/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/llvm/lib/Analysis/ScalarEvolution.cpp

Bug Summary

File:	llvm/lib/Analysis/ScalarEvolution.cpp
Warning:	line 10785, column 32 Called C++ object pointer is null
Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name ScalarEvolution.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 -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mframe-pointer=none -fmath-errno -ffp-contract=on -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/build-llvm -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I lib/Analysis -I /build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/llvm/lib/Analysis -I include -I /build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/llvm/include -D _FORTIFY_SOURCE=2 -D NDEBUG -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/x86_64-linux-gnu/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10/backward -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -fmacro-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/build-llvm=build-llvm -fmacro-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/= -fcoverage-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/build-llvm=build-llvm -fcoverage-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/= -O3 -Wno-unused-command-line-argument -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-class-memaccess -Wno-redundant-move -Wno-pessimizing-move -Wno-noexcept-type -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/build-llvm -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/build-llvm=build-llvm -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/= -ferror-limit 19 -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -fcolor-diagnostics -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2022-01-28-233020-220964-1 -x c++ /build/llvm-toolchain-snapshot-14~++20220128100846+e1a12767ee62/llvm/lib/Analysis/ScalarEvolution.cpp
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
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 contains the implementation of the scalar evolution analysis
10// engine, which is used primarily to analyze expressions involving induction
11// variables in loops.
12//
13// There are several aspects to this library.  First is the representation of
14// scalar expressions, which are represented as subclasses of the SCEV class.
15// These classes are used to represent certain types of subexpressions that we
16// can handle. We only create one SCEV of a particular shape, so
17// pointer-comparisons for equality are legal.
18//
19// One important aspect of the SCEV objects is that they are never cyclic, even
20// if there is a cycle in the dataflow for an expression (ie, a PHI node).  If
21// the PHI node is one of the idioms that we can represent (e.g., a polynomial
22// recurrence) then we represent it directly as a recurrence node, otherwise we
23// represent it as a SCEVUnknown node.
24//
25// In addition to being able to represent expressions of various types, we also
26// have folders that are used to build the *canonical* representation for a
27// particular expression.  These folders are capable of using a variety of
28// rewrite rules to simplify the expressions.
29//
30// Once the folders are defined, we can implement the more interesting
31// higher-level code, such as the code that recognizes PHI nodes of various
32// types, computes the execution count of a loop, etc.
33//
34// TODO: We should use these routines and value representations to implement
35// dependence analysis!
36//
37//===----------------------------------------------------------------------===//
38//
39// There are several good references for the techniques used in this analysis.
40//
41//  Chains of recurrences -- a method to expedite the evaluation
42//  of closed-form functions
43//  Olaf Bachmann, Paul S. Wang, Eugene V. Zima
44//
45//  On computational properties of chains of recurrences
46//  Eugene V. Zima
47//
48//  Symbolic Evaluation of Chains of Recurrences for Loop Optimization
49//  Robert A. van Engelen
50//
51//  Efficient Symbolic Analysis for Optimizing Compilers
52//  Robert A. van Engelen
53//
54//  Using the chains of recurrences algebra for data dependence testing and
55//  induction variable substitution
56//  MS Thesis, Johnie Birch
57//
58//===----------------------------------------------------------------------===//

60#include "llvm/Analysis/ScalarEvolution.h"
61#include "llvm/ADT/APInt.h"
62#include "llvm/ADT/ArrayRef.h"
63#include "llvm/ADT/DenseMap.h"
64#include "llvm/ADT/DepthFirstIterator.h"
65#include "llvm/ADT/EquivalenceClasses.h"
66#include "llvm/ADT/FoldingSet.h"
67#include "llvm/ADT/None.h"
68#include "llvm/ADT/Optional.h"
69#include "llvm/ADT/STLExtras.h"
70#include "llvm/ADT/ScopeExit.h"
71#include "llvm/ADT/Sequence.h"
72#include "llvm/ADT/SetVector.h"
73#include "llvm/ADT/SmallPtrSet.h"
74#include "llvm/ADT/SmallSet.h"
75#include "llvm/ADT/SmallVector.h"
76#include "llvm/ADT/Statistic.h"
77#include "llvm/ADT/StringRef.h"
78#include "llvm/Analysis/AssumptionCache.h"
79#include "llvm/Analysis/ConstantFolding.h"
80#include "llvm/Analysis/InstructionSimplify.h"
81#include "llvm/Analysis/LoopInfo.h"
82#include "llvm/Analysis/ScalarEvolutionDivision.h"
83#include "llvm/Analysis/ScalarEvolutionExpressions.h"
84#include "llvm/Analysis/TargetLibraryInfo.h"
85#include "llvm/Analysis/ValueTracking.h"
86#include "llvm/Config/llvm-config.h"
87#include "llvm/IR/Argument.h"
88#include "llvm/IR/BasicBlock.h"
89#include "llvm/IR/CFG.h"
90#include "llvm/IR/Constant.h"
91#include "llvm/IR/ConstantRange.h"
92#include "llvm/IR/Constants.h"
93#include "llvm/IR/DataLayout.h"
94#include "llvm/IR/DerivedTypes.h"
95#include "llvm/IR/Dominators.h"
96#include "llvm/IR/Function.h"
97#include "llvm/IR/GlobalAlias.h"
98#include "llvm/IR/GlobalValue.h"
99#include "llvm/IR/GlobalVariable.h"
100#include "llvm/IR/InstIterator.h"
101#include "llvm/IR/InstrTypes.h"
102#include "llvm/IR/Instruction.h"
103#include "llvm/IR/Instructions.h"
104#include "llvm/IR/IntrinsicInst.h"
105#include "llvm/IR/Intrinsics.h"
106#include "llvm/IR/LLVMContext.h"
107#include "llvm/IR/Metadata.h"
108#include "llvm/IR/Operator.h"
109#include "llvm/IR/PatternMatch.h"
110#include "llvm/IR/Type.h"
111#include "llvm/IR/Use.h"
112#include "llvm/IR/User.h"
113#include "llvm/IR/Value.h"
114#include "llvm/IR/Verifier.h"
115#include "llvm/InitializePasses.h"
116#include "llvm/Pass.h"
117#include "llvm/Support/Casting.h"
118#include "llvm/Support/CommandLine.h"
119#include "llvm/Support/Compiler.h"
120#include "llvm/Support/Debug.h"
121#include "llvm/Support/ErrorHandling.h"
122#include "llvm/Support/KnownBits.h"
123#include "llvm/Support/SaveAndRestore.h"
124#include "llvm/Support/raw_ostream.h"
125#include <algorithm>
126#include <cassert>
127#include <climits>
128#include <cstddef>
129#include <cstdint>
130#include <cstdlib>
131#include <map>
132#include <memory>
133#include <tuple>
134#include <utility>
135#include <vector>

137using namespace llvm;
138using namespace PatternMatch;

140#define DEBUG_TYPE"scalar-evolution" "scalar-evolution"

142STATISTIC(NumTripCountsComputed,static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
}
        "Number of loops with predictable loop counts")static llvm::Statistic NumTripCountsComputed = {"scalar-evolution"
, "NumTripCountsComputed", "Number of loops with predictable loop counts"
};
144STATISTIC(NumTripCountsNotComputed,static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
}
        "Number of loops without predictable loop counts")static llvm::Statistic NumTripCountsNotComputed = {"scalar-evolution"
, "NumTripCountsNotComputed", "Number of loops without predictable loop counts"
};
146STATISTIC(NumBruteForceTripCountsComputed,static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
}
        "Number of loops with trip counts computed by force")static llvm::Statistic NumBruteForceTripCountsComputed = {"scalar-evolution"
, "NumBruteForceTripCountsComputed", "Number of loops with trip counts computed by force"
};

149static cl::opt<unsigned>
150MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
                      cl::ZeroOrMore,
                      cl::desc("Maximum number of iterations SCEV will "
                               "symbolically execute a constant "
                               "derived loop"),
                      cl::init(100));

157// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
158static cl::opt<bool> VerifySCEV(
  "verify-scev", cl::Hidden,
  cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
161static cl::opt<bool> VerifySCEVStrict(
  "verify-scev-strict", cl::Hidden,
  cl::desc("Enable stricter verification with -verify-scev is passed"));
164static cl::opt<bool>
  VerifySCEVMap("verify-scev-maps", cl::Hidden,
                cl::desc("Verify no dangling value in ScalarEvolution's "
                         "ExprValueMap (slow)"));

169static cl::opt<bool> VerifyIR(
  "scev-verify-ir", cl::Hidden,
  cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
  cl::init(false));

174static cl::opt<unsigned> MulOpsInlineThreshold(
  "scev-mulops-inline-threshold", cl::Hidden,
  cl::desc("Threshold for inlining multiplication operands into a SCEV"),
  cl::init(32));

179static cl::opt<unsigned> AddOpsInlineThreshold(
  "scev-addops-inline-threshold", cl::Hidden,
  cl::desc("Threshold for inlining addition operands into a SCEV"),
  cl::init(500));

184static cl::opt<unsigned> MaxSCEVCompareDepth(
  "scalar-evolution-max-scev-compare-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
  cl::init(32));

189static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
  "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
  cl::init(2));

194static cl::opt<unsigned> MaxValueCompareDepth(
  "scalar-evolution-max-value-compare-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive value complexity comparisons"),
  cl::init(2));

199static cl::opt<unsigned>
  MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
                cl::desc("Maximum depth of recursive arithmetics"),
                cl::init(32));

204static cl::opt<unsigned> MaxConstantEvolvingDepth(
  "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));

208static cl::opt<unsigned>
  MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
               cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
               cl::init(8));

213static cl::opt<unsigned>
  MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
                cl::desc("Max coefficients in AddRec during evolving"),
                cl::init(8));

218static cl::opt<unsigned>
  HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
                cl::desc("Size of the expression which is considered huge"),
                cl::init(4096));

223static cl::opt<bool>
224ClassifyExpressions("scalar-evolution-classify-expressions",
  cl::Hidden, cl::init(true),
  cl::desc("When printing analysis, include information on every instruction"));

228static cl::opt<bool> UseExpensiveRangeSharpening(
  "scalar-evolution-use-expensive-range-sharpening", cl::Hidden,
  cl::init(false),
  cl::desc("Use more powerful methods of sharpening expression ranges. May "
           "be costly in terms of compile time"));

234//===----------------------------------------------------------------------===//
235//                           SCEV class definitions
236//===----------------------------------------------------------------------===//

238//===----------------------------------------------------------------------===//
239// Implementation of the SCEV class.
240//

242#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
243LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void SCEV::dump() const {
print(dbgs());
dbgs() << '\n';
246}
247#endif

249void SCEV::print(raw_ostream &OS) const {
switch (getSCEVType()) {
case scConstant:
  cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
  return;
case scPtrToInt: {
  const SCEVPtrToIntExpr *PtrToInt = cast<SCEVPtrToIntExpr>(this);
  const SCEV *Op = PtrToInt->getOperand();
  OS << "(ptrtoint " << *Op->getType() << " " << *Op << " to "
     << *PtrToInt->getType() << ")";
  return;
}
case scTruncate: {
  const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
  const SCEV *Op = Trunc->getOperand();
  OS << "(trunc " << *Op->getType() << " " << *Op << " to "
     << *Trunc->getType() << ")";
  return;
}
case scZeroExtend: {
  const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
  const SCEV *Op = ZExt->getOperand();
  OS << "(zext " << *Op->getType() << " " << *Op << " to "
     << *ZExt->getType() << ")";
  return;
}
case scSignExtend: {
  const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
  const SCEV *Op = SExt->getOperand();
  OS << "(sext " << *Op->getType() << " " << *Op << " to "
     << *SExt->getType() << ")";
  return;
}
case scAddRecExpr: {
  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
  OS << "{" << *AR->getOperand(0);
  for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
    OS << ",+," << *AR->getOperand(i);
  OS << "}<";
  if (AR->hasNoUnsignedWrap())
    OS << "nuw><";
  if (AR->hasNoSignedWrap())
    OS << "nsw><";
  if (AR->hasNoSelfWrap() &&
      !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
    OS << "nw><";
  AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
  OS << ">";
  return;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
case scSequentialUMinExpr: {
  const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
  const char *OpStr = nullptr;
  switch (NAry->getSCEVType()) {
  case scAddExpr: OpStr = " + "; break;
  case scMulExpr: OpStr = " * "; break;
  case scUMaxExpr: OpStr = " umax "; break;
  case scSMaxExpr: OpStr = " smax "; break;
  case scUMinExpr:
    OpStr = " umin ";
    break;
  case scSMinExpr:
    OpStr = " smin ";
    break;
  case scSequentialUMinExpr:
    OpStr = " umin_seq ";
    break;
  default:
    llvm_unreachable("There are no other nary expression types.")::llvm::llvm_unreachable_internal("There are no other nary expression types."
, "llvm/lib/Analysis/ScalarEvolution.cpp", 323);
  }
  OS << "(";
  ListSeparator LS(OpStr);
  for (const SCEV *Op : NAry->operands())
    OS << LS << *Op;
  OS << ")";
  switch (NAry->getSCEVType()) {
  case scAddExpr:
  case scMulExpr:
    if (NAry->hasNoUnsignedWrap())
      OS << "<nuw>";
    if (NAry->hasNoSignedWrap())
      OS << "<nsw>";
    break;
  default:
    // Nothing to print for other nary expressions.
    break;
  }
  return;
}
case scUDivExpr: {
  const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
  OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
  return;
}
case scUnknown: {
  const SCEVUnknown *U = cast<SCEVUnknown>(this);
  Type *AllocTy;
  if (U->isSizeOf(AllocTy)) {
    OS << "sizeof(" << *AllocTy << ")";
    return;
  }
  if (U->isAlignOf(AllocTy)) {
    OS << "alignof(" << *AllocTy << ")";
    return;
  }

  Type *CTy;
  Constant *FieldNo;
  if (U->isOffsetOf(CTy, FieldNo)) {
    OS << "offsetof(" << *CTy << ", ";
    FieldNo->printAsOperand(OS, false);
    OS << ")";
    return;
  }

  // Otherwise just print it normally.
  U->getValue()->printAsOperand(OS, false);
  return;
}
case scCouldNotCompute:
  OS << "***COULDNOTCOMPUTE***";
  return;
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 378);
379}

381Type *SCEV::getType() const {
switch (getSCEVType()) {
case scConstant:
  return cast<SCEVConstant>(this)->getType();
case scPtrToInt:
case scTruncate:
case scZeroExtend:
case scSignExtend:
  return cast<SCEVCastExpr>(this)->getType();
case scAddRecExpr:
  return cast<SCEVAddRecExpr>(this)->getType();
case scMulExpr:
  return cast<SCEVMulExpr>(this)->getType();
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
  return cast<SCEVMinMaxExpr>(this)->getType();
case scSequentialUMinExpr:
  return cast<SCEVSequentialMinMaxExpr>(this)->getType();
case scAddExpr:
  return cast<SCEVAddExpr>(this)->getType();
case scUDivExpr:
  return cast<SCEVUDivExpr>(this)->getType();
case scUnknown:
  return cast<SCEVUnknown>(this)->getType();
case scCouldNotCompute:
  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 408);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 410);
411}

413bool SCEV::isZero() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isZero();
return false;
417}

419bool SCEV::isOne() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isOne();
return false;
423}

425bool SCEV::isAllOnesValue() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isMinusOne();
return false;
429}

431bool SCEV::isNonConstantNegative() const {
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
if (!Mul) return false;

// If there is a constant factor, it will be first.
const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
if (!SC) return false;

// Return true if the value is negative, this matches things like (-42 * V).
return SC->getAPInt().isNegative();
441}

443SCEVCouldNotCompute::SCEVCouldNotCompute() :
SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}

446bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
448}

450const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
FoldingSetNodeID ID;
ID.AddInteger(scConstant);
ID.AddPointer(V);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
UniqueSCEVs.InsertNode(S, IP);
return S;
459}

461const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
return getConstant(ConstantInt::get(getContext(), Val));
463}

465const SCEV *
466ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
return getConstant(ConstantInt::get(ITy, V, isSigned));
469}

471SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
                         const SCEV *op, Type *ty)
  : SCEV(ID, SCEVTy, computeExpressionSize(op)), Ty(ty) {
Operands[0] = op;
475}

477SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op,
                                 Type *ITy)
  : SCEVCastExpr(ID, scPtrToInt, Op, ITy) {
assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() &&(static_cast <bool> (getOperand()->getType()->isPointerTy
() && Ty->isIntegerTy() && "Must be a non-bit-width-changing pointer-to-integer cast!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && \"Must be a non-bit-width-changing pointer-to-integer cast!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 481, __extension__
 __PRETTY_FUNCTION__))
       "Must be a non-bit-width-changing pointer-to-integer cast!")(static_cast <bool> (getOperand()->getType()->isPointerTy
() && Ty->isIntegerTy() && "Must be a non-bit-width-changing pointer-to-integer cast!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && \"Must be a non-bit-width-changing pointer-to-integer cast!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 481, __extension__
 __PRETTY_FUNCTION__));
482}

484SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
                                         SCEVTypes SCEVTy, const SCEV *op,
                                         Type *ty)
  : SCEVCastExpr(ID, SCEVTy, op, ty) {}

489SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op,
                                 Type *ty)
  : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot truncate non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 493, __extension__
 __PRETTY_FUNCTION__))
       "Cannot truncate non-integer value!")(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot truncate non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 493, __extension__
 __PRETTY_FUNCTION__));
494}

496SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
                                     const SCEV *op, Type *ty)
  : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot zero extend non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 500, __extension__
 __PRETTY_FUNCTION__))
       "Cannot zero extend non-integer value!")(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot zero extend non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 500, __extension__
 __PRETTY_FUNCTION__));
501}

503SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
                                     const SCEV *op, Type *ty)
  : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot sign extend non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 507, __extension__
 __PRETTY_FUNCTION__))
       "Cannot sign extend non-integer value!")(static_cast <bool> (getOperand()->getType()->isIntOrPtrTy
() && Ty->isIntOrPtrTy() && "Cannot sign extend non-integer value!"
) ? void (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 507, __extension__
 __PRETTY_FUNCTION__));
508}

510void SCEVUnknown::deleted() {
// Clear this SCEVUnknown from various maps.
SE->forgetMemoizedResults(this);

// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);

// Release the value.
setValPtr(nullptr);
519}

521void SCEVUnknown::allUsesReplacedWith(Value *New) {
// Remove this SCEVUnknown from the uniquing map.
SE->UniqueSCEVs.RemoveNode(this);

// Update this SCEVUnknown to point to the new value. This is needed
// because there may still be outstanding SCEVs which still point to
// this SCEVUnknown.
setValPtr(New);
529}

531bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
  if (VCE->getOpcode() == Instruction::PtrToInt)
    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
      if (CE->getOpcode() == Instruction::GetElementPtr &&
          CE->getOperand(0)->isNullValue() &&
          CE->getNumOperands() == 2)
        if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
          if (CI->isOne()) {
            AllocTy = cast<GEPOperator>(CE)->getSourceElementType();
            return true;
          }

return false;
545}

547bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
  if (VCE->getOpcode() == Instruction::PtrToInt)
    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
      if (CE->getOpcode() == Instruction::GetElementPtr &&
          CE->getOperand(0)->isNullValue()) {
        Type *Ty = cast<GEPOperator>(CE)->getSourceElementType();
        if (StructType *STy = dyn_cast<StructType>(Ty))
          if (!STy->isPacked() &&
              CE->getNumOperands() == 3 &&
              CE->getOperand(1)->isNullValue()) {
            if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
              if (CI->isOne() &&
                  STy->getNumElements() == 2 &&
                  STy->getElementType(0)->isIntegerTy(1)) {
                AllocTy = STy->getElementType(1);
                return true;
              }
          }
      }

return false;
569}

571bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
  if (VCE->getOpcode() == Instruction::PtrToInt)
    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
      if (CE->getOpcode() == Instruction::GetElementPtr &&
          CE->getNumOperands() == 3 &&
          CE->getOperand(0)->isNullValue() &&
          CE->getOperand(1)->isNullValue()) {
        Type *Ty = cast<GEPOperator>(CE)->getSourceElementType();
        // Ignore vector types here so that ScalarEvolutionExpander doesn't
        // emit getelementptrs that index into vectors.
        if (Ty->isStructTy() || Ty->isArrayTy()) {
          CTy = Ty;
          FieldNo = CE->getOperand(2);
          return true;
        }
      }

return false;
590}

592//===----------------------------------------------------------------------===//
593//                               SCEV Utilities
594//===----------------------------------------------------------------------===//

596/// Compare the two values \p LV and \p RV in terms of their "complexity" where
597/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
598/// operands in SCEV expressions.  \p EqCache is a set of pairs of values that
599/// have been previously deemed to be "equally complex" by this routine.  It is
600/// intended to avoid exponential time complexity in cases like:
601///
602///   %a = f(%x, %y)
603///   %b = f(%a, %a)
604///   %c = f(%b, %b)
605///
606///   %d = f(%x, %y)
607///   %e = f(%d, %d)
608///   %f = f(%e, %e)
609///
610///   CompareValueComplexity(%f, %c)
611///
612/// Since we do not continue running this routine on expression trees once we
613/// have seen unequal values, there is no need to track them in the cache.
614static int
615CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
                     const LoopInfo *const LI, Value *LV, Value *RV,
                     unsigned Depth) {
if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
  return 0;

// Order pointer values after integer values. This helps SCEVExpander form
// GEPs.
bool LIsPointer = LV->getType()->isPointerTy(),
     RIsPointer = RV->getType()->isPointerTy();
if (LIsPointer != RIsPointer)
  return (int)LIsPointer - (int)RIsPointer;

// Compare getValueID values.
unsigned LID = LV->getValueID(), RID = RV->getValueID();
if (LID != RID)
  return (int)LID - (int)RID;

// Sort arguments by their position.
if (const auto *LA = dyn_cast<Argument>(LV)) {
  const auto *RA = cast<Argument>(RV);
  unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
  return (int)LArgNo - (int)RArgNo;
}

if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
  const auto *RGV = cast<GlobalValue>(RV);

  const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
    auto LT = GV->getLinkage();
    return !(GlobalValue::isPrivateLinkage(LT) ||
             GlobalValue::isInternalLinkage(LT));
  };

  // Use the names to distinguish the two values, but only if the
  // names are semantically important.
  if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
    return LGV->getName().compare(RGV->getName());
}

// For instructions, compare their loop depth, and their operand count.  This
// is pretty loose.
if (const auto *LInst = dyn_cast<Instruction>(LV)) {
  const auto *RInst = cast<Instruction>(RV);

  // Compare loop depths.
  const BasicBlock *LParent = LInst->getParent(),
                   *RParent = RInst->getParent();
  if (LParent != RParent) {
    unsigned LDepth = LI->getLoopDepth(LParent),
             RDepth = LI->getLoopDepth(RParent);
    if (LDepth != RDepth)
      return (int)LDepth - (int)RDepth;
  }

  // Compare the number of operands.
  unsigned LNumOps = LInst->getNumOperands(),
           RNumOps = RInst->getNumOperands();
  if (LNumOps != RNumOps)
    return (int)LNumOps - (int)RNumOps;

  for (unsigned Idx : seq(0u, LNumOps)) {
    int Result =
        CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
                               RInst->getOperand(Idx), Depth + 1);
    if (Result != 0)
      return Result;
  }
}

EqCacheValue.unionSets(LV, RV);
return 0;
687}

689// Return negative, zero, or positive, if LHS is less than, equal to, or greater
690// than RHS, respectively. A three-way result allows recursive comparisons to be
691// more efficient.
692// If the max analysis depth was reached, return None, assuming we do not know
693// if they are equivalent for sure.
694static Optional<int>
695CompareSCEVComplexity(EquivalenceClasses<const SCEV *> &EqCacheSCEV,
                    EquivalenceClasses<const Value *> &EqCacheValue,
                    const LoopInfo *const LI, const SCEV *LHS,
                    const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) {
// Fast-path: SCEVs are uniqued so we can do a quick equality check.
if (LHS == RHS)
  return 0;

// Primarily, sort the SCEVs by their getSCEVType().
SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
if (LType != RType)
  return (int)LType - (int)RType;

if (EqCacheSCEV.isEquivalent(LHS, RHS))
  return 0;

if (Depth > MaxSCEVCompareDepth)
  return None;

// Aside from the getSCEVType() ordering, the particular ordering
// isn't very important except that it's beneficial to be consistent,
// so that (a + b) and (b + a) don't end up as different expressions.
switch (LType) {
case scUnknown: {
  const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
  const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);

  int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
                                 RU->getValue(), Depth + 1);
  if (X == 0)
    EqCacheSCEV.unionSets(LHS, RHS);
  return X;
}

case scConstant: {
  const SCEVConstant *LC = cast<SCEVConstant>(LHS);
  const SCEVConstant *RC = cast<SCEVConstant>(RHS);

  // Compare constant values.
  const APInt &LA = LC->getAPInt();
  const APInt &RA = RC->getAPInt();
  unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
  if (LBitWidth != RBitWidth)
    return (int)LBitWidth - (int)RBitWidth;
  return LA.ult(RA) ? -1 : 1;
}

case scAddRecExpr: {
  const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
  const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);

  // There is always a dominance between two recs that are used by one SCEV,
  // so we can safely sort recs by loop header dominance. We require such
  // order in getAddExpr.
  const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
  if (LLoop != RLoop) {
    const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
    assert(LHead != RHead && "Two loops share the same header?")(static_cast <bool> (LHead != RHead && "Two loops share the same header?"
) ? void (0) : __assert_fail ("LHead != RHead && \"Two loops share the same header?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 752, __extension__
 __PRETTY_FUNCTION__));
    if (DT.dominates(LHead, RHead))
      return 1;
    else
      assert(DT.dominates(RHead, LHead) &&(static_cast <bool> (DT.dominates(RHead, LHead) &&
 "No dominance between recurrences used by one SCEV?") ? void
 (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 757, __extension__
 __PRETTY_FUNCTION__))
             "No dominance between recurrences used by one SCEV?")(static_cast <bool> (DT.dominates(RHead, LHead) &&
 "No dominance between recurrences used by one SCEV?") ? void
 (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 757, __extension__
 __PRETTY_FUNCTION__));
    return -1;
  }

  // Addrec complexity grows with operand count.
  unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
  if (LNumOps != RNumOps)
    return (int)LNumOps - (int)RNumOps;

  // Lexicographically compare.
  for (unsigned i = 0; i != LNumOps; ++i) {
    auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
                                   LA->getOperand(i), RA->getOperand(i), DT,
                                   Depth + 1);
    if (X != 0)
      return X;
  }
  EqCacheSCEV.unionSets(LHS, RHS);
  return 0;
}

case scAddExpr:
case scMulExpr:
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr:
case scSequentialUMinExpr: {
  const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
  const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);

  // Lexicographically compare n-ary expressions.
  unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
  if (LNumOps != RNumOps)
    return (int)LNumOps - (int)RNumOps;

  for (unsigned i = 0; i != LNumOps; ++i) {
    auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
                                   LC->getOperand(i), RC->getOperand(i), DT,
                                   Depth + 1);
    if (X != 0)
      return X;
  }
  EqCacheSCEV.unionSets(LHS, RHS);
  return 0;
}

case scUDivExpr: {
  const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
  const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);

  // Lexicographically compare udiv expressions.
  auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
                                 RC->getLHS(), DT, Depth + 1);
  if (X != 0)
    return X;
  X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
                            RC->getRHS(), DT, Depth + 1);
  if (X == 0)
    EqCacheSCEV.unionSets(LHS, RHS);
  return X;
}

case scPtrToInt:
case scTruncate:
case scZeroExtend:
case scSignExtend: {
  const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
  const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);

  // Compare cast expressions by operand.
  auto X =
      CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getOperand(),
                            RC->getOperand(), DT, Depth + 1);
  if (X == 0)
    EqCacheSCEV.unionSets(LHS, RHS);
  return X;
}

case scCouldNotCompute:
  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 837);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 839);
840}

842/// Given a list of SCEV objects, order them by their complexity, and group
843/// objects of the same complexity together by value.  When this routine is
844/// finished, we know that any duplicates in the vector are consecutive and that
845/// complexity is monotonically increasing.
846///
847/// Note that we go take special precautions to ensure that we get deterministic
848/// results from this routine.  In other words, we don't want the results of
849/// this to depend on where the addresses of various SCEV objects happened to
850/// land in memory.
851static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
                            LoopInfo *LI, DominatorTree &DT) {
if (Ops.size() < 2) return;  // Noop

EquivalenceClasses<const SCEV *> EqCacheSCEV;
EquivalenceClasses<const Value *> EqCacheValue;

// Whether LHS has provably less complexity than RHS.
auto IsLessComplex = [&](const SCEV *LHS, const SCEV *RHS) {
  auto Complexity =
      CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT);
  return Complexity && *Complexity < 0;
};
if (Ops.size() == 2) {
  // This is the common case, which also happens to be trivially simple.
  // Special case it.
  const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
  if (IsLessComplex(RHS, LHS))
    std::swap(LHS, RHS);
  return;
}

// Do the rough sort by complexity.
llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
  return IsLessComplex(LHS, RHS);
});

// Now that we are sorted by complexity, group elements of the same
// complexity.  Note that this is, at worst, N^2, but the vector is likely to
// be extremely short in practice.  Note that we take this approach because we
// do not want to depend on the addresses of the objects we are grouping.
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
  const SCEV *S = Ops[i];
  unsigned Complexity = S->getSCEVType();

  // If there are any objects of the same complexity and same value as this
  // one, group them.
  for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
    if (Ops[j] == S) { // Found a duplicate.
      // Move it to immediately after i'th element.
      std::swap(Ops[i+1], Ops[j]);
      ++i;   // no need to rescan it.
      if (i == e-2) return;  // Done!
    }
  }
}
897}

899/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
900/// least HugeExprThreshold nodes).
901static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
return any_of(Ops, [](const SCEV *S) {
  return S->getExpressionSize() >= HugeExprThreshold;
});
905}

907//===----------------------------------------------------------------------===//
908//                      Simple SCEV method implementations
909//===----------------------------------------------------------------------===//

911/// Compute BC(It, K).  The result has width W.  Assume, K > 0.
912static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
                                     ScalarEvolution &SE,
                                     Type *ResultTy) {
// Handle the simplest case efficiently.
if (K == 1)
  return SE.getTruncateOrZeroExtend(It, ResultTy);

// We are using the following formula for BC(It, K):
//
//   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
//
// Suppose, W is the bitwidth of the return value.  We must be prepared for
// overflow.  Hence, we must assure that the result of our computation is
// equal to the accurate one modulo 2^W.  Unfortunately, division isn't
// safe in modular arithmetic.
//
// However, this code doesn't use exactly that formula; the formula it uses
// is something like the following, where T is the number of factors of 2 in
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
// exponentiation:
//
//   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
//
// This formula is trivially equivalent to the previous formula.  However,
// this formula can be implemented much more efficiently.  The trick is that
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
// arithmetic.  To do exact division in modular arithmetic, all we have
// to do is multiply by the inverse.  Therefore, this step can be done at
// width W.
//
// The next issue is how to safely do the division by 2^T.  The way this
// is done is by doing the multiplication step at a width of at least W + T
// bits.  This way, the bottom W+T bits of the product are accurate. Then,
// when we perform the division by 2^T (which is equivalent to a right shift
// by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
// truncated out after the division by 2^T.
//
// In comparison to just directly using the first formula, this technique
// is much more efficient; using the first formula requires W * K bits,
// but this formula less than W + K bits. Also, the first formula requires
// a division step, whereas this formula only requires multiplies and shifts.
//
// It doesn't matter whether the subtraction step is done in the calculation
// width or the input iteration count's width; if the subtraction overflows,
// the result must be zero anyway.  We prefer here to do it in the width of
// the induction variable because it helps a lot for certain cases; CodeGen
// isn't smart enough to ignore the overflow, which leads to much less
// efficient code if the width of the subtraction is wider than the native
// register width.
//
// (It's possible to not widen at all by pulling out factors of 2 before
// the multiplication; for example, K=2 can be calculated as
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
// extra arithmetic, so it's not an obvious win, and it gets
// much more complicated for K > 3.)

// Protection from insane SCEVs; this bound is conservative,
// but it probably doesn't matter.
if (K > 1000)
  return SE.getCouldNotCompute();

unsigned W = SE.getTypeSizeInBits(ResultTy);

// Calculate K! / 2^T and T; we divide out the factors of two before
// multiplying for calculating K! / 2^T to avoid overflow.
// Other overflow doesn't matter because we only care about the bottom
// W bits of the result.
APInt OddFactorial(W, 1);
unsigned T = 1;
for (unsigned i = 3; i <= K; ++i) {
  APInt Mult(W, i);
  unsigned TwoFactors = Mult.countTrailingZeros();
  T += TwoFactors;
  Mult.lshrInPlace(TwoFactors);
  OddFactorial *= Mult;
}

// We need at least W + T bits for the multiplication step
unsigned CalculationBits = W + T;

// Calculate 2^T, at width T+W.
APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);

// Calculate the multiplicative inverse of K! / 2^T;
// this multiplication factor will perform the exact division by
// K! / 2^T.
APInt Mod = APInt::getSignedMinValue(W+1);
APInt MultiplyFactor = OddFactorial.zext(W+1);
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
MultiplyFactor = MultiplyFactor.trunc(W);

// Calculate the product, at width T+W
IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
                                                    CalculationBits);
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
for (unsigned i = 1; i != K; ++i) {
  const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
  Dividend = SE.getMulExpr(Dividend,
                           SE.getTruncateOrZeroExtend(S, CalculationTy));
}

// Divide by 2^T
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));

// Truncate the result, and divide by K! / 2^T.

return SE.getMulExpr(SE.getConstant(MultiplyFactor),
                     SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1020}

1022/// Return the value of this chain of recurrences at the specified iteration
1023/// number.  We can evaluate this recurrence by multiplying each element in the
1024/// chain by the binomial coefficient corresponding to it.  In other words, we
1025/// can evaluate {A,+,B,+,C,+,D} as:
1026///
1027///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1028///
1029/// where BC(It, k) stands for binomial coefficient.
1030const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
                                              ScalarEvolution &SE) const {
return evaluateAtIteration(makeArrayRef(op_begin(), op_end()), It, SE);
1033}

1035const SCEV *
1036SCEVAddRecExpr::evaluateAtIteration(ArrayRef<const SCEV *> Operands,
                                  const SCEV *It, ScalarEvolution &SE) {
assert(Operands.size() > 0)(static_cast <bool> (Operands.size() > 0) ? void (0)
 : __assert_fail ("Operands.size() > 0", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 1038, __extension__ __PRETTY_FUNCTION__));
const SCEV *Result = Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
  // The computation is correct in the face of overflow provided that the
  // multiplication is performed _after_ the evaluation of the binomial
  // coefficient.
  const SCEV *Coeff = BinomialCoefficient(It, i, SE, Result->getType());
  if (isa<SCEVCouldNotCompute>(Coeff))
    return Coeff;

  Result = SE.getAddExpr(Result, SE.getMulExpr(Operands[i], Coeff));
}
return Result;
1051}

1053//===----------------------------------------------------------------------===//
1054//                    SCEV Expression folder implementations
1055//===----------------------------------------------------------------------===//

1057const SCEV *ScalarEvolution::getLosslessPtrToIntExpr(const SCEV *Op,
                                                   unsigned Depth) {
assert(Depth <= 1 &&(static_cast <bool> (Depth <= 1 && "getLosslessPtrToIntExpr() should self-recurse at most once."
) ? void (0) : __assert_fail ("Depth <= 1 && \"getLosslessPtrToIntExpr() should self-recurse at most once.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1060, __extension__
 __PRETTY_FUNCTION__))
       "getLosslessPtrToIntExpr() should self-recurse at most once.")(static_cast <bool> (Depth <= 1 && "getLosslessPtrToIntExpr() should self-recurse at most once."
) ? void (0) : __assert_fail ("Depth <= 1 && \"getLosslessPtrToIntExpr() should self-recurse at most once.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1060, __extension__
 __PRETTY_FUNCTION__));

// We could be called with an integer-typed operands during SCEV rewrites.
// Since the operand is an integer already, just perform zext/trunc/self cast.
if (!Op->getType()->isPointerTy())
  return Op;

// What would be an ID for such a SCEV cast expression?
FoldingSetNodeID ID;
ID.AddInteger(scPtrToInt);
ID.AddPointer(Op);

void *IP = nullptr;

// Is there already an expression for such a cast?
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
  return S;

// It isn't legal for optimizations to construct new ptrtoint expressions
// for non-integral pointers.
if (getDataLayout().isNonIntegralPointerType(Op->getType()))
  return getCouldNotCompute();

Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType());

// We can only trivially model ptrtoint if SCEV's effective (integer) type
// is sufficiently wide to represent all possible pointer values.
// We could theoretically teach SCEV to truncate wider pointers, but
// that isn't implemented for now.
if (getDataLayout().getTypeSizeInBits(getEffectiveSCEVType(Op->getType())) !=
    getDataLayout().getTypeSizeInBits(IntPtrTy))
  return getCouldNotCompute();

// If not, is this expression something we can't reduce any further?
if (auto *U = dyn_cast<SCEVUnknown>(Op)) {
  // Perform some basic constant folding. If the operand of the ptr2int cast
  // is a null pointer, don't create a ptr2int SCEV expression (that will be
  // left as-is), but produce a zero constant.
  // NOTE: We could handle a more general case, but lack motivational cases.
  if (isa<ConstantPointerNull>(U->getValue()))
    return getZero(IntPtrTy);

  // Create an explicit cast node.
  // We can reuse the existing insert position since if we get here,
  // we won't have made any changes which would invalidate it.
  SCEV *S = new (SCEVAllocator)
      SCEVPtrToIntExpr(ID.Intern(SCEVAllocator), Op, IntPtrTy);
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Op);
  return S;
}

assert(Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for "(static_cast <bool> (Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for "
 "non-SCEVUnknown's.") ? void (0) : __assert_fail ("Depth == 0 && \"getLosslessPtrToIntExpr() should not self-recurse for \" \"non-SCEVUnknown's.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1113, __extension__
 __PRETTY_FUNCTION__))
                     "non-SCEVUnknown's.")(static_cast <bool> (Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for "
 "non-SCEVUnknown's.") ? void (0) : __assert_fail ("Depth == 0 && \"getLosslessPtrToIntExpr() should not self-recurse for \" \"non-SCEVUnknown's.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1113, __extension__
 __PRETTY_FUNCTION__));

// Otherwise, we've got some expression that is more complex than just a
// single SCEVUnknown. But we don't want to have a SCEVPtrToIntExpr of an
// arbitrary expression, we want to have SCEVPtrToIntExpr of an SCEVUnknown
// only, and the expressions must otherwise be integer-typed.
// So sink the cast down to the SCEVUnknown's.

/// The SCEVPtrToIntSinkingRewriter takes a scalar evolution expression,
/// which computes a pointer-typed value, and rewrites the whole expression
/// tree so that *all* the computations are done on integers, and the only
/// pointer-typed operands in the expression are SCEVUnknown.
class SCEVPtrToIntSinkingRewriter
    : public SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter> {
  using Base = SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter>;

public:
  SCEVPtrToIntSinkingRewriter(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {}

  static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE) {
    SCEVPtrToIntSinkingRewriter Rewriter(SE);
    return Rewriter.visit(Scev);
  }

  const SCEV *visit(const SCEV *S) {
    Type *STy = S->getType();
    // If the expression is not pointer-typed, just keep it as-is.
    if (!STy->isPointerTy())
      return S;
    // Else, recursively sink the cast down into it.
    return Base::visit(S);
  }

  const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
    SmallVector<const SCEV *, 2> Operands;
    bool Changed = false;
    for (auto *Op : Expr->operands()) {
      Operands.push_back(visit(Op));
      Changed |= Op != Operands.back();
    }
    return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags());
  }

  const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
    SmallVector<const SCEV *, 2> Operands;
    bool Changed = false;
    for (auto *Op : Expr->operands()) {
      Operands.push_back(visit(Op));
      Changed |= Op != Operands.back();
    }
    return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags());
  }

  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    assert(Expr->getType()->isPointerTy() &&(static_cast <bool> (Expr->getType()->isPointerTy
() && "Should only reach pointer-typed SCEVUnknown's."
) ? void (0) : __assert_fail ("Expr->getType()->isPointerTy() && \"Should only reach pointer-typed SCEVUnknown's.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1168, __extension__
 __PRETTY_FUNCTION__))
           "Should only reach pointer-typed SCEVUnknown's.")(static_cast <bool> (Expr->getType()->isPointerTy
() && "Should only reach pointer-typed SCEVUnknown's."
) ? void (0) : __assert_fail ("Expr->getType()->isPointerTy() && \"Should only reach pointer-typed SCEVUnknown's.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1168, __extension__
 __PRETTY_FUNCTION__));
    return SE.getLosslessPtrToIntExpr(Expr, /*Depth=*/1);
  }
};

// And actually perform the cast sinking.
const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Op, *this);
assert(IntOp->getType()->isIntegerTy() &&(static_cast <bool> (IntOp->getType()->isIntegerTy
() && "We must have succeeded in sinking the cast, " "and ending up with an integer-typed expression!"
) ? void (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1177, __extension__
 __PRETTY_FUNCTION__))
       "We must have succeeded in sinking the cast, "(static_cast <bool> (IntOp->getType()->isIntegerTy
() && "We must have succeeded in sinking the cast, " "and ending up with an integer-typed expression!"
) ? void (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1177, __extension__
 __PRETTY_FUNCTION__))
       "and ending up with an integer-typed expression!")(static_cast <bool> (IntOp->getType()->isIntegerTy
() && "We must have succeeded in sinking the cast, " "and ending up with an integer-typed expression!"
) ? void (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1177, __extension__
 __PRETTY_FUNCTION__));
return IntOp;
1179}

1181const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty) {
assert(Ty->isIntegerTy() && "Target type must be an integer type!")(static_cast <bool> (Ty->isIntegerTy() && "Target type must be an integer type!"
) ? void (0) : __assert_fail ("Ty->isIntegerTy() && \"Target type must be an integer type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1182, __extension__
 __PRETTY_FUNCTION__));

const SCEV *IntOp = getLosslessPtrToIntExpr(Op);
if (isa<SCEVCouldNotCompute>(IntOp))
  return IntOp;

return getTruncateOrZeroExtend(IntOp, Ty);
1189}

1191const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
                                           unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(Op->getType()
) > getTypeSizeInBits(Ty) && "This is not a truncating conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1194, __extension__
 __PRETTY_FUNCTION__))
       "This is not a truncating conversion!")(static_cast <bool> (getTypeSizeInBits(Op->getType()
) > getTypeSizeInBits(Ty) && "This is not a truncating conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1194, __extension__
 __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1196, __extension__
 __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1196, __extension__
 __PRETTY_FUNCTION__));
assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!")(static_cast <bool> (!Op->getType()->isPointerTy(
) && "Can't truncate pointer!") ? void (0) : __assert_fail
 ("!Op->getType()->isPointerTy() && \"Can't truncate pointer!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1197, __extension__
 __PRETTY_FUNCTION__));
Ty = getEffectiveSCEVType(Ty);

FoldingSetNodeID ID;
ID.AddInteger(scTruncate);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;

// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
  return getConstant(
    cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));

// trunc(trunc(x)) --> trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
  return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);

// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
  return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);

// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
  return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);

if (Depth > MaxCastDepth) {
  SCEV *S =
      new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Op);
  return S;
}

// trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
// trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
// if after transforming we have at most one truncate, not counting truncates
// that replace other casts.
if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
  auto *CommOp = cast<SCEVCommutativeExpr>(Op);
  SmallVector<const SCEV *, 4> Operands;
  unsigned numTruncs = 0;
  for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
       ++i) {
    const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
    if (!isa<SCEVIntegralCastExpr>(CommOp->getOperand(i)) &&
        isa<SCEVTruncateExpr>(S))
      numTruncs++;
    Operands.push_back(S);
  }
  if (numTruncs < 2) {
    if (isa<SCEVAddExpr>(Op))
      return getAddExpr(Operands);
    else if (isa<SCEVMulExpr>(Op))
      return getMulExpr(Operands);
    else
      llvm_unreachable("Unexpected SCEV type for Op.")::llvm::llvm_unreachable_internal("Unexpected SCEV type for Op."
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1254);
  }
  // Although we checked in the beginning that ID is not in the cache, it is
  // possible that during recursion and different modification ID was inserted
  // into the cache. So if we find it, just return it.
  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
    return S;
}

// If the input value is a chrec scev, truncate the chrec's operands.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
  SmallVector<const SCEV *, 4> Operands;
  for (const SCEV *Op : AddRec->operands())
    Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
  return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
}

// Return zero if truncating to known zeros.
uint32_t MinTrailingZeros = GetMinTrailingZeros(Op);
if (MinTrailingZeros >= getTypeSizeInBits(Ty))
  return getZero(Ty);

// The cast wasn't folded; create an explicit cast node. We can reuse
// the existing insert position since if we get here, we won't have
// made any changes which would invalidate it.
SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
                                               Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
registerUser(S, Op);
return S;
1284}

1286// Get the limit of a recurrence such that incrementing by Step cannot cause
1287// signed overflow as long as the value of the recurrence within the
1288// loop does not exceed this limit before incrementing.
1289static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
                                               ICmpInst::Predicate *Pred,
                                               ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
if (SE->isKnownPositive(Step)) {
  *Pred = ICmpInst::ICMP_SLT;
  return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
                         SE->getSignedRangeMax(Step));
}
if (SE->isKnownNegative(Step)) {
  *Pred = ICmpInst::ICMP_SGT;
  return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
                         SE->getSignedRangeMin(Step));
}
return nullptr;
1304}

1306// Get the limit of a recurrence such that incrementing by Step cannot cause
1307// unsigned overflow as long as the value of the recurrence within the loop does
1308// not exceed this limit before incrementing.
1309static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
                                                 ICmpInst::Predicate *Pred,
                                                 ScalarEvolution *SE) {
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
*Pred = ICmpInst::ICMP_ULT;

return SE->getConstant(APInt::getMinValue(BitWidth) -
                       SE->getUnsignedRangeMax(Step));
1317}

1319namespace {

1321struct ExtendOpTraitsBase {
typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
                                                        unsigned);
1324};

1326// Used to make code generic over signed and unsigned overflow.
1327template <typename ExtendOp> struct ExtendOpTraits {
// Members present:
//
// static const SCEV::NoWrapFlags WrapType;
//
// static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
//
// static const SCEV *getOverflowLimitForStep(const SCEV *Step,
//                                           ICmpInst::Predicate *Pred,
//                                           ScalarEvolution *SE);
1337};

1339template <>
1340struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;

static const GetExtendExprTy GetExtendExpr;

static const SCEV *getOverflowLimitForStep(const SCEV *Step,
                                           ICmpInst::Predicate *Pred,
                                           ScalarEvolution *SE) {
  return getSignedOverflowLimitForStep(Step, Pred, SE);
}
1350};

1352const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
  SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;

1355template <>
1356struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;

static const GetExtendExprTy GetExtendExpr;

static const SCEV *getOverflowLimitForStep(const SCEV *Step,
                                           ICmpInst::Predicate *Pred,
                                           ScalarEvolution *SE) {
  return getUnsignedOverflowLimitForStep(Step, Pred, SE);
}
1366};

1368const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
  SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;

1371} // end anonymous namespace

1373// The recurrence AR has been shown to have no signed/unsigned wrap or something
1374// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1375// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1376// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1377// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1378// expression "Step + sext/zext(PreIncAR)" is congruent with
1379// "sext/zext(PostIncAR)"
1380template <typename ExtendOpTy>
1381static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
                                      ScalarEvolution *SE, unsigned Depth) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;

const Loop *L = AR->getLoop();
const SCEV *Start = AR->getStart();
const SCEV *Step = AR->getStepRecurrence(*SE);

// Check for a simple looking step prior to loop entry.
const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
if (!SA)
  return nullptr;

// Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
// subtraction is expensive. For this purpose, perform a quick and dirty
// difference, by checking for Step in the operand list.
SmallVector<const SCEV *, 4> DiffOps;
for (const SCEV *Op : SA->operands())
  if (Op != Step)
    DiffOps.push_back(Op);

if (DiffOps.size() == SA->getNumOperands())
  return nullptr;

// Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
// `Step`:

// 1. NSW/NUW flags on the step increment.
auto PreStartFlags =
  ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
    SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));

// "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
// "S+X does not sign/unsign-overflow".
//

const SCEV *BECount = SE->getBackedgeTakenCount(L);
if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
    !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
  return PreStart;

// 2. Direct overflow check on the step operation's expression.
unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
const SCEV *OperandExtendedStart =
    SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
                   (SE->*GetExtendExpr)(Step, WideTy, Depth));
if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
  if (PreAR && AR->getNoWrapFlags(WrapType)) {
    // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
    // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
    // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`.  Cache this fact.
    SE->setNoWrapFlags(const_cast<SCEVAddRecExpr *>(PreAR), WrapType);
  }
  return PreStart;
}

// 3. Loop precondition.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
    ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);

if (OverflowLimit &&
    SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
  return PreStart;

return nullptr;
1451}

1453// Get the normalized zero or sign extended expression for this AddRec's Start.
1454template <typename ExtendOpTy>
1455static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
                                      ScalarEvolution *SE,
                                      unsigned Depth) {
auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;

const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
if (!PreStart)
  return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);

return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
                                           Depth),
                      (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1467}

1469// Try to prove away overflow by looking at "nearby" add recurrences.  A
1470// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1471// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1472//
1473// Formally:
1474//
1475//     {S,+,X} == {S-T,+,X} + T
1476//  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1477//
1478// If ({S-T,+,X} + T) does not overflow  ... (1)
1479//
1480//  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1481//
1482// If {S-T,+,X} does not overflow  ... (2)
1483//
1484//  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1485//      == {Ext(S-T)+Ext(T),+,Ext(X)}
1486//
1487// If (S-T)+T does not overflow  ... (3)
1488//
1489//  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1490//      == {Ext(S),+,Ext(X)} == LHS
1491//
1492// Thus, if (1), (2) and (3) are true for some T, then
1493//   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1494//
1495// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1496// does not overflow" restricted to the 0th iteration.  Therefore we only need
1497// to check for (1) and (2).
1498//
1499// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1500// is `Delta` (defined below).
1501template <typename ExtendOpTy>
1502bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
                                              const SCEV *Step,
                                              const Loop *L) {
auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;

// We restrict `Start` to a constant to prevent SCEV from spending too much
// time here.  It is correct (but more expensive) to continue with a
// non-constant `Start` and do a general SCEV subtraction to compute
// `PreStart` below.
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
if (!StartC)
  return false;

APInt StartAI = StartC->getAPInt();

for (unsigned Delta : {-2, -1, 1, 2}) {
  const SCEV *PreStart = getConstant(StartAI - Delta);

  FoldingSetNodeID ID;
  ID.AddInteger(scAddRecExpr);
  ID.AddPointer(PreStart);
  ID.AddPointer(Step);
  ID.AddPointer(L);
  void *IP = nullptr;
  const auto *PreAR =
    static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));

  // Give up if we don't already have the add recurrence we need because
  // actually constructing an add recurrence is relatively expensive.
  if (PreAR && PreAR->getNoWrapFlags(WrapType)) {  // proves (2)
    const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
    ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
    const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
        DeltaS, &Pred, this);
    if (Limit && isKnownPredicate(Pred, PreAR, Limit))  // proves (1)
      return true;
  }
}

return false;
1542}

1544// Finds an integer D for an expression (C + x + y + ...) such that the top
1545// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1546// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1547// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1548// the (C + x + y + ...) expression is \p WholeAddExpr.
1549static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
                                          const SCEVConstant *ConstantTerm,
                                          const SCEVAddExpr *WholeAddExpr) {
const APInt &C = ConstantTerm->getAPInt();
const unsigned BitWidth = C.getBitWidth();
// Find number of trailing zeros of (x + y + ...) w/o the C first:
uint32_t TZ = BitWidth;
for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
  TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
if (TZ) {
  // Set D to be as many least significant bits of C as possible while still
  // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
  return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
}
return APInt(BitWidth, 0);
1564}

1566// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1567// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1568// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1569// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1570static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
                                          const APInt &ConstantStart,
                                          const SCEV *Step) {
const unsigned BitWidth = ConstantStart.getBitWidth();
const uint32_t TZ = SE.GetMinTrailingZeros(Step);
if (TZ)
  return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
                       : ConstantStart;
return APInt(BitWidth, 0);
1579}

1581const SCEV *
1582ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1584, __extension__
 __PRETTY_FUNCTION__))
       "This is not an extending conversion!")(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1584, __extension__
 __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1586, __extension__
 __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1586, __extension__
 __PRETTY_FUNCTION__));
assert(!Op->getType()->isPointerTy() && "Can't extend pointer!")(static_cast <bool> (!Op->getType()->isPointerTy(
) && "Can't extend pointer!") ? void (0) : __assert_fail
 ("!Op->getType()->isPointerTy() && \"Can't extend pointer!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1587, __extension__
 __PRETTY_FUNCTION__));
Ty = getEffectiveSCEVType(Ty);

// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
  return getConstant(
    cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));

// zext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);

// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scZeroExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
if (Depth > MaxCastDepth) {
  SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
                                                   Op, Ty);
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Op);
  return S;
}

// zext(trunc(x)) --> zext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
  // It's possible the bits taken off by the truncate were all zero bits. If
  // so, we should be able to simplify this further.
  const SCEV *X = ST->getOperand();
  ConstantRange CR = getUnsignedRange(X);
  unsigned TruncBits = getTypeSizeInBits(ST->getType());
  unsigned NewBits = getTypeSizeInBits(Ty);
  if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
          CR.zextOrTrunc(NewBits)))
    return getTruncateOrZeroExtend(X, Ty, Depth);
}

// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
// operands (often constants).  This allows analysis of something like
// this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
  if (AR->isAffine()) {
    const SCEV *Start = AR->getStart();
    const SCEV *Step = AR->getStepRecurrence(*this);
    unsigned BitWidth = getTypeSizeInBits(AR->getType());
    const Loop *L = AR->getLoop();

    if (!AR->hasNoUnsignedWrap()) {
      auto NewFlags = proveNoWrapViaConstantRanges(AR);
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
    }

    // If we have special knowledge that this addrec won't overflow,
    // we don't need to do any further analysis.
    if (AR->hasNoUnsignedWrap())
      return getAddRecExpr(
          getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
          getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());

    // Check whether the backedge-taken count is SCEVCouldNotCompute.
    // Note that this serves two purposes: It filters out loops that are
    // simply not analyzable, and it covers the case where this code is
    // being called from within backedge-taken count analysis, such that
    // attempting to ask for the backedge-taken count would likely result
    // in infinite recursion. In the later case, the analysis code will
    // cope with a conservative value, and it will take care to purge
    // that value once it has finished.
    const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
    if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
      // Manually compute the final value for AR, checking for overflow.

      // Check whether the backedge-taken count can be losslessly casted to
      // the addrec's type. The count is always unsigned.
      const SCEV *CastedMaxBECount =
          getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
      const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
          CastedMaxBECount, MaxBECount->getType(), Depth);
      if (MaxBECount == RecastedMaxBECount) {
        Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
        // Check whether Start+Step*MaxBECount has no unsigned overflow.
        const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
                                      SCEV::FlagAnyWrap, Depth + 1);
        const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
                                                        SCEV::FlagAnyWrap,
                                                        Depth + 1),
                                             WideTy, Depth + 1);
        const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
        const SCEV *WideMaxBECount =
          getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
        const SCEV *OperandExtendedAdd =
          getAddExpr(WideStart,
                     getMulExpr(WideMaxBECount,
                                getZeroExtendExpr(Step, WideTy, Depth + 1),
                                SCEV::FlagAnyWrap, Depth + 1),
                     SCEV::FlagAnyWrap, Depth + 1);
        if (ZAdd == OperandExtendedAdd) {
          // Cache knowledge of AR NUW, which is propagated to this AddRec.
          setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
          // Return the expression with the addrec on the outside.
          return getAddRecExpr(
              getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getZeroExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
        }
        // Similar to above, only this time treat the step value as signed.
        // This covers loops that count down.
        OperandExtendedAdd =
          getAddExpr(WideStart,
                     getMulExpr(WideMaxBECount,
                                getSignExtendExpr(Step, WideTy, Depth + 1),
                                SCEV::FlagAnyWrap, Depth + 1),
                     SCEV::FlagAnyWrap, Depth + 1);
        if (ZAdd == OperandExtendedAdd) {
          // Cache knowledge of AR NW, which is propagated to this AddRec.
          // Negative step causes unsigned wrap, but it still can't self-wrap.
          setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
          // Return the expression with the addrec on the outside.
          return getAddRecExpr(
              getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getSignExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
        }
      }
    }

    // Normally, in the cases we can prove no-overflow via a
    // backedge guarding condition, we can also compute a backedge
    // taken count for the loop.  The exceptions are assumptions and
    // guards present in the loop -- SCEV is not great at exploiting
    // these to compute max backedge taken counts, but can still use
    // these to prove lack of overflow.  Use this fact to avoid
    // doing extra work that may not pay off.
    if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
        !AC.assumptions().empty()) {

      auto NewFlags = proveNoUnsignedWrapViaInduction(AR);
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
      if (AR->hasNoUnsignedWrap()) {
        // Same as nuw case above - duplicated here to avoid a compile time
        // issue.  It's not clear that the order of checks does matter, but
        // it's one of two issue possible causes for a change which was
        // reverted.  Be conservative for the moment.
        return getAddRecExpr(
              getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getZeroExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
      }
      
      // For a negative step, we can extend the operands iff doing so only
      // traverses values in the range zext([0,UINT_MAX]). 
      if (isKnownNegative(Step)) {
        const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
                                    getSignedRangeMin(Step));
        if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
            isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
          // Cache knowledge of AR NW, which is propagated to this
          // AddRec.  Negative step causes unsigned wrap, but it
          // still can't self-wrap.
          setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);
          // Return the expression with the addrec on the outside.
          return getAddRecExpr(
              getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getSignExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
        }
      }
    }

    // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
    // if D + (C - D + Step * n) could be proven to not unsigned wrap
    // where D maximizes the number of trailing zeros of (C - D + Step * n)
    if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
      const APInt &C = SC->getAPInt();
      const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
      if (D != 0) {
        const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
        const SCEV *SResidual =
            getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
        const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
        return getAddExpr(SZExtD, SZExtR,
                          (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
                          Depth + 1);
      }
    }

    if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW);
      return getAddRecExpr(
          getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
          getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    }
  }

// zext(A % B) --> zext(A) % zext(B)
{
  const SCEV *LHS;
  const SCEV *RHS;
  if (matchURem(Op, LHS, RHS))
    return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
                       getZeroExtendExpr(RHS, Ty, Depth + 1));
}

// zext(A / B) --> zext(A) / zext(B).
if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
  return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
                     getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));

if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
  // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
  if (SA->hasNoUnsignedWrap()) {
    // If the addition does not unsign overflow then we can, by definition,
    // commute the zero extension with the addition operation.
    SmallVector<const SCEV *, 4> Ops;
    for (const auto *Op : SA->operands())
      Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
    return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
  }

  // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
  // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
  // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
  //
  // Often address arithmetics contain expressions like
  // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
  // This transformation is useful while proving that such expressions are
  // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
  if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
    const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
    if (D != 0) {
      const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
      const SCEV *SResidual =
          getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
      const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
      return getAddExpr(SZExtD, SZExtR,
                        (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
                        Depth + 1);
    }
  }
}

if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
  // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
  if (SM->hasNoUnsignedWrap()) {
    // If the multiply does not unsign overflow then we can, by definition,
    // commute the zero extension with the multiply operation.
    SmallVector<const SCEV *, 4> Ops;
    for (const auto *Op : SM->operands())
      Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
    return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
  }

  // zext(2^K * (trunc X to iN)) to iM ->
  // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
  //
  // Proof:
  //
  //     zext(2^K * (trunc X to iN)) to iM
  //   = zext((trunc X to iN) << K) to iM
  //   = zext((trunc X to i{N-K}) << K)<nuw> to iM
  //     (because shl removes the top K bits)
  //   = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
  //   = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
  //
  if (SM->getNumOperands() == 2)
    if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
      if (MulLHS->getAPInt().isPowerOf2())
        if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
          int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
                             MulLHS->getAPInt().logBase2();
          Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
          return getMulExpr(
              getZeroExtendExpr(MulLHS, Ty),
              getZeroExtendExpr(
                  getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
              SCEV::FlagNUW, Depth + 1);
        }
}

// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
                                                 Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
registerUser(S, Op);
return S;
1882}

1884const SCEV *
1885ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1887, __extension__
 __PRETTY_FUNCTION__))
       "This is not an extending conversion!")(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1887, __extension__
 __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1889, __extension__
 __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1889, __extension__
 __PRETTY_FUNCTION__));
assert(!Op->getType()->isPointerTy() && "Can't extend pointer!")(static_cast <bool> (!Op->getType()->isPointerTy(
) && "Can't extend pointer!") ? void (0) : __assert_fail
 ("!Op->getType()->isPointerTy() && \"Can't extend pointer!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 1890, __extension__
 __PRETTY_FUNCTION__));
Ty = getEffectiveSCEVType(Ty);

// Fold if the operand is constant.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
  return getConstant(
    cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));

// sext(sext(x)) --> sext(x)
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
  return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);

// sext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);

// Before doing any expensive analysis, check to see if we've already
// computed a SCEV for this Op and Ty.
FoldingSetNodeID ID;
ID.AddInteger(scSignExtend);
ID.AddPointer(Op);
ID.AddPointer(Ty);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
// Limit recursion depth.
if (Depth > MaxCastDepth) {
  SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
                                                   Op, Ty);
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Op);
  return S;
}

// sext(trunc(x)) --> sext(x) or x or trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
  // It's possible the bits taken off by the truncate were all sign bits. If
  // so, we should be able to simplify this further.
  const SCEV *X = ST->getOperand();
  ConstantRange CR = getSignedRange(X);
  unsigned TruncBits = getTypeSizeInBits(ST->getType());
  unsigned NewBits = getTypeSizeInBits(Ty);
  if (CR.truncate(TruncBits).signExtend(NewBits).contains(
          CR.sextOrTrunc(NewBits)))
    return getTruncateOrSignExtend(X, Ty, Depth);
}

if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
  // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
  if (SA->hasNoSignedWrap()) {
    // If the addition does not sign overflow then we can, by definition,
    // commute the sign extension with the addition operation.
    SmallVector<const SCEV *, 4> Ops;
    for (const auto *Op : SA->operands())
      Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
    return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
  }

  // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
  // if D + (C - D + x + y + ...) could be proven to not signed wrap
  // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
  //
  // For instance, this will bring two seemingly different expressions:
  //     1 + sext(5 + 20 * %x + 24 * %y)  and
  //         sext(6 + 20 * %x + 24 * %y)
  // to the same form:
  //     2 + sext(4 + 20 * %x + 24 * %y)
  if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
    const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
    if (D != 0) {
      const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
      const SCEV *SResidual =
          getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
      const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
      return getAddExpr(SSExtD, SSExtR,
                        (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
                        Depth + 1);
    }
  }
}
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can sign extend all of the
// operands (often constants).  This allows analysis of something like
// this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
  if (AR->isAffine()) {
    const SCEV *Start = AR->getStart();
    const SCEV *Step = AR->getStepRecurrence(*this);
    unsigned BitWidth = getTypeSizeInBits(AR->getType());
    const Loop *L = AR->getLoop();

    if (!AR->hasNoSignedWrap()) {
      auto NewFlags = proveNoWrapViaConstantRanges(AR);
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
    }

    // If we have special knowledge that this addrec won't overflow,
    // we don't need to do any further analysis.
    if (AR->hasNoSignedWrap())
      return getAddRecExpr(
          getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
          getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);

    // Check whether the backedge-taken count is SCEVCouldNotCompute.
    // Note that this serves two purposes: It filters out loops that are
    // simply not analyzable, and it covers the case where this code is
    // being called from within backedge-taken count analysis, such that
    // attempting to ask for the backedge-taken count would likely result
    // in infinite recursion. In the later case, the analysis code will
    // cope with a conservative value, and it will take care to purge
    // that value once it has finished.
    const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
    if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
      // Manually compute the final value for AR, checking for
      // overflow.

      // Check whether the backedge-taken count can be losslessly casted to
      // the addrec's type. The count is always unsigned.
      const SCEV *CastedMaxBECount =
          getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
      const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
          CastedMaxBECount, MaxBECount->getType(), Depth);
      if (MaxBECount == RecastedMaxBECount) {
        Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
        // Check whether Start+Step*MaxBECount has no signed overflow.
        const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
                                      SCEV::FlagAnyWrap, Depth + 1);
        const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
                                                        SCEV::FlagAnyWrap,
                                                        Depth + 1),
                                             WideTy, Depth + 1);
        const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
        const SCEV *WideMaxBECount =
          getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
        const SCEV *OperandExtendedAdd =
          getAddExpr(WideStart,
                     getMulExpr(WideMaxBECount,
                                getSignExtendExpr(Step, WideTy, Depth + 1),
                                SCEV::FlagAnyWrap, Depth + 1),
                     SCEV::FlagAnyWrap, Depth + 1);
        if (SAdd == OperandExtendedAdd) {
          // Cache knowledge of AR NSW, which is propagated to this AddRec.
          setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
          // Return the expression with the addrec on the outside.
          return getAddRecExpr(
              getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getSignExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
        }
        // Similar to above, only this time treat the step value as unsigned.
        // This covers loops that count up with an unsigned step.
        OperandExtendedAdd =
          getAddExpr(WideStart,
                     getMulExpr(WideMaxBECount,
                                getZeroExtendExpr(Step, WideTy, Depth + 1),
                                SCEV::FlagAnyWrap, Depth + 1),
                     SCEV::FlagAnyWrap, Depth + 1);
        if (SAdd == OperandExtendedAdd) {
          // If AR wraps around then
          //
          //    abs(Step) * MaxBECount > unsigned-max(AR->getType())
          // => SAdd != OperandExtendedAdd
          //
          // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
          // (SAdd == OperandExtendedAdd => AR is NW)

          setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW);

          // Return the expression with the addrec on the outside.
          return getAddRecExpr(
              getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
                                                       Depth + 1),
              getZeroExtendExpr(Step, Ty, Depth + 1), L,
              AR->getNoWrapFlags());
        }
      }
    }

    auto NewFlags = proveNoSignedWrapViaInduction(AR);
    setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags);
    if (AR->hasNoSignedWrap()) {
      // Same as nsw case above - duplicated here to avoid a compile time
      // issue.  It's not clear that the order of checks does matter, but
      // it's one of two issue possible causes for a change which was
      // reverted.  Be conservative for the moment.
      return getAddRecExpr(
          getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
          getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    }

    // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
    // if D + (C - D + Step * n) could be proven to not signed wrap
    // where D maximizes the number of trailing zeros of (C - D + Step * n)
    if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
      const APInt &C = SC->getAPInt();
      const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
      if (D != 0) {
        const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
        const SCEV *SResidual =
            getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
        const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
        return getAddExpr(SSExtD, SSExtR,
                          (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
                          Depth + 1);
      }
    }

    if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW);
      return getAddRecExpr(
          getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
          getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    }
  }

// If the input value is provably positive and we could not simplify
// away the sext build a zext instead.
if (isKnownNonNegative(Op))
  return getZeroExtendExpr(Op, Ty, Depth + 1);

// The cast wasn't folded; create an explicit cast node.
// Recompute the insert position, as it may have been invalidated.
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
                                                 Op, Ty);
UniqueSCEVs.InsertNode(S, IP);
registerUser(S, { Op });
return S;
2118}

2120const SCEV *ScalarEvolution::getCastExpr(SCEVTypes Kind, const SCEV *Op,
                                       Type *Ty) {
switch (Kind) {
case scTruncate:
  return getTruncateExpr(Op, Ty);
case scZeroExtend:
  return getZeroExtendExpr(Op, Ty);
case scSignExtend:
  return getSignExtendExpr(Op, Ty);
case scPtrToInt:
  return getPtrToIntExpr(Op, Ty);
default:
  llvm_unreachable("Not a SCEV cast expression!")::llvm::llvm_unreachable_internal("Not a SCEV cast expression!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2132);
}
2134}

2136/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2137/// unspecified bits out to the given type.
2138const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
                                            Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2141, __extension__
 __PRETTY_FUNCTION__))
       "This is not an extending conversion!")(static_cast <bool> (getTypeSizeInBits(Op->getType()
) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2141, __extension__
 __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2143, __extension__
 __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")(static_cast <bool> (isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2143, __extension__
 __PRETTY_FUNCTION__));
Ty = getEffectiveSCEVType(Ty);

// Sign-extend negative constants.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
  if (SC->getAPInt().isNegative())
    return getSignExtendExpr(Op, Ty);

// Peel off a truncate cast.
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
  const SCEV *NewOp = T->getOperand();
  if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
    return getAnyExtendExpr(NewOp, Ty);
  return getTruncateOrNoop(NewOp, Ty);
}

// Next try a zext cast. If the cast is folded, use it.
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
if (!isa<SCEVZeroExtendExpr>(ZExt))
  return ZExt;

// Next try a sext cast. If the cast is folded, use it.
const SCEV *SExt = getSignExtendExpr(Op, Ty);
if (!isa<SCEVSignExtendExpr>(SExt))
  return SExt;

// Force the cast to be folded into the operands of an addrec.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
  SmallVector<const SCEV *, 4> Ops;
  for (const SCEV *Op : AR->operands())
    Ops.push_back(getAnyExtendExpr(Op, Ty));
  return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
}

// If the expression is obviously signed, use the sext cast value.
if (isa<SCEVSMaxExpr>(Op))
  return SExt;

// Absent any other information, use the zext cast value.
return ZExt;
2183}

2185/// Process the given Ops list, which is a list of operands to be added under
2186/// the given scale, update the given map. This is a helper function for
2187/// getAddRecExpr. As an example of what it does, given a sequence of operands
2188/// that would form an add expression like this:
2189///
2190///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2191///
2192/// where A and B are constants, update the map with these values:
2193///
2194///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2195///
2196/// and add 13 + A*B*29 to AccumulatedConstant.
2197/// This will allow getAddRecExpr to produce this:
2198///
2199///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2200///
2201/// This form often exposes folding opportunities that are hidden in
2202/// the original operand list.
2203///
2204/// Return true iff it appears that any interesting folding opportunities
2205/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2206/// the common case where no interesting opportunities are present, and
2207/// is also used as a check to avoid infinite recursion.
2208static bool
2209CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
                           SmallVectorImpl<const SCEV *> &NewOps,
                           APInt &AccumulatedConstant,
                           const SCEV *const *Ops, size_t NumOperands,
                           const APInt &Scale,
                           ScalarEvolution &SE) {
bool Interesting = false;

// Iterate over the add operands. They are sorted, with constants first.
unsigned i = 0;
while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
  ++i;
  // Pull a buried constant out to the outside.
  if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
    Interesting = true;
  AccumulatedConstant += Scale * C->getAPInt();
}

// Next comes everything else. We're especially interested in multiplies
// here, but they're in the middle, so just visit the rest with one loop.
for (; i != NumOperands; ++i) {
  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
  if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
    APInt NewScale =
        Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
    if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
      // A multiplication of a constant with another add; recurse.
      const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
      Interesting |=
        CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
                                     Add->op_begin(), Add->getNumOperands(),
                                     NewScale, SE);
    } else {
      // A multiplication of a constant with some other value. Update
      // the map.
      SmallVector<const SCEV *, 4> MulOps(drop_begin(Mul->operands()));
      const SCEV *Key = SE.getMulExpr(MulOps);
      auto Pair = M.insert({Key, NewScale});
      if (Pair.second) {
        NewOps.push_back(Pair.first->first);
      } else {
        Pair.first->second += NewScale;
        // The map already had an entry for this value, which may indicate
        // a folding opportunity.
        Interesting = true;
      }
    }
  } else {
    // An ordinary operand. Update the map.
    std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
        M.insert({Ops[i], Scale});
    if (Pair.second) {
      NewOps.push_back(Pair.first->first);
    } else {
      Pair.first->second += Scale;
      // The map already had an entry for this value, which may indicate
      // a folding opportunity.
      Interesting = true;
    }
  }
}

return Interesting;
2272}

2274bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed,
                                    const SCEV *LHS, const SCEV *RHS) {
const SCEV *(ScalarEvolution::*Operation)(const SCEV *, const SCEV *,
                                          SCEV::NoWrapFlags, unsigned);
switch (BinOp) {
default:
  llvm_unreachable("Unsupported binary op")::llvm::llvm_unreachable_internal("Unsupported binary op", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 2280);
case Instruction::Add:
  Operation = &ScalarEvolution::getAddExpr;
  break;
case Instruction::Sub:
  Operation = &ScalarEvolution::getMinusSCEV;
  break;
case Instruction::Mul:
  Operation = &ScalarEvolution::getMulExpr;
  break;
}

const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) =
    Signed ? &ScalarEvolution::getSignExtendExpr
           : &ScalarEvolution::getZeroExtendExpr;

// Check ext(LHS op RHS) == ext(LHS) op ext(RHS)
auto *NarrowTy = cast<IntegerType>(LHS->getType());
auto *WideTy =
    IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2);

const SCEV *A = (this->*Extension)(
    (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0);
const SCEV *B = (this->*Operation)((this->*Extension)(LHS, WideTy, 0),
                                   (this->*Extension)(RHS, WideTy, 0),
                                   SCEV::FlagAnyWrap, 0);
return A == B;
2307}

2309std::pair<SCEV::NoWrapFlags, bool /*Deduced*/>
2310ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp(
  const OverflowingBinaryOperator *OBO) {
SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap;

if (OBO->hasNoUnsignedWrap())
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
if (OBO->hasNoSignedWrap())
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);

bool Deduced = false;

if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap())
  return {Flags, Deduced};

if (OBO->getOpcode() != Instruction::Add &&
    OBO->getOpcode() != Instruction::Sub &&
    OBO->getOpcode() != Instruction::Mul)
  return {Flags, Deduced};

const SCEV *LHS = getSCEV(OBO->getOperand(0));
const SCEV *RHS = getSCEV(OBO->getOperand(1));

if (!OBO->hasNoUnsignedWrap() &&
    willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(),
                    /* Signed */ false, LHS, RHS)) {
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
  Deduced = true;
}

if (!OBO->hasNoSignedWrap() &&
    willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(),
                    /* Signed */ true, LHS, RHS)) {
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
  Deduced = true;
}

return {Flags, Deduced};
2347}

2349// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2350// `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
2351// can't-overflow flags for the operation if possible.
2352static SCEV::NoWrapFlags
2353StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
                    const ArrayRef<const SCEV *> Ops,
                    SCEV::NoWrapFlags Flags) {
using namespace std::placeholders;

using OBO = OverflowingBinaryOperator;

bool CanAnalyze =
    Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
(void)CanAnalyze;
assert(CanAnalyze && "don't call from other places!")(static_cast <bool> (CanAnalyze && "don't call from other places!"
) ? void (0) : __assert_fail ("CanAnalyze && \"don't call from other places!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2363, __extension__
 __PRETTY_FUNCTION__));

int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
SCEV::NoWrapFlags SignOrUnsignWrap =
    ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);

// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
auto IsKnownNonNegative = [&](const SCEV *S) {
  return SE->isKnownNonNegative(S);
};

if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
  Flags =
      ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);

SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);

if (SignOrUnsignWrap != SignOrUnsignMask &&
    (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
    isa<SCEVConstant>(Ops[0])) {

  auto Opcode = [&] {
    switch (Type) {
    case scAddExpr:
      return Instruction::Add;
    case scMulExpr:
      return Instruction::Mul;
    default:
      llvm_unreachable("Unexpected SCEV op.")::llvm::llvm_unreachable_internal("Unexpected SCEV op.", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 2391);
    }
  }();

  const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();

  // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
  if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
    auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
        Opcode, C, OBO::NoSignedWrap);
    if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
      Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
  }

  // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
  if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
    auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
        Opcode, C, OBO::NoUnsignedWrap);
    if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
      Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
  }
}

// <0,+,nonnegative><nw> is also nuw
// TODO: Add corresponding nsw case
if (Type == scAddRecExpr && ScalarEvolution::hasFlags(Flags, SCEV::FlagNW) &&
    !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) && Ops.size() == 2 &&
    Ops[0]->isZero() && IsKnownNonNegative(Ops[1]))
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);

// both (udiv X, Y) * Y and Y * (udiv X, Y) are always NUW
if (Type == scMulExpr && !ScalarEvolution::hasFlags(Flags, SCEV::FlagNUW) &&
    Ops.size() == 2) {
  if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[0]))
    if (UDiv->getOperand(1) == Ops[1])
      Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
  if (auto *UDiv = dyn_cast<SCEVUDivExpr>(Ops[1]))
    if (UDiv->getOperand(1) == Ops[0])
      Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
}

return Flags;
2433}

2435bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2437}

2439/// Get a canonical add expression, or something simpler if possible.
2440const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
                                      SCEV::NoWrapFlags OrigFlags,
                                      unsigned Depth) {
assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&(static_cast <bool> (!(OrigFlags & ~(SCEV::FlagNUW |
 SCEV::FlagNSW)) && "only nuw or nsw allowed") ? void
 (0) : __assert_fail ("!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2444, __extension__
 __PRETTY_FUNCTION__))
       "only nuw or nsw allowed")(static_cast <bool> (!(OrigFlags & ~(SCEV::FlagNUW |
 SCEV::FlagNSW)) && "only nuw or nsw allowed") ? void
 (0) : __assert_fail ("!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2444, __extension__
 __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty add!")(static_cast <bool> (!Ops.empty() && "Cannot get empty add!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty add!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2445, __extension__
 __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
2447#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "SCEVAddExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2451, __extension__
 __PRETTY_FUNCTION__))
         "SCEVAddExpr operand types don't match!")(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "SCEVAddExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2451, __extension__
 __PRETTY_FUNCTION__));
unsigned NumPtrs = count_if(
    Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); });
assert(NumPtrs <= 1 && "add has at most one pointer operand")(static_cast <bool> (NumPtrs <= 1 && "add has at most one pointer operand"
) ? void (0) : __assert_fail ("NumPtrs <= 1 && \"add has at most one pointer operand\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2454, __extension__
 __PRETTY_FUNCTION__));
2455#endif

// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);

// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
  ++Idx;
  assert(Idx < Ops.size())(static_cast <bool> (Idx < Ops.size()) ? void (0) : __assert_fail
 ("Idx < Ops.size()", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 2464, __extension__ __PRETTY_FUNCTION__));
  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    // We found two constants, fold them together!
    Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
    if (Ops.size() == 2) return Ops[0];
    Ops.erase(Ops.begin()+1);  // Erase the folded element
    LHSC = cast<SCEVConstant>(Ops[0]);
  }

  // If we are left with a constant zero being added, strip it off.
  if (LHSC->getValue()->isZero()) {
    Ops.erase(Ops.begin());
    --Idx;
  }

  if (Ops.size() == 1) return Ops[0];
}

// Delay expensive flag strengthening until necessary.
auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
  return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags);
};

// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
  return getOrCreateAddExpr(Ops, ComputeFlags(Ops));

if (SCEV *S = findExistingSCEVInCache(scAddExpr, Ops)) {
  // Don't strengthen flags if we have no new information.
  SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S);
  if (Add->getNoWrapFlags(OrigFlags) != OrigFlags)
    Add->setNoWrapFlags(ComputeFlags(Ops));
  return S;
}

// Okay, check to see if the same value occurs in the operand list more than
// once.  If so, merge them together into an multiply expression.  Since we
// sorted the list, these values are required to be adjacent.
Type *Ty = Ops[0]->getType();
bool FoundMatch = false;
for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
  if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
    // Scan ahead to count how many equal operands there are.
    unsigned Count = 2;
    while (i+Count != e && Ops[i+Count] == Ops[i])
      ++Count;
    // Merge the values into a multiply.
    const SCEV *Scale = getConstant(Ty, Count);
    const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
    if (Ops.size() == Count)
      return Mul;
    Ops[i] = Mul;
    Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
    --i; e -= Count - 1;
    FoundMatch = true;
  }
if (FoundMatch)
  return getAddExpr(Ops, OrigFlags, Depth + 1);

// Check for truncates. If all the operands are truncated from the same
// type, see if factoring out the truncate would permit the result to be
// folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
// if the contents of the resulting outer trunc fold to something simple.
auto FindTruncSrcType = [&]() -> Type * {
  // We're ultimately looking to fold an addrec of truncs and muls of only
  // constants and truncs, so if we find any other types of SCEV
  // as operands of the addrec then we bail and return nullptr here.
  // Otherwise, we return the type of the operand of a trunc that we find.
  if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
    return T->getOperand()->getType();
  if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
    const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
    if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
      return T->getOperand()->getType();
  }
  return nullptr;
};
if (auto *SrcType = FindTruncSrcType()) {
  SmallVector<const SCEV *, 8> LargeOps;
  bool Ok = true;
  // Check all the operands to see if they can be represented in the
  // source type of the truncate.
  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
      if (T->getOperand()->getType() != SrcType) {
        Ok = false;
        break;
      }
      LargeOps.push_back(T->getOperand());
    } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
      LargeOps.push_back(getAnyExtendExpr(C, SrcType));
    } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
      SmallVector<const SCEV *, 8> LargeMulOps;
      for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
        if (const SCEVTruncateExpr *T =
              dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
          if (T->getOperand()->getType() != SrcType) {
            Ok = false;
            break;
          }
          LargeMulOps.push_back(T->getOperand());
        } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
          LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
        } else {
          Ok = false;
          break;
        }
      }
      if (Ok)
        LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
    } else {
      Ok = false;
      break;
    }
  }
  if (Ok) {
    // Evaluate the expression in the larger type.
    const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
    // If it folds to something simple, use it. Otherwise, don't.
    if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
      return getTruncateExpr(Fold, Ty);
  }
}

if (Ops.size() == 2) {
  // Check if we have an expression of the form ((X + C1) - C2), where C1 and
  // C2 can be folded in a way that allows retaining wrapping flags of (X +
  // C1).
  const SCEV *A = Ops[0];
  const SCEV *B = Ops[1];
  auto *AddExpr = dyn_cast<SCEVAddExpr>(B);
  auto *C = dyn_cast<SCEVConstant>(A);
  if (AddExpr && C && isa<SCEVConstant>(AddExpr->getOperand(0))) {
    auto C1 = cast<SCEVConstant>(AddExpr->getOperand(0))->getAPInt();
    auto C2 = C->getAPInt();
    SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap;

    APInt ConstAdd = C1 + C2;
    auto AddFlags = AddExpr->getNoWrapFlags();
    // Adding a smaller constant is NUW if the original AddExpr was NUW.
    if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNUW) &&
        ConstAdd.ule(C1)) {
      PreservedFlags =
          ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNUW);
    }

    // Adding a constant with the same sign and small magnitude is NSW, if the
    // original AddExpr was NSW.
    if (ScalarEvolution::hasFlags(AddFlags, SCEV::FlagNSW) &&
        C1.isSignBitSet() == ConstAdd.isSignBitSet() &&
        ConstAdd.abs().ule(C1.abs())) {
      PreservedFlags =
          ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNSW);
    }

    if (PreservedFlags != SCEV::FlagAnyWrap) {
      SmallVector<const SCEV *, 4> NewOps(AddExpr->operands());
      NewOps[0] = getConstant(ConstAdd);
      return getAddExpr(NewOps, PreservedFlags);
    }
  }
}

// Canonicalize (-1 * urem X, Y) + X --> (Y * X/Y)
if (Ops.size() == 2) {
  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[0]);
  if (Mul && Mul->getNumOperands() == 2 &&
      Mul->getOperand(0)->isAllOnesValue()) {
    const SCEV *X;
    const SCEV *Y;
    if (matchURem(Mul->getOperand(1), X, Y) && X == Ops[1]) {
      return getMulExpr(Y, getUDivExpr(X, Y));
    }
  }
}

// Skip past any other cast SCEVs.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
  ++Idx;

// If there are add operands they would be next.
if (Idx < Ops.size()) {
  bool DeletedAdd = false;
  // If the original flags and all inlined SCEVAddExprs are NUW, use the
  // common NUW flag for expression after inlining. Other flags cannot be
  // preserved, because they may depend on the original order of operations.
  SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW);
  while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
    if (Ops.size() > AddOpsInlineThreshold ||
        Add->getNumOperands() > AddOpsInlineThreshold)
      break;
    // If we have an add, expand the add operands onto the end of the operands
    // list.
    Ops.erase(Ops.begin()+Idx);
    Ops.append(Add->op_begin(), Add->op_end());
    DeletedAdd = true;
    CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags());
  }

  // If we deleted at least one add, we added operands to the end of the list,
  // and they are not necessarily sorted.  Recurse to resort and resimplify
  // any operands we just acquired.
  if (DeletedAdd)
    return getAddExpr(Ops, CommonFlags, Depth + 1);
}

// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
  ++Idx;

// Check to see if there are any folding opportunities present with
// operands multiplied by constant values.
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
  uint64_t BitWidth = getTypeSizeInBits(Ty);
  DenseMap<const SCEV *, APInt> M;
  SmallVector<const SCEV *, 8> NewOps;
  APInt AccumulatedConstant(BitWidth, 0);
  if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
                                   Ops.data(), Ops.size(),
                                   APInt(BitWidth, 1), *this)) {
    struct APIntCompare {
      bool operator()(const APInt &LHS, const APInt &RHS) const {
        return LHS.ult(RHS);
      }
    };

    // Some interesting folding opportunity is present, so its worthwhile to
    // re-generate the operands list. Group the operands by constant scale,
    // to avoid multiplying by the same constant scale multiple times.
    std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
    for (const SCEV *NewOp : NewOps)
      MulOpLists[M.find(NewOp)->second].push_back(NewOp);
    // Re-generate the operands list.
    Ops.clear();
    if (AccumulatedConstant != 0)
      Ops.push_back(getConstant(AccumulatedConstant));
    for (auto &MulOp : MulOpLists) {
      if (MulOp.first == 1) {
        Ops.push_back(getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1));
      } else if (MulOp.first != 0) {
        Ops.push_back(getMulExpr(
            getConstant(MulOp.first),
            getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
            SCEV::FlagAnyWrap, Depth + 1));
      }
    }
    if (Ops.empty())
      return getZero(Ty);
    if (Ops.size() == 1)
      return Ops[0];
    return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
  }
}

// If we are adding something to a multiply expression, make sure the
// something is not already an operand of the multiply.  If so, merge it into
// the multiply.
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
  const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
  for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
    const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
    if (isa<SCEVConstant>(MulOpSCEV))
      continue;
    for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
      if (MulOpSCEV == Ops[AddOp]) {
        // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
        const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
        if (Mul->getNumOperands() != 2) {
          // If the multiply has more than two operands, we must get the
          // Y*Z term.
          SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
                                              Mul->op_begin()+MulOp);
          MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
          InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
        }
        SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
        const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
        const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
                                          SCEV::FlagAnyWrap, Depth + 1);
        if (Ops.size() == 2) return OuterMul;
        if (AddOp < Idx) {
          Ops.erase(Ops.begin()+AddOp);
          Ops.erase(Ops.begin()+Idx-1);
        } else {
          Ops.erase(Ops.begin()+Idx);
          Ops.erase(Ops.begin()+AddOp-1);
        }
        Ops.push_back(OuterMul);
        return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
      }

    // Check this multiply against other multiplies being added together.
    for (unsigned OtherMulIdx = Idx+1;
         OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
         ++OtherMulIdx) {
      const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
      // If MulOp occurs in OtherMul, we can fold the two multiplies
      // together.
      for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
           OMulOp != e; ++OMulOp)
        if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
          // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
          const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
          if (Mul->getNumOperands() != 2) {
            SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
                                                Mul->op_begin()+MulOp);
            MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
            InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
          }
          const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
          if (OtherMul->getNumOperands() != 2) {
            SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
                                                OtherMul->op_begin()+OMulOp);
            MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
            InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
          }
          SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
          const SCEV *InnerMulSum =
              getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
          const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
                                            SCEV::FlagAnyWrap, Depth + 1);
          if (Ops.size() == 2) return OuterMul;
          Ops.erase(Ops.begin()+Idx);
          Ops.erase(Ops.begin()+OtherMulIdx-1);
          Ops.push_back(OuterMul);
          return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
        }
    }
  }
}

// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant.  If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
  ++Idx;

// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
  // Scan all of the other operands to this add and add them to the vector if
  // they are loop invariant w.r.t. the recurrence.
  SmallVector<const SCEV *, 8> LIOps;
  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
  const Loop *AddRecLoop = AddRec->getLoop();
  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
      LIOps.push_back(Ops[i]);
      Ops.erase(Ops.begin()+i);
      --i; --e;
    }

  // If we found some loop invariants, fold them into the recurrence.
  if (!LIOps.empty()) {
    // Compute nowrap flags for the addition of the loop-invariant ops and
    // the addrec. Temporarily push it as an operand for that purpose. These
    // flags are valid in the scope of the addrec only.
    LIOps.push_back(AddRec);
    SCEV::NoWrapFlags Flags = ComputeFlags(LIOps);
    LIOps.pop_back();

    //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
    LIOps.push_back(AddRec->getStart());

    SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());

    // It is not in general safe to propagate flags valid on an add within
    // the addrec scope to one outside it.  We must prove that the inner
    // scope is guaranteed to execute if the outer one does to be able to
    // safely propagate.  We know the program is undefined if poison is
    // produced on the inner scoped addrec.  We also know that *for this use*
    // the outer scoped add can't overflow (because of the flags we just
    // computed for the inner scoped add) without the program being undefined.
    // Proving that entry to the outer scope neccesitates entry to the inner
    // scope, thus proves the program undefined if the flags would be violated
    // in the outer scope.
    SCEV::NoWrapFlags AddFlags = Flags;
    if (AddFlags != SCEV::FlagAnyWrap) {
      auto *DefI = getDefiningScopeBound(LIOps);
      auto *ReachI = &*AddRecLoop->getHeader()->begin();
      if (!isGuaranteedToTransferExecutionTo(DefI, ReachI))
        AddFlags = SCEV::FlagAnyWrap;
    }
    AddRecOps[0] = getAddExpr(LIOps, AddFlags, Depth + 1);

    // Build the new addrec. Propagate the NUW and NSW flags if both the
    // outer add and the inner addrec are guaranteed to have no overflow.
    // Always propagate NW.
    Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
    const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);

    // If all of the other operands were loop invariant, we are done.
    if (Ops.size() == 1) return NewRec;

    // Otherwise, add the folded AddRec by the non-invariant parts.
    for (unsigned i = 0;; ++i)
      if (Ops[i] == AddRec) {
        Ops[i] = NewRec;
        break;
      }
    return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
  }

  // Okay, if there weren't any loop invariants to be folded, check to see if
  // there are multiple AddRec's with the same loop induction variable being
  // added together.  If so, we can fold them.
  for (unsigned OtherIdx = Idx+1;
       OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
       ++OtherIdx) {
    // We expect the AddRecExpr's to be sorted in reverse dominance order,
    // so that the 1st found AddRecExpr is dominated by all others.
    assert(DT.dominates((static_cast <bool> (DT.dominates( cast<SCEVAddRecExpr
>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->
getLoop()->getHeader()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? void (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2877, __extension__
 __PRETTY_FUNCTION__))
         cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),(static_cast <bool> (DT.dominates( cast<SCEVAddRecExpr
>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->
getLoop()->getHeader()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? void (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2877, __extension__
 __PRETTY_FUNCTION__))
         AddRec->getLoop()->getHeader()) &&(static_cast <bool> (DT.dominates( cast<SCEVAddRecExpr
>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->
getLoop()->getHeader()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? void (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2877, __extension__
 __PRETTY_FUNCTION__))
      "AddRecExprs are not sorted in reverse dominance order?")(static_cast <bool> (DT.dominates( cast<SCEVAddRecExpr
>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->
getLoop()->getHeader()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? void (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 2877, __extension__
 __PRETTY_FUNCTION__));
    if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
      // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
      SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands());
      for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
           ++OtherIdx) {
        const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
        if (OtherAddRec->getLoop() == AddRecLoop) {
          for (unsigned i = 0, e = OtherAddRec->getNumOperands();
               i != e; ++i) {
            if (i >= AddRecOps.size()) {
              AddRecOps.append(OtherAddRec->op_begin()+i,
                               OtherAddRec->op_end());
              break;
            }
            SmallVector<const SCEV *, 2> TwoOps = {
                AddRecOps[i], OtherAddRec->getOperand(i)};
            AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
          }
          Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
        }
      }
      // Step size has changed, so we cannot guarantee no self-wraparound.
      Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
      return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    }
  }

  // Otherwise couldn't fold anything into this recurrence.  Move onto the
  // next one.
}

// Okay, it looks like we really DO need an add expr.  Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddExpr(Ops, ComputeFlags(Ops));
2912}

2914const SCEV *
2915ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
                                  SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddExpr);
for (const SCEV *Op : Ops)
  ID.AddPointer(Op);
void *IP = nullptr;
SCEVAddExpr *S =
    static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
  S = new (SCEVAllocator)
      SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Ops);
}
S->setNoWrapFlags(Flags);
return S;
2934}

2936const SCEV *
2937ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
                                     const Loop *L, SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
for (const SCEV *Op : Ops)
  ID.AddPointer(Op);
ID.AddPointer(L);
void *IP = nullptr;
SCEVAddRecExpr *S =
    static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
  S = new (SCEVAllocator)
      SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
  UniqueSCEVs.InsertNode(S, IP);
  LoopUsers[L].push_back(S);
  registerUser(S, Ops);
}
setNoWrapFlags(S, Flags);
return S;
2958}

2960const SCEV *
2961ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
                                  SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scMulExpr);
for (const SCEV *Op : Ops)
  ID.AddPointer(Op);
void *IP = nullptr;
SCEVMulExpr *S =
  static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
if (!S) {
  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
  S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
                                      O, Ops.size());
  UniqueSCEVs.InsertNode(S, IP);
  registerUser(S, Ops);
}
S->setNoWrapFlags(Flags);
return S;
2980}

2982static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
uint64_t k = i*j;
if (j > 1 && k / j != i) Overflow = true;
return k;
2986}

2988/// Compute the result of "n choose k", the binomial coefficient.  If an
2989/// intermediate computation overflows, Overflow will be set and the return will
2990/// be garbage. Overflow is not cleared on absence of overflow.
2991static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
// We use the multiplicative formula:
//     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
// At each iteration, we take the n-th term of the numeral and divide by the
// (k-n)th term of the denominator.  This division will always produce an
// integral result, and helps reduce the chance of overflow in the
// intermediate computations. However, we can still overflow even when the
// final result would fit.

if (n == 0 || n == k) return 1;
if (k > n) return 0;

if (k > n/2)
  k = n-k;

uint64_t r = 1;
for (uint64_t i = 1; i <= k; ++i) {
  r = umul_ov(r, n-(i-1), Overflow);
  r /= i;
}
return r;
3012}

3014/// Determine if any of the operands in this SCEV are a constant or if
3015/// any of the add or multiply expressions in this SCEV contain a constant.
3016static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
struct FindConstantInAddMulChain {
  bool FoundConstant = false;

  bool follow(const SCEV *S) {
    FoundConstant |= isa<SCEVConstant>(S);
    return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
  }

  bool isDone() const {
    return FoundConstant;
  }
};

FindConstantInAddMulChain F;
SCEVTraversal<FindConstantInAddMulChain> ST(F);
ST.visitAll(StartExpr);
return F.FoundConstant;
3034}

3036/// Get a canonical multiply expression, or something simpler if possible.
3037const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
                                      SCEV::NoWrapFlags OrigFlags,
                                      unsigned Depth) {
assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&(static_cast <bool> (OrigFlags == maskFlags(OrigFlags, SCEV
::FlagNUW | SCEV::FlagNSW) && "only nuw or nsw allowed"
) ? void (0) : __assert_fail ("OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3041, __extension__
 __PRETTY_FUNCTION__))
       "only nuw or nsw allowed")(static_cast <bool> (OrigFlags == maskFlags(OrigFlags, SCEV
::FlagNUW | SCEV::FlagNSW) && "only nuw or nsw allowed"
) ? void (0) : __assert_fail ("OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3041, __extension__
 __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty mul!")(static_cast <bool> (!Ops.empty() && "Cannot get empty mul!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty mul!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3042, __extension__
 __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
3044#ifndef NDEBUG
Type *ETy = Ops[0]->getType();
assert(!ETy->isPointerTy())(static_cast <bool> (!ETy->isPointerTy()) ? void (0)
 : __assert_fail ("!ETy->isPointerTy()", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 3046, __extension__ __PRETTY_FUNCTION__));
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
  assert(Ops[i]->getType() == ETy &&(static_cast <bool> (Ops[i]->getType() == ETy &&
 "SCEVMulExpr operand types don't match!") ? void (0) : __assert_fail
 ("Ops[i]->getType() == ETy && \"SCEVMulExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3049, __extension__
 __PRETTY_FUNCTION__))
         "SCEVMulExpr operand types don't match!")(static_cast <bool> (Ops[i]->getType() == ETy &&
 "SCEVMulExpr operand types don't match!") ? void (0) : __assert_fail
 ("Ops[i]->getType() == ETy && \"SCEVMulExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3049, __extension__
 __PRETTY_FUNCTION__));
3050#endif

// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);

// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
  ++Idx;
  assert(Idx < Ops.size())(static_cast <bool> (Idx < Ops.size()) ? void (0) : __assert_fail
 ("Idx < Ops.size()", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 3059, __extension__ __PRETTY_FUNCTION__));
  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    // We found two constants, fold them together!
    Ops[0] = getConstant(LHSC->getAPInt() * RHSC->getAPInt());
    if (Ops.size() == 2) return Ops[0];
    Ops.erase(Ops.begin()+1);  // Erase the folded element
    LHSC = cast<SCEVConstant>(Ops[0]);
  }

  // If we have a multiply of zero, it will always be zero.
  if (LHSC->getValue()->isZero())
    return LHSC;

  // If we are left with a constant one being multiplied, strip it off.
  if (LHSC->getValue()->isOne()) {
    Ops.erase(Ops.begin());
    --Idx;
  }

  if (Ops.size() == 1)
    return Ops[0];
}

// Delay expensive flag strengthening until necessary.
auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) {
  return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags);
};

// Limit recursion calls depth.
if (Depth > MaxArithDepth || hasHugeExpression(Ops))
  return getOrCreateMulExpr(Ops, ComputeFlags(Ops));

if (SCEV *S = findExistingSCEVInCache(scMulExpr, Ops)) {
  // Don't strengthen flags if we have no new information.
  SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S);
  if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags)
    Mul->setNoWrapFlags(ComputeFlags(Ops));
  return S;
}

if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
  if (Ops.size() == 2) {
    // C1*(C2+V) -> C1*C2 + C1*V
    if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
      // If any of Add's ops are Adds or Muls with a constant, apply this
      // transformation as well.
      //
      // TODO: There are some cases where this transformation is not
      // profitable; for example, Add = (C0 + X) * Y + Z.  Maybe the scope of
      // this transformation should be narrowed down.
      if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
        return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
                                     SCEV::FlagAnyWrap, Depth + 1),
                          getMulExpr(LHSC, Add->getOperand(1),
                                     SCEV::FlagAnyWrap, Depth + 1),
                          SCEV::FlagAnyWrap, Depth + 1);

    if (Ops[0]->isAllOnesValue()) {
      // If we have a mul by -1 of an add, try distributing the -1 among the
      // add operands.
      if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
        SmallVector<const SCEV *, 4> NewOps;
        bool AnyFolded = false;
        for (const SCEV *AddOp : Add->operands()) {
          const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
                                       Depth + 1);
          if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
          NewOps.push_back(Mul);
        }
        if (AnyFolded)
          return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
      } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
        // Negation preserves a recurrence's no self-wrap property.
        SmallVector<const SCEV *, 4> Operands;
        for (const SCEV *AddRecOp : AddRec->operands())
          Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
                                        Depth + 1));

        return getAddRecExpr(Operands, AddRec->getLoop(),
                             AddRec->getNoWrapFlags(SCEV::FlagNW));
      }
    }
  }
}

// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
  ++Idx;

// If there are mul operands inline them all into this expression.
if (Idx < Ops.size()) {
  bool DeletedMul = false;
  while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
    if (Ops.size() > MulOpsInlineThreshold)
      break;
    // If we have an mul, expand the mul operands onto the end of the
    // operands list.
    Ops.erase(Ops.begin()+Idx);
    Ops.append(Mul->op_begin(), Mul->op_end());
    DeletedMul = true;
  }

  // If we deleted at least one mul, we added operands to the end of the
  // list, and they are not necessarily sorted.  Recurse to resort and
  // resimplify any operands we just acquired.
  if (DeletedMul)
    return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
}

// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant.  If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
  ++Idx;

// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
  // Scan all of the other operands to this mul and add them to the vector
  // if they are loop invariant w.r.t. the recurrence.
  SmallVector<const SCEV *, 8> LIOps;
  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
  const Loop *AddRecLoop = AddRec->getLoop();
  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
      LIOps.push_back(Ops[i]);
      Ops.erase(Ops.begin()+i);
      --i; --e;
    }

  // If we found some loop invariants, fold them into the recurrence.
  if (!LIOps.empty()) {
    //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
    SmallVector<const SCEV *, 4> NewOps;
    NewOps.reserve(AddRec->getNumOperands());
    const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
    for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
      NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
                                  SCEV::FlagAnyWrap, Depth + 1));

    // Build the new addrec. Propagate the NUW and NSW flags if both the
    // outer mul and the inner addrec are guaranteed to have no overflow.
    //
    // No self-wrap cannot be guaranteed after changing the step size, but
    // will be inferred if either NUW or NSW is true.
    SCEV::NoWrapFlags Flags = ComputeFlags({Scale, AddRec});
    const SCEV *NewRec = getAddRecExpr(
        NewOps, AddRecLoop, AddRec->getNoWrapFlags(Flags));

    // If all of the other operands were loop invariant, we are done.
    if (Ops.size() == 1) return NewRec;

    // Otherwise, multiply the folded AddRec by the non-invariant parts.
    for (unsigned i = 0;; ++i)
      if (Ops[i] == AddRec) {
        Ops[i] = NewRec;
        break;
      }
    return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
  }

  // Okay, if there weren't any loop invariants to be folded, check to see
  // if there are multiple AddRec's with the same loop induction variable
  // being multiplied together.  If so, we can fold them.

  // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
  // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
  //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
  //   ]]],+,...up to x=2n}.
  // Note that the arguments to choose() are always integers with values
  // known at compile time, never SCEV objects.
  //
  // The implementation avoids pointless extra computations when the two
  // addrec's are of different length (mathematically, it's equivalent to
  // an infinite stream of zeros on the right).
  bool OpsModified = false;
  for (unsigned OtherIdx = Idx+1;
       OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
       ++OtherIdx) {
    const SCEVAddRecExpr *OtherAddRec =
      dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
    if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
      continue;

    // Limit max number of arguments to avoid creation of unreasonably big
    // SCEVAddRecs with very complex operands.
    if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
        MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
      continue;

    bool Overflow = false;
    Type *Ty = AddRec->getType();
    bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
    SmallVector<const SCEV*, 7> AddRecOps;
    for (int x = 0, xe = AddRec->getNumOperands() +
           OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
      SmallVector <const SCEV *, 7> SumOps;
      for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
        uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
        for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
               ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
             z < ze && !Overflow; ++z) {
          uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
          uint64_t Coeff;
          if (LargerThan64Bits)
            Coeff = umul_ov(Coeff1, Coeff2, Overflow);
          else
            Coeff = Coeff1*Coeff2;
          const SCEV *CoeffTerm = getConstant(Ty, Coeff);
          const SCEV *Term1 = AddRec->getOperand(y-z);
          const SCEV *Term2 = OtherAddRec->getOperand(z);
          SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
                                      SCEV::FlagAnyWrap, Depth + 1));
        }
      }
      if (SumOps.empty())
        SumOps.push_back(getZero(Ty));
      AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
    }
    if (!Overflow) {
      const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
                                            SCEV::FlagAnyWrap);
      if (Ops.size() == 2) return NewAddRec;
      Ops[Idx] = NewAddRec;
      Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
      OpsModified = true;
      AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
      if (!AddRec)
        break;
    }
  }
  if (OpsModified)
    return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);

  // Otherwise couldn't fold anything into this recurrence.  Move onto the
  // next one.
}

// Okay, it looks like we really DO need an mul expr.  Check to see if we
// already have one, otherwise create a new one.
return getOrCreateMulExpr(Ops, ComputeFlags(Ops));
3299}

3301/// Represents an unsigned remainder expression based on unsigned division.
3302const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==(static_cast <bool> (getEffectiveSCEVType(LHS->getType
()) == getEffectiveSCEVType(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3306, __extension__
 __PRETTY_FUNCTION__))
       getEffectiveSCEVType(RHS->getType()) &&(static_cast <bool> (getEffectiveSCEVType(LHS->getType
()) == getEffectiveSCEVType(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3306, __extension__
 __PRETTY_FUNCTION__))
       "SCEVURemExpr operand types don't match!")(static_cast <bool> (getEffectiveSCEVType(LHS->getType
()) == getEffectiveSCEVType(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3306, __extension__
 __PRETTY_FUNCTION__));

// Short-circuit easy cases
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
  // If constant is one, the result is trivial
  if (RHSC->getValue()->isOne())
    return getZero(LHS->getType()); // X urem 1 --> 0

  // If constant is a power of two, fold into a zext(trunc(LHS)).
  if (RHSC->getAPInt().isPowerOf2()) {
    Type *FullTy = LHS->getType();
    Type *TruncTy =
        IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
    return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
  }
}

// Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
const SCEV *UDiv = getUDivExpr(LHS, RHS);
const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3327}

3329/// Get a canonical unsigned division expression, or something simpler if
3330/// possible.
3331const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
assert(!LHS->getType()->isPointerTy() &&(static_cast <bool> (!LHS->getType()->isPointerTy
() && "SCEVUDivExpr operand can't be pointer!") ? void
 (0) : __assert_fail ("!LHS->getType()->isPointerTy() && \"SCEVUDivExpr operand can't be pointer!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3334, __extension__
 __PRETTY_FUNCTION__))
       "SCEVUDivExpr operand can't be pointer!")(static_cast <bool> (!LHS->getType()->isPointerTy
() && "SCEVUDivExpr operand can't be pointer!") ? void
 (0) : __assert_fail ("!LHS->getType()->isPointerTy() && \"SCEVUDivExpr operand can't be pointer!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3334, __extension__
 __PRETTY_FUNCTION__));
assert(LHS->getType() == RHS->getType() &&(static_cast <bool> (LHS->getType() == RHS->getType
() && "SCEVUDivExpr operand types don't match!") ? void
 (0) : __assert_fail ("LHS->getType() == RHS->getType() && \"SCEVUDivExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3336, __extension__
 __PRETTY_FUNCTION__))
       "SCEVUDivExpr operand types don't match!")(static_cast <bool> (LHS->getType() == RHS->getType
() && "SCEVUDivExpr operand types don't match!") ? void
 (0) : __assert_fail ("LHS->getType() == RHS->getType() && \"SCEVUDivExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3336, __extension__
 __PRETTY_FUNCTION__));

FoldingSetNodeID ID;
ID.AddInteger(scUDivExpr);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
  return S;

// 0 udiv Y == 0
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS))
  if (LHSC->getValue()->isZero())
    return LHS;

if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
  if (RHSC->getValue()->isOne())
    return LHS;                               // X udiv 1 --> x
  // If the denominator is zero, the result of the udiv is undefined. Don't
  // try to analyze it, because the resolution chosen here may differ from
  // the resolution chosen in other parts of the compiler.
  if (!RHSC->getValue()->isZero()) {
    // Determine if the division can be folded into the operands of
    // its operands.
    // TODO: Generalize this to non-constants by using known-bits information.
    Type *Ty = LHS->getType();
    unsigned LZ = RHSC->getAPInt().countLeadingZeros();
    unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
    // For non-power-of-two values, effectively round the value up to the
    // nearest power of two.
    if (!RHSC->getAPInt().isPowerOf2())
      ++MaxShiftAmt;
    IntegerType *ExtTy =
      IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
      if (const SCEVConstant *Step =
          dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
        // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
        const APInt &StepInt = Step->getAPInt();
        const APInt &DivInt = RHSC->getAPInt();
        if (!StepInt.urem(DivInt) &&
            getZeroExtendExpr(AR, ExtTy) ==
            getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
                          getZeroExtendExpr(Step, ExtTy),
                          AR->getLoop(), SCEV::FlagAnyWrap)) {
          SmallVector<const SCEV *, 4> Operands;
          for (const SCEV *Op : AR->operands())
            Operands.push_back(getUDivExpr(Op, RHS));
          return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
        }
        /// Get a canonical UDivExpr for a recurrence.
        /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
        // We can currently only fold X%N if X is constant.
        const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
        if (StartC && !DivInt.urem(StepInt) &&
            getZeroExtendExpr(AR, ExtTy) ==
            getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
                          getZeroExtendExpr(Step, ExtTy),
                          AR->getLoop(), SCEV::FlagAnyWrap)) {
          const APInt &StartInt = StartC->getAPInt();
          const APInt &StartRem = StartInt.urem(StepInt);
          if (StartRem != 0) {
            const SCEV *NewLHS =
                getAddRecExpr(getConstant(StartInt - StartRem), Step,
                              AR->getLoop(), SCEV::FlagNW);
            if (LHS != NewLHS) {
              LHS = NewLHS;

              // Reset the ID to include the new LHS, and check if it is
              // already cached.
              ID.clear();
              ID.AddInteger(scUDivExpr);
              ID.AddPointer(LHS);
              ID.AddPointer(RHS);
              IP = nullptr;
              if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
                return S;
            }
          }
        }
      }
    // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
    if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
      SmallVector<const SCEV *, 4> Operands;
      for (const SCEV *Op : M->operands())
        Operands.push_back(getZeroExtendExpr(Op, ExtTy));
      if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
        // Find an operand that's safely divisible.
        for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
          const SCEV *Op = M->getOperand(i);
          const SCEV *Div = getUDivExpr(Op, RHSC);
          if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
            Operands = SmallVector<const SCEV *, 4>(M->operands());
            Operands[i] = Div;
            return getMulExpr(Operands);
          }
        }
    }

    // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
    if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
      if (auto *DivisorConstant =
              dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
        bool Overflow = false;
        APInt NewRHS =
            DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
        if (Overflow) {
          return getConstant(RHSC->getType(), 0, false);
        }
        return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
      }
    }

    // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
    if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
      SmallVector<const SCEV *, 4> Operands;
      for (const SCEV *Op : A->operands())
        Operands.push_back(getZeroExtendExpr(Op, ExtTy));
      if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
        Operands.clear();
        for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
          const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
          if (isa<SCEVUDivExpr>(Op) ||
              getMulExpr(Op, RHS) != A->getOperand(i))
            break;
          Operands.push_back(Op);
        }
        if (Operands.size() == A->getNumOperands())
          return getAddExpr(Operands);
      }
    }

    // Fold if both operands are constant.
    if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
      Constant *LHSCV = LHSC->getValue();
      Constant *RHSCV = RHSC->getValue();
      return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
                                                                 RHSCV)));
    }
  }
}

// The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
// changes). Make sure we get a new one.
IP = nullptr;
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
                                           LHS, RHS);
UniqueSCEVs.InsertNode(S, IP);
registerUser(S, {LHS, RHS});
return S;
3487}

3489const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
APInt A = C1->getAPInt().abs();
APInt B = C2->getAPInt().abs();
uint32_t ABW = A.getBitWidth();
uint32_t BBW = B.getBitWidth();

if (ABW > BBW)
  B = B.zext(ABW);
else if (ABW < BBW)
  A = A.zext(BBW);

return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3501}

3503/// Get a canonical unsigned division expression, or something simpler if
3504/// possible. There is no representation for an exact udiv in SCEV IR, but we
3505/// can attempt to remove factors from the LHS and RHS.  We can't do this when
3506/// it's not exact because the udiv may be clearing bits.
3507const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
                                            const SCEV *RHS) {
// TODO: we could try to find factors in all sorts of things, but for now we
// just deal with u/exact (multiply, constant). See SCEVDivision towards the
// end of this file for inspiration.

const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
if (!Mul || !Mul->hasNoUnsignedWrap())
  return getUDivExpr(LHS, RHS);

if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
  // If the mulexpr multiplies by a constant, then that constant must be the
  // first element of the mulexpr.
  if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
    if (LHSCst == RHSCst) {
      SmallVector<const SCEV *, 2> Operands(drop_begin(Mul->operands()));
      return getMulExpr(Operands);
    }

    // We can't just assume that LHSCst divides RHSCst cleanly, it could be
    // that there's a factor provided by one of the other terms. We need to
    // check.
    APInt Factor = gcd(LHSCst, RHSCst);
    if (!Factor.isIntN(1)) {
      LHSCst =
          cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
      RHSCst =
          cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
      SmallVector<const SCEV *, 2> Operands;
      Operands.push_back(LHSCst);
      Operands.append(Mul->op_begin() + 1, Mul->op_end());
      LHS = getMulExpr(Operands);
      RHS = RHSCst;
      Mul = dyn_cast<SCEVMulExpr>(LHS);
      if (!Mul)
        return getUDivExactExpr(LHS, RHS);
    }
  }
}

for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
  if (Mul->getOperand(i) == RHS) {
    SmallVector<const SCEV *, 2> Operands;
    Operands.append(Mul->op_begin(), Mul->op_begin() + i);
    Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
    return getMulExpr(Operands);
  }
}

return getUDivExpr(LHS, RHS);
3557}

3559/// Get an add recurrence expression for the specified loop.  Simplify the
3560/// expression as much as possible.
3561const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
                                         const Loop *L,
                                         SCEV::NoWrapFlags Flags) {
SmallVector<const SCEV *, 4> Operands;
Operands.push_back(Start);
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
  if (StepChrec->getLoop() == L) {
    Operands.append(StepChrec->op_begin(), StepChrec->op_end());
    return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
  }

Operands.push_back(Step);
return getAddRecExpr(Operands, L, Flags);
3574}

3576/// Get an add recurrence expression for the specified loop.  Simplify the
3577/// expression as much as possible.
3578const SCEV *
3579ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
                             const Loop *L, SCEV::NoWrapFlags Flags) {
if (Operands.size() == 1) return Operands[0];
3582#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
for (unsigned i = 1, e = Operands.size(); i != e; ++i) {
  assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&(static_cast <bool> (getEffectiveSCEVType(Operands[i]->
getType()) == ETy && "SCEVAddRecExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3586, __extension__
 __PRETTY_FUNCTION__))
         "SCEVAddRecExpr operand types don't match!")(static_cast <bool> (getEffectiveSCEVType(Operands[i]->
getType()) == ETy && "SCEVAddRecExpr operand types don't match!"
) ? void (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3586, __extension__
 __PRETTY_FUNCTION__));
  assert(!Operands[i]->getType()->isPointerTy() && "Step must be integer")(static_cast <bool> (!Operands[i]->getType()->isPointerTy
() && "Step must be integer") ? void (0) : __assert_fail
 ("!Operands[i]->getType()->isPointerTy() && \"Step must be integer\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3587, __extension__
 __PRETTY_FUNCTION__));
}
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
  assert(isLoopInvariant(Operands[i], L) &&(static_cast <bool> (isLoopInvariant(Operands[i], L) &&
 "SCEVAddRecExpr operand is not loop-invariant!") ? void (0) :
 __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3591, __extension__
 __PRETTY_FUNCTION__))
         "SCEVAddRecExpr operand is not loop-invariant!")(static_cast <bool> (isLoopInvariant(Operands[i], L) &&
 "SCEVAddRecExpr operand is not loop-invariant!") ? void (0) :
 __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3591, __extension__
 __PRETTY_FUNCTION__));
3592#endif

if (Operands.back()->isZero()) {
  Operands.pop_back();
  return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
}

// It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
// use that information to infer NUW and NSW flags. However, computing a
// BE count requires calling getAddRecExpr, so we may not yet have a
// meaningful BE count at this point (and if we don't, we'd be stuck
// with a SCEVCouldNotCompute as the cached BE count).

Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);

// Canonicalize nested AddRecs in by nesting them in order of loop depth.
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
  const Loop *NestedLoop = NestedAR->getLoop();
  if (L->contains(NestedLoop)
          ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
          : (!NestedLoop->contains(L) &&
             DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
    SmallVector<const SCEV *, 4> NestedOperands(NestedAR->operands());
    Operands[0] = NestedAR->getStart();
    // AddRecs require their operands be loop-invariant with respect to their
    // loops. Don't perform this transformation if it would break this
    // requirement.
    bool AllInvariant = all_of(
        Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });

    if (AllInvariant) {
      // Create a recurrence for the outer loop with the same step size.
      //
      // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
      // inner recurrence has the same property.
      SCEV::NoWrapFlags OuterFlags =
        maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());

      NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
      AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
        return isLoopInvariant(Op, NestedLoop);
      });

      if (AllInvariant) {
        // Ok, both add recurrences are valid after the transformation.
        //
        // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
        // the outer recurrence has the same property.
        SCEV::NoWrapFlags InnerFlags =
          maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
        return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
      }
    }
    // Reset Operands to its original state.
    Operands[0] = NestedAR;
  }
}

// Okay, it looks like we really DO need an addrec expr.  Check to see if we
// already have one, otherwise create a new one.
return getOrCreateAddRecExpr(Operands, L, Flags);
3653}

3655const SCEV *
3656ScalarEvolution::getGEPExpr(GEPOperator *GEP,
                          const SmallVectorImpl<const SCEV *> &IndexExprs) {
const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
// getSCEV(Base)->getType() has the same address space as Base->getType()
// because SCEV::getType() preserves the address space.
Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
const bool AssumeInBoundsFlags = [&]() {
  if (!GEP->isInBounds())
    return false;

  // We'd like to propagate flags from the IR to the corresponding SCEV nodes,
  // but to do that, we have to ensure that said flag is valid in the entire
  // defined scope of the SCEV.
  auto *GEPI = dyn_cast<Instruction>(GEP);
  // TODO: non-instructions have global scope.  We might be able to prove
  // some global scope cases
  return GEPI && isSCEVExprNeverPoison(GEPI);
}();

SCEV::NoWrapFlags OffsetWrap =
  AssumeInBoundsFlags ? SCEV::FlagNSW : SCEV::FlagAnyWrap;

Type *CurTy = GEP->getType();
bool FirstIter = true;
SmallVector<const SCEV *, 4> Offsets;
for (const SCEV *IndexExpr : IndexExprs) {
  // Compute the (potentially symbolic) offset in bytes for this index.
  if (StructType *STy = dyn_cast<StructType>(CurTy)) {
    // For a struct, add the member offset.
    ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
    unsigned FieldNo = Index->getZExtValue();
    const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
    Offsets.push_back(FieldOffset);

    // Update CurTy to the type of the field at Index.
    CurTy = STy->getTypeAtIndex(Index);
  } else {
    // Update CurTy to its element type.
    if (FirstIter) {
      assert(isa<PointerType>(CurTy) &&(static_cast <bool> (isa<PointerType>(CurTy) &&
 "The first index of a GEP indexes a pointer") ? void (0) : __assert_fail
 ("isa<PointerType>(CurTy) && \"The first index of a GEP indexes a pointer\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3696, __extension__
 __PRETTY_FUNCTION__))
             "The first index of a GEP indexes a pointer")(static_cast <bool> (isa<PointerType>(CurTy) &&
 "The first index of a GEP indexes a pointer") ? void (0) : __assert_fail
 ("isa<PointerType>(CurTy) && \"The first index of a GEP indexes a pointer\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3696, __extension__
 __PRETTY_FUNCTION__));
      CurTy = GEP->getSourceElementType();
      FirstIter = false;
    } else {
      CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0);
    }
    // For an array, add the element offset, explicitly scaled.
    const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
    // Getelementptr indices are signed.
    IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);

    // Multiply the index by the element size to compute the element offset.
    const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap);
    Offsets.push_back(LocalOffset);
  }
}

// Handle degenerate case of GEP without offsets.
if (Offsets.empty())
  return BaseExpr;

// Add the offsets together, assuming nsw if inbounds.
const SCEV *Offset = getAddExpr(Offsets, OffsetWrap);
// Add the base address and the offset. We cannot use the nsw flag, as the
// base address is unsigned. However, if we know that the offset is
// non-negative, we can use nuw.
SCEV::NoWrapFlags BaseWrap = AssumeInBoundsFlags && isKnownNonNegative(Offset)
                                 ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
auto *GEPExpr = getAddExpr(BaseExpr, Offset, BaseWrap);
assert(BaseExpr->getType() == GEPExpr->getType() &&(static_cast <bool> (BaseExpr->getType() == GEPExpr->
getType() && "GEP should not change type mid-flight."
) ? void (0) : __assert_fail ("BaseExpr->getType() == GEPExpr->getType() && \"GEP should not change type mid-flight.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3726, __extension__
 __PRETTY_FUNCTION__))
       "GEP should not change type mid-flight.")(static_cast <bool> (BaseExpr->getType() == GEPExpr->
getType() && "GEP should not change type mid-flight."
) ? void (0) : __assert_fail ("BaseExpr->getType() == GEPExpr->getType() && \"GEP should not change type mid-flight.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3726, __extension__
 __PRETTY_FUNCTION__));
return GEPExpr;
3728}

3730SCEV *ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
                                             ArrayRef<const SCEV *> Ops) {
FoldingSetNodeID ID;
ID.AddInteger(SCEVType);
for (const SCEV *Op : Ops)
  ID.AddPointer(Op);
void *IP = nullptr;
return UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
3738}

3740const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
return getSMaxExpr(Op, getNegativeSCEV(Op, Flags));
3743}

3745const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
                                         SmallVectorImpl<const SCEV *> &Ops) {
assert(SCEVMinMaxExpr::isMinMaxType(Kind) && "Not a SCEVMinMaxExpr!")(static_cast <bool> (SCEVMinMaxExpr::isMinMaxType(Kind)
 && "Not a SCEVMinMaxExpr!") ? void (0) : __assert_fail
 ("SCEVMinMaxExpr::isMinMaxType(Kind) && \"Not a SCEVMinMaxExpr!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3747, __extension__
 __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!")(static_cast <bool> (!Ops.empty() && "Cannot get empty (u|s)(min|max)!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty (u|s)(min|max)!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3748, __extension__
 __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
3750#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "Operand types don't match!") ? void (0
) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3754, __extension__
 __PRETTY_FUNCTION__))
         "Operand types don't match!")(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "Operand types don't match!") ? void (0
) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3754, __extension__
 __PRETTY_FUNCTION__));
  assert(Ops[0]->getType()->isPointerTy() ==(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3757, __extension__
 __PRETTY_FUNCTION__))
             Ops[i]->getType()->isPointerTy() &&(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3757, __extension__
 __PRETTY_FUNCTION__))
         "min/max should be consistently pointerish")(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3757, __extension__
 __PRETTY_FUNCTION__));
}
3759#endif

bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;

// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops, &LI, DT);

// Check if we have created the same expression before.
if (const SCEV *S = findExistingSCEVInCache(Kind, Ops)) {
  return S;
}

// If there are any constants, fold them together.
unsigned Idx = 0;
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
  ++Idx;
  assert(Idx < Ops.size())(static_cast <bool> (Idx < Ops.size()) ? void (0) : __assert_fail
 ("Idx < Ops.size()", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 3776, __extension__ __PRETTY_FUNCTION__));
  auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
    if (Kind == scSMaxExpr)
      return APIntOps::smax(LHS, RHS);
    else if (Kind == scSMinExpr)
      return APIntOps::smin(LHS, RHS);
    else if (Kind == scUMaxExpr)
      return APIntOps::umax(LHS, RHS);
    else if (Kind == scUMinExpr)
      return APIntOps::umin(LHS, RHS);
    llvm_unreachable("Unknown SCEV min/max opcode")::llvm::llvm_unreachable_internal("Unknown SCEV min/max opcode"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3786);
  };

  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    // We found two constants, fold them together!
    ConstantInt *Fold = ConstantInt::get(
        getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
    Ops[0] = getConstant(Fold);
    Ops.erase(Ops.begin()+1);  // Erase the folded element
    if (Ops.size() == 1) return Ops[0];
    LHSC = cast<SCEVConstant>(Ops[0]);
  }

  bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
  bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);

  if (IsMax ? IsMinV : IsMaxV) {
    // If we are left with a constant minimum(/maximum)-int, strip it off.
    Ops.erase(Ops.begin());
    --Idx;
  } else if (IsMax ? IsMaxV : IsMinV) {
    // If we have a max(/min) with a constant maximum(/minimum)-int,
    // it will always be the extremum.
    return LHSC;
  }

  if (Ops.size() == 1) return Ops[0];
}

// Find the first operation of the same kind
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
  ++Idx;

// Check to see if one of the operands is of the same kind. If so, expand its
// operands onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
  bool DeletedAny = false;
  while (Ops[Idx]->getSCEVType() == Kind) {
    const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
    Ops.erase(Ops.begin()+Idx);
    Ops.append(SMME->op_begin(), SMME->op_end());
    DeletedAny = true;
  }

  if (DeletedAny)
    return getMinMaxExpr(Kind, Ops);
}

// Okay, check to see if the same value occurs in the operand list twice.  If
// so, delete one.  Since we sorted the list, these values are required to
// be adjacent.
llvm::CmpInst::Predicate GEPred =
    IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
llvm::CmpInst::Predicate LEPred =
    IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
  if (Ops[i] == Ops[i + 1] ||
      isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
    //  X op Y op Y  -->  X op Y
    //  X op Y       -->  X, if we know X, Y are ordered appropriately
    Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
    --i;
    --e;
  } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
                                             Ops[i + 1])) {
    //  X op Y       -->  Y, if we know X, Y are ordered appropriately
    Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
    --i;
    --e;
  }
}

if (Ops.size() == 1) return Ops[0];

assert(!Ops.empty() && "Reduced smax down to nothing!")(static_cast <bool> (!Ops.empty() && "Reduced smax down to nothing!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"Reduced smax down to nothing!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3862, __extension__
 __PRETTY_FUNCTION__));

// Okay, it looks like we really DO need an expr.  Check to see if we
// already have one, otherwise create a new one.
FoldingSetNodeID ID;
ID.AddInteger(Kind);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
  ID.AddPointer(Ops[i]);
void *IP = nullptr;
const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
if (ExistingSCEV)
  return ExistingSCEV;
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator)
    SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());

UniqueSCEVs.InsertNode(S, IP);
registerUser(S, Ops);
return S;
3882}

3884namespace {

3886class SCEVSequentialMinMaxDeduplicatingVisitor final
  : public SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor,
                       Optional<const SCEV *>> {
using RetVal = Optional<const SCEV *>;
using Base = SCEVVisitor<SCEVSequentialMinMaxDeduplicatingVisitor, RetVal>;

ScalarEvolution &SE;
const SCEVTypes RootKind; // Must be a sequential min/max expression.
const SCEVTypes NonSequentialRootKind; // Non-sequential variant of RootKind.
SmallPtrSet<const SCEV *, 16> SeenOps;

bool canRecurseInto(SCEVTypes Kind) const {
  // We can only recurse into the SCEV expression of the same effective type
  // as the type of our root SCEV expression.
  return RootKind == Kind || NonSequentialRootKind == Kind;
};

RetVal visitAnyMinMaxExpr(const SCEV *S) {
  assert((isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) &&(static_cast <bool> ((isa<SCEVMinMaxExpr>(S) || isa
<SCEVSequentialMinMaxExpr>(S)) && "Only for min/max expressions."
) ? void (0) : __assert_fail ("(isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) && \"Only for min/max expressions.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3905, __extension__
 __PRETTY_FUNCTION__))
         "Only for min/max expressions.")(static_cast <bool> ((isa<SCEVMinMaxExpr>(S) || isa
<SCEVSequentialMinMaxExpr>(S)) && "Only for min/max expressions."
) ? void (0) : __assert_fail ("(isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) && \"Only for min/max expressions.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 3905, __extension__
 __PRETTY_FUNCTION__));
  SCEVTypes Kind = S->getSCEVType();

  if (!canRecurseInto(Kind))
    return S;

  auto *NAry = cast<SCEVNAryExpr>(S);
  SmallVector<const SCEV *> NewOps;
  bool Changed =
      visit(Kind, makeArrayRef(NAry->op_begin(), NAry->op_end()), NewOps);

  if (!Changed)
    return S;
  if (NewOps.empty())
    return None;

  return isa<SCEVSequentialMinMaxExpr>(S)
             ? SE.getSequentialMinMaxExpr(Kind, NewOps)
             : SE.getMinMaxExpr(Kind, NewOps);
}

RetVal visit(const SCEV *S) {
  // Has the whole operand been seen already?
  if (!SeenOps.insert(S).second)
    return None;
  return Base::visit(S);
}

3933public:
SCEVSequentialMinMaxDeduplicatingVisitor(ScalarEvolution &SE,
                                         SCEVTypes RootKind)
    : SE(SE), RootKind(RootKind),
      NonSequentialRootKind(
          SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(
              RootKind)) {}

bool /*Changed*/ visit(SCEVTypes Kind, ArrayRef<const SCEV *> OrigOps,
                       SmallVectorImpl<const SCEV *> &NewOps) {
  bool Changed = false;
  SmallVector<const SCEV *> Ops;
  Ops.reserve(OrigOps.size());

  for (const SCEV *Op : OrigOps) {
    RetVal NewOp = visit(Op);
    if (NewOp != Op)
      Changed = true;
    if (NewOp)
      Ops.emplace_back(*NewOp);
  }

  if (Changed)
    NewOps = std::move(Ops);
  return Changed;
}

RetVal visitConstant(const SCEVConstant *Constant) { return Constant; }

RetVal visitPtrToIntExpr(const SCEVPtrToIntExpr *Expr) { return Expr; }

RetVal visitTruncateExpr(const SCEVTruncateExpr *Expr) { return Expr; }

RetVal visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { return Expr; }

RetVal visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { return Expr; }

RetVal visitAddExpr(const SCEVAddExpr *Expr) { return Expr; }

RetVal visitMulExpr(const SCEVMulExpr *Expr) { return Expr; }

RetVal visitUDivExpr(const SCEVUDivExpr *Expr) { return Expr; }

RetVal visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }

RetVal visitSMaxExpr(const SCEVSMaxExpr *Expr) {
  return visitAnyMinMaxExpr(Expr);
}

RetVal visitUMaxExpr(const SCEVUMaxExpr *Expr) {
  return visitAnyMinMaxExpr(Expr);
}

RetVal visitSMinExpr(const SCEVSMinExpr *Expr) {
  return visitAnyMinMaxExpr(Expr);
}

RetVal visitUMinExpr(const SCEVUMinExpr *Expr) {
  return visitAnyMinMaxExpr(Expr);
}

RetVal visitSequentialUMinExpr(const SCEVSequentialUMinExpr *Expr) {
  return visitAnyMinMaxExpr(Expr);
}

RetVal visitUnknown(const SCEVUnknown *Expr) { return Expr; }

RetVal visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { return Expr; }
4001};

4003} // namespace

4005const SCEV *
4006ScalarEvolution::getSequentialMinMaxExpr(SCEVTypes Kind,
                                       SmallVectorImpl<const SCEV *> &Ops) {
assert(SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) &&(static_cast <bool> (SCEVSequentialMinMaxExpr::isSequentialMinMaxType
(Kind) && "Not a SCEVSequentialMinMaxExpr!") ? void (
0) : __assert_fail ("SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) && \"Not a SCEVSequentialMinMaxExpr!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4009, __extension__
 __PRETTY_FUNCTION__))
       "Not a SCEVSequentialMinMaxExpr!")(static_cast <bool> (SCEVSequentialMinMaxExpr::isSequentialMinMaxType
(Kind) && "Not a SCEVSequentialMinMaxExpr!") ? void (
0) : __assert_fail ("SCEVSequentialMinMaxExpr::isSequentialMinMaxType(Kind) && \"Not a SCEVSequentialMinMaxExpr!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4009, __extension__
 __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!")(static_cast <bool> (!Ops.empty() && "Cannot get empty (u|s)(min|max)!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty (u|s)(min|max)!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4010, __extension__
 __PRETTY_FUNCTION__));
if (Ops.size() == 1)
  return Ops[0];
if (Ops.size() == 2 &&
    any_of(Ops, [](const SCEV *Op) { return isa<SCEVConstant>(Op); }))
  return getMinMaxExpr(
      SCEVSequentialMinMaxExpr::getEquivalentNonSequentialSCEVType(Kind),
      Ops);
4018#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i) {
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "Operand types don't match!") ? void (0
) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4022, __extension__
 __PRETTY_FUNCTION__))
         "Operand types don't match!")(static_cast <bool> (getEffectiveSCEVType(Ops[i]->getType
()) == ETy && "Operand types don't match!") ? void (0
) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4022, __extension__
 __PRETTY_FUNCTION__));
  assert(Ops[0]->getType()->isPointerTy() ==(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4025, __extension__
 __PRETTY_FUNCTION__))
             Ops[i]->getType()->isPointerTy() &&(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4025, __extension__
 __PRETTY_FUNCTION__))
         "min/max should be consistently pointerish")(static_cast <bool> (Ops[0]->getType()->isPointerTy
() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"
) ? void (0) : __assert_fail ("Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && \"min/max should be consistently pointerish\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4025, __extension__
 __PRETTY_FUNCTION__));
}
4027#endif

// Note that SCEVSequentialMinMaxExpr is *NOT* commutative,
// so we can *NOT* do any kind of sorting of the expressions!

// Check if we have created the same expression before.
if (const SCEV *S = findExistingSCEVInCache(Kind, Ops))
  return S;

// FIXME: there are *some* simplifications that we can do here.

// Keep only the first instance of an operand.
{
  SCEVSequentialMinMaxDeduplicatingVisitor Deduplicator(*this, Kind);
  bool Changed = Deduplicator.visit(Kind, Ops, Ops);
  if (Changed)
    return getSequentialMinMaxExpr(Kind, Ops);
}

// Check to see if one of the operands is of the same kind. If so, expand its
// operands onto our operand list, and recurse to simplify.
{
  unsigned Idx = 0;
  bool DeletedAny = false;
  while (Idx < Ops.size()) {
    if (Ops[Idx]->getSCEVType() != Kind) {
      ++Idx;
      continue;
    }
    const auto *SMME = cast<SCEVSequentialMinMaxExpr>(Ops[Idx]);
    Ops.erase(Ops.begin() + Idx);
    Ops.insert(Ops.begin() + Idx, SMME->op_begin(), SMME->op_end());
    DeletedAny = true;
  }

  if (DeletedAny)
    return getSequentialMinMaxExpr(Kind, Ops);
}

// Okay, it looks like we really DO need an expr.  Check to see if we
// already have one, otherwise create a new one.
FoldingSetNodeID ID;
ID.AddInteger(Kind);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
  ID.AddPointer(Ops[i]);
void *IP = nullptr;
const SCEV *ExistingSCEV = UniqueSCEVs.FindNodeOrInsertPos(ID, IP);
if (ExistingSCEV)
  return ExistingSCEV;

const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
SCEV *S = new (SCEVAllocator)
    SCEVSequentialMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size());

UniqueSCEVs.InsertNode(S, IP);
registerUser(S, Ops);
return S;
4085}

4087const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getSMaxExpr(Ops);
4090}

4092const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMaxExpr, Ops);
4094}

4096const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getUMaxExpr(Ops);
4099}

4101const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMaxExpr, Ops);
4103}

4105const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getSMinExpr(Ops);
4109}

4111const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMinExpr, Ops);
4113}

4115const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, const SCEV *RHS,
                                       bool Sequential) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinExpr(Ops, Sequential);
4119}

4121const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops,
                                       bool Sequential) {
return Sequential ? getSequentialMinMaxExpr(scSequentialUMinExpr, Ops)
                  : getMinMaxExpr(scUMinExpr, Ops);
4125}

4127const SCEV *
4128ScalarEvolution::getSizeOfScalableVectorExpr(Type *IntTy,
                                           ScalableVectorType *ScalableTy) {
Constant *NullPtr = Constant::getNullValue(ScalableTy->getPointerTo());
Constant *One = ConstantInt::get(IntTy, 1);
Constant *GEP = ConstantExpr::getGetElementPtr(ScalableTy, NullPtr, One);
// Note that the expression we created is the final expression, we don't
// want to simplify it any further Also, if we call a normal getSCEV(),
// we'll end up in an endless recursion. So just create an SCEVUnknown.
return getUnknown(ConstantExpr::getPtrToInt(GEP, IntTy));
4137}

4139const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
if (auto *ScalableAllocTy = dyn_cast<ScalableVectorType>(AllocTy))
  return getSizeOfScalableVectorExpr(IntTy, ScalableAllocTy);
// We can bypass creating a target-independent constant expression and then
// folding it back into a ConstantInt. This is just a compile-time
// optimization.
return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
4146}

4148const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) {
if (auto *ScalableStoreTy = dyn_cast<ScalableVectorType>(StoreTy))
  return getSizeOfScalableVectorExpr(IntTy, ScalableStoreTy);
// We can bypass creating a target-independent constant expression and then
// folding it back into a ConstantInt. This is just a compile-time
// optimization.
return getConstant(IntTy, getDataLayout().getTypeStoreSize(StoreTy));
4155}

4157const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
                                           StructType *STy,
                                           unsigned FieldNo) {
// We can bypass creating a target-independent constant expression and then
// folding it back into a ConstantInt. This is just a compile-time
// optimization.
return getConstant(
    IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
4165}

4167const SCEV *ScalarEvolution::getUnknown(Value *V) {
// Don't attempt to do anything other than create a SCEVUnknown object
// here.  createSCEV only calls getUnknown after checking for all other
// interesting possibilities, and any other code that calls getUnknown
// is doing so in order to hide a value from SCEV canonicalization.

FoldingSetNodeID ID;
ID.AddInteger(scUnknown);
ID.AddPointer(V);
void *IP = nullptr;
if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
  assert(cast<SCEVUnknown>(S)->getValue() == V &&(static_cast <bool> (cast<SCEVUnknown>(S)->getValue
() == V && "Stale SCEVUnknown in uniquing map!") ? void
 (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4179, __extension__
 __PRETTY_FUNCTION__))
         "Stale SCEVUnknown in uniquing map!")(static_cast <bool> (cast<SCEVUnknown>(S)->getValue
() == V && "Stale SCEVUnknown in uniquing map!") ? void
 (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4179, __extension__
 __PRETTY_FUNCTION__));
  return S;
}
SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
                                          FirstUnknown);
FirstUnknown = cast<SCEVUnknown>(S);
UniqueSCEVs.InsertNode(S, IP);
return S;
4187}

4189//===----------------------------------------------------------------------===//
4190//            Basic SCEV Analysis and PHI Idiom Recognition Code
4191//

4193/// Test if values of the given type are analyzable within the SCEV
4194/// framework. This primarily includes integer types, and it can optionally
4195/// include pointer types if the ScalarEvolution class has access to
4196/// target-specific information.
4197bool ScalarEvolution::isSCEVable(Type *Ty) const {
// Integers and pointers are always SCEVable.
return Ty->isIntOrPtrTy();
4200}

4202/// Return the size in bits of the specified type, for which isSCEVable must
4203/// return true.
4204uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!")(static_cast <bool> (isSCEVable(Ty) && "Type is not SCEVable!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4205, __extension__
 __PRETTY_FUNCTION__));
if (Ty->isPointerTy())
  return getDataLayout().getIndexTypeSizeInBits(Ty);
return getDataLayout().getTypeSizeInBits(Ty);
4209}

4211/// Return a type with the same bitwidth as the given type and which represents
4212/// how SCEV will treat the given type, for which isSCEVable must return
4213/// true. For pointer types, this is the pointer index sized integer type.
4214Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!")(static_cast <bool> (isSCEVable(Ty) && "Type is not SCEVable!"
) ? void (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4215, __extension__
 __PRETTY_FUNCTION__));

if (Ty->isIntegerTy())
  return Ty;

// The only other support type is pointer.
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!")(static_cast <bool> (Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"
) ? void (0) : __assert_fail ("Ty->isPointerTy() && \"Unexpected non-pointer non-integer type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4221, __extension__
 __PRETTY_FUNCTION__));
return getDataLayout().getIndexType(Ty);
4223}

4225Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
return  getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
4227}

4229bool ScalarEvolution::instructionCouldExistWitthOperands(const SCEV *A,
                                                       const SCEV *B) {
/// For a valid use point to exist, the defining scope of one operand
/// must dominate the other.
bool PreciseA, PreciseB;
auto *ScopeA = getDefiningScopeBound({A}, PreciseA);
auto *ScopeB = getDefiningScopeBound({B}, PreciseB);
if (!PreciseA || !PreciseB)
  // Can't tell.
  return false;
return (ScopeA == ScopeB) || DT.dominates(ScopeA, ScopeB) ||
  DT.dominates(ScopeB, ScopeA);
4241}


4244const SCEV *ScalarEvolution::getCouldNotCompute() {
return CouldNotCompute.get();
4246}

4248bool ScalarEvolution::checkValidity(const SCEV *S) const {
bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
  auto *SU = dyn_cast<SCEVUnknown>(S);
  return SU && SU->getValue() == nullptr;
});

return !ContainsNulls;
4255}

4257bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
HasRecMapType::iterator I = HasRecMap.find(S);
if (I != HasRecMap.end())
  return I->second;

bool FoundAddRec =
    SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); });
HasRecMap.insert({S, FoundAddRec});
return FoundAddRec;
4266}

4268/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
4269/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
4270/// offset I, then return {S', I}, else return {\p S, nullptr}.
4271static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
const auto *Add = dyn_cast<SCEVAddExpr>(S);
if (!Add)
  return {S, nullptr};

if (Add->getNumOperands() != 2)
  return {S, nullptr};

auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
if (!ConstOp)
  return {S, nullptr};

return {Add->getOperand(1), ConstOp->getValue()};
4284}

4286/// Return the ValueOffsetPair set for \p S. \p S can be represented
4287/// by the value and offset from any ValueOffsetPair in the set.
4288ScalarEvolution::ValueOffsetPairSetVector *
4289ScalarEvolution::getSCEVValues(const SCEV *S) {
ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
if (SI == ExprValueMap.end())
  return nullptr;
4293#ifndef NDEBUG
if (VerifySCEVMap) {
  // Check there is no dangling Value in the set returned.
  for (const auto &VE : SI->second)
    assert(ValueExprMap.count(VE.first))(static_cast <bool> (ValueExprMap.count(VE.first)) ? void
 (0) : __assert_fail ("ValueExprMap.count(VE.first)", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 4297, __extension__ __PRETTY_FUNCTION__));
}
4299#endif
return &SI->second;
4301}

4303/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
4304/// cannot be used separately. eraseValueFromMap should be used to remove
4305/// V from ValueExprMap and ExprValueMap at the same time.
4306void ScalarEvolution::eraseValueFromMap(Value *V) {
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
  const SCEV *S = I->second;
  // Remove {V, 0} from the set of ExprValueMap[S]
  if (auto *SV = getSCEVValues(S))
    SV->remove({V, nullptr});

  // Remove {V, Offset} from the set of ExprValueMap[Stripped]
  const SCEV *Stripped;
  ConstantInt *Offset;
  std::tie(Stripped, Offset) = splitAddExpr(S);
  if (Offset != nullptr) {
    if (auto *SV = getSCEVValues(Stripped))
      SV->remove({V, Offset});
  }
  ValueExprMap.erase(V);
}
4324}

4326void ScalarEvolution::insertValueToMap(Value *V, const SCEV *S) {
// A recursive query may have already computed the SCEV. It should be
// equivalent, but may not necessarily be exactly the same, e.g. due to lazily
// inferred nowrap flags.
auto It = ValueExprMap.find_as(V);
if (It == ValueExprMap.end()) {
  ValueExprMap.insert({SCEVCallbackVH(V, this), S});
  ExprValueMap[S].insert({V, nullptr});
}
4335}

4337/// Return an existing SCEV if it exists, otherwise analyze the expression and
4338/// create a new one.
4339const SCEV *ScalarEvolution::getSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!")(static_cast <bool> (isSCEVable(V->getType()) &&
 "Value is not SCEVable!") ? void (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4340, __extension__
 __PRETTY_FUNCTION__));

const SCEV *S = getExistingSCEV(V);
if (S == nullptr) {
  S = createSCEV(V);
  // During PHI resolution, it is possible to create two SCEVs for the same
  // V, so it is needed to double check whether V->S is inserted into
  // ValueExprMap before insert S->{V, 0} into ExprValueMap.
  std::pair<ValueExprMapType::iterator, bool> Pair =
      ValueExprMap.insert({SCEVCallbackVH(V, this), S});
  if (Pair.second) {
    ExprValueMap[S].insert({V, nullptr});

    // If S == Stripped + Offset, add Stripped -> {V, Offset} into
    // ExprValueMap.
    const SCEV *Stripped = S;
    ConstantInt *Offset = nullptr;
    std::tie(Stripped, Offset) = splitAddExpr(S);
    // If stripped is SCEVUnknown, don't bother to save
    // Stripped -> {V, offset}. It doesn't simplify and sometimes even
    // increase the complexity of the expansion code.
    // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
    // because it may generate add/sub instead of GEP in SCEV expansion.
    if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
        !isa<GetElementPtrInst>(V))
      ExprValueMap[Stripped].insert({V, Offset});
  }
}
return S;
4369}

4371const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!")(static_cast <bool> (isSCEVable(V->getType()) &&
 "Value is not SCEVable!") ? void (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4372, __extension__
 __PRETTY_FUNCTION__));

ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
  const SCEV *S = I->second;
  assert(checkValidity(S) &&(static_cast <bool> (checkValidity(S) && "existing SCEV has not been properly invalidated"
) ? void (0) : __assert_fail ("checkValidity(S) && \"existing SCEV has not been properly invalidated\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4378, __extension__
 __PRETTY_FUNCTION__))
         "existing SCEV has not been properly invalidated")(static_cast <bool> (checkValidity(S) && "existing SCEV has not been properly invalidated"
) ? void (0) : __assert_fail ("checkValidity(S) && \"existing SCEV has not been properly invalidated\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4378, __extension__
 __PRETTY_FUNCTION__));
  return S;
}
return nullptr;
4382}

4384/// Return a SCEV corresponding to -V = -1*V
4385const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
                                           SCEV::NoWrapFlags Flags) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
  return getConstant(
             cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));

Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
return getMulExpr(V, getMinusOne(Ty), Flags);
4394}

4396/// If Expr computes ~A, return A else return nullptr
4397static const SCEV *MatchNotExpr(const SCEV *Expr) {
const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
if (!Add || Add->getNumOperands() != 2 ||
    !Add->getOperand(0)->isAllOnesValue())
  return nullptr;

const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
if (!AddRHS || AddRHS->getNumOperands() != 2 ||
    !AddRHS->getOperand(0)->isAllOnesValue())
  return nullptr;

return AddRHS->getOperand(1);
4409}

4411/// Return a SCEV corresponding to ~V = -1-V
4412const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
assert(!V->getType()->isPointerTy() && "Can't negate pointer")(static_cast <bool> (!V->getType()->isPointerTy()
 && "Can't negate pointer") ? void (0) : __assert_fail
 ("!V->getType()->isPointerTy() && \"Can't negate pointer\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4413, __extension__
 __PRETTY_FUNCTION__));

if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
  return getConstant(
              cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));

// Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
  auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
    SmallVector<const SCEV *, 2> MatchedOperands;
    for (const SCEV *Operand : MME->operands()) {
      const SCEV *Matched = MatchNotExpr(Operand);
      if (!Matched)
        return (const SCEV *)nullptr;
      MatchedOperands.push_back(Matched);
    }
    return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()),
                         MatchedOperands);
  };
  if (const SCEV *Replaced = MatchMinMaxNegation(MME))
    return Replaced;
}

Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
return getMinusSCEV(getMinusOne(Ty), V);
4439}

4441const SCEV *ScalarEvolution::removePointerBase(const SCEV *P) {
assert(P->getType()->isPointerTy())(static_cast <bool> (P->getType()->isPointerTy())
 ? void (0) : __assert_fail ("P->getType()->isPointerTy()"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4442, __extension__
 __PRETTY_FUNCTION__));

if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(P)) {
  // The base of an AddRec is the first operand.
  SmallVector<const SCEV *> Ops{AddRec->operands()};
  Ops[0] = removePointerBase(Ops[0]);
  // Don't try to transfer nowrap flags for now. We could in some cases
  // (for example, if pointer operand of the AddRec is a SCEVUnknown).
  return getAddRecExpr(Ops, AddRec->getLoop(), SCEV::FlagAnyWrap);
}
if (auto *Add = dyn_cast<SCEVAddExpr>(P)) {
  // The base of an Add is the pointer operand.
  SmallVector<const SCEV *> Ops{Add->operands()};
  const SCEV **PtrOp = nullptr;
  for (const SCEV *&AddOp : Ops) {
    if (AddOp->getType()->isPointerTy()) {
      assert(!PtrOp && "Cannot have multiple pointer ops")(static_cast <bool> (!PtrOp && "Cannot have multiple pointer ops"
) ? void (0) : __assert_fail ("!PtrOp && \"Cannot have multiple pointer ops\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4458, __extension__
 __PRETTY_FUNCTION__));
      PtrOp = &AddOp;
    }
  }
  *PtrOp = removePointerBase(*PtrOp);
  // Don't try to transfer nowrap flags for now. We could in some cases
  // (for example, if the pointer operand of the Add is a SCEVUnknown).
  return getAddExpr(Ops);
}
// Any other expression must be a pointer base.
return getZero(P->getType());
4469}

4471const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
                                        SCEV::NoWrapFlags Flags,
                                        unsigned Depth) {
// Fast path: X - X --> 0.
if (LHS == RHS)
  return getZero(LHS->getType());

// If we subtract two pointers with different pointer bases, bail.
// Eventually, we're going to add an assertion to getMulExpr that we
// can't multiply by a pointer.
if (RHS->getType()->isPointerTy()) {
  if (!LHS->getType()->isPointerTy() ||
      getPointerBase(LHS) != getPointerBase(RHS))
    return getCouldNotCompute();
  LHS = removePointerBase(LHS);
  RHS = removePointerBase(RHS);
}

// We represent LHS - RHS as LHS + (-1)*RHS. This transformation
// makes it so that we cannot make much use of NUW.
auto AddFlags = SCEV::FlagAnyWrap;
const bool RHSIsNotMinSigned =
    !getSignedRangeMin(RHS).isMinSignedValue();
if (hasFlags(Flags, SCEV::FlagNSW)) {
  // Let M be the minimum representable signed value. Then (-1)*RHS
  // signed-wraps if and only if RHS is M. That can happen even for
  // a NSW subtraction because e.g. (-1)*M signed-wraps even though
  // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
  // (-1)*RHS, we need to prove that RHS != M.
  //
  // If LHS is non-negative and we know that LHS - RHS does not
  // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
  // either by proving that RHS > M or that LHS >= 0.
  if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
    AddFlags = SCEV::FlagNSW;
  }
}

// FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
// RHS is NSW and LHS >= 0.
//
// The difficulty here is that the NSW flag may have been proven
// relative to a loop that is to be found in a recurrence in LHS and
// not in RHS. Applying NSW to (-1)*M may then let the NSW have a
// larger scope than intended.
auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;

return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
4519}

4521const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
                                                   unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4525, __extension__
 __PRETTY_FUNCTION__))
       "Cannot truncate or zero extend with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4525, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
  return getTruncateExpr(V, Ty, Depth);
return getZeroExtendExpr(V, Ty, Depth);
4531}

4533const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
                                                   unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4537, __extension__
 __PRETTY_FUNCTION__))
       "Cannot truncate or zero extend with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4537, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
  return getTruncateExpr(V, Ty, Depth);
return getSignExtendExpr(V, Ty, Depth);
4543}

4545const SCEV *
4546ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4549, __extension__
 __PRETTY_FUNCTION__))
       "Cannot noop or zero extend with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or zero extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4549, __extension__
 __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrZeroExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4551, __extension__
 __PRETTY_FUNCTION__))
       "getNoopOrZeroExtend cannot truncate!")(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrZeroExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4551, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getZeroExtendExpr(V, Ty);
4555}

4557const SCEV *
4558ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or sign extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4561, __extension__
 __PRETTY_FUNCTION__))
       "Cannot noop or sign extend with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or sign extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4561, __extension__
 __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrSignExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4563, __extension__
 __PRETTY_FUNCTION__))
       "getNoopOrSignExtend cannot truncate!")(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrSignExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4563, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getSignExtendExpr(V, Ty);
4567}

4569const SCEV *
4570ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or any extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4573, __extension__
 __PRETTY_FUNCTION__))
       "Cannot noop or any extend with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot noop or any extend with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4573, __extension__
 __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrAnyExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4575, __extension__
 __PRETTY_FUNCTION__))
       "getNoopOrAnyExtend cannot truncate!")(static_cast <bool> (getTypeSizeInBits(SrcTy) <= getTypeSizeInBits
(Ty) && "getNoopOrAnyExtend cannot truncate!") ? void
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4575, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getAnyExtendExpr(V, Ty);
4579}

4581const SCEV *
4582ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or noop with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4585, __extension__
 __PRETTY_FUNCTION__))
       "Cannot truncate or noop with non-integer arguments!")(static_cast <bool> (SrcTy->isIntOrPtrTy() &&
 Ty->isIntOrPtrTy() && "Cannot truncate or noop with non-integer arguments!"
) ? void (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4585, __extension__
 __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&(static_cast <bool> (getTypeSizeInBits(SrcTy) >= getTypeSizeInBits
(Ty) && "getTruncateOrNoop cannot extend!") ? void (0
) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4587, __extension__
 __PRETTY_FUNCTION__))
       "getTruncateOrNoop cannot extend!")(static_cast <bool> (getTypeSizeInBits(SrcTy) >= getTypeSizeInBits
(Ty) && "getTruncateOrNoop cannot extend!") ? void (0
) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4587, __extension__
 __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getTruncateExpr(V, Ty);
4591}

4593const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
                                                      const SCEV *RHS) {
const SCEV *PromotedLHS = LHS;
const SCEV *PromotedRHS = RHS;

if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
  PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
else
  PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());

return getUMaxExpr(PromotedLHS, PromotedRHS);
4604}

4606const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
                                                      const SCEV *RHS,
                                                      bool Sequential) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinFromMismatchedTypes(Ops, Sequential);
4611}

4613const SCEV *
4614ScalarEvolution::getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops,
                                          bool Sequential) {
assert(!Ops.empty() && "At least one operand must be!")(static_cast <bool> (!Ops.empty() && "At least one operand must be!"
) ? void (0) : __assert_fail ("!Ops.empty() && \"At least one operand must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4616, __extension__
 __PRETTY_FUNCTION__));
// Trivial case.
if (Ops.size() == 1)
  return Ops[0];

// Find the max type first.
Type *MaxType = nullptr;
for (auto *S : Ops)
  if (MaxType)
    MaxType = getWiderType(MaxType, S->getType());
  else
    MaxType = S->getType();
assert(MaxType && "Failed to find maximum type!")(static_cast <bool> (MaxType && "Failed to find maximum type!"
) ? void (0) : __assert_fail ("MaxType && \"Failed to find maximum type!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4628, __extension__
 __PRETTY_FUNCTION__));

// Extend all ops to max type.
SmallVector<const SCEV *, 2> PromotedOps;
for (auto *S : Ops)
  PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));

// Generate umin.
return getUMinExpr(PromotedOps, Sequential);
4637}

4639const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
// A pointer operand may evaluate to a nonpointer expression, such as null.
if (!V->getType()->isPointerTy())
  return V;

while (true) {
  if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
    V = AddRec->getStart();
  } else if (auto *Add = dyn_cast<SCEVAddExpr>(V)) {
    const SCEV *PtrOp = nullptr;
    for (const SCEV *AddOp : Add->operands()) {
      if (AddOp->getType()->isPointerTy()) {
        assert(!PtrOp && "Cannot have multiple pointer ops")(static_cast <bool> (!PtrOp && "Cannot have multiple pointer ops"
) ? void (0) : __assert_fail ("!PtrOp && \"Cannot have multiple pointer ops\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4651, __extension__
 __PRETTY_FUNCTION__));
        PtrOp = AddOp;
      }
    }
    assert(PtrOp && "Must have pointer op")(static_cast <bool> (PtrOp && "Must have pointer op"
) ? void (0) : __assert_fail ("PtrOp && \"Must have pointer op\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4655, __extension__
 __PRETTY_FUNCTION__));
    V = PtrOp;
  } else // Not something we can look further into.
    return V;
}
4660}

4662/// Push users of the given Instruction onto the given Worklist.
4663static void PushDefUseChildren(Instruction *I,
                             SmallVectorImpl<Instruction *> &Worklist,
                             SmallPtrSetImpl<Instruction *> &Visited) {
// Push the def-use children onto the Worklist stack.
for (User *U : I->users()) {
  auto *UserInsn = cast<Instruction>(U);
  if (Visited.insert(UserInsn).second)
    Worklist.push_back(UserInsn);
}
4672}

4674namespace {

4676/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4677/// expression in case its Loop is L. If it is not L then
4678/// if IgnoreOtherLoops is true then use AddRec itself
4679/// otherwise rewrite cannot be done.
4680/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4681class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4682public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
                           bool IgnoreOtherLoops = true) {
  SCEVInitRewriter Rewriter(L, SE);
  const SCEV *Result = Rewriter.visit(S);
  if (Rewriter.hasSeenLoopVariantSCEVUnknown())
    return SE.getCouldNotCompute();
  return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
             ? SE.getCouldNotCompute()
             : Result;
}

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  if (!SE.isLoopInvariant(Expr, L))
    SeenLoopVariantSCEVUnknown = true;
  return Expr;
}

const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
  // Only re-write AddRecExprs for this loop.
  if (Expr->getLoop() == L)
    return Expr->getStart();
  SeenOtherLoops = true;
  return Expr;
}

bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }

bool hasSeenOtherLoops() { return SeenOtherLoops; }

4712private:
explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
4719};

4721/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4722/// increment expression in case its Loop is L. If it is not L then
4723/// use AddRec itself.
4724/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4725class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4726public:
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
  SCEVPostIncRewriter Rewriter(L, SE);
  const SCEV *Result = Rewriter.visit(S);
  return Rewriter.hasSeenLoopVariantSCEVUnknown()
      ? SE.getCouldNotCompute()
      : Result;
}

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  if (!SE.isLoopInvariant(Expr, L))
    SeenLoopVariantSCEVUnknown = true;
  return Expr;
}

const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
  // Only re-write AddRecExprs for this loop.
  if (Expr->getLoop() == L)
    return Expr->getPostIncExpr(SE);
  SeenOtherLoops = true;
  return Expr;
}

bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }

bool hasSeenOtherLoops() { return SeenOtherLoops; }

4753private:
explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
4760};

4762/// This class evaluates the compare condition by matching it against the
4763/// condition of loop latch. If there is a match we assume a true value
4764/// for the condition while building SCEV nodes.
4765class SCEVBackedgeConditionFolder
  : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4767public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
                           ScalarEvolution &SE) {
  bool IsPosBECond = false;
  Value *BECond = nullptr;
  if (BasicBlock *Latch = L->getLoopLatch()) {
    BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
    if (BI && BI->isConditional()) {
      assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&(static_cast <bool> (BI->getSuccessor(0) != BI->getSuccessor
(1) && "Both outgoing branches should not target same header!"
) ? void (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4776, __extension__
 __PRETTY_FUNCTION__))
             "Both outgoing branches should not target same header!")(static_cast <bool> (BI->getSuccessor(0) != BI->getSuccessor
(1) && "Both outgoing branches should not target same header!"
) ? void (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 4776, __extension__
 __PRETTY_FUNCTION__));
      BECond = BI->getCondition();
      IsPosBECond = BI->getSuccessor(0) == L->getHeader();
    } else {
      return S;
    }
  }
  SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
  return Rewriter.visit(S);
}

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  const SCEV *Result = Expr;
  bool InvariantF = SE.isLoopInvariant(Expr, L);

  if (!InvariantF) {
    Instruction *I = cast<Instruction>(Expr->getValue());
    switch (I->getOpcode()) {
    case Instruction::Select: {
      SelectInst *SI = cast<SelectInst>(I);
      Optional<const SCEV *> Res =
          compareWithBackedgeCondition(SI->getCondition());
      if (Res.hasValue()) {
        bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
        Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
      }
      break;
    }
    default: {
      Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
      if (Res.hasValue())
        Result = Res.getValue();
      break;
    }
    }
  }
  return Result;
}

4815private:
explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
                                     bool IsPosBECond, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
      IsPositiveBECond(IsPosBECond) {}

Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);

const Loop *L;
/// Loop back condition.
Value *BackedgeCond = nullptr;
/// Set to true if loop back is on positive branch condition.
bool IsPositiveBECond;
4828};

4830Optional<const SCEV *>
4831SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {

// If value matches the backedge condition for loop latch,
// then return a constant evolution node based on loopback
// branch taken.
if (BackedgeCond == IC)
  return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
                          : SE.getZero(Type::getInt1Ty(SE.getContext()));
return None;
4840}

4842class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4843public:
static const SCEV *rewrite(const SCEV *S, const Loop *L,
                           ScalarEvolution &SE) {
  SCEVShiftRewriter Rewriter(L, SE);
  const SCEV *Result = Rewriter.visit(S);
  return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
}

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  // Only allow AddRecExprs for this loop.
  if (!SE.isLoopInvariant(Expr, L))
    Valid = false;
  return Expr;
}

const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
  if (Expr->getLoop() == L && Expr->isAffine())
    return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
  Valid = false;
  return Expr;
}

bool isValid() { return Valid; }

4867private:
explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool Valid = true;
4873};

4875} // end anonymous namespace

4877SCEV::NoWrapFlags
4878ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
if (!AR->isAffine())
  return SCEV::FlagAnyWrap;

using OBO = OverflowingBinaryOperator;

SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;

if (!AR->hasNoSignedWrap()) {
  ConstantRange AddRecRange = getSignedRange(AR);
  ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));

  auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
      Instruction::Add, IncRange, OBO::NoSignedWrap);
  if (NSWRegion.contains(AddRecRange))
    Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
}

if (!AR->hasNoUnsignedWrap()) {
  ConstantRange AddRecRange = getUnsignedRange(AR);
  ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));

  auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
      Instruction::Add, IncRange, OBO::NoUnsignedWrap);
  if (NUWRegion.contains(AddRecRange))
    Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
}

return Result;
4907}

4909SCEV::NoWrapFlags
4910ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
SCEV::NoWrapFlags Result = AR->getNoWrapFlags();

if (AR->hasNoSignedWrap())
  return Result;

if (!AR->isAffine())
  return Result;

const SCEV *Step = AR->getStepRecurrence(*this);
const Loop *L = AR->getLoop();

// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);

// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop.  The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow.  Use this fact to avoid
// doing extra work that may not pay off.

if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
    AC.assumptions().empty())
  return Result;

// If the backedge is guarded by a comparison with the pre-inc  value the
// addrec is safe. Also, if the entry is guarded by a comparison with the
// start value and the backedge is guarded by a comparison with the post-inc
// value, the addrec is safe.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
  getSignedOverflowLimitForStep(Step, &Pred, this);
if (OverflowLimit &&
    (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
     isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
  Result = setFlags(Result, SCEV::FlagNSW);
}
return Result;
4957}
4958SCEV::NoWrapFlags
4959ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
SCEV::NoWrapFlags Result = AR->getNoWrapFlags();

if (AR->hasNoUnsignedWrap())
1
Taking false branch→
  return Result;

if (!AR->isAffine())
2
←
Taking false branch→
  return Result;

const SCEV *Step = AR->getStepRecurrence(*this);
unsigned BitWidth = getTypeSizeInBits(AR->getType());
const Loop *L = AR->getLoop();

// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);

// Normally, in the cases we can prove no-overflow via a
// backedge guarding condition, we can also compute a backedge
// taken count for the loop.  The exceptions are assumptions and
// guards present in the loop -- SCEV is not great at exploiting
// these to compute max backedge taken counts, but can still use
// these to prove lack of overflow.  Use this fact to avoid
// doing extra work that may not pay off.

if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards &&
3
←
Assuming 'MaxBECount' is not a 'SCEVCouldNotCompute'→
4
←
Taking false branch→
    AC.assumptions().empty())
  return Result;

// If the backedge is guarded by a comparison with the pre-inc  value the
// addrec is safe. Also, if the entry is guarded by a comparison with the
// start value and the backedge is guarded by a comparison with the post-inc
// value, the addrec is safe.
if (isKnownPositive(Step)) {
5
←
Taking true branch→
  const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
                              getUnsignedRangeMax(Step));
  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
6
←
Calling 'ScalarEvolution::isLoopBackedgeGuardedByCond'→
18
←
Returning from 'ScalarEvolution::isLoopBackedgeGuardedByCond'→
      isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
19
←
Calling 'ScalarEvolution::isKnownOnEveryIteration'→
    Result = setFlags(Result, SCEV::FlagNUW);
  }
}

return Result;
5008}

5010namespace {

5012/// Represents an abstract binary operation.  This may exist as a
5013/// normal instruction or constant expression, or may have been
5014/// derived from an expression tree.
5015struct BinaryOp {
unsigned Opcode;
Value *LHS;
Value *RHS;
bool IsNSW = false;
bool IsNUW = false;

/// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
/// constant expression.
Operator *Op = nullptr;

explicit BinaryOp(Operator *Op)
    : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
      Op(Op) {
  if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
    IsNSW = OBO->hasNoSignedWrap();
    IsNUW = OBO->hasNoUnsignedWrap();
  }
}

explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
                  bool IsNUW = false)
    : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
5038};

5040} // end anonymous namespace

5042/// Try to map \p V into a BinaryOp, and return \c None on failure.
5043static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
auto *Op = dyn_cast<Operator>(V);
if (!Op)
  return None;

// Implementation detail: all the cleverness here should happen without
// creating new SCEV expressions -- our caller knowns tricks to avoid creating
// SCEV expressions when possible, and we should not break that.

switch (Op->getOpcode()) {
case Instruction::Add:
case Instruction::Sub:
case Instruction::Mul:
case Instruction::UDiv:
case Instruction::URem:
case Instruction::And:
case Instruction::Or:
case Instruction::AShr:
case Instruction::Shl:
  return BinaryOp(Op);

case Instruction::Xor:
  if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
    // If the RHS of the xor is a signmask, then this is just an add.
    // Instcombine turns add of signmask into xor as a strength reduction step.
    if (RHSC->getValue().isSignMask())
      return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
  return BinaryOp(Op);

case Instruction::LShr:
  // Turn logical shift right of a constant into a unsigned divide.
  if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
    uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();

    // If the shift count is not less than the bitwidth, the result of
    // the shift is undefined. Don't try to analyze it, because the
    // resolution chosen here may differ from the resolution chosen in
    // other parts of the compiler.
    if (SA->getValue().ult(BitWidth)) {
      Constant *X =
          ConstantInt::get(SA->getContext(),
                           APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
      return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
    }
  }
  return BinaryOp(Op);

case Instruction::ExtractValue: {
  auto *EVI = cast<ExtractValueInst>(Op);
  if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
    break;

  auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
  if (!WO)
    break;

  Instruction::BinaryOps BinOp = WO->getBinaryOp();
  bool Signed = WO->isSigned();
  // TODO: Should add nuw/nsw flags for mul as well.
  if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
    return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());

  // Now that we know that all uses of the arithmetic-result component of
  // CI are guarded by the overflow check, we can go ahead and pretend
  // that the arithmetic is non-overflowing.
  return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
                  /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
}

default:
  break;
}

// Recognise intrinsic loop.decrement.reg, and as this has exactly the same
// semantics as a Sub, return a binary sub expression.
if (auto *II = dyn_cast<IntrinsicInst>(V))
  if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
    return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));

return None;
5123}

5125/// Helper function to createAddRecFromPHIWithCasts. We have a phi
5126/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
5127/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
5128/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
5129/// follows one of the following patterns:
5130/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
5131/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
5132/// If the SCEV expression of \p Op conforms with one of the expected patterns
5133/// we return the type of the truncation operation, and indicate whether the
5134/// truncated type should be treated as signed/unsigned by setting
5135/// \p Signed to true/false, respectively.
5136static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
                             bool &Signed, ScalarEvolution &SE) {
// The case where Op == SymbolicPHI (that is, with no type conversions on
// the way) is handled by the regular add recurrence creating logic and
// would have already been triggered in createAddRecForPHI. Reaching it here
// means that createAddRecFromPHI had failed for this PHI before (e.g.,
// because one of the other operands of the SCEVAddExpr updating this PHI is
// not invariant).
//
// Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
// this case predicates that allow us to prove that Op == SymbolicPHI will
// be added.
if (Op == SymbolicPHI)
  return nullptr;

unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
if (SourceBits != NewBits)
  return nullptr;

const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
if (!SExt && !ZExt)
  return nullptr;
const SCEVTruncateExpr *Trunc =
    SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
         : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
if (!Trunc)
  return nullptr;
const SCEV *X = Trunc->getOperand();
if (X != SymbolicPHI)
  return nullptr;
Signed = SExt != nullptr;
return Trunc->getType();
5170}

5172static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
if (!PN->getType()->isIntegerTy())
  return nullptr;
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
  return nullptr;
return L;
5179}

5181// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
5182// computation that updates the phi follows the following pattern:
5183//   (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
5184// which correspond to a phi->trunc->sext/zext->add->phi update chain.
5185// If so, try to see if it can be rewritten as an AddRecExpr under some
5186// Predicates. If successful, return them as a pair. Also cache the results
5187// of the analysis.
5188//
5189// Example usage scenario:
5190//    Say the Rewriter is called for the following SCEV:
5191//         8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
5192//    where:
5193//         %X = phi i64 (%Start, %BEValue)
5194//    It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
5195//    and call this function with %SymbolicPHI = %X.
5196//
5197//    The analysis will find that the value coming around the backedge has
5198//    the following SCEV:
5199//         BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
5200//    Upon concluding that this matches the desired pattern, the function
5201//    will return the pair {NewAddRec, SmallPredsVec} where:
5202//         NewAddRec = {%Start,+,%Step}
5203//         SmallPredsVec = {P1, P2, P3} as follows:
5204//           P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
5205//           P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
5206//           P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
5207//    The returned pair means that SymbolicPHI can be rewritten into NewAddRec
5208//    under the predicates {P1,P2,P3}.
5209//    This predicated rewrite will be cached in PredicatedSCEVRewrites:
5210//         PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
5211//
5212// TODO's:
5213//
5214// 1) Extend the Induction descriptor to also support inductions that involve
5215//    casts: When needed (namely, when we are called in the context of the
5216//    vectorizer induction analysis), a Set of cast instructions will be
5217//    populated by this method, and provided back to isInductionPHI. This is
5218//    needed to allow the vectorizer to properly record them to be ignored by
5219//    the cost model and to avoid vectorizing them (otherwise these casts,
5220//    which are redundant under the runtime overflow checks, will be
5221//    vectorized, which can be costly).
5222//
5223// 2) Support additional induction/PHISCEV patterns: We also want to support
5224//    inductions where the sext-trunc / zext-trunc operations (partly) occur
5225//    after the induction update operation (the induction increment):
5226//
5227//      (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
5228//    which correspond to a phi->add->trunc->sext/zext->phi update chain.
5229//
5230//      (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
5231//    which correspond to a phi->trunc->add->sext/zext->phi update chain.
5232//
5233// 3) Outline common code with createAddRecFromPHI to avoid duplication.
5234Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5235ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
SmallVector<const SCEVPredicate *, 3> Predicates;

// *** Part1: Analyze if we have a phi-with-cast pattern for which we can
// return an AddRec expression under some predicate.

auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
assert(L && "Expecting an integer loop header phi")(static_cast <bool> (L && "Expecting an integer loop header phi"
) ? void (0) : __assert_fail ("L && \"Expecting an integer loop header phi\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5243, __extension__
 __PRETTY_FUNCTION__));

// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
  Value *V = PN->getIncomingValue(i);
  if (L->contains(PN->getIncomingBlock(i))) {
    if (!BEValueV) {
      BEValueV = V;
    } else if (BEValueV != V) {
      BEValueV = nullptr;
      break;
    }
  } else if (!StartValueV) {
    StartValueV = V;
  } else if (StartValueV != V) {
    StartValueV = nullptr;
    break;
  }
}
if (!BEValueV || !StartValueV)
  return None;

const SCEV *BEValue = getSCEV(BEValueV);

// If the value coming around the backedge is an add with the symbolic
// value we just inserted, possibly with casts that we can ignore under
// an appropriate runtime guard, then we found a simple induction variable!
const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
if (!Add)
  return None;

// If there is a single occurrence of the symbolic value, possibly
// casted, replace it with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
Type *TruncTy = nullptr;
bool Signed;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
  if ((TruncTy =
           isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
    if (FoundIndex == e) {
      FoundIndex = i;
      break;
    }

if (FoundIndex == Add->getNumOperands())
  return None;

// Create an add with everything but the specified operand.
SmallVector<const SCEV *, 8> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
  if (i != FoundIndex)
    Ops.push_back(Add->getOperand(i));
const SCEV *Accum = getAddExpr(Ops);

// The runtime checks will not be valid if the step amount is
// varying inside the loop.
if (!isLoopInvariant(Accum, L))
  return None;

// *** Part2: Create the predicates

// Analysis was successful: we have a phi-with-cast pattern for which we
// can return an AddRec expression under the following predicates:
//
// P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
//     fits within the truncated type (does not overflow) for i = 0 to n-1.
// P2: An Equal predicate that guarantees that
//     Start = (Ext ix (Trunc iy (Start) to ix) to iy)
// P3: An Equal predicate that guarantees that
//     Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
//
// As we next prove, the above predicates guarantee that:
//     Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
//
//
// More formally, we want to prove that:
//     Expr(i+1) = Start + (i+1) * Accum
//               = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// Given that:
// 1) Expr(0) = Start
// 2) Expr(1) = Start + Accum
//            = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
// 3) Induction hypothesis (step i):
//    Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
//
// Proof:
//  Expr(i+1) =
//   = Start + (i+1)*Accum
//   = (Start + i*Accum) + Accum
//   = Expr(i) + Accum
//   = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
//                                                             :: from step i
//
//   = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
//
//   = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
//     + (Ext ix (Trunc iy (Accum) to ix) to iy)
//     + Accum                                                     :: from P3
//
//   = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
//     + Accum                            :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
//
//   = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
//   = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
//
// By induction, the same applies to all iterations 1<=i<n:
//

// Create a truncated addrec for which we will add a no overflow check (P1).
const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV =
    getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
                  getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);

// PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
// ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
// will be constant.
//
//  If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
// add P1.
if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
  SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
      Signed ? SCEVWrapPredicate::IncrementNSSW
             : SCEVWrapPredicate::IncrementNUSW;
  const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
  Predicates.push_back(AddRecPred);
}

// Create the Equal Predicates P2,P3:

// It is possible that the predicates P2 and/or P3 are computable at
// compile time due to StartVal and/or Accum being constants.
// If either one is, then we can check that now and escape if either P2
// or P3 is false.

// Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
// for each of StartVal and Accum
auto getExtendedExpr = [&](const SCEV *Expr,
                           bool CreateSignExtend) -> const SCEV * {
  assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant")(static_cast <bool> (isLoopInvariant(Expr, L) &&
 "Expr is expected to be invariant") ? void (0) : __assert_fail
 ("isLoopInvariant(Expr, L) && \"Expr is expected to be invariant\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5386, __extension__
 __PRETTY_FUNCTION__));
  const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
  const SCEV *ExtendedExpr =
      CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
                       : getZeroExtendExpr(TruncatedExpr, Expr->getType());
  return ExtendedExpr;
};

// Given:
//  ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
//               = getExtendedExpr(Expr)
// Determine whether the predicate P: Expr == ExtendedExpr
// is known to be false at compile time
auto PredIsKnownFalse = [&](const SCEV *Expr,
                            const SCEV *ExtendedExpr) -> bool {
  return Expr != ExtendedExpr &&
         isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
};

const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
if (PredIsKnownFalse(StartVal, StartExtended)) {
  LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "P2 is compile-time false\n"
;; } } while (false);
  return None;
}

// The Step is always Signed (because the overflow checks are either
// NSSW or NUSW)
const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
if (PredIsKnownFalse(Accum, AccumExtended)) {
  LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "P3 is compile-time false\n"
;; } } while (false);
  return None;
}

auto AppendPredicate = [&](const SCEV *Expr,
                           const SCEV *ExtendedExpr) -> void {
  if (Expr != ExtendedExpr &&
      !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
    const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
    LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "Added Predicate: " <<
 *Pred; } } while (false);
    Predicates.push_back(Pred);
  }
};

AppendPredicate(StartVal, StartExtended);
AppendPredicate(Accum, AccumExtended);

// *** Part3: Predicates are ready. Now go ahead and create the new addrec in
// which the casts had been folded away. The caller can rewrite SymbolicPHI
// into NewAR if it will also add the runtime overflow checks specified in
// Predicates.
auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);

std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
    std::make_pair(NewAR, Predicates);
// Remember the result of the analysis for this SCEV at this locayyytion.
PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
return PredRewrite;
5443}

5445Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
5446ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
auto *PN = cast<PHINode>(SymbolicPHI->getValue());
const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
if (!L)
  return None;

// Check to see if we already analyzed this PHI.
auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
if (I != PredicatedSCEVRewrites.end()) {
  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
      I->second;
  // Analysis was done before and failed to create an AddRec:
  if (Rewrite.first == SymbolicPHI)
    return None;
  // Analysis was done before and succeeded to create an AddRec under
  // a predicate:
  assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec")(static_cast <bool> (isa<SCEVAddRecExpr>(Rewrite.
first) && "Expected an AddRec") ? void (0) : __assert_fail
 ("isa<SCEVAddRecExpr>(Rewrite.first) && \"Expected an AddRec\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5462, __extension__
 __PRETTY_FUNCTION__));
  assert(!(Rewrite.second).empty() && "Expected to find Predicates")(static_cast <bool> (!(Rewrite.second).empty() &&
 "Expected to find Predicates") ? void (0) : __assert_fail ("!(Rewrite.second).empty() && \"Expected to find Predicates\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5463, __extension__
 __PRETTY_FUNCTION__));
  return Rewrite;
}

Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
  Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);

// Record in the cache that the analysis failed
if (!Rewrite) {
  SmallVector<const SCEVPredicate *, 3> Predicates;
  PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
  return None;
}

return Rewrite;
5478}

5480// FIXME: This utility is currently required because the Rewriter currently
5481// does not rewrite this expression:
5482// {0, +, (sext ix (trunc iy to ix) to iy)}
5483// into {0, +, %step},
5484// even when the following Equal predicate exists:
5485// "%step == (sext ix (trunc iy to ix) to iy)".
5486bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
  const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
if (AR1 == AR2)
  return true;

auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
  if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
      !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
    return false;
  return true;
};

if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
    !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
  return false;
return true;
5502}

5504/// A helper function for createAddRecFromPHI to handle simple cases.
5505///
5506/// This function tries to find an AddRec expression for the simplest (yet most
5507/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
5508/// If it fails, createAddRecFromPHI will use a more general, but slow,
5509/// technique for finding the AddRec expression.
5510const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
                                                    Value *BEValueV,
                                                    Value *StartValueV) {
const Loop *L = LI.getLoopFor(PN->getParent());
assert(L && L->getHeader() == PN->getParent())(static_cast <bool> (L && L->getHeader() == PN
->getParent()) ? void (0) : __assert_fail ("L && L->getHeader() == PN->getParent()"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5514, __extension__
 __PRETTY_FUNCTION__));
assert(BEValueV && StartValueV)(static_cast <bool> (BEValueV && StartValueV) ?
 void (0) : __assert_fail ("BEValueV && StartValueV",
 "llvm/lib/Analysis/ScalarEvolution.cpp", 5515, __extension__
 __PRETTY_FUNCTION__));

auto BO = MatchBinaryOp(BEValueV, DT);
if (!BO)
  return nullptr;

if (BO->Opcode != Instruction::Add)
  return nullptr;

const SCEV *Accum = nullptr;
if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
  Accum = getSCEV(BO->RHS);
else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
  Accum = getSCEV(BO->LHS);

if (!Accum)
  return nullptr;

SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BO->IsNUW)
  Flags = setFlags(Flags, SCEV::FlagNUW);
if (BO->IsNSW)
  Flags = setFlags(Flags, SCEV::FlagNSW);

const SCEV *StartVal = getSCEV(StartValueV);
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
insertValueToMap(PN, PHISCEV);

// We can add Flags to the post-inc expression only if we
// know that it is *undefined behavior* for BEValueV to
// overflow.
if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) {
  assert(isLoopInvariant(Accum, L) &&(static_cast <bool> (isLoopInvariant(Accum, L) &&
 "Accum is defined outside L, but is not invariant?") ? void (
0) : __assert_fail ("isLoopInvariant(Accum, L) && \"Accum is defined outside L, but is not invariant?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5548, __extension__
 __PRETTY_FUNCTION__))
         "Accum is defined outside L, but is not invariant?")(static_cast <bool> (isLoopInvariant(Accum, L) &&
 "Accum is defined outside L, but is not invariant?") ? void (
0) : __assert_fail ("isLoopInvariant(Accum, L) && \"Accum is defined outside L, but is not invariant?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5548, __extension__
 __PRETTY_FUNCTION__));
  if (isAddRecNeverPoison(BEInst, L))
    (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
}

return PHISCEV;
5554}

5556const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
const Loop *L = LI.getLoopFor(PN->getParent());
if (!L || L->getHeader() != PN->getParent())
  return nullptr;

// The loop may have multiple entrances or multiple exits; we can analyze
// this phi as an addrec if it has a unique entry value and a unique
// backedge value.
Value *BEValueV = nullptr, *StartValueV = nullptr;
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
  Value *V = PN->getIncomingValue(i);
  if (L->contains(PN->getIncomingBlock(i))) {
    if (!BEValueV) {
      BEValueV = V;
    } else if (BEValueV != V) {
      BEValueV = nullptr;
      break;
    }
  } else if (!StartValueV) {
    StartValueV = V;
  } else if (StartValueV != V) {
    StartValueV = nullptr;
    break;
  }
}
if (!BEValueV || !StartValueV)
  return nullptr;

assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&(static_cast <bool> (ValueExprMap.find_as(PN) == ValueExprMap
.end() && "PHI node already processed?") ? void (0) :
 __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5585, __extension__
 __PRETTY_FUNCTION__))
       "PHI node already processed?")(static_cast <bool> (ValueExprMap.find_as(PN) == ValueExprMap
.end() && "PHI node already processed?") ? void (0) :
 __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5585, __extension__
 __PRETTY_FUNCTION__));

// First, try to find AddRec expression without creating a fictituos symbolic
// value for PN.
if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
  return S;

// Handle PHI node value symbolically.
const SCEV *SymbolicName = getUnknown(PN);
insertValueToMap(PN, SymbolicName);

// Using this symbolic name for the PHI, analyze the value coming around
// the back-edge.
const SCEV *BEValue = getSCEV(BEValueV);

// NOTE: If BEValue is loop invariant, we know that the PHI node just
// has a special value for the first iteration of the loop.

// If the value coming around the backedge is an add with the symbolic
// value we just inserted, then we found a simple induction variable!
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
  // If there is a single occurrence of the symbolic value, replace it
  // with a recurrence.
  unsigned FoundIndex = Add->getNumOperands();
  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
    if (Add->getOperand(i) == SymbolicName)
      if (FoundIndex == e) {
        FoundIndex = i;
        break;
      }

  if (FoundIndex != Add->getNumOperands()) {
    // Create an add with everything but the specified operand.
    SmallVector<const SCEV *, 8> Ops;
    for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
      if (i != FoundIndex)
        Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
                                                           L, *this));
    const SCEV *Accum = getAddExpr(Ops);

    // This is not a valid addrec if the step amount is varying each
    // loop iteration, but is not itself an addrec in this loop.
    if (isLoopInvariant(Accum, L) ||
        (isa<SCEVAddRecExpr>(Accum) &&
         cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
      SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;

      if (auto BO = MatchBinaryOp(BEValueV, DT)) {
        if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
          if (BO->IsNUW)
            Flags = setFlags(Flags, SCEV::FlagNUW);
          if (BO->IsNSW)
            Flags = setFlags(Flags, SCEV::FlagNSW);
        }
      } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
        // If the increment is an inbounds GEP, then we know the address
        // space cannot be wrapped around. We cannot make any guarantee
        // about signed or unsigned overflow because pointers are
        // unsigned but we may have a negative index from the base
        // pointer. We can guarantee that no unsigned wrap occurs if the
        // indices form a positive value.
        if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
          Flags = setFlags(Flags, SCEV::FlagNW);

          const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
          if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
            Flags = setFlags(Flags, SCEV::FlagNUW);
        }

        // We cannot transfer nuw and nsw flags from subtraction
        // operations -- sub nuw X, Y is not the same as add nuw X, -Y
        // for instance.
      }

      const SCEV *StartVal = getSCEV(StartValueV);
      const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);

      // Okay, for the entire analysis of this edge we assumed the PHI
      // to be symbolic.  We now need to go back and purge all of the
      // entries for the scalars that use the symbolic expression.
      forgetMemoizedResults(SymbolicName);
      insertValueToMap(PN, PHISCEV);

      // We can add Flags to the post-inc expression only if we
      // know that it is *undefined behavior* for BEValueV to
      // overflow.
      if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
        if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
          (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);

      return PHISCEV;
    }
  }
} else {
  // Otherwise, this could be a loop like this:
  //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
  // In this case, j = {1,+,1}  and BEValue is j.
  // Because the other in-value of i (0) fits the evolution of BEValue
  // i really is an addrec evolution.
  //
  // We can generalize this saying that i is the shifted value of BEValue
  // by one iteration:
  //   PHI(f(0), f({1,+,1})) --> f({0,+,1})
  const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
  const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
  if (Shifted != getCouldNotCompute() &&
      Start != getCouldNotCompute()) {
    const SCEV *StartVal = getSCEV(StartValueV);
    if (Start == StartVal) {
      // Okay, for the entire analysis of this edge we assumed the PHI
      // to be symbolic.  We now need to go back and purge all of the
      // entries for the scalars that use the symbolic expression.
      forgetMemoizedResults(SymbolicName);
      insertValueToMap(PN, Shifted);
      return Shifted;
    }
  }
}

// Remove the temporary PHI node SCEV that has been inserted while intending
// to create an AddRecExpr for this PHI node. We can not keep this temporary
// as it will prevent later (possibly simpler) SCEV expressions to be added
// to the ValueExprMap.
eraseValueFromMap(PN);

return nullptr;
5711}

5713// Checks if the SCEV S is available at BB.  S is considered available at BB
5714// if S can be materialized at BB without introducing a fault.
5715static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
                             BasicBlock *BB) {
struct CheckAvailable {
  bool TraversalDone = false;
  bool Available = true;

  const Loop *L = nullptr;  // The loop BB is in (can be nullptr)
  BasicBlock *BB = nullptr;
  DominatorTree &DT;

  CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
    : L(L), BB(BB), DT(DT) {}

  bool setUnavailable() {
    TraversalDone = true;
    Available = false;
    return false;
  }

  bool follow(const SCEV *S) {
    switch (S->getSCEVType()) {
    case scConstant:
    case scPtrToInt:
    case scTruncate:
    case scZeroExtend:
    case scSignExtend:
    case scAddExpr:
    case scMulExpr:
    case scUMaxExpr:
    case scSMaxExpr:
    case scUMinExpr:
    case scSMinExpr:
    case scSequentialUMinExpr:
      // These expressions are available if their operand(s) is/are.
      return true;

    case scAddRecExpr: {
      // We allow add recurrences that are on the loop BB is in, or some
      // outer loop.  This guarantees availability because the value of the
      // add recurrence at BB is simply the "current" value of the induction
      // variable.  We can relax this in the future; for instance an add
      // recurrence on a sibling dominating loop is also available at BB.
      const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
      if (L && (ARLoop == L || ARLoop->contains(L)))
        return true;

      return setUnavailable();
    }

    case scUnknown: {
      // For SCEVUnknown, we check for simple dominance.
      const auto *SU = cast<SCEVUnknown>(S);
      Value *V = SU->getValue();

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

      if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
        return false;

      return setUnavailable();
    }

    case scUDivExpr:
    case scCouldNotCompute:
      // We do not try to smart about these at all.
      return setUnavailable();
    }
    llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 5783);
  }

  bool isDone() { return TraversalDone; }
};

CheckAvailable CA(L, BB, DT);
SCEVTraversal<CheckAvailable> ST(CA);

ST.visitAll(S);
return CA.Available;
5794}

5796// Try to match a control flow sequence that branches out at BI and merges back
5797// at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
5798// match.
5799static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
                        Value *&C, Value *&LHS, Value *&RHS) {
C = BI->getCondition();

BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));

if (!LeftEdge.isSingleEdge())
  return false;

assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()")(static_cast <bool> (RightEdge.isSingleEdge() &&
 "Follows from LeftEdge.isSingleEdge()") ? void (0) : __assert_fail
 ("RightEdge.isSingleEdge() && \"Follows from LeftEdge.isSingleEdge()\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5809, __extension__
 __PRETTY_FUNCTION__));

Use &LeftUse = Merge->getOperandUse(0);
Use &RightUse = Merge->getOperandUse(1);

if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
  LHS = LeftUse;
  RHS = RightUse;
  return true;
}

if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
  LHS = RightUse;
  RHS = LeftUse;
  return true;
}

return false;
5827}

5829const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
auto IsReachable =
    [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
  const Loop *L = LI.getLoopFor(PN->getParent());

  // We don't want to break LCSSA, even in a SCEV expression tree.
  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
    if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
      return nullptr;

  // Try to match
  //
  //  br %cond, label %left, label %right
  // left:
  //  br label %merge
  // right:
  //  br label %merge
  // merge:
  //  V = phi [ %x, %left ], [ %y, %right ]
  //
  // as "select %cond, %x, %y"

  BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
  assert(IDom && "At least the entry block should dominate PN")(static_cast <bool> (IDom && "At least the entry block should dominate PN"
) ? void (0) : __assert_fail ("IDom && \"At least the entry block should dominate PN\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 5853, __extension__
 __PRETTY_FUNCTION__));

  auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
  Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;

  if (BI && BI->isConditional() &&
      BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
      IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
      IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
    return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
}

return nullptr;
5866}

5868const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
if (const SCEV *S = createAddRecFromPHI(PN))
  return S;

if (const SCEV *S = createNodeFromSelectLikePHI(PN))
  return S;

// If the PHI has a single incoming value, follow that value, unless the
// PHI's incoming blocks are in a different loop, in which case doing so
// risks breaking LCSSA form. Instcombine would normally zap these, but
// it doesn't have DominatorTree information, so it may miss cases.
if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
  if (LI.replacementPreservesLCSSAForm(PN, V))
    return getSCEV(V);

// If it's not a loop phi, we can't handle it yet.
return getUnknown(PN);
5885}

5887const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
                                                    Value *Cond,
                                                    Value *TrueVal,
                                                    Value *FalseVal) {
// Handle "constant" branch or select. This can occur for instance when a
// loop pass transforms an inner loop and moves on to process the outer loop.
if (auto *CI = dyn_cast<ConstantInt>(Cond))
  return getSCEV(CI->isOne() ? TrueVal : FalseVal);

// Try to match some simple smax or umax patterns.
auto *ICI = dyn_cast<ICmpInst>(Cond);
if (!ICI)
  return getUnknown(I);

Value *LHS = ICI->getOperand(0);
Value *RHS = ICI->getOperand(1);

switch (ICI->getPredicate()) {
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
  // a > b ? a+x : b+x  ->  max(a, b)+x
  // a > b ? b+x : a+x  ->  min(a, b)+x
  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
    bool Signed = ICI->isSigned();
    const SCEV *LA = getSCEV(TrueVal);
    const SCEV *RA = getSCEV(FalseVal);
    const SCEV *LS = getSCEV(LHS);
    const SCEV *RS = getSCEV(RHS);
    if (LA->getType()->isPointerTy()) {
      // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA.
      // Need to make sure we can't produce weird expressions involving
      // negated pointers.
      if (LA == LS && RA == RS)
        return Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS);
      if (LA == RS && RA == LS)
        return Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS);
    }
    auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * {
      if (Op->getType()->isPointerTy()) {
        Op = getLosslessPtrToIntExpr(Op);
        if (isa<SCEVCouldNotCompute>(Op))
          return Op;
      }
      if (Signed)
        Op = getNoopOrSignExtend(Op, I->getType());
      else
        Op = getNoopOrZeroExtend(Op, I->getType());
      return Op;
    };
    LS = CoerceOperand(LS);
    RS = CoerceOperand(RS);
    if (isa<SCEVCouldNotCompute>(LS) || isa<SCEVCouldNotCompute>(RS))
      break;
    const SCEV *LDiff = getMinusSCEV(LA, LS);
    const SCEV *RDiff = getMinusSCEV(RA, RS);
    if (LDiff == RDiff)
      return getAddExpr(Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS),
                        LDiff);
    LDiff = getMinusSCEV(LA, RS);
    RDiff = getMinusSCEV(RA, LS);
    if (LDiff == RDiff)
      return getAddExpr(Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS),
                        LDiff);
  }
  break;
case ICmpInst::ICMP_NE:
  // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
      isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
    const SCEV *One = getOne(I->getType());
    const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    const SCEV *LA = getSCEV(TrueVal);
    const SCEV *RA = getSCEV(FalseVal);
    const SCEV *LDiff = getMinusSCEV(LA, LS);
    const SCEV *RDiff = getMinusSCEV(RA, One);
    if (LDiff == RDiff)
      return getAddExpr(getUMaxExpr(One, LS), LDiff);
  }
  break;
case ICmpInst::ICMP_EQ:
  // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
      isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
    const SCEV *One = getOne(I->getType());
    const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    const SCEV *LA = getSCEV(TrueVal);
    const SCEV *RA = getSCEV(FalseVal);
    const SCEV *LDiff = getMinusSCEV(LA, One);
    const SCEV *RDiff = getMinusSCEV(RA, LS);
    if (LDiff == RDiff)
      return getAddExpr(getUMaxExpr(One, LS), LDiff);
  }
  break;
default:
  break;
}

return getUnknown(I);
5993}

5995/// Expand GEP instructions into add and multiply operations. This allows them
5996/// to be analyzed by regular SCEV code.
5997const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
// Don't attempt to analyze GEPs over unsized objects.
if (!GEP->getSourceElementType()->isSized())
  return getUnknown(GEP);

SmallVector<const SCEV *, 4> IndexExprs;
for (Value *Index : GEP->indices())
  IndexExprs.push_back(getSCEV(Index));
return getGEPExpr(GEP, IndexExprs);
6006}

6008uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
  return C->getAPInt().countTrailingZeros();

if (const SCEVPtrToIntExpr *I = dyn_cast<SCEVPtrToIntExpr>(S))
  return GetMinTrailingZeros(I->getOperand());

if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
  return std::min(GetMinTrailingZeros(T->getOperand()),
                  (uint32_t)getTypeSizeInBits(T->getType()));

if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
             ? getTypeSizeInBits(E->getType())
             : OpRes;
}

if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
             ? getTypeSizeInBits(E->getType())
             : OpRes;
}

if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
  // The result is the min of all operands results.
  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
    MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
  return MinOpRes;
}

if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
  // The result is the sum of all operands results.
  uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
  uint32_t BitWidth = getTypeSizeInBits(M->getType());
  for (unsigned i = 1, e = M->getNumOperands();
       SumOpRes != BitWidth && i != e; ++i)
    SumOpRes =
        std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
  return SumOpRes;
}

if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
  // The result is the min of all operands results.
  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
    MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
  return MinOpRes;
}

if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
  // The result is the min of all operands results.
  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
    MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
  return MinOpRes;
}

if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
  // The result is the min of all operands results.
  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
    MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
  return MinOpRes;
}

if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
  // For a SCEVUnknown, ask ValueTracking.
  KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
  return Known.countMinTrailingZeros();
}

// SCEVUDivExpr
return 0;
6084}

6086uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
auto I = MinTrailingZerosCache.find(S);
if (I != MinTrailingZerosCache.end())
  return I->second;

uint32_t Result = GetMinTrailingZerosImpl(S);
auto InsertPair = MinTrailingZerosCache.insert({S, Result});
assert(InsertPair.second && "Should insert a new key")(static_cast <bool> (InsertPair.second && "Should insert a new key"
) ? void (0) : __assert_fail ("InsertPair.second && \"Should insert a new key\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6093, __extension__
 __PRETTY_FUNCTION__));
return InsertPair.first->second;
6095}

6097/// Helper method to assign a range to V from metadata present in the IR.
6098static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
if (Instruction *I = dyn_cast<Instruction>(V))
  if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
    return getConstantRangeFromMetadata(*MD);

return None;
6104}

6106void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
                                   SCEV::NoWrapFlags Flags) {
if (AddRec->getNoWrapFlags(Flags) != Flags) {
  AddRec->setNoWrapFlags(Flags);
  UnsignedRanges.erase(AddRec);
  SignedRanges.erase(AddRec);
}
6113}

6115ConstantRange ScalarEvolution::
6116getRangeForUnknownRecurrence(const SCEVUnknown *U) {
const DataLayout &DL = getDataLayout();

unsigned BitWidth = getTypeSizeInBits(U->getType());
const ConstantRange FullSet(BitWidth, /*isFullSet=*/true);

// Match a simple recurrence of the form: <start, ShiftOp, Step>, and then
// use information about the trip count to improve our available range.  Note
// that the trip count independent cases are already handled by known bits.
// WARNING: The definition of recurrence used here is subtly different than
// the one used by AddRec (and thus most of this file).  Step is allowed to
// be arbitrarily loop varying here, where AddRec allows only loop invariant
// and other addrecs in the same loop (for non-affine addrecs).  The code
// below intentionally handles the case where step is not loop invariant.
auto *P = dyn_cast<PHINode>(U->getValue());
if (!P)
  return FullSet;

// Make sure that no Phi input comes from an unreachable block. Otherwise,
// even the values that are not available in these blocks may come from them,
// and this leads to false-positive recurrence test.
for (auto *Pred : predecessors(P->getParent()))
  if (!DT.isReachableFromEntry(Pred))
    return FullSet;

BinaryOperator *BO;
Value *Start, *Step;
if (!matchSimpleRecurrence(P, BO, Start, Step))
  return FullSet;

// If we found a recurrence in reachable code, we must be in a loop. Note
// that BO might be in some subloop of L, and that's completely okay.
auto *L = LI.getLoopFor(P->getParent());
assert(L && L->getHeader() == P->getParent())(static_cast <bool> (L && L->getHeader() == P
->getParent()) ? void (0) : __assert_fail ("L && L->getHeader() == P->getParent()"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6149, __extension__
 __PRETTY_FUNCTION__));
if (!L->contains(BO->getParent()))
  // NOTE: This bailout should be an assert instead.  However, asserting
  // the condition here exposes a case where LoopFusion is querying SCEV
  // with malformed loop information during the midst of the transform.
  // There doesn't appear to be an obvious fix, so for the moment bailout
  // until the caller issue can be fixed.  PR49566 tracks the bug.
  return FullSet;

// TODO: Extend to other opcodes such as mul, and div
switch (BO->getOpcode()) {
default:
  return FullSet;
case Instruction::AShr:
case Instruction::LShr:
case Instruction::Shl:
  break;
};

if (BO->getOperand(0) != P)
  // TODO: Handle the power function forms some day.
  return FullSet;

unsigned TC = getSmallConstantMaxTripCount(L);
if (!TC || TC >= BitWidth)
  return FullSet;

auto KnownStart = computeKnownBits(Start, DL, 0, &AC, nullptr, &DT);
auto KnownStep = computeKnownBits(Step, DL, 0, &AC, nullptr, &DT);
assert(KnownStart.getBitWidth() == BitWidth &&(static_cast <bool> (KnownStart.getBitWidth() == BitWidth
 && KnownStep.getBitWidth() == BitWidth) ? void (0) :
 __assert_fail ("KnownStart.getBitWidth() == BitWidth && KnownStep.getBitWidth() == BitWidth"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6179, __extension__
 __PRETTY_FUNCTION__))
       KnownStep.getBitWidth() == BitWidth)(static_cast <bool> (KnownStart.getBitWidth() == BitWidth
 && KnownStep.getBitWidth() == BitWidth) ? void (0) :
 __assert_fail ("KnownStart.getBitWidth() == BitWidth && KnownStep.getBitWidth() == BitWidth"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6179, __extension__
 __PRETTY_FUNCTION__));

// Compute total shift amount, being careful of overflow and bitwidths.
auto MaxShiftAmt = KnownStep.getMaxValue();
APInt TCAP(BitWidth, TC-1);
bool Overflow = false;
auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow);
if (Overflow)
  return FullSet;

switch (BO->getOpcode()) {
default:
  llvm_unreachable("filtered out above")::llvm::llvm_unreachable_internal("filtered out above", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 6191);
case Instruction::AShr: {
  // For each ashr, three cases:
  //   shift = 0 => unchanged value
  //   saturation => 0 or -1
  //   other => a value closer to zero (of the same sign)
  // Thus, the end value is closer to zero than the start.
  auto KnownEnd = KnownBits::ashr(KnownStart,
                                  KnownBits::makeConstant(TotalShift));
  if (KnownStart.isNonNegative())
    // Analogous to lshr (simply not yet canonicalized)
    return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
                                      KnownStart.getMaxValue() + 1);
  if (KnownStart.isNegative())
    // End >=u Start && End <=s Start
    return ConstantRange::getNonEmpty(KnownStart.getMinValue(),
                                      KnownEnd.getMaxValue() + 1);
  break;
}
case Instruction::LShr: {
  // For each lshr, three cases:
  //   shift = 0 => unchanged value
  //   saturation => 0
  //   other => a smaller positive number
  // Thus, the low end of the unsigned range is the last value produced.
  auto KnownEnd = KnownBits::lshr(KnownStart,
                                  KnownBits::makeConstant(TotalShift));
  return ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
                                    KnownStart.getMaxValue() + 1);
}
case Instruction::Shl: {
  // Iff no bits are shifted out, value increases on every shift.
  auto KnownEnd = KnownBits::shl(KnownStart,
                                 KnownBits::makeConstant(TotalShift));
  if (TotalShift.ult(KnownStart.countMinLeadingZeros()))
    return ConstantRange(KnownStart.getMinValue(),
                         KnownEnd.getMaxValue() + 1);
  break;
}
};
return FullSet;
6232}

6234/// Determine the range for a particular SCEV.  If SignHint is
6235/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
6236/// with a "cleaner" unsigned (resp. signed) representation.
6237const ConstantRange &
6238ScalarEvolution::getRangeRef(const SCEV *S,
                           ScalarEvolution::RangeSignHint SignHint) {
DenseMap<const SCEV *, ConstantRange> &Cache =
    SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
                                                     : SignedRanges;
ConstantRange::PreferredRangeType RangeType =
    SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
        ? ConstantRange::Unsigned : ConstantRange::Signed;

// See if we've computed this range already.
DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
if (I != Cache.end())
  return I->second;

if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
  return setRange(C, SignHint, ConstantRange(C->getAPInt()));

unsigned BitWidth = getTypeSizeInBits(S->getType());
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
using OBO = OverflowingBinaryOperator;

// If the value has known zeros, the maximum value will have those known zeros
// as well.
uint32_t TZ = GetMinTrailingZeros(S);
if (TZ != 0) {
  if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
    ConservativeResult =
        ConstantRange(APInt::getMinValue(BitWidth),
                      APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
  else
    ConservativeResult = ConstantRange(
        APInt::getSignedMinValue(BitWidth),
        APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
}

if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
  ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
  unsigned WrapType = OBO::AnyWrap;
  if (Add->hasNoSignedWrap())
    WrapType |= OBO::NoSignedWrap;
  if (Add->hasNoUnsignedWrap())
    WrapType |= OBO::NoUnsignedWrap;
  for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
    X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint),
                        WrapType, RangeType);
  return setRange(Add, SignHint,
                  ConservativeResult.intersectWith(X, RangeType));
}

if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
  ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
  for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
    X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
  return setRange(Mul, SignHint,
                  ConservativeResult.intersectWith(X, RangeType));
}

if (isa<SCEVMinMaxExpr>(S) || isa<SCEVSequentialMinMaxExpr>(S)) {
  Intrinsic::ID ID;
  switch (S->getSCEVType()) {
  case scUMaxExpr:
    ID = Intrinsic::umax;
    break;
  case scSMaxExpr:
    ID = Intrinsic::smax;
    break;
  case scUMinExpr:
  case scSequentialUMinExpr:
    ID = Intrinsic::umin;
    break;
  case scSMinExpr:
    ID = Intrinsic::smin;
    break;
  default:
    llvm_unreachable("Unknown SCEVMinMaxExpr/SCEVSequentialMinMaxExpr.")::llvm::llvm_unreachable_internal("Unknown SCEVMinMaxExpr/SCEVSequentialMinMaxExpr."
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6312);
  }

  const auto *NAry = cast<SCEVNAryExpr>(S);
  ConstantRange X = getRangeRef(NAry->getOperand(0), SignHint);
  for (unsigned i = 1, e = NAry->getNumOperands(); i != e; ++i)
    X = X.intrinsic(ID, {X, getRangeRef(NAry->getOperand(i), SignHint)});
  return setRange(S, SignHint,
                  ConservativeResult.intersectWith(X, RangeType));
}

if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
  ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
  ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
  return setRange(UDiv, SignHint,
                  ConservativeResult.intersectWith(X.udiv(Y), RangeType));
}

if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
  ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
  return setRange(ZExt, SignHint,
                  ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
                                                   RangeType));
}

if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
  ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
  return setRange(SExt, SignHint,
                  ConservativeResult.intersectWith(X.signExtend(BitWidth),
                                                   RangeType));
}

if (const SCEVPtrToIntExpr *PtrToInt = dyn_cast<SCEVPtrToIntExpr>(S)) {
  ConstantRange X = getRangeRef(PtrToInt->getOperand(), SignHint);
  return setRange(PtrToInt, SignHint, X);
}

if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
  ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
  return setRange(Trunc, SignHint,
                  ConservativeResult.intersectWith(X.truncate(BitWidth),
                                                   RangeType));
}

if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
  // If there's no unsigned wrap, the value will never be less than its
  // initial value.
  if (AddRec->hasNoUnsignedWrap()) {
    APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
    if (!UnsignedMinValue.isZero())
      ConservativeResult = ConservativeResult.intersectWith(
          ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
  }

  // If there's no signed wrap, and all the operands except initial value have
  // the same sign or zero, the value won't ever be:
  // 1: smaller than initial value if operands are non negative,
  // 2: bigger than initial value if operands are non positive.
  // For both cases, value can not cross signed min/max boundary.
  if (AddRec->hasNoSignedWrap()) {
    bool AllNonNeg = true;
    bool AllNonPos = true;
    for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
      if (!isKnownNonNegative(AddRec->getOperand(i)))
        AllNonNeg = false;
      if (!isKnownNonPositive(AddRec->getOperand(i)))
        AllNonPos = false;
    }
    if (AllNonNeg)
      ConservativeResult = ConservativeResult.intersectWith(
          ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
                                     APInt::getSignedMinValue(BitWidth)),
          RangeType);
    else if (AllNonPos)
      ConservativeResult = ConservativeResult.intersectWith(
          ConstantRange::getNonEmpty(
              APInt::getSignedMinValue(BitWidth),
              getSignedRangeMax(AddRec->getStart()) + 1),
          RangeType);
  }

  // TODO: non-affine addrec
  if (AddRec->isAffine()) {
    const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
    if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
        getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
      auto RangeFromAffine = getRangeForAffineAR(
          AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
          BitWidth);
      ConservativeResult =
          ConservativeResult.intersectWith(RangeFromAffine, RangeType);

      auto RangeFromFactoring = getRangeViaFactoring(
          AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
          BitWidth);
      ConservativeResult =
          ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
    }

    // Now try symbolic BE count and more powerful methods.
    if (UseExpensiveRangeSharpening) {
      const SCEV *SymbolicMaxBECount =
          getSymbolicMaxBackedgeTakenCount(AddRec->getLoop());
      if (!isa<SCEVCouldNotCompute>(SymbolicMaxBECount) &&
          getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
          AddRec->hasNoSelfWrap()) {
        auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR(
            AddRec, SymbolicMaxBECount, BitWidth, SignHint);
        ConservativeResult =
            ConservativeResult.intersectWith(RangeFromAffineNew, RangeType);
      }
    }
  }

  return setRange(AddRec, SignHint, std::move(ConservativeResult));
}

if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {

  // Check if the IR explicitly contains !range metadata.
  Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
  if (MDRange.hasValue())
    ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
                                                          RangeType);

  // Use facts about recurrences in the underlying IR.  Note that add
  // recurrences are AddRecExprs and thus don't hit this path.  This
  // primarily handles shift recurrences.
  auto CR = getRangeForUnknownRecurrence(U);
  ConservativeResult = ConservativeResult.intersectWith(CR);

  // See if ValueTracking can give us a useful range.
  const DataLayout &DL = getDataLayout();
  KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
  if (Known.getBitWidth() != BitWidth)
    Known = Known.zextOrTrunc(BitWidth);

  // ValueTracking may be able to compute a tighter result for the number of
  // sign bits than for the value of those sign bits.
  unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
  if (U->getType()->isPointerTy()) {
    // If the pointer size is larger than the index size type, this can cause
    // NS to be larger than BitWidth. So compensate for this.
    unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
    int ptrIdxDiff = ptrSize - BitWidth;
    if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
      NS -= ptrIdxDiff;
  }

  if (NS > 1) {
    // If we know any of the sign bits, we know all of the sign bits.
    if (!Known.Zero.getHiBits(NS).isZero())
      Known.Zero.setHighBits(NS);
    if (!Known.One.getHiBits(NS).isZero())
      Known.One.setHighBits(NS);
  }

  if (Known.getMinValue() != Known.getMaxValue() + 1)
    ConservativeResult = ConservativeResult.intersectWith(
        ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
        RangeType);
  if (NS > 1)
    ConservativeResult = ConservativeResult.intersectWith(
        ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
                      APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
        RangeType);

  // A range of Phi is a subset of union of all ranges of its input.
  if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
    // Make sure that we do not run over cycled Phis.
    if (PendingPhiRanges.insert(Phi).second) {
      ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
      for (auto &Op : Phi->operands()) {
        auto OpRange = getRangeRef(getSCEV(Op), SignHint);
        RangeFromOps = RangeFromOps.unionWith(OpRange);
        // No point to continue if we already have a full set.
        if (RangeFromOps.isFullSet())
          break;
      }
      ConservativeResult =
          ConservativeResult.intersectWith(RangeFromOps, RangeType);
      bool Erased = PendingPhiRanges.erase(Phi);
      assert(Erased && "Failed to erase Phi properly?")(static_cast <bool> (Erased && "Failed to erase Phi properly?"
) ? void (0) : __assert_fail ("Erased && \"Failed to erase Phi properly?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6494, __extension__
 __PRETTY_FUNCTION__));
      (void) Erased;
    }
  }

  return setRange(U, SignHint, std::move(ConservativeResult));
}

return setRange(S, SignHint, std::move(ConservativeResult));
6503}

6505// Given a StartRange, Step and MaxBECount for an expression compute a range of
6506// values that the expression can take. Initially, the expression has a value
6507// from StartRange and then is changed by Step up to MaxBECount times. Signed
6508// argument defines if we treat Step as signed or unsigned.
6509static ConstantRange getRangeForAffineARHelper(APInt Step,
                                             const ConstantRange &StartRange,
                                             const APInt &MaxBECount,
                                             unsigned BitWidth, bool Signed) {
// If either Step or MaxBECount is 0, then the expression won't change, and we
// just need to return the initial range.
if (Step == 0 || MaxBECount == 0)
  return StartRange;

// If we don't know anything about the initial value (i.e. StartRange is
// FullRange), then we don't know anything about the final range either.
// Return FullRange.
if (StartRange.isFullSet())
  return ConstantRange::getFull(BitWidth);

// If Step is signed and negative, then we use its absolute value, but we also
// note that we're moving in the opposite direction.
bool Descending = Signed && Step.isNegative();

if (Signed)
  // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
  // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
  // This equations hold true due to the well-defined wrap-around behavior of
  // APInt.
  Step = Step.abs();

// Check if Offset is more than full span of BitWidth. If it is, the
// expression is guaranteed to overflow.
if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
  return ConstantRange::getFull(BitWidth);

// Offset is by how much the expression can change. Checks above guarantee no
// overflow here.
APInt Offset = Step * MaxBECount;

// Minimum value of the final range will match the minimal value of StartRange
// if the expression is increasing and will be decreased by Offset otherwise.
// Maximum value of the final range will match the maximal value of StartRange
// if the expression is decreasing and will be increased by Offset otherwise.
APInt StartLower = StartRange.getLower();
APInt StartUpper = StartRange.getUpper() - 1;
APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
                                 : (StartUpper + std::move(Offset));

// It's possible that the new minimum/maximum value will fall into the initial
// range (due to wrap around). This means that the expression can take any
// value in this bitwidth, and we have to return full range.
if (StartRange.contains(MovedBoundary))
  return ConstantRange::getFull(BitWidth);

APInt NewLower =
    Descending ? std::move(MovedBoundary) : std::move(StartLower);
APInt NewUpper =
    Descending ? std::move(StartUpper) : std::move(MovedBoundary);
NewUpper += 1;

// No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
6567}

6569ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
                                                 const SCEV *Step,
                                                 const SCEV *MaxBECount,
                                                 unsigned BitWidth) {
assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&(static_cast <bool> (!isa<SCEVCouldNotCompute>(MaxBECount
) && getTypeSizeInBits(MaxBECount->getType()) <=
 BitWidth && "Precondition!") ? void (0) : __assert_fail
 ("!isa<SCEVCouldNotCompute>(MaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && \"Precondition!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6575, __extension__
 __PRETTY_FUNCTION__))
       getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&(static_cast <bool> (!isa<SCEVCouldNotCompute>(MaxBECount
) && getTypeSizeInBits(MaxBECount->getType()) <=
 BitWidth && "Precondition!") ? void (0) : __assert_fail
 ("!isa<SCEVCouldNotCompute>(MaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && \"Precondition!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6575, __extension__
 __PRETTY_FUNCTION__))
       "Precondition!")(static_cast <bool> (!isa<SCEVCouldNotCompute>(MaxBECount
) && getTypeSizeInBits(MaxBECount->getType()) <=
 BitWidth && "Precondition!") ? void (0) : __assert_fail
 ("!isa<SCEVCouldNotCompute>(MaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && \"Precondition!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6575, __extension__
 __PRETTY_FUNCTION__));

MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);

// First, consider step signed.
ConstantRange StartSRange = getSignedRange(Start);
ConstantRange StepSRange = getSignedRange(Step);

// If Step can be both positive and negative, we need to find ranges for the
// maximum absolute step values in both directions and union them.
ConstantRange SR =
    getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
                              MaxBECountValue, BitWidth, /* Signed = */ true);
SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
                                            StartSRange, MaxBECountValue,
                                            BitWidth, /* Signed = */ true));

// Next, consider step unsigned.
ConstantRange UR = getRangeForAffineARHelper(
    getUnsignedRangeMax(Step), getUnsignedRange(Start),
    MaxBECountValue, BitWidth, /* Signed = */ false);

// Finally, intersect signed and unsigned ranges.
return SR.intersectWith(UR, ConstantRange::Smallest);
6600}

6602ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR(
  const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth,
  ScalarEvolution::RangeSignHint SignHint) {
assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n")(static_cast <bool> (AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n"
) ? void (0) : __assert_fail ("AddRec->isAffine() && \"Non-affine AddRecs are not suppored!\\n\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6605, __extension__
 __PRETTY_FUNCTION__));
assert(AddRec->hasNoSelfWrap() &&(static_cast <bool> (AddRec->hasNoSelfWrap() &&
 "This only works for non-self-wrapping AddRecs!") ? void (0)
 : __assert_fail ("AddRec->hasNoSelfWrap() && \"This only works for non-self-wrapping AddRecs!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6607, __extension__
 __PRETTY_FUNCTION__))
       "This only works for non-self-wrapping AddRecs!")(static_cast <bool> (AddRec->hasNoSelfWrap() &&
 "This only works for non-self-wrapping AddRecs!") ? void (0)
 : __assert_fail ("AddRec->hasNoSelfWrap() && \"This only works for non-self-wrapping AddRecs!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6607, __extension__
 __PRETTY_FUNCTION__));
const bool IsSigned = SignHint == HINT_RANGE_SIGNED;
const SCEV *Step = AddRec->getStepRecurrence(*this);
// Only deal with constant step to save compile time.
if (!isa<SCEVConstant>(Step))
  return ConstantRange::getFull(BitWidth);
// Let's make sure that we can prove that we do not self-wrap during
// MaxBECount iterations. We need this because MaxBECount is a maximum
// iteration count estimate, and we might infer nw from some exit for which we
// do not know max exit count (or any other side reasoning).
// TODO: Turn into assert at some point.
if (getTypeSizeInBits(MaxBECount->getType()) >
    getTypeSizeInBits(AddRec->getType()))
  return ConstantRange::getFull(BitWidth);
MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType());
const SCEV *RangeWidth = getMinusOne(AddRec->getType());
const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step));
const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs);
if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount,
                                       MaxItersWithoutWrap))
  return ConstantRange::getFull(BitWidth);

ICmpInst::Predicate LEPred =
    IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
ICmpInst::Predicate GEPred =
    IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);

// We know that there is no self-wrap. Let's take Start and End values and
// look at all intermediate values V1, V2, ..., Vn that IndVar takes during
// the iteration. They either lie inside the range [Min(Start, End),
// Max(Start, End)] or outside it:
//
// Case 1:   RangeMin    ...    Start V1 ... VN End ...           RangeMax;
// Case 2:   RangeMin Vk ... V1 Start    ...    End Vn ... Vk + 1 RangeMax;
//
// No self wrap flag guarantees that the intermediate values cannot be BOTH
// outside and inside the range [Min(Start, End), Max(Start, End)]. Using that
// knowledge, let's try to prove that we are dealing with Case 1. It is so if
// Start <= End and step is positive, or Start >= End and step is negative.
const SCEV *Start = AddRec->getStart();
ConstantRange StartRange = getRangeRef(Start, SignHint);
ConstantRange EndRange = getRangeRef(End, SignHint);
ConstantRange RangeBetween = StartRange.unionWith(EndRange);
// If they already cover full iteration space, we will know nothing useful
// even if we prove what we want to prove.
if (RangeBetween.isFullSet())
  return RangeBetween;
// Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax).
bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet()
                             : RangeBetween.isWrappedSet();
if (IsWrappedSet)
  return ConstantRange::getFull(BitWidth);

if (isKnownPositive(Step) &&
    isKnownPredicateViaConstantRanges(LEPred, Start, End))
  return RangeBetween;
else if (isKnownNegative(Step) &&
         isKnownPredicateViaConstantRanges(GEPred, Start, End))
  return RangeBetween;
return ConstantRange::getFull(BitWidth);
6668}

6670ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
                                                  const SCEV *Step,
                                                  const SCEV *MaxBECount,
                                                  unsigned BitWidth) {
//    RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
// == RangeOf({A,+,P}) union RangeOf({B,+,Q})

struct SelectPattern {
  Value *Condition = nullptr;
  APInt TrueValue;
  APInt FalseValue;

  explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
                         const SCEV *S) {
    Optional<unsigned> CastOp;
    APInt Offset(BitWidth, 0);

    assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&(static_cast <bool> (SE.getTypeSizeInBits(S->getType
()) == BitWidth && "Should be!") ? void (0) : __assert_fail
 ("SE.getTypeSizeInBits(S->getType()) == BitWidth && \"Should be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6688, __extension__
 __PRETTY_FUNCTION__))
           "Should be!")(static_cast <bool> (SE.getTypeSizeInBits(S->getType
()) == BitWidth && "Should be!") ? void (0) : __assert_fail
 ("SE.getTypeSizeInBits(S->getType()) == BitWidth && \"Should be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6688, __extension__
 __PRETTY_FUNCTION__));

    // Peel off a constant offset:
    if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
      // In the future we could consider being smarter here and handle
      // {Start+Step,+,Step} too.
      if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
        return;

      Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
      S = SA->getOperand(1);
    }

    // Peel off a cast operation
    if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(S)) {
      CastOp = SCast->getSCEVType();
      S = SCast->getOperand();
    }

    using namespace llvm::PatternMatch;

    auto *SU = dyn_cast<SCEVUnknown>(S);
    const APInt *TrueVal, *FalseVal;
    if (!SU ||
        !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
                                        m_APInt(FalseVal)))) {
      Condition = nullptr;
      return;
    }

    TrueValue = *TrueVal;
    FalseValue = *FalseVal;

    // Re-apply the cast we peeled off earlier
    if (CastOp.hasValue())
      switch (*CastOp) {
      default:
        llvm_unreachable("Unknown SCEV cast type!")::llvm::llvm_unreachable_internal("Unknown SCEV cast type!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 6725);

      case scTruncate:
        TrueValue = TrueValue.trunc(BitWidth);
        FalseValue = FalseValue.trunc(BitWidth);
        break;
      case scZeroExtend:
        TrueValue = TrueValue.zext(BitWidth);
        FalseValue = FalseValue.zext(BitWidth);
        break;
      case scSignExtend:
        TrueValue = TrueValue.sext(BitWidth);
        FalseValue = FalseValue.sext(BitWidth);
        break;
      }

    // Re-apply the constant offset we peeled off earlier
    TrueValue += Offset;
    FalseValue += Offset;
  }

  bool isRecognized() { return Condition != nullptr; }
};

SelectPattern StartPattern(*this, BitWidth, Start);
if (!StartPattern.isRecognized())
  return ConstantRange::getFull(BitWidth);

SelectPattern StepPattern(*this, BitWidth, Step);
if (!StepPattern.isRecognized())
  return ConstantRange::getFull(BitWidth);

if (StartPattern.Condition != StepPattern.Condition) {
  // We don't handle this case today; but we could, by considering four
  // possibilities below instead of two. I'm not sure if there are cases where
  // that will help over what getRange already does, though.
  return ConstantRange::getFull(BitWidth);
}

// NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
// construct arbitrary general SCEV expressions here.  This function is called
// from deep in the call stack, and calling getSCEV (on a sext instruction,
// say) can end up caching a suboptimal value.

// FIXME: without the explicit `this` receiver below, MSVC errors out with
// C2352 and C2512 (otherwise it isn't needed).

const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);

ConstantRange TrueRange =
    this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
ConstantRange FalseRange =
    this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);

return TrueRange.unionWith(FalseRange);
6783}

6785SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
const BinaryOperator *BinOp = cast<BinaryOperator>(V);

// Return early if there are no flags to propagate to the SCEV.
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
if (BinOp->hasNoUnsignedWrap())
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
if (BinOp->hasNoSignedWrap())
  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
if (Flags == SCEV::FlagAnyWrap)
  return SCEV::FlagAnyWrap;

return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
6799}

6801const Instruction *
6802ScalarEvolution::getNonTrivialDefiningScopeBound(const SCEV *S) {
if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(S))
  return &*AddRec->getLoop()->getHeader()->begin();
if (auto *U = dyn_cast<SCEVUnknown>(S))
  if (auto *I = dyn_cast<Instruction>(U->getValue()))
    return I;
return nullptr;
6809}

6811/// Fills \p Ops with unique operands of \p S, if it has operands. If not,
6812/// \p Ops remains unmodified.
6813static void collectUniqueOps(const SCEV *S,
                           SmallVectorImpl<const SCEV *> &Ops) {
SmallPtrSet<const SCEV *, 4> Unique;
auto InsertUnique = [&](const SCEV *S) {
  if (Unique.insert(S).second)
    Ops.push_back(S);
};
if (auto *S2 = dyn_cast<SCEVCastExpr>(S))
  for (auto *Op : S2->operands())
    InsertUnique(Op);
else if (auto *S2 = dyn_cast<SCEVNAryExpr>(S))
  for (auto *Op : S2->operands())
    InsertUnique(Op);
else if (auto *S2 = dyn_cast<SCEVUDivExpr>(S))
  for (auto *Op : S2->operands())
    InsertUnique(Op);
6829}

6831const Instruction *
6832ScalarEvolution::getDefiningScopeBound(ArrayRef<const SCEV *> Ops,
                                     bool &Precise) {
Precise = true;
// Do a bounded search of the def relation of the requested SCEVs.
SmallSet<const SCEV *, 16> Visited;
SmallVector<const SCEV *> Worklist;
auto pushOp = [&](const SCEV *S) {
  if (!Visited.insert(S).second)
    return;
  // Threshold of 30 here is arbitrary.
  if (Visited.size() > 30) {
    Precise = false;
    return;
  }
  Worklist.push_back(S);
};

for (auto *S : Ops)
  pushOp(S);

const Instruction *Bound = nullptr;
while (!Worklist.empty()) {
  auto *S = Worklist.pop_back_val();
  if (auto *DefI = getNonTrivialDefiningScopeBound(S)) {
    if (!Bound || DT.dominates(Bound, DefI))
      Bound = DefI;
  } else {
    SmallVector<const SCEV *, 4> Ops;
    collectUniqueOps(S, Ops);
    for (auto *Op : Ops)
      pushOp(Op);
  }
}
return Bound ? Bound : &*F.getEntryBlock().begin();
6866}

6868const Instruction *
6869ScalarEvolution::getDefiningScopeBound(ArrayRef<const SCEV *> Ops) {
bool Discard;
return getDefiningScopeBound(Ops, Discard);
6872}

6874bool ScalarEvolution::isGuaranteedToTransferExecutionTo(const Instruction *A,
                                                      const Instruction *B) {
if (A->getParent() == B->getParent() &&
    isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
                                               B->getIterator()))
  return true;

auto *BLoop = LI.getLoopFor(B->getParent());
if (BLoop && BLoop->getHeader() == B->getParent() &&
    BLoop->getLoopPreheader() == A->getParent() &&
    isGuaranteedToTransferExecutionToSuccessor(A->getIterator(),
                                               A->getParent()->end()) &&
    isGuaranteedToTransferExecutionToSuccessor(B->getParent()->begin(),
                                               B->getIterator()))
  return true;
return false;
6890}


6893bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
// Only proceed if we can prove that I does not yield poison.
if (!programUndefinedIfPoison(I))
  return false;

// At this point we know that if I is executed, then it does not wrap
// according to at least one of NSW or NUW. If I is not executed, then we do
// not know if the calculation that I represents would wrap. Multiple
// instructions can map to the same SCEV. If we apply NSW or NUW from I to
// the SCEV, we must guarantee no wrapping for that SCEV also when it is
// derived from other instructions that map to the same SCEV. We cannot make
// that guarantee for cases where I is not executed. So we need to find a
// upper bound on the defining scope for the SCEV, and prove that I is
// executed every time we enter that scope.  When the bounding scope is a
// loop (the common case), this is equivalent to proving I executes on every
// iteration of that loop.
SmallVector<const SCEV *> SCEVOps;
for (const Use &Op : I->operands()) {
  // I could be an extractvalue from a call to an overflow intrinsic.
  // TODO: We can do better here in some cases.
  if (isSCEVable(Op->getType()))
    SCEVOps.push_back(getSCEV(Op));
}
auto *DefI = getDefiningScopeBound(SCEVOps);
return isGuaranteedToTransferExecutionTo(DefI, I);
6918}

6920bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
// If we know that \c I can never be poison period, then that's enough.
if (isSCEVExprNeverPoison(I))
  return true;

// For an add recurrence specifically, we assume that infinite loops without
// side effects are undefined behavior, and then reason as follows:
//
// If the add recurrence is poison in any iteration, it is poison on all
// future iterations (since incrementing poison yields poison). If the result
// of the add recurrence is fed into the loop latch condition and the loop
// does not contain any throws or exiting blocks other than the latch, we now
// have the ability to "choose" whether the backedge is taken or not (by
// choosing a sufficiently evil value for the poison feeding into the branch)
// for every iteration including and after the one in which \p I first became
// poison.  There are two possibilities (let's call the iteration in which \p
// I first became poison as K):
//
//  1. In the set of iterations including and after K, the loop body executes
//     no side effects.  In this case executing the backege an infinte number
//     of times will yield undefined behavior.
//
//  2. In the set of iterations including and after K, the loop body executes
//     at least one side effect.  In this case, that specific instance of side
//     effect is control dependent on poison, which also yields undefined
//     behavior.

auto *ExitingBB = L->getExitingBlock();
auto *LatchBB = L->getLoopLatch();
if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
  return false;

SmallPtrSet<const Instruction *, 16> Pushed;
SmallVector<const Instruction *, 8> PoisonStack;

// We start by assuming \c I, the post-inc add recurrence, is poison.  Only
// things that are known to be poison under that assumption go on the
// PoisonStack.
Pushed.insert(I);
PoisonStack.push_back(I);

bool LatchControlDependentOnPoison = false;
while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
  const Instruction *Poison = PoisonStack.pop_back_val();

  for (auto *PoisonUser : Poison->users()) {
    if (propagatesPoison(cast<Operator>(PoisonUser))) {
      if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
        PoisonStack.push_back(cast<Instruction>(PoisonUser));
    } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
      assert(BI->isConditional() && "Only possibility!")(static_cast <bool> (BI->isConditional() && "Only possibility!"
) ? void (0) : __assert_fail ("BI->isConditional() && \"Only possibility!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 6970, __extension__
 __PRETTY_FUNCTION__));
      if (BI->getParent() == LatchBB) {
        LatchControlDependentOnPoison = true;
        break;
      }
    }
  }
}

return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
6980}

6982ScalarEvolution::LoopProperties
6983ScalarEvolution::getLoopProperties(const Loop *L) {
using LoopProperties = ScalarEvolution::LoopProperties;

auto Itr = LoopPropertiesCache.find(L);
if (Itr == LoopPropertiesCache.end()) {
  auto HasSideEffects = [](Instruction *I) {
    if (auto *SI = dyn_cast<StoreInst>(I))
      return !SI->isSimple();

    return I->mayThrow() || I->mayWriteToMemory();
  };

  LoopProperties LP = {/* HasNoAbnormalExits */ true,
                       /*HasNoSideEffects*/ true};

  for (auto *BB : L->getBlocks())
    for (auto &I : *BB) {
      if (!isGuaranteedToTransferExecutionToSuccessor(&I))
        LP.HasNoAbnormalExits = false;
      if (HasSideEffects(&I))
        LP.HasNoSideEffects = false;
      if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
        break; // We're already as pessimistic as we can get.
    }

  auto InsertPair = LoopPropertiesCache.insert({L, LP});
  assert(InsertPair.second && "We just checked!")(static_cast <bool> (InsertPair.second && "We just checked!"
) ? void (0) : __assert_fail ("InsertPair.second && \"We just checked!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7009, __extension__
 __PRETTY_FUNCTION__));
  Itr = InsertPair.first;
}

return Itr->second;
7014}

7016bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) {
// A mustprogress loop without side effects must be finite.
// TODO: The check used here is very conservative.  It's only *specific*
// side effects which are well defined in infinite loops.
return isFinite(L) || (isMustProgress(L) && loopHasNoSideEffects(L));
7021}

7023const SCEV *ScalarEvolution::createSCEV(Value *V) {
if (!isSCEVable(V->getType()))
  return getUnknown(V);

if (Instruction *I = dyn_cast<Instruction>(V)) {
  // Don't attempt to analyze instructions in blocks that aren't
  // reachable. Such instructions don't matter, and they aren't required
  // to obey basic rules for definitions dominating uses which this
  // analysis depends on.
  if (!DT.isReachableFromEntry(I->getParent()))
    return getUnknown(UndefValue::get(V->getType()));
} else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
  return getConstant(CI);
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
  return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
else if (!isa<ConstantExpr>(V))
  return getUnknown(V);

Operator *U = cast<Operator>(V);
if (auto BO = MatchBinaryOp(U, DT)) {
  switch (BO->Opcode) {
  case Instruction::Add: {
    // The simple thing to do would be to just call getSCEV on both operands
    // and call getAddExpr with the result. However if we're looking at a
    // bunch of things all added together, this can be quite inefficient,
    // because it leads to N-1 getAddExpr calls for N ultimate operands.
    // Instead, gather up all the operands and make a single getAddExpr call.
    // LLVM IR canonical form means we need only traverse the left operands.
    SmallVector<const SCEV *, 4> AddOps;
    do {
      if (BO->Op) {
        if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
          AddOps.push_back(OpSCEV);
          break;
        }

        // If a NUW or NSW flag can be applied to the SCEV for this
        // addition, then compute the SCEV for this addition by itself
        // with a separate call to getAddExpr. We need to do that
        // instead of pushing the operands of the addition onto AddOps,
        // since the flags are only known to apply to this particular
        // addition - they may not apply to other additions that can be
        // formed with operands from AddOps.
        const SCEV *RHS = getSCEV(BO->RHS);
        SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
        if (Flags != SCEV::FlagAnyWrap) {
          const SCEV *LHS = getSCEV(BO->LHS);
          if (BO->Opcode == Instruction::Sub)
            AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
          else
            AddOps.push_back(getAddExpr(LHS, RHS, Flags));
          break;
        }
      }

      if (BO->Opcode == Instruction::Sub)
        AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
      else
        AddOps.push_back(getSCEV(BO->RHS));

      auto NewBO = MatchBinaryOp(BO->LHS, DT);
      if (!NewBO || (NewBO->Opcode != Instruction::Add &&
                     NewBO->Opcode != Instruction::Sub)) {
        AddOps.push_back(getSCEV(BO->LHS));
        break;
      }
      BO = NewBO;
    } while (true);

    return getAddExpr(AddOps);
  }

  case Instruction::Mul: {
    SmallVector<const SCEV *, 4> MulOps;
    do {
      if (BO->Op) {
        if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
          MulOps.push_back(OpSCEV);
          break;
        }

        SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
        if (Flags != SCEV::FlagAnyWrap) {
          MulOps.push_back(
              getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
          break;
        }
      }

      MulOps.push_back(getSCEV(BO->RHS));
      auto NewBO = MatchBinaryOp(BO->LHS, DT);
      if (!NewBO || NewBO->Opcode != Instruction::Mul) {
        MulOps.push_back(getSCEV(BO->LHS));
        break;
      }
      BO = NewBO;
    } while (true);

    return getMulExpr(MulOps);
  }
  case Instruction::UDiv:
    return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
  case Instruction::URem:
    return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
  case Instruction::Sub: {
    SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
    if (BO->Op)
      Flags = getNoWrapFlagsFromUB(BO->Op);
    return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
  }
  case Instruction::And:
    // For an expression like x&255 that merely masks off the high bits,
    // use zext(trunc(x)) as the SCEV expression.
    if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
      if (CI->isZero())
        return getSCEV(BO->RHS);
      if (CI->isMinusOne())
        return getSCEV(BO->LHS);
      const APInt &A = CI->getValue();

      // Instcombine's ShrinkDemandedConstant may strip bits out of
      // constants, obscuring what would otherwise be a low-bits mask.
      // Use computeKnownBits to compute what ShrinkDemandedConstant
      // knew about to reconstruct a low-bits mask value.
      unsigned LZ = A.countLeadingZeros();
      unsigned TZ = A.countTrailingZeros();
      unsigned BitWidth = A.getBitWidth();
      KnownBits Known(BitWidth);
      computeKnownBits(BO->LHS, Known, getDataLayout(),
                       0, &AC, nullptr, &DT);

      APInt EffectiveMask =
          APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
      if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
        const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
        const SCEV *LHS = getSCEV(BO->LHS);
        const SCEV *ShiftedLHS = nullptr;
        if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
          if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
            // For an expression like (x * 8) & 8, simplify the multiply.
            unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
            unsigned GCD = std::min(MulZeros, TZ);
            APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
            SmallVector<const SCEV*, 4> MulOps;
            MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
            MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
            auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
            ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
          }
        }
        if (!ShiftedLHS)
          ShiftedLHS = getUDivExpr(LHS, MulCount);
        return getMulExpr(
            getZeroExtendExpr(
                getTruncateExpr(ShiftedLHS,
                    IntegerType::get(getContext(), BitWidth - LZ - TZ)),
                BO->LHS->getType()),
            MulCount);
      }
    }
    break;

  case Instruction::Or:
    // If the RHS of the Or is a constant, we may have something like:
    // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
    // optimizations will transparently handle this case.
    //
    // In order for this transformation to be safe, the LHS must be of the
    // form X*(2^n) and the Or constant must be less than 2^n.
    if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
      const SCEV *LHS = getSCEV(BO->LHS);
      const APInt &CIVal = CI->getValue();
      if (GetMinTrailingZeros(LHS) >=
          (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
        // Build a plain add SCEV.
        return getAddExpr(LHS, getSCEV(CI),
                          (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW));
      }
    }
    break;

  case Instruction::Xor:
    if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
      // If the RHS of xor is -1, then this is a not operation.
      if (CI->isMinusOne())
        return getNotSCEV(getSCEV(BO->LHS));

      // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
      // This is a variant of the check for xor with -1, and it handles
      // the case where instcombine has trimmed non-demanded bits out
      // of an xor with -1.
      if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
        if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
          if (LBO->getOpcode() == Instruction::And &&
              LCI->getValue() == CI->getValue())
            if (const SCEVZeroExtendExpr *Z =
                    dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
              Type *UTy = BO->LHS->getType();
              const SCEV *Z0 = Z->getOperand();
              Type *Z0Ty = Z0->getType();
              unsigned Z0TySize = getTypeSizeInBits(Z0Ty);

              // If C is a low-bits mask, the zero extend is serving to
              // mask off the high bits. Complement the operand and
              // re-apply the zext.
              if (CI->getValue().isMask(Z0TySize))
                return getZeroExtendExpr(getNotSCEV(Z0), UTy);

              // If C is a single bit, it may be in the sign-bit position
              // before the zero-extend. In this case, represent the xor
              // using an add, which is equivalent, and re-apply the zext.
              APInt Trunc = CI->getValue().trunc(Z0TySize);
              if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
                  Trunc.isSignMask())
                return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
                                         UTy);
            }
    }
    break;

  case Instruction::Shl:
    // Turn shift left of a constant amount into a multiply.
    if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
      uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();

      // If the shift count is not less than the bitwidth, the result of
      // the shift is undefined. Don't try to analyze it, because the
      // resolution chosen here may differ from the resolution chosen in
      // other parts of the compiler.
      if (SA->getValue().uge(BitWidth))
        break;

      // We can safely preserve the nuw flag in all cases. It's also safe to
      // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
      // requires special handling. It can be preserved as long as we're not
      // left shifting by bitwidth - 1.
      auto Flags = SCEV::FlagAnyWrap;
      if (BO->Op) {
        auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
        if ((MulFlags & SCEV::FlagNSW) &&
            ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1)))
          Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW);
        if (MulFlags & SCEV::FlagNUW)
          Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW);
      }

      Constant *X = ConstantInt::get(
          getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
      return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
    }
    break;

  case Instruction::AShr: {
    // AShr X, C, where C is a constant.
    ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
    if (!CI)
      break;

    Type *OuterTy = BO->LHS->getType();
    uint64_t BitWidth = getTypeSizeInBits(OuterTy);
    // If the shift count is not less than the bitwidth, the result of
    // the shift is undefined. Don't try to analyze it, because the
    // resolution chosen here may differ from the resolution chosen in
    // other parts of the compiler.
    if (CI->getValue().uge(BitWidth))
      break;

    if (CI->isZero())
      return getSCEV(BO->LHS); // shift by zero --> noop

    uint64_t AShrAmt = CI->getZExtValue();
    Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);

    Operator *L = dyn_cast<Operator>(BO->LHS);
    if (L && L->getOpcode() == Instruction::Shl) {
      // X = Shl A, n
      // Y = AShr X, m
      // Both n and m are constant.

      const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
      if (L->getOperand(1) == BO->RHS)
        // For a two-shift sext-inreg, i.e. n = m,
        // use sext(trunc(x)) as the SCEV expression.
        return getSignExtendExpr(
            getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);

      ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
      if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
        uint64_t ShlAmt = ShlAmtCI->getZExtValue();
        if (ShlAmt > AShrAmt) {
          // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
          // expression. We already checked that ShlAmt < BitWidth, so
          // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
          // ShlAmt - AShrAmt < Amt.
          APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
                                          ShlAmt - AShrAmt);
          return getSignExtendExpr(
              getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
              getConstant(Mul)), OuterTy);
        }
      }
    }
    break;
  }
  }
}

switch (U->getOpcode()) {
case Instruction::Trunc:
  return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());

case Instruction::ZExt:
  return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());

case Instruction::SExt:
  if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
    // The NSW flag of a subtract does not always survive the conversion to
    // A + (-1)*B.  By pushing sign extension onto its operands we are much
    // more likely to preserve NSW and allow later AddRec optimisations.
    //
    // NOTE: This is effectively duplicating this logic from getSignExtend:
    //   sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
    // but by that point the NSW information has potentially been lost.
    if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
      Type *Ty = U->getType();
      auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
      auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
      return getMinusSCEV(V1, V2, SCEV::FlagNSW);
    }
  }
  return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());

case Instruction::BitCast:
  // BitCasts are no-op casts so we just eliminate the cast.
  if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
    return getSCEV(U->getOperand(0));
  break;

case Instruction::PtrToInt: {
  // Pointer to integer cast is straight-forward, so do model it.
  const SCEV *Op = getSCEV(U->getOperand(0));
  Type *DstIntTy = U->getType();
  // But only if effective SCEV (integer) type is wide enough to represent
  // all possible pointer values.
  const SCEV *IntOp = getPtrToIntExpr(Op, DstIntTy);
  if (isa<SCEVCouldNotCompute>(IntOp))
    return getUnknown(V);
  return IntOp;
}
case Instruction::IntToPtr:
  // Just don't deal with inttoptr casts.
  return getUnknown(V);

case Instruction::SDiv:
  // If both operands are non-negative, this is just an udiv.
  if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
      isKnownNonNegative(getSCEV(U->getOperand(1))))
    return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
  break;

case Instruction::SRem:
  // If both operands are non-negative, this is just an urem.
  if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
      isKnownNonNegative(getSCEV(U->getOperand(1))))
    return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
  break;

case Instruction::GetElementPtr:
  return createNodeForGEP(cast<GEPOperator>(U));

case Instruction::PHI:
  return createNodeForPHI(cast<PHINode>(U));

case Instruction::Select:
  // U can also be a select constant expr, which let fall through.  Since
  // createNodeForSelect only works for a condition that is an `ICmpInst`, and
  // constant expressions cannot have instructions as operands, we'd have
  // returned getUnknown for a select constant expressions anyway.
  if (isa<Instruction>(U))
    return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
                                    U->getOperand(1), U->getOperand(2));
  break;

case Instruction::Call:
case Instruction::Invoke:
  if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand())
    return getSCEV(RV);

  if (auto *II = dyn_cast<IntrinsicInst>(U)) {
    switch (II->getIntrinsicID()) {
    case Intrinsic::abs:
      return getAbsExpr(
          getSCEV(II->getArgOperand(0)),
          /*IsNSW=*/cast<ConstantInt>(II->getArgOperand(1))->isOne());
    case Intrinsic::umax:
      return getUMaxExpr(getSCEV(II->getArgOperand(0)),
                         getSCEV(II->getArgOperand(1)));
    case Intrinsic::umin:
      return getUMinExpr(getSCEV(II->getArgOperand(0)),
                         getSCEV(II->getArgOperand(1)));
    case Intrinsic::smax:
      return getSMaxExpr(getSCEV(II->getArgOperand(0)),
                         getSCEV(II->getArgOperand(1)));
    case Intrinsic::smin:
      return getSMinExpr(getSCEV(II->getArgOperand(0)),
                         getSCEV(II->getArgOperand(1)));
    case Intrinsic::usub_sat: {
      const SCEV *X = getSCEV(II->getArgOperand(0));
      const SCEV *Y = getSCEV(II->getArgOperand(1));
      const SCEV *ClampedY = getUMinExpr(X, Y);
      return getMinusSCEV(X, ClampedY, SCEV::FlagNUW);
    }
    case Intrinsic::uadd_sat: {
      const SCEV *X = getSCEV(II->getArgOperand(0));
      const SCEV *Y = getSCEV(II->getArgOperand(1));
      const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y));
      return getAddExpr(ClampedX, Y, SCEV::FlagNUW);
    }
    case Intrinsic::start_loop_iterations:
      // A start_loop_iterations is just equivalent to the first operand for
      // SCEV purposes.
      return getSCEV(II->getArgOperand(0));
    default:
      break;
    }
  }
  break;
}

return getUnknown(V);
7453}

7455//===----------------------------------------------------------------------===//
7456//                   Iteration Count Computation Code
7457//

7459const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount,
                                                     bool Extend) {
if (isa<SCEVCouldNotCompute>(ExitCount))
  return getCouldNotCompute();

auto *ExitCountType = ExitCount->getType();
assert(ExitCountType->isIntegerTy())(static_cast <bool> (ExitCountType->isIntegerTy()) ?
 void (0) : __assert_fail ("ExitCountType->isIntegerTy()",
 "llvm/lib/Analysis/ScalarEvolution.cpp", 7465, __extension__
 __PRETTY_FUNCTION__));

if (!Extend)
  return getAddExpr(ExitCount, getOne(ExitCountType));

auto *WiderType = Type::getIntNTy(ExitCountType->getContext(),
                                  1 + ExitCountType->getScalarSizeInBits());
return getAddExpr(getNoopOrZeroExtend(ExitCount, WiderType),
                  getOne(WiderType));
7474}

7476static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
if (!ExitCount)
  return 0;

ConstantInt *ExitConst = ExitCount->getValue();

// Guard against huge trip counts.
if (ExitConst->getValue().getActiveBits() > 32)
  return 0;

// In case of integer overflow, this returns 0, which is correct.
return ((unsigned)ExitConst->getZExtValue()) + 1;
7488}

7490unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
auto *ExitCount = dyn_cast<SCEVConstant>(getBackedgeTakenCount(L, Exact));
return getConstantTripCount(ExitCount);
7493}

7495unsigned
7496ScalarEvolution::getSmallConstantTripCount(const Loop *L,
                                         const BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!")(static_cast <bool> (ExitingBlock && "Must pass a non-null exiting block!"
) ? void (0) : __assert_fail ("ExitingBlock && \"Must pass a non-null exiting block!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7498, __extension__
 __PRETTY_FUNCTION__));
assert(L->isLoopExiting(ExitingBlock) &&(static_cast <bool> (L->isLoopExiting(ExitingBlock) &&
 "Exiting block must actually branch out of the loop!") ? void
 (0) : __assert_fail ("L->isLoopExiting(ExitingBlock) && \"Exiting block must actually branch out of the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7500, __extension__
 __PRETTY_FUNCTION__))
       "Exiting block must actually branch out of the loop!")(static_cast <bool> (L->isLoopExiting(ExitingBlock) &&
 "Exiting block must actually branch out of the loop!") ? void
 (0) : __assert_fail ("L->isLoopExiting(ExitingBlock) && \"Exiting block must actually branch out of the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7500, __extension__
 __PRETTY_FUNCTION__));
const SCEVConstant *ExitCount =
    dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
return getConstantTripCount(ExitCount);
7504}

7506unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
const auto *MaxExitCount =
    dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L));
return getConstantTripCount(MaxExitCount);
7510}

7512const SCEV *ScalarEvolution::getConstantMaxTripCountFromArray(const Loop *L) {
// We can't infer from Array in Irregular Loop.
// FIXME: It's hard to infer loop bound from array operated in Nested Loop.
if (!L->isLoopSimplifyForm() || !L->isInnermost())
  return getCouldNotCompute();

// FIXME: To make the scene more typical, we only analysis loops that have
// one exiting block and that block must be the latch. To make it easier to
// capture loops that have memory access and memory access will be executed
// in each iteration.
const BasicBlock *LoopLatch = L->getLoopLatch();
assert(LoopLatch && "See defination of simplify form loop.")(static_cast <bool> (LoopLatch && "See defination of simplify form loop."
) ? void (0) : __assert_fail ("LoopLatch && \"See defination of simplify form loop.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7523, __extension__
 __PRETTY_FUNCTION__));
if (L->getExitingBlock() != LoopLatch)
  return getCouldNotCompute();

const DataLayout &DL = getDataLayout();
SmallVector<const SCEV *> InferCountColl;
for (auto *BB : L->getBlocks()) {
  // Go here, we can know that Loop is a single exiting and simplified form
  // loop. Make sure that infer from Memory Operation in those BBs must be
  // executed in loop. First step, we can make sure that max execution time
  // of MemAccessBB in loop represents latch max excution time.
  // If MemAccessBB does not dom Latch, skip.
  //            Entry
  //              │
  //        ┌─────▼─────┐
  //        │Loop Header◄─────┐
  //        └──┬──────┬─┘     │
  //           │      │       │
  //  ┌────────▼──┐ ┌─▼─────┐ │
  //  │MemAccessBB│ │OtherBB│ │
  //  └────────┬──┘ └─┬─────┘ │
  //           │      │       │
  //         ┌─▼──────▼─┐     │
  //         │Loop Latch├─────┘
  //         └────┬─────┘
  //              ▼
  //             Exit
  if (!DT.dominates(BB, LoopLatch))
    continue;

  for (Instruction &Inst : *BB) {
    // Find Memory Operation Instruction.
    auto *GEP = getLoadStorePointerOperand(&Inst);
    if (!GEP)
      continue;

    auto *ElemSize = dyn_cast<SCEVConstant>(getElementSize(&Inst));
    // Do not infer from scalar type, eg."ElemSize = sizeof()".
    if (!ElemSize)
      continue;

    // Use a existing polynomial recurrence on the trip count.
    auto *AddRec = dyn_cast<SCEVAddRecExpr>(getSCEV(GEP));
    if (!AddRec)
      continue;
    auto *ArrBase = dyn_cast<SCEVUnknown>(getPointerBase(AddRec));
    auto *Step = dyn_cast<SCEVConstant>(AddRec->getStepRecurrence(*this));
    if (!ArrBase || !Step)
      continue;
    assert(isLoopInvariant(ArrBase, L) && "See addrec definition")(static_cast <bool> (isLoopInvariant(ArrBase, L) &&
 "See addrec definition") ? void (0) : __assert_fail ("isLoopInvariant(ArrBase, L) && \"See addrec definition\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7572, __extension__
 __PRETTY_FUNCTION__));

    // Only handle { %array + step },
    // FIXME: {(SCEVAddRecExpr) + step } could not be analysed here.
    if (AddRec->getStart() != ArrBase)
      continue;

    // Memory operation pattern which have gaps.
    // Or repeat memory opreation.
    // And index of GEP wraps arround.
    if (Step->getAPInt().getActiveBits() > 32 ||
        Step->getAPInt().getZExtValue() !=
            ElemSize->getAPInt().getZExtValue() ||
        Step->isZero() || Step->getAPInt().isNegative())
      continue;

    // Only infer from stack array which has certain size.
    // Make sure alloca instruction is not excuted in loop.
    AllocaInst *AllocateInst = dyn_cast<AllocaInst>(ArrBase->getValue());
    if (!AllocateInst || L->contains(AllocateInst->getParent()))
      continue;

    // Make sure only handle normal array.
    auto *Ty = dyn_cast<ArrayType>(AllocateInst->getAllocatedType());
    auto *ArrSize = dyn_cast<ConstantInt>(AllocateInst->getArraySize());
    if (!Ty || !ArrSize || !ArrSize->isOne())
      continue;

    // FIXME: Since gep indices are silently zext to the indexing type,
    // we will have a narrow gep index which wraps around rather than
    // increasing strictly, we shoule ensure that step is increasing
    // strictly by the loop iteration.
    // Now we can infer a max execution time by MemLength/StepLength.
    const SCEV *MemSize =
        getConstant(Step->getType(), DL.getTypeAllocSize(Ty));
    auto *MaxExeCount =
        dyn_cast<SCEVConstant>(getUDivCeilSCEV(MemSize, Step));
    if (!MaxExeCount || MaxExeCount->getAPInt().getActiveBits() > 32)
      continue;

    // If the loop reaches the maximum number of executions, we can not
    // access bytes starting outside the statically allocated size without
    // being immediate UB. But it is allowed to enter loop header one more
    // time.
    auto *InferCount = dyn_cast<SCEVConstant>(
        getAddExpr(MaxExeCount, getOne(MaxExeCount->getType())));
    // Discard the maximum number of execution times under 32bits.
    if (!InferCount || InferCount->getAPInt().getActiveBits() > 32)
      continue;

    InferCountColl.push_back(InferCount);
  }
}

if (InferCountColl.size() == 0)
  return getCouldNotCompute();

return getUMinFromMismatchedTypes(InferCountColl);
7630}

7632unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);

Optional<unsigned> Res = None;
for (auto *ExitingBB : ExitingBlocks) {
  unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB);
  if (!Res)
    Res = Multiple;
  Res = (unsigned)GreatestCommonDivisor64(*Res, Multiple);
}
return Res.getValueOr(1);
7644}

7646unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
                                                     const SCEV *ExitCount) {
if (ExitCount == getCouldNotCompute())
  return 1;

// Get the trip count
const SCEV *TCExpr = getTripCountFromExitCount(ExitCount);

const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
if (!TC)
  // Attempt to factor more general cases. Returns the greatest power of
  // two divisor. If overflow happens, the trip count expression is still
  // divisible by the greatest power of 2 divisor returned.
  return 1U << std::min((uint32_t)31,
                        GetMinTrailingZeros(applyLoopGuards(TCExpr, L)));

ConstantInt *Result = TC->getValue();

// Guard against huge trip counts (this requires checking
// for zero to handle the case where the trip count == -1 and the
// addition wraps).
if (!Result || Result->getValue().getActiveBits() > 32 ||
    Result->getValue().getActiveBits() == 0)
  return 1;

return (unsigned)Result->getZExtValue();
7672}

7674/// Returns the largest constant divisor of the trip count of this loop as a
7675/// normal unsigned value, if possible. This means that the actual trip count is
7676/// always a multiple of the returned value (don't forget the trip count could
7677/// very well be zero as well!).
7678///
7679/// Returns 1 if the trip count is unknown or not guaranteed to be the
7680/// multiple of a constant (which is also the case if the trip count is simply
7681/// constant, use getSmallConstantTripCount for that case), Will also return 1
7682/// if the trip count is very large (>= 2^32).
7683///
7684/// As explained in the comments for getSmallConstantTripCount, this assumes
7685/// that control exits the loop via ExitingBlock.
7686unsigned
7687ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
                                            const BasicBlock *ExitingBlock) {
assert(ExitingBlock && "Must pass a non-null exiting block!")(static_cast <bool> (ExitingBlock && "Must pass a non-null exiting block!"
) ? void (0) : __assert_fail ("ExitingBlock && \"Must pass a non-null exiting block!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7689, __extension__
 __PRETTY_FUNCTION__));
assert(L->isLoopExiting(ExitingBlock) &&(static_cast <bool> (L->isLoopExiting(ExitingBlock) &&
 "Exiting block must actually branch out of the loop!") ? void
 (0) : __assert_fail ("L->isLoopExiting(ExitingBlock) && \"Exiting block must actually branch out of the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7691, __extension__
 __PRETTY_FUNCTION__))
       "Exiting block must actually branch out of the loop!")(static_cast <bool> (L->isLoopExiting(ExitingBlock) &&
 "Exiting block must actually branch out of the loop!") ? void
 (0) : __assert_fail ("L->isLoopExiting(ExitingBlock) && \"Exiting block must actually branch out of the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7691, __extension__
 __PRETTY_FUNCTION__));
const SCEV *ExitCount = getExitCount(L, ExitingBlock);
return getSmallConstantTripMultiple(L, ExitCount);
7694}

7696const SCEV *ScalarEvolution::getExitCount(const Loop *L,
                                        const BasicBlock *ExitingBlock,
                                        ExitCountKind Kind) {
switch (Kind) {
case Exact:
case SymbolicMaximum:
  return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
case ConstantMaximum:
  return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this);
};
llvm_unreachable("Invalid ExitCountKind!")::llvm::llvm_unreachable_internal("Invalid ExitCountKind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 7706);
7707}

7709const SCEV *
7710ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
                                               SCEVUnionPredicate &Preds) {
return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
7713}

7715const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
                                                 ExitCountKind Kind) {
switch (Kind) {
case Exact:
  return getBackedgeTakenInfo(L).getExact(L, this);
case ConstantMaximum:
  return getBackedgeTakenInfo(L).getConstantMax(this);
case SymbolicMaximum:
  return getBackedgeTakenInfo(L).getSymbolicMax(L, this);
};
llvm_unreachable("Invalid ExitCountKind!")::llvm::llvm_unreachable_internal("Invalid ExitCountKind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 7725);
7726}

7728bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
return getBackedgeTakenInfo(L).isConstantMaxOrZero(this);
7730}

7732/// Push PHI nodes in the header of the given loop onto the given Worklist.
7733static void PushLoopPHIs(const Loop *L,
                       SmallVectorImpl<Instruction *> &Worklist,
                       SmallPtrSetImpl<Instruction *> &Visited) {
BasicBlock *Header = L->getHeader();

// Push all Loop-header PHIs onto the Worklist stack.
for (PHINode &PN : Header->phis())
  if (Visited.insert(&PN).second)
    Worklist.push_back(&PN);
7742}

7744const ScalarEvolution::BackedgeTakenInfo &
7745ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
auto &BTI = getBackedgeTakenInfo(L);
if (BTI.hasFullInfo())
  return BTI;

auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});

if (!Pair.second)
  return Pair.first->second;

BackedgeTakenInfo Result =
    computeBackedgeTakenCount(L, /*AllowPredicates=*/true);

return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
7759}

7761ScalarEvolution::BackedgeTakenInfo &
7762ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
// Initially insert an invalid entry for this loop. If the insertion
// succeeds, proceed to actually compute a backedge-taken count and
// update the value. The temporary CouldNotCompute value tells SCEV
// code elsewhere that it shouldn't attempt to request a new
// backedge-taken count, which could result in infinite recursion.
std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
    BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
if (!Pair.second)
  return Pair.first->second;

// computeBackedgeTakenCount may allocate memory for its result. Inserting it
// into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
// must be cleared in this scope.
BackedgeTakenInfo Result = computeBackedgeTakenCount(L);

// In product build, there are no usage of statistic.
(void)NumTripCountsComputed;
(void)NumTripCountsNotComputed;
7781#if LLVM_ENABLE_STATS1 || !defined(NDEBUG)
const SCEV *BEExact = Result.getExact(L, this);
if (BEExact != getCouldNotCompute()) {
  assert(isLoopInvariant(BEExact, L) &&(static_cast <bool> (isLoopInvariant(BEExact, L) &&
 isLoopInvariant(Result.getConstantMax(this), L) && "Computed backedge-taken count isn't loop invariant for loop!"
) ? void (0) : __assert_fail ("isLoopInvariant(BEExact, L) && isLoopInvariant(Result.getConstantMax(this), L) && \"Computed backedge-taken count isn't loop invariant for loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7786, __extension__
 __PRETTY_FUNCTION__))
         isLoopInvariant(Result.getConstantMax(this), L) &&(static_cast <bool> (isLoopInvariant(BEExact, L) &&
 isLoopInvariant(Result.getConstantMax(this), L) && "Computed backedge-taken count isn't loop invariant for loop!"
) ? void (0) : __assert_fail ("isLoopInvariant(BEExact, L) && isLoopInvariant(Result.getConstantMax(this), L) && \"Computed backedge-taken count isn't loop invariant for loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7786, __extension__
 __PRETTY_FUNCTION__))
         "Computed backedge-taken count isn't loop invariant for loop!")(static_cast <bool> (isLoopInvariant(BEExact, L) &&
 isLoopInvariant(Result.getConstantMax(this), L) && "Computed backedge-taken count isn't loop invariant for loop!"
) ? void (0) : __assert_fail ("isLoopInvariant(BEExact, L) && isLoopInvariant(Result.getConstantMax(this), L) && \"Computed backedge-taken count isn't loop invariant for loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7786, __extension__
 __PRETTY_FUNCTION__));
  ++NumTripCountsComputed;
} else if (Result.getConstantMax(this) == getCouldNotCompute() &&
           isa<PHINode>(L->getHeader()->begin())) {
  // Only count loops that have phi nodes as not being computable.
  ++NumTripCountsNotComputed;
}
7793#endif // LLVM_ENABLE_STATS || !defined(NDEBUG)

// Now that we know more about the trip count for this loop, forget any
// existing SCEV values for PHI nodes in this loop since they are only
// conservative estimates made without the benefit of trip count
// information. This invalidation is not necessary for correctness, and is
// only done to produce more precise results.
if (Result.hasAnyInfo()) {
  // Invalidate any expression using an addrec in this loop.
  SmallVector<const SCEV *, 8> ToForget;
  auto LoopUsersIt = LoopUsers.find(L);
  if (LoopUsersIt != LoopUsers.end())
    append_range(ToForget, LoopUsersIt->second);
  forgetMemoizedResults(ToForget);

  // Invalidate constant-evolved loop header phis.
  for (PHINode &PN : L->getHeader()->phis())
    ConstantEvolutionLoopExitValue.erase(&PN);
}

// Re-lookup the insert position, since the call to
// computeBackedgeTakenCount above could result in a
// recusive call to getBackedgeTakenInfo (on a different
// loop), which would invalidate the iterator computed
// earlier.
return BackedgeTakenCounts.find(L)->second = std::move(Result);
7819}

7821void ScalarEvolution::forgetAllLoops() {
// This method is intended to forget all info about loops. It should
// invalidate caches as if the following happened:
// - The trip counts of all loops have changed arbitrarily
// - Every llvm::Value has been updated in place to produce a different
// result.
BackedgeTakenCounts.clear();
PredicatedBackedgeTakenCounts.clear();
BECountUsers.clear();
LoopPropertiesCache.clear();
ConstantEvolutionLoopExitValue.clear();
ValueExprMap.clear();
ValuesAtScopes.clear();
ValuesAtScopesUsers.clear();
LoopDispositions.clear();
BlockDispositions.clear();
UnsignedRanges.clear();
SignedRanges.clear();
ExprValueMap.clear();
HasRecMap.clear();
MinTrailingZerosCache.clear();
PredicatedSCEVRewrites.clear();
7843}

7845void ScalarEvolution::forgetLoop(const Loop *L) {
SmallVector<const Loop *, 16> LoopWorklist(1, L);
SmallVector<Instruction *, 32> Worklist;
SmallPtrSet<Instruction *, 16> Visited;
SmallVector<const SCEV *, 16> ToForget;

// Iterate over all the loops and sub-loops to drop SCEV information.
while (!LoopWorklist.empty()) {
  auto *CurrL = LoopWorklist.pop_back_val();

  // Drop any stored trip count value.
  forgetBackedgeTakenCounts(CurrL, /* Predicated */ false);
  forgetBackedgeTakenCounts(CurrL, /* Predicated */ true);

  // Drop information about predicated SCEV rewrites for this loop.
  for (auto I = PredicatedSCEVRewrites.begin();
       I != PredicatedSCEVRewrites.end();) {
    std::pair<const SCEV *, const Loop *> Entry = I->first;
    if (Entry.second == CurrL)
      PredicatedSCEVRewrites.erase(I++);
    else
      ++I;
  }

  auto LoopUsersItr = LoopUsers.find(CurrL);
  if (LoopUsersItr != LoopUsers.end()) {
    ToForget.insert(ToForget.end(), LoopUsersItr->second.begin(),
              LoopUsersItr->second.end());
    LoopUsers.erase(LoopUsersItr);
  }

  // Drop information about expressions based on loop-header PHIs.
  PushLoopPHIs(CurrL, Worklist, Visited);

  while (!Worklist.empty()) {
    Instruction *I = Worklist.pop_back_val();

    ValueExprMapType::iterator It =
        ValueExprMap.find_as(static_cast<Value *>(I));
    if (It != ValueExprMap.end()) {
      eraseValueFromMap(It->first);
      ToForget.push_back(It->second);
      if (PHINode *PN = dyn_cast<PHINode>(I))
        ConstantEvolutionLoopExitValue.erase(PN);
    }

    PushDefUseChildren(I, Worklist, Visited);
  }

  LoopPropertiesCache.erase(CurrL);
  // Forget all contained loops too, to avoid dangling entries in the
  // ValuesAtScopes map.
  LoopWorklist.append(CurrL->begin(), CurrL->end());
}
forgetMemoizedResults(ToForget);
7900}

7902void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
while (Loop *Parent = L->getParentLoop())
  L = Parent;
forgetLoop(L);
7906}

7908void ScalarEvolution::forgetValue(Value *V) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return;

// Drop information about expressions based on loop-header PHIs.
SmallVector<Instruction *, 16> Worklist;
SmallPtrSet<Instruction *, 8> Visited;
SmallVector<const SCEV *, 8> ToForget;
Worklist.push_back(I);
Visited.insert(I);

while (!Worklist.empty()) {
  I = Worklist.pop_back_val();
  ValueExprMapType::iterator It =
    ValueExprMap.find_as(static_cast<Value *>(I));
  if (It != ValueExprMap.end()) {
    eraseValueFromMap(It->first);
    ToForget.push_back(It->second);
    if (PHINode *PN = dyn_cast<PHINode>(I))
      ConstantEvolutionLoopExitValue.erase(PN);
  }

  PushDefUseChildren(I, Worklist, Visited);
}
forgetMemoizedResults(ToForget);
7933}

7935void ScalarEvolution::forgetLoopDispositions(const Loop *L) {
LoopDispositions.clear();
7937}

7939/// Get the exact loop backedge taken count considering all loop exits. A
7940/// computable result can only be returned for loops with all exiting blocks
7941/// dominating the latch. howFarToZero assumes that the limit of each loop test
7942/// is never skipped. This is a valid assumption as long as the loop exits via
7943/// that test. For precise results, it is the caller's responsibility to specify
7944/// the relevant loop exiting block using getExact(ExitingBlock, SE).
7945const SCEV *
7946ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
                                           SCEVUnionPredicate *Preds) const {
// If any exits were not computable, the loop is not computable.
if (!isComplete() || ExitNotTaken.empty())
  return SE->getCouldNotCompute();

const BasicBlock *Latch = L->getLoopLatch();
// All exiting blocks we have collected must dominate the only backedge.
if (!Latch)
  return SE->getCouldNotCompute();

// All exiting blocks we have gathered dominate loop's latch, so exact trip
// count is simply a minimum out of all these calculated exit counts.
SmallVector<const SCEV *, 2> Ops;
for (auto &ENT : ExitNotTaken) {
  const SCEV *BECount = ENT.ExactNotTaken;
  assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!")(static_cast <bool> (BECount != SE->getCouldNotCompute
() && "Bad exit SCEV!") ? void (0) : __assert_fail ("BECount != SE->getCouldNotCompute() && \"Bad exit SCEV!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7962, __extension__
 __PRETTY_FUNCTION__));
  assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&(static_cast <bool> (SE->DT.dominates(ENT.ExitingBlock
, Latch) && "We should only have known counts for exiting blocks that dominate "
 "latch!") ? void (0) : __assert_fail ("SE->DT.dominates(ENT.ExitingBlock, Latch) && \"We should only have known counts for exiting blocks that dominate \" \"latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7965, __extension__
 __PRETTY_FUNCTION__))
         "We should only have known counts for exiting blocks that dominate "(static_cast <bool> (SE->DT.dominates(ENT.ExitingBlock
, Latch) && "We should only have known counts for exiting blocks that dominate "
 "latch!") ? void (0) : __assert_fail ("SE->DT.dominates(ENT.ExitingBlock, Latch) && \"We should only have known counts for exiting blocks that dominate \" \"latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7965, __extension__
 __PRETTY_FUNCTION__))
         "latch!")(static_cast <bool> (SE->DT.dominates(ENT.ExitingBlock
, Latch) && "We should only have known counts for exiting blocks that dominate "
 "latch!") ? void (0) : __assert_fail ("SE->DT.dominates(ENT.ExitingBlock, Latch) && \"We should only have known counts for exiting blocks that dominate \" \"latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7965, __extension__
 __PRETTY_FUNCTION__));

  Ops.push_back(BECount);

  if (Preds && !ENT.hasAlwaysTruePredicate())
    Preds->add(ENT.Predicate.get());

  assert((Preds || ENT.hasAlwaysTruePredicate()) &&(static_cast <bool> ((Preds || ENT.hasAlwaysTruePredicate
()) && "Predicate should be always true!") ? void (0)
 : __assert_fail ("(Preds || ENT.hasAlwaysTruePredicate()) && \"Predicate should be always true!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7973, __extension__
 __PRETTY_FUNCTION__))
         "Predicate should be always true!")(static_cast <bool> ((Preds || ENT.hasAlwaysTruePredicate
()) && "Predicate should be always true!") ? void (0)
 : __assert_fail ("(Preds || ENT.hasAlwaysTruePredicate()) && \"Predicate should be always true!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 7973, __extension__
 __PRETTY_FUNCTION__));
}

return SE->getUMinFromMismatchedTypes(Ops);
7977}

7979/// Get the exact not taken count for this loop exit.
7980const SCEV *
7981ScalarEvolution::BackedgeTakenInfo::getExact(const BasicBlock *ExitingBlock,
                                           ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
  if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
    return ENT.ExactNotTaken;

return SE->getCouldNotCompute();
7988}

7990const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax(
  const BasicBlock *ExitingBlock, ScalarEvolution *SE) const {
for (auto &ENT : ExitNotTaken)
  if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
    return ENT.MaxNotTaken;

return SE->getCouldNotCompute();
7997}

7999/// getConstantMax - Get the constant max backedge taken count for the loop.
8000const SCEV *
8001ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
  return !ENT.hasAlwaysTruePredicate();
};

if (!getConstantMax() || any_of(ExitNotTaken, PredicateNotAlwaysTrue))
  return SE->getCouldNotCompute();

assert((isa<SCEVCouldNotCompute>(getConstantMax()) ||(static_cast <bool> ((isa<SCEVCouldNotCompute>(getConstantMax
()) || isa<SCEVConstant>(getConstantMax())) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(getConstantMax()) || isa<SCEVConstant>(getConstantMax())) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8011, __extension__
 __PRETTY_FUNCTION__))
        isa<SCEVConstant>(getConstantMax())) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(getConstantMax
()) || isa<SCEVConstant>(getConstantMax())) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(getConstantMax()) || isa<SCEVConstant>(getConstantMax())) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8011, __extension__
 __PRETTY_FUNCTION__))
       "No point in having a non-constant max backedge taken count!")(static_cast <bool> ((isa<SCEVCouldNotCompute>(getConstantMax
()) || isa<SCEVConstant>(getConstantMax())) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(getConstantMax()) || isa<SCEVConstant>(getConstantMax())) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8011, __extension__
 __PRETTY_FUNCTION__));
return getConstantMax();
8013}

8015const SCEV *
8016ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(const Loop *L,
                                                 ScalarEvolution *SE) {
if (!SymbolicMax)
  SymbolicMax = SE->computeSymbolicMaxBackedgeTakenCount(L);
return SymbolicMax;
8021}

8023bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
  ScalarEvolution *SE) const {
auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
  return !ENT.hasAlwaysTruePredicate();
};
return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
8029}

8031ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
  : ExitLimit(E, E, false, None) {
8033}

8035ScalarEvolution::ExitLimit::ExitLimit(
  const SCEV *E, const SCEV *M, bool MaxOrZero,
  ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
  : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
// If we prove the max count is zero, so is the symbolic bound.  This happens
// in practice due to differences in a) how context sensitive we've chosen
// to be and b) how we reason about bounds impied by UB.
if (MaxNotTaken->isZero())
  ExactNotTaken = MaxNotTaken;

assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||(static_cast <bool> ((isa<SCEVCouldNotCompute>(ExactNotTaken
) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
 "Exact is not allowed to be less precise than Max") ? void (
0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ExactNotTaken) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) && \"Exact is not allowed to be less precise than Max\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8047, __extension__
 __PRETTY_FUNCTION__))
        !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(ExactNotTaken
) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
 "Exact is not allowed to be less precise than Max") ? void (
0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ExactNotTaken) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) && \"Exact is not allowed to be less precise than Max\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8047, __extension__
 __PRETTY_FUNCTION__))
       "Exact is not allowed to be less precise than Max")(static_cast <bool> ((isa<SCEVCouldNotCompute>(ExactNotTaken
) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
 "Exact is not allowed to be less precise than Max") ? void (
0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ExactNotTaken) || !isa<SCEVCouldNotCompute>(MaxNotTaken)) && \"Exact is not allowed to be less precise than Max\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8047, __extension__
 __PRETTY_FUNCTION__));
assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||(static_cast <bool> ((isa<SCEVCouldNotCompute>(MaxNotTaken
) || isa<SCEVConstant>(MaxNotTaken)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(MaxNotTaken) || isa<SCEVConstant>(MaxNotTaken)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8050, __extension__
 __PRETTY_FUNCTION__))
        isa<SCEVConstant>(MaxNotTaken)) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(MaxNotTaken
) || isa<SCEVConstant>(MaxNotTaken)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(MaxNotTaken) || isa<SCEVConstant>(MaxNotTaken)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8050, __extension__
 __PRETTY_FUNCTION__))
       "No point in having a non-constant max backedge taken count!")(static_cast <bool> ((isa<SCEVCouldNotCompute>(MaxNotTaken
) || isa<SCEVConstant>(MaxNotTaken)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(MaxNotTaken) || isa<SCEVConstant>(MaxNotTaken)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8050, __extension__
 __PRETTY_FUNCTION__));
for (auto *PredSet : PredSetList)
  for (auto *P : *PredSet)
    addPredicate(P);
assert((isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(E)
 || !E->getType()->isPointerTy()) && "Backedge count should be int"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) && \"Backedge count should be int\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8055, __extension__
 __PRETTY_FUNCTION__))
       "Backedge count should be int")(static_cast <bool> ((isa<SCEVCouldNotCompute>(E)
 || !E->getType()->isPointerTy()) && "Backedge count should be int"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(E) || !E->getType()->isPointerTy()) && \"Backedge count should be int\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8055, __extension__
 __PRETTY_FUNCTION__));
assert((isa<SCEVCouldNotCompute>(M) || !M->getType()->isPointerTy()) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(M)
 || !M->getType()->isPointerTy()) && "Max backedge count should be int"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(M) || !M->getType()->isPointerTy()) && \"Max backedge count should be int\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8057, __extension__
 __PRETTY_FUNCTION__))
       "Max backedge count should be int")(static_cast <bool> ((isa<SCEVCouldNotCompute>(M)
 || !M->getType()->isPointerTy()) && "Max backedge count should be int"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(M) || !M->getType()->isPointerTy()) && \"Max backedge count should be int\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8057, __extension__
 __PRETTY_FUNCTION__));
8058}

8060ScalarEvolution::ExitLimit::ExitLimit(
  const SCEV *E, const SCEV *M, bool MaxOrZero,
  const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
  : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
8064}

8066ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
                                    bool MaxOrZero)
  : ExitLimit(E, M, MaxOrZero, None) {
8069}

8071/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
8072/// computable exit into a persistent ExitNotTakenInfo array.
8073ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
  ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts,
  bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero)
  : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) {
using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;

ExitNotTaken.reserve(ExitCounts.size());
std::transform(
    ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
    [&](const EdgeExitInfo &EEI) {
      BasicBlock *ExitBB = EEI.first;
      const ExitLimit &EL = EEI.second;
      if (EL.Predicates.empty())
        return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
                                nullptr);

      std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
      for (auto *Pred : EL.Predicates)
        Predicate->add(Pred);

      return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
                              std::move(Predicate));
    });
assert((isa<SCEVCouldNotCompute>(ConstantMax) ||(static_cast <bool> ((isa<SCEVCouldNotCompute>(ConstantMax
) || isa<SCEVConstant>(ConstantMax)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ConstantMax) || isa<SCEVConstant>(ConstantMax)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8098, __extension__
 __PRETTY_FUNCTION__))
        isa<SCEVConstant>(ConstantMax)) &&(static_cast <bool> ((isa<SCEVCouldNotCompute>(ConstantMax
) || isa<SCEVConstant>(ConstantMax)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ConstantMax) || isa<SCEVConstant>(ConstantMax)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8098, __extension__
 __PRETTY_FUNCTION__))
       "No point in having a non-constant max backedge taken count!")(static_cast <bool> ((isa<SCEVCouldNotCompute>(ConstantMax
) || isa<SCEVConstant>(ConstantMax)) && "No point in having a non-constant max backedge taken count!"
) ? void (0) : __assert_fail ("(isa<SCEVCouldNotCompute>(ConstantMax) || isa<SCEVConstant>(ConstantMax)) && \"No point in having a non-constant max backedge taken count!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8098, __extension__
 __PRETTY_FUNCTION__));
8099}

8101/// Compute the number of times the backedge of the specified loop will execute.
8102ScalarEvolution::BackedgeTakenInfo
8103ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
                                         bool AllowPredicates) {
SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);

using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;

SmallVector<EdgeExitInfo, 4> ExitCounts;
bool CouldComputeBECount = true;
BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
const SCEV *MustExitMaxBECount = nullptr;
const SCEV *MayExitMaxBECount = nullptr;
bool MustExitMaxOrZero = false;

// Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
// and compute maxBECount.
// Do a union of all the predicates here.
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
  BasicBlock *ExitBB = ExitingBlocks[i];

  // We canonicalize untaken exits to br (constant), ignore them so that
  // proving an exit untaken doesn't negatively impact our ability to reason
  // about the loop as whole.
  if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator()))
    if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
      bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
      if (ExitIfTrue == CI->isZero())
        continue;
    }

  ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);

  assert((AllowPredicates || EL.Predicates.empty()) &&(static_cast <bool> ((AllowPredicates || EL.Predicates.
empty()) && "Predicated exit limit when predicates are not allowed!"
) ? void (0) : __assert_fail ("(AllowPredicates || EL.Predicates.empty()) && \"Predicated exit limit when predicates are not allowed!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8136, __extension__
 __PRETTY_FUNCTION__))
         "Predicated exit limit when predicates are not allowed!")(static_cast <bool> ((AllowPredicates || EL.Predicates.
empty()) && "Predicated exit limit when predicates are not allowed!"
) ? void (0) : __assert_fail ("(AllowPredicates || EL.Predicates.empty()) && \"Predicated exit limit when predicates are not allowed!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8136, __extension__
 __PRETTY_FUNCTION__));

  // 1. For each exit that can be computed, add an entry to ExitCounts.
  // CouldComputeBECount is true only if all exits can be computed.
  if (EL.ExactNotTaken == getCouldNotCompute())
    // We couldn't compute an exact value for this exit, so
    // we won't be able to compute an exact value for the loop.
    CouldComputeBECount = false;
  else
    ExitCounts.emplace_back(ExitBB, EL);

  // 2. Derive the loop's MaxBECount from each exit's max number of
  // non-exiting iterations. Partition the loop exits into two kinds:
  // LoopMustExits and LoopMayExits.
  //
  // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
  // is a LoopMayExit.  If any computable LoopMustExit is found, then
  // MaxBECount is the minimum EL.MaxNotTaken of computable
  // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
  // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
  // computable EL.MaxNotTaken.
  if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
      DT.dominates(ExitBB, Latch)) {
    if (!MustExitMaxBECount) {
      MustExitMaxBECount = EL.MaxNotTaken;
      MustExitMaxOrZero = EL.MaxOrZero;
    } else {
      MustExitMaxBECount =
          getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
    }
  } else if (MayExitMaxBECount != getCouldNotCompute()) {
    if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
      MayExitMaxBECount = EL.MaxNotTaken;
    else {
      MayExitMaxBECount =
          getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
    }
  }
}
const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
  (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
// The loop backedge will be taken the maximum or zero times if there's
// a single exit that must be taken the maximum or zero times.
bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);

// Remember which SCEVs are used in exit limits for invalidation purposes.
// We only care about non-constant SCEVs here, so we can ignore EL.MaxNotTaken
// and MaxBECount, which must be SCEVConstant.
for (const auto &Pair : ExitCounts)
  if (!isa<SCEVConstant>(Pair.second.ExactNotTaken))
    BECountUsers[Pair.second.ExactNotTaken].insert({L, AllowPredicates});
return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
                         MaxBECount, MaxOrZero);
8189}

8191ScalarEvolution::ExitLimit
8192ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
                                    bool AllowPredicates) {
assert(L->contains(ExitingBlock) && "Exit count for non-loop block?")(static_cast <bool> (L->contains(ExitingBlock) &&
 "Exit count for non-loop block?") ? void (0) : __assert_fail
 ("L->contains(ExitingBlock) && \"Exit count for non-loop block?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8194, __extension__
 __PRETTY_FUNCTION__));
// If our exiting block does not dominate the latch, then its connection with
// loop's exit limit may be far from trivial.
const BasicBlock *Latch = L->getLoopLatch();
if (!Latch || !DT.dominates(ExitingBlock, Latch))
  return getCouldNotCompute();

bool IsOnlyExit = (L->getExitingBlock() != nullptr);
Instruction *Term = ExitingBlock->getTerminator();
if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
  assert(BI->isConditional() && "If unconditional, it can't be in loop!")(static_cast <bool> (BI->isConditional() && "If unconditional, it can't be in loop!"
) ? void (0) : __assert_fail ("BI->isConditional() && \"If unconditional, it can't be in loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8204, __extension__
 __PRETTY_FUNCTION__));
  bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
  assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&(static_cast <bool> (ExitIfTrue == L->contains(BI->
getSuccessor(1)) && "It should have one successor in loop and one exit block!"
) ? void (0) : __assert_fail ("ExitIfTrue == L->contains(BI->getSuccessor(1)) && \"It should have one successor in loop and one exit block!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8207, __extension__
 __PRETTY_FUNCTION__))
         "It should have one successor in loop and one exit block!")(static_cast <bool> (ExitIfTrue == L->contains(BI->
getSuccessor(1)) && "It should have one successor in loop and one exit block!"
) ? void (0) : __assert_fail ("ExitIfTrue == L->contains(BI->getSuccessor(1)) && \"It should have one successor in loop and one exit block!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8207, __extension__
 __PRETTY_FUNCTION__));
  // Proceed to the next level to examine the exit condition expression.
  return computeExitLimitFromCond(
      L, BI->getCondition(), ExitIfTrue,
      /*ControlsExit=*/IsOnlyExit, AllowPredicates);
}

if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
  // For switch, make sure that there is a single exit from the loop.
  BasicBlock *Exit = nullptr;
  for (auto *SBB : successors(ExitingBlock))
    if (!L->contains(SBB)) {
      if (Exit) // Multiple exit successors.
        return getCouldNotCompute();
      Exit = SBB;
    }
  assert(Exit && "Exiting block must have at least one exit")(static_cast <bool> (Exit && "Exiting block must have at least one exit"
) ? void (0) : __assert_fail ("Exit && \"Exiting block must have at least one exit\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8223, __extension__
 __PRETTY_FUNCTION__));
  return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
                                              /*ControlsExit=*/IsOnlyExit);
}

return getCouldNotCompute();
8229}

8231ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
  const Loop *L, Value *ExitCond, bool ExitIfTrue,
  bool ControlsExit, bool AllowPredicates) {
ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
                                      ControlsExit, AllowPredicates);
8237}

8239Optional<ScalarEvolution::ExitLimit>
8240ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
                                    bool ExitIfTrue, bool ControlsExit,
                                    bool AllowPredicates) {
(void)this->L;
(void)this->ExitIfTrue;
(void)this->AllowPredicates;

assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8249, __extension__
 __PRETTY_FUNCTION__))
       this->AllowPredicates == AllowPredicates &&(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8249, __extension__
 __PRETTY_FUNCTION__))
       "Variance in assumed invariant key components!")(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8249, __extension__
 __PRETTY_FUNCTION__));
auto Itr = TripCountMap.find({ExitCond, ControlsExit});
if (Itr == TripCountMap.end())
  return None;
return Itr->second;
8254}

8256void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
                                           bool ExitIfTrue,
                                           bool ControlsExit,
                                           bool AllowPredicates,
                                           const ExitLimit &EL) {
assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8263, __extension__
 __PRETTY_FUNCTION__))
       this->AllowPredicates == AllowPredicates &&(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8263, __extension__
 __PRETTY_FUNCTION__))
       "Variance in assumed invariant key components!")(static_cast <bool> (this->L == L && this->
ExitIfTrue == ExitIfTrue && this->AllowPredicates ==
 AllowPredicates && "Variance in assumed invariant key components!"
) ? void (0) : __assert_fail ("this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && \"Variance in assumed invariant key components!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8263, __extension__
 __PRETTY_FUNCTION__));

auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
assert(InsertResult.second && "Expected successful insertion!")(static_cast <bool> (InsertResult.second && "Expected successful insertion!"
) ? void (0) : __assert_fail ("InsertResult.second && \"Expected successful insertion!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8266, __extension__
 __PRETTY_FUNCTION__));
(void)InsertResult;
(void)ExitIfTrue;
8269}

8271ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
  ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
  bool ControlsExit, bool AllowPredicates) {

if (auto MaybeEL =
        Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
  return *MaybeEL;

ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
                                            ControlsExit, AllowPredicates);
Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
return EL;
8283}

8285ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
  ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
  bool ControlsExit, bool AllowPredicates) {
// Handle BinOp conditions (And, Or).
if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp(
        Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
  return *LimitFromBinOp;

// With an icmp, it may be feasible to compute an exact backedge-taken count.
// Proceed to the next level to examine the icmp.
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
  ExitLimit EL =
      computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
  if (EL.hasFullInfo() || !AllowPredicates)
    return EL;

  // Try again, but use SCEV predicates this time.
  return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
                                  /*AllowPredicates=*/true);
}

// Check for a constant condition. These are normally stripped out by
// SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
// preserve the CFG and is temporarily leaving constant conditions
// in place.
if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
  if (ExitIfTrue == !CI->getZExtValue())
    // The backedge is always taken.
    return getCouldNotCompute();
  else
    // The backedge is never taken.
    return getZero(CI->getType());
}

// If we're exiting based on the overflow flag of an x.with.overflow intrinsic
// with a constant step, we can form an equivalent icmp predicate and figure
// out how many iterations will be taken before we exit.
const WithOverflowInst *WO;
const APInt *C;
if (match(ExitCond, m_ExtractValue<1>(m_WithOverflowInst(WO))) &&
    match(WO->getRHS(), m_APInt(C))) {
  ConstantRange NWR =
    ConstantRange::makeExactNoWrapRegion(WO->getBinaryOp(), *C,
                                         WO->getNoWrapKind());
  CmpInst::Predicate Pred;
  APInt NewRHSC, Offset;
  NWR.getEquivalentICmp(Pred, NewRHSC, Offset);
  if (!ExitIfTrue)
    Pred = ICmpInst::getInversePredicate(Pred);
  auto *LHS = getSCEV(WO->getLHS());
  if (Offset != 0)
    LHS = getAddExpr(LHS, getConstant(Offset));
  auto EL = computeExitLimitFromICmp(L, Pred, LHS, getConstant(NewRHSC),
                                     ControlsExit, AllowPredicates);
  if (EL.hasAnyInfo()) return EL;
}

// If it's not an integer or pointer comparison then compute it the hard way.
return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
8344}

8346Optional<ScalarEvolution::ExitLimit>
8347ScalarEvolution::computeExitLimitFromCondFromBinOp(
  ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
  bool ControlsExit, bool AllowPredicates) {
// Check if the controlling expression for this loop is an And or Or.
Value *Op0, *Op1;
bool IsAnd = false;
if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1))))
  IsAnd = true;
else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1))))
  IsAnd = false;
else
  return None;

// EitherMayExit is true in these two cases:
//   br (and Op0 Op1), loop, exit
//   br (or  Op0 Op1), exit, loop
bool EitherMayExit = IsAnd ^ ExitIfTrue;
ExitLimit EL0 = computeExitLimitFromCondCached(Cache, L, Op0, ExitIfTrue,
                                               ControlsExit && !EitherMayExit,
                                               AllowPredicates);
ExitLimit EL1 = computeExitLimitFromCondCached(Cache, L, Op1, ExitIfTrue,
                                               ControlsExit && !EitherMayExit,
                                               AllowPredicates);

// Be robust against unsimplified IR for the form "op i1 X, NeutralElement"
const Constant *NeutralElement = ConstantInt::get(ExitCond->getType(), IsAnd);
if (isa<ConstantInt>(Op1))
  return Op1 == NeutralElement ? EL0 : EL1;
if (isa<ConstantInt>(Op0))
  return Op0 == NeutralElement ? EL1 : EL0;

const SCEV *BECount = getCouldNotCompute();
const SCEV *MaxBECount = getCouldNotCompute();
if (EitherMayExit) {
  // Both conditions must be same for the loop to continue executing.
  // Choose the less conservative count.
  if (EL0.ExactNotTaken != getCouldNotCompute() &&
      EL1.ExactNotTaken != getCouldNotCompute()) {
    BECount = getUMinFromMismatchedTypes(
        EL0.ExactNotTaken, EL1.ExactNotTaken,
        /*Sequential=*/!isa<BinaryOperator>(ExitCond));

    // If EL0.ExactNotTaken was zero and ExitCond was a short-circuit form,
    // it should have been simplified to zero (see the condition (3) above)
    assert(!isa<BinaryOperator>(ExitCond) || !EL0.ExactNotTaken->isZero() ||(static_cast <bool> (!isa<BinaryOperator>(ExitCond
) || !EL0.ExactNotTaken->isZero() || BECount->isZero())
 ? void (0) : __assert_fail ("!isa<BinaryOperator>(ExitCond) || !EL0.ExactNotTaken->isZero() || BECount->isZero()"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8392, __extension__
 __PRETTY_FUNCTION__))
           BECount->isZero())(static_cast <bool> (!isa<BinaryOperator>(ExitCond
) || !EL0.ExactNotTaken->isZero() || BECount->isZero())
 ? void (0) : __assert_fail ("!isa<BinaryOperator>(ExitCond) || !EL0.ExactNotTaken->isZero() || BECount->isZero()"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8392, __extension__
 __PRETTY_FUNCTION__));
  }
  if (EL0.MaxNotTaken == getCouldNotCompute())
    MaxBECount = EL1.MaxNotTaken;
  else if (EL1.MaxNotTaken == getCouldNotCompute())
    MaxBECount = EL0.MaxNotTaken;
  else
    MaxBECount = getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
} else {
  // Both conditions must be same at the same time for the loop to exit.
  // For now, be conservative.
  if (EL0.ExactNotTaken == EL1.ExactNotTaken)
    BECount = EL0.ExactNotTaken;
}

// There are cases (e.g. PR26207) where computeExitLimitFromCond is able
// to be more aggressive when computing BECount than when computing
// MaxBECount.  In these cases it is possible for EL0.ExactNotTaken and
// EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
// to not.
if (isa<SCEVCouldNotCompute>(MaxBECount) &&
    !isa<SCEVCouldNotCompute>(BECount))
  MaxBECount = getConstant(getUnsignedRangeMax(BECount));

return ExitLimit(BECount, MaxBECount, false,
                 { &EL0.Predicates, &EL1.Predicates });
8418}

8420ScalarEvolution::ExitLimit
8421ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
                                        ICmpInst *ExitCond,
                                        bool ExitIfTrue,
                                        bool ControlsExit,
                                        bool AllowPredicates) {
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Pred;
if (!ExitIfTrue)
  Pred = ExitCond->getPredicate();
else
  Pred = ExitCond->getInversePredicate();
const ICmpInst::Predicate OriginalPred = Pred;

const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));

ExitLimit EL = computeExitLimitFromICmp(L, Pred, LHS, RHS, ControlsExit,
                                        AllowPredicates);
if (EL.hasAnyInfo()) return EL;

auto *ExhaustiveCount =
    computeExitCountExhaustively(L, ExitCond, ExitIfTrue);

if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
  return ExhaustiveCount;

return computeShiftCompareExitLimit(ExitCond->getOperand(0),
                                    ExitCond->getOperand(1), L, OriginalPred);
8449}
8450ScalarEvolution::ExitLimit
8451ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
                                        ICmpInst::Predicate Pred,
                                        const SCEV *LHS, const SCEV *RHS,
                                        bool ControlsExit,
                                        bool AllowPredicates) {

// Try to evaluate any dependencies out of the loop.
LHS = getSCEVAtScope(LHS, L);
RHS = getSCEVAtScope(RHS, L);

// At this point, we would like to compute how many iterations of the
// loop the predicate will return true for these inputs.
if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
  // If there is a loop-invariant, force it into the RHS.
  std::swap(LHS, RHS);
  Pred = ICmpInst::getSwappedPredicate(Pred);
}

// Simplify the operands before analyzing them.
(void)SimplifyICmpOperands(Pred, LHS, RHS);

// If we have a comparison of a chrec against a constant, try to use value
// ranges to answer this query.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
  if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
    if (AddRec->getLoop() == L) {
      // Form the constant range.
      ConstantRange CompRange =
          ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());

      const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
      if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
    }

// If this loop must exit based on this condition (or execute undefined
// behaviour), and we can prove the test sequence produced must repeat
// the same values on self-wrap of the IV, then we can infer that IV
// doesn't self wrap because if it did, we'd have an infinite (undefined)
// loop.
if (ControlsExit && isLoopInvariant(RHS, L) && loopHasNoAbnormalExits(L) &&
    loopIsFiniteByAssumption(L)) {

  // TODO: We can peel off any functions which are invertible *in L*.  Loop
  // invariant terms are effectively constants for our purposes here.
  auto *InnerLHS = LHS;
  if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS))
    InnerLHS = ZExt->getOperand();
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(InnerLHS)) {
    auto *StrideC = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this));
    if (!AR->hasNoSelfWrap() && AR->getLoop() == L && AR->isAffine() && 
        StrideC && StrideC->getAPInt().isPowerOf2()) {
      auto Flags = AR->getNoWrapFlags();
      Flags = setFlags(Flags, SCEV::FlagNW);
      SmallVector<const SCEV*> Operands{AR->operands()};
      Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
    }
  }
}

switch (Pred) {
case ICmpInst::ICMP_NE: {                     // while (X != Y)
  // Convert to: while (X-Y != 0)
  if (LHS->getType()->isPointerTy()) {
    LHS = getLosslessPtrToIntExpr(LHS);
    if (isa<SCEVCouldNotCompute>(LHS))
      return LHS;
  }
  if (RHS->getType()->isPointerTy()) {
    RHS = getLosslessPtrToIntExpr(RHS);
    if (isa<SCEVCouldNotCompute>(RHS))
      return RHS;
  }
  ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
                              AllowPredicates);
  if (EL.hasAnyInfo()) return EL;
  break;
}
case ICmpInst::ICMP_EQ: {                     // while (X == Y)
  // Convert to: while (X-Y == 0)
  if (LHS->getType()->isPointerTy()) {
    LHS = getLosslessPtrToIntExpr(LHS);
    if (isa<SCEVCouldNotCompute>(LHS))
      return LHS;
  }
  if (RHS->getType()->isPointerTy()) {
    RHS = getLosslessPtrToIntExpr(RHS);
    if (isa<SCEVCouldNotCompute>(RHS))
      return RHS;
  }
  ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
  if (EL.hasAnyInfo()) return EL;
  break;
}
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_ULT: {                    // while (X < Y)
  bool IsSigned = Pred == ICmpInst::ICMP_SLT;
  ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
                                  AllowPredicates);
  if (EL.hasAnyInfo()) return EL;
  break;
}
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_UGT: {                    // while (X > Y)
  bool IsSigned = Pred == ICmpInst::ICMP_SGT;
  ExitLimit EL =
      howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
                          AllowPredicates);
  if (EL.hasAnyInfo()) return EL;
  break;
}
default:
  break;
}

return getCouldNotCompute();
8567}

8569ScalarEvolution::ExitLimit
8570ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
                                                    SwitchInst *Switch,
                                                    BasicBlock *ExitingBlock,
                                                    bool ControlsExit) {
assert(!L->contains(ExitingBlock) && "Not an exiting block!")(static_cast <bool> (!L->contains(ExitingBlock) &&
 "Not an exiting block!") ? void (0) : __assert_fail ("!L->contains(ExitingBlock) && \"Not an exiting block!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8574, __extension__
 __PRETTY_FUNCTION__));

// Give up if the exit is the default dest of a switch.
if (Switch->getDefaultDest() == ExitingBlock)
  return getCouldNotCompute();

assert(L->contains(Switch->getDefaultDest()) &&(static_cast <bool> (L->contains(Switch->getDefaultDest
()) && "Default case must not exit the loop!") ? void
 (0) : __assert_fail ("L->contains(Switch->getDefaultDest()) && \"Default case must not exit the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8581, __extension__
 __PRETTY_FUNCTION__))
       "Default case must not exit the loop!")(static_cast <bool> (L->contains(Switch->getDefaultDest
()) && "Default case must not exit the loop!") ? void
 (0) : __assert_fail ("L->contains(Switch->getDefaultDest()) && \"Default case must not exit the loop!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8581, __extension__
 __PRETTY_FUNCTION__));
const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));

// while (X != Y) --> while (X-Y != 0)
ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
if (EL.hasAnyInfo())
  return EL;

return getCouldNotCompute();
8591}

8593static ConstantInt *
8594EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
                              ScalarEvolution &SE) {
const SCEV *InVal = SE.getConstant(C);
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
assert(isa<SCEVConstant>(Val) &&(static_cast <bool> (isa<SCEVConstant>(Val) &&
 "Evaluation of SCEV at constant didn't fold correctly?") ? void
 (0) : __assert_fail ("isa<SCEVConstant>(Val) && \"Evaluation of SCEV at constant didn't fold correctly?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8599, __extension__
 __PRETTY_FUNCTION__))
       "Evaluation of SCEV at constant didn't fold correctly?")(static_cast <bool> (isa<SCEVConstant>(Val) &&
 "Evaluation of SCEV at constant didn't fold correctly?") ? void
 (0) : __assert_fail ("isa<SCEVConstant>(Val) && \"Evaluation of SCEV at constant didn't fold correctly?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8599, __extension__
 __PRETTY_FUNCTION__));
return cast<SCEVConstant>(Val)->getValue();
8601}

8603ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
  Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
if (!RHS)
  return getCouldNotCompute();

const BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
  return getCouldNotCompute();

const BasicBlock *Predecessor = L->getLoopPredecessor();
if (!Predecessor)
  return getCouldNotCompute();

// Return true if V is of the form "LHS `shift_op` <positive constant>".
// Return LHS in OutLHS and shift_opt in OutOpCode.
auto MatchPositiveShift =
    [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {

  using namespace PatternMatch;

  ConstantInt *ShiftAmt;
  if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    OutOpCode = Instruction::LShr;
  else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    OutOpCode = Instruction::AShr;
  else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    OutOpCode = Instruction::Shl;
  else
    return false;

  return ShiftAmt->getValue().isStrictlyPositive();
};

// Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
//
// loop:
//   %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
//   %iv.shifted = lshr i32 %iv, <positive constant>
//
// Return true on a successful match.  Return the corresponding PHI node (%iv
// above) in PNOut and the opcode of the shift operation in OpCodeOut.
auto MatchShiftRecurrence =
    [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
  Optional<Instruction::BinaryOps> PostShiftOpCode;

  {
    Instruction::BinaryOps OpC;
    Value *V;

    // If we encounter a shift instruction, "peel off" the shift operation,
    // and remember that we did so.  Later when we inspect %iv's backedge
    // value, we will make sure that the backedge value uses the same
    // operation.
    //
    // Note: the peeled shift operation does not have to be the same
    // instruction as the one feeding into the PHI's backedge value.  We only
    // really care about it being the same *kind* of shift instruction --
    // that's all that is required for our later inferences to hold.
    if (MatchPositiveShift(LHS, V, OpC)) {
      PostShiftOpCode = OpC;
      LHS = V;
    }
  }

  PNOut = dyn_cast<PHINode>(LHS);
  if (!PNOut || PNOut->getParent() != L->getHeader())
    return false;

  Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
  Value *OpLHS;

  return
      // The backedge value for the PHI node must be a shift by a positive
      // amount
      MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&

      // of the PHI node itself
      OpLHS == PNOut &&

      // and the kind of shift should be match the kind of shift we peeled
      // off, if any.
      (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
};

PHINode *PN;
Instruction::BinaryOps OpCode;
if (!MatchShiftRecurrence(LHS, PN, OpCode))
  return getCouldNotCompute();

const DataLayout &DL = getDataLayout();

// The key rationale for this optimization is that for some kinds of shift
// recurrences, the value of the recurrence "stabilizes" to either 0 or -1
// within a finite number of iterations.  If the condition guarding the
// backedge (in the sense that the backedge is taken if the condition is true)
// is false for the value the shift recurrence stabilizes to, then we know
// that the backedge is taken only a finite number of times.

ConstantInt *StableValue = nullptr;
switch (OpCode) {
default:
  llvm_unreachable("Impossible case!")::llvm::llvm_unreachable_internal("Impossible case!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 8705);

case Instruction::AShr: {
  // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
  // bitwidth(K) iterations.
  Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
  KnownBits Known = computeKnownBits(FirstValue, DL, 0, &AC,
                                     Predecessor->getTerminator(), &DT);
  auto *Ty = cast<IntegerType>(RHS->getType());
  if (Known.isNonNegative())
    StableValue = ConstantInt::get(Ty, 0);
  else if (Known.isNegative())
    StableValue = ConstantInt::get(Ty, -1, true);
  else
    return getCouldNotCompute();

  break;
}
case Instruction::LShr:
case Instruction::Shl:
  // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
  // stabilize to 0 in at most bitwidth(K) iterations.
  StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
  break;
}

auto *Result =
    ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
assert(Result->getType()->isIntegerTy(1) &&(static_cast <bool> (Result->getType()->isIntegerTy
(1) && "Otherwise cannot be an operand to a branch instruction"
) ? void (0) : __assert_fail ("Result->getType()->isIntegerTy(1) && \"Otherwise cannot be an operand to a branch instruction\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8734, __extension__
 __PRETTY_FUNCTION__))
       "Otherwise cannot be an operand to a branch instruction")(static_cast <bool> (Result->getType()->isIntegerTy
(1) && "Otherwise cannot be an operand to a branch instruction"
) ? void (0) : __assert_fail ("Result->getType()->isIntegerTy(1) && \"Otherwise cannot be an operand to a branch instruction\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8734, __extension__
 __PRETTY_FUNCTION__));

if (Result->isZeroValue()) {
  unsigned BitWidth = getTypeSizeInBits(RHS->getType());
  const SCEV *UpperBound =
      getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
  return ExitLimit(getCouldNotCompute(), UpperBound, false);
}

return getCouldNotCompute();
8744}

8746/// Return true if we can constant fold an instruction of the specified type,
8747/// assuming that all operands were constants.
8748static bool CanConstantFold(const Instruction *I) {
if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
    isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
    isa<LoadInst>(I) || isa<ExtractValueInst>(I))
  return true;

if (const CallInst *CI = dyn_cast<CallInst>(I))
  if (const Function *F = CI->getCalledFunction())
    return canConstantFoldCallTo(CI, F);
return false;
8758}

8760/// Determine whether this instruction can constant evolve within this loop
8761/// assuming its operands can all constant evolve.
8762static bool canConstantEvolve(Instruction *I, const Loop *L) {
// An instruction outside of the loop can't be derived from a loop PHI.
if (!L->contains(I)) return false;

if (isa<PHINode>(I)) {
  // We don't currently keep track of the control flow needed to evaluate
  // PHIs, so we cannot handle PHIs inside of loops.
  return L->getHeader() == I->getParent();
}

// If we won't be able to constant fold this expression even if the operands
// are constants, bail early.
return CanConstantFold(I);
8775}

8777/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
8778/// recursing through each instruction operand until reaching a loop header phi.
8779static PHINode *
8780getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
                             DenseMap<Instruction *, PHINode *> &PHIMap,
                             unsigned Depth) {
if (Depth > MaxConstantEvolvingDepth)
  return nullptr;

// Otherwise, we can evaluate this instruction if all of its operands are
// constant or derived from a PHI node themselves.
PHINode *PHI = nullptr;
for (Value *Op : UseInst->operands()) {
  if (isa<Constant>(Op)) continue;

  Instruction *OpInst = dyn_cast<Instruction>(Op);
  if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;

  PHINode *P = dyn_cast<PHINode>(OpInst);
  if (!P)
    // If this operand is already visited, reuse the prior result.
    // We may have P != PHI if this is the deepest point at which the
    // inconsistent paths meet.
    P = PHIMap.lookup(OpInst);
  if (!P) {
    // Recurse and memoize the results, whether a phi is found or not.
    // This recursive call invalidates pointers into PHIMap.
    P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
    PHIMap[OpInst] = P;
  }
  if (!P)
    return nullptr;  // Not evolving from PHI
  if (PHI && PHI != P)
    return nullptr;  // Evolving from multiple different PHIs.
  PHI = P;
}
// This is a expression evolving from a constant PHI!
return PHI;
8815}

8817/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
8818/// in the loop that V is derived from.  We allow arbitrary operations along the
8819/// way, but the operands of an operation must either be constants or a value
8820/// derived from a constant PHI.  If this expression does not fit with these
8821/// constraints, return null.
8822static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
Instruction *I = dyn_cast<Instruction>(V);
if (!I || !canConstantEvolve(I, L)) return nullptr;

if (PHINode *PN = dyn_cast<PHINode>(I))
  return PN;

// Record non-constant instructions contained by the loop.
DenseMap<Instruction *, PHINode *> PHIMap;
return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
8832}

8834/// EvaluateExpression - Given an expression that passes the
8835/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
8836/// in the loop has the value PHIVal.  If we can't fold this expression for some
8837/// reason, return null.
8838static Constant *EvaluateExpression(Value *V, const Loop *L,
                                  DenseMap<Instruction *, Constant *> &Vals,
                                  const DataLayout &DL,
                                  const TargetLibraryInfo *TLI) {
// Convenient constant check, but redundant for recursive calls.
if (Constant *C = dyn_cast<Constant>(V)) return C;
Instruction *I = dyn_cast<Instruction>(V);
if (!I) return nullptr;

if (Constant *C = Vals.lookup(I)) return C;

// An instruction inside the loop depends on a value outside the loop that we
// weren't given a mapping for, or a value such as a call inside the loop.
if (!canConstantEvolve(I, L)) return nullptr;

// An unmapped PHI can be due to a branch or another loop inside this loop,
// or due to this not being the initial iteration through a loop where we
// couldn't compute the evolution of this particular PHI last time.
if (isa<PHINode>(I)) return nullptr;

std::vector<Constant*> Operands(I->getNumOperands());

for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
  Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
  if (!Operand) {
    Operands[i] = dyn_cast<Constant>(I->getOperand(i));
    if (!Operands[i]) return nullptr;
    continue;
  }
  Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
  Vals[Operand] = C;
  if (!C) return nullptr;
  Operands[i] = C;
}

if (CmpInst *CI = dyn_cast<CmpInst>(I))
  return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
                                         Operands[1], DL, TLI);
if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
  if (!LI->isVolatile())
    return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
}
return ConstantFoldInstOperands(I, Operands, DL, TLI);
8881}


8884// If every incoming value to PN except the one for BB is a specific Constant,
8885// return that, else return nullptr.
8886static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
Constant *IncomingVal = nullptr;

for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
  if (PN->getIncomingBlock(i) == BB)
    continue;

  auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
  if (!CurrentVal)
    return nullptr;

  if (IncomingVal != CurrentVal) {
    if (IncomingVal)
      return nullptr;
    IncomingVal = CurrentVal;
  }
}

return IncomingVal;
8905}

8907/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
8908/// in the header of its containing loop, we know the loop executes a
8909/// constant number of times, and the PHI node is just a recurrence
8910/// involving constants, fold it.
8911Constant *
8912ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
                                                 const APInt &BEs,
                                                 const Loop *L) {
auto I = ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
  return I->second;

if (BEs.ugt(MaxBruteForceIterations))
  return ConstantEvolutionLoopExitValue[PN] = nullptr;  // Not going to evaluate it.

Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];

DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!")(static_cast <bool> (PN->getParent() == Header &&
 "Can't evaluate PHI not in loop header!") ? void (0) : __assert_fail
 ("PN->getParent() == Header && \"Can't evaluate PHI not in loop header!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8926, __extension__
 __PRETTY_FUNCTION__));

BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
  return nullptr;

for (PHINode &PHI : Header->phis()) {
  if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
    CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
  return RetVal = nullptr;

Value *BEValue = PN->getIncomingValueForBlock(Latch);

// Execute the loop symbolically to determine the exit value.
assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&(static_cast <bool> (BEs.getActiveBits() < 8 * sizeof
(unsigned) && "BEs is <= MaxBruteForceIterations which is an 'unsigned'!"
) ? void (0) : __assert_fail ("BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) && \"BEs is <= MaxBruteForceIterations which is an 'unsigned'!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8943, __extension__
 __PRETTY_FUNCTION__))
       "BEs is <= MaxBruteForceIterations which is an 'unsigned'!")(static_cast <bool> (BEs.getActiveBits() < 8 * sizeof
(unsigned) && "BEs is <= MaxBruteForceIterations which is an 'unsigned'!"
) ? void (0) : __assert_fail ("BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) && \"BEs is <= MaxBruteForceIterations which is an 'unsigned'!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 8943, __extension__
 __PRETTY_FUNCTION__));

unsigned NumIterations = BEs.getZExtValue(); // must be in range
unsigned IterationNum = 0;
const DataLayout &DL = getDataLayout();
for (; ; ++IterationNum) {
  if (IterationNum == NumIterations)
    return RetVal = CurrentIterVals[PN];  // Got exit value!

  // Compute the value of the PHIs for the next iteration.
  // EvaluateExpression adds non-phi values to the CurrentIterVals map.
  DenseMap<Instruction *, Constant *> NextIterVals;
  Constant *NextPHI =
      EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
  if (!NextPHI)
    return nullptr;        // Couldn't evaluate!
  NextIterVals[PN] = NextPHI;

  bool StoppedEvolving = NextPHI == CurrentIterVals[PN];

  // Also evaluate the other PHI nodes.  However, we don't get to stop if we
  // cease to be able to evaluate one of them or if they stop evolving,
  // because that doesn't necessarily prevent us from computing PN.
  SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
  for (const auto &I : CurrentIterVals) {
    PHINode *PHI = dyn_cast<PHINode>(I.first);
    if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
    PHIsToCompute.emplace_back(PHI, I.second);
  }
  // We use two distinct loops because EvaluateExpression may invalidate any
  // iterators into CurrentIterVals.
  for (const auto &I : PHIsToCompute) {
    PHINode *PHI = I.first;
    Constant *&NextPHI = NextIterVals[PHI];
    if (!NextPHI) {   // Not already computed.
      Value *BEValue = PHI->getIncomingValueForBlock(Latch);
      NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
    }
    if (NextPHI != I.second)
      StoppedEvolving = false;
  }

  // If all entries in CurrentIterVals == NextIterVals then we can stop
  // iterating, the loop can't continue to change.
  if (StoppedEvolving)
    return RetVal = CurrentIterVals[PN];

  CurrentIterVals.swap(NextIterVals);
}
8992}

8994const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
                                                        Value *Cond,
                                                        bool ExitWhen) {
PHINode *PN = getConstantEvolvingPHI(Cond, L);
if (!PN) return getCouldNotCompute();

// If the loop is canonicalized, the PHI will have exactly two entries.
// That's the only form we support here.
if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();

DenseMap<Instruction *, Constant *> CurrentIterVals;
BasicBlock *Header = L->getHeader();
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!")(static_cast <bool> (PN->getParent() == Header &&
 "Can't evaluate PHI not in loop header!") ? void (0) : __assert_fail
 ("PN->getParent() == Header && \"Can't evaluate PHI not in loop header!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9006, __extension__
 __PRETTY_FUNCTION__));

BasicBlock *Latch = L->getLoopLatch();
assert(Latch && "Should follow from NumIncomingValues == 2!")(static_cast <bool> (Latch && "Should follow from NumIncomingValues == 2!"
) ? void (0) : __assert_fail ("Latch && \"Should follow from NumIncomingValues == 2!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9009, __extension__
 __PRETTY_FUNCTION__));

for (PHINode &PHI : Header->phis()) {
  if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
    CurrentIterVals[&PHI] = StartCST;
}
if (!CurrentIterVals.count(PN))
  return getCouldNotCompute();

// Okay, we find a PHI node that defines the trip count of this loop.  Execute
// the loop symbolically to determine when the condition gets a value of
// "ExitWhen".
unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
const DataLayout &DL = getDataLayout();
for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
  auto *CondVal = dyn_cast_or_null<ConstantInt>(
      EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));

  // Couldn't symbolically evaluate.
  if (!CondVal) return getCouldNotCompute();

  if (CondVal->getValue() == uint64_t(ExitWhen)) {
    ++NumBruteForceTripCountsComputed;
    return getConstant(Type::getInt32Ty(getContext()), IterationNum);
  }

  // Update all the PHI nodes for the next iteration.
  DenseMap<Instruction *, Constant *> NextIterVals;

  // Create a list of which PHIs we need to compute. We want to do this before
  // calling EvaluateExpression on them because that may invalidate iterators
  // into CurrentIterVals.
  SmallVector<PHINode *, 8> PHIsToCompute;
  for (const auto &I : CurrentIterVals) {
    PHINode *PHI = dyn_cast<PHINode>(I.first);
    if (!PHI || PHI->getParent() != Header) continue;
    PHIsToCompute.push_back(PHI);
  }
  for (PHINode *PHI : PHIsToCompute) {
    Constant *&NextPHI = NextIterVals[PHI];
    if (NextPHI) continue;    // Already computed!

    Value *BEValue = PHI->getIncomingValueForBlock(Latch);
    NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
  }
  CurrentIterVals.swap(NextIterVals);
}

// Too many iterations were needed to evaluate.
return getCouldNotCompute();
9059}

9061const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
    ValuesAtScopes[V];
// Check to see if we've folded this expression at this loop before.
for (auto &LS : Values)
  if (LS.first == L)
    return LS.second ? LS.second : V;

Values.emplace_back(L, nullptr);

// Otherwise compute it.
const SCEV *C = computeSCEVAtScope(V, L);
for (auto &LS : reverse(ValuesAtScopes[V]))
  if (LS.first == L) {
    LS.second = C;
    if (!isa<SCEVConstant>(C))
      ValuesAtScopesUsers[C].push_back({L, V});
    break;
  }
return C;
9081}

9083/// This builds up a Constant using the ConstantExpr interface.  That way, we
9084/// will return Constants for objects which aren't represented by a
9085/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
9086/// Returns NULL if the SCEV isn't representable as a Constant.
9087static Constant *BuildConstantFromSCEV(const SCEV *V) {
switch (V->getSCEVType()) {
case scCouldNotCompute:
case scAddRecExpr:
  return nullptr;
case scConstant:
  return cast<SCEVConstant>(V)->getValue();
case scUnknown:
  return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
case scSignExtend: {
  const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
  if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
    return ConstantExpr::getSExt(CastOp, SS->getType());
  return nullptr;
}
case scZeroExtend: {
  const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
  if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
    return ConstantExpr::getZExt(CastOp, SZ->getType());
  return nullptr;
}
case scPtrToInt: {
  const SCEVPtrToIntExpr *P2I = cast<SCEVPtrToIntExpr>(V);
  if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand()))
    return ConstantExpr::getPtrToInt(CastOp, P2I->getType());

  return nullptr;
}
case scTruncate: {
  const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
  if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
    return ConstantExpr::getTrunc(CastOp, ST->getType());
  return nullptr;
}
case scAddExpr: {
  const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
  if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
    if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
      unsigned AS = PTy->getAddressSpace();
      Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
      C = ConstantExpr::getBitCast(C, DestPtrTy);
    }
    for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
      Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
      if (!C2)
        return nullptr;

      // First pointer!
      if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
        unsigned AS = C2->getType()->getPointerAddressSpace();
        std::swap(C, C2);
        Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
        // The offsets have been converted to bytes.  We can add bytes to an
        // i8* by GEP with the byte count in the first index.
        C = ConstantExpr::getBitCast(C, DestPtrTy);
      }

      // Don't bother trying to sum two pointers. We probably can't
      // statically compute a load that results from it anyway.
      if (C2->getType()->isPointerTy())
        return nullptr;

      if (C->getType()->isPointerTy()) {
        C = ConstantExpr::getGetElementPtr(Type::getInt8Ty(C->getContext()),
                                           C, C2);
      } else {
        C = ConstantExpr::getAdd(C, C2);
      }
    }
    return C;
  }
  return nullptr;
}
case scMulExpr: {
  const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
  if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
    // Don't bother with pointers at all.
    if (C->getType()->isPointerTy())
      return nullptr;
    for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
      Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
      if (!C2 || C2->getType()->isPointerTy())
        return nullptr;
      C = ConstantExpr::getMul(C, C2);
    }
    return C;
  }
  return nullptr;
}
case scUDivExpr: {
  const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
  if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
    if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
      if (LHS->getType() == RHS->getType())
        return ConstantExpr::getUDiv(LHS, RHS);
  return nullptr;
}
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr:
case scSequentialUMinExpr:
  return nullptr; // TODO: smax, umax, smin, umax, umin_seq.
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 9191);
9192}

9194const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
if (isa<SCEVConstant>(V)) return V;

// If this instruction is evolved from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
  if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
    if (PHINode *PN = dyn_cast<PHINode>(I)) {
      const Loop *CurrLoop = this->LI[I->getParent()];
      // Looking for loop exit value.
      if (CurrLoop && CurrLoop->getParentLoop() == L &&
          PN->getParent() == CurrLoop->getHeader()) {
        // Okay, there is no closed form solution for the PHI node.  Check
        // to see if the loop that contains it has a known backedge-taken
        // count.  If so, we may be able to force computation of the exit
        // value.
        const SCEV *BackedgeTakenCount = getBackedgeTakenCount(CurrLoop);
        // This trivial case can show up in some degenerate cases where
        // the incoming IR has not yet been fully simplified.
        if (BackedgeTakenCount->isZero()) {
          Value *InitValue = nullptr;
          bool MultipleInitValues = false;
          for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
            if (!CurrLoop->contains(PN->getIncomingBlock(i))) {
              if (!InitValue)
                InitValue = PN->getIncomingValue(i);
              else if (InitValue != PN->getIncomingValue(i)) {
                MultipleInitValues = true;
                break;
              }
            }
          }
          if (!MultipleInitValues && InitValue)
            return getSCEV(InitValue);
        }
        // Do we have a loop invariant value flowing around the backedge
        // for a loop which must execute the backedge?
        if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
            isKnownPositive(BackedgeTakenCount) &&
            PN->getNumIncomingValues() == 2) {

          unsigned InLoopPred =
              CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1;
          Value *BackedgeVal = PN->getIncomingValue(InLoopPred);
          if (CurrLoop->isLoopInvariant(BackedgeVal))
            return getSCEV(BackedgeVal);
        }
        if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
          // Okay, we know how many times the containing loop executes.  If
          // this is a constant evolving PHI node, get the final value at
          // the specified iteration number.
          Constant *RV = getConstantEvolutionLoopExitValue(
              PN, BTCC->getAPInt(), CurrLoop);
          if (RV) return getSCEV(RV);
        }
      }

      // If there is a single-input Phi, evaluate it at our scope. If we can
      // prove that this replacement does not break LCSSA form, use new value.
      if (PN->getNumOperands() == 1) {
        const SCEV *Input = getSCEV(PN->getOperand(0));
        const SCEV *InputAtScope = getSCEVAtScope(Input, L);
        // TODO: We can generalize it using LI.replacementPreservesLCSSAForm,
        // for the simplest case just support constants.
        if (isa<SCEVConstant>(InputAtScope)) return InputAtScope;
      }
    }

    // Okay, this is an expression that we cannot symbolically evaluate
    // into a SCEV.  Check to see if it's possible to symbolically evaluate
    // the arguments into constants, and if so, try to constant propagate the
    // result.  This is particularly useful for computing loop exit values.
    if (CanConstantFold(I)) {
      SmallVector<Constant *, 4> Operands;
      bool MadeImprovement = false;
      for (Value *Op : I->operands()) {
        if (Constant *C = dyn_cast<Constant>(Op)) {
          Operands.push_back(C);
          continue;
        }

        // If any of the operands is non-constant and if they are
        // non-integer and non-pointer, don't even try to analyze them
        // with scev techniques.
        if (!isSCEVable(Op->getType()))
          return V;

        const SCEV *OrigV = getSCEV(Op);
        const SCEV *OpV = getSCEVAtScope(OrigV, L);
        MadeImprovement |= OrigV != OpV;

        Constant *C = BuildConstantFromSCEV(OpV);
        if (!C) return V;
        if (C->getType() != Op->getType())
          C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
                                                            Op->getType(),
                                                            false),
                                    C, Op->getType());
        Operands.push_back(C);
      }

      // Check to see if getSCEVAtScope actually made an improvement.
      if (MadeImprovement) {
        Constant *C = nullptr;
        const DataLayout &DL = getDataLayout();
        if (const CmpInst *CI = dyn_cast<CmpInst>(I))
          C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
                                              Operands[1], DL, &TLI);
        else if (const LoadInst *Load = dyn_cast<LoadInst>(I)) {
          if (!Load->isVolatile())
            C = ConstantFoldLoadFromConstPtr(Operands[0], Load->getType(),
                                             DL);
        } else
          C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
        if (!C) return V;
        return getSCEV(C);
      }
    }
  }

  // This is some other type of SCEVUnknown, just return it.
  return V;
}

if (isa<SCEVCommutativeExpr>(V) || isa<SCEVSequentialMinMaxExpr>(V)) {
  const auto *Comm = cast<SCEVNAryExpr>(V);
  // Avoid performing the look-up in the common case where the specified
  // expression has no loop-variant portions.
  for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
    const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
    if (OpAtScope != Comm->getOperand(i)) {
      // Okay, at least one of these operands is loop variant but might be
      // foldable.  Build a new instance of the folded commutative expression.
      SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
                                          Comm->op_begin()+i);
      NewOps.push_back(OpAtScope);

      for (++i; i != e; ++i) {
        OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
        NewOps.push_back(OpAtScope);
      }
      if (isa<SCEVAddExpr>(Comm))
        return getAddExpr(NewOps, Comm->getNoWrapFlags());
      if (isa<SCEVMulExpr>(Comm))
        return getMulExpr(NewOps, Comm->getNoWrapFlags());
      if (isa<SCEVMinMaxExpr>(Comm))
        return getMinMaxExpr(Comm->getSCEVType(), NewOps);
      if (isa<SCEVSequentialMinMaxExpr>(Comm))
        return getSequentialMinMaxExpr(Comm->getSCEVType(), NewOps);
      llvm_unreachable("Unknown commutative / sequential min/max SCEV type!")::llvm::llvm_unreachable_internal("Unknown commutative / sequential min/max SCEV type!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9343);
    }
  }
  // If we got here, all operands are loop invariant.
  return Comm;
}

if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
  const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
  const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
  if (LHS == Div->getLHS() && RHS == Div->getRHS())
    return Div;   // must be loop invariant
  return getUDivExpr(LHS, RHS);
}

// If this is a loop recurrence for a loop that does not contain L, then we
// are dealing with the final value computed by the loop.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
  // First, attempt to evaluate each operand.
  // Avoid performing the look-up in the common case where the specified
  // expression has no loop-variant portions.
  for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
    const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
    if (OpAtScope == AddRec->getOperand(i))
      continue;

    // Okay, at least one of these operands is loop variant but might be
    // foldable.  Build a new instance of the folded commutative expression.
    SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
                                        AddRec->op_begin()+i);
    NewOps.push_back(OpAtScope);
    for (++i; i != e; ++i)
      NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));

    const SCEV *FoldedRec =
      getAddRecExpr(NewOps, AddRec->getLoop(),
                    AddRec->getNoWrapFlags(SCEV::FlagNW));
    AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
    // The addrec may be folded to a nonrecurrence, for example, if the
    // induction variable is multiplied by zero after constant folding. Go
    // ahead and return the folded value.
    if (!AddRec)
      return FoldedRec;
    break;
  }

  // If the scope is outside the addrec's loop, evaluate it by using the
  // loop exit value of the addrec.
  if (!AddRec->getLoop()->contains(L)) {
    // To evaluate this recurrence, we need to know how many times the AddRec
    // loop iterates.  Compute this now.
    const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
    if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;

    // Then, evaluate the AddRec.
    return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
  }

  return AddRec;
}

if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
  const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
  if (Op == Cast->getOperand())
    return Cast;  // must be loop invariant
  return getCastExpr(Cast->getSCEVType(), Op, Cast->getType());
}

llvm_unreachable("Unknown SCEV type!")::llvm::llvm_unreachable_internal("Unknown SCEV type!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 9411);
9412}

9414const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
return getSCEVAtScope(getSCEV(V), L);
9416}

9418const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
  return stripInjectiveFunctions(ZExt->getOperand());
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
  return stripInjectiveFunctions(SExt->getOperand());
return S;
9424}

9426/// Finds the minimum unsigned root of the following equation:
9427///
9428///     A * X = B (mod N)
9429///
9430/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
9431/// A and B isn't important.
9432///
9433/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
9434static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
                                             ScalarEvolution &SE) {
uint32_t BW = A.getBitWidth();
assert(BW == SE.getTypeSizeInBits(B->getType()))(static_cast <bool> (BW == SE.getTypeSizeInBits(B->getType
())) ? void (0) : __assert_fail ("BW == SE.getTypeSizeInBits(B->getType())"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9437, __extension__
 __PRETTY_FUNCTION__));
assert(A != 0 && "A must be non-zero.")(static_cast <bool> (A != 0 && "A must be non-zero."
) ? void (0) : __assert_fail ("A != 0 && \"A must be non-zero.\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9438, __extension__
 __PRETTY_FUNCTION__));

// 1. D = gcd(A, N)
//
// The gcd of A and N may have only one prime factor: 2. The number of
// trailing zeros in A is its multiplicity
uint32_t Mult2 = A.countTrailingZeros();
// D = 2^Mult2

// 2. Check if B is divisible by D.
//
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
// is not less than multiplicity of this prime factor for D.
if (SE.GetMinTrailingZeros(B) < Mult2)
  return SE.getCouldNotCompute();

// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
// modulo (N / D).
//
// If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
// (N / D) in general. The inverse itself always fits into BW bits, though,
// so we immediately truncate it.
APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
APInt Mod(BW + 1, 0);
Mod.setBit(BW - Mult2);  // Mod = N / D
APInt I = AD.multiplicativeInverse(Mod).trunc(BW);

// 4. Compute the minimum unsigned root of the equation:
// I * (B / D) mod (N / D)
// To simplify the computation, we factor out the divide by D:
// (I * B mod N) / D
const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
9471}

9473/// For a given quadratic addrec, generate coefficients of the corresponding
9474/// quadratic equation, multiplied by a common value to ensure that they are
9475/// integers.
9476/// The returned value is a tuple { A, B, C, M, BitWidth }, where
9477/// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
9478/// were multiplied by, and BitWidth is the bit width of the original addrec
9479/// coefficients.
9480/// This function returns None if the addrec coefficients are not compile-
9481/// time constants.
9482static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
9483GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!")(static_cast <bool> (AddRec->getNumOperands() == 3 &&
 "This is not a quadratic chrec!") ? void (0) : __assert_fail
 ("AddRec->getNumOperands() == 3 && \"This is not a quadratic chrec!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9484, __extension__
 __PRETTY_FUNCTION__));
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": analyzing quadratic addrec: "
 << *AddRec << '\n'; } } while (false)
                  << *AddRec << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": analyzing quadratic addrec: "
 << *AddRec << '\n'; } } while (false);

// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
  LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": coefficients are not constant\n"
; } } while (false);
  return None;
}

APInt L = LC->getAPInt();
APInt M = MC->getAPInt();
APInt N = NC->getAPInt();
assert(!N.isZero() && "This is not a quadratic addrec")(static_cast <bool> (!N.isZero() && "This is not a quadratic addrec"
) ? void (0) : __assert_fail ("!N.isZero() && \"This is not a quadratic addrec\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9500, __extension__
 __PRETTY_FUNCTION__));

unsigned BitWidth = LC->getAPInt().getBitWidth();
unsigned NewWidth = BitWidth + 1;
LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": addrec coeff bw: "
 << BitWidth << '\n'; } } while (false)
                  << BitWidth << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": addrec coeff bw: "
 << BitWidth << '\n'; } } while (false);
// The sign-extension (as opposed to a zero-extension) here matches the
// extension used in SolveQuadraticEquationWrap (with the same motivation).
N = N.sext(NewWidth);
M = M.sext(NewWidth);
L = L.sext(NewWidth);

// The increments are M, M+N, M+2N, ..., so the accumulated values are
//   L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
//   L+M, L+2M+N, L+3M+3N, ...
// After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
//
// The equation Acc = 0 is then
//   L + nM + n(n-1)/2 N = 0,  or  2L + 2M n + n(n-1) N = 0.
// In a quadratic form it becomes:
//   N n^2 + (2M-N) n + 2L = 0.

APInt A = N;
APInt B = 2 * M - A;
APInt C = 2 * L;
APInt T = APInt(NewWidth, 2);
LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << Bdo { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": equation "
 << A << "x^2 + " << B << "x + " <<
 C << ", coeff bw: " << NewWidth << ", multiplied by "
 << T << '\n'; } } while (false)
                  << "x + " << C << ", coeff bw: " << NewWidthdo { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": equation "
 << A << "x^2 + " << B << "x + " <<
 C << ", coeff bw: " << NewWidth << ", multiplied by "
 << T << '\n'; } } while (false)
                  << ", multiplied by " << T << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": equation "
 << A << "x^2 + " << B << "x + " <<
 C << ", coeff bw: " << NewWidth << ", multiplied by "
 << T << '\n'; } } while (false);
return std::make_tuple(A, B, C, T, BitWidth);
9530}

9532/// Helper function to compare optional APInts:
9533/// (a) if X and Y both exist, return min(X, Y),
9534/// (b) if neither X nor Y exist, return None,
9535/// (c) if exactly one of X and Y exists, return that value.
9536static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
if (X.hasValue() && Y.hasValue()) {
  unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
  APInt XW = X->sextOrSelf(W);
  APInt YW = Y->sextOrSelf(W);
  return XW.slt(YW) ? *X : *Y;
}
if (!X.hasValue() && !Y.hasValue())
  return None;
return X.hasValue() ? *X : *Y;
9546}

9548/// Helper function to truncate an optional APInt to a given BitWidth.
9549/// When solving addrec-related equations, it is preferable to return a value
9550/// that has the same bit width as the original addrec's coefficients. If the
9551/// solution fits in the original bit width, truncate it (except for i1).
9552/// Returning a value of a different bit width may inhibit some optimizations.
9553///
9554/// In general, a solution to a quadratic equation generated from an addrec
9555/// may require BW+1 bits, where BW is the bit width of the addrec's
9556/// coefficients. The reason is that the coefficients of the quadratic
9557/// equation are BW+1 bits wide (to avoid truncation when converting from
9558/// the addrec to the equation).
9559static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
if (!X.hasValue())
  return None;
unsigned W = X->getBitWidth();
if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
  return X->trunc(BitWidth);
return X;
9566}

9568/// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
9569/// iterations. The values L, M, N are assumed to be signed, and they
9570/// should all have the same bit widths.
9571/// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
9572/// where BW is the bit width of the addrec's coefficients.
9573/// If the calculated value is a BW-bit integer (for BW > 1), it will be
9574/// returned as such, otherwise the bit width of the returned value may
9575/// be greater than BW.
9576///
9577/// This function returns None if
9578/// (a) the addrec coefficients are not constant, or
9579/// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
9580///     like x^2 = 5, no integer solutions exist, in other cases an integer
9581///     solution may exist, but SolveQuadraticEquationWrap may fail to find it.
9582static Optional<APInt>
9583SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
  return None;

std::tie(A, B, C, M, BitWidth) = *T;
LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": solving for unsigned overflow\n"
; } } while (false);
Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
if (!X.hasValue())
  return None;

ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
if (!V->isZero())
  return None;

return TruncIfPossible(X, BitWidth);
9602}

9604/// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
9605/// iterations. The values M, N are assumed to be signed, and they
9606/// should all have the same bit widths.
9607/// Find the least n such that c(n) does not belong to the given range,
9608/// while c(n-1) does.
9609///
9610/// This function returns None if
9611/// (a) the addrec coefficients are not constant, or
9612/// (b) SolveQuadraticEquationWrap was unable to find a solution for the
9613///     bounds of the range.
9614static Optional<APInt>
9615SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
                        const ConstantRange &Range, ScalarEvolution &SE) {
assert(AddRec->getOperand(0)->isZero() &&(static_cast <bool> (AddRec->getOperand(0)->isZero
() && "Starting value of addrec should be 0") ? void (
0) : __assert_fail ("AddRec->getOperand(0)->isZero() && \"Starting value of addrec should be 0\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9618, __extension__
 __PRETTY_FUNCTION__))
       "Starting value of addrec should be 0")(static_cast <bool> (AddRec->getOperand(0)->isZero
() && "Starting value of addrec should be 0") ? void (
0) : __assert_fail ("AddRec->getOperand(0)->isZero() && \"Starting value of addrec should be 0\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9618, __extension__
 __PRETTY_FUNCTION__));
LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": solving boundary crossing for range "
 << Range << ", addrec " << *AddRec <<
 '\n'; } } while (false)
                  << Range << ", addrec " << *AddRec << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << __func__ << ": solving boundary crossing for range "
 << Range << ", addrec " << *AddRec <<
 '\n'; } } while (false);
// This case is handled in getNumIterationsInRange. Here we can assume that
// we start in the range.
assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&(static_cast <bool> (Range.contains(APInt(SE.getTypeSizeInBits
(AddRec->getType()), 0)) && "Addrec's initial value should be in range"
) ? void (0) : __assert_fail ("Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) && \"Addrec's initial value should be in range\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9624, __extension__
 __PRETTY_FUNCTION__))
       "Addrec's initial value should be in range")(static_cast <bool> (Range.contains(APInt(SE.getTypeSizeInBits
(AddRec->getType()), 0)) && "Addrec's initial value should be in range"
) ? void (0) : __assert_fail ("Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) && \"Addrec's initial value should be in range\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 9624, __extension__
 __PRETTY_FUNCTION__));

APInt A, B, C, M;
unsigned BitWidth;
auto T = GetQuadraticEquation(AddRec);
if (!T.hasValue())
  return None;

// Be careful about the return value: there can be two reasons for not
// returning an actual number. First, if no solutions to the equations
// were found, and second, if the solutions don't leave the given range.
// The first case means that the actual solution is "unknown", the second
// means that it's known, but not valid. If the solution is unknown, we
// cannot make any conclusions.
// Return a pair: the optional solution and a flag indicating if the
// solution was found.
auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
  // Solve for signed overflow and unsigned overflow, pick the lower
  // solution.
  LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: checking boundary "
 << Bound << " (before multiplying by " << M
 << ")\n"; } } while (false)
                    << Bound << " (before multiplying by " << M << ")\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: checking boundary "
 << Bound << " (before multiplying by " << M
 << ")\n"; } } while (false);
  Bound *= M; // The quadratic equation multiplier.

  Optional<APInt> SO = None;
  if (BitWidth > 1) {
    LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: solving for "
 "signed overflow\n"; } } while (false)
                         "signed overflow\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: solving for "
 "signed overflow\n"; } } while (false);
    SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
  }
  LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: solving for "
 "unsigned overflow\n"; } } while (false)
                       "unsigned overflow\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("scalar-evolution")) { dbgs() << "SolveQuadraticAddRecRange: solving for "
 "unsigned overflow\n"; } } while (false);
  Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
                                                            BitWidth+1);

  auto LeavesRange = [&] (const APInt &X) {
    ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
    ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
    if (Range.contains(V0->getValue()))
      return false;
    // X should be at least 1, so X-1 is non-negative.
    ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
    ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
    if (Range.contains(V1->getValue()))
      return true;
    return false;
  };

  // If SolveQuadraticEquationWrap returns None, it means that there can
  // be a solution, but the function failed to find it. We cannot treat it
  // as "no solution".
  if (!SO.hasValue() || !UO.hasValue())
    return { None, false };

  // Check the smaller value first to see if it leaves the range.
  // At this point, both SO and UO must have values.
  Optional<APInt> Min = MinOptional(SO, UO);
  if (LeavesRange(*Min))
    return { Min, true };
  Optional<APInt> Max = Min == SO ? UO : SO;
  if (LeavesRange(*Max))
    return { Max, true };

  // Solutions were found, but were eliminated, hence the "true".
  return { None, true };
};

std::tie(A, B, C, M, BitWidth) = *T;
// Lower bound is inclusive, subtract 1 to represent the exiting value.
APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
auto SL = SolveForBoundary(Lower);
auto SU = SolveForBoundary(Upper);
// If any of the solutions was unknown, no meaninigful conclusions can
// be made.
if (!SL.second || !SU.second)
  return None;

// Claim: The correct solution is not some value between Min and Max.
//
// Justification: Assuming that Min and Max are different values, one of
// them is when the first signed overflow happens, the other is when the
// first unsigned overflow happens. Crossing the range boundary is only
// possible via an overflow (treating 0 as a special case of it, modeling
// an overflow as crossing k*2^W for some k).
//
// The interesting case here is when Min was eliminated as an invalid
// solution, but Max was not. The argument is that if there was another
// overflow between Min and Max, it would also have been eliminated if
// it was considered.
//
// For a given boundary, it is possible to have two overflows of the same
// type (signed/unsigned) without having the other type in between: this
// can happen when the vertex of the parabola is between the iterations
// corresponding to the overflows. This is only possible when the two
// overflows cross k*2^W for the same k. In such case, if the second one
// left the range (and was the first one to do so), the first overflow
// would have to enter the range, which would mean that either we had left
// the range before or that we started outside of it. Both of these cases
// are contradictions.
//
// Claim: In the case where SolveForBoundary returns None, the correct
// solution is not some value between the Max for this boundary and the
// Min of the other boundary.
//
// Justification: Assume that we had such Max_A and Min_B corresponding
// to range boundaries A and B and such that Max_A < Min_B. If there was
// a solution between Max_A and Min_B, it would have to be caused by an
// overflow corresponding to either A or B. It cannot correspond to B,
// since Min_B is the first occurrence of such an overflow. If it
// corresponded to A, it would have to be either a signed or an unsigned
// overflow that is larger than both eliminated overflows for A. But
// between the eliminated overflows and this overflow, the values would
// cover the entire value space, thus crossing the other boundary, which
// is a contradiction.

return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
9740}

9742ScalarEvolution::ExitLimit
9743ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
                            bool AllowPredicates) {

// This is only used for loops with a "x != y" exit test. The exit condition
// is now expressed as a single expression, V = x-y. So the exit test is
// effectively V != 0.  We know and take advantage of the fact that this
// expression only being used in a comparison by zero context.

SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// If the value is a constant
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
  // If the value is already zero, the branch will execute zero times.
  if (C->getValue()->isZero()) return C;
  return getCouldNotCompute();  // Otherwise it will loop infinitely.
}

const SCEVAddRecExpr *AddRec =
    dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));

if (!AddRec && AllowPredicates)
  // Try to make this an AddRec using runtime tests, in the first X
  // iterations of this loop, where X is the SCEV expression found by the
  // algorithm below.
  AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);

if (!AddRec || AddRec->getLoop() != L)
  return getCouldNotCompute();

// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
// the quadratic equation to solve it.
if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
  // We can only use this value if the chrec ends up with an exact zero
  // value at this index.  When solving for "X*X != 5", for example, we
  // should not accept a root of 2.
  if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
    const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
    return ExitLimit(R, R, false, Predicates);
  }
  return getCouldNotCompute();
}

// Otherwise we can only handle this if it is affine.
if (!AddRec->isAffine())
  return getCouldNotCompute();

// If this is an affine expression, the execution count of this branch is
// the minimum unsigned root of the following equation:
//
//     Start + Step*N = 0 (mod 2^BW)
//
// equivalent to:
//
//             Step*N = -Start (mod 2^BW)
//
// where BW is the common bit width of Start and Step.

// Get the initial value for the loop.
const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());

// For now we handle only constant steps.
//
// TODO: Handle a nonconstant Step given AddRec<NUW>. If the
// AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
// to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
// We have not yet seen any such cases.
const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
if (!StepC || StepC->getValue()->isZero())
  return getCouldNotCompute();

// For positive steps (counting up until unsigned overflow):
//   N = -Start/Step (as unsigned)
// For negative steps (counting down to zero):
//   N = Start/-Step
// First compute the unsigned distance from zero in the direction of Step.
bool CountDown = StepC->getAPInt().isNegative();
const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);

// Handle unitary steps, which cannot wraparound.
// 1*N = -Start; -1*N = Start (mod 2^BW), so:
//   N = Distance (as unsigned)
if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
  APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, L));
  MaxBECount = APIntOps::umin(MaxBECount, getUnsignedRangeMax(Distance));

  // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
  // we end up with a loop whose backedge-taken count is n - 1.  Detect this
  // case, and see if we can improve the bound.
  //
  // Explicitly handling this here is necessary because getUnsignedRange
  // isn't context-sensitive; it doesn't know that we only care about the
  // range inside the loop.
  const SCEV *Zero = getZero(Distance->getType());
  const SCEV *One = getOne(Distance->getType());
  const SCEV *DistancePlusOne = getAddExpr(Distance, One);
  if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
    // If Distance + 1 doesn't overflow, we can compute the maximum distance
    // as "unsigned_max(Distance + 1) - 1".
    ConstantRange CR = getUnsignedRange(DistancePlusOne);
    MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
  }
  return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
}

// If the condition controls loop exit (the loop exits only if the expression
// is true) and the addition is no-wrap we can use unsigned divide to
// compute the backedge count.  In this case, the step may not divide the
// distance, but we don't care because if the condition is "missed" the loop
// will have undefined behavior due to wrapping.
if (ControlsExit && AddRec->hasNoSelfWrap() &&
    loopHasNoAbnormalExits(AddRec->getLoop())) {
  const SCEV *Exact =
      getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
  const SCEV *Max = getCouldNotCompute();
  if (Exact != getCouldNotCompute()) {
    APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, L));
    Max = getConstant(APIntOps::umin(MaxInt, getUnsignedRangeMax(Exact)));
  }
  return ExitLimit(Exact, Max, false, Predicates);
}

// Solve the general equation.
const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
                                             getNegativeSCEV(Start), *this);

const SCEV *M = E;
if (E != getCouldNotCompute()) {
  APInt MaxWithGuards = getUnsignedRangeMax(applyLoopGuards(E, L));
  M = getConstant(APIntOps::umin(MaxWithGuards, getUnsignedRangeMax(E)));
}
return ExitLimit(E, M, false, Predicates);
9874}

9876ScalarEvolution::ExitLimit
9877ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
// Loops that look like: while (X == 0) are very strange indeed.  We don't
// handle them yet except for the trivial case.  This could be expanded in the
// future as needed.

// If the value is a constant, check to see if it is known to be non-zero
// already.  If so, the backedge will execute zero times.
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
  if (!C->getValue()->isZero())
    return getZero(C->getType());
  return getCouldNotCompute();  // Otherwise it will loop infinitely.
}

// We could implement others, but I really doubt anyone writes loops like
// this, and if they did, they would already be constant folded.
return getCouldNotCompute();
9893}

9895std::pair<const BasicBlock *, const BasicBlock *>
9896ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB)
  const {
// If the block has a unique predecessor, then there is no path from the
// predecessor to the block that does not go through the direct edge
// from the predecessor to the block.
if (const BasicBlock *Pred = BB->getSinglePredecessor())
  return {Pred, BB};

// A loop's header is defined to be a block that dominates the loop.
// If the header has a unique predecessor outside the loop, it must be
// a block that has exactly one successor that can reach the loop.
if (const Loop *L = LI.getLoopFor(BB))
  return {L->getLoopPredecessor(), L->getHeader()};

return {nullptr, nullptr};
9911}

9913/// SCEV structural equivalence is usually sufficient for testing whether two
9914/// expressions are equal, however for the purposes of looking for a condition
9915/// guarding a loop, it can be useful to be a little more general, since a
9916/// front-end may have replicated the controlling expression.
9917static bool HasSameValue(const SCEV *A, const SCEV *B) {
// Quick check to see if they are the same SCEV.
if (A == B) return true;

auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
  // Not all instructions that are "identical" compute the same value.  For
  // instance, two distinct alloca instructions allocating the same type are
  // identical and do not read memory; but compute distinct values.
  return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
};

// Otherwise, if they're both SCEVUnknown, it's possible that they hold
// two different instructions with the same value. Check for this case.
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
  if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
    if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
      if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
        if (ComputesEqualValues(AI, BI))
          return true;

// Otherwise assume they may have a different value.
return false;
9939}

9941bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
                                         const SCEV *&LHS, const SCEV *&RHS,
                                         unsigned Depth) {
bool Changed = false;
// Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
// '0 != 0'.
auto TrivialCase = [&](bool TriviallyTrue) {
  LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
  Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
  return true;
};
// If we hit the max recursion limit bail out.
if (Depth >= 3)
  return false;

// Canonicalize a constant to the right side.
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
  // Check for both operands constant.
  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
    if (ConstantExpr::getICmp(Pred,
                              LHSC->getValue(),
                              RHSC->getValue())->isNullValue())
      return TrivialCase(false);
    else
      return TrivialCase(true);
  }
  // Otherwise swap the operands to put the constant on the right.
  std::swap(LHS, RHS);
  Pred = ICmpInst::getSwappedPredicate(Pred);
  Changed = true;
}

// If we're comparing an addrec with a value which is loop-invariant in the
// addrec's loop, put the addrec on the left. Also make a dominance check,
// as both operands could be addrecs loop-invariant in each other's loop.
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
  const Loop *L = AR->getLoop();
  if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
    std::swap(LHS, RHS);
    Pred = ICmpInst::getSwappedPredicate(Pred);
    Changed = true;
  }
}

// If there's a constant operand, canonicalize comparisons with boundary
// cases, and canonicalize *-or-equal comparisons to regular comparisons.
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
  const APInt &RA = RC->getAPInt();

  bool SimplifiedByConstantRange = false;

  if (!ICmpInst::isEquality(Pred)) {
    ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
    if (ExactCR.isFullSet())
      return TrivialCase(true);
    else if (ExactCR.isEmptySet())
      return TrivialCase(false);

    APInt NewRHS;
    CmpInst::Predicate NewPred;
    if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
        ICmpInst::isEquality(NewPred)) {
      // We were able to convert an inequality to an equality.
      Pred = NewPred;
      RHS = getConstant(NewRHS);
      Changed = SimplifiedByConstantRange = true;
    }
  }

  if (!SimplifiedByConstantRange) {
    switch (Pred) {
    default:
      break;
    case ICmpInst::ICMP_EQ:
    case ICmpInst::ICMP_NE:
      // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
      if (!RA)
        if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
          if (const SCEVMulExpr *ME =
                  dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
            if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
                ME->getOperand(0)->isAllOnesValue()) {
              RHS = AE->getOperand(1);
              LHS = ME->getOperand(1);
              Changed = true;
            }
      break;


      // The "Should have been caught earlier!" messages refer to the fact
      // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
      // should have fired on the corresponding cases, and canonicalized the
      // check to trivial case.

    case ICmpInst::ICMP_UGE:
      assert(!RA.isMinValue() && "Should have been caught earlier!")(static_cast <bool> (!RA.isMinValue() && "Should have been caught earlier!"
) ? void (0) : __assert_fail ("!RA.isMinValue() && \"Should have been caught earlier!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10036, __extension__
 __PRETTY_FUNCTION__));
      Pred = ICmpInst::ICMP_UGT;
      RHS = getConstant(RA - 1);
      Changed = true;
      break;
    case ICmpInst::ICMP_ULE:
      assert(!RA.isMaxValue() && "Should have been caught earlier!")(static_cast <bool> (!RA.isMaxValue() && "Should have been caught earlier!"
) ? void (0) : __assert_fail ("!RA.isMaxValue() && \"Should have been caught earlier!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10042, __extension__
 __PRETTY_FUNCTION__));
      Pred = ICmpInst::ICMP_ULT;
      RHS = getConstant(RA + 1);
      Changed = true;
      break;
    case ICmpInst::ICMP_SGE:
      assert(!RA.isMinSignedValue() && "Should have been caught earlier!")(static_cast <bool> (!RA.isMinSignedValue() && "Should have been caught earlier!"
) ? void (0) : __assert_fail ("!RA.isMinSignedValue() && \"Should have been caught earlier!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10048, __extension__
 __PRETTY_FUNCTION__));
      Pred = ICmpInst::ICMP_SGT;
      RHS = getConstant(RA - 1);
      Changed = true;
      break;
    case ICmpInst::ICMP_SLE:
      assert(!RA.isMaxSignedValue() && "Should have been caught earlier!")(static_cast <bool> (!RA.isMaxSignedValue() && "Should have been caught earlier!"
) ? void (0) : __assert_fail ("!RA.isMaxSignedValue() && \"Should have been caught earlier!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10054, __extension__
 __PRETTY_FUNCTION__));
      Pred = ICmpInst::ICMP_SLT;
      RHS = getConstant(RA + 1);
      Changed = true;
      break;
    }
  }
}

// Check for obvious equality.
if (HasSameValue(LHS, RHS)) {
  if (ICmpInst::isTrueWhenEqual(Pred))
    return TrivialCase(true);
  if (ICmpInst::isFalseWhenEqual(Pred))
    return TrivialCase(false);
}

// If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
// adding or subtracting 1 from one of the operands.
switch (Pred) {
case ICmpInst::ICMP_SLE:
  if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
    RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
                     SCEV::FlagNSW);
    Pred = ICmpInst::ICMP_SLT;
    Changed = true;
  } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
    LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
                     SCEV::FlagNSW);
    Pred = ICmpInst::ICMP_SLT;
    Changed = true;
  }
  break;
case ICmpInst::ICMP_SGE:
  if (!getSignedRangeMin(RHS).isMinSignedValue()) {
    RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
                     SCEV::FlagNSW);
    Pred = ICmpInst::ICMP_SGT;
    Changed = true;
  } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
    LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
                     SCEV::FlagNSW);
    Pred = ICmpInst::ICMP_SGT;
    Changed = true;
  }
  break;
case ICmpInst::ICMP_ULE:
  if (!getUnsignedRangeMax(RHS).isMaxValue()) {
    RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
                     SCEV::FlagNUW);
    Pred = ICmpInst::ICMP_ULT;
    Changed = true;
  } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
    LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
    Pred = ICmpInst::ICMP_ULT;
    Changed = true;
  }
  break;
case ICmpInst::ICMP_UGE:
  if (!getUnsignedRangeMin(RHS).isMinValue()) {
    RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
    Pred = ICmpInst::ICMP_UGT;
    Changed = true;
  } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
    LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
                     SCEV::FlagNUW);
    Pred = ICmpInst::ICMP_UGT;
    Changed = true;
  }
  break;
default:
  break;
}

// TODO: More simplifications are possible here.

// Recursively simplify until we either hit a recursion limit or nothing
// changes.
if (Changed)
  return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);

return Changed;
10136}

10138bool ScalarEvolution::isKnownNegative(const SCEV *S) {
return getSignedRangeMax(S).isNegative();
10140}

10142bool ScalarEvolution::isKnownPositive(const SCEV *S) {
return getSignedRangeMin(S).isStrictlyPositive();
10144}

10146bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
return !getSignedRangeMin(S).isNegative();
10148}

10150bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
return !getSignedRangeMax(S).isStrictlyPositive();
10152}

10154bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
return getUnsignedRangeMin(S) != 0;
10156}

10158std::pair<const SCEV *, const SCEV *>
10159ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
// Compute SCEV on entry of loop L.
const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
if (Start == getCouldNotCompute())
  return { Start, Start };
// Compute post increment SCEV for loop L.
const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
assert(PostInc != getCouldNotCompute() && "Unexpected could not compute")(static_cast <bool> (PostInc != getCouldNotCompute() &&
 "Unexpected could not compute") ? void (0) : __assert_fail (
"PostInc != getCouldNotCompute() && \"Unexpected could not compute\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10166, __extension__
 __PRETTY_FUNCTION__));
return { Start, PostInc };
10168}

10170bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
                                        const SCEV *LHS, const SCEV *RHS) {
// First collect all loops.
SmallPtrSet<const Loop *, 8> LoopsUsed;
getUsedLoops(LHS, LoopsUsed);
getUsedLoops(RHS, LoopsUsed);

if (LoopsUsed.empty())
  return false;

// Domination relationship must be a linear order on collected loops.
10181#ifndef NDEBUG
for (auto *L1 : LoopsUsed)
  for (auto *L2 : LoopsUsed)
    assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||(static_cast <bool> ((DT.dominates(L1->getHeader(), L2
->getHeader()) || DT.dominates(L2->getHeader(), L1->
getHeader())) && "Domination relationship is not a linear order"
) ? void (0) : __assert_fail ("(DT.dominates(L1->getHeader(), L2->getHeader()) || DT.dominates(L2->getHeader(), L1->getHeader())) && \"Domination relationship is not a linear order\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10186, __extension__
 __PRETTY_FUNCTION__))
            DT.dominates(L2->getHeader(), L1->getHeader())) &&(static_cast <bool> ((DT.dominates(L1->getHeader(), L2
->getHeader()) || DT.dominates(L2->getHeader(), L1->
getHeader())) && "Domination relationship is not a linear order"
) ? void (0) : __assert_fail ("(DT.dominates(L1->getHeader(), L2->getHeader()) || DT.dominates(L2->getHeader(), L1->getHeader())) && \"Domination relationship is not a linear order\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10186, __extension__
 __PRETTY_FUNCTION__))
           "Domination relationship is not a linear order")(static_cast <bool> ((DT.dominates(L1->getHeader(), L2
->getHeader()) || DT.dominates(L2->getHeader(), L1->
getHeader())) && "Domination relationship is not a linear order"
) ? void (0) : __assert_fail ("(DT.dominates(L1->getHeader(), L2->getHeader()) || DT.dominates(L2->getHeader(), L1->getHeader())) && \"Domination relationship is not a linear order\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10186, __extension__
 __PRETTY_FUNCTION__));
10187#endif

const Loop *MDL =
    *std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
                      [&](const Loop *L1, const Loop *L2) {
       return DT.properlyDominates(L1->getHeader(), L2->getHeader());
     });

// Get init and post increment value for LHS.
auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
// if LHS contains unknown non-invariant SCEV then bail out.
if (SplitLHS.first == getCouldNotCompute())
  return false;
assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC")(static_cast <bool> (SplitLHS.second != getCouldNotCompute
() && "Unexpected CNC") ? void (0) : __assert_fail ("SplitLHS.second != getCouldNotCompute() && \"Unexpected CNC\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10200, __extension__
 __PRETTY_FUNCTION__));
// Get init and post increment value for RHS.
auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
// if RHS contains unknown non-invariant SCEV then bail out.
if (SplitRHS.first == getCouldNotCompute())
  return false;
assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC")(static_cast <bool> (SplitRHS.second != getCouldNotCompute
() && "Unexpected CNC") ? void (0) : __assert_fail ("SplitRHS.second != getCouldNotCompute() && \"Unexpected CNC\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10206, __extension__
 __PRETTY_FUNCTION__));
// It is possible that init SCEV contains an invariant load but it does
// not dominate MDL and is not available at MDL loop entry, so we should
// check it here.
if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
    !isAvailableAtLoopEntry(SplitRHS.first, MDL))
  return false;

// It seems backedge guard check is faster than entry one so in some cases
// it can speed up whole estimation by short circuit
return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
                                   SplitRHS.second) &&
       isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
10219}

10221bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
                                     const SCEV *LHS, const SCEV *RHS) {
// Canonicalize the inputs first.
(void)SimplifyICmpOperands(Pred, LHS, RHS);

if (isKnownViaInduction(Pred, LHS, RHS))
  return true;

if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
  return true;

// Otherwise see what can be done with some simple reasoning.
return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
10234}

10236Optional<bool> ScalarEvolution::evaluatePredicate(ICmpInst::Predicate Pred,
                                                const SCEV *LHS,
                                                const SCEV *RHS) {
if (isKnownPredicate(Pred, LHS, RHS))
  return true;
else if (isKnownPredicate(ICmpInst::getInversePredicate(Pred), LHS, RHS))
  return false;
return None;
10244}

10246bool ScalarEvolution::isKnownPredicateAt(ICmpInst::Predicate Pred,
                                       const SCEV *LHS, const SCEV *RHS,
                                       const Instruction *CtxI) {
// TODO: Analyze guards and assumes from Context's block.
return isKnownPredicate(Pred, LHS, RHS) ||
       isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS);
10252}

10254Optional<bool> ScalarEvolution::evaluatePredicateAt(ICmpInst::Predicate Pred,
                                                  const SCEV *LHS,
                                                  const SCEV *RHS,
                                                  const Instruction *CtxI) {
Optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS);
if (KnownWithoutContext)
  return KnownWithoutContext;

if (isBasicBlockEntryGuardedByCond(CtxI->getParent(), Pred, LHS, RHS))
  return true;
else if (isBasicBlockEntryGuardedByCond(CtxI->getParent(),
                                        ICmpInst::getInversePredicate(Pred),
                                        LHS, RHS))
  return false;
return None;
10269}

10271bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
                                            const SCEVAddRecExpr *LHS,
                                            const SCEV *RHS) {
const Loop *L = LHS->getLoop();
return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
20
←
Calling 'ScalarEvolution::isLoopEntryGuardedByCond'→
       isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
10277}

10279Optional<ScalarEvolution::MonotonicPredicateType>
10280ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS,
                                         ICmpInst::Predicate Pred) {
auto Result = getMonotonicPredicateTypeImpl(LHS, Pred);

10284#ifndef NDEBUG
// Verify an invariant: inverting the predicate should turn a monotonically
// increasing change to a monotonically decreasing one, and vice versa.
if (Result) {
  auto ResultSwapped =
      getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred));

  assert(ResultSwapped.hasValue() && "should be able to analyze both!")(static_cast <bool> (ResultSwapped.hasValue() &&
 "should be able to analyze both!") ? void (0) : __assert_fail
 ("ResultSwapped.hasValue() && \"should be able to analyze both!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10291, __extension__
 __PRETTY_FUNCTION__));
  assert(ResultSwapped.getValue() != Result.getValue() &&(static_cast <bool> (ResultSwapped.getValue() != Result
.getValue() && "monotonicity should flip as we flip the predicate"
) ? void (0) : __assert_fail ("ResultSwapped.getValue() != Result.getValue() && \"monotonicity should flip as we flip the predicate\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10293, __extension__
 __PRETTY_FUNCTION__))
         "monotonicity should flip as we flip the predicate")(static_cast <bool> (ResultSwapped.getValue() != Result
.getValue() && "monotonicity should flip as we flip the predicate"
) ? void (0) : __assert_fail ("ResultSwapped.getValue() != Result.getValue() && \"monotonicity should flip as we flip the predicate\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10293, __extension__
 __PRETTY_FUNCTION__));
}
10295#endif

return Result;
10298}

10300Optional<ScalarEvolution::MonotonicPredicateType>
10301ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS,
                                             ICmpInst::Predicate Pred) {
// A zero step value for LHS means the induction variable is essentially a
// loop invariant value. We don't really depend on the predicate actually
// flipping from false to true (for increasing predicates, and the other way
// around for decreasing predicates), all we care about is that *if* the
// predicate changes then it only changes from false to true.
//
// A zero step value in itself is not very useful, but there may be places
// where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
// as general as possible.

// Only handle LE/LT/GE/GT predicates.
if (!ICmpInst::isRelational(Pred))
  return None;

bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred);
assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) &&(static_cast <bool> ((IsGreater || ICmpInst::isLE(Pred)
 || ICmpInst::isLT(Pred)) && "Should be greater or less!"
) ? void (0) : __assert_fail ("(IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) && \"Should be greater or less!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10319, __extension__
 __PRETTY_FUNCTION__))
       "Should be greater or less!")(static_cast <bool> ((IsGreater || ICmpInst::isLE(Pred)
 || ICmpInst::isLT(Pred)) && "Should be greater or less!"
) ? void (0) : __assert_fail ("(IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) && \"Should be greater or less!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10319, __extension__
 __PRETTY_FUNCTION__));

// Check that AR does not wrap.
if (ICmpInst::isUnsigned(Pred)) {
  if (!LHS->hasNoUnsignedWrap())
    return None;
  return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;
} else {
  assert(ICmpInst::isSigned(Pred) &&(static_cast <bool> (ICmpInst::isSigned(Pred) &&
 "Relational predicate is either signed or unsigned!") ? void
 (0) : __assert_fail ("ICmpInst::isSigned(Pred) && \"Relational predicate is either signed or unsigned!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10328, __extension__
 __PRETTY_FUNCTION__))
         "Relational predicate is either signed or unsigned!")(static_cast <bool> (ICmpInst::isSigned(Pred) &&
 "Relational predicate is either signed or unsigned!") ? void
 (0) : __assert_fail ("ICmpInst::isSigned(Pred) && \"Relational predicate is either signed or unsigned!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10328, __extension__
 __PRETTY_FUNCTION__));
  if (!LHS->hasNoSignedWrap())
    return None;

  const SCEV *Step = LHS->getStepRecurrence(*this);

  if (isKnownNonNegative(Step))
    return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;

  if (isKnownNonPositive(Step))
    return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing;

  return None;
}
10342}

10344Optional<ScalarEvolution::LoopInvariantPredicate>
10345ScalarEvolution::getLoopInvariantPredicate(ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS,
                                         const Loop *L) {

// If there is a loop-invariant, force it into the RHS, otherwise bail out.
if (!isLoopInvariant(RHS, L)) {
  if (!isLoopInvariant(LHS, L))
    return None;

  std::swap(LHS, RHS);
  Pred = ICmpInst::getSwappedPredicate(Pred);
}

const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!ArLHS || ArLHS->getLoop() != L)
  return None;

auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred);
if (!MonotonicType)
  return None;
// If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
// true as the loop iterates, and the backedge is control dependent on
// "ArLHS `Pred` RHS" == true then we can reason as follows:
//
//   * if the predicate was false in the first iteration then the predicate
//     is never evaluated again, since the loop exits without taking the
//     backedge.
//   * if the predicate was true in the first iteration then it will
//     continue to be true for all future iterations since it is
//     monotonically increasing.
//
// For both the above possibilities, we can replace the loop varying
// predicate with its value on the first iteration of the loop (which is
// loop invariant).
//
// A similar reasoning applies for a monotonically decreasing predicate, by
// replacing true with false and false with true in the above two bullets.
bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing;
auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);

if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
  return None;

return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(), RHS);
10389}

10391Optional<ScalarEvolution::LoopInvariantPredicate>
10392ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations(
  ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
  const Instruction *CtxI, const SCEV *MaxIter) {
// Try to prove the following set of facts:
// - The predicate is monotonic in the iteration space.
// - If the check does not fail on the 1st iteration:
//   - No overflow will happen during first MaxIter iterations;
//   - It will not fail on the MaxIter'th iteration.
// If the check does fail on the 1st iteration, we leave the loop and no
// other checks matter.

// If there is a loop-invariant, force it into the RHS, otherwise bail out.
if (!isLoopInvariant(RHS, L)) {
  if (!isLoopInvariant(LHS, L))
    return None;

  std::swap(LHS, RHS);
  Pred = ICmpInst::getSwappedPredicate(Pred);
}

auto *AR = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AR || AR->getLoop() != L)
  return None;

// The predicate must be relational (i.e. <, <=, >=, >).
if (!ICmpInst::isRelational(Pred))
  return None;

// TODO: Support steps other than +/- 1.
const SCEV *Step = AR->getStepRecurrence(*this);
auto *One = getOne(Step->getType());
auto *MinusOne = getNegativeSCEV(One);
if (Step != One && Step != MinusOne)
  return None;

// Type mismatch here means that MaxIter is potentially larger than max
// unsigned value in start type, which mean we cannot prove no wrap for the
// indvar.
if (AR->getType() != MaxIter->getType())
  return None;

// Value of IV on suggested last iteration.
const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this);
// Does it still meet the requirement?
if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS))
  return None;
// Because step is +/- 1 and MaxIter has same type as Start (i.e. it does
// not exceed max unsigned value of this type), this effectively proves
// that there is no wrap during the iteration. To prove that there is no
// signed/unsigned wrap, we need to check that
// Start <= Last for step = 1 or Start >= Last for step = -1.
ICmpInst::Predicate NoOverflowPred =
    CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
if (Step == MinusOne)
  NoOverflowPred = CmpInst::getSwappedPredicate(NoOverflowPred);
const SCEV *Start = AR->getStart();
if (!isKnownPredicateAt(NoOverflowPred, Start, Last, CtxI))
  return None;

// Everything is fine.
return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS);
10453}

10455bool ScalarEvolution::isKnownPredicateViaConstantRanges(
  ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
if (HasSameValue(LHS, RHS))
  return ICmpInst::isTrueWhenEqual(Pred);

// This code is split out from isKnownPredicate because it is called from
// within isLoopEntryGuardedByCond.

auto CheckRanges = [&](const ConstantRange &RangeLHS,
                       const ConstantRange &RangeRHS) {
  return RangeLHS.icmp(Pred, RangeRHS);
};

// The check at the top of the function catches the case where the values are
// known to be equal.
if (Pred == CmpInst::ICMP_EQ)
  return false;

if (Pred == CmpInst::ICMP_NE) {
  if (CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
      CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)))
    return true;
  auto *Diff = getMinusSCEV(LHS, RHS);
  return !isa<SCEVCouldNotCompute>(Diff) && isKnownNonZero(Diff);
}

if (CmpInst::isSigned(Pred))
  return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));

return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
10485}

10487bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
                                                  const SCEV *LHS,
                                                  const SCEV *RHS) {
// Match X to (A + C1)<ExpectedFlags> and Y to (A + C2)<ExpectedFlags>, where
// C1 and C2 are constant integers. If either X or Y are not add expressions,
// consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via
// OutC1 and OutC2.
auto MatchBinaryAddToConst = [this](const SCEV *X, const SCEV *Y,
                                    APInt &OutC1, APInt &OutC2,
                                    SCEV::NoWrapFlags ExpectedFlags) {
  const SCEV *XNonConstOp, *XConstOp;
  const SCEV *YNonConstOp, *YConstOp;
  SCEV::NoWrapFlags XFlagsPresent;
  SCEV::NoWrapFlags YFlagsPresent;

  if (!splitBinaryAdd(X, XConstOp, XNonConstOp, XFlagsPresent)) {
    XConstOp = getZero(X->getType());
    XNonConstOp = X;
    XFlagsPresent = ExpectedFlags;
  }
  if (!isa<SCEVConstant>(XConstOp) ||
      (XFlagsPresent & ExpectedFlags) != ExpectedFlags)
    return false;

  if (!splitBinaryAdd(Y, YConstOp, YNonConstOp, YFlagsPresent)) {
    YConstOp = getZero(Y->getType());
    YNonConstOp = Y;
    YFlagsPresent = ExpectedFlags;
  }

  if (!isa<SCEVConstant>(YConstOp) ||
      (YFlagsPresent & ExpectedFlags) != ExpectedFlags)
    return false;

  if (YNonConstOp != XNonConstOp)
    return false;

  OutC1 = cast<SCEVConstant>(XConstOp)->getAPInt();
  OutC2 = cast<SCEVConstant>(YConstOp)->getAPInt();

  return true;
};

APInt C1;
APInt C2;

switch (Pred) {
default:
  break;

case ICmpInst::ICMP_SGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SLE:
  // (X + C1)<nsw> s<= (X + C2)<nsw> if C1 s<= C2.
  if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(C2))
    return true;

  break;

case ICmpInst::ICMP_SGT:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SLT:
  // (X + C1)<nsw> s< (X + C2)<nsw> if C1 s< C2.
  if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(C2))
    return true;

  break;

case ICmpInst::ICMP_UGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_ULE:
  // (X + C1)<nuw> u<= (X + C2)<nuw> for C1 u<= C2.
  if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ule(C2))
    return true;

  break;

case ICmpInst::ICMP_UGT:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_ULT:
  // (X + C1)<nuw> u< (X + C2)<nuw> if C1 u< C2.
  if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ult(C2))
    return true;
  break;
}

return false;
10578}

10580bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
                                                 const SCEV *LHS,
                                                 const SCEV *RHS) {
if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
  return false;

// Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
// the stack can result in exponential time complexity.
SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);

// If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
//
// To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
// isKnownPredicate.  isKnownPredicate is more powerful, but also more
// expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
// interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
// use isKnownPredicate later if needed.
return isKnownNonNegative(RHS) &&
       isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
       isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
10600}

10602bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB,
                                      ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS) {
// No need to even try if we know the module has no guards.
if (!HasGuards)
  return false;

return any_of(*BB, [&](const Instruction &I) {
  using namespace llvm::PatternMatch;

  Value *Condition;
  return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
                       m_Value(Condition))) &&
         isImpliedCond(Pred, LHS, RHS, Condition, false);
});
10617}

10619/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
10620/// protected by a conditional between LHS and RHS.  This is used to
10621/// to eliminate casts.
10622bool
10623ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
                                           ICmpInst::Predicate Pred,
                                           const SCEV *LHS, const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L) return true;
7
←
Assuming 'L' is non-null→
8
←
Taking false branch→

if (VerifyIR)
9
←
Assuming the condition is false→
10
←
Taking false branch→
  assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&(static_cast <bool> (!verifyFunction(*L->getHeader()
->getParent(), &dbgs()) && "This cannot be done on broken IR!"
) ? void (0) : __assert_fail ("!verifyFunction(*L->getHeader()->getParent(), &dbgs()) && \"This cannot be done on broken IR!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10632, __extension__
 __PRETTY_FUNCTION__))
         "This cannot be done on broken IR!")(static_cast <bool> (!verifyFunction(*L->getHeader()
->getParent(), &dbgs()) && "This cannot be done on broken IR!"
) ? void (0) : __assert_fail ("!verifyFunction(*L->getHeader()->getParent(), &dbgs()) && \"This cannot be done on broken IR!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10632, __extension__
 __PRETTY_FUNCTION__));


if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
11
←
Assuming the condition is false→
12
←
Taking false branch→
  return true;

BasicBlock *Latch = L->getLoopLatch();
if (!Latch)
13
←
Assuming 'Latch' is non-null→
14
←
Taking false branch→
  return false;

BranchInst *LoopContinuePredicate =
  dyn_cast<BranchInst>(Latch->getTerminator());
15
←
Assuming the object is not a 'BranchInst'→
if (LoopContinuePredicate15.1
'LoopContinuePredicate' is null
 && LoopContinuePredicate->isConditional() &&
    isImpliedCond(Pred, LHS, RHS,
                  LoopContinuePredicate->getCondition(),
                  LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
  return true;

// We don't want more than one activation of the following loops on the stack
// -- that can lead to O(n!) time complexity.
if (WalkingBEDominatingConds)
16
←
Assuming field 'WalkingBEDominatingConds' is true→
17
←
Taking true branch→
  return false;

SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);

// See if we can exploit a trip count to prove the predicate.
const auto &BETakenInfo = getBackedgeTakenInfo(L);
const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
if (LatchBECount != getCouldNotCompute()) {
  // We know that Latch branches back to the loop header exactly
  // LatchBECount times.  This means the backdege condition at Latch is
  // equivalent to  "{0,+,1} u< LatchBECount".
  Type *Ty = LatchBECount->getType();
  auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
  const SCEV *LoopCounter =
    getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
  if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
                    LatchBECount))
    return true;
}

// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
  if (!AssumeVH)
    continue;
  auto *CI = cast<CallInst>(AssumeVH);
  if (!DT.dominates(CI, Latch->getTerminator()))
    continue;

  if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
    return true;
}

// If the loop is not reachable from the entry block, we risk running into an
// infinite loop as we walk up into the dom tree.  These loops do not matter
// anyway, so we just return a conservative answer when we see them.
if (!DT.isReachableFromEntry(L->getHeader()))
  return false;

if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
  return true;

for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
     DTN != HeaderDTN; DTN = DTN->getIDom()) {
  assert(DTN && "should reach the loop header before reaching the root!")(static_cast <bool> (DTN && "should reach the loop header before reaching the root!"
) ? void (0) : __assert_fail ("DTN && \"should reach the loop header before reaching the root!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10696, __extension__
 __PRETTY_FUNCTION__));

  BasicBlock *BB = DTN->getBlock();
  if (isImpliedViaGuard(BB, Pred, LHS, RHS))
    return true;

  BasicBlock *PBB = BB->getSinglePredecessor();
  if (!PBB)
    continue;

  BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
  if (!ContinuePredicate || !ContinuePredicate->isConditional())
    continue;

  Value *Condition = ContinuePredicate->getCondition();

  // If we have an edge `E` within the loop body that dominates the only
  // latch, the condition guarding `E` also guards the backedge.  This
  // reasoning works only for loops with a single latch.

  BasicBlockEdge DominatingEdge(PBB, BB);
  if (DominatingEdge.isSingleEdge()) {
    // We're constructively (and conservatively) enumerating edges within the
    // loop body that dominate the latch.  The dominator tree better agree
    // with us on this:
    assert(DT.dominates(DominatingEdge, Latch) && "should be!")(static_cast <bool> (DT.dominates(DominatingEdge, Latch
) && "should be!") ? void (0) : __assert_fail ("DT.dominates(DominatingEdge, Latch) && \"should be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10721, __extension__
 __PRETTY_FUNCTION__));

    if (isImpliedCond(Pred, LHS, RHS, Condition,
                      BB != ContinuePredicate->getSuccessor(0)))
      return true;
  }
}

return false;
10730}

10732bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB,
                                                   ICmpInst::Predicate Pred,
                                                   const SCEV *LHS,
                                                   const SCEV *RHS) {
if (VerifyIR)
34
←
Assuming the condition is false→
35
←
Taking false branch→
  assert(!verifyFunction(*BB->getParent(), &dbgs()) &&(static_cast <bool> (!verifyFunction(*BB->getParent(
), &dbgs()) && "This cannot be done on broken IR!"
) ? void (0) : __assert_fail ("!verifyFunction(*BB->getParent(), &dbgs()) && \"This cannot be done on broken IR!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10738, __extension__
 __PRETTY_FUNCTION__))
         "This cannot be done on broken IR!")(static_cast <bool> (!verifyFunction(*BB->getParent(
), &dbgs()) && "This cannot be done on broken IR!"
) ? void (0) : __assert_fail ("!verifyFunction(*BB->getParent(), &dbgs()) && \"This cannot be done on broken IR!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10738, __extension__
 __PRETTY_FUNCTION__));

// If we cannot prove strict comparison (e.g. a > b), maybe we can prove
// the facts (a >= b && a != b) separately. A typical situation is when the
// non-strict comparison is known from ranges and non-equality is known from
// dominating predicates. If we are proving strict comparison, we always try
// to prove non-equality and non-strict comparison separately.
auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
36
←
Assuming 'Pred' is equal to 'NonStrictPredicate'→
bool ProvedNonStrictComparison = false;
bool ProvedNonEquality = false;

auto SplitAndProve =
  [&](std::function<bool(ICmpInst::Predicate)> Fn) -> bool {
  if (!ProvedNonStrictComparison)
    ProvedNonStrictComparison = Fn(NonStrictPredicate);
  if (!ProvedNonEquality)
    ProvedNonEquality = Fn(ICmpInst::ICMP_NE);
  if (ProvedNonStrictComparison && ProvedNonEquality)
    return true;
  return false;
};

if (ProvingStrictComparison36.1
'ProvingStrictComparison' is false
) {
37
←
Taking false branch→
  auto ProofFn = [&](ICmpInst::Predicate P) {
    return isKnownViaNonRecursiveReasoning(P, LHS, RHS);
  };
  if (SplitAndProve(ProofFn))
    return true;
}

// Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
auto ProveViaGuard = [&](const BasicBlock *Block) {
  if (isImpliedViaGuard(Block, Pred, LHS, RHS))
    return true;
  if (ProvingStrictComparison) {
    auto ProofFn = [&](ICmpInst::Predicate P) {
      return isImpliedViaGuard(Block, P, LHS, RHS);
    };
    if (SplitAndProve(ProofFn))
      return true;
  }
  return false;
};

// Try to prove (Pred, LHS, RHS) using isImpliedCond.
auto ProveViaCond = [&](const Value *Condition, bool Inverse) {
  const Instruction *CtxI = &BB->front();
47
←
Called C++ object pointer is null
  if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, CtxI))
    return true;
  if (ProvingStrictComparison) {
    auto ProofFn = [&](ICmpInst::Predicate P) {
      return isImpliedCond(P, LHS, RHS, Condition, Inverse, CtxI);
    };
    if (SplitAndProve(ProofFn))
      return true;
  }
  return false;
};

// Starting at the block's predecessor, climb up the predecessor chain, as long
// as there are predecessors that can be found that have unique successors
// leading to the original block.
const Loop *ContainingLoop = LI.getLoopFor(BB);
const BasicBlock *PredBB;
if (ContainingLoop && ContainingLoop->getHeader() == BB)
38
←
Assuming 'ContainingLoop' is non-null→
39
←
Assuming the condition is true→
40
←
Taking true branch→
  PredBB = ContainingLoop->getLoopPredecessor();
else
  PredBB = BB->getSinglePredecessor();
for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB);
41
←
Loop condition is true.  Entering loop body→
     Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
  if (ProveViaGuard(Pair.first))
42
←
Taking false branch→
    return true;

  const BranchInst *LoopEntryPredicate =
      dyn_cast<BranchInst>(Pair.first->getTerminator());
43
←
Assuming the object is a 'BranchInst'→
  if (!LoopEntryPredicate43.1
'LoopEntryPredicate' is non-null
 ||
44
←
Taking false branch→
      LoopEntryPredicate->isUnconditional())
    continue;

  if (ProveViaCond(LoopEntryPredicate->getCondition(),
46
←
Calling 'operator()'→
                   LoopEntryPredicate->getSuccessor(0) != Pair.second))
45
←
Assuming pointer value is null→
    return true;
}

// Check conditions due to any @llvm.assume intrinsics.
for (auto &AssumeVH : AC.assumptions()) {
  if (!AssumeVH)
    continue;
  auto *CI = cast<CallInst>(AssumeVH);
  if (!DT.dominates(CI, BB))
    continue;

  if (ProveViaCond(CI->getArgOperand(0), false))
    return true;
}

return false;
10836}

10838bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
                                             ICmpInst::Predicate Pred,
                                             const SCEV *LHS,
                                             const SCEV *RHS) {
// Interpret a null as meaning no loop, where there is obviously no guard
// (interprocedural conditions notwithstanding).
if (!L20.1
'L' is non-null
)
  return false;

// Both LHS and RHS must be available at loop entry.
assert(isAvailableAtLoopEntry(LHS, L) &&(static_cast <bool> (isAvailableAtLoopEntry(LHS, L) &&
 "LHS is not available at Loop Entry") ? void (0) : __assert_fail
 ("isAvailableAtLoopEntry(LHS, L) && \"LHS is not available at Loop Entry\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10849, __extension__
 __PRETTY_FUNCTION__))
21
←
Taking false branch→
22
←
'?' condition is true→
       "LHS is not available at Loop Entry")(static_cast <bool> (isAvailableAtLoopEntry(LHS, L) &&
 "LHS is not available at Loop Entry") ? void (0) : __assert_fail
 ("isAvailableAtLoopEntry(LHS, L) && \"LHS is not available at Loop Entry\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10849, __extension__
 __PRETTY_FUNCTION__));
assert(isAvailableAtLoopEntry(RHS, L) &&(static_cast <bool> (isAvailableAtLoopEntry(RHS, L) &&
 "RHS is not available at Loop Entry") ? void (0) : __assert_fail
 ("isAvailableAtLoopEntry(RHS, L) && \"RHS is not available at Loop Entry\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10851, __extension__
 __PRETTY_FUNCTION__))
23
←
'?' condition is true→
       "RHS is not available at Loop Entry")(static_cast <bool> (isAvailableAtLoopEntry(RHS, L) &&
 "RHS is not available at Loop Entry") ? void (0) : __assert_fail
 ("isAvailableAtLoopEntry(RHS, L) && \"RHS is not available at Loop Entry\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10851, __extension__
 __PRETTY_FUNCTION__));

if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
24
←
Calling 'ScalarEvolution::isKnownViaNonRecursiveReasoning'→
29
←
Returning from 'ScalarEvolution::isKnownViaNonRecursiveReasoning'→
30
←
Assuming the condition is false→
31
←
Taking false branch→
  return true;

return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS);
32
←
Passing value via 1st parameter 'BB'→
33
←
Calling 'ScalarEvolution::isBasicBlockEntryGuardedByCond'→
10857}

10859bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
                                  const SCEV *RHS,
                                  const Value *FoundCondValue, bool Inverse,
                                  const Instruction *CtxI) {
// False conditions implies anything. Do not bother analyzing it further.
if (FoundCondValue ==
    ConstantInt::getBool(FoundCondValue->getContext(), Inverse))
  return true;

if (!PendingLoopPredicates.insert(FoundCondValue).second)
  return false;

auto ClearOnExit =
    make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });

// Recursively handle And and Or conditions.
const Value *Op0, *Op1;
if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) {
  if (!Inverse)
    return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
           isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
} else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) {
  if (Inverse)
    return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, CtxI) ||
           isImpliedCond(Pred, LHS, RHS, Op1, Inverse, CtxI);
}

const ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
if (!ICI) return false;

// Now that we found a conditional branch that dominates the loop or controls
// the loop latch. Check to see if it is the comparison we are looking for.
ICmpInst::Predicate FoundPred;
if (Inverse)
  FoundPred = ICI->getInversePredicate();
else
  FoundPred = ICI->getPredicate();

const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));

return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, CtxI);
10901}

10903bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
                                  const SCEV *RHS,
                                  ICmpInst::Predicate FoundPred,
                                  const SCEV *FoundLHS, const SCEV *FoundRHS,
                                  const Instruction *CtxI) {
// Balance the types.
if (getTypeSizeInBits(LHS->getType()) <
    getTypeSizeInBits(FoundLHS->getType())) {
  // For unsigned and equality predicates, try to prove that both found
  // operands fit into narrow unsigned range. If so, try to prove facts in
  // narrow types.
  if (!CmpInst::isSigned(FoundPred) && !FoundLHS->getType()->isPointerTy()) {
    auto *NarrowType = LHS->getType();
    auto *WideType = FoundLHS->getType();
    auto BitWidth = getTypeSizeInBits(NarrowType);
    const SCEV *MaxValue = getZeroExtendExpr(
        getConstant(APInt::getMaxValue(BitWidth)), WideType);
    if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundLHS,
                                        MaxValue) &&
        isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, FoundRHS,
                                        MaxValue)) {
      const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType);
      const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType);
      if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, TruncFoundLHS,
                                     TruncFoundRHS, CtxI))
        return true;
    }
  }

  if (LHS->getType()->isPointerTy())
    return false;
  if (CmpInst::isSigned(Pred)) {
    LHS = getSignExtendExpr(LHS, FoundLHS->getType());
    RHS = getSignExtendExpr(RHS, FoundLHS->getType());
  } else {
    LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
    RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
  }
} else if (getTypeSizeInBits(LHS->getType()) >
    getTypeSizeInBits(FoundLHS->getType())) {
  if (FoundLHS->getType()->isPointerTy())
    return false;
  if (CmpInst::isSigned(FoundPred)) {
    FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
    FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
  } else {
    FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
    FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
  }
}
return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS,
                                  FoundRHS, CtxI);
10955}

10957bool ScalarEvolution::isImpliedCondBalancedTypes(
  ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
  ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS,
  const Instruction *CtxI) {
assert(getTypeSizeInBits(LHS->getType()) ==(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(FoundLHS->getType()) && "Types should be balanced!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(FoundLHS->getType()) && \"Types should be balanced!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10963, __extension__
 __PRETTY_FUNCTION__))
           getTypeSizeInBits(FoundLHS->getType()) &&(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(FoundLHS->getType()) && "Types should be balanced!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(FoundLHS->getType()) && \"Types should be balanced!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10963, __extension__
 __PRETTY_FUNCTION__))
       "Types should be balanced!")(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(FoundLHS->getType()) && "Types should be balanced!"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(FoundLHS->getType()) && \"Types should be balanced!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 10963, __extension__
 __PRETTY_FUNCTION__));
// Canonicalize the query to match the way instcombine will have
// canonicalized the comparison.
if (SimplifyICmpOperands(Pred, LHS, RHS))
  if (LHS == RHS)
    return CmpInst::isTrueWhenEqual(Pred);
if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
  if (FoundLHS == FoundRHS)
    return CmpInst::isFalseWhenEqual(FoundPred);

// Check to see if we can make the LHS or RHS match.
if (LHS == FoundRHS || RHS == FoundLHS) {
  if (isa<SCEVConstant>(RHS)) {
    std::swap(FoundLHS, FoundRHS);
    FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
  } else {
    std::swap(LHS, RHS);
    Pred = ICmpInst::getSwappedPredicate(Pred);
  }
}

// Check whether the found predicate is the same as the desired predicate.
if (FoundPred == Pred)
  return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);

// Check whether swapping the found predicate makes it the same as the
// desired predicate.
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
  // We can write the implication
  // 0.  LHS Pred      RHS  <-   FoundLHS SwapPred  FoundRHS
  // using one of the following ways:
  // 1.  LHS Pred      RHS  <-   FoundRHS Pred      FoundLHS
  // 2.  RHS SwapPred  LHS  <-   FoundLHS SwapPred  FoundRHS
  // 3.  LHS Pred      RHS  <-  ~FoundLHS Pred     ~FoundRHS
  // 4. ~LHS SwapPred ~RHS  <-   FoundLHS SwapPred  FoundRHS
  // Forms 1. and 2. require swapping the operands of one condition. Don't
  // do this if it would break canonical constant/addrec ordering.
  if (!isa<SCEVConstant>(RHS) && !isa<SCEVAddRecExpr>(LHS))
    return isImpliedCondOperands(FoundPred, RHS, LHS, FoundLHS, FoundRHS,
                                 CtxI);
  if (!isa<SCEVConstant>(FoundRHS) && !isa<SCEVAddRecExpr>(FoundLHS))
    return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS, CtxI);

  // There's no clear preference between forms 3. and 4., try both.  Avoid
  // forming getNotSCEV of pointer values as the resulting subtract is
  // not legal.
  if (!LHS->getType()->isPointerTy() && !RHS->getType()->isPointerTy() &&
      isImpliedCondOperands(FoundPred, getNotSCEV(LHS), getNotSCEV(RHS),
                            FoundLHS, FoundRHS, CtxI))
    return true;

  if (!FoundLHS->getType()->isPointerTy() &&
      !FoundRHS->getType()->isPointerTy() &&
      isImpliedCondOperands(Pred, LHS, RHS, getNotSCEV(FoundLHS),
                            getNotSCEV(FoundRHS), CtxI))
    return true;

  return false;
}

auto IsSignFlippedPredicate = [](CmpInst::Predicate P1,
                                 CmpInst::Predicate P2) {
  assert(P1 != P2 && "Handled earlier!")(static_cast <bool> (P1 != P2 && "Handled earlier!"
) ? void (0) : __assert_fail ("P1 != P2 && \"Handled earlier!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11025, __extension__
 __PRETTY_FUNCTION__));
  return CmpInst::isRelational(P2) &&
         P1 == CmpInst::getFlippedSignednessPredicate(P2);
};
if (IsSignFlippedPredicate(Pred, FoundPred)) {
  // Unsigned comparison is the same as signed comparison when both the
  // operands are non-negative or negative.
  if ((isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) ||
      (isKnownNegative(FoundLHS) && isKnownNegative(FoundRHS)))
    return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);
  // Create local copies that we can freely swap and canonicalize our
  // conditions to "le/lt".
  ICmpInst::Predicate CanonicalPred = Pred, CanonicalFoundPred = FoundPred;
  const SCEV *CanonicalLHS = LHS, *CanonicalRHS = RHS,
             *CanonicalFoundLHS = FoundLHS, *CanonicalFoundRHS = FoundRHS;
  if (ICmpInst::isGT(CanonicalPred) || ICmpInst::isGE(CanonicalPred)) {
    CanonicalPred = ICmpInst::getSwappedPredicate(CanonicalPred);
    CanonicalFoundPred = ICmpInst::getSwappedPredicate(CanonicalFoundPred);
    std::swap(CanonicalLHS, CanonicalRHS);
    std::swap(CanonicalFoundLHS, CanonicalFoundRHS);
  }
  assert((ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) &&(static_cast <bool> ((ICmpInst::isLT(CanonicalPred) || ICmpInst
::isLE(CanonicalPred)) && "Must be!") ? void (0) : __assert_fail
 ("(ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11047, __extension__
 __PRETTY_FUNCTION__))
         "Must be!")(static_cast <bool> ((ICmpInst::isLT(CanonicalPred) || ICmpInst
::isLE(CanonicalPred)) && "Must be!") ? void (0) : __assert_fail
 ("(ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11047, __extension__
 __PRETTY_FUNCTION__));
  assert((ICmpInst::isLT(CanonicalFoundPred) ||(static_cast <bool> ((ICmpInst::isLT(CanonicalFoundPred
) || ICmpInst::isLE(CanonicalFoundPred)) && "Must be!"
) ? void (0) : __assert_fail ("(ICmpInst::isLT(CanonicalFoundPred) || ICmpInst::isLE(CanonicalFoundPred)) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11050, __extension__
 __PRETTY_FUNCTION__))
          ICmpInst::isLE(CanonicalFoundPred)) &&(static_cast <bool> ((ICmpInst::isLT(CanonicalFoundPred
) || ICmpInst::isLE(CanonicalFoundPred)) && "Must be!"
) ? void (0) : __assert_fail ("(ICmpInst::isLT(CanonicalFoundPred) || ICmpInst::isLE(CanonicalFoundPred)) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11050, __extension__
 __PRETTY_FUNCTION__))
         "Must be!")(static_cast <bool> ((ICmpInst::isLT(CanonicalFoundPred
) || ICmpInst::isLE(CanonicalFoundPred)) && "Must be!"
) ? void (0) : __assert_fail ("(ICmpInst::isLT(CanonicalFoundPred) || ICmpInst::isLE(CanonicalFoundPred)) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11050, __extension__
 __PRETTY_FUNCTION__));
  if (ICmpInst::isSigned(CanonicalPred) && isKnownNonNegative(CanonicalRHS))
    // Use implication:
    // x <u y && y >=s 0 --> x <s y.
    // If we can prove the left part, the right part is also proven.
    return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
                                 CanonicalRHS, CanonicalFoundLHS,
                                 CanonicalFoundRHS);
  if (ICmpInst::isUnsigned(CanonicalPred) && isKnownNegative(CanonicalRHS))
    // Use implication:
    // x <s y && y <s 0 --> x <u y.
    // If we can prove the left part, the right part is also proven.
    return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
                                 CanonicalRHS, CanonicalFoundLHS,
                                 CanonicalFoundRHS);
}

// Check if we can make progress by sharpening ranges.
if (FoundPred == ICmpInst::ICMP_NE &&
    (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {

  const SCEVConstant *C = nullptr;
  const SCEV *V = nullptr;

  if (isa<SCEVConstant>(FoundLHS)) {
    C = cast<SCEVConstant>(FoundLHS);
    V = FoundRHS;
  } else {
    C = cast<SCEVConstant>(FoundRHS);
    V = FoundLHS;
  }

  // The guarding predicate tells us that C != V. If the known range
  // of V is [C, t), we can sharpen the range to [C + 1, t).  The
  // range we consider has to correspond to same signedness as the
  // predicate we're interested in folding.

  APInt Min = ICmpInst::isSigned(Pred) ?
      getSignedRangeMin(V) : getUnsignedRangeMin(V);

  if (Min == C->getAPInt()) {
    // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
    // This is true even if (Min + 1) wraps around -- in case of
    // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).

    APInt SharperMin = Min + 1;

    switch (Pred) {
      case ICmpInst::ICMP_SGE:
      case ICmpInst::ICMP_UGE:
        // We know V `Pred` SharperMin.  If this implies LHS `Pred`
        // RHS, we're done.
        if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin),
                                  CtxI))
          return true;
        LLVM_FALLTHROUGH[[gnu::fallthrough]];

      case ICmpInst::ICMP_SGT:
      case ICmpInst::ICMP_UGT:
        // We know from the range information that (V `Pred` Min ||
        // V == Min).  We know from the guarding condition that !(V
        // == Min).  This gives us
        //
        //       V `Pred` Min || V == Min && !(V == Min)
        //   =>  V `Pred` Min
        //
        // If V `Pred` Min implies LHS `Pred` RHS, we're done.

        if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min), CtxI))
          return true;
        break;

      // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively.
      case ICmpInst::ICMP_SLE:
      case ICmpInst::ICMP_ULE:
        if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS,
                                  LHS, V, getConstant(SharperMin), CtxI))
          return true;
        LLVM_FALLTHROUGH[[gnu::fallthrough]];

      case ICmpInst::ICMP_SLT:
      case ICmpInst::ICMP_ULT:
        if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS,
                                  LHS, V, getConstant(Min), CtxI))
          return true;
        break;

      default:
        // No change
        break;
    }
  }
}

// Check whether the actual condition is beyond sufficient.
if (FoundPred == ICmpInst::ICMP_EQ)
  if (ICmpInst::isTrueWhenEqual(Pred))
    if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
      return true;
if (Pred == ICmpInst::ICMP_NE)
  if (!ICmpInst::isTrueWhenEqual(FoundPred))
    if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS, CtxI))
      return true;

// Otherwise assume the worst.
return false;
11156}

11158bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
                                   const SCEV *&L, const SCEV *&R,
                                   SCEV::NoWrapFlags &Flags) {
const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
if (!AE || AE->getNumOperands() != 2)
  return false;

L = AE->getOperand(0);
R = AE->getOperand(1);
Flags = AE->getNoWrapFlags();
return true;
11169}

11171Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
                                                         const SCEV *Less) {
// We avoid subtracting expressions here because this function is usually
// fairly deep in the call stack (i.e. is called many times).

// X - X = 0.
if (More == Less)
  return APInt(getTypeSizeInBits(More->getType()), 0);

if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
  const auto *LAR = cast<SCEVAddRecExpr>(Less);
  const auto *MAR = cast<SCEVAddRecExpr>(More);

  if (LAR->getLoop() != MAR->getLoop())
    return None;

  // We look at affine expressions only; not for correctness but to keep
  // getStepRecurrence cheap.
  if (!LAR->isAffine() || !MAR->isAffine())
    return None;

  if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
    return None;

  Less = LAR->getStart();
  More = MAR->getStart();

  // fall through
}

if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
  const auto &M = cast<SCEVConstant>(More)->getAPInt();
  const auto &L = cast<SCEVConstant>(Less)->getAPInt();
  return M - L;
}

SCEV::NoWrapFlags Flags;
const SCEV *LLess = nullptr, *RLess = nullptr;
const SCEV *LMore = nullptr, *RMore = nullptr;
const SCEVConstant *C1 = nullptr, *C2 = nullptr;
// Compare (X + C1) vs X.
if (splitBinaryAdd(Less, LLess, RLess, Flags))
  if ((C1 = dyn_cast<SCEVConstant>(LLess)))
    if (RLess == More)
      return -(C1->getAPInt());

// Compare X vs (X + C2).
if (splitBinaryAdd(More, LMore, RMore, Flags))
  if ((C2 = dyn_cast<SCEVConstant>(LMore)))
    if (RMore == Less)
      return C2->getAPInt();

// Compare (X + C1) vs (X + C2).
if (C1 && C2 && RLess == RMore)
  return C2->getAPInt() - C1->getAPInt();

return None;
11228}

11230bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart(
  ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
  const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *CtxI) {
// Try to recognize the following pattern:
//
//   FoundRHS = ...
// ...
// loop:
//   FoundLHS = {Start,+,W}
// context_bb: // Basic block from the same loop
//   known(Pred, FoundLHS, FoundRHS)
//
// If some predicate is known in the context of a loop, it is also known on
// each iteration of this loop, including the first iteration. Therefore, in
// this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to
// prove the original pred using this fact.
if (!CtxI)
  return false;
const BasicBlock *ContextBB = CtxI->getParent();
// Make sure AR varies in the context block.
if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundLHS)) {
  const Loop *L = AR->getLoop();
  // Make sure that context belongs to the loop and executes on 1st iteration
  // (if it ever executes at all).
  if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch()))
    return false;
  if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop()))
    return false;
  return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS);
}

if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundRHS)) {
  const Loop *L = AR->getLoop();
  // Make sure that context belongs to the loop and executes on 1st iteration
  // (if it ever executes at all).
  if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch()))
    return false;
  if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop()))
    return false;
  return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart());
}

return false;
11273}

11275bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
  ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
  const SCEV *FoundLHS, const SCEV *FoundRHS) {
if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
  return false;

const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AddRecLHS)
  return false;

const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
if (!AddRecFoundLHS)
  return false;

// We'd like to let SCEV reason about control dependencies, so we constrain
// both the inequalities to be about add recurrences on the same loop.  This
// way we can use isLoopEntryGuardedByCond later.

const Loop *L = AddRecFoundLHS->getLoop();
if (L != AddRecLHS->getLoop())
  return false;

//  FoundLHS u< FoundRHS u< -C =>  (FoundLHS + C) u< (FoundRHS + C) ... (1)
//
//  FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
//                                                                  ... (2)
//
// Informal proof for (2), assuming (1) [*]:
//
// We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
//
// Then
//
//       FoundLHS s< FoundRHS s< INT_MIN - C
// <=>  (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C   [ using (3) ]
// <=>  (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
// <=>  (FoundLHS + INT_MIN + C + INT_MIN) s<
//                        (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
// <=>  FoundLHS + C s< FoundRHS + C
//
// [*]: (1) can be proved by ruling out overflow.
//
// [**]: This can be proved by analyzing all the four possibilities:
//    (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
//    (A s>= 0, B s>= 0).
//
// Note:
// Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
// will not sign underflow.  For instance, say FoundLHS = (i8 -128), FoundRHS
// = (i8 -127) and C = (i8 -100).  Then INT_MIN - C = (i8 -28), and FoundRHS
// s< (INT_MIN - C).  Lack of sign overflow / underflow in "FoundRHS + C" is
// neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
// C)".

Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
if (!LDiff || !RDiff || *LDiff != *RDiff)
  return false;

if (LDiff->isMinValue())
  return true;

APInt FoundRHSLimit;

if (Pred == CmpInst::ICMP_ULT) {
  FoundRHSLimit = -(*RDiff);
} else {
  assert(Pred == CmpInst::ICMP_SLT && "Checked above!")(static_cast <bool> (Pred == CmpInst::ICMP_SLT &&
 "Checked above!") ? void (0) : __assert_fail ("Pred == CmpInst::ICMP_SLT && \"Checked above!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11342, __extension__
 __PRETTY_FUNCTION__));
  FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
}

// Try to prove (1) or (2), as needed.
return isAvailableAtLoopEntry(FoundRHS, L) &&
       isLoopEntryGuardedByCond(L, Pred, FoundRHS,
                                getConstant(FoundRHSLimit));
11350}

11352bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS,
                                      const SCEV *FoundLHS,
                                      const SCEV *FoundRHS, unsigned Depth) {
const PHINode *LPhi = nullptr, *RPhi = nullptr;

auto ClearOnExit = make_scope_exit([&]() {
  if (LPhi) {
    bool Erased = PendingMerges.erase(LPhi);
    assert(Erased && "Failed to erase LPhi!")(static_cast <bool> (Erased && "Failed to erase LPhi!"
) ? void (0) : __assert_fail ("Erased && \"Failed to erase LPhi!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11361, __extension__
 __PRETTY_FUNCTION__));
    (void)Erased;
  }
  if (RPhi) {
    bool Erased = PendingMerges.erase(RPhi);
    assert(Erased && "Failed to erase RPhi!")(static_cast <bool> (Erased && "Failed to erase RPhi!"
) ? void (0) : __assert_fail ("Erased && \"Failed to erase RPhi!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11366, __extension__
 __PRETTY_FUNCTION__));
    (void)Erased;
  }
});

// Find respective Phis and check that they are not being pending.
if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
  if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
    if (!PendingMerges.insert(Phi).second)
      return false;
    LPhi = Phi;
  }
if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
  if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
    // If we detect a loop of Phi nodes being processed by this method, for
    // example:
    //
    //   %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
    //   %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
    //
    // we don't want to deal with a case that complex, so return conservative
    // answer false.
    if (!PendingMerges.insert(Phi).second)
      return false;
    RPhi = Phi;
  }

// If none of LHS, RHS is a Phi, nothing to do here.
if (!LPhi && !RPhi)
  return false;

// If there is a SCEVUnknown Phi we are interested in, make it left.
if (!LPhi) {
  std::swap(LHS, RHS);
  std::swap(FoundLHS, FoundRHS);
  std::swap(LPhi, RPhi);
  Pred = ICmpInst::getSwappedPredicate(Pred);
}

assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!")(static_cast <bool> (LPhi && "LPhi should definitely be a SCEVUnknown Phi!"
) ? void (0) : __assert_fail ("LPhi && \"LPhi should definitely be a SCEVUnknown Phi!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11405, __extension__
 __PRETTY_FUNCTION__));
const BasicBlock *LBB = LPhi->getParent();
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);

auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
  return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
         isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
         isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
};

if (RPhi && RPhi->getParent() == LBB) {
  // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
  // If we compare two Phis from the same block, and for each entry block
  // the predicate is true for incoming values from this block, then the
  // predicate is also true for the Phis.
  for (const BasicBlock *IncBB : predecessors(LBB)) {
    const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
    const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
    if (!ProvedEasily(L, R))
      return false;
  }
} else if (RAR && RAR->getLoop()->getHeader() == LBB) {
  // Case two: RHS is also a Phi from the same basic block, and it is an
  // AddRec. It means that there is a loop which has both AddRec and Unknown
  // PHIs, for it we can compare incoming values of AddRec from above the loop
  // and latch with their respective incoming values of LPhi.
  // TODO: Generalize to handle loops with many inputs in a header.
  if (LPhi->getNumIncomingValues() != 2) return false;

  auto *RLoop = RAR->getLoop();
  auto *Predecessor = RLoop->getLoopPredecessor();
  assert(Predecessor && "Loop with AddRec with no predecessor?")(static_cast <bool> (Predecessor && "Loop with AddRec with no predecessor?"
) ? void (0) : __assert_fail ("Predecessor && \"Loop with AddRec with no predecessor?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11436, __extension__
 __PRETTY_FUNCTION__));
  const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
  if (!ProvedEasily(L1, RAR->getStart()))
    return false;
  auto *Latch = RLoop->getLoopLatch();
  assert(Latch && "Loop with AddRec with no latch?")(static_cast <bool> (Latch && "Loop with AddRec with no latch?"
) ? void (0) : __assert_fail ("Latch && \"Loop with AddRec with no latch?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11441, __extension__
 __PRETTY_FUNCTION__));
  const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
  if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
    return false;
} else {
  // In all other cases go over inputs of LHS and compare each of them to RHS,
  // the predicate is true for (LHS, RHS) if it is true for all such pairs.
  // At this point RHS is either a non-Phi, or it is a Phi from some block
  // different from LBB.
  for (const BasicBlock *IncBB : predecessors(LBB)) {
    // Check that RHS is available in this block.
    if (!dominates(RHS, IncBB))
      return false;
    const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
    // Make sure L does not refer to a value from a potentially previous
    // iteration of a loop.
    if (!properlyDominates(L, IncBB))
      return false;
    if (!ProvedEasily(L, RHS))
      return false;
  }
}
return true;
11464}

11466bool ScalarEvolution::isImpliedCondOperandsViaShift(ICmpInst::Predicate Pred,
                                                  const SCEV *LHS,
                                                  const SCEV *RHS,
                                                  const SCEV *FoundLHS,
                                                  const SCEV *FoundRHS) {
// We want to imply LHS < RHS from LHS < (RHS >> shiftvalue).  First, make
// sure that we are dealing with same LHS.
if (RHS == FoundRHS) {
  std::swap(LHS, RHS);
  std::swap(FoundLHS, FoundRHS);
  Pred = ICmpInst::getSwappedPredicate(Pred);
}
if (LHS != FoundLHS)
  return false;

auto *SUFoundRHS = dyn_cast<SCEVUnknown>(FoundRHS);
if (!SUFoundRHS)
  return false;

Value *Shiftee, *ShiftValue;

using namespace PatternMatch;
if (match(SUFoundRHS->getValue(),
          m_LShr(m_Value(Shiftee), m_Value(ShiftValue)))) {
  auto *ShifteeS = getSCEV(Shiftee);
  // Prove one of the following:
  // LHS <u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <u RHS
  // LHS <=u (shiftee >> shiftvalue) && shiftee <=u RHS ---> LHS <=u RHS
  // LHS <s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
  //   ---> LHS <s RHS
  // LHS <=s (shiftee >> shiftvalue) && shiftee <=s RHS && shiftee >=s 0
  //   ---> LHS <=s RHS
  if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE)
    return isKnownPredicate(ICmpInst::ICMP_ULE, ShifteeS, RHS);
  if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE)
    if (isKnownNonNegative(ShifteeS))
      return isKnownPredicate(ICmpInst::ICMP_SLE, ShifteeS, RHS);
}

return false;
11506}

11508bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
                                          const SCEV *LHS, const SCEV *RHS,
                                          const SCEV *FoundLHS,
                                          const SCEV *FoundRHS,
                                          const Instruction *CtxI) {
if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
  return true;

if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
  return true;

if (isImpliedCondOperandsViaShift(Pred, LHS, RHS, FoundLHS, FoundRHS))
  return true;

if (isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS,
                                        CtxI))
  return true;

return isImpliedCondOperandsHelper(Pred, LHS, RHS,
                                   FoundLHS, FoundRHS);
11528}

11530/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
11531template <typename MinMaxExprType>
11532static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
                               const SCEV *Candidate) {
const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
if (!MinMaxExpr)
  return false;

return is_contained(MinMaxExpr->operands(), Candidate);
11539}

11541static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
                                         ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS) {
// If both sides are affine addrecs for the same loop, with equal
// steps, and we know the recurrences don't wrap, then we only
// need to check the predicate on the starting values.

if (!ICmpInst::isRelational(Pred))
  return false;

const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
if (!LAR)
  return false;
const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
if (!RAR)
  return false;
if (LAR->getLoop() != RAR->getLoop())
  return false;
if (!LAR->isAffine() || !RAR->isAffine())
  return false;

if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
  return false;

SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
                       SCEV::FlagNSW : SCEV::FlagNUW;
if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
  return false;

return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
11571}

11573/// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
11574/// expression?
11575static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
                                      ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS) {
switch (Pred) {
default:
  return false;

case ICmpInst::ICMP_SGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SLE:
  return
      // min(A, ...) <= A
      IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
      // A <= max(A, ...)
      IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);

case ICmpInst::ICMP_UGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_ULE:
  return
      // min(A, ...) <= A
      // FIXME: what about umin_seq?
      IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
      // A <= max(A, ...)
      IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
}

llvm_unreachable("covered switch fell through?!")::llvm::llvm_unreachable_internal("covered switch fell through?!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11604);
11605}

11607bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
                                           const SCEV *LHS, const SCEV *RHS,
                                           const SCEV *FoundLHS,
                                           const SCEV *FoundRHS,
                                           unsigned Depth) {
assert(getTypeSizeInBits(LHS->getType()) ==(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(RHS->getType()) && "LHS and RHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(RHS->getType()) && \"LHS and RHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11614, __extension__
 __PRETTY_FUNCTION__))
           getTypeSizeInBits(RHS->getType()) &&(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(RHS->getType()) && "LHS and RHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(RHS->getType()) && \"LHS and RHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11614, __extension__
 __PRETTY_FUNCTION__))
       "LHS and RHS have different sizes?")(static_cast <bool> (getTypeSizeInBits(LHS->getType(
)) == getTypeSizeInBits(RHS->getType()) && "LHS and RHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(RHS->getType()) && \"LHS and RHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11614, __extension__
 __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(FoundLHS->getType()) ==(static_cast <bool> (getTypeSizeInBits(FoundLHS->getType
()) == getTypeSizeInBits(FoundRHS->getType()) && "FoundLHS and FoundRHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(FoundLHS->getType()) == getTypeSizeInBits(FoundRHS->getType()) && \"FoundLHS and FoundRHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11617, __extension__
 __PRETTY_FUNCTION__))
           getTypeSizeInBits(FoundRHS->getType()) &&(static_cast <bool> (getTypeSizeInBits(FoundLHS->getType
()) == getTypeSizeInBits(FoundRHS->getType()) && "FoundLHS and FoundRHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(FoundLHS->getType()) == getTypeSizeInBits(FoundRHS->getType()) && \"FoundLHS and FoundRHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11617, __extension__
 __PRETTY_FUNCTION__))
       "FoundLHS and FoundRHS have different sizes?")(static_cast <bool> (getTypeSizeInBits(FoundLHS->getType
()) == getTypeSizeInBits(FoundRHS->getType()) && "FoundLHS and FoundRHS have different sizes?"
) ? void (0) : __assert_fail ("getTypeSizeInBits(FoundLHS->getType()) == getTypeSizeInBits(FoundRHS->getType()) && \"FoundLHS and FoundRHS have different sizes?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11617, __extension__
 __PRETTY_FUNCTION__));
// We want to avoid hurting the compile time with analysis of too big trees.
if (Depth > MaxSCEVOperationsImplicationDepth)
  return false;

// We only want to work with GT comparison so far.
if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SLT) {
  Pred = CmpInst::getSwappedPredicate(Pred);
  std::swap(LHS, RHS);
  std::swap(FoundLHS, FoundRHS);
}

// For unsigned, try to reduce it to corresponding signed comparison.
if (Pred == ICmpInst::ICMP_UGT)
  // We can replace unsigned predicate with its signed counterpart if all
  // involved values are non-negative.
  // TODO: We could have better support for unsigned.
  if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) {
    // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing
    // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us
    // use this fact to prove that LHS and RHS are non-negative.
    const SCEV *MinusOne = getMinusOne(LHS->getType());
    if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS,
                              FoundRHS) &&
        isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS,
                              FoundRHS))
      Pred = ICmpInst::ICMP_SGT;
  }

if (Pred != ICmpInst::ICMP_SGT)
  return false;

auto GetOpFromSExt = [&](const SCEV *S) {
  if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
    return Ext->getOperand();
  // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
  // the constant in some cases.
  return S;
};

// Acquire values from extensions.
auto *OrigLHS = LHS;
auto *OrigFoundLHS = FoundLHS;
LHS = GetOpFromSExt(LHS);
FoundLHS = GetOpFromSExt(FoundLHS);

// Is the SGT predicate can be proved trivially or using the found context.
auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
  return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
         isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
                                FoundRHS, Depth + 1);
};

if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
  // We want to avoid creation of any new non-constant SCEV. Since we are
  // going to compare the operands to RHS, we should be certain that we don't
  // need any size extensions for this. So let's decline all cases when the
  // sizes of types of LHS and RHS do not match.
  // TODO: Maybe try to get RHS from sext to catch more cases?
  if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
    return false;

  // Should not overflow.
  if (!LHSAddExpr->hasNoSignedWrap())
    return false;

  auto *LL = LHSAddExpr->getOperand(0);
  auto *LR = LHSAddExpr->getOperand(1);
  auto *MinusOne = getMinusOne(RHS->getType());

  // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
  auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
    return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
  };
  // Try to prove the following rule:
  // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
  // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
  if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
    return true;
} else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
  Value *LL, *LR;
  // FIXME: Once we have SDiv implemented, we can get rid of this matching.

  using namespace llvm::PatternMatch;

  if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
    // Rules for division.
    // We are going to perform some comparisons with Denominator and its
    // derivative expressions. In general case, creating a SCEV for it may
    // lead to a complex analysis of the entire graph, and in particular it
    // can request trip count recalculation for the same loop. This would
    // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
    // this, we only want to create SCEVs that are constants in this section.
    // So we bail if Denominator is not a constant.
    if (!isa<ConstantInt>(LR))
      return false;

    auto *Denominator = cast<SCEVConstant>(getSCEV(LR));

    // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
    // then a SCEV for the numerator already exists and matches with FoundLHS.
    auto *Numerator = getExistingSCEV(LL);
    if (!Numerator || Numerator->getType() != FoundLHS->getType())
      return false;

    // Make sure that the numerator matches with FoundLHS and the denominator
    // is positive.
    if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
      return false;

    auto *DTy = Denominator->getType();
    auto *FRHSTy = FoundRHS->getType();
    if (DTy->isPointerTy() != FRHSTy->isPointerTy())
      // One of types is a pointer and another one is not. We cannot extend
      // them properly to a wider type, so let us just reject this case.
      // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
      // to avoid this check.
      return false;

    // Given that:
    // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
    auto *WTy = getWiderType(DTy, FRHSTy);
    auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
    auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);

    // Try to prove the following rule:
    // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
    // For example, given that FoundLHS > 2. It means that FoundLHS is at
    // least 3. If we divide it by Denominator < 4, we will have at least 1.
    auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
    if (isKnownNonPositive(RHS) &&
        IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
      return true;

    // Try to prove the following rule:
    // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
    // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
    // If we divide it by Denominator > 2, then:
    // 1. If FoundLHS is negative, then the result is 0.
    // 2. If FoundLHS is non-negative, then the result is non-negative.
    // Anyways, the result is non-negative.
    auto *MinusOne = getMinusOne(WTy);
    auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
    if (isKnownNegative(RHS) &&
        IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
      return true;
  }
}

// If our expression contained SCEVUnknown Phis, and we split it down and now
// need to prove something for them, try to prove the predicate for every
// possible incoming values of those Phis.
if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
  return true;

return false;
11773}

11775static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS) {
// zext x u<= sext x, sext x s<= zext x
switch (Pred) {
case ICmpInst::ICMP_SGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SLE: {
  // If operand >=s 0 then ZExt == SExt.  If operand <s 0 then SExt <s ZExt.
  const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS);
  const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS);
  if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
    return true;
  break;
}
case ICmpInst::ICMP_UGE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_ULE: {
  // If operand >=s 0 then ZExt == SExt.  If operand <s 0 then ZExt <u SExt.
  const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS);
  const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS);
  if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
    return true;
  break;
}
default:
  break;
};
return false;
11805}

11807bool
11808ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS) {
return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
25
←
Assuming the condition is false→
28
←
Returning value, which participates in a condition later→
       isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
26
←
Assuming the condition is false→
       IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
       IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
27
←
Assuming the condition is false→
       isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
11815}

11817bool
11818ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
                                           const SCEV *LHS, const SCEV *RHS,
                                           const SCEV *FoundLHS,
                                           const SCEV *FoundRHS) {
switch (Pred) {
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!")::llvm::llvm_unreachable_internal("Unexpected ICmpInst::Predicate value!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11823);
case ICmpInst::ICMP_EQ:
case ICmpInst::ICMP_NE:
  if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
    return true;
  break;
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
  if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
      isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
    return true;
  break;
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
  if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
      isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
    return true;
  break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
  if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
      isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
    return true;
  break;
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
  if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
      isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
    return true;
  break;
}

// Maybe it can be proved via operations?
if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
  return true;

return false;
11860}

11862bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
                                                   const SCEV *LHS,
                                                   const SCEV *RHS,
                                                   const SCEV *FoundLHS,
                                                   const SCEV *FoundRHS) {
if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
  // The restriction on `FoundRHS` be lifted easily -- it exists only to
  // reduce the compile time impact of this optimization.
  return false;

Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
if (!Addend)
  return false;

const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();

// `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
// antecedent "`FoundLHS` `Pred` `FoundRHS`".
ConstantRange FoundLHSRange =
    ConstantRange::makeExactICmpRegion(Pred, ConstFoundRHS);

// Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));

// We can also compute the range of values for `LHS` that satisfy the
// consequent, "`LHS` `Pred` `RHS`":
const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
// The antecedent implies the consequent if every value of `LHS` that
// satisfies the antecedent also satisfies the consequent.
return LHSRange.icmp(Pred, ConstRHS);
11892}

11894bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
                                      bool IsSigned) {
assert(isKnownPositive(Stride) && "Positive stride expected!")(static_cast <bool> (isKnownPositive(Stride) &&
 "Positive stride expected!") ? void (0) : __assert_fail ("isKnownPositive(Stride) && \"Positive stride expected!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11896, __extension__
 __PRETTY_FUNCTION__));

unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());

if (IsSigned) {
  APInt MaxRHS = getSignedRangeMax(RHS);
  APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
  APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));

  // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
  return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
}

APInt MaxRHS = getUnsignedRangeMax(RHS);
APInt MaxValue = APInt::getMaxValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));

// UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
11916}

11918bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
                                      bool IsSigned) {

unsigned BitWidth = getTypeSizeInBits(RHS->getType());
const SCEV *One = getOne(Stride->getType());

if (IsSigned) {
  APInt MinRHS = getSignedRangeMin(RHS);
  APInt MinValue = APInt::getSignedMinValue(BitWidth);
  APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));

  // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
  return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
}

APInt MinRHS = getUnsignedRangeMin(RHS);
APInt MinValue = APInt::getMinValue(BitWidth);
APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));

// UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
11939}

11941const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) {
// umin(N, 1) + floor((N - umin(N, 1)) / D)
// This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin
// expression fixes the case of N=0.
const SCEV *MinNOne = getUMinExpr(N, getOne(N->getType()));
const SCEV *NMinusOne = getMinusSCEV(N, MinNOne);
return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D));
11948}

11950const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
                                                  const SCEV *Stride,
                                                  const SCEV *End,
                                                  unsigned BitWidth,
                                                  bool IsSigned) {
// The logic in this function assumes we can represent a positive stride.
// If we can't, the backedge-taken count must be zero.
if (IsSigned && BitWidth == 1)
  return getZero(Stride->getType());

// This code has only been closely audited for negative strides in the
// unsigned comparison case, it may be correct for signed comparison, but
// that needs to be established.
assert((!IsSigned || !isKnownNonPositive(Stride)) &&(static_cast <bool> ((!IsSigned || !isKnownNonPositive(
Stride)) && "Stride is expected strictly positive for signed case!"
) ? void (0) : __assert_fail ("(!IsSigned || !isKnownNonPositive(Stride)) && \"Stride is expected strictly positive for signed case!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11964, __extension__
 __PRETTY_FUNCTION__))
       "Stride is expected strictly positive for signed case!")(static_cast <bool> ((!IsSigned || !isKnownNonPositive(
Stride)) && "Stride is expected strictly positive for signed case!"
) ? void (0) : __assert_fail ("(!IsSigned || !isKnownNonPositive(Stride)) && \"Stride is expected strictly positive for signed case!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 11964, __extension__
 __PRETTY_FUNCTION__));

// Calculate the maximum backedge count based on the range of values
// permitted by Start, End, and Stride.
APInt MinStart =
    IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);

APInt MinStride =
    IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);

// We assume either the stride is positive, or the backedge-taken count
// is zero. So force StrideForMaxBECount to be at least one.
APInt One(BitWidth, 1);
APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(One, MinStride)
                                     : APIntOps::umax(One, MinStride);

APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
                          : APInt::getMaxValue(BitWidth);
APInt Limit = MaxValue - (StrideForMaxBECount - 1);

// Although End can be a MAX expression we estimate MaxEnd considering only
// the case End = RHS of the loop termination condition. This is safe because
// in the other case (End - Start) is zero, leading to a zero maximum backedge
// taken count.
APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
                        : APIntOps::umin(getUnsignedRangeMax(End), Limit);

// MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride)
MaxEnd = IsSigned ? APIntOps::smax(MaxEnd, MinStart)
                  : APIntOps::umax(MaxEnd, MinStart);

return getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */,
                       getConstant(StrideForMaxBECount) /* Step */);
11997}

11999ScalarEvolution::ExitLimit
12000ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
                                const Loop *L, bool IsSigned,
                                bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;

const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
bool PredicatedIV = false;

auto canAssumeNoSelfWrap = [&](const SCEVAddRecExpr *AR) {
  // Can we prove this loop *must* be UB if overflow of IV occurs?
  // Reasoning goes as follows:
  // * Suppose the IV did self wrap.
  // * If Stride evenly divides the iteration space, then once wrap
  //   occurs, the loop must revisit the same values.
  // * We know that RHS is invariant, and that none of those values
  //   caused this exit to be taken previously.  Thus, this exit is
  //   dynamically dead.
  // * If this is the sole exit, then a dead exit implies the loop
  //   must be infinite if there are no abnormal exits.
  // * If the loop were infinite, then it must either not be mustprogress
  //   or have side effects. Otherwise, it must be UB.
  // * It can't (by assumption), be UB so we have contradicted our
  //   premise and can conclude the IV did not in fact self-wrap.
  if (!isLoopInvariant(RHS, L))
    return false;

  auto *StrideC = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this));
  if (!StrideC || !StrideC->getAPInt().isPowerOf2())
    return false;

  if (!ControlsExit || !loopHasNoAbnormalExits(L))
    return false;

  return loopIsFiniteByAssumption(L);
};

if (!IV) {
  if (auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS)) {
    const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(ZExt->getOperand());
    if (AR && AR->getLoop() == L && AR->isAffine()) {
      auto canProveNUW = [&]() {
        if (!isLoopInvariant(RHS, L))
          return false;

        if (!isKnownNonZero(AR->getStepRecurrence(*this)))
          // We need the sequence defined by AR to strictly increase in the
          // unsigned integer domain for the logic below to hold.
          return false;

        const unsigned InnerBitWidth = getTypeSizeInBits(AR->getType());
        const unsigned OuterBitWidth = getTypeSizeInBits(RHS->getType());
        // If RHS <=u Limit, then there must exist a value V in the sequence
        // defined by AR (e.g. {Start,+,Step}) such that V >u RHS, and
        // V <=u UINT_MAX.  Thus, we must exit the loop before unsigned
        // overflow occurs.  This limit also implies that a signed comparison
        // (in the wide bitwidth) is equivalent to an unsigned comparison as
        // the high bits on both sides must be zero.
        APInt StrideMax = getUnsignedRangeMax(AR->getStepRecurrence(*this));
        APInt Limit = APInt::getMaxValue(InnerBitWidth) - (StrideMax - 1);
        Limit = Limit.zext(OuterBitWidth);
        return getUnsignedRangeMax(applyLoopGuards(RHS, L)).ule(Limit);
      };
      auto Flags = AR->getNoWrapFlags();
      if (!hasFlags(Flags, SCEV::FlagNUW) && canProveNUW())
        Flags = setFlags(Flags, SCEV::FlagNUW);

      setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), Flags);
      if (AR->hasNoUnsignedWrap()) {
        // Emulate what getZeroExtendExpr would have done during construction
        // if we'd been able to infer the fact just above at that time.
        const SCEV *Step = AR->getStepRecurrence(*this);
        Type *Ty = ZExt->getType();
        auto *S = getAddRecExpr(
          getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 0),
          getZeroExtendExpr(Step, Ty, 0), L, AR->getNoWrapFlags());
        IV = dyn_cast<SCEVAddRecExpr>(S);
      }
    }
  }
}


if (!IV && AllowPredicates) {
  // Try to make this an AddRec using runtime tests, in the first X
  // iterations of this loop, where X is the SCEV expression found by the
  // algorithm below.
  IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
  PredicatedIV = true;
}

// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
  return getCouldNotCompute();

// A precondition of this method is that the condition being analyzed
// reaches an exiting branch which dominates the latch.  Given that, we can
// assume that an increment which violates the nowrap specification and
// produces poison must cause undefined behavior when the resulting poison
// value is branched upon and thus we can conclude that the backedge is
// taken no more often than would be required to produce that poison value.
// Note that a well defined loop can exit on the iteration which violates
// the nowrap specification if there is another exit (either explicit or
// implicit/exceptional) which causes the loop to execute before the
// exiting instruction we're analyzing would trigger UB.
auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType);
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT;

const SCEV *Stride = IV->getStepRecurrence(*this);

bool PositiveStride = isKnownPositive(Stride);

// Avoid negative or zero stride values.
if (!PositiveStride) {
  // We can compute the correct backedge taken count for loops with unknown
  // strides if we can prove that the loop is not an infinite loop with side
  // effects. Here's the loop structure we are trying to handle -
  //
  // i = start
  // do {
  //   A[i] = i;
  //   i += s;
  // } while (i < end);
  //
  // The backedge taken count for such loops is evaluated as -
  // (max(end, start + stride) - start - 1) /u stride
  //
  // The additional preconditions that we need to check to prove correctness
  // of the above formula is as follows -
  //
  // a) IV is either nuw or nsw depending upon signedness (indicated by the
  //    NoWrap flag).
  // b) the loop is guaranteed to be finite (e.g. is mustprogress and has
  //    no side effects within the loop)
  // c) loop has a single static exit (with no abnormal exits)
  //
  // Precondition a) implies that if the stride is negative, this is a single
  // trip loop. The backedge taken count formula reduces to zero in this case.
  //
  // Precondition b) and c) combine to imply that if rhs is invariant in L,
  // then a zero stride means the backedge can't be taken without executing
  // undefined behavior.
  //
  // The positive stride case is the same as isKnownPositive(Stride) returning
  // true (original behavior of the function).
  //
  if (PredicatedIV || !NoWrap || !loopIsFiniteByAssumption(L) ||
      !loopHasNoAbnormalExits(L))
    return getCouldNotCompute();

  // This bailout is protecting the logic in computeMaxBECountForLT which
  // has not yet been sufficiently auditted or tested with negative strides.
  // We used to filter out all known-non-positive cases here, we're in the
  // process of being less restrictive bit by bit.
  if (IsSigned && isKnownNonPositive(Stride))
    return getCouldNotCompute();

  if (!isKnownNonZero(Stride)) {
    // If we have a step of zero, and RHS isn't invariant in L, we don't know
    // if it might eventually be greater than start and if so, on which
    // iteration.  We can't even produce a useful upper bound.
    if (!isLoopInvariant(RHS, L))
      return getCouldNotCompute();

    // We allow a potentially zero stride, but we need to divide by stride
    // below.  Since the loop can't be infinite and this check must control
    // the sole exit, we can infer the exit must be taken on the first
    // iteration (e.g. backedge count = 0) if the stride is zero.  Given that,
    // we know the numerator in the divides below must be zero, so we can
    // pick an arbitrary non-zero value for the denominator (e.g. stride)
    // and produce the right result.
    // FIXME: Handle the case where Stride is poison?
    auto wouldZeroStrideBeUB = [&]() {
      // Proof by contradiction.  Suppose the stride were zero.  If we can
      // prove that the backedge *is* taken on the first iteration, then since
      // we know this condition controls the sole exit, we must have an
      // infinite loop.  We can't have a (well defined) infinite loop per
      // check just above.
      // Note: The (Start - Stride) term is used to get the start' term from
      // (start' + stride,+,stride). Remember that we only care about the
      // result of this expression when stride == 0 at runtime.
      auto *StartIfZero = getMinusSCEV(IV->getStart(), Stride);
      return isLoopEntryGuardedByCond(L, Cond, StartIfZero, RHS);
    };
    if (!wouldZeroStrideBeUB()) {
      Stride = getUMaxExpr(Stride, getOne(Stride->getType()));
    }
  }
} else if (!Stride->isOne() && !NoWrap) {
  auto isUBOnWrap = [&]() {
    // From no-self-wrap, we need to then prove no-(un)signed-wrap.  This
    // follows trivially from the fact that every (un)signed-wrapped, but
    // not self-wrapped value must be LT than the last value before
    // (un)signed wrap.  Since we know that last value didn't exit, nor
    // will any smaller one.
    return canAssumeNoSelfWrap(IV);
  };

  // Avoid proven overflow cases: this will ensure that the backedge taken
  // count will not generate any unsigned overflow. Relaxed no-overflow
  // conditions exploit NoWrapFlags, allowing to optimize in presence of
  // undefined behaviors like the case of C language.
  if (canIVOverflowOnLT(RHS, Stride, IsSigned) && !isUBOnWrap())
    return getCouldNotCompute();
}

// On all paths just preceeding, we established the following invariant:
//   IV can be assumed not to overflow up to and including the exiting
//   iteration.  We proved this in one of two ways:
//   1) We can show overflow doesn't occur before the exiting iteration
//      1a) canIVOverflowOnLT, and b) step of one
//   2) We can show that if overflow occurs, the loop must execute UB
//      before any possible exit.
// Note that we have not yet proved RHS invariant (in general).

const SCEV *Start = IV->getStart();

// Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond.
// If we convert to integers, isLoopEntryGuardedByCond will miss some cases.
// Use integer-typed versions for actual computation; we can't subtract
// pointers in general.
const SCEV *OrigStart = Start;
const SCEV *OrigRHS = RHS;
if (Start->getType()->isPointerTy()) {
  Start = getLosslessPtrToIntExpr(Start);
  if (isa<SCEVCouldNotCompute>(Start))
    return Start;
}
if (RHS->getType()->isPointerTy()) {
  RHS = getLosslessPtrToIntExpr(RHS);
  if (isa<SCEVCouldNotCompute>(RHS))
    return RHS;
}

// When the RHS is not invariant, we do not know the end bound of the loop and
// cannot calculate the ExactBECount needed by ExitLimit. However, we can
// calculate the MaxBECount, given the start, stride and max value for the end
// bound of the loop (RHS), and the fact that IV does not overflow (which is
// checked above).
if (!isLoopInvariant(RHS, L)) {
  const SCEV *MaxBECount = computeMaxBECountForLT(
      Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
  return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
                   false /*MaxOrZero*/, Predicates);
}

// We use the expression (max(End,Start)-Start)/Stride to describe the
// backedge count, as if the backedge is taken at least once max(End,Start)
// is End and so the result is as above, and if not max(End,Start) is Start
// so we get a backedge count of zero.
const SCEV *BECount = nullptr;
auto *OrigStartMinusStride = getMinusSCEV(OrigStart, Stride);
assert(isAvailableAtLoopEntry(OrigStartMinusStride, L) && "Must be!")(static_cast <bool> (isAvailableAtLoopEntry(OrigStartMinusStride
, L) && "Must be!") ? void (0) : __assert_fail ("isAvailableAtLoopEntry(OrigStartMinusStride, L) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12252, __extension__
 __PRETTY_FUNCTION__));
assert(isAvailableAtLoopEntry(OrigStart, L) && "Must be!")(static_cast <bool> (isAvailableAtLoopEntry(OrigStart, L
) && "Must be!") ? void (0) : __assert_fail ("isAvailableAtLoopEntry(OrigStart, L) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12253, __extension__
 __PRETTY_FUNCTION__));
assert(isAvailableAtLoopEntry(OrigRHS, L) && "Must be!")(static_cast <bool> (isAvailableAtLoopEntry(OrigRHS, L)
 && "Must be!") ? void (0) : __assert_fail ("isAvailableAtLoopEntry(OrigRHS, L) && \"Must be!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12254, __extension__
 __PRETTY_FUNCTION__));
// Can we prove (max(RHS,Start) > Start - Stride?
if (isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigStart) &&
    isLoopEntryGuardedByCond(L, Cond, OrigStartMinusStride, OrigRHS)) {
  // In this case, we can use a refined formula for computing backedge taken
  // count.  The general formula remains:
  //   "End-Start /uceiling Stride" where "End = max(RHS,Start)"
  // We want to use the alternate formula:
  //   "((End - 1) - (Start - Stride)) /u Stride"
  // Let's do a quick case analysis to show these are equivalent under
  // our precondition that max(RHS,Start) > Start - Stride.
  // * For RHS <= Start, the backedge-taken count must be zero.
  //   "((End - 1) - (Start - Stride)) /u Stride" reduces to
  //   "((Start - 1) - (Start - Stride)) /u Stride" which simplies to
  //   "Stride - 1 /u Stride" which is indeed zero for all non-zero values
  //     of Stride.  For 0 stride, we've use umin(1,Stride) above, reducing
  //     this to the stride of 1 case.
  // * For RHS >= Start, the backedge count must be "RHS-Start /uceil Stride".
  //   "((End - 1) - (Start - Stride)) /u Stride" reduces to
  //   "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
  //   "((RHS - (Start - Stride) - 1) /u Stride".
  //   Our preconditions trivially imply no overflow in that form.
  const SCEV *MinusOne = getMinusOne(Stride->getType());
  const SCEV *Numerator =
      getMinusSCEV(getAddExpr(RHS, MinusOne), getMinusSCEV(Start, Stride));
  BECount = getUDivExpr(Numerator, Stride);
}

const SCEV *BECountIfBackedgeTaken = nullptr;
if (!BECount) {
  auto canProveRHSGreaterThanEqualStart = [&]() {
    auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
    if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart))
      return true;

    // (RHS > Start - 1) implies RHS >= Start.
    // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
    //   "Start - 1" doesn't overflow.
    // * For signed comparison, if Start - 1 does overflow, it's equal
    //   to INT_MAX, and "RHS >s INT_MAX" is trivially false.
    // * For unsigned comparison, if Start - 1 does overflow, it's equal
    //   to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
    //
    // FIXME: Should isLoopEntryGuardedByCond do this for us?
    auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
    auto *StartMinusOne = getAddExpr(OrigStart,
                                     getMinusOne(OrigStart->getType()));
    return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne);
  };

  // If we know that RHS >= Start in the context of loop, then we know that
  // max(RHS, Start) = RHS at this point.
  const SCEV *End;
  if (canProveRHSGreaterThanEqualStart()) {
    End = RHS;
  } else {
    // If RHS < Start, the backedge will be taken zero times.  So in
    // general, we can write the backedge-taken count as:
    //
    //     RHS >= Start ? ceil(RHS - Start) / Stride : 0
    //
    // We convert it to the following to make it more convenient for SCEV:
    //
    //     ceil(max(RHS, Start) - Start) / Stride
    End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);

    // See what would happen if we assume the backedge is taken. This is
    // used to compute MaxBECount.
    BECountIfBackedgeTaken = getUDivCeilSCEV(getMinusSCEV(RHS, Start), Stride);
  }

  // At this point, we know:
  //
  // 1. If IsSigned, Start <=s End; otherwise, Start <=u End
  // 2. The index variable doesn't overflow.
  //
  // Therefore, we know N exists such that
  // (Start + Stride * N) >= End, and computing "(Start + Stride * N)"
  // doesn't overflow.
  //
  // Using this information, try to prove whether the addition in
  // "(Start - End) + (Stride - 1)" has unsigned overflow.
  const SCEV *One = getOne(Stride->getType());
  bool MayAddOverflow = [&] {
    if (auto *StrideC = dyn_cast<SCEVConstant>(Stride)) {
      if (StrideC->getAPInt().isPowerOf2()) {
        // Suppose Stride is a power of two, and Start/End are unsigned
        // integers.  Let UMAX be the largest representable unsigned
        // integer.
        //
        // By the preconditions of this function, we know
        // "(Start + Stride * N) >= End", and this doesn't overflow.
        // As a formula:
        //
        //   End <= (Start + Stride * N) <= UMAX
        //
        // Subtracting Start from all the terms:
        //
        //   End - Start <= Stride * N <= UMAX - Start
        //
        // Since Start is unsigned, UMAX - Start <= UMAX.  Therefore:
        //
        //   End - Start <= Stride * N <= UMAX
        //
        // Stride * N is a multiple of Stride. Therefore,
        //
        //   End - Start <= Stride * N <= UMAX - (UMAX mod Stride)
        //
        // Since Stride is a power of two, UMAX + 1 is divisible by Stride.
        // Therefore, UMAX mod Stride == Stride - 1.  So we can write:
        //
        //   End - Start <= Stride * N <= UMAX - Stride - 1
        //
        // Dropping the middle term:
        //
        //   End - Start <= UMAX - Stride - 1
        //
        // Adding Stride - 1 to both sides:
        //
        //   (End - Start) + (Stride - 1) <= UMAX
        //
        // In other words, the addition doesn't have unsigned overflow.
        //
        // A similar proof works if we treat Start/End as signed values.
        // Just rewrite steps before "End - Start <= Stride * N <= UMAX" to
        // use signed max instead of unsigned max. Note that we're trying
        // to prove a lack of unsigned overflow in either case.
        return false;
      }
    }
    if (Start == Stride || Start == getMinusSCEV(Stride, One)) {
      // If Start is equal to Stride, (End - Start) + (Stride - 1) == End - 1.
      // If !IsSigned, 0 <u Stride == Start <=u End; so 0 <u End - 1 <u End.
      // If IsSigned, 0 <s Stride == Start <=s End; so 0 <s End - 1 <s End.
      //
      // If Start is equal to Stride - 1, (End - Start) + Stride - 1 == End.
      return false;
    }
    return true;
  }();

  const SCEV *Delta = getMinusSCEV(End, Start);
  if (!MayAddOverflow) {
    // floor((D + (S - 1)) / S)
    // We prefer this formulation if it's legal because it's fewer operations.
    BECount =
        getUDivExpr(getAddExpr(Delta, getMinusSCEV(Stride, One)), Stride);
  } else {
    BECount = getUDivCeilSCEV(Delta, Stride);
  }
}

const SCEV *MaxBECount;
bool MaxOrZero = false;
if (isa<SCEVConstant>(BECount)) {
  MaxBECount = BECount;
} else if (BECountIfBackedgeTaken &&
           isa<SCEVConstant>(BECountIfBackedgeTaken)) {
  // If we know exactly how many times the backedge will be taken if it's
  // taken at least once, then the backedge count will either be that or
  // zero.
  MaxBECount = BECountIfBackedgeTaken;
  MaxOrZero = true;
} else {
  MaxBECount = computeMaxBECountForLT(
      Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
}

if (isa<SCEVCouldNotCompute>(MaxBECount) &&
    !isa<SCEVCouldNotCompute>(BECount))
  MaxBECount = getConstant(getUnsignedRangeMax(BECount));

return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
12427}

12429ScalarEvolution::ExitLimit
12430ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
                                   const Loop *L, bool IsSigned,
                                   bool ControlsExit, bool AllowPredicates) {
SmallPtrSet<const SCEVPredicate *, 4> Predicates;
// We handle only IV > Invariant
if (!isLoopInvariant(RHS, L))
  return getCouldNotCompute();

const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
if (!IV && AllowPredicates)
  // Try to make this an AddRec using runtime tests, in the first X
  // iterations of this loop, where X is the SCEV expression found by the
  // algorithm below.
  IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);

// Avoid weird loops
if (!IV || IV->getLoop() != L || !IV->isAffine())
  return getCouldNotCompute();

auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW;
bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType);
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;

const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));

// Avoid negative or zero stride values
if (!isKnownPositive(Stride))
  return getCouldNotCompute();

// Avoid proven overflow cases: this will ensure that the backedge taken count
// will not generate any unsigned overflow. Relaxed no-overflow conditions
// exploit NoWrapFlags, allowing to optimize in presence of undefined
// behaviors like the case of C language.
if (!Stride->isOne() && !NoWrap)
  if (canIVOverflowOnGT(RHS, Stride, IsSigned))
    return getCouldNotCompute();

const SCEV *Start = IV->getStart();
const SCEV *End = RHS;
if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
  // If we know that Start >= RHS in the context of loop, then we know that
  // min(RHS, Start) = RHS at this point.
  if (isLoopEntryGuardedByCond(
          L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS))
    End = RHS;
  else
    End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
}

if (Start->getType()->isPointerTy()) {
  Start = getLosslessPtrToIntExpr(Start);
  if (isa<SCEVCouldNotCompute>(Start))
    return Start;
}
if (End->getType()->isPointerTy()) {
  End = getLosslessPtrToIntExpr(End);
  if (isa<SCEVCouldNotCompute>(End))
    return End;
}

// Compute ((Start - End) + (Stride - 1)) / Stride.
// FIXME: This can overflow. Holding off on fixing this for now;
// howManyGreaterThans will hopefully be gone soon.
const SCEV *One = getOne(Stride->getType());
const SCEV *BECount = getUDivExpr(
    getAddExpr(getMinusSCEV(Start, End), getMinusSCEV(Stride, One)), Stride);

APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
                          : getUnsignedRangeMax(Start);

APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
                           : getUnsignedRangeMin(Stride);

unsigned BitWidth = getTypeSizeInBits(LHS->getType());
APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
                       : APInt::getMinValue(BitWidth) + (MinStride - 1);

// Although End can be a MIN expression we estimate MinEnd considering only
// the case End = RHS. This is safe because in the other case (Start - End)
// is zero, leading to a zero maximum backedge taken count.
APInt MinEnd =
  IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
           : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);

const SCEV *MaxBECount = isa<SCEVConstant>(BECount)
                             ? BECount
                             : getUDivCeilSCEV(getConstant(MaxStart - MinEnd),
                                               getConstant(MinStride));

if (isa<SCEVCouldNotCompute>(MaxBECount))
  MaxBECount = BECount;

return ExitLimit(BECount, MaxBECount, false, Predicates);
12523}

12525const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
                                                  ScalarEvolution &SE) const {
if (Range.isFullSet())  // Infinite loop.
  return SE.getCouldNotCompute();

// If the start is a non-zero constant, shift the range to simplify things.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
  if (!SC->getValue()->isZero()) {
    SmallVector<const SCEV *, 4> Operands(operands());
    Operands[0] = SE.getZero(SC->getType());
    const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
                                           getNoWrapFlags(FlagNW));
    if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
      return ShiftedAddRec->getNumIterationsInRange(
          Range.subtract(SC->getAPInt()), SE);
    // This is strange and shouldn't happen.
    return SE.getCouldNotCompute();
  }

// The only time we can solve this is when we have all constant indices.
// Otherwise, we cannot determine the overflow conditions.
if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
  return SE.getCouldNotCompute();

// Okay at this point we know that all elements of the chrec are constants and
// that the start element is zero.

// First check to see if the range contains zero.  If not, the first
// iteration exits.
unsigned BitWidth = SE.getTypeSizeInBits(getType());
if (!Range.contains(APInt(BitWidth, 0)))
  return SE.getZero(getType());

if (isAffine()) {
  // If this is an affine expression then we have this situation:
  //   Solve {0,+,A} in Range  ===  Ax in Range

  // We know that zero is in the range.  If A is positive then we know that
  // the upper value of the range must be the first possible exit value.
  // If A is negative then the lower of the range is the last possible loop
  // value.  Also note that we already checked for a full range.
  APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
  APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();

  // The exit value should be (End+A)/A.
  APInt ExitVal = (End + A).udiv(A);
  ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);

  // Evaluate at the exit value.  If we really did fall out of the valid
  // range, then we computed our trip count, otherwise wrap around or other
  // things must have happened.
  ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
  if (Range.contains(Val->getValue()))
    return SE.getCouldNotCompute();  // Something strange happened

  // Ensure that the previous value is in the range.
  assert(Range.contains((static_cast <bool> (Range.contains( EvaluateConstantChrecAtConstant
(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->
getValue()) && "Linear scev computation is off in a bad way!"
) ? void (0) : __assert_fail ("Range.contains( EvaluateConstantChrecAtConstant(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && \"Linear scev computation is off in a bad way!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12584, __extension__
 __PRETTY_FUNCTION__))
         EvaluateConstantChrecAtConstant(this,(static_cast <bool> (Range.contains( EvaluateConstantChrecAtConstant
(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->
getValue()) && "Linear scev computation is off in a bad way!"
) ? void (0) : __assert_fail ("Range.contains( EvaluateConstantChrecAtConstant(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && \"Linear scev computation is off in a bad way!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12584, __extension__
 __PRETTY_FUNCTION__))
         ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&(static_cast <bool> (Range.contains( EvaluateConstantChrecAtConstant
(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->
getValue()) && "Linear scev computation is off in a bad way!"
) ? void (0) : __assert_fail ("Range.contains( EvaluateConstantChrecAtConstant(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && \"Linear scev computation is off in a bad way!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12584, __extension__
 __PRETTY_FUNCTION__))
         "Linear scev computation is off in a bad way!")(static_cast <bool> (Range.contains( EvaluateConstantChrecAtConstant
(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->
getValue()) && "Linear scev computation is off in a bad way!"
) ? void (0) : __assert_fail ("Range.contains( EvaluateConstantChrecAtConstant(this, ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && \"Linear scev computation is off in a bad way!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12584, __extension__
 __PRETTY_FUNCTION__));
  return SE.getConstant(ExitValue);
}

if (isQuadratic()) {
  if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
    return SE.getConstant(S.getValue());
}

return SE.getCouldNotCompute();
12594}

12596const SCEVAddRecExpr *
12597SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
assert(getNumOperands() > 1 && "AddRec with zero step?")(static_cast <bool> (getNumOperands() > 1 &&
 "AddRec with zero step?") ? void (0) : __assert_fail ("getNumOperands() > 1 && \"AddRec with zero step?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12598, __extension__
 __PRETTY_FUNCTION__));
// There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
// but in this case we cannot guarantee that the value returned will be an
// AddRec because SCEV does not have a fixed point where it stops
// simplification: it is legal to return ({rec1} + {rec2}). For example, it
// may happen if we reach arithmetic depth limit while simplifying. So we
// construct the returned value explicitly.
SmallVector<const SCEV *, 3> Ops;
// If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
// (this + Step) is {A+B,+,B+C,+...,+,N}.
for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
  Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
// We know that the last operand is not a constant zero (otherwise it would
// have been popped out earlier). This guarantees us that if the result has
// the same last operand, then it will also not be popped out, meaning that
// the returned value will be an AddRec.
const SCEV *Last = getOperand(getNumOperands() - 1);
assert(!Last->isZero() && "Recurrency with zero step?")(static_cast <bool> (!Last->isZero() && "Recurrency with zero step?"
) ? void (0) : __assert_fail ("!Last->isZero() && \"Recurrency with zero step?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12615, __extension__
 __PRETTY_FUNCTION__));
Ops.push_back(Last);
return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
                                             SCEV::FlagAnyWrap));
12619}

12621// Return true when S contains at least an undef value.
12622bool ScalarEvolution::containsUndefs(const SCEV *S) const {
return SCEVExprContains(S, [](const SCEV *S) {
  if (const auto *SU = dyn_cast<SCEVUnknown>(S))
    return isa<UndefValue>(SU->getValue());
  return false;
});
12628}

12630/// Return the size of an element read or written by Inst.
12631const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
Type *Ty;
if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
  Ty = Store->getValueOperand()->getType();
else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
  Ty = Load->getType();
else
  return nullptr;

Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
return getSizeOfExpr(ETy, Ty);
12642}

12644//===----------------------------------------------------------------------===//
12645//                   SCEVCallbackVH Class Implementation
12646//===----------------------------------------------------------------------===//

12648void ScalarEvolution::SCEVCallbackVH::deleted() {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!")(static_cast <bool> (SE && "SCEVCallbackVH called with a null ScalarEvolution!"
) ? void (0) : __assert_fail ("SE && \"SCEVCallbackVH called with a null ScalarEvolution!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12649, __extension__
 __PRETTY_FUNCTION__));
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
  SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(getValPtr());
// this now dangles!
12654}

12656void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!")(static_cast <bool> (SE && "SCEVCallbackVH called with a null ScalarEvolution!"
) ? void (0) : __assert_fail ("SE && \"SCEVCallbackVH called with a null ScalarEvolution!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12657, __extension__
 __PRETTY_FUNCTION__));

// Forget all the expressions associated with users of the old value,
// so that future queries will recompute the expressions using the new
// value.
Value *Old = getValPtr();
SmallVector<User *, 16> Worklist(Old->users());
SmallPtrSet<User *, 8> Visited;
while (!Worklist.empty()) {
  User *U = Worklist.pop_back_val();
  // Deleting the Old value will cause this to dangle. Postpone
  // that until everything else is done.
  if (U == Old)
    continue;
  if (!Visited.insert(U).second)
    continue;
  if (PHINode *PN = dyn_cast<PHINode>(U))
    SE->ConstantEvolutionLoopExitValue.erase(PN);
  SE->eraseValueFromMap(U);
  llvm::append_range(Worklist, U->users());
}
// Delete the Old value.
if (PHINode *PN = dyn_cast<PHINode>(Old))
  SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->eraseValueFromMap(Old);
// this now dangles!
12683}

12685ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
: CallbackVH(V), SE(se) {}

12688//===----------------------------------------------------------------------===//
12689//                   ScalarEvolution Class Implementation
12690//===----------------------------------------------------------------------===//

12692ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
                               AssumptionCache &AC, DominatorTree &DT,
                               LoopInfo &LI)
  : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
    CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
    LoopDispositions(64), BlockDispositions(64) {
// To use guards for proving predicates, we need to scan every instruction in
// relevant basic blocks, and not just terminators.  Doing this is a waste of
// time if the IR does not actually contain any calls to
// @llvm.experimental.guard, so do a quick check and remember this beforehand.
//
// This pessimizes the case where a pass that preserves ScalarEvolution wants
// to _add_ guards to the module when there weren't any before, and wants
// ScalarEvolution to optimize based on those guards.  For now we prefer to be
// efficient in lieu of being smart in that rather obscure case.

auto *GuardDecl = F.getParent()->getFunction(
    Intrinsic::getName(Intrinsic::experimental_guard));
HasGuards = GuardDecl && !GuardDecl->use_empty();
12711}

12713ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
  : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
    LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
    ValueExprMap(std::move(Arg.ValueExprMap)),
    PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
    PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
    PendingMerges(std::move(Arg.PendingMerges)),
    MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
    BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
    PredicatedBackedgeTakenCounts(
        std::move(Arg.PredicatedBackedgeTakenCounts)),
    BECountUsers(std::move(Arg.BECountUsers)),
    ConstantEvolutionLoopExitValue(
        std::move(Arg.ConstantEvolutionLoopExitValue)),
    ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
    ValuesAtScopesUsers(std::move(Arg.ValuesAtScopesUsers)),
    LoopDispositions(std::move(Arg.LoopDispositions)),
    LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
    BlockDispositions(std::move(Arg.BlockDispositions)),
    SCEVUsers(std::move(Arg.SCEVUsers)),
    UnsignedRanges(std::move(Arg.UnsignedRanges)),
    SignedRanges(std::move(Arg.SignedRanges)),
    UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
    UniquePreds(std::move(Arg.UniquePreds)),
    SCEVAllocator(std::move(Arg.SCEVAllocator)),
    LoopUsers(std::move(Arg.LoopUsers)),
    PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
    FirstUnknown(Arg.FirstUnknown) {
Arg.FirstUnknown = nullptr;
12742}

12744ScalarEvolution::~ScalarEvolution() {
// Iterate through all the SCEVUnknown instances and call their
// destructors, so that they release their references to their values.
for (SCEVUnknown *U = FirstUnknown; U;) {
  SCEVUnknown *Tmp = U;
  U = U->Next;
  Tmp->~SCEVUnknown();
}
FirstUnknown = nullptr;

ExprValueMap.clear();
ValueExprMap.clear();
HasRecMap.clear();
BackedgeTakenCounts.clear();
PredicatedBackedgeTakenCounts.clear();

assert(PendingLoopPredicates.empty() && "isImpliedCond garbage")(static_cast <bool> (PendingLoopPredicates.empty() &&
 "isImpliedCond garbage") ? void (0) : __assert_fail ("PendingLoopPredicates.empty() && \"isImpliedCond garbage\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12760, __extension__
 __PRETTY_FUNCTION__));
assert(PendingPhiRanges.empty() && "getRangeRef garbage")(static_cast <bool> (PendingPhiRanges.empty() &&
 "getRangeRef garbage") ? void (0) : __assert_fail ("PendingPhiRanges.empty() && \"getRangeRef garbage\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12761, __extension__
 __PRETTY_FUNCTION__));
assert(PendingMerges.empty() && "isImpliedViaMerge garbage")(static_cast <bool> (PendingMerges.empty() && "isImpliedViaMerge garbage"
) ? void (0) : __assert_fail ("PendingMerges.empty() && \"isImpliedViaMerge garbage\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12762, __extension__
 __PRETTY_FUNCTION__));
assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!")(static_cast <bool> (!WalkingBEDominatingConds &&
 "isLoopBackedgeGuardedByCond garbage!") ? void (0) : __assert_fail
 ("!WalkingBEDominatingConds && \"isLoopBackedgeGuardedByCond garbage!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12763, __extension__
 __PRETTY_FUNCTION__));
assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!")(static_cast <bool> (!ProvingSplitPredicate && "ProvingSplitPredicate garbage!"
) ? void (0) : __assert_fail ("!ProvingSplitPredicate && \"ProvingSplitPredicate garbage!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12764, __extension__
 __PRETTY_FUNCTION__));
12765}

12767bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
12769}

12771static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
                        const Loop *L) {
// Print all inner loops first
for (Loop *I : *L)
  PrintLoopInfo(OS, SE, I);

OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";

SmallVector<BasicBlock *, 8> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);
if (ExitingBlocks.size() != 1)
  OS << "<multiple exits> ";

if (SE->hasLoopInvariantBackedgeTakenCount(L))
  OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n";
else
  OS << "Unpredictable backedge-taken count.\n";

if (ExitingBlocks.size() > 1)
  for (BasicBlock *ExitingBlock : ExitingBlocks) {
    OS << "  exit count for " << ExitingBlock->getName() << ": "
       << *SE->getExitCount(L, ExitingBlock) << "\n";
  }

OS << "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";

if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) {
  OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L);
  if (SE->isBackedgeTakenCountMaxOrZero(L))
    OS << ", actual taken count either this or zero.";
} else {
  OS << "Unpredictable max backedge-taken count. ";
}

OS << "\n"
      "Loop ";
L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
OS << ": ";

SCEVUnionPredicate Pred;
auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
if (!isa<SCEVCouldNotCompute>(PBT)) {
  OS << "Predicated backedge-taken count is " << *PBT << "\n";
  OS << " Predicates:\n";
  Pred.print(OS, 4);
} else {
  OS << "Unpredictable predicated backedge-taken count. ";
}
OS << "\n";

if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
  OS << "Loop ";
  L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
  OS << ": ";
  OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
}
12831}

12833static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
switch (LD) {
case ScalarEvolution::LoopVariant:
  return "Variant";
case ScalarEvolution::LoopInvariant:
  return "Invariant";
case ScalarEvolution::LoopComputable:
  return "Computable";
}
llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!")::llvm::llvm_unreachable_internal("Unknown ScalarEvolution::LoopDisposition kind!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12842);
12843}

12845void ScalarEvolution::print(raw_ostream &OS) const {
// ScalarEvolution's implementation of the print method is to print
// out SCEV values of all instructions that are interesting. Doing
// this potentially causes it to create new SCEV objects though,
// which technically conflicts with the const qualifier. This isn't
// observable from outside the class though, so casting away the
// const isn't dangerous.
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);

if (ClassifyExpressions) {
  OS << "Classifying expressions for: ";
  F.printAsOperand(OS, /*PrintType=*/false);
  OS << "\n";
  for (Instruction &I : instructions(F))
    if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
      OS << I << '\n';
      OS << "  -->  ";
      const SCEV *SV = SE.getSCEV(&I);
      SV->print(OS);
      if (!isa<SCEVCouldNotCompute>(SV)) {
        OS << " U: ";
        SE.getUnsignedRange(SV).print(OS);
        OS << " S: ";
        SE.getSignedRange(SV).print(OS);
      }

      const Loop *L = LI.getLoopFor(I.getParent());

      const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
      if (AtUse != SV) {
        OS << "  -->  ";
        AtUse->print(OS);
        if (!isa<SCEVCouldNotCompute>(AtUse)) {
          OS << " U: ";
          SE.getUnsignedRange(AtUse).print(OS);
          OS << " S: ";
          SE.getSignedRange(AtUse).print(OS);
        }
      }

      if (L) {
        OS << "\t\t" "Exits: ";
        const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
        if (!SE.isLoopInvariant(ExitValue, L)) {
          OS << "<<Unknown>>";
        } else {
          OS << *ExitValue;
        }

        bool First = true;
        for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
          if (First) {
            OS << "\t\t" "LoopDispositions: { ";
            First = false;
          } else {
            OS << ", ";
          }

          Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
          OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
        }

        for (auto *InnerL : depth_first(L)) {
          if (InnerL == L)
            continue;
          if (First) {
            OS << "\t\t" "LoopDispositions: { ";
            First = false;
          } else {
            OS << ", ";
          }

          InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
          OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
        }

        OS << " }";
      }

      OS << "\n";
    }
}

OS << "Determining loop execution counts for: ";
F.printAsOperand(OS, /*PrintType=*/false);
OS << "\n";
for (Loop *I : LI)
  PrintLoopInfo(OS, &SE, I);
12933}

12935ScalarEvolution::LoopDisposition
12936ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
auto &Values = LoopDispositions[S];
for (auto &V : Values) {
  if (V.getPointer() == L)
    return V.getInt();
}
Values.emplace_back(L, LoopVariant);
LoopDisposition D = computeLoopDisposition(S, L);
auto &Values2 = LoopDispositions[S];
for (auto &V : llvm::reverse(Values2)) {
  if (V.getPointer() == L) {
    V.setInt(D);
    break;
  }
}
return D;
12952}

12954ScalarEvolution::LoopDisposition
12955ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
switch (S->getSCEVType()) {
case scConstant:
  return LoopInvariant;
case scPtrToInt:
case scTruncate:
case scZeroExtend:
case scSignExtend:
  return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
case scAddRecExpr: {
  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);

  // If L is the addrec's loop, it's computable.
  if (AR->getLoop() == L)
    return LoopComputable;

  // Add recurrences are never invariant in the function-body (null loop).
  if (!L)
    return LoopVariant;

  // Everything that is not defined at loop entry is variant.
  if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
    return LoopVariant;
  assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"(static_cast <bool> (!L->contains(AR->getLoop()) &&
 "Containing loop's header does not" " dominate the contained loop's header?"
) ? void (0) : __assert_fail ("!L->contains(AR->getLoop()) && \"Containing loop's header does not\" \" dominate the contained loop's header?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12979, __extension__
 __PRETTY_FUNCTION__))
         " dominate the contained loop's header?")(static_cast <bool> (!L->contains(AR->getLoop()) &&
 "Containing loop's header does not" " dominate the contained loop's header?"
) ? void (0) : __assert_fail ("!L->contains(AR->getLoop()) && \"Containing loop's header does not\" \" dominate the contained loop's header?\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 12979, __extension__
 __PRETTY_FUNCTION__));

  // This recurrence is invariant w.r.t. L if AR's loop contains L.
  if (AR->getLoop()->contains(L))
    return LoopInvariant;

  // This recurrence is variant w.r.t. L if any of its operands
  // are variant.
  for (auto *Op : AR->operands())
    if (!isLoopInvariant(Op, L))
      return LoopVariant;

  // Otherwise it's loop-invariant.
  return LoopInvariant;
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
case scSequentialUMinExpr: {
  bool HasVarying = false;
  for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
    LoopDisposition D = getLoopDisposition(Op, L);
    if (D == LoopVariant)
      return LoopVariant;
    if (D == LoopComputable)
      HasVarying = true;
  }
  return HasVarying ? LoopComputable : LoopInvariant;
}
case scUDivExpr: {
  const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
  LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
  if (LD == LoopVariant)
    return LoopVariant;
  LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
  if (RD == LoopVariant)
    return LoopVariant;
  return (LD == LoopInvariant && RD == LoopInvariant) ?
         LoopInvariant : LoopComputable;
}
case scUnknown:
  // All non-instruction values are loop invariant.  All instructions are loop
  // invariant if they are not contained in the specified loop.
  // Instructions are never considered invariant in the function body
  // (null loop) because they are defined within the "loop".
  if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
    return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
  return LoopInvariant;
case scCouldNotCompute:
  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13031);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 13033);
13034}

13036bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopInvariant;
13038}

13040bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
return getLoopDisposition(S, L) == LoopComputable;
13042}

13044ScalarEvolution::BlockDisposition
13045ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
auto &Values = BlockDispositions[S];
for (auto &V : Values) {
  if (V.getPointer() == BB)
    return V.getInt();
}
Values.emplace_back(BB, DoesNotDominateBlock);
BlockDisposition D = computeBlockDisposition(S, BB);
auto &Values2 = BlockDispositions[S];
for (auto &V : llvm::reverse(Values2)) {
  if (V.getPointer() == BB) {
    V.setInt(D);
    break;
  }
}
return D;
13061}

13063ScalarEvolution::BlockDisposition
13064ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
switch (S->getSCEVType()) {
case scConstant:
  return ProperlyDominatesBlock;
case scPtrToInt:
case scTruncate:
case scZeroExtend:
case scSignExtend:
  return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
case scAddRecExpr: {
  // This uses a "dominates" query instead of "properly dominates" query
  // to test for proper dominance too, because the instruction which
  // produces the addrec's value is a PHI, and a PHI effectively properly
  // dominates its entire containing block.
  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
  if (!DT.dominates(AR->getLoop()->getHeader(), BB))
    return DoesNotDominateBlock;

  // Fall through into SCEVNAryExpr handling.
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
}
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
case scSequentialUMinExpr: {
  const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
  bool Proper = true;
  for (const SCEV *NAryOp : NAry->operands()) {
    BlockDisposition D = getBlockDisposition(NAryOp, BB);
    if (D == DoesNotDominateBlock)
      return DoesNotDominateBlock;
    if (D == DominatesBlock)
      Proper = false;
  }
  return Proper ? ProperlyDominatesBlock : DominatesBlock;
}
case scUDivExpr: {
  const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
  const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
  BlockDisposition LD = getBlockDisposition(LHS, BB);
  if (LD == DoesNotDominateBlock)
    return DoesNotDominateBlock;
  BlockDisposition RD = getBlockDisposition(RHS, BB);
  if (RD == DoesNotDominateBlock)
    return DoesNotDominateBlock;
  return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
    ProperlyDominatesBlock : DominatesBlock;
}
case scUnknown:
  if (Instruction *I =
        dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
    if (I->getParent() == BB)
      return DominatesBlock;
    if (DT.properlyDominates(I->getParent(), BB))
      return ProperlyDominatesBlock;
    return DoesNotDominateBlock;
  }
  return ProperlyDominatesBlock;
case scCouldNotCompute:
  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!")::llvm::llvm_unreachable_internal("Attempt to use a SCEVCouldNotCompute object!"
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13126);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 13128);
13129}

13131bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) >= DominatesBlock;
13133}

13135bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
13137}

13139bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
13141}

13143void ScalarEvolution::forgetBackedgeTakenCounts(const Loop *L,
                                              bool Predicated) {
auto &BECounts =
    Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
auto It = BECounts.find(L);
if (It != BECounts.end()) {
  for (const ExitNotTakenInfo &ENT : It->second.ExitNotTaken) {
    if (!isa<SCEVConstant>(ENT.ExactNotTaken)) {
      auto UserIt = BECountUsers.find(ENT.ExactNotTaken);
      assert(UserIt != BECountUsers.end())(static_cast <bool> (UserIt != BECountUsers.end()) ? void
 (0) : __assert_fail ("UserIt != BECountUsers.end()", "llvm/lib/Analysis/ScalarEvolution.cpp"
, 13152, __extension__ __PRETTY_FUNCTION__));
      UserIt->second.erase({L, Predicated});
    }
  }
  BECounts.erase(It);
}
13158}

13160void ScalarEvolution::forgetMemoizedResults(ArrayRef<const SCEV *> SCEVs) {
SmallPtrSet<const SCEV *, 8> ToForget(SCEVs.begin(), SCEVs.end());
SmallVector<const SCEV *, 8> Worklist(ToForget.begin(), ToForget.end());

while (!Worklist.empty()) {
  const SCEV *Curr = Worklist.pop_back_val();
  auto Users = SCEVUsers.find(Curr);
  if (Users != SCEVUsers.end())
    for (auto *User : Users->second)
      if (ToForget.insert(User).second)
        Worklist.push_back(User);
}

for (auto *S : ToForget)
  forgetMemoizedResultsImpl(S);

for (auto I = PredicatedSCEVRewrites.begin();
     I != PredicatedSCEVRewrites.end();) {
  std::pair<const SCEV *, const Loop *> Entry = I->first;
  if (ToForget.count(Entry.first))
    PredicatedSCEVRewrites.erase(I++);
  else
    ++I;
}
13184}

13186void ScalarEvolution::forgetMemoizedResultsImpl(const SCEV *S) {
LoopDispositions.erase(S);
BlockDispositions.erase(S);
UnsignedRanges.erase(S);
SignedRanges.erase(S);
HasRecMap.erase(S);
MinTrailingZerosCache.erase(S);

auto ExprIt = ExprValueMap.find(S);
if (ExprIt != ExprValueMap.end()) {
  for (auto &ValueAndOffset : ExprIt->second) {
    if (ValueAndOffset.second == nullptr) {
      auto ValueIt = ValueExprMap.find_as(ValueAndOffset.first);
      if (ValueIt != ValueExprMap.end())
        ValueExprMap.erase(ValueIt);
    }
  }
  ExprValueMap.erase(ExprIt);
}

auto ScopeIt = ValuesAtScopes.find(S);
if (ScopeIt != ValuesAtScopes.end()) {
  for (const auto &Pair : ScopeIt->second)
    if (!isa_and_nonnull<SCEVConstant>(Pair.second))
      erase_value(ValuesAtScopesUsers[Pair.second],
                  std::make_pair(Pair.first, S));
  ValuesAtScopes.erase(ScopeIt);
}

auto ScopeUserIt = ValuesAtScopesUsers.find(S);
if (ScopeUserIt != ValuesAtScopesUsers.end()) {
  for (const auto &Pair : ScopeUserIt->second)
    erase_value(ValuesAtScopes[Pair.second], std::make_pair(Pair.first, S));
  ValuesAtScopesUsers.erase(ScopeUserIt);
}

auto BEUsersIt = BECountUsers.find(S);
if (BEUsersIt != BECountUsers.end()) {
  // Work on a copy, as forgetBackedgeTakenCounts() will modify the original.
  auto Copy = BEUsersIt->second;
  for (const auto &Pair : Copy)
    forgetBackedgeTakenCounts(Pair.getPointer(), Pair.getInt());
  BECountUsers.erase(BEUsersIt);
}
13230}

13232void
13233ScalarEvolution::getUsedLoops(const SCEV *S,
                            SmallPtrSetImpl<const Loop *> &LoopsUsed) {
struct FindUsedLoops {
  FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
      : LoopsUsed(LoopsUsed) {}
  SmallPtrSetImpl<const Loop *> &LoopsUsed;
  bool follow(const SCEV *S) {
    if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
      LoopsUsed.insert(AR->getLoop());
    return true;
  }

  bool isDone() const { return false; }
};

FindUsedLoops F(LoopsUsed);
SCEVTraversal<FindUsedLoops>(F).visitAll(S);
13250}

13252void ScalarEvolution::verify() const {
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
ScalarEvolution SE2(F, TLI, AC, DT, LI);

SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());

// Map's SCEV expressions from one ScalarEvolution "universe" to another.
struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
  SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}

  const SCEV *visitConstant(const SCEVConstant *Constant) {
    return SE.getConstant(Constant->getAPInt());
  }

  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    return SE.getUnknown(Expr->getValue());
  }

  const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
    return SE.getCouldNotCompute();
  }
};

SCEVMapper SCM(SE2);

while (!LoopStack.empty()) {
  auto *L = LoopStack.pop_back_val();
  llvm::append_range(LoopStack, *L);

  auto *CurBECount = SCM.visit(
      const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
  auto *NewBECount = SE2.getBackedgeTakenCount(L);

  if (CurBECount == SE2.getCouldNotCompute() ||
      NewBECount == SE2.getCouldNotCompute()) {
    // NB! This situation is legal, but is very suspicious -- whatever pass
    // change the loop to make a trip count go from could not compute to
    // computable or vice-versa *should have* invalidated SCEV.  However, we
    // choose not to assert here (for now) since we don't want false
    // positives.
    continue;
  }

  if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
    // SCEV treats "undef" as an unknown but consistent value (i.e. it does
    // not propagate undef aggressively).  This means we can (and do) fail
    // verification in cases where a transform makes the trip count of a loop
    // go from "undef" to "undef+1" (say).  The transform is fine, since in
    // both cases the loop iterates "undef" times, but SCEV thinks we
    // increased the trip count of the loop by 1 incorrectly.
    continue;
  }

  if (SE.getTypeSizeInBits(CurBECount->getType()) >
      SE.getTypeSizeInBits(NewBECount->getType()))
    NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
  else if (SE.getTypeSizeInBits(CurBECount->getType()) <
           SE.getTypeSizeInBits(NewBECount->getType()))
    CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());

  const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount);

  // Unless VerifySCEVStrict is set, we only compare constant deltas.
  if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) {
    dbgs() << "Trip Count for " << *L << " Changed!\n";
    dbgs() << "Old: " << *CurBECount << "\n";
    dbgs() << "New: " << *NewBECount << "\n";
    dbgs() << "Delta: " << *Delta << "\n";
    std::abort();
  }
}

// Collect all valid loops currently in LoopInfo.
SmallPtrSet<Loop *, 32> ValidLoops;
SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end());
while (!Worklist.empty()) {
  Loop *L = Worklist.pop_back_val();
  if (ValidLoops.contains(L))
    continue;
  ValidLoops.insert(L);
  Worklist.append(L->begin(), L->end());
}
for (auto &KV : ValueExprMap) {
13335#ifndef NDEBUG
  // Check for SCEV expressions referencing invalid/deleted loops.
  if (auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second)) {
    assert(ValidLoops.contains(AR->getLoop()) &&(static_cast <bool> (ValidLoops.contains(AR->getLoop
()) && "AddRec references invalid loop") ? void (0) :
 __assert_fail ("ValidLoops.contains(AR->getLoop()) && \"AddRec references invalid loop\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13339, __extension__
 __PRETTY_FUNCTION__))
           "AddRec references invalid loop")(static_cast <bool> (ValidLoops.contains(AR->getLoop
()) && "AddRec references invalid loop") ? void (0) :
 __assert_fail ("ValidLoops.contains(AR->getLoop()) && \"AddRec references invalid loop\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13339, __extension__
 __PRETTY_FUNCTION__));
  }
13341#endif

  // Check that the value is also part of the reverse map.
  auto It = ExprValueMap.find(KV.second);
  if (It == ExprValueMap.end() || !It->second.contains({KV.first, nullptr})) {
    dbgs() << "Value " << *KV.first
           << " is in ValueExprMap but not in ExprValueMap\n";
    std::abort();
  }
}

for (const auto &KV : ExprValueMap) {
  for (const auto &ValueAndOffset : KV.second) {
    if (ValueAndOffset.second != nullptr)
      continue;

    auto It = ValueExprMap.find_as(ValueAndOffset.first);
    if (It == ValueExprMap.end()) {
      dbgs() << "Value " << *ValueAndOffset.first
             << " is in ExprValueMap but not in ValueExprMap\n";
      std::abort();
    }
    if (It->second != KV.first) {
      dbgs() << "Value " << *ValueAndOffset.first
             << " mapped to " << *It->second
             << " rather than " << *KV.first << "\n";
      std::abort();
    }
  }
}

// Verify integrity of SCEV users.
for (const auto &S : UniqueSCEVs) {
  SmallVector<const SCEV *, 4> Ops;
  collectUniqueOps(&S, Ops);
  for (const auto *Op : Ops) {
    // We do not store dependencies of constants.
    if (isa<SCEVConstant>(Op))
      continue;
    auto It = SCEVUsers.find(Op);
    if (It != SCEVUsers.end() && It->second.count(&S))
      continue;
    dbgs() << "Use of operand  " << *Op << " by user " << S
           << " is not being tracked!\n";
    std::abort();
  }
}

// Verify integrity of ValuesAtScopes users.
for (const auto &ValueAndVec : ValuesAtScopes) {
  const SCEV *Value = ValueAndVec.first;
  for (const auto &LoopAndValueAtScope : ValueAndVec.second) {
    const Loop *L = LoopAndValueAtScope.first;
    const SCEV *ValueAtScope = LoopAndValueAtScope.second;
    if (!isa<SCEVConstant>(ValueAtScope)) {
      auto It = ValuesAtScopesUsers.find(ValueAtScope);
      if (It != ValuesAtScopesUsers.end() &&
          is_contained(It->second, std::make_pair(L, Value)))
        continue;
      dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
             << *ValueAtScope << " missing in ValuesAtScopesUsers\n";
      std::abort();
    }
  }
}

for (const auto &ValueAtScopeAndVec : ValuesAtScopesUsers) {
  const SCEV *ValueAtScope = ValueAtScopeAndVec.first;
  for (const auto &LoopAndValue : ValueAtScopeAndVec.second) {
    const Loop *L = LoopAndValue.first;
    const SCEV *Value = LoopAndValue.second;
    assert(!isa<SCEVConstant>(Value))(static_cast <bool> (!isa<SCEVConstant>(Value)) ?
 void (0) : __assert_fail ("!isa<SCEVConstant>(Value)",
 "llvm/lib/Analysis/ScalarEvolution.cpp", 13412, __extension__
 __PRETTY_FUNCTION__));
    auto It = ValuesAtScopes.find(Value);
    if (It != ValuesAtScopes.end() &&
        is_contained(It->second, std::make_pair(L, ValueAtScope)))
      continue;
    dbgs() << "Value: " << *Value << ", Loop: " << *L << ", ValueAtScope: "
           << *ValueAtScope << " missing in ValuesAtScopes\n";
    std::abort();
  }
}

// Verify integrity of BECountUsers.
auto VerifyBECountUsers = [&](bool Predicated) {
  auto &BECounts =
      Predicated ? PredicatedBackedgeTakenCounts : BackedgeTakenCounts;
  for (const auto &LoopAndBEInfo : BECounts) {
    for (const ExitNotTakenInfo &ENT : LoopAndBEInfo.second.ExitNotTaken) {
      if (!isa<SCEVConstant>(ENT.ExactNotTaken)) {
        auto UserIt = BECountUsers.find(ENT.ExactNotTaken);
        if (UserIt != BECountUsers.end() &&
            UserIt->second.contains({ LoopAndBEInfo.first, Predicated }))
          continue;
        dbgs() << "Value " << *ENT.ExactNotTaken << " for loop "
               << *LoopAndBEInfo.first << " missing from BECountUsers\n";
        std::abort();
      }
    }
  }
};
VerifyBECountUsers(/* Predicated */ false);
VerifyBECountUsers(/* Predicated */ true);
13443}

13445bool ScalarEvolution::invalidate(
  Function &F, const PreservedAnalyses &PA,
  FunctionAnalysisManager::Invalidator &Inv) {
// Invalidate the ScalarEvolution object whenever it isn't preserved or one
// of its dependencies is invalidated.
auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
       Inv.invalidate<AssumptionAnalysis>(F, PA) ||
       Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
       Inv.invalidate<LoopAnalysis>(F, PA);
13455}

13457AnalysisKey ScalarEvolutionAnalysis::Key;

13459ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
                                           FunctionAnalysisManager &AM) {
return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
                       AM.getResult<AssumptionAnalysis>(F),
                       AM.getResult<DominatorTreeAnalysis>(F),
                       AM.getResult<LoopAnalysis>(F));
13465}

13467PreservedAnalyses
13468ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
AM.getResult<ScalarEvolutionAnalysis>(F).verify();
return PreservedAnalyses::all();
13471}

13473PreservedAnalyses
13474ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
// For compatibility with opt's -analyze feature under legacy pass manager
// which was not ported to NPM. This keeps tests using
// update_analyze_test_checks.py working.
OS << "Printing analysis 'Scalar Evolution Analysis' for function '"
   << F.getName() << "':\n";
AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
return PreservedAnalyses::all();
13482}

13484INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",static void *initializeScalarEvolutionWrapperPassPassOnce(PassRegistry
 &Registry) {
                    "Scalar Evolution Analysis", false, true)static void *initializeScalarEvolutionWrapperPassPassOnce(PassRegistry
 &Registry) {
13486INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)initializeAssumptionCacheTrackerPass(Registry);
13487INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)initializeLoopInfoWrapperPassPass(Registry);
13488INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)initializeDominatorTreeWrapperPassPass(Registry);
13489INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)initializeTargetLibraryInfoWrapperPassPass(Registry);
13490INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",PassInfo *PI = new PassInfo( "Scalar Evolution Analysis", "scalar-evolution"
, &ScalarEvolutionWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<ScalarEvolutionWrapperPass>), false, true
); Registry.registerPass(*PI, true); return PI; } static llvm
::once_flag InitializeScalarEvolutionWrapperPassPassFlag; void
 llvm::initializeScalarEvolutionWrapperPassPass(PassRegistry &
Registry) { llvm::call_once(InitializeScalarEvolutionWrapperPassPassFlag
, initializeScalarEvolutionWrapperPassPassOnce, std::ref(Registry
)); }
                  "Scalar Evolution Analysis", false, true)PassInfo *PI = new PassInfo( "Scalar Evolution Analysis", "scalar-evolution"
, &ScalarEvolutionWrapperPass::ID, PassInfo::NormalCtor_t
(callDefaultCtor<ScalarEvolutionWrapperPass>), false, true
); Registry.registerPass(*PI, true); return PI; } static llvm
::once_flag InitializeScalarEvolutionWrapperPassPassFlag; void
 llvm::initializeScalarEvolutionWrapperPassPass(PassRegistry &
Registry) { llvm::call_once(InitializeScalarEvolutionWrapperPassPassFlag
, initializeScalarEvolutionWrapperPassPassOnce, std::ref(Registry
)); }

13493char ScalarEvolutionWrapperPass::ID = 0;

13495ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
13497}

13499bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
SE.reset(new ScalarEvolution(
    F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
    getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
    getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
    getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
return false;
13506}

13508void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }

13510void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
SE->print(OS);
13512}

13514void ScalarEvolutionWrapperPass::verifyAnalysis() const {
if (!VerifySCEV)
  return;

SE->verify();
13519}

13521void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AssumptionCacheTracker>();
AU.addRequiredTransitive<LoopInfoWrapperPass>();
AU.addRequiredTransitive<DominatorTreeWrapperPass>();
AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
13527}

13529const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
                                                      const SCEV *RHS) {
FoldingSetNodeID ID;
assert(LHS->getType() == RHS->getType() &&(static_cast <bool> (LHS->getType() == RHS->getType
() && "Type mismatch between LHS and RHS") ? void (0)
 : __assert_fail ("LHS->getType() == RHS->getType() && \"Type mismatch between LHS and RHS\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13533, __extension__
 __PRETTY_FUNCTION__))
       "Type mismatch between LHS and RHS")(static_cast <bool> (LHS->getType() == RHS->getType
() && "Type mismatch between LHS and RHS") ? void (0)
 : __assert_fail ("LHS->getType() == RHS->getType() && \"Type mismatch between LHS and RHS\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13533, __extension__
 __PRETTY_FUNCTION__));
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Equal);
ID.AddPointer(LHS);
ID.AddPointer(RHS);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
  return S;
SCEVEqualPredicate *Eq = new (SCEVAllocator)
    SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
UniquePreds.InsertNode(Eq, IP);
return Eq;
13545}

13547const SCEVPredicate *ScalarEvolution::getWrapPredicate(
  const SCEVAddRecExpr *AR,
  SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
FoldingSetNodeID ID;
// Unique this node based on the arguments
ID.AddInteger(SCEVPredicate::P_Wrap);
ID.AddPointer(AR);
ID.AddInteger(AddedFlags);
void *IP = nullptr;
if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
  return S;
auto *OF = new (SCEVAllocator)
    SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
UniquePreds.InsertNode(OF, IP);
return OF;
13562}

13564namespace {

13566class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
13567public:

/// Rewrites \p S in the context of a loop L and the SCEV predication
/// infrastructure.
///
/// If \p Pred is non-null, the SCEV expression is rewritten to respect the
/// equivalences present in \p Pred.
///
/// If \p NewPreds is non-null, rewrite is free to add further predicates to
/// \p NewPreds such that the result will be an AddRecExpr.
static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
                           SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
                           SCEVUnionPredicate *Pred) {
  SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
  return Rewriter.visit(S);
}

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  if (Pred) {
    auto ExprPreds = Pred->getPredicatesForExpr(Expr);
    for (auto *Pred : ExprPreds)
      if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
        if (IPred->getLHS() == Expr)
          return IPred->getRHS();
  }
  return convertToAddRecWithPreds(Expr);
}

const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
  const SCEV *Operand = visit(Expr->getOperand());
  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
  if (AR && AR->getLoop() == L && AR->isAffine()) {
    // This couldn't be folded because the operand didn't have the nuw
    // flag. Add the nusw flag as an assumption that we could make.
    const SCEV *Step = AR->getStepRecurrence(SE);
    Type *Ty = Expr->getType();
    if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
      return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
                              SE.getSignExtendExpr(Step, Ty), L,
                              AR->getNoWrapFlags());
  }
  return SE.getZeroExtendExpr(Operand, Expr->getType());
}

const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
  const SCEV *Operand = visit(Expr->getOperand());
  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
  if (AR && AR->getLoop() == L && AR->isAffine()) {
    // This couldn't be folded because the operand didn't have the nsw
    // flag. Add the nssw flag as an assumption that we could make.
    const SCEV *Step = AR->getStepRecurrence(SE);
    Type *Ty = Expr->getType();
    if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
      return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
                              SE.getSignExtendExpr(Step, Ty), L,
                              AR->getNoWrapFlags());
  }
  return SE.getSignExtendExpr(Operand, Expr->getType());
}

13627private:
explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
                      SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
                      SCEVUnionPredicate *Pred)
    : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}

bool addOverflowAssumption(const SCEVPredicate *P) {
  if (!NewPreds) {
    // Check if we've already made this assumption.
    return Pred && Pred->implies(P);
  }
  NewPreds->insert(P);
  return true;
}

bool addOverflowAssumption(const SCEVAddRecExpr *AR,
                           SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
  auto *A = SE.getWrapPredicate(AR, AddedFlags);
  return addOverflowAssumption(A);
}

// If \p Expr represents a PHINode, we try to see if it can be represented
// as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
// to add this predicate as a runtime overflow check, we return the AddRec.
// If \p Expr does not meet these conditions (is not a PHI node, or we
// couldn't create an AddRec for it, or couldn't add the predicate), we just
// return \p Expr.
const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
  if (!isa<PHINode>(Expr->getValue()))
    return Expr;
  Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
  PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
  if (!PredicatedRewrite)
    return Expr;
  for (auto *P : PredicatedRewrite->second){
    // Wrap predicates from outer loops are not supported.
    if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
      auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr());
      if (L != AR->getLoop())
        return Expr;
    }
    if (!addOverflowAssumption(P))
      return Expr;
  }
  return PredicatedRewrite->first;
}

SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
SCEVUnionPredicate *Pred;
const Loop *L;
13677};

13679} // end anonymous namespace

13681const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
                                                 SCEVUnionPredicate &Preds) {
return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
13684}

13686const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
  const SCEV *S, const Loop *L,
  SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);

if (!AddRec)
  return nullptr;

// Since the transformation was successful, we can now transfer the SCEV
// predicates.
for (auto *P : TransformPreds)
  Preds.insert(P);

return AddRec;
13702}

13704/// SCEV predicates
13705SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
                           SCEVPredicateKind Kind)
  : FastID(ID), Kind(Kind) {}

13709SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
                                     const SCEV *LHS, const SCEV *RHS)
  : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match")(static_cast <bool> (LHS->getType() == RHS->getType
() && "LHS and RHS types don't match") ? void (0) : __assert_fail
 ("LHS->getType() == RHS->getType() && \"LHS and RHS types don't match\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13712, __extension__
 __PRETTY_FUNCTION__));
assert(LHS != RHS && "LHS and RHS are the same SCEV")(static_cast <bool> (LHS != RHS && "LHS and RHS are the same SCEV"
) ? void (0) : __assert_fail ("LHS != RHS && \"LHS and RHS are the same SCEV\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13713, __extension__
 __PRETTY_FUNCTION__));
13714}

13716bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVEqualPredicate>(N);

if (!Op)
  return false;

return Op->LHS == LHS && Op->RHS == RHS;
13723}

13725bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }

13727const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }

13729void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
13731}

13733SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
                                   const SCEVAddRecExpr *AR,
                                   IncrementWrapFlags Flags)
  : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}

13738const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }

13740bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
const auto *Op = dyn_cast<SCEVWrapPredicate>(N);

return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
13744}

13746bool SCEVWrapPredicate::isAlwaysTrue() const {
SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
IncrementWrapFlags IFlags = Flags;

if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
  IFlags = clearFlags(IFlags, IncrementNSSW);

return IFlags == IncrementAnyWrap;
13754}

13756void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
OS.indent(Depth) << *getExpr() << " Added Flags: ";
if (SCEVWrapPredicate::IncrementNUSW & getFlags())
  OS << "<nusw>";
if (SCEVWrapPredicate::IncrementNSSW & getFlags())
  OS << "<nssw>";
OS << "\n";
13763}

13765SCEVWrapPredicate::IncrementWrapFlags
13766SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
                                 ScalarEvolution &SE) {
IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();

// We can safely transfer the NSW flag as NSSW.
if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
  ImpliedFlags = IncrementNSSW;

if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
  // If the increment is positive, the SCEV NUW flag will also imply the
  // WrapPredicate NUSW flag.
  if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
    if (Step->getValue()->getValue().isNonNegative())
      ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
}

return ImpliedFlags;
13784}

13786/// Union predicates don't get cached so create a dummy set ID for it.
13787SCEVUnionPredicate::SCEVUnionPredicate()
  : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}

13790bool SCEVUnionPredicate::isAlwaysTrue() const {
return all_of(Preds,
              [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
13793}

13795ArrayRef<const SCEVPredicate *>
13796SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
auto I = SCEVToPreds.find(Expr);
if (I == SCEVToPreds.end())
  return ArrayRef<const SCEVPredicate *>();
return I->second;
13801}

13803bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
  return all_of(Set->Preds,
                [this](const SCEVPredicate *I) { return this->implies(I); });

auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
if (ScevPredsIt == SCEVToPreds.end())
  return false;
auto &SCEVPreds = ScevPredsIt->second;

return any_of(SCEVPreds,
              [N](const SCEVPredicate *I) { return I->implies(N); });
13815}

13817const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }

13819void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
for (auto Pred : Preds)
  Pred->print(OS, Depth);
13822}

13824void SCEVUnionPredicate::add(const SCEVPredicate *N) {
if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
  for (auto Pred : Set->Preds)
    add(Pred);
  return;
}

if (implies(N))
  return;

const SCEV *Key = N->getExpr();
assert(Key && "Only SCEVUnionPredicate doesn't have an "(static_cast <bool> (Key && "Only SCEVUnionPredicate doesn't have an "
 " associated expression!") ? void (0) : __assert_fail ("Key && \"Only SCEVUnionPredicate doesn't have an \" \" associated expression!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13836, __extension__
 __PRETTY_FUNCTION__))
              " associated expression!")(static_cast <bool> (Key && "Only SCEVUnionPredicate doesn't have an "
 " associated expression!") ? void (0) : __assert_fail ("Key && \"Only SCEVUnionPredicate doesn't have an \" \" associated expression!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 13836, __extension__
 __PRETTY_FUNCTION__));

SCEVToPreds[Key].push_back(N);
Preds.push_back(N);
13840}

13842PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
                                                   Loop &L)
  : SE(SE), L(L) {}

13846void ScalarEvolution::registerUser(const SCEV *User,
                                 ArrayRef<const SCEV *> Ops) {
for (auto *Op : Ops)
  // We do not expect that forgetting cached data for SCEVConstants will ever
  // open any prospects for sharpening or introduce any correctness issues,
  // so we don't bother storing their dependencies.
  if (!isa<SCEVConstant>(Op))
    SCEVUsers[Op].insert(User);
13854}

13856const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
const SCEV *Expr = SE.getSCEV(V);
RewriteEntry &Entry = RewriteMap[Expr];

// If we already have an entry and the version matches, return it.
if (Entry.second && Generation == Entry.first)
  return Entry.second;

// We found an entry but it's stale. Rewrite the stale entry
// according to the current predicate.
if (Entry.second)
  Expr = Entry.second;

const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
Entry = {Generation, NewSCEV};

return NewSCEV;
13873}

13875const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
if (!BackedgeCount) {
  SCEVUnionPredicate BackedgePred;
  BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
  addPredicate(BackedgePred);
}
return BackedgeCount;
13882}

13884void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
if (Preds.implies(&Pred))
  return;
Preds.add(&Pred);
updateGeneration();
13889}

13891const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
return Preds;
13893}

13895void PredicatedScalarEvolution::updateGeneration() {
// If the generation number wrapped recompute everything.
if (++Generation == 0) {
  for (auto &II : RewriteMap) {
    const SCEV *Rewritten = II.second.second;
    II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
  }
}
13903}

13905void PredicatedScalarEvolution::setNoOverflow(
  Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);

auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);

// Clear the statically implied flags.
Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
addPredicate(*SE.getWrapPredicate(AR, Flags));

auto II = FlagsMap.insert({V, Flags});
if (!II.second)
  II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
13919}

13921bool PredicatedScalarEvolution::hasNoOverflow(
  Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
const SCEV *Expr = getSCEV(V);
const auto *AR = cast<SCEVAddRecExpr>(Expr);

Flags = SCEVWrapPredicate::clearFlags(
    Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));

auto II = FlagsMap.find(V);

if (II != FlagsMap.end())
  Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);

return Flags == SCEVWrapPredicate::IncrementAnyWrap;
13935}

13937const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
const SCEV *Expr = this->getSCEV(V);
SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);

if (!New)
  return nullptr;

for (auto *P : NewPreds)
  Preds.add(P);

updateGeneration();
RewriteMap[SE.getSCEV(V)] = {Generation, New};
return New;
13951}

13953PredicatedScalarEvolution::PredicatedScalarEvolution(
  const PredicatedScalarEvolution &Init)
  : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
    Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
for (auto I : Init.FlagsMap)
  FlagsMap.insert(I);
13959}

13961void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
// For each block.
for (auto *BB : L.getBlocks())
  for (auto &I : *BB) {
    if (!SE.isSCEVable(I.getType()))
      continue;

    auto *Expr = SE.getSCEV(&I);
    auto II = RewriteMap.find(Expr);

    if (II == RewriteMap.end())
      continue;

    // Don't print things that are not interesting.
    if (II->second.second == Expr)
      continue;

    OS.indent(Depth) << "[PSE]" << I << ":\n";
    OS.indent(Depth + 2) << *Expr << "\n";
    OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
  }
13982}

13984// Match the mathematical pattern A - (A / B) * B, where A and B can be
13985// arbitrary expressions. Also match zext (trunc A to iB) to iY, which is used
13986// for URem with constant power-of-2 second operands.
13987// It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
13988// 4, A / B becomes X / 8).
13989bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
                              const SCEV *&RHS) {
// Try to match 'zext (trunc A to iB) to iY', which is used
// for URem with constant power-of-2 second operands. Make sure the size of
// the operand A matches the size of the whole expressions.
if (const auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Expr))
  if (const auto *Trunc = dyn_cast<SCEVTruncateExpr>(ZExt->getOperand(0))) {
    LHS = Trunc->getOperand();
    // Bail out if the type of the LHS is larger than the type of the
    // expression for now.
    if (getTypeSizeInBits(LHS->getType()) >
        getTypeSizeInBits(Expr->getType()))
      return false;
    if (LHS->getType() != Expr->getType())
      LHS = getZeroExtendExpr(LHS, Expr->getType());
    RHS = getConstant(APInt(getTypeSizeInBits(Expr->getType()), 1)
                      << getTypeSizeInBits(Trunc->getType()));
    return true;
  }
const auto *Add = dyn_cast<SCEVAddExpr>(Expr);
if (Add == nullptr || Add->getNumOperands() != 2)
  return false;

const SCEV *A = Add->getOperand(1);
const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0));

if (Mul == nullptr)
  return false;

const auto MatchURemWithDivisor = [&](const SCEV *B) {
  // (SomeExpr + (-(SomeExpr / B) * B)).
  if (Expr == getURemExpr(A, B)) {
    LHS = A;
    RHS = B;
    return true;
  }
  return false;
};

// (SomeExpr + (-1 * (SomeExpr / B) * B)).
if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0)))
  return MatchURemWithDivisor(Mul->getOperand(1)) ||
         MatchURemWithDivisor(Mul->getOperand(2));

// (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
if (Mul->getNumOperands() == 2)
  return MatchURemWithDivisor(Mul->getOperand(1)) ||
         MatchURemWithDivisor(Mul->getOperand(0)) ||
         MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) ||
         MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0)));
return false;
14040}

14042const SCEV *
14043ScalarEvolution::computeSymbolicMaxBackedgeTakenCount(const Loop *L) {
SmallVector<BasicBlock*, 16> ExitingBlocks;
L->getExitingBlocks(ExitingBlocks);

// Form an expression for the maximum exit count possible for this loop. We
// merge the max and exact information to approximate a version of
// getConstantMaxBackedgeTakenCount which isn't restricted to just constants.
SmallVector<const SCEV*, 4> ExitCounts;
for (BasicBlock *ExitingBB : ExitingBlocks) {
  const SCEV *ExitCount = getExitCount(L, ExitingBB);
  if (isa<SCEVCouldNotCompute>(ExitCount))
    ExitCount = getExitCount(L, ExitingBB,
                                ScalarEvolution::ConstantMaximum);
  if (!isa<SCEVCouldNotCompute>(ExitCount)) {
    assert(DT.dominates(ExitingBB, L->getLoopLatch()) &&(static_cast <bool> (DT.dominates(ExitingBB, L->getLoopLatch
()) && "We should only have known counts for exiting blocks that "
 "dominate latch!") ? void (0) : __assert_fail ("DT.dominates(ExitingBB, L->getLoopLatch()) && \"We should only have known counts for exiting blocks that \" \"dominate latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 14059, __extension__
 __PRETTY_FUNCTION__))
           "We should only have known counts for exiting blocks that "(static_cast <bool> (DT.dominates(ExitingBB, L->getLoopLatch
()) && "We should only have known counts for exiting blocks that "
 "dominate latch!") ? void (0) : __assert_fail ("DT.dominates(ExitingBB, L->getLoopLatch()) && \"We should only have known counts for exiting blocks that \" \"dominate latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 14059, __extension__
 __PRETTY_FUNCTION__))
           "dominate latch!")(static_cast <bool> (DT.dominates(ExitingBB, L->getLoopLatch
()) && "We should only have known counts for exiting blocks that "
 "dominate latch!") ? void (0) : __assert_fail ("DT.dominates(ExitingBB, L->getLoopLatch()) && \"We should only have known counts for exiting blocks that \" \"dominate latch!\""
, "llvm/lib/Analysis/ScalarEvolution.cpp", 14059, __extension__
 __PRETTY_FUNCTION__));
    ExitCounts.push_back(ExitCount);
  }
}
if (ExitCounts.empty())
  return getCouldNotCompute();
return getUMinFromMismatchedTypes(ExitCounts);
14066}

14068/// A rewriter to replace SCEV expressions in Map with the corresponding entry
14069/// in the map. It skips AddRecExpr because we cannot guarantee that the
14070/// replacement is loop invariant in the loop of the AddRec.
14071///
14072/// At the moment only rewriting SCEVUnknown and SCEVZeroExtendExpr is
14073/// supported.
14074class SCEVLoopGuardRewriter : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> {
const DenseMap<const SCEV *, const SCEV *> &Map;

14077public:
SCEVLoopGuardRewriter(ScalarEvolution &SE,
                      DenseMap<const SCEV *, const SCEV *> &M)
    : SCEVRewriteVisitor(SE), Map(M) {}

const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; }

const SCEV *visitUnknown(const SCEVUnknown *Expr) {
  auto I = Map.find(Expr);
  if (I == Map.end())
    return Expr;
  return I->second;
}

const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
  auto I = Map.find(Expr);
  if (I == Map.end())
    return SCEVRewriteVisitor<SCEVLoopGuardRewriter>::visitZeroExtendExpr(
        Expr);
  return I->second;
}
14098};

14100const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) {
SmallVector<const SCEV *> ExprsToRewrite;
auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS,
                            const SCEV *RHS,
                            DenseMap<const SCEV *, const SCEV *>
                                &RewriteMap) {
  // WARNING: It is generally unsound to apply any wrap flags to the proposed
  // replacement SCEV which isn't directly implied by the structure of that
  // SCEV.  In particular, using contextual facts to imply flags is *NOT*
  // legal.  See the scoping rules for flags in the header to understand why.

  // If LHS is a constant, apply information to the other expression.
  if (isa<SCEVConstant>(LHS)) {
    std::swap(LHS, RHS);
    Predicate = CmpInst::getSwappedPredicate(Predicate);
  }

  // Check for a condition of the form (-C1 + X < C2).  InstCombine will
  // create this form when combining two checks of the form (X u< C2 + C1) and
  // (X >=u C1).
  auto MatchRangeCheckIdiom = [this, Predicate, LHS, RHS, &RewriteMap,
                               &ExprsToRewrite]() {
    auto *AddExpr = dyn_cast<SCEVAddExpr>(LHS);
    if (!AddExpr || AddExpr->getNumOperands() != 2)
      return false;

    auto *C1 = dyn_cast<SCEVConstant>(AddExpr->getOperand(0));
    auto *LHSUnknown = dyn_cast<SCEVUnknown>(AddExpr->getOperand(1));
    auto *C2 = dyn_cast<SCEVConstant>(RHS);
    if (!C1 || !C2 || !LHSUnknown)
      return false;

    auto ExactRegion =
        ConstantRange::makeExactICmpRegion(Predicate, C2->getAPInt())
            .sub(C1->getAPInt());

    // Bail out, unless we have a non-wrapping, monotonic range.
    if (ExactRegion.isWrappedSet() || ExactRegion.isFullSet())
      return false;
    auto I = RewriteMap.find(LHSUnknown);
    const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHSUnknown;
    RewriteMap[LHSUnknown] = getUMaxExpr(
        getConstant(ExactRegion.getUnsignedMin()),
        getUMinExpr(RewrittenLHS, getConstant(ExactRegion.getUnsignedMax())));
    ExprsToRewrite.push_back(LHSUnknown);
    return true;
  };
  if (MatchRangeCheckIdiom())
    return;

  // If we have LHS == 0, check if LHS is computing a property of some unknown
  // SCEV %v which we can rewrite %v to express explicitly.
  const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS);
  if (Predicate == CmpInst::ICMP_EQ && RHSC &&
      RHSC->getValue()->isNullValue()) {
    // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to
    // explicitly express that.
    const SCEV *URemLHS = nullptr;
    const SCEV *URemRHS = nullptr;
    if (matchURem(LHS, URemLHS, URemRHS)) {
      if (const SCEVUnknown *LHSUnknown = dyn_cast<SCEVUnknown>(URemLHS)) {
        auto Multiple = getMulExpr(getUDivExpr(URemLHS, URemRHS), URemRHS);
        RewriteMap[LHSUnknown] = Multiple;
        ExprsToRewrite.push_back(LHSUnknown);
        return;
      }
    }
  }

  // Do not apply information for constants or if RHS contains an AddRec.
  if (isa<SCEVConstant>(LHS) || containsAddRecurrence(RHS))
    return;

  // If RHS is SCEVUnknown, make sure the information is applied to it.
  if (!isa<SCEVUnknown>(LHS) && isa<SCEVUnknown>(RHS)) {
    std::swap(LHS, RHS);
    Predicate = CmpInst::getSwappedPredicate(Predicate);
  }

  // Limit to expressions that can be rewritten.
  if (!isa<SCEVUnknown>(LHS) && !isa<SCEVZeroExtendExpr>(LHS))
    return;

  // Check whether LHS has already been rewritten. In that case we want to
  // chain further rewrites onto the already rewritten value.
  auto I = RewriteMap.find(LHS);
  const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHS;

  const SCEV *RewrittenRHS = nullptr;
  switch (Predicate) {
  case CmpInst::ICMP_ULT:
    RewrittenRHS =
        getUMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType())));
    break;
  case CmpInst::ICMP_SLT:
    RewrittenRHS =
        getSMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType())));
    break;
  case CmpInst::ICMP_ULE:
    RewrittenRHS = getUMinExpr(RewrittenLHS, RHS);
    break;
  case CmpInst::ICMP_SLE:
    RewrittenRHS = getSMinExpr(RewrittenLHS, RHS);
    break;
  case CmpInst::ICMP_UGT:
    RewrittenRHS =
        getUMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType())));
    break;
  case CmpInst::ICMP_SGT:
    RewrittenRHS =
        getSMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType())));
    break;
  case CmpInst::ICMP_UGE:
    RewrittenRHS = getUMaxExpr(RewrittenLHS, RHS);
    break;
  case CmpInst::ICMP_SGE:
    RewrittenRHS = getSMaxExpr(RewrittenLHS, RHS);
    break;
  case CmpInst::ICMP_EQ:
    if (isa<SCEVConstant>(RHS))
      RewrittenRHS = RHS;
    break;
  case CmpInst::ICMP_NE:
    if (isa<SCEVConstant>(RHS) &&
        cast<SCEVConstant>(RHS)->getValue()->isNullValue())
      RewrittenRHS = getUMaxExpr(RewrittenLHS, getOne(RHS->getType()));
    break;
  default:
    break;
  }

  if (RewrittenRHS) {
    RewriteMap[LHS] = RewrittenRHS;
    if (LHS == RewrittenLHS)
      ExprsToRewrite.push_back(LHS);
  }
};
// First, collect conditions from dominating branches. Starting at the loop
// predecessor, climb up the predecessor chain, as long as there are
// predecessors that can be found that have unique successors leading to the
// original header.
// TODO: share this logic with isLoopEntryGuardedByCond.
SmallVector<std::pair<Value *, bool>> Terms;
for (std::pair<const BasicBlock *, const BasicBlock *> Pair(
         L->getLoopPredecessor(), L->getHeader());
     Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {

  const BranchInst *LoopEntryPredicate =
      dyn_cast<BranchInst>(Pair.first->getTerminator());
  if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional())
    continue;

  Terms.emplace_back(LoopEntryPredicate->getCondition(),
                     LoopEntryPredicate->getSuccessor(0) == Pair.second);
}

// Now apply the information from the collected conditions to RewriteMap.
// Conditions are processed in reverse order, so the earliest conditions is
// processed first. This ensures the SCEVs with the shortest dependency chains
// are constructed first.
DenseMap<const SCEV *, const SCEV *> RewriteMap;
for (auto &E : reverse(Terms)) {
  bool EnterIfTrue = E.second;
  SmallVector<Value *, 8> Worklist;
  SmallPtrSet<Value *, 8> Visited;
  Worklist.push_back(E.first);
  while (!Worklist.empty()) {
    Value *Cond = Worklist.pop_back_val();
    if (!Visited.insert(Cond).second)
      continue;

    if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) {
      auto Predicate =
          EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate();
      CollectCondition(Predicate, getSCEV(Cmp->getOperand(0)),
                       getSCEV(Cmp->getOperand(1)), RewriteMap);
      continue;
    }

    Value *L, *R;
    if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R)))
                    : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) {
      Worklist.push_back(L);
      Worklist.push_back(R);
    }
  }
}

// Also collect information from assumptions dominating the loop.
for (auto &AssumeVH : AC.assumptions()) {
  if (!AssumeVH)
    continue;
  auto *AssumeI = cast<CallInst>(AssumeVH);
  auto *Cmp = dyn_cast<ICmpInst>(AssumeI->getOperand(0));
  if (!Cmp || !DT.dominates(AssumeI, L->getHeader()))
    continue;
  CollectCondition(Cmp->getPredicate(), getSCEV(Cmp->getOperand(0)),
                   getSCEV(Cmp->getOperand(1)), RewriteMap);
}

if (RewriteMap.empty())
  return Expr;

// Now that all rewrite information is collect, rewrite the collected
// expressions with the information in the map. This applies information to
// sub-expressions.
if (ExprsToRewrite.size() > 1) {
  for (const SCEV *Expr : ExprsToRewrite) {
    const SCEV *RewriteTo = RewriteMap[Expr];
    RewriteMap.erase(Expr);
    SCEVLoopGuardRewriter Rewriter(*this, RewriteMap);
    RewriteMap.insert({Expr, Rewriter.visit(RewriteTo)});
  }
}

SCEVLoopGuardRewriter Rewriter(*this, RewriteMap);
return Rewriter.visit(Expr);
14317}