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Diffstat (limited to 'powerpc/ConstpropOp.v')
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diff --git a/powerpc/ConstpropOp.v b/powerpc/ConstpropOp.v new file mode 100644 index 00000000..87b2cfa4 --- /dev/null +++ b/powerpc/ConstpropOp.v @@ -0,0 +1,872 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* *********************************************************************) + +(** Static analysis and strength reduction for operators + and conditions. This is the machine-dependent part of [Constprop]. *) + +Require Import Coqlib. +Require Import AST. +Require Import Integers. +Require Import Floats. +Require Import Values. +Require Import Op. +Require Import Registers. + +(** * Static analysis *) + +(** To each pseudo-register at each program point, the static analysis + associates a compile-time approximation taken from the following set. *) + +Inductive approx : Type := + | Novalue: approx (** No value possible, code is unreachable. *) + | Unknown: approx (** All values are possible, + no compile-time information is available. *) + | I: int -> approx (** A known integer value. *) + | F: float -> approx (** A known floating-point value. *) + | S: ident -> int -> approx. + (** The value is the address of the given global + symbol plus the given integer offset. *) + +(** We now define the abstract interpretations of conditions and operators + over this set of approximations. For instance, the abstract interpretation + of the operator [Oaddf] applied to two expressions [a] and [b] is + [F(Float.add f g)] if [a] and [b] have static approximations [Vfloat f] + and [Vfloat g] respectively, and [Unknown] otherwise. + + The static approximations are defined by large pattern-matchings over + the approximations of the results. We write these matchings in the + indirect style described in file [Cmconstr] to avoid excessive + duplication of cases in proofs. *) + +(* +Definition eval_static_condition (cond: condition) (vl: list approx) := + match cond, vl with + | Ccomp c, I n1 :: I n2 :: nil => Some(Int.cmp c n1 n2) + | Ccompu c, I n1 :: I n2 :: nil => Some(Int.cmpu c n1 n2) + | Ccompimm c n, I n1 :: nil => Some(Int.cmp c n1 n) + | Ccompuimm c n, I n1 :: nil => Some(Int.cmpu c n1 n) + | Ccompf c, F n1 :: F n2 :: nil => Some(Float.cmp c n1 n2) + | Cnotcompf c, F n1 :: F n2 :: nil => Some(negb(Float.cmp c n1 n2)) + | Cmaskzero n, I n1 :: nil => Some(Int.eq (Int.and n1 n) Int.zero) + | Cmasknotzero n, n1::nil => Some(negb(Int.eq (Int.and n1 n) Int.zero)) + | _, _ => None + end. +*) + +Inductive eval_static_condition_cases: forall (cond: condition) (vl: list approx), Type := + | eval_static_condition_case1: + forall c n1 n2, + eval_static_condition_cases (Ccomp c) (I n1 :: I n2 :: nil) + | eval_static_condition_case2: + forall c n1 n2, + eval_static_condition_cases (Ccompu c) (I n1 :: I n2 :: nil) + | eval_static_condition_case3: + forall c n n1, + eval_static_condition_cases (Ccompimm c n) (I n1 :: nil) + | eval_static_condition_case4: + forall c n n1, + eval_static_condition_cases (Ccompuimm c n) (I n1 :: nil) + | eval_static_condition_case5: + forall c n1 n2, + eval_static_condition_cases (Ccompf c) (F n1 :: F n2 :: nil) + | eval_static_condition_case6: + forall c n1 n2, + eval_static_condition_cases (Cnotcompf c) (F n1 :: F n2 :: nil) + | eval_static_condition_case7: + forall n n1, + eval_static_condition_cases (Cmaskzero n) (I n1 :: nil) + | eval_static_condition_case8: + forall n n1, + eval_static_condition_cases (Cmasknotzero n) (I n1 :: nil) + | eval_static_condition_default: + forall (cond: condition) (vl: list approx), + eval_static_condition_cases cond vl. + +Definition eval_static_condition_match (cond: condition) (vl: list approx) := + match cond as z1, vl as z2 return eval_static_condition_cases z1 z2 with + | Ccomp c, I n1 :: I n2 :: nil => + eval_static_condition_case1 c n1 n2 + | Ccompu c, I n1 :: I n2 :: nil => + eval_static_condition_case2 c n1 n2 + | Ccompimm c n, I n1 :: nil => + eval_static_condition_case3 c n n1 + | Ccompuimm c n, I n1 :: nil => + eval_static_condition_case4 c n n1 + | Ccompf c, F n1 :: F n2 :: nil => + eval_static_condition_case5 c n1 n2 + | Cnotcompf c, F n1 :: F n2 :: nil => + eval_static_condition_case6 c n1 n2 + | Cmaskzero n, I n1 :: nil => + eval_static_condition_case7 n n1 + | Cmasknotzero n, I n1 :: nil => + eval_static_condition_case8 n n1 + | cond, vl => + eval_static_condition_default cond vl + end. + +Definition eval_static_condition (cond: condition) (vl: list approx) := + match eval_static_condition_match cond vl with + | eval_static_condition_case1 c n1 n2 => + Some(Int.cmp c n1 n2) + | eval_static_condition_case2 c n1 n2 => + Some(Int.cmpu c n1 n2) + | eval_static_condition_case3 c n n1 => + Some(Int.cmp c n1 n) + | eval_static_condition_case4 c n n1 => + Some(Int.cmpu c n1 n) + | eval_static_condition_case5 c n1 n2 => + Some(Float.cmp c n1 n2) + | eval_static_condition_case6 c n1 n2 => + Some(negb(Float.cmp c n1 n2)) + | eval_static_condition_case7 n n1 => + Some(Int.eq (Int.and n1 n) Int.zero) + | eval_static_condition_case8 n n1 => + Some(negb(Int.eq (Int.and n1 n) Int.zero)) + | eval_static_condition_default cond vl => + None + end. + +(* +Definition eval_static_operation (op: operation) (vl: list approx) := + match op, vl with + | Omove, v1::nil => v1 + | Ointconst n, nil => I n + | Ofloatconst n, nil => F n + | Oaddrsymbol s n, nil => S s n + | Ocast8signed, I n1 :: nil => I(Int.sign_ext 8 n) + | Ocast8unsigned, I n1 :: nil => I(Int.zero_ext 8 n) + | Ocast16signed, I n1 :: nil => I(Int.sign_ext 16 n) + | Ocast16unsigned, I n1 :: nil => I(Int.zero_ext 16 n) + | Oadd, I n1 :: I n2 :: nil => I(Int.add n1 n2) + | Oadd, S s1 n1 :: I n2 :: nil => S s1 (Int.add n1 n2) + | Oaddimm n, I n1 :: nil => I (Int.add n1 n) + | Oaddimm n, S s1 n1 :: nil => S s1 (Int.add n1 n) + | Osub, I n1 :: I n2 :: nil => I(Int.sub n1 n2) + | Osub, S s1 n1 :: I n2 :: nil => S s1 (Int.sub n1 n2) + | Osubimm n, I n1 :: nil => I (Int.sub n n1) + | Omul, I n1 :: I n2 :: nil => I(Int.mul n1 n2) + | Omulimm n, I n1 :: nil => I(Int.mul n1 n) + | Odiv, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2) + | Odivu, I n1 :: I n2 :: nil => if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2) + | Oand, I n1 :: I n2 :: nil => I(Int.and n1 n2) + | Oandimm n, I n1 :: nil => I(Int.and n1 n) + | Oor, I n1 :: I n2 :: nil => I(Int.or n1 n2) + | Oorimm n, I n1 :: nil => I(Int.or n1 n) + | Oxor, I n1 :: I n2 :: nil => I(Int.xor n1 n2) + | Oxorimm n, I n1 :: nil => I(Int.xor n1 n) + | Onand, I n1 :: I n2 :: nil => I(Int.xor (Int.and n1 n2) Int.mone) + | Onor, I n1 :: I n2 :: nil => I(Int.xor (Int.or n1 n2) Int.mone) + | Onxor, I n1 :: I n2 :: nil => I(Int.xor (Int.xor n1 n2) Int.mone) + | Oshl, I n1 :: I n2 :: nil => if Int.ltu n2 (Int.repr 32) then I(Int.shl n1 n2) else Unknown + | Oshr, I n1 :: I n2 :: nil => if Int.ltu n2 (Int.repr 32) then I(Int.shr n1 n2) else Unknown + | Oshrimm n, I n1 :: nil => if Int.ltu n (Int.repr 32) then I(Int.shr n1 n) else Unknown + | Oshrximm n, I n1 :: nil => if Int.ltu n (Int.repr 32) then I(Int.shrx n1 n) else Unknown + | Oshru, I n1 :: I n2 :: nil => if Int.ltu n2 (Int.repr 32) then I(Int.shru n1 n2) else Unknown + | Orolm amount mask, I n1 :: nil => I(Int.rolm n1 amount mask) + | Onegf, F n1 :: nil => F(Float.neg n1) + | Oabsf, F n1 :: nil => F(Float.abs n1) + | Oaddf, F n1 :: F n2 :: nil => F(Float.add n1 n2) + | Osubf, F n1 :: F n2 :: nil => F(Float.sub n1 n2) + | Omulf, F n1 :: F n2 :: nil => F(Float.mul n1 n2) + | Odivf, F n1 :: F n2 :: nil => F(Float.div n1 n2) + | Omuladdf, F n1 :: F n2 :: F n3 :: nil => F(Float.add (Float.mul n1 n2) n3) + | Omulsubf, F n1 :: F n2 :: F n3 :: nil => F(Float.sub (Float.mul n1 n2) n3) + | Osingleoffloat, F n1 :: nil => F(Float.singleoffloat n1) + | Ointoffloat, F n1 :: nil => I(Float.intoffloat n1) + | Ointuoffloat, F n1 :: nil => I(Float.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 + | _, _ => Unknown + end. +*) + +Inductive eval_static_operation_cases: forall (op: operation) (vl: list approx), Type := + | eval_static_operation_case1: + forall v1, + eval_static_operation_cases (Omove) (v1::nil) + | eval_static_operation_case2: + forall n, + eval_static_operation_cases (Ointconst n) (nil) + | eval_static_operation_case3: + forall n, + eval_static_operation_cases (Ofloatconst n) (nil) + | eval_static_operation_case4: + forall s n, + eval_static_operation_cases (Oaddrsymbol s n) (nil) + | eval_static_operation_case6: + forall n1, + eval_static_operation_cases (Ocast8signed) (I n1 :: nil) + | eval_static_operation_case7: + forall n1, + eval_static_operation_cases (Ocast16signed) (I n1 :: nil) + | eval_static_operation_case8: + forall n1 n2, + eval_static_operation_cases (Oadd) (I n1 :: I n2 :: nil) + | eval_static_operation_case9: + forall s1 n1 n2, + eval_static_operation_cases (Oadd) (S s1 n1 :: I n2 :: nil) + | eval_static_operation_case11: + forall n n1, + eval_static_operation_cases (Oaddimm n) (I n1 :: nil) + | eval_static_operation_case12: + forall n s1 n1, + eval_static_operation_cases (Oaddimm n) (S s1 n1 :: nil) + | eval_static_operation_case13: + forall n1 n2, + eval_static_operation_cases (Osub) (I n1 :: I n2 :: nil) + | eval_static_operation_case14: + forall s1 n1 n2, + eval_static_operation_cases (Osub) (S s1 n1 :: I n2 :: nil) + | eval_static_operation_case15: + forall n n1, + eval_static_operation_cases (Osubimm n) (I n1 :: nil) + | eval_static_operation_case16: + forall n1 n2, + eval_static_operation_cases (Omul) (I n1 :: I n2 :: nil) + | eval_static_operation_case17: + forall n n1, + eval_static_operation_cases (Omulimm n) (I n1 :: nil) + | eval_static_operation_case18: + forall n1 n2, + eval_static_operation_cases (Odiv) (I n1 :: I n2 :: nil) + | eval_static_operation_case19: + forall n1 n2, + eval_static_operation_cases (Odivu) (I n1 :: I n2 :: nil) + | eval_static_operation_case20: + forall n1 n2, + eval_static_operation_cases (Oand) (I n1 :: I n2 :: nil) + | eval_static_operation_case21: + forall n n1, + eval_static_operation_cases (Oandimm n) (I n1 :: nil) + | eval_static_operation_case22: + forall n1 n2, + eval_static_operation_cases (Oor) (I n1 :: I n2 :: nil) + | eval_static_operation_case23: + forall n n1, + eval_static_operation_cases (Oorimm n) (I n1 :: nil) + | eval_static_operation_case24: + forall n1 n2, + eval_static_operation_cases (Oxor) (I n1 :: I n2 :: nil) + | eval_static_operation_case25: + forall n n1, + eval_static_operation_cases (Oxorimm n) (I n1 :: nil) + | eval_static_operation_case26: + forall n1 n2, + eval_static_operation_cases (Onand) (I n1 :: I n2 :: nil) + | eval_static_operation_case27: + forall n1 n2, + eval_static_operation_cases (Onor) (I n1 :: I n2 :: nil) + | eval_static_operation_case28: + forall n1 n2, + eval_static_operation_cases (Onxor) (I n1 :: I n2 :: nil) + | eval_static_operation_case29: + forall n1 n2, + eval_static_operation_cases (Oshl) (I n1 :: I n2 :: nil) + | eval_static_operation_case30: + forall n1 n2, + eval_static_operation_cases (Oshr) (I n1 :: I n2 :: nil) + | eval_static_operation_case31: + forall n n1, + eval_static_operation_cases (Oshrimm n) (I n1 :: nil) + | eval_static_operation_case32: + forall n n1, + eval_static_operation_cases (Oshrximm n) (I n1 :: nil) + | eval_static_operation_case33: + forall n1 n2, + eval_static_operation_cases (Oshru) (I n1 :: I n2 :: nil) + | eval_static_operation_case34: + forall amount mask n1, + eval_static_operation_cases (Orolm amount mask) (I n1 :: nil) + | eval_static_operation_case35: + forall n1, + eval_static_operation_cases (Onegf) (F n1 :: nil) + | eval_static_operation_case36: + forall n1, + eval_static_operation_cases (Oabsf) (F n1 :: nil) + | eval_static_operation_case37: + forall n1 n2, + eval_static_operation_cases (Oaddf) (F n1 :: F n2 :: nil) + | eval_static_operation_case38: + forall n1 n2, + eval_static_operation_cases (Osubf) (F n1 :: F n2 :: nil) + | eval_static_operation_case39: + forall n1 n2, + eval_static_operation_cases (Omulf) (F n1 :: F n2 :: nil) + | eval_static_operation_case40: + forall n1 n2, + eval_static_operation_cases (Odivf) (F n1 :: F n2 :: nil) + | eval_static_operation_case41: + forall n1 n2 n3, + eval_static_operation_cases (Omuladdf) (F n1 :: F n2 :: F n3 :: nil) + | eval_static_operation_case42: + forall n1 n2 n3, + eval_static_operation_cases (Omulsubf) (F n1 :: F n2 :: F n3 :: nil) + | eval_static_operation_case43: + forall n1, + eval_static_operation_cases (Osingleoffloat) (F n1 :: nil) + | eval_static_operation_case44: + forall n1, + eval_static_operation_cases (Ointoffloat) (F n1 :: nil) + | eval_static_operation_case45: + forall n1, + eval_static_operation_cases (Ofloatofint) (I n1 :: nil) + | eval_static_operation_case46: + forall n1, + eval_static_operation_cases (Ofloatofintu) (I n1 :: nil) + | eval_static_operation_case47: + forall c vl, + eval_static_operation_cases (Ocmp c) (vl) + | eval_static_operation_case48: + forall n1, + eval_static_operation_cases (Ocast8unsigned) (I n1 :: nil) + | eval_static_operation_case49: + forall n1, + eval_static_operation_cases (Ocast16unsigned) (I n1 :: nil) + | eval_static_operation_case50: + forall n1, + eval_static_operation_cases (Ointuoffloat) (F n1 :: nil) + | eval_static_operation_default: + forall (op: operation) (vl: list approx), + eval_static_operation_cases op vl. + +Definition eval_static_operation_match (op: operation) (vl: list approx) := + match op as z1, vl as z2 return eval_static_operation_cases z1 z2 with + | Omove, v1::nil => + eval_static_operation_case1 v1 + | Ointconst n, nil => + eval_static_operation_case2 n + | Ofloatconst n, nil => + eval_static_operation_case3 n + | Oaddrsymbol s n, nil => + eval_static_operation_case4 s n + | Ocast8signed, I n1 :: nil => + eval_static_operation_case6 n1 + | Ocast16signed, I n1 :: nil => + eval_static_operation_case7 n1 + | Oadd, I n1 :: I n2 :: nil => + eval_static_operation_case8 n1 n2 + | Oadd, S s1 n1 :: I n2 :: nil => + eval_static_operation_case9 s1 n1 n2 + | Oaddimm n, I n1 :: nil => + eval_static_operation_case11 n n1 + | Oaddimm n, S s1 n1 :: nil => + eval_static_operation_case12 n s1 n1 + | Osub, I n1 :: I n2 :: nil => + eval_static_operation_case13 n1 n2 + | Osub, S s1 n1 :: I n2 :: nil => + eval_static_operation_case14 s1 n1 n2 + | Osubimm n, I n1 :: nil => + eval_static_operation_case15 n n1 + | Omul, I n1 :: I n2 :: nil => + eval_static_operation_case16 n1 n2 + | Omulimm n, I n1 :: nil => + eval_static_operation_case17 n n1 + | Odiv, I n1 :: I n2 :: nil => + eval_static_operation_case18 n1 n2 + | Odivu, I n1 :: I n2 :: nil => + eval_static_operation_case19 n1 n2 + | Oand, I n1 :: I n2 :: nil => + eval_static_operation_case20 n1 n2 + | Oandimm n, I n1 :: nil => + eval_static_operation_case21 n n1 + | Oor, I n1 :: I n2 :: nil => + eval_static_operation_case22 n1 n2 + | Oorimm n, I n1 :: nil => + eval_static_operation_case23 n n1 + | Oxor, I n1 :: I n2 :: nil => + eval_static_operation_case24 n1 n2 + | Oxorimm n, I n1 :: nil => + eval_static_operation_case25 n n1 + | Onand, I n1 :: I n2 :: nil => + eval_static_operation_case26 n1 n2 + | Onor, I n1 :: I n2 :: nil => + eval_static_operation_case27 n1 n2 + | Onxor, I n1 :: I n2 :: nil => + eval_static_operation_case28 n1 n2 + | Oshl, I n1 :: I n2 :: nil => + eval_static_operation_case29 n1 n2 + | Oshr, I n1 :: I n2 :: nil => + eval_static_operation_case30 n1 n2 + | Oshrimm n, I n1 :: nil => + eval_static_operation_case31 n n1 + | Oshrximm n, I n1 :: nil => + eval_static_operation_case32 n n1 + | Oshru, I n1 :: I n2 :: nil => + eval_static_operation_case33 n1 n2 + | Orolm amount mask, I n1 :: nil => + eval_static_operation_case34 amount mask n1 + | Onegf, F n1 :: nil => + eval_static_operation_case35 n1 + | Oabsf, F n1 :: nil => + eval_static_operation_case36 n1 + | Oaddf, F n1 :: F n2 :: nil => + eval_static_operation_case37 n1 n2 + | Osubf, F n1 :: F n2 :: nil => + eval_static_operation_case38 n1 n2 + | Omulf, F n1 :: F n2 :: nil => + eval_static_operation_case39 n1 n2 + | Odivf, F n1 :: F n2 :: nil => + eval_static_operation_case40 n1 n2 + | Omuladdf, F n1 :: F n2 :: F n3 :: nil => + eval_static_operation_case41 n1 n2 n3 + | Omulsubf, F n1 :: F n2 :: F n3 :: nil => + eval_static_operation_case42 n1 n2 n3 + | Osingleoffloat, F n1 :: nil => + eval_static_operation_case43 n1 + | Ointoffloat, F n1 :: nil => + eval_static_operation_case44 n1 + | Ofloatofint, I n1 :: nil => + eval_static_operation_case45 n1 + | Ofloatofintu, I n1 :: nil => + eval_static_operation_case46 n1 + | Ocmp c, vl => + eval_static_operation_case47 c vl + | Ocast8unsigned, I n1 :: nil => + eval_static_operation_case48 n1 + | Ocast16unsigned, I n1 :: nil => + eval_static_operation_case49 n1 + | Ointuoffloat, F n1 :: nil => + eval_static_operation_case50 n1 + | op, vl => + eval_static_operation_default op vl + end. + +Definition eval_static_operation (op: operation) (vl: list approx) := + match eval_static_operation_match op vl with + | eval_static_operation_case1 v1 => + v1 + | eval_static_operation_case2 n => + I n + | eval_static_operation_case3 n => + F n + | eval_static_operation_case4 s n => + S s n + | eval_static_operation_case6 n1 => + I(Int.sign_ext 8 n1) + | eval_static_operation_case7 n1 => + I(Int.sign_ext 16 n1) + | eval_static_operation_case8 n1 n2 => + I(Int.add n1 n2) + | eval_static_operation_case9 s1 n1 n2 => + S s1 (Int.add n1 n2) + | eval_static_operation_case11 n n1 => + I (Int.add n1 n) + | eval_static_operation_case12 n s1 n1 => + S s1 (Int.add n1 n) + | eval_static_operation_case13 n1 n2 => + I(Int.sub n1 n2) + | eval_static_operation_case14 s1 n1 n2 => + S s1 (Int.sub n1 n2) + | eval_static_operation_case15 n n1 => + I (Int.sub n n1) + | eval_static_operation_case16 n1 n2 => + I(Int.mul n1 n2) + | eval_static_operation_case17 n n1 => + I(Int.mul n1 n) + | eval_static_operation_case18 n1 n2 => + if Int.eq n2 Int.zero then Unknown else I(Int.divs n1 n2) + | eval_static_operation_case19 n1 n2 => + if Int.eq n2 Int.zero then Unknown else I(Int.divu n1 n2) + | eval_static_operation_case20 n1 n2 => + I(Int.and n1 n2) + | eval_static_operation_case21 n n1 => + I(Int.and n1 n) + | eval_static_operation_case22 n1 n2 => + I(Int.or n1 n2) + | eval_static_operation_case23 n n1 => + I(Int.or n1 n) + | eval_static_operation_case24 n1 n2 => + I(Int.xor n1 n2) + | eval_static_operation_case25 n n1 => + I(Int.xor n1 n) + | eval_static_operation_case26 n1 n2 => + I(Int.xor (Int.and n1 n2) Int.mone) + | eval_static_operation_case27 n1 n2 => + I(Int.xor (Int.or n1 n2) Int.mone) + | eval_static_operation_case28 n1 n2 => + I(Int.xor (Int.xor n1 n2) Int.mone) + | eval_static_operation_case29 n1 n2 => + if Int.ltu n2 (Int.repr 32) then I(Int.shl n1 n2) else Unknown + | eval_static_operation_case30 n1 n2 => + if Int.ltu n2 (Int.repr 32) then I(Int.shr n1 n2) else Unknown + | eval_static_operation_case31 n n1 => + if Int.ltu n (Int.repr 32) then I(Int.shr n1 n) else Unknown + | eval_static_operation_case32 n n1 => + if Int.ltu n (Int.repr 32) then I(Int.shrx n1 n) else Unknown + | eval_static_operation_case33 n1 n2 => + if Int.ltu n2 (Int.repr 32) then I(Int.shru n1 n2) else Unknown + | eval_static_operation_case34 amount mask n1 => + I(Int.rolm n1 amount mask) + | eval_static_operation_case35 n1 => + F(Float.neg n1) + | eval_static_operation_case36 n1 => + F(Float.abs n1) + | eval_static_operation_case37 n1 n2 => + F(Float.add n1 n2) + | eval_static_operation_case38 n1 n2 => + F(Float.sub n1 n2) + | eval_static_operation_case39 n1 n2 => + F(Float.mul n1 n2) + | eval_static_operation_case40 n1 n2 => + F(Float.div n1 n2) + | eval_static_operation_case41 n1 n2 n3 => + F(Float.add (Float.mul n1 n2) n3) + | eval_static_operation_case42 n1 n2 n3 => + F(Float.sub (Float.mul n1 n2) n3) + | eval_static_operation_case43 n1 => + F(Float.singleoffloat n1) + | eval_static_operation_case44 n1 => + I(Float.intoffloat n1) + | eval_static_operation_case45 n1 => + F(Float.floatofint n1) + | eval_static_operation_case46 n1 => + F(Float.floatofintu n1) + | eval_static_operation_case47 c vl => + match eval_static_condition c vl with + | None => Unknown + | Some b => I(if b then Int.one else Int.zero) + end + | eval_static_operation_case48 n1 => + I(Int.zero_ext 8 n1) + | eval_static_operation_case49 n1 => + I(Int.zero_ext 16 n1) + | eval_static_operation_case50 n1 => + I(Float.intuoffloat n1) + | eval_static_operation_default op vl => + Unknown + end. + +(** * Operator strength reduction *) + +(** We now define auxiliary functions for strength reduction of + operators and addressing modes: replacing an operator with a cheaper + one if some of its arguments are statically known. These are again + large pattern-matchings expressed in indirect style. *) + +Section STRENGTH_REDUCTION. + +Variable app: reg -> approx. + +Definition intval (r: reg) : option int := + match app r with I n => Some n | _ => None end. + +Inductive cond_strength_reduction_cases: condition -> list reg -> Type := + | csr_case1: + forall c r1 r2, + cond_strength_reduction_cases (Ccomp c) (r1 :: r2 :: nil) + | csr_case2: + forall c r1 r2, + cond_strength_reduction_cases (Ccompu c) (r1 :: r2 :: nil) + | csr_default: + forall c rl, + cond_strength_reduction_cases c rl. + +Definition cond_strength_reduction_match (cond: condition) (rl: list reg) := + match cond as x, rl as y return cond_strength_reduction_cases x y with + | Ccomp c, r1 :: r2 :: nil => + csr_case1 c r1 r2 + | Ccompu c, r1 :: r2 :: nil => + csr_case2 c r1 r2 + | cond, rl => + csr_default cond rl + end. + +Definition cond_strength_reduction + (cond: condition) (args: list reg) : condition * list reg := + match cond_strength_reduction_match cond args with + | csr_case1 c r1 r2 => + match intval r1, intval r2 with + | Some n, _ => + (Ccompimm (swap_comparison c) n, r2 :: nil) + | _, Some n => + (Ccompimm c n, r1 :: nil) + | _, _ => + (cond, args) + end + | csr_case2 c r1 r2 => + match intval r1, intval r2 with + | Some n, _ => + (Ccompuimm (swap_comparison c) n, r2 :: nil) + | _, Some n => + (Ccompuimm c n, r1 :: nil) + | _, _ => + (cond, args) + end + | csr_default cond args => + (cond, args) + end. + +Definition make_addimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Oaddimm n, r :: nil). + +Definition make_shlimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Orolm n (Int.shl Int.mone n), r :: nil). + +Definition make_shrimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Oshrimm n, r :: nil). + +Definition make_shruimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Orolm (Int.sub (Int.repr 32) n) (Int.shru Int.mone n), r :: nil). + +Definition make_mulimm (n: int) (r: reg) := + if Int.eq n Int.zero then + (Ointconst Int.zero, nil) + else if Int.eq n Int.one then + (Omove, r :: nil) + else + match Int.is_power2 n with + | Some l => make_shlimm l r + | None => (Omulimm n, r :: nil) + end. + +Definition make_andimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Ointconst Int.zero, nil) + else if Int.eq n Int.mone then (Omove, r :: nil) + else (Oandimm n, r :: nil). + +Definition make_orimm (n: int) (r: reg) := + if Int.eq n Int.zero then (Omove, r :: nil) + else if Int.eq n Int.mone then (Ointconst Int.mone, nil) + else (Oorimm n, r :: nil). + +Definition make_xorimm (n: int) (r: reg) := + if Int.eq n Int.zero + then (Omove, r :: nil) + else (Oxorimm n, r :: nil). + +Inductive op_strength_reduction_cases: operation -> list reg -> Type := + | op_strength_reduction_case1: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oadd (r1 :: r2 :: nil) + | op_strength_reduction_case2: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Osub (r1 :: r2 :: nil) + | op_strength_reduction_case3: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Omul (r1 :: r2 :: nil) + | op_strength_reduction_case4: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Odiv (r1 :: r2 :: nil) + | op_strength_reduction_case5: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Odivu (r1 :: r2 :: nil) + | op_strength_reduction_case6: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oand (r1 :: r2 :: nil) + | op_strength_reduction_case7: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oor (r1 :: r2 :: nil) + | op_strength_reduction_case8: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oxor (r1 :: r2 :: nil) + | op_strength_reduction_case9: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oshl (r1 :: r2 :: nil) + | op_strength_reduction_case10: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oshr (r1 :: r2 :: nil) + | op_strength_reduction_case11: + forall (r1: reg) (r2: reg), + op_strength_reduction_cases Oshru (r1 :: r2 :: nil) + | op_strength_reduction_case12: + forall (c: condition) (rl: list reg), + op_strength_reduction_cases (Ocmp c) rl + | op_strength_reduction_default: + forall (op: operation) (args: list reg), + op_strength_reduction_cases op args. + +Definition op_strength_reduction_match (op: operation) (args: list reg) := + match op as z1, args as z2 return op_strength_reduction_cases z1 z2 with + | Oadd, r1 :: r2 :: nil => + op_strength_reduction_case1 r1 r2 + | Osub, r1 :: r2 :: nil => + op_strength_reduction_case2 r1 r2 + | Omul, r1 :: r2 :: nil => + op_strength_reduction_case3 r1 r2 + | Odiv, r1 :: r2 :: nil => + op_strength_reduction_case4 r1 r2 + | Odivu, r1 :: r2 :: nil => + op_strength_reduction_case5 r1 r2 + | Oand, r1 :: r2 :: nil => + op_strength_reduction_case6 r1 r2 + | Oor, r1 :: r2 :: nil => + op_strength_reduction_case7 r1 r2 + | Oxor, r1 :: r2 :: nil => + op_strength_reduction_case8 r1 r2 + | Oshl, r1 :: r2 :: nil => + op_strength_reduction_case9 r1 r2 + | Oshr, r1 :: r2 :: nil => + op_strength_reduction_case10 r1 r2 + | Oshru, r1 :: r2 :: nil => + op_strength_reduction_case11 r1 r2 + | Ocmp c, rl => + op_strength_reduction_case12 c rl + | op, args => + op_strength_reduction_default op args + end. + +Definition op_strength_reduction (op: operation) (args: list reg) := + match op_strength_reduction_match op args with + | op_strength_reduction_case1 r1 r2 => (* Oadd *) + match intval r1, intval r2 with + | Some n, _ => make_addimm n r2 + | _, Some n => make_addimm n r1 + | _, _ => (op, args) + end + | op_strength_reduction_case2 r1 r2 => (* Osub *) + match intval r1, intval r2 with + | Some n, _ => (Osubimm n, r2 :: nil) + | _, Some n => make_addimm (Int.neg n) r1 + | _, _ => (op, args) + end + | op_strength_reduction_case3 r1 r2 => (* Omul *) + match intval r1, intval r2 with + | Some n, _ => make_mulimm n r2 + | _, Some n => make_mulimm n r1 + | _, _ => (op, args) + end + | op_strength_reduction_case4 r1 r2 => (* Odiv *) + match intval r2 with + | Some n => + match Int.is_power2 n with + | Some l => (Oshrximm l, r1 :: nil) + | None => (op, args) + end + | None => + (op, args) + end + | op_strength_reduction_case5 r1 r2 => (* Odivu *) + match intval r2 with + | Some n => + match Int.is_power2 n with + | Some l => make_shruimm l r1 + | None => (op, args) + end + | None => + (op, args) + end + | op_strength_reduction_case6 r1 r2 => (* Oand *) + match intval r1, intval r2 with + | Some n, _ => make_andimm n r2 + | _, Some n => make_andimm n r1 + | _, _ => (op, args) + end + | op_strength_reduction_case7 r1 r2 => (* Oor *) + match intval r1, intval r2 with + | Some n, _ => make_orimm n r2 + | _, Some n => make_orimm n r1 + | _, _ => (op, args) + end + | op_strength_reduction_case8 r1 r2 => (* Oxor *) + match intval r1, intval r2 with + | Some n, _ => make_xorimm n r2 + | _, Some n => make_xorimm n r1 + | _, _ => (op, args) + end + | op_strength_reduction_case9 r1 r2 => (* Oshl *) + match intval r2 with + | Some n => + if Int.ltu n (Int.repr 32) + then make_shlimm n r1 + else (op, args) + | _ => (op, args) + end + | op_strength_reduction_case10 r1 r2 => (* Oshr *) + match intval r2 with + | Some n => + if Int.ltu n (Int.repr 32) + then make_shrimm n r1 + else (op, args) + | _ => (op, args) + end + | op_strength_reduction_case11 r1 r2 => (* Oshru *) + match intval r2 with + | Some n => + if Int.ltu n (Int.repr 32) + then make_shruimm n r1 + else (op, args) + | _ => (op, args) + end + | op_strength_reduction_case12 c args => (* Ocmp *) + let (c', args') := cond_strength_reduction c args in + (Ocmp c', args') + | op_strength_reduction_default op args => (* default *) + (op, args) + end. + +Inductive addr_strength_reduction_cases: forall (addr: addressing) (args: list reg), Type := + | addr_strength_reduction_case1: + forall (r1: reg) (r2: reg), + addr_strength_reduction_cases (Aindexed2) (r1 :: r2 :: nil) + | addr_strength_reduction_case2: + forall (symb: ident) (ofs: int) (r1: reg), + addr_strength_reduction_cases (Abased symb ofs) (r1 :: nil) + | addr_strength_reduction_case3: + forall n r1, + addr_strength_reduction_cases (Aindexed n) (r1 :: nil) + | addr_strength_reduction_default: + forall (addr: addressing) (args: list reg), + addr_strength_reduction_cases addr args. + +Definition addr_strength_reduction_match (addr: addressing) (args: list reg) := + match addr as z1, args as z2 return addr_strength_reduction_cases z1 z2 with + | Aindexed2, r1 :: r2 :: nil => + addr_strength_reduction_case1 r1 r2 + | Abased symb ofs, r1 :: nil => + addr_strength_reduction_case2 symb ofs r1 + | Aindexed n, r1 :: nil => + addr_strength_reduction_case3 n r1 + | addr, args => + addr_strength_reduction_default addr args + end. + +Definition addr_strength_reduction (addr: addressing) (args: list reg) := + match addr_strength_reduction_match addr args with + | addr_strength_reduction_case1 r1 r2 => (* Aindexed2 *) + match app r1, app r2 with + | S symb n1, I n2 => (Aglobal symb (Int.add n1 n2), nil) + | S symb n1, _ => (Abased symb n1, r2 :: nil) + | I n1, S symb n2 => (Aglobal symb (Int.add n1 n2), nil) + | I n1, _ => (Aindexed n1, r2 :: nil) + | _, S symb n2 => (Abased symb n2, r1 :: nil) + | _, I n2 => (Aindexed n2, r1 :: nil) + | _, _ => (addr, args) + end + | addr_strength_reduction_case2 symb ofs r1 => (* Abased *) + match intval r1 with + | Some n => (Aglobal symb (Int.add ofs n), nil) + | _ => (addr, args) + end + | addr_strength_reduction_case3 n r1 => (* Aindexed *) + match app r1 with + | S symb ofs => (Aglobal symb (Int.add ofs n), nil) + | _ => (addr, args) + end + | addr_strength_reduction_default addr args => (* default *) + (addr, args) + end. + +End STRENGTH_REDUCTION. |