A computer stores data (e.g., the values of variables) in units called bytes. A byte is a unit of storage consisting of 8 bits. A bit (short for binary digit) is a binary numeric representation, which is capable of storing only the digits 0 or 1. Computers can store data using either 2, 4, 8, or 16 bytes per value. For instance, a computer that uses 4 bytes (32 bits) to store a real variable is referred to as having a 4-byte wordsize or a 32-bit wordlength.
A variable defines a storage location in the computer's memory. Some processors assign initial values to variables, so that all variables are defined at the start of program execution. Alternatively, the DATA statement is used to explicitly provide initial values for variables. During execution, values can be changed at any time and as many times as needed, simply by assigning a new value to the variable. At any time, the value of a variable is the value currently stored in that variable's storage location.
A variable name identifies a variable within a program unit. A valid variable name must begin with a letter (A through Z), and is limited to a maximum of 31 letters or digits (0 through 9). Some processors accept the use of the special characters currency symbol $ and underscore _ as part of variable names. Examples of valid variable names are
MASS
Examples of invalid variable names are
5MASS When declaring variables, several data types are used in Fortran. These data types are specified by means of dec laration statements. Declaration statements are nonexecutable; therefore, they must precede all executable statements. A variable name can be declared only once within a program unit. Multiple declaration of a variable name (i.e., using the same name in two declaration statements) is not allowed. Fortran has six data types and six corresponding declaration statements:
1. INTEGER 3.1 INTEGER STATEMENT
The INTEGER declaration statement is used to explicitly
declare the data type of a variable as integer. An integer
is an arithmetic value lacking a fractional component, for
instance the value 3, or the value -25.
In the absence of an INTEGER statement, an integer
variable is declared implicitly by the sole action of naming
its variable name starting with either of the letters I, J, K,
L, M, or N.
An example of the INTEGER statement is
INTEGER COUNTER,FILEID
This statement declares the variables COUNTER and
FILEID to be of integer type. In the absence of this state
ment, the variables COUNTER and FILEID would be subject to the rules governing implicit type declaration. Since
they start with the letters C and F, they would not be assumed to be integers.
The variables declared using an INTEGER statement
can have a 2- or 4-byte wordsize, specified during program
compilation in a processor-dependent mode. If no word
size is specified, the default value is 4 bytes. The range of
values that an integer variable can take (from largest negative to largest positive) is processor dependent.
Some processors accept the following alternate forms
of the INTEGER statement:
INTEGER*2 COUNTER,FILEID
These statements explicitly state the wordsize as 2 or 4
bytes, overriding the wordsize specified during program
compilation, if any. Note that processors may assign an
initial value of zero (0) to all integer variables.
Tips regarding allowable range of values:
3.2 REAL STATEMENT
The REAL declaration statement is used to explicitly declare the data type of a variable name as real. Real arithmetic values can take fractional components, such as
2.468, or -135.79.
In the absence of a REAL statement, a real variable is
declared implicitly by the sole action of naming its variable name starting with any letter other than I, J, K, L, M,
or N.
An example of the REAL statement is
REAL LENGTH,MASS
This statement declares the variables LENGTH and MASS
to be of real type. In the absence of this statement, the
variables LENGTH and MASS would be subject to the
rules governing implicit type declaration. In this case,
since they start with the letters L and M, they would be assumed to be integers.
Typically, the variables declared using a REAL state
ment have a 4-byte wordsize. The approximate range of
values that a real variable can take is processor dependent.
The precision of a real value (i.e., the number of significant digits) is closely linked to the wordsize. A 4-byte
wordsize usually has a precision of 7 digits. Some processors accept the following alternate forms
of the REAL statement:
REAL*4 LENGTH,MASS
These statements explicitly state the wordsize as being
either 4, 8, or 16 bytes. In this case, the statement
REAL*4 amounts to single precision, accomplishing the
same purpose as the REAL statement.
REAL*8 amounts to double precision, accomplishing
the same as the DOUBLE PRECISION statement (Section
3.5). REAL*16 amounts to quadruple precision, about 4
times that of single precision. Note that processors may
assign an initial value of zero (0.0) to all real variables.
3.3 COMPLEX SATEMENT
The COMPLEX declaration statement declares the data
type of a variable name as complex. A complex data type
consists of a pair of real values representing the complex
number (a + bi), with a being the real part and b the
imaginary part. In Fortran, the two real numbers are separated by a comma and enclosed in parentheses. For example, the complex number 3 + 4i is written as (3.,4.)
An example of the COMPLEX statement is
COMPLEX C1,C2,C3
which declares the variable names C1, C2, and C3 to be of
complex type.
Typically, the real and imaginary parts of a complex
value have each a 4-byte wordsize, which usually has a
precision of 7 digits. Unlike integer and real variables,
which may be declared implicitly, complex variables may
only be declared explicitly, by means of the COMPLEX
statement. Note that a processor may assign an initial
value of zero (0.0) to both real and imaginary parts of all
complex variables.
The following example illustrates the declaration of
complex variables. The assignment of complex variables
may be done in two ways: (1) using a DATA statement,
which is more permanent, and (2) using an arithmetic assignment statement.
Example: Complex Declaration and Assignment
C-----COMPLEX DECLARATION STATEMENTS
COMPLEX C1,C2,C3
C-----COMPLEX VARIABLE ASSIGNMENT USING DATA
DATA C1,C2 /(3.,4.5),(3.5,6.7)/
C-----COMPLEX VARIABLE ASSIGNMENT USING
C-----ARITHMETIC ASSIGNMENT STATEMENT
C3= (23.,-34.)
Complex Unformatted Input/Output
In unformatted input, complex values (two real numbers, separated by a comma and enclosed in parenthesis)
should be separated among themselves either by: (1) a
comma, (2) one or more blank spaces, or (3) a combination of a comma and one or more blank spaces in any or
der. In unformatted output, the characteristics of complex
values are processor dependent.
3.4 DOUBLE PRECISION STATEMENT
The DOUBLE PRECISION declaration statement declares
the data type of a variable name as double precision. A
double-precision variable is stored using twice as many
bytes as the single-precision real variable. For instance, if
a real variable is stored in 4 bytes (REAL*4), a double-
precision variable is stored in 8 bytes (REAL*8).
An example of the DOUBLE PRECISION statement is
DOUBLE PRECISION A,B,C
where A, B, and C are double-precision variable names.
Typically, the variables declared using a DOUBLE
PRECISION statement have an 8-byte wordsize, which
usually has a precision of 15 to 16 digits.
Unlike integer and real variables, which may be declared implicitly, double precision variables may only be
declared explicitly, by means of the DOUBLE PRECISION statement. Note that a processor may assign an
initial value of zero (0.) to all double precision variables. In
FORTRAN, the double-precision zero is written as 0.0D0,
in which D stands for "times ten to the power...", i.e.,
0.0 X 100. Likewise, 5.3D6 stands for 5.3 times ten to
sixth power (that is, 5300000.00000000). The declaration
and assignment of DOUBLE PRECISION variables is
shown in the following example.
Example: Double-Precision Variable
Declaration and Assignment
C234567890 C-----DOUBLE PRECISION DECLARATION STATEMENT
DOUBLE PRECISION A,B,C C-----DOUBLE PRECISION ASSIGNMENT USING C-----DATA STATEMENT
DATA A,B /0.123456789D35,0.987654321D-29/ C-----DOUBLE PRECISION ASSIGNMENT USING C-----ARITHMETIC ASSIGNMENT STATEMENT
C= 0.2468D-22
Double-precision Unformatted Input/Output
In unformatted input, double-precision values should
be separated among themselves either by: (1) a comma,
(2) one or more blank spaces, or (3) a combination of a
comma and one or more blank spaces in any order. In unformatted output, the characteristics of complex values are
processor dependent.
3.5 LOGICAL STATEMENT
The LOGICAL declaration statement declares the data
type of a variable name as logical, i.e., a variable that can
take a value of either true (.TRUE.) or false (.FALSE.).
The delimiting periods encompassing the values TRUE
and FALSE are required.
An example of the LOGICAL statement is
LOGICAL SWITCH1,SWITCH2
where SWITCH1 and SWITCH2 as logical variable
names; thereby, admitting only the logical values .TRUE.
or .FALSE. Logical variables may only be declared explicitly. Some processors assign an initial value of .FALSE. to
all logical variables.
The declaration and assignment of logical variables is
shown in the following example.
Example: Logical Variable Declaration
and Assignment
C234567890
C-----LOGICAL DECLARATION STATEMENT
LOGICAL SWITCH1,SWITCH2
C-----LOGICAL ASSIGNMENT WITH DATA STATEMENT
DATA SWITCH1 /.TRUE./
C-----LOGICAL ASSIGNMENT WITH
C-----LOGICAL ASSIGNMENT STATEMENT
SWITCH2= .FALSE.
Logical Unformatted Input/Output
In unformatted input, logical values should be sepa
rated among themselves either by: (1) a comma, (2) one
or more blank spaces, or (3) a combination of a comma
and one or more blank spaces in any order. The logical
values themselves can be .TRUE. or .FALSE., or
.T. or .F., T or F (or any other word starting with
either T or F). In unformatted output, logical values are
written as either T or F.
3.6 CHARACTER STATEMENT
The CHARACTER declaration statement declares the data
type of a variable name as character, i.e., one whose
value is a character constant (also referred to as a character
string).
An example of the CHARACTER statement is
CHARACTER*15 NAME,ADDRESS,SSNO
This statement declares the variables NAME, ADDRESS,
and SSNO as character. Each of these variables can have
up to 15 characters, as indicated by the length specifier
immediately following the * after CHARACTER.
Alternatively, the statement
CHARACTER*15 NAME,ADDRESS,SSNO*11
declares these variables of character type, with length
equal to 15 characters, excepting SSNO, whose length is
equal to 11 characters. It is seen that the length specifier
following the * after CHARACTER applies to all listed
variables, unless it is overridden by affecting one or more
variables with their own lengths. In addition, if the length
specifier following CHARACTER is omitted, a default
value equal to 1 is assumed. For example, in
CHARACTER ABC,DEF,GHI*5
the character variables ABC and DEF have length equal to
1, and the variable GHI has length equal to 5.
Example: Character Variable Declaration
and Assignment
C234567890 C-----CHARACTER VARIABLE DECLARATION
CHARACTER*15 NAME,ADDRESS,SSNO*11 C-----CHARACTER ASSIGNMENT USING DATA STATEMENT
DATA NAME, ADDRESS 1/'JOHN DOE','30 F STREET, NW'/
C-----CHARACTER ASSIGNMENT STATEMENT
SSNO= '555-32-9876'
Character variables remain unfilled until an assignment
is made during program program execution. It is not necessary that the character value fill the entire space allocated by the CHARACTER statement. In the preceding
example, the variable NAME has been assigned the value
JOHN DOEbbbbbbb, and it has 7 trailing blank spaces,
represented here with the letter b.
Character Variable Input/Output Example Program
In data management, it is important to know how to read
and write CHARACTER variables. The following exam
ple program reads three character variables NAME, AD
DRESS, and SSNO, each having a maximum length of 15
characters, from a file named CHARACTER.DAT using
at least one and at most three unformatted record(s). It
proceeds to write them to a file named CHARACTER.OUT using three separate unformatted records. In
unformatted input, the character constants should be en
closed by apostrophes and separated among themselves
either by: (1) a comma, (2) one or more blank spaces, or
(3) a combination of a comma and one or more blank
spaces in any order.
Example Program: Character Variable Input/Output
C234567890
PROGRAM CHARACTER_IO
CHARACTER*15 NAME,ADDRESS,SSNO
OPEN(5,FILE='CHARACTER.DAT',STATUS='UNKNOWN')
OPEN(6,FILE='CHARACTER.OUT',STATUS='UNKNOWN')
READ(5,*) NAME,ADDRESS,SSNO
WRITE(6,*) NAME
WRITE(6,*) SSNO
END
Character Variable Example Program:
Printing a Banner
The example below prints the following banner to the
Character Example Program: Printing a Banner
C234567890
PROGRAM BANNER
CHARACTER*36 XSOLID,XSPACE
DATA XSOLID/
1'XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX'/
DATA XSPACE/
1'X X X X X X X X'/
WRITE(6,*) XSOLID
WRITE(6,*) XSPACE
WRITE(6,*) XSPACE
WRITE(6,*) XSPACE
WRITE(6,*) XSOLID
END
Note the features of this program:
3.7 DECLARATION STATEMENTS IN FORTRAN 90
In general, data types can be either (1) intrinsic, i.e., predefined by the language, or (2)
derived, i.e., subject to definition by the programmer. In FORTRAN 77, all data types
and their declaration statements are intrinsic (see Sections
3.1 to 3.6). Fortran 90 allows the use of either intrinsic or
derived data types.
Fortran 90 has five intrinsic data types: (1) integer, (2)
real, (3) complex, (4) character, and (5) logical. Note that
the double precision data type of FORTRAN 77 is missing
from this list. Also, note that since FORTRAN 77 is contained entirely within Fortran 90,
the DOUBLE PRECISION statement can still be used with Fortran 90. In Fortran 90, derived data types are defined with a
TYPE statement. A derived data type can have one or
more components. Each of the component can be in itself
either intrinsic or derived. A derived data type needs a
TYPE definition to supply the name of the derived data
type, and the data type(s) and name(s) of its components. For example, if the complex type were not intrinsic but
had to be derived, a type definition would be required to
supply the name "complex" and declare two components,
each of real type, as follows.
TYPE COMPLEX Note that the type definition is written in several lines,
with optional indentation of the components. The TYPE
and END TYPE statements encompass the components.
To define a double precision data type, Fotran 90 does
not use the TYPE statement, but rather, it uses the intrinsic
type REAL affected with a KIND parameter, as in the fol
lowing example REAL (KIND (0.0D0)) DPMASS
where the variable DPMASS is declared as double preci
sion. The value of the KIND parameter (0.0D0) represents
double precision. On the other hand, the statement
REAL (KIND (0.0)) MASS
defines a real single-precision variable MASS, as does the
statement
REAL MASS The following is an example of a derived data type
having two components, an integer and a character.
TYPE PERSON
This example defines a data type PERSON, having two
components: (1) a character NAME, of length 30 spaces,
and (2) an integer AGE.
The variable declaration of the previously defined
derived-type PERSON is: TYPE (PERSON):: EMPLOYEE
A corresponding derived-type constant expression is
PERSON ('JOHN SMITH',28)
such that
EMPLOYEE = PERSON ('JOHN SMITH',28) 3.8 SUMMARY
This chapter introduces six statements: INTEGER,
REAL, COMPLEX, DOUBLE PRECISION, LOGICAL
and CHARACTER. These declaration statements declare
the data types of corresponding variables. They are nonexecutable; therefore, they should precede all executable
statements in a program unit.
The use of the INTEGER and REAL statements is not
absolutely necessary; their usage can be avoided by following certain simple rules in naming variables. All other
declaration statements are absolutely necessary to declare
their respective data types. PROBLEMS
1. Write a program to do the following tasks: (1) declare a logical variable
FLAG; (2) initialize it with the value .FALSE. using a DATA statement;
(3) write this initial value to an output file FLAG.OLD; (4) assign
FLAG a new value .TRUE.; and (5) write this new value to an output
file FLAG.NEW. Look at the output files to examine the results.
2. Write a program to do the following tasks: (1) using a DATA
statement, initialize the double precision variables DA=
0.1234567890123456D-16, and DB= 0.9876543210987654D16; (2)
multiply (DA*DB) and divide them (DA/DB) to generate the double
precision variables DC and DD, respectively; and (3) write the results
directly to the screen, preceded by an appropriate character label.
3. Using the CHARACTER statement, write a program to write the following banner to a file E_BANNER.OUT:
EEEEEEEEEEE
E
E
E
E
EEEEEEEEEEE
E
E
E
E
EEEEEEEEEEE
4. Write a program to do the following tasks: (1) initialize two variables
X= 0.1234567890123456, and Y= 0.1234567 as double precision; (2)
calculate Z= X/(X - Y) using single-precision data types for X, Y, and Z;
(3) calculate Z using double precision data types for X, Y, and Z; (4)
calculate the difference between the Z values obtained using double and
single precision; and (5) write the result directly to the screen. What can
you surmise from this exercise? Assuming the Z calculated using double
precision as the correct answer, what is the precision of the Z calculated
using single precision? [Precision is the number of correct or significant
digits].
5. Write a program to do the following tasks: (1) initialize two variables
X= 0.2468, and Y= 0.24675 as single precision; (2) calculate Z= Y/(X -
Y)0.95 using single-precision (real) data types for X, Y, and Z; (3) calculate
Z using double precision data types for X, Y, and Z; (4) calculate the
difference between the Z values obtained using single and double precision; and (5) write the result directly to the screen. Assuming the Z calculated
using double precision as correct, what is the precision of the Z
calculated using single precision? [Precision is the number of correct or
significant digits].
6. Write a program to do the following tasks: (1) declare a logical variable
FLAG; (2) initialize it with the value .FALSE. using a DATA statement;
(3) write this initial value directly to the screen, using a label such as
THE INITIAL VALUE OF FLAG IS ; (4) assign FLAG a new value
.TRUE.; and (5) write this new value directly to the screen using a label
such as THE UPDATED VALUE OF FLAG IS .
7. Write a program that initializes the value π with 15 significant digits
(π= 3.141592653589793). Then, it multiplies it by 2., and writes the
value 2π to an output file TWOPI.OUT, preceded by an appropriate label.
8. Using the CHARACTER statement, write a program to write the following banner to a file X_BANNER.OUT.
X X
X X
X X
X X
X X
X
X X
X X
X X
X X
X X
9. Write a program to calculate the value of eγ, in which e is the natural
log base and γ is Euler's constant, using single and double precision.
Use e= 2.718281828459045, and γ= 0.5772156649015328. How many
correct or significant digits does single precision have in this example?
10. Write an interactive program to calculate the hyperbolic tangent of an
angle x in radians. Use: tanh x= (ex - e-x)/(ex + e-x). Test your program
using: (a) x= π; and (b) x= π/2.
11. Repeat Problem 10, this time calculating both the hyperbolic tangent
and the hyperbolic cotangent. Calculate and write the hyperbolic tangent first. Then, calculate and write the hyperbolic cotangent. Test your
program using: (a) x= 2π; and (b) x= 0. What happens for coth 0?
12. Write a program to do the following tasks: (1) initialize two complex
variables COMP1= (1.,3.) and COMP2= (2.,4.); (2) sum, subtract,
multiply, and divide them; and (3) write the results directly to the
screen, preceded with appropriate labels.
13. Find out if your processor can accept a double-precision complex data
type (either COMPLEX*16 or DOUBLE COMPLEX statement). If so,
repeat Problem 12 using instead DCOMP1= (1.23456789, 3.57913579),
and DCOMP2= (2.46802468, 4.68024680). Write the results directly to
the screen, preceded with appropriate labels.
14. Using the CHARACTER statement, write a program to print the following geometric design of a tic-tac-toe board:
X X
O O
X X
XOXOXOXOXOXOXOXOX
X X
O O
X X
XOXOXOXOXOXOXOXOX
X X
O O
X X
15. Using CHARACTER and DATA statements, write a program to print
the following numeric design directly to the screen:
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
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