(* *********************************************************************)
(*                                                                     *)
(*              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.     *)
(*                                                                     *)
(* *********************************************************************)
(** Value analysis for ARM operators *)
Definition eval_static_shift (s: shift) (v: aval): aval :=
match s with
| Slsl x => shl v (I x)
| Slsr x => shru v (I x)
| Sasr x => shr v (I x)
| Sror x => ror v (I x)
end.
Definition eval_static_condition (cond: condition) (vl: list aval): abool :=
match cond, vl with
| Ccomp c, v1 :: v2 :: nil => cmp_bool c v1 v2
| Ccompu c, v1 :: v2 :: nil => cmpu_bool c v1 v2
| Ccompshift c s, v1 :: v2 :: nil => cmp_bool c v1 (eval_static_shift s v2)
| Ccompushift c s, v1 :: v2 :: nil => cmpu_bool c v1 (eval_static_shift s v2)
| Ccompimm c n, v1 :: nil => cmp_bool c v1 (I n)
| Ccompuimm c n, v1 :: nil => cmpu_bool c v1 (I n)
| Ccompf c, v1 :: v2 :: nil => cmpf_bool c v1 v2
| Cnotcompf c, v1 :: v2 :: nil => cnot (cmpf_bool c v1 v2)
| Ccompfzero c, v1 :: nil => cmpf_bool c v1 (F Float.zero)
| Cnotcompfzero c, v1 :: nil => cnot (cmpf_bool c v1 (F Float.zero))
| Ccompfs c, v1 :: v2 :: nil => cmpfs_bool c v1 v2
| Cnotcompfs c, v1 :: v2 :: nil => cnot (cmpfs_bool c v1 v2)
| Ccompfszero c, v1 :: nil => cmpfs_bool c v1 (FS Float32.zero)
| Cnotcompfszero c, v1 :: nil => cnot (cmpfs_bool c v1 (FS Float32.zero))
| _, _ => Bnone
end.
Definition eval_static_addressing (addr: addressing) (vl: list aval): aval :=
match addr, vl with
| Aindexed n, v1::nil => add v1 (I n)
| Aindexed2, v1::v2::nil => add v1 v2
| Aindexed2shift s, v1::v2::nil => add v1 (eval_static_shift s v2)
| Ainstack ofs, nil => Ptr(Stk ofs)
| _, _ => Vbot
end.
Definition eval_static_operation (op: operation) (vl: list aval): aval :=
match op, vl with
| Omove, v1::nil => v1
| Ointconst n, nil => I n
| Ofloatconst n, nil => if propagate_float_constants tt then F n else ntop
| Osingleconst n, nil => if propagate_float_constants tt then FS n else ntop
| Oaddrsymbol id ofs, nil => Ptr (Gl id ofs)
| Oaddrstack ofs, nil => Ptr (Stk ofs)
| Ocast8signed, v1 :: nil => sign_ext 8 v1
| Ocast16signed, v1 :: nil => sign_ext 16 v1
| Oadd, v1::v2::nil => add v1 v2
| Oaddshift s, v1::v2::nil => add v1 (eval_static_shift s v2)
| Oaddimm n, v1::nil => add v1 (I n)
| Osub, v1::v2::nil => sub v1 v2
| Osubshift s, v1::v2::nil => sub v1 (eval_static_shift s v2)
| Orsubshift s, v1::v2::nil => sub (eval_static_shift s v2) v1
| Orsubimm n, v1::nil => sub (I n) v1
| Omul, v1::v2::nil => mul v1 v2
| Omla, v1::v2::v3::nil => add (mul v1 v2) v3
| Omulhs, v1::v2::nil => mulhs v1 v2
| Omulhu, v1::v2::nil => mulhu v1 v2
| Odiv, v1::v2::nil => divs v1 v2
| Odivu, v1::v2::nil => divu v1 v2
| Oand, v1::v2::nil => and v1 v2
| Oandshift s, v1::v2::nil => and v1 (eval_static_shift s v2)
| Oandimm n, v1::nil => and v1 (I n)
| Oor, v1::v2::nil => or v1 v2
| Oorshift s, v1::v2::nil => or v1 (eval_static_shift s v2)
| Oorimm n, v1::nil => or v1 (I n)
| Oxor, v1::v2::nil => xor v1 v2
| Oxorshift s, v1::v2::nil => xor v1 (eval_static_shift s v2)
| Oxorimm n, v1::nil => xor v1 (I n)
| Obic, v1::v2::nil => and v1 (notint v2)
| Obicshift s, v1::v2::nil => and v1 (notint (eval_static_shift s v2))
| Onot, v1::nil => notint v1
| Onotshift s, v1::nil => notint (eval_static_shift s v1)
| Oshl, v1::v2::nil => shl v1 v2
| Oshr, v1::v2::nil => shr v1 v2
| Oshru, v1::v2::nil => shru v1 v2
| Oshift s, v1::nil => eval_static_shift s v1
| Oshrximm n, v1::nil => shrx v1 (I n)
| Onegf, v1::nil => negf v1
| Oabsf, v1::nil => absf v1
| Oaddf, v1::v2::nil => addf v1 v2
| Osubf, v1::v2::nil => subf v1 v2
| Omulf, v1::v2::nil => mulf v1 v2
| Odivf, v1::v2::nil => divf v1 v2
| Onegfs, v1::nil => negfs v1
| Oabsfs, v1::nil => absfs v1
| Oaddfs, v1::v2::nil => addfs v1 v2
| Osubfs, v1::v2::nil => subfs v1 v2
| Omulfs, v1::v2::nil => mulfs v1 v2
| Odivfs, v1::v2::nil => divfs v1 v2
| Osingleoffloat, v1::nil => singleoffloat v1
| Ofloatofsingle, v1::nil => floatofsingle v1
| Ointoffloat, v1::nil => intoffloat v1
| Ointuoffloat, v1::nil => intuoffloat v1
| Ofloatofint, v1::nil => floatofint v1
| Ofloatofintu, v1::nil => floatofintu v1
| Ointofsingle, v1::nil => intofsingle v1
| Ointuofsingle, v1::nil => intuofsingle v1
| Osingleofint, v1::nil => singleofint v1
| Osingleofintu, v1::nil => singleofintu v1
| Omakelong, v1::v2::nil => longofwords v1 v2
| Olowlong, v1::nil => loword v1
| Ohighlong, v1::nil => hiword v1
| Ocmp c, _ => of_optbool (eval_static_condition c vl)
| _, _ => Vbot
end.
Section SOUNDNESS.
Variable bc: block_classification.
Variable ge: genv.
Hypothesis GENV: genv_match bc ge.
Variable sp: block.
Hypothesis STACK: bc sp = BCstack.

(* Specifications: *)
Lemma eval_static_shift_sound:
forall s v a,
vmatch bc v a ->
vmatch bc (eval_shift s v) (eval_static_shift s a).