5.6. Overloading Methods

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5.9. The Math Class

The Math class contains the methods needed to perform basic mathematical functions. You have already used the pow(a, b) method to compute a ^b in Listing 2.6, ComputeLoan.java, and the Math.random() in Listing 3.5, SubtractionTutor.java. This section introduces other useful methods in the Math class. They can be categorized as trigonometric methods , exponent methods , and service methods . Besides methods, the Math class provides two useful double constants, PI and E (the base of natural logarithms). You can use these constants as Math.PI and Math.E in any program.

5.9.1. Trigonometric Methods

The Math class contains the following trigonometric methods:

   public static double   sin(double radians)   public static double   cos(double radians)   public static double   tan(double radians)   public static double   asin(double radians)   public static double   acos(double radians)   public static double   atan(double radians)   public static double   toRadians(double degree)   public static double   toDegrees(double radians) 

Each method has a single double parameter, and its return type is double . The parameter represents an angle in radians. One degree is equal to p/180 in radians. For example, Math.sin(Math.PI) returns the trigonometric sine of p. Since JDK 1.2, the Math class has also provided the method toRadians(double angdeg) for converting an angle in degrees to radians, and the method toDegrees(double angrad) for converting an angle in radians to degrees.

For example,

 Math.sin(     ) returns   0.0   Math.sin(Math.toRadians(   270   )) returns   -1.0   Math.sin(Math.PI /   6   ) returns   0.5   Math.sin(Math.PI /   2   ) returns   1.0   Math.cos(     ) returns   1.0   Math.cos(Math.PI /   6   ) returns   0.866   Math.cos(Math.PI /   2   ) returns     

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5.9.2. Exponent Methods

There are five methods related to exponents in the Math class:

  /** Return e raised to the power of x (ex) */    public static double   exp(   double   x)  /** Return the natural logarithm of x (ln(x) = loge(x)) */    public static double   log(   double   x)  /** Return the base 10 logarithm of x (log10(x)) */    public static double   log10(   double   x)  /** Return a raised to the power of b (xb) */    public static double   pow(   double   x,   double   b)  /** Return the square root of a (  ) */    public static double   sqrt(   double   x) 

Note that the parameter in the sqrt method must not be negative.

For example,

 Math.exp(   1   ) returns   2.71828   Math.log(   Math.E   ) returns   1.0   Math.log10(   10   ) returns   1.0   Math.pow(   2   ,   3   ) returns   8.0   Math.pow(   3   ,   2   ) returns   9.0   Math.pow(   3.5   ,   2.5   ) returns   22.91765   Math.sqrt(   4   ) returns   2.0   Math.sqrt(   10.5   ) returns   3.24   

5.9.3. The Rounding Methods

The Math class contains five rounding methods:

  /** x rounded up to its nearest integer. This integer is   * returned as a double value. */    public static double   ceil(   double   x)  /** x is rounded down to its nearest integer. This integer is   * returned as a double value. */    public static double   floor(   double   x)  /** x is rounded to its nearest integer. If x is equally close   * to two integers, the even one is returned as a double. */    public static double   rint(   double   x)  /** Return (int)Math.floor(x + 0.5). */    public static int   round(   float   x)  /** Return (long)Math.floor(x + 0.5). */    public static long   round(   double   x) 

For example,

 Math.ceil(   2.1   ) returns   3.0   Math.ceil(   2.0   ) returns   2.0   Math.ceil(   “2.0   ) returns   “2.0   Math.ceil(   “2.1   ) returns   -2.0   Math.floor(   2.1   ) returns   2.0   Math.floor(   2.0   ) returns   2.0   

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 Math.floor(   -2.0   ) returns   “2.0   Math.floor(   -2.1   ) returns   -3.0   Math.rint(   2.1   ) returns   2.0   Math.rint(   2.0   ) returns   2.0   Math.rint(   -2.0   ) returns   “2.0   Math.rint(   -2.1   ) returns   “2.0   Math.rint(   2.5   ) returns   2.0   Math.rint(   -2.5   ) returns   -2.0   Math.round(   2.6f   ) returns   3    // Returns int  Math.round(   2.0   ) returns   2    // Returns long  Math.round(   “2.0f   ) returns   -2   Math.round(   “2.6   ) returns   -3   

5.9.4. The min , max , and abs Methods

The min and max methods are overloaded to return the minimum and maximum numbers between two numbers ( int , long , float , or double ). For example, max(3.4, 5.0) returns 5.0 , and min(3, 2) returns 2 .

The abs method is overloaded to return the absolute value of the number ( int , long , float , and double ). For example,

 Math.max(   2   ,   3   ) returns   3   Math.max(   2.5   ,   3   ) returns   3.0   Math.min(   2.5   ,   3.6   ) returns   2.5   Math.abs(   -2   ) returns   2   Math.abs(   -2.1   ) returns   2.1   

5.9.5. The random Method

The Math class also has a powerful method, random , which generates a random double value greater than or equal to 0.0 and less than 1.0 ( 0.0 <= Math.random() < 1.0 ). This method is very useful. Listing 3.5, SubtractionTutor.java, uses this method to generate a single-digit integer. You can use it to write a simple expression to generate random numbers in any range. For example,

In general,

Tip

You can view the complete documentation for the Math class online at http://java.sun.com/j2se/1.5.0/docs/api/index.html, as shown in Figure 5.10. You can also download jdk-1_5_0-doc.zip from the same website and install it on your PC so that you can browse the documents locally.

Figure 5.10. You can view the documentation for Java API online.

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Note

Not all classes need a main method. The Math class and JOptionPane class do not have main methods. These classes contain methods for other classes to use.