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4.11 Floating-Point Numbers and Type decimal

In our next application, we depart temporarily from our GradeBook case study to declare a class called Account that maintains a bank account's balance. Most account balances are not whole numbers (such as 0, –22 and 1024). For this reason, class Account represents the account balance as a real number (i.e., a number with a decimal point, such as 7.33, 0.0975 or 1000.12345). C# provides three simple types for storing real numbers—float, double , and decimal. Types float and double are called floating-point types. The primary difference between them and decimal is that decimal variables store a limited range of real numbers precisely, whereas floating-point variables store only approximations of real numbers, but across a much greater range of values. Also, double variables can store numbers with larger magnitude and finer detail (i.e., more digits to the right of the decimal point—also known as the number's precision) than float variables. A key application of type decimal is representing monetary amounts.

Real-Number Precision and Storage Requirements

Variables of type float represent single-precision floating-point numbers and have seven significant digits. Variables of type double represent double-precision floating-point numbers. These require twice as much storage as float variables and provide 15–16 significant digits—approximately double the precision of float variables. Furthermore, variables of type decimal require twice as much storage as double variables and provide 28–29 significant digits. In some applications, even variables of type double and decimal will be inadequate—such applications are beyond the scope of this book.

Most programmers represent floating-point numbers with type double. In fact, C# treats all real numbers you type in an application's source code (such as 7.33 and 0.0975) as double values by default. Such values in the source code are known as floating-point literals. To type a decimal literal, you must type the letter "M" or "m" (which stands for "money") at the end of a real number (for example, 7.33M is a decimal literal rather than a double). Integer literals are implicitly converted into type float, double or decimal when they're assigned to a variable of one of these types. See Appendix B for the ranges of values for floats, doubles, decimals and all the other simple types.

Although floating-point numbers are not always 100% precise, they have numerous applications. For example, when we speak of a "normal" body temperature of 98.6, we do not need to be precise to a large number of digits. When we read the temperature on a thermometer as 98.6, it may actually be 98.5999473210643. Calling this number simply 98.6 is fine for most applications involving body temperatures. Due to the imprecise nature of floating-point numbers, type decimal is preferred over the floating-point types whenever the calculations need to be exact, as with monetary calculations. In cases where approximation is enough, double is preferred over type float because double variables can represent floating-point numbers more accurately. For this reason, we use type decimal throughout the book for monetary amounts and type double for other real numbers.

Real numbers also arise as a result of division. In conventional arithmetic, for example, when we divide 10 by 3, the result is 3.3333333..., with the sequence of 3s repeating infinitely. The computer allocates only a fixed amount of space to hold such a value, so clearly the stored floating-point value can be only an approximation.

Account Class with an Instance Variable of Type decimal

Our next application (Figs. 4.15–4.16) contains a simple class named Account (Fig. 4.15) that maintains the balance of a bank account. A typical bank services many accounts, each with its own balance, so line 7 declares an instance variable named balance of type decimal. Variable balance is an instance variable because it's declared in the body of the class (lines 6–36) but outside the class's method and property declarations (lines 10–13, 16–19 and 22–35). Every instance (i.e., object) of class Account contains its own copy of balance.

Fig 4.15. Account class with a constructor to initialize instance variable balance.

 1  // Fig. 4.15: Account.cs
 2  // Account class with a constructor to
 3  // initialize instance variable balance.
 4
 5  public class Account
 6  {
 7     private decimal balance; // instance variable that stores the balance
 8
 9     // constructor
10     public Account(  decimal  initialBalance )
11     {
12        Balance = initialBalance;  // set balance using property
13     }  // end Account constructor
14
15     // credit (add) an amount to the account
16     public void Credit( decimal amount )
17     {
18        Balance = Balance + amount;  // add amount to balance
19     }  // end method Credit
20
21     // a property to get and set the account balance
22     public decimal Balance
23     {
24        get
25        {
26           return balance;
27        }  // end get
28        set
29        {
30           // validate that value is greater than or equal to 0;
31           // if it is not, balance is left unchanged
32            if ( value >=  0 )
33              balance = value;
34        }  // end set
35     }  // end property Balance
36  }  // end class Account

Fig 4.16. Create and manipulate an Account object.

 1  // Fig. 4.16: AccountTest.cs
 2  // Create and manipulate Account objects.
 3  using System;
 4
 5  public class AccountTest
 6  {
 7     // Main method begins execution of C# application
 8     public static void Main( string[] args )
 9     {
10        Account account1 = new Account( 50.00M ); // create Account object
11        Account account2 = new Account( -7.53M ); // create Account object
12
13        // display initial balance of each object using a property
14        Console.WriteLine( "account1 balance: " {0:C},
15           account1.Balance ); // display Balance property
16        Console.WriteLine( "account2 balance: {0:C} \n",
17           account2.Balance ); // display Balance property
18
19        decimal depositAmount; // deposit amount read from user
20
21        // prompt and obtain user input
22        Console.Write( "Enter deposit amount for account1: " );
23        depositAmount = Convert.ToDecimal( Console.ReadLine() );
24        Console.WriteLine( "adding  {0:C} to account1 balance\n",
25           depositAmount );
26        account1.Credit( depositAmount ); // add to account1 balance
27
28        // display balances
29        Console.WriteLine( "account1 balance:  {0:C} ",
30           account1.Balance );
31        Console.WriteLine( "account2 balance:  {0:C} \n",
32           account2.Balance );
33
34        // prompt and obtain user input
35        Console.Write( "Enter deposit amount for account2: " );
36        depositAmount = Convert.ToDecimal( Console.ReadLine() );
37        Console.WriteLine( "adding {0:C} to account2 balance\n",
38           depositAmount );
39        account2.Credit( depositAmount );  // add to account2 balance
40
41        // display balances
42        Console.WriteLine( "account1 balance: {0:C} ", account1.Balance );
43        Console.WriteLine( "account2 balance: {0:C} ", account2.Balance );
44     }  // end Main
45  }  // end class AccountTest

Class Account contains a constructor, a method, and a property. Since it's common for someone opening an account to place money in the account immediately, the constructor (lines 10–13) receives a parameter initialBalance of type decimal that represents the account's starting balance. Line 12 assigns initialBalance to the property Balance, invoking Balance's set accessor to initialize the instance variable balance.

Method Credit (lines 16–19) doesn't return data when it completes its task, so its return type is void. The method receives one parameter named amount—a decimal value that's added to the property Balance. Line 18 uses both the get and set accessors of Balance. The expression Balance + amount invokes property Balance's get accessor to obtain the current value of instance variable balance, then adds amount to it. We then assign the result to instance variable balance by invoking the Balance property's set accessor (thus replacing the prior balance value).

Property Balance (lines 22–35) provides a get accessor, which allows clients of the class (i.e., other classes that use this class) to obtain the value of a particular Account object's balance. The property has type decimal (line 22). Balance also provides an enhanced set accessor.

In Section 4.5, we introduced properties whose set accessors allow clients of a class to modify the value of a private instance variable. In Fig. 4.7, class GradeBook defines property CourseName's set accessor to assign the value received in its parameter value to instance variable courseName (line 19). This CourseName property does not ensure that courseName contains only valid data.

The application of Figs. 4.15–4.16 enhances the set accessor of class Account's property Balance to perform this validation (also known as validity checking). Line 32 (Fig. 4.15) ensures that value is nonnegative. If the value is greater than or equal to 0, the amount stored in value is assigned to instance variable balance in line 33. Otherwise, balance is left unchanged.

AccountTest Class to Use Class Account

Class AccountTest (Fig. 4.16) creates two Account objects (lines 10–11) and initializes them respectively with 50.00M and -7.53M (the decimal literals representing the real numbers 50.00 and -7.53). The Account constructor (lines 10–13 of Fig. 4.15) references property Balance to initialize balance. In previous examples, the benefit of referencing the property in the constructor was not evident. Now, however, the constructor takes advantage of the validation provided by the set accessor of the Balance property. The constructor simply assigns a value to Balance rather than duplicating the set accessor's validation code. When line 11 of Fig. 4.16 passes an initial balance of -7.53 to the Account constructor, the constructor passes this value to the set accessor of property Balance, where the actual initialization occurs. This value is less than 0, so the set accessor does not modify balance, leaving this instance variable with its default value of 0.

Lines 14–17 in Fig. 4.16 output the balance in each Account by using the Account's Balance property. When Balance is used for account1 (line 15), the value of account1's balance is returned by the get accessor in line 26 of Fig. 4.15 and displayed by the Console.WriteLine statement (Fig. 4.16, lines 14–15). Similarly, when property Balance is called for account2 from line 17, the value of the account2's balance is returned from line 26 of Fig. 4.15 and displayed by the Console.WriteLine statement (Fig. 4.16, lines 16–17). The balance of account2 is 0 because the constructor ensured that the account could not begin with a negative balance. The value is output by WriteLine with the format item {0:C}, which formats the account balance as a monetary amount. The : after the 0 indicates that the next character represents a format specifier, and the C format specifier after the : specifies a monetary amount (C is for currency). The cultural settings on the user's machine determine the format for displaying monetary amounts. For example, in the United States, 50 displays as $50.00. In Germany, 50 displays as 50,00 €. Figure 4.17 lists a few other format specifiers in addition to C.

Fig 4.17. string format specifiers.

Format specifier

Description

C or c

Formats the string as currency. Displays an appropriate currency symbol ($ in the U.S.) next to the number. Separates digits with an appropriate separator character (comma in the U.S.) and sets the number of decimal places to two by default.

D or d

Formats the string as a whole number. Displays number as an integer.

N or n

Formats the string with a thousands separator and a default of two decimal places.

E or e

Formats the number using scientific notation with a default of six decimal places.

F or f

Formats the string with a fixed number of decimal places (two by default).

G or g

Formats the number normally with decimal places or using scientific notation, depending on context. If a format item does not contain a format specifier, format G is assumed implicitly.

X or x

Formats the string as hexadecimal.

Line 19 declares local variable depositAmount to store each deposit amount entered by the user. Unlike the instance variable balance in class Account, the local variable depositAmount in Main is not initialized to 0 by default. Also, a local variable can be used only in the method in which it's declared. However, this variable does not need to be initialized here because its value will be determined by the user's input. The compiler does not allow a local variable's value to be read until it's initialized.

Line 22 prompts the user to enter a deposit amount for account1. Line 23 obtains the input from the user by calling the Console class's ReadLine method, then passing the string entered by the user to the Convert class's ToDecimal method, which returns the decimal value in this string. Lines 24–25 display the deposit amount. Line 26 calls object account1's Credit method and supplies depositAmount as the method's argument. When the method is called, the argument's value is assigned to parameter amount of method Credit (lines 16–19 of Fig. 4.15), then method Credit adds that value to the balance (line 18 of Fig. 4.15). Lines 29–32 (Fig. 4.16) output the balances of both Accounts again to show that only account1's balance changed.

Line 35 prompts the user to enter a deposit amount for account2. Line 36 obtains the input from the user by calling method Console.ReadLine, and passing the return value to the Convert class's ToDecimal method. Lines 37–38 display the deposit amount. Line 39 calls object account2's Credit method and supplies depositAmount as the method's argument, then method Credit adds that value to the balance. Finally, lines 42–43 output the balances of both Accounts again to show that only account2's balance changed.

set and get Accessors with Different Access Modifiers

By default, the get and set accessors of a property have the same access as the property—for example, for a public property, the accessors are public. It's possible to declare the get and set accessors with different access modifiers. In this case, one of the accessors must implicitly have the same access as the property and the other must be declared with a more restrictive access modifier than the property. For example, in a public property, the get accessor might be public and the set accessor might be private. We demonstrate this feature in Section 10.5.

UML Class Diagram for Class Account

The UML class diagram in Fig. 4.18 models class Account of Fig. 4.15. The diagrammodels the Balance property as a UML attribute of type decimal (because the corresponding C# property had type decimal). The diagram models class Account's constructor with a parameter initialBalance of type decimal in the third compartment of the class. The diagram models operation Credit in the third compartment with an amount parameter of type decimal (because the corresponding method has an amount parameter of C# type decimal).

Fig. 4.18

Fig. 4.18 UML class diagram indicating that class Account has a public Balance property of type decimal, a constructor and a method.

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