intervalarith.c
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23 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
37 * certain optimizations should be omitted (http://www.cplusplus.com/reference/cfenv/FENV_ACCESS/).
46 * There are ways to work around this by declaring variables volatile or inserting more assembler code,
48 * A more drastic but safer way seems to be to just disable all compiler optimizations for this file.
230 #if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__)) /* gcc or icc compiler on x86 32bit or 64bit */
233 * Do this in a way that the compiler does not "optimize" it away, which usually does not considers rounding modes.
235 * @todo We now set the FENV_ACCESS pragma to on, which is the same as -frounding-math, so we might be able to eliminate this.
239 /* we explicitly use double here, since I'm not sure the assembler code would work as it for other float's */
254 * Do this in a way that the compiler does not "optimize" it away, which usually does not considers rounding modes.
258 /* we explicitly use double here, since I'm not sure the assembler code would work as it for other float's */
534 /* [a,...] + [-inf,...] = [-inf,...] for all a, in particular, [+inf,...] + [-inf,...] = [-inf,...] */
561 /* [...,b] + [...,+inf] = [...,+inf] for all b, in particular, [...,-inf] + [...,+inf] = [...,+inf] */
720 assert(resultant->inf == -infinity); /* should be set above, since operand1.inf <= operand1.sup <= -infinity */ /*lint !e777*/
890 /** multiplies operand1 with scalar operand2 and stores infimum of result in infimum of resultant */
946 /** multiplies operand1 with scalar operand2 and stores supremum of result in supremum of resultant */
1225 /** computes scalar product of a vector of intervals and a vector of scalars and stores infimum of result in infimum of
1253 /** computes the scalar product of a vector of intervals and a vector of scalars and stores supremum of result in
1281 /** computes the scalar product of a vector of intervals and a vector of scalars and stores result in resultant */
1408 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1426 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1434 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1605 /* use a binary exponentiation algorithm... see comments in SCIPintervalPowerScalarIntegerInf */
1669 SCIPintervalReciprocal(SCIP_REAL_MAX, resultant, *resultant); /* value for infinity does not matter, since there should be no 0.0 in the interval, so just use something large enough */
1720 * need to have operand1 >= 0 or operand2 integer and need to have operand2 >= 0 if operand1 == 0
1755 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1843 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1853 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1874 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1883 assert(SCIPintervalGetRoundingMode() == SCIP_ROUND_NEAREST); /* usually, no-one should have changed rounding mode */
1958 assert(resultant->inf <= resultant->sup || resultant->inf >= infinity || resultant->sup <= -infinity);
1962 assert(op2isint); /* otherwise we had set operand1.inf == 0.0, which was handled in first case */
1970 resultant->sup = SCIPintervalPowerScalarIntegerSup(MAX(-operand1.inf, operand1.sup), (int)operand2);
1979 resultant->inf = SCIPintervalPowerScalarIntegerInf(MAX(-operand1.inf, operand1.sup), (int)operand2);
2012 * 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
2065 if( basedomain.inf <= -resultant->inf && EPSISINT(exponent, 0.0) && (int)exponent % 2 == 0 ) /*lint !e835 */
2078 /* invert negative part of image, if any and if base can take negative value and if exponent is such that negative values are possible */
2079 if( image.inf < 0.0 && basedomain.inf < 0.0 && EPSISINT(exponent, 0.0) && ((int)exponent % 2 != 0) ) /*lint !e835 */
2093 * @attention we assume correctly rounded sqrt(double) and pow(double) functions when rounding is to nearest
2399 /* make sure we do not exceed value for infinity, so interval is not declared as empty if inf and sup are both > infinity */
2625 * so extend the computed interval slightly to increase the chance that it will contain the complete sin(operand)
2711 * so extend the computed interval slightly to increase the chance that it will contain the complete cos(operand)
2748 /** computes exact upper bound on \f$ a x^2 + b x \f$ for x in [xlb, xub], b an interval, and a scalar
2750 * Uses Algorithm 2.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008) */
2877 /** computes interval with positive solutions of a quadratic equation with interval coefficients
2879 * Given intervals a, b, and c, this function computes an interval that contains all positive solutions of \f$ a x^2 + b x \in c\f$ within xbnds.
2900 SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(infinity, resultant, -sqrcoeff.inf, -lincoeff.inf, -rhs.sup, xbnds);
2901 SCIPdebugMessage("solve %g*x^2 + %g*x >= %g gives [%.20f, %.20f]\n", -sqrcoeff.inf, -lincoeff.inf, -rhs.sup, resultant->inf, resultant->sup);
2909 SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(infinity, &res2, sqrcoeff.sup, lincoeff.sup, rhs.inf, xbnds);
2910 SCIPdebugMessage("solve %g*x^2 + %g*x >= %g gives [%.20f, %.20f]\n", sqrcoeff.sup, lincoeff.sup, rhs.inf, res2.inf, res2.sup);
2911 SCIPdebugMessage("intersection of [%.20f, %.20f] and [%.20f, %.20f]", resultant->inf, resultant->sup, res2.inf, res2.sup);
2924 /** computes interval with negative solutions of a quadratic equation with interval coefficients
2926 * Given intervals a, b, and c, this function computes an interval that contains all negative solutions of \f$ a x^2 + b x \in c\f$ within xbnds.
2951 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, resultant, sqrcoeff, lincoeff, rhs, xbnds);
2961 * Given scalar a, b, and c, this function computes an interval that contains all positive solutions of \f$ a x^2 + b x \geq c\f$ within xbnds.
2962 * Implements Algorithm 3.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008).
2992 * The same should have been computed below, but without the sqrcoeff, terms simplify (thus, also less rounding).
3166 * Given intervals a, b and c, this function computes an interval that contains all solutions of \f$ a x^2 + b x \in c\f$ within xbnds
3187 * the code below would also work, but uses many more case distinctions to get to a result that should be the same (though epsilon differences can sometimes be observed)
3193 SCIPdebugMessage("solving [%g,%g]*x = [%g,%g] for x in [%g,%g] gives [%g,%g]\n", lincoeff.inf, lincoeff.sup, rhs.inf, rhs.sup, xbnds.inf, xbnds.sup, resultant->inf, resultant->sup);
3197 SCIPdebugMessage("solving [%g,%g]*x^2 + [%g,%g]*x = [%g,%g] for x in [%g,%g]\n", sqrcoeff.inf, sqrcoeff.sup, lincoeff.inf, lincoeff.sup, rhs.inf, rhs.sup, xbnds.inf, xbnds.sup);
3202 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, &xpos, sqrcoeff, lincoeff, rhs, xbnds);
3203 SCIPdebugMessage(" solutions of [%g,%g]*x^2 + [%g,%g]*x in [%g,%g] for x in [%g,%g] are [%.15g,%.15g]\n",
3204 sqrcoeff.inf, sqrcoeff.sup, lincoeff.inf, lincoeff.sup, rhs.inf, rhs.sup, MAX(xbnds.inf, 0.0), xbnds.sup, xpos.inf, xpos.sup);
3214 SCIPintervalSolveUnivariateQuadExpressionNegative(infinity, &xneg, sqrcoeff, lincoeff, rhs, xbnds);
3215 SCIPdebugMessage(" solutions of [%g,%g]*x^2 + [%g,%g]*x in [%g,%g] for x in [%g,%g] are [%g,%g]\n",
3216 sqrcoeff.inf, sqrcoeff.sup, lincoeff.inf, lincoeff.sup, rhs.inf, rhs.sup, xbnds.inf, MIN(xbnds.sup, 0.0), xneg.inf, xneg.sup);
3224 SCIPdebugMessage(" unify gives [%g,%g]\n", SCIPintervalGetInf(*resultant), SCIPintervalGetSup(*resultant));
3228 * given scalars ax, ay, axy, bx, and by and intervals for x and y, computes interval for \f$ ax x^2 + ay y^2 + axy x y + bx x + by y \f$
3243 /* we use double double precision and finally widen the computed range by 1e-8% to compensate for not computing rounding-safe here */
3291 /* The whole line (x, -bx/axy - (axy/2ay) x) defines an extreme point with value -ay bx^2 / axy^2
3292 * If x is unbounded, then there is an (x,y) with y in ybnds where the extreme value is assumed.
3293 * If x is bounded on at least one side, then we can rely that the checks below for x at one of its bounds will check this extreme point.
3343 SCIPintervalAddScalar(infinity, &tmp, tmp, (SCIP_Real)(ax * xbnds.inf * xbnds.inf + bx * xbnds.inf));
3386 SCIPintervalAddScalar(infinity, &tmp, tmp, (SCIP_Real)(ax * xbnds.sup * xbnds.sup + bx * xbnds.sup));
3472 SCIPintervalAddScalar(infinity, &tmp, tmp, (SCIP_Real)(ay * ybnds.sup * ybnds.sup + by * ybnds.sup));
3481 SCIPdebugMessage("range for %gx^2 + %gy^2 + %gxy + %gx + %gy = [%g, %g] for x = [%g, %g], y=[%g, %g]\n",
3487 * computes \f$ \{ 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}} \} \f$
3503 /* we use double double precision and finally widen the computed range by 1e-8% to compensate for not computing rounding-safe here */
3527 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, &pos, sqrcoef, lincoef, rhs, xbnds);
3538 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, &neg, sqrcoef, lincoef, rhs, xbndsneg);
3553 * fall back to univariate case by solving a_x x^2 + b_x x + a_y y^2 + (a_xy xbnds + b_y) y in rhs
3589 SCIPintervalSolveBivariateQuadExpressionAllScalar(infinity, resultant, -ax, -ay, -axy, -bx, -by, rhs, xbnds, ybnds);
3629 ub = (SCIP_Real)(SCIPintervalQuadUpperBound(infinity, (SCIP_Real)rcoef_yy, ycoef, ybnds) + rhs.sup + rcoef_const);
3638 /* it looks like there will be no solution (rhs < 0), but we are very close and above operations did not take care of careful rounding
3639 * thus, we relax rhs a be feasible a bit (-ub would be sufficient, but that would put us exactly onto the boundary)
3694 /* here axy * axy < 4 * ax * ay, so need to check for zeros of r(rhs,y), which is done below */
3768 /* here axy * axy < 4 * ax * ay, so need to check for zeros of r(rhs,y), which will happen below */
3825 sqrtterm = axy * axy * ay * (ay * bx * bx - axy * bx * by + ax * by * by - axy * axy * rhs.sup + 4.0 * ax * ay * rhs.sup);
3879 sqrtterm = axy * axy * ay * (ay * bx * bx - axy * bx * by + ax * by * by - axy * axy * rhs.inf + 4.0 * ax * ay * rhs.inf);
4004 SCIPintervalSetBounds(&rhs2, (SCIP_Real)(-rhs.sup - rcoef_const), (SCIP_Real)(-rhs.inf - rcoef_const));
4013 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, &ypos, rcoef_yy_int, rcoef_y_int, rhs2, ybnds);
4056 SCIPintervalSolveUnivariateQuadExpressionNegative(infinity, &yneg, rcoef_yy_int, rcoef_y_int, rhs2, ybnds);
4092 if( rhs.inf > -infinity && xbnds.inf > -infinity && EPSGT(xbnds.inf, maxvalleft / sqrtax, 1e-9) )
4094 /* if sqrt(ax)*x > -sqrt(r(rhs,y))-b(y), then tighten lower bound of sqrt(ax)*x to lower bound of sqrt(r(rhs,y))-b(y)
4095 * this is only possible if rhs.inf > -infinity, otherwise the value for maxvalleft is not valid (but tightening wouldn't be possible for sure anyway) */
4096 assert(EPSGE(minvalright, minvalleft, 1e-9)); /* right interval should not be above lower bound of left interval */
4113 if( rhs.inf > -infinity && xbnds.sup < infinity && EPSLT(xbnds.sup, minvalright / sqrtax, 1e-9) )
4115 /* if sqrt(ax)*x < sqrt(r(rhs,y))-b(y), then tighten upper bound of sqrt(ax)*x to upper bound of -sqrt(r(rhs,y))-b(y)
4116 * this is only possible if rhs.inf > -infinity, otherwise the value for minvalright is not valid (but tightening wouldn't be possible for sure anyway) */
4117 assert(EPSLE(maxvalleft, maxvalright, 1e-9)); /* left interval should not be above upper bound of right interval */
4193 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, resultant, a_, lincoef, myrhs, xbnds);
4206 SCIPintervalSolveUnivariateQuadExpressionPositive(infinity, resultant, a_, lincoef, myrhs, xbndsneg);
4367 /* pop -O0 from beginning, though it probably doesn't matter here at the end of the compilation unit */
void SCIPintervalSignPowerScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:2095
void SCIPintervalDivScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:1083
void SCIPintervalMulSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:804
void SCIPintervalSubScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:733
void SCIPintervalMax(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:2508
SCIP_Bool SCIPintervalIsEmpty(SCIP_Real infinity, SCIP_INTERVAL operand)
Definition: intervalarith.c:405
void SCIPintervalSign(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2722
Definition: intervalarith.h:37
void SCIPintervalAddSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:551
void SCIPintervalSolveUnivariateQuadExpressionNegative(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
Definition: intervalarith.c:2928
void SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_Real lincoeff, SCIP_Real rhs, SCIP_INTERVAL xbnds)
Definition: intervalarith.c:2964
void SCIPintervalSetRoundingMode(SCIP_ROUNDMODE roundmode)
Definition: intervalarith.c:211
void SCIPintervalMul(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:864
SCIP_Real SCIPintervalPowerScalarIntegerInf(SCIP_Real operand1, int operand2)
Definition: intervalarith.c:1476
void SCIPintervalMin(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:2492
void SCIPintervalSetBounds(SCIP_INTERVAL *resultant, SCIP_Real inf, SCIP_Real sup)
Definition: intervalarith.c:380
void SCIPintervalPowerScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:1766
SCIP_Bool SCIPintervalIsNegativeInfinity(SCIP_Real infinity, SCIP_INTERVAL operand)
Definition: intervalarith.c:447
void SCIPintervalDiv(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:1029
void SCIPintervalAddVectors(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)
Definition: intervalarith.c:655
SCIP_Bool SCIPintervalIsPositiveInfinity(SCIP_Real infinity, SCIP_INTERVAL operand)
Definition: intervalarith.c:438
void SCIPintervalSin(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2552
void SCIPintervalPowerScalarScalar(SCIP_INTERVAL *resultant, SCIP_Real operand1, SCIP_Real operand2)
Definition: intervalarith.c:1723
SCIP_Bool SCIPintervalIsEntire(SCIP_Real infinity, SCIP_INTERVAL operand)
Definition: intervalarith.c:429
void SCIPintervalScalprod(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)
Definition: intervalarith.c:1186
interval arithmetics for provable bounds
void SCIPintervalSetEmpty(SCIP_INTERVAL *resultant)
Definition: intervalarith.c:394
SCIP_Real SCIPintervalGetInf(SCIP_INTERVAL interval)
Definition: intervalarith.c:352
void SCIPintervalLog(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2424
void SCIPintervalScalprodScalarsInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
Definition: intervalarith.c:1228
internal miscellaneous methods
void SCIPintervalSet(SCIP_INTERVAL *resultant, SCIP_Real value)
Definition: intervalarith.c:368
void SCIPintervalPowerScalarInteger(SCIP_INTERVAL *resultant, SCIP_Real operand1, int operand2)
Definition: intervalarith.c:1632
void SCIPintervalCos(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2638
void SCIPintervalSolveUnivariateQuadExpression(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
Definition: intervalarith.c:3168
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)
Definition: intervalarith.c:3490
void SCIPintervalSquareRoot(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:1382
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)
Definition: intervalarith.c:3231
void SCIPintervalSquare(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:1310
void SCIPintervalScalprodScalars(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
Definition: intervalarith.c:1282
SCIP_Bool SCIPintervalHasRoundingControl(void)
Definition: intervalarith.c:203
void SCIPintervalSetRoundingModeTowardsZero(void)
Definition: intervalarith.c:315
void SCIPintervalAdd(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:578
SCIP_Real SCIPintervalGetSup(SCIP_INTERVAL interval)
Definition: intervalarith.c:360
SCIP_Bool SCIPintervalAreDisjoint(SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:475
void SCIPintervalMulScalarSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:947
void SCIPintervalAbs(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2524
void SCIPintervalMulScalarInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:891
void SCIPintervalSetEntire(SCIP_Real infinity, SCIP_INTERVAL *resultant)
Definition: intervalarith.c:417
SCIP_Real SCIPintervalQuadUpperBound(SCIP_Real infinity, SCIP_Real a, SCIP_INTERVAL b_, SCIP_INTERVAL x)
Definition: intervalarith.c:2751
void SCIPintervalSetRoundingModeUpwards(void)
Definition: intervalarith.c:299
void SCIPintervalExp(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2340
public methods for message output
#define CALCB(y)
SCIP_Real SCIPintervalPowerScalarIntegerSup(SCIP_Real operand1, int operand2)
Definition: intervalarith.c:1558
void SCIPintervalIntersect(SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:484
void SCIPintervalMulScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:1003
void SCIPintervalSolveUnivariateQuadExpressionPositive(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
Definition: intervalarith.c:2881
void SCIPintervalSetRoundingModeToNearest(void)
Definition: intervalarith.c:307
void SCIPintervalMulInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:744
void SCIPintervalSub(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:685
#define CALCR(c, y)
common defines and data types used in all packages of SCIP
void SCIPintervalAddScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
Definition: intervalarith.c:605
SCIP_ROUNDMODE SCIPintervalGetRoundingMode(void)
Definition: intervalarith.c:219
void SCIPintervalPower(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:1443
void SCIPintervalSetRoundingModeDownwards(void)
Definition: intervalarith.c:291
void SCIPintervalReciprocal(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
Definition: intervalarith.c:2267
void SCIPintervalPowerScalarInverse(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL basedomain, SCIP_Real exponent, SCIP_INTERVAL image)
Definition: intervalarith.c:2014
SCIP_Bool SCIPintervalIsSubsetEQ(SCIP_Real infinity, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:456
void SCIPintervalAddInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:524
void SCIPintervalScalprodScalarsSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
Definition: intervalarith.c:1256
void SCIPintervalUnify(SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
Definition: intervalarith.c:497
void SCIPintervalQuad(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL xrng)
Definition: intervalarith.c:2846