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1//===- DependenceInfo.cpp - Calculate dependency information for a Scop. --===//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// Calculate the data dependency relations for a Scop using ISL.10//11// The integer set library (ISL) from Sven, has a integrated dependency analysis12// to calculate data dependences. This pass takes advantage of this and13// calculate those dependences a Scop.14//15// The dependences in this pass are exact in terms that for a specific read16// statement instance only the last write statement instance is returned. In17// case of may writes a set of possible write instances is returned. This18// analysis will never produce redundant dependences.19//20//===----------------------------------------------------------------------===//21//22#include "polly/DependenceInfo.h"23#include "polly/Options.h"24#include "polly/ScopInfo.h"25#include "polly/Support/GICHelper.h"26#include "polly/Support/ISLTools.h"27#include "llvm/ADT/Sequence.h"28#include "llvm/Support/Debug.h"29#include "isl/aff.h"30#include "isl/ctx.h"31#include "isl/flow.h"32#include "isl/map.h"33#include "isl/schedule.h"34#include "isl/set.h"35#include "isl/union_map.h"36#include "isl/union_set.h"37 38using namespace polly;39using namespace llvm;40 41#include "polly/Support/PollyDebug.h"42#define DEBUG_TYPE "polly-dependence"43 44namespace polly {45Dependences::AnalysisLevel OptAnalysisLevel;46}47 48static cl::opt<int> OptComputeOut(49    "polly-dependences-computeout",50    cl::desc("Bound the dependence analysis by a maximal amount of "51             "computational steps (0 means no bound)"),52    cl::Hidden, cl::init(500000), cl::cat(PollyCategory));53 54static cl::opt<bool>55    LegalityCheckDisabled("disable-polly-legality",56                          cl::desc("Disable polly legality check"), cl::Hidden,57                          cl::cat(PollyCategory));58 59static cl::opt<bool>60    UseReductions("polly-dependences-use-reductions",61                  cl::desc("Exploit reductions in dependence analysis"),62                  cl::Hidden, cl::init(true), cl::cat(PollyCategory));63 64enum AnalysisType { VALUE_BASED_ANALYSIS, MEMORY_BASED_ANALYSIS };65 66static cl::opt<enum AnalysisType> OptAnalysisType(67    "polly-dependences-analysis-type",68    cl::desc("The kind of dependence analysis to use"),69    cl::values(clEnumValN(VALUE_BASED_ANALYSIS, "value-based",70                          "Exact dependences without transitive dependences"),71               clEnumValN(MEMORY_BASED_ANALYSIS, "memory-based",72                          "Overapproximation of dependences")),73    cl::Hidden, cl::init(VALUE_BASED_ANALYSIS), cl::cat(PollyCategory));74 75static cl::opt<Dependences::AnalysisLevel, true> XOptAnalysisLevel(76    "polly-dependences-analysis-level",77    cl::desc("The level of dependence analysis"),78    cl::location(OptAnalysisLevel),79    cl::values(clEnumValN(Dependences::AL_Statement, "statement-wise",80                          "Statement-level analysis"),81               clEnumValN(Dependences::AL_Reference, "reference-wise",82                          "Memory reference level analysis that distinguish"83                          " accessed references in the same statement"),84               clEnumValN(Dependences::AL_Access, "access-wise",85                          "Memory reference level analysis that distinguish"86                          " access instructions in the same statement")),87    cl::Hidden, cl::init(Dependences::AL_Statement), cl::cat(PollyCategory));88 89//===----------------------------------------------------------------------===//90 91/// Tag the @p Relation domain with @p TagId92static __isl_give isl_map *tag(__isl_take isl_map *Relation,93                               __isl_take isl_id *TagId) {94  isl_space *Space = isl_map_get_space(Relation);95  Space = isl_space_drop_dims(Space, isl_dim_out, 0,96                              isl_map_dim(Relation, isl_dim_out));97  Space = isl_space_set_tuple_id(Space, isl_dim_out, TagId);98  isl_multi_aff *Tag = isl_multi_aff_domain_map(Space);99  Relation = isl_map_preimage_domain_multi_aff(Relation, Tag);100  return Relation;101}102 103/// Tag the @p Relation domain with either MA->getArrayId() or104///        MA->getId() based on @p TagLevel105static __isl_give isl_map *tag(__isl_take isl_map *Relation, MemoryAccess *MA,106                               Dependences::AnalysisLevel TagLevel) {107  if (TagLevel == Dependences::AL_Reference)108    return tag(Relation, MA->getArrayId().release());109 110  if (TagLevel == Dependences::AL_Access)111    return tag(Relation, MA->getId().release());112 113  // No need to tag at the statement level.114  return Relation;115}116 117/// Collect information about the SCoP @p S.118static void collectInfo(Scop &S, isl_union_map *&Read,119                        isl_union_map *&MustWrite, isl_union_map *&MayWrite,120                        isl_union_map *&ReductionTagMap,121                        isl_union_set *&TaggedStmtDomain,122                        Dependences::AnalysisLevel Level) {123  isl_space *Space = S.getParamSpace().release();124  Read = isl_union_map_empty(isl_space_copy(Space));125  MustWrite = isl_union_map_empty(isl_space_copy(Space));126  MayWrite = isl_union_map_empty(isl_space_copy(Space));127  ReductionTagMap = isl_union_map_empty(isl_space_copy(Space));128  isl_union_map *StmtSchedule = isl_union_map_empty(Space);129 130  SmallPtrSet<const ScopArrayInfo *, 8> ReductionArrays;131  if (UseReductions)132    for (ScopStmt &Stmt : S)133      for (MemoryAccess *MA : Stmt)134        if (MA->isReductionLike())135          ReductionArrays.insert(MA->getScopArrayInfo());136 137  for (ScopStmt &Stmt : S) {138    for (MemoryAccess *MA : Stmt) {139      isl_set *domcp = Stmt.getDomain().release();140      isl_map *accdom = MA->getAccessRelation().release();141 142      accdom = isl_map_intersect_domain(accdom, domcp);143 144      if (ReductionArrays.count(MA->getScopArrayInfo())) {145        // Wrap the access domain and adjust the schedule accordingly.146        //147        // An access domain like148        //   Stmt[i0, i1] -> MemAcc_A[i0 + i1]149        // will be transformed into150        //   [Stmt[i0, i1] -> MemAcc_A[i0 + i1]] -> MemAcc_A[i0 + i1]151        //152        // We collect all the access domains in the ReductionTagMap.153        // This is used in Dependences::calculateDependences to create154        // a tagged Schedule tree.155 156        ReductionTagMap =157            isl_union_map_add_map(ReductionTagMap, isl_map_copy(accdom));158        accdom = isl_map_range_map(accdom);159      } else {160        accdom = tag(accdom, MA, Level);161        if (Level > Dependences::AL_Statement) {162          isl_map *StmtScheduleMap = Stmt.getSchedule().release();163          assert(StmtScheduleMap &&164                 "Schedules that contain extension nodes require special "165                 "handling.");166          isl_map *Schedule = tag(StmtScheduleMap, MA, Level);167          StmtSchedule = isl_union_map_add_map(StmtSchedule, Schedule);168        }169      }170 171      if (MA->isRead())172        Read = isl_union_map_add_map(Read, accdom);173      else if (MA->isMayWrite())174        MayWrite = isl_union_map_add_map(MayWrite, accdom);175      else176        MustWrite = isl_union_map_add_map(MustWrite, accdom);177    }178 179    if (!ReductionArrays.empty() && Level == Dependences::AL_Statement)180      StmtSchedule =181          isl_union_map_add_map(StmtSchedule, Stmt.getSchedule().release());182  }183 184  StmtSchedule = isl_union_map_intersect_params(185      StmtSchedule, S.getAssumedContext().release());186  TaggedStmtDomain = isl_union_map_domain(StmtSchedule);187 188  ReductionTagMap = isl_union_map_coalesce(ReductionTagMap);189  Read = isl_union_map_coalesce(Read);190  MustWrite = isl_union_map_coalesce(MustWrite);191  MayWrite = isl_union_map_coalesce(MayWrite);192}193 194/// Fix all dimension of @p Zero to 0 and add it to @p user195static void fixSetToZero(isl::set Zero, isl::union_set *User) {196  for (auto i : rangeIslSize(0, Zero.tuple_dim()))197    Zero = Zero.fix_si(isl::dim::set, i, 0);198  *User = User->unite(Zero);199}200 201/// Compute the privatization dependences for a given dependency @p Map202///203/// Privatization dependences are widened original dependences which originate204/// or end in a reduction access. To compute them we apply the transitive close205/// of the reduction dependences (which maps each iteration of a reduction206/// statement to all following ones) on the RAW/WAR/WAW dependences. The207/// dependences which start or end at a reduction statement will be extended to208/// depend on all following reduction statement iterations as well.209/// Note: "Following" here means according to the reduction dependences.210///211/// For the input:212///213///  S0:   *sum = 0;214///        for (int i = 0; i < 1024; i++)215///  S1:     *sum += i;216///  S2:   *sum = *sum * 3;217///218/// we have the following dependences before we add privatization dependences:219///220///   RAW:221///     { S0[] -> S1[0]; S1[1023] -> S2[] }222///   WAR:223///     {  }224///   WAW:225///     { S0[] -> S1[0]; S1[1024] -> S2[] }226///   RED:227///     { S1[i0] -> S1[1 + i0] : i0 >= 0 and i0 <= 1022 }228///229/// and afterwards:230///231///   RAW:232///     { S0[] -> S1[i0] : i0 >= 0 and i0 <= 1023;233///       S1[i0] -> S2[] : i0 >= 0 and i0 <= 1023}234///   WAR:235///     {  }236///   WAW:237///     { S0[] -> S1[i0] : i0 >= 0 and i0 <= 1023;238///       S1[i0] -> S2[] : i0 >= 0 and i0 <= 1023}239///   RED:240///     { S1[i0] -> S1[1 + i0] : i0 >= 0 and i0 <= 1022 }241///242/// Note: This function also computes the (reverse) transitive closure of the243///       reduction dependences.244void Dependences::addPrivatizationDependences() {245  isl_union_map *PrivRAW, *PrivWAW, *PrivWAR;246 247  // The transitive closure might be over approximated, thus could lead to248  // dependency cycles in the privatization dependences. To make sure this249  // will not happen we remove all negative dependences after we computed250  // the transitive closure.251  TC_RED = isl_union_map_transitive_closure(isl_union_map_copy(RED), nullptr);252 253  // FIXME: Apply the current schedule instead of assuming the identity schedule254  //        here. The current approach is only valid as long as we compute the255  //        dependences only with the initial (identity schedule). Any other256  //        schedule could change "the direction of the backward dependences" we257  //        want to eliminate here.258  isl_union_set *UDeltas = isl_union_map_deltas(isl_union_map_copy(TC_RED));259  isl_union_set *Universe = isl_union_set_universe(isl_union_set_copy(UDeltas));260  isl::union_set Zero =261      isl::manage(isl_union_set_empty(isl_union_set_get_space(Universe)));262 263  for (isl::set Set : isl::manage_copy(Universe).get_set_list())264    fixSetToZero(Set, &Zero);265 266  isl_union_map *NonPositive =267      isl_union_set_lex_le_union_set(UDeltas, Zero.release());268 269  TC_RED = isl_union_map_subtract(TC_RED, NonPositive);270 271  TC_RED = isl_union_map_union(272      TC_RED, isl_union_map_reverse(isl_union_map_copy(TC_RED)));273  TC_RED = isl_union_map_coalesce(TC_RED);274 275  isl_union_map **Maps[] = {&RAW, &WAW, &WAR};276  isl_union_map **PrivMaps[] = {&PrivRAW, &PrivWAW, &PrivWAR};277  for (unsigned u = 0; u < 3; u++) {278    isl_union_map **Map = Maps[u], **PrivMap = PrivMaps[u];279 280    *PrivMap = isl_union_map_apply_range(isl_union_map_copy(*Map),281                                         isl_union_map_copy(TC_RED));282    *PrivMap = isl_union_map_union(283        *PrivMap, isl_union_map_apply_range(isl_union_map_copy(TC_RED),284                                            isl_union_map_copy(*Map)));285 286    *Map = isl_union_map_union(*Map, *PrivMap);287  }288 289  isl_union_set_free(Universe);290}291 292static __isl_give isl_union_flow *buildFlow(__isl_keep isl_union_map *Snk,293                                            __isl_keep isl_union_map *Src,294                                            __isl_keep isl_union_map *MaySrc,295                                            __isl_keep isl_union_map *Kill,296                                            __isl_keep isl_schedule *Schedule) {297  isl_union_access_info *AI;298 299  AI = isl_union_access_info_from_sink(isl_union_map_copy(Snk));300  if (MaySrc)301    AI = isl_union_access_info_set_may_source(AI, isl_union_map_copy(MaySrc));302  if (Src)303    AI = isl_union_access_info_set_must_source(AI, isl_union_map_copy(Src));304  if (Kill)305    AI = isl_union_access_info_set_kill(AI, isl_union_map_copy(Kill));306  AI = isl_union_access_info_set_schedule(AI, isl_schedule_copy(Schedule));307  auto Flow = isl_union_access_info_compute_flow(AI);308  POLLY_DEBUG(if (!Flow) dbgs()309                  << "last error: "310                  << isl_ctx_last_error(isl_schedule_get_ctx(Schedule))311                  << '\n';);312  return Flow;313}314 315void Dependences::calculateDependences(Scop &S) {316  isl_union_map *Read, *MustWrite, *MayWrite, *ReductionTagMap;317  isl_schedule *Schedule;318  isl_union_set *TaggedStmtDomain;319 320  POLLY_DEBUG(dbgs() << "Scop: \n" << S << "\n");321 322  collectInfo(S, Read, MustWrite, MayWrite, ReductionTagMap, TaggedStmtDomain,323              Level);324 325  bool HasReductions = !isl_union_map_is_empty(ReductionTagMap);326 327  POLLY_DEBUG(dbgs() << "Read: " << Read << '\n';328              dbgs() << "MustWrite: " << MustWrite << '\n';329              dbgs() << "MayWrite: " << MayWrite << '\n';330              dbgs() << "ReductionTagMap: " << ReductionTagMap << '\n';331              dbgs() << "TaggedStmtDomain: " << TaggedStmtDomain << '\n';);332 333  Schedule = S.getScheduleTree().release();334 335  if (!HasReductions) {336    isl_union_map_free(ReductionTagMap);337    // Tag the schedule tree if we want fine-grain dependence info338    if (Level > AL_Statement) {339      auto TaggedMap =340          isl_union_set_unwrap(isl_union_set_copy(TaggedStmtDomain));341      auto Tags = isl_union_map_domain_map_union_pw_multi_aff(TaggedMap);342      Schedule = isl_schedule_pullback_union_pw_multi_aff(Schedule, Tags);343    }344  } else {345    isl_union_map *IdentityMap;346    isl_union_pw_multi_aff *ReductionTags, *IdentityTags, *Tags;347 348    // Extract Reduction tags from the combined access domains in the given349    // SCoP. The result is a map that maps each tagged element in the domain to350    // the memory location it accesses. ReductionTags = {[Stmt[i] ->351    // Array[f(i)]] -> Stmt[i] }352    ReductionTags =353        isl_union_map_domain_map_union_pw_multi_aff(ReductionTagMap);354 355    // Compute an identity map from each statement in domain to itself.356    // IdentityTags = { [Stmt[i] -> Stmt[i] }357    IdentityMap = isl_union_set_identity(isl_union_set_copy(TaggedStmtDomain));358    IdentityTags = isl_union_pw_multi_aff_from_union_map(IdentityMap);359 360    Tags = isl_union_pw_multi_aff_union_add(ReductionTags, IdentityTags);361 362    // By pulling back Tags from Schedule, we have a schedule tree that can363    // be used to compute normal dependences, as well as 'tagged' reduction364    // dependences.365    Schedule = isl_schedule_pullback_union_pw_multi_aff(Schedule, Tags);366  }367 368  POLLY_DEBUG(dbgs() << "Read: " << Read << "\n";369              dbgs() << "MustWrite: " << MustWrite << "\n";370              dbgs() << "MayWrite: " << MayWrite << "\n";371              dbgs() << "Schedule: " << Schedule << "\n");372 373  isl_union_map *StrictWAW = nullptr;374  {375    IslMaxOperationsGuard MaxOpGuard(IslCtx.get(), OptComputeOut);376 377    RAW = WAW = WAR = RED = nullptr;378    isl_union_map *Write = isl_union_map_union(isl_union_map_copy(MustWrite),379                                               isl_union_map_copy(MayWrite));380 381    // We are interested in detecting reductions that do not have intermediate382    // computations that are captured by other statements.383    //384    // Example:385    // void f(int *A, int *B) {386    //     for(int i = 0; i <= 100; i++) {387    //388    //            *-WAR (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*389    //            |                                                   |390    //            *-WAW (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*391    //            |                                                   |392    //            v                                                   |393    //     S0:    *A += i; >------------------*-----------------------*394    //                                        |395    //         if (i >= 98) {          WAR (S0[i] -> S1[i]) 98 <= i <= 100396    //                                        |397    //     S1:        *B = *A; <--------------*398    //         }399    //     }400    // }401    //402    // S0[0 <= i <= 100] has a reduction. However, the values in403    // S0[98 <= i <= 100] is captured in S1[98 <= i <= 100].404    // Since we allow free reordering on our reduction dependences, we need to405    // remove all instances of a reduction statement that have data dependences406    // originating from them.407    // In the case of the example, we need to remove S0[98 <= i <= 100] from408    // our reduction dependences.409    //410    // When we build up the WAW dependences that are used to detect reductions,411    // we consider only **Writes that have no intermediate Reads**.412    //413    // `isl_union_flow_get_must_dependence` gives us dependences of the form:414    // (sink <- must_source).415    //416    // It *will not give* dependences of the form:417    // 1. (sink <- ... <- may_source <- ... <- must_source)418    // 2. (sink <- ... <- must_source <- ... <- must_source)419    //420    // For a detailed reference on ISL's flow analysis, see:421    // "Presburger Formulas and Polyhedral Compilation" - Approximate Dataflow422    //  Analysis.423    //424    // Since we set "Write" as a must-source, "Read" as a may-source, and ask425    // for must dependences, we get all Writes to Writes that **do not flow426    // through a Read**.427    //428    // ScopInfo::checkForReductions makes sure that if something captures429    // the reduction variable in the same basic block, then it is rejected430    // before it is even handed here. This makes sure that there is exactly431    // one read and one write to a reduction variable in a Statement.432    // Example:433    //     void f(int *sum, int A[N], int B[N]) {434    //       for (int i = 0; i < N; i++) {435    //         *sum += A[i]; < the store and the load is not tagged as a436    //         B[i] = *sum;  < reduction-like access due to the overlap.437    //       }438    //     }439 440    isl_union_flow *Flow = buildFlow(Write, Write, Read, nullptr, Schedule);441    StrictWAW = isl_union_flow_get_must_dependence(Flow);442    isl_union_flow_free(Flow);443 444    if (OptAnalysisType == VALUE_BASED_ANALYSIS) {445      Flow = buildFlow(Read, MustWrite, MayWrite, nullptr, Schedule);446      RAW = isl_union_flow_get_may_dependence(Flow);447      isl_union_flow_free(Flow);448 449      Flow = buildFlow(Write, MustWrite, MayWrite, nullptr, Schedule);450      WAW = isl_union_flow_get_may_dependence(Flow);451      isl_union_flow_free(Flow);452 453      // ISL now supports "kills" in approximate dataflow analysis, we can454      // specify the MustWrite as kills, Read as source and Write as sink.455      Flow = buildFlow(Write, nullptr, Read, MustWrite, Schedule);456      WAR = isl_union_flow_get_may_dependence(Flow);457      isl_union_flow_free(Flow);458    } else {459      Flow = buildFlow(Read, nullptr, Write, nullptr, Schedule);460      RAW = isl_union_flow_get_may_dependence(Flow);461      isl_union_flow_free(Flow);462 463      Flow = buildFlow(Write, nullptr, Read, nullptr, Schedule);464      WAR = isl_union_flow_get_may_dependence(Flow);465      isl_union_flow_free(Flow);466 467      Flow = buildFlow(Write, nullptr, Write, nullptr, Schedule);468      WAW = isl_union_flow_get_may_dependence(Flow);469      isl_union_flow_free(Flow);470    }471 472    isl_union_map_free(Write);473    isl_union_map_free(MustWrite);474    isl_union_map_free(MayWrite);475    isl_union_map_free(Read);476    isl_schedule_free(Schedule);477 478    RAW = isl_union_map_coalesce(RAW);479    WAW = isl_union_map_coalesce(WAW);480    WAR = isl_union_map_coalesce(WAR);481 482    // End of max_operations scope.483  }484 485  if (isl_ctx_last_error(IslCtx.get()) == isl_error_quota) {486    isl_union_map_free(RAW);487    isl_union_map_free(WAW);488    isl_union_map_free(WAR);489    isl_union_map_free(StrictWAW);490    RAW = WAW = WAR = StrictWAW = nullptr;491    isl_ctx_reset_error(IslCtx.get());492  }493 494  // Drop out early, as the remaining computations are only needed for495  // reduction dependences or dependences that are finer than statement496  // level dependences.497  if (!HasReductions && Level == AL_Statement) {498    RED = isl_union_map_empty(isl_union_map_get_space(RAW));499    TC_RED = isl_union_map_empty(isl_union_set_get_space(TaggedStmtDomain));500    isl_union_set_free(TaggedStmtDomain);501    isl_union_map_free(StrictWAW);502    return;503  }504 505  isl_union_map *STMT_RAW, *STMT_WAW, *STMT_WAR;506  STMT_RAW = isl_union_map_intersect_domain(507      isl_union_map_copy(RAW), isl_union_set_copy(TaggedStmtDomain));508  STMT_WAW = isl_union_map_intersect_domain(509      isl_union_map_copy(WAW), isl_union_set_copy(TaggedStmtDomain));510  STMT_WAR =511      isl_union_map_intersect_domain(isl_union_map_copy(WAR), TaggedStmtDomain);512  POLLY_DEBUG({513    dbgs() << "Wrapped Dependences:\n";514    dump();515    dbgs() << "\n";516  });517 518  // To handle reduction dependences we proceed as follows:519  // 1) Aggregate all possible reduction dependences, namely all self520  //    dependences on reduction like statements.521  // 2) Intersect them with the actual RAW & WAW dependences to the get the522  //    actual reduction dependences. This will ensure the load/store memory523  //    addresses were __identical__ in the two iterations of the statement.524  // 3) Relax the original RAW, WAW and WAR dependences by subtracting the525  //    actual reduction dependences. Binary reductions (sum += A[i]) cause526  //    the same, RAW, WAW and WAR dependences.527  // 4) Add the privatization dependences which are widened versions of528  //    already present dependences. They model the effect of manual529  //    privatization at the outermost possible place (namely after the last530  //    write and before the first access to a reduction location).531 532  // Step 1)533  RED = isl_union_map_empty(isl_union_map_get_space(RAW));534  for (ScopStmt &Stmt : S) {535    for (MemoryAccess *MA : Stmt) {536      if (!MA->isReductionLike())537        continue;538      isl_set *AccDomW = isl_map_wrap(MA->getAccessRelation().release());539      isl_map *Identity =540          isl_map_from_domain_and_range(isl_set_copy(AccDomW), AccDomW);541      RED = isl_union_map_add_map(RED, Identity);542    }543  }544 545  // Step 2)546  RED = isl_union_map_intersect(RED, isl_union_map_copy(RAW));547  RED = isl_union_map_intersect(RED, StrictWAW);548 549  if (!isl_union_map_is_empty(RED)) {550 551    // Step 3)552    RAW = isl_union_map_subtract(RAW, isl_union_map_copy(RED));553    WAW = isl_union_map_subtract(WAW, isl_union_map_copy(RED));554    WAR = isl_union_map_subtract(WAR, isl_union_map_copy(RED));555 556    // Step 4)557    addPrivatizationDependences();558  } else559    TC_RED = isl_union_map_empty(isl_union_map_get_space(RED));560 561  POLLY_DEBUG({562    dbgs() << "Final Wrapped Dependences:\n";563    dump();564    dbgs() << "\n";565  });566 567  // RED_SIN is used to collect all reduction dependences again after we568  // split them according to the causing memory accesses. The current assumption569  // is that our method of splitting will not have any leftovers. In the end570  // we validate this assumption until we have more confidence in this method.571  isl_union_map *RED_SIN = isl_union_map_empty(isl_union_map_get_space(RAW));572 573  // For each reduction like memory access, check if there are reduction574  // dependences with the access relation of the memory access as a domain575  // (wrapped space!). If so these dependences are caused by this memory access.576  // We then move this portion of reduction dependences back to the statement ->577  // statement space and add a mapping from the memory access to these578  // dependences.579  for (ScopStmt &Stmt : S) {580    for (MemoryAccess *MA : Stmt) {581      if (!MA->isReductionLike())582        continue;583 584      isl_set *AccDomW = isl_map_wrap(MA->getAccessRelation().release());585      isl_union_map *AccRedDepU = isl_union_map_intersect_domain(586          isl_union_map_copy(TC_RED), isl_union_set_from_set(AccDomW));587      if (isl_union_map_is_empty(AccRedDepU)) {588        isl_union_map_free(AccRedDepU);589        continue;590      }591 592      isl_map *AccRedDep = isl_map_from_union_map(AccRedDepU);593      RED_SIN = isl_union_map_add_map(RED_SIN, isl_map_copy(AccRedDep));594      AccRedDep = isl_map_zip(AccRedDep);595      AccRedDep = isl_set_unwrap(isl_map_domain(AccRedDep));596      setReductionDependences(MA, AccRedDep);597    }598  }599 600  assert(isl_union_map_is_equal(RED_SIN, TC_RED) &&601         "Intersecting the reduction dependence domain with the wrapped access "602         "relation is not enough, we need to loosen the access relation also");603  isl_union_map_free(RED_SIN);604 605  RAW = isl_union_map_zip(RAW);606  WAW = isl_union_map_zip(WAW);607  WAR = isl_union_map_zip(WAR);608  RED = isl_union_map_zip(RED);609  TC_RED = isl_union_map_zip(TC_RED);610 611  POLLY_DEBUG({612    dbgs() << "Zipped Dependences:\n";613    dump();614    dbgs() << "\n";615  });616 617  RAW = isl_union_set_unwrap(isl_union_map_domain(RAW));618  WAW = isl_union_set_unwrap(isl_union_map_domain(WAW));619  WAR = isl_union_set_unwrap(isl_union_map_domain(WAR));620  RED = isl_union_set_unwrap(isl_union_map_domain(RED));621  TC_RED = isl_union_set_unwrap(isl_union_map_domain(TC_RED));622 623  POLLY_DEBUG({624    dbgs() << "Unwrapped Dependences:\n";625    dump();626    dbgs() << "\n";627  });628 629  RAW = isl_union_map_union(RAW, STMT_RAW);630  WAW = isl_union_map_union(WAW, STMT_WAW);631  WAR = isl_union_map_union(WAR, STMT_WAR);632 633  RAW = isl_union_map_coalesce(RAW);634  WAW = isl_union_map_coalesce(WAW);635  WAR = isl_union_map_coalesce(WAR);636  RED = isl_union_map_coalesce(RED);637  TC_RED = isl_union_map_coalesce(TC_RED);638 639  POLLY_DEBUG(dump());640}641 642bool Dependences::isValidSchedule(Scop &S, isl::schedule NewSched) const {643  // TODO: Also check permutable/coincident flags as well.644 645  StatementToIslMapTy NewSchedules;646  for (auto NewMap : NewSched.get_map().get_map_list()) {647    auto Stmt = reinterpret_cast<ScopStmt *>(648        NewMap.get_tuple_id(isl::dim::in).get_user());649    NewSchedules[Stmt] = NewMap;650  }651 652  return isValidSchedule(S, NewSchedules);653}654 655bool Dependences::isValidSchedule(656    Scop &S, const StatementToIslMapTy &NewSchedule) const {657  if (LegalityCheckDisabled)658    return true;659 660  isl::union_map Dependences = getDependences(TYPE_RAW | TYPE_WAW | TYPE_WAR);661  isl::union_map Schedule = isl::union_map::empty(S.getIslCtx());662 663  isl::space ScheduleSpace;664 665  for (ScopStmt &Stmt : S) {666    isl::map StmtScat;667 668    auto Lookup = NewSchedule.find(&Stmt);669    if (Lookup == NewSchedule.end())670      StmtScat = Stmt.getSchedule();671    else672      StmtScat = Lookup->second;673    assert(!StmtScat.is_null() &&674           "Schedules that contain extension nodes require special handling.");675 676    if (ScheduleSpace.is_null())677      ScheduleSpace = StmtScat.get_space().range();678 679    Schedule = Schedule.unite(StmtScat);680  }681 682  Dependences = Dependences.apply_domain(Schedule);683  Dependences = Dependences.apply_range(Schedule);684 685  isl::set Zero = isl::set::universe(ScheduleSpace);686  for (auto i : rangeIslSize(0, Zero.tuple_dim()))687    Zero = Zero.fix_si(isl::dim::set, i, 0);688 689  isl::union_set UDeltas = Dependences.deltas();690  isl::set Deltas = singleton(UDeltas, ScheduleSpace);691 692  isl::space Space = Deltas.get_space();693  isl::map NonPositive = isl::map::universe(Space.map_from_set());694  NonPositive =695      NonPositive.lex_le_at(isl::multi_pw_aff::identity_on_domain(Space));696  NonPositive = NonPositive.intersect_domain(Deltas);697  NonPositive = NonPositive.intersect_range(Zero);698 699  return NonPositive.is_empty();700}701 702// Check if the current scheduling dimension is parallel.703//704// We check for parallelism by verifying that the loop does not carry any705// dependences.706//707// Parallelism test: if the distance is zero in all outer dimensions, then it708// has to be zero in the current dimension as well.709//710// Implementation: first, translate dependences into time space, then force711// outer dimensions to be equal. If the distance is zero in the current712// dimension, then the loop is parallel. The distance is zero in the current713// dimension if it is a subset of a map with equal values for the current714// dimension.715bool Dependences::isParallel(__isl_keep isl_union_map *Schedule,716                             __isl_take isl_union_map *Deps,717                             __isl_give isl_pw_aff **MinDistancePtr) const {718  isl_set *Deltas, *Distance;719  isl_map *ScheduleDeps;720  unsigned Dimension;721  bool IsParallel;722 723  Deps = isl_union_map_apply_range(Deps, isl_union_map_copy(Schedule));724  Deps = isl_union_map_apply_domain(Deps, isl_union_map_copy(Schedule));725 726  if (isl_union_map_is_empty(Deps)) {727    isl_union_map_free(Deps);728    return true;729  }730 731  ScheduleDeps = isl_map_from_union_map(Deps);732  Dimension = isl_map_dim(ScheduleDeps, isl_dim_out) - 1;733 734  for (unsigned i = 0; i < Dimension; i++)735    ScheduleDeps = isl_map_equate(ScheduleDeps, isl_dim_out, i, isl_dim_in, i);736 737  Deltas = isl_map_deltas(ScheduleDeps);738  Distance = isl_set_universe(isl_set_get_space(Deltas));739 740  // [0, ..., 0, +] - All zeros and last dimension larger than zero741  for (unsigned i = 0; i < Dimension; i++)742    Distance = isl_set_fix_si(Distance, isl_dim_set, i, 0);743 744  Distance = isl_set_lower_bound_si(Distance, isl_dim_set, Dimension, 1);745  Distance = isl_set_intersect(Distance, Deltas);746 747  IsParallel = isl_set_is_empty(Distance);748  if (IsParallel || !MinDistancePtr) {749    isl_set_free(Distance);750    return IsParallel;751  }752 753  Distance = isl_set_project_out(Distance, isl_dim_set, 0, Dimension);754  Distance = isl_set_coalesce(Distance);755 756  // This last step will compute a expression for the minimal value in the757  // distance polyhedron Distance with regards to the first (outer most)758  // dimension.759  *MinDistancePtr = isl_pw_aff_coalesce(isl_set_dim_min(Distance, 0));760 761  return false;762}763 764static void printDependencyMap(raw_ostream &OS, __isl_keep isl_union_map *DM) {765  if (DM)766    OS << DM << "\n";767  else768    OS << "n/a\n";769}770 771void Dependences::print(raw_ostream &OS) const {772  OS << "\tRAW dependences:\n\t\t";773  printDependencyMap(OS, RAW);774  OS << "\tWAR dependences:\n\t\t";775  printDependencyMap(OS, WAR);776  OS << "\tWAW dependences:\n\t\t";777  printDependencyMap(OS, WAW);778  OS << "\tReduction dependences:\n\t\t";779  printDependencyMap(OS, RED);780  OS << "\tTransitive closure of reduction dependences:\n\t\t";781  printDependencyMap(OS, TC_RED);782}783 784void Dependences::dump() const { print(dbgs()); }785 786void Dependences::releaseMemory() {787  isl_union_map_free(RAW);788  isl_union_map_free(WAR);789  isl_union_map_free(WAW);790  isl_union_map_free(RED);791  isl_union_map_free(TC_RED);792 793  RED = RAW = WAR = WAW = TC_RED = nullptr;794 795  for (auto &ReductionDeps : ReductionDependences)796    isl_map_free(ReductionDeps.second);797  ReductionDependences.clear();798}799 800isl::union_map Dependences::getDependences(int Kinds) const {801  assert(hasValidDependences() && "No valid dependences available");802  isl::space Space = isl::manage_copy(RAW).get_space();803  isl::union_map Deps = Deps.empty(Space.ctx());804 805  if (Kinds & TYPE_RAW)806    Deps = Deps.unite(isl::manage_copy(RAW));807 808  if (Kinds & TYPE_WAR)809    Deps = Deps.unite(isl::manage_copy(WAR));810 811  if (Kinds & TYPE_WAW)812    Deps = Deps.unite(isl::manage_copy(WAW));813 814  if (Kinds & TYPE_RED)815    Deps = Deps.unite(isl::manage_copy(RED));816 817  if (Kinds & TYPE_TC_RED)818    Deps = Deps.unite(isl::manage_copy(TC_RED));819 820  Deps = Deps.coalesce();821  Deps = Deps.detect_equalities();822  return Deps;823}824 825bool Dependences::hasValidDependences() const {826  return (RAW != nullptr) && (WAR != nullptr) && (WAW != nullptr);827}828 829__isl_give isl_map *830Dependences::getReductionDependences(MemoryAccess *MA) const {831  return isl_map_copy(ReductionDependences.lookup(MA));832}833 834void Dependences::setReductionDependences(MemoryAccess *MA,835                                          __isl_take isl_map *D) {836  assert(ReductionDependences.count(MA) == 0 &&837         "Reduction dependences set twice!");838  ReductionDependences[MA] = D;839}840 841const Dependences &842DependenceAnalysis::Result::getDependences(Dependences::AnalysisLevel Level) {843  if (Dependences *d = D[Level].get())844    return *d;845 846  return recomputeDependences(Level);847}848 849const Dependences &DependenceAnalysis::Result::recomputeDependences(850    Dependences::AnalysisLevel Level) {851  D[Level].reset(new Dependences(S.getSharedIslCtx(), Level));852  D[Level]->calculateDependences(S);853  return *D[Level];854}855 856void DependenceAnalysis::Result::abandonDependences() {857  for (std::unique_ptr<Dependences> &Deps : D)858    Deps.release();859}860 861DependenceAnalysis::Result polly::runDependenceAnalysis(Scop &S) {862  DependenceAnalysis::Result Result{S, {}};863  return Result;864}865