polly/lib/Transform/FlattenAlgo.cpp

   1 //===------ FlattenAlgo.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-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // Main algorithm of the FlattenSchedulePass. This is a separate file to avoid
  10 // the unittest for this requiring linking against LLVM.
  11 //
  12 //===----------------------------------------------------------------------===//
  13
  14 #include "polly/FlattenAlgo.h"
  15 #include "polly/Support/ISLOStream.h"
  16 #include "polly/Support/ISLTools.h"
  17 #include "llvm/Support/Debug.h"
  18 #define DEBUG_TYPE "polly-flatten-algo"
  19
  20 using namespace polly;
  21 using namespace llvm;
  22
  23 namespace {
  24
  25 /// Whether a dimension of a set is bounded (lower and upper) by a constant,
  26 /// i.e. there are two constants Min and Max, such that every value x of the
  27 /// chosen dimensions is Min <= x <= Max.
  28 bool isDimBoundedByConstant(isl::set Set, unsigned dim) {
  29   auto ParamDims = unsignedFromIslSize(Set.dim(isl::dim::param));
  30   Set = Set.project_out(isl::dim::param, 0, ParamDims);
  31   Set = Set.project_out(isl::dim::set, 0, dim);
  32   auto SetDims = unsignedFromIslSize(Set.tuple_dim());
  33   assert(SetDims >= 1);
  34   Set = Set.project_out(isl::dim::set, 1, SetDims - 1);
  35   return bool(Set.is_bounded());
  36 }
  37
  38 /// Whether a dimension of a set is (lower and upper) bounded by a constant or
  39 /// parameters, i.e. there are two expressions Min_p and Max_p of the parameters
  40 /// p, such that every value x of the chosen dimensions is
  41 /// Min_p <= x <= Max_p.
  42 bool isDimBoundedByParameter(isl::set Set, unsigned dim) {
  43   Set = Set.project_out(isl::dim::set, 0, dim);
  44   auto SetDims = unsignedFromIslSize(Set.tuple_dim());
  45   assert(SetDims >= 1);
  46   Set = Set.project_out(isl::dim::set, 1, SetDims - 1);
  47   return bool(Set.is_bounded());
  48 }
  49
  50 /// Whether BMap's first out-dimension is not a constant.
  51 bool isVariableDim(const isl::basic_map &BMap) {
  52   auto FixedVal = BMap.plain_get_val_if_fixed(isl::dim::out, 0);
  53   return FixedVal.is_null() || FixedVal.is_nan();
  54 }
  55
  56 /// Whether Map's first out dimension is no constant nor piecewise constant.
  57 bool isVariableDim(const isl::map &Map) {
  58   for (isl::basic_map BMap : Map.get_basic_map_list())
  59     if (isVariableDim(BMap))
  60       return false;
  61
  62   return true;
  63 }
  64
  65 /// Whether UMap's first out dimension is no (piecewise) constant.
  66 bool isVariableDim(const isl::union_map &UMap) {
  67   for (isl::map Map : UMap.get_map_list())
  68     if (isVariableDim(Map))
  69       return false;
  70   return true;
  71 }
  72
  73 /// Compute @p UPwAff - @p Val.
  74 isl::union_pw_aff subtract(isl::union_pw_aff UPwAff, isl::val Val) {
  75   if (Val.is_zero())
  76     return UPwAff;
  77
  78   auto Result = isl::union_pw_aff::empty(UPwAff.get_space());
  79   isl::stat Stat =
  80       UPwAff.foreach_pw_aff([=, &Result](isl::pw_aff PwAff) -> isl::stat {
  81         auto ValAff =
  82             isl::pw_aff(isl::set::universe(PwAff.get_space().domain()), Val);
  83         auto Subtracted = PwAff.sub(ValAff);
  84         Result = Result.union_add(isl::union_pw_aff(Subtracted));
  85         return isl::stat::ok();
  86       });
  87   if (Stat.is_error())
  88     return {};
  89   return Result;
  90 }
  91
  92 /// Compute @UPwAff * @p Val.
  93 isl::union_pw_aff multiply(isl::union_pw_aff UPwAff, isl::val Val) {
  94   if (Val.is_one())
  95     return UPwAff;
  96
  97   auto Result = isl::union_pw_aff::empty(UPwAff.get_space());
  98   isl::stat Stat =
  99       UPwAff.foreach_pw_aff([=, &Result](isl::pw_aff PwAff) -> isl::stat {
 100         auto ValAff =
 101             isl::pw_aff(isl::set::universe(PwAff.get_space().domain()), Val);
 102         auto Multiplied = PwAff.mul(ValAff);
 103         Result = Result.union_add(Multiplied);
 104         return isl::stat::ok();
 105       });
 106   if (Stat.is_error())
 107     return {};
 108   return Result;
 109 }
 110
 111 /// Remove @p n dimensions from @p UMap's range, starting at @p first.
 112 ///
 113 /// It is assumed that all maps in the maps have at least the necessary number
 114 /// of out dimensions.
 115 isl::union_map scheduleProjectOut(const isl::union_map &UMap, unsigned first,
 116                                   unsigned n) {
 117   if (n == 0)
 118     return UMap; /* isl_map_project_out would also reset the tuple, which should
 119                     have no effect on schedule ranges */
 120
 121   auto Result = isl::union_map::empty(UMap.ctx());
 122   for (isl::map Map : UMap.get_map_list()) {
 123     auto Outprojected = Map.project_out(isl::dim::out, first, n);
 124     Result = Result.unite(Outprojected);
 125   }
 126   return Result;
 127 }
 128
 129 /// Return the @p pos' range dimension, converted to an isl_union_pw_aff.
 130 isl::union_pw_aff scheduleExtractDimAff(isl::union_map UMap, unsigned pos) {
 131   auto SingleUMap = isl::union_map::empty(UMap.ctx());
 132   for (isl::map Map : UMap.get_map_list()) {
 133     unsigned MapDims = unsignedFromIslSize(Map.range_tuple_dim());
 134     assert(MapDims > pos);
 135     isl::map SingleMap = Map.project_out(isl::dim::out, 0, pos);
 136     SingleMap = SingleMap.project_out(isl::dim::out, 1, MapDims - pos - 1);
 137     SingleUMap = SingleUMap.unite(SingleMap);
 138   };
 139
 140   auto UAff = isl::union_pw_multi_aff(SingleUMap);
 141   auto FirstMAff = isl::multi_union_pw_aff(UAff);
 142   return FirstMAff.at(0);
 143 }
 144
 145 /// Flatten a sequence-like first dimension.
 146 ///
 147 /// A sequence-like scatter dimension is constant, or at least only small
 148 /// variation, typically the result of ordering a sequence of different
 149 /// statements. An example would be:
 150 ///   { Stmt_A[] -> [0, X, ...]; Stmt_B[] -> [1, Y, ...] }
 151 /// to schedule all instances of Stmt_A before any instance of Stmt_B.
 152 ///
 153 /// To flatten, first begin with an offset of zero. Then determine the lowest
 154 /// possible value of the dimension, call it "i" [In the example we start at 0].
 155 /// Considering only schedules with that value, consider only instances with
 156 /// that value and determine the extent of the next dimension. Let l_X(i) and
 157 /// u_X(i) its minimum (lower bound) and maximum (upper bound) value. Add them
 158 /// as "Offset + X - l_X(i)" to the new schedule, then add "u_X(i) - l_X(i) + 1"
 159 /// to Offset and remove all i-instances from the old schedule. Repeat with the
 160 /// remaining lowest value i' until there are no instances in the old schedule
 161 /// left.
 162 /// The example schedule would be transformed to:
 163 ///   { Stmt_X[] -> [X - l_X, ...]; Stmt_B -> [l_X - u_X + 1 + Y - l_Y, ...] }
 164 isl::union_map tryFlattenSequence(isl::union_map Schedule) {
 165   auto IslCtx = Schedule.ctx();
 166   auto ScatterSet = isl::set(Schedule.range());
 167
 168   auto ParamSpace = Schedule.get_space().params();
 169   auto Dims = unsignedFromIslSize(ScatterSet.tuple_dim());
 170   assert(Dims >= 2u);
 171
 172   // Would cause an infinite loop.
 173   if (!isDimBoundedByConstant(ScatterSet, 0)) {
 174     LLVM_DEBUG(dbgs() << "Abort; dimension is not of fixed size\n");
 175     return {};
 176   }
 177
 178   auto AllDomains = Schedule.domain();
 179   auto AllDomainsToNull = isl::union_pw_multi_aff(AllDomains);
 180
 181   auto NewSchedule = isl::union_map::empty(ParamSpace.ctx());
 182   auto Counter = isl::pw_aff(isl::local_space(ParamSpace.set_from_params()));
 183
 184   while (!ScatterSet.is_empty()) {
 185     LLVM_DEBUG(dbgs() << "Next counter:\n  " << Counter << "\n");
 186     LLVM_DEBUG(dbgs() << "Remaining scatter set:\n  " << ScatterSet << "\n");
 187     auto ThisSet = ScatterSet.project_out(isl::dim::set, 1, Dims - 1);
 188     auto ThisFirst = ThisSet.lexmin();
 189     auto ScatterFirst = ThisFirst.add_dims(isl::dim::set, Dims - 1);
 190
 191     auto SubSchedule = Schedule.intersect_range(ScatterFirst);
 192     SubSchedule = scheduleProjectOut(SubSchedule, 0, 1);
 193     SubSchedule = flattenSchedule(SubSchedule);
 194
 195     unsigned SubDims = getNumScatterDims(SubSchedule);
 196     assert(SubDims >= 1);
 197     auto FirstSubSchedule = scheduleProjectOut(SubSchedule, 1, SubDims - 1);
 198     auto FirstScheduleAff = scheduleExtractDimAff(FirstSubSchedule, 0);
 199     auto RemainingSubSchedule = scheduleProjectOut(SubSchedule, 0, 1);
 200
 201     auto FirstSubScatter = isl::set(FirstSubSchedule.range());
 202     LLVM_DEBUG(dbgs() << "Next step in sequence is:\n  " << FirstSubScatter
 203                       << "\n");
 204
 205     if (!isDimBoundedByParameter(FirstSubScatter, 0)) {
 206       LLVM_DEBUG(dbgs() << "Abort; sequence step is not bounded\n");
 207       return {};
 208     }
 209
 210     auto FirstSubScatterMap = isl::map::from_range(FirstSubScatter);
 211
 212     // isl_set_dim_max returns a strange isl_pw_aff with domain tuple_id of
 213     // 'none'. It doesn't match with any space including a 0-dimensional
 214     // anonymous tuple.
 215     // Interesting, one can create such a set using
 216     // isl_set_universe(ParamSpace). Bug?
 217     auto PartMin = FirstSubScatterMap.dim_min(0);
 218     auto PartMax = FirstSubScatterMap.dim_max(0);
 219     auto One = isl::pw_aff(isl::set::universe(ParamSpace.set_from_params()),
 220                            isl::val::one(IslCtx));
 221     auto PartLen = PartMax.add(PartMin.neg()).add(One);
 222
 223     auto AllPartMin = isl::union_pw_aff(PartMin).pullback(AllDomainsToNull);
 224     auto FirstScheduleAffNormalized = FirstScheduleAff.sub(AllPartMin);
 225     auto AllCounter = isl::union_pw_aff(Counter).pullback(AllDomainsToNull);
 226     auto FirstScheduleAffWithOffset =
 227         FirstScheduleAffNormalized.add(AllCounter);
 228
 229     auto ScheduleWithOffset =
 230         isl::union_map::from(
 231             isl::union_pw_multi_aff(FirstScheduleAffWithOffset))
 232             .flat_range_product(RemainingSubSchedule);
 233     NewSchedule = NewSchedule.unite(ScheduleWithOffset);
 234
 235     ScatterSet = ScatterSet.subtract(ScatterFirst);
 236     Counter = Counter.add(PartLen);
 237   }
 238
 239   LLVM_DEBUG(dbgs() << "Sequence-flatten result is:\n  " << NewSchedule
 240                     << "\n");
 241   return NewSchedule;
 242 }
 243
 244 /// Flatten a loop-like first dimension.
 245 ///
 246 /// A loop-like dimension is one that depends on a variable (usually a loop's
 247 /// induction variable). Let the input schedule look like this:
 248 ///   { Stmt[i] -> [i, X, ...] }
 249 ///
 250 /// To flatten, we determine the largest extent of X which may not depend on the
 251 /// actual value of i. Let l_X() the smallest possible value of X and u_X() its
 252 /// largest value. Then, construct a new schedule
 253 ///   { Stmt[i] -> [i * (u_X() - l_X() + 1), ...] }
 254 isl::union_map tryFlattenLoop(isl::union_map Schedule) {
 255   assert(getNumScatterDims(Schedule) >= 2);
 256
 257   auto Remaining = scheduleProjectOut(Schedule, 0, 1);
 258   auto SubSchedule = flattenSchedule(Remaining);
 259   unsigned SubDims = getNumScatterDims(SubSchedule);
 260
 261   assert(SubDims >= 1);
 262
 263   auto SubExtent = isl::set(SubSchedule.range());
 264   auto SubExtentDims = unsignedFromIslSize(SubExtent.dim(isl::dim::param));
 265   SubExtent = SubExtent.project_out(isl::dim::param, 0, SubExtentDims);
 266   SubExtent = SubExtent.project_out(isl::dim::set, 1, SubDims - 1);
 267
 268   if (!isDimBoundedByConstant(SubExtent, 0)) {
 269     LLVM_DEBUG(dbgs() << "Abort; dimension not bounded by constant\n");
 270     return {};
 271   }
 272
 273   auto Min = SubExtent.dim_min(0);
 274   LLVM_DEBUG(dbgs() << "Min bound:\n  " << Min << "\n");
 275   auto MinVal = getConstant(Min, false, true);
 276   auto Max = SubExtent.dim_max(0);
 277   LLVM_DEBUG(dbgs() << "Max bound:\n  " << Max << "\n");
 278   auto MaxVal = getConstant(Max, true, false);
 279
 280   if (MinVal.is_null() || MaxVal.is_null() || MinVal.is_nan() ||
 281       MaxVal.is_nan()) {
 282     LLVM_DEBUG(dbgs() << "Abort; dimension bounds could not be determined\n");
 283     return {};
 284   }
 285
 286   auto FirstSubScheduleAff = scheduleExtractDimAff(SubSchedule, 0);
 287   auto RemainingSubSchedule = scheduleProjectOut(std::move(SubSchedule), 0, 1);
 288
 289   auto LenVal = MaxVal.sub(MinVal).add(1);
 290   auto FirstSubScheduleNormalized = subtract(FirstSubScheduleAff, MinVal);
 291
 292   // TODO: Normalize FirstAff to zero (convert to isl_map, determine minimum,
 293   // subtract it)
 294   auto FirstAff = scheduleExtractDimAff(Schedule, 0);
 295   auto Offset = multiply(FirstAff, LenVal);
 296   isl::union_pw_multi_aff Index = FirstSubScheduleNormalized.add(Offset);
 297   auto IndexMap = isl::union_map::from(Index);
 298
 299   auto Result = IndexMap.flat_range_product(RemainingSubSchedule);
 300   LLVM_DEBUG(dbgs() << "Loop-flatten result is:\n  " << Result << "\n");
 301   return Result;
 302 }
 303 } // anonymous namespace
 304
 305 isl::union_map polly::flattenSchedule(isl::union_map Schedule) {
 306   unsigned Dims = getNumScatterDims(Schedule);
 307   LLVM_DEBUG(dbgs() << "Recursive schedule to process:\n  " << Schedule
 308                     << "\n");
 309
 310   // Base case; no dimensions left
 311   if (Dims == 0) {
 312     // TODO: Add one dimension?
 313     return Schedule;
 314   }
 315
 316   // Base case; already one-dimensional
 317   if (Dims == 1)
 318     return Schedule;
 319
 320   // Fixed dimension; no need to preserve variabledness.
 321   if (!isVariableDim(Schedule)) {
 322     LLVM_DEBUG(dbgs() << "Fixed dimension; try sequence flattening\n");
 323     auto NewScheduleSequence = tryFlattenSequence(Schedule);
 324     if (!NewScheduleSequence.is_null())
 325       return NewScheduleSequence;
 326   }
 327
 328   // Constant stride
 329   LLVM_DEBUG(dbgs() << "Try loop flattening\n");
 330   auto NewScheduleLoop = tryFlattenLoop(Schedule);
 331   if (!NewScheduleLoop.is_null())
 332     return NewScheduleLoop;
 333
 334   // Try again without loop condition (may blow up the number of pieces!!)
 335   LLVM_DEBUG(dbgs() << "Try sequence flattening again\n");
 336   auto NewScheduleSequence = tryFlattenSequence(Schedule);
 337   if (!NewScheduleSequence.is_null())
 338     return NewScheduleSequence;
 339
 340   // Cannot flatten
 341   return Schedule;
 342 }