Strength reduction for operators and conditions. This is the machine-dependent part of Constprop.

Require Import Coqlib Compopts.
Require Import AST Integers Floats.
Require Import Op Registers.
Require Import ValueDomain ValueAOp.
Require SelectOp.

Converting known values to constants

Definition Olea_ptr (a: addressing) := if Archi.ptr64 then Oleal a else Olea a.

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) =>
      if SelectOp.symbol_is_external id then
        if Ptrofs.eq ofs Ptrofs.zero then Some (Oindirectsymbol id) else None
      else
        Some (Olea_ptr (Aglobal id ofs))
  | Ptr(Stk ofs) => Some(Olea_ptr (Ainstack 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 =>
      (Ccompimm (swap_comparison c) n1, r2 :: nil)
  | cond_strength_reduction_case2 c r1 r2 v1 n2 =>
      (Ccompimm c n2, r1 :: nil)
  | cond_strength_reduction_case3 c r1 r2 n1 v2 =>
      (Ccompuimm (swap_comparison c) n1, r2 :: nil)
  | cond_strength_reduction_case4 c r1 r2 v1 n2 =>
      (Ccompuimm c n2, r1 :: nil)
  | cond_strength_reduction_case5 c r1 r2 n1 v2 =>
      (Ccomplimm (swap_comparison c) n1, r2 :: nil)
  | cond_strength_reduction_case6 c r1 r2 v1 n2 =>
      (Ccomplimm c n2, r1 :: nil)
  | cond_strength_reduction_case7 c r1 r2 n1 v2 =>
      (Ccompluimm (swap_comparison c) n1, r2 :: nil)
  | cond_strength_reduction_case8 c r1 r2 v1 n2 =>
      (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 =>
      make_cmp_imm_eq c args vl n r1 v1
  | make_cmp_case2 n r1 v1 =>
      make_cmp_imm_ne c args vl n r1 v1
  | make_cmp_case3 n r1 v1 =>
      make_cmp_imm_eq c args vl n r1 v1
  | make_cmp_case4 n r1 v1 =>
      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_select (c: condition) (ty: typ)
                       (r1 r2: reg) (args: list reg) (vl: list aval) :=
  match resolve_branch (eval_static_condition c vl) with
  | Some b => (Omove, (if b then r1 else r2) :: nil)
  | None =>
      let (c', args') := cond_strength_reduction c args vl in
      (Osel c' ty, r1 :: r2 :: args')
  end.

For addressing modes, we need to distinguish

reductions that produce pointers (i.e. that produce Aglobal, Ainstack, Abased and Abasedscaled addressing modes), which are valid only if the pointer size is right;
other reductions (producing Aindexed or Aindexed2 modes), which are valid independently of the pointer size.

Original definition:

Nondetfunction addr_strength_reduction_32_generic
                (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr, args, vl with
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
      (Aindexed (Int.signed n1 + ofs), r2 :: nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
      (Aindexed (Int.signed n2 + ofs), r1 :: nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
      (Aindexed (Int.signed n2 * sc + ofs), r1 :: nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
      (Ascaled sc (Int.signed n1 + ofs), r2 :: nil)
  | _, _ =>
      (addr, args)
  end.

Inductive addr_strength_reduction_32_generic_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
  | addr_strength_reduction_32_generic_case1: forall ofs r1 r2 n1 v2, addr_strength_reduction_32_generic_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
  | addr_strength_reduction_32_generic_case2: forall ofs r1 r2 v1 n2, addr_strength_reduction_32_generic_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | addr_strength_reduction_32_generic_case3: forall sc ofs r1 r2 v1 n2, addr_strength_reduction_32_generic_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | addr_strength_reduction_32_generic_case4: forall sc ofs r1 r2 n1 v2, addr_strength_reduction_32_generic_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
  | addr_strength_reduction_32_generic_default: forall (addr: addressing) (args: list reg) (vl: list aval), addr_strength_reduction_32_generic_cases addr args vl.

Definition addr_strength_reduction_32_generic_match (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_32_generic_cases zz1 zz2 zz3 with
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_32_generic_case1 ofs r1 r2 n1 v2
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_32_generic_case2 ofs r1 r2 v1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_32_generic_case3 sc ofs r1 r2 v1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_32_generic_case4 sc ofs r1 r2 n1 v2
  | addr, args, vl => addr_strength_reduction_32_generic_default addr args vl
  end.

Definition addr_strength_reduction_32_generic (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr_strength_reduction_32_generic_match addr args vl with
  | addr_strength_reduction_32_generic_case1 ofs r1 r2 n1 v2 =>
      (Aindexed (Int.signed n1 + ofs), r2 :: nil)
  | addr_strength_reduction_32_generic_case2 ofs r1 r2 v1 n2 =>
      (Aindexed (Int.signed n2 + ofs), r1 :: nil)
  | addr_strength_reduction_32_generic_case3 sc ofs r1 r2 v1 n2 =>
      (Aindexed (Int.signed n2 * sc + ofs), r1 :: nil)
  | addr_strength_reduction_32_generic_case4 sc ofs r1 r2 n1 v2 =>
      (Ascaled sc (Int.signed n1 + ofs), r2 :: nil)
  | addr_strength_reduction_32_generic_default addr args vl =>
      (addr, args)
  end.

Original definition:

Nondetfunction addr_strength_reduction_32
                (addr: addressing) (args: list reg) (vl: list aval) :=

  if Archi.ptr64 then addr_strength_reduction_32_generic addr args vl else

  match addr, args, vl with

  | Aindexed ofs, r1 :: nil, Ptr(Gl symb n) :: nil =>
      (Aglobal symb (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | Aindexed ofs, r1 :: nil, Ptr(Stk n) :: nil =>
      (Ainstack (Ptrofs.add n (Ptrofs.repr ofs)), nil)

  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int n2)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Gl symb n2) :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n2 (Ptrofs.of_int n1)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil =>
      (Ainstack (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int n2)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Stk n2) :: nil =>
      (Ainstack (Ptrofs.add (Ptrofs.add (Ptrofs.of_int n1) n2) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil =>
      (Abased symb (Ptrofs.add n1 (Ptrofs.repr ofs)), r2 :: nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: Ptr(Gl symb n2) :: nil =>
      (Abased symb (Ptrofs.add n2 (Ptrofs.repr ofs)), r1 :: nil)

  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int (Int.mul n2 (Int.repr sc)))) (Ptrofs.repr ofs)), nil)

  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil =>
      (Abasedscaled sc symb (Ptrofs.add n1 (Ptrofs.repr ofs)), r2 :: nil)

  | Abased id ofs, r1 :: nil, I n1 :: nil =>
      (Aglobal id (Ptrofs.add ofs (Ptrofs.of_int n1)), nil)

  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil =>
      (Aglobal id (Ptrofs.add ofs (Ptrofs.of_int (Int.mul n1 (Int.repr sc)))), nil)

  | _, _ =>
      addr_strength_reduction_32_generic addr args vl
  end.

Inductive addr_strength_reduction_32_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
  | addr_strength_reduction_32_case1: forall ofs r1 symb n, addr_strength_reduction_32_cases (Aindexed ofs) (r1 :: nil) (Ptr(Gl symb n) :: nil)
  | addr_strength_reduction_32_case2: forall ofs r1 n, addr_strength_reduction_32_cases (Aindexed ofs) (r1 :: nil) (Ptr(Stk n) :: nil)
  | addr_strength_reduction_32_case3: forall ofs r1 r2 symb n1 n2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: I n2 :: nil)
  | addr_strength_reduction_32_case4: forall ofs r1 r2 n1 symb n2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: Ptr(Gl symb n2) :: nil)
  | addr_strength_reduction_32_case5: forall ofs r1 r2 n1 n2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Stk n1) :: I n2 :: nil)
  | addr_strength_reduction_32_case6: forall ofs r1 r2 n1 n2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: Ptr(Stk n2) :: nil)
  | addr_strength_reduction_32_case7: forall ofs r1 r2 symb n1 v2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: v2 :: nil)
  | addr_strength_reduction_32_case8: forall ofs r1 r2 v1 symb n2, addr_strength_reduction_32_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: Ptr(Gl symb n2) :: nil)
  | addr_strength_reduction_32_case9: forall sc ofs r1 r2 symb n1 n2, addr_strength_reduction_32_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: I n2 :: nil)
  | addr_strength_reduction_32_case10: forall sc ofs r1 r2 symb n1 v2, addr_strength_reduction_32_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: v2 :: nil)
  | addr_strength_reduction_32_case11: forall id ofs r1 n1, addr_strength_reduction_32_cases (Abased id ofs) (r1 :: nil) (I n1 :: nil)
  | addr_strength_reduction_32_case12: forall sc id ofs r1 n1, addr_strength_reduction_32_cases (Abasedscaled sc id ofs) (r1 :: nil) (I n1 :: nil)
  | addr_strength_reduction_32_default: forall (addr: addressing) (args: list reg) (vl: list aval), addr_strength_reduction_32_cases addr args vl.

Definition addr_strength_reduction_32_match (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_32_cases zz1 zz2 zz3 with
  | Aindexed ofs, r1 :: nil, Ptr(Gl symb n) :: nil => addr_strength_reduction_32_case1 ofs r1 symb n
  | Aindexed ofs, r1 :: nil, Ptr(Stk n) :: nil => addr_strength_reduction_32_case2 ofs r1 n
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil => addr_strength_reduction_32_case3 ofs r1 r2 symb n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Gl symb n2) :: nil => addr_strength_reduction_32_case4 ofs r1 r2 n1 symb n2
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil => addr_strength_reduction_32_case5 ofs r1 r2 n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Stk n2) :: nil => addr_strength_reduction_32_case6 ofs r1 r2 n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil => addr_strength_reduction_32_case7 ofs r1 r2 symb n1 v2
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: Ptr(Gl symb n2) :: nil => addr_strength_reduction_32_case8 ofs r1 r2 v1 symb n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil => addr_strength_reduction_32_case9 sc ofs r1 r2 symb n1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil => addr_strength_reduction_32_case10 sc ofs r1 r2 symb n1 v2
  | Abased id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_32_case11 id ofs r1 n1
  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_32_case12 sc id ofs r1 n1
  | addr, args, vl => addr_strength_reduction_32_default addr args vl
  end.

Definition addr_strength_reduction_32 (addr: addressing) (args: list reg) (vl: list aval) :=
if Archi.ptr64 then addr_strength_reduction_32_generic addr args vl else match addr_strength_reduction_32_match addr args vl with
  | addr_strength_reduction_32_case1 ofs r1 symb n =>
      (Aglobal symb (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case2 ofs r1 n =>
      (Ainstack (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case3 ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int n2)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case4 ofs r1 r2 n1 symb n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n2 (Ptrofs.of_int n1)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case5 ofs r1 r2 n1 n2 =>
      (Ainstack (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int n2)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case6 ofs r1 r2 n1 n2 =>
      (Ainstack (Ptrofs.add (Ptrofs.add (Ptrofs.of_int n1) n2) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case7 ofs r1 r2 symb n1 v2 =>
      (Abased symb (Ptrofs.add n1 (Ptrofs.repr ofs)), r2 :: nil)
  | addr_strength_reduction_32_case8 ofs r1 r2 v1 symb n2 =>
      (Abased symb (Ptrofs.add n2 (Ptrofs.repr ofs)), r1 :: nil)
  | addr_strength_reduction_32_case9 sc ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int (Int.mul n2 (Int.repr sc)))) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_32_case10 sc ofs r1 r2 symb n1 v2 =>
      (Abasedscaled sc symb (Ptrofs.add n1 (Ptrofs.repr ofs)), r2 :: nil)
  | addr_strength_reduction_32_case11 id ofs r1 n1 =>
      (Aglobal id (Ptrofs.add ofs (Ptrofs.of_int n1)), nil)
  | addr_strength_reduction_32_case12 sc id ofs r1 n1 =>
      (Aglobal id (Ptrofs.add ofs (Ptrofs.of_int (Int.mul n1 (Int.repr sc)))), nil)
  | addr_strength_reduction_32_default addr args vl =>
      addr_strength_reduction_32_generic addr args vl
  end.

Original definition:

Nondetfunction addr_strength_reduction_64_generic
                (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr, args, vl with
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: v2 :: nil =>
      (Aindexed (Int64.signed n1 + ofs), r2 :: nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: L n2 :: nil =>
      (Aindexed (Int64.signed n2 + ofs), r1 :: nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: L n2 :: nil =>
      (Aindexed (Int64.signed n2 * sc + ofs), r1 :: nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, L n1 :: v2 :: nil =>
      (Ascaled sc (Int64.signed n1 + ofs), r2 :: nil)
  | _, _ =>
      (addr, args)
  end.

Inductive addr_strength_reduction_64_generic_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
  | addr_strength_reduction_64_generic_case1: forall ofs r1 r2 n1 v2, addr_strength_reduction_64_generic_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | addr_strength_reduction_64_generic_case2: forall ofs r1 r2 v1 n2, addr_strength_reduction_64_generic_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | addr_strength_reduction_64_generic_case3: forall sc ofs r1 r2 v1 n2, addr_strength_reduction_64_generic_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | addr_strength_reduction_64_generic_case4: forall sc ofs r1 r2 n1 v2, addr_strength_reduction_64_generic_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | addr_strength_reduction_64_generic_default: forall (addr: addressing) (args: list reg) (vl: list aval), addr_strength_reduction_64_generic_cases addr args vl.

Definition addr_strength_reduction_64_generic_match (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_64_generic_cases zz1 zz2 zz3 with
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: v2 :: nil => addr_strength_reduction_64_generic_case1 ofs r1 r2 n1 v2
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: L n2 :: nil => addr_strength_reduction_64_generic_case2 ofs r1 r2 v1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: L n2 :: nil => addr_strength_reduction_64_generic_case3 sc ofs r1 r2 v1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, L n1 :: v2 :: nil => addr_strength_reduction_64_generic_case4 sc ofs r1 r2 n1 v2
  | addr, args, vl => addr_strength_reduction_64_generic_default addr args vl
  end.

Definition addr_strength_reduction_64_generic (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr_strength_reduction_64_generic_match addr args vl with
  | addr_strength_reduction_64_generic_case1 ofs r1 r2 n1 v2 =>
      (Aindexed (Int64.signed n1 + ofs), r2 :: nil)
  | addr_strength_reduction_64_generic_case2 ofs r1 r2 v1 n2 =>
      (Aindexed (Int64.signed n2 + ofs), r1 :: nil)
  | addr_strength_reduction_64_generic_case3 sc ofs r1 r2 v1 n2 =>
      (Aindexed (Int64.signed n2 * sc + ofs), r1 :: nil)
  | addr_strength_reduction_64_generic_case4 sc ofs r1 r2 n1 v2 =>
      (Ascaled sc (Int64.signed n1 + ofs), r2 :: nil)
  | addr_strength_reduction_64_generic_default addr args vl =>
      (addr, args)
  end.

Original definition:

Nondetfunction addr_strength_reduction_64
                (addr: addressing) (args: list reg) (vl: list aval) :=

  if negb Archi.ptr64 then addr_strength_reduction_64_generic addr args vl else

  match addr, args, vl with

  | Aindexed ofs, r1 :: nil, Ptr(Gl symb n) :: nil =>
      (Aglobal symb (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | Aindexed ofs, r1 :: nil, Ptr(Stk n) :: nil =>
      (Ainstack (Ptrofs.add n (Ptrofs.repr ofs)), nil)

  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: L n2 :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 n2)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: Ptr(Gl symb n2) :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n2 (Ptrofs.of_int64 n1)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Stk n1) :: L n2 :: nil =>
      (Ainstack (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 n2)) (Ptrofs.repr ofs)), nil)
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: Ptr(Stk n2) :: nil =>
      (Ainstack (Ptrofs.add (Ptrofs.add (Ptrofs.of_int64 n1) n2) (Ptrofs.repr ofs)), nil)

  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: L n2 :: nil =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 (Int64.mul n2 (Int64.repr sc)))) (Ptrofs.repr ofs)), nil)

  | _, _ =>
      addr_strength_reduction_64_generic addr args vl
  end.

Inductive addr_strength_reduction_64_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
  | addr_strength_reduction_64_case1: forall ofs r1 symb n, addr_strength_reduction_64_cases (Aindexed ofs) (r1 :: nil) (Ptr(Gl symb n) :: nil)
  | addr_strength_reduction_64_case2: forall ofs r1 n, addr_strength_reduction_64_cases (Aindexed ofs) (r1 :: nil) (Ptr(Stk n) :: nil)
  | addr_strength_reduction_64_case3: forall ofs r1 r2 symb n1 n2, addr_strength_reduction_64_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: L n2 :: nil)
  | addr_strength_reduction_64_case4: forall ofs r1 r2 n1 symb n2, addr_strength_reduction_64_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (L n1 :: Ptr(Gl symb n2) :: nil)
  | addr_strength_reduction_64_case5: forall ofs r1 r2 n1 n2, addr_strength_reduction_64_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Stk n1) :: L n2 :: nil)
  | addr_strength_reduction_64_case6: forall ofs r1 r2 n1 n2, addr_strength_reduction_64_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (L n1 :: Ptr(Stk n2) :: nil)
  | addr_strength_reduction_64_case7: forall sc ofs r1 r2 symb n1 n2, addr_strength_reduction_64_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: L n2 :: nil)
  | addr_strength_reduction_64_default: forall (addr: addressing) (args: list reg) (vl: list aval), addr_strength_reduction_64_cases addr args vl.

Definition addr_strength_reduction_64_match (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_64_cases zz1 zz2 zz3 with
  | Aindexed ofs, r1 :: nil, Ptr(Gl symb n) :: nil => addr_strength_reduction_64_case1 ofs r1 symb n
  | Aindexed ofs, r1 :: nil, Ptr(Stk n) :: nil => addr_strength_reduction_64_case2 ofs r1 n
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: L n2 :: nil => addr_strength_reduction_64_case3 ofs r1 r2 symb n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: Ptr(Gl symb n2) :: nil => addr_strength_reduction_64_case4 ofs r1 r2 n1 symb n2
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Stk n1) :: L n2 :: nil => addr_strength_reduction_64_case5 ofs r1 r2 n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, L n1 :: Ptr(Stk n2) :: nil => addr_strength_reduction_64_case6 ofs r1 r2 n1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: L n2 :: nil => addr_strength_reduction_64_case7 sc ofs r1 r2 symb n1 n2
  | addr, args, vl => addr_strength_reduction_64_default addr args vl
  end.

Definition addr_strength_reduction_64 (addr: addressing) (args: list reg) (vl: list aval) :=
if negb Archi.ptr64 then addr_strength_reduction_64_generic addr args vl else match addr_strength_reduction_64_match addr args vl with
  | addr_strength_reduction_64_case1 ofs r1 symb n =>
      (Aglobal symb (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case2 ofs r1 n =>
      (Ainstack (Ptrofs.add n (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case3 ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 n2)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case4 ofs r1 r2 n1 symb n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n2 (Ptrofs.of_int64 n1)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case5 ofs r1 r2 n1 n2 =>
      (Ainstack (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 n2)) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case6 ofs r1 r2 n1 n2 =>
      (Ainstack (Ptrofs.add (Ptrofs.add (Ptrofs.of_int64 n1) n2) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_case7 sc ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Ptrofs.add (Ptrofs.add n1 (Ptrofs.of_int64 (Int64.mul n2 (Int64.repr sc)))) (Ptrofs.repr ofs)), nil)
  | addr_strength_reduction_64_default addr args vl =>
      addr_strength_reduction_64_generic addr args vl
  end.

Definition addr_strength_reduction
                (addr: addressing) (args: list reg) (vl: list aval) :=
  let addr_args' :=
    if Archi.ptr64
    then addr_strength_reduction_64 addr args vl
    else addr_strength_reduction_32 addr args vl in
  if addressing_valid (fst addr_args') then addr_args' else (addr, args).

Definition make_addimm (n: int) (r: reg) :=
  if Int.eq n Int.zero
  then (Omove, r :: nil)
  else (Olea (Aindexed (Int.signed 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) (r: reg) :=
  if Int.eq n Int.zero then
    (Ointconst Int.zero, nil)
  else if Int.eq n Int.one then
    (Omove, r :: nil)
  else
    match Int.is_power2 n with
    | Some l => (Oshlimm l, r :: nil)
    | None => (Omulimm n, r :: 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 if Int.eq n Int.mone then (Onot, 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 (Oleal (Aindexed (Int64.signed 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) (r: reg) :=
  if Int64.eq n Int64.zero then
    (Olongconst Int64.zero, nil)
  else if Int64.eq n Int64.one then
    (Omove, r :: nil)
  else
    match Int64.is_power2' n with
    | Some l => (Oshllimm l, r :: nil)
    | None => (Omullimm n, r :: 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 if Int64.eq n Int64.mone then (Onotl, 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_cast8unsigned (r: reg) (a: aval) :=
  if vincl a (Uns Ptop 8) then (Omove, r :: nil) else (Ocast8unsigned, r :: nil).
Definition make_cast16signed (r: reg) (a: aval) :=
  if vincl a (Sgn Ptop 16) then (Omove, r :: nil) else (Ocast16signed, r :: nil).
Definition make_cast16unsigned (r: reg) (a: aval) :=
  if vincl a (Uns Ptop 16) then (Omove, r :: nil) else (Ocast16unsigned, 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
  | Ocast8unsigned, r1 :: nil, v1 :: nil => make_cast8unsigned r1 v1
  | Ocast16signed, r1 :: nil, v1 :: nil => make_cast16signed r1 v1
  | Ocast16unsigned, r1 :: nil, v1 :: nil => make_cast16unsigned r1 v1
  | 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
  | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1
  | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2
  | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2
  | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_moduimm n2 r1 r2
  | Oand, r1 :: r2 :: nil, 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
  | Olea addr, args, vl =>
      let (addr', args') := addr_strength_reduction_32 addr args vl in
      (Olea addr', args')
  | 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
  | Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_mullimm n2 r1
  | 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
  | Oleal addr, args, vl =>
      let (addr', args') := addr_strength_reduction_64 addr args vl in
      (Oleal addr', args')
  | Ocmp c, args, vl => make_cmp c args vl
  | Osel c ty, r1 :: r2 :: args, v1 :: v2 :: vl => make_select c ty r1 r2 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 (Ocast8unsigned) (r1 :: nil) (v1 :: nil)
  | op_strength_reduction_case3: forall r1 v1, op_strength_reduction_cases (Ocast16signed) (r1 :: nil) (v1 :: nil)
  | op_strength_reduction_case4: forall r1 v1, op_strength_reduction_cases (Ocast16unsigned) (r1 :: nil) (v1 :: 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 addr args vl, op_strength_reduction_cases (Olea addr) (args) (vl)
  | op_strength_reduction_case22: forall r1 r2 v1 n2, op_strength_reduction_cases (Osubl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case23: forall r1 r2 n1 v2, op_strength_reduction_cases (Omull) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | op_strength_reduction_case24: forall r1 r2 v1 n2, op_strength_reduction_cases (Omull) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case25: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case26: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivlu) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case27: forall r1 r2 v1 n2, op_strength_reduction_cases (Omodlu) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case28: forall r1 r2 n1 v2, op_strength_reduction_cases (Oandl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | op_strength_reduction_case29: forall r1 r2 v1 n2, op_strength_reduction_cases (Oandl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case30: forall n r1 v1, op_strength_reduction_cases (Oandlimm n) (r1 :: nil) (v1 :: nil)
  | op_strength_reduction_case31: forall r1 r2 n1 v2, op_strength_reduction_cases (Oorl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | op_strength_reduction_case32: forall r1 r2 v1 n2, op_strength_reduction_cases (Oorl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case33: forall r1 r2 n1 v2, op_strength_reduction_cases (Oxorl) (r1 :: r2 :: nil) (L n1 :: v2 :: nil)
  | op_strength_reduction_case34: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxorl) (r1 :: r2 :: nil) (v1 :: L n2 :: nil)
  | op_strength_reduction_case35: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshll) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | op_strength_reduction_case36: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshrl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | op_strength_reduction_case37: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshrlu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | op_strength_reduction_case38: forall addr args vl, op_strength_reduction_cases (Oleal addr) (args) (vl)
  | op_strength_reduction_case39: forall c args vl, op_strength_reduction_cases (Ocmp c) (args) (vl)
  | op_strength_reduction_case40: forall c ty r1 r2 args v1 v2 vl, op_strength_reduction_cases (Osel c ty) (r1 :: r2 :: args) (v1 :: v2 :: vl)
  | op_strength_reduction_case41: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (v1 :: F n2 :: nil)
  | op_strength_reduction_case42: forall r1 r2 n1 v2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (F n1 :: v2 :: nil)
  | op_strength_reduction_case43: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulfs) (r1 :: r2 :: nil) (v1 :: FS n2 :: nil)
  | op_strength_reduction_case44: 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
  | Ocast8unsigned, r1 :: nil, v1 :: nil => op_strength_reduction_case2 r1 v1
  | Ocast16signed, r1 :: nil, v1 :: nil => op_strength_reduction_case3 r1 v1
  | Ocast16unsigned, r1 :: nil, v1 :: nil => op_strength_reduction_case4 r1 v1
  | 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
  | Olea addr, args, vl => op_strength_reduction_case21 addr args vl
  | Osubl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case22 r1 r2 v1 n2
  | Omull, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case23 r1 r2 n1 v2
  | Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case24 r1 r2 v1 n2
  | Odivl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case25 r1 r2 v1 n2
  | Odivlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case26 r1 r2 v1 n2
  | Omodlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case27 r1 r2 v1 n2
  | Oandl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case28 r1 r2 n1 v2
  | Oandl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case29 r1 r2 v1 n2
  | Oandlimm n, r1 :: nil, v1 :: nil => op_strength_reduction_case30 n r1 v1
  | Oorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case31 r1 r2 n1 v2
  | Oorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case32 r1 r2 v1 n2
  | Oxorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => op_strength_reduction_case33 r1 r2 n1 v2
  | Oxorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => op_strength_reduction_case34 r1 r2 v1 n2
  | Oshll, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case35 r1 r2 v1 n2
  | Oshrl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case36 r1 r2 v1 n2
  | Oshrlu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case37 r1 r2 v1 n2
  | Oleal addr, args, vl => op_strength_reduction_case38 addr args vl
  | Ocmp c, args, vl => op_strength_reduction_case39 c args vl
  | Osel c ty, r1 :: r2 :: args, v1 :: v2 :: vl => op_strength_reduction_case40 c ty r1 r2 args v1 v2 vl
  | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => op_strength_reduction_case41 r1 r2 v1 n2
  | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => op_strength_reduction_case42 r1 r2 n1 v2
  | Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => op_strength_reduction_case43 r1 r2 v1 n2
  | Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => op_strength_reduction_case44 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 =>
      make_cast8signed r1 v1
  | op_strength_reduction_case2 r1 v1 =>
      make_cast8unsigned r1 v1
  | op_strength_reduction_case3 r1 v1 =>
      make_cast16signed r1 v1
  | op_strength_reduction_case4 r1 v1 =>
      make_cast16unsigned r1 v1
  | op_strength_reduction_case5 r1 r2 v1 n2 =>
      make_addimm (Int.neg n2) r1
  | op_strength_reduction_case6 r1 r2 n1 v2 =>
      make_mulimm n1 r2
  | op_strength_reduction_case7 r1 r2 v1 n2 =>
      make_mulimm n2 r1
  | op_strength_reduction_case8 r1 r2 v1 n2 =>
      make_divimm n2 r1 r2
  | op_strength_reduction_case9 r1 r2 v1 n2 =>
      make_divuimm n2 r1 r2
  | op_strength_reduction_case10 r1 r2 v1 n2 =>
      make_moduimm n2 r1 r2
  | op_strength_reduction_case11 r1 r2 n1 v2 =>
      make_andimm n1 r2 v2
  | op_strength_reduction_case12 r1 r2 v1 n2 =>
      make_andimm n2 r1 v1
  | op_strength_reduction_case13 n r1 v1 =>
      make_andimm n r1 v1
  | op_strength_reduction_case14 r1 r2 n1 v2 =>
      make_orimm n1 r2
  | op_strength_reduction_case15 r1 r2 v1 n2 =>
      make_orimm n2 r1
  | op_strength_reduction_case16 r1 r2 n1 v2 =>
      make_xorimm n1 r2
  | op_strength_reduction_case17 r1 r2 v1 n2 =>
      make_xorimm n2 r1
  | op_strength_reduction_case18 r1 r2 v1 n2 =>
      make_shlimm n2 r1 r2
  | op_strength_reduction_case19 r1 r2 v1 n2 =>
      make_shrimm n2 r1 r2
  | op_strength_reduction_case20 r1 r2 v1 n2 =>
      make_shruimm n2 r1 r2
  | op_strength_reduction_case21 addr args vl =>
      let (addr', args') := addr_strength_reduction_32 addr args vl in (Olea addr', args')
  | op_strength_reduction_case22 r1 r2 v1 n2 =>
      make_addlimm (Int64.neg n2) r1
  | op_strength_reduction_case23 r1 r2 n1 v2 =>
      make_mullimm n1 r2
  | op_strength_reduction_case24 r1 r2 v1 n2 =>
      make_mullimm n2 r1
  | op_strength_reduction_case25 r1 r2 v1 n2 =>
      make_divlimm n2 r1 r2
  | op_strength_reduction_case26 r1 r2 v1 n2 =>
      make_divluimm n2 r1 r2
  | op_strength_reduction_case27 r1 r2 v1 n2 =>
      make_modluimm n2 r1 r2
  | op_strength_reduction_case28 r1 r2 n1 v2 =>
      make_andlimm n1 r2 v2
  | op_strength_reduction_case29 r1 r2 v1 n2 =>
      make_andlimm n2 r1 v1
  | op_strength_reduction_case30 n r1 v1 =>
      make_andlimm n r1 v1
  | op_strength_reduction_case31 r1 r2 n1 v2 =>
      make_orlimm n1 r2
  | op_strength_reduction_case32 r1 r2 v1 n2 =>
      make_orlimm n2 r1
  | op_strength_reduction_case33 r1 r2 n1 v2 =>
      make_xorlimm n1 r2
  | op_strength_reduction_case34 r1 r2 v1 n2 =>
      make_xorlimm n2 r1
  | op_strength_reduction_case35 r1 r2 v1 n2 =>
      make_shllimm n2 r1 r2
  | op_strength_reduction_case36 r1 r2 v1 n2 =>
      make_shrlimm n2 r1 r2
  | op_strength_reduction_case37 r1 r2 v1 n2 =>
      make_shrluimm n2 r1 r2
  | op_strength_reduction_case38 addr args vl =>
      let (addr', args') := addr_strength_reduction_64 addr args vl in (Oleal addr', args')
  | op_strength_reduction_case39 c args vl =>
      make_cmp c args vl
  | op_strength_reduction_case40 c ty r1 r2 args v1 v2 vl =>
      make_select c ty r1 r2 args vl
  | op_strength_reduction_case41 r1 r2 v1 n2 =>
      make_mulfimm n2 r1 r1 r2
  | op_strength_reduction_case42 r1 r2 n1 v2 =>
      make_mulfimm n1 r2 r1 r2
  | op_strength_reduction_case43 r1 r2 v1 n2 =>
      make_mulfsimm n2 r1 r1 r2
  | op_strength_reduction_case44 r1 r2 n1 v2 =>
      make_mulfsimm n1 r2 r1 r2
  | op_strength_reduction_default op args vl =>
      (op, args)
  end.

Module ConstpropOp

Converting known values to constants

Operator strength reduction