math.java

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/* java.lang.Math -- common mathematical functions, native allowed
   Copyright (C) 1998, 2001, 2002 Free Software Foundation, Inc.

This file is part of GNU Classpath.

GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING.  If not, write to the
Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.

As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module.  An independent module is a module which is not derived from
or based on this library.  If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so.  If you do not wish to do so, delete this
exception statement from your version. */

package java.lang;

import java.util.Random;

/**
 * Helper class containing useful mathematical functions and constants.
 * <P>
 *
 * Note that angles are specified in radians.  Conversion functions are
 * provided for your convenience.
 *
 * @author Paul Fisher
 * @author John Keiser
 * @author Eric Blake <[e-mail]>
 * @since 1.0
 */
public final class Math {
	/**
	 * Math is non-instantiable
	 */
	private Math() {
	}

	/**
	 * A random number generator, initialized on first use.
	 */
	private static Random rand;

	/**
	 * The most accurate approximation to the mathematical constant <em>e</em>:
	 * <code>2.718281828459045</code>. Used in natural log and exp.
	 *
	 * @see #log(double)
	 * @see #exp(double)
	 */
	public static final double E = 2.718281828459045;

	/**
	 * The most accurate approximation to the mathematical constant <em>pi</em>:
	 * <code>3.141592653589793</code>. This is the ratio of a circle's diameter
	 * to its circumference.
	 */
	public static final double PI = 3.141592653589793;

	/**
	 * Take the absolute value of the argument.
	 * (Absolute value means make it positive.)
	 * <P>
	 *
	 * Note that the the largest negative value (Integer.MIN_VALUE) cannot
	 * be made positive.  In this case, because of the rules of negation in
	 * a computer, MIN_VALUE is what will be returned.
	 * This is a <em>negative</em> value.  You have been warned.
	 *
	 * @param i the number to take the absolute value of
	 * @return the absolute value
	 * @see Integer#MIN_VALUE
	 */
	public static int abs(int i) {
		return (i < 0) ? -i : i;
	}

	/**
	 * Take the absolute value of the argument.
	 * (Absolute value means make it positive.)
	 * <P>
	 *
	 * Note that the the largest negative value (Long.MIN_VALUE) cannot
	 * be made positive.  In this case, because of the rules of negation in
	 * a computer, MIN_VALUE is what will be returned.
	 * This is a <em>negative</em> value.  You have been warned.
	 *
	 * @param l the number to take the absolute value of
	 * @return the absolute value
	 * @see Long#MIN_VALUE
	 */
	public static long abs(long l) {
		return (l < 0) ? -l : l;
	}

	/**
	 * Take the absolute value of the argument.
	 * (Absolute value means make it positive.)
	 * <P>
	 *
	 * This is equivalent, but faster than, calling
	 * <code>Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))</code>.
	 *
	 * @param f the number to take the absolute value of
	 * @return the absolute value
	 */
	public static float abs(float f) {
		return (f <= 0) ? 0 - f : f;
	}

	/**
	 * Take the absolute value of the argument.
	 * (Absolute value means make it positive.)
	 *
	 * This is equivalent, but faster than, calling
	 * <code>Double.longBitsToDouble(Double.doubleToLongBits(a)
	 *       &lt;&lt; 1) &gt;&gt;&gt; 1);</code>.
	 *
	 * @param d the number to take the absolute value of
	 * @return the absolute value
	 */
	public static double abs(double d) {
		return (d <= 0) ? 0 - d : d;
	}

	/**
	 * Return whichever argument is smaller.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the smaller of the two numbers
	 */
	public static int min(int a, int b) {
		return (a < b) ? a : b;
	}

	/**
	 * Return whichever argument is smaller.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the smaller of the two numbers
	 */
	public static long min(long a, long b) {
		return (a < b) ? a : b;
	}

	/**
	 * Return whichever argument is smaller. If either argument is NaN, the
	 * result is NaN, and when comparing 0 and -0, -0 is always smaller.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the smaller of the two numbers
	 */
	public static float min(float a, float b) {
		// this check for NaN, from JLS 15.21.1, saves a method call
		if (Float.isNaN(a))
			return a;
		// no need to check if b is NaN; < will work correctly
		// recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special
		if (a == 0 && b == 0)
			return - (-a - b);
		return (a < b) ? a : b;
	}

	/**
	 * Return whichever argument is smaller. If either argument is NaN, the
	 * result is NaN, and when comparing 0 and -0, -0 is always smaller.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the smaller of the two numbers
	 */
	public static double min(double a, double b) {
		// this check for NaN, from JLS 15.21.1, saves a method call
		if (Double.isNaN(a))
			return a;
		// no need to check if b is NaN; < will work correctly
		// recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special
		if (a == 0 && b == 0)
			return - (-a - b);
		return (a < b) ? a : b;
	}

	/**
	 * Return whichever argument is larger.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the larger of the two numbers
	 */
	public static int max(int a, int b) {
		return (a > b) ? a : b;
	}

	/**
	 * Return whichever argument is larger.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the larger of the two numbers
	 */
	public static long max(long a, long b) {
		return (a > b) ? a : b;
	}

	/**
	 * Return whichever argument is larger. If either argument is NaN, the
	 * result is NaN, and when comparing 0 and -0, 0 is always larger.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the larger of the two numbers
	 */
	public static float max(float a, float b) {
		// this check for NaN, from JLS 15.21.1, saves a method call
		if (Float.isNaN(a))
			return a;
		// no need to check if b is NaN; > will work correctly
		// recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special
		if (a == 0 && b == 0)
			return a - -b;
		return (a > b) ? a : b;
	}

	/**
	 * Return whichever argument is larger. If either argument is NaN, the
	 * result is NaN, and when comparing 0 and -0, 0 is always larger.
	 *
	 * @param a the first number
	 * @param b a second number
	 * @return the larger of the two numbers
	 */
	public static double max(double a, double b) {
		// this check for NaN, from JLS 15.21.1, saves a method call
		if (Double.isNaN(a))
			return a;
		// no need to check if b is NaN; > will work correctly
		// recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special
		if (a == 0 && b == 0)
			return a - -b;
		return (a > b) ? a : b;
	}

	/**
	 * The trigonometric function <em>sin</em>. The sine of NaN or infinity is
	 * NaN, and the sine of 0 retains its sign. This is accurate within 1 ulp,
	 * and is semi-monotonic.
	 *
	 * @param a the angle (in radians)
	 * @return sin(a)
	 */
	public static double sin(double a) {
		return StrictMath.sin(a);
	}

	/**
	 * The trigonometric function <em>cos</em>. The cosine of NaN or infinity is
	 * NaN. This is accurate within 1 ulp, and is semi-monotonic.
	 *
	 * @param a the angle (in radians)
	 * @return cos(a)
	 */
	public static double cos(double a) {
		return StrictMath.cos(a);
	}

	/**
	 * The trigonometric function <em>tan</em>. The tangent of NaN or infinity
	 * is NaN, and the tangent of 0 retains its sign. This is accurate within 1
	 * ulp, and is semi-monotonic.
	 *
	 * @param a the angle (in radians)
	 * @return tan(a)
	 */
	public static double tan(double a) {
		return StrictMath.tan(a);
	}

	/**
	 * The trigonometric function <em>arcsin</em>. The range of angles returned
	 * is -pi/2 to pi/2 radians (-90 to 90 degrees). If the argument is NaN or
	 * its absolute value is beyond 1, the result is NaN; and the arcsine of
	 * 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic.
	 *
	 * @param a the sin to turn back into an angle
	 * @return arcsin(a)
	 */
	public static double asin(double a) {
		return StrictMath.asin(a);
	}

	/**
	 * The trigonometric function <em>arccos</em>. The range of angles returned
	 * is 0 to pi radians (0 to 180 degrees). If the argument is NaN or
	 * its absolute value is beyond 1, the result is NaN. This is accurate
	 * within 1 ulp, and is semi-monotonic.
	 *
	 * @param a the cos to turn back into an angle
	 * @return arccos(a)
	 */
	public static double acos(double a) {