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authorSylvain Boulmé <sylvain.boulme@univ-grenoble-alpes.fr>2020-06-21 08:17:08 +0200
committerSylvain Boulmé <sylvain.boulme@univ-grenoble-alpes.fr>2020-06-21 08:17:08 +0200
commitd5c95e0799e3b0541b07760178e68a1e72ee1b24 (patch)
tree3fe458373a722d5362c1ac2e0c37644598798547
parentacc68982e9beb5c26acf336312605c824691f392 (diff)
downloadcompcert-kvx-d5c95e0799e3b0541b07760178e68a1e72ee1b24.tar.gz
compcert-kvx-d5c95e0799e3b0541b07760178e68a1e72ee1b24.zip
[WIP: Coq compilation broken] Stub for Asmgen
-rw-r--r--aarch64/Asm.v530
-rw-r--r--aarch64/Asmblock.v14
-rw-r--r--aarch64/Asmblockgen.v1197
-rw-r--r--aarch64/Asmblockgenproof.v1104
-rw-r--r--aarch64/Asmblockgenproof1.v (renamed from aarch64/Asmgenproof1.v)3
-rw-r--r--aarch64/Asmgen.v1185
-rw-r--r--aarch64/Asmgenproof.v1101
-rwxr-xr-xconfigure4
8 files changed, 2370 insertions, 2768 deletions
diff --git a/aarch64/Asm.v b/aarch64/Asm.v
index 47cd3051..0959d9ca 100644
--- a/aarch64/Asm.v
+++ b/aarch64/Asm.v
@@ -10,149 +10,28 @@
(* *)
(* *********************************************************************)
-(** Abstract syntax and semantics for AArch64 assembly language *)
+(** Abstract syntax and semantics for AArch64 assembly language
+
+
+W.r.t Asmblock, this is a "flat" syntax and semantics of "Aarch64" assembly:
+ - without the basic block structure
+ - without the hierarchy of instructions.
+
+
+TODO: with respect to original file, remove parts of the syntax/semantics
+that have been already defined in Asmblock.
+
+*)
Require Import Coqlib Zbits Maps.
Require Import AST Integers Floats.
Require Import Values Memory Events Globalenvs Smallstep.
Require Import Locations Conventions.
Require Stacklayout.
+Require Import OptionMonad Asmblock.
(** * Abstract syntax *)
-(** Integer registers, floating-point registers. *)
-
-(** In assembly files, [Xn] denotes the full 64-bit register
- and [Wn] the low 32 bits of [Xn]. *)
-
-Inductive ireg: Type :=
- | X0 | X1 | X2 | X3 | X4 | X5 | X6 | X7
- | X8 | X9 | X10 | X11 | X12 | X13 | X14 | X15
- | X16 | X17 | X18 | X19 | X20 | X21 | X22 | X23
- | X24 | X25 | X26 | X27 | X28 | X29 | X30.
-
-Inductive ireg0: Type :=
- | RR0 (r: ireg) | XZR.
-
-Inductive iregsp: Type :=
- | RR1 (r: ireg) | XSP.
-
-Coercion RR0: ireg >-> ireg0.
-Coercion RR1: ireg >-> iregsp.
-
-Lemma ireg_eq: forall (x y: ireg), {x=y} + {x<>y}.
-Proof. decide equality. Defined.
-
-(** In assembly files, [Dn] denotes the low 64-bit of a vector register,
- and [Sn] the low 32 bits. *)
-
-Inductive freg: Type :=
- | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7
- | D8 | D9 | D10 | D11 | D12 | D13 | D14 | D15
- | D16 | D17 | D18 | D19 | D20 | D21 | D22 | D23
- | D24 | D25 | D26 | D27 | D28 | D29 | D30 | D31.
-
-Lemma freg_eq: forall (x y: freg), {x=y} + {x<>y}.
-Proof. decide equality. Defined.
-
-(** Bits in the condition register. *)
-
-Inductive crbit: Type :=
- | CN: crbit (**r negative *)
- | CZ: crbit (**r zero *)
- | CC: crbit (**r carry *)
- | CV: crbit. (**r overflow *)
-
-Lemma crbit_eq: forall (x y: crbit), {x=y} + {x<>y}.
-Proof. decide equality. Defined.
-
-(** We model the following registers of the ARM architecture. *)
-
-Inductive preg: Type :=
- | IR: ireg -> preg (**r 64- or 32-bit integer registers *)
- | FR: freg -> preg (**r double- or single-precision float registers *)
- | CR: crbit -> preg (**r bits in the condition register *)
- | SP: preg (**r register X31 used as stack pointer *)
- | PC: preg. (**r program counter *)
-
-Coercion IR: ireg >-> preg.
-Coercion FR: freg >-> preg.
-Coercion CR: crbit >-> preg.
-
-Lemma preg_eq: forall (x y: preg), {x=y} + {x<>y}.
-Proof. decide equality. apply ireg_eq. apply freg_eq. apply crbit_eq. Defined.
-
-Module PregEq.
- Definition t := preg.
- Definition eq := preg_eq.
-End PregEq.
-
-Module Pregmap := EMap(PregEq).
-
-Definition preg_of_iregsp (r: iregsp) : preg :=
- match r with RR1 r => IR r | XSP => SP end.
-
-Coercion preg_of_iregsp: iregsp >-> preg.
-
-(** Conventional name for return address ([RA]) *)
-
-Notation "'RA'" := X30 (only parsing) : asm.
-
-(** The instruction set. Most instructions correspond exactly to
- actual AArch64 instructions. See the ARM reference manuals for more
- details. Some instructions, described below, are
- pseudo-instructions: they expand to canned instruction sequences
- during the printing of the assembly code. *)
-
-Definition label := positive.
-
-Inductive isize: Type :=
- | W (**r 32-bit integer operation *)
- | X. (**r 64-bit integer operation *)
-
-Inductive fsize: Type :=
- | S (**r 32-bit, single-precision FP operation *)
- | D. (**r 64-bit, double-precision FP operation *)
-
-Inductive testcond : Type :=
- | TCeq: testcond (**r equal *)
- | TCne: testcond (**r not equal *)
- | TChs: testcond (**r unsigned higher or same *)
- | TClo: testcond (**r unsigned lower *)
- | TCmi: testcond (**r negative *)
- | TCpl: testcond (**r positive *)
- | TChi: testcond (**r unsigned higher *)
- | TCls: testcond (**r unsigned lower or same *)
- | TCge: testcond (**r signed greater or equal *)
- | TClt: testcond (**r signed less than *)
- | TCgt: testcond (**r signed greater *)
- | TCle: testcond. (**r signed less than or equal *)
-
-Inductive addressing: Type :=
- | ADimm (base: iregsp) (n: int64) (**r base plus immediate offset *)
- | ADreg (base: iregsp) (r: ireg) (**r base plus reg *)
- | ADlsl (base: iregsp) (r: ireg) (n: int) (**r base plus reg LSL n *)
- | ADsxt (base: iregsp) (r: ireg) (n: int) (**r base plus SIGN-EXT(reg) LSL n *)
- | ADuxt (base: iregsp) (r: ireg) (n: int) (**r base plus ZERO-EXT(reg) LSL n *)
- | ADadr (base: iregsp) (id: ident) (ofs: ptrofs) (**r base plus low address of [id + ofs] *)
- | ADpostincr (base: iregsp) (n: int64). (**r base plus offset; base is updated after *)
-
-Inductive shift_op: Type :=
- | SOnone
- | SOlsl (n: int)
- | SOlsr (n: int)
- | SOasr (n: int)
- | SOror (n: int).
-
-Inductive extend_op: Type :=
- | EOsxtb (n: int)
- | EOsxth (n: int)
- | EOsxtw (n: int)
- | EOuxtb (n: int)
- | EOuxth (n: int)
- | EOuxtw (n: int)
- | EOuxtx (n: int).
-
Inductive instruction: Type :=
(** Branches *)
| Pb (lbl: label) (**r branch *)
@@ -307,65 +186,8 @@ Definition code := list instruction.
Record function : Type := mkfunction { fn_sig: signature; fn_code: code }.
Definition fundef := AST.fundef function.
Definition program := AST.program fundef unit.
-
-(** * Operational semantics *)
-
-(** The semantics operates over a single mapping from registers
- (type [preg]) to values. We maintain (but do not enforce)
- the convention that integer registers are mapped to values of
- type [Tint], float registers to values of type [Tfloat],
- and condition bits to either [Vzero] or [Vone]. *)
-
-Definition regset := Pregmap.t val.
Definition genv := Genv.t fundef unit.
-(** The value of an [ireg0] is either the value of the integer register,
- or 0. *)
-
-Definition ir0w (rs: regset) (r: ireg0) : val :=
- match r with RR0 r => rs (IR r) | XZR => Vint Int.zero end.
-Definition ir0x (rs: regset) (r: ireg0) : val :=
- match r with RR0 r => rs (IR r) | XZR => Vlong Int64.zero end.
-
-(** Concise notations for accessing and updating the values of registers. *)
-
-Notation "a # b" := (a b) (at level 1, only parsing) : asm.
-Notation "a # b <- c" := (Pregmap.set b c a) (at level 1, b at next level) : asm.
-Notation "a ## b" := (ir0w a b) (at level 1, only parsing) : asm.
-Notation "a ### b" := (ir0x a b) (at level 1, only parsing) : asm.
-
-Open Scope asm.
-
-(** Undefining some registers *)
-
-Fixpoint undef_regs (l: list preg) (rs: regset) : regset :=
- match l with
- | nil => rs
- | r :: l' => undef_regs l' (rs#r <- Vundef)
- end.
-
-(** Undefining the condition codes *)
-
-Definition undef_flags (rs: regset) : regset :=
- fun r => match r with CR _ => Vundef | _ => rs r end.
-
-(** Assigning a register pair *)
-
-Definition set_pair (p: rpair preg) (v: val) (rs: regset) : regset :=
- match p with
- | One r => rs#r <- v
- | Twolong rhi rlo => rs#rhi <- (Val.hiword v) #rlo <- (Val.loword v)
- end.
-
-(** Assigning the result of a builtin *)
-
-Fixpoint set_res (res: builtin_res preg) (v: val) (rs: regset) : regset :=
- match res with
- | BR r => rs#r <- v
- | BR_none => rs
- | BR_splitlong hi lo => set_res lo (Val.loword v) (set_res hi (Val.hiword v) rs)
- end.
-
(** The two functions below axiomatize how the linker processes
symbolic references [symbol + offset]. It computes the
difference between the address and the PC, and splits it into:
@@ -385,6 +207,8 @@ Axiom symbol_high_low:
forall (ge: genv) (id: ident) (ofs: ptrofs),
Val.addl (symbol_high ge id ofs) (symbol_low ge id ofs) = Genv.symbol_address ge id ofs.
+(** * Operational semantics *)
+
Section RELSEM.
Variable ge: genv.
@@ -419,19 +243,6 @@ Fixpoint label_pos (lbl: label) (pos: Z) (c: code) {struct c} : option Z :=
if is_label lbl instr then Some (pos + 1) else label_pos lbl (pos + 1) c'
end.
-(** The semantics is purely small-step and defined as a function
- from the current state (a register set + a memory state)
- to either [Next rs' m'] where [rs'] and [m'] are the updated register
- set and memory state after execution of the instruction at [rs#PC],
- or [Stuck] if the processor is stuck. *)
-
-Inductive outcome: Type :=
- | Next: regset -> mem -> outcome
- | Stuck: outcome.
-
-(** Manipulations over the [PC] register: continuing with the next
- instruction ([nextinstr]) or branching to a label ([goto_label]). *)
-
Definition nextinstr (rs: regset) :=
rs#PC <- (Val.offset_ptr rs#PC Ptrofs.one).
@@ -445,88 +256,6 @@ Definition goto_label (f: function) (lbl: label) (rs: regset) (m: mem) :=
end
end.
-(** Testing a condition *)
-
-Definition eval_testcond (c: testcond) (rs: regset) : option bool :=
- match c with
- | TCeq => (**r equal *)
- match rs#CZ with
- | Vint n => Some (Int.eq n Int.one)
- | _ => None
- end
- | TCne => (**r not equal *)
- match rs#CZ with
- | Vint n => Some (Int.eq n Int.zero)
- | _ => None
- end
- | TClo => (**r unsigned less than *)
- match rs#CC with
- | Vint n => Some (Int.eq n Int.zero)
- | _ => None
- end
- | TCls => (**r unsigned less or equal *)
- match rs#CC, rs#CZ with
- | Vint c, Vint z => Some (Int.eq c Int.zero || Int.eq z Int.one)
- | _, _ => None
- end
- | TChs => (**r unsigned greater or equal *)
- match rs#CC with
- | Vint n => Some (Int.eq n Int.one)
- | _ => None
- end
- | TChi => (**r unsigned greater *)
- match rs#CC, rs#CZ with
- | Vint c, Vint z => Some (Int.eq c Int.one && Int.eq z Int.zero)
- | _, _ => None
- end
- | TClt => (**r signed less than *)
- match rs#CV, rs#CN with
- | Vint o, Vint s => Some (Int.eq (Int.xor o s) Int.one)
- | _, _ => None
- end
- | TCle => (**r signed less or equal *)
- match rs#CV, rs#CN, rs#CZ with
- | Vint o, Vint s, Vint z => Some (Int.eq (Int.xor o s) Int.one || Int.eq z Int.one)
- | _, _, _ => None
- end
- | TCge => (**r signed greater or equal *)
- match rs#CV, rs#CN with
- | Vint o, Vint s => Some (Int.eq (Int.xor o s) Int.zero)
- | _, _ => None
- end
- | TCgt => (**r signed greater *)
- match rs#CV, rs#CN, rs#CZ with
- | Vint o, Vint s, Vint z => Some (Int.eq (Int.xor o s) Int.zero && Int.eq z Int.zero)
- | _, _, _ => None
- end
- | TCpl => (**r positive *)
- match rs#CN with
- | Vint n => Some (Int.eq n Int.zero)
- | _ => None
- end
- | TCmi => (**r negative *)
- match rs#CN with
- | Vint n => Some (Int.eq n Int.one)
- | _ => None
- end
- end.
-
-(** Integer "is zero?" test *)
-
-Definition eval_testzero (sz: isize) (v: val) (m: mem): option bool :=
- match sz with
- | W => Val.cmpu_bool (Mem.valid_pointer m) Ceq v (Vint Int.zero)
- | X => Val.cmplu_bool (Mem.valid_pointer m) Ceq v (Vlong Int64.zero)
- end.
-
-(** Integer "bit is set?" test *)
-
-Definition eval_testbit (sz: isize) (v: val) (n: int): option bool :=
- match sz with
- | W => Val.cmp_bool Cne (Val.and v (Vint (Int.shl Int.one n))) (Vint Int.zero)
- | X => Val.cmpl_bool Cne (Val.andl v (Vlong (Int64.shl' Int64.one n))) (Vlong Int64.zero)
- end.
-
(** Evaluating an addressing mode *)
Definition eval_addressing (a: addressing) (rs: regset): val :=
@@ -557,130 +286,6 @@ Definition exec_store (chunk: memory_chunk)
| Some m' => Next (nextinstr rs) m'
end.
-(** Comparisons *)
-
-Definition compare_int (rs: regset) (v1 v2: val) (m: mem) :=
- rs#CN <- (Val.negative (Val.sub v1 v2))
- #CZ <- (Val.cmpu (Mem.valid_pointer m) Ceq v1 v2)
- #CC <- (Val.cmpu (Mem.valid_pointer m) Cge v1 v2)
- #CV <- (Val.sub_overflow v1 v2).
-
-Definition compare_long (rs: regset) (v1 v2: val) (m: mem) :=
- rs#CN <- (Val.negativel (Val.subl v1 v2))
- #CZ <- (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Ceq v1 v2))
- #CC <- (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Cge v1 v2))
- #CV <- (Val.subl_overflow v1 v2).
-
-(** Semantics of [fcmp] instructions:
-<<
-== N=0 Z=1 C=1 V=0
-< N=1 Z=0 C=0 V=0
-> N=0 Z=0 C=1 V=0
-unord N=0 Z=0 C=1 V=1
->>
-*)
-
-Definition compare_float (rs: regset) (v1 v2: val) :=
- match v1, v2 with
- | Vfloat f1, Vfloat f2 =>
- rs#CN <- (Val.of_bool (Float.cmp Clt f1 f2))
- #CZ <- (Val.of_bool (Float.cmp Ceq f1 f2))
- #CC <- (Val.of_bool (negb (Float.cmp Clt f1 f2)))
- #CV <- (Val.of_bool (negb (Float.ordered f1 f2)))
- | _, _ =>
- rs#CN <- Vundef
- #CZ <- Vundef
- #CC <- Vundef
- #CV <- Vundef
- end.
-
-Definition compare_single (rs: regset) (v1 v2: val) :=
- match v1, v2 with
- | Vsingle f1, Vsingle f2 =>
- rs#CN <- (Val.of_bool (Float32.cmp Clt f1 f2))
- #CZ <- (Val.of_bool (Float32.cmp Ceq f1 f2))
- #CC <- (Val.of_bool (negb (Float32.cmp Clt f1 f2)))
- #CV <- (Val.of_bool (negb (Float32.ordered f1 f2)))
- | _, _ =>
- rs#CN <- Vundef
- #CZ <- Vundef
- #CC <- Vundef
- #CV <- Vundef
- end.
-
-(** Insertion of bits into an integer *)
-
-Definition insert_in_int (x: val) (y: Z) (pos: Z) (len: Z) : val :=
- match x with
- | Vint n => Vint (Int.repr (Zinsert (Int.unsigned n) y pos len))
- | _ => Vundef
- end.
-
-Definition insert_in_long (x: val) (y: Z) (pos: Z) (len: Z) : val :=
- match x with
- | Vlong n => Vlong (Int64.repr (Zinsert (Int64.unsigned n) y pos len))
- | _ => Vundef
- end.
-
-(** Evaluation of shifted operands *)
-
-Definition eval_shift_op_int (v: val) (s: shift_op): val :=
- match s with
- | SOnone => v
- | SOlsl n => Val.shl v (Vint n)
- | SOlsr n => Val.shru v (Vint n)
- | SOasr n => Val.shr v (Vint n)
- | SOror n => Val.ror v (Vint n)
- end.
-
-Definition eval_shift_op_long (v: val) (s: shift_op): val :=
- match s with
- | SOnone => v
- | SOlsl n => Val.shll v (Vint n)
- | SOlsr n => Val.shrlu v (Vint n)
- | SOasr n => Val.shrl v (Vint n)
- | SOror n => Val.rorl v (Vint n)
- end.
-
-(** Evaluation of sign- or zero- extended operands *)
-
-Definition eval_extend (v: val) (x: extend_op): val :=
- match x with
- | EOsxtb n => Val.shll (Val.longofint (Val.sign_ext 8 v)) (Vint n)
- | EOsxth n => Val.shll (Val.longofint (Val.sign_ext 16 v)) (Vint n)
- | EOsxtw n => Val.shll (Val.longofint v) (Vint n)
- | EOuxtb n => Val.shll (Val.longofintu (Val.zero_ext 8 v)) (Vint n)
- | EOuxth n => Val.shll (Val.longofintu (Val.zero_ext 16 v)) (Vint n)
- | EOuxtw n => Val.shll (Val.longofintu v) (Vint n)
- | EOuxtx n => Val.shll v (Vint n)
- end.
-
-(** Bit-level conversion from integers to FP numbers *)
-
-Definition float32_of_bits (v: val): val :=
- match v with
- | Vint n => Vsingle (Float32.of_bits n)
- | _ => Vundef
- end.
-
-Definition float64_of_bits (v: val): val :=
- match v with
- | Vlong n => Vfloat (Float.of_bits n)
- | _ => Vundef
- end.
-
-(** Execution of a single instruction [i] in initial state
- [rs] and [m]. Return updated state. For instructions
- that correspond to actual AArch64 instructions, the cases are
- straightforward transliterations of the informal descriptions
- given in the ARMv8 reference manuals. For pseudo-instructions,
- refer to the informal descriptions given above.
-
- Note that we set to [Vundef] the registers used as temporaries by
- the expansions of the pseudo-instructions, so that the code we
- generate cannot use those registers to hold values that must
- survive the execution of the pseudo-instruction.
-*)
Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : outcome :=
match i with
@@ -704,13 +309,13 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
| Pret r =>
Next (rs#PC <- (rs#r)) m
| Pcbnz sz r lbl =>
- match eval_testzero sz rs#r m with
+ match eval_testzero sz rs#r with
| Some true => Next (nextinstr rs) m
| Some false => goto_label f lbl rs m
| None => Stuck
end
| Pcbz sz r lbl =>
- match eval_testzero sz rs#r m with
+ match eval_testzero sz rs#r with
| Some true => goto_label f lbl rs m
| Some false => Next (nextinstr rs) m
| None => Stuck
@@ -778,13 +383,13 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
| Psubimm X rd r1 n =>
Next (nextinstr (rs#rd <- (Val.subl rs#r1 (Vlong (Int64.repr n))))) m
| Pcmpimm W r1 n =>
- Next (nextinstr (compare_int rs rs#r1 (Vint (Int.repr n)) m)) m
+ Next (nextinstr (compare_int rs rs#r1 (Vint (Int.repr n)))) m
| Pcmpimm X r1 n =>
- Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.repr n)) m)) m
+ Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.repr n)))) m
| Pcmnimm W r1 n =>
- Next (nextinstr (compare_int rs rs#r1 (Vint (Int.neg (Int.repr n))) m)) m
+ Next (nextinstr (compare_int rs rs#r1 (Vint (Int.neg (Int.repr n))))) m
| Pcmnimm X r1 n =>
- Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.neg (Int64.repr n))) m)) m
+ Next (nextinstr (compare_long rs rs#r1 (Vlong (Int64.neg (Int64.repr n))))) m
(** Move integer register *)
| Pmov rd r1 =>
Next (nextinstr (rs#rd <- (rs#r1))) m
@@ -802,9 +407,9 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
| Porrimm X rd r1 n =>
Next (nextinstr (rs#rd <- (Val.orl rs###r1 (Vlong (Int64.repr n))))) m
| Ptstimm W r1 n =>
- Next (nextinstr (compare_int rs (Val.and rs#r1 (Vint (Int.repr n))) (Vint Int.zero) m)) m
+ Next (nextinstr (compare_int rs (Val.and rs#r1 (Vint (Int.repr n))) (Vint Int.zero))) m
| Ptstimm X r1 n =>
- Next (nextinstr (compare_long rs (Val.andl rs#r1 (Vlong (Int64.repr n))) (Vlong Int64.zero) m)) m
+ Next (nextinstr (compare_long rs (Val.andl rs#r1 (Vlong (Int64.repr n))) (Vlong Int64.zero))) m
(** Move wide immediate *)
| Pmovz W rd n pos =>
Next (nextinstr (rs#rd <- (Vint (Int.repr (Z.shiftl n pos))))) m
@@ -850,22 +455,22 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
| Psub X rd r1 r2 s =>
Next (nextinstr (rs#rd <- (Val.subl rs###r1 (eval_shift_op_long rs#r2 s)))) m
| Pcmp W r1 r2 s =>
- Next (nextinstr (compare_int rs rs##r1 (eval_shift_op_int rs#r2 s) m)) m
+ Next (nextinstr (compare_int rs rs##r1 (eval_shift_op_int rs#r2 s))) m
| Pcmp X r1 r2 s =>
- Next (nextinstr (compare_long rs rs###r1 (eval_shift_op_long rs#r2 s) m)) m
+ Next (nextinstr (compare_long rs rs###r1 (eval_shift_op_long rs#r2 s))) m
| Pcmn W r1 r2 s =>
- Next (nextinstr (compare_int rs rs##r1 (Val.neg (eval_shift_op_int rs#r2 s)) m)) m
+ Next (nextinstr (compare_int rs rs##r1 (Val.neg (eval_shift_op_int rs#r2 s)))) m
| Pcmn X r1 r2 s =>
- Next (nextinstr (compare_long rs rs###r1 (Val.negl (eval_shift_op_long rs#r2 s)) m)) m
+ Next (nextinstr (compare_long rs rs###r1 (Val.negl (eval_shift_op_long rs#r2 s)))) m
(** Integer arithmetic, extending register *)
| Paddext rd r1 r2 x =>
Next (nextinstr (rs#rd <- (Val.addl rs#r1 (eval_extend rs#r2 x)))) m
| Psubext rd r1 r2 x =>
Next (nextinstr (rs#rd <- (Val.subl rs#r1 (eval_extend rs#r2 x)))) m
| Pcmpext r1 r2 x =>
- Next (nextinstr (compare_long rs rs#r1 (eval_extend rs#r2 x) m)) m
+ Next (nextinstr (compare_long rs rs#r1 (eval_extend rs#r2 x))) m
| Pcmnext r1 r2 x =>
- Next (nextinstr (compare_long rs rs#r1 (Val.negl (eval_extend rs#r2 x)) m)) m
+ Next (nextinstr (compare_long rs rs#r1 (Val.negl (eval_extend rs#r2 x)))) m
(** Logical, shifted register *)
| Pand W rd r1 r2 s =>
Next (nextinstr (rs#rd <- (Val.and rs##r1 (eval_shift_op_int rs#r2 s)))) m
@@ -892,9 +497,9 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
| Porn X rd r1 r2 s =>
Next (nextinstr (rs#rd <- (Val.orl rs###r1 (Val.notl (eval_shift_op_long rs#r2 s))))) m
| Ptst W r1 r2 s =>
- Next (nextinstr (compare_int rs (Val.and rs##r1 (eval_shift_op_int rs#r2 s)) (Vint Int.zero) m)) m
+ Next (nextinstr (compare_int rs (Val.and rs##r1 (eval_shift_op_int rs#r2 s)) (Vint Int.zero))) m
| Ptst X r1 r2 s =>
- Next (nextinstr (compare_long rs (Val.andl rs###r1 (eval_shift_op_long rs#r2 s)) (Vlong Int64.zero) m)) m
+ Next (nextinstr (compare_long rs (Val.andl rs###r1 (eval_shift_op_long rs#r2 s)) (Vlong Int64.zero))) m
(** Variable shifts *)
| Pasrv W rd r1 r2 =>
Next (nextinstr (rs#rd <- (Val.shr rs#r1 rs#r2))) m
@@ -1118,80 +723,9 @@ Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : out
Stuck
end.
-(** Translation of the LTL/Linear/Mach view of machine registers
- to the AArch64 view. Note that no LTL register maps to [X16],
- [X18], nor [X30].
- [X18] is reserved as the platform register and never used by the
- code generated by CompCert.
- [X30] is used for the return address, and can also be used as temporary.
- [X16] can be used as temporary. *)
-
-Definition preg_of (r: mreg) : preg :=
- match r with
- | R0 => X0 | R1 => X1 | R2 => X2 | R3 => X3
- | R4 => X4 | R5 => X5 | R6 => X6 | R7 => X7
- | R8 => X8 | R9 => X9 | R10 => X10 | R11 => X11
- | R12 => X12 | R13 => X13 | R14 => X14 | R15 => X15
- | R17 => X17 | R19 => X19
- | R20 => X20 | R21 => X21 | R22 => X22 | R23 => X23
- | R24 => X24 | R25 => X25 | R26 => X26 | R27 => X27
- | R28 => X28 | R29 => X29
- | F0 => D0 | F1 => D1 | F2 => D2 | F3 => D3
- | F4 => D4 | F5 => D5 | F6 => D6 | F7 => D7
- | F8 => D8 | F9 => D9 | F10 => D10 | F11 => D11
- | F12 => D12 | F13 => D13 | F14 => D14 | F15 => D15
- | F16 => D16 | F17 => D17 | F18 => D18 | F19 => D19
- | F20 => D20 | F21 => D21 | F22 => D22 | F23 => D23
- | F24 => D24 | F25 => D25 | F26 => D26 | F27 => D27
- | F28 => D28 | F29 => D29 | F30 => D30 | F31 => D31
- end.
-
-(** Undefine all registers except SP and callee-save registers *)
-
-Definition undef_caller_save_regs (rs: regset) : regset :=
- fun r =>
- if preg_eq r SP
- || In_dec preg_eq r (List.map preg_of (List.filter is_callee_save all_mregs))
- then rs r
- else Vundef.
-
-(** Extract the values of the arguments of an external call.
- We exploit the calling conventions from module [Conventions], except that
- we use AArch64 registers instead of locations. *)
-
-Inductive extcall_arg (rs: regset) (m: mem): loc -> val -> Prop :=
- | extcall_arg_reg: forall r,
- extcall_arg rs m (R r) (rs (preg_of r))
- | extcall_arg_stack: forall ofs ty bofs v,
- bofs = Stacklayout.fe_ofs_arg + 4 * ofs ->
- Mem.loadv (chunk_of_type ty) m
- (Val.offset_ptr rs#SP (Ptrofs.repr bofs)) = Some v ->
- extcall_arg rs m (Locations.S Outgoing ofs ty) v.
-
-Inductive extcall_arg_pair (rs: regset) (m: mem): rpair loc -> val -> Prop :=
- | extcall_arg_one: forall l v,
- extcall_arg rs m l v ->
- extcall_arg_pair rs m (One l) v
- | extcall_arg_twolong: forall hi lo vhi vlo,
- extcall_arg rs m hi vhi ->
- extcall_arg rs m lo vlo ->
- extcall_arg_pair rs m (Twolong hi lo) (Val.longofwords vhi vlo).
-
-Definition extcall_arguments
- (rs: regset) (m: mem) (sg: signature) (args: list val) : Prop :=
- list_forall2 (extcall_arg_pair rs m) (loc_arguments sg) args.
-
-Definition loc_external_result (sg: signature) : rpair preg :=
- map_rpair preg_of (loc_result sg).
-
-(** Execution of the instruction at [rs#PC]. *)
-
-Inductive state: Type :=
- | State: regset -> mem -> state.
-
Inductive step: state -> trace -> state -> Prop :=
| exec_step_internal:
- forall b ofs f i rs m rs' m',
+ forall b ofs (f:function) i rs m rs' m',
rs PC = Vptr b ofs ->
Genv.find_funct_ptr ge b = Some (Internal f) ->
find_instr (Ptrofs.unsigned ofs) f.(fn_code) = Some i ->
diff --git a/aarch64/Asmblock.v b/aarch64/Asmblock.v
index 71c0dba3..d52f3c24 100644
--- a/aarch64/Asmblock.v
+++ b/aarch64/Asmblock.v
@@ -475,11 +475,6 @@ Inductive instruction: Type :=
| Pcfi_adjust (ofs: int) (**r .cfi_adjust debug directive *)
| Pcfi_rel_offset (ofs: int) (**r .cfi_rel_offset debug directive *)
.
-
-Definition code := list instruction.
-Record function : Type := mkfunction { fn_sig: signature; fn_code: code }.
-Definition fundef := AST.fundef function.
-Definition program := AST.program fundef unit.
*)
@@ -541,6 +536,15 @@ Fixpoint set_res (res: builtin_res preg) (v: val) (rs: regset) : regset :=
| BR_splitlong hi lo => set_res lo (Val.loword v) (set_res hi (Val.hiword v) rs)
end.
+
+(** FIXME: not clear howto deal with these axioms in Asmblock.
+ The dependency over genv will get us in troubles...
+
+TODO: The solution is probably to put [symbol_low] and [symbol_high] [symbol_high_low] with any dependency on "ge"
+as an hypothesis in RELSEM section.
+
+*)
+
(** The two functions below axiomatize how the linker processes
symbolic references [symbol + offset]. It computes the
difference between the address and the PC, and splits it into:
diff --git a/aarch64/Asmblockgen.v b/aarch64/Asmblockgen.v
new file mode 100644
index 00000000..83f2b96b
--- /dev/null
+++ b/aarch64/Asmblockgen.v
@@ -0,0 +1,1197 @@
+(* *************************************************************)
+(* *)
+(* 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 *)
+(* *)
+(* Copyright Kalray. Copyright VERIMAG. All rights reserved. *)
+(* This file is distributed under the terms of the INRIA *)
+(* Non-Commercial License Agreement. *)
+(* *)
+(* *************************************************************)
+
+(** * Translation from Machblock to AArch64 assembly block language (Asmblock)
+ Inspired from the Mach->Asm pass of original Leroy's backend, but adapted to the block structure like the KVX backend. *)
+
+Require Import Recdef Coqlib Zwf Zbits.
+Require Import Errors AST Integers Floats Op.
+Require Import Locations Machblock Asmblock.
+
+(* STUB *)
+Definition transf_function (f: Machblock.function) : res Asmblock.function :=
+ Error (msg "Asmblockgen not yet implmented").
+
+Definition transf_fundef (f: Machblock.fundef) : res Asmblock.fundef :=
+ transf_partial_fundef transf_function f.
+
+Definition transf_program (p: Machblock.program) : res Asmblock.program :=
+ transform_partial_program transf_fundef p.
+
+(* ORIGINAL aarch64/Asmgen file that needs to be adapted
+
+(* *********************************************************************)
+(* *)
+(* The Compcert verified compiler *)
+(* *)
+(* Xavier Leroy, Collège de France and INRIA Paris *)
+(* *)
+(* Copyright Institut National de Recherche en Informatique et en *)
+(* Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the INRIA Non-Commercial License Agreement. *)
+(* *)
+(* *********************************************************************)
+
+(** Translation from Mach to AArch64. *)
+
+Require Import Recdef Coqlib Zwf Zbits.
+Require Import Errors AST Integers Floats Op.
+Require Import Locations Mach Asm.
+
+Local Open Scope string_scope.
+Local Open Scope list_scope.
+Local Open Scope error_monad_scope.
+
+(** 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).
+
+(** Arithmetic immediates are 12-bit unsigned numbers, possibly shifted left 12 bits *)
+
+Definition is_arith_imm32 (x: int) : bool :=
+ Int.eq x (Int.zero_ext 12 x)
+ || Int.eq x (Int.shl (Int.zero_ext 12 (Int.shru x (Int.repr 12))) (Int.repr 12)).
+
+Definition is_arith_imm64 (x: int64) : bool :=
+ Int64.eq x (Int64.zero_ext 12 x)
+ || Int64.eq x (Int64.shl (Int64.zero_ext 12 (Int64.shru x (Int64.repr 12))) (Int64.repr 12)).
+
+(** Decompose integer literals into 16-bit fragments *)
+
+Fixpoint decompose_int (N: nat) (n p: Z) {struct N} : list (Z * Z) :=
+ match N with
+ | Datatypes.O => nil
+ | Datatypes.S N =>
+ let frag := Zzero_ext 16 (Z.shiftr n p) in
+ if Z.eqb frag 0 then
+ decompose_int N n (p + 16)
+ else
+ (frag, p) :: decompose_int N (Z.ldiff n (Z.shiftl 65535 p)) (p + 16)
+ end.
+
+Definition negate_decomposition (l: list (Z * Z)) :=
+ List.map (fun np => (Z.lxor (fst np) 65535, snd np)) l.
+
+Definition loadimm_k (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
+ List.fold_right (fun np k => Pmovk sz rd (fst np) (snd np) :: k) k l.
+
+Definition loadimm_z (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
+ match l with
+ | nil => Pmovz sz rd 0 0 :: k
+ | (n1, p1) :: l => Pmovz sz rd n1 p1 :: loadimm_k sz rd l k
+ end.
+
+Definition loadimm_n (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
+ match l with
+ | nil => Pmovn sz rd 0 0 :: k
+ | (n1, p1) :: l => Pmovn sz rd n1 p1 :: loadimm_k sz rd (negate_decomposition l) k
+ end.
+
+Definition loadimm (sz: isize) (rd: ireg) (n: Z) (k: code) : code :=
+ let N := match sz with W => 2%nat | X => 4%nat end in
+ let dz := decompose_int N n 0 in
+ let dn := decompose_int N (Z.lnot n) 0 in
+ if Nat.leb (List.length dz) (List.length dn)
+ then loadimm_z sz rd dz k
+ else loadimm_n sz rd dn k.
+
+Definition loadimm32 (rd: ireg) (n: int) (k: code) : code :=
+ if is_logical_imm32 n
+ then Porrimm W rd XZR (Int.unsigned n) :: k
+ else loadimm W rd (Int.unsigned n) k.
+
+Definition loadimm64 (rd: ireg) (n: int64) (k: code) : code :=
+ if is_logical_imm64 n
+ then Porrimm X rd XZR (Int64.unsigned n) :: k
+ else loadimm X rd (Int64.unsigned n) k.
+
+(** Add immediate *)
+
+Definition addimm_aux (insn: iregsp -> iregsp -> Z -> instruction)
+ (rd r1: iregsp) (n: Z) (k: code) :=
+ let nlo := Zzero_ext 12 n in
+ let nhi := n - nlo in
+ if Z.eqb nhi 0 then
+ insn rd r1 nlo :: k
+ else if Z.eqb nlo 0 then
+ insn rd r1 nhi :: k
+ else
+ insn rd r1 nhi :: insn rd rd nlo :: k.
+
+Definition addimm32 (rd r1: ireg) (n: int) (k: code) : code :=
+ let m := Int.neg n in
+ if Int.eq n (Int.zero_ext 24 n) then
+ addimm_aux (Paddimm W) rd r1 (Int.unsigned n) k
+ else if Int.eq m (Int.zero_ext 24 m) then
+ addimm_aux (Psubimm W) rd r1 (Int.unsigned m) k
+ else if Int.lt n Int.zero then
+ loadimm32 X16 m (Psub W rd r1 X16 SOnone :: k)
+ else
+ loadimm32 X16 n (Padd W rd r1 X16 SOnone :: k).
+
+Definition addimm64 (rd r1: iregsp) (n: int64) (k: code) : code :=
+ let m := Int64.neg n in
+ if Int64.eq n (Int64.zero_ext 24 n) then
+ addimm_aux (Paddimm X) rd r1 (Int64.unsigned n) k
+ else if Int64.eq m (Int64.zero_ext 24 m) then
+ addimm_aux (Psubimm X) rd r1 (Int64.unsigned m) k
+ else if Int64.lt n Int64.zero then
+ loadimm64 X16 m (Psubext rd r1 X16 (EOuxtx Int.zero) :: k)
+ else
+ loadimm64 X16 n (Paddext rd r1 X16 (EOuxtx Int.zero) :: k).
+
+(** Logical immediate *)
+
+Definition logicalimm32
+ (insn1: ireg -> ireg0 -> Z -> instruction)
+ (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction)
+ (rd r1: ireg) (n: int) (k: code) : code :=
+ if is_logical_imm32 n
+ then insn1 rd r1 (Int.unsigned n) :: k
+ else loadimm32 X16 n (insn2 rd r1 X16 SOnone :: k).
+
+Definition logicalimm64
+ (insn1: ireg -> ireg0 -> Z -> instruction)
+ (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction)
+ (rd r1: ireg) (n: int64) (k: code) : code :=
+ if is_logical_imm64 n
+ then insn1 rd r1 (Int64.unsigned n) :: k
+ else loadimm64 X16 n (insn2 rd r1 X16 SOnone :: k).
+
+(** Sign- or zero-extended arithmetic *)
+
+Definition transl_extension (ex: extension) (a: int) : extend_op :=
+ match ex with Xsgn32 => EOsxtw a | Xuns32 => EOuxtw a end.
+
+Definition move_extended_base
+ (rd: ireg) (r1: ireg) (ex: extension) (k: code) : code :=
+ match ex with
+ | Xsgn32 => Pcvtsw2x rd r1 :: k
+ | Xuns32 => Pcvtuw2x rd r1 :: k
+ end.
+
+Definition move_extended
+ (rd: ireg) (r1: ireg) (ex: extension) (a: int) (k: code) : code :=
+ if Int.eq a Int.zero then
+ move_extended_base rd r1 ex k
+ else
+ move_extended_base rd r1 ex (Padd X rd XZR rd (SOlsl a) :: k).
+
+Definition arith_extended
+ (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction)
+ (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction)
+ (rd r1 r2: ireg) (ex: extension) (a: int) (k: code) : code :=
+ if Int.ltu a (Int.repr 5) then
+ insnX rd r1 r2 (transl_extension ex a) :: k
+ else
+ move_extended_base X16 r2 ex (insnS rd r1 X16 (SOlsl a) :: k).
+
+(** Extended right shift *)
+
+Definition shrx32 (rd r1: ireg) (n: int) (k: code) : code :=
+ if Int.eq n Int.zero then
+ Pmov rd r1 :: k
+ else if Int.eq n Int.one then
+ Padd W X16 r1 r1 (SOlsr (Int.repr 31)) ::
+ Porr W rd XZR X16 (SOasr n) :: 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 if Int.eq n Int.one then
+ Padd X X16 r1 r1 (SOlsr (Int.repr 63)) ::
+ Porr X rd XZR X16 (SOasr n) :: k
+ else
+ Porr X X16 XZR r1 (SOasr (Int.repr 63)) ::
+ Padd X X16 r1 X16 (SOlsr (Int.sub Int64.iwordsize' n)) ::
+ Porr X rd XZR X16 (SOasr n) :: k.
+
+(** Load the address [id + ofs] in [rd] *)
+
+Definition loadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (k: code) : code :=
+ if Archi.pic_code tt then
+ if Ptrofs.eq ofs Ptrofs.zero then
+ Ploadsymbol rd id :: k
+ else
+ Ploadsymbol rd id :: addimm64 rd rd (Ptrofs.to_int64 ofs) k
+ else
+ Padrp rd id ofs :: Paddadr rd rd id ofs :: k.
+
+(** Translate a shifted operand *)
+
+Definition transl_shift (s: Op.shift) (a: int): Asm.shift_op :=
+ match s with
+ | Slsl => SOlsl a
+ | Slsr => SOlsr a
+ | Sasr => SOasr a
+ | Sror => SOror a
+ end.
+
+(** Translation of a condition. Prepends to [k] the instructions
+ that evaluate the condition and leave its boolean result in one of
+ the bits of the condition register. The bit in question is
+ determined by the [crbit_for_cond] function. *)
+
+Definition transl_cond
+ (cond: condition) (args: list mreg) (k: code) :=
+ match cond, args with
+ | (Ccomp c | Ccompu c), a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pcmp W r1 r2 SOnone :: k)
+ | (Ccompshift c s a | Ccompushift c s a), a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pcmp W r1 r2 (transl_shift s a) :: k)
+ | (Ccompimm c n | Ccompuimm c n), a1 :: nil =>
+ do r1 <- ireg_of a1;
+ OK (if is_arith_imm32 n then
+ Pcmpimm W r1 (Int.unsigned n) :: k
+ else if is_arith_imm32 (Int.neg n) then
+ Pcmnimm W r1 (Int.unsigned (Int.neg n)) :: k
+ else
+ loadimm32 X16 n (Pcmp W r1 X16 SOnone :: k))
+ | (Cmaskzero n | Cmasknotzero n), a1 :: nil =>
+ do r1 <- ireg_of a1;
+ OK (if is_logical_imm32 n then
+ Ptstimm W r1 (Int.unsigned n) :: k
+ else
+ loadimm32 X16 n (Ptst W r1 X16 SOnone :: k))
+ | (Ccompl c | Ccomplu c), a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pcmp X r1 r2 SOnone :: k)
+ | (Ccomplshift c s a | Ccomplushift c s a), a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pcmp X r1 r2 (transl_shift s a) :: k)
+ | (Ccomplimm c n | Ccompluimm c n), a1 :: nil =>
+ do r1 <- ireg_of a1;
+ OK (if is_arith_imm64 n then
+ Pcmpimm X r1 (Int64.unsigned n) :: k
+ else if is_arith_imm64 (Int64.neg n) then
+ Pcmnimm X r1 (Int64.unsigned (Int64.neg n)) :: k
+ else
+ loadimm64 X16 n (Pcmp X r1 X16 SOnone :: k))
+ | (Cmasklzero n | Cmasklnotzero n), a1 :: nil =>
+ do r1 <- ireg_of a1;
+ OK (if is_logical_imm64 n then
+ Ptstimm X r1 (Int64.unsigned n) :: k
+ else
+ loadimm64 X16 n (Ptst X r1 X16 SOnone :: k))
+ | Ccompf cmp, a1 :: a2 :: nil =>
+ do r1 <- freg_of a1; do r2 <- freg_of a2;
+ OK (Pfcmp D r1 r2 :: k)
+ | Cnotcompf cmp, a1 :: a2 :: nil =>
+ do r1 <- freg_of a1; do r2 <- freg_of a2;
+ OK (Pfcmp D r1 r2 :: k)
+ | Ccompfzero cmp, a1 :: nil =>
+ do r1 <- freg_of a1;
+ OK (Pfcmp0 D r1 :: k)
+ | Cnotcompfzero cmp, a1 :: nil =>
+ do r1 <- freg_of a1;
+ OK (Pfcmp0 D r1 :: k)
+ | Ccompfs cmp, a1 :: a2 :: nil =>
+ do r1 <- freg_of a1; do r2 <- freg_of a2;
+ OK (Pfcmp S r1 r2 :: k)
+ | Cnotcompfs cmp, a1 :: a2 :: nil =>
+ do r1 <- freg_of a1; do r2 <- freg_of a2;
+ OK (Pfcmp S r1 r2 :: k)
+ | Ccompfszero cmp, a1 :: nil =>
+ do r1 <- freg_of a1;
+ OK (Pfcmp0 S r1 :: k)
+ | Cnotcompfszero cmp, a1 :: nil =>
+ do r1 <- freg_of a1;
+ OK (Pfcmp0 S r1 :: k)
+ | _, _ =>
+ Error(msg "Asmgen.transl_cond")
+ end.
+
+Definition cond_for_signed_cmp (cmp: comparison) :=
+ match cmp with
+ | Ceq => TCeq
+ | Cne => TCne
+ | Clt => TClt
+ | Cle => TCle
+ | Cgt => TCgt
+ | Cge => TCge
+ end.
+
+Definition cond_for_unsigned_cmp (cmp: comparison) :=
+ match cmp with
+ | Ceq => TCeq
+ | Cne => TCne
+ | Clt => TClo
+ | Cle => TCls
+ | Cgt => TChi
+ | Cge => TChs
+ end.
+
+Definition cond_for_float_cmp (cmp: comparison) :=
+ match cmp with
+ | Ceq => TCeq
+ | Cne => TCne
+ | Clt => TCmi
+ | Cle => TCls
+ | Cgt => TCgt
+ | Cge => TCge
+ end.
+
+Definition cond_for_float_not_cmp (cmp: comparison) :=
+ match cmp with
+ | Ceq => TCne
+ | Cne => TCeq
+ | Clt => TCpl
+ | Cle => TChi
+ | Cgt => TCle
+ | Cge => TClt
+ end.
+
+Definition cond_for_cond (cond: condition) :=
+ match cond with
+ | Ccomp cmp => cond_for_signed_cmp cmp
+ | Ccompu cmp => cond_for_unsigned_cmp cmp
+ | Ccompshift cmp s a => cond_for_signed_cmp cmp
+ | Ccompushift cmp s a => cond_for_unsigned_cmp cmp
+ | Ccompimm cmp n => cond_for_signed_cmp cmp
+ | Ccompuimm cmp n => cond_for_unsigned_cmp cmp
+ | Cmaskzero n => TCeq
+ | Cmasknotzero n => TCne
+ | Ccompl cmp => cond_for_signed_cmp cmp
+ | Ccomplu cmp => cond_for_unsigned_cmp cmp
+ | Ccomplshift cmp s a => cond_for_signed_cmp cmp
+ | Ccomplushift cmp s a => cond_for_unsigned_cmp cmp
+ | Ccomplimm cmp n => cond_for_signed_cmp cmp
+ | Ccompluimm cmp n => cond_for_unsigned_cmp cmp
+ | Cmasklzero n => TCeq
+ | Cmasklnotzero n => TCne
+ | Ccompf cmp => cond_for_float_cmp cmp
+ | Cnotcompf cmp => cond_for_float_not_cmp cmp
+ | Ccompfzero cmp => cond_for_float_cmp cmp
+ | Cnotcompfzero cmp => cond_for_float_not_cmp cmp
+ | Ccompfs cmp => cond_for_float_cmp cmp
+ | Cnotcompfs cmp => cond_for_float_not_cmp cmp
+ | Ccompfszero cmp => cond_for_float_cmp cmp
+ | Cnotcompfszero cmp => cond_for_float_not_cmp cmp
+ end.
+
+(** Translation of a conditional branch. Prepends to [k] the instructions
+ that evaluate the condition and ranch to [lbl] if it holds.
+ We recognize some conditional branches that can be implemented
+ without setting then testing condition flags. *)
+
+Definition transl_cond_branch_default
+ (c: condition) (args: list mreg) (lbl: label) (k: code) :=
+ transl_cond c args (Pbc (cond_for_cond c) lbl :: k).
+
+Definition transl_cond_branch
+ (c: condition) (args: list mreg) (lbl: label) (k: code) :=
+ match args, c with
+ | a1 :: nil, (Ccompimm Cne n | Ccompuimm Cne n) =>
+ if Int.eq n Int.zero
+ then (do r1 <- ireg_of a1; OK (Pcbnz W r1 lbl :: k))
+ else transl_cond_branch_default c args lbl k
+ | a1 :: nil, (Ccompimm Ceq n | Ccompuimm Ceq n) =>
+ if Int.eq n Int.zero
+ then (do r1 <- ireg_of a1; OK (Pcbz W r1 lbl :: k))
+ else transl_cond_branch_default c args lbl k
+ | a1 :: nil, (Ccomplimm Cne n | Ccompluimm Cne n) =>
+ if Int64.eq n Int64.zero
+ then (do r1 <- ireg_of a1; OK (Pcbnz X r1 lbl :: k))
+ else transl_cond_branch_default c args lbl k
+ | a1 :: nil, (Ccomplimm Ceq n | Ccompluimm Ceq n) =>
+ if Int64.eq n Int64.zero
+ then (do r1 <- ireg_of a1; OK (Pcbz X r1 lbl :: k))
+ else transl_cond_branch_default c args lbl k
+ | a1 :: nil, Cmaskzero n =>
+ match Int.is_power2 n with
+ | Some bit => do r1 <- ireg_of a1; OK (Ptbz W r1 bit lbl :: k)
+ | None => transl_cond_branch_default c args lbl k
+ end
+ | a1 :: nil, Cmasknotzero n =>
+ match Int.is_power2 n with
+ | Some bit => do r1 <- ireg_of a1; OK (Ptbnz W r1 bit lbl :: k)
+ | None => transl_cond_branch_default c args lbl k
+ end
+ | a1 :: nil, Cmasklzero n =>
+ match Int64.is_power2' n with
+ | Some bit => do r1 <- ireg_of a1; OK (Ptbz X r1 bit lbl :: k)
+ | None => transl_cond_branch_default c args lbl k
+ end
+ | a1 :: nil, Cmasklnotzero n =>
+ match Int64.is_power2' n with
+ | Some bit => do r1 <- ireg_of a1; OK (Ptbnz X r1 bit lbl :: k)
+ | None => transl_cond_branch_default c args lbl k
+ end
+ | _, _ =>
+ transl_cond_branch_default c args lbl k
+ end.
+
+(** Translation of the arithmetic operation [res <- op(args)].
+ The corresponding instructions are prepended to [k]. *)
+
+Definition transl_op
+ (op: operation) (args: list mreg) (res: mreg) (k: code) :=
+ match op, args with
+ | Omove, a1 :: nil =>
+ match preg_of res, preg_of a1 with
+ | IR r, IR a => OK (Pmov r a :: k)
+ | FR r, FR a => OK (Pfmov r a :: k)
+ | _ , _ => Error(msg "Asmgen.Omove")
+ end
+ | Ointconst n, nil =>
+ do rd <- ireg_of res;
+ OK (loadimm32 rd n k)
+ | Olongconst n, nil =>
+ do rd <- ireg_of res;
+ OK (loadimm64 rd n k)
+ | Ofloatconst f, nil =>
+ do rd <- freg_of res;
+ OK (if Float.eq_dec f Float.zero
+ then Pfmovi D rd XZR :: k
+ else Pfmovimmd rd f :: k)
+ | Osingleconst f, nil =>
+ do rd <- freg_of res;
+ OK (if Float32.eq_dec f Float32.zero
+ then Pfmovi S rd XZR :: k
+ else Pfmovimms rd f :: k)
+ | Oaddrsymbol id ofs, nil =>
+ do rd <- ireg_of res;
+ OK (loadsymbol rd id ofs k)
+ | Oaddrstack ofs, nil =>
+ do rd <- ireg_of res;
+ OK (addimm64 rd XSP (Ptrofs.to_int64 ofs) k)
+(** 32-bit integer arithmetic *)
+ | Oshift s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porr W rd XZR r1 (transl_shift s a) :: k)
+ | Oadd, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Padd W rd r1 r2 SOnone :: k)
+ | Oaddshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Padd W rd r1 r2 (transl_shift s a) :: k)
+ | Oaddimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (addimm32 rd r1 n k)
+ | Oneg, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psub W rd XZR r1 SOnone :: k)
+ | Onegshift s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psub W rd XZR r1 (transl_shift s a) :: k)
+ | Osub, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psub W rd r1 r2 SOnone :: k)
+ | Osubshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psub W rd r1 r2 (transl_shift s a) :: k)
+ | Omul, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pmadd W rd r1 r2 XZR :: k)
+ | Omuladd, a1 :: a2 :: a3 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
+ OK (Pmadd W rd r2 r3 r1 :: k)
+ | Omulsub, a1 :: a2 :: a3 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
+ OK (Pmsub W rd r2 r3 r1 :: k)
+ | Odiv, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psdiv W rd r1 r2 :: k)
+ | Odivu, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pudiv W rd r1 r2 :: k)
+ | Oand, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pand W rd r1 r2 SOnone :: k)
+ | Oandshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pand W rd r1 r2 (transl_shift s a) :: k)
+ | Oandimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm32 (Pandimm W) (Pand W) rd r1 n k)
+ | Oor, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porr W rd r1 r2 SOnone :: k)
+ | Oorshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porr W rd r1 r2 (transl_shift s a) :: k)
+ | Oorimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm32 (Porrimm W) (Porr W) rd r1 n k)
+ | Oxor, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peor W rd r1 r2 SOnone :: k)
+ | Oxorshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peor W rd r1 r2 (transl_shift s a) :: k)
+ | Oxorimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm32 (Peorimm W) (Peor W) rd r1 n k)
+ | Onot, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porn W rd XZR r1 SOnone :: k)
+ | Onotshift s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porn W rd XZR r1 (transl_shift s a) :: k)
+ | Obic, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pbic W rd r1 r2 SOnone :: k)
+ | Obicshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pbic W rd r1 r2 (transl_shift s a) :: k)
+ | Oorn, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porn W rd r1 r2 SOnone :: k)
+ | Oornshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porn W rd r1 r2 (transl_shift s a) :: k)
+ | Oeqv, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peon W rd r1 r2 SOnone :: k)
+ | Oeqvshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peon W rd r1 r2 (transl_shift s a) :: k)
+ | Oshl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Plslv W rd r1 r2 :: k)
+ | Oshr, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pasrv W rd r1 r2 :: k)
+ | Oshru, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Plsrv W rd r1 r2 :: k)
+ | Oshrximm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (shrx32 rd r1 n k)
+ | Ozext s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfiz W rd r1 Int.zero s :: k)
+ | Osext s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfiz W rd r1 Int.zero s :: k)
+ | Oshlzext s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
+ | Oshlsext s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
+ | Ozextshr a s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
+ | Osextshr a s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
+(** 64-bit integer arithmetic *)
+ | Oshiftl s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porr X rd XZR r1 (transl_shift s a) :: k)
+ | Oextend x a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (move_extended rd r1 x a k)
+ (* [Omakelong] and [Ohighlong] should not occur *)
+ | Olowlong, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ assertion (ireg_eq rd r1);
+ OK (Pcvtx2w rd :: k)
+ | Oaddl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Padd X rd r1 r2 SOnone :: k)
+ | Oaddlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Padd X rd r1 r2 (transl_shift s a) :: k)
+ | Oaddlext x a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (arith_extended Paddext (Padd X) rd r1 r2 x a k)
+ | Oaddlimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (addimm64 rd r1 n k)
+ | Onegl, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psub X rd XZR r1 SOnone :: k)
+ | Oneglshift s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psub X rd XZR r1 (transl_shift s a) :: k)
+ | Osubl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psub X rd r1 r2 SOnone :: k)
+ | Osublshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psub X rd r1 r2 (transl_shift s a) :: k)
+ | Osublext x a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (arith_extended Psubext (Psub X) rd r1 r2 x a k)
+ | Omull, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pmadd X rd r1 r2 XZR :: k)
+ | Omulladd, a1 :: a2 :: a3 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
+ OK (Pmadd X rd r2 r3 r1 :: k)
+ | Omullsub, a1 :: a2 :: a3 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
+ OK (Pmsub X rd r2 r3 r1 :: k)
+ | Omullhs, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psmulh rd r1 r2 :: k)
+ | Omullhu, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pumulh rd r1 r2 :: k)
+ | Odivl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Psdiv X rd r1 r2 :: k)
+ | Odivlu, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pudiv X rd r1 r2 :: k)
+ | Oandl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pand X rd r1 r2 SOnone :: k)
+ | Oandlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pand X rd r1 r2 (transl_shift s a) :: k)
+ | Oandlimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm64 (Pandimm X) (Pand X) rd r1 n k)
+ | Oorl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porr X rd r1 r2 SOnone :: k)
+ | Oorlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porr X rd r1 r2 (transl_shift s a) :: k)
+ | Oorlimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm64 (Porrimm X) (Porr X) rd r1 n k)
+ | Oxorl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peor X rd r1 r2 SOnone :: k)
+ | Oxorlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peor X rd r1 r2 (transl_shift s a) :: k)
+ | Oxorlimm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (logicalimm64 (Peorimm X) (Peor X) rd r1 n k)
+ | Onotl, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porn X rd XZR r1 SOnone :: k)
+ | Onotlshift s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Porn X rd XZR r1 (transl_shift s a) :: k)
+ | Obicl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pbic X rd r1 r2 SOnone :: k)
+ | Obiclshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pbic X rd r1 r2 (transl_shift s a) :: k)
+ | Oornl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porn X rd r1 r2 SOnone :: k)
+ | Oornlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Porn X rd r1 r2 (transl_shift s a) :: k)
+ | Oeqvl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peon X rd r1 r2 SOnone :: k)
+ | Oeqvlshift s a, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Peon X rd r1 r2 (transl_shift s a) :: k)
+ | Oshll, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Plslv X rd r1 r2 :: k)
+ | Oshrl, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Pasrv X rd r1 r2 :: k)
+ | Oshrlu, a1 :: a2 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (Plsrv X rd r1 r2 :: k)
+ | Oshrlximm n, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (shrx64 rd r1 n k)
+ | Ozextl s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfiz X rd r1 Int.zero s :: k)
+ | Osextl s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfiz X rd r1 Int.zero s :: k)
+ | Oshllzext s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
+ | Oshllsext s a, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
+ | Ozextshrl a s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Pubfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
+ | Osextshrl a s, a1 :: nil =>
+ do rd <- ireg_of res; do r1 <- ireg_of a1;
+ OK (Psbfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
+(** 64-bit floating-point arithmetic *)
+ | Onegf, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfneg D rd rs :: k)
+ | Oabsf, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfabs D rd rs :: k)
+ | Oaddf, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfadd D rd rs1 rs2 :: k)
+ | Osubf, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfsub D rd rs1 rs2 :: k)
+ | Omulf, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfmul D rd rs1 rs2 :: k)
+ | Odivf, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfdiv D rd rs1 rs2 :: k)
+(** 32-bit floating-point arithmetic *)
+ | Onegfs, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfneg S rd rs :: k)
+ | Oabsfs, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfabs S rd rs :: k)
+ | Oaddfs, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfadd S rd rs1 rs2 :: k)
+ | Osubfs, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfsub S rd rs1 rs2 :: k)
+ | Omulfs, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfmul S rd rs1 rs2 :: k)
+ | Odivfs, a1 :: a2 :: nil =>
+ do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
+ OK (Pfdiv S rd rs1 rs2 :: k)
+ | Osingleoffloat, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfcvtsd rd rs :: k)
+ | Ofloatofsingle, a1 :: nil =>
+ do rd <- freg_of res; do rs <- freg_of a1;
+ OK (Pfcvtds rd rs :: k)
+(** Conversions between int and float *)
+ | Ointoffloat, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzs W D rd rs :: k)
+ | Ointuoffloat, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzu W D rd rs :: k)
+ | Ofloatofint, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pscvtf D W rd rs :: k)
+ | Ofloatofintu, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pucvtf D W rd rs :: k)
+ | Ointofsingle, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzs W S rd rs :: k)
+ | Ointuofsingle, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzu W S rd rs :: k)
+ | Osingleofint, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pscvtf S W rd rs :: k)
+ | Osingleofintu, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pucvtf S W rd rs :: k)
+ | Olongoffloat, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzs X D rd rs :: k)
+ | Olonguoffloat, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzu X D rd rs :: k)
+ | Ofloatoflong, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pscvtf D X rd rs :: k)
+ | Ofloatoflongu, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pucvtf D X rd rs :: k)
+ | Olongofsingle, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzs X S rd rs :: k)
+ | Olonguofsingle, a1 :: nil =>
+ do rd <- ireg_of res; do rs <- freg_of a1;
+ OK (Pfcvtzu X S rd rs :: k)
+ | Osingleoflong, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pscvtf S X rd rs :: k)
+ | Osingleoflongu, a1 :: nil =>
+ do rd <- freg_of res; do rs <- ireg_of a1;
+ OK (Pucvtf S X rd rs :: k)
+(** Boolean tests *)
+ | Ocmp c, _ =>
+ do rd <- ireg_of res;
+ transl_cond c args (Pcset rd (cond_for_cond c) :: k)
+(** Conditional move *)
+ | Osel cmp ty, a1 :: a2 :: args =>
+ match preg_of res with
+ | IR r =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ transl_cond cmp args (Pcsel r r1 r2 (cond_for_cond cmp) :: k)
+ | FR r =>
+ do r1 <- freg_of a1; do r2 <- freg_of a2;
+ transl_cond cmp args (Pfsel r r1 r2 (cond_for_cond cmp) :: k)
+ | _ =>
+ Error(msg "Asmgen.Osel")
+ end
+ | _, _ =>
+ Error(msg "Asmgen.transl_op")
+ end.
+
+(** Translation of addressing modes *)
+
+Definition offset_representable (sz: Z) (ofs: int64) : bool :=
+ let isz := Int64.repr sz in
+ (** either unscaled 9-bit signed *)
+ Int64.eq ofs (Int64.sign_ext 9 ofs) ||
+ (** or scaled 12-bit unsigned *)
+ (Int64.eq (Int64.modu ofs isz) Int64.zero
+ && Int64.ltu ofs (Int64.shl isz (Int64.repr 12))).
+
+Definition transl_addressing (sz: Z) (addr: Op.addressing) (args: list mreg)
+ (insn: Asm.addressing -> instruction) (k: code) : res code :=
+ match addr, args with
+ | Aindexed ofs, a1 :: nil =>
+ do r1 <- ireg_of a1;
+ if offset_representable sz ofs then
+ OK (insn (ADimm r1 ofs) :: k)
+ else
+ OK (loadimm64 X16 ofs (insn (ADreg r1 X16) :: k))
+ | Aindexed2, a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ OK (insn (ADreg r1 r2) :: k)
+ | Aindexed2shift a, a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ if Int.eq a Int.zero then
+ OK (insn (ADreg r1 r2) :: k)
+ else if Int.eq (Int.shl Int.one a) (Int.repr sz) then
+ OK (insn (ADlsl r1 r2 a) :: k)
+ else
+ OK (Padd X X16 r1 r2 (SOlsl a) :: insn (ADimm X16 Int64.zero) :: k)
+ | Aindexed2ext x a, a1 :: a2 :: nil =>
+ do r1 <- ireg_of a1; do r2 <- ireg_of a2;
+ if Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz) then
+ OK (insn (match x with Xsgn32 => ADsxt r1 r2 a
+ | Xuns32 => ADuxt r1 r2 a end) :: k)
+ else
+ OK (arith_extended Paddext (Padd X) X16 r1 r2 x a
+ (insn (ADimm X16 Int64.zero) :: k))
+ | Aglobal id ofs, nil =>
+ assertion (negb (Archi.pic_code tt));
+ if Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero && 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")
+ end.
+
+(** Translation of loads and stores *)
+
+Definition transl_load (trap: trapping_mode)
+ (chunk: memory_chunk) (addr: Op.addressing)
+ (args: list mreg) (dst: mreg) (k: code) : res code :=
+ match trap with
+ | NOTRAP => Error (msg "Asmgen.transl_load non-trapping loads unsupported on aarch64")
+ | TRAP =>
+ match chunk with
+ | Mint8unsigned =>
+ do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrb W rd) k
+ | Mint8signed =>
+ do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrsb W rd) k
+ | Mint16unsigned =>
+ do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrh W rd) k
+ | Mint16signed =>
+ do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrsh W rd) k
+ | Mint32 =>
+ do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw rd) k
+ | Mint64 =>
+ do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx rd) k
+ | Mfloat32 =>
+ do rd <- freg_of dst; transl_addressing 4 addr args (Pldrs rd) k
+ | Mfloat64 =>
+ do rd <- freg_of dst; transl_addressing 8 addr args (Pldrd rd) k
+ | Many32 =>
+ do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw_a rd) k
+ | Many64 =>
+ do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx_a rd) k
+ end
+ end.
+
+Definition transl_store (chunk: memory_chunk) (addr: Op.addressing)
+ (args: list mreg) (src: mreg) (k: code) : res code :=
+ match chunk with
+ | Mint8unsigned | Mint8signed =>
+ do r1 <- ireg_of src; transl_addressing 1 addr args (Pstrb r1) k
+ | Mint16unsigned | Mint16signed =>
+ do r1 <- ireg_of src; transl_addressing 2 addr args (Pstrh r1) k
+ | Mint32 =>
+ do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw r1) k
+ | Mint64 =>
+ do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx r1) k
+ | Mfloat32 =>
+ do r1 <- freg_of src; transl_addressing 4 addr args (Pstrs r1) k
+ | Mfloat64 =>
+ do r1 <- freg_of src; transl_addressing 8 addr args (Pstrd r1) k
+ | Many32 =>
+ do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw_a r1) k
+ | Many64 =>
+ do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx_a r1) k
+ end.
+
+(** Register-indexed loads and stores *)
+
+Definition indexed_memory_access (insn: Asm.addressing -> instruction)
+ (sz: Z) (base: iregsp) (ofs: ptrofs) (k: code) :=
+ let ofs := Ptrofs.to_int64 ofs in
+ if offset_representable sz ofs
+ then insn (ADimm base ofs) :: k
+ else loadimm64 X16 ofs (insn (ADreg base X16) :: k).
+
+Definition loadind (base: iregsp) (ofs: ptrofs) (ty: typ) (dst: mreg) (k: code) :=
+ match ty, preg_of dst with
+ | Tint, IR rd => OK (indexed_memory_access (Pldrw rd) 4 base ofs k)
+ | Tlong, IR rd => OK (indexed_memory_access (Pldrx rd) 8 base ofs k)
+ | Tsingle, FR rd => OK (indexed_memory_access (Pldrs rd) 4 base ofs k)
+ | Tfloat, FR rd => OK (indexed_memory_access (Pldrd rd) 8 base ofs k)
+ | Tany32, IR rd => OK (indexed_memory_access (Pldrw_a rd) 4 base ofs k)
+ | Tany64, IR rd => OK (indexed_memory_access (Pldrx_a rd) 8 base ofs k)
+ | Tany64, FR rd => OK (indexed_memory_access (Pldrd_a rd) 8 base ofs k)
+ | _, _ => Error (msg "Asmgen.loadind")
+ end.
+
+Definition storeind (src: mreg) (base: iregsp) (ofs: ptrofs) (ty: typ) (k: code) :=
+ match ty, preg_of src with
+ | Tint, IR rd => OK (indexed_memory_access (Pstrw rd) 4 base ofs k)
+ | Tlong, IR rd => OK (indexed_memory_access (Pstrx rd) 8 base ofs k)
+ | Tsingle, FR rd => OK (indexed_memory_access (Pstrs rd) 4 base ofs k)
+ | Tfloat, FR rd => OK (indexed_memory_access (Pstrd rd) 8 base ofs k)
+ | Tany32, IR rd => OK (indexed_memory_access (Pstrw_a rd) 4 base ofs k)
+ | Tany64, IR rd => OK (indexed_memory_access (Pstrx_a rd) 8 base ofs k)
+ | Tany64, FR rd => OK (indexed_memory_access (Pstrd_a rd) 8 base ofs k)
+ | _, _ => Error (msg "Asmgen.storeind")
+ end.
+
+Definition loadptr (base: iregsp) (ofs: ptrofs) (dst: ireg) (k: code) :=
+ indexed_memory_access (Pldrx dst) 8 base ofs k.
+
+Definition storeptr (src: ireg) (base: iregsp) (ofs: ptrofs) (k: code) :=
+ indexed_memory_access (Pstrx src) 8 base ofs k.
+
+(** Function epilogue *)
+
+Definition make_epilogue (f: Mach.function) (k: code) :=
+ (* FIXME
+ Cannot be used because memcpy destroys X30;
+ issue being discussed with X. Leroy *)
+ (* if is_leaf_function f
+ then Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) :: k
+ else*) loadptr XSP f.(fn_retaddr_ofs) RA
+ (Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) :: k).
+
+(** Translation of a Mach instruction. *)
+
+Definition transl_instr (f: Mach.function) (i: Mach.instruction)
+ (r29_is_parent: bool) (k: code) : res code :=
+ match i with
+ | Mgetstack ofs ty dst =>
+ loadind XSP ofs ty dst k
+ | Msetstack src ofs ty =>
+ storeind src XSP ofs ty k
+ | Mgetparam ofs ty dst =>
+ (* load via the frame pointer if it is valid *)
+ do c <- loadind X29 ofs ty dst k;
+ OK (if r29_is_parent then c else loadptr XSP f.(fn_link_ofs) X29 c)
+ | Mop op args res =>
+ transl_op op args res k
+ | Mload trap chunk addr args dst =>
+ transl_load trap chunk addr args dst k
+ | Mstore chunk addr args src =>
+ transl_store chunk addr args src k
+ | Mcall sig (inl r) =>
+ do r1 <- ireg_of r; OK (Pblr r1 sig :: k)
+ | Mcall sig (inr symb) =>
+ OK (Pbl symb sig :: k)
+ | Mtailcall sig (inl r) =>
+ do r1 <- ireg_of r;
+ OK (make_epilogue f (Pbr r1 sig :: k))
+ | Mtailcall sig (inr symb) =>
+ OK (make_epilogue f (Pbs symb sig :: k))
+ | Mbuiltin ef args res =>
+ OK (Pbuiltin ef (List.map (map_builtin_arg preg_of) args) (map_builtin_res preg_of res) :: k)
+ | Mlabel lbl =>
+ OK (Plabel lbl :: k)
+ | Mgoto lbl =>
+ OK (Pb lbl :: k)
+ | Mcond cond args lbl =>
+ transl_cond_branch cond args lbl k
+ | Mjumptable arg tbl =>
+ do r <- ireg_of arg;
+ OK (Pbtbl r tbl :: k)
+ | Mreturn =>
+ OK (make_epilogue f (Pret RA :: k))
+ end.
+
+(** Translation of a code sequence *)
+
+Definition it1_is_parent (before: bool) (i: Mach.instruction) : bool :=
+ match i with
+ | Msetstack src ofs ty => before
+ | Mgetparam ofs ty dst => negb (mreg_eq dst R29)
+ | Mop op args res => before && negb (mreg_eq res R29)
+ | _ => false
+ end.
+
+(** This is the naive definition that we no longer use because it
+ is not tail-recursive. It is kept as specification. *)
+
+Fixpoint transl_code (f: Mach.function) (il: list Mach.instruction) (it1p: bool) :=
+ match il with
+ | nil => OK nil
+ | i1 :: il' =>
+ do k <- transl_code f il' (it1_is_parent it1p i1);
+ transl_instr f i1 it1p k
+ end.
+
+(** This is an equivalent definition in continuation-passing style
+ that runs in constant stack space. *)
+
+Fixpoint transl_code_rec (f: Mach.function) (il: list Mach.instruction)
+ (it1p: bool) (k: code -> res code) :=
+ match il with
+ | nil => k nil
+ | i1 :: il' =>
+ transl_code_rec f il' (it1_is_parent it1p i1)
+ (fun c1 => do c2 <- transl_instr f i1 it1p c1; k c2)
+ end.
+
+Definition transl_code' (f: Mach.function) (il: list Mach.instruction) (it1p: bool) :=
+ transl_code_rec f il it1p (fun c => OK c).
+
+(** Translation of a whole function. Note that we must check
+ that the generated code contains less than [2^32] instructions,
+ otherwise the offset part of the [PC] code pointer could wrap
+ around, leading to incorrect executions. *)
+
+Definition transl_function (f: Mach.function) :=
+ do c <- transl_code' f f.(Mach.fn_code) true;
+ OK (mkfunction f.(Mach.fn_sig)
+ (Pallocframe f.(fn_stacksize) f.(fn_link_ofs) ::
+ storeptr RA XSP f.(fn_retaddr_ofs) c)).
+
+*) \ No newline at end of file
diff --git a/aarch64/Asmblockgenproof.v b/aarch64/Asmblockgenproof.v
new file mode 100644
index 00000000..bcd4495f
--- /dev/null
+++ b/aarch64/Asmblockgenproof.v
@@ -0,0 +1,1104 @@
+(* ORIGINAL aarch64/Asmgenproof file that needs to be adapted
+
+(* *********************************************************************)
+(* *)
+(* The Compcert verified compiler *)
+(* *)
+(* Xavier Leroy, Collège de France and INRIA Paris *)
+(* *)
+(* Copyright Institut National de Recherche en Informatique et en *)
+(* Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the INRIA Non-Commercial License Agreement. *)
+(* *)
+(* *********************************************************************)
+
+(** Correctness proof for AArch64 code generation. *)
+
+Require Import Coqlib Errors.
+Require Import Integers Floats AST Linking.
+Require Import Values Memory Events Globalenvs Smallstep.
+Require Import Op Locations Mach Conventions Asm.
+Require Import Asmgen Asmgenproof0 Asmgenproof1.
+
+Definition match_prog (p: Mach.program) (tp: Asm.program) :=
+ match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp.
+
+Lemma transf_program_match:
+ forall p tp, transf_program p = OK tp -> match_prog p tp.
+Proof.
+ intros. eapply match_transform_partial_program; eauto.
+Qed.
+
+Section PRESERVATION.
+
+Variable prog: Mach.program.
+Variable tprog: Asm.program.
+Hypothesis TRANSF: match_prog prog tprog.
+Let ge := Genv.globalenv prog.
+Let tge := Genv.globalenv tprog.
+
+Lemma symbols_preserved:
+ forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s.
+Proof (Genv.find_symbol_match TRANSF).
+
+Lemma senv_preserved:
+ Senv.equiv ge tge.
+Proof (Genv.senv_match TRANSF).
+
+Lemma functions_translated:
+ forall b f,
+ Genv.find_funct_ptr ge b = Some f ->
+ exists tf,
+ Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf.
+Proof (Genv.find_funct_ptr_transf_partial TRANSF).
+
+Lemma functions_transl:
+ forall fb f tf,
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ transf_function f = OK tf ->
+ Genv.find_funct_ptr tge fb = Some (Internal tf).
+Proof.
+ intros. exploit functions_translated; eauto. intros [tf' [A B]].
+ monadInv B. rewrite H0 in EQ; inv EQ; auto.
+Qed.
+
+(** * Properties of control flow *)
+
+Lemma transf_function_no_overflow:
+ forall f tf,
+ transf_function f = OK tf -> list_length_z tf.(fn_code) <= Ptrofs.max_unsigned.
+Proof.
+ intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0.
+ omega.
+Qed.
+
+Lemma exec_straight_exec:
+ forall fb f c ep tf tc c' rs m rs' m',
+ transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
+ exec_straight tge tf tc rs m c' rs' m' ->
+ plus step tge (State rs m) E0 (State rs' m').
+Proof.
+ intros. inv H.
+ eapply exec_straight_steps_1; eauto.
+ eapply transf_function_no_overflow; eauto.
+ eapply functions_transl; eauto.
+Qed.
+
+Lemma exec_straight_at:
+ forall fb f c ep tf tc c' ep' tc' rs m rs' m',
+ transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
+ transl_code f c' ep' = OK tc' ->
+ exec_straight tge tf tc rs m tc' rs' m' ->
+ transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'.
+Proof.
+ intros. inv H.
+ exploit exec_straight_steps_2; eauto.
+ eapply transf_function_no_overflow; eauto.
+ eapply functions_transl; eauto.
+ intros [ofs' [PC' CT']].
+ rewrite PC'. constructor; auto.
+Qed.
+
+(** The following lemmas show that the translation from Mach to Asm
+ preserves labels, in the sense that the following diagram commutes:
+<<
+ translation
+ Mach code ------------------------ Asm instr sequence
+ | |
+ | Mach.find_label lbl find_label lbl |
+ | |
+ v v
+ Mach code tail ------------------- Asm instr seq tail
+ translation
+>>
+ The proof demands many boring lemmas showing that Asm constructor
+ functions do not introduce new labels.
+*)
+
+Section TRANSL_LABEL.
+
+Remark loadimm_z_label: forall sz rd l k, tail_nolabel k (loadimm_z sz rd l k).
+Proof.
+ intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel.
+ induction l as [ | [n p] l]; simpl; TailNoLabel.
+Qed.
+
+Remark loadimm_n_label: forall sz rd l k, tail_nolabel k (loadimm_n sz rd l k).
+Proof.
+ intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel.
+ induction l as [ | [n p] l]; simpl; TailNoLabel.
+Qed.
+
+Remark loadimm_label: forall sz rd n k, tail_nolabel k (loadimm sz rd n k).
+Proof.
+ unfold loadimm; intros. destruct Nat.leb; [apply loadimm_z_label|apply loadimm_n_label].
+Qed.
+Hint Resolve loadimm_label: labels.
+
+Remark loadimm32_label: forall r n k, tail_nolabel k (loadimm32 r n k).
+Proof.
+ unfold loadimm32; intros. destruct (is_logical_imm32 n); TailNoLabel.
+Qed.
+Hint Resolve loadimm32_label: labels.
+
+Remark loadimm64_label: forall r n k, tail_nolabel k (loadimm64 r n k).
+Proof.
+ unfold loadimm64; intros. destruct (is_logical_imm64 n); TailNoLabel.
+Qed.
+Hint Resolve loadimm64_label: labels.
+
+Remark addimm_aux: forall insn rd r1 n k,
+ (forall rd r1 n, nolabel (insn rd r1 n)) ->
+ tail_nolabel k (addimm_aux insn rd r1 n k).
+Proof.
+ unfold addimm_aux; intros.
+ destruct Z.eqb. TailNoLabel. destruct Z.eqb; TailNoLabel.
+Qed.
+
+Remark addimm32_label: forall rd r1 n k, tail_nolabel k (addimm32 rd r1 n k).
+Proof.
+ unfold addimm32; intros.
+ destruct Int.eq. apply addimm_aux; intros; red; auto.
+ destruct Int.eq. apply addimm_aux; intros; red; auto.
+ destruct Int.lt; eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+Hint Resolve addimm32_label: labels.
+
+Remark addimm64_label: forall rd r1 n k, tail_nolabel k (addimm64 rd r1 n k).
+Proof.
+ unfold addimm64; intros.
+ destruct Int64.eq. apply addimm_aux; intros; red; auto.
+ destruct Int64.eq. apply addimm_aux; intros; red; auto.
+ destruct Int64.lt; eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+Hint Resolve addimm64_label: labels.
+
+Remark logicalimm32_label: forall insn1 insn2 rd r1 n k,
+ (forall rd r1 n, nolabel (insn1 rd r1 n)) ->
+ (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) ->
+ tail_nolabel k (logicalimm32 insn1 insn2 rd r1 n k).
+Proof.
+ unfold logicalimm32; intros.
+ destruct (is_logical_imm32 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+
+Remark logicalimm64_label: forall insn1 insn2 rd r1 n k,
+ (forall rd r1 n, nolabel (insn1 rd r1 n)) ->
+ (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) ->
+ tail_nolabel k (logicalimm64 insn1 insn2 rd r1 n k).
+Proof.
+ unfold logicalimm64; intros.
+ destruct (is_logical_imm64 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+
+Remark move_extended_label: forall rd r1 ex a k, tail_nolabel k (move_extended rd r1 ex a k).
+Proof.
+ unfold move_extended, move_extended_base; intros. destruct Int.eq, ex; TailNoLabel.
+Qed.
+Hint Resolve move_extended_label: labels.
+
+Remark arith_extended_label: forall insnX insnS rd r1 r2 ex a k,
+ (forall rd r1 r2 x, nolabel (insnX rd r1 r2 x)) ->
+ (forall rd r1 r2 s, nolabel (insnS rd r1 r2 s)) ->
+ tail_nolabel k (arith_extended insnX insnS rd r1 r2 ex a k).
+Proof.
+ unfold arith_extended; intros. destruct Int.ltu.
+ TailNoLabel.
+ destruct ex; simpl; TailNoLabel.
+Qed.
+
+Remark loadsymbol_label: forall r id ofs k, tail_nolabel k (loadsymbol r id ofs k).
+Proof.
+ intros; unfold loadsymbol.
+ destruct (Archi.pic_code tt); TailNoLabel. destruct Ptrofs.eq; TailNoLabel.
+Qed.
+Hint Resolve loadsymbol_label: labels.
+
+Remark transl_cond_label: forall cond args k c,
+ transl_cond cond args k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_cond; intros; destruct cond; TailNoLabel.
+- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+
+Remark transl_cond_branch_default_label: forall cond args lbl k c,
+ transl_cond_branch_default cond args lbl k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_cond_branch_default; intros.
+ eapply tail_nolabel_trans; [eapply transl_cond_label;eauto|TailNoLabel].
+Qed.
+Hint Resolve transl_cond_branch_default_label: labels.
+
+Remark transl_cond_branch_label: forall cond args lbl k c,
+ transl_cond_branch cond args lbl k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_cond_branch; intros; destruct args; TailNoLabel; destruct cond; TailNoLabel.
+- destruct c0; TailNoLabel.
+- destruct c0; TailNoLabel.
+- destruct (Int.is_power2 n); TailNoLabel.
+- destruct (Int.is_power2 n); TailNoLabel.
+- destruct c0; TailNoLabel.
+- destruct c0; TailNoLabel.
+- destruct (Int64.is_power2' n); TailNoLabel.
+- destruct (Int64.is_power2' n); TailNoLabel.
+Qed.
+
+Remark transl_op_label:
+ forall op args r k c,
+ transl_op op args r k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_op; intros; destruct op; TailNoLabel.
+- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel.
+- destruct (Float.eq_dec n Float.zero); TailNoLabel.
+- destruct (Float32.eq_dec n Float32.zero); TailNoLabel.
+- apply logicalimm32_label; unfold nolabel; auto.
+- apply logicalimm32_label; unfold nolabel; auto.
+- apply logicalimm32_label; unfold nolabel; auto.
+- unfold shrx32. destruct (Int.eq _ _); try destruct (Int.eq _ _); TailNoLabel.
+- apply arith_extended_label; unfold nolabel; auto.
+- apply arith_extended_label; unfold nolabel; auto.
+- apply logicalimm64_label; unfold nolabel; auto.
+- apply logicalimm64_label; unfold nolabel; auto.
+- apply logicalimm64_label; unfold nolabel; auto.
+- unfold shrx64. destruct (Int.eq _ _); try destruct (Int.eq _ _); TailNoLabel.
+- eapply tail_nolabel_trans. eapply transl_cond_label; eauto. TailNoLabel.
+- destruct (preg_of r); try discriminate; TailNoLabel;
+ (eapply tail_nolabel_trans; [eapply transl_cond_label; eauto | TailNoLabel]).
+Qed.
+
+Remark transl_addressing_label:
+ forall sz addr args insn k c,
+ transl_addressing sz addr args insn k = OK c ->
+ (forall ad, nolabel (insn ad)) ->
+ tail_nolabel k c.
+Proof.
+ unfold transl_addressing; intros; destruct addr; TailNoLabel;
+ eapply tail_nolabel_trans; TailNoLabel.
+ eapply tail_nolabel_trans. apply arith_extended_label; unfold nolabel; auto. TailNoLabel.
+Qed.
+
+Remark transl_load_label:
+ forall trap chunk addr args dst k c,
+ transl_load trap chunk addr args dst k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_load; intros; destruct trap; try discriminate; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto.
+Qed.
+
+Remark transl_store_label:
+ forall chunk addr args src k c,
+ transl_store chunk addr args src k = OK c -> tail_nolabel k c.
+Proof.
+ unfold transl_store; intros; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto.
+Qed.
+
+Remark indexed_memory_access_label:
+ forall insn sz base ofs k,
+ (forall ad, nolabel (insn ad)) ->
+ tail_nolabel k (indexed_memory_access insn sz base ofs k).
+Proof.
+ unfold indexed_memory_access; intros. destruct offset_representable.
+ TailNoLabel.
+ eapply tail_nolabel_trans; TailNoLabel.
+Qed.
+
+Remark loadind_label:
+ forall base ofs ty dst k c,
+ loadind base ofs ty dst k = OK c -> tail_nolabel k c.
+Proof.
+ unfold loadind; intros.
+ destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I.
+Qed.
+
+Remark storeind_label:
+ forall src base ofs ty k c,
+ storeind src base ofs ty k = OK c -> tail_nolabel k c.
+Proof.
+ unfold storeind; intros.
+ destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I.
+Qed.
+
+Remark loadptr_label:
+ forall base ofs dst k, tail_nolabel k (loadptr base ofs dst k).
+Proof.
+ intros. apply indexed_memory_access_label. unfold nolabel; auto.
+Qed.
+
+Remark storeptr_label:
+ forall src base ofs k, tail_nolabel k (storeptr src base ofs k).
+Proof.
+ intros. apply indexed_memory_access_label. unfold nolabel; auto.
+Qed.
+
+Remark make_epilogue_label:
+ forall f k, tail_nolabel k (make_epilogue f k).
+Proof.
+ unfold make_epilogue; intros.
+ (* FIXME destruct is_leaf_function.
+ { TailNoLabel. } *)
+ eapply tail_nolabel_trans.
+ apply loadptr_label.
+ TailNoLabel.
+Qed.
+
+Lemma transl_instr_label:
+ forall f i ep k c,
+ transl_instr f i ep k = OK c ->
+ match i with Mlabel lbl => c = Plabel lbl :: k | _ => tail_nolabel k c end.
+Proof.
+ unfold transl_instr; intros; destruct i; TailNoLabel.
+- eapply loadind_label; eauto.
+- eapply storeind_label; eauto.
+- destruct ep. eapply loadind_label; eauto.
+ eapply tail_nolabel_trans. apply loadptr_label. eapply loadind_label; eauto.
+- eapply transl_op_label; eauto.
+- eapply transl_load_label; eauto.
+- eapply transl_store_label; eauto.
+- destruct s0; monadInv H; TailNoLabel.
+- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]).
+- eapply transl_cond_branch_label; eauto.
+- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel].
+Qed.
+
+Lemma transl_instr_label':
+ forall lbl f i ep k c,
+ transl_instr f i ep k = OK c ->
+ find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k.
+Proof.
+ intros. exploit transl_instr_label; eauto.
+ destruct i; try (intros [A B]; apply B).
+ intros. subst c. simpl. auto.
+Qed.
+
+Lemma transl_code_label:
+ forall lbl f c ep tc,
+ transl_code f c ep = OK tc ->
+ match Mach.find_label lbl c with
+ | None => find_label lbl tc = None
+ | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc'
+ end.
+Proof.
+ induction c; simpl; intros.
+ inv H. auto.
+ monadInv H. rewrite (transl_instr_label' lbl _ _ _ _ _ EQ0).
+ generalize (Mach.is_label_correct lbl a).
+ destruct (Mach.is_label lbl a); intros.
+ subst a. simpl in EQ. exists x; auto.
+ eapply IHc; eauto.
+Qed.
+
+Lemma transl_find_label:
+ forall lbl f tf,
+ transf_function f = OK tf ->
+ match Mach.find_label lbl f.(Mach.fn_code) with
+ | None => find_label lbl tf.(fn_code) = None
+ | Some c => exists tc, find_label lbl tf.(fn_code) = Some tc /\ transl_code f c false = OK tc
+ end.
+Proof.
+ intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0.
+ monadInv EQ. rewrite transl_code'_transl_code in EQ0. unfold fn_code.
+ simpl. destruct (storeptr_label X30 XSP (fn_retaddr_ofs f) x) as [A B]; rewrite B.
+ eapply transl_code_label; eauto.
+Qed.
+
+End TRANSL_LABEL.
+
+(** A valid branch in a piece of Mach code translates to a valid ``go to''
+ transition in the generated Asm code. *)
+
+Lemma find_label_goto_label:
+ forall f tf lbl rs m c' b ofs,
+ Genv.find_funct_ptr ge b = Some (Internal f) ->
+ transf_function f = OK tf ->
+ rs PC = Vptr b ofs ->
+ Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+ exists tc', exists rs',
+ goto_label tf lbl rs m = Next rs' m
+ /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc'
+ /\ forall r, r <> PC -> rs'#r = rs#r.
+Proof.
+ intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2.
+ intros [tc [A B]].
+ exploit label_pos_code_tail; eauto. instantiate (1 := 0).
+ intros [pos' [P [Q R]]].
+ exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))).
+ split. unfold goto_label. rewrite P. rewrite H1. auto.
+ split. rewrite Pregmap.gss. constructor; auto.
+ rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q.
+ auto. omega.
+ generalize (transf_function_no_overflow _ _ H0). omega.
+ intros. apply Pregmap.gso; auto.
+Qed.
+
+(** Existence of return addresses *)
+
+Lemma return_address_exists:
+ forall f sg ros c, is_tail (Mcall sg ros :: c) f.(Mach.fn_code) ->
+ exists ra, return_address_offset f c ra.
+Proof.
+ intros. eapply Asmgenproof0.return_address_exists; eauto.
+- intros. exploit transl_instr_label; eauto.
+ destruct i; try (intros [A B]; apply A). intros. subst c0. repeat constructor.
+- intros. monadInv H0.
+ destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. monadInv EQ.
+ rewrite transl_code'_transl_code in EQ0.
+ exists x; exists true; split; auto. unfold fn_code.
+ constructor. apply (storeptr_label X30 XSP (fn_retaddr_ofs f0) x).
+- exact transf_function_no_overflow.
+Qed.
+
+(** * Proof of semantic preservation *)
+
+(** Semantic preservation is proved using simulation diagrams
+ of the following form.
+<<
+ st1 --------------- st2
+ | |
+ t| *|t
+ | |
+ v v
+ st1'--------------- st2'
+>>
+ The invariant is the [match_states] predicate below, which includes:
+- The Asm code pointed by the PC register is the translation of
+ the current Mach code sequence.
+- Mach register values and Asm register values agree.
+*)
+
+Inductive match_states: Mach.state -> Asm.state -> Prop :=
+ | match_states_intro:
+ forall s fb sp c ep ms m m' rs f tf tc
+ (STACKS: match_stack ge s)
+ (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
+ (MEXT: Mem.extends m m')
+ (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc)
+ (AG: agree ms sp rs)
+ (DXP: ep = true -> rs#X29 = parent_sp s)
+ (LEAF: is_leaf_function f = true -> rs#RA = parent_ra s),
+ match_states (Mach.State s fb sp c ms m)
+ (Asm.State rs m')
+ | match_states_call:
+ forall s fb ms m m' rs
+ (STACKS: match_stack ge s)
+ (MEXT: Mem.extends m m')
+ (AG: agree ms (parent_sp s) rs)
+ (ATPC: rs PC = Vptr fb Ptrofs.zero)
+ (ATLR: rs RA = parent_ra s),
+ match_states (Mach.Callstate s fb ms m)
+ (Asm.State rs m')
+ | match_states_return:
+ forall s ms m m' rs
+ (STACKS: match_stack ge s)
+ (MEXT: Mem.extends m m')
+ (AG: agree ms (parent_sp s) rs)
+ (ATPC: rs PC = parent_ra s),
+ match_states (Mach.Returnstate s ms m)
+ (Asm.State rs m').
+
+Lemma exec_straight_steps:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2,
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists rs2,
+ exec_straight tge tf c rs1 m1' k rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ (it1_is_parent ep i = true -> rs2#X29 = parent_sp s)
+ /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c ms2 m2) st'.
+Proof.
+ intros. inversion H2. subst. monadInv H7.
+ exploit H3; eauto. intros [rs2 [A [B [C D]]]].
+ exists (State rs2 m2'); split.
+ - eapply exec_straight_exec; eauto.
+ - econstructor; eauto. eapply exec_straight_at; eauto.
+Qed.
+
+Lemma exec_straight_steps_goto:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ it1_is_parent ep i = false ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists jmp, exists k', exists rs2,
+ exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2'
+ /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c' ms2 m2) st'.
+Proof.
+ intros. inversion H3. subst. monadInv H9.
+ exploit H5; eauto. intros [jmp [k' [rs2 [A [B [C D]]]]]].
+ generalize (functions_transl _ _ _ H7 H8); intro FN.
+ generalize (transf_function_no_overflow _ _ H8); intro NOOV.
+ exploit exec_straight_steps_2; eauto.
+ intros [ofs' [PC2 CT2]].
+ exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ eapply plus_right'.
+ eapply exec_straight_steps_1; eauto.
+ econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ traceEq.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+ rewrite OTH by congruence; auto.
+Qed.
+
+Lemma exec_straight_opt_steps_goto:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ it1_is_parent ep i = false ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists jmp, exists k', exists rs2,
+ exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2'
+ /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c' ms2 m2) st'.
+Proof.
+ intros. inversion H3. subst. monadInv H9.
+ exploit H5; eauto. intros [jmp [k' [rs2 [A [B [C D]]]]]].
+ generalize (functions_transl _ _ _ H7 H8); intro FN.
+ generalize (transf_function_no_overflow _ _ H8); intro NOOV.
+ inv A.
+- exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ apply plus_one. econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+ rewrite OTH by congruence; auto.
+- exploit exec_straight_steps_2; eauto.
+ intros [ofs' [PC2 CT2]].
+ exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ eapply plus_right'.
+ eapply exec_straight_steps_1; eauto.
+ econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ traceEq.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+ rewrite OTH by congruence; auto.
+Qed.
+
+(** We need to show that, in the simulation diagram, we cannot
+ take infinitely many Mach transitions that correspond to zero
+ transitions on the Asm side. Actually, all Mach transitions
+ correspond to at least one Asm transition, except the
+ transition from [Machsem.Returnstate] to [Machsem.State].
+ So, the following integer measure will suffice to rule out
+ the unwanted behaviour. *)
+
+Definition measure (s: Mach.state) : nat :=
+ match s with
+ | Mach.State _ _ _ _ _ _ => 0%nat
+ | Mach.Callstate _ _ _ _ => 0%nat
+ | Mach.Returnstate _ _ _ => 1%nat
+ end.
+
+Remark preg_of_not_X29: forall r, negb (mreg_eq r R29) = true -> IR X29 <> preg_of r.
+Proof.
+ intros. change (IR X29) with (preg_of R29). red; intros.
+ exploit preg_of_injective; eauto. intros; subst r; discriminate.
+Qed.
+
+Lemma sp_val': forall ms sp rs, agree ms sp rs -> sp = rs XSP.
+Proof.
+ intros. eapply sp_val; eauto.
+Qed.
+
+(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *)
+
+Theorem step_simulation:
+ forall S1 t S2, Mach.step return_address_offset ge S1 t S2 ->
+ forall S1' (MS: match_states S1 S1') (WF: wf_state ge 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. }
+ split. { simpl; congruence. }
+ rewrite nextinstr_inv by congruence; assumption.
+
+- (* 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 S]]]].
+ exists rs'; split. eauto.
+ split. { eapply agree_set_mreg; eauto with asmgen. congruence. }
+ split. { simpl; congruence. }
+ rewrite S. assumption.
+
+- (* 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 R]]].
+ exists rs'; split. eauto.
+ split. eapply agree_undef_regs; eauto with asmgen.
+ simpl; intros.
+ split. rewrite Q; auto with asmgen.
+ rewrite R. assumption.
+
+- (* 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 S]]]].
+ exists rs1; split. eauto.
+ split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen.
+ simpl; split; intros.
+ { rewrite R; auto with asmgen.
+ apply preg_of_not_X29; auto.
+ }
+ { rewrite S; 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 V]]]].
+ 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.
+ split; simpl; intros. rewrite U; auto with asmgen.
+ apply preg_of_not_X29; auto.
+ rewrite V. rewrite R by congruence. 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 S]]]].
+ exists rs2; split. eauto. split.
+ apply agree_set_undef_mreg with rs0; auto.
+ apply Val.lessdef_trans with v'; auto.
+ split; simpl; intros. InvBooleans.
+ rewrite R; auto. apply preg_of_not_X29; auto.
+Local Transparent destroyed_by_op.
+ destruct op; try exact I; simpl; congruence.
+ rewrite S.
+ auto.
+- (* Mload *)
+ destruct trap.
+ {
+ 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 S]]]].
+ exists rs2; split. eauto.
+ split. eapply agree_set_undef_mreg; eauto. congruence.
+ split. simpl; congruence.
+ rewrite S. assumption.
+ }
+
+ (* Mload notrap1 *)
+ inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
+
+- (* Mload notrap *)
+ inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
+
+- (* Mload notrap *)
+ inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
+
+- (* 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 R]]].
+ exists rs2; split. eauto.
+ split. eapply agree_undef_regs; eauto with asmgen.
+ split. simpl; congruence.
+ rewrite R. assumption.
+
+- (* Mcall *)
+ assert (f0 = f) by congruence. subst f0.
+ inv AT.
+ assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned).
+ { eapply transf_function_no_overflow; eauto. }
+ destruct ros as [rf|fid]; simpl in H; monadInv H5.
++ (* Indirect call *)
+ assert (rs rf = Vptr f' Ptrofs.zero).
+ { destruct (rs rf); try discriminate.
+ revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. }
+ assert (rs0 x0 = Vptr f' Ptrofs.zero).
+ { exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. }
+ generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1.
+ assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x).
+ { econstructor; eauto. }
+ exploit return_address_offset_correct; eauto. intros; subst ra.
+ left; econstructor; split.
+ apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto.
+ eapply functions_transl; eauto. eapply find_instr_tail; eauto.
+ simpl. eauto.
+ econstructor; eauto.
+ econstructor; eauto.
+ eapply agree_sp_def; eauto.
+ simpl. eapply agree_exten; eauto. intros. Simpl.
+ Simpl. rewrite <- H2. auto.
++ (* Direct call *)
+ generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1.
+ assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x).
+ econstructor; eauto.
+ exploit return_address_offset_correct; eauto. intros; subst ra.
+ left; econstructor; split.
+ apply plus_one. eapply exec_step_internal. eauto.
+ eapply functions_transl; eauto. eapply find_instr_tail; eauto.
+ simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto.
+ econstructor; eauto.
+ econstructor; eauto.
+ eapply agree_sp_def; eauto.
+ simpl. eapply agree_exten; eauto. intros. Simpl.
+ Simpl. rewrite <- H2. auto.
+
+- (* Mtailcall *)
+ assert (f0 = f) by congruence. subst f0.
+ inversion AT; subst.
+ assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned).
+ { eapply transf_function_no_overflow; eauto. }
+ exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]].
+ destruct ros as [rf|fid]; simpl in H; monadInv H7.
++ (* Indirect call *)
+ assert (rs rf = Vptr f' Ptrofs.zero).
+ { destruct (rs rf); try discriminate.
+ revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. }
+ assert (rs0 x0 = Vptr f' Ptrofs.zero).
+ { exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. }
+ exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
+ exploit exec_straight_steps_2; eauto using functions_transl.
+ intros (ofs' & P & Q).
+ left; econstructor; split.
+ (* execution *)
+ eapply plus_right'. eapply exec_straight_exec; eauto.
+ econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q.
+ simpl. reflexivity.
+ traceEq.
+ (* match states *)
+ econstructor; eauto.
+ apply agree_set_other; auto with asmgen.
+ Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption.
++ (* Direct call *)
+ exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
+ exploit exec_straight_steps_2; eauto using functions_transl.
+ intros (ofs' & P & Q).
+ left; econstructor; split.
+ (* execution *)
+ eapply plus_right'. eapply exec_straight_exec; eauto.
+ econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q.
+ simpl. reflexivity.
+ traceEq.
+ (* match states *)
+ econstructor; eauto.
+ apply agree_set_other; auto with asmgen.
+ Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto.
+
+- (* Mbuiltin *)
+ inv AT. monadInv H4.
+ exploit functions_transl; eauto. intro FN.
+ generalize (transf_function_no_overflow _ _ H3); intro NOOV.
+ exploit builtin_args_match; eauto. intros [vargs' [P Q]].
+ exploit external_call_mem_extends; eauto.
+ intros [vres' [m2' [A [B [C D]]]]].
+ left. econstructor; split. apply plus_one.
+ eapply exec_step_builtin. eauto. eauto.
+ eapply find_instr_tail; eauto.
+ erewrite <- sp_val by eauto.
+ eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved.
+ eapply external_call_symbols_preserved; eauto. apply senv_preserved.
+ eauto.
+ econstructor; eauto.
+ instantiate (2 := tf); instantiate (1 := x).
+ unfold nextinstr. rewrite Pregmap.gss.
+ rewrite set_res_other. rewrite undef_regs_other_2.
+ rewrite <- H1. simpl. econstructor; eauto.
+ eapply code_tail_next_int; eauto.
+ rewrite preg_notin_charact. intros. auto with asmgen.
+ auto with asmgen.
+ apply agree_nextinstr. eapply agree_set_res; auto.
+ eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto.
+ congruence.
+
+ Simpl.
+ rewrite set_res_other by trivial.
+ rewrite undef_regs_other.
+ assumption.
+ intro.
+ rewrite in_map_iff.
+ intros (x0 & PREG & IN).
+ subst r'.
+ intro.
+ apply (preg_of_not_RA x0).
+ 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.
+
+ rewrite INV by congruence.
+ assumption.
+
+- (* 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 & D).
+ exists jmp; exists k; exists rs'.
+ split. eexact A.
+ split. apply agree_exten with rs0; auto with asmgen.
+ split.
+ exact B.
+ rewrite D. exact LEAF.
+
+- (* 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 & D).
+ 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.
+ split.
+ simpl; congruence.
+ Simpl. rewrite D.
+ exact LEAF.
+
+- (* Mjumptable *)
+ assert (f0 = f) by congruence. subst f0.
+ inv AT. monadInv H6.
+ exploit functions_transl; eauto. intro FN.
+ generalize (transf_function_no_overflow _ _ H5); intro NOOV.
+ exploit find_label_goto_label. eauto. eauto.
+ instantiate (2 := rs0#X16 <- Vundef #X17 <- Vundef).
+ Simpl. eauto.
+ eauto.
+ intros [tc' [rs' [A [B C]]]].
+ exploit ireg_val; eauto. rewrite H. intros LD; inv LD.
+ left; econstructor; split.
+ apply plus_one. econstructor; eauto.
+ eapply find_instr_tail; eauto.
+ simpl. Simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A.
+ econstructor; eauto.
+ eapply agree_undef_regs; eauto.
+ simpl. intros. rewrite C; auto with asmgen. Simpl.
+ congruence.
+
+ rewrite C by congruence.
+ repeat rewrite Pregmap.gso by congruence.
+ assumption.
+
+- (* 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 & W).
+ assert (EXEC_PROLOGUE:
+ exec_straight tge tf
+ tf.(fn_code) rs0 m'
+ x0 rs3 m3').
+ { change (fn_code tf) with tfbody; unfold tfbody.
+ apply exec_straight_step with rs2 m2'.
+ unfold exec_instr. rewrite C. fold sp.
+ rewrite <- (sp_val _ _ _ AG). rewrite F. reflexivity.
+ reflexivity.
+ eexact U. }
+ exploit exec_straight_steps_2; eauto using functions_transl. omega. constructor.
+ intros (ofs' & X & Y).
+ left; exists (State rs3 m3'); split.
+ eapply exec_straight_steps_1; eauto. omega. constructor.
+ econstructor; eauto.
+ rewrite X; econstructor; eauto.
+ apply agree_exten with rs2; eauto with asmgen.
+ unfold rs2.
+ apply agree_nextinstr. apply agree_set_other; auto with asmgen.
+ apply agree_change_sp with (parent_sp s).
+ apply agree_undef_regs with rs0. auto.
+Local Transparent destroyed_at_function_entry. simpl.
+ simpl; intros; Simpl.
+ unfold sp; congruence.
+ intros. rewrite V by auto with asmgen. reflexivity.
+
+ rewrite W.
+ unfold rs2.
+ Simpl.
+
+- (* external function *)
+ exploit functions_translated; eauto.
+ intros [tf [A B]]. simpl in B. inv B.
+ exploit extcall_arguments_match; eauto.
+ intros [args' [C D]].
+ exploit external_call_mem_extends; eauto.
+ intros [res' [m2' [P [Q [R S]]]]].
+ left; econstructor; split.
+ apply plus_one. eapply exec_step_external; eauto.
+ eapply external_call_symbols_preserved; eauto. apply senv_preserved.
+ econstructor; eauto.
+ unfold loc_external_result. apply agree_set_other; auto. apply agree_set_pair; auto.
+ apply agree_undef_caller_save_regs; auto.
+
+- (* return *)
+ inv STACKS. simpl in *.
+ right. split. omega. split. auto.
+ rewrite <- ATPC in H5.
+ econstructor; eauto. congruence.
+ inv WF.
+ inv STACK.
+ inv H1.
+ congruence.
+Qed.
+
+Lemma transf_initial_states:
+ forall st1, Mach.initial_state prog st1 ->
+ exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2.
+Proof.
+ intros. inversion H. unfold ge0 in *.
+ econstructor; split.
+ econstructor.
+ eapply (Genv.init_mem_transf_partial TRANSF); eauto.
+ replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero)
+ with (Vptr fb Ptrofs.zero).
+ econstructor; eauto.
+ constructor.
+ apply Mem.extends_refl.
+ split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence.
+ intros. rewrite Regmap.gi. auto.
+ unfold Genv.symbol_address.
+ rewrite (match_program_main TRANSF).
+ rewrite symbols_preserved.
+ unfold ge; rewrite H1. auto.
+Qed.
+
+Lemma transf_final_states:
+ forall st1 st2 r,
+ match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r.
+Proof.
+ intros. inv H0. inv H. constructor. assumption.
+ compute in H1. inv H1.
+ generalize (preg_val _ _ _ R0 AG). rewrite H2. intros LD; inv LD. auto.
+Qed.
+
+Theorem transf_program_correct:
+ forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog).
+Proof.
+ eapply forward_simulation_star with (measure := measure)
+ (match_states := fun S1 S2 => match_states S1 S2 /\ wf_state ge S1).
+ - apply senv_preserved.
+ - simpl; intros. exploit transf_initial_states; eauto.
+ intros (s2 & A & B).
+ exists s2; intuition auto. apply wf_initial; auto.
+ - simpl; intros. destruct H as [MS WF]. eapply transf_final_states; eauto.
+ - simpl; intros. destruct H0 as [MS WF].
+ exploit step_simulation; eauto. intros [ (s2' & A & B) | (A & B & C) ].
+ + left; exists s2'; intuition auto. eapply wf_step; eauto.
+ + right; intuition auto. eapply wf_step; eauto.
+Qed.
+
+End PRESERVATION.
+*) \ No newline at end of file
diff --git a/aarch64/Asmgenproof1.v b/aarch64/Asmblockgenproof1.v
index 0e36bd05..b42309bc 100644
--- a/aarch64/Asmgenproof1.v
+++ b/aarch64/Asmblockgenproof1.v
@@ -1,3 +1,5 @@
+(* ORIGINAL aarch64/Asmgenproof1 file that needs to be adapted
+
(* *********************************************************************)
(* *)
(* The Compcert verified compiler *)
@@ -2136,3 +2138,4 @@ Proof.
Qed.
End CONSTRUCTORS.
+*) \ No newline at end of file
diff --git a/aarch64/Asmgen.v b/aarch64/Asmgen.v
index 024c9a17..f81f37d6 100644
--- a/aarch64/Asmgen.v
+++ b/aarch64/Asmgen.v
@@ -1,1172 +1,33 @@
-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Xavier Leroy, Collège de France and INRIA Paris *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-(** Translation from Mach to AArch64. *)
+(* *************************************************************)
+(* *)
+(* 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 *)
+(* *)
+(* 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.
-Require Import Locations Mach Asm.
-
-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).
-
-(** Arithmetic immediates are 12-bit unsigned numbers, possibly shifted left 12 bits *)
-
-Definition is_arith_imm32 (x: int) : bool :=
- Int.eq x (Int.zero_ext 12 x)
- || Int.eq x (Int.shl (Int.zero_ext 12 (Int.shru x (Int.repr 12))) (Int.repr 12)).
-
-Definition is_arith_imm64 (x: int64) : bool :=
- Int64.eq x (Int64.zero_ext 12 x)
- || Int64.eq x (Int64.shl (Int64.zero_ext 12 (Int64.shru x (Int64.repr 12))) (Int64.repr 12)).
-
-(** Decompose integer literals into 16-bit fragments *)
-
-Fixpoint decompose_int (N: nat) (n p: Z) {struct N} : list (Z * Z) :=
- match N with
- | Datatypes.O => nil
- | Datatypes.S N =>
- let frag := Zzero_ext 16 (Z.shiftr n p) in
- if Z.eqb frag 0 then
- decompose_int N n (p + 16)
- else
- (frag, p) :: decompose_int N (Z.ldiff n (Z.shiftl 65535 p)) (p + 16)
- end.
-
-Definition negate_decomposition (l: list (Z * Z)) :=
- List.map (fun np => (Z.lxor (fst np) 65535, snd np)) l.
-
-Definition loadimm_k (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
- List.fold_right (fun np k => Pmovk sz rd (fst np) (snd np) :: k) k l.
-
-Definition loadimm_z (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
- match l with
- | nil => Pmovz sz rd 0 0 :: k
- | (n1, p1) :: l => Pmovz sz rd n1 p1 :: loadimm_k sz rd l k
- end.
-
-Definition loadimm_n (sz: isize) (rd: ireg) (l: list (Z * Z)) (k: code) : code :=
- match l with
- | nil => Pmovn sz rd 0 0 :: k
- | (n1, p1) :: l => Pmovn sz rd n1 p1 :: loadimm_k sz rd (negate_decomposition l) k
- end.
-
-Definition loadimm (sz: isize) (rd: ireg) (n: Z) (k: code) : code :=
- let N := match sz with W => 2%nat | X => 4%nat end in
- let dz := decompose_int N n 0 in
- let dn := decompose_int N (Z.lnot n) 0 in
- if Nat.leb (List.length dz) (List.length dn)
- then loadimm_z sz rd dz k
- else loadimm_n sz rd dn k.
-
-Definition loadimm32 (rd: ireg) (n: int) (k: code) : code :=
- if is_logical_imm32 n
- then Porrimm W rd XZR (Int.unsigned n) :: k
- else loadimm W rd (Int.unsigned n) k.
-
-Definition loadimm64 (rd: ireg) (n: int64) (k: code) : code :=
- if is_logical_imm64 n
- then Porrimm X rd XZR (Int64.unsigned n) :: k
- else loadimm X rd (Int64.unsigned n) k.
-
-(** Add immediate *)
-
-Definition addimm_aux (insn: iregsp -> iregsp -> Z -> instruction)
- (rd r1: iregsp) (n: Z) (k: code) :=
- let nlo := Zzero_ext 12 n in
- let nhi := n - nlo in
- if Z.eqb nhi 0 then
- insn rd r1 nlo :: k
- else if Z.eqb nlo 0 then
- insn rd r1 nhi :: k
- else
- insn rd r1 nhi :: insn rd rd nlo :: k.
-
-Definition addimm32 (rd r1: ireg) (n: int) (k: code) : code :=
- let m := Int.neg n in
- if Int.eq n (Int.zero_ext 24 n) then
- addimm_aux (Paddimm W) rd r1 (Int.unsigned n) k
- else if Int.eq m (Int.zero_ext 24 m) then
- addimm_aux (Psubimm W) rd r1 (Int.unsigned m) k
- else if Int.lt n Int.zero then
- loadimm32 X16 m (Psub W rd r1 X16 SOnone :: k)
- else
- loadimm32 X16 n (Padd W rd r1 X16 SOnone :: k).
-
-Definition addimm64 (rd r1: iregsp) (n: int64) (k: code) : code :=
- let m := Int64.neg n in
- if Int64.eq n (Int64.zero_ext 24 n) then
- addimm_aux (Paddimm X) rd r1 (Int64.unsigned n) k
- else if Int64.eq m (Int64.zero_ext 24 m) then
- addimm_aux (Psubimm X) rd r1 (Int64.unsigned m) k
- else if Int64.lt n Int64.zero then
- loadimm64 X16 m (Psubext rd r1 X16 (EOuxtx Int.zero) :: k)
- else
- loadimm64 X16 n (Paddext rd r1 X16 (EOuxtx Int.zero) :: k).
-
-(** Logical immediate *)
-
-Definition logicalimm32
- (insn1: ireg -> ireg0 -> Z -> instruction)
- (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction)
- (rd r1: ireg) (n: int) (k: code) : code :=
- if is_logical_imm32 n
- then insn1 rd r1 (Int.unsigned n) :: k
- else loadimm32 X16 n (insn2 rd r1 X16 SOnone :: k).
-
-Definition logicalimm64
- (insn1: ireg -> ireg0 -> Z -> instruction)
- (insn2: ireg -> ireg0 -> ireg -> shift_op -> instruction)
- (rd r1: ireg) (n: int64) (k: code) : code :=
- if is_logical_imm64 n
- then insn1 rd r1 (Int64.unsigned n) :: k
- else loadimm64 X16 n (insn2 rd r1 X16 SOnone :: k).
-
-(** Sign- or zero-extended arithmetic *)
-
-Definition transl_extension (ex: extension) (a: int) : extend_op :=
- match ex with Xsgn32 => EOsxtw a | Xuns32 => EOuxtw a end.
-
-Definition move_extended_base
- (rd: ireg) (r1: ireg) (ex: extension) (k: code) : code :=
- match ex with
- | Xsgn32 => Pcvtsw2x rd r1 :: k
- | Xuns32 => Pcvtuw2x rd r1 :: k
- end.
-
-Definition move_extended
- (rd: ireg) (r1: ireg) (ex: extension) (a: int) (k: code) : code :=
- if Int.eq a Int.zero then
- move_extended_base rd r1 ex k
- else
- move_extended_base rd r1 ex (Padd X rd XZR rd (SOlsl a) :: k).
-
-Definition arith_extended
- (insnX: iregsp -> iregsp -> ireg -> extend_op -> instruction)
- (insnS: ireg -> ireg0 -> ireg -> shift_op -> instruction)
- (rd r1 r2: ireg) (ex: extension) (a: int) (k: code) : code :=
- if Int.ltu a (Int.repr 5) then
- insnX rd r1 r2 (transl_extension ex a) :: k
- else
- move_extended_base X16 r2 ex (insnS rd r1 X16 (SOlsl a) :: k).
-
-(** Extended right shift *)
-
-Definition shrx32 (rd r1: ireg) (n: int) (k: code) : code :=
- if Int.eq n Int.zero then
- Pmov rd r1 :: k
- else if Int.eq n Int.one then
- Padd W X16 r1 r1 (SOlsr (Int.repr 31)) ::
- Porr W rd XZR X16 (SOasr n) :: 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 if Int.eq n Int.one then
- Padd X X16 r1 r1 (SOlsr (Int.repr 63)) ::
- Porr X rd XZR X16 (SOasr n) :: k
- else
- Porr X X16 XZR r1 (SOasr (Int.repr 63)) ::
- Padd X X16 r1 X16 (SOlsr (Int.sub Int64.iwordsize' n)) ::
- Porr X rd XZR X16 (SOasr n) :: k.
-
-(** Load the address [id + ofs] in [rd] *)
-
-Definition loadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (k: code) : code :=
- if Archi.pic_code tt then
- if Ptrofs.eq ofs Ptrofs.zero then
- Ploadsymbol rd id :: k
- else
- Ploadsymbol rd id :: addimm64 rd rd (Ptrofs.to_int64 ofs) k
- else
- Padrp rd id ofs :: Paddadr rd rd id ofs :: k.
-
-(** Translate a shifted operand *)
-
-Definition transl_shift (s: Op.shift) (a: int): Asm.shift_op :=
- match s with
- | Slsl => SOlsl a
- | Slsr => SOlsr a
- | Sasr => SOasr a
- | Sror => SOror a
- end.
-
-(** Translation of a condition. Prepends to [k] the instructions
- that evaluate the condition and leave its boolean result in one of
- the bits of the condition register. The bit in question is
- determined by the [crbit_for_cond] function. *)
-
-Definition transl_cond
- (cond: condition) (args: list mreg) (k: code) :=
- match cond, args with
- | (Ccomp c | Ccompu c), a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pcmp W r1 r2 SOnone :: k)
- | (Ccompshift c s a | Ccompushift c s a), a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pcmp W r1 r2 (transl_shift s a) :: k)
- | (Ccompimm c n | Ccompuimm c n), a1 :: nil =>
- do r1 <- ireg_of a1;
- OK (if is_arith_imm32 n then
- Pcmpimm W r1 (Int.unsigned n) :: k
- else if is_arith_imm32 (Int.neg n) then
- Pcmnimm W r1 (Int.unsigned (Int.neg n)) :: k
- else
- loadimm32 X16 n (Pcmp W r1 X16 SOnone :: k))
- | (Cmaskzero n | Cmasknotzero n), a1 :: nil =>
- do r1 <- ireg_of a1;
- OK (if is_logical_imm32 n then
- Ptstimm W r1 (Int.unsigned n) :: k
- else
- loadimm32 X16 n (Ptst W r1 X16 SOnone :: k))
- | (Ccompl c | Ccomplu c), a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pcmp X r1 r2 SOnone :: k)
- | (Ccomplshift c s a | Ccomplushift c s a), a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pcmp X r1 r2 (transl_shift s a) :: k)
- | (Ccomplimm c n | Ccompluimm c n), a1 :: nil =>
- do r1 <- ireg_of a1;
- OK (if is_arith_imm64 n then
- Pcmpimm X r1 (Int64.unsigned n) :: k
- else if is_arith_imm64 (Int64.neg n) then
- Pcmnimm X r1 (Int64.unsigned (Int64.neg n)) :: k
- else
- loadimm64 X16 n (Pcmp X r1 X16 SOnone :: k))
- | (Cmasklzero n | Cmasklnotzero n), a1 :: nil =>
- do r1 <- ireg_of a1;
- OK (if is_logical_imm64 n then
- Ptstimm X r1 (Int64.unsigned n) :: k
- else
- loadimm64 X16 n (Ptst X r1 X16 SOnone :: k))
- | Ccompf cmp, a1 :: a2 :: nil =>
- do r1 <- freg_of a1; do r2 <- freg_of a2;
- OK (Pfcmp D r1 r2 :: k)
- | Cnotcompf cmp, a1 :: a2 :: nil =>
- do r1 <- freg_of a1; do r2 <- freg_of a2;
- OK (Pfcmp D r1 r2 :: k)
- | Ccompfzero cmp, a1 :: nil =>
- do r1 <- freg_of a1;
- OK (Pfcmp0 D r1 :: k)
- | Cnotcompfzero cmp, a1 :: nil =>
- do r1 <- freg_of a1;
- OK (Pfcmp0 D r1 :: k)
- | Ccompfs cmp, a1 :: a2 :: nil =>
- do r1 <- freg_of a1; do r2 <- freg_of a2;
- OK (Pfcmp S r1 r2 :: k)
- | Cnotcompfs cmp, a1 :: a2 :: nil =>
- do r1 <- freg_of a1; do r2 <- freg_of a2;
- OK (Pfcmp S r1 r2 :: k)
- | Ccompfszero cmp, a1 :: nil =>
- do r1 <- freg_of a1;
- OK (Pfcmp0 S r1 :: k)
- | Cnotcompfszero cmp, a1 :: nil =>
- do r1 <- freg_of a1;
- OK (Pfcmp0 S r1 :: k)
- | _, _ =>
- Error(msg "Asmgen.transl_cond")
- end.
-
-Definition cond_for_signed_cmp (cmp: comparison) :=
- match cmp with
- | Ceq => TCeq
- | Cne => TCne
- | Clt => TClt
- | Cle => TCle
- | Cgt => TCgt
- | Cge => TCge
- end.
-
-Definition cond_for_unsigned_cmp (cmp: comparison) :=
- match cmp with
- | Ceq => TCeq
- | Cne => TCne
- | Clt => TClo
- | Cle => TCls
- | Cgt => TChi
- | Cge => TChs
- end.
-
-Definition cond_for_float_cmp (cmp: comparison) :=
- match cmp with
- | Ceq => TCeq
- | Cne => TCne
- | Clt => TCmi
- | Cle => TCls
- | Cgt => TCgt
- | Cge => TCge
- end.
-
-Definition cond_for_float_not_cmp (cmp: comparison) :=
- match cmp with
- | Ceq => TCne
- | Cne => TCeq
- | Clt => TCpl
- | Cle => TChi
- | Cgt => TCle
- | Cge => TClt
- end.
-
-Definition cond_for_cond (cond: condition) :=
- match cond with
- | Ccomp cmp => cond_for_signed_cmp cmp
- | Ccompu cmp => cond_for_unsigned_cmp cmp
- | Ccompshift cmp s a => cond_for_signed_cmp cmp
- | Ccompushift cmp s a => cond_for_unsigned_cmp cmp
- | Ccompimm cmp n => cond_for_signed_cmp cmp
- | Ccompuimm cmp n => cond_for_unsigned_cmp cmp
- | Cmaskzero n => TCeq
- | Cmasknotzero n => TCne
- | Ccompl cmp => cond_for_signed_cmp cmp
- | Ccomplu cmp => cond_for_unsigned_cmp cmp
- | Ccomplshift cmp s a => cond_for_signed_cmp cmp
- | Ccomplushift cmp s a => cond_for_unsigned_cmp cmp
- | Ccomplimm cmp n => cond_for_signed_cmp cmp
- | Ccompluimm cmp n => cond_for_unsigned_cmp cmp
- | Cmasklzero n => TCeq
- | Cmasklnotzero n => TCne
- | Ccompf cmp => cond_for_float_cmp cmp
- | Cnotcompf cmp => cond_for_float_not_cmp cmp
- | Ccompfzero cmp => cond_for_float_cmp cmp
- | Cnotcompfzero cmp => cond_for_float_not_cmp cmp
- | Ccompfs cmp => cond_for_float_cmp cmp
- | Cnotcompfs cmp => cond_for_float_not_cmp cmp
- | Ccompfszero cmp => cond_for_float_cmp cmp
- | Cnotcompfszero cmp => cond_for_float_not_cmp cmp
- end.
-
-(** Translation of a conditional branch. Prepends to [k] the instructions
- that evaluate the condition and ranch to [lbl] if it holds.
- We recognize some conditional branches that can be implemented
- without setting then testing condition flags. *)
-
-Definition transl_cond_branch_default
- (c: condition) (args: list mreg) (lbl: label) (k: code) :=
- transl_cond c args (Pbc (cond_for_cond c) lbl :: k).
-
-Definition transl_cond_branch
- (c: condition) (args: list mreg) (lbl: label) (k: code) :=
- match args, c with
- | a1 :: nil, (Ccompimm Cne n | Ccompuimm Cne n) =>
- if Int.eq n Int.zero
- then (do r1 <- ireg_of a1; OK (Pcbnz W r1 lbl :: k))
- else transl_cond_branch_default c args lbl k
- | a1 :: nil, (Ccompimm Ceq n | Ccompuimm Ceq n) =>
- if Int.eq n Int.zero
- then (do r1 <- ireg_of a1; OK (Pcbz W r1 lbl :: k))
- else transl_cond_branch_default c args lbl k
- | a1 :: nil, (Ccomplimm Cne n | Ccompluimm Cne n) =>
- if Int64.eq n Int64.zero
- then (do r1 <- ireg_of a1; OK (Pcbnz X r1 lbl :: k))
- else transl_cond_branch_default c args lbl k
- | a1 :: nil, (Ccomplimm Ceq n | Ccompluimm Ceq n) =>
- if Int64.eq n Int64.zero
- then (do r1 <- ireg_of a1; OK (Pcbz X r1 lbl :: k))
- else transl_cond_branch_default c args lbl k
- | a1 :: nil, Cmaskzero n =>
- match Int.is_power2 n with
- | Some bit => do r1 <- ireg_of a1; OK (Ptbz W r1 bit lbl :: k)
- | None => transl_cond_branch_default c args lbl k
- end
- | a1 :: nil, Cmasknotzero n =>
- match Int.is_power2 n with
- | Some bit => do r1 <- ireg_of a1; OK (Ptbnz W r1 bit lbl :: k)
- | None => transl_cond_branch_default c args lbl k
- end
- | a1 :: nil, Cmasklzero n =>
- match Int64.is_power2' n with
- | Some bit => do r1 <- ireg_of a1; OK (Ptbz X r1 bit lbl :: k)
- | None => transl_cond_branch_default c args lbl k
- end
- | a1 :: nil, Cmasklnotzero n =>
- match Int64.is_power2' n with
- | Some bit => do r1 <- ireg_of a1; OK (Ptbnz X r1 bit lbl :: k)
- | None => transl_cond_branch_default c args lbl k
- end
- | _, _ =>
- transl_cond_branch_default c args lbl k
- end.
-
-(** Translation of the arithmetic operation [res <- op(args)].
- The corresponding instructions are prepended to [k]. *)
-
-Definition transl_op
- (op: operation) (args: list mreg) (res: mreg) (k: code) :=
- match op, args with
- | Omove, a1 :: nil =>
- match preg_of res, preg_of a1 with
- | IR r, IR a => OK (Pmov r a :: k)
- | FR r, FR a => OK (Pfmov r a :: k)
- | _ , _ => Error(msg "Asmgen.Omove")
- end
- | Ointconst n, nil =>
- do rd <- ireg_of res;
- OK (loadimm32 rd n k)
- | Olongconst n, nil =>
- do rd <- ireg_of res;
- OK (loadimm64 rd n k)
- | Ofloatconst f, nil =>
- do rd <- freg_of res;
- OK (if Float.eq_dec f Float.zero
- then Pfmovi D rd XZR :: k
- else Pfmovimmd rd f :: k)
- | Osingleconst f, nil =>
- do rd <- freg_of res;
- OK (if Float32.eq_dec f Float32.zero
- then Pfmovi S rd XZR :: k
- else Pfmovimms rd f :: k)
- | Oaddrsymbol id ofs, nil =>
- do rd <- ireg_of res;
- OK (loadsymbol rd id ofs k)
- | Oaddrstack ofs, nil =>
- do rd <- ireg_of res;
- OK (addimm64 rd XSP (Ptrofs.to_int64 ofs) k)
-(** 32-bit integer arithmetic *)
- | Oshift s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porr W rd XZR r1 (transl_shift s a) :: k)
- | Oadd, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Padd W rd r1 r2 SOnone :: k)
- | Oaddshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Padd W rd r1 r2 (transl_shift s a) :: k)
- | Oaddimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (addimm32 rd r1 n k)
- | Oneg, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psub W rd XZR r1 SOnone :: k)
- | Onegshift s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psub W rd XZR r1 (transl_shift s a) :: k)
- | Osub, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psub W rd r1 r2 SOnone :: k)
- | Osubshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psub W rd r1 r2 (transl_shift s a) :: k)
- | Omul, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pmadd W rd r1 r2 XZR :: k)
- | Omuladd, a1 :: a2 :: a3 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
- OK (Pmadd W rd r2 r3 r1 :: k)
- | Omulsub, a1 :: a2 :: a3 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
- OK (Pmsub W rd r2 r3 r1 :: k)
- | Odiv, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psdiv W rd r1 r2 :: k)
- | Odivu, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pudiv W rd r1 r2 :: k)
- | Oand, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pand W rd r1 r2 SOnone :: k)
- | Oandshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pand W rd r1 r2 (transl_shift s a) :: k)
- | Oandimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm32 (Pandimm W) (Pand W) rd r1 n k)
- | Oor, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porr W rd r1 r2 SOnone :: k)
- | Oorshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porr W rd r1 r2 (transl_shift s a) :: k)
- | Oorimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm32 (Porrimm W) (Porr W) rd r1 n k)
- | Oxor, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peor W rd r1 r2 SOnone :: k)
- | Oxorshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peor W rd r1 r2 (transl_shift s a) :: k)
- | Oxorimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm32 (Peorimm W) (Peor W) rd r1 n k)
- | Onot, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porn W rd XZR r1 SOnone :: k)
- | Onotshift s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porn W rd XZR r1 (transl_shift s a) :: k)
- | Obic, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pbic W rd r1 r2 SOnone :: k)
- | Obicshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pbic W rd r1 r2 (transl_shift s a) :: k)
- | Oorn, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porn W rd r1 r2 SOnone :: k)
- | Oornshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porn W rd r1 r2 (transl_shift s a) :: k)
- | Oeqv, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peon W rd r1 r2 SOnone :: k)
- | Oeqvshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peon W rd r1 r2 (transl_shift s a) :: k)
- | Oshl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Plslv W rd r1 r2 :: k)
- | Oshr, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pasrv W rd r1 r2 :: k)
- | Oshru, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Plsrv W rd r1 r2 :: k)
- | Oshrximm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (shrx32 rd r1 n k)
- | Ozext s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfiz W rd r1 Int.zero s :: k)
- | Osext s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfiz W rd r1 Int.zero s :: k)
- | Oshlzext s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
- | Oshlsext s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfiz W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
- | Ozextshr a s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
- | Osextshr a s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfx W rd r1 a (Z.min s (Int.zwordsize - Int.unsigned a)) :: k)
-(** 64-bit integer arithmetic *)
- | Oshiftl s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porr X rd XZR r1 (transl_shift s a) :: k)
- | Oextend x a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (move_extended rd r1 x a k)
- (* [Omakelong] and [Ohighlong] should not occur *)
- | Olowlong, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- assertion (ireg_eq rd r1);
- OK (Pcvtx2w rd :: k)
- | Oaddl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Padd X rd r1 r2 SOnone :: k)
- | Oaddlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Padd X rd r1 r2 (transl_shift s a) :: k)
- | Oaddlext x a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (arith_extended Paddext (Padd X) rd r1 r2 x a k)
- | Oaddlimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (addimm64 rd r1 n k)
- | Onegl, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psub X rd XZR r1 SOnone :: k)
- | Oneglshift s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psub X rd XZR r1 (transl_shift s a) :: k)
- | Osubl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psub X rd r1 r2 SOnone :: k)
- | Osublshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psub X rd r1 r2 (transl_shift s a) :: k)
- | Osublext x a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (arith_extended Psubext (Psub X) rd r1 r2 x a k)
- | Omull, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pmadd X rd r1 r2 XZR :: k)
- | Omulladd, a1 :: a2 :: a3 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
- OK (Pmadd X rd r2 r3 r1 :: k)
- | Omullsub, a1 :: a2 :: a3 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2; do r3 <- ireg_of a3;
- OK (Pmsub X rd r2 r3 r1 :: k)
- | Omullhs, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psmulh rd r1 r2 :: k)
- | Omullhu, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pumulh rd r1 r2 :: k)
- | Odivl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Psdiv X rd r1 r2 :: k)
- | Odivlu, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pudiv X rd r1 r2 :: k)
- | Oandl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pand X rd r1 r2 SOnone :: k)
- | Oandlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pand X rd r1 r2 (transl_shift s a) :: k)
- | Oandlimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm64 (Pandimm X) (Pand X) rd r1 n k)
- | Oorl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porr X rd r1 r2 SOnone :: k)
- | Oorlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porr X rd r1 r2 (transl_shift s a) :: k)
- | Oorlimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm64 (Porrimm X) (Porr X) rd r1 n k)
- | Oxorl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peor X rd r1 r2 SOnone :: k)
- | Oxorlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peor X rd r1 r2 (transl_shift s a) :: k)
- | Oxorlimm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (logicalimm64 (Peorimm X) (Peor X) rd r1 n k)
- | Onotl, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porn X rd XZR r1 SOnone :: k)
- | Onotlshift s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Porn X rd XZR r1 (transl_shift s a) :: k)
- | Obicl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pbic X rd r1 r2 SOnone :: k)
- | Obiclshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pbic X rd r1 r2 (transl_shift s a) :: k)
- | Oornl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porn X rd r1 r2 SOnone :: k)
- | Oornlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Porn X rd r1 r2 (transl_shift s a) :: k)
- | Oeqvl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peon X rd r1 r2 SOnone :: k)
- | Oeqvlshift s a, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Peon X rd r1 r2 (transl_shift s a) :: k)
- | Oshll, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Plslv X rd r1 r2 :: k)
- | Oshrl, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Pasrv X rd r1 r2 :: k)
- | Oshrlu, a1 :: a2 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (Plsrv X rd r1 r2 :: k)
- | Oshrlximm n, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (shrx64 rd r1 n k)
- | Ozextl s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfiz X rd r1 Int.zero s :: k)
- | Osextl s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfiz X rd r1 Int.zero s :: k)
- | Oshllzext s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
- | Oshllsext s a, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfiz X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
- | Ozextshrl a s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Pubfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
- | Osextshrl a s, a1 :: nil =>
- do rd <- ireg_of res; do r1 <- ireg_of a1;
- OK (Psbfx X rd r1 a (Z.min s (Int64.zwordsize - Int.unsigned a)) :: k)
-(** 64-bit floating-point arithmetic *)
- | Onegf, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfneg D rd rs :: k)
- | Oabsf, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfabs D rd rs :: k)
- | Oaddf, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfadd D rd rs1 rs2 :: k)
- | Osubf, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfsub D rd rs1 rs2 :: k)
- | Omulf, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfmul D rd rs1 rs2 :: k)
- | Odivf, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfdiv D rd rs1 rs2 :: k)
-(** 32-bit floating-point arithmetic *)
- | Onegfs, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfneg S rd rs :: k)
- | Oabsfs, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfabs S rd rs :: k)
- | Oaddfs, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfadd S rd rs1 rs2 :: k)
- | Osubfs, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfsub S rd rs1 rs2 :: k)
- | Omulfs, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfmul S rd rs1 rs2 :: k)
- | Odivfs, a1 :: a2 :: nil =>
- do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2;
- OK (Pfdiv S rd rs1 rs2 :: k)
- | Osingleoffloat, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfcvtsd rd rs :: k)
- | Ofloatofsingle, a1 :: nil =>
- do rd <- freg_of res; do rs <- freg_of a1;
- OK (Pfcvtds rd rs :: k)
-(** Conversions between int and float *)
- | Ointoffloat, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzs W D rd rs :: k)
- | Ointuoffloat, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzu W D rd rs :: k)
- | Ofloatofint, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pscvtf D W rd rs :: k)
- | Ofloatofintu, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pucvtf D W rd rs :: k)
- | Ointofsingle, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzs W S rd rs :: k)
- | Ointuofsingle, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzu W S rd rs :: k)
- | Osingleofint, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pscvtf S W rd rs :: k)
- | Osingleofintu, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pucvtf S W rd rs :: k)
- | Olongoffloat, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzs X D rd rs :: k)
- | Olonguoffloat, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzu X D rd rs :: k)
- | Ofloatoflong, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pscvtf D X rd rs :: k)
- | Ofloatoflongu, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pucvtf D X rd rs :: k)
- | Olongofsingle, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzs X S rd rs :: k)
- | Olonguofsingle, a1 :: nil =>
- do rd <- ireg_of res; do rs <- freg_of a1;
- OK (Pfcvtzu X S rd rs :: k)
- | Osingleoflong, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pscvtf S X rd rs :: k)
- | Osingleoflongu, a1 :: nil =>
- do rd <- freg_of res; do rs <- ireg_of a1;
- OK (Pucvtf S X rd rs :: k)
-(** Boolean tests *)
- | Ocmp c, _ =>
- do rd <- ireg_of res;
- transl_cond c args (Pcset rd (cond_for_cond c) :: k)
-(** Conditional move *)
- | Osel cmp ty, a1 :: a2 :: args =>
- match preg_of res with
- | IR r =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- transl_cond cmp args (Pcsel r r1 r2 (cond_for_cond cmp) :: k)
- | FR r =>
- do r1 <- freg_of a1; do r2 <- freg_of a2;
- transl_cond cmp args (Pfsel r r1 r2 (cond_for_cond cmp) :: k)
- | _ =>
- Error(msg "Asmgen.Osel")
- end
- | _, _ =>
- Error(msg "Asmgen.transl_op")
- end.
-
-(** Translation of addressing modes *)
-
-Definition offset_representable (sz: Z) (ofs: int64) : bool :=
- let isz := Int64.repr sz in
- (** either unscaled 9-bit signed *)
- Int64.eq ofs (Int64.sign_ext 9 ofs) ||
- (** or scaled 12-bit unsigned *)
- (Int64.eq (Int64.modu ofs isz) Int64.zero
- && Int64.ltu ofs (Int64.shl isz (Int64.repr 12))).
-
-Definition transl_addressing (sz: Z) (addr: Op.addressing) (args: list mreg)
- (insn: Asm.addressing -> instruction) (k: code) : res code :=
- match addr, args with
- | Aindexed ofs, a1 :: nil =>
- do r1 <- ireg_of a1;
- if offset_representable sz ofs then
- OK (insn (ADimm r1 ofs) :: k)
- else
- OK (loadimm64 X16 ofs (insn (ADreg r1 X16) :: k))
- | Aindexed2, a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- OK (insn (ADreg r1 r2) :: k)
- | Aindexed2shift a, a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- if Int.eq a Int.zero then
- OK (insn (ADreg r1 r2) :: k)
- else if Int.eq (Int.shl Int.one a) (Int.repr sz) then
- OK (insn (ADlsl r1 r2 a) :: k)
- else
- OK (Padd X X16 r1 r2 (SOlsl a) :: insn (ADimm X16 Int64.zero) :: k)
- | Aindexed2ext x a, a1 :: a2 :: nil =>
- do r1 <- ireg_of a1; do r2 <- ireg_of a2;
- if Int.eq a Int.zero || Int.eq (Int.shl Int.one a) (Int.repr sz) then
- OK (insn (match x with Xsgn32 => ADsxt r1 r2 a
- | Xuns32 => ADuxt r1 r2 a end) :: k)
- else
- OK (arith_extended Paddext (Padd X) X16 r1 r2 x a
- (insn (ADimm X16 Int64.zero) :: k))
- | Aglobal id ofs, nil =>
- assertion (negb (Archi.pic_code tt));
- if Ptrofs.eq (Ptrofs.modu ofs (Ptrofs.repr sz)) Ptrofs.zero && 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")
- end.
-
-(** Translation of loads and stores *)
-
-Definition transl_load (trap: trapping_mode)
- (chunk: memory_chunk) (addr: Op.addressing)
- (args: list mreg) (dst: mreg) (k: code) : res code :=
- match trap with
- | NOTRAP => Error (msg "Asmgen.transl_load non-trapping loads unsupported on aarch64")
- | TRAP =>
- match chunk with
- | Mint8unsigned =>
- do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrb W rd) k
- | Mint8signed =>
- do rd <- ireg_of dst; transl_addressing 1 addr args (Pldrsb W rd) k
- | Mint16unsigned =>
- do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrh W rd) k
- | Mint16signed =>
- do rd <- ireg_of dst; transl_addressing 2 addr args (Pldrsh W rd) k
- | Mint32 =>
- do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw rd) k
- | Mint64 =>
- do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx rd) k
- | Mfloat32 =>
- do rd <- freg_of dst; transl_addressing 4 addr args (Pldrs rd) k
- | Mfloat64 =>
- do rd <- freg_of dst; transl_addressing 8 addr args (Pldrd rd) k
- | Many32 =>
- do rd <- ireg_of dst; transl_addressing 4 addr args (Pldrw_a rd) k
- | Many64 =>
- do rd <- ireg_of dst; transl_addressing 8 addr args (Pldrx_a rd) k
- end
- end.
-
-Definition transl_store (chunk: memory_chunk) (addr: Op.addressing)
- (args: list mreg) (src: mreg) (k: code) : res code :=
- match chunk with
- | Mint8unsigned | Mint8signed =>
- do r1 <- ireg_of src; transl_addressing 1 addr args (Pstrb r1) k
- | Mint16unsigned | Mint16signed =>
- do r1 <- ireg_of src; transl_addressing 2 addr args (Pstrh r1) k
- | Mint32 =>
- do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw r1) k
- | Mint64 =>
- do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx r1) k
- | Mfloat32 =>
- do r1 <- freg_of src; transl_addressing 4 addr args (Pstrs r1) k
- | Mfloat64 =>
- do r1 <- freg_of src; transl_addressing 8 addr args (Pstrd r1) k
- | Many32 =>
- do r1 <- ireg_of src; transl_addressing 4 addr args (Pstrw_a r1) k
- | Many64 =>
- do r1 <- ireg_of src; transl_addressing 8 addr args (Pstrx_a r1) k
- end.
-
-(** Register-indexed loads and stores *)
-
-Definition indexed_memory_access (insn: Asm.addressing -> instruction)
- (sz: Z) (base: iregsp) (ofs: ptrofs) (k: code) :=
- let ofs := Ptrofs.to_int64 ofs in
- if offset_representable sz ofs
- then insn (ADimm base ofs) :: k
- else loadimm64 X16 ofs (insn (ADreg base X16) :: k).
-
-Definition loadind (base: iregsp) (ofs: ptrofs) (ty: typ) (dst: mreg) (k: code) :=
- match ty, preg_of dst with
- | Tint, IR rd => OK (indexed_memory_access (Pldrw rd) 4 base ofs k)
- | Tlong, IR rd => OK (indexed_memory_access (Pldrx rd) 8 base ofs k)
- | Tsingle, FR rd => OK (indexed_memory_access (Pldrs rd) 4 base ofs k)
- | Tfloat, FR rd => OK (indexed_memory_access (Pldrd rd) 8 base ofs k)
- | Tany32, IR rd => OK (indexed_memory_access (Pldrw_a rd) 4 base ofs k)
- | Tany64, IR rd => OK (indexed_memory_access (Pldrx_a rd) 8 base ofs k)
- | Tany64, FR rd => OK (indexed_memory_access (Pldrd_a rd) 8 base ofs k)
- | _, _ => Error (msg "Asmgen.loadind")
- end.
-
-Definition storeind (src: mreg) (base: iregsp) (ofs: ptrofs) (ty: typ) (k: code) :=
- match ty, preg_of src with
- | Tint, IR rd => OK (indexed_memory_access (Pstrw rd) 4 base ofs k)
- | Tlong, IR rd => OK (indexed_memory_access (Pstrx rd) 8 base ofs k)
- | Tsingle, FR rd => OK (indexed_memory_access (Pstrs rd) 4 base ofs k)
- | Tfloat, FR rd => OK (indexed_memory_access (Pstrd rd) 8 base ofs k)
- | Tany32, IR rd => OK (indexed_memory_access (Pstrw_a rd) 4 base ofs k)
- | Tany64, IR rd => OK (indexed_memory_access (Pstrx_a rd) 8 base ofs k)
- | Tany64, FR rd => OK (indexed_memory_access (Pstrd_a rd) 8 base ofs k)
- | _, _ => Error (msg "Asmgen.storeind")
- end.
-
-Definition loadptr (base: iregsp) (ofs: ptrofs) (dst: ireg) (k: code) :=
- indexed_memory_access (Pldrx dst) 8 base ofs k.
-
-Definition storeptr (src: ireg) (base: iregsp) (ofs: ptrofs) (k: code) :=
- indexed_memory_access (Pstrx src) 8 base ofs k.
-
-(** Function epilogue *)
-
-Definition make_epilogue (f: Mach.function) (k: code) :=
- (* FIXME
- Cannot be used because memcpy destroys X30;
- issue being discussed with X. Leroy *)
- (* if is_leaf_function f
- then Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) :: k
- else*) loadptr XSP f.(fn_retaddr_ofs) RA
- (Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) :: k).
-
-(** Translation of a Mach instruction. *)
-
-Definition transl_instr (f: Mach.function) (i: Mach.instruction)
- (r29_is_parent: bool) (k: code) : res code :=
- match i with
- | Mgetstack ofs ty dst =>
- loadind XSP ofs ty dst k
- | Msetstack src ofs ty =>
- storeind src XSP ofs ty k
- | Mgetparam ofs ty dst =>
- (* load via the frame pointer if it is valid *)
- do c <- loadind X29 ofs ty dst k;
- OK (if r29_is_parent then c else loadptr XSP f.(fn_link_ofs) X29 c)
- | Mop op args res =>
- transl_op op args res k
- | Mload trap chunk addr args dst =>
- transl_load trap chunk addr args dst k
- | Mstore chunk addr args src =>
- transl_store chunk addr args src k
- | Mcall sig (inl r) =>
- do r1 <- ireg_of r; OK (Pblr r1 sig :: k)
- | Mcall sig (inr symb) =>
- OK (Pbl symb sig :: k)
- | Mtailcall sig (inl r) =>
- do r1 <- ireg_of r;
- OK (make_epilogue f (Pbr r1 sig :: k))
- | Mtailcall sig (inr symb) =>
- OK (make_epilogue f (Pbs symb sig :: k))
- | Mbuiltin ef args res =>
- OK (Pbuiltin ef (List.map (map_builtin_arg preg_of) args) (map_builtin_res preg_of res) :: k)
- | Mlabel lbl =>
- OK (Plabel lbl :: k)
- | Mgoto lbl =>
- OK (Pb lbl :: k)
- | Mcond cond args lbl =>
- transl_cond_branch cond args lbl k
- | Mjumptable arg tbl =>
- do r <- ireg_of arg;
- OK (Pbtbl r tbl :: k)
- | Mreturn =>
- OK (make_epilogue f (Pret RA :: k))
- end.
-
-(** Translation of a code sequence *)
-
-Definition it1_is_parent (before: bool) (i: Mach.instruction) : bool :=
- match i with
- | Msetstack src ofs ty => before
- | Mgetparam ofs ty dst => negb (mreg_eq dst R29)
- | Mop op args res => before && negb (mreg_eq res R29)
- | _ => false
- end.
-
-(** This is the naive definition that we no longer use because it
- is not tail-recursive. It is kept as specification. *)
-
-Fixpoint transl_code (f: Mach.function) (il: list Mach.instruction) (it1p: bool) :=
- match il with
- | nil => OK nil
- | i1 :: il' =>
- do k <- transl_code f il' (it1_is_parent it1p i1);
- transl_instr f i1 it1p k
- end.
-
-(** This is an equivalent definition in continuation-passing style
- that runs in constant stack space. *)
-
-Fixpoint transl_code_rec (f: Mach.function) (il: list Mach.instruction)
- (it1p: bool) (k: code -> res code) :=
- match il with
- | nil => k nil
- | i1 :: il' =>
- transl_code_rec f il' (it1_is_parent it1p i1)
- (fun c1 => do c2 <- transl_instr f i1 it1p c1; k c2)
- end.
-
-Definition transl_code' (f: Mach.function) (il: list Mach.instruction) (it1p: bool) :=
- transl_code_rec f il it1p (fun c => OK c).
+Require Import Locations Asmblock Asm.
-(** Translation of a whole function. Note that we must check
- that the generated code contains less than [2^32] instructions,
- otherwise the offset part of the [PC] code pointer could wrap
- around, leading to incorrect executions. *)
+(** * Translation from Asmblock to assembly language
+ Inspired from the KVX backend. *)
-Definition transl_function (f: Mach.function) :=
- do c <- transl_code' f f.(Mach.fn_code) true;
- OK (mkfunction f.(Mach.fn_sig)
- (Pallocframe f.(fn_stacksize) f.(fn_link_ofs) ::
- storeptr RA XSP f.(fn_retaddr_ofs) c)).
+(* STUB *)
-Definition transf_function (f: Mach.function) : res Asm.function :=
- do tf <- transl_function f;
- if zlt Ptrofs.max_unsigned (list_length_z tf.(fn_code))
- then Error (msg "code size exceeded")
- else OK tf.
+Definition transf_function (f: Asmblock.function) : res Asm.function :=
+ Error (msg "Asmgen not yet implmented").
-Definition transf_fundef (f: Mach.fundef) : res Asm.fundef :=
+Definition transf_fundef (f: Asmblock.fundef) : res Asm.fundef :=
transf_partial_fundef transf_function f.
-Definition transf_program (p: Mach.program) : res Asm.program :=
+Definition transf_program (p: Asmblock.program) : res Asm.program :=
transform_partial_program transf_fundef p.
diff --git a/aarch64/Asmgenproof.v b/aarch64/Asmgenproof.v
index 6831509f..e69de29b 100644
--- a/aarch64/Asmgenproof.v
+++ b/aarch64/Asmgenproof.v
@@ -1,1101 +0,0 @@
-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Xavier Leroy, Collège de France and INRIA Paris *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-(** Correctness proof for AArch64 code generation. *)
-
-Require Import Coqlib Errors.
-Require Import Integers Floats AST Linking.
-Require Import Values Memory Events Globalenvs Smallstep.
-Require Import Op Locations Mach Conventions Asm.
-Require Import Asmgen Asmgenproof0 Asmgenproof1.
-
-Definition match_prog (p: Mach.program) (tp: Asm.program) :=
- match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp.
-
-Lemma transf_program_match:
- forall p tp, transf_program p = OK tp -> match_prog p tp.
-Proof.
- intros. eapply match_transform_partial_program; eauto.
-Qed.
-
-Section PRESERVATION.
-
-Variable prog: Mach.program.
-Variable tprog: Asm.program.
-Hypothesis TRANSF: match_prog prog tprog.
-Let ge := Genv.globalenv prog.
-Let tge := Genv.globalenv tprog.
-
-Lemma symbols_preserved:
- forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s.
-Proof (Genv.find_symbol_match TRANSF).
-
-Lemma senv_preserved:
- Senv.equiv ge tge.
-Proof (Genv.senv_match TRANSF).
-
-Lemma functions_translated:
- forall b f,
- Genv.find_funct_ptr ge b = Some f ->
- exists tf,
- Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf.
-Proof (Genv.find_funct_ptr_transf_partial TRANSF).
-
-Lemma functions_transl:
- forall fb f tf,
- Genv.find_funct_ptr ge fb = Some (Internal f) ->
- transf_function f = OK tf ->
- Genv.find_funct_ptr tge fb = Some (Internal tf).
-Proof.
- intros. exploit functions_translated; eauto. intros [tf' [A B]].
- monadInv B. rewrite H0 in EQ; inv EQ; auto.
-Qed.
-
-(** * Properties of control flow *)
-
-Lemma transf_function_no_overflow:
- forall f tf,
- transf_function f = OK tf -> list_length_z tf.(fn_code) <= Ptrofs.max_unsigned.
-Proof.
- intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0.
- omega.
-Qed.
-
-Lemma exec_straight_exec:
- forall fb f c ep tf tc c' rs m rs' m',
- transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
- exec_straight tge tf tc rs m c' rs' m' ->
- plus step tge (State rs m) E0 (State rs' m').
-Proof.
- intros. inv H.
- eapply exec_straight_steps_1; eauto.
- eapply transf_function_no_overflow; eauto.
- eapply functions_transl; eauto.
-Qed.
-
-Lemma exec_straight_at:
- forall fb f c ep tf tc c' ep' tc' rs m rs' m',
- transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
- transl_code f c' ep' = OK tc' ->
- exec_straight tge tf tc rs m tc' rs' m' ->
- transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'.
-Proof.
- intros. inv H.
- exploit exec_straight_steps_2; eauto.
- eapply transf_function_no_overflow; eauto.
- eapply functions_transl; eauto.
- intros [ofs' [PC' CT']].
- rewrite PC'. constructor; auto.
-Qed.
-
-(** The following lemmas show that the translation from Mach to Asm
- preserves labels, in the sense that the following diagram commutes:
-<<
- translation
- Mach code ------------------------ Asm instr sequence
- | |
- | Mach.find_label lbl find_label lbl |
- | |
- v v
- Mach code tail ------------------- Asm instr seq tail
- translation
->>
- The proof demands many boring lemmas showing that Asm constructor
- functions do not introduce new labels.
-*)
-
-Section TRANSL_LABEL.
-
-Remark loadimm_z_label: forall sz rd l k, tail_nolabel k (loadimm_z sz rd l k).
-Proof.
- intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel.
- induction l as [ | [n p] l]; simpl; TailNoLabel.
-Qed.
-
-Remark loadimm_n_label: forall sz rd l k, tail_nolabel k (loadimm_n sz rd l k).
-Proof.
- intros; destruct l as [ | [n1 p1] l]; simpl; TailNoLabel.
- induction l as [ | [n p] l]; simpl; TailNoLabel.
-Qed.
-
-Remark loadimm_label: forall sz rd n k, tail_nolabel k (loadimm sz rd n k).
-Proof.
- unfold loadimm; intros. destruct Nat.leb; [apply loadimm_z_label|apply loadimm_n_label].
-Qed.
-Hint Resolve loadimm_label: labels.
-
-Remark loadimm32_label: forall r n k, tail_nolabel k (loadimm32 r n k).
-Proof.
- unfold loadimm32; intros. destruct (is_logical_imm32 n); TailNoLabel.
-Qed.
-Hint Resolve loadimm32_label: labels.
-
-Remark loadimm64_label: forall r n k, tail_nolabel k (loadimm64 r n k).
-Proof.
- unfold loadimm64; intros. destruct (is_logical_imm64 n); TailNoLabel.
-Qed.
-Hint Resolve loadimm64_label: labels.
-
-Remark addimm_aux: forall insn rd r1 n k,
- (forall rd r1 n, nolabel (insn rd r1 n)) ->
- tail_nolabel k (addimm_aux insn rd r1 n k).
-Proof.
- unfold addimm_aux; intros.
- destruct Z.eqb. TailNoLabel. destruct Z.eqb; TailNoLabel.
-Qed.
-
-Remark addimm32_label: forall rd r1 n k, tail_nolabel k (addimm32 rd r1 n k).
-Proof.
- unfold addimm32; intros.
- destruct Int.eq. apply addimm_aux; intros; red; auto.
- destruct Int.eq. apply addimm_aux; intros; red; auto.
- destruct Int.lt; eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-Hint Resolve addimm32_label: labels.
-
-Remark addimm64_label: forall rd r1 n k, tail_nolabel k (addimm64 rd r1 n k).
-Proof.
- unfold addimm64; intros.
- destruct Int64.eq. apply addimm_aux; intros; red; auto.
- destruct Int64.eq. apply addimm_aux; intros; red; auto.
- destruct Int64.lt; eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-Hint Resolve addimm64_label: labels.
-
-Remark logicalimm32_label: forall insn1 insn2 rd r1 n k,
- (forall rd r1 n, nolabel (insn1 rd r1 n)) ->
- (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) ->
- tail_nolabel k (logicalimm32 insn1 insn2 rd r1 n k).
-Proof.
- unfold logicalimm32; intros.
- destruct (is_logical_imm32 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-
-Remark logicalimm64_label: forall insn1 insn2 rd r1 n k,
- (forall rd r1 n, nolabel (insn1 rd r1 n)) ->
- (forall rd r1 r2 s, nolabel (insn2 rd r1 r2 s)) ->
- tail_nolabel k (logicalimm64 insn1 insn2 rd r1 n k).
-Proof.
- unfold logicalimm64; intros.
- destruct (is_logical_imm64 n). TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-
-Remark move_extended_label: forall rd r1 ex a k, tail_nolabel k (move_extended rd r1 ex a k).
-Proof.
- unfold move_extended, move_extended_base; intros. destruct Int.eq, ex; TailNoLabel.
-Qed.
-Hint Resolve move_extended_label: labels.
-
-Remark arith_extended_label: forall insnX insnS rd r1 r2 ex a k,
- (forall rd r1 r2 x, nolabel (insnX rd r1 r2 x)) ->
- (forall rd r1 r2 s, nolabel (insnS rd r1 r2 s)) ->
- tail_nolabel k (arith_extended insnX insnS rd r1 r2 ex a k).
-Proof.
- unfold arith_extended; intros. destruct Int.ltu.
- TailNoLabel.
- destruct ex; simpl; TailNoLabel.
-Qed.
-
-Remark loadsymbol_label: forall r id ofs k, tail_nolabel k (loadsymbol r id ofs k).
-Proof.
- intros; unfold loadsymbol.
- destruct (Archi.pic_code tt); TailNoLabel. destruct Ptrofs.eq; TailNoLabel.
-Qed.
-Hint Resolve loadsymbol_label: labels.
-
-Remark transl_cond_label: forall cond args k c,
- transl_cond cond args k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_cond; intros; destruct cond; TailNoLabel.
-- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_arith_imm32; TailNoLabel. destruct is_arith_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_logical_imm32; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_arith_imm64; TailNoLabel. destruct is_arith_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-- destruct is_logical_imm64; TailNoLabel. eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-
-Remark transl_cond_branch_default_label: forall cond args lbl k c,
- transl_cond_branch_default cond args lbl k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_cond_branch_default; intros.
- eapply tail_nolabel_trans; [eapply transl_cond_label;eauto|TailNoLabel].
-Qed.
-Hint Resolve transl_cond_branch_default_label: labels.
-
-Remark transl_cond_branch_label: forall cond args lbl k c,
- transl_cond_branch cond args lbl k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_cond_branch; intros; destruct args; TailNoLabel; destruct cond; TailNoLabel.
-- destruct c0; TailNoLabel.
-- destruct c0; TailNoLabel.
-- destruct (Int.is_power2 n); TailNoLabel.
-- destruct (Int.is_power2 n); TailNoLabel.
-- destruct c0; TailNoLabel.
-- destruct c0; TailNoLabel.
-- destruct (Int64.is_power2' n); TailNoLabel.
-- destruct (Int64.is_power2' n); TailNoLabel.
-Qed.
-
-Remark transl_op_label:
- forall op args r k c,
- transl_op op args r k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_op; intros; destruct op; TailNoLabel.
-- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel.
-- destruct (Float.eq_dec n Float.zero); TailNoLabel.
-- destruct (Float32.eq_dec n Float32.zero); TailNoLabel.
-- apply logicalimm32_label; unfold nolabel; auto.
-- apply logicalimm32_label; unfold nolabel; auto.
-- apply logicalimm32_label; unfold nolabel; auto.
-- unfold shrx32. destruct (Int.eq _ _); try destruct (Int.eq _ _); TailNoLabel.
-- apply arith_extended_label; unfold nolabel; auto.
-- apply arith_extended_label; unfold nolabel; auto.
-- apply logicalimm64_label; unfold nolabel; auto.
-- apply logicalimm64_label; unfold nolabel; auto.
-- apply logicalimm64_label; unfold nolabel; auto.
-- unfold shrx64. destruct (Int.eq _ _); try destruct (Int.eq _ _); TailNoLabel.
-- eapply tail_nolabel_trans. eapply transl_cond_label; eauto. TailNoLabel.
-- destruct (preg_of r); try discriminate; TailNoLabel;
- (eapply tail_nolabel_trans; [eapply transl_cond_label; eauto | TailNoLabel]).
-Qed.
-
-Remark transl_addressing_label:
- forall sz addr args insn k c,
- transl_addressing sz addr args insn k = OK c ->
- (forall ad, nolabel (insn ad)) ->
- tail_nolabel k c.
-Proof.
- unfold transl_addressing; intros; destruct addr; TailNoLabel;
- eapply tail_nolabel_trans; TailNoLabel.
- eapply tail_nolabel_trans. apply arith_extended_label; unfold nolabel; auto. TailNoLabel.
-Qed.
-
-Remark transl_load_label:
- forall trap chunk addr args dst k c,
- transl_load trap chunk addr args dst k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_load; intros; destruct trap; try discriminate; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto.
-Qed.
-
-Remark transl_store_label:
- forall chunk addr args src k c,
- transl_store chunk addr args src k = OK c -> tail_nolabel k c.
-Proof.
- unfold transl_store; intros; destruct chunk; TailNoLabel; eapply transl_addressing_label; eauto; unfold nolabel; auto.
-Qed.
-
-Remark indexed_memory_access_label:
- forall insn sz base ofs k,
- (forall ad, nolabel (insn ad)) ->
- tail_nolabel k (indexed_memory_access insn sz base ofs k).
-Proof.
- unfold indexed_memory_access; intros. destruct offset_representable.
- TailNoLabel.
- eapply tail_nolabel_trans; TailNoLabel.
-Qed.
-
-Remark loadind_label:
- forall base ofs ty dst k c,
- loadind base ofs ty dst k = OK c -> tail_nolabel k c.
-Proof.
- unfold loadind; intros.
- destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I.
-Qed.
-
-Remark storeind_label:
- forall src base ofs ty k c,
- storeind src base ofs ty k = OK c -> tail_nolabel k c.
-Proof.
- unfold storeind; intros.
- destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I.
-Qed.
-
-Remark loadptr_label:
- forall base ofs dst k, tail_nolabel k (loadptr base ofs dst k).
-Proof.
- intros. apply indexed_memory_access_label. unfold nolabel; auto.
-Qed.
-
-Remark storeptr_label:
- forall src base ofs k, tail_nolabel k (storeptr src base ofs k).
-Proof.
- intros. apply indexed_memory_access_label. unfold nolabel; auto.
-Qed.
-
-Remark make_epilogue_label:
- forall f k, tail_nolabel k (make_epilogue f k).
-Proof.
- unfold make_epilogue; intros.
- (* FIXME destruct is_leaf_function.
- { TailNoLabel. } *)
- eapply tail_nolabel_trans.
- apply loadptr_label.
- TailNoLabel.
-Qed.
-
-Lemma transl_instr_label:
- forall f i ep k c,
- transl_instr f i ep k = OK c ->
- match i with Mlabel lbl => c = Plabel lbl :: k | _ => tail_nolabel k c end.
-Proof.
- unfold transl_instr; intros; destruct i; TailNoLabel.
-- eapply loadind_label; eauto.
-- eapply storeind_label; eauto.
-- destruct ep. eapply loadind_label; eauto.
- eapply tail_nolabel_trans. apply loadptr_label. eapply loadind_label; eauto.
-- eapply transl_op_label; eauto.
-- eapply transl_load_label; eauto.
-- eapply transl_store_label; eauto.
-- destruct s0; monadInv H; TailNoLabel.
-- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]).
-- eapply transl_cond_branch_label; eauto.
-- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel].
-Qed.
-
-Lemma transl_instr_label':
- forall lbl f i ep k c,
- transl_instr f i ep k = OK c ->
- find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k.
-Proof.
- intros. exploit transl_instr_label; eauto.
- destruct i; try (intros [A B]; apply B).
- intros. subst c. simpl. auto.
-Qed.
-
-Lemma transl_code_label:
- forall lbl f c ep tc,
- transl_code f c ep = OK tc ->
- match Mach.find_label lbl c with
- | None => find_label lbl tc = None
- | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc'
- end.
-Proof.
- induction c; simpl; intros.
- inv H. auto.
- monadInv H. rewrite (transl_instr_label' lbl _ _ _ _ _ EQ0).
- generalize (Mach.is_label_correct lbl a).
- destruct (Mach.is_label lbl a); intros.
- subst a. simpl in EQ. exists x; auto.
- eapply IHc; eauto.
-Qed.
-
-Lemma transl_find_label:
- forall lbl f tf,
- transf_function f = OK tf ->
- match Mach.find_label lbl f.(Mach.fn_code) with
- | None => find_label lbl tf.(fn_code) = None
- | Some c => exists tc, find_label lbl tf.(fn_code) = Some tc /\ transl_code f c false = OK tc
- end.
-Proof.
- intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0.
- monadInv EQ. rewrite transl_code'_transl_code in EQ0. unfold fn_code.
- simpl. destruct (storeptr_label X30 XSP (fn_retaddr_ofs f) x) as [A B]; rewrite B.
- eapply transl_code_label; eauto.
-Qed.
-
-End TRANSL_LABEL.
-
-(** A valid branch in a piece of Mach code translates to a valid ``go to''
- transition in the generated Asm code. *)
-
-Lemma find_label_goto_label:
- forall f tf lbl rs m c' b ofs,
- Genv.find_funct_ptr ge b = Some (Internal f) ->
- transf_function f = OK tf ->
- rs PC = Vptr b ofs ->
- Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
- exists tc', exists rs',
- goto_label tf lbl rs m = Next rs' m
- /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc'
- /\ forall r, r <> PC -> rs'#r = rs#r.
-Proof.
- intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2.
- intros [tc [A B]].
- exploit label_pos_code_tail; eauto. instantiate (1 := 0).
- intros [pos' [P [Q R]]].
- exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))).
- split. unfold goto_label. rewrite P. rewrite H1. auto.
- split. rewrite Pregmap.gss. constructor; auto.
- rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q.
- auto. omega.
- generalize (transf_function_no_overflow _ _ H0). omega.
- intros. apply Pregmap.gso; auto.
-Qed.
-
-(** Existence of return addresses *)
-
-Lemma return_address_exists:
- forall f sg ros c, is_tail (Mcall sg ros :: c) f.(Mach.fn_code) ->
- exists ra, return_address_offset f c ra.
-Proof.
- intros. eapply Asmgenproof0.return_address_exists; eauto.
-- intros. exploit transl_instr_label; eauto.
- destruct i; try (intros [A B]; apply A). intros. subst c0. repeat constructor.
-- intros. monadInv H0.
- destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. monadInv EQ.
- rewrite transl_code'_transl_code in EQ0.
- exists x; exists true; split; auto. unfold fn_code.
- constructor. apply (storeptr_label X30 XSP (fn_retaddr_ofs f0) x).
-- exact transf_function_no_overflow.
-Qed.
-
-(** * Proof of semantic preservation *)
-
-(** Semantic preservation is proved using simulation diagrams
- of the following form.
-<<
- st1 --------------- st2
- | |
- t| *|t
- | |
- v v
- st1'--------------- st2'
->>
- The invariant is the [match_states] predicate below, which includes:
-- The Asm code pointed by the PC register is the translation of
- the current Mach code sequence.
-- Mach register values and Asm register values agree.
-*)
-
-Inductive match_states: Mach.state -> Asm.state -> Prop :=
- | match_states_intro:
- forall s fb sp c ep ms m m' rs f tf tc
- (STACKS: match_stack ge s)
- (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
- (MEXT: Mem.extends m m')
- (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc)
- (AG: agree ms sp rs)
- (DXP: ep = true -> rs#X29 = parent_sp s)
- (LEAF: is_leaf_function f = true -> rs#RA = parent_ra s),
- match_states (Mach.State s fb sp c ms m)
- (Asm.State rs m')
- | match_states_call:
- forall s fb ms m m' rs
- (STACKS: match_stack ge s)
- (MEXT: Mem.extends m m')
- (AG: agree ms (parent_sp s) rs)
- (ATPC: rs PC = Vptr fb Ptrofs.zero)
- (ATLR: rs RA = parent_ra s),
- match_states (Mach.Callstate s fb ms m)
- (Asm.State rs m')
- | match_states_return:
- forall s ms m m' rs
- (STACKS: match_stack ge s)
- (MEXT: Mem.extends m m')
- (AG: agree ms (parent_sp s) rs)
- (ATPC: rs PC = parent_ra s),
- match_states (Mach.Returnstate s ms m)
- (Asm.State rs m').
-
-Lemma exec_straight_steps:
- forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2,
- match_stack ge s ->
- Mem.extends m2 m2' ->
- Genv.find_funct_ptr ge fb = Some (Internal f) ->
- transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
- (forall k c (TR: transl_instr f i ep k = OK c),
- exists rs2,
- exec_straight tge tf c rs1 m1' k rs2 m2'
- /\ agree ms2 sp rs2
- /\ (it1_is_parent ep i = true -> rs2#X29 = parent_sp s)
- /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
- exists st',
- plus step tge (State rs1 m1') E0 st' /\
- match_states (Mach.State s fb sp c ms2 m2) st'.
-Proof.
- intros. inversion H2. subst. monadInv H7.
- exploit H3; eauto. intros [rs2 [A [B [C D]]]].
- exists (State rs2 m2'); split.
- - eapply exec_straight_exec; eauto.
- - econstructor; eauto. eapply exec_straight_at; eauto.
-Qed.
-
-Lemma exec_straight_steps_goto:
- forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
- match_stack ge s ->
- Mem.extends m2 m2' ->
- Genv.find_funct_ptr ge fb = Some (Internal f) ->
- Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
- transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
- it1_is_parent ep i = false ->
- (forall k c (TR: transl_instr f i ep k = OK c),
- exists jmp, exists k', exists rs2,
- exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2'
- /\ agree ms2 sp rs2
- /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2'
- /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
- exists st',
- plus step tge (State rs1 m1') E0 st' /\
- match_states (Mach.State s fb sp c' ms2 m2) st'.
-Proof.
- intros. inversion H3. subst. monadInv H9.
- exploit H5; eauto. intros [jmp [k' [rs2 [A [B [C D]]]]]].
- generalize (functions_transl _ _ _ H7 H8); intro FN.
- generalize (transf_function_no_overflow _ _ H8); intro NOOV.
- exploit exec_straight_steps_2; eauto.
- intros [ofs' [PC2 CT2]].
- exploit find_label_goto_label; eauto.
- intros [tc' [rs3 [GOTO [AT' OTH]]]].
- exists (State rs3 m2'); split.
- eapply plus_right'.
- eapply exec_straight_steps_1; eauto.
- econstructor; eauto.
- eapply find_instr_tail. eauto.
- rewrite C. eexact GOTO.
- traceEq.
- econstructor; eauto.
- apply agree_exten with rs2; auto with asmgen.
- congruence.
- rewrite OTH by congruence; auto.
-Qed.
-
-Lemma exec_straight_opt_steps_goto:
- forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
- match_stack ge s ->
- Mem.extends m2 m2' ->
- Genv.find_funct_ptr ge fb = Some (Internal f) ->
- Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
- transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
- it1_is_parent ep i = false ->
- (forall k c (TR: transl_instr f i ep k = OK c),
- exists jmp, exists k', exists rs2,
- exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2'
- /\ agree ms2 sp rs2
- /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2'
- /\ (is_leaf_function f = true -> rs2#RA = parent_ra s)) ->
- exists st',
- plus step tge (State rs1 m1') E0 st' /\
- match_states (Mach.State s fb sp c' ms2 m2) st'.
-Proof.
- intros. inversion H3. subst. monadInv H9.
- exploit H5; eauto. intros [jmp [k' [rs2 [A [B [C D]]]]]].
- generalize (functions_transl _ _ _ H7 H8); intro FN.
- generalize (transf_function_no_overflow _ _ H8); intro NOOV.
- inv A.
-- exploit find_label_goto_label; eauto.
- intros [tc' [rs3 [GOTO [AT' OTH]]]].
- exists (State rs3 m2'); split.
- apply plus_one. econstructor; eauto.
- eapply find_instr_tail. eauto.
- rewrite C. eexact GOTO.
- econstructor; eauto.
- apply agree_exten with rs2; auto with asmgen.
- congruence.
- rewrite OTH by congruence; auto.
-- exploit exec_straight_steps_2; eauto.
- intros [ofs' [PC2 CT2]].
- exploit find_label_goto_label; eauto.
- intros [tc' [rs3 [GOTO [AT' OTH]]]].
- exists (State rs3 m2'); split.
- eapply plus_right'.
- eapply exec_straight_steps_1; eauto.
- econstructor; eauto.
- eapply find_instr_tail. eauto.
- rewrite C. eexact GOTO.
- traceEq.
- econstructor; eauto.
- apply agree_exten with rs2; auto with asmgen.
- congruence.
- rewrite OTH by congruence; auto.
-Qed.
-
-(** We need to show that, in the simulation diagram, we cannot
- take infinitely many Mach transitions that correspond to zero
- transitions on the Asm side. Actually, all Mach transitions
- correspond to at least one Asm transition, except the
- transition from [Machsem.Returnstate] to [Machsem.State].
- So, the following integer measure will suffice to rule out
- the unwanted behaviour. *)
-
-Definition measure (s: Mach.state) : nat :=
- match s with
- | Mach.State _ _ _ _ _ _ => 0%nat
- | Mach.Callstate _ _ _ _ => 0%nat
- | Mach.Returnstate _ _ _ => 1%nat
- end.
-
-Remark preg_of_not_X29: forall r, negb (mreg_eq r R29) = true -> IR X29 <> preg_of r.
-Proof.
- intros. change (IR X29) with (preg_of R29). red; intros.
- exploit preg_of_injective; eauto. intros; subst r; discriminate.
-Qed.
-
-Lemma sp_val': forall ms sp rs, agree ms sp rs -> sp = rs XSP.
-Proof.
- intros. eapply sp_val; eauto.
-Qed.
-
-(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *)
-
-Theorem step_simulation:
- forall S1 t S2, Mach.step return_address_offset ge S1 t S2 ->
- forall S1' (MS: match_states S1 S1') (WF: wf_state ge 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. }
- split. { simpl; congruence. }
- rewrite nextinstr_inv by congruence; assumption.
-
-- (* 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 S]]]].
- exists rs'; split. eauto.
- split. { eapply agree_set_mreg; eauto with asmgen. congruence. }
- split. { simpl; congruence. }
- rewrite S. assumption.
-
-- (* 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 R]]].
- exists rs'; split. eauto.
- split. eapply agree_undef_regs; eauto with asmgen.
- simpl; intros.
- split. rewrite Q; auto with asmgen.
- rewrite R. assumption.
-
-- (* 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 S]]]].
- exists rs1; split. eauto.
- split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen.
- simpl; split; intros.
- { rewrite R; auto with asmgen.
- apply preg_of_not_X29; auto.
- }
- { rewrite S; 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 V]]]].
- 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.
- split; simpl; intros. rewrite U; auto with asmgen.
- apply preg_of_not_X29; auto.
- rewrite V. rewrite R by congruence. 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 S]]]].
- exists rs2; split. eauto. split.
- apply agree_set_undef_mreg with rs0; auto.
- apply Val.lessdef_trans with v'; auto.
- split; simpl; intros. InvBooleans.
- rewrite R; auto. apply preg_of_not_X29; auto.
-Local Transparent destroyed_by_op.
- destruct op; try exact I; simpl; congruence.
- rewrite S.
- auto.
-- (* Mload *)
- destruct trap.
- {
- 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 S]]]].
- exists rs2; split. eauto.
- split. eapply agree_set_undef_mreg; eauto. congruence.
- split. simpl; congruence.
- rewrite S. assumption.
- }
-
- (* Mload notrap1 *)
- inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
-
-- (* Mload notrap *)
- inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
-
-- (* Mload notrap *)
- inv AT. simpl in *. unfold bind in *. destruct (transl_code _ _ _) in *; discriminate.
-
-- (* 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 R]]].
- exists rs2; split. eauto.
- split. eapply agree_undef_regs; eauto with asmgen.
- split. simpl; congruence.
- rewrite R. assumption.
-
-- (* Mcall *)
- assert (f0 = f) by congruence. subst f0.
- inv AT.
- assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned).
- { eapply transf_function_no_overflow; eauto. }
- destruct ros as [rf|fid]; simpl in H; monadInv H5.
-+ (* Indirect call *)
- assert (rs rf = Vptr f' Ptrofs.zero).
- { destruct (rs rf); try discriminate.
- revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. }
- assert (rs0 x0 = Vptr f' Ptrofs.zero).
- { exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. }
- generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1.
- assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x).
- { econstructor; eauto. }
- exploit return_address_offset_correct; eauto. intros; subst ra.
- left; econstructor; split.
- apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto.
- eapply functions_transl; eauto. eapply find_instr_tail; eauto.
- simpl. eauto.
- econstructor; eauto.
- econstructor; eauto.
- eapply agree_sp_def; eauto.
- simpl. eapply agree_exten; eauto. intros. Simpl.
- Simpl. rewrite <- H2. auto.
-+ (* Direct call *)
- generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1.
- assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x).
- econstructor; eauto.
- exploit return_address_offset_correct; eauto. intros; subst ra.
- left; econstructor; split.
- apply plus_one. eapply exec_step_internal. eauto.
- eapply functions_transl; eauto. eapply find_instr_tail; eauto.
- simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto.
- econstructor; eauto.
- econstructor; eauto.
- eapply agree_sp_def; eauto.
- simpl. eapply agree_exten; eauto. intros. Simpl.
- Simpl. rewrite <- H2. auto.
-
-- (* Mtailcall *)
- assert (f0 = f) by congruence. subst f0.
- inversion AT; subst.
- assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned).
- { eapply transf_function_no_overflow; eauto. }
- exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]].
- destruct ros as [rf|fid]; simpl in H; monadInv H7.
-+ (* Indirect call *)
- assert (rs rf = Vptr f' Ptrofs.zero).
- { destruct (rs rf); try discriminate.
- revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. }
- assert (rs0 x0 = Vptr f' Ptrofs.zero).
- { exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. }
- exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
- exploit exec_straight_steps_2; eauto using functions_transl.
- intros (ofs' & P & Q).
- left; econstructor; split.
- (* execution *)
- eapply plus_right'. eapply exec_straight_exec; eauto.
- econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q.
- simpl. reflexivity.
- traceEq.
- (* match states *)
- econstructor; eauto.
- apply agree_set_other; auto with asmgen.
- Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption.
-+ (* Direct call *)
- exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
- exploit exec_straight_steps_2; eauto using functions_transl.
- intros (ofs' & P & Q).
- left; econstructor; split.
- (* execution *)
- eapply plus_right'. eapply exec_straight_exec; eauto.
- econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q.
- simpl. reflexivity.
- traceEq.
- (* match states *)
- econstructor; eauto.
- apply agree_set_other; auto with asmgen.
- Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto.
-
-- (* Mbuiltin *)
- inv AT. monadInv H4.
- exploit functions_transl; eauto. intro FN.
- generalize (transf_function_no_overflow _ _ H3); intro NOOV.
- exploit builtin_args_match; eauto. intros [vargs' [P Q]].
- exploit external_call_mem_extends; eauto.
- intros [vres' [m2' [A [B [C D]]]]].
- left. econstructor; split. apply plus_one.
- eapply exec_step_builtin. eauto. eauto.
- eapply find_instr_tail; eauto.
- erewrite <- sp_val by eauto.
- eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved.
- eapply external_call_symbols_preserved; eauto. apply senv_preserved.
- eauto.
- econstructor; eauto.
- instantiate (2 := tf); instantiate (1 := x).
- unfold nextinstr. rewrite Pregmap.gss.
- rewrite set_res_other. rewrite undef_regs_other_2.
- rewrite <- H1. simpl. econstructor; eauto.
- eapply code_tail_next_int; eauto.
- rewrite preg_notin_charact. intros. auto with asmgen.
- auto with asmgen.
- apply agree_nextinstr. eapply agree_set_res; auto.
- eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto.
- congruence.
-
- Simpl.
- rewrite set_res_other by trivial.
- rewrite undef_regs_other.
- assumption.
- intro.
- rewrite in_map_iff.
- intros (x0 & PREG & IN).
- subst r'.
- intro.
- apply (preg_of_not_RA x0).
- 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.
-
- rewrite INV by congruence.
- assumption.
-
-- (* 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 & D).
- exists jmp; exists k; exists rs'.
- split. eexact A.
- split. apply agree_exten with rs0; auto with asmgen.
- split.
- exact B.
- rewrite D. exact LEAF.
-
-- (* 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 & D).
- 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.
- split.
- simpl; congruence.
- Simpl. rewrite D.
- exact LEAF.
-
-- (* Mjumptable *)
- assert (f0 = f) by congruence. subst f0.
- inv AT. monadInv H6.
- exploit functions_transl; eauto. intro FN.
- generalize (transf_function_no_overflow _ _ H5); intro NOOV.
- exploit find_label_goto_label. eauto. eauto.
- instantiate (2 := rs0#X16 <- Vundef #X17 <- Vundef).
- Simpl. eauto.
- eauto.
- intros [tc' [rs' [A [B C]]]].
- exploit ireg_val; eauto. rewrite H. intros LD; inv LD.
- left; econstructor; split.
- apply plus_one. econstructor; eauto.
- eapply find_instr_tail; eauto.
- simpl. Simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A.
- econstructor; eauto.
- eapply agree_undef_regs; eauto.
- simpl. intros. rewrite C; auto with asmgen. Simpl.
- congruence.
-
- rewrite C by congruence.
- repeat rewrite Pregmap.gso by congruence.
- assumption.
-
-- (* 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 & W).
- assert (EXEC_PROLOGUE:
- exec_straight tge tf
- tf.(fn_code) rs0 m'
- x0 rs3 m3').
- { change (fn_code tf) with tfbody; unfold tfbody.
- apply exec_straight_step with rs2 m2'.
- unfold exec_instr. rewrite C. fold sp.
- rewrite <- (sp_val _ _ _ AG). rewrite F. reflexivity.
- reflexivity.
- eexact U. }
- exploit exec_straight_steps_2; eauto using functions_transl. omega. constructor.
- intros (ofs' & X & Y).
- left; exists (State rs3 m3'); split.
- eapply exec_straight_steps_1; eauto. omega. constructor.
- econstructor; eauto.
- rewrite X; econstructor; eauto.
- apply agree_exten with rs2; eauto with asmgen.
- unfold rs2.
- apply agree_nextinstr. apply agree_set_other; auto with asmgen.
- apply agree_change_sp with (parent_sp s).
- apply agree_undef_regs with rs0. auto.
-Local Transparent destroyed_at_function_entry. simpl.
- simpl; intros; Simpl.
- unfold sp; congruence.
- intros. rewrite V by auto with asmgen. reflexivity.
-
- rewrite W.
- unfold rs2.
- Simpl.
-
-- (* external function *)
- exploit functions_translated; eauto.
- intros [tf [A B]]. simpl in B. inv B.
- exploit extcall_arguments_match; eauto.
- intros [args' [C D]].
- exploit external_call_mem_extends; eauto.
- intros [res' [m2' [P [Q [R S]]]]].
- left; econstructor; split.
- apply plus_one. eapply exec_step_external; eauto.
- eapply external_call_symbols_preserved; eauto. apply senv_preserved.
- econstructor; eauto.
- unfold loc_external_result. apply agree_set_other; auto. apply agree_set_pair; auto.
- apply agree_undef_caller_save_regs; auto.
-
-- (* return *)
- inv STACKS. simpl in *.
- right. split. omega. split. auto.
- rewrite <- ATPC in H5.
- econstructor; eauto. congruence.
- inv WF.
- inv STACK.
- inv H1.
- congruence.
-Qed.
-
-Lemma transf_initial_states:
- forall st1, Mach.initial_state prog st1 ->
- exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2.
-Proof.
- intros. inversion H. unfold ge0 in *.
- econstructor; split.
- econstructor.
- eapply (Genv.init_mem_transf_partial TRANSF); eauto.
- replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero)
- with (Vptr fb Ptrofs.zero).
- econstructor; eauto.
- constructor.
- apply Mem.extends_refl.
- split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence.
- intros. rewrite Regmap.gi. auto.
- unfold Genv.symbol_address.
- rewrite (match_program_main TRANSF).
- rewrite symbols_preserved.
- unfold ge; rewrite H1. auto.
-Qed.
-
-Lemma transf_final_states:
- forall st1 st2 r,
- match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r.
-Proof.
- intros. inv H0. inv H. constructor. assumption.
- compute in H1. inv H1.
- generalize (preg_val _ _ _ R0 AG). rewrite H2. intros LD; inv LD. auto.
-Qed.
-
-Theorem transf_program_correct:
- forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog).
-Proof.
- eapply forward_simulation_star with (measure := measure)
- (match_states := fun S1 S2 => match_states S1 S2 /\ wf_state ge S1).
- - apply senv_preserved.
- - simpl; intros. exploit transf_initial_states; eauto.
- intros (s2 & A & B).
- exists s2; intuition auto. apply wf_initial; auto.
- - simpl; intros. destruct H as [MS WF]. eapply transf_final_states; eauto.
- - simpl; intros. destruct H0 as [MS WF].
- exploit step_simulation; eauto. intros [ (s2' & A & B) | (A & B & C) ].
- + left; exists s2'; intuition auto. eapply wf_step; eauto.
- + right; intuition auto. eapply wf_step; eauto.
-Qed.
-
-End PRESERVATION.
diff --git a/configure b/configure
index 339c9bce..a7c9df9d 100755
--- a/configure
+++ b/configure
@@ -847,8 +847,8 @@ ARCHDIRS=$arch kvx/lib kvx/abstractbb kvx/abstractbb/Impure
BACKENDLIB=Machblock.v Machblockgen.v Machblockgenproof.v OptionMonad.v IterList.v PseudoAsmblock.v PseudoAsmblockproof.v ForwardSimulationBlock.v\\
AbstractBasicBlocksDef.v SeqSimuTheory.v ImpSimuTest.v Parallelizability.v\\
ImpConfig.v ImpCore.v ImpExtern.v ImpHCons.v ImpIO.v ImpLoops.v ImpMonads.v ImpPrelude.v\\
- Asmblock.v\\
- Asmgenproof0.v Asmgenproof1.v Asmgenproof.v # TODO: CHANGE THIS
+ Asmblock.v Asmblockgen.v\\
+ Asmgenproof.v # TODO: CHANGE THIS
EOF
fi