llvm / llvm-project / f15a8545672a643f2a3e0a9ad7d1958470ee488d / . / polly / include / polly / Support / ISLTools.h

//===------ ISLTools.h ------------------------------------------*- C++ -*-===// | |

// | |

// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. | |

// See https://llvm.org/LICENSE.txt for license information. | |

// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception | |

// | |

//===----------------------------------------------------------------------===// | |

// | |

// Tools, utilities, helpers and extensions useful in conjunction with the | |

// Integer Set Library (isl). | |

// | |

//===----------------------------------------------------------------------===// | |

#ifndef POLLY_ISLTOOLS_H | |

#define POLLY_ISLTOOLS_H | |

#include "llvm/ADT/Sequence.h" | |

#include "llvm/ADT/iterator.h" | |

#include "isl/isl-noexceptions.h" | |

#include <cassert> | |

/// In debug builds assert that the @p Size is valid, in non-debug builds | |

/// disable the mandatory state checking but do not enforce the error checking. | |

inline void islAssert(const isl::size &Size) { | |

#ifdef NDEBUG | |

// Calling is_error() marks that the error status has been checked which | |

// disables the error-status-not-checked errors that would otherwise occur | |

// when using the value. | |

(void)Size.is_error(); | |

#else | |

// Assert on error in debug builds. | |

assert(!Size.is_error()); | |

#endif | |

} | |

/// Check that @p Size is valid (only on debug builds) and cast it to unsigned. | |

/// Cast the @p Size to unsigned. If the @p Size is not valid (Size.is_error() | |

/// == true) then an assert and an abort are triggered. | |

inline unsigned unsignedFromIslSize(const isl::size &Size) { | |

islAssert(Size); | |

return static_cast<unsigned>(Size); | |

} | |

namespace isl { | |

inline namespace noexceptions { | |

template <typename ListT> | |

using list_element_type = decltype(std::declval<ListT>().get_at(0)); | |

template <typename ListT> | |

struct isl_iterator | |

: public llvm::iterator_facade_base<isl_iterator<ListT>, | |

std::forward_iterator_tag, | |

list_element_type<ListT>> { | |

using ElementT = list_element_type<ListT>; | |

explicit isl_iterator(const ListT &List) | |

: List(&List), Position(std::max(List.size().release(), 0)) {} | |

isl_iterator(const ListT &List, int Position) | |

: List(&List), Position(Position) {} | |

bool operator==(const isl_iterator &O) const { | |

return List == O.List && Position == O.Position; | |

} | |

isl_iterator &operator++() { | |

++Position; | |

return *this; | |

} | |

isl_iterator operator++(int) { | |

isl_iterator Copy{*this}; | |

++Position; | |

return Copy; | |

} | |

ElementT operator*() const { return List->get_at(this->Position); } | |

protected: | |

const ListT *List; | |

int Position = 0; | |

}; | |

template <typename T> isl_iterator<T> begin(const T &t) { | |

return isl_iterator<T>(t, 0); | |

} | |

template <typename T> isl_iterator<T> end(const T &t) { | |

return isl_iterator<T>(t); | |

} | |

} // namespace noexceptions | |

} // namespace isl | |

namespace polly { | |

/// Return the range elements that are lexicographically smaller. | |

/// | |

/// @param Map { Space[] -> Scatter[] } | |

/// @param Strict True for strictly lexicographically smaller elements (exclude | |

/// same timepoints from the result). | |

/// | |

/// @return { Space[] -> Scatter[] } | |

/// A map to all timepoints that happen before the timepoints the input | |

/// mapped to. | |

isl::map beforeScatter(isl::map Map, bool Strict); | |

/// Piecewise beforeScatter(isl::map,bool). | |

isl::union_map beforeScatter(isl::union_map UMap, bool Strict); | |

/// Return the range elements that are lexicographically larger. | |

/// | |

/// @param Map { Space[] -> Scatter[] } | |

/// @param Strict True for strictly lexicographically larger elements (exclude | |

/// same timepoints from the result). | |

/// | |

/// @return { Space[] -> Scatter[] } | |

/// A map to all timepoints that happen after the timepoints the input | |

/// map originally mapped to. | |

isl::map afterScatter(isl::map Map, bool Strict); | |

/// Piecewise afterScatter(isl::map,bool). | |

isl::union_map afterScatter(const isl::union_map &UMap, bool Strict); | |

/// Construct a range of timepoints between two timepoints. | |

/// | |

/// Example: | |

/// From := { A[] -> [0]; B[] -> [0] } | |

/// To := { B[] -> [10]; C[] -> [20] } | |

/// | |

/// Result: | |

/// { B[] -> [i] : 0 < i < 10 } | |

/// | |

/// Note that A[] and C[] are not in the result because they do not have a start | |

/// or end timepoint. If a start (or end) timepoint is not unique, the first | |

/// (respectively last) is chosen. | |

/// | |

/// @param From { Space[] -> Scatter[] } | |

/// Map to start timepoints. | |

/// @param To { Space[] -> Scatter[] } | |

/// Map to end timepoints. | |

/// @param InclFrom Whether to include the start timepoints in the result. In | |

/// the example, this would add { B[] -> [0] } | |

/// @param InclTo Whether to include the end timepoints in the result. In this | |

/// example, this would add { B[] -> [10] } | |

/// | |

/// @return { Space[] -> Scatter[] } | |

/// A map for each domain element of timepoints between two extreme | |

/// points, or nullptr if @p From or @p To is nullptr, or the isl max | |

/// operations is exceeded. | |

isl::map betweenScatter(isl::map From, isl::map To, bool InclFrom, bool InclTo); | |

/// Piecewise betweenScatter(isl::map,isl::map,bool,bool). | |

isl::union_map betweenScatter(isl::union_map From, isl::union_map To, | |

bool InclFrom, bool InclTo); | |

/// If by construction a union map is known to contain only a single map, return | |

/// it. | |

/// | |

/// This function combines isl_map_from_union_map() and | |

/// isl_union_map_extract_map(). isl_map_from_union_map() fails if the map is | |

/// empty because it does not know which space it would be in. | |

/// isl_union_map_extract_map() on the other hand does not check whether there | |

/// is (at most) one isl_map in the union, i.e. how it has been constructed is | |

/// probably wrong. | |

isl::map singleton(isl::union_map UMap, isl::space ExpectedSpace); | |

/// If by construction an isl_union_set is known to contain only a single | |

/// isl_set, return it. | |

/// | |

/// This function combines isl_set_from_union_set() and | |

/// isl_union_set_extract_set(). isl_map_from_union_set() fails if the set is | |

/// empty because it does not know which space it would be in. | |

/// isl_union_set_extract_set() on the other hand does not check whether there | |

/// is (at most) one isl_set in the union, i.e. how it has been constructed is | |

/// probably wrong. | |

isl::set singleton(isl::union_set USet, isl::space ExpectedSpace); | |

/// Determine how many dimensions the scatter space of @p Schedule has. | |

/// | |

/// The schedule must not be empty and have equal number of dimensions of any | |

/// subspace it contains. | |

/// | |

/// The implementation currently returns the maximum number of dimensions it | |

/// encounters, if different, and 0 if none is encountered. However, most other | |

/// code will most likely fail if one of these happen. | |

unsigned getNumScatterDims(const isl::union_map &Schedule); | |

/// Return the scatter space of a @p Schedule. | |

/// | |

/// This is basically the range space of the schedule map, but harder to | |

/// determine because it is an isl_union_map. | |

isl::space getScatterSpace(const isl::union_map &Schedule); | |

/// Construct an identity map for the given domain values. | |

/// | |

/// @param USet { Space[] } | |

/// The returned map's domain and range. | |

/// @param RestrictDomain If true, the returned map only maps elements contained | |

/// in @p Set and no other. If false, it returns an | |

/// overapproximation with the identity maps of any space | |

/// in @p Set, not just the elements in it. | |

/// | |

/// @return { Space[] -> Space[] } | |

/// A map that maps each value of @p Set to itself. | |

isl::map makeIdentityMap(const isl::set &Set, bool RestrictDomain); | |

/// Construct an identity map for the given domain values. | |

/// | |

/// There is no type resembling isl_union_space, hence we have to pass an | |

/// isl_union_set as the map's domain and range space. | |

/// | |

/// @param USet { Space[] } | |

/// The returned map's domain and range. | |

/// @param RestrictDomain If true, the returned map only maps elements contained | |

/// in @p USet and no other. If false, it returns an | |

/// overapproximation with the identity maps of any space | |

/// in @p USet, not just the elements in it. | |

/// | |

/// @return { Space[] -> Space[] } | |

/// A map that maps each value of @p USet to itself. | |

isl::union_map makeIdentityMap(const isl::union_set &USet, bool RestrictDomain); | |

/// Reverse the nested map tuple in @p Map's domain. | |

/// | |

/// @param Map { [Space1[] -> Space2[]] -> Space3[] } | |

/// | |

/// @return { [Space2[] -> Space1[]] -> Space3[] } | |

isl::map reverseDomain(isl::map Map); | |

/// Piecewise reverseDomain(isl::map). | |

isl::union_map reverseDomain(const isl::union_map &UMap); | |

/// Add a constant to one dimension of a set. | |

/// | |

/// @param Map The set to shift a dimension in. | |

/// @param Pos The dimension to shift. If negative, the dimensions are | |

/// counted from the end instead from the beginning. E.g. -1 is | |

/// the last dimension in the tuple. | |

/// @param Amount The offset to add to the specified dimension. | |

/// | |

/// @return The modified set. | |

isl::set shiftDim(isl::set Set, int Pos, int Amount); | |

/// Piecewise shiftDim(isl::set,int,int). | |

isl::union_set shiftDim(isl::union_set USet, int Pos, int Amount); | |

/// Add a constant to one dimension of a map. | |

/// | |

/// @param Map The map to shift a dimension in. | |

/// @param Type A tuple of @p Map which contains the dimension to shift. | |

/// @param Pos The dimension to shift. If negative, the dimensions are | |

/// counted from the end instead from the beginning. Eg. -1 is the last | |

/// dimension in the tuple. | |

/// @param Amount The offset to add to the specified dimension. | |

/// | |

/// @return The modified map. | |

isl::map shiftDim(isl::map Map, isl::dim Dim, int Pos, int Amount); | |

/// Add a constant to one dimension of a each map in a union map. | |

/// | |

/// @param UMap The maps to shift a dimension in. | |

/// @param Type The tuple which contains the dimension to shift. | |

/// @param Pos The dimension to shift. If negative, the dimensions are | |

/// counted from the ends of each map of union instead from their | |

/// beginning. E.g. -1 is the last dimension of any map. | |

/// @param Amount The offset to add to the specified dimension. | |

/// | |

/// @return The union of all modified maps. | |

isl::union_map shiftDim(isl::union_map UMap, isl::dim Dim, int Pos, int Amount); | |

/// Simplify a set inplace. | |

void simplify(isl::set &Set); | |

/// Simplify a union set inplace. | |

void simplify(isl::union_set &USet); | |

/// Simplify a map inplace. | |

void simplify(isl::map &Map); | |

/// Simplify a union map inplace. | |

void simplify(isl::union_map &UMap); | |

/// Compute the reaching definition statement or the next overwrite for each | |

/// definition of an array element. | |

/// | |

/// The reaching definition of an array element at a specific timepoint is the | |

/// statement instance that has written the current element's content. | |

/// Alternatively, this function determines for each timepoint and element which | |

/// write is going to overwrite an element at a future timepoint. This can be | |

/// seen as "reaching definition in reverse" where definitions are found in the | |

/// past. | |

/// | |

/// For example: | |

/// | |

/// Schedule := { Write[] -> [0]; Overwrite[] -> [10] } | |

/// Defs := { Write[] -> A[5]; Overwrite[] -> A[5] } | |

/// | |

/// If index 5 of array A is written at timepoint 0 and 10, the resulting | |

/// reaching definitions are: | |

/// | |

/// { [A[5] -> [i]] -> Write[] : 0 < i < 10; | |

/// [A[5] -> [i]] -> Overwrite[] : 10 < i } | |

/// | |

/// Between timepoint 0 (Write[]) and timepoint 10 (Overwrite[]), the | |

/// content of A[5] is written by statement instance Write[] and after | |

/// timepoint 10 by Overwrite[]. Values not defined in the map have no known | |

/// definition. This includes the statement instance timepoints themselves, | |

/// because reads at those timepoints could either read the old or the new | |

/// value, defined only by the statement itself. But this can be changed by @p | |

/// InclPrevDef and @p InclNextDef. InclPrevDef=false and InclNextDef=true | |

/// returns a zone. Unless @p InclPrevDef and @p InclNextDef are both true, | |

/// there is only one unique definition per element and timepoint. | |

/// | |

/// @param Schedule { DomainWrite[] -> Scatter[] } | |

/// Schedule of (at least) all array writes. Instances not in | |

/// @p Writes are ignored. | |

/// @param Writes { DomainWrite[] -> Element[] } | |

/// Elements written to by the statement instances. | |

/// @param Reverse If true, look for definitions in the future. That is, | |

/// find the write that is overwrites the current value. | |

/// @param InclPrevDef Include the definition's timepoint to the set of | |

/// well-defined elements (any load at that timepoint happen | |

/// at the writes). In the example, enabling this option adds | |

/// {[A[5] -> [0]] -> Write[]; [A[5] -> [10]] -> Overwrite[]} | |

/// to the result. | |

/// @param InclNextDef Whether to assume that at the timepoint where an element | |

/// is overwritten, it still contains the old value (any load | |

/// at that timepoint would happen before the overwrite). In | |

/// this example, enabling this adds | |

/// { [A[] -> [10]] -> Write[] } to the result. | |

/// | |

/// @return { [Element[] -> Scatter[]] -> DomainWrite[] } | |

/// The reaching definitions or future overwrite as described above, or | |

/// nullptr if either @p Schedule or @p Writes is nullptr, or the isl | |

/// max operations count has exceeded. | |

isl::union_map computeReachingWrite(isl::union_map Schedule, | |

isl::union_map Writes, bool Reverse, | |

bool InclPrevDef, bool InclNextDef); | |

/// Compute the timepoints where the contents of an array element are not used. | |

/// | |

/// An element is unused at a timepoint when the element is overwritten in | |

/// the future, but it is not read in between. Another way to express this: the | |

/// time from when the element is written, to the most recent read before it, or | |

/// infinitely into the past if there is no read before. Such unused elements | |

/// can be overwritten by any value without changing the scop's semantics. An | |

/// example: | |

/// | |

/// Schedule := { Read[] -> [0]; Write[] -> [10]; Def[] -> [20] } | |

/// Writes := { Write[] -> A[5]; Def[] -> A[6] } | |

/// Reads := { Read[] -> A[5] } | |

/// | |

/// The result is: | |

/// | |

/// { A[5] -> [i] : 0 < i < 10; | |

/// A[6] -> [i] : i < 20 } | |

/// | |

/// That is, A[5] is unused between timepoint 0 (the read) and timepoint 10 (the | |

/// write). A[6] is unused before timepoint 20, but might be used after the | |

/// scop's execution (A[5] and any other A[i] as well). Use InclLastRead=false | |

/// and InclWrite=true to interpret the result as zone. | |

/// | |

/// @param Schedule { Domain[] -> Scatter[] } | |

/// The schedule of (at least) all statement instances | |

/// occurring in @p Writes or @p Reads. All other | |

/// instances are ignored. | |

/// @param Writes { DomainWrite[] -> Element[] } | |

/// Elements written to by the statement instances. | |

/// @param Reads { DomainRead[] -> Element[] } | |

/// Elements read from by the statement instances. | |

/// @param ReadEltInSameInst Whether a load reads the value from a write | |

/// that is scheduled at the same timepoint (Writes | |

/// happen before reads). Otherwise, loads use the | |

/// value of an element that it had before the | |

/// timepoint (Reads before writes). For example: | |

/// { Read[] -> [0]; Write[] -> [0] } | |

/// With ReadEltInSameInst=false it is assumed that the | |

/// read happens before the write, such that the | |

/// element is never unused, or just at timepoint 0, | |

/// depending on InclLastRead/InclWrite. | |

/// With ReadEltInSameInst=false it assumes that the | |

/// value just written is used. Anything before | |

/// timepoint 0 is considered unused. | |

/// @param InclLastRead Whether a timepoint where an element is last read | |

/// counts as unused (the read happens at the beginning | |

/// of its timepoint, and nothing (else) can use it | |

/// during the timepoint). In the example, this option | |

/// adds { A[5] -> [0] } to the result. | |

/// @param InclWrite Whether the timepoint where an element is written | |

/// itself counts as unused (the write happens at the | |

/// end of its timepoint; no (other) operations uses | |

/// the element during the timepoint). In this example, | |

/// this adds | |

/// { A[5] -> [10]; A[6] -> [20] } to the result. | |

/// | |

/// @return { Element[] -> Scatter[] } | |

/// The unused timepoints as defined above, or nullptr if either @p | |

/// Schedule, @p Writes are @p Reads is nullptr, or the ISL max | |

/// operations count is exceeded. | |

isl::union_map computeArrayUnused(isl::union_map Schedule, | |

isl::union_map Writes, isl::union_map Reads, | |

bool ReadEltInSameInst, bool InclLastRead, | |

bool InclWrite); | |

/// Convert a zone (range between timepoints) to timepoints. | |

/// | |

/// A zone represents the time between (integer) timepoints, but not the | |

/// timepoints themselves. This function can be used to determine whether a | |

/// timepoint lies within a zone. | |

/// | |

/// For instance, the range (1,3), representing the time between 1 and 3, is | |

/// represented by the zone | |

/// | |

/// { [i] : 1 < i <= 3 } | |

/// | |

/// The set of timepoints that lie completely within this range is | |

/// | |

/// { [i] : 1 < i < 3 } | |

/// | |

/// A typical use-case is the range in which a value written by a store is | |

/// available until it is overwritten by another value. If the write is at | |

/// timepoint 1 and its value is overwritten by another value at timepoint 3, | |

/// the value is available between those timepoints: timepoint 2 in this | |

/// example. | |

/// | |

/// | |

/// When InclStart is true, the range is interpreted left-inclusive, i.e. adds | |

/// the timepoint 1 to the result: | |

/// | |

/// { [i] : 1 <= i < 3 } | |

/// | |

/// In the use-case mentioned above that means that the value written at | |

/// timepoint 1 is already available in timepoint 1 (write takes place before | |

/// any read of it even if executed at the same timepoint) | |

/// | |

/// When InclEnd is true, the range is interpreted right-inclusive, i.e. adds | |

/// the timepoint 3 to the result: | |

/// | |

/// { [i] : 1 < i <= 3 } | |

/// | |

/// In the use-case mentioned above that means that although the value is | |

/// overwritten in timepoint 3, the old value is still available at timepoint 3 | |

/// (write takes place after any read even if executed at the same timepoint) | |

/// | |

/// @param Zone { Zone[] } | |

/// @param InclStart Include timepoints adjacent to the beginning of a zone. | |

/// @param InclEnd Include timepoints adjacent to the ending of a zone. | |

/// | |

/// @return { Scatter[] } | |

isl::union_set convertZoneToTimepoints(isl::union_set Zone, bool InclStart, | |

bool InclEnd); | |

/// Like convertZoneToTimepoints(isl::union_set,InclStart,InclEnd), but convert | |

/// either the domain or the range of a map. | |

isl::union_map convertZoneToTimepoints(isl::union_map Zone, isl::dim Dim, | |

bool InclStart, bool InclEnd); | |

/// Overload of convertZoneToTimepoints(isl::map,InclStart,InclEnd) to process | |

/// only a single map. | |

isl::map convertZoneToTimepoints(isl::map Zone, isl::dim Dim, bool InclStart, | |

bool InclEnd); | |

/// Distribute the domain to the tuples of a wrapped range map. | |

/// | |

/// @param Map { Domain[] -> [Range1[] -> Range2[]] } | |

/// | |

/// @return { [Domain[] -> Range1[]] -> [Domain[] -> Range2[]] } | |

isl::map distributeDomain(isl::map Map); | |

/// Apply distributeDomain(isl::map) to each map in the union. | |

isl::union_map distributeDomain(isl::union_map UMap); | |

/// Prepend a space to the tuples of a map. | |

/// | |

/// @param UMap { Domain[] -> Range[] } | |

/// @param Factor { Factor[] } | |

/// | |

/// @return { [Factor[] -> Domain[]] -> [Factor[] -> Range[]] } | |

isl::union_map liftDomains(isl::union_map UMap, isl::union_set Factor); | |

/// Apply a map to the 'middle' of another relation. | |

/// | |

/// @param UMap { [DomainDomain[] -> DomainRange[]] -> Range[] } | |

/// @param Func { DomainRange[] -> NewDomainRange[] } | |

/// | |

/// @return { [DomainDomain[] -> NewDomainRange[]] -> Range[] } | |

isl::union_map applyDomainRange(isl::union_map UMap, isl::union_map Func); | |

/// Intersect the range of @p Map with @p Range. | |

/// | |

/// Since @p Map is an isl::map, the result will be a single space, even though | |

/// @p Range is an isl::union_set. This is the only difference to | |

/// isl::map::intersect_range and isl::union_map::interset_range. | |

/// | |

/// @param Map { Domain[] -> Range[] } | |

/// @param Range { Range[] } | |

/// | |

/// @return { Domain[] -> Range[] } | |

isl::map intersectRange(isl::map Map, isl::union_set Range); | |

/// Subtract the parameter space @p Params from @p Map. | |

/// This is akin to isl::map::intersect_params. | |

/// | |

/// Example: | |

/// subtractParams( | |

/// { [i] -> [i] }, | |

/// [x] -> { : x < 0 } | |

/// ) = [x] -> { [i] -> [i] : x >= 0 } | |

/// | |

/// @param Map Remove the conditions of @p Params from this map. | |

/// @param Params Parameter set to subtract. | |

/// | |

/// @param The map with the parameter conditions removed. | |

isl::map subtractParams(isl::map Map, isl::set Params); | |

/// Subtract the parameter space @p Params from @p Set. | |

isl::set subtractParams(isl::set Set, isl::set Params); | |

/// If @p PwAff maps to a constant, return said constant. If @p Max/@p Min, it | |

/// can also be a piecewise constant and it would return the minimum/maximum | |

/// value. Otherwise, return NaN. | |

isl::val getConstant(isl::pw_aff PwAff, bool Max, bool Min); | |

/// Check that @p End is valid and return an iterator from @p Begin to @p End | |

/// | |

/// Use case example: | |

/// for (unsigned i : rangeIslSize(0, Map.domain_tuple_dim())) | |

/// // do stuff | |

llvm::iota_range<unsigned> rangeIslSize(unsigned Begin, isl::size End); | |

/// Dump a description of the argument to llvm::errs(). | |

/// | |

/// In contrast to isl's dump function, there are a few differences: | |

/// - Each polyhedron (pieces) is written on its own line. | |

/// - Spaces are sorted by structure. E.g. maps with same domain space are | |

/// grouped. Isl sorts them according to the space's hash function. | |

/// - Pieces of the same space are sorted using their lower bound. | |

/// - A more compact to_str representation is used instead of Isl's dump | |

/// functions that try to show the internal representation. | |

/// | |

/// The goal is to get a better understandable representation that is also | |

/// useful to compare two sets. As all dump() functions, its intended use is to | |

/// be called in a debugger only. | |

/// | |

/// isl_map_dump example: | |

/// [p_0, p_1, p_2] -> { Stmt0[i0] -> [o0, o1] : (o0 = i0 and o1 = 0 and i0 > 0 | |

/// and i0 <= 5 - p_2) or (i0 = 0 and o0 = 0 and o1 = 0); Stmt3[i0] -> [o0, o1] | |

/// : (o0 = i0 and o1 = 3 and i0 > 0 and i0 <= 5 - p_2) or (i0 = 0 and o0 = 0 | |

/// and o1 = 3); Stmt2[i0] -> [o0, o1] : (o0 = i0 and o1 = 1 and i0 >= 3 + p_0 - | |

/// p_1 and i0 > 0 and i0 <= 5 - p_2) or (o0 = i0 and o1 = 1 and i0 > 0 and i0 | |

/// <= 5 - p_2 and i0 < p_0 - p_1) or (i0 = 0 and o0 = 0 and o1 = 1 and p_1 >= 3 | |

/// + p_0) or (i0 = 0 and o0 = 0 and o1 = 1 and p_1 < p_0) or (p_0 = 0 and i0 = | |

/// 2 - p_1 and o0 = 2 - p_1 and o1 = 1 and p_2 <= 3 + p_1 and p_1 <= 1) or (p_1 | |

/// = 1 + p_0 and i0 = 0 and o0 = 0 and o1 = 1) or (p_0 = 0 and p_1 = 2 and i0 = | |

/// 0 and o0 = 0 and o1 = 1) or (p_0 = -1 and p_1 = -1 and i0 = 0 and o0 = 0 and | |

/// o1 = 1); Stmt1[i0] -> [o0, o1] : (p_0 = -1 and i0 = 1 - p_1 and o0 = 1 - p_1 | |

/// and o1 = 2 and p_2 <= 4 + p_1 and p_1 <= 0) or (p_0 = 0 and i0 = -p_1 and o0 | |

/// = -p_1 and o1 = 2 and p_2 <= 5 + p_1 and p_1 < 0) or (p_0 = -1 and p_1 = 1 | |

/// and i0 = 0 and o0 = 0 and o1 = 2) or (p_0 = 0 and p_1 = 0 and i0 = 0 and o0 | |

/// = 0 and o1 = 2) } | |

/// | |

/// dumpPw example (same set): | |

/// [p_0, p_1, p_2] -> { | |

/// Stmt0[0] -> [0, 0]; | |

/// Stmt0[i0] -> [i0, 0] : 0 < i0 <= 5 - p_2; | |

/// Stmt1[0] -> [0, 2] : p_1 = 1 and p_0 = -1; | |

/// Stmt1[0] -> [0, 2] : p_1 = 0 and p_0 = 0; | |

/// Stmt1[1 - p_1] -> [1 - p_1, 2] : p_0 = -1 and p_1 <= 0 and p_2 <= 4 + p_1; | |

/// Stmt1[-p_1] -> [-p_1, 2] : p_0 = 0 and p_1 < 0 and p_2 <= 5 + p_1; | |

/// Stmt2[0] -> [0, 1] : p_1 >= 3 + p_0; | |

/// Stmt2[0] -> [0, 1] : p_1 < p_0; | |

/// Stmt2[0] -> [0, 1] : p_1 = 1 + p_0; | |

/// Stmt2[0] -> [0, 1] : p_1 = 2 and p_0 = 0; | |

/// Stmt2[0] -> [0, 1] : p_1 = -1 and p_0 = -1; | |

/// Stmt2[i0] -> [i0, 1] : i0 >= 3 + p_0 - p_1 and 0 < i0 <= 5 - p_2; | |

/// Stmt2[i0] -> [i0, 1] : 0 < i0 <= 5 - p_2 and i0 < p_0 - p_1; | |

/// Stmt2[2 - p_1] -> [2 - p_1, 1] : p_0 = 0 and p_1 <= 1 and p_2 <= 3 + p_1; | |

/// Stmt3[0] -> [0, 3]; | |

/// Stmt3[i0] -> [i0, 3] : 0 < i0 <= 5 - p_2 | |

/// } | |

/// @{ | |

void dumpPw(const isl::set &Set); | |

void dumpPw(const isl::map &Map); | |

void dumpPw(const isl::union_set &USet); | |

void dumpPw(const isl::union_map &UMap); | |

void dumpPw(__isl_keep isl_set *Set); | |

void dumpPw(__isl_keep isl_map *Map); | |

void dumpPw(__isl_keep isl_union_set *USet); | |

void dumpPw(__isl_keep isl_union_map *UMap); | |

/// @} | |

/// Dump all points of the argument to llvm::errs(). | |

/// | |

/// Before being printed by dumpPw(), the argument's pieces are expanded to | |

/// contain only single points. If a dimension is unbounded, it keeps its | |

/// representation. | |

/// | |

/// This is useful for debugging reduced cases where parameters are set to | |

/// constants to keep the example simple. Such sets can still contain | |

/// existential dimensions which makes the polyhedral hard to compare. | |

/// | |

/// Example: | |

/// { [MemRef_A[i0] -> [i1]] : (exists (e0 = floor((1 + i1)/3): i0 = 1 and 3e0 | |

/// <= i1 and 3e0 >= -1 + i1 and i1 >= 15 and i1 <= 25)) or (exists (e0 = | |

/// floor((i1)/3): i0 = 0 and 3e0 < i1 and 3e0 >= -2 + i1 and i1 > 0 and i1 <= | |

/// 11)) } | |

/// | |

/// dumpExpanded: | |

/// { | |

/// [MemRef_A[0] ->[1]]; | |

/// [MemRef_A[0] ->[2]]; | |

/// [MemRef_A[0] ->[4]]; | |

/// [MemRef_A[0] ->[5]]; | |

/// [MemRef_A[0] ->[7]]; | |

/// [MemRef_A[0] ->[8]]; | |

/// [MemRef_A[0] ->[10]]; | |

/// [MemRef_A[0] ->[11]]; | |

/// [MemRef_A[1] ->[15]]; | |

/// [MemRef_A[1] ->[16]]; | |

/// [MemRef_A[1] ->[18]]; | |

/// [MemRef_A[1] ->[19]]; | |

/// [MemRef_A[1] ->[21]]; | |

/// [MemRef_A[1] ->[22]]; | |

/// [MemRef_A[1] ->[24]]; | |

/// [MemRef_A[1] ->[25]] | |

/// } | |

/// @{ | |

void dumpExpanded(const isl::set &Set); | |

void dumpExpanded(const isl::map &Map); | |

void dumpExpanded(const isl::union_set &USet); | |

void dumpExpanded(const isl::union_map &UMap); | |

void dumpExpanded(__isl_keep isl_set *Set); | |

void dumpExpanded(__isl_keep isl_map *Map); | |

void dumpExpanded(__isl_keep isl_union_set *USet); | |

void dumpExpanded(__isl_keep isl_union_map *UMap); | |

/// @} | |

} // namespace polly | |

#endif /* POLLY_ISLTOOLS_H */ |