void AnalyseAssignment(Variable variable, List <Tuple <IRegion, Expr> > defs, Graph <Block> cfg, HashSet <Variable> modSet)
{
// Ensure defs[0] refers to the definition from the outermost region
// This also checks that the definitions are in different regions
if (!OrderDefs(defs, cfg))
{
return;
}
var regionId = defs[1].Item1.Identifier();
var varDefAnalysis = verifier.varDefAnalysesRegion[impl];
var varDef = varDefAnalysis.GetPossibleInductionVariableDefintion(variable.Name, regionId);
if (varDef == null)
{
return;
}
HashSet <string> loopFreeVars;
var defInd = varDefAnalysis.SubstDefinitions(varDef, impl.Name, out loopFreeVars);
if (loopFreeVars.Any(i => i != variable.Name))
{
return;
}
var modSetLoop = LoopInvariantGenerator.GetModifiedVariables(defs[1].Item1);
var v = new VariablesOccurringInExpressionVisitor();
v.Visit(defs[0].Item2);
if (v.GetVariables().Intersect(modSetLoop).Any())
{
return;
}
AddDefinitionPair(variable, defInd, defs[0].Item2, regionId, modSet);
}
private void DiscoverVariableAssignments(Variable variable)
{
Absy assignment = null;
foreach (Block block in cfg.Nodes)
{
foreach (Cmd cmd in block.Cmds)
{
if (cmd is AssignCmd)
{
AssignCmd assignCmd = cmd as AssignCmd;
var lhss = assignCmd.Lhss.OfType <SimpleAssignLhs>();
foreach (var LhsRhs in lhss.Zip(assignCmd.Rhss))
{
if (LhsRhs.Item1.DeepAssignedVariable.Name == variable.Name)
{
assignment = LhsRhs.Item2;
if (variable.Name == this.initialVariable.Name)
{
unexpandedExpr = LhsRhs.Item2;
}
goto AnalyseAssignment;
}
}
}
else if (cmd is CallCmd)
{
CallCmd call = cmd as CallCmd;
foreach (IdentifierExpr outParam in call.Outs)
{
if (outParam.Name == variable.Name)
{
assignment = cmd;
goto AnalyseAssignment;
}
}
}
}
}
// Label used to allow exit from multiple levels in the previous loop nest
AnalyseAssignment:
if (assignment != null)
{
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(assignment);
foreach (Variable discovered in visitor.GetVariables())
{
if (TEMP_VARIABLE.IsMatch(discovered.Name) && discovered.Name != variable.Name)
{
DiscoverVariableAssignments(discovered);
}
else if (GPU_VARIABLE.IsMatch(discovered.Name))
{
GPUVariables.Add(discovered);
}
}
}
}
public ExprTree(Expr expr)
{
this.expr = expr;
root = Node.CreateFromExpr(expr);
levels[0] = new HashSet <Node>();
levels[0].Add(root);
SetLevels(root, 0);
// Set node IDs and see if any scalar node is a race offset variable
int nodeID = 0;
foreach (Node node in nodes)
{
node.ID = nodeID++;
if (node is ScalarSymbolNode)
{
ScalarSymbolNode scalarNode = node as ScalarSymbolNode;
if (BoogieInterpreter.RegularExpressions.OffsetVariable.IsMatch(scalarNode.Symbol))
{
OffsetVariables.Add(scalarNode.Symbol);
}
if (BoogieInterpreter.RegularExpressions.WatchdoVariable.IsMatch(scalarNode.Symbol))
{
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(this.expr);
string offsetVariable = string.Empty;
foreach (Variable variable in visitor.GetVariables())
{
if (BoogieInterpreter.RegularExpressions.TrackingVariable.IsMatch(variable.Name))
{
int index = variable.Name.IndexOf('$');
string arrayName = variable.Name.Substring(index);
string accessType = variable.Name.Substring(0, index);
if (accessType == "_WRITE_HAS_OCCURRED_")
{
offsetVariable = "_WRITE_OFFSET_" + arrayName;
}
else if (accessType == "_READ_HAS_OCCURRED_")
{
offsetVariable = "_READ_OFFSET_" + arrayName;
}
else
{
offsetVariable = "_ATOMIC_OFFSET_" + arrayName;
}
break;
}
}
OffsetVariables.Add(offsetVariable);
}
}
}
}
public HashSet <Variable> PartitionVariablesOfHeader()
{
if (header == null)
{
return(new HashSet <Variable>());
}
HashSet <Variable> partitionVars = new HashSet <Variable>();
var visitor = new VariablesOccurringInExpressionVisitor();
var dualBlockGraph = blockGraph.Dual(new Block());
Block loopConditionDominator = header;
// The dominator might have multiple successors, traverse these
while (blockGraph.Successors(loopConditionDominator).Count(item => loopNodes[header].Contains(item)) > 1)
{
foreach (Block b in blockGraph.Successors(loopConditionDominator))
{
foreach (var assume in b.Cmds.OfType <AssumeCmd>().Where(x => QKeyValue.FindBoolAttribute(x.Attributes, "partition")))
{
visitor.Visit(assume.Expr);
partitionVars.UnionWith(visitor.GetVariables());
}
}
// Find the immediate post-dominator of the successors
Block block = null;
foreach (var succ in blockGraph.Successors(loopConditionDominator).Where(item => loopNodes[header].Contains(item)))
{
if (block == null)
{
block = succ;
}
else
{
block = dualBlockGraph.DominatorMap.LeastCommonAncestor(block, succ);
}
}
// Use the immediate post-dominator
loopConditionDominator = block;
}
foreach (Block b in blockGraph.Successors(loopConditionDominator))
{
foreach (var assume in b.Cmds.OfType <AssumeCmd>().Where(x => QKeyValue.FindBoolAttribute(x.Attributes, "partition")))
{
visitor.Visit(assume.Expr);
partitionVars.UnionWith(visitor.GetVariables());
}
}
return(partitionVars);
}
private static void GenerateCandidateForLoopBounds(GPUVerifier verifier, Implementation impl, IRegion region)
{
HashSet <Variable> loopCounters = new HashSet <Variable>();
HashSet <Variable> modifiedVariables = region.GetModifiedVariables();
// Get the partition variables associated with the header
HashSet <Variable> partitionVars = region.PartitionVariablesOfRegion();
foreach (Variable v in partitionVars)
{
// Find the expression which defines a particular partition variable.
// Visit the expression and select any variable in the mod set of the loop.
// We assume that any variable satisfying these conditions is a loop counter
Expr partitionDefExpr = verifier.VarDefAnalysesRegion[impl].DefOfVariableName(v.Name);
if (partitionDefExpr == null) // multiple definitions or no definition
{
continue;
}
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(partitionDefExpr);
foreach (Variable variable in visitor.GetVariables())
{
if (modifiedVariables.Contains(variable))
{
loopCounters.Add(variable);
}
}
}
foreach (Variable loopCounter in loopCounters)
{
foreach (Block preheader in region.PreHeaders())
{
foreach (AssignCmd cmd in preheader.Cmds.Where(x => x is AssignCmd).Reverse <Cmd>())
{
var lhss = cmd.Lhss.Where(x => x is SimpleAssignLhs);
foreach (var lhsRhs in lhss.Zip(cmd.Rhss))
{
if (lhsRhs.Item1.DeepAssignedVariable.Name == loopCounter.Name)
{
verifier.AddCandidateInvariant(region, verifier.IntRep.MakeSle(new IdentifierExpr(loopCounter.tok, loopCounter), lhsRhs.Item2), "loopBound");
verifier.AddCandidateInvariant(region, verifier.IntRep.MakeSge(new IdentifierExpr(loopCounter.tok, loopCounter), lhsRhs.Item2), "loopBound");
verifier.AddCandidateInvariant(region, verifier.IntRep.MakeUle(new IdentifierExpr(loopCounter.tok, loopCounter), lhsRhs.Item2), "loopBound");
verifier.AddCandidateInvariant(region, verifier.IntRep.MakeUge(new IdentifierExpr(loopCounter.tok, loopCounter), lhsRhs.Item2), "loopBound");
}
}
}
}
}
}
private static void GenerateCandidateForNonNegativeGuardVariables(GPUVerifier verifier, Implementation impl, IRegion region)
{
HashSet <Variable> partitionVars = region.PartitionVariablesOfHeader();
HashSet <Variable> nonnegVars = new HashSet <Variable>();
var formals = impl.InParams.Select(x => x.Name);
var modset = GetModifiedVariables(region).Select(x => x.Name);
Regex pattern = new Regex(@"\bBV\d*_((SLE)|(SLT)|(SGE)|(SGT))\b");
foreach (var v in partitionVars)
{
var expr = verifier.varDefAnalysesRegion[impl].DefOfVariableName(v.Name);
if (!(expr is NAryExpr))
{
continue;
}
var nary = expr as NAryExpr;
if (!pattern.Match(nary.Fun.FunctionName).Success)
{
continue;
}
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(nary);
nonnegVars.UnionWith(
visitor.GetVariables().Where(
x => x.Name.StartsWith("$") &&
!formals.Contains(x.Name) &&
modset.Contains(x.Name) &&
x.TypedIdent.Type.IsBv
)
);
}
foreach (var v in nonnegVars)
{
int BVWidth = v.TypedIdent.Type.BvBits;
// REVISIT: really we only want to guess for /integer/ variables.
if (BVWidth >= 8)
{
var inv = verifier.IntRep.MakeSle(verifier.Zero(BVWidth), new IdentifierExpr(v.tok, v));
verifier.AddCandidateInvariant(region, inv, "guardNonNeg");
}
}
}
private void ExprMayAffectControlFlow(string proc, Expr e)
{
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.VisitExpr(e);
foreach (Variable v in visitor.GetVariables())
{
if (!mayBeDerivedFrom[proc].ContainsKey(v.Name))
{
continue;
}
foreach (string s in mayBeDerivedFrom[proc][v.Name])
{
if (!arraysWhichMayAffectControlFlow.Contains(s))
{
SetArrayMayAffectControlFlow(s);
}
}
}
}
public IEnumerable <Tuple <Variable, Expr> > FindSelfReferentialVariables(Dictionary <Block, VarDefs> blockVarDefs)
{
var predVarDefs = MergePredecessors(blockVarDefs, predecessors);
foreach (var p in predVarDefs)
{
if (p.Value == null || p.Value is IdentifierExpr)
{
continue;
}
var v = new VariablesOccurringInExpressionVisitor();
v.Visit(p.Value);
var modVars = v.GetVariables()
.Where(i => i is Variable && modSet.Contains(i as Variable));
if (modVars.Count() == 1 && modVars.Single() as Variable == p.Key)
{
yield return(new Tuple <Variable, Expr>(p.Key, p.Value));
}
}
}
public HashSet <Variable> PartitionVariablesOfRegion()
{
if (header == null)
{
return(new HashSet <Variable>());
}
HashSet <Variable> partitionVars = new HashSet <Variable>();
foreach (Block loopNode in loopNodes[header])
{
var visitor = new VariablesOccurringInExpressionVisitor();
foreach (Block succ in blockGraph.Successors(loopNode))
{
foreach (var assume in succ.Cmds.OfType <AssumeCmd>().Where(x => QKeyValue.FindBoolAttribute(x.Attributes, "partition")))
{
visitor.Visit(assume.Expr);
partitionVars.UnionWith(visitor.GetVariables());
}
}
}
return(partitionVars);
}
private static void GetReadAndWrittenVariables(IRegion region, out IEnumerable <Variable> ReadVariables, out IEnumerable <Variable> WrittenVariables)
{
var readVisitor = new VariablesOccurringInExpressionVisitor();
var writeVisitor = new VariablesOccurringInExpressionVisitor();
foreach (AssignCmd assignment in region.Cmds().OfType <AssignCmd>())
{
var mapLhss = assignment.Lhss.OfType <MapAssignLhs>();
foreach (var LhsRhs in mapLhss.Zip(assignment.Rhss))
{
writeVisitor.Visit(LhsRhs.Item1);
readVisitor.Visit(LhsRhs.Item2);
}
var simpleLhss = assignment.Lhss.OfType <SimpleAssignLhs>();
foreach (var LhsRhs in simpleLhss.Zip(assignment.Rhss))
{
readVisitor.Visit(LhsRhs.Item2);
}
}
ReadVariables = readVisitor.GetVariables();
WrittenVariables = writeVisitor.GetVariables();
}
private static void GenerateCandidateForNonUniformGuardVariables(GPUVerifier verifier, Implementation impl, IRegion region)
{
if (!verifier.ContainsBarrierCall(region) && !GPUVerifyVCGenCommandLineOptions.WarpSync)
{
return;
}
HashSet <Variable> partitionVars = region.PartitionVariablesOfHeader();
HashSet <Variable> guardVars = new HashSet <Variable>();
var formals = impl.InParams.Select(x => x.Name);
var modset = region.GetModifiedVariables().Select(x => x.Name);
foreach (var v in partitionVars)
{
Expr expr = verifier.VarDefAnalysesRegion[impl].DefOfVariableName(v.Name);
if (expr == null)
{
continue;
}
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(expr);
guardVars.UnionWith(
visitor.GetVariables().Where(x => x.Name.StartsWith("$") &&
!formals.Contains(x.Name) && modset.Contains(x.Name) &&
!verifier.UniformityAnalyser.IsUniform(impl.Name, x.Name) &&
x.TypedIdent.Type.IsBv && (x.TypedIdent.Type.BvBits % 8 == 0)));
}
List <AssignCmd> assignments = new List <AssignCmd>();
foreach (Block b in region.PreHeaders())
{
foreach (AssignCmd c in b.Cmds.Where(x => x is AssignCmd))
{
assignments.Add(c);
}
}
foreach (var v in guardVars)
{
foreach (AssignCmd c in assignments)
{
foreach (var a in c.Lhss.Zip(c.Rhss))
{
var lhs = a.Item1;
var rhs = a.Item2;
if (!(lhs is SimpleAssignLhs))
{
continue;
}
var sLhs = (SimpleAssignLhs)lhs;
var theVar = sLhs.DeepAssignedVariable;
if (theVar.Name == v.Name)
{
var sub = verifier.IntRep.MakeSub(new IdentifierExpr(Token.NoToken, v), rhs as Expr);
List <Expr> args = new List <Expr>();
args.Add(sub);
Function otherbv = verifier.FindOrCreateOther(sub.Type);
var inv = Expr.Eq(sub, new NAryExpr(Token.NoToken, new FunctionCall(otherbv), args));
verifier.AddCandidateInvariant(region, inv, "guardMinusInitialIsUniform");
var groupInv = Expr.Imp(verifier.ThreadsInSameGroup(), inv);
verifier.AddCandidateInvariant(region, groupInv, "guardMinusInitialIsUniform");
}
}
}
}
}
private void Analyse(Implementation impl, List <Cmd> cs)
{
foreach (var c in cs)
{
if (c is AssignCmd)
{
AssignCmd assignCmd = c as AssignCmd;
for (int i = 0; i != assignCmd.Lhss.Count; i++)
{
if (assignCmd.Lhss[i] is SimpleAssignLhs)
{
SimpleAssignLhs lhs = assignCmd.Lhss[i] as SimpleAssignLhs;
Expr rhs = assignCmd.Rhss[i];
VariablesOccurringInExpressionVisitor visitor = new VariablesOccurringInExpressionVisitor();
visitor.VisitExpr(rhs);
foreach (Variable v in visitor.GetVariables())
{
if (!mayBeDerivedFrom[impl.Name].ContainsKey(v.Name))
{
continue;
}
foreach (string s in mayBeDerivedFrom[impl.Name][v.Name])
{
if (mayBeDerivedFrom[impl.Name].ContainsKey(lhs.AssignedVariable.Name) && !mayBeDerivedFrom[impl.Name][lhs.AssignedVariable.Name].Contains(s))
{
SetMayBeDerivedFrom(impl.Name, lhs.AssignedVariable.Name, s);
}
}
}
}
}
}
else if (c is CallCmd)
{
CallCmd callCmd = c as CallCmd;
if (QKeyValue.FindBoolAttribute(callCmd.Proc.Attributes, "barrier_invariant") ||
QKeyValue.FindBoolAttribute(callCmd.Proc.Attributes, "binary_barrier_invariant"))
{
foreach (Expr param in callCmd.Ins)
{
ExprMayAffectControlFlow(impl.Name, param);
}
}
else if (!GPUVerifier.IsBarrier(callCmd.Proc))
{
Implementation CalleeImplementation = verifier.GetImplementation(callCmd.callee);
if (CalleeImplementation != null)
{
for (int i = 0; i < CalleeImplementation.InParams.Count(); i++)
{
VariablesOccurringInExpressionVisitor visitor = new VariablesOccurringInExpressionVisitor();
visitor.VisitExpr(callCmd.Ins[i]);
foreach (Variable v in visitor.GetVariables())
{
if (!mayBeDerivedFrom[impl.Name].ContainsKey(v.Name))
{
continue;
}
foreach (string s in mayBeDerivedFrom[impl.Name][v.Name])
{
if (!mayBeDerivedFrom[callCmd.callee][CalleeImplementation.InParams[i].Name].Contains(s))
{
SetMayBeDerivedFrom(callCmd.callee, CalleeImplementation.InParams[i].Name, s);
}
}
}
}
for (int i = 0; i < CalleeImplementation.OutParams.Count(); i++)
{
foreach (string s in mayBeDerivedFrom[callCmd.callee][CalleeImplementation.OutParams[i].Name])
{
if (!mayBeDerivedFrom[impl.Name][callCmd.Outs[i].Name].Contains(s))
{
SetMayBeDerivedFrom(impl.Name, callCmd.Outs[i].Name, s);
}
}
}
}
}
}
else if (c is AssumeCmd)
{
var assumeCmd = c as AssumeCmd;
ExprMayAffectControlFlow(impl.Name, assumeCmd.Expr);
}
else if (c is AssertCmd)
{
var assertCmd = c as AssertCmd;
ExprMayAffectControlFlow(impl.Name, assertCmd.Expr);
}
}
}