StackProtector.cpp

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//===- StackProtector.cpp - Stack Protector Insertion ---------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This pass inserts stack protectors into functions which need them. A variable
// with a random value in it is stored onto the stack before the local variables
// are allocated. Upon exiting the block, the stored value is checked. If it's
// changed, then there was some sort of violation and the program aborts.
//
//===----------------------------------------------------------------------===//
 
#include "llvm/CodeGen/StackProtector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/BranchProbabilityInfo.h"
#include "llvm/Analysis/EHPersonalities.h"
#include "llvm/Analysis/MemoryLocation.h"
#include "llvm/Analysis/OptimizationRemarkEmitter.h"
#include "llvm/CodeGen/Passes.h"
#include "llvm/CodeGen/TargetLowering.h"
#include "llvm/CodeGen/TargetPassConfig.h"
#include "llvm/CodeGen/TargetSubtargetInfo.h"
#include "llvm/IR/Attributes.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/MDBuilder.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/User.h"
#include "llvm/InitializePasses.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Target/TargetMachine.h"
#include "llvm/Target/TargetOptions.h"
#include <optional>
#include <utility>
 
using namespace llvm;
 
#define DEBUG_TYPE "stack-protector"
 
STATISTIC(NumFunProtected, "Number of functions protected");
STATISTIC(NumAddrTaken, "Number of local variables that have their address"
                        " taken.");
 
static cl::opt<bool> EnableSelectionDAGSP("enable-selectiondag-sp",
                                          cl::init(true), cl::Hidden);
 
char StackProtector::ID = 0;
 
StackProtector::StackProtector() : FunctionPass(ID), SSPBufferSize(8) {
  initializeStackProtectorPass(*PassRegistry::getPassRegistry());
}
 
INITIALIZE_PASS_BEGIN(StackProtector, DEBUG_TYPE,
                      "Insert stack protectors", false, true)
INITIALIZE_PASS_DEPENDENCY(TargetPassConfig)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_END(StackProtector, DEBUG_TYPE,
                    "Insert stack protectors", false, true)
 
FunctionPass *llvm::createStackProtectorPass() { return new StackProtector(); }
 
void StackProtector::getAnalysisUsage(AnalysisUsage &AU) const {
  AU.addRequired<TargetPassConfig>();
  AU.addPreserved<DominatorTreeWrapperPass>();
}
 
bool StackProtector::runOnFunction(Function &Fn) {
  F = &Fn;
  M = F->getParent();
  DominatorTreeWrapperPass *DTWP =
      getAnalysisIfAvailable<DominatorTreeWrapperPass>();
  DT = DTWP ? &DTWP->getDomTree() : nullptr;
  TM = &getAnalysis<TargetPassConfig>().getTM<TargetMachine>();
  Trip = TM->getTargetTriple();
  TLI = TM->getSubtargetImpl(Fn)->getTargetLowering();
  HasPrologue = false;
  HasIRCheck = false;
 
  Attribute Attr = Fn.getFnAttribute("stack-protector-buffer-size");
  if (Attr.isStringAttribute() &&
      Attr.getValueAsString().getAsInteger(10, SSPBufferSize))
    return false; // Invalid integer string
 
  if (!RequiresStackProtector())
    return false;
 
  // TODO(etienneb): Functions with funclets are not correctly supported now.
  // Do nothing if this is funclet-based personality.
  if (Fn.hasPersonalityFn()) {
    EHPersonality Personality = classifyEHPersonality(Fn.getPersonalityFn());
    if (isFuncletEHPersonality(Personality))
      return false;
  }
 
  ++NumFunProtected;
  return InsertStackProtectors();
}
 
/// \param [out] IsLarge is set to true if a protectable array is found and
/// it is "large" ( >= ssp-buffer-size).  In the case of a structure with
/// multiple arrays, this gets set if any of them is large.
bool StackProtector::ContainsProtectableArray(Type *Ty, bool &IsLarge,
                                              bool Strong,
                                              bool InStruct) const {
  if (!Ty)
    return false;
  if (ArrayType *AT = dyn_cast<ArrayType>(Ty)) {
    if (!AT->getElementType()->isIntegerTy(8)) {
      // If we're on a non-Darwin platform or we're inside of a structure, don't
      // add stack protectors unless the array is a character array.
      // However, in strong mode any array, regardless of type and size,
      // triggers a protector.
      if (!Strong && (InStruct || !Trip.isOSDarwin()))
        return false;
    }
 
    // If an array has more than SSPBufferSize bytes of allocated space, then we
    // emit stack protectors.
    if (SSPBufferSize <= M->getDataLayout().getTypeAllocSize(AT)) {
      IsLarge = true;
      return true;
    }
 
    if (Strong)
      // Require a protector for all arrays in strong mode
      return true;
  }
 
  const StructType *ST = dyn_cast<StructType>(Ty);
  if (!ST)
    return false;
 
  bool NeedsProtector = false;
  for (Type *ET : ST->elements())
    if (ContainsProtectableArray(ET, IsLarge, Strong, true)) {
      // If the element is a protectable array and is large (>= SSPBufferSize)
      // then we are done.  If the protectable array is not large, then
      // keep looking in case a subsequent element is a large array.
      if (IsLarge)
        return true;
      NeedsProtector = true;
    }
 
  return NeedsProtector;
}
 
bool StackProtector::HasAddressTaken(const Instruction *AI,
                                     TypeSize AllocSize) {
  const DataLayout &DL = M->getDataLayout();
  for (const User *U : AI->users()) {
    const auto *I = cast<Instruction>(U);
    // If this instruction accesses memory make sure it doesn't access beyond
    // the bounds of the allocated object.
    std::optional<MemoryLocation> MemLoc = MemoryLocation::getOrNone(I);
    if (MemLoc && MemLoc->Size.hasValue() &&
        !TypeSize::isKnownGE(AllocSize,
                             TypeSize::getFixed(MemLoc->Size.getValue())))
      return true;
    switch (I->getOpcode()) {
    case Instruction::Store:
      if (AI == cast<StoreInst>(I)->getValueOperand())
        return true;
      break;
    case Instruction::AtomicCmpXchg:
      // cmpxchg conceptually includes both a load and store from the same
      // location. So, like store, the value being stored is what matters.
      if (AI == cast<AtomicCmpXchgInst>(I)->getNewValOperand())
        return true;
      break;
    case Instruction::PtrToInt:
      if (AI == cast<PtrToIntInst>(I)->getOperand(0))
        return true;
      break;
    case Instruction::Call: {
      // Ignore intrinsics that do not become real instructions.
      // TODO: Narrow this to intrinsics that have store-like effects.
      const auto *CI = cast<CallInst>(I);
      if (!CI->isDebugOrPseudoInst() && !CI->isLifetimeStartOrEnd())
        return true;
      break;
    }
    case Instruction::Invoke:
      return true;
    case Instruction::GetElementPtr: {
      // If the GEP offset is out-of-bounds, or is non-constant and so has to be
      // assumed to be potentially out-of-bounds, then any memory access that
      // would use it could also be out-of-bounds meaning stack protection is
      // required.
      const GetElementPtrInst *GEP = cast<GetElementPtrInst>(I);
      unsigned IndexSize = DL.getIndexTypeSizeInBits(I->getType());
      APInt Offset(IndexSize, 0);
      if (!GEP->accumulateConstantOffset(DL, Offset))
        return true;
      TypeSize OffsetSize = TypeSize::Fixed(Offset.getLimitedValue());
      if (!TypeSize::isKnownGT(AllocSize, OffsetSize))
        return true;
      // Adjust AllocSize to be the space remaining after this offset.
      // We can't subtract a fixed size from a scalable one, so in that case
      // assume the scalable value is of minimum size.
      TypeSize NewAllocSize =
          TypeSize::Fixed(AllocSize.getKnownMinValue()) - OffsetSize;
      if (HasAddressTaken(I, NewAllocSize))
        return true;
      break;
    }
    case Instruction::BitCast:
    case Instruction::Select:
    case Instruction::AddrSpaceCast:
      if (HasAddressTaken(I, AllocSize))
        return true;
      break;
    case Instruction::PHI: {
      // Keep track of what PHI nodes we have already visited to ensure
      // they are only visited once.
      const auto *PN = cast<PHINode>(I);
      if (VisitedPHIs.insert(PN).second)
        if (HasAddressTaken(PN, AllocSize))
          return true;
      break;
    }
    case Instruction::Load:
    case Instruction::AtomicRMW:
    case Instruction::Ret:
      // These instructions take an address operand, but have load-like or
      // other innocuous behavior that should not trigger a stack protector.
      // atomicrmw conceptually has both load and store semantics, but the
      // value being stored must be integer; so if a pointer is being stored,
      // we'll catch it in the PtrToInt case above.
      break;
    default:
      // Conservatively return true for any instruction that takes an address
      // operand, but is not handled above.
      return true;
    }
  }
  return false;
}
 
/// Search for the first call to the llvm.stackprotector intrinsic and return it
/// if present.
static const CallInst *findStackProtectorIntrinsic(Function &F) {
  for (const BasicBlock &BB : F)
    for (const Instruction &I : BB)
      if (const auto *II = dyn_cast<IntrinsicInst>(&I))
        if (II->getIntrinsicID() == Intrinsic::stackprotector)
          return II;
  return nullptr;
}
 
/// Check whether or not this function needs a stack protector based
/// upon the stack protector level.
///
/// We use two heuristics: a standard (ssp) and strong (sspstrong).
/// The standard heuristic which will add a guard variable to functions that
/// call alloca with a either a variable size or a size >= SSPBufferSize,
/// functions with character buffers larger than SSPBufferSize, and functions
/// with aggregates containing character buffers larger than SSPBufferSize. The
/// strong heuristic will add a guard variables to functions that call alloca
/// regardless of size, functions with any buffer regardless of type and size,
/// functions with aggregates that contain any buffer regardless of type and
/// size, and functions that contain stack-based variables that have had their
/// address taken.
bool StackProtector::RequiresStackProtector() {
  bool Strong = false;
  bool NeedsProtector = false;
 
  if (F->hasFnAttribute(Attribute::SafeStack))
    return false;
 
  // We are constructing the OptimizationRemarkEmitter on the fly rather than
  // using the analysis pass to avoid building DominatorTree and LoopInfo which
  // are not available this late in the IR pipeline.
  OptimizationRemarkEmitter ORE(F);
 
  if (F->hasFnAttribute(Attribute::StackProtectReq)) {
    ORE.emit([&]() {
      return OptimizationRemark(DEBUG_TYPE, "StackProtectorRequested", F)
             << "Stack protection applied to function "
             << ore::NV("Function", F)
             << " due to a function attribute or command-line switch";
    });
    NeedsProtector = true;
    Strong = true; // Use the same heuristic as strong to determine SSPLayout
  } else if (F->hasFnAttribute(Attribute::StackProtectStrong))
    Strong = true;
  else if (!F->hasFnAttribute(Attribute::StackProtect))
    return false;
 
  for (const BasicBlock &BB : *F) {
    for (const Instruction &I : BB) {
      if (const AllocaInst *AI = dyn_cast<AllocaInst>(&I)) {
        if (AI->isArrayAllocation()) {
          auto RemarkBuilder = [&]() {
            return OptimizationRemark(DEBUG_TYPE, "StackProtectorAllocaOrArray",
                                      &I)
                   << "Stack protection applied to function "
                   << ore::NV("Function", F)
                   << " due to a call to alloca or use of a variable length "
                      "array";
          };
          if (const auto *CI = dyn_cast<ConstantInt>(AI->getArraySize())) {
            if (CI->getLimitedValue(SSPBufferSize) >= SSPBufferSize) {
              // A call to alloca with size >= SSPBufferSize requires
              // stack protectors.
              Layout.insert(std::make_pair(AI,
                                           MachineFrameInfo::SSPLK_LargeArray));
              ORE.emit(RemarkBuilder);
              NeedsProtector = true;
            } else if (Strong) {
              // Require protectors for all alloca calls in strong mode.
              Layout.insert(std::make_pair(AI,
                                           MachineFrameInfo::SSPLK_SmallArray));
              ORE.emit(RemarkBuilder);
              NeedsProtector = true;
            }
          } else {
            // A call to alloca with a variable size requires protectors.
            Layout.insert(std::make_pair(AI,
                                         MachineFrameInfo::SSPLK_LargeArray));
            ORE.emit(RemarkBuilder);
            NeedsProtector = true;
          }
          continue;
        }
 
        bool IsLarge = false;
        if (ContainsProtectableArray(AI->getAllocatedType(), IsLarge, Strong)) {
          Layout.insert(std::make_pair(AI, IsLarge
                                       ? MachineFrameInfo::SSPLK_LargeArray
                                       : MachineFrameInfo::SSPLK_SmallArray));
          ORE.emit([&]() {
            return OptimizationRemark(DEBUG_TYPE, "StackProtectorBuffer", &I)
                   << "Stack protection applied to function "
                   << ore::NV("Function", F)
                   << " due to a stack allocated buffer or struct containing a "
                      "buffer";
          });
          NeedsProtector = true;
          continue;
        }
 
        if (Strong && HasAddressTaken(AI, M->getDataLayout().getTypeAllocSize(
                                              AI->getAllocatedType()))) {
          ++NumAddrTaken;
          Layout.insert(std::make_pair(AI, MachineFrameInfo::SSPLK_AddrOf));
          ORE.emit([&]() {
            return OptimizationRemark(DEBUG_TYPE, "StackProtectorAddressTaken",
                                      &I)
                   << "Stack protection applied to function "
                   << ore::NV("Function", F)
                   << " due to the address of a local variable being taken";
          });
          NeedsProtector = true;
        }
        // Clear any PHIs that we visited, to make sure we examine all uses of
        // any subsequent allocas that we look at.
        VisitedPHIs.clear();
      }
    }
  }
 
  return NeedsProtector;
}
 
/// Create a stack guard loading and populate whether SelectionDAG SSP is
/// supported.
static Value *getStackGuard(const TargetLoweringBase *TLI, Module *M,
                            IRBuilder<> &B,
                            bool *SupportsSelectionDAGSP = nullptr) {
  Value *Guard = TLI->getIRStackGuard(B);
  StringRef GuardMode = M->getStackProtectorGuard();
  if ((GuardMode == "tls" || GuardMode.empty()) && Guard)
    return B.CreateLoad(B.getInt8PtrTy(), Guard, true, "StackGuard");
 
  // Use SelectionDAG SSP handling, since there isn't an IR guard.
  //
  // This is more or less weird, since we optionally output whether we
  // should perform a SelectionDAG SP here. The reason is that it's strictly
  // defined as !TLI->getIRStackGuard(B), where getIRStackGuard is also
  // mutating. There is no way to get this bit without mutating the IR, so
  // getting this bit has to happen in this right time.
  //
  // We could have define a new function TLI::supportsSelectionDAGSP(), but that
  // will put more burden on the backends' overriding work, especially when it
  // actually conveys the same information getIRStackGuard() already gives.
  if (SupportsSelectionDAGSP)
    *SupportsSelectionDAGSP = true;
  TLI->insertSSPDeclarations(*M);
  return B.CreateCall(Intrinsic::getDeclaration(M, Intrinsic::stackguard));
}
 
/// Insert code into the entry block that stores the stack guard
/// variable onto the stack:
///
///   entry:
///     StackGuardSlot = alloca i8*
///     StackGuard = <stack guard>
///     call void @llvm.stackprotector(StackGuard, StackGuardSlot)
///
/// Returns true if the platform/triple supports the stackprotectorcreate pseudo
/// node.
static bool CreatePrologue(Function *F, Module *M, ReturnInst *RI,
                           const TargetLoweringBase *TLI, AllocaInst *&AI) {
  bool SupportsSelectionDAGSP = false;
  IRBuilder<> B(&F->getEntryBlock().front());
  PointerType *PtrTy = Type::getInt8PtrTy(RI->getContext());
  AI = B.CreateAlloca(PtrTy, nullptr, "StackGuardSlot");
 
  Value *GuardSlot = getStackGuard(TLI, M, B, &SupportsSelectionDAGSP);
  B.CreateCall(Intrinsic::getDeclaration(M, Intrinsic::stackprotector),
               {GuardSlot, AI});
  return SupportsSelectionDAGSP;
}
 
/// InsertStackProtectors - Insert code into the prologue and epilogue of the
/// function.
///
///  - The prologue code loads and stores the stack guard onto the stack.
///  - The epilogue checks the value stored in the prologue against the original
///    value. It calls __stack_chk_fail if they differ.
bool StackProtector::InsertStackProtectors() {
  // If the target wants to XOR the frame pointer into the guard value, it's
  // impossible to emit the check in IR, so the target *must* support stack
  // protection in SDAG.
  bool SupportsSelectionDAGSP =
      TLI->useStackGuardXorFP() ||
      (EnableSelectionDAGSP && !TM->Options.EnableFastISel);
  AllocaInst *AI = nullptr; // Place on stack that stores the stack guard.
 
  for (BasicBlock &BB : llvm::make_early_inc_range(*F)) {
    ReturnInst *RI = dyn_cast<ReturnInst>(BB.getTerminator());
    if (!RI)
      continue;
 
    // Generate prologue instrumentation if not already generated.
    if (!HasPrologue) {
      HasPrologue = true;
      SupportsSelectionDAGSP &= CreatePrologue(F, M, RI, TLI, AI);
    }
 
    // SelectionDAG based code generation. Nothing else needs to be done here.
    // The epilogue instrumentation is postponed to SelectionDAG.
    if (SupportsSelectionDAGSP)
      break;
 
    // Find the stack guard slot if the prologue was not created by this pass
    // itself via a previous call to CreatePrologue().
    if (!AI) {
      const CallInst *SPCall = findStackProtectorIntrinsic(*F);
      assert(SPCall && "Call to llvm.stackprotector is missing");
      AI = cast<AllocaInst>(SPCall->getArgOperand(1));
    }
 
    // Set HasIRCheck to true, so that SelectionDAG will not generate its own
    // version. SelectionDAG called 'shouldEmitSDCheck' to check whether
    // instrumentation has already been generated.
    HasIRCheck = true;
 
    // If we're instrumenting a block with a tail call, the check has to be
    // inserted before the call rather than between it and the return. The
    // verifier guarantees that a tail call is either directly before the
    // return or with a single correct bitcast of the return value in between so
    // we don't need to worry about many situations here.
    Instruction *CheckLoc = RI;
    Instruction *Prev = RI->getPrevNonDebugInstruction();
    if (Prev && isa<CallInst>(Prev) && cast<CallInst>(Prev)->isTailCall())
      CheckLoc = Prev;
    else if (Prev) {
      Prev = Prev->getPrevNonDebugInstruction();
      if (Prev && isa<CallInst>(Prev) && cast<CallInst>(Prev)->isTailCall())
        CheckLoc = Prev;
    }
 
    // Generate epilogue instrumentation. The epilogue intrumentation can be
    // function-based or inlined depending on which mechanism the target is
    // providing.
    if (Function *GuardCheck = TLI->getSSPStackGuardCheck(*M)) {
      // Generate the function-based epilogue instrumentation.
      // The target provides a guard check function, generate a call to it.
      IRBuilder<> B(CheckLoc);
      LoadInst *Guard = B.CreateLoad(B.getInt8PtrTy(), AI, true, "Guard");
      CallInst *Call = B.CreateCall(GuardCheck, {Guard});
      Call->setAttributes(GuardCheck->getAttributes());
      Call->setCallingConv(GuardCheck->getCallingConv());
    } else {
      // Generate the epilogue with inline instrumentation.
      // If we do not support SelectionDAG based calls, generate IR level
      // calls.
      //
      // For each block with a return instruction, convert this:
      //
      //   return:
      //     ...
      //     ret ...
      //
      // into this:
      //
      //   return:
      //     ...
      //     %1 = <stack guard>
      //     %2 = load StackGuardSlot
      //     %3 = cmp i1 %1, %2
      //     br i1 %3, label %SP_return, label %CallStackCheckFailBlk
      //
      //   SP_return:
      //     ret ...
      //
      //   CallStackCheckFailBlk:
      //     call void @__stack_chk_fail()
      //     unreachable
 
      // Create the FailBB. We duplicate the BB every time since the MI tail
      // merge pass will merge together all of the various BB into one including
      // fail BB generated by the stack protector pseudo instruction.
      BasicBlock *FailBB = CreateFailBB();
 
      // Split the basic block before the return instruction.
      BasicBlock *NewBB =
          BB.splitBasicBlock(CheckLoc->getIterator(), "SP_return");
 
      // Update the dominator tree if we need to.
      if (DT && DT->isReachableFromEntry(&BB)) {
        DT->addNewBlock(NewBB, &BB);
        DT->addNewBlock(FailBB, &BB);
      }
 
      // Remove default branch instruction to the new BB.
      BB.getTerminator()->eraseFromParent();
 
      // Move the newly created basic block to the point right after the old
      // basic block so that it's in the "fall through" position.
      NewBB->moveAfter(&BB);
 
      // Generate the stack protector instructions in the old basic block.
      IRBuilder<> B(&BB);
      Value *Guard = getStackGuard(TLI, M, B);
      LoadInst *LI2 = B.CreateLoad(B.getInt8PtrTy(), AI, true);
      Value *Cmp = B.CreateICmpEQ(Guard, LI2);
      auto SuccessProb =
          BranchProbabilityInfo::getBranchProbStackProtector(true);
      auto FailureProb =
          BranchProbabilityInfo::getBranchProbStackProtector(false);
      MDNode *Weights = MDBuilder(F->getContext())
                            .createBranchWeights(SuccessProb.getNumerator(),
                                                 FailureProb.getNumerator());
      B.CreateCondBr(Cmp, NewBB, FailBB, Weights);
    }
  }
 
  // Return if we didn't modify any basic blocks. i.e., there are no return
  // statements in the function.
  return HasPrologue;
}
 
/// CreateFailBB - Create a basic block to jump to when the stack protector
/// check fails.
BasicBlock *StackProtector::CreateFailBB() {
  LLVMContext &Context = F->getContext();
  BasicBlock *FailBB = BasicBlock::Create(Context, "CallStackCheckFailBlk", F);
  IRBuilder<> B(FailBB);
  if (F->getSubprogram())
    B.SetCurrentDebugLocation(
        DILocation::get(Context, 0, 0, F->getSubprogram()));
  if (Trip.isOSOpenBSD()) {
    FunctionCallee StackChkFail = M->getOrInsertFunction(
        "__stack_smash_handler", Type::getVoidTy(Context),
        Type::getInt8PtrTy(Context));
 
    B.CreateCall(StackChkFail, B.CreateGlobalStringPtr(F->getName(), "SSH"));
  } else {
    FunctionCallee StackChkFail =
        M->getOrInsertFunction("__stack_chk_fail", Type::getVoidTy(Context));
 
    B.CreateCall(StackChkFail, {});
  }
  B.CreateUnreachable();
  return FailBB;
}
 
bool StackProtector::shouldEmitSDCheck(const BasicBlock &BB) const {
  return HasPrologue && !HasIRCheck && isa<ReturnInst>(BB.getTerminator());
}
 
void StackProtector::copyToMachineFrameInfo(MachineFrameInfo &MFI) const {
  if (Layout.empty())
    return;
 
  for (int I = 0, E = MFI.getObjectIndexEnd(); I != E; ++I) {
    if (MFI.isDeadObjectIndex(I))
      continue;
 
    const AllocaInst *AI = MFI.getObjectAllocation(I);
    if (!AI)
      continue;
 
    SSPLayoutMap::const_iterator LI = Layout.find(AI);
    if (LI == Layout.end())
      continue;
 
    MFI.setObjectSSPLayout(I, LI->second);
  }
}