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Diffstat (limited to 'powerpc/ConstpropOp.v')
| -rw-r--r-- | powerpc/ConstpropOp.v | 856 |
1 files changed, 0 insertions, 856 deletions
diff --git a/powerpc/ConstpropOp.v b/powerpc/ConstpropOp.v deleted file mode 100644 index 07a1872e..00000000 --- a/powerpc/ConstpropOp.v +++ /dev/null @@ -1,856 +0,0 @@ -(* *********************************************************************) -(* *) -(* 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 AST. -Require Import Integers. -Require Import Floats. -Require Import Values. -Require Import Op. -Require Import Registers. - -(** * Static analysis *) - -(** To each pseudo-register at each program point, the static analysis - associates a compile-time approximation taken from the following set. *) - -Inductive approx : Type := - | Novalue: approx (** No value possible, code is unreachable. *) - | Unknown: approx (** All values are possible, - no compile-time information is available. *) - | I: int -> approx (** A known integer value. *) - | F: float -> approx (** A known floating-point value. *) - | S: ident -> int -> approx. - (** The value is the address of the given global - symbol plus the given integer offset. *) - -(** We now define the abstract interpretations of conditions and operators - over this set of approximations. For instance, the abstract interpretation - of the operator [Oaddf] applied to two expressions [a] and [b] is - [F(Float.add f g)] if [a] and [b] have static approximations [Vfloat f] - and [Vfloat g] respectively, and [Unknown] otherwise. - - The static approximations are defined by large pattern-matchings over - the approximations of the results. We write these matchings in the - indirect style described in file [Cmconstr] to avoid excessive - duplication of cases in proofs. *) - -(* -Definition eval_static_condition (cond: condition) (vl: list approx) := - match cond, vl with - | Ccomp c, I n1 :: I n2 :: nil => Some(Int.cmp c n1 n2) - | Ccompu c, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 n2) - | Ccompimm c n, I n1 :: nil => Some(Int.cmp c n1 n) - | Ccompuimm c n, I n1 :: nil => Some(Int.cmpu c n1 n) - | Ccompf c, F n1 :: F n2 :: nil => Some(Float.cmp c n1 n2) - | Cnotcompf c, F n1 :: F n2 :: nil => Some(negb(Float.cmp c n1 n2)) - | Cmaskzero n, I n1 :: nil => Some(Int.eq (Int.and n1 n) Int.zero) - | Cmasknotzero n, n1::nil => Some(negb(Int.eq (Int.and n1 n) Int.zero)) - | _, _ => None - end. -*) - -Inductive eval_static_condition_cases: forall (cond: condition) (vl: list approx), Type := - | eval_static_condition_case1: - forall c n1 n2, - eval_static_condition_cases (Ccomp c) (I n1 :: I n2 :: nil) - | eval_static_condition_case2: - forall c n1 n2, - eval_static_condition_cases (Ccompu c) (I n1 :: I n2 :: nil) - | eval_static_condition_case3: - forall c n n1, - eval_static_condition_cases (Ccompimm c n) (I n1 :: nil) - | eval_static_condition_case4: - forall c n n1, - eval_static_condition_cases (Ccompuimm c n) (I n1 :: nil) - | eval_static_condition_case5: - forall c n1 n2, - eval_static_condition_cases (Ccompf c) (F n1 :: F n2 :: nil) - | eval_static_condition_case6: - forall c n1 n2, - eval_static_condition_cases (Cnotcompf c) (F n1 :: F n2 :: nil) - | eval_static_condition_case7: - forall n n1, - eval_static_condition_cases (Cmaskzero n) (I n1 :: nil) - | eval_static_condition_case8: - forall n n1, - eval_static_condition_cases (Cmasknotzero n) (I n1 :: nil) - | eval_static_condition_default: - forall (cond: condition) (vl: list approx), - eval_static_condition_cases cond vl. - -Definition eval_static_condition_match (cond: condition) (vl: list approx) := - match cond as z1, vl as z2 return eval_static_condition_cases z1 z2 with - | Ccomp c, I n1 :: I n2 :: nil => - eval_static_condition_case1 c n1 n2 - | Ccompu c, I n1 :: I n2 :: nil => - eval_static_condition_case2 c n1 n2 - | Ccompimm c n, I n1 :: nil => - eval_static_condition_case3 c n n1 - | Ccompuimm c n, I n1 :: nil => - eval_static_condition_case4 c n n1 - | Ccompf c, F n1 :: F n2 :: nil => - eval_static_condition_case5 c n1 n2 - | Cnotcompf c, F n1 :: F n2 :: nil => - eval_static_condition_case6 c n1 n2 - | Cmaskzero n, I n1 :: nil => - eval_static_condition_case7 n n1 - | Cmasknotzero n, I n1 :: nil => - eval_static_condition_case8 n n1 - | cond, vl => - eval_static_condition_default cond vl - end. - -Definition eval_static_condition (cond: condition) (vl: list approx) := - match eval_static_condition_match cond vl with - | eval_static_condition_case1 c n1 n2 => - Some(Int.cmp c n1 n2) - | eval_static_condition_case2 c n1 n2 => - Some(Int.cmpu c n1 n2) - | eval_static_condition_case3 c n n1 => - Some(Int.cmp c n1 n) - | eval_static_condition_case4 c n n1 => - Some(Int.cmpu c n1 n) - | eval_static_condition_case5 c n1 n2 => - Some(Float.cmp c n1 n2) - | eval_static_condition_case6 c n1 n2 => - Some(negb(Float.cmp c n1 n2)) - | eval_static_condition_case7 n n1 => - Some(Int.eq (Int.and n1 n) Int.zero) - | eval_static_condition_case8 n n1 => - Some(negb(Int.eq (Int.and n1 n) Int.zero)) - | eval_static_condition_default cond vl => - None - end. - -(* -Definition eval_static_operation (op: operation) (vl: list approx) := - match op, vl with - | Omove, v1::nil => v1 - | Ointconst n, nil => I n - | Ofloatconst n, nil => F n - | Oaddrsymbol s n, nil => S s n - | Ocast8signed, I n1 :: nil => I(Int.sign_ext 8 n) - | Ocast8unsigned, I n1 :: nil => I(Int.zero_ext 8 n) - | Ocast16signed, I n1 :: nil => I(Int.sign_ext 16 n) - | Ocast16unsigned, I n1 :: nil => I(Int.zero_ext 16 n) - | Oadd, I n1 :: I n2 :: nil => I(Int.add n1 n2) - | Oadd, S s1 n1 :: I n2 :: nil => S s1 (Int.add n1 n2) - | Oaddimm n, I n1 :: nil => I (Int.add n1 n) - | Oaddimm n, S s1 n1 :: nil => S s1 (Int.add n1 n) - | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2) - | Osub, S s1 n1 :: I n2 :: nil => S s1 (Int.sub n1 n2) - | Osubimm n, I n1 :: nil => I (Int.sub n n1) - | Omul, I n1 :: I n2 :: nil => I(Int.mul n1 n2) - | Omulimm n, I n1 :: nil => I(Int.mul n1 n) - | Odiv, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2) - | Odivu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2) - | Oand, I n1 :: I n2 :: nil => I(Int.and n1 n2) - | Oandimm n, I n1 :: nil => I(Int.and n1 n) - | Oor, I n1 :: I n2 :: nil => I(Int.or n1 n2) - | Oorimm n, I n1 :: nil => I(Int.or n1 n) - | Oxor, I n1 :: I n2 :: nil => I(Int.xor n1 n2) - | Oxorimm n, I n1 :: nil => I(Int.xor n1 n) - | Onand, I n1 :: I n2 :: nil => I(Int.xor (Int.and n1 n2) Int.mone) - | Onor, I n1 :: I n2 :: nil => I(Int.xor (Int.or n1 n2) Int.mone) - | Onxor, I n1 :: I n2 :: nil => I(Int.xor (Int.xor n1 n2) Int.mone) - | Oshl, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown - | Oshr, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown - | Oshrimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown - | Oshrximm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shrx n1 n) else Unknown - | Oshru, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown - | Orolm amount mask, I n1 :: nil => I(Int.rolm n1 amount mask) - | Onegf, F n1 :: nil => F(Float.neg n1) - | Oabsf, F n1 :: nil => F(Float.abs n1) - | Oaddf, F n1 :: F n2 :: nil => F(Float.add n1 n2) - | Osubf, F n1 :: F n2 :: nil => F(Float.sub n1 n2) - | Omulf, F n1 :: F n2 :: nil => F(Float.mul n1 n2) - | Odivf, F n1 :: F n2 :: nil => F(Float.div n1 n2) - | Omuladdf, F n1 :: F n2 :: F n3 :: nil => F(Float.add (Float.mul n1 n2) n3) - | Omulsubf, F n1 :: F n2 :: F n3 :: nil => F(Float.sub (Float.mul n1 n2) n3) - | Osingleoffloat, F n1 :: nil => F(Float.singleoffloat n1) - | Ointoffloat, F n1 :: nil => match Float.intoffloat n1 with Some x => I x | None => Unknown end - | Ofloatofwords, I n1 :: I n2 :: nil => F(Float.from_words n1 n2) - | Ocmp c, vl => - match eval_static_condition c vl with - | None => Unknown - | Some b => I(if b then Int.one else Int.zero) - end - | _, _ => Unknown - end. -*) - -Inductive eval_static_operation_cases: forall (op: operation) (vl: list approx), Type := - | eval_static_operation_case1: - forall v1, - eval_static_operation_cases (Omove) (v1::nil) - | eval_static_operation_case2: - forall n, - eval_static_operation_cases (Ointconst n) (nil) - | eval_static_operation_case3: - forall n, - eval_static_operation_cases (Ofloatconst n) (nil) - | eval_static_operation_case4: - forall s n, - eval_static_operation_cases (Oaddrsymbol s n) (nil) - | eval_static_operation_case6: - forall n1, - eval_static_operation_cases (Ocast8signed) (I n1 :: nil) - | eval_static_operation_case7: - forall n1, - eval_static_operation_cases (Ocast16signed) (I n1 :: nil) - | eval_static_operation_case8: - forall n1 n2, - eval_static_operation_cases (Oadd) (I n1 :: I n2 :: nil) - | eval_static_operation_case9: - forall s1 n1 n2, - eval_static_operation_cases (Oadd) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case11: - forall n n1, - eval_static_operation_cases (Oaddimm n) (I n1 :: nil) - | eval_static_operation_case12: - forall n s1 n1, - eval_static_operation_cases (Oaddimm n) (S s1 n1 :: nil) - | eval_static_operation_case13: - forall n1 n2, - eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) - | eval_static_operation_case14: - forall s1 n1 n2, - eval_static_operation_cases (Osub) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case15: - forall n n1, - eval_static_operation_cases (Osubimm n) (I n1 :: nil) - | eval_static_operation_case16: - forall n1 n2, - eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) - | eval_static_operation_case17: - forall n n1, - eval_static_operation_cases (Omulimm n) (I n1 :: nil) - | eval_static_operation_case18: - forall n1 n2, - eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) - | eval_static_operation_case19: - forall n1 n2, - eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) - | eval_static_operation_case20: - forall n1 n2, - eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) - | eval_static_operation_case21: - forall n n1, - eval_static_operation_cases (Oandimm n) (I n1 :: nil) - | eval_static_operation_case22: - forall n1 n2, - eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) - | eval_static_operation_case23: - forall n n1, - eval_static_operation_cases (Oorimm n) (I n1 :: nil) - | eval_static_operation_case24: - forall n1 n2, - eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) - | eval_static_operation_case25: - forall n n1, - eval_static_operation_cases (Oxorimm n) (I n1 :: nil) - | eval_static_operation_case26: - forall n1 n2, - eval_static_operation_cases (Onand) (I n1 :: I n2 :: nil) - | eval_static_operation_case27: - forall n1 n2, - eval_static_operation_cases (Onor) (I n1 :: I n2 :: nil) - | eval_static_operation_case28: - forall n1 n2, - eval_static_operation_cases (Onxor) (I n1 :: I n2 :: nil) - | eval_static_operation_case29: - forall n1 n2, - eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) - | eval_static_operation_case30: - forall n1 n2, - eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) - | eval_static_operation_case31: - forall n n1, - eval_static_operation_cases (Oshrimm n) (I n1 :: nil) - | eval_static_operation_case32: - forall n n1, - eval_static_operation_cases (Oshrximm n) (I n1 :: nil) - | eval_static_operation_case33: - forall n1 n2, - eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) - | eval_static_operation_case34: - forall amount mask n1, - eval_static_operation_cases (Orolm amount mask) (I n1 :: nil) - | eval_static_operation_case35: - forall n1, - eval_static_operation_cases (Onegf) (F n1 :: nil) - | eval_static_operation_case36: - forall n1, - eval_static_operation_cases (Oabsf) (F n1 :: nil) - | eval_static_operation_case37: - forall n1 n2, - eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) - | eval_static_operation_case38: - forall n1 n2, - eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) - | eval_static_operation_case39: - forall n1 n2, - eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) - | eval_static_operation_case40: - forall n1 n2, - eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) - | eval_static_operation_case41: - forall n1 n2 n3, - eval_static_operation_cases (Omuladdf) (F n1 :: F n2 :: F n3 :: nil) - | eval_static_operation_case42: - forall n1 n2 n3, - eval_static_operation_cases (Omulsubf) (F n1 :: F n2 :: F n3 :: nil) - | eval_static_operation_case43: - forall n1, - eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) - | eval_static_operation_case44: - forall n1, - eval_static_operation_cases (Ointoffloat) (F n1 :: nil) - | eval_static_operation_case45: - forall n1 n2, - eval_static_operation_cases (Ofloatofwords) (I n1 :: I n2 :: nil) - | eval_static_operation_case47: - forall c vl, - eval_static_operation_cases (Ocmp c) (vl) - | eval_static_operation_case48: - forall n1, - eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil) - | eval_static_operation_case49: - forall n1, - eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil) - | eval_static_operation_default: - forall (op: operation) (vl: list approx), - eval_static_operation_cases op vl. - -Definition eval_static_operation_match (op: operation) (vl: list approx) := - match op as z1, vl as z2 return eval_static_operation_cases z1 z2 with - | Omove, v1::nil => - eval_static_operation_case1 v1 - | Ointconst n, nil => - eval_static_operation_case2 n - | Ofloatconst n, nil => - eval_static_operation_case3 n - | Oaddrsymbol s n, nil => - eval_static_operation_case4 s n - | Ocast8signed, I n1 :: nil => - eval_static_operation_case6 n1 - | Ocast16signed, I n1 :: nil => - eval_static_operation_case7 n1 - | Oadd, I n1 :: I n2 :: nil => - eval_static_operation_case8 n1 n2 - | Oadd, S s1 n1 :: I n2 :: nil => - eval_static_operation_case9 s1 n1 n2 - | Oaddimm n, I n1 :: nil => - eval_static_operation_case11 n n1 - | Oaddimm n, S s1 n1 :: nil => - eval_static_operation_case12 n s1 n1 - | Osub, I n1 :: I n2 :: nil => - eval_static_operation_case13 n1 n2 - | Osub, S s1 n1 :: I n2 :: nil => - eval_static_operation_case14 s1 n1 n2 - | Osubimm n, I n1 :: nil => - eval_static_operation_case15 n n1 - | Omul, I n1 :: I n2 :: nil => - eval_static_operation_case16 n1 n2 - | Omulimm n, I n1 :: nil => - eval_static_operation_case17 n n1 - | Odiv, I n1 :: I n2 :: nil => - eval_static_operation_case18 n1 n2 - | Odivu, I n1 :: I n2 :: nil => - eval_static_operation_case19 n1 n2 - | Oand, I n1 :: I n2 :: nil => - eval_static_operation_case20 n1 n2 - | Oandimm n, I n1 :: nil => - eval_static_operation_case21 n n1 - | Oor, I n1 :: I n2 :: nil => - eval_static_operation_case22 n1 n2 - | Oorimm n, I n1 :: nil => - eval_static_operation_case23 n n1 - | Oxor, I n1 :: I n2 :: nil => - eval_static_operation_case24 n1 n2 - | Oxorimm n, I n1 :: nil => - eval_static_operation_case25 n n1 - | Onand, I n1 :: I n2 :: nil => - eval_static_operation_case26 n1 n2 - | Onor, I n1 :: I n2 :: nil => - eval_static_operation_case27 n1 n2 - | Onxor, I n1 :: I n2 :: nil => - eval_static_operation_case28 n1 n2 - | Oshl, I n1 :: I n2 :: nil => - eval_static_operation_case29 n1 n2 - | Oshr, I n1 :: I n2 :: nil => - eval_static_operation_case30 n1 n2 - | Oshrimm n, I n1 :: nil => - eval_static_operation_case31 n n1 - | Oshrximm n, I n1 :: nil => - eval_static_operation_case32 n n1 - | Oshru, I n1 :: I n2 :: nil => - eval_static_operation_case33 n1 n2 - | Orolm amount mask, I n1 :: nil => - eval_static_operation_case34 amount mask n1 - | Onegf, F n1 :: nil => - eval_static_operation_case35 n1 - | Oabsf, F n1 :: nil => - eval_static_operation_case36 n1 - | Oaddf, F n1 :: F n2 :: nil => - eval_static_operation_case37 n1 n2 - | Osubf, F n1 :: F n2 :: nil => - eval_static_operation_case38 n1 n2 - | Omulf, F n1 :: F n2 :: nil => - eval_static_operation_case39 n1 n2 - | Odivf, F n1 :: F n2 :: nil => - eval_static_operation_case40 n1 n2 - | Omuladdf, F n1 :: F n2 :: F n3 :: nil => - eval_static_operation_case41 n1 n2 n3 - | Omulsubf, F n1 :: F n2 :: F n3 :: nil => - eval_static_operation_case42 n1 n2 n3 - | Osingleoffloat, F n1 :: nil => - eval_static_operation_case43 n1 - | Ointoffloat, F n1 :: nil => - eval_static_operation_case44 n1 - | Ofloatofwords, I n1 :: I n2 :: nil => - eval_static_operation_case45 n1 n2 - | Ocmp c, vl => - eval_static_operation_case47 c vl - | Ocast8unsigned, I n1 :: nil => - eval_static_operation_case48 n1 - | Ocast16unsigned, I n1 :: nil => - eval_static_operation_case49 n1 - | op, vl => - eval_static_operation_default op vl - end. - -Definition eval_static_operation (op: operation) (vl: list approx) := - match eval_static_operation_match op vl with - | eval_static_operation_case1 v1 => - v1 - | eval_static_operation_case2 n => - I n - | eval_static_operation_case3 n => - F n - | eval_static_operation_case4 s n => - S s n - | eval_static_operation_case6 n1 => - I(Int.sign_ext 8 n1) - | eval_static_operation_case7 n1 => - I(Int.sign_ext 16 n1) - | eval_static_operation_case8 n1 n2 => - I(Int.add n1 n2) - | eval_static_operation_case9 s1 n1 n2 => - S s1 (Int.add n1 n2) - | eval_static_operation_case11 n n1 => - I (Int.add n1 n) - | eval_static_operation_case12 n s1 n1 => - S s1 (Int.add n1 n) - | eval_static_operation_case13 n1 n2 => - I(Int.sub n1 n2) - | eval_static_operation_case14 s1 n1 n2 => - S s1 (Int.sub n1 n2) - | eval_static_operation_case15 n n1 => - I (Int.sub n n1) - | eval_static_operation_case16 n1 n2 => - I(Int.mul n1 n2) - | eval_static_operation_case17 n n1 => - I(Int.mul n1 n) - | eval_static_operation_case18 n1 n2 => - if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2) - | eval_static_operation_case19 n1 n2 => - if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2) - | eval_static_operation_case20 n1 n2 => - I(Int.and n1 n2) - | eval_static_operation_case21 n n1 => - I(Int.and n1 n) - | eval_static_operation_case22 n1 n2 => - I(Int.or n1 n2) - | eval_static_operation_case23 n n1 => - I(Int.or n1 n) - | eval_static_operation_case24 n1 n2 => - I(Int.xor n1 n2) - | eval_static_operation_case25 n n1 => - I(Int.xor n1 n) - | eval_static_operation_case26 n1 n2 => - I(Int.xor (Int.and n1 n2) Int.mone) - | eval_static_operation_case27 n1 n2 => - I(Int.xor (Int.or n1 n2) Int.mone) - | eval_static_operation_case28 n1 n2 => - I(Int.xor (Int.xor n1 n2) Int.mone) - | eval_static_operation_case29 n1 n2 => - if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown - | eval_static_operation_case30 n1 n2 => - if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown - | eval_static_operation_case31 n n1 => - if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown - | eval_static_operation_case32 n n1 => - if Int.ltu n Int.iwordsize then I(Int.shrx n1 n) else Unknown - | eval_static_operation_case33 n1 n2 => - if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown - | eval_static_operation_case34 amount mask n1 => - I(Int.rolm n1 amount mask) - | eval_static_operation_case35 n1 => - F(Float.neg n1) - | eval_static_operation_case36 n1 => - F(Float.abs n1) - | eval_static_operation_case37 n1 n2 => - F(Float.add n1 n2) - | eval_static_operation_case38 n1 n2 => - F(Float.sub n1 n2) - | eval_static_operation_case39 n1 n2 => - F(Float.mul n1 n2) - | eval_static_operation_case40 n1 n2 => - F(Float.div n1 n2) - | eval_static_operation_case41 n1 n2 n3 => - F(Float.add (Float.mul n1 n2) n3) - | eval_static_operation_case42 n1 n2 n3 => - F(Float.sub (Float.mul n1 n2) n3) - | eval_static_operation_case43 n1 => - F(Float.singleoffloat n1) - | eval_static_operation_case44 n1 => - match Float.intoffloat n1 with Some x => I x | None => Unknown end - | eval_static_operation_case45 n1 n2 => - F(Float.from_words n1 n2) - | eval_static_operation_case47 c vl => - match eval_static_condition c vl with - | None => Unknown - | Some b => I(if b then Int.one else Int.zero) - end - | eval_static_operation_case48 n1 => - I(Int.zero_ext 8 n1) - | eval_static_operation_case49 n1 => - I(Int.zero_ext 16 n1) - | eval_static_operation_default op vl => - Unknown - 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. - -Variable app: reg -> approx. - -Definition intval (r: reg) : option int := - match app r with I n => Some n | _ => None end. - -Inductive cond_strength_reduction_cases: condition -> list reg -> Type := - | csr_case1: - forall c r1 r2, - cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) - | csr_case2: - forall c r1 r2, - cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) - | csr_default: - forall c rl, - cond_strength_reduction_cases c rl. - -Definition cond_strength_reduction_match (cond: condition) (rl: list reg) := - match cond as x, rl as y return cond_strength_reduction_cases x y with - | Ccomp c, r1 :: r2 :: nil => - csr_case1 c r1 r2 - | Ccompu c, r1 :: r2 :: nil => - csr_case2 c r1 r2 - | cond, rl => - csr_default cond rl - end. - -Definition cond_strength_reduction - (cond: condition) (args: list reg) : condition * list reg := - match cond_strength_reduction_match cond args with - | csr_case1 c r1 r2 => - match intval r1, intval r2 with - | Some n, _ => - (Ccompimm (swap_comparison c) n, r2 :: nil) - | _, Some n => - (Ccompimm c n, r1 :: nil) - | _, _ => - (cond, args) - end - | csr_case2 c r1 r2 => - match intval r1, intval r2 with - | Some n, _ => - (Ccompuimm (swap_comparison c) n, r2 :: nil) - | _, Some n => - (Ccompuimm c n, r1 :: nil) - | _, _ => - (cond, args) - end - | csr_default cond args => - (cond, 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) (r: reg) := - if Int.eq n Int.zero - then (Omove, r :: nil) - else (Orolm n (Int.shl Int.mone n), r :: nil). - -Definition make_shrimm (n: int) (r: reg) := - if Int.eq n Int.zero - then (Omove, r :: nil) - else (Oshrimm n, r :: nil). - -Definition make_shruimm (n: int) (r: reg) := - if Int.eq n Int.zero - then (Omove, r :: nil) - else (Orolm (Int.sub Int.iwordsize n) (Int.shru Int.mone n), r :: nil). - -Definition make_mulimm (n: int) (r: reg) := - if Int.eq n Int.zero then - (Ointconst Int.zero, nil) - else if Int.eq n Int.one then - (Omove, r :: nil) - else - match Int.is_power2 n with - | Some l => make_shlimm l r - | None => (Omulimm n, r :: nil) - end. - -Definition make_andimm (n: int) (r: reg) := - if Int.eq n Int.zero - then (Ointconst Int.zero, nil) - else if Int.eq n Int.mone 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 (Oxorimm n, r :: nil). - -Inductive op_strength_reduction_cases: operation -> list reg -> Type := - | op_strength_reduction_case1: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oadd (r1 :: r2 :: nil) - | op_strength_reduction_case2: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Osub (r1 :: r2 :: nil) - | op_strength_reduction_case3: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Omul (r1 :: r2 :: nil) - | op_strength_reduction_case4: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Odiv (r1 :: r2 :: nil) - | op_strength_reduction_case5: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Odivu (r1 :: r2 :: nil) - | op_strength_reduction_case6: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oand (r1 :: r2 :: nil) - | op_strength_reduction_case7: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oor (r1 :: r2 :: nil) - | op_strength_reduction_case8: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oxor (r1 :: r2 :: nil) - | op_strength_reduction_case9: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oshl (r1 :: r2 :: nil) - | op_strength_reduction_case10: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oshr (r1 :: r2 :: nil) - | op_strength_reduction_case11: - forall (r1: reg) (r2: reg), - op_strength_reduction_cases Oshru (r1 :: r2 :: nil) - | op_strength_reduction_case12: - forall (c: condition) (rl: list reg), - op_strength_reduction_cases (Ocmp c) rl - | op_strength_reduction_default: - forall (op: operation) (args: list reg), - op_strength_reduction_cases op args. - -Definition op_strength_reduction_match (op: operation) (args: list reg) := - match op as z1, args as z2 return op_strength_reduction_cases z1 z2 with - | Oadd, r1 :: r2 :: nil => - op_strength_reduction_case1 r1 r2 - | Osub, r1 :: r2 :: nil => - op_strength_reduction_case2 r1 r2 - | Omul, r1 :: r2 :: nil => - op_strength_reduction_case3 r1 r2 - | Odiv, r1 :: r2 :: nil => - op_strength_reduction_case4 r1 r2 - | Odivu, r1 :: r2 :: nil => - op_strength_reduction_case5 r1 r2 - | Oand, r1 :: r2 :: nil => - op_strength_reduction_case6 r1 r2 - | Oor, r1 :: r2 :: nil => - op_strength_reduction_case7 r1 r2 - | Oxor, r1 :: r2 :: nil => - op_strength_reduction_case8 r1 r2 - | Oshl, r1 :: r2 :: nil => - op_strength_reduction_case9 r1 r2 - | Oshr, r1 :: r2 :: nil => - op_strength_reduction_case10 r1 r2 - | Oshru, r1 :: r2 :: nil => - op_strength_reduction_case11 r1 r2 - | Ocmp c, rl => - op_strength_reduction_case12 c rl - | op, args => - op_strength_reduction_default op args - end. - -Definition op_strength_reduction (op: operation) (args: list reg) := - match op_strength_reduction_match op args with - | op_strength_reduction_case1 r1 r2 => (* Oadd *) - match intval r1, intval r2 with - | Some n, _ => make_addimm n r2 - | _, Some n => make_addimm n r1 - | _, _ => (op, args) - end - | op_strength_reduction_case2 r1 r2 => (* Osub *) - match intval r1, intval r2 with - | Some n, _ => (Osubimm n, r2 :: nil) - | _, Some n => make_addimm (Int.neg n) r1 - | _, _ => (op, args) - end - | op_strength_reduction_case3 r1 r2 => (* Omul *) - match intval r1, intval r2 with - | Some n, _ => make_mulimm n r2 - | _, Some n => make_mulimm n r1 - | _, _ => (op, args) - end - | op_strength_reduction_case4 r1 r2 => (* Odiv *) - match intval r2 with - | Some n => - match Int.is_power2 n with - | Some l => (Oshrximm l, r1 :: nil) - | None => (op, args) - end - | None => - (op, args) - end - | op_strength_reduction_case5 r1 r2 => (* Odivu *) - match intval r2 with - | Some n => - match Int.is_power2 n with - | Some l => make_shruimm l r1 - | None => (op, args) - end - | None => - (op, args) - end - | op_strength_reduction_case6 r1 r2 => (* Oand *) - match intval r1, intval r2 with - | Some n, _ => make_andimm n r2 - | _, Some n => make_andimm n r1 - | _, _ => (op, args) - end - | op_strength_reduction_case7 r1 r2 => (* Oor *) - match intval r1, intval r2 with - | Some n, _ => make_orimm n r2 - | _, Some n => make_orimm n r1 - | _, _ => (op, args) - end - | op_strength_reduction_case8 r1 r2 => (* Oxor *) - match intval r1, intval r2 with - | Some n, _ => make_xorimm n r2 - | _, Some n => make_xorimm n r1 - | _, _ => (op, args) - end - | op_strength_reduction_case9 r1 r2 => (* Oshl *) - match intval r2 with - | Some n => - if Int.ltu n Int.iwordsize - then make_shlimm n r1 - else (op, args) - | _ => (op, args) - end - | op_strength_reduction_case10 r1 r2 => (* Oshr *) - match intval r2 with - | Some n => - if Int.ltu n Int.iwordsize - then make_shrimm n r1 - else (op, args) - | _ => (op, args) - end - | op_strength_reduction_case11 r1 r2 => (* Oshru *) - match intval r2 with - | Some n => - if Int.ltu n Int.iwordsize - then make_shruimm n r1 - else (op, args) - | _ => (op, args) - end - | op_strength_reduction_case12 c args => (* Ocmp *) - let (c', args') := cond_strength_reduction c args in - (Ocmp c', args') - | op_strength_reduction_default op args => (* default *) - (op, args) - end. - -Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg), Type := - | addr_strength_reduction_case1: - forall (r1: reg) (r2: reg), - addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) - | addr_strength_reduction_case2: - forall (symb: ident) (ofs: int) (r1: reg), - addr_strength_reduction_cases (Abased symb ofs) (r1 :: nil) - | addr_strength_reduction_case3: - forall n r1, - addr_strength_reduction_cases (Aindexed n) (r1 :: nil) - | addr_strength_reduction_default: - forall (addr: addressing) (args: list reg), - addr_strength_reduction_cases addr args. - -Definition addr_strength_reduction_match (addr: addressing) (args: list reg) := - match addr as z1, args as z2 return addr_strength_reduction_cases z1 z2 with - | Aindexed2, r1 :: r2 :: nil => - addr_strength_reduction_case1 r1 r2 - | Abased symb ofs, r1 :: nil => - addr_strength_reduction_case2 symb ofs r1 - | Aindexed n, r1 :: nil => - addr_strength_reduction_case3 n r1 - | addr, args => - addr_strength_reduction_default addr args - end. - -Definition addr_strength_reduction (addr: addressing) (args: list reg) := - match addr_strength_reduction_match addr args with - | addr_strength_reduction_case1 r1 r2 => (* Aindexed2 *) - match app r1, app r2 with - | S symb n1, I n2 => (Aglobal symb (Int.add n1 n2), nil) - | S symb n1, _ => (Abased symb n1, r2 :: nil) - | I n1, S symb n2 => (Aglobal symb (Int.add n1 n2), nil) - | I n1, _ => (Aindexed n1, r2 :: nil) - | _, S symb n2 => (Abased symb n2, r1 :: nil) - | _, I n2 => (Aindexed n2, r1 :: nil) - | _, _ => (addr, args) - end - | addr_strength_reduction_case2 symb ofs r1 => (* Abased *) - match intval r1 with - | Some n => (Aglobal symb (Int.add ofs n), nil) - | _ => (addr, args) - end - | addr_strength_reduction_case3 n r1 => (* Aindexed *) - match app r1 with - | S symb ofs => (Aglobal symb (Int.add ofs n), nil) - | _ => (addr, args) - end - | addr_strength_reduction_default addr args => (* default *) - (addr, args) - end. - -End STRENGTH_REDUCTION. |