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//===- SCCP.cpp - Sparse Conditional Constant Propagation -----------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements sparse conditional constant propagation and merging:
//
// Specifically, this:
// * Assumes values are constant unless proven otherwise
// * Assumes BasicBlocks are dead unless proven otherwise
// * Proves values to be constant, and replaces them with constants
// * Proves conditional branches to be unconditional
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "sccp"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/IPO.h"
#include "llvm/Constants.h"
#include "llvm/DerivedTypes.h"
#include "llvm/Instructions.h"
#include "llvm/Pass.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Target/TargetData.h"
#include "llvm/Support/CallSite.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/InstVisitor.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/DenseSet.h"
#include "llvm/ADT/PointerIntPair.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/STLExtras.h"
#include <algorithm>
#include <map>
using namespace llvm;
STATISTIC(NumInstRemoved, "Number of instructions removed");
STATISTIC(NumDeadBlocks , "Number of basic blocks unreachable");
STATISTIC(IPNumInstRemoved, "Number of instructions removed by IPSCCP");
STATISTIC(IPNumArgsElimed ,"Number of arguments constant propagated by IPSCCP");
STATISTIC(IPNumGlobalConst, "Number of globals found to be constant by IPSCCP");
namespace {
/// LatticeVal class - This class represents the different lattice values that
/// an LLVM value may occupy. It is a simple class with value semantics.
///
class LatticeVal {
enum LatticeValueTy {
/// undefined - This LLVM Value has no known value yet.
undefined,
/// constant - This LLVM Value has a specific constant value.
constant,
/// forcedconstant - This LLVM Value was thought to be undef until
/// ResolvedUndefsIn. This is treated just like 'constant', but if merged
/// with another (different) constant, it goes to overdefined, instead of
/// asserting.
forcedconstant,
/// overdefined - This instruction is not known to be constant, and we know
/// it has a value.
overdefined
};
/// Val: This stores the current lattice value along with the Constant* for
/// the constant if this is a 'constant' or 'forcedconstant' value.
PointerIntPair<Constant *, 2, LatticeValueTy> Val;
LatticeValueTy getLatticeValue() const {
return Val.getInt();
}
public:
LatticeVal() : Val(0, undefined) {}
bool isUndefined() const { return getLatticeValue() == undefined; }
bool isConstant() const {
return getLatticeValue() == constant || getLatticeValue() == forcedconstant;
}
bool isOverdefined() const { return getLatticeValue() == overdefined; }
Constant *getConstant() const {
assert(isConstant() && "Cannot get the constant of a non-constant!");
return Val.getPointer();
}
/// markOverdefined - Return true if this is a change in status.
bool markOverdefined() {
if (isOverdefined())
return false;
Val.setInt(overdefined);
return true;
}
/// markConstant - Return true if this is a change in status.
bool markConstant(Constant *V) {
if (getLatticeValue() == constant) { // Constant but not forcedconstant.
assert(getConstant() == V && "Marking constant with different value");
return false;
}
if (isUndefined()) {
Val.setInt(constant);
assert(V && "Marking constant with NULL");
Val.setPointer(V);
} else {
assert(getLatticeValue() == forcedconstant &&
"Cannot move from overdefined to constant!");
// Stay at forcedconstant if the constant is the same.
if (V == getConstant()) return false;
// Otherwise, we go to overdefined. Assumptions made based on the
// forced value are possibly wrong. Assuming this is another constant
// could expose a contradiction.
Val.setInt(overdefined);
}
return true;
}
/// getConstantInt - If this is a constant with a ConstantInt value, return it
/// otherwise return null.
ConstantInt *getConstantInt() const {
if (isConstant())
return dyn_cast<ConstantInt>(getConstant());
return 0;
}
void markForcedConstant(Constant *V) {
assert(isUndefined() && "Can't force a defined value!");
Val.setInt(forcedconstant);
Val.setPointer(V);
}
};
} // end anonymous namespace.
namespace {
//===----------------------------------------------------------------------===//
//
/// SCCPSolver - This class is a general purpose solver for Sparse Conditional
/// Constant Propagation.
///
class SCCPSolver : public InstVisitor<SCCPSolver> {
const TargetData *TD;
SmallPtrSet<BasicBlock*, 8> BBExecutable; // The BBs that are executable.
DenseMap<Value*, LatticeVal> ValueState; // The state each value is in.
/// StructValueState - This maintains ValueState for values that have
/// StructType, for example for formal arguments, calls, insertelement, etc.
///
DenseMap<std::pair<Value*, unsigned>, LatticeVal> StructValueState;
/// GlobalValue - If we are tracking any values for the contents of a global
/// variable, we keep a mapping from the constant accessor to the element of
/// the global, to the currently known value. If the value becomes
/// overdefined, it's entry is simply removed from this map.
DenseMap<GlobalVariable*, LatticeVal> TrackedGlobals;
/// TrackedRetVals - If we are tracking arguments into and the return
/// value out of a function, it will have an entry in this map, indicating
/// what the known return value for the function is.
DenseMap<Function*, LatticeVal> TrackedRetVals;
/// TrackedMultipleRetVals - Same as TrackedRetVals, but used for functions
/// that return multiple values.
DenseMap<std::pair<Function*, unsigned>, LatticeVal> TrackedMultipleRetVals;
/// MRVFunctionsTracked - Each function in TrackedMultipleRetVals is
/// represented here for efficient lookup.
SmallPtrSet<Function*, 16> MRVFunctionsTracked;
/// TrackingIncomingArguments - This is the set of functions for whose
/// arguments we make optimistic assumptions about and try to prove as
/// constants.
SmallPtrSet<Function*, 16> TrackingIncomingArguments;
/// The reason for two worklists is that overdefined is the lowest state
/// on the lattice, and moving things to overdefined as fast as possible
/// makes SCCP converge much faster.
///
/// By having a separate worklist, we accomplish this because everything
/// possibly overdefined will become overdefined at the soonest possible
/// point.
SmallVector<Value*, 64> OverdefinedInstWorkList;
SmallVector<Value*, 64> InstWorkList;
SmallVector<BasicBlock*, 64> BBWorkList; // The BasicBlock work list
/// UsersOfOverdefinedPHIs - Keep track of any users of PHI nodes that are not
/// overdefined, despite the fact that the PHI node is overdefined.
std::multimap<PHINode*, Instruction*> UsersOfOverdefinedPHIs;
/// KnownFeasibleEdges - Entries in this set are edges which have already had
/// PHI nodes retriggered.
typedef std::pair<BasicBlock*, BasicBlock*> Edge;
DenseSet<Edge> KnownFeasibleEdges;
public:
SCCPSolver(const TargetData *td) : TD(td) {}
/// MarkBlockExecutable - This method can be used by clients to mark all of
/// the blocks that are known to be intrinsically live in the processed unit.
///
/// This returns true if the block was not considered live before.
bool MarkBlockExecutable(BasicBlock *BB) {
if (!BBExecutable.insert(BB)) return false;
DEBUG(dbgs() << "Marking Block Executable: " << BB->getName() << "\n");
BBWorkList.push_back(BB); // Add the block to the work list!
return true;
}
/// TrackValueOfGlobalVariable - Clients can use this method to
/// inform the SCCPSolver that it should track loads and stores to the
/// specified global variable if it can. This is only legal to call if
/// performing Interprocedural SCCP.
void TrackValueOfGlobalVariable(GlobalVariable *GV) {
// We only track the contents of scalar globals.
if (GV->getType()->getElementType()->isSingleValueType()) {
LatticeVal &IV = TrackedGlobals[GV];
if (!isa<UndefValue>(GV->getInitializer()))
IV.markConstant(GV->getInitializer());
}
}
/// AddTrackedFunction - If the SCCP solver is supposed to track calls into
/// and out of the specified function (which cannot have its address taken),
/// this method must be called.
void AddTrackedFunction(Function *F) {
// Add an entry, F -> undef.
if (StructType *STy = dyn_cast<StructType>(F->getReturnType())) {
MRVFunctionsTracked.insert(F);
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i)
TrackedMultipleRetVals.insert(std::make_pair(std::make_pair(F, i),
LatticeVal()));
} else
TrackedRetVals.insert(std::make_pair(F, LatticeVal()));
}
void AddArgumentTrackedFunction(Function *F) {
TrackingIncomingArguments.insert(F);
}
/// Solve - Solve for constants and executable blocks.
///
void Solve();
/// ResolvedUndefsIn - While solving the dataflow for a function, we assume
/// that branches on undef values cannot reach any of their successors.
/// However, this is not a safe assumption. After we solve dataflow, this
/// method should be use to handle this. If this returns true, the solver
/// should be rerun.
bool ResolvedUndefsIn(Function &F);
bool isBlockExecutable(BasicBlock *BB) const {
return BBExecutable.count(BB);
}
LatticeVal getLatticeValueFor(Value *V) const {
DenseMap<Value*, LatticeVal>::const_iterator I = ValueState.find(V);
assert(I != ValueState.end() && "V is not in valuemap!");
return I->second;
}
/*LatticeVal getStructLatticeValueFor(Value *V, unsigned i) const {
DenseMap<std::pair<Value*, unsigned>, LatticeVal>::const_iterator I =
StructValueState.find(std::make_pair(V, i));
assert(I != StructValueState.end() && "V is not in valuemap!");
return I->second;
}*/
/// getTrackedRetVals - Get the inferred return value map.
///
const DenseMap<Function*, LatticeVal> &getTrackedRetVals() {
return TrackedRetVals;
}
/// getTrackedGlobals - Get and return the set of inferred initializers for
/// global variables.
const DenseMap<GlobalVariable*, LatticeVal> &getTrackedGlobals() {
return TrackedGlobals;
}
void markOverdefined(Value *V) {
assert(!V->getType()->isStructTy() && "Should use other method");
markOverdefined(ValueState[V], V);
}
/// markAnythingOverdefined - Mark the specified value overdefined. This
/// works with both scalars and structs.
void markAnythingOverdefined(Value *V) {
if (StructType *STy = dyn_cast<StructType>(V->getType()))
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i)
markOverdefined(getStructValueState(V, i), V);
else
markOverdefined(V);
}
private:
// markConstant - Make a value be marked as "constant". If the value
// is not already a constant, add it to the instruction work list so that
// the users of the instruction are updated later.
//
void markConstant(LatticeVal &IV, Value *V, Constant *C) {
if (!IV.markConstant(C)) return;
DEBUG(dbgs() << "markConstant: " << *C << ": " << *V << '\n');
if (IV.isOverdefined())
OverdefinedInstWorkList.push_back(V);
else
InstWorkList.push_back(V);
}
void markConstant(Value *V, Constant *C) {
assert(!V->getType()->isStructTy() && "Should use other method");
markConstant(ValueState[V], V, C);
}
void markForcedConstant(Value *V, Constant *C) {
assert(!V->getType()->isStructTy() && "Should use other method");
LatticeVal &IV = ValueState[V];
IV.markForcedConstant(C);
DEBUG(dbgs() << "markForcedConstant: " << *C << ": " << *V << '\n');
if (IV.isOverdefined())
OverdefinedInstWorkList.push_back(V);
else
InstWorkList.push_back(V);
}
// markOverdefined - Make a value be marked as "overdefined". If the
// value is not already overdefined, add it to the overdefined instruction
// work list so that the users of the instruction are updated later.
void markOverdefined(LatticeVal &IV, Value *V) {
if (!IV.markOverdefined()) return;
DEBUG(dbgs() << "markOverdefined: ";
if (Function *F = dyn_cast<Function>(V))
dbgs() << "Function '" << F->getName() << "'\n";
else
dbgs() << *V << '\n');
// Only instructions go on the work list
OverdefinedInstWorkList.push_back(V);
}
void mergeInValue(LatticeVal &IV, Value *V, LatticeVal MergeWithV) {
if (IV.isOverdefined() || MergeWithV.isUndefined())
return; // Noop.
if (MergeWithV.isOverdefined())
markOverdefined(IV, V);
else if (IV.isUndefined())
markConstant(IV, V, MergeWithV.getConstant());
else if (IV.getConstant() != MergeWithV.getConstant())
markOverdefined(IV, V);
}
void mergeInValue(Value *V, LatticeVal MergeWithV) {
assert(!V->getType()->isStructTy() && "Should use other method");
mergeInValue(ValueState[V], V, MergeWithV);
}
/// getValueState - Return the LatticeVal object that corresponds to the
/// value. This function handles the case when the value hasn't been seen yet
/// by properly seeding constants etc.
LatticeVal &getValueState(Value *V) {
assert(!V->getType()->isStructTy() && "Should use getStructValueState");
std::pair<DenseMap<Value*, LatticeVal>::iterator, bool> I =
ValueState.insert(std::make_pair(V, LatticeVal()));
LatticeVal &LV = I.first->second;
if (!I.second)
return LV; // Common case, already in the map.
if (Constant *C = dyn_cast<Constant>(V)) {
// Undef values remain undefined.
if (!isa<UndefValue>(V))
LV.markConstant(C); // Constants are constant
}
// All others are underdefined by default.
return LV;
}
/// getStructValueState - Return the LatticeVal object that corresponds to the
/// value/field pair. This function handles the case when the value hasn't
/// been seen yet by properly seeding constants etc.
LatticeVal &getStructValueState(Value *V, unsigned i) {
assert(V->getType()->isStructTy() && "Should use getValueState");
assert(i < cast<StructType>(V->getType())->getNumElements() &&
"Invalid element #");
std::pair<DenseMap<std::pair<Value*, unsigned>, LatticeVal>::iterator,
bool> I = StructValueState.insert(
std::make_pair(std::make_pair(V, i), LatticeVal()));
LatticeVal &LV = I.first->second;
if (!I.second)
return LV; // Common case, already in the map.
if (Constant *C = dyn_cast<Constant>(V)) {
if (isa<UndefValue>(C))
; // Undef values remain undefined.
else if (ConstantStruct *CS = dyn_cast<ConstantStruct>(C))
LV.markConstant(CS->getOperand(i)); // Constants are constant.
else if (isa<ConstantAggregateZero>(C)) {
Type *FieldTy = cast<StructType>(V->getType())->getElementType(i);
LV.markConstant(Constant::getNullValue(FieldTy));
} else
LV.markOverdefined(); // Unknown sort of constant.
}
// All others are underdefined by default.
return LV;
}
/// markEdgeExecutable - Mark a basic block as executable, adding it to the BB
/// work list if it is not already executable.
void markEdgeExecutable(BasicBlock *Source, BasicBlock *Dest) {
if (!KnownFeasibleEdges.insert(Edge(Source, Dest)).second)
return; // This edge is already known to be executable!
if (!MarkBlockExecutable(Dest)) {
// If the destination is already executable, we just made an *edge*
// feasible that wasn't before. Revisit the PHI nodes in the block
// because they have potentially new operands.
DEBUG(dbgs() << "Marking Edge Executable: " << Source->getName()
<< " -> " << Dest->getName() << "\n");
PHINode *PN;
for (BasicBlock::iterator I = Dest->begin();
(PN = dyn_cast<PHINode>(I)); ++I)
visitPHINode(*PN);
}
}
// getFeasibleSuccessors - Return a vector of booleans to indicate which
// successors are reachable from a given terminator instruction.
//
void getFeasibleSuccessors(TerminatorInst &TI, SmallVector<bool, 16> &Succs);
// isEdgeFeasible - Return true if the control flow edge from the 'From' basic
// block to the 'To' basic block is currently feasible.
//
bool isEdgeFeasible(BasicBlock *From, BasicBlock *To);
// OperandChangedState - This method is invoked on all of the users of an
// instruction that was just changed state somehow. Based on this
// information, we need to update the specified user of this instruction.
//
void OperandChangedState(Instruction *I) {
if (BBExecutable.count(I->getParent())) // Inst is executable?
visit(*I);
}
/// RemoveFromOverdefinedPHIs - If I has any entries in the
/// UsersOfOverdefinedPHIs map for PN, remove them now.
void RemoveFromOverdefinedPHIs(Instruction *I, PHINode *PN) {
if (UsersOfOverdefinedPHIs.empty()) return;
typedef std::multimap<PHINode*, Instruction*>::iterator ItTy;
std::pair<ItTy, ItTy> Range = UsersOfOverdefinedPHIs.equal_range(PN);
for (ItTy It = Range.first, E = Range.second; It != E;) {
if (It->second == I)
UsersOfOverdefinedPHIs.erase(It++);
else
++It;
}
}
/// InsertInOverdefinedPHIs - Insert an entry in the UsersOfOverdefinedPHIS
/// map for I and PN, but if one is there already, do not create another.
/// (Duplicate entries do not break anything directly, but can lead to
/// exponential growth of the table in rare cases.)
void InsertInOverdefinedPHIs(Instruction *I, PHINode *PN) {
typedef std::multimap<PHINode*, Instruction*>::iterator ItTy;
std::pair<ItTy, ItTy> Range = UsersOfOverdefinedPHIs.equal_range(PN);
for (ItTy J = Range.first, E = Range.second; J != E; ++J)
if (J->second == I)
return;
UsersOfOverdefinedPHIs.insert(std::make_pair(PN, I));
}
private:
friend class InstVisitor<SCCPSolver>;
// visit implementations - Something changed in this instruction. Either an
// operand made a transition, or the instruction is newly executable. Change
// the value type of I to reflect these changes if appropriate.
void visitPHINode(PHINode &I);
// Terminators
void visitReturnInst(ReturnInst &I);
void visitTerminatorInst(TerminatorInst &TI);
void visitCastInst(CastInst &I);
void visitSelectInst(SelectInst &I);
void visitBinaryOperator(Instruction &I);
void visitCmpInst(CmpInst &I);
void visitExtractElementInst(ExtractElementInst &I);
void visitInsertElementInst(InsertElementInst &I);
void visitShuffleVectorInst(ShuffleVectorInst &I);
void visitExtractValueInst(ExtractValueInst &EVI);
void visitInsertValueInst(InsertValueInst &IVI);
void visitLandingPadInst(LandingPadInst &I) { markAnythingOverdefined(&I); }
// Instructions that cannot be folded away.
void visitStoreInst (StoreInst &I);
void visitLoadInst (LoadInst &I);
void visitGetElementPtrInst(GetElementPtrInst &I);
void visitCallInst (CallInst &I) {
visitCallSite(&I);
}
void visitInvokeInst (InvokeInst &II) {
visitCallSite(&II);
visitTerminatorInst(II);
}
void visitCallSite (CallSite CS);
void visitResumeInst (TerminatorInst &I) { /*returns void*/ }
void visitUnwindInst (TerminatorInst &I) { /*returns void*/ }
void visitUnreachableInst(TerminatorInst &I) { /*returns void*/ }
void visitFenceInst (FenceInst &I) { /*returns void*/ }
void visitAtomicCmpXchgInst (AtomicCmpXchgInst &I) { markOverdefined(&I); }
void visitAtomicRMWInst (AtomicRMWInst &I) { markOverdefined(&I); }
void visitAllocaInst (Instruction &I) { markOverdefined(&I); }
void visitVAArgInst (Instruction &I) { markAnythingOverdefined(&I); }
void visitInstruction(Instruction &I) {
// If a new instruction is added to LLVM that we don't handle.
dbgs() << "SCCP: Don't know how to handle: " << I;
markAnythingOverdefined(&I); // Just in case
}
};
} // end anonymous namespace
// getFeasibleSuccessors - Return a vector of booleans to indicate which
// successors are reachable from a given terminator instruction.
//
void SCCPSolver::getFeasibleSuccessors(TerminatorInst &TI,
SmallVector<bool, 16> &Succs) {
Succs.resize(TI.getNumSuccessors());
if (BranchInst *BI = dyn_cast<BranchInst>(&TI)) {
if (BI->isUnconditional()) {
Succs[0] = true;
return;
}
LatticeVal BCValue = getValueState(BI->getCondition());
ConstantInt *CI = BCValue.getConstantInt();
if (CI == 0) {
// Overdefined condition variables, and branches on unfoldable constant
// conditions, mean the branch could go either way.
if (!BCValue.isUndefined())
Succs[0] = Succs[1] = true;
return;
}
// Constant condition variables mean the branch can only go a single way.
Succs[CI->isZero()] = true;
return;
}
if (isa<InvokeInst>(TI)) {
// Invoke instructions successors are always executable.
Succs[0] = Succs[1] = true;
return;
}
if (SwitchInst *SI = dyn_cast<SwitchInst>(&TI)) {
if (TI.getNumSuccessors() < 2) {
Succs[0] = true;
return;
}
LatticeVal SCValue = getValueState(SI->getCondition());
ConstantInt *CI = SCValue.getConstantInt();
if (CI == 0) { // Overdefined or undefined condition?
// All destinations are executable!
if (!SCValue.isUndefined())
Succs.assign(TI.getNumSuccessors(), true);
return;
}
Succs[SI->findCaseValue(CI)] = true;
return;
}
// TODO: This could be improved if the operand is a [cast of a] BlockAddress.
if (isa<IndirectBrInst>(&TI)) {
// Just mark all destinations executable!
Succs.assign(TI.getNumSuccessors(), true);
return;
}
#ifndef NDEBUG
dbgs() << "Unknown terminator instruction: " << TI << '\n';
#endif
llvm_unreachable("SCCP: Don't know how to handle this terminator!");
}
// isEdgeFeasible - Return true if the control flow edge from the 'From' basic
// block to the 'To' basic block is currently feasible.
//
bool SCCPSolver::isEdgeFeasible(BasicBlock *From, BasicBlock *To) {
assert(BBExecutable.count(To) && "Dest should always be alive!");
// Make sure the source basic block is executable!!
if (!BBExecutable.count(From)) return false;
// Check to make sure this edge itself is actually feasible now.
TerminatorInst *TI = From->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(TI)) {
if (BI->isUnconditional())
return true;
LatticeVal BCValue = getValueState(BI->getCondition());
// Overdefined condition variables mean the branch could go either way,
// undef conditions mean that neither edge is feasible yet.
ConstantInt *CI = BCValue.getConstantInt();
if (CI == 0)
return !BCValue.isUndefined();
// Constant condition variables mean the branch can only go a single way.
return BI->getSuccessor(CI->isZero()) == To;
}
// Invoke instructions successors are always executable.
if (isa<InvokeInst>(TI))
return true;
if (SwitchInst *SI = dyn_cast<SwitchInst>(TI)) {
if (SI->getNumSuccessors() < 2)
return true;
LatticeVal SCValue = getValueState(SI->getCondition());
ConstantInt *CI = SCValue.getConstantInt();
if (CI == 0)
return !SCValue.isUndefined();
// Make sure to skip the "default value" which isn't a value
for (unsigned i = 1, E = SI->getNumSuccessors(); i != E; ++i)
if (SI->getSuccessorValue(i) == CI) // Found the taken branch.
return SI->getSuccessor(i) == To;
// If the constant value is not equal to any of the branches, we must
// execute default branch.
return SI->getDefaultDest() == To;
}
// Just mark all destinations executable!
// TODO: This could be improved if the operand is a [cast of a] BlockAddress.
if (isa<IndirectBrInst>(TI))
return true;
#ifndef NDEBUG
dbgs() << "Unknown terminator instruction: " << *TI << '\n';
#endif
llvm_unreachable(0);
}
// visit Implementations - Something changed in this instruction, either an
// operand made a transition, or the instruction is newly executable. Change
// the value type of I to reflect these changes if appropriate. This method
// makes sure to do the following actions:
//
// 1. If a phi node merges two constants in, and has conflicting value coming
// from different branches, or if the PHI node merges in an overdefined
// value, then the PHI node becomes overdefined.
// 2. If a phi node merges only constants in, and they all agree on value, the
// PHI node becomes a constant value equal to that.
// 3. If V <- x (op) y && isConstant(x) && isConstant(y) V = Constant
// 4. If V <- x (op) y && (isOverdefined(x) || isOverdefined(y)) V = Overdefined
// 5. If V <- MEM or V <- CALL or V <- (unknown) then V = Overdefined
// 6. If a conditional branch has a value that is constant, make the selected
// destination executable
// 7. If a conditional branch has a value that is overdefined, make all
// successors executable.
//
void SCCPSolver::visitPHINode(PHINode &PN) {
// If this PN returns a struct, just mark the result overdefined.
// TODO: We could do a lot better than this if code actually uses this.
if (PN.getType()->isStructTy())
return markAnythingOverdefined(&PN);
if (getValueState(&PN).isOverdefined()) {
// There may be instructions using this PHI node that are not overdefined
// themselves. If so, make sure that they know that the PHI node operand
// changed.
typedef std::multimap<PHINode*, Instruction*>::iterator ItTy;
std::pair<ItTy, ItTy> Range = UsersOfOverdefinedPHIs.equal_range(&PN);
if (Range.first == Range.second)
return;
SmallVector<Instruction*, 16> Users;
for (ItTy I = Range.first, E = Range.second; I != E; ++I)
Users.push_back(I->second);
while (!Users.empty())
visit(Users.pop_back_val());
return; // Quick exit
}
// Super-extra-high-degree PHI nodes are unlikely to ever be marked constant,
// and slow us down a lot. Just mark them overdefined.
if (PN.getNumIncomingValues() > 64)
return markOverdefined(&PN);
// Look at all of the executable operands of the PHI node. If any of them
// are overdefined, the PHI becomes overdefined as well. If they are all
// constant, and they agree with each other, the PHI becomes the identical
// constant. If they are constant and don't agree, the PHI is overdefined.
// If there are no executable operands, the PHI remains undefined.
//
Constant *OperandVal = 0;
for (unsigned i = 0, e = PN.getNumIncomingValues(); i != e; ++i) {
LatticeVal IV = getValueState(PN.getIncomingValue(i));
if (IV.isUndefined()) continue; // Doesn't influence PHI node.
if (!isEdgeFeasible(PN.getIncomingBlock(i), PN.getParent()))
continue;
if (IV.isOverdefined()) // PHI node becomes overdefined!
return markOverdefined(&PN);
if (OperandVal == 0) { // Grab the first value.
OperandVal = IV.getConstant();
continue;
}
// There is already a reachable operand. If we conflict with it,
// then the PHI node becomes overdefined. If we agree with it, we
// can continue on.
// Check to see if there are two different constants merging, if so, the PHI
// node is overdefined.
if (IV.getConstant() != OperandVal)
return markOverdefined(&PN);
}
// If we exited the loop, this means that the PHI node only has constant
// arguments that agree with each other(and OperandVal is the constant) or
// OperandVal is null because there are no defined incoming arguments. If
// this is the case, the PHI remains undefined.
//
if (OperandVal)
markConstant(&PN, OperandVal); // Acquire operand value
}
void SCCPSolver::visitReturnInst(ReturnInst &I) {
if (I.getNumOperands() == 0) return; // ret void
Function *F = I.getParent()->getParent();
Value *ResultOp = I.getOperand(0);
// If we are tracking the return value of this function, merge it in.
if (!TrackedRetVals.empty() && !ResultOp->getType()->isStructTy()) {
DenseMap<Function*, LatticeVal>::iterator TFRVI =
TrackedRetVals.find(F);
if (TFRVI != TrackedRetVals.end()) {
mergeInValue(TFRVI->second, F, getValueState(ResultOp));
return;
}
}
// Handle functions that return multiple values.
if (!TrackedMultipleRetVals.empty()) {
if (StructType *STy = dyn_cast<StructType>(ResultOp->getType()))
if (MRVFunctionsTracked.count(F))
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i)
mergeInValue(TrackedMultipleRetVals[std::make_pair(F, i)], F,
getStructValueState(ResultOp, i));
}
}
void SCCPSolver::visitTerminatorInst(TerminatorInst &TI) {
SmallVector<bool, 16> SuccFeasible;
getFeasibleSuccessors(TI, SuccFeasible);
BasicBlock *BB = TI.getParent();
// Mark all feasible successors executable.
for (unsigned i = 0, e = SuccFeasible.size(); i != e; ++i)
if (SuccFeasible[i])
markEdgeExecutable(BB, TI.getSuccessor(i));
}
void SCCPSolver::visitCastInst(CastInst &I) {
LatticeVal OpSt = getValueState(I.getOperand(0));
if (OpSt.isOverdefined()) // Inherit overdefinedness of operand
markOverdefined(&I);
else if (OpSt.isConstant()) // Propagate constant value
markConstant(&I, ConstantExpr::getCast(I.getOpcode(),
OpSt.getConstant(), I.getType()));
}
void SCCPSolver::visitExtractValueInst(ExtractValueInst &EVI) {
// If this returns a struct, mark all elements over defined, we don't track
// structs in structs.
if (EVI.getType()->isStructTy())
return markAnythingOverdefined(&EVI);
// If this is extracting from more than one level of struct, we don't know.
if (EVI.getNumIndices() != 1)
return markOverdefined(&EVI);
Value *AggVal = EVI.getAggregateOperand();
if (AggVal->getType()->isStructTy()) {
unsigned i = *EVI.idx_begin();
LatticeVal EltVal = getStructValueState(AggVal, i);
mergeInValue(getValueState(&EVI), &EVI, EltVal);
} else {
// Otherwise, must be extracting from an array.
return markOverdefined(&EVI);
}
}
void SCCPSolver::visitInsertValueInst(InsertValueInst &IVI) {
StructType *STy = dyn_cast<StructType>(IVI.getType());
if (STy == 0)
return markOverdefined(&IVI);
// If this has more than one index, we can't handle it, drive all results to
// undef.
if (IVI.getNumIndices() != 1)
return markAnythingOverdefined(&IVI);
Value *Aggr = IVI.getAggregateOperand();
unsigned Idx = *IVI.idx_begin();
// Compute the result based on what we're inserting.
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
// This passes through all values that aren't the inserted element.
if (i != Idx) {
LatticeVal EltVal = getStructValueState(Aggr, i);
mergeInValue(getStructValueState(&IVI, i), &IVI, EltVal);
continue;
}
Value *Val = IVI.getInsertedValueOperand();
if (Val->getType()->isStructTy())
// We don't track structs in structs.
markOverdefined(getStructValueState(&IVI, i), &IVI);
else {
LatticeVal InVal = getValueState(Val);
mergeInValue(getStructValueState(&IVI, i), &IVI, InVal);
}
}
}
void SCCPSolver::visitSelectInst(SelectInst &I) {
// If this select returns a struct, just mark the result overdefined.
// TODO: We could do a lot better than this if code actually uses this.
if (I.getType()->isStructTy())
return markAnythingOverdefined(&I);
LatticeVal CondValue = getValueState(I.getCondition());
if (CondValue.isUndefined())
return;
if (ConstantInt *CondCB = CondValue.getConstantInt()) {
Value *OpVal = CondCB->isZero() ? I.getFalseValue() : I.getTrueValue();
mergeInValue(&I, getValueState(OpVal));
return;
}
// Otherwise, the condition is overdefined or a constant we can't evaluate.
// See if we can produce something better than overdefined based on the T/F
// value.
LatticeVal TVal = getValueState(I.getTrueValue());
LatticeVal FVal = getValueState(I.getFalseValue());
// select ?, C, C -> C.
if (TVal.isConstant() && FVal.isConstant() &&
TVal.getConstant() == FVal.getConstant())
return markConstant(&I, FVal.getConstant());
if (TVal.isUndefined()) // select ?, undef, X -> X.
return mergeInValue(&I, FVal);
if (FVal.isUndefined()) // select ?, X, undef -> X.
return mergeInValue(&I, TVal);
markOverdefined(&I);
}
// Handle Binary Operators.
void SCCPSolver::visitBinaryOperator(Instruction &I) {
LatticeVal V1State = getValueState(I.getOperand(0));
LatticeVal V2State = getValueState(I.getOperand(1));
LatticeVal &IV = ValueState[&I];
if (IV.isOverdefined()) return;
if (V1State.isConstant() && V2State.isConstant())
return markConstant(IV, &I,
ConstantExpr::get(I.getOpcode(), V1State.getConstant(),
V2State.getConstant()));
// If something is undef, wait for it to resolve.
if (!V1State.isOverdefined() && !V2State.isOverdefined())
return;
// Otherwise, one of our operands is overdefined. Try to produce something
// better than overdefined with some tricks.
// If this is an AND or OR with 0 or -1, it doesn't matter that the other
// operand is overdefined.
if (I.getOpcode() == Instruction::And || I.getOpcode() == Instruction::Or) {
LatticeVal *NonOverdefVal = 0;
if (!V1State.isOverdefined())
NonOverdefVal = &V1State;
else if (!V2State.isOverdefined())
NonOverdefVal = &V2State;
if (NonOverdefVal) {
if (NonOverdefVal->isUndefined()) {
// Could annihilate value.
if (I.getOpcode() == Instruction::And)
markConstant(IV, &I, Constant::getNullValue(I.getType()));
else if (VectorType *PT = dyn_cast<VectorType>(I.getType()))
markConstant(IV, &I, Constant::getAllOnesValue(PT));
else
markConstant(IV, &I,
Constant::getAllOnesValue(I.getType()));
return;
}
if (I.getOpcode() == Instruction::And) {
// X and 0 = 0
if (NonOverdefVal->getConstant()->isNullValue())
return markConstant(IV, &I, NonOverdefVal->getConstant());
} else {
if (ConstantInt *CI = NonOverdefVal->getConstantInt())
if (CI->isAllOnesValue()) // X or -1 = -1
return markConstant(IV, &I, NonOverdefVal->getConstant());
}
}
}
// If both operands are PHI nodes, it is possible that this instruction has
// a constant value, despite the fact that the PHI node doesn't. Check for
// this condition now.
if (PHINode *PN1 = dyn_cast<PHINode>(I.getOperand(0)))
if (PHINode *PN2 = dyn_cast<PHINode>(I.getOperand(1)))
if (PN1->getParent() == PN2->getParent()) {
// Since the two PHI nodes are in the same basic block, they must have
// entries for the same predecessors. Walk the predecessor list, and
// if all of the incoming values are constants, and the result of
// evaluating this expression with all incoming value pairs is the
// same, then this expression is a constant even though the PHI node
// is not a constant!
LatticeVal Result;
for (unsigned i = 0, e = PN1->getNumIncomingValues(); i != e; ++i) {
LatticeVal In1 = getValueState(PN1->getIncomingValue(i));
BasicBlock *InBlock = PN1->getIncomingBlock(i);
LatticeVal In2 =getValueState(PN2->getIncomingValueForBlock(InBlock));
if (In1.isOverdefined() || In2.isOverdefined()) {
Result.markOverdefined();
break; // Cannot fold this operation over the PHI nodes!
}
if (In1.isConstant() && In2.isConstant()) {
Constant *V = ConstantExpr::get(I.getOpcode(), In1.getConstant(),
In2.getConstant());
if (Result.isUndefined())
Result.markConstant(V);
else if (Result.isConstant() && Result.getConstant() != V) {
Result.markOverdefined();
break;
}
}
}
// If we found a constant value here, then we know the instruction is
// constant despite the fact that the PHI nodes are overdefined.
if (Result.isConstant()) {
markConstant(IV, &I, Result.getConstant());
// Remember that this instruction is virtually using the PHI node
// operands.
InsertInOverdefinedPHIs(&I, PN1);
InsertInOverdefinedPHIs(&I, PN2);
return;
}
if (Result.isUndefined())
return;
// Okay, this really is overdefined now. Since we might have
// speculatively thought that this was not overdefined before, and
// added ourselves to the UsersOfOverdefinedPHIs list for the PHIs,
// make sure to clean out any entries that we put there, for
// efficiency.
RemoveFromOverdefinedPHIs(&I, PN1);
RemoveFromOverdefinedPHIs(&I, PN2);
}
markOverdefined(&I);
}
// Handle ICmpInst instruction.
void SCCPSolver::visitCmpInst(CmpInst &I) {
LatticeVal V1State = getValueState(I.getOperand(0));
LatticeVal V2State = getValueState(I.getOperand(1));
LatticeVal &IV = ValueState[&I];
if (IV.isOverdefined()) return;
if (V1State.isConstant() && V2State.isConstant())
return markConstant(IV, &I, ConstantExpr::getCompare(I.getPredicate(),
V1State.getConstant(),
V2State.getConstant()));
// If operands are still undefined, wait for it to resolve.
if (!V1State.isOverdefined() && !V2State.isOverdefined())
return;
// If something is overdefined, use some tricks to avoid ending up and over
// defined if we can.
// If both operands are PHI nodes, it is possible that this instruction has
// a constant value, despite the fact that the PHI node doesn't. Check for
// this condition now.
if (PHINode *PN1 = dyn_cast<PHINode>(I.getOperand(0)))
if (PHINode *PN2 = dyn_cast<PHINode>(I.getOperand(1)))
if (PN1->getParent() == PN2->getParent()) {
// Since the two PHI nodes are in the same basic block, they must have
// entries for the same predecessors. Walk the predecessor list, and
// if all of the incoming values are constants, and the result of
// evaluating this expression with all incoming value pairs is the
// same, then this expression is a constant even though the PHI node
// is not a constant!
LatticeVal Result;
for (unsigned i = 0, e = PN1->getNumIncomingValues(); i != e; ++i) {
LatticeVal In1 = getValueState(PN1->getIncomingValue(i));
BasicBlock *InBlock = PN1->getIncomingBlock(i);
LatticeVal In2 =getValueState(PN2->getIncomingValueForBlock(InBlock));
if (In1.isOverdefined() || In2.isOverdefined()) {
Result.markOverdefined();
break; // Cannot fold this operation over the PHI nodes!
}
if (In1.isConstant() && In2.isConstant()) {
Constant *V = ConstantExpr::getCompare(I.getPredicate(),
In1.getConstant(),
In2.getConstant());
if (Result.isUndefined())
Result.markConstant(V);
else if (Result.isConstant() && Result.getConstant() != V) {
Result.markOverdefined();
break;
}
}
}
// If we found a constant value here, then we know the instruction is
// constant despite the fact that the PHI nodes are overdefined.
if (Result.isConstant()) {
markConstant(&I, Result.getConstant());
// Remember that this instruction is virtually using the PHI node
// operands.
InsertInOverdefinedPHIs(&I, PN1);
InsertInOverdefinedPHIs(&I, PN2);
return;
}
if (Result.isUndefined())
return;
// Okay, this really is overdefined now. Since we might have
// speculatively thought that this was not overdefined before, and
// added ourselves to the UsersOfOverdefinedPHIs list for the PHIs,
// make sure to clean out any entries that we put there, for
// efficiency.
RemoveFromOverdefinedPHIs(&I, PN1);
RemoveFromOverdefinedPHIs(&I, PN2);
}
markOverdefined(&I);
}
void SCCPSolver::visitExtractElementInst(ExtractElementInst &I) {
// TODO : SCCP does not handle vectors properly.
return markOverdefined(&I);
#if 0
LatticeVal &ValState = getValueState(I.getOperand(0));
LatticeVal &IdxState = getValueState(I.getOperand(1));
if (ValState.isOverdefined() || IdxState.isOverdefined())
markOverdefined(&I);
else if(ValState.isConstant() && IdxState.isConstant())
markConstant(&I, ConstantExpr::getExtractElement(ValState.getConstant(),
IdxState.getConstant()));
#endif
}
void SCCPSolver::visitInsertElementInst(InsertElementInst &I) {
// TODO : SCCP does not handle vectors properly.
return markOverdefined(&I);
#if 0
LatticeVal &ValState = getValueState(I.getOperand(0));
LatticeVal &EltState = getValueState(I.getOperand(1));
LatticeVal &IdxState = getValueState(I.getOperand(2));
if (ValState.isOverdefined() || EltState.isOverdefined() ||
IdxState.isOverdefined())
markOverdefined(&I);
else if(ValState.isConstant() && EltState.isConstant() &&
IdxState.isConstant())
markConstant(&I, ConstantExpr::getInsertElement(ValState.getConstant(),
EltState.getConstant(),
IdxState.getConstant()));
else if (ValState.isUndefined() && EltState.isConstant() &&
IdxState.isConstant())
markConstant(&I,ConstantExpr::getInsertElement(UndefValue::get(I.getType()),
EltState.getConstant(),
IdxState.getConstant()));
#endif
}
void SCCPSolver::visitShuffleVectorInst(ShuffleVectorInst &I) {
// TODO : SCCP does not handle vectors properly.
return markOverdefined(&I);
#if 0
LatticeVal &V1State = getValueState(I.getOperand(0));
LatticeVal &V2State = getValueState(I.getOperand(1));
LatticeVal &MaskState = getValueState(I.getOperand(2));
if (MaskState.isUndefined() ||
(V1State.isUndefined() && V2State.isUndefined()))
return; // Undefined output if mask or both inputs undefined.
if (V1State.isOverdefined() || V2State.isOverdefined() ||
MaskState.isOverdefined()) {
markOverdefined(&I);
} else {
// A mix of constant/undef inputs.
Constant *V1 = V1State.isConstant() ?
V1State.getConstant() : UndefValue::get(I.getType());
Constant *V2 = V2State.isConstant() ?
V2State.getConstant() : UndefValue::get(I.getType());
Constant *Mask = MaskState.isConstant() ?
MaskState.getConstant() : UndefValue::get(I.getOperand(2)->getType());
markConstant(&I, ConstantExpr::getShuffleVector(V1, V2, Mask));
}
#endif
}
// Handle getelementptr instructions. If all operands are constants then we
// can turn this into a getelementptr ConstantExpr.
//
void SCCPSolver::visitGetElementPtrInst(GetElementPtrInst &I) {
if (ValueState[&I].isOverdefined()) return;
SmallVector<Constant*, 8> Operands;
Operands.reserve(I.getNumOperands());
for (unsigned i = 0, e = I.getNumOperands(); i != e; ++i) {
LatticeVal State = getValueState(I.getOperand(i));
if (State.isUndefined())
return; // Operands are not resolved yet.
if (State.isOverdefined())
return markOverdefined(&I);
assert(State.isConstant() && "Unknown state!");
Operands.push_back(State.getConstant());
}
Constant *Ptr = Operands[0];
ArrayRef<Constant *> Indices(Operands.begin() + 1, Operands.end());
markConstant(&I, ConstantExpr::getGetElementPtr(Ptr, Indices));
}
void SCCPSolver::visitStoreInst(StoreInst &SI) {
// If this store is of a struct, ignore it.
if (SI.getOperand(0)->getType()->isStructTy())
return;
if (TrackedGlobals.empty() || !isa<GlobalVariable>(SI.getOperand(1)))
return;
GlobalVariable *GV = cast<GlobalVariable>(SI.getOperand(1));
DenseMap<GlobalVariable*, LatticeVal>::iterator I = TrackedGlobals.find(GV);
if (I == TrackedGlobals.end() || I->second.isOverdefined()) return;
// Get the value we are storing into the global, then merge it.
mergeInValue(I->second, GV, getValueState(SI.getOperand(0)));
if (I->second.isOverdefined())
TrackedGlobals.erase(I); // No need to keep tracking this!
}
// Handle load instructions. If the operand is a constant pointer to a constant
// global, we can replace the load with the loaded constant value!
void SCCPSolver::visitLoadInst(LoadInst &I) {
// If this load is of a struct, just mark the result overdefined.
if (I.getType()->isStructTy())
return markAnythingOverdefined(&I);
LatticeVal PtrVal = getValueState(I.getOperand(0));
if (PtrVal.isUndefined()) return; // The pointer is not resolved yet!
LatticeVal &IV = ValueState[&I];
if (IV.isOverdefined()) return;
if (!PtrVal.isConstant() || I.isVolatile())
return markOverdefined(IV, &I);
Constant *Ptr = PtrVal.getConstant();
// load null -> null
if (isa<ConstantPointerNull>(Ptr) && I.getPointerAddressSpace() == 0)
return markConstant(IV, &I, Constant::getNullValue(I.getType()));
// Transform load (constant global) into the value loaded.
if (GlobalVariable *GV = dyn_cast<GlobalVariable>(Ptr)) {
if (!TrackedGlobals.empty()) {
// If we are tracking this global, merge in the known value for it.
DenseMap<GlobalVariable*, LatticeVal>::iterator It =
TrackedGlobals.find(GV);
if (It != TrackedGlobals.end()) {
mergeInValue(IV, &I, It->second);
return;
}
}
}
// Transform load from a constant into a constant if possible.
if (Constant *C = ConstantFoldLoadFromConstPtr(Ptr, TD))
return markConstant(IV, &I, C);
// Otherwise we cannot say for certain what value this load will produce.
// Bail out.
markOverdefined(IV, &I);
}
void SCCPSolver::visitCallSite(CallSite CS) {
Function *F = CS.getCalledFunction();
Instruction *I = CS.getInstruction();
// The common case is that we aren't tracking the callee, either because we
// are not doing interprocedural analysis or the callee is indirect, or is
// external. Handle these cases first.
if (F == 0 || F->isDeclaration()) {
CallOverdefined:
// Void return and not tracking callee, just bail.
if (I->getType()->isVoidTy()) return;
// Otherwise, if we have a single return value case, and if the function is
// a declaration, maybe we can constant fold it.
if (F && F->isDeclaration() && !I->getType()->isStructTy() &&
canConstantFoldCallTo(F)) {
SmallVector<Constant*, 8> Operands;
for (CallSite::arg_iterator AI = CS.arg_begin(), E = CS.arg_end();
AI != E; ++AI) {
LatticeVal State = getValueState(*AI);
if (State.isUndefined())
return; // Operands are not resolved yet.
if (State.isOverdefined())
return markOverdefined(I);
assert(State.isConstant() && "Unknown state!");
Operands.push_back(State.getConstant());
}
// If we can constant fold this, mark the result of the call as a
// constant.
if (Constant *C = ConstantFoldCall(F, Operands))
return markConstant(I, C);
}
// Otherwise, we don't know anything about this call, mark it overdefined.
return markAnythingOverdefined(I);
}
// If this is a local function that doesn't have its address taken, mark its
// entry block executable and merge in the actual arguments to the call into
// the formal arguments of the function.
if (!TrackingIncomingArguments.empty() && TrackingIncomingArguments.count(F)){
MarkBlockExecutable(F->begin());
// Propagate information from this call site into the callee.
CallSite::arg_iterator CAI = CS.arg_begin();
for (Function::arg_iterator AI = F->arg_begin(), E = F->arg_end();
AI != E; ++AI, ++CAI) {
// If this argument is byval, and if the function is not readonly, there
// will be an implicit copy formed of the input aggregate.
if (AI->hasByValAttr() && !F->onlyReadsMemory()) {
markOverdefined(AI);
continue;
}
if (StructType *STy = dyn_cast<StructType>(AI->getType())) {
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
LatticeVal CallArg = getStructValueState(*CAI, i);
mergeInValue(getStructValueState(AI, i), AI, CallArg);
}
} else {
mergeInValue(AI, getValueState(*CAI));
}
}
}
// If this is a single/zero retval case, see if we're tracking the function.
if (StructType *STy = dyn_cast<StructType>(F->getReturnType())) {
if (!MRVFunctionsTracked.count(F))
goto CallOverdefined; // Not tracking this callee.
// If we are tracking this callee, propagate the result of the function
// into this call site.
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i)
mergeInValue(getStructValueState(I, i), I,
TrackedMultipleRetVals[std::make_pair(F, i)]);
} else {
DenseMap<Function*, LatticeVal>::iterator TFRVI = TrackedRetVals.find(F);
if (TFRVI == TrackedRetVals.end())
goto CallOverdefined; // Not tracking this callee.
// If so, propagate the return value of the callee into this call result.
mergeInValue(I, TFRVI->second);
}
}
void SCCPSolver::Solve() {
// Process the work lists until they are empty!
while (!BBWorkList.empty() || !InstWorkList.empty() ||
!OverdefinedInstWorkList.empty()) {
// Process the overdefined instruction's work list first, which drives other
// things to overdefined more quickly.
while (!OverdefinedInstWorkList.empty()) {
Value *I = OverdefinedInstWorkList.pop_back_val();
DEBUG(dbgs() << "\nPopped off OI-WL: " << *I << '\n');
// "I" got into the work list because it either made the transition from
// bottom to constant
//
// Anything on this worklist that is overdefined need not be visited
// since all of its users will have already been marked as overdefined
// Update all of the users of this instruction's value.
//
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
UI != E; ++UI)
if (Instruction *I = dyn_cast<Instruction>(*UI))
OperandChangedState(I);
}
// Process the instruction work list.
while (!InstWorkList.empty()) {
Value *I = InstWorkList.pop_back_val();
DEBUG(dbgs() << "\nPopped off I-WL: " << *I << '\n');
// "I" got into the work list because it made the transition from undef to
// constant.
//
// Anything on this worklist that is overdefined need not be visited
// since all of its users will have already been marked as overdefined.
// Update all of the users of this instruction's value.
//
if (I->getType()->isStructTy() || !getValueState(I).isOverdefined())
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
UI != E; ++UI)
if (Instruction *I = dyn_cast<Instruction>(*UI))
OperandChangedState(I);
}
// Process the basic block work list.
while (!BBWorkList.empty()) {
BasicBlock *BB = BBWorkList.back();
BBWorkList.pop_back();
DEBUG(dbgs() << "\nPopped off BBWL: " << *BB << '\n');
// Notify all instructions in this basic block that they are newly
// executable.
visit(BB);
}
}
}
/// ResolvedUndefsIn - While solving the dataflow for a function, we assume
/// that branches on undef values cannot reach any of their successors.
/// However, this is not a safe assumption. After we solve dataflow, this
/// method should be use to handle this. If this returns true, the solver
/// should be rerun.
///
/// This method handles this by finding an unresolved branch and marking it one
/// of the edges from the block as being feasible, even though the condition
/// doesn't say it would otherwise be. This allows SCCP to find the rest of the
/// CFG and only slightly pessimizes the analysis results (by marking one,
/// potentially infeasible, edge feasible). This cannot usefully modify the
/// constraints on the condition of the branch, as that would impact other users
/// of the value.
///
/// This scan also checks for values that use undefs, whose results are actually
/// defined. For example, 'zext i8 undef to i32' should produce all zeros
/// conservatively, as "(zext i8 X -> i32) & 0xFF00" must always return zero,
/// even if X isn't defined.
bool SCCPSolver::ResolvedUndefsIn(Function &F) {
for (Function::iterator BB = F.begin(), E = F.end(); BB != E; ++BB) {
if (!BBExecutable.count(BB))
continue;
for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I) {
// Look for instructions which produce undef values.
if (I->getType()->isVoidTy()) continue;
if (StructType *STy = dyn_cast<StructType>(I->getType())) {
// Only a few things that can be structs matter for undef.
// Tracked calls must never be marked overdefined in ResolvedUndefsIn.
if (CallSite CS = CallSite(I))
if (Function *F = CS.getCalledFunction())
if (MRVFunctionsTracked.count(F))
continue;
// extractvalue and insertvalue don't need to be marked; they are
// tracked as precisely as their operands.
if (isa<ExtractValueInst>(I) || isa<InsertValueInst>(I))
continue;
// Send the results of everything else to overdefined. We could be
// more precise than this but it isn't worth bothering.
for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
LatticeVal &LV = getStructValueState(I, i);
if (LV.isUndefined())
markOverdefined(LV, I);
}
continue;
}
LatticeVal &LV = getValueState(I);
if (!LV.isUndefined()) continue;
// extractvalue is safe; check here because the argument is a struct.
if (isa<ExtractValueInst>(I))
continue;
// Compute the operand LatticeVals, for convenience below.
// Anything taking a struct is conservatively assumed to require
// overdefined markings.
if (I->getOperand(0)->getType()->isStructTy()) {
markOverdefined(I);
return true;
}
LatticeVal Op0LV = getValueState(I->getOperand(0));
LatticeVal Op1LV;
if (I->getNumOperands() == 2) {
if (I->getOperand(1)->getType()->isStructTy()) {
markOverdefined(I);
return true;
}
Op1LV = getValueState(I->getOperand(1));
}
// If this is an instructions whose result is defined even if the input is
// not fully defined, propagate the information.
Type *ITy = I->getType();
switch (I->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::Trunc:
case Instruction::FPTrunc:
case Instruction::BitCast:
break; // Any undef -> undef
case Instruction::FSub:
case Instruction::FAdd:
case Instruction::FMul:
case Instruction::FDiv:
case Instruction::FRem:
// Floating-point binary operation: be conservative.
if (Op0LV.isUndefined() && Op1LV.isUndefined())
markForcedConstant(I, Constant::getNullValue(ITy));
else
markOverdefined(I);
return true;
case Instruction::ZExt:
case Instruction::SExt:
case Instruction::FPToUI:
case Instruction::FPToSI:
case Instruction::FPExt:
case Instruction::PtrToInt:
case Instruction::IntToPtr:
case Instruction::SIToFP:
case Instruction::UIToFP:
// undef -> 0; some outputs are impossible
markForcedConstant(I, Constant::getNullValue(ITy));
return true;
case Instruction::Mul:
case Instruction::And:
// Both operands undef -> undef
if (Op0LV.isUndefined() && Op1LV.isUndefined())
break;
// undef * X -> 0. X could be zero.
// undef & X -> 0. X could be zero.
markForcedConstant(I, Constant::getNullValue(ITy));
return true;
case Instruction::Or:
// Both operands undef -> undef
if (Op0LV.isUndefined() && Op1LV.isUndefined())
break;
// undef | X -> -1. X could be -1.
markForcedConstant(I, Constant::getAllOnesValue(ITy));
return true;
case Instruction::Xor:
// undef ^ undef -> 0; strictly speaking, this is not strictly
// necessary, but we try to be nice to people who expect this
// behavior in simple cases
if (Op0LV.isUndefined() && Op1LV.isUndefined()) {
markForcedConstant(I, Constant::getNullValue(ITy));
return true;
}
// undef ^ X -> undef
break;
case Instruction::SDiv:
case Instruction::UDiv:
case Instruction::SRem:
case Instruction::URem:
// X / undef -> undef. No change.
// X % undef -> undef. No change.
if (Op1LV.isUndefined()) break;
// undef / X -> 0. X could be maxint.
// undef % X -> 0. X could be 1.
markForcedConstant(I, Constant::getNullValue(ITy));
return true;
case Instruction::AShr:
// X >>a undef -> undef.
if (Op1LV.isUndefined()) break;
// undef >>a X -> all ones
markForcedConstant(I, Constant::getAllOnesValue(ITy));
return true;
case Instruction::LShr:
case Instruction::Shl:
// X << undef -> undef.
// X >> undef -> undef.
if (Op1LV.isUndefined()) break;
// undef << X -> 0
// undef >> X -> 0
markForcedConstant(I, Constant::getNullValue(ITy));
return true;
case Instruction::Select:
Op1LV = getValueState(I->getOperand(1));
// undef ? X : Y -> X or Y. There could be commonality between X/Y.
if (Op0LV.isUndefined()) {
if (!Op1LV.isConstant()) // Pick the constant one if there is any.
Op1LV = getValueState(I->getOperand(2));
} else if (Op1LV.isUndefined()) {
// c ? undef : undef -> undef. No change.
Op1LV = getValueState(I->getOperand(2));
if (Op1LV.isUndefined())
break;
// Otherwise, c ? undef : x -> x.
} else {
// Leave Op1LV as Operand(1)'s LatticeValue.
}
if (Op1LV.isConstant())
markForcedConstant(I, Op1LV.getConstant());
else
markOverdefined(I);
return true;
case Instruction::Load:
// A load here means one of two things: a load of undef from a global,
// a load from an unknown pointer. Either way, having it return undef
// is okay.
break;
case Instruction::ICmp:
// X == undef -> undef. Other comparisons get more complicated.
if (cast<ICmpInst>(I)->isEquality())
break;
markOverdefined(I);
return true;
case Instruction::Call:
case Instruction::Invoke: {
// There are two reasons a call can have an undef result
// 1. It could be tracked.
// 2. It could be constant-foldable.
// Because of the way we solve return values, tracked calls must
// never be marked overdefined in ResolvedUndefsIn.
if (Function *F = CallSite(I).getCalledFunction())
if (TrackedRetVals.count(F))
break;
// If the call is constant-foldable, we mark it overdefined because
// we do not know what return values are valid.
markOverdefined(I);
return true;
}
default:
// If we don't know what should happen here, conservatively mark it
// overdefined.
markOverdefined(I);
return true;
}
}
// Check to see if we have a branch or switch on an undefined value. If so
// we force the branch to go one way or the other to make the successor
// values live. It doesn't really matter which way we force it.
TerminatorInst *TI = BB->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(TI)) {
if (!BI->isConditional()) continue;
if (!getValueState(BI->getCondition()).isUndefined())
continue;
// If the input to SCCP is actually branch on undef, fix the undef to
// false.
if (isa<UndefValue>(BI->getCondition())) {
BI->setCondition(ConstantInt::getFalse(BI->getContext()));
markEdgeExecutable(BB, TI->getSuccessor(1));
return true;
}
// Otherwise, it is a branch on a symbolic value which is currently
// considered to be undef. Handle this by forcing the input value to the
// branch to false.
markForcedConstant(BI->getCondition(),
ConstantInt::getFalse(TI->getContext()));
return true;
}
if (SwitchInst *SI = dyn_cast<SwitchInst>(TI)) {
if (SI->getNumSuccessors() < 2) // no cases
continue;
if (!getValueState(SI->getCondition()).isUndefined())
continue;
// If the input to SCCP is actually switch on undef, fix the undef to
// the first constant.
if (isa<UndefValue>(SI->getCondition())) {
SI->setCondition(SI->getCaseValue(1));
markEdgeExecutable(BB, TI->getSuccessor(1));
return true;
}
markForcedConstant(SI->getCondition(), SI->getCaseValue(1));
return true;
}
}
return false;
}
namespace {
//===--------------------------------------------------------------------===//
//
/// SCCP Class - This class uses the SCCPSolver to implement a per-function
/// Sparse Conditional Constant Propagator.
///
struct SCCP : public FunctionPass {
static char ID; // Pass identification, replacement for typeid
SCCP() : FunctionPass(ID) {
initializeSCCPPass(*PassRegistry::getPassRegistry());
}
// runOnFunction - Run the Sparse Conditional Constant Propagation
// algorithm, and return true if the function was modified.
//
bool runOnFunction(Function &F);
};
} // end anonymous namespace
char SCCP::ID = 0;
INITIALIZE_PASS(SCCP, "sccp",
"Sparse Conditional Constant Propagation", false, false)
// createSCCPPass - This is the public interface to this file.
FunctionPass *llvm::createSCCPPass() {
return new SCCP();
}
static void DeleteInstructionInBlock(BasicBlock *BB) {
DEBUG(dbgs() << " BasicBlock Dead:" << *BB);
++NumDeadBlocks;
// Check to see if there are non-terminating instructions to delete.
if (isa<TerminatorInst>(BB->begin()))
return;
// Delete the instructions backwards, as it has a reduced likelihood of having
// to update as many def-use and use-def chains.
Instruction *EndInst = BB->getTerminator(); // Last not to be deleted.
while (EndInst != BB->begin()) {
// Delete the next to last instruction.
BasicBlock::iterator I = EndInst;
Instruction *Inst = --I;
if (!Inst->use_empty())
Inst->replaceAllUsesWith(UndefValue::get(Inst->getType()));
if (isa<LandingPadInst>(Inst)) {
EndInst = Inst;
continue;
}
BB->getInstList().erase(Inst);
++NumInstRemoved;
}
}
// runOnFunction() - Run the Sparse Conditional Constant Propagation algorithm,
// and return true if the function was modified.
//
bool SCCP::runOnFunction(Function &F) {
DEBUG(dbgs() << "SCCP on function '" << F.getName() << "'\n");
SCCPSolver Solver(getAnalysisIfAvailable<TargetData>());
// Mark the first block of the function as being executable.
Solver.MarkBlockExecutable(F.begin());
// Mark all arguments to the function as being overdefined.
for (Function::arg_iterator AI = F.arg_begin(), E = F.arg_end(); AI != E;++AI)
Solver.markAnythingOverdefined(AI);
// Solve for constants.
bool ResolvedUndefs = true;
while (ResolvedUndefs) {
Solver.Solve();
DEBUG(dbgs() << "RESOLVING UNDEFs\n");
ResolvedUndefs = Solver.ResolvedUndefsIn(F);
}
bool MadeChanges = false;
// If we decided that there are basic blocks that are dead in this function,
// delete their contents now. Note that we cannot actually delete the blocks,
// as we cannot modify the CFG of the function.
for (Function::iterator BB = F.begin(), E = F.end(); BB != E; ++BB) {
if (!Solver.isBlockExecutable(BB)) {
DeleteInstructionInBlock(BB);
MadeChanges = true;
continue;
}
// Iterate over all of the instructions in a function, replacing them with
// constants if we have found them to be of constant values.
//
for (BasicBlock::iterator BI = BB->begin(), E = BB->end(); BI != E; ) {
Instruction *Inst = BI++;
if (Inst->getType()->isVoidTy() || isa<TerminatorInst>(Inst))
continue;
// TODO: Reconstruct structs from their elements.
if (Inst->getType()->isStructTy())
continue;
LatticeVal IV = Solver.getLatticeValueFor(Inst);
if (IV.isOverdefined())
continue;
Constant *Const = IV.isConstant()
? IV.getConstant() : UndefValue::get(Inst->getType());
DEBUG(dbgs() << " Constant: " << *Const << " = " << *Inst);
// Replaces all of the uses of a variable with uses of the constant.
Inst->replaceAllUsesWith(Const);
// Delete the instruction.
Inst->eraseFromParent();
// Hey, we just changed something!
MadeChanges = true;
++NumInstRemoved;
}
}
return MadeChanges;
}
namespace {
//===--------------------------------------------------------------------===//
//
/// IPSCCP Class - This class implements interprocedural Sparse Conditional
/// Constant Propagation.
///
struct IPSCCP : public ModulePass {
static char ID;
IPSCCP() : ModulePass(ID) {
initializeIPSCCPPass(*PassRegistry::getPassRegistry());
}
bool runOnModule(Module &M);
};
} // end anonymous namespace
char IPSCCP::ID = 0;
INITIALIZE_PASS(IPSCCP, "ipsccp",
"Interprocedural Sparse Conditional Constant Propagation",
false, false)
// createIPSCCPPass - This is the public interface to this file.
ModulePass *llvm::createIPSCCPPass() {
return new IPSCCP();
}
static bool AddressIsTaken(const GlobalValue *GV) {
// Delete any dead constantexpr klingons.
GV->removeDeadConstantUsers();
for (Value::const_use_iterator UI = GV->use_begin(), E = GV->use_end();
UI != E; ++UI) {
const User *U = *UI;
if (const StoreInst *SI = dyn_cast<StoreInst>(U)) {
if (SI->getOperand(0) == GV || SI->isVolatile())
return true; // Storing addr of GV.
} else if (isa<InvokeInst>(U) || isa<CallInst>(U)) {
// Make sure we are calling the function, not passing the address.
ImmutableCallSite CS(cast<Instruction>(U));
if (!CS.isCallee(UI))
return true;
} else if (const LoadInst *LI = dyn_cast<LoadInst>(U)) {
if (LI->isVolatile())
return true;
} else if (isa<BlockAddress>(U)) {
// blockaddress doesn't take the address of the function, it takes addr
// of label.
} else {
return true;
}
}
return false;
}
bool IPSCCP::runOnModule(Module &M) {
SCCPSolver Solver(getAnalysisIfAvailable<TargetData>());
// AddressTakenFunctions - This set keeps track of the address-taken functions
// that are in the input. As IPSCCP runs through and simplifies code,
// functions that were address taken can end up losing their
// address-taken-ness. Because of this, we keep track of their addresses from
// the first pass so we can use them for the later simplification pass.
SmallPtrSet<Function*, 32> AddressTakenFunctions;
// Loop over all functions, marking arguments to those with their addresses
// taken or that are external as overdefined.
//
for (Module::iterator F = M.begin(), E = M.end(); F != E; ++F) {
if (F->isDeclaration())
continue;
// If this is a strong or ODR definition of this function, then we can
// propagate information about its result into callsites of it.
if (!F->mayBeOverridden())
Solver.AddTrackedFunction(F);
// If this function only has direct calls that we can see, we can track its
// arguments and return value aggressively, and can assume it is not called
// unless we see evidence to the contrary.
if (F->hasLocalLinkage()) {
if (AddressIsTaken(F))
AddressTakenFunctions.insert(F);
else {
Solver.AddArgumentTrackedFunction(F);
continue;
}
}
// Assume the function is called.
Solver.MarkBlockExecutable(F->begin());
// Assume nothing about the incoming arguments.
for (Function::arg_iterator AI = F->arg_begin(), E = F->arg_end();
AI != E; ++AI)
Solver.markAnythingOverdefined(AI);
}
// Loop over global variables. We inform the solver about any internal global
// variables that do not have their 'addresses taken'. If they don't have
// their addresses taken, we can propagate constants through them.
for (Module::global_iterator G = M.global_begin(), E = M.global_end();
G != E; ++G)
if (!G->isConstant() && G->hasLocalLinkage() && !AddressIsTaken(G))
Solver.TrackValueOfGlobalVariable(G);
// Solve for constants.
bool ResolvedUndefs = true;
while (ResolvedUndefs) {
Solver.Solve();
DEBUG(dbgs() << "RESOLVING UNDEFS\n");
ResolvedUndefs = false;
for (Module::iterator F = M.begin(), E = M.end(); F != E; ++F)
ResolvedUndefs |= Solver.ResolvedUndefsIn(*F);
}
bool MadeChanges = false;
// Iterate over all of the instructions in the module, replacing them with
// constants if we have found them to be of constant values.
//
SmallVector<BasicBlock*, 512> BlocksToErase;
for (Module::iterator F = M.begin(), E = M.end(); F != E; ++F) {
if (Solver.isBlockExecutable(F->begin())) {
for (Function::arg_iterator AI = F->arg_begin(), E = F->arg_end();
AI != E; ++AI) {
if (AI->use_empty() || AI->getType()->isStructTy()) continue;
// TODO: Could use getStructLatticeValueFor to find out if the entire
// result is a constant and replace it entirely if so.
LatticeVal IV = Solver.getLatticeValueFor(AI);
if (IV.isOverdefined()) continue;
Constant *CST = IV.isConstant() ?
IV.getConstant() : UndefValue::get(AI->getType());
DEBUG(dbgs() << "*** Arg " << *AI << " = " << *CST <<"\n");
// Replaces all of the uses of a variable with uses of the
// constant.
AI->replaceAllUsesWith(CST);
++IPNumArgsElimed;
}
}
for (Function::iterator BB = F->begin(), E = F->end(); BB != E; ++BB) {
if (!Solver.isBlockExecutable(BB)) {
DeleteInstructionInBlock(BB);
MadeChanges = true;
TerminatorInst *TI = BB->getTerminator();
for (unsigned i = 0, e = TI->getNumSuccessors(); i != e; ++i) {
BasicBlock *Succ = TI->getSuccessor(i);
if (!Succ->empty() && isa<PHINode>(Succ->begin()))
TI->getSuccessor(i)->removePredecessor(BB);
}
if (!TI->use_empty())
TI->replaceAllUsesWith(UndefValue::get(TI->getType()));
TI->eraseFromParent();
if (&*BB != &F->front())
BlocksToErase.push_back(BB);
else
new UnreachableInst(M.getContext(), BB);
continue;
}
for (BasicBlock::iterator BI = BB->begin(), E = BB->end(); BI != E; ) {
Instruction *Inst = BI++;
if (Inst->getType()->isVoidTy() || Inst->getType()->isStructTy())
continue;
// TODO: Could use getStructLatticeValueFor to find out if the entire
// result is a constant and replace it entirely if so.
LatticeVal IV = Solver.getLatticeValueFor(Inst);
if (IV.isOverdefined())
continue;
Constant *Const = IV.isConstant()
? IV.getConstant() : UndefValue::get(Inst->getType());
DEBUG(dbgs() << " Constant: " << *Const << " = " << *Inst);
// Replaces all of the uses of a variable with uses of the
// constant.
Inst->replaceAllUsesWith(Const);
// Delete the instruction.
if (!isa<CallInst>(Inst) && !isa<TerminatorInst>(Inst))
Inst->eraseFromParent();
// Hey, we just changed something!
MadeChanges = true;
++IPNumInstRemoved;
}
}
// Now that all instructions in the function are constant folded, erase dead
// blocks, because we can now use ConstantFoldTerminator to get rid of
// in-edges.
for (unsigned i = 0, e = BlocksToErase.size(); i != e; ++i) {
// If there are any PHI nodes in this successor, drop entries for BB now.
BasicBlock *DeadBB = BlocksToErase[i];
for (Value::use_iterator UI = DeadBB->use_begin(), UE = DeadBB->use_end();
UI != UE; ) {
// Grab the user and then increment the iterator early, as the user
// will be deleted. Step past all adjacent uses from the same user.
Instruction *I = dyn_cast<Instruction>(*UI);
do { ++UI; } while (UI != UE && *UI == I);
// Ignore blockaddress users; BasicBlock's dtor will handle them.
if (!I) continue;
bool Folded = ConstantFoldTerminator(I->getParent());
if (!Folded) {
// The constant folder may not have been able to fold the terminator
// if this is a branch or switch on undef. Fold it manually as a
// branch to the first successor.
#ifndef NDEBUG
if (BranchInst *BI = dyn_cast<BranchInst>(I)) {
assert(BI->isConditional() && isa<UndefValue>(BI->getCondition()) &&
"Branch should be foldable!");
} else if (SwitchInst *SI = dyn_cast<SwitchInst>(I)) {
assert(isa<UndefValue>(SI->getCondition()) && "Switch should fold");
} else {
llvm_unreachable("Didn't fold away reference to block!");
}
#endif
// Make this an uncond branch to the first successor.
TerminatorInst *TI = I->getParent()->getTerminator();
BranchInst::Create(TI->getSuccessor(0), TI);
// Remove entries in successor phi nodes to remove edges.
for (unsigned i = 1, e = TI->getNumSuccessors(); i != e; ++i)
TI->getSuccessor(i)->removePredecessor(TI->getParent());
// Remove the old terminator.
TI->eraseFromParent();
}
}
// Finally, delete the basic block.
F->getBasicBlockList().erase(DeadBB);
}
BlocksToErase.clear();
}
// If we inferred constant or undef return values for a function, we replaced
// all call uses with the inferred value. This means we don't need to bother
// actually returning anything from the function. Replace all return
// instructions with return undef.
//
// Do this in two stages: first identify the functions we should process, then
// actually zap their returns. This is important because we can only do this
// if the address of the function isn't taken. In cases where a return is the
// last use of a function, the order of processing functions would affect
// whether other functions are optimizable.
SmallVector<ReturnInst*, 8> ReturnsToZap;
// TODO: Process multiple value ret instructions also.
const DenseMap<Function*, LatticeVal> &RV = Solver.getTrackedRetVals();
for (DenseMap<Function*, LatticeVal>::const_iterator I = RV.begin(),
E = RV.end(); I != E; ++I) {
Function *F = I->first;
if (I->second.isOverdefined() || F->getReturnType()->isVoidTy())
continue;
// We can only do this if we know that nothing else can call the function.
if (!F->hasLocalLinkage() || AddressTakenFunctions.count(F))
continue;
for (Function::iterator BB = F->begin(), E = F->end(); BB != E; ++BB)
if (ReturnInst *RI = dyn_cast<ReturnInst>(BB->getTerminator()))
if (!isa<UndefValue>(RI->getOperand(0)))
ReturnsToZap.push_back(RI);
}
// Zap all returns which we've identified as zap to change.
for (unsigned i = 0, e = ReturnsToZap.size(); i != e; ++i) {
Function *F = ReturnsToZap[i]->getParent()->getParent();
ReturnsToZap[i]->setOperand(0, UndefValue::get(F->getReturnType()));
}
// If we inferred constant or undef values for globals variables, we can delete
// the global and any stores that remain to it.
const DenseMap<GlobalVariable*, LatticeVal> &TG = Solver.getTrackedGlobals();
for (DenseMap<GlobalVariable*, LatticeVal>::const_iterator I = TG.begin(),
E = TG.end(); I != E; ++I) {
GlobalVariable *GV = I->first;
assert(!I->second.isOverdefined() &&
"Overdefined values should have been taken out of the map!");
DEBUG(dbgs() << "Found that GV '" << GV->getName() << "' is constant!\n");
while (!GV->use_empty()) {
StoreInst *SI = cast<StoreInst>(GV->use_back());
SI->eraseFromParent();
}
M.getGlobalList().erase(GV);
++IPNumGlobalConst;
}
return MadeChanges;
}