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Chapter 3


3.1 Floating-point

In the last chapter we had some problems dealing with numbers that were not integers. We worked around the problem by measuring percentages instead of fractions, but a more general solution is to use floating-point numbers, which can represent fractions as well as integers. In Java, the floating-point type is called double.

You can create floating-point variables and assign values to them using the same syntax we used for the other types. For example:

    double pi;
    pi = 3.14159;

It is also legal to declare a variable and assign a value to it at the same time:

    int x = 1;
    String empty = "";
    double pi = 3.14159;

In fact, this syntax is quite common. A combined declaration and assignment is sometimes called an initialization.

Although floating-point numbers are useful, they are often a source of confusion because there seems to be an overlap between integers and floating-point numbers. For example, if you have the value 1, is that an integer, a floating-point number, or both?

Strictly speaking, Java distinguishes the integer value 1 from the floating-point value 1.0, even though they seem to be the same number. They belong to different types, and strictly speaking, you are not allowed to make assignments between types. For example, the following is illegal:

    int x = 1.1;

because the variable on the left is an int and the value on the right is a double. But it is easy to forget this rule, especially because there are places where Java will automatically convert from one type to another. For example:

    double y = 1;

should technically not be legal, but Java allows it by converting the int to a double automatically. This leniency is convenient, but it can cause problems; for example:

    double y = 1 / 3;

You might expect the variable y to be given the value 0.333333, which is a legal floating-point value, but in fact it will get the value 0.0. The reason is that the expression on the right appears to be the ratio of two integers, so Java does integer division, which yields the integer value 0. Converted to floating-point, the result is 0.0.

One way to solve this problem (once you figure out what it is) is to make the right-hand side a floating-point expression:

    double y = 1.0 / 3.0;

This sets y to 0.333333, as expected.

All the operations we have seen so far---addition, subtraction, multiplication, and division---also work on floating-point values, although you might be interested to know that the underlying mechanism is completely different. In fact, most processors have special hardware just for performing floating-point operations.

3.2 Converting from double to int

As I mentioned, Java converts a ints to doubles automatically if necessary, because no information is lost in the translation. On the other hand, going from a double to an int requires rounding off. Java doesn't perform this operation automatically, in order to make sure that you, as the programmer, are aware of the loss of the fractional part of the number.

The simplest way to convert a floating-point value to an integer is to use a typecast. Typecasting is so called because it allows you to take a value that belongs to one type and "cast" it into another type (in the sense of molding or reforming, not throwing).

Unfortunately, the syntax for typecasting is ugly: you put the name of the type in parentheses and use it as an operator. For example,

    int x = (int) Math.PI;

The (int) operator has the effect of converting what follows into an integer, so x gets the value 3.

Typecasting takes precedence over arithmetic operations, so in the following example, the value of PI gets converted to an integer first, and the result is 60, not 62.

    int x = (int) Math.PI * 20.0;

Converting to an integer always rounds down, even if the fraction part is 0.99999999.

These two properties (precedence and rounding) can make typecasting awkward.

3.3 Math methods

In mathematics, you have probably seen functions like sin and log, and you have learned to evaluate expressions like sin(pi/2) and log(1/x). First, you evaluate the expression in parentheses, which is called the argument of the function. For example, pi/2 is approximately 1.571, and 1/x is 0.1 (assuming that x is 10).

Then you can evaluate the function itself, either by looking it up in a table or by performing various computations. The sin of 1.571 is 1, and the log of 0.1 is -1 (assuming that log indicates the logarithm base 10).

This process can be applied repeatedly to evaluate more complicated expressions like log(1/sin(pi/2)). First we evaluate the argument of the innermost function, then evaluate the function, and so on.

Java provides a set of built-in functions that includes most of the mathematical operations you can think of. These functions are called methods. Most math methods operate on doubles.

The math methods are invoked using a syntax that is similar to the print commands we have already seen:

     double root = Math.sqrt (17.0);
     double angle = 1.5;
     double height = Math.sin (angle);

The first example sets root to the square root of 17. The second example finds the sine of 1.5, which is the value of the variable angle. Java assumes that the values you use with sin and the other trigonometric functions (cos, tan) are in radians. To convert from degrees to radians, you can divide by 360 and multiply by 2 pi. Conveniently, Java provides pi as a built-in value:

     double degrees = 90;
     double angle = degrees * 2 * Math.PI / 360.0;

Notice that PI is in all capital letters. Java does not recognize Pi, pi, or pie.

Another useful method in the Math class is round, which rounds a floating-point value off to the nearest integer and returns an int.

    int x = Math.round (Math.PI * 20.0);

In this case the multiplication happens first, before the method is invoked. The result is 63 (rounded up from 62.8319).

3.4 Composition

Just as with mathematical functions, Java methods can be composed, meaning that you use one expression as part of another. For example, you can use any expression as an argument to a method:

    double x = Math.cos (angle + Math.PI/2);

This statement takes the value Math.PI, divides it by two and adds the result to the value of the variable angle. The sum is then passed as an argument to the cos method. (Notice that PI is the name of a variable, not a method, so there are no arguments, not even the empty argument ()).

You can also take the result of one method and pass it as an argument to another:

    double x = Math.exp (Math.log (10.0));

In Java, the log function always uses base e, so this statement finds the log base e of 10 and then raises e to that power. The result gets assigned to x; I hope you know what it is.

3.5 Adding new methods

So far we have only been using the methods that are built into Java, but it is also possible to add new methods. Actually, we have already seen one method definition: main. The method named main is special in that it indicates where the execution of the program begins, but the syntax for main is the same as for any other method definition:

  public static void NAME ( LIST OF PARAMETERS ) {

You can make up any name you want for your method, except that you can't call it main or any other Java keyword. The list of parameters specifies what information, if any, you have to provide in order to use (or invoke) the new function.

The single parameter for main is String[] args, which indicates that whoever invokes main has to provide an array of Strings (we'll get to arrays in Chapter 10). The first couple of methods we are going to write have no parameters, so the syntax looks like this:

  public static void newLine () {
    System.out.println ("");

This method is named newLine, and the empty parentheses indicate that it takes no parameters. It contains only a single statement, which prints an empty String, indicated by "". Printing a String with no letters in it may not seem all that useful, except remember that println skips to the next line after it prints, so this statement has the effect of skipping to the next line.

In main we can invoke this new method using syntax that is similar to the way we invoke the built-in Java commands:

  public static void main (String[] args) {
    System.out.println ("First line.");
    newLine ();
    System.out.println ("Second line.");

The output of this program is

First line.

Second line.

Notice the extra space between the two lines. What if we wanted more space between the lines? We could invoke the same method repeatedly:

  public static void main (String[] args) {
    System.out.println ("First line.");
    newLine ();
    newLine ();
    newLine ();
    System.out.println ("Second line.");

Or we could write a new method, named threeLine, that prints three new lines:

  public static void threeLine () {
    newLine ();  newLine ();  newLine ();

  public static void main (String[] args) {
    System.out.println ("First line.");
    threeLine ();
    System.out.println ("Second line.");

You should notice a few things about this program:

So far, it may not be clear why it is worth the trouble to create all these new methods. Actually, there are a lot of reasons, but this example only demonstrates two:

  1. Creating a new method gives you an opportunity to give a name to a group of statements. Methods can simplify a program by hiding a complex computation behind a single command, and by using English words in place of arcane code. Which is clearer, newLine or System.out.println ("")?
  2. Creating a new method can make a program smaller by eliminating repetitive code. For example, how would you print nine consecutive new lines? You could just invoke threeLine three times.

3.6 Classes and methods

Pulling together all the code fragments from the previous section, the whole class definition looks like this:

class NewLine {

  public static void newLine () {
    System.out.println ("");

  public static void threeLine () {
    newLine ();  newLine ();  newLine ();

  public static void main (String[] args) {
    System.out.println ("First line.");
    threeLine ();
    System.out.println ("Second line.");

The first line indicates that this is the class definition for a new class called NewLine. A class is a collection of related methods. In this case, the class named NewLine contains three methods, named newLine, threeLine, and main.

The other class we've seen is the Math class. It contains methods named sqrt, sin, and many others. When we invoke a mathematical function, we have to specify the name of the class (Math) and the name of the function. That's why the syntax is slightly different for built-in methods and the methods that we write:

    Math.pow (2.0, 10.0);
    newLine ();

The first statement invokes the pow method in the Math class (which raises the first argument to the power of the second argument). The second statement invokes the newLine method, which Java assumes (correctly) is in the NewLine class, which is what we are writing.

If you try to invoke a method from the wrong class, the compiler will generate an error. For example, if you type:

    pow (2.0, 10.0);

The compiler will say something like, "Can't find a method named pow in class NewLine." If you have seen this message, you might have wondered why it was looking for pow in your class definition. Now you know.

3.7 Programs with multiple methods

When you look at a class definition that contains several methods, it is tempting to read it from top to bottom, but that is likely to be confusing, because that is not the order of execution of the program.

Execution always begins at the first statement of main, regardless of where it is in the program (in this case I deliberately put it at the bottom). Statements are executed one at a time, in order, until you reach a method invocation. Method invocations are like a detour in the flow of execution. Instead of going to the next statement, you go to the first line of the invoked method, execute all the statements there, and then come back and pick up again where you left off.

That sounds simple enough, except that you have to remember that one method can invoke another. Thus, while we are in the middle of main, we might have to go off and execute the statements in threeLine. But while we are executing threeLine, we get interrupted three times to go off and execute newLine.

For its part, newLine invokes the built-in method println, which causes yet another detour. Fortunately, Java is quite adept at keeping track of where it is, so when println completes, it picks up where it left off in newLine, and then gets back to threeLine, and then finally gets back to main so the program can terminate.

Actually, technically, the program does not terminate at the end of main. Instead, execution picks up where it left off in the program that invoked main, which is the Java interpreter. The Java interpreter takes care of things like deleting windows and general cleanup, and then the program terminates.

What's the moral of this sordid tale? When you read a program, don't read from top to bottom. Instead, follow the flow of execution.

3.8 Parameters and arguments

Some of the built-in methods we have used have parameters, which are values that you provide to let the method do its job. For example, if you want to find the sine of a number, you have to indicate what the number is. Thus, sin takes a double value as a parameter. To print a string, you have to provide the string, which is why println takes a String as an parameter.

Some methods take more than one parameter, like pow, which takes two doubles, the base and the exponent.

Notice that in each of these cases we have to specify not only how many parameters there are, but also what type they are. So it shouldn't surprise you that when you write a class definition, the parameter list indicates the type of each parameter. For example:

  public static void printTwice (String phil) {
    System.out.println (phil);
    System.out.println (phil);

This method takes a single parameter, named phil, that has type String. Whatever that parameter is (and at this point we have no idea what it is), it gets printed twice. I chose the name phil to suggest that the name you give a parameter is up to you, but in general you want to choose something more illustrative than phil.

In order to invoke this method, we have to provide a String. For example, we might have a main method like this:

  public static void main (String[] args) {
    printTwice ("Don't make me say this twice!");

The string you provide is called an argument, and we say that the argument is passed to the method. In this case we are creating a string value that contains the text "Don't make me say this twice!" and passing that string as an argument to printTwice where, contrary to its wishes, it will get printed twice.

Alternatively, if we had a String variable, we could use it as an argument instead:

  public static void main (String[] args) {
    String argument = "Never say never.");
    printTwice (argument);

Notice something very important here: the name of the variable we pass as an argument (argument) has nothing to do with the name of the parameter (phil). Let me say that again:

The name of the variable we pass as an argument has nothing to do with the name of the parameter.

They can be the same or they can be different, but it is important to realize that they are not the same thing, except that they happen to have the same value (in this case the string "Never say never.").

The value you provide as an argument must have the same type as the parameter of the method you invoke. This rule is very important, but it often gets complicated in Java for two reasons:

One last thing you should realize is that parameters and other variables only exist inside their own methods. Within the confines of main, there is no such thing as phil. If you try to use it, the compiler will complain. Similarly, inside printTwice there is no such thing as argument.

3.9 Methods with multiple parameters

The syntax for declaring and invoking methods with multiple parameters is a common source of errors. First, remember that you have to declare the type of every parameter. For example

  public static void printTime (int hour, int minute) {
    System.out.print (hour);
    System.out.print (":");
    System.out.println (minute);

It might be tempting to write int hour, minute, but that format is only legal for variable declarations, not for parameters.

Another common source of confusion is that you do not have to declare the types of arguments. The following is wrong!

    int hour = 11;
    int minute = 59;
    printTime (int hour, int minute);   // WRONG!

In this case, Java can tell the type of hour and minute by looking at their declarations. It is unnecessary and illegal to include the type when you pass them as arguments. The correct syntax is printTime (hour, minute).

3.10 Methods with results

You might have noticed by now that some of the methods we are using, like the Math methods, yield results. Other methods, like println and newLine, perform some action but they don't return a value. That raises some questions:

The answer to the third question is "yes, you can write methods that return values," and we'll do it in a couple of chapters. I will leave it up to you to answer the other two questions by trying them out. In fact, any time you have a question about what is legal or illegal in Java, a good way to find out is to ask the compiler.

3.11 Glossary

A type of variable (or value) that can contain fractions as well as integers. In Java this type is called double.
A named collection of methods. So far, we have used the Math class and the System class, and we have written classes named Hello and NewLine.
A named sequence of statements that performs some useful function. Methods may or may not take parameters, and may or may not produce a result.
A piece of information you provide in order to invoke a method. Parameters are like variables in the sense that they contain values and have types.
A value that you provide when you invoke a method. This value must have the same type as the corresponding parameter.
Cause a method to be executed.

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