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2413bf3004
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@208343 91177308-0d34-0410-b5e6-96231b3b80d8
600 lines
24 KiB
C++
600 lines
24 KiB
C++
//===- GlobalsModRef.cpp - Simple Mod/Ref Analysis for Globals ------------===//
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//
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// The LLVM Compiler Infrastructure
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//
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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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//===----------------------------------------------------------------------===//
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//
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// This simple pass provides alias and mod/ref information for global values
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// that do not have their address taken, and keeps track of whether functions
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// read or write memory (are "pure"). For this simple (but very common) case,
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// we can provide pretty accurate and useful information.
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/Analysis/Passes.h"
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#include "llvm/ADT/SCCIterator.h"
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#include "llvm/ADT/Statistic.h"
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#include "llvm/Analysis/AliasAnalysis.h"
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#include "llvm/Analysis/CallGraph.h"
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#include "llvm/Analysis/MemoryBuiltins.h"
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#include "llvm/Analysis/ValueTracking.h"
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#include "llvm/IR/Constants.h"
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#include "llvm/IR/DerivedTypes.h"
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#include "llvm/IR/InstIterator.h"
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#include "llvm/IR/Instructions.h"
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#include "llvm/IR/IntrinsicInst.h"
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#include "llvm/IR/Module.h"
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#include "llvm/Pass.h"
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#include "llvm/Support/CommandLine.h"
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#include <set>
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using namespace llvm;
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#define DEBUG_TYPE "globalsmodref-aa"
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STATISTIC(NumNonAddrTakenGlobalVars,
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"Number of global vars without address taken");
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STATISTIC(NumNonAddrTakenFunctions,"Number of functions without address taken");
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STATISTIC(NumNoMemFunctions, "Number of functions that do not access memory");
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STATISTIC(NumReadMemFunctions, "Number of functions that only read memory");
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STATISTIC(NumIndirectGlobalVars, "Number of indirect global objects");
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namespace {
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/// FunctionRecord - One instance of this structure is stored for every
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/// function in the program. Later, the entries for these functions are
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/// removed if the function is found to call an external function (in which
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/// case we know nothing about it.
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struct FunctionRecord {
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/// GlobalInfo - Maintain mod/ref info for all of the globals without
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/// addresses taken that are read or written (transitively) by this
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/// function.
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std::map<const GlobalValue*, unsigned> GlobalInfo;
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/// MayReadAnyGlobal - May read global variables, but it is not known which.
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bool MayReadAnyGlobal;
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unsigned getInfoForGlobal(const GlobalValue *GV) const {
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unsigned Effect = MayReadAnyGlobal ? AliasAnalysis::Ref : 0;
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std::map<const GlobalValue*, unsigned>::const_iterator I =
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GlobalInfo.find(GV);
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if (I != GlobalInfo.end())
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Effect |= I->second;
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return Effect;
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}
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/// FunctionEffect - Capture whether or not this function reads or writes to
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/// ANY memory. If not, we can do a lot of aggressive analysis on it.
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unsigned FunctionEffect;
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FunctionRecord() : MayReadAnyGlobal (false), FunctionEffect(0) {}
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};
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/// GlobalsModRef - The actual analysis pass.
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class GlobalsModRef : public ModulePass, public AliasAnalysis {
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/// NonAddressTakenGlobals - The globals that do not have their addresses
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/// taken.
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std::set<const GlobalValue*> NonAddressTakenGlobals;
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/// IndirectGlobals - The memory pointed to by this global is known to be
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/// 'owned' by the global.
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std::set<const GlobalValue*> IndirectGlobals;
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/// AllocsForIndirectGlobals - If an instruction allocates memory for an
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/// indirect global, this map indicates which one.
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std::map<const Value*, const GlobalValue*> AllocsForIndirectGlobals;
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/// FunctionInfo - For each function, keep track of what globals are
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/// modified or read.
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std::map<const Function*, FunctionRecord> FunctionInfo;
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public:
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static char ID;
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GlobalsModRef() : ModulePass(ID) {
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initializeGlobalsModRefPass(*PassRegistry::getPassRegistry());
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}
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bool runOnModule(Module &M) override {
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InitializeAliasAnalysis(this);
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// Find non-addr taken globals.
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AnalyzeGlobals(M);
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// Propagate on CG.
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AnalyzeCallGraph(getAnalysis<CallGraphWrapperPass>().getCallGraph(), M);
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return false;
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}
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void getAnalysisUsage(AnalysisUsage &AU) const override {
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AliasAnalysis::getAnalysisUsage(AU);
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AU.addRequired<CallGraphWrapperPass>();
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AU.setPreservesAll(); // Does not transform code
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}
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//------------------------------------------------
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// Implement the AliasAnalysis API
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//
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AliasResult alias(const Location &LocA, const Location &LocB) override;
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ModRefResult getModRefInfo(ImmutableCallSite CS,
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const Location &Loc) override;
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ModRefResult getModRefInfo(ImmutableCallSite CS1,
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ImmutableCallSite CS2) override {
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return AliasAnalysis::getModRefInfo(CS1, CS2);
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}
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/// getModRefBehavior - Return the behavior of the specified function if
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/// called from the specified call site. The call site may be null in which
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/// case the most generic behavior of this function should be returned.
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ModRefBehavior getModRefBehavior(const Function *F) override {
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ModRefBehavior Min = UnknownModRefBehavior;
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if (FunctionRecord *FR = getFunctionInfo(F)) {
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if (FR->FunctionEffect == 0)
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Min = DoesNotAccessMemory;
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else if ((FR->FunctionEffect & Mod) == 0)
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Min = OnlyReadsMemory;
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}
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return ModRefBehavior(AliasAnalysis::getModRefBehavior(F) & Min);
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}
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/// getModRefBehavior - Return the behavior of the specified function if
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/// called from the specified call site. The call site may be null in which
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/// case the most generic behavior of this function should be returned.
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ModRefBehavior getModRefBehavior(ImmutableCallSite CS) override {
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ModRefBehavior Min = UnknownModRefBehavior;
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if (const Function* F = CS.getCalledFunction())
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if (FunctionRecord *FR = getFunctionInfo(F)) {
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if (FR->FunctionEffect == 0)
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Min = DoesNotAccessMemory;
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else if ((FR->FunctionEffect & Mod) == 0)
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Min = OnlyReadsMemory;
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}
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return ModRefBehavior(AliasAnalysis::getModRefBehavior(CS) & Min);
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}
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void deleteValue(Value *V) override;
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void copyValue(Value *From, Value *To) override;
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void addEscapingUse(Use &U) override;
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/// getAdjustedAnalysisPointer - This method is used when a pass implements
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/// an analysis interface through multiple inheritance. If needed, it
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/// should override this to adjust the this pointer as needed for the
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/// specified pass info.
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void *getAdjustedAnalysisPointer(AnalysisID PI) override {
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if (PI == &AliasAnalysis::ID)
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return (AliasAnalysis*)this;
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return this;
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}
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private:
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/// getFunctionInfo - Return the function info for the function, or null if
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/// we don't have anything useful to say about it.
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FunctionRecord *getFunctionInfo(const Function *F) {
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std::map<const Function*, FunctionRecord>::iterator I =
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FunctionInfo.find(F);
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if (I != FunctionInfo.end())
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return &I->second;
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return nullptr;
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}
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void AnalyzeGlobals(Module &M);
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void AnalyzeCallGraph(CallGraph &CG, Module &M);
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bool AnalyzeUsesOfPointer(Value *V, std::vector<Function*> &Readers,
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std::vector<Function*> &Writers,
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GlobalValue *OkayStoreDest = nullptr);
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bool AnalyzeIndirectGlobalMemory(GlobalValue *GV);
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};
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}
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char GlobalsModRef::ID = 0;
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INITIALIZE_AG_PASS_BEGIN(GlobalsModRef, AliasAnalysis,
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"globalsmodref-aa", "Simple mod/ref analysis for globals",
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false, true, false)
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INITIALIZE_PASS_DEPENDENCY(CallGraphWrapperPass)
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INITIALIZE_AG_PASS_END(GlobalsModRef, AliasAnalysis,
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"globalsmodref-aa", "Simple mod/ref analysis for globals",
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false, true, false)
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Pass *llvm::createGlobalsModRefPass() { return new GlobalsModRef(); }
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/// AnalyzeGlobals - Scan through the users of all of the internal
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/// GlobalValue's in the program. If none of them have their "address taken"
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/// (really, their address passed to something nontrivial), record this fact,
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/// and record the functions that they are used directly in.
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void GlobalsModRef::AnalyzeGlobals(Module &M) {
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std::vector<Function*> Readers, Writers;
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for (Module::iterator I = M.begin(), E = M.end(); I != E; ++I)
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if (I->hasLocalLinkage()) {
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if (!AnalyzeUsesOfPointer(I, Readers, Writers)) {
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// Remember that we are tracking this global.
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NonAddressTakenGlobals.insert(I);
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++NumNonAddrTakenFunctions;
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}
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Readers.clear(); Writers.clear();
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}
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for (Module::global_iterator I = M.global_begin(), E = M.global_end();
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I != E; ++I)
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if (I->hasLocalLinkage()) {
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if (!AnalyzeUsesOfPointer(I, Readers, Writers)) {
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// Remember that we are tracking this global, and the mod/ref fns
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NonAddressTakenGlobals.insert(I);
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for (unsigned i = 0, e = Readers.size(); i != e; ++i)
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FunctionInfo[Readers[i]].GlobalInfo[I] |= Ref;
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if (!I->isConstant()) // No need to keep track of writers to constants
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for (unsigned i = 0, e = Writers.size(); i != e; ++i)
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FunctionInfo[Writers[i]].GlobalInfo[I] |= Mod;
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++NumNonAddrTakenGlobalVars;
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// If this global holds a pointer type, see if it is an indirect global.
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if (I->getType()->getElementType()->isPointerTy() &&
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AnalyzeIndirectGlobalMemory(I))
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++NumIndirectGlobalVars;
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}
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Readers.clear(); Writers.clear();
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}
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}
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/// AnalyzeUsesOfPointer - Look at all of the users of the specified pointer.
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/// If this is used by anything complex (i.e., the address escapes), return
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/// true. Also, while we are at it, keep track of those functions that read and
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/// write to the value.
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///
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/// If OkayStoreDest is non-null, stores into this global are allowed.
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bool GlobalsModRef::AnalyzeUsesOfPointer(Value *V,
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std::vector<Function*> &Readers,
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std::vector<Function*> &Writers,
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GlobalValue *OkayStoreDest) {
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if (!V->getType()->isPointerTy()) return true;
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for (Use &U : V->uses()) {
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User *I = U.getUser();
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if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
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Readers.push_back(LI->getParent()->getParent());
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} else if (StoreInst *SI = dyn_cast<StoreInst>(I)) {
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if (V == SI->getOperand(1)) {
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Writers.push_back(SI->getParent()->getParent());
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} else if (SI->getOperand(1) != OkayStoreDest) {
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return true; // Storing the pointer
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}
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} else if (Operator::getOpcode(I) == Instruction::GetElementPtr) {
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if (AnalyzeUsesOfPointer(I, Readers, Writers))
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return true;
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} else if (Operator::getOpcode(I) == Instruction::BitCast) {
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if (AnalyzeUsesOfPointer(I, Readers, Writers, OkayStoreDest))
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return true;
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} else if (CallSite CS = I) {
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// Make sure that this is just the function being called, not that it is
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// passing into the function.
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if (!CS.isCallee(&U)) {
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// Detect calls to free.
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if (isFreeCall(I, TLI))
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Writers.push_back(CS->getParent()->getParent());
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else
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return true; // Argument of an unknown call.
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}
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} else if (ICmpInst *ICI = dyn_cast<ICmpInst>(I)) {
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if (!isa<ConstantPointerNull>(ICI->getOperand(1)))
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return true; // Allow comparison against null.
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} else {
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return true;
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}
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}
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return false;
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}
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/// AnalyzeIndirectGlobalMemory - We found an non-address-taken global variable
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/// which holds a pointer type. See if the global always points to non-aliased
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/// heap memory: that is, all initializers of the globals are allocations, and
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/// those allocations have no use other than initialization of the global.
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/// Further, all loads out of GV must directly use the memory, not store the
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/// pointer somewhere. If this is true, we consider the memory pointed to by
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/// GV to be owned by GV and can disambiguate other pointers from it.
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bool GlobalsModRef::AnalyzeIndirectGlobalMemory(GlobalValue *GV) {
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// Keep track of values related to the allocation of the memory, f.e. the
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// value produced by the malloc call and any casts.
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std::vector<Value*> AllocRelatedValues;
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// Walk the user list of the global. If we find anything other than a direct
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// load or store, bail out.
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for (User *U : GV->users()) {
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if (LoadInst *LI = dyn_cast<LoadInst>(U)) {
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// The pointer loaded from the global can only be used in simple ways:
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// we allow addressing of it and loading storing to it. We do *not* allow
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// storing the loaded pointer somewhere else or passing to a function.
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std::vector<Function*> ReadersWriters;
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if (AnalyzeUsesOfPointer(LI, ReadersWriters, ReadersWriters))
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return false; // Loaded pointer escapes.
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// TODO: Could try some IP mod/ref of the loaded pointer.
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} else if (StoreInst *SI = dyn_cast<StoreInst>(U)) {
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// Storing the global itself.
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if (SI->getOperand(0) == GV) return false;
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// If storing the null pointer, ignore it.
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if (isa<ConstantPointerNull>(SI->getOperand(0)))
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continue;
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// Check the value being stored.
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Value *Ptr = GetUnderlyingObject(SI->getOperand(0));
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if (!isAllocLikeFn(Ptr, TLI))
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return false; // Too hard to analyze.
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// Analyze all uses of the allocation. If any of them are used in a
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// non-simple way (e.g. stored to another global) bail out.
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std::vector<Function*> ReadersWriters;
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if (AnalyzeUsesOfPointer(Ptr, ReadersWriters, ReadersWriters, GV))
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return false; // Loaded pointer escapes.
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// Remember that this allocation is related to the indirect global.
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AllocRelatedValues.push_back(Ptr);
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} else {
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// Something complex, bail out.
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return false;
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}
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}
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// Okay, this is an indirect global. Remember all of the allocations for
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// this global in AllocsForIndirectGlobals.
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while (!AllocRelatedValues.empty()) {
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AllocsForIndirectGlobals[AllocRelatedValues.back()] = GV;
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AllocRelatedValues.pop_back();
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}
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IndirectGlobals.insert(GV);
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return true;
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}
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/// AnalyzeCallGraph - At this point, we know the functions where globals are
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/// immediately stored to and read from. Propagate this information up the call
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/// graph to all callers and compute the mod/ref info for all memory for each
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/// function.
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void GlobalsModRef::AnalyzeCallGraph(CallGraph &CG, Module &M) {
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// We do a bottom-up SCC traversal of the call graph. In other words, we
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// visit all callees before callers (leaf-first).
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for (scc_iterator<CallGraph*> I = scc_begin(&CG); !I.isAtEnd(); ++I) {
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const std::vector<CallGraphNode *> &SCC = *I;
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assert(!SCC.empty() && "SCC with no functions?");
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if (!SCC[0]->getFunction()) {
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// Calls externally - can't say anything useful. Remove any existing
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// function records (may have been created when scanning globals).
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for (unsigned i = 0, e = SCC.size(); i != e; ++i)
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FunctionInfo.erase(SCC[i]->getFunction());
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continue;
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}
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FunctionRecord &FR = FunctionInfo[SCC[0]->getFunction()];
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bool KnowNothing = false;
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unsigned FunctionEffect = 0;
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// Collect the mod/ref properties due to called functions. We only compute
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// one mod-ref set.
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for (unsigned i = 0, e = SCC.size(); i != e && !KnowNothing; ++i) {
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Function *F = SCC[i]->getFunction();
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if (!F) {
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KnowNothing = true;
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break;
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}
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if (F->isDeclaration()) {
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// Try to get mod/ref behaviour from function attributes.
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if (F->doesNotAccessMemory()) {
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// Can't do better than that!
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} else if (F->onlyReadsMemory()) {
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FunctionEffect |= Ref;
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if (!F->isIntrinsic())
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// This function might call back into the module and read a global -
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// consider every global as possibly being read by this function.
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FR.MayReadAnyGlobal = true;
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} else {
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FunctionEffect |= ModRef;
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// Can't say anything useful unless it's an intrinsic - they don't
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// read or write global variables of the kind considered here.
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KnowNothing = !F->isIntrinsic();
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}
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continue;
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}
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for (CallGraphNode::iterator CI = SCC[i]->begin(), E = SCC[i]->end();
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CI != E && !KnowNothing; ++CI)
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if (Function *Callee = CI->second->getFunction()) {
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if (FunctionRecord *CalleeFR = getFunctionInfo(Callee)) {
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// Propagate function effect up.
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FunctionEffect |= CalleeFR->FunctionEffect;
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// Incorporate callee's effects on globals into our info.
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for (const auto &G : CalleeFR->GlobalInfo)
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FR.GlobalInfo[G.first] |= G.second;
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FR.MayReadAnyGlobal |= CalleeFR->MayReadAnyGlobal;
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} else {
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// Can't say anything about it. However, if it is inside our SCC,
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// then nothing needs to be done.
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CallGraphNode *CalleeNode = CG[Callee];
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if (std::find(SCC.begin(), SCC.end(), CalleeNode) == SCC.end())
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KnowNothing = true;
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}
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} else {
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KnowNothing = true;
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}
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}
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// If we can't say anything useful about this SCC, remove all SCC functions
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// from the FunctionInfo map.
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if (KnowNothing) {
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for (unsigned i = 0, e = SCC.size(); i != e; ++i)
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FunctionInfo.erase(SCC[i]->getFunction());
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continue;
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}
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// Scan the function bodies for explicit loads or stores.
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for (unsigned i = 0, e = SCC.size(); i != e && FunctionEffect != ModRef;++i)
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for (inst_iterator II = inst_begin(SCC[i]->getFunction()),
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E = inst_end(SCC[i]->getFunction());
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II != E && FunctionEffect != ModRef; ++II)
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if (LoadInst *LI = dyn_cast<LoadInst>(&*II)) {
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FunctionEffect |= Ref;
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if (LI->isVolatile())
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// Volatile loads may have side-effects, so mark them as writing
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// memory (for example, a flag inside the processor).
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FunctionEffect |= Mod;
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} else if (StoreInst *SI = dyn_cast<StoreInst>(&*II)) {
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FunctionEffect |= Mod;
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if (SI->isVolatile())
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// Treat volatile stores as reading memory somewhere.
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FunctionEffect |= Ref;
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} else if (isAllocationFn(&*II, TLI) || isFreeCall(&*II, TLI)) {
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FunctionEffect |= ModRef;
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} else if (IntrinsicInst *Intrinsic = dyn_cast<IntrinsicInst>(&*II)) {
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// The callgraph doesn't include intrinsic calls.
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Function *Callee = Intrinsic->getCalledFunction();
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ModRefBehavior Behaviour = AliasAnalysis::getModRefBehavior(Callee);
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FunctionEffect |= (Behaviour & ModRef);
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}
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if ((FunctionEffect & Mod) == 0)
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|
++NumReadMemFunctions;
|
|
if (FunctionEffect == 0)
|
|
++NumNoMemFunctions;
|
|
FR.FunctionEffect = FunctionEffect;
|
|
|
|
// Finally, now that we know the full effect on this SCC, clone the
|
|
// information to each function in the SCC.
|
|
for (unsigned i = 1, e = SCC.size(); i != e; ++i)
|
|
FunctionInfo[SCC[i]->getFunction()] = FR;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
/// alias - If one of the pointers is to a global that we are tracking, and the
|
|
/// other is some random pointer, we know there cannot be an alias, because the
|
|
/// address of the global isn't taken.
|
|
AliasAnalysis::AliasResult
|
|
GlobalsModRef::alias(const Location &LocA,
|
|
const Location &LocB) {
|
|
// Get the base object these pointers point to.
|
|
const Value *UV1 = GetUnderlyingObject(LocA.Ptr);
|
|
const Value *UV2 = GetUnderlyingObject(LocB.Ptr);
|
|
|
|
// If either of the underlying values is a global, they may be non-addr-taken
|
|
// globals, which we can answer queries about.
|
|
const GlobalValue *GV1 = dyn_cast<GlobalValue>(UV1);
|
|
const GlobalValue *GV2 = dyn_cast<GlobalValue>(UV2);
|
|
if (GV1 || GV2) {
|
|
// If the global's address is taken, pretend we don't know it's a pointer to
|
|
// the global.
|
|
if (GV1 && !NonAddressTakenGlobals.count(GV1)) GV1 = nullptr;
|
|
if (GV2 && !NonAddressTakenGlobals.count(GV2)) GV2 = nullptr;
|
|
|
|
// If the two pointers are derived from two different non-addr-taken
|
|
// globals, or if one is and the other isn't, we know these can't alias.
|
|
if ((GV1 || GV2) && GV1 != GV2)
|
|
return NoAlias;
|
|
|
|
// Otherwise if they are both derived from the same addr-taken global, we
|
|
// can't know the two accesses don't overlap.
|
|
}
|
|
|
|
// These pointers may be based on the memory owned by an indirect global. If
|
|
// so, we may be able to handle this. First check to see if the base pointer
|
|
// is a direct load from an indirect global.
|
|
GV1 = GV2 = nullptr;
|
|
if (const LoadInst *LI = dyn_cast<LoadInst>(UV1))
|
|
if (GlobalVariable *GV = dyn_cast<GlobalVariable>(LI->getOperand(0)))
|
|
if (IndirectGlobals.count(GV))
|
|
GV1 = GV;
|
|
if (const LoadInst *LI = dyn_cast<LoadInst>(UV2))
|
|
if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(LI->getOperand(0)))
|
|
if (IndirectGlobals.count(GV))
|
|
GV2 = GV;
|
|
|
|
// These pointers may also be from an allocation for the indirect global. If
|
|
// so, also handle them.
|
|
if (AllocsForIndirectGlobals.count(UV1))
|
|
GV1 = AllocsForIndirectGlobals[UV1];
|
|
if (AllocsForIndirectGlobals.count(UV2))
|
|
GV2 = AllocsForIndirectGlobals[UV2];
|
|
|
|
// Now that we know whether the two pointers are related to indirect globals,
|
|
// use this to disambiguate the pointers. If either pointer is based on an
|
|
// indirect global and if they are not both based on the same indirect global,
|
|
// they cannot alias.
|
|
if ((GV1 || GV2) && GV1 != GV2)
|
|
return NoAlias;
|
|
|
|
return AliasAnalysis::alias(LocA, LocB);
|
|
}
|
|
|
|
AliasAnalysis::ModRefResult
|
|
GlobalsModRef::getModRefInfo(ImmutableCallSite CS,
|
|
const Location &Loc) {
|
|
unsigned Known = ModRef;
|
|
|
|
// If we are asking for mod/ref info of a direct call with a pointer to a
|
|
// global we are tracking, return information if we have it.
|
|
if (const GlobalValue *GV =
|
|
dyn_cast<GlobalValue>(GetUnderlyingObject(Loc.Ptr)))
|
|
if (GV->hasLocalLinkage())
|
|
if (const Function *F = CS.getCalledFunction())
|
|
if (NonAddressTakenGlobals.count(GV))
|
|
if (const FunctionRecord *FR = getFunctionInfo(F))
|
|
Known = FR->getInfoForGlobal(GV);
|
|
|
|
if (Known == NoModRef)
|
|
return NoModRef; // No need to query other mod/ref analyses
|
|
return ModRefResult(Known & AliasAnalysis::getModRefInfo(CS, Loc));
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Methods to update the analysis as a result of the client transformation.
|
|
//
|
|
void GlobalsModRef::deleteValue(Value *V) {
|
|
if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) {
|
|
if (NonAddressTakenGlobals.erase(GV)) {
|
|
// This global might be an indirect global. If so, remove it and remove
|
|
// any AllocRelatedValues for it.
|
|
if (IndirectGlobals.erase(GV)) {
|
|
// Remove any entries in AllocsForIndirectGlobals for this global.
|
|
for (std::map<const Value*, const GlobalValue*>::iterator
|
|
I = AllocsForIndirectGlobals.begin(),
|
|
E = AllocsForIndirectGlobals.end(); I != E; ) {
|
|
if (I->second == GV) {
|
|
AllocsForIndirectGlobals.erase(I++);
|
|
} else {
|
|
++I;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Otherwise, if this is an allocation related to an indirect global, remove
|
|
// it.
|
|
AllocsForIndirectGlobals.erase(V);
|
|
|
|
AliasAnalysis::deleteValue(V);
|
|
}
|
|
|
|
void GlobalsModRef::copyValue(Value *From, Value *To) {
|
|
AliasAnalysis::copyValue(From, To);
|
|
}
|
|
|
|
void GlobalsModRef::addEscapingUse(Use &U) {
|
|
// For the purposes of this analysis, it is conservatively correct to treat
|
|
// a newly escaping value equivalently to a deleted one. We could perhaps
|
|
// be more precise by processing the new use and attempting to update our
|
|
// saved analysis results to accommodate it.
|
|
deleteValue(U);
|
|
|
|
AliasAnalysis::addEscapingUse(U);
|
|
}
|