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Beginning with version 20, C# has included a feature that provides an elegant solution to what is both a common and irritating problem The feature is the nullable type The problem is how to recognize and handle fields that do not contain values (in other words, unassigned fields) To understand the problem, consider a simple customer database that keeps a record of the customer s name, address, customer ID, invoice number, and current balance In such a situation, it is possible to create a customer entry in which one or more of those fields would be unassigned For example, a customer may simply request a catalog In this case, no invoice number would be needed and the field would be unused In the past, handling the possibility of unused fields required the use of either placeholder values or an extra field that simply indicated whether a field was in use Of course, placeholder values could work only if there was a value that would otherwise be invalid, which won t be the case in all situations Adding an extra field to indicate if a field is in use works in all cases, but having to manually create and manage such a field is an annoyance The nullable type solves both problems

the beginning of motion, point B the end of motion, and point P the mid-stroke transition point APB is the constant velocity line M is the midpoint between A and P The sine amplitudes are added to the constant-velocity line in this true cycloidal case The modi ed cycloidal curve was developed to maximize the orientation of the superimposed sine wave amplitude on the straight line; see geometric construction in b Fig 312b In this gure, a point D equal to 057 the distance is the rst chosen and 2 then is joined to M by a straight line The base of the sine curve is then constructed

1 3x

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A nullable type is a special version of a value type that is represented by a structure In addition to the values defined by the underlying type, a nullable type can also store the value null Thus, a nullable type has the same range and characteristics as its underlying type It simply adds the ability to represent a value that indicates that a variable of that type is unassigned Nullable types are objects of SystemNullable<T>, where T must be a nonnullable value type

A nullable type can be specified two different ways First, you can explicitly declare objects of type Nullable<T>, which is defined in the System namespace For example, this creates int and bool nullable types:

50 48 46 44 42 40 38 36 34 32 0 10 20 30 40 50 60

SystemNullable<int> count; SystemNullable<bool> done;

20:

Cam rotation (deg)

SOLUTION We put the fractions over a common denominator to rewrite our limit as lim 3x sin 3x 3x sin 3x

U n s a f e C o d e , P o i n t e r s , N u l l a b l e Ty p e s , a n d M i s c e l l a n e o u s To p i c s

The second way to declare a nullable type is much shorter and is more commonly used Simply follow the type name with a For example, the following shows the more common way to declare a nullable int and bool type:

(a) Displacement 18 16 y Velocity (in/sec) 14 12 10 8 6 4 2 0 10 20 30 Cam rotation (deg) (b) Velocity 40 50 60

int count; bool done;

Both numerator and denominator vanish as x 0 Thus the quotient has indeterminate form 0/0 By l H pital s Rule, the limit is therefore equal to

When using nullable types, you will often see a nullable object created like this:

FIGURE 310 Comparison of popular curves (cam has 2-inch rise in 60-degree rotation and 3-inch pitch diameter) (Erdman and Sandor (1997) with permission by Prentice Hall, Upper Saddle River, NJ)

int count = null;

This explicitly initializes count to null This satisfies the constraint that a variable must be given a value before it is used In this case, the value simply means undefined You can assign a value to a nullable variable in the normal way because a conversion from the underlying type to the nullable type is predefined For example, this assigns the value 100 to count

250 200 150 y Acceleration (in/sec)2 100 50 0 50 100 150 200 250

This quotient is still indeterminate; we apply l H pital s Rule again to obtain 9 sin 3x = 0 x 0 18 cos 3x 27x sin 3x lim EXAMPLE 511

count = 100;

There are two ways to determine if a variable of a nullable type is null or contains a value First, you can test its value against null For example, using count declared by the preceding statement, the following determines if it has a value:

30 10 20 Cam rotation (degrees) 40 50

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