C++ Primer Plus

The 4 appears to be an operand for both the + and * operators. When more than one operator can be applied to the same operand, C++ uses precedence rules to decide which operator is used first. The arithmetic operators follow the usual algebraic precedence, with multiplication, division, and the taking of the modulus done before addition and subtraction. Thus 3 + 4 * 5 means 3 + (4 * 5), not (3 + 4) * 5. So the answer is 23, not 35. Of course, you can use parentheses to enforce your own priorities. Appendix D, “Operator Precedence,” shows precedence for all the C++ operators. Note that *, /, and % are all in the same row in Appendix D. That means they have equal precedence. Similarly, addition and subtraction share a lower precedence.

Sometimes the precedence list is not enough. Consider the following statement:

float logs = 120 / 4 * 5;    // 150 or 6?

Once again, 4 is an operand for two operators. But the / and * operators have the same precedence, so precedence alone doesn’t tell the program whether to first divide 120 by 4 or multiply 4 by 5. Because the first choice leads to a result of 150 and the second to a result of 6, the choice is an important one. When two operators have the same precedence, C++ looks at whether the operators have a left-to-right associativity or a right-to-left associativity. Left-to-right associativity means that if two operators acting on the same operand have the same precedence, you apply the left-hand operator first. For right-to-left associativity, you apply the right-hand operator first. The associativity information, too, is in Appendix D. Appendix D shows that multiplication and division associate left-to-right. That means you use 4 with the leftmost operator first. That is, you divide 120 by 4, get 30 as a result, and then multiply the result by 5 to get 150.

Note that the precedence and associativity rules come into play only when two operators share the same operand. Consider the following expression:

int dues = 20 * 5 + 24 * 6;

Operator precedence tells you two things: The program must evaluate 20 * 5 before doing addition, and the program must evaluate 24 * 6 before doing addition. But neither precedence nor associativity says which multiplication takes place first. You might think that associativity says to do the leftmost multiplication first, but in this case, the two * operators do not share a common operand, so the rules don’t apply. In fact, C++ leaves it to the implementation to decide which order works best on a system. For this example, either order gives the same result, but there are circumstances in which the order can make a difference. You’ll see one in Chapter 5, which discusses the increment operator.

Division Diversions

You have yet to see the rest of the story about the division operator (/). The behavior of this operator depends on the type of the operands. If both operands are integers, C++ performs integer division. That means any fractional part of the answer is discarded, making the result an integer. If one or both operands are floating-point values, the fractional part is kept, making the result floating-point. Listing 3.11 illustrates how C++ division works with different types of values. As in Listing 3.10, Listing 3.11 invokes the setf() member function to modify how the results are displayed.

Listing 3.11. divide.cpp

// divide.cpp -- integer and floating-point division

#include

int main()

{

    using namespace std;

    cout.setf(ios_base::fixed, ios_base::floatfield);

    cout << "Integer division: 9/5 = " << 9 / 5  << endl;

    cout << "Floating-point division: 9.0/5.0 = ";

    cout << 9.0 / 5.0 << endl;

    cout << "Mixed division: 9.0/5 = " << 9.0 / 5  << endl;

    cout << "double constants: 1e7/9.0 = ";

    cout << 1.e7 / 9.0 <<  endl;

    cout << "float constants: 1e7f/9.0f = ";

    cout << 1.e7f / 9.0f <<  endl;

    return 0;

}

Here is the output from the program in Listing 3.11 for one implementation:

Integer division: 9/5 = 1

Floating-point division: 9.0/5.0 = 1.800000

Mixed division: 9.0/5 = 1.800000

double constants: 1e7/9.0 = 1111111.111111

float constants: 1e7f/9.0f = 1111111.125000

The first output line shows that dividing the integer 9 by the integer 5 yields the integer 1. The fractional part of 4 / 5 (or 0.8) is discarded. (You’ll see a practical use for this kind of division when you learn about the modulus operator, later in this chapter.) The next two lines show that when at least one of the operands is floating-point, you get a floating-point answer of 1.8. Actually, when you try to combine mixed types, C++ converts all the concerned types to the same type. You’ll learn about these automatic conversions later in this chapter. The relative precisions of the last two lines show that the result is type double if both operands are double and that it is float if both operands are float. Remember, floating-point constants are type double by default.

A Glimpse at Operator Overloading