(* * Vericert: Verified high-level synthesis. * Copyright (C) 2023 Yann Herklotz * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program. If not, see . *) Require Import Coq.micromega.Lia. Require Import compcert.lib.Maps. Require Import compcert.common.Errors. Require compcert.common.Globalenvs. Require compcert.lib.Integers. Require Import compcert.common.AST. Require Import vericert.common.Statemonad. Require Import vericert.common.Vericertlib. Require Import vericert.hls.AssocMap. Require Import vericert.hls.DHTL. Require Import vericert.hls.ValueInt. Require Import vericert.hls.Verilog. Require Import vericert.hls.Gible. Require Import vericert.hls.GiblePar. Require Import vericert.hls.Predicate. Require Import vericert.common.Errormonad. Import ErrorMonad. Import ErrorMonadExtra. Import MonadNotation. #[local] Open Scope monad_scope. #[local] Hint Resolve AssocMap.gempty : htlh. #[local] Hint Resolve AssocMap.gso : htlh. #[local] Hint Resolve AssocMap.gss : htlh. #[local] Hint Resolve Ple_refl : htlh. #[local] Hint Resolve Ple_succ : htlh. Record control_regs: Type := mk_control_regs { ctrl_st : reg; ctrl_stack : reg; ctrl_fin : reg; ctrl_return : reg; }. (* Definition pred_lit (preg: reg) (pred: predicate) := *) (* Vrange preg (Vlit (posToValue pred)) (Vlit (posToValue pred)). *) (* Fixpoint pred_expr (preg: reg) (p: pred_op) := *) (* match p with *) (* | Plit (b, pred) => *) (* if b *) (* then pred_lit preg pred *) (* else Vunop Vnot (pred_lit preg pred) *) (* | Ptrue => Vlit (ZToValue 1) *) (* | Pfalse => Vlit (ZToValue 0) *) (* | Pand p1 p2 => *) (* Vbinop Vand (pred_expr preg p1) (pred_expr preg p2) *) (* | Por p1 p2 => *) (* Vbinop Vor (pred_expr preg p1) (pred_expr preg p2) *) (* end. *) Definition pred_enc (pred: predicate) := xI pred. Definition reg_enc (r: reg) := xO r. Fixpoint pred_expr (p: pred_op) := match p with | Plit (b, pred) => if b then Vvar (pred_enc pred) else (Vbinop Veq (Vvar (pred_enc pred)) (Vlit Integers.Int.zero)) | Ptrue => Vlit (boolToValue true) | Pfalse => Vlit (boolToValue false) | Pand p1 p2 => Vbinop Vand (pred_expr p1) (pred_expr p2) | Por p1 p2 => Vbinop Vor (pred_expr p1) (pred_expr p2) end. Definition assignment : Type := expr -> expr -> stmnt. Definition translate_predicate (a : assignment) (p: option pred_op) (dst e: expr) := match p with | None => a dst e | Some pos => let pos' := deep_simplify peq pos in match sat_pred_simple (negate pos') with | None => a dst e | Some _ => a dst (Vternary (pred_expr pos') e dst) end end. Definition state_goto (p: option pred_op) (st : reg) (n : node) : stmnt := translate_predicate Vblock p (Vvar st) (Vlit (posToValue n)). Definition state_cond (p: option pred_op) (st : reg) (c : expr) (n1 n2 : node) : stmnt := translate_predicate Vblock p (Vvar st) (Vternary c (posToExpr n1) (posToExpr n2)). Definition nonblock (dst : reg) (e : expr) := Vnonblock (Vvar (reg_enc dst)) e. Definition block (dst : reg) (e : expr) := Vblock (Vvar (reg_enc dst)) e. Definition bop (op : binop) (r1 r2 : reg) : expr := Vbinop op (Vvar (reg_enc r1)) (Vvar (reg_enc r2)). Definition boplit (op : binop) (r : reg) (l : Integers.int) : expr := Vbinop op (Vvar (reg_enc r)) (Vlit (intToValue l)). Definition boplitz (op: binop) (r: reg) (l: Z) : expr := Vbinop op (Vvar (reg_enc r)) (Vlit (ZToValue l)). Definition error {A} m := @Errors.Error A (Errors.msg m). Definition translate_comparison (c : Integers.comparison) (args : list reg) : Errors.res expr := match c, args with | Integers.Ceq, r1::r2::nil => ret (bop Veq r1 r2) | Integers.Cne, r1::r2::nil => ret (bop Vne r1 r2) | Integers.Clt, r1::r2::nil => ret (bop Vlt r1 r2) | Integers.Cgt, r1::r2::nil => ret (bop Vgt r1 r2) | Integers.Cle, r1::r2::nil => ret (bop Vle r1 r2) | Integers.Cge, r1::r2::nil => ret (bop Vge r1 r2) | _, _ => error "Htlpargen: comparison instruction not implemented: other" end. Definition translate_comparison_imm (c : Integers.comparison) (args : list reg) (i: Integers.int) : Errors.res expr := match c, args with | Integers.Ceq, r1::nil => Errors.OK (boplit Veq r1 i) | Integers.Cne, r1::nil => Errors.OK (boplit Vne r1 i) | Integers.Clt, r1::nil => Errors.OK (boplit Vlt r1 i) | Integers.Cgt, r1::nil => Errors.OK (boplit Vgt r1 i) | Integers.Cle, r1::nil => Errors.OK (boplit Vle r1 i) | Integers.Cge, r1::nil => Errors.OK (boplit Vge r1 i) | _, _ => error "Htlpargen: comparison_imm instruction not implemented: other" end. Definition translate_comparisonu (c : Integers.comparison) (args : list reg) : Errors.res expr := match c, args with | Integers.Clt, r1::r2::nil => Errors.OK (bop Vltu r1 r2) | Integers.Cgt, r1::r2::nil => Errors.OK (bop Vgtu r1 r2) | Integers.Cle, r1::r2::nil => Errors.OK (bop Vleu r1 r2) | Integers.Cge, r1::r2::nil => Errors.OK (bop Vgeu r1 r2) | _, _ => Errors.Error (Errors.msg "Htlpargen: comparison instruction not implemented: other") end. Definition translate_comparison_immu (c : Integers.comparison) (args : list reg) (i: Integers.int) : Errors.res expr := match c, args with | Integers.Clt, r1::nil => Errors.OK (boplit Vltu r1 i) | Integers.Cgt, r1::nil => Errors.OK (boplit Vgtu r1 i) | Integers.Cle, r1::nil => Errors.OK (boplit Vleu r1 i) | Integers.Cge, r1::nil => Errors.OK (boplit Vgeu r1 i) | _, _ => Errors.Error (Errors.msg "Htlpargen: comparison_imm instruction not implemented: other") end. Definition translate_condition (c : Op.condition) (args : list reg) : Errors.res expr := match c, args with | Op.Ccomp c, _ => translate_comparison c args | Op.Ccompu c, _ => translate_comparisonu c args | Op.Ccompimm c i, _ => translate_comparison_imm c args i | Op.Ccompuimm c i, _ => translate_comparison_immu c args i | Op.Cmaskzero n, _ => Errors.Error (Errors.msg "Htlpargen: condition instruction not implemented: Cmaskzero") | Op.Cmasknotzero n, _ => Errors.Error (Errors.msg "Htlpargen: condition instruction not implemented: Cmasknotzero") | _, _ => Errors.Error (Errors.msg "Htlpargen: condition instruction not implemented: other") end. Definition check_address_parameter_signed (p : Z) : bool := Z.leb Integers.Ptrofs.min_signed p && Z.leb p Integers.Ptrofs.max_signed. Definition check_address_parameter_unsigned (p : Z) : bool := Z.leb p Integers.Ptrofs.max_unsigned. Definition translate_eff_addressing (a: Op.addressing) (args: list reg) : Errors.res expr := match a, args with (* TODO: We should be more methodical here; what are the possibilities?*) | Op.Aindexed off, r1::nil => if (check_address_parameter_signed off) then Errors.OK (boplitz Vadd r1 off) else Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed): address out of bounds") | Op.Ascaled scale offset, r1::nil => if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) then Errors.OK (Vbinop Vadd (boplitz Vmul r1 scale) (Vlit (ZToValue offset))) else Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing (Ascaled): address out of bounds") | Op.Aindexed2 offset, r1::r2::nil => if (check_address_parameter_signed offset) then Errors.OK (Vbinop Vadd (bop Vadd r1 r2) (Vlit (ZToValue offset))) else Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed2): address out of bounds") | Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *) if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) then Errors.OK (Vbinop Vadd (Vvar (reg_enc r1)) (Vbinop Vadd (boplitz Vmul r2 scale) (Vlit (ZToValue offset)))) else Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed2scaled): address out of bounds") | Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *) let a := Integers.Ptrofs.unsigned a in if (check_address_parameter_unsigned a) then Errors.OK (Vlit (ZToValue a)) else Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing (Ainstack): address out of bounds") | _, _ => Errors.Error (Errors.msg "Veriloggen: translate_eff_addressing unsuported addressing") end. #[local] Close Scope monad_scope. #[local] Open Scope error_monad_scope. (** Translate an instruction to a statement. FIX mulhs mulhu *) Definition translate_instr (op : Op.operation) (args : list reg) : Errors.res expr := match op, args with | Op.Omove, r::nil => Errors.OK (Vvar (reg_enc r)) | Op.Ointconst n, _ => Errors.OK (Vlit (intToValue n)) | Op.Oneg, r::nil => Errors.OK (Vunop Vneg (Vvar (reg_enc r))) | Op.Osub, r1::r2::nil => Errors.OK (bop Vsub r1 r2) | Op.Omul, r1::r2::nil => Errors.OK (bop Vmul r1 r2) | Op.Omulimm n, r::nil => Errors.OK (boplit Vmul r n) | Op.Omulhs, r1::r2::nil => Errors.Error (Errors.msg "Htlpargen: Instruction not implemented: mulhs") | Op.Omulhu, r1::r2::nil => Errors.Error (Errors.msg "Htlpargen: Instruction not implemented: mulhu") | Op.Odiv, r1::r2::nil => Errors.OK (bop Vdiv r1 r2) | Op.Odivu, r1::r2::nil => Errors.OK (bop Vdivu r1 r2) | Op.Omod, r1::r2::nil => Errors.OK (bop Vmod r1 r2) | Op.Omodu, r1::r2::nil => Errors.OK (bop Vmodu r1 r2) | Op.Oand, r1::r2::nil => Errors.OK (bop Vand r1 r2) | Op.Oandimm n, r::nil => Errors.OK (boplit Vand r n) | Op.Oor, r1::r2::nil => Errors.OK (bop Vor r1 r2) | Op.Oorimm n, r::nil => Errors.OK (boplit Vor r n) | Op.Oxor, r1::r2::nil => Errors.OK (bop Vxor r1 r2) | Op.Oxorimm n, r::nil => Errors.OK (boplit Vxor r n) | Op.Onot, r::nil => Errors.OK (Vunop Vnot (Vvar (reg_enc r))) | Op.Oshl, r1::r2::nil => Errors.OK (bop Vshl r1 r2) | Op.Oshlimm n, r::nil => Errors.OK (boplit Vshl r n) | Op.Oshr, r1::r2::nil => Errors.OK (bop Vshr r1 r2) | Op.Oshrimm n, r::nil => Errors.OK (boplit Vshr r n) | Op.Oshrximm n, r::nil => Errors.OK (Vternary (Vbinop Vlt (Vvar (reg_enc r)) (Vlit (ZToValue 0))) (Vunop Vneg (Vbinop Vshru (Vunop Vneg (Vvar (reg_enc r))) (Vlit n))) (Vbinop Vshru (Vvar (reg_enc r)) (Vlit n))) | Op.Oshru, r1::r2::nil => Errors.OK (bop Vshru r1 r2) | Op.Oshruimm n, r::nil => Errors.OK (boplit Vshru r n) | Op.Ororimm n, r::nil => Errors.Error (Errors.msg "Htlpargen: Instruction not implemented: Ororimm") (*Errors.OK (Vbinop Vor (boplit Vshru r (Integers.Int.modu n (Integers.Int.repr 32))) (boplit Vshl r (Integers.Int.sub (Integers.Int.repr 32) (Integers.Int.modu n (Integers.Int.repr 32)))))*) | Op.Oshldimm n, r::nil => Errors.OK (Vbinop Vor (boplit Vshl r n) (boplit Vshr r (Integers.Int.sub (Integers.Int.repr 32) n))) | Op.Ocmp c, _ => translate_condition c args | Op.Osel c AST.Tint, r1::r2::rl => do tc <- translate_condition c rl; Errors.OK (Vternary tc (Vvar (reg_enc r1)) (Vvar (reg_enc r2))) | Op.Olea a, _ => translate_eff_addressing a args | _, _ => Errors.Error (Errors.msg "Htlpargen: Instruction not implemented: other") end. Definition translate_arr_access (mem : AST.memory_chunk) (addr : Op.addressing) (args : list reg) (stack : reg) : Errors.res expr := match mem, addr, args with (* TODO: We should be more methodical here; what are the possibilities?*) | Mint32, Op.Aindexed off, r1::nil => if (check_address_parameter_signed off) then Errors.OK (Vvari stack (Vbinop Vdivu (boplitz Vadd r1 off) (Vlit (ZToValue 4)))) else Errors.Error (Errors.msg "HTLPargen: translate_arr_access address out of bounds") | Mint32, Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *) if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) then Errors.OK (Vvari stack (Vbinop Vdivu (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale)) (Vlit (ZToValue 4)))) else Errors.Error (Errors.msg "HTLPargen: translate_arr_access address out of bounds") | Mint32, Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *) let a := Integers.Ptrofs.unsigned a in if (check_address_parameter_unsigned a) then Errors.OK (Vvari stack (Vlit (ZToValue (a / 4)))) else Errors.Error (Errors.msg "HTLPargen: eff_addressing out of bounds stack offset") | _, _, _ => Errors.Error (Errors.msg "HTLPargen: translate_arr_access unsuported addressing") end. Fixpoint enumerate (i : nat) (ns : list node) {struct ns} : list (nat * node) := match ns with | n :: ns' => (i, n) :: enumerate (i+1) ns' | nil => nil end. Definition tbl_to_case_expr (st : reg) (ns : list node) : list (expr * stmnt) := List.map (fun a => match a with (i, n) => (Vlit (natToValue i), Vblock (Vvar st) (Vlit (posToValue n))) end) (enumerate 0 ns). Definition translate_cfi (ctrl: control_regs) p (cfi: cf_instr) : Errors.res stmnt := match cfi with | RBgoto n' => Errors.OK (state_goto p ctrl.(ctrl_st) n') | RBcond c args n1 n2 => do e <- translate_condition c args; Errors.OK (state_cond p ctrl.(ctrl_st) e n1 n2) | RBreturn r => match r with | Some r' => Errors.OK (Vseq (block ctrl.(ctrl_fin) (Vlit (ZToValue 1%Z))) (block ctrl.(ctrl_return) (Vvar r'))) | None => Errors.OK (Vseq (block ctrl.(ctrl_fin) (Vlit (ZToValue 1%Z))) (block ctrl.(ctrl_return) (Vlit (ZToValue 0%Z)))) end | RBjumptable r tbl => Errors.OK (Vcase (Vvar r) (list_to_stmnt (tbl_to_case_expr ctrl.(ctrl_st) tbl)) (Some Vskip)) | RBcall sig ri rl r n => Errors.Error (Errors.msg "HTLPargen: RBcall not supported.") | RBtailcall sig ri lr => Errors.Error (Errors.msg "HTLPargen: RBtailcall not supported.") | RBbuiltin e lb b n => Errors.Error (Errors.msg "HTLPargen: RBbuildin not supported.") end. Definition transf_instr (ctrl: control_regs) (dc: pred_op * stmnt) (i: instr) : Errors.res (pred_op * stmnt) := let '(curr_p, d) := dc in let npred p := Some (Pand curr_p (dfltp p)) in match i with | RBnop => Errors.OK dc | RBop p op args dst => do instr <- translate_instr op args; let stmnt := translate_predicate Vblock (npred p) (Vvar dst) instr in Errors.OK (curr_p, Vseq d stmnt) | RBload p mem addr args dst => do src <- translate_arr_access mem addr args ctrl.(ctrl_stack); let stmnt := translate_predicate Vblock (npred p) (Vvar dst) src in Errors.OK (curr_p, Vseq d stmnt) | RBstore p mem addr args src => do dst <- translate_arr_access mem addr args ctrl.(ctrl_stack); let stmnt := translate_predicate Vblock (npred p) dst (Vvar src) in Errors.OK (curr_p, Vseq d stmnt) | RBsetpred p' cond args p => do cond' <- translate_condition cond args; let stmnt := translate_predicate Vblock (npred p') (pred_expr (Plit (true, p))) cond' in Errors.OK (curr_p, Vseq d stmnt) | RBexit p cf => do d_stmnt <- translate_cfi ctrl (npred p) cf; Errors.OK (Pand curr_p (negate (dfltp p)), Vseq d d_stmnt) end. Definition transf_chained_block (ctrl: control_regs) (dc: @pred_op positive * stmnt) (block: list instr) : Errors.res (pred_op * stmnt) := mfold_left (transf_instr ctrl) block (ret dc). Definition transf_parallel_block (ctrl: control_regs) (dc: @pred_op positive * stmnt) (block: list (list instr)) : Errors.res (pred_op * stmnt) := mfold_left (transf_chained_block ctrl) block (ret dc). Definition transf_parallel_full_stmnt ctrl curr_p n block := do ctrl_init_stmnt <- translate_cfi ctrl (Some curr_p) (RBgoto (n - 1)%positive); transf_parallel_block ctrl (curr_p, ctrl_init_stmnt) block. Definition transf_parallel_full_block (ctrl: control_regs) (dc: node * @pred_op positive * datapath) (block: list (list instr)) : Errors.res (node * pred_op * datapath) := let '(n, curr_p, dt) := dc in match AssocMap.get n dt with | None => do (curr_p', dt_stmnt) <- transf_parallel_full_stmnt ctrl curr_p n block; Errors.OK ((n - 1)%positive, curr_p', AssocMap.set n dt_stmnt dt) | _ => Errors.Error (msg "HtlPargen.transf_parallel_full_block: block not empty") end. Definition transf_seq_block (ctrl: control_regs) (d: datapath) (ni: node * ParBB.t) : Errors.res datapath := let (n, block) := ni in do res <- mfold_left (transf_parallel_full_block ctrl) block (ret (n, Ptrue, d)); let '(_, _, d') := res in Errors.OK d'. Definition stack_correct (sz : Z) : bool := (0 <=? sz) && (sz Pos.max m pc) m 1%positive. Lemma max_pc_map_sound: forall m pc i, m!pc = Some i -> Ple pc (max_pc_map m). Proof. intros until i. unfold max_pc_function. apply PTree_Properties.fold_rec with (P := fun c m => c!pc = Some i -> Ple pc m). (* extensionality *) intros. apply H0. rewrite H; auto. (* base case *) rewrite PTree.gempty. congruence. (* inductive case *) intros. rewrite PTree.gsspec in H2. destruct (peq pc k). inv H2. unfold Ple; lia. apply Ple_trans with a. auto. unfold Ple; lia. Qed. Lemma max_pc_wf : forall m, Z.pos (max_pc_map m) <= Integers.Int.max_unsigned -> map_well_formed m. Proof. unfold map_well_formed. intros. exploit list_in_map_inv. eassumption. intros [x [A B]]. destruct x. apply Maps.PTree.elements_complete in B. apply max_pc_map_sound in B. unfold Ple in B. apply Pos2Z.pos_le_pos in B. subst. simplify. transitivity (Z.pos (max_pc_map m)); eauto. Qed. Definition decide_order a b c d e f g : {module_ordering a b c d e f g} + {True}. refine (match bool_dec ((a left _ | _ => _ end); auto. simplify; repeat match goal with | H: context[(_ apply Pos.ltb_lt in H end; unfold module_ordering; auto. Defined. Definition max_resource_function (f: function) := Pos.max (reg_enc (max_reg_function f)) (pred_enc (max_pred_function f)). Program Definition transl_module (f: function) : res DHTL.module := if stack_correct f.(fn_stacksize) then let st := Pos.succ (max_resource_function f) in let fin := Pos.succ st in let rtrn := Pos.succ fin in let stack := Pos.succ rtrn in let start := Pos.succ stack in let rst := Pos.succ start in let clk := Pos.succ rst in do _stmnt <- mfold_left (transf_seq_block (mk_control_regs st stack fin rtrn)) (Maps.PTree.elements f.(GiblePar.fn_code)) (ret (PTree.empty _)); match zle (Z.pos (max_pc_map _stmnt)) Integers.Int.max_unsigned, decide_order st fin rtrn stack start rst clk, max_list_dec (List.map reg_enc (GiblePar.fn_params f)) st with | left LEDATA, left MORD, left WFPARAMS => ret (DHTL.mkmodule (List.map reg_enc f.(GiblePar.fn_params)) _stmnt f.(fn_entrypoint) st stack (Z.to_nat (f.(fn_stacksize) / 4)) fin rtrn start rst clk (AssocMap.empty _) (AssocMap.empty _) None (max_pc_wf _ LEDATA) MORD _ WFPARAMS) | _, _, _ => error "More than 2^32 states" end else error "Stack size misalignment". Definition transl_fundef := transf_partial_fundef transl_module. Definition main_is_internal (p : GiblePar.program) : bool := let ge := Globalenvs.Genv.globalenv p in match Globalenvs.Genv.find_symbol ge p.(AST.prog_main) with | Some b => match Globalenvs.Genv.find_funct_ptr ge b with | Some (AST.Internal _) => true | _ => false end | _ => false end. Definition transl_program (p : GiblePar.program) : Errors.res DHTL.program := if main_is_internal p then transform_partial_program transl_fundef p else Errors.Error (Errors.msg "Main function is not Internal").