CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational Class Reference

#include <theory_arith_old.h>

Collaboration diagram for CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational:

[legend]List of all members.

Public Member Functions

bool isFinite () const
bool isRational () const
bool isInteger () const
Rational getFloor () const
Rational getRational () const
Rational getEpsilon () const
EpsRational ()
EpsRational (const EpsRational &r)
EpsRational (const Rational &q)
EpsRational (const Rational &q, const Rational &k)
EpsRational operator+ (const EpsRational &r) const
EpsRational & operator+= (const EpsRational &r)
EpsRational operator- (const EpsRational &r) const
EpsRational operator- ()
EpsRational operator * (const Rational &a) const
EpsRational operator/ (const Rational &a) const
bool operator== (const EpsRational &r) const
bool operator<= (const EpsRational &r) const
bool operator< (const EpsRational &r) const
bool operator> (const EpsRational &r) const
std::string toString () const

Static Public Attributes

static const EpsRational PlusInfinity
static const EpsRational MinusInfinity
static const EpsRational Zero

Protected Types

enum RationalType { FINITE, PLUS_INFINITY, MINUS_INFINITY }

Protected Member Functions

EpsRational (RationalType type)

Protected Attributes

Detailed Description

EpsRational class ecapsulates the rationals with a symbolic small $\epsilon$ added. Each rational number is presented as a pair $(q, k) = q + k\epsilon$ , where $\epsilon$ is treated symbolically. The operations on the new rationals are defined as

$(q_1, k_1) + (q_2, k_2) \equiv (q_1 + q_2, k_1 + k_2)$
$a \times (q, k) \equiv (a \times q, a \times k)$
$(q_1, k_1) \leq (q_2, k_2) \equiv (q_1 < q_2) \vee (q_1 = q_2 \wedge k_1 \leq k_2)$

Note that the operations on the infinite values are not defined, as they are never used currently. Infinities can only be asigned or compared.

Definition at line 473 of file theory_arith_old.h.

Member Enumeration Documentation

enum CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::RationalType [protected]

Type of rationals, normal and the two infinities

Enumerator:

FINITE
PLUS_INFINITY
MINUS_INFINITY

Definition at line 478 of file theory_arith_old.h.

Constructor & Destructor Documentation

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::EpsRational ( RationalType type ) [inline, protected]

Private constructor to construt infinities.

Definition at line 492 of file theory_arith_old.h.

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::EpsRational ( ) [inline]

The blank constructor

Definition at line 559 of file theory_arith_old.h.

Referenced by operator *(), operator+(), operator-(), and operator/().

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::EpsRational ( const EpsRational & r ) [inline]

Copy constructor

Definition at line 562 of file theory_arith_old.h.

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::EpsRational ( const Rational & q ) [inline]

Constructor from a rational, constructs a new pair (q, 0).

Parameters:

the rational

Definition at line 569 of file theory_arith_old.h.

CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::EpsRational	(	const Rational &	q,
		const Rational &	k
	)			`[inline]`

Constructor from a rational and a given epsilon multiplier, constructs a new pair (q, k).

Parameters:

	q	the rational
	k	the epsilon multiplier

Definition at line 578 of file theory_arith_old.h.

Member Function Documentation

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::isFinite ( ) const [inline]

Returns if the numbe is finite.

Definition at line 499 of file theory_arith_old.h.

References FINITE, and type.

Referenced by CVC3::TheoryArithOld::computeTermBounds(), CVC3::TheoryArithOld::getLowerBound(), CVC3::TheoryArithOld::getUpperBound(), CVC3::TheoryArithOld::hasLowerBound(), and CVC3::TheoryArithOld::hasUpperBound().

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::isRational ( ) const [inline]

Returns if the number is a plain rational.

Returns:: true if rational, false otherwise

Definition at line 506 of file theory_arith_old.h.

References k.

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::isInteger ( ) const [inline]

Returns if the number is a plain integer.

Returns:: true if rational, false otherwise

Definition at line 513 of file theory_arith_old.h.

References CVC3::Rational::isInteger(), k, and q.

Rational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::getFloor ( ) const [inline]

Returns the floor of the number $x = q + k \epsilon$ using the following fomula

$\lfloor \beta(x) \rfloor = \begin{cases} \lfloor q \rfloor & \text{ if } q \notin Z\\ q & \text{ if } q \in Z \text{ and } k \geq 0\\ q - 1 & \text{ if } q \in Z \text{ and } k < 0 \end{cases}$

Definition at line 526 of file theory_arith_old.h.

References CVC3::Rational::isInteger(), k, and q.

Rational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::getRational ( ) const [inline]

Returns the rational part of the number

Returns:: the rational

Definition at line 541 of file theory_arith_old.h.

References q.

Referenced by CVC3::TheoryArithOld::DifferenceLogicGraph::addEdge(), CVC3::TheoryArithOld::DifferenceLogicGraph::getValuation(), and CVC3::TheoryArithOld::DifferenceLogicGraph::tryUpdate().

Rational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::getEpsilon ( ) const [inline]

Returns the epsilon part of the number

Returns:: the epsilon

Definition at line 548 of file theory_arith_old.h.

References k.

Referenced by CVC3::TheoryArithOld::DifferenceLogicGraph::addEdge(), CVC3::TheoryArithOld::DifferenceLogicGraph::getValuation(), and CVC3::TheoryArithOld::DifferenceLogicGraph::tryUpdate().

EpsRational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator+ ( const EpsRational & r ) const [inline]

Addition operator for two EpsRational numbers.

Parameters:

the number to be added

Returns:: the sum as defined in the class

Definition at line 586 of file theory_arith_old.h.

References DebugAssert, EpsRational(), FINITE, k, q, and type.

EpsRational& CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator+= ( const EpsRational & r ) [inline]

Addition operator for two EpsRational numbers.

Parameters:

the number to be added

Returns:: the sum as defined in the class

Definition at line 598 of file theory_arith_old.h.

References DebugAssert, FINITE, k, q, and type.

EpsRational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator- ( const EpsRational & r ) const [inline]

Subtraction operator for two EpsRational numbers.

Parameters:

the number to be added

Returns:: the sum as defined in the class

Definition at line 611 of file theory_arith_old.h.

References DebugAssert, EpsRational(), FINITE, k, q, and type.

EpsRational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator- ( ) [inline]

Unary minus operator

Definition at line 620 of file theory_arith_old.h.

References DebugAssert, FINITE, k, q, and type.

EpsRational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator * ( const Rational & a ) const [inline]

Multiplication operator EpsRational number and a rational number.

Parameters:

the number to be multiplied

Returns:: the product as defined in the class

Definition at line 634 of file theory_arith_old.h.

References DebugAssert, EpsRational(), FINITE, k, q, and type.

EpsRational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator/ ( const Rational & a ) const [inline]

Division operator EpsRational number and a rational number.

Parameters:

the number to be multiplied

Returns:: the product as defined in the class

Definition at line 645 of file theory_arith_old.h.

References DebugAssert, EpsRational(), FINITE, k, q, and type.

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator== ( const EpsRational & r ) const [inline]

Equality comparison operator.

Definition at line 653 of file theory_arith_old.h.

References k, and q.

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator<= ( const EpsRational & r ) const [inline]

Less than or equal comparison operator.

Definition at line 658 of file theory_arith_old.h.

References FatalAssert, FINITE, k, MINUS_INFINITY, PLUS_INFINITY, q, and type.

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator< ( const EpsRational & r ) const [inline]

Less than comparison operator.

Definition at line 683 of file theory_arith_old.h.

bool CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::operator> ( const EpsRational & r ) const [inline]

Greater than comparison operator.

Definition at line 688 of file theory_arith_old.h.

std::string CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::toString ( ) const [inline]

Returns the string representation of the number.

Returns:: the string representation of the number

Definition at line 695 of file theory_arith_old.h.

References FatalAssert, FINITE, k, MINUS_INFINITY, PLUS_INFINITY, q, CVC3::Rational::toString(), and type.

Referenced by CVC3::TheoryArithOld::DifferenceLogicGraph::getEdgeTheorems(), CVC3::TheoryArithOld::getLowerBound(), and CVC3::TheoryArithOld::getUpperBound().

Member Data Documentation

RationalType CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::type [protected]

The type of this rational

Definition at line 481 of file theory_arith_old.h.

Referenced by isFinite(), operator *(), operator+(), operator+=(), operator-(), operator/(), operator<=(), and toString().

Rational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::q [protected]

The rational part

Definition at line 484 of file theory_arith_old.h.

Referenced by getFloor(), getRational(), isInteger(), operator *(), operator+(), operator+=(), operator-(), operator/(), operator<=(), operator==(), and toString().

Rational CVC3::TheoryArithOld::DifferenceLogicGraph::EpsRational::k [protected]

The epsilon multiplier

Definition at line 487 of file theory_arith_old.h.

Referenced by getEpsilon(), getFloor(), isInteger(), isRational(), operator *(), operator+(), operator+=(), operator-(), operator/(), operator<=(), operator==(), and toString().

const TheoryArithOld::DifferenceLogicGraph::EpsRational TheoryArithOld::DifferenceLogicGraph::EpsRational::PlusInfinity [static]

The infinity constant

Definition at line 551 of file theory_arith_old.h.

Referenced by CVC3::TheoryArithOld::DifferenceLogicGraph::getEdgeWeight(), and CVC3::TheoryArithOld::getUpperBound().

const TheoryArithOld::DifferenceLogicGraph::EpsRational TheoryArithOld::DifferenceLogicGraph::EpsRational::MinusInfinity [static]

The negative infinity constant

Definition at line 553 of file theory_arith_old.h.

Referenced by CVC3::TheoryArithOld::computeTermBounds(), and CVC3::TheoryArithOld::getLowerBound().

const TheoryArithOld::DifferenceLogicGraph::EpsRational TheoryArithOld::DifferenceLogicGraph::EpsRational::Zero [static]

The zero constant

Definition at line 555 of file theory_arith_old.h.

Referenced by CVC3::TheoryArithOld::getLowerBound(), CVC3::TheoryArithOld::getUpperBound(), and CVC3::TheoryArithOld::DifferenceLogicGraph::tryUpdate().

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

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