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/*
 * @(#)BinaryRelations.java        5.0.4    2022-05-22
 *
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 * PRODUCT: MathParser.org-mXparser SOFTWARE
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 */
package org.mariuszgromada.math.mxparser.mathcollection;

/**
 * BinaryRelations - class for dealing with binary relations on integers or doubles.
 *
 * @author         Mariusz Gromada

 *                 MathParser.org - mXparser project page

 *                 mXparser on GitHub

 *                 INFIMA place to purchase a commercial MathParser.org-mXparser software license

 *                 [email protected]

 *                 ScalarMath.org - a powerful math engine and math scripting language

 *                 Scalar Lite

 *                 Scalar Pro

 *                 MathSpace.pl

 *
 * @version        5.0.0
 */
public final class BinaryRelations {
	/**
	 * Default epsilon for comparison
	 */
	public static final double DEFAULT_COMPARISON_EPSILON = 0.00000000000001;
	/**
	 * Epsilon for comparison
	 */
	static double epsilon = DEFAULT_COMPARISON_EPSILON;
	/**
	 * COmparison mode indicator
	 */
	static boolean epsilonComparison = true;
	/**
	 * Sets comparison mode to EXACT.
	 */
	public static void setExactComparison() {
		epsilonComparison = false;
	}
	/**
	 * Sets comparison mode to EPSILON.
	 */
	public static void setEpsilonComparison() {
		epsilonComparison = true;
	}
	/**
	 * Sets epsilon value.
	 * @param epsilon   Epsilon value (grater than 0).
	 *
	 * @see #setEpsilonComparison()
	 */
	public static void setEpsilon(double epsilon) {
		if (epsilon > 0) BinaryRelations.epsilon = epsilon;
	}
	/**
	 * Sets default epsilon value.
	 *
	 * @see #setEpsilonComparison()
	 * @see #DEFAULT_COMPARISON_EPSILON
	 */
	public static void setDefaultEpsilon() {
		BinaryRelations.epsilon = DEFAULT_COMPARISON_EPSILON;
	}
	/**
	 * Returns current epsilon value.
	 * @return  Returns current epsilon value.
	 *
	 * @see #setEpsilonComparison()
	 */
	public static double getEpsilon() {
		return epsilon;
	}
	/**
	 * Checks if epsilon comparison mode is active;
	 * @return  True if epsilon mode is active, otherwise returns false.
	 * @see #setEpsilonComparison()
	 * @see #setExactComparison()
	 */
	public static boolean checkIfEpsilonMode() {
		return epsilonComparison;
	}
	/**
	 * Checks if exact comparison mode is active;
	 * @return  True if exact mode is active, otherwise returns false.
	 * @see #setEpsilonComparison()
	 * @see #setExactComparison()
	 */
	public static boolean checkIfExactMode() {
		return !epsilonComparison;
	}
	/**
	 * Equality relation.
	 *
	 * @param      a                   the a number (a = b)
	 * @param      b                   the b number (a = b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a = b return 1,
	 *             otherwise return 0.
	 */
	public static double eq(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( MathFunctions.abs(a-b) <= eps ) result = BooleanAlgebra.TRUE;
		} else if ( a == b ) result = BooleanAlgebra.TRUE;
		return result;
	}
	/**
	 * Test for equality or almost equality.
	 *
	 * @param a   First number
	 * @param b   Second number
	 * @return    Returns true if both number are equal or are almost equal.
	 *
	 * @see #DEFAULT_COMPARISON_EPSILON
	 */
	public static boolean isEqualOrAlmost(double a, double b) {
		if (Math.abs(a - b) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return true;
		else return false;
	}
	/**
	 * Inequality relation.
	 *
	 * @param      a                   the a number (a <> b)
	 * @param      b                   the b number (a <> b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a <> b return 1,
	 *             otherwise return 0.
	 */
	public static double neq(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( MathFunctions.abs(a-b) > eps ) result = BooleanAlgebra.TRUE;
		} else if ( a != b ) result = BooleanAlgebra.TRUE;
		return result;
	}
	/**
	 * Lower than relation.
	 *
	 * @param      a                   the a number (a < b)
	 * @param      b                   the b number (a < b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a < b return 1,
	 *             otherwise return 0.
	 */
	public static double lt(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( a < b - eps ) result = BooleanAlgebra.TRUE;
		} else if ( a < b ) result = BooleanAlgebra.TRUE;
		return result;
	}
	/**
	 * Greater than relation.
	 *
	 * @param      a                   the a number (a > b)
	 * @param      b                   the b number (a > b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a > b return 1,
	 *             otherwise return 0.
	 */
	public static double gt(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( a > b + eps ) result = BooleanAlgebra.TRUE;
		} else if ( a > b ) result = BooleanAlgebra.TRUE;
		return result;
	}
	/**
	 * Lower or equal relation.
	 *
	 * @param      a                   the a number (a <= b)
	 * @param      b                   the b number (a <= b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a <= b return 1,
	 *             otherwise return 0.
	 */
	public static double leq(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( a <= b + eps ) result = BooleanAlgebra.TRUE;
		} else if ( a <= b ) result = BooleanAlgebra.TRUE;
		return result;
	}
	/**
	 * Greater or equal relation.
	 *
	 * @param      a                   the a number (a >= b)
	 * @param      b                   the b number (a >= b)
	 *
	 * @return     if a = Double.NaN or b = Double.NaN return Double.NaN,
	 *             else if a >= b return 1,
	 *             otherwise return 0.
	 */
	public static double geq(double a, double b) {
		if ( ( Double.isNaN(a) ) || ( Double.isNaN(b) ) ) return Double.NaN;
		double eps = NumberTheory.max(epsilon, MathFunctions.ulp(b) );
		if ( Double.isInfinite(a) || Double.isInfinite(b) ) eps = 0;
		double result = BooleanAlgebra.FALSE;
		if (epsilonComparison) {
			if ( a >= b - eps ) result = BooleanAlgebra.TRUE;
		} else if ( a >= b ) result = BooleanAlgebra.TRUE;
		return result;
	}
}