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 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:

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.

Warning

It is important that you initialize any and all variables that you declare. Failure to do so will generate an error (if you’re lucky), or C++ will initialize the variable to leftover memory, which could lead to undefined behavior.

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:

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

double y = 1;

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:

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 C++ does integer division, which yields the integer value 0. Converted to floating-point, the result is 0.0.

Warning

It’s crucial that you understand that when given two integers, C++ performs integer division! This is a common logic error that can be hard to catch, since your program will compile without problems.

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—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.

Q-3: In the lab, we measured a temperature of 7.99999999 degrees C, using an extremely precise measuring device. Now we are writing a program to perform some calculations with our data. Consider the following C++ code.

double e = 2.71828;
int e_int = e;
double e_double = e_int;
cout << e_double;

What is the value of e_double that is printed to the terminal?

• e
• This is the name of a variable. Only the value of a variable will print with cout.
• 3
• Converting to an int always rounds down.
• 2
• When we converted e to an int, e was rounded down to 2. When we converted e_nt to e_double, the decimal places from e were lost, and the value of e_double is 2.
• 3.0
• Converting to an int always rounds down.
• 2.71828
• When we converted e to an int, e was rounded down to 2. When we converted e_nt to e_double, the decimal places from e were lost.

Identifying whether an operation carries out integer division or floating point division can get tricky when we have a mix of integers and doubles in our expression. The thing to remeber is if either the divisor or the dividend is a double then the program will carry out floating point division.

Run the code below to see what type of division occurs each time.

#include <iostream> using namespace std; int main () { double value = 5.0/2; //(a) cout<<"current value (a) is "<<value<<endl; value = 5/2.0; //(b) cout<<"current value (b) is "<<value<<endl; value = 5/2; //(c) cout<<"current value (c) is "<<value<<endl; value = 5.0/2.0; //(d) cout<<"current value (d) is "<<value<<endl; return 0; }

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