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Require Import Coqlib.
Require Import Integers.
Require Import Values.
Require Import Floats.
Require Import Memory.
Require Import Lia.
Axiom address_of_ptr : mem -> block -> ptrofs -> int64.
Axiom ptr_of_address : mem -> int64 -> option (block*ptrofs).
Axiom ptr_address_correct :
forall m b ofs, (ptr_of_address m (address_of_ptr m b ofs)) = Some (b, ofs).
Definition int64_of_value m v : int64 :=
match v with
| Vint x => Int64.repr (Int.signed x)
| Vlong x => x
| Vsingle x => Int64.repr (Int.signed (Float32.to_bits x))
| Vfloat x => Float.to_bits x
| Vptr b ofs => address_of_ptr m b ofs
| Vundef => Int64.zero
end.
Inductive vtype := VTint | VTlong | VTsingle | VTfloat | VTptr | VTundef.
Definition vtype_of v :=
match v with
| Vint _ => VTint
| Vlong _ => VTlong
| Vfloat _ => VTfloat
| Vsingle _ => VTsingle
| Vptr _ _ => VTptr
| Vundef => VTundef
end.
Definition value_of_int64 (ty : vtype) (m : mem) (l : int64) : val :=
match ty with
| VTint => Vint (Int.repr (Int64.signed l))
| VTlong => Vlong l
| VTsingle => Vsingle (Float32.of_bits (Int.repr (Int64.signed l)))
| VTfloat => Vfloat (Float.of_bits l)
| VTptr => match ptr_of_address m l with
| Some(b, ofs) => Vptr b ofs
| None => Vundef
end
| VTundef => Vundef
end.
Remark min_signed_order: Int64.min_signed <= Int.min_signed.
Proof.
cbv. discriminate.
Qed.
Remark max_signed_order: Int.max_signed <= Int64.max_signed.
Proof.
cbv. discriminate.
Qed.
Lemma int64_of_value_correct :
forall m v,
value_of_int64 (vtype_of v) m (int64_of_value m v) = v.
Proof.
destruct v; cbn; trivial; f_equal.
- rewrite Int64.signed_repr.
apply Int.repr_signed.
pose proof (Int.signed_range i) as RANGE.
pose proof min_signed_order.
pose proof max_signed_order.
lia.
- apply Float.of_to_bits.
- rewrite Int64.signed_repr.
{ rewrite Int.repr_signed.
apply Float32.of_to_bits. }
pose proof (Int.signed_range (Float32.to_bits f)) as RANGE.
pose proof min_signed_order.
pose proof max_signed_order.
lia.
- pose proof (ptr_address_correct m b i).
destruct (ptr_of_address m (address_of_ptr m b i)).
+ inv H. trivial.
+ discriminate.
Qed.
Definition bits_of_float x :=
match x with
| Vfloat f => Vlong (Float.to_bits f)
| _ => Vundef
end.
Definition bits_of_single x :=
match x with
| Vsingle f => Vint (Float32.to_bits f)
| _ => Vundef
end.
Definition float_of_bits x :=
match x with
| Vlong f => Vfloat (Float.of_bits f)
| _ => Vundef
end.
Definition single_of_bits x :=
match x with
| Vint f => Vsingle (Float32.of_bits f)
| _ => Vundef
end.
Definition bitwise_select_int b vtrue vfalse :=
Val.or (Val.and (Val.neg b) vtrue)
(Val.and (Val.sub b Vone) vfalse).
Lemma bitwise_select_int_true :
forall vtrue vfalse,
bitwise_select_int (Val.of_optbool (Some true)) (Vint vtrue) (Vint vfalse)
= Vint vtrue.
Proof.
intros. cbn. f_equal.
change (Int.neg Int.one) with Int.mone.
rewrite Int.and_commut.
rewrite Int.and_mone.
rewrite Int.sub_idem.
rewrite Int.and_commut.
rewrite Int.and_zero.
apply Int.or_zero.
Qed.
Lemma bitwise_select_int_false :
forall vtrue vfalse,
bitwise_select_int (Val.of_optbool (Some false)) (Vint vtrue) (Vint vfalse)
= Vint vfalse.
Proof.
intros. cbn. f_equal.
rewrite Int.neg_zero.
rewrite Int.and_commut.
rewrite Int.and_zero.
rewrite Int.sub_zero_r.
change (Int.neg Int.one) with Int.mone.
rewrite Int.and_commut.
rewrite Int.and_mone.
rewrite Int.or_commut.
apply Int.or_zero.
Qed.
Definition bitwise_select_long b vtrue vfalse :=
let b' := Val.longofint b in
Val.orl (Val.andl (Val.negl b') vtrue)
(Val.andl (Val.subl b' (Vlong Int64.one)) vfalse).
Lemma bitwise_select_long_true :
forall vtrue vfalse,
bitwise_select_long (Val.of_optbool (Some true)) (Vlong vtrue) (Vlong vfalse)
= Vlong vtrue.
Proof.
intros. cbn. f_equal.
change (Int64.neg Int64.one) with Int64.mone.
rewrite Int64.and_commut.
rewrite Int64.and_mone.
rewrite Int64.sub_idem.
rewrite Int64.and_commut.
rewrite Int64.and_zero.
apply Int64.or_zero.
Qed.
Lemma bitwise_select_long_false :
forall vtrue vfalse,
bitwise_select_long (Val.of_optbool (Some false)) (Vlong vtrue) (Vlong vfalse)
= Vlong vfalse.
Proof.
intros. cbn. f_equal.
change (Int64.repr (Int.signed Int.zero)) with Int64.zero.
rewrite Int64.neg_zero.
rewrite Int64.and_commut.
rewrite Int64.and_zero.
rewrite Int64.sub_zero_r.
change (Int64.neg Int64.one) with Int64.mone.
rewrite Int64.and_commut.
rewrite Int64.and_mone.
rewrite Int64.or_commut.
apply Int64.or_zero.
Qed.
(*
Compute (Int.unsigned (Float32.to_bits (Float32.of_int (Int.repr 4200)))).
Compute (Int64.unsigned (Float.to_bits (Float.of_int (Int.repr 4233)))).
*)
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