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using System;
using Microsoft.Boogie;
using System.Collections.Generic;
using System.Linq;
namespace GPUVerify {
using VarDef = Tuple<Expr, bool>;
class VariableDefinitionAnalysis {
GPUVerifier verifier;
Implementation impl;
Dictionary<Variable, VarDef> defMap = new Dictionary<Variable, VarDef>();
Dictionary<string, VarDef> namedDefMap = new Dictionary<string, VarDef>();
bool changed;
VariableDefinitionAnalysis(GPUVerifier v, Implementation i) {
verifier = v;
impl = i;
}
private class IsConstantVisitor : StandardVisitor {
public bool isConstant = true;
public IsConstantVisitor() {}
public override Expr VisitNAryExpr(NAryExpr expr) {
if (expr.Fun is MapSelect) {
isConstant = false;
return expr;
} else
return base.VisitNAryExpr(expr);
}
};
private class IsDerivedFromConstantsVisitor : StandardVisitor {
private VariableDefinitionAnalysis analysis;
public bool isDerivedFromConstants = true;
public IsDerivedFromConstantsVisitor(VariableDefinitionAnalysis a) {
analysis = a;
}
public override Expr VisitIdentifierExpr(IdentifierExpr expr) {
if (expr.Decl is Constant)
return expr;
if (!analysis.defMap.ContainsKey(expr.Decl) || !analysis.defMap[expr.Decl].Item2)
isDerivedFromConstants = false;
return expr;
}
};
bool IsConstant(Expr e) {
var v = new IsConstantVisitor();
v.Visit(e);
return v.isConstant;
}
bool IsDerivedFromConstants(Expr e) {
var v = new IsDerivedFromConstantsVisitor(this);
v.Visit(e);
return v.isDerivedFromConstants;
}
void UpdateDefMap(Variable v, Expr def, bool isConstant) {
if (!defMap.ContainsKey(v)) {
changed = true;
defMap[v] = new VarDef(def, isConstant);
return;
}
var d = defMap[v];
if (d.Item1 != def || d.Item2 != isConstant) {
changed = true;
defMap[v] = new VarDef(def, isConstant);
}
}
void AddAssignment(AssignLhs lhs, Expr rhs) {
if (lhs is SimpleAssignLhs) {
var sLhs = (SimpleAssignLhs)lhs;
var theVar = sLhs.DeepAssignedVariable;
if ((defMap.ContainsKey(theVar) && defMap[theVar].Item1 != rhs) || !IsConstant(rhs)) {
UpdateDefMap(theVar, null, false);
} else {
UpdateDefMap(theVar, rhs, IsDerivedFromConstants(rhs));
}
}
}
void Analyse() {
do {
changed = false;
foreach (var c in verifier.RootRegion(impl).Cmds()) {
if (c is AssignCmd) {
var aCmd = (AssignCmd)c;
foreach (var a in aCmd.Lhss.Zip(aCmd.Rhss)) {
AddAssignment(a.Item1, a.Item2);
}
}
if (c is HavocCmd) {
var hCmd = (HavocCmd)c;
foreach (Variable v in hCmd.Vars)
UpdateDefMap(v, null, false);
}
}
} while (changed);
}
private class BuildNamedDefVisitor : Duplicator {
private VariableDefinitionAnalysis analysis;
public BuildNamedDefVisitor(VariableDefinitionAnalysis a) {
analysis = a;
}
public override Expr VisitIdentifierExpr(IdentifierExpr expr) {
if (expr.Decl is Constant)
return expr;
return analysis.BuildNamedDefFor(expr.Decl, expr);
}
}
Expr BuildNamedDefFor(Variable v, Expr e = null) {
VarDef def;
if (namedDefMap.TryGetValue(v.Name, out def))
return def.Item1;
if (!defMap.TryGetValue(v, out def))
return e;
Expr defExpr;
if (def.Item1 == null)
defExpr = e;
else
defExpr = (Expr)new BuildNamedDefVisitor(this).Visit(def.Item1.Clone());
namedDefMap[v.Name] = new VarDef(defExpr, def.Item2);
return defExpr;
}
void BuildNamedDefMap() {
foreach (var v in defMap.Keys)
if (defMap[v].Item1 != null)
BuildNamedDefFor(v);
}
private class SubstDefVisitor : Duplicator {
private VariableDefinitionAnalysis analysis;
private string procName;
public bool isSubstitutable = true;
public bool isConstant = true;
public SubstDefVisitor(VariableDefinitionAnalysis a, string p) {
analysis = a;
procName = p;
}
public override Expr VisitIdentifierExpr(IdentifierExpr expr) {
if (expr.Decl is Constant)
return expr;
int id;
var varName = GPUVerifier.StripThreadIdentifier(expr.Decl.Name, out id);
VarDef def;
if (!analysis.namedDefMap.TryGetValue(varName, out def)) {
isSubstitutable = false;
return null;
}
if (!def.Item2)
isConstant = false;
return analysis.verifier.MaybeDualise(def.Item1, id, procName);
}
}
public Expr SubstDefinitions(Expr e, string procName, out bool isConstant) {
var v = new SubstDefVisitor(this, procName);
Expr result = (Expr)v.Visit(e.Clone());
isConstant = v.isConstant;
if (!v.isSubstitutable)
return null;
return result;
}
public Expr SubstDefinitions(Expr e, string procName) {
bool isConstant;
var result = SubstDefinitions(e, procName, out isConstant);
if (!isConstant)
return null;
return result;
}
public static VariableDefinitionAnalysis Analyse(GPUVerifier verifier, Implementation impl) {
var a = new VariableDefinitionAnalysis(verifier, impl);
a.Analyse();
a.BuildNamedDefMap();
a.defMap = null;
return a;
}
}
}
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