THE INTEGER TYPE VARIABLE
OUR FIRST INTEGER VARIABLE
Example program ------> e_c03_p1.ada
Examine the program named e_c03_p1.ada for our first example program with a variable. Some programming languages do not require you to predefine a variable before you use it. Instead, you simply begin using it and the system has some mechanism by which it creates the variable and makes it ready for your use. Ada requires you to specifically define every variable before you use it. You must give the variable a name, which is any valid identifier, and you tell the compiler how you plan to use the variable by assigning a type to the variable.
WHAT IS A TYPE?
The type defines a set of values which the variable can have assigned to it, and it also defines a set of operations that can be performed on the variable. Ada is a strongly typed language since it has very strict rules limiting how a variable can be used. The compiler will not give you a usable program unless you follow all of the rules very carefully. A major part of the study of Ada involves the study of types and how to use typing as a programming aid.
AN UNBROKEN RULE OF ADA, NEVER BROKEN
Ada requires that anything you use must have been previously defined. This includes variables as well as constants, procedures, functions, and all other entities. At least one language, Pascal, makes this claim but breaks it in a few instances. Ada never breaks this rule.
THE with AND use STATEMENTS
The with and use statements, in lines 2 and 3 of this program, contain Ada.Integer_Text_IO in addition to Ada.Text_IO and a few comments are in order at this point, event though they will be completely defined later in this tutorial. The term Ada.Text_IO refers to an Ada package of the same name that provides us with the ability to output text to the monitor including characters, strings, carriage returns, and various other entities so that we can generate some formatted text output to the monitor. It also gives us the ability to input text from the keyboard, and it provides some file input/output capabilities.
The term Ada.Integer_Text_IO refers to another Ada package of that name which gives us the ability to output INTEGER type variables to the monitor in a well formatted way since it gives us control over how many columns are used, and what base to use for the numbering system, such as binary, decimal, hexadecimal, and other options. The with statement, because it mentions both of these library packages, provides us with the ability to output both text and numeric values to the monitor, because it makes a copy of both of these libraries available for use by our program. The use statement, because it mentions both of these packages, makes it very easy to "use" these packages within our program. Without the use statement, we would have to qualify every input or output statement, which makes for very ugly code, but which some programers find preferable for various reasons.
We will cover all of this in great detail later in this tutorial, but it would be best for you to simply include the appropriate packages in a with statement and a use statement for your initial programming efforts and pick up the additional knowledge later. There is only so much you can absorb and understand at one time, and the author of this tutorial desires to simplify your study of Ada as much as possible by deferring some topics until later.
HOW DO WE DECLARE A VARIABLE?
Back to the program named e_c03_p1.ada. To understand the definition of a variable, examine the program at hand and specifically line 7. This declares a variable, which we will call Index, to be of type INTEGER, therefore defining an allowable range of values which can be assigned to it. Most 16 bit computers allow an INTEGER type variable to cover a range of -32,768 to 32,767. The corresponding range for 32 bit computers is from -2,147,483,648 to 2,147,483,647 but the definition of Ada allows for flexibility in both of these ranges. We will see a way to determine exactly what the limits are for your compiler later in this chapter.
The type also defines a number of operations which can be performed on the variable. More will be said of that later. The type INTEGER is used to declare a scalar variable, which is a variable that can contain a single value.
The word INTEGER is not a reserved word but a predefined word which we can redefine if we so choose. We will not be doing that for a long time since it could cause untold problems in a program. You should know that it is possible for you to redefine this word, and many other similarly predefined words, to mean something entirely different from their predefined meanings.
In the last chapter, we said that the declarative part of the program goes between the reserved words is and begin, and you will notice that we did indeed declare the variable named Index in that area of the program. The end result of line 7 is that we have a variable named Index which is of type INTEGER. As yet however, it does not contain a useful value.
HOW DO WE USE THE VARIABLE IN A PROGRAM?
In the last chapter we also said that the executable statements went between the begin and the end reserved words and you will see that we have some executable statements within that range, in lines 11 through 18 of this program. In line 11 we assign the value of 23 to the variable Index which is valid to do because 23 is within the range of allowable values that can be assigned to an INTEGER type variable.
THE ASSIGNMENT OPERATOR
The combination := can be read as "gets the value of". Line 11 can then be read as, "Index gets the value of 23." The equal sign alone is reserved for another use. Actually, if we say that Index = 23, it is only mathematically correct if Index is never changed, but since it is a variable and will be changed, the equality is not true.
We have succeeded in assigning a value of 23 to the variable named Index and can use it in many different ways in an Ada program, but we will illustrate only very simple uses at this point.
Line 12 instructs the system to output a line of text to the monitor and leave the cursor at the end of the line. In line 13, we use the predefined procedure named Put to tell the system to display the value of Index, which has the value of 23, on the monitor. The system will right justify the output in a field width that depends on the size of an INTEGER on your system, because of its definition. This Put is part of the Ada.Integer_Text_IO package we declared earlier. The Put in line 12 is from Ada.Text_IO. Later in this tutorial you will understand which Put is from which package and why. Line 14 returns the cursor to the beginning of the next line. The New_Line procedure is from the Ada.Text_IO package.
OUR FIRST ARITHMETIC
Line 15 contains our first arithmetic statement and it will do exactly what it appears to do, "Index gets the value of Index with 12 added to it." The variable Index should now have a stored value of 23 + 12, or 35, which we verify by telling the system to display the new value of Index. The numeral 8 in line 17 tells the system to display the value right justified in a field 8 columns wide. We will discuss the Put procedure in detail later in this tutorial. If you remember that the statements are executed sequentially, you should have no difficulty following this program.
Compile and execute this program being careful to observe that the two values of Index are displayed in fields of different widths.
LET'S USE LOTS OF INTEGERS NOW
Example program ------> e_c03_p2.ada
Examine the program named e_c03_p2.ada and you will see an example of using many variables of type INTEGER in a program. Lines 7 and 8 illustrate that you can define one or more variables on a single line. All four variables are of type INTEGER and can be assigned values within the range of integer variables as defined for your particular compiler. Each of these variables have no value associated with them since they were created without an initial value. The executable part of the program can assign a value to each of them. The variable named Cat is also an INTEGER type variable but after being created, it is assigned an initial value of 12. Likewise Dog is created and initialized to a value of -5. It should not come as a surprise to you that the three variables in line 11 are created, and each is assigned an initial value of 1000.
According to the Ada definition, line 11 is merely a shorthand for three different lines with a single variable declaration on each line as far as the Ada compiler is concerned. The same is true of line 8. This is a very subtle point, and has no consequence on the program at hand, but will make a difference later when we commence the study of arrays.
NOW TO EXERCISE SOME OF THOSE VARIABLES
Examining the executable part of the program we find the four arithmetic operations in lines 15 through 18 which should be self explanatory. Note that integer division in line 18 results in truncation, not rounding. The four values are displayed on the monitor in lines 19 through 22 in a format utilizing several statements per line which is simply a matter of style.
Continuing with lines 24 and 25, we have examples of more complex mathematical calculations which should be clear to you. The order of precedence of mathematical operators is given in detail in section 4.5 of the Ada 95 Reference Manual (ARM). The order of precedence is similar to other languages and follows common sense. A discussion of the order of precedence will be given at the end of the next chapter of this tutorial.
Lines 26 and 27 illustrate use of the mod and rem operators, each of which return the remainder which would be obtained following an integer divide operation. They differ only in the sign when negative numbers are involved and since negative numbers are rare when using these operators, little will be said except to give a brief statement of the differences.
mod - gets the sign of the second operator. rem - gets the sign of the first operator.TWO MORE OPERATIONS
After displaying the results, four more values are calculated, the first being the absolute value of the variable Dog in line 33. This is not a function, it is an operation defined with the reserved word abs. The fact that it is an operator will be very significant when we come to the portion of this tutorial that deals with overloading operators. The abs operator returns the absolute value of the variable given to it as a parameter.
The operation in line 34 is an illustration of exponentiation of integer numbers. Since Cat has the value of 12, this line says that Index_2 gets the value of 12 raised to the 3rd power. The only rules for using exponentiation with integer values are, the exponent must be an integer type value, and it cannot be negative. Note that a zero value for an exponent is legal. Line 35 is a combination of several of the previous operations, and line 36 is an illustration of unary negation.
Be sure to compile and execute this program and study the results.
HOW DO WE DECLARE A CONSTANT?
Example program ------> e_c03_p3.ada
Examine e_c03_p3.ada for an example of a program with some INTEGER type variables and some INTEGER type constants declared and used in it. Lines 7 and 8 should be familiar to you now, but when we get to lines 10 through 13 we have a few new things to observe. DOZEN and GROSS are INTEGER type constants because of the reserved word constant in their declaration. The only difference between a constant and a variable is that a constant cannot be changed during execution of the program and in the present example, it would probably be silly to redefine how many elements are in a dozen. This is one of the things Ada can do to help you if you analyze your program right, because if you ever tried to change the value of DOZEN during program execution, Ada would give you an error message and you would eliminate one bug immediately.
Notice that GROSS is defined in terms of DOZEN since the constant DOZEN is available when GROSS is initialized. Likewise, the constant TWO is defined in terms of BIG_NO in the next two lines. It should be obvious that a constant must have an initialization value assigned to it at the point of declaration.
TWO MORE DEFINITIONS
Lines 12 and 13 contain underlines in the numeric values that the Ada compiler will simply ignore. You can put them in wherever you please to make the numeric literals more readable for you, but you cannot put more than one underline between each digit. The poor choice of underline locations in this example do not add to the ease of reading the numbers but illustrate the places where they can be located. The word INTEGER has been omitted from lines 12 and 13, which makes the type of these constants slightly different from the other two but we will have to learn a bit more before we can understand or appreciate the value of doing this.
Lines 17 through 25, in the executable part of the program, should be easy for you to understand on your own, so they will be left to your study.
DECLARING LITERAL CONSTANTS
Lines 27 through 29 give examples of declaration of literal values using the exponential notation. The exponent can be indicated with either case of "E" and the number following it must be positive for an INTEGER literal. Lines 30 through 33 give examples of the use of a base other than 10. The radix of the number is given prior to the first "#" sign, and can be any value from 2 through 16, the radix itself being given in decimal notation. The value is given between "#" signs and can be followed by an optional exponent, the exponent being given in the defined base. If no radix is given, base 10 is assumed as in lines 27 through 29 of this example program.
The executable part of this program should be very clear to you. Be sure to compile and execute it.
TYPES AND SUBTYPES
Example program ------> e_c03_p4.ada
Examine the program e_c03_p4.ada for your first look at a user defined type. We mentioned earlier that the range of a variable of type INTEGER could be different on different computers or with different compilers on the same computer. Ada gives us the ability to define our own type in such a way that it will be identical on every computer and with every Ada compiler.
A DIFFERENT TYPE IS INCOMPATIBLE
Line 7 defines a new integer type which will cover the range of -10,000 to 20,000 because of the use of the reserved word range to limit the available range of values that can be assigned to a variable of this type. Notice carefully that we called this an integer type, not a type INTEGER. Since it is an integer type, it has all of the properties defined earlier in this chapter but a variable of this type can only be assigned a value from -10,000 to 20,000. The actual range is given by specifying the lower and upper limits separated by two decimal points.
We have actually defined an entirely new type, and since Ada does very strong type checking, it will not allow you to assign a value directly from a variable of type INTEGER to a variable of our new type, or vice versa. The variable My_Int is defined with the new type in line 8. We will return to consideration of this variable later.
The package declaration in line 10 is completely new to us, so a few comments on it are in order. The complete definition of line 10 in Ada terminology will be given first, including a lot of new words which will mean very little to you until you gain some additional knowledge which will be given later in this tutorial. Line 10 is an instantiation of the generic package named Ada.Text_IO.Integer_IO with the type MY_INT_TYPE to provide the ability to output values of MY_INT_TYPE to the monitor or to files, or to input from the keyboard or from files. Saying the same thing in a more useful way, if you want to input or output values in some integral class type other than the predefined type INTEGER, you must include the line as shown with the desired type in the parentheses. Line 11 is included to make the new package easy to use. You will notice that it tells the system to use the package named in line 10 immediately following the keyword package.
As stated earlier, in an attempt to simplify the Ada learning curve, some topics will be deferred until later to give you a chance to absorb a few topics at a time, so don't spend any time trying to understand the previous paragraph at this time.
A NEW SUBTYPE IS COMPATIBLE WITH ITS PARENT
In line 13, we define a new subtype which is of the parent type INTEGER except that it covers a limited range, then we declare a variable named Thing of the new subtype in line 14. Any attempt to assign a value to the variable Thing which is outside of its assigned range, will result in an error. If you were running a small company with 23 employees and you assigned them each a unique number from 1 to 23, you would be interested if the payroll program tried to generate a paycheck for employee numbered 36, for example, because there would definitely be something wrong. A limited subrange could save you a lot of money in a case such as that.
ASSIGNMENT MUST BE TYPE COMPATIBLE
Anytime a value is assigned to a variable, the type assigned to it must be of its declared type or a compiler error will be generated. This will always be true in Ada and is one of the most important concepts behind its design. This is to prevent us from making the silly little mistakes which we humans are so good at making.
The variable Count is defined as an INTEGER type variable and Stuff is defined as a limited range INTEGER also. Remember that Thing is declared to be a subtype of INTEGER, so it is also a limited range INTEGER type variable. Because of the way these three variables are defined, they can be freely assigned to each other as long as the values assigned are within their respective ranges. This is because they are all of their parent type of INTEGER, and various assignments among them are illustrated in lines 25 through 27.
If we tried to assign the value of Thing to My_Int, the computer would give a compile error because they are of different types, but an explicit type conversion can be used to do the assignment as illustrated in line 30. By including the variable to convert to a new type in parentheses and preceding the parentheses with the desired type name, the system will convert the type as illustrated. The addition to Thing is completed and the entire expression inside of the parentheses is changed in type, by the explicit type conversion, to the desired type of the left side of the assignment statement. Note that explicit type conversion can only be done from within the same type class, in this case the integer class.
In line 31, the type is changed to the new type before the value of 17 is added to it, which should lead you to ask a question about the type of the constant 17.
HOW CAN 17 BE ADDED TO EITHER TYPE?
The constant 17 is of a very special type defined by Ada as type "universal_integer" which can be combined with any of the integer types without specific conversion. This term will be used in many ways in future lessons. The type universal_integer is compatible with all integer types and has a range with no limits. The range is effectively minus infinity to plus infinity. The type universal_integer is used for all literal values, but it is not available for your use in declaring a variable.
NOW FOR A SUBRANGE ERROR
Lines 30 and 31 are essentially the same because they result in the same answer, and lines 33 and 34 would appear to be the same, but they are not. In line 33, the value of Thing, which is 18, is converted to type MY_INT_TYPE and 10 is subtracted from it. Both 18 and 8 are within the specified range of MY_INT_TYPE so there is no error. In line 34 however, the result of the subtraction has the type of Thing and even the intermediate result is required to be within the range of 12 to 144. The result of 8 is outside of the required range so a run-time error is signaled in a special way called raising an exception. We will discuss the exception shortly but first notice that if we could get past the error, we could change the type of the result to MY_INT_TYPE and everything would work as desired.
INTERMEDIATE RESULTS OF CALCULATIONS
The ARM allows the limits of intermediate results to be checked against the limits of the parent type rather than the limits of the subtype. Line 34 therefore, may not give an error indicating that the intermediate result is out of the allowable range. This will depend on your compiler.
WHAT IS AN EXCEPTION?
We will have a lot to say about exceptions as we progress through this tutorial but a very brief description is needed at this time. When an Ada program is running, and a potentially disastrous error is detected, it would be good for you, the programmer, to be able to tell the system what to do with the error rather than cause a complete termination of the program. Ada gives you that capability through the use of exception handlers that you write and include in your program. In the above case, when the program detected the value of 8 as being out of the allowable range of that type of variable, it would signal your program that the error occurred, and if you did nothing, the Ada system would terminate the program. The proper Ada terminology for signaling you is called "raising an exception", and in the case of an out-of-bounds value, the exception named Constraint_Error would be raised. You could then trap this error and handle it any way you choose to.
There are several different exceptions that the system can raise and you can define your own exceptions which your program can raise and respond to. We will have a lot more to say about exceptions later in this tutorial.
A little study on your part should reveal why line 38 also has a run time error that will raise the exception Constraint_Error, if execution continues to that statement.
ANOTHER LOOK AT THE universal_integer
Before we leave this program we must look at lines 18 and 19 where we first define START and STOP as constants with no type indication. These constants are therefore of type "universal_integer" and can be used in the range definitions of the next two lines even though the two lines are of different parent types. If we had included the word INTEGER in the definitions in lines 18 and 19, they could not be used to define the limits of Example2 because it is of a different type. The example program named e_c03_p3.ada had examples of INTEGER constants (DOZEN and GROSS) and universal_integer type constants (BIG_NO and TWO). The type universal_integer is actually a hidden type that is type compatible with all integer types.
It should also be observed that the limits of the range in these definitions are based on previously defined entities and can be of arbitrary complexity as long as they evaluate to the right types. The limits must also be within the range of the parent type or a compile error will result.
HOW TO DEFINE TYPES AND SUBTYPES
To declare types or subtypes, here are two simple formulas which can be followed.
type <type_name> is <type_definition>; subtype <subtype_name> is <subtype_definition>;Note that each declaration starts with a reserved word and includes the reserved word is between the name and the definition. It should be pointed out that Ada permits new types, subtypes, and variable declarations to be done in any order as long as everything is defined before it is used.
Compile and execute e_c03_p4.ada and observe the exception error as reported by your runtime system. The exception may be raised at line 34, depending on your compiler, where the value of 8 is outside of the allowable range of 12 through 144. The error message will vary with different compilers.
Much more will be said about types and subtypes in chapter 7 of this tutorial.
WHAT ARE ATTRIBUTES?
Example program ------> e_c03_p5.ada
Ada has a rather large list of attributes available for you as a programming aid. For an example of a program that contains, and therefore illustrates the use of attributes, examine the program named e_c03_p5.ada.
A new type is defined in line 7 with a limited range to illustrate that attributes are available even for user defined types.
Two additional predefined integer types are introduced in lines 10 and 11, the NATURAL and POSITIVE types. The POSITIVE type includes all integers greater than or equal to 1, and the NATURAL type includes all integers greater than or equal to 0. Both of these are available with your Ada compiler, and both are subtypes of INTEGER, so all variables of these three types can be freely mixed with no type errors.
Attributes are used to gain access to various limits within the program. For example, it may be necessary to know the upper limit of a variable of some type because it is of some strange subtype. An attribute can be used to find this limit, specifically the attribute LAST as illustrated in line 28 of this program. By combining the type name and the attribute in question with a "tick" or apostrophe, the upper limit of the range of the type is returned. The attribute FIRST is used to find the lowest value allowed by the subrange. The attribute SIZE gives the storage size of the type in bits of memory. Other attributes are available for integer types. A complete list of available attributes is given in Annex K of the ARM. You should spend a few minutes reviewing the list at this time even though you will understand little of what is presented there. In the near future, you will understand most of the material included there.
TYPE CONVERSIONS
Note the type conversions in lines 63, 67, 69, and 72. The values could be output directly with the BUG_RANGE type by instantiating a copy of Ada.Text_IO.Integer_IO in a manner similar to that done in the example program named e_c03_p4.ada, but we choose to use type conversion rather than instantiating a new copy of the I/O package. Because NATURAL and POSITIVE are subtypes of INTEGER, they use the copy of the I/O package pre-instantiated for the INTEGER type by the Ada system.
Compile and run this program and you will get a listing of the number of bits required by your compiler to store each of the four types along with the range covered by each of the four types.
PROGRAMMING EXERCISES
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