Hook for MPPA_K1c (generates Risc-V code for now)

1 files changed, 1219 insertions, 0 deletions

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+(* *********************************************************************)
+(*                                                                     *)
+(*              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.                                       *)
+(*                                                                     *)
+(* *********************************************************************)
+
+(** Instruction selection for operators *)
+
+(** The instruction selection pass recognizes opportunities for using
+  combined arithmetic and logical operations and addressing modes
+  offered by the target processor.  For instance, the expression [x + 1]
+  can take advantage of the "immediate add" instruction of the processor,
+  and on the PowerPC, the expression [(x >> 6) & 0xFF] can be turned
+  into a "rotate and mask" instruction.
+
+  This file defines functions for building CminorSel expressions and
+  statements, especially expressions consisting of operator
+  applications.  These functions examine their arguments to choose
+  cheaper forms of operators whenever possible.
+
+  For instance, [add e1 e2] will return a CminorSel expression semantically
+  equivalent to [Eop Oadd (e1 ::: e2 ::: Enil)], but will use a
+  [Oaddimm] operator if one of the arguments is an integer constant,
+  or suppress the addition altogether if one of the arguments is the
+  null integer.  In passing, we perform operator reassociation
+  ([(e + c1) * c2] becomes [(e * c2) + (c1 * c2)]) and a small amount
+  of constant propagation.
+
+  On top of the "smart constructor" functions defined below,
+  module [Selection] implements the actual instruction selection pass.
+*)
+
+Require Archi.
+Require Import Coqlib.
+Require Import Compopts.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Op.
+Require Import CminorSel.
+
+Local Open Scope cminorsel_scope.
+
+(** ** Constants **)
+
+Definition addrsymbol (id: ident) (ofs: ptrofs) :=
+  Eop (Oaddrsymbol id ofs) Enil.
+
+Definition addrstack (ofs: ptrofs) :=
+  Eop (Oaddrstack ofs) Enil.
+
+(** ** Integer addition and pointer addition *)
+
+(** Original definition:
+<<
+Nondetfunction addimm (n: int) (e: expr) :=
+  if Int.eq n Int.zero then e else
+  match e with
+  | Eop (Ointconst m) Enil => Eop (Ointconst (Int.add n m)) Enil
+  | Eop (Oaddrsymbol s m) Enil   => Eop (Oaddrsymbol s (Ptrofs.add (Ptrofs.of_int n) m)) Enil
+  | Eop (Oaddrstack m) Enil      => Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n) m)) Enil
+  | Eop (Oaddimm m) (t ::: Enil) => Eop (Oaddimm(Int.add n m)) (t ::: Enil)
+  | _ => Eop (Oaddimm n) (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive addimm_cases: forall (e: expr), Type :=
+  | addimm_case1: forall m, addimm_cases (Eop (Ointconst m) Enil)
+  | addimm_case2: forall s m, addimm_cases (Eop (Oaddrsymbol s m) Enil)
+  | addimm_case3: forall m, addimm_cases (Eop (Oaddrstack m) Enil)
+  | addimm_case4: forall m t, addimm_cases (Eop (Oaddimm m) (t ::: Enil))
+  | addimm_default: forall (e: expr), addimm_cases e.
+
+Definition addimm_match (e: expr) :=
+  match e as zz1 return addimm_cases zz1 with
+  | Eop (Ointconst m) Enil => addimm_case1 m
+  | Eop (Oaddrsymbol s m) Enil => addimm_case2 s m
+  | Eop (Oaddrstack m) Enil => addimm_case3 m
+  | Eop (Oaddimm m) (t ::: Enil) => addimm_case4 m t
+  | e => addimm_default e
+  end.
+
+Definition addimm (n: int) (e: expr) :=
+ if Int.eq n Int.zero then e else match addimm_match e with
+  | addimm_case1 m => (* Eop (Ointconst m) Enil *) 
+      Eop (Ointconst (Int.add n m)) Enil
+  | addimm_case2 s m => (* Eop (Oaddrsymbol s m) Enil *) 
+      Eop (Oaddrsymbol s (Ptrofs.add (Ptrofs.of_int n) m)) Enil
+  | addimm_case3 m => (* Eop (Oaddrstack m) Enil *) 
+      Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n) m)) Enil
+  | addimm_case4 m t => (* Eop (Oaddimm m) (t ::: Enil) *) 
+      Eop (Oaddimm(Int.add n m)) (t ::: Enil)
+  | addimm_default e =>
+      Eop (Oaddimm n) (e ::: Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction add (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 => addimm n1 t2
+  | t1, Eop (Ointconst n2) Enil => addimm n2 t1
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) =>
+      addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil))
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil =>
+      Eop Oadd (Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n1) n2)) Enil ::: t1 ::: Enil)
+  | Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) =>
+      Eop Oadd (Eop (Oaddrstack (Ptrofs.add n1 (Ptrofs.of_int n2))) Enil ::: t2 ::: Enil)
+  | Eop (Oaddimm n1) (t1:::Enil), t2 =>
+      addimm n1 (Eop Oadd (t1:::t2:::Enil))
+  | t1, Eop (Oaddimm n2) (t2:::Enil) =>
+      addimm n2 (Eop Oadd (t1:::t2:::Enil))
+  | _, _ => Eop Oadd (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive add_cases: forall (e1: expr) (e2: expr), Type :=
+  | add_case1: forall n1 t2, add_cases (Eop (Ointconst n1) Enil) (t2)
+  | add_case2: forall t1 n2, add_cases (t1) (Eop (Ointconst n2) Enil)
+  | add_case3: forall n1 t1 n2 t2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil))
+  | add_case4: forall n1 t1 n2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddrstack n2) Enil)
+  | add_case5: forall n1 n2 t2, add_cases (Eop (Oaddrstack n1) Enil) (Eop (Oaddimm n2) (t2:::Enil))
+  | add_case6: forall n1 t1 t2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (t2)
+  | add_case7: forall t1 n2 t2, add_cases (t1) (Eop (Oaddimm n2) (t2:::Enil))
+  | add_default: forall (e1: expr) (e2: expr), add_cases e1 e2.
+
+Definition add_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return add_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => add_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => add_case2 t1 n2
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => add_case3 n1 t1 n2 t2
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil => add_case4 n1 t1 n2
+  | Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) => add_case5 n1 n2 t2
+  | Eop (Oaddimm n1) (t1:::Enil), t2 => add_case6 n1 t1 t2
+  | t1, Eop (Oaddimm n2) (t2:::Enil) => add_case7 t1 n2 t2
+  | e1, e2 => add_default e1 e2
+  end.
+
+Definition add (e1: expr) (e2: expr) :=
+  match add_match e1 e2 with
+  | add_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      addimm n1 t2
+  | add_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      addimm n2 t1
+  | add_case3 n1 t1 n2 t2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) *) 
+      addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil))
+  | add_case4 n1 t1 n2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil *) 
+      Eop Oadd (Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n1) n2)) Enil ::: t1 ::: Enil)
+  | add_case5 n1 n2 t2 => (* Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) *) 
+      Eop Oadd (Eop (Oaddrstack (Ptrofs.add n1 (Ptrofs.of_int n2))) Enil ::: t2 ::: Enil)
+  | add_case6 n1 t1 t2 => (* Eop (Oaddimm n1) (t1:::Enil), t2 *) 
+      addimm n1 (Eop Oadd (t1:::t2:::Enil))
+  | add_case7 t1 n2 t2 => (* t1, Eop (Oaddimm n2) (t2:::Enil) *) 
+      addimm n2 (Eop Oadd (t1:::t2:::Enil))
+  | add_default e1 e2 =>
+      Eop Oadd (e1:::e2:::Enil)
+  end.
+
+
+(** ** Integer and pointer subtraction *)
+
+(** Original definition:
+<<
+Nondetfunction sub (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | t1, Eop (Ointconst n2) Enil =>
+      addimm (Int.neg n2) t1
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) =>
+      addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil))
+  | Eop (Oaddimm n1) (t1:::Enil), t2 =>
+      addimm n1 (Eop Osub (t1:::t2:::Enil))
+  | t1, Eop (Oaddimm n2) (t2:::Enil) =>
+      addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil))
+  | _, _ => Eop Osub (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive sub_cases: forall (e1: expr) (e2: expr), Type :=
+  | sub_case1: forall t1 n2, sub_cases (t1) (Eop (Ointconst n2) Enil)
+  | sub_case2: forall n1 t1 n2 t2, sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil))
+  | sub_case3: forall n1 t1 t2, sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (t2)
+  | sub_case4: forall t1 n2 t2, sub_cases (t1) (Eop (Oaddimm n2) (t2:::Enil))
+  | sub_default: forall (e1: expr) (e2: expr), sub_cases e1 e2.
+
+Definition sub_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return sub_cases zz1 zz2 with
+  | t1, Eop (Ointconst n2) Enil => sub_case1 t1 n2
+  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => sub_case2 n1 t1 n2 t2
+  | Eop (Oaddimm n1) (t1:::Enil), t2 => sub_case3 n1 t1 t2
+  | t1, Eop (Oaddimm n2) (t2:::Enil) => sub_case4 t1 n2 t2
+  | e1, e2 => sub_default e1 e2
+  end.
+
+Definition sub (e1: expr) (e2: expr) :=
+  match sub_match e1 e2 with
+  | sub_case1 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      addimm (Int.neg n2) t1
+  | sub_case2 n1 t1 n2 t2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) *) 
+      addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil))
+  | sub_case3 n1 t1 t2 => (* Eop (Oaddimm n1) (t1:::Enil), t2 *) 
+      addimm n1 (Eop Osub (t1:::t2:::Enil))
+  | sub_case4 t1 n2 t2 => (* t1, Eop (Oaddimm n2) (t2:::Enil) *) 
+      addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil))
+  | sub_default e1 e2 =>
+      Eop Osub (e1:::e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction negint (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.neg n)) Enil
+  | _ => Eop Oneg (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive negint_cases: forall (e: expr), Type :=
+  | negint_case1: forall n, negint_cases (Eop (Ointconst n) Enil)
+  | negint_default: forall (e: expr), negint_cases e.
+
+Definition negint_match (e: expr) :=
+  match e as zz1 return negint_cases zz1 with
+  | Eop (Ointconst n) Enil => negint_case1 n
+  | e => negint_default e
+  end.
+
+Definition negint (e: expr) :=
+  match negint_match e with
+  | negint_case1 n => (* Eop (Ointconst n) Enil *) 
+      Eop (Ointconst (Int.neg n)) Enil
+  | negint_default e =>
+      Eop Oneg (e ::: Enil)
+  end.
+
+
+(** ** Immediate shifts *)
+
+(** Original definition:
+<<
+Nondetfunction shlimm (e1: expr) (n: int) :=
+  if Int.eq n Int.zero then
+    e1
+  else if negb (Int.ltu n Int.iwordsize) then
+    Eop Oshl (e1 ::: Eop (Ointconst n) Enil ::: Enil)
+  else match e1 with
+    | Eop (Ointconst n1) Enil =>
+        Eop (Ointconst (Int.shl n1 n)) Enil
+    | Eop (Oshlimm n1) (t1:::Enil) =>
+        if Int.ltu (Int.add n n1) Int.iwordsize
+        then Eop (Oshlimm (Int.add n n1)) (t1:::Enil)
+        else Eop (Oshlimm n) (e1:::Enil)
+    | _ =>
+        Eop (Oshlimm n) (e1:::Enil)
+  end.
+>>
+*)
+
+Inductive shlimm_cases: forall (e1: expr) , Type :=
+  | shlimm_case1: forall n1, shlimm_cases (Eop (Ointconst n1) Enil)
+  | shlimm_case2: forall n1 t1, shlimm_cases (Eop (Oshlimm n1) (t1:::Enil))
+  | shlimm_default: forall (e1: expr) , shlimm_cases e1.
+
+Definition shlimm_match (e1: expr)  :=
+  match e1 as zz1 return shlimm_cases zz1 with
+  | Eop (Ointconst n1) Enil => shlimm_case1 n1
+  | Eop (Oshlimm n1) (t1:::Enil) => shlimm_case2 n1 t1
+  | e1 => shlimm_default e1
+  end.
+
+Definition shlimm (e1: expr) (n: int) :=
+ if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshl (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shlimm_match e1 with
+  | shlimm_case1 n1 => (* Eop (Ointconst n1) Enil *) 
+      Eop (Ointconst (Int.shl n1 n)) Enil
+  | shlimm_case2 n1 t1 => (* Eop (Oshlimm n1) (t1:::Enil) *) 
+      if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshlimm (Int.add n n1)) (t1:::Enil) else Eop (Oshlimm n) (e1:::Enil)
+  | shlimm_default e1 =>
+      Eop (Oshlimm n) (e1:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction shruimm (e1: expr) (n: int) :=
+  if Int.eq n Int.zero then
+    e1
+  else if negb (Int.ltu n Int.iwordsize) then
+    Eop Oshru (e1 ::: Eop (Ointconst n) Enil ::: Enil)
+  else match e1 with
+    | Eop (Ointconst n1) Enil =>
+        Eop (Ointconst (Int.shru n1 n)) Enil
+    | Eop (Oshruimm n1) (t1:::Enil) =>
+        if Int.ltu (Int.add n n1) Int.iwordsize
+        then Eop (Oshruimm (Int.add n n1)) (t1:::Enil)
+        else Eop (Oshruimm n) (e1:::Enil)
+    | _ =>
+        Eop (Oshruimm n) (e1:::Enil)
+    end.
+>>
+*)
+
+Inductive shruimm_cases: forall (e1: expr) , Type :=
+  | shruimm_case1: forall n1, shruimm_cases (Eop (Ointconst n1) Enil)
+  | shruimm_case2: forall n1 t1, shruimm_cases (Eop (Oshruimm n1) (t1:::Enil))
+  | shruimm_default: forall (e1: expr) , shruimm_cases e1.
+
+Definition shruimm_match (e1: expr)  :=
+  match e1 as zz1 return shruimm_cases zz1 with
+  | Eop (Ointconst n1) Enil => shruimm_case1 n1
+  | Eop (Oshruimm n1) (t1:::Enil) => shruimm_case2 n1 t1
+  | e1 => shruimm_default e1
+  end.
+
+Definition shruimm (e1: expr) (n: int) :=
+ if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshru (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shruimm_match e1 with
+  | shruimm_case1 n1 => (* Eop (Ointconst n1) Enil *) 
+      Eop (Ointconst (Int.shru n1 n)) Enil
+  | shruimm_case2 n1 t1 => (* Eop (Oshruimm n1) (t1:::Enil) *) 
+      if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshruimm (Int.add n n1)) (t1:::Enil) else Eop (Oshruimm n) (e1:::Enil)
+  | shruimm_default e1 =>
+      Eop (Oshruimm n) (e1:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction shrimm (e1: expr) (n: int) :=
+  if Int.eq n Int.zero then
+    e1
+  else if negb (Int.ltu n Int.iwordsize) then
+    Eop Oshr (e1 ::: Eop (Ointconst n) Enil ::: Enil)
+  else match e1 with
+    | Eop (Ointconst n1) Enil =>
+        Eop (Ointconst (Int.shr n1 n)) Enil
+    | Eop (Oshrimm n1) (t1:::Enil) =>
+        if Int.ltu (Int.add n n1) Int.iwordsize
+        then Eop (Oshrimm (Int.add n n1)) (t1:::Enil)
+        else Eop (Oshrimm n) (e1:::Enil)
+    | _ =>
+        Eop (Oshrimm n) (e1:::Enil)
+    end.
+>>
+*)
+
+Inductive shrimm_cases: forall (e1: expr) , Type :=
+  | shrimm_case1: forall n1, shrimm_cases (Eop (Ointconst n1) Enil)
+  | shrimm_case2: forall n1 t1, shrimm_cases (Eop (Oshrimm n1) (t1:::Enil))
+  | shrimm_default: forall (e1: expr) , shrimm_cases e1.
+
+Definition shrimm_match (e1: expr)  :=
+  match e1 as zz1 return shrimm_cases zz1 with
+  | Eop (Ointconst n1) Enil => shrimm_case1 n1
+  | Eop (Oshrimm n1) (t1:::Enil) => shrimm_case2 n1 t1
+  | e1 => shrimm_default e1
+  end.
+
+Definition shrimm (e1: expr) (n: int) :=
+ if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshr (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shrimm_match e1 with
+  | shrimm_case1 n1 => (* Eop (Ointconst n1) Enil *) 
+      Eop (Ointconst (Int.shr n1 n)) Enil
+  | shrimm_case2 n1 t1 => (* Eop (Oshrimm n1) (t1:::Enil) *) 
+      if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshrimm (Int.add n n1)) (t1:::Enil) else Eop (Oshrimm n) (e1:::Enil)
+  | shrimm_default e1 =>
+      Eop (Oshrimm n) (e1:::Enil)
+  end.
+
+
+(** ** Integer multiply *)
+
+Definition mulimm_base (n1: int) (e2: expr) :=
+  match Int.one_bits n1 with
+  | i :: nil =>
+      shlimm e2 i
+  | i :: j :: nil =>
+      Elet e2 (add (shlimm (Eletvar 0) i) (shlimm (Eletvar 0) j))
+  | _ =>
+      Eop Omul (Eop (Ointconst n1) Enil ::: e2 ::: Enil)
+  end.
+
+(** Original definition:
+<<
+Nondetfunction mulimm (n1: int) (e2: expr) :=
+  if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil
+  else if Int.eq n1 Int.one then e2
+  else match e2 with
+  | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.mul n1 n2)) Enil
+  | Eop (Oaddimm n2) (t2:::Enil) => addimm (Int.mul n1 n2) (mulimm_base n1 t2)
+  | _ => mulimm_base n1 e2
+  end.
+>>
+*)
+
+Inductive mulimm_cases: forall (e2: expr), Type :=
+  | mulimm_case1: forall n2, mulimm_cases (Eop (Ointconst n2) Enil)
+  | mulimm_case2: forall n2 t2, mulimm_cases (Eop (Oaddimm n2) (t2:::Enil))
+  | mulimm_default: forall (e2: expr), mulimm_cases e2.
+
+Definition mulimm_match (e2: expr) :=
+  match e2 as zz1 return mulimm_cases zz1 with
+  | Eop (Ointconst n2) Enil => mulimm_case1 n2
+  | Eop (Oaddimm n2) (t2:::Enil) => mulimm_case2 n2 t2
+  | e2 => mulimm_default e2
+  end.
+
+Definition mulimm (n1: int) (e2: expr) :=
+ if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else if Int.eq n1 Int.one then e2 else match mulimm_match e2 with
+  | mulimm_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      Eop (Ointconst (Int.mul n1 n2)) Enil
+  | mulimm_case2 n2 t2 => (* Eop (Oaddimm n2) (t2:::Enil) *) 
+      addimm (Int.mul n1 n2) (mulimm_base n1 t2)
+  | mulimm_default e2 =>
+      mulimm_base n1 e2
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction mul (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 => mulimm n1 t2
+  | t1, Eop (Ointconst n2) Enil => mulimm n2 t1
+  | _, _ => Eop Omul (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive mul_cases: forall (e1: expr) (e2: expr), Type :=
+  | mul_case1: forall n1 t2, mul_cases (Eop (Ointconst n1) Enil) (t2)
+  | mul_case2: forall t1 n2, mul_cases (t1) (Eop (Ointconst n2) Enil)
+  | mul_default: forall (e1: expr) (e2: expr), mul_cases e1 e2.
+
+Definition mul_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return mul_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => mul_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => mul_case2 t1 n2
+  | e1, e2 => mul_default e1 e2
+  end.
+
+Definition mul (e1: expr) (e2: expr) :=
+  match mul_match e1 e2 with
+  | mul_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      mulimm n1 t2
+  | mul_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      mulimm n2 t1
+  | mul_default e1 e2 =>
+      Eop Omul (e1:::e2:::Enil)
+  end.
+
+
+Definition mulhs (e1: expr) (e2: expr) :=
+  if Archi.ptr64 then
+    Eop Olowlong
+      (Eop (Oshrlimm (Int.repr 32))
+         (Eop Omull (Eop Ocast32signed (e1 ::: Enil) :::
+                     Eop Ocast32signed (e2 ::: Enil) ::: Enil) ::: Enil)
+          ::: Enil)
+  else
+    Eop Omulhs (e1 ::: e2 ::: Enil).
+
+Definition mulhu (e1: expr) (e2: expr) :=
+  if Archi.ptr64 then
+    Eop Olowlong
+      (Eop (Oshrluimm (Int.repr 32))
+         (Eop Omull (Eop Ocast32unsigned (e1 ::: Enil) :::
+                     Eop Ocast32unsigned (e2 ::: Enil) ::: Enil) ::: Enil)
+          ::: Enil)
+  else
+    Eop Omulhu (e1 ::: e2 ::: Enil).
+
+(** ** Bitwise and, or, xor *)
+
+(** Original definition:
+<<
+Nondetfunction andimm (n1: int) (e2: expr) :=
+  if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil
+  else if Int.eq n1 Int.mone then e2
+  else match e2 with
+  | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.and n1 n2)) Enil
+  | Eop (Oandimm n2) (t2:::Enil) => Eop (Oandimm (Int.and n1 n2)) (t2:::Enil)
+  | _ => Eop (Oandimm n1) (e2:::Enil)
+  end.
+>>
+*)
+
+Inductive andimm_cases: forall (e2: expr), Type :=
+  | andimm_case1: forall n2, andimm_cases (Eop (Ointconst n2) Enil)
+  | andimm_case2: forall n2 t2, andimm_cases (Eop (Oandimm n2) (t2:::Enil))
+  | andimm_default: forall (e2: expr), andimm_cases e2.
+
+Definition andimm_match (e2: expr) :=
+  match e2 as zz1 return andimm_cases zz1 with
+  | Eop (Ointconst n2) Enil => andimm_case1 n2
+  | Eop (Oandimm n2) (t2:::Enil) => andimm_case2 n2 t2
+  | e2 => andimm_default e2
+  end.
+
+Definition andimm (n1: int) (e2: expr) :=
+ if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else if Int.eq n1 Int.mone then e2 else match andimm_match e2 with
+  | andimm_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      Eop (Ointconst (Int.and n1 n2)) Enil
+  | andimm_case2 n2 t2 => (* Eop (Oandimm n2) (t2:::Enil) *) 
+      Eop (Oandimm (Int.and n1 n2)) (t2:::Enil)
+  | andimm_default e2 =>
+      Eop (Oandimm n1) (e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction and (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 => andimm n1 t2
+  | t1, Eop (Ointconst n2) Enil => andimm n2 t1
+  | _, _ => Eop Oand (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive and_cases: forall (e1: expr) (e2: expr), Type :=
+  | and_case1: forall n1 t2, and_cases (Eop (Ointconst n1) Enil) (t2)
+  | and_case2: forall t1 n2, and_cases (t1) (Eop (Ointconst n2) Enil)
+  | and_default: forall (e1: expr) (e2: expr), and_cases e1 e2.
+
+Definition and_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return and_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => and_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => and_case2 t1 n2
+  | e1, e2 => and_default e1 e2
+  end.
+
+Definition and (e1: expr) (e2: expr) :=
+  match and_match e1 e2 with
+  | and_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      andimm n1 t2
+  | and_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      andimm n2 t1
+  | and_default e1 e2 =>
+      Eop Oand (e1:::e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction orimm (n1: int) (e2: expr) :=
+  if Int.eq n1 Int.zero then e2
+  else if Int.eq n1 Int.mone then Eop (Ointconst Int.mone) Enil
+  else match e2 with
+       | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.or n1 n2)) Enil
+       | Eop (Oorimm n2) (t2:::Enil) => Eop (Oorimm (Int.or n1 n2)) (t2:::Enil)
+       | _ => Eop (Oorimm n1) (e2:::Enil)
+  end.
+>>
+*)
+
+Inductive orimm_cases: forall (e2: expr), Type :=
+  | orimm_case1: forall n2, orimm_cases (Eop (Ointconst n2) Enil)
+  | orimm_case2: forall n2 t2, orimm_cases (Eop (Oorimm n2) (t2:::Enil))
+  | orimm_default: forall (e2: expr), orimm_cases e2.
+
+Definition orimm_match (e2: expr) :=
+  match e2 as zz1 return orimm_cases zz1 with
+  | Eop (Ointconst n2) Enil => orimm_case1 n2
+  | Eop (Oorimm n2) (t2:::Enil) => orimm_case2 n2 t2
+  | e2 => orimm_default e2
+  end.
+
+Definition orimm (n1: int) (e2: expr) :=
+ if Int.eq n1 Int.zero then e2 else if Int.eq n1 Int.mone then Eop (Ointconst Int.mone) Enil else match orimm_match e2 with
+  | orimm_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      Eop (Ointconst (Int.or n1 n2)) Enil
+  | orimm_case2 n2 t2 => (* Eop (Oorimm n2) (t2:::Enil) *) 
+      Eop (Oorimm (Int.or n1 n2)) (t2:::Enil)
+  | orimm_default e2 =>
+      Eop (Oorimm n1) (e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction or (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 => orimm n1 t2
+  | t1, Eop (Ointconst n2) Enil => orimm n2 t1
+  | _, _ => Eop Oor (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive or_cases: forall (e1: expr) (e2: expr), Type :=
+  | or_case1: forall n1 t2, or_cases (Eop (Ointconst n1) Enil) (t2)
+  | or_case2: forall t1 n2, or_cases (t1) (Eop (Ointconst n2) Enil)
+  | or_default: forall (e1: expr) (e2: expr), or_cases e1 e2.
+
+Definition or_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return or_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => or_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => or_case2 t1 n2
+  | e1, e2 => or_default e1 e2
+  end.
+
+Definition or (e1: expr) (e2: expr) :=
+  match or_match e1 e2 with
+  | or_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      orimm n1 t2
+  | or_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      orimm n2 t1
+  | or_default e1 e2 =>
+      Eop Oor (e1:::e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction xorimm (n1: int) (e2: expr) :=
+  if Int.eq n1 Int.zero then e2 else
+  match e2 with
+  | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.xor n1 n2)) Enil
+  | Eop (Oxorimm n2) (t2:::Enil) =>
+      let n := Int.xor n1 n2 in
+      if Int.eq n Int.zero then t2 else Eop (Oxorimm n) (t2:::Enil)
+  | _ => Eop (Oxorimm n1) (e2:::Enil)
+  end.
+>>
+*)
+
+Inductive xorimm_cases: forall (e2: expr), Type :=
+  | xorimm_case1: forall n2, xorimm_cases (Eop (Ointconst n2) Enil)
+  | xorimm_case2: forall n2 t2, xorimm_cases (Eop (Oxorimm n2) (t2:::Enil))
+  | xorimm_default: forall (e2: expr), xorimm_cases e2.
+
+Definition xorimm_match (e2: expr) :=
+  match e2 as zz1 return xorimm_cases zz1 with
+  | Eop (Ointconst n2) Enil => xorimm_case1 n2
+  | Eop (Oxorimm n2) (t2:::Enil) => xorimm_case2 n2 t2
+  | e2 => xorimm_default e2
+  end.
+
+Definition xorimm (n1: int) (e2: expr) :=
+ if Int.eq n1 Int.zero then e2 else match xorimm_match e2 with
+  | xorimm_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      Eop (Ointconst (Int.xor n1 n2)) Enil
+  | xorimm_case2 n2 t2 => (* Eop (Oxorimm n2) (t2:::Enil) *) 
+      let n := Int.xor n1 n2 in if Int.eq n Int.zero then t2 else Eop (Oxorimm n) (t2:::Enil)
+  | xorimm_default e2 =>
+      Eop (Oxorimm n1) (e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction xor (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 => xorimm n1 t2
+  | t1, Eop (Ointconst n2) Enil => xorimm n2 t1
+  | _, _ => Eop Oxor (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive xor_cases: forall (e1: expr) (e2: expr), Type :=
+  | xor_case1: forall n1 t2, xor_cases (Eop (Ointconst n1) Enil) (t2)
+  | xor_case2: forall t1 n2, xor_cases (t1) (Eop (Ointconst n2) Enil)
+  | xor_default: forall (e1: expr) (e2: expr), xor_cases e1 e2.
+
+Definition xor_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return xor_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => xor_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => xor_case2 t1 n2
+  | e1, e2 => xor_default e1 e2
+  end.
+
+Definition xor (e1: expr) (e2: expr) :=
+  match xor_match e1 e2 with
+  | xor_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      xorimm n1 t2
+  | xor_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      xorimm n2 t1
+  | xor_default e1 e2 =>
+      Eop Oxor (e1:::e2:::Enil)
+  end.
+
+
+(** ** Integer logical negation *)
+
+Definition notint (e: expr) := xorimm Int.mone e.
+
+(** ** Integer division and modulus *)
+
+Definition divs_base (e1: expr) (e2: expr) := Eop Odiv (e1:::e2:::Enil).
+Definition mods_base (e1: expr) (e2: expr) := Eop Omod (e1:::e2:::Enil).
+Definition divu_base (e1: expr) (e2: expr) := Eop Odivu (e1:::e2:::Enil).
+Definition modu_base (e1: expr) (e2: expr) := Eop Omodu (e1:::e2:::Enil).
+
+Definition shrximm (e1: expr) (n2: int) :=
+  if Int.eq n2 Int.zero then e1 else Eop (Oshrximm n2) (e1:::Enil).
+
+(* Alternate definition, not convenient for strength reduction during constant propagation *)
+(*
+(* n2 will be less than 31. *)
+
+Definition shrximm_inner (e1: expr) (n2: int) :=
+  Eop (Oshruimm (Int.sub Int.iwordsize n2))
+      ((Eop (Oshrimm (Int.repr (Int.zwordsize - 1)))
+            (e1 ::: Enil))
+         ::: Enil).
+
+Definition shrximm (e1: expr) (n2: int) :=
+  if Int.eq n2 Int.zero then e1
+  else Eop (Oshrimm n2)
+           ((Eop Oadd (e1 ::: shrximm_inner e1 n2 ::: Enil))
+              ::: Enil).
+*)
+
+(** ** General shifts *)
+
+(** Original definition:
+<<
+Nondetfunction shl (e1: expr) (e2: expr) :=
+  match e2 with
+  | Eop (Ointconst n2) Enil => shlimm e1 n2
+  | _ => Eop Oshl (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive shl_cases: forall (e2: expr), Type :=
+  | shl_case1: forall n2, shl_cases (Eop (Ointconst n2) Enil)
+  | shl_default: forall (e2: expr), shl_cases e2.
+
+Definition shl_match (e2: expr) :=
+  match e2 as zz1 return shl_cases zz1 with
+  | Eop (Ointconst n2) Enil => shl_case1 n2
+  | e2 => shl_default e2
+  end.
+
+Definition shl (e1: expr) (e2: expr) :=
+  match shl_match e2 with
+  | shl_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      shlimm e1 n2
+  | shl_default e2 =>
+      Eop Oshl (e1:::e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction shr (e1: expr) (e2: expr) :=
+  match e2 with
+  | Eop (Ointconst n2) Enil => shrimm e1 n2
+  | _ => Eop Oshr (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive shr_cases: forall (e2: expr), Type :=
+  | shr_case1: forall n2, shr_cases (Eop (Ointconst n2) Enil)
+  | shr_default: forall (e2: expr), shr_cases e2.
+
+Definition shr_match (e2: expr) :=
+  match e2 as zz1 return shr_cases zz1 with
+  | Eop (Ointconst n2) Enil => shr_case1 n2
+  | e2 => shr_default e2
+  end.
+
+Definition shr (e1: expr) (e2: expr) :=
+  match shr_match e2 with
+  | shr_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      shrimm e1 n2
+  | shr_default e2 =>
+      Eop Oshr (e1:::e2:::Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction shru (e1: expr) (e2: expr) :=
+  match e2 with
+  | Eop (Ointconst n2) Enil => shruimm e1 n2
+  | _ => Eop Oshru (e1:::e2:::Enil)
+  end.
+>>
+*)
+
+Inductive shru_cases: forall (e2: expr), Type :=
+  | shru_case1: forall n2, shru_cases (Eop (Ointconst n2) Enil)
+  | shru_default: forall (e2: expr), shru_cases e2.
+
+Definition shru_match (e2: expr) :=
+  match e2 as zz1 return shru_cases zz1 with
+  | Eop (Ointconst n2) Enil => shru_case1 n2
+  | e2 => shru_default e2
+  end.
+
+Definition shru (e1: expr) (e2: expr) :=
+  match shru_match e2 with
+  | shru_case1 n2 => (* Eop (Ointconst n2) Enil *) 
+      shruimm e1 n2
+  | shru_default e2 =>
+      Eop Oshru (e1:::e2:::Enil)
+  end.
+
+
+(** ** Floating-point arithmetic *)
+
+Definition negf (e: expr) :=  Eop Onegf (e ::: Enil).
+Definition absf (e: expr) :=  Eop Oabsf (e ::: Enil).
+Definition addf (e1 e2: expr) :=  Eop Oaddf (e1 ::: e2 ::: Enil).
+Definition subf (e1 e2: expr) :=  Eop Osubf (e1 ::: e2 ::: Enil).
+Definition mulf (e1 e2: expr) :=  Eop Omulf (e1 ::: e2 ::: Enil).
+
+Definition negfs (e: expr) :=  Eop Onegfs (e ::: Enil).
+Definition absfs (e: expr) :=  Eop Oabsfs (e ::: Enil).
+Definition addfs (e1 e2: expr) :=  Eop Oaddfs (e1 ::: e2 ::: Enil).
+Definition subfs (e1 e2: expr) :=  Eop Osubfs (e1 ::: e2 ::: Enil).
+Definition mulfs (e1 e2: expr) :=  Eop Omulfs (e1 ::: e2 ::: Enil).
+
+(** ** Comparisons *)
+
+(** Original definition:
+<<
+Nondetfunction compimm (default: comparison -> int -> condition)
+                       (sem: comparison -> int -> int -> bool)
+                       (c: comparison) (e1: expr) (n2: int) :=
+  match c, e1 with
+  | c, Eop (Ointconst n1) Enil =>
+      Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil
+  | Ceq, Eop (Ocmp c) el =>
+      if Int.eq_dec n2 Int.zero then
+        Eop (Ocmp (negate_condition c)) el
+      else if Int.eq_dec n2 Int.one then
+        Eop (Ocmp c) el
+      else
+        Eop (Ointconst Int.zero) Enil
+  | Cne, Eop (Ocmp c) el =>
+      if Int.eq_dec n2 Int.zero then
+        Eop (Ocmp c) el
+      else if Int.eq_dec n2 Int.one then
+        Eop (Ocmp (negate_condition c)) el
+      else
+        Eop (Ointconst Int.one) Enil
+  | _, _ =>
+       Eop (Ocmp (default c n2)) (e1 ::: Enil)
+  end.
+>>
+*)
+
+Inductive compimm_cases: forall (c: comparison) (e1: expr) , Type :=
+  | compimm_case1: forall c n1, compimm_cases (c) (Eop (Ointconst n1) Enil)
+  | compimm_case2: forall c el, compimm_cases (Ceq) (Eop (Ocmp c) el)
+  | compimm_case3: forall c el, compimm_cases (Cne) (Eop (Ocmp c) el)
+  | compimm_default: forall (c: comparison) (e1: expr) , compimm_cases c e1.
+
+Definition compimm_match (c: comparison) (e1: expr)  :=
+  match c as zz1, e1 as zz2 return compimm_cases zz1 zz2 with
+  | c, Eop (Ointconst n1) Enil => compimm_case1 c n1
+  | Ceq, Eop (Ocmp c) el => compimm_case2 c el
+  | Cne, Eop (Ocmp c) el => compimm_case3 c el
+  | c, e1 => compimm_default c e1
+  end.
+
+Definition compimm (default: comparison -> int -> condition) (sem: comparison -> int -> int -> bool) (c: comparison) (e1: expr) (n2: int) :=
+  match compimm_match c e1 with
+  | compimm_case1 c n1 => (* c, Eop (Ointconst n1) Enil *) 
+      Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil
+  | compimm_case2 c el => (* Ceq, Eop (Ocmp c) el *) 
+      if Int.eq_dec n2 Int.zero then Eop (Ocmp (negate_condition c)) el else if Int.eq_dec n2 Int.one then Eop (Ocmp c) el else Eop (Ointconst Int.zero) Enil
+  | compimm_case3 c el => (* Cne, Eop (Ocmp c) el *) 
+      if Int.eq_dec n2 Int.zero then Eop (Ocmp c) el else if Int.eq_dec n2 Int.one then Eop (Ocmp (negate_condition c)) el else Eop (Ointconst Int.one) Enil
+  | compimm_default c e1 =>
+      Eop (Ocmp (default c n2)) (e1 ::: Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction comp (c: comparison) (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 =>
+      compimm Ccompimm Int.cmp (swap_comparison c) t2 n1
+  | t1, Eop (Ointconst n2) Enil =>
+      compimm Ccompimm Int.cmp c t1 n2
+  | _, _ =>
+      Eop (Ocmp (Ccomp c)) (e1 ::: e2 ::: Enil)
+  end.
+>>
+*)
+
+Inductive comp_cases: forall (e1: expr) (e2: expr), Type :=
+  | comp_case1: forall n1 t2, comp_cases (Eop (Ointconst n1) Enil) (t2)
+  | comp_case2: forall t1 n2, comp_cases (t1) (Eop (Ointconst n2) Enil)
+  | comp_default: forall (e1: expr) (e2: expr), comp_cases e1 e2.
+
+Definition comp_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return comp_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => comp_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => comp_case2 t1 n2
+  | e1, e2 => comp_default e1 e2
+  end.
+
+Definition comp (c: comparison) (e1: expr) (e2: expr) :=
+  match comp_match e1 e2 with
+  | comp_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      compimm Ccompimm Int.cmp (swap_comparison c) t2 n1
+  | comp_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      compimm Ccompimm Int.cmp c t1 n2
+  | comp_default e1 e2 =>
+      Eop (Ocmp (Ccomp c)) (e1 ::: e2 ::: Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction compu (c: comparison) (e1: expr) (e2: expr) :=
+  match e1, e2 with
+  | Eop (Ointconst n1) Enil, t2 =>
+      compimm Ccompuimm Int.cmpu (swap_comparison c) t2 n1
+  | t1, Eop (Ointconst n2) Enil =>
+      compimm Ccompuimm Int.cmpu c t1 n2
+  | _, _ =>
+      Eop (Ocmp (Ccompu c)) (e1 ::: e2 ::: Enil)
+  end.
+>>
+*)
+
+Inductive compu_cases: forall (e1: expr) (e2: expr), Type :=
+  | compu_case1: forall n1 t2, compu_cases (Eop (Ointconst n1) Enil) (t2)
+  | compu_case2: forall t1 n2, compu_cases (t1) (Eop (Ointconst n2) Enil)
+  | compu_default: forall (e1: expr) (e2: expr), compu_cases e1 e2.
+
+Definition compu_match (e1: expr) (e2: expr) :=
+  match e1 as zz1, e2 as zz2 return compu_cases zz1 zz2 with
+  | Eop (Ointconst n1) Enil, t2 => compu_case1 n1 t2
+  | t1, Eop (Ointconst n2) Enil => compu_case2 t1 n2
+  | e1, e2 => compu_default e1 e2
+  end.
+
+Definition compu (c: comparison) (e1: expr) (e2: expr) :=
+  match compu_match e1 e2 with
+  | compu_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) 
+      compimm Ccompuimm Int.cmpu (swap_comparison c) t2 n1
+  | compu_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) 
+      compimm Ccompuimm Int.cmpu c t1 n2
+  | compu_default e1 e2 =>
+      Eop (Ocmp (Ccompu c)) (e1 ::: e2 ::: Enil)
+  end.
+
+
+Definition compf (c: comparison) (e1: expr) (e2: expr) :=
+  Eop (Ocmp (Ccompf c)) (e1 ::: e2 ::: Enil).
+
+Definition compfs (c: comparison) (e1: expr) (e2: expr) :=
+  Eop (Ocmp (Ccompfs c)) (e1 ::: e2 ::: Enil).
+
+(** ** Integer conversions *)
+
+Definition cast8unsigned (e: expr) := andimm (Int.repr 255) e.
+
+(** Original definition:
+<<
+Nondetfunction cast8signed (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.sign_ext 8 n)) Enil
+  | _ =>  Eop Ocast8signed (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive cast8signed_cases: forall (e: expr), Type :=
+  | cast8signed_case1: forall n, cast8signed_cases (Eop (Ointconst n) Enil)
+  | cast8signed_default: forall (e: expr), cast8signed_cases e.
+
+Definition cast8signed_match (e: expr) :=
+  match e as zz1 return cast8signed_cases zz1 with
+  | Eop (Ointconst n) Enil => cast8signed_case1 n
+  | e => cast8signed_default e
+  end.
+
+Definition cast8signed (e: expr) :=
+  match cast8signed_match e with
+  | cast8signed_case1 n => (* Eop (Ointconst n) Enil *) 
+      Eop (Ointconst (Int.sign_ext 8 n)) Enil
+  | cast8signed_default e =>
+      Eop Ocast8signed (e ::: Enil)
+  end.
+
+
+Definition cast16unsigned (e: expr) := andimm (Int.repr 65535) e.
+
+(** Original definition:
+<<
+Nondetfunction cast16signed (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.sign_ext 16 n)) Enil
+  | _ => Eop Ocast16signed (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive cast16signed_cases: forall (e: expr), Type :=
+  | cast16signed_case1: forall n, cast16signed_cases (Eop (Ointconst n) Enil)
+  | cast16signed_default: forall (e: expr), cast16signed_cases e.
+
+Definition cast16signed_match (e: expr) :=
+  match e as zz1 return cast16signed_cases zz1 with
+  | Eop (Ointconst n) Enil => cast16signed_case1 n
+  | e => cast16signed_default e
+  end.
+
+Definition cast16signed (e: expr) :=
+  match cast16signed_match e with
+  | cast16signed_case1 n => (* Eop (Ointconst n) Enil *) 
+      Eop (Ointconst (Int.sign_ext 16 n)) Enil
+  | cast16signed_default e =>
+      Eop Ocast16signed (e ::: Enil)
+  end.
+
+
+(** ** Floating-point conversions *)
+
+Definition intoffloat  (e: expr) := Eop Ointoffloat (e ::: Enil).
+Definition intuoffloat (e: expr) := Eop Ointuoffloat (e ::: Enil).
+
+(** Original definition:
+<<
+Nondetfunction floatofintu (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_intu n)) Enil
+  | _ => Eop Ofloatofintu (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive floatofintu_cases: forall (e: expr), Type :=
+  | floatofintu_case1: forall n, floatofintu_cases (Eop (Ointconst n) Enil)
+  | floatofintu_default: forall (e: expr), floatofintu_cases e.
+
+Definition floatofintu_match (e: expr) :=
+  match e as zz1 return floatofintu_cases zz1 with
+  | Eop (Ointconst n) Enil => floatofintu_case1 n
+  | e => floatofintu_default e
+  end.
+
+Definition floatofintu (e: expr) :=
+  match floatofintu_match e with
+  | floatofintu_case1 n => (* Eop (Ointconst n) Enil *) 
+      Eop (Ofloatconst (Float.of_intu n)) Enil
+  | floatofintu_default e =>
+      Eop Ofloatofintu (e ::: Enil)
+  end.
+
+
+(** Original definition:
+<<
+Nondetfunction floatofint (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_int n)) Enil
+  | _ => Eop Ofloatofint (e ::: Enil)
+  end.
+>>
+*)
+
+Inductive floatofint_cases: forall (e: expr), Type :=
+  | floatofint_case1: forall n, floatofint_cases (Eop (Ointconst n) Enil)
+  | floatofint_default: forall (e: expr), floatofint_cases e.
+
+Definition floatofint_match (e: expr) :=
+  match e as zz1 return floatofint_cases zz1 with
+  | Eop (Ointconst n) Enil => floatofint_case1 n
+  | e => floatofint_default e
+  end.
+
+Definition floatofint (e: expr) :=
+  match floatofint_match e with
+  | floatofint_case1 n => (* Eop (Ointconst n) Enil *) 
+      Eop (Ofloatconst (Float.of_int n)) Enil
+  | floatofint_default e =>
+      Eop Ofloatofint (e ::: Enil)
+  end.
+
+
+Definition intofsingle (e: expr) := Eop Ointofsingle (e ::: Enil).
+Definition singleofint (e: expr) := Eop Osingleofint (e ::: Enil).
+
+Definition intuofsingle (e: expr) := Eop Ointuofsingle (e ::: Enil).
+Definition singleofintu (e: expr) := Eop Osingleofintu (e ::: Enil).
+
+Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil).
+Definition floatofsingle (e: expr) := Eop Ofloatofsingle (e ::: Enil).
+
+(** ** Recognition of addressing modes for load and store operations *)
+
+(** Original definition:
+<<
+Nondetfunction addressing (chunk: memory_chunk) (e: expr) :=
+  match e with
+  | Eop (Oaddrstack n) Enil => (Ainstack n, Enil)
+  | Eop (Oaddrsymbol id ofs) Enil => if Archi.pic_code tt then (Aindexed Ptrofs.zero, e:::Enil) else (Aglobal id ofs, Enil)
+  | Eop (Oaddimm n) (e1:::Enil) => (Aindexed (Ptrofs.of_int n), e1:::Enil)
+  | Eop (Oaddlimm n) (e1:::Enil) => (Aindexed (Ptrofs.of_int64 n), e1:::Enil)
+  | _ => (Aindexed Ptrofs.zero, e:::Enil)
+  end.
+>>
+*)
+
+Inductive addressing_cases: forall (e: expr), Type :=
+  | addressing_case1: forall n, addressing_cases (Eop (Oaddrstack n) Enil)
+  | addressing_case2: forall id ofs, addressing_cases (Eop (Oaddrsymbol id ofs) Enil)
+  | addressing_case3: forall n e1, addressing_cases (Eop (Oaddimm n) (e1:::Enil))
+  | addressing_case4: forall n e1, addressing_cases (Eop (Oaddlimm n) (e1:::Enil))
+  | addressing_default: forall (e: expr), addressing_cases e.
+
+Definition addressing_match (e: expr) :=
+  match e as zz1 return addressing_cases zz1 with
+  | Eop (Oaddrstack n) Enil => addressing_case1 n
+  | Eop (Oaddrsymbol id ofs) Enil => addressing_case2 id ofs
+  | Eop (Oaddimm n) (e1:::Enil) => addressing_case3 n e1
+  | Eop (Oaddlimm n) (e1:::Enil) => addressing_case4 n e1
+  | e => addressing_default e
+  end.
+
+Definition addressing (chunk: memory_chunk) (e: expr) :=
+  match addressing_match e with
+  | addressing_case1 n => (* Eop (Oaddrstack n) Enil *) 
+      (Ainstack n, Enil)
+  | addressing_case2 id ofs => (* Eop (Oaddrsymbol id ofs) Enil *) 
+      if Archi.pic_code tt then (Aindexed Ptrofs.zero, e:::Enil) else (Aglobal id ofs, Enil)
+  | addressing_case3 n e1 => (* Eop (Oaddimm n) (e1:::Enil) *) 
+      (Aindexed (Ptrofs.of_int n), e1:::Enil)
+  | addressing_case4 n e1 => (* Eop (Oaddlimm n) (e1:::Enil) *) 
+      (Aindexed (Ptrofs.of_int64 n), e1:::Enil)
+  | addressing_default e =>
+      (Aindexed Ptrofs.zero, e:::Enil)
+  end.
+
+
+(** ** Arguments of builtins *)
+
+(** Original definition:
+<<
+Nondetfunction builtin_arg (e: expr) :=
+  match e with
+  | Eop (Ointconst n) Enil => BA_int n
+  | Eop (Oaddrsymbol id ofs) Enil => BA_addrglobal id ofs
+  | Eop (Oaddrstack ofs) Enil => BA_addrstack ofs
+  | Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) =>
+        BA_long (Int64.ofwords h l)
+  | Eop Omakelong (h ::: l ::: Enil) => BA_splitlong (BA h) (BA l)
+  | Eload chunk (Ainstack ofs) Enil => BA_loadstack chunk ofs
+  | Eop (Oaddimm n) (e1:::Enil) =>
+      if Archi.ptr64 then BA e else BA_addptr (BA e1) (BA_int n)
+  | Eop (Oaddlimm n) (e1:::Enil) =>
+      if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e
+  | _ => BA e
+  end.
+>>
+*)
+
+Inductive builtin_arg_cases: forall (e: expr), Type :=
+  | builtin_arg_case1: forall n, builtin_arg_cases (Eop (Ointconst n) Enil)
+  | builtin_arg_case2: forall id ofs, builtin_arg_cases (Eop (Oaddrsymbol id ofs) Enil)
+  | builtin_arg_case3: forall ofs, builtin_arg_cases (Eop (Oaddrstack ofs) Enil)
+  | builtin_arg_case4: forall h l, builtin_arg_cases (Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil))
+  | builtin_arg_case5: forall h l, builtin_arg_cases (Eop Omakelong (h ::: l ::: Enil))
+  | builtin_arg_case6: forall chunk ofs, builtin_arg_cases (Eload chunk (Ainstack ofs) Enil)
+  | builtin_arg_case7: forall n e1, builtin_arg_cases (Eop (Oaddimm n) (e1:::Enil))
+  | builtin_arg_case8: forall n e1, builtin_arg_cases (Eop (Oaddlimm n) (e1:::Enil))
+  | builtin_arg_default: forall (e: expr), builtin_arg_cases e.
+
+Definition builtin_arg_match (e: expr) :=
+  match e as zz1 return builtin_arg_cases zz1 with
+  | Eop (Ointconst n) Enil => builtin_arg_case1 n
+  | Eop (Oaddrsymbol id ofs) Enil => builtin_arg_case2 id ofs
+  | Eop (Oaddrstack ofs) Enil => builtin_arg_case3 ofs
+  | Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) => builtin_arg_case4 h l
+  | Eop Omakelong (h ::: l ::: Enil) => builtin_arg_case5 h l
+  | Eload chunk (Ainstack ofs) Enil => builtin_arg_case6 chunk ofs
+  | Eop (Oaddimm n) (e1:::Enil) => builtin_arg_case7 n e1
+  | Eop (Oaddlimm n) (e1:::Enil) => builtin_arg_case8 n e1
+  | e => builtin_arg_default e
+  end.
+
+Definition builtin_arg (e: expr) :=
+  match builtin_arg_match e with
+  | builtin_arg_case1 n => (* Eop (Ointconst n) Enil *) 
+      BA_int n
+  | builtin_arg_case2 id ofs => (* Eop (Oaddrsymbol id ofs) Enil *) 
+      BA_addrglobal id ofs
+  | builtin_arg_case3 ofs => (* Eop (Oaddrstack ofs) Enil *) 
+      BA_addrstack ofs
+  | builtin_arg_case4 h l => (* Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) *) 
+      BA_long (Int64.ofwords h l)
+  | builtin_arg_case5 h l => (* Eop Omakelong (h ::: l ::: Enil) *) 
+      BA_splitlong (BA h) (BA l)
+  | builtin_arg_case6 chunk ofs => (* Eload chunk (Ainstack ofs) Enil *) 
+      BA_loadstack chunk ofs
+  | builtin_arg_case7 n e1 => (* Eop (Oaddimm n) (e1:::Enil) *) 
+      if Archi.ptr64 then BA e else BA_addptr (BA e1) (BA_int n)
+  | builtin_arg_case8 n e1 => (* Eop (Oaddlimm n) (e1:::Enil) *) 
+      if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e
+  | builtin_arg_default e =>
+      BA e
+  end.
+