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1//===--------- SCEVAffinator.cpp  - Create Scops from LLVM IR -------------===//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-exception6//7//===----------------------------------------------------------------------===//8//9// Create a polyhedral description for a SCEV value.10//11//===----------------------------------------------------------------------===//12 13#include "polly/Support/SCEVAffinator.h"14#include "polly/Options.h"15#include "polly/ScopInfo.h"16#include "polly/Support/GICHelper.h"17#include "polly/Support/SCEVValidator.h"18#include "llvm/IR/DataLayout.h"19#include "isl/aff.h"20#include "isl/local_space.h"21#include "isl/set.h"22#include "isl/val.h"23 24using namespace llvm;25using namespace polly;26 27static cl::opt<bool> IgnoreIntegerWrapping(28    "polly-ignore-integer-wrapping",29    cl::desc("Do not build run-time checks to proof absence of integer "30             "wrapping"),31    cl::Hidden, cl::cat(PollyCategory));32 33// The maximal number of basic sets we allow during the construction of a34// piecewise affine function. More complex ones will result in very high35// compile time.36static int const MaxDisjunctionsInPwAff = 100;37 38// The maximal number of bits for which a general expression is modeled39// precisely.40static unsigned const MaxSmallBitWidth = 7;41 42/// Add the number of basic sets in @p Domain to @p User43static isl_stat addNumBasicSets(__isl_take isl_set *Domain,44                                __isl_take isl_aff *Aff, void *User) {45  auto *NumBasicSets = static_cast<unsigned *>(User);46  *NumBasicSets += isl_set_n_basic_set(Domain);47  isl_set_free(Domain);48  isl_aff_free(Aff);49  return isl_stat_ok;50}51 52/// Determine if @p PWAC is too complex to continue.53static bool isTooComplex(PWACtx PWAC) {54  unsigned NumBasicSets = 0;55  isl_pw_aff_foreach_piece(PWAC.first.get(), addNumBasicSets, &NumBasicSets);56  if (NumBasicSets <= MaxDisjunctionsInPwAff)57    return false;58  return true;59}60 61/// Return the flag describing the possible wrapping of @p Expr.62static SCEV::NoWrapFlags getNoWrapFlags(const SCEV *Expr) {63  if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))64    return NAry->getNoWrapFlags();65  return SCEV::NoWrapMask;66}67 68static PWACtx combine(PWACtx PWAC0, PWACtx PWAC1,69                      __isl_give isl_pw_aff *(Fn)(__isl_take isl_pw_aff *,70                                                  __isl_take isl_pw_aff *)) {71  PWAC0.first = isl::manage(Fn(PWAC0.first.release(), PWAC1.first.release()));72  PWAC0.second = PWAC0.second.unite(PWAC1.second);73  return PWAC0;74}75 76static __isl_give isl_pw_aff *getWidthExpValOnDomain(unsigned Width,77                                                     __isl_take isl_set *Dom) {78  auto *Ctx = isl_set_get_ctx(Dom);79  auto *WidthVal = isl_val_int_from_ui(Ctx, Width);80  auto *ExpVal = isl_val_2exp(WidthVal);81  return isl_pw_aff_val_on_domain(Dom, ExpVal);82}83 84SCEVAffinator::SCEVAffinator(Scop *S, LoopInfo &LI)85    : S(S), Ctx(S->getIslCtx().get()), SE(*S->getSE()), LI(LI),86      TD(S->getFunction().getDataLayout()) {}87 88Loop *SCEVAffinator::getScope() { return BB ? LI.getLoopFor(BB) : nullptr; }89 90void SCEVAffinator::interpretAsUnsigned(PWACtx &PWAC, unsigned Width) {91  auto *NonNegDom = isl_pw_aff_nonneg_set(PWAC.first.copy());92  auto *NonNegPWA =93      isl_pw_aff_intersect_domain(PWAC.first.copy(), isl_set_copy(NonNegDom));94  auto *ExpPWA = getWidthExpValOnDomain(Width, isl_set_complement(NonNegDom));95  PWAC.first = isl::manage(isl_pw_aff_union_add(96      NonNegPWA, isl_pw_aff_add(PWAC.first.release(), ExpPWA)));97}98 99void SCEVAffinator::takeNonNegativeAssumption(100    PWACtx &PWAC, RecordedAssumptionsTy *RecordedAssumptions) {101  this->RecordedAssumptions = RecordedAssumptions;102 103  auto *NegPWA = isl_pw_aff_neg(PWAC.first.copy());104  auto *NegDom = isl_pw_aff_pos_set(NegPWA);105  PWAC.second =106      isl::manage(isl_set_union(PWAC.second.release(), isl_set_copy(NegDom)));107  auto *Restriction = BB ? NegDom : isl_set_params(NegDom);108  auto DL = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();109  recordAssumption(RecordedAssumptions, UNSIGNED, isl::manage(Restriction), DL,110                   AS_RESTRICTION, BB);111}112 113PWACtx SCEVAffinator::getPWACtxFromPWA(isl::pw_aff PWA) {114  return std::make_pair(PWA, isl::set::empty(isl::space(Ctx, 0, NumIterators)));115}116 117PWACtx SCEVAffinator::getPwAff(const SCEV *Expr, BasicBlock *BB,118                               RecordedAssumptionsTy *RecordedAssumptions) {119  this->BB = BB;120  this->RecordedAssumptions = RecordedAssumptions;121 122  if (BB) {123    auto *DC = S->getDomainConditions(BB).release();124    NumIterators = isl_set_n_dim(DC);125    isl_set_free(DC);126  } else127    NumIterators = 0;128 129  return visit(Expr);130}131 132PWACtx SCEVAffinator::checkForWrapping(const SCEV *Expr, PWACtx PWAC) const {133  // If the SCEV flags do contain NSW (no signed wrap) then PWA already134  // represents Expr in modulo semantic (it is not allowed to overflow), thus we135  // are done. Otherwise, we will compute:136  //   PWA = ((PWA + 2^(n-1)) mod (2 ^ n)) - 2^(n-1)137  // whereas n is the number of bits of the Expr, hence:138  //   n = bitwidth(ExprType)139 140  if (IgnoreIntegerWrapping || (getNoWrapFlags(Expr) & SCEV::FlagNSW))141    return PWAC;142 143  isl::pw_aff PWAMod = addModuloSemantic(PWAC.first, Expr->getType());144 145  isl::set NotEqualSet = PWAC.first.ne_set(PWAMod);146  PWAC.second = PWAC.second.unite(NotEqualSet).coalesce();147 148  const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();149  if (!BB)150    NotEqualSet = NotEqualSet.params();151  NotEqualSet = NotEqualSet.coalesce();152 153  if (!NotEqualSet.is_empty())154    recordAssumption(RecordedAssumptions, WRAPPING, NotEqualSet, Loc,155                     AS_RESTRICTION, BB);156 157  return PWAC;158}159 160isl::pw_aff SCEVAffinator::addModuloSemantic(isl::pw_aff PWA,161                                             Type *ExprType) const {162  unsigned Width = TD.getTypeSizeInBits(ExprType);163 164  auto ModVal = isl::val::int_from_ui(Ctx, Width);165  ModVal = ModVal.pow2();166 167  isl::set Domain = PWA.domain();168  isl::pw_aff AddPW =169      isl::manage(getWidthExpValOnDomain(Width - 1, Domain.release()));170 171  return PWA.add(AddPW).mod(ModVal).sub(AddPW);172}173 174bool SCEVAffinator::hasNSWAddRecForLoop(Loop *L) const {175  for (const auto &CachedPair : CachedExpressions) {176    auto *AddRec = dyn_cast<SCEVAddRecExpr>(CachedPair.first.first);177    if (!AddRec)178      continue;179    if (AddRec->getLoop() != L)180      continue;181    if (AddRec->getNoWrapFlags() & SCEV::FlagNSW)182      return true;183  }184 185  return false;186}187 188bool SCEVAffinator::computeModuloForExpr(const SCEV *Expr) {189  unsigned Width = TD.getTypeSizeInBits(Expr->getType());190  // We assume nsw expressions never overflow.191  if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))192    if (NAry->getNoWrapFlags() & SCEV::FlagNSW)193      return false;194  return Width <= MaxSmallBitWidth;195}196 197PWACtx SCEVAffinator::visit(const SCEV *Expr) {198 199  auto Key = std::make_pair(Expr, BB);200  PWACtx PWAC = CachedExpressions[Key];201  if (!PWAC.first.is_null())202    return PWAC;203 204  auto ConstantAndLeftOverPair = extractConstantFactor(Expr, SE);205  auto *Factor = ConstantAndLeftOverPair.first;206  Expr = ConstantAndLeftOverPair.second;207 208  auto *Scope = getScope();209  S->addParams(getParamsInAffineExpr(&S->getRegion(), Scope, Expr, SE));210 211  // In case the scev is a valid parameter, we do not further analyze this212  // expression, but create a new parameter in the isl_pw_aff. This allows us213  // to treat subexpressions that we cannot translate into an piecewise affine214  // expression, as constant parameters of the piecewise affine expression.215  if (isl_id *Id = S->getIdForParam(Expr).release()) {216    isl_space *Space = isl_space_set_alloc(Ctx.get(), 1, NumIterators);217    Space = isl_space_set_dim_id(Space, isl_dim_param, 0, Id);218 219    isl_set *Domain = isl_set_universe(isl_space_copy(Space));220    isl_aff *Affine = isl_aff_zero_on_domain(isl_local_space_from_space(Space));221    Affine = isl_aff_add_coefficient_si(Affine, isl_dim_param, 0, 1);222 223    PWAC = getPWACtxFromPWA(isl::manage(isl_pw_aff_alloc(Domain, Affine)));224  } else {225    PWAC = SCEVVisitor<SCEVAffinator, PWACtx>::visit(Expr);226    if (computeModuloForExpr(Expr))227      PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());228    else229      PWAC = checkForWrapping(Expr, PWAC);230  }231 232  if (!Factor->getType()->isIntegerTy(1)) {233    PWAC = combine(PWAC, visitConstant(Factor), isl_pw_aff_mul);234    if (computeModuloForExpr(Key.first))235      PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());236  }237 238  // For compile time reasons we need to simplify the PWAC before we cache and239  // return it.240  PWAC.first = PWAC.first.coalesce();241  if (!computeModuloForExpr(Key.first))242    PWAC = checkForWrapping(Key.first, PWAC);243 244  CachedExpressions[Key] = PWAC;245  return PWAC;246}247 248PWACtx SCEVAffinator::visitConstant(const SCEVConstant *Expr) {249  ConstantInt *Value = Expr->getValue();250  isl_val *v;251 252  // LLVM does not define if an integer value is interpreted as a signed or253  // unsigned value. Hence, without further information, it is unknown how254  // this value needs to be converted to GMP. At the moment, we only support255  // signed operations. So we just interpret it as signed. Later, there are256  // two options:257  //258  // 1. We always interpret any value as signed and convert the values on259  //    demand.260  // 2. We pass down the signedness of the calculation and use it to interpret261  //    this constant correctly.262  v = isl_valFromAPInt(Ctx.get(), Value->getValue(), /* isSigned */ true);263 264  isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);265  isl_local_space *ls = isl_local_space_from_space(Space);266  return getPWACtxFromPWA(267      isl::manage(isl_pw_aff_from_aff(isl_aff_val_on_domain(ls, v))));268}269 270PWACtx SCEVAffinator::visitVScale(const SCEVVScale *VScale) {271  llvm_unreachable("SCEVVScale not yet supported");272}273 274PWACtx SCEVAffinator::visitPtrToIntExpr(const SCEVPtrToIntExpr *Expr) {275  return visit(Expr->getOperand(0));276}277 278PWACtx SCEVAffinator::visitTruncateExpr(const SCEVTruncateExpr *Expr) {279  // Truncate operations are basically modulo operations, thus we can280  // model them that way. However, for large types we assume the operand281  // to fit in the new type size instead of introducing a modulo with a very282  // large constant.283 284  const SCEV *Op = Expr->getOperand();285  auto OpPWAC = visit(Op);286 287  unsigned Width = TD.getTypeSizeInBits(Expr->getType());288 289  if (computeModuloForExpr(Expr))290    return OpPWAC;291 292  auto *Dom = OpPWAC.first.domain().release();293  auto *ExpPWA = getWidthExpValOnDomain(Width - 1, Dom);294  auto *GreaterDom =295      isl_pw_aff_ge_set(OpPWAC.first.copy(), isl_pw_aff_copy(ExpPWA));296  auto *SmallerDom =297      isl_pw_aff_lt_set(OpPWAC.first.copy(), isl_pw_aff_neg(ExpPWA));298  auto *OutOfBoundsDom = isl_set_union(SmallerDom, GreaterDom);299  OpPWAC.second = OpPWAC.second.unite(isl::manage_copy(OutOfBoundsDom));300 301  if (!BB) {302    assert(isl_set_dim(OutOfBoundsDom, isl_dim_set) == 0 &&303           "Expected a zero dimensional set for non-basic-block domains");304    OutOfBoundsDom = isl_set_params(OutOfBoundsDom);305  }306 307  recordAssumption(RecordedAssumptions, UNSIGNED, isl::manage(OutOfBoundsDom),308                   DebugLoc(), AS_RESTRICTION, BB);309 310  return OpPWAC;311}312 313PWACtx SCEVAffinator::visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {314  // A zero-extended value can be interpreted as a piecewise defined signed315  // value. If the value was non-negative it stays the same, otherwise it316  // is the sum of the original value and 2^n where n is the bit-width of317  // the original (or operand) type. Examples:318  //   zext i8 127 to i32 -> { [127] }319  //   zext i8  -1 to i32 -> { [256 + (-1)] } = { [255] }320  //   zext i8  %v to i32 -> [v] -> { [v] | v >= 0; [256 + v] | v < 0 }321  //322  // However, LLVM/Scalar Evolution uses zero-extend (potentially lead by a323  // truncate) to represent some forms of modulo computation. The left-hand side324  // of the condition in the code below would result in the SCEV325  // "zext i1 <false, +, true>for.body" which is just another description326  // of the C expression "i & 1 != 0" or, equivalently, "i % 2 != 0".327  //328  //   for (i = 0; i < N; i++)329  //     if (i & 1 != 0 /* == i % 2 */)330  //       /* do something */331  //332  // If we do not make the modulo explicit but only use the mechanism described333  // above we will get the very restrictive assumption "N < 3", because for all334  // values of N >= 3 the SCEVAddRecExpr operand of the zero-extend would wrap.335  // Alternatively, we can make the modulo in the operand explicit in the336  // resulting piecewise function and thereby avoid the assumption on N. For the337  // example this would result in the following piecewise affine function:338  // { [i0] -> [(1)] : 2*floor((-1 + i0)/2) = -1 + i0;339  //   [i0] -> [(0)] : 2*floor((i0)/2) = i0 }340  // To this end we can first determine if the (immediate) operand of the341  // zero-extend can wrap and, in case it might, we will use explicit modulo342  // semantic to compute the result instead of emitting non-wrapping343  // assumptions.344  //345  // Note that operands with large bit-widths are less likely to be negative346  // because it would result in a very large access offset or loop bound after347  // the zero-extend. To this end one can optimistically assume the operand to348  // be positive and avoid the piecewise definition if the bit-width is bigger349  // than some threshold (here MaxZextSmallBitWidth).350  //351  // We choose to go with a hybrid solution of all modeling techniques described352  // above. For small bit-widths (up to MaxZextSmallBitWidth) we will model the353  // wrapping explicitly and use a piecewise defined function. However, if the354  // bit-width is bigger than MaxZextSmallBitWidth we will employ overflow355  // assumptions and assume the "former negative" piece will not exist.356 357  const SCEV *Op = Expr->getOperand();358  auto OpPWAC = visit(Op);359 360  // If the width is to big we assume the negative part does not occur.361  if (!computeModuloForExpr(Op)) {362    takeNonNegativeAssumption(OpPWAC, RecordedAssumptions);363    return OpPWAC;364  }365 366  // If the width is small build the piece for the non-negative part and367  // the one for the negative part and unify them.368  unsigned Width = TD.getTypeSizeInBits(Op->getType());369  interpretAsUnsigned(OpPWAC, Width);370  return OpPWAC;371}372 373PWACtx SCEVAffinator::visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {374  // As all values are represented as signed, a sign extension is a noop.375  return visit(Expr->getOperand());376}377 378PWACtx SCEVAffinator::visitAddExpr(const SCEVAddExpr *Expr) {379  PWACtx Sum = visit(Expr->getOperand(0));380 381  for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {382    Sum = combine(Sum, visit(Expr->getOperand(i)), isl_pw_aff_add);383    if (isTooComplex(Sum))384      return complexityBailout();385  }386 387  return Sum;388}389 390PWACtx SCEVAffinator::visitMulExpr(const SCEVMulExpr *Expr) {391  PWACtx Prod = visit(Expr->getOperand(0));392 393  for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {394    Prod = combine(Prod, visit(Expr->getOperand(i)), isl_pw_aff_mul);395    if (isTooComplex(Prod))396      return complexityBailout();397  }398 399  return Prod;400}401 402PWACtx SCEVAffinator::visitAddRecExpr(const SCEVAddRecExpr *Expr) {403  assert(Expr->isAffine() && "Only affine AddRecurrences allowed");404 405  auto Flags = Expr->getNoWrapFlags();406 407  // Directly generate isl_pw_aff for Expr if 'start' is zero.408  if (Expr->getStart()->isZero()) {409    assert(S->contains(Expr->getLoop()) &&410           "Scop does not contain the loop referenced in this AddRec");411 412    PWACtx Step = visit(Expr->getOperand(1));413    isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);414    isl_local_space *LocalSpace = isl_local_space_from_space(Space);415 416    unsigned loopDimension = S->getRelativeLoopDepth(Expr->getLoop());417 418    isl_aff *LAff = isl_aff_set_coefficient_si(419        isl_aff_zero_on_domain(LocalSpace), isl_dim_in, loopDimension, 1);420    isl_pw_aff *LPwAff = isl_pw_aff_from_aff(LAff);421 422    Step.first = Step.first.mul(isl::manage(LPwAff));423    return Step;424  }425 426  // Translate AddRecExpr from '{start, +, inc}' into 'start + {0, +, inc}'427  // if 'start' is not zero.428  // TODO: Using the original SCEV no-wrap flags is not always safe, however429  //       as our code generation is reordering the expression anyway it doesn't430  //       really matter.431  const SCEV *ZeroStartExpr =432      SE.getAddRecExpr(SE.getConstant(Expr->getStart()->getType(), 0),433                       Expr->getStepRecurrence(SE), Expr->getLoop(), Flags);434 435  PWACtx Result = visit(ZeroStartExpr);436  PWACtx Start = visit(Expr->getStart());437  Result = combine(Result, Start, isl_pw_aff_add);438  return Result;439}440 441PWACtx SCEVAffinator::visitSMaxExpr(const SCEVSMaxExpr *Expr) {442  PWACtx Max = visit(Expr->getOperand(0));443 444  for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {445    Max = combine(Max, visit(Expr->getOperand(i)), isl_pw_aff_max);446    if (isTooComplex(Max))447      return complexityBailout();448  }449 450  return Max;451}452 453PWACtx SCEVAffinator::visitSMinExpr(const SCEVSMinExpr *Expr) {454  PWACtx Min = visit(Expr->getOperand(0));455 456  for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {457    Min = combine(Min, visit(Expr->getOperand(i)), isl_pw_aff_min);458    if (isTooComplex(Min))459      return complexityBailout();460  }461 462  return Min;463}464 465PWACtx SCEVAffinator::visitUMaxExpr(const SCEVUMaxExpr *Expr) {466  llvm_unreachable("SCEVUMaxExpr not yet supported");467}468 469PWACtx SCEVAffinator::visitUMinExpr(const SCEVUMinExpr *Expr) {470  llvm_unreachable("SCEVUMinExpr not yet supported");471}472 473PWACtx474SCEVAffinator::visitSequentialUMinExpr(const SCEVSequentialUMinExpr *Expr) {475  llvm_unreachable("SCEVSequentialUMinExpr not yet supported");476}477 478PWACtx SCEVAffinator::visitUDivExpr(const SCEVUDivExpr *Expr) {479  // The handling of unsigned division is basically the same as for signed480  // division, except the interpretation of the operands. As the divisor481  // has to be constant in both cases we can simply interpret it as an482  // unsigned value without additional complexity in the representation.483  // For the dividend we could choose from the different representation484  // schemes introduced for zero-extend operations but for now we will485  // simply use an assumption.486  const SCEV *Dividend = Expr->getLHS();487  const SCEV *Divisor = Expr->getRHS();488  assert(isa<SCEVConstant>(Divisor) &&489         "UDiv is no parameter but has a non-constant RHS.");490 491  auto DividendPWAC = visit(Dividend);492  auto DivisorPWAC = visit(Divisor);493 494  if (SE.isKnownNegative(Divisor)) {495    // Interpret negative divisors unsigned. This is a special case of the496    // piece-wise defined value described for zero-extends as we already know497    // the actual value of the constant divisor.498    unsigned Width = TD.getTypeSizeInBits(Expr->getType());499    auto *DivisorDom = DivisorPWAC.first.domain().release();500    auto *WidthExpPWA = getWidthExpValOnDomain(Width, DivisorDom);501    DivisorPWAC.first = DivisorPWAC.first.add(isl::manage(WidthExpPWA));502  }503 504  // TODO: One can represent the dividend as piece-wise function to be more505  //       precise but therefore a heuristic is needed.506 507  // Assume a non-negative dividend.508  takeNonNegativeAssumption(DividendPWAC, RecordedAssumptions);509 510  DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_div);511  DividendPWAC.first = DividendPWAC.first.floor();512 513  return DividendPWAC;514}515 516PWACtx SCEVAffinator::visitSDivInstruction(Instruction *SDiv) {517  assert(SDiv->getOpcode() == Instruction::SDiv && "Assumed SDiv instruction!");518 519  auto *Scope = getScope();520  auto *Divisor = SDiv->getOperand(1);521  const SCEV *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);522  auto DivisorPWAC = visit(DivisorSCEV);523  assert(isa<SCEVConstant>(DivisorSCEV) &&524         "SDiv is no parameter but has a non-constant RHS.");525 526  auto *Dividend = SDiv->getOperand(0);527  const SCEV *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);528  auto DividendPWAC = visit(DividendSCEV);529  DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_q);530  return DividendPWAC;531}532 533PWACtx SCEVAffinator::visitSRemInstruction(Instruction *SRem) {534  assert(SRem->getOpcode() == Instruction::SRem && "Assumed SRem instruction!");535 536  auto *Scope = getScope();537  auto *Divisor = SRem->getOperand(1);538  const SCEV *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);539  auto DivisorPWAC = visit(DivisorSCEV);540  assert(isa<ConstantInt>(Divisor) &&541         "SRem is no parameter but has a non-constant RHS.");542 543  auto *Dividend = SRem->getOperand(0);544  const SCEV *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);545  auto DividendPWAC = visit(DividendSCEV);546  DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_r);547  return DividendPWAC;548}549 550PWACtx SCEVAffinator::visitUnknown(const SCEVUnknown *Expr) {551  if (Instruction *I = dyn_cast<Instruction>(Expr->getValue())) {552    switch (I->getOpcode()) {553    case Instruction::IntToPtr:554      return visit(SE.getSCEVAtScope(I->getOperand(0), getScope()));555    case Instruction::SDiv:556      return visitSDivInstruction(I);557    case Instruction::SRem:558      return visitSRemInstruction(I);559    default:560      break; // Fall through.561    }562  }563 564  if (isa<ConstantPointerNull>(Expr->getValue())) {565    isl::val v{Ctx, 0};566    isl::space Space{Ctx, 0, NumIterators};567    isl::local_space ls{Space};568    return getPWACtxFromPWA(isl::aff(ls, v));569  }570 571  llvm_unreachable("Unknowns SCEV was neither a parameter, a constant nor a "572                   "valid instruction.");573}574 575PWACtx SCEVAffinator::complexityBailout() {576  // We hit the complexity limit for affine expressions; invalidate the scop577  // and return a constant zero.578  const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();579  S->invalidate(COMPLEXITY, Loc);580  return visit(SE.getZero(Type::getInt32Ty(S->getFunction().getContext())));581}582