136 files changed, 595 insertions, 877 deletions

diff --git a/Makefile b/Makefile
index ed9059db..d8cd428a 100644
--- a/Makefile
+++ b/Makefile
@@ -72,7 +72,7 @@ COMMON=Errors.v AST.v Linking.v \
 # Back-end modules (in backend/, $(ARCH)/)
 
 BACKEND=\
-  Cminor.v Op.v CminorSel.v \
+  Cminor.v Op.v CminorSel.v OpHelpers.v OpHelpersproof.v \
   SelectOp.v SelectDiv.v SplitLong.v SelectLong.v Selection.v \
   SelectOpproof.v SelectDivproof.v SplitLongproof.v \
   SelectLongproof.v Selectionproof.v \
diff --git a/arm/Machregsaux.ml b/arm/Machregsaux.ml
index ce5c67f6..14c75155 100644
--- a/arm/Machregsaux.ml
+++ b/arm/Machregsaux.ml
@@ -33,3 +33,8 @@ let register_by_name s =
 let can_reserve_register r =
   List.mem r Conventions1.int_callee_save_regs
   || List.mem r Conventions1.float_callee_save_regs
+                                              
+let class_of_type = function
+  | AST.Tint | AST.Tlong -> 0
+  | AST.Tfloat | AST.Tsingle -> 1
+  | AST.Tany32 | AST.Tany64 -> assert false
diff --git a/arm/Machregsaux.mli b/arm/Machregsaux.mli
index 9404568d..d7117c21 100644
--- a/arm/Machregsaux.mli
+++ b/arm/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/arm/SelectLong.vp b/arm/SelectLong.vp
index cc7a38f6..b4cdd0e3 100644
--- a/arm/SelectLong.vp
+++ b/arm/SelectLong.vp
@@ -16,6 +16,6 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
-Require Import SelectOp SplitLong.
+Require Import OpHelpers SelectOp SplitLong.
 
 (** This file is empty because we use the default implementation provided in [SplitLong]. *)
diff --git a/arm/SelectLongproof.v b/arm/SelectLongproof.v
index a82c082c..a65a38d4 100644
--- a/arm/SelectLongproof.v
+++ b/arm/SelectLongproof.v
@@ -16,6 +16,7 @@ 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/arm/SelectOp.vp b/arm/SelectOp.vp
index c361df65..f3f01730 100644
--- a/arm/SelectOp.vp
+++ b/arm/SelectOp.vp
@@ -42,6 +42,7 @@ Require Import AST.
 Require Import Integers.
 Require Import Floats.
 Require Import Op.
+Require Import OpHelpers.
 Require Import CminorSel.
 
 Local Open Scope cminorsel_scope.
@@ -508,3 +509,10 @@ Nondetfunction builtin_arg (e: expr) :=
   | Eop (Oaddimm n) (e1:::Enil) => BA_addptr (BA e1) (BA_int n)
   | _ => BA e
   end.
+
+(* floats *)
+Definition divf_base (e1: expr) (e2: expr) :=
+  Eop Odivf (e1 ::: e2 ::: Enil).
+
+Definition divfs_base (e1: expr) (e2: expr) :=
+  Eop Odivfs (e1 ::: e2 ::: Enil).
diff --git a/arm/SelectOpproof.v b/arm/SelectOpproof.v
index d4aac9b6..212bcfd7 100644
--- a/arm/SelectOpproof.v
+++ b/arm/SelectOpproof.v
@@ -24,6 +24,7 @@ Require Import Cminor.
 Require Import Op.
 Require Import CminorSel.
 Require Import SelectOp.
+Require Import OpHelpers OpHelpersproof.
 
 Local Open Scope cminorsel_scope.
 Local Transparent Archi.ptr64.
@@ -76,8 +77,10 @@ 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.
@@ -893,4 +896,25 @@ Proof.
 - constructor; auto.
 Qed.
 
+
+(* floating-point division without HELPERS *)
+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.
+  TrivialExists.
+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.
+  TrivialExists.
+Qed.
 End CMCONSTR.
diff --git a/backend/IRC.ml b/backend/IRC.ml
index c7b1bf04..67da47da 100644
--- a/backend/IRC.ml
+++ b/backend/IRC.ml
@@ -15,6 +15,7 @@ open Camlcoq
 open AST
 open Registers
 open Machregs
+open Machregsaux
 open Locations
 open Conventions1
 open XTL
@@ -237,13 +238,9 @@ type graph = {
    according to their types.  A variable can be forced into class 2
    by giving it a negative spill cost. *)
 
-let class_of_type = function
-  | Tint | Tlong -> 0
-  | Tfloat | Tsingle -> 0 (* normal: 1 *)
-  | Tany32 | Tany64 -> assert false
 
-let class_of_reg r = 0
-  (* normal: if Conventions1.is_float_reg r then 1 else 0 *)
+let class_of_reg r =
+  if Conventions1.is_float_reg r then 1 else 0
 
 let class_of_loc = function
   | R r -> class_of_reg r
diff --git a/backend/IRC.mli b/backend/IRC.mli
index 30b6d5c1..f7bbf9c5 100644
--- a/backend/IRC.mli
+++ b/backend/IRC.mli
@@ -43,5 +43,4 @@ val coloring: graph -> (var -> loc)
 val reserved_registers: mreg list ref
 
 (* Auxiliaries to deal with register classes *)
-val class_of_type: AST.typ -> int
 val class_of_loc: loc -> int
diff --git a/backend/OpHelpers.v b/backend/OpHelpers.v
new file mode 100644
index 00000000..53414dab
--- /dev/null
+++ b/backend/OpHelpers.v
@@ -0,0 +1,42 @@
+Require Import Coqlib.
+Require Import AST Integers Floats.
+Require Import Op CminorSel.
+
+(** Some arithmetic operations are transformed into calls to
+  runtime library functions.  The following type class collects
+  the names of these functions. *)
+
+Definition sig_l_l := mksignature (Tlong :: nil) (Some Tlong) cc_default.
+Definition sig_l_f := mksignature (Tlong :: nil) (Some Tfloat) cc_default.
+Definition sig_l_s := mksignature (Tlong :: nil) (Some Tsingle) cc_default.
+Definition sig_f_l := mksignature (Tfloat :: nil) (Some Tlong) cc_default.
+Definition sig_ll_l := mksignature (Tlong :: Tlong :: nil) (Some Tlong) cc_default.
+Definition sig_li_l := mksignature (Tlong :: Tint :: nil) (Some Tlong) cc_default.
+Definition sig_ii_l := mksignature (Tint :: Tint :: nil) (Some Tlong) cc_default.
+Definition sig_ii_i := mksignature (Tint :: Tint :: nil) (Some Tint) cc_default.
+Definition sig_ff_f := mksignature (Tfloat :: Tfloat :: nil) (Some Tfloat) cc_default.
+Definition sig_ss_s := mksignature (Tsingle :: Tsingle :: nil) (Some Tsingle) cc_default.
+
+Class helper_functions := mk_helper_functions {
+  i64_dtos: ident;                      (**r float64 -> signed long *)
+  i64_dtou: ident;                      (**r float64 -> unsigned long *)
+  i64_stod: ident;                      (**r signed long -> float64 *)
+  i64_utod: ident;                      (**r unsigned long -> float64 *)
+  i64_stof: ident;                      (**r signed long -> float32 *)
+  i64_utof: ident;                      (**r unsigned long -> float32 *)
+  i64_sdiv: ident;                      (**r signed division *)
+  i64_udiv: ident;                      (**r unsigned division *)
+  i64_smod: ident;                      (**r signed remainder *)
+  i64_umod: ident;                      (**r unsigned remainder *)
+  i64_shl: ident;                       (**r shift left *)
+  i64_shr: ident;                       (**r shift right unsigned *)
+  i64_sar: ident;                       (**r shift right signed *)
+  i64_umulh: ident;                     (**r unsigned multiply high *)
+  i64_smulh: ident;                     (**r signed multiply high *)
+  i32_sdiv: ident;                      (**r signed division *)
+  i32_udiv: ident;                      (**r unsigned division *)
+  i32_smod: ident;                      (**r signed remainder *)
+  i32_umod: ident;                      (**r unsigned remainder *)
+  f64_div: ident;                       (**float division*)
+  f32_div: ident;                       (**float division*)
+}.
diff --git a/backend/OpHelpersproof.v b/backend/OpHelpersproof.v
new file mode 100644
index 00000000..63040c5f
--- /dev/null
+++ b/backend/OpHelpersproof.v
@@ -0,0 +1,78 @@
+Require Import Coqlib.
+Require Import Maps.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Values.
+Require Import Memory.
+Require Import Globalenvs.
+Require Import Cminor.
+Require Import Op.
+Require Import CminorSel.
+Require Import Events.
+Require Import OpHelpers.
+
+(** * Axiomatization of the helper functions *)
+
+Definition external_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
+  forall F V (ge: Genv.t F V) m,
+  external_call (EF_runtime name sg) ge vargs m E0 vres m.
+
+Definition builtin_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
+  forall F V (ge: Genv.t F V) m,
+  external_call (EF_builtin name sg) ge vargs m E0 vres m.
+
+Axiom arith_helpers_correct :
+    (forall x z, Val.longoffloat x = Some z -> external_implements "__compcert_i64_dtos" sig_f_l (x::nil) z)
+ /\ (forall x z, Val.longuoffloat x = Some z -> external_implements "__compcert_i64_dtou" sig_f_l (x::nil) z)
+ /\ (forall x z, Val.floatoflong x = Some z -> external_implements "__compcert_i64_stod" sig_l_f (x::nil) z)
+ /\ (forall x z, Val.floatoflongu x = Some z -> external_implements "__compcert_i64_utod" sig_l_f (x::nil) z)
+ /\ (forall x z, Val.singleoflong x = Some z -> external_implements "__compcert_i64_stof" sig_l_s (x::nil) z)
+ /\ (forall x z, Val.singleoflongu x = Some z -> external_implements "__compcert_i64_utof" sig_l_s (x::nil) z)
+ /\ (forall x, builtin_implements "__builtin_negl" sig_l_l (x::nil) (Val.negl x))
+ /\ (forall x y, builtin_implements "__builtin_addl" sig_ll_l (x::y::nil) (Val.addl x y))
+ /\ (forall x y, builtin_implements "__builtin_subl" sig_ll_l (x::y::nil) (Val.subl x y))
+ /\ (forall x y, builtin_implements "__builtin_mull" sig_ii_l (x::y::nil) (Val.mull' x y))
+ /\ (forall x y z, Val.divls x y = Some z -> external_implements "__compcert_i64_sdiv" sig_ll_l (x::y::nil) z)
+ /\ (forall x y z, Val.divlu x y = Some z -> external_implements "__compcert_i64_udiv" sig_ll_l (x::y::nil) z)
+ /\ (forall x y z, Val.modls x y = Some z -> external_implements "__compcert_i64_smod" sig_ll_l (x::y::nil) z)
+ /\ (forall x y z, Val.modlu x y = Some z -> external_implements "__compcert_i64_umod" sig_ll_l (x::y::nil) z)
+ /\ (forall x y, external_implements "__compcert_i64_shl" sig_li_l (x::y::nil) (Val.shll x y))
+ /\ (forall x y, external_implements "__compcert_i64_shr" sig_li_l (x::y::nil) (Val.shrlu x y))
+ /\ (forall x y, external_implements "__compcert_i64_sar" sig_li_l (x::y::nil) (Val.shrl x y))
+ /\ (forall x y, external_implements "__compcert_i64_umulh" sig_ll_l (x::y::nil) (Val.mullhu x y))
+ /\ (forall x y, external_implements "__compcert_i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y))
+ /\ (forall x y z, Val.divs x y = Some z -> external_implements "__compcert_i32_sdiv" sig_ii_i (x::y::nil) z)
+ /\ (forall x y z, Val.divu x y = Some z -> external_implements "__compcert_i32_udiv" sig_ii_i (x::y::nil) z)
+ /\ (forall x y z, Val.mods x y = Some z -> external_implements "__compcert_i32_smod" sig_ii_i (x::y::nil) z)
+ /\ (forall x y z, Val.modu x y = Some z -> external_implements "__compcert_i32_umod" sig_ii_i (x::y::nil) z)
+ /\ (forall x y z, Val.divfs x y = z -> external_implements "__compcert_f32_div" sig_ss_s (x::y::nil) z)
+ /\ (forall x y z, Val.divf x y = z -> external_implements "__compcert_f64_div" sig_ff_f (x::y::nil) z)
+.
+
+Definition helper_declared {F V: Type} (p: AST.program (AST.fundef F) V) (id: ident) (name: string) (sg: signature) : Prop :=
+  (prog_defmap p)!id = Some (Gfun (External (EF_runtime name sg))).
+
+Definition helper_functions_declared {F V: Type} (p: AST.program (AST.fundef F) V) (hf: helper_functions) : Prop :=
+     helper_declared p i64_dtos "__compcert_i64_dtos" sig_f_l
+  /\ helper_declared p i64_dtou "__compcert_i64_dtou" sig_f_l
+  /\ helper_declared p i64_stod "__compcert_i64_stod" sig_l_f
+  /\ helper_declared p i64_utod "__compcert_i64_utod" sig_l_f
+  /\ helper_declared p i64_stof "__compcert_i64_stof" sig_l_s
+  /\ helper_declared p i64_utof "__compcert_i64_utof" sig_l_s
+  /\ helper_declared p i64_sdiv "__compcert_i64_sdiv" sig_ll_l
+  /\ helper_declared p i64_udiv "__compcert_i64_udiv" sig_ll_l
+  /\ helper_declared p i64_smod "__compcert_i64_smod" sig_ll_l
+  /\ helper_declared p i64_umod "__compcert_i64_umod" sig_ll_l
+  /\ helper_declared p i64_shl "__compcert_i64_shl" sig_li_l
+  /\ helper_declared p i64_shr "__compcert_i64_shr" sig_li_l
+  /\ helper_declared p i64_sar "__compcert_i64_sar" sig_li_l
+  /\ helper_declared p i64_umulh "__compcert_i64_umulh" sig_ll_l
+  /\ helper_declared p i64_smulh "__compcert_i64_smulh" sig_ll_l
+  /\ helper_declared p i32_sdiv "__compcert_i32_sdiv" sig_ii_i
+  /\ helper_declared p i32_udiv "__compcert_i32_udiv" sig_ii_i
+  /\ helper_declared p i32_smod "__compcert_i32_smod" sig_ii_i
+  /\ helper_declared p i32_umod "__compcert_i32_umod" sig_ii_i
+  /\ helper_declared p f32_div  "__compcert_f32_div"  sig_ss_s
+  /\ helper_declared p f64_div  "__compcert_f64_div"  sig_ff_f
+.
diff --git a/backend/Regalloc.ml b/backend/Regalloc.ml
index 19aba4f6..7db8a866 100644
--- a/backend/Regalloc.ml
+++ b/backend/Regalloc.ml
@@ -1067,7 +1067,7 @@ let make_parmove srcs dsts itmp ftmp k =
     | Locations.S(sl, ofs, ty), R rd ->
         code := LTL.Lgetstack(sl, ofs, ty, rd) :: !code
     | Locations.S(sls, ofss, tys), Locations.S(sld, ofsd, tyd) ->
-        let tmp = temp_for (class_of_type tys) in
+        let tmp = temp_for (Machregsaux.class_of_type tys) in
         (* code will be reversed at the end *)
         code := LTL.Lsetstack(tmp, sld, ofsd, tyd) ::
                 LTL.Lgetstack(sls, ofss, tys, tmp) :: !code
diff --git a/backend/SelectDiv.vp b/backend/SelectDiv.vp
index 7241d028..9f852616 100644
--- a/backend/SelectDiv.vp
+++ b/backend/SelectDiv.vp
@@ -15,7 +15,7 @@
 Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
-Require Import Op CminorSel SelectOp SplitLong SelectLong.
+Require Import Op CminorSel OpHelpers SelectOp SplitLong SelectLong.
 
 Local Open Scope cminorsel_scope.
 
diff --git a/backend/SelectDivproof.v b/backend/SelectDivproof.v
index dbd3f58d..e2249ddb 100644
--- a/backend/SelectDivproof.v
+++ b/backend/SelectDivproof.v
@@ -15,6 +15,7 @@
 Require Import Zquot Coqlib.
 Require Import AST Integers Floats Values Memory Globalenvs Events.
 Require Import Cminor Op CminorSel.
+Require Import OpHelpers OpHelpersproof.
 Require Import SelectOp SelectOpproof SplitLong SplitLongproof SelectLong SelectLongproof SelectDiv.
 
 Local Open Scope cminorsel_scope.
diff --git a/backend/Selection.v b/backend/Selection.v
index aba84049..05a06abf 100644
--- a/backend/Selection.v
+++ b/backend/Selection.v
@@ -26,7 +26,7 @@ Require String.
 Require Import Coqlib Maps.
 Require Import AST Errors Integers Globalenvs Switch.
 Require Cminor.
-Require Import Op CminorSel.
+Require Import Op CminorSel OpHelpers.
 Require Import SelectOp SplitLong SelectLong SelectDiv.
 Require Machregs.
 
diff --git a/backend/Selectionproof.v b/backend/Selectionproof.v
index 5a0fafaf..50ff377a 100644
--- a/backend/Selectionproof.v
+++ b/backend/Selectionproof.v
@@ -16,6 +16,7 @@ Require Import FunInd.
 Require Import Coqlib Maps.
 Require Import AST Linking Errors Integers Values Memory Events Globalenvs Smallstep.
 Require Import Switch Cminor Op CminorSel.
+Require Import OpHelpers OpHelpersproof.
 Require Import SelectOp SelectDiv SplitLong SelectLong Selection.
 Require Import SelectOpproof SelectDivproof SplitLongproof SelectLongproof.
 
diff --git a/backend/SplitLong.vp b/backend/SplitLong.vp
index 6a7d4f5c..dfe42df0 100644
--- a/backend/SplitLong.vp
+++ b/backend/SplitLong.vp
@@ -16,6 +16,7 @@ Require String.
 Require Import Coqlib.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
+Require Import OpHelpers.
 Require Import SelectOp.
 
 Local Open Scope cminorsel_scope.
diff --git a/backend/SplitLongproof.v b/backend/SplitLongproof.v
index a74276c7..6718ba5b 100644
--- a/backend/SplitLongproof.v
+++ b/backend/SplitLongproof.v
@@ -16,6 +16,7 @@ Require Import String.
 Require Import Coqlib Maps.
 Require Import AST Errors Integers Floats.
 Require Import Values Memory Globalenvs Events Cminor Op CminorSel.
+Require Import OpHelpers OpHelpersproof.
 Require Import SelectOp SelectOpproof SplitLong.
 
 Local Open Scope cminorsel_scope.
@@ -33,7 +34,7 @@ Variable sp: val.
 Variable e: env.
 Variable m: mem.
 
-Ltac UseHelper := decompose [Logic.and] i64_helpers_correct; eauto.
+Ltac UseHelper := decompose [Logic.and] arith_helpers_correct; eauto.
 Ltac DeclHelper := red in HELPERS; decompose [Logic.and] HELPERS; eauto.
 
 Lemma eval_helper:
diff --git a/mppa_k1c/Asm.v b/mppa_k1c/Asm.v
index 493f4a05..0ca554ab 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)

@@ -218,8 +215,6 @@ 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 d335801e..fdec8ed2 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 !
 
@@ -1486,17 +1483,6 @@ 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 501ec212..ad96ae87 100644
--- a/mppa_k1c/Asmblockdeps.v
+++ b/mppa_k1c/Asmblockdeps.v
@@ -540,8 +540,6 @@ Definition trans_control (ctl: control) : macro :=
   | Pj_l l => [(#PC, Op (Control (Oj_l l)) (Name (#PC) @ Enil))]
   | Pcb bt r l => [(#PC, Op (Control (Ocb bt l)) (Name (#r) @ Name (#PC) @ Enil))]
   | Pcbu bt r l => [(#PC, Op (Control (Ocbu bt l)) (Name (#r) @ Name (#PC) @ 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.
 
@@ -863,22 +861,6 @@ 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.
     (* Pj_l *)
     + unfold goto_label in H0. destruct (label_pos _ _ _) eqn:LPOS; try discriminate. destruct (nextblock _ _ _) eqn:NB; try discriminate. inv H0.
       eexists; split; try split.
@@ -1070,12 +1052,6 @@ 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.
 (* Pj_l *)
   - simpl in *. pose (H3 PC); simpl in e; rewrite e in H1. clear e.
     unfold goto_label_deps in H1. unfold goto_label.
@@ -1187,11 +1163,6 @@ 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.
 (* Pj_l *)
   - simpl in *. pose (H3 PC); simpl in e; rewrite e. unfold goto_label_deps. unfold goto_label in H0.
     destruct (label_pos _ _ _); auto. clear e. destruct (rs PC); auto. discriminate.
diff --git a/mppa_k1c/Asmblockgen.v b/mppa_k1c/Asmblockgen.v
index 5b00a64f..c03e319c 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/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 2c39e342..56b00c7e 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 19712d2f..f6605c11 100644
--- a/mppa_k1c/SelectOp.vp
+++ b/mppa_k1c/SelectOp.vp
@@ -50,6 +50,7 @@ Require Import Integers.
 Require Import Floats.
 Require Import Op.
 Require Import CminorSel.
+Require Import OpHelpers.
 
 Local Open Scope cminorsel_scope.
 
@@ -57,44 +58,6 @@ Local Open Scope string_scope.
 Local Open Scope error_monad_scope.
 
 Section SELECT.
-(** Some operations on 64-bit integers are transformed into calls to
-  runtime library functions.  The following type class collects
-  the names of these functions. *)
-
-Definition sig_l_l := mksignature (Tlong :: nil) (Some Tlong) cc_default.
-Definition sig_l_f := mksignature (Tlong :: nil) (Some Tfloat) cc_default.
-Definition sig_l_s := mksignature (Tlong :: nil) (Some Tsingle) cc_default.
-Definition sig_f_l := mksignature (Tfloat :: nil) (Some Tlong) cc_default.
-Definition sig_ll_l := mksignature (Tlong :: Tlong :: nil) (Some Tlong) cc_default.
-Definition sig_li_l := mksignature (Tlong :: Tint :: nil) (Some Tlong) cc_default.
-Definition sig_ii_l := mksignature (Tint :: Tint :: nil) (Some Tlong) cc_default.
-Definition sig_ii_i := mksignature (Tint :: Tint :: nil) (Some Tint) cc_default.
-Definition sig_ff_f := mksignature (Tfloat :: Tfloat :: nil) (Some Tfloat) cc_default.
-Definition sig_ss_s := mksignature (Tsingle :: Tsingle :: nil) (Some Tsingle) cc_default.
-
-Class helper_functions := mk_helper_functions {
-  i64_dtos: ident;                      (**r float64 -> signed long *)
-  i64_dtou: ident;                      (**r float64 -> unsigned long *)
-  i64_stod: ident;                      (**r signed long -> float64 *)
-  i64_utod: ident;                      (**r unsigned long -> float64 *)
-  i64_stof: ident;                      (**r signed long -> float32 *)
-  i64_utof: ident;                      (**r unsigned long -> float32 *)
-  i64_sdiv: ident;                      (**r signed division *)
-  i64_udiv: ident;                      (**r unsigned division *)
-  i64_smod: ident;                      (**r signed remainder *)
-  i64_umod: ident;                      (**r unsigned remainder *)
-  i64_shl: ident;                       (**r shift left *)
-  i64_shr: ident;                       (**r shift right unsigned *)
-  i64_sar: ident;                       (**r shift right signed *)
-  i64_umulh: ident;                     (**r unsigned multiply high *)
-  i64_smulh: ident;                     (**r signed multiply high *)
-  i32_sdiv: ident;                      (**r signed division *)
-  i32_udiv: ident;                      (**r unsigned division *)
-  i32_smod: ident;                      (**r signed remainder *)
-  i32_umod: ident;                      (**r unsigned remainder *)
-  f64_div: ident;                       (**float division*)
-  f32_div: ident;                       (**float division*)
-}.
 
 Context {hf: helper_functions}.
 
diff --git a/mppa_k1c/SelectOpproof.v b/mppa_k1c/SelectOpproof.v
index a4a5f72b..89af39ee 100644
--- a/mppa_k1c/SelectOpproof.v
+++ b/mppa_k1c/SelectOpproof.v
@@ -30,76 +30,13 @@ 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.
 
 
-(** * Axiomatization of the helper functions *)
-
-Definition external_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
-  forall F V (ge: Genv.t F V) m,
-  external_call (EF_runtime name sg) ge vargs m E0 vres m.
-
-Definition builtin_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
-  forall F V (ge: Genv.t F V) m,
-  external_call (EF_builtin name sg) ge vargs m E0 vres m.
-
-Axiom i64_helpers_correct :
-    (forall x z, Val.longoffloat x = Some z -> external_implements "__compcert_i64_dtos" sig_f_l (x::nil) z)
- /\ (forall x z, Val.longuoffloat x = Some z -> external_implements "__compcert_i64_dtou" sig_f_l (x::nil) z)
- /\ (forall x z, Val.floatoflong x = Some z -> external_implements "__compcert_i64_stod" sig_l_f (x::nil) z)
- /\ (forall x z, Val.floatoflongu x = Some z -> external_implements "__compcert_i64_utod" sig_l_f (x::nil) z)
- /\ (forall x z, Val.singleoflong x = Some z -> external_implements "__compcert_i64_stof" sig_l_s (x::nil) z)
- /\ (forall x z, Val.singleoflongu x = Some z -> external_implements "__compcert_i64_utof" sig_l_s (x::nil) z)
- /\ (forall x, builtin_implements "__builtin_negl" sig_l_l (x::nil) (Val.negl x))
- /\ (forall x y, builtin_implements "__builtin_addl" sig_ll_l (x::y::nil) (Val.addl x y))
- /\ (forall x y, builtin_implements "__builtin_subl" sig_ll_l (x::y::nil) (Val.subl x y))
- /\ (forall x y, builtin_implements "__builtin_mull" sig_ii_l (x::y::nil) (Val.mull' x y))
- /\ (forall x y z, Val.divls x y = Some z -> external_implements "__compcert_i64_sdiv" sig_ll_l (x::y::nil) z)
- /\ (forall x y z, Val.divlu x y = Some z -> external_implements "__compcert_i64_udiv" sig_ll_l (x::y::nil) z)
- /\ (forall x y z, Val.modls x y = Some z -> external_implements "__compcert_i64_smod" sig_ll_l (x::y::nil) z)
- /\ (forall x y z, Val.modlu x y = Some z -> external_implements "__compcert_i64_umod" sig_ll_l (x::y::nil) z)
- /\ (forall x y, external_implements "__compcert_i64_shl" sig_li_l (x::y::nil) (Val.shll x y))
- /\ (forall x y, external_implements "__compcert_i64_shr" sig_li_l (x::y::nil) (Val.shrlu x y))
- /\ (forall x y, external_implements "__compcert_i64_sar" sig_li_l (x::y::nil) (Val.shrl x y))
- /\ (forall x y, external_implements "__compcert_i64_umulh" sig_ll_l (x::y::nil) (Val.mullhu x y))
- /\ (forall x y, external_implements "__compcert_i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y))
- /\ (forall x y z, Val.divs x y = Some z -> external_implements "__compcert_i32_sdiv" sig_ii_i (x::y::nil) z)
- /\ (forall x y z, Val.divu x y = Some z -> external_implements "__compcert_i32_udiv" sig_ii_i (x::y::nil) z)
- /\ (forall x y z, Val.mods x y = Some z -> external_implements "__compcert_i32_smod" sig_ii_i (x::y::nil) z)
- /\ (forall x y z, Val.modu x y = Some z -> external_implements "__compcert_i32_umod" sig_ii_i (x::y::nil) z)
- /\ (forall x y z, Val.divfs x y = z -> external_implements "__compcert_f32_div" sig_ss_s (x::y::nil) z)
- /\ (forall x y z, Val.divf x y = z -> external_implements "__compcert_f64_div" sig_ff_f (x::y::nil) z)
-.
-
-Definition helper_declared {F V: Type} (p: AST.program (AST.fundef F) V) (id: ident) (name: string) (sg: signature) : Prop :=
-  (prog_defmap p)!id = Some (Gfun (External (EF_runtime name sg))).
-
-Definition helper_functions_declared {F V: Type} (p: AST.program (AST.fundef F) V) (hf: helper_functions) : Prop :=
-     helper_declared p i64_dtos "__compcert_i64_dtos" sig_f_l
-  /\ helper_declared p i64_dtou "__compcert_i64_dtou" sig_f_l
-  /\ helper_declared p i64_stod "__compcert_i64_stod" sig_l_f
-  /\ helper_declared p i64_utod "__compcert_i64_utod" sig_l_f
-  /\ helper_declared p i64_stof "__compcert_i64_stof" sig_l_s
-  /\ helper_declared p i64_utof "__compcert_i64_utof" sig_l_s
-  /\ helper_declared p i64_sdiv "__compcert_i64_sdiv" sig_ll_l
-  /\ helper_declared p i64_udiv "__compcert_i64_udiv" sig_ll_l
-  /\ helper_declared p i64_smod "__compcert_i64_smod" sig_ll_l
-  /\ helper_declared p i64_umod "__compcert_i64_umod" sig_ll_l
-  /\ helper_declared p i64_shl "__compcert_i64_shl" sig_li_l
-  /\ helper_declared p i64_shr "__compcert_i64_shr" sig_li_l
-  /\ helper_declared p i64_sar "__compcert_i64_sar" sig_li_l
-  /\ helper_declared p i64_umulh "__compcert_i64_umulh" sig_ll_l
-  /\ helper_declared p i64_smulh "__compcert_i64_smulh" sig_ll_l
-  /\ helper_declared p i32_sdiv "__compcert_i32_sdiv" sig_ii_i
-  /\ helper_declared p i32_udiv "__compcert_i32_udiv" sig_ii_i
-  /\ helper_declared p i32_smod "__compcert_i32_smod" sig_ii_i
-  /\ helper_declared p i32_umod "__compcert_i32_umod" sig_ii_i
-  /\ helper_declared p f32_div  "__compcert_f32_div"  sig_ss_s
-  /\ helper_declared p f64_div  "__compcert_f64_div"  sig_ff_f
-.
-
 (** * Useful lemmas and tactics *)
 
 (** The following are trivial lemmas and custom tactics that help
@@ -158,7 +95,7 @@ Variable m: mem.
 
 (* Helper lemmas - from SplitLongproof.v *)
 
-Ltac UseHelper := decompose [Logic.and] i64_helpers_correct; eauto.
+Ltac UseHelper := decompose [Logic.and] arith_helpers_correct; eauto.
 Ltac DeclHelper := red in HELPERS; decompose [Logic.and] HELPERS; eauto.
 
 Lemma eval_helper:
diff --git a/mppa_k1c/TargetPrinter.ml b/mppa_k1c/TargetPrinter.ml
index d4e2afc9..69824852 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) ->
diff --git a/powerpc/Machregsaux.ml b/powerpc/Machregsaux.ml
index 664f71a0..0b0d4548 100644
--- a/powerpc/Machregsaux.ml
+++ b/powerpc/Machregsaux.ml
@@ -33,3 +33,8 @@ let register_by_name s =
 let can_reserve_register r =
   List.mem r Conventions1.int_callee_save_regs
   || List.mem r Conventions1.float_callee_save_regs
+                                              
+let class_of_type = function
+  | AST.Tint | AST.Tlong -> 0
+  | AST.Tfloat | AST.Tsingle -> 1
+  | AST.Tany32 | AST.Tany64 -> assert false
diff --git a/powerpc/Machregsaux.mli b/powerpc/Machregsaux.mli
index 9404568d..d7117c21 100644
--- a/powerpc/Machregsaux.mli
+++ b/powerpc/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/powerpc/SelectLong.vp b/powerpc/SelectLong.vp
index 5f13774b..e4274ba5 100644
--- a/powerpc/SelectLong.vp
+++ b/powerpc/SelectLong.vp
@@ -16,7 +16,7 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
-Require Import SelectOp SplitLong.
+Require Import OpHelpers SelectOp SplitLong.
 
 Local Open Scope cminorsel_scope.
 Local Open Scope string_scope.
diff --git a/powerpc/SelectLongproof.v b/powerpc/SelectLongproof.v
index a214d131..b4e48596 100644
--- a/powerpc/SelectLongproof.v
+++ b/powerpc/SelectLongproof.v
@@ -16,6 +16,7 @@ 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/powerpc/SelectOp.vp b/powerpc/SelectOp.vp
index d2ca408a..478ce251 100644
--- a/powerpc/SelectOp.vp
+++ b/powerpc/SelectOp.vp
@@ -43,6 +43,7 @@ Require Import Integers.
 Require Import Floats.
 Require Import Op.
 Require Import CminorSel.
+Require Import OpHelpers.
 
 Local Open Scope cminorsel_scope.
 
@@ -552,3 +553,10 @@ Nondetfunction builtin_arg (e: expr) :=
   | Eop Oadd (e1:::e2:::Enil) => BA_addptr (BA e1) (BA e2)
   | _ => BA e
   end.
+
+(* floats *)
+Definition divf_base (e1: expr) (e2: expr) :=
+  Eop Odivf (e1 ::: e2 ::: Enil).
+
+Definition divfs_base (e1: expr) (e2: expr) :=
+  Eop Odivfs (e1 ::: e2 ::: Enil).
diff --git a/powerpc/SelectOpproof.v b/powerpc/SelectOpproof.v
index 5f87d9b9..00b91e70 100644
--- a/powerpc/SelectOpproof.v
+++ b/powerpc/SelectOpproof.v
@@ -25,6 +25,8 @@ Require Import Cminor.
 Require Import Op.
 Require Import CminorSel.
 Require Import SelectOp.
+Require Import OpHelpers.
+Require Import OpHelpersproof.
 
 Local Open Scope cminorsel_scope.
 Local Transparent Archi.ptr64.
@@ -77,8 +79,10 @@ 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.
@@ -1044,4 +1048,24 @@ Proof.
 - constructor; auto.
 Qed.
 
+(* floating-point division without HELPERS *)
+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.
+  TrivialExists.
+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.
+  TrivialExists.
+Qed.
 End CMCONSTR.
diff --git a/riscV/Machregsaux.ml b/riscV/Machregsaux.ml
index 473e0602..07097eaf 100644
--- a/riscV/Machregsaux.ml
+++ b/riscV/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 -> 0
+  | AST.Tfloat | AST.Tsingle -> 1
+  | AST.Tany32 | AST.Tany64 -> assert false
diff --git a/riscV/Machregsaux.mli b/riscV/Machregsaux.mli
index 9404568d..d7117c21 100644
--- a/riscV/Machregsaux.mli
+++ b/riscV/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/riscV/SelectLong.vp b/riscV/SelectLong.vp
index b3e07bf5..0ccc4725 100644
--- a/riscV/SelectLong.vp
+++ b/riscV/SelectLong.vp
@@ -21,7 +21,7 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
-Require Import SelectOp SplitLong.
+Require Import OpHelpers SelectOp SplitLong.
 
 Local Open Scope cminorsel_scope.
 Local Open Scope string_scope.
diff --git a/riscV/SelectLongproof.v b/riscV/SelectLongproof.v
index 78a1935d..d47b6d64 100644
--- a/riscV/SelectLongproof.v
+++ b/riscV/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/riscV/SelectOp.vp b/riscV/SelectOp.vp
index bb8af2ed..181b9d05 100644
--- a/riscV/SelectOp.vp
+++ b/riscV/SelectOp.vp
@@ -448,3 +448,10 @@ Nondetfunction builtin_arg (e: expr) :=
       if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e
   | _ => BA e
   end.
+
+(* floats *)
+Definition divf_base (e1: expr) (e2: expr) :=
+  Eop Odivf (e1 ::: e2 ::: Enil).
+
+Definition divfs_base (e1: expr) (e2: expr) :=
+  Eop Odivfs (e1 ::: e2 ::: Enil).
diff --git a/riscV/SelectOpproof.v b/riscV/SelectOpproof.v
index 90f077db..9966305c 100644
--- a/riscV/SelectOpproof.v
+++ b/riscV/SelectOpproof.v
@@ -29,6 +29,8 @@ Require Import Cminor.
 Require Import Op.
 Require Import CminorSel.
 Require Import SelectOp.
+Require Import OpHelpers.
+Require Import OpHelpersproof.
 
 Local Open Scope cminorsel_scope.
 
@@ -80,8 +82,10 @@ 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.
@@ -922,4 +926,25 @@ Proof.
 - constructor; auto.
 Qed.
 
+
+(* floating-point division without HELPERS *)
+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.
+  TrivialExists.
+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.
+  TrivialExists.
+Qed.
 End CMCONSTR.
diff --git a/test/monniaux/mbedtls/mbedtls_Kalray.patch b/test/monniaux/mbedtls/mbedtls_Kalray.patch
index 25cd5922..594ee7fa 100644
--- a/test/monniaux/mbedtls/mbedtls_Kalray.patch
+++ b/test/monniaux/mbedtls/mbedtls_Kalray.patch
@@ -39,56 +39,6 @@ index f89bf9604..9f8a4faeb 100644
  
  /**
   * \def MBEDTLS_VERSION_C
-diff --git a/library/bignum.c b/library/bignum.c
-index 87015af0c..a2bad7b84 100644
---- a/library/bignum.c
-+++ b/library/bignum.c
-@@ -1696,6 +1696,8 @@ cleanup:
-     return( ret );
- }
- 
-+#define INT_DIV(x,y) ((x) / (y))
-+
- /*
-  * Modulo: r = A mod b
-  */
-@@ -1734,12 +1736,12 @@ int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_
-     {
-         x  = A->p[i - 1];
-         y  = ( y << biH ) | ( x >> biH );
--        z  = y / b;
-+        z  = INT_DIV(y, b);
-         y -= z * b;
- 
-         x <<= biH;
-         y  = ( y << biH ) | ( x >> biH );
--        z  = y / b;
-+        z  = INT_DIV(y, b);
-         y -= z * b;
-     }
- 
-diff --git a/library/ssl_tls.c b/library/ssl_tls.c
-index 8710a5076..e47c859fe 100644
---- a/library/ssl_tls.c
-+++ b/library/ssl_tls.c
-@@ -2482,6 +2482,8 @@ static int ssl_decompress_buf( mbedtls_ssl_context *ssl )
- }
- #endif /* MBEDTLS_ZLIB_SUPPORT */
- 
-+#define INT_DIV(x, y)  (((long)(x))/(y))
-+
- #if defined(MBEDTLS_SSL_SRV_C) && defined(MBEDTLS_SSL_RENEGOTIATION)
- static int ssl_write_hello_request( mbedtls_ssl_context *ssl );
- 
-@@ -2492,7 +2494,7 @@ static int ssl_resend_hello_request( mbedtls_ssl_context *ssl )
-      * timeout if we were using the usual handshake doubling scheme */
-     if( ssl->conf->renego_max_records < 0 )
-     {
--        uint32_t ratio = ssl->conf->hs_timeout_max / ssl->conf->hs_timeout_min + 1;
-+      uint32_t ratio = INT_DIV(ssl->conf->hs_timeout_max, ssl->conf->hs_timeout_min + 1);
-         unsigned char doublings = 1;
- 
-         while( ratio != 0 )
 diff --git a/tests/suites/helpers.function b/tests/suites/helpers.function
 index 1255ff4be..103abe9a8 100644
 --- a/tests/suites/helpers.function
@@ -105,3 +55,16 @@ index 1255ff4be..103abe9a8 100644
  #endif
  
  /* Type for Hex parameters */
+diff --git a/tests/scripts/run-test-suites.pl b/tests/scripts/run-test-suites.pl
+index d0d4046..00cff26 100755
+--- a/tests/scripts/run-test-suites.pl
++++ b/tests/scripts/run-test-suites.pl
+@@ -59,7 +59,7 @@ for my $suite (@suites)
+     if( $verbose ) {
+         $command .= ' -v';
+     }
+-    my $result = `$command`;
++    my $result = `k1-cluster -- $command`;
+ 
+     $suite_cases_passed = () = $result =~ /.. PASS/g;
+     $suite_cases_failed = () = $result =~ /.. FAILED/g;
diff --git a/test/mppa/instr/andd.c b/test/mppa/instr/andd.c
deleted file mode 100644
index e3221bd7..00000000
--- a/test/mppa/instr/andd.c
+++ /dev/null
@@ -1,5 +0,0 @@
-#include "framework.h"
-
-BEGIN_TEST(long long)
-    c = a&b;
-END_TEST64()
diff --git a/test/mppa/instr/addw.c b/test/mppa/instr/div32.c
index e22024cf..83c3a0e3 100644
--- a/test/mppa/instr/addw.c
+++ b/test/mppa/instr/div32.c
@@ -1,5 +1,5 @@
 #include "framework.h"
 
 BEGIN_TEST(int)
-    c = a+b;
+    c = a/b;
 END_TEST32()
diff --git a/test/mppa/instr/faddw.c b/test/mppa/instr/divf32.c
index e0e635ae..513a3293 100644
--- a/test/mppa/instr/faddw.c
+++ b/test/mppa/instr/divf32.c
@@ -1,5 +1,5 @@
 #include "framework.h"
 
 BEGIN_TEST(float)
-    c = ((float)a + (float)b);
+  c = a / b;
 END_TESTF32()
diff --git a/test/mppa/instr/faddd.c b/test/mppa/instr/divf64.c
index 35b7fc92..0dd23826 100644
--- a/test/mppa/instr/faddd.c
+++ b/test/mppa/instr/divf64.c
@@ -1,5 +1,5 @@
 #include "framework.h"
 
 BEGIN_TEST(double)
-    c = ((double)a + (double)b);
+  c = a / b;
 END_TESTF64()
diff --git a/test/mppa/instr/cast_U32_S64.c b/test/mppa/instr/divu32.c
index 6f9cd059..1fe196c4 100644
--- a/test/mppa/instr/cast_U32_S64.c
+++ b/test/mppa/instr/divu32.c
@@ -2,6 +2,6 @@
 
 BEGIN_TEST(unsigned int)
 {
-    c = (long long) a;
+    c = a/b;
 }
 END_TEST32()
diff --git a/test/mppa/instr/f32.c b/test/mppa/instr/f32.c
new file mode 100644
index 00000000..7e304aeb
--- /dev/null
+++ b/test/mppa/instr/f32.c
@@ -0,0 +1,8 @@
+#include "framework.h"
+
+BEGIN_TEST(float)
+    c = ((float)a + (float)b);
+    c += ((float)a * (float)b);
+    c += (-(float)a);
+    c += ((float)a - (float)b);
+END_TESTF32()
diff --git a/test/mppa/instr/f64.c b/test/mppa/instr/f64.c
new file mode 100644
index 00000000..be8094c9
--- /dev/null
+++ b/test/mppa/instr/f64.c
@@ -0,0 +1,8 @@
+#include "framework.h"
+
+BEGIN_TEST(double)
+    c = ((double)a + (double)b);
+    c += ((double)a * (double)b);
+    c += (-(double)a);
+    c += ((double)a - (double)b);
+END_TESTF64()
diff --git a/test/mppa/instr/i32.c b/test/mppa/instr/i32.c
new file mode 100644
index 00000000..c48531b1
--- /dev/null
+++ b/test/mppa/instr/i32.c
@@ -0,0 +1,87 @@
+#include "framework.h"
+
+int sum(int a, int b){
+    return a+b;
+}
+
+int make(int a){
+    return a;
+}
+
+int tailsum(int a, int b){
+    return make(a+b);
+}
+
+float int2float(int v){
+  return v;
+}
+
+BEGIN_TEST(int)
+    c = a+b;
+    c += a&b;
+
+    if ((a & 0x1) == 1)
+        c += 1;
+    else
+        c += 2;
+
+    if (a & 0x1 == 0)
+        c += 4;
+    else
+        c += 8;
+
+    b = !(a & 0x01);
+    if (!b)
+        c += 16;
+    else
+        c += 32;
+
+    c += sum(make(a), make(b));
+    c += (long long) a;
+
+    if (0 > (a & 0x1) - 1)
+        c += 64;
+    else
+        c += 128;
+
+    if (0 >= (a & 0x1))
+        c += 256;
+    else
+        c += 512;
+
+    if ((a & 0x1) > 0)
+        c += 1024;
+    else
+        c += 2048;
+
+    if ((a & 0x1) - 1 >= 0)
+        c += 4096;
+    else
+        c += 8192;
+
+    c += ((a & 0x1) == (b & 0x1));
+    c += (a > b);
+    c += (a <= b);
+    c += (a < b);
+    c += (a + b) / 2;
+    c += (int) int2float(a) + (int) int2float(b) + (int) int2float(42.3);
+
+    int j;
+    for (j = 0 ; j < 10 ; j++)
+        c += a;
+    int k;
+    for (k = 0 ; k < (b & 0x8) ; k++)
+        c += a;
+
+    char s[] = "Tome and Cherry at the playa\n";
+    c += s[(a & (sizeof(s)-1))];
+
+    unsigned char s2[] = "Tim is sorry at the playa\n";
+    c += s2[a & (sizeof(s) - 1)];
+
+    c += a*b;
+    c += a-b;
+    c += a << (b & 0x8);
+
+    c += sum(a, b);
+END_TEST32()
diff --git a/test/mppa/instr/i64.c b/test/mppa/instr/i64.c
new file mode 100644
index 00000000..00eb159d
--- /dev/null
+++ b/test/mppa/instr/i64.c
@@ -0,0 +1,107 @@
+#include "framework.h"
+
+long long sum(long long a, long long b){
+  return a+b;
+}
+
+long long diff(long long a, long long b){
+  return a-b;
+}
+
+long long mul(long long a, long long b){
+  return a*b;
+}
+
+long long make(long long a){
+  return a;
+}
+
+long long random_op(long long a, long long b){
+  long long d = 3;
+  long long (*op)(long long, long long);
+
+  if (a % d == 0)
+    op = sum;
+  else if (a % d == 1)
+    op = diff;
+  else
+    op = mul;
+
+  return op(a, b);
+}
+
+double long2double(long v){
+  return v;
+}
+
+BEGIN_TEST(long long)
+    c = a&b;
+    c += a*b;
+    c += -a;
+    c += a | b;
+    c += a-b;
+    c += a >> (b & 0x8LL);
+    c += a >> (b & 0x8ULL);
+    c += a % b;
+
+  long long d = 3;
+  long long (*op)(long long, long long);
+
+  if (a % d == 0)
+    op = sum;
+  else if (a % d == 1)
+    op = diff;
+  else
+    op = mul;
+
+  c += op(make(a), make(b));
+  c += random_op(a, b);
+    c += a/b;
+    c += a^b;
+    c += (unsigned int) a;
+
+    if (0 != (a & 0x1LL))
+        c += 1;
+    else
+        c += 2;
+
+    if (0 > (a & 0x1LL))
+        c += 4;
+    else
+        c += 8;
+
+    if (0 >= (a & 0x1LL) - 1)
+        c += 16;
+    else
+        c += 32;
+
+    if (a & 0x1LL > 0)
+        c += 64;
+    else
+        c += 128;
+
+    if ((a & 0x1LL) - 1 >= 0)
+        c += 256;
+    else
+        c += 512;
+
+    if (0 == (a & 0x1LL))
+        c += 1024;
+    else
+        c += 2048;
+
+    c += ((a & 0x1LL) == (b & 0x1LL));
+    c += (a >= b);
+    c += (a > b);
+    c += (a <= b);
+    c += (a < b);
+    c += (long) long2double(a) + (long) long2double(b) + (long) long2double(42.3);
+
+    int j;
+
+    for (j = 0 ; j < (b & 0x8LL) ; j++)
+        c += a;
+
+    c += ((a & 0x1LL) == (b & 0x1LL));
+
+END_TEST64()
diff --git a/test/mppa/instr/andw.c b/test/mppa/instr/individual/andw.c
index 799dc7fb..799dc7fb 100644
--- a/test/mppa/instr/andw.c
+++ b/test/mppa/instr/individual/andw.c
diff --git a/test/mppa/instr/branch.c b/test/mppa/instr/individual/branch.c
index c9937e31..c9937e31 100644
--- a/test/mppa/instr/branch.c
+++ b/test/mppa/instr/individual/branch.c
diff --git a/test/mppa/instr/branchz.c b/test/mppa/instr/individual/branchz.c
index d3e021b5..d3e021b5 100644
--- a/test/mppa/instr/branchz.c
+++ b/test/mppa/instr/individual/branchz.c
diff --git a/test/mppa/instr/branchzu.c b/test/mppa/instr/individual/branchzu.c
index d0169174..d0169174 100644
--- a/test/mppa/instr/branchzu.c
+++ b/test/mppa/instr/individual/branchzu.c
diff --git a/test/mppa/instr/call.c b/test/mppa/instr/individual/call.c
index ba2ec323..ba2ec323 100644
--- a/test/mppa/instr/call.c
+++ b/test/mppa/instr/individual/call.c
diff --git a/test/mppa/instr/cast_S32_S64.c b/test/mppa/instr/individual/cast_S32_S64.c
index 09c97e00..09c97e00 100644
--- a/test/mppa/instr/cast_S32_S64.c
+++ b/test/mppa/instr/individual/cast_S32_S64.c
diff --git a/test/mppa/instr/cast_S64_U32.c b/test/mppa/instr/individual/cast_S64_U32.c
index 2d9dc723..2d9dc723 100644
--- a/test/mppa/instr/cast_S64_U32.c
+++ b/test/mppa/instr/individual/cast_S64_U32.c
diff --git a/test/mppa/instr/cb.deqz.c b/test/mppa/instr/individual/cb.deqz.c
index 6da2ab07..6da2ab07 100644
--- a/test/mppa/instr/cb.deqz.c
+++ b/test/mppa/instr/individual/cb.deqz.c
diff --git a/test/mppa/instr/cb.dgez.c b/test/mppa/instr/individual/cb.dgez.c
index 7bef25ad..7bef25ad 100644
--- a/test/mppa/instr/cb.dgez.c
+++ b/test/mppa/instr/individual/cb.dgez.c
diff --git a/test/mppa/instr/cb.dgtz.c b/test/mppa/instr/individual/cb.dgtz.c
index 1a43fb1f..1a43fb1f 100644
--- a/test/mppa/instr/cb.dgtz.c
+++ b/test/mppa/instr/individual/cb.dgtz.c
diff --git a/test/mppa/instr/cb.dlez.c b/test/mppa/instr/individual/cb.dlez.c
index 2fb97939..2fb97939 100644
--- a/test/mppa/instr/cb.dlez.c
+++ b/test/mppa/instr/individual/cb.dlez.c
diff --git a/test/mppa/instr/cb.dltz.c b/test/mppa/instr/individual/cb.dltz.c
index a431d5d0..a431d5d0 100644
--- a/test/mppa/instr/cb.dltz.c
+++ b/test/mppa/instr/individual/cb.dltz.c
diff --git a/test/mppa/instr/cb.dnez.c b/test/mppa/instr/individual/cb.dnez.c
index 44516cbe..44516cbe 100644
--- a/test/mppa/instr/cb.dnez.c
+++ b/test/mppa/instr/individual/cb.dnez.c
diff --git a/test/mppa/instr/cb.wgez.c b/test/mppa/instr/individual/cb.wgez.c
index 5779ad92..5779ad92 100644
--- a/test/mppa/instr/cb.wgez.c
+++ b/test/mppa/instr/individual/cb.wgez.c
diff --git a/test/mppa/instr/cb.wgtz.c b/test/mppa/instr/individual/cb.wgtz.c
index abb695bd..abb695bd 100644
--- a/test/mppa/instr/cb.wgtz.c
+++ b/test/mppa/instr/individual/cb.wgtz.c
diff --git a/test/mppa/instr/cb.wlez.c b/test/mppa/instr/individual/cb.wlez.c
index 3a2e08c1..3a2e08c1 100644
--- a/test/mppa/instr/cb.wlez.c
+++ b/test/mppa/instr/individual/cb.wlez.c
diff --git a/test/mppa/instr/cb.wltz.c b/test/mppa/instr/individual/cb.wltz.c
index 5d52c72a..5d52c72a 100644
--- a/test/mppa/instr/cb.wltz.c
+++ b/test/mppa/instr/individual/cb.wltz.c
diff --git a/test/mppa/instr/compd.eq.c b/test/mppa/instr/individual/compd.eq.c
index 4fe8de2a..4fe8de2a 100644
--- a/test/mppa/instr/compd.eq.c
+++ b/test/mppa/instr/individual/compd.eq.c
diff --git a/test/mppa/instr/compd.geu.c b/test/mppa/instr/individual/compd.geu.c
index fccf0804..fccf0804 100644
--- a/test/mppa/instr/compd.geu.c
+++ b/test/mppa/instr/individual/compd.geu.c
diff --git a/test/mppa/instr/compd.gt.c b/test/mppa/instr/individual/compd.gt.c
index b9901436..b9901436 100644
--- a/test/mppa/instr/compd.gt.c
+++ b/test/mppa/instr/individual/compd.gt.c
diff --git a/test/mppa/instr/compd.le.c b/test/mppa/instr/individual/compd.le.c
index 6fa0f103..6fa0f103 100644
--- a/test/mppa/instr/compd.le.c
+++ b/test/mppa/instr/individual/compd.le.c
diff --git a/test/mppa/instr/compd.leu.c b/test/mppa/instr/individual/compd.leu.c
index 1ad18281..1ad18281 100644
--- a/test/mppa/instr/compd.leu.c
+++ b/test/mppa/instr/individual/compd.leu.c
diff --git a/test/mppa/instr/compd.lt.c b/test/mppa/instr/individual/compd.lt.c
index c42cda56..c42cda56 100644
--- a/test/mppa/instr/compd.lt.c
+++ b/test/mppa/instr/individual/compd.lt.c
diff --git a/test/mppa/instr/compd.ltu.c b/test/mppa/instr/individual/compd.ltu.c
index b03d4d53..b03d4d53 100644
--- a/test/mppa/instr/compd.ltu.c
+++ b/test/mppa/instr/individual/compd.ltu.c
diff --git a/test/mppa/instr/compd.ne.c b/test/mppa/instr/individual/compd.ne.c
index fd9d0b28..fd9d0b28 100644
--- a/test/mppa/instr/compd.ne.c
+++ b/test/mppa/instr/individual/compd.ne.c
diff --git a/test/mppa/instr/compw.eq.c b/test/mppa/instr/individual/compw.eq.c
index cd93f365..cd93f365 100644
--- a/test/mppa/instr/compw.eq.c
+++ b/test/mppa/instr/individual/compw.eq.c
diff --git a/test/mppa/instr/compw.geu.c b/test/mppa/instr/individual/compw.geu.c
index b8fb1adf..b8fb1adf 100644
--- a/test/mppa/instr/compw.geu.c
+++ b/test/mppa/instr/individual/compw.geu.c
diff --git a/test/mppa/instr/compw.gt.c b/test/mppa/instr/individual/compw.gt.c
index 5f6bc907..5f6bc907 100644
--- a/test/mppa/instr/compw.gt.c
+++ b/test/mppa/instr/individual/compw.gt.c
diff --git a/test/mppa/instr/compw.gtu.c b/test/mppa/instr/individual/compw.gtu.c
index 947f6a14..947f6a14 100644
--- a/test/mppa/instr/compw.gtu.c
+++ b/test/mppa/instr/individual/compw.gtu.c
diff --git a/test/mppa/instr/compw.le.c b/test/mppa/instr/individual/compw.le.c
index 35ec6b7d..35ec6b7d 100644
--- a/test/mppa/instr/compw.le.c
+++ b/test/mppa/instr/individual/compw.le.c
diff --git a/test/mppa/instr/compw.leu.c b/test/mppa/instr/individual/compw.leu.c
index 74ebfb42..74ebfb42 100644
--- a/test/mppa/instr/compw.leu.c
+++ b/test/mppa/instr/individual/compw.leu.c
diff --git a/test/mppa/instr/compw.lt.c b/test/mppa/instr/individual/compw.lt.c
index cb1f30bd..cb1f30bd 100644
--- a/test/mppa/instr/compw.lt.c
+++ b/test/mppa/instr/individual/compw.lt.c
diff --git a/test/mppa/instr/compw.ltu.c b/test/mppa/instr/individual/compw.ltu.c
index 6a0c5af1..6a0c5af1 100644
--- a/test/mppa/instr/compw.ltu.c
+++ b/test/mppa/instr/individual/compw.ltu.c
diff --git a/test/mppa/instr/compw.ne.c b/test/mppa/instr/individual/compw.ne.c
index 7035e2c7..7035e2c7 100644
--- a/test/mppa/instr/compw.ne.c
+++ b/test/mppa/instr/individual/compw.ne.c
diff --git a/test/mppa/instr/div2.c b/test/mppa/instr/individual/div2.c
index b5dfe63a..b5dfe63a 100644
--- a/test/mppa/instr/div2.c
+++ b/test/mppa/instr/individual/div2.c
diff --git a/test/mppa/instr/doubleconv.c b/test/mppa/instr/individual/doubleconv.c
index 55b1ddab..55b1ddab 100644
--- a/test/mppa/instr/doubleconv.c
+++ b/test/mppa/instr/individual/doubleconv.c
diff --git a/test/mppa/instr/floatconv.c b/test/mppa/instr/individual/floatconv.c
index 32b798e1..32b798e1 100644
--- a/test/mppa/instr/floatconv.c
+++ b/test/mppa/instr/individual/floatconv.c
diff --git a/test/mppa/instr/fmuld.c b/test/mppa/instr/individual/fmuld.c
index 03c990fa..03c990fa 100644
--- a/test/mppa/instr/fmuld.c
+++ b/test/mppa/instr/individual/fmuld.c
diff --git a/test/mppa/instr/fmulw.c b/test/mppa/instr/individual/fmulw.c
index f85eba64..f85eba64 100644
--- a/test/mppa/instr/fmulw.c
+++ b/test/mppa/instr/individual/fmulw.c
diff --git a/test/mppa/instr/fnegd.c b/test/mppa/instr/individual/fnegd.c
index 974eb7e8..974eb7e8 100644
--- a/test/mppa/instr/fnegd.c
+++ b/test/mppa/instr/individual/fnegd.c
diff --git a/test/mppa/instr/fnegw.c b/test/mppa/instr/individual/fnegw.c
index fbeaab8e..fbeaab8e 100644
--- a/test/mppa/instr/fnegw.c
+++ b/test/mppa/instr/individual/fnegw.c
diff --git a/test/mppa/instr/for.c b/test/mppa/instr/individual/for.c
index 373ab6bd..373ab6bd 100644
--- a/test/mppa/instr/for.c
+++ b/test/mppa/instr/individual/for.c
diff --git a/test/mppa/instr/forvar.c b/test/mppa/instr/individual/forvar.c
index 9e43c198..9e43c198 100644
--- a/test/mppa/instr/forvar.c
+++ b/test/mppa/instr/individual/forvar.c
diff --git a/test/mppa/instr/forvarl.c b/test/mppa/instr/individual/forvarl.c
index c1fe90fd..c1fe90fd 100644
--- a/test/mppa/instr/forvarl.c
+++ b/test/mppa/instr/individual/forvarl.c
diff --git a/test/mppa/instr/fsbfd.c b/test/mppa/instr/individual/fsbfd.c
index f80c1efe..f80c1efe 100644
--- a/test/mppa/instr/fsbfd.c
+++ b/test/mppa/instr/individual/fsbfd.c
diff --git a/test/mppa/instr/fsbfw.c b/test/mppa/instr/individual/fsbfw.c
index 067c40b5..067c40b5 100644
--- a/test/mppa/instr/fsbfw.c
+++ b/test/mppa/instr/individual/fsbfw.c
diff --git a/test/mppa/instr/indirect_call.c b/test/mppa/instr/individual/indirect_call.c
index f376c00a..f376c00a 100644
--- a/test/mppa/instr/indirect_call.c
+++ b/test/mppa/instr/individual/indirect_call.c
diff --git a/test/mppa/instr/indirect_tailcall.c b/test/mppa/instr/individual/indirect_tailcall.c
index e6c16ea1..e6c16ea1 100644
--- a/test/mppa/instr/indirect_tailcall.c
+++ b/test/mppa/instr/individual/indirect_tailcall.c
diff --git a/test/mppa/instr/lbs.c b/test/mppa/instr/individual/lbs.c
index 22a50632..22a50632 100644
--- a/test/mppa/instr/lbs.c
+++ b/test/mppa/instr/individual/lbs.c
diff --git a/test/mppa/instr/lbz.c b/test/mppa/instr/individual/lbz.c
index 04ba098d..04ba098d 100644
--- a/test/mppa/instr/lbz.c
+++ b/test/mppa/instr/individual/lbz.c
diff --git a/test/mppa/instr/muld.c b/test/mppa/instr/individual/muld.c
index f7e23850..f7e23850 100644
--- a/test/mppa/instr/muld.c
+++ b/test/mppa/instr/individual/muld.c
diff --git a/test/mppa/instr/mulw.c b/test/mppa/instr/individual/mulw.c
index a91d966e..a91d966e 100644
--- a/test/mppa/instr/mulw.c
+++ b/test/mppa/instr/individual/mulw.c
diff --git a/test/mppa/instr/negd.c b/test/mppa/instr/individual/negd.c
index 837b9828..837b9828 100644
--- a/test/mppa/instr/negd.c
+++ b/test/mppa/instr/individual/negd.c
diff --git a/test/mppa/instr/ord.c b/test/mppa/instr/individual/ord.c
index cae1ae8b..cae1ae8b 100644
--- a/test/mppa/instr/ord.c
+++ b/test/mppa/instr/individual/ord.c
diff --git a/test/mppa/instr/sbfd.c b/test/mppa/instr/individual/sbfd.c
index 77c28c77..77c28c77 100644
--- a/test/mppa/instr/sbfd.c
+++ b/test/mppa/instr/individual/sbfd.c
diff --git a/test/mppa/instr/sbfw.c b/test/mppa/instr/individual/sbfw.c
index e38a1fff..e38a1fff 100644
--- a/test/mppa/instr/sbfw.c
+++ b/test/mppa/instr/individual/sbfw.c
diff --git a/test/mppa/instr/simple.c b/test/mppa/instr/individual/simple.c
index 944f09c9..944f09c9 100644
--- a/test/mppa/instr/simple.c
+++ b/test/mppa/instr/individual/simple.c
diff --git a/test/mppa/instr/sllw.c b/test/mppa/instr/individual/sllw.c
index 6dd41a6c..6dd41a6c 100644
--- a/test/mppa/instr/sllw.c
+++ b/test/mppa/instr/individual/sllw.c
diff --git a/test/mppa/instr/srad.c b/test/mppa/instr/individual/srad.c
index 00be9d0c..00be9d0c 100644
--- a/test/mppa/instr/srad.c
+++ b/test/mppa/instr/individual/srad.c
diff --git a/test/mppa/instr/srld.c b/test/mppa/instr/individual/srld.c
index 14970efd..14970efd 100644
--- a/test/mppa/instr/srld.c
+++ b/test/mppa/instr/individual/srld.c
diff --git a/test/mppa/instr/tailcall.c b/test/mppa/instr/individual/tailcall.c
index 6c659a01..6c659a01 100644
--- a/test/mppa/instr/tailcall.c
+++ b/test/mppa/instr/individual/tailcall.c
diff --git a/test/mppa/instr/udivd.c b/test/mppa/instr/individual/udivd.c
index cfb31881..cfb31881 100644
--- a/test/mppa/instr/udivd.c
+++ b/test/mppa/instr/individual/udivd.c
diff --git a/test/mppa/instr/umodd.c b/test/mppa/instr/individual/umodd.c
index a7f25f1c..a7f25f1c 100644
--- a/test/mppa/instr/umodd.c
+++ b/test/mppa/instr/individual/umodd.c
diff --git a/test/mppa/instr/xord.c b/test/mppa/instr/individual/xord.c
index b6a90cb0..b6a90cb0 100644
--- a/test/mppa/instr/xord.c
+++ b/test/mppa/instr/individual/xord.c
diff --git a/test/mppa/instr/modi32.c b/test/mppa/instr/modi32.c
new file mode 100644
index 00000000..958ae920
--- /dev/null
+++ b/test/mppa/instr/modi32.c
@@ -0,0 +1,5 @@
+#include "framework.h"
+
+BEGIN_TEST(int)
+    c = a%b;
+END_TEST32()
diff --git a/test/mppa/instr/modui32.c b/test/mppa/instr/modui32.c
new file mode 100644
index 00000000..a39034a8
--- /dev/null
+++ b/test/mppa/instr/modui32.c
@@ -0,0 +1,7 @@
+#include "framework.h"
+
+BEGIN_TEST(unsigned int)
+{
+    c = a%b;
+}
+END_TEST32()
diff --git a/test/mppa/instr/ui32.c b/test/mppa/instr/ui32.c
new file mode 100644
index 00000000..f56a9b95
--- /dev/null
+++ b/test/mppa/instr/ui32.c
@@ -0,0 +1,12 @@
+#include "framework.h"
+
+BEGIN_TEST(unsigned int)
+{
+    c = (long long) a;
+    c += (a >= b);
+    c += (a > b);
+    c += (a <= b);
+    c += (a < b);
+    c += ((a & 0x1U) != (b & 0x1U));
+}
+END_TEST32()
diff --git a/test/mppa/instr/compd.gtu.c b/test/mppa/instr/ui64.c
index 7b2b96a6..908dec3c 100644
--- a/test/mppa/instr/compd.gtu.c
+++ b/test/mppa/instr/ui64.c
@@ -3,5 +3,8 @@
 BEGIN_TEST(unsigned long long)
 {
     c = (a > b);
+    c += (a <= b);
+    c += (a < b);
+    c += ((a & 0x1ULL) != (b & 0x1ULL));
 }
 END_TEST64()
diff --git a/test/mppa/interop/i_manyiargs.c b/test/mppa/interop/i32.c
index d674c26f..6bc2705c 100644
--- a/test/mppa/interop/i_manyiargs.c
+++ b/test/mppa/interop/i32.c
@@ -5,5 +5,9 @@ BEGIN_TEST(int)
   c = i_manyiargs(a, b, a-b, a+b, a*2, b*2, a*2-b, a+b*2, (a-b)*2, (a+b)*2,
                   -2*a, -2*b, a-b, a+b, a*3, b*3, a*3-b, a+b*3, (a-b)*3, (a+b)*3,
                   -3*a, -3*b, a-b, a+b, a*4, b*4, a*4-b, a+b*4, (a-b)*4, (a+b)*4);
-END_TEST()
+  c += i_multiiargs(a, b, a-b, a+b);
+  c += i_oneiarg(a);
+  void_void();
+  c += a;
+END_TEST32()
 
diff --git a/test/mppa/interop/ll_manyllargs.c b/test/mppa/interop/i64.c
index 6e0b3b36..3e7240f7 100644
--- a/test/mppa/interop/ll_manyllargs.c
+++ b/test/mppa/interop/i64.c
@@ -5,4 +5,10 @@ BEGIN_TEST(long long)
   c = ll_manyllargs(a, b, a-b, a+b, a*2, b*2, a*2-b, a+b*2, (a-b)*2, (a+b)*2,
                   -2*a, -2*b, a-b, a+b, a*3, b*3, a*3-b, a+b*3, (a-b)*3, (a+b)*3,
                   -3*a, -3*b, a-b, a+b, a*4, b*4, a*4-b, a+b*4, (a-b)*4, (a+b)*4);
-END_TEST()
+  c += ll_multillargs(a, b, a-b, a+b);
+  c += ll_onellarg(a);
+  c = ll_void();
+  c += a;
+  void_void();
+  c += a;
+END_TEST64()
diff --git a/test/mppa/interop/i_multiiargs.c b/test/mppa/interop/individual/i_multiiargs.c
index 0e8c8936..888742b5 100644
--- a/test/mppa/interop/i_multiiargs.c
+++ b/test/mppa/interop/individual/i_multiiargs.c
@@ -3,4 +3,4 @@
 
 BEGIN_TEST(int)
   c = i_multiiargs(a, b, a-b, a+b);
-END_TEST()
+END_TEST32()
diff --git a/test/mppa/interop/i_oneiarg.c b/test/mppa/interop/individual/i_oneiarg.c
index 42cd1540..9c969fb8 100644
--- a/test/mppa/interop/i_oneiarg.c
+++ b/test/mppa/interop/individual/i_oneiarg.c
@@ -3,4 +3,4 @@
 
 BEGIN_TEST(int)
   c = i_oneiarg(a);
-END_TEST()
+END_TEST32()
diff --git a/test/mppa/interop/ll_multillargs.c b/test/mppa/interop/individual/ll_multillargs.c
index edb03b12..34b422eb 100644
--- a/test/mppa/interop/ll_multillargs.c
+++ b/test/mppa/interop/individual/ll_multillargs.c
@@ -3,5 +3,5 @@
 
 BEGIN_TEST(long long)
   c = ll_multillargs(a, b, a-b, a+b);
-END_TEST()
+END_TEST64()
 
diff --git a/test/mppa/interop/ll_onellarg.c b/test/mppa/interop/individual/ll_onellarg.c
index 0d182166..a2fbbbe9 100644
--- a/test/mppa/interop/ll_onellarg.c
+++ b/test/mppa/interop/individual/ll_onellarg.c
@@ -3,5 +3,5 @@
 
 BEGIN_TEST(long long)
   c = ll_onellarg(a);
-END_TEST()
+END_TEST64()
 
diff --git a/test/mppa/interop/ll_void.c b/test/mppa/interop/individual/ll_void.c
index fa350c9b..da128fdd 100644
--- a/test/mppa/interop/ll_void.c
+++ b/test/mppa/interop/individual/ll_void.c
@@ -4,4 +4,4 @@
 BEGIN_TEST(long long)
   c = ll_void();
   c += a;
-END_TEST()
+END_TEST64()
diff --git a/test/mppa/interop/void_void.c b/test/mppa/interop/individual/void_void.c
index e729edb2..976a721b 100644
--- a/test/mppa/interop/void_void.c
+++ b/test/mppa/interop/individual/void_void.c
@@ -4,4 +4,4 @@
 BEGIN_TEST(long long)
   void_void();
   c = a;
-END_TEST()
+END_TEST64()
diff --git a/x86/Conventions1.v b/x86/Conventions1.v
index 646c4afb..35d555f9 100644
--- a/x86/Conventions1.v
+++ b/x86/Conventions1.v
@@ -15,6 +15,7 @@
 
 Require Import Coqlib Decidableplus.
 Require Import AST Machregs Locations.
+Require Import Errors.
 
 (** * Classification of machine registers *)
 
@@ -26,7 +27,7 @@ Require Import AST Machregs Locations.
   We follow the x86-32 and x86-64 application binary interfaces (ABI)
   in our choice of callee- and caller-save registers.
 *)
-
+  
 Definition is_callee_save (r: mreg) : bool :=
   match r with
   | AX | CX | DX => false
diff --git a/x86/Machregsaux.ml b/x86/Machregsaux.ml
index 473e0602..80066b00 100644
--- a/x86/Machregsaux.ml
+++ b/x86/Machregsaux.ml
@@ -14,9 +14,9 @@
 
 open Camlcoq
 open Machregs
-
+   
 let register_names : (mreg, string) Hashtbl.t = Hashtbl.create 31
-
+                                              
 let _ =
   List.iter
     (fun (s, r) -> Hashtbl.add register_names r (camlstring_of_coqstring s))
@@ -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 -> 0
+  | AST.Tfloat | AST.Tsingle -> 1
+  | AST.Tany32 | AST.Tany64 -> assert false
diff --git a/x86/Machregsaux.mli b/x86/Machregsaux.mli
index 9404568d..d7117c21 100644
--- a/x86/Machregsaux.mli
+++ b/x86/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/x86/SelectLong.vp b/x86/SelectLong.vp
index b213e23f..4f9fb518 100644
--- a/x86/SelectLong.vp
+++ b/x86/SelectLong.vp
@@ -16,7 +16,7 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
-Require Import SelectOp SplitLong.
+Require Import OpHelpers SelectOp SplitLong.
 
 Local Open Scope cminorsel_scope.
 Local Open Scope string_scope.
diff --git a/x86/SelectLongproof.v b/x86/SelectLongproof.v
index 3bef632d..f008f39e 100644
--- a/x86/SelectLongproof.v
+++ b/x86/SelectLongproof.v
@@ -16,6 +16,7 @@ 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/x86/SelectOp.vp b/x86/SelectOp.vp
index a1583600..eadda093 100644
--- a/x86/SelectOp.vp
+++ b/x86/SelectOp.vp
@@ -40,6 +40,7 @@ Require Import Coqlib.
 Require Import Compopts.
 Require Import AST Integers Floats.
 Require Import Op CminorSel.
+Require Import OpHelpers.
 
 Local Open Scope cminorsel_scope.
 
@@ -540,3 +541,10 @@ Nondetfunction builtin_arg (e: expr) :=
   | Eload chunk (Ainstack ofs) Enil => BA_loadstack chunk ofs
   | _ => BA e
   end.
+
+(* floats *)
+Definition divf_base (e1: expr) (e2: expr) :=
+  Eop Odivf (e1 ::: e2 ::: Enil).
+
+Definition divfs_base (e1: expr) (e2: expr) :=
+  Eop Odivfs (e1 ::: e2 ::: Enil).
diff --git a/x86/SelectOpproof.v b/x86/SelectOpproof.v
index fdbadaa8..1eeb5906 100644
--- a/x86/SelectOpproof.v
+++ b/x86/SelectOpproof.v
@@ -23,6 +23,8 @@ Require Import Cminor.
 Require Import Op.
 Require Import CminorSel.
 Require Import SelectOp.
+Require Import OpHelpers.
+Require Import OpHelpersproof.
 
 Local Open Scope cminorsel_scope.
 
@@ -74,8 +76,10 @@ 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.
@@ -984,4 +988,25 @@ Proof.
 - constructor; auto.
 Qed.
 
+
+(* floating-point division without HELPERS *)
+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.
+  TrivialExists.
+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.
+  TrivialExists.
+Qed.
 End CMCONSTR.