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diff --git a/verilog/SelectOp.v b/verilog/SelectOp.v new file mode 100644 index 00000000..d477d7bd --- /dev/null +++ b/verilog/SelectOp.v @@ -0,0 +1,1549 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris *) +(* *) +(* 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 Compopts. +Require Import AST Integers Floats Builtins. +Require Import Op CminorSel. +Require Archi. + +Local Open Scope cminorsel_scope. + +(** ** Constants **) + +(** External oracle to determine whether a symbol should be addressed + through [Oindirectsymbol] or can be addressed via [Oleal Aglobal]. + This is to accommodate MacOS X's limitations on references to data + symbols imported from shared libraries. It can also help with PIC + code under ELF. *) + +Parameter symbol_is_external: ident -> bool. + +Definition Olea_ptr (a: addressing) := if Archi.ptr64 then Oleal a else Olea a. + +Definition addrsymbol (id: ident) (ofs: ptrofs) := + if symbol_is_external id then + if Ptrofs.eq ofs Ptrofs.zero + then Eop (Oindirectsymbol id) Enil + else Eop (Olea_ptr (Aindexed (Ptrofs.unsigned ofs))) (Eop (Oindirectsymbol id) Enil ::: Enil) + else + Eop (Olea_ptr (Aglobal id ofs)) Enil. + +Definition addrstack (ofs: ptrofs) := + Eop (Olea_ptr (Ainstack ofs)) Enil. + +(** ** Integer logical negation *) + +(** Original definition: +<< +Nondetfunction notint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.not n)) Enil + | Eop (Oxorimm n) (e1 ::: Enil) => Eop (Oxorimm (Int.not n)) (e1 ::: Enil) + | _ => Eop Onot (e ::: Enil) + end. +>> +*) + +Inductive notint_cases: forall (e: expr), Type := + | notint_case1: forall n, notint_cases (Eop (Ointconst n) Enil) + | notint_case2: forall n e1, notint_cases (Eop (Oxorimm n) (e1 ::: Enil)) + | notint_default: forall (e: expr), notint_cases e. + +Definition notint_match (e: expr) := + match e as zz1 return notint_cases zz1 with + | Eop (Ointconst n) Enil => notint_case1 n + | Eop (Oxorimm n) (e1 ::: Enil) => notint_case2 n e1 + | e => notint_default e + end. + +Definition notint (e: expr) := + match notint_match e with + | notint_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.not n)) Enil + | notint_case2 n e1 => (* Eop (Oxorimm n) (e1 ::: Enil) *) + Eop (Oxorimm (Int.not n)) (e1 ::: Enil) + | notint_default e => + Eop Onot (e ::: Enil) + 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 (Olea addr) args => Eop (Olea (offset_addressing_total addr (Int.signed n))) args + | _ => Eop (Olea (Aindexed (Int.signed n))) (e ::: Enil) + end. +>> +*) + +Inductive addimm_cases: forall (e: expr), Type := + | addimm_case1: forall m, addimm_cases (Eop (Ointconst m) Enil) + | addimm_case2: forall addr args, addimm_cases (Eop (Olea addr) args) + | 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 (Olea addr) args => addimm_case2 addr args + | 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 addr args => (* Eop (Olea addr) args *) + Eop (Olea (offset_addressing_total addr (Int.signed n))) args + | addimm_default e => + Eop (Olea (Aindexed (Int.signed n))) (e ::: Enil) + end. + + +(** Original definition: +<< +Nondetfunction add (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Ointconst n1) Enil, t2 => addimm n1 t2 + | t1, Eop (Ointconst n2) Enil => addimm n2 t1 + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => + Eop (Olea (Aindexed2 (n1 + n2))) (t1:::t2:::Enil) + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Ascaled sc n2)) (t2:::Enil) => + Eop (Olea (Aindexed2scaled sc (n1 + n2))) (t1:::t2:::Enil) + | Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => + Eop (Olea (Aindexed2scaled sc (n1 + n2))) (t2:::t1:::Enil) + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil => + Eop (Olea (Abased id (Ptrofs.add ofs (Ptrofs.repr n1)))) (t1:::Enil) + | Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Aindexed n2)) (t2:::Enil) => + Eop (Olea (Abased id (Ptrofs.add ofs (Ptrofs.repr n2)))) (t2:::Enil) + | Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil => + Eop (Olea (Abasedscaled sc id (Ptrofs.add ofs (Ptrofs.repr n1)))) (t1:::Enil) + | Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Ascaled sc n2)) (t2:::Enil) => + Eop (Olea (Abasedscaled sc id (Ptrofs.add ofs (Ptrofs.repr n2)))) (t2:::Enil) + | Eop (Olea (Ascaled sc n)) (t1:::Enil), t2 => + Eop (Olea (Aindexed2scaled sc n)) (t2:::t1:::Enil) + | t1, Eop (Olea (Ascaled sc n)) (t2:::Enil) => + Eop (Olea (Aindexed2scaled sc n)) (t1:::t2:::Enil) + | Eop (Olea (Aindexed n)) (t1:::Enil), t2 => + Eop (Olea (Aindexed2 n)) (t1:::t2:::Enil) + | t1, Eop (Olea (Aindexed n)) (t2:::Enil) => + Eop (Olea (Aindexed2 n)) (t1:::t2:::Enil) + | _, _ => + Eop (Olea (Aindexed2 0)) (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 t1 n2, add_cases (t1) (Eop (Ointconst n2) Enil) + | add_case3: forall n1 t1 n2 t2, add_cases (Eop (Olea (Aindexed n1)) (t1:::Enil)) (Eop (Olea (Aindexed n2)) (t2:::Enil)) + | add_case4: forall n1 t1 sc n2 t2, add_cases (Eop (Olea (Aindexed n1)) (t1:::Enil)) (Eop (Olea (Ascaled sc n2)) (t2:::Enil)) + | add_case5: forall sc n1 t1 n2 t2, add_cases (Eop (Olea (Ascaled sc n1)) (t1:::Enil)) (Eop (Olea (Aindexed n2)) (t2:::Enil)) + | add_case6: forall n1 t1 id ofs, add_cases (Eop (Olea (Aindexed n1)) (t1:::Enil)) (Eop (Olea (Aglobal id ofs)) Enil) + | add_case7: forall id ofs n2 t2, add_cases (Eop (Olea (Aglobal id ofs)) Enil) (Eop (Olea (Aindexed n2)) (t2:::Enil)) + | add_case8: forall sc n1 t1 id ofs, add_cases (Eop (Olea (Ascaled sc n1)) (t1:::Enil)) (Eop (Olea (Aglobal id ofs)) Enil) + | add_case9: forall id ofs sc n2 t2, add_cases (Eop (Olea (Aglobal id ofs)) Enil) (Eop (Olea (Ascaled sc n2)) (t2:::Enil)) + | add_case10: forall sc n t1 t2, add_cases (Eop (Olea (Ascaled sc n)) (t1:::Enil)) (t2) + | add_case11: forall t1 sc n t2, add_cases (t1) (Eop (Olea (Ascaled sc n)) (t2:::Enil)) + | add_case12: forall n t1 t2, add_cases (Eop (Olea (Aindexed n)) (t1:::Enil)) (t2) + | add_case13: forall t1 n t2, add_cases (t1) (Eop (Olea (Aindexed n)) (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 + | t1, Eop (Ointconst n2) Enil => add_case2 t1 n2 + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => add_case3 n1 t1 n2 t2 + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Ascaled sc n2)) (t2:::Enil) => add_case4 n1 t1 sc n2 t2 + | Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => add_case5 sc n1 t1 n2 t2 + | Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil => add_case6 n1 t1 id ofs + | Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Aindexed n2)) (t2:::Enil) => add_case7 id ofs n2 t2 + | Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil => add_case8 sc n1 t1 id ofs + | Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Ascaled sc n2)) (t2:::Enil) => add_case9 id ofs sc n2 t2 + | Eop (Olea (Ascaled sc n)) (t1:::Enil), t2 => add_case10 sc n t1 t2 + | t1, Eop (Olea (Ascaled sc n)) (t2:::Enil) => add_case11 t1 sc n t2 + | Eop (Olea (Aindexed n)) (t1:::Enil), t2 => add_case12 n t1 t2 + | t1, Eop (Olea (Aindexed n)) (t2:::Enil) => add_case13 t1 n 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 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) + addimm n2 t1 + | add_case3 n1 t1 n2 t2 => (* Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) *) + Eop (Olea (Aindexed2 (n1 + n2))) (t1:::t2:::Enil) + | add_case4 n1 t1 sc n2 t2 => (* Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Ascaled sc n2)) (t2:::Enil) *) + Eop (Olea (Aindexed2scaled sc (n1 + n2))) (t1:::t2:::Enil) + | add_case5 sc n1 t1 n2 t2 => (* Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) *) + Eop (Olea (Aindexed2scaled sc (n1 + n2))) (t2:::t1:::Enil) + | add_case6 n1 t1 id ofs => (* Eop (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil *) + Eop (Olea (Abased id (Ptrofs.add ofs (Ptrofs.repr n1)))) (t1:::Enil) + | add_case7 id ofs n2 t2 => (* Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Aindexed n2)) (t2:::Enil) *) + Eop (Olea (Abased id (Ptrofs.add ofs (Ptrofs.repr n2)))) (t2:::Enil) + | add_case8 sc n1 t1 id ofs => (* Eop (Olea (Ascaled sc n1)) (t1:::Enil), Eop (Olea (Aglobal id ofs)) Enil *) + Eop (Olea (Abasedscaled sc id (Ptrofs.add ofs (Ptrofs.repr n1)))) (t1:::Enil) + | add_case9 id ofs sc n2 t2 => (* Eop (Olea (Aglobal id ofs)) Enil, Eop (Olea (Ascaled sc n2)) (t2:::Enil) *) + Eop (Olea (Abasedscaled sc id (Ptrofs.add ofs (Ptrofs.repr n2)))) (t2:::Enil) + | add_case10 sc n t1 t2 => (* Eop (Olea (Ascaled sc n)) (t1:::Enil), t2 *) + Eop (Olea (Aindexed2scaled sc n)) (t2:::t1:::Enil) + | add_case11 t1 sc n t2 => (* t1, Eop (Olea (Ascaled sc n)) (t2:::Enil) *) + Eop (Olea (Aindexed2scaled sc n)) (t1:::t2:::Enil) + | add_case12 n t1 t2 => (* Eop (Olea (Aindexed n)) (t1:::Enil), t2 *) + Eop (Olea (Aindexed2 n)) (t1:::t2:::Enil) + | add_case13 t1 n t2 => (* t1, Eop (Olea (Aindexed n)) (t2:::Enil) *) + Eop (Olea (Aindexed2 n)) (t1:::t2:::Enil) + | add_default e1 e2 => + Eop (Olea (Aindexed2 0)) (e1:::e2:::Enil) + end. + + +(** ** Opposite *) + +(** Original definition: +<< +Nondetfunction negint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ointconst (Int.neg n)) Enil + | _ => Eop Oneg (e ::: Enil) + end. +>> +*) + +Inductive negint_cases: forall (e: expr), Type := + | negint_case1: forall n, negint_cases (Eop (Ointconst n) Enil) + | negint_default: forall (e: expr), negint_cases e. + +Definition negint_match (e: expr) := + match e as zz1 return negint_cases zz1 with + | Eop (Ointconst n) Enil => negint_case1 n + | e => negint_default e + end. + +Definition negint (e: expr) := + match negint_match e with + | negint_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.neg n)) Enil + | negint_default e => + Eop Oneg (e ::: 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 (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => + addimm (Int.repr (n1 - n2)) (Eop Osub (t1:::t2:::Enil)) + | Eop (Olea (Aindexed n1)) (t1:::Enil), t2 => + addimm (Int.repr n1) (Eop Osub (t1:::t2:::Enil)) + | t1, Eop (Olea (Aindexed n2)) (t2:::Enil) => + addimm (Int.repr (-n2)) (Eop Osub (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 (Olea (Aindexed n1)) (t1:::Enil)) (Eop (Olea (Aindexed n2)) (t2:::Enil)) + | sub_case3: forall n1 t1 t2, sub_cases (Eop (Olea (Aindexed n1)) (t1:::Enil)) (t2) + | sub_case4: forall t1 n2 t2, sub_cases (t1) (Eop (Olea (Aindexed n2)) (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 (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) => sub_case2 n1 t1 n2 t2 + | Eop (Olea (Aindexed n1)) (t1:::Enil), t2 => sub_case3 n1 t1 t2 + | t1, Eop (Olea (Aindexed n2)) (t2:::Enil) => sub_case4 t1 n2 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 (Olea (Aindexed n1)) (t1:::Enil), Eop (Olea (Aindexed n2)) (t2:::Enil) *) + addimm (Int.repr (n1 - n2)) (Eop Osub (t1:::t2:::Enil)) + | sub_case3 n1 t1 t2 => (* Eop (Olea (Aindexed n1)) (t1:::Enil), t2 *) + addimm (Int.repr n1) (Eop Osub (t1:::t2:::Enil)) + | sub_case4 t1 n2 t2 => (* t1, Eop (Olea (Aindexed n2)) (t2:::Enil) *) + addimm (Int.repr (-n2)) (Eop Osub (t1:::t2:::Enil)) + | sub_default e1 e2 => + Eop Osub (e1:::e2:::Enil) + end. + + +(** ** Immediate shifts *) + +Definition shift_is_scale (n: int) : bool := + Int.eq n (Int.repr 1) || Int.eq n (Int.repr 2) || Int.eq n (Int.repr 3). + +(** 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 (Oshlimm n1) (t1:::Enil) => + if Int.ltu (Int.add n n1) Int.iwordsize + then Eop (Oshlimm (Int.add n n1)) (t1:::Enil) + else Eop (Oshlimm n) (e1:::Enil) + | Eop (Olea (Aindexed n1)) (t1:::Enil) => + if shift_is_scale n + then Eop (Olea (Ascaled (Int.unsigned (Int.shl Int.one n)) + (Int.unsigned (Int.shl (Int.repr n1) n)))) (t1:::Enil) + else Eop (Oshlimm n) (e1:::Enil) + | _ => + if shift_is_scale n + then Eop (Olea (Ascaled (Int.unsigned (Int.shl Int.one n)) 0)) (e1:::Enil) + else Eop (Oshlimm 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 (Oshlimm n1) (t1:::Enil)) + | shlimm_case3: forall n1 t1, shlimm_cases (Eop (Olea (Aindexed 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 (Oshlimm n1) (t1:::Enil) => shlimm_case2 n1 t1 + | Eop (Olea (Aindexed n1)) (t1:::Enil) => shlimm_case3 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 (Oshlimm n1) (t1:::Enil) *) + if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshlimm (Int.add n n1)) (t1:::Enil) else Eop (Oshlimm n) (e1:::Enil) + | shlimm_case3 n1 t1 => (* Eop (Olea (Aindexed n1)) (t1:::Enil) *) + if shift_is_scale n then Eop (Olea (Ascaled (Int.unsigned (Int.shl Int.one n)) (Int.unsigned (Int.shl (Int.repr n1) n)))) (t1:::Enil) else Eop (Oshlimm n) (e1:::Enil) + | shlimm_default e1 => + if shift_is_scale n then Eop (Olea (Ascaled (Int.unsigned (Int.shl Int.one n)) 0)) (e1:::Enil) else Eop (Oshlimm 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 (Oshruimm n1) (t1:::Enil) => + if Int.ltu (Int.add n n1) Int.iwordsize + then Eop (Oshruimm (Int.add n n1)) (t1:::Enil) + else Eop (Oshruimm n) (e1:::Enil) + | _ => + Eop (Oshruimm 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 (Oshruimm 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 (Oshruimm 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 (Oshruimm n1) (t1:::Enil) *) + if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshruimm (Int.add n n1)) (t1:::Enil) else Eop (Oshruimm n) (e1:::Enil) + | shruimm_default e1 => + Eop (Oshruimm 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 (Oshrimm n1) (t1:::Enil) => + if Int.ltu (Int.add n n1) Int.iwordsize + then Eop (Oshrimm (Int.add n n1)) (t1:::Enil) + else Eop (Oshrimm n) (e1:::Enil) + | _ => + Eop (Oshrimm 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 (Oshrimm 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 (Oshrimm 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 (Oshrimm n1) (t1:::Enil) *) + if Int.ltu (Int.add n n1) Int.iwordsize then Eop (Oshrimm (Int.add n n1)) (t1:::Enil) else Eop (Oshrimm n) (e1:::Enil) + | shrimm_default e1 => + Eop (Oshrimm 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 (Omulimm n1) (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 (Olea (Aindexed n2)) (t2:::Enil) => addimm (Int.mul n1 (Int.repr 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 (Olea (Aindexed 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 (Olea (Aindexed 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 (Olea (Aindexed n2)) (t2:::Enil) *) + addimm (Int.mul n1 (Int.repr 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. + + +Definition mulhs (e1: expr) (e2: expr) := Eop Omulhs (e1 ::: e2 ::: Enil). +Definition mulhu (e1: expr) (e2: expr) := Eop Omulhu (e1 ::: e2 ::: Enil). + +(** ** 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 if Int.eq n1 Int.mone then e2 + 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 Ocast8unsigned (t2:::Enil) => + Eop (Oandimm (Int.and n1 (Int.repr 255))) (t2:::Enil) + | Eop Ocast16unsigned (t2:::Enil) => + Eop (Oandimm (Int.and n1 (Int.repr 65535))) (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_case3: forall t2, andimm_cases (Eop Ocast8unsigned (t2:::Enil)) + | andimm_case4: forall t2, andimm_cases (Eop Ocast16unsigned (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 + | Eop Ocast8unsigned (t2:::Enil) => andimm_case3 t2 + | Eop Ocast16unsigned (t2:::Enil) => andimm_case4 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 if Int.eq n1 Int.mone then e2 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_case3 t2 => (* Eop Ocast8unsigned (t2:::Enil) *) + Eop (Oandimm (Int.and n1 (Int.repr 255))) (t2:::Enil) + | andimm_case4 t2 => (* Eop Ocast16unsigned (t2:::Enil) *) + Eop (Oandimm (Int.and n1 (Int.repr 65535))) (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 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_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 + | 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_default e1 e2 => + Eop Oand (e1:::e2:::Enil) + end. + + +(** Original definition: +<< +Nondetfunction orimm (n1: int) (e2: expr) := + if Int.eq n1 Int.zero then e2 + else if Int.eq n1 Int.mone then Eop (Ointconst Int.mone) Enil + 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 if Int.eq n1 Int.mone then Eop (Ointconst Int.mone) Enil 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. + + +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 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 (Oshlimm n1) (t1:::Enil), Eop (Oshruimm n2) (t2:::Enil) => + if Int.eq (Int.add n1 n2) Int.iwordsize then + if same_expr_pure t1 t2 + then Eop (Ororimm n2) (t1:::Enil) + else Eop (Oshldimm n1) (t1:::t2:::Enil) + else Eop Oor (e1:::e2:::Enil) + | Eop (Oshruimm n2) (t2:::Enil), Eop (Oshlimm n1) (t1:::Enil) => + if Int.eq (Int.add n1 n2) Int.iwordsize then + if same_expr_pure t1 t2 + then Eop (Ororimm n2) (t1:::Enil) + else Eop (Oshldimm n1) (t1:::t2:::Enil) + else Eop Oor (e1:::e2:::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 (Oshlimm n1) (t1:::Enil)) (Eop (Oshruimm n2) (t2:::Enil)) + | or_case4: forall n2 t2 n1 t1, or_cases (Eop (Oshruimm n2) (t2:::Enil)) (Eop (Oshlimm n1) (t1:::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 (Oshlimm n1) (t1:::Enil), Eop (Oshruimm n2) (t2:::Enil) => or_case3 n1 t1 n2 t2 + | Eop (Oshruimm n2) (t2:::Enil), Eop (Oshlimm n1) (t1:::Enil) => or_case4 n2 t2 n1 t1 + | 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 (Oshlimm n1) (t1:::Enil), Eop (Oshruimm n2) (t2:::Enil) *) + if Int.eq (Int.add n1 n2) Int.iwordsize then if same_expr_pure t1 t2 then Eop (Ororimm n2) (t1:::Enil) else Eop (Oshldimm n1) (t1:::t2:::Enil) else Eop Oor (e1:::e2:::Enil) + | or_case4 n2 t2 n1 t1 => (* Eop (Oshruimm n2) (t2:::Enil), Eop (Oshlimm n1) (t1:::Enil) *) + if Int.eq (Int.add n1 n2) Int.iwordsize then if same_expr_pure t1 t2 then Eop (Ororimm n2) (t1:::Enil) else Eop (Oshldimm n1) (t1:::t2:::Enil) else Eop Oor (e1:::e2:::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 Onot (t2:::Enil) => + Eop (Oxorimm (Int.not n1)) (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_case3: forall t2, xorimm_cases (Eop Onot (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 + | Eop Onot (t2:::Enil) => xorimm_case3 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_case3 t2 => (* Eop Onot (t2:::Enil) *) + Eop (Oxorimm (Int.not n1)) (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 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_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 + | 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_default e1 e2 => + Eop Oxor (e1:::e2:::Enil) + end. + + +(** ** Integer division and modulus *) + +Definition divu_base (e1: expr) (e2: expr) := Eop Odivu (e1:::e2:::Enil). +Definition modu_base (e1: expr) (e2: expr) := Eop Omodu (e1:::e2:::Enil). +Definition divs_base (e1: expr) (e2: expr) := Eop Odiv (e1:::e2:::Enil). +Definition mods_base (e1: expr) (e2: expr) := Eop Omod (e1:::e2:::Enil). + +Definition shrximm (e1: expr) (n2: int) := + if Int.eq n2 Int.zero then e1 else Eop (Oshrximm n2) (e1:::Enil). + +(** ** 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 negfs (e: expr) := Eop Onegfs (e ::: Enil). +Definition absfs (e: expr) := Eop Oabsfs (e ::: Enil). +Definition addfs (e1 e2: expr) := Eop Oaddfs (e1 ::: e2 ::: Enil). +Definition subfs (e1 e2: expr) := Eop Osubfs (e1 ::: e2 ::: Enil). +Definition mulfs (e1 e2: expr) := Eop Omulfs (e1 ::: e2 ::: Enil). + +(** ** Comparisons *) + +(** Original definition: +<< +Nondetfunction compimm (default: comparison -> int -> condition) + (sem: comparison -> int -> int -> bool) + (c: comparison) (e1: expr) (n2: int) := + match c, e1 with + | c, Eop (Ointconst n1) Enil => + Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil + | Ceq, Eop (Ocmp c) el => + if Int.eq_dec n2 Int.zero then + Eop (Ocmp (negate_condition c)) el + else if Int.eq_dec n2 Int.one then + Eop (Ocmp c) el + else + Eop (Ointconst Int.zero) Enil + | Cne, Eop (Ocmp c) el => + if Int.eq_dec n2 Int.zero then + Eop (Ocmp c) el + else if Int.eq_dec n2 Int.one then + Eop (Ocmp (negate_condition c)) el + else + Eop (Ointconst Int.one) Enil + | Ceq, Eop (Oandimm n1) (t1 ::: Enil) => + if Int.eq_dec n2 Int.zero then + Eop (Ocmp (Cmaskzero n1)) (t1 ::: Enil) + else + Eop (Ocmp (default c n2)) (e1 ::: Enil) + | Cne, Eop (Oandimm n1) (t1 ::: Enil) => + if Int.eq_dec n2 Int.zero then + Eop (Ocmp (Cmasknotzero n1)) (t1 ::: Enil) + else + Eop (Ocmp (default c n2)) (e1 ::: Enil) + | _, _ => + Eop (Ocmp (default c n2)) (e1 ::: Enil) + end. +>> +*) + +Inductive compimm_cases: forall (c: comparison) (e1: expr) , Type := + | compimm_case1: forall c n1, compimm_cases (c) (Eop (Ointconst n1) Enil) + | compimm_case2: forall c el, compimm_cases (Ceq) (Eop (Ocmp c) el) + | compimm_case3: forall c el, compimm_cases (Cne) (Eop (Ocmp c) el) + | compimm_case4: forall n1 t1, compimm_cases (Ceq) (Eop (Oandimm n1) (t1 ::: Enil)) + | compimm_case5: forall n1 t1, compimm_cases (Cne) (Eop (Oandimm n1) (t1 ::: Enil)) + | compimm_default: forall (c: comparison) (e1: expr) , compimm_cases c e1. + +Definition compimm_match (c: comparison) (e1: expr) := + match c as zz1, e1 as zz2 return compimm_cases zz1 zz2 with + | c, Eop (Ointconst n1) Enil => compimm_case1 c n1 + | Ceq, Eop (Ocmp c) el => compimm_case2 c el + | Cne, Eop (Ocmp c) el => compimm_case3 c el + | Ceq, Eop (Oandimm n1) (t1 ::: Enil) => compimm_case4 n1 t1 + | Cne, Eop (Oandimm n1) (t1 ::: Enil) => compimm_case5 n1 t1 + | c, e1 => compimm_default c e1 + end. + +Definition compimm (default: comparison -> int -> condition) (sem: comparison -> int -> int -> bool) (c: comparison) (e1: expr) (n2: int) := + match compimm_match c e1 with + | compimm_case1 c n1 => (* c, Eop (Ointconst n1) Enil *) + Eop (Ointconst (if sem c n1 n2 then Int.one else Int.zero)) Enil + | compimm_case2 c el => (* Ceq, Eop (Ocmp c) el *) + if Int.eq_dec n2 Int.zero then Eop (Ocmp (negate_condition c)) el else if Int.eq_dec n2 Int.one then Eop (Ocmp c) el else Eop (Ointconst Int.zero) Enil + | compimm_case3 c el => (* Cne, Eop (Ocmp c) el *) + if Int.eq_dec n2 Int.zero then Eop (Ocmp c) el else if Int.eq_dec n2 Int.one then Eop (Ocmp (negate_condition c)) el else Eop (Ointconst Int.one) Enil + | compimm_case4 n1 t1 => (* Ceq, Eop (Oandimm n1) (t1 ::: Enil) *) + if Int.eq_dec n2 Int.zero then Eop (Ocmp (Cmaskzero n1)) (t1 ::: Enil) else Eop (Ocmp (default c n2)) (e1 ::: Enil) + | compimm_case5 n1 t1 => (* Cne, Eop (Oandimm n1) (t1 ::: Enil) *) + if Int.eq_dec n2 Int.zero then Eop (Ocmp (Cmasknotzero n1)) (t1 ::: Enil) else Eop (Ocmp (default c n2)) (e1 ::: Enil) + | compimm_default c e1 => + Eop (Ocmp (default c n2)) (e1 ::: Enil) + end. + + +(** Original definition: +<< +Nondetfunction comp (c: comparison) (e1: expr) (e2: expr) := + match e1, e2 with + | Eop (Ointconst n1) Enil, t2 => + compimm Ccompimm Int.cmp (swap_comparison c) t2 n1 + | t1, Eop (Ointconst n2) Enil => + compimm Ccompimm Int.cmp c t1 n2 + | _, _ => + 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_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 + | 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 *) + compimm Ccompimm Int.cmp (swap_comparison c) t2 n1 + | comp_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) + compimm Ccompimm Int.cmp c t1 n2 + | 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 => + compimm Ccompuimm Int.cmpu (swap_comparison c) t2 n1 + | t1, Eop (Ointconst n2) Enil => + compimm Ccompuimm Int.cmpu c t1 n2 + | _, _ => + 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_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 + | 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 *) + compimm Ccompuimm Int.cmpu (swap_comparison c) t2 n1 + | compu_case2 t1 n2 => (* t1, Eop (Ointconst n2) Enil *) + compimm Ccompuimm Int.cmpu c t1 n2 + | 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). + +Definition compfs (c: comparison) (e1: expr) (e2: expr) := + Eop (Ocmp (Ccompfs c)) (e1 ::: e2 ::: Enil). + +(** ** Integer conversions *) + +(** Original definition: +<< +Nondetfunction cast8unsigned (e: expr) := + match e with + | Eop (Ointconst n) Enil => + Eop (Ointconst (Int.zero_ext 8 n)) Enil + | Eop (Oandimm n) (t:::Enil) => + andimm (Int.and (Int.repr 255) n) t + | _ => + Eop Ocast8unsigned (e:::Enil) + end. +>> +*) + +Inductive cast8unsigned_cases: forall (e: expr), Type := + | cast8unsigned_case1: forall n, cast8unsigned_cases (Eop (Ointconst n) Enil) + | cast8unsigned_case2: forall n t, cast8unsigned_cases (Eop (Oandimm n) (t:::Enil)) + | cast8unsigned_default: forall (e: expr), cast8unsigned_cases e. + +Definition cast8unsigned_match (e: expr) := + match e as zz1 return cast8unsigned_cases zz1 with + | Eop (Ointconst n) Enil => cast8unsigned_case1 n + | Eop (Oandimm n) (t:::Enil) => cast8unsigned_case2 n t + | e => cast8unsigned_default e + end. + +Definition cast8unsigned (e: expr) := + match cast8unsigned_match e with + | cast8unsigned_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.zero_ext 8 n)) Enil + | cast8unsigned_case2 n t => (* Eop (Oandimm n) (t:::Enil) *) + andimm (Int.and (Int.repr 255) n) t + | cast8unsigned_default e => + Eop Ocast8unsigned (e:::Enil) + end. + + +(** Original definition: +<< +Nondetfunction cast8signed (e: expr) := + match e with + | Eop (Ointconst n) Enil => + Eop (Ointconst (Int.sign_ext 8 n)) Enil + | _ => + Eop Ocast8signed (e ::: Enil) + end. +>> +*) + +Inductive cast8signed_cases: forall (e: expr), Type := + | cast8signed_case1: forall n, cast8signed_cases (Eop (Ointconst n) Enil) + | cast8signed_default: forall (e: expr), cast8signed_cases e. + +Definition cast8signed_match (e: expr) := + match e as zz1 return cast8signed_cases zz1 with + | Eop (Ointconst n) Enil => cast8signed_case1 n + | e => cast8signed_default e + end. + +Definition cast8signed (e: expr) := + match cast8signed_match e with + | cast8signed_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.sign_ext 8 n)) Enil + | cast8signed_default e => + Eop Ocast8signed (e ::: Enil) + end. + + +(** Original definition: +<< +Nondetfunction cast16unsigned (e: expr) := + match e with + | Eop (Ointconst n) Enil => + Eop (Ointconst (Int.zero_ext 16 n)) Enil + | Eop (Oandimm n) (t:::Enil) => + andimm (Int.and (Int.repr 65535) n) t + | _ => + Eop Ocast16unsigned (e:::Enil) + end. +>> +*) + +Inductive cast16unsigned_cases: forall (e: expr), Type := + | cast16unsigned_case1: forall n, cast16unsigned_cases (Eop (Ointconst n) Enil) + | cast16unsigned_case2: forall n t, cast16unsigned_cases (Eop (Oandimm n) (t:::Enil)) + | cast16unsigned_default: forall (e: expr), cast16unsigned_cases e. + +Definition cast16unsigned_match (e: expr) := + match e as zz1 return cast16unsigned_cases zz1 with + | Eop (Ointconst n) Enil => cast16unsigned_case1 n + | Eop (Oandimm n) (t:::Enil) => cast16unsigned_case2 n t + | e => cast16unsigned_default e + end. + +Definition cast16unsigned (e: expr) := + match cast16unsigned_match e with + | cast16unsigned_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.zero_ext 16 n)) Enil + | cast16unsigned_case2 n t => (* Eop (Oandimm n) (t:::Enil) *) + andimm (Int.and (Int.repr 65535) n) t + | cast16unsigned_default e => + Eop Ocast16unsigned (e:::Enil) + end. + + +(** Original definition: +<< +Nondetfunction cast16signed (e: expr) := + match e with + | Eop (Ointconst n) Enil => + Eop (Ointconst (Int.sign_ext 16 n)) Enil + | _ => + Eop Ocast16signed (e ::: Enil) + end. +>> +*) + +Inductive cast16signed_cases: forall (e: expr), Type := + | cast16signed_case1: forall n, cast16signed_cases (Eop (Ointconst n) Enil) + | cast16signed_default: forall (e: expr), cast16signed_cases e. + +Definition cast16signed_match (e: expr) := + match e as zz1 return cast16signed_cases zz1 with + | Eop (Ointconst n) Enil => cast16signed_case1 n + | e => cast16signed_default e + end. + +Definition cast16signed (e: expr) := + match cast16signed_match e with + | cast16signed_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ointconst (Int.sign_ext 16 n)) Enil + | cast16signed_default e => + Eop Ocast16signed (e ::: Enil) + end. + + +(** ** Selection *) + +Definition select_supported (ty: typ) : bool := + match ty with + | Tint => true + | Tlong => Archi.ptr64 + | _ => false + end. + +(** [Asmgen.mk_sel] cannot always handle the conditions that are + implemented as a "and" of two processor flags. However it can + handle the negation of those conditions, which are implemented + as an "or". So, for the risky conditions we just take their + negation and swap the two arguments of the [select]. *) + +Definition select_swap (cond: condition) := + match cond with + | Ccompf Cne | Ccompfs Cne | Cnotcompf Ceq | Cnotcompfs Ceq => true + | _ => false + end. + +Definition select (ty: typ) (cond: condition) (args: exprlist) (e1 e2: expr) := + if select_supported ty then + if select_swap cond + then Some (Eop (Osel (negate_condition cond) ty) (e2 ::: e1 ::: args)) + else Some (Eop (Osel cond ty) (e1 ::: e2 ::: args)) + else None. + +(** ** Floating-point conversions *) + +Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil). +Definition floatofsingle (e: expr) := Eop Ofloatofsingle (e ::: Enil). + +Definition intoffloat (e: expr) := Eop Ointoffloat (e ::: Enil). + +(** Original definition: +<< +Nondetfunction floatofint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_int n)) Enil + | _ => Eop Ofloatofint (e ::: Enil) + end. +>> +*) + +Inductive floatofint_cases: forall (e: expr), Type := + | floatofint_case1: forall n, floatofint_cases (Eop (Ointconst n) Enil) + | floatofint_default: forall (e: expr), floatofint_cases e. + +Definition floatofint_match (e: expr) := + match e as zz1 return floatofint_cases zz1 with + | Eop (Ointconst n) Enil => floatofint_case1 n + | e => floatofint_default e + end. + +Definition floatofint (e: expr) := + match floatofint_match e with + | floatofint_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ofloatconst (Float.of_int n)) Enil + | floatofint_default e => + Eop Ofloatofint (e ::: Enil) + end. + + +Definition intuoffloat (e: expr) := + if Archi.splitlong then + Elet e + (Elet (Eop (Ofloatconst (Float.of_intu Float.ox8000_0000)) Enil) + (Econdition (CEcond (Ccompf Clt) (Eletvar 1 ::: Eletvar 0 ::: Enil)) + (intoffloat (Eletvar 1)) + (addimm Float.ox8000_0000 (intoffloat (subf (Eletvar 1) (Eletvar 0))))))%nat + else + Eop Olowlong (Eop Olongoffloat (e ::: Enil) ::: Enil). + +(** Original definition: +<< +Nondetfunction floatofintu (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_intu n)) Enil + | _ => + if Archi.splitlong then + let f := Eop (Ofloatconst (Float.of_intu Float.ox8000_0000)) Enil in + Elet e + (Econdition (CEcond (Ccompuimm Clt Float.ox8000_0000) (Eletvar O ::: Enil)) + (floatofint (Eletvar O)) + (addf (floatofint (addimm (Int.neg Float.ox8000_0000) (Eletvar O))) f)) + else + Eop Ofloatoflong (Eop Ocast32unsigned (e ::: Enil) ::: Enil) + end. +>> +*) + +Inductive floatofintu_cases: forall (e: expr), Type := + | floatofintu_case1: forall n, floatofintu_cases (Eop (Ointconst n) Enil) + | floatofintu_default: forall (e: expr), floatofintu_cases e. + +Definition floatofintu_match (e: expr) := + match e as zz1 return floatofintu_cases zz1 with + | Eop (Ointconst n) Enil => floatofintu_case1 n + | e => floatofintu_default e + end. + +Definition floatofintu (e: expr) := + match floatofintu_match e with + | floatofintu_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Ofloatconst (Float.of_intu n)) Enil + | floatofintu_default e => + if Archi.splitlong then let f := Eop (Ofloatconst (Float.of_intu Float.ox8000_0000)) Enil in Elet e (Econdition (CEcond (Ccompuimm Clt Float.ox8000_0000) (Eletvar O ::: Enil)) (floatofint (Eletvar O)) (addf (floatofint (addimm (Int.neg Float.ox8000_0000) (Eletvar O))) f)) else Eop Ofloatoflong (Eop Ocast32unsigned (e ::: Enil) ::: Enil) + end. + + +Definition intofsingle (e: expr) := Eop Ointofsingle (e ::: Enil). + +(** Original definition: +<< +Nondetfunction singleofint (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Osingleconst (Float32.of_int n)) Enil + | _ => Eop Osingleofint (e ::: Enil) + end. +>> +*) + +Inductive singleofint_cases: forall (e: expr), Type := + | singleofint_case1: forall n, singleofint_cases (Eop (Ointconst n) Enil) + | singleofint_default: forall (e: expr), singleofint_cases e. + +Definition singleofint_match (e: expr) := + match e as zz1 return singleofint_cases zz1 with + | Eop (Ointconst n) Enil => singleofint_case1 n + | e => singleofint_default e + end. + +Definition singleofint (e: expr) := + match singleofint_match e with + | singleofint_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Osingleconst (Float32.of_int n)) Enil + | singleofint_default e => + Eop Osingleofint (e ::: Enil) + end. + + +Definition intuofsingle (e: expr) := intuoffloat (floatofsingle e). + +(** Original definition: +<< +Nondetfunction singleofintu (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Osingleconst (Float32.of_intu n)) Enil + | _ => singleoffloat (floatofintu e) + end. +>> +*) + +Inductive singleofintu_cases: forall (e: expr), Type := + | singleofintu_case1: forall n, singleofintu_cases (Eop (Ointconst n) Enil) + | singleofintu_default: forall (e: expr), singleofintu_cases e. + +Definition singleofintu_match (e: expr) := + match e as zz1 return singleofintu_cases zz1 with + | Eop (Ointconst n) Enil => singleofintu_case1 n + | e => singleofintu_default e + end. + +Definition singleofintu (e: expr) := + match singleofintu_match e with + | singleofintu_case1 n => (* Eop (Ointconst n) Enil *) + Eop (Osingleconst (Float32.of_intu n)) Enil + | singleofintu_default e => + singleoffloat (floatofintu e) + end. + + +(** ** Addressing modes *) + +(** Original definition: +<< +Nondetfunction addressing (chunk: memory_chunk) (e: expr) := + match e with + | Eop (Olea addr) args => + if (negb Archi.ptr64) && addressing_valid addr then (addr, args) else (Aindexed 0, e:::Enil) + | Eop (Oleal addr) args => + if Archi.ptr64 && addressing_valid addr then (addr, args) else (Aindexed 0, e:::Enil) + | _ => (Aindexed 0, e:::Enil) + end. +>> +*) + +Inductive addressing_cases: forall (e: expr), Type := + | addressing_case1: forall addr args, addressing_cases (Eop (Olea addr) args) + | addressing_case2: forall addr args, addressing_cases (Eop (Oleal addr) args) + | addressing_default: forall (e: expr), addressing_cases e. + +Definition addressing_match (e: expr) := + match e as zz1 return addressing_cases zz1 with + | Eop (Olea addr) args => addressing_case1 addr args + | Eop (Oleal addr) args => addressing_case2 addr args + | e => addressing_default e + end. + +Definition addressing (chunk: memory_chunk) (e: expr) := + match addressing_match e with + | addressing_case1 addr args => (* Eop (Olea addr) args *) + if (negb Archi.ptr64) && addressing_valid addr then (addr, args) else (Aindexed 0, e:::Enil) + | addressing_case2 addr args => (* Eop (Oleal addr) args *) + if Archi.ptr64 && addressing_valid addr then (addr, args) else (Aindexed 0, e:::Enil) + | addressing_default e => + (Aindexed 0, e:::Enil) + end. + + +(** ** Arguments of builtins *) + +(** Original definition: +<< +Nondetfunction builtin_arg_addr (addr: Op.addressing) (el: exprlist) := + match addr, el with + | Aindexed n, e1 ::: Enil => + BA_addptr (BA e1) (if Archi.ptr64 then BA_long (Int64.repr n) else BA_int (Int.repr n)) + | Aglobal id ofs, Enil => BA_addrglobal id ofs + | Ainstack ofs, Enil => BA_addrstack ofs + | _, _ => BA (Eop (Olea_ptr addr) el) + end. +>> +*) + +Inductive builtin_arg_addr_cases: forall (addr: Op.addressing) (el: exprlist), Type := + | builtin_arg_addr_case1: forall n e1, builtin_arg_addr_cases (Aindexed n) (e1 ::: Enil) + | builtin_arg_addr_case2: forall id ofs, builtin_arg_addr_cases (Aglobal id ofs) (Enil) + | builtin_arg_addr_case3: forall ofs, builtin_arg_addr_cases (Ainstack ofs) (Enil) + | builtin_arg_addr_default: forall (addr: Op.addressing) (el: exprlist), builtin_arg_addr_cases addr el. + +Definition builtin_arg_addr_match (addr: Op.addressing) (el: exprlist) := + match addr as zz1, el as zz2 return builtin_arg_addr_cases zz1 zz2 with + | Aindexed n, e1 ::: Enil => builtin_arg_addr_case1 n e1 + | Aglobal id ofs, Enil => builtin_arg_addr_case2 id ofs + | Ainstack ofs, Enil => builtin_arg_addr_case3 ofs + | addr, el => builtin_arg_addr_default addr el + end. + +Definition builtin_arg_addr (addr: Op.addressing) (el: exprlist) := + match builtin_arg_addr_match addr el with + | builtin_arg_addr_case1 n e1 => (* Aindexed n, e1 ::: Enil *) + BA_addptr (BA e1) (if Archi.ptr64 then BA_long (Int64.repr n) else BA_int (Int.repr n)) + | builtin_arg_addr_case2 id ofs => (* Aglobal id ofs, Enil *) + BA_addrglobal id ofs + | builtin_arg_addr_case3 ofs => (* Ainstack ofs, Enil *) + BA_addrstack ofs + | builtin_arg_addr_default addr el => + BA (Eop (Olea_ptr addr) el) + end. + + +(** Original definition: +<< +Nondetfunction builtin_arg (e: expr) := + match e with + | Eop (Ointconst n) Enil => BA_int n + | Eop (Olongconst n) Enil => BA_long n + | Eop (Olea addr) el => + if Archi.ptr64 then BA e else builtin_arg_addr addr el + | Eop (Oleal addr) el => + if Archi.ptr64 then builtin_arg_addr addr el else BA e + | Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) => + BA_long (Int64.ofwords h l) + | Eop Omakelong (h ::: l ::: Enil) => BA_splitlong (BA h) (BA l) + | Eload chunk (Aglobal id ofs) Enil => BA_loadglobal chunk id ofs + | Eload chunk (Ainstack ofs) Enil => BA_loadstack chunk ofs + | _ => BA e + end. +>> +*) + +Inductive builtin_arg_cases: forall (e: expr), Type := + | builtin_arg_case1: forall n, builtin_arg_cases (Eop (Ointconst n) Enil) + | builtin_arg_case2: forall n, builtin_arg_cases (Eop (Olongconst n) Enil) + | builtin_arg_case3: forall addr el, builtin_arg_cases (Eop (Olea addr) el) + | builtin_arg_case4: forall addr el, builtin_arg_cases (Eop (Oleal addr) el) + | builtin_arg_case5: forall h l, builtin_arg_cases (Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil)) + | builtin_arg_case6: forall h l, builtin_arg_cases (Eop Omakelong (h ::: l ::: Enil)) + | builtin_arg_case7: forall chunk id ofs, builtin_arg_cases (Eload chunk (Aglobal id ofs) Enil) + | builtin_arg_case8: forall chunk ofs, builtin_arg_cases (Eload chunk (Ainstack ofs) Enil) + | builtin_arg_default: forall (e: expr), builtin_arg_cases e. + +Definition builtin_arg_match (e: expr) := + match e as zz1 return builtin_arg_cases zz1 with + | Eop (Ointconst n) Enil => builtin_arg_case1 n + | Eop (Olongconst n) Enil => builtin_arg_case2 n + | Eop (Olea addr) el => builtin_arg_case3 addr el + | Eop (Oleal addr) el => builtin_arg_case4 addr el + | Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) => builtin_arg_case5 h l + | Eop Omakelong (h ::: l ::: Enil) => builtin_arg_case6 h l + | Eload chunk (Aglobal id ofs) Enil => builtin_arg_case7 chunk id ofs + | Eload chunk (Ainstack ofs) Enil => builtin_arg_case8 chunk ofs + | e => builtin_arg_default e + end. + +Definition builtin_arg (e: expr) := + match builtin_arg_match e with + | builtin_arg_case1 n => (* Eop (Ointconst n) Enil *) + BA_int n + | builtin_arg_case2 n => (* Eop (Olongconst n) Enil *) + BA_long n + | builtin_arg_case3 addr el => (* Eop (Olea addr) el *) + if Archi.ptr64 then BA e else builtin_arg_addr addr el + | builtin_arg_case4 addr el => (* Eop (Oleal addr) el *) + if Archi.ptr64 then builtin_arg_addr addr el else BA e + | builtin_arg_case5 h l => (* Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) *) + BA_long (Int64.ofwords h l) + | builtin_arg_case6 h l => (* Eop Omakelong (h ::: l ::: Enil) *) + BA_splitlong (BA h) (BA l) + | builtin_arg_case7 chunk id ofs => (* Eload chunk (Aglobal id ofs) Enil *) + BA_loadglobal chunk id ofs + | builtin_arg_case8 chunk ofs => (* Eload chunk (Ainstack ofs) Enil *) + BA_loadstack chunk ofs + | builtin_arg_default e => + BA e + end. + + +(** Platform-specific known builtins *) + +Definition platform_builtin (b: platform_builtin) (args: exprlist) : option expr := + None. |