/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp

Bug Summary

File:	llvm/lib/Analysis/ScalarEvolution.cpp
Warning:	line 10001, column 35 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 -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 -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -fno-split-dwarf-inlining -debugger-tuning=gdb -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-12/lib/clang/12.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/build-llvm/lib/Analysis -I /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis -I /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/build-llvm/include -I /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/include -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0/backward -internal-isystem /usr/local/include -internal-isystem /usr/lib/llvm-12/lib/clang/12.0.0/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/build-llvm/lib/Analysis -fdebug-prefix-map=/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d=. -ferror-limit 19 -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -o /tmp/scan-build-2020-11-29-190409-37574-1 -x c++ /build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/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;

139#define DEBUG_TYPE"scalar-evolution" "scalar-evolution"

141STATISTIC(NumArrayLenItCounts,static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
}
        "Number of trip counts computed with array length")static llvm::Statistic NumArrayLenItCounts = {"scalar-evolution"
, "NumArrayLenItCounts", "Number of trip counts computed with array length"
};
143STATISTIC(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"
};
145STATISTIC(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"
};
147STATISTIC(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"
};

150static cl::opt<unsigned>
151MaxBruteForceIterations("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));

158// FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
159static cl::opt<bool> VerifySCEV(
  "verify-scev", cl::Hidden,
  cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
162static cl::opt<bool> VerifySCEVStrict(
  "verify-scev-strict", cl::Hidden,
  cl::desc("Enable stricter verification with -verify-scev is passed"));
165static cl::opt<bool>
  VerifySCEVMap("verify-scev-maps", cl::Hidden,
                cl::desc("Verify no dangling value in ScalarEvolution's "
                         "ExprValueMap (slow)"));

170static cl::opt<bool> VerifyIR(
  "scev-verify-ir", cl::Hidden,
  cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
  cl::init(false));

175static cl::opt<unsigned> MulOpsInlineThreshold(
  "scev-mulops-inline-threshold", cl::Hidden,
  cl::desc("Threshold for inlining multiplication operands into a SCEV"),
  cl::init(32));

180static cl::opt<unsigned> AddOpsInlineThreshold(
  "scev-addops-inline-threshold", cl::Hidden,
  cl::desc("Threshold for inlining addition operands into a SCEV"),
  cl::init(500));

185static cl::opt<unsigned> MaxSCEVCompareDepth(
  "scalar-evolution-max-scev-compare-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
  cl::init(32));

190static 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));

195static cl::opt<unsigned> MaxValueCompareDepth(
  "scalar-evolution-max-value-compare-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive value complexity comparisons"),
  cl::init(2));

200static cl::opt<unsigned>
  MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
                cl::desc("Maximum depth of recursive arithmetics"),
                cl::init(32));

205static cl::opt<unsigned> MaxConstantEvolvingDepth(
  "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
  cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));

209static cl::opt<unsigned>
  MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
               cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
               cl::init(8));

214static cl::opt<unsigned>
  MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
                cl::desc("Max coefficients in AddRec during evolving"),
                cl::init(8));

219static cl::opt<unsigned>
  HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
                cl::desc("Size of the expression which is considered huge"),
                cl::init(4096));

224static cl::opt<bool>
225ClassifyExpressions("scalar-evolution-classify-expressions",
  cl::Hidden, cl::init(true),
  cl::desc("When printing analysis, include information on every instruction"));

229static 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"));

235//===----------------------------------------------------------------------===//
236//                           SCEV class definitions
237//===----------------------------------------------------------------------===//

239//===----------------------------------------------------------------------===//
240// Implementation of the SCEV class.
241//

243#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
244LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void SCEV::dump() const {
print(dbgs());
dbgs() << '\n';
247}
248#endif

250void 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: {
  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;
  default:
    llvm_unreachable("There are no other nary expression types.")::llvm::llvm_unreachable_internal("There are no other nary expression types."
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 320);
  }
  OS << "(";
  for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
       I != E; ++I) {
    OS << **I;
    if (std::next(I) != E)
      OS << OpStr;
  }
  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!", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/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:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
  return cast<SCEVNAryExpr>(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!"
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 404);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 406);
407}

409bool SCEV::isZero() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isZero();
return false;
413}

415bool SCEV::isOne() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isOne();
return false;
419}

421bool SCEV::isAllOnesValue() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
  return SC->getValue()->isMinusOne();
return false;
425}

427bool 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();
437}

439SCEVCouldNotCompute::SCEVCouldNotCompute() :
SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}

442bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
444}

446const 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;
455}

457const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
return getConstant(ConstantInt::get(getContext(), Val));
459}

461const SCEV *
462ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
return getConstant(ConstantInt::get(ITy, V, isSigned));
465}

467SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
                         const SCEV *op, Type *ty)
  : SCEV(ID, SCEVTy, computeExpressionSize(op)), Ty(ty) {
Operands[0] = op;
471}

473SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op,
                                 Type *ITy)
  : SCEVCastExpr(ID, scPtrToInt, Op, ITy) {
assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() &&((getOperand()->getType()->isPointerTy() && Ty->
isIntegerTy() && "Must be a non-bit-width-changing pointer-to-integer cast!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && \"Must be a non-bit-width-changing pointer-to-integer cast!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 477, __PRETTY_FUNCTION__))
       "Must be a non-bit-width-changing pointer-to-integer cast!")((getOperand()->getType()->isPointerTy() && Ty->
isIntegerTy() && "Must be a non-bit-width-changing pointer-to-integer cast!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && \"Must be a non-bit-width-changing pointer-to-integer cast!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 477, __PRETTY_FUNCTION__));
478}

480SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID,
                                         SCEVTypes SCEVTy, const SCEV *op,
                                         Type *ty)
  : SCEVCastExpr(ID, SCEVTy, op, ty) {}

485SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op,
                                 Type *ty)
  : SCEVIntegralCastExpr(ID, scTruncate, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot truncate non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 489, __PRETTY_FUNCTION__))
       "Cannot truncate non-integer value!")((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot truncate non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 489, __PRETTY_FUNCTION__));
490}

492SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
                                     const SCEV *op, Type *ty)
  : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot zero extend non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 496, __PRETTY_FUNCTION__))
       "Cannot zero extend non-integer value!")((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot zero extend non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot zero extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 496, __PRETTY_FUNCTION__));
497}

499SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
                                     const SCEV *op, Type *ty)
  : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) {
assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot sign extend non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 503, __PRETTY_FUNCTION__))
       "Cannot sign extend non-integer value!")((getOperand()->getType()->isIntOrPtrTy() && Ty
->isIntOrPtrTy() && "Cannot sign extend non-integer value!"
) ? static_cast<void> (0) : __assert_fail ("getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot sign extend non-integer value!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 503, __PRETTY_FUNCTION__));
504}

506void 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);
515}

517void 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);
525}

527bool 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<PointerType>(CE->getOperand(0)->getType())
                               ->getElementType();
            return true;
          }

return false;
542}

544bool 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<PointerType>(CE->getOperand(0)->getType())->getElementType();
        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;
567}

569bool 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<PointerType>(CE->getOperand(0)->getType())->getElementType();
        // 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;
589}

591//===----------------------------------------------------------------------===//
592//                               SCEV Utilities
593//===----------------------------------------------------------------------===//

595/// Compare the two values \p LV and \p RV in terms of their "complexity" where
596/// "complexity" is a partial (and somewhat ad-hoc) relation used to order
597/// operands in SCEV expressions.  \p EqCache is a set of pairs of values that
598/// have been previously deemed to be "equally complex" by this routine.  It is
599/// intended to avoid exponential time complexity in cases like:
600///
601///   %a = f(%x, %y)
602///   %b = f(%a, %a)
603///   %c = f(%b, %b)
604///
605///   %d = f(%x, %y)
606///   %e = f(%d, %d)
607///   %f = f(%e, %e)
608///
609///   CompareValueComplexity(%f, %c)
610///
611/// Since we do not continue running this routine on expression trees once we
612/// have seen unequal values, there is no need to track them in the cache.
613static int
614CompareValueComplexity(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;
686}

688// Return negative, zero, or positive, if LHS is less than, equal to, or greater
689// than RHS, respectively. A three-way result allows recursive comparisons to be
690// more efficient.
691static int CompareSCEVComplexity(
  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 (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
  return 0;
// 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?")((LHead != RHead && "Two loops share the same header?"
) ? static_cast<void> (0) : __assert_fail ("LHead != RHead && \"Two loops share the same header?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 745, __PRETTY_FUNCTION__));
    if (DT.dominates(LHead, RHead))
      return 1;
    else
      assert(DT.dominates(RHead, LHead) &&((DT.dominates(RHead, LHead) && "No dominance between recurrences used by one SCEV?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 750, __PRETTY_FUNCTION__))
             "No dominance between recurrences used by one SCEV?")((DT.dominates(RHead, LHead) && "No dominance between recurrences used by one SCEV?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates(RHead, LHead) && \"No dominance between recurrences used by one SCEV?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 750, __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) {
    int 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: {
  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) {
    int 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.
  int 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.
  int 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!"
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 829);
}
llvm_unreachable("Unknown SCEV kind!")::llvm::llvm_unreachable_internal("Unknown SCEV kind!", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 831);
832}

834/// Given a list of SCEV objects, order them by their complexity, and group
835/// objects of the same complexity together by value.  When this routine is
836/// finished, we know that any duplicates in the vector are consecutive and that
837/// complexity is monotonically increasing.
838///
839/// Note that we go take special precautions to ensure that we get deterministic
840/// results from this routine.  In other words, we don't want the results of
841/// this to depend on where the addresses of various SCEV objects happened to
842/// land in memory.
843static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
                            LoopInfo *LI, DominatorTree &DT) {
if (Ops.size() < 2) return;  // Noop

EquivalenceClasses<const SCEV *> EqCacheSCEV;
EquivalenceClasses<const Value *> EqCacheValue;
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 (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
    std::swap(LHS, RHS);
  return;
}

// Do the rough sort by complexity.
llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
  return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
         0;
});

// 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!
    }
  }
}
883}

885/// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
886/// least HugeExprThreshold nodes).
887static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
return any_of(Ops, [](const SCEV *S) {
  return S->getExpressionSize() >= HugeExprThreshold;
});
891}

893//===----------------------------------------------------------------------===//
894//                      Simple SCEV method implementations
895//===----------------------------------------------------------------------===//

897/// Compute BC(It, K).  The result has width W.  Assume, K > 0.
898static 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));
1006}

1008/// Return the value of this chain of recurrences at the specified iteration
1009/// number.  We can evaluate this recurrence by multiplying each element in the
1010/// chain by the binomial coefficient corresponding to it.  In other words, we
1011/// can evaluate {A,+,B,+,C,+,D} as:
1012///
1013///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1014///
1015/// where BC(It, k) stands for binomial coefficient.
1016const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
                                              ScalarEvolution &SE) const {
const SCEV *Result = getStart();
for (unsigned i = 1, e = getNumOperands(); 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, getType());
  if (isa<SCEVCouldNotCompute>(Coeff))
    return Coeff;

  Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
}
return Result;
1030}

1032//===----------------------------------------------------------------------===//
1033//                    SCEV Expression folder implementations
1034//===----------------------------------------------------------------------===//

1036const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty,
                                           unsigned Depth) {
assert(Ty->isIntegerTy() && "Target type must be an integer type!")((Ty->isIntegerTy() && "Target type must be an integer type!"
) ? static_cast<void> (0) : __assert_fail ("Ty->isIntegerTy() && \"Target type must be an integer type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1038, __PRETTY_FUNCTION__));
assert(Depth <= 1 && "getPtrToIntExpr() should self-recurse at most once.")((Depth <= 1 && "getPtrToIntExpr() should self-recurse at most once."
) ? static_cast<void> (0) : __assert_fail ("Depth <= 1 && \"getPtrToIntExpr() should self-recurse at most once.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1039, __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 getTruncateOrZeroExtend(Op, Ty);

// 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 getTruncateOrZeroExtend(S, Ty);

// If not, is this expression something we can't reduce any further?
if (isa<SCEVUnknown>(Op)) {
  // 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.
  Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType());
  assert(getDataLayout().getTypeSizeInBits(getEffectiveSCEVType(((getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->
getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) &&
 "We can only model ptrtoint if SCEV's effective (integer) type is "
 "sufficiently wide to represent all possible pointer values."
) ? static_cast<void> (0) : __assert_fail ("getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) && \"We can only model ptrtoint if SCEV's effective (integer) type is \" \"sufficiently wide to represent all possible pointer values.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1066, __PRETTY_FUNCTION__))
             Op->getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) &&((getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->
getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) &&
 "We can only model ptrtoint if SCEV's effective (integer) type is "
 "sufficiently wide to represent all possible pointer values."
) ? static_cast<void> (0) : __assert_fail ("getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) && \"We can only model ptrtoint if SCEV's effective (integer) type is \" \"sufficiently wide to represent all possible pointer values.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1066, __PRETTY_FUNCTION__))
         "We can only model ptrtoint if SCEV's effective (integer) type is "((getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->
getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) &&
 "We can only model ptrtoint if SCEV's effective (integer) type is "
 "sufficiently wide to represent all possible pointer values."
) ? static_cast<void> (0) : __assert_fail ("getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) && \"We can only model ptrtoint if SCEV's effective (integer) type is \" \"sufficiently wide to represent all possible pointer values.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1066, __PRETTY_FUNCTION__))
         "sufficiently wide to represent all possible pointer values.")((getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->
getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) &&
 "We can only model ptrtoint if SCEV's effective (integer) type is "
 "sufficiently wide to represent all possible pointer values."
) ? static_cast<void> (0) : __assert_fail ("getDataLayout().getTypeSizeInBits(getEffectiveSCEVType( Op->getType())) == getDataLayout().getTypeSizeInBits(IntPtrTy) && \"We can only model ptrtoint if SCEV's effective (integer) type is \" \"sufficiently wide to represent all possible pointer values.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1066, __PRETTY_FUNCTION__));
  SCEV *S = new (SCEVAllocator)
      SCEVPtrToIntExpr(ID.Intern(SCEVAllocator), Op, IntPtrTy);
  UniqueSCEVs.InsertNode(S, IP);
  addToLoopUseLists(S);
  return getTruncateOrZeroExtend(S, Ty);
}

assert(Depth == 0 &&((Depth == 0 && "getPtrToIntExpr() should not self-recurse for non-SCEVUnknown's."
) ? static_cast<void> (0) : __assert_fail ("Depth == 0 && \"getPtrToIntExpr() should not self-recurse for non-SCEVUnknown's.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1075, __PRETTY_FUNCTION__))
       "getPtrToIntExpr() should not self-recurse for non-SCEVUnknown's.")((Depth == 0 && "getPtrToIntExpr() should not self-recurse for non-SCEVUnknown's."
) ? static_cast<void> (0) : __assert_fail ("Depth == 0 && \"getPtrToIntExpr() should not self-recurse for non-SCEVUnknown's.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1075, __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) {
    Type *ExprPtrTy = Expr->getType();
    assert(ExprPtrTy->isPointerTy() &&((ExprPtrTy->isPointerTy() && "Should only reach pointer-typed SCEVUnknown's."
) ? static_cast<void> (0) : __assert_fail ("ExprPtrTy->isPointerTy() && \"Should only reach pointer-typed SCEVUnknown's.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1131, __PRETTY_FUNCTION__))
           "Should only reach pointer-typed SCEVUnknown's.")((ExprPtrTy->isPointerTy() && "Should only reach pointer-typed SCEVUnknown's."
) ? static_cast<void> (0) : __assert_fail ("ExprPtrTy->isPointerTy() && \"Should only reach pointer-typed SCEVUnknown's.\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1131, __PRETTY_FUNCTION__));
    Type *ExprIntPtrTy = SE.getDataLayout().getIntPtrType(ExprPtrTy);
    return SE.getPtrToIntExpr(Expr, ExprIntPtrTy, /*Depth=*/1);
  }
};

// And actually perform the cast sinking.
const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Op, *this);
assert(IntOp->getType()->isIntegerTy() &&((IntOp->getType()->isIntegerTy() && "We must have succeeded in sinking the cast, "
 "and ending up with an integer-typed expression!") ? static_cast
<void> (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1141, __PRETTY_FUNCTION__))
       "We must have succeeded in sinking the cast, "((IntOp->getType()->isIntegerTy() && "We must have succeeded in sinking the cast, "
 "and ending up with an integer-typed expression!") ? static_cast
<void> (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1141, __PRETTY_FUNCTION__))
       "and ending up with an integer-typed expression!")((IntOp->getType()->isIntegerTy() && "We must have succeeded in sinking the cast, "
 "and ending up with an integer-typed expression!") ? static_cast
<void> (0) : __assert_fail ("IntOp->getType()->isIntegerTy() && \"We must have succeeded in sinking the cast, \" \"and ending up with an integer-typed expression!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1141, __PRETTY_FUNCTION__));
return getTruncateOrZeroExtend(IntOp, Ty);
1143}

1145const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
                                           unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(
Ty) && "This is not a truncating conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1148, __PRETTY_FUNCTION__))
       "This is not a truncating conversion!")((getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(
Ty) && "This is not a truncating conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && \"This is not a truncating conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1148, __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1150, __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1150, __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);
  addToLoopUseLists(S);
  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."
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1207);
  }
  // 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);
}

// 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);
addToLoopUseLists(S);
return S;
1232}

1234// Get the limit of a recurrence such that incrementing by Step cannot cause
1235// signed overflow as long as the value of the recurrence within the
1236// loop does not exceed this limit before incrementing.
1237static 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;
1252}

1254// Get the limit of a recurrence such that incrementing by Step cannot cause
1255// unsigned overflow as long as the value of the recurrence within the loop does
1256// not exceed this limit before incrementing.
1257static 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));
1265}

1267namespace {

1269struct ExtendOpTraitsBase {
typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
                                                        unsigned);
1272};

1274// Used to make code generic over signed and unsigned overflow.
1275template <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);
1285};

1287template <>
1288struct 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);
}
1298};

1300const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
  SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;

1303template <>
1304struct 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);
}
1314};

1316const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
  SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;

1319} // end anonymous namespace

1321// The recurrence AR has been shown to have no signed/unsigned wrap or something
1322// close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1323// easily prove NSW/NUW for its preincrement or postincrement sibling. This
1324// allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1325// Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1326// expression "Step + sext/zext(PreIncAR)" is congruent with
1327// "sext/zext(PostIncAR)"
1328template <typename ExtendOpTy>
1329static 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;
1399}

1401// Get the normalized zero or sign extended expression for this AddRec's Start.
1402template <typename ExtendOpTy>
1403static 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));
1415}

1417// Try to prove away overflow by looking at "nearby" add recurrences.  A
1418// motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1419// does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1420//
1421// Formally:
1422//
1423//     {S,+,X} == {S-T,+,X} + T
1424//  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1425//
1426// If ({S-T,+,X} + T) does not overflow  ... (1)
1427//
1428//  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1429//
1430// If {S-T,+,X} does not overflow  ... (2)
1431//
1432//  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1433//      == {Ext(S-T)+Ext(T),+,Ext(X)}
1434//
1435// If (S-T)+T does not overflow  ... (3)
1436//
1437//  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1438//      == {Ext(S),+,Ext(X)} == LHS
1439//
1440// Thus, if (1), (2) and (3) are true for some T, then
1441//   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1442//
1443// (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1444// does not overflow" restricted to the 0th iteration.  Therefore we only need
1445// to check for (1) and (2).
1446//
1447// In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1448// is `Delta` (defined below).
1449template <typename ExtendOpTy>
1450bool 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;
1490}

1492// Finds an integer D for an expression (C + x + y + ...) such that the top
1493// level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1494// unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1495// maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1496// the (C + x + y + ...) expression is \p WholeAddExpr.
1497static 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);
1512}

1514// Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1515// level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1516// number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1517// ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1518static 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);
1527}

1529const SCEV *
1530ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1532, __PRETTY_FUNCTION__))
       "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1532, __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1534, __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1534, __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);
  addToLoopUseLists(S);
  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);
addToLoopUseLists(S);
return S;
1829}

1831const SCEV *
1832ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1834, __PRETTY_FUNCTION__))
       "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1834, __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1836, __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 1836, __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);
  addToLoopUseLists(S);
  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);
addToLoopUseLists(S);
return S;
2064}

2066/// getAnyExtendExpr - Return a SCEV for the given operand extended with
2067/// unspecified bits out to the given type.
2068const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
                                            Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2071, __PRETTY_FUNCTION__))
       "This is not an extending conversion!")((getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(
Ty) && "This is not an extending conversion!") ? static_cast
<void> (0) : __assert_fail ("getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && \"This is not an extending conversion!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2071, __PRETTY_FUNCTION__));
assert(isSCEVable(Ty) &&((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2073, __PRETTY_FUNCTION__))
       "This is not a conversion to a SCEVable type!")((isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(Ty) && \"This is not a conversion to a SCEVable type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2073, __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;
2113}

2115/// Process the given Ops list, which is a list of operands to be added under
2116/// the given scale, update the given map. This is a helper function for
2117/// getAddRecExpr. As an example of what it does, given a sequence of operands
2118/// that would form an add expression like this:
2119///
2120///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2121///
2122/// where A and B are constants, update the map with these values:
2123///
2124///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2125///
2126/// and add 13 + A*B*29 to AccumulatedConstant.
2127/// This will allow getAddRecExpr to produce this:
2128///
2129///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2130///
2131/// This form often exposes folding opportunities that are hidden in
2132/// the original operand list.
2133///
2134/// Return true iff it appears that any interesting folding opportunities
2135/// may be exposed. This helps getAddRecExpr short-circuit extra work in
2136/// the common case where no interesting opportunities are present, and
2137/// is also used as a check to avoid infinite recursion.
2138static bool
2139CollectAddOperandsWithScales(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(Mul->op_begin()+1, Mul->op_end());
      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;
2202}

2204// We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2205// `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
2206// can't-overflow flags for the operation if possible.
2207static SCEV::NoWrapFlags
2208StrengthenNoWrapFlags(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!")((CanAnalyze && "don't call from other places!") ? static_cast
<void> (0) : __assert_fail ("CanAnalyze && \"don't call from other places!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2218, __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.", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2246);
    }
  }();

  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);
  }
}

return Flags;
2270}

2272bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2274}

2276/// Get a canonical add expression, or something simpler if possible.
2277const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
                                      SCEV::NoWrapFlags OrigFlags,
                                      unsigned Depth) {
assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&((!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
 "only nuw or nsw allowed") ? static_cast<void> (0) : __assert_fail
 ("!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2281, __PRETTY_FUNCTION__))
       "only nuw or nsw allowed")((!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
 "only nuw or nsw allowed") ? static_cast<void> (0) : __assert_fail
 ("!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2281, __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty add!")((!Ops.empty() && "Cannot get empty add!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty add!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2282, __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
2284#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "SCEVAddExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2288, __PRETTY_FUNCTION__))
         "SCEVAddExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "SCEVAddExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVAddExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2288, __PRETTY_FUNCTION__));
2289#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())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
 ("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2298, __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 = std::get<0>(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);
  }
}

// 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;
  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;
  }

  // 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, SCEV::FlagAnyWrap, 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 != 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.
    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->op_begin(),
                                           AddRec->op_end());
    // This follows from the fact that the no-wrap flags on the outer add
    // expression are applicable on the 0th iteration, when the add recurrence
    // will be equal to its start value.
    AddRecOps[0] = getAddExpr(LIOps, Flags, 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(((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2635, __PRETTY_FUNCTION__))
         cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2635, __PRETTY_FUNCTION__))
         AddRec->getLoop()->getHeader()) &&((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2635, __PRETTY_FUNCTION__))
      "AddRecExprs are not sorted in reverse dominance order?")((DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->
getLoop()->getHeader(), AddRec->getLoop()->getHeader
()) && "AddRecExprs are not sorted in reverse dominance order?"
) ? static_cast<void> (0) : __assert_fail ("DT.dominates( cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && \"AddRecExprs are not sorted in reverse dominance order?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2635, __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->op_begin(),
                                             AddRec->op_end());
      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));
2671}

2673const SCEV *
2674ScalarEvolution::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);
  addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
2693}

2695const SCEV *
2696ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
                                     const Loop *L, SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scAddRecExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
  ID.AddPointer(Ops[i]);
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);
  addToLoopUseLists(S);
}
setNoWrapFlags(S, Flags);
return S;
2716}

2718const SCEV *
2719ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
                                  SCEV::NoWrapFlags Flags) {
FoldingSetNodeID ID;
ID.AddInteger(scMulExpr);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
  ID.AddPointer(Ops[i]);
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);
  addToLoopUseLists(S);
}
S->setNoWrapFlags(Flags);
return S;
2738}

2740static 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;
2744}

2746/// Compute the result of "n choose k", the binomial coefficient.  If an
2747/// intermediate computation overflows, Overflow will be set and the return will
2748/// be garbage. Overflow is not cleared on absence of overflow.
2749static 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;
2770}

2772/// Determine if any of the operands in this SCEV are a constant or if
2773/// any of the add or multiply expressions in this SCEV contain a constant.
2774static 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;
2792}

2794/// Get a canonical multiply expression, or something simpler if possible.
2795const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
                                      SCEV::NoWrapFlags OrigFlags,
                                      unsigned Depth) {
assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) &&((OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW
) && "only nuw or nsw allowed") ? static_cast<void
> (0) : __assert_fail ("OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2799, __PRETTY_FUNCTION__))
       "only nuw or nsw allowed")((OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW
) && "only nuw or nsw allowed") ? static_cast<void
> (0) : __assert_fail ("OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) && \"only nuw or nsw allowed\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2799, __PRETTY_FUNCTION__));
assert(!Ops.empty() && "Cannot get empty mul!")((!Ops.empty() && "Cannot get empty mul!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty mul!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2800, __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
2802#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "SCEVMulExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVMulExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2806, __PRETTY_FUNCTION__))
         "SCEVMulExpr operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "SCEVMulExpr operand types don't match!") ? static_cast<void
> (0) : __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"SCEVMulExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2806, __PRETTY_FUNCTION__));
2807#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())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
 ("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 2816, __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 = std::get<0>(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));
3056}

3058/// Represents an unsigned remainder expression based on unsigned division.
3059const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3063, __PRETTY_FUNCTION__))
       getEffectiveSCEVType(RHS->getType()) &&((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3063, __PRETTY_FUNCTION__))
       "SCEVURemExpr operand types don't match!")((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVURemExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVURemExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3063, __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);
3084}

3086/// Get a canonical unsigned division expression, or something simpler if
3087/// possible.
3088const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
assert(getEffectiveSCEVType(LHS->getType()) ==((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3092, __PRETTY_FUNCTION__))
       getEffectiveSCEVType(RHS->getType()) &&((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3092, __PRETTY_FUNCTION__))
       "SCEVUDivExpr operand types don't match!")((getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType
(RHS->getType()) && "SCEVUDivExpr operand types don't match!"
) ? static_cast<void> (0) : __assert_fail ("getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && \"SCEVUDivExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3092, __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;

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->op_begin(),
                                                    M->op_end());
            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);
addToLoopUseLists(S);
return S;
3239}

3241static const 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));
3253}

3255/// Get a canonical unsigned division expression, or something simpler if
3256/// possible. There is no representation for an exact udiv in SCEV IR, but we
3257/// can attempt to remove factors from the LHS and RHS.  We can't do this when
3258/// it's not exact because the udiv may be clearing bits.
3259const 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;
      Operands.append(Mul->op_begin() + 1, Mul->op_end());
      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);
3310}

3312/// Get an add recurrence expression for the specified loop.  Simplify the
3313/// expression as much as possible.
3314const 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);
3327}

3329/// Get an add recurrence expression for the specified loop.  Simplify the
3330/// expression as much as possible.
3331const SCEV *
3332ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
                             const Loop *L, SCEV::NoWrapFlags Flags) {
if (Operands.size() == 1) return Operands[0];
3335#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
  assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&((getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
 "SCEVAddRecExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3339, __PRETTY_FUNCTION__))
         "SCEVAddRecExpr operand types don't match!")((getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
 "SCEVAddRecExpr operand types don't match!") ? static_cast<
void> (0) : __assert_fail ("getEffectiveSCEVType(Operands[i]->getType()) == ETy && \"SCEVAddRecExpr operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3339, __PRETTY_FUNCTION__));
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
  assert(isLoopInvariant(Operands[i], L) &&((isLoopInvariant(Operands[i], L) && "SCEVAddRecExpr operand is not loop-invariant!"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3342, __PRETTY_FUNCTION__))
         "SCEVAddRecExpr operand is not loop-invariant!")((isLoopInvariant(Operands[i], L) && "SCEVAddRecExpr operand is not loop-invariant!"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Operands[i], L) && \"SCEVAddRecExpr operand is not loop-invariant!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3342, __PRETTY_FUNCTION__));
3343#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->op_begin(),
                                                NestedAR->op_end());
    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);
3405}

3407const SCEV *
3408ScalarEvolution::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());
// FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
// instruction to its SCEV, because the Instruction may be guarded by control
// flow and the no-overflow bits may not be valid for the expression in any
// context. This can be fixed similarly to how these flags are handled for
// adds.
SCEV::NoWrapFlags OffsetWrap =
    GEP->isInBounds() ? 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) &&((isa<PointerType>(CurTy) && "The first index of a GEP indexes a pointer"
) ? static_cast<void> (0) : __assert_fail ("isa<PointerType>(CurTy) && \"The first index of a GEP indexes a pointer\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3440, __PRETTY_FUNCTION__))
             "The first index of a GEP indexes a pointer")((isa<PointerType>(CurTy) && "The first index of a GEP indexes a pointer"
) ? static_cast<void> (0) : __assert_fail ("isa<PointerType>(CurTy) && \"The first index of a GEP indexes a pointer\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3440, __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 = GEP->isInBounds() && isKnownNonNegative(Offset)
                                 ? SCEV::FlagNUW : SCEV::FlagAnyWrap;
return getAddExpr(BaseExpr, Offset, BaseWrap);
3469}

3471std::tuple<SCEV *, FoldingSetNodeID, void *>
3472ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType,
                                       ArrayRef<const SCEV *> Ops) {
FoldingSetNodeID ID;
void *IP = nullptr;
ID.AddInteger(SCEVType);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
  ID.AddPointer(Ops[i]);
return std::tuple<SCEV *, FoldingSetNodeID, void *>(
    UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
3481}

3483const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) {
SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
return getSMaxExpr(Op, getNegativeSCEV(Op, Flags));
3486}

3488const SCEV *ScalarEvolution::getSignumExpr(const SCEV *Op) {
Type *Ty = Op->getType();
return getSMinExpr(getSMaxExpr(Op, getMinusOne(Ty)), getOne(Ty));
3491}

3493const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind,
                                         SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!")((!Ops.empty() && "Cannot get empty (u|s)(min|max)!")
 ? static_cast<void> (0) : __assert_fail ("!Ops.empty() && \"Cannot get empty (u|s)(min|max)!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3495, __PRETTY_FUNCTION__));
if (Ops.size() == 1) return Ops[0];
3497#ifndef NDEBUG
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "Operand types don't match!") ? static_cast<void> (0) :
 __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3501, __PRETTY_FUNCTION__))
         "Operand types don't match!")((getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
 "Operand types don't match!") ? static_cast<void> (0) :
 __assert_fail ("getEffectiveSCEVType(Ops[i]->getType()) == ETy && \"Operand types don't match!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3501, __PRETTY_FUNCTION__));
3502#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 = std::get<0>(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())((Idx < Ops.size()) ? static_cast<void> (0) : __assert_fail
 ("Idx < Ops.size()", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3519, __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"
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3529);
  };

  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!")((!Ops.empty() && "Reduced smax down to nothing!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"Reduced smax down to nothing!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3605, __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.
const SCEV *ExistingSCEV;
FoldingSetNodeID ID;
void *IP;
std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
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);
addToLoopUseLists(S);
return S;
3623}

3625const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getSMaxExpr(Ops);
3628}

3630const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMaxExpr, Ops);
3632}

3634const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
return getUMaxExpr(Ops);
3637}

3639const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMaxExpr, Ops);
3641}

3643const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getSMinExpr(Ops);
3647}

3649const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scSMinExpr, Ops);
3651}

3653const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
                                       const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinExpr(Ops);
3657}

3659const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
return getMinMaxExpr(scUMinExpr, Ops);
3661}

3663const SCEV *
3664ScalarEvolution::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));
3673}

3675const 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));
3682}

3684const 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));
3691}

3693const 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));
3701}

3703const 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 &&((cast<SCEVUnknown>(S)->getValue() == V && "Stale SCEVUnknown in uniquing map!"
) ? static_cast<void> (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3715, __PRETTY_FUNCTION__))
         "Stale SCEVUnknown in uniquing map!")((cast<SCEVUnknown>(S)->getValue() == V && "Stale SCEVUnknown in uniquing map!"
) ? static_cast<void> (0) : __assert_fail ("cast<SCEVUnknown>(S)->getValue() == V && \"Stale SCEVUnknown in uniquing map!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3715, __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;
3723}

3725//===----------------------------------------------------------------------===//
3726//            Basic SCEV Analysis and PHI Idiom Recognition Code
3727//

3729/// Test if values of the given type are analyzable within the SCEV
3730/// framework. This primarily includes integer types, and it can optionally
3731/// include pointer types if the ScalarEvolution class has access to
3732/// target-specific information.
3733bool ScalarEvolution::isSCEVable(Type *Ty) const {
// Integers and pointers are always SCEVable.
return Ty->isIntOrPtrTy();
3736}

3738/// Return the size in bits of the specified type, for which isSCEVable must
3739/// return true.
3740uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!")((isSCEVable(Ty) && "Type is not SCEVable!") ? static_cast
<void> (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3741, __PRETTY_FUNCTION__));
if (Ty->isPointerTy())
  return getDataLayout().getIndexTypeSizeInBits(Ty);
return getDataLayout().getTypeSizeInBits(Ty);
3745}

3747/// Return a type with the same bitwidth as the given type and which represents
3748/// how SCEV will treat the given type, for which isSCEVable must return
3749/// true. For pointer types, this is the pointer index sized integer type.
3750Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!")((isSCEVable(Ty) && "Type is not SCEVable!") ? static_cast
<void> (0) : __assert_fail ("isSCEVable(Ty) && \"Type is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3751, __PRETTY_FUNCTION__));

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

// The only other support type is pointer.
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!")((Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"
) ? static_cast<void> (0) : __assert_fail ("Ty->isPointerTy() && \"Unexpected non-pointer non-integer type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3757, __PRETTY_FUNCTION__));
return getDataLayout().getIndexType(Ty);
3759}

3761Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
return  getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3763}

3765const SCEV *ScalarEvolution::getCouldNotCompute() {
return CouldNotCompute.get();
3767}

3769bool 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;
3776}

3778bool 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;
3787}

3789/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3790/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3791/// offset I, then return {S', I}, else return {\p S, nullptr}.
3792static 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()};
3805}

3807/// Return the ValueOffsetPair set for \p S. \p S can be represented
3808/// by the value and offset from any ValueOffsetPair in the set.
3809SetVector<ScalarEvolution::ValueOffsetPair> *
3810ScalarEvolution::getSCEVValues(const SCEV *S) {
ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
if (SI == ExprValueMap.end())
  return nullptr;
3814#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))((ValueExprMap.count(VE.first)) ? static_cast<void> (0)
 : __assert_fail ("ValueExprMap.count(VE.first)", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3818, __PRETTY_FUNCTION__));
}
3820#endif
return &SI->second;
3822}

3824/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3825/// cannot be used separately. eraseValueFromMap should be used to remove
3826/// V from ValueExprMap and ExprValueMap at the same time.
3827void 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 (SetVector<ValueOffsetPair> *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 (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
      SV->remove({V, Offset});
  }
  ValueExprMap.erase(V);
}
3845}

3847/// Check whether value has nuw/nsw/exact set but SCEV does not.
3848/// TODO: In reality it is better to check the poison recursively
3849/// but this is better than nothing.
3850static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
if (auto *I = dyn_cast<Instruction>(V)) {
  if (isa<OverflowingBinaryOperator>(I)) {
    if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
      if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
        return true;
      if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
        return true;
    }
  } else if (isa<PossiblyExactOperator>(I) && I->isExact())
    return true;
}
return false;
3863}

3865/// Return an existing SCEV if it exists, otherwise analyze the expression and
3866/// create a new one.
3867const SCEV *ScalarEvolution::getSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((isSCEVable(V->getType()) && "Value is not SCEVable!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3868, __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 && !SCEVLostPoisonFlags(S, V)) {
    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;
3897}

3899const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!")((isSCEVable(V->getType()) && "Value is not SCEVable!"
) ? static_cast<void> (0) : __assert_fail ("isSCEVable(V->getType()) && \"Value is not SCEVable!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 3900, __PRETTY_FUNCTION__));

ValueExprMapType::iterator I = ValueExprMap.find_as(V);
if (I != ValueExprMap.end()) {
  const SCEV *S = I->second;
  if (checkValidity(S))
    return S;
  eraseValueFromMap(V);
  forgetMemoizedResults(S);
}
return nullptr;
3911}

3913/// Return a SCEV corresponding to -V = -1*V
3914const 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);
3923}

3925/// If Expr computes ~A, return A else return nullptr
3926static 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);
3938}

3940/// Return a SCEV corresponding to ~V = -1-V
3941const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
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);
3966}

3968const 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());

// 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 (maskFlags(Flags, SCEV::FlagNSW) == 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);
4005}

4007const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
                                                   unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4011, __PRETTY_FUNCTION__))
       "Cannot truncate or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4011, __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);
4017}

4019const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
                                                   unsigned Depth) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4023, __PRETTY_FUNCTION__))
       "Cannot truncate or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or zero extend with non-integer arguments!"
) ? static_cast<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4023, __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);
4029}

4031const SCEV *
4032ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or zero extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4035, __PRETTY_FUNCTION__))
       "Cannot noop or zero extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or zero extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or zero extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4035, __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrZeroExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4037, __PRETTY_FUNCTION__))
       "getNoopOrZeroExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrZeroExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrZeroExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4037, __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getZeroExtendExpr(V, Ty);
4041}

4043const SCEV *
4044ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or sign extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4047, __PRETTY_FUNCTION__))
       "Cannot noop or sign extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or sign extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or sign extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4047, __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrSignExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4049, __PRETTY_FUNCTION__))
       "getNoopOrSignExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrSignExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrSignExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4049, __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getSignExtendExpr(V, Ty);
4053}

4055const SCEV *
4056ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or any extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4059, __PRETTY_FUNCTION__))
       "Cannot noop or any extend with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot noop or any extend with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot noop or any extend with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4059, __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrAnyExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4061, __PRETTY_FUNCTION__))
       "getNoopOrAnyExtend cannot truncate!")((getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
 "getNoopOrAnyExtend cannot truncate!") ? static_cast<void
> (0) : __assert_fail ("getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && \"getNoopOrAnyExtend cannot truncate!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4061, __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getAnyExtendExpr(V, Ty);
4065}

4067const SCEV *
4068ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
Type *SrcTy = V->getType();
assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or noop with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4071, __PRETTY_FUNCTION__))
       "Cannot truncate or noop with non-integer arguments!")((SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
 "Cannot truncate or noop with non-integer arguments!") ? static_cast
<void> (0) : __assert_fail ("SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && \"Cannot truncate or noop with non-integer arguments!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4071, __PRETTY_FUNCTION__));
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&((getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
 "getTruncateOrNoop cannot extend!") ? static_cast<void>
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4073, __PRETTY_FUNCTION__))
       "getTruncateOrNoop cannot extend!")((getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
 "getTruncateOrNoop cannot extend!") ? static_cast<void>
 (0) : __assert_fail ("getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && \"getTruncateOrNoop cannot extend!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4073, __PRETTY_FUNCTION__));
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
  return V;  // No conversion
return getTruncateExpr(V, Ty);
4077}

4079const 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);
4090}

4092const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
                                                      const SCEV *RHS) {
SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
return getUMinFromMismatchedTypes(Ops);
4096}

4098const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
  SmallVectorImpl<const SCEV *> &Ops) {
assert(!Ops.empty() && "At least one operand must be!")((!Ops.empty() && "At least one operand must be!") ? static_cast
<void> (0) : __assert_fail ("!Ops.empty() && \"At least one operand must be!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4100, __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!")((MaxType && "Failed to find maximum type!") ? static_cast
<void> (0) : __assert_fail ("MaxType && \"Failed to find maximum type!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4112, __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);
4121}

4123const 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 (const SCEVIntegralCastExpr *Cast = dyn_cast<SCEVIntegralCastExpr>(V)) {
    V = Cast->getOperand();
  } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
    const SCEV *PtrOp = nullptr;
    for (const SCEV *NAryOp : NAry->operands()) {
      if (NAryOp->getType()->isPointerTy()) {
        // Cannot find the base of an expression with multiple pointer ops.
        if (PtrOp)
          return V;
        PtrOp = NAryOp;
      }
    }
    if (!PtrOp) // All operands were non-pointer.
      return V;
    V = PtrOp;
  } else // Not something we can look further into.
    return V;
}
4147}

4149/// Push users of the given Instruction onto the given Worklist.
4150static void
4151PushDefUseChildren(Instruction *I,
                 SmallVectorImpl<Instruction *> &Worklist) {
// Push the def-use children onto the Worklist stack.
for (User *U : I->users())
  Worklist.push_back(cast<Instruction>(U));
4156}

4158void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
SmallVector<Instruction *, 16> Worklist;
PushDefUseChildren(PN, Worklist);

SmallPtrSet<Instruction *, 8> Visited;
Visited.insert(PN);
while (!Worklist.empty()) {
  Instruction *I = Worklist.pop_back_val();
  if (!Visited.insert(I).second)
    continue;

  auto It = ValueExprMap.find_as(static_cast<Value *>(I));
  if (It != ValueExprMap.end()) {
    const SCEV *Old = It->second;

    // Short-circuit the def-use traversal if the symbolic name
    // ceases to appear in expressions.
    if (Old != SymName && !hasOperand(Old, SymName))
      continue;

    // SCEVUnknown for a PHI either means that it has an unrecognized
    // structure, it's a PHI that's in the progress of being computed
    // by createNodeForPHI, or it's a single-value PHI. In the first case,
    // additional loop trip count information isn't going to change anything.
    // In the second case, createNodeForPHI will perform the necessary
    // updates on its own when it gets to that point. In the third, we do
    // want to forget the SCEVUnknown.
    if (!isa<PHINode>(I) ||
        !isa<SCEVUnknown>(Old) ||
        (I != PN && Old == SymName)) {
      eraseValueFromMap(It->first);
      forgetMemoizedResults(Old);
    }
  }

  PushDefUseChildren(I, Worklist);
}
4195}

4197namespace {

4199/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4200/// expression in case its Loop is L. If it is not L then
4201/// if IgnoreOtherLoops is true then use AddRec itself
4202/// otherwise rewrite cannot be done.
4203/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4204class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4205public:
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; }

4235private:
explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
4242};

4244/// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4245/// increment expression in case its Loop is L. If it is not L then
4246/// use AddRec itself.
4247/// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4248class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4249public:
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; }

4276private:
explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool SeenLoopVariantSCEVUnknown = false;
bool SeenOtherLoops = false;
4283};

4285/// This class evaluates the compare condition by matching it against the
4286/// condition of loop latch. If there is a match we assume a true value
4287/// for the condition while building SCEV nodes.
4288class SCEVBackedgeConditionFolder
  : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4290public:
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) &&((BI->getSuccessor(0) != BI->getSuccessor(1) &&
 "Both outgoing branches should not target same header!") ? static_cast
<void> (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4299, __PRETTY_FUNCTION__))
             "Both outgoing branches should not target same header!")((BI->getSuccessor(0) != BI->getSuccessor(1) &&
 "Both outgoing branches should not target same header!") ? static_cast
<void> (0) : __assert_fail ("BI->getSuccessor(0) != BI->getSuccessor(1) && \"Both outgoing branches should not target same header!\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4299, __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;
}

4338private:
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;
4351};

4353Optional<const SCEV *>
4354SCEVBackedgeConditionFolder::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;
4363}

4365class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4366public:
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; }

4390private:
explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
    : SCEVRewriteVisitor(SE), L(L) {}

const Loop *L;
bool Valid = true;
4396};

4398} // end anonymous namespace

4400SCEV::NoWrapFlags
4401ScalarEvolution::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;
4430}

4432SCEV::NoWrapFlags
4433ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) {
SCEV::NoWrapFlags Result = AR->getNoWrapFlags();

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

if (!AR->isAffine())
2
←
Taking false branch→
  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 &&
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.
ICmpInst::Predicate Pred;
const SCEV *OverflowLimit =
  getSignedOverflowLimitForStep(Step, &Pred, this);
if (OverflowLimit &&
5
←
Assuming 'OverflowLimit' is non-null→
    (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
6
←
Assuming the condition is false→
     isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
7
←
Calling 'ScalarEvolution::isKnownOnEveryIteration'→
  Result = setFlags(Result, SCEV::FlagNSW);
}
return Result;
4480}
4481SCEV::NoWrapFlags
4482ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) {
SCEV::NoWrapFlags Result = AR->getNoWrapFlags();

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

if (!AR->isAffine())
  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 &&
    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)) {
  const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
                              getUnsignedRangeMax(Step));
  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
      isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
    Result = setFlags(Result, SCEV::FlagNUW);
  }
}

return Result;
4531}

4533namespace {

4535/// Represents an abstract binary operation.  This may exist as a
4536/// normal instruction or constant expression, or may have been
4537/// derived from an expression tree.
4538struct BinaryOp {
unsigned Opcode;
Value *LHS;
Value *RHS;
bool IsNSW = false;
bool IsNUW = false;
bool IsExact = 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();
  }
  if (auto *PEO = dyn_cast<PossiblyExactOperator>(Op))
    IsExact = PEO->isExact();
}

explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
                  bool IsNUW = false, bool IsExact = false)
    : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
      IsExact(IsExact) {}
4565};

4567} // end anonymous namespace

4569/// Try to map \p V into a BinaryOp, and return \c None on failure.
4570static 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;
4650}

4652/// Helper function to createAddRecFromPHIWithCasts. We have a phi
4653/// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4654/// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4655/// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4656/// follows one of the following patterns:
4657/// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4658/// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4659/// If the SCEV expression of \p Op conforms with one of the expected patterns
4660/// we return the type of the truncation operation, and indicate whether the
4661/// truncated type should be treated as signed/unsigned by setting
4662/// \p Signed to true/false, respectively.
4663static 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();
4697}

4699static 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;
4706}

4708// Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4709// computation that updates the phi follows the following pattern:
4710//   (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4711// which correspond to a phi->trunc->sext/zext->add->phi update chain.
4712// If so, try to see if it can be rewritten as an AddRecExpr under some
4713// Predicates. If successful, return them as a pair. Also cache the results
4714// of the analysis.
4715//
4716// Example usage scenario:
4717//    Say the Rewriter is called for the following SCEV:
4718//         8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4719//    where:
4720//         %X = phi i64 (%Start, %BEValue)
4721//    It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4722//    and call this function with %SymbolicPHI = %X.
4723//
4724//    The analysis will find that the value coming around the backedge has
4725//    the following SCEV:
4726//         BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4727//    Upon concluding that this matches the desired pattern, the function
4728//    will return the pair {NewAddRec, SmallPredsVec} where:
4729//         NewAddRec = {%Start,+,%Step}
4730//         SmallPredsVec = {P1, P2, P3} as follows:
4731//           P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4732//           P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4733//           P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4734//    The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4735//    under the predicates {P1,P2,P3}.
4736//    This predicated rewrite will be cached in PredicatedSCEVRewrites:
4737//         PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4738//
4739// TODO's:
4740//
4741// 1) Extend the Induction descriptor to also support inductions that involve
4742//    casts: When needed (namely, when we are called in the context of the
4743//    vectorizer induction analysis), a Set of cast instructions will be
4744//    populated by this method, and provided back to isInductionPHI. This is
4745//    needed to allow the vectorizer to properly record them to be ignored by
4746//    the cost model and to avoid vectorizing them (otherwise these casts,
4747//    which are redundant under the runtime overflow checks, will be
4748//    vectorized, which can be costly).
4749//
4750// 2) Support additional induction/PHISCEV patterns: We also want to support
4751//    inductions where the sext-trunc / zext-trunc operations (partly) occur
4752//    after the induction update operation (the induction increment):
4753//
4754//      (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4755//    which correspond to a phi->add->trunc->sext/zext->phi update chain.
4756//
4757//      (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4758//    which correspond to a phi->trunc->add->sext/zext->phi update chain.
4759//
4760// 3) Outline common code with createAddRecFromPHI to avoid duplication.
4761Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4762ScalarEvolution::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")((L && "Expecting an integer loop header phi") ? static_cast
<void> (0) : __assert_fail ("L && \"Expecting an integer loop header phi\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4770, __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")((isLoopInvariant(Expr, L) && "Expr is expected to be invariant"
) ? static_cast<void> (0) : __assert_fail ("isLoopInvariant(Expr, L) && \"Expr is expected to be invariant\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4913, __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;
4970}

4972Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4973ScalarEvolution::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")((isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec"
) ? static_cast<void> (0) : __assert_fail ("isa<SCEVAddRecExpr>(Rewrite.first) && \"Expected an AddRec\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4989, __PRETTY_FUNCTION__));
  assert(!(Rewrite.second).empty() && "Expected to find Predicates")((!(Rewrite.second).empty() && "Expected to find Predicates"
) ? static_cast<void> (0) : __assert_fail ("!(Rewrite.second).empty() && \"Expected to find Predicates\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 4990, __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;
5005}

5007// FIXME: This utility is currently required because the Rewriter currently
5008// does not rewrite this expression:
5009// {0, +, (sext ix (trunc iy to ix) to iy)}
5010// into {0, +, %step},
5011// even when the following Equal predicate exists:
5012// "%step == (sext ix (trunc iy to ix) to iy)".
5013bool 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;
5029}

5031/// A helper function for createAddRecFromPHI to handle simple cases.
5032///
5033/// This function tries to find an AddRec expression for the simplest (yet most
5034/// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
5035/// If it fails, createAddRecFromPHI will use a more general, but slow,
5036/// technique for finding the AddRec expression.
5037const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
                                                    Value *BEValueV,
                                                    Value *StartValueV) {
const Loop *L = LI.getLoopFor(PN->getParent());
assert(L && L->getHeader() == PN->getParent())((L && L->getHeader() == PN->getParent()) ? static_cast
<void> (0) : __assert_fail ("L && L->getHeader() == PN->getParent()"
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5041, __PRETTY_FUNCTION__));
assert(BEValueV && StartValueV)((BEValueV && StartValueV) ? static_cast<void> (
0) : __assert_fail ("BEValueV && StartValueV", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5042, __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);

ValueExprMap[SCEVCallbackVH(PN, this)] = 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;
5079}

5081const 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() &&((ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"
) ? static_cast<void> (0) : __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5110, __PRETTY_FUNCTION__))
       "PHI node already processed?")((ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"
) ? static_cast<void> (0) : __assert_fail ("ValueExprMap.find_as(PN) == ValueExprMap.end() && \"PHI node already processed?\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5110, __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);
ValueExprMap.insert({SCEVCallbackVH(PN, this), 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.
      forgetSymbolicName(PN, SymbolicName);
      ValueExprMap[SCEVCallbackVH(PN, this)] = 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.
      forgetSymbolicName(PN, SymbolicName);
      ValueExprMap[SCEVCallbackVH(PN, this)] = 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;
5236}

5238// Checks if the SCEV S is available at BB.  S is considered available at BB
5239// if S can be materialized at BB without introducing a fault.
5240static 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:
      // 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!", "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5307);
  }

  bool isDone() { return TraversalDone; }
};

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

ST.visitAll(S);
return CA.Available;
5318}

5320// Try to match a control flow sequence that branches out at BI and merges back
5321// at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
5322// match.
5323static 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()")((RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()"
) ? static_cast<void> (0) : __assert_fail ("RightEdge.isSingleEdge() && \"Follows from LeftEdge.isSingleEdge()\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5333, __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;
5351}

5353const 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")((IDom && "At least the entry block should dominate PN"
) ? static_cast<void> (0) : __assert_fail ("IDom && \"At least the entry block should dominate PN\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5377, __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;
5390}

5392const 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);
5409}

5411const 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:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
  // a >s b ? a+x : b+x  ->  smax(a, b)+x
  // a >s b ? b+x : a+x  ->  smin(a, b)+x
  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
    const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
    const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
    const SCEV *LA = getSCEV(TrueVal);
    const SCEV *RA = getSCEV(FalseVal);
    const SCEV *LDiff = getMinusSCEV(LA, LS);
    const SCEV *RDiff = getMinusSCEV(RA, RS);
    if (LDiff == RDiff)
      return getAddExpr(getSMaxExpr(LS, RS), LDiff);
    LDiff = getMinusSCEV(LA, RS);
    RDiff = getMinusSCEV(RA, LS);
    if (LDiff == RDiff)
      return getAddExpr(getSMinExpr(LS, RS), LDiff);
  }
  break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
  std::swap(LHS, RHS);
  LLVM_FALLTHROUGH[[gnu::fallthrough]];
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
  // a >u b ? a+x : b+x  ->  umax(a, b)+x
  // a >u b ? b+x : a+x  ->  umin(a, b)+x
  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
    const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
    const SCEV *LA = getSCEV(TrueVal);
    const SCEV *RA = getSCEV(FalseVal);
    const SCEV *LDiff = getMinusSCEV(LA, LS);
    const SCEV *RDiff = getMinusSCEV(RA, RS);
    if (LDiff == RDiff)
      return getAddExpr(getUMaxExpr(LS, RS), LDiff);
    LDiff = getMinusSCEV(LA, RS);
    RDiff = getMinusSCEV(RA, LS);
    if (LDiff == RDiff)
      return getAddExpr(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);
5508}

5510/// Expand GEP instructions into add and multiply operations. This allows them
5511/// to be analyzed by regular SCEV code.
5512const 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 (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
  IndexExprs.push_back(getSCEV(*Index));
return getGEPExpr(GEP, IndexExprs);
5521}

5523uint32_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;
5599}

5601uint32_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")((InsertPair.second && "Should insert a new key") ? static_cast
<void> (0) : __assert_fail ("InsertPair.second && \"Should insert a new key\""
, "/build/llvm-toolchain-snapshot-12~++20201129111111+e987fbdd85d/llvm/lib/Analysis/ScalarEvolution.cpp"
, 5608, __PRETTY_FUNCTION__));
return InsertPair.first->second;
5610}

5612/// Helper method to assign a range to V from metadata present in the IR.
5613static 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;
5619}

5621void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec,
                                   SCEV::NoWrapFlags Flags) {
if (AddRec->getNoWrapFlags(Flags) != Flags) {
  AddRec->setNoWrapFlags(Flags);
  UnsignedRanges.erase(AddRec);
  SignedRanges.erase(AddRec);
}
5628}

5630/// Determine the range for a particular SCEV.  If SignHint is
5631/// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5632/// with a "cleaner" unsigned (resp. signed) representation.
5633const ConstantRange &
5634ScalarEvolution::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),