Package it.unive.lisa.analysis.numeric

Class Interval

java.lang.Object

it.unive.lisa.analysis.numeric.Interval

All Implemented Interfaces:

it.unive.lisa.analysis.BaseLattice<Interval>, it.unive.lisa.analysis.Lattice<Interval>, it.unive.lisa.analysis.nonrelational.NonRelationalDomain<Interval,it.unive.lisa.symbolic.value.ValueExpression,it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval>>, it.unive.lisa.analysis.nonrelational.NonRelationalElement<Interval,it.unive.lisa.symbolic.value.ValueExpression,it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval>>, it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>, it.unive.lisa.analysis.nonrelational.value.NonRelationalValueDomain<Interval>, it.unive.lisa.analysis.SemanticEvaluator, it.unive.lisa.util.representation.StructuredObject, java.lang.Comparable<Interval>

public class Interval
extends java.lang.Object
implements it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>, java.lang.Comparable<Interval>

The overflow-insensitive interval abstract domain, approximating integer values as the minimum integer interval containing them. It is implemented as a BaseNonRelationalValueDomain, handling top and bottom values for the expression evaluation and bottom values for the expression satisfiability. Top and bottom cases for least upper bounds, widening and less or equals operations are handled by BaseLattice in BaseLattice.lub(L), BaseLattice.widening(L) and BaseLattice.lessOrEqual(L) methods, respectively.

Nested Class Summary

Nested classes/interfaces inherited from interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain

it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain.EvaluationVisitor<T extends it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<T>>

Field Summary

Fields

Modifier and Type	Field	Description
static Interval	BOTTOM	The abstract bottom element.
it.unive.lisa.util.numeric.IntInterval	interval	The interval represented by this domain element.
static Interval	TOP	The abstract top ([-Inf, +Inf]) element.
static Interval	ZERO	The abstract zero ([0, 0]) element.

Fields inherited from interface it.unive.lisa.analysis.Lattice

BOTTOM_STRING, TOP_STRING

Constructor Summary

Constructors

Constructor	Description
Interval()	Builds the top interval.
Interval(int low, int high)	Builds the interval.
Interval(it.unive.lisa.util.numeric.IntInterval interval)	Builds the interval.
Interval(it.unive.lisa.util.numeric.MathNumber low, it.unive.lisa.util.numeric.MathNumber high)	Builds the interval.

Method Summary

Modifier and Type	Method	Description
it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval>	assumeBinaryExpression(it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval> environment, it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator, it.unive.lisa.symbolic.value.ValueExpression left, it.unive.lisa.symbolic.value.ValueExpression right, it.unive.lisa.program.cfg.ProgramPoint src, it.unive.lisa.program.cfg.ProgramPoint dest, it.unive.lisa.analysis.SemanticOracle oracle)
Interval	bottom()
int	compareTo(Interval o)
boolean	equals(java.lang.Object obj)
Interval	evalBinaryExpression(it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator, Interval left, Interval right, it.unive.lisa.program.cfg.ProgramPoint pp, it.unive.lisa.analysis.SemanticOracle oracle)
Interval	evalNonNullConstant(it.unive.lisa.symbolic.value.Constant constant, it.unive.lisa.program.cfg.ProgramPoint pp, it.unive.lisa.analysis.SemanticOracle oracle)
Interval	evalUnaryExpression(it.unive.lisa.symbolic.value.operator.unary.UnaryOperator operator, Interval arg, it.unive.lisa.program.cfg.ProgramPoint pp, it.unive.lisa.analysis.SemanticOracle oracle)
Interval	glbAux(Interval other)
int	hashCode()
boolean	is(int n)	Tests whether this interval instance corresponds (i.e., concretizes) exactly to the given integer.
boolean	isBottom()
boolean	isTop()
boolean	lessOrEqualAux(Interval other)
Interval	lubAux(Interval other)
Interval	narrowingAux(Interval other)
it.unive.lisa.util.representation.StructuredRepresentation	representation()
it.unive.lisa.analysis.lattices.Satisfiability	satisfiesBinaryExpression(it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator, Interval left, Interval right, it.unive.lisa.program.cfg.ProgramPoint pp, it.unive.lisa.analysis.SemanticOracle oracle)
Interval	top()
java.lang.String	toString()
Interval	wideningAux(Interval other)

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface it.unive.lisa.analysis.BaseLattice

glb, lessOrEqual, lub, narrowing, widening

Methods inherited from interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain

assume, assumeTernaryExpression, assumeUnaryExpression, canProcess, eval, evalIdentifier, evalNullConstant, evalPushAny, evalPushInv, evalSkip, evalTernaryExpression, evalTypeCast, evalTypeConv, evalValueExpression, satisfies, satisfiesAbstractValue, satisfiesNonNullConstant, satisfiesNullConstant, satisfiesTernaryExpression, satisfiesUnaryExpression

Methods inherited from interface it.unive.lisa.analysis.nonrelational.NonRelationalElement

fixedVariable, unknownVariable

Field Detail

ZERO

public static final Interval ZERO

The abstract zero ([0, 0]) element.

TOP

public static final Interval TOP

The abstract top ([-Inf, +Inf]) element.

BOTTOM

public static final Interval BOTTOM

The abstract bottom element.

interval

public final it.unive.lisa.util.numeric.IntInterval interval

The interval represented by this domain element.

Constructor Detail

Interval

public Interval(it.unive.lisa.util.numeric.IntInterval interval)

Builds the interval.

Parameters:

interval - the underlying IntInterval

Interval

public Interval(it.unive.lisa.util.numeric.MathNumber low,
                it.unive.lisa.util.numeric.MathNumber high)

Builds the interval.

Parameters:

low - the lower bound

high - the higher bound

Interval

public Interval(int low,
                int high)

Builds the interval.

Parameters:

low - the lower bound

high - the higher bound

Interval

public Interval()

Builds the top interval.

Method Detail

top

public Interval top()

Specified by:

top in interface it.unive.lisa.analysis.Lattice<Interval>

isTop

public boolean isTop()

Specified by:

isTop in interface it.unive.lisa.analysis.Lattice<Interval>

bottom

public Interval bottom()

Specified by:

bottom in interface it.unive.lisa.analysis.Lattice<Interval>

isBottom

public boolean isBottom()

Specified by:

isBottom in interface it.unive.lisa.analysis.Lattice<Interval>

representation

public it.unive.lisa.util.representation.StructuredRepresentation representation()

Specified by:

representation in interface it.unive.lisa.util.representation.StructuredObject

toString

public java.lang.String toString()

Specified by:

toString in interface it.unive.lisa.analysis.BaseLattice<Interval>

Overrides:

toString in class java.lang.Object

evalNonNullConstant

public Interval evalNonNullConstant(it.unive.lisa.symbolic.value.Constant constant,
                                    it.unive.lisa.program.cfg.ProgramPoint pp,
                                    it.unive.lisa.analysis.SemanticOracle oracle)

Specified by:

evalNonNullConstant in interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>

evalUnaryExpression

public Interval evalUnaryExpression(it.unive.lisa.symbolic.value.operator.unary.UnaryOperator operator,
                                    Interval arg,
                                    it.unive.lisa.program.cfg.ProgramPoint pp,
                                    it.unive.lisa.analysis.SemanticOracle oracle)

Specified by:

evalUnaryExpression in interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>

is

public boolean is(int n)

Tests whether this interval instance corresponds (i.e., concretizes) exactly to the given integer. The tests is performed through IntInterval.is(int).

Parameters:

n - the integer value

Returns:

true if that condition holds

evalBinaryExpression

public Interval evalBinaryExpression(it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator,
                                     Interval left,
                                     Interval right,
                                     it.unive.lisa.program.cfg.ProgramPoint pp,
                                     it.unive.lisa.analysis.SemanticOracle oracle)

Specified by:

evalBinaryExpression in interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>

lubAux

public Interval lubAux(Interval other)
                throws it.unive.lisa.analysis.SemanticException

Specified by:

lubAux in interface it.unive.lisa.analysis.BaseLattice<Interval>

Throws:

it.unive.lisa.analysis.SemanticException

glbAux

public Interval glbAux(Interval other)

Specified by:

glbAux in interface it.unive.lisa.analysis.BaseLattice<Interval>

wideningAux

public Interval wideningAux(Interval other)
                     throws it.unive.lisa.analysis.SemanticException

Specified by:

wideningAux in interface it.unive.lisa.analysis.BaseLattice<Interval>

Throws:

it.unive.lisa.analysis.SemanticException

narrowingAux

public Interval narrowingAux(Interval other)
                      throws it.unive.lisa.analysis.SemanticException

Specified by:

narrowingAux in interface it.unive.lisa.analysis.BaseLattice<Interval>

Throws:

it.unive.lisa.analysis.SemanticException

lessOrEqualAux

public boolean lessOrEqualAux(Interval other)
                       throws it.unive.lisa.analysis.SemanticException

Specified by:

lessOrEqualAux in interface it.unive.lisa.analysis.BaseLattice<Interval>

Throws:

it.unive.lisa.analysis.SemanticException

satisfiesBinaryExpression

public it.unive.lisa.analysis.lattices.Satisfiability satisfiesBinaryExpression(it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator,
                                                                                Interval left,
                                                                                Interval right,
                                                                                it.unive.lisa.program.cfg.ProgramPoint pp,
                                                                                it.unive.lisa.analysis.SemanticOracle oracle)

Specified by:

satisfiesBinaryExpression in interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>

hashCode

public int hashCode()

Specified by:

hashCode in interface it.unive.lisa.analysis.BaseLattice<Interval>

Overrides:

hashCode in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Specified by:

equals in interface it.unive.lisa.analysis.BaseLattice<Interval>

Overrides:

equals in class java.lang.Object

assumeBinaryExpression

public it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval> assumeBinaryExpression(it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<Interval> environment,
                                                                                                    it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator,
                                                                                                    it.unive.lisa.symbolic.value.ValueExpression left,
                                                                                                    it.unive.lisa.symbolic.value.ValueExpression right,
                                                                                                    it.unive.lisa.program.cfg.ProgramPoint src,
                                                                                                    it.unive.lisa.program.cfg.ProgramPoint dest,
                                                                                                    it.unive.lisa.analysis.SemanticOracle oracle)
                                                                                             throws it.unive.lisa.analysis.SemanticException

Specified by:

assumeBinaryExpression in interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<Interval>

Throws:

it.unive.lisa.analysis.SemanticException

compareTo

public int compareTo(Interval o)

Specified by:

compareTo in interface java.lang.Comparable<Interval>