Merge branch 'mppa-mul' into mppa-jumptable

14 files changed, 123 insertions, 719 deletions

diff --git a/mppa_k1c/Asm.v b/mppa_k1c/Asm.v
index 8c918c2d..421f3d2c 100644
--- a/mppa_k1c/Asm.v
+++ b/mppa_k1c/Asm.v
@@ -50,9 +50,6 @@ Inductive instruction : Type :=
   | Psemi                                           (**r semi colon separating bundles *)

   | Pnop                                            (**r instruction that does nothing *)

 

-  | Pdiv                                            (**r 32 bits integer division *)

-  | Pdivu                                           (**r 32 bits integer division *)

-

   (** builtins *)

   | Pclzll (rd rs: ireg)

   | Pstsud (rd rs1 rs2: ireg)

@@ -219,8 +216,6 @@ Inductive instruction : Type :=
 Definition control_to_instruction (c: control) :=

   match c with

   | PExpand (Asmblock.Pbuiltin ef args res) => Pbuiltin ef args res

-  | PExpand (Asmblock.Pdiv)                 => Pdiv

-  | PExpand (Asmblock.Pdivu)                => Pdivu

   | PCtlFlow Asmblock.Pret                  => Pret

   | PCtlFlow (Asmblock.Pcall l)             => Pcall l

   | PCtlFlow (Asmblock.Picall r)            => Picall r

diff --git a/mppa_k1c/Asmblock.v b/mppa_k1c/Asmblock.v
index dfe46e04..d630e767 100644
--- a/mppa_k1c/Asmblock.v
+++ b/mppa_k1c/Asmblock.v
@@ -178,10 +178,7 @@ Inductive ex_instruction : Type :=
   | Pbtbl   (r: ireg)  (tbl: list label)            (**r N-way branch through a jump table *) *)
 
   | Pbuiltin: external_function -> list (builtin_arg preg)
-              -> builtin_res preg -> ex_instruction   (**r built-in function (pseudo) *)
-  | Pdiv                                              (**r 32 bits integer division, call to __divdi3 *)
-  | Pdivu                                             (**r 32 bits integer division, call to __udivdi3 *)
-.
+              -> builtin_res preg -> ex_instruction   (**r built-in function (pseudo) *).
 
 (** FIXME: comment not up to date !
 
@@ -1497,17 +1494,6 @@ Definition exec_control (f: function) (oc: option control) (rs: regset) (m: mem)
 (** Pseudo-instructions *)
   | Pbuiltin ef args res =>
       Stuck (**r treated specially below *)
-  | Pdiv =>
-      match Val.divs (rs GPR0) (rs GPR1) with
-      | Some v => Next (rs # GPR0 <- v # RA <- (rs RA)) m
-      | None => Stuck
-      end
-
-  | Pdivu =>
-      match Val.divu (rs GPR0) (rs GPR1) with
-      | Some v => Next (rs # GPR0 <- v # RA <- (rs RA)) m
-      | None => Stuck
-      end
   end
   | None => Next rs m
 end.
diff --git a/mppa_k1c/Asmblockdeps.v b/mppa_k1c/Asmblockdeps.v
index 1acc3b58..845a26ed 100644
--- a/mppa_k1c/Asmblockdeps.v
+++ b/mppa_k1c/Asmblockdeps.v
@@ -555,8 +555,6 @@ Definition trans_control (ctl: control) : macro :=
   | Pjumptable r labels => [(#PC, Op (Control (Ojumptable labels)) (Name (#r) @ Name (#PC) @ Enil));
                             (#GPR62, Op (Constant Vundef) Enil);
                             (#GPR63, Op (Constant Vundef) Enil) ]
-  | Pdiv => [(#GPR0, Op (Control Odiv) (Name (#GPR0) @ Name (#GPR1) @ Enil)); (#RA, Name (#RA))]
-  | Pdivu => [(#GPR0, Op (Control Odivu) (Name (#GPR0) @ Name (#GPR1) @ Enil)); (#RA, Name (#RA))]
   | Pbuiltin ef args res => [(#PC, Op (Control (OError)) Enil)]
   end.
 
@@ -878,22 +876,6 @@ Proof.
   intros. destruct ex.
   - simpl in *. inv H1. destruct c; destruct i; try discriminate.
     all: try (inv H0; eexists; split; try split; [ simpl control_eval; pose (H3 PC); simpl in e; rewrite e; reflexivity | Simpl | intros rr; destruct rr; Simpl]).
-    (* Pdiv *)
-    + destruct (Val.divs _ _) eqn:DIVS; try discriminate. inv H0. unfold nextblock in DIVS. repeat (rewrite Pregmap.gso in DIVS; try discriminate).
-      eexists; split; try split.
-      * simpl control_eval. pose (H3 PC); simpl in e; rewrite e; clear e. simpl.
-        Simpl. pose (H3 GPR0); rewrite e; clear e. pose (H3 GPR1); rewrite e; clear e. rewrite DIVS.
-        Simpl.
-      * Simpl.
-      * intros rr; destruct rr; Simpl. destruct (preg_eq GPR0 g); Simpl. rewrite e. Simpl.
-    (* Pdivu *)
-    + destruct (Val.divu _ _) eqn:DIVU; try discriminate. inv H0. unfold nextblock in DIVU. repeat (rewrite Pregmap.gso in DIVU; try discriminate).
-      eexists; split; try split.
-      * simpl control_eval. pose (H3 PC); simpl in e; rewrite e; clear e. simpl.
-        Simpl. pose (H3 GPR0); rewrite e; clear e. pose (H3 GPR1); rewrite e; clear e. rewrite DIVU.
-        Simpl.
-      * Simpl.
-      * intros rr; destruct rr; Simpl. destruct (preg_eq GPR0 g); Simpl. rewrite e. Simpl.
     (* Pjumptable *)
     + unfold goto_label in *.
       repeat (rewrite Pregmap.gso in H0; try discriminate).
@@ -1104,12 +1086,6 @@ Lemma exec_exit_none:
 Proof.
   intros. inv H0. destruct ex as [ctl|]; try discriminate.
   destruct ctl; destruct i; try reflexivity; try discriminate.
-(* Pdiv *)
-  - simpl in *. pose (H3 GPR0); rewrite e in H1; clear e. pose (H3 GPR1); rewrite e in H1; clear e.
-    destruct (Val.divs _ _); try discriminate; auto.
-(* Pdivu *)
-  - simpl in *. pose (H3 GPR0); rewrite e in H1; clear e. pose (H3 GPR1); rewrite e in H1; clear e.
-    destruct (Val.divu _ _); try discriminate; auto.
 (* Pjumptable *)
   - simpl in *. repeat (rewrite H3 in H1).
     destruct (rs r); try discriminate; auto. destruct (list_nth_z _ _); try discriminate; auto.
@@ -1226,11 +1202,7 @@ Lemma forward_simu_exit_stuck:
 Proof.
   intros. inv H1. destruct ex as [ctl|]; try discriminate.
   destruct ctl; destruct i; try discriminate; try (simpl; reflexivity).
-(* Pdiv *)
-  - simpl in *. pose (H3 GPR0); simpl in e; rewrite e; clear e. pose (H3 GPR1); simpl in e; rewrite e; clear e.
-    destruct (Val.divs _ _); try discriminate; auto.
-  - simpl in *. pose (H3 GPR0); simpl in e; rewrite e; clear e. pose (H3 GPR1); simpl in e; rewrite e; clear e.
-    destruct (Val.divu _ _); try discriminate; auto.
+  (* Pjumptable *)
   - simpl in *. repeat (rewrite H3). destruct (rs r); try discriminate; auto. destruct (list_nth_z _ _); try discriminate; auto.
     unfold goto_label_deps. unfold goto_label in H0.
     destruct (label_pos _ _ _); auto. repeat (rewrite Pregmap.gso in H0; try discriminate). destruct (rs PC); auto. discriminate.
diff --git a/mppa_k1c/Asmblockgen.v b/mppa_k1c/Asmblockgen.v
index f3b4b921..1afb627a 100644
--- a/mppa_k1c/Asmblockgen.v
+++ b/mppa_k1c/Asmblockgen.v
@@ -425,18 +425,6 @@ Definition transl_op
       OK (mulimm32 rd rs1 n ::i k)
   | Omulhs, _ => Error(msg "Asmblockgen.transl_op: Omulhs") (* Normalement pas émis *)
   | Omulhu, _ => Error(msg "Asmblockgen.transl_op: Omulhu") (* Normalement pas émis *)
-  | Odiv, a1 :: a2 :: nil => Error(msg "Asmblockgen.transl_op: Odiv: 32-bits division not supported yet. Please use 64-bits.")
-      (* do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2;
-      OK (Pdivw rd rs1 rs2 :: k) *)
-  | Odivu, a1 :: a2 :: nil => Error(msg "Asmblockgen.transl_op: Odivu: 32-bits division not supported yet. Please use 64-bits.")
-      (* do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2;
-      OK (Pdivuw rd rs1 rs2 :: k) *)
-  | Omod, a1 :: a2 :: nil => Error(msg "Asmblockgen.transl_op: Omod: 32-bits modulo not supported yet. Please use 64-bits.")
-      (* do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2;
-      OK (Premw rd rs1 rs2 :: k) *)
-  | Omodu, a1 :: a2 :: nil => Error(msg "Asmblockgen.transl_op: Omodu: 32-bits modulo not supported yet. Please use 64-bits.")
-      (* do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2;
-      OK (Premuw rd rs1 rs2 :: k) *)
   | Oand, a1 :: a2 :: nil =>
       do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2;
       OK (Pandw rd rs1 rs2 ::i k)
diff --git a/mppa_k1c/Asmexpand.ml b/mppa_k1c/Asmexpand.ml
index 1c9e4e4c..f1528389 100644
--- a/mppa_k1c/Asmexpand.ml
+++ b/mppa_k1c/Asmexpand.ml
@@ -124,9 +124,6 @@ let expand_annot_val kind txt targ args res = assert false
 
 (* Handling of memcpy *)
 
-let offset_in_range ofs =
-  let ofs = Z.to_int64 ofs in -2048L <= ofs && ofs < 2048L
-
 let emit_move dst r =
   if dst <> r
   then emit (Paddil(dst, r, Z.zero));;
@@ -175,7 +172,7 @@ let expand_builtin_memcpy  sz al args =
   | _ -> assert false;;
 
 (* Handling of volatile reads and writes *)
-
+(* FIXME probably need to check for size of displacement *)
 let expand_builtin_vload_common chunk base ofs res =
   match chunk, res with
   | Mint8unsigned, BR(Asmblock.IR res) ->
@@ -211,21 +208,9 @@ let expand_builtin_vload chunk args res =
   | [BA(Asmblock.IR addr)] ->
       expand_builtin_vload_common chunk addr _0 res
   | [BA_addrstack ofs] ->
-      if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then
-        expand_builtin_vload_common chunk stack_pointer ofs res
-      else begin
-        assert false (* FIXME
-        expand_addptrofs Asmblock.GPR32 stack_pointer ofs; (* X31 <- sp + ofs *)
-        expand_builtin_vload_common chunk GPR32 _0 res *)
-      end
+     expand_builtin_vload_common chunk stack_pointer ofs res
   | [BA_addptr(BA(Asmblock.IR addr), (BA_int ofs | BA_long ofs))] ->
-      if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then
-        expand_builtin_vload_common chunk addr ofs res
-      else begin
-          assert false (* FIXME
-        expand_addptrofs Asmblock.GPR32 addr ofs; (* X31 <- addr + ofs *)
-        expand_builtin_vload_common chunk Asmblock.GPR32 _0 res *)
-      end
+     expand_builtin_vload_common chunk addr ofs res
   | _ ->
       assert false
 
@@ -256,19 +241,9 @@ let expand_builtin_vstore chunk args =
   | [BA(Asmblock.IR addr); src] ->
       expand_builtin_vstore_common chunk addr _0 src
   | [BA_addrstack ofs; src] ->
-      if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then
-        expand_builtin_vstore_common chunk stack_pointer ofs src
-      else begin (* FIXME 
-        expand_addptrofs X31 X2 ofs; (* X31 <- sp + ofs *)
-        expand_builtin_vstore_common chunk X31 _0 src *)
-      end
+     expand_builtin_vstore_common chunk stack_pointer ofs src
   | [BA_addptr(BA(Asmblock.IR addr), (BA_int ofs | BA_long ofs)); src] ->
-      if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then
-        expand_builtin_vstore_common chunk addr ofs src
-      else begin (* FIXME
-        expand_addptrofs X31 addr ofs; (* X31 <- addr + ofs *)
-        expand_builtin_vstore_common chunk X31 _0 src *)
-      end
+     expand_builtin_vstore_common chunk addr ofs src
   | _ ->
       assert false
 
diff --git a/mppa_k1c/ConstpropOp.v b/mppa_k1c/ConstpropOp.v
deleted file mode 100644
index e7391ab5..00000000
--- a/mppa_k1c/ConstpropOp.v
+++ /dev/null
@@ -1,613 +0,0 @@
-(* *********************************************************************)
-(*                                                                     *)
-(*              The Compcert verified compiler                         *)
-(*                                                                     *)
-(*                  Xavier Leroy, INRIA Paris                          *)
-(*                                                                     *)
-(*  Copyright Institut National de Recherche en Informatique et en     *)
-(*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
-(*                                                                     *)
-(* *********************************************************************)
-
-(** Strength reduction for operators and conditions.
-    This is the machine-dependent part of [Constprop]. *)
-
-Require Archi.
-Require Import Coqlib Compopts.
-Require Import AST Integers Floats.
-Require Import Op Registers.
-Require Import ValueDomain.
-
-(** * Converting known values to constants *)
-
-Definition const_for_result (a: aval) : option operation :=
-  match a with
-  | I n => Some(Ointconst n)
-  | L n => if Archi.ptr64 then Some(Olongconst n) else None
-  | F n => if Compopts.generate_float_constants tt then Some(Ofloatconst n) else None
-  | FS n => if Compopts.generate_float_constants tt then Some(Osingleconst n) else None
-  | Ptr(Gl id ofs) => Some(Oaddrsymbol id ofs)
-  | Ptr(Stk ofs) => Some(Oaddrstack ofs)
-  | _ => None
-  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. *)
-
-(** Original definition:
-<<
-Nondetfunction cond_strength_reduction 
-              (cond: condition) (args: list reg) (vl: list aval) :=
-  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)
-  | Ccompl c, r1 :: r2 :: nil, L n1 :: v2 :: nil =>
-      (Ccomplimm (swap_comparison c) n1, r2 :: nil)
-  | Ccompl c, r1 :: r2 :: nil, v1 :: L n2 :: nil =>
-      (Ccomplimm c n2, r1 :: nil)
-  | Ccomplu c, r1 :: r2 :: nil, L n1 :: v2 :: nil =>
-      (Ccompluimm (swap_comparison c) n1, r2 :: nil)
-  | Ccomplu c, r1 :: r2 :: nil, v1 :: L n2 :: nil =>
-      (Ccompluimm c n2, r1 :: nil)
-  | _, _, _ => 
-      (cond, args)
-  end.
->>
-*)
-
-Inductive cond_strength_reduction_cases: forall (cond: condition) (args: list reg) (vl: list aval), 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_case5: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccompl c) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | cond_strength_reduction_case6: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccompl c) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | cond_strength_reduction_case7: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccomplu c) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | cond_strength_reduction_case8: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccomplu c) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | cond_strength_reduction_default: forall (cond: condition) (args: list reg) (vl: list aval), cond_strength_reduction_cases cond args vl.
-
-Definition cond_strength_reduction_match (cond: condition) (args: list reg) (vl: list aval) :=
-  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
-  | Ccompl c, r1 :: r2 :: nil, L n1 :: v2 :: nil => cond_strength_reduction_case5 c r1 r2 n1 v2
-  | Ccompl c, r1 :: r2 :: nil, v1 :: L n2 :: nil => cond_strength_reduction_case6 c r1 r2 v1 n2
-  | Ccomplu c, r1 :: r2 :: nil, L n1 :: v2 :: nil => cond_strength_reduction_case7 c r1 r2 n1 v2
-  | Ccomplu c, r1 :: r2 :: nil, v1 :: L n2 :: nil => cond_strength_reduction_case8 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 aval) :=
-  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_case5 c r1 r2 n1 v2 => (* Ccompl c, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      (Ccomplimm (swap_comparison c) n1, r2 :: nil)
-  | cond_strength_reduction_case6 c r1 r2 v1 n2 => (* Ccompl c, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      (Ccomplimm c n2, r1 :: nil)
-  | cond_strength_reduction_case7 c r1 r2 n1 v2 => (* Ccomplu c, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      (Ccompluimm (swap_comparison c) n1, r2 :: nil)
-  | cond_strength_reduction_case8 c r1 r2 v1 n2 => (* Ccomplu c, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      (Ccompluimm c n2, r1 :: nil)
-  | cond_strength_reduction_default cond args vl =>
-      (cond, args)
-  end.
-
-
-Definition make_cmp_base (c: condition) (args: list reg) (vl: list aval) :=
-  let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args').
-
-Definition make_cmp_imm_eq (c: condition) (args: list reg) (vl: list aval) 
-                           (n: int) (r1: reg) (v1: aval) :=
-  if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil)
-  else if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil)
-  else make_cmp_base c args vl.
-
-Definition make_cmp_imm_ne (c: condition) (args: list reg) (vl: list aval) 
-                           (n: int) (r1: reg) (v1: aval) :=
-  if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil)
-  else if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil)
-  else make_cmp_base c args vl.
-
-(** Original definition:
-<<
-Nondetfunction make_cmp (c: condition) (args: list reg) (vl: list aval) :=
-  match c, args, vl with
-  | Ccompimm Ceq n, r1 :: nil, v1 :: nil =>
-      make_cmp_imm_eq c args vl n r1 v1
-  | Ccompimm Cne n, r1 :: nil, v1 :: nil =>
-      make_cmp_imm_ne c args vl n r1 v1
-  | Ccompuimm Ceq n, r1 :: nil, v1 :: nil =>
-      make_cmp_imm_eq c args vl n r1 v1
-  | Ccompuimm Cne n, r1 :: nil, v1 :: nil =>
-      make_cmp_imm_ne c args vl n r1 v1
-  | _, _, _ =>
-      make_cmp_base c args vl
-  end.
->>
-*)
-
-Inductive make_cmp_cases: forall (c: condition) (args: list reg) (vl: list aval), Type :=
-  | make_cmp_case1: forall n r1 v1, make_cmp_cases (Ccompimm Ceq n) (r1 :: nil) (v1 :: nil)
-  | make_cmp_case2: forall n r1 v1, make_cmp_cases (Ccompimm Cne n) (r1 :: nil) (v1 :: nil)
-  | make_cmp_case3: forall n r1 v1, make_cmp_cases (Ccompuimm Ceq n) (r1 :: nil) (v1 :: nil)
-  | make_cmp_case4: forall n r1 v1, make_cmp_cases (Ccompuimm Cne n) (r1 :: nil) (v1 :: nil)
-  | make_cmp_default: forall (c: condition) (args: list reg) (vl: list aval), make_cmp_cases c args vl.
-
-Definition make_cmp_match (c: condition) (args: list reg) (vl: list aval) :=
-  match c as zz1, args as zz2, vl as zz3 return make_cmp_cases zz1 zz2 zz3 with
-  | Ccompimm Ceq n, r1 :: nil, v1 :: nil => make_cmp_case1 n r1 v1
-  | Ccompimm Cne n, r1 :: nil, v1 :: nil => make_cmp_case2 n r1 v1
-  | Ccompuimm Ceq n, r1 :: nil, v1 :: nil => make_cmp_case3 n r1 v1
-  | Ccompuimm Cne n, r1 :: nil, v1 :: nil => make_cmp_case4 n r1 v1
-  | c, args, vl => make_cmp_default c args vl
-  end.
-
-Definition make_cmp (c: condition) (args: list reg) (vl: list aval) :=
-  match make_cmp_match c args vl with
-  | make_cmp_case1 n r1 v1 => (* Ccompimm Ceq n, r1 :: nil, v1 :: nil *) 
-      make_cmp_imm_eq c args vl n r1 v1
-  | make_cmp_case2 n r1 v1 => (* Ccompimm Cne n, r1 :: nil, v1 :: nil *) 
-      make_cmp_imm_ne c args vl n r1 v1
-  | make_cmp_case3 n r1 v1 => (* Ccompuimm Ceq n, r1 :: nil, v1 :: nil *) 
-      make_cmp_imm_eq c args vl n r1 v1
-  | make_cmp_case4 n r1 v1 => (* Ccompuimm Cne n, r1 :: nil, v1 :: nil *) 
-      make_cmp_imm_ne c args vl n r1 v1
-  | make_cmp_default c args vl =>
-      make_cmp_base c args vl
-  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) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int.iwordsize then (Oshlimm n, r1 :: nil)
-  else (Oshl, r1 :: r2 :: nil).
-
-Definition make_shrimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int.iwordsize then (Oshrimm n, r1 :: nil)
-  else (Oshr, r1 :: r2 :: nil).
-
-Definition make_shruimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int.iwordsize then (Oshruimm n, r1 :: nil)
-  else (Oshru, r1 :: r2 :: nil).
-
-Definition make_mulimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then
-    (Ointconst Int.zero, nil)
-  else if Int.eq n Int.one then
-    (Omove, r1 :: nil)
-  else
-    match Int.is_power2 n with
-    | Some l => (Oshlimm l, r1 :: nil)
-    | None => (Omul, r1 :: r2 :: nil)
-    end.
-
-Definition make_andimm (n: int) (r: reg) (a: aval) :=
-  if Int.eq n Int.zero then (Ointconst Int.zero, nil)
-  else if Int.eq n Int.mone then (Omove, r :: nil)
-  else if match a with Uns _ m => Int.eq (Int.zero_ext m (Int.not n)) Int.zero
-                     | _ => false end
-  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) :=
-  if Int.eq n Int.one then
-    (Omove, r1 :: nil)
-  else
-    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) :=
-  if Int.eq n Int.one then
-    (Omove, r1 :: nil)
-  else
-    match Int.is_power2 n with
-    | Some l => (Oshruimm l, r1 :: nil)
-    | 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.
-
-Definition make_addlimm (n: int64) (r: reg) :=
-  if Int64.eq n Int64.zero
-  then (Omove, r :: nil)
-  else (Oaddlimm n, r :: nil).
-
-Definition make_shllimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int64.iwordsize' then (Oshllimm n, r1 :: nil)
-  else (Oshll, r1 :: r2 :: nil).
-
-Definition make_shrlimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int64.iwordsize' then (Oshrlimm n, r1 :: nil)
-  else (Oshrl, r1 :: r2 :: nil).
-
-Definition make_shrluimm (n: int) (r1 r2: reg) :=
-  if Int.eq n Int.zero then (Omove, r1 :: nil)
-  else if Int.ltu n Int64.iwordsize' then (Oshrluimm n, r1 :: nil)
-  else (Oshrlu, r1 :: r2 :: nil).
-
-Definition make_mullimm (n: int64) (r1 r2: reg) :=
-  if Int64.eq n Int64.zero then
-    (Olongconst Int64.zero, nil)
-  else if Int64.eq n Int64.one then
-    (Omove, r1 :: nil)
-  else
-    match Int64.is_power2' n with
-    | Some l => (Oshllimm l, r1 :: nil)
-    | None => (Omull, r1 :: r2 :: nil)
-    end.
-
-Definition make_andlimm (n: int64) (r: reg) (a: aval) :=
-  if Int64.eq n Int64.zero then (Olongconst Int64.zero, nil)
-  else if Int64.eq n Int64.mone then (Omove, r :: nil)
-  else (Oandlimm n, r :: nil).
-
-Definition make_orlimm (n: int64) (r: reg) :=
-  if Int64.eq n Int64.zero then (Omove, r :: nil)
-  else if Int64.eq n Int64.mone then (Olongconst Int64.mone, nil)
-  else (Oorlimm n, r :: nil).
-
-Definition make_xorlimm (n: int64) (r: reg) :=
-  if Int64.eq n Int64.zero then (Omove, r :: nil)
-  else (Oxorlimm n, r :: nil).
-
-Definition make_divlimm n (r1 r2: reg) :=
-  match Int64.is_power2' n with
-  | Some l => if Int.ltu l (Int.repr 63)
-              then (Oshrxlimm l, r1 :: nil)
-              else (Odivl, r1 :: r2 :: nil)
-  | None   => (Odivl, r1 :: r2 :: nil)
-  end.
-
-Definition make_divluimm n (r1 r2: reg) :=
-  match Int64.is_power2' n with
-  | Some l => (Oshrluimm l, r1 :: nil)
-  | None   => (Odivlu, r1 :: r2 :: nil)
-  end.
-
-Definition make_modluimm n (r1 r2: reg) :=
-  match Int64.is_power2 n with
-  | Some l => (Oandlimm (Int64.sub n Int64.one), r1 :: nil)
-  | None   => (Omodlu, r1 :: r2 :: nil)
-  end.
-
-Definition make_mulfimm (n: float) (r r1 r2: reg) :=
-  if Float.eq_dec n (Float.of_int (Int.repr 2))
-  then (Oaddf, r :: r :: nil)
-  else (Omulf, r1 :: r2 :: nil).
-
-Definition make_mulfsimm (n: float32) (r r1 r2: reg) :=
-  if Float32.eq_dec n (Float32.of_int (Int.repr 2))
-  then (Oaddfs, r :: r :: nil)
-  else (Omulfs, r1 :: r2 :: nil).
-
-Definition make_cast8signed (r: reg) (a: aval) :=
-  if vincl a (Sgn Ptop 8) then (Omove, r :: nil) else (Ocast8signed, r :: nil).
-Definition make_cast16signed (r: reg) (a: aval) :=
-  if vincl a (Sgn Ptop 16) then (Omove, r :: nil) else (Ocast16signed, r :: nil).
-
-(** Original definition:
-<<
-Nondetfunction op_strength_reduction 
-              (op: operation) (args: list reg) (vl: list aval) :=
-  match op, args, vl with
-  | Ocast8signed, r1 :: nil, v1 :: nil => make_cast8signed r1 v1
-  | Ocast16signed, r1 :: nil, v1 :: nil => make_cast16signed r1 v1
-  | Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_addimm n1 r2
-  | Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm n2 r1
-  | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1
-  | Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_mulimm n1 r2 r1
-  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1 r2
-  | 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, I n1 :: v2 :: nil => make_andimm n1 r2 v2
-  | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1 v1
-  | Oandimm n, r1 :: nil, v1 :: nil => make_andimm n r1 v1
-  | Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_orimm n1 r2
-  | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1
-  | Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_xorimm n1 r2
-  | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1
-  | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1 r2
-  | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1 r2
-  | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 r2
-  | Oaddl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_addlimm n1 r2
-  | Oaddl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm n2 r1
-  | Osubl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm (Int64.neg n2) r1
-  | Omull, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_mullimm n1 r2 r1
-  | Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_mullimm n2 r1 r2
-  | Odivl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_divlimm n2 r1 r2
-  | Odivlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_divluimm n2 r1 r2
-  | Omodlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_modluimm n2 r1 r2
-  | Oandl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_andlimm n1 r2 v2
-  | Oandl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_andlimm n2 r1 v1
-  | Oandlimm n, r1 :: nil, v1 :: nil => make_andlimm n r1 v1
-  | Oorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_orlimm n1 r2
-  | Oorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_orlimm n2 r1
-  | Oxorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_xorlimm n1 r2
-  | Oxorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_xorlimm n2 r1
-  | Oshll, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shllimm n2 r1 r2
-  | Oshrl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrlimm n2 r1 r2
-  | Oshrlu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrluimm n2 r1 r2
-  | Ocmp c, args, vl => make_cmp c args vl
-  | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => make_mulfimm n2 r1 r1 r2
-  | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => make_mulfimm n1 r2 r1 r2
-  | Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => make_mulfsimm n2 r1 r1 r2
-  | Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => make_mulfsimm n1 r2 r1 r2
-  | _, _, _ => (op, args)
-  end.
->>
-*)
-
-Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg) (vl: list aval), Type :=
-  | op_strength_reduction_case1: forall r1 v1, op_strength_reduction_cases (Ocast8signed) (r1 :: nil) (v1 :: nil)
-  | op_strength_reduction_case2: forall r1 v1, op_strength_reduction_cases (Ocast16signed) (r1 :: nil) (v1 :: nil)
-  | op_strength_reduction_case3: forall r1 r2 n1 v2, op_strength_reduction_cases (Oadd) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | op_strength_reduction_case4: forall r1 r2 v1 n2, op_strength_reduction_cases (Oadd) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case5: forall r1 r2 v1 n2, op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case6: forall r1 r2 n1 v2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | op_strength_reduction_case7: forall r1 r2 v1 n2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case8: forall r1 r2 v1 n2, op_strength_reduction_cases (Odiv) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case9: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case10: forall r1 r2 v1 n2, op_strength_reduction_cases (Omodu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case11: forall r1 r2 n1 v2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | op_strength_reduction_case12: forall r1 r2 v1 n2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case13: forall n r1 v1, op_strength_reduction_cases (Oandimm n) (r1 :: nil) (v1 :: nil)
-  | op_strength_reduction_case14: forall r1 r2 n1 v2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | op_strength_reduction_case15: forall r1 r2 v1 n2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case16: forall r1 r2 n1 v2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
-  | op_strength_reduction_case17: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case18: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case19: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case20: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case21: forall r1 r2 n1 v2, op_strength_reduction_cases (Oaddl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | op_strength_reduction_case22: forall r1 r2 v1 n2, op_strength_reduction_cases (Oaddl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case23: forall r1 r2 v1 n2, op_strength_reduction_cases (Osubl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case24: forall r1 r2 n1 v2, op_strength_reduction_cases (Omull) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | op_strength_reduction_case25: forall r1 r2 v1 n2, op_strength_reduction_cases (Omull) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case26: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case27: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivlu) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case28: forall r1 r2 v1 n2, op_strength_reduction_cases (Omodlu) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case29: forall r1 r2 n1 v2, op_strength_reduction_cases (Oandl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | op_strength_reduction_case30: forall r1 r2 v1 n2, op_strength_reduction_cases (Oandl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case31: forall n r1 v1, op_strength_reduction_cases (Oandlimm n) (r1 :: nil) (v1 :: nil)
-  | op_strength_reduction_case32: forall r1 r2 n1 v2, op_strength_reduction_cases (Oorl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | op_strength_reduction_case33: forall r1 r2 v1 n2, op_strength_reduction_cases (Oorl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case34: forall r1 r2 n1 v2, op_strength_reduction_cases (Oxorl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
-  | op_strength_reduction_case35: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxorl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
-  | op_strength_reduction_case36: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshll) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case37: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshrl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case38: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshrlu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
-  | op_strength_reduction_case39: forall c args vl, op_strength_reduction_cases (Ocmp c) (args) (vl)
-  | op_strength_reduction_case40: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (v1 :: F n2 :: nil)
-  | op_strength_reduction_case41: forall r1 r2 n1 v2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (F n1 :: v2 :: nil)
-  | op_strength_reduction_case42: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulfs) (r1 :: r2 :: nil) (v1 :: FS n2 :: nil)
-  | op_strength_reduction_case43: forall r1 r2 n1 v2, op_strength_reduction_cases (Omulfs) (r1 :: r2 :: nil) (FS n1 :: v2 :: nil)
-  | op_strength_reduction_default: forall (op: operation) (args: list reg) (vl: list aval), op_strength_reduction_cases op args vl.
-
-Definition op_strength_reduction_match (op: operation) (args: list reg) (vl: list aval) :=
-  match op as zz1, args as zz2, vl as zz3 return op_strength_reduction_cases zz1 zz2 zz3 with
-  | Ocast8signed, r1 :: nil, v1 :: nil => op_strength_reduction_case1 r1 v1
-  | Ocast16signed, r1 :: nil, v1 :: nil => op_strength_reduction_case2 r1 v1
-  | Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case3 r1 r2 n1 v2
-  | Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case4 r1 r2 v1 n2
-  | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case5 r1 r2 v1 n2
-  | Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case6 r1 r2 n1 v2
-  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case7 r1 r2 v1 n2
-  | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case8 r1 r2 v1 n2
-  | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case9 r1 r2 v1 n2
-  | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case10 r1 r2 v1 n2
-  | Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case11 r1 r2 n1 v2
-  | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case12 r1 r2 v1 n2
-  | Oandimm n, r1 :: nil, v1 :: nil => op_strength_reduction_case13 n r1 v1
-  | Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case14 r1 r2 n1 v2
-  | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case15 r1 r2 v1 n2
-  | Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case16 r1 r2 n1 v2
-  | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case17 r1 r2 v1 n2
-  | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case18 r1 r2 v1 n2
-  | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case19 r1 r2 v1 n2
-  | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case20 r1 r2 v1 n2
-  | Oaddl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case21 r1 r2 n1 v2
-  | Oaddl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case22 r1 r2 v1 n2
-  | Osubl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case23 r1 r2 v1 n2
-  | Omull, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case24 r1 r2 n1 v2
-  | Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case25 r1 r2 v1 n2
-  | Odivl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case26 r1 r2 v1 n2
-  | Odivlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case27 r1 r2 v1 n2
-  | Omodlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case28 r1 r2 v1 n2
-  | Oandl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case29 r1 r2 n1 v2
-  | Oandl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case30 r1 r2 v1 n2
-  | Oandlimm n, r1 :: nil, v1 :: nil => op_strength_reduction_case31 n r1 v1
-  | Oorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case32 r1 r2 n1 v2
-  | Oorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case33 r1 r2 v1 n2
-  | Oxorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case34 r1 r2 n1 v2
-  | Oxorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case35 r1 r2 v1 n2
-  | Oshll, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case36 r1 r2 v1 n2
-  | Oshrl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case37 r1 r2 v1 n2
-  | Oshrlu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case38 r1 r2 v1 n2
-  | Ocmp c, args, vl => op_strength_reduction_case39 c args vl
-  | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => op_strength_reduction_case40 r1 r2 v1 n2
-  | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => op_strength_reduction_case41 r1 r2 n1 v2
-  | Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => op_strength_reduction_case42 r1 r2 v1 n2
-  | Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => op_strength_reduction_case43 r1 r2 n1 v2
-  | op, args, vl => op_strength_reduction_default op args vl
-  end.
-
-Definition op_strength_reduction (op: operation) (args: list reg) (vl: list aval) :=
-  match op_strength_reduction_match op args vl with
-  | op_strength_reduction_case1 r1 v1 => (* Ocast8signed, r1 :: nil, v1 :: nil *) 
-      make_cast8signed r1 v1
-  | op_strength_reduction_case2 r1 v1 => (* Ocast16signed, r1 :: nil, v1 :: nil *) 
-      make_cast16signed r1 v1
-  | op_strength_reduction_case3 r1 r2 n1 v2 => (* Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      make_addimm n1 r2
-  | op_strength_reduction_case4 r1 r2 v1 n2 => (* Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_addimm n2 r1
-  | op_strength_reduction_case5 r1 r2 v1 n2 => (* Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_addimm (Int.neg n2) r1
-  | op_strength_reduction_case6 r1 r2 n1 v2 => (* Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      make_mulimm n1 r2 r1
-  | op_strength_reduction_case7 r1 r2 v1 n2 => (* Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_mulimm n2 r1 r2
-  | op_strength_reduction_case8 r1 r2 v1 n2 => (* Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_divimm n2 r1 r2
-  | op_strength_reduction_case9 r1 r2 v1 n2 => (* Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_divuimm n2 r1 r2
-  | op_strength_reduction_case10 r1 r2 v1 n2 => (* Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_moduimm n2 r1 r2
-  | op_strength_reduction_case11 r1 r2 n1 v2 => (* Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      make_andimm n1 r2 v2
-  | op_strength_reduction_case12 r1 r2 v1 n2 => (* Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_andimm n2 r1 v1
-  | op_strength_reduction_case13 n r1 v1 => (* Oandimm n, r1 :: nil, v1 :: nil *) 
-      make_andimm n r1 v1
-  | op_strength_reduction_case14 r1 r2 n1 v2 => (* Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      make_orimm n1 r2
-  | op_strength_reduction_case15 r1 r2 v1 n2 => (* Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_orimm n2 r1
-  | op_strength_reduction_case16 r1 r2 n1 v2 => (* Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil *) 
-      make_xorimm n1 r2
-  | op_strength_reduction_case17 r1 r2 v1 n2 => (* Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_xorimm n2 r1
-  | op_strength_reduction_case18 r1 r2 v1 n2 => (* Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shlimm n2 r1 r2
-  | op_strength_reduction_case19 r1 r2 v1 n2 => (* Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shrimm n2 r1 r2
-  | op_strength_reduction_case20 r1 r2 v1 n2 => (* Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shruimm n2 r1 r2
-  | op_strength_reduction_case21 r1 r2 n1 v2 => (* Oaddl, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      make_addlimm n1 r2
-  | op_strength_reduction_case22 r1 r2 v1 n2 => (* Oaddl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_addlimm n2 r1
-  | op_strength_reduction_case23 r1 r2 v1 n2 => (* Osubl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_addlimm (Int64.neg n2) r1
-  | op_strength_reduction_case24 r1 r2 n1 v2 => (* Omull, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      make_mullimm n1 r2 r1
-  | op_strength_reduction_case25 r1 r2 v1 n2 => (* Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_mullimm n2 r1 r2
-  | op_strength_reduction_case26 r1 r2 v1 n2 => (* Odivl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_divlimm n2 r1 r2
-  | op_strength_reduction_case27 r1 r2 v1 n2 => (* Odivlu, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_divluimm n2 r1 r2
-  | op_strength_reduction_case28 r1 r2 v1 n2 => (* Omodlu, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_modluimm n2 r1 r2
-  | op_strength_reduction_case29 r1 r2 n1 v2 => (* Oandl, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      make_andlimm n1 r2 v2
-  | op_strength_reduction_case30 r1 r2 v1 n2 => (* Oandl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_andlimm n2 r1 v1
-  | op_strength_reduction_case31 n r1 v1 => (* Oandlimm n, r1 :: nil, v1 :: nil *) 
-      make_andlimm n r1 v1
-  | op_strength_reduction_case32 r1 r2 n1 v2 => (* Oorl, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      make_orlimm n1 r2
-  | op_strength_reduction_case33 r1 r2 v1 n2 => (* Oorl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_orlimm n2 r1
-  | op_strength_reduction_case34 r1 r2 n1 v2 => (* Oxorl, r1 :: r2 :: nil, L n1 :: v2 :: nil *) 
-      make_xorlimm n1 r2
-  | op_strength_reduction_case35 r1 r2 v1 n2 => (* Oxorl, r1 :: r2 :: nil, v1 :: L n2 :: nil *) 
-      make_xorlimm n2 r1
-  | op_strength_reduction_case36 r1 r2 v1 n2 => (* Oshll, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shllimm n2 r1 r2
-  | op_strength_reduction_case37 r1 r2 v1 n2 => (* Oshrl, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shrlimm n2 r1 r2
-  | op_strength_reduction_case38 r1 r2 v1 n2 => (* Oshrlu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) 
-      make_shrluimm n2 r1 r2
-  | op_strength_reduction_case39 c args vl => (* Ocmp c, args, vl *) 
-      make_cmp c args vl
-  | op_strength_reduction_case40 r1 r2 v1 n2 => (* Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil *) 
-      make_mulfimm n2 r1 r1 r2
-  | op_strength_reduction_case41 r1 r2 n1 v2 => (* Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil *) 
-      make_mulfimm n1 r2 r1 r2
-  | op_strength_reduction_case42 r1 r2 v1 n2 => (* Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil *) 
-      make_mulfsimm n2 r1 r1 r2
-  | op_strength_reduction_case43 r1 r2 n1 v2 => (* Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil *) 
-      make_mulfsimm n1 r2 r1 r2
-  | op_strength_reduction_default op args vl =>
-      (op, args)
-  end.
-
-
-(** Original definition:
-<<
-Nondetfunction addr_strength_reduction
-                (addr: addressing) (args: list reg) (vl: list aval) :=
-  match addr, args, vl with
-  | Aindexed n, r1 :: nil, Ptr(Gl symb n1) :: nil =>
-      if Archi.pic_code tt
-      then (addr, args)
-      else (Aglobal symb (Ptrofs.add n1 n), nil)
-  | Aindexed n, r1 :: nil, Ptr(Stk n1) :: nil =>
-      (Ainstack (Ptrofs.add n1 n), nil)
-  | _, _, _ =>
-      (addr, args)
-  end.
->>
-*)
-
-Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
-  | addr_strength_reduction_case1: forall n r1 symb n1, addr_strength_reduction_cases (Aindexed n) (r1 :: nil) (Ptr(Gl symb n1) :: nil)
-  | addr_strength_reduction_case2: forall n r1 n1, addr_strength_reduction_cases (Aindexed n) (r1 :: nil) (Ptr(Stk n1) :: nil)
-  | addr_strength_reduction_default: forall (addr: addressing) (args: list reg) (vl: list aval), addr_strength_reduction_cases addr args vl.
-
-Definition addr_strength_reduction_match (addr: addressing) (args: list reg) (vl: list aval) :=
-  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_cases zz1 zz2 zz3 with
-  | Aindexed n, r1 :: nil, Ptr(Gl symb n1) :: nil => addr_strength_reduction_case1 n r1 symb n1
-  | Aindexed n, r1 :: nil, Ptr(Stk n1) :: nil => addr_strength_reduction_case2 n r1 n1
-  | addr, args, vl => addr_strength_reduction_default addr args vl
-  end.
-
-Definition addr_strength_reduction (addr: addressing) (args: list reg) (vl: list aval) :=
-  match addr_strength_reduction_match addr args vl with
-  | addr_strength_reduction_case1 n r1 symb n1 => (* Aindexed n, r1 :: nil, Ptr(Gl symb n1) :: nil *) 
-      if Archi.pic_code tt then (addr, args) else (Aglobal symb (Ptrofs.add n1 n), nil)
-  | addr_strength_reduction_case2 n r1 n1 => (* Aindexed n, r1 :: nil, Ptr(Stk n1) :: nil *) 
-      (Ainstack (Ptrofs.add n1 n), nil)
-  | addr_strength_reduction_default addr args vl =>
-      (addr, args)
-  end.
-
-
diff --git a/mppa_k1c/Machregsaux.ml b/mppa_k1c/Machregsaux.ml
index 473e0602..9c4175ed 100644
--- a/mppa_k1c/Machregsaux.ml
+++ b/mppa_k1c/Machregsaux.ml
@@ -31,3 +31,8 @@ let register_by_name s =
   Machregs.register_by_name (coqstring_uppercase_ascii_of_camlstring s)
 
 let can_reserve_register r = Conventions1.is_callee_save r
+
+let class_of_type = function
+  | AST.Tint | AST.Tlong 
+  | AST.Tfloat | AST.Tsingle -> 0
+  | AST.Tany32 | AST.Tany64 -> assert false
diff --git a/mppa_k1c/Machregsaux.mli b/mppa_k1c/Machregsaux.mli
index 9404568d..d7117c21 100644
--- a/mppa_k1c/Machregsaux.mli
+++ b/mppa_k1c/Machregsaux.mli
@@ -16,3 +16,5 @@ val name_of_register: Machregs.mreg -> string option
 val register_by_name: string -> Machregs.mreg option
 val is_scratch_register: string -> bool
 val can_reserve_register: Machregs.mreg -> bool
+
+val class_of_type: AST.typ -> int
diff --git a/mppa_k1c/PostpassSchedulingOracle.ml b/mppa_k1c/PostpassSchedulingOracle.ml
index 25262af2..62df124a 100644
--- a/mppa_k1c/PostpassSchedulingOracle.ml
+++ b/mppa_k1c/PostpassSchedulingOracle.ml
@@ -222,7 +222,6 @@ let basic_rec i =
   | Pnop -> { inst = "nop"; write_locs = []; read_locs = []; imm = None ; is_control = false}
 
 let expand_rec = function
-  | Pdiv | Pdivu -> { inst = "Pdiv"; write_locs = [Reg (IR GPR0)]; read_locs = [Reg (IR GPR0); Reg (IR GPR1)]; imm = None; is_control = true }
   | Pbuiltin _ -> raise OpaqueInstruction
 
 let ctl_flow_rec = function
diff --git a/mppa_k1c/SelectLong.vp b/mppa_k1c/SelectLong.vp
index 3a17ab17..0c3618d7 100644
--- a/mppa_k1c/SelectLong.vp
+++ b/mppa_k1c/SelectLong.vp
@@ -21,6 +21,7 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
+Require Import OpHelpers.
 Require Import SelectOp SplitLong.
 
 Local Open Scope cminorsel_scope.
diff --git a/mppa_k1c/SelectLongproof.v b/mppa_k1c/SelectLongproof.v
index 4723278a..79187338 100644
--- a/mppa_k1c/SelectLongproof.v
+++ b/mppa_k1c/SelectLongproof.v
@@ -21,6 +21,7 @@ Require Import String Coqlib Maps Integers Floats Errors.
 Require Archi.
 Require Import AST Values Memory Globalenvs Events.
 Require Import Cminor Op CminorSel.
+Require Import OpHelpers OpHelpersproof.
 Require Import SelectOp SelectOpproof SplitLong SplitLongproof.
 Require Import SelectLong.
 
diff --git a/mppa_k1c/SelectOp.vp b/mppa_k1c/SelectOp.vp
index e4d65ced..f6605c11 100644
--- a/mppa_k1c/SelectOp.vp
+++ b/mppa_k1c/SelectOp.vp
@@ -15,6 +15,7 @@
 (*                                                                     *)
 (* *********************************************************************)
 
+
 (** Instruction selection for operators *)
 
 (** The instruction selection pass recognizes opportunities for using
@@ -49,9 +50,17 @@ Require Import Integers.
 Require Import Floats.
 Require Import Op.
 Require Import CminorSel.
+Require Import OpHelpers.
 
 Local Open Scope cminorsel_scope.
 
+Local Open Scope string_scope.
+Local Open Scope error_monad_scope.
+
+Section SELECT.
+
+Context {hf: helper_functions}.
+
 (** ** Constants **)
 
 Definition addrsymbol (id: ident) (ofs: ptrofs) :=
@@ -302,10 +311,17 @@ Nondetfunction notint (e: expr) :=
 
 (** ** 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 divs_base (e1: expr) (e2: expr) :=
+  Eexternal i32_sdiv sig_ii_i (e1 ::: e2 ::: Enil).
+  
+Definition mods_base (e1: expr) (e2: expr) :=
+  Eexternal i32_smod sig_ii_i (e1 ::: e2 ::: Enil).
+
+Definition divu_base (e1: expr) (e2: expr) :=
+  Eexternal i32_udiv sig_ii_i (e1 ::: e2 ::: Enil).
+  
+Definition modu_base (e1: expr) (e2: expr) :=
+  Eexternal i32_umod sig_ii_i (e1 ::: e2 ::: Enil).
 
 Definition shrximm (e1: expr) (n2: int) :=
   if Int.eq n2 Int.zero then e1 else Eop (Oshrximm n2) (e1:::Enil).
@@ -485,3 +501,14 @@ Nondetfunction builtin_arg (e: expr) :=
       if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e
   | _ => BA e
   end.
+
+(* float division *)
+
+Definition divf_base (e1: expr) (e2: expr) :=
+  (* Eop Odivf (e1 ::: e2 ::: Enil). *)
+  Eexternal f64_div sig_ff_f (e1 ::: e2 ::: Enil).
+
+Definition divfs_base (e1: expr) (e2: expr) :=
+  (* Eop Odivf (e1 ::: e2 ::: Enil). *)
+  Eexternal f32_div sig_ss_s (e1 ::: e2 ::: Enil).
+End SELECT.
diff --git a/mppa_k1c/SelectOpproof.v b/mppa_k1c/SelectOpproof.v
index 94d162a2..89af39ee 100644
--- a/mppa_k1c/SelectOpproof.v
+++ b/mppa_k1c/SelectOpproof.v
@@ -29,8 +29,13 @@ Require Import Cminor.
 Require Import Op.
 Require Import CminorSel.
 Require Import SelectOp.
+Require Import Events.
+Require Import OpHelpers.
+Require Import OpHelpersproof.
 
 Local Open Scope cminorsel_scope.
+Local Open Scope string_scope.
+
 
 (** * Useful lemmas and tactics *)
 
@@ -80,12 +85,53 @@ Ltac TrivialExists :=
 (** * Correctness of the smart constructors *)
 
 Section CMCONSTR.
-
-Variable ge: genv.
+Variable prog: program.
+Variable hf: helper_functions.
+Hypothesis HELPERS: helper_functions_declared prog hf.
+Let ge := Genv.globalenv prog.
 Variable sp: val.
 Variable e: env.
 Variable m: mem.
 
+(* Helper lemmas - from SplitLongproof.v *)
+
+Ltac UseHelper := decompose [Logic.and] arith_helpers_correct; eauto.
+Ltac DeclHelper := red in HELPERS; decompose [Logic.and] HELPERS; eauto.
+
+Lemma eval_helper:
+  forall le id name sg args vargs vres,
+  eval_exprlist ge sp e m le args vargs ->
+  helper_declared prog id name sg  ->
+  external_implements name sg vargs vres ->
+  eval_expr ge sp e m le (Eexternal id sg args) vres.
+Proof.
+  intros.
+  red in H0. apply Genv.find_def_symbol in H0. destruct H0 as (b & P & Q).
+  rewrite <- Genv.find_funct_ptr_iff in Q.
+  econstructor; eauto.
+Qed.
+
+Corollary eval_helper_1:
+  forall le id name sg arg1 varg1 vres,
+  eval_expr ge sp e m le arg1 varg1 ->
+  helper_declared prog id name sg  ->
+  external_implements name sg (varg1::nil) vres ->
+  eval_expr ge sp e m le (Eexternal id sg (arg1 ::: Enil)) vres.
+Proof.
+  intros. eapply eval_helper; eauto. constructor; auto. constructor.
+Qed.
+
+Corollary eval_helper_2:
+  forall le id name sg arg1 arg2 varg1 varg2 vres,
+  eval_expr ge sp e m le arg1 varg1 ->
+  eval_expr ge sp e m le arg2 varg2 ->
+  helper_declared prog id name sg  ->
+  external_implements name sg (varg1::varg2::nil) vres ->
+  eval_expr ge sp e m le (Eexternal id sg (arg1 ::: arg2 ::: Enil)) vres.
+Proof.
+  intros. eapply eval_helper; eauto. constructor; auto. constructor; auto. constructor.
+Qed.
+
 (** We now show that the code generated by "smart constructor" functions
   such as [Selection.notint] behaves as expected.  Continuing the
   [notint] example, we show that if the expression [e]
@@ -557,7 +603,8 @@ Theorem eval_divs_base:
     Val.divs x y = Some z ->
     exists v, eval_expr ge sp e m le (divs_base a b) v /\ Val.lessdef z v.
 Proof.
-  intros. unfold divs_base. exists z; split. EvalOp. auto.
+  intros; unfold divs_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
 Qed.
 
 Theorem eval_mods_base:
@@ -567,7 +614,8 @@ Theorem eval_mods_base:
     Val.mods x y = Some z ->
     exists v, eval_expr ge sp e m le (mods_base a b) v /\ Val.lessdef z v.
 Proof.
-  intros. unfold mods_base. exists z; split. EvalOp. auto.
+  intros; unfold mods_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
 Qed.
 
 Theorem eval_divu_base:
@@ -577,7 +625,8 @@ Theorem eval_divu_base:
     Val.divu x y = Some z ->
     exists v, eval_expr ge sp e m le (divu_base a b) v /\ Val.lessdef z v.
 Proof.
-  intros. unfold divu_base. exists z; split. EvalOp. auto.
+  intros; unfold divu_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
 Qed.
 
 Theorem eval_modu_base:
@@ -587,7 +636,8 @@ Theorem eval_modu_base:
     Val.modu x y = Some z ->
     exists v, eval_expr ge sp e m le (modu_base a b) v /\ Val.lessdef z v.
 Proof.
-  intros. unfold modu_base. exists z; split. EvalOp. auto.
+  intros; unfold modu_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
 Qed.
 
 Theorem eval_shrximm:
@@ -968,4 +1018,24 @@ Proof.
 - constructor; auto.
 Qed.
 
+(* floating-point division *)
+Theorem eval_divf_base:
+  forall le a b x y,
+  eval_expr ge sp e m le a x ->
+  eval_expr ge sp e m le b y ->
+  exists v, eval_expr ge sp e m le (divf_base a b) v /\ Val.lessdef (Val.divf x y) v.
+Proof.
+  intros; unfold divf_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
+Qed.
+
+Theorem eval_divfs_base:
+  forall le a b x y,
+  eval_expr ge sp e m le a x ->
+  eval_expr ge sp e m le b y ->
+  exists v, eval_expr ge sp e m le (divfs_base a b) v /\ Val.lessdef (Val.divfs x y) v.
+Proof.
+  intros; unfold divfs_base.
+  econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto.
+Qed.
 End CMCONSTR.
diff --git a/mppa_k1c/TargetPrinter.ml b/mppa_k1c/TargetPrinter.ml
index 5bcb5cc8..233dffec 100644
--- a/mppa_k1c/TargetPrinter.ml
+++ b/mppa_k1c/TargetPrinter.ml
@@ -258,10 +258,6 @@ module Target (*: TARGET*) =
          fprintf oc "	goto	%a\n" symbol s
       | Pigoto(rs) ->
          fprintf oc "	igoto	%a\n" ireg rs
-      | Pdiv ->
-         fprintf oc "	call	__divdi3\n"
-      | Pdivu ->
-         fprintf oc "	call	__udivdi3\n"
       | Pj_l(s) ->
          fprintf oc "	goto	%a\n" print_label s
       | Pcb (bt, r, lbl) | Pcbu (bt, r, lbl) ->