llvm/lib/Analysis/TypeBasedAliasAnalysis.cpp

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//===- TypeBasedAliasAnalysis.cpp - Type-Based Alias Analysis -------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines the TypeBasedAliasAnalysis pass, which implements
// metadata-based TBAA.
//
// In LLVM IR, memory does not have types, so LLVM's own type system is not
// suitable for doing TBAA. Instead, metadata is added to the IR to describe
// a type system of a higher level language. This can be used to implement
// typical C/C++ TBAA, but it can also be used to implement custom alias
// analysis behavior for other languages.
//
// We now support two types of metadata format: scalar TBAA and struct-path
// aware TBAA. After all testing cases are upgraded to use struct-path aware
// TBAA and we can auto-upgrade existing bc files, the support for scalar TBAA
// can be dropped.
//
// The scalar TBAA metadata format is very simple. TBAA MDNodes have up to
// three fields, e.g.:
// !0 = metadata !{ metadata !"an example type tree" }
// !1 = metadata !{ metadata !"int", metadata !0 }
// !2 = metadata !{ metadata !"float", metadata !0 }
// !3 = metadata !{ metadata !"const float", metadata !2, i64 1 }
//
// The first field is an identity field. It can be any value, usually
// an MDString, which uniquely identifies the type. The most important
// name in the tree is the name of the root node. Two trees with
// different root node names are entirely disjoint, even if they
// have leaves with common names.
//
// The second field identifies the type's parent node in the tree, or
// is null or omitted for a root node. A type is considered to alias
// all of its descendants and all of its ancestors in the tree. Also,
// a type is considered to alias all types in other trees, so that
// bitcode produced from multiple front-ends is handled conservatively.
//
// If the third field is present, it's an integer which if equal to 1
// indicates that the type is "constant" (meaning pointsToConstantMemory
// should return true; see
// http://llvm.org/docs/AliasAnalysis.html#OtherItfs).
//
// With struct-path aware TBAA, the MDNodes attached to an instruction using
// "!tbaa" are called path tag nodes.
//
// The path tag node has 4 fields with the last field being optional.
//
// The first field is the base type node, it can be a struct type node
// or a scalar type node. The second field is the access type node, it
// must be a scalar type node. The third field is the offset into the base type.
// The last field has the same meaning as the last field of our scalar TBAA:
// it's an integer which if equal to 1 indicates that the access is "constant".
//
// The struct type node has a name and a list of pairs, one pair for each member
// of the struct. The first element of each pair is a type node (a struct type
// node or a sclar type node), specifying the type of the member, the second
// element of each pair is the offset of the member.
//
// Given an example
// typedef struct {
// short s;
// } A;
// typedef struct {
// uint16_t s;
// A a;
// } B;
//
// For an acess to B.a.s, we attach !5 (a path tag node) to the load/store
// instruction. The base type is !4 (struct B), the access type is !2 (scalar
// type short) and the offset is 4.
//
// !0 = metadata !{metadata !"Simple C/C++ TBAA"}
// !1 = metadata !{metadata !"omnipotent char", metadata !0} // Scalar type node
// !2 = metadata !{metadata !"short", metadata !1} // Scalar type node
// !3 = metadata !{metadata !"A", metadata !2, i64 0} // Struct type node
// !4 = metadata !{metadata !"B", metadata !2, i64 0, metadata !3, i64 4}
// // Struct type node
// !5 = metadata !{metadata !4, metadata !2, i64 4} // Path tag node
//
// The struct type nodes and the scalar type nodes form a type DAG.
// Root (!0)
// char (!1) -- edge to Root
// short (!2) -- edge to char
// A (!3) -- edge with offset 0 to short
// B (!4) -- edge with offset 0 to short and edge with offset 4 to A
//
// To check if two tags (tagX and tagY) can alias, we start from the base type
// of tagX, follow the edge with the correct offset in the type DAG and adjust
// the offset until we reach the base type of tagY or until we reach the Root
// node.
// If we reach the base type of tagY, compare the adjusted offset with
// offset of tagY, return Alias if the offsets are the same, return NoAlias
// otherwise.
// If we reach the Root node, perform the above starting from base type of tagY
// to see if we reach base type of tagX.
//
// If they have different roots, they're part of different potentially
// unrelated type systems, so we return Alias to be conservative.
// If neither node is an ancestor of the other and they have the same root,
// then we say NoAlias.
//
// TODO: The current metadata format doesn't support struct
// fields. For example:
// struct X {
// double d;
// int i;
// };
// void foo(struct X *x, struct X *y, double *p) {
// *x = *y;
// *p = 0.0;
// }
// Struct X has a double member, so the store to *x can alias the store to *p.
// Currently it's not possible to precisely describe all the things struct X
// aliases, so struct assignments must use conservative TBAA nodes. There's
// no scheme for attaching metadata to @llvm.memcpy yet either.
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/Passes.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Module.h"
#include "llvm/Pass.h"
#include "llvm/Support/CommandLine.h"
using namespace llvm;
// A handy option for disabling TBAA functionality. The same effect can also be
// achieved by stripping the !tbaa tags from IR, but this option is sometimes
// more convenient.
static cl::opt<bool> EnableTBAA("enable-tbaa", cl::init(true));
namespace {
/// TBAANode - This is a simple wrapper around an MDNode which provides a
/// higher-level interface by hiding the details of how alias analysis
/// information is encoded in its operands.
class TBAANode {
const MDNode *Node;
public:
TBAANode() : Node(nullptr) {}
explicit TBAANode(const MDNode *N) : Node(N) {}
/// getNode - Get the MDNode for this TBAANode.
const MDNode *getNode() const { return Node; }
/// getParent - Get this TBAANode's Alias tree parent.
TBAANode getParent() const {
if (Node->getNumOperands() < 2)
return TBAANode();
MDNode *P = dyn_cast_or_null<MDNode>(Node->getOperand(1));
if (!P)
return TBAANode();
// Ok, this node has a valid parent. Return it.
return TBAANode(P);
}
/// TypeIsImmutable - Test if this TBAANode represents a type for objects
/// which are not modified (by any means) in the context where this
/// AliasAnalysis is relevant.
bool TypeIsImmutable() const {
if (Node->getNumOperands() < 3)
return false;
ConstantInt *CI = dyn_cast<ConstantInt>(Node->getOperand(2));
if (!CI)
return false;
return CI->getValue()[0];
}
};
/// This is a simple wrapper around an MDNode which provides a
/// higher-level interface by hiding the details of how alias analysis
/// information is encoded in its operands.
class TBAAStructTagNode {
/// This node should be created with createTBAAStructTagNode.
const MDNode *Node;
public:
explicit TBAAStructTagNode(const MDNode *N) : Node(N) {}
/// Get the MDNode for this TBAAStructTagNode.
const MDNode *getNode() const { return Node; }
const MDNode *getBaseType() const {
return dyn_cast_or_null<MDNode>(Node->getOperand(0));
}
const MDNode *getAccessType() const {
return dyn_cast_or_null<MDNode>(Node->getOperand(1));
}
uint64_t getOffset() const {
return cast<ConstantInt>(Node->getOperand(2))->getZExtValue();
}
/// TypeIsImmutable - Test if this TBAAStructTagNode represents a type for
/// objects which are not modified (by any means) in the context where this
/// AliasAnalysis is relevant.
bool TypeIsImmutable() const {
if (Node->getNumOperands() < 4)
return false;
ConstantInt *CI = dyn_cast<ConstantInt>(Node->getOperand(3));
if (!CI)
return false;
return CI->getValue()[0];
}
};
/// This is a simple wrapper around an MDNode which provides a
/// higher-level interface by hiding the details of how alias analysis
/// information is encoded in its operands.
class TBAAStructTypeNode {
/// This node should be created with createTBAAStructTypeNode.
const MDNode *Node;
public:
TBAAStructTypeNode() : Node(nullptr) {}
explicit TBAAStructTypeNode(const MDNode *N) : Node(N) {}
/// Get the MDNode for this TBAAStructTypeNode.
const MDNode *getNode() const { return Node; }
/// Get this TBAAStructTypeNode's field in the type DAG with
/// given offset. Update the offset to be relative to the field type.
TBAAStructTypeNode getParent(uint64_t &Offset) const {
// Parent can be omitted for the root node.
if (Node->getNumOperands() < 2)
return TBAAStructTypeNode();
// Fast path for a scalar type node and a struct type node with a single
// field.
if (Node->getNumOperands() <= 3) {
uint64_t Cur = Node->getNumOperands() == 2 ? 0 :
cast<ConstantInt>(Node->getOperand(2))->getZExtValue();
Offset -= Cur;
MDNode *P = dyn_cast_or_null<MDNode>(Node->getOperand(1));
if (!P)
return TBAAStructTypeNode();
return TBAAStructTypeNode(P);
}
// Assume the offsets are in order. We return the previous field if
// the current offset is bigger than the given offset.
unsigned TheIdx = 0;
for (unsigned Idx = 1; Idx < Node->getNumOperands(); Idx += 2) {
uint64_t Cur = cast<ConstantInt>(Node->getOperand(Idx + 1))->
getZExtValue();
if (Cur > Offset) {
assert(Idx >= 3 &&
"TBAAStructTypeNode::getParent should have an offset match!");
TheIdx = Idx - 2;
break;
}
}
// Move along the last field.
if (TheIdx == 0)
TheIdx = Node->getNumOperands() - 2;
uint64_t Cur = cast<ConstantInt>(Node->getOperand(TheIdx + 1))->
getZExtValue();
Offset -= Cur;
MDNode *P = dyn_cast_or_null<MDNode>(Node->getOperand(TheIdx));
if (!P)
return TBAAStructTypeNode();
return TBAAStructTypeNode(P);
}
};
}
namespace {
/// TypeBasedAliasAnalysis - This is a simple alias analysis
/// implementation that uses TypeBased to answer queries.
class TypeBasedAliasAnalysis : public ImmutablePass,
public AliasAnalysis {
public:
static char ID; // Class identification, replacement for typeinfo
TypeBasedAliasAnalysis() : ImmutablePass(ID) {
initializeTypeBasedAliasAnalysisPass(*PassRegistry::getPassRegistry());
}
void initializePass() override {
InitializeAliasAnalysis(this);
}
/// getAdjustedAnalysisPointer - This method is used when a pass implements
/// an analysis interface through multiple inheritance. If needed, it
/// should override this to adjust the this pointer as needed for the
/// specified pass info.
void *getAdjustedAnalysisPointer(const void *PI) override {
if (PI == &AliasAnalysis::ID)
return (AliasAnalysis*)this;
return this;
}
bool Aliases(const MDNode *A, const MDNode *B) const;
bool PathAliases(const MDNode *A, const MDNode *B) const;
private:
void getAnalysisUsage(AnalysisUsage &AU) const override;
AliasResult alias(const Location &LocA, const Location &LocB) override;
bool pointsToConstantMemory(const Location &Loc, bool OrLocal) override;
ModRefBehavior getModRefBehavior(ImmutableCallSite CS) override;
ModRefBehavior getModRefBehavior(const Function *F) override;
ModRefResult getModRefInfo(ImmutableCallSite CS,
const Location &Loc) override;
ModRefResult getModRefInfo(ImmutableCallSite CS1,
ImmutableCallSite CS2) override;
};
} // End of anonymous namespace
// Register this pass...
char TypeBasedAliasAnalysis::ID = 0;
INITIALIZE_AG_PASS(TypeBasedAliasAnalysis, AliasAnalysis, "tbaa",
"Type-Based Alias Analysis", false, true, false)
ImmutablePass *llvm::createTypeBasedAliasAnalysisPass() {
return new TypeBasedAliasAnalysis();
}
void
TypeBasedAliasAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AliasAnalysis::getAnalysisUsage(AU);
}
/// Check the first operand of the tbaa tag node, if it is a MDNode, we treat
/// it as struct-path aware TBAA format, otherwise, we treat it as scalar TBAA
/// format.
static bool isStructPathTBAA(const MDNode *MD) {
// Anonymous TBAA root starts with a MDNode and dragonegg uses it as
// a TBAA tag.
return isa<MDNode>(MD->getOperand(0)) && MD->getNumOperands() >= 3;
}
/// Aliases - Test whether the type represented by A may alias the
/// type represented by B.
bool
TypeBasedAliasAnalysis::Aliases(const MDNode *A,
const MDNode *B) const {
// Make sure that both MDNodes are struct-path aware.
if (isStructPathTBAA(A) && isStructPathTBAA(B))
return PathAliases(A, B);
// Keep track of the root node for A and B.
TBAANode RootA, RootB;
// Climb the tree from A to see if we reach B.
for (TBAANode T(A); ; ) {
if (T.getNode() == B)
// B is an ancestor of A.
return true;
RootA = T;
T = T.getParent();
if (!T.getNode())
break;
}
// Climb the tree from B to see if we reach A.
for (TBAANode T(B); ; ) {
if (T.getNode() == A)
// A is an ancestor of B.
return true;
RootB = T;
T = T.getParent();
if (!T.getNode())
break;
}
// Neither node is an ancestor of the other.
// If they have different roots, they're part of different potentially
// unrelated type systems, so we must be conservative.
if (RootA.getNode() != RootB.getNode())
return true;
// If they have the same root, then we've proved there's no alias.
return false;
}
/// Test whether the struct-path tag represented by A may alias the
/// struct-path tag represented by B.
bool
TypeBasedAliasAnalysis::PathAliases(const MDNode *A,
const MDNode *B) const {
// Verify that both input nodes are struct-path aware.
assert(isStructPathTBAA(A) && "MDNode A is not struct-path aware.");
assert(isStructPathTBAA(B) && "MDNode B is not struct-path aware.");
// Keep track of the root node for A and B.
TBAAStructTypeNode RootA, RootB;
TBAAStructTagNode TagA(A), TagB(B);
// TODO: We need to check if AccessType of TagA encloses AccessType of
// TagB to support aggregate AccessType. If yes, return true.
// Start from the base type of A, follow the edge with the correct offset in
// the type DAG and adjust the offset until we reach the base type of B or
// until we reach the Root node.
// Compare the adjusted offset once we have the same base.
// Climb the type DAG from base type of A to see if we reach base type of B.
const MDNode *BaseA = TagA.getBaseType();
const MDNode *BaseB = TagB.getBaseType();
uint64_t OffsetA = TagA.getOffset(), OffsetB = TagB.getOffset();
for (TBAAStructTypeNode T(BaseA); ; ) {
if (T.getNode() == BaseB)
// Base type of A encloses base type of B, check if the offsets match.
return OffsetA == OffsetB;
RootA = T;
// Follow the edge with the correct offset, OffsetA will be adjusted to
// be relative to the field type.
T = T.getParent(OffsetA);
if (!T.getNode())
break;
}
// Reset OffsetA and climb the type DAG from base type of B to see if we reach
// base type of A.
OffsetA = TagA.getOffset();
for (TBAAStructTypeNode T(BaseB); ; ) {
if (T.getNode() == BaseA)
// Base type of B encloses base type of A, check if the offsets match.
return OffsetA == OffsetB;
RootB = T;
// Follow the edge with the correct offset, OffsetB will be adjusted to
// be relative to the field type.
T = T.getParent(OffsetB);
if (!T.getNode())
break;
}
// Neither node is an ancestor of the other.
// If they have different roots, they're part of different potentially
// unrelated type systems, so we must be conservative.
if (RootA.getNode() != RootB.getNode())
return true;
// If they have the same root, then we've proved there's no alias.
return false;
}
AliasAnalysis::AliasResult
TypeBasedAliasAnalysis::alias(const Location &LocA,
const Location &LocB) {
if (!EnableTBAA)
return AliasAnalysis::alias(LocA, LocB);
// Get the attached MDNodes. If either value lacks a tbaa MDNode, we must
// be conservative.
const MDNode *AM = LocA.AATags.TBAA;
if (!AM) return AliasAnalysis::alias(LocA, LocB);
const MDNode *BM = LocB.AATags.TBAA;
if (!BM) return AliasAnalysis::alias(LocA, LocB);
// If they may alias, chain to the next AliasAnalysis.
if (Aliases(AM, BM))
return AliasAnalysis::alias(LocA, LocB);
// Otherwise return a definitive result.
return NoAlias;
}
bool TypeBasedAliasAnalysis::pointsToConstantMemory(const Location &Loc,
bool OrLocal) {
if (!EnableTBAA)
return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
const MDNode *M = Loc.AATags.TBAA;
if (!M) return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
// If this is an "immutable" type, we can assume the pointer is pointing
// to constant memory.
if ((!isStructPathTBAA(M) && TBAANode(M).TypeIsImmutable()) ||
(isStructPathTBAA(M) && TBAAStructTagNode(M).TypeIsImmutable()))
return true;
return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
}
AliasAnalysis::ModRefBehavior
TypeBasedAliasAnalysis::getModRefBehavior(ImmutableCallSite CS) {
if (!EnableTBAA)
return AliasAnalysis::getModRefBehavior(CS);
ModRefBehavior Min = UnknownModRefBehavior;
// If this is an "immutable" type, we can assume the call doesn't write
// to memory.
if (const MDNode *M = CS.getInstruction()->getMetadata(LLVMContext::MD_tbaa))
if ((!isStructPathTBAA(M) && TBAANode(M).TypeIsImmutable()) ||
(isStructPathTBAA(M) && TBAAStructTagNode(M).TypeIsImmutable()))
Min = OnlyReadsMemory;
return ModRefBehavior(AliasAnalysis::getModRefBehavior(CS) & Min);
}
AliasAnalysis::ModRefBehavior
TypeBasedAliasAnalysis::getModRefBehavior(const Function *F) {
// Functions don't have metadata. Just chain to the next implementation.
return AliasAnalysis::getModRefBehavior(F);
}
AliasAnalysis::ModRefResult
TypeBasedAliasAnalysis::getModRefInfo(ImmutableCallSite CS,
const Location &Loc) {
if (!EnableTBAA)
return AliasAnalysis::getModRefInfo(CS, Loc);
if (const MDNode *L = Loc.AATags.TBAA)
if (const MDNode *M =
CS.getInstruction()->getMetadata(LLVMContext::MD_tbaa))
if (!Aliases(L, M))
return NoModRef;
return AliasAnalysis::getModRefInfo(CS, Loc);
}
AliasAnalysis::ModRefResult
TypeBasedAliasAnalysis::getModRefInfo(ImmutableCallSite CS1,
ImmutableCallSite CS2) {
if (!EnableTBAA)
return AliasAnalysis::getModRefInfo(CS1, CS2);
if (const MDNode *M1 =
CS1.getInstruction()->getMetadata(LLVMContext::MD_tbaa))
if (const MDNode *M2 =
CS2.getInstruction()->getMetadata(LLVMContext::MD_tbaa))
if (!Aliases(M1, M2))
return NoModRef;
return AliasAnalysis::getModRefInfo(CS1, CS2);
}
bool MDNode::isTBAAVtableAccess() const {
if (!isStructPathTBAA(this)) {
if (getNumOperands() < 1) return false;
if (MDString *Tag1 = dyn_cast<MDString>(getOperand(0))) {
if (Tag1->getString() == "vtable pointer") return true;
}
return false;
}
// For struct-path aware TBAA, we use the access type of the tag.
if (getNumOperands() < 2) return false;
MDNode *Tag = cast_or_null<MDNode>(getOperand(1));
if (!Tag) return false;
if (MDString *Tag1 = dyn_cast<MDString>(Tag->getOperand(0))) {
if (Tag1->getString() == "vtable pointer") return true;
}
return false;
}
MDNode *MDNode::getMostGenericTBAA(MDNode *A, MDNode *B) {
if (!A || !B)
return nullptr;
if (A == B)
return A;
// For struct-path aware TBAA, we use the access type of the tag.
bool StructPath = isStructPathTBAA(A) && isStructPathTBAA(B);
if (StructPath) {
A = cast_or_null<MDNode>(A->getOperand(1));
if (!A) return nullptr;
B = cast_or_null<MDNode>(B->getOperand(1));
if (!B) return nullptr;
}
SmallVector<MDNode *, 4> PathA;
MDNode *T = A;
while (T) {
PathA.push_back(T);
T = T->getNumOperands() >= 2 ? cast_or_null<MDNode>(T->getOperand(1))
: nullptr;
}
SmallVector<MDNode *, 4> PathB;
T = B;
while (T) {
PathB.push_back(T);
T = T->getNumOperands() >= 2 ? cast_or_null<MDNode>(T->getOperand(1))
: nullptr;
}
int IA = PathA.size() - 1;
int IB = PathB.size() - 1;
MDNode *Ret = nullptr;
while (IA >= 0 && IB >=0) {
if (PathA[IA] == PathB[IB])
Ret = PathA[IA];
else
break;
--IA;
--IB;
}
if (!StructPath)
return Ret;
if (!Ret)
return nullptr;
// We need to convert from a type node to a tag node.
Type *Int64 = IntegerType::get(A->getContext(), 64);
Value *Ops[3] = { Ret, Ret, ConstantInt::get(Int64, 0) };
return MDNode::get(A->getContext(), Ops);
}
void Instruction::getAAMetadata(AAMDNodes &N, bool Merge) const {
if (Merge)
N.TBAA = MDNode::getMostGenericTBAA(N.TBAA,
getMetadata(LLVMContext::MD_tbaa));
else
N.TBAA = getMetadata(LLVMContext::MD_tbaa);
Add scoped-noalias metadata This commit adds scoped noalias metadata. The primary motivations for this feature are: 1. To preserve noalias function attribute information when inlining 2. To provide the ability to model block-scope C99 restrict pointers Neither of these two abilities are added here, only the necessary infrastructure. In fact, there should be no change to existing functionality, only the addition of new features. The logic that converts noalias function parameters into this metadata during inlining will come in a follow-up commit. What is added here is the ability to generally specify noalias memory-access sets. Regarding the metadata, alias-analysis scopes are defined similar to TBAA nodes: !scope0 = metadata !{ metadata !"scope of foo()" } !scope1 = metadata !{ metadata !"scope 1", metadata !scope0 } !scope2 = metadata !{ metadata !"scope 2", metadata !scope0 } !scope3 = metadata !{ metadata !"scope 2.1", metadata !scope2 } !scope4 = metadata !{ metadata !"scope 2.2", metadata !scope2 } Loads and stores can be tagged with an alias-analysis scope, and also, with a noalias tag for a specific scope: ... = load %ptr1, !alias.scope !{ !scope1 } ... = load %ptr2, !alias.scope !{ !scope1, !scope2 }, !noalias !{ !scope1 } When evaluating an aliasing query, if one of the instructions is associated with an alias.scope id that is identical to the noalias scope associated with the other instruction, or is a descendant (in the scope hierarchy) of the noalias scope associated with the other instruction, then the two memory accesses are assumed not to alias. Note that is the first element of the scope metadata is a string, then it can be combined accross functions and translation units. The string can be replaced by a self-reference to create globally unqiue scope identifiers. [Note: This overview is slightly stylized, since the metadata nodes really need to just be numbers (!0 instead of !scope0), and the scope lists are also global unnamed metadata.] Existing noalias metadata in a callee is "cloned" for use by the inlined code. This is necessary because the aliasing scopes are unique to each call site (because of possible control dependencies on the aliasing properties). For example, consider a function: foo(noalias a, noalias b) { *a = *b; } that gets inlined into bar() { ... if (...) foo(a1, b1); ... if (...) foo(a2, b2); } -- now just because we know that a1 does not alias with b1 at the first call site, and a2 does not alias with b2 at the second call site, we cannot let inlining these functons have the metadata imply that a1 does not alias with b2. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@213864 91177308-0d34-0410-b5e6-96231b3b80d8
2014-07-24 14:25:39 +00:00
if (Merge)
N.Scope = MDNode::intersect(N.Scope,
getMetadata(LLVMContext::MD_alias_scope));
else
N.Scope = getMetadata(LLVMContext::MD_alias_scope);
if (Merge)
N.NoAlias = MDNode::intersect(N.NoAlias,
getMetadata(LLVMContext::MD_noalias));
else
N.NoAlias = getMetadata(LLVMContext::MD_noalias);
}