Module ConstpropOp


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.
Require SelectOp.

Converting known values to constants


Definition const_for_result (a: aval) : option operation :=
  match a with
  | I n | IU 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 =>
      (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_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 =>
      make_cast8signed r1 v1
  | op_strength_reduction_case2 r1 v1 =>
      make_cast16signed r1 v1
  | op_strength_reduction_case3 r1 r2 n1 v2 =>
      make_addimm n1 r2
  | op_strength_reduction_case4 r1 r2 v1 n2 =>
      make_addimm n2 r1
  | 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 r1
  | op_strength_reduction_case7 r1 r2 v1 n2 =>
      make_mulimm n2 r1 r2
  | 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 r1 r2 n1 v2 =>
      make_addlimm n1 r2
  | op_strength_reduction_case22 r1 r2 v1 n2 =>
      make_addlimm n2 r1
  | op_strength_reduction_case23 r1 r2 v1 n2 =>
      make_addlimm (Int64.neg n2) r1
  | op_strength_reduction_case24 r1 r2 n1 v2 =>
      make_mullimm n1 r2 r1
  | op_strength_reduction_case25 r1 r2 v1 n2 =>
      make_mullimm n2 r1 r2
  | op_strength_reduction_case26 r1 r2 v1 n2 =>
      make_divlimm n2 r1 r2
  | op_strength_reduction_case27 r1 r2 v1 n2 =>
      make_divluimm n2 r1 r2
  | op_strength_reduction_case28 r1 r2 v1 n2 =>
      make_modluimm n2 r1 r2
  | op_strength_reduction_case29 r1 r2 n1 v2 =>
      make_andlimm n1 r2 v2
  | op_strength_reduction_case30 r1 r2 v1 n2 =>
      make_andlimm n2 r1 v1
  | op_strength_reduction_case31 n r1 v1 =>
      make_andlimm n r1 v1
  | op_strength_reduction_case32 r1 r2 n1 v2 =>
      make_orlimm n1 r2
  | op_strength_reduction_case33 r1 r2 v1 n2 =>
      make_orlimm n2 r1
  | op_strength_reduction_case34 r1 r2 n1 v2 =>
      make_xorlimm n1 r2
  | op_strength_reduction_case35 r1 r2 v1 n2 =>
      make_xorlimm n2 r1
  | op_strength_reduction_case36 r1 r2 v1 n2 =>
      make_shllimm n2 r1 r2
  | op_strength_reduction_case37 r1 r2 v1 n2 =>
      make_shrlimm n2 r1 r2
  | op_strength_reduction_case38 r1 r2 v1 n2 =>
      make_shrluimm n2 r1 r2
  | op_strength_reduction_case39 c args vl =>
      make_cmp c args vl
  | op_strength_reduction_case40 r1 r2 v1 n2 =>
      make_mulfimm n2 r1 r1 r2
  | op_strength_reduction_case41 r1 r2 n1 v2 =>
      make_mulfimm n1 r2 r1 r2
  | op_strength_reduction_case42 r1 r2 v1 n2 =>
      make_mulfsimm n2 r1 r1 r2
  | op_strength_reduction_case43 r1 r2 n1 v2 =>
      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 SelectOp.symbol_is_relocatable symb
      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 =>
      if SelectOp.symbol_is_relocatable symb then (addr, args) else (Aglobal symb (Ptrofs.add n1 n), nil)
  | addr_strength_reduction_case2 n r1 n1 =>
      (Ainstack (Ptrofs.add n1 n), nil)
  | addr_strength_reduction_default addr args vl =>
      (addr, args)
  end.


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