Detailed Description

interval arithmetics for provable bounds

Author: Tobias Achterberg; Stefan Vigerske; Kati Wolter

#include <stdlib.h>
#include <assert.h>
#include "scip/def.h"
#include "scip/intervalarith.h"
#include "scip/pub_message.h"
#include "scip/misc.h"

Go to the source code of this file.

Macros
#define	SCIP_ROUND_DOWNWARDS 0

#define	SCIP_ROUND_UPWARDS 1

#define	SCIP_ROUND_NEAREST 2

#define	SCIP_ROUND_ZERO 3

#define	CALCB(y) ((bx + axy * (y)) / (2.0 * sqrtax))

#define	CALCR(c, y) (rcoef_const + (c) + (rcoef_y + rcoef_yy * (y)) * (y))

Functions
SCIP_Bool	SCIPintervalHasRoundingControl (void)

void	SCIPintervalSetRoundingMode (SCIP_ROUNDMODE roundmode)

SCIP_ROUNDMODE	SCIPintervalGetRoundingMode (void)

static SCIP_Real	negate (SCIP_Real x)

void	SCIPintervalSetRoundingModeDownwards (void)

void	SCIPintervalSetRoundingModeUpwards (void)

void	SCIPintervalSetRoundingModeToNearest (void)

void	SCIPintervalSetRoundingModeTowardsZero (void)

SCIP_Real	SCIPintervalNegateReal (SCIP_Real x)

SCIP_Real	SCIPintervalGetInf (SCIP_INTERVAL interval)

SCIP_Real	SCIPintervalGetSup (SCIP_INTERVAL interval)

void	SCIPintervalSet (SCIP_INTERVAL *resultant, SCIP_Real value)

void	SCIPintervalSetBounds (SCIP_INTERVAL *resultant, SCIP_Real inf, SCIP_Real sup)

void	SCIPintervalSetEmpty (SCIP_INTERVAL *resultant)

SCIP_Bool	SCIPintervalIsEmpty (SCIP_Real infinity, SCIP_INTERVAL operand)

void	SCIPintervalSetEntire (SCIP_Real infinity, SCIP_INTERVAL *resultant)

SCIP_Bool	SCIPintervalIsEntire (SCIP_Real infinity, SCIP_INTERVAL operand)

SCIP_Bool	SCIPintervalIsPositiveInfinity (SCIP_Real infinity, SCIP_INTERVAL operand)

SCIP_Bool	SCIPintervalIsNegativeInfinity (SCIP_Real infinity, SCIP_INTERVAL operand)

SCIP_Bool	SCIPintervalIsSubsetEQ (SCIP_Real infinity, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

SCIP_Bool	SCIPintervalAreDisjoint (SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalIntersect (SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalUnify (SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalAddInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalAddSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalAdd (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalAddScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalAddVectors (SCIP_Real infinity, SCIP_INTERVAL resultant, int length, SCIP_INTERVAL operand1, SCIP_INTERVAL *operand2)

void	SCIPintervalSub (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalSubScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalMulInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalMulSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalMul (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalMulScalarInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalMulScalarSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalMulScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalDiv (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalDivScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalScalprod (SCIP_Real infinity, SCIP_INTERVAL resultant, int length, SCIP_INTERVAL operand1, SCIP_INTERVAL *operand2)

void	SCIPintervalScalprodScalarsInf (SCIP_Real infinity, SCIP_INTERVAL resultant, int length, SCIP_INTERVAL operand1, SCIP_Real *operand2)

void	SCIPintervalScalprodScalarsSup (SCIP_Real infinity, SCIP_INTERVAL resultant, int length, SCIP_INTERVAL operand1, SCIP_Real *operand2)

void	SCIPintervalScalprodScalars (SCIP_Real infinity, SCIP_INTERVAL resultant, int length, SCIP_INTERVAL operand1, SCIP_Real *operand2)

void	SCIPintervalSquare (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalSquareRoot (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalPower (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

SCIP_Real	SCIPintervalPowerScalarIntegerInf (SCIP_Real operand1, int operand2)

SCIP_Real	SCIPintervalPowerScalarIntegerSup (SCIP_Real operand1, int operand2)

void	SCIPintervalPowerScalarInteger (SCIP_INTERVAL *resultant, SCIP_Real operand1, int operand2)

void	SCIPintervalPowerScalarScalar (SCIP_INTERVAL *resultant, SCIP_Real operand1, SCIP_Real operand2)

void	SCIPintervalPowerScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalPowerScalarInverse (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL basedomain, SCIP_Real exponent, SCIP_INTERVAL image)

void	SCIPintervalSignPowerScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void	SCIPintervalReciprocal (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalExp (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalLog (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalMin (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalMax (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void	SCIPintervalAbs (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void	SCIPintervalSign (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

SCIP_Real	SCIPintervalQuadUpperBound (SCIP_Real infinity, SCIP_Real a, SCIP_INTERVAL b_, SCIP_INTERVAL x)

void	SCIPintervalQuad (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL xrng)

void	SCIPintervalSolveUnivariateQuadExpressionPositive (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs)

void	SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_Real lincoeff, SCIP_Real rhs)

void	SCIPintervalSolveUnivariateQuadExpression (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs)

void	SCIPintervalQuadBivar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)

void	SCIPintervalSolveBivariateQuadExpressionAllScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)

Macro Definition Documentation

#define SCIP_ROUND_DOWNWARDS 0

#define SCIP_ROUND_NEAREST 2

round always to nearest

Definition at line 176 of file intervalarith.c.

Referenced by SCIPintervalExp(), SCIPintervalGetRoundingMode(), SCIPintervalLog(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarScalar(), SCIPintervalSetRoundingModeToNearest(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIPintervalSquareRoot().

#define SCIP_ROUND_ZERO 3

round always towards zero

Definition at line 177 of file intervalarith.c.

Referenced by SCIPintervalSetRoundingModeTowardsZero().

#define CALCB ( y ) ((bx + axy * (y)) / (2.0 * sqrtax))

Referenced by SCIPintervalSolveBivariateQuadExpressionAllScalar().

#define CALCR	(	c,
		y
	)	(rcoef_const + (c) + (rcoef_y + rcoef_yy * (y)) * (y))

Referenced by SCIPintervalSolveBivariateQuadExpressionAllScalar().

Function Documentation

SCIP_Bool SCIPintervalHasRoundingControl ( void )

returns whether rounding mode control is available

Definition at line 180 of file intervalarith.c.

References FALSE.

Referenced by SCIPfindSimpleRational().

void SCIPintervalSetRoundingMode ( SCIP_ROUNDMODE roundmode )

sets rounding mode of floating point operations

Parameters

roundmode rounding mode to activate

Definition at line 188 of file intervalarith.c.

References SCIPerrorMessage.

Referenced by consdataUpdateLinearActivity(), consdataUpdateLinearActivityLbChange(), consdataUpdateLinearActivityUbChange(), exprgraphNodePropagateBounds(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateConstraintSides(), SCIPfindSimpleRational(), SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalAddVectors(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalMul(), SCIPintervalMulScalar(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalScalprod(), SCIPintervalScalprodScalars(), SCIPintervalSetRoundingModeDownwards(), SCIPintervalSetRoundingModeToNearest(), SCIPintervalSetRoundingModeTowardsZero(), SCIPintervalSetRoundingModeUpwards(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), SCIPintervalSquare(), and SCIPintervalSub().

SCIP_ROUNDMODE SCIPintervalGetRoundingMode ( void )

gets current rounding mode of floating point operations

Definition at line 196 of file intervalarith.c.

References negate(), and SCIP_ROUND_NEAREST.

Referenced by consdataUpdateLinearActivity(), consdataUpdateLinearActivityLbChange(), consdataUpdateLinearActivityUbChange(), exprgraphNodePropagateBounds(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateConstraintSides(), SCIPfindSimpleRational(), SCIPintervalAdd(), SCIPintervalAddInf(), SCIPintervalAddScalar(), SCIPintervalAddSup(), SCIPintervalAddVectors(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalExp(), SCIPintervalLog(), SCIPintervalMul(), SCIPintervalMulInf(), SCIPintervalMulScalar(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), SCIPintervalMulSup(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalPowerScalarScalar(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalScalprod(), SCIPintervalScalprodScalars(), SCIPintervalScalprodScalarsInf(), SCIPintervalScalprodScalarsSup(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), SCIPintervalSquare(), SCIPintervalSquareRoot(), and SCIPintervalSub().

static SCIP_Real negate ( SCIP_Real x )

static

gets the negation of a double

Fallback implementation that calls the negation method from misc.o. Having the implementation in a different object file will hopefully prevent it from being "optimized away".

Parameters

x	number that should be negated

Definition at line 266 of file intervalarith.c.

References SCIPnegateReal().

Referenced by SCIPintervalGetRoundingMode(), SCIPintervalNegateReal(), SCIPintervalPowerScalarInteger(), SCIPintervalQuadUpperBound(), SCIPintervalSignPowerScalar(), and SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar().

void SCIPintervalSetRoundingModeDownwards ( void )

sets rounding mode of floating point operations to downwards rounding

Definition at line 390 of file intervalarith.c.

References SCIP_ROUND_DOWNWARDS, and SCIPintervalSetRoundingMode().

Referenced by consdataUpdateLinearActivity(), consdataUpdateLinearActivityLbChange(), consdataUpdateLinearActivityUbChange(), exprgraphNodePropagateBounds(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateConstraintSides(), and SCIPfindSimpleRational().

void SCIPintervalSetRoundingModeUpwards ( void )

sets rounding mode of floating point operations to upwards rounding

Definition at line 398 of file intervalarith.c.

References SCIP_ROUND_UPWARDS, and SCIPintervalSetRoundingMode().

Referenced by consdataUpdateLinearActivity(), consdataUpdateLinearActivityLbChange(), consdataUpdateLinearActivityUbChange(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), and propagateBoundsQuadVar().

void SCIPintervalSetRoundingModeToNearest ( void )

sets rounding mode of floating point operations to nearest rounding

Definition at line 406 of file intervalarith.c.

References SCIP_ROUND_NEAREST, and SCIPintervalSetRoundingMode().

void SCIPintervalSetRoundingModeTowardsZero ( void )

sets rounding mode of floating point operations to towards zero rounding

Definition at line 414 of file intervalarith.c.

References SCIP_ROUND_ZERO, and SCIPintervalSetRoundingMode().

SCIP_Real SCIPintervalNegateReal ( SCIP_Real x )

negates a number in a way that the compiler does not optimize it away

Parameters

x	number to negate

Definition at line 422 of file intervalarith.c.

References negate().

Referenced by consdataUpdateLinearActivityLbChange(), consdataUpdateLinearActivityUbChange(), exprgraphNodePropagateBounds(), propagateBoundsCons(), and propagateConstraintSides().

SCIP_Real SCIPintervalGetInf ( SCIP_INTERVAL interval )

returns infimum of interval

Parameters

interval interval

Definition at line 451 of file intervalarith.c.

References SCIP_Interval::inf.

Referenced by addIntervalGradientEstimator(), enforceViolatedFixedNonlinear(), lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), presolveTryAddLinearReform(), propagateBounds(), propagateBoundsBilinearTerm(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateBoundsTightenVar(), propagateConstraintSides(), provedBound(), reformNode2Var(), reformulate(), replaceViolatedByLinearConstraints(), SCIP_DECL_EXPRGRAPHNODEREFORM(), SCIP_DECL_NONLINCONSUPGD(), SCIPintervalSolveUnivariateQuadExpression(), SCIPlpGetModifiedProvedPseudoObjval(), and tightenBounds().

SCIP_Real SCIPintervalGetSup ( SCIP_INTERVAL interval )

returns supremum of interval

Parameters

interval interval

Definition at line 459 of file intervalarith.c.

References SCIP_Interval::sup.

Referenced by addIntervalGradientEstimator(), enforceViolatedFixedNonlinear(), nlrowCalcActivityBounds(), presolveTryAddLinearReform(), propagateBounds(), propagateBoundsBilinearTerm(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateBoundsTightenVar(), propagateConstraintSides(), reformNode2Var(), reformulate(), replaceViolatedByLinearConstraints(), SCIP_DECL_EXPRGRAPHNODEREFORM(), SCIP_DECL_NONLINCONSUPGD(), SCIPintervalSolveUnivariateQuadExpression(), and tightenBounds().

void SCIPintervalSet	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	value
	)

stores given value as interval

Parameters

resultant	interval to store value into
value	value to store

Definition at line 467 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by checkFixedVariables(), consdataCreate(), exprgraphNodePropagateBounds(), lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), presolveTryAddLinearReform(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIPexprgraphAddNode(), SCIPexprgraphReplaceVarByLinearSum(), SCIPintervalDiv(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarScalar(), SCIPintervalQuadBivar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPlpGetModifiedProvedPseudoObjval().

void SCIPintervalSetBounds	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	inf,
		SCIP_Real	sup
	)

stores given infimum and supremum as interval

Parameters

resultant	interval to store value into
inf	value to store as infimum
sup	value to store as supremum

Definition at line 479 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by addIntervalGradientEstimator(), addUserEstimator(), checkCurvature(), exprgraphNodePropagateBounds(), getImpliedBounds(), nlrowCalcActivityBounds(), operator-(), propagateBounds(), propagateBoundsBilinearTerm(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateCons(), provedBound(), SCIP_DECL_EXPRCURV(), SCIP_DECL_EXPRGRAPHVARADDED(), SCIP_DECL_EXPRINTEVAL(), SCIPevalExprtreeGlobalBounds(), SCIPevalExprtreeLocalBounds(), SCIPexprcurvPower(), SCIPintervalPowerScalarInverse(), SCIPintervalQuadBivar(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

void SCIPintervalSetEmpty ( SCIP_INTERVAL * resultant )

sets interval to empty interval, which will be [infinity, -infinity]

Parameters

resultant resultant interval of operation

Definition at line 493 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by addBilinearTerm(), addQuadVarTerm(), catchQuadVarEvents(), consdataCreate(), delQuadVarTermPos(), mergeAndCleanLinearVars(), mergeAndCleanQuadVarTerms(), removeBilinearTermsPos(), replaceQuadVarTermPos(), SCIP_DECL_EVENTEXEC(), SCIP_DECL_EXPRINTEVAL(), SCIPaddQuadVarLinearCoefQuadratic(), SCIPaddSquareCoefQuadratic(), SCIPchgBilinCoefQuadratic(), SCIPchgLinearCoefQuadratic(), SCIPchgSquareCoefQuadratic(), SCIPintervalLog(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarInverse(), SCIPintervalQuad(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIPintervalSquareRoot().

SCIP_Bool SCIPintervalIsEmpty	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is empty, i.e., whether inf > sup

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 504 of file intervalarith.c.

References FALSE, SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by computeBoundsX(), computeBoundsZ(), enforceViolatedFixedNonlinear(), exprgraphNodePropagateBounds(), exprgraphNodeUpdateBounds(), propagateBounds(), propagateBoundsBilinearTerm(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), propagateBoundsTightenVar(), reformEnsureChildrenMinCurvature(), reformMonomial(), reformulate(), SCIP_DECL_EXPRINTEVAL(), SCIPexprgraphCheckCurvature(), SCIPexprgraphGetNodePolynomialMonomialCurvature(), SCIPexprgraphPropagateVarBounds(), SCIPexprgraphTightenNodeBounds(), SCIPexprgraphUpdateNodeBoundsCurvature(), SCIPintervalAbs(), SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalExp(), SCIPintervalLog(), SCIPintervalMax(), SCIPintervalMin(), SCIPintervalMul(), SCIPintervalMulInf(), SCIPintervalMulScalar(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), SCIPintervalMulSup(), SCIPintervalPower(), SCIPintervalPowerScalar(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalSign(), SCIPintervalSignPowerScalar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSquare(), SCIPintervalSquareRoot(), and SCIPintervalSub().

void SCIPintervalSetEntire	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant
	)

sets interval to entire [-infinity, +infinity]

Parameters

infinity	value for infinity
resultant	resultant interval of operation

Definition at line 516 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by computeBoundsX(), computeBoundsZ(), exprgraphCreateNode(), exprgraphNodePropagateBounds(), SCIP_DECL_EXPRINTEVAL(), SCIPexprEvalIntUser(), SCIPexprgraphAddNode(), SCIPexprgraphAddVars(), SCIPexprgraphEnableNode(), SCIPexprgraphNodeSplitOffLinear(), SCIPexprgraphReplaceVarByLinearSum(), SCIPintervalScalprod(), SCIPintervalScalprodScalarsInf(), SCIPintervalScalprodScalarsSup(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpression().

SCIP_Bool SCIPintervalIsEntire	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is entire, i.e., whether inf <= -infinity and sup >= infinity

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 528 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), nlrowCalcActivityBounds(), propagateBoundsBilinearTerm(), propagateBoundsCons(), propagateBoundsQuadVar(), and SCIP_DECL_EXPRINTEVAL().

SCIP_Bool SCIPintervalIsPositiveInfinity	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is positive infinity, i.e., [infinity, infinity]

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 537 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by propagateBoundsTightenVar().

SCIP_Bool SCIPintervalIsNegativeInfinity	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is negative infinity, i.e., [-infinity, -infinity]

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 546 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by propagateBoundsTightenVar().

SCIP_Bool SCIPintervalIsSubsetEQ	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

indicates whether operand1 is contained in operand2

Parameters

infinity	value for infinity
operand1	first operand of operation
operand2	second operand of operation

Definition at line 555 of file intervalarith.c.

References FALSE, SCIP_Interval::inf, MAX, MIN, SCIP_Interval::sup, and TRUE.

Referenced by propagateBoundsCons().

SCIP_Bool SCIPintervalAreDisjoint	(	SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

indicates whether operand1 and operand2 are disjoint

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 574 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by propagateBoundsCons().

void SCIPintervalIntersect	(	SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

intersection of two intervals

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 583 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, and SCIP_Interval::sup.

Referenced by exprgraphNodeUpdateBounds(), SCIPexprgraphTightenNodeBounds(), SCIPexprgraphUpdateNodeBoundsCurvature(), SCIPintervalPowerScalarInverse(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpressionPositive().

void SCIPintervalUnify	(	SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

interval enclosure of the union of two intervals

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 596 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, and SCIP_Interval::sup.

Referenced by SCIPintervalPowerScalarInverse(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpression().

void SCIPintervalAddInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 623 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, and SCIPintervalGetRoundingMode().

Referenced by SCIPintervalAdd(), SCIPintervalAddVectors(), SCIPintervalScalprod(), and SCIPintervalScalprodScalarsInf().

void SCIPintervalAddSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 650 of file intervalarith.c.

References NULL, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), and SCIP_Interval::sup.

Referenced by SCIPintervalAdd(), SCIPintervalAddVectors(), SCIPintervalScalprod(), and SCIPintervalScalprodScalarsSup().

void SCIPintervalAdd	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 677 of file intervalarith.c.

References NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), SCIPintervalAddSup(), SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), and SCIPintervalSetRoundingMode().

Referenced by exprgraphNodePropagateBounds(), lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), operator+(), presolveTryAddLinearReform(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalQuadBivar(), and SCIPlpGetModifiedProvedPseudoObjval().

void SCIPintervalAddScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

adds operand1 and scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 704 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), propagateBounds(), propagateBoundsQuadVar(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalQuadBivar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSubScalar().

void SCIPintervalAddVectors	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_INTERVAL *	operand2
	)

adds vector operand1 and vector operand2 and stores result in vector resultant

Parameters

infinity	value for infinity
resultant	array of resultant intervals of operation
length	length of arrays
operand1	array of first operands of operation
operand2	array of second operands of operation

Definition at line 754 of file intervalarith.c.

References SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), SCIPintervalAddSup(), SCIPintervalGetRoundingMode(), and SCIPintervalSetRoundingMode().

void SCIPintervalSub	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

subtracts operand2 from operand1 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 784 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), lpUpdateVarColumnProved(), lpUpdateVarProved(), operator-(), propagateBounds(), propagateBoundsCons(), propagateBoundsQuadVar(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPlpGetModifiedProvedPseudoObjval().

void SCIPintervalSubScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

subtracts scalar operand2 from operand1 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 832 of file intervalarith.c.

References SCIPintervalAddScalar().

Referenced by exprgraphNodePropagateBounds(), and propagateBounds().

void SCIPintervalMulInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 843 of file intervalarith.c.

References SCIP_Interval::inf, MIN, NULL, SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMulScalarInf(), and SCIP_Interval::sup.

Referenced by propagateBoundsCons(), SCIPintervalMul(), and SCIPintervalScalprod().

void SCIPintervalMulSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 903 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMulScalarSup(), and SCIP_Interval::sup.

Referenced by propagateBoundsCons(), SCIPintervalMul(), and SCIPintervalScalprod().

void SCIPintervalMul	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 963 of file intervalarith.c.

References NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMulInf(), SCIPintervalMulSup(), and SCIPintervalSetRoundingMode().

Referenced by exprgraphNodePropagateBounds(), lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), operator*(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalDiv(), SCIPintervalPower(), SCIPintervalQuad(), and SCIPlpGetModifiedProvedPseudoObjval().

void SCIPintervalMulScalarInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation; can be +/- inf

Definition at line 990 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIPintervalMulInf(), SCIPintervalMulScalar(), and SCIPintervalScalprodScalarsInf().

void SCIPintervalMulScalarSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation; can be +/- inf

Definition at line 1046 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIPintervalMulScalar(), SCIPintervalMulSup(), and SCIPintervalScalprodScalarsSup().

void SCIPintervalMulScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1102 of file intervalarith.c.

References NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), and SCIPintervalSetRoundingMode().

Referenced by addIntervalGradientEstimator(), exprgraphNodePropagateBounds(), nlrowCalcActivityBounds(), presolveTryAddLinearReform(), propagateBounds(), propagateBoundsCons(), propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), replaceViolatedByLinearConstraints(), SCIP_DECL_EXPRINTEVAL(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

void SCIPintervalDiv	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

divides operand1 by operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1128 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMul(), SCIPintervalSet(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), operator/(), SCIP_DECL_EXPRINTEVAL(), and SCIPintervalSolveUnivariateQuadExpression().

void SCIPintervalDivScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

divides operand1 by scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1182 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by presolveTryAddLinearReform(), propagateBounds(), and propagateBoundsCons().

void SCIPintervalScalprod	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_INTERVAL *	operand2
	)

computes the scalar product of two vectors of intervals and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals; can have +/-inf entries
operand2	second vector as array of intervals; can have +/-inf entries

Definition at line 1285 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), SCIPintervalAddSup(), SCIPintervalGetRoundingMode(), SCIPintervalMulInf(), SCIPintervalMulSup(), SCIPintervalSetEntire(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

void SCIPintervalScalprodScalarsInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes scalar product of a vector of intervals and a vector of scalars and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1327 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_ROUND_DOWNWARDS, SCIPintervalAddInf(), SCIPintervalGetRoundingMode(), SCIPintervalMulScalarInf(), SCIPintervalSetEntire(), and SCIP_Interval::sup.

Referenced by SCIPintervalScalprodScalars().

void SCIPintervalScalprodScalarsSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes the scalar product of a vector of intervals and a vector of scalars and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1355 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_ROUND_UPWARDS, SCIPintervalAddSup(), SCIPintervalGetRoundingMode(), SCIPintervalMulScalarSup(), SCIPintervalSetEntire(), and SCIP_Interval::sup.

Referenced by SCIPintervalScalprodScalars().

void SCIPintervalScalprodScalars	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes the scalar product of a vector of intervals and a vector of scalars and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1381 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalScalprodScalarsInf(), SCIPintervalScalprodScalarsSup(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

void SCIPintervalSquare	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

squares operand and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 1409 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), propagateBounds(), SCIP_DECL_EXPRINTEVAL(), and square().

void SCIPintervalSquareRoot	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores (positive part of) square root of operand in resultant

Attention: we assume a correctly rounded sqrt(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 1481 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetEmpty(), sqrt(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), propagateBounds(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalSolveUnivariateQuadExpression(), and sqrt().

void SCIPintervalPower	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores operand1 to the power of operand2 in resultant

uses SCIPintervalPowerScalar if operand2 is a scalar, otherwise computes exp(op2*log(op1))

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1542 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPintervalExp(), SCIPintervalIsEmpty(), SCIPintervalLog(), SCIPintervalMul(), SCIPintervalPowerScalar(), and SCIP_Interval::sup.

Referenced by pow(), and SCIPintervalPowerScalarInverse().

SCIP_Real SCIPintervalPowerScalarIntegerInf	(	SCIP_Real	operand1,
		int	operand2
	)

computes lower bound on power of a scalar operand1 to an integer operand2 both operands need to be finite numbers need to have operand1 >= 0 and need to have operand2 >= 0 if operand1 == 0

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 1575 of file intervalarith.c.

References SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIPintervalGetRoundingMode(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalSetRoundingMode(), and TRUE.

Referenced by SCIPintervalPowerScalar(), and SCIPintervalPowerScalarIntegerSup().

SCIP_Real SCIPintervalPowerScalarIntegerSup	(	SCIP_Real	operand1,
		int	operand2
	)

computes upper bound on power of a scalar operand1 to an integer operand2 both operands need to be finite numbers need to have operand1 >= 0 and need to have operand2 >= 0 if operand1 == 0

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 1657 of file intervalarith.c.

References SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalSetRoundingMode(), and TRUE.

Referenced by SCIPintervalPowerScalar(), and SCIPintervalPowerScalarIntegerInf().

void SCIPintervalPowerScalarInteger	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	operand1,
		int	operand2
	)

computes bounds on power of a scalar operand1 to an integer operand2 both operands need to be finite numbers need to have operand1 >= 0 and need to have operand2 >= 0 if operand1 == 0

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1731 of file intervalarith.c.

References SCIP_Interval::inf, negate(), SCIP_Real, SCIP_REAL_MAX, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalPowerScalarInteger(), SCIPintervalReciprocal(), SCIPintervalSet(), SCIPintervalSetRoundingMode(), SCIP_Interval::sup, and TRUE.

Referenced by SCIPintervalPowerScalarInteger().

void SCIPintervalPowerScalarScalar	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	operand1,
		SCIP_Real	operand2
	)

stores bounds on the power of a scalar operand1 to a scalar operand2 in resultant both operands need to be finite numbers need to have operand1 >= 0 or operand2 integer and need to have operand2 >= 0 if operand1 == 0

Attention: we assume a correctly rounded pow(double) function when rounding is to nearest

Parameters

resultant	resultant of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1822 of file intervalarith.c.

References SCIP_Interval::inf, NULL, pow(), SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalSet(), and SCIP_Interval::sup.

void SCIPintervalPowerScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

stores operand1 to the power of the scalar operand2 in resultant

Attention: we assume a correctly rounded pow(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1865 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, pow(), SCIP_Bool, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalSetEmpty(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), pow(), SCIP_DECL_EXPRINTEVAL(), and SCIPintervalPower().

void SCIPintervalPowerScalarInverse	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	basedomain,
		SCIP_Real	exponent,
		SCIP_INTERVAL	image
	)

given an interval for the image of a power operation, computes an interval for the origin that is, for y = x^p with p = exponent a given scalar and y = image a given interval, computes a subinterval x of basedomain such that y in x^p and such that for all z in basedomain less x, z^p not in y

Parameters

infinity	value for infinity
resultant	resultant interval of operation
basedomain	domain of base
exponent	exponent
image	interval image of power

Definition at line 2113 of file intervalarith.c.

References EPSISINT, SCIP_Interval::inf, MAX, MIN, NULL, SCIPintervalIntersect(), SCIPintervalPower(), SCIPintervalReciprocal(), SCIPintervalSetBounds(), SCIPintervalSetEmpty(), SCIPintervalUnify(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds().

void SCIPintervalSignPowerScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

stores operand1 to the signed power of the scalar positive operand2 in resultant

the signed power of x w.r.t. an exponent n >= 0 is given as sign(x) * abs(x)^n

Attention: we assume correctly rounded sqrt(double) and pow(double) functions when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2194 of file intervalarith.c.

References SCIP_Interval::inf, negate(), NULL, pow(), SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_NEAREST, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), sqrt(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), SCIP_DECL_EXPRINTEVAL(), and signpow().

void SCIPintervalReciprocal	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

computes the reciprocal of an interval

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2366 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by SCIPintervalPowerScalarInteger(), and SCIPintervalPowerScalarInverse().

void SCIPintervalExp	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores exponential of operand in resultant

Attention: we assume a correctly rounded exp(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2439 of file intervalarith.c.

References exp(), SCIP_Interval::inf, NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by exp(), exprgraphNodePropagateBounds(), SCIP_DECL_EXPRINTEVAL(), and SCIPintervalPower().

void SCIPintervalLog	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores natural logarithm of operand in resultant

Attention: we assume a correctly rounded log(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2519 of file intervalarith.c.

References SCIP_Interval::inf, log(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSetEmpty(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), log(), SCIP_DECL_EXPRINTEVAL(), and SCIPintervalPower().

void SCIPintervalMin	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores minimum of operands in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2593 of file intervalarith.c.

References SCIP_Interval::inf, MIN, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

void SCIPintervalMax	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores maximum of operands in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2609 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

void SCIPintervalAbs	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores absolute value of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2625 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by abs(), and SCIP_DECL_EXPRINTEVAL().

void SCIPintervalSign	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores sign of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2651 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), and sign().

SCIP_Real SCIPintervalQuadUpperBound	(	SCIP_Real	infinity,
		SCIP_Real	a,
		SCIP_INTERVAL	b_,
		SCIP_INTERVAL	x
	)

computes exact upper bound on $ a x^2 + b x $ for x in [xlb, xub], b an interval, and a scalar

Uses Algorithm 2.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008)

Parameters

infinity	value for infinity
a	coefficient of x^2
b_	coefficient of x
x	range of x

Definition at line 2680 of file intervalarith.c.

References SCIP_Interval::inf, MAX, negate(), SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalQuadUpperBound(), SCIPintervalSetRoundingMode(), and SCIP_Interval::sup.

Referenced by propagateBoundsGetQuadActivity(), propagateBoundsQuadVar(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

void SCIPintervalQuad	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	xrng
	)

stores range of quadratic term in resultant

given scalar a and intervals b and x, computes interval for $ a x^2 + b x $

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
xrng	range of x

Definition at line 2775 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_Real, SCIPintervalIsEmpty(), SCIPintervalMul(), SCIPintervalQuadUpperBound(), SCIPintervalSetEmpty(), and SCIP_Interval::sup.

Referenced by nlrowCalcActivityBounds(), propagateBoundsQuadVar(), SCIP_DECL_EXPRINTEVAL(), SCIPintervalQuadBivar(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

void SCIPintervalSolveUnivariateQuadExpressionPositive	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	rhs
	)

computes interval with positive solutions of a quadratic equation with interval coefficients

Given intervals a, b, and c, this function computes an interval that contains all positive solutions of $a x^2 + b x \in c$ .

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation

Definition at line 2810 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPdebugMessage, SCIPdebugPrintf, SCIPintervalIntersect(), SCIPintervalSetEmpty(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIP_Interval::sup.

Referenced by propagateBoundsQuadVar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpression().

void SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	sqrcoeff,
		SCIP_Real	lincoeff,
		SCIP_Real	rhs
	)

computes positive solutions of a quadratic equation with scalar coefficients

Given scalar a, b, and c, this function computes an interval that contains all positive solutions of $a x^2 + b x \geq c$ . Implements Algorithm 3.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008).

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation

Definition at line 2856 of file intervalarith.c.

References SCIP_Interval::inf, negate(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_NEAREST, SCIP_ROUND_UPWARDS, SCIPintervalGetRoundingMode(), SCIPintervalSetEmpty(), SCIPintervalSetRoundingMode(), sqrt(), and SCIP_Interval::sup.

Referenced by SCIPintervalSolveUnivariateQuadExpressionPositive().

void SCIPintervalSolveUnivariateQuadExpression	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	rhs
	)

solves a quadratic equation with interval coefficients

Given intervals a, b and c, this function computes an interval that contains all solutions of $a x^2 + b x \in c$

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation

Definition at line 2957 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIP_Real, SCIPdebugMessage, SCIPintervalDiv(), SCIPintervalGetInf(), SCIPintervalGetSup(), SCIPintervalSetEmpty(), SCIPintervalSetEntire(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalSquareRoot(), SCIPintervalUnify(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), and propagateBoundsQuadVar().

void SCIPintervalQuadBivar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	ax,
		SCIP_Real	ay,
		SCIP_Real	axy,
		SCIP_Real	bx,
		SCIP_Real	by,
		SCIP_INTERVAL	xbnds,
		SCIP_INTERVAL	ybnds
	)

stores range of bivariate quadratic term in resultant given scalars ax, ay, axy, bx, and by and intervals for x and y, computes interval for $ ax x^2 + ay y^2 + axy x y + bx x + by y $ NOTE: the operations are not applied rounding-safe here

Parameters

infinity	value for infinity in interval arithmetics
resultant	buffer where to store result of operation
ax	square coefficient of x
ay	square coefficient of y
axy	bilinear coefficients
bx	linear coefficient of x
by	linear coefficient of y
xbnds	bounds on x
ybnds	bounds on y

Definition at line 3019 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, REALABS, SCIP_Real, SCIPdebugMessage, SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalQuad(), SCIPintervalSet(), SCIPintervalSetBounds(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

void SCIPintervalSolveBivariateQuadExpressionAllScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	ax,
		SCIP_Real	ay,
		SCIP_Real	axy,
		SCIP_Real	bx,
		SCIP_Real	by,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL	xbnds,
		SCIP_INTERVAL	ybnds
	)

solves a bivariate quadratic equation for the first variable given scalars ax, ay, axy, bx and by, and intervals for x, y, and rhs, computes $\{ x \in \mathbf{x} : \exists y \in \mathbf{y} : a_x x^2 + a_y y^2 + a_{xy} x y + b_x x + b_y y \in \mathbf{\mbox{rhs}} \}$ NOTE: the operations are not applied rounding-safe here

Parameters

infinity	value for infinity in interval arithmetics
resultant	buffer where to store result of operation
ax	square coefficient of x
ay	square coefficient of y
axy	bilinear coefficients
bx	linear coefficient of x
by	linear coefficient of y
rhs	right-hand-side of equation
xbnds	bounds on x
ybnds	bounds on y

Definition at line 3278 of file intervalarith.c.

References CALCB, CALCR, EPSGE, EPSGT, EPSLE, EPSLT, EPSN, EPSZ, SCIP_Interval::inf, MAX, MIN, NULL, REALABS, SCIP_Real, SCIPintervalAddScalar(), SCIPintervalIntersect(), SCIPintervalIsEmpty(), SCIPintervalMulScalar(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), SCIPintervalSet(), SCIPintervalSetBounds(), SCIPintervalSetEmpty(), SCIPintervalSetEntire(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalSub(), SCIPintervalUnify(), sqrt(), and SCIP_Interval::sup.

Referenced by exprgraphNodePropagateBounds(), propagateBoundsBilinearTerm(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIP

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