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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. *)
(* *)
(* *********************************************************************)
(** Static analysis and strength reduction for operators
and conditions. This is the machine-dependent part of [Constprop]. *)
Require Import Coqlib.
Require Import Compopts.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Op.
Require Import Registers.
Require Import ValueDomain ValueAOp.
(** * Converting known values to constants *)
Definition const_for_result (a: aval) : option operation :=
match a with
| I n => Some(Ointconst n)
| F n => if Compopts.generate_float_constants tt then Some(Ofloatconst n) else None
| FS n => if Compopts.generate_float_constants tt then Some(Osingleconst n) else None
| Ptr(Gl id ofs) => Some (Oaddrsymbol id ofs)
| Ptr(Stk ofs) => Some(Oaddrstack ofs)
| _ => None
end.
(** * Operator strength reduction *)
(** We now define auxiliary functions for strength reduction of
operators and addressing modes: replacing an operator with a cheaper
one if some of its arguments are statically known. These are again
large pattern-matchings expressed in indirect style. *)
Section STRENGTH_REDUCTION.
Definition eval_static_shift (s: shift) (n: int) : int :=
match s with
| Slsl x => Int.shl n x
| Slsr x => Int.shru n x
| Sasr x => Int.shr n x
| Sror x => Int.ror n x
end.
Nondetfunction cond_strength_reduction
(cond: condition) (args: list reg) (vl: list aval) :=
match cond, args, vl with
| Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
(Ccompimm (swap_comparison c) n1, r2 :: nil)
| Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Ccompimm c n2, r1 :: nil)
| Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
(Ccompuimm (swap_comparison c) n1, r2 :: nil)
| Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Ccompuimm c n2, r1 :: nil)
| Ccompshift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Ccompimm c (eval_static_shift s n2), r1 :: nil)
| Ccompushift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Ccompuimm c (eval_static_shift s n2), r1 :: nil)
| Ccompf c, r1 :: r2 :: nil, F n1 :: v2 :: nil =>
if Float.eq_dec n1 Float.zero
then (Ccompfzero (swap_comparison c), r2 :: nil)
else (cond, args)
| Ccompf c, r1 :: r2 :: nil, v1 :: F n2 :: nil =>
if Float.eq_dec n2 Float.zero
then (Ccompfzero c, r1 :: nil)
else (cond, args)
| Cnotcompf c, r1 :: r2 :: nil, F n1 :: v2 :: nil =>
if Float.eq_dec n1 Float.zero
then (Cnotcompfzero (swap_comparison c), r2 :: nil)
else (cond, args)
| Cnotcompf c, r1 :: r2 :: nil, v1 :: F n2 :: nil =>
if Float.eq_dec n2 Float.zero
then (Cnotcompfzero c, r1 :: nil)
else (cond, args)
| Ccompfs c, r1 :: r2 :: nil, FS n1 :: v2 :: nil =>
if Float32.eq_dec n1 Float32.zero
then (Ccompfszero (swap_comparison c), r2 :: nil)
else (cond, args)
| Ccompfs c, r1 :: r2 :: nil, v1 :: FS n2 :: nil =>
if Float32.eq_dec n2 Float32.zero
then (Ccompfszero c, r1 :: nil)
else (cond, args)
| Cnotcompfs c, r1 :: r2 :: nil, FS n1 :: v2 :: nil =>
if Float32.eq_dec n1 Float32.zero
then (Cnotcompfszero (swap_comparison c), r2 :: nil)
else (cond, args)
| Cnotcompfs c, r1 :: r2 :: nil, v1 :: FS n2 :: nil =>
if Float32.eq_dec n2 Float32.zero
then (Cnotcompfszero c, r1 :: nil)
else (cond, args)
| _, _, _ =>
(cond, args)
end.
Definition make_cmp_base (c: condition) (args: list reg) (vl: list aval) :=
let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args').
Definition make_cmp_imm_eq (c: condition) (args: list reg) (vl: list aval)
(n: int) (r1: reg) (v1: aval) :=
if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil)
else if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil)
else make_cmp_base c args vl.
Definition make_cmp_imm_ne (c: condition) (args: list reg) (vl: list aval)
(n: int) (r1: reg) (v1: aval) :=
if Int.eq_dec n Int.zero && vincl v1 (Uns Ptop 1) then (Omove, r1 :: nil)
else if Int.eq_dec n Int.one && vincl v1 (Uns Ptop 1) then (Oxorimm Int.one, r1 :: nil)
else make_cmp_base c args vl.
Nondetfunction make_cmp (c: condition) (args: list reg) (vl: list aval) :=
match c, args, vl with
| Ccompimm Ceq n, r1 :: nil, v1 :: nil =>
make_cmp_imm_eq c args vl n r1 v1
| Ccompimm Cne n, r1 :: nil, v1 :: nil =>
make_cmp_imm_ne c args vl n r1 v1
| Ccompuimm Ceq n, r1 :: nil, v1 :: nil =>
make_cmp_imm_eq c args vl n r1 v1
| Ccompuimm Cne n, r1 :: nil, v1 :: nil =>
make_cmp_imm_ne c args vl n r1 v1
| _, _, _ =>
make_cmp_base c args vl
end.
Definition make_select (c: condition) (ty: typ)
(r1 r2: reg) (args: list reg) (vl: list aval) :=
match resolve_branch (eval_static_condition c vl) with
| Some b => (Omove, (if b then r1 else r2) :: nil)
| None =>
let (c', args') := cond_strength_reduction c args vl in
(Osel c' ty, r1 :: r2 :: args')
end.
Definition make_addimm (n: int) (r: reg) :=
if Int.eq n Int.zero
then (Omove, r :: nil)
else (Oaddimm n, r :: nil).
Definition make_shlimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.zero then
(Omove, r1 :: nil)
else if Int.ltu n Int.iwordsize then
(Oshift (Slsl (mk_shift_amount n)), r1 :: nil)
else
(Oshl, r1 :: r2 :: nil).
Definition make_shrimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.zero then
(Omove, r1 :: nil)
else if Int.ltu n Int.iwordsize then
(Oshift (Sasr (mk_shift_amount n)), r1 :: nil)
else
(Oshr, r1 :: r2 :: nil).
Definition make_shruimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.zero then
(Omove, r1 :: nil)
else if Int.ltu n Int.iwordsize then
(Oshift (Slsr (mk_shift_amount n)), r1 :: nil)
else
(Oshru, r1 :: r2 :: nil).
Definition make_mulimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.zero then
(Ointconst Int.zero, nil)
else if Int.eq n Int.one then
(Omove, r1 :: nil)
else
match Int.is_power2 n with
| Some l => (Oshift (Slsl (mk_shift_amount l)), r1 :: nil)
| None => (Omul, r1 :: r2 :: nil)
end.
Definition make_divimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.one then
(Omove, r1 :: nil)
else
match Int.is_power2 n with
| Some l => if Int.ltu l (Int.repr 31)
then (Oshrximm l, r1 :: nil)
else (Odiv, r1 :: r2 :: nil)
| None => (Odiv, r1 :: r2 :: nil)
end.
Definition make_divuimm (n: int) (r1 r2: reg) :=
if Int.eq n Int.one then
(Omove, r1 :: nil)
else
match Int.is_power2 n with
| Some l => (Oshift (Slsr (mk_shift_amount l)), r1 :: nil)
| None => (Odivu, r1 :: r2 :: nil)
end.
Definition make_andimm (n: int) (r: reg) (a: aval) :=
if Int.eq n Int.zero then (Ointconst Int.zero, nil)
else if Int.eq n Int.mone then (Omove, r :: nil)
else if match a with Uns _ m => Int.eq (Int.zero_ext m (Int.not n)) Int.zero
| _ => false end
then (Omove, r :: nil)
else (Oandimm n, r :: nil).
Definition make_orimm (n: int) (r: reg) :=
if Int.eq n Int.zero then (Omove, r :: nil)
else if Int.eq n Int.mone then (Ointconst Int.mone, nil)
else (Oorimm n, r :: nil).
Definition make_xorimm (n: int) (r: reg) :=
if Int.eq n Int.zero then (Omove, r :: nil)
else if Int.eq n Int.mone then (Onot, r :: nil)
else (Oxorimm n, r :: nil).
Definition make_mulfimm (n: float) (r r1 r2: reg) :=
if Float.eq_dec n (Float.of_int (Int.repr 2))
then (Oaddf, r :: r :: nil)
else (Omulf, r1 :: r2 :: nil).
Definition make_mulfsimm (n: float32) (r r1 r2: reg) :=
if Float32.eq_dec n (Float32.of_int (Int.repr 2))
then (Oaddfs, r :: r :: nil)
else (Omulfs, r1 :: r2 :: nil).
Definition make_cast8signed (r: reg) (a: aval) :=
if vincl a (Sgn Ptop 8) then (Omove, r :: nil) else (Ocast8signed, r :: nil).
Definition make_cast16signed (r: reg) (a: aval) :=
if vincl a (Sgn Ptop 16) then (Omove, r :: nil) else (Ocast16signed, r :: nil).
Definition make_mla_mulimm (n1: int) (r1 r2 r3: reg) :=
if Int.eq n1 Int.zero then
(Omove, r3 :: nil)
else if Int.eq n1 Int.one then
(Oadd, r2 :: r3 :: nil)
else
(Omla, r1 :: r2 :: r3 :: nil).
Definition make_mla_addimm (n3: int) (r1 r2 r3: reg) :=
if Int.eq n3 Int.zero then
(Omul, r1 :: r2 :: nil)
else
(Omla, r1 :: r2 :: r3 :: nil).
Definition make_mla_bothimm (n1 n3: int) (r1 r2 r3: reg) :=
if Int.eq n1 Int.zero then
(Ointconst n3, nil)
else if Int.eq n1 Int.one then
make_addimm n3 r2
else if Int.eq n3 Int.zero then
make_mulimm n1 r2 r1
else
(Omla, r1 :: r2 :: r3 :: nil).
Nondetfunction op_strength_reduction
(op: operation) (args: list reg) (vl: list aval) :=
match op, args, vl with
| Ocast8signed, r1 :: nil, v1 :: nil => make_cast8signed r1 v1
| Ocast16signed, r1 :: nil, v1 :: nil => make_cast16signed r1 v1
| Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_addimm n1 r2
| Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm n2 r1
| Oaddshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (eval_static_shift s n2) r1
| Osub, r1 :: r2 :: nil, I n1 :: v2 :: nil => (Orsubimm n1, r2 :: nil)
| Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1
| Osubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg (eval_static_shift s n2)) r1
| Orsubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => (Orsubimm (eval_static_shift s n2), r1 :: nil)
| Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_mulimm n1 r2 r1
| Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1 r2
| Omla, r1 :: r2 :: r3 :: nil, I n1 :: v2 :: I n3 :: nil => make_mla_bothimm n1 n3 r1 r2 r3
| Omla, r1 :: r2 :: r3 :: nil, v1 :: I n2 :: I n3 :: nil => make_mla_bothimm n2 n3 r2 r1 r3
| Omla, r1 :: r2 :: r3 :: nil, I n1 :: v2 :: v3 :: nil => make_mla_mulimm n1 r1 r2 r3
| Omla, r1 :: r2 :: r3 :: nil, v1 :: I n2 :: v3 :: nil => make_mla_mulimm n2 r2 r1 r3
| Omla, r1 :: r2 :: r3 :: nil, v1 :: v2 :: I n3 :: nil => make_mla_addimm n3 r1 r2 r3
| Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2
| Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2
| Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_andimm n1 r2 v2
| Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1 v1
| Oandshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (eval_static_shift s n2) r1 v1
| Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_orimm n1 r2
| Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1
| Oorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm (eval_static_shift s n2) r1
| Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_xorimm n1 r2
| Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1
| Oxorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm (eval_static_shift s n2) r1
| Obic, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not n2) r1 v1
| Obicshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not (eval_static_shift s n2)) r1 v1
| Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1 r2
| Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1 r2
| Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 r2
| Ocmp c, args, vl => make_cmp c args vl
| Osel c ty, r1 :: r2 :: args, v1 :: v2 :: vl => make_select c ty r1 r2 args vl
| Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => make_mulfimm n2 r1 r1 r2
| Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => make_mulfimm n1 r2 r1 r2
| Omulfs, r1 :: r2 :: nil, v1 :: FS n2 :: nil => make_mulfsimm n2 r1 r1 r2
| Omulfs, r1 :: r2 :: nil, FS n1 :: v2 :: nil => make_mulfsimm n1 r2 r1 r2
| _, _, _ => (op, args)
end.
Nondetfunction addr_strength_reduction
(addr: addressing) (args: list reg) (vl: list aval) :=
match addr, args, vl with
| Aindexed2, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil =>
(Ainstack (Ptrofs.add n1 (Ptrofs.of_int n2)), nil)
| Aindexed2, r1 :: r2 :: nil, I n1 :: Ptr(Stk n2) :: nil =>
(Ainstack (Ptrofs.add (Ptrofs.of_int n1) n2), nil)
| Aindexed2, r1 :: r2 :: nil, I n1 :: v2 :: nil =>
(Aindexed n1, r2 :: nil)
| Aindexed2, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Aindexed n2, r1 :: nil)
| Aindexed2shift s, r1 :: r2 :: nil, Ptr(Stk n1) :: I n2 :: nil =>
(Ainstack (Ptrofs.add n1 (Ptrofs.of_int (eval_static_shift s n2))), nil)
| Aindexed2shift s, r1 :: r2 :: nil, v1 :: I n2 :: nil =>
(Aindexed (eval_static_shift s n2), r1 :: nil)
| Aindexed n, r1 :: nil, Ptr(Stk n1) :: nil =>
(Ainstack (Ptrofs.add n1 (Ptrofs.of_int n)), nil)
| _, _, _ =>
(addr, args)
end.
End STRENGTH_REDUCTION.
|
