diff options
Diffstat (limited to 'ia32/ConstpropOp.v')
| -rw-r--r-- | ia32/ConstpropOp.v | 1261 |
1 files changed, 528 insertions, 733 deletions
diff --git a/ia32/ConstpropOp.v b/ia32/ConstpropOp.v index 815ba0e0..3d07a4d4 100644 --- a/ia32/ConstpropOp.v +++ b/ia32/ConstpropOp.v @@ -32,9 +32,10 @@ Inductive approx : Type := 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. + | G: ident -> int -> approx (** The value is the address of the given global symbol plus the given integer offset. *) + | S: int -> approx. (** The value is the stack pointer plus the offset. *) (** We now define the abstract interpretations of conditions and operators over this set of approximations. For instance, the abstract interpretation @@ -44,11 +45,12 @@ Inductive approx : Type := 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 + indirect style described in file [SelectOp] to avoid excessive duplication of cases in proofs. *) -(* -Definition eval_static_condition (cond: condition) (vl: list approx) := +(** Original definition: +<< +Nondetfunction 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) @@ -57,198 +59,175 @@ Definition eval_static_condition (cond: condition) (vl: list approx) := | 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)) + | Cmasknotzero n, I 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. + | 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 + match cond as zz1, vl as zz2 return eval_static_condition_cases zz1 zz2 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 => + | eval_static_condition_case1 c n1 n2 => (* Ccomp c, I n1 :: I n2 :: nil *) Some(Int.cmp c n1 n2) - | eval_static_condition_case2 c n1 n2 => + | eval_static_condition_case2 c n1 n2 => (* Ccompu c, I n1 :: I n2 :: nil *) Some(Int.cmpu c n1 n2) - | eval_static_condition_case3 c n n1 => + | eval_static_condition_case3 c n n1 => (* Ccompimm c n, I n1 :: nil *) Some(Int.cmp c n1 n) - | eval_static_condition_case4 c n n1 => + | eval_static_condition_case4 c n n1 => (* Ccompuimm c n, I n1 :: nil *) Some(Int.cmpu c n1 n) - | eval_static_condition_case5 c n1 n2 => + | eval_static_condition_case5 c n1 n2 => (* Ccompf c, F n1 :: F n2 :: nil *) Some(Float.cmp c n1 n2) - | eval_static_condition_case6 c n1 n2 => + | eval_static_condition_case6 c n1 n2 => (* Cnotcompf c, F n1 :: F n2 :: nil *) Some(negb(Float.cmp c n1 n2)) - | eval_static_condition_case7 n n1 => + | eval_static_condition_case7 n n1 => (* Cmaskzero n, I n1 :: nil *) Some(Int.eq (Int.and n1 n) Int.zero) - | eval_static_condition_case8 n n1 => + | eval_static_condition_case8 n n1 => (* Cmasknotzero n, I n1::nil *) Some(negb(Int.eq (Int.and n1 n) Int.zero)) | eval_static_condition_default cond vl => None end. -(* -Definition eval_static_addressing (addr: addressing) (vl: list approx) := - match op, vl with + +Definition eval_static_condition_val (cond: condition) (vl: list approx) := + match eval_static_condition cond vl with + | None => Unknown + | Some b => I(if b then Int.one else Int.zero) + end. + +Definition eval_static_intoffloat (f: float) := + match Float.intoffloat f with Some x => I x | None => Unknown end. + +(** Original definition: +<< +Nondetfunction eval_static_addressing (addr: addressing) (vl: list approx) := + match addr, vl with | Aindexed n, I n1::nil => I (Int.add n1 n) - | Aindexed n, S id ofs::nil => S id (Int.add ofs n) + | Aindexed n, G id ofs::nil => G id (Int.add ofs n) + | Aindexed n, S ofs::nil => S (Int.add ofs n) | Aindexed2 n, I n1::I n2::nil => I (Int.add (Int.add n1 n2) n) - | Aindexed2 n, S id ofs::I n2::nil => S id (Int.add (Int.add ofs n2) n) - | Aindexed2 n, I n1::S id ofs::nil => S id (Int.add (Int.add ofs n1) n) + | Aindexed2 n, G id ofs::I n2::nil => G id (Int.add (Int.add ofs n2) n) + | Aindexed2 n, I n1::G id ofs::nil => G id (Int.add (Int.add ofs n1) n) + | Aindexed2 n, S ofs::I n2::nil => S (Int.add (Int.add ofs n2) n) + | Aindexed2 n, I n1::S ofs::nil => S (Int.add (Int.add ofs n1) n) | Ascaled sc n, I n1::nil => I (Int.add (Int.mul n1 sc) n) | Aindexed2scaled sc n, I n1::I n2::nil => I (Int.add n1 (Int.add (Int.mul n2 sc) n)) - | Aindexed2scaled sc n, S id ofs::I n2::nil => S id (Int.add ofs (Int.add (Int.mul n2 sc) n)) - | Aglobal id ofs, nil => S id ofs - | Abased id ofs, I n1::nil => S id (Int.add ofs n1) - | Abasedscaled sc id ofs, I n1::nil => S id (Int.add ofs (Int.mul sc n1)) + | Aindexed2scaled sc n, G id ofs::I n2::nil => G id (Int.add ofs (Int.add (Int.mul n2 sc) n)) + | Aindexed2scaled sc n, S ofs::I n2::nil => S (Int.add ofs (Int.add (Int.mul n2 sc) n)) + | Aglobal id ofs, nil => G id ofs + | Abased id ofs, I n1::nil => G id (Int.add ofs n1) + | Abasedscaled sc id ofs, I n1::nil => G id (Int.add ofs (Int.mul sc n1)) + | Ainstack ofs, nil => S ofs | _, _ => Unknown end. +>> *) Inductive eval_static_addressing_cases: forall (addr: addressing) (vl: list approx), Type := - | eval_static_addressing_case1: - forall n n1, - eval_static_addressing_cases (Aindexed n) (I n1::nil) - | eval_static_addressing_case2: - forall n id ofs, - eval_static_addressing_cases (Aindexed n) (S id ofs::nil) - | eval_static_addressing_case3: - forall n n1 n2, - eval_static_addressing_cases (Aindexed2 n) (I n1::I n2::nil) - | eval_static_addressing_case4: - forall n id ofs n2, - eval_static_addressing_cases (Aindexed2 n) (S id ofs::I n2::nil) - | eval_static_addressing_case5: - forall n n1 id ofs, - eval_static_addressing_cases (Aindexed2 n) (I n1::S id ofs::nil) - | eval_static_addressing_case6: - forall sc n n1, - eval_static_addressing_cases (Ascaled sc n) (I n1::nil) - | eval_static_addressing_case7: - forall sc n n1 n2, - eval_static_addressing_cases (Aindexed2scaled sc n) (I n1::I n2::nil) - | eval_static_addressing_case8: - forall sc n id ofs n2, - eval_static_addressing_cases (Aindexed2scaled sc n) (S id ofs::I n2::nil) - | eval_static_addressing_case9: - forall id ofs, - eval_static_addressing_cases (Aglobal id ofs) (nil) - | eval_static_addressing_case10: - forall id ofs n1, - eval_static_addressing_cases (Abased id ofs) (I n1::nil) - | eval_static_addressing_case11: - forall sc id ofs n1, - eval_static_addressing_cases (Abasedscaled sc id ofs) (I n1::nil) - | eval_static_addressing_default: - forall (addr: addressing) (vl: list approx), - eval_static_addressing_cases addr vl. + | eval_static_addressing_case1: forall n n1, eval_static_addressing_cases (Aindexed n) (I n1::nil) + | eval_static_addressing_case2: forall n id ofs, eval_static_addressing_cases (Aindexed n) (G id ofs::nil) + | eval_static_addressing_case3: forall n ofs, eval_static_addressing_cases (Aindexed n) (S ofs::nil) + | eval_static_addressing_case4: forall n n1 n2, eval_static_addressing_cases (Aindexed2 n) (I n1::I n2::nil) + | eval_static_addressing_case5: forall n id ofs n2, eval_static_addressing_cases (Aindexed2 n) (G id ofs::I n2::nil) + | eval_static_addressing_case6: forall n n1 id ofs, eval_static_addressing_cases (Aindexed2 n) (I n1::G id ofs::nil) + | eval_static_addressing_case7: forall n ofs n2, eval_static_addressing_cases (Aindexed2 n) (S ofs::I n2::nil) + | eval_static_addressing_case8: forall n n1 ofs, eval_static_addressing_cases (Aindexed2 n) (I n1::S ofs::nil) + | eval_static_addressing_case9: forall sc n n1, eval_static_addressing_cases (Ascaled sc n) (I n1::nil) + | eval_static_addressing_case10: forall sc n n1 n2, eval_static_addressing_cases (Aindexed2scaled sc n) (I n1::I n2::nil) + | eval_static_addressing_case11: forall sc n id ofs n2, eval_static_addressing_cases (Aindexed2scaled sc n) (G id ofs::I n2::nil) + | eval_static_addressing_case12: forall sc n ofs n2, eval_static_addressing_cases (Aindexed2scaled sc n) (S ofs::I n2::nil) + | eval_static_addressing_case13: forall id ofs, eval_static_addressing_cases (Aglobal id ofs) (nil) + | eval_static_addressing_case14: forall id ofs n1, eval_static_addressing_cases (Abased id ofs) (I n1::nil) + | eval_static_addressing_case15: forall sc id ofs n1, eval_static_addressing_cases (Abasedscaled sc id ofs) (I n1::nil) + | eval_static_addressing_case16: forall ofs, eval_static_addressing_cases (Ainstack ofs) (nil) + | eval_static_addressing_default: forall (addr: addressing) (vl: list approx), eval_static_addressing_cases addr vl. Definition eval_static_addressing_match (addr: addressing) (vl: list approx) := - match addr as z1, vl as z2 return eval_static_addressing_cases z1 z2 with - | Aindexed n, I n1::nil => - eval_static_addressing_case1 n n1 - | Aindexed n, S id ofs::nil => - eval_static_addressing_case2 n id ofs - | Aindexed2 n, I n1::I n2::nil => - eval_static_addressing_case3 n n1 n2 - | Aindexed2 n, S id ofs::I n2::nil => - eval_static_addressing_case4 n id ofs n2 - | Aindexed2 n, I n1::S id ofs::nil => - eval_static_addressing_case5 n n1 id ofs - | Ascaled sc n, I n1::nil => - eval_static_addressing_case6 sc n n1 - | Aindexed2scaled sc n, I n1::I n2::nil => - eval_static_addressing_case7 sc n n1 n2 - | Aindexed2scaled sc n, S id ofs::I n2::nil => - eval_static_addressing_case8 sc n id ofs n2 - | Aglobal id ofs, nil => - eval_static_addressing_case9 id ofs - | Abased id ofs, I n1::nil => - eval_static_addressing_case10 id ofs n1 - | Abasedscaled sc id ofs, I n1::nil => - eval_static_addressing_case11 sc id ofs n1 - | addr, vl => - eval_static_addressing_default addr vl + match addr as zz1, vl as zz2 return eval_static_addressing_cases zz1 zz2 with + | Aindexed n, I n1::nil => eval_static_addressing_case1 n n1 + | Aindexed n, G id ofs::nil => eval_static_addressing_case2 n id ofs + | Aindexed n, S ofs::nil => eval_static_addressing_case3 n ofs + | Aindexed2 n, I n1::I n2::nil => eval_static_addressing_case4 n n1 n2 + | Aindexed2 n, G id ofs::I n2::nil => eval_static_addressing_case5 n id ofs n2 + | Aindexed2 n, I n1::G id ofs::nil => eval_static_addressing_case6 n n1 id ofs + | Aindexed2 n, S ofs::I n2::nil => eval_static_addressing_case7 n ofs n2 + | Aindexed2 n, I n1::S ofs::nil => eval_static_addressing_case8 n n1 ofs + | Ascaled sc n, I n1::nil => eval_static_addressing_case9 sc n n1 + | Aindexed2scaled sc n, I n1::I n2::nil => eval_static_addressing_case10 sc n n1 n2 + | Aindexed2scaled sc n, G id ofs::I n2::nil => eval_static_addressing_case11 sc n id ofs n2 + | Aindexed2scaled sc n, S ofs::I n2::nil => eval_static_addressing_case12 sc n ofs n2 + | Aglobal id ofs, nil => eval_static_addressing_case13 id ofs + | Abased id ofs, I n1::nil => eval_static_addressing_case14 id ofs n1 + | Abasedscaled sc id ofs, I n1::nil => eval_static_addressing_case15 sc id ofs n1 + | Ainstack ofs, nil => eval_static_addressing_case16 ofs + | addr, vl => eval_static_addressing_default addr vl end. Definition eval_static_addressing (addr: addressing) (vl: list approx) := match eval_static_addressing_match addr vl with - | eval_static_addressing_case1 n n1 => + | eval_static_addressing_case1 n n1 => (* Aindexed n, I n1::nil *) I (Int.add n1 n) - | eval_static_addressing_case2 n id ofs => - S id (Int.add ofs n) - | eval_static_addressing_case3 n n1 n2 => + | eval_static_addressing_case2 n id ofs => (* Aindexed n, G id ofs::nil *) + G id (Int.add ofs n) + | eval_static_addressing_case3 n ofs => (* Aindexed n, S ofs::nil *) + S (Int.add ofs n) + | eval_static_addressing_case4 n n1 n2 => (* Aindexed2 n, I n1::I n2::nil *) I (Int.add (Int.add n1 n2) n) - | eval_static_addressing_case4 n id ofs n2 => - S id (Int.add (Int.add ofs n2) n) - | eval_static_addressing_case5 n n1 id ofs => - S id (Int.add (Int.add ofs n1) n) - | eval_static_addressing_case6 sc n n1 => + | eval_static_addressing_case5 n id ofs n2 => (* Aindexed2 n, G id ofs::I n2::nil *) + G id (Int.add (Int.add ofs n2) n) + | eval_static_addressing_case6 n n1 id ofs => (* Aindexed2 n, I n1::G id ofs::nil *) + G id (Int.add (Int.add ofs n1) n) + | eval_static_addressing_case7 n ofs n2 => (* Aindexed2 n, S ofs::I n2::nil *) + S (Int.add (Int.add ofs n2) n) + | eval_static_addressing_case8 n n1 ofs => (* Aindexed2 n, I n1::S ofs::nil *) + S (Int.add (Int.add ofs n1) n) + | eval_static_addressing_case9 sc n n1 => (* Ascaled sc n, I n1::nil *) I (Int.add (Int.mul n1 sc) n) - | eval_static_addressing_case7 sc n n1 n2 => + | eval_static_addressing_case10 sc n n1 n2 => (* Aindexed2scaled sc n, I n1::I n2::nil *) I (Int.add n1 (Int.add (Int.mul n2 sc) n)) - | eval_static_addressing_case8 sc n id ofs n2 => - S id (Int.add ofs (Int.add (Int.mul n2 sc) n)) - | eval_static_addressing_case9 id ofs => - S id ofs - | eval_static_addressing_case10 id ofs n1 => - S id (Int.add ofs n1) - | eval_static_addressing_case11 sc id ofs n1 => - S id (Int.add ofs (Int.mul sc n1)) + | eval_static_addressing_case11 sc n id ofs n2 => (* Aindexed2scaled sc n, G id ofs::I n2::nil *) + G id (Int.add ofs (Int.add (Int.mul n2 sc) n)) + | eval_static_addressing_case12 sc n ofs n2 => (* Aindexed2scaled sc n, S ofs::I n2::nil *) + S (Int.add ofs (Int.add (Int.mul n2 sc) n)) + | eval_static_addressing_case13 id ofs => (* Aglobal id ofs, nil *) + G id ofs + | eval_static_addressing_case14 id ofs n1 => (* Abased id ofs, I n1::nil *) + G id (Int.add ofs n1) + | eval_static_addressing_case15 sc id ofs n1 => (* Abasedscaled sc id ofs, I n1::nil *) + G id (Int.add ofs (Int.mul sc n1)) + | eval_static_addressing_case16 ofs => (* Ainstack ofs, nil *) + S ofs | eval_static_addressing_default addr vl => Unknown end. -(* -Definition eval_static_operation (op: operation) (vl: list approx) := + +(** Original definition: +<< +Nondetfunction eval_static_operation (op: operation) (vl: list approx) := match op, vl with | Omove, v1::nil => v1 | Ointconst n, nil => I n @@ -259,7 +238,7 @@ Definition eval_static_operation (op: operation) (vl: list approx) := | Ocast16unsigned, I n1 :: nil => I(Int.zero_ext 16 n1) | Oneg, I n1 :: nil => I(Int.neg n1) | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2) - | Osub, S s1 n1 :: I n2 :: nil => S s1 (Int.sub n1 n2) + | Osub, G s1 n1 :: I n2 :: nil => G s1 (Int.sub n1 n2) | 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) @@ -276,7 +255,7 @@ Definition eval_static_operation (op: operation) (vl: list approx) := | Oshlimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shl n1 n) 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 + | Oshrximm n, I n1 :: nil => if Int.ltu n (Int.repr 31) 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 | Oshruimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.shru n1 n) else Unknown | Ororimm n, I n1 :: nil => if Int.ltu n Int.iwordsize then I(Int.ror n1 n) else Unknown @@ -288,320 +267,193 @@ Definition eval_static_operation (op: operation) (vl: list approx) := | Omulf, F n1 :: F n2 :: nil => F(Float.mul n1 n2) | Odivf, F n1 :: F n2 :: nil => F(Float.div n1 n2) | Osingleoffloat, F n1 :: nil => F(Float.singleoffloat n1) - | Ointoffloat, F n1 :: nil => match Float.intoffloat n1 with Some x => I x | None => Unknown end + | Ointoffloat, F n1 :: nil => eval_static_intoffloat n1 | Ofloatofint, I n1 :: nil => F(Float.floatofint n1) - | Ocmp c, vl => match eval_static_condition c vl with None => Unknown | Some b => I(if b then Int.one else Int.zero) end + | Ocmp c, vl => eval_static_condition_val c vl | _, _ => 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 n1, - eval_static_operation_cases (Ocast8signed) (I n1 :: nil) - | eval_static_operation_case5: - forall n1, - eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil) - | eval_static_operation_case6: - forall n1, - eval_static_operation_cases (Ocast16signed) (I n1 :: nil) - | eval_static_operation_case7: - forall n1, - eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil) - | eval_static_operation_case8: - forall n1, - eval_static_operation_cases (Oneg) (I n1 :: nil) - | eval_static_operation_case9: - forall n1 n2, - eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) - | eval_static_operation_case10: - forall s1 n1 n2, - eval_static_operation_cases (Osub) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case11: - forall n1 n2, - eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) - | eval_static_operation_case12: - forall n n1, - eval_static_operation_cases (Omulimm n) (I n1 :: nil) - | eval_static_operation_case13: - forall n1 n2, - eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) - | eval_static_operation_case14: - forall n1 n2, - eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) - | eval_static_operation_case15: - forall n1 n2, - eval_static_operation_cases (Omod) (I n1 :: I n2 :: nil) - | eval_static_operation_case16: - forall n1 n2, - eval_static_operation_cases (Omodu) (I n1 :: I n2 :: nil) - | eval_static_operation_case17: - forall n1 n2, - eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) - | eval_static_operation_case18: - forall n n1, - eval_static_operation_cases (Oandimm n) (I n1 :: nil) - | eval_static_operation_case19: - forall n1 n2, - eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) - | eval_static_operation_case20: - forall n n1, - eval_static_operation_cases (Oorimm n) (I n1 :: nil) - | eval_static_operation_case21: - forall n1 n2, - eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) - | eval_static_operation_case22: - forall n n1, - eval_static_operation_cases (Oxorimm n) (I n1 :: nil) - | eval_static_operation_case23: - forall n1 n2, - eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) - | eval_static_operation_case24: - forall n n1, - eval_static_operation_cases (Oshlimm n) (I n1 :: nil) - | eval_static_operation_case25: - forall n1 n2, - eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) - | eval_static_operation_case26: - forall n n1, - eval_static_operation_cases (Oshrimm n) (I n1 :: nil) - | eval_static_operation_case27: - forall n n1, - eval_static_operation_cases (Oshrximm n) (I n1 :: nil) - | eval_static_operation_case28: - forall n1 n2, - eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) - | eval_static_operation_case29: - forall n n1, - eval_static_operation_cases (Oshruimm n) (I n1 :: nil) - | eval_static_operation_case30: - forall n n1, - eval_static_operation_cases (Ororimm n) (I n1 :: nil) - | eval_static_operation_case31: - forall mode vl, - eval_static_operation_cases (Olea mode) (vl) - | eval_static_operation_case32: - forall n1, - eval_static_operation_cases (Onegf) (F n1 :: nil) - | eval_static_operation_case33: - forall n1, - eval_static_operation_cases (Oabsf) (F n1 :: nil) - | eval_static_operation_case34: - forall n1 n2, - eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) - | eval_static_operation_case35: - forall n1 n2, - eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) - | eval_static_operation_case36: - forall n1 n2, - eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) - | eval_static_operation_case37: - forall n1 n2, - eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) - | eval_static_operation_case38: - forall n1, - eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) - | eval_static_operation_case39: - forall n1, - eval_static_operation_cases (Ointoffloat) (F n1 :: nil) - | eval_static_operation_case41: - forall n1, - eval_static_operation_cases (Ofloatofint) (I n1 :: nil) - | eval_static_operation_case43: - forall c vl, - eval_static_operation_cases (Ocmp c) vl - | eval_static_operation_default: - forall (op: operation) (vl: list approx), - eval_static_operation_cases op vl. + | 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 n1, eval_static_operation_cases (Ocast8signed) (I n1 :: nil) + | eval_static_operation_case5: forall n1, eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil) + | eval_static_operation_case6: forall n1, eval_static_operation_cases (Ocast16signed) (I n1 :: nil) + | eval_static_operation_case7: forall n1, eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil) + | eval_static_operation_case8: forall n1, eval_static_operation_cases (Oneg) (I n1 :: nil) + | eval_static_operation_case9: forall n1 n2, eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) + | eval_static_operation_case10: forall s1 n1 n2, eval_static_operation_cases (Osub) (G s1 n1 :: I n2 :: nil) + | eval_static_operation_case11: forall n1 n2, eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) + | eval_static_operation_case12: forall n n1, eval_static_operation_cases (Omulimm n) (I n1 :: nil) + | eval_static_operation_case13: forall n1 n2, eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) + | eval_static_operation_case14: forall n1 n2, eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) + | eval_static_operation_case15: forall n1 n2, eval_static_operation_cases (Omod) (I n1 :: I n2 :: nil) + | eval_static_operation_case16: forall n1 n2, eval_static_operation_cases (Omodu) (I n1 :: I n2 :: nil) + | eval_static_operation_case17: forall n1 n2, eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) + | eval_static_operation_case18: forall n n1, eval_static_operation_cases (Oandimm n) (I n1 :: nil) + | eval_static_operation_case19: forall n1 n2, eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) + | eval_static_operation_case20: forall n n1, eval_static_operation_cases (Oorimm n) (I n1 :: nil) + | eval_static_operation_case21: forall n1 n2, eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) + | eval_static_operation_case22: forall n n1, eval_static_operation_cases (Oxorimm n) (I n1 :: nil) + | eval_static_operation_case23: forall n1 n2, eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) + | eval_static_operation_case24: forall n n1, eval_static_operation_cases (Oshlimm n) (I n1 :: nil) + | eval_static_operation_case25: forall n1 n2, eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) + | eval_static_operation_case26: forall n n1, eval_static_operation_cases (Oshrimm n) (I n1 :: nil) + | eval_static_operation_case27: forall n n1, eval_static_operation_cases (Oshrximm n) (I n1 :: nil) + | eval_static_operation_case28: forall n1 n2, eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) + | eval_static_operation_case29: forall n n1, eval_static_operation_cases (Oshruimm n) (I n1 :: nil) + | eval_static_operation_case30: forall n n1, eval_static_operation_cases (Ororimm n) (I n1 :: nil) + | eval_static_operation_case31: forall mode vl, eval_static_operation_cases (Olea mode) (vl) + | eval_static_operation_case32: forall n1, eval_static_operation_cases (Onegf) (F n1 :: nil) + | eval_static_operation_case33: forall n1, eval_static_operation_cases (Oabsf) (F n1 :: nil) + | eval_static_operation_case34: forall n1 n2, eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) + | eval_static_operation_case35: forall n1 n2, eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) + | eval_static_operation_case36: forall n1 n2, eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) + | eval_static_operation_case37: forall n1 n2, eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) + | eval_static_operation_case38: forall n1, eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) + | eval_static_operation_case39: forall n1, eval_static_operation_cases (Ointoffloat) (F n1 :: nil) + | eval_static_operation_case40: forall n1, eval_static_operation_cases (Ofloatofint) (I n1 :: nil) + | eval_static_operation_case41: forall c vl, eval_static_operation_cases (Ocmp c) (vl) + | 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 - | Ocast8signed, I n1 :: nil => - eval_static_operation_case4 n1 - | Ocast8unsigned, I n1 :: nil => - eval_static_operation_case5 n1 - | Ocast16signed, I n1 :: nil => - eval_static_operation_case6 n1 - | Ocast16unsigned, I n1 :: nil => - eval_static_operation_case7 n1 - | Oneg, I n1 :: nil => - eval_static_operation_case8 n1 - | Osub, I n1 :: I n2 :: nil => - eval_static_operation_case9 n1 n2 - | Osub, S s1 n1 :: I n2 :: nil => - eval_static_operation_case10 s1 n1 n2 - | Omul, I n1 :: I n2 :: nil => - eval_static_operation_case11 n1 n2 - | Omulimm n, I n1 :: nil => - eval_static_operation_case12 n n1 - | Odiv, I n1 :: I n2 :: nil => - eval_static_operation_case13 n1 n2 - | Odivu, I n1 :: I n2 :: nil => - eval_static_operation_case14 n1 n2 - | Omod, I n1 :: I n2 :: nil => - eval_static_operation_case15 n1 n2 - | Omodu, I n1 :: I n2 :: nil => - eval_static_operation_case16 n1 n2 - | Oand, I n1 :: I n2 :: nil => - eval_static_operation_case17 n1 n2 - | Oandimm n, I n1 :: nil => - eval_static_operation_case18 n n1 - | Oor, I n1 :: I n2 :: nil => - eval_static_operation_case19 n1 n2 - | Oorimm n, I n1 :: nil => - eval_static_operation_case20 n n1 - | Oxor, I n1 :: I n2 :: nil => - eval_static_operation_case21 n1 n2 - | Oxorimm n, I n1 :: nil => - eval_static_operation_case22 n n1 - | Oshl, I n1 :: I n2 :: nil => - eval_static_operation_case23 n1 n2 - | Oshlimm n, I n1 :: nil => - eval_static_operation_case24 n n1 - | Oshr, I n1 :: I n2 :: nil => - eval_static_operation_case25 n1 n2 - | Oshrimm n, I n1 :: nil => - eval_static_operation_case26 n n1 - | Oshrximm n, I n1 :: nil => - eval_static_operation_case27 n n1 - | Oshru, I n1 :: I n2 :: nil => - eval_static_operation_case28 n1 n2 - | Oshruimm n, I n1 :: nil => - eval_static_operation_case29 n n1 - | Ororimm n, I n1 :: nil => - eval_static_operation_case30 n n1 - | Olea mode, vl => - eval_static_operation_case31 mode vl - | Onegf, F n1 :: nil => - eval_static_operation_case32 n1 - | Oabsf, F n1 :: nil => - eval_static_operation_case33 n1 - | Oaddf, F n1 :: F n2 :: nil => - eval_static_operation_case34 n1 n2 - | Osubf, F n1 :: F n2 :: nil => - eval_static_operation_case35 n1 n2 - | Omulf, F n1 :: F n2 :: nil => - eval_static_operation_case36 n1 n2 - | Odivf, F n1 :: F n2 :: nil => - eval_static_operation_case37 n1 n2 - | Osingleoffloat, F n1 :: nil => - eval_static_operation_case38 n1 - | Ointoffloat, F n1 :: nil => - eval_static_operation_case39 n1 - | Ofloatofint, I n1 :: nil => - eval_static_operation_case41 n1 - | Ocmp c, vl => - eval_static_operation_case43 c vl - | op, vl => - eval_static_operation_default op vl + match op as zz1, vl as zz2 return eval_static_operation_cases zz1 zz2 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 + | Ocast8signed, I n1 :: nil => eval_static_operation_case4 n1 + | Ocast8unsigned, I n1 :: nil => eval_static_operation_case5 n1 + | Ocast16signed, I n1 :: nil => eval_static_operation_case6 n1 + | Ocast16unsigned, I n1 :: nil => eval_static_operation_case7 n1 + | Oneg, I n1 :: nil => eval_static_operation_case8 n1 + | Osub, I n1 :: I n2 :: nil => eval_static_operation_case9 n1 n2 + | Osub, G s1 n1 :: I n2 :: nil => eval_static_operation_case10 s1 n1 n2 + | Omul, I n1 :: I n2 :: nil => eval_static_operation_case11 n1 n2 + | Omulimm n, I n1 :: nil => eval_static_operation_case12 n n1 + | Odiv, I n1 :: I n2 :: nil => eval_static_operation_case13 n1 n2 + | Odivu, I n1 :: I n2 :: nil => eval_static_operation_case14 n1 n2 + | Omod, I n1 :: I n2 :: nil => eval_static_operation_case15 n1 n2 + | Omodu, I n1 :: I n2 :: nil => eval_static_operation_case16 n1 n2 + | Oand, I n1 :: I n2 :: nil => eval_static_operation_case17 n1 n2 + | Oandimm n, I n1 :: nil => eval_static_operation_case18 n n1 + | Oor, I n1 :: I n2 :: nil => eval_static_operation_case19 n1 n2 + | Oorimm n, I n1 :: nil => eval_static_operation_case20 n n1 + | Oxor, I n1 :: I n2 :: nil => eval_static_operation_case21 n1 n2 + | Oxorimm n, I n1 :: nil => eval_static_operation_case22 n n1 + | Oshl, I n1 :: I n2 :: nil => eval_static_operation_case23 n1 n2 + | Oshlimm n, I n1 :: nil => eval_static_operation_case24 n n1 + | Oshr, I n1 :: I n2 :: nil => eval_static_operation_case25 n1 n2 + | Oshrimm n, I n1 :: nil => eval_static_operation_case26 n n1 + | Oshrximm n, I n1 :: nil => eval_static_operation_case27 n n1 + | Oshru, I n1 :: I n2 :: nil => eval_static_operation_case28 n1 n2 + | Oshruimm n, I n1 :: nil => eval_static_operation_case29 n n1 + | Ororimm n, I n1 :: nil => eval_static_operation_case30 n n1 + | Olea mode, vl => eval_static_operation_case31 mode vl + | Onegf, F n1 :: nil => eval_static_operation_case32 n1 + | Oabsf, F n1 :: nil => eval_static_operation_case33 n1 + | Oaddf, F n1 :: F n2 :: nil => eval_static_operation_case34 n1 n2 + | Osubf, F n1 :: F n2 :: nil => eval_static_operation_case35 n1 n2 + | Omulf, F n1 :: F n2 :: nil => eval_static_operation_case36 n1 n2 + | Odivf, F n1 :: F n2 :: nil => eval_static_operation_case37 n1 n2 + | Osingleoffloat, F n1 :: nil => eval_static_operation_case38 n1 + | Ointoffloat, F n1 :: nil => eval_static_operation_case39 n1 + | Ofloatofint, I n1 :: nil => eval_static_operation_case40 n1 + | Ocmp c, vl => eval_static_operation_case41 c vl + | 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 => + | eval_static_operation_case1 v1 => (* Omove, v1::nil *) v1 - | eval_static_operation_case2 n => + | eval_static_operation_case2 n => (* Ointconst n, nil *) I n - | eval_static_operation_case3 n => + | eval_static_operation_case3 n => (* Ofloatconst n, nil *) F n - | eval_static_operation_case4 n1 => + | eval_static_operation_case4 n1 => (* Ocast8signed, I n1 :: nil *) I(Int.sign_ext 8 n1) - | eval_static_operation_case5 n1 => + | eval_static_operation_case5 n1 => (* Ocast8unsigned, I n1 :: nil *) I(Int.zero_ext 8 n1) - | eval_static_operation_case6 n1 => + | eval_static_operation_case6 n1 => (* Ocast16signed, I n1 :: nil *) I(Int.sign_ext 16 n1) - | eval_static_operation_case7 n1 => + | eval_static_operation_case7 n1 => (* Ocast16unsigned, I n1 :: nil *) I(Int.zero_ext 16 n1) - | eval_static_operation_case8 n1 => + | eval_static_operation_case8 n1 => (* Oneg, I n1 :: nil *) I(Int.neg n1) - | eval_static_operation_case9 n1 n2 => + | eval_static_operation_case9 n1 n2 => (* Osub, I n1 :: I n2 :: nil *) I(Int.sub n1 n2) - | eval_static_operation_case10 s1 n1 n2 => - S s1 (Int.sub n1 n2) - | eval_static_operation_case11 n1 n2 => + | eval_static_operation_case10 s1 n1 n2 => (* Osub, G s1 n1 :: I n2 :: nil *) + G s1 (Int.sub n1 n2) + | eval_static_operation_case11 n1 n2 => (* Omul, I n1 :: I n2 :: nil *) I(Int.mul n1 n2) - | eval_static_operation_case12 n n1 => + | eval_static_operation_case12 n n1 => (* Omulimm n, I n1 :: nil *) I(Int.mul n1 n) - | eval_static_operation_case13 n1 n2 => + | eval_static_operation_case13 n1 n2 => (* Odiv, I n1 :: I n2 :: nil *) if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2) - | eval_static_operation_case14 n1 n2 => + | eval_static_operation_case14 n1 n2 => (* Odivu, I n1 :: I n2 :: nil *) if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2) - | eval_static_operation_case15 n1 n2 => + | eval_static_operation_case15 n1 n2 => (* Omod, I n1 :: I n2 :: nil *) if Int.eq n2 Int.zero then Unknown else I(Int.mods n1 n2) - | eval_static_operation_case16 n1 n2 => + | eval_static_operation_case16 n1 n2 => (* Omodu, I n1 :: I n2 :: nil *) if Int.eq n2 Int.zero then Unknown else I(Int.modu n1 n2) - | eval_static_operation_case17 n1 n2 => + | eval_static_operation_case17 n1 n2 => (* Oand, I n1 :: I n2 :: nil *) I(Int.and n1 n2) - | eval_static_operation_case18 n n1 => + | eval_static_operation_case18 n n1 => (* Oandimm n, I n1 :: nil *) I(Int.and n1 n) - | eval_static_operation_case19 n1 n2 => + | eval_static_operation_case19 n1 n2 => (* Oor, I n1 :: I n2 :: nil *) I(Int.or n1 n2) - | eval_static_operation_case20 n n1 => + | eval_static_operation_case20 n n1 => (* Oorimm n, I n1 :: nil *) I(Int.or n1 n) - | eval_static_operation_case21 n1 n2 => + | eval_static_operation_case21 n1 n2 => (* Oxor, I n1 :: I n2 :: nil *) I(Int.xor n1 n2) - | eval_static_operation_case22 n n1 => + | eval_static_operation_case22 n n1 => (* Oxorimm n, I n1 :: nil *) I(Int.xor n1 n) - | eval_static_operation_case23 n1 n2 => + | eval_static_operation_case23 n1 n2 => (* Oshl, I n1 :: I n2 :: nil *) if Int.ltu n2 Int.iwordsize then I(Int.shl n1 n2) else Unknown - | eval_static_operation_case24 n n1 => + | eval_static_operation_case24 n n1 => (* Oshlimm n, I n1 :: nil *) if Int.ltu n Int.iwordsize then I(Int.shl n1 n) else Unknown - | eval_static_operation_case25 n1 n2 => + | eval_static_operation_case25 n1 n2 => (* Oshr, I n1 :: I n2 :: nil *) if Int.ltu n2 Int.iwordsize then I(Int.shr n1 n2) else Unknown - | eval_static_operation_case26 n n1 => + | eval_static_operation_case26 n n1 => (* Oshrimm n, I n1 :: nil *) if Int.ltu n Int.iwordsize then I(Int.shr n1 n) else Unknown - | eval_static_operation_case27 n n1 => + | eval_static_operation_case27 n n1 => (* Oshrximm n, I n1 :: nil *) if Int.ltu n (Int.repr 31) then I(Int.shrx n1 n) else Unknown - | eval_static_operation_case28 n1 n2 => + | eval_static_operation_case28 n1 n2 => (* Oshru, I n1 :: I n2 :: nil *) if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown - | eval_static_operation_case29 n n1 => + | eval_static_operation_case29 n n1 => (* Oshruimm n, I n1 :: nil *) if Int.ltu n Int.iwordsize then I(Int.shru n1 n) else Unknown - | eval_static_operation_case30 n n1 => + | eval_static_operation_case30 n n1 => (* Ororimm n, I n1 :: nil *) if Int.ltu n Int.iwordsize then I(Int.ror n1 n) else Unknown - | eval_static_operation_case31 mode vl => + | eval_static_operation_case31 mode vl => (* Olea mode, vl *) eval_static_addressing mode vl - | eval_static_operation_case32 n1 => + | eval_static_operation_case32 n1 => (* Onegf, F n1 :: nil *) F(Float.neg n1) - | eval_static_operation_case33 n1 => + | eval_static_operation_case33 n1 => (* Oabsf, F n1 :: nil *) F(Float.abs n1) - | eval_static_operation_case34 n1 n2 => + | eval_static_operation_case34 n1 n2 => (* Oaddf, F n1 :: F n2 :: nil *) F(Float.add n1 n2) - | eval_static_operation_case35 n1 n2 => + | eval_static_operation_case35 n1 n2 => (* Osubf, F n1 :: F n2 :: nil *) F(Float.sub n1 n2) - | eval_static_operation_case36 n1 n2 => + | eval_static_operation_case36 n1 n2 => (* Omulf, F n1 :: F n2 :: nil *) F(Float.mul n1 n2) - | eval_static_operation_case37 n1 n2 => + | eval_static_operation_case37 n1 n2 => (* Odivf, F n1 :: F n2 :: nil *) F(Float.div n1 n2) - | eval_static_operation_case38 n1 => + | eval_static_operation_case38 n1 => (* Osingleoffloat, F n1 :: nil *) F(Float.singleoffloat n1) - | eval_static_operation_case39 n1 => - match Float.intoffloat n1 with Some x => I x | None => Unknown end - | eval_static_operation_case41 n1 => + | eval_static_operation_case39 n1 => (* Ointoffloat, F n1 :: nil *) + eval_static_intoffloat n1 + | eval_static_operation_case40 n1 => (* Ofloatofint, I n1 :: nil *) F(Float.floatofint n1) - | eval_static_operation_case43 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_case41 c vl => (* Ocmp c, vl *) + eval_static_condition_val c vl | eval_static_operation_default op vl => Unknown end. + (** * Operator strength reduction *) (** We now define auxiliary functions for strength reduction of @@ -613,146 +465,178 @@ 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 +(** Original definition: +<< +Nondetfunction cond_strength_reduction + (cond: condition) (args: list reg) (vl: list approx) := + 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) + | _, _, _ => + (cond, args) + end. +>> +*) + +Inductive cond_strength_reduction_cases: forall (cond: condition) (args: list reg) (vl: list approx), Type := + | cond_strength_reduction_case1: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | cond_strength_reduction_case2: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | cond_strength_reduction_case3: forall c r1 r2 n1 v2, cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | cond_strength_reduction_case4: forall c r1 r2 v1 n2, cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | cond_strength_reduction_default: forall (cond: condition) (args: list reg) (vl: list approx), cond_strength_reduction_cases cond args vl. + +Definition cond_strength_reduction_match (cond: condition) (args: list reg) (vl: list approx) := + match cond as zz1, args as zz2, vl as zz3 return cond_strength_reduction_cases zz1 zz2 zz3 with + | Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil => cond_strength_reduction_case1 c r1 r2 n1 v2 + | Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case2 c r1 r2 v1 n2 + | Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil => cond_strength_reduction_case3 c r1 r2 n1 v2 + | Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case4 c r1 r2 v1 n2 + | cond, args, vl => cond_strength_reduction_default cond args vl 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 => +Definition cond_strength_reduction (cond: condition) (args: list reg) (vl: list approx) := + match cond_strength_reduction_match cond args vl with + | cond_strength_reduction_case1 c r1 r2 n1 v2 => (* Ccomp c, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + (Ccompimm (swap_comparison c) n1, r2 :: nil) + | cond_strength_reduction_case2 c r1 r2 v1 n2 => (* Ccomp c, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Ccompimm c n2, r1 :: nil) + | cond_strength_reduction_case3 c r1 r2 n1 v2 => (* Ccompu c, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + (Ccompuimm (swap_comparison c) n1, r2 :: nil) + | cond_strength_reduction_case4 c r1 r2 v1 n2 => (* Ccompu c, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Ccompuimm c n2, r1 :: nil) + | cond_strength_reduction_default cond args vl => (cond, args) end. -(* -Definition addr_strength_reduction (addr: addressing) (args: list reg) := - match addr, args with - | Aindexed ofs, r1 :: nil => (* Aindexed *) - | Aindexed2 ofs, r1 :: r2 :: nil => (* Aindexed2 *) - | Aindexed2scaled sc ofs, r1 :: r2 :: nil => (* Aindexed2scaled *) - | Abased id ofs, r1 :: nil => (* Abased *) - | Abasedscaled sc id ofs, r1 :: nil => (* Abasedscaled *) - | _, _ => (* default *) + +(** Original definition: +<< +Nondetfunction addr_strength_reduction + (addr: addressing) (args: list reg) (vl: list approx) := + match addr, args, vl with + + | Aindexed ofs, r1 :: nil, G symb n :: nil => + (Aglobal symb (Int.add n ofs), nil) + | Aindexed ofs, r1 :: nil, S n :: nil => + (Ainstack (Int.add n ofs), nil) + + | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => + (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil => + (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) + | Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil => + (Ainstack (Int.add (Int.add n1 n2) ofs), nil) + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil => + (Ainstack (Int.add (Int.add n1 n2) ofs), nil) + | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => + (Abased symb (Int.add n1 ofs), r2 :: nil) + | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil => + (Abased symb (Int.add n2 ofs), r1 :: nil) + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => + (Aindexed (Int.add n1 ofs), r2 :: nil) + | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Aindexed (Int.add n2 ofs), r1 :: nil) + + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => + (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil) + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => + (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil) + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil) + + | Abased id ofs, r1 :: nil, I n1 :: nil => + (Aglobal id (Int.add ofs n1), nil) + + | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil => + (Aglobal id (Int.add ofs (Int.mul sc n1)), nil) + + | _, _ => + (addr, args) end. +>> *) -Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg), Type := - | addr_strength_reduction_case1: - forall ofs r1, - addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) - | addr_strength_reduction_case2: - forall ofs r1 r2, - addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) - | addr_strength_reduction_case3: - forall sc ofs r1 r2, - addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) - | addr_strength_reduction_case4: - forall id ofs r1, - addr_strength_reduction_cases (Abased id ofs) (r1 :: nil) - | addr_strength_reduction_case5: - forall sc id ofs r1, - addr_strength_reduction_cases (Abasedscaled sc id ofs) (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 - | Aindexed ofs, r1 :: nil => - addr_strength_reduction_case1 ofs r1 - | Aindexed2 ofs, r1 :: r2 :: nil => - addr_strength_reduction_case2 ofs r1 r2 - | Aindexed2scaled sc ofs, r1 :: r2 :: nil => - addr_strength_reduction_case3 sc ofs r1 r2 - | Abased id ofs, r1 :: nil => - addr_strength_reduction_case4 id ofs r1 - | Abasedscaled sc id ofs, r1 :: nil => - addr_strength_reduction_case5 sc id ofs r1 - | addr, args => - addr_strength_reduction_default addr args +Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg) (vl: list approx), Type := + | addr_strength_reduction_case1: forall ofs r1 symb n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (G symb n :: nil) + | addr_strength_reduction_case2: forall ofs r1 n, addr_strength_reduction_cases (Aindexed ofs) (r1 :: nil) (S n :: nil) + | addr_strength_reduction_case3: forall ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (G symb n1 :: I n2 :: nil) + | addr_strength_reduction_case4: forall ofs r1 r2 n1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: G symb n2 :: nil) + | addr_strength_reduction_case5: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (S n1 :: I n2 :: nil) + | addr_strength_reduction_case6: forall ofs r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: S n2 :: nil) + | addr_strength_reduction_case7: forall ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (G symb n1 :: v2 :: nil) + | addr_strength_reduction_case8: forall ofs r1 r2 v1 symb n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: G symb n2 :: nil) + | addr_strength_reduction_case9: forall ofs r1 r2 n1 v2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | addr_strength_reduction_case10: forall ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2 ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | addr_strength_reduction_case11: forall sc ofs r1 r2 symb n1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (G symb n1 :: I n2 :: nil) + | addr_strength_reduction_case12: forall sc ofs r1 r2 symb n1 v2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (G symb n1 :: v2 :: nil) + | addr_strength_reduction_case13: forall sc ofs r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2scaled sc ofs) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | addr_strength_reduction_case14: forall id ofs r1 n1, addr_strength_reduction_cases (Abased id ofs) (r1 :: nil) (I n1 :: nil) + | addr_strength_reduction_case15: forall sc id ofs r1 n1, addr_strength_reduction_cases (Abasedscaled sc id ofs) (r1 :: nil) (I n1 :: nil) + | addr_strength_reduction_default: forall (addr: addressing) (args: list reg) (vl: list approx), addr_strength_reduction_cases addr args vl. + +Definition addr_strength_reduction_match (addr: addressing) (args: list reg) (vl: list approx) := + match addr as zz1, args as zz2, vl as zz3 return addr_strength_reduction_cases zz1 zz2 zz3 with + | Aindexed ofs, r1 :: nil, G symb n :: nil => addr_strength_reduction_case1 ofs r1 symb n + | Aindexed ofs, r1 :: nil, S n :: nil => addr_strength_reduction_case2 ofs r1 n + | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => addr_strength_reduction_case3 ofs r1 r2 symb n1 n2 + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil => addr_strength_reduction_case4 ofs r1 r2 n1 symb n2 + | Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil => addr_strength_reduction_case5 ofs r1 r2 n1 n2 + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil => addr_strength_reduction_case6 ofs r1 r2 n1 n2 + | Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => addr_strength_reduction_case7 ofs r1 r2 symb n1 v2 + | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil => addr_strength_reduction_case8 ofs r1 r2 v1 symb n2 + | Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_case9 ofs r1 r2 n1 v2 + | Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case10 ofs r1 r2 v1 n2 + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil => addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2 + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil => addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2 + | Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case13 sc ofs r1 r2 v1 n2 + | Abased id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case14 id ofs r1 n1 + | Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil => addr_strength_reduction_case15 sc id ofs r1 n1 + | addr, args, vl => addr_strength_reduction_default addr args vl end. -Definition addr_strength_reduction (addr: addressing) (args: list reg) := - match addr_strength_reduction_match addr args with - | addr_strength_reduction_case1 ofs r1 => - (* Aindexed *) - match app r1 with - | S symb n => (Aglobal symb (Int.add ofs n), nil) - | _ => (addr, args) - end - | addr_strength_reduction_case2 ofs r1 r2 => - (* Aindexed2 *) - match app r1, app r2 with - | S symb n1, I n2 => (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) - | I n1, S symb n2 => (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) - | S symb n1, _ => (Abased symb (Int.add n1 ofs), r2 :: nil) - | _, S symb n2 => (Abased symb (Int.add n2 ofs), r1 :: nil) - | I n1, _ => (Aindexed (Int.add n1 ofs), r2 :: nil) - | _, I n2 => (Aindexed (Int.add n2 ofs), r1 :: nil) - | _, _ => (addr, args) - end - | addr_strength_reduction_case3 sc ofs r1 r2 => - (* Aindexed2scaled *) - match app r1, app r2 with - | S symb n1, I n2 => (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil) - | S symb n1, _ => (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil) - | _, I n2 => (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil) - | _, _ => (addr, args) - end - | addr_strength_reduction_case4 id ofs r1 => - (* Abased *) - match app r1 with - | I n1 => (Aglobal id (Int.add ofs n1), nil) - | _ => (addr, args) - end - | addr_strength_reduction_case5 sc id ofs r1 => - (* Abasedscaled *) - match app r1 with - | I n1 => (Aglobal id (Int.add ofs (Int.mul sc n1)), nil) - | _ => (addr, args) - end - | addr_strength_reduction_default addr args => +Definition addr_strength_reduction (addr: addressing) (args: list reg) (vl: list approx) := + match addr_strength_reduction_match addr args vl with + | addr_strength_reduction_case1 ofs r1 symb n => (* Aindexed ofs, r1 :: nil, G symb n :: nil *) + (Aglobal symb (Int.add n ofs), nil) + | addr_strength_reduction_case2 ofs r1 n => (* Aindexed ofs, r1 :: nil, S n :: nil *) + (Ainstack (Int.add n ofs), nil) + | addr_strength_reduction_case3 ofs r1 r2 symb n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil *) + (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) + | addr_strength_reduction_case4 ofs r1 r2 n1 symb n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: G symb n2 :: nil *) + (Aglobal symb (Int.add (Int.add n1 n2) ofs), nil) + | addr_strength_reduction_case5 ofs r1 r2 n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, S n1 :: I n2 :: nil *) + (Ainstack (Int.add (Int.add n1 n2) ofs), nil) + | addr_strength_reduction_case6 ofs r1 r2 n1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: S n2 :: nil *) + (Ainstack (Int.add (Int.add n1 n2) ofs), nil) + | addr_strength_reduction_case7 ofs r1 r2 symb n1 v2 => (* Aindexed2 ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil *) + (Abased symb (Int.add n1 ofs), r2 :: nil) + | addr_strength_reduction_case8 ofs r1 r2 v1 symb n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, v1 :: G symb n2 :: nil *) + (Abased symb (Int.add n2 ofs), r1 :: nil) + | addr_strength_reduction_case9 ofs r1 r2 n1 v2 => (* Aindexed2 ofs, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + (Aindexed (Int.add n1 ofs), r2 :: nil) + | addr_strength_reduction_case10 ofs r1 r2 v1 n2 => (* Aindexed2 ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Aindexed (Int.add n2 ofs), r1 :: nil) + | addr_strength_reduction_case11 sc ofs r1 r2 symb n1 n2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: I n2 :: nil *) + (Aglobal symb (Int.add (Int.add n1 (Int.mul n2 sc)) ofs), nil) + | addr_strength_reduction_case12 sc ofs r1 r2 symb n1 v2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, G symb n1 :: v2 :: nil *) + (Abasedscaled sc symb (Int.add n1 ofs), r2 :: nil) + | addr_strength_reduction_case13 sc ofs r1 r2 v1 n2 => (* Aindexed2scaled sc ofs, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Aindexed (Int.add (Int.mul n2 sc) ofs), r1 :: nil) + | addr_strength_reduction_case14 id ofs r1 n1 => (* Abased id ofs, r1 :: nil, I n1 :: nil *) + (Aglobal id (Int.add ofs n1), nil) + | addr_strength_reduction_case15 sc id ofs r1 n1 => (* Abasedscaled sc id ofs, r1 :: nil, I n1 :: nil *) + (Aglobal id (Int.add ofs (Int.mul sc n1)), nil) + | addr_strength_reduction_default addr args vl => (addr, args) end. + Definition make_addimm (n: int) (r: reg) := if Int.eq n Int.zero then (Omove, r :: nil) @@ -800,211 +684,122 @@ Definition make_xorimm (n: int) (r: reg) := then (Omove, r :: nil) else (Oxorimm n, r :: nil). -(* -Definition op_strength_reduction (op: operation) (args: list reg) := - match op, args with - | Osub, r1 :: r2 :: nil => (* Osub *) - | Omul, r1 :: r2 :: nil => (* Omul *) - | Odiv, r1 :: r2 :: nil => (* Odiv *) - | Odivu, r1 :: r2 :: nil => (* Odivu *) - | Omodu, r1 :: r2 :: nil => (* Omodu *) - | Oand, r1 :: r2 :: nil => (* Oand *) - | Oor, r1 :: r2 :: nil => (* Oor *) - | Oxor, r1 :: r2 :: nil => (* Oxor *) - | Oshl, r1 :: r2 :: nil => (* Oshl *) - | Oshr, r1 :: r2 :: nil => (* Oshr *) - | Oshru, r1 :: r2 :: nil => (* Oshru *) - | Olea addr, args => (* Olea *) - | Ocmp c, args => (* Ocmp *) - | _, _ => (* default *) +Definition make_divimm n (r1 r2: reg) := + 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 (r1 r2: reg) := + match Int.is_power2 n with + | Some l => make_shruimm l r1 + | None => (Odivu, r1 :: r2 :: nil) end. -*) -Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg), Type := - | op_strength_reduction_case2: - forall r1 r2, - op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) - | op_strength_reduction_case3: - forall r1 r2, - op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) - | op_strength_reduction_case4: - forall r1 r2, - op_strength_reduction_cases (Odiv) (r1 :: r2 :: nil) - | op_strength_reduction_case5: - forall r1 r2, - op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) - | op_strength_reduction_case7: - forall r1 r2, - op_strength_reduction_cases (Omodu) (r1 :: r2 :: nil) - | op_strength_reduction_case8: - forall r1 r2, - op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) - | op_strength_reduction_case9: - forall r1 r2, - op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) - | op_strength_reduction_case10: - forall r1 r2, - op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) - | op_strength_reduction_case11: - forall r1 r2, - op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) - | op_strength_reduction_case12: - forall r1 r2, - op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) - | op_strength_reduction_case13: - forall r1 r2, - op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) - | op_strength_reduction_case14: - forall addr args, - op_strength_reduction_cases (Olea addr) (args) - | op_strength_reduction_case15: - forall c args, - op_strength_reduction_cases (Ocmp c) (args) - | 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 - | 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 - | Omodu, r1 :: r2 :: nil => - op_strength_reduction_case7 r1 r2 - | Oand, r1 :: r2 :: nil => - op_strength_reduction_case8 r1 r2 - | Oor, r1 :: r2 :: nil => - op_strength_reduction_case9 r1 r2 - | Oxor, r1 :: r2 :: nil => - op_strength_reduction_case10 r1 r2 - | Oshl, r1 :: r2 :: nil => - op_strength_reduction_case11 r1 r2 - | Oshr, r1 :: r2 :: nil => - op_strength_reduction_case12 r1 r2 - | Oshru, r1 :: r2 :: nil => - op_strength_reduction_case13 r1 r2 - | Olea addr, args => - op_strength_reduction_case14 addr args - | Ocmp c, args => - op_strength_reduction_case15 c args - | op, args => - op_strength_reduction_default op args +Definition make_moduimm n (r1 r2: reg) := + match Int.is_power2 n with + | Some l => (Oandimm (Int.sub n Int.one), r1 :: nil) + | None => (Omodu, r1 :: r2 :: nil) end. (** We must be careful to preserve 2-address constraints over the RTL code, which means that commutative operations cannot be specialized if their first argument is a constant. *) -Definition op_strength_reduction (op: operation) (args: list reg) := - match op_strength_reduction_match op args with - | op_strength_reduction_case2 r1 r2 => - (* Osub *) - match intval r2 with - | Some n => make_addimm (Int.neg n) r1 - | _ => (op, args) - end - | op_strength_reduction_case3 r1 r2 => - (* Omul *) - match intval r2 with - | 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 => if Int.ltu l (Int.repr 31) - then (Oshrximm l, r1 :: nil) - else (op, args) - | 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_case7 r1 r2 => - (* Omodu *) - match intval r2 with - | Some n => - match Int.is_power2 n with - | Some l => (Oandimm (Int.sub n Int.one), r1 :: nil) - | None => (op, args) - end - | None => - (op, args) - end - | op_strength_reduction_case8 r1 r2 => - (* Oand *) - match intval r2 with - | Some n => make_andimm n r1 - | _ => (op, args) - end - | op_strength_reduction_case9 r1 r2 => - (* Oor *) - match intval r2 with - | Some n => make_orimm n r1 - | _ => (op, args) - end - | op_strength_reduction_case10 r1 r2 => - (* Oxor *) - match intval r2 with - | Some n => make_xorimm n r1 - | _ => (op, args) - end - | op_strength_reduction_case11 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_case12 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_case13 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_case14 addr args => - (* Olea *) - let (addr', args') := addr_strength_reduction addr args in +(** Original definition: +<< +Nondetfunction op_strength_reduction + (op: operation) (args: list reg) (vl: list approx) := + match op, args, vl with + | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1 + | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1 + | 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 + | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_moduimm n2 r1 r2 + | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1 + | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1 + | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1 + | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1 + | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1 + | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 + | Olea addr, args, vl => + let (addr', args') := addr_strength_reduction addr args vl in (Olea addr', args') - | op_strength_reduction_case15 c args => - (* Ocmp *) - let (c', args') := cond_strength_reduction c args in + | Ocmp c, args, vl => + let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args') - | op_strength_reduction_default op args => - (* default *) + | _, _, _ => (op, args) + end. +>> +*) + +Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg) (vl: list approx), Type := + | op_strength_reduction_case1: forall r1 r2 v1 n2, op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case2: forall r1 r2 v1 n2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case3: forall r1 r2 v1 n2, op_strength_reduction_cases (Odiv) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case4: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case5: forall r1 r2 v1 n2, op_strength_reduction_cases (Omodu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case6: forall r1 r2 v1 n2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case7: forall r1 r2 v1 n2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case8: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case9: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case10: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case11: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case12: forall addr args vl, op_strength_reduction_cases (Olea addr) (args) (vl) + | op_strength_reduction_case13: forall c args vl, op_strength_reduction_cases (Ocmp c) (args) (vl) + | op_strength_reduction_default: forall (op: operation) (args: list reg) (vl: list approx), op_strength_reduction_cases op args vl. + +Definition op_strength_reduction_match (op: operation) (args: list reg) (vl: list approx) := + match op as zz1, args as zz2, vl as zz3 return op_strength_reduction_cases zz1 zz2 zz3 with + | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case1 r1 r2 v1 n2 + | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case2 r1 r2 v1 n2 + | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case3 r1 r2 v1 n2 + | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case4 r1 r2 v1 n2 + | Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case5 r1 r2 v1 n2 + | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case6 r1 r2 v1 n2 + | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case7 r1 r2 v1 n2 + | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case8 r1 r2 v1 n2 + | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case9 r1 r2 v1 n2 + | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case10 r1 r2 v1 n2 + | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case11 r1 r2 v1 n2 + | Olea addr, args, vl => op_strength_reduction_case12 addr args vl + | Ocmp c, args, vl => op_strength_reduction_case13 c args vl + | op, args, vl => op_strength_reduction_default op args vl + end. + +Definition op_strength_reduction (op: operation) (args: list reg) (vl: list approx) := + match op_strength_reduction_match op args vl with + | op_strength_reduction_case1 r1 r2 v1 n2 => (* Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_addimm (Int.neg n2) r1 + | op_strength_reduction_case2 r1 r2 v1 n2 => (* Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_mulimm n2 r1 + | op_strength_reduction_case3 r1 r2 v1 n2 => (* Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_divimm n2 r1 r2 + | op_strength_reduction_case4 r1 r2 v1 n2 => (* Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_divuimm n2 r1 r2 + | op_strength_reduction_case5 r1 r2 v1 n2 => (* Omodu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_moduimm n2 r1 r2 + | op_strength_reduction_case6 r1 r2 v1 n2 => (* Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_andimm n2 r1 + | op_strength_reduction_case7 r1 r2 v1 n2 => (* Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_orimm n2 r1 + | op_strength_reduction_case8 r1 r2 v1 n2 => (* Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_xorimm n2 r1 + | op_strength_reduction_case9 r1 r2 v1 n2 => (* Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shlimm n2 r1 + | op_strength_reduction_case10 r1 r2 v1 n2 => (* Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shrimm n2 r1 + | op_strength_reduction_case11 r1 r2 v1 n2 => (* Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shruimm n2 r1 + | op_strength_reduction_case12 addr args vl => (* Olea addr, args, vl *) + let (addr', args') := addr_strength_reduction addr args vl in (Olea addr', args') + | op_strength_reduction_case13 c args vl => (* Ocmp c, args, vl *) + let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args') + | op_strength_reduction_default op args vl => (op, args) end. + End STRENGTH_REDUCTION. |