Advantages and Disadvantages of Floating-Point Numbers

Floating-point numbers have two advantages over integers. First, they can represent values between integers. Second, because of the scaling factor, they can represent a much greater range of values. On the other hand, floating point operations usually are slightly slower than integer operations, and you can lose precision. Listing 3.9 illustrates the last point.

Listing 3.9. fltadd.cpp

// fltadd.cpp -- precision problems with float
#include <iostream>
int main()
{
    using namespace std;
    float a = 2.34E+22f;
    float b = a + 1.0f;

    cout << "a = " << a << endl;
    cout << "b - a = " << b - a << endl;
    return 0;
}

The program in Listing 3.9 takes a number, adds 1, and then subtracts the original number. That should result in a value of 1. Does it? Here is the output from the program in Listing 3.9 for one system:

a = 2.34e+022
b - a = 0

The problem is that 2.34E+22 represents a number with 23 digits to the left of the decimal. By adding 1, you are attempting to add 1 to the 23rd digit in that number. But type float can represent only the first 6 or 7 digits in a number, so trying to change the 23rd digit has no effect on the value.

C++ Arithmetic Operators

Perhaps you have warm memories of doing arithmetic drills in grade school. You can give that same pleasure to your computer. C++ uses operators to do arithmetic. It provides operators for five basic arithmetic calculations: addition, subtraction, multiplication, division, and taking the modulus. Each of these operators uses two values (called operands) to calculate a final answer. Together, the operator and its operands constitute an expression. For example, consider the following statement:

int wheels = 4 + 2;

The values 4 and 2 are operands, the + symbol is the addition operator, and 4 + 2 is an expression whose value is 6.

Here are C++’s five basic arithmetic operators:

• The + operator adds its operands. For example, 4 + 20 evaluates to 24.

• The - operator subtracts the second operand from the first. For example, 12 - 3 evaluates to 9.

• The * operator multiplies its operands. For example, 28 * 4 evaluates to 112.

• The / operator divides its first operand by the second. For example, 1000 / 5 evaluates to 200. If both operands are integers, the result is the integer portion of the quotient. For example, 17 / 3 is 5, with the fractional part discarded.

• The % operator finds the modulus of its first operand with respect to the second. That is, it produces the remainder of dividing the first by the second. For example, 19 % 6 is 1 because 6 goes into 19 three times, with a remainder of 1. Both operands must be integer types; using the % operator with floating-point values causes a compile-time error. If one of the operands is negative, the sign of the result satisfies the following rule: (a/b)*b + a%b equals a.

Of course, you can use variables as well as constants for operands. Listing 3.10 does just that. Because the % operator works only with integers, we’ll leave it for a later example.

Listing 3.10. arith.cpp

// arith.cpp -- some C++ arithmetic
#include <iostream>
int main()
{
    using namespace std;
    float hats, heads;

    cout.setf(ios_base::fixed, ios_base::floatfield); // fixed-point
    cout << "Enter a number: ";
    cin >> hats;
    cout << "Enter another number: ";
    cin >> heads;

    cout << "hats = " << hats << "; heads = " << heads << endl;
    cout << "hats + heads = " << hats + heads << endl;
    cout << "hats - heads = " << hats - heads << endl;
    cout << "hats * heads = " << hats * heads << endl;
    cout << "hats / heads = " << hats / heads << endl;
    return 0;
}

As you can see in the following sample output from the program in Listing 3.10, you can trust C++ to do simple arithmetic:

Enter a number: 50.25
Enter another number: 11.17
hats = 50.250000; heads = 11.170000
hats + heads = 61.419998
hats - heads = 39.080002
hats * heads = 561.292480
hats / heads = 4.498657

Well, maybe you can’t trust it completely. Adding 11.17 to 50.25 should yield 61.42, but the output reports 61.419998. This is not an arithmetic problem; it’s a problem with the limited capacity of type float to represent significant figures. Remember, C++ guarantees just six significant figures for float. If you round 61.419998 to six figures, you get 61.4200, which is the correct value to the guaranteed precision. The moral is that if you need greater accuracy, you should use double or long double.