/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT/APInt.h

Bug Summary

File:	src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT/APInt.h
Warning:	line 927, column 15 Assigned value is garbage or undefined

Annotated Source Code

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clang -cc1 -cc1 -triple amd64-unknown-openbsd7.0 -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name BasicAliasAnalysis.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -mrelocation-model pic -pic-level 1 -fhalf-no-semantic-interposition -mframe-pointer=all -relaxed-aliasing -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -resource-dir /usr/local/lib/clang/13.0.0 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I 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/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenACC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenMP -I /include/llvm/CodeGen/GlobalISel -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/IRReader -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/LTO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Linker -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC/MCParser -I /include/llvm/CodeGen/MIRParser -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Object -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Option -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Passes -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ProfileData -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Scalar -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Support -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/Symbolize -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Target -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Utils -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Vectorize -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/IPO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include -I /usr/src/gnu/usr.bin/clang/libLLVM/../include -I /usr/src/gnu/usr.bin/clang/libLLVM/obj -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include -D NDEBUG -D __STDC_LIMIT_MACROS -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D LLVM_PREFIX="/usr" -D PIC -internal-isystem /usr/include/c++/v1 -internal-isystem /usr/local/lib/clang/13.0.0/include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -ferror-limit 19 -fvisibility-inlines-hidden -fwrapv -D_RET_PROTECTOR -ret-protector -fno-rtti -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -fno-builtin-malloc -fno-builtin-calloc -fno-builtin-realloc -fno-builtin-valloc -fno-builtin-free -fno-builtin-strdup -fno-builtin-strndup -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /home/ben/Projects/vmm/scan-build/2022-01-12-194120-40624-1 -x c++ /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Analysis/BasicAliasAnalysis.cpp

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Analysis/BasicAliasAnalysis.cpp

→

1//===- BasicAliasAnalysis.cpp - Stateless Alias Analysis Impl -------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file defines the primary stateless implementation of the
10// Alias Analysis interface that implements identities (two different
11// globals cannot alias, etc), but does no stateful analysis.
12//
13//===----------------------------------------------------------------------===//

15#include "llvm/Analysis/BasicAliasAnalysis.h"
16#include "llvm/ADT/APInt.h"
17#include "llvm/ADT/ScopeExit.h"
18#include "llvm/ADT/SmallPtrSet.h"
19#include "llvm/ADT/SmallVector.h"
20#include "llvm/ADT/Statistic.h"
21#include "llvm/Analysis/AliasAnalysis.h"
22#include "llvm/Analysis/AssumptionCache.h"
23#include "llvm/Analysis/CFG.h"
24#include "llvm/Analysis/CaptureTracking.h"
25#include "llvm/Analysis/InstructionSimplify.h"
26#include "llvm/Analysis/MemoryBuiltins.h"
27#include "llvm/Analysis/MemoryLocation.h"
28#include "llvm/Analysis/PhiValues.h"
29#include "llvm/Analysis/TargetLibraryInfo.h"
30#include "llvm/Analysis/ValueTracking.h"
31#include "llvm/IR/Argument.h"
32#include "llvm/IR/Attributes.h"
33#include "llvm/IR/Constant.h"
34#include "llvm/IR/Constants.h"
35#include "llvm/IR/DataLayout.h"
36#include "llvm/IR/DerivedTypes.h"
37#include "llvm/IR/Dominators.h"
38#include "llvm/IR/Function.h"
39#include "llvm/IR/GetElementPtrTypeIterator.h"
40#include "llvm/IR/GlobalAlias.h"
41#include "llvm/IR/GlobalVariable.h"
42#include "llvm/IR/InstrTypes.h"
43#include "llvm/IR/Instruction.h"
44#include "llvm/IR/Instructions.h"
45#include "llvm/IR/IntrinsicInst.h"
46#include "llvm/IR/Intrinsics.h"
47#include "llvm/IR/Metadata.h"
48#include "llvm/IR/Operator.h"
49#include "llvm/IR/Type.h"
50#include "llvm/IR/User.h"
51#include "llvm/IR/Value.h"
52#include "llvm/InitializePasses.h"
53#include "llvm/Pass.h"
54#include "llvm/Support/Casting.h"
55#include "llvm/Support/CommandLine.h"
56#include "llvm/Support/Compiler.h"
57#include "llvm/Support/KnownBits.h"
58#include <cassert>
59#include <cstdint>
60#include <cstdlib>
61#include <utility>

63#define DEBUG_TYPE"basicaa" "basicaa"

65using namespace llvm;

67/// Enable analysis of recursive PHI nodes.
68static cl::opt<bool> EnableRecPhiAnalysis("basic-aa-recphi", cl::Hidden,
                                        cl::init(true));

71/// By default, even on 32-bit architectures we use 64-bit integers for
72/// calculations. This will allow us to more-aggressively decompose indexing
73/// expressions calculated using i64 values (e.g., long long in C) which is
74/// common enough to worry about.
75static cl::opt<bool> ForceAtLeast64Bits("basic-aa-force-at-least-64b",
                                      cl::Hidden, cl::init(true));
77static cl::opt<bool> DoubleCalcBits("basic-aa-double-calc-bits",
                                  cl::Hidden, cl::init(false));

80/// SearchLimitReached / SearchTimes shows how often the limit of
81/// to decompose GEPs is reached. It will affect the precision
82/// of basic alias analysis.
83STATISTIC(SearchLimitReached, "Number of times the limit to "static llvm::Statistic SearchLimitReached = {"basicaa", "SearchLimitReached"
, "Number of times the limit to " "decompose GEPs is reached"
}
                            "decompose GEPs is reached")static llvm::Statistic SearchLimitReached = {"basicaa", "SearchLimitReached"
, "Number of times the limit to " "decompose GEPs is reached"
};
85STATISTIC(SearchTimes, "Number of times a GEP is decomposed")static llvm::Statistic SearchTimes = {"basicaa", "SearchTimes"
, "Number of times a GEP is decomposed"};

87/// Cutoff after which to stop analysing a set of phi nodes potentially involved
88/// in a cycle. Because we are analysing 'through' phi nodes, we need to be
89/// careful with value equivalence. We use reachability to make sure a value
90/// cannot be involved in a cycle.
91const unsigned MaxNumPhiBBsValueReachabilityCheck = 20;

93// The max limit of the search depth in DecomposeGEPExpression() and
94// getUnderlyingObject(), both functions need to use the same search
95// depth otherwise the algorithm in aliasGEP will assert.
96static const unsigned MaxLookupSearchDepth = 6;

98bool BasicAAResult::invalidate(Function &Fn, const PreservedAnalyses &PA,
                             FunctionAnalysisManager::Invalidator &Inv) {
// We don't care if this analysis itself is preserved, it has no state. But
// we need to check that the analyses it depends on have been. Note that we
// may be created without handles to some analyses and in that case don't
// depend on them.
if (Inv.invalidate<AssumptionAnalysis>(Fn, PA) ||
    (DT && Inv.invalidate<DominatorTreeAnalysis>(Fn, PA)) ||
    (PV && Inv.invalidate<PhiValuesAnalysis>(Fn, PA)))
  return true;

// Otherwise this analysis result remains valid.
return false;
111}

113//===----------------------------------------------------------------------===//
114// Useful predicates
115//===----------------------------------------------------------------------===//

117/// Returns true if the pointer is one which would have been considered an
118/// escape by isNonEscapingLocalObject.
119static bool isEscapeSource(const Value *V) {
if (isa<CallBase>(V))
  return true;

if (isa<Argument>(V))
  return true;

// The load case works because isNonEscapingLocalObject considers all
// stores to be escapes (it passes true for the StoreCaptures argument
// to PointerMayBeCaptured).
if (isa<LoadInst>(V))
  return true;

// The inttoptr case works because isNonEscapingLocalObject considers all
// means of converting or equating a pointer to an int (ptrtoint, ptr store
// which could be followed by an integer load, ptr<->int compare) as
// escaping, and objects located at well-known addresses via platform-specific
// means cannot be considered non-escaping local objects.
if (isa<IntToPtrInst>(V))
  return true;

return false;
141}

143/// Returns the size of the object specified by V or UnknownSize if unknown.
144static uint64_t getObjectSize(const Value *V, const DataLayout &DL,
                            const TargetLibraryInfo &TLI,
                            bool NullIsValidLoc,
                            bool RoundToAlign = false) {
uint64_t Size;
ObjectSizeOpts Opts;
Opts.RoundToAlign = RoundToAlign;
Opts.NullIsUnknownSize = NullIsValidLoc;
if (getObjectSize(V, Size, DL, &TLI, Opts))
  return Size;
return MemoryLocation::UnknownSize;
155}

157/// Returns true if we can prove that the object specified by V is smaller than
158/// Size.
159static bool isObjectSmallerThan(const Value *V, uint64_t Size,
                              const DataLayout &DL,
                              const TargetLibraryInfo &TLI,
                              bool NullIsValidLoc) {
// Note that the meanings of the "object" are slightly different in the
// following contexts:
//    c1: llvm::getObjectSize()
//    c2: llvm.objectsize() intrinsic
//    c3: isObjectSmallerThan()
// c1 and c2 share the same meaning; however, the meaning of "object" in c3
// refers to the "entire object".
//
//  Consider this example:
//     char *p = (char*)malloc(100)
//     char *q = p+80;
//
//  In the context of c1 and c2, the "object" pointed by q refers to the
// stretch of memory of q[0:19]. So, getObjectSize(q) should return 20.
//
//  However, in the context of c3, the "object" refers to the chunk of memory
// being allocated. So, the "object" has 100 bytes, and q points to the middle
// the "object". In case q is passed to isObjectSmallerThan() as the 1st
// parameter, before the llvm::getObjectSize() is called to get the size of
// entire object, we should:
//    - either rewind the pointer q to the base-address of the object in
//      question (in this case rewind to p), or
//    - just give up. It is up to caller to make sure the pointer is pointing
//      to the base address the object.
//
// We go for 2nd option for simplicity.
if (!isIdentifiedObject(V))
  return false;

// This function needs to use the aligned object size because we allow
// reads a bit past the end given sufficient alignment.
uint64_t ObjectSize = getObjectSize(V, DL, TLI, NullIsValidLoc,
                                    /*RoundToAlign*/ true);

return ObjectSize != MemoryLocation::UnknownSize && ObjectSize < Size;
198}

200/// Return the minimal extent from \p V to the end of the underlying object,
201/// assuming the result is used in an aliasing query. E.g., we do use the query
202/// location size and the fact that null pointers cannot alias here.
203static uint64_t getMinimalExtentFrom(const Value &V,
                                   const LocationSize &LocSize,
                                   const DataLayout &DL,
                                   bool NullIsValidLoc) {
// If we have dereferenceability information we know a lower bound for the
// extent as accesses for a lower offset would be valid. We need to exclude
// the "or null" part if null is a valid pointer.
bool CanBeNull, CanBeFreed;
uint64_t DerefBytes =
  V.getPointerDereferenceableBytes(DL, CanBeNull, CanBeFreed);
DerefBytes = (CanBeNull && NullIsValidLoc) ? 0 : DerefBytes;
DerefBytes = CanBeFreed ? 0 : DerefBytes;
// If queried with a precise location size, we assume that location size to be
// accessed, thus valid.
if (LocSize.isPrecise())
  DerefBytes = std::max(DerefBytes, LocSize.getValue());
return DerefBytes;
220}

222/// Returns true if we can prove that the object specified by V has size Size.
223static bool isObjectSize(const Value *V, uint64_t Size, const DataLayout &DL,
                       const TargetLibraryInfo &TLI, bool NullIsValidLoc) {
uint64_t ObjectSize = getObjectSize(V, DL, TLI, NullIsValidLoc);
return ObjectSize != MemoryLocation::UnknownSize && ObjectSize == Size;
227}

229//===----------------------------------------------------------------------===//
230// GetElementPtr Instruction Decomposition and Analysis
231//===----------------------------------------------------------------------===//

233namespace {
234/// Represents zext(sext(V)).
235struct ExtendedValue {
const Value *V;
unsigned ZExtBits;
unsigned SExtBits;

explicit ExtendedValue(const Value *V, unsigned ZExtBits = 0,
                       unsigned SExtBits = 0)
    : V(V), ZExtBits(ZExtBits), SExtBits(SExtBits) {}

unsigned getBitWidth() const {
  return V->getType()->getPrimitiveSizeInBits() + ZExtBits + SExtBits;
}

ExtendedValue withValue(const Value *NewV) const {
  return ExtendedValue(NewV, ZExtBits, SExtBits);
}

ExtendedValue withZExtOfValue(const Value *NewV) const {
  unsigned ExtendBy = V->getType()->getPrimitiveSizeInBits() -
                      NewV->getType()->getPrimitiveSizeInBits();
  // zext(sext(zext(NewV))) == zext(zext(zext(NewV)))
  return ExtendedValue(NewV, ZExtBits + SExtBits + ExtendBy, 0);
}

ExtendedValue withSExtOfValue(const Value *NewV) const {
  unsigned ExtendBy = V->getType()->getPrimitiveSizeInBits() -
                      NewV->getType()->getPrimitiveSizeInBits();
  // zext(sext(sext(NewV)))
  return ExtendedValue(NewV, ZExtBits, SExtBits + ExtendBy);
}

APInt evaluateWith(APInt N) const {
  assert(N.getBitWidth() == V->getType()->getPrimitiveSizeInBits() &&((void)0)
         "Incompatible bit width")((void)0);
  if (SExtBits) N = N.sext(N.getBitWidth() + SExtBits);
  if (ZExtBits) N = N.zext(N.getBitWidth() + ZExtBits);
  return N;
}

bool canDistributeOver(bool NUW, bool NSW) const {
  // zext(x op<nuw> y) == zext(x) op<nuw> zext(y)
  // sext(x op<nsw> y) == sext(x) op<nsw> sext(y)
  return (!ZExtBits43.1
Field 'ZExtBits' is 0
1
Field 'ZExtBits' is 0
 || NUW) && (!SExtBits43.2
Field 'SExtBits' is 0
2
Field 'SExtBits' is 0
 || NSW);
44
←
Returning the value 1, which participates in a condition later→
}
279};

281/// Represents zext(sext(V)) * Scale + Offset.
282struct LinearExpression {
ExtendedValue Val;
APInt Scale;
APInt Offset;

/// True if all operations in this expression are NSW.
bool IsNSW;

LinearExpression(const ExtendedValue &Val, const APInt &Scale,
                 const APInt &Offset, bool IsNSW)
    : Val(Val), Scale(Scale), Offset(Offset), IsNSW(IsNSW) {}

LinearExpression(const ExtendedValue &Val) : Val(Val), IsNSW(true) {
  unsigned BitWidth = Val.getBitWidth();
  Scale = APInt(BitWidth, 1);
  Offset = APInt(BitWidth, 0);
}
299};
300}

302/// Analyzes the specified value as a linear expression: "A*V + B", where A and
303/// B are constant integers.
304static LinearExpression GetLinearExpression(
  const ExtendedValue &Val,  const DataLayout &DL, unsigned Depth,
  AssumptionCache *AC, DominatorTree *DT) {
// Limit our recursion depth.
if (Depth22.1
'Depth' is not equal to 6
1
'Depth' is not equal to 6
1
'Depth' is not equal to 6
1
'Depth' is not equal to 6
 == 6)
23
←
Taking false branch→
34
←
Taking false branch→
  return Val;

if (const ConstantInt *Const24.1
'Const' is null
1
'Const' is null
1
'Const' is null
1
'Const' is null
 = dyn_cast<ConstantInt>(Val.V))
24
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Field 'V' is not a 'ConstantInt'→
25
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Taking false branch→
35
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Assuming field 'V' is not a 'ConstantInt'→
36
←
Taking false branch→
  return LinearExpression(Val, APInt(Val.getBitWidth(), 0),
                          Val.evaluateWith(Const->getValue()), true);

if (const BinaryOperator *BOp26.1
'BOp' is null
1
'BOp' is non-null
1
'BOp' is null
1
'BOp' is non-null
 = dyn_cast<BinaryOperator>(Val.V)) {
26
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Assuming field 'V' is not a 'BinaryOperator'→
27
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Taking false branch→
37
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Assuming field 'V' is a 'BinaryOperator'→
38
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Taking true branch→
  if (ConstantInt *RHSC = dyn_cast<ConstantInt>(BOp->getOperand(1))) {
39
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Assuming 'RHSC' is non-null→
40
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Taking true branch→
    APInt RHS = Val.evaluateWith(RHSC->getValue());
    // The only non-OBO case we deal with is or, and only limited to the
    // case where it is both nuw and nsw.
    bool NUW = true, NSW = true;
    if (isa<OverflowingBinaryOperator>(BOp)) {
41
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Assuming 'BOp' is not a 'OverflowingBinaryOperator'→
42
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Taking false branch→
      NUW &= BOp->hasNoUnsignedWrap();
      NSW &= BOp->hasNoSignedWrap();
    }
    if (!Val.canDistributeOver(NUW, NSW))
43
←
Calling 'ExtendedValue::canDistributeOver'→
45
←
Returning from 'ExtendedValue::canDistributeOver'→
46
←
Taking false branch→
      return Val;

    LinearExpression E(Val);
    switch (BOp->getOpcode()) {
47
←
Control jumps to 'case Shl:'  at line 364→
    default:
      // We don't understand this instruction, so we can't decompose it any
      // further.
      return Val;
    case Instruction::Or:
      // X|C == X+C if all the bits in C are unset in X.  Otherwise we can't
      // analyze it.
      if (!MaskedValueIsZero(BOp->getOperand(0), RHSC->getValue(), DL, 0, AC,
                             BOp, DT))
        return Val;

      LLVM_FALLTHROUGH[[gnu::fallthrough]];
    case Instruction::Add: {
      E = GetLinearExpression(Val.withValue(BOp->getOperand(0)), DL,
                              Depth + 1, AC, DT);
      E.Offset += RHS;
      E.IsNSW &= NSW;
      break;
    }
    case Instruction::Sub: {
      E = GetLinearExpression(Val.withValue(BOp->getOperand(0)), DL,
                              Depth + 1, AC, DT);
      E.Offset -= RHS;
      E.IsNSW &= NSW;
      break;
    }
    case Instruction::Mul: {
      E = GetLinearExpression(Val.withValue(BOp->getOperand(0)), DL,
                              Depth + 1, AC, DT);
      E.Offset *= RHS;
      E.Scale *= RHS;
      E.IsNSW &= NSW;
      break;
    }
    case Instruction::Shl:
      // We're trying to linearize an expression of the kind:
      //   shl i8 -128, 36
      // where the shift count exceeds the bitwidth of the type.
      // We can't decompose this further (the expression would return
      // a poison value).
      if (RHS.getLimitedValue() > Val.getBitWidth())
48
←
Assuming the condition is false→
49
←
Taking false branch→
        return Val;

      E = GetLinearExpression(Val.withValue(BOp->getOperand(0)), DL,
                              Depth + 1, AC, DT);
      E.Offset <<= RHS.getLimitedValue();
50
←
Passing the value 18446744073709551615 via 1st parameter 'Limit'→
51
←
Calling 'APInt::getLimitedValue'→
55
←
Returning from 'APInt::getLimitedValue'→
56
←
Passing the value 4294967295 via 1st parameter 'ShiftAmt'→
57
←
Calling 'APInt::operator<<='→
      E.Scale <<= RHS.getLimitedValue();
      E.IsNSW &= NSW;
      break;
    }
    return E;
  }
}

if (isa<ZExtInst>(Val.V))
28
←
Assuming field 'V' is not a 'ZExtInst'→
29
←
Taking false branch→
  return GetLinearExpression(
      Val.withZExtOfValue(cast<CastInst>(Val.V)->getOperand(0)),
      DL, Depth + 1, AC, DT);

if (isa<SExtInst>(Val.V))
30
←
Assuming field 'V' is a 'SExtInst'→
31
←
Taking true branch→
  return GetLinearExpression(
33
←
Calling 'GetLinearExpression'→
      Val.withSExtOfValue(cast<CastInst>(Val.V)->getOperand(0)),
32
←
Field 'V' is a 'CastInst'→
      DL, Depth + 1, AC, DT);

return Val;
395}

397/// To ensure a pointer offset fits in an integer of size PointerSize
398/// (in bits) when that size is smaller than the maximum pointer size. This is
399/// an issue, for example, in particular for 32b pointers with negative indices
400/// that rely on two's complement wrap-arounds for precise alias information
401/// where the maximum pointer size is 64b.
402static APInt adjustToPointerSize(const APInt &Offset, unsigned PointerSize) {
assert(PointerSize <= Offset.getBitWidth() && "Invalid PointerSize!")((void)0);
unsigned ShiftBits = Offset.getBitWidth() - PointerSize;
return (Offset << ShiftBits).ashr(ShiftBits);
406}

408static unsigned getMaxPointerSize(const DataLayout &DL) {
unsigned MaxPointerSize = DL.getMaxPointerSizeInBits();
if (MaxPointerSize < 64 && ForceAtLeast64Bits) MaxPointerSize = 64;
if (DoubleCalcBits) MaxPointerSize *= 2;

return MaxPointerSize;
414}

416/// If V is a symbolic pointer expression, decompose it into a base pointer
417/// with a constant offset and a number of scaled symbolic offsets.
418///
419/// The scaled symbolic offsets (represented by pairs of a Value* and a scale
420/// in the VarIndices vector) are Value*'s that are known to be scaled by the
421/// specified amount, but which may have other unrepresented high bits. As
422/// such, the gep cannot necessarily be reconstructed from its decomposed form.
423///
424/// This function is capable of analyzing everything that getUnderlyingObject
425/// can look through. To be able to do that getUnderlyingObject and
426/// DecomposeGEPExpression must use the same search depth
427/// (MaxLookupSearchDepth).
428BasicAAResult::DecomposedGEP
429BasicAAResult::DecomposeGEPExpression(const Value *V, const DataLayout &DL,
                                    AssumptionCache *AC, DominatorTree *DT) {
// Limit recursion depth to limit compile time in crazy cases.
unsigned MaxLookup = MaxLookupSearchDepth;
SearchTimes++;
const Instruction *CxtI = dyn_cast<Instruction>(V);
2
←
Assuming 'V' is not a 'Instruction'→

unsigned MaxPointerSize = getMaxPointerSize(DL);
DecomposedGEP Decomposed;
Decomposed.Offset = APInt(MaxPointerSize, 0);
Decomposed.HasCompileTimeConstantScale = true;
do {
  // See if this is a bitcast or GEP.
  const Operator *Op = dyn_cast<Operator>(V);
3
←
Assuming 'V' is a 'Operator'→
  if (!Op3.1
'Op' is non-null
1
'Op' is non-null
) {
4
←
Taking false branch→
    // The only non-operator case we can handle are GlobalAliases.
    if (const GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
      if (!GA->isInterposable()) {
        V = GA->getAliasee();
        continue;
      }
    }
    Decomposed.Base = V;
    return Decomposed;
  }

  if (Op->getOpcode() == Instruction::BitCast ||
5
←
Assuming the condition is false→
7
←
Taking false branch→
      Op->getOpcode() == Instruction::AddrSpaceCast) {
6
←
Assuming the condition is false→
    V = Op->getOperand(0);
    continue;
  }

  const GEPOperator *GEPOp = dyn_cast<GEPOperator>(Op);
8
←
Assuming 'Op' is a 'GEPOperator'→
  if (!GEPOp8.1
'GEPOp' is non-null
1
'GEPOp' is non-null
) {
9
←
Taking false branch→
    if (const auto *PHI = dyn_cast<PHINode>(V)) {
      // Look through single-arg phi nodes created by LCSSA.
      if (PHI->getNumIncomingValues() == 1) {
        V = PHI->getIncomingValue(0);
        continue;
      }
    } else if (const auto *Call = dyn_cast<CallBase>(V)) {
      // CaptureTracking can know about special capturing properties of some
      // intrinsics like launder.invariant.group, that can't be expressed with
      // the attributes, but have properties like returning aliasing pointer.
      // Because some analysis may assume that nocaptured pointer is not
      // returned from some special intrinsic (because function would have to
      // be marked with returns attribute), it is crucial to use this function
      // because it should be in sync with CaptureTracking. Not using it may
      // cause weird miscompilations where 2 aliasing pointers are assumed to
      // noalias.
      if (auto *RP = getArgumentAliasingToReturnedPointer(Call, false)) {
        V = RP;
        continue;
      }
    }

    Decomposed.Base = V;
    return Decomposed;
  }

  // Track whether we've seen at least one in bounds gep, and if so, whether
  // all geps parsed were in bounds.
  if (Decomposed.InBounds == None)
10
←
Taking true branch→
    Decomposed.InBounds = GEPOp->isInBounds();
  else if (!GEPOp->isInBounds())
    Decomposed.InBounds = false;

  // Don't attempt to analyze GEPs over unsized objects.
  if (!GEPOp->getSourceElementType()->isSized()) {
11
←
Taking false branch→
    Decomposed.Base = V;
    return Decomposed;
  }

  // Don't attempt to analyze GEPs if index scale is not a compile-time
  // constant.
  if (isa<ScalableVectorType>(GEPOp->getSourceElementType())) {
12
←
Assuming the object is not a 'ScalableVectorType'→
13
←
Taking false branch→
    Decomposed.Base = V;
    Decomposed.HasCompileTimeConstantScale = false;
    return Decomposed;
  }

  unsigned AS = GEPOp->getPointerAddressSpace();
  // Walk the indices of the GEP, accumulating them into BaseOff/VarIndices.
  gep_type_iterator GTI = gep_type_begin(GEPOp);
  unsigned PointerSize = DL.getPointerSizeInBits(AS);
  // Assume all GEP operands are constants until proven otherwise.
  bool GepHasConstantOffset = true;
  for (User::const_op_iterator I = GEPOp->op_begin() + 1, E = GEPOp->op_end();
15
←
Loop condition is true.  Entering loop body→
       I != E; ++I, ++GTI) {
14
←
Assuming 'I' is not equal to 'E'→
    const Value *Index = *I;
    // Compute the (potentially symbolic) offset in bytes for this index.
    if (StructType *STy = GTI.getStructTypeOrNull()) {
16
←
Assuming 'STy' is null→
17
←
Taking false branch→
      // For a struct, add the member offset.
      unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
      if (FieldNo == 0)
        continue;

      Decomposed.Offset += DL.getStructLayout(STy)->getElementOffset(FieldNo);
      continue;
    }

    // For an array/pointer, add the element offset, explicitly scaled.
    if (const ConstantInt *CIdx18.1
'CIdx' is null
1
'CIdx' is null
 = dyn_cast<ConstantInt>(Index)) {
18
←
Assuming 'Index' is not a 'ConstantInt'→
19
←
Taking false branch→
      if (CIdx->isZero())
        continue;
      Decomposed.Offset +=
          DL.getTypeAllocSize(GTI.getIndexedType()).getFixedSize() *
          CIdx->getValue().sextOrTrunc(MaxPointerSize);
      continue;
    }

    GepHasConstantOffset = false;

    APInt Scale(MaxPointerSize,
                DL.getTypeAllocSize(GTI.getIndexedType()).getFixedSize());
    // If the integer type is smaller than the pointer size, it is implicitly
    // sign extended to pointer size.
    unsigned Width = Index->getType()->getIntegerBitWidth();
    unsigned SExtBits = PointerSize > Width ? PointerSize - Width : 0;
20
←
Assuming 'PointerSize' is <= 'Width'→
21
←
'?' condition is false→
    LinearExpression LE = GetLinearExpression(
22
←
Calling 'GetLinearExpression'→
        ExtendedValue(Index, 0, SExtBits), DL, 0, AC, DT);

    // The GEP index scale ("Scale") scales C1*V+C2, yielding (C1*V+C2)*Scale.
    // This gives us an aggregate computation of (C1*Scale)*V + C2*Scale.

    // It can be the case that, even through C1*V+C2 does not overflow for
    // relevant values of V, (C2*Scale) can overflow. In that case, we cannot
    // decompose the expression in this way.
    //
    // FIXME: C1*Scale and the other operations in the decomposed
    // (C1*Scale)*V+C2*Scale can also overflow. We should check for this
    // possibility.
    bool Overflow;
    APInt ScaledOffset = LE.Offset.sextOrTrunc(MaxPointerSize)
                         .smul_ov(Scale, Overflow);
    if (Overflow) {
      LE = LinearExpression(ExtendedValue(Index, 0, SExtBits));
    } else {
      Decomposed.Offset += ScaledOffset;
      Scale *= LE.Scale.sextOrTrunc(MaxPointerSize);
    }

    // If we already had an occurrence of this index variable, merge this
    // scale into it.  For example, we want to handle:
    //   A[x][x] -> x*16 + x*4 -> x*20
    // This also ensures that 'x' only appears in the index list once.
    for (unsigned i = 0, e = Decomposed.VarIndices.size(); i != e; ++i) {
      if (Decomposed.VarIndices[i].V == LE.Val.V &&
          Decomposed.VarIndices[i].ZExtBits == LE.Val.ZExtBits &&
          Decomposed.VarIndices[i].SExtBits == LE.Val.SExtBits) {
        Scale += Decomposed.VarIndices[i].Scale;
        Decomposed.VarIndices.erase(Decomposed.VarIndices.begin() + i);
        break;
      }
    }

    // Make sure that we have a scale that makes sense for this target's
    // pointer size.
    Scale = adjustToPointerSize(Scale, PointerSize);

    if (!!Scale) {
      VariableGEPIndex Entry = {
          LE.Val.V, LE.Val.ZExtBits, LE.Val.SExtBits, Scale, CxtI, LE.IsNSW};
      Decomposed.VarIndices.push_back(Entry);
    }
  }

  // Take care of wrap-arounds
  if (GepHasConstantOffset)
    Decomposed.Offset = adjustToPointerSize(Decomposed.Offset, PointerSize);

  // Analyze the base pointer next.
  V = GEPOp->getOperand(0);
} while (--MaxLookup);

// If the chain of expressions is too deep, just return early.
Decomposed.Base = V;
SearchLimitReached++;
return Decomposed;
608}

610/// Returns whether the given pointer value points to memory that is local to
611/// the function, with global constants being considered local to all
612/// functions.
613bool BasicAAResult::pointsToConstantMemory(const MemoryLocation &Loc,
                                         AAQueryInfo &AAQI, bool OrLocal) {
assert(Visited.empty() && "Visited must be cleared after use!")((void)0);

unsigned MaxLookup = 8;
SmallVector<const Value *, 16> Worklist;
Worklist.push_back(Loc.Ptr);
do {
  const Value *V = getUnderlyingObject(Worklist.pop_back_val());
  if (!Visited.insert(V).second) {
    Visited.clear();
    return AAResultBase::pointsToConstantMemory(Loc, AAQI, OrLocal);
  }

  // An alloca instruction defines local memory.
  if (OrLocal && isa<AllocaInst>(V))
    continue;

  // A global constant counts as local memory for our purposes.
  if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(V)) {
    // Note: this doesn't require GV to be "ODR" because it isn't legal for a
    // global to be marked constant in some modules and non-constant in
    // others.  GV may even be a declaration, not a definition.
    if (!GV->isConstant()) {
      Visited.clear();
      return AAResultBase::pointsToConstantMemory(Loc, AAQI, OrLocal);
    }
    continue;
  }

  // If both select values point to local memory, then so does the select.
  if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
    Worklist.push_back(SI->getTrueValue());
    Worklist.push_back(SI->getFalseValue());
    continue;
  }

  // If all values incoming to a phi node point to local memory, then so does
  // the phi.
  if (const PHINode *PN = dyn_cast<PHINode>(V)) {
    // Don't bother inspecting phi nodes with many operands.
    if (PN->getNumIncomingValues() > MaxLookup) {
      Visited.clear();
      return AAResultBase::pointsToConstantMemory(Loc, AAQI, OrLocal);
    }
    append_range(Worklist, PN->incoming_values());
    continue;
  }

  // Otherwise be conservative.
  Visited.clear();
  return AAResultBase::pointsToConstantMemory(Loc, AAQI, OrLocal);
} while (!Worklist.empty() && --MaxLookup);

Visited.clear();
return Worklist.empty();
669}

671static bool isIntrinsicCall(const CallBase *Call, Intrinsic::ID IID) {
const IntrinsicInst *II = dyn_cast<IntrinsicInst>(Call);
return II && II->getIntrinsicID() == IID;
674}

676/// Returns the behavior when calling the given call site.
677FunctionModRefBehavior BasicAAResult::getModRefBehavior(const CallBase *Call) {
if (Call->doesNotAccessMemory())
  // Can't do better than this.
  return FMRB_DoesNotAccessMemory;

FunctionModRefBehavior Min = FMRB_UnknownModRefBehavior;

// If the callsite knows it only reads memory, don't return worse
// than that.
if (Call->onlyReadsMemory())
  Min = FMRB_OnlyReadsMemory;
else if (Call->doesNotReadMemory())
  Min = FMRB_OnlyWritesMemory;

if (Call->onlyAccessesArgMemory())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);
else if (Call->onlyAccessesInaccessibleMemory())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleMem);
else if (Call->onlyAccessesInaccessibleMemOrArgMem())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleOrArgMem);

// If the call has operand bundles then aliasing attributes from the function
// it calls do not directly apply to the call.  This can be made more precise
// in the future.
if (!Call->hasOperandBundles())
  if (const Function *F = Call->getCalledFunction())
    Min =
        FunctionModRefBehavior(Min & getBestAAResults().getModRefBehavior(F));

return Min;
707}

709/// Returns the behavior when calling the given function. For use when the call
710/// site is not known.
711FunctionModRefBehavior BasicAAResult::getModRefBehavior(const Function *F) {
// If the function declares it doesn't access memory, we can't do better.
if (F->doesNotAccessMemory())
  return FMRB_DoesNotAccessMemory;

FunctionModRefBehavior Min = FMRB_UnknownModRefBehavior;

// If the function declares it only reads memory, go with that.
if (F->onlyReadsMemory())
  Min = FMRB_OnlyReadsMemory;
else if (F->doesNotReadMemory())
  Min = FMRB_OnlyWritesMemory;

if (F->onlyAccessesArgMemory())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);
else if (F->onlyAccessesInaccessibleMemory())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleMem);
else if (F->onlyAccessesInaccessibleMemOrArgMem())
  Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleOrArgMem);

return Min;
732}

734/// Returns true if this is a writeonly (i.e Mod only) parameter.
735static bool isWriteOnlyParam(const CallBase *Call, unsigned ArgIdx,
                           const TargetLibraryInfo &TLI) {
if (Call->paramHasAttr(ArgIdx, Attribute::WriteOnly))
  return true;

// We can bound the aliasing properties of memset_pattern16 just as we can
// for memcpy/memset.  This is particularly important because the
// LoopIdiomRecognizer likes to turn loops into calls to memset_pattern16
// whenever possible.
// FIXME Consider handling this in InferFunctionAttr.cpp together with other
// attributes.
LibFunc F;
if (Call->getCalledFunction() &&
    TLI.getLibFunc(*Call->getCalledFunction(), F) &&
    F == LibFunc_memset_pattern16 && TLI.has(F))
  if (ArgIdx == 0)
    return true;

// TODO: memset_pattern4, memset_pattern8
// TODO: _chk variants
// TODO: strcmp, strcpy

return false;
758}

760ModRefInfo BasicAAResult::getArgModRefInfo(const CallBase *Call,
                                         unsigned ArgIdx) {
// Checking for known builtin intrinsics and target library functions.
if (isWriteOnlyParam(Call, ArgIdx, TLI))
  return ModRefInfo::Mod;

if (Call->paramHasAttr(ArgIdx, Attribute::ReadOnly))
  return ModRefInfo::Ref;

if (Call->paramHasAttr(ArgIdx, Attribute::ReadNone))
  return ModRefInfo::NoModRef;

return AAResultBase::getArgModRefInfo(Call, ArgIdx);
773}

775#ifndef NDEBUG1
776static const Function *getParent(const Value *V) {
if (const Instruction *inst = dyn_cast<Instruction>(V)) {
  if (!inst->getParent())
    return nullptr;
  return inst->getParent()->getParent();
}

if (const Argument *arg = dyn_cast<Argument>(V))
  return arg->getParent();

return nullptr;
787}

789static bool notDifferentParent(const Value *O1, const Value *O2) {

const Function *F1 = getParent(O1);
const Function *F2 = getParent(O2);

return !F1 || !F2 || F1 == F2;
795}
796#endif

798AliasResult BasicAAResult::alias(const MemoryLocation &LocA,
                               const MemoryLocation &LocB,
                               AAQueryInfo &AAQI) {
assert(notDifferentParent(LocA.Ptr, LocB.Ptr) &&((void)0)
       "BasicAliasAnalysis doesn't support interprocedural queries.")((void)0);
return aliasCheck(LocA.Ptr, LocA.Size, LocB.Ptr, LocB.Size, AAQI);
804}

806/// Checks to see if the specified callsite can clobber the specified memory
807/// object.
808///
809/// Since we only look at local properties of this function, we really can't
810/// say much about this query.  We do, however, use simple "address taken"
811/// analysis on local objects.
812ModRefInfo BasicAAResult::getModRefInfo(const CallBase *Call,
                                      const MemoryLocation &Loc,
                                      AAQueryInfo &AAQI) {
assert(notDifferentParent(Call, Loc.Ptr) &&((void)0)
       "AliasAnalysis query involving multiple functions!")((void)0);

const Value *Object = getUnderlyingObject(Loc.Ptr);

// Calls marked 'tail' cannot read or write allocas from the current frame
// because the current frame might be destroyed by the time they run. However,
// a tail call may use an alloca with byval. Calling with byval copies the
// contents of the alloca into argument registers or stack slots, so there is
// no lifetime issue.
if (isa<AllocaInst>(Object))
  if (const CallInst *CI = dyn_cast<CallInst>(Call))
    if (CI->isTailCall() &&
        !CI->getAttributes().hasAttrSomewhere(Attribute::ByVal))
      return ModRefInfo::NoModRef;

// Stack restore is able to modify unescaped dynamic allocas. Assume it may
// modify them even though the alloca is not escaped.
if (auto *AI = dyn_cast<AllocaInst>(Object))
  if (!AI->isStaticAlloca() && isIntrinsicCall(Call, Intrinsic::stackrestore))
    return ModRefInfo::Mod;

// If the pointer is to a locally allocated object that does not escape,
// then the call can not mod/ref the pointer unless the call takes the pointer
// as an argument, and itself doesn't capture it.
if (!isa<Constant>(Object) && Call != Object &&
    isNonEscapingLocalObject(Object, &AAQI.IsCapturedCache)) {

  // Optimistically assume that call doesn't touch Object and check this
  // assumption in the following loop.
  ModRefInfo Result = ModRefInfo::NoModRef;
  bool IsMustAlias = true;

  unsigned OperandNo = 0;
  for (auto CI = Call->data_operands_begin(), CE = Call->data_operands_end();
       CI != CE; ++CI, ++OperandNo) {
    // Only look at the no-capture or byval pointer arguments.  If this
    // pointer were passed to arguments that were neither of these, then it
    // couldn't be no-capture.
    if (!(*CI)->getType()->isPointerTy() ||
        (!Call->doesNotCapture(OperandNo) &&
         OperandNo < Call->getNumArgOperands() &&
         !Call->isByValArgument(OperandNo)))
      continue;

    // Call doesn't access memory through this operand, so we don't care
    // if it aliases with Object.
    if (Call->doesNotAccessMemory(OperandNo))
      continue;

    // If this is a no-capture pointer argument, see if we can tell that it
    // is impossible to alias the pointer we're checking.
    AliasResult AR = getBestAAResults().alias(
        MemoryLocation::getBeforeOrAfter(*CI),
        MemoryLocation::getBeforeOrAfter(Object), AAQI);
    if (AR != AliasResult::MustAlias)
      IsMustAlias = false;
    // Operand doesn't alias 'Object', continue looking for other aliases
    if (AR == AliasResult::NoAlias)
      continue;
    // Operand aliases 'Object', but call doesn't modify it. Strengthen
    // initial assumption and keep looking in case if there are more aliases.
    if (Call->onlyReadsMemory(OperandNo)) {
      Result = setRef(Result);
      continue;
    }
    // Operand aliases 'Object' but call only writes into it.
    if (Call->doesNotReadMemory(OperandNo)) {
      Result = setMod(Result);
      continue;
    }
    // This operand aliases 'Object' and call reads and writes into it.
    // Setting ModRef will not yield an early return below, MustAlias is not
    // used further.
    Result = ModRefInfo::ModRef;
    break;
  }

  // No operand aliases, reset Must bit. Add below if at least one aliases
  // and all aliases found are MustAlias.
  if (isNoModRef(Result))
    IsMustAlias = false;

  // Early return if we improved mod ref information
  if (!isModAndRefSet(Result)) {
    if (isNoModRef(Result))
      return ModRefInfo::NoModRef;
    return IsMustAlias ? setMust(Result) : clearMust(Result);
  }
}

// If the call is malloc/calloc like, we can assume that it doesn't
// modify any IR visible value.  This is only valid because we assume these
// routines do not read values visible in the IR.  TODO: Consider special
// casing realloc and strdup routines which access only their arguments as
// well.  Or alternatively, replace all of this with inaccessiblememonly once
// that's implemented fully.
if (isMallocOrCallocLikeFn(Call, &TLI)) {
  // Be conservative if the accessed pointer may alias the allocation -
  // fallback to the generic handling below.
  if (getBestAAResults().alias(MemoryLocation::getBeforeOrAfter(Call), Loc,
                               AAQI) == AliasResult::NoAlias)
    return ModRefInfo::NoModRef;
}

// The semantics of memcpy intrinsics either exactly overlap or do not
// overlap, i.e., source and destination of any given memcpy are either
// no-alias or must-alias.
if (auto *Inst = dyn_cast<AnyMemCpyInst>(Call)) {
  AliasResult SrcAA =
      getBestAAResults().alias(MemoryLocation::getForSource(Inst), Loc, AAQI);
  AliasResult DestAA =
      getBestAAResults().alias(MemoryLocation::getForDest(Inst), Loc, AAQI);
  // It's also possible for Loc to alias both src and dest, or neither.
  ModRefInfo rv = ModRefInfo::NoModRef;
  if (SrcAA != AliasResult::NoAlias)
    rv = setRef(rv);
  if (DestAA != AliasResult::NoAlias)
    rv = setMod(rv);
  return rv;
}

// Guard intrinsics are marked as arbitrarily writing so that proper control
// dependencies are maintained but they never mods any particular memory
// location.
//
// *Unlike* assumes, guard intrinsics are modeled as reading memory since the
// heap state at the point the guard is issued needs to be consistent in case
// the guard invokes the "deopt" continuation.
if (isIntrinsicCall(Call, Intrinsic::experimental_guard))
  return ModRefInfo::Ref;
// The same applies to deoptimize which is essentially a guard(false).
if (isIntrinsicCall(Call, Intrinsic::experimental_deoptimize))
  return ModRefInfo::Ref;

// Like assumes, invariant.start intrinsics were also marked as arbitrarily
// writing so that proper control dependencies are maintained but they never
// mod any particular memory location visible to the IR.
// *Unlike* assumes (which are now modeled as NoModRef), invariant.start
// intrinsic is now modeled as reading memory. This prevents hoisting the
// invariant.start intrinsic over stores. Consider:
// *ptr = 40;
// *ptr = 50;
// invariant_start(ptr)
// int val = *ptr;
// print(val);
//
// This cannot be transformed to:
//
// *ptr = 40;
// invariant_start(ptr)
// *ptr = 50;
// int val = *ptr;
// print(val);
//
// The transformation will cause the second store to be ignored (based on
// rules of invariant.start)  and print 40, while the first program always
// prints 50.
if (isIntrinsicCall(Call, Intrinsic::invariant_start))
  return ModRefInfo::Ref;

// The AAResultBase base class has some smarts, lets use them.
return AAResultBase::getModRefInfo(Call, Loc, AAQI);
978}

980ModRefInfo BasicAAResult::getModRefInfo(const CallBase *Call1,
                                      const CallBase *Call2,
                                      AAQueryInfo &AAQI) {
// Guard intrinsics are marked as arbitrarily writing so that proper control
// dependencies are maintained but they never mods any particular memory
// location.
//
// *Unlike* assumes, guard intrinsics are modeled as reading memory since the
// heap state at the point the guard is issued needs to be consistent in case
// the guard invokes the "deopt" continuation.

// NB! This function is *not* commutative, so we special case two
// possibilities for guard intrinsics.

if (isIntrinsicCall(Call1, Intrinsic::experimental_guard))
  return isModSet(createModRefInfo(getModRefBehavior(Call2)))
             ? ModRefInfo::Ref
             : ModRefInfo::NoModRef;

if (isIntrinsicCall(Call2, Intrinsic::experimental_guard))
  return isModSet(createModRefInfo(getModRefBehavior(Call1)))
             ? ModRefInfo::Mod
             : ModRefInfo::NoModRef;

// The AAResultBase base class has some smarts, lets use them.
return AAResultBase::getModRefInfo(Call1, Call2, AAQI);
1006}

1008/// Return true if we know V to the base address of the corresponding memory
1009/// object.  This implies that any address less than V must be out of bounds
1010/// for the underlying object.  Note that just being isIdentifiedObject() is
1011/// not enough - For example, a negative offset from a noalias argument or call
1012/// can be inbounds w.r.t the actual underlying object.
1013static bool isBaseOfObject(const Value *V) {
// TODO: We can handle other cases here
// 1) For GC languages, arguments to functions are often required to be
//    base pointers.
// 2) Result of allocation routines are often base pointers.  Leverage TLI.
return (isa<AllocaInst>(V) || isa<GlobalVariable>(V));
1019}

1021/// Provides a bunch of ad-hoc rules to disambiguate a GEP instruction against
1022/// another pointer.
1023///
1024/// We know that V1 is a GEP, but we don't know anything about V2.
1025/// UnderlyingV1 is getUnderlyingObject(GEP1), UnderlyingV2 is the same for
1026/// V2.
1027AliasResult BasicAAResult::aliasGEP(
  const GEPOperator *GEP1, LocationSize V1Size,
  const Value *V2, LocationSize V2Size,
  const Value *UnderlyingV1, const Value *UnderlyingV2, AAQueryInfo &AAQI) {
if (!V1Size.hasValue() && !V2Size.hasValue()) {
  // TODO: This limitation exists for compile-time reasons. Relax it if we
  // can avoid exponential pathological cases.
  if (!isa<GEPOperator>(V2))
    return AliasResult::MayAlias;

  // If both accesses have unknown size, we can only check whether the base
  // objects don't alias.
  AliasResult BaseAlias = getBestAAResults().alias(
      MemoryLocation::getBeforeOrAfter(UnderlyingV1),
      MemoryLocation::getBeforeOrAfter(UnderlyingV2), AAQI);
  return BaseAlias == AliasResult::NoAlias ? AliasResult::NoAlias
                                           : AliasResult::MayAlias;
}

DecomposedGEP DecompGEP1 = DecomposeGEPExpression(GEP1, DL, &AC, DT);
1
Calling 'BasicAAResult::DecomposeGEPExpression'→
DecomposedGEP DecompGEP2 = DecomposeGEPExpression(V2, DL, &AC, DT);

// Don't attempt to analyze the decomposed GEP if index scale is not a
// compile-time constant.
if (!DecompGEP1.HasCompileTimeConstantScale ||
    !DecompGEP2.HasCompileTimeConstantScale)
  return AliasResult::MayAlias;

assert(DecompGEP1.Base == UnderlyingV1 && DecompGEP2.Base == UnderlyingV2 &&((void)0)
       "DecomposeGEPExpression returned a result different from "((void)0)
       "getUnderlyingObject")((void)0);

// Subtract the GEP2 pointer from the GEP1 pointer to find out their
// symbolic difference.
DecompGEP1.Offset -= DecompGEP2.Offset;
GetIndexDifference(DecompGEP1.VarIndices, DecompGEP2.VarIndices);

// If an inbounds GEP would have to start from an out of bounds address
// for the two to alias, then we can assume noalias.
if (*DecompGEP1.InBounds && DecompGEP1.VarIndices.empty() &&
    V2Size.hasValue() && DecompGEP1.Offset.sge(V2Size.getValue()) &&
    isBaseOfObject(DecompGEP2.Base))
  return AliasResult::NoAlias;

if (isa<GEPOperator>(V2)) {
  // Symmetric case to above.
  if (*DecompGEP2.InBounds && DecompGEP1.VarIndices.empty() &&
      V1Size.hasValue() && DecompGEP1.Offset.sle(-V1Size.getValue()) &&
      isBaseOfObject(DecompGEP1.Base))
    return AliasResult::NoAlias;
}

// For GEPs with identical offsets, we can preserve the size and AAInfo
// when performing the alias check on the underlying objects.
if (DecompGEP1.Offset == 0 && DecompGEP1.VarIndices.empty())
  return getBestAAResults().alias(
      MemoryLocation(UnderlyingV1, V1Size),
      MemoryLocation(UnderlyingV2, V2Size), AAQI);

// Do the base pointers alias?
AliasResult BaseAlias = getBestAAResults().alias(
    MemoryLocation::getBeforeOrAfter(UnderlyingV1),
    MemoryLocation::getBeforeOrAfter(UnderlyingV2), AAQI);

// If we get a No or May, then return it immediately, no amount of analysis
// will improve this situation.
if (BaseAlias != AliasResult::MustAlias) {
  assert(BaseAlias == AliasResult::NoAlias ||((void)0)
         BaseAlias == AliasResult::MayAlias)((void)0);
  return BaseAlias;
}

// If there is a constant difference between the pointers, but the difference
// is less than the size of the associated memory object, then we know
// that the objects are partially overlapping.  If the difference is
// greater, we know they do not overlap.
if (DecompGEP1.Offset != 0 && DecompGEP1.VarIndices.empty()) {
  APInt &Off = DecompGEP1.Offset;

  // Initialize for Off >= 0 (V2 <= GEP1) case.
  const Value *LeftPtr = V2;
  const Value *RightPtr = GEP1;
  LocationSize VLeftSize = V2Size;
  LocationSize VRightSize = V1Size;
  const bool Swapped = Off.isNegative();

  if (Swapped) {
    // Swap if we have the situation where:
    // +                +
    // | BaseOffset     |
    // ---------------->|
    // |-->V1Size       |-------> V2Size
    // GEP1             V2
    std::swap(LeftPtr, RightPtr);
    std::swap(VLeftSize, VRightSize);
    Off = -Off;
  }

  if (VLeftSize.hasValue()) {
    const uint64_t LSize = VLeftSize.getValue();
    if (Off.ult(LSize)) {
      // Conservatively drop processing if a phi was visited and/or offset is
      // too big.
      AliasResult AR = AliasResult::PartialAlias;
      if (VRightSize.hasValue() && Off.ule(INT32_MAX0x7fffffff) &&
          (Off + VRightSize.getValue()).ule(LSize)) {
        // Memory referenced by right pointer is nested. Save the offset in
        // cache. Note that originally offset estimated as GEP1-V2, but
        // AliasResult contains the shift that represents GEP1+Offset=V2.
        AR.setOffset(-Off.getSExtValue());
        AR.swap(Swapped);
      }
      return AR;
    }
    return AliasResult::NoAlias;
  }
}

if (!DecompGEP1.VarIndices.empty()) {
  APInt GCD;
  bool AllNonNegative = DecompGEP1.Offset.isNonNegative();
  bool AllNonPositive = DecompGEP1.Offset.isNonPositive();
  for (unsigned i = 0, e = DecompGEP1.VarIndices.size(); i != e; ++i) {
    APInt Scale = DecompGEP1.VarIndices[i].Scale;
    APInt ScaleForGCD = DecompGEP1.VarIndices[i].Scale;
    if (!DecompGEP1.VarIndices[i].IsNSW)
      ScaleForGCD = APInt::getOneBitSet(Scale.getBitWidth(),
                                        Scale.countTrailingZeros());

    if (i == 0)
      GCD = ScaleForGCD.abs();
    else
      GCD = APIntOps::GreatestCommonDivisor(GCD, ScaleForGCD.abs());

    if (AllNonNegative || AllNonPositive) {
      // If the Value could change between cycles, then any reasoning about
      // the Value this cycle may not hold in the next cycle. We'll just
      // give up if we can't determine conditions that hold for every cycle:
      const Value *V = DecompGEP1.VarIndices[i].V;
      const Instruction *CxtI = DecompGEP1.VarIndices[i].CxtI;

      KnownBits Known = computeKnownBits(V, DL, 0, &AC, CxtI, DT);
      bool SignKnownZero = Known.isNonNegative();
      bool SignKnownOne = Known.isNegative();

      // Zero-extension widens the variable, and so forces the sign
      // bit to zero.
      bool IsZExt = DecompGEP1.VarIndices[i].ZExtBits > 0 || isa<ZExtInst>(V);
      SignKnownZero |= IsZExt;
      SignKnownOne &= !IsZExt;

      AllNonNegative &= (SignKnownZero && Scale.isNonNegative()) ||
                        (SignKnownOne && Scale.isNonPositive());
      AllNonPositive &= (SignKnownZero && Scale.isNonPositive()) ||
                        (SignKnownOne && Scale.isNonNegative());
    }
  }

  // We now have accesses at two offsets from the same base:
  //  1. (...)*GCD + DecompGEP1.Offset with size V1Size
  //  2. 0 with size V2Size
  // Using arithmetic modulo GCD, the accesses are at
  // [ModOffset..ModOffset+V1Size) and [0..V2Size). If the first access fits
  // into the range [V2Size..GCD), then we know they cannot overlap.
  APInt ModOffset = DecompGEP1.Offset.srem(GCD);
  if (ModOffset.isNegative())
    ModOffset += GCD; // We want mod, not rem.
  if (V1Size.hasValue() && V2Size.hasValue() &&
      ModOffset.uge(V2Size.getValue()) &&
      (GCD - ModOffset).uge(V1Size.getValue()))
    return AliasResult::NoAlias;

  // If we know all the variables are non-negative, then the total offset is
  // also non-negative and >= DecompGEP1.Offset. We have the following layout:
  // [0, V2Size) ... [TotalOffset, TotalOffer+V1Size]
  // If DecompGEP1.Offset >= V2Size, the accesses don't alias.
  if (AllNonNegative && V2Size.hasValue() &&
      DecompGEP1.Offset.uge(V2Size.getValue()))
    return AliasResult::NoAlias;
  // Similarly, if the variables are non-positive, then the total offset is
  // also non-positive and <= DecompGEP1.Offset. We have the following layout:
  // [TotalOffset, TotalOffset+V1Size) ... [0, V2Size)
  // If -DecompGEP1.Offset >= V1Size, the accesses don't alias.
  if (AllNonPositive && V1Size.hasValue() &&
      (-DecompGEP1.Offset).uge(V1Size.getValue()))
    return AliasResult::NoAlias;

  if (V1Size.hasValue() && V2Size.hasValue()) {
    // Try to determine whether abs(VarIndex) > 0.
    Optional<APInt> MinAbsVarIndex;
    if (DecompGEP1.VarIndices.size() == 1) {
      // VarIndex = Scale*V. If V != 0 then abs(VarIndex) >= abs(Scale).
      const VariableGEPIndex &Var = DecompGEP1.VarIndices[0];
      if (isKnownNonZero(Var.V, DL, 0, &AC, Var.CxtI, DT))
        MinAbsVarIndex = Var.Scale.abs();
    } else if (DecompGEP1.VarIndices.size() == 2) {
      // VarIndex = Scale*V0 + (-Scale)*V1.
      // If V0 != V1 then abs(VarIndex) >= abs(Scale).
      // Check that VisitedPhiBBs is empty, to avoid reasoning about
      // inequality of values across loop iterations.
      const VariableGEPIndex &Var0 = DecompGEP1.VarIndices[0];
      const VariableGEPIndex &Var1 = DecompGEP1.VarIndices[1];
      if (Var0.Scale == -Var1.Scale && Var0.ZExtBits == Var1.ZExtBits &&
          Var0.SExtBits == Var1.SExtBits && VisitedPhiBBs.empty() &&
          isKnownNonEqual(Var0.V, Var1.V, DL, &AC, /* CxtI */ nullptr, DT))
        MinAbsVarIndex = Var0.Scale.abs();
    }

    if (MinAbsVarIndex) {
      // The constant offset will have added at least +/-MinAbsVarIndex to it.
      APInt OffsetLo = DecompGEP1.Offset - *MinAbsVarIndex;
      APInt OffsetHi = DecompGEP1.Offset + *MinAbsVarIndex;
      // Check that an access at OffsetLo or lower, and an access at OffsetHi
      // or higher both do not alias.
      if (OffsetLo.isNegative() && (-OffsetLo).uge(V1Size.getValue()) &&
          OffsetHi.isNonNegative() && OffsetHi.uge(V2Size.getValue()))
        return AliasResult::NoAlias;
    }
  }

  if (constantOffsetHeuristic(DecompGEP1.VarIndices, V1Size, V2Size,
                              DecompGEP1.Offset, &AC, DT))
    return AliasResult::NoAlias;
}

// Statically, we can see that the base objects are the same, but the
// pointers have dynamic offsets which we can't resolve. And none of our
// little tricks above worked.
return AliasResult::MayAlias;
1256}

1258static AliasResult MergeAliasResults(AliasResult A, AliasResult B) {
// If the results agree, take it.
if (A == B)
  return A;
// A mix of PartialAlias and MustAlias is PartialAlias.
if ((A == AliasResult::PartialAlias && B == AliasResult::MustAlias) ||
    (B == AliasResult::PartialAlias && A == AliasResult::MustAlias))
  return AliasResult::PartialAlias;
// Otherwise, we don't know anything.
return AliasResult::MayAlias;
1268}

1270/// Provides a bunch of ad-hoc rules to disambiguate a Select instruction
1271/// against another.
1272AliasResult
1273BasicAAResult::aliasSelect(const SelectInst *SI, LocationSize SISize,
                         const Value *V2, LocationSize V2Size,
                         AAQueryInfo &AAQI) {
// If the values are Selects with the same condition, we can do a more precise
// check: just check for aliases between the values on corresponding arms.
if (const SelectInst *SI2 = dyn_cast<SelectInst>(V2))
  if (SI->getCondition() == SI2->getCondition()) {
    AliasResult Alias = getBestAAResults().alias(
        MemoryLocation(SI->getTrueValue(), SISize),
        MemoryLocation(SI2->getTrueValue(), V2Size), AAQI);
    if (Alias == AliasResult::MayAlias)
      return AliasResult::MayAlias;
    AliasResult ThisAlias = getBestAAResults().alias(
        MemoryLocation(SI->getFalseValue(), SISize),
        MemoryLocation(SI2->getFalseValue(), V2Size), AAQI);
    return MergeAliasResults(ThisAlias, Alias);
  }

// If both arms of the Select node NoAlias or MustAlias V2, then returns
// NoAlias / MustAlias. Otherwise, returns MayAlias.
AliasResult Alias = getBestAAResults().alias(
    MemoryLocation(V2, V2Size),
    MemoryLocation(SI->getTrueValue(), SISize), AAQI);
if (Alias == AliasResult::MayAlias)
  return AliasResult::MayAlias;

AliasResult ThisAlias = getBestAAResults().alias(
    MemoryLocation(V2, V2Size),
    MemoryLocation(SI->getFalseValue(), SISize), AAQI);
return MergeAliasResults(ThisAlias, Alias);
1303}

1305/// Provide a bunch of ad-hoc rules to disambiguate a PHI instruction against
1306/// another.
1307AliasResult BasicAAResult::aliasPHI(const PHINode *PN, LocationSize PNSize,
                                  const Value *V2, LocationSize V2Size,
                                  AAQueryInfo &AAQI) {
if (!PN->getNumIncomingValues())
  return AliasResult::NoAlias;
// If the values are PHIs in the same block, we can do a more precise
// as well as efficient check: just check for aliases between the values
// on corresponding edges.
if (const PHINode *PN2 = dyn_cast<PHINode>(V2))
  if (PN2->getParent() == PN->getParent()) {
    Optional<AliasResult> Alias;
    for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
      AliasResult ThisAlias = getBestAAResults().alias(
          MemoryLocation(PN->getIncomingValue(i), PNSize),
          MemoryLocation(
              PN2->getIncomingValueForBlock(PN->getIncomingBlock(i)), V2Size),
          AAQI);
      if (Alias)
        *Alias = MergeAliasResults(*Alias, ThisAlias);
      else
        Alias = ThisAlias;
      if (*Alias == AliasResult::MayAlias)
        break;
    }
    return *Alias;
  }

SmallVector<Value *, 4> V1Srcs;
// If a phi operand recurses back to the phi, we can still determine NoAlias
// if we don't alias the underlying objects of the other phi operands, as we
// know that the recursive phi needs to be based on them in some way.
bool isRecursive = false;
auto CheckForRecPhi = [&](Value *PV) {
  if (!EnableRecPhiAnalysis)
    return false;
  if (getUnderlyingObject(PV) == PN) {
    isRecursive = true;
    return true;
  }
  return false;
};

if (PV) {
  // If we have PhiValues then use it to get the underlying phi values.
  const PhiValues::ValueSet &PhiValueSet = PV->getValuesForPhi(PN);
  // If we have more phi values than the search depth then return MayAlias
  // conservatively to avoid compile time explosion. The worst possible case
  // is if both sides are PHI nodes. In which case, this is O(m x n) time
  // where 'm' and 'n' are the number of PHI sources.
  if (PhiValueSet.size() > MaxLookupSearchDepth)
    return AliasResult::MayAlias;
  // Add the values to V1Srcs
  for (Value *PV1 : PhiValueSet) {
    if (CheckForRecPhi(PV1))
      continue;
    V1Srcs.push_back(PV1);
  }
} else {
  // If we don't have PhiInfo then just look at the operands of the phi itself
  // FIXME: Remove this once we can guarantee that we have PhiInfo always
  SmallPtrSet<Value *, 4> UniqueSrc;
  Value *OnePhi = nullptr;
  for (Value *PV1 : PN->incoming_values()) {
    if (isa<PHINode>(PV1)) {
      if (OnePhi && OnePhi != PV1) {
        // To control potential compile time explosion, we choose to be
        // conserviate when we have more than one Phi input.  It is important
        // that we handle the single phi case as that lets us handle LCSSA
        // phi nodes and (combined with the recursive phi handling) simple
        // pointer induction variable patterns.
        return AliasResult::MayAlias;
      }
      OnePhi = PV1;
    }

    if (CheckForRecPhi(PV1))
      continue;

    if (UniqueSrc.insert(PV1).second)
      V1Srcs.push_back(PV1);
  }

  if (OnePhi && UniqueSrc.size() > 1)
    // Out of an abundance of caution, allow only the trivial lcssa and
    // recursive phi cases.
    return AliasResult::MayAlias;
}

// If V1Srcs is empty then that means that the phi has no underlying non-phi
// value. This should only be possible in blocks unreachable from the entry
// block, but return MayAlias just in case.
if (V1Srcs.empty())
  return AliasResult::MayAlias;

// If this PHI node is recursive, indicate that the pointer may be moved
// across iterations. We can only prove NoAlias if different underlying
// objects are involved.
if (isRecursive)
  PNSize = LocationSize::beforeOrAfterPointer();

// In the recursive alias queries below, we may compare values from two
// different loop iterations. Keep track of visited phi blocks, which will
// be used when determining value equivalence.
bool BlockInserted = VisitedPhiBBs.insert(PN->getParent()).second;
auto _ = make_scope_exit([&]() {
  if (BlockInserted)
    VisitedPhiBBs.erase(PN->getParent());
});

// If we inserted a block into VisitedPhiBBs, alias analysis results that
// have been cached earlier may no longer be valid. Perform recursive queries
// with a new AAQueryInfo.
AAQueryInfo NewAAQI = AAQI.withEmptyCache();
AAQueryInfo *UseAAQI = BlockInserted ? &NewAAQI : &AAQI;

AliasResult Alias = getBestAAResults().alias(
    MemoryLocation(V2, V2Size),
    MemoryLocation(V1Srcs[0], PNSize), *UseAAQI);

// Early exit if the check of the first PHI source against V2 is MayAlias.
// Other results are not possible.
if (Alias == AliasResult::MayAlias)
  return AliasResult::MayAlias;
// With recursive phis we cannot guarantee that MustAlias/PartialAlias will
// remain valid to all elements and needs to conservatively return MayAlias.
if (isRecursive && Alias != AliasResult::NoAlias)
  return AliasResult::MayAlias;

// If all sources of the PHI node NoAlias or MustAlias V2, then returns
// NoAlias / MustAlias. Otherwise, returns MayAlias.
for (unsigned i = 1, e = V1Srcs.size(); i != e; ++i) {
  Value *V = V1Srcs[i];

  AliasResult ThisAlias = getBestAAResults().alias(
      MemoryLocation(V2, V2Size), MemoryLocation(V, PNSize), *UseAAQI);
  Alias = MergeAliasResults(ThisAlias, Alias);
  if (Alias == AliasResult::MayAlias)
    break;
}

return Alias;
1448}

1450/// Provides a bunch of ad-hoc rules to disambiguate in common cases, such as
1451/// array references.
1452AliasResult BasicAAResult::aliasCheck(const Value *V1, LocationSize V1Size,
                                    const Value *V2, LocationSize V2Size,
                                    AAQueryInfo &AAQI) {
// If either of the memory references is empty, it doesn't matter what the
// pointer values are.
if (V1Size.isZero() || V2Size.isZero())
  return AliasResult::NoAlias;

// Strip off any casts if they exist.
V1 = V1->stripPointerCastsForAliasAnalysis();
V2 = V2->stripPointerCastsForAliasAnalysis();

// If V1 or V2 is undef, the result is NoAlias because we can always pick a
// value for undef that aliases nothing in the program.
if (isa<UndefValue>(V1) || isa<UndefValue>(V2))
  return AliasResult::NoAlias;

// Are we checking for alias of the same value?
// Because we look 'through' phi nodes, we could look at "Value" pointers from
// different iterations. We must therefore make sure that this is not the
// case. The function isValueEqualInPotentialCycles ensures that this cannot
// happen by looking at the visited phi nodes and making sure they cannot
// reach the value.
if (isValueEqualInPotentialCycles(V1, V2))
  return AliasResult::MustAlias;

if (!V1->getType()->isPointerTy() || !V2->getType()->isPointerTy())
  return AliasResult::NoAlias; // Scalars cannot alias each other

// Figure out what objects these things are pointing to if we can.
const Value *O1 = getUnderlyingObject(V1, MaxLookupSearchDepth);
const Value *O2 = getUnderlyingObject(V2, MaxLookupSearchDepth);

// Null values in the default address space don't point to any object, so they
// don't alias any other pointer.
if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O1))
  if (!NullPointerIsDefined(&F, CPN->getType()->getAddressSpace()))
    return AliasResult::NoAlias;
if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O2))
  if (!NullPointerIsDefined(&F, CPN->getType()->getAddressSpace()))
    return AliasResult::NoAlias;

if (O1 != O2) {
  // If V1/V2 point to two different objects, we know that we have no alias.
  if (isIdentifiedObject(O1) && isIdentifiedObject(O2))
    return AliasResult::NoAlias;

  // Constant pointers can't alias with non-const isIdentifiedObject objects.
  if ((isa<Constant>(O1) && isIdentifiedObject(O2) && !isa<Constant>(O2)) ||
      (isa<Constant>(O2) && isIdentifiedObject(O1) && !isa<Constant>(O1)))
    return AliasResult::NoAlias;

  // Function arguments can't alias with things that are known to be
  // unambigously identified at the function level.
  if ((isa<Argument>(O1) && isIdentifiedFunctionLocal(O2)) ||
      (isa<Argument>(O2) && isIdentifiedFunctionLocal(O1)))
    return AliasResult::NoAlias;

  // If one pointer is the result of a call/invoke or load and the other is a
  // non-escaping local object within the same function, then we know the
  // object couldn't escape to a point where the call could return it.
  //
  // Note that if the pointers are in different functions, there are a
  // variety of complications. A call with a nocapture argument may still
  // temporary store the nocapture argument's value in a temporary memory
  // location if that memory location doesn't escape. Or it may pass a
  // nocapture value to other functions as long as they don't capture it.
  if (isEscapeSource(O1) &&
      isNonEscapingLocalObject(O2, &AAQI.IsCapturedCache))
    return AliasResult::NoAlias;
  if (isEscapeSource(O2) &&
      isNonEscapingLocalObject(O1, &AAQI.IsCapturedCache))
    return AliasResult::NoAlias;
}

// If the size of one access is larger than the entire object on the other
// side, then we know such behavior is undefined and can assume no alias.
bool NullIsValidLocation = NullPointerIsDefined(&F);
if ((isObjectSmallerThan(
        O2, getMinimalExtentFrom(*V1, V1Size, DL, NullIsValidLocation), DL,
        TLI, NullIsValidLocation)) ||
    (isObjectSmallerThan(
        O1, getMinimalExtentFrom(*V2, V2Size, DL, NullIsValidLocation), DL,
        TLI, NullIsValidLocation)))
  return AliasResult::NoAlias;

// If one the accesses may be before the accessed pointer, canonicalize this
// by using unknown after-pointer sizes for both accesses. This is
// equivalent, because regardless of which pointer is lower, one of them
// will always came after the other, as long as the underlying objects aren't
// disjoint. We do this so that the rest of BasicAA does not have to deal
// with accesses before the base pointer, and to improve cache utilization by
// merging equivalent states.
if (V1Size.mayBeBeforePointer() || V2Size.mayBeBeforePointer()) {
  V1Size = LocationSize::afterPointer();
  V2Size = LocationSize::afterPointer();
}

// FIXME: If this depth limit is hit, then we may cache sub-optimal results
// for recursive queries. For this reason, this limit is chosen to be large
// enough to be very rarely hit, while still being small enough to avoid
// stack overflows.
if (AAQI.Depth >= 512)
  return AliasResult::MayAlias;

// Check the cache before climbing up use-def chains. This also terminates
// otherwise infinitely recursive queries.
AAQueryInfo::LocPair Locs({V1, V1Size}, {V2, V2Size});
const bool Swapped = V1 > V2;
if (Swapped)
  std::swap(Locs.first, Locs.second);
const auto &Pair = AAQI.AliasCache.try_emplace(
    Locs, AAQueryInfo::CacheEntry{AliasResult::NoAlias, 0});
if (!Pair.second) {
  auto &Entry = Pair.first->second;
  if (!Entry.isDefinitive()) {
    // Remember that we used an assumption.
    ++Entry.NumAssumptionUses;
    ++AAQI.NumAssumptionUses;
  }
  // Cache contains sorted {V1,V2} pairs but we should return original order.
  auto Result = Entry.Result;
  Result.swap(Swapped);
  return Result;
}

int OrigNumAssumptionUses = AAQI.NumAssumptionUses;
unsigned OrigNumAssumptionBasedResults = AAQI.AssumptionBasedResults.size();
AliasResult Result =
    aliasCheckRecursive(V1, V1Size, V2, V2Size, AAQI, O1, O2);

auto It = AAQI.AliasCache.find(Locs);
assert(It != AAQI.AliasCache.end() && "Must be in cache")((void)0);
auto &Entry = It->second;

// Check whether a NoAlias assumption has been used, but disproven.
bool AssumptionDisproven =
    Entry.NumAssumptionUses > 0 && Result != AliasResult::NoAlias;
if (AssumptionDisproven)
  Result = AliasResult::MayAlias;

// This is a definitive result now, when considered as a root query.
AAQI.NumAssumptionUses -= Entry.NumAssumptionUses;
Entry.Result = Result;
// Cache contains sorted {V1,V2} pairs.
Entry.Result.swap(Swapped);
Entry.NumAssumptionUses = -1;

// If the assumption has been disproven, remove any results that may have
// been based on this assumption. Do this after the Entry updates above to
// avoid iterator invalidation.
if (AssumptionDisproven)
  while (AAQI.AssumptionBasedResults.size() > OrigNumAssumptionBasedResults)
    AAQI.AliasCache.erase(AAQI.AssumptionBasedResults.pop_back_val());

// The result may still be based on assumptions higher up in the chain.
// Remember it, so it can be purged from the cache later.
if (OrigNumAssumptionUses != AAQI.NumAssumptionUses &&
    Result != AliasResult::MayAlias)
  AAQI.AssumptionBasedResults.push_back(Locs);
return Result;
1613}

1615AliasResult BasicAAResult::aliasCheckRecursive(
  const Value *V1, LocationSize V1Size,
  const Value *V2, LocationSize V2Size,
  AAQueryInfo &AAQI, const Value *O1, const Value *O2) {
if (const GEPOperator *GV1 = dyn_cast<GEPOperator>(V1)) {
  AliasResult Result = aliasGEP(GV1, V1Size, V2, V2Size, O1, O2, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
} else if (const GEPOperator *GV2 = dyn_cast<GEPOperator>(V2)) {
  AliasResult Result = aliasGEP(GV2, V2Size, V1, V1Size, O2, O1, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
}

if (const PHINode *PN = dyn_cast<PHINode>(V1)) {
  AliasResult Result = aliasPHI(PN, V1Size, V2, V2Size, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
} else if (const PHINode *PN = dyn_cast<PHINode>(V2)) {
  AliasResult Result = aliasPHI(PN, V2Size, V1, V1Size, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
}

if (const SelectInst *S1 = dyn_cast<SelectInst>(V1)) {
  AliasResult Result = aliasSelect(S1, V1Size, V2, V2Size, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
} else if (const SelectInst *S2 = dyn_cast<SelectInst>(V2)) {
  AliasResult Result = aliasSelect(S2, V2Size, V1, V1Size, AAQI);
  if (Result != AliasResult::MayAlias)
    return Result;
}

// If both pointers are pointing into the same object and one of them
// accesses the entire object, then the accesses must overlap in some way.
if (O1 == O2) {
  bool NullIsValidLocation = NullPointerIsDefined(&F);
  if (V1Size.isPrecise() && V2Size.isPrecise() &&
      (isObjectSize(O1, V1Size.getValue(), DL, TLI, NullIsValidLocation) ||
       isObjectSize(O2, V2Size.getValue(), DL, TLI, NullIsValidLocation)))
    return AliasResult::PartialAlias;
}

return AliasResult::MayAlias;
1660}

1662/// Check whether two Values can be considered equivalent.
1663///
1664/// In addition to pointer equivalence of \p V1 and \p V2 this checks whether
1665/// they can not be part of a cycle in the value graph by looking at all
1666/// visited phi nodes an making sure that the phis cannot reach the value. We
1667/// have to do this because we are looking through phi nodes (That is we say
1668/// noalias(V, phi(VA, VB)) if noalias(V, VA) and noalias(V, VB).
1669bool BasicAAResult::isValueEqualInPotentialCycles(const Value *V,
                                                const Value *V2) {
if (V != V2)
  return false;

const Instruction *Inst = dyn_cast<Instruction>(V);
if (!Inst)
  return true;

if (VisitedPhiBBs.empty())
  return true;

if (VisitedPhiBBs.size() > MaxNumPhiBBsValueReachabilityCheck)
  return false;

// Make sure that the visited phis cannot reach the Value. This ensures that
// the Values cannot come from different iterations of a potential cycle the
// phi nodes could be involved in.
for (auto *P : VisitedPhiBBs)
  if (isPotentiallyReachable(&P->front(), Inst, nullptr, DT))
    return false;

return true;
1692}

1694/// Computes the symbolic difference between two de-composed GEPs.
1695///
1696/// Dest and Src are the variable indices from two decomposed GetElementPtr
1697/// instructions GEP1 and GEP2 which have common base pointers.
1698void BasicAAResult::GetIndexDifference(
  SmallVectorImpl<VariableGEPIndex> &Dest,
  const SmallVectorImpl<VariableGEPIndex> &Src) {
if (Src.empty())
  return;

for (unsigned i = 0, e = Src.size(); i != e; ++i) {
  const Value *V = Src[i].V;
  unsigned ZExtBits = Src[i].ZExtBits, SExtBits = Src[i].SExtBits;
  APInt Scale = Src[i].Scale;

  // Find V in Dest.  This is N^2, but pointer indices almost never have more
  // than a few variable indexes.
  for (unsigned j = 0, e = Dest.size(); j != e; ++j) {
    if (!isValueEqualInPotentialCycles(Dest[j].V, V) ||
        Dest[j].ZExtBits != ZExtBits || Dest[j].SExtBits != SExtBits)
      continue;

    // If we found it, subtract off Scale V's from the entry in Dest.  If it
    // goes to zero, remove the entry.
    if (Dest[j].Scale != Scale) {
      Dest[j].Scale -= Scale;
      Dest[j].IsNSW = false;
    } else
      Dest.erase(Dest.begin() + j);
    Scale = 0;
    break;
  }

  // If we didn't consume this entry, add it to the end of the Dest list.
  if (!!Scale) {
    VariableGEPIndex Entry = {V,      ZExtBits,    SExtBits,
                              -Scale, Src[i].CxtI, Src[i].IsNSW};
    Dest.push_back(Entry);
  }
}
1734}

1736bool BasicAAResult::constantOffsetHeuristic(
  const SmallVectorImpl<VariableGEPIndex> &VarIndices,
  LocationSize MaybeV1Size, LocationSize MaybeV2Size, const APInt &BaseOffset,
  AssumptionCache *AC, DominatorTree *DT) {
if (VarIndices.size() != 2 || !MaybeV1Size.hasValue() ||
    !MaybeV2Size.hasValue())
  return false;

const uint64_t V1Size = MaybeV1Size.getValue();
const uint64_t V2Size = MaybeV2Size.getValue();

const VariableGEPIndex &Var0 = VarIndices[0], &Var1 = VarIndices[1];

if (Var0.ZExtBits != Var1.ZExtBits || Var0.SExtBits != Var1.SExtBits ||
    Var0.Scale != -Var1.Scale || Var0.V->getType() != Var1.V->getType())
  return false;

// We'll strip off the Extensions of Var0 and Var1 and do another round
// of GetLinearExpression decomposition. In the example above, if Var0
// is zext(%x + 1) we should get V1 == %x and V1Offset == 1.

LinearExpression E0 =
    GetLinearExpression(ExtendedValue(Var0.V), DL, 0, AC, DT);
LinearExpression E1 =
    GetLinearExpression(ExtendedValue(Var1.V), DL, 0, AC, DT);
if (E0.Scale != E1.Scale || E0.Val.ZExtBits != E1.Val.ZExtBits ||
    E0.Val.SExtBits != E1.Val.SExtBits ||
    !isValueEqualInPotentialCycles(E0.Val.V, E1.Val.V))
  return false;

// We have a hit - Var0 and Var1 only differ by a constant offset!

// If we've been sext'ed then zext'd the maximum difference between Var0 and
// Var1 is possible to calculate, but we're just interested in the absolute
// minimum difference between the two. The minimum distance may occur due to
// wrapping; consider "add i3 %i, 5": if %i == 7 then 7 + 5 mod 8 == 4, and so
// the minimum distance between %i and %i + 5 is 3.
APInt MinDiff = E0.Offset - E1.Offset, Wrapped = -MinDiff;
MinDiff = APIntOps::umin(MinDiff, Wrapped);
APInt MinDiffBytes =
  MinDiff.zextOrTrunc(Var0.Scale.getBitWidth()) * Var0.Scale.abs();

// We can't definitely say whether GEP1 is before or after V2 due to wrapping
// arithmetic (i.e. for some values of GEP1 and V2 GEP1 < V2, and for other
// values GEP1 > V2). We'll therefore only declare NoAlias if both V1Size and
// V2Size can fit in the MinDiffBytes gap.
return MinDiffBytes.uge(V1Size + BaseOffset.abs()) &&
       MinDiffBytes.uge(V2Size + BaseOffset.abs());
1784}

1786//===----------------------------------------------------------------------===//
1787// BasicAliasAnalysis Pass
1788//===----------------------------------------------------------------------===//

1790AnalysisKey BasicAA::Key;

1792BasicAAResult BasicAA::run(Function &F, FunctionAnalysisManager &AM) {
auto &TLI = AM.getResult<TargetLibraryAnalysis>(F);
auto &AC = AM.getResult<AssumptionAnalysis>(F);
auto *DT = &AM.getResult<DominatorTreeAnalysis>(F);
auto *PV = AM.getCachedResult<PhiValuesAnalysis>(F);
return BasicAAResult(F.getParent()->getDataLayout(), F, TLI, AC, DT, PV);
1798}

1800BasicAAWrapperPass::BasicAAWrapperPass() : FunctionPass(ID) {
initializeBasicAAWrapperPassPass(*PassRegistry::getPassRegistry());
1802}

1804char BasicAAWrapperPass::ID = 0;

1806void BasicAAWrapperPass::anchor() {}

1808INITIALIZE_PASS_BEGIN(BasicAAWrapperPass, "basic-aa",static void *initializeBasicAAWrapperPassPassOnce(PassRegistry
 &Registry) {
                    "Basic Alias Analysis (stateless AA impl)", true, true)static void *initializeBasicAAWrapperPassPassOnce(PassRegistry
 &Registry) {
1810INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)initializeAssumptionCacheTrackerPass(Registry);
1811INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)initializeDominatorTreeWrapperPassPass(Registry);
1812INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)initializeTargetLibraryInfoWrapperPassPass(Registry);
1813INITIALIZE_PASS_DEPENDENCY(PhiValuesWrapperPass)initializePhiValuesWrapperPassPass(Registry);
1814INITIALIZE_PASS_END(BasicAAWrapperPass, "basic-aa",PassInfo *PI = new PassInfo( "Basic Alias Analysis (stateless AA impl)"
, "basic-aa", &BasicAAWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<BasicAAWrapperPass>), true, true); Registry
.registerPass(*PI, true); return PI; } static llvm::once_flag
 InitializeBasicAAWrapperPassPassFlag; void llvm::initializeBasicAAWrapperPassPass
(PassRegistry &Registry) { llvm::call_once(InitializeBasicAAWrapperPassPassFlag
, initializeBasicAAWrapperPassPassOnce, std::ref(Registry)); }
                  "Basic Alias Analysis (stateless AA impl)", true, true)PassInfo *PI = new PassInfo( "Basic Alias Analysis (stateless AA impl)"
, "basic-aa", &BasicAAWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<BasicAAWrapperPass>), true, true); Registry
.registerPass(*PI, true); return PI; } static llvm::once_flag
 InitializeBasicAAWrapperPassPassFlag; void llvm::initializeBasicAAWrapperPassPass
(PassRegistry &Registry) { llvm::call_once(InitializeBasicAAWrapperPassPassFlag
, initializeBasicAAWrapperPassPassOnce, std::ref(Registry)); }

1817FunctionPass *llvm::createBasicAAWrapperPass() {
return new BasicAAWrapperPass();
1819}

1821bool BasicAAWrapperPass::runOnFunction(Function &F) {
auto &ACT = getAnalysis<AssumptionCacheTracker>();
auto &TLIWP = getAnalysis<TargetLibraryInfoWrapperPass>();
auto &DTWP = getAnalysis<DominatorTreeWrapperPass>();
auto *PVWP = getAnalysisIfAvailable<PhiValuesWrapperPass>();

Result.reset(new BasicAAResult(F.getParent()->getDataLayout(), F,
                               TLIWP.getTLI(F), ACT.getAssumptionCache(F),
                               &DTWP.getDomTree(),
                               PVWP ? &PVWP->getResult() : nullptr));

return false;
1833}

1835void BasicAAWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AssumptionCacheTracker>();
AU.addRequiredTransitive<DominatorTreeWrapperPass>();
AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
AU.addUsedIfAvailable<PhiValuesWrapperPass>();
1841}

1843BasicAAResult llvm::createLegacyPMBasicAAResult(Pass &P, Function &F) {
return BasicAAResult(
    F.getParent()->getDataLayout(), F,
    P.getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
    P.getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F));
1848}

←

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT/APInt.h

1//===-- llvm/ADT/APInt.h - For Arbitrary Precision Integer -----*- C++ -*--===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8///
9/// \file
10/// This file implements a class to represent arbitrary precision
11/// integral constant values and operations on them.
12///
13//===----------------------------------------------------------------------===//

15#ifndef LLVM_ADT_APINT_H
16#define LLVM_ADT_APINT_H

18#include "llvm/Support/Compiler.h"
19#include "llvm/Support/MathExtras.h"
20#include <cassert>
21#include <climits>
22#include <cstring>
23#include <utility>

25namespace llvm {
26class FoldingSetNodeID;
27class StringRef;
28class hash_code;
29class raw_ostream;

31template <typename T> class SmallVectorImpl;
32template <typename T> class ArrayRef;
33template <typename T> class Optional;
34template <typename T> struct DenseMapInfo;

36class APInt;

38inline APInt operator-(APInt);

40//===----------------------------------------------------------------------===//
41//                              APInt Class
42//===----------------------------------------------------------------------===//

44/// Class for arbitrary precision integers.
45///
46/// APInt is a functional replacement for common case unsigned integer type like
47/// "unsigned", "unsigned long" or "uint64_t", but also allows non-byte-width
48/// integer sizes and large integer value types such as 3-bits, 15-bits, or more
49/// than 64-bits of precision. APInt provides a variety of arithmetic operators
50/// and methods to manipulate integer values of any bit-width. It supports both
51/// the typical integer arithmetic and comparison operations as well as bitwise
52/// manipulation.
53///
54/// The class has several invariants worth noting:
55///   * All bit, byte, and word positions are zero-based.
56///   * Once the bit width is set, it doesn't change except by the Truncate,
57///     SignExtend, or ZeroExtend operations.
58///   * All binary operators must be on APInt instances of the same bit width.
59///     Attempting to use these operators on instances with different bit
60///     widths will yield an assertion.
61///   * The value is stored canonically as an unsigned value. For operations
62///     where it makes a difference, there are both signed and unsigned variants
63///     of the operation. For example, sdiv and udiv. However, because the bit
64///     widths must be the same, operations such as Mul and Add produce the same
65///     results regardless of whether the values are interpreted as signed or
66///     not.
67///   * In general, the class tries to follow the style of computation that LLVM
68///     uses in its IR. This simplifies its use for LLVM.
69///
70class LLVM_NODISCARD[[clang::warn_unused_result]] APInt {
71public:
typedef uint64_t WordType;

/// This enum is used to hold the constants we needed for APInt.
enum : unsigned {
  /// Byte size of a word.
  APINT_WORD_SIZE = sizeof(WordType),
  /// Bits in a word.
  APINT_BITS_PER_WORD = APINT_WORD_SIZE * CHAR_BIT8
};

enum class Rounding {
  DOWN,
  TOWARD_ZERO,
  UP,
};

static constexpr WordType WORDTYPE_MAX = ~WordType(0);

90private:
/// This union is used to store the integer value. When the
/// integer bit-width <= 64, it uses VAL, otherwise it uses pVal.
union {
  uint64_t VAL;   ///< Used to store the <= 64 bits integer value.
  uint64_t *pVal; ///< Used to store the >64 bits integer value.
} U;

unsigned BitWidth; ///< The number of bits in this APInt.

friend struct DenseMapInfo<APInt>;

friend class APSInt;

/// Fast internal constructor
///
/// This constructor is used only internally for speed of construction of
/// temporaries. It is unsafe for general use so it is not public.
APInt(uint64_t *val, unsigned bits) : BitWidth(bits) {
  U.pVal = val;
}

/// Determine which word a bit is in.
///
/// \returns the word position for the specified bit position.
static unsigned whichWord(unsigned bitPosition) {
  return bitPosition / APINT_BITS_PER_WORD;
}

/// Determine which bit in a word a bit is in.
///
/// \returns the bit position in a word for the specified bit position
/// in the APInt.
static unsigned whichBit(unsigned bitPosition) {
  return bitPosition % APINT_BITS_PER_WORD;
}

/// Get a single bit mask.
///
/// \returns a uint64_t with only bit at "whichBit(bitPosition)" set
/// This method generates and returns a uint64_t (word) mask for a single
/// bit at a specific bit position. This is used to mask the bit in the
/// corresponding word.
static uint64_t maskBit(unsigned bitPosition) {
  return 1ULL << whichBit(bitPosition);
}

/// Clear unused high order bits
///
/// This method is used internally to clear the top "N" bits in the high order
/// word that are not used by the APInt. This is needed after the most
/// significant word is assigned a value to ensure that those bits are
/// zero'd out.
APInt &clearUnusedBits() {
  // Compute how many bits are used in the final word
  unsigned WordBits = ((BitWidth-1) % APINT_BITS_PER_WORD) + 1;

  // Mask out the high bits.
  uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - WordBits);
  if (isSingleWord())
    U.VAL &= mask;
  else
    U.pVal[getNumWords() - 1] &= mask;
  return *this;
}

/// Get the word corresponding to a bit position
/// \returns the corresponding word for the specified bit position.
uint64_t getWord(unsigned bitPosition) const {
  return isSingleWord() ? U.VAL : U.pVal[whichWord(bitPosition)];
}

/// Utility method to change the bit width of this APInt to new bit width,
/// allocating and/or deallocating as necessary. There is no guarantee on the
/// value of any bits upon return. Caller should populate the bits after.
void reallocate(unsigned NewBitWidth);

/// Convert a char array into an APInt
///
/// \param radix 2, 8, 10, 16, or 36
/// Converts a string into a number.  The string must be non-empty
/// and well-formed as a number of the given base. The bit-width
/// must be sufficient to hold the result.
///
/// This is used by the constructors that take string arguments.
///
/// StringRef::getAsInteger is superficially similar but (1) does
/// not assume that the string is well-formed and (2) grows the
/// result to hold the input.
void fromString(unsigned numBits, StringRef str, uint8_t radix);

/// An internal division function for dividing APInts.
///
/// This is used by the toString method to divide by the radix. It simply
/// provides a more convenient form of divide for internal use since KnuthDiv
/// has specific constraints on its inputs. If those constraints are not met
/// then it provides a simpler form of divide.
static void divide(const WordType *LHS, unsigned lhsWords,
                   const WordType *RHS, unsigned rhsWords, WordType *Quotient,
                   WordType *Remainder);

/// out-of-line slow case for inline constructor
void initSlowCase(uint64_t val, bool isSigned);

/// shared code between two array constructors
void initFromArray(ArrayRef<uint64_t> array);

/// out-of-line slow case for inline copy constructor
void initSlowCase(const APInt &that);

/// out-of-line slow case for shl
void shlSlowCase(unsigned ShiftAmt);

/// out-of-line slow case for lshr.
void lshrSlowCase(unsigned ShiftAmt);

/// out-of-line slow case for ashr.
void ashrSlowCase(unsigned ShiftAmt);

/// out-of-line slow case for operator=
void AssignSlowCase(const APInt &RHS);

/// out-of-line slow case for operator==
bool EqualSlowCase(const APInt &RHS) const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for countLeadingZeros
unsigned countLeadingZerosSlowCase() const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for countLeadingOnes.
unsigned countLeadingOnesSlowCase() const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for countTrailingZeros.
unsigned countTrailingZerosSlowCase() const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for countTrailingOnes
unsigned countTrailingOnesSlowCase() const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for countPopulation
unsigned countPopulationSlowCase() const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for intersects.
bool intersectsSlowCase(const APInt &RHS) const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for isSubsetOf.
bool isSubsetOfSlowCase(const APInt &RHS) const LLVM_READONLY__attribute__((__pure__));

/// out-of-line slow case for setBits.
void setBitsSlowCase(unsigned loBit, unsigned hiBit);

/// out-of-line slow case for flipAllBits.
void flipAllBitsSlowCase();

/// out-of-line slow case for operator&=.
void AndAssignSlowCase(const APInt& RHS);

/// out-of-line slow case for operator|=.
void OrAssignSlowCase(const APInt& RHS);

/// out-of-line slow case for operator^=.
void XorAssignSlowCase(const APInt& RHS);

/// Unsigned comparison. Returns -1, 0, or 1 if this APInt is less than, equal
/// to, or greater than RHS.
int compare(const APInt &RHS) const LLVM_READONLY__attribute__((__pure__));

/// Signed comparison. Returns -1, 0, or 1 if this APInt is less than, equal
/// to, or greater than RHS.
int compareSigned(const APInt &RHS) const LLVM_READONLY__attribute__((__pure__));

259public:
/// \name Constructors
/// @{

/// Create a new APInt of numBits width, initialized as val.
///
/// If isSigned is true then val is treated as if it were a signed value
/// (i.e. as an int64_t) and the appropriate sign extension to the bit width
/// will be done. Otherwise, no sign extension occurs (high order bits beyond
/// the range of val are zero filled).
///
/// \param numBits the bit width of the constructed APInt
/// \param val the initial value of the APInt
/// \param isSigned how to treat signedness of val
APInt(unsigned numBits, uint64_t val, bool isSigned = false)
    : BitWidth(numBits) {
  assert(BitWidth && "bitwidth too small")((void)0);
  if (isSingleWord()) {
    U.VAL = val;
    clearUnusedBits();
  } else {
    initSlowCase(val, isSigned);
  }
}

/// Construct an APInt of numBits width, initialized as bigVal[].
///
/// Note that bigVal.size() can be smaller or larger than the corresponding
/// bit width but any extraneous bits will be dropped.
///
/// \param numBits the bit width of the constructed APInt
/// \param bigVal a sequence of words to form the initial value of the APInt
APInt(unsigned numBits, ArrayRef<uint64_t> bigVal);

/// Equivalent to APInt(numBits, ArrayRef<uint64_t>(bigVal, numWords)), but
/// deprecated because this constructor is prone to ambiguity with the
/// APInt(unsigned, uint64_t, bool) constructor.
///
/// If this overload is ever deleted, care should be taken to prevent calls
/// from being incorrectly captured by the APInt(unsigned, uint64_t, bool)
/// constructor.
APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]);

/// Construct an APInt from a string representation.
///
/// This constructor interprets the string \p str in the given radix. The
/// interpretation stops when the first character that is not suitable for the
/// radix is encountered, or the end of the string. Acceptable radix values
/// are 2, 8, 10, 16, and 36. It is an error for the value implied by the
/// string to require more bits than numBits.
///
/// \param numBits the bit width of the constructed APInt
/// \param str the string to be interpreted
/// \param radix the radix to use for the conversion
APInt(unsigned numBits, StringRef str, uint8_t radix);

/// Simply makes *this a copy of that.
/// Copy Constructor.
APInt(const APInt &that) : BitWidth(that.BitWidth) {
  if (isSingleWord())
    U.VAL = that.U.VAL;
  else
    initSlowCase(that);
}

/// Move Constructor.
APInt(APInt &&that) : BitWidth(that.BitWidth) {
  memcpy(&U, &that.U, sizeof(U));
  that.BitWidth = 0;
}

/// Destructor.
~APInt() {
  if (needsCleanup())
    delete[] U.pVal;
}

/// Default constructor that creates an uninteresting APInt
/// representing a 1-bit zero value.
///
/// This is useful for object deserialization (pair this with the static
///  method Read).
explicit APInt() : BitWidth(1) { U.VAL = 0; }

/// Returns whether this instance allocated memory.
bool needsCleanup() const { return !isSingleWord(); }

/// Used to insert APInt objects, or objects that contain APInt objects, into
///  FoldingSets.
void Profile(FoldingSetNodeID &id) const;

/// @}
/// \name Value Tests
/// @{

/// Determine if this APInt just has one word to store value.
///
/// \returns true if the number of bits <= 64, false otherwise.
bool isSingleWord() const { return BitWidth <= APINT_BITS_PER_WORD; }
59
←
Assuming field 'BitWidth' is <= APINT_BITS_PER_WORD→
60
←
Returning the value 1, which participates in a condition later→

/// Determine sign of this APInt.
///
/// This tests the high bit of this APInt to determine if it is set.
///
/// \returns true if this APInt is negative, false otherwise
bool isNegative() const { return (*this)[BitWidth - 1]; }

/// Determine if this APInt Value is non-negative (>= 0)
///
/// This tests the high bit of the APInt to determine if it is unset.
bool isNonNegative() const { return !isNegative(); }

/// Determine if sign bit of this APInt is set.
///
/// This tests the high bit of this APInt to determine if it is set.
///
/// \returns true if this APInt has its sign bit set, false otherwise.
bool isSignBitSet() const { return (*this)[BitWidth-1]; }

/// Determine if sign bit of this APInt is clear.
///
/// This tests the high bit of this APInt to determine if it is clear.
///
/// \returns true if this APInt has its sign bit clear, false otherwise.
bool isSignBitClear() const { return !isSignBitSet(); }

/// Determine if this APInt Value is positive.
///
/// This tests if the value of this APInt is positive (> 0). Note
/// that 0 is not a positive value.
///
/// \returns true if this APInt is positive.
bool isStrictlyPositive() const { return isNonNegative() && !isNullValue(); }

/// Determine if this APInt Value is non-positive (<= 0).
///
/// \returns true if this APInt is non-positive.
bool isNonPositive() const { return !isStrictlyPositive(); }

/// Determine if all bits are set
///
/// This checks to see if the value has all bits of the APInt are set or not.
bool isAllOnesValue() const {
  if (isSingleWord())
    return U.VAL == WORDTYPE_MAX >> (APINT_BITS_PER_WORD - BitWidth);
  return countTrailingOnesSlowCase() == BitWidth;
}

/// Determine if all bits are clear
///
/// This checks to see if the value has all bits of the APInt are clear or
/// not.
bool isNullValue() const { return !*this; }

/// Determine if this is a value of 1.
///
/// This checks to see if the value of this APInt is one.
bool isOneValue() const {
  if (isSingleWord())
    return U.VAL == 1;
  return countLeadingZerosSlowCase() == BitWidth - 1;
}

/// Determine if this is the largest unsigned value.
///
/// This checks to see if the value of this APInt is the maximum unsigned
/// value for the APInt's bit width.
bool isMaxValue() const { return isAllOnesValue(); }

/// Determine if this is the largest signed value.
///
/// This checks to see if the value of this APInt is the maximum signed
/// value for the APInt's bit width.
bool isMaxSignedValue() const {
  if (isSingleWord())
    return U.VAL == ((WordType(1) << (BitWidth - 1)) - 1);
  return !isNegative() && countTrailingOnesSlowCase() == BitWidth - 1;
}

/// Determine if this is the smallest unsigned value.
///
/// This checks to see if the value of this APInt is the minimum unsigned
/// value for the APInt's bit width.
bool isMinValue() const { return isNullValue(); }

/// Determine if this is the smallest signed value.
///
/// This checks to see if the value of this APInt is the minimum signed
/// value for the APInt's bit width.
bool isMinSignedValue() const {
  if (isSingleWord())
    return U.VAL == (WordType(1) << (BitWidth - 1));
  return isNegative() && countTrailingZerosSlowCase() == BitWidth - 1;
}

/// Check if this APInt has an N-bits unsigned integer value.
bool isIntN(unsigned N) const {
  assert(N && "N == 0 ???")((void)0);
  return getActiveBits() <= N;
}

/// Check if this APInt has an N-bits signed integer value.
bool isSignedIntN(unsigned N) const {
  assert(N && "N == 0 ???")((void)0);
  return getMinSignedBits() <= N;
}

/// Check if this APInt's value is a power of two greater than zero.
///
/// \returns true if the argument APInt value is a power of two > 0.
bool isPowerOf2() const {
  if (isSingleWord())
    return isPowerOf2_64(U.VAL);
  return countPopulationSlowCase() == 1;
}

/// Check if the APInt's value is returned by getSignMask.
///
/// \returns true if this is the value returned by getSignMask.
bool isSignMask() const { return isMinSignedValue(); }

/// Convert APInt to a boolean value.
///
/// This converts the APInt to a boolean value as a test against zero.
bool getBoolValue() const { return !!*this; }

/// If this value is smaller than the specified limit, return it, otherwise
/// return the limit value.  This causes the value to saturate to the limit.
uint64_t getLimitedValue(uint64_t Limit = UINT64_MAX0xffffffffffffffffULL) const {
  return ugt(Limit) ? Limit : getZExtValue();
52
←
Assuming the condition is true→
53
←
'?' condition is true→
54
←
Returning the value 18446744073709551615→
}

/// Check if the APInt consists of a repeated bit pattern.
///
/// e.g. 0x01010101 satisfies isSplat(8).
/// \param SplatSizeInBits The size of the pattern in bits. Must divide bit
/// width without remainder.
bool isSplat(unsigned SplatSizeInBits) const;

/// \returns true if this APInt value is a sequence of \param numBits ones
/// starting at the least significant bit with the remainder zero.
bool isMask(unsigned numBits) const {
  assert(numBits != 0 && "numBits must be non-zero")((void)0);
  assert(numBits <= BitWidth && "numBits out of range")((void)0);
  if (isSingleWord())
    return U.VAL == (WORDTYPE_MAX >> (APINT_BITS_PER_WORD - numBits));
  unsigned Ones = countTrailingOnesSlowCase();
  return (numBits == Ones) &&
         ((Ones + countLeadingZerosSlowCase()) == BitWidth);
}

/// \returns true if this APInt is a non-empty sequence of ones starting at
/// the least significant bit with the remainder zero.
/// Ex. isMask(0x0000FFFFU) == true.
bool isMask() const {
  if (isSingleWord())
    return isMask_64(U.VAL);
  unsigned Ones = countTrailingOnesSlowCase();
  return (Ones > 0) && ((Ones + countLeadingZerosSlowCase()) == BitWidth);
}

/// Return true if this APInt value contains a sequence of ones with
/// the remainder zero.
bool isShiftedMask() const {
  if (isSingleWord())
    return isShiftedMask_64(U.VAL);
  unsigned Ones = countPopulationSlowCase();
  unsigned LeadZ = countLeadingZerosSlowCase();
  return (Ones + LeadZ + countTrailingZeros()) == BitWidth;
}

/// @}
/// \name Value Generators
/// @{

/// Gets maximum unsigned value of APInt for specific bit width.
static APInt getMaxValue(unsigned numBits) {
  return getAllOnesValue(numBits);
}

/// Gets maximum signed value of APInt for a specific bit width.
static APInt getSignedMaxValue(unsigned numBits) {
  APInt API = getAllOnesValue(numBits);
  API.clearBit(numBits - 1);
  return API;
}

/// Gets minimum unsigned value of APInt for a specific bit width.
static APInt getMinValue(unsigned numBits) { return APInt(numBits, 0); }

/// Gets minimum signed value of APInt for a specific bit width.
static APInt getSignedMinValue(unsigned numBits) {
  APInt API(numBits, 0);
  API.setBit(numBits - 1);
  return API;
}

/// Get the SignMask for a specific bit width.
///
/// This is just a wrapper function of getSignedMinValue(), and it helps code
/// readability when we want to get a SignMask.
static APInt getSignMask(unsigned BitWidth) {
  return getSignedMinValue(BitWidth);
}

/// Get the all-ones value.
///
/// \returns the all-ones value for an APInt of the specified bit-width.
static APInt getAllOnesValue(unsigned numBits) {
  return APInt(numBits, WORDTYPE_MAX, true);
}

/// Get the '0' value.
///
/// \returns the '0' value for an APInt of the specified bit-width.
static APInt getNullValue(unsigned numBits) { return APInt(numBits, 0); }

/// Compute an APInt containing numBits highbits from this APInt.
///
/// Get an APInt with the same BitWidth as this APInt, just zero mask
/// the low bits and right shift to the least significant bit.
///
/// \returns the high "numBits" bits of this APInt.
APInt getHiBits(unsigned numBits) const;

/// Compute an APInt containing numBits lowbits from this APInt.
///
/// Get an APInt with the same BitWidth as this APInt, just zero mask
/// the high bits.
///
/// \returns the low "numBits" bits of this APInt.
APInt getLoBits(unsigned numBits) const;

/// Return an APInt with exactly one bit set in the result.
static APInt getOneBitSet(unsigned numBits, unsigned BitNo) {
  APInt Res(numBits, 0);
  Res.setBit(BitNo);
  return Res;
}

/// Get a value with a block of bits set.
///
/// Constructs an APInt value that has a contiguous range of bits set. The
/// bits from loBit (inclusive) to hiBit (exclusive) will be set. All other
/// bits will be zero. For example, with parameters(32, 0, 16) you would get
/// 0x0000FFFF. Please call getBitsSetWithWrap if \p loBit may be greater than
/// \p hiBit.
///
/// \param numBits the intended bit width of the result
/// \param loBit the index of the lowest bit set.
/// \param hiBit the index of the highest bit set.
///
/// \returns An APInt value with the requested bits set.
static APInt getBitsSet(unsigned numBits, unsigned loBit, unsigned hiBit) {
  assert(loBit <= hiBit && "loBit greater than hiBit")((void)0);
  APInt Res(numBits, 0);
  Res.setBits(loBit, hiBit);
  return Res;
}

/// Wrap version of getBitsSet.
/// If \p hiBit is bigger than \p loBit, this is same with getBitsSet.
/// If \p hiBit is not bigger than \p loBit, the set bits "wrap". For example,
/// with parameters (32, 28, 4), you would get 0xF000000F.
/// If \p hiBit is equal to \p loBit, you would get a result with all bits
/// set.
static APInt getBitsSetWithWrap(unsigned numBits, unsigned loBit,
                                unsigned hiBit) {
  APInt Res(numBits, 0);
  Res.setBitsWithWrap(loBit, hiBit);
  return Res;
}

/// Get a value with upper bits starting at loBit set.
///
/// Constructs an APInt value that has a contiguous range of bits set. The
/// bits from loBit (inclusive) to numBits (exclusive) will be set. All other
/// bits will be zero. For example, with parameters(32, 12) you would get
/// 0xFFFFF000.
///
/// \param numBits the intended bit width of the result
/// \param loBit the index of the lowest bit to set.
///
/// \returns An APInt value with the requested bits set.
static APInt getBitsSetFrom(unsigned numBits, unsigned loBit) {
  APInt Res(numBits, 0);
  Res.setBitsFrom(loBit);
  return Res;
}

/// Get a value with high bits set
///
/// Constructs an APInt value that has the top hiBitsSet bits set.
///
/// \param numBits the bitwidth of the result
/// \param hiBitsSet the number of high-order bits set in the result.
static APInt getHighBitsSet(unsigned numBits, unsigned hiBitsSet) {
  APInt Res(numBits, 0);
  Res.setHighBits(hiBitsSet);
  return Res;
}

/// Get a value with low bits set
///
/// Constructs an APInt value that has the bottom loBitsSet bits set.
///
/// \param numBits the bitwidth of the result
/// \param loBitsSet the number of low-order bits set in the result.
static APInt getLowBitsSet(unsigned numBits, unsigned loBitsSet) {
  APInt Res(numBits, 0);
  Res.setLowBits(loBitsSet);
  return Res;
}

/// Return a value containing V broadcasted over NewLen bits.
static APInt getSplat(unsigned NewLen, const APInt &V);

/// Determine if two APInts have the same value, after zero-extending
/// one of them (if needed!) to ensure that the bit-widths match.
static bool isSameValue(const APInt &I1, const APInt &I2) {
  if (I1.getBitWidth() == I2.getBitWidth())
    return I1 == I2;

  if (I1.getBitWidth() > I2.getBitWidth())
    return I1 == I2.zext(I1.getBitWidth());

  return I1.zext(I2.getBitWidth()) == I2;
}

/// Overload to compute a hash_code for an APInt value.
friend hash_code hash_value(const APInt &Arg);

/// This function returns a pointer to the internal storage of the APInt.
/// This is useful for writing out the APInt in binary form without any
/// conversions.
const uint64_t *getRawData() const {
  if (isSingleWord())
    return &U.VAL;
  return &U.pVal[0];
}

/// @}
/// \name Unary Operators
/// @{

/// Postfix increment operator.
///
/// Increments *this by 1.
///
/// \returns a new APInt value representing the original value of *this.
const APInt operator++(int) {
  APInt API(*this);
  ++(*this);
  return API;
}

/// Prefix increment operator.
///
/// \returns *this incremented by one
APInt &operator++();

/// Postfix decrement operator.
///
/// Decrements *this by 1.
///
/// \returns a new APInt value representing the original value of *this.
const APInt operator--(int) {
  APInt API(*this);
  --(*this);
  return API;
}

/// Prefix decrement operator.
///
/// \returns *this decremented by one.
APInt &operator--();

/// Logical negation operator.
///
/// Performs logical negation operation on this APInt.
///
/// \returns true if *this is zero, false otherwise.
bool operator!() const {
  if (isSingleWord())
    return U.VAL == 0;
  return countLeadingZerosSlowCase() == BitWidth;
}

/// @}
/// \name Assignment Operators
/// @{

/// Copy assignment operator.
///
/// \returns *this after assignment of RHS.
APInt &operator=(const APInt &RHS) {
  // If the bitwidths are the same, we can avoid mucking with memory
  if (isSingleWord() && RHS.isSingleWord()) {
    U.VAL = RHS.U.VAL;
    BitWidth = RHS.BitWidth;
    return clearUnusedBits();
  }

  AssignSlowCase(RHS);
  return *this;
}

/// Move assignment operator.
APInt &operator=(APInt &&that) {
768#ifdef EXPENSIVE_CHECKS
  // Some std::shuffle implementations still do self-assignment.
  if (this == &that)
    return *this;
772#endif
  assert(this != &that && "Self-move not supported")((void)0);
  if (!isSingleWord())
    delete[] U.pVal;

  // Use memcpy so that type based alias analysis sees both VAL and pVal
  // as modified.
  memcpy(&U, &that.U, sizeof(U));

  BitWidth = that.BitWidth;
  that.BitWidth = 0;

  return *this;
}

/// Assignment operator.
///
/// The RHS value is assigned to *this. If the significant bits in RHS exceed
/// the bit width, the excess bits are truncated. If the bit width is larger
/// than 64, the value is zero filled in the unspecified high order bits.
///
/// \returns *this after assignment of RHS value.
APInt &operator=(uint64_t RHS) {
  if (isSingleWord()) {
    U.VAL = RHS;
    return clearUnusedBits();
  }
  U.pVal[0] = RHS;
  memset(U.pVal + 1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
  return *this;
}

/// Bitwise AND assignment operator.
///
/// Performs a bitwise AND operation on this APInt and RHS. The result is
/// assigned to *this.
///
/// \returns *this after ANDing with RHS.
APInt &operator&=(const APInt &RHS) {
  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")((void)0);
  if (isSingleWord())
    U.VAL &= RHS.U.VAL;
  else
    AndAssignSlowCase(RHS);
  return *this;
}

/// Bitwise AND assignment operator.
///
/// Performs a bitwise AND operation on this APInt and RHS. RHS is
/// logically zero-extended or truncated to match the bit-width of
/// the LHS.
APInt &operator&=(uint64_t RHS) {
  if (isSingleWord()) {
    U.VAL &= RHS;
    return *this;
  }
  U.pVal[0] &= RHS;
  memset(U.pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
  return *this;
}

/// Bitwise OR assignment operator.
///
/// Performs a bitwise OR operation on this APInt and RHS. The result is
/// assigned *this;
///
/// \returns *this after ORing with RHS.
APInt &operator|=(const APInt &RHS) {
  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")((void)0);
  if (isSingleWord())
    U.VAL |= RHS.U.VAL;
  else
    OrAssignSlowCase(RHS);
  return *this;
}

/// Bitwise OR assignment operator.
///
/// Performs a bitwise OR operation on this APInt and RHS. RHS is
/// logically zero-extended or truncated to match the bit-width of
/// the LHS.
APInt &operator|=(uint64_t RHS) {
  if (isSingleWord()) {
    U.VAL |= RHS;
    return clearUnusedBits();
  }
  U.pVal[0] |= RHS;
  return *this;
}

/// Bitwise XOR assignment operator.
///
/// Performs a bitwise XOR operation on this APInt and RHS. The result is
/// assigned to *this.
///
/// \returns *this after XORing with RHS.
APInt &operator^=(const APInt &RHS) {
  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")((void)0);
  if (isSingleWord())
    U.VAL ^= RHS.U.VAL;
  else
    XorAssignSlowCase(RHS);
  return *this;
}

/// Bitwise XOR assignment operator.
///
/// Performs a bitwise XOR operation on this APInt and RHS. RHS is
/// logically zero-extended or truncated to match the bit-width of
/// the LHS.
APInt &operator^=(uint64_t RHS) {
  if (isSingleWord()) {
    U.VAL ^= RHS;
    return clearUnusedBits();
  }
  U.pVal[0] ^= RHS;
  return *this;
}

/// Multiplication assignment operator.
///
/// Multiplies this APInt by RHS and assigns the result to *this.
///
/// \returns *this
APInt &operator*=(const APInt &RHS);
APInt &operator*=(uint64_t RHS);

/// Addition assignment operator.
///
/// Adds RHS to *this and assigns the result to *this.
///
/// \returns *this
APInt &operator+=(const APInt &RHS);
APInt &operator+=(uint64_t RHS);

/// Subtraction assignment operator.
///
/// Subtracts RHS from *this and assigns the result to *this.
///
/// \returns *this
APInt &operator-=(const APInt &RHS);
APInt &operator-=(uint64_t RHS);

/// Left-shift assignment function.
///
/// Shifts *this left by shiftAmt and assigns the result to *this.
///
/// \returns *this after shifting left by ShiftAmt
APInt &operator<<=(unsigned ShiftAmt) {
  assert(ShiftAmt <= BitWidth && "Invalid shift amount")((void)0);
  if (isSingleWord()) {
58
←
Calling 'APInt::isSingleWord'→
61
←
Returning from 'APInt::isSingleWord'→
62
←
Taking true branch→
    if (ShiftAmt62.1
'ShiftAmt' is not equal to field 'BitWidth'
1
'ShiftAmt' is not equal to field 'BitWidth'
 == BitWidth)
63
←
Taking false branch→
      U.VAL = 0;
    else
      U.VAL <<= ShiftAmt;
64
←
Assigned value is garbage or undefined
    return clearUnusedBits();
  }
  shlSlowCase(ShiftAmt);
  return *this;
}

/// Left-shift assignment function.
///
/// Shifts *this left by shiftAmt and assigns the result to *this.
///
/// \returns *this after shifting left by ShiftAmt
APInt &operator<<=(const APInt &ShiftAmt);

/// @}
/// \name Binary Operators
/// @{

/// Multiplication operator.
///
/// Multiplies this APInt by RHS and returns the result.
APInt operator*(const APInt &RHS) const;

/// Left logical shift operator.
///
/// Shifts this APInt left by \p Bits and returns the result.
APInt operator<<(unsigned Bits) const { return shl(Bits); }

/// Left logical shift operator.
///
/// Shifts this APInt left by \p Bits and returns the result.
APInt operator<<(const APInt &Bits) const { return shl(Bits); }

/// Arithmetic right-shift function.
///
/// Arithmetic right-shift this APInt by shiftAmt.
APInt ashr(unsigned ShiftAmt) const {
  APInt R(*this);
  R.ashrInPlace(ShiftAmt);
  return R;
}

/// Arithmetic right-shift this APInt by ShiftAmt in place.
void ashrInPlace(unsigned ShiftAmt) {
  assert(ShiftAmt <= BitWidth && "Invalid shift amount")((void)0);
  if (isSingleWord()) {
    int64_t SExtVAL = SignExtend64(U.VAL, BitWidth);
    if (ShiftAmt == BitWidth)
      U.VAL = SExtVAL >> (APINT_BITS_PER_WORD - 1); // Fill with sign bit.
    else
      U.VAL = SExtVAL >> ShiftAmt;
    clearUnusedBits();
    return;
  }
  ashrSlowCase(ShiftAmt);
}

/// Logical right-shift function.
///
/// Logical right-shift this APInt by shiftAmt.
APInt lshr(unsigned shiftAmt) const {
  APInt R(*this);
  R.lshrInPlace(shiftAmt);
  return R;
}

/// Logical right-shift this APInt by ShiftAmt in place.
void lshrInPlace(unsigned ShiftAmt) {
  assert(ShiftAmt <= BitWidth && "Invalid shift amount")((void)0);
  if (isSingleWord()) {
    if (ShiftAmt == BitWidth)
      U.VAL = 0;
    else
      U.VAL >>= ShiftAmt;
    return;
  }
  lshrSlowCase(ShiftAmt);
}

/// Left-shift function.
///
/// Left-shift this APInt by shiftAmt.
APInt shl(unsigned shiftAmt) const {
  APInt R(*this);
  R <<= shiftAmt;
  return R;
}

/// Rotate left by rotateAmt.
APInt rotl(unsigned rotateAmt) const;

/// Rotate right by rotateAmt.
APInt rotr(unsigned rotateAmt) const;

/// Arithmetic right-shift function.
///
/// Arithmetic right-shift this APInt by shiftAmt.
APInt ashr(const APInt &ShiftAmt) const {
  APInt R(*this);
  R.ashrInPlace(ShiftAmt);
  return R;
}

/// Arithmetic right-shift this APInt by shiftAmt in place.
void ashrInPlace(const APInt &shiftAmt);

/// Logical right-shift function.
///
/// Logical right-shift this APInt by shiftAmt.
APInt lshr(const APInt &ShiftAmt) const {
  APInt R(*this);
  R.lshrInPlace(ShiftAmt);
  return R;
}

/// Logical right-shift this APInt by ShiftAmt in place.
void lshrInPlace(const APInt &ShiftAmt);

/// Left-shift function.
///
/// Left-shift this APInt by shiftAmt.
APInt shl(const APInt &ShiftAmt) const {
  APInt R(*this);
  R <<= ShiftAmt;
  return R;
}

/// Rotate left by rotateAmt.
APInt rotl(const APInt &rotateAmt) const;

/// Rotate right by rotateAmt.
APInt rotr(const APInt &rotateAmt) const;

/// Unsigned division operation.
///
/// Perform an unsigned divide operation on this APInt by RHS. Both this and
/// RHS are treated as unsigned quantities for purposes of this division.
///
/// \returns a new APInt value containing the division result, rounded towards
/// zero.
APInt udiv(const APInt &RHS) const;
APInt udiv(uint64_t RHS) const;

/// Signed division function for APInt.
///
/// Signed divide this APInt by APInt RHS.
///
/// The result is rounded towards zero.
APInt sdiv(const APInt &RHS) const;
APInt sdiv(int64_t RHS) const;

/// Unsigned remainder operation.
///
/// Perform an unsigned remainder operation on this APInt with RHS being the
/// divisor. Both this and RHS are treated as unsigned quantities for purposes
/// of this operation. Note that this is a true remainder operation and not a
/// modulo operation because the sign follows the sign of the dividend which
/// is *this.
///
/// \returns a new APInt value containing the remainder result
APInt urem(const APInt &RHS) const;
uint64_t urem(uint64_t RHS) const;

/// Function for signed remainder operation.
///
/// Signed remainder operation on APInt.
APInt srem(const APInt &RHS) const;
int64_t srem(int64_t RHS) const;

/// Dual division/remainder interface.
///
/// Sometimes it is convenient to divide two APInt values and obtain both the
/// quotient and remainder. This function does both operations in the same
/// computation making it a little more efficient. The pair of input arguments
/// may overlap with the pair of output arguments. It is safe to call
/// udivrem(X, Y, X, Y), for example.
static void udivrem(const APInt &LHS, const APInt &RHS, APInt &Quotient,
                    APInt &Remainder);
static void udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient,
                    uint64_t &Remainder);

static void sdivrem(const APInt &LHS, const APInt &RHS, APInt &Quotient,
                    APInt &Remainder);
static void sdivrem(const APInt &LHS, int64_t RHS, APInt &Quotient,
                    int64_t &Remainder);

// Operations that return overflow indicators.
APInt sadd_ov(const APInt &RHS, bool &Overflow) const;
APInt uadd_ov(const APInt &RHS, bool &Overflow) const;
APInt ssub_ov(const APInt &RHS, bool &Overflow) const;
APInt usub_ov(const APInt &RHS, bool &Overflow) const;
APInt sdiv_ov(const APInt &RHS, bool &Overflow) const;
APInt smul_ov(const APInt &RHS, bool &Overflow) const;
APInt umul_ov(const APInt &RHS, bool &Overflow) const;
APInt sshl_ov(const APInt &Amt, bool &Overflow) const;
APInt ushl_ov(const APInt &Amt, bool &Overflow) const;

// Operations that saturate
APInt sadd_sat(const APInt &RHS) const;
APInt uadd_sat(const APInt &RHS) const;
APInt ssub_sat(const APInt &RHS) const;
APInt usub_sat(const APInt &RHS) const;
APInt smul_sat(const APInt &RHS) const;
APInt umul_sat(const APInt &RHS) const;
APInt sshl_sat(const APInt &RHS) const;
APInt ushl_sat(const APInt &RHS) const;

/// Array-indexing support.
///
/// \returns the bit value at bitPosition
bool operator[](unsigned bitPosition) const {
  assert(bitPosition < getBitWidth() && "Bit position out of bounds!")((void)0);
  return (maskBit(bitPosition) & getWord(bitPosition)) != 0;
}

/// @}
/// \name Comparison Operators
/// @{

/// Equality operator.
///
/// Compares this APInt with RHS for the validity of the equality
/// relationship.
bool operator==(const APInt &RHS) const {
  assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths")((void)0);
  if (isSingleWord())
    return U.VAL == RHS.U.VAL;
  return EqualSlowCase(RHS);
}

/// Equality operator.
///
/// Compares this APInt with a uint64_t for the validity of the equality
/// relationship.
///
/// \returns true if *this == Val
bool operator==(uint64_t Val) const {
  return (isSingleWord() || getActiveBits() <= 64) && getZExtValue() == Val;
}

/// Equality comparison.
///
/// Compares this APInt with RHS for the validity of the equality
/// relationship.
///
/// \returns true if *this == Val
bool eq(const APInt &RHS) const { return (*this) == RHS; }

/// Inequality operator.
///
/// Compares this APInt with RHS for the validity of the inequality
/// relationship.
///
/// \returns true if *this != Val
bool operator!=(const APInt &RHS) const { return !((*this) == RHS); }

/// Inequality operator.
///
/// Compares this APInt with a uint64_t for the validity of the inequality
/// relationship.
///
/// \returns true if *this != Val
bool operator!=(uint64_t Val) const { return !((*this) == Val); }

/// Inequality comparison
///
/// Compares this APInt with RHS for the validity of the inequality
/// relationship.
///
/// \returns true if *this != Val
bool ne(const APInt &RHS) const { return !((*this) == RHS); }

/// Unsigned less than comparison
///
/// Regards both *this and RHS as unsigned quantities and compares them for
/// the validity of the less-than relationship.
///
/// \returns true if *this < RHS when both are considered unsigned.
bool ult(const APInt &RHS) const { return compare(RHS) < 0; }

/// Unsigned less than comparison
///
/// Regards both *this as an unsigned quantity and compares it with RHS for
/// the validity of the less-than relationship.
///
/// \returns true if *this < RHS when considered unsigned.
bool ult(uint64_t RHS) const {
  // Only need to check active bits if not a single word.
  return (isSingleWord() || getActiveBits() <= 64) && getZExtValue() < RHS;
}

/// Signed less than comparison
///
/// Regards both *this and RHS as signed quantities and compares them for
/// validity of the less-than relationship.
///
/// \returns true if *this < RHS when both are considered signed.
bool slt(const APInt &RHS) const { return compareSigned(RHS) < 0; }

/// Signed less than comparison
///
/// Regards both *this as a signed quantity and compares it with RHS for
/// the validity of the less-than relationship.
///
/// \returns true if *this < RHS when considered signed.
bool slt(int64_t RHS) const {
  return (!isSingleWord() && getMinSignedBits() > 64) ? isNegative()
                                                      : getSExtValue() < RHS;
}

/// Unsigned less or equal comparison
///
/// Regards both *this and RHS as unsigned quantities and compares them for
/// validity of the less-or-equal relationship.
///
/// \returns true if *this <= RHS when both are considered unsigned.
bool ule(const APInt &RHS) const { return compare(RHS) <= 0; }

/// Unsigned less or equal comparison
///
/// Regards both *this as an unsigned quantity and compares it with RHS for
/// the validity of the less-or-equal relationship.
///
/// \returns true if *this <= RHS when considered unsigned.
bool ule(uint64_t RHS) const { return !ugt(RHS); }

/// Signed less or equal comparison
///
/// Regards both *this and RHS as signed quantities and compares them for
/// validity of the less-or-equal relationship.
///
/// \returns true if *this <= RHS when both are considered signed.
bool sle(const APInt &RHS) const { return compareSigned(RHS) <= 0; }

/// Signed less or equal comparison
///
/// Regards both *this as a signed quantity and compares it with RHS for the
/// validity of the less-or-equal relationship.
///
/// \returns true if *this <= RHS when considered signed.
bool sle(uint64_t RHS) const { return !sgt(RHS); }

/// Unsigned greater than comparison
///
/// Regards both *this and RHS as unsigned quantities and compares them for
/// the validity of the greater-than relationship.
///
/// \returns true if *this > RHS when both are considered unsigned.
bool ugt(const APInt &RHS) const { return !ule(RHS); }

/// Unsigned greater than comparison
///
/// Regards both *this as an unsigned quantity and compares it with RHS for
/// the validity of the greater-than relationship.
///
/// \returns true if *this > RHS when considered unsigned.
bool ugt(uint64_t RHS) const {
  // Only need to check active bits if not a single word.
  return (!isSingleWord() && getActiveBits() > 64) || getZExtValue() > RHS;
}

/// Signed greater than comparison
///
/// Regards both *this and RHS as signed quantities and compares them for the
/// validity of the greater-than relationship.
///
/// \returns true if *this > RHS when both are considered signed.
bool sgt(const APInt &RHS) const { return !sle(RHS); }

/// Signed greater than comparison
///
/// Regards both *this as a signed quantity and compares it with RHS for
/// the validity of the greater-than relationship.
///
/// \returns true if *this > RHS when considered signed.
bool sgt(int64_t RHS) const {
  return (!isSingleWord() && getMinSignedBits() > 64) ? !isNegative()
                                                      : getSExtValue() > RHS;
}

/// Unsigned greater or equal comparison
///
/// Regards both *this and RHS as unsigned quantities and compares them for
/// validity of the greater-or-equal relationship.
///
/// \returns true if *this >= RHS when both are considered unsigned.
bool uge(const APInt &RHS) const { return !ult(RHS); }

/// Unsigned greater or equal comparison
///
/// Regards both *this as an unsigned quantity and compares it with RHS for
/// the validity of the greater-or-equal relationship.
///
/// \returns true if *this >= RHS when considered unsigned.
bool uge(uint64_t RHS) const { return !ult(RHS); }

/// Signed greater or equal comparison
///
/// Regards both *this and RHS as signed quantities and compares them for
/// validity of the greater-or-equal relationship.
///
/// \returns true if *this >= RHS when both are considered signed.
bool sge(const APInt &RHS) const { return !slt(RHS); }

/// Signed greater or equal comparison
///
/// Regards both *this as a signed quantity and compares it with RHS for
/// the validity of the greater-or-equal relationship.
///
/// \returns true if *this >= RHS when considered signed.
bool sge(int64_t RHS) const { return !slt(RHS); }

/// This operation tests if there are any pairs of corresponding bits
/// between this APInt and RHS that are both set.
bool intersects(const APInt &RHS) const {
  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")((void)0);
  if (isSingleWord())
    return (U.VAL & RHS.U.VAL) != 0;
  return intersectsSlowCase(RHS);
}

/// This operation checks that all bits set in this APInt are also set in RHS.
bool isSubsetOf(const APInt &RHS) const {
  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")((void)0);
  if (isSingleWord())
    return (U.VAL & ~RHS.U.VAL) == 0;
  return isSubsetOfSlowCase(RHS);
}

/// @}
/// \name Resizing Operators
/// @{

/// Truncate to new width.
///
/// Truncate the APInt to a specified width. It is an error to specify a width
/// that is greater than or equal to the current width.
APInt trunc(unsigned width) const;

/// Truncate to new width with unsigned saturation.
///
/// If the APInt, treated as unsigned integer, can be losslessly truncated to
/// the new bitwidth, then return truncated APInt. Else, return max value.
APInt truncUSat(unsigned width) const;

/// Truncate to new width with signed saturation.
///
/// If this APInt, treated as signed integer, can be losslessly truncated to
/// the new bitwidth, then return truncated APInt. Else, return either
/// signed min value if the APInt was negative, or signed max value.
APInt truncSSat(unsigned width) const;

/// Sign extend to a new width.
///
/// This operation sign extends the APInt to a new width. If the high order
/// bit is set, the fill on the left will be done with 1 bits, otherwise zero.
/// It is an error to specify a width that is less than or equal to the
/// current width.
APInt sext(unsigned width) const;

/// Zero extend to a new width.
///
/// This operation zero extends the APInt to a new width. The high order bits
/// are filled with 0 bits.  It is an error to specify a width that is less
/// than or equal to the current width.
APInt zext(unsigned width) const;

/// Sign extend or truncate to width
///
/// Make this APInt have the bit width given by \p width. The value is sign
/// extended, truncated, or left alone to make it that width.
APInt sextOrTrunc(unsigned width) const;

/// Zero extend or truncate to width
///
/// Make this APInt have the bit width given by \p width. The value is zero
/// extended, truncated, or left alone to make it that width.
APInt zextOrTrunc(unsigned width) const;

/// Truncate to width
///
/// Make this APInt have the bit width given by \p width. The value is
/// truncated or left alone to make it that width.
APInt truncOrSelf(unsigned width) const;

/// Sign extend or truncate to width
///
/// Make this APInt have the bit width given by \p width. The value is sign
/// extended, or left alone to make it that width.
APInt sextOrSelf(unsigned width) const;

/// Zero extend or truncate to width
///
/// Make this APInt have the bit width given by \p width. The value is zero
/// extended, or left alone to make it that width.
APInt zextOrSelf(unsigned width) const;

/// @}
/// \name Bit Manipulation Operators
/// @{

/// Set every bit to 1.
void setAllBits() {
  if (isSingleWord())
    U.VAL = WORDTYPE_MAX;
  else
    // Set all the bits in all the words.
    memset(U.pVal, -1, getNumWords() * APINT_WORD_SIZE);
  // Clear the unused ones
  clearUnusedBits();
}

/// Set a given bit to 1.
///
/// Set the given bit to 1 whose position is given as "bitPosition".
void setBit(unsigned BitPosition) {
  assert(BitPosition < BitWidth && "BitPosition out of range")((void)0);
  WordType Mask = maskBit(BitPosition);
  if (isSingleWord())
    U.VAL |= Mask;
  else
    U.pVal[whichWord(BitPosition)] |= Mask;
}

/// Set the sign bit to 1.
void setSignBit() {
  setBit(BitWidth - 1);
}

/// Set a given bit to a given value.
void setBitVal(unsigned BitPosition, bool BitValue) {
  if (BitValue)
    setBit(BitPosition);
  else
    clearBit(BitPosition);
}

/// Set the bits from loBit (inclusive) to hiBit (exclusive) to 1.
/// This function handles "wrap" case when \p loBit >= \p hiBit, and calls
/// setBits when \p loBit < \p hiBit.
/// For \p loBit == \p hiBit wrap case, set every bit to 1.
void setBitsWithWrap(unsigned loBit, unsigned hiBit) {
  assert(hiBit <= BitWidth && "hiBit out of range")((void)0);
  assert(loBit <= BitWidth && "loBit out of range")((void)0);
  if (loBit < hiBit) {
    setBits(loBit, hiBit);
    return;
  }
  setLowBits(hiBit);
  setHighBits(BitWidth - loBit);
}

/// Set the bits from loBit (inclusive) to hiBit (exclusive) to 1.
/// This function handles case when \p loBit <= \p hiBit.
void setBits(unsigned loBit, unsigned hiBit) {
  assert(hiBit <= BitWidth && "hiBit out of range")((void)0);
  assert(loBit <= BitWidth && "loBit out of range")((void)0);
  assert(loBit <= hiBit && "loBit greater than hiBit")((void)0);
  if (loBit == hiBit)
    return;
  if (loBit < APINT_BITS_PER_WORD && hiBit <= APINT_BITS_PER_WORD) {
    uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - (hiBit - loBit));
    mask <<= loBit;
    if (isSingleWord())
      U.VAL |= mask;
    else
      U.pVal[0] |= mask;
  } else {
    setBitsSlowCase(loBit, hiBit);
  }
}

/// Set the top bits starting from loBit.
void setBitsFrom(unsigned loBit) {
  return setBits(loBit, BitWidth);
}

/// Set the bottom loBits bits.
void setLowBits(unsigned loBits) {
  return setBits(0, loBits);
}

/// Set the top hiBits bits.
void setHighBits(unsigned hiBits) {
  return setBits(BitWidth - hiBits, BitWidth);
}

/// Set every bit to 0.
void clearAllBits() {
  if (isSingleWord())
    U.VAL = 0;
  else
    memset(U.pVal, 0, getNumWords() * APINT_WORD_SIZE);
}

/// Set a given bit to 0.
///
/// Set the given bit to 0 whose position is given as "bitPosition".
void clearBit(unsigned BitPosition) {
  assert(BitPosition < BitWidth && "BitPosition out of range")((void)0);
  WordType Mask = ~maskBit(BitPosition);
  if (isSingleWord())
    U.VAL &= Mask;
  else
    U.pVal[whichWord(BitPosition)] &= Mask;
}

/// Set bottom loBits bits to 0.
void clearLowBits(unsigned loBits) {
  assert(loBits <= BitWidth && "More bits than bitwidth")((void)0);
  APInt Keep = getHighBitsSet(BitWidth, BitWidth - loBits);
  *this &= Keep;
}

/// Set the sign bit to 0.
void clearSignBit() {
  clearBit(BitWidth - 1);
}

/// Toggle every bit to its opposite value.
void flipAllBits() {
  if (isSingleWord()) {
    U.VAL ^= WORDTYPE_MAX;
    clearUnusedBits();
  } else {
    flipAllBitsSlowCase();
  }
}

/// Toggles a given bit to its opposite value.
///
/// Toggle a given bit to its opposite value whose position is given
/// as "bitPosition".
void flipBit(unsigned bitPosition);

/// Negate this APInt in place.
void negate() {
  flipAllBits();
  ++(*this);
}

/// Insert the bits from a smaller APInt starting at bitPosition.
void insertBits(const APInt &SubBits, unsigned bitPosition);
void insertBits(uint64_t SubBits, unsigned bitPosition, unsigned numBits);

/// Return an APInt with the extracted bits [bitPosition,bitPosition+numBits).
APInt extractBits(unsigned numBits, unsigned bitPosition) const;
uint64_t extractBitsAsZExtValue(unsigned numBits, unsigned bitPosition) const;

/// @}
/// \name Value Characterization Functions
/// @{

/// Return the number of bits in the APInt.
unsigned getBitWidth() const { return BitWidth; }

/// Get the number of words.
///
/// Here one word's bitwidth equals to that of uint64_t.
///
/// \returns the number of words to hold the integer value of this APInt.
unsigned getNumWords() const { return getNumWords(BitWidth); }

/// Get the number of words.
///
/// *NOTE* Here one word's bitwidth equals to that of uint64_t.
///
/// \returns the number of words to hold the integer value with a given bit
/// width.
static unsigned getNumWords(unsigned BitWidth) {
  return ((uint64_t)BitWidth + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
}

/// Compute the number of active bits in the value
///
/// This function returns the number of active bits which is defined as the
/// bit width minus the number of leading zeros. This is used in several
/// computations to see how "wide" the value is.
unsigned getActiveBits() const { return BitWidth - countLeadingZeros(); }

/// Compute the number of active words in the value of this APInt.
///
/// This is used in conjunction with getActiveData to extract the raw value of
/// the APInt.
unsigned getActiveWords() const {
  unsigned numActiveBits = getActiveBits();
  return numActiveBits ? whichWord(numActiveBits - 1) + 1 : 1;
}

/// Get the minimum bit size for this signed APInt
///
/// Computes the minimum bit width for this APInt while considering it to be a
/// signed (and probably negative) value. If the value is not negative, this
/// function returns the same value as getActiveBits()+1. Otherwise, it
/// returns the smallest bit width that will retain the negative value. For
/// example, -1 can be written as 0b1 or 0xFFFFFFFFFF. 0b1 is shorter and so
/// for -1, this function will always return 1.
unsigned getMinSignedBits() const { return BitWidth - getNumSignBits() + 1; }

/// Get zero extended value
///
/// This method attempts to return the value of this APInt as a zero extended
/// uint64_t. The bitwidth must be <= 64 or the value must fit within a
/// uint64_t. Otherwise an assertion will result.
uint64_t getZExtValue() const {
  if (isSingleWord())
    return U.VAL;
  assert(getActiveBits() <= 64 && "Too many bits for uint64_t")((void)0);
  return U.pVal[0];
}

/// Get sign extended value
///
/// This method attempts to return the value of this APInt as a sign extended
/// int64_t. The bit width must be <= 64 or the value must fit within an
/// int64_t. Otherwise an assertion will result.
int64_t getSExtValue() const {
  if (isSingleWord())
    return SignExtend64(U.VAL, BitWidth);
  assert(getMinSignedBits() <= 64 && "Too many bits for int64_t")((void)0);
  return int64_t(U.pVal[0]);
}

/// Get bits required for string value.
///
/// This method determines how many bits are required to hold the APInt
/// equivalent of the string given by \p str.
static unsigned getBitsNeeded(StringRef str, uint8_t radix);

/// The APInt version of the countLeadingZeros functions in
///   MathExtras.h.
///
/// It counts the number of zeros from the most significant bit to the first
/// one bit.
///
/// \returns BitWidth if the value is zero, otherwise returns the number of
///   zeros from the most significant bit to the first one bits.
unsigned countLeadingZeros() const {
  if (isSingleWord()) {
    unsigned unusedBits = APINT_BITS_PER_WORD - BitWidth;
    return llvm::countLeadingZeros(U.VAL) - unusedBits;
  }
  return countLeadingZerosSlowCase();
}

/// Count the number of leading one bits.
///
/// This function is an APInt version of the countLeadingOnes
/// functions in MathExtras.h. It counts the number of ones from the most
/// significant bit to the first zero bit.
///
/// \returns 0 if the high order bit is not set, otherwise returns the number
/// of 1 bits from the most significant to the least
unsigned countLeadingOnes() const {
  if (isSingleWord())
    return llvm::countLeadingOnes(U.VAL << (APINT_BITS_PER_WORD - BitWidth));
  return countLeadingOnesSlowCase();
}

/// Computes the number of leading bits of this APInt that are equal to its
/// sign bit.
unsigned getNumSignBits() const {
  return isNegative() ? countLeadingOnes() : countLeadingZeros();
}

/// Count the number of trailing zero bits.
///
/// This function is an APInt version of the countTrailingZeros
/// functions in MathExtras.h. It counts the number of zeros from the least
/// significant bit to the first set bit.
///
/// \returns BitWidth if the value is zero, otherwise returns the number of
/// zeros from the least significant bit to the first one bit.
unsigned countTrailingZeros() const {
  if (isSingleWord()) {
    unsigned TrailingZeros = llvm::countTrailingZeros(U.VAL);
    return (TrailingZeros > BitWidth ? BitWidth : TrailingZeros);
  }
  return countTrailingZerosSlowCase();
}

/// Count the number of trailing one bits.
///
/// This function is an APInt version of the countTrailingOnes
/// functions in MathExtras.h. It counts the number of ones from the least
/// significant bit to the first zero bit.
///
/// \returns BitWidth if the value is all ones, otherwise returns the number
/// of ones from the least significant bit to the first zero bit.
unsigned countTrailingOnes() const {
  if (isSingleWord())
    return llvm::countTrailingOnes(U.VAL);
  return countTrailingOnesSlowCase();
}

/// Count the number of bits set.
///
/// This function is an APInt version of the countPopulation functions
/// in MathExtras.h. It counts the number of 1 bits in the APInt value.
///
/// \returns 0 if the value is zero, otherwise returns the number of set bits.
unsigned countPopulation() const {
  if (isSingleWord())
    return llvm::countPopulation(U.VAL);
  return countPopulationSlowCase();
}

/// @}
/// \name Conversion Functions
/// @{
void print(raw_ostream &OS, bool isSigned) const;

/// Converts an APInt to a string and append it to Str.  Str is commonly a
/// SmallString.
void toString(SmallVectorImpl<char> &Str, unsigned Radix, bool Signed,
              bool formatAsCLiteral = false) const;

/// Considers the APInt to be unsigned and converts it into a string in the
/// radix given. The radix can be 2, 8, 10 16, or 36.
void toStringUnsigned(SmallVectorImpl<char> &Str, unsigned Radix = 10) const {
  toString(Str, Radix, false, false);
}

/// Considers the APInt to be signed and converts it into a string in the
/// radix given. The radix can be 2, 8, 10, 16, or 36.
void toStringSigned(SmallVectorImpl<char> &Str, unsigned Radix = 10) const {
  toString(Str, Radix, true, false);
}

/// \returns a byte-swapped representation of this APInt Value.
APInt byteSwap() const;

/// \returns the value with the bit representation reversed of this APInt
/// Value.
APInt reverseBits() const;

/// Converts this APInt to a double value.
double roundToDouble(bool isSigned) const;

/// Converts this unsigned APInt to a double value.
double roundToDouble() const { return roundToDouble(false); }

/// Converts this signed APInt to a double value.
double signedRoundToDouble() const { return roundToDouble(true); }

/// Converts APInt bits to a double
///
/// The conversion does not do a translation from integer to double, it just
/// re-interprets the bits as a double. Note that it is valid to do this on
/// any bit width. Exactly 64 bits will be translated.
double bitsToDouble() const {
  return BitsToDouble(getWord(0));
}

/// Converts APInt bits to a float
///
/// The conversion does not do a translation from integer to float, it just
/// re-interprets the bits as a float. Note that it is valid to do this on
/// any bit width. Exactly 32 bits will be translated.
float bitsToFloat() const {
  return BitsToFloat(static_cast<uint32_t>(getWord(0)));
}

/// Converts a double to APInt bits.
///
/// The conversion does not do a translation from double to integer, it just
/// re-interprets the bits of the double.
static APInt doubleToBits(double V) {
  return APInt(sizeof(double) * CHAR_BIT8, DoubleToBits(V));
}

/// Converts a float to APInt bits.
///
/// The conversion does not do a translation from float to integer, it just
/// re-interprets the bits of the float.
static APInt floatToBits(float V) {
  return APInt(sizeof(float) * CHAR_BIT8, FloatToBits(V));
}

/// @}
/// \name Mathematics Operations
/// @{

/// \returns the floor log base 2 of this APInt.
unsigned logBase2() const { return getActiveBits() -  1; }

/// \returns the ceil log base 2 of this APInt.
unsigned ceilLogBase2() const {
  APInt temp(*this);
  --temp;
  return temp.getActiveBits();
}

/// \returns the nearest log base 2 of this APInt. Ties round up.
///
/// NOTE: When we have a BitWidth of 1, we define:
///
///   log2(0) = UINT32_MAX
///   log2(1) = 0
///
/// to get around any mathematical concerns resulting from
/// referencing 2 in a space where 2 does no exist.
unsigned nearestLogBase2() const {
  // Special case when we have a bitwidth of 1. If VAL is 1, then we
  // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to
  // UINT32_MAX.
  if (BitWidth == 1)
    return U.VAL - 1;

  // Handle the zero case.
  if (isNullValue())
    return UINT32_MAX0xffffffffU;

  // The non-zero case is handled by computing:
  //
  //   nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1].
  //
  // where x[i] is referring to the value of the ith bit of x.
  unsigned lg = logBase2();
  return lg + unsigned((*this)[lg - 1]);
}

/// \returns the log base 2 of this APInt if its an exact power of two, -1
/// otherwise
int32_t exactLogBase2() const {
  if (!isPowerOf2())
    return -1;
  return logBase2();
}

/// Compute the square root
APInt sqrt() const;

/// Get the absolute value;
///
/// If *this is < 0 then return -(*this), otherwise *this;
APInt abs() const {
  if (isNegative())
    return -(*this);
  return *this;
}

/// \returns the multiplicative inverse for a given modulo.
APInt multiplicativeInverse(const APInt &modulo) const;

/// @}
/// \name Support for division by constant
/// @{

/// Calculate the magic number for signed division by a constant.
struct ms;
ms magic() const;

/// Calculate the magic number for unsigned division by a constant.
struct mu;
mu magicu(unsigned LeadingZeros = 0) const;

/// @}
/// \name Building-block Operations for APInt and APFloat
/// @{

// These building block operations operate on a representation of arbitrary
// precision, two's-complement, bignum integer values. They should be
// sufficient to implement APInt and APFloat bignum requirements. Inputs are
// generally a pointer to the base of an array of integer parts, representing
// an unsigned bignum, and a count of how many parts there are.

/// Sets the least significant part of a bignum to the input value, and zeroes
/// out higher parts.
static void tcSet(WordType *, WordType, unsigned);

/// Assign one bignum to another.
static void tcAssign(WordType *, const WordType *, unsigned);

/// Returns true if a bignum is zero, false otherwise.
static bool tcIsZero(const WordType *, unsigned);

/// Extract the given bit of a bignum; returns 0 or 1.  Zero-based.
static int tcExtractBit(const WordType *, unsigned bit);

/// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to
/// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least
/// significant bit of DST.  All high bits above srcBITS in DST are
/// zero-filled.
static void tcExtract(WordType *, unsigned dstCount,
                      const WordType *, unsigned srcBits,
                      unsigned srcLSB);

/// Set the given bit of a bignum.  Zero-based.
static void tcSetBit(WordType *, unsigned bit);

/// Clear the given bit of a bignum.  Zero-based.
static void tcClearBit(WordType *, unsigned bit);

/// Returns the bit number of the least or most significant set bit of a
/// number.  If the input number has no bits set -1U is returned.
static unsigned tcLSB(const WordType *, unsigned n);
static unsigned tcMSB(const WordType *parts, unsigned n);

/// Negate a bignum in-place.
static void tcNegate(WordType *, unsigned);

/// DST += RHS + CARRY where CARRY is zero or one.  Returns the carry flag.
static WordType tcAdd(WordType *, const WordType *,
                      WordType carry, unsigned);
/// DST += RHS.  Returns the carry flag.
static WordType tcAddPart(WordType *, WordType, unsigned);

/// DST -= RHS + CARRY where CARRY is zero or one. Returns the carry flag.
static WordType tcSubtract(WordType *, const WordType *,
                           WordType carry, unsigned);
/// DST -= RHS.  Returns the carry flag.
static WordType tcSubtractPart(WordType *, WordType, unsigned);

/// DST += SRC * MULTIPLIER + PART   if add is true
/// DST  = SRC * MULTIPLIER + PART   if add is false
///
/// Requires 0 <= DSTPARTS <= SRCPARTS + 1.  If DST overlaps SRC they must
/// start at the same point, i.e. DST == SRC.
///
/// If DSTPARTS == SRC_PARTS + 1 no overflow occurs and zero is returned.
/// Otherwise DST is filled with the least significant DSTPARTS parts of the
/// result, and if all of the omitted higher parts were zero return zero,
/// otherwise overflow occurred and return one.
static int tcMultiplyPart(WordType *dst, const WordType *src,
                          WordType multiplier, WordType carry,
                          unsigned srcParts, unsigned dstParts,
                          bool add);

/// DST = LHS * RHS, where DST has the same width as the operands and is
/// filled with the least significant parts of the result.  Returns one if
/// overflow occurred, otherwise zero.  DST must be disjoint from both
/// operands.
static int tcMultiply(WordType *, const WordType *, const WordType *,
                      unsigned);

/// DST = LHS * RHS, where DST has width the sum of the widths of the
/// operands. No overflow occurs. DST must be disjoint from both operands.
static void tcFullMultiply(WordType *, const WordType *,
                           const WordType *, unsigned, unsigned);

/// If RHS is zero LHS and REMAINDER are left unchanged, return one.
/// Otherwise set LHS to LHS / RHS with the fractional part discarded, set
/// REMAINDER to the remainder, return zero.  i.e.
///
///  OLD_LHS = RHS * LHS + REMAINDER
///
/// SCRATCH is a bignum of the same size as the operands and result for use by
/// the routine; its contents need not be initialized and are destroyed.  LHS,
/// REMAINDER and SCRATCH must be distinct.
static int tcDivide(WordType *lhs, const WordType *rhs,
                    WordType *remainder, WordType *scratch,
                    unsigned parts);

/// Shift a bignum left Count bits. Shifted in bits are zero. There are no
/// restrictions on Count.
static void tcShiftLeft(WordType *, unsigned Words, unsigned Count);

/// Shift a bignum right Count bits.  Shifted in bits are zero.  There are no
/// restrictions on Count.
static void tcShiftRight(WordType *, unsigned Words, unsigned Count);

/// The obvious AND, OR and XOR and complement operations.
static void tcAnd(WordType *, const WordType *, unsigned);
static void tcOr(WordType *, const WordType *, unsigned);
static void tcXor(WordType *, const WordType *, unsigned);
static void tcComplement(WordType *, unsigned);

/// Comparison (unsigned) of two bignums.
static int tcCompare(const WordType *, const WordType *, unsigned);

/// Increment a bignum in-place.  Return the carry flag.
static WordType tcIncrement(WordType *dst, unsigned parts) {
  return tcAddPart(dst, 1, parts);
}

/// Decrement a bignum in-place.  Return the borrow flag.
static WordType tcDecrement(WordType *dst, unsigned parts) {
  return tcSubtractPart(dst, 1, parts);
}

/// Set the least significant BITS and clear the rest.
static void tcSetLeastSignificantBits(WordType *, unsigned, unsigned bits);

/// debug method
void dump() const;

/// @}
2015};

2017/// Magic data for optimising signed division by a constant.
2018struct APInt::ms {
APInt m;    ///< magic number
unsigned s; ///< shift amount
2021};

2023/// Magic data for optimising unsigned division by a constant.
2024struct APInt::mu {
APInt m;    ///< magic number
bool a;     ///< add indicator
unsigned s; ///< shift amount
2028};

2030inline bool operator==(uint64_t V1, const APInt &V2) { return V2 == V1; }

2032inline bool operator!=(uint64_t V1, const APInt &V2) { return V2 != V1; }

2034/// Unary bitwise complement operator.
2035///
2036/// \returns an APInt that is the bitwise complement of \p v.
2037inline APInt operator~(APInt v) {
v.flipAllBits();
return v;
2040}

2042inline APInt operator&(APInt a, const APInt &b) {
a &= b;
return a;
2045}

2047inline APInt operator&(const APInt &a, APInt &&b) {
b &= a;
return std::move(b);
2050}

2052inline APInt operator&(APInt a, uint64_t RHS) {
a &= RHS;
return a;
2055}

2057inline APInt operator&(uint64_t LHS, APInt b) {
b &= LHS;
return b;
2060}

2062inline APInt operator|(APInt a, const APInt &b) {
a |= b;
return a;
2065}

2067inline APInt operator|(const APInt &a, APInt &&b) {
b |= a;
return std::move(b);
2070}

2072inline APInt operator|(APInt a, uint64_t RHS) {
a |= RHS;
return a;
2075}

2077inline APInt operator|(uint64_t LHS, APInt b) {
b |= LHS;
return b;
2080}

2082inline APInt operator^(APInt a, const APInt &b) {
a ^= b;
return a;
2085}

2087inline APInt operator^(const APInt &a, APInt &&b) {
b ^= a;
return std::move(b);
2090}

2092inline APInt operator^(APInt a, uint64_t RHS) {
a ^= RHS;
return a;
2095}

2097inline APInt operator^(uint64_t LHS, APInt b) {
b ^= LHS;
return b;
2100}

2102inline raw_ostream &operator<<(raw_ostream &OS, const APInt &I) {
I.print(OS, true);
return OS;
2105}

2107inline APInt operator-(APInt v) {
v.negate();
return v;
2110}

2112inline APInt operator+(APInt a, const APInt &b) {
a += b;
return a;
2115}

2117inline APInt operator+(const APInt &a, APInt &&b) {
b += a;
return std::move(b);
2120}

2122inline APInt operator+(APInt a, uint64_t RHS) {
a += RHS;
return a;
2125}

2127inline APInt operator+(uint64_t LHS, APInt b) {
b += LHS;
return b;
2130}

2132inline APInt operator-(APInt a, const APInt &b) {
a -= b;
return a;
2135}

2137inline APInt operator-(const APInt &a, APInt &&b) {
b.negate();
b += a;
return std::move(b);
2141}

2143inline APInt operator-(APInt a, uint64_t RHS) {
a -= RHS;
return a;
2146}

2148inline APInt operator-(uint64_t LHS, APInt b) {
b.negate();
b += LHS;
return b;
2152}

2154inline APInt operator*(APInt a, uint64_t RHS) {
a *= RHS;
return a;
2157}

2159inline APInt operator*(uint64_t LHS, APInt b) {
b *= LHS;
return b;
2162}


2165namespace APIntOps {

2167/// Determine the smaller of two APInts considered to be signed.
2168inline const APInt &smin(const APInt &A, const APInt &B) {
return A.slt(B) ? A : B;
2170}

2172/// Determine the larger of two APInts considered to be signed.
2173inline const APInt &smax(const APInt &A, const APInt &B) {
return A.sgt(B) ? A : B;
2175}

2177/// Determine the smaller of two APInts considered to be unsigned.
2178inline const APInt &umin(const APInt &A, const APInt &B) {
return A.ult(B) ? A : B;
2180}

2182/// Determine the larger of two APInts considered to be unsigned.
2183inline const APInt &umax(const APInt &A, const APInt &B) {
return A.ugt(B) ? A : B;
2185}

2187/// Compute GCD of two unsigned APInt values.
2188///
2189/// This function returns the greatest common divisor of the two APInt values
2190/// using Stein's algorithm.
2191///
2192/// \returns the greatest common divisor of A and B.
2193APInt GreatestCommonDivisor(APInt A, APInt B);

2195/// Converts the given APInt to a double value.
2196///
2197/// Treats the APInt as an unsigned value for conversion purposes.
2198inline double RoundAPIntToDouble(const APInt &APIVal) {
return APIVal.roundToDouble();
2200}

2202/// Converts the given APInt to a double value.
2203///
2204/// Treats the APInt as a signed value for conversion purposes.
2205inline double RoundSignedAPIntToDouble(const APInt &APIVal) {
return APIVal.signedRoundToDouble();
2207}

2209/// Converts the given APInt to a float value.
2210inline float RoundAPIntToFloat(const APInt &APIVal) {
return float(RoundAPIntToDouble(APIVal));
2212}

2214/// Converts the given APInt to a float value.
2215///
2216/// Treats the APInt as a signed value for conversion purposes.
2217inline float RoundSignedAPIntToFloat(const APInt &APIVal) {
return float(APIVal.signedRoundToDouble());
2219}

2221/// Converts the given double value into a APInt.
2222///
2223/// This function convert a double value to an APInt value.
2224APInt RoundDoubleToAPInt(double Double, unsigned width);

2226/// Converts a float value into a APInt.
2227///
2228/// Converts a float value into an APInt value.
2229inline APInt RoundFloatToAPInt(float Float, unsigned width) {
return RoundDoubleToAPInt(double(Float), width);
2231}

2233/// Return A unsign-divided by B, rounded by the given rounding mode.
2234APInt RoundingUDiv(const APInt &A, const APInt &B, APInt::Rounding RM);

2236/// Return A sign-divided by B, rounded by the given rounding mode.
2237APInt RoundingSDiv(const APInt &A, const APInt &B, APInt::Rounding RM);

2239/// Let q(n) = An^2 + Bn + C, and BW = bit width of the value range
2240/// (e.g. 32 for i32).
2241/// This function finds the smallest number n, such that
2242/// (a) n >= 0 and q(n) = 0, or
2243/// (b) n >= 1 and q(n-1) and q(n), when evaluated in the set of all
2244///     integers, belong to two different intervals [Rk, Rk+R),
2245///     where R = 2^BW, and k is an integer.
2246/// The idea here is to find when q(n) "overflows" 2^BW, while at the
2247/// same time "allowing" subtraction. In unsigned modulo arithmetic a
2248/// subtraction (treated as addition of negated numbers) would always
2249/// count as an overflow, but here we want to allow values to decrease
2250/// and increase as long as they are within the same interval.
2251/// Specifically, adding of two negative numbers should not cause an
2252/// overflow (as long as the magnitude does not exceed the bit width).
2253/// On the other hand, given a positive number, adding a negative
2254/// number to it can give a negative result, which would cause the
2255/// value to go from [-2^BW, 0) to [0, 2^BW). In that sense, zero is
2256/// treated as a special case of an overflow.
2257///
2258/// This function returns None if after finding k that minimizes the
2259/// positive solution to q(n) = kR, both solutions are contained between
2260/// two consecutive integers.
2261///
2262/// There are cases where q(n) > T, and q(n+1) < T (assuming evaluation
2263/// in arithmetic modulo 2^BW, and treating the values as signed) by the
2264/// virtue of *signed* overflow. This function will *not* find such an n,
2265/// however it may find a value of n satisfying the inequalities due to
2266/// an *unsigned* overflow (if the values are treated as unsigned).
2267/// To find a solution for a signed overflow, treat it as a problem of
2268/// finding an unsigned overflow with a range with of BW-1.
2269///
2270/// The returned value may have a different bit width from the input
2271/// coefficients.
2272Optional<APInt> SolveQuadraticEquationWrap(APInt A, APInt B, APInt C,
                                         unsigned RangeWidth);

2275/// Compare two values, and if they are different, return the position of the
2276/// most significant bit that is different in the values.
2277Optional<unsigned> GetMostSignificantDifferentBit(const APInt &A,
                                                const APInt &B);

2280} // End of APIntOps namespace

2282// See friend declaration above. This additional declaration is required in
2283// order to compile LLVM with IBM xlC compiler.
2284hash_code hash_value(const APInt &Arg);

2286/// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst
2287/// with the integer held in IntVal.
2288void StoreIntToMemory(const APInt &IntVal, uint8_t *Dst, unsigned StoreBytes);

2290/// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting
2291/// from Src into IntVal, which is assumed to be wide enough and to hold zero.
2292void LoadIntFromMemory(APInt &IntVal, const uint8_t *Src, unsigned LoadBytes);

2294/// Provide DenseMapInfo for APInt.
2295template <> struct DenseMapInfo<APInt> {
static inline APInt getEmptyKey() {
  APInt V(nullptr, 0);
  V.U.VAL = 0;
  return V;
}

static inline APInt getTombstoneKey() {
  APInt V(nullptr, 0);
  V.U.VAL = 1;
  return V;
}

static unsigned getHashValue(const APInt &Key);

static bool isEqual(const APInt &LHS, const APInt &RHS) {
  return LHS.getBitWidth() == RHS.getBitWidth() && LHS == RHS;
}
2313};

2315} // namespace llvm

2317#endif