diff options
Diffstat (limited to 'arm/ConstpropOp.v')
| -rw-r--r-- | arm/ConstpropOp.v | 1407 |
1 files changed, 584 insertions, 823 deletions
diff --git a/arm/ConstpropOp.v b/arm/ConstpropOp.v index 86b6d66..9e51e25 100644 --- a/arm/ConstpropOp.v +++ b/arm/ConstpropOp.v @@ -32,9 +32,11 @@ 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 @@ -44,140 +46,140 @@ 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 [Selection] 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) := +Definition eval_static_shift (s: shift) (n: int) : int := + match s with + | Slsl x => Int.shl n x + | Slsr x => Int.shru n x + | Sasr x => Int.shr n x + | Sror x => Int.ror n x + end. + +(** 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) - | Ccompshift c s, I n1 :: I n2 :: nil => Some(Int.cmp c n1 (eval_shift s n2)) - | Ccompushift c s, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 (eval_shift s n2)) + | Ccompshift c s, I n1 :: I n2 :: nil => Some(Int.cmp c n1 (eval_static_shift s n2)) + | Ccompushift c s, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 (eval_static_shift s 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)) | _, _ => 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 s n1 n2, - eval_static_condition_cases (Ccompshift c s) (I n1 :: I n2 :: nil) - | eval_static_condition_case4: - forall c s n1 n2, - eval_static_condition_cases (Ccompushift c s) (I n1 :: I n2 :: nil) - | eval_static_condition_case5: - forall c n n1, - eval_static_condition_cases (Ccompimm c n) (I n1 :: nil) - | eval_static_condition_case6: - forall c n n1, - eval_static_condition_cases (Ccompuimm c n) (I n1 :: nil) - | eval_static_condition_case7: - forall c n1 n2, - eval_static_condition_cases (Ccompf c) (F n1 :: F n2 :: nil) - | eval_static_condition_case8: - forall c n1 n2, - eval_static_condition_cases (Cnotcompf c) (F n1 :: F n2 :: 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 s n1 n2, eval_static_condition_cases (Ccompshift c s) (I n1 :: I n2 :: nil) + | eval_static_condition_case4: forall c s n1 n2, eval_static_condition_cases (Ccompushift c s) (I n1 :: I n2 :: nil) + | eval_static_condition_case5: forall c n n1, eval_static_condition_cases (Ccompimm c n) (I n1 :: nil) + | eval_static_condition_case6: forall c n n1, eval_static_condition_cases (Ccompuimm c n) (I n1 :: nil) + | eval_static_condition_case7: forall c n1 n2, eval_static_condition_cases (Ccompf c) (F n1 :: F n2 :: nil) + | eval_static_condition_case8: forall c n1 n2, eval_static_condition_cases (Cnotcompf c) (F n1 :: F n2 :: 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 - | Ccompshift c s, I n1 :: I n2 :: nil => - eval_static_condition_case3 c s n1 n2 - | Ccompushift c s, I n1 :: I n2 :: nil => - eval_static_condition_case4 c s n1 n2 - | Ccompimm c n, I n1 :: nil => - eval_static_condition_case5 c n n1 - | Ccompuimm c n, I n1 :: nil => - eval_static_condition_case6 c n n1 - | Ccompf c, F n1 :: F n2 :: nil => - eval_static_condition_case7 c n1 n2 - | Cnotcompf c, F n1 :: F n2 :: nil => - eval_static_condition_case8 c n1 n2 - | 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 + | Ccompshift c s, I n1 :: I n2 :: nil => eval_static_condition_case3 c s n1 n2 + | Ccompushift c s, I n1 :: I n2 :: nil => eval_static_condition_case4 c s n1 n2 + | Ccompimm c n, I n1 :: nil => eval_static_condition_case5 c n n1 + | Ccompuimm c n, I n1 :: nil => eval_static_condition_case6 c n n1 + | Ccompf c, F n1 :: F n2 :: nil => eval_static_condition_case7 c n1 n2 + | Cnotcompf c, F n1 :: F n2 :: nil => eval_static_condition_case8 c n1 n2 + | 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 s n1 n2 => - Some(Int.cmp c n1 (eval_shift s n2)) - | eval_static_condition_case4 c s n1 n2 => - Some(Int.cmpu c n1 (eval_shift s n2)) - | eval_static_condition_case5 c n n1 => + | eval_static_condition_case3 c s n1 n2 => (* Ccompshift c s, I n1 :: I n2 :: nil *) + Some(Int.cmp c n1 (eval_static_shift s n2)) + | eval_static_condition_case4 c s n1 n2 => (* Ccompushift c s, I n1 :: I n2 :: nil *) + Some(Int.cmpu c n1 (eval_static_shift s n2)) + | eval_static_condition_case5 c n n1 => (* Ccompimm c n, I n1 :: nil *) Some(Int.cmp c n1 n) - | eval_static_condition_case6 c n n1 => + | eval_static_condition_case6 c n n1 => (* Ccompuimm c n, I n1 :: nil *) Some(Int.cmpu c n1 n) - | eval_static_condition_case7 c n1 n2 => + | eval_static_condition_case7 c n1 n2 => (* Ccompf c, F n1 :: F n2 :: nil *) Some(Float.cmp c n1 n2) - | eval_static_condition_case8 c n1 n2 => + | eval_static_condition_case8 c n1 n2 => (* Cnotcompf c, F n1 :: F n2 :: nil *) Some(negb(Float.cmp c n1 n2)) | eval_static_condition_default cond vl => None end. -(* -Definition eval_static_operation (op: operation) (vl: list approx) := + +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. + +Definition eval_static_intuoffloat (f: float) := + match Float.intuoffloat f with Some x => I x | None => Unknown end. + +(** Original definition: +<< +Nondetfunction 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) + | Oaddrsymbol s n, nil => G s n + | Oaddrstack n, nil => S n | Oadd, I n1 :: I n2 :: nil => I(Int.add n1 n2) - | Oaddshift s, I n1 :: I n2 :: nil => I(Int.add n1 (eval_shift s n2)) - | Oadd, S s1 n1 :: I n2 :: nil => S s1 (Int.add n1 n2) - | Oaddshift s, S s1 n1 :: I n2 :: nil => S s1 (Int.add n1 (eval_shift s n2)) + | Oaddshift s, I n1 :: I n2 :: nil => I(Int.add n1 (eval_static_shift s n2)) + | Oadd, G s1 n1 :: I n2 :: nil => G s1 (Int.add n1 n2) + | Oaddshift s, G s1 n1 :: I n2 :: nil => G s1 (Int.add n1 (eval_static_shift s n2)) + | Oadd, S n1 :: I n2 :: nil => S (Int.add n1 n2) + | Oaddshift s, S n1 :: I n2 :: nil => S (Int.add n1 (eval_static_shift s n2)) + | Oadd, I n1 :: G s2 n2 :: nil => G s2 (Int.add n1 n2) + | Oadd, I n1 :: S n2 :: nil => S (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) + | Oaddimm n, G s1 n1 :: nil => G s1 (Int.add n1 n) + | Oaddimm n, S n1 :: nil => S (Int.add n1 n) | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2) - | Osubshift s, I n1 :: I n2 :: nil => I(Int.sub n1 (eval_shift s n2)) - | Osub, S s1 n1 :: I n2 :: nil => S s1 (Int.sub n1 n2) - | Osubshift s, S s1 n1 :: I n2 :: nil => S s1 (Int.sub n1 (eval_shift s n2)) - | Orsubshift s, I n1 :: I n2 :: nil => I(Int.sub (eval_shift s n2) n1) + | Osubshift s, I n1 :: I n2 :: nil => I(Int.sub n1 (eval_static_shift s n2)) + | Osub, G s1 n1 :: I n2 :: nil => G s1 (Int.sub n1 n2) + | Osub, S n1 :: I n2 :: nil => S (Int.sub n1 n2) + | Osubshift s, G s1 n1 :: I n2 :: nil => G s1 (Int.sub n1 (eval_static_shift s n2)) + | Orsubshift s, I n1 :: I n2 :: nil => I(Int.sub (eval_static_shift s n2) n1) | Orsubimm n, I n1 :: nil => I (Int.sub n n1) | Omul, I n1 :: I n2 :: nil => I(Int.mul n1 n2) | 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) - | Oandshift s, I n1 :: I n2 :: nil => I(Int.and n1 (eval_shift s n2)) + | Oandshift s, I n1 :: I n2 :: nil => I(Int.and n1 (eval_static_shift s n2)) | Oandimm n, I n1 :: nil => I(Int.and n1 n) | Oor, I n1 :: I n2 :: nil => I(Int.or n1 n2) - | Oorshift s, I n1 :: I n2 :: nil => I(Int.or n1 (eval_shift s n2)) + | Oorshift s, I n1 :: I n2 :: nil => I(Int.or n1 (eval_static_shift s n2)) | Oorimm n, I n1 :: nil => I(Int.or n1 n) | Oxor, I n1 :: I n2 :: nil => I(Int.xor n1 n2) - | Oxorshift s, I n1 :: I n2 :: nil => I(Int.xor n1 (eval_shift s n2)) + | Oxorshift s, I n1 :: I n2 :: nil => I(Int.xor n1 (eval_static_shift s n2)) | Oxorimm n, I n1 :: nil => I(Int.xor n1 n) | Obic, I n1 :: I n2 :: nil => I(Int.and n1 (Int.not n2)) - | Obicshift s, I n1 :: I n2 :: nil => I(Int.and n1 (Int.not (eval_shift s n2))) + | Obicshift s, I n1 :: I n2 :: nil => I(Int.and n1 (Int.not (eval_static_shift s n2))) | Onot, I n1 :: nil => I(Int.not n1) - | Onotshift s, I n1 :: nil => I(Int.not (eval_shift s n1)) + | Onotshift s, I n1 :: nil => I(Int.not (eval_static_shift s n1)) | 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 | Oshru, I n1 :: I n2 :: nil => if Int.ltu n2 Int.iwordsize then I(Int.shru n1 n2) else Unknown - | Oshift s, I n1 :: nil => I(eval_shift s n1) + | Oshift s, I n1 :: nil => I(eval_static_shift s n1) | 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) @@ -185,409 +187,251 @@ 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 + | Ointuoffloat, F n1 :: nil => eval_static_intuoffloat n1 | Ofloatofint, I n1 :: nil => F(Float.floatofint n1) | Ofloatofintu, I n1 :: nil => F(Float.floatofintu 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 s n, - eval_static_operation_cases (Oaddrsymbol s n) (nil) - | eval_static_operation_case5: - forall n1, - eval_static_operation_cases (Ocast8signed) (I n1 :: nil) - | eval_static_operation_case6: - forall n1, - eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil) - | eval_static_operation_case7: - forall n1, - eval_static_operation_cases (Ocast16signed) (I n1 :: nil) - | eval_static_operation_case8: - forall n1, - eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil) - | eval_static_operation_case9: - forall n1 n2, - eval_static_operation_cases (Oadd) (I n1 :: I n2 :: nil) - | eval_static_operation_case10: - forall s n1 n2, - eval_static_operation_cases (Oaddshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case11: - forall s1 n1 n2, - eval_static_operation_cases (Oadd) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case12: - forall s s1 n1 n2, - eval_static_operation_cases (Oaddshift s) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case13: - forall n n1, - eval_static_operation_cases (Oaddimm n) (I n1 :: nil) - | eval_static_operation_case14: - forall n s1 n1, - eval_static_operation_cases (Oaddimm n) (S s1 n1 :: nil) - | eval_static_operation_case15: - forall n1 n2, - eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) - | eval_static_operation_case16: - forall s n1 n2, - eval_static_operation_cases (Osubshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case17: - forall s1 n1 n2, - eval_static_operation_cases (Osub) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case18: - forall s s1 n1 n2, - eval_static_operation_cases (Osubshift s) (S s1 n1 :: I n2 :: nil) - | eval_static_operation_case19: - forall s n1 n2, - eval_static_operation_cases (Orsubshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case20: - forall n n1, - eval_static_operation_cases (Orsubimm n) (I n1 :: nil) - | eval_static_operation_case21: - forall n1 n2, - eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) - | eval_static_operation_case22: - forall n1 n2, - eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) - | eval_static_operation_case23: - forall n1 n2, - eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) - | eval_static_operation_case24: - forall n1 n2, - eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) - | eval_static_operation_case25: - forall s n1 n2, - eval_static_operation_cases (Oandshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case26: - forall n n1, - eval_static_operation_cases (Oandimm n) (I n1 :: nil) - | eval_static_operation_case27: - forall n1 n2, - eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) - | eval_static_operation_case28: - forall s n1 n2, - eval_static_operation_cases (Oorshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case29: - forall n n1, - eval_static_operation_cases (Oorimm n) (I n1 :: nil) - | eval_static_operation_case30: - forall n1 n2, - eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) - | eval_static_operation_case31: - forall s n1 n2, - eval_static_operation_cases (Oxorshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case32: - forall n n1, - eval_static_operation_cases (Oxorimm n) (I n1 :: nil) - | eval_static_operation_case33: - forall n1 n2, - eval_static_operation_cases (Obic) (I n1 :: I n2 :: nil) - | eval_static_operation_case34: - forall s n1 n2, - eval_static_operation_cases (Obicshift s) (I n1 :: I n2 :: nil) - | eval_static_operation_case35: - forall n1, - eval_static_operation_cases (Onot) (I n1 :: nil) - | eval_static_operation_case36: - forall s n1, - eval_static_operation_cases (Onotshift s) (I n1 :: nil) - | eval_static_operation_case37: - forall n1 n2, - eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) - | eval_static_operation_case38: - forall n1 n2, - eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) - | eval_static_operation_case39: - forall n1 n2, - eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) - | eval_static_operation_case40: - forall s n1, - eval_static_operation_cases (Oshift s) (I n1 :: nil) - | eval_static_operation_case41: - forall n1, - eval_static_operation_cases (Onegf) (F n1 :: nil) - | eval_static_operation_case42: - forall n1, - eval_static_operation_cases (Oabsf) (F n1 :: nil) - | eval_static_operation_case43: - forall n1 n2, - eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) - | eval_static_operation_case44: - forall n1 n2, - eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) - | eval_static_operation_case45: - forall n1 n2, - eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) - | eval_static_operation_case46: - forall n1 n2, - eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) - | eval_static_operation_case47: - forall n1, - eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) - | eval_static_operation_case48: - forall n1, - eval_static_operation_cases (Ointoffloat) (F n1 :: nil) - | eval_static_operation_case49: - forall n1, - eval_static_operation_cases (Ofloatofint) (I n1 :: nil) - | eval_static_operation_case50: - forall n1, - eval_static_operation_cases (Ointuoffloat) (F n1 :: nil) - | eval_static_operation_case53: - forall n1, - eval_static_operation_cases (Ofloatofintu) (I n1 :: nil) - | eval_static_operation_case51: - forall c vl, - eval_static_operation_cases (Ocmp c) (vl) - | eval_static_operation_case52: - forall n n1, - eval_static_operation_cases (Oshrximm n) (I n1 :: nil) - | 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 s n, eval_static_operation_cases (Oaddrsymbol s n) (nil) + | eval_static_operation_case5: forall n, eval_static_operation_cases (Oaddrstack n) (nil) + | eval_static_operation_case6: forall n1 n2, eval_static_operation_cases (Oadd) (I n1 :: I n2 :: nil) + | eval_static_operation_case7: forall s n1 n2, eval_static_operation_cases (Oaddshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case8: forall s1 n1 n2, eval_static_operation_cases (Oadd) (G s1 n1 :: I n2 :: nil) + | eval_static_operation_case9: forall s s1 n1 n2, eval_static_operation_cases (Oaddshift s) (G s1 n1 :: I n2 :: nil) + | eval_static_operation_case10: forall n1 n2, eval_static_operation_cases (Oadd) (S n1 :: I n2 :: nil) + | eval_static_operation_case11: forall s n1 n2, eval_static_operation_cases (Oaddshift s) (S n1 :: I n2 :: nil) + | eval_static_operation_case12: forall n1 s2 n2, eval_static_operation_cases (Oadd) (I n1 :: G s2 n2 :: nil) + | eval_static_operation_case13: forall n1 n2, eval_static_operation_cases (Oadd) (I n1 :: S n2 :: nil) + | eval_static_operation_case14: forall n n1, eval_static_operation_cases (Oaddimm n) (I n1 :: nil) + | eval_static_operation_case15: forall n s1 n1, eval_static_operation_cases (Oaddimm n) (G s1 n1 :: nil) + | eval_static_operation_case16: forall n n1, eval_static_operation_cases (Oaddimm n) (S n1 :: nil) + | eval_static_operation_case17: forall n1 n2, eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) + | eval_static_operation_case18: forall s n1 n2, eval_static_operation_cases (Osubshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case19: forall s1 n1 n2, eval_static_operation_cases (Osub) (G s1 n1 :: I n2 :: nil) + | eval_static_operation_case20: forall n1 n2, eval_static_operation_cases (Osub) (S n1 :: I n2 :: nil) + | eval_static_operation_case21: forall s s1 n1 n2, eval_static_operation_cases (Osubshift s) (G s1 n1 :: I n2 :: nil) + | eval_static_operation_case22: forall s n1 n2, eval_static_operation_cases (Orsubshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case23: forall n n1, eval_static_operation_cases (Orsubimm n) (I n1 :: nil) + | eval_static_operation_case24: forall n1 n2, eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) + | eval_static_operation_case25: forall n1 n2, eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) + | eval_static_operation_case26: forall n1 n2, eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) + | eval_static_operation_case27: forall n1 n2, eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) + | eval_static_operation_case28: forall s n1 n2, eval_static_operation_cases (Oandshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case29: forall n n1, eval_static_operation_cases (Oandimm n) (I n1 :: nil) + | eval_static_operation_case30: forall n1 n2, eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) + | eval_static_operation_case31: forall s n1 n2, eval_static_operation_cases (Oorshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case32: forall n n1, eval_static_operation_cases (Oorimm n) (I n1 :: nil) + | eval_static_operation_case33: forall n1 n2, eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) + | eval_static_operation_case34: forall s n1 n2, eval_static_operation_cases (Oxorshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case35: forall n n1, eval_static_operation_cases (Oxorimm n) (I n1 :: nil) + | eval_static_operation_case36: forall n1 n2, eval_static_operation_cases (Obic) (I n1 :: I n2 :: nil) + | eval_static_operation_case37: forall s n1 n2, eval_static_operation_cases (Obicshift s) (I n1 :: I n2 :: nil) + | eval_static_operation_case38: forall n1, eval_static_operation_cases (Onot) (I n1 :: nil) + | eval_static_operation_case39: forall s n1, eval_static_operation_cases (Onotshift s) (I n1 :: nil) + | eval_static_operation_case40: forall n1 n2, eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) + | eval_static_operation_case41: forall n1 n2, eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) + | eval_static_operation_case42: forall n1 n2, eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) + | eval_static_operation_case43: forall s n1, eval_static_operation_cases (Oshift s) (I n1 :: nil) + | eval_static_operation_case44: forall n1, eval_static_operation_cases (Onegf) (F n1 :: nil) + | eval_static_operation_case45: forall n1, eval_static_operation_cases (Oabsf) (F n1 :: nil) + | eval_static_operation_case46: forall n1 n2, eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) + | eval_static_operation_case47: forall n1 n2, eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) + | eval_static_operation_case48: forall n1 n2, eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) + | eval_static_operation_case49: forall n1 n2, eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) + | eval_static_operation_case50: forall n1, eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) + | eval_static_operation_case51: forall n1, eval_static_operation_cases (Ointoffloat) (F n1 :: nil) + | eval_static_operation_case52: forall n1, eval_static_operation_cases (Ointuoffloat) (F n1 :: nil) + | eval_static_operation_case53: forall n1, eval_static_operation_cases (Ofloatofint) (I n1 :: nil) + | eval_static_operation_case54: forall n1, eval_static_operation_cases (Ofloatofintu) (I n1 :: nil) + | eval_static_operation_case55: 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 - | Oaddrsymbol s n, nil => - eval_static_operation_case4 s n - | Ocast8signed, I n1 :: nil => - eval_static_operation_case5 n1 - | Ocast8unsigned, I n1 :: nil => - eval_static_operation_case6 n1 - | Ocast16signed, I n1 :: nil => - eval_static_operation_case7 n1 - | Ocast16unsigned, I n1 :: nil => - eval_static_operation_case8 n1 - | Oadd, I n1 :: I n2 :: nil => - eval_static_operation_case9 n1 n2 - | Oaddshift s, I n1 :: I n2 :: nil => - eval_static_operation_case10 s n1 n2 - | Oadd, S s1 n1 :: I n2 :: nil => - eval_static_operation_case11 s1 n1 n2 - | Oaddshift s, S s1 n1 :: I n2 :: nil => - eval_static_operation_case12 s s1 n1 n2 - | Oaddimm n, I n1 :: nil => - eval_static_operation_case13 n n1 - | Oaddimm n, S s1 n1 :: nil => - eval_static_operation_case14 n s1 n1 - | Osub, I n1 :: I n2 :: nil => - eval_static_operation_case15 n1 n2 - | Osubshift s, I n1 :: I n2 :: nil => - eval_static_operation_case16 s n1 n2 - | Osub, S s1 n1 :: I n2 :: nil => - eval_static_operation_case17 s1 n1 n2 - | Osubshift s, S s1 n1 :: I n2 :: nil => - eval_static_operation_case18 s s1 n1 n2 - | Orsubshift s, I n1 :: I n2 :: nil => - eval_static_operation_case19 s n1 n2 - | Orsubimm n, I n1 :: nil => - eval_static_operation_case20 n n1 - | Omul, I n1 :: I n2 :: nil => - eval_static_operation_case21 n1 n2 - | Odiv, I n1 :: I n2 :: nil => - eval_static_operation_case22 n1 n2 - | Odivu, I n1 :: I n2 :: nil => - eval_static_operation_case23 n1 n2 - | Oand, I n1 :: I n2 :: nil => - eval_static_operation_case24 n1 n2 - | Oandshift s, I n1 :: I n2 :: nil => - eval_static_operation_case25 s n1 n2 - | Oandimm n, I n1 :: nil => - eval_static_operation_case26 n n1 - | Oor, I n1 :: I n2 :: nil => - eval_static_operation_case27 n1 n2 - | Oorshift s, I n1 :: I n2 :: nil => - eval_static_operation_case28 s n1 n2 - | Oorimm n, I n1 :: nil => - eval_static_operation_case29 n n1 - | Oxor, I n1 :: I n2 :: nil => - eval_static_operation_case30 n1 n2 - | Oxorshift s, I n1 :: I n2 :: nil => - eval_static_operation_case31 s n1 n2 - | Oxorimm n, I n1 :: nil => - eval_static_operation_case32 n n1 - | Obic, I n1 :: I n2 :: nil => - eval_static_operation_case33 n1 n2 - | Obicshift s, I n1 :: I n2 :: nil => - eval_static_operation_case34 s n1 n2 - | Onot, I n1 :: nil => - eval_static_operation_case35 n1 - | Onotshift s, I n1 :: nil => - eval_static_operation_case36 s n1 - | Oshl, I n1 :: I n2 :: nil => - eval_static_operation_case37 n1 n2 - | Oshr, I n1 :: I n2 :: nil => - eval_static_operation_case38 n1 n2 - | Oshru, I n1 :: I n2 :: nil => - eval_static_operation_case39 n1 n2 - | Oshift s, I n1 :: nil => - eval_static_operation_case40 s n1 - | Onegf, F n1 :: nil => - eval_static_operation_case41 n1 - | Oabsf, F n1 :: nil => - eval_static_operation_case42 n1 - | Oaddf, F n1 :: F n2 :: nil => - eval_static_operation_case43 n1 n2 - | Osubf, F n1 :: F n2 :: nil => - eval_static_operation_case44 n1 n2 - | Omulf, F n1 :: F n2 :: nil => - eval_static_operation_case45 n1 n2 - | Odivf, F n1 :: F n2 :: nil => - eval_static_operation_case46 n1 n2 - | Osingleoffloat, F n1 :: nil => - eval_static_operation_case47 n1 - | Ointoffloat, F n1 :: nil => - eval_static_operation_case48 n1 - | Ofloatofint, I n1 :: nil => - eval_static_operation_case49 n1 - | Ointuoffloat, F n1 :: nil => - eval_static_operation_case50 n1 - | Ofloatofintu, I n1 :: nil => - eval_static_operation_case53 n1 - | Ocmp c, vl => - eval_static_operation_case51 c vl - | Oshrximm n, I n1 :: nil => - eval_static_operation_case52 n n1 - | 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 + | Oaddrsymbol s n, nil => eval_static_operation_case4 s n + | Oaddrstack n, nil => eval_static_operation_case5 n + | Oadd, I n1 :: I n2 :: nil => eval_static_operation_case6 n1 n2 + | Oaddshift s, I n1 :: I n2 :: nil => eval_static_operation_case7 s n1 n2 + | Oadd, G s1 n1 :: I n2 :: nil => eval_static_operation_case8 s1 n1 n2 + | Oaddshift s, G s1 n1 :: I n2 :: nil => eval_static_operation_case9 s s1 n1 n2 + | Oadd, S n1 :: I n2 :: nil => eval_static_operation_case10 n1 n2 + | Oaddshift s, S n1 :: I n2 :: nil => eval_static_operation_case11 s n1 n2 + | Oadd, I n1 :: G s2 n2 :: nil => eval_static_operation_case12 n1 s2 n2 + | Oadd, I n1 :: S n2 :: nil => eval_static_operation_case13 n1 n2 + | Oaddimm n, I n1 :: nil => eval_static_operation_case14 n n1 + | Oaddimm n, G s1 n1 :: nil => eval_static_operation_case15 n s1 n1 + | Oaddimm n, S n1 :: nil => eval_static_operation_case16 n n1 + | Osub, I n1 :: I n2 :: nil => eval_static_operation_case17 n1 n2 + | Osubshift s, I n1 :: I n2 :: nil => eval_static_operation_case18 s n1 n2 + | Osub, G s1 n1 :: I n2 :: nil => eval_static_operation_case19 s1 n1 n2 + | Osub, S n1 :: I n2 :: nil => eval_static_operation_case20 n1 n2 + | Osubshift s, G s1 n1 :: I n2 :: nil => eval_static_operation_case21 s s1 n1 n2 + | Orsubshift s, I n1 :: I n2 :: nil => eval_static_operation_case22 s n1 n2 + | Orsubimm n, I n1 :: nil => eval_static_operation_case23 n n1 + | Omul, I n1 :: I n2 :: nil => eval_static_operation_case24 n1 n2 + | Odiv, I n1 :: I n2 :: nil => eval_static_operation_case25 n1 n2 + | Odivu, I n1 :: I n2 :: nil => eval_static_operation_case26 n1 n2 + | Oand, I n1 :: I n2 :: nil => eval_static_operation_case27 n1 n2 + | Oandshift s, I n1 :: I n2 :: nil => eval_static_operation_case28 s n1 n2 + | Oandimm n, I n1 :: nil => eval_static_operation_case29 n n1 + | Oor, I n1 :: I n2 :: nil => eval_static_operation_case30 n1 n2 + | Oorshift s, I n1 :: I n2 :: nil => eval_static_operation_case31 s n1 n2 + | Oorimm n, I n1 :: nil => eval_static_operation_case32 n n1 + | Oxor, I n1 :: I n2 :: nil => eval_static_operation_case33 n1 n2 + | Oxorshift s, I n1 :: I n2 :: nil => eval_static_operation_case34 s n1 n2 + | Oxorimm n, I n1 :: nil => eval_static_operation_case35 n n1 + | Obic, I n1 :: I n2 :: nil => eval_static_operation_case36 n1 n2 + | Obicshift s, I n1 :: I n2 :: nil => eval_static_operation_case37 s n1 n2 + | Onot, I n1 :: nil => eval_static_operation_case38 n1 + | Onotshift s, I n1 :: nil => eval_static_operation_case39 s n1 + | Oshl, I n1 :: I n2 :: nil => eval_static_operation_case40 n1 n2 + | Oshr, I n1 :: I n2 :: nil => eval_static_operation_case41 n1 n2 + | Oshru, I n1 :: I n2 :: nil => eval_static_operation_case42 n1 n2 + | Oshift s, I n1 :: nil => eval_static_operation_case43 s n1 + | Onegf, F n1 :: nil => eval_static_operation_case44 n1 + | Oabsf, F n1 :: nil => eval_static_operation_case45 n1 + | Oaddf, F n1 :: F n2 :: nil => eval_static_operation_case46 n1 n2 + | Osubf, F n1 :: F n2 :: nil => eval_static_operation_case47 n1 n2 + | Omulf, F n1 :: F n2 :: nil => eval_static_operation_case48 n1 n2 + | Odivf, F n1 :: F n2 :: nil => eval_static_operation_case49 n1 n2 + | Osingleoffloat, F n1 :: nil => eval_static_operation_case50 n1 + | Ointoffloat, F n1 :: nil => eval_static_operation_case51 n1 + | Ointuoffloat, F n1 :: nil => eval_static_operation_case52 n1 + | Ofloatofint, I n1 :: nil => eval_static_operation_case53 n1 + | Ofloatofintu, I n1 :: nil => eval_static_operation_case54 n1 + | Ocmp c, vl => eval_static_operation_case55 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 s n => - S s n - | eval_static_operation_case5 n => - I(Int.sign_ext 8 n) - | eval_static_operation_case6 n => - I(Int.zero_ext 8 n) - | eval_static_operation_case7 n => - I(Int.sign_ext 16 n) - | eval_static_operation_case8 n => - I(Int.zero_ext 16 n) - | eval_static_operation_case9 n1 n2 => + | eval_static_operation_case4 s n => (* Oaddrsymbol s n, nil *) + G s n + | eval_static_operation_case5 n => (* Oaddrstack n, nil *) + S n + | eval_static_operation_case6 n1 n2 => (* Oadd, I n1 :: I n2 :: nil *) I(Int.add n1 n2) - | eval_static_operation_case10 s n1 n2 => - I(Int.add n1 (eval_shift s n2)) - | eval_static_operation_case11 s1 n1 n2 => - S s1 (Int.add n1 n2) - | eval_static_operation_case12 s s1 n1 n2 => - S s1 (Int.add n1 (eval_shift s n2)) - | eval_static_operation_case13 n n1 => + | eval_static_operation_case7 s n1 n2 => (* Oaddshift s, I n1 :: I n2 :: nil *) + I(Int.add n1 (eval_static_shift s n2)) + | eval_static_operation_case8 s1 n1 n2 => (* Oadd, G s1 n1 :: I n2 :: nil *) + G s1 (Int.add n1 n2) + | eval_static_operation_case9 s s1 n1 n2 => (* Oaddshift s, G s1 n1 :: I n2 :: nil *) + G s1 (Int.add n1 (eval_static_shift s n2)) + | eval_static_operation_case10 n1 n2 => (* Oadd, S n1 :: I n2 :: nil *) + S (Int.add n1 n2) + | eval_static_operation_case11 s n1 n2 => (* Oaddshift s, S n1 :: I n2 :: nil *) + S (Int.add n1 (eval_static_shift s n2)) + | eval_static_operation_case12 n1 s2 n2 => (* Oadd, I n1 :: G s2 n2 :: nil *) + G s2 (Int.add n1 n2) + | eval_static_operation_case13 n1 n2 => (* Oadd, I n1 :: S n2 :: nil *) + S (Int.add n1 n2) + | eval_static_operation_case14 n n1 => (* Oaddimm n, I n1 :: nil *) I (Int.add n1 n) - | eval_static_operation_case14 n s1 n1 => - S s1 (Int.add n1 n) - | eval_static_operation_case15 n1 n2 => + | eval_static_operation_case15 n s1 n1 => (* Oaddimm n, G s1 n1 :: nil *) + G s1 (Int.add n1 n) + | eval_static_operation_case16 n n1 => (* Oaddimm n, S n1 :: nil *) + S (Int.add n1 n) + | eval_static_operation_case17 n1 n2 => (* Osub, I n1 :: I n2 :: nil *) I(Int.sub n1 n2) - | eval_static_operation_case16 s n1 n2 => - I(Int.sub n1 (eval_shift s n2)) - | eval_static_operation_case17 s1 n1 n2 => - S s1 (Int.sub n1 n2) - | eval_static_operation_case18 s s1 n1 n2 => - S s1 (Int.sub n1 (eval_shift s n2)) - | eval_static_operation_case19 s n1 n2 => - I(Int.sub (eval_shift s n2) n1) - | eval_static_operation_case20 n n1 => + | eval_static_operation_case18 s n1 n2 => (* Osubshift s, I n1 :: I n2 :: nil *) + I(Int.sub n1 (eval_static_shift s n2)) + | eval_static_operation_case19 s1 n1 n2 => (* Osub, G s1 n1 :: I n2 :: nil *) + G s1 (Int.sub n1 n2) + | eval_static_operation_case20 n1 n2 => (* Osub, S n1 :: I n2 :: nil *) + S (Int.sub n1 n2) + | eval_static_operation_case21 s s1 n1 n2 => (* Osubshift s, G s1 n1 :: I n2 :: nil *) + G s1 (Int.sub n1 (eval_static_shift s n2)) + | eval_static_operation_case22 s n1 n2 => (* Orsubshift s, I n1 :: I n2 :: nil *) + I(Int.sub (eval_static_shift s n2) n1) + | eval_static_operation_case23 n n1 => (* Orsubimm n, I n1 :: nil *) I (Int.sub n n1) - | eval_static_operation_case21 n1 n2 => + | eval_static_operation_case24 n1 n2 => (* Omul, I n1 :: I n2 :: nil *) I(Int.mul n1 n2) - | eval_static_operation_case22 n1 n2 => + | eval_static_operation_case25 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_case23 n1 n2 => + | eval_static_operation_case26 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_case24 n1 n2 => + | eval_static_operation_case27 n1 n2 => (* Oand, I n1 :: I n2 :: nil *) I(Int.and n1 n2) - | eval_static_operation_case25 s n1 n2 => - I(Int.and n1 (eval_shift s n2)) - | eval_static_operation_case26 n n1 => + | eval_static_operation_case28 s n1 n2 => (* Oandshift s, I n1 :: I n2 :: nil *) + I(Int.and n1 (eval_static_shift s n2)) + | eval_static_operation_case29 n n1 => (* Oandimm n, I n1 :: nil *) I(Int.and n1 n) - | eval_static_operation_case27 n1 n2 => + | eval_static_operation_case30 n1 n2 => (* Oor, I n1 :: I n2 :: nil *) I(Int.or n1 n2) - | eval_static_operation_case28 s n1 n2 => - I(Int.or n1 (eval_shift s n2)) - | eval_static_operation_case29 n n1 => + | eval_static_operation_case31 s n1 n2 => (* Oorshift s, I n1 :: I n2 :: nil *) + I(Int.or n1 (eval_static_shift s n2)) + | eval_static_operation_case32 n n1 => (* Oorimm n, I n1 :: nil *) I(Int.or n1 n) - | eval_static_operation_case30 n1 n2 => + | eval_static_operation_case33 n1 n2 => (* Oxor, I n1 :: I n2 :: nil *) I(Int.xor n1 n2) - | eval_static_operation_case31 s n1 n2 => - I(Int.xor n1 (eval_shift s n2)) - | eval_static_operation_case32 n n1 => + | eval_static_operation_case34 s n1 n2 => (* Oxorshift s, I n1 :: I n2 :: nil *) + I(Int.xor n1 (eval_static_shift s n2)) + | eval_static_operation_case35 n n1 => (* Oxorimm n, I n1 :: nil *) I(Int.xor n1 n) - | eval_static_operation_case33 n1 n2 => + | eval_static_operation_case36 n1 n2 => (* Obic, I n1 :: I n2 :: nil *) I(Int.and n1 (Int.not n2)) - | eval_static_operation_case34 s n1 n2 => - I(Int.and n1 (Int.not (eval_shift s n2))) - | eval_static_operation_case35 n1 => + | eval_static_operation_case37 s n1 n2 => (* Obicshift s, I n1 :: I n2 :: nil *) + I(Int.and n1 (Int.not (eval_static_shift s n2))) + | eval_static_operation_case38 n1 => (* Onot, I n1 :: nil *) I(Int.not n1) - | eval_static_operation_case36 s n1 => - I(Int.not (eval_shift s n1)) - | eval_static_operation_case37 n1 n2 => + | eval_static_operation_case39 s n1 => (* Onotshift s, I n1 :: nil *) + I(Int.not (eval_static_shift s n1)) + | eval_static_operation_case40 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_case38 n1 n2 => + | eval_static_operation_case41 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_case39 n1 n2 => + | eval_static_operation_case42 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_case40 s n1 => - I(eval_shift s n1) - | eval_static_operation_case41 n1 => + | eval_static_operation_case43 s n1 => (* Oshift s, I n1 :: nil *) + I(eval_static_shift s n1) + | eval_static_operation_case44 n1 => (* Onegf, F n1 :: nil *) F(Float.neg n1) - | eval_static_operation_case42 n1 => + | eval_static_operation_case45 n1 => (* Oabsf, F n1 :: nil *) F(Float.abs n1) - | eval_static_operation_case43 n1 n2 => + | eval_static_operation_case46 n1 n2 => (* Oaddf, F n1 :: F n2 :: nil *) F(Float.add n1 n2) - | eval_static_operation_case44 n1 n2 => + | eval_static_operation_case47 n1 n2 => (* Osubf, F n1 :: F n2 :: nil *) F(Float.sub n1 n2) - | eval_static_operation_case45 n1 n2 => + | eval_static_operation_case48 n1 n2 => (* Omulf, F n1 :: F n2 :: nil *) F(Float.mul n1 n2) - | eval_static_operation_case46 n1 n2 => + | eval_static_operation_case49 n1 n2 => (* Odivf, F n1 :: F n2 :: nil *) F(Float.div n1 n2) - | eval_static_operation_case47 n1 => + | eval_static_operation_case50 n1 => (* Osingleoffloat, F n1 :: nil *) F(Float.singleoffloat n1) - | eval_static_operation_case48 n1 => - match Float.intoffloat n1 with Some x => I x | None => Unknown end - | eval_static_operation_case49 n1 => + | eval_static_operation_case51 n1 => (* Ointoffloat, F n1 :: nil *) + eval_static_intoffloat n1 + | eval_static_operation_case52 n1 => (* Ointuoffloat, F n1 :: nil *) + eval_static_intuoffloat n1 + | eval_static_operation_case53 n1 => (* Ofloatofint, I n1 :: nil *) F(Float.floatofint n1) - | eval_static_operation_case50 n1 => - match Float.intuoffloat n1 with Some x => I x | None => Unknown end - | eval_static_operation_case53 n1 => + | eval_static_operation_case54 n1 => (* Ofloatofintu, I n1 :: nil *) F(Float.floatofintu n1) - | eval_static_operation_case51 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_case52 n n1 => - if Int.ltu n (Int.repr 31) then I(Int.shrx n1 n) else Unknown + | eval_static_operation_case55 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 @@ -597,134 +441,124 @@ Definition eval_static_operation (op: operation) (vl: list approx) := Section STRENGTH_REDUCTION. -Variable app: reg -> approx. - -Definition intval (r: reg) : option int := - match app r with I n => Some n | _ => None end. - -(* -Definition cond_strength_reduction (cond: condition) (args: list reg) := - match cond, args with - | Ccomp c, r1 :: r2 :: nil => - | Ccompu c, r1 :: r2 :: nil => - | Ccompshift c s, r1 :: r2 :: nil => - | Ccompushift c s, r1 :: r2 :: nil => - | _ => +(** 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) + | Ccompshift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompimm c (eval_static_shift s n2), r1 :: nil) + | Ccompushift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Ccompuimm c (eval_static_shift s n2), r1 :: nil) + | _, _, _ => + (cond, args) end. +>> *) -Inductive cond_strength_reduction_cases: forall (cond: condition) (args: list reg), Type := - | cond_strength_reduction_case1: - forall c r1 r2, - cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) - | cond_strength_reduction_case2: - forall c r1 r2, - cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) - | cond_strength_reduction_case3: - forall c s r1 r2, - cond_strength_reduction_cases (Ccompshift c s) (r1 :: r2 :: nil) - | cond_strength_reduction_case4: - forall c s r1 r2, - cond_strength_reduction_cases (Ccompushift c s) (r1 :: r2 :: nil) - | cond_strength_reduction_default: - forall (cond: condition) (args: list reg), - cond_strength_reduction_cases cond args. - -Definition cond_strength_reduction_match (cond: condition) (args: list reg) := - match cond as z1, args as z2 return cond_strength_reduction_cases z1 z2 with - | Ccomp c, r1 :: r2 :: nil => - cond_strength_reduction_case1 c r1 r2 - | Ccompu c, r1 :: r2 :: nil => - cond_strength_reduction_case2 c r1 r2 - | Ccompshift c s, r1 :: r2 :: nil => - cond_strength_reduction_case3 c s r1 r2 - | Ccompushift c s, r1 :: r2 :: nil => - cond_strength_reduction_case4 c s r1 r2 - | cond, args => - cond_strength_reduction_default cond args +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_case5: forall c s r1 r2 v1 n2, cond_strength_reduction_cases (Ccompshift c s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | cond_strength_reduction_case6: forall c s r1 r2 v1 n2, cond_strength_reduction_cases (Ccompushift c s) (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 + | Ccompshift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case5 c s r1 r2 v1 n2 + | Ccompushift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil => cond_strength_reduction_case6 c s r1 r2 v1 n2 + | cond, args, vl => cond_strength_reduction_default cond args vl end. -Definition cond_strength_reduction (cond: condition) (args: list reg) := - match cond_strength_reduction_match cond args with - | cond_strength_reduction_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 - | cond_strength_reduction_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 - | cond_strength_reduction_case3 c s r1 r2 => - match intval r2 with - | Some n => - (Ccompimm c (eval_shift s n), r1 :: nil) - | None => - (cond, args) - end - | cond_strength_reduction_case4 c s r1 r2 => - match intval r2 with - | Some n => - (Ccompuimm c (eval_shift s n), r1 :: nil) - | None => - (cond, args) - end - | cond_strength_reduction_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_case5 c s r1 r2 v1 n2 => (* Ccompshift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Ccompimm c (eval_static_shift s n2), r1 :: nil) + | cond_strength_reduction_case6 c s r1 r2 v1 n2 => (* Ccompushift c s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Ccompuimm c (eval_static_shift s n2), r1 :: nil) + | cond_strength_reduction_default cond args vl => (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) := +Definition make_shlimm (n: int) (r1 r2: reg) := if Int.eq n Int.zero then - (Omove, r :: nil) - else match is_shift_amount n with - | Some n' => (Oshift (Slsl n'), r :: nil) - | None => (Ointconst Int.zero, nil) (* never happens *) - end. + (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then + (Oshift (Slsl (mk_shift_amount n)), r1 :: nil) + else + (Oshl, r1 :: r2 :: nil). -Definition make_shrimm (n: int) (r: reg) := +Definition make_shrimm (n: int) (r1 r2: reg) := if Int.eq n Int.zero then - (Omove, r :: nil) - else match is_shift_amount n with - | Some n' => (Oshift (Sasr n'), r :: nil) - | None => (Ointconst Int.zero, nil) (* never happens *) - end. + (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then + (Oshift (Sasr (mk_shift_amount n)), r1 :: nil) + else + (Oshr, r1 :: r2 :: nil). -Definition make_shruimm (n: int) (r: reg) := +Definition make_shruimm (n: int) (r1 r2: reg) := if Int.eq n Int.zero then - (Omove, r :: nil) - else match is_shift_amount n with - | Some n' => (Oshift (Slsr n'), r :: nil) - | None => (Ointconst Int.zero, nil) (* never happens *) - end. + (Omove, r1 :: nil) + else if Int.ltu n Int.iwordsize then + (Oshift (Slsr (mk_shift_amount n)), r1 :: nil) + else + (Oshru, r1 :: r2 :: nil). -Definition make_mulimm (n: int) (r: reg) (r': reg) := +Definition make_mulimm (n: int) (r1 r2: reg) := if Int.eq n Int.zero then (Ointconst Int.zero, nil) else if Int.eq n Int.one then - (Omove, r :: nil) + (Omove, r1 :: nil) else match Int.is_power2 n with - | Some l => make_shlimm l r - | None => (Omul, r :: r' :: nil) + | Some l => (Oshift (Slsl (mk_shift_amount l)), r1 :: nil) + | None => (Omul, r1 :: r2 :: nil) end. +Definition make_divimm (n: int) (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: int) (r1 r2: reg) := + match Int.is_power2 n with + | Some l => (Oshift (Slsr (mk_shift_amount l)), r1 :: nil) + | None => (Odivu, r1 :: r2 :: nil) + end. + Definition make_andimm (n: int) (r: reg) := - if Int.eq n Int.zero - then (Ointconst Int.zero, nil) + 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). @@ -738,302 +572,229 @@ Definition make_xorimm (n: int) (r: reg) := else if Int.eq n Int.mone then (Onot, r :: nil) else (Oxorimm n, r :: nil). -(* -Definition op_strength_reduction (op: operation) (args: list reg) := - match op, args with - | Oadd, r1 :: r2 :: nil => - | Oaddshift s, r1 :: r2 :: nil => - | Osub, r1 :: r2 :: nil => - | Osubshift s, r1 :: r2 :: nil => - | Orsubshift s, r1 :: r2 :: nil => - | Omul, r1 :: r2 :: nil => - | Odivu, r1 :: r2 :: nil => - | Oand, r1 :: r2 :: nil => - | Oandshift s, r1 :: r2 :: nil => - | Oor, r1 :: r2 :: nil => - | Oorshift s, r1 :: r2 :: nil => - | Oxor, r1 :: r2 :: nil => - | Oxorshift s, r1 :: r2 :: nil => - | Obic, r1 :: r2 :: nil => - | Obicshift s, r1 :: r2 :: nil => - | Oshl, r1 :: r2 :: nil => - | Oshr, r1 :: r2 :: nil => - | Oshru, r1 :: r2 :: nil => - | Ocmp c, rl => - | _, _ => +(** Original definition: +<< +Nondetfunction op_strength_reduction + (op: operation) (args: list reg) (vl: list approx) := + match op, args, vl with + | Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_addimm n1 r2 + | Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm n2 r1 + | Oaddshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (eval_static_shift s n2) r1 + | Osub, r1 :: r2 :: nil, I n1 :: v2 :: nil => (Orsubimm n1, r2 :: nil) + | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg n2) r1 + | Osubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_addimm (Int.neg (eval_static_shift s n2)) r1 + | Orsubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => (Orsubimm (eval_static_shift s n2), r1 :: nil) + | Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_mulimm n1 r2 r1 + | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_mulimm n2 r1 r2 + | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divimm n2 r1 r2 + | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_divuimm n2 r1 r2 + | Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_andimm n1 r2 + | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm n2 r1 + | Oandshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (eval_static_shift s n2) r1 + | Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_orimm n1 r2 + | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm n2 r1 + | Oorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_orimm (eval_static_shift s n2) r1 + | Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => make_xorimm n1 r2 + | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm n2 r1 + | Oxorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_xorimm (eval_static_shift s n2) r1 + | Obic, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not n2) r1 + | Obicshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_andimm (Int.not (eval_static_shift s n2)) r1 + | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shlimm n2 r1 r2 + | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shrimm n2 r1 r2 + | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 r2 + | Ocmp c, args, vl => + let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args') + | _, _, _ => (op, args) end. +>> *) -Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg), Type := - | op_strength_reduction_case1: - forall r1 r2, - op_strength_reduction_cases (Oadd) (r1 :: r2 :: nil) - | op_strength_reduction_case2: - forall s r1 r2, - op_strength_reduction_cases (Oaddshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case3: - forall r1 r2, - op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) - | op_strength_reduction_case4: - forall s r1 r2, - op_strength_reduction_cases (Osubshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case5: - forall s r1 r2, - op_strength_reduction_cases (Orsubshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case6: - forall r1 r2, - op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) - | op_strength_reduction_case7: - forall r1 r2, - op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) - | op_strength_reduction_case8: - forall r1 r2, - op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) - | op_strength_reduction_case9: - forall s r1 r2, - op_strength_reduction_cases (Oandshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case10: - forall r1 r2, - op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) - | op_strength_reduction_case11: - forall s r1 r2, - op_strength_reduction_cases (Oorshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case12: - forall r1 r2, - op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) - | op_strength_reduction_case13: - forall s r1 r2, - op_strength_reduction_cases (Oxorshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case14: - forall r1 r2, - op_strength_reduction_cases (Obic) (r1 :: r2 :: nil) - | op_strength_reduction_case15: - forall s r1 r2, - op_strength_reduction_cases (Obicshift s) (r1 :: r2 :: nil) - | op_strength_reduction_case16: - forall r1 r2, - op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) - | op_strength_reduction_case17: - forall r1 r2, - op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) - | op_strength_reduction_case18: - forall r1 r2, - op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) - | op_strength_reduction_case19: - forall c rl, - 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 - | Oaddshift s, r1 :: r2 :: nil => - op_strength_reduction_case2 s r1 r2 - | Osub, r1 :: r2 :: nil => - op_strength_reduction_case3 r1 r2 - | Osubshift s, r1 :: r2 :: nil => - op_strength_reduction_case4 s r1 r2 - | Orsubshift s, r1 :: r2 :: nil => - op_strength_reduction_case5 s r1 r2 - | Omul, r1 :: r2 :: nil => - op_strength_reduction_case6 r1 r2 - | Odivu, r1 :: r2 :: nil => - op_strength_reduction_case7 r1 r2 - | Oand, r1 :: r2 :: nil => - op_strength_reduction_case8 r1 r2 - | Oandshift s, r1 :: r2 :: nil => - op_strength_reduction_case9 s r1 r2 - | Oor, r1 :: r2 :: nil => - op_strength_reduction_case10 r1 r2 - | Oorshift s, r1 :: r2 :: nil => - op_strength_reduction_case11 s r1 r2 - | Oxor, r1 :: r2 :: nil => - op_strength_reduction_case12 r1 r2 - | Oxorshift s, r1 :: r2 :: nil => - op_strength_reduction_case13 s r1 r2 - | Obic, r1 :: r2 :: nil => - op_strength_reduction_case14 r1 r2 - | Obicshift s, r1 :: r2 :: nil => - op_strength_reduction_case15 s r1 r2 - | Oshl, r1 :: r2 :: nil => - op_strength_reduction_case16 r1 r2 - | Oshr, r1 :: r2 :: nil => - op_strength_reduction_case17 r1 r2 - | Oshru, r1 :: r2 :: nil => - op_strength_reduction_case18 r1 r2 - | Ocmp c, rl => - op_strength_reduction_case19 c rl - | op, args => - op_strength_reduction_default op args +Inductive op_strength_reduction_cases: forall (op: operation) (args: list reg) (vl: list approx), Type := + | op_strength_reduction_case1: forall r1 r2 n1 v2, op_strength_reduction_cases (Oadd) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case2: forall r1 r2 v1 n2, op_strength_reduction_cases (Oadd) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case3: forall s r1 r2 v1 n2, op_strength_reduction_cases (Oaddshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case4: forall r1 r2 n1 v2, op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case5: forall r1 r2 v1 n2, op_strength_reduction_cases (Osub) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case6: forall s r1 r2 v1 n2, op_strength_reduction_cases (Osubshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case7: forall s r1 r2 v1 n2, op_strength_reduction_cases (Orsubshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case8: forall r1 r2 n1 v2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case9: forall r1 r2 v1 n2, op_strength_reduction_cases (Omul) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case10: forall r1 r2 v1 n2, op_strength_reduction_cases (Odiv) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case11: forall r1 r2 v1 n2, op_strength_reduction_cases (Odivu) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case12: forall r1 r2 n1 v2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case13: forall r1 r2 v1 n2, op_strength_reduction_cases (Oand) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case14: forall s r1 r2 v1 n2, op_strength_reduction_cases (Oandshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case15: forall r1 r2 n1 v2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case16: forall r1 r2 v1 n2, op_strength_reduction_cases (Oor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case17: forall s r1 r2 v1 n2, op_strength_reduction_cases (Oorshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case18: forall r1 r2 n1 v2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | op_strength_reduction_case19: forall r1 r2 v1 n2, op_strength_reduction_cases (Oxor) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case20: forall s r1 r2 v1 n2, op_strength_reduction_cases (Oxorshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case21: forall r1 r2 v1 n2, op_strength_reduction_cases (Obic) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case22: forall s r1 r2 v1 n2, op_strength_reduction_cases (Obicshift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case23: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshl) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case24: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshr) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case25: forall r1 r2 v1 n2, op_strength_reduction_cases (Oshru) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | op_strength_reduction_case26: 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 + | Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case1 r1 r2 n1 v2 + | Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case2 r1 r2 v1 n2 + | Oaddshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case3 s r1 r2 v1 n2 + | Osub, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case4 r1 r2 n1 v2 + | Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case5 r1 r2 v1 n2 + | Osubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case6 s r1 r2 v1 n2 + | Orsubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case7 s r1 r2 v1 n2 + | Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case8 r1 r2 n1 v2 + | Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case9 r1 r2 v1 n2 + | Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case10 r1 r2 v1 n2 + | Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case11 r1 r2 v1 n2 + | Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case12 r1 r2 n1 v2 + | Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case13 r1 r2 v1 n2 + | Oandshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case14 s r1 r2 v1 n2 + | Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case15 r1 r2 n1 v2 + | Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case16 r1 r2 v1 n2 + | Oorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case17 s r1 r2 v1 n2 + | Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil => op_strength_reduction_case18 r1 r2 n1 v2 + | Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case19 r1 r2 v1 n2 + | Oxorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case20 s r1 r2 v1 n2 + | Obic, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case21 r1 r2 v1 n2 + | Obicshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case22 s r1 r2 v1 n2 + | Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case23 r1 r2 v1 n2 + | Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case24 r1 r2 v1 n2 + | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => op_strength_reduction_case25 r1 r2 v1 n2 + | Ocmp c, args, vl => op_strength_reduction_case26 c args vl + | op, args, vl => op_strength_reduction_default op args vl 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 s r1 r2 => (* Oaddshift *) - match intval r2 with - | Some n => make_addimm (eval_shift s n) r1 - | _ => (op, args) - end - | op_strength_reduction_case3 r1 r2 => (* Osub *) - match intval r1, intval r2 with - | Some n, _ => (Orsubimm n, r2 :: nil) - | _, Some n => make_addimm (Int.neg n) r1 - | _, _ => (op, args) - end - | op_strength_reduction_case4 s r1 r2 => (* Osubshift *) - match intval r2 with - | Some n => make_addimm (Int.neg (eval_shift s n)) r1 - | _ => (op, args) - end - | op_strength_reduction_case5 s r1 r2 => (* Orsubshift *) - match intval r2 with - | Some n => (Orsubimm (eval_shift s n), r1 :: nil) - | _ => (op, args) - end - | op_strength_reduction_case6 r1 r2 => (* Omul *) - match intval r1, intval r2 with - | Some n, _ => make_mulimm n r2 r1 - | _, Some n => make_mulimm n r1 r2 - | _, _ => (op, args) - end - | op_strength_reduction_case7 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_case8 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_case9 s r1 r2 => (* Oandshift *) - match intval r2 with - | Some n => make_andimm (eval_shift s n) r1 - | _ => (op, args) - end - | op_strength_reduction_case10 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_case11 s r1 r2 => (* Oorshift *) - match intval r2 with - | Some n => make_orimm (eval_shift s n) r1 - | _ => (op, args) - end - | op_strength_reduction_case12 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_case13 s r1 r2 => (* Oxorshift *) - match intval r2 with - | Some n => make_xorimm (eval_shift s n) r1 - | _ => (op, args) - end - | op_strength_reduction_case14 r1 r2 => (* Obic *) - match intval r2 with - | Some n => make_andimm (Int.not n) r1 - | _ => (op, args) - end - | op_strength_reduction_case15 s r1 r2 => (* Obicshift *) - match intval r2 with - | Some n => make_andimm (Int.not (eval_shift s n)) r1 - | _ => (op, args) - end - | op_strength_reduction_case16 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_case17 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_case18 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_case19 c rl => (* Ocmp *) - let (c', args') := cond_strength_reduction c args in - (Ocmp c', args') - | op_strength_reduction_default op args => (* default *) +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 n1 v2 => (* Oadd, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + make_addimm n1 r2 + | op_strength_reduction_case2 r1 r2 v1 n2 => (* Oadd, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_addimm n2 r1 + | op_strength_reduction_case3 s r1 r2 v1 n2 => (* Oaddshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_addimm (eval_static_shift s n2) r1 + | op_strength_reduction_case4 r1 r2 n1 v2 => (* Osub, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + (Orsubimm n1, r2 :: nil) + | op_strength_reduction_case5 r1 r2 v1 n2 => (* Osub, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_addimm (Int.neg n2) r1 + | op_strength_reduction_case6 s r1 r2 v1 n2 => (* Osubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_addimm (Int.neg (eval_static_shift s n2)) r1 + | op_strength_reduction_case7 s r1 r2 v1 n2 => (* Orsubshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Orsubimm (eval_static_shift s n2), r1 :: nil) + | op_strength_reduction_case8 r1 r2 n1 v2 => (* Omul, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + make_mulimm n1 r2 r1 + | op_strength_reduction_case9 r1 r2 v1 n2 => (* Omul, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_mulimm n2 r1 r2 + | op_strength_reduction_case10 r1 r2 v1 n2 => (* Odiv, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_divimm n2 r1 r2 + | op_strength_reduction_case11 r1 r2 v1 n2 => (* Odivu, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_divuimm n2 r1 r2 + | op_strength_reduction_case12 r1 r2 n1 v2 => (* Oand, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + make_andimm n1 r2 + | op_strength_reduction_case13 r1 r2 v1 n2 => (* Oand, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_andimm n2 r1 + | op_strength_reduction_case14 s r1 r2 v1 n2 => (* Oandshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_andimm (eval_static_shift s n2) r1 + | op_strength_reduction_case15 r1 r2 n1 v2 => (* Oor, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + make_orimm n1 r2 + | op_strength_reduction_case16 r1 r2 v1 n2 => (* Oor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_orimm n2 r1 + | op_strength_reduction_case17 s r1 r2 v1 n2 => (* Oorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_orimm (eval_static_shift s n2) r1 + | op_strength_reduction_case18 r1 r2 n1 v2 => (* Oxor, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + make_xorimm n1 r2 + | op_strength_reduction_case19 r1 r2 v1 n2 => (* Oxor, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_xorimm n2 r1 + | op_strength_reduction_case20 s r1 r2 v1 n2 => (* Oxorshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_xorimm (eval_static_shift s n2) r1 + | op_strength_reduction_case21 r1 r2 v1 n2 => (* Obic, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_andimm (Int.not n2) r1 + | op_strength_reduction_case22 s r1 r2 v1 n2 => (* Obicshift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_andimm (Int.not (eval_static_shift s n2)) r1 + | op_strength_reduction_case23 r1 r2 v1 n2 => (* Oshl, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shlimm n2 r1 r2 + | op_strength_reduction_case24 r1 r2 v1 n2 => (* Oshr, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shrimm n2 r1 r2 + | op_strength_reduction_case25 r1 r2 v1 n2 => (* Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + make_shruimm n2 r1 r2 + | op_strength_reduction_case26 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. -(* -Definition addr_strength_reduction (addr: addressing) (args: list reg) := - match addr, args with - | Aindexed2, r1 :: r2 :: nil => - | Aindexed2shift s, r1 :: r2 :: nil => - | _, _ => + + +(** Original definition: +<< +Nondetfunction addr_strength_reduction + (addr: addressing) (args: list reg) (vl: list approx) := + match addr, args, vl with + | Aindexed2, r1 :: r2 :: nil, S n1 :: I n2 :: nil => + (Ainstack (Int.add n1 n2), nil) + | Aindexed2, r1 :: r2 :: nil, I n1 :: S n2 :: nil => + (Ainstack (Int.add n1 n2), nil) + | Aindexed2, r1 :: r2 :: nil, I n1 :: v2 :: nil => + (Aindexed n1, r2 :: nil) + | Aindexed2, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Aindexed n2, r1 :: nil) + | Aindexed2shift s, r1 :: r2 :: nil, S n1 :: I n2 :: nil => + (Ainstack (Int.add n1 (eval_static_shift s n2)), nil) + | Aindexed2shift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => + (Aindexed (eval_static_shift s n2), r1 :: nil) + | Aindexed n, r1 :: nil, S n1 :: nil => + (Ainstack (Int.add n1 n), nil) + | _, _, _ => + (addr, args) end. +>> *) -Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg), Type := - | addr_strength_reduction_case1: - forall r1 r2, - addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) - | addr_strength_reduction_case2: - forall s r1 r2, - addr_strength_reduction_cases (Aindexed2shift s) (r1 :: r2 :: 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 - | Aindexed2shift s, r1 :: r2 :: nil => - addr_strength_reduction_case2 s r1 r2 - | 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 r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) (S n1 :: I n2 :: nil) + | addr_strength_reduction_case2: forall r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) (I n1 :: S n2 :: nil) + | addr_strength_reduction_case3: forall r1 r2 n1 v2, addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) (I n1 :: v2 :: nil) + | addr_strength_reduction_case4: forall r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | addr_strength_reduction_case5: forall s r1 r2 n1 n2, addr_strength_reduction_cases (Aindexed2shift s) (r1 :: r2 :: nil) (S n1 :: I n2 :: nil) + | addr_strength_reduction_case6: forall s r1 r2 v1 n2, addr_strength_reduction_cases (Aindexed2shift s) (r1 :: r2 :: nil) (v1 :: I n2 :: nil) + | addr_strength_reduction_case7: forall n r1 n1, addr_strength_reduction_cases (Aindexed n) (r1 :: nil) (S 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 + | Aindexed2, r1 :: r2 :: nil, S n1 :: I n2 :: nil => addr_strength_reduction_case1 r1 r2 n1 n2 + | Aindexed2, r1 :: r2 :: nil, I n1 :: S n2 :: nil => addr_strength_reduction_case2 r1 r2 n1 n2 + | Aindexed2, r1 :: r2 :: nil, I n1 :: v2 :: nil => addr_strength_reduction_case3 r1 r2 n1 v2 + | Aindexed2, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case4 r1 r2 v1 n2 + | Aindexed2shift s, r1 :: r2 :: nil, S n1 :: I n2 :: nil => addr_strength_reduction_case5 s r1 r2 n1 n2 + | Aindexed2shift s, r1 :: r2 :: nil, v1 :: I n2 :: nil => addr_strength_reduction_case6 s r1 r2 v1 n2 + | Aindexed n, r1 :: nil, S n1 :: nil => addr_strength_reduction_case7 n 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 r1 r2 => (* Aindexed2 *) - match intval r1, intval r2 with - | Some n1, _ => (Aindexed n1, r2 :: nil) - | _, Some n2 => (Aindexed n2, r1 :: nil) - | _, _ => (addr, args) - end - | addr_strength_reduction_case2 s r1 r2 => (* Aindexed2shift *) - match intval r2 with - | Some n2 => (Aindexed (eval_shift s n2), r1 :: nil) - | _ => (addr, args) - end - | addr_strength_reduction_default addr args => - (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 r1 r2 n1 n2 => (* Aindexed2, r1 :: r2 :: nil, S n1 :: I n2 :: nil *) + (Ainstack (Int.add n1 n2), nil) + | addr_strength_reduction_case2 r1 r2 n1 n2 => (* Aindexed2, r1 :: r2 :: nil, I n1 :: S n2 :: nil *) + (Ainstack (Int.add n1 n2), nil) + | addr_strength_reduction_case3 r1 r2 n1 v2 => (* Aindexed2, r1 :: r2 :: nil, I n1 :: v2 :: nil *) + (Aindexed n1, r2 :: nil) + | addr_strength_reduction_case4 r1 r2 v1 n2 => (* Aindexed2, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Aindexed n2, r1 :: nil) + | addr_strength_reduction_case5 s r1 r2 n1 n2 => (* Aindexed2shift s, r1 :: r2 :: nil, S n1 :: I n2 :: nil *) + (Ainstack (Int.add n1 (eval_static_shift s n2)), nil) + | addr_strength_reduction_case6 s r1 r2 v1 n2 => (* Aindexed2shift s, r1 :: r2 :: nil, v1 :: I n2 :: nil *) + (Aindexed (eval_static_shift s n2), r1 :: nil) + | addr_strength_reduction_case7 n r1 n1 => (* Aindexed n, r1 :: nil, S n1 :: nil *) + (Ainstack (Int.add n1 n), nil) + | addr_strength_reduction_default addr args vl => + (addr, args) end. + End STRENGTH_REDUCTION. |