diff options
Diffstat (limited to 'docs')
| -rw-r--r-- | docs/basic-block-generation.org | 497 | ||||
| -rw-r--r-- | docs/scheduler-languages.org | 682 | ||||
| -rw-r--r-- | docs/scheduler.org | 2317 |
3 files changed, 0 insertions, 3496 deletions
diff --git a/docs/basic-block-generation.org b/docs/basic-block-generation.org deleted file mode 100644 index 1d78dad..0000000 --- a/docs/basic-block-generation.org +++ /dev/null @@ -1,497 +0,0 @@ -#+title: Basic Block Generation -#+author: Yann Herklotz -#+email: yann [at] yannherklotz [dot] com - -* RTLBlockgen -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLBlockgen.v -:END: - -Refers to [[rtlblockgen-equalities][rtlblockgen-equalities]]. - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlblockgen-imports -#+begin_src coq -Require compcert.backend.RTL. -Require Import compcert.common.AST. -Require Import compcert.lib.Maps. -Require Import compcert.lib.Integers. -Require Import compcert.lib.Floats. - -Require Import vericert.common.Vericertlib. -Require Import vericert.hls.RTLBlockInstr. -Require Import vericert.hls.RTLBlock. - -#[local] Open Scope positive. -#+end_src - -#+name: rtlblockgen-equalities-insert -#+begin_src coq :comments no -<<rtlblockgen-equalities>> -#+end_src - -#+name: rtlblockgen-main -#+begin_src coq -Parameter partition : RTL.function -> Errors.res function. - -(** [find_block max nodes index]: Does not need to be sorted, because we use filter and the max fold - function to find the desired element. *) -Definition find_block (max: positive) (nodes: list positive) (index: positive) : positive := - List.fold_right Pos.min max (List.filter (fun x => (index <=? x)) nodes). - -(*Compute find_block (2::94::28::40::19::nil) 40.*) - -Definition check_instr (n: positive) (istr: RTL.instruction) (istr': instr) := - match istr, istr' with - | RTL.Inop n', RBnop => (n' + 1 =? n) - | RTL.Iop op args dst n', RBop None op' args' dst' => - ceq operation_eq op op' && - ceq list_pos_eq args args' && - ceq peq dst dst' && (n' + 1 =? n) - | RTL.Iload chunk addr args dst n', RBload None chunk' addr' args' dst' => - ceq memory_chunk_eq chunk chunk' && - ceq addressing_eq addr addr' && - ceq list_pos_eq args args' && - ceq peq dst dst' && - (n' + 1 =? n) - | RTL.Istore chunk addr args src n', RBstore None chunk' addr' args' src' => - ceq memory_chunk_eq chunk chunk' && - ceq addressing_eq addr addr' && - ceq list_pos_eq args args' && - ceq peq src src' && - (n' + 1 =? n) - | _, _ => false - end. - -Definition check_cf_instr_body (istr: RTL.instruction) (istr': instr): bool := - match istr, istr' with - | RTL.Iop op args dst _, RBop None op' args' dst' => - ceq operation_eq op op' && - ceq list_pos_eq args args' && - ceq peq dst dst' - | RTL.Iload chunk addr args dst _, RBload None chunk' addr' args' dst' => - ceq memory_chunk_eq chunk chunk' && - ceq addressing_eq addr addr' && - ceq list_pos_eq args args' && - ceq peq dst dst' - | RTL.Istore chunk addr args src _, RBstore None chunk' addr' args' src' => - ceq memory_chunk_eq chunk chunk' && - ceq addressing_eq addr addr' && - ceq list_pos_eq args args' && - ceq peq src src' - | RTL.Inop _, RBnop - | RTL.Icall _ _ _ _ _, RBnop - | RTL.Itailcall _ _ _, RBnop - | RTL.Ibuiltin _ _ _ _, RBnop - | RTL.Icond _ _ _ _, RBnop - | RTL.Ijumptable _ _, RBnop - | RTL.Ireturn _, RBnop => true - | _, _ => false - end. - -Definition check_cf_instr (istr: RTL.instruction) (istr': cf_instr) := - match istr, istr' with - | RTL.Inop n, RBgoto n' => (n =? n') - | RTL.Iop _ _ _ n, RBgoto n' => (n =? n') - | RTL.Iload _ _ _ _ n, RBgoto n' => (n =? n') - | RTL.Istore _ _ _ _ n, RBgoto n' => (n =? n') - | RTL.Icall sig (inl r) args dst n, RBcall sig' (inl r') args' dst' n' => - ceq signature_eq sig sig' && - ceq peq r r' && - ceq list_pos_eq args args' && - ceq peq dst dst' && - (n =? n') - | RTL.Icall sig (inr i) args dst n, RBcall sig' (inr i') args' dst' n' => - ceq signature_eq sig sig' && - ceq peq i i' && - ceq list_pos_eq args args' && - ceq peq dst dst' && - (n =? n') - | RTL.Itailcall sig (inl r) args, RBtailcall sig' (inl r') args' => - ceq signature_eq sig sig' && - ceq peq r r' && - ceq list_pos_eq args args' - | RTL.Itailcall sig (inr r) args, RBtailcall sig' (inr r') args' => - ceq signature_eq sig sig' && - ceq peq r r' && - ceq list_pos_eq args args' - | RTL.Icond cond args n1 n2, RBcond cond' args' n1' n2' => - ceq condition_eq cond cond' && - ceq list_pos_eq args args' && - ceq peq n1 n1' && ceq peq n2 n2' - | RTL.Ijumptable r ns, RBjumptable r' ns' => - ceq peq r r' && ceq list_pos_eq ns ns' - | RTL.Ireturn (Some r), RBreturn (Some r') => - ceq peq r r' - | RTL.Ireturn None, RBreturn None => true - | _, _ => false - end. - -Definition is_cf_instr (n: positive) (i: RTL.instruction) := - match i with - | RTL.Inop n' => negb (n' + 1 =? n) - | RTL.Iop _ _ _ n' => negb (n' + 1 =? n) - | RTL.Iload _ _ _ _ n' => negb (n' + 1 =? n) - | RTL.Istore _ _ _ _ n' => negb (n' + 1 =? n) - | RTL.Icall _ _ _ _ _ => true - | RTL.Itailcall _ _ _ => true - | RTL.Ibuiltin _ _ _ _ => true - | RTL.Icond _ _ _ _ => true - | RTL.Ijumptable _ _ => true - | RTL.Ireturn _ => true - end. - -Definition check_present_blocks (c: code) (n: list positive) (max: positive) (i: positive) (istr: RTL.instruction) := - let blockn := find_block max n i in - match c ! blockn with - | Some istrs => - match List.nth_error istrs.(bb_body) (Pos.to_nat blockn - Pos.to_nat i)%nat with - | Some istr' => - if is_cf_instr i istr - then check_cf_instr istr istrs.(bb_exit) && check_cf_instr_body istr istr' - else check_instr i istr istr' - | None => false - end - | None => false - end. - -Definition transl_function (f: RTL.function) := - match partition f with - | Errors.OK f' => - let blockids := map fst (PTree.elements f'.(fn_code)) in - if forall_ptree (check_present_blocks f'.(fn_code) blockids (fold_right Pos.max 1 blockids)) - f.(RTL.fn_code) then - Errors.OK f' - else Errors.Error (Errors.msg "check_present_blocks failed") - | Errors.Error msg => Errors.Error msg - end. - -Definition transl_fundef := transf_partial_fundef transl_function. - -Definition transl_program : RTL.program -> Errors.res program := - transform_partial_program transl_fundef. -#+end_src - -** Equalities - -#+name: rtlblockgen-equalities -#+begin_src coq :tangle no -Lemma comparison_eq: forall (x y : comparison), {x = y} + {x <> y}. -Proof. - decide equality. -Defined. - -Lemma condition_eq: forall (x y : Op.condition), {x = y} + {x <> y}. -Proof. - generalize comparison_eq; intro. - generalize Int.eq_dec; intro. - generalize Int64.eq_dec; intro. - decide equality. -Defined. - -Lemma addressing_eq : forall (x y : Op.addressing), {x = y} + {x <> y}. -Proof. - generalize Int.eq_dec; intro. - generalize AST.ident_eq; intro. - generalize Z.eq_dec; intro. - generalize Ptrofs.eq_dec; intro. - decide equality. -Defined. - -Lemma typ_eq : forall (x y : AST.typ), {x = y} + {x <> y}. -Proof. - decide equality. -Defined. - -Lemma operation_eq: forall (x y : Op.operation), {x = y} + {x <> y}. -Proof. - generalize Int.eq_dec; intro. - generalize Int64.eq_dec; intro. - generalize Float.eq_dec; intro. - generalize Float32.eq_dec; intro. - generalize AST.ident_eq; intro. - generalize condition_eq; intro. - generalize addressing_eq; intro. - generalize typ_eq; intro. - decide equality. -Defined. - -Lemma memory_chunk_eq : forall (x y : AST.memory_chunk), {x = y} + {x <> y}. -Proof. - decide equality. -Defined. - -Lemma list_typ_eq: forall (x y : list AST.typ), {x = y} + {x <> y}. -Proof. - generalize typ_eq; intro. - decide equality. -Defined. - -Lemma option_typ_eq : forall (x y : option AST.typ), {x = y} + {x <> y}. -Proof. - generalize typ_eq; intro. - decide equality. -Defined. - -Lemma signature_eq: forall (x y : AST.signature), {x = y} + {x <> y}. -Proof. - repeat decide equality. -Defined. - -Lemma list_operation_eq : forall (x y : list Op.operation), {x = y} + {x <> y}. -Proof. - generalize operation_eq; intro. - decide equality. -Defined. - -Lemma list_pos_eq : forall (x y : list positive), {x = y} + {x <> y}. -Proof. - generalize Pos.eq_dec; intros. - decide equality. -Defined. - -Lemma sig_eq : forall (x y : AST.signature), {x = y} + {x <> y}. -Proof. - repeat decide equality. -Defined. - -Lemma instr_eq: forall (x y : instr), {x = y} + {x <> y}. -Proof. - generalize Pos.eq_dec; intro. - generalize typ_eq; intro. - generalize Int.eq_dec; intro. - generalize memory_chunk_eq; intro. - generalize addressing_eq; intro. - generalize operation_eq; intro. - generalize condition_eq; intro. - generalize signature_eq; intro. - generalize list_operation_eq; intro. - generalize list_pos_eq; intro. - generalize AST.ident_eq; intro. - repeat decide equality. -Defined. - -Lemma cf_instr_eq: forall (x y : cf_instr), {x = y} + {x <> y}. -Proof. - generalize Pos.eq_dec; intro. - generalize typ_eq; intro. - generalize Int.eq_dec; intro. - generalize Int64.eq_dec; intro. - generalize Float.eq_dec; intro. - generalize Float32.eq_dec; intro. - generalize Ptrofs.eq_dec; intro. - generalize memory_chunk_eq; intro. - generalize addressing_eq; intro. - generalize operation_eq; intro. - generalize condition_eq; intro. - generalize signature_eq; intro. - generalize list_operation_eq; intro. - generalize list_pos_eq; intro. - generalize AST.ident_eq; intro. - repeat decide equality. -Defined. - -Definition ceq {A: Type} (eqd: forall a b: A, {a = b} + {a <> b}) (a b: A): bool := - if eqd a b then true else false. -#+end_src - -* RTLBlockgenproof -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLBlockgenproof.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -** Imports - -#+name: rtlblockgenproof-imports -#+begin_src coq -Require compcert.backend.RTL. -Require Import compcert.common.AST. -Require Import compcert.lib.Maps. - -Require Import vericert.hls.RTLBlock. -Require Import vericert.hls.RTLBlockgen. -#+end_src - -** Match states - -The ~match_states~ predicate describes which states are equivalent between the two languages, in this -case ~RTL~ and ~RTLBlock~. - -#+name: rtlblockgenproof-match-states -#+begin_src coq -Inductive match_states : RTL.state -> RTLBlock.state -> Prop := -| match_state : - forall stk f tf sp pc rs m - (TF: transl_function f = OK tf), - match_states (RTL.State stk f sp pc rs m) - (RTLBlock.State stk tf sp (find_block max n i) rs m). -#+end_src - -** Correctness - -#+name: rtlblockgenproof-correctness -#+begin_src coq -Section CORRECTNESS. - - Context (prog : RTL.program). - Context (tprog : RTLBlock.program). - - Context (TRANSL : match_prog prog tprog). - - Theorem transf_program_correct: - Smallstep.forward_simulation (RTL.semantics prog) (RTLBlock.semantics tprog). - Proof. - eapply Smallstep.forward_simulation_plus; eauto with htlproof. - apply senv_preserved. - -End CORRECTNESS. -#+end_src - -* Partition -:PROPERTIES: -:header-args:ocaml: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/Partition.ml -:END: - -#+begin_src ocaml :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: partition-main -#+begin_src ocaml -open Printf -open Clflags -open Camlcoq -open Datatypes -open Coqlib -open Maps -open AST -open Kildall -open Op -open RTLBlockInstr -open RTLBlock - -(** Assuming that the nodes of the CFG [code] are numbered in reverse postorder (cf. pass - [Renumber]), an edge from [n] to [s] is a normal edge if [s < n] and a back-edge otherwise. *) -let find_edge i n = - let succ = RTL.successors_instr i in - let filt = List.filter (fun s -> P.lt n s || P.lt s (P.pred n)) succ in - ((match filt with [] -> [] | _ -> [n]), filt) - -let find_edges c = - PTree.fold (fun l n i -> - let f = find_edge i n in - (List.append (fst f) (fst l), List.append (snd f) (snd l))) c ([], []) - -let prepend_instr i = function - | {bb_body = bb; bb_exit = e} -> {bb_body = (i :: bb); bb_exit = e} - -let translate_inst = function - | RTL.Inop _ -> Some RBnop - | RTL.Iop (op, ls, dst, _) -> Some (RBop (None, op, ls, dst)) - | RTL.Iload (m, addr, ls, dst, _) -> Some (RBload (None, m, addr, ls, dst)) - | RTL.Istore (m, addr, ls, src, _) -> Some (RBstore (None, m, addr, ls, src)) - | _ -> None - -let translate_cfi = function - | RTL.Icall (s, r, ls, dst, n) -> Some (RBcall (s, r, ls, dst, n)) - | RTL.Itailcall (s, r, ls) -> Some (RBtailcall (s, r, ls)) - | RTL.Ibuiltin (e, ls, r, n) -> Some (RBbuiltin (e, ls, r, n)) - | RTL.Icond (c, ls, dst1, dst2) -> Some (RBcond (c, ls, dst1, dst2)) - | RTL.Ijumptable (r, ls) -> Some (RBjumptable (r, ls)) - | RTL.Ireturn r -> Some (RBreturn r) - | _ -> None - -let rec next_bblock_from_RTL is_start e (c : RTL.code) s i = - let succ = List.map (fun i -> (i, PTree.get i c)) (RTL.successors_instr i) in - let trans_inst = (translate_inst i, translate_cfi i) in - match trans_inst, succ with - | (None, Some i'), _ -> - if List.exists (fun x -> x = s) (snd e) && not is_start then - Errors.OK { bb_body = [RBnop]; bb_exit = RBgoto s } - else - Errors.OK { bb_body = [RBnop]; bb_exit = i' } - | (Some i', None), (s', Some i_n)::[] -> - if List.exists (fun x -> x = s) (fst e) then - Errors.OK { bb_body = [i']; bb_exit = RBgoto s' } - else if List.exists (fun x -> x = s) (snd e) && not is_start then - Errors.OK { bb_body = [RBnop]; bb_exit = RBgoto s } - else begin - match next_bblock_from_RTL false e c s' i_n with - | Errors.OK bb -> - Errors.OK (prepend_instr i' bb) - | Errors.Error msg -> Errors.Error msg - end - | _, _ -> - Errors.Error (Errors.msg (coqstring_of_camlstring "next_bblock_from_RTL went wrong.")) - -let rec traverseacc f l c = - match l with - | [] -> Errors.OK c - | x::xs -> - match f x c with - | Errors.Error msg -> Errors.Error msg - | Errors.OK x' -> - match traverseacc f xs x' with - | Errors.Error msg -> Errors.Error msg - | Errors.OK xs' -> Errors.OK xs' - -let rec translate_all edge c s res = - let c_bb, translated = res in - if List.exists (fun x -> P.eq x s) translated then Errors.OK (c_bb, translated) else - (match PTree.get s c with - | None -> Errors.Error (Errors.msg (coqstring_of_camlstring "Could not translate all.")) - | Some i -> - match next_bblock_from_RTL true edge c s i with - | Errors.Error msg -> Errors.Error msg - | Errors.OK {bb_body = bb; bb_exit = e} -> - let succ = List.filter (fun x -> P.lt x s) (successors_instr e) in - (match traverseacc (translate_all edge c) succ (c_bb, s :: translated) with - | Errors.Error msg -> Errors.Error msg - | Errors.OK (c', t') -> - Errors.OK (PTree.set s {bb_body = bb; bb_exit = e} c', t'))) - -(* Partition a function and transform it into RTLBlock. *) -let function_from_RTL f = - let e = find_edges f.RTL.fn_code in - match translate_all e f.RTL.fn_code f.RTL.fn_entrypoint (PTree.empty, []) with - | Errors.Error msg -> Errors.Error msg - | Errors.OK (c, _) -> - Errors.OK { fn_sig = f.RTL.fn_sig; - fn_stacksize = f.RTL.fn_stacksize; - fn_params = f.RTL.fn_params; - fn_entrypoint = f.RTL.fn_entrypoint; - fn_code = c - } - -let partition = function_from_RTL -#+end_src - -* License - -#+name: license -#+begin_src coq :tangle no -(* - * Vericert: Verified high-level synthesis. - * Copyright (C) 2020-2022 Yann Herklotz <yann@yannherklotz.com> - * - * 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 <https://www.gnu.org/licenses/>. - *) -#+end_src diff --git a/docs/scheduler-languages.org b/docs/scheduler-languages.org deleted file mode 100644 index 02249f8..0000000 --- a/docs/scheduler-languages.org +++ /dev/null @@ -1,682 +0,0 @@ -#+title: Scheduler Languages -#+author: Yann Herklotz -#+email: yann [at] yannherklotz [dot] com - -* RTLBlockInstr -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLBlockInstr.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlblockinstr-imports -#+begin_src coq -Require Import Coq.micromega.Lia. - -Require Import compcert.backend.Registers. -Require Import compcert.common.AST. -Require Import compcert.common.Events. -Require Import compcert.common.Globalenvs. -Require Import compcert.common.Memory. -Require Import compcert.common.Values. -Require Import compcert.lib.Integers. -Require Import compcert.lib.Maps. -Require Import compcert.verilog.Op. - -Require Import Predicate. -Require Import Vericertlib. -#+end_src - -These instructions are used for ~RTLBlock~ and ~RTLPar~, so that they have consistent instructions, -which greatly simplifies the proofs, as they will by default have the same instruction syntax and -semantics. The only changes are therefore at the top-level of the instructions. - -** Instruction Definition - -First, we define the instructions that can be placed into a basic block, meaning they won't branch. -The main changes to how instructions are defined in [RTL], is that these instructions don't have a -next node, as they will be in a basic block, and they also have an optional predicate ([pred_op]). - -#+name: rtlblockinstr-instr-def -#+begin_src coq -Definition node := positive. - -Inductive instr : Type := -| RBnop : instr -| RBop : option pred_op -> operation -> list reg -> reg -> instr -| RBload : option pred_op -> memory_chunk -> addressing -> list reg -> reg -> instr -| RBstore : option pred_op -> memory_chunk -> addressing -> list reg -> reg -> instr -| RBsetpred : option pred_op -> condition -> list reg -> predicate -> instr. -#+end_src - -** Control-Flow Instruction Definition - -These are the instructions that count as control-flow, and will be placed at the end of the basic -blocks. - -#+name: rtlblockinstr-cf-instr-def -#+begin_src coq -Inductive cf_instr : Type := -| RBcall : signature -> reg + ident -> list reg -> reg -> node -> cf_instr -| RBtailcall : signature -> reg + ident -> list reg -> cf_instr -| RBbuiltin : external_function -> list (builtin_arg reg) -> - builtin_res reg -> node -> cf_instr -| RBcond : condition -> list reg -> node -> node -> cf_instr -| RBjumptable : reg -> list node -> cf_instr -| RBreturn : option reg -> cf_instr -| RBgoto : node -> cf_instr -| RBpred_cf : pred_op -> cf_instr -> cf_instr -> cf_instr. -#+end_src - -** Helper functions - -#+name: rtlblockinstr-helpers -#+begin_src coq -Fixpoint successors_instr (i : cf_instr) : list node := - match i with - | RBcall sig ros args res s => s :: nil - | RBtailcall sig ros args => nil - | RBbuiltin ef args res s => s :: nil - | RBcond cond args ifso ifnot => ifso :: ifnot :: nil - | RBjumptable arg tbl => tbl - | RBreturn optarg => nil - | RBgoto n => n :: nil - | RBpred_cf p c1 c2 => concat (successors_instr c1 :: successors_instr c2 :: nil) - end. - -Definition max_reg_instr (m: positive) (i: instr) := - match i with - | RBnop => m - | RBop p op args res => - fold_left Pos.max args (Pos.max res m) - | RBload p chunk addr args dst => - fold_left Pos.max args (Pos.max dst m) - | RBstore p chunk addr args src => - fold_left Pos.max args (Pos.max src m) - | RBsetpred p' c args p => - fold_left Pos.max args m - end. - -Fixpoint max_reg_cfi (m : positive) (i : cf_instr) := - match i with - | RBcall sig (inl r) args res s => - fold_left Pos.max args (Pos.max r (Pos.max res m)) - | RBcall sig (inr id) args res s => - fold_left Pos.max args (Pos.max res m) - | RBtailcall sig (inl r) args => - fold_left Pos.max args (Pos.max r m) - | RBtailcall sig (inr id) args => - fold_left Pos.max args m - | RBbuiltin ef args res s => - fold_left Pos.max (params_of_builtin_args args) - (fold_left Pos.max (params_of_builtin_res res) m) - | RBcond cond args ifso ifnot => fold_left Pos.max args m - | RBjumptable arg tbl => Pos.max arg m - | RBreturn None => m - | RBreturn (Some arg) => Pos.max arg m - | RBgoto n => m - | RBpred_cf p c1 c2 => Pos.max (max_reg_cfi m c1) (max_reg_cfi m c2) - end. - -Definition regset := Regmap.t val. -Definition predset := PMap.t bool. - -Definition eval_predf (pr: predset) (p: pred_op) := - sat_predicate p (fun x => pr !! (Pos.of_nat x)). - -#[global] -Instance eval_predf_Proper : Proper (eq ==> equiv ==> eq) eval_predf. -Proof. - unfold Proper. simplify. unfold "==>". - intros. - unfold sat_equiv in *. intros. unfold eval_predf. subst. apply H0. -Qed. - -#[local] Open Scope pred_op. - -Lemma eval_predf_Pand : - forall ps p p', - eval_predf ps (p ∧ p') = eval_predf ps p && eval_predf ps p'. -Proof. unfold eval_predf; split; simplify; auto with bool. Qed. - -Lemma eval_predf_Por : - forall ps p p', - eval_predf ps (p ∨ p') = eval_predf ps p || eval_predf ps p'. -Proof. unfold eval_predf; split; simplify; auto with bool. Qed. - -Lemma eval_predf_pr_equiv : - forall p ps ps', - (forall x, ps !! x = ps' !! x) -> - eval_predf ps p = eval_predf ps' p. -Proof. - induction p; simplify; auto; - try (unfold eval_predf; simplify; repeat (destruct_match; []); inv Heqp0; rewrite <- H; auto); - [repeat rewrite eval_predf_Pand|repeat rewrite eval_predf_Por]; - erewrite IHp1; try eassumption; erewrite IHp2; eauto. -Qed. - -Fixpoint init_regs (vl: list val) (rl: list reg) {struct rl} : regset := - match rl, vl with - | r1 :: rs, v1 :: vs => Regmap.set r1 v1 (init_regs vs rs) - | _, _ => Regmap.init Vundef - end. -#+end_src - -*** Instruction State - -Definition of the instruction state, which contains the following: - -- ~is_rs~ :: This is the current state of the registers. -- ~is_ps~ :: This is the current state of the predicate registers, which is in a separate namespace - and area compared to the standard registers in [is_rs]. -- ~is_mem~ :: The current state of the memory. - -#+name: rtlblockinstr-instr-state -#+begin_src coq -Record instr_state := mk_instr_state { - is_rs: regset; - is_ps: predset; - is_mem: mem; -}. -#+end_src - -** Top-Level Type Definitions - -#+name: rtlblockinstr-type-def -#+begin_src coq -Section DEFINITION. - - Context {bblock_body: Type}. - - Record bblock : Type := mk_bblock { - bb_body: bblock_body; - bb_exit: cf_instr - }. - - Definition code: Type := PTree.t bblock. - - Record function: Type := mkfunction { - fn_sig: signature; - fn_params: list reg; - fn_stacksize: Z; - fn_code: code; - fn_entrypoint: node - }. - - Definition fundef := AST.fundef function. - - Definition program := AST.program fundef unit. - - Definition funsig (fd: fundef) := - match fd with - | Internal f => fn_sig f - | External ef => ef_sig ef - end. - - Inductive stackframe : Type := - | Stackframe: - forall (res: reg) (**r where to store the result *) - (f: function) (**r calling function *) - (sp: val) (**r stack pointer in calling function *) - (pc: node) (**r program point in calling function *) - (rs: regset) (**r register state in calling function *) - (pr: predset), (**r predicate state of the calling function *) - stackframe. -#+end_src - -*** State definition -:PROPERTIES: -:CUSTOM_ID: state -:END: - -Definition of the ~state~ type, which is used by the ~step~ functions. - -#+name: rtlblockinstr-state -#+begin_src coq - Variant state : Type := - | State: - forall (stack: list stackframe) (**r call stack *) - (f: function) (**r current function *) - (sp: val) (**r stack pointer *) - (pc: node) (**r current program point in [c] *) - (rs: regset) (**r register state *) - (pr: predset) (**r predicate register state *) - (m: mem), (**r memory state *) - state - | Callstate: - forall (stack: list stackframe) (**r call stack *) - (f: fundef) (**r function to call *) - (args: list val) (**r arguments to the call *) - (m: mem), (**r memory state *) - state - | Returnstate: - forall (stack: list stackframe) (**r call stack *) - (v: val) (**r return value for the call *) - (m: mem), (**r memory state *) - state. -#+end_src - -#+name: rtlblockinstr-state -#+begin_src coq -End DEFINITION. -#+end_src - -** Semantics - -#+name: rtlblockinstr-semantics -#+begin_src coq -Section RELSEM. - - Context {bblock_body : Type}. - - Definition genv := Genv.t (@fundef bblock_body) unit. - - Context (ge: genv). - - Definition find_function - (ros: reg + ident) (rs: regset) : option fundef := - match ros with - | inl r => Genv.find_funct ge rs#r - | inr symb => - match Genv.find_symbol ge symb with - | None => None - | Some b => Genv.find_funct_ptr ge b - end - end. - - Inductive eval_pred: option pred_op -> instr_state -> instr_state -> instr_state -> Prop := - | eval_pred_true: - forall i i' p, - eval_predf (is_ps i) p = true -> - eval_pred (Some p) i i' i' - | eval_pred_false: - forall i i' p, - eval_predf (is_ps i) p = false -> - eval_pred (Some p) i i' i - | eval_pred_none: - forall i i', eval_pred None i i' i. -#+end_src - -*** Step a single instruction -:PROPERTIES: -:CUSTOM_ID: step_instr -:END: - -#+name: rtlblockinstr-step_instr -#+begin_src coq - Inductive step_instr: val -> instr_state -> instr -> instr_state -> Prop := - | exec_RBnop: - forall sp ist, - step_instr sp ist RBnop ist - | exec_RBop: - forall op v res args rs m sp p ist pr, - eval_operation ge sp op rs##args m = Some v -> - eval_pred p (mk_instr_state rs pr m) (mk_instr_state (rs#res <- v) pr m) ist -> - step_instr sp (mk_instr_state rs pr m) (RBop p op args res) ist - | exec_RBload: - forall addr rs args a chunk m v dst sp p pr ist, - eval_addressing ge sp addr rs##args = Some a -> - Mem.loadv chunk m a = Some v -> - eval_pred p (mk_instr_state rs pr m) (mk_instr_state (rs#dst <- v) pr m) ist -> - step_instr sp (mk_instr_state rs pr m) (RBload p chunk addr args dst) ist - | exec_RBstore: - forall addr rs args a chunk m src m' sp p pr ist, - eval_addressing ge sp addr rs##args = Some a -> - Mem.storev chunk m a rs#src = Some m' -> - eval_pred p (mk_instr_state rs pr m) (mk_instr_state rs pr m') ist -> - step_instr sp (mk_instr_state rs pr m) (RBstore p chunk addr args src) ist - | exec_RBsetpred: - forall sp rs pr m p c b args p' ist, - Op.eval_condition c rs##args m = Some b -> - eval_pred p' (mk_instr_state rs pr m) (mk_instr_state rs (pr#p <- b) m) ist -> - step_instr sp (mk_instr_state rs pr m) (RBsetpred p' c args p) ist. -#+end_src - -*** Step a control-flow instruction -:PROPERTIES: -:CUSTOM_ID: step_cf_instr -:END: - -#+name: rtlblockinstr-step_cf_instr -#+begin_src coq - Inductive step_cf_instr: state -> cf_instr -> trace -> state -> Prop := - | exec_RBcall: - forall s f sp rs m res fd ros sig args pc pc' pr, - find_function ros rs = Some fd -> - funsig fd = sig -> - step_cf_instr (State s f sp pc rs pr m) (RBcall sig ros args res pc') - E0 (Callstate (Stackframe res f sp pc' rs pr :: s) fd rs##args m) - | exec_RBtailcall: - forall s f stk rs m sig ros args fd m' pc pr, - find_function ros rs = Some fd -> - funsig fd = sig -> - Mem.free m stk 0 f.(fn_stacksize) = Some m' -> - step_cf_instr (State s f (Vptr stk Ptrofs.zero) pc rs pr m) (RBtailcall sig ros args) - E0 (Callstate s fd rs##args m') - | exec_RBbuiltin: - forall s f sp rs m ef args res pc' vargs t vres m' pc pr, - eval_builtin_args ge (fun r => rs#r) sp m args vargs -> - external_call ef ge vargs m t vres m' -> - step_cf_instr (State s f sp pc rs pr m) (RBbuiltin ef args res pc') - t (State s f sp pc' (regmap_setres res vres rs) pr m') - | exec_RBcond: - forall s f sp rs m cond args ifso ifnot b pc pc' pr, - eval_condition cond rs##args m = Some b -> - pc' = (if b then ifso else ifnot) -> - step_cf_instr (State s f sp pc rs pr m) (RBcond cond args ifso ifnot) - E0 (State s f sp pc' rs pr m) - | exec_RBjumptable: - forall s f sp rs m arg tbl n pc pc' pr, - rs#arg = Vint n -> - list_nth_z tbl (Int.unsigned n) = Some pc' -> - step_cf_instr (State s f sp pc rs pr m) (RBjumptable arg tbl) - E0 (State s f sp pc' rs pr m) - | exec_RBreturn: - forall s f stk rs m or pc m' pr, - Mem.free m stk 0 f.(fn_stacksize) = Some m' -> - step_cf_instr (State s f (Vptr stk Ptrofs.zero) pc rs pr m) (RBreturn or) - E0 (Returnstate s (regmap_optget or Vundef rs) m') - | exec_RBgoto: - forall s f sp pc rs pr m pc', - step_cf_instr (State s f sp pc rs pr m) (RBgoto pc') E0 (State s f sp pc' rs pr m) - | exec_RBpred_cf: - forall s f sp pc rs pr m cf1 cf2 st' p t, - step_cf_instr (State s f sp pc rs pr m) (if eval_predf pr p then cf1 else cf2) t st' -> - step_cf_instr (State s f sp pc rs pr m) (RBpred_cf p cf1 cf2) t st'. -#+end_src - -#+name: rtlblockinstr-end_RELSEM -#+begin_src coq -End RELSEM. -#+end_src - -* RTLBlock -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLBlock.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlblock-main -#+begin_src coq -Require Import compcert.backend.Registers. -Require Import compcert.common.AST. -Require Import compcert.common.Events. -Require Import compcert.common.Globalenvs. -Require Import compcert.common.Memory. -Require Import compcert.common.Smallstep. -Require Import compcert.common.Values. -Require Import compcert.lib.Coqlib. -Require Import compcert.lib.Integers. -Require Import compcert.lib.Maps. -Require Import compcert.verilog.Op. - -Require Import vericert.hls.RTLBlockInstr. - -Definition bb := list instr. - -Definition bblock := @bblock bb. -Definition code := @code bb. -Definition function := @function bb. -Definition fundef := @fundef bb. -Definition program := @program bb. -Definition funsig := @funsig bb. -Definition stackframe := @stackframe bb. -Definition state := @state bb. - -Definition genv := @genv bb. -#+end_src - -** Semantics - -We first describe the semantics by assuming a global program environment with type ~genv~ which was -declared earlier. - -#+name: rtlblock-semantics -#+begin_src coq -Section RELSEM. - - Context (ge: genv). -#+end_src - -*** Instruction list step -:PROPERTIES: -:CUSTOM_ID: step_instr_list -:END: - -The ~step_instr_list~ definition describes the execution of a list of instructions in one big step, -inductively traversing the list of instructions and applying the ~step_instr~ ([[#step_instr][step_instr]]). - -#+name: rtlblock-step_instr_list -#+begin_src coq - Inductive step_instr_list: val -> instr_state -> list instr -> instr_state -> Prop := - | exec_RBcons: - forall state i state' state'' instrs sp, - step_instr ge sp state i state' -> - step_instr_list sp state' instrs state'' -> - step_instr_list sp state (i :: instrs) state'' - | exec_RBnil: - forall state sp, - step_instr_list sp state nil state. -#+end_src - -*** Top-level step -:PROPERTIES: -:CUSTOM_ID: rtlblock-step -:END: - -The step function itself then uses this big step of the list of instructions to then show a -transition from basic block to basic block. - -#+name: rtlblock-step -#+begin_src coq - Variant step: state -> trace -> state -> Prop := - | exec_bblock: - forall s f sp pc rs rs' m m' t s' bb pr pr', - f.(fn_code)!pc = Some bb -> - step_instr_list sp (mk_instr_state rs pr m) bb.(bb_body) (mk_instr_state rs' pr' m') -> - step_cf_instr ge (State s f sp pc rs' pr' m') bb.(bb_exit) t s' -> - step (State s f sp pc rs pr m) t s' - | exec_function_internal: - forall s f args m m' stk, - Mem.alloc m 0 f.(fn_stacksize) = (m', stk) -> - step (Callstate s (Internal f) args m) - E0 (State s f - (Vptr stk Ptrofs.zero) - f.(fn_entrypoint) - (init_regs args f.(fn_params)) - (PMap.init false) - m') - | exec_function_external: - forall s ef args res t m m', - external_call ef ge args m t res m' -> - step (Callstate s (External ef) args m) - t (Returnstate s res m') - | exec_return: - forall res f sp pc rs s vres m pr, - step (Returnstate (Stackframe res f sp pc rs pr :: s) vres m) - E0 (State s f sp pc (rs#res <- vres) pr m). -#+end_src - -#+name: rtlblock-rest -#+begin_src coq -End RELSEM. - -Inductive initial_state (p: program): state -> Prop := -| initial_state_intro: forall b f m0, - let ge := Genv.globalenv p in - Genv.init_mem p = Some m0 -> - Genv.find_symbol ge p.(prog_main) = Some b -> - Genv.find_funct_ptr ge b = Some f -> - funsig f = signature_main -> - initial_state p (Callstate nil f nil m0). - -Inductive final_state: state -> int -> Prop := -| final_state_intro: forall r m, - final_state (Returnstate nil (Vint r) m) r. - -Definition semantics (p: program) := - Semantics step (initial_state p) final_state (Genv.globalenv p). -#+end_src - -* RTLPar -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLPar.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlpar-main -#+begin_src coq -Require Import compcert.backend.Registers. -Require Import compcert.common.AST. -Require Import compcert.common.Events. -Require Import compcert.common.Globalenvs. -Require Import compcert.common.Memory. -Require Import compcert.common.Smallstep. -Require Import compcert.common.Values. -Require Import compcert.lib.Coqlib. -Require Import compcert.lib.Integers. -Require Import compcert.lib.Maps. -Require Import compcert.verilog.Op. - -Require Import vericert.hls.RTLBlockInstr. - -Definition bb := list (list (list instr)). - -Definition bblock := @bblock bb. -Definition code := @code bb. -Definition function := @function bb. -Definition fundef := @fundef bb. -Definition program := @program bb. -Definition funsig := @funsig bb. -Definition stackframe := @stackframe bb. -Definition state := @state bb. -Definition genv := @genv bb. - -Section RELSEM. - - Context (ge: genv). - - Inductive step_instr_list: val -> instr_state -> list instr -> instr_state -> Prop := - | exec_RBcons: - forall state i state' state'' instrs sp, - step_instr ge sp state i state' -> - step_instr_list sp state' instrs state'' -> - step_instr_list sp state (i :: instrs) state'' - | exec_RBnil: - forall state sp, - step_instr_list sp state nil state. - - Inductive step_instr_seq (sp : val) - : instr_state -> list (list instr) -> instr_state -> Prop := - | exec_instr_seq_cons: - forall state i state' state'' instrs, - step_instr_list sp state i state' -> - step_instr_seq sp state' instrs state'' -> - step_instr_seq sp state (i :: instrs) state'' - | exec_instr_seq_nil: - forall state, - step_instr_seq sp state nil state. - - Inductive step_instr_block (sp : val) - : instr_state -> bb -> instr_state -> Prop := - | exec_instr_block_cons: - forall state i state' state'' instrs, - step_instr_seq sp state i state' -> - step_instr_block sp state' instrs state'' -> - step_instr_block sp state (i :: instrs) state'' - | exec_instr_block_nil: - forall state, - step_instr_block sp state nil state. - - Inductive step: state -> trace -> state -> Prop := - | exec_bblock: - forall s f sp pc rs rs' m m' t s' bb pr pr', - f.(fn_code)!pc = Some bb -> - step_instr_block sp (mk_instr_state rs pr m) bb.(bb_body) (mk_instr_state rs' pr' m') -> - step_cf_instr ge (State s f sp pc rs' pr' m') bb.(bb_exit) t s' -> - step (State s f sp pc rs pr m) t s' - | exec_function_internal: - forall s f args m m' stk, - Mem.alloc m 0 f.(fn_stacksize) = (m', stk) -> - step (Callstate s (Internal f) args m) - E0 (State s - f - (Vptr stk Ptrofs.zero) - f.(fn_entrypoint) - (init_regs args f.(fn_params)) - (PMap.init false) - m') - | exec_function_external: - forall s ef args res t m m', - external_call ef ge args m t res m' -> - step (Callstate s (External ef) args m) - t (Returnstate s res m') - | exec_return: - forall res f sp pc rs s vres m pr, - step (Returnstate (Stackframe res f sp pc rs pr :: s) vres m) - E0 (State s f sp pc (rs#res <- vres) pr m). - -End RELSEM. - -Inductive initial_state (p: program): state -> Prop := - | initial_state_intro: forall b f m0, - let ge := Genv.globalenv p in - Genv.init_mem p = Some m0 -> - Genv.find_symbol ge p.(prog_main) = Some b -> - Genv.find_funct_ptr ge b = Some f -> - funsig f = signature_main -> - initial_state p (Callstate nil f nil m0). - -Inductive final_state: state -> int -> Prop := - | final_state_intro: forall r m, - final_state (Returnstate nil (Vint r) m) r. - -Definition semantics (p: program) := - Semantics step (initial_state p) final_state (Genv.globalenv p). - -Definition max_reg_bblock (m : positive) (pc : node) (bb : bblock) := - let max_body := fold_left (fun x l => fold_left (fun x' l' => fold_left max_reg_instr l' x') l x) bb.(bb_body) m in - max_reg_cfi max_body bb.(bb_exit). - -Definition max_reg_function (f: function) := - Pos.max - (PTree.fold max_reg_bblock f.(fn_code) 1%positive) - (fold_left Pos.max f.(fn_params) 1%positive). - -Definition max_pc_function (f: function) : positive := - PTree.fold (fun m pc i => (Pos.max m - (pc + match Zlength i.(bb_body) - with Z.pos p => p | _ => 1 end))%positive) - f.(fn_code) 1%positive. -#+end_src - -* License - -#+name: license -#+begin_src coq :tangle no -(* - * Vericert: Verified high-level synthesis. - * Copyright (C) 2020-2022 Yann Herklotz <yann@yannherklotz.com> - * - * 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 <https://www.gnu.org/licenses/>. - *) -#+end_src diff --git a/docs/scheduler.org b/docs/scheduler.org deleted file mode 100644 index c8b00ff..0000000 --- a/docs/scheduler.org +++ /dev/null @@ -1,2317 +0,0 @@ -#+title: Basic Block Generation -#+author: Yann Herklotz -#+email: yann [at] yannherklotz [dot] com - -* Scheduler -:PROPERTIES: -:header-args:ocaml: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/Schedule.ml -:END: - -#+begin_src ocaml :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: scheduler-main -#+begin_src ocaml -open Printf -open Clflags -open Camlcoq -open Datatypes -open Coqlib -open Maps -open AST -open Kildall -open Op -open RTLBlockInstr -open Predicate -open RTLBlock -open HTL -open Verilog -open HTLgen -open HTLMonad -open HTLMonadExtra - -module SS = Set.Make(P) - -type svtype = - | BBType of int - | VarType of int * int - -type sv = { - sv_type: svtype; - sv_num: int; -} - -let print_sv v = - match v with - | { sv_type = BBType bbi; sv_num = n } -> sprintf "bb%d_%d" bbi n - | { sv_type = VarType (bbi, i); sv_num = n } -> sprintf "var%dn%d_%d" bbi i n - -module G = Graph.Persistent.Digraph.ConcreteLabeled(struct - type t = sv - let compare = compare - let equal = (=) - let hash = Hashtbl.hash -end)(struct - type t = int - let compare = compare - let hash = Hashtbl.hash - let equal = (=) - let default = 0 -end) - -module GDot = Graph.Graphviz.Dot(struct - let graph_attributes _ = [] - let default_vertex_attributes _ = [] - let vertex_name = print_sv - let vertex_attributes _ = [] - let get_subgraph _ = None - let default_edge_attributes _ = [] - let edge_attributes _ = [] - - include G - end) - -module DFG = Graph.Persistent.Digraph.ConcreteLabeled(struct - type t = int * instr - let compare = compare - let equal = (=) - let hash = Hashtbl.hash -end)(struct - type t = int - let compare = compare - let hash = Hashtbl.hash - let equal = (=) - let default = 0 -end) - -module DFGSimp = Graph.Persistent.Graph.Concrete(struct - type t = int * instr - let compare = compare - let equal = (=) - let hash = Hashtbl.hash - end) - -let convert dfg = - DFG.fold_vertex (fun v g -> DFGSimp.add_vertex g v) dfg DFGSimp.empty - |> DFG.fold_edges (fun v1 v2 g -> DFGSimp.add_edge (DFGSimp.add_edge g v1 v2) v2 v1) dfg - -let reg r = sprintf "r%d" (P.to_int r) -let print_pred r = sprintf "p%d" (P.to_int r) - -let print_instr = function - | RBnop -> "" - | RBload (_, _, _, _, r) -> sprintf "load(%s)" (reg r) - | RBstore (_, _, _, _, r) -> sprintf "store(%s)" (reg r) - | RBsetpred (_, _, _, p) -> sprintf "setpred(%s)" (print_pred p) - | RBop (_, op, args, d) -> - (match op, args with - | Omove, _ -> "mov" - | Ointconst n, _ -> sprintf "%s=%ld" (reg d) (camlint_of_coqint n) - | Olongconst n, _ -> sprintf "%s=%LdL" (reg d) (camlint64_of_coqint n) - | Ofloatconst n, _ -> sprintf "%s=%.15F" (reg d) (camlfloat_of_coqfloat n) - | Osingleconst n, _ -> sprintf "%s=%.15Ff" (reg d) (camlfloat_of_coqfloat32 n) - | Oindirectsymbol id, _ -> sprintf "%s=&%s" (reg d) (extern_atom id) - | Ocast8signed, [r1] -> sprintf "%s=int8signed(%s)" (reg d) (reg r1) - | Ocast8unsigned, [r1] -> sprintf "%s=int8unsigned(%s)" (reg d) (reg r1) - | Ocast16signed, [r1] -> sprintf "%s=int16signed(%s)" (reg d) (reg r1) - | Ocast16unsigned, [r1] -> sprintf "%s=int16unsigned(%s)" (reg d) (reg r1) - | Oneg, [r1] -> sprintf "%s=-%s" (reg d) (reg r1) - | Osub, [r1;r2] -> sprintf "%s=%s-%s" (reg d) (reg r1) (reg r2) - | Omul, [r1;r2] -> sprintf "%s=%s*%s" (reg d) (reg r1) (reg r2) - | Omulimm n, [r1] -> sprintf "%s=%s*%ld" (reg d) (reg r1) (camlint_of_coqint n) - | Omulhs, [r1;r2] -> sprintf "%s=mulhs(%s,%s)" (reg d) (reg r1) (reg r2) - | Omulhu, [r1;r2] -> sprintf "%s=mulhu(%s,%s)" (reg d) (reg r1) (reg r2) - | Odiv, [r1;r2] -> sprintf "%s=%s /s %s" (reg d) (reg r1) (reg r2) - | Odivu, [r1;r2] -> sprintf "%s=%s /u %s" (reg d) (reg r1) (reg r2) - | Omod, [r1;r2] -> sprintf "%s=%s %%s %s" (reg d) (reg r1) (reg r2) - | Omodu, [r1;r2] -> sprintf "%s=%s %%u %s" (reg d) (reg r1) (reg r2) - | Oand, [r1;r2] -> sprintf "%s=%s & %s" (reg d) (reg r1) (reg r2) - | Oandimm n, [r1] -> sprintf "%s=%s & %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oor, [r1;r2] -> sprintf "%s=%s | %s" (reg d) (reg r1) (reg r2) - | Oorimm n, [r1] -> sprintf "%s=%s | %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oxor, [r1;r2] -> sprintf "%s=%s ^ %s" (reg d) (reg r1) (reg r2) - | Oxorimm n, [r1] -> sprintf "%s=%s ^ %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Onot, [r1] -> sprintf "%s=not(%s)" (reg d) (reg r1) - | Oshl, [r1;r2] -> sprintf "%s=%s << %s" (reg d) (reg r1) (reg r2) - | Oshlimm n, [r1] -> sprintf "%s=%s << %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshr, [r1;r2] -> sprintf "%s=%s >>s %s" (reg d) (reg r1) (reg r2) - | Oshrimm n, [r1] -> sprintf "%s=%s >>s %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshrximm n, [r1] -> sprintf "%s=%s >>x %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshru, [r1;r2] -> sprintf "%s=%s >>u %s" (reg d) (reg r1) (reg r2) - | Oshruimm n, [r1] -> sprintf "%s=%s >>u %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Ororimm n, [r1] -> sprintf "%s=%s ror %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshldimm n, [r1;r2] -> sprintf "%s=(%s, %s) << %ld" (reg d) (reg r1) (reg r2) (camlint_of_coqint n) - | Olea addr, args -> sprintf "%s=addr" (reg d) - | Omakelong, [r1;r2] -> sprintf "%s=makelong(%s,%s)" (reg d) (reg r1) (reg r2) - | Olowlong, [r1] -> sprintf "%s=lowlong(%s)" (reg d) (reg r1) - | Ohighlong, [r1] -> sprintf "%s=highlong(%s)" (reg d) (reg r1) - | Ocast32signed, [r1] -> sprintf "%s=long32signed(%s)" (reg d) (reg r1) - | Ocast32unsigned, [r1] -> sprintf "%s=long32unsigned(%s)" (reg d) (reg r1) - | Onegl, [r1] -> sprintf "%s=-l %s" (reg d) (reg r1) - | Osubl, [r1;r2] -> sprintf "%s=%s -l %s" (reg d) (reg r1) (reg r2) - | Omull, [r1;r2] -> sprintf "%s=%s *l %s" (reg d) (reg r1) (reg r2) - | Omullimm n, [r1] -> sprintf "%s=%s *l %Ld" (reg d) (reg r1) (camlint64_of_coqint n) - | Omullhs, [r1;r2] -> sprintf "%s=mullhs(%s,%s)" (reg d) (reg r1) (reg r2) - | Omullhu, [r1;r2] -> sprintf "%s=mullhu(%s,%s)" (reg d) (reg r1) (reg r2) - | Odivl, [r1;r2] -> sprintf "%s=%s /ls %s" (reg d) (reg r1) (reg r2) - | Odivlu, [r1;r2] -> sprintf "%s=%s /lu %s" (reg d) (reg r1) (reg r2) - | Omodl, [r1;r2] -> sprintf "%s=%s %%ls %s" (reg d) (reg r1) (reg r2) - | Omodlu, [r1;r2] -> sprintf "%s=%s %%lu %s" (reg d) (reg r1) (reg r2) - | Oandl, [r1;r2] -> sprintf "%s=%s &l %s" (reg d) (reg r1) (reg r2) - | Oandlimm n, [r1] -> sprintf "%s=%s &l %Ld" (reg d) (reg r1) (camlint64_of_coqint n) - | Oorl, [r1;r2] -> sprintf "%s=%s |l %s" (reg d) (reg r1) (reg r2) - | Oorlimm n, [r1] -> sprintf "%s=%s |l %Ld" (reg d) (reg r1) (camlint64_of_coqint n) - | Oxorl, [r1;r2] -> sprintf "%s=%s ^l %s" (reg d) (reg r1) (reg r2) - | Oxorlimm n, [r1] -> sprintf "%s=%s ^l %Ld" (reg d) (reg r1) (camlint64_of_coqint n) - | Onotl, [r1] -> sprintf "%s=notl(%s)" (reg d) (reg r1) - | Oshll, [r1;r2] -> sprintf "%s=%s <<l %s" (reg d) (reg r1) (reg r2) - | Oshllimm n, [r1] -> sprintf "%s=%s <<l %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshrl, [r1;r2] -> sprintf "%s=%s >>ls %s" (reg d) (reg r1) (reg r2) - | Oshrlimm n, [r1] -> sprintf "%s=%s >>ls %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshrxlimm n, [r1] -> sprintf "%s=%s >>lx %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oshrlu, [r1;r2] -> sprintf "%s=%s >>lu %s" (reg d) (reg r1) (reg r2) - | Oshrluimm n, [r1] -> sprintf "%s=%s >>lu %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Ororlimm n, [r1] -> sprintf "%s=%s rorl %ld" (reg d) (reg r1) (camlint_of_coqint n) - | Oleal addr, args -> sprintf "%s=addr" (reg d) - | Onegf, [r1] -> sprintf "%s=negf(%s)" (reg d) (reg r1) - | Oabsf, [r1] -> sprintf "%s=absf(%s)" (reg d) (reg r1) - | Oaddf, [r1;r2] -> sprintf "%s=%s +f %s" (reg d) (reg r1) (reg r2) - | Osubf, [r1;r2] -> sprintf "%s=%s -f %s" (reg d) (reg r1) (reg r2) - | Omulf, [r1;r2] -> sprintf "%s=%s *f %s" (reg d) (reg r1) (reg r2) - | Odivf, [r1;r2] -> sprintf "%s=%s /f %s" (reg d) (reg r1) (reg r2) - | Onegfs, [r1] -> sprintf "%s=negfs(%s)" (reg d) (reg r1) - | Oabsfs, [r1] -> sprintf "%s=absfs(%s)" (reg d) (reg r1) - | Oaddfs, [r1;r2] -> sprintf "%s=%s +fs %s" (reg d) (reg r1) (reg r2) - | Osubfs, [r1;r2] -> sprintf "%s=%s -fs %s" (reg d) (reg r1) (reg r2) - | Omulfs, [r1;r2] -> sprintf "%s=%s *fs %s" (reg d) (reg r1) (reg r2) - | Odivfs, [r1;r2] -> sprintf "%s=%s /fs %s" (reg d) (reg r1) (reg r2) - | Osingleoffloat, [r1] -> sprintf "%s=singleoffloat(%s)" (reg d) (reg r1) - | Ofloatofsingle, [r1] -> sprintf "%s=floatofsingle(%s)" (reg d) (reg r1) - | Ointoffloat, [r1] -> sprintf "%s=intoffloat(%s)" (reg d) (reg r1) - | Ofloatofint, [r1] -> sprintf "%s=floatofint(%s)" (reg d) (reg r1) - | Ointofsingle, [r1] -> sprintf "%s=intofsingle(%s)" (reg d) (reg r1) - | Osingleofint, [r1] -> sprintf "%s=singleofint(%s)" (reg d) (reg r1) - | Olongoffloat, [r1] -> sprintf "%s=longoffloat(%s)" (reg d) (reg r1) - | Ofloatoflong, [r1] -> sprintf "%s=floatoflong(%s)" (reg d) (reg r1) - | Olongofsingle, [r1] -> sprintf "%s=longofsingle(%s)" (reg d) (reg r1) - | Osingleoflong, [r1] -> sprintf "%s=singleoflong(%s)" (reg d) (reg r1) - | Ocmp c, args -> sprintf "%s=cmp" (reg d) - | Osel (c, ty), r1::r2::args -> sprintf "%s=sel" (reg d) - | _, _ -> sprintf "N/a") - -module DFGDot = Graph.Graphviz.Dot(struct - let graph_attributes _ = [] - let default_vertex_attributes _ = [] - let vertex_name = function (i, instr) -> sprintf "\"%d:%s\"" i (print_instr instr) - let vertex_attributes _ = [] - let get_subgraph _ = None - let default_edge_attributes _ = [] - let edge_attributes _ = [] - - include DFG - end) - -module DFGDfs = Graph.Traverse.Dfs(DFG) - -module IMap = Map.Make (struct - type t = int - - let compare = compare -end) - -let gen_vertex instrs i = (i, List.nth instrs i) - -(** The DFG type defines a list of instructions with their data dependencies as [edges], which are - the pairs of integers that represent the index of the instruction in the [nodes]. The edges - always point from left to right. *) - -let print_list f out_chan a = - fprintf out_chan "[ "; - List.iter (fprintf out_chan "%a " f) a; - fprintf out_chan "]" - -let print_tuple out_chan a = - let l, r = a in - fprintf out_chan "(%d,%d)" l r - -(*let print_dfg out_chan dfg = - fprintf out_chan "{ nodes = %a, edges = %a }" - (print_list PrintRTLBlockInstr.print_bblock_body) - dfg.nodes (print_list print_tuple) dfg.edges*) - -let print_dfg = DFGDot.output_graph - -let read_process command = - let buffer_size = 2048 in - let buffer = Buffer.create buffer_size in - let string = Bytes.create buffer_size in - let in_channel = Unix.open_process_in command in - let chars_read = ref 1 in - while !chars_read <> 0 do - chars_read := input in_channel string 0 buffer_size; - Buffer.add_substring buffer (Bytes.to_string string) 0 !chars_read - done; - ignore (Unix.close_process_in in_channel); - Buffer.contents buffer - -let comb_delay = function - | RBnop -> 0 - | RBop (_, op, _, _) -> - (match op with - | Omove -> 0 - | Ointconst _ -> 0 - | Olongconst _ -> 0 - | Ocast8signed -> 0 - | Ocast8unsigned -> 0 - | Ocast16signed -> 0 - | Ocast16unsigned -> 0 - | Oneg -> 0 - | Onot -> 0 - | Oor -> 0 - | Oorimm _ -> 0 - | Oand -> 0 - | Oandimm _ -> 0 - | Oxor -> 0 - | Oxorimm _ -> 0 - | Omul -> 8 - | Omulimm _ -> 8 - | Omulhs -> 8 - | Omulhu -> 8 - | Odiv -> 72 - | Odivu -> 72 - | Omod -> 72 - | Omodu -> 72 - | _ -> 1) - | _ -> 1 - -let pipeline_stages = function - | RBload _ -> 2 - | RBop (_, op, _, _) -> - (match op with - | Odiv -> 32 - | Odivu -> 32 - | Omod -> 32 - | Omodu -> 32 - | _ -> 0) - | _ -> 0 - -(** Add a dependency if it uses a register that was written to previously. *) -let add_dep map i tree dfg curr = - match PTree.get curr tree with - | None -> dfg - | Some ip -> - let ipv = (List.nth map ip) in - DFG.add_edge_e dfg (ipv, comb_delay (snd (List.nth map i)), List.nth map i) - -(** This function calculates the dependencies of each instruction. The nodes correspond to previous - registers that were allocated and show which instruction caused it. - - This function only gathers the RAW constraints, and will therefore only be active for operations - that modify registers, which is this case only affects loads and operations. *) -let accumulate_RAW_deps map dfg curr = - let i, dst_map, graph = dfg in - let acc_dep_instruction rs dst = - ( i + 1, - PTree.set dst i dst_map, - List.fold_left (add_dep map i dst_map) graph rs - ) - in - let acc_dep_instruction_nodst rs = - ( i + 1, - dst_map, - List.fold_left (add_dep map i dst_map) graph rs) - in - match curr with - | RBop (op, _, rs, dst) -> acc_dep_instruction rs dst - | RBload (op, _mem, _addr, rs, dst) -> acc_dep_instruction rs dst - | RBsetpred (_op, _mem, rs, _p) -> acc_dep_instruction_nodst rs - | RBstore (op, _mem, _addr, rs, src) -> acc_dep_instruction_nodst (src :: rs) - | _ -> (i + 1, dst_map, graph) - -(** Finds the next write to the [dst] register. This is a small optimisation so that only one - dependency is generated for a data dependency. *) -let rec find_next_dst_write i dst i' curr = - let check_dst dst' curr' = - if dst = dst' then Some (i, i') - else find_next_dst_write i dst (i' + 1) curr' - in - match curr with - | [] -> None - | RBop (_, _, _, dst') :: curr' -> check_dst dst' curr' - | RBload (_, _, _, _, dst') :: curr' -> check_dst dst' curr' - | _ :: curr' -> find_next_dst_write i dst (i' + 1) curr' - -let rec find_all_next_dst_read i dst i' curr = - let check_dst rs curr' = - if List.exists (fun x -> x = dst) rs - then (i, i') :: find_all_next_dst_read i dst (i' + 1) curr' - else find_all_next_dst_read i dst (i' + 1) curr' - in - match curr with - | [] -> [] - | RBop (_, _, rs, _) :: curr' -> check_dst rs curr' - | RBload (_, _, _, rs, _) :: curr' -> check_dst rs curr' - | RBstore (_, _, _, rs, src) :: curr' -> check_dst (src :: rs) curr' - | RBnop :: curr' -> find_all_next_dst_read i dst (i' + 1) curr' - | RBsetpred (_, _, rs, _) :: curr' -> check_dst rs curr' - -let drop i lst = - let rec drop' i' lst' = - match lst' with - | _ :: ls -> if i' = i then ls else drop' (i' + 1) ls - | [] -> [] - in - if i = 0 then lst else drop' 1 lst - -let take i lst = - let rec take' i' lst' = - match lst' with - | l :: ls -> if i' = i then [ l ] else l :: take' (i' + 1) ls - | [] -> [] - in - if i = 0 then [] else take' 1 lst - -let rec next_store i = function - | [] -> None - | RBstore (_, _, _, _, _) :: _ -> Some i - | _ :: rst -> next_store (i + 1) rst - -let rec next_load i = function - | [] -> None - | RBload (_, _, _, _, _) :: _ -> Some i - | _ :: rst -> next_load (i + 1) rst - -let accumulate_RAW_mem_deps instrs dfg curri = - let i, curr = curri in - match curr with - | RBload (_, _, _, _, _) -> ( - match next_store 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i) ) - | _ -> dfg - -let accumulate_WAR_mem_deps instrs dfg curri = - let i, curr = curri in - match curr with - | RBstore (_, _, _, _, _) -> ( - match next_load 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i) ) - | _ -> dfg - -let accumulate_WAW_mem_deps instrs dfg curri = - let i, curr = curri in - match curr with - | RBstore (_, _, _, _, _) -> ( - match next_store 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i)) - | _ -> dfg - -(** Predicate dependencies. *) - -let rec in_predicate p p' = - match p' with - | Plit p'' -> P.to_int p = P.to_int (snd p'') - | Pand (p1, p2) -> in_predicate p p1 || in_predicate p p2 - | Por (p1, p2) -> in_predicate p p1 || in_predicate p p2 - | Ptrue -> false - | Pfalse -> false - -let get_predicate = function - | RBop (p, _, _, _) -> p - | RBload (p, _, _, _, _) -> p - | RBstore (p, _, _, _, _) -> p - | RBsetpred (p, _, _, _) -> p - | _ -> None - -let rec next_setpred p i = function - | [] -> None - | RBsetpred (_, _, _, p') :: rst -> - if in_predicate p' p then - Some i - else - next_setpred p (i + 1) rst - | _ :: rst -> next_setpred p (i + 1) rst - -let rec next_preduse p i instr= - let next p' rst = - if in_predicate p p' then - Some i - else - next_preduse p (i + 1) rst - in - match instr with - | [] -> None - | RBload (Some p', _, _, _, _) :: rst -> next p' rst - | RBstore (Some p', _, _, _, _) :: rst -> next p' rst - | RBop (Some p', _, _, _) :: rst -> next p' rst - | RBsetpred (Some p', _, _, _) :: rst -> next p' rst - | _ :: rst -> next_load (i + 1) rst - -let accumulate_RAW_pred_deps instrs dfg curri = - let i, curr = curri in - match get_predicate curr with - | Some p -> ( - match next_setpred p 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i) ) - | _ -> dfg - -let accumulate_WAR_pred_deps instrs dfg curri = - let i, curr = curri in - match curr with - | RBsetpred (_, _, _, p) -> ( - match next_preduse p 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i) ) - | _ -> dfg - -let accumulate_WAW_pred_deps instrs dfg curri = - let i, curr = curri in - match curr with - | RBsetpred (_, _, _, p) -> ( - match next_setpred (Plit (true, p)) 0 (take i instrs |> List.rev) with - | None -> dfg - | Some d -> DFG.add_edge dfg (gen_vertex instrs (i - d - 1)) (gen_vertex instrs i) ) - | _ -> dfg - -(** This function calculates the WAW dependencies, which happen when two writes are ordered one - after another and therefore have to be kept in that order. This accumulation might be redundant - if register renaming is done before hand, because then these dependencies can be avoided. *) -let accumulate_WAW_deps instrs dfg curri = - let i, curr = curri in - let dst_dep dst = - match find_next_dst_write i dst (i + 1) (drop (i + 1) instrs) with - | Some (a, b) -> DFG.add_edge dfg (gen_vertex instrs a) (gen_vertex instrs b) - | _ -> dfg - in - match curr with - | RBop (_, _, _, dst) -> dst_dep dst - | RBload (_, _, _, _, dst) -> dst_dep dst - | RBstore (_, _, _, _, _) -> ( - match next_store (i + 1) (drop (i + 1) instrs) with - | None -> dfg - | Some i' -> DFG.add_edge dfg (gen_vertex instrs i) (gen_vertex instrs i') ) - | _ -> dfg - -let accumulate_WAR_deps instrs dfg curri = - let i, curr = curri in - let dst_dep dst = - let dep_list = find_all_next_dst_read i dst 0 (take i instrs |> List.rev) - |> List.map (function (d, d') -> (i - d' - 1, d)) - in - List.fold_left (fun g -> - function (d, d') -> DFG.add_edge g (gen_vertex instrs d) (gen_vertex instrs d')) dfg dep_list - in - match curr with - | RBop (_, _, _, dst) -> dst_dep dst - | RBload (_, _, _, _, dst) -> dst_dep dst - | _ -> dfg - -let assigned_vars vars = function - | RBnop -> vars - | RBop (_, _, _, dst) -> dst :: vars - | RBload (_, _, _, _, dst) -> dst :: vars - | RBstore (_, _, _, _, _) -> vars - | RBsetpred (_, _, _, _) -> vars - -let get_pred = function - | RBnop -> None - | RBop (op, _, _, _) -> op - | RBload (op, _, _, _, _) -> op - | RBstore (op, _, _, _, _) -> op - | RBsetpred (_, _, _, _) -> None - -let independant_pred p p' = - match sat_pred_simple (Pand (p, p')) with - | None -> true - | _ -> false - -let check_dependent op1 op2 = - match op1, op2 with - | Some p, Some p' -> not (independant_pred p p') - | _, _ -> true - -let remove_unnecessary_deps graph = - let is_dependent v1 v2 g = - let (_, instr1) = v1 in - let (_, instr2) = v2 in - if check_dependent (get_pred instr1) (get_pred instr2) - then g - else DFG.remove_edge g v1 v2 - in - DFG.fold_edges is_dependent graph graph - -(** All the nodes in the DFG have to come after the source of the basic block, and should terminate - before the sink of the basic block. After that, there should be constraints for data - dependencies between nodes. *) -let gather_bb_constraints debug bb = - let ibody = List.mapi (fun i a -> (i, a)) bb.bb_body in - let dfg = List.fold_left (fun dfg v -> DFG.add_vertex dfg v) DFG.empty ibody in - let _, _, dfg' = - List.fold_left (accumulate_RAW_deps ibody) - (0, PTree.empty, dfg) - bb.bb_body - in - let dfg'' = List.fold_left (fun dfg f -> List.fold_left (f bb.bb_body) dfg ibody) dfg' - [ accumulate_WAW_deps; - accumulate_WAR_deps; - accumulate_RAW_mem_deps; - accumulate_WAR_mem_deps; - accumulate_WAW_mem_deps; - accumulate_RAW_pred_deps; - accumulate_WAR_pred_deps; - accumulate_WAW_pred_deps - ] - in - let dfg''' = remove_unnecessary_deps dfg'' in - (List.length bb.bb_body, dfg''', successors_instr bb.bb_exit) - -let encode_var bbn n i = { sv_type = VarType (bbn, n); sv_num = i } -let encode_bb bbn i = { sv_type = BBType bbn; sv_num = i } - -let add_initial_sv n dfg constr = - let add_initial_sv' (i, instr) g = - let pipes = pipeline_stages instr in - if pipes > 0 then - List.init pipes (fun i' -> i') - |> List.fold_left (fun g i' -> - G.add_edge_e g (encode_var n i i', -1, encode_var n i (i'+1)) - ) g - else g - in - DFG.fold_vertex add_initial_sv' dfg constr - -let add_super_nodes n dfg = - DFG.fold_vertex (function v1 -> fun g -> - (if DFG.in_degree dfg v1 = 0 - then G.add_edge_e g (encode_bb n 0, 0, encode_var n (fst v1) 0) - else g) |> - (fun g' -> - if DFG.out_degree dfg v1 = 0 - then G.add_edge_e g' (encode_var n (fst v1) (pipeline_stages (snd v1)), - 0, encode_bb n 1) - else g')) dfg - -let add_data_deps n = - DFG.fold_edges_e (function ((i1, instr1), _, (i2, _)) -> fun g -> - let end_sv = pipeline_stages instr1 in - G.add_edge_e g (encode_var n i1 end_sv, 0, encode_var n i2 0) - ) - -let add_ctrl_deps n succs constr = - List.fold_left (fun g n' -> - G.add_edge_e g (encode_bb n 1, -1, encode_bb n' 0) - ) constr succs - -module BFDFG = Graph.Path.BellmanFord(DFG)(struct - include DFG - type t = int - let weight = DFG.E.label - let compare = compare - let add = (+) - let zero = 0 - end) - -module TopoDFG = Graph.Topological.Make(DFG) - -let negate_graph constr = - DFG.fold_edges_e (function (v1, e, v2) -> fun g -> - DFG.add_edge_e g (v1, -e, v2) - ) constr DFG.empty - -let add_cycle_constr maxf n dfg constr = - let negated_dfg = negate_graph dfg in - let max_initial_del = DFG.fold_vertex (fun v1 g -> - if DFG.in_degree dfg v1 = 0 - then max g (comb_delay (snd v1)) - else g) dfg 0 in - let longest_path v = BFDFG.all_shortest_paths negated_dfg v - |> BFDFG.H.to_seq |> List.of_seq - |> List.map (function (x, y) -> (x, y - max_initial_del)) in - let constrained_paths = List.filter (function (_, m) -> - m > maxf) in - List.fold_left (fun g -> function (v, v', w) -> - G.add_edge_e g (encode_var n (fst v) 0, - - (int_of_float (Float.ceil (Float.div (float_of_int w) (float_of_int maxf))) - 1), - encode_var n (fst v') 0) - ) constr (DFG.fold_vertex (fun v l -> - List.append l (longest_path v (*|> (function l -> List.iter (function (a, x) -> - printf "c: %d %d\n" (fst a) x) l; l)*) |> constrained_paths (* |> (function l -> List.iter (function (a, x) -> - printf "%d %d\n" (fst a) x) l; l)*) - |> List.map (function (v', w) -> (v, v', - w))) - ) dfg []) - -type resource = - | Mem - | SDiv - | UDiv - -type resources = { - res_mem: DFG.V.t list; - res_udiv: DFG.V.t list; - res_sdiv: DFG.V.t list; -} - -let find_resource = function - | RBload _ -> Some Mem - | RBstore _ -> Some Mem - | RBop (_, op, _, _) -> - ( match op with - | Odiv -> Some SDiv - | Odivu -> Some UDiv - | Omod -> Some SDiv - | Omodu -> Some UDiv - | _ -> None ) - | _ -> None - -let add_resource_constr n dfg constr = - let res = TopoDFG.fold (function (i, instr) -> - function {res_mem = ml; res_sdiv = sdl; res_udiv = udl} as r -> - match find_resource instr with - | Some SDiv -> {r with res_sdiv = (i, instr) :: sdl} - | Some UDiv -> {r with res_udiv = (i, instr) :: udl} - | Some Mem -> {r with res_mem = (i, instr) :: ml} - | None -> r - ) dfg {res_mem = []; res_sdiv = []; res_udiv = []} - in - let get_constraints l g = List.fold_left (fun gv v' -> - match gv with - | (g, None) -> (g, Some v') - | (g, Some v) -> - (G.add_edge_e g (encode_var n (fst v) 0, -1, encode_var n (fst v') 0), Some v') - ) (g, None) l |> fst - in - get_constraints (List.rev res.res_mem) constr - |> get_constraints (List.rev res.res_udiv) - |> get_constraints (List.rev res.res_sdiv) - -let gather_cfg_constraints c constr curr = - let (n, dfg) = curr in - match PTree.get (P.of_int n) c with - | None -> assert false - | Some { bb_exit = ctrl; _ } -> - add_super_nodes n dfg constr - |> add_initial_sv n dfg - |> add_data_deps n dfg - |> add_ctrl_deps n (successors_instr ctrl - |> List.map P.to_int - |> List.filter (fun n' -> n' < n)) - |> add_cycle_constr 8 n dfg - |> add_resource_constr n dfg - -let rec intersperse s = function - | [] -> [] - | [ a ] -> [ a ] - | x :: xs -> x :: s :: intersperse s xs - -let print_objective constr = - let vars = G.fold_vertex (fun v1 l -> - match v1 with - | { sv_type = VarType _; sv_num = 0 } -> print_sv v1 :: l - | _ -> l - ) constr [] - in - "min: " ^ String.concat "" (intersperse " + " vars) ^ ";\n" - -let print_lp constr = - print_objective constr ^ - (G.fold_edges_e (function (e1, w, e2) -> fun s -> - s ^ sprintf "%s - %s <= %d;\n" (print_sv e1) (print_sv e2) w - ) constr "" |> - G.fold_vertex (fun v1 s -> - s ^ sprintf "int %s;\n" (print_sv v1) - ) constr) - -let update_schedule v = function Some l -> Some (v :: l) | None -> Some [ v ] - -let parse_soln (tree, bbtree) s = - let r = Str.regexp "var\\([0-9]+\\)n\\([0-9]+\\)_0[ ]+\\([0-9]+\\)" in - let bb = Str.regexp "bb\\([0-9]+\\)_\\([0-9]+\\)[ ]+\\([0-9]+\\)" in - let upd s = IMap.update - (Str.matched_group 1 s |> int_of_string) - (update_schedule - ( Str.matched_group 2 s |> int_of_string, - Str.matched_group 3 s |> int_of_string )) - in - if Str.string_match r s 0 - then (upd s tree, bbtree) - else - (if Str.string_match bb s 0 - then (tree, upd s bbtree) - else (tree, bbtree)) - -let solve_constraints constr = - let (fn, oc) = Filename.open_temp_file "vericert_" "_lp_solve" in - fprintf oc "%s\n" (print_lp constr); - close_out oc; - - let res = Str.split (Str.regexp_string "\n") (read_process ("lp_solve " ^ fn)) - |> drop 3 - |> List.fold_left parse_soln (IMap.empty, IMap.empty) - in - (*Sys.remove fn;*) res - -let subgraph dfg l = - let dfg' = List.fold_left (fun g v -> DFG.add_vertex g v) DFG.empty l in - List.fold_left (fun g v -> - List.fold_left (fun g' v' -> - let edges = DFG.find_all_edges dfg v v' in - List.fold_left DFG.add_edge_e g' edges - ) g l - ) dfg' l - -let rec all_successors dfg v = - List.concat (List.fold_left (fun l v -> - all_successors dfg v :: l - ) [] (DFG.succ dfg v)) - -let order_instr dfg = - DFG.fold_vertex (fun v li -> - if DFG.in_degree dfg v = 0 - then (List.map snd (v :: all_successors dfg v)) :: li - else li - ) dfg [] - -let combine_bb_schedule schedule s = - let i, st = s in - IMap.update st (update_schedule i) schedule - -(**let add_el dfg i l = - List.*) - -let check_in el = - List.exists (List.exists ((=) el)) - -let all_dfs dfg = - let roots = DFG.fold_vertex (fun v li -> - if DFG.in_degree dfg v = 0 then v :: li else li - ) dfg [] in - let dfg' = DFG.fold_edges (fun v1 v2 g -> DFG.add_edge g v2 v1) dfg dfg in - List.fold_left (fun a el -> - if check_in el a then a else - (DFGDfs.fold_component (fun v l -> v :: l) [] dfg' el) :: a) [] roots - -let range s e = - List.init (e - s) (fun i -> i) - |> List.map (fun x -> x + s) - -(** Should generate the [RTLPar] code based on the input [RTLBlock] description. *) -let transf_rtlpar c c' schedule = - let f i bb : RTLPar.bblock = - match bb with - | { bb_body = []; bb_exit = c } -> { bb_body = []; bb_exit = c } - | { bb_body = bb_body'; bb_exit = ctrl_flow } -> - let dfg = match PTree.get i c' with None -> assert false | Some x -> x in - let bb_st_e = - let m = IMap.find (P.to_int i) (snd schedule) in - (List.assq 0 m, List.assq 1 m) in - let i_sched = IMap.find (P.to_int i) (fst schedule) in - let i_sched_tree = - List.fold_left combine_bb_schedule IMap.empty i_sched - in - let body = IMap.to_seq i_sched_tree |> List.of_seq |> List.map snd - |> List.map (List.map (fun x -> (x, List.nth bb_body' x))) - in - let body2 = List.fold_left (fun x b -> - match IMap.find_opt b i_sched_tree with - | Some i -> i :: x - | None -> [] :: x - ) [] (range (fst bb_st_e) (snd bb_st_e + 1)) - |> List.map (List.map (fun x -> (x, List.nth bb_body' x))) - |> List.rev - in - (*let final_body = List.map (fun x -> subgraph dfg x |> order_instr) body in*) - let final_body2 = List.map (fun x -> subgraph dfg x - |> (fun x -> - all_dfs x - |> List.map (subgraph x) - |> List.map (fun y -> - TopoDFG.fold (fun i l -> snd i :: l) y [] - |> List.rev))) body2 - (*|> (fun x -> TopoDFG.fold (fun i l -> snd i :: l) x []) - |> List.rev) body2*) - in - { bb_body = final_body2; - bb_exit = ctrl_flow - } - in - PTree.map f c - -let schedule entry (c : RTLBlock.bb RTLBlockInstr.code) = - let debug = true in - let transf_graph (_, dfg, _) = dfg in - let c' = PTree.map1 (fun x -> gather_bb_constraints false x |> transf_graph) c in - (*let _ = if debug then PTree.map (fun r o -> printf "##### %d #####\n%a\n\n" (P.to_int r) print_dfg o) c' else PTree.empty in*) - let cgraph = PTree.elements c' - |> List.map (function (x, y) -> (P.to_int x, y)) - |> List.fold_left (gather_cfg_constraints c) G.empty - in - let graph = open_out "constr_graph.dot" in - fprintf graph "%a\n" GDot.output_graph cgraph; - close_out graph; - let schedule' = solve_constraints cgraph in - (**IMap.iter (fun a b -> printf "##### %d #####\n%a\n\n" a (print_list print_tuple) b) schedule';*) - (**printf "Schedule: %a\n" (fun a x -> IMap.iter (fun d -> fprintf a "%d: %a\n" d (print_list print_tuple)) x) schedule';*) - transf_rtlpar c c' schedule' - -let rec find_reachable_states c e = - match PTree.get e c with - | Some { bb_exit = ex; _ } -> - e :: List.fold_left (fun x a -> List.concat [x; find_reachable_states c a]) [] - (successors_instr ex |> List.filter (fun x -> P.lt x e)) - | None -> assert false - -let add_to_tree c nt i = - match PTree.get i c with - | Some p -> PTree.set i p nt - | None -> assert false - -let schedule_fn (f : RTLBlock.coq_function) : RTLPar.coq_function = - let scheduled = schedule f.fn_entrypoint f.fn_code in - let reachable = find_reachable_states scheduled f.fn_entrypoint - |> List.to_seq |> SS.of_seq |> SS.to_seq |> List.of_seq in - { fn_sig = f.fn_sig; - fn_params = f.fn_params; - fn_stacksize = f.fn_stacksize; - fn_code = scheduled (*List.fold_left (add_to_tree scheduled) PTree.empty reachable*); - fn_entrypoint = f.fn_entrypoint - } -#+end_src - -* RTLPargen -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLPargen.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlpargen-main -#+begin_src coq -Require Import compcert.backend.Registers. -Require Import compcert.common.AST. -Require Import compcert.common.Globalenvs. -Require Import compcert.common.Memory. -Require Import compcert.common.Values. -Require Import compcert.lib.Floats. -Require Import compcert.lib.Integers. -Require Import compcert.lib.Maps. -Require compcert.verilog.Op. - -Require Import vericert.common.Vericertlib. -Require Import vericert.hls.RTLBlock. -Require Import vericert.hls.RTLPar. -Require Import vericert.hls.RTLBlockInstr. -Require Import vericert.hls.Predicate. -Require Import vericert.hls.Abstr. -Import NE.NonEmptyNotation. - -#[local] Open Scope positive. -#[local] Open Scope forest. -#[local] Open Scope pred_op. -#+end_src - -** Abstract Computations - -Define the abstract computation using the [update] function, which will set each register to its -symbolic value. First we need to define a few helper functions to correctly translate the -predicates. - -#+name: rtlpargen-generation -#+begin_src coq -Fixpoint list_translation (l : list reg) (f : forest) {struct l} : list pred_expr := - match l with - | nil => nil - | i :: l => (f # (Reg i)) :: (list_translation l f) - end. - -Fixpoint replicate {A} (n: nat) (l: A) := - match n with - | O => nil - | S n => l :: replicate n l - end. - -Definition merge''' x y := - match x, y with - | Some p1, Some p2 => Some (Pand p1 p2) - | Some p, None | None, Some p => Some p - | None, None => None - end. - -Definition merge'' x := - match x with - | ((a, e), (b, el)) => (merge''' a b, Econs e el) - end. - -Definition map_pred_op {A B} (pf: option pred_op * (A -> B)) (pa: option pred_op * A): option pred_op * B := - match pa, pf with - | (p, a), (p', f) => (merge''' p p', f a) - end. - -Definition predicated_prod {A B: Type} (p1: predicated A) (p2: predicated B) := - NE.map (fun x => match x with ((a, b), (c, d)) => (Pand a c, (b, d)) end) - (NE.non_empty_prod p1 p2). - -Definition predicated_map {A B: Type} (f: A -> B) (p: predicated A): predicated B := - NE.map (fun x => (fst x, f (snd x))) p. - -(*map (fun x => (fst x, Econs (snd x) Enil)) pel*) -Definition merge' (pel: pred_expr) (tpel: predicated expression_list) := - predicated_map (uncurry Econs) (predicated_prod pel tpel). - -Fixpoint merge (pel: list pred_expr): predicated expression_list := - match pel with - | nil => NE.singleton (T, Enil) - | a :: b => merge' a (merge b) - end. - -Definition map_predicated {A B} (pf: predicated (A -> B)) (pa: predicated A): predicated B := - predicated_map (fun x => (fst x) (snd x)) (predicated_prod pf pa). - -Definition predicated_apply1 {A B} (pf: predicated (A -> B)) (pa: A): predicated B := - NE.map (fun x => (fst x, (snd x) pa)) pf. - -Definition predicated_apply2 {A B C} (pf: predicated (A -> B -> C)) (pa: A) (pb: B): predicated C := - NE.map (fun x => (fst x, (snd x) pa pb)) pf. - -Definition predicated_apply3 {A B C D} (pf: predicated (A -> B -> C -> D)) (pa: A) (pb: B) (pc: C): predicated D := - NE.map (fun x => (fst x, (snd x) pa pb pc)) pf. - -Definition predicated_from_opt {A: Type} (p: option pred_op) (a: A) := - match p with - | Some p' => NE.singleton (p', a) - | None => NE.singleton (T, a) - end. - -#[local] Open Scope non_empty_scope. -#[local] Open Scope pred_op. - -Fixpoint NEfold_left {A B} (f: A -> B -> A) (l: NE.non_empty B) (a: A) : A := - match l with - | NE.singleton a' => f a a' - | a' ::| b => NEfold_left f b (f a a') - end. - -Fixpoint NEapp {A} (l m: NE.non_empty A) := - match l with - | NE.singleton a => a ::| m - | a ::| b => a ::| NEapp b m - end. - -Definition app_predicated' {A: Type} (a b: predicated A) := - let negation := ¬ (NEfold_left (fun a b => a ∨ (fst b)) b ⟂) in - NEapp (NE.map (fun x => (negation ∧ fst x, snd x)) a) b. - -Definition app_predicated {A: Type} (p: option pred_op) (a b: predicated A) := - match p with - | Some p' => NEapp (NE.map (fun x => (¬ p' ∧ fst x, snd x)) a) - (NE.map (fun x => (p' ∧ fst x, snd x)) b) - | None => b - end. - -Definition pred_ret {A: Type} (a: A) : predicated A := - NE.singleton (T, a). - -#+end_src - -*** Update Function -:PROPERTIES: -:CUSTOM_ID: update-function -:END: - -The [update] function will generate a new forest given an existing forest and a new instruction, so -that it can evaluate a symbolic expression by folding over a list of instructions. The main problem -is that predicates need to be merged as well, so that: - -1. The predicates are *independent*. -2. The expression assigned to the register should still be correct. - -This is done by multiplying the predicates together, and assigning the negation of the expression to -the other predicates. - -#+name: rtlpargen-update-function -#+begin_src coq -Definition update (f : forest) (i : instr) : forest := - match i with - | RBnop => f - | RBop p op rl r => - f # (Reg r) <- - (app_predicated p - (f # (Reg r)) - (map_predicated (pred_ret (Eop op)) (merge (list_translation rl f)))) - | RBload p chunk addr rl r => - f # (Reg r) <- - (app_predicated p - (f # (Reg r)) - (map_predicated - (map_predicated (pred_ret (Eload chunk addr)) (merge (list_translation rl f))) - (f # Mem))) - | RBstore p chunk addr rl r => - f # Mem <- - (app_predicated p - (f # Mem) - (map_predicated - (map_predicated - (predicated_apply2 (map_predicated (pred_ret Estore) (f # (Reg r))) chunk addr) - (merge (list_translation rl f))) (f # Mem))) - | RBsetpred p' c args p => - f # (Pred p) <- - (app_predicated p' - (f # (Pred p)) - (map_predicated (pred_ret (Esetpred c)) (merge (list_translation args f)))) - end. -#+end_src - -Implementing which are necessary to show the correctness of the translation validation by -showing that there aren't any more effects in the resultant RTLPar code than in the RTLBlock code. - -Get a sequence from the basic block. - -#+name: rtlpargen-abstract-seq -#+begin_src coq -Fixpoint abstract_sequence (f : forest) (b : list instr) : forest := - match b with - | nil => f - | i :: l => abstract_sequence (update f i) l - end. -#+end_src - -Check equivalence of control flow instructions. As none of the basic blocks should have been -moved, none of the labels should be different, meaning the control-flow instructions should match -exactly. - -#+name: rtlpargen-check-functions -#+begin_src coq -Definition check_control_flow_instr (c1 c2: cf_instr) : bool := - if cf_instr_eq c1 c2 then true else false. -#+end_src - -We define the top-level oracle that will check if two basic blocks are equivalent after a -scheduling transformation. - -#+name: rtlpargen-top-check-functions -#+begin_src coq -Definition empty_trees (bb: RTLBlock.bb) (bbt: RTLPar.bb) : bool := - match bb with - | nil => - match bbt with - | nil => true - | _ => false - end - | _ => true - end. - -Definition schedule_oracle (bb: RTLBlock.bblock) (bbt: RTLPar.bblock) : bool := - check (abstract_sequence empty (bb_body bb)) - (abstract_sequence empty (concat (concat (bb_body bbt)))) && - check_control_flow_instr (bb_exit bb) (bb_exit bbt) && - empty_trees (bb_body bb) (bb_body bbt). - -Definition check_scheduled_trees := beq2 schedule_oracle. - -Ltac solve_scheduled_trees_correct := - intros; unfold check_scheduled_trees in *; - match goal with - | [ H: context[beq2 _ _ _], x: positive |- _ ] => - rewrite beq2_correct in H; specialize (H x) - end; repeat destruct_match; crush. - -Lemma check_scheduled_trees_correct: - forall f1 f2 x y1, - check_scheduled_trees f1 f2 = true -> - PTree.get x f1 = Some y1 -> - exists y2, PTree.get x f2 = Some y2 /\ schedule_oracle y1 y2 = true. -Proof. solve_scheduled_trees_correct; eexists; crush. Qed. - -Lemma check_scheduled_trees_correct2: - forall f1 f2 x, - check_scheduled_trees f1 f2 = true -> - PTree.get x f1 = None -> - PTree.get x f2 = None. -Proof. solve_scheduled_trees_correct. Qed. - -#+end_src - -** Top-level Functions - -#+name: rtlpargen-top-level-functions -#+begin_src coq -Parameter schedule : RTLBlock.function -> RTLPar.function. - -Definition transl_function (f: RTLBlock.function) : Errors.res RTLPar.function := - let tfcode := fn_code (schedule f) in - if check_scheduled_trees f.(fn_code) tfcode then - Errors.OK (mkfunction f.(fn_sig) - f.(fn_params) - f.(fn_stacksize) - tfcode - f.(fn_entrypoint)) - else - Errors.Error (Errors.msg "RTLPargen: Could not prove the blocks equivalent."). - -Definition transl_fundef := transf_partial_fundef transl_function. - -Definition transl_program (p : RTLBlock.program) : Errors.res RTLPar.program := - transform_partial_program transl_fundef p. -#+end_src - -* RTLPargenproof -:PROPERTIES: -:header-args:coq: :comments noweb :noweb no-export :padline yes :tangle ../src/hls/RTLPargenproof.v -:END: - -#+begin_src coq :comments no :padline no :exports none -<<license>> -#+end_src - -#+name: rtlpargenproof-imports -#+begin_src coq -Require Import compcert.backend.Registers. -Require Import compcert.common.AST. -Require Import compcert.common.Errors. -Require Import compcert.common.Linking. -Require Import compcert.common.Globalenvs. -Require Import compcert.common.Memory. -Require Import compcert.common.Values. -Require Import compcert.lib.Maps. - -Require Import vericert.common.Vericertlib. -Require Import vericert.hls.RTLBlock. -Require Import vericert.hls.RTLPar. -Require Import vericert.hls.RTLBlockInstr. -Require Import vericert.hls.RTLPargen. -Require Import vericert.hls.Predicate. -Require Import vericert.hls.Abstr. - -#[local] Open Scope positive. -#[local] Open Scope forest. -#[local] Open Scope pred_op. -#+end_src - -** RTLBlock to abstract translation - -Correctness of translation from RTLBlock to the abstract interpretation language. - -#+name: rtlpargenproof-main -#+begin_src coq -(*Definition is_regs i := match i with mk_instr_state rs _ => rs end. -Definition is_mem i := match i with mk_instr_state _ m => m end. - -Inductive state_lessdef : instr_state -> instr_state -> Prop := - state_lessdef_intro : - forall rs1 rs2 m1, - (forall x, rs1 !! x = rs2 !! x) -> - state_lessdef (mk_instr_state rs1 m1) (mk_instr_state rs2 m1). - -Ltac inv_simp := - repeat match goal with - | H: exists _, _ |- _ => inv H - end; simplify. - -*) - -Definition check_dest i r' := - match i with - | RBop p op rl r => (r =? r')%positive - | RBload p chunk addr rl r => (r =? r')%positive - | _ => false - end. - -Lemma check_dest_dec i r : {check_dest i r = true} + {check_dest i r = false}. -Proof. destruct (check_dest i r); tauto. Qed. - -Fixpoint check_dest_l l r := - match l with - | nil => false - | a :: b => check_dest a r || check_dest_l b r - end. - -Lemma check_dest_l_forall : - forall l r, - check_dest_l l r = false -> - Forall (fun x => check_dest x r = false) l. -Proof. induction l; crush. Qed. - -Lemma check_dest_l_dec i r : {check_dest_l i r = true} + {check_dest_l i r = false}. -Proof. destruct (check_dest_l i r); tauto. Qed. - -Lemma check_dest_update : - forall f i r, - check_dest i r = false -> - (update f i) # (Reg r) = f # (Reg r). -Proof. - destruct i; crush; try apply Pos.eqb_neq in H; apply genmap1; crush. -Qed. - -Lemma check_dest_l_forall2 : - forall l r, - Forall (fun x => check_dest x r = false) l -> - check_dest_l l r = false. -Proof. - induction l; crush. - inv H. apply orb_false_intro; crush. -Qed. - -Lemma check_dest_l_ex2 : - forall l r, - (exists a, In a l /\ check_dest a r = true) -> - check_dest_l l r = true. -Proof. - induction l; crush. - specialize (IHl r). inv H. - apply orb_true_intro; crush. - apply orb_true_intro; crush. - right. apply IHl. exists x. auto. -Qed. - -Lemma check_list_l_false : - forall l x r, - check_dest_l (l ++ x :: nil) r = false -> - check_dest_l l r = false /\ check_dest x r = false. -Proof. - simplify. - apply check_dest_l_forall in H. apply Forall_app in H. - simplify. apply check_dest_l_forall2; auto. - apply check_dest_l_forall in H. apply Forall_app in H. - simplify. inv H1. auto. -Qed. - -Lemma check_dest_l_ex : - forall l r, - check_dest_l l r = true -> - exists a, In a l /\ check_dest a r = true. -Proof. - induction l; crush. - destruct (check_dest a r) eqn:?; try solve [econstructor; crush]. - simplify. - exploit IHl. apply H. simplify. econstructor. simplify. right. eassumption. - auto. -Qed. - -Lemma check_list_l_true : - forall l x r, - check_dest_l (l ++ x :: nil) r = true -> - check_dest_l l r = true \/ check_dest x r = true. -Proof. - simplify. - apply check_dest_l_ex in H; simplify. - apply in_app_or in H. inv H. left. - apply check_dest_l_ex2. exists x0. auto. - inv H0; auto. -Qed. - -Lemma check_dest_l_dec2 l r : - {Forall (fun x => check_dest x r = false) l} - + {exists a, In a l /\ check_dest a r = true}. -Proof. - destruct (check_dest_l_dec l r); [right | left]; - auto using check_dest_l_ex, check_dest_l_forall. -Qed. - -Lemma abstr_comp : - forall l i f x x0, - abstract_sequence f (l ++ i :: nil) = x -> - abstract_sequence f l = x0 -> - x = update x0 i. -Proof. induction l; intros; crush; eapply IHl; eauto. Qed. - -(* - -Lemma gen_list_base: - forall FF ge sp l rs exps st1, - (forall x, @sem_value FF ge sp st1 (exps # (Reg x)) (rs !! x)) -> - sem_val_list ge sp st1 (list_translation l exps) rs ## l. -Proof. - induction l. - intros. simpl. constructor. - intros. simpl. eapply Scons; eauto. -Qed. - -Lemma check_dest_update2 : - forall f r rl op p, - (update f (RBop p op rl r)) # (Reg r) = Eop op (list_translation rl f) (f # Mem). -Proof. crush; rewrite map2; auto. Qed. - -Lemma check_dest_update3 : - forall f r rl p addr chunk, - (update f (RBload p chunk addr rl r)) # (Reg r) = Eload chunk addr (list_translation rl f) (f # Mem). -Proof. crush; rewrite map2; auto. Qed. - -Lemma abstract_seq_correct_aux: - forall FF ge sp i st1 st2 st3 f, - @step_instr FF ge sp st3 i st2 -> - sem ge sp st1 f st3 -> - sem ge sp st1 (update f i) st2. -Proof. - intros; inv H; simplify. - { simplify; eauto. } (*apply match_states_refl. }*) - { inv H0. inv H6. destruct st1. econstructor. simplify. - constructor. intros. - destruct (resource_eq (Reg res) (Reg x)). inv e. - rewrite map2. econstructor. eassumption. apply gen_list_base; eauto. - rewrite Regmap.gss. eauto. - assert (res <> x). { unfold not in *. intros. apply n. rewrite H0. auto. } - rewrite Regmap.gso by auto. - rewrite genmap1 by auto. auto. - - rewrite genmap1; crush. } - { inv H0. inv H7. constructor. constructor. intros. - destruct (Pos.eq_dec dst x); subst. - rewrite map2. econstructor; eauto. - apply gen_list_base. auto. rewrite Regmap.gss. auto. - rewrite genmap1. rewrite Regmap.gso by auto. auto. - unfold not in *; intros. inv H0. auto. - rewrite genmap1; crush. - } - { inv H0. inv H7. constructor. constructor; intros. - rewrite genmap1; crush. - rewrite map2. econstructor; eauto. - apply gen_list_base; auto. - } -Qed. - -Lemma regmap_list_equiv : - forall A (rs1: Regmap.t A) rs2, - (forall x, rs1 !! x = rs2 !! x) -> - forall rl, rs1##rl = rs2##rl. -Proof. induction rl; crush. Qed. - -Lemma sem_update_Op : - forall A ge sp st f st' r l o0 o m rs v, - @sem A ge sp st f st' -> - Op.eval_operation ge sp o0 rs ## l m = Some v -> - match_states st' (mk_instr_state rs m) -> - exists tst, - sem ge sp st (update f (RBop o o0 l r)) tst /\ match_states (mk_instr_state (Regmap.set r v rs) m) tst. -Proof. - intros. inv H1. simplify. - destruct st. - econstructor. simplify. - { constructor. - { constructor. intros. destruct (Pos.eq_dec x r); subst. - { pose proof (H5 r). rewrite map2. pose proof H. inv H. econstructor; eauto. - { inv H9. eapply gen_list_base; eauto. } - { instantiate (1 := (Regmap.set r v rs0)). rewrite Regmap.gss. erewrite regmap_list_equiv; eauto. } } - { rewrite Regmap.gso by auto. rewrite genmap1; crush. inv H. inv H7; eauto. } } - { inv H. rewrite genmap1; crush. eauto. } } - { constructor; eauto. intros. - destruct (Pos.eq_dec r x); - subst; [repeat rewrite Regmap.gss | repeat rewrite Regmap.gso]; auto. } -Qed. - -Lemma sem_update_load : - forall A ge sp st f st' r o m a l m0 rs v a0, - @sem A ge sp st f st' -> - Op.eval_addressing ge sp a rs ## l = Some a0 -> - Mem.loadv m m0 a0 = Some v -> - match_states st' (mk_instr_state rs m0) -> - exists tst : instr_state, - sem ge sp st (update f (RBload o m a l r)) tst - /\ match_states (mk_instr_state (Regmap.set r v rs) m0) tst. -Proof. - intros. inv H2. pose proof H. inv H. inv H9. - destruct st. - econstructor; simplify. - { constructor. - { constructor. intros. - destruct (Pos.eq_dec x r); subst. - { rewrite map2. econstructor; eauto. eapply gen_list_base. intros. - rewrite <- H6. eauto. - instantiate (1 := (Regmap.set r v rs0)). rewrite Regmap.gss. auto. } - { rewrite Regmap.gso by auto. rewrite genmap1; crush. } } - { rewrite genmap1; crush. eauto. } } - { constructor; auto; intros. destruct (Pos.eq_dec r x); - subst; [repeat rewrite Regmap.gss | repeat rewrite Regmap.gso]; auto. } -Qed. - -Lemma sem_update_store : - forall A ge sp a0 m a l r o f st m' rs m0 st', - @sem A ge sp st f st' -> - Op.eval_addressing ge sp a rs ## l = Some a0 -> - Mem.storev m m0 a0 rs !! r = Some m' -> - match_states st' (mk_instr_state rs m0) -> - exists tst, sem ge sp st (update f (RBstore o m a l r)) tst - /\ match_states (mk_instr_state rs m') tst. -Proof. - intros. inv H2. pose proof H. inv H. inv H9. - destruct st. - econstructor; simplify. - { econstructor. - { econstructor; intros. rewrite genmap1; crush. } - { rewrite map2. econstructor; eauto. eapply gen_list_base. intros. rewrite <- H6. - eauto. specialize (H6 r). rewrite H6. eauto. } } - { econstructor; eauto. } -Qed. - -Lemma sem_update : - forall A ge sp st x st' st'' st''' f, - sem ge sp st f st' -> - match_states st' st''' -> - @step_instr A ge sp st''' x st'' -> - exists tst, sem ge sp st (update f x) tst /\ match_states st'' tst. -Proof. - intros. destruct x; inv H1. - { econstructor. split. - apply sem_update_RBnop. eassumption. - apply match_states_commut. auto. } - { eapply sem_update_Op; eauto. } - { eapply sem_update_load; eauto. } - { eapply sem_update_store; eauto. } -Qed. - -Lemma sem_update2_Op : - forall A ge sp st f r l o0 o m rs v, - @sem A ge sp st f (mk_instr_state rs m) -> - Op.eval_operation ge sp o0 rs ## l m = Some v -> - sem ge sp st (update f (RBop o o0 l r)) (mk_instr_state (Regmap.set r v rs) m). -Proof. - intros. destruct st. constructor. - inv H. inv H6. - { constructor; intros. simplify. - destruct (Pos.eq_dec r x); subst. - { rewrite map2. econstructor. eauto. - apply gen_list_base. eauto. - rewrite Regmap.gss. auto. } - { rewrite genmap1; crush. rewrite Regmap.gso; auto. } } - { simplify. rewrite genmap1; crush. inv H. eauto. } -Qed. - -Lemma sem_update2_load : - forall A ge sp st f r o m a l m0 rs v a0, - @sem A ge sp st f (mk_instr_state rs m0) -> - Op.eval_addressing ge sp a rs ## l = Some a0 -> - Mem.loadv m m0 a0 = Some v -> - sem ge sp st (update f (RBload o m a l r)) (mk_instr_state (Regmap.set r v rs) m0). -Proof. - intros. simplify. inv H. inv H7. constructor. - { constructor; intros. destruct (Pos.eq_dec r x); subst. - { rewrite map2. rewrite Regmap.gss. econstructor; eauto. - apply gen_list_base; eauto. } - { rewrite genmap1; crush. rewrite Regmap.gso; eauto. } - } - { simplify. rewrite genmap1; crush. } -Qed. - -Lemma sem_update2_store : - forall A ge sp a0 m a l r o f st m' rs m0, - @sem A ge sp st f (mk_instr_state rs m0) -> - Op.eval_addressing ge sp a rs ## l = Some a0 -> - Mem.storev m m0 a0 rs !! r = Some m' -> - sem ge sp st (update f (RBstore o m a l r)) (mk_instr_state rs m'). -Proof. - intros. simplify. inv H. inv H7. constructor; simplify. - { econstructor; intros. rewrite genmap1; crush. } - { rewrite map2. econstructor; eauto. apply gen_list_base; eauto. } -Qed. - -Lemma sem_update2 : - forall A ge sp st x st' st'' f, - sem ge sp st f st' -> - @step_instr A ge sp st' x st'' -> - sem ge sp st (update f x) st''. -Proof. - intros. - destruct x; inv H0; - eauto using sem_update_RBnop, sem_update2_Op, sem_update2_load, sem_update2_store. -Qed. - -Lemma abstr_sem_val_mem : - forall A B ge tge st tst sp a, - ge_preserved ge tge -> - forall v m, - (@sem_mem A ge sp st a m /\ match_states st tst -> @sem_mem B tge sp tst a m) /\ - (@sem_value A ge sp st a v /\ match_states st tst -> @sem_value B tge sp tst a v). -Proof. - intros * H. - apply expression_ind2 with - - (P := fun (e1: expression) => - forall v m, - (@sem_mem A ge sp st e1 m /\ match_states st tst -> @sem_mem B tge sp tst e1 m) /\ - (@sem_value A ge sp st e1 v /\ match_states st tst -> @sem_value B tge sp tst e1 v)) - - (P0 := fun (e1: expression_list) => - forall lv, @sem_val_list A ge sp st e1 lv /\ match_states st tst -> @sem_val_list B tge sp tst e1 lv); - simplify; intros; simplify. - { inv H1. inv H2. constructor. } - { inv H2. inv H1. rewrite H0. constructor. } - { inv H3. } - { inv H3. inv H4. econstructor. apply H1; auto. simplify. eauto. constructor. auto. auto. - apply H0; simplify; eauto. constructor; eauto. - unfold ge_preserved in *. simplify. rewrite <- H2. auto. - } - { inv H3. } - { inv H3. inv H4. econstructor. apply H1; eauto; simplify; eauto. constructor; eauto. - apply H0; simplify; eauto. constructor; eauto. - inv H. rewrite <- H4. eauto. - auto. - } - { inv H4. inv H5. econstructor. apply H0; eauto. simplify; eauto. constructor; eauto. - apply H2; eauto. simplify; eauto. constructor; eauto. - apply H1; eauto. simplify; eauto. constructor; eauto. - inv H. rewrite <- H5. eauto. auto. - } - { inv H4. } - { inv H1. constructor. } - { inv H3. constructor; auto. apply H0; eauto. apply Mem.empty. } -Qed. - -Lemma abstr_sem_value : - forall a A B ge tge sp st tst v, - @sem_value A ge sp st a v -> - ge_preserved ge tge -> - match_states st tst -> - @sem_value B tge sp tst a v. -Proof. intros; eapply abstr_sem_val_mem; eauto; apply Mem.empty. Qed. - -Lemma abstr_sem_mem : - forall a A B ge tge sp st tst v, - @sem_mem A ge sp st a v -> - ge_preserved ge tge -> - match_states st tst -> - @sem_mem B tge sp tst a v. -Proof. intros; eapply abstr_sem_val_mem; eauto. Qed. - -Lemma abstr_sem_regset : - forall a a' A B ge tge sp st tst rs, - @sem_regset A ge sp st a rs -> - ge_preserved ge tge -> - (forall x, a # x = a' # x) -> - match_states st tst -> - exists rs', @sem_regset B tge sp tst a' rs' /\ (forall x, rs !! x = rs' !! x). -Proof. - inversion 1; intros. - inv H7. - econstructor. simplify. econstructor. intros. - eapply abstr_sem_value; eauto. rewrite <- H6. - eapply H0. constructor; eauto. - auto. -Qed. - -Lemma abstr_sem : - forall a a' A B ge tge sp st tst st', - @sem A ge sp st a st' -> - ge_preserved ge tge -> - (forall x, a # x = a' # x) -> - match_states st tst -> - exists tst', @sem B tge sp tst a' tst' /\ match_states st' tst'. -Proof. - inversion 1; subst; intros. - inversion H4; subst. - exploit abstr_sem_regset; eauto; inv_simp. - do 3 econstructor; eauto. - rewrite <- H3. - eapply abstr_sem_mem; eauto. -Qed. - -Lemma abstract_execution_correct': - forall A B ge tge sp st' a a' st tst, - @sem A ge sp st a st' -> - ge_preserved ge tge -> - check a a' = true -> - match_states st tst -> - exists tst', @sem B tge sp tst a' tst' /\ match_states st' tst'. -Proof. - intros; - pose proof (check_correct a a' H1); - eapply abstr_sem; eauto. -Qed. - -Lemma states_match : - forall st1 st2 st3 st4, - match_states st1 st2 -> - match_states st2 st3 -> - match_states st3 st4 -> - match_states st1 st4. -Proof. - intros * H1 H2 H3; destruct st1; destruct st2; destruct st3; destruct st4. - inv H1. inv H2. inv H3; constructor. - unfold regs_lessdef in *. intros. - repeat match goal with - | H: forall _, _, r : positive |- _ => specialize (H r) - end. - congruence. - auto. -Qed. - -Lemma step_instr_block_same : - forall ge sp st st', - step_instr_block ge sp st nil st' -> - st = st'. -Proof. inversion 1; auto. Qed. - -Lemma step_instr_seq_same : - forall ge sp st st', - step_instr_seq ge sp st nil st' -> - st = st'. -Proof. inversion 1; auto. Qed. - -Lemma sem_update' : - forall A ge sp st a x st', - sem ge sp st (update (abstract_sequence empty a) x) st' -> - exists st'', - @step_instr A ge sp st'' x st' /\ - sem ge sp st (abstract_sequence empty a) st''. -Proof. - Admitted. - -Lemma rtlpar_trans_correct : - forall bb ge sp sem_st' sem_st st, - sem ge sp sem_st (abstract_sequence empty (concat (concat bb))) sem_st' -> - match_states sem_st st -> - exists st', RTLPar.step_instr_block ge sp st bb st' - /\ match_states sem_st' st'. -Proof. - induction bb using rev_ind. - { repeat econstructor. eapply abstract_interp_empty3 in H. - inv H. inv H0. constructor; congruence. } - { simplify. inv H0. repeat rewrite concat_app in H. simplify. - rewrite app_nil_r in H. - exploit sem_separate; eauto; inv_simp. - repeat econstructor. admit. admit. - } -Admitted. - -(*Lemma abstract_execution_correct_ld: - forall bb bb' cfi ge tge sp st st' tst, - RTLBlock.step_instr_list ge sp st bb st' -> - ge_preserved ge tge -> - schedule_oracle (mk_bblock bb cfi) (mk_bblock bb' cfi) = true -> - match_states_ld st tst -> - exists tst', RTLPar.step_instr_block tge sp tst bb' tst' - /\ match_states st' tst'. -Proof. - intros.*) -*) - -Lemma match_states_list : - forall A (rs: Regmap.t A) rs', - (forall r, rs !! r = rs' !! r) -> - forall l, rs ## l = rs' ## l. -Proof. induction l; crush. Qed. - -Lemma PTree_matches : - forall A (v: A) res rs rs', - (forall r, rs !! r = rs' !! r) -> - forall x, (Regmap.set res v rs) !! x = (Regmap.set res v rs') !! x. -Proof. - intros; destruct (Pos.eq_dec x res); subst; - [ repeat rewrite Regmap.gss by auto - | repeat rewrite Regmap.gso by auto ]; auto. -Qed. - -Lemma abstract_interp_empty3 : - forall A ctx st', - @sem A ctx empty st' -> match_states (ctx_is ctx) st'. -Proof. - inversion 1; subst; simplify. destruct ctx. - destruct ctx_is. - constructor; intros. - - inv H0. specialize (H3 x). inv H3. inv H8. reflexivity. - - inv H1. specialize (H3 x). inv H3. inv H8. reflexivity. - - inv H2. inv H8. reflexivity. -Qed. - -Lemma step_instr_matches : - forall A a ge sp st st', - @step_instr A ge sp st a st' -> - forall tst, - match_states st tst -> - exists tst', step_instr ge sp tst a tst' - /\ match_states st' tst'. -Proof. - induction 1; simplify; - match goal with H: match_states _ _ |- _ => inv H end; - try solve [repeat econstructor; try erewrite match_states_list; - try apply PTree_matches; eauto; - match goal with - H: forall _, _ |- context[Mem.storev] => erewrite <- H; eauto - end]. - - destruct p. match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - erewrite <- eval_predf_pr_equiv; eassumption. - apply PTree_matches; assumption. - repeat (econstructor; try apply eval_pred_false); eauto. try erewrite match_states_list; eauto. - erewrite <- eval_predf_pr_equiv; eassumption. - econstructor; auto. - match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - - destruct p. match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - erewrite <- eval_predf_pr_equiv; eassumption. - apply PTree_matches; assumption. - repeat (econstructor; try apply eval_pred_false); eauto. try erewrite match_states_list; eauto. - erewrite <- eval_predf_pr_equiv; eassumption. - econstructor; auto. - match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - - destruct p. match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - match goal with - H: forall _, _ |- context[Mem.storev] => erewrite <- H; eauto - end. - erewrite <- eval_predf_pr_equiv; eassumption. - repeat (econstructor; try apply eval_pred_false); eauto. try erewrite match_states_list; eauto. - match goal with - H: forall _, _ |- context[Mem.storev] => erewrite <- H; eauto - end. - erewrite <- eval_predf_pr_equiv; eassumption. - match goal with H: eval_pred _ _ _ _ |- _ => inv H end. - repeat econstructor; try erewrite match_states_list; eauto. - match goal with - H: forall _, _ |- context[Mem.storev] => erewrite <- H; eauto - end. - - admit. Admitted. - -Lemma step_instr_list_matches : - forall a ge sp st st', - step_instr_list ge sp st a st' -> - forall tst, match_states st tst -> - exists tst', step_instr_list ge sp tst a tst' - /\ match_states st' tst'. -Proof. - induction a; intros; inv H; - try (exploit step_instr_matches; eauto; []; simplify; - exploit IHa; eauto; []; simplify); repeat econstructor; eauto. -Qed. - -Lemma step_instr_seq_matches : - forall a ge sp st st', - step_instr_seq ge sp st a st' -> - forall tst, match_states st tst -> - exists tst', step_instr_seq ge sp tst a tst' - /\ match_states st' tst'. -Proof. - induction a; intros; inv H; - try (exploit step_instr_list_matches; eauto; []; simplify; - exploit IHa; eauto; []; simplify); repeat econstructor; eauto. -Qed. - -Lemma step_instr_block_matches : - forall bb ge sp st st', - step_instr_block ge sp st bb st' -> - forall tst, match_states st tst -> - exists tst', step_instr_block ge sp tst bb tst' - /\ match_states st' tst'. -Proof. - induction bb; intros; inv H; - try (exploit step_instr_seq_matches; eauto; []; simplify; - exploit IHbb; eauto; []; simplify); repeat econstructor; eauto. -Qed. - -Lemma rtlblock_trans_correct' : - forall bb ge sp st x st'', - RTLBlock.step_instr_list ge sp st (bb ++ x :: nil) st'' -> - exists st', RTLBlock.step_instr_list ge sp st bb st' - /\ step_instr ge sp st' x st''. -Proof. - induction bb. - crush. exists st. - split. constructor. inv H. inv H6. auto. - crush. inv H. exploit IHbb. eassumption. simplify. - econstructor. split. - econstructor; eauto. eauto. -Qed. - -Lemma abstract_interp_empty A st : @sem A st empty (ctx_is st). -Proof. destruct st, ctx_is. simpl. repeat econstructor. Qed. - -Lemma abstract_seq : - forall l f i, - abstract_sequence f (l ++ i :: nil) = update (abstract_sequence f l) i. -Proof. induction l; crush. Qed. - -Lemma abstract_sequence_update : - forall l r f, - check_dest_l l r = false -> - (abstract_sequence f l) # (Reg r) = f # (Reg r). -Proof. - induction l using rev_ind; crush. - rewrite abstract_seq. rewrite check_dest_update. apply IHl. - apply check_list_l_false in H. tauto. - apply check_list_l_false in H. tauto. -Qed. - -(*Lemma sem_separate : - forall A ctx b a st', - sem ctx (abstract_sequence empty (a ++ b)) st' -> - exists st'', - @sem A ctx (abstract_sequence empty a) st'' - /\ @sem A (mk_ctx st'' (ctx_sp ctx) (ctx_ge ctx)) (abstract_sequence empty b) st'. -Proof. - induction b using rev_ind; simplify. - { econstructor. simplify. rewrite app_nil_r in H. eauto. apply abstract_interp_empty. } - { simplify. rewrite app_assoc in H. rewrite abstract_seq in H. - exploit sem_update'; eauto; simplify. - exploit IHb; eauto; inv_simp. - econstructor; split; eauto. - rewrite abstract_seq. - eapply sem_update2; eauto. - } -Qed.*) - -Lemma sem_update_RBnop : - forall A ctx f st', - @sem A ctx f st' -> sem ctx (update f RBnop) st'. -Proof. auto. Qed. - -Lemma sem_update_Op : - forall A ge sp ist f st' r l o0 o m rs v ps, - @sem A (mk_ctx ist sp ge) f st' -> - eval_predf ps o = true -> - Op.eval_operation ge sp o0 (rs ## l) m = Some v -> - match_states st' (mk_instr_state rs ps m) -> - exists tst, - sem (mk_ctx ist sp ge) (update f (RBop (Some o) o0 l r)) tst - /\ match_states (mk_instr_state (Regmap.set r v rs) ps m) tst. -Proof. - intros. inv H1. inv H. inv H1. inv H3. simplify. - econstructor. simplify. - { constructor; try constructor; intros; try solve [rewrite genmap1; now eauto]. - destruct (Pos.eq_dec x r); subst. - { rewrite map2. specialize (H1 r). inv H1. -(*} - } - destruct st. - econstructor. simplify. - { constructor. - { constructor. intros. destruct (Pos.eq_dec x r); subst. - { pose proof (H5 r). rewrite map2. pose proof H. inv H. econstructor; eauto. - { inv H9. eapply gen_list_base; eauto. } - { instantiate (1 := (Regmap.set r v rs0)). rewrite Regmap.gss. erewrite regmap_list_equiv; eauto. } } - { rewrite Regmap.gso by auto. rewrite genmap1; crush. inv H. inv H7; eauto. } } - { inv H. rewrite genmap1; crush. eauto. } } - { constructor; eauto. intros. - destruct (Pos.eq_dec r x); - subst; [repeat rewrite Regmap.gss | repeat rewrite Regmap.gso]; auto. } -Qed.*) Admitted. - -Lemma sem_update : - forall A ge sp st x st' st'' st''' f, - sem (mk_ctx st sp ge) f st' -> - match_states st' st''' -> - @step_instr A ge sp st''' x st'' -> - exists tst, sem (mk_ctx st sp ge) (update f x) tst /\ match_states st'' tst. -Proof. - intros. destruct x. - - inv H1. econstructor. simplify. eauto. symmetry; auto. - - inv H1. inv H0. econstructor. - Admitted. - -Lemma rtlblock_trans_correct : - forall bb ge sp st st', - RTLBlock.step_instr_list ge sp st bb st' -> - forall tst, - match_states st tst -> - exists tst', sem (mk_ctx tst sp ge) (abstract_sequence empty bb) tst' - /\ match_states st' tst'. -Proof. - induction bb using rev_ind; simplify. - { econstructor. simplify. apply abstract_interp_empty. - inv H. auto. } - { apply rtlblock_trans_correct' in H. simplify. - rewrite abstract_seq. - exploit IHbb; try eassumption; []; simplify. - exploit sem_update. apply H1. symmetry; eassumption. - eauto. simplify. econstructor. split. apply H3. - auto. } -Qed. - -Lemma abstract_execution_correct: - forall bb bb' cfi cfi' ge tge sp st st' tst, - RTLBlock.step_instr_list ge sp st bb st' -> - ge_preserved ge tge -> - schedule_oracle (mk_bblock bb cfi) (mk_bblock bb' cfi') = true -> - match_states st tst -> - exists tst', RTLPar.step_instr_block tge sp tst bb' tst' - /\ match_states st' tst'. -Proof. - intros. - unfold schedule_oracle in *. simplify. unfold empty_trees in H4. - exploit rtlblock_trans_correct; try eassumption; []; simplify. -(*) exploit abstract_execution_correct'; - try solve [eassumption | apply state_lessdef_match_sem; eassumption]. - apply match_states_commut. eauto. inv_simp. - exploit rtlpar_trans_correct; try eassumption; []; inv_simp. - exploit step_instr_block_matches; eauto. apply match_states_commut; eauto. inv_simp. - repeat match goal with | H: match_states _ _ |- _ => inv H end. - do 2 econstructor; eauto. - econstructor; congruence. -Qed.*)Admitted. - -Definition match_prog (prog : RTLBlock.program) (tprog : RTLPar.program) := - match_program (fun cu f tf => transl_fundef f = Errors.OK tf) eq prog tprog. - -Inductive match_stackframes: RTLBlock.stackframe -> RTLPar.stackframe -> Prop := -| match_stackframe: - forall f tf res sp pc rs rs' ps ps', - transl_function f = OK tf -> - (forall x, rs !! x = rs' !! x) -> - (forall x, ps !! x = ps' !! x) -> - match_stackframes (Stackframe res f sp pc rs ps) - (Stackframe res tf sp pc rs' ps'). - -Inductive match_states: RTLBlock.state -> RTLPar.state -> Prop := -| match_state: - forall sf f sp pc rs rs' m sf' tf ps ps' - (TRANSL: transl_function f = OK tf) - (STACKS: list_forall2 match_stackframes sf sf') - (REG: forall x, rs !! x = rs' !! x) - (REG: forall x, ps !! x = ps' !! x), - match_states (State sf f sp pc rs ps m) - (State sf' tf sp pc rs' ps' m) -| match_returnstate: - forall stack stack' v m - (STACKS: list_forall2 match_stackframes stack stack'), - match_states (Returnstate stack v m) - (Returnstate stack' v m) -| match_callstate: - forall stack stack' f tf args m - (TRANSL: transl_fundef f = OK tf) - (STACKS: list_forall2 match_stackframes stack stack'), - match_states (Callstate stack f args m) - (Callstate stack' tf args m). - -Section CORRECTNESS. - - Context (prog: RTLBlock.program) (tprog : RTLPar.program). - Context (TRANSL: match_prog prog tprog). - - Let ge : RTLBlock.genv := Globalenvs.Genv.globalenv prog. - Let tge : RTLPar.genv := Globalenvs.Genv.globalenv tprog. - - Lemma symbols_preserved: - forall (s: AST.ident), Genv.find_symbol tge s = Genv.find_symbol ge s. - Proof using TRANSL. intros. eapply (Genv.find_symbol_match TRANSL). Qed. - Hint Resolve symbols_preserved : rtlgp. - - Lemma function_ptr_translated: - forall (b: Values.block) (f: RTLBlock.fundef), - Genv.find_funct_ptr ge b = Some f -> - exists tf, - Genv.find_funct_ptr tge b = Some tf /\ transl_fundef f = Errors.OK tf. - Proof using TRANSL. - intros. exploit (Genv.find_funct_ptr_match TRANSL); eauto. - intros (cu & tf & P & Q & R); exists tf; auto. - Qed. - - Lemma functions_translated: - forall (v: Values.val) (f: RTLBlock.fundef), - Genv.find_funct ge v = Some f -> - exists tf, - Genv.find_funct tge v = Some tf /\ transl_fundef f = Errors.OK tf. - Proof using TRANSL. - intros. exploit (Genv.find_funct_match TRANSL); eauto. - intros (cu & tf & P & Q & R); exists tf; auto. - Qed. - - Lemma senv_preserved: - Senv.equiv (Genv.to_senv ge) (Genv.to_senv tge). - Proof (Genv.senv_transf_partial TRANSL). - Hint Resolve senv_preserved : rtlgp. - - Lemma sig_transl_function: - forall (f: RTLBlock.fundef) (tf: RTLPar.fundef), - transl_fundef f = OK tf -> - funsig tf = funsig f. - Proof using . - unfold transl_fundef, transf_partial_fundef, transl_function; intros; - repeat destruct_match; crush; - match goal with H: OK _ = OK _ |- _ => inv H end; auto. - Qed. - Hint Resolve sig_transl_function : rtlgp. - - Hint Resolve Val.lessdef_same : rtlgp. - Hint Resolve regs_lessdef_regs : rtlgp. - - Lemma find_function_translated: - forall ros rs rs' f, - (forall x, rs !! x = rs' !! x) -> - find_function ge ros rs = Some f -> - exists tf, find_function tge ros rs' = Some tf - /\ transl_fundef f = OK tf. - Proof using TRANSL. - Ltac ffts := match goal with - | [ H: forall _, Val.lessdef _ _, r: Registers.reg |- _ ] => - specialize (H r); inv H - | [ H: Vundef = ?r, H1: Genv.find_funct _ ?r = Some _ |- _ ] => - rewrite <- H in H1 - | [ H: Genv.find_funct _ Vundef = Some _ |- _] => solve [inv H] - | _ => solve [exploit functions_translated; eauto] - end. - destruct ros; simplify; try rewrite <- H; - [| rewrite symbols_preserved; destruct_match; - try (apply function_ptr_translated); crush ]; - intros; - repeat ffts. - Qed. - - Lemma schedule_oracle_nil: - forall bb cfi, - schedule_oracle {| bb_body := nil; bb_exit := cfi |} bb = true -> - bb_body bb = nil /\ bb_exit bb = cfi. - Proof using . - unfold schedule_oracle, check_control_flow_instr. - simplify; repeat destruct_match; crush. - Qed. - - Lemma schedule_oracle_nil2: - forall cfi, - schedule_oracle {| bb_body := nil; bb_exit := cfi |} - {| bb_body := nil; bb_exit := cfi |} = true. - Proof using . - unfold schedule_oracle, check_control_flow_instr. - simplify; repeat destruct_match; crush. - Qed. - - Lemma eval_op_eq: - forall (sp0 : Values.val) (op : Op.operation) (vl : list Values.val) m, - Op.eval_operation ge sp0 op vl m = Op.eval_operation tge sp0 op vl m. - Proof using TRANSL. - intros. - destruct op; auto; unfold Op.eval_operation, Genv.symbol_address, Op.eval_addressing32; - [| destruct a; unfold Genv.symbol_address ]; - try rewrite symbols_preserved; auto. - Qed. - Hint Resolve eval_op_eq : rtlgp. - - Lemma eval_addressing_eq: - forall sp addr vl, - Op.eval_addressing ge sp addr vl = Op.eval_addressing tge sp addr vl. - Proof using TRANSL. - intros. - destruct addr; - unfold Op.eval_addressing, Op.eval_addressing32; - unfold Genv.symbol_address; - try rewrite symbols_preserved; auto. - Qed. - Hint Resolve eval_addressing_eq : rtlgp. - - Lemma ge_preserved_lem: - ge_preserved ge tge. - Proof using TRANSL. - unfold ge_preserved. - eauto with rtlgp. - Qed. - Hint Resolve ge_preserved_lem : rtlgp. - - Lemma lessdef_regmap_optget: - forall or rs rs', - regs_lessdef rs rs' -> - Val.lessdef (regmap_optget or Vundef rs) (regmap_optget or Vundef rs'). - Proof using. destruct or; crush. Qed. - Hint Resolve lessdef_regmap_optget : rtlgp. - - Lemma regmap_equiv_lessdef: - forall rs rs', - (forall x, rs !! x = rs' !! x) -> - regs_lessdef rs rs'. - Proof using. - intros; unfold regs_lessdef; intros. - rewrite H. apply Val.lessdef_refl. - Qed. - Hint Resolve regmap_equiv_lessdef : rtlgp. - - Lemma int_lessdef: - forall rs rs', - regs_lessdef rs rs' -> - (forall arg v, - rs !! arg = Vint v -> - rs' !! arg = Vint v). - Proof using. intros ? ? H; intros; specialize (H arg); inv H; crush. Qed. - Hint Resolve int_lessdef : rtlgp. - - Ltac semantics_simpl := - match goal with - | [ H: match_states _ _ |- _ ] => - let H2 := fresh "H" in - learn H as H2; inv H2 - | [ H: transl_function ?f = OK _ |- _ ] => - let H2 := fresh "TRANSL" in - learn H as H2; - unfold transl_function in H2; - destruct (check_scheduled_trees - (@fn_code RTLBlock.bb f) - (@fn_code RTLPar.bb (schedule f))) eqn:?; - [| discriminate ]; inv H2 - | [ H: context[check_scheduled_trees] |- _ ] => - let H2 := fresh "CHECK" in - learn H as H2; - eapply check_scheduled_trees_correct in H2; [| solve [eauto] ] - | [ H: schedule_oracle {| bb_body := nil; bb_exit := _ |} ?bb = true |- _ ] => - let H2 := fresh "SCHED" in - learn H as H2; - apply schedule_oracle_nil in H2 - | [ H: find_function _ _ _ = Some _, H2: forall x, ?rs !! x = ?rs' !! x |- _ ] => - learn H; exploit find_function_translated; try apply H2; eauto; inversion 1 - | [ H: Mem.free ?m _ _ _ = Some ?m', H2: Mem.extends ?m ?m'' |- _ ] => - learn H; exploit Mem.free_parallel_extends; eauto; intros - | [ H: Events.eval_builtin_args _ _ _ _ _ _, H2: regs_lessdef ?rs ?rs' |- _ ] => - let H3 := fresh "H" in - learn H; exploit Events.eval_builtin_args_lessdef; [apply H2 | | |]; - eauto with rtlgp; intro H3; learn H3 - | [ H: Events.external_call _ _ _ _ _ _ _ |- _ ] => - let H2 := fresh "H" in - learn H; exploit Events.external_call_mem_extends; - eauto; intro H2; learn H2 - | [ H: exists _, _ |- _ ] => inv H - | _ => progress simplify - end. - - Hint Resolve Events.eval_builtin_args_preserved : rtlgp. - Hint Resolve Events.external_call_symbols_preserved : rtlgp. - Hint Resolve set_res_lessdef : rtlgp. - Hint Resolve set_reg_lessdef : rtlgp. - Hint Resolve Op.eval_condition_lessdef : rtlgp. - - Hint Constructors Events.eval_builtin_arg: barg. - - Lemma eval_builtin_arg_eq: - forall A ge a v1 m1 e1 e2 sp, - (forall x, e1 x = e2 x) -> - @Events.eval_builtin_arg A ge e1 sp m1 a v1 -> - Events.eval_builtin_arg ge e2 sp m1 a v1. -Proof. induction 2; try rewrite H; eauto with barg. Qed. - - Lemma eval_builtin_args_eq: - forall A ge e1 sp m1 e2 al vl1, - (forall x, e1 x = e2 x) -> - @Events.eval_builtin_args A ge e1 sp m1 al vl1 -> - Events.eval_builtin_args ge e2 sp m1 al vl1. - Proof. - induction 2. - - econstructor; split. - - exploit eval_builtin_arg_eq; eauto. intros. - destruct IHlist_forall2 as [| y]. constructor; eauto. - constructor. constructor; auto. - constructor; eauto. - Qed. - - Lemma step_cf_instr_correct: - forall cfi t s s', - step_cf_instr ge s cfi t s' -> - forall r, - match_states s r -> - exists r', step_cf_instr tge r cfi t r' /\ match_states s' r'. - Proof using TRANSL. - induction 1; repeat semantics_simpl; - try solve [repeat (try erewrite match_states_list; eauto; econstructor; eauto with rtlgp)]. - { do 3 (try erewrite match_states_list by eauto; econstructor; eauto with rtlgp). - eapply eval_builtin_args_eq. eapply REG. - eapply Events.eval_builtin_args_preserved. eapply symbols_preserved. - eauto. - intros. - unfold regmap_setres. destruct res. - destruct (Pos.eq_dec x0 x); subst. - repeat rewrite Regmap.gss; auto. - repeat rewrite Regmap.gso; auto. - eapply REG. eapply REG. - } - { repeat (try erewrite match_states_list; eauto; econstructor; eauto with rtlgp). - unfold regmap_optget. destruct or. rewrite REG. constructor; eauto. - constructor; eauto. - } - { exploit IHstep_cf_instr; eauto. simplify. - repeat (try erewrite match_states_list; eauto; econstructor; eauto with rtlgp). - erewrite eval_predf_pr_equiv; eauto. - } - Qed. - - Theorem transl_step_correct : - forall (S1 : RTLBlock.state) t S2, - RTLBlock.step ge S1 t S2 -> - forall (R1 : RTLPar.state), - match_states S1 R1 -> - exists R2, Smallstep.plus RTLPar.step tge R1 t R2 /\ match_states S2 R2. - Proof. - - induction 1; repeat semantics_simpl. - - { destruct bb; destruct x. - assert (bb_exit = bb_exit0). - { unfold schedule_oracle in *. simplify. - unfold check_control_flow_instr in *. - destruct_match; crush. - } - subst. - - exploit abstract_execution_correct; try eassumption. eapply ge_preserved_lem. - econstructor; eauto. - simplify. destruct x. inv H7. - - exploit step_cf_instr_correct; try eassumption. econstructor; eauto. - simplify. - - econstructor. econstructor. eapply Smallstep.plus_one. econstructor. - eauto. eauto. simplify. eauto. eauto. } - { unfold bind in *. inv TRANSL0. clear Learn. inv H0. destruct_match; crush. - inv H2. unfold transl_function in Heqr. destruct_match; crush. - inv Heqr. - repeat econstructor; eauto. - unfold bind in *. destruct_match; crush. } - { inv TRANSL0. repeat econstructor; eauto using Events.external_call_symbols_preserved, symbols_preserved, senv_preserved, Events.E0_right. } - { inv STACKS. inv H2. repeat econstructor; eauto. - intros. apply PTree_matches; eauto. } - Qed. - - Lemma transl_initial_states: - forall S, - RTLBlock.initial_state prog S -> - exists R, RTLPar.initial_state tprog R /\ match_states S R. - Proof. - induction 1. - exploit function_ptr_translated; eauto. intros [tf [A B]]. - econstructor; split. - econstructor. apply (Genv.init_mem_transf_partial TRANSL); eauto. - replace (prog_main tprog) with (prog_main prog). rewrite symbols_preserved; eauto. - symmetry; eapply match_program_main; eauto. - eexact A. - rewrite <- H2. apply sig_transl_function; auto. - constructor. auto. constructor. - Qed. - - Lemma transl_final_states: - forall S R r, - match_states S R -> RTLBlock.final_state S r -> RTLPar.final_state R r. - Proof. - intros. inv H0. inv H. inv STACKS. constructor. - Qed. - - Theorem transf_program_correct: - Smallstep.forward_simulation (RTLBlock.semantics prog) (RTLPar.semantics tprog). - Proof. - eapply Smallstep.forward_simulation_plus. - apply senv_preserved. - eexact transl_initial_states. - eexact transl_final_states. - exact transl_step_correct. - Qed. - -End CORRECTNESS. -#+end_src - -* License - -#+name: license -#+begin_src coq :tangle no -(* - * Vericert: Verified high-level synthesis. - * Copyright (C) 2020-2022 Yann Herklotz <yann@yannherklotz.com> - * - * 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 <https://www.gnu.org/licenses/>. - *) -#+end_src |