Home > Articles > Programming > C/C++

  • Print
  • + Share This
This chapter is from the book

This chapter is from the book

2.6 Arithmetic

Most programs perform arithmetic calculations. Figure 2.9 summarizes the C++ arithmetic operators. Note the use of various special symbols not used in algebra. The asterisk (*) indicates multiplication and the percent sign (%) is the modulus operator that will be discussed shortly. The arithmetic operators in Fig. 2.9 are all binary operators, i.e., operators that take two operands. For example, the expression number1 + number2 contains the binary operator + and the two operands number1 and number2.

Fig 2.9. 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 xbyy.jpg 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. 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).

Arithmetic Expressions in Straight-Line Form

Arithmetic expressions in C++ must be entered into the computer in straight-line form. Thus, expressions such as "a divided by b" must be written as a / b, so that all constants, variables and operators appear in a straight line. The algebraic notation

048equ01.jpg

is generally not acceptable to compilers, although some special-purpose software packages do support more natural notation for complex mathematical expressions.

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 order determined by these rules of operator precedence, which are generally the same as those 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.

  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, the addition operators (+) in the expression

a + b + c

associate from left to right, so a + b is calculated first, then c is added to that sum to determine the whole expression's value. We'll see that some operators associate from right to left. Figure 2.10 summarizes these rules of operator precedence. We expand this table as we introduce additional C++ operators. A complete precedence chart is included in Appendix A.

Fig 2.10. 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. [Caution: If you have an expression such as (a + b) * (c - d) in which two sets of parentheses are not nested, but appear "on the same level," the C++ Standard does not specify the order in which these parenthesized subexpressions will be evaluated.]

*, /, %

Multiplication, Division, Modulus

Evaluated second. If there are several, they're evaluated left to right.

+

-

Addition

Subtraction

Evaluated last. If there are several, they're evaluated left to right.

Sample Algebraic and C++ Expressions

Now consider several expressions in light of the rules of operator precedence. Each example lists an algebraic expression and its C++ equivalent. The following is an example of an arithmetic mean (average) of five terms:

049equ01.jpg

The parentheses are required because division has higher precedence than addition. The entire quantity ( a + b + c + d + e ) is to be divided by 5. If the parentheses are erroneously omitted, we obtain a + b + c + d + e / 5, which evaluates incorrectly as

050equ01.jpg

The following is an example of the equation of a straight line:

Algebra:

y = mx + b

C++:

y = m * x + b;

No parentheses are required. The multiplication is applied first because multiplication has a higher precedence than addition.

The following example contains modulus (%), multiplication, division, addition, subtraction and assignment operations:

050fig01.jpg

The circled numbers under the statement indicate the order in which C++ applies the operators. The multiplication, modulus and division are evaluated first in left-to-right order (i.e., they associate from left to right) because they have higher precedence than addition and subtraction. The addition and subtraction are applied next. These are also applied left to right. The assignment operator is applied last because its precedence is lower than that of any of the arithmetic operators.

Evaluation of a Second-Degree Polynomial

To develop a better understanding of the rules of operator precedence, consider the evaluation of a second-degree polynomial y = ax 2 + bx + c:

050fig02.jpg

The circled numbers under the statement indicate the order in which C++ applies the operators. There is no arithmetic operator for exponentiation in C++, so we've represented x 2 as x * x. We'll soon discuss the standard library function pow ("power") that performs exponentiation. Because of some subtle issues related to the data types required by pow, we defer a detailed explanation of pow until Chapter 6.

Suppose variables a, b, c and x in the preceding second-degree polynomial are initialized as follows: a = 2, b = 3, c = 7 and x = 5. Figure 2.11 illustrates the order in which the operators are applied and the final value of the expression.

Fig. 2.11

Fig. 2.11 Order in which a second-degree polynomial is evaluated.

As in algebra, it's acceptable to place unnecessary parentheses in an expression to make the expression clearer. These are called redundant parentheses. For example, the preceding assignment statement could be parenthesized as follows:

y = ( a * x * x ) + ( b * x ) + c;
  • + Share This
  • 🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020