phanerozoic/Coq-CompCert · Datasets at AI快站

statement stringlengths 1 2.09k	proof stringlengths 0 22.1k	type stringclasses 25 values	symbolic_name stringlengths 1 49	library stringclasses 14 values	filename stringclasses 212 values	imports listlengths 0 63	deps listlengths 0 64	docstring stringlengths 0 1.82k	source_url stringclasses 1 value	commit stringclasses 1 value
platform_builtin_table : list (string * platform_builtin)	:= nil.	Definition	platform_builtin_table	aarch64	aarch64/Builtins1.v	[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]	[ "platform_builtin", "string" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
platform_builtin_sig (b: platform_builtin) : signature	:= match b with end.	Definition	platform_builtin_sig	aarch64	aarch64/Builtins1.v	[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]	[ "platform_builtin", "signature" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
platform_builtin_sem (b: platform_builtin) : builtin_sem (sig_res (platform_builtin_sig b))	:= match b with end.	Definition	platform_builtin_sem	aarch64	aarch64/Builtins1.v	[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]	[ "builtin_sem", "platform_builtin", "platform_builtin_sig" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
eq_platform_builtin: forall (x y: platform_builtin), {x=y} + {x<>y}.	Proof. intros. destruct x. Defined.	Definition	eq_platform_builtin	aarch64	aarch64/Builtins1.v	[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]	[ "platform_builtin" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
combine_compimm_ne_0 (x: valnum) : option(condition * list valnum)	:= match get x with \| Some(Op (Ocmp c) ys) => Some (c, ys) \| Some(Op (Oxorimm n) ys) => if Int.eq n (Int.zero_ext 12 n) then Some (Ccompimm Cne n, ys) else None \| _ => None end.	Function	combine_compimm_ne_0	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "condition", "eq", "get", "valnum", "zero_ext" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
combine_compimm_eq_0 (x: valnum) : option(condition * list valnum)	:= match get x with \| Some(Op (Ocmp c) ys) => Some (negate_condition c, ys) \| Some(Op (Oxorimm n) ys) => if Int.eq n (Int.zero_ext 12 n) then Some (Ccompimm Ceq n, ys) else None \| _ => None end.	Function	combine_compimm_eq_0	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "condition", "eq", "get", "negate_condition", "valnum", "zero_ext" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_eq_1	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "condition", "get", "valnum" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_compimm_ne_1	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "condition", "get", "negate_condition", "valnum" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 t...	Function	combine_cond	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "combine_compimm_eq_0", "combine_compimm_eq_1", "combine_compimm_ne_0", "combine_compimm_ne_1", "condition", "eq_dec", "one", "valnum", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
combine_cond' (cond: condition) (args: list valnum) : option bool	:= match cond, args with \| (Ccomp c \| Ccompu c \| Ccompl c \| Ccomplu c), x :: y :: nil => combine_comparison c x y \| _, _ => None end.	Definition	combine_cond'	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "combine_comparison", "condition", "valnum" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_addr	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "add", "addressing", "get", "valnum" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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...	Function	combine_op	aarch64	aarch64/CombineOp.v	[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]	[ "add", "and", "combine_cond", "combine_cond'", "eq", "eq_valnum", "get", "one", "operation", "or", "valnum", "xor", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
get_sound: forall v rhs, get v = Some rhs -> rhs_eval_to valu ge sp m rhs (valu v).		Hypothesis	get_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "ge", "get", "rhs", "rhs_eval_to" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.	Lemma	get_op_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "eval_operation", "exploit", "ge", "get", "get_sound", "inv", "map" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
UseGetSound	:= match goal with \| [ H: get _ = Some _ \|- _ ] => let x := fresh "EQ" in (generalize (get_op_sound _ _ _ H); intros x; simpl in x; FuncInv) end.	Ltac	UseGetSound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "FuncInv", "get", "get_op_sound" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. ( of xorimm *) UseGetSound. rewrite <- H. destruct v; simpl; auto. rewrite Int.xor_is_ze...	Lemma	combine_compimm_ne_0_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_ne_0", "eval_condition", "get", "inv", "map", "valid_pointer", "xor_is_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. ( of xorimm *) UseGetSound. rewrite <- H. destruct v; simp...	Lemma	combine_compimm_eq_0_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_eq_0", "eval_condition", "eval_negate_condition", "get", "inv", "map", "valid_pointer", "xor_is_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_eq_1_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_eq_1", "eval_condition", "get", "inv", "map", "one", "valid_pointer" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.	Lemma	combine_compimm_ne_1_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_ne_1", "eval_condition", "eval_negate_condition", "get", "inv", "map", "one", "valid_pointer" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 c...	Theorem	combine_cond_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "combine_compimm_eq_0_sound", "combine_compimm_eq_1_sound", "combine_compimm_ne_0_sound", "combine_compimm_ne_1_sound", "combine_cond", "eval_condition", "get", "map" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
combine_cond'_sound: forall cond args res res', combine_cond' cond args = Some res' -> eval_condition cond (map valu args) m = Some res -> res = res'.	Proof. intros. unfold combine_cond' in *. destruct cond; inv H; destruct args; inv H2; destruct args; inv H1; destruct args; inv H2. apply (combine_comparison_cmp_sound valu c v v0 res res'); auto. apply (combine_comparison_cmpu_sound valu m c v v0 res res'); auto. apply (combine_comparison_cmpl_sound valu c...	Theorem	combine_cond'_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "combine_comparison_cmp_sound", "combine_comparison_cmpl_sound", "combine_comparison_cmplu_sound", "combine_comparison_cmpu_sound", "combine_cond'", "eval_condition", "inv", "map", "res" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_addr_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "addl_assoc", "combine_addr", "eval_addressing", "ge", "get", "map" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
combine_op_sound: forall op args op' args' r, combine_op get op args = Some(op', args') -> eval_operation ge sp op (map valu args) m = Some r -> exists r', eval_operation ge sp op' (map valu args') m = Some r' /\ Val.lessdef r r'.	Proof. intros. functional inversion H; subst. (* addimm - addimm ) - UseGetSound. exists r; split; auto. rewrite <- H0. simpl. rewrite <- H1. rewrite Val.add_assoc. auto. ( andimm - andimm *) - UseGetSound; simpl. generalize (Int.eq_spec p m0); rewrite H8; intros. exists r; split; auto. rewrite ...	Theorem	combine_op_sound	aarch64	aarch64/CombineOpproof.v	[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]	[ "UseGetSound", "Vfalse", "Vtrue", "add_assoc", "addl_assoc", "and_assoc", "andl_assoc", "combine_cond'_sound", "combine_cond_sound", "combine_op", "decEq", "eq_spec", "eval_condition", "eval_operation", "fold", "ge", "get", "inv", "lessdef", "map", "or_assoc", "orl_assoc", ...		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
GENV: genv_match bc ge.		Hypothesis	GENV	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "ge", "genv_match" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
STACK: bc sp = BCstack.		Hypothesis	STACK	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
MATCH: ematch bc e ae.		Hypothesis	MATCH	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "ematch" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_G	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Genv", "MATCH", "ge", "get", "lessdef", "symbol_address", "vmatch_ptr_gl" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.	Lemma	match_S	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "MATCH", "get", "lessdef", "vmatch_ptr_stk" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	InvApproxRegs	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "MATCH", "get" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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...	Ltac	SimplVM	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Genv", "ge", "lessdef", "symbol_address", "vmatch", "vmatch_ptr_gl", "vmatch_ptr_stk" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. - ( integer or undef ) exists (Vint n); split; auto. inv H0; auto. - ( long ) exists (Vlong n); auto. - ( float *) destruct (Compopts.generate_float_constants tt); inv H2. exists (Vfloat f); auto. -...	Lemma	const_for_result_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Genv", "SimplVM", "add_zero_l", "eval_operation", "ge", "generate_float_constants", "inv", "lessdef", "symbol_address", "vmatch", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_shift_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eval_shift", "eval_static_shift" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_shiftl_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eval_shiftl", "eval_static_shiftl" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	eval_static_extend_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eval_extend", "eval_static_extend" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.s...	Lemma	cond_strength_reduction_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "InvApproxRegs", "SimplVM", "cmp_swap", "eq_dec", "eval_condition", "eval_static_shift_correct", "eval_static_shiftl_correct", "get", "map", "swap_cmp_bool", "swap_cmpl_bool", "swap_cmplu_bool", "swap_cmpu_bool", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_base_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "cond_strength_reduction_correct", "eval_condition", "eval_operation", "ge", "get", "lessdef", "map", "of_optbool", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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); ...	Lemma	make_cmp_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "E0", "InvBooleans", "MATCH", "Ptop", "eq_dec", "eval_condition", "eval_operation", "exploit", "ge", "get", "inv", "lessdef", "make_cmp", "make_cmp_base_correct", "map", "of_optbool", "one", "vincl", "vincl_ge", "vmatch_Uns_1", "vmatch_ge", "xor", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. rewri...	Lemma	make_select_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "MATCH", "aregs_sound", "cond_strength_reduction_correct", "eval_condition", "eval_operation", "eval_static_condition", "eval_static_condition_sound", "ge", "get", "lessdef", "lessdef_normalize", "map", "resolve_branch", "resolve_branch_sound", "select", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_addimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "add", "add_zero", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. ...	Lemma	make_shlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32", "mk_amount32_eq", "predSpec", "shl", "shl_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. simp...	Lemma	make_shrimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32_eq", "predSpec", "shr", "shr_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. si...	Lemma	make_shruimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32_eq", "predSpec", "shru", "shru_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.m...	Lemma	make_mulimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "is_power2", "is_power2_range", "lessdef", "mk_amount32_eq", "mul", "mul_one", "mul_pow2", "mul_zero", "one", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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)) eq...	Lemma	make_divimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "divs", "divs_one", "divs_pow2", "eq", "eq_spec", "eval_operation", "ge", "inv", "is_power2", "lessdef", "ltu", "one", "predSpec", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. ...	Lemma	make_divuimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "divu", "divu_one", "divu_pow2", "eq", "eq_spec", "eval_operation", "ge", "inv", "is_power2", "is_power2_range", "lessdef", "mk_amount32_eq", "one", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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...	Lemma	make_andimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "and", "and_mone", "and_zero", "bit_solve", "bits_not", "bits_zero", "bits_zero_ext", "eq", "eq_spec", "eval_operation", "ge", "inv", "lessdef", "mone", "not", "predSpec", "testbit", "vmatch", "zero", "zero_ext", "zlt", "zlt_true" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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.o...	Lemma	make_orimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "or", "or_mone", "or_zero", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_xorimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "notint", "predSpec", "xor", "xor_zero", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_addlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "add_zero", "addl", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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....	Lemma	make_shllimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64", "mk_amount64_eq", "predSpec", "repr_unsigned", "shl'", "shll", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_am...	Lemma	make_shrlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64_eq", "predSpec", "repr_signed", "shr'", "shrl", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 m...	Lemma	make_shrluimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64_eq", "predSpec", "repr_unsigned", "shrlu", "shru'", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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; a...	Lemma	make_mullimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "is_power2'", "is_power2'_range", "lessdef", "mk_amount64_eq", "mul_one", "mul_pow2'", "mul_zero", "mull", "one", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_divlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "divls", "divls_pow2", "eval_operation", "ge", "is_power2'", "lessdef", "ltu", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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....	Lemma	make_divluimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "divlu", "divu_pow2'", "eq", "eval_operation", "ge", "inv", "is_power2'", "is_power2'_range", "lessdef", "mk_amount64_eq", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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;...	Lemma	make_andlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "and_mone", "and_zero", "andl", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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; a...	Lemma	make_orlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "or_mone", "or_zero", "orl", "predSpec", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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; eau...	Lemma	make_xorlimm_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "notl", "predSpec", "xor_zero", "xorl", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mulf", "of_int", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_mulfimm_correct_2	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mul_commut", "mulf", "of_int", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mulfs", "of_int", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_mulfsimm_correct_2	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mul_commut", "mulfs", "of_int", "repr", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_zext_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Ptop", "eval_operation", "ge", "inv", "is_uns_zero_ext", "lessdef", "vincl", "vincl_ge", "vmatch", "vmatch_ge", "zero", "zero_ext" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	make_sext_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Ptop", "eval_operation", "ge", "inv", "is_sgn_sign_ext", "lessdef", "sign_ext", "vincl", "vincl_ge", "vmatch", "vmatch_ge", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. - ( adds...	Lemma	op_strength_reduction_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "InvApproxRegs", "SimplVM", "add_commut", "addl_commut", "and_commut", "andl_commut", "eval_operation", "eval_static_extend_correct", "eval_static_shift_correct", "eval_static_shiftl_correct", "fold", "ge", "get", "inv", "lessdef", "make_addimm_correct", "make_addlimm_correct", "ma...		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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' /...	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. - rewri...	Lemma	addr_strength_reduction_correct	aarch64	aarch64/ConstpropOpproof.v	[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]	[ "Genv", "InvApproxRegs", "SimplVM", "add_commut", "add_zero_l", "addl_commut", "eval_addressing", "eval_static_extend_correct", "find_symbol", "ge", "get", "inv", "lessdef", "map", "res", "symbol_address", "zero" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 => true \| F0 \| F1 \| F2 \| F3 \| F4 \| F5 \| F6 \| F7 => false \| F8 \| F9 ...	Definition	is_callee_save	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "mreg" ]	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 ...	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
int_caller_save_regs	:= R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: R11 :: R12 :: R13 :: R14 :: R15 :: R17 :: nil.	Definition	int_caller_save_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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	float_caller_save_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
int_callee_save_regs	:= R19 :: R20 :: R21 :: R22 :: R23 :: R24 :: R25 :: R26 :: R27 :: R28 :: R29 :: nil.	Definition	int_callee_save_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
float_callee_save_regs	:= F8 :: F9 :: F10 :: F11 :: F12 :: F13 :: F14 :: F15 :: nil.	Definition	float_callee_save_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
destroyed_at_call	:= List.filter (fun r => negb (is_callee_save r)) all_mregs.	Definition	destroyed_at_call	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "all_mregs", "is_callee_save" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
dummy_int_reg	:= R0.	Definition	dummy_int_reg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
dummy_float_reg	:= F0.	Definition	dummy_float_reg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]	r Used in [Coloring].	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
callee_save_type	:= mreg_type.	Definition	callee_save_type	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "mreg_type" ]	r Used in [Coloring].	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 \| ...	Definition	is_float_reg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "mreg" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
alloc_regs	:= mk_alloc_regs { preferred_int_regs: list mreg; remaining_int_regs: list mreg; preferred_float_regs: list mreg; remaining_float_regs: list mreg }.	Record	alloc_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "mreg" ]	How to use registers for register allocation. We favor the use of caller-save registers, using callee-save registers only when no caller-save is available.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
allocatable_registers (_: unit)	:= {\| preferred_int_regs := int_caller_save_regs; remaining_int_regs := int_callee_save_regs; preferred_float_regs := float_caller_save_regs; remaining_float_regs := float_callee_save_regs \|}.	Definition	allocatable_registers	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "float_callee_save_regs", "float_caller_save_regs", "int_callee_save_regs", "int_caller_save_regs" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_result (s: signature) : rpair mreg	:= match proj_sig_res s with \| Tint \| Tlong \| Tany32 \| Tany64 => One R0 \| Tfloat \| Tsingle => One F0 end.	Definition	loc_result	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "mreg", "proj_sig_res", "rpair", "signature" ]	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.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_result_type: forall sig, subtype (proj_sig_res sig) (typ_rpair mreg_type (loc_result sig)) = true.	Proof. intros. unfold loc_result. destruct (proj_sig_res sig); auto. Qed.	Lemma	loc_result_type	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "loc_result", "mreg_type", "proj_sig_res", "subtype", "typ_rpair" ]	The result registers have types compatible with that given in the signature.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 (proj_sig_res s); simpl; auto. Qed.	Lemma	loc_result_caller_save	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "forall_rpair", "is_callee_save", "loc_result", "proj_sig_res", "signature" ]	The result locations are caller-save registers	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_result_pair: forall sg, match loc_result sg with \| One _ => True \| Twolong r1 r2 => r1 <> r2 /\ proj_sig_res sg = Tlong /\ subtype Tint (mreg_type r1) = true /\ subtype Tint (mreg_type r2) = true /\ Archi.ptr64 = false end.	Proof. intros; unfold loc_result; destruct (proj_sig_res sg); exact I. Qed.	Lemma	loc_result_pair	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "loc_result", "mreg_type", "proj_sig_res", "ptr64", "subtype" ]	If the result is in a pair of registers, those registers are distinct and have type [Tint] at least.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_result_exten: forall s1 s2, s1.(sig_res) = s2.(sig_res) -> loc_result s1 = loc_result s2.	Proof. intros. unfold loc_result, proj_sig_res. rewrite H; auto. Qed.	Lemma	loc_result_exten	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "loc_result", "proj_sig_res" ]	The location of the result depends only on the result part of the signature	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
int_param_regs	:= R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 :: nil.	Definition	int_param_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]	- 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, consecutively assigned, starting at word offset 0. In the standard AAPCS64, all stack slots are 8-byte wide (2 words). In t...	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
float_param_regs	:= F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: nil.	Definition	float_param_regs	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
stack_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))	:= match Archi.abi with \| Archi.AAPCS64 => let ofs := align ofs 2 in One (S Outgoing ofs ty) :: rec ir fr (ofs + 2) \| Archi.Apple => let ofs := align ofs (typesize ty) in One (S Outgoing ofs ty) :: rec ir fr (ofs + typesize ty) end.	Definition	stack_arg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "abi", "align", "loc", "rpair", "typ", "typesize" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
int_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))	:= match list_nth_z int_param_regs ir with \| None => stack_arg ty ir fr ofs rec \| Some ireg => One (R ireg) :: rec (ir + 1) fr ofs end.	Definition	int_arg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "int_param_regs", "ireg", "list_nth_z", "loc", "rpair", "stack_arg", "typ" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
float_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))	:= match list_nth_z float_param_regs fr with \| None => stack_arg ty ir fr ofs rec \| Some freg => One (R freg) :: rec ir (fr + 1) ofs end.	Definition	float_arg	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "float_param_regs", "freg", "list_nth_z", "loc", "rpair", "stack_arg", "typ" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_arguments_stack (tyl: list typ) (ofs: Z) {struct tyl} : list (rpair loc)	:= match tyl with \| nil => nil \| ty :: tys => One (S Outgoing ofs Tany64) :: loc_arguments_stack tys (ofs + 2) end.	Fixpoint	loc_arguments_stack	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "loc", "rpair", "typ" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_arguments_rec (tyl: list typ) (fixed ir fr ofs: Z) {struct tyl} : list (rpair loc)	:= match tyl with \| nil => nil \| ty :: tys => if zle fixed 0 then loc_arguments_stack tyl (align ofs 2) else match ty with \| Tint \| Tlong \| Tany32 \| Tany64 => int_arg ty ir fr ofs (loc_arguments_rec tys (fixed - 1)) \| Tfloat \| Tsingle => float_arg ty ir fr ofs (loc_argu...	Fixpoint	loc_arguments_rec	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "align", "float_arg", "int_arg", "loc", "loc_arguments_stack", "rpair", "typ", "zle" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
fixed_arguments (s: signature) : Z	:= match Archi.abi, s.(sig_cc).(cc_vararg) with \| Archi.Apple, Some n => n \| _, _ => list_length_z s.(sig_args) end.	Definition	fixed_arguments	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "abi", "list_length_z", "signature" ]	Number of fixed arguments for a function with signature [s]. For AAPCS64, all arguments are treated as fixed, even for a vararg function.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_arguments (s: signature) : list (rpair loc)	:= loc_arguments_rec (proj_sig_args s) (fixed_arguments s) 0 0 0.	Definition	loc_arguments	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "fixed_arguments", "loc", "loc_arguments_rec", "proj_sig_args", "rpair", "signature" ]	[loc_arguments s] returns the list of locations where to store arguments when calling a function with signature [s].	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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_acceptable	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "is_callee_save", "loc", "typealign" ]	Argument locations are either caller-save registers or [Outgoing] stack slots at nonnegative offsets.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_arguments_rec_charact: forall tyl fixed ri rf ofs p, ofs >= 0 -> In p (loc_arguments_rec tyl fixed ri rf ofs) -> forall_rpair loc_argument_acceptable p.	Proof. set (OK := fun (l: list (rpair loc)) => forall p, In p l -> forall_rpair loc_argument_acceptable p). set (OKF := fun (f: Z -> Z -> Z -> list (rpair loc)) => forall ri rf ofs, ofs >= 0 -> OK (f ri rf ofs)). assert (CSI: forall r, In r int_param_regs -> is_callee_save r = false). ...	Lemma	loc_arguments_rec_charact	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "In", "abi", "align", "align_divides", "align_le", "decide_goal", "float_arg", "float_param_regs", "forall_rpair", "int_arg", "int_param_regs", "is_callee_save", "list_nth_z", "list_nth_z_in", "loc", "loc_argument_acceptable", "loc_arguments_rec", "loc_arguments_stack", "rpair", ...		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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. eapply loc_arguments_rec_charact; eauto. lia. Qed.	Lemma	loc_arguments_acceptable	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "In", "forall_rpair", "loc", "loc_argument_acceptable", "loc_arguments", "loc_arguments_rec_charact", "rpair", "signature" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
loc_arguments_main: loc_arguments signature_main = nil.	Proof. unfold loc_arguments; reflexivity. Qed.	Lemma	loc_arguments_main	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "loc_arguments", "signature_main" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
return_value_needs_normalization (t: xtype) : bool	:= match Archi.abi with \| Archi.Apple => false \| Archi.AAPCS64 => match t with \| Xbool \| Xint8signed \| Xint8unsigned \| Xint16signed \| Xint16unsigned => true \| _ => false end end.	Definition	return_value_needs_normalization	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "abi", "xtype" ]	According to the AAPCS64 ABI specification, "padding bits" in the return value of a function or in a function parameter have unpredictable values and must be ignored. Consequently, we force normalization of return values and of function parameters when they have small integer types (8- and 16-bit integ...	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
parameter_needs_normalization	:= return_value_needs_normalization.	Definition	parameter_needs_normalization	aarch64	aarch64/Conventions1.v	[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]	[ "return_value_needs_normalization" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
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 \| F...	Inductive	mreg	aarch64	aarch64/Machregs.v	[ "Coq", "String", "Coqlib", "Decidableplus", "Maps", "AST", "Op" ]	[]	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.	https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401
mreg_eq: forall (r1 r2: mreg), {r1 = r2} + {r1 <> r2}.	Proof. decide equality. Defined.	Lemma	mreg_eq	aarch64	aarch64/Machregs.v	[ "Coq", "String", "Coqlib", "Decidableplus", "Maps", "AST", "Op" ]	[ "mreg" ]		https://github.com/AbsInt/CompCert	0ef26dad76446c803da02d7368eb4f9d074c1401

platform_builtin_table : list (string * platform_builtin)

:= nil.

Definition

platform_builtin_table

aarch64

aarch64/Builtins1.v

[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]

[ "platform_builtin", "string" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

platform_builtin_sig (b: platform_builtin) : signature

:= match b with end.

Definition

platform_builtin_sig

aarch64

aarch64/Builtins1.v

[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]

[ "platform_builtin", "signature" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

platform_builtin_sem (b: platform_builtin) : builtin_sem (sig_res (platform_builtin_sig b))

:= match b with end.

Definition

platform_builtin_sem

aarch64

aarch64/Builtins1.v

[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]

[ "builtin_sem", "platform_builtin", "platform_builtin_sig" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

eq_platform_builtin: forall (x y: platform_builtin), {x=y} + {x<>y}.

Proof. intros. destruct x. Defined.

Definition

eq_platform_builtin

aarch64

aarch64/Builtins1.v

[ "Coq", "String", "Coqlib", "AST", "Integers", "Floats", "Values", "Builtins0" ]

[ "platform_builtin" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_compimm_ne_0 (x: valnum) : option(condition * list valnum)

:= match get x with | Some(Op (Ocmp c) ys) => Some (c, ys) | Some(Op (Oxorimm n) ys) => if Int.eq n (Int.zero_ext 12 n) then Some (Ccompimm Cne n, ys) else None | _ => None end.

Function

combine_compimm_ne_0

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "condition", "eq", "get", "valnum", "zero_ext" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_compimm_eq_0 (x: valnum) : option(condition * list valnum)

:= match get x with | Some(Op (Ocmp c) ys) => Some (negate_condition c, ys) | Some(Op (Oxorimm n) ys) => if Int.eq n (Int.zero_ext 12 n) then Some (Ccompimm Ceq n, ys) else None | _ => None end.

Function

combine_compimm_eq_0

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "condition", "eq", "get", "negate_condition", "valnum", "zero_ext" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_eq_1

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "condition", "get", "valnum" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_compimm_ne_1

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "condition", "get", "negate_condition", "valnum" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 t...

Function

combine_cond

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "combine_compimm_eq_0", "combine_compimm_eq_1", "combine_compimm_ne_0", "combine_compimm_ne_1", "condition", "eq_dec", "one", "valnum", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_cond' (cond: condition) (args: list valnum) : option bool

Definition

combine_cond'

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "combine_comparison", "condition", "valnum" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_addr

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "add", "addressing", "get", "valnum" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_op (op: operation) (args: list valnum) : option(operation * list valnum)

Function

combine_op

aarch64

aarch64/CombineOp.v

[ "Coqlib", "AST", "Integers", "Op", "CSEdomain" ]

[ "add", "and", "combine_cond", "combine_cond'", "eq", "eq_valnum", "get", "one", "operation", "or", "valnum", "xor", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

get_sound: forall v rhs, get v = Some rhs -> rhs_eval_to valu ge sp m rhs (valu v).

Hypothesis

get_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "ge", "get", "rhs", "rhs_eval_to" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.

Lemma

get_op_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "eval_operation", "exploit", "ge", "get", "get_sound", "inv", "map" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

UseGetSound

:= match goal with | [ H: get _ = Some _ |- _ ] => let x := fresh "EQ" in (generalize (get_op_sound _ _ _ H); intros x; simpl in x; FuncInv) end.

Ltac

UseGetSound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "FuncInv", "get", "get_op_sound" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. (* of xorimm *) UseGetSound. rewrite <- H. destruct v; simpl; auto. rewrite Int.xor_is_ze...

Lemma

combine_compimm_ne_0_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_ne_0", "eval_condition", "get", "inv", "map", "valid_pointer", "xor_is_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. (* of xorimm *) UseGetSound. rewrite <- H. destruct v; simp...

Lemma

combine_compimm_eq_0_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_eq_0", "eval_condition", "eval_negate_condition", "get", "inv", "map", "valid_pointer", "xor_is_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_eq_1_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_eq_1", "eval_condition", "get", "inv", "map", "one", "valid_pointer" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.

Lemma

combine_compimm_ne_1_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "cmp_bool", "cmpu_bool", "combine_compimm_ne_1", "eval_condition", "eval_negate_condition", "get", "inv", "map", "one", "valid_pointer" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 c...

Theorem

combine_cond_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "combine_compimm_eq_0_sound", "combine_compimm_eq_1_sound", "combine_compimm_ne_0_sound", "combine_compimm_ne_1_sound", "combine_cond", "eval_condition", "get", "map" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_cond'_sound: forall cond args res res', combine_cond' cond args = Some res' -> eval_condition cond (map valu args) m = Some res -> res = res'.

Proof. intros. unfold combine_cond' in *. destruct cond; inv H; destruct args; inv H2; destruct args; inv H1; destruct args; inv H2. apply (combine_comparison_cmp_sound valu c v v0 res res'); auto. apply (combine_comparison_cmpu_sound valu m c v v0 res res'); auto. apply (combine_comparison_cmpl_sound valu c...

Theorem

combine_cond'_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "combine_comparison_cmp_sound", "combine_comparison_cmpl_sound", "combine_comparison_cmplu_sound", "combine_comparison_cmpu_sound", "combine_cond'", "eval_condition", "inv", "map", "res" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_addr_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "addl_assoc", "combine_addr", "eval_addressing", "ge", "get", "map" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

combine_op_sound: forall op args op' args' r, combine_op get op args = Some(op', args') -> eval_operation ge sp op (map valu args) m = Some r -> exists r', eval_operation ge sp op' (map valu args') m = Some r' /\ Val.lessdef r r'.

Proof. intros. functional inversion H; subst. (* addimm - addimm *) - UseGetSound. exists r; split; auto. rewrite <- H0. simpl. rewrite <- H1. rewrite Val.add_assoc. auto. (* andimm - andimm *) - UseGetSound; simpl. generalize (Int.eq_spec p m0); rewrite H8; intros. exists r; split; auto. rewrite ...

Theorem

combine_op_sound

aarch64

aarch64/CombineOpproof.v

[ "Coq", "FunInd", "Coqlib", "AST", "Integers", "Values", "Memory", "Op", "Registers", "RTL", "CSEdomain", "CombineOp" ]

[ "UseGetSound", "Vfalse", "Vtrue", "add_assoc", "addl_assoc", "and_assoc", "andl_assoc", "combine_cond'_sound", "combine_cond_sound", "combine_op", "decEq", "eq_spec", "eval_condition", "eval_operation", "fold", "ge", "get", "inv", "lessdef", "map", "or_assoc", "orl_assoc", ...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

GENV: genv_match bc ge.

Hypothesis

GENV

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "ge", "genv_match" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

STACK: bc sp = BCstack.

Hypothesis

STACK

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

MATCH: ematch bc e ae.

Hypothesis

MATCH

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "ematch" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_G

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Genv", "MATCH", "ge", "get", "lessdef", "symbol_address", "vmatch_ptr_gl" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.

Lemma

match_S

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "MATCH", "get", "lessdef", "vmatch_ptr_stk" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

InvApproxRegs

Ltac

InvApproxRegs

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "MATCH", "get" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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...

Ltac

SimplVM

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Genv", "ge", "lessdef", "symbol_address", "vmatch", "vmatch_ptr_gl", "vmatch_ptr_stk" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. - (* integer or undef *) exists (Vint n); split; auto. inv H0; auto. - (* long *) exists (Vlong n); auto. - (* float *) destruct (Compopts.generate_float_constants tt); inv H2. exists (Vfloat f); auto. -...

Lemma

const_for_result_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Genv", "SimplVM", "add_zero_l", "eval_operation", "ge", "generate_float_constants", "inv", "lessdef", "symbol_address", "vmatch", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_shift_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eval_shift", "eval_static_shift" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_shiftl_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eval_shiftl", "eval_static_shiftl" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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

eval_static_extend_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eval_extend", "eval_static_extend" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.s...

Lemma

cond_strength_reduction_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "InvApproxRegs", "SimplVM", "cmp_swap", "eq_dec", "eval_condition", "eval_static_shift_correct", "eval_static_shiftl_correct", "get", "map", "swap_cmp_bool", "swap_cmpl_bool", "swap_cmplu_bool", "swap_cmpu_bool", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_base_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "cond_strength_reduction_correct", "eval_condition", "eval_operation", "ge", "get", "lessdef", "map", "of_optbool", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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); ...

Lemma

make_cmp_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "E0", "InvBooleans", "MATCH", "Ptop", "eq_dec", "eval_condition", "eval_operation", "exploit", "ge", "get", "inv", "lessdef", "make_cmp", "make_cmp_base_correct", "map", "of_optbool", "one", "vincl", "vincl_ge", "vmatch_Uns_1", "vmatch_ge", "xor", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. rewri...

Lemma

make_select_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "MATCH", "aregs_sound", "cond_strength_reduction_correct", "eval_condition", "eval_operation", "eval_static_condition", "eval_static_condition_sound", "ge", "get", "lessdef", "lessdef_normalize", "map", "resolve_branch", "resolve_branch_sound", "select", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_addimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "add", "add_zero", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. ...

Lemma

make_shlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32", "mk_amount32_eq", "predSpec", "shl", "shl_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. simp...

Lemma

make_shrimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32_eq", "predSpec", "shr", "shr_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. si...

Lemma

make_shruimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize", "lessdef", "ltu", "mk_amount32_eq", "predSpec", "shru", "shru_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.m...

Lemma

make_mulimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "is_power2", "is_power2_range", "lessdef", "mk_amount32_eq", "mul", "mul_one", "mul_pow2", "mul_zero", "one", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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)) eq...

Lemma

make_divimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "divs", "divs_one", "divs_pow2", "eq", "eq_spec", "eval_operation", "ge", "inv", "is_power2", "lessdef", "ltu", "one", "predSpec", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. ...

Lemma

make_divuimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "divu", "divu_one", "divu_pow2", "eq", "eq_spec", "eval_operation", "ge", "inv", "is_power2", "is_power2_range", "lessdef", "mk_amount32_eq", "one", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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...

Lemma

make_andimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "and", "and_mone", "and_zero", "bit_solve", "bits_not", "bits_zero", "bits_zero_ext", "eq", "eq_spec", "eval_operation", "ge", "inv", "lessdef", "mone", "not", "predSpec", "testbit", "vmatch", "zero", "zero_ext", "zlt", "zlt_true" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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.o...

Lemma

make_orimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "or", "or_mone", "or_zero", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_xorimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "notint", "predSpec", "xor", "xor_zero", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_addlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "add_zero", "addl", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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....

Lemma

make_shllimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64", "mk_amount64_eq", "predSpec", "repr_unsigned", "shl'", "shll", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_am...

Lemma

make_shrlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64_eq", "predSpec", "repr_signed", "shr'", "shrl", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 m...

Lemma

make_shrluimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "iwordsize'", "lessdef", "ltu", "mk_amount64_eq", "predSpec", "repr_unsigned", "shrlu", "shru'", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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; a...

Lemma

make_mullimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "is_power2'", "is_power2'_range", "lessdef", "mk_amount64_eq", "mul_one", "mul_pow2'", "mul_zero", "mull", "one", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_divlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "divls", "divls_pow2", "eval_operation", "ge", "is_power2'", "lessdef", "ltu", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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....

Lemma

make_divluimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "divlu", "divu_pow2'", "eq", "eval_operation", "ge", "inv", "is_power2'", "is_power2'_range", "lessdef", "mk_amount64_eq", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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;...

Lemma

make_andlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "and_mone", "and_zero", "andl", "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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; a...

Lemma

make_orlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "or_mone", "or_zero", "orl", "predSpec", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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; eau...

Lemma

make_xorlimm_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq", "eq_spec", "eval_operation", "ge", "lessdef", "mone", "notl", "predSpec", "xor_zero", "xorl", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mulf", "of_int", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_mulfimm_correct_2

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mul_commut", "mulf", "of_int", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mulfs", "of_int", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_mulfsimm_correct_2

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "eq_dec", "eval_operation", "ge", "lessdef", "mul2_add", "mul_commut", "mulfs", "of_int", "repr", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_zext_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Ptop", "eval_operation", "ge", "inv", "is_uns_zero_ext", "lessdef", "vincl", "vincl_ge", "vmatch", "vmatch_ge", "zero", "zero_ext" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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

make_sext_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Ptop", "eval_operation", "ge", "inv", "is_sgn_sign_ext", "lessdef", "sign_ext", "vincl", "vincl_ge", "vmatch", "vmatch_ge", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. - (* adds...

Lemma

op_strength_reduction_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "InvApproxRegs", "SimplVM", "add_commut", "addl_commut", "and_commut", "andl_commut", "eval_operation", "eval_static_extend_correct", "eval_static_shift_correct", "eval_static_shiftl_correct", "fold", "ge", "get", "inv", "lessdef", "make_addimm_correct", "make_addlimm_correct", "ma...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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' /...

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. - rewri...

Lemma

addr_strength_reduction_correct

aarch64

aarch64/ConstpropOpproof.v

[ "Coqlib", "Compopts", "Integers", "Floats", "Values", "Memory", "Globalenvs", "Events", "Op", "Registers", "RTL", "ValueDomain", "ValueAOp", "ValueAnalysis", "ConstpropOp" ]

[ "Genv", "InvApproxRegs", "SimplVM", "add_commut", "add_zero_l", "addl_commut", "eval_addressing", "eval_static_extend_correct", "find_symbol", "ge", "get", "inv", "lessdef", "map", "res", "symbol_address", "zero" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 => true | F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 => false | F8 | F9 ...

Definition

is_callee_save

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "mreg" ]

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 ...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

int_caller_save_regs

:= R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: R11 :: R12 :: R13 :: R14 :: R15 :: R17 :: nil.

Definition

int_caller_save_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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

float_caller_save_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

int_callee_save_regs

:= R19 :: R20 :: R21 :: R22 :: R23 :: R24 :: R25 :: R26 :: R27 :: R28 :: R29 :: nil.

Definition

int_callee_save_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

float_callee_save_regs

:= F8 :: F9 :: F10 :: F11 :: F12 :: F13 :: F14 :: F15 :: nil.

Definition

float_callee_save_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

destroyed_at_call

:= List.filter (fun r => negb (is_callee_save r)) all_mregs.

Definition

destroyed_at_call

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "all_mregs", "is_callee_save" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

dummy_int_reg

:= R0.

Definition

dummy_int_reg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

dummy_float_reg

:= F0.

Definition

dummy_float_reg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

r Used in [Coloring].

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

callee_save_type

:= mreg_type.

Definition

callee_save_type

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "mreg_type" ]

r Used in [Coloring].

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 | ...

Definition

is_float_reg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "mreg" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

alloc_regs

:= mk_alloc_regs { preferred_int_regs: list mreg; remaining_int_regs: list mreg; preferred_float_regs: list mreg; remaining_float_regs: list mreg }.

Record

alloc_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "mreg" ]

How to use registers for register allocation. We favor the use of caller-save registers, using callee-save registers only when no caller-save is available.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

allocatable_registers (_: unit)

:= {| preferred_int_regs := int_caller_save_regs; remaining_int_regs := int_callee_save_regs; preferred_float_regs := float_caller_save_regs; remaining_float_regs := float_callee_save_regs |}.

Definition

allocatable_registers

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "float_callee_save_regs", "float_caller_save_regs", "int_callee_save_regs", "int_caller_save_regs" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_result (s: signature) : rpair mreg

Definition

loc_result

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "mreg", "proj_sig_res", "rpair", "signature" ]

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.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_result_type: forall sig, subtype (proj_sig_res sig) (typ_rpair mreg_type (loc_result sig)) = true.

Proof. intros. unfold loc_result. destruct (proj_sig_res sig); auto. Qed.

Lemma

loc_result_type

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "loc_result", "mreg_type", "proj_sig_res", "subtype", "typ_rpair" ]

The result registers have types compatible with that given in the signature.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 (proj_sig_res s); simpl; auto. Qed.

Lemma

loc_result_caller_save

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "forall_rpair", "is_callee_save", "loc_result", "proj_sig_res", "signature" ]

The result locations are caller-save registers

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_result_pair: forall sg, match loc_result sg with | One _ => True | Twolong r1 r2 => r1 <> r2 /\ proj_sig_res sg = Tlong /\ subtype Tint (mreg_type r1) = true /\ subtype Tint (mreg_type r2) = true /\ Archi.ptr64 = false end.

Proof. intros; unfold loc_result; destruct (proj_sig_res sg); exact I. Qed.

Lemma

loc_result_pair

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "loc_result", "mreg_type", "proj_sig_res", "ptr64", "subtype" ]

If the result is in a pair of registers, those registers are distinct and have type [Tint] at least.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_result_exten: forall s1 s2, s1.(sig_res) = s2.(sig_res) -> loc_result s1 = loc_result s2.

Proof. intros. unfold loc_result, proj_sig_res. rewrite H; auto. Qed.

Lemma

loc_result_exten

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "loc_result", "proj_sig_res" ]

The location of the result depends only on the result part of the signature

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

int_param_regs

:= R0 :: R1 :: R2 :: R3 :: R4 :: R5 :: R6 :: R7 :: nil.

Definition

int_param_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

- 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, consecutively assigned, starting at word offset 0. In the standard AAPCS64, all stack slots are 8-byte wide (2 words). In t...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

float_param_regs

:= F0 :: F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: nil.

Definition

float_param_regs

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

stack_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))

:= match Archi.abi with | Archi.AAPCS64 => let ofs := align ofs 2 in One (S Outgoing ofs ty) :: rec ir fr (ofs + 2) | Archi.Apple => let ofs := align ofs (typesize ty) in One (S Outgoing ofs ty) :: rec ir fr (ofs + typesize ty) end.

Definition

stack_arg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "abi", "align", "loc", "rpair", "typ", "typesize" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

int_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))

:= match list_nth_z int_param_regs ir with | None => stack_arg ty ir fr ofs rec | Some ireg => One (R ireg) :: rec (ir + 1) fr ofs end.

Definition

int_arg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "int_param_regs", "ireg", "list_nth_z", "loc", "rpair", "stack_arg", "typ" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

float_arg (ty: typ) (ir fr ofs: Z) (rec: Z -> Z -> Z -> list (rpair loc))

:= match list_nth_z float_param_regs fr with | None => stack_arg ty ir fr ofs rec | Some freg => One (R freg) :: rec ir (fr + 1) ofs end.

Definition

float_arg

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "float_param_regs", "freg", "list_nth_z", "loc", "rpair", "stack_arg", "typ" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_arguments_stack (tyl: list typ) (ofs: Z) {struct tyl} : list (rpair loc)

:= match tyl with | nil => nil | ty :: tys => One (S Outgoing ofs Tany64) :: loc_arguments_stack tys (ofs + 2) end.

Fixpoint

loc_arguments_stack

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "loc", "rpair", "typ" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_arguments_rec (tyl: list typ) (fixed ir fr ofs: Z) {struct tyl} : list (rpair loc)

Fixpoint

loc_arguments_rec

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "align", "float_arg", "int_arg", "loc", "loc_arguments_stack", "rpair", "typ", "zle" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

fixed_arguments (s: signature) : Z

:= match Archi.abi, s.(sig_cc).(cc_vararg) with | Archi.Apple, Some n => n | _, _ => list_length_z s.(sig_args) end.

Definition

fixed_arguments

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "abi", "list_length_z", "signature" ]

Number of fixed arguments for a function with signature [s]. For AAPCS64, all arguments are treated as fixed, even for a vararg function.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_arguments (s: signature) : list (rpair loc)

:= loc_arguments_rec (proj_sig_args s) (fixed_arguments s) 0 0 0.

Definition

loc_arguments

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "fixed_arguments", "loc", "loc_arguments_rec", "proj_sig_args", "rpair", "signature" ]

[loc_arguments s] returns the list of locations where to store arguments when calling a function with signature [s].

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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_acceptable

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "is_callee_save", "loc", "typealign" ]

Argument locations are either caller-save registers or [Outgoing] stack slots at nonnegative offsets.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_arguments_rec_charact: forall tyl fixed ri rf ofs p, ofs >= 0 -> In p (loc_arguments_rec tyl fixed ri rf ofs) -> forall_rpair loc_argument_acceptable p.

Proof. set (OK := fun (l: list (rpair loc)) => forall p, In p l -> forall_rpair loc_argument_acceptable p). set (OKF := fun (f: Z -> Z -> Z -> list (rpair loc)) => forall ri rf ofs, ofs >= 0 -> OK (f ri rf ofs)). assert (CSI: forall r, In r int_param_regs -> is_callee_save r = false). ...

Lemma

loc_arguments_rec_charact

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "In", "abi", "align", "align_divides", "align_le", "decide_goal", "float_arg", "float_param_regs", "forall_rpair", "int_arg", "int_param_regs", "is_callee_save", "list_nth_z", "list_nth_z_in", "loc", "loc_argument_acceptable", "loc_arguments_rec", "loc_arguments_stack", "rpair", ...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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. eapply loc_arguments_rec_charact; eauto. lia. Qed.

Lemma

loc_arguments_acceptable

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "In", "forall_rpair", "loc", "loc_argument_acceptable", "loc_arguments", "loc_arguments_rec_charact", "rpair", "signature" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

loc_arguments_main: loc_arguments signature_main = nil.

Proof. unfold loc_arguments; reflexivity. Qed.

Lemma

loc_arguments_main

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "loc_arguments", "signature_main" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

return_value_needs_normalization (t: xtype) : bool

Definition

return_value_needs_normalization

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "abi", "xtype" ]

According to the AAPCS64 ABI specification, "padding bits" in the return value of a function or in a function parameter have unpredictable values and must be ignored. Consequently, we force normalization of return values and of function parameters when they have small integer types (8- and 16-bit integ...

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

parameter_needs_normalization

:= return_value_needs_normalization.

Definition

parameter_needs_normalization

aarch64

aarch64/Conventions1.v

[ "Coqlib", "Decidableplus", "AST", "Events", "Locations", "Archi" ]

[ "return_value_needs_normalization" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

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 | F...

Inductive

mreg

aarch64

aarch64/Machregs.v

[ "Coq", "String", "Coqlib", "Decidableplus", "Maps", "AST", "Op" ]

[]

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.

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401

mreg_eq: forall (r1 r2: mreg), {r1 = r2} + {r1 <> r2}.

Proof. decide equality. Defined.

Lemma

mreg_eq

aarch64

aarch64/Machregs.v

[ "Coq", "String", "Coqlib", "Decidableplus", "Maps", "AST", "Op" ]

[ "mreg" ]

https://github.com/AbsInt/CompCert

0ef26dad76446c803da02d7368eb4f9d074c1401