Module ConstpropOp


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

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

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)
  | _, _, _ => 
      (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_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
  | 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_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').

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 =>
      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
  | Ccompimm Cne n, r1 :: nil, v1 :: nil =>
      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
  | _, _, _ =>
      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_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
  | 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 =>
      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
  | make_cmp_case2 n r1 v1 =>
      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
  | make_cmp_default c args vl =>
      make_cmp_base c args vl
  end.


Original definition: 
Nondetfunction addr_strength_reduction
                (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr, args, vl with

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

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

  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil =>
      (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil =>
      (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil)
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
      (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil)

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

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

  | _, _ =>
      (addr, args)
  end.

Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg) (vl: list aval), Type :=
  | addr_strength_reduction_case1: forall ofs r1 symb n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (Ptr(Gl symb n) :: nil)
  | addr_strength_reduction_case2: forall ofs r1 n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (Ptr(Stk n) :: nil)
  | addr_strength_reduction_case3: forall ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: I n2 :: nil)
  | addr_strength_reduction_case4: forall ofs r1 r2 n1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: Ptr(Gl symb n2) :: nil)
  | addr_strength_reduction_case5: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Stk n1) :: I n2 :: nil)
  | addr_strength_reduction_case6: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: Ptr(Stk n2) :: nil)
  | addr_strength_reduction_case7: forall ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: v2 :: nil)
  | addr_strength_reduction_case8: forall ofs r1 r2 v1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: Ptr(Gl symb n2) :: nil)
  | addr_strength_reduction_case9: forall ofs r1 r2 n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: v2 :: nil)
  | addr_strength_reduction_case10: forall ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | addr_strength_reduction_case11: forall sc ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: I n2 :: nil)
  | addr_strength_reduction_case12: forall sc ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (Ptr(Gl symb n1) :: v2 :: nil)
  | addr_strength_reduction_case13: forall sc ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil)
  | addr_strength_reduction_case14: forall id ofs r1 n1, addr_strength_reduction_cases (Abased id ofs) (r1 :: nil) (I n1 :: nil)
  | addr_strength_reduction_case15: forall sc id ofs r1 n1, addr_strength_reduction_cases (Abasedscaled sc id ofs) (r1 :: nil) (I n1 :: nil)
  | addr_strength_reduction_default: forall (addr: addressing) (args: list reg) (vl: list 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 ofs, r1 :: nil, Ptr(Gl symb n) :: nil => addr_strength_reduction_case1 ofs r1 symb n
  | Aindexed ofs, r1 :: nil, Ptr(Stk n) :: nil => addr_strength_reduction_case2 ofs r1 n
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil => addr_strength_reduction_case3 ofs r1 r2 symb n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Gl symb n2) :: nil => addr_strength_reduction_case4 ofs r1 r2 n1 symb n2
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil => addr_strength_reduction_case5 ofs r1 r2 n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: Ptr(Stk n2) :: nil => addr_strength_reduction_case6 ofs r1 r2 n1 n2
  | Aindexed2 ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil => addr_strength_reduction_case7 ofs r1 r2 symb n1 v2
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: Ptr(Gl symb n2) :: nil => addr_strength_reduction_case8 ofs r1 r2 v1 symb n2
  | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_case9 ofs r1 r2 n1 v2
  | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case10 ofs r1 r2 v1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: I n2 :: nil => addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, Ptr(Gl symb n1) :: v2 :: nil => addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2
  | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case13 sc ofs r1 r2 v1 n2
  | Abased id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case14 id ofs r1 n1
  | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case15 sc id ofs r1 n1
  | addr, args, vl => addr_strength_reduction_default addr args vl
  end.

Definition addr_strength_reduction (addr: addressing) (args: list reg) (vl: list aval) :=
  match addr_strength_reduction_match addr args vl with
  | addr_strength_reduction_case1 ofs r1 symb n =>
      (Aglobal symb (Int.add n ofs), nil)
  | addr_strength_reduction_case2 ofs r1 n =>
      (Ainstack (Int.add n ofs), nil)
  | addr_strength_reduction_case3 ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
  | addr_strength_reduction_case4 ofs r1 r2 n1 symb n2 =>
      (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil)
  | addr_strength_reduction_case5 ofs r1 r2 n1 n2 =>
      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
  | addr_strength_reduction_case6 ofs r1 r2 n1 n2 =>
      (Ainstack (Int.add (Int.add n1 n2) ofs), nil)
  | addr_strength_reduction_case7 ofs r1 r2 symb n1 v2 =>
      (Abased symb (Int.add n1 ofs), r2 :: nil)
  | addr_strength_reduction_case8 ofs r1 r2 v1 symb n2 =>
      (Abased symb (Int.add n2 ofs), r1 :: nil)
  | addr_strength_reduction_case9 ofs r1 r2 n1 v2 =>
      (Aindexed (Int.add n1 ofs), r2 :: nil)
  | addr_strength_reduction_case10 ofs r1 r2 v1 n2 =>
      (Aindexed (Int.add n2 ofs), r1 :: nil)
  | addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2 =>
      (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil)
  | addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2 =>
      (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil)
  | addr_strength_reduction_case13 sc ofs r1 r2 v1 n2 =>
      (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil)
  | addr_strength_reduction_case14 id ofs r1 n1 =>
      (Aglobal id (Int.add ofs n1), nil)
  | addr_strength_reduction_case15 sc id ofs r1 n1 =>
      (Aglobal id (Int.add ofs (Int.mul sc n1)), nil)
  | addr_strength_reduction_default addr args vl =>
      (addr, args)
  end.


Definition make_addimm (n: int) (r: reg) :=
  if Int.eq n Int.zero
  then (Omove, r :: nil)
  else (Olea (Aindexed 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) :=
  match Int.is_power2 n with
  | Some l => if Int.ltu l (Int.repr 31)
              then (Oshrximm l, r1 :: nil)
              else (Odiv, r1 :: r2 :: nil)
  | None => (Odiv, r1 :: r2 :: nil)
  end.

Definition make_divuimm n (r1 r2: reg) :=
  match Int.is_power2 n with
  | Some l => (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_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 addr args vl in
      (Olea addr', args')
  | 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 (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 c args vl, op_strength_reduction_cases (Ocmp c) (args) (vl)
  | op_strength_reduction_case23: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (v1 :: F n2 :: nil)
  | op_strength_reduction_case24: forall r1 r2 n1 v2, op_strength_reduction_cases (Omulf) (r1 :: r2 :: nil) (F n1 :: v2 :: nil)
  | op_strength_reduction_case25: forall r1 r2 v1 n2, op_strength_reduction_cases (Omulfs) (r1 :: r2 :: nil) (v1 :: FS n2 :: nil)
  | op_strength_reduction_case26: 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
  | Ocmp c, args, vl => op_strength_reduction_case22 c args vl
  | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => op_strength_reduction_case23 r1 r2 v1 n2
  | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => op_strength_reduction_case24 r1 r2 n1 v2
  | Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => op_strength_reduction_case25 r1 r2 v1 n2
  | Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => op_strength_reduction_case26 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 addr args vl in (Olea addr', args')
  | op_strength_reduction_case22 c args vl =>
      make_cmp c args vl
  | op_strength_reduction_case23 r1 r2 v1 n2 =>
      make_mulfimm n2 r1 r1 r2
  | op_strength_reduction_case24 r1 r2 n1 v2 =>
      make_mulfimm n1 r2 r1 r2
  | op_strength_reduction_case25 r1 r2 v1 n2 =>
      make_mulfsimm n2 r1 r1 r2
  | op_strength_reduction_case26 r1 r2 n1 v2 =>
      make_mulfsimm n1 r2 r1 r2
  | op_strength_reduction_default op args vl =>
      (op, args)
  end.

Generated by coq2html