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JCP Standard JSR331 “Java Constraint Programming API”. It is used for Modeling and Solving Constraint Satisfaction and Optimization Problems using Java and off-the-shelf Constraint/Linear Solvers
package javax.constraints.impl;
import javax.constraints.Problem;
import javax.constraints.VarReal;
// IEEE 754 NAN and inf RULES
// - result of any operation with the operand NAN = NAN
// - (-inf)+(+inf) = NAN
// - (+inf)-(+inf) = NAN
// - (-inf)-(-inf) = NAN
// - inf*0 = NAN
// - inf/inf = NAN
// - 0/0 = NAN ((!0)/0 = (+/-)inf)
//
// We have to try the rules:
// - values can be finite doubles, +inf, -inf but not NaN
/**
* A helper for the floating-point arithmetic.
*/
public final class Real {
/**
* A Not-a-Number (NaN) value of type double.
*
* @see Double#NaN
*/
// static public final double NaN = Double.NaN;
/**
* The positive infinity of type double.
*
* @see Double#POSITIVE_INFINITY
*/
// static public final double pInf = Double.POSITIVE_INFINITY;
/**
* The negative infinity of type double.
*
* @see Double#NEGATIVE_INFINITY
*/
// static public final double nInf = Double.NEGATIVE_INFINITY;
/**
* Returns true if the specified numbers are equal with the precision
*/
public static boolean eq(Problem p, double d1, double d2) {
return Math.abs(d1 - d2) < p.getRealPrecision();
}
/**
* Returns true if the first number more than the second number with the
* precision
*/
public static boolean gt(Problem p, double d1, double d2) {
return (d1 - d2) > p.getRealPrecision();
}
/**
* Returns true if the first number is more or equal to the second number
* with the precision
*/
public static boolean ge(Problem p, double d1, double d2) {
return d1 - d2 > -p.getRealPrecision();
}
/**
* Returns true if the specified number is the special Not-a-Number (NaN)
* value.
*
* @see Double#isNaN
*/
public static boolean isNan(double v) {
return Double.isNaN(v);
}
/**
* Returns true if the specified number is infinitely large in magnitude.
*
* @see Double#isInfinite
*/
public static boolean isInf(double v) {
return Double.isInfinite(v);
}
/**
* Returns the expression: min(1 / [min..max]). Result may be
* finite number or -inf.
*/
public static double inverseMin(double min, double max) {
assertMinMax(min, max);
double _min;
// strictly positive or strictly negative
if (min > 0 || max < 0) {
_min = 1 / max;
}
// [0..>0]
else if (min == 0 && max > 0) {
_min = 1 / max;
}
// [<0..0]
else if (max == 0 && min < 0) {
_min = Double.NEGATIVE_INFINITY;
}
// [<0..>0] or [0..0]
else {
_min = Double.NEGATIVE_INFINITY;
}
return _min;
}
/**
* Returns the expression: max(1 / [min..max]). Result may be
* finite number or +inf.
*/
public static double inverseMax(double min, double max) {
assertMinMax(min, max);
double _max;
// strictly positive or strictly negative
if (min > 0 || max < 0) {
_max = 1 / min;
}
// [0..>0]
else if (min == 0 && max > 0) {
_max = Double.POSITIVE_INFINITY;
}
// [<0..0]
else if (max == 0 && min < 0) {
_max = 1 / min;
}
// [<0..>0] or [0..0]
else {
_max = Double.POSITIVE_INFINITY;
}
return _max;
}
/**
* Returns the expression: min(1 / [v..v]). Result may be
* finite number or -inf.
*/
public static double inverseMin(double v) {
return v != 0 ? 1 / v : Double.NEGATIVE_INFINITY;
}
/**
* Returns the expression: max(1 / [v..v]). Result may be
* finite number or +inf.
*/
public static double inverseMax(double v) {
return v != 0 ? 1 / v : Double.POSITIVE_INFINITY;
}
/**
* Returns the expression: log(x,base).
*/
public static double log(double x, double base) {
// log(x,e)=log(x,base)*log(base,e)
return Math.log(x) / Math.log(base);
}
/**
* Returns x satisfying the equation: y = pow(x,v).
*/
public static double pow(double y, double v) {
// y=pow(x,v) -> pow(y,1/v)=pow(pow(x,v),1/v)=x
double x = Math.pow(y, 1 / v);
// System.out.println(y+"=pow("+x+","+v+")["+Math.pow(x,v)+"]"); //
// check
return x;
}
/**
* Returns the expression: min([min1..max1]*[min2..max2]) where
* [min1..max1] is more or equal 0.
*/
public static double productMinP(double min1, double max1, double min2) {
if (min2 >= 0)
return min1 * min2;
else
return max1 * min2;
}
/**
* Returns the expression: max([min1..max1]*[min2..max2]) where
* [min1..max1] is more or equal to 0.
*/
public static double productMaxP(double min1, double max1, double max2) {
if (max2 >= 0)
return max1 * max2;
else
return min1 * max2;
}
/**
* Returns the expression: min([min1..max1]*[min2..max2]) where
* [min1..max1] is less or equal to 0.
*/
public static double productMinN(double min1, double max1, double max2) {
if (max2 >= 0)
return min1 * max2;
else
return max1 * max2;
}
/**
* Returns the expression: max([min1..max1]*[min2..max2]) where
* [min1..max1] is less or equal to 0.
*/
public static double productMaxN(double min1, double max1, double min2) {
if (min2 >= 0)
return max1 * min2;
else
return min1 * min2;
}
/**
* Returns the expression: min([min1..max1]*[min2..max2]).
*/
public static double productMin(double min1, double max1, double min2,
double max2) {
// exp1 >= 0
if (min1 >= 0)
return productMinP(min1, max1, min2);
// exp1 <= 0
else if (max1 <= 0)
return productMinN(min1, max1, max2);
// exp1 changes sign
else {
// exp2 >= 0
if (min2 >= 0)
return min1 * max2;
// exp2 <= 0
else if (max2 <= 0)
return max1 * min2;
// exp2 changes sign
else {
return Math.min(max1 * min2, min1 * max2);
}
}
}
/**
* Returns the expression: max([min1..max1]*[min2..max2]).
*/
public static double productMax(double min1, double max1, double min2,
double max2) {
// exp1 >= 0
if (min1 >= 0)
return productMaxP(min1, max1, max2);
// exp1 <= 0
else if (max1 <= 0)
return productMaxN(min1, max1, min2);
// exp1 changes sign
else {
// exp2 >= 0
if (min2 >= 0)
return max1 * max2;
// exp2 <= 0
else if (max2 <= 0)
return min1 * min2;
// exp2 changes sign
else {
return Math.max(min1 * min2, max1 * max2);
}
}
}
// /**
// * Adjust the expression exp2 so that:
// * min([min1..max1]*[min2..max2]) >= min where
// * [min1..max1] >= 0.
// */
// static public void productSetMinP(double min, double min1, double max1,
// VarReal var) throws RuntimeException {
// if (min == 0) {
// if (min1 > 0)
// var.setMin(0);
// } else {
// double v = min > 0 ? max1 : min1;
// if (v != 0) {
// double min2 = min / v;
// var.setMin(min2);
// }
// }
// }
//
// /**
// * Adjust the expression exp2 so that:
// * min([min1..max1]*[min2..max2]) <= max where
// * [min1..max1] >= 0.
// */
// static public void productSetMaxP(double max, double min1, double max1,
// FloatExp exp2) throws Failure {
// if (max == 0) {
// if (min1 > 0)
// exp2.setMax(0);
// } else {
// double v = max > 0 ? min1 : max1;
// if (v != 0) {
// double max2 = max / v;
// exp2.setMax(max2);
// }
// }
// }
//
// /**
// * Adjust the expression exp2 so that:
// * min([min1..max1]*[min2..max2]) >= min where
// * [min1..max1] <= 0.
// */
// static public void productSetMinN(double min, double min1, double max1,
// FloatExp exp2) throws Failure {
// if (min == 0) {
// if (max1 < 0)
// exp2.setMax(0);
// } else {
// double v = min > 0 ? min1 : max1;
// if (v != 0) {
// double max2 = min / v;
// exp2.setMax(max2);
// }
// }
// }
//
// /**
// * Adjust the expression exp2 so that:
// * min([min1..max1]*[min2..max2]) <= max where
// * [min1..max1] <= 0.
// */
// static public void productSetMaxN(double max, double min1, double max1,
// FloatExp exp2) throws Failure {
// if (max == 0) {
// if (max1 < 0)
// exp2.setMin(0);
// } else {
// double v = max > 0 ? max1 : min1;
// if (v != 0) {
// double min2 = max / v;
// exp2.setMin(min2);
// }
// }
// }
//
// /**
// * Adjust the expression exp2 so that:
// * min([min1..max1]*[min2..max2]) >= min.
// */
// static public void productSetMin(double min, FloatExp exp1, FloatExp exp2)
// throws Failure {
// double min1, max1;
// // exp1 >= 0
// if ((min1 = exp1.min()) >= 0) {
// productSetMinP(min, min1, exp1.max(), exp2);
// }
// // exp1 <= 0
// else if ((max1 = exp1.max()) <= 0) {
// productSetMinN(min, min1, max1, exp2);
// } else // exp1 changes sign
// {
// if (min > 0) {
// double m = min1 / min;
// double M = max1 / min;
// exp2.removeRange(m, M);
// }
// }
// }
//
// /**
// * Adjust the expression exp2 so that:
// * max([min1..max1]*[min2..max2]) <= max.
// */
// static public void productSetMax(double max, FloatExp exp1, FloatExp exp2)
// throws Failure {
// double min1, max1;
// // exp1 >= 0
// if ((min1 = exp1.min()) >= 0) {
// productSetMaxP(max, min1, exp1.max(), exp2);
// }
// // exp1 <= 0
// else if ((max1 = exp1.max()) <= 0) {
// productSetMaxN(max, min1, max1, exp2);
// } else // exp1 changes sign
// {
// if (max < 0) {
// double m = max1 / max;
// double M = min1 / max;
// exp2.removeRange(m, M);
// }
// }
// }
/**
* Returns the expression: max(sqr(min),sqr(max)).
*/
public static double sqrMax(double min, double max) {
return Math.max(min * min, max * max);
}
/**
* Returns the expression: min(sqr(min),sqr(max)).
*/
public static double sqrMin(double min, double max) {
// min >= 0 && max >= 0
if (min >= 0)
return min * min;
// min < 0 && max >= 0
if (max >= 0)
return 0;
// min < 0 && max < 0
return max * max;
}
public static void doAssert(boolean v, String s) {
if (v)
return;
System.out.println("Assertion failed: " + s);
}
public static void assertMinMax(double min, double max) {
doAssert(!isNan(min), "min not NaN");
doAssert(!isNan(max), "max not NaN");
doAssert(min <= max, "min <= max");
}
} // ~ Real