A PresburgerRelation represents a union of IntegerRelations that live in the same PresburgerSpace with support for union, intersection, subtraction, and complement operations, as well as sampling. More...

#include "mlir/Analysis/Presburger/PresburgerRelation.h"

Inheritance diagram for mlir::presburger::PresburgerRelation:

Public Member Functions
	PresburgerRelation (const IntegerRelation &disjunct)

unsigned	getNumDomainVars () const

unsigned	getNumRangeVars () const

unsigned	getNumSymbolVars () const

unsigned	getNumLocalVars () const

unsigned	getNumVars () const

unsigned	getNumDisjuncts () const
	Return the number of disjuncts in the union. More...

const PresburgerSpace &	getSpace () const

void	setSpace (const PresburgerSpace &oSpace)
	Set the space to `oSpace`. More...

ArrayRef< IntegerRelation >	getAllDisjuncts () const
	Return a reference to the list of disjuncts. More...

const IntegerRelation &	getDisjunct (unsigned index) const
	Return the disjunct at the specified index. More...

void	unionInPlace (const IntegerRelation &disjunct)
	Mutate this set, turning it into the union of this set and the given disjunct. More...

void	unionInPlace (const PresburgerRelation &set)
	Mutate this set, turning it into the union of this set and the given set. More...

PresburgerRelation	unionSet (const PresburgerRelation &set) const
	Return the union of this set and the given set. More...

PresburgerRelation	intersect (const PresburgerRelation &set) const
	Return the intersection of this set and the given set. More...

bool	containsPoint (ArrayRef< MPInt > point) const
	Return true if the set contains the given point, and false otherwise. More...

bool	containsPoint (ArrayRef< int64_t > point) const

PresburgerRelation	complement () const
	Return the complement of this set. More...

PresburgerRelation	subtract (const PresburgerRelation &set) const
	Return the set difference of this set and the given set, i.e., return `this \ set`. More...

bool	isSubsetOf (const PresburgerRelation &set) const
	Return true if this set is a subset of the given set, and false otherwise. More...

bool	isEqual (const PresburgerRelation &set) const
	Return true if this set is equal to the given set, and false otherwise. More...

bool	isIntegerEmpty () const
	Return true if all the sets in the union are known to be integer empty false otherwise. More...

bool	findIntegerSample (SmallVectorImpl< MPInt > &sample)
	Find an integer sample from the given set. More...

std::optional< MPInt >	computeVolume () const
	Compute an overapproximation of the number of integer points in the disjunct. More...

PresburgerRelation	coalesce () const
	Simplifies the representation of a PresburgerRelation. More...

bool	hasOnlyDivLocals () const
	Check whether all local ids in all disjuncts have a div representation. More...

PresburgerRelation	computeReprWithOnlyDivLocals () const
	Compute an equivalent representation of the same relation, such that all local ids in all disjuncts have division representations. More...

void	print (raw_ostream &os) const
	Print the set's internal state. More...

void	dump () const

Static Public Member Functions
static PresburgerRelation	getUniverse (const PresburgerSpace &space)
	Return a universe set of the specified type that contains all points. More...

static PresburgerRelation	getEmpty (const PresburgerSpace &space)
	Return an empty set of the specified type that contains no points. More...

Protected Member Functions
	PresburgerRelation (const PresburgerSpace &space)
	Construct an empty PresburgerRelation with the specified number of dimension and symbols. More...

Protected Attributes
PresburgerSpace	space

SmallVector< IntegerRelation, 2 >	disjuncts
	The list of disjuncts that this set is the union of. More...

Friends
class	SetCoalescer

Detailed Description

A PresburgerRelation represents a union of IntegerRelations that live in the same PresburgerSpace with support for union, intersection, subtraction, and complement operations, as well as sampling.

The IntegerRelations (disjuncts) are stored in a vector, and the set represents the union of these relations. An empty list corresponds to the empty set.

Note that there are no invariants guaranteed on the list of disjuncts other than that they are all in the same PresburgerSpace. For example, the relations may overlap with each other.

Definition at line 38 of file PresburgerRelation.h.

Constructor & Destructor Documentation

◆ PresburgerRelation() [1/2]

PresburgerRelation::PresburgerRelation ( const IntegerRelation & disjunct )

explicit

Definition at line 20 of file PresburgerRelation.cpp.

References unionInPlace().

Referenced by getEmpty().

◆ PresburgerRelation() [2/2]

mlir::presburger::PresburgerRelation::PresburgerRelation ( const PresburgerSpace & space )

inlineexplicitprotected

Construct an empty PresburgerRelation with the specified number of dimension and symbols.

Definition at line 148 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumLocalVars(), and space.

Member Function Documentation

◆ coalesce()

PresburgerRelation PresburgerRelation::coalesce ( ) const

Simplifies the representation of a PresburgerRelation.

In particular, removes all disjuncts which are subsets of other disjuncts in the union.

Definition at line 813 of file PresburgerRelation.cpp.

References SetCoalescer.

Referenced by mlir::presburger::PresburgerSet::coalesce().

◆ complement()

PresburgerRelation PresburgerRelation::complement ( ) const

Return the complement of this set.

All local variables in the set must correspond to floor divisions.

Definition at line 427 of file PresburgerRelation.cpp.

References getSetDifference(), getSpace(), and mlir::presburger::IntegerRelation::getUniverse().

Referenced by mlir::presburger::PresburgerSet::complement().

◆ computeReprWithOnlyDivLocals()

PresburgerRelation PresburgerRelation::computeReprWithOnlyDivLocals ( ) const

Compute an equivalent representation of the same relation, such that all local ids in all disjuncts have division representations.

This representation may involve local ids that correspond to divisions, and may also be a union of convex disjuncts.

Definition at line 140 of file PresburgerRelation.cpp.

References disjuncts, getSpace(), hasOnlyDivLocals(), and unionInPlace().

Referenced by getSetDifference().

◆ computeVolume()

std::optional< MPInt > PresburgerRelation::computeVolume ( ) const

Compute an overapproximation of the number of integer points in the disjunct.

Symbol vars are currently not supported. If the computed overapproximation is infinite, an empty optional is returned.

This currently just sums up the overapproximations of the volumes of the disjuncts, so the approximation might be far from the true volume in the case when there is a lot of overlap between disjuncts.

Definition at line 475 of file PresburgerRelation.cpp.

References disjuncts, and getNumSymbolVars().

◆ containsPoint() [1/2]

bool mlir::presburger::PresburgerRelation::containsPoint ( ArrayRef< int64_t > point ) const

inline

Definition at line 88 of file PresburgerRelation.h.

References containsPoint(), and mlir::presburger::getMPIntVec().

◆ containsPoint() [2/2]

bool PresburgerRelation::containsPoint ( ArrayRef< MPInt > point ) const

Return true if the set contains the given point, and false otherwise.

A point is contained in the union iff any of the parts contain the point.

Definition at line 72 of file PresburgerRelation.cpp.

References mlir::presburger::IntegerRelation::containsPointNoLocal(), and disjuncts.

Referenced by containsPoint().

◆ dump()

void PresburgerRelation::dump ( ) const

Definition at line 831 of file PresburgerRelation.cpp.

References print().

◆ findIntegerSample()

bool PresburgerRelation::findIntegerSample ( SmallVectorImpl< MPInt > & sample )

Find an integer sample from the given set.

This should not be called if any of the disjuncts in the union are unbounded.

Definition at line 463 of file PresburgerRelation.cpp.

References disjuncts.

◆ getAllDisjuncts()

ArrayRef< IntegerRelation > PresburgerRelation::getAllDisjuncts ( ) const

Return a reference to the list of disjuncts.

Definition at line 36 of file PresburgerRelation.cpp.

References disjuncts.

Referenced by mlir::presburger::MultiAffineFunction::isEqual().

◆ getDisjunct()

const IntegerRelation & PresburgerRelation::getDisjunct ( unsigned index ) const

Return the disjunct at the specified index.

Definition at line 40 of file PresburgerRelation.cpp.

References disjuncts.

Referenced by getSetDifference().

◆ getEmpty()

PresburgerRelation PresburgerRelation::getEmpty ( const PresburgerSpace & space )

static

Return an empty set of the specified type that contains no points.

Definition at line 85 of file PresburgerRelation.cpp.

References PresburgerRelation(), and space.

Referenced by getSetDifference().

◆ getNumDisjuncts()

unsigned PresburgerRelation::getNumDisjuncts ( ) const

Return the number of disjuncts in the union.

Definition at line 32 of file PresburgerRelation.cpp.

References disjuncts.

Referenced by getSetDifference(), print(), and mlir::presburger::SetCoalescer::SetCoalescer().

◆ getNumDomainVars()

unsigned mlir::presburger::PresburgerRelation::getNumDomainVars ( ) const

inline

Definition at line 48 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumDomainVars(), and space.

◆ getNumLocalVars()

unsigned mlir::presburger::PresburgerRelation::getNumLocalVars ( ) const

inline

Definition at line 51 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumLocalVars(), and space.

◆ getNumRangeVars()

unsigned mlir::presburger::PresburgerRelation::getNumRangeVars ( ) const

inline

Definition at line 49 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumRangeVars(), and space.

◆ getNumSymbolVars()

unsigned mlir::presburger::PresburgerRelation::getNumSymbolVars ( ) const

inline

Definition at line 50 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumSymbolVars(), and space.

Referenced by computeVolume().

◆ getNumVars()

unsigned mlir::presburger::PresburgerRelation::getNumVars ( ) const

inline

Definition at line 52 of file PresburgerRelation.h.

References mlir::presburger::PresburgerSpace::getNumVars(), and space.

◆ getSpace()

const PresburgerSpace& mlir::presburger::PresburgerRelation::getSpace ( ) const

inline

Definition at line 57 of file PresburgerRelation.h.

References space.

Referenced by complement(), computeReprWithOnlyDivLocals(), getSetDifference(), intersect(), mlir::presburger::PWMAFunction::Piece::isConsistent(), isEqual(), subtract(), unionInPlace(), and unionSet().

◆ getUniverse()

PresburgerRelation PresburgerRelation::getUniverse ( const PresburgerSpace & space )

static

Return a universe set of the specified type that contains all points.

Definition at line 79 of file PresburgerRelation.cpp.

References mlir::presburger::IntegerRelation::getUniverse(), space, and unionInPlace().

◆ hasOnlyDivLocals()

bool PresburgerRelation::hasOnlyDivLocals ( ) const

Check whether all local ids in all disjuncts have a div representation.

Definition at line 817 of file PresburgerRelation.cpp.

References disjuncts, and mlir::presburger::IntegerRelation::hasOnlyDivLocals().

Referenced by computeReprWithOnlyDivLocals(), and getSetDifference().

◆ intersect()

PresburgerRelation PresburgerRelation::intersect ( const PresburgerRelation & set ) const

Return the intersection of this set and the given set.

Definition at line 97 of file PresburgerRelation.cpp.

References disjuncts, getSpace(), mlir::presburger::IntegerRelation::intersect(), mlir::presburger::PresburgerSpace::isCompatible(), mlir::presburger::IntegerRelation::isEmpty(), space, and unionInPlace().

Referenced by mlir::presburger::PresburgerSet::intersect().

◆ isEqual()

bool PresburgerRelation::isEqual ( const PresburgerRelation & set ) const

Return true if this set is equal to the given set, and false otherwise.

Two sets are equal iff they are subsets of each other.

All local variables in both sets must correspond to floor divisions.

Definition at line 451 of file PresburgerRelation.cpp.

References getSpace(), mlir::presburger::PresburgerSpace::isCompatible(), isSubsetOf(), and space.

Referenced by mlir::presburger::IntegerRelation::isEqual().

◆ isIntegerEmpty()

bool PresburgerRelation::isIntegerEmpty ( ) const

Return true if all the sets in the union are known to be integer empty false otherwise.

Return true if all the sets in the union are known to be integer empty, false otherwise.

Definition at line 458 of file PresburgerRelation.cpp.

References disjuncts, and mlir::presburger::IntegerRelation::isIntegerEmpty().

Referenced by mlir::affine::ComputationSliceState::isMaximal(), mlir::affine::ComputationSliceState::isSliceValid(), and isSubsetOf().

◆ isSubsetOf()

bool PresburgerRelation::isSubsetOf ( const PresburgerRelation & set ) const

Return true if this set is a subset of the given set, and false otherwise.

T is a subset of S iff T \ S is empty, since if T \ S contains a point then this is a point that is contained in T but not S, and if T contains a point that is not in S, this also lies in T \ S.

Definition at line 446 of file PresburgerRelation.cpp.

References isIntegerEmpty(), and subtract().

Referenced by isEqual(), and mlir::presburger::IntegerRelation::isSubsetOf().

◆ print()

void PresburgerRelation::print ( raw_ostream & os ) const

Print the set's internal state.

Definition at line 823 of file PresburgerRelation.cpp.

References disjuncts, getNumDisjuncts(), and mlir::presburger::IntegerRelation::print().

Referenced by dump().

◆ setSpace()

void PresburgerRelation::setSpace ( const PresburgerSpace & oSpace )

Set the space to oSpace.

oSpace should not contain any local ids. oSpace need not have the same number of ids as the current space; it could have more or less. If it has less, the extra ids become locals of the disjuncts. It can also have more, in which case the disjuncts will have fewer locals. If its total number of ids exceeds that of some disjunct, an assert failure will occur.

Definition at line 25 of file PresburgerRelation.cpp.

References disjuncts, mlir::presburger::PresburgerSpace::getNumLocalVars(), and space.

Referenced by mlir::presburger::IntegerRelation::computeReprWithOnlyDivLocals().

◆ subtract()

PresburgerRelation PresburgerRelation::subtract ( const PresburgerRelation & set ) const

Return the set difference of this set and the given set, i.e., return this \ set.

Return the result of subtract the given set from this set, i.e., return this \ set.

All local variables in set must correspond to floor divisions, but local variables in this need not correspond to divisions.

Definition at line 434 of file PresburgerRelation.cpp.

References disjuncts, getSetDifference(), getSpace(), mlir::presburger::PresburgerSpace::isCompatible(), space, and unionInPlace().

Referenced by isSubsetOf(), mlir::presburger::IntegerRelation::subtract(), and mlir::presburger::PresburgerSet::subtract().

◆ unionInPlace() [1/2]

void PresburgerRelation::unionInPlace ( const IntegerRelation & disjunct )

Mutate this set, turning it into the union of this set and the given disjunct.

Mutate this set, turning it into the union of this set and the given IntegerRelation.

Definition at line 47 of file PresburgerRelation.cpp.

References disjuncts, mlir::presburger::IntegerRelation::getSpace(), mlir::presburger::PresburgerSpace::isCompatible(), and space.

Referenced by mlir::presburger::SetCoalescer::coalesce(), computeReprWithOnlyDivLocals(), mlir::presburger::PWMAFunction::getDomain(), mlir::presburger::MultiAffineFunction::getLexSet(), getSetDifference(), getUniverse(), mlir::presburger::PresburgerSet::getUniverse(), intersect(), PresburgerRelation(), subtract(), unionInPlace(), and unionSet().

◆ unionInPlace() [2/2]

void PresburgerRelation::unionInPlace ( const PresburgerRelation & set )

Mutate this set, turning it into the union of this set and the given set.

This is accomplished by simply adding all the disjuncts of the given set to this set.

Definition at line 56 of file PresburgerRelation.cpp.

References disjuncts, getSpace(), mlir::presburger::PresburgerSpace::isCompatible(), space, and unionInPlace().

◆ unionSet()

PresburgerRelation PresburgerRelation::unionSet ( const PresburgerRelation & set ) const

Return the union of this set and the given set.

Definition at line 64 of file PresburgerRelation.cpp.

References getSpace(), mlir::presburger::PresburgerSpace::isCompatible(), space, and unionInPlace().

Referenced by mlir::presburger::PresburgerSet::unionSet().

Friends And Related Function Documentation

◆ SetCoalescer

friend class SetCoalescer

friend

Definition at line 158 of file PresburgerRelation.h.

Referenced by coalesce().

Member Data Documentation

◆ disjuncts

SmallVector<IntegerRelation, 2> mlir::presburger::PresburgerRelation::disjuncts

protected

The list of disjuncts that this set is the union of.

Definition at line 156 of file PresburgerRelation.h.

Referenced by computeReprWithOnlyDivLocals(), computeVolume(), containsPoint(), findIntegerSample(), getAllDisjuncts(), getDisjunct(), getNumDisjuncts(), hasOnlyDivLocals(), intersect(), isIntegerEmpty(), print(), mlir::presburger::SetCoalescer::SetCoalescer(), setSpace(), subtract(), and unionInPlace().

◆ space

PresburgerSpace mlir::presburger::PresburgerRelation::space

protected

The documentation for this class was generated from the following files:

include/mlir/Analysis/Presburger/PresburgerRelation.h
lib/Analysis/Presburger/PresburgerRelation.cpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PresburgerRelation() [1/2]

◆ PresburgerRelation() [2/2]

Member Function Documentation

◆ coalesce()

◆ complement()

◆ computeReprWithOnlyDivLocals()

◆ computeVolume()

◆ containsPoint() [1/2]

◆ containsPoint() [2/2]

◆ dump()

◆ findIntegerSample()

◆ getAllDisjuncts()

◆ getDisjunct()

◆ getEmpty()

◆ getNumDisjuncts()

◆ getNumDomainVars()

◆ getNumLocalVars()

◆ getNumRangeVars()

◆ getNumSymbolVars()

◆ getNumVars()

◆ getSpace()

◆ getUniverse()

◆ hasOnlyDivLocals()

◆ intersect()

◆ isEqual()

◆ isIntegerEmpty()

◆ isSubsetOf()

◆ print()

◆ setSpace()

◆ subtract()

◆ unionInPlace() [1/2]

◆ unionInPlace() [2/2]

◆ unionSet()

Friends And Related Function Documentation

◆ SetCoalescer

Member Data Documentation

◆ disjuncts

◆ space