private void AnalyseRegion(IRegion region, Graph <Block> cfg)
{
var header = region.Header();
var blockVarDefs = new Dictionary <Block, VarDefs>();
var blocks = region.SubBlocks().Where(i => i != header);
var modSet = region.GetModifiedVariables();
blockVarDefs[header] = new VarDefs(header, cfg.BackEdgeNodes(header), modSet);
blockVarDefs[header].Initialize();
foreach (var b in blocks)
{
blockVarDefs[b] = new VarDefs(b, cfg.Predecessors(b), modSet);
}
var changed = true;
while (changed)
{
changed = false;
foreach (var b in blocks)
{
if (blockVarDefs[b].ComputeTransfer(blockVarDefs))
{
changed = true;
}
}
}
possibleInductionVarDefs[region.Identifier()]
= blockVarDefs[header].FindSelfReferentialVariables(blockVarDefs)
.ToDictionary(i => i.Item1.Name, i => i.Item2);
}
public override void GenerateCandidates(Implementation impl, IRegion region)
{
HashSet <Variable> modset = region.GetModifiedVariables();
foreach (Variable v in impl.LocVars)
{
string basicName = Utilities.StripThreadIdentifier(v.Name);
if (Verifier.MayBePowerOfTwoAnalyser.MayBePowerOfTwo(impl.Name, basicName))
{
if (Verifier.ContainsNamedVariable(modset, basicName))
{
var type = v.TypedIdent.Type;
var bitwiseInv = Expr.Or(
Expr.Eq(new IdentifierExpr(v.tok, v), Verifier.IntRep.GetZero(type)),
Expr.Eq(
Verifier.IntRep.MakeAnd(
new IdentifierExpr(v.tok, v),
Verifier.IntRep.MakeSub(
new IdentifierExpr(v.tok, v), Verifier.IntRep.GetLiteral(1, type))),
Verifier.IntRep.GetZero(type)));
Verifier.AddCandidateInvariant(region, bitwiseInv, "pow2");
Verifier.AddCandidateInvariant(
region,
Expr.Neq(new IdentifierExpr(v.tok, v), Verifier.IntRep.GetZero(type)),
"pow2NotZero");
}
}
}
// Relational Power Of Two
var incs = modset.Where(v => Verifier.RelationalPowerOfTwoAnalyser.IsInc(impl.Name, v.Name));
var decs = modset.Where(v => Verifier.RelationalPowerOfTwoAnalyser.IsDec(impl.Name, v.Name));
if (incs.ToList().Count() == 1 && decs.ToList().Count() == 1)
{
var inc = incs.Single();
var dec = decs.Single();
var type = inc.TypedIdent.Type;
if (type.Equals(dec.TypedIdent.Type))
{
for (int i = 1 << 15; i > 0; i >>= 1)
{
var mulInv = Expr.Eq(
Verifier.IntRep.MakeMul(
new IdentifierExpr(inc.tok, inc),
new IdentifierExpr(dec.tok, dec)),
Verifier.IntRep.GetLiteral(i, type));
Verifier.AddCandidateInvariant(region, mulInv, "relationalPow2");
var disjInv = Expr.Or(
Expr.And(
Expr.Eq(new IdentifierExpr(dec.tok, dec), Verifier.IntRep.GetZero(type)),
Expr.Eq(new IdentifierExpr(inc.tok, inc), Verifier.IntRep.GetLiteral(2 * i, type))),
mulInv);
Verifier.AddCandidateInvariant(region, disjInv, "relationalPow2");
}
}
}
}
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 = region.GetModifiedVariables().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("$") &&
!formals.Contains(x.Name) && modset.Contains(x.Name) &&
x.TypedIdent.Type.IsBv));
}
foreach (var v in nonnegVars)
{
// REVISIT: really we only want to guess for /integer/ variables.
var type = v.TypedIdent.Type;
if (type.BvBits >= 8)
{
var inv = verifier.IntRep.MakeSle(verifier.IntRep.GetZero(type), new IdentifierExpr(v.tok, v));
verifier.AddCandidateInvariant(region, inv, "guardNonNeg");
}
}
}
private void AddBarrierDivergenceCandidates(HashSet <Variable> localVars, Implementation impl, IRegion region)
{
if (!verifier.ContainsBarrierCall(region) && !GPUVerifyVCGenCommandLineOptions.WarpSync)
{
return;
}
Expr guard = region.Guard();
if (guard != null && verifier.UniformityAnalyser.IsUniform(impl.Name, guard))
{
return;
}
if (IsDisjunctionOfPredicates(guard))
{
string loopPredicate = ((guard as NAryExpr).Args[0] as IdentifierExpr).Name;
loopPredicate = loopPredicate.Substring(0, loopPredicate.IndexOf('$'));
// Int type used here, but it doesn't matter as we will print and then re-parse the program
var uniformEnabledPredicate = Expr.Eq(
new IdentifierExpr(Token.NoToken, new LocalVariable(Token.NoToken, new TypedIdent(Token.NoToken, loopPredicate + "$1", Type.Int))),
new IdentifierExpr(Token.NoToken, new LocalVariable(Token.NoToken, new TypedIdent(Token.NoToken, loopPredicate + "$2", Type.Int))));
verifier.AddCandidateInvariant(region, uniformEnabledPredicate, "loopPredicateEquality");
verifier.AddCandidateInvariant(region, Expr.Imp(verifier.ThreadsInSameGroup(), uniformEnabledPredicate), "loopPredicateEquality");
Dictionary <string, int> assignmentCounts = GetAssignmentCounts(impl);
HashSet <string> alreadyConsidered = new HashSet <string>();
foreach (var v in localVars)
{
string lv = Utilities.StripThreadIdentifier(v.Name);
if (alreadyConsidered.Contains(lv))
{
continue;
}
alreadyConsidered.Add(lv);
if (verifier.UniformityAnalyser.IsUniform(impl.Name, v.Name))
{
continue;
}
if (GPUVerifier.IsPredicate(lv))
{
continue;
}
if (!assignmentCounts.ContainsKey(lv) || assignmentCounts[lv] <= 1)
{
continue;
}
if (!verifier.ContainsNamedVariable(region.GetModifiedVariables(), lv))
{
continue;
}
AddPredicatedEqualityCandidateInvariant(region, loopPredicate, new LocalVariable(Token.NoToken, new TypedIdent(Token.NoToken, lv, Type.Int)));
}
}
}
private static void GenerateCandidateForNonUniformGuardVariables(GPUVerifier verifier, Implementation impl, IRegion region)
{
if (!verifier.ContainsBarrierCall(region) && !GPUVerifyVCGenCommandLineOptions.WarpSync)
{
return;
}
HashSet <Variable> partitionVars = region.PartitionVariablesOfHeader();
HashSet <Variable> guardVars = new HashSet <Variable>();
var formals = impl.InParams.Select(x => x.Name);
var modset = region.GetModifiedVariables().Select(x => x.Name);
foreach (var v in partitionVars)
{
Expr expr = verifier.VarDefAnalysesRegion[impl].DefOfVariableName(v.Name);
if (expr == null)
{
continue;
}
var visitor = new VariablesOccurringInExpressionVisitor();
visitor.Visit(expr);
guardVars.UnionWith(
visitor.GetVariables().Where(x => x.Name.StartsWith("$") &&
!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");
}
}
}
}
}