diff options
Diffstat (limited to 'aarch64/TO_MERGE')
| -rw-r--r-- | aarch64/TO_MERGE/Archi.v | 100 | ||||
| -rw-r--r-- | aarch64/TO_MERGE/Asmgen.v | 712 | ||||
| -rw-r--r-- | aarch64/TO_MERGE/Asmgenproof.v | 2787 | ||||
| -rw-r--r-- | aarch64/TO_MERGE/Asmgenproof1.v | 1836 | ||||
| -rw-r--r-- | aarch64/TO_MERGE/TargetPrinter.ml | 862 | ||||
| -rw-r--r-- | aarch64/TO_MERGE/extractionMachdep.v | 45 |
6 files changed, 6342 insertions, 0 deletions
diff --git a/aarch64/TO_MERGE/Archi.v b/aarch64/TO_MERGE/Archi.v new file mode 100644 index 00000000..eb022db9 --- /dev/null +++ b/aarch64/TO_MERGE/Archi.v @@ -0,0 +1,100 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the GNU General Public License as published by *) +(* the Free Software Foundation, either version 2 of the License, or *) +(* (at your option) any later version. This file is also distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Architecture-dependent parameters for AArch64 *) + +From Flocq Require Import Binary Bits. +Require Import ZArith List. + +Definition ptr64 := true. + +Definition big_endian := false. + +Definition align_int64 := 8%Z. +Definition align_float64 := 8%Z. + +Definition splitlong := false. + +Lemma splitlong_ptr32: splitlong = true -> ptr64 = false. +Proof. + unfold splitlong, ptr64; congruence. +Qed. + +Definition default_nan_64 := (false, iter_nat 51 _ xO xH). +Definition default_nan_32 := (false, iter_nat 22 _ xO xH). + +(** Choose the first signaling NaN, if any; + otherwise choose the first NaN; + otherwise use default. *) + +Definition choose_nan (is_signaling: positive -> bool) + (default: bool * positive) + (l0: list (bool * positive)) : bool * positive := + let fix choose_snan (l1: list (bool * positive)) := + match l1 with + | nil => + match l0 with nil => default | n :: _ => n end + | ((s, p) as n) :: l1 => + if is_signaling p then n else choose_snan l1 + end + in choose_snan l0. + +Lemma choose_nan_idem: forall is_signaling default n, + choose_nan is_signaling default (n :: n :: nil) = + choose_nan is_signaling default (n :: nil). +Proof. + intros. destruct n as [s p]; unfold choose_nan; simpl. + destruct (is_signaling p); auto. +Qed. + +Definition choose_nan_64 := + choose_nan (fun p => negb (Pos.testbit p 51)) default_nan_64. + +Definition choose_nan_32 := + choose_nan (fun p => negb (Pos.testbit p 22)) default_nan_32. + +Lemma choose_nan_64_idem: forall n, + choose_nan_64 (n :: n :: nil) = choose_nan_64 (n :: nil). +Proof. intros; apply choose_nan_idem. Qed. + +Lemma choose_nan_32_idem: forall n, + choose_nan_32 (n :: n :: nil) = choose_nan_32 (n :: nil). +Proof. intros; apply choose_nan_idem. Qed. + +Definition fma_order {A: Type} (x y z: A) := (z, x, y). + +Definition fma_invalid_mul_is_nan := true. + +Definition float_of_single_preserves_sNaN := false. + +Global Opaque ptr64 big_endian splitlong + default_nan_64 choose_nan_64 + default_nan_32 choose_nan_32 + fma_order fma_invalid_mul_is_nan + float_of_single_preserves_sNaN. + +(** Which ABI to implement *) + +<<<<<<< HEAD +Parameter pic_code: unit -> bool. + +Definition has_notrap_loads := false. +======= +Inductive abi_kind: Type := + | AAPCS64 (**r ARM's standard as used in Linux and other ELF platforms *) + | Apple. (**r the variant used in macOS and iOS *) + +Parameter abi: abi_kind. +>>>>>>> master diff --git a/aarch64/TO_MERGE/Asmgen.v b/aarch64/TO_MERGE/Asmgen.v new file mode 100644 index 00000000..c8e48b40 --- /dev/null +++ b/aarch64/TO_MERGE/Asmgen.v @@ -0,0 +1,712 @@ +(* *************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Sylvain Boulmé Grenoble-INP, VERIMAG *) +(* Justus Fasse UGA, VERIMAG *) +(* Xavier Leroy INRIA Paris-Rocquencourt *) +(* David Monniaux CNRS, VERIMAG *) +(* Cyril Six Kalray *) +(* Léo Gourdin UGA, VERIMAG *) +(* *) +(* Copyright Kalray. Copyright VERIMAG. All rights reserved. *) +(* This file is distributed under the terms of the INRIA *) +(* Non-Commercial License Agreement. *) +(* *) +(* *************************************************************) + +Require Import Recdef Coqlib Zwf Zbits. +Require Import Errors AST Integers Floats Op. +<<<<<<< HEAD +Require Import Locations Compopts. +Require Import Mach Asm Asmblock Asmblockgen Machblockgen PostpassScheduling. +======= +Require Import Locations Mach Asm. +Require SelectOp. + +Local Open Scope string_scope. +Local Open Scope list_scope. +Local Open Scope error_monad_scope. + +(** Alignment check for symbols *) + +Parameter symbol_is_aligned : ident -> Z -> bool. +(** [symbol_is_aligned id sz] checks whether the symbol [id] is [sz] aligned *) + +(** Extracting integer or float registers. *) + +Definition ireg_of (r: mreg) : res ireg := + match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.ireg_of") end. + +Definition freg_of (r: mreg) : res freg := + match preg_of r with FR mr => OK mr | _ => Error(msg "Asmgen.freg_of") end. + +(** Recognition of immediate arguments for logical integer operations.*) + +(** Valid immediate arguments are repetitions of a bit pattern [B] + of length [e] = 2, 4, 8, 16, 32 or 64. + The bit pattern [B] must be of the form [0*1*0*] or [1*0*1*] + but must not be all zeros or all ones. *) + +(** The following automaton recognizes [0*1*0*|1*0*1*]. +<< + 0 1 0 + / \ / \ / \ + \ / \ / \ / + -0--> [B] --1--> [D] --0--> [F] + / + [A] + \ + -1--> [C] --0--> [E] --1--> [G] + / \ / \ / \ + \ / \ / \ / + 1 0 1 +>> +*) + +Module Automaton. + +Inductive state : Type := SA | SB | SC | SD | SE | SF | SG | Sbad. + +Definition start := SA. + +Definition next (s: state) (b: bool) := + match s, b with + | SA,false => SB | SA,true => SC + | SB,false => SB | SB,true => SD + | SC,false => SE | SC,true => SC + | SD,false => SF | SD,true => SD + | SE,false => SE | SE,true => SG + | SF,false => SF | SF,true => Sbad + | SG,false => Sbad | SG,true => SG + | Sbad,_ => Sbad + end. + +Definition accepting (s: state) := + match s with + | SA | SB | SC | SD | SE | SF | SG => true + | Sbad => false + end. + +Fixpoint run (len: nat) (s: state) (x: Z) : bool := + match len with + | Datatypes.O => accepting s + | Datatypes.S len => run len (next s (Z.odd x)) (Z.div2 x) + end. + +End Automaton. + +(** The following function determines the candidate length [e], + ensuring that [x] is a repetition [BB...B] + of a bit pattern [B] of length [e]. *) + +Definition logical_imm_length (x: Z) (sixtyfour: bool) : nat := + (** [test n] checks that the low [2n] bits of [x] are of the + form [BB], that is, two occurrences of the same [n] bits *) + let test (n: Z) : bool := + Z.eqb (Zzero_ext n x) (Zzero_ext n (Z.shiftr x n)) in + (** If [test n] fails, we know that the candidate length [e] is + at least [2n]. Hence we test with decreasing values of [n]: + 32, 16, 8, 4, 2. *) + if sixtyfour && negb (test 32) then 64%nat + else if negb (test 16) then 32%nat + else if negb (test 8) then 16%nat + else if negb (test 4) then 8%nat + else if negb (test 2) then 4%nat + else 2%nat. + +(** A valid logical immediate is +- neither [0] nor [-1]; +- composed of a repetition [BBBBB] of a bit-pattern [B] of length [e] +- the low [e] bits of the number, that is, [B], match [0*1*0*] or [1*0*1*]. +*) + +Definition is_logical_imm32 (x: int) : bool := + negb (Int.eq x Int.zero) && negb (Int.eq x Int.mone) && + Automaton.run (logical_imm_length (Int.unsigned x) false) + Automaton.start (Int.unsigned x). + +Definition is_logical_imm64 (x: int64) : bool := + negb (Int64.eq x Int64.zero) && negb (Int64.eq x Int64.mone) && + Automaton.run (logical_imm_length (Int64.unsigned x) true) + Automaton.start (Int64.unsigned x). +>>>>>>> master + + +Local Open Scope error_monad_scope. + +(** Functions called by the Asmexpand ocaml file, inspired and adapted from Asmblockgen.v *) + +Module Asmgen_expand. + +(* Load immediate *) + +Definition loadimm_k (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + List.fold_right (fun np k => Asm.Pmovk sz rd (fst np) (snd np) :: k) k l. + +Definition loadimm_z (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + match l with + | nil => Asm.Pmovz sz rd 0 0 :: k + | (n1, p1) :: l => Asm.Pmovz sz rd n1 p1 :: loadimm_k sz rd l k + end. + +Definition loadimm_n (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code := + match l with + | nil => Asm.Pmovn sz rd 0 0 :: k + | (n1, p1) :: l => Asm.Pmovn sz rd n1 p1 :: loadimm_k sz rd (negate_decomposition l) k + end. + +Definition loadimm (sz: isize) (rd: ireg) (n: Z) (k: code) : code := + let N := match sz with W => 2%nat | X => 4%nat end in + let dz := decompose_int N n 0 in + let dn := decompose_int N (Z.lnot n) 0 in + if Nat.leb (List.length dz) (List.length dn) + then loadimm_z sz rd dz k + else loadimm_n sz rd dn k. + +Definition loadimm32 (rd: ireg) (n: int) (k: code) : code := + if is_logical_imm32 n + then Asm.Porrimm W rd XZR (Int.unsigned n) :: k + else loadimm W rd (Int.unsigned n) k. + +Definition loadimm64 (rd: ireg) (n: int64) (k: code) : code := + if is_logical_imm64 n + then Asm.Porrimm X rd XZR (Int64.unsigned n) :: k + else loadimm X rd (Int64.unsigned n) k. + +(* Add immediate *) + +Definition addimm_aux (insn: iregsp -> iregsp -> Z -> instruction) + (rd r1: iregsp) (n: Z) (k: code) := + let nlo := Zzero_ext 12 n in + let nhi := n - nlo in + if Z.eqb nhi 0 then + insn rd r1 nlo :: k + else if Z.eqb nlo 0 then + insn rd r1 nhi :: k + else + insn rd r1 nhi :: insn rd rd nlo :: k. + +Definition addimm64 (rd r1: iregsp) (n: int64) (k: code) : code := + let m := Int64.neg n in + if Int64.eq n (Int64.zero_ext 24 n) then + addimm_aux (Asm.Paddimm X) rd r1 (Int64.unsigned n) k + else if Int64.eq m (Int64.zero_ext 24 m) then + addimm_aux (Asm.Psubimm X) rd r1 (Int64.unsigned m) k + else if Int64.lt n Int64.zero then +<<<<<<< HEAD + loadimm64 X16 m (Asm.Psubext rd r1 X16 (EOuxtx Int.zero) :: k) +======= + loadimm64 X16 m (Psubext rd r1 X16 (EOuxtx Int.zero) :: k) + else + loadimm64 X16 n (Paddext rd r1 X16 (EOuxtx Int.zero) :: k). + +(** Logical immediate *) + +Definition logicalimm32 + (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1: ireg) (n: int) (k: code) : code := + if is_logical_imm32 n + then insn1 rd r1 (Int.unsigned n) :: k + else loadimm32 X16 n (insn2 rd r1 X16 SOnone :: k). + +Definition logicalimm64 + (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1: ireg) (n: int64) (k: code) : code := + if is_logical_imm64 n + then insn1 rd r1 (Int64.unsigned n) :: k + else loadimm64 X16 n (insn2 rd r1 X16 SOnone :: k). + +(** Sign- or zero-extended arithmetic *) + +Definition transl_extension (ex: extension) (a: int) : extend_op := + match ex with Xsgn32 => EOsxtw a | Xuns32 => EOuxtw a end. + +Definition move_extended_base + (rd: ireg) (r1: ireg) (ex: extension) (k: code) : code := + match ex with + | Xsgn32 => Pcvtsw2x rd r1 :: k + | Xuns32 => Pcvtuw2x rd r1 :: k + end. + +Definition move_extended + (rd: ireg) (r1: ireg) (ex: extension) (a: int) (k: code) : code := + if Int.eq a Int.zero then + move_extended_base rd r1 ex k + else + move_extended_base rd r1 ex (Padd X rd XZR rd (SOlsl a) :: k). + +Definition arith_extended + (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction) + (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (rd r1 r2: ireg) (ex: extension) (a: int) (k: code) : code := + if Int.ltu a (Int.repr 5) then + insnX rd r1 r2 (transl_extension ex a) :: k + else + move_extended_base X16 r2 ex (insnS rd r1 X16 (SOlsl a) :: k). + +(** Extended right shift *) + +Definition shrx32 (rd r1: ireg) (n: int) (k: code) : code := + if Int.eq n Int.zero then + Pmov rd r1 :: k + else + Porr W X16 XZR r1 (SOasr (Int.repr 31)) :: + Padd W X16 r1 X16 (SOlsr (Int.sub Int.iwordsize n)) :: + Porr W rd XZR X16 (SOasr n) :: k. + +Definition shrx64 (rd r1: ireg) (n: int) (k: code) : code := + if Int.eq n Int.zero then + Pmov rd r1 :: k + else + Porr X X16 XZR r1 (SOasr (Int.repr 63)) :: + Padd X X16 r1 X16 (SOlsr (Int.sub Int64.iwordsize' n)) :: + Porr X rd XZR X16 (SOasr n) :: k. + +(** Load the address [id + ofs] in [rd] *) + +Definition loadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (k: code) : code := + if SelectOp.symbol_is_relocatable id then + if Ptrofs.eq ofs Ptrofs.zero then + Ploadsymbol rd id :: k + else + Ploadsymbol rd id :: addimm64 rd rd (Ptrofs.to_int64 ofs) k +>>>>>>> master + else + loadimm64 X16 n (Asm.Paddext rd r1 X16 (EOuxtx Int.zero) :: k). + +(** Register-indexed stores *) + +Definition indexed_memory_access (insn: Asm.addressing -> instruction) + (sz: Z) (base: iregsp) (ofs: ptrofs) (k: code) := + let ofs := Ptrofs.to_int64 ofs in + if offset_representable sz ofs + then insn (ADimm base ofs) :: k + else loadimm64 X16 ofs (insn (ADreg base X16) :: k). + +Definition storeptr (src: ireg) (base: iregsp) (ofs: ptrofs) (k: code) := + indexed_memory_access (Asm.Pstrx src) 8 base ofs k. + +End Asmgen_expand. + +(** * Translation from Asmblock to assembly language + Inspired from the KVX backend (see kvx/Asm.v and kvx/Asmgen.v) *) + +Module Asmblock_TRANSF. +(* STUB *) + +Definition ireg_of_preg (p : Asm.preg) : res ireg := + match p with + | DR (IR (RR1 r)) => OK r + | _ => Error (msg "Asmgen.ireg_of_preg") + end. + +Definition freg_of_preg (p : Asm.preg) : res freg := + match p with + | DR (FR r) => OK r + | _ => Error (msg "Asmgen.freg_of_preg") + end. + +Definition iregsp_of_preg (p : Asm.preg) : res iregsp := + match p with + | DR (IR r) => OK r + | _ => Error (msg "Asmgen.iregsp_of_preg") + end. + +Definition basic_to_instruction (b: basic) : res Asm.instruction := + match b with + (* Aithmetic instructions *) + | PArith (PArithP (Padrp id ofs) rd) => do rd' <- ireg_of_preg rd; + OK (Asm.Padrp rd' id ofs) + | PArith (PArithP (Pmovz sz n pos) rd) => do rd' <- ireg_of_preg rd; + OK (Asm.Pmovz sz rd' n pos) + | PArith (PArithP (Pmovn sz n pos) rd) => do rd' <- ireg_of_preg rd; + OK (Asm.Pmovn sz rd' n pos) + | PArith (PArithP (Pfmovimms f) rd) => do rd' <- freg_of_preg rd; + OK (Asm.Pfmovimms rd' f) + | PArith (PArithP (Pfmovimmd f) rd) => do rd' <- freg_of_preg rd; + OK (Asm.Pfmovimmd rd' f) + + | PArith (PArithPP (Pmovk sz n pos) rd rs) => + if (Asm.preg_eq rd rs) then ( + do rd' <- ireg_of_preg rd; + OK (Asm.Pmovk sz rd' n pos) + ) else + Error (msg "Asmgen.basic_to_instruction: Pmovk uses a single register as both source and target") + | PArith (PArithPP Pmov rd rs) => do rd' <- iregsp_of_preg rd; + do rs' <- iregsp_of_preg rs; + OK (Asm.Pmov rd' rs') + | PArith (PArithPP (Paddadr id ofs) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Paddadr rd' rs' id ofs) + | PArith (PArithPP (Psbfiz sz r s) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Psbfiz sz rd' rs' r s) + | PArith (PArithPP (Psbfx sz r s) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Psbfx sz rd' rs' r s) + | PArith (PArithPP (Pubfiz sz r s) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Pubfiz sz rd' rs' r s) + | PArith (PArithPP (Pubfx sz r s) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Pubfx sz rd' rs' r s) + | PArith (PArithPP Pfmov rd rs) => do rd' <- freg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfmov rd' rs') + | PArith (PArithPP Pfcvtds rd rs) => do rd' <- freg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfcvtds rd' rs') + | PArith (PArithPP Pfcvtsd rd rs) => do rd' <- freg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfcvtsd rd' rs') + | PArith (PArithPP (Pfabs sz) rd rs) => do rd' <- freg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfabs sz rd' rs') + | PArith (PArithPP (Pfneg sz) rd rs) => do rd' <- freg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfneg sz rd' rs') + | PArith (PArithPP (Pscvtf fsz isz) rd rs) => do rd' <- freg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Pscvtf fsz isz rd' rs') + | PArith (PArithPP (Pucvtf fsz isz) rd rs) => do rd' <- freg_of_preg rd; + do rs' <- ireg_of_preg rs; + OK (Asm.Pucvtf fsz isz rd' rs') + | PArith (PArithPP (Pfcvtzs isz fsz) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfcvtzs isz fsz rd' rs') + | PArith (PArithPP (Pfcvtzu isz fsz) rd rs) => do rd' <- ireg_of_preg rd; + do rs' <- freg_of_preg rs; + OK (Asm.Pfcvtzu isz fsz rd' rs') + | PArith (PArithPP (Paddimm sz n) rd rs) => do rd' <- iregsp_of_preg rd; + do rs' <- iregsp_of_preg rs; + OK (Asm.Paddimm sz rd' rs' n) + | PArith (PArithPP (Psubimm sz n) rd rs) => do rd' <- iregsp_of_preg rd; + do rs' <- iregsp_of_preg rs; + OK (Asm.Psubimm sz rd' rs' n) + + | PArith (PArithPPP (Pasrv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Pasrv sz rd' r1' r2') + | PArith (PArithPPP (Plslv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Plslv sz rd' r1' r2') + | PArith (PArithPPP (Plsrv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Plsrv sz rd' r1' r2') + | PArith (PArithPPP (Prorv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Prorv sz rd' r1' r2') + | PArith (PArithPPP Psmulh rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Psmulh rd' r1' r2') + | PArith (PArithPPP Pumulh rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Pumulh rd' r1' r2') + | PArith (PArithPPP (Psdiv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Psdiv sz rd' r1' r2') + | PArith (PArithPPP (Pudiv sz) rd r1 r2) => do rd' <- ireg_of_preg rd; + do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Pudiv sz rd' r1' r2') + | PArith (PArithPPP (Paddext x) rd r1 r2) => do rd' <- iregsp_of_preg rd; + do r1' <- iregsp_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Paddext rd' r1' r2' x) + | PArith (PArithPPP (Psubext x) rd r1 r2) => do rd' <- iregsp_of_preg rd; + do r1' <- iregsp_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Psubext rd' r1' r2' x) + | PArith (PArithPPP (Pfadd sz) rd r1 r2) => do rd' <- freg_of_preg rd; + do r1' <- freg_of_preg r1; + do r2' <- freg_of_preg r2; + OK (Asm.Pfadd sz rd' r1' r2') + | PArith (PArithPPP (Pfdiv sz) rd r1 r2) => do rd' <- freg_of_preg rd; + do r1' <- freg_of_preg r1; + do r2' <- freg_of_preg r2; + OK (Asm.Pfdiv sz rd' r1' r2') + | PArith (PArithPPP (Pfmul sz) rd r1 r2) => do rd' <- freg_of_preg rd; + do r1' <- freg_of_preg r1; + do r2' <- freg_of_preg r2; + OK (Asm.Pfmul sz rd' r1' r2') + | PArith (PArithPPP (Pfsub sz) rd r1 r2) => do rd' <- freg_of_preg rd; + do r1' <- freg_of_preg r1; + do r2' <- freg_of_preg r2; + OK (Asm.Pfsub sz rd' r1' r2') + + | PArith (PArithRR0 (Pandimm sz n) rd r1) => OK (Asm.Pandimm sz rd r1 n) + | PArith (PArithRR0 (Peorimm sz n) rd r1) => OK (Asm.Peorimm sz rd r1 n) + | PArith (PArithRR0 (Porrimm sz n) rd r1) => OK (Asm.Porrimm sz rd r1 n) + + + | PArith (PArithRR0R (Padd sz s) rd r1 r2) => OK (Asm.Padd sz rd r1 r2 s) + | PArith (PArithRR0R (Psub sz s) rd r1 r2) => OK (Asm.Psub sz rd r1 r2 s) + | PArith (PArithRR0R (Pand sz s) rd r1 r2) => OK (Asm.Pand sz rd r1 r2 s) + | PArith (PArithRR0R (Pbic sz s) rd r1 r2) => OK (Asm.Pbic sz rd r1 r2 s) + | PArith (PArithRR0R (Peon sz s) rd r1 r2) => OK (Asm.Peon sz rd r1 r2 s) + | PArith (PArithRR0R (Peor sz s) rd r1 r2) => OK (Asm.Peor sz rd r1 r2 s) + | PArith (PArithRR0R (Porr sz s) rd r1 r2) => OK (Asm.Porr sz rd r1 r2 s) + | PArith (PArithRR0R (Porn sz s) rd r1 r2) => OK (Asm.Porn sz rd r1 r2 s) + + | PArith (PArithARRRR0 (Pmadd sz) rd r1 r2 r3) => OK (Asm.Pmadd sz rd r1 r2 r3) + | PArith (PArithARRRR0 (Pmsub sz) rd r1 r2 r3) => OK (Asm.Pmsub sz rd r1 r2 r3) + + | PArith (PArithComparisonPP (Pcmpext x) r1 r2) => do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Pcmpext r1' r2' x) + | PArith (PArithComparisonPP (Pcmnext x) r1 r2) => do r1' <- ireg_of_preg r1; + do r2' <- ireg_of_preg r2; + OK (Asm.Pcmnext r1' r2' x) + | PArith (PArithComparisonPP (Pfcmp sz) r1 r2) => do r1' <- freg_of_preg r1; + do r2' <- freg_of_preg r2; + OK (Asm.Pfcmp sz r1' r2') + + | PArith (PArithComparisonR0R (Pcmp is s) r1 r2) => OK (Asm.Pcmp is r1 r2 s) + | PArith (PArithComparisonR0R (Pcmn is s) r1 r2) => OK (Asm.Pcmn is r1 r2 s) + | PArith (PArithComparisonR0R (Ptst is s) r1 r2) => OK (Asm.Ptst is r1 r2 s) + + | PArith (PArithComparisonP (Pcmpimm sz n) r1) => do r1' <- ireg_of_preg r1; + OK (Asm.Pcmpimm sz r1' n) + | PArith (PArithComparisonP (Pcmnimm sz n) r1) => do r1' <- ireg_of_preg r1; + OK (Asm.Pcmnimm sz r1' n) + | PArith (PArithComparisonP (Ptstimm sz n) r1) => do r1' <- ireg_of_preg r1; + OK (Asm.Ptstimm sz r1' n) + | PArith (PArithComparisonP (Pfcmp0 sz) r1) => do r1' <- freg_of_preg r1; + OK (Asm.Pfcmp0 sz r1') + + | PArith (Pcset rd c) => OK (Asm.Pcset rd c) + | PArith (Pfmovi fsz rd r1) => OK (Asm.Pfmovi fsz rd r1) + | PArith (Pcsel rd r1 r2 c) => + match r1, r2 with + | IR r1', IR r2' => do rd' <- ireg_of_preg rd; + do r1'' <- ireg_of_preg r1'; + do r2'' <- ireg_of_preg r2'; + OK (Asm.Pcsel rd' r1'' r2'' c) + | FR r1', FR r2' => do rd' <- freg_of_preg rd; + do r1'' <- freg_of_preg r1'; + do r2'' <- freg_of_preg r2'; + OK (Asm.Pfsel rd' r1'' r2'' c) + | _, _ => Error (msg "Asmgen.basic_to_instruction: Pcsel is only defind on iregs and fregs.") + end + | PArith (Pfnmul fsz rd r1 r2) => OK (Asm.Pfnmul fsz rd r1 r2) + + | PLoad (PLd_rd_a Pldrw rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrw rd' a) + | PLoad (PLd_rd_a Pldrw_a rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrw_a rd' a) + | PLoad (PLd_rd_a Pldrx rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrx rd' a) + | PLoad (PLd_rd_a Pldrx_a rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrx_a rd' a) + | PLoad (PLd_rd_a (Pldrb sz) rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrb sz rd' a) + | PLoad (PLd_rd_a (Pldrsb sz) rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrsb sz rd' a) + | PLoad (PLd_rd_a (Pldrh sz) rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrh sz rd' a) + | PLoad (PLd_rd_a (Pldrsh sz) rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrsh sz rd' a) + | PLoad (PLd_rd_a Pldrzw rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrzw rd' a) + | PLoad (PLd_rd_a Pldrsw rd a) => do rd' <- ireg_of_preg rd; OK (Asm.Pldrsw rd' a) + + | PLoad (PLd_rd_a Pldrs rd a) => do rd' <- freg_of_preg rd; OK (Asm.Pldrs rd' a) + | PLoad (PLd_rd_a Pldrd rd a) => do rd' <- freg_of_preg rd; OK (Asm.Pldrd rd' a) + | PLoad (PLd_rd_a Pldrd_a rd a) => do rd' <- freg_of_preg rd; OK (Asm.Pldrd_a rd' a) + + | PLoad (Pldp Pldpw rd1 rd2 chk1 chk2 a) => do rd1' <- ireg_of_preg rd1; + do rd2' <- ireg_of_preg rd2; + OK (Asm.Pldpw rd1' rd2' chk1 chk2 a) + | PLoad (Pldp Pldpx rd1 rd2 chk1 chk2 a) => do rd1' <- ireg_of_preg rd1; + do rd2' <- ireg_of_preg rd2; + OK (Asm.Pldpx rd1' rd2' chk1 chk2 a) + | PLoad (Pldp Pldps rd1 rd2 chk1 chk2 a) => do rd1' <- freg_of_preg rd1; + do rd2' <- freg_of_preg rd2; + OK (Asm.Pldps rd1' rd2' chk1 chk2 a) + | PLoad (Pldp Pldpd rd1 rd2 chk1 chk2 a) => do rd1' <- freg_of_preg rd1; + do rd2' <- freg_of_preg rd2; + OK (Asm.Pldpd rd1' rd2' chk1 chk2 a) + + | PStore (PSt_rs_a Pstrw r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrw r' a) + | PStore (PSt_rs_a Pstrw_a r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrw_a r' a) + | PStore (PSt_rs_a Pstrx r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrx r' a) + | PStore (PSt_rs_a Pstrx_a r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrx_a r' a) + | PStore (PSt_rs_a Pstrb r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrb r' a) + | PStore (PSt_rs_a Pstrh r a) => do r' <- ireg_of_preg r; OK (Asm.Pstrh r' a) + + | PStore (PSt_rs_a Pstrs r a) => do r' <- freg_of_preg r; OK (Asm.Pstrs r' a) + | PStore (PSt_rs_a Pstrd r a) => do r' <- freg_of_preg r; OK (Asm.Pstrd r' a) + | PStore (PSt_rs_a Pstrd_a r a) => do r' <- freg_of_preg r; OK (Asm.Pstrd_a r' a) + + | PStore (Pstp Pstpw rs1 rs2 chk1 chk2 a) => do rs1' <- ireg_of_preg rs1; + do rs2' <- ireg_of_preg rs2; + OK (Asm.Pstpw rs1' rs2' chk1 chk2 a) + | PStore (Pstp Pstpx rs1 rs2 chk1 chk2 a) => do rs1' <- ireg_of_preg rs1; + do rs2' <- ireg_of_preg rs2; + OK (Asm.Pstpx rs1' rs2' chk1 chk2 a) + | PStore (Pstp Pstps rs1 rs2 chk1 chk2 a) => do rs1' <- freg_of_preg rs1; + do rs2' <- freg_of_preg rs2; + OK (Asm.Pstps rs1' rs2' chk1 chk2 a) + | PStore (Pstp Pstpd rs1 rs2 chk1 chk2 a) => do rs1' <- freg_of_preg rs1; + do rs2' <- freg_of_preg rs2; + OK (Asm.Pstpd rs1' rs2' chk1 chk2 a) + + | Pallocframe sz linkofs => OK (Asm.Pallocframe sz linkofs) + | Pfreeframe sz linkofs => OK (Asm.Pfreeframe sz linkofs) + + | Ploadsymbol rd id => OK (Asm.Ploadsymbol rd id) + + | Pcvtsw2x rd r1 => OK (Asm.Pcvtsw2x rd r1) + + | Pcvtuw2x rd r1 => OK (Asm.Pcvtuw2x rd r1) + + | Pcvtx2w rd => OK (Asm.Pcvtx2w rd) + | Pnop => OK (Asm.Pnop) + end. + +<<<<<<< HEAD +Definition cf_instruction_to_instruction (cfi: cf_instruction) : Asm.instruction := + match cfi with + | Pb l => Asm.Pb l + | Pbc c lbl => Asm.Pbc c lbl + | Pbl id sg => Asm.Pbl id sg + | Pbs id sg => Asm.Pbs id sg + | Pblr r sg => Asm.Pblr r sg + | Pbr r sg => Asm.Pbr r sg + | Pret r => Asm.Pret r + | Pcbnz sz r lbl => Asm.Pcbnz sz r lbl + | Pcbz sz r lbl => Asm.Pcbz sz r lbl + | Ptbnz sz r n lbl => Asm.Ptbnz sz r n lbl + | Ptbz sz r n lbl => Asm.Ptbz sz r n lbl + | Pbtbl r1 tbl => Asm.Pbtbl r1 tbl +======= +(** Translation of addressing modes *) + +Definition offset_representable (sz: Z) (ofs: int64) : bool := + let isz := Int64.repr sz in + (** either unscaled 9-bit signed *) + Int64.eq ofs (Int64.sign_ext 9 ofs) || + (** or scaled 12-bit unsigned *) + (Int64.eq (Int64.modu ofs isz) Int64.zero + && Int64.ltu ofs (Int64.shl isz (Int64.repr 12))). + +Definition transl_addressing (sz: Z) (addr: Op.addressing) (args: list mreg) + (insn: Asm.addressing -> instruction) (k: code) : res code := + match addr, args with + | Aindexed ofs, a1 :: nil => + do r1 <- ireg_of a1; + if offset_representable sz ofs then + OK (insn (ADimm r1 ofs) :: k) + else + OK (loadimm64 X16 ofs (insn (ADreg r1 X16) :: k)) + | Aindexed2, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (insn (ADreg r1 r2) :: k) + | Aindexed2shift a, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + if Int.eq a Int.zero then + OK (insn (ADreg r1 r2) :: k) + else if Int.eq (Int.shl Int.one a) (Int.repr sz) then + OK (insn (ADlsl r1 r2 a) :: k) + else + OK (Padd X X16 r1 r2 (SOlsl a) :: insn (ADimm X16 Int64.zero) :: k) + | Aindexed2ext x a, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + if Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz) then + OK (insn (match x with Xsgn32 => ADsxt r1 r2 a + | Xuns32 => ADuxt r1 r2 a end) :: k) + else + OK (arith_extended Paddext (Padd X) X16 r1 r2 x a + (insn (ADimm X16 Int64.zero) :: k)) + | Aglobal id ofs, nil => + assertion (negb (SelectOp.symbol_is_relocatable id)); + if Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero && symbol_is_aligned id sz + then OK (Padrp X16 id ofs :: insn (ADadr X16 id ofs) :: k) + else OK (loadsymbol X16 id ofs (insn (ADimm X16 Int64.zero) :: k)) + | Ainstack ofs, nil => + let ofs := Ptrofs.to_int64 ofs in + if offset_representable sz ofs then + OK (insn (ADimm XSP ofs) :: k) + else + OK (loadimm64 X16 ofs (insn (ADreg XSP X16) :: k)) + | _, _ => + Error(msg "Asmgen.transl_addressing") +>>>>>>> master + end. + +Definition control_to_instruction (c: control) := + match c with + | PCtlFlow i => cf_instruction_to_instruction i + | Pbuiltin ef args res => Asm.Pbuiltin ef (List.map (map_builtin_arg DR) args) (map_builtin_res DR res) + end. + +Fixpoint unfold_label (ll: list label) := + match ll with + | nil => nil + | l :: ll => Plabel l :: unfold_label ll + end. + +Fixpoint unfold_body (lb: list basic) : res Asm.code := + match lb with + | nil => OK nil + | b :: lb => + (* x_is: x's instructions *) + do b_is <- basic_to_instruction b; + do lb_is <- unfold_body lb; + OK (b_is :: lb_is) + end. + +Definition unfold_exit (oc: option control) := + match oc with + | None => nil + | Some c => control_to_instruction c :: nil + end. + +Definition unfold_bblock (bb: bblock) := + let lbl := unfold_label (header bb) in + (* + * With this dynamically checked assumption on a previous optimization we + * can show that [Asmblock.label_pos] and [Asm.label_pos] retrieve the same + * exact address. Maintaining this property allows us to use the simple + * formulation of match_states defined as equality. + * Otherwise we would have to deal with the case of a basic block header + * that has multiple labels. Asmblock.label_pos will, for all labels, point + * to the same location at the beginning of the basic block. Asm.label_pos + * on the other hand could return a position pointing into the original + * basic block. + *) + if zle (list_length_z (header bb)) 1 then + do bo_is <- unfold_body (body bb); + OK (lbl ++ bo_is ++ unfold_exit (exit bb)) + else + Error (msg "Asmgen.unfold_bblock: Multiple labels were generated."). + +Fixpoint unfold (bbs: Asmblock.bblocks) : res Asm.code := + match bbs with + | nil => OK (nil) + | bb :: bbs' => + do bb_is <- unfold_bblock bb; + do bbs'_is <- unfold bbs'; + OK (bb_is ++ bbs'_is) + end. + +Definition transf_function (f: Asmblock.function) : res Asm.function := + do c <- unfold (Asmblock.fn_blocks f); + if zlt Ptrofs.max_unsigned (list_length_z c) + then Error (msg "Asmgen.trans_function: code size exceeded") + else OK {| Asm.fn_sig := Asmblock.fn_sig f; Asm.fn_code := c |}. + +Definition transf_fundef (f: Asmblock.fundef) : res Asm.fundef := + transf_partial_fundef transf_function f. + +Definition transf_program (p: Asmblock.program) : res Asm.program := + transform_partial_program transf_fundef p. + +End Asmblock_TRANSF. + +Definition transf_program (p: Mach.program) : res Asm.program := + let mbp := Machblockgen.transf_program p in + do abp <- Asmblockgen.transf_program mbp; + do abp' <- (time "PostpassScheduling total oracle+verification" PostpassScheduling.transf_program) abp; + Asmblock_TRANSF.transf_program abp'. diff --git a/aarch64/TO_MERGE/Asmgenproof.v b/aarch64/TO_MERGE/Asmgenproof.v new file mode 100644 index 00000000..8af013fd --- /dev/null +++ b/aarch64/TO_MERGE/Asmgenproof.v @@ -0,0 +1,2787 @@ +(* *************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Sylvain Boulmé Grenoble-INP, VERIMAG *) +(* Léo Gourdin UGA, VERIMAG *) +(* Justus Fasse UGA, VERIMAG *) +(* Xavier Leroy INRIA Paris-Rocquencourt *) +(* David Monniaux CNRS, VERIMAG *) +(* Cyril Six Kalray *) +(* *) +(* Copyright Kalray. Copyright VERIMAG. All rights reserved. *) +(* This file is distributed under the terms of the INRIA *) +(* Non-Commercial License Agreement. *) +(* *) +(* *************************************************************) + +Require Import Coqlib Errors. +Require Import Integers Floats AST Linking. +Require Import Values Memory Events Globalenvs Smallstep. +Require Import Op Locations Machblock Conventions Asm Asmblock. +Require Machblockgenproof Asmblockgenproof PostpassSchedulingproof. +Require Import Asmgen. +Require Import Axioms. +Require Import IterList. +Require Import Ring Lia. + +Module Asmblock_PRESERVATION. + +Import Asmblock_TRANSF. + +Definition match_prog (p: Asmblock.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: Asmblock.program. +Variable tprog: Asm.program. +Hypothesis TRANSF: match_prog prog tprog. +Let ge := Genv.globalenv prog. +Let tge := Genv.globalenv tprog. + +Definition lk :aarch64_linker := {| Asmblock.symbol_low:=Asm.symbol_low tge; Asmblock.symbol_high:=Asm.symbol_high tge|}. + +Lemma symbols_preserved: + forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s. +Proof (Genv.find_symbol_match TRANSF). + +Lemma symbol_addresses_preserved: + forall (s: ident) (ofs: ptrofs), + Genv.symbol_address tge s ofs = Genv.symbol_address ge s ofs. +Proof. + intros; unfold Genv.symbol_address; rewrite symbols_preserved; reflexivity. +Qed. + +Lemma senv_preserved: + Senv.equiv ge tge. +Proof (Genv.senv_match TRANSF). + +Lemma symbol_high_low: forall (id: ident) (ofs: ptrofs), + Val.addl (Asmblock.symbol_high lk id ofs) (Asmblock.symbol_low lk id ofs) = Genv.symbol_address ge id ofs. +Proof. + unfold lk; simpl. intros; rewrite Asm.symbol_high_low; unfold Genv.symbol_address; + rewrite symbols_preserved; reflexivity. +Qed. + +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 internal_functions_translated: + forall b f, + Genv.find_funct_ptr ge b = Some (Internal f) -> + exists tf, + Genv.find_funct_ptr tge b = Some (Internal tf) /\ transf_function f = OK tf. +Proof. + intros; exploit functions_translated; eauto. + intros (x & FIND & TRANSf). + apply bind_inversion in TRANSf. + destruct TRANSf as (tf & TRANSf & X). + inv X. + eauto. +Qed. + +Lemma internal_functions_unfold: + forall b f, + Genv.find_funct_ptr ge b = Some (Internal f) -> + exists tc, + Genv.find_funct_ptr tge b = Some (Internal (Asm.mkfunction (fn_sig f) tc)) + /\ unfold (fn_blocks f) = OK tc + /\ list_length_z tc <= Ptrofs.max_unsigned. +Proof. + intros. + exploit internal_functions_translated; eauto. + intros (tf & FINDtf & TRANStf). + unfold transf_function in TRANStf. + monadInv TRANStf. + destruct (zlt _ _); try congruence. + inv EQ. inv EQ0. + eexists; intuition eauto. + lia. +Qed. + + +Inductive is_nth_inst (bb: bblock) (n:Z) (i:Asm.instruction): Prop := + | is_nth_label l: + list_nth_z (header bb) n = Some l -> + i = Asm.Plabel l -> + is_nth_inst bb n i + | is_nth_basic bi: + list_nth_z (body bb) (n - list_length_z (header bb)) = Some bi -> + basic_to_instruction bi = OK i -> + is_nth_inst bb n i + | is_nth_ctlflow cfi: + (exit bb) = Some cfi -> + n = size bb - 1 -> + i = control_to_instruction cfi -> + is_nth_inst bb n i. + +(* Asmblock and Asm share the same definition of state *) +Definition match_states (s1 s2 : state) := s1 = s2. + +Inductive match_internal: forall n, state -> state -> Prop := + | match_internal_intro n rs1 m1 rs2 m2 + (MEM: m1 = m2) + (AG: forall r, r <> PC -> rs1 r = rs2 r) + (AGPC: Val.offset_ptr (rs1 PC) (Ptrofs.repr n) = rs2 PC) + : match_internal n (State rs1 m1) (State rs2 m2). + +Lemma match_internal_set_parallel: + forall n rs1 m1 rs2 m2 r val, + match_internal n (State rs1 m1) (State rs2 m2) -> + r <> PC -> + match_internal n (State (rs1#r <- val) m1) (State (rs2#r <- val ) m2). +Proof. + intros n rs1 m1 rs2 m2 r v MI. + inversion MI; constructor; auto. + - intros r' NOTPC. + unfold Pregmap.set; rewrite AG. reflexivity. assumption. + - unfold Pregmap.set; destruct (PregEq.eq PC r); congruence. +Qed. + +Lemma agree_match_states: + forall rs1 m1 rs2 m2, + match_states (State rs1 m1) (State rs2 m2) -> + forall r : preg, rs1#r = rs2#r. +Proof. + intros. + unfold match_states in *. + assert (rs1 = rs2) as EQ. { congruence. } + rewrite EQ. reflexivity. +Qed. + +Lemma match_states_set_parallel: + forall rs1 m1 rs2 m2 r v, + match_states (State rs1 m1) (State rs2 m2) -> + match_states (State (rs1#r <- v) m1) (State (rs2#r <- v) m2). +Proof. + intros; unfold match_states in *. + assert (rs1 = rs2) as RSEQ. { congruence. } + assert (m1 = m2) as MEQ. { congruence. } + rewrite RSEQ in *; rewrite MEQ in *; unfold Pregmap.set; reflexivity. +Qed. + +(* match_internal from match_states *) +Lemma mi_from_ms: + forall rs1 m1 rs2 m2 b ofs, + match_states (State rs1 m1) (State rs2 m2) -> + rs1#PC = Vptr b ofs -> + match_internal 0 (State rs1 m1) (State rs2 m2). +Proof. + intros rs1 m1 rs2 m2 b ofs MS PCVAL. + inv MS; constructor; auto; unfold Val.offset_ptr; + rewrite PCVAL; rewrite Ptrofs.add_zero; reflexivity. +Qed. + +Lemma transf_initial_states: + forall s1, Asmblock.initial_state prog s1 -> + exists s2, Asm.initial_state tprog s2 /\ match_states s1 s2. +Proof. + intros ? INIT_s1. + inversion INIT_s1 as (m, ?, ge0, rs). unfold ge0 in *. + econstructor; split. + - econstructor. + eapply (Genv.init_mem_transf_partial TRANSF); eauto. + - rewrite (match_program_main TRANSF); rewrite symbol_addresses_preserved. + unfold rs; reflexivity. +Qed. + +Lemma transf_final_states: + forall s1 s2 r, + match_states s1 s2 -> Asmblock.final_state s1 r -> Asm.final_state s2 r. +Proof. + intros s1 s2 r MATCH FINAL_s1. + inv FINAL_s1; inv MATCH; constructor; assumption. +Qed. + +Definition max_pos (f : Asm.function) := list_length_z f.(Asm.fn_code). + +Lemma functions_bound_max_pos: forall fb f tf, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transf_function f = OK tf -> +<<<<<<< HEAD + max_pos tf <= Ptrofs.max_unsigned. +Proof. + intros fb f tf FINDf TRANSf. + unfold transf_function in TRANSf. + apply bind_inversion in TRANSf. + destruct TRANSf as (c & TRANSf). + destruct TRANSf as (_ & TRANSf). + destruct (zlt _ _). + - inversion TRANSf. + - unfold max_pos. + assert (Asm.fn_code tf = c) as H. { inversion TRANSf as (H'); auto. } + rewrite H; lia. +Qed. +======= + 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. + lia. +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. +*) +>>>>>>> master + +Lemma one_le_max_unsigned: + 1 <= Ptrofs.max_unsigned. +Proof. + unfold Ptrofs.max_unsigned; simpl; unfold Ptrofs.wordsize; + unfold Wordsize_Ptrofs.wordsize; destruct Archi.ptr64; simpl; lia. +Qed. + +(* NB: does not seem useful anymore, with the [exec_header_simulation] proof below +Lemma match_internal_exec_label: + forall n rs1 m1 rs2 m2 l fb f tf, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transf_function f = OK tf -> + match_internal n (State rs1 m1) (State rs2 m2) -> + n >= 0 -> + (* There is no step if n is already max_pos *) + n < (max_pos tf) -> + exists rs2' m2', Asm.exec_instr tge tf (Asm.Plabel l) rs2 m2 = Next rs2' m2' + /\ match_internal (n+1) (State rs1 m1) (State rs2' m2'). +Proof. + intros. (* XXX auto generated names *) + unfold Asm.exec_instr. + eexists; eexists; split; eauto. + inversion H1; constructor; auto. + - intros; unfold Asm.nextinstr; unfold Pregmap.set; + destruct (PregEq.eq r PC); auto; contradiction. + - unfold Asm.nextinstr; rewrite Pregmap.gss; unfold Ptrofs.one. + rewrite <- AGPC; rewrite Val.offset_ptr_assoc; unfold Ptrofs.add; + rewrite Ptrofs.unsigned_repr. rewrite Ptrofs.unsigned_repr; trivial. + + split. + * apply Z.le_0_1. + * apply one_le_max_unsigned. + + split. + * apply Z.ge_le; assumption. + * rewrite <- functions_bound_max_pos; eauto; lia. +Qed. +*) + +Lemma incrPC_agree_but_pc: + forall rs r ofs, + r <> PC -> + (incrPC ofs rs)#r = rs#r. +Proof. + intros rs r ofs NOTPC. + unfold incrPC; unfold Pregmap.set; destruct (PregEq.eq r PC). + - contradiction. + - reflexivity. +Qed. + +Lemma bblock_non_empty bb: body bb <> nil \/ exit bb <> None. +Proof. + destruct bb. simpl. + unfold non_empty_bblockb in correct. + unfold non_empty_body, non_empty_exit, Is_true in correct. + destruct body, exit. + - right. discriminate. + - contradiction. + - right. discriminate. + - left. discriminate. +Qed. + +Lemma list_length_z_aux_increase A (l: list A): forall acc, + list_length_z_aux l acc >= acc. +Proof. + induction l; simpl; intros. + - lia. + - generalize (IHl (Z.succ acc)). lia. +Qed. + +Lemma bblock_size_aux_pos bb: list_length_z (body bb) + Z.of_nat (length_opt (exit bb)) >= 1. +Proof. + destruct (bblock_non_empty bb), (body bb) as [|hd tl], (exit bb); simpl; + try (congruence || lia); + unfold list_length_z; simpl; + generalize (list_length_z_aux_increase _ tl 1); lia. +Qed. + + +Lemma list_length_add_acc A (l : list A) acc: + list_length_z_aux l acc = (list_length_z l) + acc. +Proof. + unfold list_length_z, list_length_z_aux. simpl. + fold list_length_z_aux. + rewrite (list_length_z_aux_shift l acc 0). + lia. +Qed. + +Lemma list_length_z_cons A hd (tl : list A): + list_length_z (hd :: tl) = list_length_z tl + 1. +Proof. + unfold list_length_z; simpl; rewrite list_length_add_acc; reflexivity. +Qed. + +Lemma bblock_size_aux bb: size bb = list_length_z (header bb) + list_length_z (body bb) + Z.of_nat (length_opt (exit bb)). +Proof. + unfold size. + repeat (rewrite list_length_z_nat). repeat (rewrite Nat2Z.inj_add). reflexivity. +Qed. + +Lemma header_size_lt_block_size bb: + list_length_z (header bb) < size bb. +Proof. + rewrite bblock_size_aux. + generalize (bblock_non_empty bb); intros NEMPTY; destruct NEMPTY as [HDR|EXIT]. + - destruct (body bb); try contradiction; rewrite list_length_z_cons; + repeat rewrite list_length_z_nat; lia. + - destruct (exit bb); try contradiction; simpl; repeat rewrite list_length_z_nat; lia. +Qed. + +Lemma body_size_le_block_size bb: + list_length_z (body bb) <= size bb. +Proof. + rewrite bblock_size_aux; repeat rewrite list_length_z_nat; lia. +Qed. + + +Lemma bblock_size_pos bb: size bb >= 1. +Proof. + rewrite (bblock_size_aux bb). + generalize (bblock_size_aux_pos bb). + generalize (list_length_z_pos (header bb)). + lia. +Qed. + +Lemma unfold_car_cdr bb bbs tc: + unfold (bb :: bbs) = OK tc -> + exists tbb tc', unfold_bblock bb = OK tbb + /\ unfold bbs = OK tc' + /\ unfold (bb :: bbs) = OK (tbb ++ tc'). +Proof. + intros UNFOLD. + assert (UF := UNFOLD). + unfold unfold in UNFOLD. + apply bind_inversion in UNFOLD. destruct UNFOLD as (? & UBB). destruct UBB as (UBB & REST). + apply bind_inversion in REST. destruct REST as (? & UNFOLD'). + fold unfold in UNFOLD'. destruct UNFOLD' as (UNFOLD' & UNFOLD). + rewrite <- UNFOLD in UF. + eauto. +Qed. + +Lemma unfold_cdr bb bbs tc: + unfold (bb :: bbs) = OK tc -> + exists tc', unfold bbs = OK tc'. +Proof. +<<<<<<< HEAD + intros; exploit unfold_car_cdr; eauto. intros (_ & ? & _ & ? & _). + eexists; eauto. +Qed. +======= + intros; unfold loadsymbol. + destruct (SelectOp.symbol_is_relocatable id); TailNoLabel. destruct Ptrofs.eq; TailNoLabel. +Qed. +Hint Resolve loadsymbol_label: labels. +>>>>>>> master + +Lemma unfold_car bb bbs tc: + unfold (bb :: bbs) = OK tc -> + exists tbb, unfold_bblock bb = OK tbb. +Proof. + intros; exploit unfold_car_cdr; eauto. intros (? & _ & ? & _ & _). + eexists; eauto. +Qed. + +Lemma all_blocks_translated: + forall bbs tc, + unfold bbs = OK tc -> + forall bb, In bb bbs -> + exists c, unfold_bblock bb = OK c. +Proof. + induction bbs as [| bb bbs IHbbs]. + - contradiction. + - intros ? UNFOLD ? IN. + (* unfold proceeds by unfolding the basic block at the head of the list and + * then recurring *) + exploit unfold_car_cdr; eauto. intros (? & ? & ? & ? & _). + (* basic block is either in head or tail *) + inversion IN as [EQ | NEQ]. + + rewrite <- EQ; eexists; eauto. + + eapply IHbbs; eauto. +Qed. + +Lemma entire_body_translated: + forall lbi tc, + unfold_body lbi = OK tc -> + forall bi, In bi lbi -> + exists bi', basic_to_instruction bi = OK bi'. +Proof. + induction lbi as [| a lbi IHlbi]. + - intros. contradiction. + - intros tc UNFOLD_BODY bi IN. + unfold unfold_body in UNFOLD_BODY. apply bind_inversion in UNFOLD_BODY. + destruct UNFOLD_BODY as (? & TRANSbi & REST). + apply bind_inversion in REST. destruct REST as (? & UNFOLD_BODY' & ?). + fold unfold_body in UNFOLD_BODY'. + + inversion IN as [EQ | NEQ]. + + rewrite <- EQ; eauto. + + eapply IHlbi; eauto. +Qed. + +Lemma bblock_in_bblocks bbs bb: forall + tc pos + (UNFOLD: unfold bbs = OK tc) + (FINDBB: find_bblock pos bbs = Some bb), + In bb bbs. +Proof. + induction bbs as [| b bbs IH]. + - intros. inversion FINDBB. + - destruct pos. + + intros. inversion FINDBB as (EQ). rewrite <- EQ. apply in_eq. + + intros. + exploit unfold_cdr; eauto. intros (tc' & UNFOLD'). + unfold find_bblock in FINDBB. simpl in FINDBB. + fold find_bblock in FINDBB. + apply in_cons. eapply IH; eauto. + + intros. inversion FINDBB. +Qed. + +Lemma blocks_translated tc pos bbs bb: forall + (UNFOLD: unfold bbs = OK tc) + (FINDBB: find_bblock pos bbs = Some bb), + exists tbb, unfold_bblock bb = OK tbb. +Proof. + intros; exploit bblock_in_bblocks; eauto; intros; + eapply all_blocks_translated; eauto. +Qed. + +Lemma size_header b pos f bb: forall + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock pos (fn_blocks f) = Some bb), + list_length_z (header bb) <= 1. +Proof. + intros. + exploit internal_functions_unfold; eauto. + intros (tc & FINDtf & TRANStf & ?). + exploit blocks_translated; eauto. intros TBB. + + unfold unfold_bblock in TBB. + destruct (zle (list_length_z (header bb)) 1). + - assumption. + - destruct TBB as (? & TBB). discriminate TBB. +Qed. + +Lemma list_nth_z_neg A (l: list A): forall n, + n < 0 -> list_nth_z l n = None. +Proof. + induction l; simpl; auto. + intros n H; destruct (zeq _ _); (try eapply IHl); lia. +Qed. + +Lemma find_bblock_neg bbs: forall pos, + pos < 0 -> find_bblock pos bbs = None. +Proof. + induction bbs; simpl; auto. + intros. destruct (zlt pos 0). { reflexivity. } + destruct (zeq pos 0); contradiction. +Qed. + +Lemma equal_header_size bb: + length (header bb) = length (unfold_label (header bb)). +Proof. + induction (header bb); auto. + simpl. rewrite IHl. auto. +Qed. + +Lemma equal_body_size: + forall bb tb, + unfold_body (body bb) = OK tb -> + length (body bb) = length tb. +Proof. + intros bb. induction (body bb). + - simpl. intros ? H. inversion H. auto. + - intros tb H. simpl in H. apply bind_inversion in H. destruct H as (? & BI & TAIL). + apply bind_inversion in TAIL. destruct TAIL as (tb' & BODY' & CONS). inv CONS. + simpl. specialize (IHl tb' BODY'). rewrite IHl. reflexivity. +Qed. + +Lemma equal_exit_size bb: + length_opt (exit bb) = length (unfold_exit (exit bb)). +Proof. + destruct (exit bb); trivial. +Qed. + +Lemma bblock_size_preserved bb tb: + unfold_bblock bb = OK tb -> + size bb = list_length_z tb. +Proof. + unfold unfold_bblock. intros UNFOLD_BBLOCK. + destruct (zle (list_length_z (header bb)) 1). 2: { inversion UNFOLD_BBLOCK. } + apply bind_inversion in UNFOLD_BBLOCK. destruct UNFOLD_BBLOCK as (? & UNFOLD_BODY & CONS). + inversion CONS. + unfold size. + rewrite equal_header_size, equal_exit_size. + erewrite equal_body_size; eauto. + rewrite list_length_z_nat. + repeat (rewrite app_length). + rewrite plus_assoc. auto. +Qed. + +Lemma size_of_blocks_max_pos_aux: + forall bbs tbbs pos bb, + find_bblock pos bbs = Some bb -> + unfold bbs = OK tbbs -> + pos + size bb <= list_length_z tbbs. +Proof. + induction bbs as [| bb ? IHbbs]. + - intros tbbs ? ? FINDBB; inversion FINDBB. + - simpl; intros tbbs pos bb' FINDBB UNFOLD. + apply bind_inversion in UNFOLD; destruct UNFOLD as (tbb & UNFOLD_BBLOCK & H). + apply bind_inversion in H; destruct H as (tbbs' & UNFOLD & CONS). + inv CONS. + destruct (zlt pos 0). { discriminate FINDBB. } + destruct (zeq pos 0). + + inv FINDBB. + exploit bblock_size_preserved; eauto; intros SIZE; rewrite SIZE. + repeat (rewrite list_length_z_nat). rewrite app_length, Nat2Z.inj_add. + lia. + + generalize (IHbbs tbbs' (pos - size bb) bb' FINDBB UNFOLD). intros IH. + exploit bblock_size_preserved; eauto; intros SIZE. + repeat (rewrite list_length_z_nat); rewrite app_length. + rewrite Nat2Z.inj_add; repeat (rewrite <- list_length_z_nat). + lia. +Qed. + +Lemma size_of_blocks_max_pos pos f tf bi: + find_bblock pos (fn_blocks f) = Some bi -> + transf_function f = OK tf -> + pos + size bi <= max_pos tf. +Proof. + unfold transf_function, max_pos. + intros FINDBB UNFOLD. + apply bind_inversion in UNFOLD. destruct UNFOLD as (? & UNFOLD & H). + destruct (zlt Ptrofs.max_unsigned (list_length_z x)). { discriminate H. } + inv H. simpl. + eapply size_of_blocks_max_pos_aux; eauto. +Qed. + +Lemma unfold_bblock_not_nil bb: + unfold_bblock bb = OK nil -> False. +Proof. + intros. + exploit bblock_size_preserved; eauto. unfold list_length_z; simpl. intros SIZE. + generalize (bblock_size_pos bb). intros SIZE'. lia. +Qed. + +(* same proof as list_nth_z_range (Coqlib) *) +Lemma find_instr_range: + forall c n i, + Asm.find_instr n c = Some i -> 0 <= n < list_length_z c. +Proof. + induction c; simpl; intros. + discriminate. + rewrite list_length_z_cons. destruct (zeq n 0). + generalize (list_length_z_pos c); lia. + exploit IHc; eauto. lia. +Qed. + +Lemma find_instr_tail: + forall tbb pos c i, + Asm.find_instr pos c = Some i -> + Asm.find_instr (pos + list_length_z tbb) (tbb ++ c) = Some i. +Proof. + induction tbb as [| ? ? IHtbb]. + - intros. unfold list_length_z; simpl. rewrite Z.add_0_r. assumption. + - intros. rewrite list_length_z_cons. simpl. + destruct (zeq (pos + (list_length_z tbb + 1)) 0). + + exploit find_instr_range; eauto. intros POS_RANGE. + generalize (list_length_z_pos tbb). lia. + + replace (pos + (list_length_z tbb + 1) - 1) with (pos + list_length_z tbb) by lia. + eapply IHtbb; eauto. +Qed. + +Lemma size_of_blocks_bounds fb pos f bi: + Genv.find_funct_ptr ge fb = Some (Internal f) -> + find_bblock pos (fn_blocks f) = Some bi -> + pos + size bi <= Ptrofs.max_unsigned. +Proof. + intros; exploit internal_functions_translated; eauto. + intros (tf & _ & TRANSf). + assert (pos + size bi <= max_pos tf). { eapply size_of_blocks_max_pos; eauto. } + assert (max_pos tf <= Ptrofs.max_unsigned). { eapply functions_bound_max_pos; eauto. } + lia. +Qed. + +Lemma find_instr_bblock_tail: + forall tbb bb pos c i, + Asm.find_instr pos c = Some i -> + unfold_bblock bb = OK tbb -> + Asm.find_instr (pos + size bb ) (tbb ++ c) = Some i. +Proof. + induction tbb. + - intros. exploit unfold_bblock_not_nil; eauto. intros. contradiction. + - intros. simpl. + destruct (zeq (pos + size bb) 0). + + (* absurd *) + exploit find_instr_range; eauto. intros POS_RANGE. + generalize (bblock_size_pos bb). intros SIZE. lia. + + erewrite bblock_size_preserved; eauto. + rewrite list_length_z_cons. + replace (pos + (list_length_z tbb + 1) - 1) with (pos + list_length_z tbb) by lia. + apply find_instr_tail; auto. +Qed. + +Lemma list_nth_z_find_label: + forall (ll : list label) il n l, + list_nth_z ll n = Some l -> + Asm.find_instr n ((unfold_label ll) ++ il) = Some (Asm.Plabel l). +Proof. + induction ll. + - intros. inversion H. + - intros. simpl. + destruct (zeq n 0) as [Z | NZ]. + + inversion H as (H'). rewrite Z in H'. simpl in H'. inv H'. reflexivity. + + simpl in H. destruct (zeq n 0). { contradiction. } + apply IHll; auto. +Qed. + +Lemma list_nth_z_find_bi: + forall lbi bi tlbi n bi' exit, + list_nth_z lbi n = Some bi -> + unfold_body lbi = OK tlbi -> + basic_to_instruction bi = OK bi' -> + Asm.find_instr n (tlbi ++ exit) = Some bi'. +Proof. + induction lbi. + - intros. inversion H. + - simpl. intros. + apply bind_inversion in H0. destruct H0 as (? & ? & ?). + apply bind_inversion in H2. destruct H2 as (? & ? & ?). + destruct (zeq n 0) as [Z | NZ]. + + destruct n. + * inversion H as (BI). rewrite BI in *. + inversion H3. simpl. congruence. + * (* absurd *) congruence. + * (* absurd *) congruence. + + inv H3. simpl. destruct (zeq n 0). { contradiction. } + eapply IHlbi; eauto. +Qed. + +Lemma list_nth_z_find_bi_with_header: + forall ll lbi bi tlbi n bi' (rest : list Asm.instruction), + list_nth_z lbi (n - list_length_z ll) = Some bi -> + unfold_body lbi = OK tlbi -> + basic_to_instruction bi = OK bi' -> + Asm.find_instr n ((unfold_label ll) ++ (tlbi) ++ (rest)) = Some bi'. +Proof. + induction ll. + - unfold list_length_z. simpl. intros. + replace (n - 0) with n in H by lia. eapply list_nth_z_find_bi; eauto. + - intros. simpl. destruct (zeq n 0). + + rewrite list_length_z_cons in H. rewrite e in H. + replace (0 - (list_length_z ll + 1)) with (-1 - (list_length_z ll)) in H by lia. + generalize (list_length_z_pos ll). intros. + rewrite list_nth_z_neg in H; try lia. inversion H. + + rewrite list_length_z_cons in H. + replace (n - (list_length_z ll + 1)) with (n -1 - (list_length_z ll)) in H by lia. + eapply IHll; eauto. +Qed. + +(* XXX unused *) +Lemma range_list_nth_z: + forall (A: Type) (l: list A) n, + 0 <= n < list_length_z l -> + exists x, list_nth_z l n = Some x. +Proof. + induction l. + - intros. unfold list_length_z in H. simpl in H. lia. + - intros n. destruct (zeq n 0). + + intros. simpl. destruct (zeq n 0). { eauto. } contradiction. + + intros H. rewrite list_length_z_cons in H. + simpl. destruct (zeq n 0). { contradiction. } + replace (Z.pred n) with (n - 1) by lia. + eapply IHl; lia. +Qed. + +Lemma list_nth_z_n_too_big: + forall (A: Type) (l: list A) n, + 0 <= n -> + list_nth_z l n = None -> + n >= list_length_z l. +Proof. + induction l. + - intros. unfold list_length_z. simpl. lia. + - intros. rewrite list_length_z_cons. + simpl in H0. + destruct (zeq n 0) as [N | N]. + + inversion H0. + + (* XXX there must be a more elegant way to prove this simple fact *) + assert (n > 0). { lia. } + assert (0 <= n - 1). { lia. } + generalize (IHl (n - 1)). intros IH. + assert (n - 1 >= list_length_z l). { auto. } + assert (n > list_length_z l); lia. +Qed. + +Lemma find_instr_past_header: + forall labels n rest, + list_nth_z labels n = None -> + Asm.find_instr n (unfold_label labels ++ rest) = + Asm.find_instr (n - list_length_z labels) rest. +Proof. + induction labels as [| label labels' IH]. + - unfold list_length_z; simpl; intros; rewrite Z.sub_0_r; reflexivity. + - intros. simpl. destruct (zeq n 0) as [N | N]. + + rewrite N in H. inversion H. + + rewrite list_length_z_cons. + replace (n - (list_length_z labels' + 1)) with (n - 1 - list_length_z labels') by lia. + simpl in H. destruct (zeq n 0). { contradiction. } + replace (Z.pred n) with (n - 1) in H by lia. + apply IH; auto. +Qed. + +(* very similar to find_instr_past_header *) +Lemma find_instr_past_body: + forall lbi n tlbi rest, + list_nth_z lbi n = None -> + unfold_body lbi = OK tlbi -> + Asm.find_instr n (tlbi ++ rest) = + Asm.find_instr (n - list_length_z lbi) rest. +Proof. + induction lbi. + - unfold list_length_z; simpl; intros ? ? ? ? H. inv H; rewrite Z.sub_0_r; reflexivity. + - intros n tlib ? NTH UNFOLD_BODY. + unfold unfold_body in UNFOLD_BODY. apply bind_inversion in UNFOLD_BODY. + destruct UNFOLD_BODY as (? & BI & H). + apply bind_inversion in H. destruct H as (? & UNFOLD_BODY' & CONS). + fold unfold_body in UNFOLD_BODY'. inv CONS. + simpl; destruct (zeq n 0) as [N|N]. + + rewrite N in NTH; inversion NTH. + + rewrite list_length_z_cons. + replace (n - (list_length_z lbi + 1)) with (n - 1 - list_length_z lbi) by lia. + simpl in NTH. destruct (zeq n 0). { contradiction. } + replace (Z.pred n) with (n - 1) in NTH by lia. + apply IHlbi; auto. +Qed. + +Lemma n_beyond_body: + forall bb n, + 0 <= n < size bb -> + list_nth_z (header bb) n = None -> + list_nth_z (body bb) (n - list_length_z (header bb)) = None -> + n >= Z.of_nat (length (header bb) + length (body bb)). +Proof. + intros. + assert (0 <= n). { lia. } + generalize (list_nth_z_n_too_big label (header bb) n H2 H0). intros. + generalize (list_nth_z_n_too_big _ (body bb) (n - list_length_z (header bb))). intros. + unfold size in H. + + assert (0 <= n - list_length_z (header bb)). { lia. } + assert (n - list_length_z (header bb) >= list_length_z (body bb)). { apply H4; auto. } + + assert (n >= list_length_z (header bb) + list_length_z (body bb)). { lia. } + rewrite Nat2Z.inj_add. + repeat (rewrite <- list_length_z_nat). assumption. +Qed. + +Lemma exec_arith_instr_dont_move_PC ai rs rs': forall + (BASIC: exec_arith_instr lk ai rs = rs'), + rs PC = rs' PC. +Proof. + destruct ai; simpl; intros; + try (rewrite <- BASIC; rewrite Pregmap.gso; auto; discriminate). + - destruct i; simpl in BASIC; + try destruct (negb _); rewrite <- BASIC; + repeat rewrite Pregmap.gso; try discriminate; reflexivity. + - destruct i; simpl in BASIC. + 1,2: rewrite <- BASIC; repeat rewrite Pregmap.gso; try discriminate; reflexivity. + destruct sz; + try (unfold compare_single in BASIC || unfold compare_float in BASIC); + destruct (rs r1), (rs r2); + try (rewrite <- BASIC; repeat rewrite Pregmap.gso; try (discriminate || reflexivity)). + - destruct i; simpl in BASIC; + destruct is; + try (unfold compare_int in BASIC || unfold compare_long in BASIC); + try (rewrite <- BASIC; repeat rewrite Pregmap.gso; try (discriminate || reflexivity)). + - destruct i; simpl in BASIC; destruct sz; + try (unfold compare_single in BASIC || unfold compare_float in BASIC); + destruct (rs r1); + try (rewrite <- BASIC; repeat rewrite Pregmap.gso; try (discriminate || reflexivity)). + - destruct fsz; rewrite <- BASIC; rewrite Pregmap.gso; try (discriminate || reflexivity). + - destruct fsz; rewrite <- BASIC; rewrite Pregmap.gso; try (discriminate || reflexivity). +Qed. + +Lemma exec_basic_dont_move_PC bi rs m rs' m': forall + (BASIC: exec_basic lk ge bi rs m = Next rs' m'), + rs PC = rs' PC. +Proof. + destruct bi; simpl; intros. + - inv BASIC. exploit exec_arith_instr_dont_move_PC; eauto. + - unfold exec_load in BASIC. + destruct ld. + + unfold exec_load_rd_a in BASIC. + destruct Mem.loadv. 2: { discriminate BASIC. } + inv BASIC. rewrite Pregmap.gso; try discriminate; auto. + + unfold exec_load_double, is_pair_addressing_mode_correct in BASIC. + destruct a; try discriminate BASIC. + do 2 (destruct Mem.loadv; try discriminate BASIC). + inv BASIC. rewrite Pregmap.gso; try discriminate; auto. + - unfold exec_store in BASIC. + destruct st. + + unfold exec_store_rs_a in BASIC. + destruct Mem.storev. 2: { discriminate BASIC. } + inv BASIC; reflexivity. + + unfold exec_store_double in BASIC. + destruct a; try discriminate BASIC. + do 2 (destruct Mem.storev; try discriminate BASIC). + inv BASIC; reflexivity. + - destruct Mem.alloc, Mem.store. 2: { discriminate BASIC. } + inv BASIC. repeat (rewrite Pregmap.gso; try discriminate). reflexivity. + - destruct Mem.loadv. 2: { discriminate BASIC. } + destruct rs, Mem.free; try discriminate BASIC. + inv BASIC; rewrite Pregmap.gso; try discriminate; auto. + - inv BASIC; rewrite Pregmap.gso; try discriminate; auto. + - inv BASIC; rewrite Pregmap.gso; try discriminate; auto. + - inv BASIC; rewrite Pregmap.gso; try discriminate; auto. + - inv BASIC; rewrite Pregmap.gso; try discriminate; auto. + - inv BASIC; auto. +Qed. + +Lemma exec_body_dont_move_PC_aux: + forall bis rs m rs' m' + (BODY: exec_body lk ge bis rs m = Next rs' m'), + rs PC = rs' PC. +Proof. + induction bis. + - intros; inv BODY; reflexivity. + - simpl; intros. + remember (exec_basic lk ge a rs m) as bi eqn:BI; destruct bi. 2: { discriminate BODY. } + symmetry in BI; destruct s in BODY, BI; simpl in BODY, BI. + exploit exec_basic_dont_move_PC; eauto; intros AGPC; rewrite AGPC. + eapply IHbis; eauto. +Qed. + +Lemma exec_body_dont_move_PC bb rs m rs' m': forall + (BODY: exec_body lk ge (body bb) rs m = Next rs' m'), + rs PC = rs' PC. +Proof. apply exec_body_dont_move_PC_aux. Qed. + +Lemma find_instr_bblock: + forall n lb pos bb tlb + (FINDBB: find_bblock pos lb = Some bb) + (UNFOLD: unfold lb = OK tlb) + (SIZE: 0 <= n < size bb), + exists i, is_nth_inst bb n i /\ Asm.find_instr (pos+n) tlb = Some i. +Proof. + induction lb as [| b lb IHlb]. + - intros. inversion FINDBB. + - intros pos bb tlb FINDBB UNFOLD SIZE. + destruct pos. + + inv FINDBB. simpl. + exploit unfold_car_cdr; eauto. intros (tbb & tlb' & UNFOLD_BBLOCK & UNFOLD' & UNFOLD_cons). + rewrite UNFOLD in UNFOLD_cons. inversion UNFOLD_cons. + unfold unfold_bblock in UNFOLD_BBLOCK. + destruct (zle (list_length_z (header bb)) 1). 2: { inversion UNFOLD_BBLOCK. } + apply bind_inversion in UNFOLD_BBLOCK. + destruct UNFOLD_BBLOCK as (? & UNFOLD_BODY & H). + inversion H as (UNFOLD_BBLOCK). + remember (list_nth_z (header bb) n) as label_opt eqn:LBL. destruct label_opt. + * (* nth instruction is a label *) + eexists; split. { eapply is_nth_label; eauto. } + inversion UNFOLD_cons. + symmetry in LBL. + rewrite <- app_assoc. + apply list_nth_z_find_label; auto. + * remember (list_nth_z (body bb) (n - list_length_z (header bb))) as bi_opt eqn:BI. + destruct bi_opt. + -- (* nth instruction is a basic instruction *) + exploit list_nth_z_in; eauto. intros INBB. + exploit entire_body_translated; eauto. intros BI'. + destruct BI'. + eexists; split. + ++ eapply is_nth_basic; eauto. + ++ repeat (rewrite <- app_assoc). eapply list_nth_z_find_bi_with_header; eauto. + -- (* nth instruction is the exit instruction *) + generalize n_beyond_body. intros TEMP. + assert (n >= Z.of_nat (Datatypes.length (header bb) + + Datatypes.length (body bb))) as NGE. { auto. } clear TEMP. + remember (exit bb) as exit_opt eqn:EXIT. destruct exit_opt. + ++ rewrite <- app_assoc. rewrite find_instr_past_header; auto. + rewrite <- app_assoc. erewrite find_instr_past_body; eauto. + assert (SIZE' := SIZE). + unfold size in SIZE. rewrite <- EXIT in SIZE. simpl in SIZE. + destruct SIZE as (LOWER & UPPER). + repeat (rewrite Nat2Z.inj_add in UPPER). + repeat (rewrite <- list_length_z_nat in UPPER). repeat (rewrite Nat2Z.inj_add in NGE). + repeat (rewrite <- list_length_z_nat in NGE). simpl in UPPER. + assert (n = list_length_z (header bb) + list_length_z (body bb)). { lia. } + assert (n = size bb - 1). { + unfold size. rewrite <- EXIT. simpl. + repeat (rewrite Nat2Z.inj_add). repeat (rewrite <- list_length_z_nat). simpl. lia. + } + symmetry in EXIT. + eexists; split. + ** eapply is_nth_ctlflow; eauto. + ** simpl. + destruct (zeq (n - list_length_z (header bb) - list_length_z (body bb)) 0). { reflexivity. } + (* absurd *) lia. + ++ (* absurd *) + unfold size in SIZE. rewrite <- EXIT in SIZE. simpl in SIZE. + destruct SIZE as (? & SIZE'). rewrite Nat.add_0_r in SIZE'. lia. + + unfold find_bblock in FINDBB; simpl in FINDBB; fold find_bblock in FINDBB. + inversion UNFOLD as (UNFOLD'). + apply bind_inversion in UNFOLD'. destruct UNFOLD' as (? & (UNFOLD_BBLOCK' & UNFOLD')). + apply bind_inversion in UNFOLD'. destruct UNFOLD' as (? & (UNFOLD' & TLB)). + inversion TLB. + generalize (IHlb _ _ _ FINDBB UNFOLD'). intros IH. + destruct IH as (? & (IH_is_nth & IH_find_instr)); eauto. + eexists; split. + * apply IH_is_nth. + * replace (Z.pos p + n) with (Z.pos p + n - size b + size b) by lia. + eapply find_instr_bblock_tail; try assumption. + replace (Z.pos p + n - size b) with (Z.pos p - size b + n) by lia. + apply IH_find_instr. + + (* absurd *) + generalize (Pos2Z.neg_is_neg p). intros. exploit (find_bblock_neg (b :: lb)); eauto. + rewrite FINDBB. intros CONTRA. inversion CONTRA. +Qed. + +Lemma exec_header_simulation b ofs f bb rs m: forall + (ATPC: rs PC = Vptr b ofs) + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb), + exists s', star Asm.step tge (State rs m) E0 s' + /\ match_internal (list_length_z (header bb)) (State rs m) s'. +Proof. + intros. + exploit internal_functions_unfold; eauto. + intros (tc & FINDtf & TRANStf & _). + assert (BNDhead: list_length_z (header bb) <= 1). { eapply size_header; eauto. } + destruct (header bb) as [|l[|]] eqn: EQhead. + + (* header nil *) + eexists; split. + - eapply star_refl. + - split; eauto. + unfold list_length_z; rewrite !ATPC; simpl. + rewrite Ptrofs.add_zero; auto. + + (* header one *) + assert (Lhead: list_length_z (header bb) = 1). { rewrite EQhead; unfold list_length_z; simpl. auto. } + exploit (find_instr_bblock 0); eauto. + { generalize (bblock_size_pos bb). lia. } + intros (i & NTH & FIND_INSTR). + inv NTH. + * rewrite EQhead in H; simpl in H. inv H. + replace (Ptrofs.unsigned ofs + 0) with (Ptrofs.unsigned ofs) in FIND_INSTR by lia. + eexists. split. + - eapply star_one. + eapply Asm.exec_step_internal; eauto. + simpl; eauto. + - unfold list_length_z; simpl. split; eauto. + intros r; destruct r; simpl; congruence || auto. + * (* absurd case *) + erewrite list_nth_z_neg in * |-; [ congruence | rewrite Lhead; lia]. + * (* absurd case *) + rewrite bblock_size_aux, Lhead in *. generalize (bblock_size_aux_pos bb). lia. + + (* absurd case *) + unfold list_length_z in BNDhead. simpl in *. + generalize (list_length_z_aux_increase _ l1 2); lia. +Qed. + +Lemma eval_addressing_preserved a rs1 rs2: + (forall r : preg, r <> PC -> rs1 r = rs2 r) -> + eval_addressing lk a rs1 = Asm.eval_addressing tge a rs2. +Proof. + intros EQ. + destruct a; simpl; try (rewrite !EQ; congruence). + auto. +Qed. + +Ltac next_stuck_cong := try (unfold Next, Stuck in *; congruence). + +Ltac inv_ok_eq := + repeat match goal with + | [EQ: OK ?x = OK ?y |- _ ] + => inversion EQ; clear EQ; subst + end. + +Ltac reg_rwrt := + match goal with + | [e: DR _ = DR _ |- _ ] + => rewrite e in * + end. + +Ltac destruct_reg_inv := + repeat match goal with + | [ H : match ?reg with _ => _ end = _ |- _ ] + => simpl in *; destruct reg; try congruence; try inv_ok_eq; try reg_rwrt + end. + +Ltac destruct_ireg_inv := + repeat match goal with + | [ H : match ?reg with _ => _ end = _ |- _ ] + => destruct reg as [[r|]|]; try congruence; try inv_ok_eq; subst + end. + +Ltac destruct_reg_size := + simpl in *; + match goal with + | [ |- context [ match ?reg with _ => _ end ] ] + => destruct reg; try congruence + end. + +Ltac find_rwrt_ag := + simpl in *; + match goal with + | [ AG: forall r, r <> ?PC -> _ r = _ r |- _ ] + => repeat rewrite <- AG; try congruence + end. + +Ltac inv_matchi := + match goal with + | [ MATCHI : match_internal _ _ _ |- _ ] + => inversion MATCHI; subst; find_rwrt_ag + end. + +Ltac destruct_ir0_reg := + match goal with + | [ |- context [ ir0 _ _ ?r ] ] + => unfold ir0 in *; destruct r; find_rwrt_ag; eauto + end. + +Ltac pc_not_sp := + match goal with + | [ |- ?PC <> ?SP ] + => destruct (PregEq.eq SP PC); repeat congruence; discriminate + end. + +Ltac update_x_access_x := + subst; rewrite !Pregmap.gss; auto. + +Ltac update_x_access_r := + rewrite !Pregmap.gso; auto. + +Lemma nextinstr_agree_but_pc rs1 rs2: forall + (AG: forall r, r <> PC -> rs1 r = rs2 r), + forall r, r <> PC -> rs1 r = Asm.nextinstr rs2 r. +Proof. + intros; unfold Asm.nextinstr in *; rewrite Pregmap.gso in *; eauto. +Qed. + +Lemma ptrofs_nextinstr_agree rs1 rs2 n: forall + (BOUNDED : 0 <= n <= Ptrofs.max_unsigned) + (AGPC : Val.offset_ptr (rs1 PC) (Ptrofs.repr n) = rs2 PC), + Val.offset_ptr (rs1 PC) (Ptrofs.repr (n + 1)) = Asm.nextinstr rs2 PC. +Proof. + intros; unfold Asm.nextinstr; rewrite Pregmap.gss. + rewrite <- Ptrofs.unsigned_one; rewrite <- (Ptrofs.unsigned_repr n); eauto; + rewrite <- Ptrofs.add_unsigned; rewrite <- Val.offset_ptr_assoc; rewrite AGPC; eauto. +Qed. + +Lemma load_rd_a_preserved n rs1 m1 rs1' m1' rs2 m2 rd chk f a: forall + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (HLOAD: exec_load_rd_a lk chk f a rd rs1 m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), Asm.exec_load tge chk f a rd rs2 m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + unfold exec_load_rd_a, Asm.exec_load in *. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + rewrite <- (eval_addressing_preserved a rs1 rs2); auto. + destruct (Mem.loadv _ _ _). + + inversion HLOAD; auto. repeat (econstructor; eauto). + * eapply nextinstr_agree_but_pc; intros. + destruct (PregEq.eq r rd); try update_x_access_x; try update_x_access_r. + * eapply ptrofs_nextinstr_agree; eauto. + + next_stuck_cong. +Qed. + +Lemma load_double_preserved n rs1 m1 rs1' m1' rs2 m2 rd1 rd2 chk1 chk2 f a: forall + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (HLOAD: exec_load_double lk chk1 chk2 f a rd1 rd2 rs1 m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), Asm.exec_load_double tge chk1 chk2 f a rd1 rd2 rs2 m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + unfold exec_load_double, Asm.exec_load_double in *. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + erewrite <- !eval_addressing_preserved; eauto. + destruct (is_pair_addressing_mode_correct a); try discriminate. + destruct (Mem.loadv _ _ _); + destruct (Mem.loadv chk2 m2 + (eval_addressing lk + (get_offset_addr a match chk1 with + | Mint32 | Mfloat32| Many32 => 4 + | _ => 8 + end) rs1)); + inversion HLOAD; auto. + repeat (econstructor; eauto). + * eapply nextinstr_agree_but_pc; intros. + destruct (PregEq.eq r rd2); destruct (PregEq.eq r rd1). + - try update_x_access_x. + - try update_x_access_x. + - subst; repeat rewrite Pregmap.gso, Pregmap.gss; auto. + - try update_x_access_r. + * eapply ptrofs_nextinstr_agree; eauto. +Qed. + +<<<<<<< HEAD +Lemma store_rs_a_preserved n rs1 m1 rs1' m1' rs2 m2 v chk a: forall + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (HSTORE: exec_store_rs_a lk chk a v rs1 m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), Asm.exec_store tge chk a v rs2 m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + unfold exec_store_rs_a, Asm.exec_store in *. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + rewrite <- (eval_addressing_preserved a rs1 rs2); auto. + destruct (Mem.storev _ _ _ _). + + inversion HSTORE; auto. repeat (econstructor; eauto). + * eapply nextinstr_agree_but_pc; intros. + subst. apply EQR. auto. + * eapply ptrofs_nextinstr_agree; subst; eauto. + + next_stuck_cong. +Qed. +======= +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. lia. + generalize (transf_function_no_overflow _ _ H0). lia. + intros. apply Pregmap.gso; auto. +Qed. + +(** Existence of return addresses *) +>>>>>>> master + +Lemma store_double_preserved n rs1 m1 rs1' m1' rs2 m2 v1 v2 chk1 chk2 a: forall + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (HSTORE: exec_store_double lk chk1 chk2 a v1 v2 rs1 m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), Asm.exec_store_double tge chk1 chk2 a v1 v2 rs2 m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + unfold exec_store_double, Asm.exec_store_double in *. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + erewrite <- !eval_addressing_preserved; eauto. + destruct (is_pair_addressing_mode_correct a); try discriminate. + destruct (Mem.storev _ _ _ _); + try destruct (Mem.storev chk2 m + (eval_addressing lk + (get_offset_addr a + match chk1 with + | Mint32 | Mfloat32 | Many32 => 4 + | _ => 8 + end) rs1) v2); + inversion HSTORE; auto. + repeat (econstructor; eauto). + * eapply nextinstr_agree_but_pc; intros. + subst. apply EQR. auto. + * eapply ptrofs_nextinstr_agree; subst; eauto. +Qed. + +Lemma next_inst_preserved n rs1 m1 rs1' m1' rs2 m2 (x: dreg) v: forall + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (NEXTI: Next rs1 # x <- v m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), + Next (Asm.nextinstr rs2 # x <- v) m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + inversion NEXTI. repeat (econstructor; eauto). + * eapply nextinstr_agree_but_pc; intros. + destruct (PregEq.eq r x); try update_x_access_x; try update_x_access_r. + * eapply ptrofs_nextinstr_agree; eauto. +Qed. + +Lemma match_internal_nextinstr_switch: + forall n s rs2 m2 r v, + r <> PC -> + match_internal n s (State ((Asm.nextinstr rs2)#r <- v) m2) -> + match_internal n s (State (Asm.nextinstr (rs2#r <- v)) m2). +Proof. + unfold Asm.nextinstr; intros n s rs2 m2 r v NOTPC1 MI. + inversion MI; subst; constructor; auto. + - eapply nextinstr_agree_but_pc; intros. + rewrite AG; try congruence. + destruct (PregEq.eq r r0); try update_x_access_x; try update_x_access_r. + - rewrite !Pregmap.gss, !Pregmap.gso; try congruence. + rewrite AGPC. + rewrite Pregmap.gso, Pregmap.gss; try congruence. +Qed. + +Lemma match_internal_nextinstr_set_parallel: + forall n rs1 m1 rs2 m2 r v1 v2, + r <> PC -> + match_internal n (State rs1 m1) (State (Asm.nextinstr rs2) m2) -> + v1 = v2 -> + match_internal n (State (rs1#r <- v1) m1) (State (Asm.nextinstr (rs2#r <- v2)) m2). +Proof. + intros; subst; eapply match_internal_nextinstr_switch; eauto. + intros; eapply match_internal_set_parallel; eauto. +Qed. + +Lemma exec_basic_simulation: + forall tf n rs1 m1 rs1' m1' rs2 m2 bi tbi + (BOUNDED: 0 <= n <= Ptrofs.max_unsigned) + (BASIC: exec_basic lk ge bi rs1 m1 = Next rs1' m1') + (MATCHI: match_internal n (State rs1 m1) (State rs2 m2)) + (TRANSBI: basic_to_instruction bi = OK tbi), + exists rs2' m2', Asm.exec_instr tge tf tbi + rs2 m2 = Next rs2' m2' + /\ match_internal (n + 1) (State rs1' m1') (State rs2' m2'). +Proof. + intros. + destruct bi. + { (* PArith *) + simpl in *; destruct i. + 1: { + destruct i. + 1,2,3: + try (destruct sumbool_rec; try congruence); + try (monadInv TRANSBI); + try (destruct_reg_inv); + try (inv_matchi); + try (exploit next_inst_preserved; eauto); + try (repeat destruct_reg_size); + try (destruct_ir0_reg). + 1,2: (* Special case for Pfmovimmd / Pfmovimms *) + try (monadInv TRANSBI); + try (destruct_reg_inv); + try (inv_matchi); + inversion BASIC; clear BASIC; subst; + try (destruct (is_immediate_float64 _)); + try (destruct (is_immediate_float32 _)); + eexists; eexists; split; eauto; + repeat (eapply match_internal_nextinstr_set_parallel; try congruence); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). + } + 1,2,3,4,5: (* PArithP, PArithPP, PArithPPP, PArithRR0R, PArithRR0, PArithARRRR0 *) + destruct i; + try (destruct sumbool_rec; try congruence); + try (monadInv TRANSBI); + try (destruct_reg_inv); + try (inv_matchi); + try (exploit next_inst_preserved; eauto); + try (repeat destruct_reg_size); + try (destruct_ir0_reg). + { (* PArithComparisonPP *) + destruct i; + try (monadInv TRANSBI); + try (inv_matchi); + try (destruct_reg_inv); + simpl in *. + 1,2: (* compare_long *) + inversion BASIC; clear BASIC; subst; + eexists; eexists; split; eauto; + unfold compare_long; + repeat (eapply match_internal_nextinstr_set_parallel; [ congruence | idtac | try (rewrite !AG; congruence)]); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). + + destruct sz. + - (* compare_single *) + unfold compare_single in BASIC. + destruct (rs1 x), (rs1 x0); + inversion BASIC; + eexists; eexists; split; eauto; + repeat (eapply match_internal_nextinstr_set_parallel; [ congruence | idtac | try (rewrite !AG; congruence)]); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). + - (* compare_float *) + unfold compare_float in BASIC. + destruct (rs1 x), (rs1 x0); + inversion BASIC; + eexists; eexists; split; eauto; + repeat (eapply match_internal_nextinstr_set_parallel; [ congruence | idtac | try (rewrite !AG; congruence)]); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). } + 1,2: (* PArithComparisonR0R, PArithComparisonP *) + destruct i; + try (monadInv TRANSBI); + try (inv_matchi); + try (destruct_reg_inv); + try (destruct_reg_size); + simpl in *; + inversion BASIC; clear BASIC; subst; + eexists; eexists; split; eauto; + unfold compare_long, compare_int, compare_float, compare_single; + try (destruct_reg_size); + repeat (eapply match_internal_nextinstr_set_parallel; [ congruence | idtac | try (rewrite !AG; congruence)]); + try (econstructor; eauto); + try (destruct_ir0_reg); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). + { (* Pcset *) + try (monadInv TRANSBI); + try (inv_matchi). + try (exploit next_inst_preserved; eauto); + try (simpl in *; intros; + unfold if_opt_bool_val in *; unfold eval_testcond in *; + rewrite <- !AG; try congruence; eauto). } + { (* Pfmovi *) + try (monadInv TRANSBI); + try (inv_matchi); + try (destruct_reg_size); + try (destruct_ir0_reg); + try (exploit next_inst_preserved; eauto). } + { (* Pcsel *) + try (destruct_reg_inv); + try (monadInv TRANSBI); + try (destruct_reg_inv); + try (inv_matchi); + try (exploit next_inst_preserved; eauto); + simpl in *; intros; + unfold if_opt_bool_val in *; unfold eval_testcond in *; + rewrite <- !AG; try congruence; eauto. } + { (* Pfnmul *) + try (monadInv TRANSBI); + try (inv_matchi); + try (destruct_reg_size); + try (exploit next_inst_preserved; eauto); + try (find_rwrt_ag). } } + { (* PLoad *) + destruct ld. + - destruct ld; monadInv TRANSBI; try destruct_ireg_inv; exploit load_rd_a_preserved; eauto; + intros; simpl in *; destruct sz; eauto. + - destruct ld; monadInv TRANSBI; destruct rd1 as [[rd1'|]|]; destruct rd2 as [[rd2'|]|]; + inv EQ; inv EQ1; exploit load_double_preserved; eauto. } + { (* PStore *) + destruct st. + - destruct st; monadInv TRANSBI; try destruct_ireg_inv; exploit store_rs_a_preserved; eauto; + simpl in *; inv_matchi; find_rwrt_ag. + - destruct st; monadInv TRANSBI; destruct rs0 as [[rs0'|]|]; destruct rs3 as [[rs3'|]|]; + inv EQ; inv EQ1; exploit store_double_preserved; eauto; + simpl in *; inv_matchi; find_rwrt_ag. } + { (* Pallocframe *) + monadInv TRANSBI; + inv_matchi; try pc_not_sp; + destruct sz eqn:EQSZ; + destruct Mem.alloc eqn:EQALLOC; + destruct Mem.store eqn:EQSTORE; inversion BASIC; try pc_not_sp; + eexists; eexists; split; eauto; + repeat (eapply match_internal_nextinstr_set_parallel; [ try (pc_not_sp; congruence) | idtac | try (reflexivity)]); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). } + { (* Pfreeframe *) + monadInv TRANSBI; + inv_matchi; try pc_not_sp; + destruct sz eqn:EQSZ; + destruct Mem.loadv eqn:EQLOAD; + destruct (rs1 SP) eqn:EQRS1SP; + try (destruct Mem.free eqn:EQFREE); + inversion BASIC; try pc_not_sp; + eexists; eexists; split; eauto; + repeat (eapply match_internal_nextinstr_set_parallel; [ try (pc_not_sp; congruence) | idtac | try (reflexivity)]); + try (econstructor; eauto); + try (eapply nextinstr_agree_but_pc; eauto); + try (eapply ptrofs_nextinstr_agree; eauto). } + 1,2,3,4: (* Ploadsymbol, Pcvtsw2x, Pcvtuw2x, Pcvtx2w *) + try (monadInv TRANSBI); + try (inv_matchi); + try (exploit next_inst_preserved; eauto); + rewrite symbol_addresses_preserved; eauto; + try (find_rwrt_ag). + { (* Pnop *) + monadInv TRANSBI; inv_matchi. + inversion BASIC. + repeat (econstructor; eauto). + eapply nextinstr_agree_but_pc; intros; + try rewrite <- H0, AG; auto. + try eapply ptrofs_nextinstr_agree; auto; rewrite <- H0; + assumption. } +Qed. + +Lemma find_basic_instructions b ofs f bb tc: forall + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (UNFOLD: unfold (fn_blocks f) = OK tc), + forall n, + (n < length (body bb))%nat -> + exists (i : Asm.instruction) (bi : basic), + list_nth_z (body bb) (Z.of_nat n) = Some bi + /\ basic_to_instruction bi = OK i + /\ Asm.find_instr (Ptrofs.unsigned ofs + + (list_length_z (header bb)) + + Z.of_nat n) tc + = Some i. +Proof. + intros until n; intros NLT. + exploit internal_functions_unfold; eauto. + intros (tc' & FINDtf & TRANStf & _). + assert (tc' = tc) by congruence; subst. + exploit (find_instr_bblock (list_length_z (header bb) + Z.of_nat n)); eauto. + { unfold size; split. + - rewrite list_length_z_nat; lia. + - repeat (rewrite list_length_z_nat). repeat (rewrite Nat2Z.inj_add). lia. } + intros (i & NTH & FIND_INSTR). + exists i; intros. + inv NTH. + - (* absurd *) apply list_nth_z_range in H; lia. + - exists bi; + rewrite Z.add_simpl_l in H; + rewrite Z.add_assoc in FIND_INSTR; + intuition. + - (* absurd *) rewrite bblock_size_aux in H0; + rewrite H in H0; simpl in H0; repeat rewrite list_length_z_nat in H0; lia. +Qed. + +(* TODO: remplacer find_basic_instructions directement par ce lemme ? *) +Lemma find_basic_instructions_alt b ofs f bb tc n: forall + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (UNFOLD: unfold (fn_blocks f) = OK tc) + (BOUND: 0 <= n < list_length_z (body bb)), + exists (i : Asm.instruction) (bi : basic), + list_nth_z (body bb) n = Some bi + /\ basic_to_instruction bi = OK i + /\ Asm.find_instr (Ptrofs.unsigned ofs + + (list_length_z (header bb)) + + n) tc + = Some i. +Proof. + intros; assert ((Z.to_nat n) < length (body bb))%nat. + { rewrite Nat2Z.inj_lt, <- list_length_z_nat, Z2Nat.id; try lia. } + exploit find_basic_instructions; eauto. + rewrite Z2Nat.id; try lia. intros (i & bi & X). + eexists; eexists; intuition eauto. +Qed. + +Lemma header_body_tail_bound: forall (a: basic) (li: list basic) bb ofs + (BOUNDBB : Ptrofs.unsigned ofs + size bb <= Ptrofs.max_unsigned) + (BDYLENPOS : 0 <= list_length_z (body bb) - list_length_z (a :: li) < + list_length_z (body bb)), +0 <= list_length_z (header bb) + list_length_z (body bb) - list_length_z (a :: li) <= +Ptrofs.max_unsigned. +Proof. + intros. + assert (HBBPOS: list_length_z (header bb) >= 0) by eapply list_length_z_pos. + assert (HBBSIZE: list_length_z (header bb) < size bb) by eapply header_size_lt_block_size. + assert (OFSBOUND: 0 <= Ptrofs.unsigned ofs <= Ptrofs.max_unsigned) by eapply Ptrofs.unsigned_range_2. + assert (BBSIZE: size bb <= Ptrofs.max_unsigned) by lia. + unfold size in BBSIZE. + rewrite !Nat2Z.inj_add in BBSIZE. + rewrite <- !list_length_z_nat in BBSIZE. + lia. +Qed. + +(* A more general version of the exec_body_simulation_plus lemma below. + This generalization is necessary for the induction proof inside the body. +*) +Lemma exec_body_simulation_plus_gen li: forall b ofs f bb rs m s2 rs' m' + (BLI: is_tail li (body bb)) + (ATPC: rs PC = Vptr b ofs) + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (NEMPTY_BODY: li <> nil) + (MATCHI: match_internal ((list_length_z (header bb)) + (list_length_z (body bb)) - (list_length_z li)) (State rs m) s2) + (BODY: exec_body lk ge li rs m = Next rs' m'), + exists s2', plus Asm.step tge s2 E0 s2' + /\ match_internal (size bb - (Z.of_nat (length_opt (exit bb)))) (State rs' m') s2'. +Proof. + induction li as [|a li]; simpl; try congruence. + intros. + assert (BDYLENPOS: 0 <= (list_length_z (body bb) - list_length_z (a::li)) < list_length_z (body bb)). { + assert (Z.of_nat O < list_length_z (a::li) <= list_length_z (body bb)); try lia. + rewrite !list_length_z_nat; split. + - rewrite <- Nat2Z.inj_lt. simpl. lia. + - rewrite <- Nat2Z.inj_le; eapply is_tail_bound; eauto. + } + exploit internal_functions_unfold; eauto. + intros (tc & FINDtf & TRANStf & _). + exploit find_basic_instructions_alt; eauto. + intros (tbi & (bi & (NTHBI & TRANSBI & FIND_INSTR))). + exploit is_tail_list_nth_z; eauto. + rewrite NTHBI; simpl. + intros X; inversion X; subst; clear X NTHBI. + destruct (exec_basic _ _ _ _ _) eqn:EXEC_BASIC; next_stuck_cong. + destruct s as (rs1 & m1); simpl in *. + destruct s2 as (rs2 & m2); simpl in *. + assert (BOUNDBBMAX: Ptrofs.unsigned ofs + size bb <= Ptrofs.max_unsigned) + by (eapply size_of_blocks_bounds; eauto). + exploit header_body_tail_bound; eauto. intros BDYTAIL. + exploit exec_basic_simulation; eauto. + intros (rs_next' & m_next' & EXEC_INSTR & MI_NEXT). + exploit exec_basic_dont_move_PC; eauto. intros AGPC. + inversion MI_NEXT as [A B C D E M_NEXT_AGREE RS_NEXT_AGREE ATPC_NEXT PC_OFS_NEXT RS RS']. + subst A. subst B. subst C. subst D. subst E. + rewrite ATPC in AGPC. symmetry in AGPC, ATPC_NEXT. + + inv MATCHI. symmetry in AGPC0. + rewrite ATPC in AGPC0. + unfold Val.offset_ptr in AGPC0. + + simpl in FIND_INSTR. + (* Execute internal step. *) + exploit (Asm.exec_step_internal tge b); eauto. + { + rewrite Ptrofs.add_unsigned. + repeat (rewrite Ptrofs.unsigned_repr); try lia. + 2: { + assert (BOUNDOFS: 0 <= Ptrofs.unsigned ofs <= Ptrofs.max_unsigned) by eapply Ptrofs.unsigned_range_2. + assert (list_length_z (body bb) <= size bb) by eapply body_size_le_block_size. + assert (list_length_z (header bb) <= 1). { eapply size_header; eauto. } + lia. } + try rewrite list_length_z_nat; try split; + simpl; rewrite <- !list_length_z_nat; + replace (Ptrofs.unsigned ofs + (list_length_z (header bb) + list_length_z (body bb) - + list_length_z (a :: li))) with (Ptrofs.unsigned ofs + list_length_z (header bb) + + (list_length_z (body bb) - list_length_z (a :: li))) by lia; + try assumption; try lia. } + + (* This is our STEP hypothesis. *) + intros STEP_NEXT. + destruct li as [|a' li]; simpl in *. + - (* case of a single instruction in li: this our base case in the induction *) + inversion BODY; subst. + eexists; split. + + apply plus_one. eauto. + + constructor; auto. + rewrite ATPC_NEXT. + apply f_equal. + apply f_equal. + rewrite bblock_size_aux, list_length_z_cons; simpl. + lia. + - exploit (IHli b ofs f bb rs1 m_next' (State rs_next' m_next')); congruence || eauto. + + exploit is_tail_app_def; eauto. + intros (l3 & EQ); rewrite EQ. + exploit (is_tail_app_right (l3 ++ a::nil)). + rewrite <- app_assoc; simpl; eauto. + + constructor; auto. + rewrite ATPC_NEXT. + apply f_equal. + apply f_equal. + rewrite! list_length_z_cons; simpl. + lia. + + intros (s2' & LAST_STEPS & LAST_MATCHS). + eexists. split; eauto. + eapply plus_left'; eauto. +Qed. + +Lemma exec_body_simulation_plus b ofs f bb rs m s2 rs' m': forall + (ATPC: rs PC = Vptr b ofs) + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (NEMPTY_BODY: body bb <> nil) + (MATCHI: match_internal (list_length_z (header bb)) (State rs m) s2) + (BODY: exec_body lk ge (body bb) rs m = Next rs' m'), + exists s2', plus Asm.step tge s2 E0 s2' + /\ match_internal (size bb - (Z.of_nat (length_opt (exit bb)))) (State rs' m') s2'. +Proof. + intros. + exploit exec_body_simulation_plus_gen; eauto. + - constructor. + - replace (list_length_z (header bb) + list_length_z (body bb) - list_length_z (body bb)) with (list_length_z (header bb)); auto. + lia. +Qed. + +Lemma exec_body_simulation_star b ofs f bb rs m s2 rs' m': forall + (ATPC: rs PC = Vptr b ofs) + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (MATCHI: match_internal (list_length_z (header bb)) (State rs m) s2) + (BODY: exec_body lk ge (body bb) rs m = Next rs' m'), + exists s2', star Asm.step tge s2 E0 s2' + /\ match_internal (size bb - (Z.of_nat (length_opt (exit bb)))) (State rs' m') s2'. +Proof. + intros. + destruct (body bb) eqn: Hbb. + - simpl in BODY. inv BODY. + eexists. split. + eapply star_refl; eauto. + assert (EQ: (size bb - Z.of_nat (length_opt (exit bb))) = list_length_z (header bb)). + { rewrite bblock_size_aux. rewrite Hbb; unfold list_length_z; simpl. lia. } + rewrite EQ; eauto. + - exploit exec_body_simulation_plus; congruence || eauto. + { rewrite Hbb; eauto. } + intros (s2' & PLUS & MATCHI'). + eexists; split; eauto. + eapply plus_star; eauto. +Qed. + +Lemma list_nth_z_range_exceeded A (l : list A) n: + n >= list_length_z l -> + list_nth_z l n = None. +Proof. + intros N. + remember (list_nth_z l n) as opt eqn:H. symmetry in H. + destruct opt; auto. + exploit list_nth_z_range; eauto. lia. +Qed. + +Lemma label_in_header_list lbl a: + is_label lbl a = true -> list_length_z (header a) <= 1 -> header a = lbl :: nil. +Proof. + intros. + eapply is_label_correct_true in H. + destruct (header a). + - eapply in_nil in H. contradiction. + - rewrite list_length_z_cons in H0. + assert (list_length_z l0 >= 0) by eapply list_length_z_pos. + assert (list_length_z l0 = 0) by lia. + rewrite list_length_z_nat in H2. + assert (Datatypes.length l0 = 0%nat) by lia. + eapply length_zero_iff_nil in H3. subst. + unfold In in H. destruct H. + + subst; eauto. + + destruct H. +Qed. + +Lemma no_label_in_basic_inst: forall a lbl x, + basic_to_instruction a = OK x -> Asm.is_label lbl x = false. +Proof. + intros. + destruct a; simpl in *; + repeat destruct i; + repeat destruct ld; repeat destruct st; + simpl in *; + try (try destruct_reg_inv; monadInv H; simpl in *; reflexivity). +Qed. + +Lemma label_pos_body bdy: forall c1 c2 z ex lbl + (HUNF : unfold_body bdy = OK c2), + Asm.label_pos lbl (z + Z.of_nat ((Datatypes.length bdy) + length_opt ex)) c1 = Asm.label_pos lbl (z) ((c2 ++ unfold_exit ex) ++ c1). +Proof. + induction bdy. + - intros. inversion HUNF. simpl in *. + destruct ex eqn:EQEX. + + simpl in *. unfold Asm.is_label. destruct c; simpl; try congruence. + destruct i; simpl; try congruence. + + simpl in *. ring_simplify (z + 0). auto. + - intros. inversion HUNF; clear HUNF. monadInv H0. simpl in *. + erewrite no_label_in_basic_inst; eauto. rewrite <- IHbdy; eauto. + erewrite Zpos_P_of_succ_nat. + apply f_equal2; auto. lia. +Qed. + +Lemma asm_label_pos_header: forall z a x0 x1 lbl + (HUNF: unfold_body (body a) = OK x1), + Asm.label_pos lbl (z + size a) x0 = + Asm.label_pos lbl (z + list_length_z (header a)) ((x1 ++ unfold_exit (exit a)) ++ x0). +Proof. + intros. + unfold size. + rewrite <- plus_assoc. rewrite Nat2Z.inj_add. + rewrite list_length_z_nat. + replace (z + (Z.of_nat (Datatypes.length (header a)) + Z.of_nat (Datatypes.length (body a) + length_opt (exit a)))) with (z + Z.of_nat (Datatypes.length (header a)) + Z.of_nat (Datatypes.length (body a) + length_opt (exit a))) by lia. + eapply (label_pos_body (body a) x0 x1 (z + Z.of_nat (Datatypes.length (header a))) (exit a) lbl). auto. +Qed. + +Lemma header_size_cons_nil: forall (l0: label) (l1: list label) + (HSIZE: list_length_z (l0 :: l1) <= 1), + l1 = nil. +Proof. + intros. + destruct l1; try congruence. rewrite !list_length_z_cons in HSIZE. + assert (list_length_z l1 >= 0) by eapply list_length_z_pos. + assert (list_length_z l1 + 1 + 1 >= 2) by lia. + assert (2 <= 1) by lia. contradiction H1. lia. +Qed. + +Lemma label_pos_preserved_gen bbs: forall lbl c z + (HUNF: unfold bbs = OK c), + label_pos lbl z bbs = Asm.label_pos lbl z c. +Proof. + induction bbs. + - intros. simpl in *. inversion HUNF. simpl. reflexivity. + - intros. simpl in *. monadInv HUNF. unfold unfold_bblock in EQ. + destruct (zle _ _); try congruence. monadInv EQ. + destruct (is_label _ _) eqn:EQLBL. + + erewrite label_in_header_list; eauto. + simpl in *. destruct (peq lbl lbl); try congruence. + + erewrite IHbbs; eauto. + rewrite (asm_label_pos_header z a x0 x1 lbl); auto. + unfold is_label in *. + destruct (header a). + * replace (z + list_length_z (@nil label)) with (z); eauto. + unfold list_length_z. simpl. lia. + * eapply header_size_cons_nil in l as HL1. + subst. simpl in *. destruct (in_dec _ _); try congruence. + simpl in *. + destruct (peq _ _); try intuition congruence. +Qed. + +Lemma label_pos_preserved f lbl z tf: forall + (FINDF: transf_function f = OK tf), + label_pos lbl z (fn_blocks f) = Asm.label_pos lbl z (Asm.fn_code tf). +Proof. + intros. + eapply label_pos_preserved_gen. + unfold transf_function in FINDF. monadInv FINDF. + destruct zlt; try congruence. inversion EQ0. eauto. +Qed. + +Lemma goto_label_preserved bb rs1 m1 rs1' m1' rs2 m2 lbl f tf v: forall + (FINDF: transf_function f = OK tf) + (BOUNDED: size bb <= Ptrofs.max_unsigned) + (MATCHI: match_internal (size bb - 1) (State rs1 m1) (State rs2 m2)) + (HGOTO: goto_label f lbl (incrPC v rs1) m1 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), Asm.goto_label tf lbl rs2 m2 = Next rs2' m2' + /\ match_states (State rs1' m1') (State rs2' m2'). +Proof. + intros. + unfold goto_label, Asm.goto_label in *. + rewrite <- (label_pos_preserved f); auto. + inversion MATCHI as [n0 r1 mx1 r2 mx2 EQM EQR EQPC]; subst. + destruct label_pos; next_stuck_cong. + destruct (incrPC v rs1 PC) eqn:INCRPC; next_stuck_cong. + inversion HGOTO; auto. repeat (econstructor; eauto). + rewrite <- EQPC. + unfold incrPC in *. + rewrite !Pregmap.gss in *. + destruct (rs1 PC) eqn:EQRS1; simpl in *; try congruence. + replace (rs2 # PC <- (Vptr b0 (Ptrofs.repr z))) with ((rs1 # PC <- (Vptr b0 (Ptrofs.add i0 v))) # PC <- (Vptr b (Ptrofs.repr z))); auto. + eapply functional_extensionality. intros. + destruct (PregEq.eq x PC); subst. + rewrite !Pregmap.gss. congruence. + rewrite !Pregmap.gso; auto. +Qed. + +Lemma next_inst_incr_pc_preserved bb rs1 m1 rs1' m1' rs2 m2 f tf: forall + (FINDF: transf_function f = OK tf) + (BOUNDED: size bb <= Ptrofs.max_unsigned) + (MATCHI: match_internal (size bb - 1) (State rs1 m1) (State rs2 m2)) + (NEXT: Next (incrPC (Ptrofs.repr (size bb)) rs1) m2 = Next rs1' m1'), + exists (rs2' : regset) (m2' : mem), + Next (Asm.nextinstr rs2) m2 = Next rs2' m2' + /\ match_states (State rs1' m1') (State rs2' m2'). +Proof. + intros; simpl in *; unfold incrPC in NEXT; + inv_matchi; + assert (size bb >= 1) by eapply bblock_size_pos; + assert (0 <= size bb - 1 <= Ptrofs.max_unsigned) by lia; + inversion NEXT; subst; + eexists; eexists; split; eauto. + assert (rs1 # PC <- (Val.offset_ptr (rs1 PC) (Ptrofs.repr (size bb))) = Asm.nextinstr rs2). { + unfold Pregmap.set. apply functional_extensionality. + intros x. destruct (PregEq.eq x PC). + -- unfold Asm.nextinstr. rewrite <- AGPC. + rewrite Val.offset_ptr_assoc. rewrite Ptrofs.add_unsigned. + rewrite (Ptrofs.unsigned_repr (size bb - 1)); try lia. + rewrite Ptrofs.unsigned_one. + replace (size bb - 1 + 1) with (size bb) by lia. + rewrite e. rewrite Pregmap.gss. + reflexivity. + -- eapply nextinstr_agree_but_pc; eauto. } + rewrite H1. econstructor. +Qed. + +Lemma pc_reg_overwrite: forall (r: ireg) rs1 m1 rs2 m2 bb + (MATCHI: match_internal (size bb - 1) (State rs1 m1) (State rs2 m2)), + rs2 # PC <- (rs2 r) = + (rs1 # PC <- (Val.offset_ptr (rs1 PC) (Ptrofs.repr (size bb)))) # PC <- + (rs1 r). +Proof. + intros. + unfold Pregmap.set; apply functional_extensionality. + intros x; destruct (PregEq.eq x PC) as [X | X]; try discriminate; inv_matchi. +Qed. + +Lemma exec_cfi_simulation: + forall bb f tf rs1 m1 rs1' m1' rs2 m2 cfi + (SIZE: size bb <= Ptrofs.max_unsigned) + (FINDF: transf_function f = OK tf) + (* Warning: Asmblock's PC is assumed to be already pointing on the next instruction ! *) + (CFI: exec_cfi ge f cfi (incrPC (Ptrofs.repr (size bb)) rs1) m1 = Next rs1' m1') + (MATCHI: match_internal (size bb - 1) (State rs1 m1) (State rs2 m2)), + exists rs2' m2', Asm.exec_instr tge tf (cf_instruction_to_instruction cfi) + rs2 m2 = Next rs2' m2' + /\ match_states (State rs1' m1') (State rs2' m2'). +Proof. + intros. + assert (BBPOS: size bb >= 1) by eapply bblock_size_pos. + destruct cfi; inv CFI; simpl. + - (* Pb *) + exploit goto_label_preserved; eauto. + - (* Pbc *) + inv_matchi. + unfold eval_testcond in *. destruct c; + erewrite !incrPC_agree_but_pc in H0; try rewrite <- !AG; try congruence. + all: + destruct_reg_size; + try destruct b eqn:EQB. + 1,4,7,10,13,16,19,22,25,28,31,34: + exploit goto_label_preserved; eauto. + 1,3,5,7,9,11,13,15,17,19,21,23: + exploit next_inst_incr_pc_preserved; eauto. + all: repeat (econstructor; eauto). + - (* Pbl *) + eexists; eexists; split; eauto. + assert ( ((incrPC (Ptrofs.repr (size bb)) rs1) # X30 <- (incrPC (Ptrofs.repr (size bb)) rs1 PC)) + # PC <- (Genv.symbol_address ge id Ptrofs.zero) + = (rs2 # X30 <- (Val.offset_ptr (rs2 PC) Ptrofs.one)) + # PC <- (Genv.symbol_address tge id Ptrofs.zero) + ) as EQRS. { + unfold incrPC. unfold Pregmap.set. simpl. apply functional_extensionality. + intros x. destruct (PregEq.eq x PC). + * rewrite symbol_addresses_preserved. reflexivity. + * destruct (PregEq.eq x X30). + -- inv MATCHI. rewrite <- AGPC. rewrite Val.offset_ptr_assoc. + unfold Ptrofs.add, Ptrofs.one. repeat (rewrite Ptrofs.unsigned_repr); try lia. + replace (size bb - 1 + 1) with (size bb) by lia. reflexivity. + -- inv MATCHI; rewrite AG; try assumption; reflexivity. + } rewrite EQRS; inv MATCHI; reflexivity. + - (* Pbs *) + eexists; eexists; split; eauto. + assert ( (incrPC (Ptrofs.repr (size bb)) rs1) # PC <- + (Genv.symbol_address ge id Ptrofs.zero) + = rs2 # PC <- (Genv.symbol_address tge id Ptrofs.zero) + ) as EQRS. { + unfold incrPC, Pregmap.set. rewrite symbol_addresses_preserved. inv MATCHI. + apply functional_extensionality. intros x. destruct (PregEq.eq x PC); auto. + } rewrite EQRS; inv MATCHI; reflexivity. + - (* Pblr *) + eexists; eexists; split; eauto. + unfold incrPC. rewrite Pregmap.gss. rewrite Pregmap.gso; try discriminate. + assert ( (rs2 # X30 <- (Val.offset_ptr (rs2 PC) Ptrofs.one)) # PC <- (rs2 r) + = ((rs1 # PC <- (Val.offset_ptr (rs1 PC) (Ptrofs.repr (size bb)))) + # X30 <- (Val.offset_ptr (rs1 PC) (Ptrofs.repr (size bb)))) + # PC <- (rs1 r) + ) as EQRS. { + unfold Pregmap.set. apply functional_extensionality. + intros x; destruct (PregEq.eq x PC) as [X | X]. + - inv_matchi; rewrite AG; auto. + - destruct (PregEq.eq x X30) as [X' | X']. + + inversion MATCHI; subst. rewrite <- AGPC. + rewrite Val.offset_ptr_assoc. unfold Ptrofs.one. + rewrite Ptrofs.add_unsigned. rewrite Ptrofs.unsigned_repr; try lia. rewrite Ptrofs.unsigned_repr; try lia. + rewrite Z.sub_add; reflexivity. + + inv_matchi. + } rewrite EQRS. inv_matchi. + - (* Pbr *) + eexists; eexists; split; eauto. + unfold incrPC. rewrite Pregmap.gso; try discriminate. + rewrite (pc_reg_overwrite r rs1 m1' rs2 m2 bb); auto. + inv_matchi. + - (* Pret *) + eexists; eexists; split; eauto. + unfold incrPC. rewrite Pregmap.gso; try discriminate. + rewrite (pc_reg_overwrite r rs1 m1' rs2 m2 bb); auto. + inv_matchi. + - (* Pcbnz *) + inv_matchi. + unfold eval_neg_branch in *. + erewrite incrPC_agree_but_pc in H0; try congruence. + destruct eval_testzero; next_stuck_cong. + destruct b. + * exploit next_inst_incr_pc_preserved; eauto. + * exploit goto_label_preserved; eauto. + - (* Pcbz *) + inv_matchi. + unfold eval_branch in *. + erewrite incrPC_agree_but_pc in H0; try congruence. + destruct eval_testzero; next_stuck_cong. + destruct b. + * exploit goto_label_preserved; eauto. + * exploit next_inst_incr_pc_preserved; eauto. + - (* Ptbnbz *) + inv_matchi. + unfold eval_branch in *. + erewrite incrPC_agree_but_pc in H0; try congruence. + destruct eval_testbit; next_stuck_cong. + destruct b. + * exploit goto_label_preserved; eauto. + * exploit next_inst_incr_pc_preserved; eauto. + - (* Ptbz *) + inv_matchi. + unfold eval_neg_branch in *. + erewrite incrPC_agree_but_pc in H0; try congruence. + destruct eval_testbit; next_stuck_cong. + destruct b. + * exploit next_inst_incr_pc_preserved; eauto. + * exploit goto_label_preserved; eauto. + - (* Pbtbl *) + assert (rs2 # X16 <- Vundef r1 = (incrPC (Ptrofs.repr (size bb)) rs1) # X16 <- Vundef r1) + as EQUNDEFX16. { + unfold incrPC, Pregmap.set. + destruct (PregEq.eq r1 X16) as [X16 | X16]; auto. + destruct (PregEq.eq r1 PC) as [PC' | PC']; try discriminate. + inv MATCHI; rewrite AG; auto. + } rewrite <- EQUNDEFX16 in H0. + destruct_reg_inv; next_stuck_cong. + unfold goto_label, Asm.goto_label in *. + rewrite <- (label_pos_preserved f); auto. + inversion MATCHI; subst. + destruct label_pos; next_stuck_cong. + destruct ((incrPC (Ptrofs.repr (size bb)) rs1) # X16 <- Vundef PC) eqn:INCRPC; next_stuck_cong. + inversion H0; auto. repeat (econstructor; eauto). + rewrite !Pregmap.gso; try congruence. + rewrite <- AGPC. + unfold incrPC in *. + destruct (rs1 PC) eqn:EQRS1; simpl in *; try discriminate. + replace ((rs2 # X16 <- Vundef) # PC <- (Vptr b0 (Ptrofs.repr z))) with + (((rs1 # PC <- (Vptr b0 (Ptrofs.add i1 (Ptrofs.repr (size bb))))) # X16 <- + Vundef) # PC <- (Vptr b (Ptrofs.repr z))); auto. + eapply functional_extensionality; intros x. + destruct (PregEq.eq x PC); subst. + + rewrite Pregmap.gso in INCRPC; try congruence. + rewrite Pregmap.gss in INCRPC. + rewrite !Pregmap.gss in *; congruence. + + rewrite Pregmap.gso; auto. + rewrite (Pregmap.gso (i := x) (j := PC)); auto. + destruct (PregEq.eq x X16); subst. + * rewrite !Pregmap.gss; auto. + * rewrite !Pregmap.gso; auto. +Qed. + +Lemma last_instruction_cannot_be_label bb: + list_nth_z (header bb) (size bb - 1) = None. +Proof. + assert (list_length_z (header bb) <= size bb - 1). { + rewrite bblock_size_aux. generalize (bblock_size_aux_pos bb). lia. + } + remember (list_nth_z (header bb) (size bb - 1)) as label_opt; destruct label_opt; auto; + exploit list_nth_z_range; eauto; lia. +Qed. + +Lemma pc_ptr_exec_step: forall ofs bb b rs m _rs _m + (ATPC : rs PC = Vptr b ofs) + (MATCHI : match_internal (size bb - 1) + {| _rs := rs; _m := m |} + {| _rs := _rs; _m := _m |}), + _rs PC = Vptr b (Ptrofs.add ofs (Ptrofs.repr (size bb - 1))). +Proof. + intros; inv MATCHI. rewrite <- AGPC; rewrite ATPC; unfold Val.offset_ptr; eauto. +Qed. + +Lemma find_instr_ofs_somei: forall ofs bb f tc asmi rs m _rs _m + (BOUNDOFS : Ptrofs.unsigned ofs + size bb <= Ptrofs.max_unsigned) + (FIND_INSTR : Asm.find_instr (Ptrofs.unsigned ofs + (size bb - 1)) tc = + Some (asmi)) + (MATCHI : match_internal (size bb - 1) + {| _rs := rs; _m := m |} + {| _rs := _rs; _m := _m |}), + Asm.find_instr (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr (size bb - 1)))) + (Asm.fn_code {| Asm.fn_sig := fn_sig f; Asm.fn_code := tc |}) = + Some (asmi). +Proof. + intros; simpl. + replace (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr (size bb - 1)))) + with (Ptrofs.unsigned ofs + (size bb - 1)); try assumption. + generalize (bblock_size_pos bb); generalize (Ptrofs.unsigned_range_2 ofs); intros. + unfold Ptrofs.add. + rewrite Ptrofs.unsigned_repr. rewrite Ptrofs.unsigned_repr; try lia. + rewrite Ptrofs.unsigned_repr; lia. +Qed. + +Lemma eval_builtin_arg_match: forall rs _m _rs a1 b1 + (AG : forall r : preg, r <> PC -> rs r = _rs r) + (EVAL : eval_builtin_arg tge (fun r : dreg => rs r) (rs SP) _m a1 b1), + eval_builtin_arg tge _rs (_rs SP) _m (map_builtin_arg DR a1) b1. +Proof. + intros; induction EVAL; simpl in *; try rewrite AG; try rewrite AG in EVAL; try discriminate; try congruence; eauto with barg. + econstructor. rewrite <- AG; try discriminate; auto. +Qed. + +Lemma eval_builtin_args_match: forall bb rs m _rs _m args vargs + (MATCHI : match_internal (size bb - 1) + {| _rs := rs; _m := m |} + {| _rs := _rs; _m := _m |}) + (EVAL : eval_builtin_args tge (fun r : dreg => rs r) (rs SP) m args vargs), + eval_builtin_args tge _rs (_rs SP) _m (map (map_builtin_arg DR) args) vargs. +Proof. + intros; inv MATCHI. + induction EVAL; subst. + - econstructor. + - econstructor. + + eapply eval_builtin_arg_match; eauto. + + eauto. +Qed. + +Lemma pc_both_sides: forall (rs _rs: regset) v + (AG : forall r : preg, r <> PC -> rs r = _rs r), + rs # PC <- v = _rs # PC <- v. +Proof. + intros; unfold Pregmap.set; apply functional_extensionality; intros y. + destruct (PregEq.eq y PC); try rewrite AG; eauto. +Qed. + +Lemma set_buitin_res_sym res: forall vres rs _rs r + (NPC: r <> PC) + (AG : forall r : preg, r <> PC -> rs r = _rs r), + set_res res vres rs r = set_res res vres _rs r. +Proof. + induction res; simpl; intros; unfold Pregmap.set; try rewrite AG; eauto. +Qed. + +Lemma set_builtin_res_dont_move_pc_gen res: forall vres rs _rs v1 v2 + (HV: v1 = v2) + (AG : forall r : preg, r <> PC -> rs r = _rs r), + (set_res res vres rs) # PC <- v1 = + (set_res res vres _rs) # PC <- v2. +Proof. + intros. rewrite HV. generalize res vres rs _rs AG v2. + clear res vres rs _rs AG v1 v2 HV. + induction res. + - simpl; intros. apply pc_both_sides; intros. + unfold Pregmap.set; try rewrite AG; eauto. + - simpl; intros; apply pc_both_sides; eauto. + - simpl; intros. + erewrite IHres2; eauto; intros. + eapply set_buitin_res_sym; eauto. +Qed. + +Lemma set_builtin_map_not_pc (res: builtin_res dreg): forall vres rs, + set_res (map_builtin_res DR res) vres rs PC = rs PC. +Proof. + induction res. + - intros; simpl. unfold Pregmap.set. destruct (PregEq.eq PC x); try congruence. + - intros; simpl; congruence. + - intros; simpl in *. rewrite IHres2. rewrite IHres1. reflexivity. +Qed. + +Lemma undef_reg_preserved (rl: list mreg): forall rs _rs r + (NPC: r <> PC) + (AG : forall r : preg, r <> PC -> rs r = _rs r), + undef_regs (map preg_of rl) rs r = undef_regs (map preg_of rl) _rs r. +Proof. + induction rl. + - simpl; auto. + - simpl; intros. erewrite IHrl; eauto. + intros. unfold Pregmap.set. destruct (PregEq.eq r0 (preg_of a)); try rewrite AG; eauto. +Qed. + +Lemma undef_regs_other: + forall r rl rs, + (forall r', In r' rl -> r <> r') -> + undef_regs rl rs r = rs r. +Proof. + induction rl; simpl; intros. auto. + rewrite IHrl by auto. rewrite Pregmap.gso; auto. +Qed. + +Fixpoint preg_notin (r: preg) (rl: list mreg) : Prop := + match rl with + | nil => True + | r1 :: nil => r <> preg_of r1 + | r1 :: rl => r <> preg_of r1 /\ preg_notin r rl + end. + +<<<<<<< HEAD +Remark preg_notin_charact: + forall r rl, + preg_notin r rl <-> (forall mr, In mr rl -> r <> preg_of mr). +Proof. + induction rl; simpl; intros. + tauto. + destruct rl. + simpl. split. intros. intuition congruence. auto. + rewrite IHrl. split. + intros [A B]. intros. destruct H. congruence. auto. + auto. +======= +Remark preg_of_not_X29: forall r, negb (mreg_eq r R29) = true -> IR X29 <> preg_of r. +Proof. + intros. change (IR X29) with (preg_of R29). red; intros. + exploit preg_of_injective; eauto. intros; subst r; discriminate. +Qed. + +Lemma sp_val': forall ms sp rs, agree ms sp rs -> sp = rs XSP. +Proof. + intros. eapply sp_val; eauto. +Qed. + +(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *) + +Theorem step_simulation: + forall S1 t S2, Mach.step return_address_offset ge S1 t S2 -> + forall S1' (MS: match_states S1 S1'), + (exists S2', plus step tge S1' t S2' /\ match_states S2 S2') + \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat. +Proof. + induction 1; intros; inv MS. + +- (* Mlabel *) + left; eapply exec_straight_steps; eauto; intros. + monadInv TR. econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split. apply agree_nextinstr; auto. simpl; congruence. + +- (* Mgetstack *) + unfold load_stack in H. + exploit Mem.loadv_extends; eauto. intros [v' [A B]]. + rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit loadind_correct; eauto with asmgen. intros [rs' [P [Q R]]]. + exists rs'; split. eauto. + split. eapply agree_set_mreg; eauto with asmgen. congruence. + simpl; congruence. + +- (* Msetstack *) + unfold store_stack in H. + assert (Val.lessdef (rs src) (rs0 (preg_of src))) by (eapply preg_val; eauto). + exploit Mem.storev_extends; eauto. intros [m2' [A B]]. + left; eapply exec_straight_steps; eauto. + rewrite (sp_val _ _ _ AG) in A. intros. simpl in TR. + exploit storeind_correct; eauto with asmgen. intros [rs' [P Q]]. + exists rs'; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; intros. rewrite Q; auto with asmgen. + +- (* Mgetparam *) + assert (f0 = f) by congruence; subst f0. + unfold load_stack in *. + exploit Mem.loadv_extends. eauto. eexact H0. auto. + intros [parent' [A B]]. rewrite (sp_val' _ _ _ AG) in A. + exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'. + exploit Mem.loadv_extends. eauto. eexact H1. auto. + intros [v' [C D]]. +Opaque loadind. + left; eapply exec_straight_steps; eauto; intros. monadInv TR. + destruct ep. +(* X30 contains parent *) + exploit loadind_correct. eexact EQ. + instantiate (2 := rs0). simpl; rewrite DXP; eauto. simpl; congruence. + intros [rs1 [P [Q R]]]. + exists rs1; split. eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen. + simpl; intros. rewrite R; auto with asmgen. + apply preg_of_not_X29; auto. +(* X30 does not contain parent *) + exploit loadptr_correct. eexact A. simpl; congruence. intros [rs1 [P [Q R]]]. + exploit loadind_correct. eexact EQ. instantiate (2 := rs1). simpl; rewrite Q. eauto. simpl; congruence. + intros [rs2 [S [T U]]]. + exists rs2; split. eapply exec_straight_trans; eauto. + split. eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto. + instantiate (1 := rs1#X29 <- (rs2#X29)). intros. + rewrite Pregmap.gso; auto with asmgen. + congruence. + intros. unfold Pregmap.set. destruct (PregEq.eq r' X29). congruence. auto with asmgen. + simpl; intros. rewrite U; auto with asmgen. + apply preg_of_not_X29; auto. + +- (* Mop *) + assert (eval_operation tge sp op (map rs args) m = Some v). + { rewrite <- H. apply eval_operation_preserved. exact symbols_preserved. } + exploit eval_operation_lessdef. eapply preg_vals; eauto. eauto. eexact H0. + intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. split. + apply agree_set_undef_mreg with rs0; auto. + apply Val.lessdef_trans with v'; auto. + simpl; intros. InvBooleans. + rewrite R; auto. apply preg_of_not_X29; auto. +Local Transparent destroyed_by_op. + destruct op; try exact I; simpl; congruence. + +- (* Mload *) + assert (Op.eval_addressing tge sp addr (map rs args) = Some a). + { rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. } + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + exploit Mem.loadv_extends; eauto. intros [v' [C D]]. + left; eapply exec_straight_steps; eauto; intros. simpl in TR. + exploit transl_load_correct; eauto. intros [rs2 [P [Q R]]]. + exists rs2; split. eauto. + split. eapply agree_set_undef_mreg; eauto. congruence. + simpl; congruence. + +- (* Mstore *) + assert (Op.eval_addressing tge sp addr (map rs args) = Some a). + { rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. } + exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. + intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. + assert (Val.lessdef (rs src) (rs0 (preg_of src))) by (eapply preg_val; eauto). + exploit Mem.storev_extends; eauto. intros [m2' [C D]]. + left; eapply exec_straight_steps; eauto. + intros. simpl in TR. exploit transl_store_correct; eauto. intros [rs2 [P Q]]. + exists rs2; split. eauto. + split. eapply agree_undef_regs; eauto with asmgen. + simpl; congruence. + +- (* Mcall *) + assert (f0 = f) by congruence. subst f0. + inv AT. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + { eapply transf_function_no_overflow; eauto. } + destruct ros as [rf|fid]; simpl in H; monadInv H5. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + { destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. } + assert (rs0 x0 = Vptr f' Ptrofs.zero). + { exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. } + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + { econstructor; eauto. } + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. ++ (* Direct call *) + generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. + assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). + econstructor; eauto. + exploit return_address_offset_correct; eauto. intros; subst ra. + left; econstructor; split. + apply plus_one. eapply exec_step_internal. eauto. + eapply functions_transl; eauto. eapply find_instr_tail; eauto. + simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto. + econstructor; eauto. + econstructor; eauto. + eapply agree_sp_def; eauto. + simpl. eapply agree_exten; eauto. intros. Simpl. + Simpl. rewrite <- H2. auto. + +- (* Mtailcall *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + { eapply transf_function_no_overflow; eauto. } + exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]]. + destruct ros as [rf|fid]; simpl in H; monadInv H7. ++ (* Indirect call *) + assert (rs rf = Vptr f' Ptrofs.zero). + { destruct (rs rf); try discriminate. + revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. } + assert (rs0 x0 = Vptr f' Ptrofs.zero). + { exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. } + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption. ++ (* Direct call *) + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto. + +- (* Mbuiltin *) + inv AT. monadInv H4. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H3); intro NOOV. + exploit builtin_args_match; eauto. intros [vargs' [P Q]]. + exploit external_call_mem_extends; eauto. + intros [vres' [m2' [A [B [C D]]]]]. + left. econstructor; split. apply plus_one. + eapply exec_step_builtin. eauto. eauto. + eapply find_instr_tail; eauto. + erewrite <- sp_val by eauto. + eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + eauto. + econstructor; eauto. + instantiate (2 := tf); instantiate (1 := x). + unfold nextinstr. rewrite Pregmap.gss. + rewrite set_res_other. rewrite undef_regs_other. + rewrite <- H1. simpl. econstructor; eauto. + eapply code_tail_next_int; eauto. + simpl; intros. destruct H4. congruence. destruct H4. congruence. + exploit list_in_map_inv; eauto. intros (mr & U & V). subst. + auto with asmgen. + auto with asmgen. + apply agree_nextinstr. eapply agree_set_res; auto. + eapply agree_undef_regs; eauto. intros. + simpl. rewrite undef_regs_other_2; auto. Simpl. + congruence. + +- (* Mgoto *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H4. + exploit find_label_goto_label; eauto. intros [tc' [rs' [GOTO [AT2 INV]]]]. + left; exists (State rs' m'); split. + apply plus_one. econstructor; eauto. + eapply functions_transl; eauto. + eapply find_instr_tail; eauto. + simpl; eauto. + econstructor; eauto. + eapply agree_exten; eauto with asmgen. + congruence. + +- (* Mcond true *) + assert (f0 = f) by congruence. subst f0. + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_opt_steps_goto; eauto. + intros. simpl in TR. + exploit transl_cond_branch_correct; eauto. intros (rs' & jmp & A & B & C). + exists jmp; exists k; exists rs'. + split. eexact A. + split. apply agree_exten with rs0; auto with asmgen. + exact B. + +- (* Mcond false *) + exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. + left; eapply exec_straight_steps; eauto. intros. simpl in TR. + exploit transl_cond_branch_correct; eauto. intros (rs' & jmp & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. apply exec_straight_one. eexact B. auto. + split. apply agree_exten with rs0; auto. intros. Simpl. + simpl; congruence. + +- (* Mjumptable *) + assert (f0 = f) by congruence. subst f0. + inv AT. monadInv H6. + exploit functions_transl; eauto. intro FN. + generalize (transf_function_no_overflow _ _ H5); intro NOOV. + exploit find_label_goto_label. eauto. eauto. + instantiate (2 := rs0#X16 <- Vundef). + Simpl. eauto. + eauto. + intros [tc' [rs' [A [B C]]]]. + exploit ireg_val; eauto. rewrite H. intros LD; inv LD. + left; econstructor; split. + apply plus_one. econstructor; eauto. + eapply find_instr_tail; eauto. + simpl. Simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A. + econstructor; eauto. + eapply agree_undef_regs; eauto. + simpl. intros. rewrite C; auto with asmgen. Simpl. + congruence. + +- (* Mreturn *) + assert (f0 = f) by congruence. subst f0. + inversion AT; subst. simpl in H6; monadInv H6. + assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). + eapply transf_function_no_overflow; eauto. + exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). + exploit exec_straight_steps_2; eauto using functions_transl. + intros (ofs' & P & Q). + left; econstructor; split. + (* execution *) + eapply plus_right'. eapply exec_straight_exec; eauto. + econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. + simpl. reflexivity. + traceEq. + (* match states *) + econstructor; eauto. + apply agree_set_other; auto with asmgen. + +- (* internal function *) + + exploit functions_translated; eauto. intros [tf [A B]]. monadInv B. + generalize EQ; intros EQ'. monadInv EQ'. + destruct (zlt Ptrofs.max_unsigned (list_length_z x0.(fn_code))); inversion EQ1. clear EQ1. subst x0. + unfold store_stack in *. + exploit Mem.alloc_extends. eauto. eauto. apply Z.le_refl. apply Z.le_refl. + intros [m1' [C D]]. + exploit Mem.storev_extends. eexact D. eexact H1. eauto. eauto. + intros [m2' [F G]]. + simpl chunk_of_type in F. + exploit Mem.storev_extends. eexact G. eexact H2. eauto. eauto. + intros [m3' [P Q]]. + change (chunk_of_type Tptr) with Mint64 in *. + (* Execution of function prologue *) + monadInv EQ0. rewrite transl_code'_transl_code in EQ1. + set (tfbody := Pallocframe (fn_stacksize f) (fn_link_ofs f) :: + storeptr RA XSP (fn_retaddr_ofs f) x0) in *. + set (tf := {| fn_sig := Mach.fn_sig f; fn_code := tfbody |}) in *. + set (rs2 := nextinstr (rs0#X29 <- (parent_sp s) #SP <- sp #X16 <- Vundef)). + exploit (storeptr_correct tge tf XSP (fn_retaddr_ofs f) RA x0 m2' m3' rs2). + simpl preg_of_iregsp. change (rs2 X30) with (rs0 X30). rewrite ATLR. + change (rs2 X2) with sp. eexact P. + simpl; congruence. congruence. + intros (rs3 & U & V). + assert (EXEC_PROLOGUE: + exec_straight tge tf + tf.(fn_code) rs0 m' + x0 rs3 m3'). + { change (fn_code tf) with tfbody; unfold tfbody. + apply exec_straight_step with rs2 m2'. + unfold exec_instr. rewrite C. fold sp. + rewrite <- (sp_val _ _ _ AG). rewrite F. reflexivity. + reflexivity. + eexact U. } + exploit exec_straight_steps_2; eauto using functions_transl. lia. constructor. + intros (ofs' & X & Y). + left; exists (State rs3 m3'); split. + eapply exec_straight_steps_1; eauto. lia. constructor. + econstructor; eauto. + rewrite X; econstructor; eauto. + apply agree_exten with rs2; eauto with asmgen. + unfold rs2. + apply agree_nextinstr. apply agree_set_other; auto with asmgen. + apply agree_change_sp with (parent_sp s). + apply agree_undef_regs with rs0. auto. +Local Transparent destroyed_at_function_entry. simpl. + simpl; intros; Simpl. + unfold sp; congruence. + intros. rewrite V by auto with asmgen. reflexivity. + +- (* external function *) + exploit functions_translated; eauto. + intros [tf [A B]]. simpl in B. inv B. + exploit extcall_arguments_match; eauto. + intros [args' [C D]]. + exploit external_call_mem_extends; eauto. + intros [res' [m2' [P [Q [R S]]]]]. + left; econstructor; split. + apply plus_one. eapply exec_step_external; eauto. + eapply external_call_symbols_preserved; eauto. apply senv_preserved. + econstructor; eauto. + unfold loc_external_result. apply agree_set_other; auto. apply agree_set_pair; auto. + apply agree_undef_caller_save_regs; auto. + +- (* return *) + inv STACKS. simpl in *. + right. split. lia. split. auto. + rewrite <- ATPC in H5. + econstructor; eauto. congruence. +>>>>>>> master +Qed. + +Lemma undef_regs_other_2: + forall r rl rs, + preg_notin r rl -> + undef_regs (map preg_of rl) rs r = rs r. +Proof. + intros. apply undef_regs_other. intros. + exploit list_in_map_inv; eauto. intros [mr [A B]]. subst. + rewrite preg_notin_charact in H. auto. +Qed. + +Lemma exec_exit_simulation_plus b ofs f bb s2 t rs m rs' m': forall + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (NEMPTY_EXIT: exit bb <> None) + (MATCHI: match_internal (size bb - Z.of_nat (length_opt (exit bb))) (State rs m) s2) + (EXIT: exec_exit ge f (Ptrofs.repr (size bb)) rs m (exit bb) t rs' m') + (ATPC: rs PC = Vptr b ofs), + plus Asm.step tge s2 t (State rs' m'). +Proof. + intros. + exploit internal_functions_unfold; eauto. + intros (tc & FINDtf & TRANStf & _). + + exploit (find_instr_bblock (size bb - 1)); eauto. + { generalize (bblock_size_pos bb). lia. } + intros (i' & NTH & FIND_INSTR). + + inv NTH. + + rewrite last_instruction_cannot_be_label in *. discriminate. + + destruct (exit bb) as [ctrl |] eqn:NEMPTY_EXIT'. 2: { contradiction. } + rewrite bblock_size_aux in *. rewrite NEMPTY_EXIT' in *. simpl in *. + (* XXX: Is there a better way to simplify this expression i.e. automatically? *) + replace (list_length_z (header bb) + list_length_z (body bb) + 1 - 1 - + list_length_z (header bb)) with (list_length_z (body bb)) in H by lia. + rewrite list_nth_z_range_exceeded in H; try lia. discriminate. + + assert (Ptrofs.unsigned ofs + size bb <= Ptrofs.max_unsigned). { + eapply size_of_blocks_bounds; eauto. + } + assert (size bb <= Ptrofs.max_unsigned). { generalize (Ptrofs.unsigned_range_2 ofs); lia. } + destruct cfi. + * (* control flow instruction *) + destruct s2. + rewrite H in EXIT. (* exit bb is a cfi *) + inv EXIT. + rewrite H in MATCHI. simpl in MATCHI. + exploit internal_functions_translated; eauto. + rewrite FINDtf. + intros (tf & FINDtf' & TRANSf). inversion FINDtf'; subst; clear FINDtf'. + exploit exec_cfi_simulation; eauto. + (* extract exec_cfi_simulation's conclusion as separate hypotheses *) + intros (rs2' & m2' & EXECI & MATCHS); rewrite MATCHS. + apply plus_one. + eapply Asm.exec_step_internal; eauto. + - eapply pc_ptr_exec_step; eauto. + - eapply find_instr_ofs_somei; eauto. + * (* builtin *) + destruct s2. + rewrite H in EXIT. + rewrite H in MATCHI. simpl in MATCHI. + simpl in FIND_INSTR. + inversion EXIT. + apply plus_one. + eapply external_call_symbols_preserved in H10; try (apply senv_preserved). + eapply eval_builtin_args_preserved in H6; try (apply symbols_preserved). + eapply Asm.exec_step_builtin; eauto. + - eapply pc_ptr_exec_step; eauto. + - eapply find_instr_ofs_somei; eauto. + - eapply eval_builtin_args_match; eauto. + - inv MATCHI; eauto. + - inv MATCHI. + unfold Asm.nextinstr, incrPC. + assert (HPC: Val.offset_ptr (rs PC) (Ptrofs.repr (size bb)) + = Val.offset_ptr (_rs PC) Ptrofs.one). + { rewrite <- AGPC. rewrite ATPC. unfold Val.offset_ptr. + rewrite Ptrofs.add_assoc. unfold Ptrofs.add. + assert (BBPOS: size bb >= 1) by eapply bblock_size_pos. + rewrite (Ptrofs.unsigned_repr (size bb - 1)); try lia. + rewrite Ptrofs.unsigned_one. + replace (size bb - 1 + 1) with (size bb) by lia. + reflexivity. } + apply set_builtin_res_dont_move_pc_gen. + -- erewrite !set_builtin_map_not_pc. + erewrite !undef_regs_other. + rewrite HPC; auto. + all: intros; simpl in *; destruct H3 as [HX16 | [HX30 | HDES]]; subst; try discriminate; + exploit list_in_map_inv; eauto; intros [mr [A B]]; subst; discriminate. + -- intros. eapply undef_reg_preserved; eauto. + intros. destruct (PregEq.eq X16 r0); destruct (PregEq.eq X30 r0); subst. + rewrite Pregmap.gso, Pregmap.gss; try congruence. + do 2 (rewrite Pregmap.gso, Pregmap.gss; try discriminate; auto). + rewrite 2Pregmap.gss; auto. + rewrite !Pregmap.gso; auto. +Qed. + +Lemma exec_exit_simulation_star b ofs f bb s2 t rs m rs' m': forall + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (MATCHI: match_internal (size bb - Z.of_nat (length_opt (exit bb))) (State rs m) s2) + (EXIT: exec_exit ge f (Ptrofs.repr (size bb)) rs m (exit bb) t rs' m') + (ATPC: rs PC = Vptr b ofs), + star Asm.step tge s2 t (State rs' m'). +Proof. + intros. + destruct (exit bb) eqn: Hex. + - eapply plus_star. + eapply exec_exit_simulation_plus; try rewrite Hex; congruence || eauto. + - inv MATCHI. + inv EXIT. + assert (X: rs2 = incrPC (Ptrofs.repr (size bb)) rs). { + unfold incrPC. unfold Pregmap.set. + apply functional_extensionality. intros x. + destruct (PregEq.eq x PC) as [X|]. + - rewrite X. rewrite <- AGPC. simpl. + replace (size bb - 0) with (size bb) by lia. reflexivity. + - rewrite AG; try assumption. reflexivity. + } + destruct X. + subst; eapply star_refl; eauto. +Qed. + +Lemma exec_bblock_simulation b ofs f bb t rs m rs' m': forall + (ATPC: rs PC = Vptr b ofs) + (FINDF: Genv.find_funct_ptr ge b = Some (Internal f)) + (FINDBB: find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bb) + (EXECBB: exec_bblock lk ge f bb rs m t rs' m'), + plus Asm.step tge (State rs m) t (State rs' m'). +Proof. + intros; destruct EXECBB as (rs1 & m1 & BODY & CTL). + exploit exec_header_simulation; eauto. + intros (s0 & STAR & MATCH0). + eapply star_plus_trans; traceEq || eauto. + destruct (bblock_non_empty bb). + - (* body bb <> nil *) + exploit exec_body_simulation_plus; eauto. + intros (s1 & PLUS & MATCH1). + eapply plus_star_trans; traceEq || eauto. + eapply exec_exit_simulation_star; eauto. + erewrite <- exec_body_dont_move_PC; eauto. + - (* exit bb <> None *) + exploit exec_body_simulation_star; eauto. + intros (s1 & STAR1 & MATCH1). + eapply star_plus_trans; traceEq || eauto. + eapply exec_exit_simulation_plus; eauto. + erewrite <- exec_body_dont_move_PC; eauto. +Qed. + +Lemma step_simulation s t s': + Asmblock.step lk ge s t s' -> plus Asm.step tge s t s'. +Proof. + intros STEP. + inv STEP; simpl; exploit functions_translated; eauto; + intros (tf0 & FINDtf & TRANSf); + monadInv TRANSf. + - (* internal step *) eapply exec_bblock_simulation; eauto. + - (* external step *) + apply plus_one. + exploit external_call_symbols_preserved; eauto. apply senv_preserved. + intros ?. + eapply Asm.exec_step_external; eauto. +Qed. + +Lemma transf_program_correct: + forward_simulation (Asmblock.semantics lk prog) (Asm.semantics tprog). +Proof. + eapply forward_simulation_plus. + - apply senv_preserved. + - eexact transf_initial_states. + - eexact transf_final_states. + - unfold match_states. + simpl; intros; subst; eexists; split; eauto. + eapply step_simulation; eauto. +Qed. + +End PRESERVATION. + +End Asmblock_PRESERVATION. + + +Local Open Scope linking_scope. + +Definition block_passes := + mkpass Machblockgenproof.match_prog + ::: mkpass Asmblockgenproof.match_prog + ::: mkpass PostpassSchedulingproof.match_prog + ::: mkpass Asmblock_PRESERVATION.match_prog + ::: pass_nil _. + +Definition match_prog := pass_match (compose_passes block_passes). + +Lemma transf_program_match: + forall p tp, Asmgen.transf_program p = OK tp -> match_prog p tp. +Proof. + intros p tp H. + unfold Asmgen.transf_program in H. apply bind_inversion in H. destruct H. + inversion_clear H. apply bind_inversion in H1. destruct H1. + inversion_clear H. + unfold Compopts.time in *. remember (Machblockgen.transf_program p) as mbp. + unfold match_prog; simpl. + exists mbp; split. apply Machblockgenproof.transf_program_match; auto. + exists x; split. apply Asmblockgenproof.transf_program_match; auto. + exists x0; split. apply PostpassSchedulingproof.transf_program_match; auto. + exists tp; split. apply Asmblock_PRESERVATION.transf_program_match; auto. auto. +Qed. + +(** Return Address Offset *) + +Definition return_address_offset: Mach.function -> Mach.code -> ptrofs -> Prop := + Machblockgenproof.Mach_return_address_offset (Asmblockgenproof.return_address_offset). + +Lemma return_address_exists: + forall f sg ros c, is_tail (Mach.Mcall sg ros :: c) f.(Mach.fn_code) -> + exists ra, return_address_offset f c ra. +Proof. + intros; unfold return_address_offset; eapply Machblockgenproof.Mach_return_address_exists; eauto. + intros; eapply Asmblockgenproof.return_address_exists; 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. + +Theorem transf_program_correct: + forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog). +Proof. + unfold match_prog in TRANSF. simpl in TRANSF. + inv TRANSF. inv H. inv H1. inv H. inv H2. inv H. inv H3. inv H. + eapply compose_forward_simulations. + { exploit Machblockgenproof.transf_program_correct; eauto. } + + eapply compose_forward_simulations. + + apply Asmblockgenproof.transf_program_correct; eauto. + { intros. + unfold Genv.symbol_address. + erewrite <- PostpassSchedulingproof.symbols_preserved; eauto. + erewrite Asmblock_PRESERVATION.symbol_high_low; eauto. + reflexivity. + } + + eapply compose_forward_simulations. + - apply PostpassSchedulingproof.transf_program_correct; eauto. + - apply Asmblock_PRESERVATION.transf_program_correct; eauto. +Qed. + +End PRESERVATION. + +Instance TransfAsm: TransfLink match_prog := pass_match_link (compose_passes block_passes). + +(*******************************************) +(* Stub actually needed by driver/Compiler *) + +Module Asmgenproof0. + +Definition return_address_offset := return_address_offset. + +End Asmgenproof0. diff --git a/aarch64/TO_MERGE/Asmgenproof1.v b/aarch64/TO_MERGE/Asmgenproof1.v new file mode 100644 index 00000000..93c1f1ed --- /dev/null +++ b/aarch64/TO_MERGE/Asmgenproof1.v @@ -0,0 +1,1836 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Correctness proof for AArch64 code generation: auxiliary results. *) + +Require Import Recdef Coqlib Zwf Zbits. +Require Import Maps Errors AST Integers Floats Values Memory Globalenvs. +Require Import Op Locations Mach Asm Conventions. +Require Import Asmgen. +Require Import Asmgenproof0. + +Local Transparent Archi.ptr64. + +(** Properties of registers *) + +Lemma preg_of_iregsp_not_PC: forall r, preg_of_iregsp r <> PC. +Proof. + destruct r; simpl; congruence. +Qed. +Global Hint Resolve preg_of_iregsp_not_PC: asmgen. + +Lemma preg_of_not_X16: forall r, preg_of r <> X16. +Proof. + destruct r; simpl; congruence. +Qed. + +Lemma ireg_of_not_X16: forall r x, ireg_of r = OK x -> x <> X16. +Proof. + unfold ireg_of; intros. destruct (preg_of r) eqn:E; inv H. + red; intros; subst x. elim (preg_of_not_X16 r); auto. +Qed. + +Lemma ireg_of_not_X16': forall r x, ireg_of r = OK x -> IR x <> IR X16. +Proof. + intros. apply ireg_of_not_X16 in H. congruence. +Qed. + +Global Hint Resolve preg_of_not_X16 ireg_of_not_X16 ireg_of_not_X16': asmgen. + +(** Useful simplification tactic *) + + +Ltac Simplif := + ((rewrite nextinstr_inv by eauto with asmgen) + || (rewrite nextinstr_inv1 by eauto with asmgen) + || (rewrite Pregmap.gss) + || (rewrite nextinstr_pc) + || (rewrite Pregmap.gso by eauto with asmgen)); auto with asmgen. + +Ltac Simpl := repeat Simplif. + +(** * Correctness of ARM constructor functions *) + +Section CONSTRUCTORS. + +Variable ge: genv. +Variable fn: function. + +(** Decomposition of integer literals *) + +Inductive wf_decomposition: list (Z * Z) -> Prop := + | wf_decomp_nil: + wf_decomposition nil + | wf_decomp_cons: forall m n p l, + n = Zzero_ext 16 m -> 0 <= p -> wf_decomposition l -> + wf_decomposition ((n, p) :: l). + +Lemma decompose_int_wf: + forall N n p, 0 <= p -> wf_decomposition (decompose_int N n p). +Proof. +Local Opaque Zzero_ext. + induction N as [ | N]; simpl; intros. +- constructor. +- set (frag := Zzero_ext 16 (Z.shiftr n p)) in *. destruct (Z.eqb frag 0). ++ apply IHN. lia. ++ econstructor. reflexivity. lia. apply IHN; lia. +Qed. + +Fixpoint recompose_int (accu: Z) (l: list (Z * Z)) : Z := + match l with + | nil => accu + | (n, p) :: l => recompose_int (Zinsert accu n p 16) l + end. + +Lemma decompose_int_correct: + forall N n p accu, + 0 <= p -> + (forall i, p <= i -> Z.testbit accu i = false) -> + (forall i, 0 <= i < p + Z.of_nat N * 16 -> + Z.testbit (recompose_int accu (decompose_int N n p)) i = + if zlt i p then Z.testbit accu i else Z.testbit n i). +Proof. + induction N as [ | N]; intros until accu; intros PPOS ABOVE i RANGE. +- simpl. rewrite zlt_true; auto. extlia. +- rewrite inj_S in RANGE. simpl. + set (frag := Zzero_ext 16 (Z.shiftr n p)). + assert (FRAG: forall i, p <= i < p + 16 -> Z.testbit n i = Z.testbit frag (i - p)). + { unfold frag; intros. rewrite Zzero_ext_spec by lia. rewrite zlt_true by lia. + rewrite Z.shiftr_spec by lia. f_equal; lia. } + destruct (Z.eqb_spec frag 0). ++ rewrite IHN. +* destruct (zlt i p). rewrite zlt_true by lia. auto. + destruct (zlt i (p + 16)); auto. + rewrite ABOVE by lia. rewrite FRAG by lia. rewrite e, Z.testbit_0_l. auto. +* lia. +* intros; apply ABOVE; lia. +* extlia. ++ simpl. rewrite IHN. +* destruct (zlt i (p + 16)). +** rewrite Zinsert_spec by lia. unfold proj_sumbool. + rewrite zlt_true by lia. + destruct (zlt i p). + rewrite zle_false by lia. auto. + rewrite zle_true by lia. simpl. symmetry; apply FRAG; lia. +** rewrite Z.ldiff_spec, Z.shiftl_spec by lia. + change 65535 with (two_p 16 - 1). rewrite Ztestbit_two_p_m1 by lia. + rewrite zlt_false by lia. rewrite zlt_false by lia. apply andb_true_r. +* lia. +* intros. rewrite Zinsert_spec by lia. unfold proj_sumbool. + rewrite zle_true by lia. rewrite zlt_false by lia. simpl. + apply ABOVE. lia. +* extlia. +Qed. + +Corollary decompose_int_eqmod: forall N n, + eqmod (two_power_nat (N * 16)%nat) (recompose_int 0 (decompose_int N n 0)) n. +Proof. + intros; apply eqmod_same_bits; intros. + rewrite decompose_int_correct. apply zlt_false; lia. + lia. intros; apply Z.testbit_0_l. extlia. +Qed. + +Corollary decompose_notint_eqmod: forall N n, + eqmod (two_power_nat (N * 16)%nat) + (Z.lnot (recompose_int 0 (decompose_int N (Z.lnot n) 0))) n. +Proof. + intros; apply eqmod_same_bits; intros. + rewrite Z.lnot_spec, decompose_int_correct. + rewrite zlt_false by lia. rewrite Z.lnot_spec by lia. apply negb_involutive. + lia. intros; apply Z.testbit_0_l. extlia. lia. +Qed. + +Lemma negate_decomposition_wf: + forall l, wf_decomposition l -> wf_decomposition (negate_decomposition l). +Proof. + induction 1; simpl; econstructor; auto. + instantiate (1 := (Z.lnot m)). + apply equal_same_bits; intros. + rewrite H. change 65535 with (two_p 16 - 1). + rewrite Z.lxor_spec, !Zzero_ext_spec, Z.lnot_spec, Ztestbit_two_p_m1 by lia. + destruct (zlt i 16). + apply xorb_true_r. + auto. +Qed. + +Lemma Zinsert_eqmod: + forall n x1 x2 y p l, 0 <= p -> 0 <= l -> + eqmod (two_power_nat n) x1 x2 -> + eqmod (two_power_nat n) (Zinsert x1 y p l) (Zinsert x2 y p l). +Proof. + intros. apply eqmod_same_bits; intros. rewrite ! Zinsert_spec by lia. + destruct (zle p i && zlt i (p + l)); auto. + apply same_bits_eqmod with n; auto. +Qed. + +Lemma Zinsert_0_l: + forall y p l, + 0 <= p -> 0 <= l -> + Z.shiftl (Zzero_ext l y) p = Zinsert 0 (Zzero_ext l y) p l. +Proof. + intros. apply equal_same_bits; intros. + rewrite Zinsert_spec by lia. unfold proj_sumbool. + destruct (zlt i p); [rewrite zle_false by lia|rewrite zle_true by lia]; simpl. +- rewrite Z.testbit_0_l, Z.shiftl_spec_low by auto. auto. +- rewrite Z.shiftl_spec by lia. + destruct (zlt i (p + l)); auto. + rewrite Zzero_ext_spec, zlt_false, Z.testbit_0_l by lia. auto. +Qed. + +Lemma recompose_int_negated: + forall l, wf_decomposition l -> + forall accu, recompose_int (Z.lnot accu) (negate_decomposition l) = Z.lnot (recompose_int accu l). +Proof. + induction 1; intros accu; simpl. +- auto. +- rewrite <- IHwf_decomposition. f_equal. apply equal_same_bits; intros. + rewrite Z.lnot_spec, ! Zinsert_spec, Z.lxor_spec, Z.lnot_spec by lia. + unfold proj_sumbool. + destruct (zle p i); simpl; auto. + destruct (zlt i (p + 16)); simpl; auto. + change 65535 with (two_p 16 - 1). + rewrite Ztestbit_two_p_m1 by lia. rewrite zlt_true by lia. + apply xorb_true_r. +Qed. + +Lemma exec_loadimm_k_w: + forall (rd: ireg) k m l, + wf_decomposition l -> + forall (rs: regset) accu, + rs#rd = Vint (Int.repr accu) -> + exists rs', + exec_straight_opt ge fn (loadimm_k W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (recompose_int accu l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + induction 1; intros rs accu ACCU; simpl. +- exists rs; split. apply exec_straight_opt_refl. auto. +- destruct (IHwf_decomposition + (nextinstr (rs#rd <- (insert_in_int rs#rd n p 16))) + (Zinsert accu n p 16)) + as (rs' & P & Q & R). + Simpl. rewrite ACCU. simpl. f_equal. apply Int.eqm_samerepr. + apply Zinsert_eqmod. auto. lia. apply Int.eqm_sym; apply Int.eqm_unsigned_repr. + exists rs'; split. + eapply exec_straight_opt_step_opt. simpl; eauto. auto. exact P. + split. exact Q. intros; Simpl. rewrite R by auto. Simpl. +Qed. + +Lemma exec_loadimm_z_w: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_z W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (recompose_int 0 l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_z; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Zinsert 0 n p 16). + set (rs1 := nextinstr (rs#rd <- (Vint (Int.repr accu0)))). + destruct (exec_loadimm_k_w rd k m l H1 rs1 accu0) as (rs2 & P & Q & R); auto. + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. unfold accu0. rewrite H. apply Zinsert_0_l; lia. + reflexivity. + split. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm_n_w: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_n W rd l k) rs m k rs' m + /\ rs'#rd = Vint (Int.repr (Z.lnot (recompose_int 0 l))) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_n; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Z.lnot (Zinsert 0 n p 16)). + set (rs1 := nextinstr (rs#rd <- (Vint (Int.repr accu0)))). + destruct (exec_loadimm_k_w rd k m (negate_decomposition l) + (negate_decomposition_wf l H1) + rs1 accu0) as (rs2 & P & Q & R). + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. + unfold accu0. f_equal. rewrite H. apply Zinsert_0_l; lia. + reflexivity. + split. unfold accu0 in Q; rewrite recompose_int_negated in Q by auto. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm32: + forall rd n k rs m, + exists rs', + exec_straight ge fn (loadimm32 rd n k) rs m k rs' m + /\ rs'#rd = Vint n + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm32, loadimm; intros. + destruct (is_logical_imm32 n). +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite Int.repr_unsigned, Int.or_zero_l; auto. + intros; Simpl. +- set (dz := decompose_int 2%nat (Int.unsigned n) 0). + set (dn := decompose_int 2%nat (Z.lnot (Int.unsigned n)) 0). + assert (A: Int.repr (recompose_int 0 dz) = n). + { transitivity (Int.repr (Int.unsigned n)). + apply Int.eqm_samerepr. apply decompose_int_eqmod. + apply Int.repr_unsigned. } + assert (B: Int.repr (Z.lnot (recompose_int 0 dn)) = n). + { transitivity (Int.repr (Int.unsigned n)). + apply Int.eqm_samerepr. apply decompose_notint_eqmod. + apply Int.repr_unsigned. } + destruct Nat.leb. ++ rewrite <- A. apply exec_loadimm_z_w. apply decompose_int_wf; lia. ++ rewrite <- B. apply exec_loadimm_n_w. apply decompose_int_wf; lia. +Qed. + +Lemma exec_loadimm_k_x: + forall (rd: ireg) k m l, + wf_decomposition l -> + forall (rs: regset) accu, + rs#rd = Vlong (Int64.repr accu) -> + exists rs', + exec_straight_opt ge fn (loadimm_k X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (recompose_int accu l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + induction 1; intros rs accu ACCU; simpl. +- exists rs; split. apply exec_straight_opt_refl. auto. +- destruct (IHwf_decomposition + (nextinstr (rs#rd <- (insert_in_long rs#rd n p 16))) + (Zinsert accu n p 16)) + as (rs' & P & Q & R). + Simpl. rewrite ACCU. simpl. f_equal. apply Int64.eqm_samerepr. + apply Zinsert_eqmod. auto. lia. apply Int64.eqm_sym; apply Int64.eqm_unsigned_repr. + exists rs'; split. + eapply exec_straight_opt_step_opt. simpl; eauto. auto. exact P. + split. exact Q. intros; Simpl. rewrite R by auto. Simpl. +Qed. + +Lemma exec_loadimm_z_x: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_z X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (recompose_int 0 l)) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_z; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Zinsert 0 n p 16). + set (rs1 := nextinstr (rs#rd <- (Vlong (Int64.repr accu0)))). + destruct (exec_loadimm_k_x rd k m l H1 rs1 accu0) as (rs2 & P & Q & R); auto. + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. unfold accu0. rewrite H. apply Zinsert_0_l; lia. + reflexivity. + split. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm_n_x: + forall rd l k rs m, + wf_decomposition l -> + exists rs', + exec_straight ge fn (loadimm_n X rd l k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.repr (Z.lnot (recompose_int 0 l))) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm_n; destruct 1. +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +- set (accu0 := Z.lnot (Zinsert 0 n p 16)). + set (rs1 := nextinstr (rs#rd <- (Vlong (Int64.repr accu0)))). + destruct (exec_loadimm_k_x rd k m (negate_decomposition l) + (negate_decomposition_wf l H1) + rs1 accu0) as (rs2 & P & Q & R). + unfold rs1; Simpl. + exists rs2; split. + eapply exec_straight_opt_step; eauto. + simpl. unfold rs1. do 5 f_equal. + unfold accu0. f_equal. rewrite H. apply Zinsert_0_l; lia. + reflexivity. + split. unfold accu0 in Q; rewrite recompose_int_negated in Q by auto. exact Q. + intros. rewrite R by auto. unfold rs1; Simpl. +Qed. + +Lemma exec_loadimm64: + forall rd n k rs m, + exists rs', + exec_straight ge fn (loadimm64 rd n k) rs m k rs' m + /\ rs'#rd = Vlong n + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm64, loadimm; intros. + destruct (is_logical_imm64 n). +- econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite Int64.repr_unsigned, Int64.or_zero_l; auto. + intros; Simpl. +- set (dz := decompose_int 4%nat (Int64.unsigned n) 0). + set (dn := decompose_int 4%nat (Z.lnot (Int64.unsigned n)) 0). + assert (A: Int64.repr (recompose_int 0 dz) = n). + { transitivity (Int64.repr (Int64.unsigned n)). + apply Int64.eqm_samerepr. apply decompose_int_eqmod. + apply Int64.repr_unsigned. } + assert (B: Int64.repr (Z.lnot (recompose_int 0 dn)) = n). + { transitivity (Int64.repr (Int64.unsigned n)). + apply Int64.eqm_samerepr. apply decompose_notint_eqmod. + apply Int64.repr_unsigned. } + destruct Nat.leb. ++ rewrite <- A. apply exec_loadimm_z_x. apply decompose_int_wf; lia. ++ rewrite <- B. apply exec_loadimm_n_x. apply decompose_int_wf; lia. +Qed. + +(** Add immediate *) + +Lemma exec_addimm_aux_32: + forall (insn: iregsp -> iregsp -> Z -> instruction) (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (Vint (Int.repr n))))) m) -> + (forall v n1 n2, sem (sem v (Vint n1)) (Vint n2) = sem v (Vint (Int.add n1 n2))) -> + forall rd r1 n k rs m, + exists rs', + exec_straight ge fn (addimm_aux insn rd r1 (Int.unsigned n) k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros insn sem SEM ASSOC; intros. unfold addimm_aux. + set (nlo := Zzero_ext 12 (Int.unsigned n)). set (nhi := Int.unsigned n - nlo). + assert (E: Int.unsigned n = nhi + nlo) by (unfold nhi; lia). + rewrite <- (Int.repr_unsigned n). + destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; lia. + intros; Simpl. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; lia. + intros; Simpl. +- econstructor; split. eapply exec_straight_two. + apply SEM. apply SEM. Simpl. Simpl. + split. Simpl. rewrite ASSOC. do 2 f_equal. apply Int.eqm_samerepr. + rewrite E. auto with ints. + intros; Simpl. +Qed. + +Lemma exec_addimm32: + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (addimm32 rd r1 n k) rs m k rs' m + /\ rs'#rd = Val.add rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros. unfold addimm32. set (nn := Int.neg n). + destruct (Int.eq n (Int.zero_ext 24 n)); [| destruct (Int.eq nn (Int.zero_ext 24 nn))]. +- apply exec_addimm_aux_32 with (sem := Val.add). auto. intros; apply Val.add_assoc. +- rewrite <- Val.sub_opp_add. + apply exec_addimm_aux_32 with (sem := Val.sub). auto. + intros. rewrite ! Val.sub_add_opp, Val.add_assoc. rewrite Int.neg_add_distr. auto. +- destruct (Int.lt n Int.zero). ++ rewrite <- Val.sub_opp_add; fold nn. + edestruct (exec_loadimm32 X16 nn) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite B, C; eauto with asmgen. + intros; Simpl. ++ edestruct (exec_loadimm32 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. auto. + split. Simpl. rewrite B, C; eauto with asmgen. + intros; Simpl. +Qed. + +Lemma exec_addimm_aux_64: + forall (insn: iregsp -> iregsp -> Z -> instruction) (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (Vlong (Int64.repr n))))) m) -> + (forall v n1 n2, sem (sem v (Vlong n1)) (Vlong n2) = sem v (Vlong (Int64.add n1 n2))) -> + forall rd r1 n k rs m, + exists rs', + exec_straight ge fn (addimm_aux insn rd r1 (Int64.unsigned n) k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros insn sem SEM ASSOC; intros. unfold addimm_aux. + set (nlo := Zzero_ext 12 (Int64.unsigned n)). set (nhi := Int64.unsigned n - nlo). + assert (E: Int64.unsigned n = nhi + nlo) by (unfold nhi; lia). + rewrite <- (Int64.repr_unsigned n). + destruct (Z.eqb_spec nhi 0); [|destruct (Z.eqb_spec nlo 0)]. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; lia. + intros; Simpl. +- econstructor; split. apply exec_straight_one. apply SEM. Simpl. + split. Simpl. do 3 f_equal; lia. + intros; Simpl. +- econstructor; split. eapply exec_straight_two. + apply SEM. apply SEM. Simpl. Simpl. + split. Simpl. rewrite ASSOC. do 2 f_equal. apply Int64.eqm_samerepr. + rewrite E. auto with ints. + intros; Simpl. +Qed. + +Lemma exec_addimm64: + forall rd r1 n k rs m, + preg_of_iregsp r1 <> X16 -> + exists rs', + exec_straight ge fn (addimm64 rd r1 n k) rs m k rs' m + /\ rs'#rd = Val.addl rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros. + unfold addimm64. set (nn := Int64.neg n). + destruct (Int64.eq n (Int64.zero_ext 24 n)); [| destruct (Int64.eq nn (Int64.zero_ext 24 nn))]. +- apply exec_addimm_aux_64 with (sem := Val.addl). auto. intros; apply Val.addl_assoc. +- rewrite <- Val.subl_opp_addl. + apply exec_addimm_aux_64 with (sem := Val.subl). auto. + intros. rewrite ! Val.subl_addl_opp, Val.addl_assoc. rewrite Int64.neg_add_distr. auto. +- destruct (Int64.lt n Int64.zero). ++ rewrite <- Val.subl_opp_addl; fold nn. + edestruct (exec_loadimm64 X16 nn) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. Simpl. + split. Simpl. rewrite B, C; eauto with asmgen. simpl. rewrite Int64.shl'_zero. auto. + intros; Simpl. ++ edestruct (exec_loadimm64 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. eapply exec_straight_one. simpl; eauto. Simpl. + split. Simpl. rewrite B, C; eauto with asmgen. simpl. rewrite Int64.shl'_zero. auto. + intros; Simpl. +Qed. + +(** Logical immediate *) + +Lemma exec_logicalimm32: + forall (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn1 rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs##r1 (Vint (Int.repr n))))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insn2 rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs##r1 (eval_shift_op_int rs#r2 s)))) m) -> + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (logicalimm32 insn1 insn2 rd r1 n k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vint n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros until sem; intros SEM1 SEM2; intros. unfold logicalimm32. + destruct (is_logical_imm32 n). +- econstructor; split. + apply exec_straight_one. apply SEM1. reflexivity. + split. Simpl. rewrite Int.repr_unsigned; auto. intros; Simpl. +- edestruct (exec_loadimm32 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. apply SEM2. reflexivity. + split. Simpl. f_equal; auto. apply C; auto with asmgen. + intros; Simpl. +Qed. + +Lemma exec_logicalimm64: + forall (insn1: ireg -> ireg0 -> Z -> instruction) + (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction) + (sem: val -> val -> val), + (forall rd r1 n rs m, + exec_instr ge fn (insn1 rd r1 n) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (Vlong (Int64.repr n))))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insn2 rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (eval_shift_op_long rs#r2 s)))) m) -> + forall rd r1 n k rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (logicalimm64 insn1 insn2 rd r1 n k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vlong n) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros until sem; intros SEM1 SEM2; intros. unfold logicalimm64. + destruct (is_logical_imm64 n). +- econstructor; split. + apply exec_straight_one. apply SEM1. reflexivity. + split. Simpl. rewrite Int64.repr_unsigned. auto. intros; Simpl. +- edestruct (exec_loadimm64 X16 n) as (rs1 & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. apply SEM2. reflexivity. + split. Simpl. f_equal; auto. apply C; auto with asmgen. + intros; Simpl. +Qed. + +(** Load address of symbol *) + +Lemma exec_loadsymbol: forall rd s ofs k rs m, + rd <> X16 \/ SelectOp.symbol_is_relocatable s = false -> + exists rs', + exec_straight ge fn (loadsymbol rd s ofs k) rs m k rs' m + /\ rs'#rd = Genv.symbol_address ge s ofs + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadsymbol; intros. destruct (SelectOp.symbol_is_relocatable s). +- predSpec Ptrofs.eq Ptrofs.eq_spec ofs Ptrofs.zero. ++ subst ofs. econstructor; split. + apply exec_straight_one; [simpl; eauto | reflexivity]. + split. Simpl. intros; Simpl. ++ exploit exec_addimm64. instantiate (1 := rd). simpl. destruct H; congruence. + intros (rs1 & A & B & C). + econstructor; split. + econstructor. simpl; eauto. auto. eexact A. + split. simpl in B; rewrite B. Simpl. + rewrite <- Genv.shift_symbol_address_64 by auto. + rewrite Ptrofs.add_zero_l, Ptrofs.of_int64_to_int64 by auto. auto. + intros. rewrite C by auto. Simpl. +- econstructor; split. + eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. + split. Simpl. rewrite symbol_high_low; auto. + intros; Simpl. +Qed. + +(** Shifted operands *) + +Remark transl_shift_not_none: + forall s a, transl_shift s a <> SOnone. +Proof. + destruct s; intros; simpl; congruence. +Qed. + +Remark or_zero_eval_shift_op_int: + forall v s, s <> SOnone -> Val.or (Vint Int.zero) (eval_shift_op_int v s) = eval_shift_op_int v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int.iwordsize); auto; rewrite Int.or_zero_l; auto. +Qed. + +Remark or_zero_eval_shift_op_long: + forall v s, s <> SOnone -> Val.orl (Vlong Int64.zero) (eval_shift_op_long v s) = eval_shift_op_long v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int64.iwordsize'); auto; rewrite Int64.or_zero_l; auto. +Qed. + +Remark add_zero_eval_shift_op_long: + forall v s, s <> SOnone -> Val.addl (Vlong Int64.zero) (eval_shift_op_long v s) = eval_shift_op_long v s. +Proof. + intros; destruct s; try congruence; destruct v; auto; simpl; + destruct (Int.ltu n Int64.iwordsize'); auto; rewrite Int64.add_zero_l; auto. +Qed. + +Lemma transl_eval_shift: forall s v (a: amount32), + eval_shift_op_int v (transl_shift s a) = eval_shift s v a. +Proof. + intros. destruct s; simpl; auto. +Qed. + +Lemma transl_eval_shift': forall s v (a: amount32), + Val.or (Vint Int.zero) (eval_shift_op_int v (transl_shift s a)) = eval_shift s v a. +Proof. + intros. rewrite or_zero_eval_shift_op_int by (apply transl_shift_not_none). + apply transl_eval_shift. +Qed. + +Lemma transl_eval_shiftl: forall s v (a: amount64), + eval_shift_op_long v (transl_shift s a) = eval_shiftl s v a. +Proof. + intros. destruct s; simpl; auto. +Qed. + +Lemma transl_eval_shiftl': forall s v (a: amount64), + Val.orl (Vlong Int64.zero) (eval_shift_op_long v (transl_shift s a)) = eval_shiftl s v a. +Proof. + intros. rewrite or_zero_eval_shift_op_long by (apply transl_shift_not_none). + apply transl_eval_shiftl. +Qed. + +Lemma transl_eval_shiftl'': forall s v (a: amount64), + Val.addl (Vlong Int64.zero) (eval_shift_op_long v (transl_shift s a)) = eval_shiftl s v a. +Proof. + intros. rewrite add_zero_eval_shift_op_long by (apply transl_shift_not_none). + apply transl_eval_shiftl. +Qed. + +(** Zero- and Sign- extensions *) + +Lemma exec_move_extended_base: forall rd r1 ex k rs m, + exists rs', + exec_straight ge fn (move_extended_base rd r1 ex k) rs m k rs' m + /\ rs' rd = match ex with Xsgn32 => Val.longofint rs#r1 | Xuns32 => Val.longofintu rs#r1 end + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold move_extended_base; destruct ex; econstructor; + (split; [apply exec_straight_one; [simpl;eauto|auto] | split; [Simpl|intros;Simpl]]). +Qed. + +Lemma exec_move_extended: forall rd r1 ex (a: amount64) k rs m, + exists rs', + exec_straight ge fn (move_extended rd r1 ex a k) rs m k rs' m + /\ rs' rd = Op.eval_extend ex rs#r1 a + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold move_extended; intros. predSpec Int.eq Int.eq_spec a Int.zero. +- exploit (exec_move_extended_base rd r1 ex). intros (rs' & A & B & C). + exists rs'; split. eexact A. split. unfold Op.eval_extend. rewrite H. rewrite B. + destruct ex, (rs r1); simpl; auto; rewrite Int64.shl'_zero; auto. + auto. +- Local Opaque Val.addl. + exploit (exec_move_extended_base rd r1 ex). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + unfold exec_instr. change (SOlsl a) with (transl_shift Slsl a). rewrite transl_eval_shiftl''. eauto. auto. + split. Simpl. rewrite B. auto. + intros; Simpl. +Qed. + +Lemma exec_arith_extended: + forall (sem: val -> val -> val) + (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction) + (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction), + (forall rd r1 r2 x rs m, + exec_instr ge fn (insnX rd r1 r2 x) rs m = + Next (nextinstr (rs#rd <- (sem rs#r1 (eval_extend rs#r2 x)))) m) -> + (forall rd r1 r2 s rs m, + exec_instr ge fn (insnS rd r1 r2 s) rs m = + Next (nextinstr (rs#rd <- (sem rs###r1 (eval_shift_op_long rs#r2 s)))) m) -> + forall (rd r1 r2: ireg) (ex: extension) (a: amount64) (k: code) rs m, + r1 <> X16 -> + exists rs', + exec_straight ge fn (arith_extended insnX insnS rd r1 r2 ex a k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Op.eval_extend ex rs#r2 a) + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + intros sem insnX insnS EX ES; intros. unfold arith_extended. destruct (Int.ltu a (Int.repr 5)). +- econstructor; split. + apply exec_straight_one. rewrite EX; eauto. auto. + split. Simpl. f_equal. destruct ex; auto. + intros; Simpl. +- exploit (exec_move_extended_base X16 r2 ex). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + rewrite ES. eauto. auto. + split. Simpl. unfold ir0x. rewrite C by eauto with asmgen. f_equal. + rewrite B. destruct ex; auto. + intros; Simpl. +Qed. + +(** Extended right shift *) + +Lemma exec_shrx32: forall (rd r1: ireg) (n: int) k v (rs: regset) m, + Val.shrx rs#r1 (Vint n) = Some v -> + r1 <> X16 -> + exists rs', + exec_straight ge fn (shrx32 rd r1 n k) rs m k rs' m + /\ rs'#rd = v + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold shrx32; intros. apply Val.shrx_shr_2 in H. + destruct (Int.eq n Int.zero) eqn:E. +- econstructor; split. apply exec_straight_one; [simpl;eauto|auto]. + split. Simpl. subst v; auto. intros; Simpl. +- econstructor; split. eapply exec_straight_three. + unfold exec_instr. rewrite or_zero_eval_shift_op_int by congruence. eauto. + simpl; eauto. + unfold exec_instr. rewrite or_zero_eval_shift_op_int by congruence. eauto. + auto. auto. auto. + split. subst v; Simpl. intros; Simpl. +Qed. + +Lemma exec_shrx64: forall (rd r1: ireg) (n: int) k v (rs: regset) m, + Val.shrxl rs#r1 (Vint n) = Some v -> + r1 <> X16 -> + exists rs', + exec_straight ge fn (shrx64 rd r1 n k) rs m k rs' m + /\ rs'#rd = v + /\ forall r, data_preg r = true -> r <> rd -> rs'#r = rs#r. +Proof. + unfold shrx64; intros. apply Val.shrxl_shrl_2 in H. + destruct (Int.eq n Int.zero) eqn:E. +- econstructor; split. apply exec_straight_one; [simpl;eauto|auto]. + split. Simpl. subst v; auto. intros; Simpl. +- econstructor; split. eapply exec_straight_three. + unfold exec_instr. rewrite or_zero_eval_shift_op_long by congruence. eauto. + simpl; eauto. + unfold exec_instr. rewrite or_zero_eval_shift_op_long by congruence. eauto. + auto. auto. auto. + split. subst v; Simpl. intros; Simpl. +Qed. + +(** Condition bits *) + +Lemma compare_int_spec: forall rs v1 v2 m, + let rs' := compare_int rs v1 v2 m in + rs'#CN = (Val.negative (Val.sub v1 v2)) + /\ rs'#CZ = (Val.cmpu (Mem.valid_pointer m) Ceq v1 v2) + /\ rs'#CC = (Val.cmpu (Mem.valid_pointer m) Cge v1 v2) + /\ rs'#CV = (Val.sub_overflow v1 v2). +Proof. + intros; unfold rs'; auto. +Qed. + +Lemma eval_testcond_compare_sint: forall c v1 v2 b rs m, + Val.cmp_bool c v1 v2 = Some b -> + eval_testcond (cond_for_signed_cmp c) (compare_int rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_int_spec rs v1 v2 m). + set (rs' := compare_int rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmpu; simpl. destruct c; simpl. +- destruct (Int.eq i i0); auto. +- destruct (Int.eq i i0); auto. +- rewrite Int.lt_sub_overflow. destruct (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow, Int.not_lt. + destruct (Int.eq i i0), (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow, (Int.lt_not i). + destruct (Int.eq i i0), (Int.lt i i0); auto. +- rewrite Int.lt_sub_overflow. destruct (Int.lt i i0); auto. +Qed. + +Lemma eval_testcond_compare_uint: forall c v1 v2 b rs m, + Val.cmpu_bool (Mem.valid_pointer m) c v1 v2 = Some b -> + eval_testcond (cond_for_unsigned_cmp c) (compare_int rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_int_spec rs v1 v2 m). + set (rs' := compare_int rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmpu; simpl. destruct c; simpl. +- destruct (Int.eq i i0); auto. +- destruct (Int.eq i i0); auto. +- destruct (Int.ltu i i0); auto. +- rewrite (Int.not_ltu i). destruct (Int.eq i i0), (Int.ltu i i0); auto. +- rewrite (Int.ltu_not i). destruct (Int.eq i i0), (Int.ltu i i0); auto. +- destruct (Int.ltu i i0); auto. +Qed. + +Lemma compare_long_spec: forall rs v1 v2 m, + let rs' := compare_long rs v1 v2 m in + rs'#CN = (Val.negativel (Val.subl v1 v2)) + /\ rs'#CZ = (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Ceq v1 v2)) + /\ rs'#CC = (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Cge v1 v2)) + /\ rs'#CV = (Val.subl_overflow v1 v2). +Proof. + intros; unfold rs'; auto. +Qed. + +Remark int64_sub_overflow: + forall x y, + Int.xor (Int.repr (Int64.unsigned (Int64.sub_overflow x y Int64.zero))) + (Int.repr (Int64.unsigned (Int64.negative (Int64.sub x y)))) = + (if Int64.lt x y then Int.one else Int.zero). +Proof. + intros. + transitivity (Int.repr (Int64.unsigned (if Int64.lt x y then Int64.one else Int64.zero))). + rewrite <- (Int64.lt_sub_overflow x y). + unfold Int64.sub_overflow, Int64.negative. + set (s := Int64.signed x - Int64.signed y - Int64.signed Int64.zero). + destruct (zle Int64.min_signed s && zle s Int64.max_signed); + destruct (Int64.lt (Int64.sub x y) Int64.zero); + auto. + destruct (Int64.lt x y); auto. +Qed. + +Lemma eval_testcond_compare_slong: forall c v1 v2 b rs m, + Val.cmpl_bool c v1 v2 = Some b -> + eval_testcond (cond_for_signed_cmp c) (compare_long rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_long_spec rs v1 v2 m). + set (rs' := compare_long rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. + destruct v1; try discriminate; destruct v2; try discriminate. + simpl in H; inv H. + unfold Val.cmplu; simpl. destruct c; simpl. +- destruct (Int64.eq i i0); auto. +- destruct (Int64.eq i i0); auto. +- rewrite int64_sub_overflow. destruct (Int64.lt i i0); auto. +- rewrite int64_sub_overflow, Int64.not_lt. + destruct (Int64.eq i i0), (Int64.lt i i0); auto. +- rewrite int64_sub_overflow, (Int64.lt_not i). + destruct (Int64.eq i i0), (Int64.lt i i0); auto. +- rewrite int64_sub_overflow. destruct (Int64.lt i i0); auto. +Qed. + +Lemma eval_testcond_compare_ulong: forall c v1 v2 b rs m, + Val.cmplu_bool (Mem.valid_pointer m) c v1 v2 = Some b -> + eval_testcond (cond_for_unsigned_cmp c) (compare_long rs v1 v2 m) = Some b. +Proof. + intros. generalize (compare_long_spec rs v1 v2 m). + set (rs' := compare_long rs v1 v2 m). intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E; unfold Val.cmplu. + destruct v1; try discriminate; destruct v2; try discriminate; simpl in H. +- (* int-int *) + inv H. destruct c; simpl. ++ destruct (Int64.eq i i0); auto. ++ destruct (Int64.eq i i0); auto. ++ destruct (Int64.ltu i i0); auto. ++ rewrite (Int64.not_ltu i). destruct (Int64.eq i i0), (Int64.ltu i i0); auto. ++ rewrite (Int64.ltu_not i). destruct (Int64.eq i i0), (Int64.ltu i i0); auto. ++ destruct (Int64.ltu i i0); auto. +- (* int-ptr *) + simpl. + destruct (Int64.eq i Int64.zero && + (Mem.valid_pointer m b0 (Ptrofs.unsigned i0) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i0 - 1))); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +- (* ptr-int *) + simpl. + destruct (Int64.eq i0 Int64.zero && + (Mem.valid_pointer m b0 (Ptrofs.unsigned i) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i - 1))); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +- (* ptr-ptr *) + simpl. + destruct (eq_block b0 b1). ++ destruct ((Mem.valid_pointer m b0 (Ptrofs.unsigned i) + || Mem.valid_pointer m b0 (Ptrofs.unsigned i - 1)) && + (Mem.valid_pointer m b1 (Ptrofs.unsigned i0) + || Mem.valid_pointer m b1 (Ptrofs.unsigned i0 - 1))); + inv H. + destruct c; simpl. +* destruct (Ptrofs.eq i i0); auto. +* destruct (Ptrofs.eq i i0); auto. +* destruct (Ptrofs.ltu i i0); auto. +* rewrite (Ptrofs.not_ltu i). destruct (Ptrofs.eq i i0), (Ptrofs.ltu i i0); auto. +* rewrite (Ptrofs.ltu_not i). destruct (Ptrofs.eq i i0), (Ptrofs.ltu i i0); auto. +* destruct (Ptrofs.ltu i i0); auto. ++ destruct (Mem.valid_pointer m b0 (Ptrofs.unsigned i) && + Mem.valid_pointer m b1 (Ptrofs.unsigned i0)); try discriminate. + destruct c; simpl in H; inv H; reflexivity. +Qed. + +Lemma compare_float_spec: forall rs f1 f2, + let rs' := compare_float rs (Vfloat f1) (Vfloat f2) in + rs'#CN = (Val.of_bool (Float.cmp Clt f1 f2)) + /\ rs'#CZ = (Val.of_bool (Float.cmp Ceq f1 f2)) + /\ rs'#CC = (Val.of_bool (negb (Float.cmp Clt f1 f2))) + /\ rs'#CV = (Val.of_bool (negb (Float.ordered f1 f2))). +Proof. + intros; auto. +Qed. + +Lemma eval_testcond_compare_float: forall c v1 v2 b rs, + Val.cmpf_bool c v1 v2 = Some b -> + eval_testcond (cond_for_float_cmp c) (compare_float rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_float_spec rs f f0). + set (rs' := compare_float rs (Vfloat f) (Vfloat f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float.cmp Float.ordered. + unfold Float.cmp, Float.ordered; + destruct c; destruct (Float.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma eval_testcond_compare_not_float: forall c v1 v2 b rs, + option_map negb (Val.cmpf_bool c v1 v2) = Some b -> + eval_testcond (cond_for_float_not_cmp c) (compare_float rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_float_spec rs f f0). + set (rs' := compare_float rs (Vfloat f) (Vfloat f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float.cmp Float.ordered. + unfold Float.cmp, Float.ordered; + destruct c; destruct (Float.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma compare_single_spec: forall rs f1 f2, + let rs' := compare_single rs (Vsingle f1) (Vsingle f2) in + rs'#CN = (Val.of_bool (Float32.cmp Clt f1 f2)) + /\ rs'#CZ = (Val.of_bool (Float32.cmp Ceq f1 f2)) + /\ rs'#CC = (Val.of_bool (negb (Float32.cmp Clt f1 f2))) + /\ rs'#CV = (Val.of_bool (negb (Float32.ordered f1 f2))). +Proof. + intros; auto. +Qed. + +Lemma eval_testcond_compare_single: forall c v1 v2 b rs, + Val.cmpfs_bool c v1 v2 = Some b -> + eval_testcond (cond_for_float_cmp c) (compare_single rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_single_spec rs f f0). + set (rs' := compare_single rs (Vsingle f) (Vsingle f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float32.cmp Float32.ordered. + unfold Float32.cmp, Float32.ordered; + destruct c; destruct (Float32.compare f f0) as [[]|]; reflexivity. +Qed. + +Lemma eval_testcond_compare_not_single: forall c v1 v2 b rs, + option_map negb (Val.cmpfs_bool c v1 v2) = Some b -> + eval_testcond (cond_for_float_not_cmp c) (compare_single rs v1 v2) = Some b. +Proof. + intros. destruct v1; try discriminate; destruct v2; simpl in H; inv H. + generalize (compare_single_spec rs f f0). + set (rs' := compare_single rs (Vsingle f) (Vsingle f0)). + intros (B & C & D & E). + unfold eval_testcond; rewrite B, C, D, E. +Local Transparent Float32.cmp Float32.ordered. + unfold Float32.cmp, Float32.ordered; + destruct c; destruct (Float32.compare f f0) as [[]|]; reflexivity. +Qed. + +Remark compare_float_inv: forall rs v1 v2 r, + match r with CR _ => False | _ => True end -> + (nextinstr (compare_float rs v1 v2))#r = (nextinstr rs)#r. +Proof. + intros; unfold compare_float. + destruct r; try contradiction; destruct v1; auto; destruct v2; auto. +Qed. + +Remark compare_single_inv: forall rs v1 v2 r, + match r with CR _ => False | _ => True end -> + (nextinstr (compare_single rs v1 v2))#r = (nextinstr rs)#r. +Proof. + intros; unfold compare_single. + destruct r; try contradiction; destruct v1; auto; destruct v2; auto. +Qed. + +(** Translation of conditionals *) + +Ltac ArgsInv := + repeat (match goal with + | [ H: Error _ = OK _ |- _ ] => discriminate + | [ H: match ?args with nil => _ | _ :: _ => _ end = OK _ |- _ ] => destruct args + | [ H: bind _ _ = OK _ |- _ ] => monadInv H + | [ H: match _ with left _ => _ | right _ => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + | [ H: match _ with true => _ | false => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + end); + subst; + repeat (match goal with + | [ H: ireg_of _ = OK _ |- _ ] => simpl in *; rewrite (ireg_of_eq _ _ H) in * + | [ H: freg_of _ = OK _ |- _ ] => simpl in *; rewrite (freg_of_eq _ _ H) in * + end). + +Lemma transl_cond_correct: + forall cond args k c rs m, + transl_cond cond args k = OK c -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ (forall b, + eval_condition cond (map rs (map preg_of args)) m = Some b -> + eval_testcond (cond_for_cond cond) rs' = Some b) + /\ forall r, data_preg r = true -> rs'#r = rs#r. +Proof. + intros until m; intros TR. destruct cond; simpl in TR; ArgsInv. +- (* Ccomp *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompu *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompimm *) + destruct (is_arith_imm32 n); [|destruct (is_arith_imm32 (Int.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int.repr_unsigned, Int.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_sint; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompuimm *) + destruct (is_arith_imm32 n); [|destruct (is_arith_imm32 (Int.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int.repr_unsigned, Int.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_uint; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompshift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shift. apply eval_testcond_compare_sint; auto. + destruct r; reflexivity || discriminate. +- (* Ccompushift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shift. apply eval_testcond_compare_uint; auto. + destruct r; reflexivity || discriminate. +- (* Cmaskzero *) + destruct (is_logical_imm32 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply (eval_testcond_compare_sint Ceq); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_sint Ceq); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Cmasknotzero *) + destruct (is_logical_imm32 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int.repr_unsigned. apply (eval_testcond_compare_sint Cne); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm32 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_sint Cne); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompl *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplu *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplimm *) + destruct (is_arith_imm64 n); [|destruct (is_arith_imm64 (Int64.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int64.repr_unsigned, Int64.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_slong; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompluimm *) + destruct (is_arith_imm64 n); [|destruct (is_arith_imm64 (Int64.neg n))]. ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. ++ econstructor; split. + apply exec_straight_one. simpl. rewrite Int64.repr_unsigned, Int64.neg_involutive. eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply eval_testcond_compare_ulong; auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccomplshift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shiftl. apply eval_testcond_compare_slong; auto. + destruct r; reflexivity || discriminate. +- (* Ccomplushift *) + econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite transl_eval_shiftl. apply eval_testcond_compare_ulong; auto. + destruct r; reflexivity || discriminate. +- (* Cmasklzero *) + destruct (is_logical_imm64 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply (eval_testcond_compare_slong Ceq); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_slong Ceq); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Cmasknotzero *) + destruct (is_logical_imm64 n). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros. rewrite Int64.repr_unsigned. apply (eval_testcond_compare_slong Cne); auto. + destruct r; reflexivity || discriminate. ++ exploit (exec_loadimm64 X16 n). intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. + apply exec_straight_one. simpl. rewrite B, C by eauto with asmgen. eauto. auto. + split; intros. apply (eval_testcond_compare_slong Cne); auto. + transitivity (rs' r). destruct r; reflexivity || discriminate. auto with asmgen. +- (* Ccompf *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Cnotcompf *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_not_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Ccompfzero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Cnotcompfzero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_float_inv; auto. + split; intros. apply eval_testcond_compare_not_float; auto. + destruct r; discriminate || rewrite compare_float_inv; auto. +- (* Ccompfs *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Cnotcompfs *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_not_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Ccompfszero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +- (* Cnotcompfszero *) + econstructor; split. apply exec_straight_one. simpl; eauto. + rewrite compare_single_inv; auto. + split; intros. apply eval_testcond_compare_not_single; auto. + destruct r; discriminate || rewrite compare_single_inv; auto. +Qed. + +(** Translation of conditional branches *) + +Lemma transl_cond_branch_correct: + forall cond args lbl k c rs m b, + transl_cond_branch cond args lbl k = OK c -> + eval_condition cond (map rs (map preg_of args)) m = Some b -> + exists rs' insn, + exec_straight_opt ge fn c rs m (insn :: k) rs' m + /\ exec_instr ge fn insn rs' m = + (if b then goto_label fn lbl rs' m else Next (nextinstr rs') m) + /\ forall r, data_preg r = true -> rs'#r = rs#r. +Proof. + intros until b; intros TR EV. + assert (DFL: + transl_cond_branch_default cond args lbl k = OK c -> + exists rs' insn, + exec_straight_opt ge fn c rs m (insn :: k) rs' m + /\ exec_instr ge fn insn rs' m = + (if b then goto_label fn lbl rs' m else Next (nextinstr rs') m) + /\ forall r, data_preg r = true -> rs'#r = rs#r). + { + unfold transl_cond_branch_default; intros. + exploit transl_cond_correct; eauto. intros (rs' & A & B & C). + exists rs', (Pbc (cond_for_cond cond) lbl); split. + apply exec_straight_opt_intro. eexact A. + split; auto. simpl. rewrite (B b) by auto. auto. + } +Local Opaque transl_cond transl_cond_branch_default. + destruct args as [ | a1 args]; simpl in TR; auto. + destruct args as [ | a2 args]; simpl in TR; auto. + destruct cond; simpl in TR; auto. +- (* Ccompimm *) + destruct c0; auto; destruct (Int.eq n Int.zero) eqn:N0; auto; + apply Int.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. auto. ++ (* Ccompimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. destruct (Int.eq i Int.zero); auto. +- (* Ccompuimm *) + destruct c0; auto; destruct (Int.eq n Int.zero) eqn:N0; auto; + apply Int.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompuimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite EV. auto. ++ (* Ccompuimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite (Val.negate_cmpu_bool (Mem.valid_pointer m) Cne), EV. destruct b; auto. +- (* Cmaskzero *) + destruct (Int.is_power2 n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int.mul_pow2, Int.mul_commut, Int.mul_one by eauto. + rewrite (Val.negate_cmp_bool Ceq), EV. destruct b; auto. +- (* Cmasknotzero *) + destruct (Int.is_power2 n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int.mul_pow2, Int.mul_commut, Int.mul_one by eauto. + rewrite EV. auto. +- (* Ccomplimm *) + destruct c0; auto; destruct (Int64.eq n Int64.zero) eqn:N0; auto; + apply Int64.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccomplimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. auto. ++ (* Ccomplimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. destruct (rs x); simpl in EV; inv EV. simpl. destruct (Int64.eq i Int64.zero); auto. +- (* Ccompluimm *) + destruct c0; auto; destruct (Int64.eq n Int64.zero) eqn:N0; auto; + apply Int64.same_if_eq in N0; subst n; ArgsInv. ++ (* Ccompluimm Cne 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite EV. auto. ++ (* Ccompluimm Ceq 0 *) + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. rewrite (Val.negate_cmplu_bool (Mem.valid_pointer m) Cne), EV. destruct b; auto. +- (* Cmasklzero *) + destruct (Int64.is_power2' n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int64.mul_pow2', Int64.mul_commut, Int64.mul_one by eauto. + rewrite (Val.negate_cmpl_bool Ceq), EV. destruct b; auto. +- (* Cmasklnotzero *) + destruct (Int64.is_power2' n) as [bit|] eqn:P2; auto. ArgsInv. + do 2 econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. + erewrite <- Int64.mul_pow2', Int64.mul_commut, Int64.mul_one by eauto. + rewrite EV. auto. +Qed. + +(** Translation of arithmetic operations *) + +Ltac SimplEval H := + match type of H with + | Some _ = None _ => discriminate + | Some _ = Some _ => inv H + | ?a = Some ?b => let A := fresh in assert (A: Val.maketotal a = b) by (rewrite H; reflexivity) +end. + +Ltac TranslOpSimpl := + econstructor; split; + [ apply exec_straight_one; [simpl; eauto | reflexivity] + | split; [ rewrite ? transl_eval_shift, ? transl_eval_shiftl; + apply Val.lessdef_same; Simpl; fail + | intros; Simpl; fail ] ]. + +Ltac TranslOpBase := + econstructor; split; + [ apply exec_straight_one; [simpl; eauto | reflexivity] + | split; [ rewrite ? transl_eval_shift, ? transl_eval_shiftl; Simpl + | intros; Simpl; fail ] ]. + +Lemma transl_op_correct: + forall op args res k (rs: regset) m v c, + transl_op op args res k = OK c -> + eval_operation ge (rs#SP) op (map rs (map preg_of args)) m = Some v -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ Val.lessdef v rs'#(preg_of res) + /\ forall r, data_preg r = true -> r <> preg_of res -> preg_notin r (destroyed_by_op op) -> rs' r = rs r. +Proof. +Local Opaque Int.eq Int64.eq Val.add Val.addl Int.zwordsize Int64.zwordsize. + intros until c; intros TR EV. + unfold transl_op in TR; destruct op; ArgsInv; simpl in EV; SimplEval EV; try TranslOpSimpl. +- (* move *) + destruct (preg_of res) eqn:RR; try discriminate; destruct (preg_of m0) eqn:R1; inv TR. ++ TranslOpSimpl. ++ TranslOpSimpl. +- (* intconst *) + exploit exec_loadimm32. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. intros; auto with asmgen. +- (* longconst *) + exploit exec_loadimm64. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. intros; auto with asmgen. +- (* floatconst *) + destruct (Float.eq_dec n Float.zero). ++ subst n. TranslOpSimpl. ++ TranslOpSimpl. +- (* singleconst *) + destruct (Float32.eq_dec n Float32.zero). ++ subst n. TranslOpSimpl. ++ TranslOpSimpl. +- (* loadsymbol *) + exploit (exec_loadsymbol x id ofs). eauto with asmgen. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* addrstack *) + exploit (exec_addimm64 x XSP (Ptrofs.to_int64 ofs)). simpl; eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. simpl in B; rewrite B. +Local Transparent Val.addl. + destruct (rs SP); simpl; auto. rewrite Ptrofs.of_int64_to_int64 by auto. auto. + auto. +- (* shift *) + rewrite <- transl_eval_shift'. TranslOpSimpl. +- (* addimm *) + exploit (exec_addimm32 x x0 n). eauto with asmgen. intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* mul *) + TranslOpBase. +Local Transparent Val.add. + destruct (rs x0); auto; destruct (rs x1); auto. simpl. rewrite Int.add_zero_l; auto. +- (* andimm *) + exploit (exec_logicalimm32 (Pandimm W) (Pand W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* orimm *) + exploit (exec_logicalimm32 (Porrimm W) (Porr W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* xorimm *) + exploit (exec_logicalimm32 (Peorimm W) (Peor W)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* not *) + TranslOpBase. + destruct (rs x0); auto. simpl. rewrite Int.or_zero_l; auto. +- (* notshift *) + TranslOpBase. + destruct (eval_shift s (rs x0) a); auto. simpl. rewrite Int.or_zero_l; auto. +- (* shrx *) + exploit (exec_shrx32 x x0 n); eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* zero-ext *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int.shl_zero. auto. +- (* sign-ext *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int.shl_zero. auto. +- (* shlzext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int.shl_zero_ext_min; auto using a32_range. +- (* shlsext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int.shl_sign_ext_min; auto using a32_range. +- (* zextshr *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a32_range; simpl. rewrite <- Int.zero_ext_shru_min; auto using a32_range. +- (* sextshr *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a32_range; simpl. rewrite <- Int.sign_ext_shr_min; auto using a32_range. +- (* shiftl *) + rewrite <- transl_eval_shiftl'. TranslOpSimpl. +- (* extend *) + exploit (exec_move_extended x0 x1 x a k). intros (rs' & A & B & C). + econstructor; split. eexact A. + split. rewrite B; auto. eauto with asmgen. +- (* addext *) + exploit (exec_arith_extended Val.addl Paddext (Padd X)). + auto. auto. instantiate (1 := x1). eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* addlimm *) + exploit (exec_addimm64 x x0 n). simpl. generalize (ireg_of_not_X16 _ _ EQ1). congruence. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. simpl in B; rewrite B; auto. auto. +- (* subext *) + exploit (exec_arith_extended Val.subl Psubext (Psub X)). + auto. auto. instantiate (1 := x1). eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* mull *) + TranslOpBase. + destruct (rs x0); auto; destruct (rs x1); auto. simpl. rewrite Int64.add_zero_l; auto. +- (* andlimm *) + exploit (exec_logicalimm64 (Pandimm X) (Pand X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* orlimm *) + exploit (exec_logicalimm64 (Porrimm X) (Porr X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* xorlimm *) + exploit (exec_logicalimm64 (Peorimm X) (Peor X)). + intros; reflexivity. intros; reflexivity. instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split. eexact A. split. rewrite B; auto. auto. +- (* notl *) + TranslOpBase. + destruct (rs x0); auto. simpl. rewrite Int64.or_zero_l; auto. +- (* notlshift *) + TranslOpBase. + destruct (eval_shiftl s (rs x0) a); auto. simpl. rewrite Int64.or_zero_l; auto. +- (* shrx *) + exploit (exec_shrx64 x x0 n); eauto with asmgen. intros (rs' & A & B & C). + econstructor; split. eexact A. split. rewrite B; auto. auto. +- (* zero-ext-l *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int64.shl'_zero. auto. +- (* sign-ext-l *) + TranslOpBase. + destruct (rs x0); auto; simpl. rewrite Int64.shl'_zero. auto. +- (* shllzext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int64.shl'_zero_ext_min; auto using a64_range. +- (* shllsext *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite <- Int64.shl'_sign_ext_min; auto using a64_range. +- (* zextshrl *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a64_range; simpl. rewrite <- Int64.zero_ext_shru'_min; auto using a64_range. +- (* sextshrl *) + TranslOpBase. + destruct (rs x0); simpl; auto. rewrite ! a64_range; simpl. rewrite <- Int64.sign_ext_shr'_min; auto using a64_range. +- (* condition *) + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. auto. + auto. + intros; Simpl. +- (* select *) + destruct (preg_of res) eqn:RES; monadInv TR. + + (* integer *) + generalize (ireg_of_eq _ _ EQ) (ireg_of_eq _ _ EQ1); intros E1 E2; rewrite E1, E2. + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. rewrite !C. apply Val.lessdef_normalize. + rewrite <- E2; auto with asmgen. rewrite <- E1; auto with asmgen. + auto. + intros; Simpl. + + (* FP *) + generalize (freg_of_eq _ _ EQ) (freg_of_eq _ _ EQ1); intros E1 E2; rewrite E1, E2. + exploit (transl_cond_correct cond args); eauto. intros (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (eval_condition cond (map rs (map preg_of args)) m) as [b|]; simpl in *. + rewrite (B b) by auto. rewrite !C. apply Val.lessdef_normalize. + rewrite <- E2; auto with asmgen. rewrite <- E1; auto with asmgen. + auto. + intros; Simpl. +Qed. + +(** Translation of addressing modes, loads, stores *) + +Lemma transl_addressing_correct: + forall sz addr args (insn: Asm.addressing -> instruction) k (rs: regset) m c b o, + transl_addressing sz addr args insn k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some (Vptr b o) -> + exists ad rs', + exec_straight_opt ge fn c rs m (insn ad :: k) rs' m + /\ Asm.eval_addressing ge ad rs' = Vptr b o + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros until o; intros TR EV. + unfold transl_addressing in TR; destruct addr; ArgsInv; SimplEval EV. +- (* Aindexed *) + destruct (offset_representable sz ofs); inv EQ0. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ exploit (exec_loadimm64 X16 ofs). intros (rs' & A & B & C). + econstructor; exists rs'; split. apply exec_straight_opt_intro; eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. + eauto with asmgen. +- (* Aindexed2 *) + econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. +- (* Aindexed2shift *) + destruct (Int.eq a Int.zero) eqn:E; [|destruct (Int.eq (Int.shl Int.one a) (Int.repr sz))]; inv EQ2. ++ apply Int.same_if_eq in E. rewrite E. + econstructor; econstructor; split. apply exec_straight_opt_refl. + split; auto. simpl. + rewrite Val.addl_commut in H0. destruct (rs x0); try discriminate. + unfold Val.shll. rewrite Int64.shl'_zero. auto. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ econstructor; econstructor; split. + apply exec_straight_opt_intro. apply exec_straight_one. simpl; eauto. auto. + split. simpl. Simpl. rewrite H0. simpl. rewrite Ptrofs.add_zero. auto. + intros; Simpl. +- (* Aindexed2ext *) + destruct (Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz)); inv EQ2. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + split; auto. destruct x; auto. ++ exploit (exec_arith_extended Val.addl Paddext (Padd X)); auto. + instantiate (1 := x0). eauto with asmgen. + intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. rewrite B. rewrite Val.addl_assoc. f_equal. + unfold Op.eval_extend; destruct x, (rs x1); simpl; auto; rewrite ! a64_range; + simpl; rewrite Int64.add_zero; auto. + intros. apply C; eauto with asmgen. +- (* Aglobal *) + destruct (Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero && symbol_is_aligned id sz); inv TR. ++ econstructor; econstructor; split. + apply exec_straight_opt_intro. apply exec_straight_one. simpl; eauto. auto. + split. simpl. Simpl. rewrite symbol_high_low. simpl in EV. congruence. + intros; Simpl. ++ exploit (exec_loadsymbol X16 id ofs). auto. intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. + rewrite B. rewrite <- Genv.shift_symbol_address_64, Ptrofs.add_zero by auto. + simpl in EV. congruence. + auto with asmgen. +- (* Ainstrack *) + assert (E: Val.addl (rs SP) (Vlong (Ptrofs.to_int64 ofs)) = Vptr b o). + { simpl in EV. inv EV. destruct (rs SP); simpl in H1; inv H1. simpl. + rewrite Ptrofs.of_int64_to_int64 by auto. auto. } + destruct (offset_representable sz (Ptrofs.to_int64 ofs)); inv TR. ++ econstructor; econstructor; split. apply exec_straight_opt_refl. + auto. ++ exploit (exec_loadimm64 X16 (Ptrofs.to_int64 ofs)). intros (rs' & A & B & C). + econstructor; exists rs'; split. + apply exec_straight_opt_intro. eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. + auto with asmgen. +Qed. + +Lemma transl_load_correct: + forall chunk addr args dst k c (rs: regset) m vaddr v, + transl_load chunk addr args dst k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some vaddr -> + Mem.loadv chunk m vaddr = Some v -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, data_preg r = true -> r <> preg_of dst -> rs' r = rs r. +Proof. + intros. destruct vaddr; try discriminate. + assert (A: exists sz insn, + transl_addressing sz addr args insn k = OK c + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_load ge chunk (fun v => v) ad (preg_of dst) rs' m)). + { + destruct chunk; monadInv H; + try rewrite (ireg_of_eq _ _ EQ); try rewrite (freg_of_eq _ _ EQ); + do 2 econstructor; (split; [eassumption|auto]). + } + destruct A as (sz & insn & B & C). + exploit transl_addressing_correct. eexact B. eexact H0. intros (ad & rs' & P & Q & R). + assert (X: exec_load ge chunk (fun v => v) ad (preg_of dst) rs' m = + Next (nextinstr (rs'#(preg_of dst) <- v)) m). + { unfold exec_load. rewrite Q, H1. auto. } + econstructor; split. + eapply exec_straight_opt_right. eexact P. + apply exec_straight_one. rewrite C, X; eauto. Simpl. + split. Simpl. intros; Simpl. +Qed. + +Lemma transl_store_correct: + forall chunk addr args src k c (rs: regset) m vaddr m', + transl_store chunk addr args src k = OK c -> + Op.eval_addressing ge (rs#SP) addr (map rs (map preg_of args)) = Some vaddr -> + Mem.storev chunk m vaddr rs#(preg_of src) = Some m' -> + exists rs', + exec_straight ge fn c rs m k rs' m' + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros. destruct vaddr; try discriminate. + set (chunk' := match chunk with Mint8signed => Mint8unsigned + | Mint16signed => Mint16unsigned + | _ => chunk end). + assert (A: exists sz insn, + transl_addressing sz addr args insn k = OK c + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_store ge chunk' ad rs'#(preg_of src) rs' m)). + { + unfold chunk'; destruct chunk; monadInv H; + try rewrite (ireg_of_eq _ _ EQ); try rewrite (freg_of_eq _ _ EQ); + do 2 econstructor; (split; [eassumption|auto]). + } + destruct A as (sz & insn & B & C). + exploit transl_addressing_correct. eexact B. eexact H0. intros (ad & rs' & P & Q & R). + assert (X: Mem.storev chunk' m (Vptr b i) rs#(preg_of src) = Some m'). + { rewrite <- H1. unfold chunk'. destruct chunk; auto; simpl; symmetry. + apply Mem.store_signed_unsigned_8. + apply Mem.store_signed_unsigned_16. } + assert (Y: exec_store ge chunk' ad rs'#(preg_of src) rs' m = + Next (nextinstr rs') m'). + { unfold exec_store. rewrite Q, R, X by auto with asmgen. auto. } + econstructor; split. + eapply exec_straight_opt_right. eexact P. + apply exec_straight_one. rewrite C, Y; eauto. Simpl. + intros; Simpl. +Qed. + +(** Translation of indexed memory accesses *) + +Lemma indexed_memory_access_correct: forall insn sz (base: iregsp) ofs k (rs: regset) m b i, + preg_of_iregsp base <> IR X16 -> + Val.offset_ptr rs#base ofs = Vptr b i -> + exists ad rs', + exec_straight_opt ge fn (indexed_memory_access insn sz base ofs k) rs m (insn ad :: k) rs' m + /\ Asm.eval_addressing ge ad rs' = Vptr b i + /\ forall r, r <> PC -> r <> X16 -> rs' r = rs r. +Proof. + unfold indexed_memory_access; intros. + assert (Val.addl rs#base (Vlong (Ptrofs.to_int64 ofs)) = Vptr b i). + { destruct (rs base); try discriminate. simpl in *. rewrite Ptrofs.of_int64_to_int64 by auto. auto. } + destruct offset_representable. +- econstructor; econstructor; split. apply exec_straight_opt_refl. auto. +- exploit (exec_loadimm64 X16); eauto. intros (rs' & A & B & C). + econstructor; econstructor; split. apply exec_straight_opt_intro; eexact A. + split. simpl. rewrite B, C by eauto with asmgen. auto. auto. +Qed. + +Lemma loadptr_correct: forall (base: iregsp) ofs dst k m v (rs: regset), + Mem.loadv Mint64 m (Val.offset_ptr rs#base ofs) = Some v -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn (loadptr base ofs dst k) rs m k rs' m + /\ rs'#dst = v + /\ forall r, r <> PC -> r <> X16 -> r <> dst -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. simpl. unfold exec_load. rewrite B, H. eauto. auto. + split. Simpl. intros; Simpl. +Qed. + +Lemma storeptr_correct: forall (base: iregsp) ofs (src: ireg) k m m' (rs: regset), + Mem.storev Mint64 m (Val.offset_ptr rs#base ofs) rs#src = Some m' -> + preg_of_iregsp base <> IR X16 -> + src <> X16 -> + exists rs', + exec_straight ge fn (storeptr src base ofs k) rs m k rs' m' + /\ forall r, r <> PC -> r <> X16 -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. simpl. unfold exec_store. rewrite B, C, H by eauto with asmgen. eauto. auto. + intros; Simpl. +Qed. + +Lemma loadind_correct: forall (base: iregsp) ofs ty dst k c (rs: regset) m v, + loadind base ofs ty dst k = OK c -> + Mem.loadv (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) = Some v -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn c rs m k rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, data_preg r = true -> r <> preg_of dst -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + assert (X: exists sz insn, + c = indexed_memory_access insn sz base ofs k + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_load ge (chunk_of_type ty) (fun v => v) ad (preg_of dst) rs' m)). + { + unfold loadind in H; destruct ty; destruct (preg_of dst); inv H; do 2 econstructor; eauto. + } + destruct X as (sz & insn & EQ & SEM). subst c. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. rewrite SEM. unfold exec_load. rewrite B, H0. eauto. Simpl. + split. Simpl. intros; Simpl. +Qed. + +Lemma storeind_correct: forall (base: iregsp) ofs ty src k c (rs: regset) m m', + storeind src base ofs ty k = OK c -> + Mem.storev (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) rs#(preg_of src) = Some m' -> + preg_of_iregsp base <> IR X16 -> + exists rs', + exec_straight ge fn c rs m k rs' m' + /\ forall r, data_preg r = true -> rs' r = rs r. +Proof. + intros. + destruct (Val.offset_ptr rs#base ofs) eqn:V; try discriminate. + assert (X: exists sz insn, + c = indexed_memory_access insn sz base ofs k + /\ (forall ad rs', exec_instr ge fn (insn ad) rs' m = + exec_store ge (chunk_of_type ty) ad rs'#(preg_of src) rs' m)). + { + unfold storeind in H; destruct ty; destruct (preg_of src); inv H; do 2 econstructor; eauto. + } + destruct X as (sz & insn & EQ & SEM). subst c. + exploit indexed_memory_access_correct; eauto. intros (ad & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. + apply exec_straight_one. rewrite SEM. + unfold exec_store. rewrite B, C, H0 by eauto with asmgen. eauto. + Simpl. + intros; Simpl. +Qed. + +Lemma make_epilogue_correct: + forall ge0 f m stk soff cs m' ms rs k tm, + load_stack m (Vptr stk soff) Tptr f.(fn_link_ofs) = Some (parent_sp cs) -> + load_stack m (Vptr stk soff) Tptr f.(fn_retaddr_ofs) = Some (parent_ra cs) -> + Mem.free m stk 0 f.(fn_stacksize) = Some m' -> + agree ms (Vptr stk soff) rs -> + Mem.extends m tm -> + match_stack ge0 cs -> + exists rs', exists tm', + exec_straight ge fn (make_epilogue f k) rs tm k rs' tm' + /\ agree ms (parent_sp cs) rs' + /\ Mem.extends m' tm' + /\ rs'#RA = parent_ra cs + /\ rs'#SP = parent_sp cs + /\ (forall r, r <> PC -> r <> SP -> r <> X30 -> r <> X16 -> rs'#r = rs#r). +Proof. + intros until tm; intros LP LRA FREE AG MEXT MCS. + exploit Mem.loadv_extends. eauto. eexact LP. auto. simpl. intros (parent' & LP' & LDP'). + exploit Mem.loadv_extends. eauto. eexact LRA. auto. simpl. intros (ra' & LRA' & LDRA'). + exploit lessdef_parent_sp; eauto. intros EQ; subst parent'; clear LDP'. + exploit lessdef_parent_ra; eauto. intros EQ; subst ra'; clear LDRA'. + exploit Mem.free_parallel_extends; eauto. intros (tm' & FREE' & MEXT'). + unfold make_epilogue. + exploit (loadptr_correct XSP (fn_retaddr_ofs f)). + instantiate (2 := rs). simpl. rewrite <- (sp_val _ _ _ AG). simpl. eexact LRA'. simpl; congruence. + intros (rs1 & A1 & B1 & C1). + econstructor; econstructor; split. + eapply exec_straight_trans. eexact A1. apply exec_straight_one. simpl. + simpl; rewrite (C1 SP) by auto with asmgen. rewrite <- (sp_val _ _ _ AG). simpl; rewrite LP'. + rewrite FREE'. eauto. auto. + split. apply agree_nextinstr. apply agree_set_other; auto. + apply agree_change_sp with (Vptr stk soff). + apply agree_exten with rs; auto. intros; apply C1; auto with asmgen. + eapply parent_sp_def; eauto. + split. auto. + split. Simpl. + split. Simpl. + intros. Simpl. +Qed. + +End CONSTRUCTORS. diff --git a/aarch64/TO_MERGE/TargetPrinter.ml b/aarch64/TO_MERGE/TargetPrinter.ml new file mode 100644 index 00000000..bc4279a0 --- /dev/null +++ b/aarch64/TO_MERGE/TargetPrinter.ml @@ -0,0 +1,862 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(* Printing AArch64 assembly code in asm syntax *) + +open Printf +open Camlcoq +open Sections +open AST +open Asm +open AisAnnot +open PrintAsmaux +open Fileinfo + +<<<<<<< HEAD +(* Module containing the printing functions *) + +module Target (*: TARGET*) = +======= +(* Recognition of FP numbers that are supported by the fmov #imm instructions: + "a normalized binary floating point encoding with 1 sign bit, + 4 bits of fraction and a 3-bit exponent" +*) + +let is_immediate_float64 bits = + let exp = (Int64.(to_int (shift_right_logical bits 52)) land 0x7FF) - 1023 in + let mant = Int64.logand bits 0xF_FFFF_FFFF_FFFFL in + exp >= -3 && exp <= 4 && Int64.logand mant 0xF_0000_0000_0000L = mant + +let is_immediate_float32 bits = + let exp = (Int32.(to_int (shift_right_logical bits 23)) land 0xFF) - 127 in + let mant = Int32.logand bits 0x7F_FFFFl in + exp >= -3 && exp <= 4 && Int32.logand mant 0x78_0000l = mant + +(* Naming and printing registers *) + +let intsz oc (sz, n) = + match sz with X -> coqint64 oc n | W -> coqint oc n + +let xreg_name = function + | X0 -> "x0" | X1 -> "x1" | X2 -> "x2" | X3 -> "x3" + | X4 -> "x4" | X5 -> "x5" | X6 -> "x6" | X7 -> "x7" + | X8 -> "x8" | X9 -> "x9" | X10 -> "x10" | X11 -> "x11" + | X12 -> "x12" | X13 -> "x13" | X14 -> "x14" | X15 -> "x15" + | X16 -> "x16" | X17 -> "x17" | X18 -> "x18" | X19 -> "x19" + | X20 -> "x20" | X21 -> "x21" | X22 -> "x22" | X23 -> "x23" + | X24 -> "x24" | X25 -> "x25" | X26 -> "x26" | X27 -> "x27" + | X28 -> "x28" | X29 -> "x29" | X30 -> "x30" + +let wreg_name = function + | X0 -> "w0" | X1 -> "w1" | X2 -> "w2" | X3 -> "w3" + | X4 -> "w4" | X5 -> "w5" | X6 -> "w6" | X7 -> "w7" + | X8 -> "w8" | X9 -> "w9" | X10 -> "w10" | X11 -> "w11" + | X12 -> "w12" | X13 -> "w13" | X14 -> "w14" | X15 -> "w15" + | X16 -> "w16" | X17 -> "w17" | X18 -> "w18" | X19 -> "w19" + | X20 -> "w20" | X21 -> "w21" | X22 -> "w22" | X23 -> "w23" + | X24 -> "w24" | X25 -> "w25" | X26 -> "w26" | X27 -> "w27" + | X28 -> "w28" | X29 -> "w29" | X30 -> "w30" + +let xreg0_name = function RR0 r -> xreg_name r | XZR -> "xzr" +let wreg0_name = function RR0 r -> wreg_name r | XZR -> "wzr" + +let xregsp_name = function RR1 r -> xreg_name r | XSP -> "sp" +let wregsp_name = function RR1 r -> wreg_name r | XSP -> "wsp" + +let dreg_name = function +| D0 -> "d0" | D1 -> "d1" | D2 -> "d2" | D3 -> "d3" +| D4 -> "d4" | D5 -> "d5" | D6 -> "d6" | D7 -> "d7" +| D8 -> "d8" | D9 -> "d9" | D10 -> "d10" | D11 -> "d11" +| D12 -> "d12" | D13 -> "d13" | D14 -> "d14" | D15 -> "d15" +| D16 -> "d16" | D17 -> "d17" | D18 -> "d18" | D19 -> "d19" +| D20 -> "d20" | D21 -> "d21" | D22 -> "d22" | D23 -> "d23" +| D24 -> "d24" | D25 -> "d25" | D26 -> "d26" | D27 -> "d27" +| D28 -> "d28" | D29 -> "d29" | D30 -> "d30" | D31 -> "d31" + +let sreg_name = function +| D0 -> "s0" | D1 -> "s1" | D2 -> "s2" | D3 -> "s3" +| D4 -> "s4" | D5 -> "s5" | D6 -> "s6" | D7 -> "s7" +| D8 -> "s8" | D9 -> "s9" | D10 -> "s10" | D11 -> "s11" +| D12 -> "s12" | D13 -> "s13" | D14 -> "s14" | D15 -> "s15" +| D16 -> "s16" | D17 -> "s17" | D18 -> "s18" | D19 -> "s19" +| D20 -> "s20" | D21 -> "s21" | D22 -> "s22" | D23 -> "s23" +| D24 -> "s24" | D25 -> "s25" | D26 -> "s26" | D27 -> "s27" +| D28 -> "s28" | D29 -> "s29" | D30 -> "s30" | D31 -> "s31" + +let xreg oc r = output_string oc (xreg_name r) +let wreg oc r = output_string oc (wreg_name r) +let ireg oc (sz, r) = + output_string oc (match sz with X -> xreg_name r | W -> wreg_name r) + +let xreg0 oc r = output_string oc (xreg0_name r) +let wreg0 oc r = output_string oc (wreg0_name r) +let ireg0 oc (sz, r) = + output_string oc (match sz with X -> xreg0_name r | W -> wreg0_name r) + +let xregsp oc r = output_string oc (xregsp_name r) +let iregsp oc (sz, r) = + output_string oc (match sz with X -> xregsp_name r | W -> wregsp_name r) + +let dreg oc r = output_string oc (dreg_name r) +let sreg oc r = output_string oc (sreg_name r) +let freg oc (sz, r) = + output_string oc (match sz with D -> dreg_name r | S -> sreg_name r) + +let preg_asm oc ty = function + | IR r -> if ty = Tint then wreg oc r else xreg oc r + | FR r -> if ty = Tsingle then sreg oc r else dreg oc r + | _ -> assert false + +let preg_annot = function + | IR r -> xreg_name r + | FR r -> dreg_name r + | _ -> assert false + +(* Base-2 log of a Caml integer *) +let rec log2 n = + assert (n > 0); + if n = 1 then 0 else 1 + log2 (n lsr 1) + +(* System dependent printer functions *) + +module type SYSTEM = + sig + val comment: string + val raw_symbol: out_channel -> string -> unit + val symbol: out_channel -> P.t -> unit + val symbol_offset_high: out_channel -> P.t * Z.t -> unit + val symbol_offset_low: out_channel -> P.t * Z.t -> unit + val label: out_channel -> int -> unit + val label_high: out_channel -> int -> unit + val label_low: out_channel -> int -> unit + val load_symbol_address: out_channel -> ireg -> P.t -> unit + val name_of_section: section_name -> string + val print_fun_info: out_channel -> P.t -> unit + val print_var_info: out_channel -> P.t -> unit + val print_comm_decl: out_channel -> P.t -> Z.t -> int -> unit + val print_lcomm_decl: out_channel -> P.t -> Z.t -> int -> unit + end + +module ELF_System : SYSTEM = +>>>>>>> master + struct + let comment = "//" + let raw_symbol = output_string + let symbol = elf_symbol + let symbol_offset_high = elf_symbol_offset + let symbol_offset_low oc id_ofs = + fprintf oc "#:lo12:%a" elf_symbol_offset id_ofs + + let label = elf_label + let label_high = elf_label + let label_low oc lbl = + fprintf oc "#:lo12:%a" elf_label lbl + +<<<<<<< HEAD + let print_label oc lbl = label oc (transl_label lbl) + + let intsz oc (sz, n) = + match sz with X -> coqint64 oc n | W -> coqint oc n + + let xreg_name = function + | X0 -> "x0" | X1 -> "x1" | X2 -> "x2" | X3 -> "x3" + | X4 -> "x4" | X5 -> "x5" | X6 -> "x6" | X7 -> "x7" + | X8 -> "x8" | X9 -> "x9" | X10 -> "x10" | X11 -> "x11" + | X12 -> "x12" | X13 -> "x13" | X14 -> "x14" | X15 -> "x15" + | X16 -> "x16" | X17 -> "x17" | X18 -> "x18" | X19 -> "x19" + | X20 -> "x20" | X21 -> "x21" | X22 -> "x22" | X23 -> "x23" + | X24 -> "x24" | X25 -> "x25" | X26 -> "x26" | X27 -> "x27" + | X28 -> "x28" | X29 -> "x29" | X30 -> "x30" + + let wreg_name = function + | X0 -> "w0" | X1 -> "w1" | X2 -> "w2" | X3 -> "w3" + | X4 -> "w4" | X5 -> "w5" | X6 -> "w6" | X7 -> "w7" + | X8 -> "w8" | X9 -> "w9" | X10 -> "w10" | X11 -> "w11" + | X12 -> "w12" | X13 -> "w13" | X14 -> "w14" | X15 -> "w15" + | X16 -> "w16" | X17 -> "w17" | X18 -> "w18" | X19 -> "w19" + | X20 -> "w20" | X21 -> "w21" | X22 -> "w22" | X23 -> "w23" + | X24 -> "w24" | X25 -> "w25" | X26 -> "w26" | X27 -> "w27" + | X28 -> "w28" | X29 -> "w29" | X30 -> "w30" + + let xreg0_name = function RR0 r -> xreg_name r | XZR -> "xzr" + let wreg0_name = function RR0 r -> wreg_name r | XZR -> "wzr" + + let xregsp_name = function RR1 r -> xreg_name r | XSP -> "sp" + let wregsp_name = function RR1 r -> wreg_name r | XSP -> "wsp" + + let dreg_name = function + | D0 -> "d0" | D1 -> "d1" | D2 -> "d2" | D3 -> "d3" + | D4 -> "d4" | D5 -> "d5" | D6 -> "d6" | D7 -> "d7" + | D8 -> "d8" | D9 -> "d9" | D10 -> "d10" | D11 -> "d11" + | D12 -> "d12" | D13 -> "d13" | D14 -> "d14" | D15 -> "d15" + | D16 -> "d16" | D17 -> "d17" | D18 -> "d18" | D19 -> "d19" + | D20 -> "d20" | D21 -> "d21" | D22 -> "d22" | D23 -> "d23" + | D24 -> "d24" | D25 -> "d25" | D26 -> "d26" | D27 -> "d27" + | D28 -> "d28" | D29 -> "d29" | D30 -> "d30" | D31 -> "d31" + + let sreg_name = function + | D0 -> "s0" | D1 -> "s1" | D2 -> "s2" | D3 -> "s3" + | D4 -> "s4" | D5 -> "s5" | D6 -> "s6" | D7 -> "s7" + | D8 -> "s8" | D9 -> "s9" | D10 -> "s10" | D11 -> "s11" + | D12 -> "s12" | D13 -> "s13" | D14 -> "s14" | D15 -> "s15" + | D16 -> "s16" | D17 -> "s17" | D18 -> "s18" | D19 -> "s19" + | D20 -> "s20" | D21 -> "s21" | D22 -> "s22" | D23 -> "s23" + | D24 -> "s24" | D25 -> "s25" | D26 -> "s26" | D27 -> "s27" + | D28 -> "s28" | D29 -> "s29" | D30 -> "s30" | D31 -> "s31" + + let xreg oc r = output_string oc (xreg_name r) + let wreg oc r = output_string oc (wreg_name r) + let ireg oc (sz, r) = + output_string oc (match sz with X -> xreg_name r | W -> wreg_name r) + + let xreg0 oc r = output_string oc (xreg0_name r) + let wreg0 oc r = output_string oc (wreg0_name r) + let ireg0 oc (sz, r) = + output_string oc (match sz with X -> xreg0_name r | W -> wreg0_name r) + + let xregsp oc r = output_string oc (xregsp_name r) + let iregsp oc (sz, r) = + output_string oc (match sz with X -> xregsp_name r | W -> wregsp_name r) + + let dreg oc r = output_string oc (dreg_name r) + let sreg oc r = output_string oc (sreg_name r) + let freg oc (sz, r) = + output_string oc (match sz with D -> dreg_name r | S -> sreg_name r) + + let preg_asm oc ty = function + | DR (IR (RR1 r)) -> if ty = Tint then wreg oc r else xreg oc r + | DR (FR r) -> if ty = Tsingle then sreg oc r else dreg oc r + | _ -> assert false + + let preg_annot = function + | DR (IR (RR1 r)) -> xreg_name r + | DR (FR r) -> dreg_name r + | _ -> assert false + +(* Names of sections *) + + let name_of_section = function + | Section_text -> ".text" + | Section_data(i, true) -> + failwith "_Thread_local unsupported on this platform" + | Section_data(i, false) | Section_small_data i -> + if i then ".data" else common_section () +======= + let load_symbol_address oc rd id = + fprintf oc " adrp %a, :got:%a\n" xreg rd symbol id; + fprintf oc " ldr %a, [%a, #:got_lo12:%a]\n" xreg rd xreg rd symbol id + + let name_of_section = function + | Section_text -> ".text" + | Section_data i | Section_small_data i -> + variable_section ~sec:".data" ~bss:".bss" i +>>>>>>> master + | Section_const i | Section_small_const i -> + variable_section ~sec:".section .rodata" i + | Section_string -> ".section .rodata" + | Section_literal -> ".section .rodata" + | Section_jumptable -> ".section .rodata" + | Section_debug_info _ -> ".section .debug_info,\"\",%progbits" + | Section_debug_loc -> ".section .debug_loc,\"\",%progbits" + | Section_debug_abbrev -> ".section .debug_abbrev,\"\",%progbits" + | Section_debug_line _ -> ".section .debug_line,\"\",%progbits" + | Section_debug_ranges -> ".section .debug_ranges,\"\",%progbits" + | Section_debug_str -> ".section .debug_str,\"MS\",%progbits,1" + | Section_user(s, wr, ex) -> + sprintf ".section \"%s\",\"a%s%s\",%%progbits" + s (if wr then "w" else "") (if ex then "x" else "") + | Section_ais_annotation -> sprintf ".section \"__compcert_ais_annotations\",\"\",@note" + + let print_fun_info = elf_print_fun_info + let print_var_info = elf_print_var_info + + let print_comm_decl oc name sz al = + fprintf oc " .comm %a, %s, %d\n" symbol name (Z.to_string sz) al + + let print_lcomm_decl oc name sz al = + fprintf oc " .local %a\n" symbol name; + print_comm_decl oc name sz al + + end + +module MacOS_System : SYSTEM = + struct + let comment = ";" + + let raw_symbol oc s = + fprintf oc "_%s" s + + let symbol oc symb = + raw_symbol oc (extern_atom symb) + + let symbol_offset_gen kind oc (id, ofs) = + fprintf oc "%a@%s" symbol id kind; + let ofs = camlint64_of_ptrofs ofs in + if ofs <> 0L then fprintf oc " + %Ld" ofs + + let symbol_offset_high = symbol_offset_gen "PAGE" + let symbol_offset_low = symbol_offset_gen "PAGEOFF" + + let label oc lbl = + fprintf oc "L%d" lbl + + let label_high oc lbl = + fprintf oc "%a@PAGE" label lbl + let label_low oc lbl = + fprintf oc "%a@PAGEOFF" label lbl + + let load_symbol_address oc rd id = + fprintf oc " adrp %a, %a@GOTPAGE\n" xreg rd symbol id; + fprintf oc " ldr %a, [%a, %a@GOTPAGEOFF]\n" xreg rd xreg rd symbol id + + let name_of_section = function + | Section_text -> ".text" + | Section_data i | Section_small_data i -> + variable_section ~sec:".data" i + | Section_const i | Section_small_const i -> + variable_section ~sec:".const" ~reloc:".const_data" i + | Section_string -> ".const" + | Section_literal -> ".const" + | Section_jumptable -> ".text" + | Section_user(s, wr, ex) -> + sprintf ".section \"%s\", %s, %s" + (if wr then "__DATA" else "__TEXT") s + (if ex then "regular, pure_instructions" else "regular") + | Section_debug_info _ -> ".section __DWARF,__debug_info,regular,debug" + | Section_debug_loc -> ".section __DWARF,__debug_loc,regular,debug" + | Section_debug_line _ -> ".section __DWARF,__debug_line,regular,debug" + | Section_debug_str -> ".section __DWARF,__debug_str,regular,debug" + | Section_debug_ranges -> ".section __DWARF,__debug_ranges,regular,debug" + | Section_debug_abbrev -> ".section __DWARF,__debug_abbrev,regular,debug" + | Section_ais_annotation -> assert false (* Not supported under MacOS *) + + let print_fun_info _ _ = () + let print_var_info _ _ = () + + let print_comm_decl oc name sz al = + fprintf oc " .comm %a, %s, %d\n" + symbol name (Z.to_string sz) (log2 al) + + let print_lcomm_decl oc name sz al = + fprintf oc " .lcomm %a, %s, %d\n" + symbol name (Z.to_string sz) (log2 al) + + end + +(* Module containing the printing functions *) + +module Target(System: SYSTEM): TARGET = + struct + include System + +(* Basic printing functions *) + + let print_label oc lbl = label oc (transl_label lbl) + +(* Names of sections *) + + let section oc sec = + fprintf oc " %s\n" (name_of_section sec) + +(* Associate labels to floating-point constants and to symbols. *) + + let emit_constants oc lit = + if exists_constants () then begin + section oc lit; + if Hashtbl.length literal64_labels > 0 then + begin + fprintf oc " .balign 8\n"; + Hashtbl.iter + (fun bf lbl -> fprintf oc "%a: .quad 0x%Lx\n" label lbl bf) + literal64_labels + end; + if Hashtbl.length literal32_labels > 0 then + begin + fprintf oc " .balign 4\n"; + Hashtbl.iter + (fun bf lbl -> + fprintf oc "%a: .long 0x%lx\n" label lbl bf) + literal32_labels + end; + reset_literals () + end + +(* Emit .file / .loc debugging directives *) + + let print_file_line oc file line = + print_file_line oc comment file line + +(* Name of testable condition *) + + let condition_name = function + | TCeq -> "eq" + | TCne -> "ne" + | TChs -> "hs" + | TClo -> "lo" + | TCmi -> "mi" + | TCpl -> "pl" + | TChi -> "hi" + | TCls -> "ls" + | TCge -> "ge" + | TClt -> "lt" + | TCgt -> "gt" + | TCle -> "le" + +(* Print an addressing mode *) + + let addressing oc = function + | ADimm(base, n) -> fprintf oc "[%a, #%a]" xregsp base coqint64 n + | ADreg(base, r) -> fprintf oc "[%a, %a]" xregsp base xreg r + | ADlsl(base, r, n) -> fprintf oc "[%a, %a, lsl #%a]" xregsp base xreg r coqint n + | ADsxt(base, r, n) -> fprintf oc "[%a, %a, sxtw #%a]" xregsp base wreg r coqint n + | ADuxt(base, r, n) -> fprintf oc "[%a, %a, uxtw #%a]" xregsp base wreg r coqint n + | ADadr(base, id, ofs) -> fprintf oc "[%a, %a]" xregsp base symbol_offset_low (id, ofs) + | ADpostincr(base, n) -> fprintf oc "[%a], #%a" xregsp base coqint64 n + +(* Print a shifted operand *) + let shiftop oc = function + | SOnone -> () + | SOlsl n -> fprintf oc ", lsl #%a" coqint n + | SOlsr n -> fprintf oc ", lsr #%a" coqint n + | SOasr n -> fprintf oc ", asr #%a" coqint n + | SOror n -> fprintf oc ", ror #%a" coqint n + +(* Print a sign- or zero-extended register operand *) + let regextend oc = function + | (r, EOsxtb n) -> fprintf oc "%a, sxtb #%a" wreg r coqint n + | (r, EOsxth n) -> fprintf oc "%a, sxth #%a" wreg r coqint n + | (r, EOsxtw n) -> fprintf oc "%a, sxtw #%a" wreg r coqint n + | (r, EOuxtb n) -> fprintf oc "%a, uxtb #%a" wreg r coqint n + | (r, EOuxth n) -> fprintf oc "%a, uxth #%a" wreg r coqint n + | (r, EOuxtw n) -> fprintf oc "%a, uxtw #%a" wreg r coqint n + | (r, EOuxtx n) -> fprintf oc "%a, uxtx #%a" xreg r coqint n + + let next_profiling_label = + let atomic_incr_counter = ref 0 in + fun () -> + let r = sprintf ".Lcompcert_atomic_incr%d" !atomic_incr_counter in + incr atomic_incr_counter; r;; + + let print_profiling_logger oc id kind = + assert (kind >= 0); + assert (kind <= 1); + fprintf oc "%s begin profiling %a %d: atomic increment\n" comment + Profilingaux.pp_id id kind; + let ofs = profiling_offset id kind and lbl = next_profiling_label () in + fprintf oc " adrp x15, %s+%d\n" profiling_counter_table_name ofs; + fprintf oc " add x15, x15, :lo12:(%s+%d)\n" profiling_counter_table_name ofs; + fprintf oc "%s:\n" lbl; + fprintf oc " ldaxr x17, [x15]\n"; + fprintf oc " add x17, x17, 1\n"; + fprintf oc " stlxr w17, x17, [x15]\n"; + fprintf oc " cbnz w17, %s\n" lbl; + fprintf oc "%s end profiling %a %d\n" comment + Profilingaux.pp_id id kind;; + +(* Printing of instructions *) + let print_instruction oc = function + (* Branches *) + | Pb lbl -> + fprintf oc " b %a\n" print_label lbl + | Pbc(c, lbl) -> + fprintf oc " b.%s %a\n" (condition_name c) print_label lbl + | Pbl(id, sg) -> + fprintf oc " bl %a\n" symbol id + | Pbs(id, sg) -> + fprintf oc " b %a\n" symbol id + | Pblr(r, sg) -> + fprintf oc " blr %a\n" xreg r + | Pbr(r, sg) -> + fprintf oc " br %a\n" xreg r + | Pret r -> + fprintf oc " ret %a\n" xreg r + | Pcbnz(sz, r, lbl) -> + fprintf oc " cbnz %a, %a\n" ireg (sz, r) print_label lbl + | Pcbz(sz, r, lbl) -> + fprintf oc " cbz %a, %a\n" ireg (sz, r) print_label lbl + | Ptbnz(sz, r, n, lbl) -> + fprintf oc " tbnz %a, #%a, %a\n" ireg (sz, r) coqint n print_label lbl + | Ptbz(sz, r, n, lbl) -> + fprintf oc " tbz %a, #%a, %a\n" ireg (sz, r) coqint n print_label lbl + (* Memory loads and stores *) + | Pldrw(rd, a) | Pldrw_a(rd, a) -> + fprintf oc " ldr %a, %a\n" wreg rd addressing a + | Pldrx(rd, a) | Pldrx_a(rd, a) -> + fprintf oc " ldr %a, %a\n" xreg rd addressing a + | Pldrb(sz, rd, a) -> + fprintf oc " ldrb %a, %a\n" wreg rd addressing a + | Pldrsb(sz, rd, a) -> + fprintf oc " ldrsb %a, %a\n" ireg (sz, rd) addressing a + | Pldrh(sz, rd, a) -> + fprintf oc " ldrh %a, %a\n" wreg rd addressing a + | Pldrsh(sz, rd, a) -> + fprintf oc " ldrsh %a, %a\n" ireg (sz, rd) addressing a + | Pldrzw(rd, a) -> + fprintf oc " ldr %a, %a\n" wreg rd addressing a + (* the upper 32 bits of Xrd are set to 0, performing zero-extension *) + | Pldrsw(rd, a) -> + fprintf oc " ldrsw %a, %a\n" xreg rd addressing a + | Pldpw(rd1, rd2, _, _, a) -> + fprintf oc " ldp %a, %a, %a\n" wreg rd1 wreg rd2 addressing a + | Pldpx(rd1, rd2, _, _, a) -> + fprintf oc " ldp %a, %a, %a\n" xreg rd1 xreg rd2 addressing a + | Pstrw(rs, a) | Pstrw_a(rs, a) -> + fprintf oc " str %a, %a\n" wreg rs addressing a + | Pstrx(rs, a) | Pstrx_a(rs, a) -> + fprintf oc " str %a, %a\n" xreg rs addressing a + | Pstrb(rs, a) -> + fprintf oc " strb %a, %a\n" wreg rs addressing a + | Pstrh(rs, a) -> + fprintf oc " strh %a, %a\n" wreg rs addressing a + | Pstpw(rs1, rs2, _, _, a) -> + fprintf oc " stp %a, %a, %a\n" wreg rs1 wreg rs2 addressing a + | Pstpx(rs1, rs2, _, _, a) -> + fprintf oc " stp %a, %a, %a\n" xreg rs1 xreg rs2 addressing a + (* Integer arithmetic, immediate *) + | Paddimm(sz, rd, r1, n) -> + fprintf oc " add %a, %a, #%a\n" iregsp (sz, rd) iregsp (sz, r1) intsz (sz, n) + | Psubimm(sz, rd, r1, n) -> + fprintf oc " sub %a, %a, #%a\n" iregsp (sz, rd) iregsp (sz, r1) intsz (sz, n) + | Pcmpimm(sz, r1, n) -> + fprintf oc " cmp %a, #%a\n" ireg (sz, r1) intsz (sz, n) + | Pcmnimm(sz, r1, n) -> + fprintf oc " cmn %a, #%a\n" ireg (sz, r1) intsz (sz, n) + (* Move integer register *) + | Pmov(rd, r1) -> + fprintf oc " mov %a, %a\n" xregsp rd xregsp r1 + (* Logical, immediate *) + | Pandimm(sz, rd, r1, n) -> + fprintf oc " and %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Peorimm(sz, rd, r1, n) -> + fprintf oc " eor %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Porrimm(sz, rd, r1, n) -> + fprintf oc " orr %a, %a, #%a\n" ireg (sz, rd) ireg0 (sz, r1) intsz (sz, n) + | Ptstimm(sz, r1, n) -> + fprintf oc " tst %a, #%a\n" ireg (sz, r1) intsz (sz, n) + (* Move wide immediate *) + | Pmovz(sz, rd, n, pos) -> + fprintf oc " movz %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + | Pmovn(sz, rd, n, pos) -> + fprintf oc " movn %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + | Pmovk(sz, rd, n, pos) -> + fprintf oc " movk %a, #%d, lsl #%d\n" ireg (sz, rd) (Z.to_int n) (Z.to_int pos) + (* PC-relative addressing *) + | Padrp(rd, id, ofs) -> + fprintf oc " adrp %a, %a\n" xreg rd symbol_offset_high (id, ofs) + | Paddadr(rd, r1, id, ofs) -> + fprintf oc " add %a, %a, %a\n" xreg rd xreg r1 symbol_offset_low (id, ofs) + (* Bit-field operations *) + | Psbfiz(sz, rd, r1, r, s) -> + fprintf oc " sbfiz %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Psbfx(sz, rd, r1, r, s) -> + fprintf oc " sbfx %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Pubfiz(sz, rd, r1, r, s) -> + fprintf oc " ubfiz %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + | Pubfx(sz, rd, r1, r, s) -> + fprintf oc " ubfx %a, %a, %a, %d\n" ireg (sz, rd) ireg (sz, r1) coqint r (Z.to_int s) + (* Integer arithmetic, shifted register *) + | Padd(sz, rd, r1, r2, s) -> + fprintf oc " add %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Psub(sz, rd, r1, r2, s) -> + fprintf oc " sub %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pcmp(sz, r1, r2, s) -> + fprintf oc " cmp %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pcmn(sz, r1, r2, s) -> + fprintf oc " cmn %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + (* Integer arithmetic, extending register *) + | Paddext(rd, r1, r2, x) -> + fprintf oc " add %a, %a, %a\n" xregsp rd xregsp r1 regextend (r2, x) + | Psubext(rd, r1, r2, x) -> + fprintf oc " sub %a, %a, %a\n" xregsp rd xregsp r1 regextend (r2, x) + | Pcmpext(r1, r2, x) -> + fprintf oc " cmp %a, %a\n" xreg r1 regextend (r2, x) + | Pcmnext(r1, r2, x) -> + fprintf oc " cmn %a, %a\n" xreg r1 regextend (r2, x) + (* Logical, shifted register *) + | Pand(sz, rd, r1, r2, s) -> + fprintf oc " and %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Pbic(sz, rd, r1, r2, s) -> + fprintf oc " bic %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Peon(sz, rd, r1, r2, s) -> + fprintf oc " eon %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Peor(sz, rd, r1, r2, s) -> + fprintf oc " eor %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Porr(sz, rd, r1, r2, s) -> + fprintf oc " orr %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Porn(sz, rd, r1, r2, s) -> + fprintf oc " orn %a, %a, %a%a\n" ireg (sz, rd) ireg0 (sz, r1) ireg (sz, r2) shiftop s + | Ptst(sz, r1, r2, s) -> + fprintf oc " tst %a, %a%a\n" ireg0 (sz, r1) ireg (sz, r2) shiftop s + (* Variable shifts *) + | Pasrv(sz, rd, r1, r2) -> + fprintf oc " asr %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Plslv(sz, rd, r1, r2) -> + fprintf oc " lsl %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Plsrv(sz, rd, r1, r2) -> + fprintf oc " lsr %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Prorv(sz, rd, r1, r2) -> + fprintf oc " ror %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + (* Bit operations *) + | Pcls(sz, rd, r1) -> + fprintf oc " cls %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Pclz(sz, rd, r1) -> + fprintf oc " clz %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Prev(sz, rd, r1) -> + fprintf oc " rev %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Prev16(sz, rd, r1) -> + fprintf oc " rev16 %a, %a\n" ireg (sz, rd) ireg (sz, r1) + | Prbit(sz, rd, r1) -> + fprintf oc " rbit %a, %a\n" ireg (sz, rd) ireg (sz, r1) + (* Conditional data processing *) + | Pcsel(rd, r1, r2, c) -> + fprintf oc " csel %a, %a, %a, %s\n" xreg rd xreg r1 xreg r2 (condition_name c) + | Pcset(rd, c) -> + fprintf oc " cset %a, %s\n" xreg rd (condition_name c) + (* Integer multiply/divide *) + | Pmadd(sz, rd, r1, r2, r3) -> + fprintf oc " madd %a, %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) ireg0 (sz, r3) + | Pmsub(sz, rd, r1, r2, r3) -> + fprintf oc " msub %a, %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) ireg0 (sz, r3) + | Psmulh(rd, r1, r2) -> + fprintf oc " smulh %a, %a, %a\n" xreg rd xreg r1 xreg r2 + | Pumulh(rd, r1, r2) -> + fprintf oc " umulh %a, %a, %a\n" xreg rd xreg r1 xreg r2 + | Psdiv(sz, rd, r1, r2) -> + fprintf oc " sdiv %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + | Pudiv(sz, rd, r1, r2) -> + fprintf oc " udiv %a, %a, %a\n" ireg (sz, rd) ireg (sz, r1) ireg (sz, r2) + (* Floating-point loads and stores *) + | Pldrs(rd, a) -> + fprintf oc " ldr %a, %a\n" sreg rd addressing a + | Pldrd(rd, a) | Pldrd_a(rd, a) -> + fprintf oc " ldr %a, %a\n" dreg rd addressing a + | Pstrs(rd, a) -> + fprintf oc " str %a, %a\n" sreg rd addressing a + | Pstrd(rd, a) | Pstrd_a(rd, a) -> + fprintf oc " str %a, %a\n" dreg rd addressing a + | Pldps(rd1, rd2, _, _, a) -> + fprintf oc " ldp %a, %a, %a\n" sreg rd1 sreg rd2 addressing a + | Pldpd(rd1, rd2, _, _, a) -> + fprintf oc " ldp %a, %a, %a\n" dreg rd1 dreg rd2 addressing a + | Pstps(rd1, rd2, _, _, a) -> + fprintf oc " stp %a, %a, %a\n" sreg rd1 sreg rd2 addressing a + | Pstpd(rd1, rd2, _, _, a) -> + fprintf oc " stp %a, %a, %a\n" dreg rd1 dreg rd2 addressing a + (* Floating-point move *) + | Pfmov(rd, r1) -> + fprintf oc " fmov %a, %a\n" dreg rd dreg r1 + | Pfmovimmd(rd, f) -> + let d = camlint64_of_coqint (Floats.Float.to_bits f) in + if is_immediate_float64 f then + fprintf oc " fmov %a, #%.7f\n" dreg rd (Int64.float_of_bits d) + else begin + let lbl = label_literal64 d in + fprintf oc " adrp x16, %a\n" label_high lbl; + fprintf oc " ldr %a, [x16, %a] %s %.18g\n" dreg rd label_low lbl comment (Int64.float_of_bits d) + end + | Pfmovimms(rd, f) -> + let d = camlint_of_coqint (Floats.Float32.to_bits f) in + if is_immediate_float32 f then + fprintf oc " fmov %a, #%.7f\n" sreg rd (Int32.float_of_bits d) + else begin + let lbl = label_literal32 d in + fprintf oc " adrp x16, %a\n" label_high lbl; + fprintf oc " ldr %a, [x16, %a] %s %.18g\n" sreg rd label_low lbl comment (Int32.float_of_bits d) + end + | Pfmovi(D, rd, r1) -> + fprintf oc " fmov %a, %a\n" dreg rd xreg0 r1 + | Pfmovi(S, rd, r1) -> + fprintf oc " fmov %a, %a\n" sreg rd wreg0 r1 + (* Floating-point conversions *) + | Pfcvtds(rd, r1) -> + fprintf oc " fcvt %a, %a\n" dreg rd sreg r1 + | Pfcvtsd(rd, r1) -> + fprintf oc " fcvt %a, %a\n" sreg rd dreg r1 + | Pfcvtzs(isz, fsz, rd, r1) -> + fprintf oc " fcvtzs %a, %a\n" ireg (isz, rd) freg (fsz, r1) + | Pfcvtzu(isz, fsz, rd, r1) -> + fprintf oc " fcvtzu %a, %a\n" ireg (isz, rd) freg (fsz, r1) + | Pscvtf(fsz, isz, rd, r1) -> + fprintf oc " scvtf %a, %a\n" freg (fsz, rd) ireg (isz, r1) + | Pucvtf(fsz, isz, rd, r1) -> + fprintf oc " ucvtf %a, %a\n" freg (fsz, rd) ireg (isz, r1) + (* Floating-point arithmetic *) + | Pfabs(sz, rd, r1) -> + fprintf oc " fabs %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfneg(sz, rd, r1) -> + fprintf oc " fneg %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfsqrt(sz, rd, r1) -> + fprintf oc " fsqrt %a, %a\n" freg (sz, rd) freg (sz, r1) + | Pfadd(sz, rd, r1, r2) -> + fprintf oc " fadd %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfdiv(sz, rd, r1, r2) -> + fprintf oc " fdiv %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfmul(sz, rd, r1, r2) -> + fprintf oc " fmul %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfnmul(sz, rd, r1, r2) -> + fprintf oc " fnmul %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfsub(sz, rd, r1, r2) -> + fprintf oc " fsub %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfmadd(sz, rd, r1, r2, r3) -> + fprintf oc " fmadd %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfmsub(sz, rd, r1, r2, r3) -> + fprintf oc " fmsub %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfnmadd(sz, rd, r1, r2, r3) -> + fprintf oc " fnmadd %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfnmsub(sz, rd, r1, r2, r3) -> + fprintf oc " fnmsub %a, %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) freg (sz, r3) + | Pfmax (sz, rd, r1, r2) -> + fprintf oc " fmax %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + | Pfmin (sz, rd, r1, r2) -> + fprintf oc " fmin %a, %a, %a\n" freg (sz, rd) freg (sz, r1) freg (sz, r2) + (* Floating-point comparison *) + | Pfcmp(sz, r1, r2) -> + fprintf oc " fcmp %a, %a\n" freg (sz, r1) freg (sz, r2) + | Pfcmp0(sz, r1) -> + fprintf oc " fcmp %a, #0.0\n" freg (sz, r1) + (* Floating-point conditional select *) + | Pfsel(rd, r1, r2, c) -> + fprintf oc " fcsel %a, %a, %a, %s\n" dreg rd dreg r1 dreg r2 (condition_name c) + (* No-op *) + | Pnop -> () + (*fprintf oc " nop\n"*) + (* Pseudo-instructions expanded in Asmexpand *) + | Pallocframe(sz, linkofs) -> assert false + | Pfreeframe(sz, linkofs) -> assert false + | Pcvtx2w rd -> assert false + (* Pseudo-instructions not yet expanded *) + | Plabel lbl -> + fprintf oc "%a:\n" print_label lbl + | Ploadsymbol(rd, id) -> + load_symbol_address oc rd id + | Pcvtsw2x(rd, r1) -> + fprintf oc " sxtw %a, %a\n" xreg rd wreg r1 + | Pcvtuw2x(rd, r1) -> + fprintf oc " uxtw %a, %a\n" xreg rd wreg r1 + | Pbtbl(r1, tbl) -> + let lbl = new_label() in + fprintf oc " adr x16, %a\n" label lbl; + fprintf oc " add x16, x16, %a, uxtw #2\n" wreg r1; + fprintf oc " br x16\n"; + fprintf oc "%a:" label lbl; + List.iter (fun l -> fprintf oc " b %a\n" print_label l) tbl + | Pcfi_adjust sz -> + cfi_adjust oc (camlint_of_coqint sz) + | Pcfi_rel_offset ofs -> + cfi_rel_offset oc "lr" (camlint_of_coqint ofs) + | Pbuiltin(ef, args, res) -> + begin match ef with + | EF_annot(kind,txt, targs) -> + begin match (P.to_int kind) with + | 1 -> let annot = annot_text preg_annot "sp" (camlstring_of_coqstring txt) args in + fprintf oc "%s annotation: %S\n" comment annot + | 2 -> let lbl = new_label () in + fprintf oc "%a:\n" label lbl; + add_ais_annot lbl preg_annot "sp" (camlstring_of_coqstring txt) args + | _ -> assert false + end + | EF_debug(kind, txt, targs) -> + print_debug_info comment print_file_line preg_annot "sp" oc + (P.to_int kind) (extern_atom txt) args + | EF_inline_asm(txt, sg, clob) -> + fprintf oc "%s begin inline assembly\n\t" comment; + print_inline_asm preg_asm oc (camlstring_of_coqstring txt) sg args res; + fprintf oc "%s end inline assembly\n" comment + | EF_profiling (id, coq_kind) -> + print_profiling_logger oc id (Z.to_int coq_kind) + | _ -> + assert false + end + + let get_section_names name = + let (text, lit) = + match C2C.atom_sections name with + | t :: l :: _ -> (t, l) + | _ -> (Section_text, Section_literal) in + text,lit,Section_jumptable + + let print_align oc alignment = + fprintf oc " .balign %d\n" alignment + + let print_jumptable oc jmptbl = + let print_tbl oc (lbl, tbl) = + fprintf oc "%a:\n" label lbl; + List.iter + (fun l -> fprintf oc " .long %a - %a\n" + print_label l label lbl) + tbl in + if !jumptables <> [] then + begin + section oc jmptbl; + fprintf oc " .balign 4\n"; + List.iter (print_tbl oc) !jumptables; + jumptables := [] + end + + let print_optional_fun_info _ = () + + let print_comm_symb oc sz name align = + if C2C.atom_is_static name + then print_lcomm_decl oc name sz align + else print_comm_decl oc name sz align + + let print_instructions oc fn = + current_function_sig := fn.fn_sig; + List.iter (print_instruction oc) fn.fn_code + +(* Data *) + + let address = ".quad" + + let print_prologue oc = + if !Clflags.option_g then begin + section oc Section_text; + end + + let aarch64_profiling_stub oc nr_items + profiling_id_table_name + profiling_counter_table_name = + fprintf oc " adrp x2, %s\n" profiling_counter_table_name; + fprintf oc " adrp x1, %s\n" profiling_id_table_name; + fprintf oc " add x2, x2, :lo12:%s\n" profiling_counter_table_name; + fprintf oc " add x1, x1, :lo12:%s\n" profiling_id_table_name; + fprintf oc " mov w0, %d\n" nr_items; + fprintf oc " b %s\n" profiling_write_table_helper ;; + + let print_atexit oc to_be_called = + fprintf oc " adrp x0, %s\n" to_be_called; + fprintf oc " add x0, x0, :lo12:%s\n" to_be_called; + fprintf oc " b atexit\n";; + + + let print_epilogue oc = + print_profiling_epilogue elf_text_print_fun_info (Init_atexit print_atexit) aarch64_profiling_stub oc; + if !Clflags.option_g then begin + Debug.compute_gnu_file_enum (fun f -> ignore (print_file oc f)); + section oc Section_text; + end + + let default_falignment = 4 + + let cfi_startproc oc = () + let cfi_endproc oc = () + + end + +let sel_target () = + let module S = + (val (match Configuration.system with + | "linux" -> (module ELF_System : SYSTEM) + | "macos" -> (module MacOS_System : SYSTEM) + | _ -> invalid_arg ("System " ^ Configuration.system ^ " not supported")) + : SYSTEM) in + (module Target(S) : TARGET) diff --git a/aarch64/TO_MERGE/extractionMachdep.v b/aarch64/TO_MERGE/extractionMachdep.v new file mode 100644 index 00000000..947fa38b --- /dev/null +++ b/aarch64/TO_MERGE/extractionMachdep.v @@ -0,0 +1,45 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, Collège de France and INRIA Paris *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the GNU General Public License as published by *) +(* the Free Software Foundation, either version 2 of the License, or *) +(* (at your option) any later version. This file is also distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(* Additional extraction directives specific to the AArch64 port *) + +Require Archi Asm Asmgen SelectOp. + +(* Archi *) + +Extract Constant Archi.abi => + "match Configuration.abi with + | ""apple"" -> Apple + | _ -> AAPCS64". + +(* SelectOp *) + +Extract Constant SelectOp.symbol_is_relocatable => + "match Configuration.system with + | ""macos"" -> C2C.atom_is_extern + | _ -> (fun _ -> false)". + +(* Asm *) + +Extract Constant Asm.symbol_low => "fun _ _ _ -> assert false". +Extract Constant Asm.symbol_high => "fun _ _ _ -> assert false". +<<<<<<< HEAD +Extract Constant Asmblockgen.symbol_is_aligned => "C2C.atom_is_aligned". +======= + +(* Asmgen *) + +Extract Constant Asmgen.symbol_is_aligned => "C2C.atom_is_aligned". +>>>>>>> master |