brintos

brintos / llvm-project-archived public Read only

0
0
Text · 41.9 KiB · a114a24 Raw
1174 lines · cpp
1//===------ ZoneAlgo.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// Derive information about array elements between statements ("Zones").10//11// The algorithms here work on the scatter space - the image space of the12// schedule returned by Scop::getSchedule(). We call an element in that space a13// "timepoint". Timepoints are lexicographically ordered such that we can14// defined ranges in the scatter space. We use two flavors of such ranges:15// Timepoint sets and zones. A timepoint set is simply a subset of the scatter16// space and is directly stored as isl_set.17//18// Zones are used to describe the space between timepoints as open sets, i.e.19// they do not contain the extrema. Using isl rational sets to express these20// would be overkill. We also cannot store them as the integer timepoints they21// contain; the (nonempty) zone between 1 and 2 would be empty and22// indistinguishable from e.g. the zone between 3 and 4. Also, we cannot store23// the integer set including the extrema; the set ]1,2[ + ]3,4[ could be24// coalesced to ]1,3[, although we defined the range [2,3] to be not in the set.25// Instead, we store the "half-open" integer extrema, including the lower bound,26// but excluding the upper bound. Examples:27//28// * The set { [i] : 1 <= i <= 3 } represents the zone ]0,3[ (which contains the29//   integer points 1 and 2, but not 0 or 3)30//31// * { [1] } represents the zone ]0,1[32//33// * { [i] : i = 1 or i = 3 } represents the zone ]0,1[ + ]2,3[34//35// Therefore, an integer i in the set represents the zone ]i-1,i[, i.e. strictly36// speaking the integer points never belong to the zone. However, depending an37// the interpretation, one might want to include them. Part of the38// interpretation may not be known when the zone is constructed.39//40// Reads are assumed to always take place before writes, hence we can think of41// reads taking place at the beginning of a timepoint and writes at the end.42//43// Let's assume that the zone represents the lifetime of a variable. That is,44// the zone begins with a write that defines the value during its lifetime and45// ends with the last read of that value. In the following we consider whether a46// read/write at the beginning/ending of the lifetime zone should be within the47// zone or outside of it.48//49// * A read at the timepoint that starts the live-range loads the previous50//   value. Hence, exclude the timepoint starting the zone.51//52// * A write at the timepoint that starts the live-range is not defined whether53//   it occurs before or after the write that starts the lifetime. We do not54//   allow this situation to occur. Hence, we include the timepoint starting the55//   zone to determine whether they are conflicting.56//57// * A read at the timepoint that ends the live-range reads the same variable.58//   We include the timepoint at the end of the zone to include that read into59//   the live-range. Doing otherwise would mean that the two reads access60//   different values, which would mean that the value they read are both alive61//   at the same time but occupy the same variable.62//63// * A write at the timepoint that ends the live-range starts a new live-range.64//   It must not be included in the live-range of the previous definition.65//66// All combinations of reads and writes at the endpoints are possible, but most67// of the time only the write->read (for instance, a live-range from definition68// to last use) and read->write (for instance, an unused range from last use to69// overwrite) and combinations are interesting (half-open ranges). write->write70// zones might be useful as well in some context to represent71// output-dependencies.72//73// @see convertZoneToTimepoints74//75//76// The code makes use of maps and sets in many different spaces. To not loose77// track in which space a set or map is expected to be in, variables holding an78// isl reference are usually annotated in the comments. They roughly follow isl79// syntax for spaces, but only the tuples, not the dimensions. The tuples have a80// meaning as follows:81//82// * Space[] - An unspecified tuple. Used for function parameters such that the83//             function caller can use it for anything they like.84//85// * Domain[] - A statement instance as returned by ScopStmt::getDomain()86//     isl_id_get_name: Stmt_<NameOfBasicBlock>87//     isl_id_get_user: Pointer to ScopStmt88//89// * Element[] - An array element as in the range part of90//               MemoryAccess::getAccessRelation()91//     isl_id_get_name: MemRef_<NameOfArrayVariable>92//     isl_id_get_user: Pointer to ScopArrayInfo93//94// * Scatter[] - Scatter space or space of timepoints95//     Has no tuple id96//97// * Zone[] - Range between timepoints as described above98//     Has no tuple id99//100// * ValInst[] - An llvm::Value as defined at a specific timepoint.101//102//     A ValInst[] itself can be structured as one of:103//104//     * [] - An unknown value.105//         Always zero dimensions106//         Has no tuple id107//108//     * Value[] - An llvm::Value that is read-only in the SCoP, i.e. its109//                 runtime content does not depend on the timepoint.110//         Always zero dimensions111//         isl_id_get_name: Val_<NameOfValue>112//         isl_id_get_user: A pointer to an llvm::Value113//114//     * SCEV[...] - A synthesizable llvm::SCEV Expression.115//         In contrast to a Value[] is has at least one dimension per116//         SCEVAddRecExpr in the SCEV.117//118//     * [Domain[] -> Value[]] - An llvm::Value that may change during the119//                               Scop's execution.120//         The tuple itself has no id, but it wraps a map space holding a121//         statement instance which defines the llvm::Value as the map's domain122//         and llvm::Value itself as range.123//124// @see makeValInst()125//126// An annotation "{ Domain[] -> Scatter[] }" therefore means: A map from a127// statement instance to a timepoint, aka a schedule. There is only one scatter128// space, but most of the time multiple statements are processed in one set.129// This is why most of the time isl_union_map has to be used.130//131// The basic algorithm works as follows:132// At first we verify that the SCoP is compatible with this technique. For133// instance, two writes cannot write to the same location at the same statement134// instance because we cannot determine within the polyhedral model which one135// comes first. Once this was verified, we compute zones at which an array136// element is unused. This computation can fail if it takes too long. Then the137// main algorithm is executed. Because every store potentially trails an unused138// zone, we start at stores. We search for a scalar (MemoryKind::Value or139// MemoryKind::PHI) that we can map to the array element overwritten by the140// store, preferably one that is used by the store or at least the ScopStmt.141// When it does not conflict with the lifetime of the values in the array142// element, the map is applied and the unused zone updated as it is now used. We143// continue to try to map scalars to the array element until there are no more144// candidates to map. The algorithm is greedy in the sense that the first scalar145// not conflicting will be mapped. Other scalars processed later that could have146// fit the same unused zone will be rejected. As such the result depends on the147// processing order.148//149//===----------------------------------------------------------------------===//150 151#include "polly/ZoneAlgo.h"152#include "polly/ScopInfo.h"153#include "polly/Support/GICHelper.h"154#include "polly/Support/ISLTools.h"155#include "polly/Support/VirtualInstruction.h"156#include "llvm/ADT/Statistic.h"157#include "llvm/Support/raw_ostream.h"158 159#include "polly/Support/PollyDebug.h"160#define DEBUG_TYPE "polly-zone"161 162STATISTIC(NumIncompatibleArrays, "Number of not zone-analyzable arrays");163STATISTIC(NumCompatibleArrays, "Number of zone-analyzable arrays");164STATISTIC(NumRecursivePHIs, "Number of recursive PHIs");165STATISTIC(NumNormalizablePHIs, "Number of normalizable PHIs");166STATISTIC(NumPHINormialization, "Number of PHI executed normalizations");167 168using namespace polly;169using namespace llvm;170 171static isl::union_map computeReachingDefinition(isl::union_map Schedule,172                                                isl::union_map Writes,173                                                bool InclDef, bool InclRedef) {174  return computeReachingWrite(Schedule, Writes, false, InclDef, InclRedef);175}176 177/// Compute the reaching definition of a scalar.178///179/// Compared to computeReachingDefinition, there is just one element which is180/// accessed and therefore only a set if instances that accesses that element is181/// required.182///183/// @param Schedule  { DomainWrite[] -> Scatter[] }184/// @param Writes    { DomainWrite[] }185/// @param InclDef   Include the timepoint of the definition to the result.186/// @param InclRedef Include the timepoint of the overwrite into the result.187///188/// @return { Scatter[] -> DomainWrite[] }189static isl::union_map computeScalarReachingDefinition(isl::union_map Schedule,190                                                      isl::union_set Writes,191                                                      bool InclDef,192                                                      bool InclRedef) {193  // { DomainWrite[] -> Element[] }194  isl::union_map Defs = isl::union_map::from_domain(Writes);195 196  // { [Element[] -> Scatter[]] -> DomainWrite[] }197  auto ReachDefs =198      computeReachingDefinition(Schedule, Defs, InclDef, InclRedef);199 200  // { Scatter[] -> DomainWrite[] }201  return ReachDefs.curry().range().unwrap();202}203 204/// Compute the reaching definition of a scalar.205///206/// This overload accepts only a single writing statement as an isl_map,207/// consequently the result also is only a single isl_map.208///209/// @param Schedule  { DomainWrite[] -> Scatter[] }210/// @param Writes    { DomainWrite[] }211/// @param InclDef   Include the timepoint of the definition to the result.212/// @param InclRedef Include the timepoint of the overwrite into the result.213///214/// @return { Scatter[] -> DomainWrite[] }215static isl::map computeScalarReachingDefinition(isl::union_map Schedule,216                                                isl::set Writes, bool InclDef,217                                                bool InclRedef) {218  isl::space DomainSpace = Writes.get_space();219  isl::space ScatterSpace = getScatterSpace(Schedule);220 221  //  { Scatter[] -> DomainWrite[] }222  isl::union_map UMap = computeScalarReachingDefinition(223      Schedule, isl::union_set(Writes), InclDef, InclRedef);224 225  isl::space ResultSpace = ScatterSpace.map_from_domain_and_range(DomainSpace);226  return singleton(UMap, ResultSpace);227}228 229isl::union_map polly::makeUnknownForDomain(isl::union_set Domain) {230  return isl::union_map::from_domain(Domain);231}232 233/// Create a domain-to-unknown value mapping.234///235/// @see makeUnknownForDomain(isl::union_set)236///237/// @param Domain { Domain[] }238///239/// @return { Domain[] -> ValInst[] }240static isl::map makeUnknownForDomain(isl::set Domain) {241  return isl::map::from_domain(Domain);242}243 244/// Return whether @p Map maps to an unknown value.245///246/// @param { [] -> ValInst[] }247static bool isMapToUnknown(const isl::map &Map) {248  isl::space Space = Map.get_space().range();249  return Space.has_tuple_id(isl::dim::set).is_false() &&250         Space.is_wrapping().is_false() &&251         Space.dim(isl::dim::set).release() == 0;252}253 254isl::union_map polly::filterKnownValInst(const isl::union_map &UMap) {255  isl::union_map Result = isl::union_map::empty(UMap.ctx());256  for (isl::map Map : UMap.get_map_list()) {257    if (!isMapToUnknown(Map))258      Result = Result.unite(Map);259  }260  return Result;261}262 263ZoneAlgorithm::ZoneAlgorithm(const char *PassName, Scop *S, LoopInfo *LI)264    : PassName(PassName), IslCtx(S->getSharedIslCtx()), S(S), LI(LI),265      Schedule(S->getSchedule()) {266  auto Domains = S->getDomains();267 268  Schedule = Schedule.intersect_domain(Domains);269  ParamSpace = Schedule.get_space();270  ScatterSpace = getScatterSpace(Schedule);271}272 273/// Check if all stores in @p Stmt store the very same value.274///275/// This covers a special situation occurring in Polybench's276/// covariance/correlation (which is typical for algorithms that cover symmetric277/// matrices):278///279/// for (int i = 0; i < n; i += 1)280/// 	for (int j = 0; j <= i; j += 1) {281/// 		double x = ...;282/// 		C[i][j] = x;283/// 		C[j][i] = x;284/// 	}285///286/// For i == j, the same value is written twice to the same element.Double287/// writes to the same element are not allowed in DeLICM because its algorithm288/// does not see which of the writes is effective.But if its the same value289/// anyway, it doesn't matter.290///291/// LLVM passes, however, cannot simplify this because the write is necessary292/// for i != j (unless it would add a condition for one of the writes to occur293/// only if i != j).294///295/// TODO: In the future we may want to extent this to make the checks296///       specific to different memory locations.297static bool onlySameValueWrites(ScopStmt *Stmt) {298  Value *V = nullptr;299 300  for (auto *MA : *Stmt) {301    if (!MA->isLatestArrayKind() || !MA->isMustWrite() ||302        !MA->isOriginalArrayKind())303      continue;304 305    if (!V) {306      V = MA->getAccessValue();307      continue;308    }309 310    if (V != MA->getAccessValue())311      return false;312  }313  return true;314}315 316/// Is @p InnerLoop nested inside @p OuterLoop?317static bool isInsideLoop(Loop *OuterLoop, Loop *InnerLoop) {318  // If OuterLoop is nullptr, we cannot call its contains() method. In this case319  // OuterLoop represents the 'top level' and therefore contains all loop.320  return !OuterLoop || OuterLoop->contains(InnerLoop);321}322 323void ZoneAlgorithm::collectIncompatibleElts(ScopStmt *Stmt,324                                            isl::union_set &IncompatibleElts,325                                            isl::union_set &AllElts) {326  auto Stores = makeEmptyUnionMap();327  auto Loads = makeEmptyUnionMap();328 329  // This assumes that the MemoryKind::Array MemoryAccesses are iterated in330  // order.331  for (auto *MA : *Stmt) {332    if (!MA->isOriginalArrayKind())333      continue;334 335    isl::map AccRelMap = getAccessRelationFor(MA);336    isl::union_map AccRel = AccRelMap;337 338    // To avoid solving any ILP problems, always add entire arrays instead of339    // just the elements that are accessed.340    auto ArrayElts = isl::set::universe(AccRelMap.get_space().range());341    AllElts = AllElts.unite(ArrayElts);342 343    if (MA->isRead()) {344      // Reject load after store to same location.345      if (!Stores.is_disjoint(AccRel)) {346        POLLY_DEBUG(347            dbgs() << "Load after store of same element in same statement\n");348        OptimizationRemarkMissed R(PassName, "LoadAfterStore",349                                   MA->getAccessInstruction());350        R << "load after store of same element in same statement";351        R << " (previous stores: " << Stores;352        R << ", loading: " << AccRel << ")";353        S->getFunction().getContext().diagnose(R);354 355        IncompatibleElts = IncompatibleElts.unite(ArrayElts);356      }357 358      Loads = Loads.unite(AccRel);359 360      continue;361    }362 363    // In region statements the order is less clear, eg. the load and store364    // might be in a boxed loop.365    if (Stmt->isRegionStmt() && !Loads.is_disjoint(AccRel)) {366      POLLY_DEBUG(dbgs() << "WRITE in non-affine subregion not supported\n");367      OptimizationRemarkMissed R(PassName, "StoreInSubregion",368                                 MA->getAccessInstruction());369      R << "store is in a non-affine subregion";370      S->getFunction().getContext().diagnose(R);371 372      IncompatibleElts = IncompatibleElts.unite(ArrayElts);373    }374 375    // Do not allow more than one store to the same location.376    if (!Stores.is_disjoint(AccRel) && !onlySameValueWrites(Stmt)) {377      POLLY_DEBUG(dbgs() << "WRITE after WRITE to same element\n");378      OptimizationRemarkMissed R(PassName, "StoreAfterStore",379                                 MA->getAccessInstruction());380      R << "store after store of same element in same statement";381      R << " (previous stores: " << Stores;382      R << ", storing: " << AccRel << ")";383      S->getFunction().getContext().diagnose(R);384 385      IncompatibleElts = IncompatibleElts.unite(ArrayElts);386    }387 388    Stores = Stores.unite(AccRel);389  }390}391 392void ZoneAlgorithm::addArrayReadAccess(MemoryAccess *MA) {393  assert(MA->isLatestArrayKind());394  assert(MA->isRead());395  ScopStmt *Stmt = MA->getStatement();396 397  // { DomainRead[] -> Element[] }398  auto AccRel = intersectRange(getAccessRelationFor(MA), CompatibleElts);399  AllReads = AllReads.unite(AccRel);400 401  if (LoadInst *Load = dyn_cast_or_null<LoadInst>(MA->getAccessInstruction())) {402    // { DomainRead[] -> ValInst[] }403    isl::map LoadValInst = makeValInst(404        Load, Stmt, LI->getLoopFor(Load->getParent()), Stmt->isBlockStmt());405 406    // { DomainRead[] -> [Element[] -> DomainRead[]] }407    isl::map IncludeElement = AccRel.domain_map().curry();408 409    // { [Element[] -> DomainRead[]] -> ValInst[] }410    isl::map EltLoadValInst = LoadValInst.apply_domain(IncludeElement);411 412    AllReadValInst = AllReadValInst.unite(EltLoadValInst);413  }414}415 416isl::union_map ZoneAlgorithm::getWrittenValue(MemoryAccess *MA,417                                              isl::map AccRel) {418  if (!MA->isMustWrite())419    return {};420 421  Value *AccVal = MA->getAccessValue();422  ScopStmt *Stmt = MA->getStatement();423  Instruction *AccInst = MA->getAccessInstruction();424 425  // Write a value to a single element.426  auto L = MA->isOriginalArrayKind() ? LI->getLoopFor(AccInst->getParent())427                                     : Stmt->getSurroundingLoop();428  if (AccVal &&429      AccVal->getType() == MA->getLatestScopArrayInfo()->getElementType() &&430      AccRel.is_single_valued().is_true())431    return makeNormalizedValInst(AccVal, Stmt, L);432 433  // memset(_, '0', ) is equivalent to writing the null value to all touched434  // elements. isMustWrite() ensures that all of an element's bytes are435  // overwritten.436  if (auto *Memset = dyn_cast<MemSetInst>(AccInst)) {437    auto *WrittenConstant = dyn_cast<Constant>(Memset->getValue());438    Type *Ty = MA->getLatestScopArrayInfo()->getElementType();439    if (WrittenConstant && WrittenConstant->isZeroValue()) {440      Constant *Zero = Constant::getNullValue(Ty);441      return makeNormalizedValInst(Zero, Stmt, L);442    }443  }444 445  return {};446}447 448void ZoneAlgorithm::addArrayWriteAccess(MemoryAccess *MA) {449  assert(MA->isLatestArrayKind());450  assert(MA->isWrite());451  auto *Stmt = MA->getStatement();452 453  // { Domain[] -> Element[] }454  isl::map AccRel = intersectRange(getAccessRelationFor(MA), CompatibleElts);455 456  if (MA->isMustWrite())457    AllMustWrites = AllMustWrites.unite(AccRel);458 459  if (MA->isMayWrite())460    AllMayWrites = AllMayWrites.unite(AccRel);461 462  // { Domain[] -> ValInst[] }463  isl::union_map WriteValInstance = getWrittenValue(MA, AccRel);464  if (WriteValInstance.is_null())465    WriteValInstance = makeUnknownForDomain(Stmt);466 467  // { Domain[] -> [Element[] -> Domain[]] }468  isl::map IncludeElement = AccRel.domain_map().curry();469 470  // { [Element[] -> DomainWrite[]] -> ValInst[] }471  isl::union_map EltWriteValInst =472      WriteValInstance.apply_domain(IncludeElement);473 474  AllWriteValInst = AllWriteValInst.unite(EltWriteValInst);475}476 477/// For an llvm::Value defined in @p DefStmt, compute the RAW dependency for a478/// use in every instance of @p UseStmt.479///480/// @param UseStmt Statement a scalar is used in.481/// @param DefStmt Statement a scalar is defined in.482///483/// @return { DomainUse[] -> DomainDef[] }484isl::map ZoneAlgorithm::computeUseToDefFlowDependency(ScopStmt *UseStmt,485                                                      ScopStmt *DefStmt) {486  // { DomainUse[] -> Scatter[] }487  isl::map UseScatter = getScatterFor(UseStmt);488 489  // { Zone[] -> DomainDef[] }490  isl::map ReachDefZone = getScalarReachingDefinition(DefStmt);491 492  // { Scatter[] -> DomainDef[] }493  isl::map ReachDefTimepoints =494      convertZoneToTimepoints(ReachDefZone, isl::dim::in, false, true);495 496  // { DomainUse[] -> DomainDef[] }497  return UseScatter.apply_range(ReachDefTimepoints);498}499 500/// Return whether @p PHI refers (also transitively through other PHIs) to501/// itself.502///503/// loop:504///   %phi1 = phi [0, %preheader], [%phi1, %loop]505///   br i1 %c, label %loop, label %exit506///507/// exit:508///   %phi2 = phi [%phi1, %bb]509///510/// In this example, %phi1 is recursive, but %phi2 is not.511static bool isRecursivePHI(const PHINode *PHI) {512  SmallVector<const PHINode *, 8> Worklist;513  SmallPtrSet<const PHINode *, 8> Visited;514  Worklist.push_back(PHI);515 516  while (!Worklist.empty()) {517    const PHINode *Cur = Worklist.pop_back_val();518 519    if (Visited.count(Cur))520      continue;521    Visited.insert(Cur);522 523    for (const Use &Incoming : Cur->incoming_values()) {524      Value *IncomingVal = Incoming.get();525      auto *IncomingPHI = dyn_cast<PHINode>(IncomingVal);526      if (!IncomingPHI)527        continue;528 529      if (IncomingPHI == PHI)530        return true;531      Worklist.push_back(IncomingPHI);532    }533  }534  return false;535}536 537isl::union_map ZoneAlgorithm::computePerPHI(const ScopArrayInfo *SAI) {538  // TODO: If the PHI has an incoming block from before the SCoP, it is not539  // represented in any ScopStmt.540 541  auto *PHI = cast<PHINode>(SAI->getBasePtr());542  auto It = PerPHIMaps.find(PHI);543  if (It != PerPHIMaps.end())544    return It->second;545 546  // Cannot reliably compute immediate predecessor for undefined executions, so547  // bail out if we do not know. This in particular applies to undefined control548  // flow.549  isl::set DefinedContext = S->getDefinedBehaviorContext();550  if (DefinedContext.is_null())551    return {};552 553  assert(SAI->isPHIKind());554 555  // { DomainPHIWrite[] -> Scatter[] }556  isl::union_map PHIWriteScatter = makeEmptyUnionMap();557 558  // Collect all incoming block timepoints.559  for (MemoryAccess *MA : S->getPHIIncomings(SAI)) {560    isl::map Scatter = getScatterFor(MA);561    PHIWriteScatter = PHIWriteScatter.unite(Scatter);562  }563 564  // { DomainPHIRead[] -> Scatter[] }565  isl::map PHIReadScatter = getScatterFor(S->getPHIRead(SAI));566 567  // { DomainPHIRead[] -> Scatter[] }568  isl::map BeforeRead = beforeScatter(PHIReadScatter, true);569 570  // { Scatter[] }571  isl::set WriteTimes = singleton(PHIWriteScatter.range(), ScatterSpace);572 573  // { DomainPHIRead[] -> Scatter[] }574  isl::map PHIWriteTimes = BeforeRead.intersect_range(WriteTimes);575 576  // Remove instances outside the context.577  PHIWriteTimes = PHIWriteTimes.intersect_params(DefinedContext);578 579  isl::map LastPerPHIWrites = PHIWriteTimes.lexmax();580 581  // { DomainPHIRead[] -> DomainPHIWrite[] }582  isl::union_map Result =583      isl::union_map(LastPerPHIWrites).apply_range(PHIWriteScatter.reverse());584  assert(!Result.is_single_valued().is_false());585  assert(!Result.is_injective().is_false());586 587  PerPHIMaps.insert({PHI, Result});588  return Result;589}590 591isl::union_set ZoneAlgorithm::makeEmptyUnionSet() const {592  return isl::union_set::empty(ParamSpace.ctx());593}594 595isl::union_map ZoneAlgorithm::makeEmptyUnionMap() const {596  return isl::union_map::empty(ParamSpace.ctx());597}598 599void ZoneAlgorithm::collectCompatibleElts() {600  // First find all the incompatible elements, then take the complement.601  // We compile the list of compatible (rather than incompatible) elements so602  // users can intersect with the list, not requiring a subtract operation. It603  // also allows us to define a 'universe' of all elements and makes it more604  // explicit in which array elements can be used.605  isl::union_set AllElts = makeEmptyUnionSet();606  isl::union_set IncompatibleElts = makeEmptyUnionSet();607 608  for (auto &Stmt : *S)609    collectIncompatibleElts(&Stmt, IncompatibleElts, AllElts);610 611  NumIncompatibleArrays += isl_union_set_n_set(IncompatibleElts.get());612  CompatibleElts = AllElts.subtract(IncompatibleElts);613  NumCompatibleArrays += isl_union_set_n_set(CompatibleElts.get());614}615 616isl::map ZoneAlgorithm::getScatterFor(ScopStmt *Stmt) const {617  isl::space ResultSpace =618      Stmt->getDomainSpace().map_from_domain_and_range(ScatterSpace);619  return Schedule.extract_map(ResultSpace);620}621 622isl::map ZoneAlgorithm::getScatterFor(MemoryAccess *MA) const {623  return getScatterFor(MA->getStatement());624}625 626isl::union_map ZoneAlgorithm::getScatterFor(isl::union_set Domain) const {627  return Schedule.intersect_domain(Domain);628}629 630isl::map ZoneAlgorithm::getScatterFor(isl::set Domain) const {631  auto ResultSpace = Domain.get_space().map_from_domain_and_range(ScatterSpace);632  auto UDomain = isl::union_set(Domain);633  auto UResult = getScatterFor(std::move(UDomain));634  auto Result = singleton(std::move(UResult), std::move(ResultSpace));635  assert(Result.is_null() || Result.domain().is_equal(Domain) == isl_bool_true);636  return Result;637}638 639isl::set ZoneAlgorithm::getDomainFor(ScopStmt *Stmt) const {640  return Stmt->getDomain().remove_redundancies();641}642 643isl::set ZoneAlgorithm::getDomainFor(MemoryAccess *MA) const {644  return getDomainFor(MA->getStatement());645}646 647isl::map ZoneAlgorithm::getAccessRelationFor(MemoryAccess *MA) const {648  auto Domain = getDomainFor(MA);649  auto AccRel = MA->getLatestAccessRelation();650  return AccRel.intersect_domain(Domain);651}652 653isl::map ZoneAlgorithm::getDefToTarget(ScopStmt *DefStmt,654                                       ScopStmt *TargetStmt) {655  // No translation required if the definition is already at the target.656  if (TargetStmt == DefStmt)657    return isl::map::identity(658        getDomainFor(TargetStmt).get_space().map_from_set());659 660  isl::map &Result = DefToTargetCache[std::make_pair(TargetStmt, DefStmt)];661 662  // This is a shortcut in case the schedule is still the original and663  // TargetStmt is in the same or nested inside DefStmt's loop. With the664  // additional assumption that operand trees do not cross DefStmt's loop665  // header, then TargetStmt's instance shared coordinates are the same as666  // DefStmt's coordinates. All TargetStmt instances with this prefix share667  // the same DefStmt instance.668  // Model:669  //670  //   for (int i < 0; i < N; i+=1) {671  // DefStmt:672  //    D = ...;673  //    for (int j < 0; j < N; j+=1) {674  // TargetStmt:675  //      use(D);676  //    }677  //  }678  //679  // Here, the value used in TargetStmt is defined in the corresponding680  // DefStmt, i.e.681  //682  //   { DefStmt[i] -> TargetStmt[i,j] }683  //684  // In practice, this should cover the majority of cases.685  if (Result.is_null() && S->isOriginalSchedule() &&686      isInsideLoop(DefStmt->getSurroundingLoop(),687                   TargetStmt->getSurroundingLoop())) {688    isl::set DefDomain = getDomainFor(DefStmt);689    isl::set TargetDomain = getDomainFor(TargetStmt);690    assert(unsignedFromIslSize(DefDomain.tuple_dim()) <=691           unsignedFromIslSize(TargetDomain.tuple_dim()));692 693    Result = isl::map::from_domain_and_range(DefDomain, TargetDomain);694    for (unsigned i : rangeIslSize(0, DefDomain.tuple_dim()))695      Result = Result.equate(isl::dim::in, i, isl::dim::out, i);696  }697 698  if (Result.is_null()) {699    // { DomainDef[] -> DomainTarget[] }700    Result = computeUseToDefFlowDependency(TargetStmt, DefStmt).reverse();701    simplify(Result);702  }703 704  return Result;705}706 707isl::map ZoneAlgorithm::getScalarReachingDefinition(ScopStmt *Stmt) {708  auto &Result = ScalarReachDefZone[Stmt];709  if (!Result.is_null())710    return Result;711 712  auto Domain = getDomainFor(Stmt);713  Result = computeScalarReachingDefinition(Schedule, Domain, false, true);714  simplify(Result);715 716  return Result;717}718 719isl::map ZoneAlgorithm::getScalarReachingDefinition(isl::set DomainDef) {720  auto DomId = DomainDef.get_tuple_id();721  auto *Stmt = static_cast<ScopStmt *>(isl_id_get_user(DomId.get()));722 723  auto StmtResult = getScalarReachingDefinition(Stmt);724 725  return StmtResult.intersect_range(DomainDef);726}727 728isl::map ZoneAlgorithm::makeUnknownForDomain(ScopStmt *Stmt) const {729  return ::makeUnknownForDomain(getDomainFor(Stmt));730}731 732isl::id ZoneAlgorithm::makeValueId(Value *V) {733  if (!V)734    return {};735 736  auto &Id = ValueIds[V];737  if (Id.is_null()) {738    auto Name = getIslCompatibleName("Val_", V, ValueIds.size() - 1,739                                     std::string(), UseInstructionNames);740    Id = isl::id::alloc(IslCtx.get(), Name.c_str(), V);741  }742  return Id;743}744 745isl::space ZoneAlgorithm::makeValueSpace(Value *V) {746  auto Result = ParamSpace.set_from_params();747  return Result.set_tuple_id(isl::dim::set, makeValueId(V));748}749 750isl::set ZoneAlgorithm::makeValueSet(Value *V) {751  auto Space = makeValueSpace(V);752  return isl::set::universe(Space);753}754 755isl::map ZoneAlgorithm::makeValInst(Value *Val, ScopStmt *UserStmt, Loop *Scope,756                                    bool IsCertain) {757  // If the definition/write is conditional, the value at the location could758  // be either the written value or the old value. Since we cannot know which759  // one, consider the value to be unknown.760  if (!IsCertain)761    return makeUnknownForDomain(UserStmt);762 763  auto DomainUse = getDomainFor(UserStmt);764  auto VUse = VirtualUse::create(S, UserStmt, Scope, Val, true);765  switch (VUse.getKind()) {766  case VirtualUse::Constant:767  case VirtualUse::Block:768  case VirtualUse::Hoisted:769  case VirtualUse::ReadOnly: {770    // The definition does not depend on the statement which uses it.771    auto ValSet = makeValueSet(Val);772    return isl::map::from_domain_and_range(DomainUse, ValSet);773  }774 775  case VirtualUse::Synthesizable: {776    auto *ScevExpr = VUse.getScevExpr();777    auto UseDomainSpace = DomainUse.get_space();778 779    // Construct the SCEV space.780    // TODO: Add only the induction variables referenced in SCEVAddRecExpr781    // expressions, not just all of them.782    auto ScevId = isl::manage(isl_id_alloc(UseDomainSpace.ctx().get(), nullptr,783                                           const_cast<SCEV *>(ScevExpr)));784 785    auto ScevSpace = UseDomainSpace.drop_dims(isl::dim::set, 0, 0);786    ScevSpace = ScevSpace.set_tuple_id(isl::dim::set, ScevId);787 788    // { DomainUse[] -> ScevExpr[] }789    auto ValInst =790        isl::map::identity(UseDomainSpace.map_from_domain_and_range(ScevSpace));791    return ValInst;792  }793 794  case VirtualUse::Intra: {795    // Definition and use is in the same statement. We do not need to compute796    // a reaching definition.797 798    // { llvm::Value }799    auto ValSet = makeValueSet(Val);800 801    // {  UserDomain[] -> llvm::Value }802    auto ValInstSet = isl::map::from_domain_and_range(DomainUse, ValSet);803 804    // { UserDomain[] -> [UserDomain[] - >llvm::Value] }805    auto Result = ValInstSet.domain_map().reverse();806    simplify(Result);807    return Result;808  }809 810  case VirtualUse::Inter: {811    // The value is defined in a different statement.812 813    auto *Inst = cast<Instruction>(Val);814    auto *ValStmt = S->getStmtFor(Inst);815 816    // If the llvm::Value is defined in a removed Stmt, we cannot derive its817    // domain. We could use an arbitrary statement, but this could result in818    // different ValInst[] for the same llvm::Value.819    if (!ValStmt)820      return ::makeUnknownForDomain(DomainUse);821 822    // { DomainUse[] -> DomainDef[] }823    auto UsedInstance = getDefToTarget(ValStmt, UserStmt).reverse();824 825    // { llvm::Value }826    auto ValSet = makeValueSet(Val);827 828    // { DomainUse[] -> llvm::Value[] }829    auto ValInstSet = isl::map::from_domain_and_range(DomainUse, ValSet);830 831    // { DomainUse[] -> [DomainDef[] -> llvm::Value]  }832    auto Result = UsedInstance.range_product(ValInstSet);833 834    simplify(Result);835    return Result;836  }837  }838  llvm_unreachable("Unhandled use type");839}840 841/// Remove all computed PHIs out of @p Input and replace by their incoming842/// value.843///844/// @param Input        { [] -> ValInst[] }845/// @param ComputedPHIs Set of PHIs that are replaced. Its ValInst must appear846///                     on the LHS of @p NormalizeMap.847/// @param NormalizeMap { ValInst[] -> ValInst[] }848static isl::union_map normalizeValInst(isl::union_map Input,849                                       const DenseSet<PHINode *> &ComputedPHIs,850                                       isl::union_map NormalizeMap) {851  isl::union_map Result = isl::union_map::empty(Input.ctx());852  for (isl::map Map : Input.get_map_list()) {853    isl::space Space = Map.get_space();854    isl::space RangeSpace = Space.range();855 856    // Instructions within the SCoP are always wrapped. Non-wrapped tuples857    // are therefore invariant in the SCoP and don't need normalization.858    if (!RangeSpace.is_wrapping()) {859      Result = Result.unite(Map);860      continue;861    }862 863    auto *PHI = dyn_cast<PHINode>(static_cast<Value *>(864        RangeSpace.unwrap().get_tuple_id(isl::dim::out).get_user()));865 866    // If no normalization is necessary, then the ValInst stands for itself.867    if (!ComputedPHIs.count(PHI)) {868      Result = Result.unite(Map);869      continue;870    }871 872    // Otherwise, apply the normalization.873    isl::union_map Mapped = isl::union_map(Map).apply_range(NormalizeMap);874    Result = Result.unite(Mapped);875    NumPHINormialization++;876  }877  return Result;878}879 880isl::union_map ZoneAlgorithm::makeNormalizedValInst(llvm::Value *Val,881                                                    ScopStmt *UserStmt,882                                                    llvm::Loop *Scope,883                                                    bool IsCertain) {884  isl::map ValInst = makeValInst(Val, UserStmt, Scope, IsCertain);885  isl::union_map Normalized =886      normalizeValInst(ValInst, ComputedPHIs, NormalizeMap);887  return Normalized;888}889 890bool ZoneAlgorithm::isCompatibleAccess(MemoryAccess *MA) {891  if (!MA)892    return false;893  if (!MA->isLatestArrayKind())894    return false;895  Instruction *AccInst = MA->getAccessInstruction();896  return isa<StoreInst>(AccInst) || isa<LoadInst>(AccInst);897}898 899bool ZoneAlgorithm::isNormalizable(MemoryAccess *MA) {900  assert(MA->isRead());901 902  // Exclude ExitPHIs, we are assuming that a normalizable PHI has a READ903  // MemoryAccess.904  if (!MA->isOriginalPHIKind())905    return false;906 907  // Exclude recursive PHIs, normalizing them would require a transitive908  // closure.909  auto *PHI = cast<PHINode>(MA->getAccessInstruction());910  if (RecursivePHIs.count(PHI))911    return false;912 913  // Ensure that each incoming value can be represented by a ValInst[].914  // We do represent values from statements associated to multiple incoming915  // value by the PHI itself, but we do not handle this case yet (especially916  // isNormalized()) when normalizing.917  const ScopArrayInfo *SAI = MA->getOriginalScopArrayInfo();918  auto Incomings = S->getPHIIncomings(SAI);919  for (MemoryAccess *Incoming : Incomings) {920    if (Incoming->getIncoming().size() != 1)921      return false;922  }923 924  return true;925}926 927isl::boolean ZoneAlgorithm::isNormalized(isl::map Map) {928  isl::space Space = Map.get_space();929  isl::space RangeSpace = Space.range();930 931  isl::boolean IsWrapping = RangeSpace.is_wrapping();932  if (!IsWrapping.is_true())933    return !IsWrapping;934  isl::space Unwrapped = RangeSpace.unwrap();935 936  isl::id OutTupleId = Unwrapped.get_tuple_id(isl::dim::out);937  if (OutTupleId.is_null())938    return isl::boolean();939  auto *PHI = dyn_cast<PHINode>(static_cast<Value *>(OutTupleId.get_user()));940  if (!PHI)941    return true;942 943  isl::id InTupleId = Unwrapped.get_tuple_id(isl::dim::in);944  if (OutTupleId.is_null())945    return isl::boolean();946  auto *IncomingStmt = static_cast<ScopStmt *>(InTupleId.get_user());947  MemoryAccess *PHIRead = IncomingStmt->lookupPHIReadOf(PHI);948  if (!isNormalizable(PHIRead))949    return true;950 951  return false;952}953 954isl::boolean ZoneAlgorithm::isNormalized(isl::union_map UMap) {955  isl::boolean Result = true;956  for (isl::map Map : UMap.get_map_list()) {957    Result = isNormalized(Map);958    if (Result.is_true())959      continue;960    break;961  }962  return Result;963}964 965void ZoneAlgorithm::computeCommon() {966  AllReads = makeEmptyUnionMap();967  AllMayWrites = makeEmptyUnionMap();968  AllMustWrites = makeEmptyUnionMap();969  AllWriteValInst = makeEmptyUnionMap();970  AllReadValInst = makeEmptyUnionMap();971 972  // Default to empty, i.e. no normalization/replacement is taking place. Call973  // computeNormalizedPHIs() to initialize.974  NormalizeMap = makeEmptyUnionMap();975  ComputedPHIs.clear();976 977  for (auto &Stmt : *S) {978    for (auto *MA : Stmt) {979      if (!MA->isLatestArrayKind())980        continue;981 982      if (MA->isRead())983        addArrayReadAccess(MA);984 985      if (MA->isWrite())986        addArrayWriteAccess(MA);987    }988  }989 990  // { DomainWrite[] -> Element[] }991  AllWrites = AllMustWrites.unite(AllMayWrites);992 993  // { [Element[] -> Zone[]] -> DomainWrite[] }994  WriteReachDefZone =995      computeReachingDefinition(Schedule, AllWrites, false, true);996  simplify(WriteReachDefZone);997}998 999void ZoneAlgorithm::computeNormalizedPHIs() {1000  // Determine which PHIs can reference themselves. They are excluded from1001  // normalization to avoid problems with transitive closures.1002  for (ScopStmt &Stmt : *S) {1003    for (MemoryAccess *MA : Stmt) {1004      if (!MA->isPHIKind())1005        continue;1006      if (!MA->isRead())1007        continue;1008 1009      // TODO: Can be more efficient since isRecursivePHI can theoretically1010      // determine recursiveness for multiple values and/or cache results.1011      auto *PHI = cast<PHINode>(MA->getAccessInstruction());1012      if (isRecursivePHI(PHI)) {1013        NumRecursivePHIs++;1014        RecursivePHIs.insert(PHI);1015      }1016    }1017  }1018 1019  // { PHIValInst[] -> IncomingValInst[] }1020  isl::union_map AllPHIMaps = makeEmptyUnionMap();1021 1022  // Discover new PHIs and try to normalize them.1023  DenseSet<PHINode *> AllPHIs;1024  for (ScopStmt &Stmt : *S) {1025    for (MemoryAccess *MA : Stmt) {1026      if (!MA->isOriginalPHIKind())1027        continue;1028      if (!MA->isRead())1029        continue;1030      if (!isNormalizable(MA))1031        continue;1032 1033      auto *PHI = cast<PHINode>(MA->getAccessInstruction());1034      const ScopArrayInfo *SAI = MA->getOriginalScopArrayInfo();1035 1036      // Determine which instance of the PHI statement corresponds to which1037      // incoming value. Skip if we cannot determine PHI predecessors.1038      // { PHIDomain[] -> IncomingDomain[] }1039      isl::union_map PerPHI = computePerPHI(SAI);1040      if (PerPHI.is_null())1041        continue;1042 1043      // { PHIDomain[] -> PHIValInst[] }1044      isl::map PHIValInst = makeValInst(PHI, &Stmt, Stmt.getSurroundingLoop());1045 1046      // { IncomingDomain[] -> IncomingValInst[] }1047      isl::union_map IncomingValInsts = makeEmptyUnionMap();1048 1049      // Get all incoming values.1050      for (MemoryAccess *MA : S->getPHIIncomings(SAI)) {1051        ScopStmt *IncomingStmt = MA->getStatement();1052 1053        auto Incoming = MA->getIncoming();1054        assert(Incoming.size() == 1 && "The incoming value must be "1055                                       "representable by something else than "1056                                       "the PHI itself");1057        Value *IncomingVal = Incoming[0].second;1058 1059        // { IncomingDomain[] -> IncomingValInst[] }1060        isl::map IncomingValInst = makeValInst(1061            IncomingVal, IncomingStmt, IncomingStmt->getSurroundingLoop());1062 1063        IncomingValInsts = IncomingValInsts.unite(IncomingValInst);1064      }1065 1066      // { PHIValInst[] -> IncomingValInst[] }1067      isl::union_map PHIMap =1068          PerPHI.apply_domain(PHIValInst).apply_range(IncomingValInsts);1069      assert(!PHIMap.is_single_valued().is_false());1070 1071      // Resolve transitiveness: The incoming value of the newly discovered PHI1072      // may reference a previously normalized PHI. At the same time, already1073      // normalized PHIs might be normalized to the new PHI. At the end, none of1074      // the PHIs may appear on the right-hand-side of the normalization map.1075      PHIMap = normalizeValInst(PHIMap, AllPHIs, AllPHIMaps);1076      AllPHIs.insert(PHI);1077      AllPHIMaps = normalizeValInst(AllPHIMaps, AllPHIs, PHIMap);1078 1079      AllPHIMaps = AllPHIMaps.unite(PHIMap);1080      NumNormalizablePHIs++;1081    }1082  }1083  simplify(AllPHIMaps);1084 1085  // Apply the normalization.1086  ComputedPHIs = AllPHIs;1087  NormalizeMap = AllPHIMaps;1088 1089  assert(NormalizeMap.is_null() || isNormalized(NormalizeMap));1090}1091 1092void ZoneAlgorithm::printAccesses(llvm::raw_ostream &OS, int Indent) const {1093  OS.indent(Indent) << "After accesses {\n";1094  for (auto &Stmt : *S) {1095    OS.indent(Indent + 4) << Stmt.getBaseName() << "\n";1096    for (auto *MA : Stmt)1097      MA->print(OS);1098  }1099  OS.indent(Indent) << "}\n";1100}1101 1102isl::union_map ZoneAlgorithm::computeKnownFromMustWrites() const {1103  // { [Element[] -> Zone[]] -> [Element[] -> DomainWrite[]] }1104  isl::union_map EltReachdDef = distributeDomain(WriteReachDefZone.curry());1105 1106  // { [Element[] -> DomainWrite[]] -> ValInst[] }1107  isl::union_map AllKnownWriteValInst = filterKnownValInst(AllWriteValInst);1108 1109  // { [Element[] -> Zone[]] -> ValInst[] }1110  return EltReachdDef.apply_range(AllKnownWriteValInst);1111}1112 1113isl::union_map ZoneAlgorithm::computeKnownFromLoad() const {1114  // { Element[] }1115  isl::union_set AllAccessedElts = AllReads.range().unite(AllWrites.range());1116 1117  // { Element[] -> Scatter[] }1118  isl::union_map EltZoneUniverse = isl::union_map::from_domain_and_range(1119      AllAccessedElts, isl::set::universe(ScatterSpace));1120 1121  // This assumes there are no "holes" in1122  // isl_union_map_domain(WriteReachDefZone); alternatively, compute the zone1123  // before the first write or that are not written at all.1124  // { Element[] -> Scatter[] }1125  isl::union_set NonReachDef =1126      EltZoneUniverse.wrap().subtract(WriteReachDefZone.domain());1127 1128  // { [Element[] -> Zone[]] -> ReachDefId[] }1129  isl::union_map DefZone =1130      WriteReachDefZone.unite(isl::union_map::from_domain(NonReachDef));1131 1132  // { [Element[] -> Scatter[]] -> Element[] }1133  isl::union_map EltZoneElt = EltZoneUniverse.domain_map();1134 1135  // { [Element[] -> Zone[]] -> [Element[] -> ReachDefId[]] }1136  isl::union_map DefZoneEltDefId = EltZoneElt.range_product(DefZone);1137 1138  // { Element[] -> [Zone[] -> ReachDefId[]] }1139  isl::union_map EltDefZone = DefZone.curry();1140 1141  // { [Element[] -> Zone[] -> [Element[] -> ReachDefId[]] }1142  isl::union_map EltZoneEltDefid = distributeDomain(EltDefZone);1143 1144  // { [Element[] -> Scatter[]] -> DomainRead[] }1145  isl::union_map Reads = AllReads.range_product(Schedule).reverse();1146 1147  // { [Element[] -> Scatter[]] -> [Element[] -> DomainRead[]] }1148  isl::union_map ReadsElt = EltZoneElt.range_product(Reads);1149 1150  // { [Element[] -> Scatter[]] -> ValInst[] }1151  isl::union_map ScatterKnown = ReadsElt.apply_range(AllReadValInst);1152 1153  // { [Element[] -> ReachDefId[]] -> ValInst[] }1154  isl::union_map DefidKnown =1155      DefZoneEltDefId.apply_domain(ScatterKnown).reverse();1156 1157  // { [Element[] -> Zone[]] -> ValInst[] }1158  return DefZoneEltDefId.apply_range(DefidKnown);1159}1160 1161isl::union_map ZoneAlgorithm::computeKnown(bool FromWrite,1162                                           bool FromRead) const {1163  isl::union_map Result = makeEmptyUnionMap();1164 1165  if (FromWrite)1166    Result = Result.unite(computeKnownFromMustWrites());1167 1168  if (FromRead)1169    Result = Result.unite(computeKnownFromLoad());1170 1171  simplify(Result);1172  return Result;1173}1174