_addressing_cases (Aindexed2 n) (I n1::G id ofs::nil)
-  | eval_static_addressing_case7: forall n ofs n2, eval_static_addressing_cases (Aindexed2 n) (S ofs::I n2::nil)
-  | eval_static_addressing_case8: forall n n1 ofs, eval_static_addressing_cases (Aindexed2 n) (I n1::S ofs::nil)
-  | eval_static_addressing_case9: forall sc n n1, eval_static_addressing_cases (Ascaled sc n) (I n1::nil)
-  | eval_static_addressing_case10: forall sc n n1 n2, eval_static_addressing_cases (Aindexed2scaled sc n) (I n1::I n2::nil)
-  | eval_static_addressing_case11: forall sc n id ofs n2, eval_static_addressing_cases (Aindexed2scaled sc n) (G id ofs::I n2::nil)
-  | eval_static_addressing_case12: forall sc n ofs n2, eval_static_addressing_cases (Aindexed2scaled sc n) (S ofs::I n2::nil)
-  | eval_static_addressing_case13: forall id ofs, eval_static_addressing_cases (Aglobal id ofs) (nil)
-  | eval_static_addressing_case14: forall id ofs n1, eval_static_addressing_cases (Abased id ofs) (I n1::nil)
-  | eval_static_addressing_case15: forall sc id ofs n1, eval_static_addressing_cases (Abasedscaled sc id ofs) (I n1::nil)
-  | eval_static_addressing_case16: forall ofs, eval_static_addressing_cases (Ainstack ofs) (nil)
-  | eval_static_addressing_default: forall (addr: addressing) (vl: list approx), eval_static_addressing_cases addr vl.
-
-Definition eval_static_addressing_match (addr: addressing) (vl: list approx) :=
-  match addr as zz1, vl as zz2 return eval_static_addressing_cases zz1 zz2 with
-  | Aindexed n, I n1::nil => eval_static_addressing_case1 n n1
-  | Aindexed n, G id ofs::nil => eval_static_addressing_case2 n id ofs
-  | Aindexed n, S ofs::nil => eval_static_addressing_case3 n ofs
-  | Aindexed2 n, I n1::I n2::nil => eval_static_addressing_case4 n n1 n2
-  | Aindexed2 n, G id ofs::I n2::nil => eval_static_addressing_case5 n id ofs n2
-  | Aindexed2 n, I n1::G id ofs::nil => eval_static_addressing_case6 n n1 id ofs
-  | Aindexed2 n, S ofs::I n2::nil => eval_static_addressing_case7 n ofs n2
-  | Aindexed2 n, I n1::S ofs::nil => eval_static_addressing_case8 n n1 ofs
-  | Ascaled sc n, I n1::nil => eval_static_addressing_case9 sc n n1
-  | Aindexed2scaled sc n, I n1::I n2::nil => eval_static_addressing_case10 sc n n1 n2
-  | Aindexed2scaled sc n, G id ofs::I n2::nil => eval_static_addressing_case11 sc n id ofs n2
-  | Aindexed2scaled sc n, S ofs::I n2::nil => eval_static_addressing_case12 sc n ofs n2
-  | Aglobal id ofs, nil => eval_static_addressing_case13 id ofs
-  | Abased id ofs, I n1::nil => eval_static_addressing_case14 id ofs n1
-  | Abasedscaled sc id ofs, I n1::nil => eval_static_addressing_case15 sc id ofs n1
-  | Ainstack ofs, nil => eval_static_addressing_case16 ofs
-  | addr, vl => eval_static_addressing_default addr vl
-  end.
-
-Definition eval_static_addressing (addr: addressing) (vl: list approx) :=
-  match eval_static_addressing_match addr vl with
-  | eval_static_addressing_case1 n n1 => (* Aindexed n, I n1::nil *) 
-      I (Int.add n1 n)
-  | eval_static_addressing_case2 n id ofs => (* Aindexed n, G id ofs::nil *) 
-      G id (Int.add ofs n)
-  | eval_static_addressing_case3 n ofs => (* Aindexed n, S ofs::nil *) 
-      S (Int.add ofs n)
-  | eval_static_addressing_case4 n n1 n2 => (* Aindexed2 n, I n1::I n2::nil *) 
-      I (Int.add (Int.add n1 n2) n)
-  | eval_static_addressing_case5 n id ofs n2 => (* Aindexed2 n, G id ofs::I n2::nil *) 
-      G id (Int.add (Int.add ofs n2) n)
-  | eval_static_addressing_case6 n n1 id ofs => (* Aindexed2 n, I n1::G id ofs::nil *) 
-      G id (Int.add (Int.add ofs n1) n)
-  | eval_static_addressing_case7 n ofs n2 => (* Aindexed2 n, S ofs::I n2::nil *) 
-      S (Int.add (Int.add ofs n2) n)
-  | eval_static_addressing_case8 n n1 ofs => (* Aindexed2 n, I n1::S ofs::nil *) 
-      S (Int.add (Int.add ofs n1) n)
-  | eval_static_addressing_case9 sc n n1 => (* Ascaled sc n, I n1::nil *) 
-      I (Int.add (Int.mul n1 sc) n)
-  | eval_static_addressing_case10 sc n n1 n2 => (* Aindexed2scaled sc n, I n1::I n2::nil *) 
-      I (Int.add n1 (Int.add (Int.mul n2 sc) n))
-  | eval_static_addressing_case11 sc n id ofs n2 => (* Aindexed2scaled sc n, G id ofs::I n2::nil *) 
-      G id (Int.add ofs (Int.add (Int.mul n2 sc) n))
-  | eval_static_addressing_case12 sc n ofs n2 => (* Aindexed2scaled sc n, S ofs::I n2::nil *) 
-      S (Int.add ofs (Int.add (Int.mul n2 sc) n))
-  | eval_static_addressing_case13 id ofs => (* Aglobal id ofs, nil *) 
-      G id ofs
-  | eval_static_addressing_case14 id ofs n1 => (* Abased id ofs, I n1::nil *) 
-      G id (Int.add ofs n1)
-  | eval_static_addressing_case15 sc id ofs n1 => (* Abasedscaled sc id ofs, I n1::nil *) 
-      G id (Int.add ofs (Int.mul sc n1))
-  | eval_static_addressing_case16 ofs => (* Ainstack ofs, nil *) 
-      S ofs
-  | eval_static_addressing_default addr vl =>
-      Unknown
-  end.
-
-
-(** Original definition:
-<<
-Nondetfunction eval_static_operation (op: operation) (vl: list approx) :=
-  match op, vl with
-  | Omove, v1::nil => v1
-  | Ointconst n, nil => I n
-  | Ofloatconst n, nil => F n
-  | Ocast8signed, I n1 :: nil => I(Int.sign_ext 8 n1)
-  | Ocast8unsigned, I n1 :: nil => I(Int.zero_ext 8 n1)
-  | Ocast16signed, I n1 :: nil => I(Int.sign_ext 16 n1)
-  | Ocast16unsigned, I n1 :: nil => I(Int.zero_ext 16 n1)
-  | Oneg, I n1 :: nil => I(Int.neg n1)
-  | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2)
-  | Osub, G s1 n1 :: I n2 :: nil => G s1 (Int.sub n1 n2)
-  | Omul, I n1 :: I n2 :: nil => I(Int.mul n1 n2)
-  | Omulimm n, I n1 :: nil => I(Int.mul n1 n)
-  | Odiv, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2)
-  | Odivu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2)
-  | Omod, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.mods n1 n2)
-  | Omodu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.modu n1 n2)
-  | Oand, I n1 :: I n2 :: nil => I(Int.and n1 n2)
-  | Oandimm n, I n1 :: nil => I(Int.and n1 n)
-  | Oor, I n1 :: I n2 :: nil => I(Int.or n1 n2)
-  | Oorimm n, I n1 :: nil => I(Int.or n1 n)
-  | Oxor, I n1 :: I n2 :: nil => I(Int.xor n1 n2)
-  | Oxorimm n, I n1 :: nil => I(Int.xor n1 n)
-  | Oshl, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown
-  | Oshlimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shl n1 n) else Unknown
-  | Oshr, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown
-  | Oshrimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown
-  | Oshrximm n, I n1 :: nil => if Int.ltu n (Int.repr 31) then I(Int.shrx n1 n) else Unknown
-  | Oshru, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown
-  | Oshruimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shru n1 n) else Unknown
-  | Ororimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.ror n1 n) else Unknown
-  | Olea mode, vl => eval_static_addressing mode vl
-  | Onegf, F n1 :: nil => F(Float.neg n1)
-  | Oabsf, F n1 :: nil => F(Float.abs n1)
-  | Oaddf, F n1 :: F n2 :: nil => F(Float.add n1 n2)
-  | Osubf, F n1 :: F n2 :: nil => F(Float.sub n1 n2)
-  | Omulf, F n1 :: F n2 :: nil => F(Float.mul n1 n2)
-  | Odivf, F n1 :: F n2 :: nil => F(Float.div n1 n2)
-  | Osingleoffloat, F n1 :: nil => F(Float.singleoffloat n1)
-  | Ointoffloat, F n1 :: nil => eval_static_intoffloat n1
-  | Ofloatofint, I n1 :: nil => F(Float.floatofint n1)
-  | Ocmp c, vl => eval_static_condition_val c vl
-  | _, _ => Unknown
-  end.
->>
-*)
-
-Inductive eval_static_operation_cases: forall (op: operation) (vl: list approx), Type :=
-  | eval_static_operation_case1: forall v1, eval_static_operation_cases (Omove) (v1::nil)
-  | eval_static_operation_case2: forall n, eval_static_operation_cases (Ointconst n) (nil)
-  | eval_static_operation_case3: forall n, eval_static_operation_cases (Ofloatconst n) (nil)
-  | eval_static_operation_case4: forall n1, eval_static_operation_cases (Ocast8signed) (I n1 :: nil)
-  | eval_static_operation_case5: forall n1, eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil)
-  | eval_static_operation_case6: forall n1, eval_static_operation_cases (Ocast16signed) (I n1 :: nil)
-  | eval_static_operation_case7: forall n1, eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil)
-  | eval_static_operation_case8: forall n1, eval_static_operation_cases (Oneg) (I n1 :: nil)
-  | eval_static_operation_case9: forall n1 n2, eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case10: forall s1 n1 n2, eval_static_operation_cases (Osub) (G s1 n1 :: I n2 :: nil)
-  | eval_static_operation_case11: forall n1 n2, eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case12: forall n n1, eval_static_operation_cases (Omulimm n) (I n1 :: nil)
-  | eval_static_operation_case13: forall n1 n2, eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case14: forall n1 n2, eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case15: forall n1 n2, eval_static_operation_cases (Omod) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case16: forall n1 n2, eval_static_operation_cases (Omodu) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case17: forall n1 n2, eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case18: forall n n1, eval_static_operation_cases (Oandimm n) (I n1 :: nil)
-  | eval_static_operation_case19: forall n1 n2, eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case20: forall n n1, eval_static_operation_cases (Oorimm n) (I n1 :: nil)
-  | eval_static_operation_case21: forall n1 n2, eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case22: forall n n1, eval_static_operation_cases (Oxorimm n) (I n1 :: nil)
-  | eval_static_operation_case23: forall n1 n2, eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case24: forall n n1, eval_static_operation_cases (Oshlimm n) (I n1 :: nil)
-  | eval_static_operation_case25: forall n1 n2, eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case26: forall n n1, eval_static_operation_cases (Oshrimm n) (I n1 :: nil)
-  | eval_static_operation_case27: forall n n1, eval_static_operation_cases (Oshrximm n) (I n1 :: nil)
-  | eval_static_operation_case28: forall n1 n2, eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil)
-  | eval_static_operation_case29: forall n n1, eval_static_operation_cases (Oshruimm n) (I n1 :: nil)
-  | eval_static_operation_case30: forall n n1, eval_static_operation_cases (Ororimm n) (I n1 :: nil)
-  | eval_static_operation_case31: forall mode vl, eval_static_operation_cases (Olea mode) (vl)
-  | eval_static_operation_case32: forall n1, eval_static_operation_cases (Onegf) (F n1 :: nil)
-  | eval_static_operation_case33: forall n1, eval_static_operation_cases (Oabsf) (F n1 :: nil)
-  | eval_static_operation_case34: forall n1 n2, eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil)
-  | eval_static_operation_case35: forall n1 n2, eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil)
-  | eval_static_operation_case36: forall n1 n2, eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil)
-  | eval_static_operation_case37: forall n1 n2, eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil)
-  | eval_static_operation_case38: forall n1, eval_static_operation_cases (Osingleoffloat) (F n1 :: nil)
-  | eval_static_operation_case39: forall n1, eval_static_operation_cases (Ointoffloat) (F n1 :: nil)
-  | eval_static_operation_case40: forall n1, eval_static_operation_cases (Ofloatofint) (I n1 :: nil)
-  | eval_static_operation_case41: forall c vl, eval_static_operation_cases (Ocmp c) (vl)
-  | eval_static_operation_default: forall (op: operation) (vl: list approx), eval_static_operation_cases op vl.
-
-Definition eval_static_operation_match (op: operation) (vl: list approx) :=
-  match op as zz1, vl as zz2 return eval_static_operation_cases zz1 zz2 with
-  | Omove, v1::nil => eval_static_operation_case1 v1
-  | Ointconst n, nil => eval_static_operation_case2 n
-  | Ofloatconst n, nil => eval_static_operation_case3 n
-  | Ocast8signed, I n1 :: nil => eval_static_operation_case4 n1
-  | Ocast8unsigned, I n1 :: nil => eval_static_operation_case5 n1
-  | Ocast16signed, I n1 :: nil => eval_static_operation_case6 n1
-  | Ocast16unsigned, I n1 :: nil => eval_static_operation_case7 n1
-  | Oneg, I n1 :: nil => eval_static_operation_case8 n1
-  | Osub, I n1 :: I n2 :: nil => eval_static_operation_case9 n1 n2
-  | Osub, G s1 n1 :: I n2 :: nil => eval_static_operation_case10 s1 n1 n2
-  | Omul, I n1 :: I n2 :: nil => eval_static_operation_case11 n1 n2
-  | Omulimm n, I n1 :: nil => eval_static_operation_case12 n n1
-  | Odiv, I n1 :: I n2 :: nil => eval_static_operation_case13 n1 n2
-  | Odivu, I n1 :: I n2 :: nil => eval_static_operation_case14 n1 n2
-  | Omod, I n1 :: I n2 :: nil => eval_static_operation_case15 n1 n2
-  | Omodu, I n1 :: I n2 :: nil => eval_static_operation_case16 n1 n2
-  | Oand, I n1 :: I n2 :: nil => eval_static_operation_case17 n1 n2
-  | Oandimm n, I n1 :: nil => eval_static_operation_case18 n n1
-  | Oor, I n1 :: I n2 :: nil => eval_static_operation_case19 n1 n2
-  | Oorimm n, I n1 :: nil => eval_static_operation_case20 n n1
-  | Oxor, I n1 :: I n2 :: nil => eval_static_operation_case21 n1 n2
-  | Oxorimm n, I n1 :: nil => eval_static_operation_case22 n n1
-  | Oshl, I n1 :: I n2 :: nil => eval_static_operation_case23 n1 n2
-  | Oshlimm n, I n1 :: nil => eval_static_operation_case24 n n1
-  | Oshr, I n1 :: I n2 :: nil => eval_static_operation_case25 n1 n2
-  | Oshrimm n, I n1 :: nil => eval_static_operation_case26 n n1
-  | Oshrximm n, I n1 :: nil => eval_static_operation_case27 n n1
-  | Oshru, I n1 :: I n2 :: nil => eval_static_operation_case28 n1 n2
-  | Oshruimm n, I n1 :: nil => eval_static_operation_case29 n n1
-  | Ororimm n, I n1 :: nil => eval_static_operation_case30 n n1
-  | Olea mode, vl => eval_static_operation_case31 mode vl
-  | Onegf, F n1 :: nil => eval_static_operation_case32 n1
-  | Oabsf, F n1 :: nil => eval_static_operation_case33 n1
-  | Oaddf, F n1 :: F n2 :: nil => eval_static_operation_case34 n1 n2
-  | Osubf, F n1 :: F n2 :: nil => eval_static_operation_case35 n1 n2
-  | Omulf, F n1 :: F n2 :: nil => eval_static_operation_case36 n1 n2
-  | Odivf, F n1 :: F n2 :: nil => eval_static_operation_case37 n1 n2
-  | Osingleoffloat, F n1 :: nil => eval_static_operation_case38 n1
-  | Ointoffloat, F n1 :: nil => eval_static_operation_case39 n1
-  | Ofloatofint, I n1 :: nil => eval_static_operation_case40 n1
-  | Ocmp c, vl => eval_static_operation_case41 c vl
-  | op, vl => eval_static_operation_default op vl
-  end.
-
-Definition eval_static_operation (op: operation) (vl: list approx) :=
-  match eval_static_operation_match op vl with
-  | eval_static_operation_case1 v1 => (* Omove, v1::nil *) 
-      v1
-  | eval_static_operation_case2 n => (* Ointconst n, nil *) 
-      I n
-  | eval_static_operation_case3 n => (* Ofloatconst n, nil *) 
-      F n
-  | eval_static_operation_case4 n1 => (* Ocast8signed, I n1 :: nil *) 
-      I(Int.sign_ext 8 n1)
-  | eval_static_operation_case5 n1 => (* Ocast8unsigned, I n1 :: nil *) 
-      I(Int.zero_ext 8 n1)
-  | eval_static_operation_case6 n1 => (* Ocast16signed, I n1 :: nil *) 
-      I(Int.sign_ext 16 n1)
-  | eval_static_operation_case7 n1 => (* Ocast16unsigned, I n1 :: nil *) 
-      I(Int.zero_ext 16 n1)
-  | eval_static_operation_case8 n1 => (* Oneg, I n1 :: nil *) 
-      I(Int.neg n1)
-  | eval_static_operation_case9 n1 n2 => (* Osub, I n1 :: I n2 :: nil *) 
-      I(Int.sub n1 n2)
-  | eval_static_operation_case10 s1 n1 n2 => (* Osub, G s1 n1 :: I n2 :: nil *) 
-      G s1 (Int.sub n1 n2)
-  | eval_static_operation_case11 n1 n2 => (* Omul, I n1 :: I n2 :: nil *) 
-      I(Int.mul n1 n2)
-  | eval_static_operation_case12 n n1 => (* Omulimm n, I n1 :: nil *) 
-      I(Int.mul n1 n)
-  | eval_static_operation_case13 n1 n2 => (* Odiv, I n1 :: I n2 :: nil *) 
-      if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2)
-  | eval_static_operation_case14 n1 n2 => (* Odivu, I n1 :: I n2 :: nil *) 
-      if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2)
-  | eval_static_operation_case15 n1 n2 => (* Omod, I n1 :: I n2 :: nil *) 
-      if Int.eq n2 Int.zero then Unknown else I(Int.mods n1 n2)
-  | eval_static_operation_case16 n1 n2 => (* Omodu, I n1 :: I n2 :: nil *) 
-      if Int.eq n2 Int.zero then Unknown else I(Int.modu n1 n2)
-  | eval_static_operation_case17 n1 n2 => (* Oand, I n1 :: I n2 :: nil *) 
-      I(Int.and n1 n2)
-  | eval_static_operation_case18 n n1 => (* Oandimm n, I n1 :: nil *) 
-      I(Int.and n1 n)
-  | eval_static_operation_case19 n1 n2 => (* Oor, I n1 :: I n2 :: nil *) 
-      I(Int.or n1 n2)
-  | eval_static_operation_case20 n n1 => (* Oorimm n, I n1 :: nil *) 
-      I(Int.or n1 n)
-  | eval_static_operation_case21 n1 n2 => (* Oxor, I n1 :: I n2 :: nil *) 
-      I(Int.xor n1 n2)
-  | eval_static_operation_case22 n n1 => (* Oxorimm n, I n1 :: nil *) 
-      I(Int.xor n1 n)
-  | eval_static_operation_case23 n1 n2 => (* Oshl, I n1 :: I n2 :: nil *) 
-      if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown
-  | eval_static_operation_case24 n n1 => (* Oshlimm n, I n1 :: nil *) 
-      if Int.ltu n Int.iwordsize then I(Int.shl n1 n) else Unknown
-  | eval_static_operation_case25 n1 n2 => (* Oshr, I n1 :: I n2 :: nil *) 
-      if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown
-  | eval_static_operation_case26 n n1 => (* Oshrimm n, I n1 :: nil *) 
-      if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown
-  | eval_static_operation_case27 n n1 => (* Oshrximm n, I n1 :: nil *) 
-      if Int.ltu n (Int.repr 31) then I(Int.shrx n1 n) else Unknown
-  | eval_static_operation_case28 n1 n2 => (* Oshru, I n1 :: I n2 :: nil *) 
-      if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown
-  | eval_static_operation_case29 n n1 => (* Oshruimm n, I n1 :: nil *) 
-      if Int.ltu n Int.iwordsize then I(Int.shru n1 n) else Unknown
-  | eval_static_operation_case30 n n1 => (* Ororimm n, I n1 :: nil *) 
-      if Int.ltu n Int.iwordsize then I(Int.ror n1 n) else Unknown
-  | eval_static_operation_case31 mode vl => (* Olea mode, vl *) 
-      eval_static_addressing mode vl
-  | eval_static_operation_case32 n1 => (* Onegf, F n1 :: nil *) 
-      F(Float.neg n1)
-  | eval_static_operation_case33 n1 => (* Oabsf, F n1 :: nil *) 
-      F(Float.abs n1)
-  | eval_static_operation_case34 n1 n2 => (* Oaddf, F n1 :: F n2 :: nil *) 
-      F(Float.add n1 n2)
-  | eval_static_operation_case35 n1 n2 => (* Osubf, F n1 :: F n2 :: nil *) 
-      F(Float.sub n1 n2)
-  | eval_static_operation_case36 n1 n2 => (* Omulf, F n1 :: F n2 :: nil *) 
-      F(Float.mul n1 n2)
-  | eval_static_operation_case37 n1 n2 => (* Odivf, F n1 :: F n2 :: nil *) 
-      F(Float.div n1 n2)
-  | eval_static_operation_case38 n1 => (* Osingleoffloat, F n1 :: nil *) 
-      F(Float.singleoffloat n1)
-  | eval_static_operation_case39 n1 => (* Ointoffloat, F n1 :: nil *) 
-      eval_static_intoffloat n1
-  | eval_static_operation_case40 n1 => (* Ofloatofint, I n1 :: nil *) 
-      F(Float.floatofint n1)
-  | eval_static_operation_case41 c vl => (* Ocmp c, vl *) 
-      eval_static_condition_val c vl
-  | eval_static_operation_default op vl =>
-      Unknown
-  end.
-
-
-(** * Operator strength reduction *)
-
-(** We now define auxiliary functions for strength reduction of
-  operators and addressing modes: replacing an operator with a cheaper
-  one if some of its arguments are statically known.  These are again
-  large pattern-matchings expressed in indirect style. *)
-
-Section STRENGTH_REDUCTION.
-
-Variable app: reg -> approx.
-
-(** Original definition:
-<<
-Nondetfunction cond_strength_reduction 
-              (cond: condition) (args: list reg) (vl: list approx) :=
-  match cond, args, vl with
-  | Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
-      (Ccompimm (swap_comparison c) n1, r2 :: nil)
-  | Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
-      (Ccompimm c n2, r1 :: nil)
-  | Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
-      (Ccompuimm (swap_comparison c) n1, r2 :: nil)
-  | Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
-      (Ccompuimm c n2, r1 :: nil)
-  | _, _, _ => 
-      (cond, args)
-  end.
->>
-*)
-
-Inductive cond_strength_reduction_cases: forall (cond: condition) (args: list reg) (vl: list approx), Type :=
-  | cond_strength_reduction_case1: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | cond_strength_reduction_case2: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | cond_strength_reduction_case3: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | cond_strength_reduction_case4: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | cond_strength_reduction_default: forall (cond: condition) (args: list reg) (vl: list approx), cond_strength_reduction_cases cond args vl.
-
-Definition cond_strength_reduction_match (cond: condition) (args: list reg) (vl: list approx) :=
-  match cond as zz1, args as zz2, vl as zz3 return cond_strength_reduction_cases zz1 zz2 zz3 with
-  | Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil => cond_strength_reduction_case1 c r1 r2 n1 v2
-  | Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case2 c r1 r2 v1 n2
-  | Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil => cond_strength_reduction_case3 c r1 r2 n1 v2
-  | Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case4 c r1 r2 v1 n2
-  | cond, args, vl => cond_strength_reduction_default cond args vl
-  end.
-
-Definition cond_strength_reduction (cond: condition) (args: list reg) (vl: list approx) :=
-  match cond_strength_reduction_match cond args vl with
-  | cond_strength_reduction_case1 c r1 r2 n1 v2 => (* Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      (Ccompimm (swap_comparison c) n1, r2 :: nil)
-  | cond_strength_reduction_case2 c r1 r2 v1 n2 => (* Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      (Ccompimm c n2, r1 :: nil)
-  | cond_strength_reduction_case3 c r1 r2 n1 v2 => (* Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      (Ccompuimm (swap_comparison c) n1, r2 :: nil)
-  | cond_strength_reduction_case4 c r1 r2 v1 n2 => (* Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      (Ccompuimm c n2, r1 :: nil)
-  | cond_strength_reduction_default cond args vl =>
-      (cond, args)
-  end.
-
-
-(** Original definition:
-<<
-Nondetfunction addr_strength_reduction
-                (addr: addressing) (args: list reg) (vl: list approx) :=
-  match addr, args, vl with
-
-  | Aindexed ofs, r1 :: nil, G symb n :: nil =>
-      (Aglobal symb (Int.add n ofs), nil)
-  | Aindexed ofs, r1 :: nil, S n :: nil =>
-      (Ainstack (Int.add n ofs), nil)
-
-  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil =>
-      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil =>
-      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil =>
-      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil =>
-      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil =>
-      (Abased symb (Int.add n1 ofs), r2 :: nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil =>
-      (Abased symb (Int.add n2 ofs), r1 :: nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
-      (Aindexed (Int.add n1 ofs), r2 :: nil)
-  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
-      (Aindexed (Int.add n2 ofs), r1 :: nil)
-
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil =>
-      (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil)
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil =>
-      (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil)
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
-      (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil)
-
-  | Abased id ofs, r1 :: nil, I n1 :: nil =>
-      (Aglobal id (Int.add ofs n1), nil)
-
-  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil =>
-      (Aglobal id (Int.add ofs (Int.mul sc n1)), nil)
-
-  | _, _ =>
-      (addr, args)
-  end.
->>
-*)
-
-Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg) (vl: list approx), Type :=
-  | addr_strength_reduction_case1: forall ofs r1 symb n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (G symb n :: nil)
-  | addr_strength_reduction_case2: forall ofs r1 n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (S n :: nil)
-  | addr_strength_reduction_case3: forall ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (G symb n1 :: I n2 :: nil)
-  | addr_strength_reduction_case4: forall ofs r1 r2 n1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: G symb n2 :: nil)
-  | addr_strength_reduction_case5: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (S n1 :: I n2 :: nil)
-  | addr_strength_reduction_case6: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: S n2 :: nil)
-  | addr_strength_reduction_case7: forall ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (G symb n1 :: v2 :: nil)
-  | addr_strength_reduction_case8: forall ofs r1 r2 v1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: G symb n2 :: nil)
-  | addr_strength_reduction_case9: forall ofs r1 r2 n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | addr_strength_reduction_case10: forall ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | addr_strength_reduction_case11: forall sc ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (G symb n1 :: I n2 :: nil)
-  | addr_strength_reduction_case12: forall sc ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (G symb n1 :: v2 :: nil)
-  | addr_strength_reduction_case13: forall sc ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | addr_strength_reduction_case14: forall id ofs r1 n1, addr_strength_reduction_cases (Abased id ofs) (r1 :: nil) (I n1 :: nil)
-  | addr_strength_reduction_case15: forall sc id ofs r1 n1, addr_strength_reduction_cases (Abasedscaled sc id ofs) (r1 :: nil) (I n1 :: nil)
-  | addr_strength_reduction_default: forall (addr: addressing) (args: list reg) (vl: list approx), addr_strength_reduction_cases addr args vl.
-
-Definition addr_strength_reduction_match (addr: addressing) (args: list reg) (vl: list approx) :=
-  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_cases zz1 zz2 zz3 with
-  | Aindexed ofs, r1 :: nil, G symb n :: nil => addr_strength_reduction_case1 ofs r1 symb n
-  | Aindexed ofs, r1 :: nil, S n :: nil => addr_strength_reduction_case2 ofs r1 n
-  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => addr_strength_reduction_case3 ofs r1 r2 symb n1 n2
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil => addr_strength_reduction_case4 ofs r1 r2 n1 symb n2
-  | Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil => addr_strength_reduction_case5 ofs r1 r2 n1 n2
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil => addr_strength_reduction_case6 ofs r1 r2 n1 n2
-  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => addr_strength_reduction_case7 ofs r1 r2 symb n1 v2
-  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil => addr_strength_reduction_case8 ofs r1 r2 v1 symb n2
-  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_case9 ofs r1 r2 n1 v2
-  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case10 ofs r1 r2 v1 n2
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2
-  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case13 sc ofs r1 r2 v1 n2
-  | Abased id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case14 id ofs r1 n1
-  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case15 sc id ofs r1 n1
-  | addr, args, vl => addr_strength_reduction_default addr args vl
-  end.
-
-Definition addr_strength_reduction (addr: addressing) (args: list reg) (vl: list approx) :=
-  match addr_strength_reduction_match addr args vl with
-  | addr_strength_reduction_case1 ofs r1 symb n => (* Aindexed ofs, r1 :: nil, G symb n :: nil *) 
-      (Aglobal symb (Int.add n ofs), nil)
-  | addr_strength_reduction_case2 ofs r1 n => (* Aindexed ofs, r1 :: nil, S n :: nil *) 
-      (Ainstack (Int.add n ofs), nil)
-  | addr_strength_reduction_case3 ofs r1 r2 symb n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil *) 
-      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
-  | addr_strength_reduction_case4 ofs r1 r2 n1 symb n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil *) 
-      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
-  | addr_strength_reduction_case5 ofs r1 r2 n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil *) 
-      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
-  | addr_strength_reduction_case6 ofs r1 r2 n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil *) 
-      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
-  | addr_strength_reduction_case7 ofs r1 r2 symb n1 v2 => (* Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil *) 
-      (Abased symb (Int.add n1 ofs), r2 :: nil)
-  | addr_strength_reduction_case8 ofs r1 r2 v1 symb n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil *) 
-      (Abased symb (Int.add n2 ofs), r1 :: nil)
-  | addr_strength_reduction_case9 ofs r1 r2 n1 v2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      (Aindexed (Int.add n1 ofs), r2 :: nil)
-  | addr_strength_reduction_case10 ofs r1 r2 v1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      (Aindexed (Int.add n2 ofs), r1 :: nil)
-  | addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil *) 
-      (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil)
-  | addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil *) 
-      (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil)
-  | addr_strength_reduction_case13 sc ofs r1 r2 v1 n2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil)
-  | addr_strength_reduction_case14 id ofs r1 n1 => (* Abased id ofs, r1 :: nil, I n1 :: nil *) 
-      (Aglobal id (Int.add ofs n1), nil)
-  | addr_strength_reduction_case15 sc id ofs r1 n1 => (* Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil *) 
-      (Aglobal id (Int.add ofs (Int.mul sc n1)), nil)
-  | addr_strength_reduction_default addr args vl =>
-      (addr, args)
-  end.
-
-
-Definition make_addimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Omove, r :: nil)
-  else (Oaddimm n, r :: nil).
-
-Definition make_shlimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Omove, r :: nil)
-  else (Oshlimm n, r :: nil).
-
-Definition make_shrimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Omove, r :: nil)
-  else (Oshrimm n, r :: nil).
-
-Definition make_shruimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Omove, r :: nil)
-  else (Oshruimm n, r :: nil).
-
-Definition make_mulimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero then
-    (Ointconst Int.zero, nil)
-  else if Int.eq n Int.one then
-    (Omove, r :: nil)
-  else
-    match Int.is_power2 n with
-    | Some l => make_shlimm l r
-    | None => (Omulimm n, r :: nil)
-    end.
-
-Definition make_andimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Ointconst Int.zero, nil)
-  else if Int.eq n Int.mone then (Omove, r :: nil)
-  else (Oandimm n, r :: nil).
-
-Definition make_orimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero then (Omove, r :: nil)
-  else if Int.eq n Int.mone then (Ointconst Int.mone, nil)
-  else (Oorimm n, r :: nil).
-
-Definition make_xorimm (n: int) (r: reg) :=
-  if Int.eq n Int.zero
-  then (Omove, r :: nil)
-  else (Oxorimm n, r :: nil).
-
-Definition make_divimm n (r1 r2: reg) :=
-  match Int.is_power2 n with
-  | Some l => if Int.ltu l (Int.repr 31)
-              then (Oshrximm l, r1 :: nil)
-              else (Odiv, r1 :: r2 :: nil)
-  | None   => (Odiv, r1 :: r2 :: nil)
-  end.
-
-Definition make_divuimm n (r1 r2: reg) :=
-  match Int.is_power2 n with
-  | Some l => make_shruimm l r1
-  | None   => (Odivu, r1 :: r2 :: nil)
-  end.
-
-Definition make_moduimm n (r1 r2: reg) :=
-  match Int.is_power2 n with
-  | Some l => (Oandimm (Int.sub n Int.one), r1 :: nil)
-  | None   => (Omodu, r1 :: r2 :: nil)
-  end.
-
-(** We must be careful to preserve 2-address constraints over the
-    RTL code, which means that commutative operations cannot
-    be specialized if their first argument is a constant. *)
-
-(** Original definition:
-<<
-Nondetfunction op_strength_reduction 
-              (op: operation) (args: list reg) (vl: list approx) :=
-  match op, args, vl with
-  | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1
-  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1
-  | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2
-  | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2
-  | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_moduimm n2 r1 r2
-  | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1
-  | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1
-  | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1
-  | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1
-  | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1
-  | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1
-  | Olea addr, args, vl =>
-      let (addr', args') := addr_strength_reduction addr args vl in
-      (Olea addr', args')
-  | Ocmp c, args, vl =>
-      let (c', args') := cond_strength_reduction c args vl in 
-      (Ocmp c', args')
-  | _, _, _ => (op, args)
-  end.
->>
-*)
-
-Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg) (vl: list approx), Type :=
-  | op_strength_reduction_case1: forall r1 r2 v1 n2, op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case2: forall r1 r2 v1 n2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case3: forall r1 r2 v1 n2, op_strength_reduction_cases (Odiv) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case4: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case5: forall r1 r2 v1 n2, op_strength_reduction_cases (Omodu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case6: forall r1 r2 v1 n2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case7: forall r1 r2 v1 n2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case8: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case9: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case10: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case11: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case12: forall addr args vl, op_strength_reduction_cases (Olea addr) (args) (vl)
-  | op_strength_reduction_case13: forall c args vl, op_strength_reduction_cases (Ocmp c) (args) (vl)
-  | op_strength_reduction_default: forall (op: operation) (args: list reg) (vl: list approx), op_strength_reduction_cases op args vl.
-
-Definition op_strength_reduction_match (op: operation) (args: list reg) (vl: list approx) :=
-  match op as zz1, args as zz2, vl as zz3 return op_strength_reduction_cases zz1 zz2 zz3 with
-  | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case1 r1 r2 v1 n2
-  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case2 r1 r2 v1 n2
-  | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case3 r1 r2 v1 n2
-  | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case4 r1 r2 v1 n2
-  | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case5 r1 r2 v1 n2
-  | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case6 r1 r2 v1 n2
-  | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case7 r1 r2 v1 n2
-  | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case8 r1 r2 v1 n2
-  | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case9 r1 r2 v1 n2
-  | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case10 r1 r2 v1 n2
-  | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case11 r1 r2 v1 n2
-  | Olea addr, args, vl => op_strength_reduction_case12 addr args vl
-  | Ocmp c, args, vl => op_strength_reduction_case13 c args vl
-  | op, args, vl => op_strength_reduction_default op args vl
-  end.
-
-Definition op_strength_reduction (op: operation) (args: list reg) (vl: list approx) :=
-  match op_strength_reduction_match op args vl with
-  | op_strength_reduction_case1 r1 r2 v1 n2 => (* Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_addimm (Int.neg n2) r1
-  | op_strength_reduction_case2 r1 r2 v1 n2 => (* Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_mulimm n2 r1
-  | op_strength_reduction_case3 r1 r2 v1 n2 => (* Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_divimm n2 r1 r2
-  | op_strength_reduction_case4 r1 r2 v1 n2 => (* Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_divuimm n2 r1 r2
-  | op_strength_reduction_case5 r1 r2 v1 n2 => (* Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_moduimm n2 r1 r2
-  | op_strength_reduction_case6 r1 r2 v1 n2 => (* Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_andimm n2 r1
-  | op_strength_reduction_case7 r1 r2 v1 n2 => (* Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_orimm n2 r1
-  | op_strength_reduction_case8 r1 r2 v1 n2 => (* Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_xorimm n2 r1
-  | op_strength_reduction_case9 r1 r2 v1 n2 => (* Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shlimm n2 r1
-  | op_strength_reduction_case10 r1 r2 v1 n2 => (* Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shrimm n2 r1
-  | op_strength_reduction_case11 r1 r2 v1 n2 => (* Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shruimm n2 r1
-  | op_strength_reduction_case12 addr args vl => (* Olea addr, args, vl *) 
-      let (addr', args') := addr_strength_reduction addr args vl in (Olea addr', args')
-  | op_strength_reduction_case13 c args vl => (* Ocmp c, args, vl *) 
-      let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args')
-  | op_strength_reduction_default op args vl =>
-      (op, args)
-  end.
-
-
-End STRENGTH_REDUCTION.
diff --git a/ia32/ConstpropOp.vp b/ia32/ConstpropOp.vp
new file mode 100644
index 0000000..b861107
--- /dev/null
+++ b/ia32/ConstpropOp.vp
@@ -0,0 +1,314 @@
+(* *********************************************************************)
+(*                                                                     *)
+(*              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.     *)
+(*                                                                     *)
+(* *********************************************************************)
+
+(** Static analysis and strength reduction for operators 
+  and conditions.  This is the machine-dependent part of [Constprop]. *)
+
+Require Import Coqlib.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Values.
+Require Import Op.
+Require Import Registers.
+
+(** * Static analysis *)
+
+(** To each pseudo-register at each program point, the static analysis 
+  associates a compile-time approximation taken from the following set. *)
+
+Inductive approx : Type :=
+  | Novalue: approx      (** No value possible, code is unreachable. *)
+  | Unknown: approx      (** All values are possible,
+                             no compile-time information is available. *)
+  | I: int -> approx     (** A known integer value. *)
+  | F: float -> approx   (** A known floating-point value. *)
+  | G: ident -> int -> approx
+                         (** The value is the address of the given global
+                             symbol plus the given integer offset. *)
+  | S: int -> approx.    (** The value is the stack pointer plus the offset. *)
+
+(** We now define the abstract interpretations of conditions and operators
+  over this set of approximations.  For instance, the abstract interpretation
+  of the operator [Oaddf] applied to two expressions [a] and [b] is
+  [F(Float.add f g)] if [a] and [b] have static approximations [Vfloat f]
+  and [Vfloat g] respectively, and [Unknown] otherwise.
+
+  The static approximations are defined by large pattern-matchings over
+  the approximations of the results.  We write these matchings in the
+  indirect style described in file [SelectOp] to avoid excessive
+  duplication of cases in proofs. *)
+
+Nondetfunction eval_static_condition (cond: condition) (vl: list approx) :=
+  match cond, vl with
+  | Ccomp c, I n1 :: I n2 :: nil => Some(Int.cmp c n1 n2)
+  | Ccompu c, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 n2)
+  | Ccompimm c n, I n1 :: nil => Some(Int.cmp c n1 n)
+  | Ccompuimm c n, I n1 :: nil => Some(Int.cmpu c n1 n)
+  | Ccompf c, F n1 :: F n2 :: nil => Some(Float.cmp c n1 n2)
+  | Cnotcompf c, F n1 :: F n2 :: nil => Some(negb(Float.cmp c n1 n2))
+  | Cmaskzero n, I n1 :: nil => Some(Int.eq (Int.and n1 n) Int.zero)
+  | Cmasknotzero n, I n1::nil => Some(negb(Int.eq (Int.and n1 n) Int.zero))
+  | _, _ => None
+  end.
+
+Definition eval_static_condition_val (cond: condition) (vl: list approx) :=
+  match eval_static_condition cond vl with
+  | None => Unknown
+  | Some b => I(if b then Int.one else Int.zero)
+  end.
+
+Definition eval_static_intoffloat (f: float) :=
+  match Float.intoffloat f with Some x => I x | None => Unknown end.
+
+Nondetfunction eval_static_addressing (addr: addressing) (vl: list approx) :=
+  match addr, vl with
+  | Aindexed n, I n1::nil => I (Int.add n1 n)
+  | Aindexed n, G id ofs::nil => G id (Int.add ofs n)
+  | Aindexed n, S ofs::nil => S (Int.add ofs n)
+  | Aindexed2 n, I n1::I n2::nil => I (Int.add (Int.add n1 n2) n)
+  | Aindexed2 n, G id ofs::I n2::nil => G id (Int.add (Int.add ofs n2) n)
+  | Aindexed2 n, I n1::G id ofs::nil => G id (Int.add (Int.add ofs n1) n)
+  | Aindexed2 n, S ofs::I n2::nil => S (Int.add (Int.add ofs n2) n)
+  | Aindexed2 n, I n1::S ofs::nil => S (Int.add (Int.add ofs n1) n)
+  | Ascaled sc n, I n1::nil => I (Int.add (Int.mul n1 sc) n)
+  | Aindexed2scaled sc n, I n1::I n2::nil => I (Int.add n1 (Int.add (Int.mul n2 sc) n))
+  | Aindexed2scaled sc n, G id ofs::I n2::nil => G id (Int.add ofs (Int.add (Int.mul n2 sc) n))
+  | Aindexed2scaled sc n, S ofs::I n2::nil => S (Int.add ofs (Int.add (Int.mul n2 sc) n))
+  | Aglobal id ofs, nil => G id ofs
+  | Abased id ofs, I n1::nil => G id (Int.add ofs n1)
+  | Abasedscaled sc id ofs, I n1::nil => G id (Int.add ofs (Int.mul sc n1))
+  | Ainstack ofs, nil => S ofs
+  | _, _ => Unknown
+  end.
+
+Nondetfunction eval_static_operation (op: operation) (vl: list approx) :=
+  match op, vl with
+  | Omove, v1::nil => v1
+  | Ointconst n, nil => I n
+  | Ofloatconst n, nil => F n
+  | Ocast8signed, I n1 :: nil => I(Int.sign_ext 8 n1)
+  | Ocast8unsigned, I n1 :: nil => I(Int.zero_ext 8 n1)
+  | Ocast16signed, I n1 :: nil => I(Int.sign_ext 16 n1)
+  | Ocast16unsigned, I n1 :: nil => I(Int.zero_ext 16 n1)
+  | Oneg, I n1 :: nil => I(Int.neg n1)
+  | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2)
+  | Osub, G s1 n1 :: I n2 :: nil => G s1 (Int.sub n1 n2)
+  | Omul, I n1 :: I n2 :: nil => I(Int.mul n1 n2)
+  | Omulimm n, I n1 :: nil => I(Int.mul n1 n)
+  | Odiv, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2)
+  | Odivu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2)
+  | Omod, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.mods n1 n2)
+  | Omodu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.modu n1 n2)
+  | Oand, I n1 :: I n2 :: nil => I(Int.and n1 n2)
+  | Oandimm n, I n1 :: nil => I(Int.and n1 n)
+  | Oor, I n1 :: I n2 :: nil => I(Int.or n1 n2)
+  | Oorimm n, I n1 :: nil => I(Int.or n1 n)
+  | Oxor, I n1 :: I n2 :: nil => I(Int.xor n1 n2)
+  | Oxorimm n, I n1 :: nil => I(Int.xor n1 n)
+  | Oshl, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown
+  | Oshlimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shl n1 n) else Unknown
+  | Oshr, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown
+  | Oshrimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown
+  | Oshrximm n, I n1 :: nil => if Int.ltu n (Int.repr 31) then I(Int.shrx n1 n) else Unknown
+  | Oshru, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown
+  | Oshruimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shru n1 n) else Unknown
+  | Ororimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.ror n1 n) else Unknown
+  | Olea mode, vl => eval_static_addressing mode vl
+  | Onegf, F n1 :: nil => F(Float.neg n1)
+  | Oabsf, F n1 :: nil => F(Float.abs n1)
+  | Oaddf, F n1 :: F n2 :: nil => F(Float.add n1 n2)
+  | Osubf, F n1 :: F n2 :: nil => F(Float.sub n1 n2)
+  | Omulf, F n1 :: F n2 :: nil => F(Float.mul n1 n2)
+  | Odivf, F n1 :: F n2 :: nil => F(Float.div n1 n2)
+  | Osingleoffloat, F n1 :: nil => F(Float.singleoffloat n1)
+  | Ointoffloat, F n1 :: nil => eval_static_intoffloat n1
+  | Ofloatofint, I n1 :: nil => F(Float.floatofint n1)
+  | Ocmp c, vl => eval_static_condition_val c vl
+  | _, _ => Unknown
+  end.
+
+(** * Operator strength reduction *)
+
+(** We now define auxiliary functions for strength reduction of
+  operators and addressing modes: replacing an operator with a cheaper
+  one if some of its arguments are statically known.  These are again
+  large pattern-matchings expressed in indirect style. *)
+
+Section STRENGTH_REDUCTION.
+
+Variable app: reg -> approx.
+
+Nondetfunction cond_strength_reduction 
+              (cond: condition) (args: list reg) (vl: list approx) :=
+  match cond, args, vl with
+  | Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
+      (Ccompimm (swap_comparison c) n1, r2 :: nil)
+  | Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
+      (Ccompimm c n2, r1 :: nil)
+  | Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
+      (Ccompuimm (swap_comparison c) n1, r2 :: nil)
+  | Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
+      (Ccompuimm c n2, r1 :: nil)
+  | _, _, _ => 
+      (cond, args)
+  end.
+
+Nondetfunction addr_strength_reduction
+                (addr: addressing) (args: list reg) (vl: list approx) :=
+  match addr, args, vl with
+
+  | Aindexed ofs, r1 :: nil, G symb n :: nil =>
+      (Aglobal symb (Int.add n ofs), nil)
+  | Aindexed ofs, r1 :: nil, S n :: nil =>
+      (Ainstack (Int.add n ofs), nil)
+
+  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil =>
+      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil =>
+      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil =>
+      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil =>
+      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil =>
+      (Abased symb (Int.add n1 ofs), r2 :: nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil =>
+      (Abased symb (Int.add n2 ofs), r1 :: nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
+      (Aindexed (Int.add n1 ofs), r2 :: nil)
+  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
+      (Aindexed (Int.add n2 ofs), r1 :: nil)
+
+  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil =>
+      (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil)
+  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil =>
+      (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil)
+  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
+      (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil)
+
+  | Abased id ofs, r1 :: nil, I n1 :: nil =>
+      (Aglobal id (Int.add ofs n1), nil)
+
+  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil =>
+      (Aglobal id (Int.add ofs (Int.mul sc n1)), nil)
+
+  | _, _ =>
+      (addr, args)
+  end.
+
+Definition make_addimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Omove, r :: nil)
+  else (Oaddimm n, r :: nil).
+
+Definition make_shlimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Omove, r :: nil)
+  else (Oshlimm n, r :: nil).
+
+Definition make_shrimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Omove, r :: nil)
+  else (Oshrimm n, r :: nil).
+
+Definition make_shruimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Omove, r :: nil)
+  else (Oshruimm n, r :: nil).
+
+Definition make_mulimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero then
+    (Ointconst Int.zero, nil)
+  else if Int.eq n Int.one then
+    (Omove, r :: nil)
+  else
+    match Int.is_power2 n with
+    | Some l => make_shlimm l r
+    | None => (Omulimm n, r :: nil)
+    end.
+
+Definition make_andimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Ointconst Int.zero, nil)
+  else if Int.eq n Int.mone then (Omove, r :: nil)
+  else (Oandimm n, r :: nil).
+
+Definition make_orimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero then (Omove, r :: nil)
+  else if Int.eq n Int.mone then (Ointconst Int.mone, nil)
+  else (Oorimm n, r :: nil).
+
+Definition make_xorimm (n: int) (r: reg) :=
+  if Int.eq n Int.zero
+  then (Omove, r :: nil)
+  else (Oxorimm n, r :: nil).
+
+Definition make_divimm n (r1 r2: reg) :=
+  match Int.is_power2 n with
+  | Some l => if Int.ltu l (Int.repr 31)
+              then (Oshrximm l, r1 :: nil)
+              else (Odiv, r1 :: r2 :: nil)
+  | None   => (Odiv, r1 :: r2 :: nil)
+  end.
+
+Definition make_divuimm n (r1 r2: reg) :=
+  match Int.is_power2 n with
+  | Some l => make_shruimm l r1
+  | None   => (Odivu, r1 :: r2 :: nil)
+  end.
+
+Definition make_moduimm n (r1 r2: reg) :=
+  match Int.is_power2 n with
+  | Some l => (Oandimm (Int.sub n Int.one), r1 :: nil)
+  | None   => (Omodu, r1 :: r2 :: nil)
+  end.
+
+(** We must be careful to preserve 2-address constraints over the
+    RTL code, which means that commutative operations cannot
+    be specialized if their first argument is a constant. *)
+
+Nondetfunction op_strength_reduction 
+              (op: operation) (args: list reg) (vl: list approx) :=
+  match op, args, vl with
+  | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1
+  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1
+  | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2
+  | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2
+  | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_moduimm n2 r1 r2
+  | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1
+  | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1
+  | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1
+  | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1
+  | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1
+  | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1
+  | Olea addr, args, vl =>
+      let (addr', args') := addr_strength_reduction addr args vl in
+      (Olea addr', args')
+  | Ocmp c, args, vl =>
+      let (c', args') := cond_strength_reduction c args vl in 
+      (Ocmp c', args')
+  | _, _, _ => (op, args)
+  end.
+
+Nondetfunction builtin_strength_reduction
+               (ef: external_function) (args: list reg) (vl: list approx) :=
+  match ef, args, vl with
+  | EF_vload chunk, r1 :: nil, G symb n1 :: nil =>
+      (EF_vload_global chunk symb n1, nil)
+  | EF_vstore chunk, r1 :: r2 :: nil, G symb n1 :: v2 :: nil =>
+      (EF_vstore_global chunk symb n1, r2 :: nil)
+  | _, _, _ =>
+      (ef, args)
+  end.
+
+End STRENGTH_REDUCTION.
diff --git a/ia32/ConstpropOpproof.v b/ia32/ConstpropOpproof.v
index afb284a..04a1725 100644
--- a/ia32/ConstpropOpproof.v
+++ b/ia32/ConstpropOpproof.v
@@ -19,6 +19,7 @@ Require Import Floats.
 Require Import Values.
 Require Import Memory.
 Require Import Globalenvs.
+Require Import Events.
 Require Import Op.
 Require Import Registers.
 Require Import RTL.
@@ -418,6 +419,24 @@ Proof.
   exists v; auto.
 Qed.
 
+Lemma builtin_strength_reduction_correct:
+  forall ef args vl m t vres m',
+  vl = approx_regs app args ->
+  external_call ef ge rs##args m t vres m' ->
+  let (ef', args') := builtin_strength_reduction ef args vl in
+  external_call ef' ge rs##args' m t vres m'.
+Proof.
+  intros until m'. unfold builtin_strength_reduction.
+  destruct (builtin_strength_reduction_match ef args vl); simpl; intros; InvApproxRegs; SimplVMA.
+  unfold symbol_address in H. destruct (Genv.find_symbol ge symb) as [b|]_eqn; rewrite H in H0.
+  rewrite volatile_load_global_charact. exists b; auto. 
+  inv H0.
+  unfold symbol_address in H1. destruct (Genv.find_symbol ge symb) as [b|]_eqn; rewrite H1 in H0.
+  rewrite volatile_store_global_charact. exists b; auto. 
+  inv H0.
+  auto.
+Qed.
+
 End STRENGTH_REDUCTION.
 
 End ANALYSIS.
diff --git a/ia32/PrintAsm.ml b/ia32/PrintAsm.ml
index 5ca56d7..3ee0c6e 100644
--- a/ia32/PrintAsm.ml
+++ b/ia32/PrintAsm.ml
@@ -348,52 +348,85 @@ let print_builtin_memcpy oc sz al args =
 
 (* Handling of volatile reads and writes *)
 
+let print_builtin_vload_common oc chunk addr res =
+  match chunk, res with
+  | Mint8unsigned, IR res ->
+      fprintf oc "	movzbl	%a, %a\n" addressing addr ireg res
+  | Mint8signed, IR res ->
+      fprintf oc "	movsbl	%a, %a\n" addressing addr ireg res
+  | Mint16unsigned, IR res ->
+      fprintf oc "	movzwl	%a, %a\n" addressing addr ireg res
+  | Mint16signed, IR res ->
+      fprintf oc "	movswl	%a, %a\n" addressing addr ireg res
+  | Mint32, IR res ->
+      fprintf oc "	movl	%a, %a\n" addressing addr ireg res
+  | Mfloat32, FR res ->
+      fprintf oc "	cvtss2sd %a, %a\n" addressing addr freg res
+  | Mfloat64, FR res ->
+      fprintf oc "	movsd	%a, %a\n" addressing addr freg res
+  | _ ->
+      assert false
+
 let print_builtin_vload oc chunk args res =
   fprintf oc "%s begin builtin __builtin_volatile_read\n" comment;
-  begin match chunk, args, res with
-  | Mint8unsigned, [IR addr], IR res ->
-      fprintf oc "	movzbl	0(%a), %a\n" ireg addr ireg res
-  | Mint8signed, [IR addr], IR res ->
-      fprintf oc "	movsbl	0(%a), %a\n" ireg addr ireg res
-  | Mint16unsigned, [IR addr], IR res ->
-      fprintf oc "	movzwl	0(%a), %a\n" ireg addr ireg res
-  | Mint16signed, [IR addr], IR res ->
-      fprintf oc "	movswl	0(%a), %a\n" ireg addr ireg res
-  | Mint32, [IR addr], IR res ->
-      fprintf oc "	movl	0(%a), %a\n" ireg addr ireg res
-  | Mfloat32, [IR addr], FR res ->
-      fprintf oc "	cvtss2sd 0(%a), %a\n" ireg addr freg res
-  | Mfloat64, [IR addr], FR res ->
-      fprintf oc "	movsd	0(%a), %a\n" ireg addr freg res
+  begin match args with
+  | [IR addr] ->
+      print_builtin_vload_common oc chunk
+                 (Addrmode(Some addr, None, Coq_inl Integers.Int.zero)) res
   | _ ->
       assert false
   end;
   fprintf oc "%s end builtin __builtin_volatile_read\n" comment
 
-let print_builtin_vstore oc chunk args =
-  fprintf oc "%s begin builtin __builtin_volatile_write\n" comment;
-  begin match chunk, args with
-  | (Mint8signed | Mint8unsigned), [IR addr; IR src] ->
+let print_builtin_vload_global oc chunk id ofs args res =
+  fprintf oc "%s begin builtin __builtin_volatile_read\n" comment;
+  print_builtin_vload_common oc chunk
+                 (Addrmode(None, None, Coq_inr(id,ofs))) res;
+  fprintf oc "%s end builtin __builtin_volatile_read\n" comment
+
+let print_builtin_vstore_common oc chunk addr src =
+  match chunk, src with
+  | (Mint8signed | Mint8unsigned), IR src ->
       if Asmgen.low_ireg src then
-        fprintf oc "	movb	%a, 0(%a)\n" ireg8 src ireg addr
+        fprintf oc "	movb	%a, %a\n" ireg8 src addressing addr
       else begin
         fprintf oc "	movl	%a, %%ecx\n" ireg src;
-        fprintf oc "	movb	%%cl, 0(%a)\n" ireg addr
+        fprintf oc "	movb	%%cl, %a\n" addressing addr
       end
-  | (Mint16signed | Mint16unsigned), [IR addr; IR src] ->
+  | (Mint16signed | Mint16unsigned), IR src ->
       if Asmgen.low_ireg src then
-        fprintf oc "	movw	%a, 0(%a)\n" ireg16 src ireg addr
+        fprintf oc "	movw	%a, %a\n" ireg16 src addressing addr
       else begin
         fprintf oc "	movl	%a, %%ecx\n" ireg src;
-        fprintf oc "	movw	%%cx, 0(%a)\n" ireg addr
+        fprintf oc "	movw	%%cx, %a\n" addressing addr
       end
-  | Mint32, [IR addr; IR src] ->
-      fprintf oc "	movl	%a, 0(%a)\n" ireg src ireg addr
-  | Mfloat32, [IR addr; FR src] ->
+  | Mint32, IR src ->
+      fprintf oc "	movl	%a, %a\n" ireg src addressing addr
+  | Mfloat32, FR src ->
       fprintf oc "	cvtsd2ss %a, %%xmm7\n" freg src;
-      fprintf oc "	movss	%%xmm7, 0(%a)\n" ireg addr
-  | Mfloat64, [IR addr; FR src] ->
-      fprintf oc "	movsd	%a, 0(%a)\n" freg src ireg addr
+      fprintf oc "	movss	%%xmm7, %a\n" addressing addr
+  | Mfloat64, FR src ->
+      fprintf oc "	movsd	%a, %a\n" freg src addressing addr
+  | _ ->
+      assert false
+
+let print_builtin_vstore oc chunk args =
+  fprintf oc "%s begin builtin __builtin_volatile_write\n" comment;
+  begin match args with
+  | [IR addr; src] ->
+      print_builtin_vstore_common oc chunk
+                 (Addrmode(Some addr, None, Coq_inl Integers.Int.zero)) src
+  | _ ->
+      assert false
+  end;
+  fprintf oc "%s end builtin __builtin_volatile_write\n" comment
+
+let print_builtin_vstore_global oc chunk id ofs args =
+  fprintf oc "%s begin builtin __builtin_volatile_write\n" comment;
+  begin match args with
+  | [src] ->
+      print_builtin_vstore_common oc chunk
+                       (Addrmode(None, None, Coq_inr(id,ofs))) src
   | _ ->
       assert false
   end;
@@ -677,6 +710,10 @@ let print_instruction oc = function
           print_builtin_vload oc chunk args res
       | EF_vstore chunk ->
           print_builtin_vstore oc chunk args
+      | EF_vload_global(chunk, id, ofs) ->
+          print_builtin_vload_global oc chunk id ofs args res
+      | EF_vstore_global(chunk, id, ofs) ->
+          print_builtin_vstore_global oc chunk id ofs args
       | EF_memcpy(sz, al) ->
           print_builtin_memcpy oc (Int32.to_int (camlint_of_coqint sz))
                                   (Int32.to_int (camlint_of_coqint al)) args