From f642817f0dc761e51c3bd362f75b0068a8d4b0c8 Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Fri, 28 Apr 2017 15:56:59 +0200 Subject: RISC-V port and assorted changes This commits adds code generation for the RISC-V architecture, both in 32- and 64-bit modes. The generated code was lightly tested using the simulator and cross-binutils from https://riscv.org/software-tools/ This port required the following additional changes: - Integers: More properties about shrx - SelectOp: now provides smart constructors for mulhs and mulhu - SelectDiv, 32-bit integer division and modulus: implement constant propagation, use the new smart constructors mulhs and mulhu. - Runtime library: if no asm implementation is provided, run the reference C implementation through CompCert. Since CompCert rejects the definitions of names of special functions such as __i64_shl, the reference implementation now uses "i64_" names, e.g. "i64_shl", and a renaming "i64_ -> __i64_" is performed over the generated assembly file, before assembling and building the runtime library. - test/: add SIMU make variable to run tests through a simulator - test/regression/alignas.c: make sure _Alignas and _Alignof are not #define'd by C headers commit da14495c01cf4f66a928c2feff5c53f09bde837f Author: Xavier Leroy Date: Thu Apr 13 17:36:10 2017 +0200 RISC-V port, continued Now working on Asmgen. commit 36f36eb3a5abfbb8805960443d087b6a83e86005 Author: Xavier Leroy Date: Wed Apr 12 17:26:39 2017 +0200 RISC-V port, first steps This port is based on Prashanth Mundkur's experimental RV32 port and brings it up to date with CompCert, and adds 64-bit support (RV64). Work in progress. --- riscV/Asmgenproof.v | 1028 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1028 insertions(+) create mode 100644 riscV/Asmgenproof.v (limited to 'riscV/Asmgenproof.v') diff --git a/riscV/Asmgenproof.v b/riscV/Asmgenproof.v new file mode 100644 index 00000000..da444a4b --- /dev/null +++ b/riscV/Asmgenproof.v @@ -0,0 +1,1028 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Correctness proof for RISC-V generation: main proof. *) + +Require Import Coqlib Errors. +Require Import Integers Floats AST Linking. +Require Import Values Memory Events Globalenvs Smallstep. +Require Import Op Locations Mach Conventions Asm. +Require Import Asmgen Asmgenproof0 Asmgenproof1. + +Definition match_prog (p: Mach.program) (tp: Asm.program) := + match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp. + +Lemma transf_program_match: + forall p tp, transf_program p = OK tp -> match_prog p tp. +Proof. + intros. eapply match_transform_partial_program; eauto. +Qed. + +Section PRESERVATION. + +Variable prog: Mach.program. +Variable tprog: Asm.program. +Hypothesis TRANSF: match_prog prog tprog. +Let ge := Genv.globalenv prog. +Let tge := Genv.globalenv tprog. + +Lemma symbols_preserved: + forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s. +Proof (Genv.find_symbol_match TRANSF). + +Lemma senv_preserved: + Senv.equiv ge tge. +Proof (Genv.senv_match TRANSF). + +Lemma functions_translated: + forall b f, + Genv.find_funct_ptr ge b = Some f -> + exists tf, + Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf. +Proof (Genv.find_funct_ptr_transf_partial TRANSF). + +Lemma functions_transl: + forall fb f tf, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transf_function f = OK tf -> + Genv.find_funct_ptr tge fb = Some (Internal tf). +Proof. + intros. exploit functions_translated; eauto. intros [tf' [A B]]. + monadInv B. rewrite H0 in EQ; inv EQ; auto. +Qed. + +(** * Properties of control flow *) + +Lemma transf_function_no_overflow: + forall f tf, + transf_function f = OK tf -> list_length_z tf.(fn_code) <= Ptrofs.max_unsigned. +Proof. + intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. + omega. +Qed. + +Lemma exec_straight_exec: + forall fb f c ep tf tc c' rs m rs' m', + transl_code_at_pc ge (rs PC) fb f c ep tf tc -> + exec_straight tge tf tc rs m c' rs' m' -> + plus step tge (State rs m) E0 (State rs' m'). +Proof. + intros. inv H. + eapply exec_straight_steps_1; eauto. + eapply transf_function_no_overflow; eauto. + eapply functions_transl; eauto. +Qed. + +Lemma exec_straight_at: + forall fb f c ep tf tc c' ep' tc' rs m rs' m', + transl_code_at_pc ge (rs PC) fb f c ep tf tc -> + transl_code f c' ep' = OK tc' -> + exec_straight tge tf tc rs m tc' rs' m' -> + transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'. +Proof. + intros. inv H. + exploit exec_straight_steps_2; eauto. + eapply transf_function_no_overflow; eauto. + eapply functions_transl; eauto. + intros [ofs' [PC' CT']]. + rewrite PC'. constructor; auto. +Qed. + +(** The following lemmas show that the translation from Mach to Asm + preserves labels, in the sense that the following diagram commutes: +<< + translation + Mach code ------------------------ Asm instr sequence + | | + | Mach.find_label lbl find_label lbl | + | | + v v + Mach code tail ------------------- Asm instr seq tail + translation +>> + The proof demands many boring lemmas showing that Asm constructor + functions do not introduce new labels. +*) + +Section TRANSL_LABEL. + +Remark loadimm32_label: + forall r n k, tail_nolabel k (loadimm32 r n k). +Proof. + intros; unfold loadimm32. destruct (make_immed32 n); TailNoLabel. + unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel. +Qed. +Hint Resolve loadimm32_label: labels. + +Remark opimm32_label: + forall op opimm r1 r2 n k, + (forall r1 r2 r3, nolabel (op r1 r2 r3)) -> + (forall r1 r2 n, nolabel (opimm r1 r2 n)) -> + tail_nolabel k (opimm32 op opimm r1 r2 n k). +Proof. + intros; unfold opimm32. destruct (make_immed32 n); TailNoLabel. + unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel. +Qed. +Hint Resolve opimm32_label: labels. + +Remark loadimm64_label: + forall r n k, tail_nolabel k (loadimm64 r n k). +Proof. + intros; unfold loadimm64. destruct (make_immed64 n); TailNoLabel. + unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel. +Qed. +Hint Resolve loadimm64_label: labels. + +Remark opimm64_label: + forall op opimm r1 r2 n k, + (forall r1 r2 r3, nolabel (op r1 r2 r3)) -> + (forall r1 r2 n, nolabel (opimm r1 r2 n)) -> + tail_nolabel k (opimm64 op opimm r1 r2 n k). +Proof. + intros; unfold opimm64. destruct (make_immed64 n); TailNoLabel. + unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel. +Qed. +Hint Resolve opimm64_label: labels. + +Remark addptrofs_label: + forall r1 r2 n k, tail_nolabel k (addptrofs r1 r2 n k). +Proof. + unfold addptrofs; intros. destruct (Ptrofs.eq_dec n Ptrofs.zero). TailNoLabel. + destruct Archi.ptr64. apply opimm64_label; TailNoLabel. apply opimm32_label; TailNoLabel. +Qed. +Hint Resolve addptrofs_label: labels. + +Remark transl_cond_float_nolabel: + forall c r1 r2 r3 insn normal, + transl_cond_float c r1 r2 r3 = (insn, normal) -> nolabel insn. +Proof. + unfold transl_cond_float; intros. destruct c; inv H; exact I. +Qed. + +Remark transl_cond_single_nolabel: + forall c r1 r2 r3 insn normal, + transl_cond_single c r1 r2 r3 = (insn, normal) -> nolabel insn. +Proof. + unfold transl_cond_single; intros. destruct c; inv H; exact I. +Qed. + +Remark transl_cbranch_label: + forall cond args lbl k c, + transl_cbranch cond args lbl k = OK c -> tail_nolabel k c. +Proof. + intros. unfold transl_cbranch in H; destruct cond; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- destruct (Int.eq n Int.zero). + destruct c0; simpl; TailNoLabel. + apply tail_nolabel_trans with (transl_cbranch_int32s c0 x X31 lbl :: k). + auto with labels. destruct c0; simpl; TailNoLabel. +- destruct (Int.eq n Int.zero). + destruct c0; simpl; TailNoLabel. + apply tail_nolabel_trans with (transl_cbranch_int32u c0 x X31 lbl :: k). + auto with labels. destruct c0; simpl; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- destruct (Int64.eq n Int64.zero). + destruct c0; simpl; TailNoLabel. + apply tail_nolabel_trans with (transl_cbranch_int64s c0 x X31 lbl :: k). + auto with labels. destruct c0; simpl; TailNoLabel. +- destruct (Int64.eq n Int64.zero). + destruct c0; simpl; TailNoLabel. + apply tail_nolabel_trans with (transl_cbranch_int64u c0 x X31 lbl :: k). + auto with labels. destruct c0; simpl; TailNoLabel. +- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. + destruct normal; TailNoLabel. +Qed. + +Remark transl_cond_op_label: + forall cond args r k c, + transl_cond_op cond r args k = OK c -> tail_nolabel k c. +Proof. + intros. unfold transl_cond_op in H; destruct cond; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- unfold transl_condimm_int32s. + destruct (Int.eq n Int.zero). ++ destruct c0; simpl; TailNoLabel. ++ destruct c0; simpl. +* eapply tail_nolabel_trans; [apply opimm32_label; intros; exact I | TailNoLabel]. +* eapply tail_nolabel_trans; [apply opimm32_label; intros; exact I | TailNoLabel]. +* apply opimm32_label; intros; exact I. +* destruct (Int.eq n (Int.repr Int.max_signed)). apply loadimm32_label. apply opimm32_label; intros; exact I. +* eapply tail_nolabel_trans. apply loadimm32_label. TailNoLabel. +* eapply tail_nolabel_trans. apply loadimm32_label. TailNoLabel. +- unfold transl_condimm_int32u. + destruct (Int.eq n Int.zero). ++ destruct c0; simpl; TailNoLabel. ++ destruct c0; simpl; + try (eapply tail_nolabel_trans; [apply loadimm32_label | TailNoLabel]). + apply opimm32_label; intros; exact I. +- destruct c0; simpl; TailNoLabel. +- destruct c0; simpl; TailNoLabel. +- unfold transl_condimm_int64s. + destruct (Int64.eq n Int64.zero). ++ destruct c0; simpl; TailNoLabel. ++ destruct c0; simpl. +* eapply tail_nolabel_trans; [apply opimm64_label; intros; exact I | TailNoLabel]. +* eapply tail_nolabel_trans; [apply opimm64_label; intros; exact I | TailNoLabel]. +* apply opimm64_label; intros; exact I. +* destruct (Int64.eq n (Int64.repr Int64.max_signed)). apply loadimm32_label. apply opimm64_label; intros; exact I. +* eapply tail_nolabel_trans. apply loadimm64_label. TailNoLabel. +* eapply tail_nolabel_trans. apply loadimm64_label. TailNoLabel. +- unfold transl_condimm_int64u. + destruct (Int64.eq n Int64.zero). ++ destruct c0; simpl; TailNoLabel. ++ destruct c0; simpl; + try (eapply tail_nolabel_trans; [apply loadimm64_label | TailNoLabel]). + apply opimm64_label; intros; exact I. +- destruct (transl_cond_float c0 r x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_float c0 r x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_single c0 r x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. + destruct normal; TailNoLabel. +- destruct (transl_cond_single c0 r x x0) as [insn normal] eqn:F; inv EQ2. + apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. + destruct normal; TailNoLabel. +Qed. + +Remark transl_op_label: + forall op args r k c, + transl_op op args r k = OK c -> tail_nolabel k c. +Proof. +Opaque Int.eq. + unfold transl_op; intros; destruct op; TailNoLabel. +- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel. +- destruct (Float.eq_dec n Float.zero); TailNoLabel. +- destruct (Float32.eq_dec n Float32.zero); TailNoLabel. +- destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)). ++ eapply tail_nolabel_trans; [|apply addptrofs_label]. TailNoLabel. ++ TailNoLabel. +- apply opimm32_label; intros; exact I. +- apply opimm32_label; intros; exact I. +- apply opimm32_label; intros; exact I. +- apply opimm32_label; intros; exact I. +- destruct (Int.eq n Int.zero); TailNoLabel. +- apply opimm64_label; intros; exact I. +- apply opimm64_label; intros; exact I. +- apply opimm64_label; intros; exact I. +- apply opimm64_label; intros; exact I. +- destruct (Int.eq n Int.zero); TailNoLabel. +- eapply transl_cond_op_label; eauto. +Qed. + +Remark indexed_memory_access_label: + forall (mk_instr: ireg -> offset -> instruction) base ofs k, + (forall r o, nolabel (mk_instr r o)) -> + tail_nolabel k (indexed_memory_access mk_instr base ofs k). +Proof. + unfold indexed_memory_access; intros. + destruct Archi.ptr64. + destruct (make_immed64 (Ptrofs.to_int64 ofs)); TailNoLabel. + destruct (make_immed32 (Ptrofs.to_int ofs)); TailNoLabel. +Qed. + +Remark loadind_label: + forall base ofs ty dst k c, + loadind base ofs ty dst k = OK c -> tail_nolabel k c. +Proof. + unfold loadind; intros. + destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I. +Qed. + +Remark storeind_label: + forall src base ofs ty k c, + storeind src base ofs ty k = OK c -> tail_nolabel k c. +Proof. + unfold storeind; intros. + destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I. +Qed. + +Remark loadind_ptr_label: + forall base ofs dst k, tail_nolabel k (loadind_ptr base ofs dst k). +Proof. + intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I. +Qed. + +Remark storeind_ptr_label: + forall src base ofs k, tail_nolabel k (storeind_ptr src base ofs k). +Proof. + intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I. +Qed. + +Remark transl_memory_access_label: + forall (mk_instr: ireg -> offset -> instruction) addr args k c, + (forall r o, nolabel (mk_instr r o)) -> + transl_memory_access mk_instr addr args k = OK c -> + tail_nolabel k c. +Proof. + unfold transl_memory_access; intros; destruct addr; TailNoLabel; apply indexed_memory_access_label; auto. +Qed. + +Remark make_epilogue_label: + forall f k, tail_nolabel k (make_epilogue f k). +Proof. + unfold make_epilogue; intros. eapply tail_nolabel_trans. apply loadind_ptr_label. TailNoLabel. +Qed. + +Lemma transl_instr_label: + forall f i ep k c, + transl_instr f i ep k = OK c -> + match i with Mlabel lbl => c = Plabel lbl :: k | _ => tail_nolabel k c end. +Proof. + unfold transl_instr; intros; destruct i; TailNoLabel. +- eapply loadind_label; eauto. +- eapply storeind_label; eauto. +- destruct ep. eapply loadind_label; eauto. + eapply tail_nolabel_trans. apply loadind_ptr_label. eapply loadind_label; eauto. +- eapply transl_op_label; eauto. +- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. +- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. +- destruct s0; monadInv H; TailNoLabel. +- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]). +- eapply transl_cbranch_label; eauto. +- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]. +Qed. + +Lemma transl_instr_label': + forall lbl f i ep k c, + transl_instr f i ep k = OK c -> + find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k. +Proof. + intros. exploit transl_instr_label; eauto. + destruct i; try (intros [A B]; apply B). + intros. subst c. simpl. auto. +Qed. + +Lemma transl_code_label: + forall lbl f c ep tc, + transl_code f c ep = OK tc -> + match Mach.find_label lbl c with + | None => find_label lbl tc = None + | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc' + end. +Proof. + induction c; simpl; intros. + inv H. auto. + monadInv H. rewrite (transl_instr_label' lbl _ _ _ _ _ EQ0). + generalize (Mach.is_label_correct lbl a). + destruct (Mach.is_label lbl a); intros. + subst a. simpl in EQ. exists x; auto. + eapply IHc; eauto. +Qed. + +Lemma transl_find_label: + forall lbl f tf, + transf_function f = OK tf -> + match Mach.find_label lbl f.(Mach.fn_code) with + | None => find_label lbl tf.(fn_code) = None + | Some c => exists tc, find_label lbl tf.(fn_code) = Some tc /\ transl_code f c false = OK tc + end. +Proof. + intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. + monadInv EQ. rewrite transl_code'_transl_code in EQ0. unfold fn_code. + simpl. destruct (storeind_ptr_label X1 X2 (fn_retaddr_ofs f) x) as [A B]; rewrite B. + eapply transl_code_label; eauto. +Qed. + +End TRANSL_LABEL. + +(** A valid branch in a piece of Mach code translates to a valid ``go to'' + transition in the generated Asm code. *) + +Lemma find_label_goto_label: + forall f tf lbl rs m c' b ofs, + Genv.find_funct_ptr ge b = Some (Internal f) -> + transf_function f = OK tf -> + rs PC = Vptr b ofs -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + exists tc', exists rs', + goto_label tf lbl rs m = Next rs' m + /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc' + /\ forall r, r <> PC -> rs'#r = rs#r. +Proof. + intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2. + intros [tc [A B]]. + exploit label_pos_code_tail; eauto. instantiate (1 := 0). + intros [pos' [P [Q R]]]. + exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))). + split. unfold goto_label. rewrite P. rewrite H1. auto. + split. rewrite Pregmap.gss. constructor; auto. + rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q. + auto. omega. + generalize (transf_function_no_overflow _ _ H0). omega. + intros. apply Pregmap.gso; auto. +Qed. + +(** Existence of return addresses *) + +Lemma return_address_exists: + forall f sg ros c, is_tail (Mcall sg ros :: c) f.(Mach.fn_code) -> + exists ra, return_address_offset f c ra. +Proof. + intros. eapply Asmgenproof0.return_address_exists; eauto. +- intros. exploit transl_instr_label; eauto. + destruct i; try (intros [A B]; apply A). intros. subst c0. repeat constructor. +- intros. monadInv H0. + destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. monadInv EQ. + rewrite transl_code'_transl_code in EQ0. + exists x; exists true; split; auto. unfold fn_code. + constructor. apply (storeind_ptr_label X1 X2 (fn_retaddr_ofs f0) x). +- exact transf_function_no_overflow. +Qed. + +(** * Proof of semantic preservation *) + +(** Semantic preservation is proved using simulation diagrams + of the following form. +<< + st1 --------------- st2 + | | + t| *|t + | | + v v + st1'--------------- st2' +>> + The invariant is the [match_states] predicate below, which includes: +- The Asm code pointed by the PC register is the translation of + the current Mach code sequence. +- Mach register values and Asm register values agree. +*) + +Inductive match_states: Mach.state -> Asm.state -> Prop := + | match_states_intro: + forall s fb sp c ep ms m m' rs f tf tc + (STACKS: match_stack ge s) + (FIND: Genv.find_funct_ptr ge fb = Some (Internal f)) + (MEXT: Mem.extends m m') + (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc) + (AG: agree ms sp rs) + (DXP: ep = true -> rs#X30 = parent_sp s), + match_states (Mach.State s fb sp c ms m) + (Asm.State rs m') + | match_states_call: + forall s fb ms m m' rs + (STACKS: match_stack ge s) + (MEXT: Mem.extends m m') + (AG: agree ms (parent_sp s) rs) + (ATPC: rs PC = Vptr fb Ptrofs.zero) + (ATLR: rs RA = parent_ra s), + match_states (Mach.Callstate s fb ms m) + (Asm.State rs m') + | match_states_return: + forall s ms m m' rs + (STACKS: match_stack ge s) + (MEXT: Mem.extends m m') + (AG: agree ms (parent_sp s) rs) + (ATPC: rs PC = parent_ra s), + match_states (Mach.Returnstate s ms m) + (Asm.State rs m'). + +Lemma exec_straight_steps: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2, + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists rs2, + exec_straight tge tf c rs1 m1' k rs2 m2' + /\ agree ms2 sp rs2 + /\ (it1_is_parent ep i = true -> rs2#X30 = parent_sp s)) -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c ms2 m2) st'. +Proof. + intros. inversion H2. subst. monadInv H7. + exploit H3; eauto. intros [rs2 [A [B C]]]. + exists (State rs2 m2'); split. + eapply exec_straight_exec; eauto. + econstructor; eauto. eapply exec_straight_at; eauto. +Qed. + +Lemma exec_straight_steps_goto: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + it1_is_parent ep i = false -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists jmp, exists k', exists rs2, + exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2' + /\ agree ms2 sp rs2 + /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c' ms2 m2) st'. +Proof. + intros. inversion H3. subst. monadInv H9. + exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. + generalize (functions_transl _ _ _ H7 H8); intro FN. + generalize (transf_function_no_overflow _ _ H8); intro NOOV. + exploit exec_straight_steps_2; eauto. + intros [ofs' [PC2 CT2]]. + exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + eapply plus_right'. + eapply exec_straight_steps_1; eauto. + econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + traceEq. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +Qed. + +Lemma exec_straight_opt_steps_goto: + forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', + match_stack ge s -> + Mem.extends m2 m2' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + Mach.find_label lbl f.(Mach.fn_code) = Some c' -> + transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> + it1_is_parent ep i = false -> + (forall k c (TR: transl_instr f i ep k = OK c), + exists jmp, exists k', exists rs2, + exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2' + /\ agree ms2 sp rs2 + /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> + exists st', + plus step tge (State rs1 m1') E0 st' /\ + match_states (Mach.State s fb sp c' ms2 m2) st'. +Proof. + intros. inversion H3. subst. monadInv H9. + exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. + generalize (functions_transl _ _ _ H7 H8); intro FN. + generalize (transf_function_no_overflow _ _ H8); intro NOOV. + inv A. +- exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + apply plus_one. econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +- exploit exec_straight_steps_2; eauto. + intros [ofs' [PC2 CT2]]. + exploit find_label_goto_label; eauto. + intros [tc' [rs3 [GOTO [AT' OTH]]]]. + exists (State rs3 m2'); split. + eapply plus_right'. + eapply exec_straight_steps_1; eauto. + econstructor; eauto. + eapply find_instr_tail. eauto. + rewrite C. eexact GOTO. + traceEq. + econstructor; eauto. + apply agree_exten with rs2; auto with asmgen. + congruence. +Qed. + +(** We need to show that, in the simulation diagram, we cannot + take infinitely many Mach transitions that correspond to zero + transitions on the Asm side. Actually, all Mach transitions + correspond to at least one Asm transition, except the + transition from [Machsem.Returnstate] to [Machsem.State]. + So, the following integer measure will suffice to rule out + the unwanted behaviour. *) + +Definition measure (s: Mach.state) : nat := + match s with + | Mach.State _ _ _ _ _ _ => 0%nat + | Mach.Callstate _ _ _ _ => 0%nat + | Mach.Returnstate _ _ _ => 1%nat + end. + +Remark preg_of_not_X30: forall r, negb (mreg_eq r R30) = true -> IR X30 <> preg_of r. +Proof. + intros. change (IR X30) with (preg_of R30). red; intros. + exploit preg_of_injective; eauto. intros; subst r; discriminate. +Qed. + +(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *) + +Theorem step_simulation: + forall S1 t S2, Mach.step return_address_offset ge S1 t S2 -> + forall S1' (MS: match_states S1 S1'), + (exists S2', plus step tge S1' t S2' /\ match_states S2 S2') + \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat. +Proof. + induction 1; intros; inv MS. + +- (* Mlabel *) + left; eapply exec_straight_steps; eauto; intros. + monadInv TR. econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split. apply agree_nextinstr; auto. simpl; congruence. + +- (* Mgetstack *) + unfold load_stack in H. + exploit Mem.loadv_extends; eauto. intros [v' [A B]]. + rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit loadind_correct; eauto with asmgen. intros [rs' [P [Q R]]]. + exists rs'; split. eauto. + split. eapply agree_set_mreg; eauto with asmgen. congruence. + simpl; congruence. + +- (* Msetstack *) + unfold store_stack in H. + assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto. + exploit Mem.storev_extends; eauto. intros [m2' [A B]]. + left; eapply exec_straight_steps; eauto. + rewrite (sp_val _ _ _ AG) in A. intros. simpl in TR. + exploit storeind_correct; eauto with asmgen. intros [rs' [P Q]]. + exists rs'; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; intros. rewrite Q; auto with asmgen. + +- (* Mgetparam *) + assert (f0 = f) by congruence; subst f0. + unfold load_stack in *. + exploit Mem.loadv_extends. eauto. eexact H0. auto. + intros [parent' [A B]]. rewrite (sp_val _ _ _ AG) in A. + exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'. + exploit Mem.loadv_extends. eauto. eexact H1. auto. + intros [v' [C D]]. +Opaque loadind. + left; eapply exec_straight_steps; eauto; intros. monadInv TR. + destruct ep. +(* X30 contains parent *) + exploit loadind_correct. eexact EQ. + instantiate (2 := rs0). rewrite DXP; eauto. congruence. + intros [rs1 [P [Q R]]]. + exists rs1; split. eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen. + simpl; intros. rewrite R; auto with asmgen. + apply preg_of_not_X30; auto. +(* GPR11 does not contain parent *) + rewrite chunk_of_Tptr in A. + exploit loadind_ptr_correct. eexact A. congruence. intros [rs1 [P [Q R]]]. + exploit loadind_correct. eexact EQ. instantiate (2 := rs1). rewrite Q. eauto. congruence. + intros [rs2 [S [T U]]]. + exists rs2; split. eapply exec_straight_trans; eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto. + instantiate (1 := rs1#X30 <- (rs2#X30)). intros. + rewrite Pregmap.gso; auto with asmgen. + congruence. + intros. unfold Pregmap.set. destruct (PregEq.eq r' X30). congruence. auto with asmgen. + simpl; intros. rewrite U; auto with asmgen. + apply preg_of_not_X30; auto. + +- (* Mop *) + assert (eval_operation tge sp op (map rs args) m = Some v). + rewrite <- H. apply eval_operation_preserved. exact symbols_preserved. + exploit eval_operation_lessdef. eapply preg_vals; eauto. eauto. eexact H0. + intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. split. auto. + apply agree_set_undef_mreg with rs0; auto. + apply Val.lessdef_trans with v'; auto. + simpl; intros. destruct (andb_prop _ _ H1); clear H1. + rewrite R; auto. apply preg_of_not_X30; auto. +Local Transparent destroyed_by_op. + destruct op; simpl; auto; congruence. + +- (* Mload *) + assert (eval_addressing tge sp addr (map rs args) = Some a). + rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + exploit Mem.loadv_extends; eauto. intros [v' [C D]]. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_load_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. + split. eapply agree_set_undef_mreg; eauto. congruence. + intros; auto with asmgen. + simpl; congruence. + +- (* Mstore *) + assert (eval_addressing tge sp addr (map rs args) = Some a). + rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto. + exploit Mem.storev_extends; eauto. intros [m2' [C D]]. + left; eapply exec_straight_steps; eauto. + intros. simpl in TR. exploit transl_store_correct; eauto. intros [rs2 [P Q]]. + exists rs2; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; congruence. + +- (* Mcall *) + assert (f0 = f) by congruence. subst f0. + inv AT. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + eapply transf_function_no_overflow; eauto. + destruct ros as [rf|fid]; simpl in H; monadInv H5. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. + assert (rs0 x0 = Vptr f' Ptrofs.zero). + exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + econstructor; eauto. + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. ++ (* Direct call *) + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + econstructor; eauto. + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. + +- (* Mtailcall *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + eapply transf_function_no_overflow; eauto. exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]]. + destruct ros as [rf|fid]; simpl in H; monadInv H7. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. + assert (rs0 x0 = Vptr f' Ptrofs.zero). + exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption. ++ (* Direct call *) + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto. + +- (* Mbuiltin *) + inv AT. monadInv H4. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H3); intro NOOV. + exploit builtin_args_match; eauto. intros [vargs' [P Q]]. + exploit external_call_mem_extends; eauto. + intros [vres' [m2' [A [B [C D]]]]]. + left. econstructor; split. apply plus_one. + eapply exec_step_builtin. eauto. eauto. + eapply find_instr_tail; eauto. + erewrite <- sp_val by eauto. + eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + eauto. + econstructor; eauto. + instantiate (2 := tf); instantiate (1 := x). + unfold nextinstr. rewrite Pregmap.gss. + rewrite set_res_other. rewrite undef_regs_other_2. rewrite Pregmap.gso by congruence. + rewrite <- H1. simpl. econstructor; eauto. + eapply code_tail_next_int; eauto. + rewrite preg_notin_charact. intros. auto with asmgen. + auto with asmgen. + apply agree_nextinstr. eapply agree_set_res; auto. + eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto. apply Pregmap.gso; auto with asmgen. + congruence. + +- (* Mgoto *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H4. + exploit find_label_goto_label; eauto. intros [tc' [rs' [GOTO [AT2 INV]]]]. + left; exists (State rs' m'); split. + apply plus_one. econstructor; eauto. + eapply functions_transl; eauto. + eapply find_instr_tail; eauto. + simpl; eauto. + econstructor; eauto. + eapply agree_exten; eauto with asmgen. + congruence. + +- (* Mcond true *) + assert (f0 = f) by congruence. subst f0. + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_opt_steps_goto; eauto. + intros. simpl in TR. + exploit transl_cbranch_correct_true; eauto. intros (rs' & jmp & A & B & C). + exists jmp; exists k; exists rs'. + split. eexact A. + split. apply agree_exten with rs0; auto with asmgen. + exact B. + +- (* Mcond false *) + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit transl_cbranch_correct_false; eauto. intros (rs' & A & B). + exists rs'. + split. eexact A. + split. apply agree_exten with rs0; auto with asmgen. + simpl. congruence. + +- (* Mjumptable *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H6. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H5); intro NOOV. + exploit find_label_goto_label. eauto. eauto. + instantiate (2 := rs0#X5 <- Vundef #X31 <- Vundef). + Simpl. eauto. + eauto. + intros [tc' [rs' [A [B C]]]]. + exploit ireg_val; eauto. rewrite H. intros LD; inv LD. + left; econstructor; split. + apply plus_one. econstructor; eauto. + eapply find_instr_tail; eauto. + simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A. + econstructor; eauto. + eapply agree_undef_regs; eauto. + simpl. intros. rewrite C; auto with asmgen. Simpl. + congruence. + +- (* Mreturn *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. simpl in H6; monadInv H6. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + eapply transf_function_no_overflow; eauto. + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + +- (* internal function *) + exploit functions_translated; eauto. intros [tf [A B]]. monadInv B. + generalize EQ; intros EQ'. monadInv EQ'. + destruct (zlt Ptrofs.max_unsigned (list_length_z x0.(fn_code))); inversion EQ1. clear EQ1. subst x0. + unfold store_stack in *. + exploit Mem.alloc_extends. eauto. eauto. apply Zle_refl. apply Zle_refl. + intros [m1' [C D]]. + exploit Mem.storev_extends. eexact D. eexact H1. eauto. eauto. + intros [m2' [F G]]. + simpl chunk_of_type in F. + exploit Mem.storev_extends. eexact G. eexact H2. eauto. eauto. + intros [m3' [P Q]]. + (* Execution of function prologue *) + monadInv EQ0. rewrite transl_code'_transl_code in EQ1. + set (tfbody := Pallocframe (fn_stacksize f) (fn_link_ofs f) :: + storeind_ptr RA SP (fn_retaddr_ofs f) x0) in *. + set (tf := {| fn_sig := Mach.fn_sig f; fn_code := tfbody |}) in *. + set (rs2 := nextinstr (rs0#X30 <- (parent_sp s) #SP <- sp #X31 <- Vundef)). + exploit (storeind_ptr_correct tge tf SP (fn_retaddr_ofs f) RA x0 rs2 m2'). + rewrite chunk_of_Tptr in P. change (rs2 X1) with (rs0 X1). rewrite ATLR. + change (rs2 X2) with sp. eexact P. + congruence. congruence. + intros (rs3 & U & V). + assert (EXEC_PROLOGUE: + exec_straight tge tf + tf.(fn_code) rs0 m' + x0 rs3 m3'). + { change (fn_code tf) with tfbody; unfold tfbody. + apply exec_straight_step with rs2 m2'. + unfold exec_instr. rewrite C. fold sp. + rewrite <- (sp_val _ _ _ AG). rewrite chunk_of_Tptr in F. rewrite F. reflexivity. + reflexivity. + eexact U. } + exploit exec_straight_steps_2; eauto using functions_transl. omega. constructor. + intros (ofs' & X & Y). + left; exists (State rs3 m3'); split. + eapply exec_straight_steps_1; eauto. omega. constructor. + econstructor; eauto. + rewrite X; econstructor; eauto. + apply agree_exten with rs2; eauto with asmgen. + unfold rs2. + apply agree_nextinstr. apply agree_set_other; auto with asmgen. + apply agree_change_sp with (parent_sp s). + apply agree_undef_regs with rs0. auto. +Local Transparent destroyed_at_function_entry. + simpl; intros; Simpl. + unfold sp; congruence. + intros. rewrite V by auto with asmgen. reflexivity. + +- (* external function *) + exploit functions_translated; eauto. + intros [tf [A B]]. simpl in B. inv B. + exploit extcall_arguments_match; eauto. + intros [args' [C D]]. + exploit external_call_mem_extends; eauto. + intros [res' [m2' [P [Q [R S]]]]]. + left; econstructor; split. + apply plus_one. eapply exec_step_external; eauto. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + econstructor; eauto. + unfold loc_external_result. + apply agree_set_other; auto. apply agree_set_pair; auto. + +- (* return *) + inv STACKS. simpl in *. + right. split. omega. split. auto. + rewrite <- ATPC in H5. + econstructor; eauto. congruence. +Qed. + +Lemma transf_initial_states: + forall st1, Mach.initial_state prog st1 -> + exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2. +Proof. + intros. inversion H. unfold ge0 in *. + econstructor; split. + econstructor. + eapply (Genv.init_mem_transf_partial TRANSF); eauto. + replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero) + with (Vptr fb Ptrofs.zero). + econstructor; eauto. + constructor. + apply Mem.extends_refl. + split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence. + intros. rewrite Regmap.gi. auto. + unfold Genv.symbol_address. + rewrite (match_program_main TRANSF). + rewrite symbols_preserved. + unfold ge; rewrite H1. auto. +Qed. + +Lemma transf_final_states: + forall st1 st2 r, + match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r. +Proof. + intros. inv H0. inv H. constructor. assumption. + compute in H1. inv H1. + generalize (preg_val _ _ _ R10 AG). rewrite H2. intros LD; inv LD. auto. +Qed. + +Theorem transf_program_correct: + forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog). +Proof. + eapply forward_simulation_star with (measure := measure). + apply senv_preserved. + eexact transf_initial_states. + eexact transf_final_states. + exact step_simulation. +Qed. + +End PRESERVATION. -- cgit