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diff --git a/mppa_k1c/SelectOp.v b/mppa_k1c/SelectOp.v new file mode 100644 index 00000000..c42f0340 --- /dev/null +++ b/mppa_k1c/SelectOp.v @@ -0,0 +1,1219 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* Prashanth Mundkur, SRI International *) +(* *) +(* 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. *) +(* *) +(* The contributions by Prashanth Mundkur are reused and adapted *) +(* under the terms of a Contributor License Agreement between *) +(* SRI International and INRIA. *) +(* *) +(* *********************************************************************) + +(** 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 Archi. +Require Import Coqlib. +Require Import Compopts. +Require Import AST. +Require Import Integers. +Require Import Floats. +Require Import Op. +Require Import CminorSel. + +Local Open Scope cminorsel_scope. + +(** ** Constants **) + +Definition addrsymbol (id: ident) (ofs: ptrofs) := + Eop (Oaddrsymbol id ofs) Enil. + +Definition addrstack (ofs: ptrofs) := + Eop (Oaddrstack ofs) Enil. + +(** ** 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 (Ptrofs.add (Ptrofs.of_int n) m)) Enil + | Eop (Oaddrstack m) Enil => Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int 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 (Ptrofs.add (Ptrofs.of_int n) m)) Enil + | addimm_case3 m => (* Eop (Oaddrstack m) Enil *) + Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int 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 + | t1, Eop (Ointconst n2) Enil => addimm n2 t1 + | 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), Eop (Oaddrstack n2) Enil => + Eop Oadd (Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n1) n2)) Enil ::: t1 ::: Enil) + | Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) => + Eop Oadd (Eop (Oaddrstack (Ptrofs.add n1 (Ptrofs.of_int n2))) Enil ::: t2 ::: Enil) + | Eop (Oaddimm n1) (t1:::Enil), t2 => + addimm n1 (Eop Oadd (t1:::t2:::Enil)) + | t1, Eop (Oaddimm n2) (t2:::Enil) => + addimm n2 (Eop Oadd (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 t1 n2, add_cases (t1) (Eop (Ointconst n2) Enil) + | add_case3: forall n1 t1 n2 t2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddimm n2) (t2:::Enil)) + | add_case4: forall n1 t1 n2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (Eop (Oaddrstack n2) Enil) + | add_case5: forall n1 n2 t2, add_cases (Eop (Oaddrstack n1) Enil) (Eop (Oaddimm n2) (t2:::Enil)) + | add_case6: forall n1 t1 t2, add_cases (Eop (Oaddimm n1) (t1:::Enil)) (t2) + | add_case7: forall t1 n2 t2, add_cases (t1) (Eop (Oaddimm n2) (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 (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) => add_case3 n1 t1 n2 t2 + | Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil => add_case4 n1 t1 n2 + | Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) => add_case5 n1 n2 t2 + | Eop (Oaddimm n1) (t1:::Enil), t2 => add_case6 n1 t1 t2 + | t1, Eop (Oaddimm n2) (t2:::Enil) => add_case7 t1 n2 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 (Oaddimm n1) (t1:::Enil), Eop (Oaddimm n2) (t2:::Enil) *) + addimm (Int.add n1 n2) (Eop Oadd (t1:::t2:::Enil)) + | add_case4 n1 t1 n2 => (* Eop (Oaddimm n1) (t1:::Enil), Eop (Oaddrstack n2) Enil *) + Eop Oadd (Eop (Oaddrstack (Ptrofs.add (Ptrofs.of_int n1) n2)) Enil ::: t1 ::: Enil) + | add_case5 n1 n2 t2 => (* Eop (Oaddrstack n1) Enil, Eop (Oaddimm n2) (t2:::Enil) *) + Eop Oadd (Eop (Oaddrstack (Ptrofs.add n1 (Ptrofs.of_int n2))) Enil ::: t2 ::: Enil) + | add_case6 n1 t1 t2 => (* Eop (Oaddimm n1) (t1:::Enil), t2 *) + addimm n1 (Eop Oadd (t1:::t2:::Enil)) + | add_case7 t1 n2 t2 => (* t1, Eop (Oaddimm n2) (t2:::Enil) *) + addimm n2 (Eop Oadd (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 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_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 + | 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_default e1 e2 => + Eop Osub (e1:::e2:::Enil) + end. + + +(** 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. + + +(** ** 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 (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 (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_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 + | 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_default e1 => + 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 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. + + +Definition mulhs (e1: expr) (e2: expr) := + if Archi.ptr64 then + Eop Olowlong + (Eop (Oshrlimm (Int.repr 32)) + (Eop Omull (Eop Ocast32signed (e1 ::: Enil) ::: + Eop Ocast32signed (e2 ::: Enil) ::: Enil) ::: Enil) + ::: Enil) + else + Eop Omulhs (e1 ::: e2 ::: Enil). + +Definition mulhu (e1: expr) (e2: expr) := + if Archi.ptr64 then + Eop Olowlong + (Eop (Oshrluimm (Int.repr 32)) + (Eop Omull (Eop Ocast32unsigned (e1 ::: Enil) ::: + Eop Ocast32unsigned (e2 ::: Enil) ::: Enil) ::: Enil) + ::: Enil) + else + 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 (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 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_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. + + +(** 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 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_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 + | 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_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) => + let n := Int.xor n1 n2 in + if Int.eq n Int.zero then t2 else Eop (Oxorimm n) (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) *) + let n := Int.xor n1 n2 in if Int.eq n Int.zero then t2 else Eop (Oxorimm n) (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 logical negation *) + +Definition notint (e: expr) := xorimm Int.mone e. + +(** ** Integer division and modulus *) + +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 divu_base (e1: expr) (e2: expr) := Eop Odivu (e1:::e2:::Enil). +Definition modu_base (e1: expr) (e2: expr) := Eop Omodu (e1:::e2:::Enil). + +Definition shrximm (e1: expr) (n2: int) := + if Int.eq n2 Int.zero then e1 else Eop (Oshrximm n2) (e1:::Enil). + +(* Alternate definition, not convenient for strength reduction during constant propagation *) +(* +(* n2 will be less than 31. *) + +Definition shrximm_inner (e1: expr) (n2: int) := + Eop (Oshruimm (Int.sub Int.iwordsize n2)) + ((Eop (Oshrimm (Int.repr (Int.zwordsize - 1))) + (e1 ::: Enil)) + ::: Enil). + +Definition shrximm (e1: expr) (n2: int) := + if Int.eq n2 Int.zero then e1 + else Eop (Oshrimm n2) + ((Eop Oadd (e1 ::: shrximm_inner e1 n2 ::: Enil)) + ::: 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 + | _, _ => + 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_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 + | 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_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 *) + +Definition cast8unsigned (e: expr) := andimm (Int.repr 255) e. + +(** 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. + + +Definition cast16unsigned (e: expr) := andimm (Int.repr 65535) e. + +(** 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. + + +(** ** Floating-point conversions *) + +Definition intoffloat (e: expr) := Eop Ointoffloat (e ::: Enil). +Definition intuoffloat (e: expr) := Eop Ointuoffloat (e ::: Enil). + +(** Original definition: +<< +Nondetfunction floatofintu (e: expr) := + match e with + | Eop (Ointconst n) Enil => Eop (Ofloatconst (Float.of_intu n)) Enil + | _ => Eop Ofloatofintu (e ::: 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 => + Eop Ofloatofintu (e ::: Enil) + end. + + +(** 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 intofsingle (e: expr) := Eop Ointofsingle (e ::: Enil). +Definition singleofint (e: expr) := Eop Osingleofint (e ::: Enil). + +Definition intuofsingle (e: expr) := Eop Ointuofsingle (e ::: Enil). +Definition singleofintu (e: expr) := Eop Osingleofintu (e ::: Enil). + +Definition singleoffloat (e: expr) := Eop Osingleoffloat (e ::: Enil). +Definition floatofsingle (e: expr) := Eop Ofloatofsingle (e ::: Enil). + +(** ** Recognition of addressing modes for load and store operations *) + +(** Original definition: +<< +Nondetfunction addressing (chunk: memory_chunk) (e: expr) := + match e with + | Eop (Oaddrstack n) Enil => (Ainstack n, Enil) + | Eop (Oaddrsymbol id ofs) Enil => if Archi.pic_code tt then (Aindexed Ptrofs.zero, e:::Enil) else (Aglobal id ofs, Enil) + | Eop (Oaddimm n) (e1:::Enil) => (Aindexed (Ptrofs.of_int n), e1:::Enil) + | Eop (Oaddlimm n) (e1:::Enil) => (Aindexed (Ptrofs.of_int64 n), e1:::Enil) + | _ => (Aindexed Ptrofs.zero, e:::Enil) + end. +>> +*) + +Inductive addressing_cases: forall (e: expr), Type := + | addressing_case1: forall n, addressing_cases (Eop (Oaddrstack n) Enil) + | addressing_case2: forall id ofs, addressing_cases (Eop (Oaddrsymbol id ofs) Enil) + | addressing_case3: forall n e1, addressing_cases (Eop (Oaddimm n) (e1:::Enil)) + | addressing_case4: forall n e1, addressing_cases (Eop (Oaddlimm n) (e1:::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 (Oaddrsymbol id ofs) Enil => addressing_case2 id ofs + | Eop (Oaddimm n) (e1:::Enil) => addressing_case3 n e1 + | Eop (Oaddlimm n) (e1:::Enil) => addressing_case4 n e1 + | 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 id ofs => (* Eop (Oaddrsymbol id ofs) Enil *) + if Archi.pic_code tt then (Aindexed Ptrofs.zero, e:::Enil) else (Aglobal id ofs, Enil) + | addressing_case3 n e1 => (* Eop (Oaddimm n) (e1:::Enil) *) + (Aindexed (Ptrofs.of_int n), e1:::Enil) + | addressing_case4 n e1 => (* Eop (Oaddlimm n) (e1:::Enil) *) + (Aindexed (Ptrofs.of_int64 n), e1:::Enil) + | addressing_default e => + (Aindexed Ptrofs.zero, e:::Enil) + end. + + +(** ** Arguments of builtins *) + +(** Original definition: +<< +Nondetfunction builtin_arg (e: expr) := + match e with + | Eop (Ointconst n) Enil => BA_int n + | Eop (Oaddrsymbol id ofs) Enil => BA_addrglobal id ofs + | Eop (Oaddrstack ofs) Enil => BA_addrstack ofs + | 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 (Ainstack ofs) Enil => BA_loadstack chunk ofs + | Eop (Oaddimm n) (e1:::Enil) => + if Archi.ptr64 then BA e else BA_addptr (BA e1) (BA_int n) + | Eop (Oaddlimm n) (e1:::Enil) => + if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e + | _ => 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 id ofs, builtin_arg_cases (Eop (Oaddrsymbol id ofs) Enil) + | builtin_arg_case3: forall ofs, builtin_arg_cases (Eop (Oaddrstack ofs) Enil) + | builtin_arg_case4: forall h l, builtin_arg_cases (Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil)) + | builtin_arg_case5: forall h l, builtin_arg_cases (Eop Omakelong (h ::: l ::: Enil)) + | builtin_arg_case6: forall chunk ofs, builtin_arg_cases (Eload chunk (Ainstack ofs) Enil) + | builtin_arg_case7: forall n e1, builtin_arg_cases (Eop (Oaddimm n) (e1:::Enil)) + | builtin_arg_case8: forall n e1, builtin_arg_cases (Eop (Oaddlimm n) (e1:::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 (Oaddrsymbol id ofs) Enil => builtin_arg_case2 id ofs + | Eop (Oaddrstack ofs) Enil => builtin_arg_case3 ofs + | Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) => builtin_arg_case4 h l + | Eop Omakelong (h ::: l ::: Enil) => builtin_arg_case5 h l + | Eload chunk (Ainstack ofs) Enil => builtin_arg_case6 chunk ofs + | Eop (Oaddimm n) (e1:::Enil) => builtin_arg_case7 n e1 + | Eop (Oaddlimm n) (e1:::Enil) => builtin_arg_case8 n e1 + | 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 id ofs => (* Eop (Oaddrsymbol id ofs) Enil *) + BA_addrglobal id ofs + | builtin_arg_case3 ofs => (* Eop (Oaddrstack ofs) Enil *) + BA_addrstack ofs + | builtin_arg_case4 h l => (* Eop Omakelong (Eop (Ointconst h) Enil ::: Eop (Ointconst l) Enil ::: Enil) *) + BA_long (Int64.ofwords h l) + | builtin_arg_case5 h l => (* Eop Omakelong (h ::: l ::: Enil) *) + BA_splitlong (BA h) (BA l) + | builtin_arg_case6 chunk ofs => (* Eload chunk (Ainstack ofs) Enil *) + BA_loadstack chunk ofs + | builtin_arg_case7 n e1 => (* Eop (Oaddimm n) (e1:::Enil) *) + if Archi.ptr64 then BA e else BA_addptr (BA e1) (BA_int n) + | builtin_arg_case8 n e1 => (* Eop (Oaddlimm n) (e1:::Enil) *) + if Archi.ptr64 then BA_addptr (BA e1) (BA_long n) else BA e + | builtin_arg_default e => + BA e + end. + |