intervalarith.c File Reference

Detailed Description

interval arithmetics for provable bounds

Author

Tobias Achterberg

Stefan Vigerske

Kati Wolter

Definition in file intervalarith.c.

#include <stdlib.h>
#include <assert.h>
#include <math.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)
static void	intervalSetRoundingMode (SCIP_ROUNDMODE roundmode)
static SCIP_ROUNDMODE	intervalGetRoundingMode (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)
SCIP_Bool	SCIPintervalAreDisjointEps (SCIP_Real eps, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalIntersect (SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalIntersectEps (SCIP_INTERVAL *resultant, SCIP_Real eps, 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	SCIPintervalSin (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalCos (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalSign (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalEntropy (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, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpressionNegative (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_Real lincoeff, SCIP_Real rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpression (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
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)
int	SCIPintervalPropagateWeightedSum (SCIP_Real infinity, int noperands, SCIP_INTERVAL *operands, SCIP_Real *weights, SCIP_Real constant, SCIP_INTERVAL rhs, SCIP_INTERVAL *resultants, SCIP_Bool *infeasible)

Variables
static const double	pi_d_l = (3373259426.0 + 273688.0 / (1<<21)) / (1<<30)
static const double	pi_d_u = (3373259426.0 + 273689.0 / (1<<21)) / (1<<30)

Macro Definition Documentation

SCIP_ROUND_DOWNWARDS

#define SCIP_ROUND_DOWNWARDS   0

round always down

Definition at line 233 of file intervalarith.c.

SCIP_ROUND_UPWARDS

#define SCIP_ROUND_UPWARDS   1

round always up

Definition at line 234 of file intervalarith.c.

SCIP_ROUND_NEAREST

#define SCIP_ROUND_NEAREST   2

round always to nearest

Definition at line 235 of file intervalarith.c.

SCIP_ROUND_ZERO

#define SCIP_ROUND_ZERO   3

round always towards zero

Definition at line 236 of file intervalarith.c.

CALCB

#define CALCB

(

y

)

((bx + axy * (y)) / (2.0 * sqrtax))

CALCR

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

Function Documentation

intervalSetRoundingMode()

static void intervalSetRoundingMode ( SCIP_ROUNDMODE  roundmode )

static

sets rounding mode of floating point operations

Parameters

roundmode

rounding mode to activate

Definition at line 248 of file intervalarith.c.

References SCIPerrorMessage.

Referenced by SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalAddVectors(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalMul(), SCIPintervalMulScalar(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalScalprod(), SCIPintervalScalprodScalars(), SCIPintervalSetRoundingMode(), SCIPintervalSetRoundingModeDownwards(), SCIPintervalSetRoundingModeToNearest(), SCIPintervalSetRoundingModeTowardsZero(), SCIPintervalSetRoundingModeUpwards(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), SCIPintervalSquare(), and SCIPintervalSub().

intervalGetRoundingMode()

static SCIP_ROUNDMODE intervalGetRoundingMode ( void  )

static

gets current rounding mode of floating point operations

Definition at line 257 of file intervalarith.c.

References SCIP_ROUND_NEAREST.

Referenced by SCIPintervalAdd(), SCIPintervalAddInf(), SCIPintervalAddScalar(), SCIPintervalAddSup(), SCIPintervalAddVectors(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalExp(), SCIPintervalGetRoundingMode(), SCIPintervalLog(), SCIPintervalMul(), SCIPintervalMulInf(), SCIPintervalMulScalar(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), SCIPintervalMulSup(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalPowerScalarScalar(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalScalprod(), SCIPintervalScalprodScalars(), SCIPintervalScalprodScalarsInf(), SCIPintervalScalprodScalarsSup(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), SCIPintervalSquare(), SCIPintervalSquareRoot(), and SCIPintervalSub().

negate()

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 333 of file intervalarith.c.

References SCIPnegateReal(), and x.

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

Variable Documentation

pi_d_l

const double pi_d_l = (3373259426.0 + 273688.0 / (1<<21)) / (1<<30)

static

Definition at line 2692 of file intervalarith.c.

Referenced by SCIPintervalCos(), and SCIPintervalSin().

pi_d_u

const double pi_d_u = (3373259426.0 + 273689.0 / (1<<21)) / (1<<30)

static

Definition at line 2693 of file intervalarith.c.

Referenced by SCIPintervalCos(), and SCIPintervalSin().