math.java

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   * 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 native static double asin(double 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 native static double acos(double 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, the
   * result is NaN; and the arctangent of 0 retains its sign. This is accurate
   * within 1 ulp, and is semi-monotonic.
   *
   * @param a the tan to turn back into an angle
   * @return arcsin(a)
   * @see #atan2(double, double)
   */
  public native static double atan(double a);

  /**
   * A special version of the trigonometric function <em>arctan</em>, for
   * converting rectangular coordinates <em>(x, y)</em> to polar
   * <em>(r, theta)</em>. This computes the arctangent of x/y in the range
   * of -pi to pi radians (-180 to 180 degrees). Special cases:<ul>
   * <li>If either argument is NaN, the result is NaN.</li>
   * <li>If the first argument is positive zero and the second argument is
   * positive, or the first argument is positive and finite and the second
   * argument is positive infinity, then the result is positive zero.</li>
   * <li>If the first argument is negative zero and the second argument is
   * positive, or the first argument is negative and finite and the second
   * argument is positive infinity, then the result is negative zero.</li>
   * <li>If the first argument is positive zero and the second argument is
   * negative, or the first argument is positive and finite and the second
   * argument is negative infinity, then the result is the double value
   * closest to pi.</li>
   * <li>If the first argument is negative zero and the second argument is
   * negative, or the first argument is negative and finite and the second
   * argument is negative infinity, then the result is the double value
   * closest to -pi.</li>
   * <li>If the first argument is positive and the second argument is
   * positive zero or negative zero, or the first argument is positive
   * infinity and the second argument is finite, then the result is the
   * double value closest to pi/2.</li>
   * <li>If the first argument is negative and the second argument is
   * positive zero or negative zero, or the first argument is negative
   * infinity and the second argument is finite, then the result is the
   * double value closest to -pi/2.</li>
   * <li>If both arguments are positive infinity, then the result is the
   * double value closest to pi/4.</li>
   * <li>If the first argument is positive infinity and the second argument
   * is negative infinity, then the result is the double value closest to
   * 3*pi/4.</li>
   * <li>If the first argument is negative infinity and the second argument
   * is positive infinity, then the result is the double value closest to
   * -pi/4.</li>
   * <li>If both arguments are negative infinity, then the result is the
   * double value closest to -3*pi/4.</li>
   *
   * </ul><p>This is accurate within 2 ulps, and is semi-monotonic. To get r,
   * use sqrt(x*x+y*y).
   *
   * @param y the y position
   * @param x the x position
   * @return <em>theta</em> in the conversion of (x, y) to (r, theta)
   * @see #atan(double)
   */
  public native static double atan2(double y, double x);

  /**
   * Take <em>e</em><sup>a</sup>.  The opposite of <code>log()</code>. If the
   * argument is NaN, the result is NaN; if the argument is positive infinity,
   * the result is positive infinity; and if the argument is negative
   * infinity, the result is positive zero. This is accurate within 1 ulp,
   * and is semi-monotonic.
   *
   * @param a the number to raise to the power
   * @return the number raised to the power of <em>e</em>
   * @see #log(double)
   * @see #pow(double, double)
   */
  public native static double exp(double a);

  /**
   * Take ln(a) (the natural log).  The opposite of <code>exp()</code>. If the
   * argument is NaN or negative, the result is NaN; if the argument is
   * positive infinity, the result is positive infinity; and if the argument
   * is either zero, the result is negative infinity. This is accurate within
   * 1 ulp, and is semi-monotonic.
   *
   * <p>Note that the way to get log<sub>b</sub>(a) is to do this:
   * <code>ln(a) / ln(b)</code>.
   *
   * @param a the number to take the natural log of
   * @return the natural log of <code>a</code>
   * @see #exp(double)
   */
  public native static double log(double a);

  /**
   * Take a square root. If the argument is NaN or negative, the result is
   * NaN; if the argument is positive infinity, the result is positive
   * infinity; and if the result is either zero, the result is the same.
   * This is accurate within the limits of doubles.
   *
   * <p>For other roots, use pow(a, 1 / rootNumber).
   *
   * @param a the numeric argument
   * @return the square root of the argument
   * @see #pow(double, double)
   */
  public native static double sqrt(double a);

  /**
   * Raise a number to a power. Special cases:<ul>
   * <li>If the second argument is positive or negative zero, then the result
   * is 1.0.</li>
   * <li>If the second argument is 1.0, then the result is the same as the
   * first argument.</li>
   * <li>If the second argument is NaN, then the result is NaN.</li>
   * <li>If the first argument is NaN and the second argument is nonzero,
   * then the result is NaN.</li>
   * <li>If the absolute value of the first argument is greater than 1 and
   * the second argument is positive infinity, or the absolute value of the
   * first argument is less than 1 and the second argument is negative
   * infinity, then the result is positive infinity.</li>
   * <li>If the absolute value of the first argument is greater than 1 and
   * the second argument is negative infinity, or the absolute value of the
   * first argument is less than 1 and the second argument is positive
   * infinity, then the result is positive zero.</li>
   * <li>If the absolute value of the first argument equals 1 and the second
   * argument is infinite, then the result is NaN.</li>
   * <li>If the first argument is positive zero and the second argument is
   * greater than zero, or the first argument is positive infinity and the
   * second argument is less than zero, then the result is positive zero.</li>
   * <li>If the first argument is positive zero and the second argument is
   * less than zero, or the first argument is positive infinity and the
   * second argument is greater than zero, then the result is positive
   * infinity.</li>
   * <li>If the first argument is negative zero and the second argument is
   * greater than zero but not a finite odd integer, or the first argument is
   * negative infinity and the second argument is less than zero but not a
   * finite odd integer, then the result is positive zero.</li>
   * <li>If the first argument is negative zero and the second argument is a
   * positive finite odd integer, or the first argument is negative infinity
   * and the second argument is a negative finite odd integer, then the result
   * is negative zero.</li>
   * <li>If the first argument is negative zero and the second argument is
   * less than zero but not a finite odd integer, or the first argument is
   * negative infinity and the second argument is greater than zero but not a
   * finite odd integer, then the result is positive infinity.</li>
   * <li>If the first argument is negative zero and the second argument is a
   * negative finite odd integer, or the first argument is negative infinity
   * and the second argument is a positive finite odd integer, then the result
   * is negative infinity.</li>
   * <li>If the first argument is less than zero and the second argument is a
   * finite even integer, then the result is equal to the result of raising
   * the absolute value of the first argument to the power of the second
   * argument.</li>
   * <li>If the first argument is less than zero and the second argument is a
   * finite odd integer, then the result is equal to the negative of the
   * result of raising the absolute value of the first argument to the power
   * of the second argument.</li>
   * <li>If the first argument is finite and less than zero and the second
   * argument is finite and not an integer, then the result is NaN.</li>
   * <li>If both arguments are integers, then the result is exactly equal to
   * the mathematical result of raising the first argument to the power of
   * the second argument if that result can in fact be represented exactly as
   * a double value.</li>
   *
   * </ul><p>(In the foregoing descriptions, a floating-point value is
   * considered to be an integer if and only if it is a fixed point of the
   * method {@link #ceil(double)} or, equivalently, a fixed point of the
   * method {@link #floor(double)}. A value is a fixed point of a one-argument
   * method if and only if the result of applying the method to the value is
   * equal to the value.) This is accurate within 1 ulp, and is semi-monotonic.
   *
   * @param a the number to raise
   * @param b the power to raise it to
   * @return a<sup>b</sup>
   */
  public native static double pow(double a, double b);

  /**
   * Get the IEEE 754 floating point remainder on two numbers. This is the
   * value of <code>x - y * <em>n</em></code>, where <em>n</em> is the closest
   * double to <code>x / y</code> (ties go to the even n); for a zero
   * remainder, the sign is that of <code>x</code>. If either argument is NaN,
   * the first argument is infinite, or the second argument is zero, the result
   * is NaN; if x is finite but y is infinte, the result is x. This is
   * accurate within the limits of doubles.
   *
   * @param x the dividend (the top half)
   * @param y the divisor (the bottom half)
   * @return the IEEE 754-defined floating point remainder of x/y
   * @see #rint(double)
   */
  public native static double IEEEremainder(double x, double y);

  /**
   * Take the nearest integer that is that is greater than or equal to the
   * argument. If the argument is NaN, infinite, or zero, the result is the
   * same; if the argument is between -1 and 0, the result is negative zero.
   * Note that <code>Math.ceil(x) == -Math.floor(-x)</code>.
   *
   * @param a the value to act upon
   * @return the nearest integer &gt;= <code>a</code>
   */
  public native static double ceil(double a);

  /**
   * Take the nearest integer that is that is less than or equal to the
   * argument. If the argument is NaN, infinite, or zero, the result is the
   * same. Note that <code>Math.ceil(x) == -Math.floor(-x)</code>.
   *
   * @param a the value to act upon
   * @return the nearest integer &lt;= <code>a</code>
   */
  public native static double floor(double a);

  /**
   * Take the nearest integer to the argument.  If it is exactly between
   * two integers, the even integer is taken. If the argument is NaN,
   * infinite, or zero, the result is the same.
   *
   * @param a the value to act upon
   * @return the nearest integer to <code>a</code>
   */
  public native static double rint(double a);

  /**
   * Take the nearest integer to the argument.  This is equivalent to
   * <code>(int) Math.floor(a + 0.5f). If the argument is NaN, the result
   * is 0; otherwise if the argument is outside the range of int, the result
   * will be Integer.MIN_VALUE or Integer.MAX_VALUE, as appropriate.
   *
   * @param a the argument to round
   * @return the nearest integer to the argument
   * @see Integer#MIN_VALUE
   * @see Integer#MAX_VALUE
   */
  public static int round(float a)
  {
    return (int) floor(a + 0.5f);
  }

  /**
   * Take the nearest long to the argument.  This is equivalent to
   * <code>(long) Math.floor(a + 0.5)</code>. If the argument is NaN, the
   * result is 0; otherwise if the argument is outside the range of long, the
   * result will be Long.MIN_VALUE or Long.MAX_VALUE, as appropriate.
   *
   * @param a the argument to round
   * @return the nearest long to the argument
   * @see Long#MIN_VALUE
   * @see Long#MAX_VALUE
   */
  public static long round(double a)
  {
    return (long) floor(a + 0.5d);
  }

  /**
   * Get a random number.  This behaves like Random.nextDouble(), seeded by
   * System.currentTimeMillis() when first called. In other words, the number
   * is from a pseudorandom sequence, and lies in the range [+0.0, 1.0).
   * This random sequence is only used by this method, and is threadsafe,
   * although you may want your own random number generator if it is shared
   * among threads.
   *
   * @return a random number
   * @see Random#nextDouble()
   * @see System#currentTimeMillis()
   */
  public static synchronized double random()
  {
    if (rand == null)
      rand = new Random();
    return rand.nextDouble();
  }

  /**
   * Convert from degrees to radians. The formula for this is
   * radians = degrees * (pi/180); however it is not always exact given the
   * limitations of floating point numbers.
   *
   * @param degrees an angle in degrees
   * @return the angle in radians
   * @since 1.2
   */
  public static double toRadians(double degrees)
  {
    return degrees * (PI / 180);
  }

  /**
   * Convert from radians to degrees. The formula for this is
   * degrees = radians * (180/pi); however it is not always exact given the
   * limitations of floating point numbers.
   *
   * @param rads an angle in radians
   * @return the angle in degrees
   * @since 1.2
   */
  public static double toDegrees(double rads)
  {
    return rads * (180 / PI);
  }
}