math.java

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/*
 * @(#)Math.java	1.24 97/01/31
 * 
 * Copyright (c) 1995, 1996 Sun Microsystems, Inc. All Rights Reserved.
 * 
 * This software is the confidential and proprietary information of Sun
 * Microsystems, Inc. ("Confidential Information").  You shall not
 * disclose such Confidential Information and shall use it only in
 * accordance with the terms of the license agreement you entered into
 * with Sun.
 * 
 * SUN MAKES NO REPRESENTATIONS OR WARRANTIES ABOUT THE SUITABILITY OF THE
 * SOFTWARE, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
 * PURPOSE, OR NON-INFRINGEMENT. SUN SHALL NOT BE LIABLE FOR ANY DAMAGES
 * SUFFERED BY LICENSEE AS A RESULT OF USING, MODIFYING OR DISTRIBUTING
 * THIS SOFTWARE OR ITS DERIVATIVES.
 * 
 * CopyrightVersion 1.1_beta
 * 
 */

package java.lang;
import java.util.Random;


/**
 * The class <code>Math</code> contains methods for performing basic 
 * numeric operations such as the elementary exponential, logarithm, 
 * square root, and trigonometric functions. 
 * <p>
 * To help ensure portability of Java programs, the definitions of 
 * many of the numeric functions in this package require that they 
 * produce the same results as certain published algorithms. These 
 * algorithms are available from the well-known network library 
 * <code>netlib</code> as the package "Freely Distributable 
 * Math Library" (<code>fdlibm</code>). These algorithms, which 
 * are written in the C programming language, are then to be 
 * understood as executed with all floating-point operations 
 * following the rules of Java floating-point arithmetic. 
 * <p>
 * The network library may be found on the World Wide Web at 
 * <ul><code>
 *   http://netlib.att.com/
 * </code></ul>
 * <p>
 * then perform a keyword search for "<code>fdlibm</code>".
 * <p>
 * The Java math library is defined with respect to the version of 
 * <code>fdlibm</code> dated January 4, 1995. Where 
 * <code>fdlibm</code> provides more than one definition for a 
 * function (such as <code>acos</code>), use the "IEEE 754 core 
 * function" version (residing in a file whose name begins with 
 * the letter <code>e</code>). 
 *
 * @author  unascribed
 * @version 1.24, 01/31/97
 * @since   JDK1.0
 */

public final class Math {

    /**
     * Don't let anyone instantiate this class.
     */
    private Math() {}

    /**
     * The <code>double</code> value that is closer than any other to 
     * <code>e</code>, the base of the natural logarithms. 
     *
     * @since   JDK1.0
     */
    public static final double E = 2.7182818284590452354;

    /**
     * The <code>double</code> value that is closer than any other to 
     * <i>pi</i>, the ratio of the circumference of a circle to its diameter. 
     *
     * @since   JDK1.0
     */
    public static final double PI = 3.14159265358979323846;

    /**
     * Returns the trigonometric sine of an angle.
     *
     * @param   a   an angle, in radians.
     * @return  the sine of the argument.
     * @since   JDK1.0
     */
    public static native double sin(double a);
    
    /**
     * Returns the trigonometric cosine of an angle.
     *
     * @param   a   an angle, in radians.
     * @return  the cosine of the argument.
     * @since   JDK1.0
     */
    public static native double cos(double a);
   
    /**
     * Returns the trigonometric tangent of an angle.
     *
     * @param   a   an angle, in radians.
     * @return  the tangent of the argument.
     * @since   JDK1.0
     */
    public static native double tan(double a);

    /**
     * Returns the arc sine of an angle, in the range of -<i>pi</i>/2 through
     * <i>pi</i>/2.
     *
     * @param   a   an angle, in radians.
     * @return  the arc sine of the argument.
     * @since   JDK1.0
     */
    public static native double asin(double a);

    /**
     * Returns the arc cosine of an angle, in the range of 0.0 through
     * <i>pi</i>.
     *
     * @param   a   an angle, in radians.
     * @return  the arc cosine of the argument.
     * @since   JDK1.0
     */
    public static native double acos(double a); 

    /**
     * Returns the arc tangent of an angle, in the range of -<i>pi</i>/2
     * through <i>pi</i>/2.
     *
     * @param   a   an angle, in radians.
     * @return  the arc tangent of the argument.
     * @since   JDK1.0
     */
    public static native double atan(double a);

    /**
     * Returns the exponential number <i>e</i> (i.e., 2.718...) raised to
     * the power of a <code>double</code> value.
     *
     * @param   a   a <code>double</code> value.
     * @return  the value <i>e</i><sup>a</sup>, where <i>e</i> is the base of
     *          the natural logarithms.
     * @since   JDK1.0
     */
    public static native double exp(double a);

    /**
     * Returns the natural logarithm (base <i>e</i>) of a <code>double</code>
     * value.
     *
     * @param   a   a number greater than <code>0.0</code>.
     * @return  the value ln&nbsp;<code>a</code>, the natural logarithm of
     *          <code>a</code>.
     * @since   JDK1.0
     */
    public static native double log(double a);

    /**
     * Returns the square root of a <code>double</code> value.
     *
     * @param   a   a <code>double</code> value.
     * <!--@return  the value of &radic;&nbsp;<code>a</code>.-->
     * @return  the square root of <code>a</code>.
     *          If the argument is NaN or less than zero, the result is NaN.
     * @since   JDK1.0
     */
    public static native double sqrt(double a);

    /**
     * Computes the remainder operation on two arguments as prescribed 
     * by the IEEE 754 standard.
     * The remainder value is mathematically equal to 
     * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
     * where <i>n</i> is the mathematical integer closest to the exact 
     * mathematical value of the quotient <code>f1/f2</code>, and if two 
     * mathematical integers are equally close to <code>f1/f2</code>, 
     * then <i>n</i> is the integer that is even. If the remainder is 
     * zero, its sign is the same as the sign of the first argument. 
     *
     * @param   f1   the dividend.
     * @param   f2   the divisor.
     * @return  the remainder when <code>f1</code> is divided by
     *          <code>f2</code>.
     * @since   JDK1.0
     */
    public static native double IEEEremainder(double f1, double f2);

    /**
     * Returns the smallest (closest to negative infinity) 
     * <code>double</code> value that is not less than the argument and is 
     * equal to a mathematical integer. 
     *
     * @param   a   a <code>double</code> value.
     * <!--@return  the value &lceil;&nbsp;<code>a</code>&nbsp;&rceil;.-->
     * @return  the smallest (closest to negative infinity) 
     *          <code>double</code> value that is not less than the argument
     *          and is equal to a mathematical integer. 
     * @since   JDK1.0
     */
    public static native double ceil(double a);

    /**
     * Returns the largest (closest to positive infinity) 
     * <code>double</code> value that is not greater than the argument and 
     * is equal to a mathematical integer. 
     *
     * @param   a   a <code>double</code> value.
     * @param   a   an assigned value.
     * <!--@return  the value &lfloor;&nbsp;<code>a</code>&nbsp;&rfloor;.-->
     * @return  the largest (closest to positive infinity) 
     *          <code>double</code> value that is not greater than the argument
     *          and is equal to a mathematical integer. 
     * @since   JDK1.0
     */
    public static native double floor(double a);

    /**
     * returns the closest integer to the argument. 
     *
     * @param   a   a <code>double</code> value.
     * @return  the closest <code>double</code> value to <code>a</code> that is
     *          equal to a mathematical integer. If two <code>double</code>
     *          values that are mathematical integers are equally close to the
     *          value of the argument, the result is the integer value that
     *          is even.
     * @since   JDK1.0
     */
    public static native double rint(double a);

    /**
     * Converts rectangular coordinates (<code>b</code>,&nbsp;<code>a</code>)
     * to polar (r,&nbsp;<i>theta</i>).
     * This method computes the phase <i>theta</i> by computing an arc tangent
     * of <code>b/a</code> in the range of -<i>pi</i> to <i>pi</i>.
     *
     * @param   a   a <code>double</code> value.
     * @param   b   a <code>double</code> value.
     * @return  the <i>theta</i> component of the point
     *          (<i>r</i>,&nbsp;<i>theta</i>)
     *          in polar coordinates that corresponds to the point
     *          (<i>b</i>,&nbsp;<i>a</i>) in Cartesian coordinates.
     * @since   JDK1.0
     */
    public static native double atan2(double a, double b);


    /**
     * Returns of value of the first argument raised to the power of the
     * second argument.
     * <p>
     * If (<code>a&nbsp;==&nbsp;0.0</code>), then <code>b</code> must be
     * greater than <code>0.0</code>; otherwise an exception is thrown. 
     * An exception also will occur if (<code>a&nbsp;&lt;=&nbsp;0.0</code>)
     * and <code>b</code> is not equal to a whole number.
     *
     * @param   a   a <code>double</code> value.
     * @param   b   a <code>double</code> value.
     * @return  the value <code>a<sup>b</sup></code>.
     * @exception ArithmeticException  if (<code>a&nbsp;==&nbsp;0.0</code>) and
     *              (<code>b&nbsp;&lt;=&nbsp0.0</code>), or
     *              if (<code>a&nbsp;&lt;=&nbsp;0.0</code>) and <code>b</code>