From fb9d0d19cd76383b42ccbf6cc7c9698998c729f4 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 3 Aug 2019 09:11:42 +0200 Subject: Simplify invocation of Emacs + Proof General PG now uses the _Coqproject file and finds relevant paths there. --- pg | 20 +++----------------- 1 file changed, 3 insertions(+), 17 deletions(-) diff --git a/pg b/pg index 28926baa..398d618f 100755 --- a/pg +++ b/pg @@ -1,10 +1,7 @@ #!/bin/sh -# Start Proof General with the right -I options +# Start Proof General with the right Coq version # Use the Makefile to rebuild dependencies if needed -# Recompile the modified file after coqide editing - -PWD=`pwd` -INCLUDES=`make print-includes` +# Recompile the modified file after editing make -q ${1}o || { make -n ${1}o | grep -v "\\b${1}\\b" | \ @@ -15,16 +12,5 @@ make -q ${1}o || { COQPROGNAME="${COQBIN}coqtop" -COQPROGARGS="" -for arg in $INCLUDES; do - case "$arg" in - -I|-R|-as|compcert*) - COQPROGARGS="$COQPROGARGS \"$arg\"";; - *) - COQPROGARGS="$COQPROGARGS \"$PWD/$arg\"";; - esac -done - -emacs --eval "(setq coq-prog-name \"$COQPROGNAME\")" \ - --eval "(setq coq-prog-args '($COQPROGARGS))" $1 \ +emacs --eval "(setq coq-prog-name \"$COQPROGNAME\")" $1 \ && make ${1}o -- cgit From 136d25dcbf2829e63c20b96acf86d34c94474fde Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Fri, 2 Aug 2019 10:41:29 +0200 Subject: Coq 8.10 compatibility: make explicit the "core" hint database "Hint Resolve foo." becomes "Hint Resolve foo : core", or "Local Hint Resolve foo : core". --- backend/Conventions.v | 2 -- cfrontend/Cexec.v | 11 ++++++----- cfrontend/Cop.v | 4 ++-- cfrontend/Cstrategy.v | 10 +++++----- cfrontend/SimplExprspec.v | 2 +- common/Separation.v | 2 +- common/Values.v | 10 +++++----- lib/Floats.v | 4 ++-- 8 files changed, 22 insertions(+), 23 deletions(-) diff --git a/backend/Conventions.v b/backend/Conventions.v index 989bfa05..6025c6b4 100644 --- a/backend/Conventions.v +++ b/backend/Conventions.v @@ -128,8 +128,6 @@ Definition callee_save_loc (l: loc) := | S sl ofs ty => sl <> Outgoing end. -Hint Unfold callee_save_loc. - Definition agree_callee_save (ls1 ls2: Locmap.t) : Prop := forall l, callee_save_loc l -> ls1 l = ls2 l. diff --git a/cfrontend/Cexec.v b/cfrontend/Cexec.v index e6bf2129..2942080b 100644 --- a/cfrontend/Cexec.v +++ b/cfrontend/Cexec.v @@ -1124,8 +1124,8 @@ Proof. induction 1; intros; constructor; eauto. Qed. -Hint Constructors context contextlist. -Hint Resolve context_compose contextlist_compose. +Local Hint Constructors context contextlist : core. +Local Hint Resolve context_compose contextlist_compose : core. Definition reduction_ok (k: kind) (a: expr) (m: mem) (rd: reduction) : Prop := match k, rd with @@ -1691,8 +1691,9 @@ Proof. change (In (f (C0, rd)) (map f res2)). apply in_map; auto. Qed. -Hint Resolve reducts_incl_val reducts_incl_loc reducts_incl_listval - reducts_incl_incontext reducts_incl_incontext2_left reducts_incl_incontext2_right. +Local Hint Resolve reducts_incl_val reducts_incl_loc reducts_incl_listval + reducts_incl_incontext reducts_incl_incontext2_left + reducts_incl_incontext2_right : core. Lemma step_expr_context: forall from to C, context from to C -> @@ -2077,7 +2078,7 @@ Ltac myinv := | _ => idtac end. -Hint Extern 3 => exact I. +Local Hint Extern 3 => exact I : core. Theorem do_step_sound: forall w S rule t S', diff --git a/cfrontend/Cop.v b/cfrontend/Cop.v index 782fb32a..aa73abb0 100644 --- a/cfrontend/Cop.v +++ b/cfrontend/Cop.v @@ -1131,7 +1131,7 @@ Qed. Remark val_inject_vptrofs: forall n, Val.inject f (Vptrofs n) (Vptrofs n). Proof. intros. unfold Vptrofs. destruct Archi.ptr64; auto. Qed. -Hint Resolve val_inject_vtrue val_inject_vfalse val_inject_of_bool val_inject_vptrofs. +Local Hint Resolve val_inject_vtrue val_inject_vfalse val_inject_of_bool val_inject_vptrofs : core. Ltac TrivialInject := match goal with @@ -1517,7 +1517,7 @@ Inductive val_casted: val -> type -> Prop := | val_casted_void: forall v, val_casted v Tvoid. -Hint Constructors val_casted. +Local Hint Constructors val_casted : core. Remark cast_int_int_idem: forall sz sg i, cast_int_int sz sg (cast_int_int sz sg i) = cast_int_int sz sg i. diff --git a/cfrontend/Cstrategy.v b/cfrontend/Cstrategy.v index 28c8eeb8..c235031f 100644 --- a/cfrontend/Cstrategy.v +++ b/cfrontend/Cstrategy.v @@ -222,7 +222,7 @@ Proof. induction 1; constructor; auto. Qed. -Hint Resolve leftcontext_context. +Local Hint Resolve leftcontext_context : core. (** Strategy for reducing expressions. We reduce the leftmost innermost non-simple subexpression, evaluating its arguments (which are necessarily @@ -398,8 +398,8 @@ Proof. induction 1; intros; constructor; eauto. Qed. -Hint Constructors context contextlist. -Hint Resolve context_compose contextlist_compose. +Local Hint Constructors context contextlist : core. +Local Hint Resolve context_compose contextlist_compose : core. (** * Safe executions. *) @@ -975,7 +975,7 @@ Proof. apply extensionality; intros. f_equal. f_equal. apply exprlist_app_assoc. Qed. -Hint Resolve contextlist'_head contextlist'_tail. +Local Hint Resolve contextlist'_head contextlist'_tail : core. Lemma eval_simple_list_steps: forall rl vl, eval_simple_list' rl vl -> @@ -1049,7 +1049,7 @@ Scheme expr_ind2 := Induction for expr Sort Prop with exprlist_ind2 := Induction for exprlist Sort Prop. Combined Scheme expr_expr_list_ind from expr_ind2, exprlist_ind2. -Hint Constructors leftcontext leftcontextlist. +Local Hint Constructors leftcontext leftcontextlist : core. Lemma decompose_expr: (forall a from C, diff --git a/cfrontend/SimplExprspec.v b/cfrontend/SimplExprspec.v index 37e2cd96..e7d57a1c 100644 --- a/cfrontend/SimplExprspec.v +++ b/cfrontend/SimplExprspec.v @@ -687,7 +687,7 @@ Hint Resolve gensym_within within_widen contained_widen in_eq in_cons Ple_trans Ple_refl: gensym. -Hint Resolve dest_for_val_below dest_for_effect_below. +Local Hint Resolve dest_for_val_below dest_for_effect_below : core. (** ** Correctness of the translation functions *) diff --git a/common/Separation.v b/common/Separation.v index 1493b535..27065d1f 100644 --- a/common/Separation.v +++ b/common/Separation.v @@ -113,7 +113,7 @@ Proof. intros P Q [[A B] [C D]]. split; auto. Qed. -Hint Resolve massert_imp_refl massert_eqv_refl. +Hint Resolve massert_imp_refl massert_eqv_refl : core. (** * Separating conjunction *) diff --git a/common/Values.v b/common/Values.v index a51a390f..2eb778a5 100644 --- a/common/Values.v +++ b/common/Values.v @@ -1949,7 +1949,7 @@ Inductive lessdef_list: list val -> list val -> Prop := lessdef v1 v2 -> lessdef_list vl1 vl2 -> lessdef_list (v1 :: vl1) (v2 :: vl2). -Hint Resolve lessdef_refl lessdef_undef lessdef_list_nil lessdef_list_cons. +Hint Resolve lessdef_refl lessdef_undef lessdef_list_nil lessdef_list_cons : core. Lemma lessdef_list_inv: forall vl1 vl2, lessdef_list vl1 vl2 -> vl1 = vl2 \/ In Vundef vl1. @@ -2174,7 +2174,7 @@ Inductive inject (mi: meminj): val -> val -> Prop := | val_inject_undef: forall v, inject mi Vundef v. -Hint Constructors inject. +Hint Constructors inject : core. Inductive inject_list (mi: meminj): list val -> list val-> Prop:= | inject_list_nil : @@ -2183,7 +2183,7 @@ Inductive inject_list (mi: meminj): list val -> list val-> Prop:= inject mi v v' -> inject_list mi vl vl'-> inject_list mi (v :: vl) (v' :: vl'). -Hint Resolve inject_list_nil inject_list_cons. +Hint Resolve inject_list_nil inject_list_cons : core. Lemma inject_ptrofs: forall mi i, inject mi (Vptrofs i) (Vptrofs i). @@ -2191,7 +2191,7 @@ Proof. unfold Vptrofs; intros. destruct Archi.ptr64; auto. Qed. -Hint Resolve inject_ptrofs. +Hint Resolve inject_ptrofs : core. Section VAL_INJ_OPS. @@ -2494,7 +2494,7 @@ Proof. constructor. eapply val_inject_incr; eauto. auto. Qed. -Hint Resolve inject_incr_refl val_inject_incr val_inject_list_incr. +Hint Resolve inject_incr_refl val_inject_incr val_inject_list_incr : core. Lemma val_inject_lessdef: forall v1 v2, Val.lessdef v1 v2 <-> Val.inject (fun b => Some(b, 0)) v1 v2. diff --git a/lib/Floats.v b/lib/Floats.v index 7677e3c8..13350dd0 100644 --- a/lib/Floats.v +++ b/lib/Floats.v @@ -139,8 +139,8 @@ Definition default_nan_32 := quiet_nan_32 Archi.default_nan_32. Local Notation __ := (eq_refl Datatypes.Lt). -Local Hint Extern 1 (Prec_gt_0 _) => exact (eq_refl Datatypes.Lt). -Local Hint Extern 1 (_ < _) => exact (eq_refl Datatypes.Lt). +Local Hint Extern 1 (Prec_gt_0 _) => exact (eq_refl Datatypes.Lt) : core. +Local Hint Extern 1 (_ < _) => exact (eq_refl Datatypes.Lt) : core. (** * Double-precision FP numbers *) -- cgit From efb5f52493345a1e17cc10b56023dfe00beb6074 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Fri, 2 Aug 2019 10:48:27 +0200 Subject: Coq 8.10 compatibility: tweak Argument command --- lib/Maps.v | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/Maps.v b/lib/Maps.v index cfb866ba..9e44a7fe 100644 --- a/lib/Maps.v +++ b/lib/Maps.v @@ -190,7 +190,7 @@ Module PTree <: TREE. | Leaf : tree A | Node : tree A -> option A -> tree A -> tree A. - Arguments Leaf [A]. + Arguments Leaf {A}. Arguments Node [A]. Scheme tree_ind := Induction for tree Sort Prop. -- cgit From f19b7fd7a0b87d7fcce021a264f9b95c43a24a09 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Mon, 5 Aug 2019 16:01:46 +0200 Subject: Coq 8.10 compatibility: (temporarily) silence new warning The "undeclared-scope" warning fires when we use a "notation" scope before having declared it. This is a good thing, except that the "Declare Scope" vernacular that declares a scope was introduced in Coq 8.10 and is not available in earlier versions. Hence there is no way to avoid triggering the warning yet remain compatible with pre-8.10 Coq versions. This commit silences the warning. It will have to revisited when Coq 8.10 is the oldest version of Coq we support in CompCert. --- Makefile | 1 + 1 file changed, 1 insertion(+) diff --git a/Makefile b/Makefile index ae19225a..80eca80d 100644 --- a/Makefile +++ b/Makefile @@ -30,6 +30,7 @@ RECDIRS=lib common $(ARCHDIRS) backend cfrontend driver flocq exportclight \ COQINCLUDES=$(foreach d, $(RECDIRS), -R $(d) compcert.$(d)) +COQCOPTS ?= -w -undeclared-scope COQC="$(COQBIN)coqc" -q $(COQINCLUDES) $(COQCOPTS) COQDEP="$(COQBIN)coqdep" $(COQINCLUDES) COQDOC="$(COQBIN)coqdoc" -- cgit From 5148617b7961c1d67acb70bfc783bc5616537486 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Mon, 5 Aug 2019 16:05:53 +0200 Subject: Add support for Coq 8.10 --- configure | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/configure b/configure index d586436a..9a2db366 100755 --- a/configure +++ b/configure @@ -503,14 +503,14 @@ missingtools=false echo "Testing Coq... " | tr -d '\n' coq_ver=$(${COQBIN}coqc -v 2>/dev/null | sed -n -e 's/The Coq Proof Assistant, version \([^ ]*\).*$/\1/p') case "$coq_ver" in - 8.7.0|8.7.1|8.7.2|8.8.0|8.8.1|8.8.2|8.9.0|8.9.1) + 8.7.0|8.7.1|8.7.2|8.8.0|8.8.1|8.8.2|8.9.0|8.9.1|8.10) echo "version $coq_ver -- good!";; ?*) echo "version $coq_ver -- UNSUPPORTED" if $ignore_coq_version; then echo "Warning: this version of Coq is unsupported, proceed at your own risks." else - echo "Error: CompCert requires one of the following Coq versions: 8.9.1, 8.9.0, 8.8.2, 8.8.1, 8.8.0, 8.7.2, 8.7.1, 8.7.0" + echo "Error: CompCert requires one of the following Coq versions: 8.10, 8.9.1, 8.9.0, 8.8.2, 8.8.1, 8.8.0, 8.7.2, 8.7.1, 8.7.0" missingtools=true fi;; "") -- cgit From 4e3d57e84a0ebf96723fc7a6deeb9fd27f56770a Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Tue, 6 Aug 2019 13:34:23 +0200 Subject: x86: wrong expansion of __builtin_fmadd et al There was a misunderstanding on the asm syntax for 3-operand instructions such as vfmadd132: when the Intel manual reads vfmadd132 res, arg2, arg3 the corresponding GNU asm syntax is vfmadd132 arg3, arg2, res but not vfmadd132 arg2, arg3, res Closes: #188 --- x86/TargetPrinter.ml | 32 +++++++++++++++++++------------- 1 file changed, 19 insertions(+), 13 deletions(-) diff --git a/x86/TargetPrinter.ml b/x86/TargetPrinter.ml index cd54e08b..6159437e 100644 --- a/x86/TargetPrinter.ml +++ b/x86/TargetPrinter.ml @@ -399,7 +399,13 @@ module Target(System: SYSTEM):TARGET = (* Printing of instructions *) -(* Reminder on AT&T syntax: op source, dest *) +(* Reminder on X86 assembly syntaxes: + AT&T syntax Intel syntax + (used by GNU as) (used in reference manuals) + dst <- op(src) op src, dst op dst, src + dst <- op(dst, src2) op src2, dst op dst, src2 + dst <- op(dst, src2, src3) op src3, src2, dst op dst, src2, src3 +*) let print_instruction oc = function (* Moves *) @@ -752,29 +758,29 @@ module Target(System: SYSTEM):TARGET = | Pcfi_adjust sz -> cfi_adjust oc (camlint_of_coqint sz) | Pfmadd132 (res,a1,a2) -> - fprintf oc " vfmadd132sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmadd132sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfmadd213 (res,a1,a2) -> - fprintf oc " vfmadd213sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmadd213sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfmadd231 (res,a1,a2) -> - fprintf oc " vfmadd231sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmadd231sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfmsub132 (res,a1,a2) -> - fprintf oc " vfmsub132sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmsub132sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfmsub213 (res,a1,a2) -> - fprintf oc " vfmsub213sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmsub213sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfmsub231 (res,a1,a2) -> - fprintf oc " vfmsub231sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfmsub231sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmadd132 (res,a1,a2) -> - fprintf oc " vfnmadd132sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmadd132sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmadd213 (res,a1,a2) -> - fprintf oc " vfnmadd213sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmadd213sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmadd231 (res,a1,a2) -> - fprintf oc " vfnmadd231sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmadd231sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmsub132 (res,a1,a2) -> - fprintf oc " vfnmsub132sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmsub132sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmsub213 (res,a1,a2) -> - fprintf oc " vfnmsub213sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmsub213sd %a, %a, %a\n" freg a2 freg a1 freg res | Pfnmsub231 (res,a1,a2) -> - fprintf oc " vfnmsub231sd %a, %a, %a\n" freg a1 freg a2 freg res + fprintf oc " vfnmsub231sd %a, %a, %a\n" freg a2 freg a1 freg res | Pmaxsd (res,a1) -> fprintf oc " maxsd %a, %a\n" freg a1 freg res | Pminsd (res,a1) -> -- cgit From 1f73810ca4f9754f3da8bd02f85a6e294129813a Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Mon, 6 May 2019 15:30:48 +0200 Subject: Zbits.v: add bit extraction and bit insertion --- lib/Zbits.v | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) diff --git a/lib/Zbits.v b/lib/Zbits.v index dca2a5a2..459e891b 100644 --- a/lib/Zbits.v +++ b/lib/Zbits.v @@ -1026,3 +1026,60 @@ Proof. exploit (Zsize_interval_1 y). omega. omega. Qed. + +(** ** Bit insertion, bit extraction *) + +(** Extract and optionally sign-extend bits [from...from+len-1] of [x] *) +Definition Zextract_u (x: Z) (from: Z) (len: Z) : Z := + Zzero_ext len (Z.shiftr x from). + +Definition Zextract_s (x: Z) (from: Z) (len: Z) : Z := + Zsign_ext len (Z.shiftr x from). + +Lemma Zextract_u_spec: + forall x from len i, + 0 <= from -> 0 <= len -> 0 <= i -> + Z.testbit (Zextract_u x from len) i = + if zlt i len then Z.testbit x (from + i) else false. +Proof. + unfold Zextract_u; intros. rewrite Zzero_ext_spec, Z.shiftr_spec by auto. + rewrite Z.add_comm. auto. +Qed. + +Lemma Zextract_s_spec: + forall x from len i, + 0 <= from -> 0 < len -> 0 <= i -> + Z.testbit (Zextract_s x from len) i = + Z.testbit x (from + (if zlt i len then i else len - 1)). +Proof. + unfold Zextract_s; intros. rewrite Zsign_ext_spec by auto. rewrite Z.shiftr_spec. + rewrite Z.add_comm. auto. + destruct (zlt i len); omega. +Qed. + +(** Insert bits [0...len-1] of [y] into bits [to...to+len-1] of [x] *) + +Definition Zinsert (x y: Z) (to: Z) (len: Z) : Z := + let mask := Z.shiftl (two_p len - 1) to in + Z.lor (Z.land (Z.shiftl y to) mask) (Z.ldiff x mask). + +Lemma Zinsert_spec: + forall x y to len i, + 0 <= to -> 0 <= len -> 0 <= i -> + Z.testbit (Zinsert x y to len) i = + if zle to i && zlt i (to + len) + then Z.testbit y (i - to) + else Z.testbit x i. +Proof. + unfold Zinsert; intros. set (mask := two_p len - 1). + assert (M: forall j, 0 <= j -> Z.testbit mask j = if zlt j len then true else false). + { intros; apply Ztestbit_two_p_m1; auto. } + rewrite Z.lor_spec, Z.land_spec, Z.ldiff_spec by auto. + destruct (zle to i). +- rewrite ! Z.shiftl_spec by auto. rewrite ! M by omega. + unfold proj_sumbool; destruct (zlt (i - to) len); simpl; + rewrite andb_true_r, andb_false_r. ++ rewrite zlt_true by omega. apply orb_false_r. ++ rewrite zlt_false by omega; auto. +- rewrite ! Z.shiftl_spec_low by omega. simpl. apply andb_true_r. +Qed. -- cgit From 62c92241a69cd4597650d8408744ff922ca34245 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Wed, 8 May 2019 16:05:56 +0200 Subject: Define integer sign extension for zero bits Just ensure sign_ext 0 x = zero. This simplifies some statements and proofs. --- lib/Integers.v | 41 +++++++++++++++++++++++++++-------------- lib/Zbits.v | 58 ++++++++++++++++++++++++++++++---------------------------- 2 files changed, 57 insertions(+), 42 deletions(-) diff --git a/lib/Integers.v b/lib/Integers.v index f4213332..1b0375b1 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -1139,6 +1139,12 @@ Proof. intros. apply Ztestbit_above with wordsize; auto. apply unsigned_range. Qed. +Lemma bits_below: + forall x i, i < 0 -> testbit x i = false. +Proof. + intros. apply Z.testbit_neg_r; auto. +Qed. + Lemma bits_zero: forall i, testbit zero i = false. Proof. @@ -2511,12 +2517,11 @@ Proof. Qed. Lemma bits_sign_ext: - forall n x i, 0 <= i < zwordsize -> 0 < n -> + forall n x i, 0 <= i < zwordsize -> testbit (sign_ext n x) i = testbit x (if zlt i n then i else n - 1). Proof. intros. unfold sign_ext. - rewrite testbit_repr; auto. rewrite Zsign_ext_spec. destruct (zlt i n); auto. - omega. auto. + rewrite testbit_repr; auto. apply Zsign_ext_spec. omega. Qed. Hint Rewrite bits_zero_ext bits_sign_ext: ints. @@ -2528,12 +2533,24 @@ Proof. rewrite bits_zero_ext. apply zlt_true. omega. omega. Qed. +Theorem zero_ext_below: + forall n x, n <= 0 -> zero_ext n x = zero. +Proof. + intros. bit_solve. destruct (zlt i n); auto. apply bits_below; omega. omega. +Qed. + Theorem sign_ext_above: forall n x, n >= zwordsize -> sign_ext n x = x. Proof. intros. apply same_bits_eq; intros. unfold sign_ext; rewrite testbit_repr; auto. - rewrite Zsign_ext_spec. rewrite zlt_true. auto. omega. omega. omega. + rewrite Zsign_ext_spec. rewrite zlt_true. auto. omega. omega. +Qed. + +Theorem sign_ext_below: + forall n x, n <= 0 -> sign_ext n x = zero. +Proof. + intros. bit_solve. apply bits_below. destruct (zlt i n); omega. Qed. Theorem zero_ext_and: @@ -2570,7 +2587,7 @@ Proof. Qed. Theorem sign_ext_widen: - forall x n n', 0 < n <= n' -> + forall x n n', 0 < n <= n' -> sign_ext n' (sign_ext n x) = sign_ext n x. Proof. intros. destruct (zlt n' zwordsize). @@ -2578,9 +2595,8 @@ Proof. auto. rewrite (zlt_false _ i n). destruct (zlt (n' - 1) n); f_equal; omega. - omega. omega. + omega. destruct (zlt i n'); omega. - omega. omega. apply sign_ext_above; auto. Qed. @@ -2594,7 +2610,6 @@ Proof. auto. rewrite !zlt_false. auto. omega. omega. omega. destruct (zlt i n'); omega. - omega. apply sign_ext_above; auto. Qed. @@ -2614,9 +2629,7 @@ Theorem sign_ext_narrow: Proof. intros. destruct (zlt n zwordsize). bit_solve. destruct (zlt i n); f_equal; apply zlt_true; omega. - omega. destruct (zlt i n); omega. - omega. omega. rewrite (sign_ext_above n'). auto. omega. Qed. @@ -2628,7 +2641,7 @@ Proof. bit_solve. destruct (zlt i n); auto. rewrite zlt_true; auto. omega. - omega. omega. omega. + omega. omega. rewrite sign_ext_above; auto. Qed. @@ -2643,7 +2656,7 @@ Theorem sign_ext_idem: Proof. intros. apply sign_ext_widen. omega. Qed. - + Theorem sign_ext_zero_ext: forall n x, 0 < n -> sign_ext n (zero_ext n x) = sign_ext n x. Proof. @@ -2706,7 +2719,7 @@ Proof. rewrite zlt_true. rewrite bits_shl. rewrite zlt_false. f_equal. omega. omega. omega. omega. rewrite zlt_false. rewrite bits_shl. rewrite zlt_false. f_equal. omega. - omega. omega. omega. omega. omega. + omega. omega. omega. omega. Qed. (** [zero_ext n x] is the unique integer congruent to [x] modulo [2^n] @@ -2766,7 +2779,7 @@ Proof. apply eqmod_same_bits; intros. rewrite H0 in H1. rewrite H0. fold (testbit (sign_ext n x) i). rewrite bits_sign_ext. - rewrite zlt_true. auto. omega. omega. omega. + rewrite zlt_true. auto. omega. omega. Qed. Lemma eqmod_sign_ext: diff --git a/lib/Zbits.v b/lib/Zbits.v index 459e891b..fb40ccb5 100644 --- a/lib/Zbits.v +++ b/lib/Zbits.v @@ -557,7 +557,7 @@ Definition Zzero_ext (n: Z) (x: Z) : Z := Definition Zsign_ext (n: Z) (x: Z) : Z := Z.iter (Z.pred n) (fun rec x => Zshiftin (Z.odd x) (rec (Z.div2 x))) - (fun x => if Z.odd x then -1 else 0) + (fun x => if Z.odd x && zlt 0 n then -1 else 0) x. Lemma Ziter_base: @@ -606,32 +606,34 @@ Proof. Qed. Lemma Zsign_ext_spec: - forall n x i, 0 <= i -> 0 < n -> + forall n x i, 0 <= i -> Z.testbit (Zsign_ext n x) i = Z.testbit x (if zlt i n then i else n - 1). Proof. - intros n0 x i I0 N0. - revert x i I0. pattern n0. apply Zlt_lower_bound_ind with (z := 1). - - unfold Zsign_ext. intros. - destruct (zeq x 1). - + subst x; simpl. - replace (if zlt i 1 then i else 0) with 0. - rewrite Ztestbit_base. - destruct (Z.odd x0). - apply Ztestbit_m1; auto. - apply Ztestbit_0. - destruct (zlt i 1); omega. - + set (x1 := Z.pred x). replace x1 with (Z.succ (Z.pred x1)). - rewrite Ziter_succ. rewrite Ztestbit_shiftin. - destruct (zeq i 0). - * subst i. rewrite zlt_true. rewrite Ztestbit_base; auto. omega. - * rewrite H. unfold x1. destruct (zlt (Z.pred i) (Z.pred x)). - rewrite zlt_true. rewrite (Ztestbit_eq i x0); auto. rewrite zeq_false; auto. omega. - rewrite zlt_false. rewrite (Ztestbit_eq (x - 1) x0). rewrite zeq_false; auto. - omega. omega. omega. unfold x1; omega. omega. - * omega. - * unfold x1; omega. - * omega. - - omega. + intros n0 x i I0. unfold Zsign_ext. + unfold proj_sumbool; destruct (zlt 0 n0) as [N0|N0]; simpl. +- revert x i I0. pattern n0. apply Zlt_lower_bound_ind with (z := 1); [ | omega ]. + unfold Zsign_ext. intros. + destruct (zeq x 1). + + subst x; simpl. + replace (if zlt i 1 then i else 0) with 0. + rewrite Ztestbit_base. + destruct (Z.odd x0); [ apply Ztestbit_m1; auto | apply Ztestbit_0 ]. + destruct (zlt i 1); omega. + + set (x1 := Z.pred x). replace x1 with (Z.succ (Z.pred x1)) by omega. + rewrite Ziter_succ by (unfold x1; omega). rewrite Ztestbit_shiftin by auto. + destruct (zeq i 0). + * subst i. rewrite zlt_true. rewrite Ztestbit_base; auto. omega. + * rewrite H by (unfold x1; omega). + unfold x1; destruct (zlt (Z.pred i) (Z.pred x)). + ** rewrite zlt_true by omega. + rewrite (Ztestbit_eq i x0) by omega. + rewrite zeq_false by omega. auto. + ** rewrite zlt_false by omega. + rewrite (Ztestbit_eq (x - 1) x0) by omega. + rewrite zeq_false by omega. auto. +- rewrite Ziter_base by omega. rewrite andb_false_r. + rewrite Z.testbit_0_l, Z.testbit_neg_r. auto. + destruct (zlt i n0); omega. Qed. (** [Zzero_ext n x] is [x modulo 2^n] *) @@ -661,7 +663,7 @@ Qed. (** Relation between [Zsign_ext n x] and (Zzero_ext n x] *) Lemma Zsign_ext_zero_ext: - forall n, 0 < n -> forall x, + forall n, 0 <= n -> forall x, Zsign_ext n x = Zzero_ext n x - (if Z.testbit x (n - 1) then two_p n else 0). Proof. intros. apply equal_same_bits; intros. @@ -698,12 +700,12 @@ Proof. assert (C: two_p n = 2 * two_p (n - 1)). { rewrite <- two_p_S by omega. f_equal; omega. } rewrite Zzero_ext_spec, zlt_true in B by omega. - rewrite Zsign_ext_zero_ext by auto. rewrite B. + rewrite Zsign_ext_zero_ext by omega. rewrite B. destruct (zlt (Zzero_ext n x) (two_p (n - 1))); omega. Qed. Lemma eqmod_Zsign_ext: - forall n x, 0 < n -> + forall n x, 0 <= n -> eqmod (two_p n) (Zsign_ext n x) x. Proof. intros. rewrite Zsign_ext_zero_ext by auto. -- cgit From 862b0a23ad6c2caf2b81e502584d369fe9bc0d14 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Wed, 8 May 2019 18:37:54 +0200 Subject: Properties of combinations of shifts and zero-/sign-extension --- lib/Integers.v | 249 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 249 insertions(+) diff --git a/lib/Integers.v b/lib/Integers.v index 1b0375b1..369584c3 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -2794,6 +2794,132 @@ Proof. apply eqmod_sign_ext'; auto. Qed. +(** Combinations of shifts and zero/sign extensions *) + +Lemma shl_zero_ext: + forall n m x, 0 <= n -> + shl (zero_ext n x) m = zero_ext (n + unsigned m) (shl x m). +Proof. + intros. apply same_bits_eq; intros. + rewrite bits_zero_ext, ! bits_shl by omega. + destruct (zlt i (unsigned m)). +- rewrite zlt_true by omega; auto. +- rewrite bits_zero_ext by omega. + destruct (zlt (i - unsigned m) n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. +Qed. + +Lemma shl_sign_ext: + forall n m x, 0 < n -> + shl (sign_ext n x) m = sign_ext (n + unsigned m) (shl x m). +Proof. + intros. generalize (unsigned_range m); intros. + apply same_bits_eq; intros. + rewrite bits_sign_ext, ! bits_shl by omega. + destruct (zlt i (n + unsigned m)). +- rewrite bits_shl by auto. destruct (zlt i (unsigned m)); auto. + rewrite bits_sign_ext by omega. f_equal. apply zlt_true. omega. +- rewrite zlt_false by omega. rewrite bits_shl by omega. rewrite zlt_false by omega. + rewrite bits_sign_ext by omega. f_equal. rewrite zlt_false by omega. omega. +Qed. + +Lemma shru_zero_ext: + forall n m x, 0 <= n -> + shru (zero_ext (n + unsigned m) x) m = zero_ext n (shru x m). +Proof. + intros. bit_solve. +- destruct (zlt (i + unsigned m) zwordsize). +* destruct (zlt i n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. +* destruct (zlt i n); auto. +- generalize (unsigned_range m); omega. +- omega. +Qed. + +Lemma shru_zero_ext_0: + forall n m x, n <= unsigned m -> + shru (zero_ext n x) m = zero. +Proof. + intros. bit_solve. +- destruct (zlt (i + unsigned m) zwordsize); auto. + apply zlt_false. omega. +- generalize (unsigned_range m); omega. +Qed. + +Lemma shr_sign_ext: + forall n m x, 0 < n -> n + unsigned m < zwordsize -> + shr (sign_ext (n + unsigned m) x) m = sign_ext n (shr x m). +Proof. + intros. generalize (unsigned_range m); intros. + apply same_bits_eq; intros. + rewrite bits_sign_ext, bits_shr by auto. + rewrite bits_sign_ext, bits_shr. +- f_equal. + destruct (zlt i n), (zlt (i + unsigned m) zwordsize). ++ apply zlt_true; omega. ++ apply zlt_true; omega. ++ rewrite zlt_false by omega. rewrite zlt_true by omega. omega. ++ rewrite zlt_false by omega. rewrite zlt_true by omega. omega. +- destruct (zlt i n); omega. +- destruct (zlt (i + unsigned m) zwordsize); omega. +Qed. + +Lemma zero_ext_shru_min: + forall s x n, ltu n iwordsize = true -> + zero_ext s (shru x n) = zero_ext (Z.min s (zwordsize - unsigned n)) (shru x n). +Proof. + intros. apply ltu_iwordsize_inv in H. + apply Z.min_case_strong; intros; auto. + bit_solve; try omega. + destruct (zlt i (zwordsize - unsigned n)). + rewrite zlt_true by omega. auto. + destruct (zlt i s); auto. rewrite zlt_false by omega; auto. +Qed. + +Lemma sign_ext_shr_min: + forall s x n, ltu n iwordsize = true -> + sign_ext s (shr x n) = sign_ext (Z.min s (zwordsize - unsigned n)) (shr x n). +Proof. + intros. apply ltu_iwordsize_inv in H. + rewrite Z.min_comm. + destruct (Z.min_spec (zwordsize - unsigned n) s) as [[A B] | [A B]]; rewrite B; auto. + apply same_bits_eq; intros. rewrite ! bits_sign_ext by auto. + destruct (zlt i (zwordsize - unsigned n)). + rewrite zlt_true by omega. auto. + assert (C: testbit (shr x n) (zwordsize - unsigned n - 1) = testbit x (zwordsize - 1)). + { rewrite bits_shr by omega. rewrite zlt_true by omega. f_equal; omega. } + rewrite C. destruct (zlt i s); rewrite bits_shr by omega. + rewrite zlt_false by omega. auto. + rewrite zlt_false by omega. auto. +Qed. + +Lemma shl_zero_ext_min: + forall s x n, ltu n iwordsize = true -> + shl (zero_ext s x) n = shl (zero_ext (Z.min s (zwordsize - unsigned n)) x) n. +Proof. + intros. apply ltu_iwordsize_inv in H. + apply Z.min_case_strong; intros; auto. + apply same_bits_eq; intros. rewrite ! bits_shl by auto. + destruct (zlt i (unsigned n)); auto. + rewrite ! bits_zero_ext by omega. + destruct (zlt (i - unsigned n) s). + rewrite zlt_true by omega; auto. + rewrite zlt_false by omega; auto. +Qed. + +Lemma shl_sign_ext_min: + forall s x n, ltu n iwordsize = true -> + shl (sign_ext s x) n = shl (sign_ext (Z.min s (zwordsize - unsigned n)) x) n. +Proof. + intros. apply ltu_iwordsize_inv in H. + rewrite Z.min_comm. + destruct (Z.min_spec (zwordsize - unsigned n) s) as [[A B] | [A B]]; rewrite B; auto. + apply same_bits_eq; intros. rewrite ! bits_shl by auto. + destruct (zlt i (unsigned n)); auto. + rewrite ! bits_sign_ext by omega. f_equal. + destruct (zlt (i - unsigned n) s). + rewrite zlt_true by omega; auto. + omegaContradiction. +Qed. + (** ** Properties of [one_bits] (decomposition in sum of powers of two) *) Theorem one_bits_range: @@ -3512,6 +3638,129 @@ Proof. unfold shr, shr'; rewrite <- A; auto. Qed. +Lemma shl'_zero_ext: + forall n m x, 0 <= n -> + shl' (zero_ext n x) m = zero_ext (n + Int.unsigned m) (shl' x m). +Proof. + intros. apply same_bits_eq; intros. + rewrite bits_zero_ext, ! bits_shl' by omega. + destruct (zlt i (Int.unsigned m)). +- rewrite zlt_true by omega; auto. +- rewrite bits_zero_ext by omega. + destruct (zlt (i - Int.unsigned m) n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. +Qed. + +Lemma shl'_sign_ext: + forall n m x, 0 < n -> + shl' (sign_ext n x) m = sign_ext (n + Int.unsigned m) (shl' x m). +Proof. + intros. generalize (Int.unsigned_range m); intros. + apply same_bits_eq; intros. + rewrite bits_sign_ext, ! bits_shl' by omega. + destruct (zlt i (n + Int.unsigned m)). +- rewrite bits_shl' by auto. destruct (zlt i (Int.unsigned m)); auto. + rewrite bits_sign_ext by omega. f_equal. apply zlt_true. omega. +- rewrite zlt_false by omega. rewrite bits_shl' by omega. rewrite zlt_false by omega. + rewrite bits_sign_ext by omega. f_equal. rewrite zlt_false by omega. omega. +Qed. + +Lemma shru'_zero_ext: + forall n m x, 0 <= n -> + shru' (zero_ext (n + Int.unsigned m) x) m = zero_ext n (shru' x m). +Proof. + intros. generalize (Int.unsigned_range m); intros. + bit_solve; [|omega]. rewrite bits_shru', bits_zero_ext, bits_shru' by omega. + destruct (zlt (i + Int.unsigned m) zwordsize). +* destruct (zlt i n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. +* destruct (zlt i n); auto. +Qed. + +Lemma shru'_zero_ext_0: + forall n m x, n <= Int.unsigned m -> + shru' (zero_ext n x) m = zero. +Proof. + intros. generalize (Int.unsigned_range m); intros. + bit_solve. rewrite bits_shru', bits_zero_ext by omega. + destruct (zlt (i + Int.unsigned m) zwordsize); auto. + apply zlt_false. omega. +Qed. + +Lemma shr'_sign_ext: + forall n m x, 0 < n -> n + Int.unsigned m < zwordsize -> + shr' (sign_ext (n + Int.unsigned m) x) m = sign_ext n (shr' x m). +Proof. + intros. generalize (Int.unsigned_range m); intros. + apply same_bits_eq; intros. + rewrite bits_sign_ext, bits_shr' by auto. + rewrite bits_sign_ext, bits_shr'. +- f_equal. + destruct (zlt i n), (zlt (i + Int.unsigned m) zwordsize). ++ apply zlt_true; omega. ++ apply zlt_true; omega. ++ rewrite zlt_false by omega. rewrite zlt_true by omega. omega. ++ rewrite zlt_false by omega. rewrite zlt_true by omega. omega. +- destruct (zlt i n); omega. +- destruct (zlt (i + Int.unsigned m) zwordsize); omega. +Qed. + +Lemma zero_ext_shru'_min: + forall s x n, Int.ltu n iwordsize' = true -> + zero_ext s (shru' x n) = zero_ext (Z.min s (zwordsize - Int.unsigned n)) (shru' x n). +Proof. + intros. apply Int.ltu_inv in H. change (Int.unsigned iwordsize') with zwordsize in H. + apply Z.min_case_strong; intros; auto. + bit_solve; try omega. rewrite ! bits_shru' by omega. + destruct (zlt i (zwordsize - Int.unsigned n)). + rewrite zlt_true by omega. auto. + destruct (zlt i s); auto. rewrite zlt_false by omega; auto. +Qed. + +Lemma sign_ext_shr'_min: + forall s x n, Int.ltu n iwordsize' = true -> + sign_ext s (shr' x n) = sign_ext (Z.min s (zwordsize - Int.unsigned n)) (shr' x n). +Proof. + intros. apply Int.ltu_inv in H. change (Int.unsigned iwordsize') with zwordsize in H. + rewrite Z.min_comm. + destruct (Z.min_spec (zwordsize - Int.unsigned n) s) as [[A B] | [A B]]; rewrite B; auto. + apply same_bits_eq; intros. rewrite ! bits_sign_ext by auto. + destruct (zlt i (zwordsize - Int.unsigned n)). + rewrite zlt_true by omega. auto. + assert (C: testbit (shr' x n) (zwordsize - Int.unsigned n - 1) = testbit x (zwordsize - 1)). + { rewrite bits_shr' by omega. rewrite zlt_true by omega. f_equal; omega. } + rewrite C. destruct (zlt i s); rewrite bits_shr' by omega. + rewrite zlt_false by omega. auto. + rewrite zlt_false by omega. auto. +Qed. + +Lemma shl'_zero_ext_min: + forall s x n, Int.ltu n iwordsize' = true -> + shl' (zero_ext s x) n = shl' (zero_ext (Z.min s (zwordsize - Int.unsigned n)) x) n. +Proof. + intros. apply Int.ltu_inv in H. change (Int.unsigned iwordsize') with zwordsize in H. + apply Z.min_case_strong; intros; auto. + apply same_bits_eq; intros. rewrite ! bits_shl' by auto. + destruct (zlt i (Int.unsigned n)); auto. + rewrite ! bits_zero_ext by omega. + destruct (zlt (i - Int.unsigned n) s). + rewrite zlt_true by omega; auto. + rewrite zlt_false by omega; auto. +Qed. + +Lemma shl'_sign_ext_min: + forall s x n, Int.ltu n iwordsize' = true -> + shl' (sign_ext s x) n = shl' (sign_ext (Z.min s (zwordsize - Int.unsigned n)) x) n. +Proof. + intros. apply Int.ltu_inv in H. change (Int.unsigned iwordsize') with zwordsize in H. + rewrite Z.min_comm. + destruct (Z.min_spec (zwordsize - Int.unsigned n) s) as [[A B] | [A B]]; rewrite B; auto. + apply same_bits_eq; intros. rewrite ! bits_shl' by auto. + destruct (zlt i (Int.unsigned n)); auto. + rewrite ! bits_sign_ext by omega. f_equal. + destruct (zlt (i - Int.unsigned n) s). + rewrite zlt_true by omega; auto. + omegaContradiction. +Qed. + (** Powers of two with exponents given as 32-bit ints *) Definition one_bits' (x: int) : list Int.int := -- cgit From 8be12dfcd60d40cc5ba90657bc6a2f5528b45e55 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sun, 12 May 2019 19:16:40 +0200 Subject: Added Int.same_if_eq Should simplify reasoning over Boolean equalities. --- lib/Integers.v | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/lib/Integers.v b/lib/Integers.v index 369584c3..066e6b04 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -668,6 +668,11 @@ Proof. intros. generalize (eq_spec x y); case (eq x y); intros; congruence. Qed. +Theorem same_if_eq: forall x y, eq x y = true -> x = y. +Proof. + intros. generalize (eq_spec x y); rewrite H; auto. +Qed. + Theorem eq_signed: forall x y, eq x y = if zeq (signed x) (signed y) then true else false. Proof. -- cgit From 659c06eb4fabce59751476ddeb2e065759f19765 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sun, 12 May 2019 19:17:14 +0200 Subject: Values: add functions for zero- and sign-extension of 64-bit integers --- common/Values.v | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/common/Values.v b/common/Values.v index 2eb778a5..52474f99 100644 --- a/common/Values.v +++ b/common/Values.v @@ -783,6 +783,18 @@ Definition rolml (v: val) (amount: int) (mask: int64): val := | _ => Vundef end. +Definition zero_ext_l (nbits: Z) (v: val) : val := + match v with + | Vlong n => Vlong(Int64.zero_ext nbits n) + | _ => Vundef + end. + +Definition sign_ext_l (nbits: Z) (v: val) : val := + match v with + | Vlong n => Vlong(Int64.sign_ext nbits n) + | _ => Vundef + end. + (** Comparisons *) Section COMPARISONS. -- cgit From b4130798bd428ad3586baa17b0f991018854997a Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sun, 12 May 2019 19:18:22 +0200 Subject: Asmgenproof0: add predicate exec_straight0 This is a variant of exec_straight where it is allowed to take zero steps. In other words, exec_straight0 is the "star" relation, while exec_straight is the "plus" relation. In the end we need "plus" relations in simulation diagrams, to show the absence of stuttering. But the "star" relation exec_straight0 is useful to reason about code fragments that are always preceded or followed by at least one instruction. --- backend/Asmgenproof0.v | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) diff --git a/backend/Asmgenproof0.v b/backend/Asmgenproof0.v index 70c4323c..111e435f 100644 --- a/backend/Asmgenproof0.v +++ b/backend/Asmgenproof0.v @@ -897,6 +897,32 @@ Proof. apply code_tail_next_int with i; auto. Qed. +(** A variant that supports zero steps of execution *) + +Inductive exec_straight0: code -> regset -> mem -> + code -> regset -> mem -> Prop := + | exec_straight0_none: + forall c rs m, + exec_straight0 c rs m c rs m + | exec_straight0_step: + forall i c rs1 m1 rs2 m2 c' rs3 m3, + exec_instr ge fn i rs1 m1 = Next rs2 m2 -> + rs2#PC = Val.offset_ptr rs1#PC Ptrofs.one -> + exec_straight0 c rs2 m2 c' rs3 m3 -> + exec_straight0 (i :: c) rs1 m1 c' rs3 m3. + +Lemma exec_straight_step': + forall i c rs1 m1 rs2 m2 c' rs3 m3, + exec_instr ge fn i rs1 m1 = Next rs2 m2 -> + rs2#PC = Val.offset_ptr rs1#PC Ptrofs.one -> + exec_straight0 c rs2 m2 c' rs3 m3 -> + exec_straight (i :: c) rs1 m1 c' rs3 m3. +Proof. + intros. revert i rs1 m1 H H0. revert H1. induction 1; intros. +- apply exec_straight_one; auto. +- eapply exec_straight_step; eauto. +Qed. + End STRAIGHTLINE. (** * Properties of the Mach call stack *) -- cgit From dd243f5f35200aa9fdcc400300990192ed4bc0b6 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Tue, 11 Jun 2019 17:51:12 +0200 Subject: Errors: fixed a loop in tactic MonadInv --- common/Errors.v | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/common/Errors.v b/common/Errors.v index 28933313..6807735a 100644 --- a/common/Errors.v +++ b/common/Errors.v @@ -164,7 +164,7 @@ Ltac monadInv1 H := | (match ?X with left _ => _ | right _ => assertion_failed end = OK _) => destruct X; [try (monadInv1 H) | discriminate] | (match (negb ?X) with true => _ | false => assertion_failed end = OK _) => - destruct X as [] eqn:?; [discriminate | try (monadInv1 H)] + destruct X as [] eqn:?; simpl negb in H; [discriminate | try (monadInv1 H)] | (match ?X with true => _ | false => assertion_failed end = OK _) => destruct X as [] eqn:?; [try (monadInv1 H) | discriminate] | (mmap ?F ?L = OK ?M) => -- cgit From f86e6618b62769b1c3e78175f95f882d3960d54b Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 8 Jun 2019 18:17:13 +0200 Subject: More lemmas about powers of 2 --- lib/Zbits.v | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/lib/Zbits.v b/lib/Zbits.v index fb40ccb5..27586aff 100644 --- a/lib/Zbits.v +++ b/lib/Zbits.v @@ -824,6 +824,14 @@ Proof. apply Z.log2_nonneg. - reflexivity. Qed. + +Lemma Z_is_power2_nonneg: + forall x i, Z_is_power2 x = Some i -> 0 <= i. +Proof. + unfold Z_is_power2; intros. destruct x; try discriminate. + destruct (P_is_power2 p) eqn:P; try discriminate. + replace i with (Z.log2 (Z.pos p)) by congruence. apply Z.log2_nonneg. +Qed. Lemma Z_is_power2_sound: forall x i, Z_is_power2 x = Some i -> x = two_p i /\ i = Z.log2 x. @@ -859,6 +867,12 @@ Qed. Definition Z_is_power2m1 (x: Z) : option Z := Z_is_power2 (Z.succ x). +Lemma Z_is_power2m1_nonneg: + forall x i, Z_is_power2m1 x = Some i -> 0 <= i. +Proof. + unfold Z_is_power2m1; intros. eapply Z_is_power2_nonneg; eauto. +Qed. + Lemma Z_is_power2m1_sound: forall x i, Z_is_power2m1 x = Some i -> x = two_p i - 1. Proof. -- cgit From e61e2dffaac5f5ffbffdbd87c3d3466bd9a2e83b Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 15 Jun 2019 10:13:31 +0200 Subject: ndfun: add support for guards on patterns Syntax is "pat ?? bexpr => action". The whole case is selected only when "pat" matches and then "bexpr" evaluates to "true". --- tools/ndfun.ml | 21 ++++++++++++++++----- 1 file changed, 16 insertions(+), 5 deletions(-) diff --git a/tools/ndfun.ml b/tools/ndfun.ml index 2b8bcb19..b6a87ede 100644 --- a/tools/ndfun.ml +++ b/tools/ndfun.ml @@ -41,7 +41,9 @@ let trim s = let str_match n re s = if not (Str.string_match re s 0) then [||] else begin let res = Array.make (n+1) "" in - for i = 1 to n do res.(i) <- Str.matched_group i s done; + for i = 1 to n do + res.(i) <- (try Str.matched_group i s with Not_found -> "") + done; for i = 1 to n do res.(i) <- trim res.(i) done; res end @@ -87,6 +89,11 @@ let match_temps args = let parenpats p = "(" ^ Str.global_replace re_comma ") (" p ^ ")" +(* "foo, bar, gee" -> "_ _ _" *) + +let underscores_for s = + Str.global_replace re_arg "_" (remove_commas s) + (* Extract the bound variables in a pattern. Heuristic: any identifier that starts with a lowercase letter and is not "nil". *) @@ -123,7 +130,7 @@ let re_nd = Str.regexp( let re_split_cases = Str.regexp "|" -let re_case = Str.regexp "\\(.*\\)=>\\(.*\\)" +let re_case = Str.regexp "\\([^?]*\\)\\(\\?\\?\\(.*\\)\\)?=>\\(.*\\)" let re_default_pat = Str.regexp "[ _,]*$" @@ -165,16 +172,20 @@ let transl_ndfun filename lineno s = (* Adding each case *) let numcase = ref 0 in let transl_case s = - let res = str_match 2 re_case s in + let res = str_match 4 re_case s in if Array.length res = 0 then error filename lineno ("ill-formed case: " ^ s); - let patlist = res.(1) and rhs = res.(2) in + let patlist = res.(1) and guard = res.(3) and rhs = res.(4) in let bv = boundvarspat patlist in if not (Str.string_match re_default_pat patlist 0) then begin incr numcase; bprintf a " | %s_case%d: forall %s, %s_cases %s\n" name !numcase bv name (parenpats patlist); - bprintf b " | %s => %s_case%d %s\n" patlist name !numcase bv; + if guard = "" then + bprintf b " | %s => %s_case%d %s\n" patlist name !numcase bv + else + bprintf b " | %s => if %s then %s_case%d %s else %s_default %s\n" + patlist guard name !numcase bv name (underscores_for args); bprintf c " | %s_case%d %s => (* %s *) \n" name !numcase bv patlist; bprintf c " %s\n" rhs end else begin -- cgit From b839084a1731b09542eedff0cfac8e1a7b072c69 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 15 Jun 2019 14:00:49 +0200 Subject: Factor out endianness determination between tests --- test/c/aes.c | 10 +--------- test/endian.h | 8 ++++++++ test/regression/floats-basics.c | 14 +++----------- test/regression/floats.c | 12 ++---------- 4 files changed, 14 insertions(+), 30 deletions(-) create mode 100644 test/endian.h diff --git a/test/c/aes.c b/test/c/aes.c index 0aa02595..16f02e47 100644 --- a/test/c/aes.c +++ b/test/c/aes.c @@ -27,6 +27,7 @@ #include #include #include +#include "../endian.h" #define MAXKC (256/32) #define MAXKB (256/8) @@ -36,15 +37,6 @@ typedef unsigned char u8; typedef unsigned short u16; typedef unsigned int u32; -#if defined(__ppc__) || defined(__PPC__) || defined(__ARMEB__) -#define ARCH_BIG_ENDIAN -#elif defined(__i386__) || defined(__x86_64__) || defined(__ARMEL__) \ - || defined(__riscv) -#undef ARCH_BIG_ENDIAN -#else -#error "unknown endianness" -#endif - #ifdef ARCH_BIG_ENDIAN #define GETU32(pt) (*(u32 *)(pt)) #define PUTU32(ct,st) (*(u32 *)(ct) = (st)) diff --git a/test/endian.h b/test/endian.h new file mode 100644 index 00000000..8be2850c --- /dev/null +++ b/test/endian.h @@ -0,0 +1,8 @@ +#if defined(__ppc__) || defined(__PPC__) || defined(__ARMEB__) +#define ARCH_BIG_ENDIAN +#elif defined(__i386__) || defined(__x86_64__) || defined(__ARMEL__) \ + || defined(__riscv) || defined(__aarch64__) +#undef ARCH_BIG_ENDIAN +#else +#error "unknown endianness" +#endif diff --git a/test/regression/floats-basics.c b/test/regression/floats-basics.c index a7ba3623..876a0d42 100644 --- a/test/regression/floats-basics.c +++ b/test/regression/floats-basics.c @@ -1,18 +1,10 @@ -#include -#include +#include +#include +#include "../endian.h" #define STR_EXPAND(tok) #tok #define STR(tok) STR_EXPAND(tok) -#if defined(__ppc__) || defined(__PPC__) || defined(__ARMEB__) -#define ARCH_BIG_ENDIAN -#elif defined(__i386__) || defined(__x86_64__) || defined(__ARMEL__) \ - || defined(__riscv) -#undef ARCH_BIG_ENDIAN -#else -#error "unknown endianness" -#endif - union converter64 { double dbl; struct { diff --git a/test/regression/floats.c b/test/regression/floats.c index 84c4e062..58c202ae 100644 --- a/test/regression/floats.c +++ b/test/regression/floats.c @@ -1,17 +1,9 @@ -#include +#include +#include "../endian.h" #define STR_EXPAND(tok) #tok #define STR(tok) STR_EXPAND(tok) -#if defined(__ppc__) || defined(__PPC__) || defined(__ARMEB__) -#define ARCH_BIG_ENDIAN -#elif defined(__i386__) || defined(__x86_64__) || defined(__ARMEL__) \ - || defined(__riscv) -#undef ARCH_BIG_ENDIAN -#else -#error "unknown endianness" -#endif - union converter64 { double dbl; struct { -- cgit From eb85803875c5a4e90be60d870f01fac380ca18b0 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sun, 16 Jun 2019 18:55:17 +0200 Subject: Relax lemma Val.zero_ext_and and add Val.zero_ext_andl --- common/Values.v | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/common/Values.v b/common/Values.v index 52474f99..de317734 100644 --- a/common/Values.v +++ b/common/Values.v @@ -1910,10 +1910,18 @@ Qed. Lemma zero_ext_and: forall n v, - 0 < n < Int.zwordsize -> + 0 <= n -> Val.zero_ext n v = Val.and v (Vint (Int.repr (two_p n - 1))). Proof. - intros. destruct v; simpl; auto. decEq. apply Int.zero_ext_and; auto. omega. + intros. destruct v; simpl; auto. decEq. apply Int.zero_ext_and; auto. +Qed. + +Lemma zero_ext_andl: + forall n v, + 0 <= n -> + Val.zero_ext_l n v = Val.andl v (Vlong (Int64.repr (two_p n - 1))). +Proof. + intros. destruct v; simpl; auto. decEq. apply Int64.zero_ext_and; auto. Qed. Lemma rolm_lt_zero: -- cgit From 7cdd676d002e33015b496f609538a9e86d77c543 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Thu, 8 Aug 2019 11:18:38 +0200 Subject: AArch64 port This commit adds a back-end for the AArch64 architecture, namely ARMv8 in 64-bit mode. --- .gitignore | 3 + aarch64/Archi.v | 88 ++ aarch64/Asm.v | 1312 +++++++++++++++++++++ aarch64/AsmToJSON.ml | 24 + aarch64/Asmexpand.ml | 436 +++++++ aarch64/Asmgen.v | 1151 +++++++++++++++++++ aarch64/Asmgenproof.v | 1026 +++++++++++++++++ aarch64/Asmgenproof1.v | 1836 ++++++++++++++++++++++++++++++ aarch64/Builtins1.v | 33 + aarch64/CBuiltins.ml | 72 ++ aarch64/CombineOp.v | 137 +++ aarch64/CombineOpproof.v | 161 +++ aarch64/ConstpropOp.vp | 401 +++++++ aarch64/ConstpropOpproof.v | 838 ++++++++++++++ aarch64/Conventions1.v | 380 +++++++ aarch64/Machregs.v | 210 ++++ aarch64/Machregsaux.ml | 35 + aarch64/NeedOp.v | 253 ++++ aarch64/Op.v | 1778 +++++++++++++++++++++++++++++ aarch64/PrintOp.ml | 247 ++++ aarch64/SelectLong.vp | 478 ++++++++ aarch64/SelectLongproof.v | 764 +++++++++++++ aarch64/SelectOp.vp | 566 +++++++++ aarch64/SelectOpproof.v | 1070 +++++++++++++++++ aarch64/Stacklayout.v | 140 +++ aarch64/TargetPrinter.ml | 592 ++++++++++ aarch64/ValueAOp.v | 319 ++++++ aarch64/extractionMachdep.v | 23 + backend/Asmgenproof0.v | 51 +- backend/Lineartyping.v | 2 +- backend/NeedDomain.v | 24 +- backend/SelectDivproof.v | 20 +- backend/Selectionaux.ml | 2 + backend/Selectionproof.v | 4 +- backend/ValueDomain.v | 31 +- configure | 38 +- cparser/Machine.ml | 5 + cparser/Machine.mli | 1 + driver/Configuration.ml | 2 +- driver/Frontend.ml | 1 + lib/Integers.v | 160 ++- riscV/Asmgenproof1.v | 16 - runtime/Makefile | 2 + runtime/aarch64/sysdeps.h | 45 + runtime/aarch64/vararg.S | 109 ++ test/regression/Results/builtins-aarch64 | 15 + test/regression/builtins-aarch64.c | 47 + test/regression/extasm.c | 13 +- 48 files changed, 14874 insertions(+), 87 deletions(-) create mode 100644 aarch64/Archi.v create mode 100644 aarch64/Asm.v create mode 100644 aarch64/AsmToJSON.ml create mode 100644 aarch64/Asmexpand.ml create mode 100644 aarch64/Asmgen.v create mode 100644 aarch64/Asmgenproof.v create mode 100644 aarch64/Asmgenproof1.v create mode 100644 aarch64/Builtins1.v create mode 100644 aarch64/CBuiltins.ml create mode 100644 aarch64/CombineOp.v create mode 100644 aarch64/CombineOpproof.v create mode 100644 aarch64/ConstpropOp.vp create mode 100644 aarch64/ConstpropOpproof.v create mode 100644 aarch64/Conventions1.v create mode 100644 aarch64/Machregs.v create mode 100644 aarch64/Machregsaux.ml create mode 100644 aarch64/NeedOp.v create mode 100644 aarch64/Op.v create mode 100644 aarch64/PrintOp.ml create mode 100644 aarch64/SelectLong.vp create mode 100644 aarch64/SelectLongproof.v create mode 100644 aarch64/SelectOp.vp create mode 100644 aarch64/SelectOpproof.v create mode 100644 aarch64/Stacklayout.v create mode 100644 aarch64/TargetPrinter.ml create mode 100644 aarch64/ValueAOp.v create mode 100644 aarch64/extractionMachdep.v create mode 100644 runtime/aarch64/sysdeps.h create mode 100644 runtime/aarch64/vararg.S create mode 100644 test/regression/Results/builtins-aarch64 create mode 100644 test/regression/builtins-aarch64.c diff --git a/.gitignore b/.gitignore index f33b2173..4b497387 100644 --- a/.gitignore +++ b/.gitignore @@ -40,6 +40,9 @@ /riscV/ConstpropOp.v /riscV/SelectOp.v /riscV/SelectLong.v +/aarch64/ConstpropOp.v +/aarch64/SelectOp.v +/aarch64/SelectLong.v /backend/SelectDiv.v /backend/SplitLong.v /cparser/Parser.v diff --git a/aarch64/Archi.v b/aarch64/Archi.v new file mode 100644 index 00000000..aef4ab77 --- /dev/null +++ b/aarch64/Archi.v @@ -0,0 +1,88 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Architecture-dependent parameters for AArch64 *) + +Require Import ZArith List. +(*From Flocq*) +Require Import Binary Bits. + +Definition ptr64 := true. + +Definition big_endian := false. + +Definition align_int64 := 8%Z. +Definition align_float64 := 8%Z. + +Definition splitlong := false. + +Lemma splitlong_ptr32: splitlong = true -> ptr64 = false. +Proof. + unfold splitlong, ptr64; congruence. +Qed. + +Definition default_nan_64 := (false, iter_nat 51 _ xO xH). +Definition default_nan_32 := (false, iter_nat 22 _ xO xH). + +(** Choose the first signaling NaN, if any; + otherwise choose the first NaN; + otherwise use default. *) + +Definition choose_nan (is_signaling: positive -> bool) + (default: bool * positive) + (l0: list (bool * positive)) : bool * positive := + let fix choose_snan (l1: list (bool * positive)) := + match l1 with + | nil => + match l0 with nil => default | n :: _ => n end + | ((s, p) as n) :: l1 => + if is_signaling p then n else choose_snan l1 + end + in choose_snan l0. + +Lemma choose_nan_idem: forall is_signaling default n, + choose_nan is_signaling default (n :: n :: nil) = + choose_nan is_signaling default (n :: nil). +Proof. + intros. destruct n as [s p]; unfold choose_nan; simpl. + destruct (is_signaling p); auto. +Qed. + +Definition choose_nan_64 := + choose_nan (fun p => negb (Pos.testbit p 51)) default_nan_64. + +Definition choose_nan_32 := + choose_nan (fun p => negb (Pos.testbit p 22)) default_nan_32. + +Lemma choose_nan_64_idem: forall n, + choose_nan_64 (n :: n :: nil) = choose_nan_64 (n :: nil). +Proof. intros; apply choose_nan_idem. Qed. + +Lemma choose_nan_32_idem: forall n, + choose_nan_32 (n :: n :: nil) = choose_nan_32 (n :: nil). +Proof. intros; apply choose_nan_idem. Qed. + +Definition fma_order {A: Type} (x y z: A) := (z, x, y). + +Definition fma_invalid_mul_is_nan := true. + +Definition float_of_single_preserves_sNaN := false. + +Global Opaque ptr64 big_endian splitlong + default_nan_64 choose_nan_64 + default_nan_32 choose_nan_32 + fma_order fma_invalid_mul_is_nan + float_of_single_preserves_sNaN. + +(** Whether to generate position-independent code or not *) + +Parameter pic_code: unit -> bool. diff --git a/aarch64/Asm.v b/aarch64/Asm.v new file mode 100644 index 00000000..47cd3051 --- /dev/null +++ b/aarch64/Asm.v @@ -0,0 +1,1312 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Abstract syntax and semantics for AArch64 assembly language *) + +Require Import Coqlib Zbits Maps. +Require Import AST Integers Floats. +Require Import Values Memory Events Globalenvs Smallstep. +Require Import Locations Conventions. +Require Stacklayout. + +(** * Abstract syntax *) + +(** Integer registers, floating-point registers. *) + +(** In assembly files, [Xn] denotes the full 64-bit register + and [Wn] the low 32 bits of [Xn]. *) + +Inductive ireg: Type := + | X0 | X1 | X2 | X3 | X4 | X5 | X6 | X7 + | X8 | X9 | X10 | X11 | X12 | X13 | X14 | X15 + | X16 | X17 | X18 | X19 | X20 | X21 | X22 | X23 + | X24 | X25 | X26 | X27 | X28 | X29 | X30. + +Inductive ireg0: Type := + | RR0 (r: ireg) | XZR. + +Inductive iregsp: Type := + | RR1 (r: ireg) | XSP. + +Coercion RR0: ireg >-> ireg0. +Coercion RR1: ireg >-> iregsp. + +Lemma ireg_eq: forall (x y: ireg), {x=y} + {x<>y}. +Proof. decide equality. Defined. + +(** In assembly files, [Dn] denotes the low 64-bit of a vector register, + and [Sn] the low 32 bits. *) + +Inductive freg: Type := + | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 + | D8 | D9 | D10 | D11 | D12 | D13 | D14 | D15 + | D16 | D17 | D18 | D19 | D20 | D21 | D22 | D23 + | D24 | D25 | D26 | D27 | D28 | D29 | D30 | D31. + +Lemma freg_eq: forall (x y: freg), {x=y} + {x<>y}. +Proof. decide equality. Defined. + +(** Bits in the condition register. *) + +Inductive crbit: Type := + | CN: crbit (**r negative *) + | CZ: crbit (**r zero *) + | CC: crbit (**r carry *) + | CV: crbit. (**r overflow *) + +Lemma crbit_eq: forall (x y: crbit), {x=y} + {x<>y}. +Proof. decide equality. Defined. + +(** We model the following registers of the ARM architecture. *) + +Inductive preg: Type := + | IR: ireg -> preg (**r 64- or 32-bit integer registers *) + | FR: freg -> preg (**r double- or single-precision float registers *) + | CR: crbit -> preg (**r bits in the condition register *) + | SP: preg (**r register X31 used as stack pointer *) + | PC: preg. (**r program counter *) + +Coercion IR: ireg >-> preg. +Coercion FR: freg >-> preg. +Coercion CR: crbit >-> preg. + +Lemma preg_eq: forall (x y: preg), {x=y} + {x<>y}. +Proof. decide equality. apply ireg_eq. apply freg_eq. apply crbit_eq. Defined. + +Module PregEq. + Definition t := preg. + Definition eq := preg_eq. +End PregEq. + +Module Pregmap := EMap(PregEq). + +Definition preg_of_iregsp (r: iregsp) : preg := + match r with RR1 r => IR r | XSP => SP end. + +Coercion preg_of_iregsp: iregsp >-> preg. + +(** Conventional name for return address ([RA]) *) + +Notation "'RA'" := X30 (only parsing) : asm. + +(** The instruction set. Most instructions correspond exactly to + actual AArch64 instructions. See the ARM reference manuals for more + details. Some instructions, described below, are + pseudo-instructions: they expand to canned instruction sequences + during the printing of the assembly code. *) + +Definition label := positive. + +Inductive isize: Type := + | W (**r 32-bit integer operation *) + | X. (**r 64-bit integer operation *) + +Inductive fsize: Type := + | S (**r 32-bit, single-precision FP operation *) + | D. (**r 64-bit, double-precision FP operation *) + +Inductive testcond : Type := + | TCeq: testcond (**r equal *) + | TCne: testcond (**r not equal *) + | TChs: testcond (**r unsigned higher or same *) + | TClo: testcond (**r unsigned lower *) + | TCmi: testcond (**r negative *) + | TCpl: testcond (**r positive *) + | TChi: testcond (**r unsigned higher *) + | TCls: testcond (**r unsigned lower or same *) + | TCge: testcond (**r signed greater or equal *) + | TClt: testcond (**r signed less than *) + | TCgt: testcond (**r signed greater *) + | TCle: testcond. (**r signed less than or equal *) + +Inductive addressing: Type := + | ADimm (base: iregsp) (n: int64) (**r base plus immediate offset *) + | ADreg (base: iregsp) (r: ireg) (**r base plus reg *) + | ADlsl (base: iregsp) (r: ireg) (n: int) (**r base plus reg LSL n *) + | ADsxt (base: iregsp) (r: ireg) (n: int) (**r base plus SIGN-EXT(reg) LSL n *) + | ADuxt (base: iregsp) (r: ireg) (n: int) (**r base plus ZERO-EXT(reg) LSL n *) + | ADadr (base: iregsp) (id: ident) (ofs: ptrofs) (**r base plus low address of [id + ofs] *) + | ADpostincr (base: iregsp) (n: int64). (**r base plus offset; base is updated after *) + +Inductive shift_op: Type := + | SOnone + | SOlsl (n: int) + | SOlsr (n: int) + | SOasr (n: int) + | SOror (n: int). + +Inductive extend_op: Type := + | EOsxtb (n: int) + | EOsxth (n: int) + | EOsxtw (n: int) + | EOuxtb (n: int) + | EOuxth (n: int) + | EOuxtw (n: int) + | EOuxtx (n: int). + +Inductive instruction: Type := + (** Branches *) + | Pb (lbl: label) (**r branch *) + | Pbc (c: testcond) (lbl: label) (**r conditional branch *) + | Pbl (id: ident) (sg: signature) (**r jump to function and link *) + | Pbs (id: ident) (sg: signature) (**r jump to function *) + | Pblr (r: ireg) (sg: signature) (**r indirect jump and link *) + | Pbr (r: ireg) (sg: signature) (**r indirect jump *) + | Pret (r: ireg) (**r return *) + | Pcbnz (sz: isize) (r: ireg) (lbl: label) (**r branch if not zero *) + | Pcbz (sz: isize) (r: ireg) (lbl: label) (**r branch if zero *) + | Ptbnz (sz: isize) (r: ireg) (n: int) (lbl: label) (**r branch if bit n is not zero *) + | Ptbz (sz: isize) (r: ireg) (n: int) (lbl: label) (**r branch if bit n is zero *) + (** Memory loads and stores *) + | Pldrw (rd: ireg) (a: addressing) (**r load int32 *) + | Pldrw_a (rd: ireg) (a: addressing) (**r load int32 as any32 *) + | Pldrx (rd: ireg) (a: addressing) (**r load int64 *) + | Pldrx_a (rd: ireg) (a: addressing) (**r load int64 as any64 *) + | Pldrb (sz: isize) (rd: ireg) (a: addressing) (**r load int8, zero-extend *) + | Pldrsb (sz: isize) (rd: ireg) (a: addressing) (**r load int8, sign-extend *) + | Pldrh (sz: isize) (rd: ireg) (a: addressing) (**r load int16, zero-extend *) + | Pldrsh (sz: isize) (rd: ireg) (a: addressing) (**r load int16, sign-extend *) + | Pldrzw (rd: ireg) (a: addressing) (**r load int32, zero-extend to int64 *) + | Pldrsw (rd: ireg) (a: addressing) (**r load int32, sign-extend to int64 *) + | Pldp (rd1 rd2: ireg) (a: addressing) (**r load two int64 *) + | Pstrw (rs: ireg) (a: addressing) (**r store int32 *) + | Pstrw_a (rs: ireg) (a: addressing) (**r store int32 as any32 *) + | Pstrx (rs: ireg) (a: addressing) (**r store int64 *) + | Pstrx_a (rs: ireg) (a: addressing) (**r store int64 as any64 *) + | Pstrb (rs: ireg) (a: addressing) (**r store int8 *) + | Pstrh (rs: ireg) (a: addressing) (**r store int16 *) + | Pstp (rs1 rs2: ireg) (a: addressing) (**r store two int64 *) + (** Integer arithmetic, immediate *) + | Paddimm (sz: isize) (rd: iregsp) (r1: iregsp) (n: Z) (**r addition *) + | Psubimm (sz: isize) (rd: iregsp) (r1: iregsp) (n: Z) (**r subtraction *) + | Pcmpimm (sz: isize) (r1: ireg) (n: Z) (**r compare *) + | Pcmnimm (sz: isize) (r1: ireg) (n: Z) (**r compare negative *) + (** Move integer register *) + | Pmov (rd: iregsp) (r1: iregsp) + (** Logical, immediate *) + | Pandimm (sz: isize) (rd: ireg) (r1: ireg0) (n: Z) (**r and *) + | Peorimm (sz: isize) (rd: ireg) (r1: ireg0) (n: Z) (**r xor *) + | Porrimm (sz: isize) (rd: ireg) (r1: ireg0) (n: Z) (**r or *) + | Ptstimm (sz: isize) (r1: ireg) (n: Z) (**r and, then set flags *) + (** Move wide immediate *) + | Pmovz (sz: isize) (rd: ireg) (n: Z) (pos: Z) (**r move [n << pos] to [rd] *) + | Pmovn (sz: isize) (rd: ireg) (n: Z) (pos: Z) (**r move [NOT(n << pos)] to [rd] *) + | Pmovk (sz: isize) (rd: ireg) (n: Z) (pos: Z) (**r insert 16 bits of [n] at [pos] in rd *) + (** PC-relative addressing *) + | Padrp (rd: ireg) (id: ident) (ofs: ptrofs) (**r set [rd] to high address of [id + ofs] *) + | Paddadr (rd: ireg) (r1: ireg) (id: ident) (ofs: ptrofs) (**r add the low address of [id + ofs] *) + (** Bit-field operations *) + | Psbfiz (sz: isize) (rd: ireg) (r1: ireg) (r: int) (s: Z) (**r sign extend and shift left *) + | Psbfx (sz: isize) (rd: ireg) (r1: ireg) (r: int) (s: Z) (**r shift right and sign extend *) + | Pubfiz (sz: isize) (rd: ireg) (r1: ireg) (r: int) (s: Z) (**r zero extend and shift left *) + | Pubfx (sz: isize) (rd: ireg) (r1: ireg) (r: int) (s: Z) (**r shift right and zero extend *) + (** Integer arithmetic, shifted register *) + | Padd (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r addition *) + | Psub (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r subtraction *) + | Pcmp (sz: isize) (r1: ireg0) (r2: ireg) (s: shift_op) (**r compare *) + | Pcmn (sz: isize) (r1: ireg0) (r2: ireg) (s: shift_op) (**r compare negative *) + (** Integer arithmetic, extending register *) + | Paddext (rd: iregsp) (r1: iregsp) (r2: ireg) (x: extend_op) (**r int64-int32 add *) + | Psubext (rd: iregsp) (r1: iregsp) (r2: ireg) (x: extend_op) (**r int64-int32 sub *) + | Pcmpext (r1: ireg) (r2: ireg) (x: extend_op) (**r int64-int32 cmp *) + | Pcmnext (r1: ireg) (r2: ireg) (x: extend_op) (**r int64-int32 cmn *) + (** Logical, shifted register *) + | Pand (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r and *) + | Pbic (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r and-not *) + | Peon (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r xor-not *) + | Peor (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r xor *) + | Porr (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r or *) + | Porn (sz: isize) (rd: ireg) (r1: ireg0) (r2: ireg) (s: shift_op) (**r or-not *) + | Ptst (sz: isize) (r1: ireg0) (r2: ireg) (s: shift_op) (**r and, then set flags *) + (** Variable shifts *) + | Pasrv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r arithmetic right shift *) + | Plslv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r left shift *) + | Plsrv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r logical right shift *) + | Prorv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r rotate right *) + (** Bit operations *) + | Pcls (sz: isize) (rd r1: ireg) (**r count leading sign bits *) + | Pclz (sz: isize) (rd r1: ireg) (**r count leading zero bits *) + | Prev (sz: isize) (rd r1: ireg) (**r reverse bytes *) + | Prev16 (sz: isize) (rd r1: ireg) (**r reverse bytes in each 16-bit word *) + (** Conditional data processing *) + | Pcsel (rd: ireg) (r1 r2: ireg) (c: testcond) (**r int conditional move *) + | Pcset (rd: ireg) (c: testcond) (**r set to 1/0 if cond is true/false *) +(* + | Pcsetm (rd: ireg) (c: testcond) (**r set to -1/0 if cond is true/false *) +*) + (** Integer multiply/divide *) + | Pmadd (sz: isize) (rd: ireg) (r1 r2: ireg) (r3: ireg0) (**r multiply-add *) + | Pmsub (sz: isize) (rd: ireg) (r1 r2: ireg) (r3: ireg0) (**r multiply-sub *) + | Psmulh (rd: ireg) (r1 r2: ireg) (**r signed multiply high *) + | Pumulh (rd: ireg) (r1 r2: ireg) (**r unsigned multiply high *) + | Psdiv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r signed division *) + | Pudiv (sz: isize) (rd: ireg) (r1 r2: ireg) (**r unsigned division *) + (** Floating-point loads and stores *) + | Pldrs (rd: freg) (a: addressing) (**r load float32 (single precision) *) + | Pldrd (rd: freg) (a: addressing) (**r load float64 (double precision) *) + | Pldrd_a (rd: freg) (a: addressing) (**r load float64 as any64 *) + | Pstrs (rs: freg) (a: addressing) (**r store float32 *) + | Pstrd (rs: freg) (a: addressing) (**r store float64 *) + | Pstrd_a (rs: freg) (a: addressing) (**r store float64 as any64 *) + (** Floating-point move *) + | Pfmov (rd r1: freg) + | Pfmovimms (rd: freg) (f: float32) (**r load float32 constant *) + | Pfmovimmd (rd: freg) (f: float) (**r load float64 constant *) + | Pfmovi (fsz: fsize) (rd: freg) (r1: ireg0) (**r copy int reg to FP reg *) + (** Floating-point conversions *) + | Pfcvtds (rd r1: freg) (**r convert float32 to float64 *) + | Pfcvtsd (rd r1: freg) (**r convert float64 to float32 *) + | Pfcvtzs (isz: isize) (fsz: fsize) (rd: ireg) (r1: freg) (**r convert float to signed int *) + | Pfcvtzu (isz: isize) (fsz: fsize) (rd: ireg) (r1: freg) (**r convert float to unsigned int *) + | Pscvtf (fsz: fsize) (isz: isize) (rd: freg) (r1: ireg) (**r convert signed int to float *) + | Pucvtf (fsz: fsize) (isz: isize) (rd: freg) (r1: ireg) (**r convert unsigned int to float *) + (** Floating-point arithmetic *) + | Pfabs (sz: fsize) (rd r1: freg) (**r absolute value *) + | Pfneg (sz: fsize) (rd r1: freg) (**r negation *) + | Pfsqrt (sz: fsize) (rd r1: freg) (**r square root *) + | Pfadd (sz: fsize) (rd r1 r2: freg) (**r addition *) + | Pfdiv (sz: fsize) (rd r1 r2: freg) (**r division *) + | Pfmul (sz: fsize) (rd r1 r2: freg) (**r multiplication *) + | Pfnmul (sz: fsize) (rd r1 r2: freg) (**r multiply-negate *) + | Pfsub (sz: fsize) (rd r1 r2: freg) (**r subtraction *) + | Pfmadd (sz: fsize) (rd r1 r2 r3: freg) (**r [rd = r3 + r1 * r2] *) + | Pfmsub (sz: fsize) (rd r1 r2 r3: freg) (**r [rd = r3 - r1 * r2] *) + | Pfnmadd (sz: fsize) (rd r1 r2 r3: freg) (**r [rd = - r3 - r1 * r2] *) + | Pfnmsub (sz: fsize) (rd r1 r2 r3: freg) (**r [rd = - r3 + r1 * r2] *) + (** Floating-point comparison *) + | Pfcmp (sz: fsize) (r1 r2: freg) (**r compare [r1] and [r2] *) + | Pfcmp0 (sz: fsize) (r1: freg) (**r compare [r1] and [+0.0] *) + (** Floating-point conditional select *) + | Pfsel (rd r1 r2: freg) (cond: testcond) + (** Pseudo-instructions *) + | Pallocframe (sz: Z) (linkofs: ptrofs) (**r allocate new stack frame *) + | Pfreeframe (sz: Z) (linkofs: ptrofs) (**r deallocate stack frame and restore previous frame *) + | Plabel (lbl: label) (**r define a code label *) + | Ploadsymbol (rd: ireg) (id: ident) (**r load the address of [id] *) + | Pcvtsw2x (rd: ireg) (r1: ireg) (**r sign-extend 32-bit int to 64-bit *) + | Pcvtuw2x (rd: ireg) (r1: ireg) (**r zero-extend 32-bit int to 64-bit *) + | Pcvtx2w (rd: ireg) (**r retype a 64-bit int as a 32-bit int *) + | Pbtbl (r1: ireg) (tbl: list label) (**r N-way branch through a jump table *) + | Pbuiltin (ef: external_function) + (args: list (builtin_arg preg)) (res: builtin_res preg) (**r built-in function (pseudo) *) + | Pnop (**r no operation *) + | Pcfi_adjust (ofs: int) (**r .cfi_adjust debug directive *) + | Pcfi_rel_offset (ofs: int) (**r .cfi_rel_offset debug directive *) +. + +Definition code := list instruction. +Record function : Type := mkfunction { fn_sig: signature; fn_code: code }. +Definition fundef := AST.fundef function. +Definition program := AST.program fundef unit. + +(** * Operational semantics *) + +(** The semantics operates over a single mapping from registers + (type [preg]) to values. We maintain (but do not enforce) + the convention that integer registers are mapped to values of + type [Tint], float registers to values of type [Tfloat], + and condition bits to either [Vzero] or [Vone]. *) + +Definition regset := Pregmap.t val. +Definition genv := Genv.t fundef unit. + +(** The value of an [ireg0] is either the value of the integer register, + or 0. *) + +Definition ir0w (rs: regset) (r: ireg0) : val := + match r with RR0 r => rs (IR r) | XZR => Vint Int.zero end. +Definition ir0x (rs: regset) (r: ireg0) : val := + match r with RR0 r => rs (IR r) | XZR => Vlong Int64.zero end. + +(** Concise notations for accessing and updating the values of registers. *) + +Notation "a # b" := (a b) (at level 1, only parsing) : asm. +Notation "a # b <- c" := (Pregmap.set b c a) (at level 1, b at next level) : asm. +Notation "a ## b" := (ir0w a b) (at level 1, only parsing) : asm. +Notation "a ### b" := (ir0x a b) (at level 1, only parsing) : asm. + +Open Scope asm. + +(** Undefining some registers *) + +Fixpoint undef_regs (l: list preg) (rs: regset) : regset := + match l with + | nil => rs + | r :: l' => undef_regs l' (rs#r <- Vundef) + end. + +(** Undefining the condition codes *) + +Definition undef_flags (rs: regset) : regset := + fun r => match r with CR _ => Vundef | _ => rs r end. + +(** Assigning a register pair *) + +Definition set_pair (p: rpair preg) (v: val) (rs: regset) : regset := + match p with + | One r => rs#r <- v + | Twolong rhi rlo => rs#rhi <- (Val.hiword v) #rlo <- (Val.loword v) + end. + +(** Assigning the result of a builtin *) + +Fixpoint set_res (res: builtin_res preg) (v: val) (rs: regset) : regset := + match res with + | BR r => rs#r <- v + | BR_none => rs + | BR_splitlong hi lo => set_res lo (Val.loword v) (set_res hi (Val.hiword v) rs) + end. + +(** The two functions below axiomatize how the linker processes + symbolic references [symbol + offset]. It computes the + difference between the address and the PC, and splits it into: + - 12 low bits usable as an offset in an addressing mode; + - 21 high bits usable as argument to the ADRP instruction. + + In CompCert's model, we cannot really describe PC-relative addressing, + but we can claim that the address of [symbol + offset] decomposes + as the sum of + - a low part, usable as an offset in an addressing mode; + - a high part, usable as argument to the ADRP instruction. *) + +Parameter symbol_low: genv -> ident -> ptrofs -> val. +Parameter symbol_high: genv -> ident -> ptrofs -> val. + +Axiom symbol_high_low: + forall (ge: genv) (id: ident) (ofs: ptrofs), + Val.addl (symbol_high ge id ofs) (symbol_low ge id ofs) = Genv.symbol_address ge id ofs. + +Section RELSEM. + +Variable ge: genv. + +(** Looking up instructions in a code sequence by position. *) + +Fixpoint find_instr (pos: Z) (c: code) {struct c} : option instruction := + match c with + | nil => None + | i :: il => if zeq pos 0 then Some i else find_instr (pos - 1) il + end. + +(** Position corresponding to a label *) + +Definition is_label (lbl: label) (instr: instruction) : bool := + match instr with + | Plabel lbl' => if peq lbl lbl' then true else false + | _ => false + end. + +Lemma is_label_correct: + forall lbl instr, + if is_label lbl instr then instr = Plabel lbl else instr <> Plabel lbl. +Proof. + intros. destruct instr; simpl; try discriminate. destruct (peq lbl lbl0); congruence. +Qed. + +Fixpoint label_pos (lbl: label) (pos: Z) (c: code) {struct c} : option Z := + match c with + | nil => None + | instr :: c' => + if is_label lbl instr then Some (pos + 1) else label_pos lbl (pos + 1) c' + end. + +(** The semantics is purely small-step and defined as a function + from the current state (a register set + a memory state) + to either [Next rs' m'] where [rs'] and [m'] are the updated register + set and memory state after execution of the instruction at [rs#PC], + or [Stuck] if the processor is stuck. *) + +Inductive outcome: Type := + | Next: regset -> mem -> outcome + | Stuck: outcome. + +(** Manipulations over the [PC] register: continuing with the next + instruction ([nextinstr]) or branching to a label ([goto_label]). *) + +Definition nextinstr (rs: regset) := + rs#PC <- (Val.offset_ptr rs#PC Ptrofs.one). + +Definition goto_label (f: function) (lbl: label) (rs: regset) (m: mem) := + match label_pos lbl 0 (fn_code f) with + | None => Stuck + | Some pos => + match rs#PC with + | Vptr b ofs => Next (rs#PC <- (Vptr b (Ptrofs.repr pos))) m + | _ => Stuck + end + end. + +(** Testing a condition *) + +Definition eval_testcond (c: testcond) (rs: regset) : option bool := + match c with + | TCeq => (**r equal *) + match rs#CZ with + | Vint n => Some (Int.eq n Int.one) + | _ => None + end + | TCne => (**r not equal *) + match rs#CZ with + | Vint n => Some (Int.eq n Int.zero) + | _ => None + end + | TClo => (**r unsigned less than *) + match rs#CC with + | Vint n => Some (Int.eq n Int.zero) + | _ => None + end + | TCls => (**r unsigned less or equal *) + match rs#CC, rs#CZ with + | Vint c, Vint z => Some (Int.eq c Int.zero || Int.eq z Int.one) + | _, _ => None + end + | TChs => (**r unsigned greater or equal *) + match rs#CC with + | Vint n => Some (Int.eq n Int.one) + | _ => None + end + | TChi => (**r unsigned greater *) + match rs#CC, rs#CZ with + | Vint c, Vint z => Some (Int.eq c Int.one && Int.eq z Int.zero) + | _, _ => None + end + | TClt => (**r signed less than *) + match rs#CV, rs#CN with + | Vint o, Vint s => Some (Int.eq (Int.xor o s) Int.one) + | _, _ => None + end + | TCle => (**r signed less or equal *) + match rs#CV, rs#CN, rs#CZ with + | Vint o, Vint s, Vint z => Some (Int.eq (Int.xor o s) Int.one || Int.eq z Int.one) + | _, _, _ => None + end + | TCge => (**r signed greater or equal *) + match rs#CV, rs#CN with + | Vint o, Vint s => Some (Int.eq (Int.xor o s) Int.zero) + | _, _ => None + end + | TCgt => (**r signed greater *) + match rs#CV, rs#CN, rs#CZ with + | Vint o, Vint s, Vint z => Some (Int.eq (Int.xor o s) Int.zero && Int.eq z Int.zero) + | _, _, _ => None + end + | TCpl => (**r positive *) + match rs#CN with + | Vint n => Some (Int.eq n Int.zero) + | _ => None + end + | TCmi => (**r negative *) + match rs#CN with + | Vint n => Some (Int.eq n Int.one) + | _ => None + end + end. + +(** Integer "is zero?" test *) + +Definition eval_testzero (sz: isize) (v: val) (m: mem): option bool := + match sz with + | W => Val.cmpu_bool (Mem.valid_pointer m) Ceq v (Vint Int.zero) + | X => Val.cmplu_bool (Mem.valid_pointer m) Ceq v (Vlong Int64.zero) + end. + +(** Integer "bit is set?" test *) + +Definition eval_testbit (sz: isize) (v: val) (n: int): option bool := + match sz with + | W => Val.cmp_bool Cne (Val.and v (Vint (Int.shl Int.one n))) (Vint Int.zero) + | X => Val.cmpl_bool Cne (Val.andl v (Vlong (Int64.shl' Int64.one n))) (Vlong Int64.zero) + end. + +(** Evaluating an addressing mode *) + +Definition eval_addressing (a: addressing) (rs: regset): val := + match a with + | ADimm base n => Val.addl rs#base (Vlong n) + | ADreg base r => Val.addl rs#base rs#r + | ADlsl base r n => Val.addl rs#base (Val.shll rs#r (Vint n)) + | ADsxt base r n => Val.addl rs#base (Val.shll (Val.longofint rs#r) (Vint n)) + | ADuxt base r n => Val.addl rs#base (Val.shll (Val.longofintu rs#r) (Vint n)) + | ADadr base id ofs => Val.addl rs#base (symbol_low ge id ofs) + | ADpostincr base n => Vundef (* not modeled yet *) + end. + +(** Auxiliaries for memory accesses *) + +Definition exec_load (chunk: memory_chunk) (transf: val -> val) + (a: addressing) (r: preg) (rs: regset) (m: mem) := + match Mem.loadv chunk m (eval_addressing a rs) with + | None => Stuck + | Some v => Next (nextinstr (rs#r <- (transf v))) m + end. + +Definition exec_store (chunk: memory_chunk) + (a: addressing) (v: val) + (rs: regset) (m: mem) := + match Mem.storev chunk m (eval_addressing a rs) v with + | None => Stuck + | Some m' => Next (nextinstr rs) m' + end. + +(** Comparisons *) + +Definition compare_int (rs: regset) (v1 v2: val) (m: mem) := + rs#CN <- (Val.negative (Val.sub v1 v2)) + #CZ <- (Val.cmpu (Mem.valid_pointer m) Ceq v1 v2) + #CC <- (Val.cmpu (Mem.valid_pointer m) Cge v1 v2) + #CV <- (Val.sub_overflow v1 v2). + +Definition compare_long (rs: regset) (v1 v2: val) (m: mem) := + rs#CN <- (Val.negativel (Val.subl v1 v2)) + #CZ <- (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Ceq v1 v2)) + #CC <- (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Cge v1 v2)) + #CV <- (Val.subl_overflow v1 v2). + +(** Semantics of [fcmp] instructions: +<< +== N=0 Z=1 C=1 V=0 +< N=1 Z=0 C=0 V=0 +> N=0 Z=0 C=1 V=0 +unord N=0 Z=0 C=1 V=1 +>> +*) + +Definition compare_float (rs: regset) (v1 v2: val) := + match v1, v2 with + | Vfloat f1, Vfloat f2 => + rs#CN <- (Val.of_bool (Float.cmp Clt f1 f2)) + #CZ <- (Val.of_bool (Float.cmp Ceq f1 f2)) + #CC <- (Val.of_bool (negb (Float.cmp Clt f1 f2))) + #CV <- (Val.of_bool (negb (Float.ordered f1 f2))) + | _, _ => + rs#CN <- Vundef + #CZ <- Vundef + #CC <- Vundef + #CV <- Vundef + end. + +Definition compare_single (rs: regset) (v1 v2: val) := + match v1, v2 with + | Vsingle f1, Vsingle f2 => + rs#CN <- (Val.of_bool (Float32.cmp Clt f1 f2)) + #CZ <- (Val.of_bool (Float32.cmp Ceq f1 f2)) + #CC <- (Val.of_bool (negb (Float32.cmp Clt f1 f2))) + #CV <- (Val.of_bool (negb (Float32.ordered f1 f2))) + | _, _ => + rs#CN <- Vundef + #CZ <- Vundef + #CC <- Vundef + #CV <- Vundef + end. + +(** Insertion of bits into an integer *) + +Definition insert_in_int (x: val) (y: Z) (pos: Z) (len: Z) : val := + match x with + | Vint n => Vint (Int.repr (Zinsert (Int.unsigned n) y pos len)) + | _ => Vundef + end. + +Definition insert_in_long (x: val) (y: Z) (pos: Z) (len: Z) : val := + match x with + | Vlong n => Vlong (Int64.repr (Zinsert (Int64.unsigned n) y pos len)) + | _ => Vundef + end. + +(** Evaluation of shifted operands *) + +Definition eval_shift_op_int (v: val) (s: shift_op): val := + match s with + | SOnone => v + | SOlsl n => Val.shl v (Vint n) + | SOlsr n => Val.shru v (Vint n) + | SOasr n => Val.shr v (Vint n) + | SOror n => Val.ror v (Vint n) + end. + +Definition eval_shift_op_long (v: val) (s: shift_op): val := + match s with + | SOnone => v + | SOlsl n => Val.shll v (Vint n) + | SOlsr n => Val.shrlu v (Vint n) + | SOasr n => Val.shrl v (Vint n) + | SOror n => Val.rorl v (Vint n) + end. + +(** Evaluation of sign- or zero- extended operands *) + +Definition eval_extend (v: val) (x: extend_op): val := + match x with + | EOsxtb n => Val.shll (Val.longofint (Val.sign_ext 8 v)) (Vint n) + | EOsxth n => Val.shll (Val.longofint (Val.sign_ext 16 v)) (Vint n) + | EOsxtw n => Val.shll (Val.longofint v) (Vint n) + | EOuxtb n => Val.shll (Val.longofintu (Val.zero_ext 8 v)) (Vint n) + | EOuxth n => Val.shll (Val.longofintu (Val.zero_ext 16 v)) (Vint n) + | EOuxtw n => Val.shll (Val.longofintu v) (Vint n) + | EOuxtx n => Val.shll v (Vint n) + end. + +(** Bit-level conversion from integers to FP numbers *) + +Definition float32_of_bits (v: val): val := + match v with + | Vint n => Vsingle (Float32.of_bits n) + | _ => Vundef + end. + +Definition float64_of_bits (v: val): val := + match v with + | Vlong n => Vfloat (Float.of_bits n) + | _ => Vundef + end. + +(** Execution of a single instruction [i] in initial state + [rs] and [m]. Return updated state. For instructions + that correspond to actual AArch64 instructions, the cases are + straightforward transliterations of the informal descriptions + given in the ARMv8 reference manuals. For pseudo-instructions, + refer to the informal descriptions given above. + + Note that we set to [Vundef] the registers used as temporaries by + the expansions of the pseudo-instructions, so that the code we + generate cannot use those registers to hold values that must + survive the execution of the pseudo-instruction. +*) + +Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : outcome := + match i with + (** Branches *) + | Pb lbl => + goto_label f lbl rs m + | Pbc cond lbl => + match eval_testcond cond rs with + | Some true => goto_label f lbl rs m + | Some false => Next (nextinstr rs) m + | None => Stuck + end + | Pbl id sg => + Next (rs#RA <- (Val.offset_ptr rs#PC Ptrofs.one) #PC <- (Genv.symbol_address ge id Ptrofs.zero)) m + | Pbs id sg => + Next (rs#PC <- (Genv.symbol_address ge id Ptrofs.zero)) m + | Pblr r sg => + Next (rs#RA <- (Val.offset_ptr rs#PC Ptrofs.one) #PC <- (rs#r)) m + | Pbr r sg => + Next (rs#PC <- (rs#r)) m + | Pret r => + Next (rs#PC <- (rs#r)) m + | Pcbnz sz r lbl => + match eval_testzero sz rs#r m with + | Some true => Next (nextinstr rs) m + | Some false => goto_label f lbl rs m + | None => Stuck + end + | Pcbz sz r lbl => + match eval_testzero sz rs#r m with + | Some true => goto_label f lbl rs m + | Some false => Next (nextinstr rs) m + | None => Stuck + end + | Ptbnz sz r n lbl => + match eval_testbit sz rs#r n with + | Some true => goto_label f lbl rs m + | Some false => Next (nextinstr rs) m + | None => Stuck + end + | Ptbz sz r n lbl => + match eval_testbit sz rs#r n with + | Some true => Next (nextinstr rs) m + | Some false => goto_label f lbl rs m + | None => Stuck + end + (** Memory loads and stores *) + | Pldrw rd a => + exec_load Mint32 (fun v => v) a rd rs m + | Pldrw_a rd a => + exec_load Many32 (fun v => v) a rd rs m + | Pldrx rd a => + exec_load Mint64 (fun v => v) a rd rs m + | Pldrx_a rd a => + exec_load Many64 (fun v => v) a rd rs m + | Pldrb W rd a => + exec_load Mint8unsigned (fun v => v) a rd rs m + | Pldrb X rd a => + exec_load Mint8unsigned Val.longofintu a rd rs m + | Pldrsb W rd a => + exec_load Mint8signed (fun v => v) a rd rs m + | Pldrsb X rd a => + exec_load Mint8signed Val.longofint a rd rs m + | Pldrh W rd a => + exec_load Mint16unsigned (fun v => v) a rd rs m + | Pldrh X rd a => + exec_load Mint16unsigned Val.longofintu a rd rs m + | Pldrsh W rd a => + exec_load Mint16signed (fun v => v) a rd rs m + | Pldrsh X rd a => + exec_load Mint16signed Val.longofint a rd rs m + | Pldrzw rd a => + exec_load Mint32 Val.longofintu a rd rs m + | Pldrsw rd a => + exec_load Mint32 Val.longofint a rd rs m + | Pstrw r a => + exec_store Mint32 a rs#r rs m + | Pstrw_a r a => + exec_store Many32 a rs#r rs m + | Pstrx r a => + exec_store Mint64 a rs#r rs m + | Pstrx_a r a => + exec_store Many64 a rs#r rs m + | Pstrb r a => + exec_store Mint8unsigned a rs#r rs m + | Pstrh r a => + exec_store Mint16unsigned a rs#r rs m + (** Integer arithmetic, immediate *) + | Paddimm W rd r1 n => + Next (nextinstr (rs#rd <- (Val.add rs#r1 (Vint (Int.repr n))))) m + | Paddimm X rd r1 n => + Next (nextinstr (rs#rd <- (Val.addl rs#r1 (Vlong (Int64.repr n))))) m + | Psubimm W rd r1 n => + Next (nextinstr (rs#rd <- (Val.sub rs#r1 (Vint (Int.repr n))))) m + | Psubimm X rd r1 n => + Next (nextinstr (rs#rd <- (Val.subl rs#r1 (Vlong (Int64.repr n))))) m + | Pcmpimm W r1 n => + Next (nextinstr (compare_int rs rs#r1 (Vint (Int.repr n)) m)) m + | Pcmpimm X r1 n => + Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.repr n)) m)) m + | Pcmnimm W r1 n => + Next (nextinstr (compare_int rs rs#r1 (Vint (Int.neg (Int.repr n))) m)) m + | Pcmnimm X r1 n => + Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.neg (Int64.repr n))) m)) m + (** Move integer register *) + | Pmov rd r1 => + Next (nextinstr (rs#rd <- (rs#r1))) m + (** Logical, immediate *) + | Pandimm W rd r1 n => + Next (nextinstr (rs#rd <- (Val.and rs##r1 (Vint (Int.repr n))))) m + | Pandimm X rd r1 n => + Next (nextinstr (rs#rd <- (Val.andl rs###r1 (Vlong (Int64.repr n))))) m + | Peorimm W rd r1 n => + Next (nextinstr (rs#rd <- (Val.xor rs##r1 (Vint (Int.repr n))))) m + | Peorimm X rd r1 n => + Next (nextinstr (rs#rd <- (Val.xorl rs###r1 (Vlong (Int64.repr n))))) m + | Porrimm W rd r1 n => + Next (nextinstr (rs#rd <- (Val.or rs##r1 (Vint (Int.repr n))))) m + | Porrimm X rd r1 n => + Next (nextinstr (rs#rd <- (Val.orl rs###r1 (Vlong (Int64.repr n))))) m + | Ptstimm W r1 n => + Next (nextinstr (compare_int rs (Val.and rs#r1 (Vint (Int.repr n))) (Vint Int.zero) m)) m + | Ptstimm X r1 n => + Next (nextinstr (compare_long rs (Val.andl rs#r1 (Vlong (Int64.repr n))) (Vlong Int64.zero) m)) m + (** Move wide immediate *) + | Pmovz W rd n pos => + Next (nextinstr (rs#rd <- (Vint (Int.repr (Z.shiftl n pos))))) m + | Pmovz X rd n pos => + Next (nextinstr (rs#rd <- (Vlong (Int64.repr (Z.shiftl n pos))))) m + | Pmovn W rd n pos => + Next (nextinstr (rs#rd <- (Vint (Int.repr (Z.lnot (Z.shiftl n pos)))))) m + | Pmovn X rd n pos => + Next (nextinstr (rs#rd <- (Vlong (Int64.repr (Z.lnot (Z.shiftl n pos)))))) m + | Pmovk W rd n pos => + Next (nextinstr (rs#rd <- (insert_in_int rs#rd n pos 16))) m + | Pmovk X rd n pos => + Next (nextinstr (rs#rd <- (insert_in_long rs#rd n pos 16))) m + (** PC-relative addressing *) + | Padrp rd id ofs => + Next (nextinstr (rs#rd <- (symbol_high ge id ofs))) m + | Paddadr rd r1 id ofs => + Next (nextinstr (rs#rd <- (Val.addl rs#r1 (symbol_low ge id ofs)))) m + (** Bit-field operations *) + | Psbfiz W rd r1 r s => + Next (nextinstr (rs#rd <- (Val.shl (Val.sign_ext s rs#r1) (Vint r)))) m + | Psbfiz X rd r1 r s => + Next (nextinstr (rs#rd <- (Val.shll (Val.sign_ext_l s rs#r1) (Vint r)))) m + | Psbfx W rd r1 r s => + Next (nextinstr (rs#rd <- (Val.sign_ext s (Val.shr rs#r1 (Vint r))))) m + | Psbfx X rd r1 r s => + Next (nextinstr (rs#rd <- (Val.sign_ext_l s (Val.shrl rs#r1 (Vint r))))) m + | Pubfiz W rd r1 r s => + Next (nextinstr (rs#rd <- (Val.shl (Val.zero_ext s rs#r1) (Vint r)))) m + | Pubfiz X rd r1 r s => + Next (nextinstr (rs#rd <- (Val.shll (Val.zero_ext_l s rs#r1) (Vint r)))) m + | Pubfx W rd r1 r s => + Next (nextinstr (rs#rd <- (Val.zero_ext s (Val.shru rs#r1 (Vint r))))) m + | Pubfx X rd r1 r s => + Next (nextinstr (rs#rd <- (Val.zero_ext_l s (Val.shrlu rs#r1 (Vint r))))) m + (** Integer arithmetic, shifted register *) + | Padd W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.add rs##r1 (eval_shift_op_int rs#r2 s)))) m + | Padd X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.addl rs###r1 (eval_shift_op_long rs#r2 s)))) m + | Psub W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.sub rs##r1 (eval_shift_op_int rs#r2 s)))) m + | Psub X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.subl rs###r1 (eval_shift_op_long rs#r2 s)))) m + | Pcmp W r1 r2 s => + Next (nextinstr (compare_int rs rs##r1 (eval_shift_op_int rs#r2 s) m)) m + | Pcmp X r1 r2 s => + Next (nextinstr (compare_long rs rs###r1 (eval_shift_op_long rs#r2 s) m)) m + | Pcmn W r1 r2 s => + Next (nextinstr (compare_int rs rs##r1 (Val.neg (eval_shift_op_int rs#r2 s)) m)) m + | Pcmn X r1 r2 s => + Next (nextinstr (compare_long rs rs###r1 (Val.negl (eval_shift_op_long rs#r2 s)) m)) m + (** Integer arithmetic, extending register *) + | Paddext rd r1 r2 x => + Next (nextinstr (rs#rd <- (Val.addl rs#r1 (eval_extend rs#r2 x)))) m + | Psubext rd r1 r2 x => + Next (nextinstr (rs#rd <- (Val.subl rs#r1 (eval_extend rs#r2 x)))) m + | Pcmpext r1 r2 x => + Next (nextinstr (compare_long rs rs#r1 (eval_extend rs#r2 x) m)) m + | Pcmnext r1 r2 x => + Next (nextinstr (compare_long rs rs#r1 (Val.negl (eval_extend rs#r2 x)) m)) m + (** Logical, shifted register *) + | Pand W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.and rs##r1 (eval_shift_op_int rs#r2 s)))) m + | Pand X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.andl rs###r1 (eval_shift_op_long rs#r2 s)))) m + | Pbic W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.and rs##r1 (Val.notint (eval_shift_op_int rs#r2 s))))) m + | Pbic X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.andl rs###r1 (Val.notl (eval_shift_op_long rs#r2 s))))) m + | Peon W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.xor rs##r1 (Val.notint (eval_shift_op_int rs#r2 s))))) m + | Peon X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.xorl rs###r1 (Val.notl (eval_shift_op_long rs#r2 s))))) m + | Peor W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.xor rs##r1 (eval_shift_op_int rs#r2 s)))) m + | Peor X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.xorl rs###r1 (eval_shift_op_long rs#r2 s)))) m + | Porr W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.or rs##r1 (eval_shift_op_int rs#r2 s)))) m + | Porr X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.orl rs###r1 (eval_shift_op_long rs#r2 s)))) m + | Porn W rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.or rs##r1 (Val.notint (eval_shift_op_int rs#r2 s))))) m + | Porn X rd r1 r2 s => + Next (nextinstr (rs#rd <- (Val.orl rs###r1 (Val.notl (eval_shift_op_long rs#r2 s))))) m + | Ptst W r1 r2 s => + Next (nextinstr (compare_int rs (Val.and rs##r1 (eval_shift_op_int rs#r2 s)) (Vint Int.zero) m)) m + | Ptst X r1 r2 s => + Next (nextinstr (compare_long rs (Val.andl rs###r1 (eval_shift_op_long rs#r2 s)) (Vlong Int64.zero) m)) m + (** Variable shifts *) + | Pasrv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shr rs#r1 rs#r2))) m + | Pasrv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shrl rs#r1 rs#r2))) m + | Plslv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shl rs#r1 rs#r2))) m + | Plslv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shll rs#r1 rs#r2))) m + | Plsrv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shru rs#r1 rs#r2))) m + | Plsrv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.shrlu rs#r1 rs#r2))) m + | Prorv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.ror rs#r1 rs#r2))) m + | Prorv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.rorl rs#r1 rs#r2))) m + (** Conditional data processing *) + | Pcsel rd r1 r2 cond => + let v := + match eval_testcond cond rs with + | Some true => rs#r1 + | Some false => rs#r2 + | None => Vundef + end in + Next (nextinstr (rs#rd <- v)) m + | Pcset rd cond => + let v := + match eval_testcond cond rs with + | Some true => Vint Int.one + | Some false => Vint Int.zero + | None => Vundef + end in + Next (nextinstr (rs#rd <- v)) m + (** Integer multiply/divide *) + | Pmadd W rd r1 r2 r3 => + Next (nextinstr (rs#rd <- (Val.add rs##r3 (Val.mul rs#r1 rs#r2)))) m + | Pmadd X rd r1 r2 r3 => + Next (nextinstr (rs#rd <- (Val.addl rs###r3 (Val.mull rs#r1 rs#r2)))) m + | Pmsub W rd r1 r2 r3 => + Next (nextinstr (rs#rd <- (Val.sub rs##r3 (Val.mul rs#r1 rs#r2)))) m + | Pmsub X rd r1 r2 r3 => + Next (nextinstr (rs#rd <- (Val.subl rs###r3 (Val.mull rs#r1 rs#r2)))) m + | Psmulh rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.mullhs rs#r1 rs#r2))) m + | Pumulh rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.mullhu rs#r1 rs#r2))) m + | Psdiv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.divs rs#r1 rs#r2)))) m + | Psdiv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.divls rs#r1 rs#r2)))) m + | Pudiv W rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.divu rs#r1 rs#r2)))) m + | Pudiv X rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.divlu rs#r1 rs#r2)))) m + (** Floating-point loads and stores *) + | Pldrs rd a => + exec_load Mfloat32 (fun v => v) a rd rs m + | Pldrd rd a => + exec_load Mfloat64 (fun v => v) a rd rs m + | Pldrd_a rd a => + exec_load Many64 (fun v => v) a rd rs m + | Pstrs r a => + exec_store Mfloat32 a rs#r rs m + | Pstrd r a => + exec_store Mfloat64 a rs#r rs m + | Pstrd_a r a => + exec_store Many64 a rs#r rs m + (** Floating-point move *) + | Pfmov rd r1 => + Next (nextinstr (rs#rd <- (rs#r1))) m + | Pfmovimms rd f => + Next (nextinstr (rs#rd <- (Vsingle f))) m + | Pfmovimmd rd f => + Next (nextinstr (rs#rd <- (Vfloat f))) m + | Pfmovi S rd r1 => + Next (nextinstr (rs#rd <- (float32_of_bits rs##r1))) m + | Pfmovi D rd r1 => + Next (nextinstr (rs#rd <- (float64_of_bits rs###r1))) m + (** Floating-point conversions *) + | Pfcvtds rd r1 => + Next (nextinstr (rs#rd <- (Val.floatofsingle rs#r1))) m + | Pfcvtsd rd r1 => + Next (nextinstr (rs#rd <- (Val.singleoffloat rs#r1))) m + | Pfcvtzs W S rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.intofsingle rs#r1)))) m + | Pfcvtzs W D rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.intoffloat rs#r1)))) m + | Pfcvtzs X S rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.longofsingle rs#r1)))) m + | Pfcvtzs X D rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.longoffloat rs#r1)))) m + | Pfcvtzu W S rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.intuofsingle rs#r1)))) m + | Pfcvtzu W D rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.intuoffloat rs#r1)))) m + | Pfcvtzu X S rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.longuofsingle rs#r1)))) m + | Pfcvtzu X D rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.longuoffloat rs#r1)))) m + | Pscvtf S W rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.singleofint rs#r1)))) m + | Pscvtf D W rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.floatofint rs#r1)))) m + | Pscvtf S X rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.singleoflong rs#r1)))) m + | Pscvtf D X rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.floatoflong rs#r1)))) m + | Pucvtf S W rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.singleofintu rs#r1)))) m + | Pucvtf D W rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.floatofintu rs#r1)))) m + | Pucvtf S X rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.singleoflongu rs#r1)))) m + | Pucvtf D X rd r1 => + Next (nextinstr (rs#rd <- (Val.maketotal (Val.floatoflongu rs#r1)))) m + (** Floating-point arithmetic *) + | Pfabs S rd r1 => + Next (nextinstr (rs#rd <- (Val.absfs rs#r1))) m + | Pfabs D rd r1 => + Next (nextinstr (rs#rd <- (Val.absf rs#r1))) m + | Pfneg S rd r1 => + Next (nextinstr (rs#rd <- (Val.negfs rs#r1))) m + | Pfneg D rd r1 => + Next (nextinstr (rs#rd <- (Val.negf rs#r1))) m + | Pfadd S rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.addfs rs#r1 rs#r2))) m + | Pfadd D rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.addf rs#r1 rs#r2))) m + | Pfdiv S rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.divfs rs#r1 rs#r2))) m + | Pfdiv D rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.divf rs#r1 rs#r2))) m + | Pfmul S rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.mulfs rs#r1 rs#r2))) m + | Pfmul D rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.mulf rs#r1 rs#r2))) m + | Pfnmul S rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.negfs (Val.mulfs rs#r1 rs#r2)))) m + | Pfnmul D rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.negf (Val.mulf rs#r1 rs#r2)))) m + | Pfsub S rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.subfs rs#r1 rs#r2))) m + | Pfsub D rd r1 r2 => + Next (nextinstr (rs#rd <- (Val.subf rs#r1 rs#r2))) m + (** Floating-point comparison *) + | Pfcmp S r1 r2 => + Next (nextinstr (compare_single rs rs#r1 rs#r2)) m + | Pfcmp D r1 r2 => + Next (nextinstr (compare_float rs rs#r1 rs#r2)) m + | Pfcmp0 S r1 => + Next (nextinstr (compare_single rs rs#r1 (Vsingle Float32.zero))) m + | Pfcmp0 D r1 => + Next (nextinstr (compare_float rs rs#r1 (Vfloat Float.zero))) m + (** Floating-point conditional select *) + | Pfsel rd r1 r2 cond => + let v := + match eval_testcond cond rs with + | Some true => rs#r1 + | Some false => rs#r2 + | None => Vundef + end in + Next (nextinstr (rs#rd <- v)) m + (** Pseudo-instructions *) + | Pallocframe sz pos => + let (m1, stk) := Mem.alloc m 0 sz in + let sp := (Vptr stk Ptrofs.zero) in + match Mem.storev Mint64 m1 (Val.offset_ptr sp pos) rs#SP with + | None => Stuck + | Some m2 => Next (nextinstr (rs #X29 <- (rs#SP) #SP <- sp #X16 <- Vundef)) m2 + end + | Pfreeframe sz pos => + match Mem.loadv Mint64 m (Val.offset_ptr rs#SP pos) with + | None => Stuck + | Some v => + match rs#SP with + | Vptr stk ofs => + match Mem.free m stk 0 sz with + | None => Stuck + | Some m' => Next (nextinstr (rs#SP <- v #X16 <- Vundef)) m' + end + | _ => Stuck + end + end + | Plabel lbl => + Next (nextinstr rs) m + | Ploadsymbol rd id => + Next (nextinstr (rs#rd <- (Genv.symbol_address ge id Ptrofs.zero))) m + | Pcvtsw2x rd r1 => + Next (nextinstr (rs#rd <- (Val.longofint rs#r1))) m + | Pcvtuw2x rd r1 => + Next (nextinstr (rs#rd <- (Val.longofintu rs#r1))) m + | Pcvtx2w rd => + Next (nextinstr (rs#rd <- (Val.loword rs#rd))) m + | Pbtbl r tbl => + match (rs#X16 <- Vundef)#r with + | Vint n => + match list_nth_z tbl (Int.unsigned n) with + | None => Stuck + | Some lbl => goto_label f lbl (rs#X16 <- Vundef #X17 <- Vundef) m + end + | _ => Stuck + end + | Pbuiltin ef args res => Stuck (**r treated specially below *) + (** The following instructions and directives are not generated directly + by Asmgen, so we do not model them. *) + | Pldp _ _ _ + | Pstp _ _ _ + | Pcls _ _ _ + | Pclz _ _ _ + | Prev _ _ _ + | Prev16 _ _ _ + | Pfsqrt _ _ _ + | Pfmadd _ _ _ _ _ + | Pfmsub _ _ _ _ _ + | Pfnmadd _ _ _ _ _ + | Pfnmsub _ _ _ _ _ + | Pnop + | Pcfi_adjust _ + | Pcfi_rel_offset _ => + Stuck + end. + +(** Translation of the LTL/Linear/Mach view of machine registers + to the AArch64 view. Note that no LTL register maps to [X16], + [X18], nor [X30]. + [X18] is reserved as the platform register and never used by the + code generated by CompCert. + [X30] is used for the return address, and can also be used as temporary. + [X16] can be used as temporary. *) + +Definition preg_of (r: mreg) : preg := + match r with + | R0 => X0 | R1 => X1 | R2 => X2 | R3 => X3 + | R4 => X4 | R5 => X5 | R6 => X6 | R7 => X7 + | R8 => X8 | R9 => X9 | R10 => X10 | R11 => X11 + | R12 => X12 | R13 => X13 | R14 => X14 | R15 => X15 + | R17 => X17 | R19 => X19 + | R20 => X20 | R21 => X21 | R22 => X22 | R23 => X23 + | R24 => X24 | R25 => X25 | R26 => X26 | R27 => X27 + | R28 => X28 | R29 => X29 + | F0 => D0 | F1 => D1 | F2 => D2 | F3 => D3 + | F4 => D4 | F5 => D5 | F6 => D6 | F7 => D7 + | F8 => D8 | F9 => D9 | F10 => D10 | F11 => D11 + | F12 => D12 | F13 => D13 | F14 => D14 | F15 => D15 + | F16 => D16 | F17 => D17 | F18 => D18 | F19 => D19 + | F20 => D20 | F21 => D21 | F22 => D22 | F23 => D23 + | F24 => D24 | F25 => D25 | F26 => D26 | F27 => D27 + | F28 => D28 | F29 => D29 | F30 => D30 | F31 => D31 + end. + +(** Undefine all registers except SP and callee-save registers *) + +Definition undef_caller_save_regs (rs: regset) : regset := + fun r => + if preg_eq r SP + || In_dec preg_eq r (List.map preg_of (List.filter is_callee_save all_mregs)) + then rs r + else Vundef. + +(** Extract the values of the arguments of an external call. + We exploit the calling conventions from module [Conventions], except that + we use AArch64 registers instead of locations. *) + +Inductive extcall_arg (rs: regset) (m: mem): loc -> val -> Prop := + | extcall_arg_reg: forall r, + extcall_arg rs m (R r) (rs (preg_of r)) + | extcall_arg_stack: forall ofs ty bofs v, + bofs = Stacklayout.fe_ofs_arg + 4 * ofs -> + Mem.loadv (chunk_of_type ty) m + (Val.offset_ptr rs#SP (Ptrofs.repr bofs)) = Some v -> + extcall_arg rs m (Locations.S Outgoing ofs ty) v. + +Inductive extcall_arg_pair (rs: regset) (m: mem): rpair loc -> val -> Prop := + | extcall_arg_one: forall l v, + extcall_arg rs m l v -> + extcall_arg_pair rs m (One l) v + | extcall_arg_twolong: forall hi lo vhi vlo, + extcall_arg rs m hi vhi -> + extcall_arg rs m lo vlo -> + extcall_arg_pair rs m (Twolong hi lo) (Val.longofwords vhi vlo). + +Definition extcall_arguments + (rs: regset) (m: mem) (sg: signature) (args: list val) : Prop := + list_forall2 (extcall_arg_pair rs m) (loc_arguments sg) args. + +Definition loc_external_result (sg: signature) : rpair preg := + map_rpair preg_of (loc_result sg). + +(** Execution of the instruction at [rs#PC]. *) + +Inductive state: Type := + | State: regset -> mem -> state. + +Inductive step: state -> trace -> state -> Prop := + | exec_step_internal: + forall b ofs f i rs m rs' m', + rs PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal f) -> + find_instr (Ptrofs.unsigned ofs) f.(fn_code) = Some i -> + exec_instr f i rs m = Next rs' m' -> + step (State rs m) E0 (State rs' m') + | exec_step_builtin: + forall b ofs f ef args res rs m vargs t vres rs' m', + rs PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal f) -> + find_instr (Ptrofs.unsigned ofs) f.(fn_code) = Some (Pbuiltin ef args res) -> + eval_builtin_args ge rs rs#SP m args vargs -> + external_call ef ge vargs m t vres m' -> + rs' = nextinstr + (set_res res vres + (undef_regs (map preg_of (destroyed_by_builtin ef)) rs)) -> + step (State rs m) t (State rs' m') + | exec_step_external: + forall b ef args res rs m t rs' m', + rs PC = Vptr b Ptrofs.zero -> + Genv.find_funct_ptr ge b = Some (External ef) -> + external_call ef ge args m t res m' -> + extcall_arguments rs m (ef_sig ef) args -> + rs' = (set_pair (loc_external_result (ef_sig ef)) res (undef_caller_save_regs rs)) #PC <- (rs RA) -> + step (State rs m) t (State rs' m'). + +End RELSEM. + +(** Execution of whole programs. *) + +Inductive initial_state (p: program): state -> Prop := + | initial_state_intro: forall m0, + Genv.init_mem p = Some m0 -> + let ge := Genv.globalenv p in + let rs0 := + (Pregmap.init Vundef) + # PC <- (Genv.symbol_address ge p.(prog_main) Ptrofs.zero) + # RA <- Vnullptr + # SP <- Vnullptr in + initial_state p (State rs0 m0). + +Inductive final_state: state -> int -> Prop := + | final_state_intro: forall rs m r, + rs#PC = Vnullptr -> + rs#X0 = Vint r -> + final_state (State rs m) r. + +Definition semantics (p: program) := + Semantics step (initial_state p) final_state (Genv.globalenv p). + +(** Determinacy of the [Asm] semantics. *) + +Remark extcall_arguments_determ: + forall rs m sg args1 args2, + extcall_arguments rs m sg args1 -> extcall_arguments rs m sg args2 -> args1 = args2. +Proof. + intros until m. + assert (A: forall l v1 v2, + extcall_arg rs m l v1 -> extcall_arg rs m l v2 -> v1 = v2). + { intros. inv H; inv H0; congruence. } + assert (B: forall p v1 v2, + extcall_arg_pair rs m p v1 -> extcall_arg_pair rs m p v2 -> v1 = v2). + { intros. inv H; inv H0. + eapply A; eauto. + f_equal; eapply A; eauto. } + assert (C: forall ll vl1, list_forall2 (extcall_arg_pair rs m) ll vl1 -> + forall vl2, list_forall2 (extcall_arg_pair rs m) ll vl2 -> vl1 = vl2). + { + induction 1; intros vl2 EA; inv EA. + auto. + f_equal; eauto. } + intros. eapply C; eauto. +Qed. + +Lemma semantics_determinate: forall p, determinate (semantics p). +Proof. +Ltac Equalities := + match goal with + | [ H1: ?a = ?b, H2: ?a = ?c |- _ ] => + rewrite H1 in H2; inv H2; Equalities + | _ => idtac + end. + intros; constructor; simpl; intros. +- (* determ *) + inv H; inv H0; Equalities. + split. constructor. auto. + discriminate. + discriminate. + assert (vargs0 = vargs) by (eapply eval_builtin_args_determ; eauto). subst vargs0. + exploit external_call_determ. eexact H5. eexact H11. intros [A B]. + split. auto. intros. destruct B; auto. subst. auto. + assert (args0 = args) by (eapply extcall_arguments_determ; eauto). subst args0. + exploit external_call_determ. eexact H3. eexact H8. intros [A B]. + split. auto. intros. destruct B; auto. subst. auto. +- (* trace length *) + red; intros. inv H; simpl. + omega. + eapply external_call_trace_length; eauto. + eapply external_call_trace_length; eauto. +- (* initial states *) + inv H; inv H0. f_equal. congruence. +- (* final no step *) + inv H. red; intros; red; intros. inv H; rewrite H0 in *; discriminate. +- (* final states *) + inv H; inv H0. congruence. +Qed. + +(** Classification functions for processor registers (used in Asmgenproof). *) + +Definition data_preg (r: preg) : bool := + match r with + | IR X16 => false + | IR X30 => false + | IR _ => true + | FR _ => true + | CR _ => false + | SP => true + | PC => false + end. diff --git a/aarch64/AsmToJSON.ml b/aarch64/AsmToJSON.ml new file mode 100644 index 00000000..b7cfc152 --- /dev/null +++ b/aarch64/AsmToJSON.ml @@ -0,0 +1,24 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(* Functions to serialize AArch64 Asm to JSON *) + +(* Dummy function *) + +let destination: string option ref = ref None + +let sdump_folder = ref "" + +let print_if prog sourcename = + () + +let pp_mnemonics pp = () diff --git a/aarch64/Asmexpand.ml b/aarch64/Asmexpand.ml new file mode 100644 index 00000000..71bd0042 --- /dev/null +++ b/aarch64/Asmexpand.ml @@ -0,0 +1,436 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(* Expanding built-ins and some pseudo-instructions by rewriting + of the AArch64 assembly code. *) + +open Asm +open Asmexpandaux +open AST +open Camlcoq +module Ptrofs = Integers.Ptrofs + +exception Error of string + +(* Useful constants *) + +let _0 = Z.zero +let _1 = Z.one +let _2 = Z.of_sint 2 +let _4 = Z.of_sint 4 +let _8 = Z.of_sint 8 +let _16 = Z.of_sint 16 +let _m1 = Z.of_sint (-1) + +(* Emit instruction sequences that set or offset a register by a constant. *) + +let expand_loadimm32 (dst: ireg) n = + List.iter emit (Asmgen.loadimm32 dst n []) + +let expand_addimm64 (dst: iregsp) (src: iregsp) n = + List.iter emit (Asmgen.addimm64 dst src n []) + +let expand_storeptr (src: ireg) (base: iregsp) ofs = + List.iter emit (Asmgen.storeptr src base ofs []) + +(* Handling of varargs *) + +(* Determine the number of int registers, FP registers, and stack locations + used to pass the fixed parameters. *) + +let rec next_arg_locations ir fr stk = function + | [] -> + (ir, fr, stk) + | (Tint | Tlong | Tany32 | Tany64) :: l -> + if ir < 8 + then next_arg_locations (ir + 1) fr stk l + else next_arg_locations ir fr (stk + 8) l + | (Tfloat | Tsingle) :: l -> + if fr < 8 + then next_arg_locations ir (fr + 1) stk l + else next_arg_locations ir fr (stk + 8) l + +(* Allocate memory on the stack and use it to save the registers + used for parameter passing. As an optimization, do not save + the registers used to pass the fixed parameters. *) + +let int_param_regs = [| X0; X1; X2; X3; X4; X5; X6; X7 |] +let float_param_regs = [| D0; D1; D2; D3; D4; D5; D6; D7 |] +let size_save_register_area = 8*8 + 8*16 + +let save_parameter_registers ir fr = + emit (Psubimm(X, XSP, XSP, Z.of_uint size_save_register_area)); + let i = ref ir in + while !i < 8 do + let pos = 8*16 + !i*8 in + if !i land 1 = 0 then begin + emit (Pstp(int_param_regs.(!i), int_param_regs.(!i + 1), + ADimm(XSP, Z.of_uint pos))); + i := !i + 2 + end else begin + emit (Pstrx(int_param_regs.(!i), ADimm(XSP, Z.of_uint pos))); + i := !i + 1 + end + done; + for i = fr to 7 do + let pos = i*16 in + emit (Pstrd(float_param_regs.(i), ADimm(XSP, Z.of_uint pos))) + done + +(* Initialize a va_list as per va_start. + Register r points to the following struct: + + typedef struct __va_list { + void *__stack; // next stack parameter + void *__gr_top; // top of the save area for int regs + void *__vr_top; // top of the save area for float regs + int__gr_offs; // offset from gr_top to next int reg + int__vr_offs; // offset from gr_top to next FP reg + } +*) + +let current_function_stacksize = ref 0L + +let expand_builtin_va_start r = + if not (is_current_function_variadic ()) then + invalid_arg "Fatal error: va_start used in non-vararg function"; + let (ir, fr, stk) = + next_arg_locations 0 0 0 (get_current_function_args ()) in + let stack_ofs = Int64.(add !current_function_stacksize (of_int stk)) + and gr_top_ofs = !current_function_stacksize + and vr_top_ofs = Int64.(sub !current_function_stacksize 64L) + and gr_offs = - ((8 - ir) * 8) + and vr_offs = - ((8 - fr) * 16) in + (* va->__stack = sp + stack_ofs *) + expand_addimm64 (RR1 X16) XSP (coqint_of_camlint64 stack_ofs); + emit (Pstrx(X16, ADimm(RR1 r, coqint_of_camlint64 0L))); + (* va->__gr_top = sp + gr_top_ofs *) + if gr_top_ofs <> stack_ofs then + expand_addimm64 (RR1 X16) XSP (coqint_of_camlint64 gr_top_ofs); + emit (Pstrx(X16, ADimm(RR1 r, coqint_of_camlint64 8L))); + (* va->__vr_top = sp + vr_top_ofs *) + expand_addimm64 (RR1 X16) XSP (coqint_of_camlint64 vr_top_ofs); + emit (Pstrx(X16, ADimm(RR1 r, coqint_of_camlint64 16L))); + (* va->__gr_offs = gr_offs *) + expand_loadimm32 X16 (coqint_of_camlint (Int32.of_int gr_offs)); + emit (Pstrw(X16, ADimm(RR1 r, coqint_of_camlint64 24L))); + (* va->__vr_offs = vr_offs *) + expand_loadimm32 X16 (coqint_of_camlint (Int32.of_int vr_offs)); + emit (Pstrw(X16, ADimm(RR1 r, coqint_of_camlint64 28L))) + +(* Handling of annotations *) + +let expand_annot_val kind txt targ args res = + emit (Pbuiltin (EF_annot(kind,txt,[targ]), args, BR_none)); + match args, res with + | [BA(IR src)], BR(IR dst) -> + if dst <> src then emit (Pmov (RR1 dst, RR1 src)) + | [BA(FR src)], BR(FR dst) -> + if dst <> src then emit (Pfmov (dst, src)) + | _, _ -> + raise (Error "ill-formed __builtin_annot_val") + +(* Handling of memcpy *) + +(* We assume unaligned memory accesses are efficient. Hence we use + memory accesses as wide as we can, up to 16 bytes. + Temporary registers used: x15 x16 x17 x29 x30. *) + +let offset_in_range ofs = + let ofs = Z.to_int64 ofs in 0L <= ofs && ofs < 0x1000L + +let memcpy_small_arg sz arg tmp = + match arg with + | BA (IR r) -> + (RR1 r, _0) + | BA_addrstack ofs -> + if offset_in_range ofs + && offset_in_range (Ptrofs.add ofs (Ptrofs.repr (Z.of_uint sz))) + then (XSP, ofs) + else begin expand_addimm64 (RR1 tmp) XSP ofs; (RR1 tmp, _0) end + | _ -> + assert false + +let expand_builtin_memcpy_small sz al src dst = + let (tsrc, tdst) = + if dst <> BA (IR X17) then (X17, X29) else (X29, X17) in + let (rsrc, osrc) = memcpy_small_arg sz src tsrc in + let (rdst, odst) = memcpy_small_arg sz dst tdst in + let rec copy osrc odst sz = + if sz >= 16 then begin + emit (Pldp(X16, X30, ADimm(rsrc, osrc))); + emit (Pstp(X16, X30, ADimm(rdst, odst))); + copy (Ptrofs.add osrc _16) (Ptrofs.add odst _16) (sz - 16) + end + else if sz >= 8 then begin + emit (Pldrx(X16, ADimm(rsrc, osrc))); + emit (Pstrx(X16, ADimm(rdst, odst))); + copy (Ptrofs.add osrc _8) (Ptrofs.add odst _8) (sz - 8) + end + else if sz >= 4 then begin + emit (Pldrw(X16, ADimm(rsrc, osrc))); + emit (Pstrw(X16, ADimm(rdst, odst))); + copy (Ptrofs.add osrc _4) (Ptrofs.add odst _4) (sz - 4) + end + else if sz >= 2 then begin + emit (Pldrh(W, X16, ADimm(rsrc, osrc))); + emit (Pstrh(X16, ADimm(rdst, odst))); + copy (Ptrofs.add osrc _2) (Ptrofs.add odst _2) (sz - 2) + end + else if sz >= 1 then begin + emit (Pldrb(W, X16, ADimm(rsrc, osrc))); + emit (Pstrb(X16, ADimm(rdst, odst))); + copy (Ptrofs.add osrc _1) (Ptrofs.add odst _1) (sz - 1) + end + in copy osrc odst sz + +let memcpy_big_arg arg tmp = + match arg with + | BA (IR r) -> emit (Pmov(RR1 tmp, RR1 r)) + | BA_addrstack ofs -> expand_addimm64 (RR1 tmp) XSP ofs + | _ -> assert false + +let expand_builtin_memcpy_big sz al src dst = + assert (sz >= 16); + memcpy_big_arg src X30; + memcpy_big_arg dst X29; + let lbl = new_label () in + expand_loadimm32 X15 (Z.of_uint (sz / 16)); + emit (Plabel lbl); + emit (Pldp(X16, X17, ADpostincr(RR1 X30, _16))); + emit (Pstp(X16, X17, ADpostincr(RR1 X29, _16))); + emit (Psubimm(W, RR1 X15, RR1 X15, _1)); + emit (Pcbnz(W, X15, lbl)); + if sz mod 16 >= 8 then begin + emit (Pldrx(X16, ADpostincr(RR1 X30, _8))); + emit (Pstrx(X16, ADpostincr(RR1 X29, _8))) + end; + if sz mod 8 >= 4 then begin + emit (Pldrw(X16, ADpostincr(RR1 X30, _4))); + emit (Pstrw(X16, ADpostincr(RR1 X29, _4))) + end; + if sz mod 4 >= 2 then begin + emit (Pldrh(W, X16, ADpostincr(RR1 X30, _2))); + emit (Pstrh(X16, ADpostincr(RR1 X29, _2))) + end; + if sz mod 2 >= 1 then begin + emit (Pldrb(W, X16, ADpostincr(RR1 X30, _1))); + emit (Pstrb(X16, ADpostincr(RR1 X29, _1))) + end + +let expand_builtin_memcpy sz al args = + let (dst, src) = + match args with [d; s] -> (d, s) | _ -> assert false in + if sz < 64 + then expand_builtin_memcpy_small sz al src dst + else expand_builtin_memcpy_big sz al src dst + +(* Handling of volatile reads and writes *) + +let expand_builtin_vload_common chunk base ofs res = + let addr = ADimm(base, ofs) in + match chunk, res with + | Mint8unsigned, BR(IR res) -> + emit (Pldrb(W, res, addr)) + | Mint8signed, BR(IR res) -> + emit (Pldrsb(W, res, addr)) + | Mint16unsigned, BR(IR res) -> + emit (Pldrh(W, res, addr)) + | Mint16signed, BR(IR res) -> + emit (Pldrsh(W, res, addr)) + | Mint32, BR(IR res) -> + emit (Pldrw(res, addr)) + | Mint64, BR(IR res) -> + emit (Pldrx(res, addr)) + | Mfloat32, BR(FR res) -> + emit (Pldrs(res, addr)) + | Mfloat64, BR(FR res) -> + emit (Pldrd(res, addr)) + | _ -> + assert false + +let expand_builtin_vload chunk args res = + match args with + | [BA(IR addr)] -> + expand_builtin_vload_common chunk (RR1 addr) _0 res + | [BA_addrstack ofs] -> + if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then + expand_builtin_vload_common chunk XSP ofs res + else begin + expand_addimm64 (RR1 X16) XSP ofs; (* X16 <- SP + ofs *) + expand_builtin_vload_common chunk (RR1 X16) _0 res + end + | [BA_addptr(BA(IR addr), BA_long ofs)] -> + if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then + expand_builtin_vload_common chunk (RR1 addr) ofs res + else begin + expand_addimm64 (RR1 X16) (RR1 addr) ofs; (* X16 <- addr + ofs *) + expand_builtin_vload_common chunk (RR1 X16) _0 res + end + | _ -> + assert false + +let expand_builtin_vstore_common chunk base ofs src = + let addr = ADimm(base, ofs) in + match chunk, src with + | (Mint8signed | Mint8unsigned), BA(IR src) -> + emit (Pstrb(src, addr)) + | (Mint16signed | Mint16unsigned), BA(IR src) -> + emit (Pstrh(src, addr)) + | Mint32, BA(IR src) -> + emit (Pstrw(src, addr)) + | Mint64, BA(IR src) -> + emit (Pstrx(src, addr)) + | Mfloat32, BA(FR src) -> + emit (Pstrs(src, addr)) + | Mfloat64, BA(FR src) -> + emit (Pstrd(src, addr)) + | _ -> + assert false + +let expand_builtin_vstore chunk args = + match args with + | [BA(IR addr); src] -> + expand_builtin_vstore_common chunk (RR1 addr) _0 src + | [BA_addrstack ofs; src] -> + if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then + expand_builtin_vstore_common chunk XSP ofs src + else begin + expand_addimm64 (RR1 X16) XSP ofs; (* X16 <- SP + ofs *) + expand_builtin_vstore_common chunk (RR1 X16) _0 src + end + | [BA_addptr(BA(IR addr), BA_long ofs); src] -> + if offset_in_range (Z.add ofs (Memdata.size_chunk chunk)) then + expand_builtin_vstore_common chunk (RR1 addr) ofs src + else begin + expand_addimm64 (RR1 X16) (RR1 addr) ofs; (* X16 <- addr + ofs *) + expand_builtin_vstore_common chunk (RR1 X16) _0 src + end + | _ -> + assert false + +(* Handling of compiler-inlined builtins *) + +let expand_builtin_inline name args res = + match name, args, res with + (* Synchronization *) + | "__builtin_membar", [], _ -> + () + | "__builtin_nop", [], _ -> + emit Pnop + (* Byte swap *) + | ("__builtin_bswap" | "__builtin_bswap32"), [BA(IR a1)], BR(IR res) -> + emit (Prev(W, res, a1)) + | "__builtin_bswap64", [BA(IR a1)], BR(IR res) -> + emit (Prev(X, res, a1)) + | "__builtin_bswap16", [BA(IR a1)], BR(IR res) -> + emit (Prev16(W, res, a1)); + emit (Pandimm(W, res, RR0 res, Z.of_uint 0xFFFF)) + (* Count leading zeros and leading sign bits *) + | "__builtin_clz", [BA(IR a1)], BR(IR res) -> + emit (Pclz(W, res, a1)) + | ("__builtin_clzl" | "__builtin_clzll"), [BA(IR a1)], BR(IR res) -> + emit (Pclz(X, res, a1)) + | "__builtin_cls", [BA(IR a1)], BR(IR res) -> + emit (Pcls(W, res, a1)) + | ("__builtin_clsl" | "__builtin_clsll"), [BA(IR a1)], BR(IR res) -> + emit (Pcls(X, res, a1)) + (* Float arithmetic *) + | "__builtin_fabs", [BA(FR a1)], BR(FR res) -> + emit (Pfabs(D, res, a1)) + | "__builtin_fsqrt", [BA(FR a1)], BR(FR res) -> + emit (Pfsqrt(D, res, a1)) + | "__builtin_fmadd", [BA(FR a1); BA(FR a2); BA(FR a3)], BR(FR res) -> + emit (Pfmadd(D, res, a1, a2, a3)) + | "__builtin_fmsub", [BA(FR a1); BA(FR a2); BA(FR a3)], BR(FR res) -> + emit (Pfmsub(D, res, a1, a2, a3)) + | "__builtin_fnmadd", [BA(FR a1); BA(FR a2); BA(FR a3)], BR(FR res) -> + emit (Pfnmadd(D, res, a1, a2, a3)) + | "__builtin_fnmsub", [BA(FR a1); BA(FR a2); BA(FR a3)], BR(FR res) -> + emit (Pfnmsub(D, res, a1, a2, a3)) + (* Vararg *) + | "__builtin_va_start", [BA(IR a)], _ -> + expand_builtin_va_start a + (* Catch-all *) + | _ -> + raise (Error ("unrecognized builtin " ^ name)) + +(* Expansion of instructions *) + +let expand_instruction instr = + match instr with + | Pallocframe (sz, ofs) -> + emit (Pmov (RR1 X29, XSP)); + if is_current_function_variadic() then begin + let (ir, fr, _) = + next_arg_locations 0 0 0 (get_current_function_args ()) in + save_parameter_registers ir fr; + current_function_stacksize := + Int64.(add (Z.to_int64 sz) (of_int size_save_register_area)) + end else begin + current_function_stacksize := Z.to_int64 sz + end; + expand_addimm64 XSP XSP (Ptrofs.repr (Z.neg sz)); + expand_storeptr X29 XSP ofs + | Pfreeframe (sz, ofs) -> + expand_addimm64 XSP XSP (coqint_of_camlint64 !current_function_stacksize) + | Pcvtx2w rd -> + (* no code generated, the upper 32 bits of rd will be ignored *) + () + | Pbuiltin (ef,args,res) -> + begin match ef with + | EF_builtin (name,sg) -> + expand_builtin_inline (camlstring_of_coqstring name) args res + | EF_vload chunk -> + expand_builtin_vload chunk args res + | EF_vstore chunk -> + expand_builtin_vstore chunk args + | EF_annot_val (kind,txt,targ) -> + expand_annot_val kind txt targ args res + | EF_memcpy(sz, al) -> + expand_builtin_memcpy (Z.to_int sz) (Z.to_int al) args + | EF_annot _ | EF_debug _ | EF_inline_asm _ -> + emit instr + | _ -> + assert false + end + | _ -> + emit instr + +let int_reg_to_dwarf r = 0 (* TODO *) + +let float_reg_to_dwarf r = 0 (* TODO *) + +let preg_to_dwarf = function + | IR r -> int_reg_to_dwarf r + | FR r -> float_reg_to_dwarf r + | _ -> assert false + +let expand_function id fn = + try + set_current_function fn; + expand id (* sp= *) 2 preg_to_dwarf expand_instruction fn.fn_code; + Errors.OK (get_current_function ()) + with Error s -> + Errors.Error (Errors.msg (coqstring_of_camlstring s)) + +let expand_fundef id = function + | Internal f -> + begin match expand_function id f with + | Errors.OK tf -> Errors.OK (Internal tf) + | Errors.Error msg -> Errors.Error msg + end + | External ef -> + Errors.OK (External ef) + +let expand_program (p: Asm.program) : Asm.program Errors.res = + AST.transform_partial_program2 expand_fundef (fun id v -> Errors.OK v) p diff --git a/aarch64/Asmgen.v b/aarch64/Asmgen.v new file mode 100644 index 00000000..1c0e41a1 --- /dev/null +++ b/aarch64/Asmgen.v @@ -0,0 +1,1151 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Translation from Mach to AArch64. *) + +Require Import Recdef Coqlib Zwf Zbits. +Require Import Errors AST Integers Floats Op. +Require Import Locations Mach Asm. + +Local Open Scope string_scope. +Local Open Scope list_scope. +Local Open Scope error_monad_scope. + +(** Extracting integer or float registers. *) + +Definition ireg_of (r: mreg) : res ireg := + match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.ireg_of") end. + +Definition freg_of (r: mreg) : res freg := + match preg_of r with FR mr => OK mr | _ => Error(msg "Asmgen.freg_of") end. + +(** Recognition of immediate arguments for logical integer operations.*) + +(** Valid immediate arguments are repetitions of a bit pattern [B] + of length [e] = 2, 4, 8, 16, 32 or 64. + The bit pattern [B] must be of the form [0*1*0*] or [1*0*1*] + but must not be all zeros or all ones. *) + +(** The following automaton recognizes [0*1*0*|1*0*1*]. +<< + 0 1 0 + / \ / \ / \ + \ / \ / \ / + -0--> [B] --1--> [D] --0--> [F] + / + [A] + \ + -1--> [C] --0--> [E] --1--> [G] + / \ / \ / \ + \ / \ / \ / + 1 0 1 +>> +*) + +Module Automaton. + +Inductive state : Type := SA | SB | SC | SD | SE | SF | SG | Sbad. + +Definition start := SA. + +Definition next (s: state) (b: bool) := + match s, b with + | SA,false => SB | SA,true => SC + | SB,false => SB | SB,true => SD + | SC,false => SE | SC,true => SC + | SD,false => SF | SD,true => SD + | SE,false => SE | SE,true => SG + | SF,false => SF | SF,true => Sbad + | SG,false => Sbad | SG,true => SG + | Sbad,_ => Sbad + end. + +Definition accepting (s: state) := + match s with + | SA | SB | SC | SD | SE | SF | SG => true + | Sbad => false + end. + +Fixpoint run (len: nat) (s: state) (x: Z) : bool := + match len with + | Datatypes.O => accepting s + | Datatypes.S len => run len (next s (Z.odd x)) (Z.div2 x) + end. + +End Automaton. + +(** The following function determines the candidate length [e], + ensuring that [x] is a repetition [BB...B] + of a bit pattern [B] of length [e]. *) + +Definition logical_imm_length (x: Z) (sixtyfour: bool) : nat := + (** [test n] checks that the low [2n] bits of [x] are of the + form [BB], that is, two occurrences of the same [n] bits *) + let test (n: Z) : bool := + Z.eqb (Zzero_ext n x) (Zzero_ext n (Z.shiftr x n)) in + (** If [test n] fails, we know that the candidate length [e] is + at least [2n]. Hence we test with decreasing values of [n]: + 32, 16, 8, 4, 2. *) + if sixtyfour && negb (test 32) then 64%nat + else if negb (test 16) then 32%nat + else if negb (test 8) then 16%nat + else if negb (test 4) then 8%nat + else if negb (test 2) then 4%nat + else 2%nat. + +(** A valid logical immediate is +- neither [0] nor [-1]; +- composed of a repetition [BBBBB] of a bit-pattern [B] of length [e] +- the low [e] bits of the number, that is, [B], match [0*1*0*] or [1*0*1*]. +*) + +Definition is_logical_imm32 (x: int) : bool := + negb (Int.eq x Int.zero) && negb (Int.eq x Int.mone) && + Automaton.run (logical_imm_length (Int.unsigned x) false) + Automaton.start (Int.unsigned x). + +Definition is_logical_imm64 (x: int64) : bool := + negb (Int64.eq x Int64.zero) && negb (Int64.eq x Int64.mone) && + Automaton.run (logical_imm_length (Int64.unsigned x) true) + Automaton.start (Int64.unsigned x). + +(** Arithmetic immediates are 12-bit unsigned numbers, possibly shifted left 12 bits *) + +Definition is_arith_imm32 (x: int) : bool := + Int.eq x (Int.zero_ext 12 x) + || Int.eq x (Int.shl (Int.zero_ext 12 (Int.shru x (Int.repr 12))) (Int.repr 12)). + +Definition is_arith_imm64 (x: int64) : bool := + Int64.eq x (Int64.zero_ext 12 x) + || Int64.eq x (Int64.shl (Int64.zero_ext 12 (Int64.shru x (Int64.repr 12))) (Int64.repr 12)). + +(** Decompose integer literals into 16-bit fragments *) + +Fixpoint decompose_int (N: nat) (n p: Z) {struct N} : list (Z * Z) := + match N with + | Datatypes.O => nil + | Datatypes.S N => + let frag := Zzero_ext 16 (Z.shiftr n p) in + if Z.eqb frag 0 then + decompose_int N n (p + 16) + else + (frag, p) :: decompose_int N (Z.ldiff n (Z.shiftl 65535 p)) (p + 16) + end. + +Definition negate_decomposition (l: list (Z * Z)) := + List.map (fun np => (Z.lxor (fst np) 65535, snd np)) l. + +Definition loadimm_k (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + List.fold_right (fun np k => Pmovk sz rd (fst np) (snd np) :: k) k l. + +Definition loadimm_z (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + match l with + | nil => Pmovz sz rd 0 0 :: k + | (n1, p1) :: l => Pmovz sz rd n1 p1 :: loadimm_k sz rd l k + end. + +Definition loadimm_n (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + match l with + | nil => Pmovn sz rd 0 0 :: k + | (n1, p1) :: l => Pmovn sz rd n1 p1 :: loadimm_k sz rd (negate_decomposition l) k + end. + +Definition loadimm (sz: isize) (rd: ireg) (n: Z) (k: code) : code := + let N := match sz with W => 2%nat | X => 4%nat end in + let dz := decompose_int N n 0 in + let dn := decompose_int N (Z.lnot n) 0 in + if Nat.leb (List.length dz) (List.length dn) + then loadimm_z sz rd dz k + else loadimm_n sz rd dn k. + +Definition loadimm32 (rd: ireg) (n: int) (k: code) : code := + if is_logical_imm32 n + then Porrimm W rd XZR (Int.unsigned n) :: k + else loadimm W rd (Int.unsigned n) k. + +Definition loadimm64 (rd: ireg) (n: int64) (k: code) : code := + if is_logical_imm64 n + then Porrimm X rd XZR (Int64.unsigned n) :: k + else loadimm X rd (Int64.unsigned n) k. + +(** Add immediate *) + +Definition addimm_aux (insn: iregsp -> iregsp -> Z -> instruction) + (rd r1: iregsp) (n: Z) (k: code) := + let nlo := Zzero_ext 12 n in + let nhi := n - nlo in + if Z.eqb nhi 0 then + insn rd r1 nlo :: k + else if Z.eqb nlo 0 then + insn rd r1 nhi :: k + else + insn rd r1 nhi :: insn rd rd nlo :: k. + +Definition addimm32 (rd r1: ireg) (n: int) (k: code) : code := + let m := Int.neg n in + if Int.eq n (Int.zero_ext 24 n) then + addimm_aux (Paddimm W) rd r1 (Int.unsigned n) k + else if Int.eq m (Int.zero_ext 24 m) then + addimm_aux (Psubimm W) rd r1 (Int.unsigned m) k + else if Int.lt n Int.zero then + loadimm32 X16 m (Psub W rd r1 X16 SOnone :: k) + else + loadimm32 X16 n (Padd W rd r1 X16 SOnone :: k). + +Definition addimm64 (rd r1: iregsp) (n: int64) (k: code) : code := + let m := Int64.neg n in + if Int64.eq n (Int64.zero_ext 24 n) then + addimm_aux (Paddimm X) rd r1 (Int64.unsigned n) k + else if Int64.eq m (Int64.zero_ext 24 m) then + addimm_aux (Psubimm X) rd r1 (Int64.unsigned m) k + else if Int64.lt n Int64.zero then + loadimm64 X16 m (Psubext rd r1 X16 (EOuxtx Int.zero) :: k) + else + loadimm64 X16 n (Paddext rd r1 X16 (EOuxtx Int.zero) :: k). + +(** Logical immediate *) + +Definition logicalimm32 + (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1: ireg) (n: int) (k: code) : code := + if is_logical_imm32 n + then insn1 rd r1 (Int.unsigned n) :: k + else loadimm32 X16 n (insn2 rd r1 X16 SOnone :: k). + +Definition logicalimm64 + (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1: ireg) (n: int64) (k: code) : code := + if is_logical_imm64 n + then insn1 rd r1 (Int64.unsigned n) :: k + else loadimm64 X16 n (insn2 rd r1 X16 SOnone :: k). + +(** Sign- or zero-extended arithmetic *) + +Definition transl_extension (ex: extension) (a: int) : extend_op := + match ex with Xsgn32 => EOsxtw a | Xuns32 => EOuxtw a end. + +Definition move_extended_base + (rd: ireg) (r1: ireg) (ex: extension) (k: code) : code := + match ex with + | Xsgn32 => Pcvtsw2x rd r1 :: k + | Xuns32 => Pcvtuw2x rd r1 :: k + end. + +Definition move_extended + (rd: ireg) (r1: ireg) (ex: extension) (a: int) (k: code) : code := + if Int.eq a Int.zero then + move_extended_base rd r1 ex k + else + move_extended_base rd r1 ex (Padd X rd XZR rd (SOlsl a) :: k). + +Definition arith_extended + (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction) + (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1 r2: ireg) (ex: extension) (a: int) (k: code) : code := + if Int.ltu a (Int.repr 5) then + insnX rd r1 r2 (transl_extension ex a) :: k + else + move_extended_base X16 r2 ex (insnS rd r1 X16 (SOlsl a) :: k). + +(** Extended right shift *) + +Definition shrx32 (rd r1: ireg) (n: int) (k: code) : code := + if Int.eq n Int.zero then + Pmov rd r1 :: k + else + Porr W X16 XZR r1 (SOasr (Int.repr 31)) :: + Padd W X16 r1 X16 (SOlsr (Int.sub Int.iwordsize n)) :: + Porr W rd XZR X16 (SOasr n) :: k. + +Definition shrx64 (rd r1: ireg) (n: int) (k: code) : code := + if Int.eq n Int.zero then + Pmov rd r1 :: k + else + Porr X X16 XZR r1 (SOasr (Int.repr 63)) :: + Padd X X16 r1 X16 (SOlsr (Int.sub Int64.iwordsize' n)) :: + Porr X rd XZR X16 (SOasr n) :: k. + +(** Load the address [id + ofs] in [rd] *) + +Definition loadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (k: code) : code := + if Archi.pic_code tt then + if Ptrofs.eq ofs Ptrofs.zero then + Ploadsymbol rd id :: k + else + Ploadsymbol rd id :: addimm64 rd rd (Ptrofs.to_int64 ofs) k + else + Padrp rd id ofs :: Paddadr rd rd id ofs :: k. + +(** Translate a shifted operand *) + +Definition transl_shift (s: Op.shift) (a: int): Asm.shift_op := + match s with + | Slsl => SOlsl a + | Slsr => SOlsr a + | Sasr => SOasr a + | Sror => SOror a + end. + +(** Translation of a condition. Prepends to [k] the instructions + that evaluate the condition and leave its boolean result in one of + the bits of the condition register. The bit in question is + determined by the [crbit_for_cond] function. *) + +Definition transl_cond + (cond: condition) (args: list mreg) (k: code) := + match cond, args with + | (Ccomp c | Ccompu c), a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pcmp W r1 r2 SOnone :: k) + | (Ccompshift c s a | Ccompushift c s a), a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pcmp W r1 r2 (transl_shift s a) :: k) + | (Ccompimm c n | Ccompuimm c n), a1 :: nil => + do r1 <- ireg_of a1; + OK (if is_arith_imm32 n then + Pcmpimm W r1 (Int.unsigned n) :: k + else if is_arith_imm32 (Int.neg n) then + Pcmnimm W r1 (Int.unsigned (Int.neg n)) :: k + else + loadimm32 X16 n (Pcmp W r1 X16 SOnone :: k)) + | (Cmaskzero n | Cmasknotzero n), a1 :: nil => + do r1 <- ireg_of a1; + OK (if is_logical_imm32 n then + Ptstimm W r1 (Int.unsigned n) :: k + else + loadimm32 X16 n (Ptst W r1 X16 SOnone :: k)) + | (Ccompl c | Ccomplu c), a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pcmp X r1 r2 SOnone :: k) + | (Ccomplshift c s a | Ccomplushift c s a), a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pcmp X r1 r2 (transl_shift s a) :: k) + | (Ccomplimm c n | Ccompluimm c n), a1 :: nil => + do r1 <- ireg_of a1; + OK (if is_arith_imm64 n then + Pcmpimm X r1 (Int64.unsigned n) :: k + else if is_arith_imm64 (Int64.neg n) then + Pcmnimm X r1 (Int64.unsigned (Int64.neg n)) :: k + else + loadimm64 X16 n (Pcmp X r1 X16 SOnone :: k)) + | (Cmasklzero n | Cmasklnotzero n), a1 :: nil => + do r1 <- ireg_of a1; + OK (if is_logical_imm64 n then + Ptstimm X r1 (Int64.unsigned n) :: k + else + loadimm64 X16 n (Ptst X r1 X16 SOnone :: k)) + | Ccompf cmp, a1 :: a2 :: nil => + do r1 <- freg_of a1; do r2 <- freg_of a2; + OK (Pfcmp D r1 r2 :: k) + | Cnotcompf cmp, a1 :: a2 :: nil => + do r1 <- freg_of a1; do r2 <- freg_of a2; + OK (Pfcmp D r1 r2 :: k) + | Ccompfzero cmp, a1 :: nil => + do r1 <- freg_of a1; + OK (Pfcmp0 D r1 :: k) + | Cnotcompfzero cmp, a1 :: nil => + do r1 <- freg_of a1; + OK (Pfcmp0 D r1 :: k) + | Ccompfs cmp, a1 :: a2 :: nil => + do r1 <- freg_of a1; do r2 <- freg_of a2; + OK (Pfcmp S r1 r2 :: k) + | Cnotcompfs cmp, a1 :: a2 :: nil => + do r1 <- freg_of a1; do r2 <- freg_of a2; + OK (Pfcmp S r1 r2 :: k) + | Ccompfszero cmp, a1 :: nil => + do r1 <- freg_of a1; + OK (Pfcmp0 S r1 :: k) + | Cnotcompfszero cmp, a1 :: nil => + do r1 <- freg_of a1; + OK (Pfcmp0 S r1 :: k) + | _, _ => + Error(msg "Asmgen.transl_cond") + end. + +Definition cond_for_signed_cmp (cmp: comparison) := + match cmp with + | Ceq => TCeq + | Cne => TCne + | Clt => TClt + | Cle => TCle + | Cgt => TCgt + | Cge => TCge + end. + +Definition cond_for_unsigned_cmp (cmp: comparison) := + match cmp with + | Ceq => TCeq + | Cne => TCne + | Clt => TClo + | Cle => TCls + | Cgt => TChi + | Cge => TChs + end. + +Definition cond_for_float_cmp (cmp: comparison) := + match cmp with + | Ceq => TCeq + | Cne => TCne + | Clt => TCmi + | Cle => TCls + | Cgt => TCgt + | Cge => TCge + end. + +Definition cond_for_float_not_cmp (cmp: comparison) := + match cmp with + | Ceq => TCne + | Cne => TCeq + | Clt => TCpl + | Cle => TChi + | Cgt => TCle + | Cge => TClt + end. + +Definition cond_for_cond (cond: condition) := + match cond with + | Ccomp cmp => cond_for_signed_cmp cmp + | Ccompu cmp => cond_for_unsigned_cmp cmp + | Ccompshift cmp s a => cond_for_signed_cmp cmp + | Ccompushift cmp s a => cond_for_unsigned_cmp cmp + | Ccompimm cmp n => cond_for_signed_cmp cmp + | Ccompuimm cmp n => cond_for_unsigned_cmp cmp + | Cmaskzero n => TCeq + | Cmasknotzero n => TCne + | Ccompl cmp => cond_for_signed_cmp cmp + | Ccomplu cmp => cond_for_unsigned_cmp cmp + | Ccomplshift cmp s a => cond_for_signed_cmp cmp + | Ccomplushift cmp s a => cond_for_unsigned_cmp cmp + | Ccomplimm cmp n => cond_for_signed_cmp cmp + | Ccompluimm cmp n => cond_for_unsigned_cmp cmp + | Cmasklzero n => TCeq + | Cmasklnotzero n => TCne + | Ccompf cmp => cond_for_float_cmp cmp + | Cnotcompf cmp => cond_for_float_not_cmp cmp + | Ccompfzero cmp => cond_for_float_cmp cmp + | Cnotcompfzero cmp => cond_for_float_not_cmp cmp + | Ccompfs cmp => cond_for_float_cmp cmp + | Cnotcompfs cmp => cond_for_float_not_cmp cmp + | Ccompfszero cmp => cond_for_float_cmp cmp + | Cnotcompfszero cmp => cond_for_float_not_cmp cmp + end. + +(** Translation of a conditional branch. Prepends to [k] the instructions + that evaluate the condition and ranch to [lbl] if it holds. + We recognize some conditional branches that can be implemented + without setting then testing condition flags. *) + +Definition transl_cond_branch_default + (c: condition) (args: list mreg) (lbl: label) (k: code) := + transl_cond c args (Pbc (cond_for_cond c) lbl :: k). + +Definition transl_cond_branch + (c: condition) (args: list mreg) (lbl: label) (k: code) := + match args, c with + | a1 :: nil, (Ccompimm Cne n | Ccompuimm Cne n) => + if Int.eq n Int.zero + then (do r1 <- ireg_of a1; OK (Pcbnz W r1 lbl :: k)) + else transl_cond_branch_default c args lbl k + | a1 :: nil, (Ccompimm Ceq n | Ccompuimm Ceq n) => + if Int.eq n Int.zero + then (do r1 <- ireg_of a1; OK (Pcbz W r1 lbl :: k)) + else transl_cond_branch_default c args lbl k + | a1 :: nil, (Ccomplimm Cne n | Ccompluimm Cne n) => + if Int64.eq n Int64.zero + then (do r1 <- ireg_of a1; OK (Pcbnz X r1 lbl :: k)) + else transl_cond_branch_default c args lbl k + | a1 :: nil, (Ccomplimm Ceq n | Ccompluimm Ceq n) => + if Int64.eq n Int64.zero + then (do r1 <- ireg_of a1; OK (Pcbz X r1 lbl :: k)) + else transl_cond_branch_default c args lbl k + | a1 :: nil, Cmaskzero n => + match Int.is_power2 n with + | Some bit => do r1 <- ireg_of a1; OK (Ptbz W r1 bit lbl :: k) + | None => transl_cond_branch_default c args lbl k + end + | a1 :: nil, Cmasknotzero n => + match Int.is_power2 n with + | Some bit => do r1 <- ireg_of a1; OK (Ptbnz W r1 bit lbl :: k) + | None => transl_cond_branch_default c args lbl k + end + | a1 :: nil, Cmasklzero n => + match Int64.is_power2' n with + | Some bit => do r1 <- ireg_of a1; OK (Ptbz X r1 bit lbl :: k) + | None => transl_cond_branch_default c args lbl k + end + | a1 :: nil, Cmasklnotzero n => + match Int64.is_power2' n with + | Some bit => do r1 <- ireg_of a1; OK (Ptbnz X r1 bit lbl :: k) + | None => transl_cond_branch_default c args lbl k + end + | _, _ => + transl_cond_branch_default c args lbl k + end. + +(** Translation of the arithmetic operation [res <- op(args)]. + The corresponding instructions are prepended to [k]. *) + +Definition transl_op + (op: operation) (args: list mreg) (res: mreg) (k: code) := + match op, args with + | Omove, a1 :: nil => + match preg_of res, preg_of a1 with + | IR r, IR a => OK (Pmov r a :: k) + | FR r, FR a => OK (Pfmov r a :: k) + | _ , _ => Error(msg "Asmgen.Omove") + end + | Ointconst n, nil => + do rd <- ireg_of res; + OK (loadimm32 rd n k) + | Olongconst n, nil => + do rd <- ireg_of res; + OK (loadimm64 rd n k) + | Ofloatconst f, nil => + do rd <- freg_of res; + OK (if Float.eq_dec f Float.zero + then Pfmovi D rd XZR :: k + else Pfmovimmd rd f :: k) + | Osingleconst f, nil => + do rd <- freg_of res; + OK (if Float32.eq_dec f Float32.zero + then Pfmovi S rd XZR :: k + else Pfmovimms rd f :: k) + | Oaddrsymbol id ofs, nil => + do rd <- ireg_of res; + OK (loadsymbol rd id ofs k) + | Oaddrstack ofs, nil => + do rd <- ireg_of res; + OK (addimm64 rd XSP (Ptrofs.to_int64 ofs) k) +(** 32-bit integer arithmetic *) + | Oshift s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porr W rd XZR r1 (transl_shift s a) :: k) + | Oadd, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Padd W rd r1 r2 SOnone :: k) + | Oaddshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Padd W rd r1 r2 (transl_shift s a) :: k) + | Oaddimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (addimm32 rd r1 n k) + | Oneg, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psub W rd XZR r1 SOnone :: k) + | Onegshift s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psub W rd XZR r1 (transl_shift s a) :: k) + | Osub, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psub W rd r1 r2 SOnone :: k) + | Osubshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psub W rd r1 r2 (transl_shift s a) :: k) + | Omul, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pmadd W rd r1 r2 XZR :: k) + | Omuladd, a1 :: a2 :: a3 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3; + OK (Pmadd W rd r2 r3 r1 :: k) + | Omulsub, a1 :: a2 :: a3 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3; + OK (Pmsub W rd r2 r3 r1 :: k) + | Odiv, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psdiv W rd r1 r2 :: k) + | Odivu, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pudiv W rd r1 r2 :: k) + | Oand, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pand W rd r1 r2 SOnone :: k) + | Oandshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pand W rd r1 r2 (transl_shift s a) :: k) + | Oandimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm32 (Pandimm W) (Pand W) rd r1 n k) + | Oor, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porr W rd r1 r2 SOnone :: k) + | Oorshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porr W rd r1 r2 (transl_shift s a) :: k) + | Oorimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm32 (Porrimm W) (Porr W) rd r1 n k) + | Oxor, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peor W rd r1 r2 SOnone :: k) + | Oxorshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peor W rd r1 r2 (transl_shift s a) :: k) + | Oxorimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm32 (Peorimm W) (Peor W) rd r1 n k) + | Onot, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porn W rd XZR r1 SOnone :: k) + | Onotshift s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porn W rd XZR r1 (transl_shift s a) :: k) + | Obic, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pbic W rd r1 r2 SOnone :: k) + | Obicshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pbic W rd r1 r2 (transl_shift s a) :: k) + | Oorn, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porn W rd r1 r2 SOnone :: k) + | Oornshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porn W rd r1 r2 (transl_shift s a) :: k) + | Oeqv, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peon W rd r1 r2 SOnone :: k) + | Oeqvshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peon W rd r1 r2 (transl_shift s a) :: k) + | Oshl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Plslv W rd r1 r2 :: k) + | Oshr, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pasrv W rd r1 r2 :: k) + | Oshru, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Plsrv W rd r1 r2 :: k) + | Oshrximm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (shrx32 rd r1 n k) + | Ozext s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfiz W rd r1 Int.zero s :: k) + | Osext s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfiz W rd r1 Int.zero s :: k) + | Oshlzext s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k) + | Oshlsext s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k) + | Ozextshr a s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k) + | Osextshr a s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k) +(** 64-bit integer arithmetic *) + | Oshiftl s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porr X rd XZR r1 (transl_shift s a) :: k) + | Oextend x a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (move_extended rd r1 x a k) + (* [Omakelong] and [Ohighlong] should not occur *) + | Olowlong, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + assertion (ireg_eq rd r1); + OK (Pcvtx2w rd :: k) + | Oaddl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Padd X rd r1 r2 SOnone :: k) + | Oaddlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Padd X rd r1 r2 (transl_shift s a) :: k) + | Oaddlext x a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (arith_extended Paddext (Padd X) rd r1 r2 x a k) + | Oaddlimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (addimm64 rd r1 n k) + | Onegl, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psub X rd XZR r1 SOnone :: k) + | Oneglshift s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psub X rd XZR r1 (transl_shift s a) :: k) + | Osubl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psub X rd r1 r2 SOnone :: k) + | Osublshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psub X rd r1 r2 (transl_shift s a) :: k) + | Osublext x a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (arith_extended Psubext (Psub X) rd r1 r2 x a k) + | Omull, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pmadd X rd r1 r2 XZR :: k) + | Omulladd, a1 :: a2 :: a3 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3; + OK (Pmadd X rd r2 r3 r1 :: k) + | Omullsub, a1 :: a2 :: a3 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3; + OK (Pmsub X rd r2 r3 r1 :: k) + | Omullhs, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psmulh rd r1 r2 :: k) + | Omullhu, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pumulh rd r1 r2 :: k) + | Odivl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Psdiv X rd r1 r2 :: k) + | Odivlu, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pudiv X rd r1 r2 :: k) + | Oandl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pand X rd r1 r2 SOnone :: k) + | Oandlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pand X rd r1 r2 (transl_shift s a) :: k) + | Oandlimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm64 (Pandimm X) (Pand X) rd r1 n k) + | Oorl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porr X rd r1 r2 SOnone :: k) + | Oorlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porr X rd r1 r2 (transl_shift s a) :: k) + | Oorlimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm64 (Porrimm X) (Porr X) rd r1 n k) + | Oxorl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peor X rd r1 r2 SOnone :: k) + | Oxorlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peor X rd r1 r2 (transl_shift s a) :: k) + | Oxorlimm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (logicalimm64 (Peorimm X) (Peor X) rd r1 n k) + | Onotl, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porn X rd XZR r1 SOnone :: k) + | Onotlshift s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Porn X rd XZR r1 (transl_shift s a) :: k) + | Obicl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pbic X rd r1 r2 SOnone :: k) + | Obiclshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pbic X rd r1 r2 (transl_shift s a) :: k) + | Oornl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porn X rd r1 r2 SOnone :: k) + | Oornlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Porn X rd r1 r2 (transl_shift s a) :: k) + | Oeqvl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peon X rd r1 r2 SOnone :: k) + | Oeqvlshift s a, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Peon X rd r1 r2 (transl_shift s a) :: k) + | Oshll, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Plslv X rd r1 r2 :: k) + | Oshrl, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Pasrv X rd r1 r2 :: k) + | Oshrlu, a1 :: a2 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (Plsrv X rd r1 r2 :: k) + | Oshrlximm n, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (shrx64 rd r1 n k) + | Ozextl s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfiz X rd r1 Int.zero s :: k) + | Osextl s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfiz X rd r1 Int.zero s :: k) + | Oshllzext s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k) + | Oshllsext s a, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k) + | Ozextshrl a s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Pubfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k) + | Osextshrl a s, a1 :: nil => + do rd <- ireg_of res; do r1 <- ireg_of a1; + OK (Psbfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k) +(** 64-bit floating-point arithmetic *) + | Onegf, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfneg D rd rs :: k) + | Oabsf, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfabs D rd rs :: k) + | Oaddf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfadd D rd rs1 rs2 :: k) + | Osubf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfsub D rd rs1 rs2 :: k) + | Omulf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfmul D rd rs1 rs2 :: k) + | Odivf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfdiv D rd rs1 rs2 :: k) +(** 32-bit floating-point arithmetic *) + | Onegfs, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfneg S rd rs :: k) + | Oabsfs, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfabs S rd rs :: k) + | Oaddfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfadd S rd rs1 rs2 :: k) + | Osubfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfsub S rd rs1 rs2 :: k) + | Omulfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfmul S rd rs1 rs2 :: k) + | Odivfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfdiv S rd rs1 rs2 :: k) + | Osingleoffloat, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfcvtsd rd rs :: k) + | Ofloatofsingle, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfcvtds rd rs :: k) +(** Conversions between int and float *) + | Ointoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzs W D rd rs :: k) + | Ointuoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzu W D rd rs :: k) + | Ofloatofint, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pscvtf D W rd rs :: k) + | Ofloatofintu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pucvtf D W rd rs :: k) + | Ointofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzs W S rd rs :: k) + | Ointuofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzu W S rd rs :: k) + | Osingleofint, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pscvtf S W rd rs :: k) + | Osingleofintu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pucvtf S W rd rs :: k) + | Olongoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzs X D rd rs :: k) + | Olonguoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzu X D rd rs :: k) + | Ofloatoflong, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pscvtf D X rd rs :: k) + | Ofloatoflongu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pucvtf D X rd rs :: k) + | Olongofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzs X S rd rs :: k) + | Olonguofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtzu X S rd rs :: k) + | Osingleoflong, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pscvtf S X rd rs :: k) + | Osingleoflongu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pucvtf S X rd rs :: k) +(** Boolean tests *) + | Ocmp c, _ => + do rd <- ireg_of res; + transl_cond c args (Pcset rd (cond_for_cond c) :: k) +(** Conditional move *) + | Osel cmp ty, a1 :: a2 :: args => + match preg_of res with + | IR r => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + transl_cond cmp args (Pcsel r r1 r2 (cond_for_cond cmp) :: k) + | FR r => + do r1 <- freg_of a1; do r2 <- freg_of a2; + transl_cond cmp args (Pfsel r r1 r2 (cond_for_cond cmp) :: k) + | _ => + Error(msg "Asmgen.Osel") + end + | _, _ => + Error(msg "Asmgen.transl_op") + end. + +(** Translation of addressing modes *) + +Definition offset_representable (sz: Z) (ofs: int64) : bool := + let isz := Int64.repr sz in + (** either unscaled 9-bit signed *) + Int64.eq ofs (Int64.sign_ext 9 ofs) || + (** or scaled 12-bit unsigned *) + (Int64.eq (Int64.modu ofs isz) Int64.zero + && Int64.ltu ofs (Int64.shl isz (Int64.repr 12))). + +Definition transl_addressing (sz: Z) (addr: Op.addressing) (args: list mreg) + (insn: Asm.addressing -> instruction) (k: code) : res code := + match addr, args with + | Aindexed ofs, a1 :: nil => + do r1 <- ireg_of a1; + if offset_representable sz ofs then + OK (insn (ADimm r1 ofs) :: k) + else + OK (loadimm64 X16 ofs (insn (ADreg r1 X16) :: k)) + | Aindexed2, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (insn (ADreg r1 r2) :: k) + | Aindexed2shift a, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + if Int.eq a Int.zero then + OK (insn (ADreg r1 r2) :: k) + else if Int.eq (Int.shl Int.one a) (Int.repr sz) then + OK (insn (ADlsl r1 r2 a) :: k) + else + OK (Padd X X16 r1 r2 (SOlsl a) :: insn (ADimm X16 Int64.zero) :: k) + | Aindexed2ext x a, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + if Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz) then + OK (insn (match x with Xsgn32 => ADsxt r1 r2 a + | Xuns32 => ADuxt r1 r2 a end) :: k) + else + OK (arith_extended Paddext (Padd X) X16 r1 r2 x a + (insn (ADimm X16 Int64.zero) :: k)) + | Aglobal id ofs, nil => + assertion (negb (Archi.pic_code tt)); + if Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero + then OK (Padrp X16 id ofs :: insn (ADadr X16 id ofs) :: k) + else OK (loadsymbol X16 id ofs (insn (ADimm X16 Int64.zero) :: k)) + | Ainstack ofs, nil => + let ofs := Ptrofs.to_int64 ofs in + if offset_representable sz ofs then + OK (insn (ADimm XSP ofs) :: k) + else + OK (loadimm64 X16 ofs (insn (ADreg XSP X16) :: k)) + | _, _ => + Error(msg "Asmgen.transl_addressing") + end. + +(** Translation of loads and stores *) + +Definition transl_load (chunk: memory_chunk) (addr: Op.addressing) + (args: list mreg) (dst: mreg) (k: code) : res code := + match chunk with + | Mint8unsigned => + do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrb W rd) k + | Mint8signed => + do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrsb W rd) k + | Mint16unsigned => + do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrh W rd) k + | Mint16signed => + do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrsh W rd) k + | Mint32 => + do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw rd) k + | Mint64 => + do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx rd) k + | Mfloat32 => + do rd <- freg_of dst; transl_addressing 4 addr args (Pldrs rd) k + | Mfloat64 => + do rd <- freg_of dst; transl_addressing 8 addr args (Pldrd rd) k + | Many32 => + do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw_a rd) k + | Many64 => + do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx_a rd) k + end. + +Definition transl_store (chunk: memory_chunk) (addr: Op.addressing) + (args: list mreg) (src: mreg) (k: code) : res code := + match chunk with + | Mint8unsigned | Mint8signed => + do r1 <- ireg_of src; transl_addressing 1 addr args (Pstrb r1) k + | Mint16unsigned | Mint16signed => + do r1 <- ireg_of src; transl_addressing 2 addr args (Pstrh r1) k + | Mint32 => + do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw r1) k + | Mint64 => + do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx r1) k + | Mfloat32 => + do r1 <- freg_of src; transl_addressing 4 addr args (Pstrs r1) k + | Mfloat64 => + do r1 <- freg_of src; transl_addressing 8 addr args (Pstrd r1) k + | Many32 => + do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw_a r1) k + | Many64 => + do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx_a r1) k + end. + +(** Register-indexed loads and stores *) + +Definition indexed_memory_access (insn: Asm.addressing -> instruction) + (sz: Z) (base: iregsp) (ofs: ptrofs) (k: code) := + let ofs := Ptrofs.to_int64 ofs in + if offset_representable sz ofs + then insn (ADimm base ofs) :: k + else loadimm64 X16 ofs (insn (ADreg base X16) :: k). + +Definition loadind (base: iregsp) (ofs: ptrofs) (ty: typ) (dst: mreg) (k: code) := + match ty, preg_of dst with + | Tint, IR rd => OK (indexed_memory_access (Pldrw rd) 4 base ofs k) + | Tlong, IR rd => OK (indexed_memory_access (Pldrx rd) 8 base ofs k) + | Tsingle, FR rd => OK (indexed_memory_access (Pldrs rd) 4 base ofs k) + | Tfloat, FR rd => OK (indexed_memory_access (Pldrd rd) 8 base ofs k) + | Tany32, IR rd => OK (indexed_memory_access (Pldrw_a rd) 4 base ofs k) + | Tany64, IR rd => OK (indexed_memory_access (Pldrx_a rd) 8 base ofs k) + | Tany64, FR rd => OK (indexed_memory_access (Pldrd_a rd) 8 base ofs k) + | _, _ => Error (msg "Asmgen.loadind") + end. + +Definition storeind (src: mreg) (base: iregsp) (ofs: ptrofs) (ty: typ) (k: code) := + match ty, preg_of src with + | Tint, IR rd => OK (indexed_memory_access (Pstrw rd) 4 base ofs k) + | Tlong, IR rd => OK (indexed_memory_access (Pstrx rd) 8 base ofs k) + | Tsingle, FR rd => OK (indexed_memory_access (Pstrs rd) 4 base ofs k) + | Tfloat, FR rd => OK (indexed_memory_access (Pstrd rd) 8 base ofs k) + | Tany32, IR rd => OK (indexed_memory_access (Pstrw_a rd) 4 base ofs k) + | Tany64, IR rd => OK (indexed_memory_access (Pstrx_a rd) 8 base ofs k) + | Tany64, FR rd => OK (indexed_memory_access (Pstrd_a rd) 8 base ofs k) + | _, _ => Error (msg "Asmgen.storeind") + end. + +Definition loadptr (base: iregsp) (ofs: ptrofs) (dst: ireg) (k: code) := + indexed_memory_access (Pldrx dst) 8 base ofs k. + +Definition storeptr (src: ireg) (base: iregsp) (ofs: ptrofs) (k: code) := + indexed_memory_access (Pstrx src) 8 base ofs k. + +(** Function epilogue *) + +Definition make_epilogue (f: Mach.function) (k: code) := + loadptr XSP f.(fn_retaddr_ofs) RA + (Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) :: k). + +(** Translation of a Mach instruction. *) + +Definition transl_instr (f: Mach.function) (i: Mach.instruction) + (r29_is_parent: bool) (k: code) : res code := + match i with + | Mgetstack ofs ty dst => + loadind XSP ofs ty dst k + | Msetstack src ofs ty => + storeind src XSP ofs ty k + | Mgetparam ofs ty dst => + (* load via the frame pointer if it is valid *) + do c <- loadind X29 ofs ty dst k; + OK (if r29_is_parent then c else loadptr XSP f.(fn_link_ofs) X29 c) + | Mop op args res => + transl_op op args res k + | Mload chunk addr args dst => + transl_load chunk addr args dst k + | Mstore chunk addr args src => + transl_store chunk addr args src k + | Mcall sig (inl r) => + do r1 <- ireg_of r; OK (Pblr r1 sig :: k) + | Mcall sig (inr symb) => + OK (Pbl symb sig :: k) + | Mtailcall sig (inl r) => + do r1 <- ireg_of r; + OK (make_epilogue f (Pbr r1 sig :: k)) + | Mtailcall sig (inr symb) => + OK (make_epilogue f (Pbs symb sig :: k)) + | Mbuiltin ef args res => + OK (Pbuiltin ef (List.map (map_builtin_arg preg_of) args) (map_builtin_res preg_of res) :: k) + | Mlabel lbl => + OK (Plabel lbl :: k) + | Mgoto lbl => + OK (Pb lbl :: k) + | Mcond cond args lbl => + transl_cond_branch cond args lbl k + | Mjumptable arg tbl => + do r <- ireg_of arg; + OK (Pbtbl r tbl :: k) + | Mreturn => + OK (make_epilogue f (Pret RA :: k)) + end. + +(** Translation of a code sequence *) + +Definition it1_is_parent (before: bool) (i: Mach.instruction) : bool := + match i with + | Msetstack src ofs ty => before + | Mgetparam ofs ty dst => negb (mreg_eq dst R29) + | Mop op args res => before && negb (mreg_eq res R29) + | _ => false + end. + +(** This is the naive definition that we no longer use because it + is not tail-recursive. It is kept as specification. *) + +Fixpoint transl_code (f: Mach.function) (il: list Mach.instruction) (it1p: bool) := + match il with + | nil => OK nil + | i1 :: il' => + do k <- transl_code f il' (it1_is_parent it1p i1); + transl_instr f i1 it1p k + end. + +(** This is an equivalent definition in continuation-passing style + that runs in constant stack space. *) + +Fixpoint transl_code_rec (f: Mach.function) (il: list Mach.instruction) + (it1p: bool) (k: code -> res code) := + match il with + | nil => k nil + | i1 :: il' => + transl_code_rec f il' (it1_is_parent it1p i1) + (fun c1 => do c2 <- transl_instr f i1 it1p c1; k c2) + end. + +Definition transl_code' (f: Mach.function) (il: list Mach.instruction) (it1p: bool) := + transl_code_rec f il it1p (fun c => OK c). + +(** Translation of a whole function. Note that we must check + that the generated code contains less than [2^32] instructions, + otherwise the offset part of the [PC] code pointer could wrap + around, leading to incorrect executions. *) + +Definition transl_function (f: Mach.function) := + do c <- transl_code' f f.(Mach.fn_code) true; + OK (mkfunction f.(Mach.fn_sig) + (Pallocframe f.(fn_stacksize) f.(fn_link_ofs) :: + storeptr RA XSP f.(fn_retaddr_ofs) c)). + +Definition transf_function (f: Mach.function) : res Asm.function := + do tf <- transl_function f; + if zlt Ptrofs.max_unsigned (list_length_z tf.(fn_code)) + then Error (msg "code size exceeded") + else OK tf. + +Definition transf_fundef (f: Mach.fundef) : res Asm.fundef := + transf_partial_fundef transf_function f. + +Definition transf_program (p: Mach.program) : res Asm.program := + transform_partial_program transf_fundef p. diff --git a/aarch64/Asmgenproof.v b/aarch64/Asmgenproof.v new file mode 100644 index 00000000..eeff1956 --- /dev/null +++ b/aarch64/Asmgenproof.v @@ -0,0 +1,1026 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Correctness proof for AArch64 code generation. *) + +Require Import Coqlib Errors. +Require Import Integers Floats AST Linking. +Require Import Values Memory Events Globalenvs Smallstep. +Require Import Op Locations Mach Conventions Asm. +Require Import Asmgen Asmgenproof0 Asmgenproof1. + +Definition match_prog (p: Mach.program) (tp: Asm.program) := + match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp. + +Lemma transf_program_match: + forall p tp, transf_program p = OK tp -> match_prog p tp. +Proof. + intros. eapply match_transform_partial_program; eauto. +Qed. + +Section PRESERVATION. + +Variable prog: Mach.program. +Variable tprog: Asm.program. +Hypothesis TRANSF: match_prog prog tprog. +Let ge := Genv.globalenv prog. +Let tge := Genv.globalenv tprog. + +Lemma symbols_preserved: + forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s. +Proof (Genv.find_symbol_match TRANSF). + +Lemma senv_preserved: + Senv.equiv ge tge. +Proof (Genv.senv_match TRANSF). + +Lemma functions_translated: + forall b f, + Genv.find_funct_ptr ge b = Some f -> + exists tf, + Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf. +Proof (Genv.find_funct_ptr_transf_partial TRANSF). + +Lemma functions_transl: + forall fb f tf, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transf_function f = OK tf -> + Genv.find_funct_ptr tge fb = Some (Internal tf). +Proof. + intros. exploit functions_translated; eauto. intros [tf' [A B]]. + monadInv B. rewrite H0 in EQ; inv EQ; auto. +Qed. + +(** * Properties of control flow *) + +Lemma transf_function_no_overflow: + forall f tf, + transf_function f = OK tf -> list_length_z tf.(fn_code) <= Ptrofs.max_unsigned. +Proof. + intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. + omega. +Qed. + +Lemma exec_straight_exec: + forall fb f c ep tf tc c' rs m rs' m', + transl_code_at_pc ge (rs PC) fb f c ep tf tc -> + exec_straight tge tf tc rs m c' rs' m' -> + plus step tge (State rs m) E0 (State rs' m'). +Proof. + intros. inv H. + eapply exec_straight_steps_1; eauto. + eapply transf_function_no_overflow; eauto. + eapply functions_transl; eauto. +Qed. + +Lemma exec_straight_at: + forall fb f c ep tf tc c' ep' tc' rs m rs' m', + transl_code_at_pc ge (rs PC) fb f c ep tf tc -> + transl_code f c' ep' = OK tc' -> + exec_straight tge tf tc rs m tc' rs' m' -> + transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'. +Proof. + intros. inv H. + exploit exec_straight_steps_2; eauto. + eapply transf_function_no_overflow; eauto. + eapply functions_transl; eauto. + intros [ofs' [PC' CT']]. + rewrite PC'. constructor; auto. +Qed. + +(** The following lemmas show that the translation from Mach to Asm + preserves labels, in the sense that the following diagram commutes: +<< + translation + Mach code ------------------------ Asm instr sequence + | | + | Mach.find_label lbl find_label lbl | + | | + v v + Mach code tail ------------------- Asm instr seq tail + translation +>> + The proof demands many boring lemmas showing that Asm constructor + functions do not introduce new labels. +*) + +Section TRANSL_LABEL. + +Remark loadimm_z_label: forall sz rd l k, tail_nolabel k (loadimm_z sz rd l k). +Proof. + intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel. + induction l as [ | [n p] l]; simpl; TailNoLabel. +Qed. + +Remark loadimm_n_label: forall sz rd l k, tail_nolabel k (loadimm_n sz rd l k). +Proof. + intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel. + induction l as [ | [n p] l]; simpl; TailNoLabel. +Qed. + +Remark loadimm_label: forall sz rd n k, tail_nolabel k (loadimm sz rd n k). +Proof. + unfold loadimm; intros. destruct Nat.leb; [apply loadimm_z_label|apply loadimm_n_label]. +Qed. +Hint Resolve loadimm_label: labels. + +Remark loadimm32_label: forall r n k, tail_nolabel k (loadimm32 r n k). +Proof. + unfold loadimm32; intros. destruct (is_logical_imm32 n); TailNoLabel. +Qed. +Hint Resolve loadimm32_label: labels. + +Remark loadimm64_label: forall r n k, tail_nolabel k (loadimm64 r n k). +Proof. + unfold loadimm64; intros. destruct (is_logical_imm64 n); TailNoLabel. +Qed. +Hint Resolve loadimm64_label: labels. + +Remark addimm_aux: forall insn rd r1 n k, + (forall rd r1 n, nolabel (insn rd r1 n)) -> + tail_nolabel k (addimm_aux insn rd r1 n k). +Proof. + unfold addimm_aux; intros. + destruct Z.eqb. TailNoLabel. destruct Z.eqb; TailNoLabel. +Qed. + +Remark addimm32_label: forall rd r1 n k, tail_nolabel k (addimm32 rd r1 n k). +Proof. + unfold addimm32; intros. + destruct Int.eq. apply addimm_aux; intros; red; auto. + destruct Int.eq. apply addimm_aux; intros; red; auto. + destruct Int.lt; eapply tail_nolabel_trans; TailNoLabel. +Qed. +Hint Resolve addimm32_label: labels. + +Remark addimm64_label: forall rd r1 n k, tail_nolabel k (addimm64 rd r1 n k). +Proof. + unfold addimm64; intros. + destruct Int64.eq. apply addimm_aux; intros; red; auto. + destruct Int64.eq. apply addimm_aux; intros; red; auto. + destruct Int64.lt; eapply tail_nolabel_trans; TailNoLabel. +Qed. +Hint Resolve addimm64_label: labels. + +Remark logicalimm32_label: forall insn1 insn2 rd r1 n k, + (forall rd r1 n, nolabel (insn1 rd r1 n)) -> + (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) -> + tail_nolabel k (logicalimm32 insn1 insn2 rd r1 n k). +Proof. + unfold logicalimm32; intros. + destruct (is_logical_imm32 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +Qed. + +Remark logicalimm64_label: forall insn1 insn2 rd r1 n k, + (forall rd r1 n, nolabel (insn1 rd r1 n)) -> + (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) -> + tail_nolabel k (logicalimm64 insn1 insn2 rd r1 n k). +Proof. + unfold logicalimm64; intros. + destruct (is_logical_imm64 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +Qed. + +Remark move_extended_label: forall rd r1 ex a k, tail_nolabel k (move_extended rd r1 ex a k). +Proof. + unfold move_extended, move_extended_base; intros. destruct Int.eq, ex; TailNoLabel. +Qed. +Hint Resolve move_extended_label: labels. + +Remark arith_extended_label: forall insnX insnS rd r1 r2 ex a k, + (forall rd r1 r2 x, nolabel (insnX rd r1 r2 x)) -> + (forall rd r1 r2 s, nolabel (insnS rd r1 r2 s)) -> + tail_nolabel k (arith_extended insnX insnS rd r1 r2 ex a k). +Proof. + unfold arith_extended; intros. destruct Int.ltu. + TailNoLabel. + destruct ex; simpl; TailNoLabel. +Qed. + +Remark loadsymbol_label: forall r id ofs k, tail_nolabel k (loadsymbol r id ofs k). +Proof. + intros; unfold loadsymbol. + destruct (Archi.pic_code tt); TailNoLabel. destruct Ptrofs.eq; TailNoLabel. +Qed. +Hint Resolve loadsymbol_label: labels. + +Remark transl_cond_label: forall cond args k c, + transl_cond cond args k = OK c -> tail_nolabel k c. +Proof. + unfold transl_cond; intros; destruct cond; TailNoLabel. +- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel. +Qed. + +Remark transl_cond_branch_default_label: forall cond args lbl k c, + transl_cond_branch_default cond args lbl k = OK c -> tail_nolabel k c. +Proof. + unfold transl_cond_branch_default; intros. + eapply tail_nolabel_trans; [eapply transl_cond_label;eauto|TailNoLabel]. +Qed. +Hint Resolve transl_cond_branch_default_label: labels. + +Remark transl_cond_branch_label: forall cond args lbl k c, + transl_cond_branch cond args lbl k = OK c -> tail_nolabel k c. +Proof. + unfold transl_cond_branch; intros; destruct args; TailNoLabel; destruct cond; TailNoLabel. +- destruct c0; TailNoLabel. +- destruct c0; TailNoLabel. +- destruct (Int.is_power2 n); TailNoLabel. +- destruct (Int.is_power2 n); TailNoLabel. +- destruct c0; TailNoLabel. +- destruct c0; TailNoLabel. +- destruct (Int64.is_power2' n); TailNoLabel. +- destruct (Int64.is_power2' n); TailNoLabel. +Qed. + +Remark transl_op_label: + forall op args r k c, + transl_op op args r k = OK c -> tail_nolabel k c. +Proof. + unfold transl_op; intros; destruct op; TailNoLabel. +- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel. +- destruct (Float.eq_dec n Float.zero); TailNoLabel. +- destruct (Float32.eq_dec n Float32.zero); TailNoLabel. +- apply logicalimm32_label; unfold nolabel; auto. +- apply logicalimm32_label; unfold nolabel; auto. +- apply logicalimm32_label; unfold nolabel; auto. +- unfold shrx32. destruct Int.eq; TailNoLabel. +- apply arith_extended_label; unfold nolabel; auto. +- apply arith_extended_label; unfold nolabel; auto. +- apply logicalimm64_label; unfold nolabel; auto. +- apply logicalimm64_label; unfold nolabel; auto. +- apply logicalimm64_label; unfold nolabel; auto. +- unfold shrx64. destruct Int.eq; TailNoLabel. +- eapply tail_nolabel_trans. eapply transl_cond_label; eauto. TailNoLabel. +- destruct (preg_of r); try discriminate; TailNoLabel; + (eapply tail_nolabel_trans; [eapply transl_cond_label; eauto | TailNoLabel]). +Qed. + +Remark transl_addressing_label: + forall sz addr args insn k c, + transl_addressing sz addr args insn k = OK c -> + (forall ad, nolabel (insn ad)) -> + tail_nolabel k c. +Proof. + unfold transl_addressing; intros; destruct addr; TailNoLabel; + eapply tail_nolabel_trans; TailNoLabel. + eapply tail_nolabel_trans. apply arith_extended_label; unfold nolabel; auto. TailNoLabel. +Qed. + +Remark transl_load_label: + forall chunk addr args dst k c, + transl_load chunk addr args dst k = OK c -> tail_nolabel k c. +Proof. + unfold transl_load; intros; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto. +Qed. + +Remark transl_store_label: + forall chunk addr args src k c, + transl_store chunk addr args src k = OK c -> tail_nolabel k c. +Proof. + unfold transl_store; intros; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto. +Qed. + +Remark indexed_memory_access_label: + forall insn sz base ofs k, + (forall ad, nolabel (insn ad)) -> + tail_nolabel k (indexed_memory_access insn sz base ofs k). +Proof. + unfold indexed_memory_access; intros. destruct offset_representable. + TailNoLabel. + eapply tail_nolabel_trans; TailNoLabel. +Qed. + +Remark loadind_label: + forall base ofs ty dst k c, + loadind base ofs ty dst k = OK c -> tail_nolabel k c. +Proof. + unfold loadind; intros. + destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I. +Qed. + +Remark storeind_label: + forall src base ofs ty k c, + storeind src base ofs ty k = OK c -> tail_nolabel k c. +Proof. + unfold storeind; intros. + destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I. +Qed. + +Remark loadptr_label: + forall base ofs dst k, tail_nolabel k (loadptr base ofs dst k). +Proof. + intros. apply indexed_memory_access_label. unfold nolabel; auto. +Qed. + +Remark storeptr_label: + forall src base ofs k, tail_nolabel k (storeptr src base ofs k). +Proof. + intros. apply indexed_memory_access_label. unfold nolabel; auto. +Qed. + +Remark make_epilogue_label: + forall f k, tail_nolabel k (make_epilogue f k). +Proof. + unfold make_epilogue; intros. eapply tail_nolabel_trans. apply loadptr_label. TailNoLabel. +Qed. + +Lemma transl_instr_label: + forall f i ep k c, + transl_instr f i ep k = OK c -> + match i with Mlabel lbl => c = Plabel lbl :: k | _ => tail_nolabel k c end. +Proof. + unfold transl_instr; intros; destruct i; TailNoLabel. +- eapply loadind_label; eauto. +- eapply storeind_label; eauto. +- destruct ep. eapply loadind_label; eauto. + eapply tail_nolabel_trans. apply loadptr_label. eapply loadind_label; eauto. +- eapply transl_op_label; eauto. +- eapply transl_load_label; eauto. +- eapply transl_store_label; eauto. +- destruct s0; monadInv H; TailNoLabel. +- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]). +- eapply transl_cond_branch_label; eauto. +- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]. +Qed. + +Lemma transl_instr_label': + forall lbl f i ep k c, + transl_instr f i ep k = OK c -> + find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k. +Proof. + intros. exploit transl_instr_label; eauto. + destruct i; try (intros [A B]; apply B). + intros. subst c. simpl. auto. +Qed. + +Lemma transl_code_label: + forall lbl f c ep tc, + transl_code f c ep = OK tc -> + match Mach.find_label lbl c with + | None => find_label lbl tc = None + | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc' + end. +Proof. + induction c; simpl; intros. + inv H. auto. + monadInv H. rewrite (transl_instr_label' lbl _ _ _ _ _ EQ0). + generalize (Mach.is_label_correct lbl a). + destruct (Mach.is_label lbl a); intros. + subst a. simpl in EQ. exists x; auto. + eapply IHc; eauto. +Qed. + +Lemma transl_find_label: + forall lbl f tf, + transf_function f = OK tf -> + match Mach.find_label lbl f.(Mach.fn_code) with + | None => find_label lbl tf.(fn_code) = None + | Some c => exists tc, find_label lbl tf.(fn_code) = Some tc /\ transl_code f c false = OK tc + end. +Proof. + intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. + monadInv EQ. rewrite transl_code'_transl_code in EQ0. unfold fn_code. + simpl. destruct (storeptr_label X30 XSP (fn_retaddr_ofs f) x) as [A B]; rewrite B. + eapply transl_code_label; eauto. +Qed. + +End TRANSL_LABEL. + +(** A valid branch in a piece of Mach code translates to a valid ``go to'' + transition in the generated Asm code. *) + +Lemma find_label_goto_label: + forall f tf lbl rs m c' b ofs, + Genv.find_funct_ptr ge b = Some (Internal f) -> + transf_function f = OK tf -> + rs PC = Vptr b ofs -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + exists tc', exists rs', + goto_label tf lbl rs m = Next rs' m + /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc' + /\ forall r, r <> PC -> rs'#r = rs#r. +Proof. + intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2. + intros [tc [A B]]. + exploit label_pos_code_tail; eauto. instantiate (1 := 0). + intros [pos' [P [Q R]]]. + exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))). + split. unfold goto_label. rewrite P. rewrite H1. auto. + split. rewrite Pregmap.gss. constructor; auto. + rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q. + auto. omega. + generalize (transf_function_no_overflow _ _ H0). omega. + intros. apply Pregmap.gso; auto. +Qed. + +(** Existence of return addresses *) + +Lemma return_address_exists: + forall f sg ros c, is_tail (Mcall sg ros :: c) f.(Mach.fn_code) -> + exists ra, return_address_offset f c ra. +Proof. + intros. eapply Asmgenproof0.return_address_exists; eauto. +- intros. exploit transl_instr_label; eauto. + destruct i; try (intros [A B]; apply A). intros. subst c0. repeat constructor. +- intros. monadInv H0. + destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. monadInv EQ. + rewrite transl_code'_transl_code in EQ0. + exists x; exists true; split; auto. unfold fn_code. + constructor. apply (storeptr_label X30 XSP (fn_retaddr_ofs f0) x). +- exact transf_function_no_overflow. +Qed. + +(** * Proof of semantic preservation *) + +(** Semantic preservation is proved using simulation diagrams + of the following form. +<< + st1 --------------- st2 + | | + t| *|t + | | + v v + st1'--------------- st2' +>> + The invariant is the [match_states] predicate below, which includes: +- The Asm code pointed by the PC register is the translation of + the current Mach code sequence. +- Mach register values and Asm register values agree. +*) + +Inductive match_states: Mach.state -> Asm.state -> Prop := + | match_states_intro: + forall s fb sp c ep ms m m' rs f tf tc + (STACKS: match_stack ge s) + (FIND: Genv.find_funct_ptr ge fb = Some (Internal f)) + (MEXT: Mem.extends m m') + (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc) + (AG: agree ms sp rs) + (DXP: ep = true -> rs#X29 = parent_sp s), + match_states (Mach.State s fb sp c ms m) + (Asm.State rs m') + | match_states_call: + forall s fb ms m m' rs + (STACKS: match_stack ge s) + (MEXT: Mem.extends m m') + (AG: agree ms (parent_sp s) rs) + (ATPC: rs PC = Vptr fb Ptrofs.zero) + (ATLR: rs RA = parent_ra s), + match_states (Mach.Callstate s fb ms m) + (Asm.State rs m') + | match_states_return: + forall s ms m m' rs + (STACKS: match_stack ge s) + (MEXT: Mem.extends m m') + (AG: agree ms (parent_sp s) rs) + (ATPC: rs PC = parent_ra s), + match_states (Mach.Returnstate s ms m) + (Asm.State rs m'). + +Lemma exec_straight_steps: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2, + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists rs2, + exec_straight tge tf c rs1 m1' k rs2 m2' + /\ agree ms2 sp rs2 + /\ (it1_is_parent ep i = true -> rs2#X29 = parent_sp s)) -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c ms2 m2) st'. +Proof. + intros. inversion H2. subst. monadInv H7. + exploit H3; eauto. intros [rs2 [A [B C]]]. + exists (State rs2 m2'); split. + eapply exec_straight_exec; eauto. + econstructor; eauto. eapply exec_straight_at; eauto. +Qed. + +Lemma exec_straight_steps_goto: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + it1_is_parent ep i = false -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists jmp, exists k', exists rs2, + exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2' + /\ agree ms2 sp rs2 + /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c' ms2 m2) st'. +Proof. + intros. inversion H3. subst. monadInv H9. + exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. + generalize (functions_transl _ _ _ H7 H8); intro FN. + generalize (transf_function_no_overflow _ _ H8); intro NOOV. + exploit exec_straight_steps_2; eauto. + intros [ofs' [PC2 CT2]]. + exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + eapply plus_right'. + eapply exec_straight_steps_1; eauto. + econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + traceEq. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +Qed. + +Lemma exec_straight_opt_steps_goto: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + it1_is_parent ep i = false -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists jmp, exists k', exists rs2, + exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2' + /\ agree ms2 sp rs2 + /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c' ms2 m2) st'. +Proof. + intros. inversion H3. subst. monadInv H9. + exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. + generalize (functions_transl _ _ _ H7 H8); intro FN. + generalize (transf_function_no_overflow _ _ H8); intro NOOV. + inv A. +- exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + apply plus_one. econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +- exploit exec_straight_steps_2; eauto. + intros [ofs' [PC2 CT2]]. + exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + eapply plus_right'. + eapply exec_straight_steps_1; eauto. + econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + traceEq. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +Qed. + +(** We need to show that, in the simulation diagram, we cannot + take infinitely many Mach transitions that correspond to zero + transitions on the Asm side. Actually, all Mach transitions + correspond to at least one Asm transition, except the + transition from [Machsem.Returnstate] to [Machsem.State]. + So, the following integer measure will suffice to rule out + the unwanted behaviour. *) + +Definition measure (s: Mach.state) : nat := + match s with + | Mach.State _ _ _ _ _ _ => 0%nat + | Mach.Callstate _ _ _ _ => 0%nat + | Mach.Returnstate _ _ _ => 1%nat + end. + +Remark preg_of_not_X29: forall r, negb (mreg_eq r R29) = true -> IR X29 <> preg_of r. +Proof. + intros. change (IR X29) with (preg_of R29). red; intros. + exploit preg_of_injective; eauto. intros; subst r; discriminate. +Qed. + +Lemma sp_val': forall ms sp rs, agree ms sp rs -> sp = rs XSP. +Proof. + intros. eapply sp_val; eauto. +Qed. + +(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *) + +Theorem step_simulation: + forall S1 t S2, Mach.step return_address_offset ge S1 t S2 -> + forall S1' (MS: match_states S1 S1'), + (exists S2', plus step tge S1' t S2' /\ match_states S2 S2') + \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat. +Proof. + induction 1; intros; inv MS. + +- (* Mlabel *) + left; eapply exec_straight_steps; eauto; intros. + monadInv TR. econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split. apply agree_nextinstr; auto. simpl; congruence. + +- (* Mgetstack *) + unfold load_stack in H. + exploit Mem.loadv_extends; eauto. intros [v' [A B]]. + rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit loadind_correct; eauto with asmgen. intros [rs' [P [Q R]]]. + exists rs'; split. eauto. + split. eapply agree_set_mreg; eauto with asmgen. congruence. + simpl; congruence. + +- (* Msetstack *) + unfold store_stack in H. + assert (Val.lessdef (rs src) (rs0 (preg_of src))) by (eapply preg_val; eauto). + exploit Mem.storev_extends; eauto. intros [m2' [A B]]. + left; eapply exec_straight_steps; eauto. + rewrite (sp_val _ _ _ AG) in A. intros. simpl in TR. + exploit storeind_correct; eauto with asmgen. intros [rs' [P Q]]. + exists rs'; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; intros. rewrite Q; auto with asmgen. + +- (* Mgetparam *) + assert (f0 = f) by congruence; subst f0. + unfold load_stack in *. + exploit Mem.loadv_extends. eauto. eexact H0. auto. + intros [parent' [A B]]. rewrite (sp_val' _ _ _ AG) in A. + exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'. + exploit Mem.loadv_extends. eauto. eexact H1. auto. + intros [v' [C D]]. +Opaque loadind. + left; eapply exec_straight_steps; eauto; intros. monadInv TR. + destruct ep. +(* X30 contains parent *) + exploit loadind_correct. eexact EQ. + instantiate (2 := rs0). simpl; rewrite DXP; eauto. simpl; congruence. + intros [rs1 [P [Q R]]]. + exists rs1; split. eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen. + simpl; intros. rewrite R; auto with asmgen. + apply preg_of_not_X29; auto. +(* X30 does not contain parent *) + exploit loadptr_correct. eexact A. simpl; congruence. intros [rs1 [P [Q R]]]. + exploit loadind_correct. eexact EQ. instantiate (2 := rs1). simpl; rewrite Q. eauto. simpl; congruence. + intros [rs2 [S [T U]]]. + exists rs2; split. eapply exec_straight_trans; eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto. + instantiate (1 := rs1#X29 <- (rs2#X29)). intros. + rewrite Pregmap.gso; auto with asmgen. + congruence. + intros. unfold Pregmap.set. destruct (PregEq.eq r' X29). congruence. auto with asmgen. + simpl; intros. rewrite U; auto with asmgen. + apply preg_of_not_X29; auto. + +- (* Mop *) + assert (eval_operation tge sp op (map rs args) m = Some v). + { rewrite <- H. apply eval_operation_preserved. exact symbols_preserved. } + exploit eval_operation_lessdef. eapply preg_vals; eauto. eauto. eexact H0. + intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. split. + apply agree_set_undef_mreg with rs0; auto. + apply Val.lessdef_trans with v'; auto. + simpl; intros. InvBooleans. + rewrite R; auto. apply preg_of_not_X29; auto. +Local Transparent destroyed_by_op. + destruct op; try exact I; simpl; congruence. + +- (* Mload *) + assert (Op.eval_addressing tge sp addr (map rs args) = Some a). + { rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. } + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + exploit Mem.loadv_extends; eauto. intros [v' [C D]]. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_load_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. + split. eapply agree_set_undef_mreg; eauto. congruence. + simpl; congruence. + +- (* Mstore *) + assert (Op.eval_addressing tge sp addr (map rs args) = Some a). + { rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. } + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + assert (Val.lessdef (rs src) (rs0 (preg_of src))) by (eapply preg_val; eauto). + exploit Mem.storev_extends; eauto. intros [m2' [C D]]. + left; eapply exec_straight_steps; eauto. + intros. simpl in TR. exploit transl_store_correct; eauto. intros [rs2 [P Q]]. + exists rs2; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; congruence. + +- (* Mcall *) + assert (f0 = f) by congruence. subst f0. + inv AT. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + { eapply transf_function_no_overflow; eauto. } + destruct ros as [rf|fid]; simpl in H; monadInv H5. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + { destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. } + assert (rs0 x0 = Vptr f' Ptrofs.zero). + { exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. } + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + { econstructor; eauto. } + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. ++ (* Direct call *) + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + econstructor; eauto. + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. + +- (* Mtailcall *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + { eapply transf_function_no_overflow; eauto. } + exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]]. + destruct ros as [rf|fid]; simpl in H; monadInv H7. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + { destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. } + assert (rs0 x0 = Vptr f' Ptrofs.zero). + { exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. } + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption. ++ (* Direct call *) + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto. + +- (* Mbuiltin *) + inv AT. monadInv H4. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H3); intro NOOV. + exploit builtin_args_match; eauto. intros [vargs' [P Q]]. + exploit external_call_mem_extends; eauto. + intros [vres' [m2' [A [B [C D]]]]]. + left. econstructor; split. apply plus_one. + eapply exec_step_builtin. eauto. eauto. + eapply find_instr_tail; eauto. + erewrite <- sp_val by eauto. + eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + eauto. + econstructor; eauto. + instantiate (2 := tf); instantiate (1 := x). + unfold nextinstr. rewrite Pregmap.gss. + rewrite set_res_other. rewrite undef_regs_other_2. + rewrite <- H1. simpl. econstructor; eauto. + eapply code_tail_next_int; eauto. + rewrite preg_notin_charact. intros. auto with asmgen. + auto with asmgen. + apply agree_nextinstr. eapply agree_set_res; auto. + eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto. + congruence. + +- (* Mgoto *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H4. + exploit find_label_goto_label; eauto. intros [tc' [rs' [GOTO [AT2 INV]]]]. + left; exists (State rs' m'); split. + apply plus_one. econstructor; eauto. + eapply functions_transl; eauto. + eapply find_instr_tail; eauto. + simpl; eauto. + econstructor; eauto. + eapply agree_exten; eauto with asmgen. + congruence. + +- (* Mcond true *) + assert (f0 = f) by congruence. subst f0. + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_opt_steps_goto; eauto. + intros. simpl in TR. + exploit transl_cond_branch_correct; eauto. intros (rs' & jmp & A & B & C). + exists jmp; exists k; exists rs'. + split. eexact A. + split. apply agree_exten with rs0; auto with asmgen. + exact B. + +- (* Mcond false *) + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit transl_cond_branch_correct; eauto. intros (rs' & jmp & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. apply exec_straight_one. eexact B. auto. + split. apply agree_exten with rs0; auto. intros. Simpl. + simpl; congruence. + +- (* Mjumptable *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H6. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H5); intro NOOV. + exploit find_label_goto_label. eauto. eauto. + instantiate (2 := rs0#X16 <- Vundef #X17 <- Vundef). + Simpl. eauto. + eauto. + intros [tc' [rs' [A [B C]]]]. + exploit ireg_val; eauto. rewrite H. intros LD; inv LD. + left; econstructor; split. + apply plus_one. econstructor; eauto. + eapply find_instr_tail; eauto. + simpl. Simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A. + econstructor; eauto. + eapply agree_undef_regs; eauto. + simpl. intros. rewrite C; auto with asmgen. Simpl. + congruence. + +- (* Mreturn *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. simpl in H6; monadInv H6. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + eapply transf_function_no_overflow; eauto. + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + +- (* internal function *) + + exploit functions_translated; eauto. intros [tf [A B]]. monadInv B. + generalize EQ; intros EQ'. monadInv EQ'. + destruct (zlt Ptrofs.max_unsigned (list_length_z x0.(fn_code))); inversion EQ1. clear EQ1. subst x0. + unfold store_stack in *. + exploit Mem.alloc_extends. eauto. eauto. apply Z.le_refl. apply Z.le_refl. + intros [m1' [C D]]. + exploit Mem.storev_extends. eexact D. eexact H1. eauto. eauto. + intros [m2' [F G]]. + simpl chunk_of_type in F. + exploit Mem.storev_extends. eexact G. eexact H2. eauto. eauto. + intros [m3' [P Q]]. + change (chunk_of_type Tptr) with Mint64 in *. + (* Execution of function prologue *) + monadInv EQ0. rewrite transl_code'_transl_code in EQ1. + set (tfbody := Pallocframe (fn_stacksize f) (fn_link_ofs f) :: + storeptr RA XSP (fn_retaddr_ofs f) x0) in *. + set (tf := {| fn_sig := Mach.fn_sig f; fn_code := tfbody |}) in *. + set (rs2 := nextinstr (rs0#X29 <- (parent_sp s) #SP <- sp #X16 <- Vundef)). + exploit (storeptr_correct tge tf XSP (fn_retaddr_ofs f) RA x0 m2' m3' rs2). + simpl preg_of_iregsp. change (rs2 X30) with (rs0 X30). rewrite ATLR. + change (rs2 X2) with sp. eexact P. + simpl; congruence. congruence. + intros (rs3 & U & V). + assert (EXEC_PROLOGUE: + exec_straight tge tf + tf.(fn_code) rs0 m' + x0 rs3 m3'). + { change (fn_code tf) with tfbody; unfold tfbody. + apply exec_straight_step with rs2 m2'. + unfold exec_instr. rewrite C. fold sp. + rewrite <- (sp_val _ _ _ AG). rewrite F. reflexivity. + reflexivity. + eexact U. } + exploit exec_straight_steps_2; eauto using functions_transl. omega. constructor. + intros (ofs' & X & Y). + left; exists (State rs3 m3'); split. + eapply exec_straight_steps_1; eauto. omega. constructor. + econstructor; eauto. + rewrite X; econstructor; eauto. + apply agree_exten with rs2; eauto with asmgen. + unfold rs2. + apply agree_nextinstr. apply agree_set_other; auto with asmgen. + apply agree_change_sp with (parent_sp s). + apply agree_undef_regs with rs0. auto. +Local Transparent destroyed_at_function_entry. simpl. + simpl; intros; Simpl. + unfold sp; congruence. + intros. rewrite V by auto with asmgen. reflexivity. + +- (* external function *) + exploit functions_translated; eauto. + intros [tf [A B]]. simpl in B. inv B. + exploit extcall_arguments_match; eauto. + intros [args' [C D]]. + exploit external_call_mem_extends; eauto. + intros [res' [m2' [P [Q [R S]]]]]. + left; econstructor; split. + apply plus_one. eapply exec_step_external; eauto. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + econstructor; eauto. + unfold loc_external_result. apply agree_set_other; auto. apply agree_set_pair; auto. + apply agree_undef_caller_save_regs; auto. + +- (* return *) + inv STACKS. simpl in *. + right. split. omega. split. auto. + rewrite <- ATPC in H5. + econstructor; eauto. congruence. +Qed. + +Lemma transf_initial_states: + forall st1, Mach.initial_state prog st1 -> + exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2. +Proof. + intros. inversion H. unfold ge0 in *. + econstructor; split. + econstructor. + eapply (Genv.init_mem_transf_partial TRANSF); eauto. + replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero) + with (Vptr fb Ptrofs.zero). + econstructor; eauto. + constructor. + apply Mem.extends_refl. + split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence. + intros. rewrite Regmap.gi. auto. + unfold Genv.symbol_address. + rewrite (match_program_main TRANSF). + rewrite symbols_preserved. + unfold ge; rewrite H1. auto. +Qed. + +Lemma transf_final_states: + forall st1 st2 r, + match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r. +Proof. + intros. inv H0. inv H. constructor. assumption. + compute in H1. inv H1. + generalize (preg_val _ _ _ R0 AG). rewrite H2. intros LD; inv LD. auto. +Qed. + +Theorem transf_program_correct: + forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog). +Proof. + eapply forward_simulation_star with (measure := measure). + apply senv_preserved. + eexact transf_initial_states. + eexact transf_final_states. + exact step_simulation. +Qed. + +End PRESERVATION. diff --git a/aarch64/Asmgenproof1.v b/aarch64/Asmgenproof1.v new file mode 100644 index 00000000..d60ad2bc --- /dev/null +++ b/aarch64/Asmgenproof1.v @@ -0,0 +1,1836 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Correctness proof for AArch64 code generation: auxiliary results. *) + +Require Import Recdef Coqlib Zwf Zbits. +Require Import Maps Errors AST Integers Floats Values Memory Globalenvs. +Require Import Op Locations Mach Asm Conventions. +Require Import Asmgen. +Require Import Asmgenproof0. + +Local Transparent Archi.ptr64. + +(** Properties of registers *) + +Lemma preg_of_iregsp_not_PC: forall r, preg_of_iregsp r <> PC. +Proof. + destruct r; simpl; congruence. +Qed. +Hint Resolve preg_of_iregsp_not_PC: asmgen. + +Lemma preg_of_not_X16: forall r, preg_of r <> X16. +Proof. + destruct r; simpl; congruence. +Qed. + +Lemma ireg_of_not_X16: forall r x, ireg_of r = OK x -> x <> X16. +Proof. + unfold ireg_of; intros. destruct (preg_of r) eqn:E; inv H. + red; intros; subst x. elim (preg_of_not_X16 r); auto. +Qed. + +Lemma ireg_of_not_X16': forall r x, ireg_of r = OK x -> IR x <> IR X16. +Proof. + intros. apply ireg_of_not_X16 in H. congruence. +Qed. + +Hint Resolve preg_of_not_X16 ireg_of_not_X16 ireg_of_not_X16': asmgen. + +(** Useful simplification tactic *) + + +Ltac Simplif := + ((rewrite nextinstr_inv by eauto with asmgen) + || (rewrite nextinstr_inv1 by eauto with asmgen) + || (rewrite Pregmap.gss) + || (rewrite nextinstr_pc) + || (rewrite Pregmap.gso by eauto with asmgen)); auto with asmgen. + +Ltac Simpl := repeat Simplif. + +(** * Correctness of ARM constructor functions *) + +Section CONSTRUCTORS. + +Variable ge: genv. +Variable fn: function. + +(** Decomposition of integer literals *) + +Inductive wf_decomposition: list (Z * Z) -> Prop := + | wf_decomp_nil: + wf_decomposition nil + | wf_decomp_cons: forall m n p l, + n = Zzero_ext 16 m -> 0 <= p -> wf_decomposition l -> + wf_decomposition ((n, p) :: l). + +Lemma decompose_int_wf: + forall N n p, 0 <= p -> wf_decomposition (decompose_int N n p). +Proof. +Local Opaque Zzero_ext. + induction N as [ | N]; simpl; intros. +- constructor. +- set (frag := Zzero_ext 16 (Z.shiftr n p)) in *. destruct (Z.eqb frag 0). ++ apply IHN. omega. ++ econstructor. reflexivity. omega. apply IHN; omega. +Qed. + +Fixpoint recompose_int (accu: Z) (l: list (Z * Z)) : Z := + match l with + | nil => accu + | (n, p) :: l => recompose_int (Zinsert accu n p 16) l + end. + +Lemma decompose_int_correct: + forall N n p accu, + 0 <= p -> + (forall i, p <= i -> Z.testbit accu i = false) -> + (forall i, 0 <= i < p + Z.of_nat N * 16 -> + Z.testbit (recompose_int accu (decompose_int N n p)) i = + if zlt i p then Z.testbit accu i else Z.testbit n i). +Proof. + induction N as [ | N]; intros until accu; intros PPOS ABOVE i RANGE. +- simpl. rewrite zlt_true; auto. xomega. +- rewrite inj_S in RANGE. simpl. + set (frag := Zzero_ext 16 (Z.shiftr n p)). + assert (FRAG: forall i, p <= i < p + 16 -> Z.testbit n i = Z.testbit frag (i - p)). + { unfold frag; intros. rewrite Zzero_ext_spec by omega. rewrite zlt_true by omega. + rewrite Z.shiftr_spec by omega. f_equal; omega. } + destruct (Z.eqb_spec frag 0). ++ rewrite IHN. +* destruct (zlt i p). rewrite zlt_true by omega. auto. + destruct (zlt i (p + 16)); auto. + rewrite ABOVE by omega. rewrite FRAG by omega. rewrite e, Z.testbit_0_l. auto. +* omega. +* intros; apply ABOVE; omega. +* xomega. ++ simpl. rewrite IHN. +* destruct (zlt i (p + 16)). +** rewrite Zinsert_spec by omega. unfold proj_sumbool. + rewrite zlt_true by omega. + destruct (zlt i p). + rewrite zle_false by omega. auto. + rewrite zle_true by omega. simpl. symmetry; apply FRAG; omega. +** rewrite Z.ldiff_spec, Z.shiftl_spec by omega. + change 65535 with (two_p 16 - 1). rewrite Ztestbit_two_p_m1 by omega. + rewrite zlt_false by omega. rewrite zlt_false by omega. apply andb_true_r. +* omega. +* intros. rewrite Zinsert_spec by omega. unfold proj_sumbool. + rewrite zle_true by omega. rewrite zlt_false by omega. simpl. + apply ABOVE. omega. +* xomega. +Qed. + +Corollary decompose_int_eqmod: forall N n, + eqmod (two_power_nat (N * 16)%nat) (recompose_int 0 (decompose_int N n 0)) n. +Proof. + intros; apply eqmod_same_bits; intros. + rewrite decompose_int_correct. apply zlt_false; omega. + omega. intros; apply Z.testbit_0_l. xomega. +Qed. + +Corollary decompose_notint_eqmod: forall N n, + eqmod (two_power_nat (N * 16)%nat) + (Z.lnot (recompose_int 0 (decompose_int N (Z.lnot n) 0))) n. +Proof. + intros; apply eqmod_same_bits; intros. + rewrite Z.lnot_spec, decompose_int_correct. + rewrite zlt_false by omega. rewrite Z.lnot_spec by omega. apply negb_involutive. + omega. intros; apply Z.testbit_0_l. xomega. omega. +Qed. + +Lemma negate_decomposition_wf: + forall l, wf_decomposition l -> wf_decomposition (negate_decomposition l). +Proof. + induction 1; simpl; econstructor; auto. + instantiate (1 := (Z.lnot m)). + apply equal_same_bits; intros. + rewrite H. change 65535 with (two_p 16 - 1). + rewrite Z.lxor_spec, !Zzero_ext_spec, Z.lnot_spec, Ztestbit_two_p_m1 by omega. + destruct (zlt i 16). + apply xorb_true_r. + auto. +Qed. + +Lemma Zinsert_eqmod: + forall n x1 x2 y p l, 0 <= p -> 0 <= l -> + eqmod (two_power_nat n) x1 x2 -> + eqmod (two_power_nat n) (Zinsert x1 y p l) (Zinsert x2 y p l). +Proof. + intros. apply eqmod_same_bits; intros. rewrite ! Zinsert_spec by omega. + destruct (zle p i && zlt i (p + l)); auto. + apply same_bits_eqmod with n; auto. +Qed. + +Lemma Zinsert_0_l: + forall y p l, + 0 <= p -> 0 <= l -> + Z.shiftl (Zzero_ext l y) p = Zinsert 0 (Zzero_ext l y) p l. +Proof. + intros. apply equal_same_bits; intros. + rewrite Zinsert_spec by omega. unfold proj_sumbool. + destruct (zlt i p); [rewrite zle_false by omega|rewrite zle_true by omega]; simpl. +- rewrite Z.testbit_0_l, Z.shiftl_spec_low by auto. auto. +- rewrite Z.shiftl_spec by omega. + destruct (zlt i (p + l)); auto. + rewrite Zzero_ext_spec, zlt_false, Z.testbit_0_l by omega. auto. +Qed. + +Lemma recompose_int_negated: + forall l, wf_decomposition l -> + forall accu, recompose_int (Z.lnot accu) (negate_decomposition l) = Z.lnot (recompose_int accu l). +Proof. + induction 1; intros accu; simpl. +- auto. +- rewrite <- IHwf_decomposition. f_equal. apply equal_same_bits; intros. + rewrite Z.lnot_spec, ! Zinsert_spec, Z.lxor_spec, Z.lnot_spec by omega. + unfold proj_sumbool. + destruct (zle p i); simpl; auto. + destruct (zlt i (p + 16)); simpl; auto. + change 65535 with (two_p 16 - 1). + rewrite Ztestbit_two_p_m1 by omega. rewrite zlt_true by omega. + apply xorb_true_r. +Qed. + +Lemma exec_loadimm_k_w: + forall (rd: ireg) k m l, + wf_decomposition l -> + forall (rs: regset) accu, + rs#rd = Vint (Int.repr accu) -> + exists rs', + exec_straight_opt ge fn (loadimm_k W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (recompose_int accu l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + induction 1; intros rs accu ACCU; simpl. +- exists rs; split. apply exec_straight_opt_refl. auto. +- destruct (IHwf_decomposition + (nextinstr (rs#rd <- (insert_in_int rs#rd n p 16))) + (Zinsert accu n p 16)) + as (rs' & P & Q & R). + Simpl. rewrite ACCU. simpl. f_equal. apply Int.eqm_samerepr. + apply Zinsert_eqmod. auto. omega. apply Int.eqm_sym; apply Int.eqm_unsigned_repr. + exists rs'; split. + eapply exec_straight_opt_step_opt. simpl; eauto. auto. exact P. + split. exact Q. intros; Simpl. rewrite R by auto. Simpl. +Qed. + +Lemma exec_loadimm_z_w: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_z W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (recompose_int 0 l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_z; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Zinsert 0 n p 16). + set (rs1 := nextinstr (rs#rd <- (Vint (Int.repr accu0)))). + destruct (exec_loadimm_k_w rd k m l H1 rs1 accu0) as (rs2 & P & Q & R); auto. + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. unfold accu0. rewrite H. apply Zinsert_0_l; omega. + reflexivity. + split. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm_n_w: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_n W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (Z.lnot (recompose_int 0 l))) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_n; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Z.lnot (Zinsert 0 n p 16)). + set (rs1 := nextinstr (rs#rd <- (Vint (Int.repr accu0)))). + destruct (exec_loadimm_k_w rd k m (negate_decomposition l) + (negate_decomposition_wf l H1) + rs1 accu0) as (rs2 & P & Q & R). + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. + unfold accu0. f_equal. rewrite H. apply Zinsert_0_l; omega. + reflexivity. + split. unfold accu0 in Q; rewrite recompose_int_negated in Q by auto. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm32: + forall rd n k rs m, + exists rs', + exec_straight ge fn (loadimm32 rd n k) rs m k rs' m + /\ rs'#rd = Vint n + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm32, loadimm; intros. + destruct (is_logical_imm32 n). +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite Int.repr_unsigned, Int.or_zero_l; auto. + intros; Simpl. +- set (dz := decompose_int 2%nat (Int.unsigned n) 0). + set (dn := decompose_int 2%nat (Z.lnot (Int.unsigned n)) 0). + assert (A: Int.repr (recompose_int 0 dz) = n). + { transitivity (Int.repr (Int.unsigned n)). + apply Int.eqm_samerepr. apply decompose_int_eqmod. + apply Int.repr_unsigned. } + assert (B: Int.repr (Z.lnot (recompose_int 0 dn)) = n). + { transitivity (Int.repr (Int.unsigned n)). + apply Int.eqm_samerepr. apply decompose_notint_eqmod. + apply Int.repr_unsigned. } + destruct Nat.leb. ++ rewrite <- A. apply exec_loadimm_z_w. apply decompose_int_wf; omega. ++ rewrite <- B. apply exec_loadimm_n_w. apply decompose_int_wf; omega. +Qed. + +Lemma exec_loadimm_k_x: + forall (rd: ireg) k m l, + wf_decomposition l -> + forall (rs: regset) accu, + rs#rd = Vlong (Int64.repr accu) -> + exists rs', + exec_straight_opt ge fn (loadimm_k X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (recompose_int accu l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + induction 1; intros rs accu ACCU; simpl. +- exists rs; split. apply exec_straight_opt_refl. auto. +- destruct (IHwf_decomposition + (nextinstr (rs#rd <- (insert_in_long rs#rd n p 16))) + (Zinsert accu n p 16)) + as (rs' & P & Q & R). + Simpl. rewrite ACCU. simpl. f_equal. apply Int64.eqm_samerepr. + apply Zinsert_eqmod. auto. omega. apply Int64.eqm_sym; apply Int64.eqm_unsigned_repr. + exists rs'; split. + eapply exec_straight_opt_step_opt. simpl; eauto. auto. exact P. + split. exact Q. intros; Simpl. rewrite R by auto. Simpl. +Qed. + +Lemma exec_loadimm_z_x: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_z X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (recompose_int 0 l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_z; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Zinsert 0 n p 16). + set (rs1 := nextinstr (rs#rd <- (Vlong (Int64.repr accu0)))). + destruct (exec_loadimm_k_x rd k m l H1 rs1 accu0) as (rs2 & P & Q & R); auto. + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. unfold accu0. rewrite H. apply Zinsert_0_l; omega. + reflexivity. + split. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm_n_x: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_n X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (Z.lnot (recompose_int 0 l))) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_n; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Z.lnot (Zinsert 0 n p 16)). + set (rs1 := nextinstr (rs#rd <- (Vlong (Int64.repr accu0)))). + destruct (exec_loadimm_k_x rd k m (negate_decomposition l) + (negate_decomposition_wf l H1) + rs1 accu0) as (rs2 & P & Q & R). + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. + unfold accu0. f_equal. rewrite H. apply Zinsert_0_l; omega. + reflexivity. + split. unfold accu0 in Q; rewrite recompose_int_negated in Q by auto. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm64: + forall rd n k rs m, + exists rs', + exec_straight ge fn (loadimm64 rd n k) rs m k rs' m + /\ rs'#rd = Vlong n + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm64, loadimm; intros. + destruct (is_logical_imm64 n). +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite Int64.repr_unsigned, Int64.or_zero_l; auto. + intros; Simpl. +- set (dz := decompose_int 4%nat (Int64.unsigned n) 0). + set (dn := decompose_int 4%nat (Z.lnot (Int64.unsigned n)) 0). + assert (A: Int64.repr (recompose_int 0 dz) = n). + { transitivity (Int64.repr (Int64.unsigned n)). + apply Int64.eqm_samerepr. apply decompose_int_eqmod. + apply Int64.repr_unsigned. } + assert (B: Int64.repr (Z.lnot (recompose_int 0 dn)) = n). + { transitivity (Int64.repr (Int64.unsigned n)). + apply Int64.eqm_samerepr. apply decompose_notint_eqmod. + apply Int64.repr_unsigned. } + destruct Nat.leb. ++ rewrite <- A. apply exec_loadimm_z_x. apply decompose_int_wf; omega. ++ rewrite <- B. apply exec_loadimm_n_x. apply decompose_int_wf; omega. +Qed. + +(** Add immediate *) + +Lemma exec_addimm_aux_32: + forall (insn: iregsp -> iregsp -> Z -> instruction) (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (Vint (Int.repr n))))) m) -> + (forall v n1 n2, sem (sem v (Vint n1)) (Vint n2) = sem v (Vint (Int.add n1 n2))) -> + forall rd r1 n k rs m, + exists rs', + exec_straight ge fn (addimm_aux insn rd r1 (Int.unsigned n) k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros insn sem SEM ASSOC; intros. unfold addimm_aux. + set (nlo := Zzero_ext 12 (Int.unsigned n)). set (nhi := Int.unsigned n - nlo). + assert (E: Int.unsigned n = nhi + nlo) by (unfold nlo, nhi; omega). + rewrite <- (Int.repr_unsigned n). + destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; omega. + intros; Simpl. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; omega. + intros; Simpl. +- econstructor; split. eapply exec_straight_two. + apply SEM. apply SEM. Simpl. Simpl. + split. Simpl. rewrite ASSOC. do 2 f_equal. apply Int.eqm_samerepr. + rewrite E. auto with ints. + intros; Simpl. +Qed. + +Lemma exec_addimm32: + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (addimm32 rd r1 n k) rs m k rs' m + /\ rs'#rd = Val.add rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros. unfold addimm32. set (nn := Int.neg n). + destruct (Int.eq n (Int.zero_ext 24 n)); [| destruct (Int.eq nn (Int.zero_ext 24 nn))]. +- apply exec_addimm_aux_32 with (sem := Val.add). auto. intros; apply Val.add_assoc. +- rewrite <- Val.sub_opp_add. + apply exec_addimm_aux_32 with (sem := Val.sub). auto. + intros. rewrite ! Val.sub_add_opp, Val.add_assoc. rewrite Int.neg_add_distr. auto. +- destruct (Int.lt n Int.zero). ++ rewrite <- Val.sub_opp_add; fold nn. + edestruct (exec_loadimm32 X16 nn) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite B, C; eauto with asmgen. + intros; Simpl. ++ edestruct (exec_loadimm32 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite B, C; eauto with asmgen. + intros; Simpl. +Qed. + +Lemma exec_addimm_aux_64: + forall (insn: iregsp -> iregsp -> Z -> instruction) (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (Vlong (Int64.repr n))))) m) -> + (forall v n1 n2, sem (sem v (Vlong n1)) (Vlong n2) = sem v (Vlong (Int64.add n1 n2))) -> + forall rd r1 n k rs m, + exists rs', + exec_straight ge fn (addimm_aux insn rd r1 (Int64.unsigned n) k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros insn sem SEM ASSOC; intros. unfold addimm_aux. + set (nlo := Zzero_ext 12 (Int64.unsigned n)). set (nhi := Int64.unsigned n - nlo). + assert (E: Int64.unsigned n = nhi + nlo) by (unfold nlo, nhi; omega). + rewrite <- (Int64.repr_unsigned n). + destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; omega. + intros; Simpl. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; omega. + intros; Simpl. +- econstructor; split. eapply exec_straight_two. + apply SEM. apply SEM. Simpl. Simpl. + split. Simpl. rewrite ASSOC. do 2 f_equal. apply Int64.eqm_samerepr. + rewrite E. auto with ints. + intros; Simpl. +Qed. + +Lemma exec_addimm64: + forall rd r1 n k rs m, + preg_of_iregsp r1 <> X16 -> + exists rs', + exec_straight ge fn (addimm64 rd r1 n k) rs m k rs' m + /\ rs'#rd = Val.addl rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros. + unfold addimm64. set (nn := Int64.neg n). + destruct (Int64.eq n (Int64.zero_ext 24 n)); [| destruct (Int64.eq nn (Int64.zero_ext 24 nn))]. +- apply exec_addimm_aux_64 with (sem := Val.addl). auto. intros; apply Val.addl_assoc. +- rewrite <- Val.subl_opp_addl. + apply exec_addimm_aux_64 with (sem := Val.subl). auto. + intros. rewrite ! Val.subl_addl_opp, Val.addl_assoc. rewrite Int64.neg_add_distr. auto. +- destruct (Int64.lt n Int64.zero). ++ rewrite <- Val.subl_opp_addl; fold nn. + edestruct (exec_loadimm64 X16 nn) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. Simpl. + split. Simpl. rewrite B, C; eauto with asmgen. simpl. rewrite Int64.shl'_zero. auto. + intros; Simpl. ++ edestruct (exec_loadimm64 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. Simpl. + split. Simpl. rewrite B, C; eauto with asmgen. simpl. rewrite Int64.shl'_zero. auto. + intros; Simpl. +Qed. + +(** Logical immediate *) + +Lemma exec_logicalimm32: + forall (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn1 rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs##r1 (Vint (Int.repr n))))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insn2 rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs##r1 (eval_shift_op_int rs#r2 s)))) m) -> + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (logicalimm32 insn1 insn2 rd r1 n k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros until sem; intros SEM1 SEM2; intros. unfold logicalimm32. + destruct (is_logical_imm32 n). +- econstructor; split. + apply exec_straight_one. apply SEM1. reflexivity. + split. Simpl. rewrite Int.repr_unsigned; auto. intros; Simpl. +- edestruct (exec_loadimm32 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. apply SEM2. reflexivity. + split. Simpl. f_equal; auto. apply C; auto with asmgen. + intros; Simpl. +Qed. + +Lemma exec_logicalimm64: + forall (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn1 rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (Vlong (Int64.repr n))))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insn2 rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (eval_shift_op_long rs#r2 s)))) m) -> + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (logicalimm64 insn1 insn2 rd r1 n k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros until sem; intros SEM1 SEM2; intros. unfold logicalimm64. + destruct (is_logical_imm64 n). +- econstructor; split. + apply exec_straight_one. apply SEM1. reflexivity. + split. Simpl. rewrite Int64.repr_unsigned. auto. intros; Simpl. +- edestruct (exec_loadimm64 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. apply SEM2. reflexivity. + split. Simpl. f_equal; auto. apply C; auto with asmgen. + intros; Simpl. +Qed. + +(** Load address of symbol *) + +Lemma exec_loadsymbol: forall rd s ofs k rs m, + rd <> X16 \/ Archi.pic_code tt = false -> + exists rs', + exec_straight ge fn (loadsymbol rd s ofs k) rs m k rs' m + /\ rs'#rd = Genv.symbol_address ge s ofs + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadsymbol; intros. destruct (Archi.pic_code tt). +- predSpec Ptrofs.eq Ptrofs.eq_spec ofs Ptrofs.zero. ++ subst ofs. econstructor; split. + apply exec_straight_one; [simpl; eauto | reflexivity]. + split. Simpl. intros; Simpl. ++ exploit exec_addimm64. instantiate (1 := rd). simpl. destruct H; congruence. + intros (rs1 & A & B & C). + econstructor; split. + econstructor. simpl; eauto. auto. eexact A. + split. simpl in B; rewrite B. Simpl. + rewrite <- Genv.shift_symbol_address_64 by auto. + rewrite Ptrofs.add_zero_l, Ptrofs.of_int64_to_int64 by auto. auto. + intros. rewrite C by auto. Simpl. +- econstructor; split. + eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. + split. Simpl. rewrite symbol_high_low; auto. + intros; Simpl. +Qed. + +(** Shifted operands *) + +Remark transl_shift_not_none: + forall s a, transl_shift s a <> SOnone. +Proof. + destruct s; intros; simpl; congruence. +Qed. + +Remark or_zero_eval_shift_op_int: + forall v s, s <> SOnone -> Val.or (Vint Int.zero) (eval_shift_op_int v s) = eval_shift_op_int v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int.iwordsize); auto; rewrite Int.or_zero_l; auto. +Qed. + +Remark or_zero_eval_shift_op_long: + forall v s, s <> SOnone -> Val.orl (Vlong Int64.zero) (eval_shift_op_long v s) = eval_shift_op_long v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int64.iwordsize'); auto; rewrite Int64.or_zero_l; auto. +Qed. + +Remark add_zero_eval_shift_op_long: + forall v s, s <> SOnone -> Val.addl (Vlong Int64.zero) (eval_shift_op_long v s) = eval_shift_op_long v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int64.iwordsize'); auto; rewrite Int64.add_zero_l; auto. +Qed. + +Lemma transl_eval_shift: forall s v (a: amount32), + eval_shift_op_int v (transl_shift s a) = eval_shift s v a. +Proof. + intros. destruct s; simpl; auto. +Qed. + +Lemma transl_eval_shift': forall s v (a: amount32), + Val.or (Vint Int.zero) (eval_shift_op_int v (transl_shift s a)) = eval_shift s v a. +Proof. + intros. rewrite or_zero_eval_shift_op_int by (apply transl_shift_not_none). + apply transl_eval_shift. +Qed. + +Lemma transl_eval_shiftl: forall s v (a: amount64), + eval_shift_op_long v (transl_shift s a) = eval_shiftl s v a. +Proof. + intros. destruct s; simpl; auto. +Qed. + +Lemma transl_eval_shiftl': forall s v (a: amount64), + Val.orl (Vlong Int64.zero) (eval_shift_op_long v (transl_shift s a)) = eval_shiftl s v a. +Proof. + intros. rewrite or_zero_eval_shift_op_long by (apply transl_shift_not_none). + apply transl_eval_shiftl. +Qed. + +Lemma transl_eval_shiftl'': forall s v (a: amount64), + Val.addl (Vlong Int64.zero) (eval_shift_op_long v (transl_shift s a)) = eval_shiftl s v a. +Proof. + intros. rewrite add_zero_eval_shift_op_long by (apply transl_shift_not_none). + apply transl_eval_shiftl. +Qed. + +(** Zero- and Sign- extensions *) + +Lemma exec_move_extended_base: forall rd r1 ex k rs m, + exists rs', + exec_straight ge fn (move_extended_base rd r1 ex k) rs m k rs' m + /\ rs' rd = match ex with Xsgn32 => Val.longofint rs#r1 | Xuns32 => Val.longofintu rs#r1 end + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold move_extended_base; destruct ex; econstructor; + (split; [apply exec_straight_one; [simpl;eauto|auto] | split; [Simpl|intros;Simpl]]). +Qed. + +Lemma exec_move_extended: forall rd r1 ex (a: amount64) k rs m, + exists rs', + exec_straight ge fn (move_extended rd r1 ex a k) rs m k rs' m + /\ rs' rd = Op.eval_extend ex rs#r1 a + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold move_extended; intros. predSpec Int.eq Int.eq_spec a Int.zero. +- exploit (exec_move_extended_base rd r1 ex). intros (rs' & A & B & C). + exists rs'; split. eexact A. split. unfold Op.eval_extend. rewrite H. rewrite B. + destruct ex, (rs r1); simpl; auto; rewrite Int64.shl'_zero; auto. + auto. +- Local Opaque Val.addl. + exploit (exec_move_extended_base rd r1 ex). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + unfold exec_instr. change (SOlsl a) with (transl_shift Slsl a). rewrite transl_eval_shiftl''. eauto. auto. + split. Simpl. rewrite B. auto. + intros; Simpl. +Qed. + +Lemma exec_arith_extended: + forall (sem: val -> val -> val) + (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction) + (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction), + (forall rd r1 r2 x rs m, + exec_instr ge fn (insnX rd r1 r2 x) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (eval_extend rs#r2 x)))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insnS rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (eval_shift_op_long rs#r2 s)))) m) -> + forall (rd r1 r2: ireg) (ex: extension) (a: amount64) (k: code) rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (arith_extended insnX insnS rd r1 r2 ex a k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Op.eval_extend ex rs#r2 a) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros sem insnX insnS EX ES; intros. unfold arith_extended. destruct (Int.ltu a (Int.repr 5)). +- econstructor; split. + apply exec_straight_one. rewrite EX; eauto. auto. + split. Simpl. f_equal. destruct ex; auto. + intros; Simpl. +- exploit (exec_move_extended_base X16 r2 ex). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + rewrite ES. eauto. auto. + split. Simpl. unfold ir0x. rewrite C by eauto with asmgen. f_equal. + rewrite B. destruct ex; auto. + intros; Simpl. +Qed. + +(** Extended right shift *) + +Lemma exec_shrx32: forall (rd r1: ireg) (n: int) k v (rs: regset) m, + Val.shrx rs#r1 (Vint n) = Some v -> + r1 <> X16 -> + exists rs', + exec_straight ge fn (shrx32 rd r1 n k) rs m k rs' m + /\ rs'#rd = v + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold shrx32; intros. apply Val.shrx_shr_2 in H. + destruct (Int.eq n Int.zero) eqn:E. +- econstructor; split. apply exec_straight_one; [simpl;eauto|auto]. + split. Simpl. subst v; auto. intros; Simpl. +- econstructor; split. eapply exec_straight_three. + unfold exec_instr. rewrite or_zero_eval_shift_op_int by congruence. eauto. + simpl; eauto. + unfold exec_instr. rewrite or_zero_eval_shift_op_int by congruence. eauto. + auto. auto. auto. + split. subst v; Simpl. intros; Simpl. +Qed. + +Lemma exec_shrx64: forall (rd r1: ireg) (n: int) k v (rs: regset) m, + Val.shrxl rs#r1 (Vint n) = Some v -> + r1 <> X16 -> + exists rs', + exec_straight ge fn (shrx64 rd r1 n k) rs m k rs' m + /\ rs'#rd = v + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold shrx64; intros. apply Val.shrxl_shrl_2 in H. + destruct (Int.eq n Int.zero) eqn:E. +- econstructor; split. apply exec_straight_one; [simpl;eauto|auto]. + split. Simpl. subst v; auto. intros; Simpl. +- econstructor; split. eapply exec_straight_three. + unfold exec_instr. rewrite or_zero_eval_shift_op_long by congruence. eauto. + simpl; eauto. + unfold exec_instr. rewrite or_zero_eval_shift_op_long by congruence. eauto. + auto. auto. auto. + split. subst v; Simpl. intros; Simpl. +Qed. + +(** Condition bits *) + +Lemma compare_int_spec: forall rs v1 v2 m, + let rs' := compare_int rs v1 v2 m in + rs'#CN = (Val.negative (Val.sub v1 v2)) + /\ rs'#CZ = (Val.cmpu (Mem.valid_pointer m) Ceq v1 v2) + /\ rs'#CC = (Val.cmpu (Mem.valid_pointer m) Cge v1 v2) + /\ rs'#CV = (Val.sub_overflow v1 v2). +Proof. + intros; unfold rs'; auto. +Qed. + +Lemma eval_testcond_compare_sint: forall c v1 v2 b rs m, + Val.cmp_bool c v1 v2 = Some b -> + eval_testcond (cond_for_signed_cmp c) (compare_int rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_int_spec rs v1 v2 m). + set (rs' := compare_int rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmpu; simpl. destruct c; simpl. +- destruct (Int.eq i i0); auto. +- destruct (Int.eq i i0); auto. +- rewrite Int.lt_sub_overflow. destruct (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow, Int.not_lt. + destruct (Int.eq i i0), (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow, (Int.lt_not i). + destruct (Int.eq i i0), (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow. destruct (Int.lt i i0); auto. +Qed. + +Lemma eval_testcond_compare_uint: forall c v1 v2 b rs m, + Val.cmpu_bool (Mem.valid_pointer m) c v1 v2 = Some b -> + eval_testcond (cond_for_unsigned_cmp c) (compare_int rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_int_spec rs v1 v2 m). + set (rs' := compare_int rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmpu; simpl. destruct c; simpl. +- destruct (Int.eq i i0); auto. +- destruct (Int.eq i i0); auto. +- destruct (Int.ltu i i0); auto. +- rewrite (Int.not_ltu i). destruct (Int.eq i i0), (Int.ltu i i0); auto. +- rewrite (Int.ltu_not i). destruct (Int.eq i i0), (Int.ltu i i0); auto. +- destruct (Int.ltu i i0); auto. +Qed. + +Lemma compare_long_spec: forall rs v1 v2 m, + let rs' := compare_long rs v1 v2 m in + rs'#CN = (Val.negativel (Val.subl v1 v2)) + /\ rs'#CZ = (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Ceq v1 v2)) + /\ rs'#CC = (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Cge v1 v2)) + /\ rs'#CV = (Val.subl_overflow v1 v2). +Proof. + intros; unfold rs'; auto. +Qed. + +Remark int64_sub_overflow: + forall x y, + Int.xor (Int.repr (Int64.unsigned (Int64.sub_overflow x y Int64.zero))) + (Int.repr (Int64.unsigned (Int64.negative (Int64.sub x y)))) = + (if Int64.lt x y then Int.one else Int.zero). +Proof. + intros. + transitivity (Int.repr (Int64.unsigned (if Int64.lt x y then Int64.one else Int64.zero))). + rewrite <- (Int64.lt_sub_overflow x y). + unfold Int64.sub_overflow, Int64.negative. + set (s := Int64.signed x - Int64.signed y - Int64.signed Int64.zero). + destruct (zle Int64.min_signed s && zle s Int64.max_signed); + destruct (Int64.lt (Int64.sub x y) Int64.zero); + auto. + destruct (Int64.lt x y); auto. +Qed. + +Lemma eval_testcond_compare_slong: forall c v1 v2 b rs m, + Val.cmpl_bool c v1 v2 = Some b -> + eval_testcond (cond_for_signed_cmp c) (compare_long rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_long_spec rs v1 v2 m). + set (rs' := compare_long rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmplu; simpl. destruct c; simpl. +- destruct (Int64.eq i i0); auto. +- destruct (Int64.eq i i0); auto. +- rewrite int64_sub_overflow. destruct (Int64.lt i i0); auto. +- rewrite int64_sub_overflow, Int64.not_lt. + destruct (Int64.eq i i0), (Int64.lt i i0); auto. +- rewrite int64_sub_overflow, (Int64.lt_not i). + destruct (Int64.eq i i0), (Int64.lt i i0); auto. +- rewrite int64_sub_overflow. destruct (Int64.lt i i0); auto. +Qed. + +Lemma eval_testcond_compare_ulong: forall c v1 v2 b rs m, + Val.cmplu_bool (Mem.valid_pointer m) c v1 v2 = Some b -> + eval_testcond (cond_for_unsigned_cmp c) (compare_long rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_long_spec rs v1 v2 m). + set (rs' := compare_long rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E; unfold Val.cmplu. + destruct v1; try discriminate; destruct v2; try discriminate; simpl in H. +- (* int-int *) + inv H. destruct c; simpl. ++ destruct (Int64.eq i i0); auto. ++ destruct (Int64.eq i i0); auto. ++ destruct (Int64.ltu i i0); auto. ++ rewrite (Int64.not_ltu i). destruct (Int64.eq i i0), (Int64.ltu i i0); auto. ++ rewrite (Int64.ltu_not i). destruct (Int64.eq i i0), (Int64.ltu i i0); auto. ++ destruct (Int64.ltu i i0); auto. +- (* int-ptr *) + simpl. + destruct (Int64.eq i Int64.zero && + (Mem.valid_pointer m b0 (Ptrofs.unsigned i0) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i0 - 1))); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +- (* ptr-int *) + simpl. + destruct (Int64.eq i0 Int64.zero && + (Mem.valid_pointer m b0 (Ptrofs.unsigned i) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i - 1))); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +- (* ptr-ptr *) + simpl. + destruct (eq_block b0 b1). ++ destruct ((Mem.valid_pointer m b0 (Ptrofs.unsigned i) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i - 1)) && + (Mem.valid_pointer m b1 (Ptrofs.unsigned i0) + || Mem.valid_pointer m b1 (Ptrofs.unsigned i0 - 1))); + inv H. + destruct c; simpl. +* destruct (Ptrofs.eq i i0); auto. +* destruct (Ptrofs.eq i i0); auto. +* destruct (Ptrofs.ltu i i0); auto. +* rewrite (Ptrofs.not_ltu i). destruct (Ptrofs.eq i i0), (Ptrofs.ltu i i0); auto. +* rewrite (Ptrofs.ltu_not i). destruct (Ptrofs.eq i i0), (Ptrofs.ltu i i0); auto. +* destruct (Ptrofs.ltu i i0); auto. ++ destruct (Mem.valid_pointer m b0 (Ptrofs.unsigned i) && + Mem.valid_pointer m b1 (Ptrofs.unsigned i0)); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +Qed. + +Lemma compare_float_spec: forall rs f1 f2, + let rs' := compare_float rs (Vfloat f1) (Vfloat f2) in + rs'#CN = (Val.of_bool (Float.cmp Clt f1 f2)) + /\ rs'#CZ = (Val.of_bool (Float.cmp Ceq f1 f2)) + /\ rs'#CC = (Val.of_bool (negb (Float.cmp Clt f1 f2))) + /\ rs'#CV = (Val.of_bool (negb (Float.ordered f1 f2))). +Proof. + intros; auto. +Qed. + +Lemma eval_testcond_compare_float: forall c v1 v2 b rs, + Val.cmpf_bool c v1 v2 = Some b -> + eval_testcond (cond_for_float_cmp c) (compare_float rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_float_spec rs f f0). + set (rs' := compare_float rs (Vfloat f) (Vfloat f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float.cmp Float.ordered. + unfold Float.cmp, Float.ordered; + destruct c; destruct (Float.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma eval_testcond_compare_not_float: forall c v1 v2 b rs, + option_map negb (Val.cmpf_bool c v1 v2) = Some b -> + eval_testcond (cond_for_float_not_cmp c) (compare_float rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_float_spec rs f f0). + set (rs' := compare_float rs (Vfloat f) (Vfloat f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float.cmp Float.ordered. + unfold Float.cmp, Float.ordered; + destruct c; destruct (Float.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma compare_single_spec: forall rs f1 f2, + let rs' := compare_single rs (Vsingle f1) (Vsingle f2) in + rs'#CN = (Val.of_bool (Float32.cmp Clt f1 f2)) + /\ rs'#CZ = (Val.of_bool (Float32.cmp Ceq f1 f2)) + /\ rs'#CC = (Val.of_bool (negb (Float32.cmp Clt f1 f2))) + /\ rs'#CV = (Val.of_bool (negb (Float32.ordered f1 f2))). +Proof. + intros; auto. +Qed. + +Lemma eval_testcond_compare_single: forall c v1 v2 b rs, + Val.cmpfs_bool c v1 v2 = Some b -> + eval_testcond (cond_for_float_cmp c) (compare_single rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_single_spec rs f f0). + set (rs' := compare_single rs (Vsingle f) (Vsingle f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float32.cmp Float32.ordered. + unfold Float32.cmp, Float32.ordered; + destruct c; destruct (Float32.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma eval_testcond_compare_not_single: forall c v1 v2 b rs, + option_map negb (Val.cmpfs_bool c v1 v2) = Some b -> + eval_testcond (cond_for_float_not_cmp c) (compare_single rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_single_spec rs f f0). + set (rs' := compare_single rs (Vsingle f) (Vsingle f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float32.cmp Float32.ordered. + unfold Float32.cmp, Float32.ordered; + destruct c; destruct (Float32.compare f f0) as [[]|]; reflexivity. +Qed. + +Remark compare_float_inv: forall rs v1 v2 r, + match r with CR _ => False | _ => True end -> + (nextinstr (compare_float rs v1 v2))#r = (nextinstr rs)#r. +Proof. + intros; unfold compare_float. + destruct r; try contradiction; destruct v1; auto; destruct v2; auto. +Qed. + +Remark compare_single_inv: forall rs v1 v2 r, + match r with CR _ => False | _ => True end -> + (nextinstr (compare_single rs v1 v2))#r = (nextinstr rs)#r. +Proof. + intros; unfold compare_single. + destruct r; try contradiction; destruct v1; auto; destruct v2; auto. +Qed. + +(** Translation of conditionals *) + +Ltac ArgsInv := + repeat (match goal with + | [ H: Error _ = OK _ |- _ ] => discriminate + | [ H: match ?args with nil => _ | _ :: _ => _ end = OK _ |- _ ] => destruct args + | [ H: bind _ _ = OK _ |- _ ] => monadInv H + | [ H: match _ with left _ => _ | right _ => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + | [ H: match _ with true => _ | false => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + end); + subst; + repeat (match goal with + | [ H: ireg_of _ = OK _ |- _ ] => simpl in *; rewrite (ireg_of_eq _ _ H) in * + | [ H: freg_of _ = OK _ |- _ ] => simpl in *; rewrite (freg_of_eq _ _ H) in * + end). + +Lemma transl_cond_correct: + forall cond args k c rs m, + transl_cond cond args k = OK c -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ (forall b, + eval_condition cond (map rs (map preg_of args)) m = Some b -> + eval_testcond (cond_for_cond cond) rs' = Some b) + /\ forall r, data_preg r = true -> rs'#r = rs#r. +Proof. + intros until m; intros TR. destruct cond; simpl in TR; ArgsInv. +- (* Ccomp *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompu *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompimm *) + destruct (is_arith_imm32 n); [|destruct (is_arith_imm32 (Int.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int.repr_unsigned, Int.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompuimm *) + destruct (is_arith_imm32 n); [|destruct (is_arith_imm32 (Int.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int.repr_unsigned, Int.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompshift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shift. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompushift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shift. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. +- (* Cmaskzero *) + destruct (is_logical_imm32 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply (eval_testcond_compare_sint Ceq); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_sint Ceq); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Cmasknotzero *) + destruct (is_logical_imm32 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply (eval_testcond_compare_sint Cne); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_sint Cne); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompl *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplu *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplimm *) + destruct (is_arith_imm64 n); [|destruct (is_arith_imm64 (Int64.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int64.repr_unsigned, Int64.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompluimm *) + destruct (is_arith_imm64 n); [|destruct (is_arith_imm64 (Int64.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int64.repr_unsigned, Int64.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccomplshift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shiftl. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplushift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shiftl. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. +- (* Cmasklzero *) + destruct (is_logical_imm64 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply (eval_testcond_compare_slong Ceq); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_slong Ceq); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Cmasknotzero *) + destruct (is_logical_imm64 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply (eval_testcond_compare_slong Cne); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_slong Cne); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompf *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Cnotcompf *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_not_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Ccompfzero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Cnotcompfzero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_not_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Ccompfs *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Cnotcompfs *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_not_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Ccompfszero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Cnotcompfszero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_not_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +Qed. + +(** Translation of conditional branches *) + +Lemma transl_cond_branch_correct: + forall cond args lbl k c rs m b, + transl_cond_branch cond args lbl k = OK c -> + eval_condition cond (map rs (map preg_of args)) m = Some b -> + exists rs' insn, + exec_straight_opt ge fn c rs m (insn :: k) rs' m + /\ exec_instr ge fn insn rs' m = + (if b then goto_label fn lbl rs' m else Next (nextinstr rs') m) + /\ forall r, data_preg r = true -> rs'#r = rs#r. +Proof. + intros until b; intros TR EV. + assert (DFL: + transl_cond_branch_default cond args lbl k = OK c -> + exists rs' insn, + exec_straight_opt ge fn c rs m (insn :: k) rs' m + /\ exec_instr ge fn insn rs' m = + (if b then goto_label fn lbl rs' m else Next (nextinstr rs') m) + /\ forall r, data_preg r = true -> rs'#r = rs#r). + { + unfold transl_cond_branch_default; intros. + exploit transl_cond_correct; eauto. intros (rs' & A & B & C). + exists rs', (Pbc (cond_for_cond cond) lbl); split. + apply exec_straight_opt_intro. eexact A. + split; auto. simpl. rewrite (B b) by auto. auto. + } +Local Opaque transl_cond transl_cond_branch_default. + destruct args as [ | a1 args]; simpl in TR; auto. + destruct args as [ | a2 args]; simpl in TR; auto. + destruct cond; simpl in TR; auto. +- (* Ccompimm *) + destruct c0; auto; destruct (Int.eq n Int.zero) eqn:N0; auto; + apply Int.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. auto. ++ (* Ccompimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. destruct (Int.eq i Int.zero); auto. +- (* Ccompuimm *) + destruct c0; auto; destruct (Int.eq n Int.zero) eqn:N0; auto; + apply Int.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompuimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite EV. auto. ++ (* Ccompuimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite (Val.negate_cmpu_bool (Mem.valid_pointer m) Cne), EV. destruct b; auto. +- (* Cmaskzero *) + destruct (Int.is_power2 n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int.mul_pow2, Int.mul_commut, Int.mul_one by eauto. + rewrite (Val.negate_cmp_bool Ceq), EV. destruct b; auto. +- (* Cmasknotzero *) + destruct (Int.is_power2 n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int.mul_pow2, Int.mul_commut, Int.mul_one by eauto. + rewrite EV. auto. +- (* Ccomplimm *) + destruct c0; auto; destruct (Int64.eq n Int64.zero) eqn:N0; auto; + apply Int64.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccomplimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. auto. ++ (* Ccomplimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. destruct (Int64.eq i Int64.zero); auto. +- (* Ccompluimm *) + destruct c0; auto; destruct (Int64.eq n Int64.zero) eqn:N0; auto; + apply Int64.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompluimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite EV. auto. ++ (* Ccompluimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite (Val.negate_cmplu_bool (Mem.valid_pointer m) Cne), EV. destruct b; auto. +- (* Cmasklzero *) + destruct (Int64.is_power2' n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int64.mul_pow2', Int64.mul_commut, Int64.mul_one by eauto. + rewrite (Val.negate_cmpl_bool Ceq), EV. destruct b; auto. +- (* Cmasklnotzero *) + destruct (Int64.is_power2' n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int64.mul_pow2', Int64.mul_commut, Int64.mul_one by eauto. + rewrite EV. auto. +Qed. + +(** Translation of arithmetic operations *) + +Ltac SimplEval H := + match type of H with + | Some _ = None _ => discriminate + | Some _ = Some _ => inv H + | ?a = Some ?b => let A := fresh in assert (A: Val.maketotal a = b) by (rewrite H; reflexivity) +end. + +Ltac TranslOpSimpl := + econstructor; split; + [ apply exec_straight_one; [simpl; eauto | reflexivity] + | split; [ rewrite ? transl_eval_shift, ? transl_eval_shiftl; + apply Val.lessdef_same; Simpl; fail + | intros; Simpl; fail ] ]. + +Ltac TranslOpBase := + econstructor; split; + [ apply exec_straight_one; [simpl; eauto | reflexivity] + | split; [ rewrite ? transl_eval_shift, ? transl_eval_shiftl; Simpl + | intros; Simpl; fail ] ]. + +Lemma transl_op_correct: + forall op args res k (rs: regset) m v c, + transl_op op args res k = OK c -> + eval_operation ge (rs#SP) op (map rs (map preg_of args)) m = Some v -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ Val.lessdef v rs'#(preg_of res) + /\ forall r, data_preg r = true -> r <> preg_of res -> preg_notin r (destroyed_by_op op) -> rs' r = rs r. +Proof. +Local Opaque Int.eq Int64.eq Val.add Val.addl Int.zwordsize Int64.zwordsize. + intros until c; intros TR EV. + unfold transl_op in TR; destruct op; ArgsInv; simpl in EV; SimplEval EV; try TranslOpSimpl. +- (* move *) + destruct (preg_of res) eqn:RR; try discriminate; destruct (preg_of m0) eqn:R1; inv TR. ++ TranslOpSimpl. ++ TranslOpSimpl. +- (* intconst *) + exploit exec_loadimm32. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. intros; auto with asmgen. +- (* longconst *) + exploit exec_loadimm64. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. intros; auto with asmgen. +- (* floatconst *) + destruct (Float.eq_dec n Float.zero). ++ subst n. TranslOpSimpl. ++ TranslOpSimpl. +- (* singleconst *) + destruct (Float32.eq_dec n Float32.zero). ++ subst n. TranslOpSimpl. ++ TranslOpSimpl. +- (* loadsymbol *) + exploit (exec_loadsymbol x id ofs). eauto with asmgen. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* addrstack *) + exploit (exec_addimm64 x XSP (Ptrofs.to_int64 ofs)). simpl; eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. simpl in B; rewrite B. +Local Transparent Val.addl. + destruct (rs SP); simpl; auto. rewrite Ptrofs.of_int64_to_int64 by auto. auto. + auto. +- (* shift *) + rewrite <- transl_eval_shift'. TranslOpSimpl. +- (* addimm *) + exploit (exec_addimm32 x x0 n). eauto with asmgen. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* mul *) + TranslOpBase. +Local Transparent Val.add. + destruct (rs x0); auto; destruct (rs x1); auto. simpl. rewrite Int.add_zero_l; auto. +- (* andimm *) + exploit (exec_logicalimm32 (Pandimm W) (Pand W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* orimm *) + exploit (exec_logicalimm32 (Porrimm W) (Porr W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* xorimm *) + exploit (exec_logicalimm32 (Peorimm W) (Peor W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* not *) + TranslOpBase. + destruct (rs x0); auto. simpl. rewrite Int.or_zero_l; auto. +- (* notshift *) + TranslOpBase. + destruct (eval_shift s (rs x0) a); auto. simpl. rewrite Int.or_zero_l; auto. +- (* shrx *) + exploit (exec_shrx32 x x0 n); eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* zero-ext *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int.shl_zero. auto. +- (* sign-ext *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int.shl_zero. auto. +- (* shlzext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int.shl_zero_ext_min; auto using a32_range. +- (* shlsext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int.shl_sign_ext_min; auto using a32_range. +- (* zextshr *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a32_range; simpl. rewrite <- Int.zero_ext_shru_min; auto using a32_range. +- (* sextshr *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a32_range; simpl. rewrite <- Int.sign_ext_shr_min; auto using a32_range. +- (* shiftl *) + rewrite <- transl_eval_shiftl'. TranslOpSimpl. +- (* extend *) + exploit (exec_move_extended x0 x1 x a k). intros (rs' & A & B & C). + econstructor; split. eexact A. + split. rewrite B; auto. eauto with asmgen. +- (* addext *) + exploit (exec_arith_extended Val.addl Paddext (Padd X)). + auto. auto. instantiate (1 := x1). eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* addlimm *) + exploit (exec_addimm64 x x0 n). simpl. generalize (ireg_of_not_X16 _ _ EQ1). congruence. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. simpl in B; rewrite B; auto. auto. +- (* subext *) + exploit (exec_arith_extended Val.subl Psubext (Psub X)). + auto. auto. instantiate (1 := x1). eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* mull *) + TranslOpBase. + destruct (rs x0); auto; destruct (rs x1); auto. simpl. rewrite Int64.add_zero_l; auto. +- (* andlimm *) + exploit (exec_logicalimm64 (Pandimm X) (Pand X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* orlimm *) + exploit (exec_logicalimm64 (Porrimm X) (Porr X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* xorlimm *) + exploit (exec_logicalimm64 (Peorimm X) (Peor X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* notl *) + TranslOpBase. + destruct (rs x0); auto. simpl. rewrite Int64.or_zero_l; auto. +- (* notlshift *) + TranslOpBase. + destruct (eval_shiftl s (rs x0) a); auto. simpl. rewrite Int64.or_zero_l; auto. +- (* shrx *) + exploit (exec_shrx64 x x0 n); eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* zero-ext-l *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int64.shl'_zero. auto. +- (* sign-ext-l *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int64.shl'_zero. auto. +- (* shllzext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int64.shl'_zero_ext_min; auto using a64_range. +- (* shllsext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int64.shl'_sign_ext_min; auto using a64_range. +- (* zextshrl *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a64_range; simpl. rewrite <- Int64.zero_ext_shru'_min; auto using a64_range. +- (* sextshrl *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a64_range; simpl. rewrite <- Int64.sign_ext_shr'_min; auto using a64_range. +- (* condition *) + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. auto. + auto. + intros; Simpl. +- (* select *) + destruct (preg_of res) eqn:RES; monadInv TR. + + (* integer *) + generalize (ireg_of_eq _ _ EQ) (ireg_of_eq _ _ EQ1); intros E1 E2; rewrite E1, E2. + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. rewrite !C. apply Val.lessdef_normalize. + rewrite <- E2; auto with asmgen. rewrite <- E1; auto with asmgen. + auto. + intros; Simpl. + + (* FP *) + generalize (freg_of_eq _ _ EQ) (freg_of_eq _ _ EQ1); intros E1 E2; rewrite E1, E2. + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. rewrite !C. apply Val.lessdef_normalize. + rewrite <- E2; auto with asmgen. rewrite <- E1; auto with asmgen. + auto. + intros; Simpl. +Qed. + +(** Translation of addressing modes, loads, stores *) + +Lemma transl_addressing_correct: + forall sz addr args (insn: Asm.addressing -> instruction) k (rs: regset) m c b o, + transl_addressing sz addr args insn k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some (Vptr b o) -> + exists ad rs', + exec_straight_opt ge fn c rs m (insn ad :: k) rs' m + /\ Asm.eval_addressing ge ad rs' = Vptr b o + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros until o; intros TR EV. + unfold transl_addressing in TR; destruct addr; ArgsInv; SimplEval EV. +- (* Aindexed *) + destruct (offset_representable sz ofs); inv EQ0. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ exploit (exec_loadimm64 X16 ofs). intros (rs' & A & B & C). + econstructor; exists rs'; split. apply exec_straight_opt_intro; eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. + eauto with asmgen. +- (* Aindexed2 *) + econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. +- (* Aindexed2shift *) + destruct (Int.eq a Int.zero) eqn:E; [|destruct (Int.eq (Int.shl Int.one a) (Int.repr sz))]; inv EQ2. ++ apply Int.same_if_eq in E. rewrite E. + econstructor; econstructor; split. apply exec_straight_opt_refl. + split; auto. simpl. + rewrite Val.addl_commut in H0. destruct (rs x0); try discriminate. + unfold Val.shll. rewrite Int64.shl'_zero. auto. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ econstructor; econstructor; split. + apply exec_straight_opt_intro. apply exec_straight_one. simpl; eauto. auto. + split. simpl. Simpl. rewrite H0. simpl. rewrite Ptrofs.add_zero. auto. + intros; Simpl. +- (* Aindexed2ext *) + destruct (Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz)); inv EQ2. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + split; auto. destruct x; auto. ++ exploit (exec_arith_extended Val.addl Paddext (Padd X)); auto. + instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. rewrite B. rewrite Val.addl_assoc. f_equal. + unfold Op.eval_extend; destruct x, (rs x1); simpl; auto; rewrite ! a64_range; + simpl; rewrite Int64.add_zero; auto. + intros. apply C; eauto with asmgen. +- (* Aglobal *) + destruct (Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero); inv TR. ++ econstructor; econstructor; split. + apply exec_straight_opt_intro. apply exec_straight_one. simpl; eauto. auto. + split. simpl. Simpl. rewrite symbol_high_low. simpl in EV. congruence. + intros; Simpl. ++ exploit (exec_loadsymbol X16 id ofs). auto. intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. + rewrite B. rewrite <- Genv.shift_symbol_address_64, Ptrofs.add_zero by auto. + simpl in EV. congruence. + auto with asmgen. +- (* Ainstrack *) + assert (E: Val.addl (rs SP) (Vlong (Ptrofs.to_int64 ofs)) = Vptr b o). + { simpl in EV. inv EV. destruct (rs SP); simpl in H1; inv H1. simpl. + rewrite Ptrofs.of_int64_to_int64 by auto. auto. } + destruct (offset_representable sz (Ptrofs.to_int64 ofs)); inv TR. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ exploit (exec_loadimm64 X16 (Ptrofs.to_int64 ofs)). intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. + auto with asmgen. +Qed. + +Lemma transl_load_correct: + forall chunk addr args dst k c (rs: regset) m vaddr v, + transl_load chunk addr args dst k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some vaddr -> + Mem.loadv chunk m vaddr = Some v -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, data_preg r = true -> r <> preg_of dst -> rs' r = rs r. +Proof. + intros. destruct vaddr; try discriminate. + assert (A: exists sz insn, + transl_addressing sz addr args insn k = OK c + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_load ge chunk (fun v => v) ad (preg_of dst) rs' m)). + { + destruct chunk; monadInv H; + try rewrite (ireg_of_eq _ _ EQ); try rewrite (freg_of_eq _ _ EQ); + do 2 econstructor; (split; [eassumption|auto]). + } + destruct A as (sz & insn & B & C). + exploit transl_addressing_correct. eexact B. eexact H0. intros (ad & rs' & P & Q & R). + assert (X: exec_load ge chunk (fun v => v) ad (preg_of dst) rs' m = + Next (nextinstr (rs'#(preg_of dst) <- v)) m). + { unfold exec_load. rewrite Q, H1. auto. } + econstructor; split. + eapply exec_straight_opt_right. eexact P. + apply exec_straight_one. rewrite C, X; eauto. Simpl. + split. Simpl. intros; Simpl. +Qed. + +Lemma transl_store_correct: + forall chunk addr args src k c (rs: regset) m vaddr m', + transl_store chunk addr args src k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some vaddr -> + Mem.storev chunk m vaddr rs#(preg_of src) = Some m' -> + exists rs', + exec_straight ge fn c rs m k rs' m' + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros. destruct vaddr; try discriminate. + set (chunk' := match chunk with Mint8signed => Mint8unsigned + | Mint16signed => Mint16unsigned + | _ => chunk end). + assert (A: exists sz insn, + transl_addressing sz addr args insn k = OK c + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_store ge chunk' ad rs'#(preg_of src) rs' m)). + { + unfold chunk'; destruct chunk; monadInv H; + try rewrite (ireg_of_eq _ _ EQ); try rewrite (freg_of_eq _ _ EQ); + do 2 econstructor; (split; [eassumption|auto]). + } + destruct A as (sz & insn & B & C). + exploit transl_addressing_correct. eexact B. eexact H0. intros (ad & rs' & P & Q & R). + assert (X: Mem.storev chunk' m (Vptr b i) rs#(preg_of src) = Some m'). + { rewrite <- H1. unfold chunk'. destruct chunk; auto; simpl; symmetry. + apply Mem.store_signed_unsigned_8. + apply Mem.store_signed_unsigned_16. } + assert (Y: exec_store ge chunk' ad rs'#(preg_of src) rs' m = + Next (nextinstr rs') m'). + { unfold exec_store. rewrite Q, R, X by auto with asmgen. auto. } + econstructor; split. + eapply exec_straight_opt_right. eexact P. + apply exec_straight_one. rewrite C, Y; eauto. Simpl. + intros; Simpl. +Qed. + +(** Translation of indexed memory accesses *) + +Lemma indexed_memory_access_correct: forall insn sz (base: iregsp) ofs k (rs: regset) m b i, + preg_of_iregsp base <> IR X16 -> + Val.offset_ptr rs#base ofs = Vptr b i -> + exists ad rs', + exec_straight_opt ge fn (indexed_memory_access insn sz base ofs k) rs m (insn ad :: k) rs' m + /\ Asm.eval_addressing ge ad rs' = Vptr b i + /\ forall r, r <> PC -> r <> X16 -> rs' r = rs r. +Proof. + unfold indexed_memory_access; intros. + assert (Val.addl rs#base (Vlong (Ptrofs.to_int64 ofs)) = Vptr b i). + { destruct (rs base); try discriminate. simpl in *. rewrite Ptrofs.of_int64_to_int64 by auto. auto. } + destruct offset_representable. +- econstructor; econstructor; split. apply exec_straight_opt_refl. auto. +- exploit (exec_loadimm64 X16); eauto. intros (rs' & A & B & C). + econstructor; econstructor; split. apply exec_straight_opt_intro; eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. auto. +Qed. + +Lemma loadptr_correct: forall (base: iregsp) ofs dst k m v (rs: regset), + Mem.loadv Mint64 m (Val.offset_ptr rs#base ofs) = Some v -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn (loadptr base ofs dst k) rs m k rs' m + /\ rs'#dst = v + /\ forall r, r <> PC -> r <> X16 -> r <> dst -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. simpl. unfold exec_load. rewrite B, H. eauto. auto. + split. Simpl. intros; Simpl. +Qed. + +Lemma storeptr_correct: forall (base: iregsp) ofs (src: ireg) k m m' (rs: regset), + Mem.storev Mint64 m (Val.offset_ptr rs#base ofs) rs#src = Some m' -> + preg_of_iregsp base <> IR X16 -> + src <> X16 -> + exists rs', + exec_straight ge fn (storeptr src base ofs k) rs m k rs' m' + /\ forall r, r <> PC -> r <> X16 -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. simpl. unfold exec_store. rewrite B, C, H by eauto with asmgen. eauto. auto. + intros; Simpl. +Qed. + +Lemma loadind_correct: forall (base: iregsp) ofs ty dst k c (rs: regset) m v, + loadind base ofs ty dst k = OK c -> + Mem.loadv (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) = Some v -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, data_preg r = true -> r <> preg_of dst -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + assert (X: exists sz insn, + c = indexed_memory_access insn sz base ofs k + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_load ge (chunk_of_type ty) (fun v => v) ad (preg_of dst) rs' m)). + { + unfold loadind in H; destruct ty; destruct (preg_of dst); inv H; do 2 econstructor; eauto. + } + destruct X as (sz & insn & EQ & SEM). subst c. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. rewrite SEM. unfold exec_load. rewrite B, H0. eauto. Simpl. + split. Simpl. intros; Simpl. +Qed. + +Lemma storeind_correct: forall (base: iregsp) ofs ty src k c (rs: regset) m m', + storeind src base ofs ty k = OK c -> + Mem.storev (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) rs#(preg_of src) = Some m' -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn c rs m k rs' m' + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + assert (X: exists sz insn, + c = indexed_memory_access insn sz base ofs k + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_store ge (chunk_of_type ty) ad rs'#(preg_of src) rs' m)). + { + unfold storeind in H; destruct ty; destruct (preg_of src); inv H; do 2 econstructor; eauto. + } + destruct X as (sz & insn & EQ & SEM). subst c. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. rewrite SEM. + unfold exec_store. rewrite B, C, H0 by eauto with asmgen. eauto. + Simpl. + intros; Simpl. +Qed. + +Lemma make_epilogue_correct: + forall ge0 f m stk soff cs m' ms rs k tm, + load_stack m (Vptr stk soff) Tptr f.(fn_link_ofs) = Some (parent_sp cs) -> + load_stack m (Vptr stk soff) Tptr f.(fn_retaddr_ofs) = Some (parent_ra cs) -> + Mem.free m stk 0 f.(fn_stacksize) = Some m' -> + agree ms (Vptr stk soff) rs -> + Mem.extends m tm -> + match_stack ge0 cs -> + exists rs', exists tm', + exec_straight ge fn (make_epilogue f k) rs tm k rs' tm' + /\ agree ms (parent_sp cs) rs' + /\ Mem.extends m' tm' + /\ rs'#RA = parent_ra cs + /\ rs'#SP = parent_sp cs + /\ (forall r, r <> PC -> r <> SP -> r <> X30 -> r <> X16 -> rs'#r = rs#r). +Proof. + intros until tm; intros LP LRA FREE AG MEXT MCS. + exploit Mem.loadv_extends. eauto. eexact LP. auto. simpl. intros (parent' & LP' & LDP'). + exploit Mem.loadv_extends. eauto. eexact LRA. auto. simpl. intros (ra' & LRA' & LDRA'). + exploit lessdef_parent_sp; eauto. intros EQ; subst parent'; clear LDP'. + exploit lessdef_parent_ra; eauto. intros EQ; subst ra'; clear LDRA'. + exploit Mem.free_parallel_extends; eauto. intros (tm' & FREE' & MEXT'). + unfold make_epilogue. + exploit (loadptr_correct XSP (fn_retaddr_ofs f)). + instantiate (2 := rs). simpl. rewrite <- (sp_val _ _ _ AG). simpl. eexact LRA'. simpl; congruence. + intros (rs1 & A1 & B1 & C1). + econstructor; econstructor; split. + eapply exec_straight_trans. eexact A1. apply exec_straight_one. simpl. + simpl; rewrite (C1 SP) by auto with asmgen. rewrite <- (sp_val _ _ _ AG). simpl; rewrite LP'. + rewrite FREE'. eauto. auto. + split. apply agree_nextinstr. apply agree_set_other; auto. + apply agree_change_sp with (Vptr stk soff). + apply agree_exten with rs; auto. intros; apply C1; auto with asmgen. + eapply parent_sp_def; eauto. + split. auto. + split. Simpl. + split. Simpl. + intros. Simpl. +Qed. + +End CONSTRUCTORS. diff --git a/aarch64/Builtins1.v b/aarch64/Builtins1.v new file mode 100644 index 00000000..f6e643d2 --- /dev/null +++ b/aarch64/Builtins1.v @@ -0,0 +1,33 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and Inria Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the GNU General Public License as published by *) +(* the Free Software Foundation, either version 2 of the License, or *) +(* (at your option) any later version. This file is also distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Platform-specific built-in functions *) + +Require Import String Coqlib. +Require Import AST Integers Floats Values. +Require Import Builtins0. + +Inductive platform_builtin : Type := . + +Local Open Scope string_scope. + +Definition platform_builtin_table : list (string * platform_builtin) := + nil. + +Definition platform_builtin_sig (b: platform_builtin) : signature := + match b with end. + +Definition platform_builtin_sem (b: platform_builtin) : builtin_sem (proj_sig_res (platform_builtin_sig b)) := + match b with end. diff --git a/aarch64/CBuiltins.ml b/aarch64/CBuiltins.ml new file mode 100644 index 00000000..fdc1372d --- /dev/null +++ b/aarch64/CBuiltins.ml @@ -0,0 +1,72 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(* Processor-dependent builtin C functions *) + +open C + +(* va_list is a struct of size 32 and alignment 8, passed by reference *) + +let va_list_type = TArray(TInt(IULong, []), Some 4L, []) +let size_va_list = 32 +let va_list_scalar = false + +let builtins = { + builtin_typedefs = [ + "__builtin_va_list", va_list_type + ]; + builtin_functions = [ + (* Synchronization *) + "__builtin_fence", + (TVoid [], [], false); + (* Integer arithmetic *) + "__builtin_bswap64", + (TInt(IULongLong, []), [TInt(IULongLong, [])], false); + "__builtin_clz", + (TInt(IInt, []), [TInt(IUInt, [])], false); + "__builtin_clzl", + (TInt(IInt, []), [TInt(IULong, [])], false); + "__builtin_clzll", + (TInt(IInt, []), [TInt(IULongLong, [])], false); + "__builtin_cls", + (TInt(IInt, []), [TInt(IInt, [])], false); + "__builtin_clsl", + (TInt(IInt, []), [TInt(ILong, [])], false); + "__builtin_clsll", + (TInt(IInt, []), [TInt(ILongLong, [])], false); + (* Float arithmetic *) + "__builtin_fmadd", + (TFloat(FDouble, []), + [TFloat(FDouble, []); TFloat(FDouble, []); TFloat(FDouble, [])], + false); + "__builtin_fmsub", + (TFloat(FDouble, []), + [TFloat(FDouble, []); TFloat(FDouble, []); TFloat(FDouble, [])], + false); + "__builtin_fnmadd", + (TFloat(FDouble, []), + [TFloat(FDouble, []); TFloat(FDouble, []); TFloat(FDouble, [])], + false); + "__builtin_fnmsub", + (TFloat(FDouble, []), + [TFloat(FDouble, []); TFloat(FDouble, []); TFloat(FDouble, [])], + false); + "__builtin_fmax", + (TFloat(FDouble, []), [TFloat(FDouble, []); TFloat(FDouble, [])], false); + "__builtin_fmin", + (TFloat(FDouble, []), [TFloat(FDouble, []); TFloat(FDouble, [])], false); + ] +} + +(* Expand memory references inside extended asm statements. Used in C2C. *) + +let asm_mem_argument arg = Printf.sprintf "[%s]" arg diff --git a/aarch64/CombineOp.v b/aarch64/CombineOp.v new file mode 100644 index 00000000..4d78c9a0 --- /dev/null +++ b/aarch64/CombineOp.v @@ -0,0 +1,137 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Recognition of combined operations, addressing modes and conditions + during the [CSE] phase. *) + +Require Import Coqlib. +Require Import AST Integers. +Require Import Op. +Require Import CSEdomain. + +Section COMBINE. + +Variable get: valnum -> option rhs. + +Function combine_compimm_ne_0 (x: valnum) : option(condition * list valnum) := + match get x with + | Some(Op (Ocmp c) ys) => Some (c, ys) + | _ => None + end. + +Function combine_compimm_eq_0 (x: valnum) : option(condition * list valnum) := + match get x with + | Some(Op (Ocmp c) ys) => Some (negate_condition c, ys) + | _ => None + end. + +Function combine_compimm_eq_1 (x: valnum) : option(condition * list valnum) := + match get x with + | Some(Op (Ocmp c) ys) => Some (c, ys) + | _ => None + end. + +Function combine_compimm_ne_1 (x: valnum) : option(condition * list valnum) := + match get x with + | Some(Op (Ocmp c) ys) => Some (negate_condition c, ys) + | _ => None + end. + +Function combine_cond (cond: condition) (args: list valnum) : option(condition * list valnum) := + match cond, args with + | Ccompimm Cne n, x::nil => + if Int.eq_dec n Int.zero then combine_compimm_ne_0 x + else if Int.eq_dec n Int.one then combine_compimm_ne_1 x + else None + | Ccompimm Ceq n, x::nil => + if Int.eq_dec n Int.zero then combine_compimm_eq_0 x + else if Int.eq_dec n Int.one then combine_compimm_eq_1 x + else None + | Ccompuimm Cne n, x::nil => + if Int.eq_dec n Int.zero then combine_compimm_ne_0 x + else if Int.eq_dec n Int.one then combine_compimm_ne_1 x + else None + | Ccompuimm Ceq n, x::nil => + if Int.eq_dec n Int.zero then combine_compimm_eq_0 x + else if Int.eq_dec n Int.one then combine_compimm_eq_1 x + else None + | _, _ => None + end. + +Function combine_addr (addr: addressing) (args: list valnum) : option(addressing * list valnum) := + match addr, args with + | Aindexed n, x::nil => + match get x with + | Some(Op (Oaddlimm m) ys) => + Some(Aindexed (Int64.add m n), ys) + | _ => None + end + | _, _ => None + end. + +Function combine_op (op: operation) (args: list valnum) : option(operation * list valnum) := + match op, args with + | Oaddimm n, x :: nil => + match get x with + | Some(Op (Oaddimm m) ys) => Some(Oaddimm (Int.add m n), ys) + | _ => None + end + | Oandimm n, x :: nil => + match get x with + | Some(Op (Oandimm m) ys) => + Some(let p := Int.and m n in + if Int.eq p m then (Omove, x :: nil) else (Oandimm p, ys)) + | _ => None + end + | Oorimm n, x :: nil => + match get x with + | Some(Op (Oorimm m) ys) => Some(Oorimm (Int.or m n), ys) + | _ => None + end + | Oxorimm n, x :: nil => + match get x with + | Some(Op (Oxorimm m) ys) => Some(Oxorimm (Int.xor m n), ys) + | _ => None + end + | Oaddlimm n, x :: nil => + match get x with + | Some(Op (Oaddlimm m) ys) => Some(Oaddlimm (Int64.add m n), ys) + | _ => None + end + | Oandlimm n, x :: nil => + match get x with + | Some(Op (Oandlimm m) ys) => + Some(let p := Int64.and m n in + if Int64.eq p m then (Omove, x :: nil) else (Oandlimm p, ys)) + | _ => None + end + | Oorlimm n, x :: nil => + match get x with + | Some(Op (Oorlimm m) ys) => Some(Oorlimm (Int64.or m n), ys) + | _ => None + end + | Oxorlimm n, x :: nil => + match get x with + | Some(Op (Oxorlimm m) ys) => Some(Oxorlimm (Int64.xor m n), ys) + | _ => None + end + | Ocmp cond, _ => + match combine_cond cond args with + | Some(cond', args') => Some(Ocmp cond', args') + | None => None + end + | _, _ => None + end. + +End COMBINE. + + diff --git a/aarch64/CombineOpproof.v b/aarch64/CombineOpproof.v new file mode 100644 index 00000000..7d13b964 --- /dev/null +++ b/aarch64/CombineOpproof.v @@ -0,0 +1,161 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +Require Import FunInd. +Require Import Coqlib. +Require Import AST Integers Values Memory. +Require Import Op Registers RTL. +Require Import CSEdomain. +Require Import CombineOp. + +Section COMBINE. + +Variable ge: genv. +Variable sp: val. +Variable m: mem. +Variable get: valnum -> option rhs. +Variable valu: valnum -> val. +Hypothesis get_sound: forall v rhs, get v = Some rhs -> rhs_eval_to valu ge sp m rhs (valu v). + +Lemma get_op_sound: + forall v op vl, get v = Some (Op op vl) -> eval_operation ge sp op (map valu vl) m = Some (valu v). +Proof. + intros. exploit get_sound; eauto. intros REV; inv REV; auto. +Qed. + +Ltac UseGetSound := + match goal with + | [ H: get _ = Some _ |- _ ] => + let x := fresh "EQ" in (generalize (get_op_sound _ _ _ H); intros x; simpl in x; FuncInv) + end. + +Lemma combine_compimm_ne_0_sound: + forall x cond args, + combine_compimm_ne_0 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Cne (valu x) (Vint Int.zero) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Cne (valu x) (Vint Int.zero). +Proof. + intros until args. functional induction (combine_compimm_ne_0 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Lemma combine_compimm_eq_0_sound: + forall x cond args, + combine_compimm_eq_0 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Ceq (valu x) (Vint Int.zero) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Ceq (valu x) (Vint Int.zero). +Proof. + intros until args. functional induction (combine_compimm_eq_0 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + rewrite eval_negate_condition. + destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Lemma combine_compimm_eq_1_sound: + forall x cond args, + combine_compimm_eq_1 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Ceq (valu x) (Vint Int.one) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Ceq (valu x) (Vint Int.one). +Proof. + intros until args. functional induction (combine_compimm_eq_1 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Lemma combine_compimm_ne_1_sound: + forall x cond args, + combine_compimm_ne_1 get x = Some(cond, args) -> + eval_condition cond (map valu args) m = Val.cmp_bool Cne (valu x) (Vint Int.one) /\ + eval_condition cond (map valu args) m = Val.cmpu_bool (Mem.valid_pointer m) Cne (valu x) (Vint Int.one). +Proof. + intros until args. functional induction (combine_compimm_ne_1 get x); intros EQ; inv EQ. + (* of cmp *) + UseGetSound. rewrite <- H. + rewrite eval_negate_condition. + destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. +Qed. + +Theorem combine_cond_sound: + forall cond args cond' args', + combine_cond get cond args = Some(cond', args') -> + eval_condition cond' (map valu args') m = eval_condition cond (map valu args) m. +Proof. + intros. functional inversion H; subst. + (* compimm ne zero *) + - simpl; eapply combine_compimm_ne_0_sound; eauto. + (* compimm ne one *) + - simpl; eapply combine_compimm_ne_1_sound; eauto. + (* compimm eq zero *) + - simpl; eapply combine_compimm_eq_0_sound; eauto. + (* compimm eq one *) + - simpl; eapply combine_compimm_eq_1_sound; eauto. + (* compuimm ne zero *) + - simpl; eapply combine_compimm_ne_0_sound; eauto. + (* compuimm ne one *) + - simpl; eapply combine_compimm_ne_1_sound; eauto. + (* compuimm eq zero *) + - simpl; eapply combine_compimm_eq_0_sound; eauto. + (* compuimm eq one *) + - simpl; eapply combine_compimm_eq_1_sound; eauto. +Qed. + +Theorem combine_addr_sound: + forall addr args addr' args', + combine_addr get addr args = Some(addr', args') -> + eval_addressing ge sp addr' (map valu args') = eval_addressing ge sp addr (map valu args). +Proof. + intros. functional inversion H; subst. +- (* indexed - addimml *) + UseGetSound. simpl. rewrite <- H0. rewrite Val.addl_assoc. auto. +Qed. + +Theorem combine_op_sound: + forall op args op' args', + combine_op get op args = Some(op', args') -> + eval_operation ge sp op' (map valu args') m = eval_operation ge sp op (map valu args) m. +Proof. + intros. functional inversion H; subst. + (* addimm - addimm *) + - UseGetSound. FuncInv. simpl. + rewrite <- H0. rewrite Val.add_assoc. auto. + (* andimm - andimm *) + - UseGetSound; simpl. + generalize (Int.eq_spec p m0); rewrite H7; intros. + rewrite <- H0. rewrite Val.and_assoc. simpl. fold p. rewrite H1. auto. + - UseGetSound; simpl. + rewrite <- H0. rewrite Val.and_assoc. auto. + (* orimm - orimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.or_assoc. auto. + (* xorimm - xorimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.xor_assoc. auto. + (* addlimm - addlimm *) + - UseGetSound. FuncInv. simpl. + rewrite <- H0. rewrite Val.addl_assoc. auto. + (* andlimm - andlimm *) + - UseGetSound; simpl. + generalize (Int64.eq_spec p m0); rewrite H7; intros. + rewrite <- H0. rewrite Val.andl_assoc. simpl. fold p. rewrite H1. auto. + - UseGetSound; simpl. + rewrite <- H0. rewrite Val.andl_assoc. auto. + (* orlimm - orlimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.orl_assoc. auto. + (* xorlimm - xorlimm *) + - UseGetSound. simpl. rewrite <- H0. rewrite Val.xorl_assoc. auto. + (* cmp *) + - simpl. decEq; decEq. eapply combine_cond_sound; eauto. +Qed. + +End COMBINE. diff --git a/aarch64/ConstpropOp.vp b/aarch64/ConstpropOp.vp new file mode 100644 index 00000000..c0a2c6bf --- /dev/null +++ b/aarch64/ConstpropOp.vp @@ -0,0 +1,401 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Strength reduction for operators and conditions. + This is the machine-dependent part of [Constprop]. *) + +Require Archi. +Require Import Coqlib Compopts. +Require Import AST Integers Floats. +Require Import Op Registers. +Require Import ValueDomain ValueAOp. + +(** * Converting known values to constants *) + +Definition const_for_result (a: aval) : option operation := + match a with + | I n => Some(Ointconst n) + | L n => Some(Olongconst n) + | F n => if Compopts.generate_float_constants tt then Some(Ofloatconst n) else None + | FS n => if Compopts.generate_float_constants tt then Some(Osingleconst n) else None + | Ptr(Gl id ofs) => Some(Oaddrsymbol id ofs) + | Ptr(Stk ofs) => Some(Oaddrstack ofs) + | _ => None + end. + +(** * Operator strength reduction *) + +Definition eval_static_shift (s: shift) (v: int) (n: amount32) : int := + match s with + | Slsl => Int.shl v n + | Slsr => Int.shru v n + | Sasr => Int.shr v n + | Sror => Int.ror v n + end. + +Definition eval_static_shiftl (s: shift) (v: int64) (n: amount64) : int64 := + match s with + | Slsl => Int64.shl' v n + | Slsr => Int64.shru' v n + | Sasr => Int64.shr' v n + | Sror => Int64.ror v (Int64.repr (Int.unsigned n)) + end. + +Definition eval_static_extend (x: extension) (v: int) (n: amount64) : int64 := + Int64.shl' (match x with Xsgn32 => Int64.repr (Int.signed v) + | Xuns32 => Int64.repr (Int.unsigned v) end) + n. + +Nondetfunction cond_strength_reduction + (cond: condition) (args: list reg) (vl: list aval) := + match cond, args, vl with + | Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil => + (Ccompimm (swap_comparison c) n1, r2 :: nil) + | Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompimm c n2, r1 :: nil) + | Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil => + (Ccompuimm (swap_comparison c) n1, r2 :: nil) + | Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompuimm c n2, r1 :: nil) + | Ccompshift c s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompimm c (eval_static_shift s n2 a), r1 :: nil) + | Ccompushift c s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompuimm c (eval_static_shift s n2 a), r1 :: nil) + | Ccompl c, r1 :: r2 :: nil, L n1 :: v2 :: nil => + (Ccomplimm (swap_comparison c) n1, r2 :: nil) + | Ccompl c, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Ccomplimm c n2, r1 :: nil) + | Ccomplu c, r1 :: r2 :: nil, L n1 :: v2 :: nil => + (Ccompluimm (swap_comparison c) n1, r2 :: nil) + | Ccomplu c, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Ccompluimm c n2, r1 :: nil) + | Ccomplshift c s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Ccomplimm c (eval_static_shiftl s n2 a), r1 :: nil) + | Ccomplushift c s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Ccompluimm c (eval_static_shiftl s n2 a), r1 :: nil) + | Ccompf c, r1 :: r2 :: nil, F n1 :: v2 :: nil => + if Float.eq_dec n1 Float.zero + then (Ccompfzero (swap_comparison c), r2 :: nil) + else (cond, args) + | Ccompf c, r1 :: r2 :: nil, v1 :: F n2 :: nil => + if Float.eq_dec n2 Float.zero + then (Ccompfzero c, r1 :: nil) + else (cond, args) + | Cnotcompf c, r1 :: r2 :: nil, F n1 :: v2 :: nil => + if Float.eq_dec n1 Float.zero + then (Cnotcompfzero (swap_comparison c), r2 :: nil) + else (cond, args) + | Cnotcompf c, r1 :: r2 :: nil, v1 :: F n2 :: nil => + if Float.eq_dec n2 Float.zero + then (Cnotcompfzero c, r1 :: nil) + else (cond, args) + | Ccompfs c, r1 :: r2 :: nil, FS n1 :: v2 :: nil => + if Float32.eq_dec n1 Float32.zero + then (Ccompfszero (swap_comparison c), r2 :: nil) + else (cond, args) + | Ccompfs c, r1 :: r2 :: nil, v1 :: FS n2 :: nil => + if Float32.eq_dec n2 Float32.zero + then (Ccompfszero c, r1 :: nil) + else (cond, args) + | Cnotcompfs c, r1 :: r2 :: nil, FS n1 :: v2 :: nil => + if Float32.eq_dec n1 Float32.zero + then (Cnotcompfszero (swap_comparison c), r2 :: nil) + else (cond, args) + | Cnotcompfs c, r1 :: r2 :: nil, v1 :: FS n2 :: nil => + if Float32.eq_dec n2 Float32.zero + then (Cnotcompfszero c, r1 :: nil) + else (cond, args) + | _, _, _ => + (cond, args) + end. + +Definition make_cmp_base (c: condition) (args: list reg) (vl: list aval) := + let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args'). + +Definition make_cmp_imm_eq (c: condition) (args: list reg) (vl: list aval) + (n: int) (r1: reg) (v1: aval) := + if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil) + else if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil) + else make_cmp_base c args vl. + +Definition make_cmp_imm_ne (c: condition) (args: list reg) (vl: list aval) + (n: int) (r1: reg) (v1: aval) := + if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil) + else if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil) + else make_cmp_base c args vl. + +Nondetfunction make_cmp (c: condition) (args: list reg) (vl: list aval) := + match c, args, vl with + | Ccompimm Ceq n, r1 :: nil, v1 :: nil => + make_cmp_imm_eq c args vl n r1 v1 + | Ccompimm Cne n, r1 :: nil, v1 :: nil => + make_cmp_imm_ne c args vl n r1 v1 + | Ccompuimm Ceq n, r1 :: nil, v1 :: nil => + make_cmp_imm_eq c args vl n r1 v1 + | Ccompuimm Cne n, r1 :: nil, v1 :: nil => + make_cmp_imm_ne c args vl n r1 v1 + | _, _, _ => + make_cmp_base c args vl + end. + +Definition make_select (c: condition) (ty: typ) + (r1 r2: reg) (args: list reg) (vl: list aval) := + match resolve_branch (eval_static_condition c vl) with + | Some b => (Omove, (if b then r1 else r2) :: nil) + | None => + let (c', args') := cond_strength_reduction c args vl in + (Osel c' ty, r1 :: r2 :: args') + end. + +Definition make_addimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Oaddimm n, r :: nil). + +Definition make_shlimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then (Oshift Slsl (mk_amount32 n), r1 :: nil) + else (Oshl, r1 :: r2 :: nil). + +Definition make_shrimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then (Oshift Sasr (mk_amount32 n), r1 :: nil) + else (Oshr, r1 :: r2 :: nil). + +Definition make_shruimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then (Oshift Slsr (mk_amount32 n), r1 :: nil) + else (Oshru, r1 :: r2 :: nil). + +Definition make_mulimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then + (Ointconst Int.zero, nil) + else if Int.eq n Int.one then + (Omove, r1 :: nil) + else + match Int.is_power2 n with + | Some l => (Oshift Slsl (mk_amount32 l), r1 :: nil) + | None => (Omul, r1 :: r2 :: nil) + end. + +Definition make_andimm (n: int) (r: reg) (a: aval) := + if Int.eq n Int.zero then (Ointconst Int.zero, nil) + else if Int.eq n Int.mone then (Omove, r :: nil) + else if match a with Uns _ m => Int.eq (Int.zero_ext m (Int.not n)) Int.zero + | _ => false end + then (Omove, r :: nil) + else (Oandimm n, r :: nil). + +Definition make_orimm (n: int) (r: reg) := + if Int.eq n Int.zero then (Omove, r :: nil) + else if Int.eq n Int.mone then (Ointconst Int.mone, nil) + else (Oorimm n, r :: nil). + +Definition make_xorimm (n: int) (r: reg) := + if Int.eq n Int.zero then (Omove, r :: nil) + else (Oxorimm n, r :: nil). + +Definition make_divimm n (r1 r2: reg) := + if Int.eq n Int.one then + (Omove, r1 :: nil) + else + match Int.is_power2 n with + | Some l => if Int.ltu l (Int.repr 31) + then (Oshrximm l, r1 :: nil) + else (Odiv, r1 :: r2 :: nil) + | None => (Odiv, r1 :: r2 :: nil) + end. + +Definition make_divuimm n (r1 r2: reg) := + if Int.eq n Int.one then + (Omove, r1 :: nil) + else + match Int.is_power2 n with + | Some l => (Oshift Slsr (mk_amount32 l), r1 :: nil) + | None => (Odivu, r1 :: r2 :: nil) + end. + +Definition make_addlimm (n: int64) (r: reg) := + if Int64.eq n Int64.zero + then (Omove, r :: nil) + else (Oaddlimm n, r :: nil). + +Definition make_shllimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int64.iwordsize' then (Oshiftl Slsl (mk_amount64 n), r1 :: nil) + else (Oshll, r1 :: r2 :: nil). + +Definition make_shrlimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int64.iwordsize' then (Oshiftl Sasr (mk_amount64 n), r1 :: nil) + else (Oshrl, r1 :: r2 :: nil). + +Definition make_shrluimm (n: int) (r1 r2: reg) := + if Int.eq n Int.zero then (Omove, r1 :: nil) + else if Int.ltu n Int64.iwordsize' then (Oshiftl Slsr (mk_amount64 n), r1 :: nil) + else (Oshrlu, r1 :: r2 :: nil). + +Definition make_mullimm (n: int64) (r1 r2: reg) := + if Int64.eq n Int64.zero then + (Olongconst Int64.zero, nil) + else if Int64.eq n Int64.one then + (Omove, r1 :: nil) + else + match Int64.is_power2' n with + | Some l => (Oshiftl Slsl (mk_amount64 l), r1 :: nil) + | None => (Omull, r1 :: r2 :: nil) + end. + +Definition make_andlimm (n: int64) (r: reg) (a: aval) := + if Int64.eq n Int64.zero then (Olongconst Int64.zero, nil) + else if Int64.eq n Int64.mone then (Omove, r :: nil) + else (Oandlimm n, r :: nil). + +Definition make_orlimm (n: int64) (r: reg) := + if Int64.eq n Int64.zero then (Omove, r :: nil) + else if Int64.eq n Int64.mone then (Olongconst Int64.mone, nil) + else (Oorlimm n, r :: nil). + +Definition make_xorlimm (n: int64) (r: reg) := + if Int64.eq n Int64.zero then (Omove, r :: nil) + else (Oxorlimm n, r :: nil). + +Definition make_divlimm n (r1 r2: reg) := + match Int64.is_power2' n with + | Some l => if Int.ltu l (Int.repr 63) + then (Oshrlximm l, r1 :: nil) + else (Odivl, r1 :: r2 :: nil) + | None => (Odivl, r1 :: r2 :: nil) + end. + +Definition make_divluimm n (r1 r2: reg) := + match Int64.is_power2' n with + | Some l => (Oshiftl Slsr (mk_amount64 l), r1 :: nil) + | None => (Odivlu, r1 :: r2 :: nil) + end. + +Definition make_mulfimm (n: float) (r r1 r2: reg) := + if Float.eq_dec n (Float.of_int (Int.repr 2)) + then (Oaddf, r :: r :: nil) + else (Omulf, r1 :: r2 :: nil). + +Definition make_mulfsimm (n: float32) (r r1 r2: reg) := + if Float32.eq_dec n (Float32.of_int (Int.repr 2)) + then (Oaddfs, r :: r :: nil) + else (Omulfs, r1 :: r2 :: nil). + +Definition make_zext (s: Z) (r: reg) (a: aval) := + if vincl a (Uns Ptop s) then (Omove, r :: nil) else (Ozext s, r :: nil). + +Definition make_sext (s: Z) (r: reg) (a: aval) := + if vincl a (Sgn Ptop s) then (Omove, r :: nil) else (Osext s, r :: nil). + +Nondetfunction op_strength_reduction + (op: operation) (args: list reg) (vl: list aval) := + match op, args, vl with + | Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_addimm n1 r2 + | Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm n2 r1 + | Oaddshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (eval_static_shift s n2 a) r1 + | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1 + | Osubshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg (eval_static_shift s n2 a)) r1 + | Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_mulimm n1 r2 r1 + | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1 r2 + | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2 + | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2 + | Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_andimm n1 r2 v2 + | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1 v1 + | Oandshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (eval_static_shift s n2 a) r1 v1 + | Oandimm n, r1 :: nil, v1 :: nil => make_andimm n r1 v1 + | Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_orimm n1 r2 + | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1 + | Oorshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm (eval_static_shift s n2 a) r1 + | Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_xorimm n1 r2 + | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1 + | Oxorshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm (eval_static_shift s n2 a) r1 + | Obic, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not n2) r1 v1 + | Obicshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not (eval_static_shift s n2 a)) r1 v1 + | Oorn, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm (Int.not n2) r1 + | Oornshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm (Int.not (eval_static_shift s n2 a)) r1 + | Oeqv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm (Int.not n2) r1 + | Oeqvshift s a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm (Int.not (eval_static_shift s n2 a)) r1 + | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1 r2 + | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1 r2 + | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 r2 + | Ozext s, r1 :: nil, v1 :: nil => make_zext s r1 v1 + | Osext s, r1 :: nil, v1 :: nil => make_sext s r1 v1 + + | Oaddl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_addlimm n1 r2 + | Oaddl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm n2 r1 + | Oaddlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm (eval_static_shiftl s n2 a) r1 + | Oaddlext x a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addlimm (eval_static_extend x n2 a) r1 + | Osubl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm (Int64.neg n2) r1 + | Osublshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_addlimm (Int64.neg (eval_static_shiftl s n2 a)) r1 + | Osublext x a, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addlimm (Int64.neg (eval_static_extend x n2 a)) r1 + | Omull, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_mullimm n1 r2 r1 + | Omull, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_mullimm n2 r1 r2 + | Odivl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_divlimm n2 r1 r2 + | Odivlu, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_divluimm n2 r1 r2 + | Oandl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_andlimm n1 r2 v2 + | Oandl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_andlimm n2 r1 v1 + | Oandlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_andlimm (eval_static_shiftl s n2 a) r1 v1 + | Oandlimm n, r1 :: nil, v1 :: nil => make_andlimm n r1 v1 + | Oorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_orlimm n1 r2 + | Oorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_orlimm n2 r1 + | Oorlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_orlimm (eval_static_shiftl s n2 a) r1 + | Oxorl, r1 :: r2 :: nil, L n1 :: v2 :: nil => make_xorlimm n1 r2 + | Oxorl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_xorlimm n2 r1 + | Oxorlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_xorlimm (eval_static_shiftl s n2 a) r1 + | Obicl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_andlimm (Int64.not n2) r1 v1 + | Obiclshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_andlimm (Int64.not (eval_static_shiftl s n2 a)) r1 v1 + | Oornl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_orlimm (Int64.not n2) r1 + | Oornlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_orlimm (Int64.not (eval_static_shiftl s n2 a)) r1 + | Oeqvl, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_xorlimm (Int64.not n2) r1 + | Oeqvlshift s a, r1 :: r2 :: nil, v1 :: L n2 :: nil => make_xorlimm (Int64.not (eval_static_shiftl s n2 a)) r1 + | Oshll, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shllimm n2 r1 r2 + | Oshrl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrlimm n2 r1 r2 + | Oshrlu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrluimm n2 r1 r2 + | Ocmp c, args, vl => make_cmp c args vl + | Osel c ty, r1 :: r2 :: args, v1 :: v2 :: vl => make_select c ty r1 r2 args vl + | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => make_mulfimm n2 r1 r1 r2 + | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => make_mulfimm n1 r2 r1 r2 + | Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => make_mulfsimm n2 r1 r1 r2 + | Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => make_mulfsimm n1 r2 r1 r2 + | _, _, _ => (op, args) + end. + +Nondetfunction addr_strength_reduction + (addr: addressing) (args: list reg) (vl: list aval) := + match addr, args, vl with + | Aindexed n, r1 :: nil, Ptr(Gl symb n1) :: nil => + (Aglobal symb (Ptrofs.add n1 (Ptrofs.of_int64 n)), nil) + | Aindexed n, r1 :: nil, Ptr(Stk n1) :: nil => + (Ainstack (Ptrofs.add n1 (Ptrofs.of_int64 n)), nil) + | Aindexed2, r1 :: r2 :: nil, Ptr(Stk n1) :: L n2 :: nil => + (Ainstack (Ptrofs.add n1 (Ptrofs.of_int64 n2)), nil) + | Aindexed2, r1 :: r2 :: nil, L n1 :: Ptr(Stk n2) :: nil => + (Ainstack (Ptrofs.add (Ptrofs.of_int64 n1) n2), nil) + | Aindexed2, r1 :: r2 :: nil, L n1 :: v2 :: nil => + (Aindexed n1, r2 :: nil) + | Aindexed2, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Aindexed n2, r1 :: nil) + | Aindexed2shift a, r1 :: r2 :: nil, Ptr(Stk n1) :: L n2 :: nil => + (Ainstack (Ptrofs.add n1 (Ptrofs.of_int64 (Int64.shl' n2 a))), nil) + | Aindexed2shift a, r1 :: r2 :: nil, v1 :: L n2 :: nil => + (Aindexed (Int64.shl' n2 a), r1 :: nil) + | Aindexed2ext x a, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil => + (Ainstack (Ptrofs.add n1 (Ptrofs.of_int64 (eval_static_extend x n2 a))), nil) + | Aindexed2ext x a, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Aindexed (eval_static_extend x n2 a), r1 :: nil) + | _, _, _ => + (addr, args) + end. + diff --git a/aarch64/ConstpropOpproof.v b/aarch64/ConstpropOpproof.v new file mode 100644 index 00000000..deab7cd4 --- /dev/null +++ b/aarch64/ConstpropOpproof.v @@ -0,0 +1,838 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Correctness proof for operator strength reduction. *) + +Require Import Coqlib Compopts. +Require Import Integers Floats Values Memory Globalenvs Events. +Require Import Op Registers RTL ValueDomain ValueAOp ValueAnalysis. +Require Import ConstpropOp. + +Local Transparent Archi.ptr64. + +Section STRENGTH_REDUCTION. + +Variable bc: block_classification. +Variable ge: genv. +Hypothesis GENV: genv_match bc ge. +Variable sp: block. +Hypothesis STACK: bc sp = BCstack. +Variable ae: AE.t. +Variable e: regset. +Variable m: mem. +Hypothesis MATCH: ematch bc e ae. + +Lemma match_G: + forall r id ofs, + AE.get r ae = Ptr(Gl id ofs) -> Val.lessdef e#r (Genv.symbol_address ge id ofs). +Proof. + intros. apply vmatch_ptr_gl with bc; auto. rewrite <- H. apply MATCH. +Qed. + +Lemma match_S: + forall r ofs, + AE.get r ae = Ptr(Stk ofs) -> Val.lessdef e#r (Vptr sp ofs). +Proof. + intros. apply vmatch_ptr_stk with bc; auto. rewrite <- H. apply MATCH. +Qed. + +Ltac InvApproxRegs := + match goal with + | [ H: _ :: _ = _ :: _ |- _ ] => + injection H; clear H; intros; InvApproxRegs + | [ H: ?v = AE.get ?r ae |- _ ] => + generalize (MATCH r); rewrite <- H; clear H; intro; InvApproxRegs + | _ => idtac + end. + +Ltac SimplVM := + match goal with + | [ H: vmatch _ ?v (I ?n) |- _ ] => + let E := fresh in + assert (E: v = Vint n) by (inversion H; auto); + rewrite E in *; clear H; SimplVM + | [ H: vmatch _ ?v (L ?n) |- _ ] => + let E := fresh in + assert (E: v = Vlong n) by (inversion H; auto); + rewrite E in *; clear H; SimplVM + | [ H: vmatch _ ?v (F ?n) |- _ ] => + let E := fresh in + assert (E: v = Vfloat n) by (inversion H; auto); + rewrite E in *; clear H; SimplVM + | [ H: vmatch _ ?v (FS ?n) |- _ ] => + let E := fresh in + assert (E: v = Vsingle n) by (inversion H; auto); + rewrite E in *; clear H; SimplVM + | [ H: vmatch _ ?v (Ptr(Gl ?id ?ofs)) |- _ ] => + let E := fresh in + assert (E: Val.lessdef v (Genv.symbol_address ge id ofs)) by (eapply vmatch_ptr_gl; eauto); + clear H; SimplVM + | [ H: vmatch _ ?v (Ptr(Stk ?ofs)) |- _ ] => + let E := fresh in + assert (E: Val.lessdef v (Vptr sp ofs)) by (eapply vmatch_ptr_stk; eauto); + clear H; SimplVM + | _ => idtac + end. + +Lemma const_for_result_correct: + forall a op v, + const_for_result a = Some op -> + vmatch bc v a -> + exists v', eval_operation ge (Vptr sp Ptrofs.zero) op nil m = Some v' /\ Val.lessdef v v'. +Proof. + unfold const_for_result; intros; destruct a; inv H; SimplVM. +- (* integer *) + exists (Vint n); auto. +- (* long *) + exists (Vlong n); auto. +- (* float *) + destruct (Compopts.generate_float_constants tt); inv H2. exists (Vfloat f); auto. +- (* single *) + destruct (Compopts.generate_float_constants tt); inv H2. exists (Vsingle f); auto. +- (* pointer *) + destruct p; try discriminate; SimplVM. + + (* global *) + inv H2. exists (Genv.symbol_address ge id ofs); auto. + + (* stack *) + inv H2. exists (Vptr sp ofs); split; auto. simpl. rewrite Ptrofs.add_zero_l; auto. +Qed. + +Lemma eval_static_shift_correct: forall s v a, + eval_shift s (Vint v) a = Vint (eval_static_shift s v a). +Proof. + intros; destruct s; simpl; rewrite ? a32_range; auto. +Qed. + +Lemma eval_static_shiftl_correct: forall s v a, + eval_shiftl s (Vlong v) a = Vlong (eval_static_shiftl s v a). +Proof. + intros; destruct s; simpl; rewrite ? a64_range; auto. +Qed. + +Lemma eval_static_extend_correct: forall x v a, + eval_extend x (Vint v) a = Vlong (eval_static_extend x v a). +Proof. + unfold eval_extend, eval_static_extend; intros; destruct x; simpl; rewrite ? a64_range; auto. +Qed. + +Lemma cond_strength_reduction_correct: + forall cond args vl, + vl = map (fun r => AE.get r ae) args -> + let (cond', args') := cond_strength_reduction cond args vl in + eval_condition cond' e##args' m = eval_condition cond e##args m. +Proof. + intros until vl. unfold cond_strength_reduction. + case (cond_strength_reduction_match cond args vl); simpl; intros; InvApproxRegs; SimplVM. +- apply Val.swap_cmp_bool. +- auto. +- apply Val.swap_cmpu_bool. +- auto. +- rewrite eval_static_shift_correct; auto. +- rewrite eval_static_shift_correct; auto. +- apply Val.swap_cmpl_bool. +- auto. +- apply Val.swap_cmplu_bool. +- auto. +- rewrite eval_static_shiftl_correct; auto. +- rewrite eval_static_shiftl_correct; auto. +- destruct (Float.eq_dec n1 Float.zero). + subst n1. simpl. destruct (e#r2); simpl; auto. rewrite Float.cmp_swap. auto. + simpl. rewrite H1; auto. +- destruct (Float.eq_dec n2 Float.zero). + subst n2. simpl. auto. + simpl. rewrite H1; auto. +- destruct (Float.eq_dec n1 Float.zero). + subst n1. simpl. destruct (e#r2); simpl; auto. rewrite Float.cmp_swap. auto. + simpl. rewrite H1; auto. +- destruct (Float.eq_dec n2 Float.zero); simpl; auto. + subst n2; auto. + rewrite H1; auto. +- destruct (Float32.eq_dec n1 Float32.zero). + subst n1. simpl. destruct (e#r2); simpl; auto. rewrite Float32.cmp_swap. auto. + simpl. rewrite H1; auto. +- destruct (Float32.eq_dec n2 Float32.zero). + subst n2. simpl. auto. + simpl. rewrite H1; auto. +- destruct (Float32.eq_dec n1 Float32.zero). + subst n1. simpl. destruct (e#r2); simpl; auto. rewrite Float32.cmp_swap. auto. + simpl. rewrite H1; auto. +- destruct (Float32.eq_dec n2 Float32.zero); simpl; auto. + subst n2; auto. + rewrite H1; auto. +- auto. +Qed. + +Lemma make_cmp_base_correct: + forall c args vl, + vl = map (fun r => AE.get r ae) args -> + let (op', args') := make_cmp_base c args vl in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op' e##args' m = Some v + /\ Val.lessdef (Val.of_optbool (eval_condition c e##args m)) v. +Proof. + intros. unfold make_cmp_base. + generalize (cond_strength_reduction_correct c args vl H). + destruct (cond_strength_reduction c args vl) as [c' args']. intros EQ. + econstructor; split. simpl; eauto. rewrite EQ. auto. +Qed. + +Lemma make_cmp_correct: + forall c args vl, + vl = map (fun r => AE.get r ae) args -> + let (op', args') := make_cmp c args vl in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op' e##args' m = Some v + /\ Val.lessdef (Val.of_optbool (eval_condition c e##args m)) v. +Proof. + intros c args vl. + assert (Y: forall r, vincl (AE.get r ae) (Uns Ptop 1) = true -> + e#r = Vundef \/ e#r = Vint Int.zero \/ e#r = Vint Int.one). + { intros. apply vmatch_Uns_1 with bc Ptop. eapply vmatch_ge. eapply vincl_ge; eauto. apply MATCH. } + unfold make_cmp. case (make_cmp_match c args vl); intros. +- unfold make_cmp_imm_eq. + destruct (Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1)) eqn:E1. ++ simpl in H; inv H. InvBooleans. subst n. + exists (e#r1); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. ++ destruct (Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1)) eqn:E0. +* simpl in H; inv H. InvBooleans. subst n. + exists (Val.xor e#r1 (Vint Int.one)); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. +* apply make_cmp_base_correct; auto. +- unfold make_cmp_imm_ne. + destruct (Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1)) eqn:E0. ++ simpl in H; inv H. InvBooleans. subst n. + exists (e#r1); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. ++ destruct (Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1)) eqn:E1. +* simpl in H; inv H. InvBooleans. subst n. + exists (Val.xor e#r1 (Vint Int.one)); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. +* apply make_cmp_base_correct; auto. +- unfold make_cmp_imm_eq. + destruct (Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1)) eqn:E1. ++ simpl in H; inv H. InvBooleans. subst n. + exists (e#r1); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. ++ destruct (Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1)) eqn:E0. +* simpl in H; inv H. InvBooleans. subst n. + exists (Val.xor e#r1 (Vint Int.one)); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. +* apply make_cmp_base_correct; auto. +- unfold make_cmp_imm_ne. + destruct (Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1)) eqn:E0. ++ simpl in H; inv H. InvBooleans. subst n. + exists (e#r1); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. ++ destruct (Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1)) eqn:E1. +* simpl in H; inv H. InvBooleans. subst n. + exists (Val.xor e#r1 (Vint Int.one)); split; auto. simpl. + exploit Y; eauto. intros [A | [A | A]]; rewrite A; simpl; auto. +* apply make_cmp_base_correct; auto. +- apply make_cmp_base_correct; auto. +Qed. + +Lemma make_select_correct: + forall c ty r1 r2 args vl, + vl = map (fun r => AE.get r ae) args -> + let (op', args') := make_select c ty r1 r2 args vl in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op' e##args' m = Some v + /\ Val.lessdef (Val.select (eval_condition c e##args m) e#r1 e#r2 ty) v. +Proof. + unfold make_select; intros. + destruct (resolve_branch (eval_static_condition c vl)) as [b|] eqn:RB. +- exists (if b then e#r1 else e#r2); split. ++ simpl. destruct b; auto. ++ destruct (eval_condition c e##args m) as [b'|] eqn:EC; simpl; auto. + assert (b = b'). + { eapply resolve_branch_sound; eauto. + rewrite <- EC. apply eval_static_condition_sound with bc. + subst vl. exact (aregs_sound _ _ _ args MATCH). } + subst b'. apply Val.lessdef_normalize. +- generalize (cond_strength_reduction_correct c args vl H). + destruct (cond_strength_reduction c args vl) as [cond' args']; intros EQ. + econstructor; split. simpl; eauto. rewrite EQ; auto. +Qed. + +Lemma make_addimm_correct: + forall n r, + let (op, args) := make_addimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.add e#r (Vint n)) v. +Proof. + intros. unfold make_addimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. + subst. exists (e#r); split; auto. + destruct (e#r); simpl; rewrite ?Int.add_zero; auto. + exists (Val.add e#r (Vint n)); split; auto. +Qed. + +Lemma make_shlimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shlimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shl e#r1 (Vint n)) v. +Proof. +Local Opaque mk_amount32. + intros; unfold make_shlimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. rewrite Int.shl_zero. auto. + destruct (Int.ltu n Int.iwordsize) eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount32_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_shrimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shrimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shr e#r1 (Vint n)) v. +Proof. + intros; unfold make_shrimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. rewrite Int.shr_zero. auto. + destruct (Int.ltu n Int.iwordsize) eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount32_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_shruimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shruimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shru e#r1 (Vint n)) v. +Proof. + intros; unfold make_shruimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. rewrite Int.shru_zero. auto. + destruct (Int.ltu n Int.iwordsize) eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount32_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_mulimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_mulimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mul e#r1 (Vint n)) v. +Proof. + intros; unfold make_mulimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (Vint Int.zero); split; auto. destruct (e#r1); simpl; auto. rewrite Int.mul_zero; auto. + predSpec Int.eq Int.eq_spec n Int.one; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. rewrite Int.mul_one; auto. + destruct (Int.is_power2 n) eqn:?; intros. + rewrite (Val.mul_pow2 e#r1 _ _ Heqo). econstructor; split. simpl; eauto. + rewrite mk_amount32_eq; auto. eapply Int.is_power2_range; eauto. + econstructor; split; eauto. simpl. rewrite H; auto. +Qed. + +Lemma make_divimm_correct: + forall n r1 r2 v, + Val.divs e#r1 e#r2 = Some v -> + e#r2 = Vint n -> + let (op, args) := make_divimm n r1 r2 in + exists w, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some w /\ Val.lessdef v w. +Proof. + intros; unfold make_divimm. + predSpec Int.eq Int.eq_spec n Int.one; intros. subst. rewrite H0 in H. + destruct (e#r1) eqn:?; + try (rewrite Val.divs_one in H; exists (Vint i); split; simpl; try rewrite Heqv0; auto); + inv H; auto. + destruct (Int.is_power2 n) eqn:?. + destruct (Int.ltu i (Int.repr 31)) eqn:?. + exists v; split; auto. simpl. eapply Val.divs_pow2; eauto. congruence. + exists v; auto. + exists v; auto. +Qed. + +Lemma make_divuimm_correct: + forall n r1 r2 v, + Val.divu e#r1 e#r2 = Some v -> + e#r2 = Vint n -> + let (op, args) := make_divuimm n r1 r2 in + exists w, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some w /\ Val.lessdef v w. +Proof. + intros; unfold make_divuimm. + predSpec Int.eq Int.eq_spec n Int.one; intros. subst. rewrite H0 in H. + destruct (e#r1) eqn:?; + try (rewrite Val.divu_one in H; exists (Vint i); split; simpl; try rewrite Heqv0; auto); + inv H; auto. + destruct (Int.is_power2 n) eqn:?. + econstructor; split. simpl; eauto. + rewrite mk_amount32_eq by (eapply Int.is_power2_range; eauto). + rewrite H0 in H. erewrite Val.divu_pow2 by eauto. auto. + exists v; auto. +Qed. + +Lemma make_andimm_correct: + forall n r x, + vmatch bc e#r x -> + let (op, args) := make_andimm n r x in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.and e#r (Vint n)) v. +Proof. + intros; unfold make_andimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. + subst n. exists (Vint Int.zero); split; auto. destruct (e#r); simpl; auto. rewrite Int.and_zero; auto. + predSpec Int.eq Int.eq_spec n Int.mone; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int.and_mone; auto. + destruct (match x with Uns _ k => Int.eq (Int.zero_ext k (Int.not n)) Int.zero + | _ => false end) eqn:UNS. + destruct x; try congruence. + exists (e#r); split; auto. + inv H; auto. simpl. replace (Int.and i n) with i; auto. + generalize (Int.eq_spec (Int.zero_ext n0 (Int.not n)) Int.zero); rewrite UNS; intro EQ. + Int.bit_solve. destruct (zlt i0 n0). + replace (Int.testbit n i0) with (negb (Int.testbit Int.zero i0)). + rewrite Int.bits_zero. simpl. rewrite andb_true_r. auto. + rewrite <- EQ. rewrite Int.bits_zero_ext by omega. rewrite zlt_true by auto. + rewrite Int.bits_not by auto. apply negb_involutive. + rewrite H6 by auto. auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_orimm_correct: + forall n r, + let (op, args) := make_orimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.or e#r (Vint n)) v. +Proof. + intros; unfold make_orimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int.or_zero; auto. + predSpec Int.eq Int.eq_spec n Int.mone; intros. + subst n. exists (Vint Int.mone); split; auto. destruct (e#r); simpl; auto. rewrite Int.or_mone; auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_xorimm_correct: + forall n r, + let (op, args) := make_xorimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.xor e#r (Vint n)) v. +Proof. + intros; unfold make_xorimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int.xor_zero; auto. + predSpec Int.eq Int.eq_spec n Int.mone; intros. + subst n. exists (Val.notint e#r); split; auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_addlimm_correct: + forall n r, + let (op, args) := make_addlimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.addl e#r (Vlong n)) v. +Proof. + intros. unfold make_addlimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero; intros. + subst. exists (e#r); split; auto. + destruct (e#r); simpl; auto; rewrite ? Int64.add_zero, ? Ptrofs.add_zero; auto. + exists (Val.addl e#r (Vlong n)); split; auto. +Qed. + +Lemma make_shllimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shllimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shll e#r1 (Vint n)) v. +Proof. +Local Opaque mk_amount64. + intros; unfold make_shllimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. + unfold Int64.shl'. rewrite Z.shiftl_0_r, Int64.repr_unsigned. auto. + destruct (Int.ltu n Int64.iwordsize') eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount64_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_shrlimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shrlimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shrl e#r1 (Vint n)) v. +Proof. + intros; unfold make_shrlimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. + unfold Int64.shr'. rewrite Z.shiftr_0_r, Int64.repr_signed. auto. + destruct (Int.ltu n Int64.iwordsize') eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount64_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_shrluimm_correct: + forall n r1 r2, + e#r2 = Vint n -> + let (op, args) := make_shrluimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.shrlu e#r1 (Vint n)) v. +Proof. + intros; unfold make_shrluimm. + predSpec Int.eq Int.eq_spec n Int.zero; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. + unfold Int64.shru'. rewrite Z.shiftr_0_r, Int64.repr_unsigned. auto. + destruct (Int.ltu n Int64.iwordsize') eqn:L. + econstructor; split. simpl. eauto. rewrite mk_amount64_eq; auto. + econstructor; split. simpl. eauto. rewrite H; auto. +Qed. + +Lemma make_mullimm_correct: + forall n r1 r2, + e#r2 = Vlong n -> + let (op, args) := make_mullimm n r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mull e#r1 (Vlong n)) v. +Proof. + intros; unfold make_mullimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero; intros. subst. + exists (Vlong Int64.zero); split; auto. destruct (e#r1); simpl; auto. rewrite Int64.mul_zero; auto. + predSpec Int64.eq Int64.eq_spec n Int64.one; intros. subst. + exists (e#r1); split; auto. destruct (e#r1); simpl; auto. rewrite Int64.mul_one; auto. + destruct (Int64.is_power2' n) eqn:?; intros. + econstructor; split. simpl; eauto. + rewrite mk_amount64_eq by (eapply Int64.is_power2'_range; eauto). + destruct (e#r1); simpl; auto. + erewrite Int64.is_power2'_range by eauto. + erewrite Int64.mul_pow2' by eauto. auto. + econstructor; split; eauto. simpl; rewrite H; auto. +Qed. + +Lemma make_divlimm_correct: + forall n r1 r2 v, + Val.divls e#r1 e#r2 = Some v -> + e#r2 = Vlong n -> + let (op, args) := make_divlimm n r1 r2 in + exists w, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some w /\ Val.lessdef v w. +Proof. + intros; unfold make_divlimm. + destruct (Int64.is_power2' n) eqn:?. destruct (Int.ltu i (Int.repr 63)) eqn:?. + rewrite H0 in H. econstructor; split. simpl; eauto. eapply Val.divls_pow2; eauto. auto. + exists v; auto. + exists v; auto. +Qed. + +Lemma make_divluimm_correct: + forall n r1 r2 v, + Val.divlu e#r1 e#r2 = Some v -> + e#r2 = Vlong n -> + let (op, args) := make_divluimm n r1 r2 in + exists w, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some w /\ Val.lessdef v w. +Proof. + intros; unfold make_divluimm. + destruct (Int64.is_power2' n) eqn:?. + econstructor; split. simpl; eauto. + rewrite mk_amount64_eq by (eapply Int64.is_power2'_range; eauto). + rewrite H0 in H. destruct (e#r1); inv H. destruct (Int64.eq n Int64.zero); inv H2. + simpl. + erewrite Int64.is_power2'_range by eauto. + erewrite Int64.divu_pow2' by eauto. auto. + exists v; auto. +Qed. + +Lemma make_andlimm_correct: + forall n r x, + let (op, args) := make_andlimm n r x in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.andl e#r (Vlong n)) v. +Proof. + intros; unfold make_andlimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero; intros. + subst n. exists (Vlong Int64.zero); split; auto. destruct (e#r); simpl; auto. rewrite Int64.and_zero; auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int64.and_mone; auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_orlimm_correct: + forall n r, + let (op, args) := make_orlimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.orl e#r (Vlong n)) v. +Proof. + intros; unfold make_orlimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int64.or_zero; auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone; intros. + subst n. exists (Vlong Int64.mone); split; auto. destruct (e#r); simpl; auto. rewrite Int64.or_mone; auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_xorlimm_correct: + forall n r, + let (op, args) := make_xorlimm n r in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.xorl e#r (Vlong n)) v. +Proof. + intros; unfold make_xorlimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero; intros. + subst n. exists (e#r); split; auto. destruct (e#r); simpl; auto. rewrite Int64.xor_zero; auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone; intros. + subst n. exists (Val.notl e#r); split; auto. + econstructor; split; eauto. auto. +Qed. + +Lemma make_mulfimm_correct: + forall n r1 r2, + e#r2 = Vfloat n -> + let (op, args) := make_mulfimm n r1 r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mulf e#r1 e#r2) v. +Proof. + intros; unfold make_mulfimm. + destruct (Float.eq_dec n (Float.of_int (Int.repr 2))); intros. + simpl. econstructor; split. eauto. rewrite H; subst n. + destruct (e#r1); simpl; auto. rewrite Float.mul2_add; auto. + simpl. econstructor; split; eauto. +Qed. + +Lemma make_mulfimm_correct_2: + forall n r1 r2, + e#r1 = Vfloat n -> + let (op, args) := make_mulfimm n r2 r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mulf e#r1 e#r2) v. +Proof. + intros; unfold make_mulfimm. + destruct (Float.eq_dec n (Float.of_int (Int.repr 2))); intros. + simpl. econstructor; split. eauto. rewrite H; subst n. + destruct (e#r2); simpl; auto. rewrite Float.mul2_add; auto. + rewrite Float.mul_commut; auto. + simpl. econstructor; split; eauto. +Qed. + +Lemma make_mulfsimm_correct: + forall n r1 r2, + e#r2 = Vsingle n -> + let (op, args) := make_mulfsimm n r1 r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mulfs e#r1 e#r2) v. +Proof. + intros; unfold make_mulfsimm. + destruct (Float32.eq_dec n (Float32.of_int (Int.repr 2))); intros. + simpl. econstructor; split. eauto. rewrite H; subst n. + destruct (e#r1); simpl; auto. rewrite Float32.mul2_add; auto. + simpl. econstructor; split; eauto. +Qed. + +Lemma make_mulfsimm_correct_2: + forall n r1 r2, + e#r1 = Vsingle n -> + let (op, args) := make_mulfsimm n r2 r1 r2 in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.mulfs e#r1 e#r2) v. +Proof. + intros; unfold make_mulfsimm. + destruct (Float32.eq_dec n (Float32.of_int (Int.repr 2))); intros. + simpl. econstructor; split. eauto. rewrite H; subst n. + destruct (e#r2); simpl; auto. rewrite Float32.mul2_add; auto. + rewrite Float32.mul_commut; auto. + simpl. econstructor; split; eauto. +Qed. + +Lemma make_zext_correct: + forall s r x, + vmatch bc e#r x -> + let (op, args) := make_zext s r x in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.zero_ext s e#r) v. +Proof. + intros; unfold make_zext. destruct (vincl x (Uns Ptop s)) eqn:INCL. +- exists e#r; split; auto. + assert (V: vmatch bc e#r (Uns Ptop s)). + { eapply vmatch_ge; eauto. apply vincl_ge; auto. } + inv V; simpl; auto. rewrite is_uns_zero_ext in H4 by auto. rewrite H4; auto. +- econstructor; split; simpl; eauto. +Qed. + +Lemma make_sext_correct: + forall s r x, + vmatch bc e#r x -> + let (op, args) := make_sext s r x in + exists v, eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v /\ Val.lessdef (Val.sign_ext s e#r) v. +Proof. + intros; unfold make_sext. destruct (vincl x (Sgn Ptop s)) eqn:INCL. +- exists e#r; split; auto. + assert (V: vmatch bc e#r (Sgn Ptop s)). + { eapply vmatch_ge; eauto. apply vincl_ge; auto. } + inv V; simpl; auto. rewrite is_sgn_sign_ext in H4 by auto. rewrite H4; auto. +- econstructor; split; simpl; eauto. +Qed. + +Lemma op_strength_reduction_correct: + forall op args vl v, + vl = map (fun r => AE.get r ae) args -> + eval_operation ge (Vptr sp Ptrofs.zero) op e##args m = Some v -> + let (op', args') := op_strength_reduction op args vl in + exists w, eval_operation ge (Vptr sp Ptrofs.zero) op' e##args' m = Some w /\ Val.lessdef v w. +Proof. + intros until v; unfold op_strength_reduction; + case (op_strength_reduction_match op args vl); simpl; intros. +- (* add 1 *) + rewrite Val.add_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_addimm_correct; auto. +- (* add 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_addimm_correct; auto. +- (* addshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_addimm_correct; auto. +- (* sub *) + InvApproxRegs; SimplVM; inv H0. rewrite Val.sub_add_opp. apply make_addimm_correct; auto. +- (* subshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct, Val.sub_add_opp. apply make_addimm_correct; auto. +- (* mul 1 *) + rewrite Val.mul_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_mulimm_correct; auto. +- (* mul 2*) + InvApproxRegs; SimplVM; inv H0. apply make_mulimm_correct; auto. +- (* divs *) + assert (e#r2 = Vint n2). clear H0. InvApproxRegs; SimplVM; auto. + apply make_divimm_correct; auto. +- (* divu *) + assert (e#r2 = Vint n2). clear H0. InvApproxRegs; SimplVM; auto. + apply make_divuimm_correct; auto. +- (* and 1 *) + rewrite Val.and_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_andimm_correct; auto. +- (* and 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_andimm_correct; auto. +- (* andshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_andimm_correct; auto. +- (* andimm *) + inv H; inv H0. apply make_andimm_correct; auto. +- (* or 1 *) + rewrite Val.or_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_orimm_correct; auto. +- (* or 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_orimm_correct; auto. +- (* orshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_orimm_correct; auto. +- (* xor 1 *) + rewrite Val.xor_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_xorimm_correct; auto. +- (* xor 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_xorimm_correct; auto. +- (* xorshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_xorimm_correct; auto. +- (* bic *) + InvApproxRegs; SimplVM; inv H0. apply make_andimm_correct; auto. +- (* bicshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_andimm_correct; auto. +- (* orn *) + InvApproxRegs; SimplVM; inv H0. apply make_orimm_correct; auto. +- (* ornshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_orimm_correct; auto. +- (* eor *) + InvApproxRegs; SimplVM; inv H0. apply make_xorimm_correct; auto. +- (* eorshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shift_correct. apply make_xorimm_correct; auto. +- (* shl *) + InvApproxRegs; SimplVM; inv H0. apply make_shlimm_correct; auto. +- (* shr *) + InvApproxRegs; SimplVM; inv H0. apply make_shrimm_correct; auto. +- (* shru *) + InvApproxRegs; SimplVM; inv H0. apply make_shruimm_correct; auto. +- (* zext *) + InvApproxRegs; SimplVM; inv H0. apply make_zext_correct; auto. +- (* sext *) + InvApproxRegs; SimplVM; inv H0. apply make_sext_correct; auto. +- (* addl 1 *) + rewrite Val.addl_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_addlimm_correct; auto. +- (* addl 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_addlimm_correct; auto. +- (* addshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_addlimm_correct; auto. +- (* addext *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_extend_correct. apply make_addlimm_correct; auto. +- (* subl *) + InvApproxRegs; SimplVM; inv H0. rewrite Val.subl_addl_opp. apply make_addlimm_correct; auto. +- (* sublshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct, Val.subl_addl_opp. apply make_addlimm_correct; auto. +- (* sublextend *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_extend_correct, Val.subl_addl_opp. apply make_addlimm_correct; auto. +- (* mull 1 *) + rewrite Val.mull_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_mullimm_correct; auto. +- (* mull 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_mullimm_correct; auto. +- (* divl *) + assert (e#r2 = Vlong n2). clear H0. InvApproxRegs; SimplVM; auto. + apply make_divlimm_correct; auto. +- (* divlu *) + assert (e#r2 = Vlong n2). clear H0. InvApproxRegs; SimplVM; auto. + apply make_divluimm_correct; auto. +- (* andl 1 *) + rewrite Val.andl_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_andlimm_correct; auto. +- (* andl 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_andlimm_correct; auto. +- (* andlshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_andlimm_correct; auto. +- (* andlimm *) + inv H; inv H0. apply make_andlimm_correct; auto. +- (* orl 1 *) + rewrite Val.orl_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_orlimm_correct; auto. +- (* orl 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_orlimm_correct; auto. +- (* orlshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_orlimm_correct; auto. +- (* xorl 1 *) + rewrite Val.xorl_commut in H0. InvApproxRegs; SimplVM; inv H0. apply make_xorlimm_correct; auto. +- (* xorl 2 *) + InvApproxRegs; SimplVM; inv H0. apply make_xorlimm_correct; auto. +- (* xorlshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_xorlimm_correct; auto. +- (* bicl *) + InvApproxRegs; SimplVM; inv H0. apply make_andlimm_correct; auto. +- (* biclshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_andlimm_correct; auto. +- (* ornl *) + InvApproxRegs; SimplVM; inv H0. apply make_orlimm_correct; auto. +- (* ornlshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_orlimm_correct; auto. +- (* eorl *) + InvApproxRegs; SimplVM; inv H0. apply make_xorlimm_correct; auto. +- (* eorlshift *) + InvApproxRegs; SimplVM; inv H0. rewrite eval_static_shiftl_correct. apply make_xorlimm_correct; auto. +- (* shll *) + InvApproxRegs; SimplVM; inv H0. apply make_shllimm_correct; auto. +- (* shrl *) + InvApproxRegs; SimplVM; inv H0. apply make_shrlimm_correct; auto. +- (* shrlu *) + InvApproxRegs; SimplVM; inv H0. apply make_shrluimm_correct; auto. +- (* cond *) + inv H0. apply make_cmp_correct; auto. +- (* select *) + inv H0. apply make_select_correct; congruence. +- (* mulf 1 *) + InvApproxRegs; SimplVM; inv H0. rewrite <- H2. apply make_mulfimm_correct; auto. +- (* mulf 2 *) + InvApproxRegs; SimplVM; inv H0. fold (Val.mulf (Vfloat n1) e#r2). + rewrite <- H2. apply make_mulfimm_correct_2; auto. +- (* mulfs 1 *) + InvApproxRegs; SimplVM; inv H0. rewrite <- H2. apply make_mulfsimm_correct; auto. +- (* mulfs 2 *) + InvApproxRegs; SimplVM; inv H0. fold (Val.mulfs (Vsingle n1) e#r2). + rewrite <- H2. apply make_mulfsimm_correct_2; auto. +- (* default *) + exists v; auto. +Qed. + +Lemma addr_strength_reduction_correct: + forall addr args vl res, + vl = map (fun r => AE.get r ae) args -> + eval_addressing ge (Vptr sp Ptrofs.zero) addr e##args = Some res -> + let (addr', args') := addr_strength_reduction addr args vl in + exists res', eval_addressing ge (Vptr sp Ptrofs.zero) addr' e##args' = Some res' /\ Val.lessdef res res'. +Proof. + intros until res. unfold addr_strength_reduction. + destruct (addr_strength_reduction_match addr args vl); simpl; + intros VL EA; InvApproxRegs; SimplVM; try (inv EA). +- econstructor; split; eauto. inv H0; simpl; auto. rewrite H2. + unfold Genv.symbol_address. destruct (Genv.find_symbol ge symb); auto. +- rewrite Ptrofs.add_zero_l. econstructor; split; eauto. + inv H0; auto. rewrite H2; auto. +- rewrite Ptrofs.add_zero_l. econstructor; split; eauto. + inv H; auto. rewrite H3; auto. +- rewrite Ptrofs.add_zero_l. econstructor; split; eauto. + inv H0; auto. rewrite H3. rewrite Ptrofs.add_commut; auto. +- econstructor; split; eauto. rewrite Val.addl_commut. auto. +- econstructor; split; eauto. +- rewrite Ptrofs.add_zero_l. rewrite a64_range. econstructor; split; eauto. + inv H; auto. rewrite H3; auto. +- rewrite a64_range. econstructor; split; eauto. +- rewrite Ptrofs.add_zero_l, eval_static_extend_correct. + econstructor; split; eauto. inv H; auto. rewrite H3; auto. +- rewrite eval_static_extend_correct. + econstructor; split; eauto. +- exists res; auto. +Qed. + +End STRENGTH_REDUCTION. diff --git a/aarch64/Conventions1.v b/aarch64/Conventions1.v new file mode 100644 index 00000000..5914e8f2 --- /dev/null +++ b/aarch64/Conventions1.v @@ -0,0 +1,380 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Function calling conventions and other conventions regarding the use of + machine registers and stack slots. *) + +Require Import Coqlib Decidableplus. +Require Import AST Events Locations. +Require Archi. + +(** * Classification of machine registers *) + +(** Machine registers (type [mreg] in module [Locations]) are divided in: +- Callee-save registers, whose value is preserved across a function call. +- Caller-save registers that can be modified during a function call. + + We follow the Procedure Call Standard for the ARM 64-bit Architecture + (AArch64) document: R19-R28 and F8-F15 are callee-save. *) + +Definition is_callee_save (r: mreg): bool := + match r with + | R0 | R1 | R2 | R3 | R4 | R5 | R6 | R7 => false + | R8 | R9 | R10 | R11 | R12 | R13 | R14 | R15 => false + | R17 => false + | R19 | R20 | R21 | R22 | R23 => true + | R24 | R25 | R26 | R27 | R28 => true + | R29 => false + | F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 => false + | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 => true + | F16 | F17 | F18 | F19 | F20 | F21 | F22 | F23 => false + | F24 | F25 | F26 | F27 | F28 | F29 | F30 | F31 => false + end. + +Definition int_caller_save_regs := + R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 + :: R8 :: R9 :: R10 :: R11 :: R12 :: R13 :: R14 :: R15 + :: R17 :: R29 :: nil. + +Definition float_caller_save_regs := + F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 + :: F16 :: F17 :: F18 :: F19 :: F20 :: F21 :: F22 :: F23 + :: F24 :: F25 :: F26 :: F27 :: F28 :: F29 :: F30 :: F31 :: nil. + +Definition int_callee_save_regs := + R19 :: R20 :: R21 :: R22 :: R23 + :: R24 :: R25 :: R26 :: R27 :: R28 :: nil. + +Definition float_callee_save_regs := + F8 :: F9 :: F10 :: F11 :: F12 :: F13 :: F14 :: F15 :: nil. + +Definition destroyed_at_call := + List.filter (fun r => negb (is_callee_save r)) all_mregs. + +Definition dummy_int_reg := R0. (**r Used in [Coloring]. *) +Definition dummy_float_reg := F0. (**r Used in [Coloring]. *) + +Definition callee_save_type := mreg_type. + +Definition is_float_reg (r: mreg): bool := + match r with + | R0 | R1 | R2 | R3 | R4 | R5 | R6 | R7 + | R8 | R9 | R10 | R11 | R12 | R13 | R14 | R15 + | R17 | R19 | R20 | R21 | R22 | R23 + | R24 | R25 | R26 | R27 | R28 + | R29 => false + | F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 + | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 + | F16 | F17 | F18 | F19 | F20 | F21 | F22 | F23 + | F24 | F25 | F26 | F27 | F28 | F29 | F30 | F31 => true + end. + +(** * Function calling conventions *) + +(** The functions in this section determine the locations (machine registers + and stack slots) used to communicate arguments and results between the + caller and the callee during function calls. These locations are functions + of the signature of the function and of the call instruction. + Agreement between the caller and the callee on the locations to use + is guaranteed by our dynamic semantics for Cminor and RTL, which demand + that the signature of the call instruction is identical to that of the + called function. + + Calling conventions are largely arbitrary: they must respect the properties + proved in this section (such as no overlapping between the locations + of function arguments), but this leaves much liberty in choosing actual + locations. *) + +(** ** Location of function result *) + +(** The result value of a function is passed back to the caller in + registers [R0] or [F0], depending on the type of the + returned value. We treat a function without result as a function + with one integer result. *) + +Definition loc_result (s: signature) : rpair mreg := + match s.(sig_res) with + | None => One R0 + | Some (Tint | Tlong | Tany32 | Tany64) => One R0 + | Some (Tfloat | Tsingle) => One F0 + end. + +(** The result registers have types compatible with that given in the signature. *) + +Lemma loc_result_type: + forall sig, + subtype (proj_sig_res sig) (typ_rpair mreg_type (loc_result sig)) = true. +Proof. + intros. unfold proj_sig_res, loc_result. destruct (sig_res sig) as [[]|]; auto. +Qed. + +(** The result locations are caller-save registers *) + +Lemma loc_result_caller_save: + forall (s: signature), + forall_rpair (fun r => is_callee_save r = false) (loc_result s). +Proof. + intros. + unfold loc_result. destruct (sig_res s) as [[]|]; simpl; auto. +Qed. + +(** If the result is in a pair of registers, those registers are distinct and have type [Tint] at least. *) + +Lemma loc_result_pair: + forall sg, + match loc_result sg with + | One _ => True + | Twolong r1 r2 => + r1 <> r2 /\ sg.(sig_res) = Some Tlong + /\ subtype Tint (mreg_type r1) = true /\ subtype Tint (mreg_type r2) = true + /\ Archi.ptr64 = false + end. +Proof. + intros; unfold loc_result; destruct (sig_res sg) as [[]|]; exact I. +Qed. + +(** The location of the result depends only on the result part of the signature *) + +Lemma loc_result_exten: + forall s1 s2, s1.(sig_res) = s2.(sig_res) -> loc_result s1 = loc_result s2. +Proof. + intros. unfold loc_result. rewrite H; auto. +Qed. + +(** ** Location of function arguments *) + +(** +- The first 8 integer arguments are passed in registers [R0...R7]. +- The first 8 FP arguments are passed in registers [F0...F7]. +- Extra arguments are passed on the stack, in [Outgoing] slots of size + 64 bits (2 words), consecutively assigned, starting at word offset 0. +**) + +Definition int_param_regs := + R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 :: nil. + +Definition float_param_regs := + F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: nil. + +Fixpoint loc_arguments_rec + (tyl: list typ) (ir fr ofs: Z) {struct tyl} : list (rpair loc) := + match tyl with + | nil => nil + | (Tint | Tlong | Tany32 | Tany64) as ty :: tys => + match list_nth_z int_param_regs ir with + | None => + One (S Outgoing ofs ty) :: loc_arguments_rec tys ir fr (ofs + 2) + | Some ireg => + One (R ireg) :: loc_arguments_rec tys (ir + 1) fr ofs + end + | (Tfloat | Tsingle) as ty :: tys => + match list_nth_z float_param_regs fr with + | None => + One (S Outgoing ofs ty) :: loc_arguments_rec tys ir fr (ofs + 2) + | Some freg => + One (R freg) :: loc_arguments_rec tys ir (fr + 1) ofs + end + end. + +(** [loc_arguments s] returns the list of locations where to store arguments + when calling a function with signature [s]. *) + +Definition loc_arguments (s: signature) : list (rpair loc) := + loc_arguments_rec s.(sig_args) 0 0 0. + +(** [size_arguments s] returns the number of [Outgoing] slots used + to call a function with signature [s]. *) + +Fixpoint size_arguments_rec (tyl: list typ) (ir fr ofs: Z) {struct tyl} : Z := + match tyl with + | nil => ofs + | (Tint | Tlong | Tany32 | Tany64) :: tys => + match list_nth_z int_param_regs ir with + | None => size_arguments_rec tys ir fr (ofs + 2) + | Some ireg => size_arguments_rec tys (ir + 1) fr ofs + end + | (Tfloat | Tsingle) :: tys => + match list_nth_z float_param_regs fr with + | None => size_arguments_rec tys ir fr (ofs + 2) + | Some freg => size_arguments_rec tys ir (fr + 1) ofs + end + end. + +Definition size_arguments (s: signature) : Z := + size_arguments_rec s.(sig_args) 0 0 0. + +(** Argument locations are either caller-save registers or [Outgoing] + stack slots at nonnegative offsets. *) + +Definition loc_argument_acceptable (l: loc) : Prop := + match l with + | R r => is_callee_save r = false + | S Outgoing ofs ty => ofs >= 0 /\ (typealign ty | ofs) + | _ => False + end. + +Definition loc_argument_charact (ofs: Z) (l: loc) : Prop := + match l with + | R r => In r int_param_regs \/ In r float_param_regs + | S Outgoing ofs' ty => ofs' >= ofs /\ (2 | ofs') + | _ => False + end. + +Remark loc_arguments_rec_charact: + forall tyl ir fr ofs p, + In p (loc_arguments_rec tyl ir fr ofs) -> (2 | ofs) -> forall_rpair (loc_argument_charact ofs) p. +Proof. + assert (X: forall ofs1 ofs2 l, loc_argument_charact ofs2 l -> ofs1 <= ofs2 -> loc_argument_charact ofs1 l). + { destruct l; simpl; intros; auto. destruct sl; auto. intuition omega. } + assert (Y: forall ofs1 ofs2 p, forall_rpair (loc_argument_charact ofs2) p -> ofs1 <= ofs2 -> forall_rpair (loc_argument_charact ofs1) p). + { destruct p; simpl; intuition eauto. } + assert (Z: forall ofs, (2 | ofs) -> (2 | ofs + 2)). + { intros. apply Z.divide_add_r; auto. apply Z.divide_refl. } +Opaque list_nth_z. + induction tyl; simpl loc_arguments_rec; intros. +- contradiction. +- assert (A: forall ty, In p + match list_nth_z int_param_regs ir with + | Some ireg => One (R ireg) :: loc_arguments_rec tyl (ir + 1) fr ofs + | None => One (S Outgoing ofs ty) :: loc_arguments_rec tyl ir fr (ofs + 2) + end -> + forall_rpair (loc_argument_charact ofs) p). + { intros. destruct (list_nth_z int_param_regs ir) as [r|] eqn:E; destruct H1. + subst. left. eapply list_nth_z_in; eauto. + eapply IHtyl; eauto. + subst. split. omega. assumption. + eapply Y; eauto. omega. } + assert (B: forall ty, In p + match list_nth_z float_param_regs fr with + | Some ireg => One (R ireg) :: loc_arguments_rec tyl ir (fr + 1) ofs + | None => One (S Outgoing ofs ty) :: loc_arguments_rec tyl ir fr (ofs + 2) + end -> + forall_rpair (loc_argument_charact ofs) p). + { intros. destruct (list_nth_z float_param_regs fr) as [r|] eqn:E; destruct H1. + subst. right. eapply list_nth_z_in; eauto. + eapply IHtyl; eauto. + subst. split. omega. assumption. + eapply Y; eauto. omega. } + destruct a; eauto. +Qed. + +Lemma loc_arguments_acceptable: + forall (s: signature) (p: rpair loc), + In p (loc_arguments s) -> forall_rpair loc_argument_acceptable p. +Proof. + unfold loc_arguments; intros. + assert (A: forall r, In r int_param_regs -> is_callee_save r = false) by decide_goal. + assert (B: forall r, In r float_param_regs -> is_callee_save r = false) by decide_goal. + assert (X: forall l, loc_argument_charact 0 l -> loc_argument_acceptable l). + { unfold loc_argument_charact, loc_argument_acceptable. + destruct l as [r | [] ofs ty]; auto. intros [C|C]; auto. + intros [C D]. split; auto. apply Z.divide_trans with 2; auto. + exists (2 / typealign ty); destruct ty; reflexivity. + } + exploit loc_arguments_rec_charact; eauto using Z.divide_0_r. + unfold forall_rpair; destruct p; intuition auto. +Qed. + +Hint Resolve loc_arguments_acceptable: locs. + +(** The offsets of [Outgoing] arguments are below [size_arguments s]. *) + +Remark size_arguments_rec_above: + forall tyl ir fr ofs0, + ofs0 <= size_arguments_rec tyl ir fr ofs0. +Proof. + induction tyl; simpl; intros. + omega. + assert (A: ofs0 <= + match list_nth_z int_param_regs ir with + | Some _ => size_arguments_rec tyl (ir + 1) fr ofs0 + | None => size_arguments_rec tyl ir fr (ofs0 + 2) + end). + { destruct (list_nth_z int_param_regs ir); eauto. + apply Z.le_trans with (ofs0 + 2); auto. omega. } + assert (B: ofs0 <= + match list_nth_z float_param_regs fr with + | Some _ => size_arguments_rec tyl ir (fr + 1) ofs0 + | None => size_arguments_rec tyl ir fr (ofs0 + 2) + end). + { destruct (list_nth_z float_param_regs fr); eauto. + apply Z.le_trans with (ofs0 + 2); auto. omega. } + destruct a; auto. +Qed. + +Lemma size_arguments_above: + forall s, size_arguments s >= 0. +Proof. + intros; unfold size_arguments. apply Z.le_ge. apply size_arguments_rec_above. +Qed. + +Lemma loc_arguments_rec_bounded: + forall ofs ty tyl ir fr ofs0, + In (S Outgoing ofs ty) (regs_of_rpairs (loc_arguments_rec tyl ir fr ofs0)) -> + ofs + typesize ty <= size_arguments_rec tyl ir fr ofs0. +Proof. + induction tyl; simpl; intros. +- contradiction. +- assert (T: forall ty0, typesize ty0 <= 2). + { destruct ty0; simpl; omega. } + assert (A: forall ty0, + In (S Outgoing ofs ty) (regs_of_rpairs + match list_nth_z int_param_regs ir with + | Some ireg => + One (R ireg) :: loc_arguments_rec tyl (ir + 1) fr ofs0 + | None => One (S Outgoing ofs0 ty0) :: loc_arguments_rec tyl ir fr (ofs0 + 2) + end) -> + ofs + typesize ty <= + match list_nth_z int_param_regs ir with + | Some _ => size_arguments_rec tyl (ir + 1) fr ofs0 + | None => size_arguments_rec tyl ir fr (ofs0 + 2) + end). + { intros. destruct (list_nth_z int_param_regs ir); simpl in H0; destruct H0. + - discriminate. + - eapply IHtyl; eauto. + - inv H0. apply Z.le_trans with (ofs + 2). specialize (T ty). omega. apply size_arguments_rec_above. + - eapply IHtyl; eauto. } + assert (B: forall ty0, + In (S Outgoing ofs ty) (regs_of_rpairs + match list_nth_z float_param_regs fr with + | Some ireg => + One (R ireg) :: loc_arguments_rec tyl ir (fr + 1) ofs0 + | None => One (S Outgoing ofs0 ty0) :: loc_arguments_rec tyl ir fr (ofs0 + 2) + end) -> + ofs + typesize ty <= + match list_nth_z float_param_regs fr with + | Some _ => size_arguments_rec tyl ir (fr + 1) ofs0 + | None => size_arguments_rec tyl ir fr (ofs0 + 2) + end). + { intros. destruct (list_nth_z float_param_regs fr); simpl in H0; destruct H0. + - discriminate. + - eapply IHtyl; eauto. + - inv H0. apply Z.le_trans with (ofs + 2). specialize (T ty). omega. apply size_arguments_rec_above. + - eapply IHtyl; eauto. } + destruct a; eauto. +Qed. + +Lemma loc_arguments_bounded: + forall (s: signature) (ofs: Z) (ty: typ), + In (S Outgoing ofs ty) (regs_of_rpairs (loc_arguments s)) -> + ofs + typesize ty <= size_arguments s. +Proof. + unfold loc_arguments, size_arguments; intros. + eauto using loc_arguments_rec_bounded. +Qed. + +Lemma loc_arguments_main: + loc_arguments signature_main = nil. +Proof. + unfold loc_arguments; reflexivity. +Qed. + diff --git a/aarch64/Machregs.v b/aarch64/Machregs.v new file mode 100644 index 00000000..b2a2308e --- /dev/null +++ b/aarch64/Machregs.v @@ -0,0 +1,210 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +Require Import String. +Require Import Coqlib Decidableplus Maps. +Require Import AST Op. + +(** ** Machine registers *) + +(** Integer register 16 is reserved as temporary and for call veeners. + Integer register 18 is reserved as the platform register. + Integer register 30 is reserved for the return address. *) + +Inductive mreg: Type := + (** Allocatable integer regs *) + | R0 | R1 | R2 | R3 | R4 | R5 | R6 | R7 + | R8 | R9 | R10 | R11 | R12 | R13 | R14 | R15 + | R17 | R19 | R20 | R21 | R22 | R23 + | R24 | R25 | R26 | R27 | R28 | R29 + (** Allocatable floating-point regs *) + | F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 + | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 + | F16 | F17 | F18 | F19 | F20 | F21 | F22 | F23 + | F24 | F25 | F26 | F27 | F28 | F29 | F30 | F31. + +Lemma mreg_eq: forall (r1 r2: mreg), {r1 = r2} + {r1 <> r2}. +Proof. decide equality. Defined. +Global Opaque mreg_eq. + +Definition all_mregs := + R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 + :: R8 :: R9 :: R10 :: R11 :: R12 :: R13 :: R14 :: R15 + :: R17 :: R19 :: R20 :: R21 :: R22 :: R23 + :: R24 :: R25 :: R26 :: R27 :: R28 :: R29 + :: F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 + :: F8 :: F9 :: F10 :: F11 :: F12 :: F13 :: F14 :: F15 + :: F16 :: F17 :: F18 :: F19 :: F20 :: F21 :: F22 :: F23 + :: F24 :: F25 :: F26 :: F27 :: F28 :: F29 :: F30 :: F31 + :: nil. + +Lemma all_mregs_complete: + forall (r: mreg), In r all_mregs. +Proof. + assert (forall r, proj_sumbool (In_dec mreg_eq r all_mregs) = true) by (destruct r; reflexivity). + intros. specialize (H r). InvBooleans. auto. +Qed. + +Instance Decidable_eq_mreg : forall (x y: mreg), Decidable (eq x y) := Decidable_eq mreg_eq. + +Instance Finite_mreg : Finite mreg := { + Finite_elements := all_mregs; + Finite_elements_spec := all_mregs_complete +}. + +Definition mreg_type (r: mreg): typ := Tany64. + +Open Scope positive_scope. + +Module IndexedMreg <: INDEXED_TYPE. + Definition t := mreg. + Definition eq := mreg_eq. + Definition index (r: mreg): positive := + match r with + | R0 => 1 | R1 => 2 | R2 => 3 | R3 => 4 + | R4 => 5 | R5 => 6 | R6 => 7 | R7 => 8 + | R8 => 9 | R9 => 10 | R10 => 11 | R11 => 12 + | R12 => 13 | R13 => 14 | R14 => 15 | R15 => 16 + | R17 => 17 | R19 => 19 + | R20 => 20 | R21 => 21 | R22 => 22 | R23 => 23 + | R24 => 24 | R25 => 25 | R26 => 26 | R27 => 27 + | R28 => 28 | R29 => 29 + | F0 => 32 | F1 => 33 | F2 => 34 | F3 => 35 + | F4 => 36 | F5 => 37 | F6 => 38 | F7 => 39 + | F8 => 40 | F9 => 41 | F10 => 42 | F11 => 43 + | F12 => 44 | F13 => 45 | F14 => 46 | F15 => 47 + | F16 => 48 | F17 => 49 | F18 => 50 | F19 => 51 + | F20 => 52 | F21 => 53 | F22 => 54 | F23 => 55 + | F24 => 56 | F25 => 57 | F26 => 58 | F27 => 59 + | F28 => 60 | F29 => 61 | F30 => 62 | F31 => 63 + end. + Lemma index_inj: + forall r1 r2, index r1 = index r2 -> r1 = r2. + Proof. + decide_goal. + Qed. +End IndexedMreg. + +Definition is_stack_reg (r: mreg) : bool := false. + +(** ** Names of registers *) + +Local Open Scope string_scope. + +Definition register_names := + ("X0", R0) :: ("X1", R1) :: ("X2", R2) :: ("X3", R3) + :: ("X4", R4) :: ("X5", R5) :: ("X6", R6) :: ("X7", R7) + :: ("X8", R8) :: ("X9", R9) :: ("X10", R10) :: ("X11", R11) + :: ("X12", R12) :: ("X13", R13) :: ("X14", R14) :: ("X15", R15) + :: ("X17", R17) :: ("X19", R19) + :: ("X20", R20) :: ("X21", R21) :: ("X22", R22) :: ("X23", R23) + :: ("X24", R24) :: ("X25", R25) :: ("X26", R26) :: ("X27", R27) + :: ("X28", R28) :: ("X29", R29) + :: ("D0", F0) :: ("D1", F1) :: ("D2", F2) :: ("D3", F3) + :: ("D4", F4) :: ("D5", F5) :: ("D6", F6) :: ("D7", F7) + :: ("D8", F8) :: ("D9", F9) :: ("D10", F10) :: ("D11", F11) + :: ("D12", F12) :: ("D13", F13) :: ("D14", F14) :: ("D15", F15) + :: ("D16", F16) :: ("D17", F17) :: ("D18", F18) :: ("D19", F19) + :: ("D20", F20) :: ("D21", F21) :: ("D22", F22) :: ("D23", F23) + :: ("D24", F24) :: ("D25", F25) :: ("D26", F26) :: ("D27", F27) + :: ("D28", F28) :: ("D29", F29) :: ("D30", F30) :: ("D31", F31) + :: nil. + +Definition register_by_name (s: string) : option mreg := + let fix assoc (l: list (string * mreg)) : option mreg := + match l with + | nil => None + | (s1, r1) :: l' => if string_dec s s1 then Some r1 else assoc l' + end + in assoc register_names. + +(** ** Destroyed registers, preferred registers *) + +Definition destroyed_by_op (op: operation): list mreg := + match op with + | Oshrximm _ | Oshrlximm _ => R17 :: nil + | _ => nil + end. + +Definition destroyed_by_load (chunk: memory_chunk) (addr: addressing): list mreg := + nil. + +Definition destroyed_by_store (chunk: memory_chunk) (addr: addressing): list mreg := nil. + +Definition destroyed_by_cond (cond: condition): list mreg := nil. + +Definition destroyed_by_jumptable: list mreg := R17 :: nil. + +Fixpoint destroyed_by_clobber (cl: list string): list mreg := + match cl with + | nil => nil + | c1 :: cl => + match register_by_name c1 with + | Some r => r :: destroyed_by_clobber cl + | None => destroyed_by_clobber cl + end + end. + +Definition destroyed_by_builtin (ef: external_function): list mreg := + match ef with + | EF_memcpy sz al => R15 :: R17 :: R29 :: nil + | EF_inline_asm txt sg clob => destroyed_by_clobber clob + | _ => nil + end. + +Definition destroyed_by_setstack (ty: typ): list mreg := nil. + +Definition destroyed_at_function_entry: list mreg := R29 :: nil. + +Definition destroyed_at_indirect_call: list mreg := nil. + +Definition temp_for_parent_frame: mreg := R29. + +Definition mregs_for_operation (op: operation): list (option mreg) * option mreg := + (nil, None). + +Definition mregs_for_builtin (ef: external_function): list (option mreg) * list(option mreg) := + (nil, nil). + +Global Opaque + destroyed_by_op destroyed_by_load destroyed_by_store + destroyed_by_cond destroyed_by_jumptable destroyed_by_builtin + destroyed_by_setstack destroyed_at_function_entry temp_for_parent_frame + destroyed_at_indirect_call + mregs_for_operation mregs_for_builtin. + +(** Two-address operations. Return [true] if the first argument and + the result must be in the same location *and* are unconstrained + by [mregs_for_operation]. There is one for AArch64: [Olowlong], + which is actually a no-operation in the generated asm code. *) + +Definition two_address_op (op: operation) : bool := + match op with + | Olowlong => true + | _ => false + end. + +Global Opaque two_address_op. + +(* Constraints on constant propagation for builtins *) + +Definition builtin_constraints (ef: external_function) : + list builtin_arg_constraint := + match ef with + | EF_vload _ => OK_addressing :: nil + | EF_vstore _ => OK_addressing :: OK_default :: nil + | EF_memcpy _ _ => OK_addrstack :: OK_addrstack :: nil + | EF_annot kind txt targs => map (fun _ => OK_all) targs + | EF_debug kind txt targs => map (fun _ => OK_all) targs + | _ => nil + end. + diff --git a/aarch64/Machregsaux.ml b/aarch64/Machregsaux.ml new file mode 100644 index 00000000..d7f10b9b --- /dev/null +++ b/aarch64/Machregsaux.ml @@ -0,0 +1,35 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Auxiliary functions on machine registers *) + +open Camlcoq +open Machregs + +let register_names : (mreg, string) Hashtbl.t = Hashtbl.create 31 + +let _ = + List.iter + (fun (s, r) -> Hashtbl.add register_names r (camlstring_of_coqstring s)) + Machregs.register_names + +let is_scratch_register s = + s = "X16" || s = "x16" || s = "X30" || s = "x30" + + +let name_of_register r = + try Some (Hashtbl.find register_names r) with Not_found -> None + +let register_by_name s = + Machregs.register_by_name (coqstring_uppercase_ascii_of_camlstring s) + +let can_reserve_register r = Conventions1.is_callee_save r diff --git a/aarch64/NeedOp.v b/aarch64/NeedOp.v new file mode 100644 index 00000000..8fcab9e1 --- /dev/null +++ b/aarch64/NeedOp.v @@ -0,0 +1,253 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +Require Import Coqlib. +Require Import AST Integers Floats. +Require Import Values Memory Globalenvs. +Require Import Op RTL. +Require Import NeedDomain. + +(** Neededness analysis for AArch64 operators *) + +Definition needs_of_shift (s: shift) (a: amount32) (nv: nval) := + match s with + | Slsl => shlimm nv a + | Sasr => shrimm nv a + | Slsr => shruimm nv a + | Sror => ror nv a + end. + +Definition zero_ext' (s: Z) (nv: nval) := + if zle 0 s then zero_ext s nv else default nv. +Definition sign_ext' (s: Z) (nv: nval) := + if zlt 0 s then sign_ext s nv else default nv. + +Definition op1 (nv: nval) := nv :: nil. +Definition op2 (nv: nval) := nv :: nv :: nil. +Definition op1shift (s: shift) (a: amount32) (nv: nval) := + needs_of_shift s a nv :: nil. +Definition op2shift (s: shift) (a: amount32) (nv: nval) := + nv :: needs_of_shift s a nv :: nil. + +Definition needs_of_condition (cond: condition): list nval := nil. + +Definition needs_of_operation (op: operation) (nv: nval): list nval := + match op with + | Omove => nv :: nil + | Ointconst _ => nil + | Olongconst _ => nil + | Ofloatconst _ => nil + | Osingleconst _ => nil + | Oaddrsymbol _ _ => nil + | Oaddrstack _ => nil + | Oshift s a => op1shift s a nv + | Oadd | Osub | Omul => op2 (modarith nv) + | Oaddshift s a | Osubshift s a => op2shift s a (modarith nv) + | Oaddimm _ => op1 (modarith nv) + | Oneg => op1 (modarith nv) + | Onegshift s a => op1shift s a (modarith nv) + | Omuladd | Omulsub => + let n := modarith nv in n :: n :: n :: nil + | Odiv | Odivu => op2 (default nv) + | Oand | Oor | Oxor => op2 (bitwise nv) + | Oandshift s a | Oorshift s a | Oxorshift s a => op2shift s a (bitwise nv) + | Oandimm n => op1 (andimm nv n) + | Oorimm n => op1 (orimm nv n) + | Oxorimm n => op1 (bitwise nv) + | Onot => op1 (bitwise nv) + | Onotshift s a => needs_of_shift s a (bitwise nv) :: nil + | Obic | Oorn | Oeqv => + let n := bitwise nv in n :: bitwise n :: nil + | Obicshift s a | Oornshift s a | Oeqvshift s a => + let n := bitwise nv in n :: needs_of_shift s a (bitwise n) :: nil + | Oshl | Oshr | Oshru => op2 (default nv) + | Oshrximm _ => op1 (default nv) + | Ozext s => op1 (zero_ext' s nv) + | Osext s => op1 (sign_ext' s nv) + | Oshlzext s a => op1 (zero_ext' s (shlimm nv a)) + | Oshlsext s a => op1 (sign_ext' s (shlimm nv a)) + | Ozextshr a s => op1 (shruimm (zero_ext' s nv) a) + | Osextshr a s => op1 (shrimm (sign_ext' s nv) a) + + | Oshiftl _ _ | Oextend _ _ => op1 (default nv) + | Omakelong | Olowlong | Ohighlong => op1 (default nv) + | Oaddl | Osubl | Omull => op2 (default nv) + | Oaddlshift _ _ | Oaddlext _ _ | Osublshift _ _ | Osublext _ _ => op2 (default nv) + | Oaddlimm _ => op1 (default nv) + | Onegl => op1 (default nv) + | Oneglshift _ _ => op1 (default nv) + | Omulladd | Omullsub => let n := default nv in n :: n :: n :: nil + | Omullhs | Omullhu | Odivl | Odivlu => op2 (default nv) + | Oandl | Oorl | Oxorl | Obicl | Oornl | Oeqvl => op2 (default nv) + | Oandlshift _ _ | Oorlshift _ _ | Oxorlshift _ _ + | Obiclshift _ _ | Oornlshift _ _ | Oeqvlshift _ _ => op2 (default nv) + | Oandlimm _ | Oorlimm _ | Oxorlimm _ => op1 (default nv) + | Onotl => op1 (default nv) + | Onotlshift _ _ => op1 (default nv) + | Oshll | Oshrl | Oshrlu => op2 (default nv) + | Oshrlximm _ => op1 (default nv) + | Ozextl _ | Osextl _ + | Oshllzext _ _ | Oshllsext _ _ | Ozextshrl _ _ | Osextshrl _ _ => op1 (default nv) + | Onegf | Oabsf => op1 (default nv) + | Oaddf | Osubf | Omulf | Odivf => op2 (default nv) + | Onegfs | Oabsfs => op1 (default nv) + | Oaddfs | Osubfs | Omulfs | Odivfs => op2 (default nv) + | Ofloatofsingle | Osingleoffloat => op1 (default nv) + | Ointoffloat | Ointuoffloat | Ofloatofint | Ofloatofintu => op1 (default nv) + | Olongoffloat | Olonguoffloat | Ofloatoflong | Ofloatoflongu => op1 (default nv) + | Ointofsingle | Ointuofsingle | Osingleofint | Osingleofintu => op1 (default nv) + | Olongofsingle | Olonguofsingle | Osingleoflong | Osingleoflongu => op1 (default nv) + | Ocmp c => needs_of_condition c + | Osel c ty => nv :: nv :: needs_of_condition c + end. + +Definition operation_is_redundant (op: operation) (nv: nval): bool := + match op with + | Ozext s => zle 0 s && zero_ext_redundant s nv + | Osext s => zlt 0 s && sign_ext_redundant s nv + | Oandimm n => andimm_redundant nv n + | Oorimm n => orimm_redundant nv n + | _ => false + end. + +Ltac InvAgree := + match goal with + | [H: vagree_list nil _ _ |- _ ] => inv H; InvAgree + | [H: vagree_list (_::_) _ _ |- _ ] => inv H; InvAgree + | _ => idtac + end. + +Ltac TrivialExists := + match goal with + | [ |- exists v, Some ?x = Some v /\ _ ] => exists x; split; auto + | _ => idtac + end. + +Lemma shift_sound: + forall v w s a x, + vagree v w (needs_of_shift s a x) -> + vagree (eval_shift s v a) (eval_shift s w a) x. +Proof. + intros until x; destruct s; simpl; intros. +- apply shlimm_sound; auto. +- apply shruimm_sound; auto. +- apply shrimm_sound; auto. +- apply ror_sound; auto. +Qed. + +Lemma zero_ext'_sound: + forall v w x n, + vagree v w (zero_ext' n x) -> + vagree (Val.zero_ext n v) (Val.zero_ext n w) x. +Proof. + unfold zero_ext'; intros. destruct (zle 0 n). +- apply zero_ext_sound; auto. +- assert (E: x = Nothing \/ Val.lessdef v w) by (destruct x; auto). + destruct E. subst x; simpl; auto. apply vagree_lessdef; apply Val.zero_ext_lessdef; auto. +Qed. + +Lemma sign_ext'_sound: + forall v w x n, + vagree v w (sign_ext' n x) -> + vagree (Val.sign_ext n v) (Val.sign_ext n w) x. +Proof. + unfold sign_ext'; intros. destruct (zlt 0 n). +- apply sign_ext_sound; auto. +- assert (E: x = Nothing \/ Val.lessdef v w) by (destruct x; auto). + destruct E. subst x; simpl; auto. apply vagree_lessdef; apply Val.sign_ext_lessdef; auto. +Qed. + +Section SOUNDNESS. + +Variable ge: genv. +Variable sp: block. +Variables m m': mem. +Hypothesis PERM: forall b ofs k p, Mem.perm m b ofs k p -> Mem.perm m' b ofs k p. + +Lemma needs_of_condition_sound: + forall cond args b args', + eval_condition cond args m = Some b -> + vagree_list args args' (needs_of_condition cond) -> + eval_condition cond args' m' = Some b. +Proof. + intros. unfold needs_of_condition in H0. + eapply default_needs_of_condition_sound; eauto. +Qed. + +Lemma needs_of_operation_sound: + forall op args v nv args', + eval_operation ge (Vptr sp Ptrofs.zero) op args m = Some v -> + vagree_list args args' (needs_of_operation op nv) -> + nv <> Nothing -> + exists v', + eval_operation ge (Vptr sp Ptrofs.zero) op args' m' = Some v' + /\ vagree v v' nv. +Proof. + unfold needs_of_operation; intros; destruct op; try (eapply default_needs_of_operation_sound; eauto; fail); + simpl in *; FuncInv; InvAgree; TrivialExists. +- apply shift_sound; auto. +- apply add_sound; auto. +- apply add_sound; auto using shift_sound. +- apply add_sound; auto with na. +- apply neg_sound; auto. +- apply neg_sound; auto using shift_sound. +- apply sub_sound; auto. +- apply sub_sound; auto using shift_sound. +- apply mul_sound; auto. +- apply add_sound; auto. apply mul_sound; rewrite modarith_idem; auto. +- apply sub_sound; auto. apply mul_sound; rewrite modarith_idem; auto. +- apply and_sound; auto. +- apply and_sound; auto using shift_sound. +- apply andimm_sound; auto. +- apply or_sound; auto. +- apply or_sound; auto using shift_sound. +- apply orimm_sound; auto. +- apply xor_sound; auto. +- apply xor_sound; auto using shift_sound. +- apply xor_sound; auto with na. +- apply notint_sound; auto. +- apply notint_sound; auto using shift_sound. +- apply and_sound; auto. apply notint_sound; rewrite bitwise_idem; auto. +- apply and_sound; auto. apply notint_sound; rewrite bitwise_idem; auto using shift_sound. +- apply or_sound; auto. apply notint_sound; rewrite bitwise_idem; auto. +- apply or_sound; auto. apply notint_sound; rewrite bitwise_idem; auto using shift_sound. +- apply xor_sound; auto. apply notint_sound; rewrite bitwise_idem; auto. +- apply xor_sound; auto. apply notint_sound; rewrite bitwise_idem; auto using shift_sound. +- apply zero_ext'_sound; auto. +- apply sign_ext'_sound; auto. +- apply shlimm_sound; apply zero_ext'_sound; auto. +- apply shlimm_sound; apply sign_ext'_sound; auto. +- apply zero_ext'_sound; apply shruimm_sound; auto. +- apply sign_ext'_sound; apply shrimm_sound; auto. +- destruct (eval_condition cond args m) as [b|] eqn:EC. + erewrite needs_of_condition_sound by eauto. + apply select_sound; auto. + simpl; auto with na. +Qed. + +Lemma operation_is_redundant_sound: + forall op nv arg1 args v arg1' args', + operation_is_redundant op nv = true -> + eval_operation ge (Vptr sp Ptrofs.zero) op (arg1 :: args) m = Some v -> + vagree_list (arg1 :: args) (arg1' :: args') (needs_of_operation op nv) -> + vagree v arg1' nv. +Proof. + intros. destruct op; simpl in *; try discriminate; inv H1; FuncInv; subst. +- apply andimm_redundant_sound; auto. +- apply orimm_redundant_sound; auto. +- InvBooleans. unfold zero_ext' in H5; rewrite zle_true in H5 by auto. + apply zero_ext_redundant_sound; auto. +- InvBooleans. unfold sign_ext' in H5; rewrite zlt_true in H5 by auto. + apply sign_ext_redundant_sound; auto. +Qed. + +End SOUNDNESS. diff --git a/aarch64/Op.v b/aarch64/Op.v new file mode 100644 index 00000000..34c03c77 --- /dev/null +++ b/aarch64/Op.v @@ -0,0 +1,1778 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Operators and addressing modes. The abstract syntax and dynamic + semantics for the CminorSel, RTL, LTL and Mach languages depend on the + following types, defined in this library: +- [condition]: boolean conditions for conditional branches; +- [operation]: arithmetic and logical operations; +- [addressing]: addressing modes for load and store operations. + + These types are processor-specific and correspond roughly to what the + processor can compute in one instruction. In other terms, these + types reflect the state of the program after instruction selection. + For a processor-independent set of operations, see the abstract + syntax and dynamic semantics of the Cminor language. +*) + +Require Import Axioms Coqlib BoolEqual. +Require Import AST Integers Floats Values Memory Globalenvs Events. + +Set Implicit Arguments. +Local Transparent Archi.ptr64. + +(** Shift amounts *) + +Record amount32 : Type := { + a32_amount :> int; + a32_range : Int.ltu a32_amount Int.iwordsize = true }. + +Record amount64 : Type := { + a64_amount :> int; + a64_range : Int.ltu a64_amount Int64.iwordsize' = true }. + +(** Shifted operands *) + +Inductive shift : Type := + | Slsl (**r left shift *) + | Slsr (**r right unsigned shift *) + | Sasr (**r right signed shift *) + | Sror. (**r rotate right *) + +(** Sign- or zero-extended operands *) + +Inductive extension : Type := + | Xsgn32 (**r from signed 32-bit integer to 64-bit integer *) + | Xuns32. (**r from unsigned 32-bit integer to 64-bit integer *) + +(** Conditions (boolean-valued operators). *) + +Inductive condition: Type := +(** Tests over 32-bit integers *) + | Ccomp (c: comparison) (**r signed comparison *) + | Ccompu (c: comparison) (**r unsigned comparison *) + | Ccompimm (c: comparison) (n: int) (**r signed comparison with constant *) + | Ccompuimm (c: comparison) (n: int) (**r unsigned comparison with constant *) + | Ccompshift (c: comparison) (s: shift) (a: amount32) (**r signed comparison with shift *) + | Ccompushift (c: comparison) (s: shift) (a: amount32)(**r unsigned comparison width shift *) + | Cmaskzero (n: int) (**r test [(arg & n) == 0] *) + | Cmasknotzero (n: int) (**r test [(arg & n) != 0] *) +(** Tests over 64-bit integers *) + | Ccompl (c: comparison) (**r signed comparison *) + | Ccomplu (c: comparison) (**r unsigned comparison *) + | Ccomplimm (c: comparison) (n: int64) (**r signed comparison with constant *) + | Ccompluimm (c: comparison) (n: int64) (**r unsigned comparison with constant *) + | Ccomplshift (c: comparison) (s: shift) (a: amount64)(**r signed comparison with shift *) + | Ccomplushift (c: comparison) (s: shift) (a: amount64)(**r unsigned comparison width shift *) + | Cmasklzero (n: int64) (**r test [(arg & n) == 0] *) + | Cmasklnotzero (n: int64) (**r test [(arg & n) != 0] *) +(** Tests over 64-bit floating-point numbers *) + | Ccompf (c: comparison) (**r FP comparison *) + | Cnotcompf (c: comparison) (**r negation of an FP comparison *) + | Ccompfzero (c: comparison) (**r comparison with 0.0 *) + | Cnotcompfzero (c: comparison) (**r negation of comparison with 0.0 *) +(** Tests over 32-bit floating-point numbers *) + | Ccompfs (c: comparison) (**r FP comparison *) + | Cnotcompfs (c: comparison) (**r negation of an FP comparison *) + | Ccompfszero (c: comparison) (**r equal to 0.0 *) + | Cnotcompfszero (c: comparison). (**r not equal to 0.0 *) + +(** Arithmetic and logical operations. In the descriptions, [rd] is the + result of the operation and [r1], [r2], etc, are the arguments. *) + +Inductive operation : Type := + | Omove (**r [rd = r1] *) + | Ointconst (n: int) (**r [rd] is set to the given integer constant *) + | Olongconst (n: int64) (**r [rd] is set to the given integer constant *) + | Ofloatconst (n: float) (**r [rd] is set to the given float constant *) + | Osingleconst (n: float32) (**r [rd] is set to the given float constant *) + | Oaddrsymbol (id: ident) (ofs: ptrofs) (**r [rd] is set to the address of the symbol plus the given offset *) + | Oaddrstack (ofs: ptrofs) (**r [rd] is set to the stack pointer plus the given offset *) +(** 32-bit integer arithmetic *) + | Oshift (s: shift) (a: amount32) (**r shift or rotate by immediate quantity *) + | Oadd (**r [rd = r1 + r2] *) + | Oaddshift (s: shift) (a: amount32) (**r [rd = r1 + shifted r2] *) + | Oaddimm (n: int) (**r [rd = r1 + n] *) + | Oneg (**r [rd = - r1] *) + | Onegshift (s: shift) (a: amount32) (**r [rd = - shifted r1] *) + | Osub (**r [rd = r1 - r2] *) + | Osubshift (s: shift) (a: amount32) (**r [rd = r1 - shifted r2] *) + | Omul (**r [rd = r1 * r2] *) + | Omuladd (**r [rd = r1 + r2 * r3] *) + | Omulsub (**r [rd = r1 - r2 * r3] *) + | Odiv (**r [rd = r1 / r2] (signed) *) + | Odivu (**r [rd = r1 / r2] (unsigned) *) + | Oand (**r [rd = r1 & r2] *) + | Oandshift (s: shift) (a: amount32) (**r [rd = r1 & shifted r2] *) + | Oandimm (n: int) (**r [rd = r1 & n] *) + | Oor (**r [rd = r1 | r2] *) + | Oorshift (s: shift) (a: amount32) (**r [rd = r1 | shifted r2] *) + | Oorimm (n: int) (**r [rd = r1 | n] *) + | Oxor (**r [rd = r1 ^ r2] *) + | Oxorshift (s: shift) (a: amount32) (**r [rd = r1 ^ shifted r2] *) + | Oxorimm (n: int) (**r [rd = r1 ^ n] *) + | Onot (**r [rd = ~r1] *) + | Onotshift (s: shift) (a: amount32) (**r [rd = ~ shifted r1] *) + | Obic (**r [rd = r1 & ~r2] *) + | Obicshift (s: shift) (a: amount32) (**r [rd = r1 ^ ~ shifted r2] *) + | Oorn (**r [rd = r1 | ~r2] *) + | Oornshift (s: shift) (a: amount32) (**r [rd = r1 | ~ shifted r2] *) + | Oeqv (**r [rd = r1 ^ ~r2] *) + | Oeqvshift (s: shift) (a: amount32) (**r [rd = r1 | ~ shifted r2] *) + | Oshl (**r [rd = r1 << r2] *) + | Oshr (**r [rd = r1 >> r2] (signed) *) + | Oshru (**r [rd = r1 >> r2] (unsigned) *) + | Oshrximm (n: int) (**r [rd = r1 / 2^n] (signed) *) + | Ozext (s: Z) (**r [rd = zero_ext(r1,s)] *) + | Osext (s: Z) (**r [rd = sign_ext(r1,s)] *) + | Oshlzext (s: Z) (a: amount32) (**r [rd = zero_ext(r1,s) << a] *) + | Oshlsext (s: Z) (a: amount32) (**r [rd = sign_ext(r1,s) << a] *) + | Ozextshr (a: amount32) (s: Z) (**r [rd = zero_ext(r1 >> a, s)] *) + | Osextshr (a: amount32) (s: Z) (**r [rd = sign_ext(r1 >> a, s)] *) +(** 64-bit integer arithmetic *) + | Oshiftl (s: shift) (a: amount64) (**r shift or rotate by immediate quantity *) + | Oextend (x: extension) (a: amount64) (**r convert from 32 to 64 bits and shift *) + | Omakelong (**r [rd = r1 << 32 | r2] *) + | Olowlong (**r [rd = low-word(r1)] *) + | Ohighlong (**r [rd = high-word(r1)] *) + | Oaddl (**r [rd = r1 + r2] *) + | Oaddlshift (s: shift) (a: amount64) (**r [rd = r1 + shifted r2] *) + | Oaddlext (x: extension) (a: amount64) (**r [rd = r1 + shifted, converted r2] *) + | Oaddlimm (n: int64) (**r [rd = r1 + n] *) + | Onegl (**r [rd = - r1] *) + | Oneglshift (s: shift) (a: amount64) (**r [rd = - shifted r1] *) + | Osubl (**r [rd = r1 - r2] *) + | Osublshift (s: shift) (a: amount64) (**r [rd = r1 - shifted r2] *) + | Osublext (x: extension) (a: amount64) (**r [rd = r1 - shifted, converted r2] *) + | Omull (**r [rd = r1 * r2] *) + | Omulladd (**r [rd = r1 + r2 * r3] *) + | Omullsub (**r [rd = r1 - r2 * r3] *) + | Omullhs (**r [rd = high part of r1 * r2 (signed)] *) + | Omullhu (**r [rd = high part of r1 * r2 (unsigned)] *) + | Odivl (**r [rd = r1 / r2] (signed) *) + | Odivlu (**r [rd = r1 / r2] (unsigned) *) + | Oandl (**r [rd = r1 & r2] *) + | Oandlshift (s: shift) (a: amount64) (**r [rd = r1 & shifted r2] *) + | Oandlimm (n: int64) (**r [rd = r1 & n] *) + | Oorl (**r [rd = r1 | r2] *) + | Oorlshift (s: shift) (a: amount64) (**r [rd = r1 | shifted r2] *) + | Oorlimm (n: int64) (**r [rd = r1 | n] *) + | Oxorl (**r [rd = r1 ^ r2] *) + | Oxorlshift (s: shift) (a: amount64) (**r [rd = r1 ^ shifted r2] *) + | Oxorlimm (n: int64) (**r [rd = r1 ^ n] *) + | Onotl (**r [rd = ~r1] *) + | Onotlshift (s: shift) (a: amount64) (**r [rd = ~ shifted r1] *) + | Obicl (**r [rd = r1 & ~r2] *) + | Obiclshift (s: shift) (a: amount64) (**r [rd = r1 ^ ~ shifted r2] *) + | Oornl (**r [rd = r1 | ~r2] *) + | Oornlshift (s: shift) (a: amount64) (**r [rd = r1 | ~ shifted r2] *) + | Oeqvl (**r [rd = r1 ^ ~r2] *) + | Oeqvlshift (s: shift) (a: amount64) (**r [rd = r1 | ~ shifted r2] *) + | Oshll (**r [rd = r1 << r2] *) + | Oshrl (**r [rd = r1 >> r2] (signed) *) + | Oshrlu (**r [rd = r1 >> r2] (unsigned) *) + | Oshrlximm (n: int) (**r [rd = r1 / 2^n] (signed) *) + | Ozextl (s: Z) (**r [rd = zero_ext(r1,s)] *) + | Osextl (s: Z) (**r [rd = sign_ext(r1,s)] *) + | Oshllzext (s: Z) (a: amount64) (**r [rd = zero_ext(r1,s) << a] *) + | Oshllsext (s: Z) (a: amount64) (**r [rd = sign_ext(r1,s) << a] *) + | Ozextshrl (a: amount64) (s: Z) (**r [rd = zero_ext(r1 >> a, s)] *) + | Osextshrl (a: amount64) (s: Z) (**r [rd = sign_ext(r1 >> a, s)] *) +(** 64-bit floating-point arithmetic *) + | Onegf (**r [rd = - r1] *) + | Oabsf (**r [rd = abs(r1)] *) + | Oaddf (**r [rd = r1 + r2] *) + | Osubf (**r [rd = r1 - r2] *) + | Omulf (**r [rd = r1 * r2] *) + | Odivf (**r [rd = r1 / r2] *) +(** 32-bit floating-point arithmetic *) + | Onegfs (**r [rd = - r1] *) + | Oabsfs (**r [rd = abs(r1)] *) + | Oaddfs (**r [rd = r1 + r2] *) + | Osubfs (**r [rd = r1 - r2] *) + | Omulfs (**r [rd = r1 * r2] *) + | Odivfs (**r [rd = r1 / r2] *) + | Osingleoffloat (**r [rd] is [r1] truncated to single-precision float *) + | Ofloatofsingle (**r [rd] is [r1] extended to double-precision float *) +(** Conversions between int and float *) + | Ointoffloat (**r [rd = signed_int_of_float64(r1)] *) + | Ointuoffloat (**r [rd = unsigned_int_of_float64(r1)] *) + | Ofloatofint (**r [rd = float64_of_signed_int(r1)] *) + | Ofloatofintu (**r [rd = float64_of_unsigned_int(r1)] *) + | Ointofsingle (**r [rd = signed_int_of_float32(r1)] *) + | Ointuofsingle (**r [rd = unsigned_int_of_float32(r1)] *) + | Osingleofint (**r [rd = float32_of_signed_int(r1)] *) + | Osingleofintu (**r [rd = float32_of_unsigned_int(r1)] *) + | Olongoffloat (**r [rd = signed_long_of_float64(r1)] *) + | Olonguoffloat (**r [rd = unsigned_long_of_float64(r1)] *) + | Ofloatoflong (**r [rd = float64_of_signed_long(r1)] *) + | Ofloatoflongu (**r [rd = float64_of_unsigned_long(r1)] *) + | Olongofsingle (**r [rd = signed_long_of_float32(r1)] *) + | Olonguofsingle (**r [rd = unsigned_long_of_float32(r1)] *) + | Osingleoflong (**r [rd = float32_of_signed_long(r1)] *) + | Osingleoflongu (**r [rd = float32_of_unsigned_int(r1)] *) +(** Boolean tests *) + | Ocmp (cond: condition) (**r [rd = 1] if condition holds, [rd = 0] otherwise. *) + | Osel (cond: condition) (ty: typ). (**r [rd = rs1] if condition holds, [rd = rs2] otherwise. *) + +(** Addressing modes. [r1], [r2], etc, are the arguments to the addressing. *) + +Inductive addressing: Type := + | Aindexed (ofs: int64) (**r Address is [r1 + offset] *) + | Aindexed2 (**r Address is [r1 + r2] *) + | Aindexed2shift (a: amount64) (**r Address is [r1 + r2 << a] *) + | Aindexed2ext (x: extension) (a: amount64) (**r Address is [r1 + sign-or-zero-ext(r2) << a] *) + | Aglobal (id: ident) (ofs: ptrofs) (**r Address is [global + offset] *) + | Ainstack (ofs: ptrofs). (**r Address is [stack_pointer + offset] *) + +(** Comparison functions (used in modules [CSE] and [Allocation]). *) + +Definition eq_amount32 (x y: amount32): {x=y} + {x<>y}. +Proof. + destruct x as [x Px], y as [y Py]. + destruct (Int.eq_dec x y). +- subst y. assert (Px = Py) by (apply proof_irr). subst Py. left; auto. +- right; congruence. +Defined. + +Definition eq_amount64 (x y: amount64): {x=y} + {x<>y}. +Proof. + destruct x as [x Px], y as [y Py]. + destruct (Int.eq_dec x y). +- subst y. assert (Px = Py) by (apply proof_irr). subst Py. left; auto. +- right; congruence. +Defined. + +Definition eq_shift (x y: shift): {x=y} + {x<>y}. +Proof. + decide equality. +Defined. + +Definition eq_extension (x y: extension): {x=y} + {x<>y}. +Proof. + decide equality. +Defined. + +Definition eq_condition (x y: condition) : {x=y} + {x<>y}. +Proof. + assert (forall (x y: comparison), {x=y}+{x<>y}) by decide equality. + generalize Int.eq_dec Int64.eq_dec eq_shift eq_amount32 eq_amount64; intro. + decide equality. +Defined. + +Definition eq_addressing (x y: addressing) : {x=y} + {x<>y}. +Proof. + generalize ident_eq Int64.eq_dec Ptrofs.eq_dec eq_extension eq_amount64; intros. + decide equality. +Defined. + +Definition eq_operation: forall (x y: operation), {x=y} + {x<>y}. +Proof. + intros. + generalize Int.eq_dec Int64.eq_dec Ptrofs.eq_dec Float.eq_dec Float32.eq_dec + zeq ident_eq eq_shift eq_extension eq_amount32 eq_amount64 + typ_eq eq_condition; + decide equality. +Defined. + +(** Alternative: + +Definition beq_operation: forall (x y: operation), bool. +Proof. + generalize Int.eq_dec Int64.eq_dec Ptrofs.eq_dec Float.eq_dec Float32.eq_dec + zeq ident_eq eq_shift eq_extension eq_amount32 eq_amount64 + eq_condition typ_eq; boolean_equality. +Defined. + +Definition eq_operation: forall (x y: operation), {x=y} + {x<>y}. +Proof. + decidable_equality_from beq_operation. +Defined. +*) + +(** * Evaluation functions *) + +(** Evaluation of conditions, operators and addressing modes applied + to lists of values. Return [None] when the computation can trigger an + error, e.g. integer division by zero. [eval_condition] returns a boolean, + [eval_operation] and [eval_addressing] return a value. *) + +Definition eval_shift (s: shift) (v: val) (n: amount32) : val := + match s with + | Slsl => Val.shl v (Vint n) + | Slsr => Val.shru v (Vint n) + | Sasr => Val.shr v (Vint n) + | Sror => Val.ror v (Vint n) + end. + +Definition eval_shiftl (s: shift) (v: val) (n: amount64) : val := + match s with + | Slsl => Val.shll v (Vint n) + | Slsr => Val.shrlu v (Vint n) + | Sasr => Val.shrl v (Vint n) + | Sror => Val.rorl v (Vint n) + end. + +Definition eval_extend (x: extension) (v: val) (n: amount64) : val := + Val.shll + (match x with + | Xsgn32 => Val.longofint v + | Xuns32 => Val.longofintu v + end) + (Vint n). + +Definition eval_condition (cond: condition) (vl: list val) (m: mem): option bool := + match cond, vl with + | Ccomp c, v1 :: v2 :: nil => Val.cmp_bool c v1 v2 + | Ccompu c, v1 :: v2 :: nil => Val.cmpu_bool (Mem.valid_pointer m) c v1 v2 + | Ccompimm c n, v1 :: nil => Val.cmp_bool c v1 (Vint n) + | Ccompuimm c n, v1 :: nil => Val.cmpu_bool (Mem.valid_pointer m) c v1 (Vint n) + | Ccompshift c s a, v1 :: v2 :: nil => Val.cmp_bool c v1 (eval_shift s v2 a) + | Ccompushift c s a, v1 :: v2 :: nil => Val.cmpu_bool (Mem.valid_pointer m) c v1 (eval_shift s v2 a) + | Cmaskzero n, v1 :: nil => Val.cmp_bool Ceq (Val.and v1 (Vint n)) (Vint Int.zero) + | Cmasknotzero n, v1 :: nil => Val.cmp_bool Cne (Val.and v1 (Vint n)) (Vint Int.zero) + + | Ccompl c, v1 :: v2 :: nil => Val.cmpl_bool c v1 v2 + | Ccomplu c, v1 :: v2 :: nil => Val.cmplu_bool (Mem.valid_pointer m) c v1 v2 + | Ccomplimm c n, v1 :: nil => Val.cmpl_bool c v1 (Vlong n) + | Ccompluimm c n, v1 :: nil => Val.cmplu_bool (Mem.valid_pointer m) c v1 (Vlong n) + | Ccomplshift c s a, v1 :: v2 :: nil => Val.cmpl_bool c v1 (eval_shiftl s v2 a) + | Ccomplushift c s a, v1 :: v2 :: nil => Val.cmplu_bool (Mem.valid_pointer m) c v1 (eval_shiftl s v2 a) + | Cmasklzero n, v1 :: nil => Val.cmpl_bool Ceq (Val.andl v1 (Vlong n)) (Vlong Int64.zero) + | Cmasklnotzero n, v1 :: nil => Val.cmpl_bool Cne (Val.andl v1 (Vlong n)) (Vlong Int64.zero) + + | Ccompf c, v1 :: v2 :: nil => Val.cmpf_bool c v1 v2 + | Cnotcompf c, v1 :: v2 :: nil => option_map negb (Val.cmpf_bool c v1 v2) + | Ccompfzero c, v1 :: nil => Val.cmpf_bool c v1 (Vfloat Float.zero) + | Cnotcompfzero c, v1 :: nil => option_map negb (Val.cmpf_bool c v1 (Vfloat Float.zero)) + + | Ccompfs c, v1 :: v2 :: nil => Val.cmpfs_bool c v1 v2 + | Cnotcompfs c, v1 :: v2 :: nil => option_map negb (Val.cmpfs_bool c v1 v2) + | Ccompfszero c, v1 :: nil => Val.cmpfs_bool c v1 (Vsingle Float32.zero) + | Cnotcompfszero c, v1 :: nil => option_map negb (Val.cmpfs_bool c v1 (Vsingle Float32.zero)) + + | _, _ => None + end. + +Definition eval_operation + (F V: Type) (genv: Genv.t F V) (sp: val) + (op: operation) (vl: list val) (m: mem): option val := + match op, vl with + | Omove, v1::nil => Some v1 + | Ointconst n, nil => Some (Vint n) + | Olongconst n, nil => Some (Vlong n) + | Ofloatconst n, nil => Some (Vfloat n) + | Osingleconst n, nil => Some (Vsingle n) + | Oaddrsymbol s ofs, nil => Some (Genv.symbol_address genv s ofs) + | Oaddrstack ofs, nil => Some (Val.offset_ptr sp ofs) + + | Oshift s a, v1 :: nil => Some (eval_shift s v1 a) + | Oadd, v1 :: v2 :: nil => Some (Val.add v1 v2) + | Oaddshift s a, v1 :: v2 :: nil => Some (Val.add v1 (eval_shift s v2 a)) + | Oaddimm n, v1 :: nil => Some (Val.add v1 (Vint n)) + | Oneg, v1 :: nil => Some (Val.neg v1) + | Onegshift s a, v1 :: nil => Some (Val.neg (eval_shift s v1 a)) + | Osub, v1 :: v2 :: nil => Some (Val.sub v1 v2) + | Osubshift s a, v1 :: v2 :: nil => Some (Val.sub v1 (eval_shift s v2 a)) + | Omul, v1 :: v2 :: nil => Some (Val.mul v1 v2) + | Omuladd, v1 :: v2 :: v3 :: nil => Some (Val.add v1 (Val.mul v2 v3)) + | Omulsub, v1 :: v2 :: v3 :: nil => Some (Val.sub v1 (Val.mul v2 v3)) + | Odiv, v1 :: v2 :: nil => Val.divs v1 v2 + | Odivu, v1 :: v2 :: nil => Val.divu v1 v2 + | Oand, v1 :: v2 :: nil => Some (Val.and v1 v2) + | Oandshift s a, v1 :: v2 :: nil => Some (Val.and v1 (eval_shift s v2 a)) + | Oandimm n, v1 :: nil => Some (Val.and v1 (Vint n)) + | Oor, v1 :: v2 :: nil => Some (Val.or v1 v2) + | Oorshift s a, v1 :: v2 :: nil => Some (Val.or v1 (eval_shift s v2 a)) + | Oorimm n, v1 :: nil => Some (Val.or v1 (Vint n)) + | Oxor, v1 :: v2 :: nil => Some (Val.xor v1 v2) + | Oxorshift s a, v1 :: v2 :: nil => Some (Val.xor v1 (eval_shift s v2 a)) + | Oxorimm n, v1 :: nil => Some (Val.xor v1 (Vint n)) + | Onot, v1 :: nil => Some (Val.notint v1) + | Onotshift s a, v1 :: nil => Some (Val.notint (eval_shift s v1 a)) + | Obic, v1 :: v2 :: nil => Some (Val.and v1 (Val.notint v2)) + | Obicshift s a, v1 :: v2 :: nil => Some (Val.and v1 (Val.notint (eval_shift s v2 a))) + | Oorn, v1 :: v2 :: nil => Some (Val.or v1 (Val.notint v2)) + | Oornshift s a, v1 :: v2 :: nil => Some (Val.or v1 (Val.notint (eval_shift s v2 a))) + | Oeqv, v1 :: v2 :: nil => Some (Val.xor v1 (Val.notint v2)) + | Oeqvshift s a, v1 :: v2 :: nil => Some (Val.xor v1 (Val.notint (eval_shift s v2 a))) + | Oshl, v1 :: v2 :: nil => Some (Val.shl v1 v2) + | Oshr, v1 :: v2 :: nil => Some (Val.shr v1 v2) + | Oshru, v1 :: v2 :: nil => Some (Val.shru v1 v2) + | Oshrximm n, v1::nil => Val.shrx v1 (Vint n) + | Ozext s, v1 :: nil => Some (Val.zero_ext s v1) + | Osext s, v1 :: nil => Some (Val.sign_ext s v1) + | Oshlzext s a, v1 :: nil => Some (Val.shl (Val.zero_ext s v1) (Vint a)) + | Oshlsext s a, v1 :: nil => Some (Val.shl (Val.sign_ext s v1) (Vint a)) + | Ozextshr a s, v1 :: nil => Some (Val.zero_ext s (Val.shru v1 (Vint a))) + | Osextshr a s, v1 :: nil => Some (Val.sign_ext s (Val.shr v1 (Vint a))) + + | Oshiftl s a, v1 :: nil => Some (eval_shiftl s v1 a) + | Oextend x a, v1 :: nil => Some (eval_extend x v1 a) + | Omakelong, v1::v2::nil => Some (Val.longofwords v1 v2) + | Olowlong, v1::nil => Some (Val.loword v1) + | Ohighlong, v1::nil => Some (Val.hiword v1) + | Oaddl, v1 :: v2 :: nil => Some (Val.addl v1 v2) + | Oaddlshift s a, v1 :: v2 :: nil => Some (Val.addl v1 (eval_shiftl s v2 a)) + | Oaddlext x a, v1 :: v2 :: nil => Some (Val.addl v1 (eval_extend x v2 a)) + | Oaddlimm n, v1 :: nil => Some (Val.addl v1 (Vlong n)) + | Onegl, v1 :: nil => Some (Val.negl v1) + | Oneglshift s a, v1 :: nil => Some (Val.negl (eval_shiftl s v1 a)) + | Osubl, v1 :: v2 :: nil => Some (Val.subl v1 v2) + | Osublshift s a, v1 :: v2 :: nil => Some (Val.subl v1 (eval_shiftl s v2 a)) + | Osublext x a, v1 :: v2 :: nil => Some (Val.subl v1 (eval_extend x v2 a)) + | Omull, v1 :: v2 :: nil => Some (Val.mull v1 v2) + | Omulladd, v1 :: v2 :: v3 :: nil => Some (Val.addl v1 (Val.mull v2 v3)) + | Omullsub, v1 :: v2 :: v3 :: nil => Some (Val.subl v1 (Val.mull v2 v3)) + | Omullhs, v1::v2::nil => Some (Val.mullhs v1 v2) + | Omullhu, v1::v2::nil => Some (Val.mullhu v1 v2) + | Odivl, v1 :: v2 :: nil => Val.divls v1 v2 + | Odivlu, v1 :: v2 :: nil => Val.divlu v1 v2 + | Oandl, v1 :: v2 :: nil => Some (Val.andl v1 v2) + | Oandlshift s a, v1 :: v2 :: nil => Some (Val.andl v1 (eval_shiftl s v2 a)) + | Oandlimm n, v1 :: nil => Some (Val.andl v1 (Vlong n)) + | Oorl, v1 :: v2 :: nil => Some (Val.orl v1 v2) + | Oorlshift s a, v1 :: v2 :: nil => Some (Val.orl v1 (eval_shiftl s v2 a)) + | Oorlimm n, v1 :: nil => Some (Val.orl v1 (Vlong n)) + | Oxorl, v1 :: v2 :: nil => Some (Val.xorl v1 v2) + | Oxorlshift s a, v1 :: v2 :: nil => Some (Val.xorl v1 (eval_shiftl s v2 a)) + | Oxorlimm n, v1 :: nil => Some (Val.xorl v1 (Vlong n)) + | Onotl, v1 :: nil => Some (Val.notl v1) + | Onotlshift s a, v1 :: nil => Some (Val.notl (eval_shiftl s v1 a)) + | Obicl, v1 :: v2 :: nil => Some (Val.andl v1 (Val.notl v2)) + | Obiclshift s a, v1 :: v2 :: nil => Some (Val.andl v1 (Val.notl (eval_shiftl s v2 a))) + | Oornl, v1 :: v2 :: nil => Some (Val.orl v1 (Val.notl v2)) + | Oornlshift s a, v1 :: v2 :: nil => Some (Val.orl v1 (Val.notl (eval_shiftl s v2 a))) + | Oeqvl, v1 :: v2 :: nil => Some (Val.xorl v1 (Val.notl v2)) + | Oeqvlshift s a, v1 :: v2 :: nil => Some (Val.xorl v1 (Val.notl (eval_shiftl s v2 a))) + | Oshll, v1 :: v2 :: nil => Some (Val.shll v1 v2) + | Oshrl, v1 :: v2 :: nil => Some (Val.shrl v1 v2) + | Oshrlu, v1 :: v2 :: nil => Some (Val.shrlu v1 v2) + | Oshrlximm n, v1::nil => Val.shrxl v1 (Vint n) + | Ozextl s, v1 :: nil => Some (Val.zero_ext_l s v1) + | Osextl s, v1 :: nil => Some (Val.sign_ext_l s v1) + | Oshllzext s a, v1 :: nil => Some (Val.shll (Val.zero_ext_l s v1) (Vint a)) + | Oshllsext s a, v1 :: nil => Some (Val.shll (Val.sign_ext_l s v1) (Vint a)) + | Ozextshrl a s, v1 :: nil => Some (Val.zero_ext_l s (Val.shrlu v1 (Vint a))) + | Osextshrl a s, v1 :: nil => Some (Val.sign_ext_l s (Val.shrl v1 (Vint a))) + + | Onegf, v1::nil => Some (Val.negf v1) + | Oabsf, v1::nil => Some (Val.absf v1) + | Oaddf, v1::v2::nil => Some (Val.addf v1 v2) + | Osubf, v1::v2::nil => Some (Val.subf v1 v2) + | Omulf, v1::v2::nil => Some (Val.mulf v1 v2) + | Odivf, v1::v2::nil => Some (Val.divf v1 v2) + + | Onegfs, v1::nil => Some (Val.negfs v1) + | Oabsfs, v1::nil => Some (Val.absfs v1) + | Oaddfs, v1::v2::nil => Some (Val.addfs v1 v2) + | Osubfs, v1::v2::nil => Some (Val.subfs v1 v2) + | Omulfs, v1::v2::nil => Some (Val.mulfs v1 v2) + | Odivfs, v1::v2::nil => Some (Val.divfs v1 v2) + + | Osingleoffloat, v1::nil => Some (Val.singleoffloat v1) + | Ofloatofsingle, v1::nil => Some (Val.floatofsingle v1) + | Ointoffloat, v1::nil => Val.intoffloat v1 + | Ointuoffloat, v1::nil => Val.intuoffloat v1 + | Ofloatofint, v1::nil => Val.floatofint v1 + | Ofloatofintu, v1::nil => Val.floatofintu v1 + | Ointofsingle, v1::nil => Val.intofsingle v1 + | Ointuofsingle, v1::nil => Val.intuofsingle v1 + | Osingleofint, v1::nil => Val.singleofint v1 + | Osingleofintu, v1::nil => Val.singleofintu v1 + | Olongoffloat, v1::nil => Val.longoffloat v1 + | Olonguoffloat, v1::nil => Val.longuoffloat v1 + | Ofloatoflong, v1::nil => Val.floatoflong v1 + | Ofloatoflongu, v1::nil => Val.floatoflongu v1 + | Olongofsingle, v1::nil => Val.longofsingle v1 + | Olonguofsingle, v1::nil => Val.longuofsingle v1 + | Osingleoflong, v1::nil => Val.singleoflong v1 + | Osingleoflongu, v1::nil => Val.singleoflongu v1 + + | Ocmp c, _ => Some (Val.of_optbool (eval_condition c vl m)) + | Osel c ty, v1::v2::vl => Some(Val.select (eval_condition c vl m) v1 v2 ty) + | _, _ => None + end. + +Definition eval_addressing + (F V: Type) (genv: Genv.t F V) (sp: val) + (addr: addressing) (vl: list val) : option val := + match addr, vl with + | Aindexed n, v1 :: nil => Some (Val.addl v1 (Vlong n)) + | Aindexed2, v1 :: v2 :: nil => Some (Val.addl v1 v2) + | Aindexed2shift a, v1 :: v2 :: nil => Some (Val.addl v1 (Val.shll v2 (Vint a))) + | Aindexed2ext x a, v1 :: v2 :: nil => Some (Val.addl v1 (eval_extend x v2 a)) + | Aglobal s ofs, nil => Some (Genv.symbol_address genv s ofs) + | Ainstack n, nil => Some (Val.offset_ptr sp n) + | _, _ => None + end. + +Remark eval_addressing_Ainstack: + forall (F V: Type) (genv: Genv.t F V) sp ofs, + eval_addressing genv sp (Ainstack ofs) nil = Some (Val.offset_ptr sp ofs). +Proof. + intros. reflexivity. +Qed. + +Remark eval_addressing_Ainstack_inv: + forall (F V: Type) (genv: Genv.t F V) sp ofs vl v, + eval_addressing genv sp (Ainstack ofs) vl = Some v -> vl = nil /\ v = Val.offset_ptr sp ofs. +Proof. + unfold eval_addressing; intros; destruct vl; inv H; auto. +Qed. + +Ltac FuncInv := + match goal with + | H: (match ?x with nil => _ | _ :: _ => _ end = Some _) |- _ => + destruct x; simpl in H; FuncInv + | H: (match ?v with Vundef => _ | Vint _ => _ | Vfloat _ => _ | Vptr _ _ => _ end = Some _) |- _ => + destruct v; simpl in H; FuncInv + | H: (if Archi.ptr64 then _ else _) = Some _ |- _ => + change Archi.ptr64 with true in H; simpl in H; FuncInv + | H: (Some _ = Some _) |- _ => + injection H; intros; clear H; FuncInv + | H: (None = Some _) |- _ => + discriminate H + | _ => + idtac + end. + +(** * Static typing of conditions, operators and addressing modes. *) + +Definition type_of_condition (c: condition) : list typ := + match c with + | Ccomp _ => Tint :: Tint :: nil + | Ccompu _ => Tint :: Tint :: nil + | Ccompimm _ _ => Tint :: nil + | Ccompuimm _ _ => Tint :: nil + | Ccompshift _ _ _ => Tint :: Tint :: nil + | Ccompushift _ _ _ => Tint :: Tint :: nil + | Cmaskzero _ => Tint :: nil + | Cmasknotzero _ => Tint :: nil + | Ccompl _ => Tlong :: Tlong :: nil + | Ccomplu _ => Tlong :: Tlong :: nil + | Ccomplimm _ _ => Tlong :: nil + | Ccompluimm _ _ => Tlong :: nil + | Ccomplshift _ _ _ => Tlong :: Tlong :: nil + | Ccomplushift _ _ _ => Tlong :: Tlong :: nil + | Cmasklzero _ => Tint :: nil + | Cmasklnotzero _ => Tint :: nil + | Ccompf _ => Tfloat :: Tfloat :: nil + | Cnotcompf _ => Tfloat :: Tfloat :: nil + | Ccompfzero _ => Tfloat :: nil + | Cnotcompfzero _ => Tfloat :: nil + | Ccompfs _ => Tsingle :: Tsingle :: nil + | Cnotcompfs _ => Tsingle :: Tsingle :: nil + | Ccompfszero _ => Tsingle :: nil + | Cnotcompfszero _ => Tsingle :: nil + end. + +Definition type_of_operation (op: operation) : list typ * typ := + match op with + | Omove => (nil, Tint) (* treated specially *) + | Ointconst _ => (nil, Tint) + | Olongconst _ => (nil, Tlong) + | Ofloatconst f => (nil, Tfloat) + | Osingleconst f => (nil, Tsingle) + | Oaddrsymbol _ _ => (nil, Tptr) + | Oaddrstack _ => (nil, Tptr) + + | Oshift _ _ => (Tint :: nil, Tint) + | Oadd => (Tint :: Tint :: nil, Tint) + | Oaddshift _ _ => (Tint :: Tint :: nil, Tint) + | Oaddimm _ => (Tint :: nil, Tint) + | Oneg => (Tint :: nil, Tint) + | Onegshift _ _ => (Tint :: nil, Tint) + | Osub => (Tint :: Tint :: nil, Tint) + | Osubshift _ _ => (Tint :: Tint :: nil, Tint) + | Omul => (Tint :: Tint :: nil, Tint) + | Omuladd => (Tint :: Tint :: Tint :: nil, Tint) + | Omulsub => (Tint :: Tint :: Tint :: nil, Tint) + | Odiv => (Tint :: Tint :: nil, Tint) + | Odivu => (Tint :: Tint :: nil, Tint) + | Oand => (Tint :: Tint :: nil, Tint) + | Oandshift _ _ => (Tint :: Tint :: nil, Tint) + | Oandimm _ => (Tint :: nil, Tint) + | Oor => (Tint :: Tint :: nil, Tint) + | Oorshift _ _ => (Tint :: Tint :: nil, Tint) + | Oorimm _ => (Tint :: nil, Tint) + | Oxor => (Tint :: Tint :: nil, Tint) + | Oxorshift _ _ => (Tint :: Tint :: nil, Tint) + | Oxorimm _ => (Tint :: nil, Tint) + | Onot => (Tint :: nil, Tint) + | Onotshift _ _ => (Tint :: nil, Tint) + | Obic => (Tint :: Tint :: nil, Tint) + | Obicshift _ _ => (Tint :: Tint :: nil, Tint) + | Oorn => (Tint :: Tint :: nil, Tint) + | Oornshift _ _ => (Tint :: Tint :: nil, Tint) + | Oeqv => (Tint :: Tint :: nil, Tint) + | Oeqvshift _ _ => (Tint :: Tint :: nil, Tint) + | Oshl => (Tint :: Tint :: nil, Tint) + | Oshr => (Tint :: Tint :: nil, Tint) + | Oshru => (Tint :: Tint :: nil, Tint) + | Oshrximm _ => (Tint :: nil, Tint) + | Ozext _ => (Tint :: nil, Tint) + | Osext _ => (Tint :: nil, Tint) + | Oshlzext _ _ => (Tint :: nil, Tint) + | Oshlsext _ _ => (Tint :: nil, Tint) + | Ozextshr _ _ => (Tint :: nil, Tint) + | Osextshr _ _ => (Tint :: nil, Tint) + + | Oshiftl _ _ => (Tlong :: nil, Tlong) + | Oextend _ _ => (Tint :: nil, Tlong) + | Omakelong => (Tint :: Tint :: nil, Tlong) + | Olowlong => (Tlong :: nil, Tint) + | Ohighlong => (Tlong :: nil, Tint) + | Oaddl => (Tlong :: Tlong :: nil, Tlong) + | Oaddlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oaddlext _ _ => (Tlong :: Tint :: nil, Tlong) + | Oaddlimm _ => (Tlong :: nil, Tlong) + | Onegl => (Tlong :: nil, Tlong) + | Oneglshift _ _ => (Tlong :: nil, Tlong) + | Osubl => (Tlong :: Tlong :: nil, Tlong) + | Osublshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Osublext _ _ => (Tlong :: Tint :: nil, Tlong) + | Omull => (Tlong :: Tlong :: nil, Tlong) + | Omulladd => (Tlong :: Tlong :: Tlong :: nil, Tlong) + | Omullsub => (Tlong :: Tlong :: Tlong :: nil, Tlong) + | Omullhs => (Tlong :: Tlong :: nil, Tlong) + | Omullhu => (Tlong :: Tlong :: nil, Tlong) + | Odivl => (Tlong :: Tlong :: nil, Tlong) + | Odivlu => (Tlong :: Tlong :: nil, Tlong) + | Oandl => (Tlong :: Tlong :: nil, Tlong) + | Oandlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oandlimm _ => (Tlong :: nil, Tlong) + | Oorl => (Tlong :: Tlong :: nil, Tlong) + | Oorlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oorlimm _ => (Tlong :: nil, Tlong) + | Oxorl => (Tlong :: Tlong :: nil, Tlong) + | Oxorlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oxorlimm _ => (Tlong :: nil, Tlong) + | Onotl => (Tlong :: nil, Tlong) + | Onotlshift _ _ => (Tlong :: nil, Tlong) + | Obicl => (Tlong :: Tlong :: nil, Tlong) + | Obiclshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oornl => (Tlong :: Tlong :: nil, Tlong) + | Oornlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oeqvl => (Tlong :: Tlong :: nil, Tlong) + | Oeqvlshift _ _ => (Tlong :: Tlong :: nil, Tlong) + | Oshll => (Tlong :: Tint :: nil, Tlong) + | Oshrl => (Tlong :: Tint :: nil, Tlong) + | Oshrlu => (Tlong :: Tint :: nil, Tlong) + | Oshrlximm _ => (Tlong :: nil, Tlong) + | Ozextl _ => (Tlong :: nil, Tlong) + | Osextl _ => (Tlong :: nil, Tlong) + | Oshllzext _ _ => (Tlong :: nil, Tlong) + | Oshllsext _ _ => (Tlong :: nil, Tlong) + | Ozextshrl _ _ => (Tlong :: nil, Tlong) + | Osextshrl _ _ => (Tlong :: nil, Tlong) + + | Onegf => (Tfloat :: nil, Tfloat) + | Oabsf => (Tfloat :: nil, Tfloat) + | Oaddf => (Tfloat :: Tfloat :: nil, Tfloat) + | Osubf => (Tfloat :: Tfloat :: nil, Tfloat) + | Omulf => (Tfloat :: Tfloat :: nil, Tfloat) + | Odivf => (Tfloat :: Tfloat :: nil, Tfloat) + + | Onegfs => (Tsingle :: nil, Tsingle) + | Oabsfs => (Tsingle :: nil, Tsingle) + | Oaddfs => (Tsingle :: Tsingle :: nil, Tsingle) + | Osubfs => (Tsingle :: Tsingle :: nil, Tsingle) + | Omulfs => (Tsingle :: Tsingle :: nil, Tsingle) + | Odivfs => (Tsingle :: Tsingle :: nil, Tsingle) + | Osingleoffloat => (Tfloat :: nil, Tsingle) + | Ofloatofsingle => (Tsingle :: nil, Tfloat) + + | Ointoffloat => (Tfloat :: nil, Tint) + | Ointuoffloat => (Tfloat :: nil, Tint) + | Ofloatofint => (Tint :: nil, Tfloat) + | Ofloatofintu => (Tint :: nil, Tfloat) + | Ointofsingle => (Tsingle :: nil, Tint) + | Ointuofsingle => (Tsingle :: nil, Tint) + | Osingleofint => (Tint :: nil, Tsingle) + | Osingleofintu => (Tint :: nil, Tsingle) + | Olongoffloat => (Tfloat :: nil, Tlong) + | Olonguoffloat => (Tfloat :: nil, Tlong) + | Ofloatoflong => (Tlong :: nil, Tfloat) + | Ofloatoflongu => (Tlong :: nil, Tfloat) + | Olongofsingle => (Tsingle :: nil, Tlong) + | Olonguofsingle => (Tsingle :: nil, Tlong) + | Osingleoflong => (Tlong :: nil, Tsingle) + | Osingleoflongu => (Tlong :: nil, Tsingle) + + | Ocmp c => (type_of_condition c, Tint) + | Osel c ty => (ty :: ty :: type_of_condition c, ty) + end. + +Definition type_of_addressing (addr: addressing) : list typ := + match addr with + | Aindexed _ => Tptr :: nil + | Aindexed2 => Tptr :: Tlong :: nil + | Aindexed2shift _ => Tptr :: Tlong :: nil + | Aindexed2ext _ _ => Tptr :: Tint :: nil + | Aglobal _ _ => nil + | Ainstack _ => nil + end. + +(** Weak type soundness results for [eval_operation]: + the result values, when defined, are always of the type predicted + by [type_of_operation]. *) + +Section SOUNDNESS. + +Variable A V: Type. +Variable genv: Genv.t A V. + +Remark type_add: + forall v1 v2, Val.has_type (Val.add v1 v2) Tint. +Proof. + intros. unfold Val.has_type, Val.add. destruct v1, v2; simpl; auto. +Qed. + +Remark type_sub: + forall v1 v2, Val.has_type (Val.sub v1 v2) Tint. +Proof. + intros. unfold Val.has_type, Val.add. destruct v1, v2; simpl; auto. +Qed. + +Remark type_addl: + forall v1 v2, Val.has_type (Val.addl v1 v2) Tlong. +Proof. + intros. unfold Val.has_type, Val.addl. destruct v1, v2; simpl; auto. +Qed. + +Remark type_subl: + forall v1 v2, Val.has_type (Val.subl v1 v2) Tlong. +Proof. + intros. unfold Val.has_type, Val.addl. destruct v1, v2; simpl; auto. + destruct (eq_block b b0); auto. +Qed. + +Lemma type_of_operation_sound: + forall op vl sp v m, + op <> Omove -> + eval_operation genv sp op vl m = Some v -> + Val.has_type v (snd (type_of_operation op)). +Proof with (try exact I; try reflexivity; auto using Val.Vptr_has_type). + intros. + destruct op; simpl; simpl in H0; FuncInv; subst; simpl. + (* move *) + - congruence. + (* intconst, longconst, floatconst, singleconst *) + - exact I. + - exact I. + - exact I. + - exact I. + (* addrsymbol *) + - unfold Genv.symbol_address. destruct (Genv.find_symbol genv id)... + (* addrstack *) + - destruct sp... + (* 32-bit integer operations *) + - destruct s, v0; try exact I; simpl; rewrite a32_range... + - apply type_add. + - apply type_add. + - apply type_add. + - destruct v0... + - destruct (eval_shift s v0 a)... + - apply type_sub. + - apply type_sub. + - destruct v0... destruct v1... + - apply type_add. + - apply type_sub. + - destruct v0; destruct v1; simpl in *; inv H0. + destruct (Int.eq i0 Int.zero || Int.eq i (Int.repr Int.min_signed) && Int.eq i0 Int.mone); inv H2... + - destruct v0; destruct v1; simpl in *; inv H0. + destruct (Int.eq i0 Int.zero); inv H2... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0... + - destruct v0... + - destruct (eval_shift s v0 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shift s v1 a)... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int.iwordsize)... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int.iwordsize)... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int.iwordsize)... + - destruct v0; simpl in H0; try discriminate. destruct (Int.ltu n (Int.repr 31)); inv H0... + - destruct v0... + - destruct v0... + - destruct (Val.zero_ext s v0)... simpl; rewrite a32_range... + - destruct (Val.sign_ext s v0)... simpl; rewrite a32_range... + - destruct (Val.shru v0 (Vint a))... + - destruct (Val.shr v0 (Vint a))... + (* 64-bit integer operations *) + - destruct s, v0; try exact I; simpl; rewrite a64_range... + - unfold eval_extend. destruct (match x with + | Xsgn32 => Val.longofint v0 + | Xuns32 => Val.longofintu v0 + end)... + simpl; rewrite a64_range... + - destruct v0... destruct v1... + - destruct v0... + - destruct v0... + - apply type_addl. + - apply type_addl. + - apply type_addl. + - apply type_addl. + - destruct v0... + - destruct (eval_shiftl s v0 a)... + - apply type_subl. + - apply type_subl. + - apply type_subl. + - destruct v0... destruct v1... + - apply type_addl. + - apply type_subl. + - destruct v0... destruct v1... + - destruct v0... destruct v1... + - destruct v0; destruct v1; simpl in *; inv H0. + destruct (Int64.eq i0 Int64.zero || Int64.eq i (Int64.repr Int64.min_signed) && Int64.eq i0 Int64.mone); inv H2... + - destruct v0; destruct v1; simpl in *; inv H0. + destruct (Int64.eq i0 Int64.zero); inv H2... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0... + - destruct v0... + - destruct (eval_shiftl s v0 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0... destruct v1... + - destruct v0... destruct (eval_shiftl s v1 a)... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int64.iwordsize')... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int64.iwordsize')... + - destruct v0; destruct v1; simpl... destruct (Int.ltu i0 Int64.iwordsize')... + - destruct v0; simpl in H0; try discriminate. destruct (Int.ltu n (Int.repr 63)); inv H0... + - destruct v0... + - destruct v0... + - destruct (Val.zero_ext_l s v0)... simpl; rewrite a64_range... + - destruct (Val.sign_ext_l s v0)... simpl; rewrite a64_range... + - destruct (Val.shrlu v0 (Vint a))... + - destruct (Val.shrl v0 (Vint a))... + + (* 64-bit FP *) + - destruct v0... + - destruct v0... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + (* 32-bit FP *) + - destruct v0... + - destruct v0... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + - destruct v0; destruct v1... + (* singleoffloat, floatofsingle *) + - destruct v0... + - destruct v0... + (* intoffloat, intuoffloat *) + - destruct v0; simpl in H0; inv H0. destruct (Float.to_int f); inv H2... + - destruct v0; simpl in H0; inv H0. destruct (Float.to_intu f); inv H2... + (* floatofint, floatofintu *) + - destruct v0; simpl in H0; inv H0... + - destruct v0; simpl in H0; inv H0... + (* intofsingle, intuofsingle *) + - destruct v0; simpl in H0; inv H0. destruct (Float32.to_int f); inv H2... + - destruct v0; simpl in H0; inv H0. destruct (Float32.to_intu f); inv H2... + (* singleofint, singleofintu *) + - destruct v0; simpl in H0; inv H0... + - destruct v0; simpl in H0; inv H0... + (* longoffloat, longuoffloat *) + - destruct v0; simpl in H0; inv H0. destruct (Float.to_long f); inv H2... + - destruct v0; simpl in H0; inv H0. destruct (Float.to_longu f); inv H2... + (* floatoflong, floatoflongu *) + - destruct v0; simpl in H0; inv H0... + - destruct v0; simpl in H0; inv H0... + (* longofsingle, longuofsingle *) + - destruct v0; simpl in H0; inv H0. destruct (Float32.to_long f); inv H2... + - destruct v0; simpl in H0; inv H0. destruct (Float32.to_longu f); inv H2... + (* singleoflong, singleoflongu *) + - destruct v0; simpl in H0; inv H0... + - destruct v0; simpl in H0; inv H0... + (* cmp *) + - destruct (eval_condition cond vl m) as [[]|]... + - unfold Val.select. destruct (eval_condition cond vl m). apply Val.normalize_type. exact I. +Qed. + +End SOUNDNESS. + +(** * Manipulating and transforming operations *) + +(** Constructing shift amounts *) + +Section SHIFT_AMOUNT. + +Variable l: Z. +Hypothesis l_range: 0 <= l < 32. +Variable N: int. +Hypothesis N_eq: Int.unsigned N = two_p l. + +Remark mk_amount_range: + forall n, Int.ltu (Int.zero_ext l n) N = true. +Proof. + intros; unfold Int.ltu. apply zlt_true. rewrite N_eq. apply (Int.zero_ext_range l n). assumption. +Qed. + +Remark mk_amount_eq: + forall n, Int.ltu n N = true -> Int.zero_ext l n = n. +Proof. + intros. + transitivity (Int.repr (Int.unsigned (Int.zero_ext l n))). + symmetry; apply Int.repr_unsigned. + transitivity (Int.repr (Int.unsigned n)). + f_equal. rewrite Int.zero_ext_mod. apply Int.ltu_inv in H. rewrite N_eq in H. + apply Z.mod_small. assumption. assumption. + apply Int.repr_unsigned. +Qed. + +End SHIFT_AMOUNT. + +Program Definition mk_amount32 (n: int): amount32 := + {| a32_amount := Int.zero_ext 5 n |}. +Next Obligation. + apply mk_amount_range. omega. reflexivity. +Qed. + +Lemma mk_amount32_eq: forall n, + Int.ltu n Int.iwordsize = true -> a32_amount (mk_amount32 n) = n. +Proof. + intros. eapply mk_amount_eq; eauto. omega. reflexivity. +Qed. + +Program Definition mk_amount64 (n: int): amount64 := + {| a64_amount := Int.zero_ext 6 n |}. +Next Obligation. + apply mk_amount_range. omega. reflexivity. +Qed. + +Lemma mk_amount64_eq: forall n, + Int.ltu n Int64.iwordsize' = true -> a64_amount (mk_amount64 n) = n. +Proof. + intros. eapply mk_amount_eq; eauto. omega. reflexivity. +Qed. + +(** Recognition of move operations. *) + +Definition is_move_operation + (A: Type) (op: operation) (args: list A) : option A := + match op, args with + | Omove, arg :: nil => Some arg + | _, _ => None + end. + +Lemma is_move_operation_correct: + forall (A: Type) (op: operation) (args: list A) (a: A), + is_move_operation op args = Some a -> + op = Omove /\ args = a :: nil. +Proof. + intros until a. unfold is_move_operation; destruct op; + try (intros; discriminate). + destruct args. intros; discriminate. + destruct args. intros. intuition congruence. + intros; discriminate. +Qed. + +(** [negate_condition cond] returns a condition that is logically + equivalent to the negation of [cond]. *) + +Definition negate_condition (cond: condition): condition := + match cond with + | Ccomp c => Ccomp (negate_comparison c) + | Ccompu c => Ccompu (negate_comparison c) + | Ccompimm c n => Ccompimm (negate_comparison c) n + | Ccompuimm c n => Ccompuimm (negate_comparison c) n + | Ccompshift c s a => Ccompshift (negate_comparison c) s a + | Ccompushift c s a => Ccompushift (negate_comparison c) s a + | Cmaskzero n => Cmasknotzero n + | Cmasknotzero n => Cmaskzero n + | Ccompl c => Ccompl (negate_comparison c) + | Ccomplu c => Ccomplu (negate_comparison c) + | Ccomplimm c n => Ccomplimm (negate_comparison c) n + | Ccompluimm c n => Ccompluimm (negate_comparison c) n + | Ccomplshift c s a => Ccomplshift (negate_comparison c) s a + | Ccomplushift c s a => Ccomplushift (negate_comparison c) s a + | Cmasklzero n => Cmasklnotzero n + | Cmasklnotzero n => Cmasklzero n + | Ccompf c => Cnotcompf c + | Cnotcompf c => Ccompf c + | Ccompfzero c => Cnotcompfzero c + | Cnotcompfzero c => Ccompfzero c + | Ccompfs c => Cnotcompfs c + | Cnotcompfs c => Ccompfs c + | Ccompfszero c => Cnotcompfszero c + | Cnotcompfszero c => Ccompfszero c + end. + +Lemma eval_negate_condition: + forall cond vl m, + eval_condition (negate_condition cond) vl m = option_map negb (eval_condition cond vl m). +Proof. + intros. destruct cond; simpl. + repeat (destruct vl; auto). apply Val.negate_cmp_bool. + repeat (destruct vl; auto). apply Val.negate_cmpu_bool. + repeat (destruct vl; auto). apply Val.negate_cmp_bool. + repeat (destruct vl; auto). apply Val.negate_cmpu_bool. + repeat (destruct vl; auto). apply Val.negate_cmp_bool. + repeat (destruct vl; auto). apply Val.negate_cmpu_bool. + repeat (destruct vl; auto). apply (Val.negate_cmp_bool Ceq). + repeat (destruct vl; auto). apply (Val.negate_cmp_bool Cne). + repeat (destruct vl; auto). apply Val.negate_cmpl_bool. + repeat (destruct vl; auto). apply Val.negate_cmplu_bool. + repeat (destruct vl; auto). apply Val.negate_cmpl_bool. + repeat (destruct vl; auto). apply Val.negate_cmplu_bool. + repeat (destruct vl; auto). apply Val.negate_cmpl_bool. + repeat (destruct vl; auto). apply Val.negate_cmplu_bool. + repeat (destruct vl; auto). apply (Val.negate_cmpl_bool Ceq). + repeat (destruct vl; auto). apply (Val.negate_cmpl_bool Cne). + repeat (destruct vl; auto). + repeat (destruct vl; auto). destruct (Val.cmpf_bool c v v0) as [[]|]; auto. + repeat (destruct vl; auto). + repeat (destruct vl; auto). destruct (Val.cmpf_bool c v (Vfloat Float.zero)) as [[]|]; auto. + repeat (destruct vl; auto). + repeat (destruct vl; auto). destruct (Val.cmpfs_bool c v v0) as [[]|]; auto. + repeat (destruct vl; auto). + repeat (destruct vl; auto). destruct (Val.cmpfs_bool c v (Vsingle Float32.zero)) as [[]|]; auto. +Qed. + +(** Shifting stack-relative references. This is used in [Stacking]. *) + +Definition shift_stack_addressing (delta: Z) (addr: addressing) := + match addr with + | Ainstack ofs => Ainstack (Ptrofs.add ofs (Ptrofs.repr delta)) + | _ => addr + end. + +Definition shift_stack_operation (delta: Z) (op: operation) := + match op with + | Oaddrstack ofs => Oaddrstack (Ptrofs.add ofs (Ptrofs.repr delta)) + | _ => op + end. + +Lemma type_shift_stack_addressing: + forall delta addr, type_of_addressing (shift_stack_addressing delta addr) = type_of_addressing addr. +Proof. + intros. destruct addr; auto. +Qed. + +Lemma type_shift_stack_operation: + forall delta op, type_of_operation (shift_stack_operation delta op) = type_of_operation op. +Proof. + intros. destruct op; auto. +Qed. + +Lemma eval_shift_stack_addressing: + forall F V (ge: Genv.t F V) sp addr vl delta, + eval_addressing ge (Vptr sp Ptrofs.zero) (shift_stack_addressing delta addr) vl = + eval_addressing ge (Vptr sp (Ptrofs.repr delta)) addr vl. +Proof. + intros. destruct addr; simpl; auto. destruct vl; auto. + rewrite Ptrofs.add_zero_l, Ptrofs.add_commut; auto. +Qed. + +Lemma eval_shift_stack_operation: + forall F V (ge: Genv.t F V) sp op vl m delta, + eval_operation ge (Vptr sp Ptrofs.zero) (shift_stack_operation delta op) vl m = + eval_operation ge (Vptr sp (Ptrofs.repr delta)) op vl m. +Proof. + intros. destruct op; simpl; auto. destruct vl; auto. + rewrite Ptrofs.add_zero_l, Ptrofs.add_commut; auto. +Qed. + +(** Offset an addressing mode [addr] by a quantity [delta], so that + it designates the pointer [delta] bytes past the pointer designated + by [addr]. May be undefined, in which case [None] is returned. *) + +Definition offset_addressing (addr: addressing) (delta: Z) : option addressing := + match addr with + | Aindexed n => Some(Aindexed (Int64.add n (Int64.repr delta))) + | Aindexed2 => None + | Aindexed2shift _ => None + | Aindexed2ext _ _ => None + | Aglobal id n => Some(Aglobal id (Ptrofs.add n (Ptrofs.repr delta))) + | Ainstack n => Some(Ainstack (Ptrofs.add n (Ptrofs.repr delta))) + end. + +Lemma eval_offset_addressing: + forall (F V: Type) (ge: Genv.t F V) sp addr args delta addr' v, + offset_addressing addr delta = Some addr' -> + eval_addressing ge sp addr args = Some v -> + Archi.ptr64 = false -> + eval_addressing ge sp addr' args = Some(Val.add v (Vint (Int.repr delta))). +Proof. + intros. discriminate. +Qed. + +(** Operations that are so cheap to recompute that CSE should not factor them out. *) + +Definition is_trivial_op (op: operation) : bool := + match op with + | Omove => true + | Ointconst n => Int.eq (Int.sign_ext 16 n) n + | Olongconst n => Int64.eq (Int64.sign_ext 16 n) n + | Oaddrstack _ => true + | _ => false + end. + +(** Operations that depend on the memory state. *) + +Definition cond_depends_on_memory (c: condition) : bool := + match c with + | Ccomplu _ | Ccompluimm _ _ | Ccomplushift _ _ _ => true + | _ => false + end. + +Lemma cond_depends_on_memory_correct: + forall c args m1 m2, + cond_depends_on_memory c = false -> + eval_condition c args m1 = eval_condition c args m2. +Proof. + intros; destruct c; simpl; discriminate || reflexivity. +Qed. + +Definition op_depends_on_memory (op: operation) : bool := + match op with + | Ocmp c => cond_depends_on_memory c + | Osel c yu => cond_depends_on_memory c + | _ => false + end. + +Lemma op_depends_on_memory_correct: + forall (F V: Type) (ge: Genv.t F V) sp op args m1 m2, + op_depends_on_memory op = false -> + eval_operation ge sp op args m1 = eval_operation ge sp op args m2. +Proof. + intros. destruct op; auto. + simpl. rewrite (cond_depends_on_memory_correct cond args m1 m2 H). auto. + simpl. destruct args; auto. destruct args; auto. + rewrite (cond_depends_on_memory_correct cond args m1 m2 H). auto. +Qed. + +(** Global variables mentioned in an operation or addressing mode *) + +Definition globals_addressing (addr: addressing) : list ident := + match addr with + | Aglobal s ofs => s :: nil + | _ => nil + end. + +Definition globals_operation (op: operation) : list ident := + match op with + | Oaddrsymbol s ofs => s :: nil + | _ => nil + end. + +(** * Invariance and compatibility properties. *) + +(** [eval_operation] and [eval_addressing] depend on a global environment + for resolving references to global symbols. We show that they give + the same results if a global environment is replaced by another that + assigns the same addresses to the same symbols. *) + +Section GENV_TRANSF. + +Variable F1 F2 V1 V2: Type. +Variable ge1: Genv.t F1 V1. +Variable ge2: Genv.t F2 V2. +Hypothesis agree_on_symbols: + forall (s: ident), Genv.find_symbol ge2 s = Genv.find_symbol ge1 s. + +Lemma eval_addressing_preserved: + forall sp addr vl, + eval_addressing ge2 sp addr vl = eval_addressing ge1 sp addr vl. +Proof. + intros. + unfold eval_addressing; destruct addr; auto. destruct vl; auto. + unfold Genv.symbol_address. rewrite agree_on_symbols; auto. +Qed. + +Lemma eval_operation_preserved: + forall sp op vl m, + eval_operation ge2 sp op vl m = eval_operation ge1 sp op vl m. +Proof. + intros. + unfold eval_operation; destruct op; auto. destruct vl; auto. + unfold Genv.symbol_address. rewrite agree_on_symbols; auto. +Qed. + +End GENV_TRANSF. + +(** Compatibility of the evaluation functions with value injections. *) + +Section EVAL_COMPAT. + +Variable F1 F2 V1 V2: Type. +Variable ge1: Genv.t F1 V1. +Variable ge2: Genv.t F2 V2. +Variable f: meminj. + +Variable m1: mem. +Variable m2: mem. + +Hypothesis valid_pointer_inj: + forall b1 ofs b2 delta, + f b1 = Some(b2, delta) -> + Mem.valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + Mem.valid_pointer m2 b2 (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr delta))) = true. + +Hypothesis weak_valid_pointer_inj: + forall b1 ofs b2 delta, + f b1 = Some(b2, delta) -> + Mem.weak_valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + Mem.weak_valid_pointer m2 b2 (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr delta))) = true. + +Hypothesis weak_valid_pointer_no_overflow: + forall b1 ofs b2 delta, + f b1 = Some(b2, delta) -> + Mem.weak_valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + 0 <= Ptrofs.unsigned ofs + Ptrofs.unsigned (Ptrofs.repr delta) <= Ptrofs.max_unsigned. + +Hypothesis valid_different_pointers_inj: + forall b1 ofs1 b2 ofs2 b1' delta1 b2' delta2, + b1 <> b2 -> + Mem.valid_pointer m1 b1 (Ptrofs.unsigned ofs1) = true -> + Mem.valid_pointer m1 b2 (Ptrofs.unsigned ofs2) = true -> + f b1 = Some (b1', delta1) -> + f b2 = Some (b2', delta2) -> + b1' <> b2' \/ + Ptrofs.unsigned (Ptrofs.add ofs1 (Ptrofs.repr delta1)) <> Ptrofs.unsigned (Ptrofs.add ofs2 (Ptrofs.repr delta2)). + +Ltac InvInject := + match goal with + | [ H: Val.inject _ (Vint _) _ |- _ ] => + inv H; InvInject + | [ H: Val.inject _ (Vfloat _) _ |- _ ] => + inv H; InvInject + | [ H: Val.inject _ (Vptr _ _) _ |- _ ] => + inv H; InvInject + | [ H: Val.inject_list _ nil _ |- _ ] => + inv H; InvInject + | [ H: Val.inject_list _ (_ :: _) _ |- _ ] => + inv H; InvInject + | _ => idtac + end. + +Lemma eval_shift_inject: + forall v1 v2 s a, + Val.inject f v1 v2 -> Val.inject f (eval_shift s v1 a) (eval_shift s v2 a). +Proof. + intros; inv H; destruct s; simpl; auto; rewrite a32_range; auto. +Qed. + +Lemma eval_shiftl_inject: + forall v1 v2 s a, + Val.inject f v1 v2 -> Val.inject f (eval_shiftl s v1 a) (eval_shiftl s v2 a). +Proof. + intros; inv H; destruct s; simpl; auto; rewrite a64_range; auto. +Qed. + +Lemma eval_extend_inject: + forall v1 v2 x a, + Val.inject f v1 v2 -> Val.inject f (eval_extend x v1 a) (eval_extend x v2 a). +Proof. + unfold eval_extend; intros; inv H; destruct x; simpl; auto; rewrite a64_range; auto. +Qed. + +Lemma eval_condition_inj: + forall cond vl1 vl2 b, + Val.inject_list f vl1 vl2 -> + eval_condition cond vl1 m1 = Some b -> + eval_condition cond vl2 m2 = Some b. +Proof. + intros. destruct cond; simpl in H0; FuncInv; InvInject; simpl; auto. +(* 32-bit integers *) +- inv H3; inv H2; simpl in H0; inv H0; auto. +- eauto 3 using Val.cmpu_bool_inject, Mem.valid_pointer_implies. +- inv H3; simpl in H0; inv H0; auto. +- eauto 3 using Val.cmpu_bool_inject, Mem.valid_pointer_implies. +- revert H0. generalize (eval_shift_inject s a H2); intros J; inv H3; inv J; simpl; congruence. +- eauto 3 using Val.cmpu_bool_inject, Mem.valid_pointer_implies, eval_shift_inject. +- inv H3; inv H0; auto. +- inv H3; inv H0; auto. +(* 64-bit integers *) +- inv H3; inv H2; simpl in H0; inv H0; auto. +- eauto 3 using Val.cmplu_bool_inject, Mem.valid_pointer_implies. +- inv H3; simpl in H0; inv H0; auto. +- eauto 3 using Val.cmplu_bool_inject, Mem.valid_pointer_implies. +- revert H0. generalize (eval_shiftl_inject s a H2); intros J; inv H3; inv J; simpl; congruence. +- eauto 3 using Val.cmplu_bool_inject, Mem.valid_pointer_implies, eval_shiftl_inject. +- inv H3; inv H0; auto. +- inv H3; inv H0; auto. +(* 64-bit floats *) +- inv H3; inv H2; simpl in H0; inv H0; auto. +- inv H3; inv H2; simpl in H0; inv H0; auto. +- inv H3; simpl in H0; inv H0; auto. +- inv H3; simpl in H0; inv H0; auto. +(* 32-bit floats *) +- inv H3; inv H2; simpl in H0; inv H0; auto. +- inv H3; inv H2; simpl in H0; inv H0; auto. +- inv H3; simpl in H0; inv H0; auto. +- inv H3; simpl in H0; inv H0; auto. +Qed. + +Ltac TrivialExists := + match goal with + | [ |- exists v2, Some ?v1 = Some v2 /\ Val.inject _ _ v2 ] => + exists v1; split; auto + | _ => idtac + end. + +Lemma eval_operation_inj: + forall op sp1 vl1 sp2 vl2 v1, + (forall id ofs, + In id (globals_operation op) -> + Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> + Val.inject f sp1 sp2 -> + Val.inject_list f vl1 vl2 -> + eval_operation ge1 sp1 op vl1 m1 = Some v1 -> + exists v2, eval_operation ge2 sp2 op vl2 m2 = Some v2 /\ Val.inject f v1 v2. +Proof. + intros until v1; intros GL; intros. destruct op; simpl in H1; simpl; FuncInv; InvInject; TrivialExists. + (* addrsymbol *) + - apply GL; simpl; auto. + (* addrstack *) + - apply Val.offset_ptr_inject; auto. + (* shift *) + - apply eval_shift_inject; auto. + (* add *) + - apply Val.add_inject; auto. + - apply Val.add_inject; auto using eval_shift_inject. + - apply Val.add_inject; auto. + (* neg, sub *) + - inv H4; simpl; auto. + - generalize (eval_shift_inject s a H4); intros J; inv J; simpl; auto. + - apply Val.sub_inject; auto. + - apply Val.sub_inject; auto using eval_shift_inject. + (* mul, muladd, mulsub *) + - inv H4; inv H2; simpl; auto. + - apply Val.add_inject; auto. inv H2; inv H3; simpl; auto. + - apply Val.sub_inject; auto. inv H2; inv H3; simpl; auto. + (* div, divu *) + - inv H4; inv H3; simpl in H1; inv H1. simpl. + destruct (Int.eq i0 Int.zero + || Int.eq i (Int.repr Int.min_signed) && Int.eq i0 Int.mone); inv H2. + TrivialExists. + - inv H4; inv H3; simpl in H1; inv H1. simpl. + destruct (Int.eq i0 Int.zero); inv H2. TrivialExists. + (* and*) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* or *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* xor *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* not *) + - inv H4; simpl; auto. + - generalize (eval_shift_inject s a H4); intros J; inv J; simpl; auto. + (* bic *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* nor *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* eqv *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shift_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* shl *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int.iwordsize); auto. + (* shr *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int.iwordsize); auto. + (* shru *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int.iwordsize); auto. + (* shrx *) + - inv H4; simpl in H1; try discriminate. simpl. + destruct (Int.ltu n (Int.repr 31)); inv H1. TrivialExists. + (* shift-ext *) + - inv H4; simpl; auto. + - inv H4; simpl; auto. + - inv H4; simpl; auto; rewrite a32_range; auto. + - inv H4; simpl; auto; rewrite a32_range; auto. + - inv H4; simpl; auto; rewrite a32_range; simpl; auto. + - inv H4; simpl; auto; rewrite a32_range; simpl; auto. + + (* shiftl *) + - apply eval_shiftl_inject; auto. + (* extend *) + - apply eval_extend_inject; auto. + (* makelong, low, high *) + - inv H4; inv H2; simpl; auto. + - inv H4; simpl; auto. + - inv H4; simpl; auto. + (* addl *) + - apply Val.addl_inject; auto. + - apply Val.addl_inject; auto using eval_shiftl_inject. + - apply Val.addl_inject; auto using eval_extend_inject. + - apply Val.addl_inject; auto. + (* negl, subl *) + - inv H4; simpl; auto. + - generalize (eval_shiftl_inject s a H4); intros J; inv J; simpl; auto. + - apply Val.subl_inject; auto. + - apply Val.subl_inject; auto using eval_shiftl_inject. + - apply Val.subl_inject; auto using eval_extend_inject. + (* mull, mulladd, mullsub, mullhs, mullhu *) + - inv H4; inv H2; simpl; auto. + - apply Val.addl_inject; auto. inv H2; inv H3; simpl; auto. + - apply Val.subl_inject; auto. inv H2; inv H3; simpl; auto. + - inv H4; inv H2; simpl; auto. + - inv H4; inv H2; simpl; auto. + (* divl, divlu *) + - inv H4; inv H3; simpl in H1; inv H1. simpl. + destruct (Int64.eq i0 Int64.zero + || Int64.eq i (Int64.repr Int64.min_signed) && Int64.eq i0 Int64.mone); inv H2. + TrivialExists. + - inv H4; inv H3; simpl in H1; inv H1. simpl. + destruct (Int64.eq i0 Int64.zero); inv H2. TrivialExists. + (* andl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* orl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* xorl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + - inv H4; simpl; auto. + (* notl *) + - inv H4; simpl; auto. + - generalize (eval_shiftl_inject s a H4); intros J; inv J; simpl; auto. + (* bicl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* norl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* eqvl *) + - inv H4; inv H2; simpl; auto. + - generalize (eval_shiftl_inject s a H2); intros J; inv H4; inv J; simpl; auto. + (* shll *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int64.iwordsize'); auto. + (* shrl *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int64.iwordsize'); auto. + (* shrlu *) + - inv H4; inv H2; simpl; auto. destruct (Int.ltu i0 Int64.iwordsize'); auto. + (* shrlx *) + - inv H4; simpl in H1; try discriminate. simpl. + destruct (Int.ltu n (Int.repr 63)); inv H1. TrivialExists. + (* shift-ext *) + - inv H4; simpl; auto. + - inv H4; simpl; auto. + - inv H4; simpl; auto; rewrite a64_range; auto. + - inv H4; simpl; auto; rewrite a64_range; auto. + - inv H4; simpl; auto; rewrite a64_range; simpl; auto. + - inv H4; simpl; auto; rewrite a64_range; simpl; auto. + + (* negf, absf *) + - inv H4; simpl; auto. + - inv H4; simpl; auto. + (* addf, subf *) + - inv H4; inv H2; simpl; auto. + - inv H4; inv H2; simpl; auto. + (* mulf, divf *) + - inv H4; inv H2; simpl; auto. + - inv H4; inv H2; simpl; auto. + (* negfs, absfs *) + - inv H4; simpl; auto. + - inv H4; simpl; auto. + (* addfs, subfs *) + - inv H4; inv H2; simpl; auto. + - inv H4; inv H2; simpl; auto. + (* mulfs, divfs *) + - inv H4; inv H2; simpl; auto. + - inv H4; inv H2; simpl; auto. + (* singleoffloat, floatofsingle *) + - inv H4; simpl; auto. + - inv H4; simpl; auto. + (* intoffloat, intuoffloat *) + - inv H4; simpl in H1; inv H1. simpl. destruct (Float.to_int f0); simpl in H2; inv H2. + exists (Vint i); auto. + - inv H4; simpl in H1; inv H1. simpl. destruct (Float.to_intu f0); simpl in H2; inv H2. + exists (Vint i); auto. + (* floatofint, floatofintu *) + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + (* intofsingle, intuofsingle *) + - inv H4; simpl in H1; inv H1. simpl. destruct (Float32.to_int f0); simpl in H2; inv H2. + exists (Vint i); auto. + - inv H4; simpl in H1; inv H1. simpl. destruct (Float32.to_intu f0); simpl in H2; inv H2. + exists (Vint i); auto. + (* singleofint, singleofintu *) + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + (* longoffloat, longuoffloat *) + - inv H4; simpl in H1; inv H1. simpl. destruct (Float.to_long f0); simpl in H2; inv H2. + exists (Vlong i); auto. + - inv H4; simpl in H1; inv H1. simpl. destruct (Float.to_longu f0); simpl in H2; inv H2. + exists (Vlong i); auto. + (* floatoflong, floatoflongu *) + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + (* longofsingle, longuofsingle *) + - inv H4; simpl in H1; inv H1. simpl. destruct (Float32.to_long f0); simpl in H2; inv H2. + exists (Vlong i); auto. + - inv H4; simpl in H1; inv H1. simpl. destruct (Float32.to_longu f0); simpl in H2; inv H2. + exists (Vlong i); auto. + (* singleoflong, singleoflongu *) + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + - inv H4; simpl in H1; inv H1. simpl. TrivialExists. + (* cmp, sel *) + - subst v1. destruct (eval_condition cond vl1 m1) eqn:?. + exploit eval_condition_inj; eauto. intros EQ; rewrite EQ. + destruct b; simpl; constructor. + simpl; constructor. + - apply Val.select_inject; auto. + destruct (eval_condition cond vl1 m1) eqn:?; auto. + right; symmetry; eapply eval_condition_inj; eauto. +Qed. + +Lemma eval_addressing_inj: + forall addr sp1 vl1 sp2 vl2 v1, + (forall id ofs, + In id (globals_addressing addr) -> + Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> + Val.inject f sp1 sp2 -> + Val.inject_list f vl1 vl2 -> + eval_addressing ge1 sp1 addr vl1 = Some v1 -> + exists v2, eval_addressing ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2. +Proof. + intros. destruct addr; simpl in H2; simpl; FuncInv; InvInject; TrivialExists. +- apply Val.addl_inject; auto. +- apply Val.addl_inject; auto. +- apply Val.addl_inject; auto. inv H3; simpl; auto; rewrite a64_range; auto. +- apply Val.addl_inject; auto using eval_extend_inject. +- apply H; simpl; auto. +- apply Val.offset_ptr_inject; auto. +Qed. + +End EVAL_COMPAT. + +(** Compatibility of the evaluation functions with the ``is less defined'' relation over values. *) + +Section EVAL_LESSDEF. + +Variable F V: Type. +Variable genv: Genv.t F V. + +Remark valid_pointer_extends: + forall m1 m2, Mem.extends m1 m2 -> + forall b1 ofs b2 delta, + Some(b1, 0) = Some(b2, delta) -> + Mem.valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + Mem.valid_pointer m2 b2 (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr delta))) = true. +Proof. + intros. inv H0. rewrite Ptrofs.add_zero. eapply Mem.valid_pointer_extends; eauto. +Qed. + +Remark weak_valid_pointer_extends: + forall m1 m2, Mem.extends m1 m2 -> + forall b1 ofs b2 delta, + Some(b1, 0) = Some(b2, delta) -> + Mem.weak_valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + Mem.weak_valid_pointer m2 b2 (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr delta))) = true. +Proof. + intros. inv H0. rewrite Ptrofs.add_zero. eapply Mem.weak_valid_pointer_extends; eauto. +Qed. + +Remark weak_valid_pointer_no_overflow_extends: + forall m1 b1 ofs b2 delta, + Some(b1, 0) = Some(b2, delta) -> + Mem.weak_valid_pointer m1 b1 (Ptrofs.unsigned ofs) = true -> + 0 <= Ptrofs.unsigned ofs + Ptrofs.unsigned (Ptrofs.repr delta) <= Ptrofs.max_unsigned. +Proof. + intros. inv H. rewrite Z.add_0_r. apply Ptrofs.unsigned_range_2. +Qed. + +Remark valid_different_pointers_extends: + forall m1 b1 ofs1 b2 ofs2 b1' delta1 b2' delta2, + b1 <> b2 -> + Mem.valid_pointer m1 b1 (Ptrofs.unsigned ofs1) = true -> + Mem.valid_pointer m1 b2 (Ptrofs.unsigned ofs2) = true -> + Some(b1, 0) = Some (b1', delta1) -> + Some(b2, 0) = Some (b2', delta2) -> + b1' <> b2' \/ + Ptrofs.unsigned(Ptrofs.add ofs1 (Ptrofs.repr delta1)) <> Ptrofs.unsigned(Ptrofs.add ofs2 (Ptrofs.repr delta2)). +Proof. + intros. inv H2; inv H3. auto. +Qed. + +Lemma eval_condition_lessdef: + forall cond vl1 vl2 b m1 m2, + Val.lessdef_list vl1 vl2 -> + Mem.extends m1 m2 -> + eval_condition cond vl1 m1 = Some b -> + eval_condition cond vl2 m2 = Some b. +Proof. + intros. eapply eval_condition_inj with (f := fun b => Some(b, 0)) (m1 := m1). + apply valid_pointer_extends; auto. + apply weak_valid_pointer_extends; auto. + apply weak_valid_pointer_no_overflow_extends. + apply valid_different_pointers_extends; auto. + rewrite <- val_inject_list_lessdef. eauto. auto. +Qed. + +Lemma eval_operation_lessdef: + forall sp op vl1 vl2 v1 m1 m2, + Val.lessdef_list vl1 vl2 -> + Mem.extends m1 m2 -> + eval_operation genv sp op vl1 m1 = Some v1 -> + exists v2, eval_operation genv sp op vl2 m2 = Some v2 /\ Val.lessdef v1 v2. +Proof. + intros. rewrite val_inject_list_lessdef in H. + assert (exists v2 : val, + eval_operation genv sp op vl2 m2 = Some v2 + /\ Val.inject (fun b => Some(b, 0)) v1 v2). + eapply eval_operation_inj with (m1 := m1) (sp1 := sp). + apply valid_pointer_extends; auto. + apply weak_valid_pointer_extends; auto. + apply weak_valid_pointer_no_overflow_extends. + apply valid_different_pointers_extends; auto. + intros. apply val_inject_lessdef. auto. + apply val_inject_lessdef; auto. + eauto. + auto. + destruct H2 as [v2 [A B]]. exists v2; split; auto. rewrite val_inject_lessdef; auto. +Qed. + +Lemma eval_addressing_lessdef: + forall sp addr vl1 vl2 v1, + Val.lessdef_list vl1 vl2 -> + eval_addressing genv sp addr vl1 = Some v1 -> + exists v2, eval_addressing genv sp addr vl2 = Some v2 /\ Val.lessdef v1 v2. +Proof. + intros. rewrite val_inject_list_lessdef in H. + assert (exists v2 : val, + eval_addressing genv sp addr vl2 = Some v2 + /\ Val.inject (fun b => Some(b, 0)) v1 v2). + eapply eval_addressing_inj with (sp1 := sp). + intros. rewrite <- val_inject_lessdef; auto. + rewrite <- val_inject_lessdef; auto. + eauto. auto. + destruct H1 as [v2 [A B]]. exists v2; split; auto. rewrite val_inject_lessdef; auto. +Qed. + +End EVAL_LESSDEF. + +(** Compatibility of the evaluation functions with memory injections. *) + +Section EVAL_INJECT. + +Variable F V: Type. +Variable genv: Genv.t F V. +Variable f: meminj. +Hypothesis globals: meminj_preserves_globals genv f. +Variable sp1: block. +Variable sp2: block. +Variable delta: Z. +Hypothesis sp_inj: f sp1 = Some(sp2, delta). + +Remark symbol_address_inject: + forall id ofs, Val.inject f (Genv.symbol_address genv id ofs) (Genv.symbol_address genv id ofs). +Proof. + intros. unfold Genv.symbol_address. destruct (Genv.find_symbol genv id) eqn:?; auto. + exploit (proj1 globals); eauto. intros. + econstructor; eauto. rewrite Ptrofs.add_zero; auto. +Qed. + +Lemma eval_condition_inject: + forall cond vl1 vl2 b m1 m2, + Val.inject_list f vl1 vl2 -> + Mem.inject f m1 m2 -> + eval_condition cond vl1 m1 = Some b -> + eval_condition cond vl2 m2 = Some b. +Proof. + intros. eapply eval_condition_inj with (f := f) (m1 := m1); eauto. + intros; eapply Mem.valid_pointer_inject_val; eauto. + intros; eapply Mem.weak_valid_pointer_inject_val; eauto. + intros; eapply Mem.weak_valid_pointer_inject_no_overflow; eauto. + intros; eapply Mem.different_pointers_inject; eauto. +Qed. + +Lemma eval_addressing_inject: + forall addr vl1 vl2 v1, + Val.inject_list f vl1 vl2 -> + eval_addressing genv (Vptr sp1 Ptrofs.zero) addr vl1 = Some v1 -> + exists v2, + eval_addressing genv (Vptr sp2 Ptrofs.zero) (shift_stack_addressing delta addr) vl2 = Some v2 + /\ Val.inject f v1 v2. +Proof. + intros. + rewrite eval_shift_stack_addressing. + eapply eval_addressing_inj with (sp1 := Vptr sp1 Ptrofs.zero); eauto. + intros. apply symbol_address_inject. + econstructor; eauto. rewrite Ptrofs.add_zero_l; auto. +Qed. + +Lemma eval_operation_inject: + forall op vl1 vl2 v1 m1 m2, + Val.inject_list f vl1 vl2 -> + Mem.inject f m1 m2 -> + eval_operation genv (Vptr sp1 Ptrofs.zero) op vl1 m1 = Some v1 -> + exists v2, + eval_operation genv (Vptr sp2 Ptrofs.zero) (shift_stack_operation delta op) vl2 m2 = Some v2 + /\ Val.inject f v1 v2. +Proof. + intros. + rewrite eval_shift_stack_operation. simpl. + eapply eval_operation_inj with (sp1 := Vptr sp1 Ptrofs.zero) (m1 := m1); eauto. + intros; eapply Mem.valid_pointer_inject_val; eauto. + intros; eapply Mem.weak_valid_pointer_inject_val; eauto. + intros; eapply Mem.weak_valid_pointer_inject_no_overflow; eauto. + intros; eapply Mem.different_pointers_inject; eauto. + intros. apply symbol_address_inject. + econstructor; eauto. rewrite Ptrofs.add_zero_l; auto. +Qed. + +End EVAL_INJECT. + +(** * Handling of builtin arguments *) + +Definition builtin_arg_ok_1 + (A: Type) (ba: builtin_arg A) (c: builtin_arg_constraint) := + match c, ba with + | OK_all, _ => true + | OK_const, (BA_int _ | BA_long _ | BA_float _ | BA_single _) => true + | OK_addrstack, BA_addrstack _ => true + | OK_addressing, BA_addrstack _ => true + | OK_addressing, BA_addptr (BA _) (BA_int _) => true + | OK_addressing, BA_addptr (BA _) (BA_long _) => true + | _, _ => false + end. + +Definition builtin_arg_ok + (A: Type) (ba: builtin_arg A) (c: builtin_arg_constraint) := + match ba with + | (BA _ | BA_splitlong (BA _) (BA _)) => true + | _ => builtin_arg_ok_1 ba c + end. diff --git a/aarch64/PrintOp.ml b/aarch64/PrintOp.ml new file mode 100644 index 00000000..1780104c --- /dev/null +++ b/aarch64/PrintOp.ml @@ -0,0 +1,247 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Pretty-printing of operators, conditions, addressing modes *) + +open Printf +open Camlcoq +open Integers +open Op + +let comparison_name = function + | Ceq -> "==" + | Cne -> "!=" + | Clt -> "<" + | Cle -> "<=" + | Cgt -> ">" + | Cge -> ">=" + +let shift pp (s, a) = + match s with + | Slsl -> fprintf pp "<< %ld" (camlint_of_coqint a) + | Slsr -> fprintf pp ">>u %ld" (camlint_of_coqint a) + | Sasr -> fprintf pp ">>s %ld" (camlint_of_coqint a) + | Sror -> fprintf pp "ror %ld" (camlint_of_coqint a) + +let shiftl pp (s, a) = + match s with + | Slsl -> fprintf pp "< fprintf pp ">>lu %ld" (camlint_of_coqint a) + | Sasr -> fprintf pp ">>ls %ld" (camlint_of_coqint a) + | Sror -> fprintf pp "rorl %ld" (camlint_of_coqint a) + +let extend_name = function + | Xsgn32 -> "sext" + | Xuns32 -> "zext" + +let print_condition reg pp = function + | (Ccomp c, [r1;r2]) -> + fprintf pp "%a %ss %a" reg r1 (comparison_name c) reg r2 + | (Ccompu c, [r1;r2]) -> + fprintf pp "%a %su %a" reg r1 (comparison_name c) reg r2 + | (Ccompimm(c, n), [r1]) -> + fprintf pp "%a %ss %ld" reg r1 (comparison_name c) (camlint_of_coqint n) + | (Ccompuimm(c, n), [r1]) -> + fprintf pp "%a %su %ld" reg r1 (comparison_name c) (camlint_of_coqint n) + | (Ccompshift(c, s, a), [r1;r2]) -> + fprintf pp "%a %ss %a %a" reg r1 (comparison_name c) reg r2 shift (s, a) + | (Ccompushift(c, s, a), [r1;r2]) -> + fprintf pp "%a %su %a %a" reg r1 (comparison_name c) reg r2 shift (s, a) + | (Cmaskzero n, [r1]) -> + fprintf pp "%a & 0x%lx == 0" reg r1 (camlint_of_coqint n) + | (Cmasknotzero n, [r1]) -> + fprintf pp "%a & 0x%lx != 0" reg r1 (camlint_of_coqint n) + | (Ccompl c, [r1;r2]) -> + fprintf pp "%a %sls %a" reg r1 (comparison_name c) reg r2 + | (Ccomplu c, [r1;r2]) -> + fprintf pp "%a %slu %a" reg r1 (comparison_name c) reg r2 + | (Ccomplimm(c, n), [r1]) -> + fprintf pp "%a %sls %Ld" reg r1 (comparison_name c) (camlint64_of_coqint n) + | (Ccompluimm(c, n), [r1]) -> + fprintf pp "%a %slu %Ld" reg r1 (comparison_name c) (camlint64_of_coqint n) + | (Ccomplshift(c, s, a), [r1;r2]) -> + fprintf pp "%a %sls %a %a" reg r1 (comparison_name c) reg r2 shift (s, a) + | (Ccomplushift(c, s, a), [r1;r2]) -> + fprintf pp "%a %slu %a %a" reg r1 (comparison_name c) reg r2 shift (s, a) + | (Cmasklzero n, [r1]) -> + fprintf pp "%a & 0x%Lx == 0" reg r1 (camlint64_of_coqint n) + | (Cmasklnotzero n, [r1]) -> + fprintf pp "%a & 0x%Lx != 0" reg r1 (camlint64_of_coqint n) + | (Ccompf c, [r1;r2]) -> + fprintf pp "%a %sf %a" reg r1 (comparison_name c) reg r2 + | (Cnotcompf c, [r1;r2]) -> + fprintf pp "%a not(%sf) %a" reg r1 (comparison_name c) reg r2 + | (Ccompfzero c, [r1]) -> + fprintf pp "%a %sf 0.0" reg r1 (comparison_name c) + | (Cnotcompfzero c, [r1]) -> + fprintf pp "%a not(%sf) 0.0" reg r1 (comparison_name c) + | (Ccompfs c, [r1;r2]) -> + fprintf pp "%a %sfs %a" reg r1 (comparison_name c) reg r2 + | (Cnotcompfs c, [r1;r2]) -> + fprintf pp "%a not(%sfs) %a" reg r1 (comparison_name c) reg r2 + | (Ccompfszero c, [r1]) -> + fprintf pp "%a %sfs 0.0" reg r1 (comparison_name c) + | (Cnotcompfszero c, [r1]) -> + fprintf pp "%a not(%sfs) 0.0" reg r1 (comparison_name c) + | _ -> + fprintf pp "" + +let print_operation reg pp = function + | Omove, [r1] -> reg pp r1 + | Ointconst n, [] -> fprintf pp "%ld" (camlint_of_coqint n) + | Olongconst n, [] -> fprintf pp "%LdL" (camlint64_of_coqint n) + | Ofloatconst n, [] -> fprintf pp "%F" (camlfloat_of_coqfloat n) + | Osingleconst n, [] -> fprintf pp "%Ff" (camlfloat_of_coqfloat32 n) + | Oaddrsymbol(id, ofs), [] -> + fprintf pp "\"%s\" + %Ld" (extern_atom id) (camlint64_of_ptrofs ofs) + | Oaddrstack ofs, [] -> + fprintf pp "stack(%Ld)" (camlint64_of_ptrofs ofs) +(* 32-bit integer arithmetic *) + | Oshift(s, a), [r1] -> fprintf pp "%a %a" reg r1 shift (s,a) + | Oadd, [r1;r2] -> fprintf pp "%a + %a" reg r1 reg r2 + | Oaddshift(s, a), [r1;r2] -> fprintf pp "%a + %a %a" reg r1 reg r2 shift (s,a) + | Oaddimm n, [r1] -> fprintf pp "%a + %ld" reg r1 (camlint_of_coqint n) + | Oneg, [r1] -> fprintf pp "- %a" reg r1 + | Onegshift(s, a), [r1] -> fprintf pp "- (%a %a)" reg r1 shift (s,a) + | Osub, [r1;r2] -> fprintf pp "%a - %a" reg r1 reg r2 + | Osubshift(s, a), [r1;r2] -> fprintf pp "%a - %a %a" reg r1 reg r2 shift (s,a) + | Omul, [r1;r2] -> fprintf pp "%a * %a" reg r1 reg r2 + | Omuladd, [r1;r2;r3] -> fprintf pp "%a + %a * %a" reg r3 reg r1 reg r2 + | Omulsub, [r1;r2;r3] -> fprintf pp "%a - %a * %a" reg r3 reg r1 reg r2 + | Odiv, [r1;r2] -> fprintf pp "%a /s %a" reg r1 reg r2 + | Odivu, [r1;r2] -> fprintf pp "%a /u %a" reg r1 reg r2 + | Oand, [r1;r2] -> fprintf pp "%a & %a" reg r1 reg r2 + | Oandshift(s, a), [r1;r2] -> fprintf pp "%a & %a %a" reg r1 reg r2 shift (s,a) + | Oandimm n, [r1] -> fprintf pp "%a & %ld" reg r1 (camlint_of_coqint n) + | Oor, [r1;r2] -> fprintf pp "%a | %a" reg r1 reg r2 + | Oorshift(s, a), [r1;r2] -> fprintf pp "%a | %a %a" reg r1 reg r2 shift (s,a) + | Oorimm n, [r1] -> fprintf pp "%a | %ld" reg r1 (camlint_of_coqint n) + | Oxor, [r1;r2] -> fprintf pp "%a ^ %a" reg r1 reg r2 + | Oxorshift(s, a), [r1;r2] -> fprintf pp "%a ^ %a %a" reg r1 reg r2 shift (s,a) + | Oxorimm n, [r1] -> fprintf pp "%a ^ %ld" reg r1 (camlint_of_coqint n) + | Onot, [r1] -> fprintf pp "~ %a" reg r1 + | Onotshift(s, a), [r1] -> fprintf pp "~ (%a %a)" reg r1 shift (s,a) + | Obic, [r1;r2] -> fprintf pp "%a & ~ %a" reg r1 reg r2 + | Obicshift(s, a), [r1;r2] -> fprintf pp "%a & ~ %a %a" reg r1 reg r2 shift (s,a) + | Oorn, [r1;r2] -> fprintf pp "%a | ~ %a" reg r1 reg r2 + | Oornshift(s, a), [r1;r2] -> fprintf pp "%a | ~ %a %a" reg r1 reg r2 shift (s,a) + | Oeqv, [r1;r2] -> fprintf pp "%a ^ ~ %a" reg r1 reg r2 + | Oeqvshift(s, a), [r1;r2] -> fprintf pp "%a ^ ~ %a %a" reg r1 reg r2 shift (s,a) + | Oshl, [r1;r2] -> fprintf pp "%a << %a" reg r1 reg r2 + | Oshr, [r1;r2] -> fprintf pp "%a >>s %a" reg r1 reg r2 + | Oshru, [r1;r2] -> fprintf pp "%a >>u %a" reg r1 reg r2 + | Oshrximm n, [r1] -> fprintf pp "%a >>x %ld" reg r1 (camlint_of_coqint n) + | Ozext s, [r1] -> fprintf pp "zext(%d, %a)" (Z.to_int s) reg r1 + | Osext s, [r1] -> fprintf pp "sext(%d, %a)" (Z.to_int s) reg r1 + | Oshlzext(s, a), [r1] -> fprintf pp "zext(%d, %a) << %ld" (Z.to_int s) reg r1 (camlint_of_coqint a) + | Oshlsext(s, a), [r1] -> fprintf pp "sext(%d, %a) << %ld" (Z.to_int s) reg r1 (camlint_of_coqint a) + | Ozextshr(a, s), [r1] -> fprintf pp "zext(%d, %a >>u %ld)" (Z.to_int s) reg r1 (camlint_of_coqint a) + | Osextshr(a, s), [r1] -> fprintf pp "sext(%d, %a >>s %ld)" (Z.to_int s) reg r1 (camlint_of_coqint a) +(* 64-bit integer arithmetic *) + | Oshiftl(s, a), [r1] -> fprintf pp "%a %a" reg r1 shiftl (s,a) + | Oextend(x, a), [r1] -> fprintf pp "%s(32, %a) < fprintf pp "makelong(%a,%a)" reg r1 reg r2 + | Olowlong, [r1] -> fprintf pp "lowlong(%a)" reg r1 + | Ohighlong, [r1] -> fprintf pp "highlong(%a)" reg r1 + | Oaddl, [r1;r2] -> fprintf pp "%a +l %a" reg r1 reg r2 + | Oaddlshift(s, a), [r1;r2] -> fprintf pp "%a +l %a %a" reg r1 reg r2 shiftl (s,a) + | Oaddlext(x, a), [r1;r2] -> fprintf pp "%a +l %s(%a) << %ld" reg r1 (extend_name x) reg r2 (camlint_of_coqint a) + | Oaddlimm n, [r1] -> fprintf pp "%a +l %Ld" reg r1 (camlint64_of_coqint n) + | Onegl, [r1] -> fprintf pp "-l %a" reg r1 + | Oneglshift(s, a), [r1] -> fprintf pp "-l (%a %a)" reg r1 shiftl (s,a) + | Osubl, [r1;r2] -> fprintf pp "%a -l %a" reg r1 reg r2 + | Osublext(x, a), [r1;r2] -> fprintf pp "%a +l %s(%a) << %ld" reg r1 (extend_name x) reg r2 (camlint_of_coqint a) + | Osublshift(s, a), [r1;r2] -> fprintf pp "%a -l %a %a" reg r1 reg r2 shiftl (s,a) + | Omull, [r1;r2] -> fprintf pp "%a *l %a" reg r1 reg r2 + | Omulladd, [r1;r2;r3] -> fprintf pp "%a +l %a *l %a" reg r3 reg r1 reg r2 + | Omullsub, [r1;r2;r3] -> fprintf pp "%a -l %a *l %a" reg r3 reg r1 reg r2 + | Omullhs, [r1;r2] -> fprintf pp "%a *hls %a" reg r1 reg r2 + | Omullhu, [r1;r2] -> fprintf pp "%a *hlu %a" reg r1 reg r2 + | Odivl, [r1;r2] -> fprintf pp "%a /ls %a" reg r1 reg r2 + | Odivlu, [r1;r2] -> fprintf pp "%a /lu %a" reg r1 reg r2 + | Oandl, [r1;r2] -> fprintf pp "%a &l %a" reg r1 reg r2 + | Oandlshift(s, a), [r1;r2] -> fprintf pp "%a &l %a %a" reg r1 reg r2 shiftl (s,a) + | Oandlimm n, [r1] -> fprintf pp "%a &l %Ld" reg r1 (camlint64_of_coqint n) + | Oorl, [r1;r2] -> fprintf pp "%a |l %a" reg r1 reg r2 + | Oorlshift(s, a), [r1;r2] -> fprintf pp "%a |l %a %a" reg r1 reg r2 shiftl (s,a) + | Oorlimm n, [r1] -> fprintf pp "%a |l %Ld" reg r1 (camlint64_of_coqint n) + | Oxorl, [r1;r2] -> fprintf pp "%a ^l %a" reg r1 reg r2 + | Oxorlshift(s, a), [r1;r2] -> fprintf pp "%a ^l %a %a" reg r1 reg r2 shiftl (s,a) + | Oxorlimm n, [r1] -> fprintf pp "%a ^l %Ld" reg r1 (camlint64_of_coqint n) + | Onotl, [r1] -> fprintf pp "~l %a" reg r1 + | Onotlshift(s, a), [r1] -> fprintf pp "~l (%a %a)" reg r1 shiftl (s,a) + | Obicl, [r1;r2] -> fprintf pp "%a &l ~l %a" reg r1 reg r2 + | Obiclshift(s, a), [r1;r2] -> fprintf pp "%a &l ~l %a %a" reg r1 reg r2 shiftl (s,a) + | Oornl, [r1;r2] -> fprintf pp "%a |l ~l %a" reg r1 reg r2 + | Oornlshift(s, a), [r1;r2] -> fprintf pp "%a |l ~l %a %a" reg r1 reg r2 shiftl (s,a) + | Oeqvl, [r1;r2] -> fprintf pp "%a ^l ~l %a" reg r1 reg r2 + | Oeqvlshift(s, a), [r1;r2] -> fprintf pp "%a ^l ~l %a %a" reg r1 reg r2 shift (s,a) + | Oshll, [r1;r2] -> fprintf pp "%a < fprintf pp "%a >>ls %a" reg r1 reg r2 + | Oshrlu, [r1;r2] -> fprintf pp "%a >>lu %a" reg r1 reg r2 + | Oshrlximm n, [r1] -> fprintf pp "%a >>lx %ld" reg r1 (camlint_of_coqint n) + | Ozextl s, [r1] -> fprintf pp "zextl(%d, %a)" (Z.to_int s) reg r1 + | Osextl s, [r1] -> fprintf pp "sextl(%d, %a)" (Z.to_int s) reg r1 + | Oshllzext(s, a), [r1] -> fprintf pp "zextl(%d, %a) < fprintf pp "sextl(%d, %a) < fprintf pp "zextl(%d, %a >>lu %ld)" (Z.to_int s) reg r1 (camlint_of_coqint a) + | Osextshrl(a, s), [r1] -> fprintf pp "sextl(%d, %a >>ls %ld)" (Z.to_int s) reg r1 (camlint_of_coqint a) +(* 64-bit floating-point arithmetic *) + | Onegf, [r1] -> fprintf pp "negf(%a)" reg r1 + | Oabsf, [r1] -> fprintf pp "absf(%a)" reg r1 + | Oaddf, [r1;r2] -> fprintf pp "%a +f %a" reg r1 reg r2 + | Osubf, [r1;r2] -> fprintf pp "%a -f %a" reg r1 reg r2 + | Omulf, [r1;r2] -> fprintf pp "%a *f %a" reg r1 reg r2 + | Odivf, [r1;r2] -> fprintf pp "%a /f %a" reg r1 reg r2 +(* 32-bit floating-point arithmetic *) + | Onegfs, [r1] -> fprintf pp "negfs(%a)" reg r1 + | Oabsfs, [r1] -> fprintf pp "absfs(%a)" reg r1 + | Oaddfs, [r1;r2] -> fprintf pp "%a +fs %a" reg r1 reg r2 + | Osubfs, [r1;r2] -> fprintf pp "%a -fs %a" reg r1 reg r2 + | Omulfs, [r1;r2] -> fprintf pp "%a *fs %a" reg r1 reg r2 + | Odivfs, [r1;r2] -> fprintf pp "%a /fs %a" reg r1 reg r2 + | Osingleoffloat, [r1] -> fprintf pp "singleoffloat(%a)" reg r1 + | Ofloatofsingle, [r1] -> fprintf pp "floatofsingle(%a)" reg r1 +(* Conversions between int and float *) + | Ointoffloat, [r1] -> fprintf pp "intoffloat(%a)" reg r1 + | Ointuoffloat, [r1] -> fprintf pp "intuoffloat(%a)" reg r1 + | Ofloatofint, [r1] -> fprintf pp "floatofint(%a)" reg r1 + | Ofloatofintu, [r1] -> fprintf pp "floatofintu(%a)" reg r1 + | Olongoffloat, [r1] -> fprintf pp "longoffloat(%a)" reg r1 + | Olonguoffloat, [r1] -> fprintf pp "longuoffloat(%a)" reg r1 + | Ofloatoflong, [r1] -> fprintf pp "floatoflong(%a)" reg r1 + | Ofloatoflongu, [r1] -> fprintf pp "floatoflongu(%a)" reg r1 + | Ointofsingle, [r1] -> fprintf pp "intofsingle(%a)" reg r1 + | Ointuofsingle, [r1] -> fprintf pp "intuofsingle(%a)" reg r1 + | Osingleofint, [r1] -> fprintf pp "singleofint(%a)" reg r1 + | Osingleofintu, [r1] -> fprintf pp "singleofintu(%a)" reg r1 + | Olongofsingle, [r1] -> fprintf pp "longofsingle(%a)" reg r1 + | Olonguofsingle, [r1] -> fprintf pp "longuofsingle(%a)" reg r1 + | Osingleoflong, [r1] -> fprintf pp "singleoflong(%a)" reg r1 + | Osingleoflongu, [r1] -> fprintf pp "singleoflongu(%a)" reg r1 +(* Boolean tests *) + | Ocmp c, args -> print_condition reg pp (c, args) + | Osel (c, ty), r1::r2::args -> + fprintf pp "%a ?%s %a : %a" + (print_condition reg) (c, args) + (PrintAST.name_of_type ty) reg r1 reg r2 + | _ -> fprintf pp "" + +let print_addressing reg pp = function + | Aindexed n, [r1] -> fprintf pp "%a + %Ld" reg r1 (camlint64_of_coqint n) + | Aindexed2, [r1; r2] -> fprintf pp "%a + %a" reg r1 reg r2 + | Aindexed2shift a, [r1; r2] -> fprintf pp "%a + %a << %ld" reg r1 reg r2 (camlint_of_coqint a) + | Aindexed2ext(x, a), [r1; r2] -> fprintf pp "%a + %s(%a) << %ld" reg r1 (extend_name x) reg r2 (camlint_of_coqint a) + | Aglobal(id, ofs), [] -> + fprintf pp "\"%s\" + %Ld" (extern_atom id) (camlint64_of_ptrofs ofs) + | Ainstack ofs, [] -> fprintf pp "stack(%Ld)" (camlint64_of_ptrofs ofs) + | _ -> fprintf pp "" diff --git a/aarch64/SelectLong.vp b/aarch64/SelectLong.vp new file mode 100644 index 00000000..ddf6e212 --- /dev/null +++ b/aarch64/SelectLong.vp @@ -0,0 +1,478 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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 64-bit integer operations *) + +Require Import Coqlib Zbits. +Require Import Compopts AST Integers Floats. +Require Import Op CminorSel SelectOp. + +Local Open Scope cminorsel_scope. + +(** ** Constants **) + +Definition longconst (n: int64) : expr := + Eop (Olongconst n) Enil. + +(** ** Conversions *) + +Nondetfunction intoflong (e: expr) := + match e with + | Eop (Olongconst n) Enil => Eop (Ointconst (Int.repr (Int64.unsigned n))) Enil + | _ => Eop Olowlong (e ::: Enil) + end. + +Nondetfunction longofint (e: expr) := + match e with + | Eop (Ointconst n) Enil => longconst (Int64.repr (Int.signed n)) + | _ => Eop (Oextend Xsgn32 (mk_amount64 Int.zero)) (e ::: Enil) + end. + +Nondetfunction longofintu (e: expr) := + match e with + | Eop (Ointconst n) Enil => longconst (Int64.repr (Int.unsigned n)) + | _ => Eop (Oextend Xuns32 (mk_amount64 Int.zero)) (e ::: Enil) + end. + +(** ** Integer addition and pointer addition *) + +Nondetfunction addlimm (n: int64) (e: expr) := + if Int64.eq n Int64.zero then e else + match e with + | Eop (Olongconst m) Enil => longconst (Int64.add n m) + | Eop (Oaddrsymbol s m) Enil => Eop (Oaddrsymbol s (Ptrofs.add (Ptrofs.of_int64 n) m)) Enil + | Eop (Oaddrstack m) Enil => Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int64 n) m)) Enil + | Eop (Oaddlimm m) (t ::: Enil) => Eop (Oaddlimm(Int64.add n m)) (t ::: Enil) + | _ => Eop (Oaddlimm n) (e ::: Enil) + end. + +Nondetfunction addl (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => addlimm n1 t2 + | t1, Eop (Olongconst n2) Enil => addlimm n2 t1 + | Eop (Oaddlimm n1) (t1:::Enil), Eop (Oaddlimm n2) (t2:::Enil) => + addlimm (Int64.add n1 n2) (Eop Oaddl (t1:::t2:::Enil)) + | Eop (Oaddlimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil => + Eop Oaddl (Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int64 n1) n2)) Enil ::: t1 ::: Enil) + | Eop (Oaddrstack n1) Enil, Eop (Oaddlimm n2) (t2:::Enil) => + Eop Oaddl (Eop (Oaddrstack (Ptrofs.add n1 (Ptrofs.of_int64 n2))) Enil ::: t2 ::: Enil) + | Eop (Oaddlimm n1) (t1:::Enil), t2 => + addlimm n1 (Eop Oaddl (t1:::t2:::Enil)) + | t1, Eop (Oaddlimm n2) (t2:::Enil) => + addlimm n2 (Eop Oaddl (t1:::t2:::Enil)) + | Eop (Oshiftl s a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Oaddlshift s a) (t2 ::: t1 ::: Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) ?? arith_shift s => + Eop (Oaddlshift s a) (t1 ::: t2 ::: Enil) + | Eop (Oextend x a) (t1:::Enil), t2 => + Eop (Oaddlext x a) (t2 ::: t1 ::: Enil) + | t1, Eop (Oextend x a) (t2:::Enil) => + Eop (Oaddlext x a) (t1 ::: t2 ::: Enil) + | Eop Omull (t1:::t2:::Enil), t3 => + Eop Omulladd (t3:::t1:::t2:::Enil) + | t1, Eop Omull (t2:::t3:::Enil) => + Eop Omulladd (t1:::t2:::t3:::Enil) + | _, _ => Eop Oaddl (e1:::e2:::Enil) + end. + +(** ** Opposite *) + +Nondetfunction negl (e: expr) := + match e with + | Eop (Olongconst n) Enil => Eop (Olongconst (Int64.neg n)) Enil + | Eop (Oshiftl s a) (t1:::Enil) ?? arith_shift s => Eop (Oneglshift s a) (t1:::Enil) + | _ => Eop Onegl (e ::: Enil) + end. + +(** ** Integer and pointer subtraction *) + +Nondetfunction subl (e1: expr) (e2: expr) := + match e1, e2 with + | t1, Eop (Olongconst n2) Enil => + addlimm (Int64.neg n2) t1 + | Eop (Oaddlimm n1) (t1:::Enil), Eop (Oaddlimm n2) (t2:::Enil) => + addlimm (Int64.sub n1 n2) (Eop Osubl (t1:::t2:::Enil)) + | Eop (Oaddlimm n1) (t1:::Enil), t2 => + addlimm n1 (Eop Osubl (t1:::t2:::Enil)) + | t1, Eop (Oaddlimm n2) (t2:::Enil) => + addlimm (Int64.neg n2) (Eop Osubl (t1:::t2:::Enil)) + | t1, Eop (Oshiftl s a) (t2:::Enil) ?? arith_shift s => + Eop (Osublshift s a) (t1:::t2::: Enil) + | t1, Eop (Oextend x a) (t2:::Enil) => + Eop (Osublext x a) (t1 ::: t2 ::: Enil) + | t1, Eop Omull (t2:::t3:::Enil) => + Eop Omullsub (t1:::t2:::t3:::Enil) + | _, _ => Eop Osubl (e1:::e2:::Enil) + end. + +(** ** Immediate shift left *) + +Definition shllimm_base (e1: expr) (n: int) := + Eop (Oshiftl Slsl (mk_amount64 n)) (e1 ::: Enil). + +Nondetfunction shllimm (e1: expr) (n: int) := + if Int.eq n Int.zero then + e1 + else if negb (Int.ltu n Int64.iwordsize') then + Eop Oshll (e1 ::: Eop (Ointconst n) Enil ::: Enil) + else match e1 with + | Eop (Olongconst n1) Enil => + Eop (Olongconst (Int64.shl' n1 n)) Enil + | Eop (Oshiftl Slsl a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then shllimm_base t1 (Int.add a n) + else shllimm_base e1 n + | Eop (Ozextl s) (t1:::Enil) => + Eop (Oshllzext s (mk_amount64 n)) (t1:::Enil) + | Eop (Osextl s) (t1:::Enil) => + Eop (Oshllsext s (mk_amount64 n)) (t1:::Enil) + | Eop (Oshllzext s a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then Eop (Oshllzext s (mk_amount64 (Int.add a n))) (t1:::Enil) + else shllimm_base e1 n + | Eop (Oshllsext s a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then Eop (Oshllsext s (mk_amount64 (Int.add a n))) (t1:::Enil) + else shllimm_base e1 n + | Eop (Oextend x a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then Eop (Oextend x (mk_amount64 (Int.add a n))) (t1:::Enil) + else shllimm_base e1 n + | _ => + shllimm_base e1 n + end. + +(** ** Immediate shift right (logical) *) + +Definition shrluimm_base (e1: expr) (n: int) := + Eop (Oshiftl Slsr (mk_amount64 n)) (e1 ::: Enil). + +Nondetfunction shrluimm (e1: expr) (n: int) := + if Int.eq n Int.zero then + e1 + else if negb (Int.ltu n Int64.iwordsize') then + Eop Oshrlu (e1 ::: Eop (Ointconst n) Enil ::: Enil) + else match e1 with + | Eop (Olongconst n1) Enil => + Eop (Olongconst (Int64.shru' n1 n)) Enil + | Eop (Oshiftl Slsl a) (t1:::Enil) => + if Int.ltu n a + then Eop (Oshllzext (Int64.zwordsize - Int.unsigned a) (mk_amount64 (Int.sub a n))) (t1:::Enil) + else Eop (Ozextshrl (mk_amount64 (Int.sub n a)) (Int64.zwordsize - Int.unsigned n)) (t1:::Enil) + | Eop (Oshiftl Slsr a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then shrluimm_base t1 (Int.add a n) + else shrluimm_base e1 n + | Eop (Ozextl s) (t1:::Enil) => + if zlt (Int.unsigned n) s + then Eop (Ozextshrl (mk_amount64 n) (s - Int.unsigned n)) (t1:::Enil) + else Eop (Olongconst Int64.zero) Enil + | _ => + shrluimm_base e1 n + end. + +(** ** Immediate shift right (arithmetic) *) + +Definition shrlimm_base (e1: expr) (n: int) := + Eop (Oshiftl Sasr (mk_amount64 n)) (e1 ::: Enil). + +Nondetfunction shrlimm (e1: expr) (n: int) := + if Int.eq n Int.zero then + e1 + else if negb (Int.ltu n Int64.iwordsize') then + Eop Oshrl (e1 ::: Eop (Ointconst n) Enil ::: Enil) + else match e1 with + | Eop (Olongconst n1) Enil => + Eop (Olongconst (Int64.shr' n1 n)) Enil + | Eop (Oshiftl Slsl a) (t1:::Enil) => + if Int.ltu n a + then Eop (Oshllsext (Int64.zwordsize - Int.unsigned a) (mk_amount64 (Int.sub a n))) (t1:::Enil) + else Eop (Osextshrl (mk_amount64 (Int.sub n a)) (Int64.zwordsize - Int.unsigned n)) (t1:::Enil) + | Eop (Oshiftl Sasr a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int64.iwordsize' + then shrlimm_base t1 (Int.add a n) + else shrlimm_base e1 n + | Eop (Osextl s) (t1:::Enil) => + if zlt (Int.unsigned n) s && zlt s Int64.zwordsize + then Eop (Osextshrl (mk_amount64 n) (s - Int.unsigned n)) (t1:::Enil) + else shrlimm_base e1 n + | _ => + shrlimm_base e1 n + end. + +(** ** Integer multiply *) + +Definition mullimm_base (n1: int64) (e2: expr) := + match Int64.one_bits' n1 with + | i :: nil => + shllimm e2 i + | i :: j :: nil => + Elet e2 (addl (shllimm (Eletvar 0) i) (shllimm (Eletvar 0) j)) + | _ => + Eop Omull (Eop (Olongconst n1) Enil ::: e2 ::: Enil) + end. + +Nondetfunction mullimm (n1: int64) (e2: expr) := + if Int64.eq n1 Int64.zero then Eop (Olongconst Int64.zero) Enil + else if Int64.eq n1 Int64.one then e2 + else match e2 with + | Eop (Olongconst n2) Enil => Eop (Olongconst (Int64.mul n1 n2)) Enil + | Eop (Oaddlimm n2) (t2:::Enil) => addlimm (Int64.mul n1 n2) (mullimm_base n1 t2) + | _ => mullimm_base n1 e2 + end. + +Nondetfunction mull (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => mullimm n1 t2 + | t1, Eop (Olongconst n2) Enil => mullimm n2 t1 + | _, _ => Eop Omull (e1:::e2:::Enil) + end. + +Definition mullhs (e1: expr) (n2: int64) := + Eop Omullhs (e1 ::: longconst n2 ::: Enil). + +Definition mullhu (e1: expr) (n2: int64) := + Eop Omullhu (e1 ::: longconst n2 ::: Enil). + +(** ** Integer conversions *) + +Nondetfunction zero_ext_l (sz: Z) (e: expr) := + match e with + | Eop (Olongconst n) Enil => Eop (Olongconst (Int64.zero_ext sz n)) Enil + | Eop (Oshiftl Slsr a) (t1:::Enil) => Eop (Ozextshrl a sz) (t1:::Enil) + | Eop (Oshiftl Slsl a) (t1:::Enil) => + if zlt (Int.unsigned a) sz + then Eop (Oshllzext (sz - Int.unsigned a) a) (t1:::Enil) + else Eop (Ozextl sz) (e:::Enil) + | _ => Eop (Ozextl sz) (e:::Enil) + end. + +(** ** Bitwise not *) + +Nondetfunction notl (e: expr) := + match e with + | Eop (Olongconst n) Enil => Eop (Olongconst (Int64.not n)) Enil + | Eop (Oshiftl s a) (t1:::Enil) => Eop (Onotlshift s a) (t1:::Enil) + | Eop Onotl (t1:::Enil) => t1 + | Eop (Onotlshift s a) (t1:::Enil) => Eop (Oshiftl s a) (t1:::Enil) + | Eop Obicl (t1:::t2:::Enil) => Eop Oornl (t2:::t1:::Enil) + | Eop Oornl (t1:::t2:::Enil) => Eop Obicl (t2:::t1:::Enil) + | Eop Oxorl (t1:::t2:::Enil) => Eop Oeqvl (t1:::t2:::Enil) + | Eop Oeqvl (t1:::t2:::Enil) => Eop Oxorl (t1:::t2:::Enil) + | _ => Eop Onotl (e:::Enil) + end. + +(** ** Bitwise and *) + +Definition andlimm_base (n1: int64) (e2: expr) := + if Int64.eq n1 Int64.zero then Eop (Olongconst Int64.zero) Enil else + if Int64.eq n1 Int64.mone then e2 else + match Z_is_power2m1 (Int64.unsigned n1) with + | Some s => zero_ext_l s e2 + | None => Eop (Oandlimm n1) (e2 ::: Enil) + end. + +Nondetfunction andlimm (n1: int64) (e2: expr) := + match e2 with + | Eop (Olongconst n2) Enil => Eop (Olongconst (Int64.and n1 n2)) Enil + | Eop (Oandlimm n2) (t2:::Enil) => andlimm_base (Int64.and n1 n2) t2 + | Eop (Ozextl s) (t2:::Enil) => + if zle 0 s + then andlimm_base (Int64.and n1 (Int64.repr (two_p s - 1))) t2 + else andlimm_base n1 e2 + | _ => andlimm_base n1 e2 + end. + +Nondetfunction andl (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => andlimm n1 t2 + | t1, Eop (Olongconst n2) Enil => andlimm n2 t1 + | Eop Onotl (t1:::Enil), t2 => Eop Obicl (t2:::t1:::Enil) + | t1, Eop Onotl (t2:::Enil) => Eop Obicl (t1:::t2:::Enil) + | Eop (Onotlshift s a) (t1:::Enil), t2 => Eop (Obiclshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotlshift s a) (t2:::Enil) => Eop (Obiclshift s a) (t1:::t2:::Enil) + | Eop (Oshiftl s a) (t1:::Enil), t2 => Eop (Oandlshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) => Eop (Oandlshift s a) (t1:::t2:::Enil) + | _, _ => Eop Oandl (e1:::e2:::Enil) + end. + +(** ** Bitwise or *) + +Nondetfunction orlimm (n1: int64) (e2: expr) := + if Int64.eq n1 Int64.zero then e2 + else if Int64.eq n1 Int64.mone then Eop (Olongconst Int64.mone) Enil + else match e2 with + | Eop (Olongconst n2) Enil => Eop (Olongconst (Int64.or n1 n2)) Enil + | Eop (Oorlimm n2) (t2:::Enil) => Eop (Oorlimm (Int64.or n1 n2)) (t2:::Enil) + | _ => Eop (Oorlimm n1) (e2:::Enil) + end. + +Nondetfunction orl (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => orlimm n1 t2 + | t1, Eop (Olongconst n2) Enil => orlimm n2 t1 + | Eop Onotl (t1:::Enil), t2 => Eop Oornl (t2:::t1:::Enil) + | t1, Eop Onotl (t2:::Enil) => Eop Oornl (t1:::t2:::Enil) + | Eop (Onotlshift s a) (t1:::Enil), t2 => Eop (Oornlshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotlshift s a) (t2:::Enil) => Eop (Oornlshift s a) (t1:::t2:::Enil) + | Eop (Oshiftl Slsl a1) (t1:::Enil), Eop (Oshiftl Slsr a2) (t2:::Enil) => + if Int.eq (Int.add a1 a2) Int64.iwordsize' && same_expr_pure t1 t2 + then Eop (Oshiftl Sror a2) (t2:::Enil) + else Eop (Oorlshift Slsr a2) (Eop (Oshiftl Slsl a1) (t1:::Enil):::t2:::Enil) + | Eop (Oshiftl Slsr a1) (t1:::Enil), Eop (Oshiftl Slsl a2) (t2:::Enil) => + if Int.eq (Int.add a2 a1) Int64.iwordsize' && same_expr_pure t1 t2 + then Eop (Oshiftl Sror a1) (t1:::Enil) + else Eop (Oorlshift Slsl a2) (Eop (Oshiftl Slsr a1) (t1:::Enil):::t2:::Enil) + | Eop (Oshiftl s a) (t1:::Enil), t2 => Eop (Oorlshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) => Eop (Oorlshift s a) (t1:::t2:::Enil) + | _, _ => Eop Oorl (e1:::e2:::Enil) + end. + +(** ** Bitwise xor *) + +Definition xorlimm_base (n1: int64) (e2: expr) := + if Int64.eq n1 Int64.zero then e2 else + if Int64.eq n1 Int64.mone then notl e2 else + Eop (Oxorlimm n1) (e2:::Enil). + +Nondetfunction xorlimm (n1: int64) (e2: expr) := + match e2 with + | Eop (Olongconst n2) Enil => Eop (Olongconst (Int64.xor n1 n2)) Enil + | Eop (Oxorlimm n2) (t2:::Enil) => xorlimm_base (Int64.xor n1 n2) t2 + | _ => xorlimm_base n1 e2 + end. + +Nondetfunction xorl (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => xorlimm n1 t2 + | t1, Eop (Olongconst n2) Enil => xorlimm n2 t1 + | Eop Onotl (t1:::Enil), t2 => Eop Oeqvl (t2:::t1:::Enil) + | t1, Eop Onotl (t2:::Enil) => Eop Oeqvl (t1:::t2:::Enil) + | Eop (Onotlshift s a) (t1:::Enil), t2 => Eop (Oeqvlshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotlshift s a) (t2:::Enil) => Eop (Oeqvlshift s a) (t1:::t2:::Enil) + | Eop (Oshiftl s a) (t1:::Enil), t2 => Eop (Oxorlshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) => Eop (Oxorlshift s a) (t1:::t2:::Enil) + | _, _ => Eop Oxorl (e1:::e2:::Enil) + end. + +(** ** Integer division and modulus *) + +Definition modl_aux (divop: operation) (e1 e2: expr) := + Elet e1 + (Elet (lift e2) + (Eop Omullsub (Eletvar 1 ::: + Eop divop (Eletvar 1 ::: Eletvar 0 ::: Enil) ::: + Eletvar 0 ::: + Enil))). + +Definition divls_base (e1: expr) (e2: expr) := Eop Odivl (e1:::e2:::Enil). +Definition modls_base := modl_aux Odivl. +Definition divlu_base (e1: expr) (e2: expr) := Eop Odivlu (e1:::e2:::Enil). +Definition modlu_base := modl_aux Odivlu. + +Definition shrxlimm (e1: expr) (n2: int) := + if Int.eq n2 Int.zero then e1 else Eop (Oshrlximm n2) (e1:::Enil). + +(** ** General shifts *) + +Nondetfunction shll (e1: expr) (e2: expr) := + match e2 with + | Eop (Ointconst n2) Enil => shllimm e1 n2 + | _ => Eop Oshll (e1:::e2:::Enil) + end. + +Nondetfunction shrl (e1: expr) (e2: expr) := + match e2 with + | Eop (Ointconst n2) Enil => shrlimm e1 n2 + | _ => Eop Oshrl (e1:::e2:::Enil) + end. + +Nondetfunction shrlu (e1: expr) (e2: expr) := + match e2 with + | Eop (Ointconst n2) Enil => shrluimm e1 n2 + | _ => Eop Oshrlu (e1:::e2:::Enil) + end. + +(** ** Comparisons *) + +Nondetfunction complimm (default: comparison -> int64 -> condition) + (sem: comparison -> int64 -> int64 -> bool) + (c: comparison) (e1: expr) (n2: int64) := + match c, e1 with + | c, Eop (Olongconst n1) Enil => + Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil + | Ceq, Eop (Oandlimm m) (t1:::Enil) => + if Int64.eq n2 Int64.zero + then Eop (Ocmp (Cmasklzero m)) (t1:::Enil) + else Eop (Ocmp (default c n2)) (e1:::Enil) + | Cne, Eop (Oandlimm m) (t1:::Enil) => + if Int64.eq n2 Int64.zero + then Eop (Ocmp (Cmasklnotzero m)) (t1:::Enil) + else Eop (Ocmp (default c n2)) (e1:::Enil) + | _, _ => + Eop (Ocmp (default c n2)) (e1:::Enil) + end. + +Nondetfunction cmpl (c: comparison) (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => + complimm Ccomplimm Int64.cmp (swap_comparison c) t2 n1 + | t1, Eop (Olongconst n2) Enil => + complimm Ccomplimm Int64.cmp c t1 n2 + | Eop (Oshiftl s a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Ocmp (Ccomplshift (swap_comparison c) s a)) (t2:::t1:::Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) ?? arith_shift s => + Eop (Ocmp (Ccomplshift c s a)) (t1:::t2:::Enil) + | _, _ => + Eop (Ocmp (Ccompl c)) (e1:::e2:::Enil) + end. + +Nondetfunction cmplu (c: comparison) (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Olongconst n1) Enil, t2 => + complimm Ccompluimm Int64.cmpu (swap_comparison c) t2 n1 + | t1, Eop (Olongconst n2) Enil => + complimm Ccompluimm Int64.cmpu c t1 n2 + | Eop (Oshiftl s a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Ocmp (Ccomplushift (swap_comparison c) s a)) (t2:::t1:::Enil) + | t1, Eop (Oshiftl s a) (t2:::Enil) ?? arith_shift s => + Eop (Ocmp (Ccomplushift c s a)) (t1:::t2:::Enil) + | _, _ => + Eop (Ocmp (Ccomplu c)) (e1:::e2:::Enil) + end. + +(** ** Floating-point conversions *) + +Definition longoffloat (e: expr) := + Eop Olongoffloat (e:::Enil). + +Definition longuoffloat (e: expr) := + Eop Olonguoffloat (e:::Enil). + +Definition floatoflong (e: expr) := + Eop Ofloatoflong (e:::Enil). + +Definition floatoflongu (e: expr) := + Eop Ofloatoflongu (e:::Enil). + +Definition longofsingle (e: expr) := + Eop Olongofsingle (e:::Enil). + +Definition longuofsingle (e: expr) := + Eop Olonguofsingle (e:::Enil). + +Definition singleoflong (e: expr) := + Eop Osingleoflong (e:::Enil). + +Definition singleoflongu (e: expr) := + Eop Osingleoflongu (e:::Enil). + diff --git a/aarch64/SelectLongproof.v b/aarch64/SelectLongproof.v new file mode 100644 index 00000000..b051369c --- /dev/null +++ b/aarch64/SelectLongproof.v @@ -0,0 +1,764 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Correctness of instruction selection for 64-bit integer operators *) + +Require Import Coqlib Zbits. +Require Import AST Integers Floats Values Memory Globalenvs. +Require Import Cminor Op CminorSel. +Require Import SelectOp SelectLong SelectOpproof. + +Local Open Scope cminorsel_scope. +Local Transparent Archi.ptr64. + +(** * Correctness of the smart constructors *) + +Section CMCONSTR. + +Variable ge: genv. +Variable sp: val. +Variable e: env. +Variable m: mem. + +Definition unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop := + forall le a x, + eval_expr ge sp e m le a x -> + exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef (sem x) v. + +Definition binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> val) : Prop := + forall le a x b y, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. + +Definition partial_unary_constructor_sound (cstr: expr -> expr) (sem: val -> option val) : Prop := + forall le a x y, + eval_expr ge sp e m le a x -> + sem x = Some y -> + exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef y v. + +Definition partial_binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> option val) : Prop := + forall le a x b y z, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + sem x y = Some z -> + exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef z v. + +(** ** Constants *) + +Theorem eval_longconst: + forall le n, eval_expr ge sp e m le (longconst n) (Vlong n). +Proof. + intros; EvalOp. +Qed. + +(** ** Conversions *) + +Theorem eval_intoflong: unary_constructor_sound intoflong Val.loword. +Proof. + unfold intoflong; red; intros until x; destruct (intoflong_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_longofintu: unary_constructor_sound longofintu Val.longofintu. +Proof. + unfold longofintu; red; intros until x; destruct (longofintu_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. simpl. unfold eval_extend. rewrite mk_amount64_eq by reflexivity. + destruct x; simpl; auto. rewrite Int64.shl'_zero. auto. +Qed. + +Theorem eval_longofint: unary_constructor_sound longofint Val.longofint. +Proof. + unfold longofint; red; intros until x; destruct (longofint_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. simpl. unfold eval_extend. rewrite mk_amount64_eq by reflexivity. + destruct x; simpl; auto. rewrite Int64.shl'_zero. auto. +Qed. + +(** ** Addition, opposite, subtraction *) + +Theorem eval_addlimm: + forall n, unary_constructor_sound (addlimm n) (fun x => Val.addl x (Vlong n)). +Proof. + red; unfold addlimm; intros until x. + predSpec Int64.eq Int64.eq_spec n Int64.zero. +- subst n. intros. exists x; split; auto. + destruct x; simpl; auto. + rewrite Int64.add_zero; auto. + rewrite Ptrofs.add_zero; auto. +- case (addlimm_match a); intros; InvEval; subst. ++ rewrite Int64.add_commut; TrivialExists. ++ TrivialExists. simpl. rewrite Ptrofs.add_commut, Genv.shift_symbol_address_64; auto. ++ econstructor; split. EvalOp. destruct sp; simpl; auto. + rewrite Ptrofs.add_assoc, (Ptrofs.add_commut m0); auto. ++ rewrite Val.addl_assoc, Int64.add_commut; TrivialExists. ++ TrivialExists. +Qed. + +Theorem eval_addl: binary_constructor_sound addl Val.addl. +Proof. + red; intros until y. + unfold addl; case (addl_match a b); intros; InvEval; subst. +- rewrite Val.addl_commut. apply eval_addlimm; auto. +- apply eval_addlimm; auto. +- replace (Val.addl (Val.addl v1 (Vlong n1)) (Val.addl v0 (Vlong n2))) + with (Val.addl (Val.addl v1 v0) (Val.addl (Vlong n1) (Vlong n2))). + apply eval_addlimm. EvalOp. + repeat rewrite Val.addl_assoc. decEq. apply Val.addl_permut. +- TrivialExists. simpl. + rewrite Val.addl_commut, Val.addl_assoc. f_equal; f_equal. + destruct sp; simpl; auto. rewrite Ptrofs.add_assoc, (Ptrofs.add_commut n2). auto. +- TrivialExists. simpl. + rewrite <- (Val.addl_commut v1), <- (Val.addl_commut (Val.addl v1 (Vlong n2))). + rewrite Val.addl_assoc. f_equal; f_equal. + destruct sp; simpl; auto. rewrite Ptrofs.add_assoc. auto. +- replace (Val.addl (Val.addl v1 (Vlong n1)) y) + with (Val.addl (Val.addl v1 y) (Vlong n1)). + apply eval_addlimm. EvalOp. + repeat rewrite Val.addl_assoc. decEq. apply Val.addl_commut. +- rewrite <- Val.addl_assoc. apply eval_addlimm. EvalOp. +- rewrite Val.addl_commut. TrivialExists. +- TrivialExists. +- rewrite Val.addl_commut. TrivialExists. +- TrivialExists. +- rewrite Val.addl_commut. TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_negl: unary_constructor_sound negl (fun v => Val.subl (Vlong Int64.zero) v). +Proof. + red; intros until x; unfold negl. case (negl_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_subl: binary_constructor_sound subl Val.subl. +Proof. + red; intros until y; unfold subl; case (subl_match a b); intros; InvEval; subst. +- rewrite Val.subl_addl_opp. apply eval_addlimm; auto. +- rewrite Val.subl_addl_l. rewrite Val.subl_addl_r. + rewrite Val.addl_assoc. simpl. rewrite Int64.add_commut. rewrite <- Int64.sub_add_opp. + apply eval_addlimm; EvalOp. +- rewrite Val.subl_addl_l. apply eval_addlimm; EvalOp. +- rewrite Val.subl_addl_r. apply eval_addlimm; EvalOp. +- TrivialExists. +- TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +(** ** Immediate shifts *) + +Remark eval_shllimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int64.iwordsize' = true -> + eval_expr ge sp e m le (shllimm_base a n) (Val.shll x (Vint n)). +Proof. +Local Opaque mk_amount64. + unfold shlimm_base; intros; EvalOp. simpl. rewrite mk_amount64_eq by auto. auto. +Qed. + +Theorem eval_shllimm: + forall n, unary_constructor_sound (fun a => shllimm a n) + (fun x => Val.shll x (Vint n)). +Proof. + red; intros until x; unfold shllimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int64.iwordsize') eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int64.shl'_zero; auto. +- destruct (shllimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* econstructor; split. eapply eval_shllimm_base; eauto. + destruct v1; simpl; auto. rewrite a64_range; simpl. rewrite L, L2. + rewrite Int64.shl'_shl'; auto using a64_range. +* econstructor; split; [|eauto]. apply eval_shllimm_base; auto. EvalOp. ++ TrivialExists. simpl. rewrite mk_amount64_eq; auto. ++ TrivialExists. simpl. rewrite mk_amount64_eq; auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* TrivialExists. simpl. rewrite mk_amount64_eq by auto. + destruct (Val.zero_ext_l s v1); simpl; auto. + rewrite a64_range; simpl; rewrite L, L2. + rewrite Int64.shl'_shl'; auto using a64_range. +* econstructor; split. eapply eval_shllimm_base; eauto. EvalOp; simpl; eauto. auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* TrivialExists. simpl. rewrite mk_amount64_eq by auto. + destruct (Val.sign_ext_l s v1); simpl; auto. + rewrite a64_range; simpl; rewrite L, L2. + rewrite Int64.shl'_shl'; auto using a64_range. +* econstructor; split. eapply eval_shllimm_base; eauto. EvalOp; simpl; eauto. auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* TrivialExists. simpl. unfold eval_extend. rewrite mk_amount64_eq by auto. + destruct (match x0 with Xsgn32 => Val.longofint v1 | Xuns32 => Val.longofintu v1 end); simpl; auto. + rewrite a64_range; simpl; rewrite L, L2. + rewrite Int64.shl'_shl'; auto using a64_range. +* econstructor; split. eapply eval_shllimm_base; eauto. EvalOp; simpl; eauto. auto. ++ econstructor; eauto using eval_shllimm_base. +- intros; TrivialExists. +Qed. + +Remark eval_shrluimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int64.iwordsize' = true -> + eval_expr ge sp e m le (shrluimm_base a n) (Val.shrlu x (Vint n)). +Proof. + unfold shrluimm_base; intros; EvalOp. simpl. rewrite mk_amount64_eq by auto. auto. +Qed. + +Remark sub_shift_amount: + forall y z, + Int.ltu y Int64.iwordsize' = true -> Int.ltu z Int64.iwordsize' = true -> Int.unsigned y <= Int.unsigned z -> + Int.ltu (Int.sub z y) Int64.iwordsize' = true. +Proof. + intros. unfold Int.ltu; apply zlt_true. + apply Int.ltu_inv in H. apply Int.ltu_inv in H0. + change (Int.unsigned Int64.iwordsize') with Int64.zwordsize in *. + unfold Int.sub; rewrite Int.unsigned_repr. omega. + assert (Int64.zwordsize < Int.max_unsigned) by reflexivity. omega. +Qed. + +Theorem eval_shrluimm: + forall n, unary_constructor_sound (fun a => shrluimm a n) + (fun x => Val.shrlu x (Vint n)). +Proof. +Local Opaque Int64.zwordsize. + red; intros until x; unfold shrluimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int64.iwordsize') eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int64.shru'_zero; auto. +- destruct (shrluimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu n a) eqn:L2. +* assert (L3: Int.ltu (Int.sub a n) Int64.iwordsize' = true). + { apply sub_shift_amount; auto using a64_range. + apply Int.ltu_inv in L2. omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount64_eq, L3, a64_range by auto. + simpl. rewrite L. rewrite Int64.shru'_shl', L2 by auto using a64_range. auto. +* assert (L3: Int.ltu (Int.sub n a) Int64.iwordsize' = true). + { apply sub_shift_amount; auto using a64_range. + unfold Int.ltu in L2. destruct zlt in L2; discriminate || omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount64_eq, L3, a64_range by auto. + simpl. rewrite L. rewrite Int64.shru'_shl', L2 by auto using a64_range. auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* econstructor; split. eapply eval_shrluimm_base; eauto. + destruct v1; simpl; auto. rewrite a64_range; simpl. rewrite L, L2. + rewrite Int64.shru'_shru'; auto using a64_range. +* econstructor; split; [|eauto]. apply eval_shrluimm_base; auto. EvalOp. ++ destruct (zlt (Int.unsigned n) s). +* econstructor; split. EvalOp. rewrite mk_amount64_eq by auto. + destruct v1; simpl; auto. rewrite ! L; simpl. + set (s' := s - Int.unsigned n). + replace s with (s' + Int.unsigned n) by (unfold s'; omega). + rewrite Int64.shru'_zero_ext. auto. unfold s'; omega. +* econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite ! L; simpl. + rewrite Int64.shru'_zero_ext_0 by omega. auto. ++ econstructor; eauto using eval_shrluimm_base. +- intros; TrivialExists. +Qed. + +Remark eval_shrlimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int64.iwordsize' = true -> + eval_expr ge sp e m le (shrlimm_base a n) (Val.shrl x (Vint n)). +Proof. + unfold shrlimm_base; intros; EvalOp. simpl. rewrite mk_amount64_eq by auto. auto. +Qed. + +Theorem eval_shrlimm: + forall n, unary_constructor_sound (fun a => shrlimm a n) + (fun x => Val.shrl x (Vint n)). +Proof. + red; intros until x; unfold shrlimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int64.iwordsize') eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int64.shr'_zero; auto. +- destruct (shrlimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu n a) eqn:L2. +* assert (L3: Int.ltu (Int.sub a n) Int64.iwordsize' = true). + { apply sub_shift_amount; auto using a64_range. + apply Int.ltu_inv in L2. omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount64_eq, L3, a64_range by auto. + simpl. rewrite L. rewrite Int64.shr'_shl', L2 by auto using a64_range. auto. +* assert (L3: Int.ltu (Int.sub n a) Int64.iwordsize' = true). + { apply sub_shift_amount; auto using a64_range. + unfold Int.ltu in L2. destruct zlt in L2; discriminate || omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount64_eq, L3, a64_range by auto. + simpl. rewrite L. rewrite Int64.shr'_shl', L2 by auto using a64_range. auto. ++ destruct (Int.ltu (Int.add a n) Int64.iwordsize') eqn:L2. +* econstructor; split. eapply eval_shrlimm_base; eauto. + destruct v1; simpl; auto. rewrite a64_range; simpl. rewrite L, L2. + rewrite Int64.shr'_shr'; auto using a64_range. +* econstructor; split; [|eauto]. apply eval_shrlimm_base; auto. EvalOp. ++ destruct (zlt (Int.unsigned n) s && zlt s Int64.zwordsize) eqn:E. +* InvBooleans. econstructor; split. EvalOp. rewrite mk_amount64_eq by auto. + destruct v1; simpl; auto. rewrite ! L; simpl. + set (s' := s - Int.unsigned n). + replace s with (s' + Int.unsigned n) by (unfold s'; omega). + rewrite Int64.shr'_sign_ext. auto. unfold s'; omega. unfold s'; omega. +* econstructor; split; [|eauto]. apply eval_shrlimm_base; auto. EvalOp. ++ econstructor; eauto using eval_shrlimm_base. +- intros; TrivialExists. +Qed. + +(** ** Multiplication *) + +Lemma eval_mullimm_base: + forall n, unary_constructor_sound (mullimm_base n) (fun x => Val.mull x (Vlong n)). +Proof. + intros; red; intros; unfold mullimm_base. + assert (DFL: exists v, eval_expr ge sp e m le (Eop Omull (Eop (Olongconst n) Enil ::: a ::: Enil)) v /\ Val.lessdef (Val.mull x (Vlong n)) v). + { rewrite Val.mull_commut; TrivialExists. } + generalize (Int64.one_bits'_decomp n); generalize (Int64.one_bits'_range n); + destruct (Int64.one_bits' n) as [ | i [ | j []]]; intros P Q. +- apply DFL. +- replace (Val.mull x (Vlong n)) with (Val.shll x (Vint i)). + apply eval_shllimm; auto. + simpl in Q. destruct x; auto; simpl. rewrite P by auto with coqlib. + rewrite Q, Int64.add_zero, Int64.shl'_mul. auto. +- exploit (eval_shllimm i (x :: le) (Eletvar 0) x). constructor; auto. intros [v1 [A1 B1]]. + exploit (eval_shllimm j (x :: le) (Eletvar 0) x). constructor; auto. intros [v2 [A2 B2]]. + exploit (eval_addl (x :: le)). eexact A1. eexact A2. intros [v [A B]]. + exists v; split. econstructor; eauto. + simpl in Q. rewrite Q, Int64.add_zero. eapply Val.lessdef_trans; [|eexact B]. + eapply Val.lessdef_trans; [|eapply Val.addl_lessdef; eauto]. + destruct x; simpl; auto; rewrite ! P by auto with coqlib. + rewrite Int64.mul_add_distr_r, <- ! Int64.shl'_mul. auto. +- apply DFL. +Qed. + +Theorem eval_mullimm: + forall n, unary_constructor_sound (mullimm n) (fun x => Val.mull x (Vlong n)). +Proof. + intros; red; intros until x; unfold mullimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero. + intros. exists (Vlong Int64.zero); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int64.mul_zero. auto. + predSpec Int64.eq Int64.eq_spec n Int64.one. + intros. exists x; split; auto. + destruct x; simpl; auto. subst n. rewrite Int64.mul_one. auto. + case (mullimm_match a); intros; InvEval; subst. +- TrivialExists. simpl. rewrite Int64.mul_commut; auto. +- rewrite Val.mull_addl_distr_l. + exploit eval_mullimm_base; eauto. instantiate (1 := n). intros [v' [A1 B1]]. + exploit (eval_addlimm (Int64.mul n n2) le (mullimm_base n t2) v'). auto. intros [v'' [A2 B2]]. + exists v''; split; auto. eapply Val.lessdef_trans. eapply Val.addl_lessdef; eauto. + rewrite Val.mull_commut; auto. +- apply eval_mullimm_base; auto. +Qed. + +Theorem eval_mull: binary_constructor_sound mull Val.mull. +Proof. + red; intros until y; unfold mull; case (mull_match a b); intros; InvEval; subst. +- rewrite Val.mull_commut. apply eval_mullimm; auto. +- apply eval_mullimm; auto. +- TrivialExists. +Qed. + +Theorem eval_mullhu: + forall n, unary_constructor_sound (fun a => mullhu a n) (fun v => Val.mullhu v (Vlong n)). +Proof. + unfold mullhu; red; intros; TrivialExists. +Qed. + +Theorem eval_mullhs: + forall n, unary_constructor_sound (fun a => mullhs a n) (fun v => Val.mullhs v (Vlong n)). +Proof. + unfold mullhs; red; intros; TrivialExists. +Qed. + +(** Integer conversions *) + +Theorem eval_zero_ext_l: + forall sz, 0 <= sz -> unary_constructor_sound (zero_ext_l sz) (Val.zero_ext_l sz). +Proof. + intros; red; intros until x; unfold zero_ext_l; case (zero_ext_l_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- destruct (zlt (Int.unsigned a0) sz). ++ econstructor; split. EvalOp. destruct v1; simpl; auto. rewrite a64_range; simpl. + apply Val.lessdef_same. f_equal. rewrite Int64.shl'_zero_ext by omega. f_equal. omega. ++ TrivialExists. +- TrivialExists. +Qed. + +(** Bitwise not, and, or, xor *) + +Theorem eval_notl: unary_constructor_sound notl Val.notl. +Proof. + assert (INV: forall v, Val.lessdef (Val.notl (Val.notl v)) v). + { destruct v; auto. simpl; rewrite Int64.not_involutive; auto. } + unfold notl; red; intros until x; case (notl_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- exists v1; auto. +- exists (eval_shiftl s v1 a0); split; auto. EvalOp. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + rewrite Int64.not_and_or_not, Int64.not_involutive, Int64.or_commut. auto. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + rewrite Int64.not_or_and_not, Int64.not_involutive, Int64.and_commut. auto. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + unfold Int64.not; rewrite ! Int64.xor_assoc. auto. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + unfold Int64.not; rewrite ! Int64.xor_assoc, Int64.xor_idem, Int64.xor_zero. auto. +- TrivialExists. +Qed. + +Lemma eval_andlimm_base: + forall n, unary_constructor_sound (andlimm_base n) (fun x => Val.andl x (Vlong n)). +Proof. + intros; red; intros. unfold andlimm_base. + predSpec Int64.eq Int64.eq_spec n Int64.zero. + exists (Vlong Int64.zero); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int64.and_zero. auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone. + exists x; split; auto. + subst. destruct x; simpl; auto. rewrite Int64.and_mone; auto. + destruct (Z_is_power2m1 (Int64.unsigned n)) as [s|] eqn:P. + assert (0 <= s) by (eapply Z_is_power2m1_nonneg; eauto). + rewrite <- (Int64.repr_unsigned n), (Z_is_power2m1_sound _ _ P), <- Val.zero_ext_andl by auto. + apply eval_zero_ext_l; auto. + TrivialExists. +Qed. + +Theorem eval_andlimm: + forall n, unary_constructor_sound (andlimm n) (fun x => Val.andl x (Vlong n)). +Proof. + intros; red; intros until x. unfold andlimm. + case (andlimm_match a); intros; InvEval; subst. +- rewrite Int64.and_commut; TrivialExists. +- rewrite Val.andl_assoc, Int64.and_commut. apply eval_andlimm_base; auto. +- destruct (zle 0 s). ++ replace (Val.zero_ext_l s v1) with (Val.andl v1 (Vlong (Int64.repr (two_p s - 1)))). + rewrite Val.andl_assoc, Int64.and_commut. + apply eval_andlimm_base; auto. + destruct v1; simpl; auto. rewrite Int64.zero_ext_and by auto. auto. ++ apply eval_andlimm_base. EvalOp. +- apply eval_andlimm_base; auto. +Qed. + +Theorem eval_andl: binary_constructor_sound andl Val.andl. +Proof. + red; intros until y; unfold andl; case (andl_match a b); intros; InvEval; subst. +- rewrite Val.andl_commut; apply eval_andlimm; auto. +- apply eval_andlimm; auto. +- rewrite Val.andl_commut; TrivialExists. +- TrivialExists. +- rewrite Val.andl_commut; TrivialExists. +- TrivialExists. +- rewrite Val.andl_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_orlimm: + forall n, unary_constructor_sound (orlimm n) (fun x => Val.orl x (Vlong n)). +Proof. + intros; red; intros until x. unfold orlimm. + predSpec Int64.eq Int64.eq_spec n Int64.zero. + intros. subst. exists x; split; auto. + destruct x; simpl; auto. rewrite Int64.or_zero; auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone. + intros. exists (Vlong Int64.mone); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int64.or_mone. auto. + destruct (orlimm_match a); intros; InvEval; subst. +- rewrite Int64.or_commut; TrivialExists. +- rewrite Val.orl_assoc, Int64.or_commut; TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_orl: binary_constructor_sound orl Val.orl. +Proof. + red; intros until y; unfold orl; case (orl_match a b); intros; InvEval; subst. +- rewrite Val.orl_commut. apply eval_orlimm; auto. +- apply eval_orlimm; auto. +- rewrite Val.orl_commut; TrivialExists. +- TrivialExists. +- rewrite Val.orl_commut; TrivialExists. +- TrivialExists. +- (* shl - shru *) + destruct (Int.eq (Int.add a1 a2) Int64.iwordsize' && same_expr_pure t1 t2) eqn:?. ++ InvBooleans. apply Int.same_if_eq in H. + exploit eval_same_expr; eauto. intros [EQ1 EQ2]. subst. + econstructor; split. EvalOp. + destruct v0; simpl; auto. rewrite ! a64_range. simpl. rewrite <- Int64.or_ror'; auto using a64_range. ++ TrivialExists. +- (* shru - shl *) + destruct (Int.eq (Int.add a2 a1) Int64.iwordsize' && same_expr_pure t1 t2) eqn:?. ++ InvBooleans. apply Int.same_if_eq in H. + exploit eval_same_expr; eauto. intros [EQ1 EQ2]. subst. + econstructor; split. EvalOp. + destruct v0; simpl; auto. rewrite ! a64_range. simpl. + rewrite Int64.or_commut, <- Int64.or_ror'; auto using a64_range. ++ TrivialExists. +- rewrite Val.orl_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Lemma eval_xorlimm_base: + forall n, unary_constructor_sound (xorlimm_base n) (fun x => Val.xorl x (Vlong n)). +Proof. + intros; red; intros. unfold xorlimm_base. + predSpec Int64.eq Int64.eq_spec n Int64.zero. + intros. exists x; split. auto. + destruct x; simpl; auto. subst n. rewrite Int64.xor_zero. auto. + predSpec Int64.eq Int64.eq_spec n Int64.mone. + subst n. change (Val.xorl x (Vlong Int64.mone)) with (Val.notl x). apply eval_notl; auto. + TrivialExists. +Qed. + +Theorem eval_xorlimm: + forall n, unary_constructor_sound (xorlimm n) (fun x => Val.xorl x (Vlong n)). +Proof. + intros; red; intros until x. unfold xorlimm. + destruct (xorlimm_match a); intros; InvEval; subst. +- rewrite Int64.xor_commut; TrivialExists. +- rewrite Val.xorl_assoc; simpl. rewrite (Int64.xor_commut n2). apply eval_xorlimm_base; auto. +- apply eval_xorlimm_base; auto. +Qed. + +Theorem eval_xorl: binary_constructor_sound xorl Val.xorl. +Proof. + red; intros until y; unfold xorl; case (xorl_match a b); intros; InvEval; subst. +- rewrite Val.xorl_commut; apply eval_xorlimm; auto. +- apply eval_xorlimm; auto. +- rewrite Val.xorl_commut; TrivialExists. +- TrivialExists. +- rewrite Val.xorl_commut; TrivialExists. +- TrivialExists. +- rewrite Val.xorl_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +(** ** Integer division and modulus *) + +Theorem eval_divls_base: partial_binary_constructor_sound divls_base Val.divls. +Proof. + red; intros; unfold divls_base; TrivialExists. +Qed. + +Theorem eval_modls_base: partial_binary_constructor_sound modls_base Val.modls. +Proof. + red; intros; unfold modls_base, modl_aux. + exploit Val.modls_divls; eauto. intros (q & A & B). subst z. + TrivialExists. repeat (econstructor; eauto with evalexpr). exact A. +Qed. + +Theorem eval_divlu_base: partial_binary_constructor_sound divlu_base Val.divlu. +Proof. + red; intros; unfold divlu_base; TrivialExists. +Qed. + +Theorem eval_modlu_base: partial_binary_constructor_sound modlu_base Val.modlu. +Proof. + red; intros; unfold modlu_base, modl_aux. + exploit Val.modlu_divlu; eauto. intros (q & A & B). subst z. + TrivialExists. repeat (econstructor; eauto with evalexpr). exact A. +Qed. + +Theorem eval_shrxlimm: + forall le a n x z, + eval_expr ge sp e m le a x -> + Val.shrxl x (Vint n) = Some z -> + exists v, eval_expr ge sp e m le (shrxlimm a n) v /\ Val.lessdef z v. +Proof. + intros; unfold shrxlimm. + predSpec Int.eq Int.eq_spec n Int.zero. +- subst n. exists x; split; auto. + destruct x; simpl in H0; try discriminate. + change (Int.ltu Int.zero (Int.repr 63)) with true in H0; inv H0. + rewrite Int64.shrx'_zero. auto. +- TrivialExists. +Qed. + +(** General shifts *) + +Theorem eval_shll: binary_constructor_sound shll Val.shll. +Proof. + red; intros until y; unfold shll; case (shll_match b); intros. + InvEval. apply eval_shllimm; auto. + TrivialExists. +Qed. + +Theorem eval_shrl: binary_constructor_sound shrl Val.shrl. +Proof. + red; intros until y; unfold shrl; case (shrl_match b); intros. + InvEval. apply eval_shrlimm; auto. + TrivialExists. +Qed. + +Theorem eval_shrlu: binary_constructor_sound shrlu Val.shrlu. +Proof. + red; intros until y; unfold shrlu; case (shrlu_match b); intros. + InvEval. apply eval_shrluimm; auto. + TrivialExists. +Qed. + +(** Comparisons *) + +Remark option_map_of_bool_inv: forall ov w, + option_map Val.of_bool ov = Some w -> Val.of_optbool ov = w. +Proof. + intros. destruct ov; inv H; auto. +Qed. + +Section COMP_IMM. + +Variable default: comparison -> int64 -> condition. +Variable intsem: comparison -> int64 -> int64 -> bool. +Variable sem: comparison -> val -> val -> option val. + +Hypothesis sem_int: forall c x y, + sem c (Vlong x) (Vlong y) = Some (Val.of_bool (intsem c x y)). +Hypothesis sem_undef: forall c v, + sem c Vundef v = None. +Hypothesis sem_eq: forall x y, + sem Ceq (Vlong x) (Vlong y) = Some (Val.of_bool (Int64.eq x y)). +Hypothesis sem_ne: forall x y, + sem Cne (Vlong x) (Vlong y) = Some (Val.of_bool (negb (Int64.eq x y))). +Hypothesis sem_default: forall c v n, + sem c v (Vlong n) = option_map Val.of_bool (eval_condition (default c n) (v :: nil) m). + +Lemma eval_complimm_default: forall le a x c n2 v, + sem c x (Vlong n2) = Some v -> + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le (Eop (Ocmp (default c n2)) (a:::Enil)) v. +Proof. + intros. EvalOp. simpl. rewrite sem_default in H. apply option_map_of_bool_inv in H. + congruence. +Qed. + +Lemma eval_complimm: + forall le c a n2 x v, + eval_expr ge sp e m le a x -> + sem c x (Vlong n2) = Some v -> + eval_expr ge sp e m le (complimm default intsem c a n2) v. +Proof. + intros until x; unfold complimm; case (complimm_match c a); intros; InvEval; subst. +- (* constant *) + rewrite sem_int in H0; inv H0. EvalOp. destruct (intsem c0 n1 n2); auto. +- (* mask zero *) + predSpec Int64.eq Int64.eq_spec n2 Int64.zero. ++ subst n2. destruct v1; simpl in H0; rewrite ? sem_undef, ? sem_eq in H0; inv H0. + EvalOp. ++ eapply eval_complimm_default; eauto. EvalOp. +- (* mask not zero *) + predSpec Int64.eq Int64.eq_spec n2 Int64.zero. ++ subst n2. destruct v1; simpl in H0; rewrite ? sem_undef, ? sem_ne in H0; inv H0. + EvalOp. ++ eapply eval_complimm_default; eauto. EvalOp. +- (* default *) + eapply eval_complimm_default; eauto. +Qed. + +Hypothesis sem_swap: + forall c x y, sem (swap_comparison c) x y = sem c y x. + +Lemma eval_complimm_swap: + forall le c a n2 x v, + eval_expr ge sp e m le a x -> + sem c (Vlong n2) x = Some v -> + eval_expr ge sp e m le (complimm default intsem (swap_comparison c) a n2) v. +Proof. + intros. eapply eval_complimm; eauto. rewrite sem_swap; auto. +Qed. + +End COMP_IMM. + +Theorem eval_cmpl: + forall c le a x b y v, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.cmpl c x y = Some v -> + eval_expr ge sp e m le (cmpl c a b) v. +Proof. + intros until y; unfold cmpl; case (cmpl_match a b); intros; InvEval; subst. +- apply eval_complimm_swap with (sem := Val.cmpl) (x := y); auto. + intros; unfold Val.cmpl; rewrite Val.swap_cmpl_bool; auto. +- apply eval_complimm with (sem := Val.cmpl) (x := x); auto. +- EvalOp. simpl. rewrite Val.swap_cmpl_bool. apply option_map_of_bool_inv in H1. congruence. +- EvalOp. simpl. apply option_map_of_bool_inv in H1. congruence. +- EvalOp. simpl. apply option_map_of_bool_inv in H1. congruence. +Qed. + +Theorem eval_cmplu: + forall c le a x b y v, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.cmplu (Mem.valid_pointer m) c x y = Some v -> + eval_expr ge sp e m le (cmplu c a b) v. +Proof. + intros until y; unfold cmplu; case (cmplu_match a b); intros; InvEval; subst. +- apply eval_complimm_swap with (sem := Val.cmplu (Mem.valid_pointer m)) (x := y); auto. + intros; unfold Val.cmplu; rewrite Val.swap_cmplu_bool; auto. +- apply eval_complimm with (sem := Val.cmplu (Mem.valid_pointer m)) (x := x); auto. +- EvalOp. simpl. rewrite Val.swap_cmplu_bool. apply option_map_of_bool_inv in H1. congruence. +- EvalOp. simpl. apply option_map_of_bool_inv in H1. congruence. +- EvalOp. simpl. apply option_map_of_bool_inv in H1. congruence. +Qed. + + +(** Floating-point conversions *) + +Theorem eval_longoffloat: partial_unary_constructor_sound longoffloat Val.longoffloat. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_longuoffloat: partial_unary_constructor_sound longuoffloat Val.longuoffloat. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_floatoflong: partial_unary_constructor_sound floatoflong Val.floatoflong. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_floatoflongu: partial_unary_constructor_sound floatoflongu Val.floatoflongu. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_longofsingle: partial_unary_constructor_sound longofsingle Val.longofsingle. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_longuofsingle: partial_unary_constructor_sound longuofsingle Val.longuofsingle. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_singleoflong: partial_unary_constructor_sound singleoflong Val.singleoflong. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_singleoflongu: partial_unary_constructor_sound singleoflongu Val.singleoflongu. +Proof. + red; intros; TrivialExists. +Qed. + +End CMCONSTR. diff --git a/aarch64/SelectOp.vp b/aarch64/SelectOp.vp new file mode 100644 index 00000000..5bd96987 --- /dev/null +++ b/aarch64/SelectOp.vp @@ -0,0 +1,566 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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 *) + +Require Import Coqlib Zbits. +Require Import Compopts AST Integers Floats Builtins. +Require Import Op CminorSel. + +Local Open Scope cminorsel_scope. + +(** "ror" shifted operands are not supported by arithmetic operations *) + +Definition arith_shift (s: shift) := + match s with Sror => false | _ => true end. + +(** ** Constants **) + +Definition addrsymbol (id: ident) (ofs: ptrofs) := + Eop (Oaddrsymbol id ofs) Enil. + +Definition addrstack (ofs: ptrofs) := + Eop (Oaddrstack ofs) Enil. + +(** ** Integer 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 (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 a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Oaddshift s a) (t2 ::: t1 ::: Enil) + | t1, Eop (Oshift s a) (t2:::Enil) ?? arith_shift s => + Eop (Oaddshift s a) (t1 ::: t2 ::: Enil) + | Eop Omul (t1:::t2:::Enil), t3 => + Eop Omuladd (t3:::t1:::t2:::Enil) + | t1, Eop Omul (t2:::t3:::Enil) => + Eop Omuladd (t1:::t2:::t3:::Enil) + | _, _ => Eop Oadd (e1:::e2:::Enil) + end. + +(** ** Opposite *) + +Nondetfunction negint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.neg n)) Enil + | Eop (Oshift s a) (t1:::Enil) ?? arith_shift s => Eop (Onegshift s a) (t1:::Enil) + | _ => Eop Oneg (e ::: Enil) + end. + +(** ** Integer and pointer subtraction *) + +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)) + | t1, Eop (Oshift s a) (t2:::Enil) ?? arith_shift s => + Eop (Osubshift s a) (t1:::t2::: Enil) + | t1, Eop Omul (t2:::t3:::Enil) => + Eop Omulsub (t1:::t2:::t3:::Enil) + | _, _ => Eop Osub (e1:::e2:::Enil) + end. + +(** ** Immediate shift left *) + +Definition shlimm_base (e1: expr) (n: int) := + Eop (Oshift Slsl (mk_amount32 n)) (e1 ::: Enil). + +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 a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int.iwordsize + then shlimm_base t1 (Int.add a n) + else shlimm_base e1 n + | Eop (Ozext s) (t1:::Enil) => + Eop (Oshlzext s (mk_amount32 n)) (t1:::Enil) + | Eop (Osext s) (t1:::Enil) => + Eop (Oshlsext s (mk_amount32 n)) (t1:::Enil) + | Eop (Oshlzext s a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int.iwordsize + then Eop (Oshlzext s (mk_amount32 (Int.add a n))) (t1:::Enil) + else shlimm_base e1 n + | Eop (Oshlsext s a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int.iwordsize + then Eop (Oshlsext s (mk_amount32 (Int.add a n))) (t1:::Enil) + else shlimm_base e1 n + | _ => + shlimm_base e1 n + end. + +(** ** Immediate shift right (logical) *) + +Definition shruimm_base (e1: expr) (n: int) := + Eop (Oshift Slsr (mk_amount32 n)) (e1 ::: Enil). + +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 Slsl a) (t1:::Enil) => + if Int.ltu n a + then Eop (Oshlzext (Int.zwordsize - Int.unsigned a) (mk_amount32 (Int.sub a n))) (t1:::Enil) + else Eop (Ozextshr (mk_amount32 (Int.sub n a)) (Int.zwordsize - Int.unsigned n)) (t1:::Enil) + | Eop (Oshift Slsr a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int.iwordsize + then shruimm_base t1 (Int.add a n) + else shruimm_base e1 n + | Eop (Ozext s) (t1:::Enil) => + if zlt (Int.unsigned n) s + then Eop (Ozextshr (mk_amount32 n) (s - Int.unsigned n)) (t1:::Enil) + else Eop (Ointconst Int.zero) Enil + | _ => + shruimm_base e1 n + end. + +(** ** Immediate shift right (arithmetic) *) + +Definition shrimm_base (e1: expr) (n: int) := + Eop (Oshift Sasr (mk_amount32 n)) (e1 ::: Enil). + +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 Slsl a) (t1:::Enil) => + if Int.ltu n a + then Eop (Oshlsext (Int.zwordsize - Int.unsigned a) (mk_amount32 (Int.sub a n))) (t1:::Enil) + else Eop (Osextshr (mk_amount32 (Int.sub n a)) (Int.zwordsize - Int.unsigned n)) (t1:::Enil) + | Eop (Oshift Sasr a) (t1:::Enil) => + if Int.ltu (Int.add a n) Int.iwordsize + then shrimm_base t1 (Int.add a n) + else shrimm_base e1 n + | Eop (Osext s) (t1:::Enil) => + if zlt (Int.unsigned n) s && zlt s Int.zwordsize + then Eop (Osextshr (mk_amount32 n) (s - Int.unsigned n)) (t1:::Enil) + else shrimm_base e1 n + | _ => + shrimm_base e1 n + 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. + +Definition mulhs (e1: expr) (e2: expr) := + Eop Olowlong + (Eop (Oshiftl Sasr (mk_amount64 (Int.repr 32))) + (Eop Omull (Eop (Oextend Xsgn32 (mk_amount64 Int.zero)) (e1 ::: Enil) ::: + Eop (Oextend Xsgn32 (mk_amount64 Int.zero)) (e2 ::: Enil) ::: Enil) ::: Enil) + ::: Enil). + +Definition mulhu (e1: expr) (e2: expr) := + Eop Olowlong + (Eop (Oshiftl Slsr (mk_amount64 (Int.repr 32))) + (Eop Omull (Eop (Oextend Xuns32 (mk_amount64 Int.zero)) (e1 ::: Enil) ::: + Eop (Oextend Xuns32 (mk_amount64 Int.zero)) (e2 ::: Enil) ::: Enil) ::: Enil) + ::: Enil). + +(** ** Integer conversions *) + +Nondetfunction zero_ext (sz: Z) (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.zero_ext sz n)) Enil + | Eop (Oshift Slsr a) (t1:::Enil) => Eop (Ozextshr a sz) (t1:::Enil) + | Eop (Oshift Slsl a) (t1:::Enil) => + if zlt (Int.unsigned a) sz + then Eop (Oshlzext (sz - Int.unsigned a) a) (t1:::Enil) + else Eop (Ozext sz) (e:::Enil) + | _ => Eop (Ozext sz) (e:::Enil) + end. + +Nondetfunction sign_ext (sz: Z) (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.sign_ext sz n)) Enil + | Eop (Oshift Sasr a) (t1:::Enil) => Eop (Osextshr a sz) (t1:::Enil) + | Eop (Oshift Slsl a) (t1:::Enil) => + if zlt (Int.unsigned a) sz + then Eop (Oshlsext (sz - Int.unsigned a) a) (t1:::Enil) + else Eop (Osext sz) (e:::Enil) + | _ => Eop (Osext sz) (e:::Enil) + end. + +Definition cast8unsigned (e: expr) := zero_ext 8 e. +Definition cast8signed (e: expr) := sign_ext 8 e. +Definition cast16unsigned (e: expr) := zero_ext 16 e. +Definition cast16signed (e: expr) := sign_ext 16 e. + +(** ** Bitwise not *) + +Nondetfunction notint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.not n)) Enil + | Eop (Oshift s a) (t1:::Enil) => Eop (Onotshift s a) (t1:::Enil) + | Eop Onot (t1:::Enil) => t1 + | Eop (Onotshift s a) (t1:::Enil) => Eop (Oshift s a) (t1:::Enil) + | Eop Obic (t1:::t2:::Enil) => Eop Oorn (t2:::t1:::Enil) + | Eop Oorn (t1:::t2:::Enil) => Eop Obic (t2:::t1:::Enil) + | Eop Oxor (t1:::t2:::Enil) => Eop Oeqv (t1:::t2:::Enil) + | Eop Oeqv (t1:::t2:::Enil) => Eop Oxor (t1:::t2:::Enil) + | _ => Eop Onot (e:::Enil) + end. + +(** ** Bitwise and *) + +Definition andimm_base (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 Z_is_power2m1 (Int.unsigned n1) with + | Some s => zero_ext s e2 + | None => Eop (Oandimm n1) (e2 ::: Enil) + end. + +Nondetfunction andimm (n1: int) (e2: expr) := + match e2 with + | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.and n1 n2)) Enil + | Eop (Oandimm n2) (t2:::Enil) => andimm_base (Int.and n1 n2) t2 + | Eop (Ozext s) (t2:::Enil) => + if zle 0 s + then andimm_base (Int.and n1 (Int.repr (two_p s - 1))) t2 + else andimm_base n1 e2 + | _ => andimm_base n1 e2 + 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 Onot (t1:::Enil), t2 => Eop Obic (t2:::t1:::Enil) + | t1, Eop Onot (t2:::Enil) => Eop Obic (t1:::t2:::Enil) + | Eop (Onotshift s a) (t1:::Enil), t2 => Eop (Obicshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotshift s a) (t2:::Enil) => Eop (Obicshift s a) (t1:::t2:::Enil) + | Eop (Oshift s a) (t1:::Enil), t2 => Eop (Oandshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshift s a) (t2:::Enil) => Eop (Oandshift s a) (t1:::t2:::Enil) + | _, _ => Eop Oand (e1:::e2:::Enil) + end. + +(** ** Bitwise or *) + +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. + +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 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 Onot (t1:::Enil), t2 => Eop Oorn (t2:::t1:::Enil) + | t1, Eop Onot (t2:::Enil) => Eop Oorn (t1:::t2:::Enil) + | Eop (Onotshift s a) (t1:::Enil), t2 => Eop (Oornshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotshift s a) (t2:::Enil) => Eop (Oornshift s a) (t1:::t2:::Enil) + | Eop (Oshift Slsl a1) (t1:::Enil), Eop (Oshift Slsr a2) (t2:::Enil) => + if Int.eq (Int.add a1 a2) Int.iwordsize && same_expr_pure t1 t2 + then Eop (Oshift Sror a2) (t2:::Enil) + else Eop (Oorshift Slsr a2) (Eop (Oshift Slsl a1) (t1:::Enil):::t2:::Enil) + | Eop (Oshift Slsr a1) (t1:::Enil), Eop (Oshift Slsl a2) (t2:::Enil) => + if Int.eq (Int.add a2 a1) Int.iwordsize && same_expr_pure t1 t2 + then Eop (Oshift Sror a1) (t1:::Enil) + else Eop (Oorshift Slsl a2) (Eop (Oshift Slsr a1) (t1:::Enil):::t2:::Enil) + | Eop (Oshift s a) (t1:::Enil), t2 => Eop (Oorshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshift s a) (t2:::Enil) => Eop (Oorshift s a) (t1:::t2:::Enil) + | _, _ => Eop Oor (e1:::e2:::Enil) + end. + +(** ** Bitwise xor *) + +Definition xorimm_base (n1: int) (e2: expr) := + if Int.eq n1 Int.zero then e2 else + if Int.eq n1 Int.mone then notint e2 else + Eop (Oxorimm n1) (e2:::Enil). + +Nondetfunction xorimm (n1: int) (e2: expr) := + match e2 with + | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.xor n1 n2)) Enil + | Eop (Oxorimm n2) (t2:::Enil) => xorimm_base (Int.xor n1 n2) t2 + | _ => xorimm_base n1 e2 + 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 Onot (t1:::Enil), t2 => Eop Oeqv (t2:::t1:::Enil) + | t1, Eop Onot (t2:::Enil) => Eop Oeqv (t1:::t2:::Enil) + | Eop (Onotshift s a) (t1:::Enil), t2 => Eop (Oeqvshift s a) (t2:::t1:::Enil) + | t1, Eop (Onotshift s a) (t2:::Enil) => Eop (Oeqvshift s a) (t1:::t2:::Enil) + | Eop (Oshift s a) (t1:::Enil), t2 => Eop (Oxorshift s a) (t2:::t1:::Enil) + | t1, Eop (Oshift s a) (t2:::Enil) => Eop (Oxorshift s a) (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 Omulsub (Eletvar 1 ::: + Eop divop (Eletvar 1 ::: Eletvar 0 ::: Enil) ::: + Eletvar 0 ::: + 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 + | Ceq, Eop (Oandimm m) (t1:::Enil) => + if Int.eq n2 Int.zero + then Eop (Ocmp (Cmaskzero m)) (t1:::Enil) + else Eop (Ocmp (default c n2)) (e1:::Enil) + | Cne, Eop (Oandimm m) (t1:::Enil) => + if Int.eq n2 Int.zero + then Eop (Ocmp (Cmasknotzero m)) (t1:::Enil) + else Eop (Ocmp (default c n2)) (e1:::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 (Oshift s a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Ocmp (Ccompshift (swap_comparison c) s a)) (t2:::t1:::Enil) + | t1, Eop (Oshift s a) (t2:::Enil) ?? arith_shift s => + Eop (Ocmp (Ccompshift c s a)) (t1:::t2:::Enil) + | _, _ => + 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 (Oshift s a) (t1:::Enil), t2 ?? arith_shift s => + Eop (Ocmp (Ccompushift (swap_comparison c) s a)) (t2:::t1:::Enil) + | t1, Eop (Oshift s a) (t2:::Enil) ?? arith_shift s => + Eop (Ocmp (Ccompushift c s a)) (t1:::t2:::Enil) + | _, _ => + 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). + +(** ** Floating-point conversions *) + +Definition intoffloat (e: expr) := Eop Ointoffloat (e ::: Enil). +Definition intuoffloat (e: expr) := Eop Ointuoffloat (e ::: Enil). + +Nondetfunction floatofintu (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_intu n)) Enil + | _ => Eop Ofloatofintu (e ::: Enil) + end. + +Nondetfunction floatofint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_int n)) Enil + | _ => Eop Ofloatofint (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. + +Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil). +Definition floatofsingle (e: expr) := Eop Ofloatofsingle (e ::: Enil). + +(** ** Selection *) + +Definition select (ty: typ) (cond: condition) (args: exprlist) (e1 e2: expr) := + if match ty with + | Tint => true + | Tlong => true + | Tfloat => true + | Tsingle => true + | _ => false + end + then Some (Eop (Osel cond ty) (e1 ::: e2 ::: args)) + else None. + +(** ** Recognition of addressing modes for load and store operations *) + +Nondetfunction addressing (chunk: memory_chunk) (e: expr) := + match e with + | Eop (Oaddrstack n) Enil => (Ainstack n, Enil) + | Eop (Oaddrsymbol id ofs) Enil => (Aglobal id ofs, Enil) + | Eop (Oaddlimm n) (e1:::Enil) => (Aindexed n, e1:::Enil) + | Eop (Oaddlshift Slsl a) (e1:::e2:::Enil) => (Aindexed2shift a, e1:::e2:::Enil) + | Eop (Oaddlext x a) (e1:::e2:::Enil) => (Aindexed2ext x a, e1:::e2:::Enil) + | Eop Oaddl (e1:::e2:::Enil) => (Aindexed2, e1:::e2:::Enil) + | _ => (Aindexed Int64.zero, e:::Enil) + end. + +(** ** Arguments of builtins *) + +Nondetfunction builtin_arg (e: expr) := + match e with + | Eop (Ointconst n) Enil => BA_int n + | Eop (Olongconst n) Enil => BA_long n + | Eop (Oaddrsymbol id ofs) Enil => BA_addrglobal id ofs + | Eop (Oaddrstack ofs) Enil => BA_addrstack ofs + | Eload chunk (Ainstack ofs) Enil => BA_loadstack chunk ofs + | Eop (Oaddlimm n) (e1:::Enil) => BA_addptr (BA e1) (BA_long n) + | _ => BA e + end. + +(** Platform-specific known builtins *) + +Definition platform_builtin (b: platform_builtin) (args: exprlist) : option expr := + None. diff --git a/aarch64/SelectOpproof.v b/aarch64/SelectOpproof.v new file mode 100644 index 00000000..b78a5ed8 --- /dev/null +++ b/aarch64/SelectOpproof.v @@ -0,0 +1,1070 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Correctness of instruction selection for operators *) + +Require Import Coqlib Zbits. +Require Import AST Integers Floats Values Memory Builtins Globalenvs. +Require Import Cminor Op CminorSel. +Require Import SelectOp. + +Local Open Scope cminorsel_scope. +Local Transparent Archi.ptr64. + +(** * Useful lemmas and tactics *) + +(** The following are trivial lemmas and custom tactics that help + perform backward (inversion) and forward reasoning over the evaluation + of operator applications. *) + +Ltac EvalOp := + eauto with evalexpr; + match goal with + | [ |- eval_expr _ _ _ _ _ _ _ ] => eapply eval_Eop; [EvalOp|try reflexivity; auto] + | [ |- eval_exprlist _ _ _ _ _ _ _ ] => econstructor; EvalOp + | _ => idtac + end. + +Ltac InvEval1 := + match goal with + | [ H: (eval_expr _ _ _ _ _ (Eop _ Enil) _) |- _ ] => + inv H; InvEval1 + | [ H: (eval_expr _ _ _ _ _ (Eop _ (_ ::: Enil)) _) |- _ ] => + inv H; InvEval1 + | [ H: (eval_expr _ _ _ _ _ (Eop _ (_ ::: _ ::: Enil)) _) |- _ ] => + inv H; InvEval1 + | [ H: (eval_exprlist _ _ _ _ _ Enil _) |- _ ] => + inv H; InvEval1 + | [ H: (eval_exprlist _ _ _ _ _ (_ ::: _) _) |- _ ] => + inv H; InvEval1 + | _ => + idtac + end. + +Ltac InvEval2 := + match goal with + | [ H: (eval_operation _ _ _ nil _ = Some _) |- _ ] => + simpl in H; inv H + | [ H: (eval_operation _ _ _ (_ :: nil) _ = Some _) |- _ ] => + simpl in H; FuncInv + | [ H: (eval_operation _ _ _ (_ :: _ :: nil) _ = Some _) |- _ ] => + simpl in H; FuncInv + | [ H: (eval_operation _ _ _ (_ :: _ :: _ :: nil) _ = Some _) |- _ ] => + simpl in H; FuncInv + | _ => + idtac + end. + +Ltac InvEval := InvEval1; InvEval2; InvEval2. + +Ltac TrivialExists := + match goal with + | [ |- exists v, _ /\ Val.lessdef ?a v ] => exists a; split; [EvalOp | auto] + end. + +(** * Correctness of the smart constructors *) + +Section CMCONSTR. + +Variable ge: genv. +Variable sp: val. +Variable e: env. +Variable m: mem. + +(** We now show that the code generated by "smart constructor" functions + such as [Selection.notint] behaves as expected. Continuing the + [notint] example, we show that if the expression [e] + evaluates to some integer value [Vint n], then [Selection.notint e] + evaluates to a value [Vint (Int.not n)] which is indeed the integer + negation of the value of [e]. + + All proofs follow a common pattern: +- Reasoning by case over the result of the classification functions + (such as [add_match] for integer addition), gathering additional + information on the shape of the argument expressions in the non-default + cases. +- Inversion of the evaluations of the arguments, exploiting the additional + information thus gathered. +- Equational reasoning over the arithmetic operations performed, + using the lemmas from the [Int] and [Float] modules. +- Construction of an evaluation derivation for the expression returned + by the smart constructor. +*) + +Definition unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop := + forall le a x, + eval_expr ge sp e m le a x -> + exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef (sem x) v. + +Definition binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> val) : Prop := + forall le a x b y, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. + +(** ** Constants *) + +Theorem eval_addrsymbol: + forall le id ofs, + exists v, eval_expr ge sp e m le (addrsymbol id ofs) v /\ Val.lessdef (Genv.symbol_address ge id ofs) v. +Proof. + intros. unfold addrsymbol. TrivialExists. +Qed. + +Theorem eval_addrstack: + forall le ofs, + exists v, eval_expr ge sp e m le (addrstack ofs) v /\ Val.lessdef (Val.offset_ptr sp ofs) v. +Proof. + intros. unfold addrstack. TrivialExists. +Qed. + +(** ** Addition, opposite, subtraction *) + +Theorem eval_addimm: + forall n, unary_constructor_sound (addimm n) (fun x => Val.add x (Vint n)). +Proof. + red; unfold addimm; intros until x. + predSpec Int.eq Int.eq_spec n Int.zero. +- subst n. intros. exists x; split; auto. + destruct x; simpl; auto. rewrite Int.add_zero; auto. +- case (addimm_match a); intros; InvEval; simpl; TrivialExists; simpl. ++ rewrite Int.add_commut. auto. ++ subst x. rewrite Val.add_assoc. rewrite Int.add_commut. auto. +Qed. + +Theorem eval_add: binary_constructor_sound add Val.add. +Proof. + red; intros until y. + unfold add; case (add_match a b); intros; InvEval; subst. +- rewrite Val.add_commut. apply eval_addimm; auto. +- apply eval_addimm; auto. +- replace (Val.add (Val.add v1 (Vint n1)) (Val.add v0 (Vint n2))) + with (Val.add (Val.add v1 v0) (Val.add (Vint n1) (Vint n2))). + apply eval_addimm. EvalOp. + repeat rewrite Val.add_assoc. decEq. apply Val.add_permut. +- replace (Val.add (Val.add v1 (Vint n1)) y) + with (Val.add (Val.add v1 y) (Vint n1)). + apply eval_addimm. EvalOp. + repeat rewrite Val.add_assoc. decEq. apply Val.add_commut. +- rewrite <- Val.add_assoc. apply eval_addimm. EvalOp. +- rewrite Val.add_commut. TrivialExists. +- TrivialExists. +- rewrite Val.add_commut. TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_negint: unary_constructor_sound negint (fun v => Val.sub Vzero v). +Proof. + red; intros until x; unfold negint. case (negint_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_sub: binary_constructor_sound sub Val.sub. +Proof. + red; intros until y; unfold sub; case (sub_match a b); intros; InvEval; subst. +- rewrite Val.sub_add_opp. apply eval_addimm; auto. +- rewrite Val.sub_add_l. rewrite Val.sub_add_r. + rewrite Val.add_assoc. simpl. rewrite Int.add_commut. rewrite <- Int.sub_add_opp. + apply eval_addimm; EvalOp. +- rewrite Val.sub_add_l. apply eval_addimm; EvalOp. +- rewrite Val.sub_add_r. apply eval_addimm; EvalOp. +- TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +(** ** Immediate shifts *) + +Remark eval_shlimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int.iwordsize = true -> + eval_expr ge sp e m le (shlimm_base a n) (Val.shl x (Vint n)). +Proof. +Local Opaque mk_amount32. + unfold shlimm_base; intros; EvalOp. simpl. rewrite mk_amount32_eq by auto. auto. +Qed. + +Theorem eval_shlimm: + forall n, unary_constructor_sound (fun a => shlimm a n) + (fun x => Val.shl x (Vint n)). +Proof. + red; intros until x; unfold shlimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int.iwordsize) eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shl_zero; auto. +- destruct (shlimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu (Int.add a n) Int.iwordsize) eqn:L2. +* econstructor; split. eapply eval_shlimm_base; eauto. + destruct v1; simpl; auto. rewrite a32_range; simpl. rewrite L, L2. + rewrite Int.shl_shl; auto using a32_range. +* econstructor; split; [|eauto]. apply eval_shlimm_base; auto. EvalOp. ++ TrivialExists. simpl. rewrite mk_amount32_eq; auto. ++ TrivialExists. simpl. rewrite mk_amount32_eq; auto. ++ destruct (Int.ltu (Int.add a n) Int.iwordsize) eqn:L2. +* TrivialExists. simpl. rewrite mk_amount32_eq by auto. + destruct (Val.zero_ext s v1); simpl; auto. + rewrite a32_range; simpl; rewrite L, L2. + rewrite Int.shl_shl; auto using a32_range. +* econstructor; split. eapply eval_shlimm_base; eauto. EvalOp; simpl; eauto. auto. ++ destruct (Int.ltu (Int.add a n) Int.iwordsize) eqn:L2. +* TrivialExists. simpl. rewrite mk_amount32_eq by auto. + destruct (Val.sign_ext s v1); simpl; auto. + rewrite a32_range; simpl; rewrite L, L2. + rewrite Int.shl_shl; auto using a32_range. +* econstructor; split. eapply eval_shlimm_base; eauto. EvalOp; simpl; eauto. auto. ++ econstructor; eauto using eval_shlimm_base. +- intros; TrivialExists. +Qed. + +Remark eval_shruimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int.iwordsize = true -> + eval_expr ge sp e m le (shruimm_base a n) (Val.shru x (Vint n)). +Proof. + unfold shruimm_base; intros; EvalOp. simpl. rewrite mk_amount32_eq by auto. auto. +Qed. + +Remark sub_shift_amount: + forall y z, + Int.ltu y Int.iwordsize = true -> Int.ltu z Int.iwordsize = true -> Int.unsigned y <= Int.unsigned z -> + Int.ltu (Int.sub z y) Int.iwordsize = true. +Proof. + intros. unfold Int.ltu; apply zlt_true. rewrite Int.unsigned_repr_wordsize. + apply Int.ltu_iwordsize_inv in H. apply Int.ltu_iwordsize_inv in H0. + unfold Int.sub; rewrite Int.unsigned_repr. omega. + generalize Int.wordsize_max_unsigned; omega. +Qed. + +Theorem eval_shruimm: + forall n, unary_constructor_sound (fun a => shruimm a n) + (fun x => Val.shru x (Vint n)). +Proof. +Local Opaque Int.zwordsize. + red; intros until x; unfold shruimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int.iwordsize) eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shru_zero; auto. +- destruct (shruimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu n a) eqn:L2. +* assert (L3: Int.ltu (Int.sub a n) Int.iwordsize = true). + { apply sub_shift_amount; auto using a32_range. + apply Int.ltu_inv in L2. omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount32_eq, L3, a32_range by auto. + simpl. rewrite L. rewrite Int.shru_shl, L2 by auto using a32_range. auto. +* assert (L3: Int.ltu (Int.sub n a) Int.iwordsize = true). + { apply sub_shift_amount; auto using a32_range. + unfold Int.ltu in L2. destruct zlt in L2; discriminate || omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount32_eq, L3, a32_range by auto. + simpl. rewrite L. rewrite Int.shru_shl, L2 by auto using a32_range. auto. ++ destruct (Int.ltu (Int.add a n) Int.iwordsize) eqn:L2. +* econstructor; split. eapply eval_shruimm_base; eauto. + destruct v1; simpl; auto. rewrite a32_range; simpl. rewrite L, L2. + rewrite Int.shru_shru; auto using a32_range. +* econstructor; split; [|eauto]. apply eval_shruimm_base; auto. EvalOp. ++ destruct (zlt (Int.unsigned n) s). +* econstructor; split. EvalOp. rewrite mk_amount32_eq by auto. + destruct v1; simpl; auto. rewrite ! L; simpl. + set (s' := s - Int.unsigned n). + replace s with (s' + Int.unsigned n) by (unfold s'; omega). + rewrite Int.shru_zero_ext. auto. unfold s'; omega. +* econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite ! L; simpl. + rewrite Int.shru_zero_ext_0 by omega. auto. ++ econstructor; eauto using eval_shruimm_base. +- intros; TrivialExists. +Qed. + +Remark eval_shrimm_base: forall le a n x, + eval_expr ge sp e m le a x -> + Int.ltu n Int.iwordsize = true -> + eval_expr ge sp e m le (shrimm_base a n) (Val.shr x (Vint n)). +Proof. + unfold shrimm_base; intros; EvalOp. simpl. rewrite mk_amount32_eq by auto. auto. +Qed. + +Theorem eval_shrimm: + forall n, unary_constructor_sound (fun a => shrimm a n) + (fun x => Val.shr x (Vint n)). +Proof. + red; intros until x; unfold shrimm. + predSpec Int.eq Int.eq_spec n Int.zero; [| destruct (Int.ltu n Int.iwordsize) eqn:L]; simpl. +- intros; subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int.shr_zero; auto. +- destruct (shrimm_match a); intros; InvEval; subst. ++ TrivialExists. simpl; rewrite L; auto. ++ destruct (Int.ltu n a) eqn:L2. +* assert (L3: Int.ltu (Int.sub a n) Int.iwordsize = true). + { apply sub_shift_amount; auto using a32_range. + apply Int.ltu_inv in L2. omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount32_eq, L3, a32_range by auto. + simpl. rewrite L. rewrite Int.shr_shl, L2 by auto using a32_range. auto. +* assert (L3: Int.ltu (Int.sub n a) Int.iwordsize = true). + { apply sub_shift_amount; auto using a32_range. + unfold Int.ltu in L2. destruct zlt in L2; discriminate || omega. } + econstructor; split. EvalOp. + destruct v1; simpl; auto. rewrite mk_amount32_eq, L3, a32_range by auto. + simpl. rewrite L. rewrite Int.shr_shl, L2 by auto using a32_range. auto. ++ destruct (Int.ltu (Int.add a n) Int.iwordsize) eqn:L2. +* econstructor; split. eapply eval_shrimm_base; eauto. + destruct v1; simpl; auto. rewrite a32_range; simpl. rewrite L, L2. + rewrite Int.shr_shr; auto using a32_range. +* econstructor; split; [|eauto]. apply eval_shrimm_base; auto. EvalOp. ++ destruct (zlt (Int.unsigned n) s && zlt s Int.zwordsize) eqn:E. +* InvBooleans. econstructor; split. EvalOp. rewrite mk_amount32_eq by auto. + destruct v1; simpl; auto. rewrite ! L; simpl. + set (s' := s - Int.unsigned n). + replace s with (s' + Int.unsigned n) by (unfold s'; omega). + rewrite Int.shr_sign_ext. auto. unfold s'; omega. unfold s'; omega. +* econstructor; split; [|eauto]. apply eval_shrimm_base; auto. EvalOp. ++ econstructor; eauto using eval_shrimm_base. +- intros; TrivialExists. +Qed. + +(** ** Multiplication *) + +Lemma eval_mulimm_base: + forall n, unary_constructor_sound (mulimm_base n) (fun x => Val.mul x (Vint n)). +Proof. + intros; red; intros; unfold mulimm_base. + assert (DFL: exists v, eval_expr ge sp e m le (Eop Omul (Eop (Ointconst n) Enil ::: a ::: Enil)) v /\ Val.lessdef (Val.mul x (Vint n)) v). + { rewrite Val.mul_commut; TrivialExists. } + generalize (Int.one_bits_decomp n); generalize (Int.one_bits_range n); + destruct (Int.one_bits n) as [ | i [ | j []]]; intros P Q. +- apply DFL. +- replace (Val.mul x (Vint n)) with (Val.shl x (Vint i)). + apply eval_shlimm; auto. + simpl in Q. rewrite <- Val.shl_mul, Q, Int.add_zero. simpl. rewrite P by auto with coqlib. auto. +- exploit (eval_shlimm i (x :: le) (Eletvar 0) x). constructor; auto. intros [v1 [A1 B1]]. + exploit (eval_shlimm j (x :: le) (Eletvar 0) x). constructor; auto. intros [v2 [A2 B2]]. + exploit (eval_add (x :: le)). eexact A1. eexact A2. intros [v [A B]]. + exists v; split. econstructor; eauto. + simpl in Q. rewrite Q, Int.add_zero. + replace (Vint (Int.add (Int.shl Int.one i) (Int.shl Int.one j))) + with (Val.add (Val.shl Vone (Vint i)) (Val.shl Vone (Vint j))). + rewrite Val.mul_add_distr_r. + repeat rewrite Val.shl_mul. eapply Val.lessdef_trans; [|eauto]. apply Val.add_lessdef; auto. + simpl. repeat rewrite P by auto with coqlib. auto. +- apply DFL. +Qed. + +Theorem eval_mulimm: + forall n, unary_constructor_sound (mulimm n) (fun x => Val.mul x (Vint n)). +Proof. + intros; red; intros until x; unfold mulimm. + predSpec Int.eq Int.eq_spec n Int.zero. + intros. exists (Vint Int.zero); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int.mul_zero. auto. + predSpec Int.eq Int.eq_spec n Int.one. + intros. exists x; split; auto. + destruct x; simpl; auto. subst n. rewrite Int.mul_one. auto. + case (mulimm_match a); intros; InvEval; subst. +- TrivialExists. simpl. rewrite Int.mul_commut; auto. +- rewrite Val.mul_add_distr_l. + exploit eval_mulimm_base; eauto. instantiate (1 := n). intros [v' [A1 B1]]. + exploit (eval_addimm (Int.mul n n2) le (mulimm_base n t2) v'). auto. intros [v'' [A2 B2]]. + exists v''; split; auto. eapply Val.lessdef_trans. eapply Val.add_lessdef; eauto. + rewrite Val.mul_commut; auto. +- apply eval_mulimm_base; auto. +Qed. + +Theorem eval_mul: binary_constructor_sound mul Val.mul. +Proof. + red; intros until y; unfold mul; case (mul_match a b); intros; InvEval; subst. +- rewrite Val.mul_commut. apply eval_mulimm; auto. +- apply eval_mulimm; auto. +- TrivialExists. +Qed. + +Theorem eval_mulhs: binary_constructor_sound mulhs Val.mulhs. +Proof. + unfold mulhs; red; intros. econstructor; split. EvalOp. + unfold eval_shiftl, eval_extend. rewrite ! mk_amount64_eq by auto. + destruct x; simpl; auto. destruct y; simpl; auto. + change (Int.ltu Int.zero Int64.iwordsize') with true; simpl. + rewrite ! Int64.shl'_zero. + change (Int.ltu (Int.repr 32) Int64.iwordsize') with true; simpl. + apply Val.lessdef_same. f_equal. + transitivity (Int.repr (Z.shiftr (Int.signed i * Int.signed i0) 32)). + unfold Int.mulhs; f_equal. rewrite Zshiftr_div_two_p by omega. reflexivity. + apply Int.same_bits_eq; intros n N. + change Int.zwordsize with 32 in *. + assert (N1: 0 <= n < 64) by omega. + rewrite Int64.bits_loword by auto. + rewrite Int64.bits_shr' by auto. + change (Int.unsigned (Int.repr 32)) with 32. change Int64.zwordsize with 64. + rewrite zlt_true by omega. + rewrite Int.testbit_repr by auto. + unfold Int64.mul. rewrite Int64.testbit_repr by (change Int64.zwordsize with 64; omega). + transitivity (Z.testbit (Int.signed i * Int.signed i0) (n + 32)). + rewrite Z.shiftr_spec by omega. auto. + apply Int64.same_bits_eqm. apply Int64.eqm_mult; apply Int64.eqm_unsigned_repr. + change Int64.zwordsize with 64; omega. +Qed. + +Theorem eval_mulhu: binary_constructor_sound mulhu Val.mulhu. +Proof. + unfold mulhu; red; intros. econstructor; split. EvalOp. + unfold eval_shiftl, eval_extend. rewrite ! mk_amount64_eq by auto. + destruct x; simpl; auto. destruct y; simpl; auto. + change (Int.ltu Int.zero Int64.iwordsize') with true; simpl. + rewrite ! Int64.shl'_zero. + change (Int.ltu (Int.repr 32) Int64.iwordsize') with true; simpl. + apply Val.lessdef_same. f_equal. + transitivity (Int.repr (Z.shiftr (Int.unsigned i * Int.unsigned i0) 32)). + unfold Int.mulhu; f_equal. rewrite Zshiftr_div_two_p by omega. reflexivity. + apply Int.same_bits_eq; intros n N. + change Int.zwordsize with 32 in *. + assert (N1: 0 <= n < 64) by omega. + rewrite Int64.bits_loword by auto. + rewrite Int64.bits_shru' by auto. + change (Int.unsigned (Int.repr 32)) with 32. change Int64.zwordsize with 64. + rewrite zlt_true by omega. + rewrite Int.testbit_repr by auto. + unfold Int64.mul. rewrite Int64.testbit_repr by (change Int64.zwordsize with 64; omega). + transitivity (Z.testbit (Int.unsigned i * Int.unsigned i0) (n + 32)). + rewrite Z.shiftr_spec by omega. auto. + apply Int64.same_bits_eqm. apply Int64.eqm_mult; apply Int64.eqm_unsigned_repr. + change Int64.zwordsize with 64; omega. +Qed. + +(** Integer conversions *) + +Theorem eval_zero_ext: + forall sz, 0 <= sz -> unary_constructor_sound (zero_ext sz) (Val.zero_ext sz). +Proof. + intros; red; intros until x; unfold zero_ext; case (zero_ext_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- destruct (zlt (Int.unsigned a0) sz). ++ econstructor; split. EvalOp. destruct v1; simpl; auto. rewrite a32_range; simpl. + apply Val.lessdef_same. f_equal. rewrite Int.shl_zero_ext by omega. f_equal. omega. ++ TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_sign_ext: + forall sz, 0 < sz -> unary_constructor_sound (sign_ext sz) (Val.sign_ext sz). +Proof. + intros; red; intros until x; unfold sign_ext; case (sign_ext_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- destruct (zlt (Int.unsigned a0) sz). ++ econstructor; split. EvalOp. destruct v1; simpl; auto. rewrite a32_range; simpl. + apply Val.lessdef_same. f_equal. rewrite Int.shl_sign_ext by omega. f_equal. omega. ++ TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_cast8signed: unary_constructor_sound cast8signed (Val.sign_ext 8). +Proof. + apply eval_sign_ext; omega. +Qed. + +Theorem eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8). +Proof. + apply eval_zero_ext; omega. +Qed. + +Theorem eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16). +Proof. + apply eval_sign_ext; omega. +Qed. + +Theorem eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16). +Proof. + apply eval_zero_ext; omega. +Qed. + +(** Bitwise not, and, or, xor *) + +Theorem eval_notint: unary_constructor_sound notint Val.notint. +Proof. + assert (INV: forall v, Val.lessdef (Val.notint (Val.notint v)) v). + { destruct v; auto. simpl; rewrite Int.not_involutive; auto. } + unfold notint; red; intros until x; case (notint_match a); intros; InvEval; subst. +- TrivialExists. +- TrivialExists. +- exists v1; auto. +- exists (eval_shift s v1 a0); split; auto. EvalOp. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + rewrite Int.not_and_or_not, Int.not_involutive, Int.or_commut. auto. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + rewrite Int.not_or_and_not, Int.not_involutive, Int.and_commut. auto. +- econstructor; split. EvalOp. + rewrite ! Val.not_xor, Val.xor_assoc; auto. +- econstructor; split. EvalOp. + destruct v1; simpl; auto; destruct v0; simpl; auto. + unfold Int.not; rewrite ! Int.xor_assoc, Int.xor_idem, Int.xor_zero. auto. +- TrivialExists. +Qed. + +Lemma eval_andimm_base: + forall n, unary_constructor_sound (andimm_base n) (fun x => Val.and x (Vint n)). +Proof. + intros; red; intros. unfold andimm_base. + predSpec Int.eq Int.eq_spec n Int.zero. + exists (Vint Int.zero); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int.and_zero. auto. + predSpec Int.eq Int.eq_spec n Int.mone. + exists x; split; auto. + subst. destruct x; simpl; auto. rewrite Int.and_mone; auto. + destruct (Z_is_power2m1 (Int.unsigned n)) as [s|] eqn:P. + assert (0 <= s) by (eapply Z_is_power2m1_nonneg; eauto). + rewrite <- (Int.repr_unsigned n), (Z_is_power2m1_sound _ _ P), <- Val.zero_ext_and by auto. + apply eval_zero_ext; auto. + TrivialExists. +Qed. + +Theorem eval_andimm: + forall n, unary_constructor_sound (andimm n) (fun x => Val.and x (Vint n)). +Proof. + intros; red; intros until x. unfold andimm. + case (andimm_match a); intros; InvEval; subst. +- rewrite Int.and_commut; TrivialExists. +- rewrite Val.and_assoc, Int.and_commut. apply eval_andimm_base; auto. +- destruct (zle 0 s). ++ rewrite Val.zero_ext_and, Val.and_assoc, Int.and_commut by auto. + apply eval_andimm_base; auto. ++ apply eval_andimm_base. EvalOp. +- apply eval_andimm_base; auto. +Qed. + +Theorem eval_and: binary_constructor_sound and Val.and. +Proof. + red; intros until y; unfold and; case (and_match a b); intros; InvEval; subst. +- rewrite Val.and_commut; apply eval_andimm; auto. +- apply eval_andimm; auto. +- rewrite Val.and_commut; TrivialExists. +- TrivialExists. +- rewrite Val.and_commut; TrivialExists. +- TrivialExists. +- rewrite Val.and_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_orimm: + forall n, unary_constructor_sound (orimm n) (fun x => Val.or x (Vint n)). +Proof. + intros; red; intros until x. unfold orimm. + predSpec Int.eq Int.eq_spec n Int.zero. + intros. subst. exists x; split; auto. + destruct x; simpl; auto. rewrite Int.or_zero; auto. + predSpec Int.eq Int.eq_spec n Int.mone. + intros. exists (Vint Int.mone); split. EvalOp. + destruct x; simpl; auto. subst n. rewrite Int.or_mone. auto. + destruct (orimm_match a); intros; InvEval; subst. +- rewrite Int.or_commut; TrivialExists. +- rewrite Val.or_assoc, Int.or_commut; TrivialExists. +- TrivialExists. +Qed. + +Remark eval_same_expr: + forall a1 a2 le v1 v2, + same_expr_pure a1 a2 = true -> + eval_expr ge sp e m le a1 v1 -> + eval_expr ge sp e m le a2 v2 -> + a1 = a2 /\ v1 = v2. +Proof. + intros. destruct a1; try discriminate. destruct a2; try discriminate. + simpl in H; destruct (ident_eq i i0); inv H. + split. auto. inv H0; inv H1; congruence. +Qed. + +Theorem eval_or: binary_constructor_sound or Val.or. +Proof. + red; intros until y; unfold or; case (or_match a b); intros; InvEval; subst. +- rewrite Val.or_commut. apply eval_orimm; auto. +- apply eval_orimm; auto. +- rewrite Val.or_commut; TrivialExists. +- TrivialExists. +- rewrite Val.or_commut; TrivialExists. +- TrivialExists. +- (* shl - shru *) + destruct (Int.eq (Int.add a1 a2) Int.iwordsize && same_expr_pure t1 t2) eqn:?. ++ InvBooleans. apply Int.same_if_eq in H. + exploit eval_same_expr; eauto. intros [EQ1 EQ2]. subst. + econstructor; split. EvalOp. + destruct v0; simpl; auto. rewrite ! a32_range. simpl. rewrite <- Int.or_ror; auto using a32_range. ++ TrivialExists. +- (* shru - shl *) + destruct (Int.eq (Int.add a2 a1) Int.iwordsize && same_expr_pure t1 t2) eqn:?. ++ InvBooleans. apply Int.same_if_eq in H. + exploit eval_same_expr; eauto. intros [EQ1 EQ2]. subst. + econstructor; split. EvalOp. + destruct v0; simpl; auto. rewrite ! a32_range. simpl. + rewrite Int.or_commut, <- Int.or_ror; auto using a32_range. ++ TrivialExists. +- rewrite Val.or_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +Lemma eval_xorimm_base: + forall n, unary_constructor_sound (xorimm_base n) (fun x => Val.xor x (Vint n)). +Proof. + intros; red; intros. unfold xorimm_base. + predSpec Int.eq Int.eq_spec n Int.zero. + intros. exists x; split. auto. + destruct x; simpl; auto. subst n. rewrite Int.xor_zero. auto. + predSpec Int.eq Int.eq_spec n Int.mone. + subst n. rewrite <- Val.not_xor. apply eval_notint; auto. + TrivialExists. +Qed. + +Theorem eval_xorimm: + forall n, unary_constructor_sound (xorimm n) (fun x => Val.xor x (Vint n)). +Proof. + intros; red; intros until x. unfold xorimm. + destruct (xorimm_match a); intros; InvEval; subst. +- rewrite Int.xor_commut; TrivialExists. +- rewrite Val.xor_assoc; simpl. rewrite (Int.xor_commut n2). apply eval_xorimm_base; auto. +- apply eval_xorimm_base; auto. +Qed. + +Theorem eval_xor: binary_constructor_sound xor Val.xor. +Proof. + red; intros until y; unfold xor; case (xor_match a b); intros; InvEval; subst. +- rewrite Val.xor_commut; apply eval_xorimm; auto. +- apply eval_xorimm; auto. +- rewrite Val.xor_commut; TrivialExists. +- TrivialExists. +- rewrite Val.xor_commut; TrivialExists. +- TrivialExists. +- rewrite Val.xor_commut; TrivialExists. +- TrivialExists. +- TrivialExists. +Qed. + +(** ** Integer division and modulus *) + +Theorem eval_divs_base: + forall le a b x y z, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.divs x y = Some z -> + exists v, eval_expr ge sp e m le (divs_base a b) v /\ Val.lessdef z v. +Proof. + intros; unfold divs_base; TrivialExists. +Qed. + +Theorem eval_mods_base: + forall le a b x y z, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.mods x y = Some z -> + exists v, eval_expr ge sp e m le (mods_base a b) v /\ Val.lessdef z v. +Proof. + intros; unfold mods_base, mod_aux. + exploit Val.mods_divs; eauto. intros (q & A & B). subst z. + TrivialExists. repeat (econstructor; eauto with evalexpr). exact A. +Qed. + +Theorem eval_divu_base: + forall le a x b y z, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.divu x y = Some z -> + exists v, eval_expr ge sp e m le (divu_base a b) v /\ Val.lessdef z v. +Proof. + intros; unfold divu_base; TrivialExists. +Qed. + +Theorem eval_modu_base: + forall le a x b y z, + eval_expr ge sp e m le a x -> + eval_expr ge sp e m le b y -> + Val.modu x y = Some z -> + exists v, eval_expr ge sp e m le (modu_base a b) v /\ Val.lessdef z v. +Proof. + intros; unfold modu_base, mod_aux. + exploit Val.modu_divu; eauto. intros (q & A & B). subst z. + TrivialExists. repeat (econstructor; eauto with evalexpr). exact A. +Qed. + +Theorem eval_shrximm: + forall le a n x z, + eval_expr ge sp e m le a x -> + Val.shrx x (Vint n) = Some z -> + exists v, eval_expr ge sp e m le (shrximm a n) v /\ Val.lessdef z v. +Proof. + intros; unfold shrximm. + predSpec Int.eq Int.eq_spec n Int.zero. +- subst n. exists x; split; auto. + destruct x; simpl in H0; try discriminate. + change (Int.ltu Int.zero (Int.repr 31)) with true in H0; inv H0. + rewrite Int.shrx_zero by (compute; auto). auto. +- TrivialExists. +Qed. + +(** General shifts *) + +Theorem eval_shl: binary_constructor_sound shl Val.shl. +Proof. + red; intros until y; unfold shl; case (shl_match b); intros. + InvEval. apply eval_shlimm; auto. + TrivialExists. +Qed. + +Theorem eval_shr: binary_constructor_sound shr Val.shr. +Proof. + red; intros until y; unfold shr; case (shr_match b); intros. + InvEval. apply eval_shrimm; auto. + TrivialExists. +Qed. + +Theorem eval_shru: binary_constructor_sound shru Val.shru. +Proof. + red; intros until y; unfold shru; case (shru_match b); intros. + InvEval. apply eval_shruimm; auto. + TrivialExists. +Qed. + +(** Floating-point operations *) + +Theorem eval_negf: unary_constructor_sound negf Val.negf. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_absf: unary_constructor_sound absf Val.absf. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_addf: binary_constructor_sound addf Val.addf. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_subf: binary_constructor_sound subf Val.subf. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_mulf: binary_constructor_sound mulf Val.mulf. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_negfs: unary_constructor_sound negfs Val.negfs. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_absfs: unary_constructor_sound absfs Val.absfs. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_addfs: binary_constructor_sound addfs Val.addfs. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_subfs: binary_constructor_sound subfs Val.subfs. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_mulfs: binary_constructor_sound mulfs Val.mulfs. +Proof. + red; intros; TrivialExists. +Qed. + +Section COMP_IMM. + +Variable default: comparison -> int -> condition. +Variable intsem: comparison -> int -> int -> bool. +Variable sem: comparison -> val -> val -> val. + +Hypothesis sem_int: forall c x y, sem c (Vint x) (Vint y) = Val.of_bool (intsem c x y). +Hypothesis sem_undef: forall c v, sem c Vundef v = Vundef. +Hypothesis sem_eq: forall x y, sem Ceq (Vint x) (Vint y) = Val.of_bool (Int.eq x y). +Hypothesis sem_ne: forall x y, sem Cne (Vint x) (Vint y) = Val.of_bool (negb (Int.eq x y)). +Hypothesis sem_default: forall c v n, sem c v (Vint n) = Val.of_optbool (eval_condition (default c n) (v :: nil) m). + +Lemma eval_compimm: + forall le c a n2 x, + eval_expr ge sp e m le a x -> + exists v, eval_expr ge sp e m le (compimm default intsem c a n2) v + /\ Val.lessdef (sem c x (Vint n2)) v. +Proof. + intros until x. + unfold compimm; case (compimm_match c a); intros; InvEval; subst. +- (* constant *) + rewrite sem_int. TrivialExists. simpl. destruct (intsem c0 n1 n2); auto. +- (* eq cmp *) + inv H. simpl in H5. inv H5. + destruct (Int.eq_dec n2 Int.zero). subst n2. TrivialExists. + simpl. rewrite eval_negate_condition. + destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_eq; auto. + rewrite sem_undef; auto. + destruct (Int.eq_dec n2 Int.one). subst n2. TrivialExists. + simpl. destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_eq; auto. + rewrite sem_undef; auto. + exists (Vint Int.zero); split. EvalOp. + destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; rewrite sem_eq; rewrite Int.eq_false; auto. + rewrite sem_undef; auto. +- (* ne cmp *) + inv H. simpl in H5. inv H5. + destruct (Int.eq_dec n2 Int.zero). subst n2. TrivialExists. + simpl. destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_ne; auto. + rewrite sem_undef; auto. + destruct (Int.eq_dec n2 Int.one). subst n2. TrivialExists. + simpl. rewrite eval_negate_condition. destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; simpl; rewrite sem_ne; auto. + rewrite sem_undef; auto. + exists (Vint Int.one); split. EvalOp. + destruct (eval_condition c0 vl m); simpl. + unfold Vtrue, Vfalse. destruct b; rewrite sem_ne; rewrite Int.eq_false; auto. + rewrite sem_undef; auto. +- (* mask zero *) + predSpec Int.eq Int.eq_spec n2 Int.zero. ++ subst n2. econstructor; split. EvalOp. simpl. + destruct v1; simpl; try (rewrite sem_undef; auto). + rewrite sem_eq. destruct (Int.eq (Int.and i m0) Int.zero); auto. ++ TrivialExists. simpl. rewrite sem_default. auto. +- (* mask not zero *) + predSpec Int.eq Int.eq_spec n2 Int.zero. ++ subst n2. econstructor; split. EvalOp. simpl. + destruct v1; simpl; try (rewrite sem_undef; auto). + rewrite sem_ne. destruct (Int.eq (Int.and i m0) Int.zero); auto. ++ TrivialExists. simpl. rewrite sem_default. auto. +- (* default *) + TrivialExists. simpl. rewrite sem_default. auto. +Qed. + +Hypothesis sem_swap: + forall c x y, sem (swap_comparison c) x y = sem c y x. + +Lemma eval_compimm_swap: + forall le c a n2 x, + eval_expr ge sp e m le a x -> + exists v, eval_expr ge sp e m le (compimm default intsem (swap_comparison c) a n2) v + /\ Val.lessdef (sem c (Vint n2) x) v. +Proof. + intros. rewrite <- sem_swap. eapply eval_compimm; eauto. +Qed. + +End COMP_IMM. + +Theorem eval_comp: + forall c, binary_constructor_sound (comp c) (Val.cmp c). +Proof. + intros; red; intros until y. unfold comp; case (comp_match a b); intros; InvEval; subst. +- eapply eval_compimm_swap; eauto. + intros. unfold Val.cmp. rewrite Val.swap_cmp_bool; auto. +- eapply eval_compimm; eauto. +- TrivialExists. simpl. rewrite Val.swap_cmp_bool. auto. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_compu: + forall c, binary_constructor_sound (compu c) (Val.cmpu (Mem.valid_pointer m) c). +Proof. + intros; red; intros until y. unfold compu; case (compu_match a b); intros; InvEval; subst. +- eapply eval_compimm_swap; eauto. + intros. unfold Val.cmpu. rewrite Val.swap_cmpu_bool; auto. +- eapply eval_compimm; eauto. +- TrivialExists. simpl. rewrite Val.swap_cmpu_bool. auto. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_compf: + forall c, binary_constructor_sound (compf c) (Val.cmpf c). +Proof. + intros; red; intros. unfold compf. TrivialExists. +Qed. + +Theorem eval_compfs: + forall c, binary_constructor_sound (compfs c) (Val.cmpfs c). +Proof. + intros; red; intros. unfold compfs. TrivialExists. +Qed. + +(** Floating-point conversions *) + +Theorem eval_singleoffloat: unary_constructor_sound singleoffloat Val.singleoffloat. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_floatofsingle: unary_constructor_sound floatofsingle Val.floatofsingle. +Proof. + red; intros; TrivialExists. +Qed. + +Theorem eval_intoffloat: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.intoffloat x = Some y -> + exists v, eval_expr ge sp e m le (intoffloat a) v /\ Val.lessdef y v. +Proof. + intros; TrivialExists. +Qed. + +Theorem eval_floatofint: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.floatofint x = Some y -> + exists v, eval_expr ge sp e m le (floatofint a) v /\ Val.lessdef y v. +Proof. + intros until y; unfold floatofint. case (floatofint_match a); intros; InvEval. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_intuoffloat: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.intuoffloat x = Some y -> + exists v, eval_expr ge sp e m le (intuoffloat a) v /\ Val.lessdef y v. +Proof. + intros; TrivialExists. +Qed. + +Theorem eval_floatofintu: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.floatofintu x = Some y -> + exists v, eval_expr ge sp e m le (floatofintu a) v /\ Val.lessdef y v. +Proof. + intros until y; unfold floatofintu. case (floatofintu_match a); intros; InvEval. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_intofsingle: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.intofsingle x = Some y -> + exists v, eval_expr ge sp e m le (intofsingle a) v /\ Val.lessdef y v. +Proof. + intros; TrivialExists. +Qed. + +Theorem eval_singleofint: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.singleofint x = Some y -> + exists v, eval_expr ge sp e m le (singleofint a) v /\ Val.lessdef y v. +Proof. + intros until y; unfold singleofint. case (singleofint_match a); intros; InvEval. +- TrivialExists. +- TrivialExists. +Qed. + +Theorem eval_intuofsingle: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.intuofsingle x = Some y -> + exists v, eval_expr ge sp e m le (intuofsingle a) v /\ Val.lessdef y v. +Proof. + intros; TrivialExists. +Qed. + +Theorem eval_singleofintu: + forall le a x y, + eval_expr ge sp e m le a x -> + Val.singleofintu x = Some y -> + exists v, eval_expr ge sp e m le (singleofintu a) v /\ Val.lessdef y v. +Proof. + intros until y; unfold singleofintu. case (singleofintu_match a); intros; InvEval. +- TrivialExists. +- TrivialExists. +Qed. + +(** Selection *) + +Theorem eval_select: + forall le ty cond al vl a1 v1 a2 v2 a b, + select ty cond al a1 a2 = Some a -> + eval_exprlist ge sp e m le al vl -> + eval_expr ge sp e m le a1 v1 -> + eval_expr ge sp e m le a2 v2 -> + eval_condition cond vl m = Some b -> + exists v, + eval_expr ge sp e m le a v + /\ Val.lessdef (Val.select (Some b) v1 v2 ty) v. +Proof. + unfold select; intros. + destruct (match ty with Tint | Tlong | Tfloat | Tsingle => true | _ => false end); inv H. + rewrite <- H3; TrivialExists. +Qed. + +(** Addressing modes *) + +Theorem eval_addressing: + forall le chunk a v b ofs, + eval_expr ge sp e m le a v -> + v = Vptr b ofs -> + match addressing chunk a with (mode, args) => + exists vl, + eval_exprlist ge sp e m le args vl /\ + eval_addressing ge sp mode vl = Some v + end. +Proof. + intros until v. unfold addressing; case (addressing_match a); intros; InvEval. +- econstructor; split. EvalOp. simpl; auto. +- econstructor; split. EvalOp. simpl; auto. +- econstructor; split. EvalOp. simpl. + destruct v1; try discriminate. rewrite <- H; auto. +- econstructor; split. EvalOp. simpl. congruence. +- econstructor; split. EvalOp. simpl. congruence. +- econstructor; split. EvalOp. simpl. congruence. +- econstructor; split. EvalOp. simpl. rewrite H0. simpl. rewrite Ptrofs.add_zero; auto. +Qed. + +(** Builtins *) + +Theorem eval_builtin_arg: + forall a v, + eval_expr ge sp e m nil a v -> + CminorSel.eval_builtin_arg ge sp e m (builtin_arg a) v. +Proof. + intros until v. unfold builtin_arg; case (builtin_arg_match a); intros; InvEval. +- constructor. +- constructor. +- constructor. +- constructor. +- inv H. InvEval. simpl in H6. inv H6. constructor; auto. +- subst v. repeat constructor; auto. +- constructor; auto. +Qed. + +(** Platform-specific known builtins *) + +Theorem eval_platform_builtin: + forall bf al a vl v le, + platform_builtin bf al = Some a -> + eval_exprlist ge sp e m le al vl -> + platform_builtin_sem bf vl = Some v -> + exists v', eval_expr ge sp e m le a v' /\ Val.lessdef v v'. +Proof. + intros. discriminate. +Qed. + +End CMCONSTR. diff --git a/aarch64/Stacklayout.v b/aarch64/Stacklayout.v new file mode 100644 index 00000000..86ba9f45 --- /dev/null +++ b/aarch64/Stacklayout.v @@ -0,0 +1,140 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(** Machine- and ABI-dependent layout information for activation records. *) + +Require Import Coqlib. +Require Import AST Memory Separation. +Require Import Bounds. + +Local Open Scope sep_scope. + +(** The general shape of activation records is as follows, + from bottom (lowest offsets) to top: +- Space for outgoing arguments to function calls. +- Back link to parent frame +- Return address +- Saved values of callee-save registers used by the function. +- Local stack slots. +- Space for the stack-allocated data declared in Cminor. + +The stack pointer is kept 16-aligned. +*) + +Definition fe_ofs_arg := 0. + +Definition make_env (b: bounds) : frame_env := + let olink := align (4 * b.(bound_outgoing)) 8 in (* back link *) + let oretaddr := olink + 8 in (* return address *) + let ocs := oretaddr + 8 in (* callee-saves *) + let ol := align (size_callee_save_area b ocs) 8 in (* locals *) + let ostkdata := align (ol + 4 * b.(bound_local)) 8 in (* stack data *) + let sz := align (ostkdata + b.(bound_stack_data)) 16 in + {| fe_size := sz; + fe_ofs_link := olink; + fe_ofs_retaddr := oretaddr; + fe_ofs_local := ol; + fe_ofs_callee_save := ocs; + fe_stack_data := ostkdata; + fe_used_callee_save := b.(used_callee_save) |}. + +Lemma frame_env_separated: + forall b sp m P, + let fe := make_env b in + m |= range sp 0 (fe_stack_data fe) ** range sp (fe_stack_data fe + bound_stack_data b) (fe_size fe) ** P -> + m |= range sp (fe_ofs_local fe) (fe_ofs_local fe + 4 * bound_local b) + ** range sp fe_ofs_arg (fe_ofs_arg + 4 * bound_outgoing b) + ** range sp (fe_ofs_link fe) (fe_ofs_link fe + size_chunk Mptr) + ** range sp (fe_ofs_retaddr fe) (fe_ofs_retaddr fe + size_chunk Mptr) + ** range sp (fe_ofs_callee_save fe) (size_callee_save_area b (fe_ofs_callee_save fe)) + ** P. +Proof. +Local Opaque Z.add Z.mul sepconj range. + intros; simpl. + set (olink := align (4 * b.(bound_outgoing)) 8). + set (oretaddr := olink + 8). + set (ocs := oretaddr + 8). + set (ol := align (size_callee_save_area b ocs) 8). + set (ostkdata := align (ol + 4 * b.(bound_local)) 8). + change (size_chunk Mptr) with 8. + generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. + assert (0 <= 4 * b.(bound_outgoing)) by omega. + assert (4 * b.(bound_outgoing) <= olink) by (apply align_le; omega). + assert (olink + 8 <= oretaddr) by (unfold oretaddr; omega). + assert (oretaddr + 8 <= ocs) by (unfold ocs; omega). + assert (ocs <= size_callee_save_area b ocs) by (apply size_callee_save_area_incr). + assert (size_callee_save_area b ocs <= ol) by (apply align_le; omega). + assert (ol + 4 * b.(bound_local) <= ostkdata) by (apply align_le; omega). +(* Reorder as: + outgoing + back link + retaddr + callee-save + local *) + rewrite sep_swap12. + rewrite sep_swap23. + rewrite sep_swap34. + rewrite sep_swap45. +(* Apply range_split and range_split2 repeatedly *) + unfold fe_ofs_arg. + apply range_split_2. fold olink; omega. omega. + apply range_split. omega. + apply range_split. omega. + apply range_split_2. fold ol. omega. omega. + apply range_drop_right with ostkdata. omega. + eapply sep_drop2. eexact H. +Qed. + +Lemma frame_env_range: + forall b, + let fe := make_env b in + 0 <= fe_stack_data fe /\ fe_stack_data fe + bound_stack_data b <= fe_size fe. +Proof. + intros; simpl. + set (olink := align (4 * b.(bound_outgoing)) 8). + set (oretaddr := olink + 8). + set (ocs := oretaddr + 8). + set (ol := align (size_callee_save_area b ocs) 8). + set (ostkdata := align (ol + 4 * b.(bound_local)) 8). + generalize b.(bound_local_pos) b.(bound_outgoing_pos) b.(bound_stack_data_pos); intros. + assert (0 <= 4 * b.(bound_outgoing)) by omega. + assert (4 * b.(bound_outgoing) <= olink) by (apply align_le; omega). + assert (olink + 8 <= oretaddr) by (unfold oretaddr; omega). + assert (oretaddr + 8 <= ocs) by (unfold ocs; omega). + assert (ocs <= size_callee_save_area b ocs) by (apply size_callee_save_area_incr). + assert (size_callee_save_area b ocs <= ol) by (apply align_le; omega). + assert (ol + 4 * b.(bound_local) <= ostkdata) by (apply align_le; omega). + split. omega. apply align_le. omega. +Qed. + +Lemma frame_env_aligned: + forall b, + let fe := make_env b in + (8 | fe_ofs_arg) + /\ (8 | fe_ofs_local fe) + /\ (8 | fe_stack_data fe) + /\ (align_chunk Mptr | fe_ofs_link fe) + /\ (align_chunk Mptr | fe_ofs_retaddr fe). +Proof. + intros; simpl. + set (olink := align (4 * b.(bound_outgoing)) 8). + set (oretaddr := olink + 8). + set (ocs := oretaddr + 8). + set (ol := align (size_callee_save_area b ocs) 8). + set (ostkdata := align (ol + 4 * b.(bound_local)) 8). + change (align_chunk Mptr) with 8. + split. apply Z.divide_0_r. + split. apply align_divides; omega. + split. apply align_divides; omega. + split. apply align_divides; omega. + apply Z.divide_add_r. apply align_divides; omega. apply Z.divide_refl. +Qed. diff --git a/aarch64/TargetPrinter.ml b/aarch64/TargetPrinter.ml new file mode 100644 index 00000000..e54673dd --- /dev/null +++ b/aarch64/TargetPrinter.ml @@ -0,0 +1,592 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(* Printing AArch64 assembly code in asm syntax *) + +open Printf +open Camlcoq +open Sections +open AST +open Asm +open AisAnnot +open PrintAsmaux +open Fileinfo + +(* Recognition of FP numbers that are supported by the fmov #imm instructions: + "a normalized binary floating point encoding with 1 sign bit, + 4 bits of fraction and a 3-bit exponent" +*) + +let is_immediate_float64 bits = + let exp = (Int64.(to_int (shift_right_logical bits 52)) land 0x7FF) - 1023 in + let mant = Int64.logand bits 0xF_FFFF_FFFF_FFFFL in + exp >= -3 && exp <= 4 && Int64.logand mant 0xF_0000_0000_0000L = mant + +let is_immediate_float32 bits = + let exp = (Int32.(to_int (shift_right_logical bits 23)) land 0xFF) - 127 in + let mant = Int32.logand bits 0x7F_FFFFl in + exp >= -3 && exp <= 4 && Int32.logand mant 0x78_0000l = mant + +(* Module containing the printing functions *) + +module Target : TARGET = + struct + +(* Basic printing functions *) + + let comment = "//" + + let symbol = elf_symbol + let symbol_offset = elf_symbol_offset + let label = elf_label + + let print_label oc lbl = label oc (transl_label lbl) + + let intsz oc (sz, n) = + match sz with X -> coqint64 oc n | W -> coqint oc n + + let xreg_name = function + | X0 -> "x0" | X1 -> "x1" | X2 -> "x2" | X3 -> "x3" + | X4 -> "x4" | X5 -> "x5" | X6 -> "x6" | X7 -> "x7" + | X8 -> "x8" | X9 -> "x9" | X10 -> "x10" | X11 -> "x11" + | X12 -> "x12" | X13 -> "x13" | X14 -> "x14" | X15 -> "x15" + | X16 -> "x16" | X17 -> "x17" | X18 -> "x18" | X19 -> "x19" + | X20 -> "x20" | X21 -> "x21" | X22 -> "x22" | X23 -> "x23" + | X24 -> "x24" | X25 -> "x25" | X26 -> "x26" | X27 -> "x27" + | X28 -> "x28" | X29 -> "x29" | X30 -> "x30" + + let wreg_name = function + | X0 -> "w0" | X1 -> "w1" | X2 -> "w2" | X3 -> "w3" + | X4 -> "w4" | X5 -> "w5" | X6 -> "w6" | X7 -> "w7" + | X8 -> "w8" | X9 -> "w9" | X10 -> "w10" | X11 -> "w11" + | X12 -> "w12" | X13 -> "w13" | X14 -> "w14" | X15 -> "w15" + | X16 -> "w16" | X17 -> "w17" | X18 -> "w18" | X19 -> "w19" + | X20 -> "w20" | X21 -> "w21" | X22 -> "w22" | X23 -> "w23" + | X24 -> "w24" | X25 -> "w25" | X26 -> "w26" | X27 -> "w27" + | X28 -> "w28" | X29 -> "w29" | X30 -> "w30" + + let xreg0_name = function RR0 r -> xreg_name r | XZR -> "xzr" + let wreg0_name = function RR0 r -> wreg_name r | XZR -> "wzr" + + let xregsp_name = function RR1 r -> xreg_name r | XSP -> "sp" + let wregsp_name = function RR1 r -> wreg_name r | XSP -> "wsp" + + let dreg_name = function + | D0 -> "d0" | D1 -> "d1" | D2 -> "d2" | D3 -> "d3" + | D4 -> "d4" | D5 -> "d5" | D6 -> "d6" | D7 -> "d7" + | D8 -> "d8" | D9 -> "d9" | D10 -> "d10" | D11 -> "d11" + | D12 -> "d12" | D13 -> "d13" | D14 -> "d14" | D15 -> "d15" + | D16 -> "d16" | D17 -> "d17" | D18 -> "d18" | D19 -> "d19" + | D20 -> "d20" | D21 -> "d21" | D22 -> "d22" | D23 -> "d23" + | D24 -> "d24" | D25 -> "d25" | D26 -> "d26" | D27 -> "d27" + | D28 -> "d28" | D29 -> "d29" | D30 -> "d30" | D31 -> "d31" + + let sreg_name = function + | D0 -> "s0" | D1 -> "s1" | D2 -> "s2" | D3 -> "s3" + | D4 -> "s4" | D5 -> "s5" | D6 -> "s6" | D7 -> "s7" + | D8 -> "s8" | D9 -> "s9" | D10 -> "s10" | D11 -> "s11" + | D12 -> "s12" | D13 -> "s13" | D14 -> "s14" | D15 -> "s15" + | D16 -> "s16" | D17 -> "s17" | D18 -> "s18" | D19 -> "s19" + | D20 -> "s20" | D21 -> "s21" | D22 -> "s22" | D23 -> "s23" + | D24 -> "s24" | D25 -> "s25" | D26 -> "s26" | D27 -> "s27" + | D28 -> "s28" | D29 -> "s29" | D30 -> "s30" | D31 -> "s31" + + let xreg oc r = output_string oc (xreg_name r) + let wreg oc r = output_string oc (wreg_name r) + let ireg oc (sz, r) = + output_string oc (match sz with X -> xreg_name r | W -> wreg_name r) + + let xreg0 oc r = output_string oc (xreg0_name r) + let wreg0 oc r = output_string oc (wreg0_name r) + let ireg0 oc (sz, r) = + output_string oc (match sz with X -> xreg0_name r | W -> wreg0_name r) + + let xregsp oc r = output_string oc (xregsp_name r) + let iregsp oc (sz, r) = + output_string oc (match sz with X -> xregsp_name r | W -> wregsp_name r) + + let dreg oc r = output_string oc (dreg_name r) + let sreg oc r = output_string oc (sreg_name r) + let freg oc (sz, r) = + output_string oc (match sz with D -> dreg_name r | S -> sreg_name r) + + let preg_asm oc ty = function + | IR r -> if ty = Tint then wreg oc r else xreg oc r + | FR r -> if ty = Tsingle then sreg oc r else dreg oc r + | _ -> assert false + + let preg_annot = function + | IR r -> xreg_name r + | FR r -> dreg_name r + | _ -> assert false + +(* Names of sections *) + + let name_of_section = function + | Section_text -> ".text" + | Section_data i | Section_small_data i -> + if i then ".data" else common_section () + | Section_const i | Section_small_const i -> + if i || (not !Clflags.option_fcommon) then ".section .rodata" else "COMM" + | Section_string -> ".section .rodata" + | Section_literal -> ".section .rodata" + | Section_jumptable -> ".section .rodata" + | Section_debug_info _ -> ".section .debug_info,\"\",%progbits" + | Section_debug_loc -> ".section .debug_loc,\"\",%progbits" + | Section_debug_abbrev -> ".section .debug_abbrev,\"\",%progbits" + | Section_debug_line _ -> ".section .debug_line,\"\",%progbits" + | Section_debug_ranges -> ".section .debug_ranges,\"\",%progbits" + | Section_debug_str -> ".section .debug_str,\"MS\",%progbits,1" + | Section_user(s, wr, ex) -> + sprintf ".section \"%s\",\"a%s%s\",%%progbits" + s (if wr then "w" else "") (if ex then "x" else "") + | Section_ais_annotation -> sprintf ".section \"__compcert_ais_annotations\",\"\",@note" + + let section oc sec = + fprintf oc " %s\n" (name_of_section sec) + +(* Associate labels to floating-point constants and to symbols. *) + + let emit_constants oc lit = + if exists_constants () then begin + section oc lit; + if Hashtbl.length literal64_labels > 0 then + begin + fprintf oc " .balign 8\n"; + Hashtbl.iter + (fun bf lbl -> fprintf oc "%a: .quad 0x%Lx\n" label lbl bf) + literal64_labels + end; + if Hashtbl.length literal32_labels > 0 then + begin + fprintf oc " .balign 4\n"; + Hashtbl.iter + (fun bf lbl -> + fprintf oc "%a: .long 0x%lx\n" label lbl bf) + literal32_labels + end; + reset_literals () + end + +(* Emit .file / .loc debugging directives *) + + let print_file_line oc file line = + print_file_line oc comment file line + +(* Name of testable condition *) + + let condition_name = function + | TCeq -> "eq" + | TCne -> "ne" + | TChs -> "hs" + | TClo -> "lo" + | TCmi -> "mi" + | TCpl -> "pl" + | TChi -> "hi" + | TCls -> "ls" + | TCge -> "ge" + | TClt -> "lt" + | TCgt -> "gt" + | TCle -> "le" + +(* Print an addressing mode *) + + let addressing oc = function + | ADimm(base, n) -> fprintf oc "[%a, #%a]" xregsp base coqint64 n + | ADreg(base, r) -> fprintf oc "[%a, %a]" xregsp base xreg r + | ADlsl(base, r, n) -> fprintf oc "[%a, %a, lsl #%a]" xregsp base xreg r coqint n + | ADsxt(base, r, n) -> fprintf oc "[%a, %a, sxtw #%a]" xregsp base wreg r coqint n + | ADuxt(base, r, n) -> fprintf oc "[%a, %a, uxtw #%a]" xregsp base wreg r coqint n + | ADadr(base, id, ofs) -> fprintf oc "[%a, #:lo12:%a]" xregsp base symbol_offset (id, ofs) + | ADpostincr(base, n) -> fprintf oc "[%a], #%a" xregsp base coqint64 n + +(* Print a shifted operand *) + let shiftop oc = function + | SOnone -> () + | SOlsl n -> fprintf oc ", lsl #%a" coqint n + | SOlsr n -> fprintf oc ", lsr #%a" coqint n + | SOasr n -> fprintf oc ", asr #%a" coqint n + | SOror n -> fprintf oc ", ror #%a" coqint n + +(* Print a sign- or zero-extended operand *) + let extendop oc = function + | EOsxtb n -> fprintf oc ", sxtb #%a" coqint n + | EOsxth n -> fprintf oc ", sxth #%a" coqint n + | EOsxtw n -> fprintf oc ", sxtw #%a" coqint n + | EOuxtb n -> fprintf oc ", uxtb #%a" coqint n + | EOuxth n -> fprintf oc ", uxth #%a" coqint n + | EOuxtw n -> fprintf oc ", uxtw #%a" coqint n + | EOuxtx n -> fprintf oc ", uxtx #%a" coqint n + +(* Printing of instructions *) + let print_instruction oc = function + (* Branches *) + | Pb lbl -> + fprintf oc " b %a\n" print_label lbl + | Pbc(c, lbl) -> + fprintf oc " b.%s %a\n" (condition_name c) print_label lbl + | Pbl(id, sg) -> + fprintf oc " bl %a\n" symbol id + | Pbs(id, sg) -> + fprintf oc " b %a\n" symbol id + | Pblr(r, sg) -> + fprintf oc " blr %a\n" xreg r + | Pbr(r, sg) -> + fprintf oc " br %a\n" xreg r + | Pret r -> + fprintf oc " ret %a\n" xreg r + | Pcbnz(sz, r, lbl) -> + fprintf oc " cbnz %a, %a\n" ireg (sz, r) print_label lbl + | Pcbz(sz, r, lbl) -> + fprintf oc " cbz %a, %a\n" ireg (sz, r) print_label lbl + | Ptbnz(sz, r, n, lbl) -> + fprintf oc " tbnz %a, #%a, %a\n" ireg (sz, r) coqint n print_label lbl + | Ptbz(sz, r, n, lbl) -> + fprintf oc " tbz %a, #%a, %a\n" ireg (sz, r) coqint n print_label lbl + (* Memory loads and stores *) + | Pldrw(rd, a) | Pldrw_a(rd, a) -> + fprintf oc " ldr %a, %a\n" wreg rd addressing a + | Pldrx(rd, a) | Pldrx_a(rd, a) -> + fprintf oc " ldr %a, %a\n" xreg rd addressing a + | Pldrb(sz, rd, a) -> + fprintf oc " ldrb %a, %a\n" wreg rd addressing a + | Pldrsb(sz, rd, a) -> + fprintf oc " ldrsb %a, %a\n" ireg (sz, rd) addressing a + | Pldrh(sz, rd, a) -> + fprintf oc " ldrh %a, %a\n" wreg rd addressing a + | Pldrsh(sz, rd, a) -> + fprintf oc " ldrsh %a, %a\n" ireg (sz, rd) addressing a + | Pldrzw(rd, a) -> + fprintf oc " ldr %a, %a\n" wreg rd addressing a + (* the upper 32 bits of Xrd are set to 0, performing zero-extension *) + | Pldrsw(rd, a) -> + fprintf oc " ldrsw %a, %a\n" xreg rd addressing a + | Pldp(rd1, rd2, a) -> + fprintf oc " ldp %a, %a, %a\n" xreg rd1 xreg rd2 addressing a + | Pstrw(rs, a) | Pstrw_a(rs, a) -> + fprintf oc " str %a, %a\n" wreg rs addressing a + | Pstrx(rs, a) | Pstrx_a(rs, a) -> + fprintf oc " str %a, %a\n" xreg rs addressing a + | Pstrb(rs, a) -> + fprintf oc " strb %a, %a\n" wreg rs addressing a + | Pstrh(rs, a) -> + fprintf oc " strh %a, %a\n" wreg rs addressing a + | Pstp(rs1, rs2, a) -> + fprintf oc " stp %a, %a, %a\n" xreg rs1 xreg rs2 addressing a + (* Integer arithmetic, immediate *) + | Paddimm(sz, rd, r1, n) -> + fprintf oc " add %a, %a, #%a\n" iregsp (sz, rd) iregsp (sz, r1) intsz (sz, n) + | Psubimm(sz, rd, r1, n) -> + fprintf oc " sub %a, %a, #%a\n" iregsp (sz, rd) iregsp (sz, r1) intsz (sz, n) + | Pcmpimm(sz, r1, n) -> + fprintf oc " cmp %a, #%a\n" ireg (sz, r1) intsz (sz, n) + | Pcmnimm(sz, r1, n) -> + fprintf oc " cmn %a, #%a\n" ireg (sz, r1) intsz (sz, n) + (* Move integer register *) + | Pmov(rd, r1) -> + fprintf oc " mov %a, %a\n" xregsp rd xregsp r1 + (* Logical, immediate *) + | Pandimm(sz, rd, r1, n) -> + fprintf oc " and %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Peorimm(sz, rd, r1, n) -> + fprintf oc " eor %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Porrimm(sz, rd, r1, n) -> + fprintf oc " orr %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Ptstimm(sz, r1, n) -> + fprintf oc " tst %a, #%a\n" ireg (sz, r1) intsz (sz, n) + (* Move wide immediate *) + | Pmovz(sz, rd, n, pos) -> + fprintf oc " movz %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + | Pmovn(sz, rd, n, pos) -> + fprintf oc " movn %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + | Pmovk(sz, rd, n, pos) -> + fprintf oc " movk %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + (* PC-relative addressing *) + | Padrp(rd, id, ofs) -> + fprintf oc " adrp %a, %a\n" xreg rd symbol_offset (id, ofs) + | Paddadr(rd, r1, id, ofs) -> + fprintf oc " add %a, %a, #:lo12:%a\n" xreg rd xreg r1 symbol_offset (id, ofs) + (* Bit-field operations *) + | Psbfiz(sz, rd, r1, r, s) -> + fprintf oc " sbfiz %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Psbfx(sz, rd, r1, r, s) -> + fprintf oc " sbfx %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Pubfiz(sz, rd, r1, r, s) -> + fprintf oc " ubfiz %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Pubfx(sz, rd, r1, r, s) -> + fprintf oc " ubfx %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + (* Integer arithmetic, shifted register *) + | Padd(sz, rd, r1, r2, s) -> + fprintf oc " add %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Psub(sz, rd, r1, r2, s) -> + fprintf oc " sub %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pcmp(sz, r1, r2, s) -> + fprintf oc " cmp %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pcmn(sz, r1, r2, s) -> + fprintf oc " cmn %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + (* Integer arithmetic, extending register *) + | Paddext(rd, r1, r2, x) -> + fprintf oc " add %a, %a, %a%a\n" xregsp rd xregsp r1 wreg r2 extendop x + | Psubext(rd, r1, r2, x) -> + fprintf oc " sub %a, %a, %a%a\n" xregsp rd xregsp r1 wreg r2 extendop x + | Pcmpext(r1, r2, x) -> + fprintf oc " cmp %a, %a%a\n" xreg r1 wreg r2 extendop x + | Pcmnext(r1, r2, x) -> + fprintf oc " cmn %a, %a%a\n" xreg r1 wreg r2 extendop x + (* Logical, shifted register *) + | Pand(sz, rd, r1, r2, s) -> + fprintf oc " and %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pbic(sz, rd, r1, r2, s) -> + fprintf oc " bic %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Peon(sz, rd, r1, r2, s) -> + fprintf oc " eon %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Peor(sz, rd, r1, r2, s) -> + fprintf oc " eor %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Porr(sz, rd, r1, r2, s) -> + fprintf oc " orr %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Porn(sz, rd, r1, r2, s) -> + fprintf oc " orn %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Ptst(sz, r1, r2, s) -> + fprintf oc " tst %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + (* Variable shifts *) + | Pasrv(sz, rd, r1, r2) -> + fprintf oc " asr %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Plslv(sz, rd, r1, r2) -> + fprintf oc " lsl %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Plsrv(sz, rd, r1, r2) -> + fprintf oc " lsr %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Prorv(sz, rd, r1, r2) -> + fprintf oc " ror %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + (* Bit operations *) + | Pcls(sz, rd, r1) -> + fprintf oc " cls %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Pclz(sz, rd, r1) -> + fprintf oc " clz %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Prev(sz, rd, r1) -> + fprintf oc " rev %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Prev16(sz, rd, r1) -> + fprintf oc " rev16 %a, %a\n" ireg (sz, rd) ireg (sz, r1) + (* Conditional data processing *) + | Pcsel(rd, r1, r2, c) -> + fprintf oc " csel %a, %a, %a, %s\n" xreg rd xreg r1 xreg r2 (condition_name c) + | Pcset(rd, c) -> + fprintf oc " cset %a, %s\n" xreg rd (condition_name c) + (* Integer multiply/divide *) + | Pmadd(sz, rd, r1, r2, r3) -> + fprintf oc " madd %a, %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) ireg0 (sz, r3) + | Pmsub(sz, rd, r1, r2, r3) -> + fprintf oc " msub %a, %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) ireg0 (sz, r3) + | Psmulh(rd, r1, r2) -> + fprintf oc " smulh %a, %a, %a\n" xreg rd xreg r1 xreg r2 + | Pumulh(rd, r1, r2) -> + fprintf oc " umulh %a, %a, %a\n" xreg rd xreg r1 xreg r2 + | Psdiv(sz, rd, r1, r2) -> + fprintf oc " sdiv %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Pudiv(sz, rd, r1, r2) -> + fprintf oc " udiv %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + (* Floating-point loads and stores *) + | Pldrs(rd, a) -> + fprintf oc " ldr %a, %a\n" sreg rd addressing a + | Pldrd(rd, a) | Pldrd_a(rd, a) -> + fprintf oc " ldr %a, %a\n" dreg rd addressing a + | Pstrs(rd, a) -> + fprintf oc " str %a, %a\n" sreg rd addressing a + | Pstrd(rd, a) | Pstrd_a(rd, a) -> + fprintf oc " str %a, %a\n" dreg rd addressing a + (* Floating-point move *) + | Pfmov(rd, r1) -> + fprintf oc " fmov %a, %a\n" dreg rd dreg r1 + | Pfmovimmd(rd, f) -> + let d = camlint64_of_coqint (Floats.Float.to_bits f) in + if is_immediate_float64 d then + fprintf oc " fmov %a, #%.7f\n" dreg rd (Int64.float_of_bits d) + else begin + let lbl = label_literal64 d in + fprintf oc " adrp x16, %a\n" label lbl; + fprintf oc " ldr %a, [x16, #:lo12:%a] %s %.18g\n" dreg rd label lbl comment (Int64.float_of_bits d) + end + | Pfmovimms(rd, f) -> + let d = camlint_of_coqint (Floats.Float32.to_bits f) in + if is_immediate_float32 d then + fprintf oc " fmov %a, #%.7f\n" sreg rd (Int32.float_of_bits d) + else begin + let lbl = label_literal32 d in + fprintf oc " adrp x16, %a\n" label lbl; + fprintf oc " ldr %a, [x16, #:lo12:%a] %s %.18g\n" sreg rd label lbl comment (Int32.float_of_bits d) + end + | Pfmovi(D, rd, r1) -> + fprintf oc " fmov %a, %a\n" dreg rd xreg0 r1 + | Pfmovi(S, rd, r1) -> + fprintf oc " fmov %a, %a\n" sreg rd wreg0 r1 + (* Floating-point conversions *) + | Pfcvtds(rd, r1) -> + fprintf oc " fcvt %a, %a\n" dreg rd sreg r1 + | Pfcvtsd(rd, r1) -> + fprintf oc " fcvt %a, %a\n" sreg rd dreg r1 + | Pfcvtzs(isz, fsz, rd, r1) -> + fprintf oc " fcvtzs %a, %a\n" ireg (isz, rd) freg (fsz, r1) + | Pfcvtzu(isz, fsz, rd, r1) -> + fprintf oc " fcvtzu %a, %a\n" ireg (isz, rd) freg (fsz, r1) + | Pscvtf(fsz, isz, rd, r1) -> + fprintf oc " scvtf %a, %a\n" freg (fsz, rd) ireg (isz, r1) + | Pucvtf(fsz, isz, rd, r1) -> + fprintf oc " ucvtf %a, %a\n" freg (fsz, rd) ireg (isz, r1) + (* Floating-point arithmetic *) + | Pfabs(sz, rd, r1) -> + fprintf oc " fabs %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfneg(sz, rd, r1) -> + fprintf oc " fneg %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfsqrt(sz, rd, r1) -> + fprintf oc " fsqrt %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfadd(sz, rd, r1, r2) -> + fprintf oc " fadd %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfdiv(sz, rd, r1, r2) -> + fprintf oc " fdiv %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfmul(sz, rd, r1, r2) -> + fprintf oc " fmul %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfnmul(sz, rd, r1, r2) -> + fprintf oc " fnmul %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfsub(sz, rd, r1, r2) -> + fprintf oc " fsub %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfmadd(sz, rd, r1, r2, r3) -> + fprintf oc " fmadd %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfmsub(sz, rd, r1, r2, r3) -> + fprintf oc " fmsub %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfnmadd(sz, rd, r1, r2, r3) -> + fprintf oc " fnmadd %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfnmsub(sz, rd, r1, r2, r3) -> + fprintf oc " fnmsub %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + (* Floating-point comparison *) + | Pfcmp(sz, r1, r2) -> + fprintf oc " fcmp %a, %a\n" freg (sz, r1) freg (sz, r2) + | Pfcmp0(sz, r1) -> + fprintf oc " fcmp %a, #0.0\n" freg (sz, r1) + (* Floating-point conditional select *) + | Pfsel(rd, r1, r2, c) -> + fprintf oc " fcsel %a, %a, %a, %s\n" dreg rd dreg r1 dreg r2 (condition_name c) + (* No-op *) + | Pnop -> + fprintf oc " nop\n" + (* Pseudo-instructions expanded in Asmexpand *) + | Pallocframe(sz, linkofs) -> assert false + | Pfreeframe(sz, linkofs) -> assert false + | Pcvtx2w rd -> assert false + (* Pseudo-instructions not yet expanded *) + | Plabel lbl -> + fprintf oc "%a:\n" print_label lbl + | Ploadsymbol(rd, id) -> + fprintf oc " adrp %a, :got:%a\n" xreg rd symbol id; + fprintf oc " ldr %a, [%a, #:got_lo12:%a]\n" xreg rd xreg rd symbol id + | Pcvtsw2x(rd, r1) -> + fprintf oc " sxtw %a, %a\n" xreg rd wreg r1 + | Pcvtuw2x(rd, r1) -> + fprintf oc " uxtw %a, %a\n" xreg rd wreg r1 + | Pbtbl(r1, tbl) -> + let lbl = new_label() in + fprintf oc " adr x16, %a\n" label lbl; + fprintf oc " add x16, x16, %a, uxtw #2\n" wreg r1; + fprintf oc " br x16\n"; + fprintf oc "%a:" label lbl; + List.iter (fun l -> fprintf oc " b %a\n" print_label l) tbl + | Pcfi_adjust sz -> + cfi_adjust oc (camlint_of_coqint sz) + | Pcfi_rel_offset ofs -> + cfi_rel_offset oc "lr" (camlint_of_coqint ofs) + | Pbuiltin(ef, args, res) -> + begin match ef with + | EF_annot(kind,txt, targs) -> + begin match (P.to_int kind) with + | 1 -> let annot = annot_text preg_annot "sp" (camlstring_of_coqstring txt) args in + fprintf oc "%s annotation: %S\n" comment annot + | 2 -> let lbl = new_label () in + fprintf oc "%a:\n" label lbl; + add_ais_annot lbl preg_annot "sp" (camlstring_of_coqstring txt) args + | _ -> assert false + end + | EF_debug(kind, txt, targs) -> + print_debug_info comment print_file_line preg_annot "sp" oc + (P.to_int kind) (extern_atom txt) args + | EF_inline_asm(txt, sg, clob) -> + fprintf oc "%s begin inline assembly\n\t" comment; + print_inline_asm preg_asm oc (camlstring_of_coqstring txt) sg args res; + fprintf oc "%s end inline assembly\n" comment + | _ -> + assert false + end + + let get_section_names name = + let (text, lit) = + match C2C.atom_sections name with + | t :: l :: _ -> (t, l) + | _ -> (Section_text, Section_literal) in + text,lit,Section_jumptable + + let print_align oc alignment = + fprintf oc " .balign %d\n" alignment + + let print_jumptable oc jmptbl = + let print_tbl oc (lbl, tbl) = + fprintf oc "%a:\n" label lbl; + List.iter + (fun l -> fprintf oc " .long %a - %a\n" + print_label l label lbl) + tbl in + if !jumptables <> [] then + begin + section oc jmptbl; + fprintf oc " .balign 4\n"; + List.iter (print_tbl oc) !jumptables; + jumptables := [] + end + + let print_fun_info = elf_print_fun_info + + let print_optional_fun_info _ = () + + let print_var_info = elf_print_var_info + + let print_comm_symb oc sz name align = + if C2C.atom_is_static name then + fprintf oc " .local %a\n" symbol name; + fprintf oc " .comm %a, %s, %d\n" + symbol name + (Z.to_string sz) + align + + let print_instructions oc fn = + current_function_sig := fn.fn_sig; + List.iter (print_instruction oc) fn.fn_code + +(* Data *) + + let address = ".quad" + + let print_prologue oc = + if !Clflags.option_g then begin + section oc Section_text; + end + + let print_epilogue oc = + if !Clflags.option_g then begin + Debug.compute_gnu_file_enum (fun f -> ignore (print_file oc f)); + section oc Section_text; + end + + let default_falignment = 2 + + let cfi_startproc oc = () + let cfi_endproc oc = () + + end + +let sel_target () = + (module Target:TARGET) diff --git a/aarch64/ValueAOp.v b/aarch64/ValueAOp.v new file mode 100644 index 00000000..e0d98c85 --- /dev/null +++ b/aarch64/ValueAOp.v @@ -0,0 +1,319 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +Require Import Coqlib Compopts. +Require Import AST Integers Floats Values Memory Globalenvs. +Require Import Op RTL ValueDomain. + +(** Value analysis for AArch64 operators *) + +Definition eval_static_shift (s: shift) (v: aval) (n: amount32) : aval := + match s with + | Slsl => shl v (I n) + | Slsr => shru v (I n) + | Sasr => shr v (I n) + | Sror => ror v (I n) + end. + +Definition eval_static_shiftl (s: shift) (v: aval) (n: amount64) : aval := + match s with + | Slsl => shll v (I n) + | Slsr => shrlu v (I n) + | Sasr => shrl v (I n) + | Sror => rorl v (I n) + end. + +Definition eval_static_extend (x: extension) (v: aval) (n: amount64) : aval := + shll (match x with Xsgn32 => longofint v | Xuns32 => longofintu v end) (I n). + +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 + | Ccompimm c n, v1 :: nil => cmp_bool c v1 (I n) + | Ccompuimm c n, v1 :: nil => cmpu_bool c v1 (I n) + | Ccompshift c s a, v1 :: v2 :: nil => cmp_bool c v1 (eval_static_shift s v2 a) + | Ccompushift c s a, v1 :: v2 :: nil => cmpu_bool c v1 (eval_static_shift s v2 a) + | Cmaskzero m, v1 :: nil => maskzero v1 m + | Cmasknotzero m, v1 :: nil => cnot (maskzero v1 m) + | Ccompl c, v1 :: v2 :: nil => cmpl_bool c v1 v2 + | Ccomplu c, v1 :: v2 :: nil => cmplu_bool c v1 v2 + | Ccomplimm c n, v1 :: nil => cmpl_bool c v1 (L n) + | Ccompluimm c n, v1 :: nil => cmplu_bool c v1 (L n) + | Ccomplshift c s a, v1 :: v2 :: nil => cmpl_bool c v1 (eval_static_shiftl s v2 a) + | Ccomplushift c s a, v1 :: v2 :: nil => cmplu_bool c v1 (eval_static_shiftl s v2 a) + | Cmasklzero m, v1 :: nil => cmpl_bool Ceq (andl v1 (L m)) (L Int64.zero) + | Cmasklnotzero m, v1 :: nil => cmpl_bool Cne (andl v1 (L m)) (L Int64.zero) + | 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 => addl v1 (L n) + | Aindexed2, v1 :: v2 :: nil => addl v1 v2 + | Aindexed2shift a, v1 :: v2 :: nil => addl v1 (shll v2 (I a)) + | Aindexed2ext x a, v1 :: v2 :: nil => addl v1 (eval_static_extend x v2 a) + | Aglobal s ofs, nil => Ptr (Gl s ofs) + | 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 + | Olongconst n, nil => L 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) + + | Oshift s a, v1::nil => eval_static_shift s v1 a + | Oadd, v1::v2::nil => add v1 v2 + | Oaddshift s a, v1::v2::nil => add v1 (eval_static_shift s v2 a) + | Oaddimm n, v1::nil => add v1 (I n) + | Oneg, v1::nil => neg v1 + | Onegshift s a, v1::nil => neg (eval_static_shift s v1 a) + | Osub, v1::v2::nil => sub v1 v2 + | Osubshift s a, v1::v2::nil => sub v1 (eval_static_shift s v2 a) + | Omul, v1::v2::nil => mul v1 v2 + | Omuladd, v1::v2::v3::nil => add v1 (mul v2 v3) + | Omulsub, v1::v2::v3::nil => sub v1 (mul v2 v3) + | Odiv, v1::v2::nil => divs v1 v2 + | Odivu, v1::v2::nil => divu v1 v2 + | Oand, v1::v2::nil => and v1 v2 + | Oandshift s a, v1::v2::nil => and v1 (eval_static_shift s v2 a) + | Oandimm n, v1::nil => and v1 (I n) + | Oor, v1::v2::nil => or v1 v2 + | Oorshift s a, v1::v2::nil => or v1 (eval_static_shift s v2 a) + | Oorimm n, v1::nil => or v1 (I n) + | Oxor, v1::v2::nil => xor v1 v2 + | Oxorshift s a, v1::v2::nil => xor v1 (eval_static_shift s v2 a) + | Oxorimm n, v1::nil => xor v1 (I n) + | Onot, v1::nil => notint v1 + | Onotshift s a, v1::nil => notint (eval_static_shift s v1 a) + | Obic, v1::v2::nil => and v1 (notint v2) + | Obicshift s a, v1::v2::nil => and v1 (notint (eval_static_shift s v2 a)) + | Oorn, v1::v2::nil => or v1 (notint v2) + | Oornshift s a, v1::v2::nil => or v1 (notint (eval_static_shift s v2 a)) + | Oeqv, v1::v2::nil => xor v1 (notint v2) + | Oeqvshift s a, v1::v2::nil => xor v1 (notint (eval_static_shift s v2 a)) + | Oshl, v1::v2::nil => shl v1 v2 + | Oshr, v1::v2::nil => shr v1 v2 + | Oshru, v1::v2::nil => shru v1 v2 + | Oshrximm n, v1::nil => shrx v1 (I n) + | Ozext s, v1::nil => zero_ext s v1 + | Osext s, v1::nil => sign_ext s v1 + | Oshlzext s a, v1::nil => shl (zero_ext s v1) (I a) + | Oshlsext s a, v1::nil => shl (sign_ext s v1) (I a) + | Ozextshr a s, v1::nil => zero_ext s (shru v1 (I a)) + | Osextshr a s, v1::nil => sign_ext s (shr v1 (I a)) + + | Oshiftl s a, v1::nil => eval_static_shiftl s v1 a + | Oextend x a, v1::nil => eval_static_extend x v1 a + | Omakelong, v1::v2::nil => longofwords v1 v2 + | Olowlong, v1::nil => loword v1 + | Ohighlong, v1::nil => hiword v1 + | Oaddl, v1::v2::nil => addl v1 v2 + | Oaddlshift s a, v1::v2::nil => addl v1 (eval_static_shiftl s v2 a) + | Oaddlext x a, v1::v2::nil => addl v1 (eval_static_extend x v2 a) + | Oaddlimm n, v1::nil => addl v1 (L n) + | Onegl, v1::nil => negl v1 + | Oneglshift s a, v1::nil => negl (eval_static_shiftl s v1 a) + | Osubl, v1::v2::nil => subl v1 v2 + | Osublshift s a, v1::v2::nil => subl v1 (eval_static_shiftl s v2 a) + | Osublext x a, v1::v2::nil => subl v1 (eval_static_extend x v2 a) + | Omull, v1::v2::nil => mull v1 v2 + | Omulladd, v1::v2::v3::nil => addl v1 (mull v2 v3) + | Omullsub, v1::v2::v3::nil => subl v1 (mull v2 v3) + | Omullhs, v1::v2::nil => mullhs v1 v2 + | Omullhu, v1::v2::nil => mullhu v1 v2 + | Odivl, v1::v2::nil => divls v1 v2 + | Odivlu, v1::v2::nil => divlu v1 v2 + | Oandl, v1::v2::nil => andl v1 v2 + | Oandlshift s a, v1::v2::nil => andl v1 (eval_static_shiftl s v2 a) + | Oandlimm n, v1::nil => andl v1 (L n) + | Oorl, v1::v2::nil => orl v1 v2 + | Oorlshift s a, v1::v2::nil => orl v1 (eval_static_shiftl s v2 a) + | Oorlimm n, v1::nil => orl v1 (L n) + | Oxorl, v1::v2::nil => xorl v1 v2 + | Oxorlshift s a, v1::v2::nil => xorl v1 (eval_static_shiftl s v2 a) + | Oxorlimm n, v1::nil => xorl v1 (L n) + | Onotl, v1::nil => notl v1 + | Onotlshift s a, v1::nil => notl (eval_static_shiftl s v1 a) + | Obicl, v1::v2::nil => andl v1 (notl v2) + | Obiclshift s a, v1::v2::nil => andl v1 (notl (eval_static_shiftl s v2 a)) + | Oornl, v1::v2::nil => orl v1 (notl v2) + | Oornlshift s a, v1::v2::nil => orl v1 (notl (eval_static_shiftl s v2 a)) + | Oeqvl, v1::v2::nil => xorl v1 (notl v2) + | Oeqvlshift s a, v1::v2::nil => xorl v1 (notl (eval_static_shiftl s v2 a)) + | Oshll, v1::v2::nil => shll v1 v2 + | Oshrl, v1::v2::nil => shrl v1 v2 + | Oshrlu, v1::v2::nil => shrlu v1 v2 + | Oshrlximm n, v1::nil => shrxl v1 (I n) + | Ozextl s, v1::nil => zero_ext_l s v1 + | Osextl s, v1::nil => sign_ext_l s v1 + | Oshllzext s a, v1::nil => shll (zero_ext_l s v1) (I a) + | Oshllsext s a, v1::nil => shll (sign_ext_l s v1) (I a) + | Ozextshrl a s, v1::nil => zero_ext_l s (shrlu v1 (I a)) + | Osextshrl a s, v1::nil => sign_ext_l s (shrl v1 (I a)) + + | 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 + | Olongoffloat, v1::nil => longoffloat v1 + | Olonguoffloat, v1::nil => longuoffloat v1 + | Ofloatoflong, v1::nil => floatoflong v1 + | Ofloatoflongu, v1::nil => floatoflongu v1 + | Olongofsingle, v1::nil => longofsingle v1 + | Olonguofsingle, v1::nil => longuofsingle v1 + | Osingleoflong, v1::nil => singleoflong v1 + | Osingleoflongu, v1::nil => singleoflongu v1 + + | Ocmp c, _ => of_optbool (eval_static_condition c vl) + | Osel c ty, v1::v2::vl => select (eval_static_condition c vl) v1 v2 + + | _, _ => 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. + +Ltac InvHyps := + match goal with + | [H: None = Some _ |- _ ] => discriminate + | [H: Some _ = Some _ |- _] => inv H + | [H1: match ?vl with nil => _ | _ :: _ => _ end = Some _ , + H2: list_forall2 _ ?vl _ |- _ ] => inv H2; InvHyps + | _ => idtac + end. + +Lemma eval_static_shift_sound: forall v av s n, + vmatch bc v av -> vmatch bc (eval_shift s v n) (eval_static_shift s av n). +Proof. + intros. unfold eval_shift, eval_static_shift; destruct s; auto with va. +Qed. + +Lemma eval_static_shiftl_sound: forall v av s n, + vmatch bc v av -> vmatch bc (eval_shiftl s v n) (eval_static_shiftl s av n). +Proof. + intros. unfold eval_shiftl, eval_static_shiftl; destruct s; auto with va. +Qed. + +Lemma eval_static_extend_sound: forall v av x n, + vmatch bc v av -> vmatch bc (eval_extend x v n) (eval_static_extend x av n). +Proof. + intros. unfold eval_extend, eval_static_extend; destruct x; auto with va. +Qed. + +Hint Resolve eval_static_shift_sound eval_static_shiftl_sound eval_static_extend_sound: va. + +Theorem eval_static_condition_sound: + forall cond vargs m aargs, + list_forall2 (vmatch bc) vargs aargs -> + cmatch (eval_condition cond vargs m) (eval_static_condition cond aargs). +Proof. + intros until aargs; intros VM. inv VM. + destruct cond; auto with va. + inv H0. + destruct cond; simpl; eauto with va. + replace (Val.cmp_bool Ceq (Val.and a1 (Vint n)) (Vint Int.zero)) + with (Val.maskzero_bool a1 n) by (destruct a1; auto). + eauto with va. + replace (Val.cmp_bool Cne (Val.and a1 (Vint n)) (Vint Int.zero)) + with (option_map negb (Val.maskzero_bool a1 n)) by (destruct a1; auto). + eauto with va. + inv H2. + destruct cond; simpl; eauto with va. + destruct cond; auto with va. +Qed. + +Lemma symbol_address_sound: + forall id ofs, + vmatch bc (Genv.symbol_address ge id ofs) (Ptr (Gl id ofs)). +Proof. + intros; apply symbol_address_sound; apply GENV. +Qed. + +Lemma symbol_address_sound_2: + forall id ofs, + vmatch bc (Genv.symbol_address ge id ofs) (Ifptr (Gl id ofs)). +Proof. + intros. unfold Genv.symbol_address. destruct (Genv.find_symbol ge id) as [b|] eqn:F. + constructor. constructor. apply GENV; auto. + constructor. +Qed. + +Hint Resolve symbol_address_sound symbol_address_sound_2: va. + +Theorem eval_static_addressing_sound: + forall addr vargs vres aargs, + eval_addressing ge (Vptr sp Ptrofs.zero) addr vargs = Some vres -> + list_forall2 (vmatch bc) vargs aargs -> + vmatch bc vres (eval_static_addressing addr aargs). +Proof. + unfold eval_addressing, eval_static_addressing; intros; + destruct addr; InvHyps; eauto with va. + rewrite Ptrofs.add_zero_l; eauto with va. +Qed. + +Theorem eval_static_operation_sound: + forall op vargs m vres aargs, + eval_operation ge (Vptr sp Ptrofs.zero) op vargs m = Some vres -> + list_forall2 (vmatch bc) vargs aargs -> + vmatch bc vres (eval_static_operation op aargs). +Proof. + unfold eval_operation, eval_static_operation; intros; + destruct op; InvHyps; eauto with va. + destruct (propagate_float_constants tt); constructor. + destruct (propagate_float_constants tt); constructor. + rewrite Ptrofs.add_zero_l; eauto with va. + apply of_optbool_sound. eapply eval_static_condition_sound; eauto. + apply select_sound; eauto using eval_static_condition_sound. +Qed. + +End SOUNDNESS. + diff --git a/aarch64/extractionMachdep.v b/aarch64/extractionMachdep.v new file mode 100644 index 00000000..a447d12f --- /dev/null +++ b/aarch64/extractionMachdep.v @@ -0,0 +1,23 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* 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. *) +(* *) +(* *********************************************************************) + +(* Additional extraction directives specific to the AArch64 port *) + +Require Archi Asm. + +(* Archi *) + +Extract Constant Archi.pic_code => "fun () -> false". (* for the time being *) + +(* Asm *) +Extract Constant Asm.symbol_low => "fun _ _ _ -> assert false". +Extract Constant Asm.symbol_high => "fun _ _ _ -> assert false". diff --git a/backend/Asmgenproof0.v b/backend/Asmgenproof0.v index 111e435f..3638c465 100644 --- a/backend/Asmgenproof0.v +++ b/backend/Asmgenproof0.v @@ -899,30 +899,53 @@ Qed. (** A variant that supports zero steps of execution *) -Inductive exec_straight0: code -> regset -> mem -> - code -> regset -> mem -> Prop := - | exec_straight0_none: - forall c rs m, - exec_straight0 c rs m c rs m - | exec_straight0_step: - forall i c rs1 m1 rs2 m2 c' rs3 m3, - exec_instr ge fn i rs1 m1 = Next rs2 m2 -> - rs2#PC = Val.offset_ptr rs1#PC Ptrofs.one -> - exec_straight0 c rs2 m2 c' rs3 m3 -> - exec_straight0 (i :: c) rs1 m1 c' rs3 m3. +Inductive exec_straight_opt: code -> regset -> mem -> code -> regset -> mem -> Prop := + | exec_straight_opt_refl: forall c rs m, + exec_straight_opt c rs m c rs m + | exec_straight_opt_intro: forall c1 rs1 m1 c2 rs2 m2, + exec_straight c1 rs1 m1 c2 rs2 m2 -> + exec_straight_opt c1 rs1 m1 c2 rs2 m2. + +Lemma exec_straight_opt_left: + forall c3 rs3 m3 c1 rs1 m1 c2 rs2 m2, + exec_straight c1 rs1 m1 c2 rs2 m2 -> + exec_straight_opt c2 rs2 m2 c3 rs3 m3 -> + exec_straight c1 rs1 m1 c3 rs3 m3. +Proof. + destruct 2; intros. auto. eapply exec_straight_trans; eauto. +Qed. + +Lemma exec_straight_opt_right: + forall c3 rs3 m3 c1 rs1 m1 c2 rs2 m2, + exec_straight_opt c1 rs1 m1 c2 rs2 m2 -> + exec_straight c2 rs2 m2 c3 rs3 m3 -> + exec_straight c1 rs1 m1 c3 rs3 m3. +Proof. + destruct 1; intros. auto. eapply exec_straight_trans; eauto. +Qed. -Lemma exec_straight_step': +Lemma exec_straight_opt_step: forall i c rs1 m1 rs2 m2 c' rs3 m3, exec_instr ge fn i rs1 m1 = Next rs2 m2 -> rs2#PC = Val.offset_ptr rs1#PC Ptrofs.one -> - exec_straight0 c rs2 m2 c' rs3 m3 -> + exec_straight_opt c rs2 m2 c' rs3 m3 -> exec_straight (i :: c) rs1 m1 c' rs3 m3. Proof. - intros. revert i rs1 m1 H H0. revert H1. induction 1; intros. + intros. inv H1. - apply exec_straight_one; auto. - eapply exec_straight_step; eauto. Qed. +Lemma exec_straight_opt_step_opt: + forall i c rs1 m1 rs2 m2 c' rs3 m3, + exec_instr ge fn i rs1 m1 = Next rs2 m2 -> + rs2#PC = Val.offset_ptr rs1#PC Ptrofs.one -> + exec_straight_opt c rs2 m2 c' rs3 m3 -> + exec_straight_opt (i :: c) rs1 m1 c' rs3 m3. +Proof. + intros. apply exec_straight_opt_intro. eapply exec_straight_opt_step; eauto. +Qed. + End STRAIGHTLINE. (** * Properties of the Mach call stack *) diff --git a/backend/Lineartyping.v b/backend/Lineartyping.v index 55fa7a67..0e3b7c8e 100644 --- a/backend/Lineartyping.v +++ b/backend/Lineartyping.v @@ -321,7 +321,7 @@ Local Opaque mreg_type. + (* other ops *) destruct (type_of_operation op) as [ty_args ty_res] eqn:TYOP. InvBooleans. econstructor; eauto. - apply wt_setreg; auto. eapply Val.has_subtype; eauto. + apply wt_setreg. eapply Val.has_subtype; eauto. change ty_res with (snd (ty_args, ty_res)). rewrite <- TYOP. eapply type_of_operation_sound; eauto. red; intros; subst op. simpl in ISMOVE. destruct args; try discriminate. destruct args; discriminate. diff --git a/backend/NeedDomain.v b/backend/NeedDomain.v index b35c90b2..3c2d8e20 100644 --- a/backend/NeedDomain.v +++ b/backend/NeedDomain.v @@ -594,7 +594,8 @@ Proof. Qed. (** Modular arithmetic operations: add, mul, opposite. - (But not subtraction because of the pointer - pointer case. *) + Also subtraction, but only on 64-bit targets, otherwise + the pointer - pointer case does not fit. *) Definition modarith (x: nval) := match x with @@ -615,6 +616,19 @@ Proof. - inv H; auto. inv H0; auto. destruct w1; auto. Qed. +Lemma sub_sound: + forall v1 w1 v2 w2 x, + vagree v1 w1 (modarith x) -> vagree v2 w2 (modarith x) -> + Archi.ptr64 = true -> + vagree (Val.sub v1 v2) (Val.sub w1 w2) x. +Proof. + unfold modarith; intros. destruct x; simpl in *. +- auto. +- unfold Val.sub; rewrite H1; InvAgree. + apply eqmod_iagree. apply eqmod_sub; apply iagree_eqmod; auto. +- inv H; auto. inv H0; auto. destruct w1; auto. +Qed. + Remark modarith_idem: forall nv, modarith (modarith nv) = modarith nv. Proof. destruct nv; simpl; auto. f_equal; apply complete_mask_idem. @@ -680,7 +694,7 @@ Definition sign_ext (n: Z) (x: nval) := Lemma sign_ext_sound: forall v w x n, vagree v w (sign_ext n x) -> - 0 < n < Int.zwordsize -> + 0 < n -> vagree (Val.sign_ext n v) (Val.sign_ext n w) x. Proof. unfold sign_ext; intros. destruct x; simpl in *. @@ -889,7 +903,8 @@ Lemma default_needs_of_operation_sound: eval_operation ge (Vptr sp Ptrofs.zero) op args1 m1 = Some v1 -> vagree_list args1 args2 nil \/ vagree_list args1 args2 (default nv :: nil) - \/ vagree_list args1 args2 (default nv :: default nv :: nil) -> + \/ vagree_list args1 args2 (default nv :: default nv :: nil) + \/ vagree_list args1 args2 (default nv :: default nv :: default nv :: nil) -> nv <> Nothing -> exists v2, eval_operation ge (Vptr sp Ptrofs.zero) op args2 m2 = Some v2 @@ -901,7 +916,8 @@ Proof. { destruct H0. auto with na. destruct H0. inv H0; constructor; auto with na. - inv H0; constructor; auto with na. inv H8; constructor; auto with na. + destruct H0. inv H0. constructor. inv H8; constructor; auto with na. + inv H0; constructor; auto with na. inv H8; constructor; auto with na. inv H9; constructor; auto with na. } exploit (@eval_operation_inj _ _ _ _ ge ge inject_id). eassumption. auto. auto. auto. diff --git a/backend/SelectDivproof.v b/backend/SelectDivproof.v index f4ff2c86..334bedf6 100644 --- a/backend/SelectDivproof.v +++ b/backend/SelectDivproof.v @@ -763,8 +763,8 @@ Lemma eval_divlu_mull: Proof. intros. unfold divlu_mull. exploit (divlu_mul_shift x); eauto. intros [A B]. assert (A0: eval_expr ge sp e m le (Eletvar O) (Vlong x)) by (constructor; auto). - exploit eval_mullhu. eauto. eexact A0. instantiate (1 := Int64.repr M). intros (v1 & A1 & B1). - exploit eval_shrluimm. eauto. eexact A1. instantiate (1 := Int.repr p). intros (v2 & A2 & B2). + exploit eval_mullhu. try apply HELPERS. eexact A0. instantiate (1 := Int64.repr M). intros (v1 & A1 & B1). + exploit eval_shrluimm. try apply HELPERS. eexact A1. instantiate (1 := Int.repr p). intros (v2 & A2 & B2). simpl in B1; inv B1. simpl in B2. replace (Int.ltu (Int.repr p) Int64.iwordsize') with true in B2. inv B2. rewrite B. assumption. unfold Int.ltu. rewrite Int.unsigned_repr. rewrite zlt_true; auto. tauto. @@ -834,17 +834,17 @@ Proof. intros. unfold divls_mull. assert (A0: eval_expr ge sp e m le (Eletvar O) (Vlong x)). { constructor; auto. } - exploit eval_mullhs. eauto. eexact A0. instantiate (1 := Int64.repr M). intros (v1 & A1 & B1). - exploit eval_addl; auto; try apply HELPERS. eexact A1. eexact A0. intros (v2 & A2 & B2). - exploit eval_shrluimm. eauto. eexact A0. instantiate (1 := Int.repr 63). intros (v3 & A3 & B3). + exploit eval_mullhs. try apply HELPERS. eexact A0. instantiate (1 := Int64.repr M). intros (v1 & A1 & B1). + exploit eval_addl. try apply HELPERS. eexact A1. eexact A0. intros (v2 & A2 & B2). + exploit eval_shrluimm. try apply HELPERS. eexact A0. instantiate (1 := Int.repr 63). intros (v3 & A3 & B3). set (a4 := if zlt M Int64.half_modulus then mullhs (Eletvar 0) (Int64.repr M) else addl (mullhs (Eletvar 0) (Int64.repr M)) (Eletvar 0)). set (v4 := if zlt M Int64.half_modulus then v1 else v2). assert (A4: eval_expr ge sp e m le a4 v4). { unfold a4, v4; destruct (zlt M Int64.half_modulus); auto. } - exploit eval_shrlimm. eauto. eexact A4. instantiate (1 := Int.repr p). intros (v5 & A5 & B5). - exploit eval_addl; auto; try apply HELPERS. eexact A5. eexact A3. intros (v6 & A6 & B6). + exploit eval_shrlimm. try apply HELPERS. eexact A4. instantiate (1 := Int.repr p). intros (v5 & A5 & B5). + exploit eval_addl. try apply HELPERS. eexact A5. eexact A3. intros (v6 & A6 & B6). assert (RANGE: forall x, 0 <= x < 64 -> Int.ltu (Int.repr x) Int64.iwordsize' = true). { intros. unfold Int.ltu. rewrite Int.unsigned_repr. rewrite zlt_true by tauto. auto. assert (64 < Int.max_unsigned) by (compute; auto). omega. } @@ -948,8 +948,7 @@ Proof. intros until y. unfold divf. destruct (divf_match b); intros. - unfold divfimm. destruct (Float.exact_inverse n2) as [n2' | ] eqn:EINV. + inv H0. inv H4. simpl in H6. inv H6. econstructor; split. - EvalOp. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor. - simpl; eauto. + repeat (econstructor; eauto). destruct x; simpl; auto. erewrite Float.div_mul_inverse; eauto. + TrivialExists. - TrivialExists. @@ -964,8 +963,7 @@ Proof. intros until y. unfold divfs. destruct (divfs_match b); intros. - unfold divfsimm. destruct (Float32.exact_inverse n2) as [n2' | ] eqn:EINV. + inv H0. inv H4. simpl in H6. inv H6. econstructor; split. - EvalOp. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor. - simpl; eauto. + repeat (econstructor; eauto). destruct x; simpl; auto. erewrite Float32.div_mul_inverse; eauto. + TrivialExists. - TrivialExists. diff --git a/backend/Selectionaux.ml b/backend/Selectionaux.ml index 4ca7dd21..8acae8f2 100644 --- a/backend/Selectionaux.ml +++ b/backend/Selectionaux.ml @@ -68,6 +68,8 @@ let rec cost_expr = function let fast_cmove ty = match Configuration.arch, Configuration.model with + | "aarch64", _ -> + (match ty with Tint | Tlong | Tfloat | Tsingle -> true | _ -> false) | "arm", _ -> (match ty with Tint | Tfloat | Tsingle -> true | _ -> false) | "powerpc", "e5500" -> diff --git a/backend/Selectionproof.v b/backend/Selectionproof.v index ee3ed358..8a3aaae6 100644 --- a/backend/Selectionproof.v +++ b/backend/Selectionproof.v @@ -1257,8 +1257,8 @@ Proof. econstructor; eauto. econstructor; eauto. apply set_var_lessdef; auto. - (* store *) - exploit sel_expr_correct. eauto. eauto. eexact H. eauto. eauto. intros [vaddr' [A B]]. - exploit sel_expr_correct. eauto. eauto. eexact H0. eauto. eauto. intros [v' [C D]]. + exploit sel_expr_correct. try apply LINK. try apply HF. eexact H. eauto. eauto. intros [vaddr' [A B]]. + exploit sel_expr_correct. try apply LINK. try apply HF. eexact H0. eauto. eauto. intros [v' [C D]]. exploit Mem.storev_extends; eauto. intros [m2' [P Q]]. left; econstructor; split. eapply eval_store; eauto. diff --git a/backend/ValueDomain.v b/backend/ValueDomain.v index fd3bd5ae..c132ce7c 100644 --- a/backend/ValueDomain.v +++ b/backend/ValueDomain.v @@ -2093,6 +2093,7 @@ Proof. Qed. Definition sign_ext (nbits: Z) (v: aval) := + if zle nbits 0 then Uns (provenance v) 0 else match v with | I i => I (Int.sign_ext nbits i) | Uns p n => if zlt n nbits then Uns p n else sgn p nbits @@ -2101,20 +2102,39 @@ Definition sign_ext (nbits: Z) (v: aval) := end. Lemma sign_ext_sound: - forall nbits v x, 0 < nbits -> vmatch v x -> vmatch (Val.sign_ext nbits v) (sign_ext nbits x). + forall nbits v x, vmatch v x -> vmatch (Val.sign_ext nbits v) (sign_ext nbits x). Proof. assert (DFL: forall p nbits i, 0 < nbits -> vmatch (Vint (Int.sign_ext nbits i)) (sgn p nbits)). { intros. apply vmatch_sgn. apply is_sign_ext_sgn; auto with va. } - intros. inv H0; simpl; auto with va. -- destruct (zlt n nbits); eauto with va. + intros. unfold sign_ext. destruct (zle nbits 0). +- destruct v; simpl; auto with va. constructor. omega. + rewrite Int.sign_ext_below by auto. red; intros; apply Int.bits_zero. +- inv H; simpl; auto with va. ++ destruct (zlt n nbits); eauto with va. constructor; auto. eapply is_sign_ext_uns; eauto with va. -- destruct (zlt n nbits); auto with va. -- apply vmatch_sgn. apply is_sign_ext_sgn; auto with va. ++ destruct (zlt n nbits); auto with va. ++ apply vmatch_sgn. apply is_sign_ext_sgn; auto with va. apply Z.min_case; auto with va. Qed. +Definition zero_ext_l (s: Z) := unop_long (Int64.zero_ext s). + +Lemma zero_ext_l_sound: + forall s v x, vmatch v x -> vmatch (Val.zero_ext_l s v) (zero_ext_l s x). +Proof. + intros s. exact (unop_long_sound (Int64.zero_ext s)). +Qed. + +Definition sign_ext_l (s: Z) := unop_long (Int64.sign_ext s). + +Lemma sign_ext_l_sound: + forall s v x, vmatch v x -> vmatch (Val.sign_ext_l s v) (sign_ext_l s x). +Proof. + intros s. exact (unop_long_sound (Int64.sign_ext s)). +Qed. + Definition longofint (v: aval) := match v with | I i => L (Int64.repr (Int.signed i)) @@ -4712,6 +4732,7 @@ Hint Resolve cnot_sound symbol_address_sound negfs_sound absfs_sound addfs_sound subfs_sound mulfs_sound divfs_sound zero_ext_sound sign_ext_sound longofint_sound longofintu_sound + zero_ext_l_sound sign_ext_l_sound singleoffloat_sound floatofsingle_sound intoffloat_sound intuoffloat_sound floatofint_sound floatofintu_sound intofsingle_sound intuofsingle_sound singleofint_sound singleofintu_sound diff --git a/configure b/configure index 9a2db366..dccf6d14 100755 --- a/configure +++ b/configure @@ -55,10 +55,12 @@ Supported targets: x86_64-macosx (x86 64 bits, MacOS X) rv32-linux (RISC-V 32 bits, Linux) rv64-linux (RISC-V 64 bits, Linux) + aarch64-linux (AArch64, i.e. ARMv8 in 64-bit mode, Linux) manual (edit configuration file by hand) For x86 targets, the "x86_32-" prefix can also be written "ia32-" or "i386-". For x86 targets, the "x86_64-" prefix can also be written "amd64-". +For AArch64 targets, the "aarch64-" prefix can also be written "arm64-". For PowerPC targets, the "ppc-" prefix can be refined into: ppc64- PowerPC 64 bits @@ -175,6 +177,8 @@ case "$target" in arch="riscV"; model="32"; endianness="little"; bitsize=32;; rv64-*) arch="riscV"; model="64"; endianness="little"; bitsize=64;; + aarch64-*|arm64-*) + arch="aarch64"; model="default"; endianness="little"; bitsize=64;; manual) ;; "") @@ -428,6 +432,29 @@ if test "$arch" = "riscV"; then system="linux" fi +# +# AArch64 (ARMv8 64 bits) Target Configuration +# +if test "$arch" = "aarch64"; then + case "$target" in + linux) + abi="standard" + casm="${toolprefix}gcc" + casm_options="-c" + cc="${toolprefix}gcc" + clinker="${toolprefix}gcc" + clinker_options="" + cprepro="${toolprefix}gcc" + cprepro_options="-std=c99 -U__GNUC__ -E" + libmath="-lm" + system="linux";; + *) + echo "Error: invalid eabi/system '$target' for architecture AArch64." 1>&2 + echo "$usage" 1>&2 + exit 2;; + esac +fi + # # Finalize Target Configuration @@ -690,6 +717,8 @@ cat >> Makefile.config <<'EOF' # ARCH=powerpc # ARCH=arm # ARCH=x86 +# ARCH=riscV +# ARCH=aarch6 ARCH= # Hardware variant @@ -703,23 +732,24 @@ ARCH= # MODEL=armv7m # for ARM # MODEL=32sse2 # for x86 in 32-bit mode # MODEL=64 # for x86 in 64-bit mode +# MODEL=default # for others MODEL= # Target ABI # ABI=eabi # for PowerPC / Linux and other SVR4 or EABI platforms # ABI=eabi # for ARM # ABI=hardfloat # for ARM -# ABI=standard # for x86 +# ABI=standard # for others ABI= # Target bit width -# BITSIZE=64 # for x86 in 64-bit mode +# BITSIZE=64 # for x86 in 64-bit mode, RiscV in 64-bit mode, AArch64 # BITSIZE=32 # otherwise BITSIZE= # Target endianness # ENDIANNESS=big # for ARM or PowerPC -# ENDIANNESS=little # for ARM or x86 +# ENDIANNESS=little # for ARM or x86 or RiscV or AArch64 ENDIANNESS= # Target operating system and development environment @@ -728,7 +758,7 @@ ENDIANNESS= # SYSTEM=linux # SYSTEM=diab # -# Possible choices for ARM: +# Possible choices for ARM, AArch64, RiscV: # SYSTEM=linux # # Possible choices for x86: diff --git a/cparser/Machine.ml b/cparser/Machine.ml index 089f2483..97bedb3b 100644 --- a/cparser/Machine.ml +++ b/cparser/Machine.ml @@ -237,6 +237,11 @@ let rv64 = struct_passing_style = SP_ref_callee; (* Wrong *) struct_return_style = SR_ref } (* to check *) +let aarch64 = + { i32lpll64 with name = "aarch64"; + struct_passing_style = SP_ref_callee; (* Wrong *) + struct_return_style = SR_ref } (* Wrong *) + (* Add GCC extensions re: sizeof and alignof *) let gcc_extensions c = diff --git a/cparser/Machine.mli b/cparser/Machine.mli index 8971e2a3..ca7de17b 100644 --- a/cparser/Machine.mli +++ b/cparser/Machine.mli @@ -86,6 +86,7 @@ val arm_littleendian : t val arm_bigendian : t val rv32 : t val rv64 : t +val aarch64 : t val gcc_extensions : t -> t val compcert_interpreter : t -> t diff --git a/driver/Configuration.ml b/driver/Configuration.ml index 68531701..2188acf0 100644 --- a/driver/Configuration.ml +++ b/driver/Configuration.ml @@ -123,7 +123,7 @@ let get_bool_config key = let arch = match get_config_string "arch" with - | "powerpc"|"arm"|"x86"|"riscV" as a -> a + | "powerpc"|"arm"|"x86"|"riscV"|"aarch64" as a -> a | v -> bad_config "arch" [v] let model = get_config_string "model" let abi = get_config_string "abi" diff --git a/driver/Frontend.ml b/driver/Frontend.ml index bfb3542b..74791247 100644 --- a/driver/Frontend.ml +++ b/driver/Frontend.ml @@ -116,6 +116,7 @@ let init () = | "riscV" -> if Configuration.model = "64" then Machine.rv64 else Machine.rv32 + | "aarch64" -> Machine.aarch64 | _ -> assert false end; Env.set_builtins C2C.builtins; diff --git a/lib/Integers.v b/lib/Integers.v index 066e6b04..3b6c35eb 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -2689,42 +2689,93 @@ Proof. rewrite <- (sign_ext_zero_ext n y H). congruence. Qed. -Theorem zero_ext_shru_shl: +Theorem shru_shl: + forall x y z, ltu y iwordsize = true -> ltu z iwordsize = true -> + shru (shl x y) z = + if ltu z y then shl (zero_ext (zwordsize - unsigned y) x) (sub y z) + else zero_ext (zwordsize - unsigned z) (shru x (sub z y)). +Proof. + intros. apply ltu_iwordsize_inv in H; apply ltu_iwordsize_inv in H0. + unfold ltu. set (Y := unsigned y) in *; set (Z := unsigned z) in *. + apply same_bits_eq; intros. rewrite bits_shru by auto. fold Z. + destruct (zlt Z Y). +- assert (A: unsigned (sub y z) = Y - Z). + { apply unsigned_repr. generalize wordsize_max_unsigned; omega. } + symmetry; rewrite bits_shl, A by omega. + destruct (zlt (i + Z) zwordsize). ++ rewrite bits_shl by omega. fold Y. + destruct (zlt i (Y - Z)); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. + rewrite bits_zero_ext by omega. rewrite zlt_true by omega. f_equal; omega. ++ rewrite bits_zero_ext by omega. rewrite ! zlt_false by omega. auto. +- assert (A: unsigned (sub z y) = Z - Y). + { apply unsigned_repr. generalize wordsize_max_unsigned; omega. } + rewrite bits_zero_ext, bits_shru, A by omega. + destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. + rewrite bits_shl by omega. fold Y. + destruct (zlt (i + Z) Y). ++ rewrite zlt_false by omega. auto. ++ rewrite zlt_true by omega. f_equal; omega. +Qed. + +Corollary zero_ext_shru_shl: forall n x, 0 < n < zwordsize -> let y := repr (zwordsize - n) in zero_ext n x = shru (shl x y) y. Proof. intros. - assert (unsigned y = zwordsize - n). - unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. - apply same_bits_eq; intros. - rewrite bits_zero_ext. - rewrite bits_shru; auto. - destruct (zlt i n). - rewrite zlt_true. rewrite bits_shl. rewrite zlt_false. f_equal. omega. - omega. omega. omega. - rewrite zlt_false. auto. omega. - omega. -Qed. - -Theorem sign_ext_shr_shl: + assert (A: unsigned y = zwordsize - n). + { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. } + assert (B: ltu y iwordsize = true). + { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; omega. } + rewrite shru_shl by auto. unfold ltu; rewrite zlt_false by omega. + rewrite sub_idem, shru_zero. f_equal. rewrite A; omega. +Qed. + +Theorem shr_shl: + forall x y z, ltu y iwordsize = true -> ltu z iwordsize = true -> + shr (shl x y) z = + if ltu z y then shl (sign_ext (zwordsize - unsigned y) x) (sub y z) + else sign_ext (zwordsize - unsigned z) (shr x (sub z y)). +Proof. + intros. apply ltu_iwordsize_inv in H; apply ltu_iwordsize_inv in H0. + unfold ltu. set (Y := unsigned y) in *; set (Z := unsigned z) in *. + apply same_bits_eq; intros. rewrite bits_shr by auto. fold Z. + rewrite bits_shl by (destruct (zlt (i + Z) zwordsize); omega). fold Y. + destruct (zlt Z Y). +- assert (A: unsigned (sub y z) = Y - Z). + { apply unsigned_repr. generalize wordsize_max_unsigned; omega. } + rewrite bits_shl, A by omega. + destruct (zlt i (Y - Z)). ++ apply zlt_true. destruct (zlt (i + Z) zwordsize); omega. ++ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega). + rewrite bits_sign_ext by omega. f_equal. + destruct (zlt (i + Z) zwordsize). + rewrite zlt_true by omega. omega. + rewrite zlt_false by omega. omega. +- assert (A: unsigned (sub z y) = Z - Y). + { apply unsigned_repr. generalize wordsize_max_unsigned; omega. } + rewrite bits_sign_ext by omega. + rewrite bits_shr by (destruct (zlt i (zwordsize - Z)); omega). + rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega). + f_equal. destruct (zlt i (zwordsize - Z)). ++ rewrite ! zlt_true by omega. omega. ++ rewrite ! zlt_false by omega. rewrite zlt_true by omega. omega. +Qed. + +Corollary sign_ext_shr_shl: forall n x, 0 < n < zwordsize -> let y := repr (zwordsize - n) in sign_ext n x = shr (shl x y) y. Proof. intros. - assert (unsigned y = zwordsize - n). - unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. - apply same_bits_eq; intros. - rewrite bits_sign_ext. - rewrite bits_shr; auto. - destruct (zlt i n). - rewrite zlt_true. rewrite bits_shl. rewrite zlt_false. f_equal. omega. - omega. omega. omega. - rewrite zlt_false. rewrite bits_shl. rewrite zlt_false. f_equal. omega. - omega. omega. omega. omega. + assert (A: unsigned y = zwordsize - n). + { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. } + assert (B: ltu y iwordsize = true). + { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; omega. } + rewrite shr_shl by auto. unfold ltu; rewrite zlt_false by omega. + rewrite sub_idem, shr_zero. f_equal. rewrite A; omega. Qed. (** [zero_ext n x] is the unique integer congruent to [x] modulo [2^n] @@ -3643,6 +3694,67 @@ Proof. unfold shr, shr'; rewrite <- A; auto. Qed. +Theorem shru'_shl': + forall x y z, Int.ltu y iwordsize' = true -> Int.ltu z iwordsize' = true -> + shru' (shl' x y) z = + if Int.ltu z y then shl' (zero_ext (zwordsize - Int.unsigned y) x) (Int.sub y z) + else zero_ext (zwordsize - Int.unsigned z) (shru' x (Int.sub z y)). +Proof. + intros. apply Int.ltu_inv in H; apply Int.ltu_inv in H0. + change (Int.unsigned iwordsize') with zwordsize in *. + unfold Int.ltu. set (Y := Int.unsigned y) in *; set (Z := Int.unsigned z) in *. + apply same_bits_eq; intros. rewrite bits_shru' by auto. fold Z. + destruct (zlt Z Y). +- assert (A: Int.unsigned (Int.sub y z) = Y - Z). + { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. } + symmetry; rewrite bits_shl', A by omega. + destruct (zlt (i + Z) zwordsize). ++ rewrite bits_shl' by omega. fold Y. + destruct (zlt i (Y - Z)); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. + rewrite bits_zero_ext by omega. rewrite zlt_true by omega. f_equal; omega. ++ rewrite bits_zero_ext by omega. rewrite ! zlt_false by omega. auto. +- assert (A: Int.unsigned (Int.sub z y) = Z - Y). + { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. } + rewrite bits_zero_ext, bits_shru', A by omega. + destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto. + rewrite bits_shl' by omega. fold Y. + destruct (zlt (i + Z) Y). ++ rewrite zlt_false by omega. auto. ++ rewrite zlt_true by omega. f_equal; omega. +Qed. + +Theorem shr'_shl': + forall x y z, Int.ltu y iwordsize' = true -> Int.ltu z iwordsize' = true -> + shr' (shl' x y) z = + if Int.ltu z y then shl' (sign_ext (zwordsize - Int.unsigned y) x) (Int.sub y z) + else sign_ext (zwordsize - Int.unsigned z) (shr' x (Int.sub z y)). +Proof. + intros. apply Int.ltu_inv in H; apply Int.ltu_inv in H0. + change (Int.unsigned iwordsize') with zwordsize in *. + unfold Int.ltu. set (Y := Int.unsigned y) in *; set (Z := Int.unsigned z) in *. + apply same_bits_eq; intros. rewrite bits_shr' by auto. fold Z. + rewrite bits_shl' by (destruct (zlt (i + Z) zwordsize); omega). fold Y. + destruct (zlt Z Y). +- assert (A: Int.unsigned (Int.sub y z) = Y - Z). + { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. } + rewrite bits_shl', A by omega. + destruct (zlt i (Y - Z)). ++ apply zlt_true. destruct (zlt (i + Z) zwordsize); omega. ++ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega). + rewrite bits_sign_ext by omega. f_equal. + destruct (zlt (i + Z) zwordsize). + rewrite zlt_true by omega. omega. + rewrite zlt_false by omega. omega. +- assert (A: Int.unsigned (Int.sub z y) = Z - Y). + { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. } + rewrite bits_sign_ext by omega. + rewrite bits_shr' by (destruct (zlt i (zwordsize - Z)); omega). + rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega). + f_equal. destruct (zlt i (zwordsize - Z)). ++ rewrite ! zlt_true by omega. omega. ++ rewrite ! zlt_false by omega. rewrite zlt_true by omega. omega. +Qed. + Lemma shl'_zero_ext: forall n m x, 0 <= n -> shl' (zero_ext n x) m = zero_ext (n + Int.unsigned m) (shl' x m). diff --git a/riscV/Asmgenproof1.v b/riscV/Asmgenproof1.v index 98d5bd33..b4d6b831 100644 --- a/riscV/Asmgenproof1.v +++ b/riscV/Asmgenproof1.v @@ -400,22 +400,6 @@ Ltac ArgsInv := | [ H: freg_of _ = OK _ |- _ ] => simpl in *; rewrite (freg_of_eq _ _ H) in * end). -Inductive exec_straight_opt: code -> regset -> mem -> code -> regset -> mem -> Prop := - | exec_straight_opt_refl: forall c rs m, - exec_straight_opt c rs m c rs m - | exec_straight_opt_intro: forall c1 rs1 m1 c2 rs2 m2, - exec_straight ge fn c1 rs1 m1 c2 rs2 m2 -> - exec_straight_opt c1 rs1 m1 c2 rs2 m2. - -Remark exec_straight_opt_right: - forall c3 rs3 m3 c1 rs1 m1 c2 rs2 m2, - exec_straight_opt c1 rs1 m1 c2 rs2 m2 -> - exec_straight ge fn c2 rs2 m2 c3 rs3 m3 -> - exec_straight ge fn c1 rs1 m1 c3 rs3 m3. -Proof. - destruct 1; intros. auto. eapply exec_straight_trans; eauto. -Qed. - Lemma transl_cbranch_correct_1: forall cond args lbl k c m ms b sp rs m', transl_cbranch cond args lbl k = OK c -> diff --git a/runtime/Makefile b/runtime/Makefile index 8fe00934..6777995d 100644 --- a/runtime/Makefile +++ b/runtime/Makefile @@ -22,6 +22,8 @@ ifeq ($(ARCH),x86_64) OBJS=i64_dtou.o i64_utod.o i64_utof.o vararg.o else ifeq ($(ARCH),powerpc64) OBJS=i64_dtou.o i64_stof.o i64_utod.o i64_utof.o vararg.o +else ifeq ($(ARCH),aarch64) +OBJS=vararg.o else OBJS=i64_dtos.o i64_dtou.o i64_sar.o i64_sdiv.o i64_shl.o \ i64_shr.o i64_smod.o i64_stod.o i64_stof.o \ diff --git a/runtime/aarch64/sysdeps.h b/runtime/aarch64/sysdeps.h new file mode 100644 index 00000000..0cee9ae3 --- /dev/null +++ b/runtime/aarch64/sysdeps.h @@ -0,0 +1,45 @@ +// ***************************************************************** +// +// The Compcert verified compiler +// +// Xavier Leroy, Collège de France and INRIA Paris +// +// Copyright (c) Institut National de Recherche en Informatique et +// en Automatique. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are met: +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// * Neither the name of the nor the +// names of its contributors may be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// ********************************************************************* + +// System dependencies + +#define FUNCTION(f) \ + .text; \ + .balign 16; \ + .globl f; \ +f: + +#define ENDFUNCTION(f) \ + .type f, @function; .size f, . - f + diff --git a/runtime/aarch64/vararg.S b/runtime/aarch64/vararg.S new file mode 100644 index 00000000..b7347d65 --- /dev/null +++ b/runtime/aarch64/vararg.S @@ -0,0 +1,109 @@ +// ***************************************************************** +// +// The Compcert verified compiler +// +// Xavier Leroy, Collège de France and INRIA Paris +// +// Copyright (c) Institut National de Recherche en Informatique et +// en Automatique. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are met: +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// * Neither the name of the nor the +// names of its contributors may be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// ********************************************************************* + +// Helper functions for variadic functions . AArch64 version. + +#include "sysdeps.h" + +// typedef struct __va_list { +// void *__stack; // next stack parameter +// void *__gr_top; // top of the save area for int regs +// void *__vr_top; // top of the save area for float regs +// int__gr_offs; // offset from gr_top to next int reg +// int__vr_offs; // offset from gr_top to next FP reg +// } +// typedef struct __va_list va_list; // struct passed by reference +// unsigned int __compcert_va_int32(va_list * ap); +// unsigned long long __compcert_va_int64(va_list * ap); +// double __compcert_va_float64(va_list * ap); + +FUNCTION(__compcert_va_int32) + ldr w1, [x0, #24] // w1 = gr_offs + cbz w1, 1f + // gr_offs is not zero: load from int save area and update gr_offs + ldr x2, [x0, #8] // x2 = gr_top + ldr w2, [x2, w1, sxtw] // w2 = the next integer + add w1, w1, #8 + str w1, [x0, #24] // update gr_offs + mov w0, w2 + ret + // gr_offs is zero: load from stack save area and update stack pointer +1: ldr x1, [x0, #0] // x1 = stack + ldr w2, [x1, #0] // w2 = the next integer + add x1, x1, #8 + str x1, [x0, #0] // update stack + mov w0, w2 + ret +ENDFUNCTION(__compcert_va_int32) + +FUNCTION(__compcert_va_int64) + ldr w1, [x0, #24] // w1 = gr_offs + cbz w1, 1f + // gr_offs is not zero: load from int save area and update gr_offs + ldr x2, [x0, #8] // x2 = gr_top + ldr x2, [x2, w1, sxtw] // w2 = the next long integer + add w1, w1, #8 + str w1, [x0, #24] // update gr_offs + mov x0, x2 + ret + // gr_offs is zero: load from stack save area and update stack pointer +1: ldr x1, [x0, #0] // x1 = stack + ldr x2, [x1, #0] // w2 = the next long integer + add x1, x1, #8 + str x1, [x0, #0] // update stack + mov x0, x2 + ret +ENDFUNCTION(__compcert_va_int64) + +FUNCTION(__compcert_va_float64) + ldr w1, [x0, #28] // w1 = vr_offs + cbz w1, 1f + // vr_offs is not zero: load from float save area and update vr_offs + ldr x2, [x0, #16] // x2 = vr_top + ldr d0, [x2, w1, sxtw] // d0 = the next float + add w1, w1, #16 + str w1, [x0, #28] // update vr_offs + ret + // gr_offs is zero: load from stack save area and update stack pointer +1: ldr x1, [x0, #0] // x1 = stack + ldr d0, [x1, #0] // d0 = the next float + add x1, x1, #8 + str x1, [x0, #0] // update stack + ret +ENDFUNCTION(__compcert_va_float64) + +// Right now we pass structs by reference. This is not ABI conformant. +FUNCTION(__compcert_va_composite) + b __compcert_va_int64 +ENDFUNCTION(__compcert_va_composite) diff --git a/test/regression/Results/builtins-aarch64 b/test/regression/Results/builtins-aarch64 new file mode 100644 index 00000000..c70432d8 --- /dev/null +++ b/test/regression/Results/builtins-aarch64 @@ -0,0 +1,15 @@ +bswap(12345678) = 78563412 +bswap16(1234) = 3412 +bswap64(123456789abcdef0) = f0debc9a78563412 +clz(12345678) = 3 +clzll(12345678) = 35 +clzll(1234567812345678) = 3 +cls(1234567) = 10 +cls(-9999) = 17 +clsll(1234567) = 42 +clsll(-9999) = 49 +fsqrt(3.141590) = 1.772453 +fmadd(3.141590, 2.718000, 1.414000) = 9.952842 +fmsub(3.141590, 2.718000, 1.414000) = -7.124842 +fnmadd(3.141590, 2.718000, 1.414000) = -9.952842 +fnmsub(3.141590, 2.718000, 1.414000) = 7.124842 diff --git a/test/regression/builtins-aarch64.c b/test/regression/builtins-aarch64.c new file mode 100644 index 00000000..2cfa2d09 --- /dev/null +++ b/test/regression/builtins-aarch64.c @@ -0,0 +1,47 @@ +/* Fun with builtin functions */ + +#include + +int main(int argc, char ** argv) +{ + unsigned int x = 0x12345678; + unsigned int y = 0xDEADBEEF; + unsigned long long xx = 0x1234567812345678ULL; + unsigned long long yy = 0x1234567800000000ULL; + unsigned long long zz = 0x123456789ABCDEF0ULL; + unsigned z; + double a = 3.14159; + double b = 2.718; + double c = 1.414; + unsigned short s = 0x1234; + signed int u = 1234567; + signed int v = -9999; + + printf("bswap(%x) = %x\n", x, __builtin_bswap(x)); + printf("bswap16(%x) = %x\n", s, __builtin_bswap16(s)); + printf("bswap64(%llx) = %llx\n", zz, __builtin_bswap64(zz)); + printf("clz(%x) = %d\n", x, __builtin_clz(x)); + printf("clzll(%llx) = %d\n", (unsigned long long) x, __builtin_clzll(x)); + printf("clzll(%llx) = %d\n", xx, __builtin_clzll(xx)); + printf("cls(%d) = %d\n", u, __builtin_cls(u)); + printf("cls(%d) = %d\n", v, __builtin_cls(v)); + printf("clsll(%lld) = %d\n", (signed long long) u, __builtin_clsll(u)); + printf("clsll(%lld) = %d\n", (signed long long) v, __builtin_clsll(v)); + + printf("fsqrt(%f) = %f\n", a, __builtin_fsqrt(a)); + printf("fmadd(%f, %f, %f) = %f\n", a, b, c, __builtin_fmadd(a, b, c)); + printf("fmsub(%f, %f, %f) = %f\n", a, b, c, __builtin_fmsub(a, b, c)); + printf("fnmadd(%f, %f, %f) = %f\n", a, b, c, __builtin_fnmadd(a, b, c)); + printf("fnmsub(%f, %f, %f) = %f\n", a, b, c, __builtin_fnmsub(a, b, c)); + + /* Make sure that ignoring the result of a builtin + doesn't cause an internal error */ + (void) __builtin_bswap(x); + (void) __builtin_fsqrt(a); + return 0; +} + + + + + diff --git a/test/regression/extasm.c b/test/regression/extasm.c index 83a07a05..297178d1 100644 --- a/test/regression/extasm.c +++ b/test/regression/extasm.c @@ -5,14 +5,16 @@ int clobbers(int x, int z) { int y; asm("TEST0 out:%0 in:%1" : "=r"(y) : "r"(x) : "cc" -#if defined(__x86_64__) +#if defined(ARCH_x86) && defined(MODEL_64) , "rax", "rdx", "rbx" -#elif defined(__i386__) +#elif defined(ARCH_x86) && !defined(MODEL_64) , "eax", "edx", "ebx" -#elif defined(__arm__) +#elif defined(ARCH_arm) , "r0", "r1", "r4" -#elif defined(__PPC__) +#elif defined(ARCH_powerpc) , "r0", "r3", "r4", "r31" +#elif defined(ARCH_aarch64) + , "x0", "x1", "x16", "x29", "x30" #endif ); return y + z; @@ -21,7 +23,8 @@ int clobbers(int x, int z) #if (defined(ARCH_x86) && defined(MODEL_64)) \ || (defined(ARCH_riscV) && defined(MODEL_64)) \ || (defined(ARCH_powerpc) && defined(MODEL_ppc64)) \ - || (defined(ARCH_powerpc) && defined(MODEL_e5500)) + || (defined(ARCH_powerpc) && defined(MODEL_e5500)) \ + || defined(ARCH_aarch64) #define SIXTYFOUR #else #undef SIXTYFOUR -- cgit From 27167c6226bbdd2856b8bb6c290b31b5e8534ba9 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Thu, 8 Aug 2019 11:19:15 +0200 Subject: Test for the compilation of floating-point literals With special emphasis on the use of the AArch64 fmov #imm instruction. --- test/regression/Makefile | 2 +- test/regression/Results/floats-lit | 2 + test/regression/floats-lit.c | 559 +++++++++++++++++++++++++++++++++++++ 3 files changed, 562 insertions(+), 1 deletion(-) create mode 100644 test/regression/Results/floats-lit create mode 100644 test/regression/floats-lit.c diff --git a/test/regression/Makefile b/test/regression/Makefile index e5b0655e..8e8d8762 100644 --- a/test/regression/Makefile +++ b/test/regression/Makefile @@ -10,7 +10,7 @@ LIBS=$(LIBMATH) # Can run, both in compiled mode and in interpreter mode, # and have reference output in Results -TESTS=int32 int64 floats floats-basics \ +TESTS=int32 int64 floats floats-basics floats-lit \ expr1 expr6 funptr2 initializers initializers2 initializers3 \ volatile1 volatile2 volatile3 volatile4 \ funct3 expr5 struct7 struct8 struct11 struct12 casts1 casts2 char1 \ diff --git a/test/regression/Results/floats-lit b/test/regression/Results/floats-lit new file mode 100644 index 00000000..6cde72fb --- /dev/null +++ b/test/regression/Results/floats-lit @@ -0,0 +1,2 @@ +--- Double-precision test +--- Single-precision test diff --git a/test/regression/floats-lit.c b/test/regression/floats-lit.c new file mode 100644 index 00000000..a1098faf --- /dev/null +++ b/test/regression/floats-lit.c @@ -0,0 +1,559 @@ +#include + +int error = 0; + +void dbl(double x, unsigned long long bits) +{ + union { double d; unsigned long long i; } u; + u.d = x; + if (u.i != bits) { + printf("Error: expected 0x%016llx, got 0x%016llx\n", bits, u.i); + error = 1; + } +} + +void sng(float x, unsigned int bits) +{ + union { float f; unsigned int i; } u; + u.f = x; + if (u.i != bits) { + printf("Error: expected 0x%08x, got 0x%08x\n", bits, u.i); + error = 1; + } +} + +void testdbl(void) +{ + printf("--- Double-precision test\n"); + dbl(0.0, 0ULL); + dbl((-0.0), 0x8000000000000000ULL); + // The following are the "fmov immediate" of aarch64 + // They include +1.0 and -1.0 + dbl(0x1p-3, 0x3fc0000000000000ULL); + dbl(0x1.1p-3, 0x3fc1000000000000ULL); + dbl(0x1.2p-3, 0x3fc2000000000000ULL); + dbl(0x1.3p-3, 0x3fc3000000000000ULL); + dbl(0x1.4p-3, 0x3fc4000000000000ULL); + dbl(0x1.5p-3, 0x3fc5000000000000ULL); + dbl(0x1.6p-3, 0x3fc6000000000000ULL); + dbl(0x1.7p-3, 0x3fc7000000000000ULL); + dbl(0x1.8p-3, 0x3fc8000000000000ULL); + dbl(0x1.9p-3, 0x3fc9000000000000ULL); + dbl(0x1.ap-3, 0x3fca000000000000ULL); + dbl(0x1.bp-3, 0x3fcb000000000000ULL); + dbl(0x1.cp-3, 0x3fcc000000000000ULL); + dbl(0x1.dp-3, 0x3fcd000000000000ULL); + dbl(0x1.ep-3, 0x3fce000000000000ULL); + dbl(0x1.fp-3, 0x3fcf000000000000ULL); + dbl(0x1p-2, 0x3fd0000000000000ULL); + dbl(0x1.1p-2, 0x3fd1000000000000ULL); + dbl(0x1.2p-2, 0x3fd2000000000000ULL); + dbl(0x1.3p-2, 0x3fd3000000000000ULL); + dbl(0x1.4p-2, 0x3fd4000000000000ULL); + dbl(0x1.5p-2, 0x3fd5000000000000ULL); + dbl(0x1.6p-2, 0x3fd6000000000000ULL); + dbl(0x1.7p-2, 0x3fd7000000000000ULL); + dbl(0x1.8p-2, 0x3fd8000000000000ULL); + dbl(0x1.9p-2, 0x3fd9000000000000ULL); + dbl(0x1.ap-2, 0x3fda000000000000ULL); + dbl(0x1.bp-2, 0x3fdb000000000000ULL); + dbl(0x1.cp-2, 0x3fdc000000000000ULL); + dbl(0x1.dp-2, 0x3fdd000000000000ULL); + dbl(0x1.ep-2, 0x3fde000000000000ULL); + dbl(0x1.fp-2, 0x3fdf000000000000ULL); + dbl(0x1p-1, 0x3fe0000000000000ULL); + dbl(0x1.1p-1, 0x3fe1000000000000ULL); + dbl(0x1.2p-1, 0x3fe2000000000000ULL); + dbl(0x1.3p-1, 0x3fe3000000000000ULL); + dbl(0x1.4p-1, 0x3fe4000000000000ULL); + dbl(0x1.5p-1, 0x3fe5000000000000ULL); + dbl(0x1.6p-1, 0x3fe6000000000000ULL); + dbl(0x1.7p-1, 0x3fe7000000000000ULL); + dbl(0x1.8p-1, 0x3fe8000000000000ULL); + dbl(0x1.9p-1, 0x3fe9000000000000ULL); + dbl(0x1.ap-1, 0x3fea000000000000ULL); + dbl(0x1.bp-1, 0x3feb000000000000ULL); + dbl(0x1.cp-1, 0x3fec000000000000ULL); + dbl(0x1.dp-1, 0x3fed000000000000ULL); + dbl(0x1.ep-1, 0x3fee000000000000ULL); + dbl(0x1.fp-1, 0x3fef000000000000ULL); + dbl(0x1p+0, 0x3ff0000000000000ULL); + dbl(0x1.1p+0, 0x3ff1000000000000ULL); + dbl(0x1.2p+0, 0x3ff2000000000000ULL); + dbl(0x1.3p+0, 0x3ff3000000000000ULL); + dbl(0x1.4p+0, 0x3ff4000000000000ULL); + dbl(0x1.5p+0, 0x3ff5000000000000ULL); + dbl(0x1.6p+0, 0x3ff6000000000000ULL); + dbl(0x1.7p+0, 0x3ff7000000000000ULL); + dbl(0x1.8p+0, 0x3ff8000000000000ULL); + dbl(0x1.9p+0, 0x3ff9000000000000ULL); + dbl(0x1.ap+0, 0x3ffa000000000000ULL); + dbl(0x1.bp+0, 0x3ffb000000000000ULL); + dbl(0x1.cp+0, 0x3ffc000000000000ULL); + dbl(0x1.dp+0, 0x3ffd000000000000ULL); + dbl(0x1.ep+0, 0x3ffe000000000000ULL); + dbl(0x1.fp+0, 0x3fff000000000000ULL); + dbl(0x1p+1, 0x4000000000000000ULL); + dbl(0x1.1p+1, 0x4001000000000000ULL); + dbl(0x1.2p+1, 0x4002000000000000ULL); + dbl(0x1.3p+1, 0x4003000000000000ULL); + dbl(0x1.4p+1, 0x4004000000000000ULL); + dbl(0x1.5p+1, 0x4005000000000000ULL); + dbl(0x1.6p+1, 0x4006000000000000ULL); + dbl(0x1.7p+1, 0x4007000000000000ULL); + dbl(0x1.8p+1, 0x4008000000000000ULL); + dbl(0x1.9p+1, 0x4009000000000000ULL); + dbl(0x1.ap+1, 0x400a000000000000ULL); + dbl(0x1.bp+1, 0x400b000000000000ULL); + dbl(0x1.cp+1, 0x400c000000000000ULL); + dbl(0x1.dp+1, 0x400d000000000000ULL); + dbl(0x1.ep+1, 0x400e000000000000ULL); + dbl(0x1.fp+1, 0x400f000000000000ULL); + dbl(0x1p+2, 0x4010000000000000ULL); + dbl(0x1.1p+2, 0x4011000000000000ULL); + dbl(0x1.2p+2, 0x4012000000000000ULL); + dbl(0x1.3p+2, 0x4013000000000000ULL); + dbl(0x1.4p+2, 0x4014000000000000ULL); + dbl(0x1.5p+2, 0x4015000000000000ULL); + dbl(0x1.6p+2, 0x4016000000000000ULL); + dbl(0x1.7p+2, 0x4017000000000000ULL); + dbl(0x1.8p+2, 0x4018000000000000ULL); + dbl(0x1.9p+2, 0x4019000000000000ULL); + dbl(0x1.ap+2, 0x401a000000000000ULL); + dbl(0x1.bp+2, 0x401b000000000000ULL); + dbl(0x1.cp+2, 0x401c000000000000ULL); + dbl(0x1.dp+2, 0x401d000000000000ULL); + dbl(0x1.ep+2, 0x401e000000000000ULL); + dbl(0x1.fp+2, 0x401f000000000000ULL); + dbl(0x1p+3, 0x4020000000000000ULL); + dbl(0x1.1p+3, 0x4021000000000000ULL); + dbl(0x1.2p+3, 0x4022000000000000ULL); + dbl(0x1.3p+3, 0x4023000000000000ULL); + dbl(0x1.4p+3, 0x4024000000000000ULL); + dbl(0x1.5p+3, 0x4025000000000000ULL); + dbl(0x1.6p+3, 0x4026000000000000ULL); + dbl(0x1.7p+3, 0x4027000000000000ULL); + dbl(0x1.8p+3, 0x4028000000000000ULL); + dbl(0x1.9p+3, 0x4029000000000000ULL); + dbl(0x1.ap+3, 0x402a000000000000ULL); + dbl(0x1.bp+3, 0x402b000000000000ULL); + dbl(0x1.cp+3, 0x402c000000000000ULL); + dbl(0x1.dp+3, 0x402d000000000000ULL); + dbl(0x1.ep+3, 0x402e000000000000ULL); + dbl(0x1.fp+3, 0x402f000000000000ULL); + dbl(0x1p+4, 0x4030000000000000ULL); + dbl(0x1.1p+4, 0x4031000000000000ULL); + dbl(0x1.2p+4, 0x4032000000000000ULL); + dbl(0x1.3p+4, 0x4033000000000000ULL); + dbl(0x1.4p+4, 0x4034000000000000ULL); + dbl(0x1.5p+4, 0x4035000000000000ULL); + dbl(0x1.6p+4, 0x4036000000000000ULL); + dbl(0x1.7p+4, 0x4037000000000000ULL); + dbl(0x1.8p+4, 0x4038000000000000ULL); + dbl(0x1.9p+4, 0x4039000000000000ULL); + dbl(0x1.ap+4, 0x403a000000000000ULL); + dbl(0x1.bp+4, 0x403b000000000000ULL); + dbl(0x1.cp+4, 0x403c000000000000ULL); + dbl(0x1.dp+4, 0x403d000000000000ULL); + dbl(0x1.ep+4, 0x403e000000000000ULL); + dbl(0x1.fp+4, 0x403f000000000000ULL); + dbl((-0x1p-3), 0xbfc0000000000000ULL); + dbl((-0x1.1p-3), 0xbfc1000000000000ULL); + dbl((-0x1.2p-3), 0xbfc2000000000000ULL); + dbl((-0x1.3p-3), 0xbfc3000000000000ULL); + dbl((-0x1.4p-3), 0xbfc4000000000000ULL); + dbl((-0x1.5p-3), 0xbfc5000000000000ULL); + dbl((-0x1.6p-3), 0xbfc6000000000000ULL); + dbl((-0x1.7p-3), 0xbfc7000000000000ULL); + dbl((-0x1.8p-3), 0xbfc8000000000000ULL); + dbl((-0x1.9p-3), 0xbfc9000000000000ULL); + dbl((-0x1.ap-3), 0xbfca000000000000ULL); + dbl((-0x1.bp-3), 0xbfcb000000000000ULL); + dbl((-0x1.cp-3), 0xbfcc000000000000ULL); + dbl((-0x1.dp-3), 0xbfcd000000000000ULL); + dbl((-0x1.ep-3), 0xbfce000000000000ULL); + dbl((-0x1.fp-3), 0xbfcf000000000000ULL); + dbl((-0x1p-2), 0xbfd0000000000000ULL); + dbl((-0x1.1p-2), 0xbfd1000000000000ULL); + dbl((-0x1.2p-2), 0xbfd2000000000000ULL); + dbl((-0x1.3p-2), 0xbfd3000000000000ULL); + dbl((-0x1.4p-2), 0xbfd4000000000000ULL); + dbl((-0x1.5p-2), 0xbfd5000000000000ULL); + dbl((-0x1.6p-2), 0xbfd6000000000000ULL); + dbl((-0x1.7p-2), 0xbfd7000000000000ULL); + dbl((-0x1.8p-2), 0xbfd8000000000000ULL); + dbl((-0x1.9p-2), 0xbfd9000000000000ULL); + dbl((-0x1.ap-2), 0xbfda000000000000ULL); + dbl((-0x1.bp-2), 0xbfdb000000000000ULL); + dbl((-0x1.cp-2), 0xbfdc000000000000ULL); + dbl((-0x1.dp-2), 0xbfdd000000000000ULL); + dbl((-0x1.ep-2), 0xbfde000000000000ULL); + dbl((-0x1.fp-2), 0xbfdf000000000000ULL); + dbl((-0x1p-1), 0xbfe0000000000000ULL); + dbl((-0x1.1p-1), 0xbfe1000000000000ULL); + dbl((-0x1.2p-1), 0xbfe2000000000000ULL); + dbl((-0x1.3p-1), 0xbfe3000000000000ULL); + dbl((-0x1.4p-1), 0xbfe4000000000000ULL); + dbl((-0x1.5p-1), 0xbfe5000000000000ULL); + dbl((-0x1.6p-1), 0xbfe6000000000000ULL); + dbl((-0x1.7p-1), 0xbfe7000000000000ULL); + dbl((-0x1.8p-1), 0xbfe8000000000000ULL); + dbl((-0x1.9p-1), 0xbfe9000000000000ULL); + dbl((-0x1.ap-1), 0xbfea000000000000ULL); + dbl((-0x1.bp-1), 0xbfeb000000000000ULL); + dbl((-0x1.cp-1), 0xbfec000000000000ULL); + dbl((-0x1.dp-1), 0xbfed000000000000ULL); + dbl((-0x1.ep-1), 0xbfee000000000000ULL); + dbl((-0x1.fp-1), 0xbfef000000000000ULL); + dbl((-0x1p+0), 0xbff0000000000000ULL); + dbl((-0x1.1p+0), 0xbff1000000000000ULL); + dbl((-0x1.2p+0), 0xbff2000000000000ULL); + dbl((-0x1.3p+0), 0xbff3000000000000ULL); + dbl((-0x1.4p+0), 0xbff4000000000000ULL); + dbl((-0x1.5p+0), 0xbff5000000000000ULL); + dbl((-0x1.6p+0), 0xbff6000000000000ULL); + dbl((-0x1.7p+0), 0xbff7000000000000ULL); + dbl((-0x1.8p+0), 0xbff8000000000000ULL); + dbl((-0x1.9p+0), 0xbff9000000000000ULL); + dbl((-0x1.ap+0), 0xbffa000000000000ULL); + dbl((-0x1.bp+0), 0xbffb000000000000ULL); + dbl((-0x1.cp+0), 0xbffc000000000000ULL); + dbl((-0x1.dp+0), 0xbffd000000000000ULL); + dbl((-0x1.ep+0), 0xbffe000000000000ULL); + dbl((-0x1.fp+0), 0xbfff000000000000ULL); + dbl((-0x1p+1), 0xc000000000000000ULL); + dbl((-0x1.1p+1), 0xc001000000000000ULL); + dbl((-0x1.2p+1), 0xc002000000000000ULL); + dbl((-0x1.3p+1), 0xc003000000000000ULL); + dbl((-0x1.4p+1), 0xc004000000000000ULL); + dbl((-0x1.5p+1), 0xc005000000000000ULL); + dbl((-0x1.6p+1), 0xc006000000000000ULL); + dbl((-0x1.7p+1), 0xc007000000000000ULL); + dbl((-0x1.8p+1), 0xc008000000000000ULL); + dbl((-0x1.9p+1), 0xc009000000000000ULL); + dbl((-0x1.ap+1), 0xc00a000000000000ULL); + dbl((-0x1.bp+1), 0xc00b000000000000ULL); + dbl((-0x1.cp+1), 0xc00c000000000000ULL); + dbl((-0x1.dp+1), 0xc00d000000000000ULL); + dbl((-0x1.ep+1), 0xc00e000000000000ULL); + dbl((-0x1.fp+1), 0xc00f000000000000ULL); + dbl((-0x1p+2), 0xc010000000000000ULL); + dbl((-0x1.1p+2), 0xc011000000000000ULL); + dbl((-0x1.2p+2), 0xc012000000000000ULL); + dbl((-0x1.3p+2), 0xc013000000000000ULL); + dbl((-0x1.4p+2), 0xc014000000000000ULL); + dbl((-0x1.5p+2), 0xc015000000000000ULL); + dbl((-0x1.6p+2), 0xc016000000000000ULL); + dbl((-0x1.7p+2), 0xc017000000000000ULL); + dbl((-0x1.8p+2), 0xc018000000000000ULL); + dbl((-0x1.9p+2), 0xc019000000000000ULL); + dbl((-0x1.ap+2), 0xc01a000000000000ULL); + dbl((-0x1.bp+2), 0xc01b000000000000ULL); + dbl((-0x1.cp+2), 0xc01c000000000000ULL); + dbl((-0x1.dp+2), 0xc01d000000000000ULL); + dbl((-0x1.ep+2), 0xc01e000000000000ULL); + dbl((-0x1.fp+2), 0xc01f000000000000ULL); + dbl((-0x1p+3), 0xc020000000000000ULL); + dbl((-0x1.1p+3), 0xc021000000000000ULL); + dbl((-0x1.2p+3), 0xc022000000000000ULL); + dbl((-0x1.3p+3), 0xc023000000000000ULL); + dbl((-0x1.4p+3), 0xc024000000000000ULL); + dbl((-0x1.5p+3), 0xc025000000000000ULL); + dbl((-0x1.6p+3), 0xc026000000000000ULL); + dbl((-0x1.7p+3), 0xc027000000000000ULL); + dbl((-0x1.8p+3), 0xc028000000000000ULL); + dbl((-0x1.9p+3), 0xc029000000000000ULL); + dbl((-0x1.ap+3), 0xc02a000000000000ULL); + dbl((-0x1.bp+3), 0xc02b000000000000ULL); + dbl((-0x1.cp+3), 0xc02c000000000000ULL); + dbl((-0x1.dp+3), 0xc02d000000000000ULL); + dbl((-0x1.ep+3), 0xc02e000000000000ULL); + dbl((-0x1.fp+3), 0xc02f000000000000ULL); + dbl((-0x1p+4), 0xc030000000000000ULL); + dbl((-0x1.1p+4), 0xc031000000000000ULL); + dbl((-0x1.2p+4), 0xc032000000000000ULL); + dbl((-0x1.3p+4), 0xc033000000000000ULL); + dbl((-0x1.4p+4), 0xc034000000000000ULL); + dbl((-0x1.5p+4), 0xc035000000000000ULL); + dbl((-0x1.6p+4), 0xc036000000000000ULL); + dbl((-0x1.7p+4), 0xc037000000000000ULL); + dbl((-0x1.8p+4), 0xc038000000000000ULL); + dbl((-0x1.9p+4), 0xc039000000000000ULL); + dbl((-0x1.ap+4), 0xc03a000000000000ULL); + dbl((-0x1.bp+4), 0xc03b000000000000ULL); + dbl((-0x1.cp+4), 0xc03c000000000000ULL); + dbl((-0x1.dp+4), 0xc03d000000000000ULL); + dbl((-0x1.ep+4), 0xc03e000000000000ULL); + dbl((-0x1.fp+4), 0xc03f000000000000ULL); +} + +void testsng(void) +{ + printf("--- Single-precision test\n"); + sng(0x0p+0, 0x0U); + sng(-0x0p+0, 0x80000000U); + sng(0x1p-3, 0x3e000000U); + sng(0x1.1p-3, 0x3e080000U); + sng(0x1.2p-3, 0x3e100000U); + sng(0x1.3p-3, 0x3e180000U); + sng(0x1.4p-3, 0x3e200000U); + sng(0x1.5p-3, 0x3e280000U); + sng(0x1.6p-3, 0x3e300000U); + sng(0x1.7p-3, 0x3e380000U); + sng(0x1.8p-3, 0x3e400000U); + sng(0x1.9p-3, 0x3e480000U); + sng(0x1.ap-3, 0x3e500000U); + sng(0x1.bp-3, 0x3e580000U); + sng(0x1.cp-3, 0x3e600000U); + sng(0x1.dp-3, 0x3e680000U); + sng(0x1.ep-3, 0x3e700000U); + sng(0x1.fp-3, 0x3e780000U); + sng(0x1p-2, 0x3e800000U); + sng(0x1.1p-2, 0x3e880000U); + sng(0x1.2p-2, 0x3e900000U); + sng(0x1.3p-2, 0x3e980000U); + sng(0x1.4p-2, 0x3ea00000U); + sng(0x1.5p-2, 0x3ea80000U); + sng(0x1.6p-2, 0x3eb00000U); + sng(0x1.7p-2, 0x3eb80000U); + sng(0x1.8p-2, 0x3ec00000U); + sng(0x1.9p-2, 0x3ec80000U); + sng(0x1.ap-2, 0x3ed00000U); + sng(0x1.bp-2, 0x3ed80000U); + sng(0x1.cp-2, 0x3ee00000U); + sng(0x1.dp-2, 0x3ee80000U); + sng(0x1.ep-2, 0x3ef00000U); + sng(0x1.fp-2, 0x3ef80000U); + sng(0x1p-1, 0x3f000000U); + sng(0x1.1p-1, 0x3f080000U); + sng(0x1.2p-1, 0x3f100000U); + sng(0x1.3p-1, 0x3f180000U); + sng(0x1.4p-1, 0x3f200000U); + sng(0x1.5p-1, 0x3f280000U); + sng(0x1.6p-1, 0x3f300000U); + sng(0x1.7p-1, 0x3f380000U); + sng(0x1.8p-1, 0x3f400000U); + sng(0x1.9p-1, 0x3f480000U); + sng(0x1.ap-1, 0x3f500000U); + sng(0x1.bp-1, 0x3f580000U); + sng(0x1.cp-1, 0x3f600000U); + sng(0x1.dp-1, 0x3f680000U); + sng(0x1.ep-1, 0x3f700000U); + sng(0x1.fp-1, 0x3f780000U); + sng(0x1p+0, 0x3f800000U); + sng(0x1.1p+0, 0x3f880000U); + sng(0x1.2p+0, 0x3f900000U); + sng(0x1.3p+0, 0x3f980000U); + sng(0x1.4p+0, 0x3fa00000U); + sng(0x1.5p+0, 0x3fa80000U); + sng(0x1.6p+0, 0x3fb00000U); + sng(0x1.7p+0, 0x3fb80000U); + sng(0x1.8p+0, 0x3fc00000U); + sng(0x1.9p+0, 0x3fc80000U); + sng(0x1.ap+0, 0x3fd00000U); + sng(0x1.bp+0, 0x3fd80000U); + sng(0x1.cp+0, 0x3fe00000U); + sng(0x1.dp+0, 0x3fe80000U); + sng(0x1.ep+0, 0x3ff00000U); + sng(0x1.fp+0, 0x3ff80000U); + sng(0x1p+1, 0x40000000U); + sng(0x1.1p+1, 0x40080000U); + sng(0x1.2p+1, 0x40100000U); + sng(0x1.3p+1, 0x40180000U); + sng(0x1.4p+1, 0x40200000U); + sng(0x1.5p+1, 0x40280000U); + sng(0x1.6p+1, 0x40300000U); + sng(0x1.7p+1, 0x40380000U); + sng(0x1.8p+1, 0x40400000U); + sng(0x1.9p+1, 0x40480000U); + sng(0x1.ap+1, 0x40500000U); + sng(0x1.bp+1, 0x40580000U); + sng(0x1.cp+1, 0x40600000U); + sng(0x1.dp+1, 0x40680000U); + sng(0x1.ep+1, 0x40700000U); + sng(0x1.fp+1, 0x40780000U); + sng(0x1p+2, 0x40800000U); + sng(0x1.1p+2, 0x40880000U); + sng(0x1.2p+2, 0x40900000U); + sng(0x1.3p+2, 0x40980000U); + sng(0x1.4p+2, 0x40a00000U); + sng(0x1.5p+2, 0x40a80000U); + sng(0x1.6p+2, 0x40b00000U); + sng(0x1.7p+2, 0x40b80000U); + sng(0x1.8p+2, 0x40c00000U); + sng(0x1.9p+2, 0x40c80000U); + sng(0x1.ap+2, 0x40d00000U); + sng(0x1.bp+2, 0x40d80000U); + sng(0x1.cp+2, 0x40e00000U); + sng(0x1.dp+2, 0x40e80000U); + sng(0x1.ep+2, 0x40f00000U); + sng(0x1.fp+2, 0x40f80000U); + sng(0x1p+3, 0x41000000U); + sng(0x1.1p+3, 0x41080000U); + sng(0x1.2p+3, 0x41100000U); + sng(0x1.3p+3, 0x41180000U); + sng(0x1.4p+3, 0x41200000U); + sng(0x1.5p+3, 0x41280000U); + sng(0x1.6p+3, 0x41300000U); + sng(0x1.7p+3, 0x41380000U); + sng(0x1.8p+3, 0x41400000U); + sng(0x1.9p+3, 0x41480000U); + sng(0x1.ap+3, 0x41500000U); + sng(0x1.bp+3, 0x41580000U); + sng(0x1.cp+3, 0x41600000U); + sng(0x1.dp+3, 0x41680000U); + sng(0x1.ep+3, 0x41700000U); + sng(0x1.fp+3, 0x41780000U); + sng(0x1p+4, 0x41800000U); + sng(0x1.1p+4, 0x41880000U); + sng(0x1.2p+4, 0x41900000U); + sng(0x1.3p+4, 0x41980000U); + sng(0x1.4p+4, 0x41a00000U); + sng(0x1.5p+4, 0x41a80000U); + sng(0x1.6p+4, 0x41b00000U); + sng(0x1.7p+4, 0x41b80000U); + sng(0x1.8p+4, 0x41c00000U); + sng(0x1.9p+4, 0x41c80000U); + sng(0x1.ap+4, 0x41d00000U); + sng(0x1.bp+4, 0x41d80000U); + sng(0x1.cp+4, 0x41e00000U); + sng(0x1.dp+4, 0x41e80000U); + sng(0x1.ep+4, 0x41f00000U); + sng(0x1.fp+4, 0x41f80000U); + sng(-0x1p-3, 0xbe000000U); + sng(-0x1.1p-3, 0xbe080000U); + sng(-0x1.2p-3, 0xbe100000U); + sng(-0x1.3p-3, 0xbe180000U); + sng(-0x1.4p-3, 0xbe200000U); + sng(-0x1.5p-3, 0xbe280000U); + sng(-0x1.6p-3, 0xbe300000U); + sng(-0x1.7p-3, 0xbe380000U); + sng(-0x1.8p-3, 0xbe400000U); + sng(-0x1.9p-3, 0xbe480000U); + sng(-0x1.ap-3, 0xbe500000U); + sng(-0x1.bp-3, 0xbe580000U); + sng(-0x1.cp-3, 0xbe600000U); + sng(-0x1.dp-3, 0xbe680000U); + sng(-0x1.ep-3, 0xbe700000U); + sng(-0x1.fp-3, 0xbe780000U); + sng(-0x1p-2, 0xbe800000U); + sng(-0x1.1p-2, 0xbe880000U); + sng(-0x1.2p-2, 0xbe900000U); + sng(-0x1.3p-2, 0xbe980000U); + sng(-0x1.4p-2, 0xbea00000U); + sng(-0x1.5p-2, 0xbea80000U); + sng(-0x1.6p-2, 0xbeb00000U); + sng(-0x1.7p-2, 0xbeb80000U); + sng(-0x1.8p-2, 0xbec00000U); + sng(-0x1.9p-2, 0xbec80000U); + sng(-0x1.ap-2, 0xbed00000U); + sng(-0x1.bp-2, 0xbed80000U); + sng(-0x1.cp-2, 0xbee00000U); + sng(-0x1.dp-2, 0xbee80000U); + sng(-0x1.ep-2, 0xbef00000U); + sng(-0x1.fp-2, 0xbef80000U); + sng(-0x1p-1, 0xbf000000U); + sng(-0x1.1p-1, 0xbf080000U); + sng(-0x1.2p-1, 0xbf100000U); + sng(-0x1.3p-1, 0xbf180000U); + sng(-0x1.4p-1, 0xbf200000U); + sng(-0x1.5p-1, 0xbf280000U); + sng(-0x1.6p-1, 0xbf300000U); + sng(-0x1.7p-1, 0xbf380000U); + sng(-0x1.8p-1, 0xbf400000U); + sng(-0x1.9p-1, 0xbf480000U); + sng(-0x1.ap-1, 0xbf500000U); + sng(-0x1.bp-1, 0xbf580000U); + sng(-0x1.cp-1, 0xbf600000U); + sng(-0x1.dp-1, 0xbf680000U); + sng(-0x1.ep-1, 0xbf700000U); + sng(-0x1.fp-1, 0xbf780000U); + sng(-0x1p+0, 0xbf800000U); + sng(-0x1.1p+0, 0xbf880000U); + sng(-0x1.2p+0, 0xbf900000U); + sng(-0x1.3p+0, 0xbf980000U); + sng(-0x1.4p+0, 0xbfa00000U); + sng(-0x1.5p+0, 0xbfa80000U); + sng(-0x1.6p+0, 0xbfb00000U); + sng(-0x1.7p+0, 0xbfb80000U); + sng(-0x1.8p+0, 0xbfc00000U); + sng(-0x1.9p+0, 0xbfc80000U); + sng(-0x1.ap+0, 0xbfd00000U); + sng(-0x1.bp+0, 0xbfd80000U); + sng(-0x1.cp+0, 0xbfe00000U); + sng(-0x1.dp+0, 0xbfe80000U); + sng(-0x1.ep+0, 0xbff00000U); + sng(-0x1.fp+0, 0xbff80000U); + sng(-0x1p+1, 0xc0000000U); + sng(-0x1.1p+1, 0xc0080000U); + sng(-0x1.2p+1, 0xc0100000U); + sng(-0x1.3p+1, 0xc0180000U); + sng(-0x1.4p+1, 0xc0200000U); + sng(-0x1.5p+1, 0xc0280000U); + sng(-0x1.6p+1, 0xc0300000U); + sng(-0x1.7p+1, 0xc0380000U); + sng(-0x1.8p+1, 0xc0400000U); + sng(-0x1.9p+1, 0xc0480000U); + sng(-0x1.ap+1, 0xc0500000U); + sng(-0x1.bp+1, 0xc0580000U); + sng(-0x1.cp+1, 0xc0600000U); + sng(-0x1.dp+1, 0xc0680000U); + sng(-0x1.ep+1, 0xc0700000U); + sng(-0x1.fp+1, 0xc0780000U); + sng(-0x1p+2, 0xc0800000U); + sng(-0x1.1p+2, 0xc0880000U); + sng(-0x1.2p+2, 0xc0900000U); + sng(-0x1.3p+2, 0xc0980000U); + sng(-0x1.4p+2, 0xc0a00000U); + sng(-0x1.5p+2, 0xc0a80000U); + sng(-0x1.6p+2, 0xc0b00000U); + sng(-0x1.7p+2, 0xc0b80000U); + sng(-0x1.8p+2, 0xc0c00000U); + sng(-0x1.9p+2, 0xc0c80000U); + sng(-0x1.ap+2, 0xc0d00000U); + sng(-0x1.bp+2, 0xc0d80000U); + sng(-0x1.cp+2, 0xc0e00000U); + sng(-0x1.dp+2, 0xc0e80000U); + sng(-0x1.ep+2, 0xc0f00000U); + sng(-0x1.fp+2, 0xc0f80000U); + sng(-0x1p+3, 0xc1000000U); + sng(-0x1.1p+3, 0xc1080000U); + sng(-0x1.2p+3, 0xc1100000U); + sng(-0x1.3p+3, 0xc1180000U); + sng(-0x1.4p+3, 0xc1200000U); + sng(-0x1.5p+3, 0xc1280000U); + sng(-0x1.6p+3, 0xc1300000U); + sng(-0x1.7p+3, 0xc1380000U); + sng(-0x1.8p+3, 0xc1400000U); + sng(-0x1.9p+3, 0xc1480000U); + sng(-0x1.ap+3, 0xc1500000U); + sng(-0x1.bp+3, 0xc1580000U); + sng(-0x1.cp+3, 0xc1600000U); + sng(-0x1.dp+3, 0xc1680000U); + sng(-0x1.ep+3, 0xc1700000U); + sng(-0x1.fp+3, 0xc1780000U); + sng(-0x1p+4, 0xc1800000U); + sng(-0x1.1p+4, 0xc1880000U); + sng(-0x1.2p+4, 0xc1900000U); + sng(-0x1.3p+4, 0xc1980000U); + sng(-0x1.4p+4, 0xc1a00000U); + sng(-0x1.5p+4, 0xc1a80000U); + sng(-0x1.6p+4, 0xc1b00000U); + sng(-0x1.7p+4, 0xc1b80000U); + sng(-0x1.8p+4, 0xc1c00000U); + sng(-0x1.9p+4, 0xc1c80000U); + sng(-0x1.ap+4, 0xc1d00000U); + sng(-0x1.bp+4, 0xc1d80000U); + sng(-0x1.cp+4, 0xc1e00000U); + sng(-0x1.dp+4, 0xc1e80000U); + sng(-0x1.ep+4, 0xc1f00000U); + sng(-0x1.fp+4, 0xc1f80000U); +} + + +int main() +{ + testdbl(); + testsng(); + return error; +} -- cgit From 7d5db993033ce049776fa290ae1ebc6051dea0f3 Mon Sep 17 00:00:00 2001 From: Bernhard Schommer Date: Sat, 17 Aug 2019 10:10:42 +0200 Subject: Fix compile for architectures other than AArch64 (#192) Some changes were not correctly propagated to all architectures. --- arm/SelectOpproof.v | 4 ++-- backend/SelectDivproof.v | 4 ++-- powerpc/SelectOpproof.v | 4 ++-- riscV/Asmgenproof1.v | 8 ++++---- riscV/SelectOpproof.v | 4 ++-- x86/SelectOpproof.v | 8 ++++---- 6 files changed, 16 insertions(+), 16 deletions(-) diff --git a/arm/SelectOpproof.v b/arm/SelectOpproof.v index 5d54d94f..70f8f191 100644 --- a/arm/SelectOpproof.v +++ b/arm/SelectOpproof.v @@ -754,7 +754,7 @@ Qed. Theorem eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8). Proof. red; intros until x. unfold cast8unsigned. - rewrite Val.zero_ext_and. apply eval_andimm. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm. omega. Qed. Theorem eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16). @@ -767,7 +767,7 @@ Qed. Theorem eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16). Proof. red; intros until x. unfold cast8unsigned. - rewrite Val.zero_ext_and. apply eval_andimm. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm. omega. Qed. Theorem eval_singleoffloat: unary_constructor_sound singleoffloat Val.singleoffloat. diff --git a/backend/SelectDivproof.v b/backend/SelectDivproof.v index 334bedf6..c57d3652 100644 --- a/backend/SelectDivproof.v +++ b/backend/SelectDivproof.v @@ -835,7 +835,7 @@ Proof. assert (A0: eval_expr ge sp e m le (Eletvar O) (Vlong x)). { constructor; auto. } exploit eval_mullhs. try apply HELPERS. eexact A0. instantiate (1 := Int64.repr M). intros (v1 & A1 & B1). - exploit eval_addl. try apply HELPERS. eexact A1. eexact A0. intros (v2 & A2 & B2). + exploit eval_addl. auto. eexact A1. eexact A0. intros (v2 & A2 & B2). exploit eval_shrluimm. try apply HELPERS. eexact A0. instantiate (1 := Int.repr 63). intros (v3 & A3 & B3). set (a4 := if zlt M Int64.half_modulus then mullhs (Eletvar 0) (Int64.repr M) @@ -844,7 +844,7 @@ Proof. assert (A4: eval_expr ge sp e m le a4 v4). { unfold a4, v4; destruct (zlt M Int64.half_modulus); auto. } exploit eval_shrlimm. try apply HELPERS. eexact A4. instantiate (1 := Int.repr p). intros (v5 & A5 & B5). - exploit eval_addl. try apply HELPERS. eexact A5. eexact A3. intros (v6 & A6 & B6). + exploit eval_addl. auto. eexact A5. eexact A3. intros (v6 & A6 & B6). assert (RANGE: forall x, 0 <= x < 64 -> Int.ltu (Int.repr x) Int64.iwordsize' = true). { intros. unfold Int.ltu. rewrite Int.unsigned_repr. rewrite zlt_true by tauto. auto. assert (64 < Int.max_unsigned) by (compute; auto). omega. } diff --git a/powerpc/SelectOpproof.v b/powerpc/SelectOpproof.v index 1f23f4bd..c3eda068 100644 --- a/powerpc/SelectOpproof.v +++ b/powerpc/SelectOpproof.v @@ -805,7 +805,7 @@ Qed. Theorem eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8). Proof. red; intros. unfold cast8unsigned. - rewrite Val.zero_ext_and. apply eval_andimm; auto. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm; auto. omega. Qed. Theorem eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16). @@ -818,7 +818,7 @@ Qed. Theorem eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16). Proof. red; intros. unfold cast16unsigned. - rewrite Val.zero_ext_and. apply eval_andimm; auto. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm; auto. omega. Qed. Theorem eval_singleoffloat: unary_constructor_sound singleoffloat Val.singleoffloat. diff --git a/riscV/Asmgenproof1.v b/riscV/Asmgenproof1.v index b4d6b831..c20c4e49 100644 --- a/riscV/Asmgenproof1.v +++ b/riscV/Asmgenproof1.v @@ -407,7 +407,7 @@ Lemma transl_cbranch_correct_1: agree ms sp rs -> Mem.extends m m' -> exists rs', exists insn, - exec_straight_opt c rs m' (insn :: k) rs' m' + exec_straight_opt ge fn c rs m' (insn :: k) rs' m' /\ exec_instr ge fn insn rs' m' = eval_branch fn lbl rs' m' (Some b) /\ forall r, r <> PC -> r <> X31 -> rs'#r = rs#r. Proof. @@ -502,7 +502,7 @@ Lemma transl_cbranch_correct_true: agree ms sp rs -> Mem.extends m m' -> exists rs', exists insn, - exec_straight_opt c rs m' (insn :: k) rs' m' + exec_straight_opt ge fn c rs m' (insn :: k) rs' m' /\ exec_instr ge fn insn rs' m' = goto_label fn lbl rs' m' /\ forall r, r <> PC -> r <> X31 -> rs'#r = rs#r. Proof. @@ -1092,7 +1092,7 @@ Lemma indexed_memory_access_correct: forall mk_instr base ofs k rs m, base <> X31 -> exists base' ofs' rs', - exec_straight_opt (indexed_memory_access mk_instr base ofs k) rs m + exec_straight_opt ge fn (indexed_memory_access mk_instr base ofs k) rs m (mk_instr base' ofs' :: k) rs' m /\ Val.offset_ptr rs'#base' (eval_offset ge ofs') = Val.offset_ptr rs#base ofs /\ forall r, r <> PC -> r <> X31 -> rs'#r = rs#r. @@ -1242,7 +1242,7 @@ Lemma transl_memory_access_correct: transl_memory_access mk_instr addr args k = OK c -> eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some v -> exists base ofs rs', - exec_straight_opt c rs m (mk_instr base ofs :: k) rs' m + exec_straight_opt ge fn c rs m (mk_instr base ofs :: k) rs' m /\ Val.offset_ptr rs'#base (eval_offset ge ofs) = v /\ forall r, r <> PC -> r <> X31 -> rs'#r = rs#r. Proof. diff --git a/riscV/SelectOpproof.v b/riscV/SelectOpproof.v index 18bc5dfe..593be1ed 100644 --- a/riscV/SelectOpproof.v +++ b/riscV/SelectOpproof.v @@ -763,7 +763,7 @@ Qed. Theorem eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8). Proof. red; intros until x. unfold cast8unsigned. - rewrite Val.zero_ext_and. apply eval_andimm. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm. omega. Qed. Theorem eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16). @@ -776,7 +776,7 @@ Qed. Theorem eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16). Proof. red; intros until x. unfold cast8unsigned. - rewrite Val.zero_ext_and. apply eval_andimm. compute; auto. + rewrite Val.zero_ext_and. apply eval_andimm. omega. Qed. Theorem eval_intoffloat: diff --git a/x86/SelectOpproof.v b/x86/SelectOpproof.v index a1bb0703..961f602c 100644 --- a/x86/SelectOpproof.v +++ b/x86/SelectOpproof.v @@ -381,9 +381,9 @@ Proof. - TrivialExists. simpl. rewrite Int.and_commut; auto. - TrivialExists. simpl. rewrite Val.and_assoc. rewrite Int.and_commut. auto. - rewrite Val.zero_ext_and. TrivialExists. rewrite Val.and_assoc. - rewrite Int.and_commut. auto. compute; auto. + rewrite Int.and_commut. auto. omega. - rewrite Val.zero_ext_and. TrivialExists. rewrite Val.and_assoc. - rewrite Int.and_commut. auto. compute; auto. + rewrite Int.and_commut. auto. omega. - TrivialExists. Qed. @@ -743,7 +743,7 @@ Proof. red; intros until x. unfold cast8unsigned. destruct (cast8unsigned_match a); intros; InvEval. TrivialExists. subst. rewrite Val.zero_ext_and. rewrite Val.and_assoc. - rewrite Int.and_commut. apply eval_andimm; auto. compute; auto. + rewrite Int.and_commut. apply eval_andimm; auto. omega. TrivialExists. Qed. @@ -759,7 +759,7 @@ Proof. red; intros until x. unfold cast16unsigned. destruct (cast16unsigned_match a); intros; InvEval. TrivialExists. subst. rewrite Val.zero_ext_and. rewrite Val.and_assoc. - rewrite Int.and_commut. apply eval_andimm; auto. compute; auto. + rewrite Int.and_commut. apply eval_andimm; auto. omega. TrivialExists. Qed. -- cgit From 25a39ae6be7a4b65e01d9bb6b1fd94688aa674b0 Mon Sep 17 00:00:00 2001 From: "xavier.leroy" Date: Fri, 23 Aug 2019 08:18:27 +0200 Subject: Offset out of range for ldp/stp instructions These instructions are generated by __builtin_memcpy. --- aarch64/Asmexpand.ml | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/aarch64/Asmexpand.ml b/aarch64/Asmexpand.ml index 71bd0042..ab155e9c 100644 --- a/aarch64/Asmexpand.ml +++ b/aarch64/Asmexpand.ml @@ -146,7 +146,9 @@ let expand_annot_val kind txt targ args res = Temporary registers used: x15 x16 x17 x29 x30. *) let offset_in_range ofs = - let ofs = Z.to_int64 ofs in 0L <= ofs && ofs < 0x1000L + (* The 512 upper bound comes from ldp/stp. Single-register load/store + instructions support bigger offsets. *) + let ofs = Z.to_int64 ofs in 0L <= ofs && ofs < 512L let memcpy_small_arg sz arg tmp = match arg with -- cgit From c243b565ab0744086e10efcfee16768f6c3cf880 Mon Sep 17 00:00:00 2001 From: "xavier.leroy" Date: Sat, 31 Aug 2019 17:00:24 +0200 Subject: AArch64: wrong expected type for arguments of Cmaskl{zero,notzero} The argument is of type Tlong, not Tint. This caused spurious errors in RTLtyping. Also: in AArch64/PrintOp.ml, print Cmaskl{zero,notzero} with "&l" to distinguish them from Cmask{zero,notzero}. --- aarch64/Op.v | 4 ++-- aarch64/PrintOp.ml | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/aarch64/Op.v b/aarch64/Op.v index 34c03c77..a7483d56 100644 --- a/aarch64/Op.v +++ b/aarch64/Op.v @@ -564,8 +564,8 @@ Definition type_of_condition (c: condition) : list typ := | Ccompluimm _ _ => Tlong :: nil | Ccomplshift _ _ _ => Tlong :: Tlong :: nil | Ccomplushift _ _ _ => Tlong :: Tlong :: nil - | Cmasklzero _ => Tint :: nil - | Cmasklnotzero _ => Tint :: nil + | Cmasklzero _ => Tlong :: nil + | Cmasklnotzero _ => Tlong :: nil | Ccompf _ => Tfloat :: Tfloat :: nil | Cnotcompf _ => Tfloat :: Tfloat :: nil | Ccompfzero _ => Tfloat :: nil diff --git a/aarch64/PrintOp.ml b/aarch64/PrintOp.ml index 1780104c..2d45e446 100644 --- a/aarch64/PrintOp.ml +++ b/aarch64/PrintOp.ml @@ -73,9 +73,9 @@ let print_condition reg pp = function | (Ccomplushift(c, s, a), [r1;r2]) -> fprintf pp "%a %slu %a %a" reg r1 (comparison_name c) reg r2 shift (s, a) | (Cmasklzero n, [r1]) -> - fprintf pp "%a & 0x%Lx == 0" reg r1 (camlint64_of_coqint n) + fprintf pp "%a &l 0x%Lx == 0" reg r1 (camlint64_of_coqint n) | (Cmasklnotzero n, [r1]) -> - fprintf pp "%a & 0x%Lx != 0" reg r1 (camlint64_of_coqint n) + fprintf pp "%a &l 0x%Lx != 0" reg r1 (camlint64_of_coqint n) | (Ccompf c, [r1;r2]) -> fprintf pp "%a %sf %a" reg r1 (comparison_name c) reg r2 | (Cnotcompf c, [r1;r2]) -> -- cgit From f3bdf0c70faa9e69359bd06b78570c60a569a7cb Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Wed, 11 Sep 2019 16:16:33 +0200 Subject: Asmgenproof1: useless unfolding in proof scripts causing "omega" to fail "omega" fails in Coq 8.7, but not in 8.8 and later. --- aarch64/Asmgenproof1.v | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/aarch64/Asmgenproof1.v b/aarch64/Asmgenproof1.v index d60ad2bc..663ee50b 100644 --- a/aarch64/Asmgenproof1.v +++ b/aarch64/Asmgenproof1.v @@ -426,7 +426,7 @@ Lemma exec_addimm_aux_32: Proof. intros insn sem SEM ASSOC; intros. unfold addimm_aux. set (nlo := Zzero_ext 12 (Int.unsigned n)). set (nhi := Int.unsigned n - nlo). - assert (E: Int.unsigned n = nhi + nlo) by (unfold nlo, nhi; omega). + assert (E: Int.unsigned n = nhi + nlo) by (unfold nhi; omega). rewrite <- (Int.repr_unsigned n). destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. - econstructor; split. apply exec_straight_one. apply SEM. Simpl. @@ -484,7 +484,7 @@ Lemma exec_addimm_aux_64: Proof. intros insn sem SEM ASSOC; intros. unfold addimm_aux. set (nlo := Zzero_ext 12 (Int64.unsigned n)). set (nhi := Int64.unsigned n - nlo). - assert (E: Int64.unsigned n = nhi + nlo) by (unfold nlo, nhi; omega). + assert (E: Int64.unsigned n = nhi + nlo) by (unfold nhi; omega). rewrite <- (Int64.repr_unsigned n). destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. - econstructor; split. apply exec_straight_one. apply SEM. Simpl. @@ -1833,4 +1833,4 @@ Proof. intros. Simpl. Qed. -End CONSTRUCTORS. +End CONSTRUCTORS. \ No newline at end of file -- cgit From a7c8e4f4ef4a5f0a15283cd3f0999f3fa24e581d Mon Sep 17 00:00:00 2001 From: Bernhard Schommer Date: Thu, 12 Sep 2019 17:03:14 +0200 Subject: Reworked json export. The json export prints formatted json, which takes a lot of additional time, however the result is only consumed by other tools and not meant for human reading. This commit implements several small changes in order to speedup the json export: * Removal of usage of the Format Module * Replacing `fprintf` calls by calls to function that print directly, such as `output_string`, etc. * Replacing list of all instruction names by a set of all instructions --- arm/AsmToJSON.ml | 40 ++++++++++++++++++--------------- backend/Json.ml | 52 +++++++++++++++++++++++++------------------ backend/JsonAST.ml | 12 +++++----- backend/JsonAST.mli | 2 +- powerpc/AsmToJSON.ml | 63 ++++++++++++++++++++++++++-------------------------- 5 files changed, 91 insertions(+), 78 deletions(-) diff --git a/arm/AsmToJSON.ml b/arm/AsmToJSON.ml index 6ba3f1bc..e850fed6 100644 --- a/arm/AsmToJSON.ml +++ b/arm/AsmToJSON.ml @@ -19,21 +19,25 @@ open BinNums open Camlcoq open Json -let mnemonic_names = [ "Padc"; "Padd"; "Padds"; "Pand";"Pannot"; "Pasr"; "Pb"; "Pbc"; "Pbic"; "Pblreg"; - "Pblsymb"; "Pbne"; "Pbreg"; "Pbsymb"; "Pbtbl"; "Pclz"; "Pcmp"; "Pcmn"; "Pconstants"; "Pfcpy_iif"; - "Pfcpy_fii"; "Pfcpy_fi"; "Pfcpy_sf"; "Pflid_lbl"; "Pflis_lbl"; "Pdmb"; "Pdsb"; "Peor"; "Pfabsd"; - "Pfabss"; "Pfaddd"; "Pfadds"; "Pfcmpd"; "Pfcmps"; "Pfcmpzd"; "Pfcmpzs"; - "Pfcpyd"; "Pfcpy_fs"; "Pfcpy_if";"Pfcvtds"; "Pfcvtsd"; "Pfdivd"; "Pfdivs"; "Pfldd"; - "Pflid"; "Pflds"; "Pflid_imm"; "Pflis_imm"; "Pfmuld"; "Pfmuls"; "Pfnegd"; - "Pfnegs"; "Pfsitod"; "Pfsitos"; "Pfsqrt"; "Pfstd"; - "Pfsts"; "Pfsubd"; "Pfsubs"; "Pftosizd"; "Pftosizs"; "Pftouizd"; - "Pftouizs"; "Pfuitod"; "Pfuitos"; "Pinlineasm"; "Pisb"; "Plabel"; "Pldr"; - "Ploadsymbol_lbl"; "Pldr_p"; "Pldrb"; "Pldrb_p"; "Pldrh"; "Pldrh_p"; "Pldrsb"; - "Pldrsh"; "Plsl"; "Plsr"; "Pmla"; "Pmov"; "Pmovite"; "Pfmovite"; - "Pmovt"; "Pmovw"; "Pmul"; "Pmvn"; "Ploadsymbol_imm"; "Pnop"; "Porr"; - "Ppush"; "Prev"; "Prev16"; "Prsb"; "Prsbs"; "Prsc"; "Psbc"; "Psbfx"; "Psdiv"; "Psmull"; - "Pstr"; "Pstr_p"; "Pstrb"; "Pstrb_p"; "Pstrh"; "Pstrh_p"; "Psub"; "Psubs"; "Pudiv"; - "Pumull" ] +module StringSet = Set.Make(String) + +let mnemonic_names = StringSet.of_list + [ "Padc"; "Padd"; "Padds"; "Pand";"Pannot"; "Pasr"; "Pb"; "Pbc"; "Pbic"; + "Pblreg"; "Pblsymb"; "Pbne"; "Pbreg"; "Pbsymb"; "Pbtbl"; "Pclz"; "Pcmp"; + "Pcmn"; "Pconstants"; "Pfcpy_iif"; "Pfcpy_fii"; "Pfcpy_fi"; "Pfcpy_sf"; + "Pflid_lbl"; "Pflis_lbl"; "Pdmb"; "Pdsb"; "Peor"; "Pfabsd"; "Pfabss"; + "Pfaddd"; "Pfadds"; "Pfcmpd"; "Pfcmps"; "Pfcmpzd"; "Pfcmpzs"; "Pfcpyd"; + "Pfcpy_fs"; "Pfcpy_if";"Pfcvtds"; "Pfcvtsd"; "Pfdivd"; "Pfdivs"; "Pfldd"; + "Pflid"; "Pflds"; "Pflid_imm"; "Pflis_imm"; "Pfmuld"; "Pfmuls"; "Pfnegd"; + "Pfnegs"; "Pfsitod"; "Pfsitos"; "Pfsqrt"; "Pfstd"; "Pfsts"; "Pfsubd"; + "Pfsubs"; "Pftosizd"; "Pftosizs"; "Pftouizd"; "Pftouizs"; "Pfuitod"; + "Pfuitos"; "Pinlineasm"; "Pisb"; "Plabel"; "Pldr"; "Ploadsymbol_lbl"; + "Pldr_p"; "Pldrb"; "Pldrb_p"; "Pldrh"; "Pldrh_p"; "Pldrsb"; "Pldrsh"; + "Plsl"; "Plsr"; "Pmla"; "Pmov"; "Pmovite"; "Pfmovite"; "Pmovt"; "Pmovw"; + "Pmul"; "Pmvn"; "Ploadsymbol_imm"; "Pnop"; "Porr"; "Ppush"; "Prev"; + "Prev16"; "Prsb"; "Prsbs"; "Prsc"; "Psbc"; "Psbfx"; "Psdiv"; "Psmull"; + "Pstr"; "Pstr_p"; "Pstrb"; "Pstrb_p"; "Pstrh"; "Pstrh_p"; "Psub"; "Psubs"; + "Pudiv";"Pumull" ] type instruction_arg = | ALabel of positive @@ -143,7 +147,7 @@ let pp_instructions pp ic = | _ -> true) ic in let instruction pp n args = - assert (List.mem n mnemonic_names); + assert (StringSet.mem n mnemonic_names); pp_jobject_start pp; pp_jmember ~first:true pp "Instruction Name" pp_jstring n; pp_jmember pp "Args" (pp_jarray pp_arg) args; @@ -313,8 +317,8 @@ let print_if prog sourcename = | Some f -> let f = Filename.concat !sdump_folder f in let oc = open_out_bin f in - JsonAST.pp_ast (Format.formatter_of_out_channel oc) pp_instructions prog sourcename; + JsonAST.pp_ast oc pp_instructions prog sourcename; close_out oc let pp_mnemonics pp = - JsonAST.pp_mnemonics pp mnemonic_names + JsonAST.pp_mnemonics pp (StringSet.elements mnemonic_names) diff --git a/backend/Json.ml b/backend/Json.ml index b8f66c08..bd4d6ff9 100644 --- a/backend/Json.ml +++ b/backend/Json.ml @@ -10,7 +10,6 @@ (* *) (* *********************************************************************) -open Format open Camlcoq @@ -18,16 +17,21 @@ open Camlcoq (* Print a string as json string *) let pp_jstring oc s = - fprintf oc "\"%s\"" s + output_string oc "\""; + output_string oc s; + output_string oc "\"" (* Print a bool as json bool *) -let pp_jbool oc = fprintf oc "%B" +let pp_jbool oc b = output_string oc (string_of_bool b) (* Print an int as json int *) -let pp_jint oc = fprintf oc "%d" +let pp_jint oc i = output_string oc (string_of_int i) (* Print an int32 as json int *) -let pp_jint32 oc = fprintf oc "%ld" +let pp_jint32 oc i = output_string oc (Int32.to_string i) + +(* Print an int64 as json int *) +let pp_jint64 oc i = output_string oc (Int64.to_string i) (* Print optional value *) let pp_jopt pp_elem oc = function @@ -36,15 +40,19 @@ let pp_jopt pp_elem oc = function (* Print opening and closing curly braces for json dictionaries *) let pp_jobject_start pp = - fprintf pp "@[{" + output_string pp "\n{" let pp_jobject_end pp = - fprintf pp "@;<0 -1>}@]" + output_string pp "}" (* Print a member of a json dictionary *) let pp_jmember ?(first=false) pp name pp_mem mem = - let sep = if first then "" else "," in - fprintf pp "%s@ \"%s\": %a" sep name pp_mem mem + if not first then output_string pp ","; + output_string pp " "; + pp_jstring pp name; + output_string pp " :"; + pp_mem pp mem; + output_string pp "\n" (* Print singleton object *) let pp_jsingle_object pp name pp_mem mem = @@ -54,29 +62,31 @@ let pp_jsingle_object pp name pp_mem mem = (* Print a list as json array *) let pp_jarray elem pp l = - match l with - | [] -> fprintf pp "[]"; + let pp_sep () = output_string pp ", " in + output_string pp "["; + begin match l with + | [] -> () | hd::tail -> - fprintf pp "@[["; - fprintf pp "%a" elem hd; - List.iter (fun l -> fprintf pp ",@ %a" elem l) tail; - fprintf pp "@;<0 -1>]@]" + elem pp hd; + List.iter (fun l -> pp_sep (); elem pp l) tail; + end; + output_string pp "]" (* Helper functions for printing coq integer and floats *) let pp_int pp i = - fprintf pp "%ld" (camlint_of_coqint i) + pp_jint32 pp (camlint_of_coqint i) let pp_int64 pp i = - fprintf pp "%Ld" (camlint64_of_coqint i) + pp_jint64 pp (camlint64_of_coqint i) let pp_float32 pp f = - fprintf pp "%ld" (camlint_of_coqint (Floats.Float32.to_bits f)) + pp_jint32 pp (camlint_of_coqint (Floats.Float32.to_bits f)) let pp_float64 pp f = - fprintf pp "%Ld" (camlint64_of_coqint (Floats.Float.to_bits f)) + pp_jint64 pp (camlint64_of_coqint (Floats.Float.to_bits f)) let pp_z pp z = - fprintf pp "%s" (Z.to_string z) + output_string pp (Z.to_string z) (* Helper functions for printing assembler constructs *) let pp_atom pp a = @@ -106,4 +116,4 @@ let reset_id () = let pp_id_const pp () = let i = next_id () in - pp_jsingle_object pp "Integer" (fun pp i -> fprintf pp "%d" i) i + pp_jsingle_object pp "Integer" pp_jint i diff --git a/backend/JsonAST.ml b/backend/JsonAST.ml index 4e57106f..8905e252 100644 --- a/backend/JsonAST.ml +++ b/backend/JsonAST.ml @@ -15,7 +15,6 @@ open Asm open AST open C2C open Json -open Format open Sections @@ -54,8 +53,8 @@ let pp_section pp sec = | Section_ais_annotation -> () (* There should be no info in the debug sections *) let pp_int_opt pp = function - | None -> fprintf pp "0" - | Some i -> fprintf pp "%d" i + | None -> output_string pp "0" + | Some i -> pp_jint pp i let pp_fundef pp_inst pp (name,fn) = let alignment = atom_alignof name @@ -119,9 +118,8 @@ let pp_program pp pp_inst prog = pp_jobject_end pp let pp_mnemonics pp mnemonic_names = - let mnemonic_names = List.sort (String.compare) mnemonic_names in - let new_line pp () = pp_print_string pp "\n" in - pp_print_list ~pp_sep:new_line pp_print_string pp mnemonic_names + let new_line pp () = Format.pp_print_string pp "\n" in + Format.pp_print_list ~pp_sep:new_line Format.pp_print_string pp mnemonic_names let jdump_magic_number = "CompCertJDUMPRelease: " ^ Version.version @@ -153,4 +151,4 @@ let pp_ast pp pp_inst ast sourcename = pp_jmember pp "Compilation Unit" pp_jstring sourcename; pp_jmember pp "Asm Ast" (fun pp prog -> pp_program pp pp_inst prog) ast; pp_jobject_end pp; - Format.pp_print_flush pp () + flush pp diff --git a/backend/JsonAST.mli b/backend/JsonAST.mli index 7afdce51..c32439e4 100644 --- a/backend/JsonAST.mli +++ b/backend/JsonAST.mli @@ -13,4 +13,4 @@ val pp_mnemonics : Format.formatter -> string list -> unit -val pp_ast : Format.formatter -> (Format.formatter -> Asm.code -> unit) -> (Asm.coq_function AST.fundef, 'a) AST.program -> string -> unit +val pp_ast : out_channel -> (out_channel -> Asm.code -> unit) -> (Asm.coq_function AST.fundef, 'a) AST.program -> string -> unit diff --git a/powerpc/AsmToJSON.ml b/powerpc/AsmToJSON.ml index 99c51e43..f4d4285a 100644 --- a/powerpc/AsmToJSON.ml +++ b/powerpc/AsmToJSON.ml @@ -17,12 +17,10 @@ open AST open BinNums open Camlcoq open Json -open Format open JsonAST let pp_reg pp t n = - let s = sprintf "%s%s" t n in - pp_jsingle_object pp "Register" pp_jstring s + pp_jsingle_object pp "Register" pp_jstring (t ^ n) let pp_ireg pp reg = pp_reg pp "r" (TargetPrinter.int_reg_name reg) @@ -31,8 +29,8 @@ let pp_freg pp reg = pp_reg pp "f" (TargetPrinter.float_reg_name reg) let preg_annot = function - | IR r -> sprintf "r%s" (TargetPrinter.int_reg_name r) - | FR r -> sprintf "f%s" (TargetPrinter.float_reg_name r) + | IR r -> "r" ^ (TargetPrinter.int_reg_name r) + | FR r -> "f" ^ (TargetPrinter.float_reg_name r) | _ -> assert false let pp_constant pp c = @@ -86,28 +84,31 @@ let pp_arg pp = function | Atom a -> pp_atom_constant pp a | String s -> pp_jsingle_object pp "String" pp_jstring s -let mnemonic_names =["Padd"; "Paddc"; "Padde"; "Paddi"; "Paddic"; "Paddis"; "Paddze"; "Pand_"; - "Pandc"; "Pandi_"; "Pandis_"; "Pannot"; "Pb"; "Pbctr"; "Pbctrl"; "Pbdnz"; - "Pbf"; "Pbl"; "Pblr"; "Pbs"; "Pbt"; "Pbtbl"; "Pcmpb"; "Pcmpd"; "Pcmpdi"; - "Pcmpld"; "Pcmpldi"; "Pcmplw"; "Pcmplwi"; "Pcmpw"; "Pcmpwi"; "Pcntlzd"; - "Pcntlzw"; "Pcreqv"; "Pcror"; "Pcrxor"; "Pdcbf"; "Pdcbi"; "Pdcbt"; - "Pdcbtls"; "Pdcbtst"; "Pdcbz"; "Pdivd"; "Pdivdu"; "Pdivw"; "Pdivwu"; - "Peieio"; "Peqv"; "Pextsb"; "Pextsh"; "Pextsw"; "Pfabs"; "Pfadd"; "Pfadds"; - "Pfcfid"; "Pfcmpu"; "Pfctidz"; "Pfctiw"; "Pfctiwz"; "Pfdiv"; "Pfdivs"; - "Pfmadd"; "Pfmr"; "Pfmsub"; "Pfmul"; "Pfmuls"; "Pfneg"; "Pfnmadd"; - "Pfnmsub"; "Pfres"; "Pfrsp"; "Pfrsqrte"; "Pfsel"; "Pfsqrt"; "Pfsub"; - "Pfsubs"; "Picbi"; "Picbtls"; "Pinlineasm"; "Pisel"; "Pisync"; "Plabel"; - "Plbz"; "Plbzx"; "Pld"; "Pldbrx"; "Pldi"; "Pldx"; "Plfd"; "Plfdx"; "Plfi"; "Plfis"; - "Plfs"; "Plfsx"; "Plha"; "Plhax"; "Plhbrx"; "Plhz"; "Plhzx"; "Plwarx"; - "Plwbrx"; "Plwsync"; "Plwz"; "Plwzu"; "Plwzx"; "Pmbar"; "Pmfcr"; "Pmflr"; - "Pmfspr"; "Pmr"; "Pmtctr"; "Pmtlr"; "Pmtspr"; "Pmulhd"; "Pmulhdu"; "Pmulhw"; - "Pmulhwu"; "Pmulld"; "Pmulli"; "Pmullw"; "Pnand"; "Pnor"; "Por"; "Porc"; - "Pori"; "Poris"; "Prldicl"; "Prldimi"; "Prldinm"; "Prlwimi"; "Prlwinm"; - "Psld"; "Pslw"; "Psrad"; "Psradi"; "Psraw"; "Psrawi"; "Psrd"; "Psrw"; - "Pstb"; "Pstbx"; "Pstd"; "Pstdbrx"; "Pstdu"; "Pstdx"; "Pstfd"; "Pstfdu"; "Pstfdx"; - "Pstfs"; "Pstfsx"; "Psth"; "Psthbrx"; "Psthx"; "Pstw"; "Pstwbrx"; "Pstwcx_"; - "Pstwu"; "Pstwux"; "Pstwx"; "Psubfc"; "Psubfe"; "Psubfic"; "Psubfze"; - "Psync"; "Ptrap"; "Pxor"; "Pxori"; "Pxoris"] +module StringSet = Set.Make(String) + +let mnemonic_names = StringSet.of_list + ["Padd"; "Paddc"; "Padde"; "Paddi"; "Paddic"; "Paddis"; "Paddze"; "Pand_"; + "Pandc"; "Pandi_"; "Pandis_"; "Pannot"; "Pb"; "Pbctr"; "Pbctrl"; "Pbdnz"; + "Pbf"; "Pbl"; "Pblr"; "Pbs"; "Pbt"; "Pbtbl"; "Pcmpb"; "Pcmpd"; "Pcmpdi"; + "Pcmpld"; "Pcmpldi"; "Pcmplw"; "Pcmplwi"; "Pcmpw"; "Pcmpwi"; "Pcntlzd"; + "Pcntlzw"; "Pcreqv"; "Pcror"; "Pcrxor"; "Pdcbf"; "Pdcbi"; "Pdcbt"; + "Pdcbtls"; "Pdcbtst"; "Pdcbz"; "Pdivd"; "Pdivdu"; "Pdivw"; "Pdivwu"; + "Peieio"; "Peqv"; "Pextsb"; "Pextsh"; "Pextsw"; "Pfabs"; "Pfadd"; "Pfadds"; + "Pfcfid"; "Pfcmpu"; "Pfctidz"; "Pfctiw"; "Pfctiwz"; "Pfdiv"; "Pfdivs"; + "Pfmadd"; "Pfmr"; "Pfmsub"; "Pfmul"; "Pfmuls"; "Pfneg"; "Pfnmadd"; + "Pfnmsub"; "Pfres"; "Pfrsp"; "Pfrsqrte"; "Pfsel"; "Pfsqrt"; "Pfsub"; + "Pfsubs"; "Picbi"; "Picbtls"; "Pinlineasm"; "Pisel"; "Pisync"; "Plabel"; + "Plbz"; "Plbzx"; "Pld"; "Pldbrx"; "Pldi"; "Pldx"; "Plfd"; "Plfdx"; "Plfi"; + "Plfis"; "Plfs"; "Plfsx"; "Plha"; "Plhax"; "Plhbrx"; "Plhz"; "Plhzx"; + "Plwarx"; "Plwbrx"; "Plwsync"; "Plwz"; "Plwzu"; "Plwzx"; "Pmbar"; "Pmfcr"; + "Pmflr"; "Pmfspr"; "Pmr"; "Pmtctr"; "Pmtlr"; "Pmtspr"; "Pmulhd"; "Pmulhdu"; + "Pmulhw"; "Pmulhwu"; "Pmulld"; "Pmulli"; "Pmullw"; "Pnand"; "Pnor"; "Por"; + "Porc"; "Pori"; "Poris"; "Prldicl"; "Prldimi"; "Prldinm"; "Prlwimi"; + "Prlwinm"; "Psld"; "Pslw"; "Psrad"; "Psradi"; "Psraw"; "Psrawi"; "Psrd"; + "Psrw"; "Pstb"; "Pstbx"; "Pstd"; "Pstdbrx"; "Pstdu"; "Pstdx"; "Pstfd"; + "Pstfdu"; "Pstfdx"; "Pstfs"; "Pstfsx"; "Psth"; "Psthbrx"; "Psthx"; "Pstw"; + "Pstwbrx"; "Pstwcx_"; "Pstwu"; "Pstwux"; "Pstwx"; "Psubfc"; "Psubfe"; + "Psubfic"; "Psubfze"; "Psync"; "Ptrap"; "Pxor"; "Pxori"; "Pxoris"] let pp_instructions pp ic = let ic = List.filter (fun s -> match s with @@ -126,7 +127,7 @@ let pp_instructions pp ic = | Pcfi_rel_offset _ -> false | _ -> true) ic in let instruction pp n args = - assert (List.mem n mnemonic_names); + assert (StringSet.mem n mnemonic_names); pp_jobject_start pp; pp_jmember ~first:true pp "Instruction Name" pp_jstring n; pp_jmember pp "Args" (pp_jarray pp_arg) args; @@ -251,7 +252,7 @@ let pp_instructions pp ic = | Plhbrx (ir1,ir2,ir3) -> instruction pp "Plhbrx" [Ireg ir1; Ireg ir2; Ireg ir3] | Plhz (ir1,c,ir2) -> instruction pp "Plhz" [Ireg ir1; Constant c; Ireg ir2] | Plhzx (ir1,ir2,ir3) -> instruction pp "Plhzx" [Ireg ir1; Ireg ir2; Ireg ir3] - | Pldi (ir,c) -> instruction pp "Pldi" [Ireg ir; Long c] (* FIXME Cint is too small, we need Clong *) + | Pldi (ir,c) -> instruction pp "Pldi" [Ireg ir; Long c] | Plmake _ (* Should not occur *) | Pllo _ (* Should not occur *) | Plhi _ -> assert false (* Should not occur *) @@ -385,8 +386,8 @@ let print_if prog sourcename = | Some f -> let f = Filename.concat !sdump_folder f in let oc = open_out_bin f in - pp_ast (formatter_of_out_channel oc) pp_instructions prog sourcename; + pp_ast oc pp_instructions prog sourcename; close_out oc let pp_mnemonics pp = - pp_mnemonics pp mnemonic_names + pp_mnemonics pp (StringSet.elements mnemonic_names) -- cgit From 3d25d06ec58f0527b6f0eee7e0df19c18f7133ed Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 14 Sep 2019 19:37:28 +0200 Subject: clightgen -dclight: print function parameters correctly The Clight output of clightgen is Clight version 2, after SimplLocals conversion, where function parameters are temporary variables, not variables. This commit makes sure the function parameters are printed as temporary variables and not as variables. In passing, it generalizes the Clight pretty-printer so that it can print both Clight version 1 and Clight version 2. Closes: #314 --- cfrontend/PrintClight.ml | 41 ++++++++++++++++++++++++++++++----------- cfrontend/PrintCsyntax.ml | 8 ++++---- exportclight/Clightgen.ml | 2 +- 3 files changed, 35 insertions(+), 16 deletions(-) diff --git a/cfrontend/PrintClight.ml b/cfrontend/PrintClight.ml index ca378c11..e63067a9 100644 --- a/cfrontend/PrintClight.ml +++ b/cfrontend/PrintClight.ml @@ -236,10 +236,20 @@ and print_stmt_for p s = | _ -> fprintf p "({ %a })" print_stmt s -let print_function p id f = +(* There are two versions of Clight, Clight1 and Clight2, that differ + only in the meaning of function parameters: + - in Clight1, function parameters are variables + - in Clight2, function parameters are temporaries. +*) + +type clight_version = Clight1 | Clight2 + +let name_param = function Clight1 -> extern_atom | Clight2 -> temp_name + +let print_function ver p id f = fprintf p "%s@ " - (name_cdecl (name_function_parameters (extern_atom id) - f.fn_params f.fn_callconv) + (name_cdecl (name_function_parameters (name_param ver) + (extern_atom id) f.fn_params f.fn_callconv) f.fn_return); fprintf p "@[{@ "; List.iter @@ -253,12 +263,12 @@ let print_function p id f = print_stmt p f.fn_body; fprintf p "@;<0 -2>}@]@ @ " -let print_fundef p id fd = +let print_fundef ver p id fd = match fd with | Ctypes.External(_, _, _, _) -> () | Internal f -> - print_function p id f + print_function ver p id f let print_fundecl p id fd = match fd with @@ -271,9 +281,9 @@ let print_fundecl p id fd = fprintf p "%s;@ " (name_cdecl (extern_atom id) (Clight.type_of_function f)) -let print_globdef p (id, gd) = +let print_globdef var p (id, gd) = match gd with - | AST.Gfun f -> print_fundef p id f + | AST.Gfun f -> print_fundef var p id f | AST.Gvar v -> print_globvar p id v (* from PrintCsyntax *) let print_globdecl p (id, gd) = @@ -281,20 +291,29 @@ let print_globdecl p (id, gd) = | AST.Gfun f -> print_fundecl p id f | AST.Gvar v -> () -let print_program p prog = +let print_program ver p prog = fprintf p "@["; List.iter (declare_composite p) prog.prog_types; List.iter (define_composite p) prog.prog_types; List.iter (print_globdecl p) prog.prog_defs; - List.iter (print_globdef p) prog.prog_defs; + List.iter (print_globdef ver p) prog.prog_defs; fprintf p "@]@." let destination : string option ref = ref None -let print_if prog = +let print_if_gen ver prog = match !destination with | None -> () | Some f -> let oc = open_out f in - print_program (formatter_of_out_channel oc) prog; + print_program ver (formatter_of_out_channel oc) prog; close_out oc + +(* print_if is called from driver/Compiler.v between the SimplExpr + and SimplLocals passes. It receives Clight1 syntax. *) +let print_if prog = print_if_gen Clight1 prog + +(* print_if_2 is called from clightgen/Clightgen.ml, after the + SimplLocals pass. It receives Clight2 syntax. *) +let print_if_2 prog = print_if_gen Clight2 prog + diff --git a/cfrontend/PrintCsyntax.ml b/cfrontend/PrintCsyntax.ml index 3a44796c..1c9729c5 100644 --- a/cfrontend/PrintCsyntax.ml +++ b/cfrontend/PrintCsyntax.ml @@ -391,7 +391,7 @@ and print_stmt_for p s = | _ -> fprintf p "({ %a })" print_stmt s -let name_function_parameters fun_name params cconv = +let name_function_parameters name_param fun_name params cconv = let b = Buffer.create 20 in Buffer.add_string b fun_name; Buffer.add_char b '('; @@ -404,7 +404,7 @@ let name_function_parameters fun_name params cconv = if cconv.cc_vararg then Buffer.add_string b ",..." | (id, ty) :: rem -> if not first then Buffer.add_string b ", "; - Buffer.add_string b (name_cdecl (extern_atom id) ty); + Buffer.add_string b (name_cdecl (name_param id) ty); add_params false rem in add_params true params end; @@ -413,8 +413,8 @@ let name_function_parameters fun_name params cconv = let print_function p id f = fprintf p "%s@ " - (name_cdecl (name_function_parameters (extern_atom id) - f.fn_params f.fn_callconv) + (name_cdecl (name_function_parameters extern_atom + (extern_atom id) f.fn_params f.fn_callconv) f.fn_return); fprintf p "@[{@ "; List.iter diff --git a/exportclight/Clightgen.ml b/exportclight/Clightgen.ml index 4209975a..f7279a5e 100644 --- a/exportclight/Clightgen.ml +++ b/exportclight/Clightgen.ml @@ -45,7 +45,7 @@ let compile_c_ast sourcename csyntax ofile = | Errors.Error msg -> fatal_error loc "%a" print_error msg in (* Dump Clight in C syntax if requested *) - PrintClight.print_if clight; + PrintClight.print_if_2 clight; (* Print Clight in Coq syntax *) let oc = open_out ofile in ExportClight.print_program (Format.formatter_of_out_channel oc) -- cgit From 8ac255f207b6864fa22552a48f84ffcf23f747b4 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sat, 14 Sep 2019 19:42:25 +0200 Subject: -dclight output: use nicer names for temporary variables The temporary variables introduced by SimplLocals reuse the same integer identifiers as the local variables they come from. This commit ensures that these variables are printed as "$var", where "var" is the original variable name, instead of "$NNN" as before. The "$NNN" form is retained for temporary variables that do not correspond to a source-level local variable, such as the temporary variables introduced by SimplExpr. This commit should make no difference for "ccomp -dclight", because the Clight that is printed is the Clight version 1 produced by SimplExpr, where every temporary is fresh and does not correspond to a source-level local variable. This commit does change the output of "clightgen -dclight", because the Clight that is printed is the Clight version 2 produced by SimplLocals. The printed Clight is much more legible thanks to the more meaningful temporary variable names. --- cfrontend/PrintClight.ml | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/cfrontend/PrintClight.ml b/cfrontend/PrintClight.ml index e63067a9..0e735d2d 100644 --- a/cfrontend/PrintClight.ml +++ b/cfrontend/PrintClight.ml @@ -23,9 +23,18 @@ open Cop open PrintCsyntax open Clight -(* Naming temporaries *) +(* Naming temporaries. + Some temporaries are obtained by lifting variables in SimplLocals. + For these we use a meaningful name "$var", as found in the table of + atoms. Other temporaries are generated during SimplExpr, and are + not in the table of atoms. We print them as "$NNN" (a unique + integer). *) -let temp_name (id: AST.ident) = "$" ^ Z.to_string (Z.Zpos id) +let temp_name (id: AST.ident) = + try + "$" ^ Hashtbl.find string_of_atom id + with Not_found -> + Printf.sprintf "$%d" (P.to_int id) (* Declarator (identifier + type) -- reuse from PrintCsyntax *) -- cgit From 1b2e0534cc60ea45b17e5e1c70c8a28be682c266 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Mon, 16 Sep 2019 15:50:31 +0200 Subject: Updates in preparation for release 3.6 --- Changelog | 62 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ VERSION | 2 +- 2 files changed, 63 insertions(+), 1 deletion(-) diff --git a/Changelog b/Changelog index e5e701d0..935f77f2 100644 --- a/Changelog +++ b/Changelog @@ -1,3 +1,65 @@ +Release 3.6, 2019-09-17 +======================= + +New features and optimizations: +- New port targeting the AArch64 architecture: ARMv8 in 64-bit mode. +- New optimization: if-conversion. Some `if`/`else` statements + and `a ? b : c` conditional expressions are compiled to branchless + conditional move instructions, when supported by the target processor +- New optimization flag: `-Obranchless`, to favor the generation of + branchless instruction sequences, even if probably slower than branches. +- Built-in functions can now be given a formal semantics within + CompCert, instead of being treated as I/O interactions. + Currently, `__builtin_fsqrt` and `__builtin_bswap*` have semantics. +- Extend constant propagation and CSE optimizations to built-in + functions that have known semantics. +- New "polymorphic" built-in function: `__builtin_sel(a,b,c)`. + Similar to `a ? b : c` but `b` and `c` are always evaluated, + and a branchless conditional move instruction is produced if possible. +- x86 64 bits: faster, branchless instruction sequences are produced + for conversions between `double` and `unsigned int`. +- `__builtin_bswap64` is now available for all platforms. + +Usability and diagnostics: +- Improved the DWARF debug information generated in -g mode. +- Added options -fcommon and -fno-common to control the generation + of "common" declarations for uninitialized global. +- Check for reserved keywords `_Complex` and `_Imaginary`. +- Reject function declarations with multiple `void` parameters. +- Define macros `__COMPCERT_MAJOR__`, `__COMPCERT_MINOR__`, and + `__COMPCERT_VERSION__` with CompCert's version number. (#284) +- Prepend `$(DESTDIR)` to the installation target. (#169) +- Extended inline asm: print register names according to the + types of the corresponding arguments (e.g. for x86_64, + `%eax` if int and `%rax` if long). + +Bug fixing: +- Introduce distinct scopes for iteration and selection statements, + as required by ISO C99. +- Handle dependencies in sequences of declarations + (e.g. `int * x, sz = sizeof(x);`). (#267) +- Corrected the check for overflow in integer literals. +- On x86, __builtin_fma was producing wrong code in some cases. +- `float` arguments to `__builtin_annot` and `__builtin_ais_annot` + were uselessly promoted to type `double`. + +Coq formalization and development: +- Improved C parser based on Menhir version 20190626: + fewer run-time checks, faster validation, no axioms. (#276) +- Compatibility with Coq versions 8.9.1 and 8.10.0. +- Compatibility with OCaml versions 4.08.0 and 4.08.1. +- Updated to Flocq version 3.1. +- Revised the construction of NaN payloads in processor descriptions + so as to accommodate FMA. +- Removed some definitions and lemmas from lib/Coqlib.v, using Coq's + standard library instead. + +The clightgen tool: +- Fix normalization of Clight `switch` statements. (#285) +- Add more tracing options: `-dprepro`, `-dall`. (#298) +- Fix the output of `-dclight`. (#314) + + Release 3.5, 2019-02-27 ======================= diff --git a/VERSION b/VERSION index d4563a62..92686b06 100644 --- a/VERSION +++ b/VERSION @@ -1,3 +1,3 @@ -version=3.5 +version=3.6 buildnr= tag= -- cgit From db96b0e2b156cfa527493f5890cd805f8aa4543a Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Sun, 25 Aug 2019 19:22:03 +0200 Subject: Revise the "bench" entries of the test suite Initially, the "bench" entries of the test suite used a "xtime" utility developed in-house and not publically available. This commit adds a version of "xtime" written in OCaml (tools/xtime.ml) and updates the "bench" entries of the test/*/Makefile to use it. --- test/c/Makefile | 7 ++-- test/compression/Makefile | 5 +-- test/raytracer/Makefile | 4 +- test/spass/Makefile | 5 +-- tools/xtime.ml | 101 ++++++++++++++++++++++++++++++++++++++++++++++ 5 files changed, 110 insertions(+), 12 deletions(-) create mode 100644 tools/xtime.ml diff --git a/test/c/Makefile b/test/c/Makefile index 51a8f105..4b521bb5 100644 --- a/test/c/Makefile +++ b/test/c/Makefile @@ -7,8 +7,7 @@ CFLAGS=-O1 -Wall LIBS=$(LIBMATH) -TIME=xtime -o /dev/null -mintime 2.0 # Xavier's hack -#TIME=time >/dev/null # Otherwise +TIME=ocaml unix.cma ../../tools/xtime.ml -o /dev/null -mintime 2.0 -minruns 4 PROGS=fib integr qsort fft fftsp fftw sha1 sha3 aes almabench \ lists binarytrees fannkuch knucleotide mandelbrot nbody \ @@ -48,12 +47,12 @@ test_gcc: bench_gcc: @for i in $(PROGS); do \ - echo -n "$$i: "; $(TIME) ./$$i.gcc; \ + $(TIME) -name $$i -- ./$$i.gcc; \ done bench: @for i in $(PROGS); do \ - echo -n "$$i: "; $(TIME) ./$$i.compcert; \ + $(TIME) -name $$i -- ./$$i.compcert; \ done clean: diff --git a/test/compression/Makefile b/test/compression/Makefile index 2e14e646..e8f3cf4d 100644 --- a/test/compression/Makefile +++ b/test/compression/Makefile @@ -3,7 +3,7 @@ include ../../Makefile.config CC=../../ccomp CFLAGS=$(CCOMPOPTS) -U__GNUC__ -stdlib ../../runtime -dclight -dasm LIBS= -TIME=xtime -o /dev/null -mintime 1.0 +TIME=ocaml unix.cma ../../tools/xtime.ml -mintime 2.0 -minruns 2 EXE=arcode lzw lzss @@ -48,8 +48,7 @@ test: bench: @rm -f $(TESTCOMPR) @for i in $(EXE); do \ - echo -n "$$i: "; \ - $(TIME) sh -c "./$$i -c -i $(TESTFILE) -o $(TESTCOMPR) && ./$$i -d -i $(TESTCOMPR) -o /dev/null"; \ + $(TIME) -name $$i -- sh -c "./$$i -c -i $(TESTFILE) -o $(TESTCOMPR) && ./$$i -d -i $(TESTCOMPR) -o /dev/null"; \ done @rm -f $(TESTCOMPR) diff --git a/test/raytracer/Makefile b/test/raytracer/Makefile index 8f6541a1..24461bd1 100644 --- a/test/raytracer/Makefile +++ b/test/raytracer/Makefile @@ -3,7 +3,7 @@ include ../../Makefile.config CC=../../ccomp CFLAGS=$(CCOMPOPTS) -stdlib ../../runtime -dparse -dclight -dasm -fstruct-return LIBS=$(LIBMATH) -TIME=xtime +TIME=ocaml unix.cma ../../tools/xtime.ml -mintime 2.0 -minruns 4 OBJS=memory.o gmllexer.o gmlparser.o eval.o \ arrays.o vector.o matrix.o object.o intersect.o surface.o light.o \ @@ -30,4 +30,4 @@ test: fi bench: - @echo -n "raytracer: "; $(TIME) sh -c './render < kal.gml' + @$(TIME) -name raytracer -- sh -c './render < kal.gml' diff --git a/test/spass/Makefile b/test/spass/Makefile index 0e89d6d1..d512ea95 100644 --- a/test/spass/Makefile +++ b/test/spass/Makefile @@ -24,11 +24,10 @@ clean: test: $(SIMU) ./spass small_problem.dfg | grep 'Proof found' -TIME=xtime -o /dev/null # Xavier's hack -#TIME=time >/dev/null # Otherwise +TIME=ocaml unix.cma ../../tools/xtime.ml -o /dev/null -mintime 5.0 bench: - @echo -n "spass: "; $(TIME) ./spass problem.dfg + @$(TIME) -name spass -- ./spass problem.dfg depend: gcc -MM $(SRCS) > .depend diff --git a/tools/xtime.ml b/tools/xtime.ml new file mode 100644 index 00000000..fbb25a49 --- /dev/null +++ b/tools/xtime.ml @@ -0,0 +1,101 @@ +(* *********************************************************************) +(* *) +(* 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 GNU General Public License as published by *) +(* the Free Software Foundation, either version 2 of the License, or *) +(* (at your option) any later version. This file is also distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(* Timing the execution of a command, with more options than the + standard Unix "time" utility. *) + +open Printf + +let outfile = ref "" +let errfile = ref "" +let command_name = ref "" +let num_runs = ref 1 +let min_runs = ref 0 +let min_time = ref 0.0 +let print_sys = ref false + +let error fmt = + eprintf "Error: "; kfprintf (fun _ -> exit 2) stderr fmt + +let open_file out dfl = + if out = "" + then dfl + else Unix.(openfile out [O_WRONLY; O_CREAT; O_TRUNC] 0o666) + +let close_file out fd = + if out <> "" then Unix.close fd + +let run1 (cmd, args) = + let fd_out = open_file !outfile Unix.stdout in + let fd_err = open_file !errfile Unix.stderr in + let pid = + Unix.create_process cmd (Array.of_list (cmd :: args)) + Unix.stdin fd_out fd_err in + close_file !outfile fd_out; + close_file !errfile fd_err; + let (_, st) = Unix.waitpid [] pid in + match st with + | Unix.WEXITED 127 -> error "cannot execute '%s'\n" cmd + | Unix.WSIGNALED signo -> error "terminated by signal %d\n" signo + | _ -> () + +let run (cmd, arg) = + let rec repeat n = + run1 (cmd, arg); + if (!min_time > 0.0 && Unix.((times()).tms_cutime) < !min_time) + || (!min_runs > 0 && n < !min_runs) + || n < !num_runs + then repeat (n + 1) + else n in + let n = repeat 1 in + let ts = Unix.times() in + let cmdname = if !command_name <> "" then !command_name else cmd in + if !print_sys then + Printf.printf "%.3f usr + %.3f sys %s\n" + (ts.Unix.tms_cutime /. float n) + (ts.Unix.tms_cstime /. float n) + cmdname + else + Printf.printf "%.3f %s\n" + (ts.Unix.tms_cutime /. float n) + cmdname + +let _ = + let cmd_and_args = ref [] in + Arg.parse [ + "-o", Arg.Set_string outfile, + " Redirect standard output of command to "; + "-e", Arg.Set_string outfile, + " Redirect standard error of command to "; + "-name", Arg.Set_string command_name, + " Name of command to report along with the time"; + "-repeat", Arg.Int (fun n -> num_runs := n), + " Run the command N times"; + "-mintime", Arg.Float (fun f -> min_time := f), + " Repeatedly run the command for a total duration of at least T seconds"; + "-minruns", Arg.Int (fun n -> num_runs := n), + " Run the command at least N times (to be used in conjunction with -mintime)"; + "-sys", Arg.Set print_sys, + " Print system time (spent in the OS) in addition to user time (spent in the command)"; + "--", Arg.Rest (fun s -> cmd_and_args := s :: !cmd_and_args), + " Specify the executable to time, with its arguments" + ] + (fun s -> raise (Arg.Bad (sprintf "Don't know what to do with '%s'" s))) + "Usage: xtime [options] -- [arguments].\n\nOptions are:"; + match List.rev !cmd_and_args with + | [] -> + error "No command to execute\n" + | cmd :: args -> + Unix.handle_unix_error run (cmd, args) -- cgit From e1725209b2b4401adc63ce5238fa5db7c134609c Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Tue, 17 Sep 2019 14:45:59 +0200 Subject: Update for release 3.6 --- doc/index.html | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/doc/index.html b/doc/index.html index edb3accd..3a4cf6ba 100644 --- a/doc/index.html +++ b/doc/index.html @@ -24,7 +24,7 @@ a:active {color : Red; text-decoration : underline; }

The CompCert verified compiler

Commented Coq development

-

Version 3.5, 2019-02-27

+

Version 3.6, 2019-09-17

Introduction

@@ -180,7 +180,8 @@ code. - Recognition of operators
and addressing modes + Recognition of operators
and addressing modes;
+ if-conversion Cminor to CminorSel Selection
SelectOp
-- cgit