strictmath.java

this gcc-g++-3.3.1.tar.gz is a source file of gcc, you can learn more about gcc through this codes f

/* java.lang.StrictMath -- common mathematical functions, strict Java
   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. */

/*
 * Some of the algorithms in this class are in the public domain, as part
 * of fdlibm (freely-distributable math library), available at
 * http://www.netlib.org/fdlibm/, and carry the following copyright:
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

package java.lang;

import java.util.Random;
import gnu.classpath.Configuration;

/**
 * Helper class containing useful mathematical functions and constants.
 * This class mirrors {@link Math}, but is 100% portable, because it uses
 * no native methods whatsoever.  Also, these algorithms are all accurate
 * to less than 1 ulp, and execute in <code>strictfp</code> mode, while
 * Math is allowed to vary in its results for some functions. Unfortunately,
 * this usually means StrictMath has less efficiency and speed, as Math can
 * use native methods.
 *
 * <p>The source of the various algorithms used is the fdlibm library, at:<br>
 * <a href="http://www.netlib.org/fdlibm/">http://www.netlib.org/fdlibm/</a>
 *
 * Note that angles are specified in radians.  Conversion functions are
 * provided for your convenience.
 *
 * @author Eric Blake <[e-mail]>
 * @since 1.3
 */
public final strictfp class StrictMath
{
  /**
   * StrictMath is non-instantiable.
   */
  private StrictMath()
  {
  }

  /**
   * A random number generator, initialized on first use.
   *
   * @see #random()
   */
  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; // Long bits 0x4005bf0z8b145769L.

  /**
   * 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; // Long bits 0x400921fb54442d18L.

  /**
   * 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.)
   *
   * @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.)
   *
   * @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 (a != 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 (a != 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 (a != 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 (a != 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.
   *
   * @param a the angle (in radians)
   * @return sin(a)
   */
  public static double sin(double a)
  {
    if (a == Double.NEGATIVE_INFINITY || ! (a < Double.POSITIVE_INFINITY))
      return Double.NaN;

    if (abs(a) <= PI / 4)
      return sin(a, 0);

    // Argument reduction needed.
    double[] y = new double[2];
    int n = remPiOver2(a, y);
    switch (n & 3)
      {
      case 0:
        return sin(y[0], y[1]);
      case 1:
        return cos(y[0], y[1]);
      case 2:
        return -sin(y[0], y[1]);
      default:
        return -cos(y[0], y[1]);
      }
  }

  /**
   * The trigonometric function <em>cos</em>. The cosine of NaN or infinity is
   * NaN.
   *
   * @param a the angle (in radians).
   * @return cos(a).
   */
  public static double cos(double a)
  {
    if (a == Double.NEGATIVE_INFINITY || ! (a < Double.POSITIVE_INFINITY))
      return Double.NaN;

    if (abs(a) <= PI / 4)
      return cos(a, 0);

    // Argument reduction needed.
    double[] y = new double[2];
    int n = remPiOver2(a, y);
    switch (n & 3)
      {
      case 0:
        return cos(y[0], y[1]);
      case 1:
        return -sin(y[0], y[1]);
      case 2:
        return -cos(y[0], y[1]);
      default:
        return sin(y[0], y[1]);
      }
  }

  /**
   * The trigonometric function <em>tan</em>. The tangent of NaN or infinity
   * is NaN, and the tangent of 0 retains its sign.
   *
   * @param a the angle (in radians)
   * @return tan(a)
   */
  public static double tan(double a)
  {
    if (a == Double.NEGATIVE_INFINITY || ! (a < Double.POSITIVE_INFINITY))
      return Double.NaN;

    if (abs(a) <= PI / 4)
      return tan(a, 0, false);

    // Argument reduction needed.
    double[] y = new double[2];
    int n = remPiOver2(a, y);
    return tan(y[0], y[1], (n & 1) == 1);
  }

  /**
   * 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.
   *
   * @param x the sin to turn back into an angle
   * @return arcsin(x)
   */
  public static double asin(double x)
  {
    boolean negative = x < 0;
    if (negative)
      x = -x;
    if (! (x <= 1))
      return Double.NaN;
    if (x == 1)
      return negative ? -PI / 2 : PI / 2;
    if (x < 0.5)
      {
        if (x < 1 / TWO_27)
          return negative ? -x : x;
        double t = x * x;
        double p = t * (PS0 + t * (PS1 + t * (PS2 + t * (PS3 + t
                                                         * (PS4 + t * PS5)))));
        double q = 1 + t * (QS1 + t * (QS2 + t * (QS3 + t * QS4)));
        return negative ? -x - x * (p / q) : x + x * (p / q);
      }
    double w = 1 - x; // 1>|x|>=0.5.
    double t = w * 0.5;
    double p = t * (PS0 + t * (PS1 + t * (PS2 + t * (PS3 + t
                                                     * (PS4 + t * PS5)))));
    double q = 1 + t * (QS1 + t * (QS2 + t * (QS3 + t * QS4)));
    double s = sqrt(t);
    if (x >= 0.975)
      {
        w = p / q;
        t = PI / 2 - (2 * (s + s * w) - PI_L / 2);
      }
    else
      {
        w = (float) s;
        double c = (t - w * w) / (s + w);
        p = 2 * s * (p / q) - (PI_L / 2 - 2 * c);
        q = PI / 4 - 2 * w;
        t = PI / 4 - (p - q);
      }
    return negative ? -t : t;
  }

  /**
   * 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.
   *
   * @param x the cos to turn back into an angle
   * @return arccos(x)
   */
  public static double acos(double x)
  {
    boolean negative = x < 0;
    if (negative)
      x = -x;
    if (! (x <= 1))
      return Double.NaN;
    if (x == 1)
      return negative ? PI : 0;
    if (x < 0.5)
      {
        if (x < 1 / TWO_57)
          return PI / 2;
        double z = x * x;
        double p = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z
                                                         * (PS4 + z * PS5)))));
        double q = 1 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
        double r = x - (PI_L / 2 - x * (p / q));
        return negative ? PI / 2 + r : PI / 2 - r;
      }
    if (negative) // x<=-0.5.
      {
        double z = (1 + x) * 0.5;
        double p = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z