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-rw-r--r--powerpc/Asmgenproof1.v144
1 files changed, 112 insertions, 32 deletions
diff --git a/powerpc/Asmgenproof1.v b/powerpc/Asmgenproof1.v
index cd961c9..d9b6cf3 100644
--- a/powerpc/Asmgenproof1.v
+++ b/powerpc/Asmgenproof1.v
@@ -103,6 +103,42 @@ Proof.
rewrite Int.sub_idem. apply Int.add_zero.
Qed.
+Lemma add_zero_symbol_offset:
+ forall ge id ofs,
+ Val.add Vzero (symbol_offset ge id ofs) = symbol_offset ge id ofs.
+Proof.
+ unfold symbol_offset; intros. destruct (Genv.find_symbol ge id); auto.
+ simpl. rewrite Int.add_zero; auto.
+Qed.
+
+Lemma csymbol_high_low:
+ forall ge id ofs,
+ Val.add (high_half (symbol_offset ge id ofs)) (low_half (symbol_offset ge id ofs))
+ = symbol_offset ge id ofs.
+Proof.
+ intros. rewrite Val.add_commut. apply low_high_half.
+Qed.
+
+Lemma csymbol_high_low_2:
+ forall ge id ofs rel,
+ Val.add (const_high ge (csymbol_high id ofs rel))
+ (const_low ge (csymbol_low id ofs rel)) = symbol_offset ge id ofs.
+Proof.
+ intros. destruct rel; apply csymbol_high_low.
+Qed.
+
+(*
+Lemma csymbol_sda_eq:
+ forall ge id ofs,
+ symbol_is_small_data id ofs = true ->
+ Val.add Vzero (const_low ge (Csymbol_sda id ofs)) = symbol_offset ge id ofs.
+Proof.
+ intros. unfold const_low. rewrite small_data_area_addressing by auto.
+ unfold symbol_offset.
+ destruct (Genv.find_symbol ge id); simpl; auto. rewrite Int.add_zero; auto.
+Qed.
+*)
+
(** Useful properties of the GPR0 registers. *)
Lemma gpr_or_zero_not_zero:
@@ -827,17 +863,14 @@ Opaque Int.eq.
set (v' := symbol_offset ge i i0).
destruct (symbol_is_small_data i i0) eqn:SD.
(* small data *)
+Opaque Val.add.
econstructor; split. apply exec_straight_one; simpl; reflexivity.
- split. Simpl. rewrite (small_data_area_addressing _ _ _ SD). unfold v', symbol_offset.
- destruct (Genv.find_symbol ge i); auto. rewrite Int.add_zero; auto.
+ split. Simpl. rewrite small_data_area_addressing by auto. apply add_zero_symbol_offset.
intros; Simpl.
(* not small data *)
-Opaque Val.add.
econstructor; split. eapply exec_straight_two; simpl; reflexivity.
- split. Simpl. rewrite gpr_or_zero_zero.
- rewrite gpr_or_zero_not_zero; eauto with asmgen. Simpl.
- rewrite (Val.add_commut Vzero). rewrite high_half_zero.
- rewrite Val.add_commut. rewrite low_high_half. auto.
+ split. Simpl. rewrite gpr_or_zero_not_zero; eauto with asmgen. Simpl.
+ rewrite Val.add_assoc. rewrite csymbol_high_low_2. apply add_zero_symbol_offset.
intros; Simpl.
(* Oaddrstack *)
destruct (addimm_correct x GPR1 i k rs m) as [rs' [EX [RES OTH]]]; eauto with asmgen.
@@ -845,6 +878,26 @@ Opaque Val.add.
(* Oaddimm *)
destruct (addimm_correct x0 x i k rs m) as [rs' [A [B C]]]; eauto with asmgen.
exists rs'; auto with asmgen.
+ (* Oaddsymbol *)
+ destruct (symbol_is_small_data i i0) eqn:SD.
+ (* small data *)
+ econstructor; split. eapply exec_straight_two; simpl; reflexivity.
+ split. Simpl. rewrite (Val.add_commut (rs x)). f_equal.
+ rewrite small_data_area_addressing by auto. apply add_zero_symbol_offset.
+ intros; Simpl.
+ destruct (symbol_is_rel_data i i0).
+ (* relative data *)
+ econstructor; split. eapply exec_straight_three; simpl; reflexivity.
+ split. Simpl. rewrite gpr_or_zero_zero. rewrite gpr_or_zero_not_zero by (eauto with asmgen).
+ Simpl. rewrite Val.add_assoc. rewrite (Val.add_commut (rs x)). f_equal.
+ rewrite Val.add_assoc. rewrite csymbol_high_low. apply add_zero_symbol_offset.
+ intros; Simpl.
+ (* absolute data *)
+ econstructor; split. eapply exec_straight_two; simpl; reflexivity.
+ split. Simpl. rewrite ! gpr_or_zero_not_zero by (eauto with asmgen). Simpl.
+ rewrite Val.add_assoc. rewrite (Val.add_commut (rs x)). f_equal.
+ apply csymbol_high_low.
+ intros; Simpl.
(* Osubimm *)
case (Int.eq (high_s i) Int.zero).
TranslOpSimpl.
@@ -935,12 +988,12 @@ Lemma transl_memory_access_correct:
temp <> GPR0 ->
(forall cst (r1: ireg) (rs1: regset) k,
Val.add (gpr_or_zero rs1 r1) (const_low ge cst) = a ->
- (forall r, r <> PC -> r <> temp -> rs1 r = rs r) ->
+ (forall r, r <> PC -> r <> temp -> r <> GPR0 -> rs1 r = rs r) ->
exists rs',
exec_straight ge fn (mk1 cst r1 :: k) rs1 m k rs' m' /\ P rs') ->
(forall (r1 r2: ireg) (rs1: regset) k,
Val.add rs1#r1 rs1#r2 = a ->
- (forall r, r <> PC -> r <> temp -> rs1 r = rs r) ->
+ (forall r, r <> PC -> r <> temp -> r <> GPR0 -> rs1 r = rs r) ->
exists rs',
exec_straight ge fn (mk2 r1 r2 :: k) rs1 m k rs' m' /\ P rs') ->
exists rs',
@@ -969,34 +1022,61 @@ Transparent Val.add.
(* Aglobal *)
destruct (symbol_is_small_data i i0) eqn:SISD; inv TR.
(* Aglobal from small data *)
- apply MK1. simpl. rewrite small_data_area_addressing; auto.
- unfold symbol_address, symbol_offset.
- destruct (Genv.find_symbol ge i); auto. rewrite Int.add_zero. auto.
+ apply MK1. unfold const_low. rewrite small_data_area_addressing by auto.
+ apply add_zero_symbol_offset.
auto.
(* Aglobal general case *)
- set (rs1 := nextinstr (rs#temp <- (const_high ge (Csymbol_high i i0)))).
- exploit (MK1 (Csymbol_low i i0) temp rs1 k).
+ set (rel := symbol_is_rel_data i i0).
+ set (rs1 := nextinstr (rs#temp <- (const_high ge (csymbol_high i i0 rel)))).
+ exploit (MK1 (csymbol_low i i0 rel) temp rs1 k).
simpl. rewrite gpr_or_zero_not_zero; eauto with asmgen.
- unfold rs1. Simpl.
- unfold const_high, const_low.
- rewrite Val.add_commut. rewrite low_high_half. auto.
+ unfold rs1. Simpl. apply csymbol_high_low_2.
intros; unfold rs1; Simpl.
intros [rs' [EX' AG']].
exists rs'. split. apply exec_straight_step with rs1 m.
unfold exec_instr. rewrite gpr_or_zero_zero.
- rewrite Val.add_commut. unfold const_high.
- rewrite high_half_zero.
- reflexivity. reflexivity.
+ rewrite Val.add_commut. unfold const_high, csymbol_high.
+ destruct rel; rewrite high_half_zero; reflexivity.
+ reflexivity.
assumption. assumption.
(* Abased *)
+ destruct (symbol_is_small_data i i0) eqn:SISD.
+ (* Abased from small data *)
+ set (rs1 := nextinstr (rs#GPR0 <- (symbol_offset ge i i0))).
+ exploit (MK2 x GPR0 rs1 k).
+ unfold rs1; Simpl. apply Val.add_commut.
+ intros. unfold rs1; Simpl.
+ intros [rs' [EX' AG']].
+ exists rs'; split. apply exec_straight_step with rs1 m.
+ unfold exec_instr. rewrite gpr_or_zero_zero. f_equal. unfold rs1. f_equal. f_equal.
+ unfold const_low. rewrite small_data_area_addressing; auto.
+ apply add_zero_symbol_offset.
+ reflexivity.
+ assumption. assumption.
+ destruct (symbol_is_rel_data i i0).
+ (* Abased relative *)
+ set (rs1 := nextinstr (rs#GPR0 <- (const_high ge (Csymbol_rel_high i i0)))).
+ set (rs2 := nextinstr (rs1#temp <- (Val.add (rs x) (const_high ge (Csymbol_rel_high i i0))))).
+ exploit (MK1 (Csymbol_rel_low i i0) temp rs2 k).
+ simpl. rewrite gpr_or_zero_not_zero; eauto with asmgen.
+ unfold rs2. Simpl. rewrite Val.add_assoc. simpl. rewrite csymbol_high_low.
+ apply Val.add_commut.
+ intros. unfold rs2; Simpl. unfold rs1; Simpl.
+ intros [rs' [EX' AG']].
+ exists rs'. split. apply exec_straight_step with rs1 m.
+ unfold exec_instr. rewrite gpr_or_zero_zero.
+ rewrite (Val.add_commut Vzero). unfold const_high. rewrite high_half_zero. auto.
+ reflexivity.
+ apply exec_straight_step with rs2 m.
+ simpl. unfold rs2, rs1. Simpl.
+ reflexivity.
+ assumption. assumption.
+ (* Abased absolute *)
set (rs1 := nextinstr (rs#temp <- (Val.add (rs x) (const_high ge (Csymbol_high i i0))))).
exploit (MK1 (Csymbol_low i i0) temp rs1 k).
simpl. rewrite gpr_or_zero_not_zero; eauto with asmgen.
unfold rs1. Simpl.
- rewrite Val.add_assoc.
- unfold const_high, const_low.
- symmetry. rewrite Val.add_commut. f_equal. f_equal.
- rewrite Val.add_commut. rewrite low_high_half. auto.
+ rewrite Val.add_assoc. simpl. rewrite csymbol_high_low. apply Val.add_commut.
intros; unfold rs1; Simpl.
intros [rs' [EX' AG']].
exists rs'. split. apply exec_straight_step with rs1 m.
@@ -1028,7 +1108,7 @@ Lemma transl_load_correct:
exists rs',
exec_straight ge fn c rs m k rs' m
/\ rs'#(preg_of dst) = v
- /\ forall r, r <> PC -> r <> GPR12 -> r <> preg_of dst -> rs' r = rs r.
+ /\ forall r, r <> PC -> r <> GPR12 -> r <> GPR0 -> r <> preg_of dst -> rs' r = rs r.
Proof.
intros.
assert (BASE: forall mk1 mk2 k' chunk' v',
@@ -1043,7 +1123,7 @@ Proof.
exists rs',
exec_straight ge fn c rs m k' rs' m
/\ rs'#(preg_of dst) = v'
- /\ forall r, r <> PC -> r <> GPR12 -> r <> preg_of dst -> rs' r = rs r).
+ /\ forall r, r <> PC -> r <> GPR12 -> r <> GPR0 -> r <> preg_of dst -> rs' r = rs r).
{
intros. eapply transl_memory_access_correct; eauto. congruence.
intros. econstructor; split. apply exec_straight_one.
@@ -1095,7 +1175,7 @@ Lemma transl_store_correct:
Mem.storev chunk m a (rs (preg_of src)) = Some m' ->
exists rs',
exec_straight ge fn c rs m k rs' m'
- /\ forall r, r <> PC -> preg_notin r (destroyed_by_store chunk addr) -> rs' r = rs r.
+ /\ forall r, r <> PC -> r <> GPR0 -> preg_notin r (destroyed_by_store chunk addr) -> rs' r = rs r.
Proof.
Local Transparent destroyed_by_store.
intros.
@@ -1119,15 +1199,15 @@ Local Transparent destroyed_by_store.
store2 chunk' (preg_of src) r1 r2 rs1 m) ->
exists rs',
exec_straight ge fn c rs m k rs' m'
- /\ forall r, r <> PC -> r <> GPR11 /\ r <> GPR12 -> rs' r = rs r).
+ /\ forall r, r <> PC -> r <> GPR0 -> r <> GPR11 /\ r <> GPR12 -> rs' r = rs r).
{
intros. eapply transl_memory_access_correct; eauto.
intros. econstructor; split. apply exec_straight_one.
rewrite H4. unfold store1. rewrite H6. rewrite H7; auto with asmgen. rewrite H3. eauto. auto.
- intros; Simpl. apply H7; auto. destruct TEMP0; destruct H9; congruence.
+ intros; Simpl. apply H7; auto. destruct TEMP0; destruct H10; congruence.
intros. econstructor; split. apply exec_straight_one.
rewrite H5. unfold store2. rewrite H6. rewrite H7; auto with asmgen. rewrite H3. eauto. auto.
- intros; Simpl. apply H7; auto. destruct TEMP0; destruct H9; congruence.
+ intros; Simpl. apply H7; auto. destruct TEMP0; destruct H10; congruence.
}
destruct chunk; monadInv H.
- (* Mint8signed *)
@@ -1150,10 +1230,10 @@ Local Transparent destroyed_by_store.
intros. econstructor; split. apply exec_straight_one.
simpl. unfold store1. rewrite H. rewrite H2; auto with asmgen. rewrite H1. eauto. auto.
Local Transparent destroyed_by_store.
- simpl; intros. destruct H4 as [A [B C]]. Simpl. apply H2; auto with asmgen. destruct TEMP0; congruence.
+ simpl; intros. destruct H5 as [A [B C]]. Simpl. apply H2; auto with asmgen. destruct TEMP0; congruence.
intros. econstructor; split. apply exec_straight_one.
simpl. unfold store2. rewrite H. rewrite H2; auto with asmgen. rewrite H1. eauto. auto.
- simpl; intros. destruct H4 as [A [B C]]. Simpl. apply H2; auto with asmgen. destruct TEMP0; congruence.
+ simpl; intros. destruct H5 as [A [B C]]. Simpl. apply H2; auto with asmgen. destruct TEMP0; congruence.
- (* Mfloat64 *)
apply Mem.storev_float64al32 in H1. eapply BASE; eauto; erewrite freg_of_eq by eauto; auto.
- (* Mfloat64al32 *)