| //===------ FlattenAlgo.cpp ------------------------------------*- C++ -*-===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is distributed under the University of Illinois Open Source |
| // License. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // Main algorithm of the FlattenSchedulePass. This is a separate file to avoid |
| // the unittest for this requiring linking against LLVM. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #include "polly/FlattenAlgo.h" |
| #include "polly/Support/ISLOStream.h" |
| #include "polly/Support/ISLTools.h" |
| #include "llvm/Support/Debug.h" |
| #define DEBUG_TYPE "polly-flatten-algo" |
| |
| using namespace polly; |
| using namespace llvm; |
| |
| namespace { |
| |
| /// Whether a dimension of a set is bounded (lower and upper) by a constant, |
| /// i.e. there are two constants Min and Max, such that every value x of the |
| /// chosen dimensions is Min <= x <= Max. |
| bool isDimBoundedByConstant(isl::set Set, unsigned dim) { |
| auto ParamDims = Set.dim(isl::dim::param); |
| Set = Set.project_out(isl::dim::param, 0, ParamDims); |
| Set = Set.project_out(isl::dim::set, 0, dim); |
| auto SetDims = Set.dim(isl::dim::set); |
| Set = Set.project_out(isl::dim::set, 1, SetDims - 1); |
| return bool(Set.is_bounded()); |
| } |
| |
| /// Whether a dimension of a set is (lower and upper) bounded by a constant or |
| /// parameters, i.e. there are two expressions Min_p and Max_p of the parameters |
| /// p, such that every value x of the chosen dimensions is |
| /// Min_p <= x <= Max_p. |
| bool isDimBoundedByParameter(isl::set Set, unsigned dim) { |
| Set = Set.project_out(isl::dim::set, 0, dim); |
| auto SetDims = Set.dim(isl::dim::set); |
| Set = Set.project_out(isl::dim::set, 1, SetDims - 1); |
| return bool(Set.is_bounded()); |
| } |
| |
| /// Whether BMap's first out-dimension is not a constant. |
| bool isVariableDim(const isl::basic_map &BMap) { |
| auto FixedVal = BMap.plain_get_val_if_fixed(isl::dim::out, 0); |
| return !FixedVal || FixedVal.is_nan(); |
| } |
| |
| /// Whether Map's first out dimension is no constant nor piecewise constant. |
| bool isVariableDim(const isl::map &Map) { |
| for (isl::basic_map BMap : Map.get_basic_map_list()) |
| if (isVariableDim(BMap)) |
| return false; |
| |
| return true; |
| } |
| |
| /// Whether UMap's first out dimension is no (piecewise) constant. |
| bool isVariableDim(const isl::union_map &UMap) { |
| for (isl::map Map : UMap.get_map_list()) |
| if (isVariableDim(Map)) |
| return false; |
| return true; |
| } |
| |
| /// Compute @p UPwAff - @p Val. |
| isl::union_pw_aff subtract(isl::union_pw_aff UPwAff, isl::val Val) { |
| if (Val.is_zero()) |
| return UPwAff; |
| |
| auto Result = isl::union_pw_aff::empty(UPwAff.get_space()); |
| isl::stat Stat = |
| UPwAff.foreach_pw_aff([=, &Result](isl::pw_aff PwAff) -> isl::stat { |
| auto ValAff = |
| isl::pw_aff(isl::set::universe(PwAff.get_space().domain()), Val); |
| auto Subtracted = PwAff.sub(ValAff); |
| Result = Result.union_add(isl::union_pw_aff(Subtracted)); |
| return isl::stat::ok(); |
| }); |
| if (Stat.is_error()) |
| return {}; |
| return Result; |
| } |
| |
| /// Compute @UPwAff * @p Val. |
| isl::union_pw_aff multiply(isl::union_pw_aff UPwAff, isl::val Val) { |
| if (Val.is_one()) |
| return UPwAff; |
| |
| auto Result = isl::union_pw_aff::empty(UPwAff.get_space()); |
| isl::stat Stat = |
| UPwAff.foreach_pw_aff([=, &Result](isl::pw_aff PwAff) -> isl::stat { |
| auto ValAff = |
| isl::pw_aff(isl::set::universe(PwAff.get_space().domain()), Val); |
| auto Multiplied = PwAff.mul(ValAff); |
| Result = Result.union_add(Multiplied); |
| return isl::stat::ok(); |
| }); |
| if (Stat.is_error()) |
| return {}; |
| return Result; |
| } |
| |
| /// Remove @p n dimensions from @p UMap's range, starting at @p first. |
| /// |
| /// It is assumed that all maps in the maps have at least the necessary number |
| /// of out dimensions. |
| isl::union_map scheduleProjectOut(const isl::union_map &UMap, unsigned first, |
| unsigned n) { |
| if (n == 0) |
| return UMap; /* isl_map_project_out would also reset the tuple, which should |
| have no effect on schedule ranges */ |
| |
| auto Result = isl::union_map::empty(UMap.get_space()); |
| for (isl::map Map : UMap.get_map_list()) { |
| auto Outprojected = Map.project_out(isl::dim::out, first, n); |
| Result = Result.add_map(Outprojected); |
| } |
| return Result; |
| } |
| |
| /// Return the number of dimensions in the input map's range. |
| /// |
| /// Because this function takes an isl_union_map, the out dimensions could be |
| /// different. We return the maximum number in this case. However, a different |
| /// number of dimensions is not supported by the other code in this file. |
| size_t scheduleScatterDims(const isl::union_map &Schedule) { |
| unsigned Dims = 0; |
| for (isl::map Map : Schedule.get_map_list()) |
| Dims = std::max(Dims, Map.dim(isl::dim::out)); |
| return Dims; |
| } |
| |
| /// Return the @p pos' range dimension, converted to an isl_union_pw_aff. |
| isl::union_pw_aff scheduleExtractDimAff(isl::union_map UMap, unsigned pos) { |
| auto SingleUMap = isl::union_map::empty(UMap.get_space()); |
| for (isl::map Map : UMap.get_map_list()) { |
| unsigned MapDims = Map.dim(isl::dim::out); |
| isl::map SingleMap = Map.project_out(isl::dim::out, 0, pos); |
| SingleMap = SingleMap.project_out(isl::dim::out, 1, MapDims - pos - 1); |
| SingleUMap = SingleUMap.add_map(SingleMap); |
| }; |
| |
| auto UAff = isl::union_pw_multi_aff(SingleUMap); |
| auto FirstMAff = isl::multi_union_pw_aff(UAff); |
| return FirstMAff.get_union_pw_aff(0); |
| } |
| |
| /// Flatten a sequence-like first dimension. |
| /// |
| /// A sequence-like scatter dimension is constant, or at least only small |
| /// variation, typically the result of ordering a sequence of different |
| /// statements. An example would be: |
| /// { Stmt_A[] -> [0, X, ...]; Stmt_B[] -> [1, Y, ...] } |
| /// to schedule all instances of Stmt_A before any instance of Stmt_B. |
| /// |
| /// To flatten, first begin with an offset of zero. Then determine the lowest |
| /// possible value of the dimension, call it "i" [In the example we start at 0]. |
| /// Considering only schedules with that value, consider only instances with |
| /// that value and determine the extent of the next dimension. Let l_X(i) and |
| /// u_X(i) its minimum (lower bound) and maximum (upper bound) value. Add them |
| /// as "Offset + X - l_X(i)" to the new schedule, then add "u_X(i) - l_X(i) + 1" |
| /// to Offset and remove all i-instances from the old schedule. Repeat with the |
| /// remaining lowest value i' until there are no instances in the old schedule |
| /// left. |
| /// The example schedule would be transformed to: |
| /// { Stmt_X[] -> [X - l_X, ...]; Stmt_B -> [l_X - u_X + 1 + Y - l_Y, ...] } |
| isl::union_map tryFlattenSequence(isl::union_map Schedule) { |
| auto IslCtx = Schedule.get_ctx(); |
| auto ScatterSet = isl::set(Schedule.range()); |
| |
| auto ParamSpace = Schedule.get_space().params(); |
| auto Dims = ScatterSet.dim(isl::dim::set); |
| assert(Dims >= 2); |
| |
| // Would cause an infinite loop. |
| if (!isDimBoundedByConstant(ScatterSet, 0)) { |
| LLVM_DEBUG(dbgs() << "Abort; dimension is not of fixed size\n"); |
| return nullptr; |
| } |
| |
| auto AllDomains = Schedule.domain(); |
| auto AllDomainsToNull = isl::union_pw_multi_aff(AllDomains); |
| |
| auto NewSchedule = isl::union_map::empty(ParamSpace); |
| auto Counter = isl::pw_aff(isl::local_space(ParamSpace.set_from_params())); |
| |
| while (!ScatterSet.is_empty()) { |
| LLVM_DEBUG(dbgs() << "Next counter:\n " << Counter << "\n"); |
| LLVM_DEBUG(dbgs() << "Remaining scatter set:\n " << ScatterSet << "\n"); |
| auto ThisSet = ScatterSet.project_out(isl::dim::set, 1, Dims - 1); |
| auto ThisFirst = ThisSet.lexmin(); |
| auto ScatterFirst = ThisFirst.add_dims(isl::dim::set, Dims - 1); |
| |
| auto SubSchedule = Schedule.intersect_range(ScatterFirst); |
| SubSchedule = scheduleProjectOut(SubSchedule, 0, 1); |
| SubSchedule = flattenSchedule(SubSchedule); |
| |
| auto SubDims = scheduleScatterDims(SubSchedule); |
| auto FirstSubSchedule = scheduleProjectOut(SubSchedule, 1, SubDims - 1); |
| auto FirstScheduleAff = scheduleExtractDimAff(FirstSubSchedule, 0); |
| auto RemainingSubSchedule = scheduleProjectOut(SubSchedule, 0, 1); |
| |
| auto FirstSubScatter = isl::set(FirstSubSchedule.range()); |
| LLVM_DEBUG(dbgs() << "Next step in sequence is:\n " << FirstSubScatter |
| << "\n"); |
| |
| if (!isDimBoundedByParameter(FirstSubScatter, 0)) { |
| LLVM_DEBUG(dbgs() << "Abort; sequence step is not bounded\n"); |
| return nullptr; |
| } |
| |
| auto FirstSubScatterMap = isl::map::from_range(FirstSubScatter); |
| |
| // isl_set_dim_max returns a strange isl_pw_aff with domain tuple_id of |
| // 'none'. It doesn't match with any space including a 0-dimensional |
| // anonymous tuple. |
| // Interesting, one can create such a set using |
| // isl_set_universe(ParamSpace). Bug? |
| auto PartMin = FirstSubScatterMap.dim_min(0); |
| auto PartMax = FirstSubScatterMap.dim_max(0); |
| auto One = isl::pw_aff(isl::set::universe(ParamSpace.set_from_params()), |
| isl::val::one(IslCtx)); |
| auto PartLen = PartMax.add(PartMin.neg()).add(One); |
| |
| auto AllPartMin = isl::union_pw_aff(PartMin).pullback(AllDomainsToNull); |
| auto FirstScheduleAffNormalized = FirstScheduleAff.sub(AllPartMin); |
| auto AllCounter = isl::union_pw_aff(Counter).pullback(AllDomainsToNull); |
| auto FirstScheduleAffWithOffset = |
| FirstScheduleAffNormalized.add(AllCounter); |
| |
| auto ScheduleWithOffset = isl::union_map(FirstScheduleAffWithOffset) |
| .flat_range_product(RemainingSubSchedule); |
| NewSchedule = NewSchedule.unite(ScheduleWithOffset); |
| |
| ScatterSet = ScatterSet.subtract(ScatterFirst); |
| Counter = Counter.add(PartLen); |
| } |
| |
| LLVM_DEBUG(dbgs() << "Sequence-flatten result is:\n " << NewSchedule |
| << "\n"); |
| return NewSchedule; |
| } |
| |
| /// Flatten a loop-like first dimension. |
| /// |
| /// A loop-like dimension is one that depends on a variable (usually a loop's |
| /// induction variable). Let the input schedule look like this: |
| /// { Stmt[i] -> [i, X, ...] } |
| /// |
| /// To flatten, we determine the largest extent of X which may not depend on the |
| /// actual value of i. Let l_X() the smallest possible value of X and u_X() its |
| /// largest value. Then, construct a new schedule |
| /// { Stmt[i] -> [i * (u_X() - l_X() + 1), ...] } |
| isl::union_map tryFlattenLoop(isl::union_map Schedule) { |
| assert(scheduleScatterDims(Schedule) >= 2); |
| |
| auto Remaining = scheduleProjectOut(Schedule, 0, 1); |
| auto SubSchedule = flattenSchedule(Remaining); |
| auto SubDims = scheduleScatterDims(SubSchedule); |
| |
| auto SubExtent = isl::set(SubSchedule.range()); |
| auto SubExtentDims = SubExtent.dim(isl::dim::param); |
| SubExtent = SubExtent.project_out(isl::dim::param, 0, SubExtentDims); |
| SubExtent = SubExtent.project_out(isl::dim::set, 1, SubDims - 1); |
| |
| if (!isDimBoundedByConstant(SubExtent, 0)) { |
| LLVM_DEBUG(dbgs() << "Abort; dimension not bounded by constant\n"); |
| return nullptr; |
| } |
| |
| auto Min = SubExtent.dim_min(0); |
| LLVM_DEBUG(dbgs() << "Min bound:\n " << Min << "\n"); |
| auto MinVal = getConstant(Min, false, true); |
| auto Max = SubExtent.dim_max(0); |
| LLVM_DEBUG(dbgs() << "Max bound:\n " << Max << "\n"); |
| auto MaxVal = getConstant(Max, true, false); |
| |
| if (!MinVal || !MaxVal || MinVal.is_nan() || MaxVal.is_nan()) { |
| LLVM_DEBUG(dbgs() << "Abort; dimension bounds could not be determined\n"); |
| return nullptr; |
| } |
| |
| auto FirstSubScheduleAff = scheduleExtractDimAff(SubSchedule, 0); |
| auto RemainingSubSchedule = scheduleProjectOut(std::move(SubSchedule), 0, 1); |
| |
| auto LenVal = MaxVal.sub(MinVal).add_ui(1); |
| auto FirstSubScheduleNormalized = subtract(FirstSubScheduleAff, MinVal); |
| |
| // TODO: Normalize FirstAff to zero (convert to isl_map, determine minimum, |
| // subtract it) |
| auto FirstAff = scheduleExtractDimAff(Schedule, 0); |
| auto Offset = multiply(FirstAff, LenVal); |
| auto Index = FirstSubScheduleNormalized.add(Offset); |
| auto IndexMap = isl::union_map(Index); |
| |
| auto Result = IndexMap.flat_range_product(RemainingSubSchedule); |
| LLVM_DEBUG(dbgs() << "Loop-flatten result is:\n " << Result << "\n"); |
| return Result; |
| } |
| } // anonymous namespace |
| |
| isl::union_map polly::flattenSchedule(isl::union_map Schedule) { |
| auto Dims = scheduleScatterDims(Schedule); |
| LLVM_DEBUG(dbgs() << "Recursive schedule to process:\n " << Schedule |
| << "\n"); |
| |
| // Base case; no dimensions left |
| if (Dims == 0) { |
| // TODO: Add one dimension? |
| return Schedule; |
| } |
| |
| // Base case; already one-dimensional |
| if (Dims == 1) |
| return Schedule; |
| |
| // Fixed dimension; no need to preserve variabledness. |
| if (!isVariableDim(Schedule)) { |
| LLVM_DEBUG(dbgs() << "Fixed dimension; try sequence flattening\n"); |
| auto NewScheduleSequence = tryFlattenSequence(Schedule); |
| if (NewScheduleSequence) |
| return NewScheduleSequence; |
| } |
| |
| // Constant stride |
| LLVM_DEBUG(dbgs() << "Try loop flattening\n"); |
| auto NewScheduleLoop = tryFlattenLoop(Schedule); |
| if (NewScheduleLoop) |
| return NewScheduleLoop; |
| |
| // Try again without loop condition (may blow up the number of pieces!!) |
| LLVM_DEBUG(dbgs() << "Try sequence flattening again\n"); |
| auto NewScheduleSequence = tryFlattenSequence(Schedule); |
| if (NewScheduleSequence) |
| return NewScheduleSequence; |
| |
| // Cannot flatten |
| return Schedule; |
| } |