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authorxleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>2008-12-30 14:48:33 +0000
committerxleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>2008-12-30 14:48:33 +0000
commit6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9 (patch)
treef7adbc5ec8accc4bec3e38939bdf570a266f0e83 /backend/Selection.v
parent1bce6b0f9f8cd614038a6e7fc21fb984724204a4 (diff)
downloadcompcert-kvx-6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9.tar.gz
compcert-kvx-6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9.zip
Reorganized the development, modularizing away machine-dependent parts.
Started to merge the ARM code generator. Started to add support for PowerPC/EABI. Use ocamlbuild to construct executable from Caml files. git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@930 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
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-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Xavier Leroy, INRIA Paris-Rocquencourt *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-(** Instruction selection *)
-
-(** The instruction selection pass recognizes opportunities for using
- combined arithmetic and logical operations and addressing modes
- offered by the target processor. For instance, the expression [x + 1]
- can take advantage of the "immediate add" instruction of the processor,
- and on the PowerPC, the expression [(x >> 6) & 0xFF] can be turned
- into a "rotate and mask" instruction.
-
- Instruction selection proceeds by bottom-up rewriting over expressions.
- The source language is Cminor and the target language is CminorSel. *)
-
-Require Import Coqlib.
-Require Import Maps.
-Require Import AST.
-Require Import Integers.
-Require Import Floats.
-Require Import Values.
-Require Import Mem.
-Require Import Globalenvs.
-Require Cminor.
-Require Import Op.
-Require Import CminorSel.
-
-Infix ":::" := Econs (at level 60, right associativity) : selection_scope.
-
-Open Local Scope selection_scope.
-
-(** * Lifting of let-bound variables *)
-
-(** Some of the instruction functions generate [Elet] constructs to
- share the evaluation of a subexpression. Owing to the use of de
- Bruijn indices for let-bound variables, we need to shift de Bruijn
- indices when an expression [b] is put in a [Elet a b] context. *)
-
-Fixpoint lift_expr (p: nat) (a: expr) {struct a}: expr :=
- match a with
- | Evar id => Evar id
- | Eop op bl => Eop op (lift_exprlist p bl)
- | Eload chunk addr bl => Eload chunk addr (lift_exprlist p bl)
- | Econdition b c d =>
- Econdition (lift_condexpr p b) (lift_expr p c) (lift_expr p d)
- | Elet b c => Elet (lift_expr p b) (lift_expr (S p) c)
- | Eletvar n =>
- if le_gt_dec p n then Eletvar (S n) else Eletvar n
- end
-
-with lift_condexpr (p: nat) (a: condexpr) {struct a}: condexpr :=
- match a with
- | CEtrue => CEtrue
- | CEfalse => CEfalse
- | CEcond cond bl => CEcond cond (lift_exprlist p bl)
- | CEcondition b c d =>
- CEcondition (lift_condexpr p b) (lift_condexpr p c) (lift_condexpr p d)
- end
-
-with lift_exprlist (p: nat) (a: exprlist) {struct a}: exprlist :=
- match a with
- | Enil => Enil
- | Econs b cl => Econs (lift_expr p b) (lift_exprlist p cl)
- end.
-
-Definition lift (a: expr): expr := lift_expr O a.
-
-(** * Smart constructors for operators *)
-
-(** This section defines functions for building CminorSel expressions
- and statements, especially expressions consisting of operator
- applications. These functions examine their arguments to choose
- cheaper forms of operators whenever possible.
-
- For instance, [add e1 e2] will return a CminorSel expression semantically
- equivalent to [Eop Oadd (e1 ::: e2 ::: Enil)], but will use a
- [Oaddimm] operator if one of the arguments is an integer constant,
- or suppress the addition altogether if one of the arguments is the
- null integer. In passing, we perform operator reassociation
- ([(e + c1) * c2] becomes [(e * c2) + (c1 * c2)]) and a small amount
- of constant propagation.
-*)
-
-(** ** Integer logical negation *)
-
-(** The natural way to write smart constructors is by pattern-matching
- on their arguments, recognizing cases where cheaper operators
- or combined operators are applicable. For instance, integer logical
- negation has three special cases (not-and, not-or and not-xor),
- along with a default case that uses not-or over its arguments and itself.
- This is written naively as follows:
-<<
-Definition notint (e: expr) :=
- match e with
- | Eop Oand (t1:::t2:::Enil) => Eop Onand (t1:::t2:::Enil)
- | Eop Oor (t1:::t2:::Enil) => Eop Onor (t1:::t2:::Enil)
- | Eop Oxor (t1:::t2:::Enil) => Eop Onxor (t1:::t2:::Enil)
- | _ => Elet(e, Eop Onor (Eletvar O ::: Eletvar O ::: Enil)
- end.
->>
- However, Coq expands complex pattern-matchings like the above into
- elementary matchings over all constructors of an inductive type,
- resulting in much duplication of the final catch-all case.
- Such duplications generate huge executable code and duplicate
- cases in the correctness proofs.
-
- To limit this duplication, we use the following trick due to
- Yves Bertot. We first define a dependent inductive type that
- characterizes the expressions that match each of the 4 cases of interest.
-*)
-
-Inductive notint_cases: forall (e: expr), Set :=
- | notint_case1:
- forall (t1: expr) (t2: expr),
- notint_cases (Eop Oand (t1:::t2:::Enil))
- | notint_case2:
- forall (t1: expr) (t2: expr),
- notint_cases (Eop Oor (t1:::t2:::Enil))
- | notint_case3:
- forall (t1: expr) (t2: expr),
- notint_cases (Eop Oxor (t1:::t2:::Enil))
- | notint_default:
- forall (e: expr),
- notint_cases e.
-
-(** We then define a classification function that takes an expression
- and return the case in which it falls. Note that the catch-all case
- [notint_default] does not state that it is mutually exclusive with
- the first three, more specific cases. The classification function
- nonetheless chooses the specific cases in preference to the catch-all
- case. *)
-
-Definition notint_match (e: expr) :=
- match e as z1 return notint_cases z1 with
- | Eop Oand (t1:::t2:::Enil) =>
- notint_case1 t1 t2
- | Eop Oor (t1:::t2:::Enil) =>
- notint_case2 t1 t2
- | Eop Oxor (t1:::t2:::Enil) =>
- notint_case3 t1 t2
- | e =>
- notint_default e
- end.
-
-(** Finally, the [notint] function we need is defined by a 4-case match
- over the result of the classification function. Thus, no duplication
- of the right-hand sides of this match occur, and the proof has only
- 4 cases to consider (it proceeds by case over [notint_match e]).
- Since the default case is not obviously exclusive with the three
- specific cases, it is important that its right-hand side is
- semantically correct for all possible values of [e], which is the
- case here and for all other smart constructors. *)
-
-Definition notint (e: expr) :=
- match notint_match e with
- | notint_case1 t1 t2 =>
- Eop Onand (t1:::t2:::Enil)
- | notint_case2 t1 t2 =>
- Eop Onor (t1:::t2:::Enil)
- | notint_case3 t1 t2 =>
- Eop Onxor (t1:::t2:::Enil)
- | notint_default e =>
- Elet e (Eop Onor (Eletvar O ::: Eletvar O ::: Enil))
- end.
-
-(** This programming pattern will be applied systematically for the
- other smart constructors in this file. *)
-
-(** ** Boolean negation *)
-
-Definition notbool_base (e: expr) :=
- Eop (Ocmp (Ccompimm Ceq Int.zero)) (e ::: Enil).
-
-Fixpoint notbool (e: expr) {struct e} : expr :=
- match e with
- | Eop (Ointconst n) Enil =>
- Eop (Ointconst (if Int.eq n Int.zero then Int.one else Int.zero)) Enil
- | Eop (Ocmp cond) args =>
- Eop (Ocmp (negate_condition cond)) args
- | Econdition e1 e2 e3 =>
- Econdition e1 (notbool e2) (notbool e3)
- | _ =>
- notbool_base e
- end.
-
-(** ** Integer addition and pointer addition *)
-
-(*
-Definition addimm (n: int) (e: expr) :=
- if Int.eq n Int.zero then e else
- match e with
- | Eop (Ointconst m) Enil => Eop (Ointconst(Int.add n m)) Enil
- | Eop (Oaddrsymbol s m) Enil => Eop (Oaddrsymbol s (Int.add n m)) Enil
- | Eop (Oaddrstack m) Enil => Eop (Oaddrstack (Int.add n m)) Enil
- | Eop (Oaddimm m) (t ::: Enil) => Eop (Oaddimm(Int.add n m)) (t ::: Enil)
- | _ => Eop (Oaddimm n) (e ::: Enil)
- end.
-*)
-
-(** Addition of an integer constant. *)
-
-Inductive addimm_cases: forall (e: expr), Set :=
- | addimm_case1:
- forall (m: int),
- addimm_cases (Eop (Ointconst m) Enil)
- | addimm_case2:
- forall (s: ident) (m: int),
- addimm_cases (Eop (Oaddrsymbol s m) Enil)
- | addimm_case3:
- forall (m: int),
- addimm_cases (Eop (Oaddrstack m) Enil)
- | addimm_case4:
- forall (m: int) (t: expr),
- addimm_cases (Eop (Oaddimm m) (t ::: Enil))
- | addimm_default:
- forall (e: expr),
- addimm_cases e.
-
-Definition addimm_match (e: expr) :=
- match e as z1 return addimm_cases z1 with
- | Eop (Ointconst m) Enil =>
- addimm_case1 m
- | Eop (Oaddrsymbol s m) Enil =>
- addimm_case2 s m
- | Eop (Oaddrstack m) Enil =>
- addimm_case3 m
- | Eop (Oaddimm m) (t ::: Enil) =>
- addimm_case4 m t
- | e =>
- addimm_default e
- end.
-
-Definition addimm (n: int) (e: expr) :=
- if Int.eq n Int.zero then e else
- match addimm_match e with
- | addimm_case1 m =>
- Eop (Ointconst(Int.add n m)) Enil
- | addimm_case2 s m =>
- Eop (Oaddrsymbol s (Int.add n m)) Enil
- | addimm_case3 m =>
- Eop (Oaddrstack (Int.add n m)) Enil
- | addimm_case4 m t =>
- Eop (Oaddimm(Int.add n m)) (t ::: Enil)
- | addimm_default e =>
- Eop (Oaddimm n) (e ::: Enil)
- end.
-
-(** Addition of two integer or pointer expressions. *)
-
-(*
-Definition add (e1: expr) (e2: expr) :=
- match e1, e2 with
- | Eop (Ointconst n1) Enil, t2 => addimm n1 t2
- | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil))
- | Eop(Oaddimm n1) (t1:::Enil)), t2 => addimm n1 (Eop Oadd (t1:::t2:::Enil))
- | t1, Eop (Ointconst n2) Enil => addimm n2 t1
- | t1, Eop (Oaddimm n2) (t2:::Enil) => addimm n2 (Eop Oadd (t1:::t2:::Enil))
- | _, _ => Eop Oadd (e1:::e2:::Enil)
- end.
-*)
-
-Inductive add_cases: forall (e1: expr) (e2: expr), Set :=
- | add_case1:
- forall (n1: int) (t2: expr),
- add_cases (Eop (Ointconst n1) Enil) (t2)
- | add_case2:
- forall (n1: int) (t1: expr) (n2: int) (t2: expr),
- add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil))
- | add_case3:
- forall (n1: int) (t1: expr) (t2: expr),
- add_cases (Eop(Oaddimm n1) (t1:::Enil)) (t2)
- | add_case4:
- forall (t1: expr) (n2: int),
- add_cases (t1) (Eop (Ointconst n2) Enil)
- | add_case5:
- forall (t1: expr) (n2: int) (t2: expr),
- add_cases (t1) (Eop (Oaddimm n2) (t2:::Enil))
- | add_default:
- forall (e1: expr) (e2: expr),
- add_cases e1 e2.
-
-Definition add_match_aux (e1: expr) (e2: expr) :=
- match e2 as z2 return add_cases e1 z2 with
- | Eop (Ointconst n2) Enil =>
- add_case4 e1 n2
- | Eop (Oaddimm n2) (t2:::Enil) =>
- add_case5 e1 n2 t2
- | e2 =>
- add_default e1 e2
- end.
-
-Definition add_match (e1: expr) (e2: expr) :=
- match e1 as z1, e2 as z2 return add_cases z1 z2 with
- | Eop (Ointconst n1) Enil, t2 =>
- add_case1 n1 t2
- | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) =>
- add_case2 n1 t1 n2 t2
- | Eop(Oaddimm n1) (t1:::Enil), t2 =>
- add_case3 n1 t1 t2
- | e1, e2 =>
- add_match_aux e1 e2
- end.
-
-Definition add (e1: expr) (e2: expr) :=
- match add_match e1 e2 with
- | add_case1 n1 t2 =>
- addimm n1 t2
- | add_case2 n1 t1 n2 t2 =>
- addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil))
- | add_case3 n1 t1 t2 =>
- addimm n1 (Eop Oadd (t1:::t2:::Enil))
- | add_case4 t1 n2 =>
- addimm n2 t1
- | add_case5 t1 n2 t2 =>
- addimm n2 (Eop Oadd (t1:::t2:::Enil))
- | add_default e1 e2 =>
- Eop Oadd (e1:::e2:::Enil)
- end.
-
-(** ** Integer and pointer subtraction *)
-
-(*
-Definition sub (e1: expr) (e2: expr) :=
- match e1, e2 with
- | t1, Eop (Ointconst n2) Enil => addimm (Int.neg n2) t1
- | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => addimm
-(intsub n1 n2) (Eop Osub (t1:::t2:::Enil))
- | Eop (Oaddimm n1) (t1:::Enil), t2 => addimm n1 (Eop Osub (t1:::t2:::Rni
-l))
- | t1, Eop (Oaddimm n2) (t2:::Enil) => addimm (Int.neg n2) (Eop Osub (t1:::
-:t2:::Enil))
- | _, _ => Eop Osub (e1:::e2:::Enil)
- end.
-*)
-
-Inductive sub_cases: forall (e1: expr) (e2: expr), Set :=
- | sub_case1:
- forall (t1: expr) (n2: int),
- sub_cases (t1) (Eop (Ointconst n2) Enil)
- | sub_case2:
- forall (n1: int) (t1: expr) (n2: int) (t2: expr),
- sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil))
- | sub_case3:
- forall (n1: int) (t1: expr) (t2: expr),
- sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (t2)
- | sub_case4:
- forall (t1: expr) (n2: int) (t2: expr),
- sub_cases (t1) (Eop (Oaddimm n2) (t2:::Enil))
- | sub_default:
- forall (e1: expr) (e2: expr),
- sub_cases e1 e2.
-
-Definition sub_match_aux (e1: expr) (e2: expr) :=
- match e1 as z1 return sub_cases z1 e2 with
- | Eop (Oaddimm n1) (t1:::Enil) =>
- sub_case3 n1 t1 e2
- | e1 =>
- sub_default e1 e2
- end.
-
-Definition sub_match (e1: expr) (e2: expr) :=
- match e2 as z2, e1 as z1 return sub_cases z1 z2 with
- | Eop (Ointconst n2) Enil, t1 =>
- sub_case1 t1 n2
- | Eop (Oaddimm n2) (t2:::Enil), Eop (Oaddimm n1) (t1:::Enil) =>
- sub_case2 n1 t1 n2 t2
- | Eop (Oaddimm n2) (t2:::Enil), t1 =>
- sub_case4 t1 n2 t2
- | e2, e1 =>
- sub_match_aux e1 e2
- end.
-
-Definition sub (e1: expr) (e2: expr) :=
- match sub_match e1 e2 with
- | sub_case1 t1 n2 =>
- addimm (Int.neg n2) t1
- | sub_case2 n1 t1 n2 t2 =>
- addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil))
- | sub_case3 n1 t1 t2 =>
- addimm n1 (Eop Osub (t1:::t2:::Enil))
- | sub_case4 t1 n2 t2 =>
- addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil))
- | sub_default e1 e2 =>
- Eop Osub (e1:::e2:::Enil)
- end.
-
-(** ** Rotates and immediate shifts *)
-
-(*
-Definition rolm (e1: expr) :=
- match e1 with
- | Eop (Ointconst n1) Enil =>
- Eop (Ointconst(Int.and (Int.rol n1 amount2) mask2)) Enil
- | Eop (Orolm amount1 mask1) (t1:::Enil) =>
- let amount := Int.and (Int.add amount1 amount2) Ox1Fl in
- let mask := Int.and (Int.rol mask1 amount2) mask2 in
- if Int.is_rlw_mask mask
- then Eop (Orolm amount mask) (t1:::Enil)
- else Eop (Orolm amount2 mask2) (e1:::Enil)
- | _ => Eop (Orolm amount2 mask2) (e1:::Enil)
- end
-*)
-
-Inductive rolm_cases: forall (e1: expr), Set :=
- | rolm_case1:
- forall (n1: int),
- rolm_cases (Eop (Ointconst n1) Enil)
- | rolm_case2:
- forall (amount1: int) (mask1: int) (t1: expr),
- rolm_cases (Eop (Orolm amount1 mask1) (t1:::Enil))
- | rolm_default:
- forall (e1: expr),
- rolm_cases e1.
-
-Definition rolm_match (e1: expr) :=
- match e1 as z1 return rolm_cases z1 with
- | Eop (Ointconst n1) Enil =>
- rolm_case1 n1
- | Eop (Orolm amount1 mask1) (t1:::Enil) =>
- rolm_case2 amount1 mask1 t1
- | e1 =>
- rolm_default e1
- end.
-
-Definition rolm (e1: expr) (amount2 mask2: int) :=
- match rolm_match e1 with
- | rolm_case1 n1 =>
- Eop (Ointconst(Int.and (Int.rol n1 amount2) mask2)) Enil
- | rolm_case2 amount1 mask1 t1 =>
- let amount := Int.and (Int.add amount1 amount2) (Int.repr 31) in
- let mask := Int.and (Int.rol mask1 amount2) mask2 in
- if Int.is_rlw_mask mask
- then Eop (Orolm amount mask) (t1:::Enil)
- else Eop (Orolm amount2 mask2) (e1:::Enil)
- | rolm_default e1 =>
- Eop (Orolm amount2 mask2) (e1:::Enil)
- end.
-
-Definition shlimm (e1: expr) (n2: int) :=
- if Int.eq n2 Int.zero then
- e1
- else if Int.ltu n2 (Int.repr 32) then
- rolm e1 n2 (Int.shl Int.mone n2)
- else
- Eop Oshl (e1:::Eop (Ointconst n2) Enil:::Enil).
-
-Definition shruimm (e1: expr) (n2: int) :=
- if Int.eq n2 Int.zero then
- e1
- else if Int.ltu n2 (Int.repr 32) then
- rolm e1 (Int.sub (Int.repr 32) n2) (Int.shru Int.mone n2)
- else
- Eop Oshru (e1:::Eop (Ointconst n2) Enil:::Enil).
-
-(** ** Integer multiply *)
-
-Definition mulimm_base (n1: int) (e2: expr) :=
- match Int.one_bits n1 with
- | i :: nil =>
- shlimm e2 i
- | i :: j :: nil =>
- Elet e2
- (Eop Oadd (shlimm (Eletvar 0) i :::
- shlimm (Eletvar 0) j ::: Enil))
- | _ =>
- Eop (Omulimm n1) (e2:::Enil)
- end.
-
-(*
-Definition mulimm (n1: int) (e2: expr) :=
- if Int.eq n1 Int.zero then
- Elet e2 (Eop (Ointconst Int.zero) Enil)
- else if Int.eq n1 Int.one then
- e2
- else match e2 with
- | Eop (Ointconst n2) Enil => Eop (Ointconst(intmul n1 n2)) Enil
- | Eop (Oaddimm n2) (t2:::Enil) => addimm (intmul n1 n2) (mulimm_base n1 t2)
- | _ => mulimm_base n1 e2
- end.
-*)
-
-Inductive mulimm_cases: forall (e2: expr), Set :=
- | mulimm_case1:
- forall (n2: int),
- mulimm_cases (Eop (Ointconst n2) Enil)
- | mulimm_case2:
- forall (n2: int) (t2: expr),
- mulimm_cases (Eop (Oaddimm n2) (t2:::Enil))
- | mulimm_default:
- forall (e2: expr),
- mulimm_cases e2.
-
-Definition mulimm_match (e2: expr) :=
- match e2 as z1 return mulimm_cases z1 with
- | Eop (Ointconst n2) Enil =>
- mulimm_case1 n2
- | Eop (Oaddimm n2) (t2:::Enil) =>
- mulimm_case2 n2 t2
- | e2 =>
- mulimm_default e2
- end.
-
-Definition mulimm (n1: int) (e2: expr) :=
- if Int.eq n1 Int.zero then
- Elet e2 (Eop (Ointconst Int.zero) Enil)
- else if Int.eq n1 Int.one then
- e2
- else match mulimm_match e2 with
- | mulimm_case1 n2 =>
- Eop (Ointconst(Int.mul n1 n2)) Enil
- | mulimm_case2 n2 t2 =>
- addimm (Int.mul n1 n2) (mulimm_base n1 t2)
- | mulimm_default e2 =>
- mulimm_base n1 e2
- end.
-
-(*
-Definition mul (e1: expr) (e2: expr) :=
- match e1, e2 with
- | Eop (Ointconst n1) Enil, t2 => mulimm n1 t2
- | t1, Eop (Ointconst n2) Enil => mulimm n2 t1
- | _, _ => Eop Omul (e1:::e2:::Enil)
- end.
-*)
-
-Inductive mul_cases: forall (e1: expr) (e2: expr), Set :=
- | mul_case1:
- forall (n1: int) (t2: expr),
- mul_cases (Eop (Ointconst n1) Enil) (t2)
- | mul_case2:
- forall (t1: expr) (n2: int),
- mul_cases (t1) (Eop (Ointconst n2) Enil)
- | mul_default:
- forall (e1: expr) (e2: expr),
- mul_cases e1 e2.
-
-Definition mul_match_aux (e1: expr) (e2: expr) :=
- match e2 as z2 return mul_cases e1 z2 with
- | Eop (Ointconst n2) Enil =>
- mul_case2 e1 n2
- | e2 =>
- mul_default e1 e2
- end.
-
-Definition mul_match (e1: expr) (e2: expr) :=
- match e1 as z1 return mul_cases z1 e2 with
- | Eop (Ointconst n1) Enil =>
- mul_case1 n1 e2
- | e1 =>
- mul_match_aux e1 e2
- end.
-
-Definition mul (e1: expr) (e2: expr) :=
- match mul_match e1 e2 with
- | mul_case1 n1 t2 =>
- mulimm n1 t2
- | mul_case2 t1 n2 =>
- mulimm n2 t1
- | mul_default e1 e2 =>
- Eop Omul (e1:::e2:::Enil)
- end.
-
-(** ** Integer division and modulus *)
-
-Definition divs (e1: expr) (e2: expr) := Eop Odiv (e1:::e2:::Enil).
-
-Definition mod_aux (divop: operation) (e1 e2: expr) :=
- Elet e1
- (Elet (lift e2)
- (Eop Osub (Eletvar 1 :::
- Eop Omul (Eop divop (Eletvar 1 ::: Eletvar 0 ::: Enil) :::
- Eletvar 0 :::
- Enil) :::
- Enil))).
-
-Definition mods := mod_aux Odiv.
-
-Inductive divu_cases: forall (e2: expr), Set :=
- | divu_case1:
- forall (n2: int),
- divu_cases (Eop (Ointconst n2) Enil)
- | divu_default:
- forall (e2: expr),
- divu_cases e2.
-
-Definition divu_match (e2: expr) :=
- match e2 as z1 return divu_cases z1 with
- | Eop (Ointconst n2) Enil =>
- divu_case1 n2
- | e2 =>
- divu_default e2
- end.
-
-Definition divu (e1: expr) (e2: expr) :=
- match divu_match e2 with
- | divu_case1 n2 =>
- match Int.is_power2 n2 with
- | Some l2 => shruimm e1 l2
- | None => Eop Odivu (e1:::e2:::Enil)
- end
- | divu_default e2 =>
- Eop Odivu (e1:::e2:::Enil)
- end.
-
-Definition modu (e1: expr) (e2: expr) :=
- match divu_match e2 with
- | divu_case1 n2 =>
- match Int.is_power2 n2 with
- | Some l2 => rolm e1 Int.zero (Int.sub n2 Int.one)
- | None => mod_aux Odivu e1 e2
- end
- | divu_default e2 =>
- mod_aux Odivu e1 e2
- end.
-
-(** ** Bitwise and, or, xor *)
-
-Definition andimm (n1: int) (e2: expr) :=
- if Int.is_rlw_mask n1
- then rolm e2 Int.zero n1
- else Eop (Oandimm n1) (e2:::Enil).
-
-Definition and (e1: expr) (e2: expr) :=
- match mul_match e1 e2 with
- | mul_case1 n1 t2 =>
- andimm n1 t2
- | mul_case2 t1 n2 =>
- andimm n2 t1
- | mul_default e1 e2 =>
- Eop Oand (e1:::e2:::Enil)
- end.
-
-Definition same_expr_pure (e1 e2: expr) :=
- match e1, e2 with
- | Evar v1, Evar v2 => if ident_eq v1 v2 then true else false
- | _, _ => false
- end.
-
-Inductive or_cases: forall (e1: expr) (e2: expr), Set :=
- | or_case1:
- forall (amount1: int) (mask1: int) (t1: expr)
- (amount2: int) (mask2: int) (t2: expr),
- or_cases (Eop (Orolm amount1 mask1) (t1:::Enil))
- (Eop (Orolm amount2 mask2) (t2:::Enil))
- | or_default:
- forall (e1: expr) (e2: expr),
- or_cases e1 e2.
-
-Definition or_match (e1: expr) (e2: expr) :=
- match e1 as z1, e2 as z2 return or_cases z1 z2 with
- | Eop (Orolm amount1 mask1) (t1:::Enil),
- Eop (Orolm amount2 mask2) (t2:::Enil) =>
- or_case1 amount1 mask1 t1 amount2 mask2 t2
- | e1, e2 =>
- or_default e1 e2
- end.
-
-Definition or (e1: expr) (e2: expr) :=
- match or_match e1 e2 with
- | or_case1 amount1 mask1 t1 amount2 mask2 t2 =>
- if Int.eq amount1 amount2
- && Int.is_rlw_mask (Int.or mask1 mask2)
- && same_expr_pure t1 t2
- then Eop (Orolm amount1 (Int.or mask1 mask2)) (t1:::Enil)
- else Eop Oor (e1:::e2:::Enil)
- | or_default e1 e2 =>
- Eop Oor (e1:::e2:::Enil)
- end.
-
-(** ** General shifts *)
-
-Inductive shift_cases: forall (e1: expr), Set :=
- | shift_case1:
- forall (n2: int),
- shift_cases (Eop (Ointconst n2) Enil)
- | shift_default:
- forall (e1: expr),
- shift_cases e1.
-
-Definition shift_match (e1: expr) :=
- match e1 as z1 return shift_cases z1 with
- | Eop (Ointconst n2) Enil =>
- shift_case1 n2
- | e1 =>
- shift_default e1
- end.
-
-Definition shl (e1: expr) (e2: expr) :=
- match shift_match e2 with
- | shift_case1 n2 =>
- shlimm e1 n2
- | shift_default e2 =>
- Eop Oshl (e1:::e2:::Enil)
- end.
-
-Definition shru (e1: expr) (e2: expr) :=
- match shift_match e2 with
- | shift_case1 n2 =>
- shruimm e1 n2
- | shift_default e2 =>
- Eop Oshru (e1:::e2:::Enil)
- end.
-
-(** ** Floating-point arithmetic *)
-
-Parameter use_fused_mul : unit -> bool.
-
-(*
-Definition addf (e1: expr) (e2: expr) :=
- match e1, e2 with
- | Eop Omulf (t1:::t2:::Enil), t3 => Eop Omuladdf (t1:::t2:::t3:::Enil)
- | t1, Eop Omulf (t2:::t3:::Enil) => Elet t1 (Eop Omuladdf (t2:::t3:::Rvar 0:::Enil))
- | _, _ => Eop Oaddf (e1:::e2:::Enil)
- end.
-*)
-
-Inductive addf_cases: forall (e1: expr) (e2: expr), Set :=
- | addf_case1:
- forall (t1: expr) (t2: expr) (t3: expr),
- addf_cases (Eop Omulf (t1:::t2:::Enil)) (t3)
- | addf_case2:
- forall (t1: expr) (t2: expr) (t3: expr),
- addf_cases (t1) (Eop Omulf (t2:::t3:::Enil))
- | addf_default:
- forall (e1: expr) (e2: expr),
- addf_cases e1 e2.
-
-Definition addf_match_aux (e1: expr) (e2: expr) :=
- match e2 as z2 return addf_cases e1 z2 with
- | Eop Omulf (t2:::t3:::Enil) =>
- addf_case2 e1 t2 t3
- | e2 =>
- addf_default e1 e2
- end.
-
-Definition addf_match (e1: expr) (e2: expr) :=
- match e1 as z1 return addf_cases z1 e2 with
- | Eop Omulf (t1:::t2:::Enil) =>
- addf_case1 t1 t2 e2
- | e1 =>
- addf_match_aux e1 e2
- end.
-
-Definition addf (e1: expr) (e2: expr) :=
- if use_fused_mul tt then
- match addf_match e1 e2 with
- | addf_case1 t1 t2 t3 =>
- Eop Omuladdf (t1:::t2:::t3:::Enil)
- | addf_case2 t1 t2 t3 =>
- Eop Omuladdf (t2:::t3:::t1:::Enil)
- | addf_default e1 e2 =>
- Eop Oaddf (e1:::e2:::Enil)
- end
- else Eop Oaddf (e1:::e2:::Enil).
-
-(*
-Definition subf (e1: expr) (e2: expr) :=
- match e1, e2 with
- | Eop Omulfloat (t1:::t2:::Enil), t3 => Eop Omulsubf (t1:::t2:::t3:::Enil)
- | _, _ => Eop Osubf (e1:::e2:::Enil)
- end.
-*)
-
-Inductive subf_cases: forall (e1: expr) (e2: expr), Set :=
- | subf_case1:
- forall (t1: expr) (t2: expr) (t3: expr),
- subf_cases (Eop Omulf (t1:::t2:::Enil)) (t3)
- | subf_default:
- forall (e1: expr) (e2: expr),
- subf_cases e1 e2.
-
-Definition subf_match (e1: expr) (e2: expr) :=
- match e1 as z1 return subf_cases z1 e2 with
- | Eop Omulf (t1:::t2:::Enil) =>
- subf_case1 t1 t2 e2
- | e1 =>
- subf_default e1 e2
- end.
-
-Definition subf (e1: expr) (e2: expr) :=
- if use_fused_mul tt then
- match subf_match e1 e2 with
- | subf_case1 t1 t2 t3 =>
- Eop Omulsubf (t1:::t2:::t3:::Enil)
- | subf_default e1 e2 =>
- Eop Osubf (e1:::e2:::Enil)
- end
- else Eop Osubf (e1:::e2:::Enil).
-
-(** ** Truncations and sign extensions *)
-
-Inductive cast8signed_cases: forall (e1: expr), Set :=
- | cast8signed_case1:
- forall (e2: expr),
- cast8signed_cases (Eop Ocast8signed (e2 ::: Enil))
- | cast8signed_default:
- forall (e1: expr),
- cast8signed_cases e1.
-
-Definition cast8signed_match (e1: expr) :=
- match e1 as z1 return cast8signed_cases z1 with
- | Eop Ocast8signed (e2 ::: Enil) =>
- cast8signed_case1 e2
- | e1 =>
- cast8signed_default e1
- end.
-
-Definition cast8signed (e: expr) :=
- match cast8signed_match e with
- | cast8signed_case1 e1 => e
- | cast8signed_default e1 => Eop Ocast8signed (e1 ::: Enil)
- end.
-
-Inductive cast8unsigned_cases: forall (e1: expr), Set :=
- | cast8unsigned_case1:
- forall (e2: expr),
- cast8unsigned_cases (Eop Ocast8unsigned (e2 ::: Enil))
- | cast8unsigned_default:
- forall (e1: expr),
- cast8unsigned_cases e1.
-
-Definition cast8unsigned_match (e1: expr) :=
- match e1 as z1 return cast8unsigned_cases z1 with
- | Eop Ocast8unsigned (e2 ::: Enil) =>
- cast8unsigned_case1 e2
- | e1 =>
- cast8unsigned_default e1
- end.
-
-Definition cast8unsigned (e: expr) :=
- match cast8unsigned_match e with
- | cast8unsigned_case1 e1 => e
- | cast8unsigned_default e1 => Eop Ocast8unsigned (e1 ::: Enil)
- end.
-
-Inductive cast16signed_cases: forall (e1: expr), Set :=
- | cast16signed_case1:
- forall (e2: expr),
- cast16signed_cases (Eop Ocast16signed (e2 ::: Enil))
- | cast16signed_default:
- forall (e1: expr),
- cast16signed_cases e1.
-
-Definition cast16signed_match (e1: expr) :=
- match e1 as z1 return cast16signed_cases z1 with
- | Eop Ocast16signed (e2 ::: Enil) =>
- cast16signed_case1 e2
- | e1 =>
- cast16signed_default e1
- end.
-
-Definition cast16signed (e: expr) :=
- match cast16signed_match e with
- | cast16signed_case1 e1 => e
- | cast16signed_default e1 => Eop Ocast16signed (e1 ::: Enil)
- end.
-
-Inductive cast16unsigned_cases: forall (e1: expr), Set :=
- | cast16unsigned_case1:
- forall (e2: expr),
- cast16unsigned_cases (Eop Ocast16unsigned (e2 ::: Enil))
- | cast16unsigned_default:
- forall (e1: expr),
- cast16unsigned_cases e1.
-
-Definition cast16unsigned_match (e1: expr) :=
- match e1 as z1 return cast16unsigned_cases z1 with
- | Eop Ocast16unsigned (e2 ::: Enil) =>
- cast16unsigned_case1 e2
- | e1 =>
- cast16unsigned_default e1
- end.
-
-Definition cast16unsigned (e: expr) :=
- match cast16unsigned_match e with
- | cast16unsigned_case1 e1 => e
- | cast16unsigned_default e1 => Eop Ocast16unsigned (e1 ::: Enil)
- end.
-
-Inductive singleoffloat_cases: forall (e1: expr), Set :=
- | singleoffloat_case1:
- forall (e2: expr),
- singleoffloat_cases (Eop Osingleoffloat (e2 ::: Enil))
- | singleoffloat_default:
- forall (e1: expr),
- singleoffloat_cases e1.
-
-Definition singleoffloat_match (e1: expr) :=
- match e1 as z1 return singleoffloat_cases z1 with
- | Eop Osingleoffloat (e2 ::: Enil) =>
- singleoffloat_case1 e2
- | e1 =>
- singleoffloat_default e1
- end.
-
-Definition singleoffloat (e: expr) :=
- match singleoffloat_match e with
- | singleoffloat_case1 e1 => e
- | singleoffloat_default e1 => Eop Osingleoffloat (e1 ::: Enil)
- end.
-
-(** ** Comparisons *)
-
-Inductive comp_cases: forall (e1: expr) (e2: expr), Set :=
- | comp_case1:
- forall n1 t2,
- comp_cases (Eop (Ointconst n1) Enil) (t2)
- | comp_case2:
- forall t1 n2,
- comp_cases (t1) (Eop (Ointconst n2) Enil)
- | comp_default:
- forall (e1: expr) (e2: expr),
- comp_cases e1 e2.
-
-Definition comp_match (e1: expr) (e2: expr) :=
- match e1 as z1, e2 as z2 return comp_cases z1 z2 with
- | Eop (Ointconst n1) Enil, t2 =>
- comp_case1 n1 t2
- | t1, Eop (Ointconst n2) Enil =>
- comp_case2 t1 n2
- | e1, e2 =>
- comp_default e1 e2
- end.
-
-Definition comp (c: comparison) (e1: expr) (e2: expr) :=
- match comp_match e1 e2 with
- | comp_case1 n1 t2 =>
- Eop (Ocmp (Ccompimm (swap_comparison c) n1)) (t2 ::: Enil)
- | comp_case2 t1 n2 =>
- Eop (Ocmp (Ccompimm c n2)) (t1 ::: Enil)
- | comp_default e1 e2 =>
- Eop (Ocmp (Ccomp c)) (e1 ::: e2 ::: Enil)
- end.
-
-Definition compu (c: comparison) (e1: expr) (e2: expr) :=
- match comp_match e1 e2 with
- | comp_case1 n1 t2 =>
- Eop (Ocmp (Ccompuimm (swap_comparison c) n1)) (t2 ::: Enil)
- | comp_case2 t1 n2 =>
- Eop (Ocmp (Ccompuimm c n2)) (t1 ::: Enil)
- | comp_default e1 e2 =>
- Eop (Ocmp (Ccompu c)) (e1 ::: e2 ::: Enil)
- end.
-
-Definition compf (c: comparison) (e1: expr) (e2: expr) :=
- Eop (Ocmp (Ccompf c)) (e1 ::: e2 ::: Enil).
-
-(** ** Conditional expressions *)
-
-Fixpoint negate_condexpr (e: condexpr): condexpr :=
- match e with
- | CEtrue => CEfalse
- | CEfalse => CEtrue
- | CEcond c el => CEcond (negate_condition c) el
- | CEcondition e1 e2 e3 =>
- CEcondition e1 (negate_condexpr e2) (negate_condexpr e3)
- end.
-
-
-Definition is_compare_neq_zero (c: condition) : bool :=
- match c with
- | Ccompimm Cne n => Int.eq n Int.zero
- | Ccompuimm Cne n => Int.eq n Int.zero
- | _ => false
- end.
-
-Definition is_compare_eq_zero (c: condition) : bool :=
- match c with
- | Ccompimm Ceq n => Int.eq n Int.zero
- | Ccompuimm Ceq n => Int.eq n Int.zero
- | _ => false
- end.
-
-Fixpoint condexpr_of_expr (e: expr) : condexpr :=
- match e with
- | Eop (Ointconst n) Enil =>
- if Int.eq n Int.zero then CEfalse else CEtrue
- | Eop (Ocmp c) (e1 ::: Enil) =>
- if is_compare_neq_zero c then
- condexpr_of_expr e1
- else if is_compare_eq_zero c then
- negate_condexpr (condexpr_of_expr e1)
- else
- CEcond c (e1 ::: Enil)
- | Eop (Ocmp c) el =>
- CEcond c el
- | Econdition ce e1 e2 =>
- CEcondition ce (condexpr_of_expr e1) (condexpr_of_expr e2)
- | _ =>
- CEcond (Ccompimm Cne Int.zero) (e:::Enil)
- end.
-
-(** ** Recognition of addressing modes for load and store operations *)
-
-(*
-Definition addressing (e: expr) :=
- match e with
- | Eop (Oaddrsymbol s n) Enil => (Aglobal s n, Enil)
- | Eop (Oaddrstack n) Enil => (Ainstack n, Enil)
- | Eop Oadd (Eop (Oaddrsymbol s n) Enil) e2 => (Abased(s, n), e2:::Enil)
- | Eop (Oaddimm n) (e1:::Enil) => (Aindexed n, e1:::Enil)
- | Eop Oadd (e1:::e2:::Enil) => (Aindexed2, e1:::e2:::Enil)
- | _ => (Aindexed Int.zero, e:::Enil)
- end.
-*)
-
-Inductive addressing_cases: forall (e: expr), Set :=
- | addressing_case1:
- forall (s: ident) (n: int),
- addressing_cases (Eop (Oaddrsymbol s n) Enil)
- | addressing_case2:
- forall (n: int),
- addressing_cases (Eop (Oaddrstack n) Enil)
- | addressing_case3:
- forall (s: ident) (n: int) (e2: expr),
- addressing_cases
- (Eop Oadd (Eop (Oaddrsymbol s n) Enil:::e2:::Enil))
- | addressing_case4:
- forall (n: int) (e1: expr),
- addressing_cases (Eop (Oaddimm n) (e1:::Enil))
- | addressing_case5:
- forall (e1: expr) (e2: expr),
- addressing_cases (Eop Oadd (e1:::e2:::Enil))
- | addressing_default:
- forall (e: expr),
- addressing_cases e.
-
-Definition addressing_match (e: expr) :=
- match e as z1 return addressing_cases z1 with
- | Eop (Oaddrsymbol s n) Enil =>
- addressing_case1 s n
- | Eop (Oaddrstack n) Enil =>
- addressing_case2 n
- | Eop Oadd (Eop (Oaddrsymbol s n) Enil:::e2:::Enil) =>
- addressing_case3 s n e2
- | Eop (Oaddimm n) (e1:::Enil) =>
- addressing_case4 n e1
- | Eop Oadd (e1:::e2:::Enil) =>
- addressing_case5 e1 e2
- | e =>
- addressing_default e
- end.
-
-Definition addressing (e: expr) :=
- match addressing_match e with
- | addressing_case1 s n =>
- (Aglobal s n, Enil)
- | addressing_case2 n =>
- (Ainstack n, Enil)
- | addressing_case3 s n e2 =>
- (Abased s n, e2:::Enil)
- | addressing_case4 n e1 =>
- (Aindexed n, e1:::Enil)
- | addressing_case5 e1 e2 =>
- (Aindexed2, e1:::e2:::Enil)
- | addressing_default e =>
- (Aindexed Int.zero, e:::Enil)
- end.
-
-Definition load (chunk: memory_chunk) (e1: expr) :=
- match addressing e1 with
- | (mode, args) => Eload chunk mode args
- end.
-
-Definition store (chunk: memory_chunk) (e1 e2: expr) :=
- match addressing e1 with
- | (mode, args) => Sstore chunk mode args e2
- end.
-
-(** * Translation from Cminor to CminorSel *)
-
-(** Instruction selection for operator applications *)
-
-Definition sel_constant (cst: Cminor.constant) : expr :=
- match cst with
- | Cminor.Ointconst n => Eop (Ointconst n) Enil
- | Cminor.Ofloatconst f => Eop (Ofloatconst f) Enil
- | Cminor.Oaddrsymbol id ofs => Eop (Oaddrsymbol id ofs) Enil
- | Cminor.Oaddrstack ofs => Eop (Oaddrstack ofs) Enil
- end.
-
-Definition sel_unop (op: Cminor.unary_operation) (arg: expr) : expr :=
- match op with
- | Cminor.Ocast8unsigned => cast8unsigned arg
- | Cminor.Ocast8signed => cast8signed arg
- | Cminor.Ocast16unsigned => cast16unsigned arg
- | Cminor.Ocast16signed => cast16signed arg
- | Cminor.Onegint => Eop (Osubimm Int.zero) (arg ::: Enil)
- | Cminor.Onotbool => notbool arg
- | Cminor.Onotint => notint arg
- | Cminor.Onegf => Eop Onegf (arg ::: Enil)
- | Cminor.Oabsf => Eop Oabsf (arg ::: Enil)
- | Cminor.Osingleoffloat => singleoffloat arg
- | Cminor.Ointoffloat => Eop Ointoffloat (arg ::: Enil)
- | Cminor.Ointuoffloat => Eop Ointuoffloat (arg ::: Enil)
- | Cminor.Ofloatofint => Eop Ofloatofint (arg ::: Enil)
- | Cminor.Ofloatofintu => Eop Ofloatofintu (arg ::: Enil)
- end.
-
-Definition sel_binop (op: Cminor.binary_operation) (arg1 arg2: expr) : expr :=
- match op with
- | Cminor.Oadd => add arg1 arg2
- | Cminor.Osub => sub arg1 arg2
- | Cminor.Omul => mul arg1 arg2
- | Cminor.Odiv => divs arg1 arg2
- | Cminor.Odivu => divu arg1 arg2
- | Cminor.Omod => mods arg1 arg2
- | Cminor.Omodu => modu arg1 arg2
- | Cminor.Oand => and arg1 arg2
- | Cminor.Oor => or arg1 arg2
- | Cminor.Oxor => Eop Oxor (arg1 ::: arg2 ::: Enil)
- | Cminor.Oshl => shl arg1 arg2
- | Cminor.Oshr => Eop Oshr (arg1 ::: arg2 ::: Enil)
- | Cminor.Oshru => shru arg1 arg2
- | Cminor.Oaddf => addf arg1 arg2
- | Cminor.Osubf => subf arg1 arg2
- | Cminor.Omulf => Eop Omulf (arg1 ::: arg2 ::: Enil)
- | Cminor.Odivf => Eop Odivf (arg1 ::: arg2 ::: Enil)
- | Cminor.Ocmp c => comp c arg1 arg2
- | Cminor.Ocmpu c => compu c arg1 arg2
- | Cminor.Ocmpf c => compf c arg1 arg2
- end.
-
-(** Conversion from Cminor expression to Cminorsel expressions *)
-
-Fixpoint sel_expr (a: Cminor.expr) : expr :=
- match a with
- | Cminor.Evar id => Evar id
- | Cminor.Econst cst => sel_constant cst
- | Cminor.Eunop op arg => sel_unop op (sel_expr arg)
- | Cminor.Ebinop op arg1 arg2 => sel_binop op (sel_expr arg1) (sel_expr arg2)
- | Cminor.Eload chunk addr => load chunk (sel_expr addr)
- | Cminor.Econdition cond ifso ifnot =>
- Econdition (condexpr_of_expr (sel_expr cond))
- (sel_expr ifso) (sel_expr ifnot)
- end.
-
-Fixpoint sel_exprlist (al: list Cminor.expr) : exprlist :=
- match al with
- | nil => Enil
- | a :: bl => Econs (sel_expr a) (sel_exprlist bl)
- end.
-
-(** Conversion from Cminor statements to Cminorsel statements. *)
-
-Fixpoint sel_stmt (s: Cminor.stmt) : stmt :=
- match s with
- | Cminor.Sskip => Sskip
- | Cminor.Sassign id e => Sassign id (sel_expr e)
- | Cminor.Sstore chunk addr rhs => store chunk (sel_expr addr) (sel_expr rhs)
- | Cminor.Scall optid sg fn args =>
- Scall optid sg (sel_expr fn) (sel_exprlist args)
- | Cminor.Stailcall sg fn args =>
- Stailcall sg (sel_expr fn) (sel_exprlist args)
- | Cminor.Salloc id b => Salloc id (sel_expr b)
- | Cminor.Sseq s1 s2 => Sseq (sel_stmt s1) (sel_stmt s2)
- | Cminor.Sifthenelse e ifso ifnot =>
- Sifthenelse (condexpr_of_expr (sel_expr e))
- (sel_stmt ifso) (sel_stmt ifnot)
- | Cminor.Sloop body => Sloop (sel_stmt body)
- | Cminor.Sblock body => Sblock (sel_stmt body)
- | Cminor.Sexit n => Sexit n
- | Cminor.Sswitch e cases dfl => Sswitch (sel_expr e) cases dfl
- | Cminor.Sreturn None => Sreturn None
- | Cminor.Sreturn (Some e) => Sreturn (Some (sel_expr e))
- | Cminor.Slabel lbl body => Slabel lbl (sel_stmt body)
- | Cminor.Sgoto lbl => Sgoto lbl
- end.
-
-(** Conversion of functions and programs. *)
-
-Definition sel_function (f: Cminor.function) : function :=
- mkfunction
- f.(Cminor.fn_sig)
- f.(Cminor.fn_params)
- f.(Cminor.fn_vars)
- f.(Cminor.fn_stackspace)
- (sel_stmt f.(Cminor.fn_body)).
-
-Definition sel_fundef (f: Cminor.fundef) : fundef :=
- transf_fundef sel_function f.
-
-Definition sel_program (p: Cminor.program) : program :=
- transform_program sel_fundef p.
-
-
-