| IDRIS adaptation of the Fortran 77 manual from: |
|
University of Strathclyde Computer Centre Curran Building -- 100 Cathedral Street -- Glasgow (See Copyright) |
A computer (often called simply a machine) is a device for the fast, accurate processing of symbolic information under the control of a stored sequence of instructions called a program.
Figure 1 is a schematic diagram of a simple computer system.
The control unit controls the operation of the whole machine. It:
Figure 2: The memory
The memory stores programs and information. It consists of an array of storage units called words, all of equal length and numbered in sequence. The number of each word is called its address.
Each word contains a row of storage elements, which can individually be set to either of two states, conventionally represented as 0 and 1. Thus information is represented by binary codes.
When a program is run, each instruction in sequence is fetched from memory and executed. An instruction can order the control unit to fetch its next instruction from an address other than the next in memory. In this way, different sequences of instructions can be executed. This makes it possible to execute instruction sequences conditionally and iteratively.
To be executable, a program must be written in the binary machine code recognised by the processor. Machine code programming is difficult and prone to error. Furthermore, since each type of processor has its own machine code, a program written for one type of processor is not executable by any other.
Today, most programs are written in high level languages, which resemble English and are therefore easier to use than machine code, but which have a limited, specialised vocabulary and a simple syntax free from ambiguity.
FORTRAN (FORmula TRANslation), introduced in 1956, was the first high level language. It has since been revised several times. Fortran 77, though not the latest version, is widely available and is compatible with later versions.
Note: although compatible with Fortran 90 standard, mind not to use old "obsolescent features" which will be progressively eliminated from future standards (see "obsolescent features" in Fortran 90/95 manuals).
High level language instructions are not executable. Instead, a high level language source program is read as input by a program called a compiler, which checks its syntax and, if it is free from errors, compiles an equivalent machine code object program. (If the source program contains syntax errors, the compiler outputs a number of messages indicating the nature of the errors and where they occur.)
Although it is in machine code, the object program is incomplete because it includes references to subprograms which it requires for such common tasks as reading input, producing output and computing mathematical functions. These subprograms are grouped together in libraries which are available for use by all object programs. To create an executable program, the object program must be linked to the subprogram libraries it requires. The executable program may then be loaded into memory and run. The steps required to compile, link and run a Fortran program are illustrated by Figure 3.
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Data are constants provided to a program for use in computation (processing).
Results are constants produced as a result of computation.
We have seen that all information is represented in the computer
in binary form. The type of information determines the
way in which it is represented and the operations which may be
performed on it.
2.1 The CHARACTER type
A constant of type CHARACTER, (often called a string) is a sequence of characters which may be upper case alphabetic, numeric, blanks, and the following:
+ - * / = ( ) , . ' $ :
When included in a Fortran statement, a string must be delimited by single quotes ('). A single quote may be included in a string by writing two consecutively. Only one is retained.
Example: 'WE''RE A'' JOCK TAMSON''S BAIRNS.'
2.2 The INTEGER type
Constants of type INTEGER are integer numbers. An INTEGER constant is written as a sequence of decimal digits, optionally preceded by a sign (unary + or -).
Examples:
123 +1 0 4356 -4
INTEGER constants are represented in exact form. Their
magnitude has a limit which depends on the word length of the
computer.
2.3 The REAL type
Constants of type REAL are numbers which may include a fractional part. A REAL constant is written in one of the following forms:
Examples:
+123.4 -123.4 .6E-3 (0.6x10-3) 4.6E3 (4.6x103) 7E-3 2.REAL constants are represented in approximate form. Their magnitude has a limit which depends on the word length of the computer.
Note: the explicit type length specification in bytes (8 bits) is often
specified after an "*". Examples: REAL*8 or INTEGER*4
It was an extension to Fortran 77, now replaced by the KIND
type parameter in Fortran 90.
2.4 Variables
A variable is a unique name which a Fortran program applies to a word of memory and uses to refer to it. A variable consists of one to six upper case alphabetic characters and decimal digits, beginning with an alphabetic character.
Examples:
VOL TEMP A2 COLUMN IBM370
Spaces are ignored by Fortran 77, e.g. 'COL UMN' is equivalent to 'COLUMN'.
Note: spaces becomes significant in the "free format" of Fortran 90 !
Clarity can be improved by choosing variables which suggest their usage, e.g.
DEGC MEAN STDDEVThe value of a variable is the constant stored in the word to which it refers. Each variable has a type, which stipulates the type of value it may have. The type of a variable may be specified explicitly, or assigned implicitly (by default).
The type of a variable may be assigned explicitly by a type specification statement. This has the form:
type variable_list
where type is the name of a type
and variable_list is a single variable or a list of variables, separated by commas.
The statement assigns the given type to all the variables in the list.
Examples:
INTEGER WIDTH
REAL NUM, K
Type specification statements are not compiled into executable
machine code instructions. Instead the compiler records the names
and types of the variables and reserves storage for them. Such
non-executable statements must be placed at the beginning
of a program, before the first executable statement.
2.4.2 Implicit (or default) typing
If a variable is used without being included in a type specification, its type is assigned implicitly (by default) according to the following rule:
If the variable begins with a character from I to N, its type is INTEGER. Otherwise, it is REAL.
Thus TEMP is a REAL variable, while ITEMP is an INTEGER.
Note: because a variable can be used without first being declared in a type specification, a misspelled variable is not in general detected as an error by the compiler. The program may compile and run, but produce incorrect results. Care should therefore be taken to get variable names right, and if unexpected results are obtained, variable names are one of the first things to check.
Note: it is strongly recommended to force explicit typing by
placing an IMPLICIT NONE statement before type
specifications. It was an extension to the Fortran 77 standard, but
it is now integral part of Fortran 90 standard.
2.4.3 Assigning a value
Before a variable can be used in computation, it must be assigned an initial value. This may be done by reading a value from input or by using an assignment statement.
The READ statement is used to assign values to variables by reading data from input. The simplest form of the READ statement is:
READ *, variable_list
where variable_list is a single variable or a list of variables separated by commas. (The asterisk will be explained later).
This statement reads constants from the terminal, separated by spaces, commas, or new lines, and assigns them in sequence to the variables in the list. Execution of the program pauses until the right number of constants has been entered.
Example:
READ *, VAR1, VAR2, VAR3
waits for three constants to be entered and assigns them in sequence
to the variables VAR1, VAR2 and VAR3.
The simplest form of assignment statement is:
variable = constant
This means that the constant is assigned as a value to the variable on the left-hand-side. Note that the '=' sign has a different meaning than in algebra. It does not indicate equality, but is an assignment operator.
Examples:
TEMP = 74.5
ITEMP = 100
Whichever method is used to assign a value to a variable, the type of the value must be consistent with that of the variable. The rules are:
Value
Assigned
N = 0.9999 0
M = -1.9999 -1
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An arithmetic expression is one which is evaluated by performing a sequence of arithmetic operations to obtain a numeric value, which replaces the expression. Arithmetic operations are denoted by the following arithmetic operators
Operator Operation + Addition or unary + - Subtraction or unary - * Multiplication / Division ** Exponentiation
Figure 4 : Arithmetic operators
An operand of an arithmetic expression may be:
An arithmetic expression has the form:
operand [operator operand] ...
The square brackets indicate that the items operator operand are optional and the ellipsis (...) that they may be repeated indefinitely.
Spaces may be used to improve readability, but are ignored by the Fortran 77 compiler.
Examples:
3.14159
K
(A+B)*(C+D)
-1.0/X + Y/Z**2
2.0 * 3.14159*RADIUS
Restrictions:
An arithmetic expression is evaluated by replacing variable operands and parenthesised expressions by their values, and performing the operations indicated in sequence, using the result of each operation as an operand of the next. Clearly, the sequence in which the operations are performed is significant, as shown by the example:
4.0+6.0*2.0
which evaluates to 20.0 if the addition is performed first, or
16.0 if the multiplication is performed first.
The sequence of operations is determined by the following precedence order, in which operators on any line have equal precedence and precedence decreases downwards.
**
* /
+ - (binary and unary)
Using this precedence order, the rules for the evaluation of an arithmetic expression may be stated as follows:
3.1.2 Type rules for arithmetic expressions
Subject to the restrictions noted under 'Restrictions:' above, REAL and INTEGER operands may be freely mixed in an arithmetic expression. The type of the expression's value is determined by applying the following rules to each operation performed in its evaluation:
This rule is inconsistent with the rules of arithmetic, in which dividing one integer by another (e.g. 7/5) or raising an integer to an integer power (e.g. 2-1) does not always result in an integer. Fortran deals with such cases by truncating, as described under "Type rules" (in the above paragraph "Assigning a value"), to obtain an INTEGER value.
Examples:
Value
99/100 0
7/3 2
-7/3 -2
N**(-1) 0
N**(1/2) 1
100*9/5 180
9/5*100 100
The last two examples show that the ordering of * and / operators with INTEGER operands is significant. It is usually best to avoid dividing one integer by another unless there are special reasons for doing so.
As noted at the beginning of the chapter, the value of an arithmetic expression is assigned to a numeric variable in a statement of the form:
numeric_variable = arithmetic_expression
If the type of the expression differs from that of the variable, the rules listed under 'Type rules' (in the above paragraph "Assigning a value"), are applied, i.e.
Expression Variable Rule type type INTEGER REAL Convert to REAL REAL INTEGER Truncate
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We are now ready to write a simple Fortran program. All that is required is some information on printing output, program layout and a few simple statements.
Output can be printed using the PRINT statement, which is very similar to the READ statement shown above:
PRINT *, output_list
where output_list is a single constant, variable or expression or a list of such items, separated by commas.
Example: PRINT *,'THE RESULTS ARE', X ,'AND',Y
The PRINT statement prints the output list on the terminal screen in a standard format. Later, we shall consider more flexible output statements which give us greater control over the appearance of the output and the device where it is printed.
A program can optionally be given a name by beginning it with a single PROGRAM statement. This has the form:
PROGRAM program_name
where program_name is a name conforming to the rules for Fortran variables.
4.3 The END and
STOP
statements
Each program must conclude with the statement END, which marks the end of the program. There must be no previous END statement.
The statement STOP stops execution of the program. In Fortran 77/90, but not in previous versions, END also has this effect. Therefore, if execution is simply to stop at the end of the program, STOP is optional. However, one or more STOP statements may be written earlier, to stop execution conditionally at points other than the end.
4.4 Program layout (fixed format of Fortran 77)
When Fortran was introduced, punched cards were a common input medium. Fortran was designed to make use of the cards' 80-column layout by ignoring spaces and reserving different fields of the card for different purposes. Although cards are no longer used, Fortran still uses this column-based layout.
All Fortran statements must be written in columns 7 to 72. A statement ends with the last character on the line, unless the next line has any character other than 0 in column 6. Any such character indicates that columns 7 to 72 are a continuation of the previous line.
Columns 73 to 80 are ignored by the compiler. Originally, these columns were used to print sequence numbers on the cards, but now they are normally unused.
Columns 1 to 5 are reserved for statement labels. These are optional unique unsigned non-zero integers used to provide a reference to statements.
The layout rules are summarised in Figure 5.
Columns Usage
1-5 Statement labels
6 Continuation character or blank
7-72 Fortran statements
73-80 Unused
Figure 5: Fortran layout
Note: the fixed format source of Fortran 77 is an obsolescent
feature of Fortran 95. It must be repaced by the new free format.
4.5 Comments
The letter 'C' or an asterisk in column one causes the compiler to ignore the rest of the line, which may therefore be used as a comment to provide information for anyone reading the program.
The following example uses the Fortran statements introduced so far to solve a simple problem.
Example 1: a driver fills his tank with petrol before setting out on a journey. Each time he stops for petrol he puts in 40 litres. At his destination, he fills the tank again and notes the distance he has travelled in kilometres. Write a program which reads the distance travelled, the number of stops and the amount of petrol put in at the end of the journey, and prints the average petrol consumption in kilometres per litre, rounded to the nearest litre.
1| PROGRAM PETROL 2| INTEGER STOPS, FILLUP 3| C 4| C THESE VARIABLES WOULD OTHERWISE BE TYPED REAL BY DEFAULT 5| C ANY TYPE SPECIFICATIONS MUST PRECEDE THE FIRST EXECUTABLE STATEMENT 6| C 7| READ *, KM,STOPS,FILLUP 8| USED = 40*STOPS + FILLUP 9| C COMPUTES THE PETROL USED AND CONVERTS IT TO REAL 10| KPL = KM/USED + 0.5 11| C 0.5 IS ADDED TO ENSURE THAT THE RESULT IS ROUNDED 12| PRINT *, 'AVERAGE KPL WAS',KPL 13| ENDFigure 6: Petrol consumption program
This program illustrates some of the points about type conversion made in the previous chapter. In line 8, the number of litres of petrol used is computed. The computed value is of type INTEGER, but is converted to REAL when assigned to the REAL variable USED.
In line 10, the expression KM/USED is evaluated as REAL, but would be truncated, not rounded, when assigned to the INTEGER variable KPL. Adding 0.5 before truncating has the effect of rounding up or down. This is a useful rounding method. It is illustrated further below.
KM/USED KM/USED + 0.5 KPL
12.0 12.5 12 12.4 12.9 12 12.5 13.0 13 12.9 13.4 13
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The Fortran statements covered so far are enough to allow us to read information, evaluate arithmetic expressions and print results. It is hardly necessary to write a program to perform such tasks, which can usually be more easily done using a calculator.
The main advantages of a computer are its ability to:
This chapter deals with conditional execution while iteration is covered in Chapter 6.
The need for conditional execution is illustrated by the following problem:
Example 1: write a program to read the coefficients of a quadratic equation and print its roots.
Solution: the roots of the quadratic equation
ax² + bx +c
are given by the formula
The outline of the program is:
In step 3, the program must test conditions such as "b² -4ac exceeds zero".
To express such conditions, Fortran uses another type, the LOGICAL type.
There are two LOGICAL constants, defined as .TRUE. and .FALSE..
A LOGICAL variable can be assigned either of these values. It may not be assigned a value of any other type. Each LOGICAL variable must be declared in a LOGICAL type specification statement, which must occur, like all other type specifications, before the first executable statement.
Example: the LOGICAL variable ERROR could be declared and initialised by the statements:
LOGICAL ERROR
ERROR = .FALSE.
A logical expresssion is one which evaluates to one of the LOGICAL constants .TRUE. or .FALSE.. Thus the simplest logical expressions are the LOGICAL constants themselves, and LOGICAL variables.
A relational expression is a logical expression which states a relationship between two expressions, evaluating to .TRUE. if the relationship applies or .FALSE. otherwise. For the present, we shall consider only relationships between arithmetic expressions. (As we shall see later, Fortran can also deal with relationships between CHARACTER expressions.)
A relational expression has the form:
arithmetic_expression relational_operator arithmetic_expression
The relational operators are:
Meaning
.LT. Less than
.LE. Less than or equal to
.EQ. Equal to
.NE. Not equal to
.GE. Greater than or equal to
.GT. Greater than
Thus examples of relational expressions are:
N.GE.0
X.LT.Y
B**2 - 4*A*C .GT. 0.
Notes:
It is often necessary to express a condition which combines two or more logical expressions. For example, to check that the value of a variable lies within a given range, we should have to check that it is greater than the lower limit AND less than the upper limit. Such conditions are expressed in Fortran by composite logical expressions, which have the form:
L1 logical_operator L2
where L1 and L2 are logical expressions (relational or composite). The logical operators and their meanings are shown below. The second column indicates the conditions under which a composite logical expression as above evaluates to .TRUE..
Meaning
.AND. Both L1 and L2 are .TRUE.
.OR. Either L1 or L2 or both are .TRUE.
.EQV. Both L1 and L2 have the same value (.TRUE. or .FALSE.)
.NEQV. L1 and L2 have different values (one .TRUE. and one .FALSE.)
Thus the following composite logical expression would evaluate to .TRUE. if the value of the variable X lay within a range with non-inclusive limits MIN and MAX:
X.GT.MIN .AND. X.LT.MAX
There is one further logical operator .NOT., which unlike the others, takes only one operand, which it precedes. The expression .NOT.L is .TRUE. if the logical expression L is .FALSE. and vice versa.
As with arithmetic operators, precedence rules are required to define the interpretation of expressions like:
.NOT. L1 .OR. L2
which could evaluate to .TRUE. under either of the following conditions,
depending on the order of evaluation:
The precedence order is shown by the following list, in which precedence decreases downwards.
| Arithmetic operators |
| Relational operators |
| .NOT. |
| .AND. |
| .OR. |
| .EQV. and .NEQV. |
Thus (1) is the correct interpretation of the above expression.
As in arithmetic expressions, parentheses can be used to group partial logical expressions and change the order of evaluation. Thus
.NOT.(L1.OR.L2)
would be evaluated according to interpretation (2).
Parentheses can also be used to improve clarity, even when not logically required, e.g.
(A.LT.B) .OR. (C.LT.D)
5.3 Logical assignment
The value of a logical expression can be assigned to a variable of type LOGICAL, e.g.
LOGICAL VALID
VALID = X.GT.MIN .AND. X.LT.MAX
Logical expressions are more commonly used in logical IF statements and structures.
The logical IF statement is used to execute an instruction conditionally. It has the form:
IF (logical_expression) executable_statement
where executable_statement is an executable Fortran statement other than another IF statement or a DO statement (see Chapter 6).
The statement is executed by evaluating logical_expression and executing executable_statement if it evaluates to .TRUE..
Example: IF (A.LT.B) SUM = SUM + A
The logical IF statement is of limited usefulness, as it permits only the execution of a single instruction depending on a single condition. The block IF structure is more powerful, permitting the conditional execution of one of a number of alternative sequences of instructions. It may be described informally as:
More formally, the structure is:
IF (Lo) THEN So ELSE IF (Li) THEN Si ..... ... ELSE Sn END IFwhere:
The structure is executed as follows:
Lo is evaluated. If it evaluates to .TRUE., the sequence So is executed and execution continues with the statement following END IF.
Otherwise:
If there are any ELSE IF clauses, each Li is evaluated, until either:
Thus, a simple block IF structure is:
IF (A.LT.B) THEN
SUM = SUM + A
PRINT *, SUM
END IF
which is equivalent to the IF statement shown earlier.
A more realistic example is the following:
Example: an employee is paid at the standard rate for the first 40 hours of work, at time and a half for the next 10, and at double time for any hours in excess of 50. If the variable HRS represents the hours worked and RATE the standard rate then the employee's salary is computed by the block IF structure:
IF (HRS.LE.40) THEN
SALARY = HRS*RATE
ELSE IF (HRS.LE.50) THEN
SALARY = 40.0*RATE + (HRS-40.0)*RATE*1.5
ELSE
SALARY = 40.0*RATE + 10.0*RATE*1.5 + (HRS-50.0)*RATE*2.0
END IF
Note the use of indentation to clarify the structure.
We are now in a position to complete the quadratic roots program of Example 1, but first the outline should be altered as follows:
The expression
"b² - 4ac exceeds zero" in step 3 should be replaced by:
b² - 4ac > e
Similarly, the expression "b² - 4ac is equal to zero"
in step 3 should be replaced by:
-e <= b² -4 ac <= e
However, the expression is evaluated only if
b² -4 ac > e
has previously been evaluated as false, which of course implies
b² -4 ac <= e. Therefore,
all that is required is:
-e <= b² -4 ac
Comparisons involving REAL values should always be expressed in this way.
In general, programs should be designed to be robust, i.e. they should take account of any exceptional data values which may cause the program to fail, and take steps to prevent this.
The program outline now becomes:
Now that the outline is complete, the program can be easily written:
PROGRAM QUAD
E = 1E-9
READ *, A,B,C
IF (A.GE. -E .AND. A.LE.E) THEN
PRINT *, 'FIRST COEFFICIENT MUST BE NON-ZERO.'
ELSE
S = B**2 - 4*A*C
IF (S.GT.E) THEN
D = S**0.5
X1 = (-B+D)/(2*A)
X2 = (-B-D)/(2*A)
PRINT *, 'TWO DISTINCT ROOTS:' X1 'AND' X2
ELSE IF (S.GT. -E) THEN
X = -B/(2*A)
PRINT *, 'TWO COINCIDENT ROOTS',X
ELSE
PRINT *, 'NO REAL ROOTS.'
END IF
END IF
END
Figure 7: Quadratic roots program
Note that most of the program consists of a block IF structure, with a second block IF included in its ELSE clause. The embedding of one structure within another in this way is called nesting.
Once again, indentation has been used to clarify the structure.
| First page |
The last chapter showed how a sequence of instructions can be executed once, if a condition is true. The need also frequently arises to execute a sequence of instructions repeatedly, while a condition is true, or until a condition becomes true. Such repetitive execution is called iteration.
Write a program to read the marks (notes in french) of a class of students in an exam, print the number of marks and compute and print the average mark. The marks are to be read one at a time, with a 'dummy' mark of 999 marking the end.
The outline of the program is:
Unlike Fortran 90 and other more modern programming languages,
Fortran 77 lacks a while
structure as such, but the effect can be obtained using an IF
structure and a new statement, the GOTO.
6.1 The GOTO statement
The GOTO statement has the form:
GOTO label
where label is the label of an executable statement, with certain restrictions which will be considered later.
A GOTO statement causes the flow of execution to 'jump' to the labelled statement and resume from there.
We can use a GOTO to complete the program of Example 1:
PROGRAM AVMARK
INTEGER TOTAL,COUNT
TOTAL = 0
COUNT = 0
READ *, MARK
10 IF (MARK.NE.999) THEN
COUNT = COUNT+1
TOTAL = TOTAL+MARK
READ *, MARK
GOTO 10
END IF
IF (COUNT.GT.0) THEN
AVER = 1.0*TOTAL/COUNT
C MULTIPLY BY 1.0 TO CONVERT TO REAL AND AVOID TRUNCATION
PRINT *, COUNT, 'MARKS WERE READ.'
PRINT *, 'AVERAGE MARK IS', AVER
ELSE
PRINT *, 'NO MARKS WERE READ.'
END IF
END
Figure 8: Average mark program
Exercise:
the average mark program provides for the possibility that the
data consists only of the terminator 999, but does no other checking.
If the range of valid marks is 0 to 100, alter the program to
check the validity of each mark, printing a suitable message if
it is invalid, and print a count of any invalid marks with the
results.
6.2 Count controlled loops
Any iterative structure is usually called a loop. As in example 1, a loop of any kind can be constructed using an IF structure and one or more GOTO's.
Often a loop is controlled by a variable which is incremented or decremented on each iteration until a limiting value is reached, so that the number of iterations is predetermined. Such a loop is shown in Example 2.
Example 2: write a program to print a table of angles in degrees and their equivalents in radians, from 0 to 360 degrees, in steps of 10 degrees.
The program outline is:
and the program is:
PROGRAM CONVRT
INTEGER DEGREE
CONFAC = 3.141593/180.0
C CONVERSION FACTOR FROM DEGREES TO RADIANS
DEGREE = 0
10 IF (DEGREE .LE. 360) THEN
RADIAN = DEGREE*CONFAC
PRINT *, DEGREE,RADIAN
DEGREE = DEGREE + 10
GOTO 10
END IF
END
Figure 9: Degrees to radians conversion program (version 1)
Loops of this kind occur frequently. Their essential features are:
Fortran provides for such loops with a structure called a DO loop, which is more concise and readable than a construction using IF and GOTO.
A DO loop is a sequence of statements beginning with a DO statement. This has the form:
DO label, var = e1, e2, [,e3]
the square brackets indicating that ',e3' may be omitted.
label is the label of an executable statement sequentially following the DO statement called the terminal statement of the DO loop.
var is an INTEGER or REAL (obsolete Fortran 90 feature) variable called the loop control variable.
e1, e2 and e3 are arithmetic expressions (i.e. INTEGER or REAL constants, variables or more complex expressions).
The sequence of statements beginning with the statement immediately following the DO statement and ending with the terminal statement is called the range of the DO loop.
A DO loop is executed as follows:
If the condition tested is "true", then:
Examples:
DO 10, I = 1,5
causes the range of statements beginning with the next and ending with the statement labelled 10 to be executed 5 times.
DO 10, I = 0,100,5
causes the range to be executed 21 times for values of I of 0,5,10...100.
DO 10, I = 100,0,-5
causes the range to be executed 21 times for values of I of 100,95...0.
DO 10, I = 0,100,-5
In this case, the range is not executed at all, as the test in step 3 fails for the initial value of I.
DO 10, J = I,4*N**2-1,K
Here, e1, e2 and e3 are more complex expressions.
We can now rewrite the program of Example 2 using a DO loop. The outline becomes:
and the program follows:
PROGRAM CONVRT
INTEGER DEGREE
CONFAC = 3.141593/180.0
C CONVERSION FACTOR FROM DEGREES TO RADIANS
DO 10, DEGREE = 0,360,10
RADIAN = DEGREE*CONFAC
PRINT *, DEGREE,RADIAN
10 CONTINUE
END
Figure 10: Degrees to radians conversion program (version 2)
This is clearer and more concise than version 1. Note the use of indentation to clarify the loop structure.
6.3.2 Restrictions and other notes
To protect the integrity of the loop structure, there are various restrictions affecting DO loops.
Examples:
GOTO 10
. . .
DO 20, I = 1,5
. . .
10 . . .
. . .
20 CONTINUE
is wrong, but
DO 20, I = 1,5
. . .
10 . . .
. . .
IF (...) GOTO 10
.
IF (...) GOTO 30
. . .
20 CONTINUE
. . .
30 . . .
is all right.
As explained under 'Execution' the control variable is incremented and tested at the end of each iteration. Thus, unless iteration is interrupted by a GOTO, the value of the control variable after execution of the loop will be the value which it was assigned at the end of the final iteration. For example, in a loop controlled by the statement:
DO 10, I = 0,100,5
the control variable I is incremented to exactly 100 at the end of the 20th iteration. This does not exceed limit, so another iteration is performed. I is then incremented to 105 and iteration stops, with I retaining this value.
If the control variable is REAL, inconsistent results may be obtained unless allowance is made for approximation. For example, in a loop controlled by:
DO 10, C = 0,100,5
the control variable C is incremented at the end of the 20th iteration to a value of approximately 100. If it is less, execution continues for a further iteration, but if it is greater, iteration stops.
To avoid such effects, a higher value of limit should be used, e.g.
DO 10, C = 0,101,5
Note: REAL control variable is a Fortran 90
obsolescent feature.
6.3.4 Nested DO loops
DO loops, like IF structures, can be nested, provided that there is no overlapping. (i.e. that the range of each nested loop is entirely within the range of any loop in which it is nested).
Example:
Valid Invalid
DO 20 ... DO 20 ...
... ...
DO 10 ... DO 10 ...
... ...
10 CONTINUE 20 CONTINUE
... ...
20 CONTINUE 10 CONTINUE
The following provides a simple, if not very useful example of a nested loop structure.
Example 3:
Write a program to print a set of multiplication tables from 2 times up to 12 times.
The outline is:
Repeat for I increasing from 2 to 12:
and the program is:
PROGRAM TABLES
DO 20, I = 2,12
PRINT *,I,' TIMES TABLE'
DO 10, J = 1,12
10 PRINT *,I,' TIMES',J,' IS',I*J
20 CONTINUE
END
Figure 11: Multiplication tables program
There is no logical need for the CONTINUE statement in this program as nested loops can share a common terminal statement. Thus the program could be rewritten as:
PROGRAM TABLES
DO 10, I = 2,12
PRINT *,I,' TIMES TABLE'
DO 10, J = 1,12
10 PRINT *,I,' TIMES',J,' IS',I*J
END
However, to clarify the structure, it is better to use separate terminal statements and indentation as in the first version.
Note: sharing terminal statement or eliminating the terminal CONTINUE is an obsolescent feature of Fortran 90.
| First page |
All our programs so far have required the storage of only a few values, and could therefore be written using only a few variables. For example, the average mark program of Figure 8 required only variables for a mark, the total mark, the count of the marks and the average. When large numbers of values have to be stored, it becomes impracticaI or impossible to use different variables for them all. If the average mark program were rewritten to compute average marks for five subjects, we should require five variables, say MARK1 ... MARK5 for the marks, five variables for the totals, and five for the averages. This could be done, but the program would be rather repetitive. The situation is even worse if, after computing the averages, the program is required to print a list showing, for each student and subject, the student's mark and the difference between the mark and the average. This could conceivably be done if the number of students were given in advance, but the program would be extremely cumbersome. If, as in the example, the number of students is not given but determined by counting, the task is impossible, as there is no way of knowing how many variables will be required.
We need to store all the marks in order in a list or other structure to which we can apply a name, and refer to individual marks by a combination of the name and a number or numbers indicating the position of a mark in the list or structure.
In mathematics, an ordered list of n items is called a vector
of dimension n. If the vector is denoted by v, the items,
usually called the components or elements of the
vector, are denoted by
v
Fortran uses a structure similar to a vector called an array.
An array A of dimension N is an
ordered list of N variables of a given type, called the
elements of the array. In Fortran, the subscript notation
used for the components of a vector is not available. Instead
the elements are denoted by the name of the array followed by
an integer expression in parentheses. Thus, the elements of A
are denoted by A(1), A(2),... A(N). The parenthesised
expressions are called array subscripts even though not
written as such.
A subscript can be any arithmetic expression which evaluates to
an integer. Thus, if A, B, and C are arrays,
the following are valid ways of writing an array element:
Since an array is a list of variables, it obviously requires several
words or other units of storage. Each array must therefore be
declared in a statement which tells the compiler how many units
to reserve for it. This can be done by including the array name
in a type specification followed by its dimension in parentheses.
For example:
This reserves 100 words of storage for array AGE, 25
for array NUM, and one word for the variable DEG.
All three items are of type INTEGER.
Space can also be reserved for arrays by the DIMENSION
statement, which reserves storage using a similar syntax, but
includes no information about type. Thus, if this method is used,
the type is either determined by the initial letter of the array
or assigned by a separate type specification. Therefore, the equivalent
to the above using a DIMENSION statement is:
(NUM is typed as INTEGER by default).
DIMENSION statements, like type specifications, are non-executable
and must be placed before the first executable statement.
When this form of declaration is used in a type or DIMENSION statement
the upper and lower bounds for the subscript are 1 and the dimension
respectively. Thus, AGE in the above example may have
any subscript from 1 to 100. Arrays can also be declared to have
subscripts with a lower bound other than 1 by using a second form
of declaration in which the lower and upper bounds are given,
separated by a colon. For example:
reserves 21 words of storage for each of the arrays C
and ERROR and stipulates that the subscripts of C
range from 0 to 20 inclusive, while those of ERROR range
from -10 to 10.
Although the declaration stipulates bounds for the subscript,
not all compilers check that a subscript actually lies within
the bounds. For example, if NUM is declared as above
to have a subscript from 1 to 25, a reference to NUM(30)may
not cause an error. The compiler may simply use the 30th word
of storage starting from the address of NUM(1) even though
this is outside the bounds of the array. This can cause unpredictable
results. Care should therefore be taken to make sure that your
subscripts are within their bounds.
Array elements can be used in the same way as variables, their
advantage being that different elements of an array can be referenced
by using a variable as a subscript and altering its value, for
example by making it the control variable of a DO loop. This is
illustrated in the following sections.
The array name without a subscript refers to the entire array
and can be used only in a number of specific ways.
Values can be assigned to the elements of an array by assignment
statements, e.g.
The DATA statement is a non-executable statement used to initialise
variables. It is particularly useful for initialising arrays.
It has the form:
DATA variable_list/constant_list/ [,variable_list/constant_list/]
...
(The square brackets and ellipsis have their usual meaning.)
Each variable_list is a list of variables, and each
constant_list a list of constants, separated by commas in each case.
Each constant_list must contain the same number of items as
the preceding variable_list and corresponding items in sequence
in the two lists must be of the same type.
The DATA statement assigns to each variable in each
variable_list a value equal to the corresponding constant
in the corresponding constant_list. For example:
A constant may be repeated by preceding it by the number of repetitions
required (an integer) and an asterisk. Thus:
Items in a variable_list may be array elements. Thus, if
A is an array of dimension 20, the DATA statement:
When a large number of array elements have to be initialised,
we can avoid writing them all individually by using an implied
DO list.
An implied DO list is used in a DATA statement or an input/output
statement to generate a list of array elements. The simplest form
of implied DO list is:
(dlist, int=c1,c2[,c3])
where dlist is a list of array elements separated by commas.
The expresssion: int=c1,c2[,c3] has a similar effect
to the expression: var=e1,e2,[,e3] in a DO loop,
but int must be a variable of type INTEGER, and c1,c2
and c3 must be constants or expressions with constant operands.
The implied DO variable int is defined only in the
implied DO list, and is distinct from any variable of the same
name used elsewhere.
The implied DO list expands dlist by repeating the list
for each value of int generated by the loop, evaluating
the array subscripts each time. Thus:
has the same effect as the previous example.
A more complex use of an implied DO list is shown by the example:
which assigns a value of zero to A(1),A(2), A(4),A(5),
... A(19),A(20) and a value of 1.0 to every third element
A(3),A(6), ... A(18) .
Finally, an entire array can be initialised by including its name,
without a subscript, in variable_list in a DATA statement.
This is equivalent to a list of all its elements in sequence.
Thus, if A has dimension 20, all the elements of A
are initialised to zero by:
Note: not placing DATA statements before the first
executable statement is an obsolescent feature of Fortran 90.
Array elements and array names can be used in input/output statements
in much the same way as in DATA statements. Thus, input and output
lists can include:
Implied DO lists in input/output statements differ in two respects
from those in DATA statements:
Example 1:
write a program to read the marks of a class of students in five
papers, and print, for each paper, the number of students sitting
it and the average mark. The marks are to be read as a list of
five marks in the same order for each student, with a negative
mark if the student did not sit a paper. The end of the data is
indicated by a dummy mark of 999.
The outline of the program is:
We shall use arrays MARK, COUNT and TOTAL
to store the five marks for a student, a count of students sitting
each paper and the total mark for each paper respectively. The
program follows.
One problem with this program is that if the last line of input
consists of the single terminating value of 999, the statement:
READ *,(MARK(I),I=1,5) will wait for another four values
to be entered. This can be avoided by following 999 by a '/' character,
which is a terminator causing the READ statement to ignore the
rest of the input list.
Suppose now that the exam marks program is to be altered to print
a list of all the marks in each paper, with the differences between
each mark and the average for the paper. This requires that all
the marks should be stored. This could be done by making the dimension
of MARK large enough to contain all the marks, and reserving the
first five elements for the first student's marks, the next five
for the second student's marks and so on. This would be rather
awkward.
The problem could be dealt with more easily if we could add a
second subscript to the MARK array to represent the number
of each student in sequence. Our array could then be declared
either by:
In fact, Fortran arrays can have up to seven dimensions,
so the above declarations are valid. The subscript bounds are
specified in the same way as for one-dimensional arrays. For example:
An array element must always be written with the number of subscripts
indicated by the declaration.
When multi-dimensional array elements are used in an implied DO
list, multiple subscripts can be dealt with by including nested
implied DO lists in dlist, for example:
We can use a two-dimensional array to solve the problem posed
at the beginning of this section.
Example 2:
write a program to read the marks of up to 100 students in five
papers, and print, for each paper, the number of students sitting
it, the average mark, and a list of the marks and their differences
from the average. The marks are to be read as a list of five marks
in the same order for each student, with a negative mark if the
student did not sit a paper. The end of the data is indicated
by a dummy mark of 999.
The outline is:
Since the marks are read five subjects at a time for each student,
it is convenient to store them in an array MARK(5,100).
The program follows:
Figure 13: Exam marks program (version 2)
This chapter introduces input, output and format statements which
give us greater flexibility than the simple
READ and PRINT statements used so far.
A statement which reads information must:
A statement which outputs information must:
The simple READ statement:
READ *, variable_list
reads a line (or record ) of information from the standard
input (defined as the keyboard for programs run from a terminal)
and stores it in the variables in variable_list. The asterisk
refers to a list-directed format used to split the
information into separate items using spaces and/or commas as
separators and convert each item to the appropriate internal representation,
which is determined by the type of the corresponding variable
in variable_list.
Similarly, the simple PRINT statement:
PRINT *, output_list
uses a list-directed format to convert each constant, and the
value of each variable, in output_list to a suitable form
for output on standard output (defined for a program
run from a terminal as the screen) and prints the list as a line
of output, with spaces between the items.
We can obtain greater control over the conversion and formatting
of input/output items by replacing the asterisk in a READ
or PRINT statement by the label of a FORMAT
statement, for example:
label FORMAT (specification_list)
label is a statement label. A FORMAT statement must always
be labelled to provide a reference for use in input/output statements.
specification_list is a list of format descriptors
(sometimes called edit descriptors), separated by commas.
These describe the layout of each input or output item, and specify
how it is to be converted (or edited) from external to internal
form or vice versa.
FORMAT statements can be placed anywhere in a program. It is often
convenient to place them all at the end (immediately before END),
especially if some of them are used by more than one input/output
statement.
The format descriptors used for input are summarised in Figure 14
and described in the following sections.
This is used to read a value into an INTEGER variable. Its form
is Iw, where w is an unsigned integer
indicating the number of characters to be read (the width
of the field). These characters must consist of decimal
digits and/or spaces, which are interpreted as zeroes, with an
optional + or - sign anywhere before the first digit. Any other
characters will cause an input error.
Example:
(b represents a blank). This assigns a value of 123 to
MEAN and -50 to INC.
This is used to read a value into a REAL variable. It has the
form Fw.d, where w is an unsigned
integer representing the width of the field and d is an
unsigned integer representing the number of digits in the fractional
part.
The corresponding input item must consist of decimal digits and/or
spaces, with an optional sign anywhere before the first digit
and an optional decimal point. As with the I format descriptor,
spaces are interpreted as zeroes. If there is no decimal point
in the item, the number of fractional digits is indicated by d.
If the item includes a decimal point, d is ignored, and
the number of fractional digits is as indicated.
Example:
Results: X: 1.5
A: 12.3
B: 0.45
C: 0.00678
D: 900.0
This is used to read a value into a REAL variable. It has a similar
form to the F format descriptor, but is more versatile, as it
can be used to read input in exponential notation.
We saw in Chapter 2 that a REAL constant can be written
in exponential notation as a REAL or INTEGER constant
followed by an exponent
in the form of the letter 'E' followed by the power of 10 by which
the number is to be multiplied. For input, the exponent can also
be a signed integer without the letter 'E'.
Example:
With a format descriptor of E9.2, all the following will be read
as 1.26
The I, F and E format descriptors may be repeated by preceding
them by a number indicating the number of repetitions. For example:
This is used with an unsigned integer prefix n to skip
n characters.
Example:
Results:
I: 1234
J: 890
The T (for tab), TL and TR format descriptors are used
to move the cursor to a given position. This is defined absolutely
by the T format descriptor or relative to the current position
by the TL and TR descriptors.
Example:
Results: I: 45 J: 89 K: 567
Notes:
Output statements use the same format descriptors as for input
and another, the literal format descriptor, which is a
string of characters for output. The descriptors are summarised
in Figure 15 and described further in the following sections.
Figure 15: Some format descriptors
for output
As well as defining the layout of a line of output via an associated
FORMAT statement, an output statement must define the vertical
placement of the line on the screen or page of printed output.
The method of doing this is described before the use of the format
descriptors of Figure 15.
The computer uses the output list and the corresponding format
specification list to build each line of output in a storage unit
called an output buffer before displaying or printing it.
When the contents of the buffer are displayed on the screen or
printed on paper, the first character is not shown, but is interpreted
as a control character, defining the vertical placement
of the line. Four control characters are recognised, as shown
in Figure 16.
Figure 16: Control characters for
vertical spacing
The effect of any other character is not defined, but is usually
the same as a space, i.e. output is on the next line.
The overprint is simulated by as many backspaces as necessary to override
the previous line: it's not always working very well!
On IBM, the available filter is called asa: for more details
consult its man.
At IDRIS, a portable Fortran 95 program (prt_filter.f90)
is available on our front-end SGI machine Rhodes
to filter such an output.
For more information, see /usr/local/public/src directory.
See also "The standard ASCII table" in chapter 14.
Incorrect output may be obtained if the control character is not
taken into account. It is therefore best to use the format specification
to insert a control character as the first character in a line,
rather than to provide it via the output list. For example:
Output: 15
The initial blank in the buffer is interpreted as a control character,
and '15' is printed on the next line. However, if the FORMAT statement
were:
The following sections describe in more detail the effect of the
format descriptors in output statements.
The format descriptor Iw is used to print
an INTEGER value right-justified in a field of width w character
positions, filling unused positions on the left with blanks and
beginning with a '-' sign if the value is negative. If the value
cannot be printed in a field of width w, the field is filled
with asterisks and an output error is reported.
Example:
Notes:
The format descriptor Fw.d (F for floating
point) is used to print a REAL value right-justified in a field
of width w, with the fractional part rounded (not
truncated) to d places of decimals. The field is filled
on the left with blanks and the first non-blank character is '-'
if the value is negative. If the value cannot be printed according
to the descriptor, the field is filled with asterisks and an error
is reported.
Example:
The value of X is rounded up, that of Y is rounded down, and that
of Z is rounded up, the 3 decimal places being filled with zeroes.
The format descriptor Ew.d is used to print a
REAL value in exponential notation right-justified in a field
of width w, with the fractional part rounded to d
places of decimals. Thus the layout for a format descriptor of
E10.3 is:
Example:
The value 0.0000231436 is printed as shown with the various format
descriptors:
The literal format descriptors 'c1c2...cn' and
nHc1c2...cn
place the string of n characters c1c2...cn
directly into the buffer. Thus a PRINT statement using either
of the following FORMAT statements will print the header:
'RESULTS'
at the top of a new page:
The quoted form is generally easier to use, but the 'H' form is
convenient for providing control characters.
Note: the nHc1c2...cn Hollerith form is an
obsolescent feature of Fortran 90 and deleted from Fortran 95.
A repetition count may be used with a literal format descriptor
if the descriptor is enclosed in parentheses, e.g.
A record is a sequence of values or characters.
A file is a sequence of records.
An external file is one contained on an external medium
(e.g. a magnetic disk).
Each Fortran input/output statement reads information from, or
writes it to, a file. The file must be connected to an
external unit, i.e. a physical device such as the keyboard
or screen, or a magnetic disk. An external unit is referred to
by a unit identifier, which may be:
The READ and PRINT statements we have
considered so far read from
the file 'standard input', normally connected to the keyboard,
and print on the file 'standard output', normally connected to
the screen. To use different files and devices and to obtain various
other options, we require a more general form of the READ statement
for input, and a new statement, the WRITE statement
for output. These statements have the form:
keyword = value
The specifiers may be in any order. In special cases noted below,
only the value is required. Some of the keywords are:
The unit specifier must always be included. Its value must be
a unit identifier, as defined above.
If the unit specifier is the first item in cilist, it may
be denoted by its value only (without 'UNIT=').
Unit identifiers 5 and 6 are preconnected to the files
'standard input' and 'standard output' respectively.
The value of the format specifier FMT is the label of a
FORMAT
statement to be used for input/output conversion, or an asterisk
to indicate list-directed formatting. A format specifier may be
denoted by its value only (without 'FMT=') if it is the second
item in cilist and follows a unit specifier also denoted
by its value only.
Examples:
if unit identifier 5 corresponds to standard input, the following
are all equivalent:
ERR = label
is included in cilist, execution continues from the statement
labelled label. This makes it possible to include statements
in the program to take special actions to deal with such errors.
If a READ statement tries to read more data than is available,
an input error normally occurs. However, if a file ends with a
special end-of-file record, a specifier of the form:
END = label
will cause execution to continue from the statement labelled label.
Note: the format specification list can be put inside the
READ or WRITE statement. By example:
As noted above, the files 'standard input' and 'standard output'
are preconnected to unit identifiers 5 and 6, and normally refer
to the keyboard and screen, respectively. If other files, e.g.
files on disk, are to be used, or if 'standard input' and 'standard
output' are to be redefined, each file must be connected to an
external unit by an OPEN statement, which has the form:
where openlist is a list of specifiers
of the form:
keyword = value
Specifiers may occur in any order. Two of the more important keywords
are:
If the unit specifier is the first item in openlist,
it may be denoted by its value only (without 'UNIT=').
The value of the file specifier is a character expression naming
a file to be opened, i.e. connected to the external unit specified
by the unit specifier. If the file does not exist, a new file
is created.
Example:
If the number of items in an input or output list exceeds the
number of format descriptors in the corresponding FORMAT statement,
a new record is taken (a new line for terminal input/output) and
the format specification list is re-used. This happens as often
as required to deal with the complete list.
Example:
The format specification list may also be re-used partially if
it includes nested parentheses. The rules are:
This is illustrated by the following examples, in which a vertical bar
indicates the point from which repetition, if required, begins:
Repetitions can be used as in the last section to read in or print
out a sequence of values on consecutive lines using the same format
specification list. It is also useful to be able to specify the
format of several consecutive lines (or records) in a single format
specification. This can be done using the / format descriptor,
which marks the end of a record. Unlike other format descriptors,
/ need not be preceded or followed by a comma.
On input, / causes the rest of the current record to be skipped,
and the next value to be read from the first item on the next
record. For example:
Consecutive slashes cause records to be skipped. Thus if the FORMAT
statement in the above example were changed to:
On output, a / marks the end of a record, and starts a new one.
Consecutive slashes cause blank records to be output. For example:
The following example illustrates the use of formatting to produce
output in tabular form with headers and regular spacing.
Example 1:
rewrite the degrees to radians conversion program (Chapter 6,
Example 2) to print angles from 1 to 360 degrees in 1 degree intervals
and their equivalents in radians. The results should be printed
40 lines to a page, with the values suitably formatted, blank
lines separating groups of 10 consecutive lines, headers for the
'Degrees' and 'Radians' columns, and a header and page number
at the start of each page.
The outline is:
and the program follows:
Example:
Note: some parameters of the OPEN statement are set
by defaut :
Example:
Notes:
Very often, a program has to perform a computation several times
using different values, producing a single value each time. An
example is the conversion of an angle in degrees to an equivalent
in radians in Example 1 of the previous chapter.
In Fortran, such a computation can be defined as a function
and referred to by a name followed by a list of the values (called
arguments) which it uses, in parentheses, i.e.
name([argument_list])
where argument_list is an optional list of arguments separated
by commas. Note that the parentheses must be included even if
argument_list is omitted, i.e.
name()
Such a function reference can be used in the same way as a variable
or array element, except that it cannot be the object of an assignment.
Like a variable or array element, a function reference is evaluated
and the value obtained is substituted for it in the expression
in which it appears. The type of a function is the type
of the value so obtained.
Thus, in the above example, a REAL function DGTORD
might be defined
to convert an angle in degrees to an equivalent in radians. The
function would have a single argument, of type INTEGER, representing
the value of the angle in degrees, and would be evaluated to obtain
the equivalent in radians. The function might be used in an assignment
statement like:
As the above example illustrates, a function reference has an
identical form to an array element, and may be used in a similar
context. Fortran distinguishes between the two by checking whether
the name has been declared as an array, and assuming that it is
a function if it has not. Thus, for example, if DGTORD were declared
as:
then DGTORD(DEGREE) would be interpreted as an array
element and not a function reference.
Fortran provides a wide range of intrinsic functions, which
are defined as part of the language. Many of them have an argument,
or list of arguments, which may be of different types in different
references. Most, though not all, of these return a value of the
same type as that of their arguments in any reference. For example,
the function ABS returns the absolute value of its argument,
which may be REAL or INTEGER. Thus
returns the absolute value of the REAL variable X as
a REAL value, while
returns the absolute value of the INTEGER variable N
as an INTEGER value.
A function of this kind is called a generic function. Its
name really refers to a group of functions, the appropriate one
being selected in each reference according to the type of the
arguments.
Figure 18 is a list of some of the more frequently used intrinsic
functions. I and R indicate INTEGER and REAL
arguments respectively. Where an argument represents an angle,
it must be in radians.
As well as using the intrinsic functions provided by the language,
a programmer may create and use his/her own external functions.
These functions may be included in the same source file as a program
which uses them and compiled along with it, or may be written
and compiled separately to obtain separate object files which
are then linked to the object version of the program to obtain
an executable program, in the same way as the library subprograms
shown in Figure 3 on page 2. In either case, the program and functions
are entirely independent program units.
A Fortran source file consists of one or more program units in
any order. One of these may be a main program unit, which
begins with an optional PROGRAM statement and ends with
an END statement. The others are subprograms, which
may be external functions or subroutines. (Subroutines
are explained later in the chapter.)
An external function program unit begins with a FUNCTION
statement and ends with an
Figure 19 illustrates a Fortran source file containing three program
units, a main program MAIN and two functions FUN1
and FUN2. The order of the program units is immaterial.
Provided that the program MAIN includes no references to any other
external functions, the file could be compiled, and the resulting
object file linked with the library subprograms to obtain an executable
program.
The functions might also be placed in one or two separate files
and compiled separately from the main program. The object file
or files thus obtained could then be linked with the library subprograms
and the object version of the program MAIN or any other program
containing references to them. In this way a programmer can create
his/her own subprogram libraries for use by any program.
As shown above, an external function must begin with a FUNCTION
statement. This has the form:
As before, square brackets indicate that an item is optional.
Each function has a type corresponding to the type of value returned
by a reference to it. As for variables, the type of a function
may be specified explicitly or assigned implicitly according to
the first letter of the function name. For example, the function:
If the type of a function differs from that implied by the first
letter of its name, it must be declared in a type specification
in any program which refers to it. Thus any program using the
second version of FUN1 above would include the name FUN1
in an INTEGER type specification statement, e.g.
argument_list is an optional list of dummy arguments,
separated by commas. Each dummy argument is a name similar to
a variable or array name, which represents a corresponding actual
argument used in a function reference. Dummy arguments, and
variables used in a function, are defined only within it. They
may therefore be identical to variable or array names used in
any other program unit.
If a dummy argument represents an array, it must appear in a type
specification or DIMENSION statement in the function.
If it represents a variable, it may appear in a type specification,
or may be typed by default.
Example:
A function may have no arguments, e.g.
As we have seen, a function reference has the form:
name(argument_list)
argument_list is a list of actual arguments, which
must match the list of dummy arguments in the FUNCTION statement
with respect to the number of arguments and the type of each argument.
For example:
If a dummy argument is a variable name, the corresponding actual
argument may be any expression of the same type, i.e. a constant,
variable, array element or more complex arithmetic expression.
If a dummy argument is an array name, the actual argument may
be an array or array element. The dimensions of the dummy array
may be variable if they are also dummy arguments.
Example:
The dummy arguments and corresponding actual arguments provide
a means of exchanging information between a program unit and a
function.
Each actual argument refers to a word or other unit of storage.
However, no storage is reserved for a dummy argument; it is simply
a name. When a function reference is evaluated, the address of
each actual argument is passed to the function, and the corresponding
dummy argument is set to refer to it. The dummy argument may therefore
be used in the function as a variable or array referring to the
same unit of storage as the actual argument.
Thus if a dummy argument represents a variable, its value on entry
to the function is that of the corresponding actual argument when
the function is referenced. If its value is changed in the function
by an assignment or READ statement, the actual argument will be
correspondingly changed after the function reference has been
evaluated.
If a dummy argument is an array, the corresponding actual argument
may be an array or array element. In the former case, the elements
of the dummy array correspond to the elements of the actual array
in the order of their storage in memory. This, however, does not
imply that the subscripts are identical, or even that the two
arrays have the same number of subscripts. For example, suppose
that the function:
Once the dummy arguments have been initialised as described above,
the statements comprising the body of the function are executed.
Any statement other than a reference to the function itself may
be used. At least one statement must assign a value to the function
name, either by assignment, or less commonly, by a READ statement.
Execution of the function is stopped, and control returned to
the program unit containing the function reference, by a
RETURN statement, written simply as:
The value of the function name when RETURN is executed is returned
as the function value to the program unit containing the function
reference.
We can now write the function DGTORD suggested at the beginning
of the chapter, to convert an INTEGER value representing an angle
in degrees, to a REAL value representing the equivalent in radians.
Our function uses the intrinsic function ATAN to compute the conversion
factor.
If a function involves only a computation which can be written
as a single statement, it may be declared as a statement function
in any program unit which refers to it. The declaration has the
form:
name(argument_list) = expression
where:
Thus the function DGTORD might be declared as a statement function
in the program ANGLES:
Note: statement functions are obsolete with the Fortran 95 standard.
They are replaced by internal functions (see
"obsolescent features" in Fortran 95 manuals).
The name of a statement function must be different from that of
any variable or array in the same program unit.
The type of a statement function may be specified explicitly in
a separate type specification or determined implicitly by the
first letter of its name.
A dummy argument may have the same name as a variable or array
in the same program unit. If so, it has the same type as the variable
or array but is otherwise distinct from it and shares none of
its attributes. For example, in the program ANGLES, the dummy
argument DEGREE of the statement function DGTORD has
the same name as the variable DEGREE declared in the
program, and therefore has the correct (INTEGER) type, but is
a different entity. If the program included the declaration:
If a dummy argument does not have the same name as a variable
or array in the same program unit, it is typed implicitly according
to its first letter, e.g.
A SUBROUTINE is a subprogram similar in most respects to
a function. Like a function, a subroutine has a list of dummy
arguments used to exchange information between the subroutine
and a program unit referring to it. Unlike a function, a subroutine
does not return a value via its name (and therefore has no type),
but it may return one or more values via its arguments.
A subroutine subprogram begins with a SUBROUTINE
statement and ends with END. The SUBROUTINE
statement has the form:
A subroutine is referenced by a CALL statement, which
has the form:
Functions (intrinsic and external) and subroutines are often called
procedures.
In Example 1 of Chapter 8, the steps required to print a page
header and column headers at the top of each page might be written
as a subroutine. The steps are:
The subroutine therefore has two dummy arguments, one representing
the page number and the other representing the output device,
and includes the WRITE statement and FORMAT
statements required to print the page and column headers. The
subroutine follows:
The degrees to radians conversion program can now be rewritten
using the subroutine HEADER and function DGTORD
as follows:
A program unit can pass the names of procedures as arguments to
a function or subroutine. The calling program unit must declare
these names in an EXTERNAL statement for external
procedures (functions or subroutines), or INTRINSIC
statement for intrinsic functions. The statements have the form:
respectively, where list is a list of external
procedures, or intrinsic functions respectively.
If an actual argument is a procedure name, the corresponding dummy
argument may be:
In this way, a procedure name can be passed from one procedure
to another for as many levels as required.
Example 1
In Figure 21, the program MAIN passes the names of the
subroutine ANALYS and the intrinsic function SQRT
as actual arguments to the subroutine SUB1, corresponding
to its dummy arguments SUB and FUN respectively.
In SUB1, SUB appears in a CALL statement
in which it is replaced in this instance by a call of ANALYS,
while FUN appears in an EXTERNAL statement and
is passed as an actual argument to SUB2, corresponding
to its dummy argument F. In SUB2, F
appears followed by a left parenthesis. Because F is
not declared as an array, this is interpreted as a function reference,
and is replaced by a reference to SQRT.
Note that although SQRT is an intrinsic function and
is declared as such in program MAIN, FUN, the
corresponding dummy argument of subroutine SUB1, is declared
in SUB1 as EXTERNAL because FUN is
a dummy procedure name corresponding to a function defined externally
to SUB1.
Example 2
In Figure 22, the subroutine TRIG has three dummy arguments,
X representing an angle in radians, F representing
a trigonometric function, and Y representing that function
of X. The main program includes four calls to TRIG,
using the intrinsic functions SIN, COS and TAN
and the external function COT, which computes the cotangent.
The variables used in a subprogram, other than its arguments,
are local variables, defined only within it, and therefore
distinct from any identically named variables used elsewhere.
When a RETURN statement is executed, they become undefined,
and their addresses may be used by other program units. Therefore,
if a subprogram is executed several times, the values of its local
variables are not preserved from one execution to the next.
The values of local variables can be preserved by a SAVE
statement, which has the form:
SAVE is a non-executable statement and must be placed before the
first executable statement or DATA statement.
Example:
each time the following function is executed, it prints a message
indicating how many times it has been referenced.
Constants of type CHARACTER were briefly introduced in Chapter
Two. You will recall that a CHARACTER constant (or string) is
a sequence of characters delimited by single quotes, and that
single quotes may be included by writing two consecutively.
Variables of type CHARACTER must be declared in a CHARACTER type
specification, which specifies the length of each variable (i.e.
the number of characters it contains). This takes the form:
var is a variable name.
Thus the simplest form of declaration is:
The form:
The form:
Finally, the form:
Example:
the following specification assigns a length of 4 characters to
the CHARACTER variables A and C, and 6 characters to B.
Example:
A CHARACTER variable may only be assigned a value of type CHARACTER.
If the length of a variable differs from that of the value assigned
to it, the following rules are applied:
Example:
Two operations are defined for character strings: concatenation
and extraction of a substring.
The concatenation operator // joins two character
string operands together in sequence.
Example:
If A is a CHARACTER variable of length 5, the assignment:
A substring is a string of contiguous characters forming
part of another string. A substring is extracted by writing a
CHARACTER variable followed
by one or two INTEGER expressions
in parentheses and separated by a colon, indicating the leftmost
and rightmost character positions of the substring in the larger
string. If the first expression is omitted, the substring begins
at the beginning of the string. If the second is omitted, it ends
at the end of the string.
Example:
If the CHARACTER variable LANG has the value
'FORTRAN', some substrings are:
Example:
The following assignment will change the value of the CHARACTER
variable LANG from 'FORTRAN' to 'FORMATS':
When a CHARACTER variable is used in a list directed input statement,
the value read must be delimited by single quotes. These are required
because the value may include characters such as blanks, commas
or slashes (/), which are normally recognised as separators between
input items.
When a CHARACTER expression is used in a list directed output
statement, it is printed in full using as many character positions
as required. This form of output has been used in earlier program
examples, e.g.
Figure 24: The A format descriptor
If w differs from the length len of the input or
output item, the rules are:
For input:
For output:
These rules ensure consistency of input and output. If a string
is written out, and the result read using the same format, the
value read in will be the same as that originally written out.
This would not be so, for example, if rule (ii) for input were
changed to store the left-most len characters as for assignment.
This is illustrated in Figure 25, in which the output of the program
CHROUT is read by the program CHRIN.
A contains 'WHAT'. B contains 'FORb'.
(b represents a blank.)
Figure 25: Character input and
output
Character strings can be used in logical expressions with the
six relational operators .GT., .GE., .EQ., .NE., .LE. and .LT..
The definition of the operators depends on the coding scheme used
to represent characters in binary form, which can be used to define
a collating sequence of all valid characters in order of
their binary codes. Two coding schemes, ASCII and EBCDIC, are
in common use. The two collating sequences are different but have
the following rules in common:
Relational expressions with single character operands are defined
with reference to the collating sequence. For example, if CHAR1
and CHAR2 are two CHARACTER variables of length
1, then CHAR1.GT.CHAR2 evaluates to .TRUE.
if CHAR1 comes after CHAR2 in the collating
sequence. The other operators are similarly defined.
A relational expression with two character string operands of
any length is evaluated in the following stages:
Examples:
'ADAM'.GT.'EVE' evaluates to .FALSE.
because 'A' precedes 'E' in the collating sequence.
'ADAM'.LE.'ADAMANT' evaluates to .TRUE.
'ADAM' is extended on the right with blanks, the first
four characters are found to be identical, and the expression:
The value of such expressions as:
A REAL variable or constant occupies one word of storage and this
limits its accuracy. When greater accuracy is required,
DOUBLE PRECISION variables and constants may be used.
These occupy two words of storage and can store a greater number
of significant digits.
DOUBLE PRECISION constants are written in exponential form, but
with the letter 'D' in place of 'E', e.g.
DOUBLE PRECISION variables must be declared in a type specification
of the form:
DOUBLE PRECISION values can be used in list-directed input and
output in the same way as REAL values. In formatted input and
output, they may be used with the F and E format specifications
and with a new format specification D, which has a similar
form to the E specification, i.e.
Dw.d
In output, this specification prints a value in exponential form
with a 'D' instead of an 'E'.
If both operands of an arithmetic operation are of type DOUBLE
PRECISION, the result is also of type DOUBLE PRECISION. If one
operand is of type REAL or INTEGER, the result is of type
DOUBLE PRECISION, but this does not imply that the other operand
is converted to this type.
All the intrinsic functions in Figure 18 on page 45 which take
REAL arguments also take DOUBLE PRECISION arguments and return
DOUBLE PRECISION values.
Fortran provides for the representation of complex numbers using
the type COMPLEX.
A COMPLEX constant is written as two REAL constants,
separated by a comma and enclosed in parentheses. The first constant
represents the real, and the second the imaginary part.
Example:
The complex number 3.0-i1.5, where i²= -1,
is represented in Fortran as:
(3.0,-1.5).
COMPLEX variables must be declared in a COMPLEX type
specification:
In list-directed output, a COMPLEX value is printed as described
under 'COMPLEX constants'. In list-directed input, two REAL values
are read for each COMPLEX variable in the input list, corresponding
to the real and imaginary parts in that order.
In formatted input and output, COMPLEX values are read or printed
with two REAL format specifications, representing the real and
imaginary parts in that order. It is good practice to use additional
format specifiers to print the values in parentheses, or in the
'' form. Both forms are illustrated in Figure 27.
An operation with two COMPLEX operands always gives a COMPLEX
result. In mixed mode expressions, COMPLEX values may be used
with REAL or INTEGER, but not with DOUBLE PRECISION values. The
REAL or INTEGER value is converted to a COMPLEX value with an
imaginary part of zero.
COMPLEX arguments may be used in generic functions such as ABS,
EXP, LOG, SQRT, SIN and COS to obtain a COMPLEX value. The following
functions are provided for use with COMPLEX values. (C, I,
R and D represent COMPLEX, INTEGER,
REAL and DOUBLE precision arguments respectively.)
Figure 28: Some functions used with COMPLEX values
Example:
Note: if the equivalenced objects have differing type, no conversion
nor mathematical equivalence is done.
The common blocks may be named and are called named common blocks,
or may be unnamed and are called blank common.
Example:
Note: an EQUIVALENCE statement must not cause storage
association of two common blocks and an EQUIVALENCE statement
association must not cause a common block storage sequence
to be extended. For example, the following is not permitted:
A block data program unit is used to provide values for data objects
in named common blocks.
Example:
Example:
Note: in Fortran 90 this feature should be replaced by the
IF construct (see IF...THEN...ELSEIF...ENDIF statements)
or the CASE construct (see select case statement).
Example:
Note: in Fortran 90 this feature should be replaced by the
CASE construct (see select case statement).
This chapter contains some general principles which should be
observed in writing and testing programs. An attempt has been
made to demonstrate them in the examples in the previous chapters.
Do not attempt to write the Fortran code straight away. Write
an outline as shown in the examples, showing the main steps in
sequence. Use indentation to indicate the logical structure.
The steps defined in 1. can initially be quite broad and general.
Revise your outline as often as required, breaking down each main
step into a sequence of simpler steps. Repeat this process until
your steps correspond to Fortran statements.
While developing your program as above, think about the main variables
and arrays you will require to represent the information. Choose
names which suggest their usage and write down each name with
its type and dimensions (if an array) and a note of what it represents.
Always use IMPLICIT NONE statement to force explicit typing
of variables and arrays.
Use functions and subroutines not only to avoid repetitive coding
but, more importantly, to keep your program simple and its structure
clear by putting the details of clearly defined computations in
separate units.
Don't hesitate to use available scientific libraries as NAG, IMSL,
LAPACK, ... which saves you development time and offers you a best
optimisation and reliability.
Your program should be designed to cope with invalid data by printing
informative error messages rather than simply failing, e.g. due
to attempted division by zero. This applies especially if your
program will be used by others.
When writing your Fortran code, use indentation to clarify its
logical structure and include explanatory comments freely.
Once you have eliminated the syntax errors from your program and
subroutines, try running them using suitable test data. Calculate
what the results should be, and check that the actual results
correspond. If they do not, you will have to revise some of the
steps above to correct the errors in your logic. To determine
the cause of an error, you may have to insert extra WRITE
statements to print out the values of variables etc. at various stages.
Many debugging options or tools can help you finding errors.
For the arrays, the "bound checking" options are very usefull
to detect errors at execution.
Your test data should be designed to test the various logical
paths through your program. For example, to test the quadratic
roots program of Figure 7 on page 16, you should use data designed
to obtain two, one and no real roots, as well as a value of zero
for a.
Try to use optimisation compiler options to get an improved version of
your exectable program. As a second step in this way, you can use
profiling tools do detect the more important parts of your program
(in term of CPU time) and try to improve them by hand...
Copyright: The University of Strathclyde Computer Centre, Glasgow, Scotland.
Permission to copy will normally be granted provided that these credits
remain intact.
We'd appreciate a request before you use these notes, partly to justify
distributing them, but also so we can distribute news of any updates.
These notes were written by John Porter of the University of Strathclyde
Computer Centre. They form the basis of the Computer Centre's Fortran 77
course. John can be reached at J.R.Porter@strath.ac.uk.
Original URL : http://www.strath.ac.uk/CC/Courses/fortran.html
IDRIS/CNRS : bâtiment 506 BP167 - 91403 ORSAY Cedex - France
A(10)
B(I+4)
C(3*I+K)
7.1 Array declarations
INTEGER AGE(100),NUM(25),DEG
INTEGER AGE,DEG
DIMENSION AGE(100),NUM(25)
REAL C(0:20)
INTEGER ERROR(-10:10)
7.2 Use of arrays and array elements
7.3 Initialising an array
NUM(1) = 0
NUM(2) = 5
If all the elements are to have equal values, or if their values
form a regular sequence, a DO loop can be used. Thus, if NUM and
DIST are arrays of dimension 5:
DO 10, I = 1,5
NUM(I) = 0
10 CONTINUE
initialises all the elements of NUM to 0, while:
DO 10, I = 1,5
DIST(I) = 1.5*I
10 CONTINUE
assigns the values 1.5, 3.0, 4.5, 6.0 and 7.5 to
DIST(1),DIST(2),DIST(3),DIST(4)
and DIST(5) respectively.
7.3.1 The DATA statement
DATA A,B,N/1.0,2.0,17/
assigns the values 1. and 2. respectively to the REAL variables
A and B, and 17 to the INTEGER variable N.
DATA N1,N2,N3,N4/4*0/
assigns a value of zero to each of the variables N1,N2,N3
and N4.
DATA A(1),A(2),A(3),A(4)/4*0.0/,A(20)/-1.0/
assigns a value of zero to the first four elements, -1.0 to the
last element, and leaves the remaining elements undefined.
7.3.2 The implied DO list
DATA (A(I),I=1,4)/4*0.0/,A(20)/-1.0/
DATA (A(I),A(I+1),I=1,19,3)/14*0.0/,(A(I),I=3,18,3)/6*1.0/
DATA A/20*0.0/
DATA statements can be placed anywhere in a program after any
specifications. In the interests of clarity, it is probably best
to put them immediately before the first executable statement.
Wherever they may be, they cause initialisation when the program
is loaded (before execution begins). Therefore they can only
be used to initialise variables and not to re-assign values
to them throughout execution of the program. For this purpose,
assignment statements or READ statements must be used.
7.4 Input and output of arrays
In an input statement, the loop parameters can depend on values
read before by the same statement, e.g.
PRINT *, (A(I),'ABC', K, I=1,4)
will print the values of A(1)...A(4) followed
in each case by 'ABC' and the value of K.
N = 5
. . .
PRINT *,(A(I),I=1,N)
READ *, N, (A(I),I=1,N)
If variables are used in this way, care should be taken to ensure
that they lie within the subscript bounds of the array, as in
the following example:
REAL A(20)
. . .
READ *, N
IF (N.GE.1 .AND. N.LE.20) THEN
READ *, (A(I),I=1,N)
ELSE
PRINT *, N, 'EXCEEDS SUBSCRIPT BOUNDS.'
END IF
We can now return to the exam marks problem mentioned at the beginning
of the chapter.
PROGRAM EXAM
INTEGER MARK(5),TOTAL(5),COUNT(5)
DATA COUNT/5*0/,TOTAL/5*0/
READ *,(MARK(I),I=1,5)
10 IF (MARK(1).NE.999) THEN
DO 20, I=1,5
IF (MARK(I).GE.0) THEN
COUNT(I) = COUNT(I)+1
TOTAL(I) = TOTAL(I)+MARK(I)
END IF
20 CONTINUE
READ *,(MARK(I),I=1,5)
GOTO 10
END IF
DO 30, I=1,5
IF (COUNT(I).GT.0) THEN
AVMARK = 1.0*TOTAL(I)/COUNT(I)
C MULTIPLY BY 1.0 TO CONVERT TO REAL AND AVOID TRUNCATION
PRINT *,COUNT(I),' STUDENTS SAT PAPER NUMBER',I
PRINT *,'THE AVERAGE MARK WAS', AVMARK
ELSE
PRINT *,'NO STUDENTS SAT PAPER NUMBER',I
END IF
30 CONTINUE
END
Figure 12: Exam marks program
7.5 Multi-dimensional arrays
INTEGER MARK(5,100)
or by:
INTEGER MARK(100,5)
and would reserve enough space to store the marks of up to 100
students in 5 subjects.
REAL THREED(5,0:5,-10:10)
declares a three-dimensional array of type REAL, with
subscript bounds of 1...5, 0...5 and -10...10 in that order.
READ *, (A(J),(MARK(I,J),I=1,5),J=1,100)
Here, dlist contains two items, A(J) and the implied
DO list (MARK(I,J),I=,5) .This inner implied DO
list is expanded once for each value of J in the outer implied
DO list. Thus the above READ statement reads values
into the elements of A and MARK in the order:
A(1), MARK(1,1), MARK(2,1),... MARK(5,1)
A(2), MARK(1,2), MARK(2,2),... MARK(5,2)
.. .. .. ..
A(100), MARK(1,100), MARK(2,100),... MARK(5,100)
The unsubscripted name of a multi-dimensional array can be used,
like that of a one-dimensional array, in input/output and DATA
statements to refer to all its elements, but it is essential to
know their order. The elements are referenced in the order
of their positions in the computer's memory. For a one-dimensional
array, the elements occur, as we might expect, in increasing order
of their subscripts, but for multi-dimensional arrays, the ordering
is less obvious. The rule is that the elements are ordered with
the first subscript increasing most rapidly, then the next and
so on, the last subscript increasing most slowly. Thus if MARK
is declared as:
INTEGER MARK(5,100)
its elements are ordered in memory as shown above, and the statement:
READ *,MARK
is equivalent to:
READ *, ((MARK(I,J),I=1,5),J=1,100)
Of course, the order could be altered by swapping the control
variables in the inner and outer implied DO loops thus:
READ *, ((MARK(I,J),J=1,100),I=1,5)
Note: if we consider a two dimensional array as a matrix, we should
say that in memory its elements are stored column after colum. With the C
language it should be row after row !
PROGRAM EXAM2
IMPLICIT NONE
REAL AVMARK
INTEGER MARK(5,100),TOTAL(5),COUNT(5),ALL,I,J,LAST
DATA COUNT/5*0/,TOTAL/5*0/,ALL/0/
DO 20, J=1,100
READ *,(MARK(I,J),I=1,5)
IF (MARK(1,J).EQ.999) GOTO 30
ALL = ALL+1
DO 10, I=1,5
IF (MARK(I,J).GE.0) THEN
COUNT(I) = COUNT(I)+1
TOTAL(I) = TOTAL(I)+MARK(I,J)
END IF
10 CONTINUE
20 CONTINUE
READ *,LAST
IF (LAST.NE.999) THEN
PRINT *,'MARKS ENTERED FOR MORE THAN 100 STUDENTS.'
STOP
END IF
30 DO 50, I=1,5
IF (COUNT(I).GT.0) THEN
AVMARK = 1.0*TOTAL(I)/COUNT(I)
C MULTIPLY BY 1.0 TO CONVERT TO REAL AND AVOID TRUNCATION
PRINT *,COUNT(I),' STUDENTS SAT PAPER NUMBER',I
PRINT *,'THE AVERAGE MARK WAS', AVMARK
PRINT *,'MARKS AND THEIR DIFFERENCES FROM THE AVERAGE:'
DO 40, J=1,ALL
IF (MARK(I,J).GE.0)PRINT *,MARK(I,J),MARK(I,J)-AVMARK
40 CONTINUE
ELSE
PRINT *,'NO STUDENTS SAT PAPER NUMBER',I
END IF
50 CONTINUE
END
First page
-8- Input and output
8.1 The FORMAT statement
READ 10,A,B,C
10 FORMAT(...)
The FORMAT statement describes the layout of each item to be read
or printed, and how it is to be converted from external to internal
form or vice versa. It also describes the movements of an imaginary
cursor which can be envisaged as scanning the input list.
Its general form is:
8.2 Formatted input
Descriptor Meaning
Iw Convert the next w characters to an INTEGER value.
Fw.d Convert the next w characters to a REAL value.
If no decimal point is included, the final d digits
are the fractional part.
Ew.d Convert the next w characters to a REAL value,
interpreting them as a number in exponential notation.
nX Skip the next n characters.
Tc Skip to character absolute position c.
TLn Skip to the character which is n characters
to the left of the current character.
TRn Skip to the character which is n characters
to the right of the current character.
Figure 14: Some format descriptors for input
8.2.1 The I format descriptor
READ 10,MEAN,INC
10 FORMAT(I4,I4)
Input: b123b-5b
8.2.2 The F format descriptor
READ 10,X,A,B,C,D
10 FORMAT(F4.5,F4.1,F2.2,F3.5,F3.0)
Input: b1.5b123456789bb
8.2.3 The E format descriptor
0.126Eb01
1.26bEb00
1.26bbbbb
12.60E-01
bbb.126E1
bbbbbb126
126bbbbbb
bbb12.6-1
8.2.4 Repeat count
10 FORMAT(3I4)
is equivalent to:
10 FORMAT(I4,I4,I4)
8.2.5 The X format descriptor
READ 10,I,J
10 FORMAT(I4,3X,I3)
Input: 123456789b
8.2.6 The T format descriptors
READ 10,I,J,K
10 FORMAT(T4,I2,TR2,I2,TL5,I3)
Input: 123456789b
8.3 Formatted output
Descriptor
Meaning
Iw
Output an INTEGER value in the next w character
positions
Fw.d
Output a REAL value in the next w character positions,
with d digits
in the fractional part.
Ew.d
Output a REAL value in exponential notation in the next w
character positions,
with d digits in the fractional part.
nX
Skip the next n character positions.
Tc
Skip to character absolute position c.
TLn
Skip to the character which is n characters to the left
of the current character.
TRn
Skip to the character which is n characters to the right
of the current character.
'c1c2...cn'
Output the string of n characters c1c2...cn starting
at the next character position.
nHc1c2...cn
Output the string of n characters c1c2...cn starting
at the next character position.
8.3.1 Vertical spacing
Character
Vertical spacing before output
Space One line
0 (zero) Two lines
1 New page
+
No vertical spacing (i.e. current line is overprinted).
Note: these vertical control characters are generally called
"Fortran ASA carriage control characters". They are ineffective on
modern displays and printers. To take them in account you must activate
a filter which is contructor dependent. It converts them to
equivalent ASCII control characters to simulate the vertical action.
Fortran char.
Equiv. ASCII control char.
Hex. value
Display
Space
Ignored
.
.
0
Line Feed
'0A'
^J / Ctrl-J
1
Form Feed
'0C'
^L / Ctrl-L
+
n Backspaces
'08'
^H / Ctrl-H
N = 15
PRINT 10,N
10 FORMAT(1X,I2)
Buffer contents: b15
10 FORMAT(I2)
the buffer contents would be '15'. On printing, the initial '1'
would be interpreted as a control character, and '5' would be
printed at the start of the next page.
8.3.2 The I format descriptor
I = 15
J = 709
K = -12
PRINT 10,I,J,K,
10 FORMAT(1X,I4,I4,I4)
Output: bb15b709b-12
10 FORMAT(1X,3I4)
8.3.3 The F format descriptor
X = 3.14159
Y = -275.3024
Z = 12.9999
PRINT 10,X,Y,Z,
10 FORMAT(1X,3F10.3)
Output: bbbbb3.142bb-275.302bbbb13.000
8.3.4 The E format descriptor
S0.XXXESXX
<d>
<---w---->
S indicates a position for a sign. The initial sign is
printed only if negative, but the sign of the exponent is always
printed. X indicates a digit.
E10.4 0.2314E-04
E12.3 bbb0.231E-04
E12.5 b0.23144E-04
8.3.5 The literal format descriptors
10 FORMAT('1','RESULTS')
10 FORMAT(1H1,7HRESULTS)
10 FORMAT(1X,3('RESULTS'))
8.4 More general input/output statements
READ (cilist) input_list
WRITE(cilist) output_list
where cilist is a list of input-output specifiers,
separated by commas. Each specifier takes the form:
UNIT
FMT
ERR
END
READ(UNIT=5, FMT=100) X,Y,Z
READ(FMT=100, UNIT=5) X,Y,Z
READ(5, FMT=100) X,Y,Z
READ(5, 100) X,Y,Z
READ(*, 100) X,Y,Z
Also, the statements:
READ(*,*) A,B,C
READ(5,*) A,B,C
are both equivalent to the list-directed input statement:
READ *, A,B,C
The last two specifiers deal with special conditions. If an error
occurs in input or output execution normally stops, but if an
error specifier of the form:
read(10, '(I4, F6.2)') K, X
8.5 The OPEN statement
OPEN(openlist)
UNIT
FILE
The unit specifier must be included. Its value must be a unit
identifier.
OPEN(8, FILE='MYFILE.DAT')
connects the file MYFILE.DAT to unit 8. If the file does not exist,
it is created. READ and WRITE statements referring to this unit
identifier will then read from or write to this file.
8.6 Repetition of format specifications
READ(5,10) A,B,C,P,Q,R,X,Y,Z
10 FORMAT(3F12.3)
This reads three values from the first line of input into the
variables A,B and C, from the second line into
P,Q and R, and from the third line into X,Y
and Z. Similarly:
WRITE(6,10) A,B,C,P,Q,R,X,Y,Z
10 FORMAT(1X,3F12.3)
prints the values of the variables three to a line on consecutive
lines.
10 FORMAT(I6, 10X,I5, 3F10.2)
|---------------------
20 FORMAT(I6, 10X,I5, (3F10.2))
|-------
30 FORMAT(I6, (10X,I5), 3F10.2)
|----------------
40 FORMAT(F6.2, (2F4.1,2X,I4, 4(I7,F7.2)))
|-------------------------
50 FORMAT(F6.2, 2(2F4.1,2X,I4), 4(I7,F7.2))
|---------
60 FORMAT(F6.2,(2(2F4.1,2X,I4), 4(I7,F7.2)))
|---------------------------
8.7 Multi-record specifications
READ(5,100) A,B,C,I,J,K
100 FORMAT(2F10.2,F12.3/I6,2I10)
reads three REAL values into A,B and C from
a line, ignores anything more on that line, and reads three INTEGER
values into I,J and K from the next line.
100 FORMAT(2F10.2,F12.3//I6,2I10)
a complete line would be skipped before the values were read into
I,J and K.
WRITE(6,200) A,B,A+B,A*B
200 FORMAT(1H1////T10,'MULTIPLE LINES EXAMPLE'///
* 1X,'THE SUM OF',F5.2,' AND',F5.2,' IS',F5.2/
* 1X,'AND THEIR PRODUCT IS',F8.2////)
prints four blank lines and a header at the top of a new page,
followed by two blank lines, then the sum and product on consecutive
lines followed by four blank lines.
PROGRAM ANGLES
IMPLICIT NONE
REAL RADIAN,CONFAC
INTEGER DEGREE,PAGENO,OUT,N
DATA OUT/6/
C UNIT NUMBER FOR OUTPUT. A DIFFERENT DEVICE COULD BE USED BY
C CHANGING THIS VALUE
DATA PAGENO/0/
CONFAC = 3.141593/180.0
C CONVERSION FACTOR FROM DEGREES TO RADIANS
DO 10, DEGREE = 1,360
N = DEGREE-1
IF (N/40*40 .EQ. N) THEN
C PRINT PAGE HEADER, NUMBER AND COLUMN HEADERS
PAGENO = PAGENO+1
WRITE(OUT,100)PAGENO
ELSE IF (N/10*10 .EQ.N) THEN
WRITE(OUT,110)
END IF
RADIAN = DEGREE*CONFAC
WRITE(OUT,120)DEGREE,RADIAN
10 CONTINUE
100 FORMAT(1H1//1X,'DEGREES TO RADIANS CONVERSION TABLE',
* T74,'PAGE',I2//1X,'DEGREES RADIANS'/)
110 FORMAT(1X)
120 FORMAT(1X,I5,T10,F7.5)
END
Figure 17: Degrees to radians conversion program (version 3)
8.8 Sequential unformatted I/O
This program writes one record containing the array T. The data are
written without any format specification (often said "binary" mode).
After having rewound it, this record is read.
REAL T(100)
DO 10 I=1, 100
T(I) = SIN(REAL(100)/123.)
10 CONTINUE
OPEN(UNIT=10, FILE='MYFIC', ACCESS='SEQUENTIAL',
1 FORM='UNFORMATTED', STATUS='NEW')
WRITE(UNIT=10) T
REWIND 10
READ(UNIT=10) T
CLOSE(UNIT=10)
END
ACCESS='SEQUENTIAL'
FORM='UNFORMATTED'
STATUS='UNKNOWN'
It could have been coded more shortly as:
OPEN(10, FILE='MYFIC', STATUS='NEW')
8.9 Direct access unformatted I/O
This program writes five records, each of then containing a part of
the array T. The data are written without any format
specification (often said "binary" mode).Then it reads the third record and
stocks it in array TR.
REAL T(100), TR(20)
DO 10 I=1, 100
T(I) = REAL(I)
10 CONTINUE
OPEN(UNIT=10, FILE='MYFIC', ACCESS='DIRECT', FORM='UNFORMATTED',
1 STATUS='UNKNOWN', RECL=80)
DO 20 K=1, 5
WRITE(UNIT=10, REC=K) (T(I), I=(K-1)*20+1, K*20)
20 CONTINUE
READ(UNIT=10, REC=3) TR
PRINT *, TR
END
First page
-9- Functions and subroutines
RADIAN = DGTORD(DEGREE)
The definition of a function must include a definition of its
type and the number and types of its arguments. In a function
reference the number and type of the arguments must be as defined.
Thus, for example:
RADIAN = DGTORD(DEGREE,X)
would be an error.
REAL DGTORD(100)
9.1 Intrinsic functions
ABS(X)
ABS(N)
Name Type Definition
ABS(IR) Generic Absolute value: |IR|
ACOS(R) REAL arccos(R)
AINT(R) REAL Truncation: REAL(INT(R))
ANINT(R) REAL Nearest whole number: REAL(INT(R+0.5)) if R>=0
REAL(INT(R-0.5)) if R<=0
ASIN(R) REAL arcsin(R)
ATAN(R) REAL arctan(R)
COS(R) REAL cos(R)
COSH(R) REAL cosh(R)
DIM(IR1,IR2) Generic Positive difference: MAX(IR1-IR2,0)
EXP(R) REAL eR
INT(R) INTEGER INTEGER portion of R
LOG(R) REAL Natural logarithm: logeR
LOG10(R) REAL Common logarithm: log10R
MAX(IR1,IR2,...) Generic Largest of IR1,IR2,...
MIN(IR1,IR2,...) Generic Smallest of IR1,IR2,...
MOD(IR1,IR2) Generic Remainder: IR1-INT(IR1/IR2)*IR2
NINT(R) INTEGER Nearest integer: INT(ANINT(R))
REAL(I) REAL Real equivalent of I
SIGN(IR1,IR2) Generic Transfer of sign: |IR1| if IR2>=0
-|IR1| if IR2<0
SIN(R) REAL sin(R)
SINH(R) REAL sinh(R)
SQRT(R) REAL R
TAN(R) REAL tan(R)
TANH(R) REAL tanh(R)
Figure 18: Some common intrinsic functions
9.2 External functions
PROGRAM MAIN
. . . .
. . . .
END
FUNCTION FUN1(arg1,...)
. . . .
. . . .
END
FUNCTION FUN2(arg1,...)
. . . .
. . . .
END
Figure 19: A Fortran source file
containing two functions
9.2.1 The FUNCTION statement
[type] FUNCTION name([argument_list])
9.2.1.1 Type
FUNCTION FUN1(arg1,...)
returns a value of type REAL, but
INTEGER FUNCTION FUN1(arg1,...)
returns a value of type INTEGER.
INTEGER FUN1
9.2.1.2 The argument list
FUNCTION FUN1(A,B,N)
REAL A(100)
INTEGER B
Here, A represents a REAL array of dimension 100, and
B and N represent INTEGER variables.
FUNCTION NOARGS()
9.2.2 The function reference
REAL X(100)
. . .
RESULT = FUN1(X,J,10)
would be a valid reference to the function FUN1(A,B,N)
shown above.
REAL X(5,10)
. . .
Y = FUN(X,5,10)
. . .
END
FUNCTION FUN(A,M,N)
REAL A(M,N)
. . .
9.2.2.1 Actual and dummy arguments
Arrays as arguments
FUNCTION FUN(A)
REAL A(9,6)
. . .
END
is referenced by program MAIN as follows:
PROGRAM MAIN
REAL X(100),Y(0:5,-10,10)
. . .
F1 = FUN(X)
F2 = FUN(Y)
. . .
END
Then the correspondence between some elements of the dummy array
A and the actual arrays X and Y in
the two function references is as shown below:
A(1,1) X(1) Y(0,-10)
A(6,1) X(6) Y(5,-10)
A(7,1) X(7) Y(0,-9)
A(1,2) X(10) Y(3,-9)
A(5,4) X(32) Y(1,-5)
A(9,6) X(54) Y(5,-2)
If the actual argument is an array element, the first element
of the dummy array corresponds to that element. Thus, if the function
references:
F3 = FUN(X(15))
F4 = FUN(Y(3,0))
were included in the program above, the following items would
correspond in the two references:
A(1,1) X(15) Y(3,0)
A(4,1) X(18) Y(0,1)
A(9,1) X(23) Y(5,1)
A(1,2) X(24) Y(0,2)
A(5,4) X(46) Y(4,5)
A(9,6) X(68) Y(2,9)
Such complicated relationships between actual and dummy arguments
can sometimes be useful, but are in general best avoided for reasons
of clarity.
9.2.3 Evaluation of a function
RETURN
FUNCTION DGTORD(DEG)
INTEGER DEG
CONFAC = ATAN(1.0)/45.0
DGTORD = DEG*CONFAC
RETURN
END
As a second example, the following function returns the mean of
an array of N real numbers.
REAL FUNCTION MEAN(A,N)
REAL A(N)
SUM = 0.0
DO 10, I=1,N
SUM = SUM+A(I)
10 CONTINUE
MEAN = SUM/N
RETURN
END
Note that, since the type of this function differs from that implied
by the first letter of its name, any program referring to it must
declare the name in a type specification, e.g.
REAL MEAN
9.3 Statement functions
name is the name of the statement function.
argument_list is a list of dummy arguments.
expression is an expression which may include constants, variables
and array elements defined in the same program unit, and
function references.
The declaration must be placed after all type specifications,
but before the first executable statement.
DGTORD(DEGREE) = DEGREE*ATAN(1.0)/45.0
INTEGER DEGREE(100)
the dummy argument DEGREE would be an INTEGER
variable, not an array.
DGTORD(IDEG) = IDEG*ATAN(1.0)/45.0
expression may include references to functions, including
statement functions. Any statement function must have been previously
defined in the same program unit.
SUBROUTINE name[(argument_list)]
where name and
argument_list
have the same meanings as in the FUNCTION statement.
The square brackets indicate that the item (argument_list)
is optional, i.e. a subroutine may have no arguments, in which
case the SUBROUTINE statement is simply:
SUBROUTINE name
As for a function, a subroutine must include at least one RETURN
statement to return control to the program unit referring to it.
CALL name[(argument_list)]
where argument_list is a list of actual arguments corresponding
to the dummy arguments in the SUBROUTINE statement. The
rules governing the relationship between actual and dummy arguments
are the same as for functions.
SUBROUTINE HEADER(PAGENO,OUTPUT)
C PRINT PAGE HEADER, NUMBER AND COLUMN HEADERS
INTEGER PAGENO,OUTPUT
PAGENO = PAGENO+1
WRITE(OUTPUT,100)PAGENO
100 FORMAT(1H1//1X,'DEGREES TO RADIANS CONVERSION TABLE',
* T74,'PAGE',I2//1X,'DEGREES RADIANS'/)
RETURN
END
Note that the argument OUTPUT is used to receive a value
from the calling program, while PAGENO both receives
and returns a value.
PROGRAM ANGLES
INTEGER DEGREE,PAGENO,OUT
DATA OUT/6/
C UNIT NUMBER FOR OUTPUT. A DIFFERENT DEVICE COULD BE USED BY
C CHANGING THIS VALUE
DATA PAGENO/0/
DO 10, DEGREE = 1,360
N = DEGREE-1
IF (N/40*40 .EQ. N) THEN
CALL HEADER(PAGENO,OUT)
ELSE IF (N/10*10 .EQ.N) THEN
WRITE(OUT,110)
END IF
WRITE(OUT,120)DEGREE,DGTORD(DEGREE)
10 CONTINUE
110 FORMAT(1X)
120 FORMAT(1X,I5,T10,F7.5)
END
Figure 20: Degrees to radians conversion program (version 4)
EXTERNAL list
INTRINSIC list
PROGRAM MAIN
EXTERNAL ANALYS
INTRINSIC SQRT
. . .
CALL SUB1(ANALYS,SQRT,A,B)
. . . .
END
SUBROUTINE SUB1(SUB,FUN,X,Y)
EXTERNAL FUN
. . .
CALL SUB(...)
. . .
CALL SUB2(FUN,X,Y)
. . .
END
SUBROUTINE SUB2(F,P,Q)
. . .
Q = F(P)
. . .
END
Figure 21: Procedures as arguments
PROGRAM MAIN
EXTERNAL COT
INTRINSIC SIN,COS,TAN
. . .
CALL TRIG(ANGLE,SIN,SINE)
. . .
CALL TRIG(ANGLE,COS,COSINE)
. . .
CALL TRIG(ANGLE,TAN,TANGT)
. . .
CALL TRIG(ANGLE,COT,COTAN)
. . .
END
SUBROUTINE TRIG(X,F,Y)
Y = F(X)
RETURN
END
FUNCTION COT(X)
COT = 1.0/TAN(X)
RETURN
END
Figure 22: Subroutine to compute
any trigonometric function.
9.6 Local variables
SAVE [variable_list]
where variable_list is a list of local
variables, separated by commas. The statement causes the values
of all variables in variable_list to be
saved. If variable_list is omitted, the values
of all local variables are saved.
FUNCTION AVE(X,Y)
INTEGER COUNT
SAVE COUNT
DATA COUNT/0/
COUNT = COUNT+1
WRITE(6,10)COUNT
. . .
10 FORMAT(1X,'FUNCTION AVE REFERENCED',I3,' TIMES.')
. . .
END
First page
-10- The type CHARACTER
10.2 CHARACTER variables
CHARACTER[*len] var[*vlen] [,var[*vlen]] ...
len and vlen are unsigned INTEGER constants or constant
expressions in parentheses.
CHARACTER var [,var]...
which specifies that each CHARACTER variable var contains
one character
CHARACTER*len var [,var]...
specifies that each CHARACTER variable var contains len
characters.
CHARACTER var[*vlen] [,var[*vlen]]...
may be used to specify a different length vlen for each
variable var. If *vlen is omitted, one
character is assigned.
CHARACTER*len var[*vlen] [,var[*vlen]]...
specifies that if a variable var is followed by *vlen
it contains vlen characters, and otherwise it contains
len characters.
CHARACTER*4 A,B*6,C
10.2.1 CHARACTER arrays
CHARACTER*4 A(3,4),B(10,20)*6
This declares two CHARACTER arrays: A with 12 elements
each 4 characters long, and B with 200 elements each
6 characters long.
PROGRAM CHAREX
CHARACTER*4 A*3,B,C
A = 'END'
B = A
C = 'FINAL'
STOP
END
Results:
Value
Figure 23: Character assignment
A 'END'
B 'END '
C 'FINA'
10.3 CHARACTER expressions
A = 'JIM'//'MY'
assigns a value of 'JIMMY' to A.
10.3.2 Extraction of a substring
Substring Value
A substring reference can be used in the same way as a CHARACTER
variable. Thus part of a string can be changed by an assignment
to a substring.
LANG(1:1) 'F'
LANG(1:7) 'FORTRAN'
LANG(2:3) 'OR'
LANG(7:7) 'N'
LANG(:4) 'FORT'
LANG(5:) 'RAN'
LANG(4:7) = 'MATS'
10.4 Input and output
PRINT *,'THIS IS A STRING.'
Character strings can be used in formatted input and output with
the A format descriptor, which has the form A or Aw,
where w is the field width in characters. The effect for
input and output is shown in Figure 24.
Descriptor Input Output
Aw
Input w characters.
Output characters in the next
w character positions.
A
Input sufficient characters
Output the output list item
to fill the input list item
with no leading or trailing
blanks.
PROGRAM CHROUT
CHARACTER*4 A,B
A = 'WHAT'
B = 'FOR '
WRITE(2,100)A,B
100 FORMAT(1H ,A6,3X,A3)
STOP
END
Output:
bbWHATbbbFOR
PROGRAM CHRIN
CHARACTER*4 A,B
READ(1,200)A,B
200 FORMAT(A6,3X,A3)
STOP
END
Result:
10.5 Logical expressions
Figure 26: Collating rules
or:
' '.LE.'A' then evaluates to .TRUE..
'XA'.LT.'X4'
'VAR-1'.LT.'VAR.1'
is undefined by the collating rules of Figure 26. In the first
example, the rules do not stipulate whether letters come before
or after digits, while in the second example, the characters '-'
and '.' are not included in the rules. The value of such expressions
depends on the coding scheme used by the computer system.
First page
-11- Additional information types
11.1.1 DOUBLE PRECISION constants
1D-7
14713D-3
12.7192D0
9.413D5
11.1.2 DOUBLE PRECISION variables
DOUBLE PRECISION variable_list
where variable_list is a list of variables, separated
by commas.
COMPLEX variable_list
PROGRAM COMPLX
COMPLEX A,B,C
READ(5,100)A,B
C = A*B
WRITE(6,200)A,B,C
100 FORMAT(2F10.3)
200 FORMAT(1HO,' A = (',F10.3,',',F10.3,')'/
1 1HO,' B = (',F10.3,',',F10.3,')'/
2 1H0,' A*B =',F8.3,' + I',F8.3)
STOP
END
Results:
A = ( 12.500, 8.400)
B = ( 6.500 9.600)
C = 0.610 + I 174.600
Figure 27: Complex numbers example
Name
Type
Definition
AIMAG(C)
REAL
Imaginary part
CMPLX(IRD1,IRD2)
COMPLEX
Complex number: (IRD1,IRD2)
CONJG(C)
COMPLEX
Complex conjugate
REAL(C)
REAL
Real part
First page
-12- Other Fortran 77 features
12.1 EQUIVALENCE
An EQUIVALENCE statement is used to specify the sharing of
the same storage units by two or more variables or arrays.
PROGRAM EQUIV
COMPLEX*16 CMPLX(2)
REAL*8 TAMPON(4)
CHARACTER*8 STR
CHARACTER*1 TC(8)
EQUIVALENCE (TAMPON(1), CMPLX(1))
EQUIVALENCE (STR, TC(1))
STR = 'ABCDEFGH'
DO 10 I=1,4
TAMPON(I)=I
10 CONTINUE
PRINT *, 'TC(3)=', TC(3), ' TC(4)=', TC(4)
PRINT *, 'CMPLX(1)=', CMPLX(1), ' CMPLX(2)=', CMPLX(2)
END
Result:
TC(3)=C TC(4)=D
CMPLX(1)=(1.0,2.0) CMPLX(2)=(3.0,4.0)
< CMPLX(1) >< CMPLX(2) >
Memoy ...==><===========><===========><==========><===========><==...
< TAMPON(1) >< TAMPON(2) >< TAMPON(3)>< TAMPON(4) >
Figure 29: equivalenced objects
12.2 COMMON
The COMMON statement specifies blocks of physical storage, called
common blocks that may be accessed by any of the functions or subroutines
of a program. Thus, the COMMON provides a global facility
based on storage association.
COMMON X1, TAB(10)
COMMON/BLOC1/ A, B, MAT(10, 15)
REAL B(50)
EQUIVALENCE (TAB(1), MAT(1,1))
EQUIVALENCE (TAB(1), B(1))
12.3 BLOCKDATA
BLOCK DATA INIT
COMMON/BLOC1/ A, B, MAT(10, 15)
DATA A /0./, B /3.14/, MAT /150 * 0.0/
END
12.4 Other obsolescent features
These features should not any more be used as they will get out of the future
Fortran standards. We document them for those who need to migrate their
Fortran 77 old programs to Fortran 90 and above.
12.4.1 Arithmetic IF
Its' a conditional GOTO. According to the value of an
INTEGER expression, this statement allows branching to one
of three specified labels.
IF(I+2) 10, 20 ,30
. . .
10 . . .
. . .
20 . . .
. . .
30 . . .
. . .
If the value of the integer expression (here I+2) is :
12.4.2 Computed GOTO
Its' a conditional GOTO. According to the value of an
INTEGER expression, this statement allows branching to one
of a list of specified labels.
IF(10, 20 ,30, 40), I+2
. . .
10 . . .
. . .
20 . . .
. . .
30 . . .
. . .
40 . . .
. . .
If the value of the integer expression (here I+2) is :
First page
-13- Writing and testing programs
First page -14- The standard ASCII table
Character
decimal
hexa.
octal
Character
decimal
hexa.
octal
C-@ (NUL) 0 0x00 000 espace 32 0x20 040
C-a (SOH) 1 0x01 001 ! 33 0x21 041
C-b (STX) 2 0x02 002 " 34 0x22 042
C-c (ETX) 3 0x03 003 # 35 0x23 043
C-d (EOT) 4 0x04 004 $ 36 0x24 044
C-e (ENQ) 5 0x05 005 % 37 0x25 045
C-f (ACK) 6 0x06 006 & 38 0x26 046
C-g (BEL) 7 0x07 007 ' 39 0x27 047
C-h (BS) 8 0x08 010 ( 40 0x28 050
C-i (HT) 9 0x09 011 ) 41 0x29 051
C-j (LF) 10 0x0a 012 * 42 0x2a 052
C-k (VT) 11 0x0b 013 + 43 0x2b 053
C-l (FF) 12 0x0c 014 , 44 0x2c 054
C-m (CR) 13 0x0d 015 - 45 0x2d 055
C-n (SO) 14 0x0e 016 . 46 0x2e 056
C-o (SI) 15 0x0f 017 / 47 0x2f 057
C-p (DLE) 16 0x10 020 0 48 0x30 060
C-q (DC1) 17 0x11 021 1 49 0x31 061
C-r (DC2) 18 0x12 022 2 50 0x32 062
C-s (DC3) 19 0x13 023 3 51 0x33 063
C-t (DC4) 20 0x14 024 4 52 0x34 064
C-u (NAK) 21 0x15 025 5 53 0x35 065
C-v (SYN) 22 0x16 026 6 54 0x36 066
C-w (ETB) 23 0x17 027 7 55 0x37 067
C-x (CAN) 24 0x18 030 8 56 0x38 070
C-y (EM) 25 0x19 031 9 57 0x39 071
C-z (SUB) 26 0x1a 032 : 58 0x3a 072
C-[ (ESC) 27 0x1b 033 ; 59 0x3b 073
C-\ (FS) 28 0x1c 034 < 60 0x3c 074
C-] (GS) 29 0x1d 035 = 61 0x3d 075
C-$ (RS) 30 0x1e 036 > 62 0x3e 076
C-_ (US) 31 0x1f 037 ? 63 0x3f 077
Character
decimal
hexa.
octal
Character
decimal
hexa.
octal
@ 64 0x40 100 ` 96 0x60 140
A 65 0x41 101 a 97 0x61 141
B 66 0x42 102 b 98 0x62 142
C 67 0x43 103 c 99 0x63 143
D 68 0x44 104 d 100 0x64 144
E 69 0x45 105 e 101 0x65 145
F 70 0x46 106 f 102 0x66 146
G 71 0x47 107 g 103 0x67 147
H 72 0x48 110 h 104 0x68 150
I 73 0x49 111 i 105 0x69 151
J 74 0x4a 112 j 106 0x6a 152
K 75 0x4b 113 k 107 0x6b 153
L 76 0x4c 114 l 108 0x6c 154
M 77 0x4d 115 m 109 0x6d 155
N 78 0x4e 116 n 110 0x6e 156
O 79 0x4f 117 o 111 0x6f 157
P 80 0x50 120 p 112 0x70 160
Q 81 0x51 121 q 113 0x71 161
R 82 0x52 122 r 114 0x72 162
S 83 0x53 123 s 115 0x73 163
T 84 0x54 124 t 116 0x74 164
U 85 0x55 125 u 117 0x75 165
V 86 0x56 126 v 118 0x76 166
W 87 0x57 127 w 119 0x77 167
X 88 0x58 130 x 120 0x78 170
Y 89 0x59 131 y 121 0x79 171
Z 90 0x5a 132 z 122 0x7a 172
[ 91 0x5b 133 { 123 0x7b 173
\ 92 0x5c 134 | 124 0x7c 174
] 93 0x5d 135 } 125 0x7d 175
^ 94 0x5e 136 ~ 126 0x7e 176
_ 95 0x5f 137 C-? 127 0x7f 177
First page
-15- Copyright
(webperson@strath.ac.uk)
IDRIS adaptation by Hervé Delouis (delouis@idris.fr)
and Patrick Corde (corde@idris.fr)
First page