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diff --git a/arm/SelectOp.v b/arm/SelectOp.v deleted file mode 100644 index 64d15cbc..00000000 --- a/arm/SelectOp.v +++ /dev/null @@ -1,1169 +0,0 @@ -(* *********************************************************************) -(* *) -(* The Compcert verified compiler *) -(* *) -(* Xavier Leroy, INRIA Paris-Rocquencourt *) -(* *) -(* Copyright Institut National de Recherche en Informatique et en *) -(* Automatique. All rights reserved. This file is distributed *) -(* under the terms of the INRIA Non-Commercial License Agreement. *) -(* *) -(* *********************************************************************) - -(** Instruction selection for operators *) - -(** The instruction selection pass recognizes opportunities for using - combined arithmetic and logical operations and addressing modes - offered by the target processor. For instance, the expression [x + 1] - can take advantage of the "immediate add" instruction of the processor, - and on the PowerPC, the expression [(x >> 6) & 0xFF] can be turned - into a "rotate and mask" instruction. - - This file defines functions for building CminorSel expressions and - statements, especially expressions consisting of operator - applications. These functions examine their arguments to choose - cheaper forms of operators whenever possible. - - For instance, [add e1 e2] will return a CminorSel expression semantically - equivalent to [Eop Oadd (e1 ::: e2 ::: Enil)], but will use a - [Oaddimm] operator if one of the arguments is an integer constant, - or suppress the addition altogether if one of the arguments is the - null integer. In passing, we perform operator reassociation - ([(e + c1) * c2] becomes [(e * c2) + (c1 * c2)]) and a small amount - of constant propagation. - - On top of the "smart constructor" functions defined below, - module [Selection] implements the actual instruction selection pass. -*) - -Require Import Coqlib. -Require Import Maps. -Require Import AST. -Require Import Integers. -Require Import Floats. -Require Import Values. -Require Import Memory. -Require Import Globalenvs. -Require Cminor. -Require Import Op. -Require Import CminorSel. - -Open Local Scope cminorsel_scope. - -(** ** Constants **) - -Definition addrsymbol (id: ident) (ofs: int) := - Eop (Oaddrsymbol id ofs) Enil. - -Definition addrstack (ofs: int) := - Eop (Oaddrstack ofs) Enil. - -(** ** Integer logical negation *) - -(** Original definition: -<< -Nondetfunction notint (e: expr) := - match e with - | Eop (Oshift s) (t1:::Enil) => Eop (Onotshift s) (t1:::Enil) - | Eop Onot (t1:::Enil) => t1 - | Eop (Onotshift s) (t1:::Enil) => Eop (Oshift s) (t1:::Enil) - | _ => Eop Onot (e:::Enil) - end. ->> -*) - -Inductive notint_cases: forall (e: expr), Type := - | notint_case1: forall s t1, notint_cases (Eop (Oshift s) (t1:::Enil)) - | notint_case2: forall t1, notint_cases (Eop Onot (t1:::Enil)) - | notint_case3: forall s t1, notint_cases (Eop (Onotshift s) (t1:::Enil)) - | notint_default: forall (e: expr), notint_cases e. - -Definition notint_match (e: expr) := - match e as zz1 return notint_cases zz1 with - | Eop (Oshift s) (t1:::Enil) => notint_case1 s t1 - | Eop Onot (t1:::Enil) => notint_case2 t1 - | Eop (Onotshift s) (t1:::Enil) => notint_case3 s t1 - | e => notint_default e - end. - -Definition notint (e: expr) := - match notint_match e with - | notint_case1 s t1 => (* Eop (Oshift s) (t1:::Enil) *) - Eop (Onotshift s) (t1:::Enil) - | notint_case2 t1 => (* Eop Onot (t1:::Enil) *) - t1 - | notint_case3 s t1 => (* Eop (Onotshift s) (t1:::Enil) *) - Eop (Oshift s) (t1:::Enil) - | notint_default e => - Eop Onot (e:::Enil) - end. - - -(** ** Boolean negation *) - -Fixpoint notbool (e: expr) {struct e} : expr := - let default := Eop (Ocmp (Ccompuimm Ceq Int.zero)) (e ::: Enil) in - match e with - | Eop (Ointconst n) Enil => - Eop (Ointconst (if Int.eq n Int.zero then Int.one else Int.zero)) Enil - | Eop (Ocmp cond) args => - Eop (Ocmp (negate_condition cond)) args - | Econdition e1 e2 e3 => - Econdition e1 (notbool e2) (notbool e3) - | _ => - default - end. - -(** ** Integer addition and pointer addition *) - -(** Original definition: -<< -Nondetfunction addimm (n: int) (e: expr) := - if Int.eq n Int.zero then e else - match e with - | Eop (Ointconst m) Enil => Eop (Ointconst(Int.add n m)) Enil - | Eop (Oaddrsymbol s m) Enil => Eop (Oaddrsymbol s (Int.add n m)) Enil - | Eop (Oaddrstack m) Enil => Eop (Oaddrstack (Int.add n m)) Enil - | Eop (Oaddimm m) (t ::: Enil) => Eop (Oaddimm(Int.add n m)) (t ::: Enil) - | _ => Eop (Oaddimm n) (e ::: Enil) - end. ->> -*) - -Inductive addimm_cases: forall (e: expr), Type := - | addimm_case1: forall m, addimm_cases (Eop (Ointconst m) Enil) - | addimm_case2: forall s m, addimm_cases (Eop (Oaddrsymbol s m) Enil) - | addimm_case3: forall m, addimm_cases (Eop (Oaddrstack m) Enil) - | addimm_case4: forall m t, addimm_cases (Eop (Oaddimm m) (t ::: Enil)) - | addimm_default: forall (e: expr), addimm_cases e. - -Definition addimm_match (e: expr) := - match e as zz1 return addimm_cases zz1 with - | Eop (Ointconst m) Enil => addimm_case1 m - | Eop (Oaddrsymbol s m) Enil => addimm_case2 s m - | Eop (Oaddrstack m) Enil => addimm_case3 m - | Eop (Oaddimm m) (t ::: Enil) => addimm_case4 m t - | e => addimm_default e - end. - -Definition addimm (n: int) (e: expr) := - if Int.eq n Int.zero then e else match addimm_match e with - | addimm_case1 m => (* Eop (Ointconst m) Enil *) - Eop (Ointconst(Int.add n m)) Enil - | addimm_case2 s m => (* Eop (Oaddrsymbol s m) Enil *) - Eop (Oaddrsymbol s (Int.add n m)) Enil - | addimm_case3 m => (* Eop (Oaddrstack m) Enil *) - Eop (Oaddrstack (Int.add n m)) Enil - | addimm_case4 m t => (* Eop (Oaddimm m) (t ::: Enil) *) - Eop (Oaddimm(Int.add n m)) (t ::: Enil) - | addimm_default e => - Eop (Oaddimm n) (e ::: Enil) - end. - - -(** Original definition: -<< -Nondetfunction add (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => addimm n1 t2 - | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => - addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil)) - | Eop(Oaddimm n1) (t1:::Enil), t2 => addimm n1 (Eop Oadd (t1:::t2:::Enil)) - | t1, Eop (Ointconst n2) Enil => addimm n2 t1 - | t1, Eop (Oaddimm n2) (t2:::Enil) => addimm n2 (Eop Oadd (t1:::t2:::Enil)) - | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oaddshift s) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oaddshift s) (t1:::t2:::Enil) - | _, _ => Eop Oadd (e1:::e2:::Enil) - end. ->> -*) - -Inductive add_cases: forall (e1: expr) (e2: expr), Type := - | add_case1: forall n1 t2, add_cases (Eop (Ointconst n1) Enil) (t2) - | add_case2: forall n1 t1 n2 t2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil)) - | add_case3: forall n1 t1 t2, add_cases (Eop(Oaddimm n1) (t1:::Enil)) (t2) - | add_case4: forall t1 n2, add_cases (t1) (Eop (Ointconst n2) Enil) - | add_case5: forall t1 n2 t2, add_cases (t1) (Eop (Oaddimm n2) (t2:::Enil)) - | add_case6: forall s t1 t2, add_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | add_case7: forall t1 s t2, add_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | add_default: forall (e1: expr) (e2: expr), add_cases e1 e2. - -Definition add_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return add_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => add_case1 n1 t2 - | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => add_case2 n1 t1 n2 t2 - | Eop(Oaddimm n1) (t1:::Enil), t2 => add_case3 n1 t1 t2 - | t1, Eop (Ointconst n2) Enil => add_case4 t1 n2 - | t1, Eop (Oaddimm n2) (t2:::Enil) => add_case5 t1 n2 t2 - | Eop (Oshift s) (t1:::Enil), t2 => add_case6 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => add_case7 t1 s t2 - | e1, e2 => add_default e1 e2 - end. - -Definition add (e1: expr) (e2: expr) := - match add_match e1 e2 with - | add_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - addimm n1 t2 - | add_case2 n1 t1 n2 t2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) *) - addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil)) - | add_case3 n1 t1 t2 => (* Eop(Oaddimm n1) (t1:::Enil), t2 *) - addimm n1 (Eop Oadd (t1:::t2:::Enil)) - | add_case4 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - addimm n2 t1 - | add_case5 t1 n2 t2 => (* t1, Eop (Oaddimm n2) (t2:::Enil) *) - addimm n2 (Eop Oadd (t1:::t2:::Enil)) - | add_case6 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Oaddshift s) (t2:::t1:::Enil) - | add_case7 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Oaddshift s) (t1:::t2:::Enil) - | add_default e1 e2 => - Eop Oadd (e1:::e2:::Enil) - end. - - -(** ** Integer and pointer subtraction *) - -(** Original definition: -<< -Nondetfunction sub (e1: expr) (e2: expr) := - match e1, e2 with - | t1, Eop (Ointconst n2) Enil => addimm (Int.neg n2) t1 - | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => - addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil)) - | Eop (Oaddimm n1) (t1:::Enil), t2 => - addimm n1 (Eop Osub (t1:::t2:::Enil)) - | t1, Eop (Oaddimm n2) (t2:::Enil) => - addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil)) - | Eop (Ointconst n1) Enil, t2 => Eop (Orsubimm n1) (t2:::Enil) - | Eop (Oshift s) (t1:::Enil), t2 => Eop (Orsubshift s) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => Eop (Osubshift s) (t1:::t2:::Enil) - | _, _ => Eop Osub (e1:::e2:::Enil) - end. ->> -*) - -Inductive sub_cases: forall (e1: expr) (e2: expr), Type := - | sub_case1: forall t1 n2, sub_cases (t1) (Eop (Ointconst n2) Enil) - | sub_case2: forall n1 t1 n2 t2, sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil)) - | sub_case3: forall n1 t1 t2, sub_cases (Eop (Oaddimm n1) (t1:::Enil)) (t2) - | sub_case4: forall t1 n2 t2, sub_cases (t1) (Eop (Oaddimm n2) (t2:::Enil)) - | sub_case5: forall n1 t2, sub_cases (Eop (Ointconst n1) Enil) (t2) - | sub_case6: forall s t1 t2, sub_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | sub_case7: forall t1 s t2, sub_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | sub_default: forall (e1: expr) (e2: expr), sub_cases e1 e2. - -Definition sub_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return sub_cases zz1 zz2 with - | t1, Eop (Ointconst n2) Enil => sub_case1 t1 n2 - | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => sub_case2 n1 t1 n2 t2 - | Eop (Oaddimm n1) (t1:::Enil), t2 => sub_case3 n1 t1 t2 - | t1, Eop (Oaddimm n2) (t2:::Enil) => sub_case4 t1 n2 t2 - | Eop (Ointconst n1) Enil, t2 => sub_case5 n1 t2 - | Eop (Oshift s) (t1:::Enil), t2 => sub_case6 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => sub_case7 t1 s t2 - | e1, e2 => sub_default e1 e2 - end. - -Definition sub (e1: expr) (e2: expr) := - match sub_match e1 e2 with - | sub_case1 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - addimm (Int.neg n2) t1 - | sub_case2 n1 t1 n2 t2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) *) - addimm (Int.sub n1 n2) (Eop Osub (t1:::t2:::Enil)) - | sub_case3 n1 t1 t2 => (* Eop (Oaddimm n1) (t1:::Enil), t2 *) - addimm n1 (Eop Osub (t1:::t2:::Enil)) - | sub_case4 t1 n2 t2 => (* t1, Eop (Oaddimm n2) (t2:::Enil) *) - addimm (Int.neg n2) (Eop Osub (t1:::t2:::Enil)) - | sub_case5 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - Eop (Orsubimm n1) (t2:::Enil) - | sub_case6 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Orsubshift s) (t2:::t1:::Enil) - | sub_case7 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Osubshift s) (t1:::t2:::Enil) - | sub_default e1 e2 => - Eop Osub (e1:::e2:::Enil) - end. - - -Definition negint (e: expr) := Eop (Orsubimm Int.zero) (e ::: Enil). - -(** ** Immediate shifts *) - -(** Original definition: -<< -Nondetfunction shlimm (e1: expr) (n: int) := - if Int.eq n Int.zero then - e1 - else if negb (Int.ltu n Int.iwordsize) then - Eop Oshl (e1 ::: Eop (Ointconst n) Enil ::: Enil) - else match e1 with - | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shl n1 n)) Enil - | Eop (Oshift (Slsl n1)) (t1:::Enil) => - if Int.ltu (Int.add n n1) Int.iwordsize - then Eop (Oshift (Slsl (mk_shift_amount(Int.add n n1)))) (t1:::Enil) - else Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil) - | _ => Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil) - end. ->> -*) - -Inductive shlimm_cases: forall (e1: expr) , Type := - | shlimm_case1: forall n1, shlimm_cases (Eop (Ointconst n1) Enil) - | shlimm_case2: forall n1 t1, shlimm_cases (Eop (Oshift (Slsl n1)) (t1:::Enil)) - | shlimm_default: forall (e1: expr) , shlimm_cases e1. - -Definition shlimm_match (e1: expr) := - match e1 as zz1 return shlimm_cases zz1 with - | Eop (Ointconst n1) Enil => shlimm_case1 n1 - | Eop (Oshift (Slsl n1)) (t1:::Enil) => shlimm_case2 n1 t1 - | e1 => shlimm_default e1 - end. - -Definition shlimm (e1: expr) (n: int) := - if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshl (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shlimm_match e1 with - | shlimm_case1 n1 => (* Eop (Ointconst n1) Enil *) - Eop (Ointconst(Int.shl n1 n)) Enil - | shlimm_case2 n1 t1 => (* Eop (Oshift (Slsl n1)) (t1:::Enil) *) - if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshift (Slsl (mk_shift_amount(Int.add n n1)))) (t1:::Enil) else Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil) - | shlimm_default e1 => - Eop (Oshift (Slsl (mk_shift_amount n))) (e1:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction shruimm (e1: expr) (n: int) := - if Int.eq n Int.zero then - e1 - else if negb (Int.ltu n Int.iwordsize) then - Eop Oshru (e1 ::: Eop (Ointconst n) Enil ::: Enil) - else match e1 with - | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shru n1 n)) Enil - | Eop (Oshift (Slsr n1)) (t1:::Enil) => - if Int.ltu (Int.add n n1) Int.iwordsize - then Eop (Oshift (Slsr (mk_shift_amount (Int.add n n1)))) (t1:::Enil) - else Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil) - | _ => Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil) - end. ->> -*) - -Inductive shruimm_cases: forall (e1: expr) , Type := - | shruimm_case1: forall n1, shruimm_cases (Eop (Ointconst n1) Enil) - | shruimm_case2: forall n1 t1, shruimm_cases (Eop (Oshift (Slsr n1)) (t1:::Enil)) - | shruimm_default: forall (e1: expr) , shruimm_cases e1. - -Definition shruimm_match (e1: expr) := - match e1 as zz1 return shruimm_cases zz1 with - | Eop (Ointconst n1) Enil => shruimm_case1 n1 - | Eop (Oshift (Slsr n1)) (t1:::Enil) => shruimm_case2 n1 t1 - | e1 => shruimm_default e1 - end. - -Definition shruimm (e1: expr) (n: int) := - if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshru (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shruimm_match e1 with - | shruimm_case1 n1 => (* Eop (Ointconst n1) Enil *) - Eop (Ointconst(Int.shru n1 n)) Enil - | shruimm_case2 n1 t1 => (* Eop (Oshift (Slsr n1)) (t1:::Enil) *) - if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshift (Slsr (mk_shift_amount (Int.add n n1)))) (t1:::Enil) else Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil) - | shruimm_default e1 => - Eop (Oshift (Slsr (mk_shift_amount n))) (e1:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction shrimm (e1: expr) (n: int) := - if Int.eq n Int.zero then - e1 - else if negb (Int.ltu n Int.iwordsize) then - Eop Oshr (e1 ::: Eop (Ointconst n) Enil ::: Enil) - else - match e1 with - | Eop (Ointconst n1) Enil => Eop (Ointconst(Int.shr n1 n)) Enil - | Eop (Oshift (Sasr n1)) (t1:::Enil) => - if Int.ltu (Int.add n n1) Int.iwordsize - then Eop (Oshift (Sasr (mk_shift_amount (Int.add n n1)))) (t1:::Enil) - else Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil) - | _ => Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil) - end. ->> -*) - -Inductive shrimm_cases: forall (e1: expr) , Type := - | shrimm_case1: forall n1, shrimm_cases (Eop (Ointconst n1) Enil) - | shrimm_case2: forall n1 t1, shrimm_cases (Eop (Oshift (Sasr n1)) (t1:::Enil)) - | shrimm_default: forall (e1: expr) , shrimm_cases e1. - -Definition shrimm_match (e1: expr) := - match e1 as zz1 return shrimm_cases zz1 with - | Eop (Ointconst n1) Enil => shrimm_case1 n1 - | Eop (Oshift (Sasr n1)) (t1:::Enil) => shrimm_case2 n1 t1 - | e1 => shrimm_default e1 - end. - -Definition shrimm (e1: expr) (n: int) := - if Int.eq n Int.zero then e1 else if negb (Int.ltu n Int.iwordsize) then Eop Oshr (e1 ::: Eop (Ointconst n) Enil ::: Enil) else match shrimm_match e1 with - | shrimm_case1 n1 => (* Eop (Ointconst n1) Enil *) - Eop (Ointconst(Int.shr n1 n)) Enil - | shrimm_case2 n1 t1 => (* Eop (Oshift (Sasr n1)) (t1:::Enil) *) - if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshift (Sasr (mk_shift_amount (Int.add n n1)))) (t1:::Enil) else Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil) - | shrimm_default e1 => - Eop (Oshift (Sasr (mk_shift_amount n))) (e1:::Enil) - end. - - -(** ** Integer multiply *) - -Definition mulimm_base (n1: int) (e2: expr) := - match Int.one_bits n1 with - | i :: nil => - shlimm e2 i - | i :: j :: nil => - Elet e2 - (add (shlimm (Eletvar 0) i) (shlimm (Eletvar 0) j)) - | _ => - Eop Omul (Eop (Ointconst n1) Enil ::: e2 ::: Enil) - end. - -(** Original definition: -<< -Nondetfunction mulimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil - else if Int.eq n1 Int.one then e2 - else match e2 with - | Eop (Ointconst n2) Enil => Eop (Ointconst(Int.mul n1 n2)) Enil - | Eop (Oaddimm n2) (t2:::Enil) => addimm (Int.mul n1 n2) (mulimm_base n1 t2) - | _ => mulimm_base n1 e2 - end. ->> -*) - -Inductive mulimm_cases: forall (e2: expr), Type := - | mulimm_case1: forall n2, mulimm_cases (Eop (Ointconst n2) Enil) - | mulimm_case2: forall n2 t2, mulimm_cases (Eop (Oaddimm n2) (t2:::Enil)) - | mulimm_default: forall (e2: expr), mulimm_cases e2. - -Definition mulimm_match (e2: expr) := - match e2 as zz1 return mulimm_cases zz1 with - | Eop (Ointconst n2) Enil => mulimm_case1 n2 - | Eop (Oaddimm n2) (t2:::Enil) => mulimm_case2 n2 t2 - | e2 => mulimm_default e2 - end. - -Definition mulimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else if Int.eq n1 Int.one then e2 else match mulimm_match e2 with - | mulimm_case1 n2 => (* Eop (Ointconst n2) Enil *) - Eop (Ointconst(Int.mul n1 n2)) Enil - | mulimm_case2 n2 t2 => (* Eop (Oaddimm n2) (t2:::Enil) *) - addimm (Int.mul n1 n2) (mulimm_base n1 t2) - | mulimm_default e2 => - mulimm_base n1 e2 - end. - - -(** Original definition: -<< -Nondetfunction mul (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => mulimm n1 t2 - | t1, Eop (Ointconst n2) Enil => mulimm n2 t1 - | _, _ => Eop Omul (e1:::e2:::Enil) - end. ->> -*) - -Inductive mul_cases: forall (e1: expr) (e2: expr), Type := - | mul_case1: forall n1 t2, mul_cases (Eop (Ointconst n1) Enil) (t2) - | mul_case2: forall t1 n2, mul_cases (t1) (Eop (Ointconst n2) Enil) - | mul_default: forall (e1: expr) (e2: expr), mul_cases e1 e2. - -Definition mul_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return mul_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => mul_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => mul_case2 t1 n2 - | e1, e2 => mul_default e1 e2 - end. - -Definition mul (e1: expr) (e2: expr) := - match mul_match e1 e2 with - | mul_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - mulimm n1 t2 - | mul_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - mulimm n2 t1 - | mul_default e1 e2 => - Eop Omul (e1:::e2:::Enil) - end. - - -(** ** Bitwise and, or, xor *) - -(** Original definition: -<< -Nondetfunction andimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else - match e2 with - | Eop (Ointconst n2) Enil => - Eop (Ointconst (Int.and n1 n2)) Enil - | Eop (Oandimm n2) (t2:::Enil) => - Eop (Oandimm (Int.and n1 n2)) (t2:::Enil) - | _ => - Eop (Oandimm n1) (e2:::Enil) - end. ->> -*) - -Inductive andimm_cases: forall (e2: expr), Type := - | andimm_case1: forall n2, andimm_cases (Eop (Ointconst n2) Enil) - | andimm_case2: forall n2 t2, andimm_cases (Eop (Oandimm n2) (t2:::Enil)) - | andimm_default: forall (e2: expr), andimm_cases e2. - -Definition andimm_match (e2: expr) := - match e2 as zz1 return andimm_cases zz1 with - | Eop (Ointconst n2) Enil => andimm_case1 n2 - | Eop (Oandimm n2) (t2:::Enil) => andimm_case2 n2 t2 - | e2 => andimm_default e2 - end. - -Definition andimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then Eop (Ointconst Int.zero) Enil else match andimm_match e2 with - | andimm_case1 n2 => (* Eop (Ointconst n2) Enil *) - Eop (Ointconst (Int.and n1 n2)) Enil - | andimm_case2 n2 t2 => (* Eop (Oandimm n2) (t2:::Enil) *) - Eop (Oandimm (Int.and n1 n2)) (t2:::Enil) - | andimm_default e2 => - Eop (Oandimm n1) (e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction and (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => andimm n1 t2 - | t1, Eop (Ointconst n2) Enil => andimm n2 t1 - | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oandshift s) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oandshift s) (t1:::t2:::Enil) - | Eop (Onotshift s) (t1:::Enil), t2 => Eop (Obicshift s) (t2:::t1:::Enil) - | t1, Eop (Onotshift s) (t2:::Enil) => Eop (Obicshift s) (t1:::t2:::Enil) - | Eop Onot (t1:::Enil), t2 => Eop Obic (t2:::t1:::Enil) - | t1, Eop Onot (t2:::Enil) => Eop Obic (t1:::t2:::Enil) - | _, _ => Eop Oand (e1:::e2:::Enil) - end. ->> -*) - -Inductive and_cases: forall (e1: expr) (e2: expr), Type := - | and_case1: forall n1 t2, and_cases (Eop (Ointconst n1) Enil) (t2) - | and_case2: forall t1 n2, and_cases (t1) (Eop (Ointconst n2) Enil) - | and_case3: forall s t1 t2, and_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | and_case4: forall t1 s t2, and_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | and_case5: forall s t1 t2, and_cases (Eop (Onotshift s) (t1:::Enil)) (t2) - | and_case6: forall t1 s t2, and_cases (t1) (Eop (Onotshift s) (t2:::Enil)) - | and_case7: forall t1 t2, and_cases (Eop Onot (t1:::Enil)) (t2) - | and_case8: forall t1 t2, and_cases (t1) (Eop Onot (t2:::Enil)) - | and_default: forall (e1: expr) (e2: expr), and_cases e1 e2. - -Definition and_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return and_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => and_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => and_case2 t1 n2 - | Eop (Oshift s) (t1:::Enil), t2 => and_case3 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => and_case4 t1 s t2 - | Eop (Onotshift s) (t1:::Enil), t2 => and_case5 s t1 t2 - | t1, Eop (Onotshift s) (t2:::Enil) => and_case6 t1 s t2 - | Eop Onot (t1:::Enil), t2 => and_case7 t1 t2 - | t1, Eop Onot (t2:::Enil) => and_case8 t1 t2 - | e1, e2 => and_default e1 e2 - end. - -Definition and (e1: expr) (e2: expr) := - match and_match e1 e2 with - | and_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - andimm n1 t2 - | and_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - andimm n2 t1 - | and_case3 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Oandshift s) (t2:::t1:::Enil) - | and_case4 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Oandshift s) (t1:::t2:::Enil) - | and_case5 s t1 t2 => (* Eop (Onotshift s) (t1:::Enil), t2 *) - Eop (Obicshift s) (t2:::t1:::Enil) - | and_case6 t1 s t2 => (* t1, Eop (Onotshift s) (t2:::Enil) *) - Eop (Obicshift s) (t1:::t2:::Enil) - | and_case7 t1 t2 => (* Eop Onot (t1:::Enil), t2 *) - Eop Obic (t2:::t1:::Enil) - | and_case8 t1 t2 => (* t1, Eop Onot (t2:::Enil) *) - Eop Obic (t1:::t2:::Enil) - | and_default e1 e2 => - Eop Oand (e1:::e2:::Enil) - end. - - -Definition same_expr_pure (e1 e2: expr) := - match e1, e2 with - | Evar v1, Evar v2 => if ident_eq v1 v2 then true else false - | _, _ => false - end. - -(** Original definition: -<< -Nondetfunction orimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then e2 else - match e2 with - | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.or n1 n2)) Enil - | Eop (Oorimm n2) (t2:::Enil) => Eop (Oorimm (Int.or n1 n2)) (t2:::Enil) - | _ => Eop (Oorimm n1) (e2:::Enil) - end. ->> -*) - -Inductive orimm_cases: forall (e2: expr), Type := - | orimm_case1: forall n2, orimm_cases (Eop (Ointconst n2) Enil) - | orimm_case2: forall n2 t2, orimm_cases (Eop (Oorimm n2) (t2:::Enil)) - | orimm_default: forall (e2: expr), orimm_cases e2. - -Definition orimm_match (e2: expr) := - match e2 as zz1 return orimm_cases zz1 with - | Eop (Ointconst n2) Enil => orimm_case1 n2 - | Eop (Oorimm n2) (t2:::Enil) => orimm_case2 n2 t2 - | e2 => orimm_default e2 - end. - -Definition orimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then e2 else match orimm_match e2 with - | orimm_case1 n2 => (* Eop (Ointconst n2) Enil *) - Eop (Ointconst (Int.or n1 n2)) Enil - | orimm_case2 n2 t2 => (* Eop (Oorimm n2) (t2:::Enil) *) - Eop (Oorimm (Int.or n1 n2)) (t2:::Enil) - | orimm_default e2 => - Eop (Oorimm n1) (e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction or (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => orimm n1 t2 - | t1, Eop (Ointconst n2) Enil => orimm n2 t1 - | Eop (Oshift (Slsl n1)) (t1:::Enil), Eop (Oshift (Slsr n2)) (t2:::Enil) => - if Int.eq (Int.add n1 n2) Int.iwordsize - && same_expr_pure t1 t2 - then Eop (Oshift (Sror n2)) (t1:::Enil) - else Eop (Oorshift (Slsr n2)) (e1:::t2:::Enil) - | Eop (Oshift (Slsr n1)) (t1:::Enil), Eop (Oshift (Slsl n2)) (t2:::Enil) => - if Int.eq (Int.add n2 n1) Int.iwordsize - && same_expr_pure t1 t2 - then Eop (Oshift (Sror n1)) (t1:::Enil) - else Eop (Oorshift (Slsl n2)) (e1:::t2:::Enil) - | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oorshift s) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oorshift s) (t1:::t2:::Enil) - | _, _ => Eop Oor (e1:::e2:::Enil) - end. ->> -*) - -Inductive or_cases: forall (e1: expr) (e2: expr), Type := - | or_case1: forall n1 t2, or_cases (Eop (Ointconst n1) Enil) (t2) - | or_case2: forall t1 n2, or_cases (t1) (Eop (Ointconst n2) Enil) - | or_case3: forall n1 t1 n2 t2, or_cases (Eop (Oshift (Slsl n1)) (t1:::Enil)) (Eop (Oshift (Slsr n2)) (t2:::Enil)) - | or_case4: forall n1 t1 n2 t2, or_cases (Eop (Oshift (Slsr n1)) (t1:::Enil)) (Eop (Oshift (Slsl n2)) (t2:::Enil)) - | or_case5: forall s t1 t2, or_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | or_case6: forall t1 s t2, or_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | or_default: forall (e1: expr) (e2: expr), or_cases e1 e2. - -Definition or_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return or_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => or_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => or_case2 t1 n2 - | Eop (Oshift (Slsl n1)) (t1:::Enil), Eop (Oshift (Slsr n2)) (t2:::Enil) => or_case3 n1 t1 n2 t2 - | Eop (Oshift (Slsr n1)) (t1:::Enil), Eop (Oshift (Slsl n2)) (t2:::Enil) => or_case4 n1 t1 n2 t2 - | Eop (Oshift s) (t1:::Enil), t2 => or_case5 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => or_case6 t1 s t2 - | e1, e2 => or_default e1 e2 - end. - -Definition or (e1: expr) (e2: expr) := - match or_match e1 e2 with - | or_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - orimm n1 t2 - | or_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - orimm n2 t1 - | or_case3 n1 t1 n2 t2 => (* Eop (Oshift (Slsl n1)) (t1:::Enil), Eop (Oshift (Slsr n2)) (t2:::Enil) *) - if Int.eq (Int.add n1 n2) Int.iwordsize && same_expr_pure t1 t2 then Eop (Oshift (Sror n2)) (t1:::Enil) else Eop (Oorshift (Slsr n2)) (e1:::t2:::Enil) - | or_case4 n1 t1 n2 t2 => (* Eop (Oshift (Slsr n1)) (t1:::Enil), Eop (Oshift (Slsl n2)) (t2:::Enil) *) - if Int.eq (Int.add n2 n1) Int.iwordsize && same_expr_pure t1 t2 then Eop (Oshift (Sror n1)) (t1:::Enil) else Eop (Oorshift (Slsl n2)) (e1:::t2:::Enil) - | or_case5 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Oorshift s) (t2:::t1:::Enil) - | or_case6 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Oorshift s) (t1:::t2:::Enil) - | or_default e1 e2 => - Eop Oor (e1:::e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction xorimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then e2 else - match e2 with - | Eop (Ointconst n2) Enil => Eop (Ointconst (Int.xor n1 n2)) Enil - | Eop (Oxorimm n2) (t2:::Enil) => Eop (Oxorimm (Int.xor n1 n2)) (t2:::Enil) - | _ => Eop (Oxorimm n1) (e2:::Enil) - end. ->> -*) - -Inductive xorimm_cases: forall (e2: expr), Type := - | xorimm_case1: forall n2, xorimm_cases (Eop (Ointconst n2) Enil) - | xorimm_case2: forall n2 t2, xorimm_cases (Eop (Oxorimm n2) (t2:::Enil)) - | xorimm_default: forall (e2: expr), xorimm_cases e2. - -Definition xorimm_match (e2: expr) := - match e2 as zz1 return xorimm_cases zz1 with - | Eop (Ointconst n2) Enil => xorimm_case1 n2 - | Eop (Oxorimm n2) (t2:::Enil) => xorimm_case2 n2 t2 - | e2 => xorimm_default e2 - end. - -Definition xorimm (n1: int) (e2: expr) := - if Int.eq n1 Int.zero then e2 else match xorimm_match e2 with - | xorimm_case1 n2 => (* Eop (Ointconst n2) Enil *) - Eop (Ointconst (Int.xor n1 n2)) Enil - | xorimm_case2 n2 t2 => (* Eop (Oxorimm n2) (t2:::Enil) *) - Eop (Oxorimm (Int.xor n1 n2)) (t2:::Enil) - | xorimm_default e2 => - Eop (Oxorimm n1) (e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction xor (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => xorimm n1 t2 - | t1, Eop (Ointconst n2) Enil => xorimm n2 t1 - | Eop (Oshift s) (t1:::Enil), t2 => Eop (Oxorshift s) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => Eop (Oxorshift s) (t1:::t2:::Enil) - | _, _ => Eop Oxor (e1:::e2:::Enil) - end. ->> -*) - -Inductive xor_cases: forall (e1: expr) (e2: expr), Type := - | xor_case1: forall n1 t2, xor_cases (Eop (Ointconst n1) Enil) (t2) - | xor_case2: forall t1 n2, xor_cases (t1) (Eop (Ointconst n2) Enil) - | xor_case3: forall s t1 t2, xor_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | xor_case4: forall t1 s t2, xor_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | xor_default: forall (e1: expr) (e2: expr), xor_cases e1 e2. - -Definition xor_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return xor_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => xor_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => xor_case2 t1 n2 - | Eop (Oshift s) (t1:::Enil), t2 => xor_case3 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => xor_case4 t1 s t2 - | e1, e2 => xor_default e1 e2 - end. - -Definition xor (e1: expr) (e2: expr) := - match xor_match e1 e2 with - | xor_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - xorimm n1 t2 - | xor_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - xorimm n2 t1 - | xor_case3 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Oxorshift s) (t2:::t1:::Enil) - | xor_case4 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Oxorshift s) (t1:::t2:::Enil) - | xor_default e1 e2 => - Eop Oxor (e1:::e2:::Enil) - end. - - -(** ** Integer division and modulus *) - -Definition mod_aux (divop: operation) (e1 e2: expr) := - Elet e1 - (Elet (lift e2) - (Eop Osub (Eletvar 1 ::: - Eop Omul (Eop divop (Eletvar 1 ::: Eletvar 0 ::: Enil) ::: - Eletvar 0 ::: - Enil) ::: - Enil))). - -Definition divs (e1: expr) (e2: expr) := Eop Odiv (e1:::e2:::Enil). - -Definition mods := mod_aux Odiv. - -Definition divuimm (e: expr) (n: int) := - match Int.is_power2 n with - | Some l => shruimm e l - | None => Eop Odivu (e ::: Eop (Ointconst n) Enil ::: Enil) - end. - -(** Original definition: -<< -Nondetfunction divu (e1: expr) (e2: expr) := - match e2 with - | Eop (Ointconst n2) Enil => divuimm e1 n2 - | _ => Eop Odivu (e1:::e2:::Enil) - end. ->> -*) - -Inductive divu_cases: forall (e2: expr), Type := - | divu_case1: forall n2, divu_cases (Eop (Ointconst n2) Enil) - | divu_default: forall (e2: expr), divu_cases e2. - -Definition divu_match (e2: expr) := - match e2 as zz1 return divu_cases zz1 with - | Eop (Ointconst n2) Enil => divu_case1 n2 - | e2 => divu_default e2 - end. - -Definition divu (e1: expr) (e2: expr) := - match divu_match e2 with - | divu_case1 n2 => (* Eop (Ointconst n2) Enil *) - divuimm e1 n2 - | divu_default e2 => - Eop Odivu (e1:::e2:::Enil) - end. - - -Definition moduimm (e: expr) (n: int) := - match Int.is_power2 n with - | Some l => Eop (Oandimm (Int.sub n Int.one)) (e ::: Enil) - | None => mod_aux Odivu e (Eop (Ointconst n) Enil) - end. - -(** Original definition: -<< -Nondetfunction modu (e1: expr) (e2: expr) := - match e2 with - | Eop (Ointconst n2) Enil => moduimm e1 n2 - | _ => mod_aux Odivu e1 e2 - end. ->> -*) - -Inductive modu_cases: forall (e2: expr), Type := - | modu_case1: forall n2, modu_cases (Eop (Ointconst n2) Enil) - | modu_default: forall (e2: expr), modu_cases e2. - -Definition modu_match (e2: expr) := - match e2 as zz1 return modu_cases zz1 with - | Eop (Ointconst n2) Enil => modu_case1 n2 - | e2 => modu_default e2 - end. - -Definition modu (e1: expr) (e2: expr) := - match modu_match e2 with - | modu_case1 n2 => (* Eop (Ointconst n2) Enil *) - moduimm e1 n2 - | modu_default e2 => - mod_aux Odivu e1 e2 - end. - - -(** ** General shifts *) - -(** Original definition: -<< -Nondetfunction shl (e1: expr) (e2: expr) := - match e2 with - | Eop (Ointconst n2) Enil => shlimm e1 n2 - | _ => Eop Oshl (e1:::e2:::Enil) - end. ->> -*) - -Inductive shl_cases: forall (e2: expr), Type := - | shl_case1: forall n2, shl_cases (Eop (Ointconst n2) Enil) - | shl_default: forall (e2: expr), shl_cases e2. - -Definition shl_match (e2: expr) := - match e2 as zz1 return shl_cases zz1 with - | Eop (Ointconst n2) Enil => shl_case1 n2 - | e2 => shl_default e2 - end. - -Definition shl (e1: expr) (e2: expr) := - match shl_match e2 with - | shl_case1 n2 => (* Eop (Ointconst n2) Enil *) - shlimm e1 n2 - | shl_default e2 => - Eop Oshl (e1:::e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction shr (e1: expr) (e2: expr) := - match e2 with - | Eop (Ointconst n2) Enil => shrimm e1 n2 - | _ => Eop Oshr (e1:::e2:::Enil) - end. ->> -*) - -Inductive shr_cases: forall (e2: expr), Type := - | shr_case1: forall n2, shr_cases (Eop (Ointconst n2) Enil) - | shr_default: forall (e2: expr), shr_cases e2. - -Definition shr_match (e2: expr) := - match e2 as zz1 return shr_cases zz1 with - | Eop (Ointconst n2) Enil => shr_case1 n2 - | e2 => shr_default e2 - end. - -Definition shr (e1: expr) (e2: expr) := - match shr_match e2 with - | shr_case1 n2 => (* Eop (Ointconst n2) Enil *) - shrimm e1 n2 - | shr_default e2 => - Eop Oshr (e1:::e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction shru (e1: expr) (e2: expr) := - match e2 with - | Eop (Ointconst n2) Enil => shruimm e1 n2 - | _ => Eop Oshru (e1:::e2:::Enil) - end. ->> -*) - -Inductive shru_cases: forall (e2: expr), Type := - | shru_case1: forall n2, shru_cases (Eop (Ointconst n2) Enil) - | shru_default: forall (e2: expr), shru_cases e2. - -Definition shru_match (e2: expr) := - match e2 as zz1 return shru_cases zz1 with - | Eop (Ointconst n2) Enil => shru_case1 n2 - | e2 => shru_default e2 - end. - -Definition shru (e1: expr) (e2: expr) := - match shru_match e2 with - | shru_case1 n2 => (* Eop (Ointconst n2) Enil *) - shruimm e1 n2 - | shru_default e2 => - Eop Oshru (e1:::e2:::Enil) - end. - - -(** ** Floating-point arithmetic *) - -Definition negf (e: expr) := Eop Onegf (e ::: Enil). -Definition absf (e: expr) := Eop Oabsf (e ::: Enil). -Definition addf (e1 e2: expr) := Eop Oaddf (e1 ::: e2 ::: Enil). -Definition subf (e1 e2: expr) := Eop Osubf (e1 ::: e2 ::: Enil). -Definition mulf (e1 e2: expr) := Eop Omulf (e1 ::: e2 ::: Enil). -Definition divf (e1 e2: expr) := Eop Odivf (e1 ::: e2 ::: Enil). - -(** ** Comparisons *) - -(** Original definition: -<< -Nondetfunction comp (c: comparison) (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => - Eop (Ocmp (Ccompimm (swap_comparison c) n1)) (t2:::Enil) - | t1, Eop (Ointconst n2) Enil => - Eop (Ocmp (Ccompimm c n2)) (t1:::Enil) - | Eop (Oshift s) (t1:::Enil), t2 => - Eop (Ocmp (Ccompshift (swap_comparison c) s)) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => - Eop (Ocmp (Ccompshift c s)) (t1:::t2:::Enil) - | _, _ => - Eop (Ocmp (Ccomp c)) (e1:::e2:::Enil) - end. ->> -*) - -Inductive comp_cases: forall (e1: expr) (e2: expr), Type := - | comp_case1: forall n1 t2, comp_cases (Eop (Ointconst n1) Enil) (t2) - | comp_case2: forall t1 n2, comp_cases (t1) (Eop (Ointconst n2) Enil) - | comp_case3: forall s t1 t2, comp_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | comp_case4: forall t1 s t2, comp_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | comp_default: forall (e1: expr) (e2: expr), comp_cases e1 e2. - -Definition comp_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return comp_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => comp_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => comp_case2 t1 n2 - | Eop (Oshift s) (t1:::Enil), t2 => comp_case3 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => comp_case4 t1 s t2 - | e1, e2 => comp_default e1 e2 - end. - -Definition comp (c: comparison) (e1: expr) (e2: expr) := - match comp_match e1 e2 with - | comp_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - Eop (Ocmp (Ccompimm (swap_comparison c) n1)) (t2:::Enil) - | comp_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - Eop (Ocmp (Ccompimm c n2)) (t1:::Enil) - | comp_case3 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Ocmp (Ccompshift (swap_comparison c) s)) (t2:::t1:::Enil) - | comp_case4 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Ocmp (Ccompshift c s)) (t1:::t2:::Enil) - | comp_default e1 e2 => - Eop (Ocmp (Ccomp c)) (e1:::e2:::Enil) - end. - - -(** Original definition: -<< -Nondetfunction compu (c: comparison) (e1: expr) (e2: expr) := - match e1, e2 with - | Eop (Ointconst n1) Enil, t2 => - Eop (Ocmp (Ccompuimm (swap_comparison c) n1)) (t2:::Enil) - | t1, Eop (Ointconst n2) Enil => - Eop (Ocmp (Ccompuimm c n2)) (t1:::Enil) - | Eop (Oshift s) (t1:::Enil), t2 => - Eop (Ocmp (Ccompushift (swap_comparison c) s)) (t2:::t1:::Enil) - | t1, Eop (Oshift s) (t2:::Enil) => - Eop (Ocmp (Ccompushift c s)) (t1:::t2:::Enil) - | _, _ => - Eop (Ocmp (Ccompu c)) (e1:::e2:::Enil) - end. ->> -*) - -Inductive compu_cases: forall (e1: expr) (e2: expr), Type := - | compu_case1: forall n1 t2, compu_cases (Eop (Ointconst n1) Enil) (t2) - | compu_case2: forall t1 n2, compu_cases (t1) (Eop (Ointconst n2) Enil) - | compu_case3: forall s t1 t2, compu_cases (Eop (Oshift s) (t1:::Enil)) (t2) - | compu_case4: forall t1 s t2, compu_cases (t1) (Eop (Oshift s) (t2:::Enil)) - | compu_default: forall (e1: expr) (e2: expr), compu_cases e1 e2. - -Definition compu_match (e1: expr) (e2: expr) := - match e1 as zz1, e2 as zz2 return compu_cases zz1 zz2 with - | Eop (Ointconst n1) Enil, t2 => compu_case1 n1 t2 - | t1, Eop (Ointconst n2) Enil => compu_case2 t1 n2 - | Eop (Oshift s) (t1:::Enil), t2 => compu_case3 s t1 t2 - | t1, Eop (Oshift s) (t2:::Enil) => compu_case4 t1 s t2 - | e1, e2 => compu_default e1 e2 - end. - -Definition compu (c: comparison) (e1: expr) (e2: expr) := - match compu_match e1 e2 with - | compu_case1 n1 t2 => (* Eop (Ointconst n1) Enil, t2 *) - Eop (Ocmp (Ccompuimm (swap_comparison c) n1)) (t2:::Enil) - | compu_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) - Eop (Ocmp (Ccompuimm c n2)) (t1:::Enil) - | compu_case3 s t1 t2 => (* Eop (Oshift s) (t1:::Enil), t2 *) - Eop (Ocmp (Ccompushift (swap_comparison c) s)) (t2:::t1:::Enil) - | compu_case4 t1 s t2 => (* t1, Eop (Oshift s) (t2:::Enil) *) - Eop (Ocmp (Ccompushift c s)) (t1:::t2:::Enil) - | compu_default e1 e2 => - Eop (Ocmp (Ccompu c)) (e1:::e2:::Enil) - end. - - -Definition compf (c: comparison) (e1: expr) (e2: expr) := - Eop (Ocmp (Ccompf c)) (e1 ::: e2 ::: Enil). - -(** ** Integer conversions *) - -Definition cast8unsigned (e: expr) := andimm (Int.repr 255) e. - -Definition cast8signed (e: expr) := shrimm (shlimm e (Int.repr 24)) (Int.repr 24). - -Definition cast16unsigned (e: expr) := andimm (Int.repr 65535) e. - -Definition cast16signed (e: expr) := shrimm (shlimm e (Int.repr 16)) (Int.repr 16). - -(** ** Floating-point conversions *) - -Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil). -Definition intoffloat (e: expr) := Eop Ointoffloat (e ::: Enil). -Definition intuoffloat (e: expr) := Eop Ointuoffloat (e ::: Enil). -Definition floatofint (e: expr) := Eop Ofloatofint (e ::: Enil). -Definition floatofintu (e: expr) := Eop Ofloatofintu (e ::: Enil). - -(** ** Recognition of addressing modes for load and store operations *) - -(** We do not recognize the [Aindexed2] and [Aindexed2shift] modes - for floating-point accesses, since these are not supported - by the hardware and emulated inefficiently in [Asmgen]. - Likewise, [Aindexed2shift] are not supported for halfword - and signed byte accesses. *) - -Definition can_use_Aindexed2 (chunk: memory_chunk): bool := - match chunk with - | Mint8signed => true - | Mint8unsigned => true - | Mint16signed => true - | Mint16unsigned => true - | Mint32 => true - | Mfloat32 => false - | Mfloat64 => false - end. - -Definition can_use_Aindexed2shift (chunk: memory_chunk): bool := - match chunk with - | Mint8signed => false - | Mint8unsigned => true - | Mint16signed => false - | Mint16unsigned => false - | Mint32 => true - | Mfloat32 => false - | Mfloat64 => false - end. - -(** Original definition: -<< -Nondetfunction addressing (chunk: memory_chunk) (e: expr) := - match e with - | Eop (Oaddrstack n) Enil => (Ainstack n, Enil) - | Eop (Oaddimm n) (e1:::Enil) => (Aindexed n, e1:::Enil) - | Eop (Oaddshift s) (e1:::e2:::Enil) => - if can_use_Aindexed2shift chunk - then (Aindexed2shift s, e1:::e2:::Enil) - else (Aindexed Int.zero, Eop (Oaddshift s) (e1:::e2:::Enil) ::: Enil) - | Eop Oadd (e1:::e2:::Enil) => - if can_use_Aindexed2 chunk - then (Aindexed2, e1:::e2:::Enil) - else (Aindexed Int.zero, Eop Oadd (e1:::e2:::Enil) ::: Enil) - | _ => (Aindexed Int.zero, e:::Enil) - end. ->> -*) - -Inductive addressing_cases: forall (e: expr), Type := - | addressing_case1: forall n, addressing_cases (Eop (Oaddrstack n) Enil) - | addressing_case2: forall n e1, addressing_cases (Eop (Oaddimm n) (e1:::Enil)) - | addressing_case3: forall s e1 e2, addressing_cases (Eop (Oaddshift s) (e1:::e2:::Enil)) - | addressing_case4: forall e1 e2, addressing_cases (Eop Oadd (e1:::e2:::Enil)) - | addressing_default: forall (e: expr), addressing_cases e. - -Definition addressing_match (e: expr) := - match e as zz1 return addressing_cases zz1 with - | Eop (Oaddrstack n) Enil => addressing_case1 n - | Eop (Oaddimm n) (e1:::Enil) => addressing_case2 n e1 - | Eop (Oaddshift s) (e1:::e2:::Enil) => addressing_case3 s e1 e2 - | Eop Oadd (e1:::e2:::Enil) => addressing_case4 e1 e2 - | e => addressing_default e - end. - -Definition addressing (chunk: memory_chunk) (e: expr) := - match addressing_match e with - | addressing_case1 n => (* Eop (Oaddrstack n) Enil *) - (Ainstack n, Enil) - | addressing_case2 n e1 => (* Eop (Oaddimm n) (e1:::Enil) *) - (Aindexed n, e1:::Enil) - | addressing_case3 s e1 e2 => (* Eop (Oaddshift s) (e1:::e2:::Enil) *) - if can_use_Aindexed2shift chunk then (Aindexed2shift s, e1:::e2:::Enil) else (Aindexed Int.zero, Eop (Oaddshift s) (e1:::e2:::Enil) ::: Enil) - | addressing_case4 e1 e2 => (* Eop Oadd (e1:::e2:::Enil) *) - if can_use_Aindexed2 chunk then (Aindexed2, e1:::e2:::Enil) else (Aindexed Int.zero, Eop Oadd (e1:::e2:::Enil) ::: Enil) - | addressing_default e => - (Aindexed Int.zero, e:::Enil) - end. - - - |