Doing Math in Java part 1: Operators

One of the most valuable uses of a computer is...computing. That is, acting as a mathematical calculator. Java has a plethora of tools for doing computation.

Operators

The standard math functions that are built into the Java language are called operators. These are the sort of math functions you would expect to find on a simple calculator, plus some extras:

+ - * / % ++ --

There are other operators used for comparisons, these are the math operators. You can learn more about them in the Java Language Specification, specifically in Integer Operations, Floating-Point Operations, and more extensively through Chapter 15, Expressions.

+ and - do what you would expect, they add and subtract one value from another. * is the symbol used for multiplication, instead of the × used in math class. * is used because it's easier for the computer to recognize it as a math operator, × just looks like a letter 'x' to the computer. Similarly, / is used for division. The ÷ sign isn't on most keyboards, but / has been common on keyboards even before they were attached to computers.

The % sign doesn't do what you might, at first, expect. It doesn't calculate a percentage, as it does on most calculators. It returns the remainder of a division. For example, if you do 10/3 (ten divided by three), the result will be 3. But what if you want to get the remainder? That's what % does. 10%3 will return a value of 1. '%' is sometimes called "modulo". It's a bit of a misnomer, mathematically, but the use of the term is common and well understood, so it's not unusual to pronounce 10%3 as "ten modulo three". This is a very valuable function for keeping a value within a certain range, such as keeping an object located onscreen in graphics by having it "wrap" from one side of the screen to the other when it reaches an edge.

++ and -- are the "increment" and "decrement" operators. Increment means "go up by one unit", and decrement "go down by one unit". So if you've got a variable like:

int i = 5;

And you do i++, the value of i will become 6. Doing i-- will take away 1. ++ and -- can be placed either before or after the value they act on, for example:

number = i++;
count = --j;

There will be different effects on your program depending on whether they come before or after the value. You can find information on that in the Java Language Specification as well, in sections 15.14 and 15.15 which cover the two ways of using these operators. In general, it's best to stick to using them after your value until you understand the differences.

Assignment Operators

You can also do math as part of assigning a value. For example, let's say we want to add three to a value in our program. The obvious way to do this would be:

i = i + 3;

This takes the prior value of i, adds 3 to it, then puts the result back into variable i. With an assignment operator we can do the same thing more tersely:

i += 3;

We've combined the + with = to create an operator. This does the same thing as i = i + 3;. Your program doesn't care which way you type it. The same thing can be done with the other operators that take two values:

i *= 4; // Multiply i by four, store result back in i.
i /= 2; // Divide i in half.
i %= 3; // Put the remainder of i/3 in i.
i -= 7; //Subtract seven from i.

More Complex Math

This is what we can do with the basic math operators built into the language. To get more operations, like those found on a scientific or programmer's calculator, we use methods of some of the standard packages of Java. Which I'll cover in a future article.

Until then, have a look at java.lang.Math.

Stars in import Statements

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import javax.swing.event.*;

These are some representative import statments. Each one has an asterisk (or "star") at the end of it. What does that mean?

The asterisk is a special pattern-matching character. It matches any combination of characters (letters, numbers, or special characters.) In other words, it will match any name of any class in the package. Let's say we want to import Frame, Panel, Component, Color, Dialog, Dimension, Graphics and Image from the java.awt package for a program we're writing. We could have the following import statements:

import java.awt.Frame;
import java.awt.Panel;
import java.awt.Component;
import java.awt.Color;
import java.awt.Dialog;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Image;

Since star can take the place of any name, we can replace all of those import statements with one:

import java.awt.*;

This imports every class in java.awt. It also imports all the interfaces, exceptions, and errors defined in java.awt. It makes absolutely everything in the java.awt package available to our program.

OK, then why do we need to do this?

import java.awt.*;
import java.awt.event.*;

If the * makes us get everything in java.awt, why do we need to then go an import java.awt.event.*?

The reason is that java.awt.event is a different package than java.awt. The stuff in java.awt.event isn't actually in java.awt. With package names, the dot notation is just a way of letting us know that the stuff in java.awt.event is related to the stuff in java.awt, and that we'll probably want to use the stuff in these packages together. But java.awt.event isn't in java.awt, the way that System.out is in the class System.

Just remember, every package with its own name is a totally different package. You can tell a class name from a package name by whether it is capitalized:

import java.awt.Color;

Color is a class in the java.awt package. This is one of the reasons we follow the convention of using a capital letter at the start of a class's name. Whereas this:

import java.awt.color.*;

is an import of the classes in the java.awt.color package. These classes are not in java.awt, so you can't import them using "import java.awt.*;"

The asterisk is a "regular expression" character. It and a number of other characters are a way of building up what are called regular expressions, which are a way of matching things without using the precise name. The asterisk is a "wildcard," it can stand for any character, or any number of any characters.