| //===------ ISLTools.cpp ----------------------------------------*- C++ -*-===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is distributed under the University of Illinois Open Source |
| // License. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // Tools, utilities, helpers and extensions useful in conjunction with the |
| // Integer Set Library (isl). |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #include "polly/Support/ISLTools.h" |
| |
| using namespace polly; |
| |
| namespace { |
| /// Create a map that shifts one dimension by an offset. |
| /// |
| /// Example: |
| /// makeShiftDimAff({ [i0, i1] -> [o0, o1] }, 1, -2) |
| /// = { [i0, i1] -> [i0, i1 - 1] } |
| /// |
| /// @param Space The map space of the result. Must have equal number of in- and |
| /// out-dimensions. |
| /// @param Pos Position to shift. |
| /// @param Amount Value added to the shifted dimension. |
| /// |
| /// @return An isl_multi_aff for the map with this shifted dimension. |
| isl::multi_aff makeShiftDimAff(isl::space Space, int Pos, int Amount) { |
| auto Identity = give(isl_multi_aff_identity(Space.take())); |
| if (Amount == 0) |
| return Identity; |
| auto ShiftAff = give(isl_multi_aff_get_aff(Identity.keep(), Pos)); |
| ShiftAff = give(isl_aff_set_constant_si(ShiftAff.take(), Amount)); |
| return give(isl_multi_aff_set_aff(Identity.take(), Pos, ShiftAff.take())); |
| } |
| |
| /// Construct a map that swaps two nested tuples. |
| /// |
| /// @param FromSpace1 { Space1[] } |
| /// @param FromSpace2 { Space2[] } |
| /// |
| /// @return { [Space1[] -> Space2[]] -> [Space2[] -> Space1[]] } |
| isl::basic_map makeTupleSwapBasicMap(isl::space FromSpace1, |
| isl::space FromSpace2) { |
| assert(isl_space_is_set(FromSpace1.keep()) != isl_bool_false); |
| assert(isl_space_is_set(FromSpace2.keep()) != isl_bool_false); |
| |
| auto Dims1 = isl_space_dim(FromSpace1.keep(), isl_dim_set); |
| auto Dims2 = isl_space_dim(FromSpace2.keep(), isl_dim_set); |
| auto FromSpace = give(isl_space_wrap(isl_space_map_from_domain_and_range( |
| FromSpace1.copy(), FromSpace2.copy()))); |
| auto ToSpace = give(isl_space_wrap(isl_space_map_from_domain_and_range( |
| FromSpace2.take(), FromSpace1.take()))); |
| auto MapSpace = give( |
| isl_space_map_from_domain_and_range(FromSpace.take(), ToSpace.take())); |
| |
| auto Result = give(isl_basic_map_universe(MapSpace.take())); |
| for (auto i = Dims1 - Dims1; i < Dims1; i += 1) { |
| Result = give(isl_basic_map_equate(Result.take(), isl_dim_in, i, |
| isl_dim_out, Dims2 + i)); |
| } |
| for (auto i = Dims2 - Dims2; i < Dims2; i += 1) { |
| Result = give(isl_basic_map_equate(Result.take(), isl_dim_in, Dims1 + i, |
| isl_dim_out, i)); |
| } |
| |
| return Result; |
| } |
| |
| /// Like makeTupleSwapBasicMap(isl::space,isl::space), but returns |
| /// an isl_map. |
| isl::map makeTupleSwapMap(isl::space FromSpace1, isl::space FromSpace2) { |
| auto BMapResult = |
| makeTupleSwapBasicMap(std::move(FromSpace1), std::move(FromSpace2)); |
| return give(isl_map_from_basic_map(BMapResult.take())); |
| } |
| } // anonymous namespace |
| |
| isl::map polly::beforeScatter(isl::map Map, bool Strict) { |
| auto RangeSpace = give(isl_space_range(isl_map_get_space(Map.keep()))); |
| auto ScatterRel = give(Strict ? isl_map_lex_gt(RangeSpace.take()) |
| : isl_map_lex_ge(RangeSpace.take())); |
| return give(isl_map_apply_range(Map.take(), ScatterRel.take())); |
| } |
| |
| isl::union_map polly::beforeScatter(isl::union_map UMap, bool Strict) { |
| auto Result = give(isl_union_map_empty(isl_union_map_get_space(UMap.keep()))); |
| UMap.foreach_map([=, &Result](isl::map Map) -> isl::stat { |
| auto After = beforeScatter(Map, Strict); |
| Result = give(isl_union_map_add_map(Result.take(), After.take())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::map polly::afterScatter(isl::map Map, bool Strict) { |
| auto RangeSpace = give(isl_space_range(isl_map_get_space(Map.keep()))); |
| auto ScatterRel = give(Strict ? isl_map_lex_lt(RangeSpace.take()) |
| : isl_map_lex_le(RangeSpace.take())); |
| return give(isl_map_apply_range(Map.take(), ScatterRel.take())); |
| } |
| |
| isl::union_map polly::afterScatter(const isl::union_map &UMap, bool Strict) { |
| auto Result = give(isl_union_map_empty(isl_union_map_get_space(UMap.keep()))); |
| UMap.foreach_map([=, &Result](isl::map Map) -> isl::stat { |
| auto After = afterScatter(Map, Strict); |
| Result = give(isl_union_map_add_map(Result.take(), After.take())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::map polly::betweenScatter(isl::map From, isl::map To, bool InclFrom, |
| bool InclTo) { |
| auto AfterFrom = afterScatter(From, !InclFrom); |
| auto BeforeTo = beforeScatter(To, !InclTo); |
| |
| return give(isl_map_intersect(AfterFrom.take(), BeforeTo.take())); |
| } |
| |
| isl::union_map polly::betweenScatter(isl::union_map From, isl::union_map To, |
| bool InclFrom, bool InclTo) { |
| auto AfterFrom = afterScatter(From, !InclFrom); |
| auto BeforeTo = beforeScatter(To, !InclTo); |
| |
| return give(isl_union_map_intersect(AfterFrom.take(), BeforeTo.take())); |
| } |
| |
| isl::map polly::singleton(isl::union_map UMap, isl::space ExpectedSpace) { |
| if (!UMap) |
| return nullptr; |
| |
| if (isl_union_map_n_map(UMap.keep()) == 0) |
| return give(isl_map_empty(ExpectedSpace.take())); |
| |
| auto Result = give(isl_map_from_union_map(UMap.take())); |
| assert(!Result || isl_space_has_equal_tuples( |
| give(isl_map_get_space(Result.keep())).keep(), |
| ExpectedSpace.keep()) == isl_bool_true); |
| return Result; |
| } |
| |
| isl::set polly::singleton(isl::union_set USet, isl::space ExpectedSpace) { |
| if (!USet) |
| return nullptr; |
| |
| if (isl_union_set_n_set(USet.keep()) == 0) |
| return give(isl_set_empty(ExpectedSpace.copy())); |
| |
| auto Result = give(isl_set_from_union_set(USet.take())); |
| assert(!Result || isl_space_has_equal_tuples( |
| give(isl_set_get_space(Result.keep())).keep(), |
| ExpectedSpace.keep()) == isl_bool_true); |
| return Result; |
| } |
| |
| unsigned polly::getNumScatterDims(const isl::union_map &Schedule) { |
| unsigned Dims = 0; |
| Schedule.foreach_map([&Dims](isl::map Map) -> isl::stat { |
| Dims = std::max(Dims, isl_map_dim(Map.keep(), isl_dim_out)); |
| return isl::stat::ok; |
| }); |
| return Dims; |
| } |
| |
| isl::space polly::getScatterSpace(const isl::union_map &Schedule) { |
| if (!Schedule) |
| return nullptr; |
| auto Dims = getNumScatterDims(Schedule); |
| auto ScatterSpace = |
| give(isl_space_set_from_params(isl_union_map_get_space(Schedule.keep()))); |
| return give(isl_space_add_dims(ScatterSpace.take(), isl_dim_set, Dims)); |
| } |
| |
| isl::union_map polly::makeIdentityMap(const isl::union_set &USet, |
| bool RestrictDomain) { |
| auto Result = give(isl_union_map_empty(isl_union_set_get_space(USet.keep()))); |
| USet.foreach_set([=, &Result](isl::set Set) -> isl::stat { |
| auto IdentityMap = give(isl_map_identity( |
| isl_space_map_from_set(isl_set_get_space(Set.keep())))); |
| if (RestrictDomain) |
| IdentityMap = |
| give(isl_map_intersect_domain(IdentityMap.take(), Set.take())); |
| Result = give(isl_union_map_add_map(Result.take(), IdentityMap.take())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::map polly::reverseDomain(isl::map Map) { |
| auto DomSpace = |
| give(isl_space_unwrap(isl_space_domain(isl_map_get_space(Map.keep())))); |
| auto Space1 = give(isl_space_domain(DomSpace.copy())); |
| auto Space2 = give(isl_space_range(DomSpace.take())); |
| auto Swap = makeTupleSwapMap(std::move(Space1), std::move(Space2)); |
| return give(isl_map_apply_domain(Map.take(), Swap.take())); |
| } |
| |
| isl::union_map polly::reverseDomain(const isl::union_map &UMap) { |
| auto Result = give(isl_union_map_empty(isl_union_map_get_space(UMap.keep()))); |
| UMap.foreach_map([=, &Result](isl::map Map) -> isl::stat { |
| auto Reversed = reverseDomain(std::move(Map)); |
| Result = give(isl_union_map_add_map(Result.take(), Reversed.take())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::set polly::shiftDim(isl::set Set, int Pos, int Amount) { |
| int NumDims = isl_set_dim(Set.keep(), isl_dim_set); |
| if (Pos < 0) |
| Pos = NumDims + Pos; |
| assert(Pos < NumDims && "Dimension index must be in range"); |
| auto Space = give(isl_set_get_space(Set.keep())); |
| Space = give(isl_space_map_from_domain_and_range(Space.copy(), Space.copy())); |
| auto Translator = makeShiftDimAff(std::move(Space), Pos, Amount); |
| auto TranslatorMap = give(isl_map_from_multi_aff(Translator.take())); |
| return give(isl_set_apply(Set.take(), TranslatorMap.take())); |
| } |
| |
| isl::union_set polly::shiftDim(isl::union_set USet, int Pos, int Amount) { |
| auto Result = give(isl_union_set_empty(isl_union_set_get_space(USet.keep()))); |
| USet.foreach_set([=, &Result](isl::set Set) -> isl::stat { |
| auto Shifted = shiftDim(Set, Pos, Amount); |
| Result = give(isl_union_set_add_set(Result.take(), Shifted.take())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::map polly::shiftDim(isl::map Map, isl::dim Dim, int Pos, int Amount) { |
| int NumDims = Map.dim(Dim); |
| if (Pos < 0) |
| Pos = NumDims + Pos; |
| assert(Pos < NumDims && "Dimension index must be in range"); |
| auto Space = give(isl_map_get_space(Map.keep())); |
| switch (Dim) { |
| case isl::dim::in: |
| Space = std::move(Space).domain(); |
| break; |
| case isl::dim::out: |
| Space = give(isl_space_range(Space.take())); |
| break; |
| default: |
| llvm_unreachable("Unsupported value for 'dim'"); |
| } |
| Space = give(isl_space_map_from_domain_and_range(Space.copy(), Space.copy())); |
| auto Translator = makeShiftDimAff(std::move(Space), Pos, Amount); |
| auto TranslatorMap = give(isl_map_from_multi_aff(Translator.take())); |
| switch (Dim) { |
| case isl::dim::in: |
| return Map.apply_domain(TranslatorMap); |
| case isl::dim::out: |
| return Map.apply_range(TranslatorMap); |
| default: |
| llvm_unreachable("Unsupported value for 'dim'"); |
| } |
| } |
| |
| isl::union_map polly::shiftDim(isl::union_map UMap, isl::dim Dim, int Pos, |
| int Amount) { |
| auto Result = isl::union_map::empty(UMap.get_space()); |
| |
| UMap.foreach_map([=, &Result](isl::map Map) -> isl::stat { |
| auto Shifted = shiftDim(Map, Dim, Pos, Amount); |
| Result = std::move(Result).add_map(Shifted); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| void polly::simplify(isl::set &Set) { |
| Set = give(isl_set_compute_divs(Set.take())); |
| Set = give(isl_set_detect_equalities(Set.take())); |
| Set = give(isl_set_coalesce(Set.take())); |
| } |
| |
| void polly::simplify(isl::union_set &USet) { |
| USet = give(isl_union_set_compute_divs(USet.take())); |
| USet = give(isl_union_set_detect_equalities(USet.take())); |
| USet = give(isl_union_set_coalesce(USet.take())); |
| } |
| |
| void polly::simplify(isl::map &Map) { |
| Map = give(isl_map_compute_divs(Map.take())); |
| Map = give(isl_map_detect_equalities(Map.take())); |
| Map = give(isl_map_coalesce(Map.take())); |
| } |
| |
| void polly::simplify(isl::union_map &UMap) { |
| UMap = give(isl_union_map_compute_divs(UMap.take())); |
| UMap = give(isl_union_map_detect_equalities(UMap.take())); |
| UMap = give(isl_union_map_coalesce(UMap.take())); |
| } |
| |
| isl::union_map polly::computeReachingWrite(isl::union_map Schedule, |
| isl::union_map Writes, bool Reverse, |
| bool InclPrevDef, bool InclNextDef) { |
| |
| // { Scatter[] } |
| auto ScatterSpace = getScatterSpace(Schedule); |
| |
| // { ScatterRead[] -> ScatterWrite[] } |
| isl::map Relation; |
| if (Reverse) |
| Relation = give(InclPrevDef ? isl_map_lex_lt(ScatterSpace.take()) |
| : isl_map_lex_le(ScatterSpace.take())); |
| else |
| Relation = give(InclNextDef ? isl_map_lex_gt(ScatterSpace.take()) |
| : isl_map_lex_ge(ScatterSpace.take())); |
| |
| // { ScatterWrite[] -> [ScatterRead[] -> ScatterWrite[]] } |
| auto RelationMap = give(isl_map_reverse(isl_map_range_map(Relation.take()))); |
| |
| // { Element[] -> ScatterWrite[] } |
| auto WriteAction = |
| give(isl_union_map_apply_domain(Schedule.copy(), Writes.take())); |
| |
| // { ScatterWrite[] -> Element[] } |
| auto WriteActionRev = give(isl_union_map_reverse(WriteAction.copy())); |
| |
| // { Element[] -> [ScatterUse[] -> ScatterWrite[]] } |
| auto DefSchedRelation = give(isl_union_map_apply_domain( |
| isl_union_map_from_map(RelationMap.take()), WriteActionRev.take())); |
| |
| // For each element, at every point in time, map to the times of previous |
| // definitions. { [Element[] -> ScatterRead[]] -> ScatterWrite[] } |
| auto ReachableWrites = give(isl_union_map_uncurry(DefSchedRelation.take())); |
| if (Reverse) |
| ReachableWrites = give(isl_union_map_lexmin(ReachableWrites.copy())); |
| else |
| ReachableWrites = give(isl_union_map_lexmax(ReachableWrites.copy())); |
| |
| // { [Element[] -> ScatterWrite[]] -> ScatterWrite[] } |
| auto SelfUse = give(isl_union_map_range_map(WriteAction.take())); |
| |
| if (InclPrevDef && InclNextDef) { |
| // Add the Def itself to the solution. |
| ReachableWrites = |
| give(isl_union_map_union(ReachableWrites.take(), SelfUse.take())); |
| ReachableWrites = give(isl_union_map_coalesce(ReachableWrites.take())); |
| } else if (!InclPrevDef && !InclNextDef) { |
| // Remove Def itself from the solution. |
| ReachableWrites = |
| give(isl_union_map_subtract(ReachableWrites.take(), SelfUse.take())); |
| } |
| |
| // { [Element[] -> ScatterRead[]] -> Domain[] } |
| auto ReachableWriteDomain = give(isl_union_map_apply_range( |
| ReachableWrites.take(), isl_union_map_reverse(Schedule.take()))); |
| |
| return ReachableWriteDomain; |
| } |
| |
| isl::union_map |
| polly::computeArrayUnused(isl::union_map Schedule, isl::union_map Writes, |
| isl::union_map Reads, bool ReadEltInSameInst, |
| bool IncludeLastRead, bool IncludeWrite) { |
| // { Element[] -> Scatter[] } |
| auto ReadActions = |
| give(isl_union_map_apply_domain(Schedule.copy(), Reads.take())); |
| auto WriteActions = |
| give(isl_union_map_apply_domain(Schedule.copy(), Writes.copy())); |
| |
| // { [Element[] -> Scatter[] } |
| auto AfterReads = afterScatter(ReadActions, ReadEltInSameInst); |
| auto WritesBeforeAnyReads = |
| give(isl_union_map_subtract(WriteActions.take(), AfterReads.take())); |
| auto BeforeWritesBeforeAnyReads = |
| beforeScatter(WritesBeforeAnyReads, !IncludeWrite); |
| |
| // { [Element[] -> DomainWrite[]] -> Scatter[] } |
| auto EltDomWrites = give(isl_union_map_apply_range( |
| isl_union_map_range_map(isl_union_map_reverse(Writes.copy())), |
| Schedule.copy())); |
| |
| // { [Element[] -> Scatter[]] -> DomainWrite[] } |
| auto ReachingOverwrite = computeReachingWrite( |
| Schedule, Writes, true, ReadEltInSameInst, !ReadEltInSameInst); |
| |
| // { [Element[] -> Scatter[]] -> DomainWrite[] } |
| auto ReadsOverwritten = give(isl_union_map_intersect_domain( |
| ReachingOverwrite.take(), isl_union_map_wrap(ReadActions.take()))); |
| |
| // { [Element[] -> DomainWrite[]] -> Scatter[] } |
| auto ReadsOverwrittenRotated = give(isl_union_map_reverse( |
| isl_union_map_curry(reverseDomain(ReadsOverwritten).take()))); |
| auto LastOverwrittenRead = |
| give(isl_union_map_lexmax(ReadsOverwrittenRotated.take())); |
| |
| // { [Element[] -> DomainWrite[]] -> Scatter[] } |
| auto BetweenLastReadOverwrite = betweenScatter( |
| LastOverwrittenRead, EltDomWrites, IncludeLastRead, IncludeWrite); |
| |
| return give(isl_union_map_union( |
| BeforeWritesBeforeAnyReads.take(), |
| isl_union_map_domain_factor_domain(BetweenLastReadOverwrite.take()))); |
| } |
| |
| isl::union_set polly::convertZoneToTimepoints(isl::union_set Zone, |
| bool InclStart, bool InclEnd) { |
| if (!InclStart && InclEnd) |
| return Zone; |
| |
| auto ShiftedZone = shiftDim(Zone, -1, -1); |
| if (InclStart && !InclEnd) |
| return ShiftedZone; |
| else if (!InclStart && !InclEnd) |
| return give(isl_union_set_intersect(Zone.take(), ShiftedZone.take())); |
| |
| assert(InclStart && InclEnd); |
| return give(isl_union_set_union(Zone.take(), ShiftedZone.take())); |
| } |
| |
| isl::union_map polly::convertZoneToTimepoints(isl::union_map Zone, isl::dim Dim, |
| bool InclStart, bool InclEnd) { |
| if (!InclStart && InclEnd) |
| return Zone; |
| |
| auto ShiftedZone = shiftDim(Zone, Dim, -1, -1); |
| if (InclStart && !InclEnd) |
| return ShiftedZone; |
| else if (!InclStart && !InclEnd) |
| return give(isl_union_map_intersect(Zone.take(), ShiftedZone.take())); |
| |
| assert(InclStart && InclEnd); |
| return give(isl_union_map_union(Zone.take(), ShiftedZone.take())); |
| } |
| |
| isl::map polly::distributeDomain(isl::map Map) { |
| // Note that we cannot take Map apart into { Domain[] -> Range1[] } and { |
| // Domain[] -> Range2[] } and combine again. We would loose any relation |
| // between Range1[] and Range2[] that is not also a constraint to Domain[]. |
| |
| auto Space = give(isl_map_get_space(Map.keep())); |
| auto DomainSpace = give(isl_space_domain(Space.copy())); |
| assert(DomainSpace); |
| auto DomainDims = isl_space_dim(DomainSpace.keep(), isl_dim_set); |
| auto RangeSpace = give(isl_space_unwrap(isl_space_range(Space.copy()))); |
| auto Range1Space = give(isl_space_domain(RangeSpace.copy())); |
| assert(Range1Space); |
| auto Range1Dims = isl_space_dim(Range1Space.keep(), isl_dim_set); |
| auto Range2Space = give(isl_space_range(RangeSpace.copy())); |
| assert(Range2Space); |
| auto Range2Dims = isl_space_dim(Range2Space.keep(), isl_dim_set); |
| |
| auto OutputSpace = give(isl_space_map_from_domain_and_range( |
| isl_space_wrap(isl_space_map_from_domain_and_range(DomainSpace.copy(), |
| Range1Space.copy())), |
| isl_space_wrap(isl_space_map_from_domain_and_range(DomainSpace.copy(), |
| Range2Space.copy())))); |
| |
| auto Translator = |
| give(isl_basic_map_universe(isl_space_map_from_domain_and_range( |
| isl_space_wrap(Space.copy()), isl_space_wrap(OutputSpace.copy())))); |
| |
| for (unsigned i = 0; i < DomainDims; i += 1) { |
| Translator = give( |
| isl_basic_map_equate(Translator.take(), isl_dim_in, i, isl_dim_out, i)); |
| Translator = |
| give(isl_basic_map_equate(Translator.take(), isl_dim_in, i, isl_dim_out, |
| DomainDims + Range1Dims + i)); |
| } |
| for (unsigned i = 0; i < Range1Dims; i += 1) { |
| Translator = |
| give(isl_basic_map_equate(Translator.take(), isl_dim_in, DomainDims + i, |
| isl_dim_out, DomainDims + i)); |
| } |
| for (unsigned i = 0; i < Range2Dims; i += 1) { |
| Translator = give(isl_basic_map_equate( |
| Translator.take(), isl_dim_in, DomainDims + Range1Dims + i, isl_dim_out, |
| DomainDims + Range1Dims + DomainDims + i)); |
| } |
| |
| return give(isl_set_unwrap(isl_set_apply( |
| isl_map_wrap(Map.copy()), isl_map_from_basic_map(Translator.copy())))); |
| } |
| |
| isl::union_map polly::distributeDomain(isl::union_map UMap) { |
| auto Result = give(isl_union_map_empty(isl_union_map_get_space(UMap.keep()))); |
| UMap.foreach_map([=, &Result](isl::map Map) { |
| auto Distributed = distributeDomain(Map); |
| Result = give(isl_union_map_add_map(Result.take(), Distributed.copy())); |
| return isl::stat::ok; |
| }); |
| return Result; |
| } |
| |
| isl::union_map polly::liftDomains(isl::union_map UMap, isl::union_set Factor) { |
| |
| // { Factor[] -> Factor[] } |
| auto Factors = makeIdentityMap(std::move(Factor), true); |
| |
| return std::move(Factors).product(std::move(UMap)); |
| } |
| |
| isl::union_map polly::applyDomainRange(isl::union_map UMap, |
| isl::union_map Func) { |
| // This implementation creates unnecessary cross products of the |
| // DomainDomain[] and Func. An alternative implementation could reverse |
| // domain+uncurry,apply Func to what now is the domain, then undo the |
| // preparing transformation. Another alternative implementation could create a |
| // translator map for each piece. |
| |
| // { DomainDomain[] } |
| auto DomainDomain = UMap.domain().unwrap().domain(); |
| |
| // { [DomainDomain[] -> DomainRange[]] -> [DomainDomain[] -> NewDomainRange[]] |
| // } |
| auto LifetedFunc = liftDomains(std::move(Func), DomainDomain); |
| |
| return std::move(UMap).apply_domain(std::move(LifetedFunc)); |
| } |