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Require Import Coqlib.
Require Import Integers.
Require Import Values.
Require Import Floats.
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.
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