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 C++, there are two floating-point types, called float and double. In this book we will use doubles exclusively.

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

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

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, C++ 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

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 C++ automatically converts from one type to another. For example,

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

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 C++ 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:

This sets y to 0.333333, as expected.

All the operations we have seen---addition, subtraction, multiplication, and division---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.