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1//===------ ISLTools.cpp ----------------------------------------*- C++ -*-===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8//9// Tools, utilities, helpers and extensions useful in conjunction with the10// Integer Set Library (isl).11//12//===----------------------------------------------------------------------===//13 14#include "polly/Support/ISLTools.h"15#include "polly/Support/GICHelper.h"16#include "llvm/Support/raw_ostream.h"17#include <cassert>18#include <vector>19 20using namespace polly;21 22namespace {23/// Create a map that shifts one dimension by an offset.24///25/// Example:26/// makeShiftDimAff({ [i0, i1] -> [o0, o1] }, 1, -2)27///   = { [i0, i1] -> [i0, i1 - 1] }28///29/// @param Space  The map space of the result. Must have equal number of in- and30///               out-dimensions.31/// @param Pos    Position to shift.32/// @param Amount Value added to the shifted dimension.33///34/// @return An isl_multi_aff for the map with this shifted dimension.35isl::multi_aff makeShiftDimAff(isl::space Space, int Pos, int Amount) {36  auto Identity = isl::multi_aff::identity(Space);37  if (Amount == 0)38    return Identity;39  auto ShiftAff = Identity.at(Pos);40  ShiftAff = ShiftAff.set_constant_si(Amount);41  return Identity.set_aff(Pos, ShiftAff);42}43 44/// Construct a map that swaps two nested tuples.45///46/// @param FromSpace1 { Space1[] }47/// @param FromSpace2 { Space2[] }48///49/// @return { [Space1[] -> Space2[]] -> [Space2[] -> Space1[]] }50isl::basic_map makeTupleSwapBasicMap(isl::space FromSpace1,51                                     isl::space FromSpace2) {52  // Fast-path on out-of-quota.53  if (FromSpace1.is_null() || FromSpace2.is_null())54    return {};55 56  assert(FromSpace1.is_set());57  assert(FromSpace2.is_set());58 59  unsigned Dims1 = unsignedFromIslSize(FromSpace1.dim(isl::dim::set));60  unsigned Dims2 = unsignedFromIslSize(FromSpace2.dim(isl::dim::set));61 62  isl::space FromSpace =63      FromSpace1.map_from_domain_and_range(FromSpace2).wrap();64  isl::space ToSpace = FromSpace2.map_from_domain_and_range(FromSpace1).wrap();65  isl::space MapSpace = FromSpace.map_from_domain_and_range(ToSpace);66 67  isl::basic_map Result = isl::basic_map::universe(MapSpace);68  for (unsigned i = 0u; i < Dims1; i += 1)69    Result = Result.equate(isl::dim::in, i, isl::dim::out, Dims2 + i);70  for (unsigned i = 0u; i < Dims2; i += 1) {71    Result = Result.equate(isl::dim::in, Dims1 + i, isl::dim::out, i);72  }73 74  return Result;75}76 77/// Like makeTupleSwapBasicMap(isl::space,isl::space), but returns78/// an isl_map.79isl::map makeTupleSwapMap(isl::space FromSpace1, isl::space FromSpace2) {80  isl::basic_map BMapResult = makeTupleSwapBasicMap(FromSpace1, FromSpace2);81  return isl::map(BMapResult);82}83} // anonymous namespace84 85isl::map polly::beforeScatter(isl::map Map, bool Strict) {86  isl::space RangeSpace = Map.get_space().range();87  isl::map ScatterRel =88      Strict ? isl::map::lex_gt(RangeSpace) : isl::map::lex_ge(RangeSpace);89  return Map.apply_range(ScatterRel);90}91 92isl::union_map polly::beforeScatter(isl::union_map UMap, bool Strict) {93  isl::union_map Result = isl::union_map::empty(UMap.ctx());94 95  for (isl::map Map : UMap.get_map_list()) {96    isl::map After = beforeScatter(Map, Strict);97    Result = Result.unite(After);98  }99 100  return Result;101}102 103isl::map polly::afterScatter(isl::map Map, bool Strict) {104  isl::space RangeSpace = Map.get_space().range();105  isl::map ScatterRel =106      Strict ? isl::map::lex_lt(RangeSpace) : isl::map::lex_le(RangeSpace);107  return Map.apply_range(ScatterRel);108}109 110isl::union_map polly::afterScatter(const isl::union_map &UMap, bool Strict) {111  isl::union_map Result = isl::union_map::empty(UMap.ctx());112  for (isl::map Map : UMap.get_map_list()) {113    isl::map After = afterScatter(Map, Strict);114    Result = Result.unite(After);115  }116  return Result;117}118 119isl::map polly::betweenScatter(isl::map From, isl::map To, bool InclFrom,120                               bool InclTo) {121  isl::map AfterFrom = afterScatter(From, !InclFrom);122  isl::map BeforeTo = beforeScatter(To, !InclTo);123 124  return AfterFrom.intersect(BeforeTo);125}126 127isl::union_map polly::betweenScatter(isl::union_map From, isl::union_map To,128                                     bool InclFrom, bool InclTo) {129  isl::union_map AfterFrom = afterScatter(From, !InclFrom);130  isl::union_map BeforeTo = beforeScatter(To, !InclTo);131 132  return AfterFrom.intersect(BeforeTo);133}134 135isl::map polly::singleton(isl::union_map UMap, isl::space ExpectedSpace) {136  if (UMap.is_null())137    return {};138 139  if (isl_union_map_n_map(UMap.get()) == 0)140    return isl::map::empty(ExpectedSpace);141 142  isl::map Result = isl::map::from_union_map(UMap);143  assert(Result.is_null() ||144         Result.get_space().has_equal_tuples(ExpectedSpace));145 146  return Result;147}148 149isl::set polly::singleton(isl::union_set USet, isl::space ExpectedSpace) {150  if (USet.is_null())151    return {};152 153  if (isl_union_set_n_set(USet.get()) == 0)154    return isl::set::empty(ExpectedSpace);155 156  isl::set Result(USet);157  assert(Result.is_null() ||158         Result.get_space().has_equal_tuples(ExpectedSpace));159 160  return Result;161}162 163unsigned polly::getNumScatterDims(const isl::union_map &Schedule) {164  unsigned Dims = 0;165  for (isl::map Map : Schedule.get_map_list()) {166    if (Map.is_null())167      continue;168 169    Dims = std::max(Dims, unsignedFromIslSize(Map.range_tuple_dim()));170  }171  return Dims;172}173 174isl::space polly::getScatterSpace(const isl::union_map &Schedule) {175  if (Schedule.is_null())176    return {};177  unsigned Dims = getNumScatterDims(Schedule);178  isl::space ScatterSpace = Schedule.get_space().set_from_params();179  return ScatterSpace.add_dims(isl::dim::set, Dims);180}181 182isl::map polly::makeIdentityMap(const isl::set &Set, bool RestrictDomain) {183  isl::map Result = isl::map::identity(Set.get_space().map_from_set());184  if (RestrictDomain)185    Result = Result.intersect_domain(Set);186  return Result;187}188 189isl::union_map polly::makeIdentityMap(const isl::union_set &USet,190                                      bool RestrictDomain) {191  isl::union_map Result = isl::union_map::empty(USet.ctx());192  for (isl::set Set : USet.get_set_list()) {193    isl::map IdentityMap = makeIdentityMap(Set, RestrictDomain);194    Result = Result.unite(IdentityMap);195  }196  return Result;197}198 199isl::map polly::reverseDomain(isl::map Map) {200  isl::space DomSpace = Map.get_space().domain().unwrap();201  isl::space Space1 = DomSpace.domain();202  isl::space Space2 = DomSpace.range();203  isl::map Swap = makeTupleSwapMap(Space1, Space2);204  return Map.apply_domain(Swap);205}206 207isl::union_map polly::reverseDomain(const isl::union_map &UMap) {208  isl::union_map Result = isl::union_map::empty(UMap.ctx());209  for (isl::map Map : UMap.get_map_list()) {210    auto Reversed = reverseDomain(std::move(Map));211    Result = Result.unite(Reversed);212  }213  return Result;214}215 216isl::set polly::shiftDim(isl::set Set, int Pos, int Amount) {217  unsigned NumDims = unsignedFromIslSize(Set.tuple_dim());218  if (Pos < 0)219    Pos = NumDims + Pos;220  assert(unsigned(Pos) < NumDims && "Dimension index must be in range");221  isl::space Space = Set.get_space();222  Space = Space.map_from_domain_and_range(Space);223  isl::multi_aff Translator = makeShiftDimAff(Space, Pos, Amount);224  isl::map TranslatorMap = isl::map::from_multi_aff(Translator);225  return Set.apply(TranslatorMap);226}227 228isl::union_set polly::shiftDim(isl::union_set USet, int Pos, int Amount) {229  isl::union_set Result = isl::union_set::empty(USet.ctx());230  for (isl::set Set : USet.get_set_list()) {231    isl::set Shifted = shiftDim(Set, Pos, Amount);232    Result = Result.unite(Shifted);233  }234  return Result;235}236 237isl::map polly::shiftDim(isl::map Map, isl::dim Dim, int Pos, int Amount) {238  unsigned NumDims = unsignedFromIslSize(Map.dim(Dim));239  if (Pos < 0)240    Pos = NumDims + Pos;241  assert(unsigned(Pos) < NumDims && "Dimension index must be in range");242  isl::space Space = Map.get_space();243  switch (Dim) {244  case isl::dim::in:245    Space = Space.domain();246    break;247  case isl::dim::out:248    Space = Space.range();249    break;250  default:251    llvm_unreachable("Unsupported value for 'dim'");252  }253  Space = Space.map_from_domain_and_range(Space);254  isl::multi_aff Translator = makeShiftDimAff(Space, Pos, Amount);255  isl::map TranslatorMap = isl::map::from_multi_aff(Translator);256  switch (Dim) {257  case isl::dim::in:258    return Map.apply_domain(TranslatorMap);259  case isl::dim::out:260    return Map.apply_range(TranslatorMap);261  default:262    llvm_unreachable("Unsupported value for 'dim'");263  }264}265 266isl::val polly::getConstant(isl::map Map, isl::dim Dim, int Pos) {267  unsigned NumDims = unsignedFromIslSize(Map.dim(Dim));268  if (Pos < 0)269    Pos = NumDims + Pos;270  assert(unsigned(Pos) < NumDims && "Dimension index must be in range");271  // TODO: The isl_map_plain_get_val_if_fixed function is not robust, since its272  // result is different depending on the internal representation.273  // Replace it with a different implementation.274  return isl::manage(isl_map_plain_get_val_if_fixed(275      Map.get(), static_cast<enum isl_dim_type>(Dim), Pos));276}277 278isl::union_map polly::shiftDim(isl::union_map UMap, isl::dim Dim, int Pos,279                               int Amount) {280  isl::union_map Result = isl::union_map::empty(UMap.ctx());281 282  for (isl::map Map : UMap.get_map_list()) {283    isl::map Shifted = shiftDim(Map, Dim, Pos, Amount);284    Result = Result.unite(Shifted);285  }286  return Result;287}288 289void polly::simplify(isl::set &Set) {290  Set = isl::manage(isl_set_compute_divs(Set.copy()));291  Set = Set.detect_equalities();292  Set = Set.coalesce();293}294 295void polly::simplify(isl::union_set &USet) {296  USet = isl::manage(isl_union_set_compute_divs(USet.copy()));297  USet = USet.detect_equalities();298  USet = USet.coalesce();299}300 301void polly::simplify(isl::map &Map) {302  Map = isl::manage(isl_map_compute_divs(Map.copy()));303  Map = Map.detect_equalities();304  Map = Map.coalesce();305}306 307void polly::simplify(isl::union_map &UMap) {308  UMap = isl::manage(isl_union_map_compute_divs(UMap.copy()));309  UMap = UMap.detect_equalities();310  UMap = UMap.coalesce();311}312 313isl::union_map polly::computeReachingWrite(isl::union_map Schedule,314                                           isl::union_map Writes, bool Reverse,315                                           bool InclPrevDef, bool InclNextDef) {316 317  // { Scatter[] }318  isl::space ScatterSpace = getScatterSpace(Schedule);319 320  // { ScatterRead[] -> ScatterWrite[] }321  isl::map Relation;322  if (Reverse)323    Relation = InclPrevDef ? isl::map::lex_lt(ScatterSpace)324                           : isl::map::lex_le(ScatterSpace);325  else326    Relation = InclNextDef ? isl::map::lex_gt(ScatterSpace)327                           : isl::map::lex_ge(ScatterSpace);328 329  // { ScatterWrite[] -> [ScatterRead[] -> ScatterWrite[]] }330  isl::map RelationMap = Relation.range_map().reverse();331 332  // { Element[] -> ScatterWrite[] }333  isl::union_map WriteAction = Schedule.apply_domain(Writes);334 335  // { ScatterWrite[] -> Element[] }336  isl::union_map WriteActionRev = WriteAction.reverse();337 338  // { Element[] -> [ScatterUse[] -> ScatterWrite[]] }339  isl::union_map DefSchedRelation =340      isl::union_map(RelationMap).apply_domain(WriteActionRev);341 342  // For each element, at every point in time, map to the times of previous343  // definitions. { [Element[] -> ScatterRead[]] -> ScatterWrite[] }344  isl::union_map ReachableWrites = DefSchedRelation.uncurry();345  if (Reverse)346    ReachableWrites = ReachableWrites.lexmin();347  else348    ReachableWrites = ReachableWrites.lexmax();349 350  // { [Element[] -> ScatterWrite[]] -> ScatterWrite[] }351  isl::union_map SelfUse = WriteAction.range_map();352 353  if (InclPrevDef && InclNextDef) {354    // Add the Def itself to the solution.355    ReachableWrites = ReachableWrites.unite(SelfUse).coalesce();356  } else if (!InclPrevDef && !InclNextDef) {357    // Remove Def itself from the solution.358    ReachableWrites = ReachableWrites.subtract(SelfUse);359  }360 361  // { [Element[] -> ScatterRead[]] -> Domain[] }362  return ReachableWrites.apply_range(Schedule.reverse());363}364 365isl::union_map366polly::computeArrayUnused(isl::union_map Schedule, isl::union_map Writes,367                          isl::union_map Reads, bool ReadEltInSameInst,368                          bool IncludeLastRead, bool IncludeWrite) {369  // { Element[] -> Scatter[] }370  isl::union_map ReadActions = Schedule.apply_domain(Reads);371  isl::union_map WriteActions = Schedule.apply_domain(Writes);372 373  // { [Element[] -> DomainWrite[]] -> Scatter[] }374  isl::union_map EltDomWrites =375      Writes.reverse().range_map().apply_range(Schedule);376 377  // { [Element[] -> Scatter[]] -> DomainWrite[] }378  isl::union_map ReachingOverwrite = computeReachingWrite(379      Schedule, Writes, true, ReadEltInSameInst, !ReadEltInSameInst);380 381  // { [Element[] -> Scatter[]] -> DomainWrite[] }382  isl::union_map ReadsOverwritten =383      ReachingOverwrite.intersect_domain(ReadActions.wrap());384 385  // { [Element[] -> DomainWrite[]] -> Scatter[] }386  isl::union_map ReadsOverwrittenRotated =387      reverseDomain(ReadsOverwritten).curry().reverse();388  isl::union_map LastOverwrittenRead = ReadsOverwrittenRotated.lexmax();389 390  // { [Element[] -> DomainWrite[]] -> Scatter[] }391  isl::union_map BetweenLastReadOverwrite = betweenScatter(392      LastOverwrittenRead, EltDomWrites, IncludeLastRead, IncludeWrite);393 394  // { [Element[] -> Scatter[]] -> DomainWrite[] }395  isl::union_map ReachingOverwriteZone = computeReachingWrite(396      Schedule, Writes, true, IncludeLastRead, IncludeWrite);397 398  // { [Element[] -> DomainWrite[]] -> Scatter[] }399  isl::union_map ReachingOverwriteRotated =400      reverseDomain(ReachingOverwriteZone).curry().reverse();401 402  // { [Element[] -> DomainWrite[]] -> Scatter[] }403  isl::union_map WritesWithoutReads = ReachingOverwriteRotated.subtract_domain(404      ReadsOverwrittenRotated.domain());405 406  return BetweenLastReadOverwrite.unite(WritesWithoutReads)407      .domain_factor_domain();408}409 410isl::union_set polly::convertZoneToTimepoints(isl::union_set Zone,411                                              bool InclStart, bool InclEnd) {412  if (!InclStart && InclEnd)413    return Zone;414 415  auto ShiftedZone = shiftDim(Zone, -1, -1);416  if (InclStart && !InclEnd)417    return ShiftedZone;418  else if (!InclStart && !InclEnd)419    return Zone.intersect(ShiftedZone);420 421  assert(InclStart && InclEnd);422  return Zone.unite(ShiftedZone);423}424 425isl::union_map polly::convertZoneToTimepoints(isl::union_map Zone, isl::dim Dim,426                                              bool InclStart, bool InclEnd) {427  if (!InclStart && InclEnd)428    return Zone;429 430  auto ShiftedZone = shiftDim(Zone, Dim, -1, -1);431  if (InclStart && !InclEnd)432    return ShiftedZone;433  else if (!InclStart && !InclEnd)434    return Zone.intersect(ShiftedZone);435 436  assert(InclStart && InclEnd);437  return Zone.unite(ShiftedZone);438}439 440isl::map polly::convertZoneToTimepoints(isl::map Zone, isl::dim Dim,441                                        bool InclStart, bool InclEnd) {442  if (!InclStart && InclEnd)443    return Zone;444 445  auto ShiftedZone = shiftDim(Zone, Dim, -1, -1);446  if (InclStart && !InclEnd)447    return ShiftedZone;448  else if (!InclStart && !InclEnd)449    return Zone.intersect(ShiftedZone);450 451  assert(InclStart && InclEnd);452  return Zone.unite(ShiftedZone);453}454 455isl::map polly::distributeDomain(isl::map Map) {456  // Note that we cannot take Map apart into { Domain[] -> Range1[] } and {457  // Domain[] -> Range2[] } and combine again. We would loose any relation458  // between Range1[] and Range2[] that is not also a constraint to Domain[].459 460  isl::space Space = Map.get_space();461  isl::space DomainSpace = Space.domain();462  if (DomainSpace.is_null())463    return {};464  unsigned DomainDims = unsignedFromIslSize(DomainSpace.dim(isl::dim::set));465  isl::space RangeSpace = Space.range().unwrap();466  isl::space Range1Space = RangeSpace.domain();467  if (Range1Space.is_null())468    return {};469  unsigned Range1Dims = unsignedFromIslSize(Range1Space.dim(isl::dim::set));470  isl::space Range2Space = RangeSpace.range();471  if (Range2Space.is_null())472    return {};473  unsigned Range2Dims = unsignedFromIslSize(Range2Space.dim(isl::dim::set));474 475  isl::space OutputSpace =476      DomainSpace.map_from_domain_and_range(Range1Space)477          .wrap()478          .map_from_domain_and_range(479              DomainSpace.map_from_domain_and_range(Range2Space).wrap());480 481  isl::basic_map Translator = isl::basic_map::universe(482      Space.wrap().map_from_domain_and_range(OutputSpace.wrap()));483 484  for (unsigned i = 0; i < DomainDims; i += 1) {485    Translator = Translator.equate(isl::dim::in, i, isl::dim::out, i);486    Translator = Translator.equate(isl::dim::in, i, isl::dim::out,487                                   DomainDims + Range1Dims + i);488  }489  for (unsigned i = 0; i < Range1Dims; i += 1)490    Translator = Translator.equate(isl::dim::in, DomainDims + i, isl::dim::out,491                                   DomainDims + i);492  for (unsigned i = 0; i < Range2Dims; i += 1)493    Translator = Translator.equate(isl::dim::in, DomainDims + Range1Dims + i,494                                   isl::dim::out,495                                   DomainDims + Range1Dims + DomainDims + i);496 497  return Map.wrap().apply(Translator).unwrap();498}499 500isl::union_map polly::distributeDomain(isl::union_map UMap) {501  isl::union_map Result = isl::union_map::empty(UMap.ctx());502  for (isl::map Map : UMap.get_map_list()) {503    auto Distributed = distributeDomain(Map);504    Result = Result.unite(Distributed);505  }506  return Result;507}508 509isl::union_map polly::liftDomains(isl::union_map UMap, isl::union_set Factor) {510 511  // { Factor[] -> Factor[] }512  isl::union_map Factors = makeIdentityMap(Factor, true);513 514  return Factors.product(UMap);515}516 517isl::union_map polly::applyDomainRange(isl::union_map UMap,518                                       isl::union_map Func) {519  // This implementation creates unnecessary cross products of the520  // DomainDomain[] and Func. An alternative implementation could reverse521  // domain+uncurry,apply Func to what now is the domain, then undo the522  // preparing transformation. Another alternative implementation could create a523  // translator map for each piece.524 525  // { DomainDomain[] }526  isl::union_set DomainDomain = UMap.domain().unwrap().domain();527 528  // { [DomainDomain[] -> DomainRange[]] -> [DomainDomain[] -> NewDomainRange[]]529  // }530  isl::union_map LifetedFunc = liftDomains(std::move(Func), DomainDomain);531 532  return UMap.apply_domain(LifetedFunc);533}534 535isl::map polly::intersectRange(isl::map Map, isl::union_set Range) {536  isl::set RangeSet = Range.extract_set(Map.get_space().range());537  return Map.intersect_range(RangeSet);538}539 540isl::map polly::subtractParams(isl::map Map, isl::set Params) {541  auto MapSpace = Map.get_space();542  auto ParamsMap = isl::map::universe(MapSpace).intersect_params(Params);543  return Map.subtract(ParamsMap);544}545 546isl::set polly::subtractParams(isl::set Set, isl::set Params) {547  isl::space SetSpace = Set.get_space();548  isl::set ParamsSet = isl::set::universe(SetSpace).intersect_params(Params);549  return Set.subtract(ParamsSet);550}551 552isl::val polly::getConstant(isl::pw_aff PwAff, bool Max, bool Min) {553  assert(!Max || !Min); // Cannot return min and max at the same time.554  isl::val Result;555  isl::stat Stat = PwAff.foreach_piece(556      [=, &Result](isl::set Set, isl::aff Aff) -> isl::stat {557        if (!Result.is_null() && Result.is_nan())558          return isl::stat::ok();559 560        // TODO: If Min/Max, we can also determine a minimum/maximum value if561        // Set is constant-bounded.562        if (!Aff.is_cst()) {563          Result = isl::val::nan(Aff.ctx());564          return isl::stat::error();565        }566 567        isl::val ThisVal = Aff.get_constant_val();568        if (Result.is_null()) {569          Result = ThisVal;570          return isl::stat::ok();571        }572 573        if (Result.eq(ThisVal))574          return isl::stat::ok();575 576        if (Max && ThisVal.gt(Result)) {577          Result = ThisVal;578          return isl::stat::ok();579        }580 581        if (Min && ThisVal.lt(Result)) {582          Result = ThisVal;583          return isl::stat::ok();584        }585 586        // Not compatible587        Result = isl::val::nan(Aff.ctx());588        return isl::stat::error();589      });590 591  if (Stat.is_error())592    return {};593 594  return Result;595}596 597llvm::iota_range<unsigned> polly::rangeIslSize(unsigned Begin, isl::size End) {598  unsigned UEnd = unsignedFromIslSize(End);599  return llvm::seq<unsigned>(std::min(Begin, UEnd), UEnd);600}601 602#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)603static void foreachPoint(const isl::set &Set,604                         const std::function<void(isl::point P)> &F) {605  Set.foreach_point([&](isl::point P) -> isl::stat {606    F(P);607    return isl::stat::ok();608  });609}610 611static void foreachPoint(isl::basic_set BSet,612                         const std::function<void(isl::point P)> &F) {613  foreachPoint(isl::set(BSet), F);614}615 616/// Determine the sorting order of the sets @p A and @p B without considering617/// the space structure.618///619/// Ordering is based on the lower bounds of the set's dimensions. First620/// dimensions are considered first.621static int flatCompare(const isl::basic_set &A, const isl::basic_set &B) {622  // Quick bail-out on out-of-quota.623  if (A.is_null() || B.is_null())624    return 0;625 626  unsigned ALen = unsignedFromIslSize(A.dim(isl::dim::set));627  unsigned BLen = unsignedFromIslSize(B.dim(isl::dim::set));628  unsigned Len = std::min(ALen, BLen);629 630  for (unsigned i = 0; i < Len; i += 1) {631    isl::basic_set ADim =632        A.project_out(isl::dim::param, 0,633                      unsignedFromIslSize(A.dim(isl::dim::param)))634            .project_out(isl::dim::set, i + 1, ALen - i - 1)635            .project_out(isl::dim::set, 0, i);636    isl::basic_set BDim =637        B.project_out(isl::dim::param, 0,638                      unsignedFromIslSize(B.dim(isl::dim::param)))639            .project_out(isl::dim::set, i + 1, BLen - i - 1)640            .project_out(isl::dim::set, 0, i);641 642    isl::basic_set AHull = isl::set(ADim).convex_hull();643    isl::basic_set BHull = isl::set(BDim).convex_hull();644 645    bool ALowerBounded =646        bool(isl::set(AHull).dim_has_any_lower_bound(isl::dim::set, 0));647    bool BLowerBounded =648        bool(isl::set(BHull).dim_has_any_lower_bound(isl::dim::set, 0));649 650    int BoundedCompare = BLowerBounded - ALowerBounded;651    if (BoundedCompare != 0)652      return BoundedCompare;653 654    if (!ALowerBounded || !BLowerBounded)655      continue;656 657    isl::pw_aff AMin = isl::set(ADim).dim_min(0);658    isl::pw_aff BMin = isl::set(BDim).dim_min(0);659 660    isl::val AMinVal = polly::getConstant(AMin, false, true);661    isl::val BMinVal = polly::getConstant(BMin, false, true);662 663    int MinCompare = AMinVal.sub(BMinVal).sgn();664    if (MinCompare != 0)665      return MinCompare;666  }667 668  // If all the dimensions' lower bounds are equal or incomparable, sort based669  // on the number of dimensions.670  return ALen - BLen;671}672 673/// Compare the sets @p A and @p B according to their nested space structure.674/// Returns 0 if the structure is considered equal.675/// If @p ConsiderTupleLen is false, the number of dimensions in a tuple are676/// ignored, i.e. a tuple with the same name but different number of dimensions677/// are considered equal.678static int structureCompare(const isl::space &ASpace, const isl::space &BSpace,679                            bool ConsiderTupleLen) {680  int WrappingCompare = bool(ASpace.is_wrapping()) - bool(BSpace.is_wrapping());681  if (WrappingCompare != 0)682    return WrappingCompare;683 684  if (ASpace.is_wrapping() && BSpace.is_wrapping()) {685    isl::space AMap = ASpace.unwrap();686    isl::space BMap = BSpace.unwrap();687 688    int FirstResult =689        structureCompare(AMap.domain(), BMap.domain(), ConsiderTupleLen);690    if (FirstResult != 0)691      return FirstResult;692 693    return structureCompare(AMap.range(), BMap.range(), ConsiderTupleLen);694  }695 696  std::string AName;697  if (!ASpace.is_params() && ASpace.has_tuple_name(isl::dim::set))698    AName = ASpace.get_tuple_name(isl::dim::set);699 700  std::string BName;701  if (!BSpace.is_params() && BSpace.has_tuple_name(isl::dim::set))702    BName = BSpace.get_tuple_name(isl::dim::set);703 704  int NameCompare = AName.compare(BName);705  if (NameCompare != 0)706    return NameCompare;707 708  if (ConsiderTupleLen) {709    int LenCompare = (int)unsignedFromIslSize(BSpace.dim(isl::dim::set)) -710                     (int)unsignedFromIslSize(ASpace.dim(isl::dim::set));711    if (LenCompare != 0)712      return LenCompare;713  }714 715  return 0;716}717 718/// Compare the sets @p A and @p B according to their nested space structure. If719/// the structure is the same, sort using the dimension lower bounds.720/// Returns an std::sort compatible bool.721static bool orderComparer(const isl::basic_set &A, const isl::basic_set &B) {722  isl::space ASpace = A.get_space();723  isl::space BSpace = B.get_space();724 725  // Ignoring number of dimensions first ensures that structures with same tuple726  // names, but different number of dimensions are still sorted close together.727  int TupleNestingCompare = structureCompare(ASpace, BSpace, false);728  if (TupleNestingCompare != 0)729    return TupleNestingCompare < 0;730 731  int TupleCompare = structureCompare(ASpace, BSpace, true);732  if (TupleCompare != 0)733    return TupleCompare < 0;734 735  return flatCompare(A, B) < 0;736}737 738/// Print a string representation of @p USet to @p OS.739///740/// The pieces of @p USet are printed in a sorted order. Spaces with equal or741/// similar nesting structure are printed together. Compared to isl's own742/// printing function the uses the structure itself as base of the sorting, not743/// a hash of it. It ensures that e.g. maps spaces with same domain structure744/// are printed together. Set pieces with same structure are printed in order of745/// their lower bounds.746///747/// @param USet     Polyhedra to print.748/// @param OS       Target stream.749/// @param Simplify Whether to simplify the polyhedron before printing.750/// @param IsMap    Whether @p USet is a wrapped map. If true, sets are751///                 unwrapped before printing to again appear as a map.752static void printSortedPolyhedra(isl::union_set USet, llvm::raw_ostream &OS,753                                 bool Simplify, bool IsMap) {754  if (USet.is_null()) {755    OS << "<null>\n";756    return;757  }758 759  if (Simplify)760    simplify(USet);761 762  // Get all the polyhedra.763  std::vector<isl::basic_set> BSets;764 765  for (isl::set Set : USet.get_set_list()) {766    for (isl::basic_set BSet : Set.get_basic_set_list()) {767      BSets.push_back(BSet);768    }769  }770 771  if (BSets.empty()) {772    OS << "{\n}\n";773    return;774  }775 776  // Sort the polyhedra.777  llvm::sort(BSets, orderComparer);778 779  // Print the polyhedra.780  bool First = true;781  for (const isl::basic_set &BSet : BSets) {782    std::string Str;783    if (IsMap)784      Str = stringFromIslObj(isl::map(BSet.unwrap()));785    else786      Str = stringFromIslObj(isl::set(BSet));787    size_t OpenPos = Str.find_first_of('{');788    assert(OpenPos != std::string::npos);789    size_t ClosePos = Str.find_last_of('}');790    assert(ClosePos != std::string::npos);791 792    if (First)793      OS << llvm::StringRef(Str).substr(0, OpenPos + 1) << "\n ";794    else795      OS << ";\n ";796 797    OS << llvm::StringRef(Str).substr(OpenPos + 1, ClosePos - OpenPos - 2);798    First = false;799  }800  assert(!First);801  OS << "\n}\n";802}803 804static void recursiveExpand(isl::basic_set BSet, unsigned Dim,805                            isl::set &Expanded) {806  unsigned Dims = unsignedFromIslSize(BSet.dim(isl::dim::set));807  if (Dim >= Dims) {808    Expanded = Expanded.unite(BSet);809    return;810  }811 812  isl::basic_set DimOnly =813      BSet.project_out(isl::dim::param, 0,814                       unsignedFromIslSize(BSet.dim(isl::dim::param)))815          .project_out(isl::dim::set, Dim + 1, Dims - Dim - 1)816          .project_out(isl::dim::set, 0, Dim);817  if (!DimOnly.is_bounded()) {818    recursiveExpand(BSet, Dim + 1, Expanded);819    return;820  }821 822  foreachPoint(DimOnly, [&, Dim](isl::point P) {823    isl::val Val = P.get_coordinate_val(isl::dim::set, 0);824    isl::basic_set FixBSet = BSet.fix_val(isl::dim::set, Dim, Val);825    recursiveExpand(FixBSet, Dim + 1, Expanded);826  });827}828 829/// Make each point of a set explicit.830///831/// "Expanding" makes each point a set contains explicit. That is, the result is832/// a set of singleton polyhedra. Unbounded dimensions are not expanded.833///834/// Example:835///   { [i] : 0 <= i < 2 }836/// is expanded to:837///   { [0]; [1] }838static isl::set expand(const isl::set &Set) {839  isl::set Expanded = isl::set::empty(Set.get_space());840  for (isl::basic_set BSet : Set.get_basic_set_list())841    recursiveExpand(BSet, 0, Expanded);842  return Expanded;843}844 845/// Expand all points of a union set explicit.846///847/// @see expand(const isl::set)848static isl::union_set expand(const isl::union_set &USet) {849  isl::union_set Expanded = isl::union_set::empty(USet.ctx());850  for (isl::set Set : USet.get_set_list()) {851    isl::set SetExpanded = expand(Set);852    Expanded = Expanded.unite(SetExpanded);853  }854  return Expanded;855}856 857LLVM_DUMP_METHOD void polly::dumpPw(const isl::set &Set) {858  printSortedPolyhedra(Set, llvm::errs(), true, false);859}860 861LLVM_DUMP_METHOD void polly::dumpPw(const isl::map &Map) {862  printSortedPolyhedra(Map.wrap(), llvm::errs(), true, true);863}864 865LLVM_DUMP_METHOD void polly::dumpPw(const isl::union_set &USet) {866  printSortedPolyhedra(USet, llvm::errs(), true, false);867}868 869LLVM_DUMP_METHOD void polly::dumpPw(const isl::union_map &UMap) {870  printSortedPolyhedra(UMap.wrap(), llvm::errs(), true, true);871}872 873LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_set *Set) {874  dumpPw(isl::manage_copy(Set));875}876 877LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_map *Map) {878  dumpPw(isl::manage_copy(Map));879}880 881LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_union_set *USet) {882  dumpPw(isl::manage_copy(USet));883}884 885LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_union_map *UMap) {886  dumpPw(isl::manage_copy(UMap));887}888 889LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::set &Set) {890  printSortedPolyhedra(expand(Set), llvm::errs(), false, false);891}892 893LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::map &Map) {894  printSortedPolyhedra(expand(Map.wrap()), llvm::errs(), false, true);895}896 897LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::union_set &USet) {898  printSortedPolyhedra(expand(USet), llvm::errs(), false, false);899}900 901LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::union_map &UMap) {902  printSortedPolyhedra(expand(UMap.wrap()), llvm::errs(), false, true);903}904 905LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_set *Set) {906  dumpExpanded(isl::manage_copy(Set));907}908 909LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_map *Map) {910  dumpExpanded(isl::manage_copy(Map));911}912 913LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_union_set *USet) {914  dumpExpanded(isl::manage_copy(USet));915}916 917LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_union_map *UMap) {918  dumpExpanded(isl::manage_copy(UMap));919}920#endif921