2.5. Arithmetic

Figure 2.6 summarizes the C++ arithmetic operators. The asterisk (*) indicates multiplication and the percent sign (%) is the modulus operator that will be discussed shortly. The arithmetic operators in Fig. 2.6 are all binary operators

Fig. 2.6. Arithmetic operators.
C++ operation C++ arithmetic operator Algebraic expression C++ expression
Addition + f + 7 f + 7
Subtraction – p – c p – c
Multiplication * bm or b · m b * m
Division / x / y or or x ÷ y x / y
Modulus % r mod s r % s


Integer division (i.e., where both the numerator and the denominator are integers) yields an integer quotient; for example, the expression 7 / 4 evaluates to 1 and the expression 17 / 5 evaluates to 3. Note that any fractional part in integer division is discarded (i.e., truncated)—no rounding occurs.

C++ provides the modulus operator, %, that yields the remainder after integer division. The modulus operator can be used only with integer operands. The expression x % y yields the remainder after x is divided by y. Thus, 7 % 4 yields 3 and 17 % 5 yields 2. In later chapters, we discuss many interesting applications of the modulus operator, such as determining whether one number is a multiple of another (a special case of this is determining whether a number is odd or even).

Common Programming Error 2.3

Attempting to use the modulus operator (%) with noninteger operands is a compilation error.


Parentheses for Grouping Subexpressions

Parentheses are used in C++ expressions in the same manner as in algebraic expressions. For example, to multiply a times the quantity b + c we write a * ( b + c ).

Rules of Operator Precedence

C++ applies the operators in arithmetic expressions in a precise sequence determined by the following rules of operator precedence, which are generally the same as those followed in algebra:

  1. Operators in expressions contained within pairs of parentheses are evaluated first. Parentheses are said to be at the "highest level of precedence." In cases of nested, or embedded, parentheses, such as

    ( ( a + b ) + c )

    the operators in the innermost pair of parentheses are applied first. [Note: As in algebra, it is acceptable to place unnecessary parentheses in an expression to make the expression clearer. These are called redundant parentheses.]

  2. Multiplication, division and modulus operations are applied next. If an expression contains several multiplication, division and modulus operations, operators are applied from left to right. Multiplication, division and modulus are said to be on the same level of precedence.

  3. Addition and subtraction operations are applied last. If an expression contains several addition and subtraction operations, operators are applied from left to right. Addition and subtraction also have the same level of precedence.

The set of rules of operator precedence defines the order in which C++ applies operators. When we say that certain operators are applied from left to right, we are referring to the associativity of the operators. For example, in the expression

a + b + c

the addition operators (+) associate from left to right, so a + b is calculated first, then c is added to that sum to determine the value of the whole expression. We'll see that some operators associate from right to left. Figure 2.7 summarizes these rules of operator precedence. This table will be expanded as additional C++ operators are introduced. A complete precedence chart is included in Appendix A.

Fig. 2.7. Precedence of arithmetic operators.
Operator(s) Operation(s) Order of evaluation (precedence)
( ) Parentheses Evaluated first. If the parentheses are nested, the expression in the innermost pair is evaluated first. If there are several pairs of parentheses "on the same level" (i.e., not nested), they are evaluated left to right.
*
/
%		 Multiplication, Division, Modulus Evaluated second. If there are several, they are evaluated left to right.
+
-		 Addition Subtraction Evaluated last. If there are several, they are evaluated left to right.


Good Programming Practice 2.5

Using redundant parentheses in complex arithmetic expressions can make the expressions clearer.