(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)

(** Instruction selection for operators *)

(** The instruction selection pass recognizes opportunities for using
  combined arithmetic and logical operations and addressing modes
  offered by the target processor.  For instance, the expression [x + 1]
  can take advantage of the "immediate add" instruction of the processor,
  and on the PowerPC, the expression [(x >> 6) & 0xFF] can be turned
  into a "rotate and mask" instruction.

  This file defines functions for building CminorSel expressions and
  statements, especially expressions consisting of operator
  applications.  These functions examine their arguments to choose
  cheaper forms of operators whenever possible.

  For instance, [add e1 e2] will return a CminorSel expression semantically
  equivalent to [Eop Oadd (e1 ::: e2 ::: Enil)], but will use a
  [Oaddimm] operator if one of the arguments is an integer constant,
  or suppress the addition altogether if one of the arguments is the
  null integer.  In passing, we perform operator reassociation
  ([(e + c1) * c2] becomes [(e * c2) + (c1 * c2)]) and a small amount
  of constant propagation.

  On top of the "smart constructor" functions defined below,
  module [Selection] implements the actual instruction selection pass.
*)

Require Import Coqlib.
Require Import Compopts.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Op.
Require Import CminorSel.

Open Local Scope cminorsel_scope.

(** ** Constants **)

Definition addrsymbol (id: ident) (ofs: int) :=
  Eop (Oaddrsymbol id ofs) Enil.

Definition addrstack (ofs: int) :=
  Eop (Oaddrstack ofs) Enil.

(** ** Integer logical negation *)

Nondetfunction notint (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.not n)) Enil
  | Eop (Oshift s) (t1:::Enil) => Eop (Onotshift s) (t1:::Enil)
  | Eop Onot (t1:::Enil) => t1
  | Eop (Onotshift s) (t1:::Enil) => Eop (Oshift s) (t1:::Enil)
  | Eop (Oxorimm n) (t1:::Enil) => Eop (Oxorimm (Int.not n)) (t1:::Enil)
  | _ => Eop Onot (e:::Enil)
  end.

(** ** Integer addition and pointer addition *)

Nondetfunction addimm (n: int) (e: expr) :=
  if Int.eq n Int.zero then e else
  match e with
  | Eop (Ointconst m) Enil       => Eop (Ointconst(Int.add n m)) Enil
  | Eop (Oaddrsymbol s m) Enil   => Eop (Oaddrsymbol s (Int.add n m)) Enil
  | Eop (Oaddrstack m) Enil      => Eop (Oaddrstack (Int.add n m)) Enil
  | Eop (Oaddimm m) (t ::: Enil) => Eop (Oaddimm(Int.add n m)) (t ::: Enil)
  | _                            => Eop (Oaddimm n) (e ::: Enil)
  end.

Nondetfunction add (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 => addimm n1 t2
  | t1, Eop (Ointconst n2) Enil => addimm n2 t1
  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) =>
      addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil))
  | Eop(Oaddimm n1) (t1:::Enil), t2 => addimm n1 (Eop Oadd (t1:::t2:::Enil))
  | t1, Eop (Oaddimm n2) (t2:::Enil) => addimm n2 (Eop Oadd (t1:::t2:::Enil))
  | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oaddshift s) (t2:::t1:::Enil)
  | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oaddshift s) (t1:::t2:::Enil)
  | Eop Omul (t1:::t2:::Enil), t3 => Eop Omla (t1:::t2:::t3:::Enil)
  | t1, Eop Omul (t2:::t3:::Enil) => Eop Omla (t2:::t3:::t1:::Enil)
  | _, _ => Eop Oadd (e1:::e2:::Enil)
  end.

(** ** Integer and pointer subtraction *)

Nondetfunction rsubimm (n: int) (e: expr) :=
  match e with
  | Eop (Ointconst m) Enil => Eop (Ointconst (Int.sub n m)) Enil
  | Eop (Oaddimm m) (t:::Enil) => Eop (Orsubimm (Int.sub n m)) (t:::Enil)
  | Eop (Orsubimm m) (t:::Enil) => Eop (Oaddimm (Int.sub n m)) (t:::Enil)
  | _ => Eop (Orsubimm n) (e:::Enil)
  end.

Nondetfunction sub (e1: expr) (e2: expr) :=
  match e1, e2 with
  | t1, Eop (Ointconst n2) Enil => addimm (Int.neg n2) t1
  | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) =>
      addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil))
  | Eop (Oaddimm n1) (t1:::Enil), t2 =>
      addimm n1 (Eop Osub (t1:::t2:::Enil))
  | t1, Eop (Oaddimm n2) (t2:::Enil) =>
      addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil))
  | Eop (Ointconst n1) Enil, t2 => rsubimm n1 t2
  | Eop (Oshift s) (t1:::Enil), t2 => Eop (Orsubshift s) (t2:::t1:::Enil)
  | t1, Eop (Oshift s) (t2:::Enil) => Eop (Osubshift s) (t1:::t2:::Enil)
  | _, _ => Eop Osub (e1:::e2:::Enil)
  end.

Definition negint (e: expr) := rsubimm Int.zero e.

(** ** Immediate shifts *)

Nondetfunction shlimm (e1: expr) (n: int) :=
  if Int.eq n Int.zero then
    e1
  else if negb (Int.ltu n Int.iwordsize) then
    Eop Oshl (e1 ::: Eop (Ointconst n) Enil ::: Enil)
  else match e1 with
    | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shl n1 n)) Enil
    | Eop (Oshift (Slsl n1)) (t1:::Enil) =>
        if Int.ltu (Int.add n n1) Int.iwordsize
        then Eop (Oshift (Slsl (mk_shift_amount(Int.add n n1)))) (t1:::Enil)
        else Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil)
    | _ => Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil)
    end.

Nondetfunction shruimm (e1: expr) (n: int) :=
  if Int.eq n Int.zero then
    e1
  else if negb (Int.ltu n Int.iwordsize) then
    Eop Oshru (e1 ::: Eop (Ointconst n) Enil ::: Enil)
  else match e1 with
    | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shru n1 n)) Enil
    | Eop (Oshift (Slsr n1)) (t1:::Enil) =>
        if Int.ltu (Int.add n n1) Int.iwordsize
        then Eop (Oshift (Slsr (mk_shift_amount (Int.add n n1)))) (t1:::Enil)
        else Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil)
    | _ => Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil)
    end.

Nondetfunction shrimm (e1: expr) (n: int) :=
  if Int.eq n Int.zero then
    e1
  else if negb (Int.ltu n Int.iwordsize) then
    Eop Oshr (e1 ::: Eop (Ointconst n) Enil ::: Enil)
  else
    match e1 with
    | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shr n1 n)) Enil
    | Eop (Oshift (Sasr n1)) (t1:::Enil) =>
        if Int.ltu (Int.add n n1) Int.iwordsize
        then Eop (Oshift (Sasr (mk_shift_amount (Int.add n n1)))) (t1:::Enil)
        else Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil)
    | _ => Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil)
    end.

(** ** Integer multiply *)

Definition mulimm_base (n1: int) (e2: expr) :=
  match Int.one_bits n1 with
  | i :: nil =>
      shlimm e2 i
  | i :: j :: nil =>
      Elet e2
        (add (shlimm (Eletvar 0) i) (shlimm (Eletvar 0) j))
  | _ =>
      Eop Omul (Eop (Ointconst n1) Enil ::: e2 ::: Enil)
  end.

Nondetfunction mulimm (n1: int) (e2: expr) :=
  if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil
  else if Int.eq n1 Int.one then e2
  else match e2 with
  | Eop (Ointconst n2) Enil => Eop (Ointconst(Int.mul n1 n2)) Enil
  | Eop (Oaddimm n2) (t2:::Enil) => addimm (Int.mul n1 n2) (mulimm_base n1 t2)
  | _ => mulimm_base n1 e2
  end.

Nondetfunction mul (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 => mulimm n1 t2
  | t1, Eop (Ointconst n2) Enil => mulimm n2 t1
  | _, _ => Eop Omul (e1:::e2:::Enil)
  end.

(** ** Bitwise and, or, xor *)

Nondetfunction andimm (n1: int) (e2: expr) := 
  if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else
  if Int.eq n1 Int.mone then e2 else
  match e2 with
  | Eop (Ointconst n2) Enil =>
      Eop (Ointconst (Int.and n1 n2)) Enil
  | Eop (Oandimm n2) (t2:::Enil) =>
      Eop (Oandimm (Int.and n1 n2)) (t2:::Enil)
  | _ =>
      Eop (Oandimm n1) (e2:::Enil)
  end.

Nondetfunction and (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 => andimm n1 t2
  | t1, Eop (Ointconst n2) Enil => andimm n2 t1
  | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oandshift s) (t2:::t1:::Enil)
  | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oandshift s) (t1:::t2:::Enil)
  | Eop (Onotshift s) (t1:::Enil), t2 => Eop (Obicshift s) (t2:::t1:::Enil)
  | t1, Eop (Onotshift s) (t2:::Enil) => Eop (Obicshift s) (t1:::t2:::Enil)
  | Eop Onot (t1:::Enil), t2 => Eop Obic (t2:::t1:::Enil)
  | t1, Eop Onot (t2:::Enil) => Eop Obic (t1:::t2:::Enil)
  | _, _ => Eop Oand (e1:::e2:::Enil)
  end.

Definition same_expr_pure (e1 e2: expr) :=
  match e1, e2 with
  | Evar v1, Evar v2 => if ident_eq v1 v2 then true else false
  | _, _ => false
  end.

Nondetfunction orimm (n1: int) (e2: expr) :=
  if Int.eq n1 Int.zero then e2 else
  if Int.eq n1 Int.mone then Eop (Ointconst Int.mone) Enil else
  match e2 with
  | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.or n1 n2)) Enil
  | Eop (Oorimm n2) (t2:::Enil) => Eop (Oorimm (Int.or n1 n2)) (t2:::Enil)
  | _ => Eop (Oorimm n1) (e2:::Enil)
  end.

Nondetfunction or (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 => orimm n1 t2
  | t1, Eop (Ointconst n2) Enil => orimm n2 t1
  | Eop (Oshift (Slsl n1)) (t1:::Enil), Eop (Oshift (Slsr n2)) (t2:::Enil) =>
      if Int.eq (Int.add n1 n2) Int.iwordsize
      && same_expr_pure t1 t2
      then Eop (Oshift (Sror n2)) (t1:::Enil)
      else Eop (Oorshift (Slsr n2)) (e1:::t2:::Enil)
  | Eop (Oshift (Slsr n1)) (t1:::Enil), Eop (Oshift (Slsl n2)) (t2:::Enil) =>
      if Int.eq (Int.add n2 n1) Int.iwordsize
      && same_expr_pure t1 t2
      then Eop (Oshift (Sror n1)) (t1:::Enil)
      else Eop (Oorshift (Slsl n2)) (e1:::t2:::Enil)
  | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oorshift s) (t2:::t1:::Enil)
  | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oorshift s) (t1:::t2:::Enil)
  | _, _ => Eop Oor (e1:::e2:::Enil)
  end.

Nondetfunction xorimm (n1: int) (e2: expr) :=
  if Int.eq n1 Int.zero then e2 else
  if Int.eq n1 Int.mone then notint e2 else
  match e2 with
  | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.xor n1 n2)) Enil
  | Eop (Oxorimm n2) (t2:::Enil) => Eop (Oxorimm (Int.xor n1 n2)) (t2:::Enil)
  | Eop Onot (t2:::Enil) => Eop (Oxorimm (Int.not n1)) (t2:::Enil)
  | _ => Eop (Oxorimm n1) (e2:::Enil)
  end.

Nondetfunction xor (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 => xorimm n1 t2
  | t1, Eop (Ointconst n2) Enil => xorimm n2 t1
  | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oxorshift s) (t2:::t1:::Enil)
  | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oxorshift s) (t1:::t2:::Enil)
  | _, _ => Eop Oxor (e1:::e2:::Enil)
  end.

(** ** Integer division and modulus *)

Definition mod_aux (divop: operation) (e1 e2: expr) :=
  Elet e1
    (Elet (lift e2)
      (Eop Osub (Eletvar 1 :::
                 Eop Omul (Eop divop (Eletvar 1 ::: Eletvar 0 ::: Enil) :::
                           Eletvar 0 :::
                           Enil) :::
                 Enil))).

Definition divs_base (e1: expr) (e2: expr) := Eop Odiv (e1:::e2:::Enil).
Definition mods_base := mod_aux Odiv.
Definition divu_base (e1: expr) (e2: expr) := Eop Odivu (e1:::e2:::Enil).
Definition modu_base := mod_aux Odivu.

Definition shrximm (e1: expr) (n2: int) :=
  if Int.eq n2 Int.zero then e1 else Eop (Oshrximm n2) (e1:::Enil).

(** ** General shifts *)

Nondetfunction shl (e1: expr) (e2: expr) :=
  match e2 with
  | Eop (Ointconst n2) Enil => shlimm e1 n2
  | _ => Eop Oshl (e1:::e2:::Enil)
  end.

Nondetfunction shr (e1: expr) (e2: expr) :=
  match e2 with
  | Eop (Ointconst n2) Enil => shrimm e1 n2
  | _ => Eop Oshr (e1:::e2:::Enil)
  end.

Nondetfunction shru (e1: expr) (e2: expr) :=
  match e2 with
  | Eop (Ointconst n2) Enil => shruimm e1 n2
  | _ => Eop Oshru (e1:::e2:::Enil)
  end.

(** ** Floating-point arithmetic *)

Definition negf (e: expr) :=  Eop Onegf (e ::: Enil).
Definition absf (e: expr) :=  Eop Oabsf (e ::: Enil).
Definition addf (e1 e2: expr) :=  Eop Oaddf (e1 ::: e2 ::: Enil).
Definition subf (e1 e2: expr) :=  Eop Osubf (e1 ::: e2 ::: Enil).
Definition mulf (e1 e2: expr) :=  Eop Omulf (e1 ::: e2 ::: Enil).

Definition negfs (e: expr) :=  Eop Onegfs (e ::: Enil).
Definition absfs (e: expr) :=  Eop Oabsfs (e ::: Enil).
Definition addfs (e1 e2: expr) :=  Eop Oaddfs (e1 ::: e2 ::: Enil).
Definition subfs (e1 e2: expr) :=  Eop Osubfs (e1 ::: e2 ::: Enil).
Definition mulfs (e1 e2: expr) :=  Eop Omulfs (e1 ::: e2 ::: Enil).

(** ** Comparisons *)

Nondetfunction compimm (default: comparison -> int -> condition)
                       (sem: comparison -> int -> int -> bool)
                       (c: comparison) (e1: expr) (n2: int) :=
  match c, e1 with
  | c, Eop (Ointconst n1) Enil =>
      Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil
  | Ceq, Eop (Ocmp c) el =>
      if Int.eq_dec n2 Int.zero then
        Eop (Ocmp (negate_condition c)) el
      else if Int.eq_dec n2 Int.one then
        Eop (Ocmp c) el
      else 
        Eop (Ointconst Int.zero) Enil
  | Cne, Eop (Ocmp c) el =>
      if Int.eq_dec n2 Int.zero then
        Eop (Ocmp c) el
      else if Int.eq_dec n2 Int.one then
        Eop (Ocmp (negate_condition c)) el
      else 
        Eop (Ointconst Int.one) Enil
  | _, _ =>
       Eop (Ocmp (default c n2)) (e1 ::: Enil)
  end.

Nondetfunction comp (c: comparison) (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 =>
      compimm Ccompimm Int.cmp (swap_comparison c) t2 n1
  | t1, Eop (Ointconst n2) Enil =>
      compimm Ccompimm Int.cmp c t1 n2
  | _, _ =>
      Eop (Ocmp (Ccomp c)) (e1 ::: e2 ::: Enil)
  end.

Nondetfunction compu (c: comparison) (e1: expr) (e2: expr) :=
  match e1, e2 with
  | Eop (Ointconst n1) Enil, t2 =>
      compimm Ccompuimm Int.cmpu (swap_comparison c) t2 n1
  | t1, Eop (Ointconst n2) Enil =>
      compimm Ccompuimm Int.cmpu c t1 n2
  | _, _ =>
      Eop (Ocmp (Ccompu c)) (e1 ::: e2 ::: Enil)
  end.

Definition compf (c: comparison) (e1: expr) (e2: expr) :=
  Eop (Ocmp (Ccompf c)) (e1 ::: e2 ::: Enil).

Definition compfs (c: comparison) (e1: expr) (e2: expr) :=
  Eop (Ocmp (Ccompfs c)) (e1 ::: e2 ::: Enil).

(** ** Integer conversions *)

Definition cast8unsigned (e: expr) := andimm (Int.repr 255) e.

Nondetfunction cast8signed (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.sign_ext 8 n)) Enil
  | _ => Eop Ocast8signed (e ::: Enil)
  end.

Definition cast16unsigned (e: expr) := andimm (Int.repr 65535) e.

Nondetfunction cast16signed (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Ointconst (Int.sign_ext 16 n)) Enil
  | _ => Eop Ocast16signed (e ::: Enil)
  end.

(** ** Floating-point conversions *)

Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil).
Definition floatofsingle (e: expr) := Eop Ofloatofsingle (e ::: Enil).

Definition intoffloat (e: expr) := Eop Ointoffloat (e ::: Enil).
Definition intuoffloat (e: expr) := Eop Ointuoffloat (e ::: Enil).

Nondetfunction floatofint (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_int n)) Enil
  | _ => Eop Ofloatofint (e ::: Enil)
  end.

Nondetfunction floatofintu (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_intu n)) Enil
  | _ => Eop Ofloatofintu (e ::: Enil)
  end.

Definition intofsingle (e: expr) := Eop Ointofsingle (e ::: Enil).
Definition intuofsingle (e: expr) := Eop Ointuofsingle (e ::: Enil).

Nondetfunction singleofint (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Osingleconst (Float32.of_int n)) Enil
  | _ => Eop Osingleofint (e ::: Enil)
  end.

Nondetfunction singleofintu (e: expr) :=
  match e with
  | Eop (Ointconst n) Enil => Eop (Osingleconst (Float32.of_intu n)) Enil
  | _ => Eop Osingleofintu (e ::: Enil)
  end.

(** ** Recognition of addressing modes for load and store operations *)

(** We do not recognize the [Aindexed2] and [Aindexed2shift] modes
    for floating-point accesses, since these are not supported
    by the hardware and emulated inefficiently in [Asmgen].
    Likewise, [Aindexed2shift] are not supported for halfword
    and signed byte accesses. *)

Definition can_use_Aindexed2 (chunk: memory_chunk): bool :=
  match chunk with
  | Mint8signed => true
  | Mint8unsigned => true
  | Mint16signed => true
  | Mint16unsigned => true
  | Mint32 => true
  | Mint64 => false
  | Mfloat32 => false
  | Mfloat64 => false
  | Many32 => true
  | Many64 => false
  end.

Definition can_use_Aindexed2shift (chunk: memory_chunk) (s: shift): bool :=
  match chunk with
  | Mint8signed => false
  | Mint8unsigned => true
  | Mint16signed => false
  | Mint16unsigned => false
  | Mint32 => true
  | Mint64 => false
  | Mfloat32 => false
  | Mfloat64 => false
  | Many32 => true
  | Many64 => false
  end &&
  (if thumb tt then
     match s with
     | Slsl s => Int.ltu s (Int.repr 4)
     | _      => false
     end
   else true).

Nondetfunction addressing (chunk: memory_chunk) (e: expr) :=
  match e with
  | Eop (Oaddrstack n) Enil => (Ainstack n, Enil)
  | Eop (Oaddimm n) (e1:::Enil) => (Aindexed n, e1:::Enil)
  | Eop (Oaddshift s) (e1:::e2:::Enil) =>
      if can_use_Aindexed2shift chunk s
      then (Aindexed2shift s, e1:::e2:::Enil)
      else (Aindexed Int.zero, Eop (Oaddshift s) (e1:::e2:::Enil) ::: Enil)
  | Eop Oadd (e1:::e2:::Enil) =>
      if can_use_Aindexed2 chunk
      then (Aindexed2, e1:::e2:::Enil)
      else (Aindexed Int.zero, Eop Oadd (e1:::e2:::Enil) ::: Enil)
  | _ => (Aindexed Int.zero, e:::Enil)
  end.