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//===- MemoryDependenceAnalysis.cpp - Mem Deps Implementation --*- C++ -*-===//
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// The LLVM Compiler Infrastructure
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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//===----------------------------------------------------------------------===//
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// This file implements an analysis that determines, for a given memory
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// operation, what preceding memory operations it depends on. It builds on
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// alias analysis information, and tries to provide a lazy, caching interface to
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// a common kind of alias information query.
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//===----------------------------------------------------------------------===//
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#define DEBUG_TYPE "memdep"
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#include "llvm/Analysis/MemoryDependenceAnalysis.h"
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#include "llvm/Instructions.h"
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#include "llvm/IntrinsicInst.h"
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#include "llvm/Function.h"
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#include "llvm/Analysis/AliasAnalysis.h"
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#include "llvm/Analysis/Dominators.h"
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#include "llvm/Analysis/InstructionSimplify.h"
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#include "llvm/Analysis/MemoryBuiltins.h"
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#include "llvm/Analysis/PHITransAddr.h"
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#include "llvm/ADT/Statistic.h"
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#include "llvm/ADT/STLExtras.h"
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#include "llvm/Support/PredIteratorCache.h"
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#include "llvm/Support/Debug.h"
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STATISTIC(NumCacheNonLocal, "Number of fully cached non-local responses");
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STATISTIC(NumCacheDirtyNonLocal, "Number of dirty cached non-local responses");
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STATISTIC(NumUncacheNonLocal, "Number of uncached non-local responses");
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STATISTIC(NumCacheNonLocalPtr,
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"Number of fully cached non-local ptr responses");
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STATISTIC(NumCacheDirtyNonLocalPtr,
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"Number of cached, but dirty, non-local ptr responses");
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STATISTIC(NumUncacheNonLocalPtr,
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"Number of uncached non-local ptr responses");
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STATISTIC(NumCacheCompleteNonLocalPtr,
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"Number of block queries that were completely cached");
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char MemoryDependenceAnalysis::ID = 0;
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// Register this pass...
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INITIALIZE_PASS(MemoryDependenceAnalysis, "memdep",
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"Memory Dependence Analysis", false, true);
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MemoryDependenceAnalysis::MemoryDependenceAnalysis()
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: FunctionPass(ID), PredCache(0) {
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MemoryDependenceAnalysis::~MemoryDependenceAnalysis() {
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/// Clean up memory in between runs
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void MemoryDependenceAnalysis::releaseMemory() {
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NonLocalPointerDeps.clear();
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ReverseLocalDeps.clear();
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ReverseNonLocalDeps.clear();
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ReverseNonLocalPtrDeps.clear();
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/// getAnalysisUsage - Does not modify anything. It uses Alias Analysis.
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void MemoryDependenceAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
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AU.addRequiredTransitive<AliasAnalysis>();
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bool MemoryDependenceAnalysis::runOnFunction(Function &) {
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AA = &getAnalysis<AliasAnalysis>();
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PredCache.reset(new PredIteratorCache());
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/// RemoveFromReverseMap - This is a helper function that removes Val from
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/// 'Inst's set in ReverseMap. If the set becomes empty, remove Inst's entry.
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template <typename KeyTy>
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static void RemoveFromReverseMap(DenseMap<Instruction*,
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SmallPtrSet<KeyTy, 4> > &ReverseMap,
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Instruction *Inst, KeyTy Val) {
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typename DenseMap<Instruction*, SmallPtrSet<KeyTy, 4> >::iterator
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InstIt = ReverseMap.find(Inst);
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assert(InstIt != ReverseMap.end() && "Reverse map out of sync?");
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bool Found = InstIt->second.erase(Val);
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assert(Found && "Invalid reverse map!"); Found=Found;
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if (InstIt->second.empty())
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ReverseMap.erase(InstIt);
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/// getCallSiteDependencyFrom - Private helper for finding the local
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/// dependencies of a call site.
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MemDepResult MemoryDependenceAnalysis::
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getCallSiteDependencyFrom(CallSite CS, bool isReadOnlyCall,
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BasicBlock::iterator ScanIt, BasicBlock *BB) {
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// Walk backwards through the block, looking for dependencies
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while (ScanIt != BB->begin()) {
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Instruction *Inst = --ScanIt;
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// If this inst is a memory op, get the pointer it accessed
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uint64_t PointerSize = 0;
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if (StoreInst *S = dyn_cast<StoreInst>(Inst)) {
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Pointer = S->getPointerOperand();
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PointerSize = AA->getTypeStoreSize(S->getOperand(0)->getType());
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} else if (VAArgInst *V = dyn_cast<VAArgInst>(Inst)) {
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Pointer = V->getOperand(0);
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PointerSize = AA->getTypeStoreSize(V->getType());
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} else if (const CallInst *CI = isFreeCall(Inst)) {
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Pointer = CI->getArgOperand(0);
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// calls to free() erase the entire structure
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} else if (CallSite InstCS = cast<Value>(Inst)) {
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// Debug intrinsics don't cause dependences.
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if (isa<DbgInfoIntrinsic>(Inst)) continue;
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// If these two calls do not interfere, look past it.
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switch (AA->getModRefInfo(CS, InstCS)) {
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case AliasAnalysis::NoModRef:
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// If the two calls are the same, return InstCS as a Def, so that
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// CS can be found redundant and eliminated.
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if (isReadOnlyCall && InstCS.onlyReadsMemory() &&
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CS.getInstruction()->isIdenticalToWhenDefined(Inst))
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return MemDepResult::getDef(Inst);
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// Otherwise if the two calls don't interact (e.g. InstCS is readnone)
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return MemDepResult::getClobber(Inst);
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// Non-memory instruction.
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if (AA->getModRefInfo(CS, Pointer, PointerSize) != AliasAnalysis::NoModRef)
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return MemDepResult::getClobber(Inst);
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// No dependence found. If this is the entry block of the function, it is a
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// clobber, otherwise it is non-local.
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if (BB != &BB->getParent()->getEntryBlock())
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return MemDepResult::getNonLocal();
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return MemDepResult::getClobber(ScanIt);
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/// getPointerDependencyFrom - Return the instruction on which a memory
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/// location depends. If isLoad is true, this routine ignore may-aliases with
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/// read-only operations.
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MemDepResult MemoryDependenceAnalysis::
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getPointerDependencyFrom(Value *MemPtr, uint64_t MemSize, bool isLoad,
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BasicBlock::iterator ScanIt, BasicBlock *BB) {
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Value *InvariantTag = 0;
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// Walk backwards through the basic block, looking for dependencies.
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while (ScanIt != BB->begin()) {
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Instruction *Inst = --ScanIt;
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// If we're in an invariant region, no dependencies can be found before
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// we pass an invariant-begin marker.
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if (InvariantTag == Inst) {
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if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(Inst)) {
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// Debug intrinsics don't cause dependences.
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if (isa<DbgInfoIntrinsic>(Inst)) continue;
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// If we pass an invariant-end marker, then we've just entered an
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// invariant region and can start ignoring dependencies.
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if (II->getIntrinsicID() == Intrinsic::invariant_end) {
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// FIXME: This only considers queries directly on the invariant-tagged
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// pointer, not on query pointers that are indexed off of them. It'd
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// be nice to handle that at some point.
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AliasAnalysis::AliasResult R = AA->alias(II->getArgOperand(2), MemPtr);
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if (R == AliasAnalysis::MustAlias) {
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InvariantTag = II->getArgOperand(0);
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// If we reach a lifetime begin or end marker, then the query ends here
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// because the value is undefined.
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} else if (II->getIntrinsicID() == Intrinsic::lifetime_start) {
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// FIXME: This only considers queries directly on the invariant-tagged
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// pointer, not on query pointers that are indexed off of them. It'd
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// be nice to handle that at some point.
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AliasAnalysis::AliasResult R = AA->alias(II->getArgOperand(1), MemPtr);
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if (R == AliasAnalysis::MustAlias)
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return MemDepResult::getDef(II);
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// If we're querying on a load and we're in an invariant region, we're done
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// at this point. Nothing a load depends on can live in an invariant region.
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if (isLoad && InvariantTag) continue;
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// Values depend on loads if the pointers are must aliased. This means that
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// a load depends on another must aliased load from the same value.
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if (LoadInst *LI = dyn_cast<LoadInst>(Inst)) {
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Value *Pointer = LI->getPointerOperand();
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uint64_t PointerSize = AA->getTypeStoreSize(LI->getType());
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// If we found a pointer, check if it could be the same as our pointer.
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AliasAnalysis::AliasResult R =
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AA->alias(Pointer, PointerSize, MemPtr, MemSize);
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if (R == AliasAnalysis::NoAlias)
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// May-alias loads don't depend on each other without a dependence.
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if (isLoad && R == AliasAnalysis::MayAlias)
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// Stores depend on may and must aliased loads, loads depend on must-alias
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return MemDepResult::getDef(Inst);
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if (StoreInst *SI = dyn_cast<StoreInst>(Inst)) {
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// There can't be stores to the value we care about inside an
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if (InvariantTag) continue;
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// If alias analysis can tell that this store is guaranteed to not modify
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// the query pointer, ignore it. Use getModRefInfo to handle cases where
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// the query pointer points to constant memory etc.
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if (AA->getModRefInfo(SI, MemPtr, MemSize) == AliasAnalysis::NoModRef)
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// Ok, this store might clobber the query pointer. Check to see if it is
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// a must alias: in this case, we want to return this as a def.
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Value *Pointer = SI->getPointerOperand();
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uint64_t PointerSize = AA->getTypeStoreSize(SI->getOperand(0)->getType());
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// If we found a pointer, check if it could be the same as our pointer.
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AliasAnalysis::AliasResult R =
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AA->alias(Pointer, PointerSize, MemPtr, MemSize);
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if (R == AliasAnalysis::NoAlias)
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if (R == AliasAnalysis::MayAlias)
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return MemDepResult::getClobber(Inst);
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return MemDepResult::getDef(Inst);
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// If this is an allocation, and if we know that the accessed pointer is to
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// the allocation, return Def. This means that there is no dependence and
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// the access can be optimized based on that. For example, a load could
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// Note: Only determine this to be a malloc if Inst is the malloc call, not
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// a subsequent bitcast of the malloc call result. There can be stores to
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// the malloced memory between the malloc call and its bitcast uses, and we
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// need to continue scanning until the malloc call.
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if (isa<AllocaInst>(Inst) ||
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(isa<CallInst>(Inst) && extractMallocCall(Inst))) {
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Value *AccessPtr = MemPtr->getUnderlyingObject();
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if (AccessPtr == Inst ||
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AA->alias(Inst, 1, AccessPtr, 1) == AliasAnalysis::MustAlias)
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return MemDepResult::getDef(Inst);
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// See if this instruction (e.g. a call or vaarg) mod/ref's the pointer.
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switch (AA->getModRefInfo(Inst, MemPtr, MemSize)) {
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case AliasAnalysis::NoModRef:
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// If the call has no effect on the queried pointer, just ignore it.
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case AliasAnalysis::Mod:
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// If we're in an invariant region, we can ignore calls that ONLY
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// modify the pointer.
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if (InvariantTag) continue;
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return MemDepResult::getClobber(Inst);
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case AliasAnalysis::Ref:
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// If the call is known to never store to the pointer, and if this is a
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// load query, we can safely ignore it (scan past it).
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// Otherwise, there is a potential dependence. Return a clobber.
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return MemDepResult::getClobber(Inst);
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// No dependence found. If this is the entry block of the function, it is a
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// clobber, otherwise it is non-local.
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if (BB != &BB->getParent()->getEntryBlock())
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return MemDepResult::getNonLocal();
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return MemDepResult::getClobber(ScanIt);
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/// getDependency - Return the instruction on which a memory operation
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MemDepResult MemoryDependenceAnalysis::getDependency(Instruction *QueryInst) {
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Instruction *ScanPos = QueryInst;
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// Check for a cached result
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MemDepResult &LocalCache = LocalDeps[QueryInst];
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// If the cached entry is non-dirty, just return it. Note that this depends
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// on MemDepResult's default constructing to 'dirty'.
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if (!LocalCache.isDirty())
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// Otherwise, if we have a dirty entry, we know we can start the scan at that
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// instruction, which may save us some work.
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if (Instruction *Inst = LocalCache.getInst()) {
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RemoveFromReverseMap(ReverseLocalDeps, Inst, QueryInst);
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BasicBlock *QueryParent = QueryInst->getParent();
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uint64_t MemSize = 0;
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if (BasicBlock::iterator(QueryInst) == QueryParent->begin()) {
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// No dependence found. If this is the entry block of the function, it is a
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// clobber, otherwise it is non-local.
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if (QueryParent != &QueryParent->getParent()->getEntryBlock())
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LocalCache = MemDepResult::getNonLocal();
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LocalCache = MemDepResult::getClobber(QueryInst);
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} else if (StoreInst *SI = dyn_cast<StoreInst>(QueryInst)) {
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// If this is a volatile store, don't mess around with it. Just return the
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// previous instruction as a clobber.
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if (SI->isVolatile())
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LocalCache = MemDepResult::getClobber(--BasicBlock::iterator(ScanPos));
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MemPtr = SI->getPointerOperand();
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MemSize = AA->getTypeStoreSize(SI->getOperand(0)->getType());
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} else if (LoadInst *LI = dyn_cast<LoadInst>(QueryInst)) {
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// If this is a volatile load, don't mess around with it. Just return the
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// previous instruction as a clobber.
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if (LI->isVolatile())
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LocalCache = MemDepResult::getClobber(--BasicBlock::iterator(ScanPos));
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MemPtr = LI->getPointerOperand();
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MemSize = AA->getTypeStoreSize(LI->getType());
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} else if (const CallInst *CI = isFreeCall(QueryInst)) {
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MemPtr = CI->getArgOperand(0);
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// calls to free() erase the entire structure, not just a field.
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} else if (isa<CallInst>(QueryInst) || isa<InvokeInst>(QueryInst)) {
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int IntrinsicID = 0; // Intrinsic IDs start at 1.
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IntrinsicInst *II = dyn_cast<IntrinsicInst>(QueryInst);
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IntrinsicID = II->getIntrinsicID();
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switch (IntrinsicID) {
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case Intrinsic::lifetime_start:
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case Intrinsic::lifetime_end:
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case Intrinsic::invariant_start:
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MemPtr = II->getArgOperand(1);
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MemSize = cast<ConstantInt>(II->getArgOperand(0))->getZExtValue();
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case Intrinsic::invariant_end:
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MemPtr = II->getArgOperand(2);
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MemSize = cast<ConstantInt>(II->getArgOperand(1))->getZExtValue();
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CallSite QueryCS(QueryInst);
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bool isReadOnly = AA->onlyReadsMemory(QueryCS);
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LocalCache = getCallSiteDependencyFrom(QueryCS, isReadOnly, ScanPos,
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// Non-memory instruction.
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LocalCache = MemDepResult::getClobber(--BasicBlock::iterator(ScanPos));
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// If we need to do a pointer scan, make it happen.
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bool isLoad = !QueryInst->mayWriteToMemory();
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if (IntrinsicInst *II = dyn_cast<MemoryUseIntrinsic>(QueryInst)) {
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isLoad |= II->getIntrinsicID() == Intrinsic::lifetime_end;
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LocalCache = getPointerDependencyFrom(MemPtr, MemSize, isLoad, ScanPos,
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// Remember the result!
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if (Instruction *I = LocalCache.getInst())
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ReverseLocalDeps[I].insert(QueryInst);
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/// AssertSorted - This method is used when -debug is specified to verify that
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/// cache arrays are properly kept sorted.
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static void AssertSorted(MemoryDependenceAnalysis::NonLocalDepInfo &Cache,
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if (Count == -1) Count = Cache.size();
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if (Count == 0) return;
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for (unsigned i = 1; i != unsigned(Count); ++i)
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assert(!(Cache[i] < Cache[i-1]) && "Cache isn't sorted!");
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/// getNonLocalCallDependency - Perform a full dependency query for the
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/// specified call, returning the set of blocks that the value is
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/// potentially live across. The returned set of results will include a
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/// "NonLocal" result for all blocks where the value is live across.
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/// This method assumes the instruction returns a "NonLocal" dependency
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/// within its own block.
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/// This returns a reference to an internal data structure that may be
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/// invalidated on the next non-local query or when an instruction is
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/// removed. Clients must copy this data if they want it around longer than
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const MemoryDependenceAnalysis::NonLocalDepInfo &
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MemoryDependenceAnalysis::getNonLocalCallDependency(CallSite QueryCS) {
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assert(getDependency(QueryCS.getInstruction()).isNonLocal() &&
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"getNonLocalCallDependency should only be used on calls with non-local deps!");
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PerInstNLInfo &CacheP = NonLocalDeps[QueryCS.getInstruction()];
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NonLocalDepInfo &Cache = CacheP.first;
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/// DirtyBlocks - This is the set of blocks that need to be recomputed. In
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/// the cached case, this can happen due to instructions being deleted etc. In
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/// the uncached case, this starts out as the set of predecessors we care
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SmallVector<BasicBlock*, 32> DirtyBlocks;
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if (!Cache.empty()) {
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// Okay, we have a cache entry. If we know it is not dirty, just return it
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// with no computation.
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if (!CacheP.second) {
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// If we already have a partially computed set of results, scan them to
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// determine what is dirty, seeding our initial DirtyBlocks worklist.
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for (NonLocalDepInfo::iterator I = Cache.begin(), E = Cache.end();
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if (I->getResult().isDirty())
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DirtyBlocks.push_back(I->getBB());
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// Sort the cache so that we can do fast binary search lookups below.
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std::sort(Cache.begin(), Cache.end());
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++NumCacheDirtyNonLocal;
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//cerr << "CACHED CASE: " << DirtyBlocks.size() << " dirty: "
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// << Cache.size() << " cached: " << *QueryInst;
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// Seed DirtyBlocks with each of the preds of QueryInst's block.
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BasicBlock *QueryBB = QueryCS.getInstruction()->getParent();
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for (BasicBlock **PI = PredCache->GetPreds(QueryBB); *PI; ++PI)
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DirtyBlocks.push_back(*PI);
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++NumUncacheNonLocal;
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// isReadonlyCall - If this is a read-only call, we can be more aggressive.
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bool isReadonlyCall = AA->onlyReadsMemory(QueryCS);
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SmallPtrSet<BasicBlock*, 64> Visited;
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unsigned NumSortedEntries = Cache.size();
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DEBUG(AssertSorted(Cache));
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// Iterate while we still have blocks to update.
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while (!DirtyBlocks.empty()) {
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BasicBlock *DirtyBB = DirtyBlocks.back();
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DirtyBlocks.pop_back();
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// Already processed this block?
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if (!Visited.insert(DirtyBB))
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// Do a binary search to see if we already have an entry for this block in
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// the cache set. If so, find it.
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DEBUG(AssertSorted(Cache, NumSortedEntries));
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NonLocalDepInfo::iterator Entry =
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std::upper_bound(Cache.begin(), Cache.begin()+NumSortedEntries,
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NonLocalDepEntry(DirtyBB));
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if (Entry != Cache.begin() && prior(Entry)->getBB() == DirtyBB)
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NonLocalDepEntry *ExistingResult = 0;
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if (Entry != Cache.begin()+NumSortedEntries &&
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Entry->getBB() == DirtyBB) {
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// If we already have an entry, and if it isn't already dirty, the block
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if (!Entry->getResult().isDirty())
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// Otherwise, remember this slot so we can update the value.
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ExistingResult = &*Entry;
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// If the dirty entry has a pointer, start scanning from it so we don't have
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// to rescan the entire block.
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BasicBlock::iterator ScanPos = DirtyBB->end();
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if (ExistingResult) {
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if (Instruction *Inst = ExistingResult->getResult().getInst()) {
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// We're removing QueryInst's use of Inst.
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RemoveFromReverseMap(ReverseNonLocalDeps, Inst,
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QueryCS.getInstruction());
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// Find out if this block has a local dependency for QueryInst.
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if (ScanPos != DirtyBB->begin()) {
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Dep = getCallSiteDependencyFrom(QueryCS, isReadonlyCall,ScanPos, DirtyBB);
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} else if (DirtyBB != &DirtyBB->getParent()->getEntryBlock()) {
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// No dependence found. If this is the entry block of the function, it is
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// a clobber, otherwise it is non-local.
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Dep = MemDepResult::getNonLocal();
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Dep = MemDepResult::getClobber(ScanPos);
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// If we had a dirty entry for the block, update it. Otherwise, just add
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ExistingResult->setResult(Dep);
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Cache.push_back(NonLocalDepEntry(DirtyBB, Dep));
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// If the block has a dependency (i.e. it isn't completely transparent to
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// the value), remember the association!
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if (!Dep.isNonLocal()) {
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// Keep the ReverseNonLocalDeps map up to date so we can efficiently
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// update this when we remove instructions.
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if (Instruction *Inst = Dep.getInst())
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ReverseNonLocalDeps[Inst].insert(QueryCS.getInstruction());
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// If the block *is* completely transparent to the load, we need to check
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// the predecessors of this block. Add them to our worklist.
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for (BasicBlock **PI = PredCache->GetPreds(DirtyBB); *PI; ++PI)
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DirtyBlocks.push_back(*PI);
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/// getNonLocalPointerDependency - Perform a full dependency query for an
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/// access to the specified (non-volatile) memory location, returning the
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/// set of instructions that either define or clobber the value.
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/// This method assumes the pointer has a "NonLocal" dependency within its
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void MemoryDependenceAnalysis::
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getNonLocalPointerDependency(Value *Pointer, bool isLoad, BasicBlock *FromBB,
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SmallVectorImpl<NonLocalDepResult> &Result) {
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assert(Pointer->getType()->isPointerTy() &&
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"Can't get pointer deps of a non-pointer!");
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// We know that the pointer value is live into FromBB find the def/clobbers
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// from presecessors.
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const Type *EltTy = cast<PointerType>(Pointer->getType())->getElementType();
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uint64_t PointeeSize = AA->getTypeStoreSize(EltTy);
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PHITransAddr Address(Pointer, TD);
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// This is the set of blocks we've inspected, and the pointer we consider in
582
// each block. Because of critical edges, we currently bail out if querying
583
// a block with multiple different pointers. This can happen during PHI
585
DenseMap<BasicBlock*, Value*> Visited;
586
if (!getNonLocalPointerDepFromBB(Address, PointeeSize, isLoad, FromBB,
587
Result, Visited, true))
590
Result.push_back(NonLocalDepResult(FromBB,
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MemDepResult::getClobber(FromBB->begin()),
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/// GetNonLocalInfoForBlock - Compute the memdep value for BB with
596
/// Pointer/PointeeSize using either cached information in Cache or by doing a
597
/// lookup (which may use dirty cache info if available). If we do a lookup,
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/// add the result to the cache.
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MemDepResult MemoryDependenceAnalysis::
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GetNonLocalInfoForBlock(Value *Pointer, uint64_t PointeeSize,
601
bool isLoad, BasicBlock *BB,
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NonLocalDepInfo *Cache, unsigned NumSortedEntries) {
604
// Do a binary search to see if we already have an entry for this block in
605
// the cache set. If so, find it.
606
NonLocalDepInfo::iterator Entry =
607
std::upper_bound(Cache->begin(), Cache->begin()+NumSortedEntries,
608
NonLocalDepEntry(BB));
609
if (Entry != Cache->begin() && (Entry-1)->getBB() == BB)
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NonLocalDepEntry *ExistingResult = 0;
613
if (Entry != Cache->begin()+NumSortedEntries && Entry->getBB() == BB)
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ExistingResult = &*Entry;
616
// If we have a cached entry, and it is non-dirty, use it as the value for
618
if (ExistingResult && !ExistingResult->getResult().isDirty()) {
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++NumCacheNonLocalPtr;
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return ExistingResult->getResult();
623
// Otherwise, we have to scan for the value. If we have a dirty cache
624
// entry, start scanning from its position, otherwise we scan from the end
626
BasicBlock::iterator ScanPos = BB->end();
627
if (ExistingResult && ExistingResult->getResult().getInst()) {
628
assert(ExistingResult->getResult().getInst()->getParent() == BB &&
629
"Instruction invalidated?");
630
++NumCacheDirtyNonLocalPtr;
631
ScanPos = ExistingResult->getResult().getInst();
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// Eliminating the dirty entry from 'Cache', so update the reverse info.
634
ValueIsLoadPair CacheKey(Pointer, isLoad);
635
RemoveFromReverseMap(ReverseNonLocalPtrDeps, ScanPos, CacheKey);
637
++NumUncacheNonLocalPtr;
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// Scan the block for the dependency.
641
MemDepResult Dep = getPointerDependencyFrom(Pointer, PointeeSize, isLoad,
644
// If we had a dirty entry for the block, update it. Otherwise, just add
647
ExistingResult->setResult(Dep);
649
Cache->push_back(NonLocalDepEntry(BB, Dep));
651
// If the block has a dependency (i.e. it isn't completely transparent to
652
// the value), remember the reverse association because we just added it
654
if (Dep.isNonLocal())
657
// Keep the ReverseNonLocalPtrDeps map up to date so we can efficiently
658
// update MemDep when we remove instructions.
659
Instruction *Inst = Dep.getInst();
660
assert(Inst && "Didn't depend on anything?");
661
ValueIsLoadPair CacheKey(Pointer, isLoad);
662
ReverseNonLocalPtrDeps[Inst].insert(CacheKey);
666
/// SortNonLocalDepInfoCache - Sort the a NonLocalDepInfo cache, given a certain
667
/// number of elements in the array that are already properly ordered. This is
668
/// optimized for the case when only a few entries are added.
670
SortNonLocalDepInfoCache(MemoryDependenceAnalysis::NonLocalDepInfo &Cache,
671
unsigned NumSortedEntries) {
672
switch (Cache.size() - NumSortedEntries) {
674
// done, no new entries.
677
// Two new entries, insert the last one into place.
678
NonLocalDepEntry Val = Cache.back();
680
MemoryDependenceAnalysis::NonLocalDepInfo::iterator Entry =
681
std::upper_bound(Cache.begin(), Cache.end()-1, Val);
682
Cache.insert(Entry, Val);
686
// One new entry, Just insert the new value at the appropriate position.
687
if (Cache.size() != 1) {
688
NonLocalDepEntry Val = Cache.back();
690
MemoryDependenceAnalysis::NonLocalDepInfo::iterator Entry =
691
std::upper_bound(Cache.begin(), Cache.end(), Val);
692
Cache.insert(Entry, Val);
696
// Added many values, do a full scale sort.
697
std::sort(Cache.begin(), Cache.end());
702
/// getNonLocalPointerDepFromBB - Perform a dependency query based on
703
/// pointer/pointeesize starting at the end of StartBB. Add any clobber/def
704
/// results to the results vector and keep track of which blocks are visited in
707
/// This has special behavior for the first block queries (when SkipFirstBlock
708
/// is true). In this special case, it ignores the contents of the specified
709
/// block and starts returning dependence info for its predecessors.
711
/// This function returns false on success, or true to indicate that it could
712
/// not compute dependence information for some reason. This should be treated
713
/// as a clobber dependence on the first instruction in the predecessor block.
714
bool MemoryDependenceAnalysis::
715
getNonLocalPointerDepFromBB(const PHITransAddr &Pointer, uint64_t PointeeSize,
716
bool isLoad, BasicBlock *StartBB,
717
SmallVectorImpl<NonLocalDepResult> &Result,
718
DenseMap<BasicBlock*, Value*> &Visited,
719
bool SkipFirstBlock) {
721
// Look up the cached info for Pointer.
722
ValueIsLoadPair CacheKey(Pointer.getAddr(), isLoad);
724
std::pair<BBSkipFirstBlockPair, NonLocalDepInfo> *CacheInfo =
725
&NonLocalPointerDeps[CacheKey];
726
NonLocalDepInfo *Cache = &CacheInfo->second;
728
// If we have valid cached information for exactly the block we are
729
// investigating, just return it with no recomputation.
730
if (CacheInfo->first == BBSkipFirstBlockPair(StartBB, SkipFirstBlock)) {
731
// We have a fully cached result for this query then we can just return the
732
// cached results and populate the visited set. However, we have to verify
733
// that we don't already have conflicting results for these blocks. Check
734
// to ensure that if a block in the results set is in the visited set that
735
// it was for the same pointer query.
736
if (!Visited.empty()) {
737
for (NonLocalDepInfo::iterator I = Cache->begin(), E = Cache->end();
739
DenseMap<BasicBlock*, Value*>::iterator VI = Visited.find(I->getBB());
740
if (VI == Visited.end() || VI->second == Pointer.getAddr())
743
// We have a pointer mismatch in a block. Just return clobber, saying
744
// that something was clobbered in this result. We could also do a
745
// non-fully cached query, but there is little point in doing this.
750
Value *Addr = Pointer.getAddr();
751
for (NonLocalDepInfo::iterator I = Cache->begin(), E = Cache->end();
753
Visited.insert(std::make_pair(I->getBB(), Addr));
754
if (!I->getResult().isNonLocal())
755
Result.push_back(NonLocalDepResult(I->getBB(), I->getResult(), Addr));
757
++NumCacheCompleteNonLocalPtr;
761
// Otherwise, either this is a new block, a block with an invalid cache
762
// pointer or one that we're about to invalidate by putting more info into it
763
// than its valid cache info. If empty, the result will be valid cache info,
764
// otherwise it isn't.
766
CacheInfo->first = BBSkipFirstBlockPair(StartBB, SkipFirstBlock);
768
CacheInfo->first = BBSkipFirstBlockPair();
770
SmallVector<BasicBlock*, 32> Worklist;
771
Worklist.push_back(StartBB);
773
// Keep track of the entries that we know are sorted. Previously cached
774
// entries will all be sorted. The entries we add we only sort on demand (we
775
// don't insert every element into its sorted position). We know that we
776
// won't get any reuse from currently inserted values, because we don't
777
// revisit blocks after we insert info for them.
778
unsigned NumSortedEntries = Cache->size();
779
DEBUG(AssertSorted(*Cache));
781
while (!Worklist.empty()) {
782
BasicBlock *BB = Worklist.pop_back_val();
784
// Skip the first block if we have it.
785
if (!SkipFirstBlock) {
786
// Analyze the dependency of *Pointer in FromBB. See if we already have
788
assert(Visited.count(BB) && "Should check 'visited' before adding to WL");
790
// Get the dependency info for Pointer in BB. If we have cached
791
// information, we will use it, otherwise we compute it.
792
DEBUG(AssertSorted(*Cache, NumSortedEntries));
793
MemDepResult Dep = GetNonLocalInfoForBlock(Pointer.getAddr(), PointeeSize,
797
// If we got a Def or Clobber, add this to the list of results.
798
if (!Dep.isNonLocal()) {
799
Result.push_back(NonLocalDepResult(BB, Dep, Pointer.getAddr()));
804
// If 'Pointer' is an instruction defined in this block, then we need to do
805
// phi translation to change it into a value live in the predecessor block.
806
// If not, we just add the predecessors to the worklist and scan them with
808
if (!Pointer.NeedsPHITranslationFromBlock(BB)) {
809
SkipFirstBlock = false;
810
for (BasicBlock **PI = PredCache->GetPreds(BB); *PI; ++PI) {
811
// Verify that we haven't looked at this block yet.
812
std::pair<DenseMap<BasicBlock*,Value*>::iterator, bool>
813
InsertRes = Visited.insert(std::make_pair(*PI, Pointer.getAddr()));
814
if (InsertRes.second) {
815
// First time we've looked at *PI.
816
Worklist.push_back(*PI);
820
// If we have seen this block before, but it was with a different
821
// pointer then we have a phi translation failure and we have to treat
822
// this as a clobber.
823
if (InsertRes.first->second != Pointer.getAddr())
824
goto PredTranslationFailure;
829
// We do need to do phi translation, if we know ahead of time we can't phi
830
// translate this value, don't even try.
831
if (!Pointer.IsPotentiallyPHITranslatable())
832
goto PredTranslationFailure;
834
// We may have added values to the cache list before this PHI translation.
835
// If so, we haven't done anything to ensure that the cache remains sorted.
836
// Sort it now (if needed) so that recursive invocations of
837
// getNonLocalPointerDepFromBB and other routines that could reuse the cache
838
// value will only see properly sorted cache arrays.
839
if (Cache && NumSortedEntries != Cache->size()) {
840
SortNonLocalDepInfoCache(*Cache, NumSortedEntries);
841
NumSortedEntries = Cache->size();
845
for (BasicBlock **PI = PredCache->GetPreds(BB); *PI; ++PI) {
846
BasicBlock *Pred = *PI;
848
// Get the PHI translated pointer in this predecessor. This can fail if
849
// not translatable, in which case the getAddr() returns null.
850
PHITransAddr PredPointer(Pointer);
851
PredPointer.PHITranslateValue(BB, Pred, 0);
853
Value *PredPtrVal = PredPointer.getAddr();
855
// Check to see if we have already visited this pred block with another
856
// pointer. If so, we can't do this lookup. This failure can occur
857
// with PHI translation when a critical edge exists and the PHI node in
858
// the successor translates to a pointer value different than the
859
// pointer the block was first analyzed with.
860
std::pair<DenseMap<BasicBlock*,Value*>::iterator, bool>
861
InsertRes = Visited.insert(std::make_pair(Pred, PredPtrVal));
863
if (!InsertRes.second) {
864
// If the predecessor was visited with PredPtr, then we already did
865
// the analysis and can ignore it.
866
if (InsertRes.first->second == PredPtrVal)
869
// Otherwise, the block was previously analyzed with a different
870
// pointer. We can't represent the result of this case, so we just
871
// treat this as a phi translation failure.
872
goto PredTranslationFailure;
875
// If PHI translation was unable to find an available pointer in this
876
// predecessor, then we have to assume that the pointer is clobbered in
877
// that predecessor. We can still do PRE of the load, which would insert
878
// a computation of the pointer in this predecessor.
879
if (PredPtrVal == 0) {
880
// Add the entry to the Result list.
881
NonLocalDepResult Entry(Pred,
882
MemDepResult::getClobber(Pred->getTerminator()),
884
Result.push_back(Entry);
886
// Since we had a phi translation failure, the cache for CacheKey won't
887
// include all of the entries that we need to immediately satisfy future
888
// queries. Mark this in NonLocalPointerDeps by setting the
889
// BBSkipFirstBlockPair pointer to null. This requires reuse of the
890
// cached value to do more work but not miss the phi trans failure.
891
NonLocalPointerDeps[CacheKey].first = BBSkipFirstBlockPair();
895
// FIXME: it is entirely possible that PHI translating will end up with
896
// the same value. Consider PHI translating something like:
897
// X = phi [x, bb1], [y, bb2]. PHI translating for bb1 doesn't *need*
898
// to recurse here, pedantically speaking.
900
// If we have a problem phi translating, fall through to the code below
901
// to handle the failure condition.
902
if (getNonLocalPointerDepFromBB(PredPointer, PointeeSize, isLoad, Pred,
904
goto PredTranslationFailure;
907
// Refresh the CacheInfo/Cache pointer so that it isn't invalidated.
908
CacheInfo = &NonLocalPointerDeps[CacheKey];
909
Cache = &CacheInfo->second;
910
NumSortedEntries = Cache->size();
912
// Since we did phi translation, the "Cache" set won't contain all of the
913
// results for the query. This is ok (we can still use it to accelerate
914
// specific block queries) but we can't do the fastpath "return all
915
// results from the set" Clear out the indicator for this.
916
CacheInfo->first = BBSkipFirstBlockPair();
917
SkipFirstBlock = false;
920
PredTranslationFailure:
923
// Refresh the CacheInfo/Cache pointer if it got invalidated.
924
CacheInfo = &NonLocalPointerDeps[CacheKey];
925
Cache = &CacheInfo->second;
926
NumSortedEntries = Cache->size();
929
// Since we failed phi translation, the "Cache" set won't contain all of the
930
// results for the query. This is ok (we can still use it to accelerate
931
// specific block queries) but we can't do the fastpath "return all
932
// results from the set". Clear out the indicator for this.
933
CacheInfo->first = BBSkipFirstBlockPair();
935
// If *nothing* works, mark the pointer as being clobbered by the first
936
// instruction in this block.
938
// If this is the magic first block, return this as a clobber of the whole
939
// incoming value. Since we can't phi translate to one of the predecessors,
940
// we have to bail out.
944
for (NonLocalDepInfo::reverse_iterator I = Cache->rbegin(); ; ++I) {
945
assert(I != Cache->rend() && "Didn't find current block??");
946
if (I->getBB() != BB)
949
assert(I->getResult().isNonLocal() &&
950
"Should only be here with transparent block");
951
I->setResult(MemDepResult::getClobber(BB->begin()));
952
ReverseNonLocalPtrDeps[BB->begin()].insert(CacheKey);
953
Result.push_back(NonLocalDepResult(I->getBB(), I->getResult(),
959
// Okay, we're done now. If we added new values to the cache, re-sort it.
960
SortNonLocalDepInfoCache(*Cache, NumSortedEntries);
961
DEBUG(AssertSorted(*Cache));
965
/// RemoveCachedNonLocalPointerDependencies - If P exists in
966
/// CachedNonLocalPointerInfo, remove it.
967
void MemoryDependenceAnalysis::
968
RemoveCachedNonLocalPointerDependencies(ValueIsLoadPair P) {
969
CachedNonLocalPointerInfo::iterator It =
970
NonLocalPointerDeps.find(P);
971
if (It == NonLocalPointerDeps.end()) return;
973
// Remove all of the entries in the BB->val map. This involves removing
974
// instructions from the reverse map.
975
NonLocalDepInfo &PInfo = It->second.second;
977
for (unsigned i = 0, e = PInfo.size(); i != e; ++i) {
978
Instruction *Target = PInfo[i].getResult().getInst();
979
if (Target == 0) continue; // Ignore non-local dep results.
980
assert(Target->getParent() == PInfo[i].getBB());
982
// Eliminating the dirty entry from 'Cache', so update the reverse info.
983
RemoveFromReverseMap(ReverseNonLocalPtrDeps, Target, P);
986
// Remove P from NonLocalPointerDeps (which deletes NonLocalDepInfo).
987
NonLocalPointerDeps.erase(It);
991
/// invalidateCachedPointerInfo - This method is used to invalidate cached
992
/// information about the specified pointer, because it may be too
993
/// conservative in memdep. This is an optional call that can be used when
994
/// the client detects an equivalence between the pointer and some other
995
/// value and replaces the other value with ptr. This can make Ptr available
996
/// in more places that cached info does not necessarily keep.
997
void MemoryDependenceAnalysis::invalidateCachedPointerInfo(Value *Ptr) {
998
// If Ptr isn't really a pointer, just ignore it.
999
if (!Ptr->getType()->isPointerTy()) return;
1000
// Flush store info for the pointer.
1001
RemoveCachedNonLocalPointerDependencies(ValueIsLoadPair(Ptr, false));
1002
// Flush load info for the pointer.
1003
RemoveCachedNonLocalPointerDependencies(ValueIsLoadPair(Ptr, true));
1006
/// invalidateCachedPredecessors - Clear the PredIteratorCache info.
1007
/// This needs to be done when the CFG changes, e.g., due to splitting
1009
void MemoryDependenceAnalysis::invalidateCachedPredecessors() {
1013
/// removeInstruction - Remove an instruction from the dependence analysis,
1014
/// updating the dependence of instructions that previously depended on it.
1015
/// This method attempts to keep the cache coherent using the reverse map.
1016
void MemoryDependenceAnalysis::removeInstruction(Instruction *RemInst) {
1017
// Walk through the Non-local dependencies, removing this one as the value
1018
// for any cached queries.
1019
NonLocalDepMapType::iterator NLDI = NonLocalDeps.find(RemInst);
1020
if (NLDI != NonLocalDeps.end()) {
1021
NonLocalDepInfo &BlockMap = NLDI->second.first;
1022
for (NonLocalDepInfo::iterator DI = BlockMap.begin(), DE = BlockMap.end();
1024
if (Instruction *Inst = DI->getResult().getInst())
1025
RemoveFromReverseMap(ReverseNonLocalDeps, Inst, RemInst);
1026
NonLocalDeps.erase(NLDI);
1029
// If we have a cached local dependence query for this instruction, remove it.
1031
LocalDepMapType::iterator LocalDepEntry = LocalDeps.find(RemInst);
1032
if (LocalDepEntry != LocalDeps.end()) {
1033
// Remove us from DepInst's reverse set now that the local dep info is gone.
1034
if (Instruction *Inst = LocalDepEntry->second.getInst())
1035
RemoveFromReverseMap(ReverseLocalDeps, Inst, RemInst);
1037
// Remove this local dependency info.
1038
LocalDeps.erase(LocalDepEntry);
1041
// If we have any cached pointer dependencies on this instruction, remove
1042
// them. If the instruction has non-pointer type, then it can't be a pointer
1045
// Remove it from both the load info and the store info. The instruction
1046
// can't be in either of these maps if it is non-pointer.
1047
if (RemInst->getType()->isPointerTy()) {
1048
RemoveCachedNonLocalPointerDependencies(ValueIsLoadPair(RemInst, false));
1049
RemoveCachedNonLocalPointerDependencies(ValueIsLoadPair(RemInst, true));
1052
// Loop over all of the things that depend on the instruction we're removing.
1054
SmallVector<std::pair<Instruction*, Instruction*>, 8> ReverseDepsToAdd;
1056
// If we find RemInst as a clobber or Def in any of the maps for other values,
1057
// we need to replace its entry with a dirty version of the instruction after
1058
// it. If RemInst is a terminator, we use a null dirty value.
1060
// Using a dirty version of the instruction after RemInst saves having to scan
1061
// the entire block to get to this point.
1062
MemDepResult NewDirtyVal;
1063
if (!RemInst->isTerminator())
1064
NewDirtyVal = MemDepResult::getDirty(++BasicBlock::iterator(RemInst));
1066
ReverseDepMapType::iterator ReverseDepIt = ReverseLocalDeps.find(RemInst);
1067
if (ReverseDepIt != ReverseLocalDeps.end()) {
1068
SmallPtrSet<Instruction*, 4> &ReverseDeps = ReverseDepIt->second;
1069
// RemInst can't be the terminator if it has local stuff depending on it.
1070
assert(!ReverseDeps.empty() && !isa<TerminatorInst>(RemInst) &&
1071
"Nothing can locally depend on a terminator");
1073
for (SmallPtrSet<Instruction*, 4>::iterator I = ReverseDeps.begin(),
1074
E = ReverseDeps.end(); I != E; ++I) {
1075
Instruction *InstDependingOnRemInst = *I;
1076
assert(InstDependingOnRemInst != RemInst &&
1077
"Already removed our local dep info");
1079
LocalDeps[InstDependingOnRemInst] = NewDirtyVal;
1081
// Make sure to remember that new things depend on NewDepInst.
1082
assert(NewDirtyVal.getInst() && "There is no way something else can have "
1083
"a local dep on this if it is a terminator!");
1084
ReverseDepsToAdd.push_back(std::make_pair(NewDirtyVal.getInst(),
1085
InstDependingOnRemInst));
1088
ReverseLocalDeps.erase(ReverseDepIt);
1090
// Add new reverse deps after scanning the set, to avoid invalidating the
1091
// 'ReverseDeps' reference.
1092
while (!ReverseDepsToAdd.empty()) {
1093
ReverseLocalDeps[ReverseDepsToAdd.back().first]
1094
.insert(ReverseDepsToAdd.back().second);
1095
ReverseDepsToAdd.pop_back();
1099
ReverseDepIt = ReverseNonLocalDeps.find(RemInst);
1100
if (ReverseDepIt != ReverseNonLocalDeps.end()) {
1101
SmallPtrSet<Instruction*, 4> &Set = ReverseDepIt->second;
1102
for (SmallPtrSet<Instruction*, 4>::iterator I = Set.begin(), E = Set.end();
1104
assert(*I != RemInst && "Already removed NonLocalDep info for RemInst");
1106
PerInstNLInfo &INLD = NonLocalDeps[*I];
1107
// The information is now dirty!
1110
for (NonLocalDepInfo::iterator DI = INLD.first.begin(),
1111
DE = INLD.first.end(); DI != DE; ++DI) {
1112
if (DI->getResult().getInst() != RemInst) continue;
1114
// Convert to a dirty entry for the subsequent instruction.
1115
DI->setResult(NewDirtyVal);
1117
if (Instruction *NextI = NewDirtyVal.getInst())
1118
ReverseDepsToAdd.push_back(std::make_pair(NextI, *I));
1122
ReverseNonLocalDeps.erase(ReverseDepIt);
1124
// Add new reverse deps after scanning the set, to avoid invalidating 'Set'
1125
while (!ReverseDepsToAdd.empty()) {
1126
ReverseNonLocalDeps[ReverseDepsToAdd.back().first]
1127
.insert(ReverseDepsToAdd.back().second);
1128
ReverseDepsToAdd.pop_back();
1132
// If the instruction is in ReverseNonLocalPtrDeps then it appears as a
1133
// value in the NonLocalPointerDeps info.
1134
ReverseNonLocalPtrDepTy::iterator ReversePtrDepIt =
1135
ReverseNonLocalPtrDeps.find(RemInst);
1136
if (ReversePtrDepIt != ReverseNonLocalPtrDeps.end()) {
1137
SmallPtrSet<ValueIsLoadPair, 4> &Set = ReversePtrDepIt->second;
1138
SmallVector<std::pair<Instruction*, ValueIsLoadPair>,8> ReversePtrDepsToAdd;
1140
for (SmallPtrSet<ValueIsLoadPair, 4>::iterator I = Set.begin(),
1141
E = Set.end(); I != E; ++I) {
1142
ValueIsLoadPair P = *I;
1143
assert(P.getPointer() != RemInst &&
1144
"Already removed NonLocalPointerDeps info for RemInst");
1146
NonLocalDepInfo &NLPDI = NonLocalPointerDeps[P].second;
1148
// The cache is not valid for any specific block anymore.
1149
NonLocalPointerDeps[P].first = BBSkipFirstBlockPair();
1151
// Update any entries for RemInst to use the instruction after it.
1152
for (NonLocalDepInfo::iterator DI = NLPDI.begin(), DE = NLPDI.end();
1154
if (DI->getResult().getInst() != RemInst) continue;
1156
// Convert to a dirty entry for the subsequent instruction.
1157
DI->setResult(NewDirtyVal);
1159
if (Instruction *NewDirtyInst = NewDirtyVal.getInst())
1160
ReversePtrDepsToAdd.push_back(std::make_pair(NewDirtyInst, P));
1163
// Re-sort the NonLocalDepInfo. Changing the dirty entry to its
1164
// subsequent value may invalidate the sortedness.
1165
std::sort(NLPDI.begin(), NLPDI.end());
1168
ReverseNonLocalPtrDeps.erase(ReversePtrDepIt);
1170
while (!ReversePtrDepsToAdd.empty()) {
1171
ReverseNonLocalPtrDeps[ReversePtrDepsToAdd.back().first]
1172
.insert(ReversePtrDepsToAdd.back().second);
1173
ReversePtrDepsToAdd.pop_back();
1178
assert(!NonLocalDeps.count(RemInst) && "RemInst got reinserted?");
1179
AA->deleteValue(RemInst);
1180
DEBUG(verifyRemoved(RemInst));
1182
/// verifyRemoved - Verify that the specified instruction does not occur
1183
/// in our internal data structures.
1184
void MemoryDependenceAnalysis::verifyRemoved(Instruction *D) const {
1185
for (LocalDepMapType::const_iterator I = LocalDeps.begin(),
1186
E = LocalDeps.end(); I != E; ++I) {
1187
assert(I->first != D && "Inst occurs in data structures");
1188
assert(I->second.getInst() != D &&
1189
"Inst occurs in data structures");
1192
for (CachedNonLocalPointerInfo::const_iterator I =NonLocalPointerDeps.begin(),
1193
E = NonLocalPointerDeps.end(); I != E; ++I) {
1194
assert(I->first.getPointer() != D && "Inst occurs in NLPD map key");
1195
const NonLocalDepInfo &Val = I->second.second;
1196
for (NonLocalDepInfo::const_iterator II = Val.begin(), E = Val.end();
1198
assert(II->getResult().getInst() != D && "Inst occurs as NLPD value");
1201
for (NonLocalDepMapType::const_iterator I = NonLocalDeps.begin(),
1202
E = NonLocalDeps.end(); I != E; ++I) {
1203
assert(I->first != D && "Inst occurs in data structures");
1204
const PerInstNLInfo &INLD = I->second;
1205
for (NonLocalDepInfo::const_iterator II = INLD.first.begin(),
1206
EE = INLD.first.end(); II != EE; ++II)
1207
assert(II->getResult().getInst() != D && "Inst occurs in data structures");
1210
for (ReverseDepMapType::const_iterator I = ReverseLocalDeps.begin(),
1211
E = ReverseLocalDeps.end(); I != E; ++I) {
1212
assert(I->first != D && "Inst occurs in data structures");
1213
for (SmallPtrSet<Instruction*, 4>::const_iterator II = I->second.begin(),
1214
EE = I->second.end(); II != EE; ++II)
1215
assert(*II != D && "Inst occurs in data structures");
1218
for (ReverseDepMapType::const_iterator I = ReverseNonLocalDeps.begin(),
1219
E = ReverseNonLocalDeps.end();
1221
assert(I->first != D && "Inst occurs in data structures");
1222
for (SmallPtrSet<Instruction*, 4>::const_iterator II = I->second.begin(),
1223
EE = I->second.end(); II != EE; ++II)
1224
assert(*II != D && "Inst occurs in data structures");
1227
for (ReverseNonLocalPtrDepTy::const_iterator
1228
I = ReverseNonLocalPtrDeps.begin(),
1229
E = ReverseNonLocalPtrDeps.end(); I != E; ++I) {
1230
assert(I->first != D && "Inst occurs in rev NLPD map");
1232
for (SmallPtrSet<ValueIsLoadPair, 4>::const_iterator II = I->second.begin(),
1233
E = I->second.end(); II != E; ++II)
1234
assert(*II != ValueIsLoadPair(D, false) &&
1235
*II != ValueIsLoadPair(D, true) &&
1236
"Inst occurs in ReverseNonLocalPtrDeps map");
added
removed
libclamav/c++/llvm/lib/Analysis/MemoryDependenceAnalysis.cpp
