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Professional Programmers Guide to Fortran77
Clive G. Page, University of Leicester, UK 22nd February 1995

This le contains the text of Professional Programmer's Guide to Fortran77 published by Pitman in 1988. Since the book has now gone out of print, it seemed reasonable to make the text available free of charge over the Internet. The ISO Standard for Fortran77 is, of course, now obsolete, since Fortran90 has replaced it. Until compilers for the latter become more widely available, however, many programmers are still using Fortran77. I am retaining all rights to this text, except that it may be copied and reproduced without fee, as long as attribution to the author is preserved. a This le is written in L TEXand is called prof77.tex: it is substantially the same as the published version but the opportunity has been taken to correct a few mistakes and make some minor updates. The book was intentionally kept as short as possible so it could be sold at a modest price. Even so it covers the entire Fortran77 language as dened in the ANSI and ISO Standards including several topics which are often omitted from much larger textbooks because they are deemed to be too \advanced". In order to encourage the writing of clear, reliable, portable, robust, and well structured code, short sections appear throughout the book oering specic guidance on the practical use of Fortran. Obsolete or super uous features of the language, mainly those which have been retained for compatibility with earlier versions of Fortran, are omitted from the main text but are covered in the section 13. This is provided solely for the assistance of those who have to cope with existing poorly-written programs or ones which pre-date the Fortran77 standard.

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Clive G. Page, 1988, 1995

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CONTENTS

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Contents
1.1 1.2 1.3 1.4

1 What Is Fortran?

Early Development : : : : Standardization : : : : : : Strengths and Weaknesses Precautions : : : : : : : :

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2 Basic Fortran Concepts
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2 3.3 3.4 3.5

Statements : : : : : : : : : : Expressions and Assignments Integer and Real Data Types DO Loops : : : : : : : : : : : Formatted Output : : : : : : Functions : : : : : : : : : : : IF-blocks : : : : : : : : : : : Arrays : : : : : : : : : : : : : The Fortran System : Creating the Source Co Compiling : : : : : : : Linking : : : : : : : : Program Development

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3 Fortran in Practice

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4 Program Structure and Layout
4.1 4.2 4.3 4.4 4.5 4.6 4.7 The Fortran Character Set : Statements and Lines : : : Program Units : : : : : : : StatementTypes and Order Symbolic Names : : : : : : PROGRAM Statement : : : : : END Statement : : : : : : : Data Types : : : : : Constants : : : : : : Specifying Data Type Named Constants : : Variables : : : : : : Arrays : : : : : : : :

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5 Constants, Variables, and Arrays
5.1 5.2 5.3 5.4 5.5 5.6

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6 Arithmetic

6.1 Arithmetic Expressions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 39 6.2 Arithmetic Intrinsic Functions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 6.3 Arithmetic Assignment Statements : : : : : : : : : : : : : : : : : : : : : : : : : : 45 7.1 Character Facilities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 46

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7 Character Handling and Logic

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CONTENTS
7.2 7.3 7.4 7.5 7.6 7.7 7.8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Character Substrings : : : : : : : Character Expressions : : : : : : Character Assignment Statements Character Intrinsic Functions : : Relational Expressions : : : : : : Logical Expressions : : : : : : : : Logical Assignment Statements : Control Structures : : : : : : : IF-Blocks : : : : : : : : : : : : DO-Loops : : : : : : : : : : : : Logical-IF Statement : : : : : : Unconditional GO TO Statement Computed GO TO Statement : : STOP Statement : : : : : : : : :

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8 Control Statements

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9 Procedures
9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12

Intrinsic Functions : : : : : : : : : : StatementFunctions : : : : : : : : : External Procedures : : : : : : : : : Arguments of External Procedures : Variables as Dummy Arguments : : Arrays as Arguments : : : : : : : : : Procedures as Arguments : : : : : : Subroutine and Call Statements : : : RETURN Statement : : : : : : : : : : FUNCTION Statement : : : : : : : : : SAVE Statement : : : : : : : : : : : : EXTERNAL and INTRINSIC Statements

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10 Input/Output Facilities

10.1 Files, I/O Units, and Records : : : : : : : 10.2 External Files : : : : : : : : : : : : : : : : 10.3 Internal Files : : : : : : : : : : : : : : : : 10.4 Pre-Connected Files : : : : : : : : : : : : 10.5 Error and End-Of-File Conditions : : : : 10.6 Format Specications : : : : : : : : : : : 10.7 Format Edit Descriptors : : : : : : : : : : 10.8 Format Data Descriptors A, E, F, G, I, 10.9 Format Control Descriptors : : : : : : : : 10.10List-Directed Formatting : : : : : : : : : : 10.11Carriage-Control and Printing : : : : : : : 10.12Input/Output Statements and Keywords : 10.13OPEN Statement : : : : : : : : : : : : : : : 10.14CLOSE Statement : : : : : : : : : : : : : : 10.15INQUIRE Statement : : : : : : : : : : : : : 10.16READ and WRITE Statements : : : : : : : :

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CONTENTS
10.17
REWIND

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DATA

11.1 11.2 11.3 11.4 11.5

Dened and Undened Values : Initialising Variables : : : : : : Initialising Arrays : : : : : : : DATA Statements in Procedures General Rules : : : : : : : : : :

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12 Common Blocks

12.1 Using Common Blocks : : : 12.2 Blank Common Blocks : : : 12.3 COMMON Statement : : : : : 12.4 BLOCK DATA Program Units

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13 Obsolete and Deprecated Features

13.1 Storage of Character Strings in Non-character 13.2 Arithmetic IF Statement : : : : : : : : : : : : 13.3 ASSIGN and assigned GO TO Statements : : : 13.4 PAUSE Statement : : : : : : : : : : : : : : : : 13.5 Alternate RETURN : : : : : : : : : : : : : : : : 13.6 ENTRY Statement : : : : : : : : : : : : : : : : 13.7 EQUIVALENCE Statement : : : : : : : : : : : : 13.8 Specic Names of Intrinsic Functions : : : : : 13.9 PRINT Statement and simplied READ : : : : : 13.10END FILE Statement : : : : : : : : : : : : : : 13.11Obsolete Format Descriptors : : : : : : : : :

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14 Appendix A { List of Intrinsic Functions 15 Appendix B { Specic Names of Generic Functions

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1 WHATIS FORTRAN?

5

1 What Is Fortran?
Fortran is the most widely used programming language in the world for numerical applications. It has achieved this position partly by being on the scene earlier than any of the other ma jor languages and partly because it seems gradually to have evolved the features which its users, especially scientists and engineers, found most useful. In order to retain compatibility with old programs, Fortran has advanced mainly by adding new features rather than by removing old ones. The net result is, of course, that some parts of the language are, by present standards, rather archaic: some of these can be avoided easily, others can still be a nuisance. This section gives a brief history of the language, outlines its future prospects, and summarises its strengths and weaknesses.

1.1 Early Development

Fortran was invented by a team of programmers working for IBM in the early nineteen-fties. This group, led by John Backus, produced the rst compiler, for an IBM 704 computer, in 1957. They used the name Fortran because one of their principal aims was \formula translation". But Fortran was in fact one of the very rst high-level language: it came complete with control structures and facilities for input/output. Fortran became popular quite rapidly and compilers were soon produced for other IBM machines. Before long other manufacturers were forced to design Fortran compilers for their own hardware. By 1963 all the ma jor manufacturers had joined in and there were dozens of dierentFortran compilers in existence, many of them rather more powerful than the original. All this resulted in a chaos of incompatible dialects. Some order was restored in 1966 when an American national standard was dened for Fortran. This was the rst time that a standard had ever been produced for a computer programming language. Although it was very valuable, it hardly checked the growth of the language. Quite deliberately the Fortran66 standard only specied a set of language features which had to be present: it did not prevent other features being added. As time went on these extensions proliferated and the need for a further standardization exercise became apparent. This eventually resulted in the current version of the language: Fortran77.

1.2 Standardization

One of the most important features of Fortran programs is their portability, that is the ease with which they can be moved from one computer system to another. Now that each generation of hardware succeeds the previous one every few years, while good software often lasts for much longer, more and more programs need to be portable. The growth in computer networks is also encouraging the development of portable programs. The rst step in achieving portability is to ensure that a standard form of programming language is acceptable everywhere. This need is now widely recognised and has resulted in the development of standards for all the ma jor programming languages. In practice, however, many of the new standards have been ignored and standard-conforming systems for languages like Basic and Pascal are still very rare. Fortunately Fortran is in much better shape: almost all currentFortran systems are designed to conform to the standard usually called Fortran77. This was produced in 1977 by a committee of the American National Standards Institute (ANSI) and was subsequently adopted by the International Standards Organisation (ISO). The denition was published as ANSI X3.9-1978 and ISO 1539-1980. The term \Standard Fortran" will be used in the rest of this book to refer

1 WHATIS FORTRAN?

6

to mean Fortran77 according to this denition. Fortran is now one of the most widely used computer languages in the world with compilers available for almost every type of computer on the market. Since Fortran77 is quite good at handling character strings as well as numbers and also has powerful le-handling and input/output facilities, it is suitable for a much wider range of applications than before.

Full and Subset Fortran
The ANSI Standard actually denes two dierent levels for Fortran77. The simpler form, subset Fortran, was intended for use on computers which were too small to handle the full language. Now that even personal computers are powerful enough to handle full Fortran77, subset Fortran is practically obsolete. This book, therefore, only describes full Fortran77.

Fortran90
The ISO Standard for Fortran90 has, ocially, replaced that for Fortran77. It introduces a wealth of new features many of them already in use in other high-level languages, which will make programming easier, and facilitate the construction of portable and robust programs. The whole of the Fortran77 Standard is included as a proper subset, so existing (standardconforming) Fortran programs will automatically conform also to the new Standard. Until well-tested compilers for Fortran90 are widespread, however, most programmers are still using Fortran77, with perhaps a few minor extensions.

1.3 Strengths and Weaknesses

Fortran has become popular and widespread because of its unique combination of properties. Its numerical and input/output facilities are almost unrivalled while those for logic and character handling are as good as most other languages. Fortran is simple enough that you do not need to be a computer specialist to become familiar with it fairly quickly,yet it has features, suchasthe independent compilation of program units, which allow it to be used on very large applications. Programs written in Fortran are also more portable than those in other ma jor languages. The eciency of compiled code also tends to be quite high because the language is straight-forward to compile and techniques for handling Fortran have reached a considerable degree of renement. Finally, the ease with which existing procedures can be incorporated into new software makes it especially easy to develop new programs out of old ones. It cannot be denied, however, that Fortran has more than its fair share of weaknesses and drawbacks. Many of these have existed in Fortran since it was rst invented and oughtto have been eliminated long ago: examples include the 6-character limit on symbolic names, the xed statementlayout, and the need to use statement labels. Fortran also has rather liberal rules and an extensive system of default values: while this reduces programming eort it also makes it harder for the system to detect the programmer's mistakes. In many other programming languages, for example, the data type of every variable has to be declared in advance. Fortran does not insist on this but, in consequence, if you make a spelling mistakein a variable name the compiler is likely to use twovariables when you only intended to use one. Such errors can be serious but are not always easy to detect. Fortran also lacks various control and data structures which simplify programming languages with a more modern design. These limitations, and others, are all eliminated with the advent of Fortran90.

1 WHATIS FORTRAN?

7

1.4 Precautions

Extensions and Portability
Computer manufacturers have a natural tendency to compete with each other by providing Fortran systems which are \better" than before, usually by providing extensions to the language. This does not con ict with the Fortran Standard, provided that standard-conforming programs are still processed correctly. Indeed in the long term languages advance by the absorbtion of such extensions. In the short term, however, their use is more problematical, since they necessarily makes programs less portable. When the latest Fortran Standard was issued in 1977 there was fairly widespread disappointment that it did not go just a little further in eliminating some of the tiresome restrictions that had persisted since the early days. The US Department of Defense issued a short list of extensions which manufacturers were encouraged to add to their Fortran77 systems. The most important of these were the following: the END DO statement the DO WHILE loop the INCLUDE statement the IMPLICIT NONE facility intrinsic functions for bit-wise operations on integers. Many Fortran systems, especially those produced in the United States, now support these extensions but they are by no means universal and should not be used in portable programs. One of the most irksome restrictions of Fortran77 is that symbolic names cannot be more than six characters long. This forces programmers to devise all manner of contractions, abbreviations, and acronyms in place of meaningful symbolic names. It is very tempting to take advantage of systems which relax this rule but this can have serious repercussions. Consider a program which makes use of variables called TEMPERATURE and TEMPERED. Many compilers will be quite happy with these, though a few will reject both names on grounds of length. Unfortunately there are also one or two compilers in existence which will simply ignore all letters after the sixth so that both names will be taken as references to the same variable, TEMPER. Such behaviour, while deplorable, is quite in accordance with the Standard which only requires systems to compile programs correctly if they conform to its rules. The only way to be certain of avoiding problems like this is to ignore such temptations entirely and just use Standard Fortran. Many compilers provide a switch or option which can be set to cause all non-standard syntax to be agged. Everything covered in this book is part of Standard Fortran unless clearly marked to the contrary.

Guidelines

Computer programming always requires a very high standard of care and accuracy if it is to be successful. This is even more vital when using Fortran than with some other languages, because, as explained above, the liberal rules of Fortran make it harder for the system to detect mistakes. To program successfully it is not enough just to conform to the rules of the language, it is also important to defend yourself against known pitfalls. There is a useful lesson to be learned from the failure of one of the earliest planetary probes launched by NASA. The cause of the failure was eventually traced to a statement in its control

2 BASIC FORTRAN CONCEPTS
software similar to this:
DO 15 I = 1.100 DO 15 I = 1,100

8

when what should have been written was: but somehow a dot had replaced the comma. Because Fortran ignores spaces, this was seen by the compiler as: which is a perfectly valid assignmentto a variable called DO15I and not at all what was intended. Fortran77 permits an additional comma to be inserted after the label in a DO statement, so it could now be written as: which has the great advantage that it is no longer as vulnerable to a single-point failure. There are many hazards of this sort in Fortran, but the risk of falling victim to them can be minimised by adopting the programming practices of more experienced users. To help you, various recommendations and guidelines are given throughout this book. Some of the most outdated and unsatisfactory features of Fortran are not described in the main part of the book at all but have been relegated to section 13. There is not room in a book of this size to go further into the techniques of program design and software engineering. As far as possible everything recommended here is consistent with the methods of modular design and structured programming, but you should study these topics in more detail before embarking on any large-scale programming pro jects.
DO 15,I = 1,100 DO15I = 1.100

2 Basic Fortran Concepts
This section presents some of the basic ideas of Fortran by showing some complete examples. In the interests of simplicity, the problems which these solve are hardly beyond the range of a good pocket calculator, and the programs shown here do not include various renements that would usually be present in professional software. They are, however, complete working programs which you can try out for yourself if you have access to a Fortran system. If not, it is still worth reading through them to see how the basic elements of Fortran can be put together into complete programs.

2.1 Statements

To start with, here is one of the simplest program that can be devised:
PROGRAM TINY WRITE(UNIT=*, FMT=*) 'Hello, world' END

As you can probably guess, all this program does is to send a rather trite message \Hello, world" to your terminal. Even so its layout and structure deserve some explanation. The program consists of three lines, each containing one statement. EachFortran statement must have a line to itself (or more than one line if necessary), but the rst six character positions on each line are reserved for statement labels and continuation markers. Since the statements in this example need neither of these features, the rst six columns of each line have been left blank. The PROGRAM statement gives a name to the program unit and declares that it is a main program unit. Other types of program unit will be covered later on. The program can be

2 BASIC FORTRAN CONCEPTS

9

called anything you like provided the name conforms to the Fortran rules; the rst character of a Fortran symbolic name must be a letter but, unfortunately, they cannot be more than six characters long in total. It is generally sensible to give the same name to the program and to the le which holds the Fortran source code (the original text). The WRITE statement produces output: the parentheses enclose a list of control items which determine where and in what form the output appears. UNIT=* selects the standard output le which is normally your own terminal; FMT=* selects a default output layout (technically known as list-directed format). Asterisks are used here, as in many places in Fortran, to select a default or standard option. This program could, in fact, have been made slightly shorter by using an abbreviated form of the WRITE statements:
WRITE(*,*) 'Hello, world'

Although the keywords UNIT= and FMT= are optional, they help to make the program more readable. The items in the control list, like those in all lists in Fortran, are separated by commas. The control information in the WRITE statement is followed by a list of the data items to be output: here there is just one item, a character constant which is enclosed in a pair of apostrophe (single quote) characters. An END statement is required at the end of every program unit. When the program is compiled (translated into machine code) it tells the compiler that the program unit is complete; when encountered at run-time the END statement stops the program running and returns control to the operating system. The Standard Fortran character set does not contain any lower-case letters so statements generally have to be written all in upper case. But Fortran programs can process as data any characters supported by the machine; character constants (such as the message in the last example) are not sub ject to this constraint.

2.2 Expressions and Assignments

The next example solves a somewhat more realistic problem: it computes the repayments on a xed-term loan (such as a home mortgage loan). The xed payments cover the interest and repay part of the capital sum; the annual payment can be calculated by the following formula: ) In this formula, rate is the annual interest rate expressed as a fraction; since it is more conventional to quote interest rates as a percentage the program does this conversion for us.
ny ear s

rate:amount payment = (1 (1 + rate)

PROGRAM LOAN WRITE(UNIT=*, FMT=*)'Enter amount, % rate, years' READ(UNIT=*, FMT=*) AMOUNT, PCRATE, NYEARS RATE = PCRATE / 100.0 REPAY = RATE * AMOUNT / (1.0 - (1.0+RATE)**(-NYEARS)) WRITE(UNIT=*, FMT=*)'Annual repayments are ', REPAY END

This example introduces two new forms of statement: the both of which can be used to assign new values to variables.

READ

and assignment statements,

2 BASIC FORTRAN CONCEPTS

10

The READ statement has a similar form to WRITE: here it reads in three numbers entered on the terminal in response to the prompt and assigns their values to the three named variables. FMT=* again selects list-directed (or free-format) input which allows the numbers to be given in any convenient form: they can be separated by spaces or commas or even given one on each line. The fourth statement is an assignment statement which divides PCRATE by 100 and assigns the result to another variable called RATE. The next assignment statement evaluates the loan repayment formula and assigns the result to a variable called REPAY. Several arithmetic operators are used in these expressions: as in most programming languages \/" represents division and \*" represents multiplication; in Fortran \**" is used for exponentiation, i.e. raising one number to the power of another. Note that two operators cannot appear in succession as this could be ambiguous, so that instead of \**-N" the form \**(-N)" has to be used. Another general point concerning program layout: spaces (blanks) are not signicant in Fortran statements so they can be inserted freely to improve the legibility of the program. When the program is run, the terminal dialogue will look something like this:
Enter amount, % rate, years 20000, 9.5, 15 Annual repayments are 2554.873

The answer given by your system may not be exactly the same as this because the number of digits provided by list-directed formatting depends on the accuracy of the arithmetic, which varies from one computer to another.

2.3 Integer and Real Data Types

The LOAN program would have been more complicated if it had not taken advantage of some implicit rules of Fortran concerning data types: this requires a little more explanation. Computers can store numbers in several dierent ways: the most common numerical data types are those called integer and real. Integer variables store numbers exactly and are mainly used to count discrete ob jects. Real variables are useful many other circumstances as they store numbers using a oating-point representation which can handle numbers with a fractional part as well as whole numbers. The disadvantage of the real data type is that oating-pointnumbers are not stored exactly: typically only the rst six or seven decimal digits will be correct. It is important to select the correct type for every data item in the program. In the last example, the number of years was an integer, but all of the other variables were of real type. The data type of a constant is always evident from its form: character constants, for example, are enclosed in a pair of apostrophes. In numerical constants the presence of a decimal point indicates that they are real and not integer constants: this is why the value one was represented as \1.0" and not just \1". There are several ways to specify the data type of a variable. One is to use explicit type statements at the beginning of the program. For example, the previous program could have begun like this:
PROGRAM LOAN INTEGER NYEARS REAL AMOUNT, PCRATE, RATE, REPAY

Although many programming languages require declarations of this sort for every symbolic name used in the program, Fortran does not. Depending on your point of view, this makes

2 BASIC FORTRAN CONCEPTS

11

Fortran programs easier to write, or allows Fortran programmers to become lazy. The reason that these declarations can often be omitted in Fortran is that, in the absence of an explicit declaration, the data type of any item is determined by the rst letter of its name. The general rule is: initial letters I-N integer type initial letters A-H and O-Z real type. In the preceding program, because the period of the loan was called NYEARS (and not simply YEARS) it automatically became an integer, while all the other variables were of real type.

2.4

DO

Although the annual repayments on a home loan are usually xed, the outstanding balance does not decline linearly with time. The next program demonstrates this with the aid of a DO-loop.
PROGRAM REDUCE WRITE(UNIT=*, FMT=*)'Enter amount, % rate, years' READ(UNIT=*, FMT=*) AMOUNT, PCRATE, NYEARS RATE = PCRATE / 100.0 REPAY = RATE * AMOUNT / (1.0 - (1.0+RATE)**(-NYEARS)) WRITE(UNIT=*, FMT=*)'Annual repayments are ', REPAY WRITE(UNIT=*, FMT=*)'End of Year Balance' DO 15,IYEAR = 1,NYEARS AMOUNT = AMOUNT + (AMOUNT * RATE) - REPAY WRITE(UNIT=*, FMT=*) IYEAR, AMOUNT CONTINUE END

Loops

15

The rst part of the program is similar to the earlier one. It continues with another WRITE statement which produces headings for the two columns of output which will be produced later on. The DO statement then denes the start of a loop: the statements in the loop are executed repeatedly with the loop-control variable IYEAR taking successivevalues from 1 to NYEARS. The rst statement in the loop updates the value of AMOUNT by adding the annual interest to it and subtracting the actual repayment. This results in AMOUNT storing the amount of the loan still owing at the end of the year. The next statement outputs the year number and the latest value of AMOUNT. After this there is a CONTINUE statement which actually does nothing but act as a place-marker. The loop ends at the CONTINUE statement because it is attached to the label, 15, that was specied in the DO statement at the start of the loop. The active statements in the loop have been indented a little to the right of those outside it: this is not required but is very common practice among Fortran programmers because it makes the structure of the program more conspicuous. The program REDUCE produces a table of values which, while mathematically correct, is not very easy to read:
Enter amount, % rate, years 2000, 9.5, 5 Annual repayments are 520.8728 End of Year Balance 1 1669.127 2 1306.822

2 BASIC FORTRAN CONCEPTS
3 4 5 910.0968 475.6832 2.9800416E-04

12

2.5 Formatted Output

The table of values would have a better appearance if the decimal points were properly aligned and if there were only two digits after them. The last gure in the table is actually less than a thirtieth of a penny, which is eectively zero to within the accuracy of the machine. A better layout can be produced easily enough by using an explicit format specication instead of the list-directed output used up to now. To do this, the last WRITE statement in the program should be replaced with one like this: The amended program will then produce a neater tabulation:
Enter amount, % rate, years 2000, 9.5, 5 Annual repayments are 520.8728 End of Year Balance 1 1669.13 2 1306.82 3 910.10 4 475.68 5 .00 WRITE(UNIT=*, FMT='(1X,I9,F11.2)') IYEAR, AMOUNT

The format specication has to be enclosed in parentheses and, as it is actually a character constant, in a pair of apostrophes as well. The rst item in the format list, 1X, is needed to cope with the carriage-control convention: it provides an additional blank at the start of each line which is later removed by the Fortran system. There is no logical explanation for this: it is there for compatibility with very early Fortran system. The remaining items specify the layout of eachnumber: I10 species that the rst number, an integer, should be occupy a eld 10 columns wide; similarly F11.2 puts the second number, a real ( oating-point) value, into a eld 11 characters wide with exactly 2 digits after the decimal point. Numbers are always rightjustied in each eld. The eld widths in this example have been chosen so that the columns of gures line up satisfactorily with the headings.

2.6 Functions

Fortran provides a useful selection of intrinsic functions to carry out various mathematical operations such as square root, maximum and minimum, sine, cosine, etc., as well as various data type conversions. You can also write your own functions. The next example, which computes the area of a triangle, shows both forms of function in action. The formulae for the area of a triangle with sides of length a, b, and c is:

area = [s:(s a):(s b):(s c)]
PROGRAM TRIANG WRITE(UNIT=*,FMT=*)'Enter lengths of three sides:'

q

s =(a + b + c)=2

2 BASIC FORTRAN CONCEPTS
READ(UNIT=*,FMT=*) SIDEA, SIDEB, SIDEC WRITE(UNIT=*,FMT=*)'Area is ', AREA3(SIDEA,SIDEB,SIDEC) END FUNCTION AREA3(A, B, C) *Computes the area of a triangle from lengths of sides S = (A + B + C)/2.0 AREA3 = SQRT(S * (S-A) * (S-B) * (S-C)) END

13

This program consists of two program units. The rst is the main program, and it has as similar form to those seen earlier. The only novel feature is that the list of items output by the WRITE statement includes a call to a function called AREA3. This computes the area of the triangle. It is an external function which is specied by means of a separate program unit technically known as a function subprogram. The external function starts with a FUNCTION statement which names the function and species its set of dummy arguments. This function has three dummy arguments called A, B, and C. The values of the actual arguments, SIDEA, SIDEB, and SIDEC, are transferred to the corresponding dummy arguments when the function is called. Variable names used in the external function have no connection with those of the main program: the actual and dummy argument values are connected only by their relative position in each list. Thus SIDEA transfers its value to A, and so on. The name of the function can be used as a variable within the subprogram unit; this variable must be assigned a value before the function returns control, as this is the value returned to the calling program. Within the function the dummy arguments can also be used as variables. The rst assignment statement computes the sum, divides it bytwo, and assigns it to a local variable, S; the second assignment statement uses the intrinsic function SQRT which computes the square-root of its argument. The result is returned to the calling program by assigning it to the variable which has the same name as the function. The END statement in a procedure does not cause the program to stop but just returns control to the calling program unit. There is one other novelty: a comment line describing the action of the function. Any line of text can be inserted as a commentanywhere except after an END statement. Comment lines have an asterisk in the rst column. These two program units could be held on separate source les and even compiled separately. An additional stage, usually called linking, is needed to construct the complete executable program out of these separately compiled ob ject modules. This seems an unnecessary overhead for such simple programs but, as described in the next section, it has advantages when building large programs. In this very simple example it was not really necessary to separate the calculation from the input/output operations but in more complicated cases this is usually a sensible practice. For one thing it allows the same calculation to be executed anywhere else that it is required. For another, it reduces the complexity of the program by dividing the work up into small independent units which are easier to manage.

2.7 IF-blocks

Another important control structure in Fortran is the IF statement which allows a block of statements to be executed conditionally, or allows a choice to be made between dierent courses

2 BASIC FORTRAN CONCEPTS

14

of action. One obvious defect of the function AREA3 is that has no protection against incorrect input. Many sets of three real numbers could not possibly form the sides of a triangle, for example 1.0, 2.0, and 7.0. A little analysis shows that in all such impossible cases the argument of the square root function will be negative, which is illegal. Fortran systems should detect errors like this at run-time but will vary in their response. Even so, a message like "negative argument for square-root" may not be enough to suggest to the user what is wrong. The next version of the function is slightly more user-friendly:
REAL FUNCTION AREA3(A, B, C) *Computes the area of a triangle from lengths of its sides. *If arguments are invalid issues error message and returns zero. REAL A, B, C S = (A + B + C)/2.0 FACTOR = S * (S-A) * (S-B) * (S-C) IF(FACTOR .LE. 0.0) THEN WRITE(UNIT=*, FMT=*)'Impossible triangle', A, B, C AREA3 = 0.0 ELSE AREA3 = SQRT(FACTOR) END IF END

The IF statement works with the ELSE and END IF statements to enclose two blocks of code. The statements in the rst block are only executed if the expression in the IF statement is true, those in the second block only if it is false. The statements in each block are indented for visibility, but this is, again, just a sensible programming practice. With this modication, the value of FACTOR is tested and if it is negative or zero then an error message is produced; AREA3 is also set to an impossible value (zero) to ag the mistake. Note that the form \.LE." is used because the less-than-or-equals character, \<", is not present in the Fortran character set. If S is positive the calculation proceeds as before.

2.8 Arrays

Fortran has good facilities for handling arrays. They can have up to seven dimensions. The program STATS reads a set of real numbers from a data le and puts them into a onedimensional array. It then computes their mean and standard deviation. Given an array of values x1 ;x2;x3; :::x , the mean standard deviation are given by:
N

= Nx
2=( (
P
i

P

i

x )2) = (P x2 N ) (N 1) (N 1)
i

To simplify this program, it will be assumed that the rst number in the le is an integer which tells the program how many real data points follow.
PROGRAM STATS CHARACTER FNAME*50

2 BASIC FORTRAN CONCEPTS
REAL X(1000) WRITE(UNIT=*, FMT=*) 'Enter data file name:' READ(UNIT=*, FMT='(A)') FNAME OPEN(UNIT=1, FILE=FNAME, STATUS='OLD') *Read number of data points NPTS READ(UNIT=1, FMT=*) NPTS WRITE(UNIT=*, FMT=*) NPTS, ' data points' IF(NPTS .GT. 1000) STOP 'Too many data points' READ(UNIT=1, FMT=*) (X(I), I = 1,NPTS) CALL MEANSD(X, NPTS, AVG, SD) WRITE(UNIT=*, FMT=*) 'Mean =', AVG, ' Std Deviation =', SD END SUBROUTINE MEANSD(X, NPTS, AVG, SD) INTEGER NPTS REAL X(NPTS), AVG, SD SUM = 0.0 SUMSQ = 0.0 DO 15, I = 1,NPTS SUM = SUM + X(I) SUMSQ = SUMSQ + X(I)**2 CONTINUE AVG = SUM / NPTS SD = SQRT(SUMSQ - NPTS * AVG)/(NPTS-1) END

15

15

This program has several new statement forms. The CHARACTER statement declares that the variable FNAME is to hold a string of 50 characters: this should be long enough for the le-names used by most operating systems. The REAL statement declares an array X with 1000 elements numbered from X(1) to X(1000). The READ statement uses a format item A which is needed to read in a character string: A originally stood for \alpha-numeric". The OPEN statement then assigns I/O unit number one (any small integer could have been used) to the le. This unit number is needed in subsequent input/output statements. The item STATUS='OLD' is used to specify that the le already exists. The IF statement is a special form which can replace an IF-block where it would only contain one statement: its eect is to stop the program running if the arraywould not be large enough. The READ statement which follows it has a special form known as an implied-DO-loop: this reads all the numbers from the le in to successive elements of the array X in one operation. The CALL statement corresponds to the SUBROUTINE statement in the same way that a function reference corresponded to a FUNCTION statement. The dierence is that the arguments X and NPTS transfer information into the subroutine, whereas AVG and SD return information from it. The direction of transfer is determined only by the way the dummy arguments are used within the subroutine. An argument can be used to pass information in either direction, or both. The INTEGER statement is, as before, not really essential but it is good practice to indicate clearly the data typeofevery procedure argument. The REAL statement declares that X is an array but uses a special option available only to dummy arguments: it uses another argument, NPTS, to specify its size and makes it an adjustable array. Normally in Fortran array bounds must be specied by constants, but the rules are relaxed

3 FORTRAN IN PRACTICE

16

for arrays passed into procedures because the actual storage space is already allocated in the calling program unit; the REAL statement here merely species how many of the 1000 elements already allocated are actually to be used within the subroutine. The rest of the subroutine uses a loop to accumulate the sum of the elements in SUM, and the sum of their squares in SUMSQ. It then computes the mean and standard deviation using the usual formulae, and returns these values to the main program, where they are printed out.

3 Fortran in Practice
This section describes the steps required to turn a Fortran program from a piece of text into executable form. The main operation is that of translating the original Fortran source code into the appropriate machine code. On a typical Fortran system this is carried out in two separate stages. This section explains how this works in more detail. These descriptions dier from those in the rest of the book in two ways. Firstly, it is not essential to understand howaFortran system works in order to use it, just as you do not have to know how an internal combustion engine works in order to drive a car. But, in both cases, those who have some basic understanding of the way in which the machine works nd it easier to get the best results. This is especially true when things start to go wrong { and most people nd that things go wrong all too easily when they start to use a new programming language. Secondly the contents of this section are much more system-dependent than all the others in the book. The Fortran Standard only species what a Fortran program should do when it is executed, it has nothing directly to say about the translation process. In practice, however, nearly all Fortran systems work in much the same way, so there should not be too many differences between the \typical" system described here and the one that you are actually using. Regrettably the underlying similarities are sometimes obscured by dierences in the terminology that dierent manufacturers use.

3.1 The Fortran System

The two main ways of translating a program into machine code are to use an interpreter or a compiler. An interpreter is a program which stays in control all the while the program is running. It translates the source code into machine code one line at a time and then executes that line immediately. It then goes on to translate the next, and so on. If an error occurs it is usually possible to correct the mistake and continue running the program from the point at which it left o. This can speed up program development considerably. The main snag is that all non-trivial programs involve forms of repetition, such as loops or procedure calls. In all these cases the same lines of source code are translated into machine code over and over again. Some interpreters are clever enough to avoid doing all the work again but the overhead cannot be eliminated entirely. The compiler works in an entirely dierentway. It is an independent program which translates the entire source code into machine code at once. The machine code is usually saved on a le, often called an executable image, which can then be run whenever it is needed. Because each statement is only translated once, but can be executed as many times as you like, the time take by the translation process is less important. Many systems provide what is called an optimising compiler which takes even more trouble and generates highly ecient machine code; optimised code will try to make the best possible use of fast internal registers and the compiler will analyse the source program in blocks rather than one line at a time. As a result, compiled programs usually run an order of magnitude faster than interpreted ones. The main disadvantage is that

3 FORTRAN IN PRACTICE

17

if the program fails in anyway, it is necessary to edit the source code and recompile the whole thing before starting again from the beginning. The error messages from a compiled program may also be less informative than those from an interpreter because the original symbolic names and line numbers may not be retained by the compiler. Interpreters, being more \user-friendly", are especially suitable for highly interactive use and for running small programs produced by beginners. Thus languages like APL, Basic, and Logo are usually handled by an interpreter. Fortran, on the other hand, is often used for jobs which consume signicant amounts of computer time: in some applications, such as weather forecasting, the results would simply be of no use if they were produced more slowly. The speed advantage of compilers is therefore of great importance and in practice almost all Fortran systems use a compiler to carry out the translation.

Separate Compilation
The principal disadvantage of a compiler is the necessity of re-compiling the whole program after making any alteration to it, no matter how small. Fortran has partly overcome this limitation by allowing program units to be compiled separately; these compiled units or modules are linked together afterwards into an executable program. A Fortran compiler turns the source code into what is usually called ob ject code: this contains the appropriate machine-code instructions but with relative memory addresses rather than absolute ones. All the program units can be compiled together, or each one can be compiled separately. Either way a set of ob ject modules is produced, one from each program unit. The second stage, which joins all the ob ject modules together, is usually known as linking, but other terms such as loading, link-editing, and task-building are also in use. The job of the linker is to collect up all these ob ject modules, allocate absolute addresses to each one, and produce a complete executable program, also called an executable image. The advantage of this two-stage system is that if changes are made to just one program unit then only that one has to be re-compiled. It is, of course, necessary to re-link the whole program. The operations which the linker performs are relatively simple so that linkers ought to be fast. Unfortunately this is not always so, and on some systems it can take longer to link a small program than to compile it.

3.2 Creating the Source Code

The rst step after writing a program is to enter it into the computer: these les are known as the source code. Fortran systems do not usually come with an editor of their own: the source les can be generated using any convenient text editor or word processor. Many text editors have options which ease the drudgery of entering Fortran statements. On some you can dene a single key-stroke to skip directly to the start of the statement eld at column 7 (but if the source les are to conform to the standard this should work by inserting a suitable number of spaces and not a tab character). An even more useful feature is a warning when you cross the right-margin of the statement eld at column 72. Most text editors makeit easy to delete and insert whole words, where a word is anything delimited by spaces. It helps with later editing, therefore, to put spaces between items in Fortran statements. This also makes the program more readable. Most programs will consist of several program units: these may go on separate les, all on one le, or any combination. On most systems it is not necessary for the main program unit to come rst. When rst keying in the program it may seem simpler to put the whole program on one le, but during program development it is usually more convenient to have each program

3 FORTRAN IN PRACTICE

18

unit on a separate le so that they can be edited and compiled independently. It minimises confusion if each source le has the same name as the (rst) program unit that it contains.
INCLUDE

Statements

Many systems provide a pseudo-statement called INCLUDE (or sometimes INSERT which inserts the entire contents of a separate text le into the source code in place of the INCLUDE statement. This feature can be particularly useful when the same set of statements, usually specication statements, has to be used in several dierent program units. Such is often the case when dening a set of constants using PARAMETER statements, or when declaring common blocks with a set of COMMON statements. INCLUDE statements reduce the key-punching eort and the risk of error. Although non-standard, INCLUDE statements do not seriously compromise portability because they merely manipulate the source les and do not alter the source code which the compiler translates.

3.3 Compiling

The main function of a Fortran compiler is to read a set of source les and write the corresponding set of ob ject modules to the ob ject le. Most compilers have a number of switches or options which can be set to control how the compiler works and what additional output it produces. Some of the more useful ones, found on many systems, are described below. Almost all compilers can produce a listing le: a text le containing a copy of the source code, with the lines numbered, and with error messages and other useful information attached. A list of all the symbolic names and labels used in the program unit is often provided: this should be checked for unexpected entries as they may be the result of spelling mistakes. An even more useful addition to the listing is a cross-reference table: this lists every place that each symbolic name has been used. Good compilers indicate which names have only been used once as these often indicate a programming mistake. Another widely available option is the detection of syntax which does not conform to the Fortran Standard: this helps to ensure program portability. Often it is possible to choose the optimization level. During program development a low level of optimization should be selected if this makes the compiler run faster; it may improve the error detection. Highly optimised machine code may execute faster but if the source code lines are rearranged error messages may be less helpful. Many systems allow additional code to be included which check for errors at run-time. Errors such as over-running the bounds of an array or a character string, or arithmetic over- ow can usually be trapped. Such errors are not uncommon, so this assistance is very valuable. Some programming manuals suggest that these options should only be selected during program development and switched-o thereafter in the interests of speed. This is rather like wearing seat-belts in the car only while you are learning to drive and ignoring them as soon as you are allowed out on the motorway. Run-time checks do not usually reduce the execution speed noticeably.

3 FORTRAN IN PRACTICE

19

3.4 Linking

At its simplest, the linker just takes the set of ob ject modules produced by the compiler and links them all together into an executable image. One of these modules must correspond to the main program unit, the other modules will correspond to procedures and to block data subprogram units. It often happens that a number of dierent programs require some of the same computations to be carried out. If these calculations can be turned into procedures and linked into each program it can save a great deal of programming eort, especially in the long run. This \building block" approach is particularly benecial for large programs. Many organisations gradually build up collections of procedures which become an important software resource. Procedures collected in this way tend to be fairly reliable and free from bugs, if only because they have been extensively tested and de-bugged in earlier applications.

Ob ject Libraries

It obviously saves on compilation time if these commonly-used procedures can be kept in compiled form as ob ject modules. Almost all operating systems allow a collection of ob ject modules to be stored in an ob ject library (sometimes known as a pre-compiled or relocatable-code library). This is a le containing a collection of ob ject modules together with an index which allows them to be extracted easily. Ob ject libraries are not only more ecient but also easier to use as there is only one le-name to specify to the linker. The linker can then work out for itself which modules are needed to satisfy the various CALL statements and function references encountered in the preceding ob ject modules. Ob ject libraries also simplify the management of a procedure collection and may reduce the amount of disc space needed. There are usually simple ways of listing the contents of an ob ject library, deleting modules from it, and replacing modules with new versions. All Fortran systems come with a system library which contains the ob ject modules for various intrinsic functions suchas SIN, COS, and SQRT. This is automatically scanned by the linker and does not have to be specied explicitly. Software is often available commercially in the form of procedure libraries containing modules which may be linked into any Fortran program. Those commonly used cover elds such as statistics, signal processing, graphics, and numerical analysis.

Linker Options
The order of the ob ject modules supplied to the linker does not usually matter although some systems require the main program to be specied rst. The order in which the library les are searched may be important, however, so that some care has to be exercised when several dierent libraries are in use at the same time. The principal output of the linker is a single le usually called the executable image. Most linkers can also produce a storage map showing the location of the various modules in memory. Sometimes other information is provided such as symbol tables whichmay be useful in debugging the program.

3.5 Program Development

The program development process consists of a number of stages some of whichmayhaveto be repeated several times until the end product is correct:

3 FORTRAN IN PRACTICE
1. Designing the program and writing the source-code text. 2. Keying in the text to produce a set of Fortran source les. 3. Compiling the source code to produce a set of ob ject modules. 4. Linking the ob ject modules and any ob ject libraries into a complete executable image. 5. Running the executable program on some test data and checking the results. The main parts of the process are shown in the diagram below.

20

Libraries...

Source-code

?

COMPILER

?

Ob ject-code

?

-

LINKER

Executable program

?

Figure 1: Compiling and Linking

-

optional source-listing

optional linker-map

4 PROGRAM STRUCTURE AND LAYOUT

21

Handling Errors
Things can go wrong at almost every stage of the program development process for a variety of reasons, most of them the fault of the programmer. Naturally the Fortran system cannot possibly detect all the mistakes that it is possible for human programmers to make. Errors in the syntax of Fortran statements can usually be detected by the compiler, which will issue error messages indicating what is wrong and, if possible, where. Other mistakes will only come to light at the linking stage. If, for example, you misspell the name of a subroutine or function the compiler will not be able to detect this as it only works on one program unit at a time, but the linker will say something like \unsatised external reference". This sort of message will sometimes appear if you misspell the name of an array since array and function references can have the same form. Most errors that occur at run-time are the result of programmer error, or at least failure to anticipate some failure mode. Even things like division by zero or attempting to access an array element which is beyond its declared bounds can be prevented by suciently careful programming. There is, however, a second category of run-time error which no amount of forethought can avoid: these nearly all involve the input/output system. Examples include trying to open a le which no longer exists, or nding corrupted data on an input le. For this reason most input/output errors can be trapped, using the IOSTAT= or ERR= keywords in any I/O statement. There is no way of trapping run-time errors in any other types of statement in Standard Fortran. But, just because a program compiles, links, and runs without apparent error, it is not safe to assume that all bugs have been eliminated. There are some types of mistake which will simply give you the wrong answer. The only way to become condent that a program is correct is to give it some test data, preferably for a case where the results can be calculated independently. When a program is too elaborate for its results to be predictable it should be split into sections which can be checked separately.

4 Program Structure and Layout
This section explains the rules for program construction and text layout. A complete Fortran program is composed of a number of separate program units. Each of these can contain both statements and comment lines. Statements are formed from items suchas keywords and symbolic names. These in turn consist of characters.

4.1 The Fortran Character Set

The only characters needed to write Fortran programs, and the only ones that should be used in portable software, are those in the Fortran character set: the 26 upper-case letters A B C ... X Y Z the 10 digits 0123456789 and 13 special characters:

4 PROGRAM STRUCTURE AND LAYOUT
+ *

22

plus - minus asterisk / slash blank = equals ( left parenthesis ) right parenthesis . decimal point , comma ' apostrophe : colon $ currency symbol Although this character set is somewhat limited, it is at least universally available, which helps to make programs portable. What suers is program legibility: lower-case letters are absent and it is necessary to resort to ugly constructions like .LT. and .GT. to represent operators like < and >. Some of the special characters, such as the asterisk and parentheses, are also rather overloaded with duties.

Blanks
The blank, or space, character is ignored everywhere in Fortran statements (except within character constants, which are enclosed in a pair of apostrophes). Although you do not need to separate items in Fortran statements with blanks, it is good practice to include a liberal helping of them since they improve legibility and often simplify editing. The only limitation (as explained below) is that statement lines must not extend beyond column 72.

Currency Symbol
The currency symbol has no xed graphic representation: it appears on most systems as the dollar \$", but other forms such as \$" equally valid. This variability does not matter much because the currency symbol is not actually needed in Standard Fortran syntax.

Other Characters
Most computers haveacharacter set which includes many other printable characters, for example lower-case letters, square brackets, ampersands and per-cent signs. Any printable characters supported by the machine may be used in comment lines and within character constants. The Fortran character set does not include any carriage-control characters such as tab, carriage-return, or form-feed, but formatted WRITE statements can be used to produce paginated and tabulated output les. Fortran programs can process as data any characters supported by the local hardware. The Fortran Standard is not based on the use of any particular character code but it requires its character comparison functions to use the collating sequence of the American Standard Code for Information Interchange (ASCII). Further details are given in section 7.6.

4.2 Statements and Lines

The statement is the smallest unit of a Fortran program, corresponding to what is called an instruction or command in some programming languages. Most types of statement start with a keyword which consists of one (or sometimes two) English words describing the main action of that statement, for example: READ, DO, ELSE IF, GO TO. Since blanks are ignored, compound keywords can be written either as one word or two: ELSEIF or ELSE IF (but the latter seems easier to read).

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The rules for statementlayout are an unfortunate relic of punched-card days. Every statement must start on a new line and each line is divided into three xed elds: columns 1 to 5 form the label eld, column 6 forms the continuation marker eld, columns 7 to 72 form the statement eld. Since labels and continuation markers are only needed on a few statements, the rst six columns of most lines are left blank. Anycharacters in column 73 or beyond are likely to be ignored (columns 73 to 80 were once used to hold card sequence numbers). This invisible boundary after column 72 demands careful attention as it can have very pernicious eects: it is possible for a statement to be truncated at the boundary but still be syntactically correct, so that the compiler will not detect anything wrong.

Continuation Lines
Statements do not have to t on a single line. The initial line of each statement should havea blank in column 6, and all subsequent lines, called continuation lines, must have some character other than blank (or the digit zero) in column 6. Up to 19 continuation lines are allowed, i.e. 20 in total. The column layout needed with continuation lines is illustrated here:
columns 123456789... IF(REPLY .EQ. 'Y' .OR. REPLY .EQ. 'y' .OR. $ REPLY .EQ. 'T' .OR. REPLY .EQ. 't') THEN

The currency symbol makes a good continuation marker since if accidentally misplaced into an adjacent column it would be almost certain to produce an error during compilation. The END statement is an exception to the continuation rule: it may not be followed by continuation lines and no other statement may have an initial line which just contains the letters \END". Neither rule causes many problems in practice. Programs which make excessive use of continuation lines can be hard to read and to modify: it is generally better, if possible, to divide a long statementinto several shorter ones.

Comment Lines
Comments form an important part of any computer program even though they are completely ignored by the compiler: their purpose is to help any human who has to read and understand the program (such as the original programmer six months later). Comments in Fortran always occupy a separate line of text; they are marked by an asterisk in the rst column. For example:
*Calculate the atmospheric refraction at PRESS mbar. REF = PRESS * (0.1594 + 1.96E-2 * A + 2E-5 * A**2) *Correct for the temperature T (Celsius) TCOR = (273.0 + T) * (1.0 + 0.505 * A + 8.45E-2 * A**2)

A commentmay appear at any point in a program unit except after the END statement (unless another program unit follows, in which case it will form the rst line of the next unit). A

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completely blank line is also allowed and is treated as a blank comment. This means that a blank line is not actually permitted after the last END statement of a program. There is no limit to the number of consecutive comment lines whichmay be used; comments may also appear in the middle of a sequence of continuation lines. To conform to the Fortran Standard, comment lines should not be over 72 characters long, but this rule is rarely enforced. Comments may include characters which are not in the Fortran character set. It helps to distinguish comments from code if they are mainly written in lower-case letters (where available). It is also good practice for comments to precede the statements they describe rather than follow them. Some systems allow end-of-line comments, usually prefaced by an exclamation mark: this is not permitted by the Fortran standard. For compatibility with Fortran66 comments can also be denoted by the letter C in column 1.

Statement Labels
A label can be attached to any statement. There are three reasons for using labels: the end of each DO-loop is specied by a label given in the DO statement; every FORMAT statementmust have a label attached as that is how READ and WRITE statements refer to it; any executable statementmayhave a label attached so that control may be transferred to it, for example bya GO TO statement. Example:
*Read numbers from input file until it ends, add them up. SUM = 0.0 100 READ(UNIT=IN, FMT=200, END=9999) VALUE 200 FORMAT(F20.0) SUM = SUM + VALUE GO TO 100 9999 WRITE(UNIT=*, FMT=*)'SUM of values is', SUM

Each label has the form of an unsigned integer in the range 1 to 99999. Blanks and leading zeros are ignored. The numerical value is irrelevant and cannot be used in a calculation at all. The label must appear in columns 1 to 5 of the initial line of the statement. In continuation lines the label eld must be blank. A label must be unique within a program unit but labels in dierent program units are quite independent. Although any statementmay be labelled, it only makes sense to attach a label to a FORMAT statement or an executable statement, since there is no way of using a label on any other type of statement. Statement labels are unsatisfactory because nearly all of them mark a point to which control could be transferred from elsewhere in the program unit. This makes it much harder to understand a program with many labelled statements. Unfortunately at present one cannot avoid using labels altogether in Fortran. If labels are used at all they should appear in ascending order and preferably in steps of 10 or 100 to allow for changes. Labels do not have to be right-justied in the label eld.

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4.3 Program Units

A complete executable program consists of one or more program units. There is always one (and only one) main program unit: this starts with a PROGRAM statement. There may also be anynumber of subprogram units of any of the three varieties: subroutine subprograms: these start with a SUBROUTINE statement function subprograms, also known as external functions: these start with a FUNCTION statement block data subprograms: these start with a BLOCK DATA statement. Subroutines and external functions are known collectively as external procedures; block data subprograms are not procedures and are used only for the special purpose of initialising the contents of named common blocks. Every program unit must end with an END statement.

Procedures

Subroutines and external functions are collectively known as external procedures: they are described in full in section 9. A procedure is a self-contained sequence of operations which can be called into action on demand from elsewhere in the program. Fortran supplies a number of intrinsic functions such as SIN, COS, TAN, MIN, MAX, etc. These are procedures which are automatically available when you need to use them in expressions. External functions can be used in similar ways: there maybe anynumber of arguments but only one value is returned via the function name. The subroutine is a procedure of more general form: it can have any number of input and output arguments but it is executed only in response to an explicit CALL statement. Procedures may call other procedures and so on, but a procedure may not call itself directly or indirectly; Fortran does not support recursive procedure calls. Most Fortran systems allow procedures to be written in other languages and linked with Fortran modules into an executable program. If the procedure interface is similar to that of a Fortran subroutine or function this presents no problem. The normal way to transfer information from one program unit to another is to use the argument list of the procedure as described in section 9, but it is also possible to use a common block: a shared area of memory. This facility, which is less modular, is described in section 12.

4.4 StatementTypes and Order

Fortran statements are either executable or non-executable. The compiler translates executable statements directly into a set of machine code instructions. Non-executable statements are mainly used to tell the compiler about the program; they are not directly translated into machine code. The END statement is executable and so are all those in the lowest right-hand box of the table below; all other statements are non-executable. The general order of statements in a program unit is: Program unit header (PROGRAM, SUBROUTINE, FUNCTION,or BLOCK DATA statement) Specication statements Executable statements

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statement. The table below shows the complete statement ordering rules: the statements listed in each box can be intermixed with those in boxes on the same horizontal level (thus PARAMETER statements can be intermixed with IMPLICIT statements) but those in boxes separated vertically must appear in the proper order in each program unit (thus all statement functions must precede all executable statements).
END PROGRAM, FUNCTION, SUBROUTINE, BLOCK DATA IMPLICIT PARAMETER Type statements: INTEGER, REAL, DOUBLE PRECISION, COMPLEX, LOGICAL, CHARACTER

Other specication statements: Statement function statements Executable statements:

COMMON, DIMENSION, EQUIVALENCE, EXTERNAL, INTRINSIC, SAVE FORMAT DATA

BACKSPACE, CALL, CLOSE, CONTINUE, DO, ELSE, ELSE IF, END IF, GO TO, IF, INQUIRE, OPEN, READ, RETURN, REWIND, STOP, WRITE, assignment statements. END

Execution Sequence
A program starts by executing the rst executable statement of the main program unit. Execution continues sequentially unless control is transferred elsewhere: an IF or GO TO statement, for example, may transfer control to another part of the same program unit, whereas a CALL statement or function reference will transfer control temporarily to a procedure. A program continues executing until it reaches a STOP statementin any program unit, or the END statement of the main program unit, or until a fatal error occurs. When a program terminates normally (at STOP or END) the Fortran system closes any les still open before returning control to the operating system. But when a program is terminated prematurely les, especially output les, may be left with incomplete or corrupted records.

4.5 Symbolic Names

Symbolic names can be given to items suchas variables, arrays, constants, functions, subroutines, and common blocks. All symbolic names must conform to the following simple rule: the rst character of each name must be a letter, this may be followed byup to ve more letters or digits. Here are some examples of valid symbolic names:
I MATRIX VOLTS PIBY4 OLDCHI TWOX R2D2 OUTPUT

And here are some names which do not conform to the rules: COMPLEX (too many letters) MAX EL (underscore is not allowed) 2PI (starts with a digit) Height (lower-case letters are not allowed).

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It is best to avoid using digits in names unless the meaning is clear, because they are often misread. The digit 1 is easily confused with the letter I, similarly 0 looks much like the letter O on many devices. The six-character limit on the length of a symbolic name is one of the most unsatisfactory features of Fortran: programs are much harder to understand if the names are cryptic acronyms or abbreviations, but with only six characters there is little choice. Although many systems do not enforce the limit (and Fortran90 allows names up to 31 characters long), at present the only way to ensure software portabilityisto keep to it strictly. There is a further problem with items which have an associated data type (constants, variables, arrays, and functions). Unless the data type is declared explicitly in a type statement, it is determined by the initial letter of the name. This may further restrict the choice.

Scope of Symbolic Names
Symbolic names which identify common blocks and program units of all types are global in scope, i.e. their name must be unique in the entire executable program. Names identifying all other items (variables, arrays, constants, statement functions, intrinsic functions, and all types of dummy argument) are local to the program unit in which they are used so that the same name may be used independently in other program units. To see the eect of these rules here is a simple example. Suppose your program contains a subroutine called SUMMIT. This is a global name so it cannot be used as the name of global item (such as an external procedure or a common block) in the same executable program. In the SUMMIT subroutine and in any other program unit which calls it the name cannot be used for a local item such asavariable or array. In all other program units, however, including those which call SUMMIT indirectly, the name SUMMIT can be used freely e.g. for a constant, variable, or array. The names of global items need to be chosen more carefully because it is harder to alter them at a later stage; it can be dicult to avoid name clashes when writing a large program or building a library of procedures unless program unit names are allocated systematically. It seems appropriate for procedures to have names which are verb-like. If you nd it dicult to devise sensible procedure names remember that the English language is well stocked with three and four-letter verbs which form a good basis, for example: DO, ASK, GET, PUT, TRY, EDIT, FORM, LIST, LOAD, SAVE, PLOT. By combining a word like one of these with one or two additional letters it is possible to make up a whole range of procedure names.

Reserved Words
In most computer languages there is a long list of words which are reserved by the system and cannot be used as symbolic names: Cobol programmers, for example, have to try to remember nearly 500 of them. In Fortran there are no reserved words. Some Fortran keywords (for instance DATA, END, and OPEN) are short enough to be perfectly valid symbolic names. Although it is not against the rules to do this, it can be somewhat confusing. The names of the intrinsic functions (such as SQRT, MIN, CHAR) are, technically, local names and there is nothing to prevent you using them for your own purposes, but this is not generally a good idea either. For example, if you choose to use the name SQRT for a local variable you will have more diculty in computing square-roots in that program unit. It is even more unwise to use the name of an intrinsic function as that of an external procedure because in this case the name has to be declared in an EXTERNAL statementin every program unit in which it is used in this way.

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4.6

PROGRAM

The PROGRAM statement can only appear at the start of the main program unit. Its only function is to indicate what type of program unit it is and to giveitsymbolic name. Although this name cannot be used anywhere else in the program, it may be used by the Fortran system to identify error messages etc. The general form is simply: PROGRAM name Where name is a symbolic name. This name is global in scope and may not be used elsewhere in the main program nor as a global name in any other program unit. For compatibility with Fortran66 the PROGRAM statement is optional. This can have unexpected eects: if you forget use a SUBROUTINE or FUNCTION statement at the start of a procedure the compiler will assume it to be a (nameless) main program unit. Since this will normally result in two main program units, the linker is likely to detect the mistake.

Statement

4.7

END

The END statementmust appear as the last statementof every program unit. It simply consists of the word: which may not be followed by any continuation lines (or comments). The END statement is executable and may have a label attached. If an END statement is executed in a subprogram unit, i.e. a procedure, it returns control to the calling unit; if an END statement is executed in the main program it closes any les which are open, stops the program, and returns control to the operating system.
END

Statement

5 Constants, Variables, and Arrays
This section deals with the data-storage elements of Fortran: constants, variables, and arrays. These all possess an important property called data type. The data type of an item determines what sort of information it holds and the operations that can be performed on it.

5.1 Data Types

All the information processed by a digital computer is held internally in the form of binary digits or bits. Suitable collections of bits can be used to represent many dierenttypes of data including numbers and strings of characters. It is not necessary to knowhow the information is represented internally in order to write Fortran programs, only that there is a dierent representation for each type of data. The data type of each item also determines what operations can be carried out on it: thus arithmetic operations can be carried out on numbers, whereas character strings can be split up or joined together. The data type of each item is xed when the program is written. Fortran, with its emphasis on numerical operations, has four data types just for numbers. These are collectively known as the arithmetic data types. Arithmetic expressions can include mixtures of data types and, in most cases, automatic type conversions are provided. In other circumstances, however, especially in procedure calls, there is no provision for automatic type conversion and it is essential for data types to match exactly. The range and precision of the arithmetic data types are not specied by the Standard: typical values are indicated below, but the only way to be sure is to check the manuals provided with your own Fortran system.

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Several intrinsic functions are available to convert from one data type to another. Conversion from character strings to numbers and vice-versa can be complicated; these are best carried out with the internal le READ and WRITE statements (see section 10.3). There are, as yet, no user-dened or structured data types in Fortran.

Standard Data Types
Integer Real

The table below summarises the properties of the six data types provided in Standard Fortran: Data type Characteristics Whole numbers stored exactly. Numbers, whichmayhave fractional parts, stored using a oatingpoint representation with limited precision. Similar to real but with greater precision.

Double Precision Complex Complex numbers: stored as an ordered pair of real numbers. Logical A Boolean value, i.e. one which is either true or false. Character A string of characters of xed length. The rst four types (integer, real, double precision, and complex) all hold numerical information and are collectively known as arithmetic data types.

Integer Type
The integer data type can only represent whole numbers but they are stored exactly in all circumstances. Integers are often used to count discrete ob jects such as elements of an array, characters in a string, or iterations of a loop. The range of numbers covered by the integer type is system-dependent. The ma jority of computers use 32 bits for their integer arithmetic (1 bit for the sign and 31 for the magnitude) giving a number range of 2; 147; 483; 648 to +2; 147; 483; 647. Some systems have an even larger integer range but a few very small systems only allow 16-bit integer arithmetic so that their integer range is only 32; 768 to +32; 767.

Real Type
Most scientic applications use the real data type more than anything else. Real values are stored internally using a oating-point representation which gives a larger range than the integer type but the values are not, in general, stored exactly. Both the range and precision are machine dependent. In practice most machines use at least 32 bits to store real numbers. Many systems now use the IEEE Standard representation: for 32-bit numbers this gives a precision of just over 7 decimal digits and allows a number range from around 10 38 to just over 10+38 . This can be something of a limitation because there are manytypes of calculation, especially in physics and astronomy, which lead to numbers in excess of 1040. Some computers designed expressly for scientic work, sometimes called \super-computers", allocate 64 bits for real numbers so that the numerical precision is much larger; the range is often larger as well. On such machines it is rarely necessary to use the double precision type.

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Double Precision Type
Double precision is an alternative oating-pointtype. The Fortran Standard only species that it should have greater precision than the real type but in practice, since the double precision storage unit is twice the size, it is safe to assume that the precision is at least doubled. The number range may,however, be the same as that for real type. Although double precision values occupy twice as much memory as real (or integer) values, computations on them do not necessarily taketwice as long.

Complex Type

The complex data type stores two real values as a single entity. There is no double precision complex type in Standard Fortran. Complex numbers arise naturally when extracting the roots of negative numbers and are used in many branches of mathematics, physics, and engineering. A complex number is often represented as (A + iB ), where A and B are the real and imaginary parts respectively and i2 = 1. Electrical engineers, having used the letter i to represent current, use the notation (A + jB ) instead. Although the rules for manipulating complex numbers are straight-forward, it is convenient to have the Fortran system to do the work. It is usually more ecient as well, because the computer can use its internal registers to store the intermediate products in complex arithmetic. Exponentiation and the four regular arithmetic operators can be used on complex values, and various intrinsic functions are also provided such as square-root, logarithms, and the trigonometric functions.

Logical Type
The logical data type is mainly used in conjunction with IF statements which select a course of action according to whether some condition is true or false. A logical variable (or array element) may be used to store such a condition value for future use. Logical variables and arrays are also useful when dealing with two-valued data such as whether a person is male or female, a le open or closed, power on or o, etc. Some programmers seem reluctant to use logical variables and arrays because they feel that it must be inecient to use an entire computer word of perhaps 32 bits to store just one bit of information. In fact the extra code needed to implement a more ecient data packing scheme usually wastes more memory than the logical variables would have occupied.

Character Type
The character type is unique in that eachcharacter item has a length dened for it: this is the number of characters that it holds. In general the length is xed when the item is declared and cannot be altered during execution. The only exception to this is for dummy arguments of procedures: here it is possible for the dummy argument to acquire the length of the corresponding actual argument. Using this facility, general-purpose procedures can be written to operate on character strings irrespective of their length. In addition, the rules for character assignment take care of mismatched lengths by truncating or padding with blanks on the right as necessary. This means that the Fortran character type has many of the properties of a genuine variable-length character-handling system. The maximum length of a character item is system-dependent: it is safe to assume that all systems will allow strings of up to 255 characters, a length limit of 32767 (or even more) is quite

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common. The minimum length of a character item is one character; empty or null strings are not permitted.

Storage Units
Although the Fortran Standard does not specify the absolute amount of memory to be allocated to each data type, it does specify the relative amounts. This is not important very often, only when constructing unformatted direct-access records or when using COMMON and EQUIVALENCE statements. The rules are as follows: Data types Storage units integer, real, logical 1 numerical storage unit complex, double precision 2 numerical storage units character*(N) N character storage units In the case of an array the number of storage units must be multiplied by the total number of elements in the array. The relationship between the numeric and character storage units is deliberately undened because it is entirely system-dependent.

Guidelines

It is usually fairly clear which data type to choose for each item in a program, though there are some borderline cases among the various arithmetic data types. When processing data which are inherently integers, such as the number of seeds which germinate in each plot, or the number of photons detected in each time interval, it is not always clear whether to use integer or real arrays to store them. They both use the same memory space but on some machines additions and subtractions are faster on integers than on oating-point numbers. In practice, however, any savings can be swallowed up in the data type conversions that are usually necessary in subsequent processing. The main snag with integers is the limited range; on some machines integer over ow is not detected whereas oating-pointover ows nearly always produce error messages. If your machine stores its real variables in 32-bit words then the precision of around 1 in 107 is likely to be inadequate in some applications. This imprecision is equivalent to an error of several pence in a million pounds, or around ten milliseconds in a day. If errors of this order are signicant you should consider using the double precision type instead. This will normally reduce the errors by at least another factor of 107. Mixing data types increases the risks of making mistakes and it is often simpler and safer to use the double precision type instead of real throughout the program, even though this may use slightly more memory and processor time. Although automatic type conversions are provided for the arithmetic types in expressions, in other cases such as procedure calls it is essential for each actual argumenttohave the same data type as the corresponding dummy argument. Since program units are compiled independently, it is dicult for either the compiler or the linker to detect type mismatches in calls to external procedures.

Non-standard Data Types
Although Standard Fortran only provides the above six data types, many systems provide additional ones. You may come across data type names such as: LOGICAL*1, INTEGER*2, REAL*8, COMPLEX*16, etc. The number after the asterisk indicates the number of bytes of storage used

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for each datum (a byte being a group of 8 bits). This notation has a certain logic but is totally non-standard. The use of a term like REAL*8 when it is simply a synonym for DOUBLE PRECISION seems particularly pointless. There are, of course, circumstances when types suchas COMPLEX*16 are necessary but the price to be paid is the loss of portability.

5.2 Constants

A constant has a value which is xed when the program is written. The data type of every constant is evident from its form. Arithmetic constants always use the decimal number base: Standard Fortran does not support other number bases such as octal or hexadecimal. Although arithmetic constants may in general have a leading sign (plus or minus) there are some circumstances in Fortran when an unsigned constant is required. If the constant is zero then any sign is ignored.

Integer Constants
The general form of an integer constant is a sign (plus or minus) followed by a string of one or more digits. All other characters (except blanks) are prohibited. If the number is positive the plus sign is optional. Here are some examples of valid integer constants: It is easier to read a large number if its digits are marked o in groups of three: traditionally the comma (or in some countries the dot) is used for this purpose. The blank can be used in the same wayin Fortran programs (but not in data les): Note that this number, although conforming to the rules of Fortran, may be too large in magnitude to be stored as an integer on some systems.
-1 000 000 000 -100 42 0 +1048576

Real Constants
A real constant must contain a decimal point or an exponent (or both) to distinguish it from one of integer type. The letter \E" is used in Fortran to represent \times 10 to the power of". For example, the constant1:234 10 5 is written as \1.234E-5". The most general form of a real constant is: sign digits . digits E sign digits {integer-part{ {decimal-part{ {exponent{ |basic-real-constant| |exponent-section| Both signs are optional; a plus sign is assumed if no sign is present. Leading zeros in the integer-part and in the exponent are ignored. Either the integer part or the decimal part may be omitted if it is zero but one or the other must be present. If the value of the exponent is zero the entire exponent section may be omitted provided a decimal point is present in the number. There is no harm in giving more decimal digits in a real (or double precision) constant than the computer can make use of: the value will be correctly rounded by the computer and the extra decimal places ignored. Here are a few examples of valid real constants: Dangling decimal points, though permitted, are easily overlooked, and it is conventional to standardize constants in exponential notation so that there is only one digit before the decimal point. Using this convention, these values would look like this:
.5 -10. 1E3 +123.456E4 .000001

5 CONSTANTS, VARIABLES, AND ARRAYS
0.5 -10.0 1000.0 1.23456E6 1.0E-6

33

Double Precision Constants
A double precision constant has a similar form to a real constant but it must contain an exponent but using the letter \D" in place of "E" even if the exponent is zero. Some examples of double precision constants are:
3.14159265358987D0 1.0D-12 -3.652564D+02

Complex Constants
A complex constant has the form of two real or integer constants separated by a comma and enclosed in a pair of parentheses. The rst number is the real component and the second the imaginary component. Some examples of valid complex constants are:
(3.14,-5.67) (+1E5,0.125) (0,0) (-0.999,2.718E15)

Logical Constants
There are only two possible logical constants, and they are expressed as: .TRUE. and .FALSE. The dots at each end are needed to distinguish these special forms from the words TRUE and FALSE, which could be used as symbolic names.

Character Constants
Acharacter constant consists of a string of characters enclosed in a pair of apostrophes which act as quotation marks. Within the quoted string anycharacters available in the character set of the machine are permitted; the blank (or space) character is signicant within character constants and counts as a single character just like any other. Examples of valid character constants are:
'X' ' 40 + 15%' 'This is a constant including spaces'

The apostrophe character can be included in a character constantby representing it as two successive apostrophes (with no intervening blanks). This pair of apostrophes only counts as a single character for the purposes of computing the length of the string. For example: 'DON''T' is a constant of length 5.

5.3 Specifying Data Type

The preceding rules ensure that the data type of an literal constant is completely determined by its form. Similarly the data type of an expression depends on the operands and operators involved. The intrinsic functions are also a special case, since their properties, including their data types, are known to the compiler. All other typed ob jects in a Fortran program are referred to by symbolic names. The rules given here apply to all of these named ob jects: variables, arrays, named constants, statement functions, and external functions. In many programming languages, especially those in the Algol family, the data type of almost every item in the program has to be specied explicitly. Many programmers regard it as a chore

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to have to provide all these type specications, although their presence does make it rather easier for the compiler to detect mistakes. In Fortran you can specify data types explicitly in a similar way by using type statements, but Fortran also makes life easier byhaving certain default types. The data type of any ob ject which has not been declared in a type statement depends on the rst letter of its name. The default rules are: First letter of the name Implicit type AtoH REAL I to N INTEGER O to Z REAL Most programs make extensive use of integer and real ob jects, so these default values reduce the number of type statements that are required, provided suitable initial letters are chosen for the symbolic names. The rst-letter rule can also be changed throughout a program unit by using an IMPLICIT statement, described below.

Type Statements
There are six dierenttype statements, one for each data type. In their simplest form they just consist of the appropriate data-type keyword followed by a list of symbolic names. For example:
INTEGER AGE, GRADE LOGICAL SUPER REAL RATE, HOURS, PAY, TAX, INSURE

In this example the rst four items declared to be real would have had that type anyway had the default rules been left to operate. Conrmatory type specication does no harm. There is no limit to the numberoftype statements that can be used but a name must not have its type specied explicitly more than once in a program unit. Type statements must precede all executable statements in the unit; it is good practice, though not essential, for them to precede other specication statements referring to the same name. Type statements can be used in a subprogram to specify the types of the dummy arguments and, in an external function, the type of the function as well. Type statements by themselves have no eect on intrinsic function names but it is not a good idea to use them in this way. The CHARACTER statement is slightly dierent from the others because it also species the length of each character item, i.e. the number of characters it holds. The length can be given separately for each item, thus: Alternatively, if several items are to have the same length, a default length for the statement can be given at the beginning: This declares the name COMET to have a length of 4 characters, whereas STAR, GALAXY, and PLANET are all 20 characters long. If the length is not specied at all it defaults to one. The length can also be specied by means of a named integer constant or an integer constant expression enclosed in parentheses. For example:
PARAMETER (NEXT=15, LAST=80) CHARACTER TEXT*(NEXT+LAST) CHARACTER*20 STAR, GALAXY, COMET*4, PLANET CHARACTER NAME*15, STREET*30, TOWN*20, PCODE*7

Note that the length of a character item is xed at compilation time. The special form:
CHARACTER NAME*(*)

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is permitted in two cases: for named constants the length of the literal constant in the PARAMETER statement is used (section 5.4); for dummy arguments of procedures the length of the associated actual argument is used (section 9.5). Type statements can also be used to declare the dimensions of arrays: this is described in section 5.6.
IMPLICIT

The IMPLICIT statement can be used to change the rst-letter default rule throughout a program unit. For example: would mean that all names starting with the letters D,X,Y, or Z would (unless declared otherwise in type statements) have the type double precision. Similarly the letters I through P, instead of just I through N, will imply integer type. The other letters (A-C,E-H, and Q-W) will still imply real type. IMPLICIT can be used with character type to specify a default length as well, for example: But this is not usually of much practical value. As with type statements, the default character length is one. More than one IMPLICIT statement can be used in a program unit but the same letter must not have its implied type specied more than once. The usual Fortran implied-type rules apply to all initial letters not listed in any IMPLICIT statements. The list of letters given after eachtype must appear in alphabetical order. IMPLICIT statements normally precede all other specication statements in a program. There is one exception to this: PARAMETER statements may precede them provided that the constants named in them are not aected by the IMPLICIT statement. Note that dummy arguments and function names may be aected by a subsequent IMPLICIT statement. IMPLICIT statements have no eect on intrinsic function names.
IMPLICIT CHARACTER*100 (C,Z), CHARACTER*4 (S) IMPLICIT DOUBLE PRECISION (D,X-Z), INTEGER (N-P)

Statement

Guidelines
There are two diametrically opposed schools of thought on type specication. The rst holds that all names should have their types specied explicitly. This certainly helps programmers to avoid mistakes, because they have to think more carefully about each item. It also helps the compiler to diagnose errors more easily, especially if the it knows that all names are going to be declared in advance. Some Fortran compilers allow a statement of the form \IMPLICIT NONE" which makes all names typeless by default and so requiring every name to be explicitly typed. Others have a compile-time switch with the same eect. If yours does not you may be able to produce a similar eect by using something like: near the beginning of each program unit which is likely to cause an error for anything not explicitly typed. One disadvantage of the practice of declaring all names in advance is that the program may become so cluttered with specication statements that it may obscure its structure and algorithm. The alternative way of working is to make maximum use of implicit types to reduce the number of statements. This means, of course, that the rst letter of each name has to be chosen to suit the type, leaving no more than ve to be chosen freely: this makes it harder than ever to devise meaningful symbolic names. As a result, Fortran programs often include names like RIMAGE or ISIZE or KOUNT. Clearly type statements are still needed for character type because it is usually necessary to use items of a number of dierent lengths. Experience suggests that either system can be satisfactory provided it is used consistently.
IMPLICIT CHARACTER*1000000 (A-Z)

5 CONSTANTS, VARIABLES, AND ARRAYS

36

However the wholesale reassignment of initial letters with IMPLICIT statements usually increases the chance of making a mistake. IMPLICIT, if used at all, should only reassign one or two rarelyused letters to the less common data types, for example:
IMPLICIT DOUBLE PRECISION (Z), LOGICAL (Q), COMPLEX (X)

It is also prudent to use an identical IMPLICIT statement in each program unit, otherwise type mismatches are more likely to be made in procedure calls.

5.4 Named Constants

The PARAMETER statement can be used to give a symbolic name to any constant. This can be useful in several rather dierent circumstances. With constants of nature (such as ) and physical conversion factors (like the number of pounds in a kilogram) it can savetyping eort and reduce the risk of error if the actual number is only given once in the program and the name used everywhere else:
REAL PI, TWOPI, HALFPI, RTOD PARAMETER (PI = 3.14159265, TWOPI = 2.0 * PI) PARAMETER (HALFPI = PI / 2.0, RTOD = 180.0 / PI)

The names PI, TWOPI, etc. can then be used in place of the literal constants elsewhere in the program unit. It is much better to use named constants than variables in such cases as they are given better protection against inadvertent corruption: constants are often protected by hardware. The use of symbolic names rather than numbers can also make the program a little more readable: it is probably harder to work out the signicance of a number like 1.570796325 than to deduce the meaning of HALFPI. Another important application of named constants is for items which are not permanent constants but parameters of a program, i.e. items xed for the present but sub ject to alteration at some later date. Named constants are often used to specify array bounds, character-string lengths, and so on. For example:
INTEGER MAXR, MAXC, NPTS PARAMETER (MAXR = 100, MAXC = 500, NPTS = MAXR*MAXC) REAL MATRIX(MAXR,MAXC), COLUMN(MAXR), ROW(MAXC)

The constants such as MAXR and MAXC can also be used in the executable part of the program, for instance to check that the array subscripts are in range:
IF(NCOL .GT. MAXC .OR. NROW .GT. MAXR) THEN STOP 'Matrix is too small' ELSE MATRIX(NROW,NCOL) = ROW(NCOL) END IF

If, at some point, the matrix turns out to be too small for your needs then you only have to alter this one PARAMETER statement: everything else will change automatically when the program is recompiled. The rules for character assignment apply to PARAMETER statements: see section 7.4. In addition a special length specication of *(*) is permitted which means that the length of item is set to that of the literal constant. The type specication must precede the PARAMETER statement.

5 CONSTANTS, VARIABLES, AND ARRAYS
CHARACTER*(*) LETTER, DIGIT, ALPNUM PARAMETER (LETTER = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ', $ DIGIT = '0123456789', ALPNUM = LETTER // DIGIT) CHARACTER WARN*(*) PARAMETER (WARN = 'This matrix is nearly singular')

37

The constant ALPNUM will be 36 characters long and contain all the alpha-numeric characters (letters and digits). Named logical constants also exist, but useful applications for them are somewhat harder to nd:
PARAMETER (NX = 100, NY = 200, NZ = 300, NTOT = NX*NY*NZ) LOGICAL LARGE PARAMETER (LARGE = (NTOT .GT. 1000000) .OR. (NZ .GT. 1000)) PARAMETER

Statement

The general form of the PARAMETER statement is: PARAMETER ( cname = cexp, cname = cexp, ... ) where each cname is a symbolic name which becomes the name of a constant, and each cexp is a constant expression of a suitable data type. The terms in a constant expression can only be literal constants or named constants dened earlier in the same program unit. Variables, array elements, and function references are not permitted at all. Otherwise the usual rules for expressions apply: parentheses can be used around sub-expressions, and the arithmetic types can be intermixed. There is one restriction on exponentiation: it can only be used to raise a number to an integer power. The normal rules for assignment statements apply: for arithmetic types suitable conversions will be applied if necessary; character strings will be truncated or padded to the required length. Note that substring references are not permitted in character constant expressions. PARAMETER statements are specication statements and may precede or follow type statements. But anytype (or IMPLICIT) statement which aects the data type or length of a named constantmust precede it. Sub ject to these rules, PARAMETER statements are permitted to precede IMPLICIT statements. This makes it possible for a named constant to set the default length for the character type for certain ranges of initial letters. For example:
PROGRAM CLEVER PARAMETER (LENCD = 40, LENE = 2 * LENCD) IMPLICIT CHARACTER*(LENCD)(C-D), CHARACTER*(LENE)(E) PARAMETER (DEMO = 'This is exactly 40 chars long')

Once dened, a named constant can be used in any expression, including a dimension-bound expression, or in a DATA statement. A named constant cannot be used just as part of another constant (for example one component of a complex constant) and named constants are not permitted at all within format specications.

Guidelines

One of the limitations of Standard Fortran at present is that there is no way of allocating memory dynamically. One of the best ways around this is to use named constants to specify array bounds; this makes it much easier to alter programs to suit new requirements.

5 CONSTANTS, VARIABLES, AND ARRAYS

38

Names should also be given to all mathematical and physical constants that your programs require. If the same constants are needed in several program units then it may be sensible to compose a suitable set of PARAMETER statements for all of them and bring them in where ever necessary using INCLUDE statements. If you dene double precision constants in a PARAMETER statement do not forget that each literal constantvalue must include an exponent using the letter D. There are no constant arrays in Fortran: the only way to overcome this limitation is to declare an ordinary arrayin a type statement and initialise its elements with a DATA statement (described in section 11).

5.5 Variables

A variable is simply a named memory location with a xed data type. As explained earlier, variables do not have to be declared in advance if the data type implied by the rst letter of the name is appropriate. Otherwise a type statement is required. At the start of execution the value of each variable is undened unless a suitable DATA statement appears in the program unit (see section 11). Undened values must not be used in expressions. Local variables in procedures do not necessarily retain their values from one invocation of the procedure to another unless a suitable SAVE statement is provided (section 9.11).

5.6 Arrays

An array is a group of memory locations given a single name. The elements of the array all have the same data type. In mathematics the elements of an array a would be denoted by a1, a2, a3, and so on. In Fortran a particular array element is identied by providing a subscript expression in parentheses after the array name: A(1), A(2), A(3), etc. Subscripts must have integer type but they may be specied by expressions of arbitrary complexity, including function calls. An array element can be used in the same way as a variable in almost all executable statements. Array elements are most often used within loops: typically an integer loop counter selects each element of the array in turn.
*Add array OLD to array NEW making array TOTAL PARAMETER (NDATA = 1024) REAL OLD(NDATA), NEW(NDATA), TOTAL(NDATA) *...... DO 100, I = 1,NDATA TOTAL(I) = OLD(I) + NEW(I) 100 CONTINUE

Declaring Arrays
Arrays can haveup toseven dimensions; the lower bound of each dimension is one unless declared otherwise. There is no limit on the upper bound provided it is not less than the lower bound. Arrays which are dummy arguments of a procedure mayhave their dimension bounds specied by integer variables which are arguments of the procedure; in all other cases each dimension bound must be an integer constant expression. This xes the size of the array at compiletime. Type, DIMENSION, and COMMON statements may all be used to declare arrays, but COMMON

5 CONSTANTS, VARIABLES, AND ARRAYS

39

statements have a specialised use (described in section 12). The DIMENSION statement has a similar form to a type statement but only declares the bounds of an array without determining its data type. It is usually simpler and neater to use a type statement which species both at once: Note that when declaring character arrays the string length follows the list of array bounds. The character array COLUMN has 5 elements each of which is 25 characters long; TITLE is, of course, just a variable 80 characters long. Although a default string length can be set for an entire type statement, it is not possible to set a default array size in a similar way. It is generally good practice to use named constants to specify array bounds as this facilitates later modications:
PARAMETER (MAXIM = 15) INTEGER POINTS(MAXIM) COMPLEX SERIES(2**MAXIM) CHARACTER COLUMN(5)*25, TITLE*80

These arrays all have a lower bound of one. A dierent lower bound can be specied for any dimension as shown below. The lower and upper bounds are separated by a colon:
REAL TAX(1985:1990), PAY(12,1985:1990) LOGICAL TRIPLE(-1:1, -1:1, -1:1, -1:1)

TAX has 6 elements from TAX(1985) to TAX(1990). PAY has 72 elements from PAY(1,1985) to PAY(12,1990). TRIPLE has 81 elements from BIN(-1,-1.-1.-1) to BIN(1,1,1,1). Although Fortran itself sets no limits to the sizes of arrays that can be dened, the nite capacity of the hardware is likely to do so. In virtual memory operating systems it is possible to use arrays larger than physical memory: those parts of the array not in active use are held on backing store such as a disc le.

Using Arrays
An array element reference must always use the same number of subscripts as the number of dimensions declared for the array. Each subscript can be an integer expression of any complexity, but there are restrictions on functions with side eects (see section 9.3). An array element reference is only valid if all of the subscript expressions are dened and if each one is in the range declared for it. An array element can only be used in an expression if a value for it has been dened. A DATA statement (section 12) can be used to dene an initial value for an entire arrayorany set of elements. An array can be used without subscripts: in a specication statement suchasatype, DIMENSION, or SAVE statement; in a function reference or CALL statement: this transfers the whole of the array to the associated dummy argument (whichmust have a compatible array declaration); in the data transfer list of a READ or WRITE statement: this causes the whole arrayto be input or output. This is not permitted for an assumed size dummy argument array. as a unit identier in a READ or WRITE statement: a character array is then an internal le with one record per element.

6 ARITHMETIC

40

as a format identier in a

READ or WRITE statement: the format specication is contained in the character array with its elements taken in sequence.

Storage Sequence
Arrays are always stored in a contiguous set of memory locations. In the case of multidimensional arrays, the order of the elements is that the rst subscript varies most rapidly, then the second subscript, and so on. For example in the following 2-dimensional array (for simplicity one of only six elements):

X (2; 3) = x1 1 x1 2 x1 3 x2 1 x2 2 x2 3
; ; ; ; ; ;

(1)

The elements are stored in the following sequence:

i.e. the sequence moves down each column rst, then across to the next row. This column order is dierent from that used in some other programming languages. The storage order may be important if you use large multi-dimensional arrays and wish to carry out some operation on all the elements of the array. It is then likely to be faster to access the array in storage order, i.e. by columns rather than rows. This means arranging loop indices with the last subscript indexed by the outer loop, and so on inwards. For example:
DOUBLE PRECISION ARRAY(100,100), SUM SUM = 0.0D0 DO 250,L = 1,100 DO 150,K = 1,100 SUM = SUM + ARRAY(K,L) CONTINUE CONTINUE

X(1,1), X(2,1), X(1,2), X(2,2), X(1,3), X(2,3)

150 250

With the loops arranged this way around the memory locations are overhead in subscript calculations.

6 Arithmetic
Fortran has good facilities for processing numbers. Arithmetic expressions and assignment statements can include integer, real, double precision, or complex items. Data type conversions are provided automatically when necessary; type conversions can also be performed explicitly using intrinsic functions. Other intrinsic functions are available for trigonometry, logarithms, and other useful operations. For example, the well-known cosine formula for the third side of a triangle, given the other two sides and the angle between them is:
q

b2 + c2 2:b:c:cos(A)

Translated into a Fortran expression it looks like this:

which makes use of the intrinsic functions SQRT and COS. Although SQRT(X) produces the same result as X**0.5, the square-root function is simpler, faster, and probably more accurate than

SQRT(B**2 + C**2 - 2.0 * B * C * COS(ANGLEA))

6 ARITHMETIC

41

raising to the power of one half, which would actually be carried out using both the EXP and LOG functions. Assignment statements evaluate an expression and assign its value to a variable (or array element). Unlike almost all other Fortran statements, they do not start with a keyword. For example:
A = SQRT(B**2 + C**2 - 2.0 * B * C * COS(ANGLEA)) TOTAL(N/2+1) = 0.0 FLUX = FLUX + 1.0

6.1 Arithmetic Expressions
RATE * HOURS + BONUS

An expression in its simplest form is just a single operand, such as a constantor variable. More complicated expressions combine various operands with operators, which specify the computations to be performed. For example: The rules of Fortran have been designed to resemble those of mathematics as far as possible, especially in determining the order in which the expression is evaluated. In this example the multiplication would always be carried out before the addition, not because if comes rst, but because it has a higher precedence. When in doubt, or to over-ride the precedence rules, parentheses can be used:
(ROOM + DINNER) * 1.15

Sub-expressions enclosed in parentheses are always evaluated rst; they can be nested to any reasonable depth. If in doubt, there is no harm in adding parentheses to determine the order of evaluation or to make a complicated expression easier to understand. Arithmetic expressions can contain any of the ve arithmetical operators + - * / ** . The double asterisk represents exponentiation, i.e. raising a number to a power. Thus the mathematical expression: (1 + RAT E =100) could be represented in Fortran as:
y ear s

(note the explicit decimal points in the constants to make them real values). Arithmetic expressions can involve operands of dierent data types: the data type of the result is determined by some simple rules explained below.

(1.0 + RATE/100.0)**YEARS

General Rules
Arithmetic expressions can contain arithmetic operands, arithmetic operators, and parentheses. There must always be at least one operand. The operands can belong to any of the four arithmetic data types (integer, real, double precision, or complex); the result also has an arithmetic data type. Operands can be any of the following: unsigned literal constants named constants variables array elements

6 ARITHMETIC

42

function references complete expressions enclosed in parentheses.
The rules for forming more complicated arithmetic expressions are as follows. An arithmetic expression can haveany of the following forms: operand +operand -operand arithmetic-expression arith-op operand where the arith-op can be any of these operators: + addition subtraction * multiplication / division ** exponentiation The eect of these rules is that an expression consists of a string of operands separated by operators and, optionally, a plus or minus at the start. A leading plus sign has no eect; a leading minus sign negates the value of the expression. All literal arithmetical constants used in expressions must be unsigned: this is to prevent the use of two consecutive operators which is confusing and possibly ambiguous: 4 / -3.0**-1 (illegal). The way around this is to use parentheses, for example: which makes the order of evaluation explicit. The order of evaluation of an expression is: 1. sub-expressions in parentheses 2. function references 3. exponentiation, i.e. raising to a power 4. multiplication and division 5. addition, subtraction, or negation. Within each of these groups evaluation proceeds from left to right, except that exponentiations are evaluated from right to left. Thus: A / B / C is equivalent to (A / B) / C whereas X ** Y ** Z is equivalent to X ** (Y ** Z). An expression does not have to be evaluated fully if its value can be determined otherwise: for example the result of: can be determined without calling the function FUNC if X happens to be zero. This will not cause problems if you only use functions that have no side eects.
X * FUNC(G) 4 / (-3.0)**(-1)

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43

Data Type Conversions
If an operator has two operands of the same data type then the result has the same type. If the operands have dierent data types then an implicit type conversion is applied to one of them to bring it to the type of the other. These conversions always go in the direction which minimises loss of information: integer =) real =) complex or double precision Since there is no way of converting a complex number to double precision type, or viceversa, without losing signicant information, both these conversions are prohibited: an operator cannot have one complex operand and one of double precision type. All other combinations are permitted. These implicit type conversions have the same result as if the appropriate intrinsic function (REAL, DBLE, or CMPLX) had been used. These are described in detail below. Note that the data typeofany operation just depends on the two operands involved; the rest of the expression has no in uence on it whatever. Exponentiation is an exception to the type conversion rule: when the exponentis aninteger it does not have to be converted to the type of the other operand and the result is evaluated as if by repeated multiplication. But if the exponent has any other data type the calculation is performed by implicit use of the LOG and EXP functions, thus: 2.0**3 =) 2.0 * 2.0 * 2.0 =) 8.0 2.0**3.0 =) EXP(3.0 * LOG(2.0)) =) 8.0 The rst result will, of course, be computed more rapidly and accurately than the second. If the exponent has a negative value the result is simply the reciprocal of the corresponding positive power, thus: 2.0**(-3) =) 1.0/2.0**3 =) 1.0/8.0 =) 0.125 Note that conversion from real to double precision cannot produce any information not present originally. Thus with a real variable R and a double precision variable D: Dmay end up with a value such as 0.3333333432674408... which is no closer to the value of one third than R was originally.
R = 1.0 / 3.0 D=R

Integer Division
Integer division always produces a result which is another integer value: any fractional part is truncated, i.e. rounded towards zero. This makes it especially important to provide a decimal point at the end of a real constanteven if the fractional part is zero. For example: 8/3=) 2-8/3=) -2 2**(-3) =) 1/(2**3) =) 1/8 =) 0 The combination of the two preceding rules mayhave unexpected eects, for example: (-2)**3 =) -2*-2*-2=) -8 whereas (-2)**3.0 is an invalid expression as the computer would try to evaluate the logarithm of -2.0, which does not exist. Similarly, the expression: 3/ 4*5.0 =) REAL(3/4) * 5.0 =) 0.0 whereas 5.0 *3/4 =) 15.0 / REAL(4) =) 3.75

Restrictions
Certain arithmetical operations are prohibited because their results are not mathematically dened. For example dividing by zero, raising a negativevalue to a real power, and raising zero

6 ARITHMETIC

44

to a negativepower. The Fortran Standard does not specify exactly what is to happen if one of these errors occurs: most systems issue an error message and abort the program. Errors can also occur because numbers are stored on a computer with nite range and precision. The results of adding or multiplying twovery large numbers may be outside the number range: this is called over ow. A similar eect on very large negative integers is called under ow. Most systems will issue a warning message for over ow or under ow, and may abort the program, but some processors cannot detect errors of this sort involving integer arithmetic. Every operand (variable, array element, or function reference) used in an expression must have a dened value at the time the expression is evaluated. Note that variables and arrays are initially undened unless a suitable DATA statement is used. Expressions must not include references to any external functions with side eects on other operands of the expression: see section 9.3 for more details.

Arithmetic Constant Expressions
Arithmetic constant expressions can be used in PARAMETER statements and to specify impliedDO parameters in DATA statements. All the operands in a constant expression must be literal constants or previously dened named constants. Variables, array elements, and function references are all prohibited. Exponentiation is only allowed if the number is raised to an integer power. The same rules apply to integer constant expressions but in addition the operands must all be integer constants: such expressions can be used to specify array bounds in type, COMMON, and DIMENSION statements, and to specify string lengths in CHARACTER statements.

Bit-wise Logical Operations on Integers
When Fortran programs communicate directly with digital hardware it may be necessary to carry out bit-wise logical operations on bit-patterns. Standard Fortran does not provide any direct way of doing this, since logical variables essentially only store one bit of information and integer variables can only be used for arithmetic. Many systems provide, as an extension, intrinsic functions to perform bit-wise operations on integers. The function names vary: typically they are IAND, IOR, ISHIFT. A few systems provide allow the normal logical operators suchas .AND. and .OR. to be used with integer arguments: this is a much more radical extension and much less satisfactory, not only because it reduces portability, but also reduces the ability of the compiler to detect errors in normal arithmetic expressions. Many systems also provide format descriptors to transfer integers using octal and hexadecimal number bases: these are also non-standard.

Guidelines
Expressions with mixed data types should be examined carefully to ensure that the typeconversion rules have the desired eect. It does no harm to use the type conversion functions explicitly and it may make the working clearer. Particular care is needed with the data types of literal constants. It is bad practice to use an integer constant where you really need a real constant. Although this will work in most expressions it is a serious mistake to use the wrong form of constant in the argument list of a procedure. Long and complicated expressions which spread over several lines can be rather trying to read oer more scope for programming errors. Sometimes it is better to split the computation

6 ARITHMETIC

45

into several shorter equations at the expense of one or two temporary variables. It is often tempting to try to write programs that are as ecient as possible. With modern compilers there is little point in trying to rearrange expressions to optimise speed. One of the few exceptions is that if an intrinsic function is provided it is always best to use it; thus SQRT(X) is likely to be faster and more accurate than X**0.5. You may nd that your system actually sets the whole of memory to zero initially, except for items dened with DATA statements, but it is very bad programming practice to rely on this.

6.2 Arithmetic Intrinsic Functions

Intrinsic functions are supplied automatically by the system and can be used in expressions in any program unit. A description of their special properties appears in section 9.1. Many of the arithmetic intrinsic functions have generic names: that is they can be used with several dierenttypes of arguments. The SQRT function, for example, can be used with a real, double precision, or complex argument. The Fortran system automatically selects the correct specic function for the job: SQRT, DSQRT, or CSQRT. These specic names can be ignored in almost all circumstances, and are listed only in the appendix. In most cases the data type of the function is the same as that of its argument but there are a few obvious exceptions suchas the type conversion functions. In the descriptions below, the number and data type of the arguments of each intrinsic function are indicated by a letter: I = integer, R = real, D = double precision, X = complex. An asterisk on the left indicates that the result has the same data type as the arguments. Note that if multiple arguments are permitted they must all have the same data type. Thus I = NINT(RD) indicates that the NINT function can take a single real or double precision argument but its result is always integer, whereas * = ANINT(RD) indicates that the result has the same type (real or double precision) as the argument.

Trignometric Functions
The functions in this group can all be used on real or double precision arguments, and SIN and COS can also be used on complex numbers. In every case the result has the same data type as the argument. * = SIN(RDX) sine of the angle in radians. * = COS(RDX) cosine of the angle in radians. * = TAN(RD) tangent of the angle in radians. * = ASIN(RD) arc-sine; the result is in the range =2to +=2. * = ACOS(RD) arc-cosine; the result is in the range 0 to + . * = ATAN(RD) arc-tangent; the result is in the range =2to+=2. * = ATAN2(RD,RD) arc-tangent of arg1/arg2; the result is in the range to + . Both arguments must not be zero. * = SINH(RD) hyperbolic sine. * = COSH(RD) hyperbolic cosine. * = TANH(RD) hyperbolic tangent. Note that the arguments of SIN, COS, and TAN must be angles measured in radians (not degrees). They can be used on angles of any size, positive or negative, but if the magnitude is very large the accuracy of the result will be reduced. Similarly all the inverse trigonometric functions deliver a result in radians; the argument of ASIN and ACOS must be in the range -1 to +1. The ATAN2 function can be useful in resolving a result into the correct quadrant of the circle, thus:

6 ARITHMETIC
ATAN(0.5) = 0.4636476 ATAN2(2.0,4.0) = 0.4636476 ATAN2(-2.0,-4.0) = -2.677945

46

( = 0.4636476 - ).

Other Transcendental Functions
* = SQRT(RDX) * = LOG(RDX) * = EXP(RDX)

square root. natural logarithm, i.e. log to base e (where e = 2.718281828...). returns the exponential, i.e. e to the power of the argument. This is the inverse of the natural logarithm. * = LOG10(RD) logarithm to base 10. Note that LOG10, whichmay be useful to compute decibel ratios etc., is the only one of this group which cannot be used on a complex argument.

Type Conversion Functions
These functions can be used to convert from any of the four arithmetic data types to anyofthe others. They are used automatically whenever mixed data types are encountered in arithmetic expressions and assignments. I = INT(IRDX) converts to integer by truncation. R = REAL(IRDX) converts to real. D = DBLE(IRDX) converts to double precision. X = CMPLX(IRDX) converts to complex. X = CMPLX(IRD,IRD) converts to complex. The integer conversion of INT rounds towards zero; if you need to round to the nearest integer use the NINT function (described below). The CMPLX function produces a value with a zero imaginary component unless it is used with two arguments (or one which is already complex). It is important to realise that many conversions lose information: in particular a double precision value is likely to lose signicant digits if converted to any other data type.

Minimum and Maximum
The MIN and MAX functions are unique in being able to take anynumber of arguments from twoupwards; the result has the same data type as the arguments. * = MIN(IRD,IRD,...) returns the smallest of its arguments. * = MAX(IRD,IRD,...) returns the largest of its arguments. These two functions can, of course, be combined to limit a value to a certain range. For example, to limit a value TEMPER to the range 32 to 212 you can use an expression such as: Note that the minimum of the range is an argument of the MAX function and vice-versa. To nd the largest (or smallest) element of a large array it is necessary use a loop.
*Find largest value in array T of N elements: TOP = T(1) DO 25,I = 2,N TOP = MAX(T(I), TOP) 25 CONTINUE *TOP now contains the largest element of T. MAX(32.0, MIN(TEMPER, 212.0))

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47

Other Functions
* = AINT(RD)

Truncates the fractional part (i.e. as INT) but preserves the data type. * = ANINT(RD) Rounds to the nearest whole number. I = NINT(RD) Converts to integer by rounding to the nearest whole number. * = ABS(IRD) Returns the absolute value of a number (i.e. it changes the sign if negative). R = ABS(X) Computes the modulus of a complex number (i.e. the square-root of the sum of the squares of the two components). * = MOD(IRD,IRD) returns A1 modulo A2, i.e. the remainder after dividing A1 by A2. * = SIGN(IRD,IRD) performs sign transfer: if A2 is negative the result is -A1, if A2 is zero or positive the result is A1. * = DIM(IRD,IRD) returns the positive dierence of A1 and A2, i.e. if A1 > A2 it returns (A1-A2), otherwise zero. D = DPROD(R,R) Computes the double precision product of two real values. R = AIMAG(X) Extracts the imaginary component of a complex number. Note that the real component can be obtained by using the REAL function. X = CONJG(X) Computes the complex conjugate of a complex number. The NINT and ANINT functions round upwards if the fractional part of the argument is 0.5 or more, whereas INT and AINT always round towards zero. Thus: The fractional part of a oating point number, X, can easily be found either by: or
X - AINT(X) MOD(X, 1.0) INT(+3.5) = 3 INT(-3.5) = -3 NINT(+3.5) = 4 NINT(-3.5) = -4

In either case, if X is negative the result will also be negative. The ABS function can always be used to alter the sign if required. The MOD function has other uses. For example it can nd the day of the week from an absolute day count such as Modied Julian Date (MJD): has a value between 0 and 6 for days from Wednesday to Tuesday. Similarly if you use the ATAN2 function but want the result to lie in the range 0 to 2 (rather than to +2 ) then, assuming the value of TWOPI is suitably dened, the required expression is:
MOD(ATAN2(X,Y) + TWOPI, TWOPI) MOD(MJD,7)

6.3 Arithmetic Assignment Statements

An arithmetic assignment statement has the form: arithmetic-var = arithmetic-expression where arithmetic-var can be an arithmetic variable or array element. For example, the following assignment statementis valid provided that N, K, and ANGLE are all dened values: If the ob ject on the left has a dierent data type from that of the expression on the right then a data type conversion is applied automatically. The type conversion function (INT, REAL,
IMAGE(N/2+1,3*K-1) = SIN(ANGLE)**2 + 1.0

7 CHARACTER HANDLING AND LOGIC

48

DBLE, or CMPLX) is selected to match the ob ject on the left. Note that many type conversions lose information. If the ob ject on the left is an array element, its subscripts can be arbitrary integer expressions, but all the operands in these expressions must be dened before the statement is executed and eachmust be in the range declared for the corresponding subscript of the array. Remember with an integer item on the left and an expression of one of the oating-point types, the INT function is invoked: if the NINT function is really needed then it must be used explicitly to convert the value of the expression.

7 Character Handling and Logic
This section describes the facilities for handling non-numerical data in Fortran. Character data are actually present in almost all programs, if only in the form of le names and error messages, but the facilities for character manipulation are now quite powerful. The logical data type is even more indispensable since a logical expression is used in every IF statement.

7.1 Character Facilities

The character data type diers from all the others in one important respect: every character item has a xed length. This species the number of characters it holds. The length of a literal character constant is just the number of characters between the enclosing apostrophes (except that two consecutive apostrophe within the string count as one). Thus: is a character constant of length four. Because the length of every character variable, array, and function has to be specied in advance it is nearly always necessary to use CHARACTER statements to declare them, for example: The same applies to named character constants but for these a special notation sets the length to that of the attached constant, which saves the trouble of counting characters:
CHARACTER TITLE*(*) PARAMETER (TITLE = 'Latest mailing list') CHARACTER NAME*20, ADDRSS(3)*40, ZIP*7 'it''s'

The xed length of character ob jects makes it easy to output data in a xed format as when printing a table with neatly aligned columns, but sometimes it would be more convenientto have avariable length string type as some other languages do. The rules for character assignmentgo some waytowards this: if an expression is too short then blanks are appended to it; if it is too long then characters are removed from the right-hand end. For many purposes, therefore, it is only necessary to ensure that character variables are at least as long as the longest string you need to store in them. When transferring character information to procedures the length of the dummy argument can be set automatically to that of the corresponding actual argument. With this passed length notation it is easy to write general-purpose character handling procedures. This is described further in section 9.5. The most common operations carried out on character strings are splitting them up and joining them together. Any section of a character variable or array element can be extracted by using the substring notation. Strings (and substrings) can be joined end to end by using the concatenation operator in a character expression. These are described in the next two sections.

7 CHARACTER HANDLING AND LOGIC

49

Another fairly common requirement is to search for a particular sequence of characters within a longer string: this can be done with the intrinsic function INDEX. Other intrinsic functions ICHAR and CHAR are provided to convert a single character to an integer or vice-versa according to its position within the nativecharacter set. More complicated conversions from a numerical data typetocharacter form and vice-versa are best carried out using the internal le READ and WRITE statements which allow the power of the format specication to applied to the task. This mechanism is described in section 10.3. Character strings can be compared to each other using relational operators or intrinsic functions. The latter use the ASCII collating sequence irrespective of the native character code. Further details are given in section 7.6.

7.2 Character Substrings

The substring notation can be used to select any contiguous section of any character variable or array element. The characters in any string are numbered starting from one on the left: the lower bound cannot be altered as it can in arrays. A substring is selected simply by giving the rst and last character positions of the extract. For example, with:
CHARACTER METAL*10 METAL = 'CADMIUM'

then METAL(1:3) has the value 'CAD' while METAL(8:8) has the value blank because the value is padded out with blanks to its declared length. Substrings must be at least one character long. They can be used in general in the same ways as character variables. Continuing with the last example, the assignment statement: will change the value of METAL to length stays at 10).
METAL(3:4) = 'ES' 'CAESIUM '

(with three blanks at the end, since the total

Substring Rules
The parentheses denoting a substring must contain a colon: there maybe aninteger expression on either side of the colon. The rst expression denotes the initial character position, the second one the last character position. Both values must be within the range 1 to LEN, where LEN is the length of the parent string, and the length of the resulting substring must not be less than one. Although the colon must always be present, the two integer expressions are optional. The default value for the rst one is one, the default for the second is the position of the last character of the parent string. Thus, staying with the last example: METAL(:2) has the value 'CA' while METAL(7:) has the value 'M' with three blanks. With array elements the substring expression follows the sub-script expression, for example:
CHARACTER PLAY(30)*80 PLAY(10) = 'AS YOU LIKE IT'

Then the substring PLAY(10)(4:11) has the value 'YOU LIKE'. Substrings can be used in expressions anywhere except in the denition of a statement function; they can also be used on the left-hand side of an assignment statement, and can be also be dened by input/output statements.

7 CHARACTER HANDLING AND LOGIC

50

7.3 Character Expressions

The character operator // is used to concatenate, or join, two character strings. It is, in fact, the only character operator that Fortran provides. Thus: 'CUP' // 'BOARD' = 'CUPBOARD' ) The length of the result is just the sum of the lengths of the operands. Parentheses may be used in character expressions but make no dierence to the result. Note that anyembedded or trailing blanks (spaces) will be reproduced exactly in the resulting string. The general form of a character-expression is thus: character-operand or character-expression // character-operand where character-operand can be any of the following: character constant (literal or named), character variable, character array element, character substring, character function reference. There is one special restriction on character concatenation in procedures: a passed-length dummy argument can only be an operand of the concatenation operator in an assignment statement. This seemingly arbitrary rule allows the compiler to determine howmuch work-space is required.

7.4 Character Assignment Statements

The character assignment statement has the general form: char-var = character-expression where char-var can be a character variable, array element, or substring. There is one important restriction on character assignment statements: none of the characters being referenced in the expression on the rightmay be dened in char-var on the left, that is to say there can be no overlap. Thus the assignment statement: is valid only as long as N is no higher than 9. It is, of course, easy to get around this restriction by using a temporary character variable with a suitable length. Note when a value is assigned to a substring (as in the last example) the other characters in the parent string are not aected at all. If the string was previously undened then the other character positions will still be undened; otherwise they will retain their previous contents. The expression and the character ob ject to which its value is assigned may have dierent lengths: if the expression is longer then the excess characters on the right are lost; if it is shorter then blanks are appended. Care is needed to declare adequate lengths or else the results can be unexpected:
CHARACTER AUTHOR*30, SHORT*5, EXPAND*10 AUTHOR = 'SHAKESPEARE, WILLIAM' SHORT = AUTHOR EXPAND = SHORT STRING(1:N) = STRING(10:)

The resulting value of

EXPAND

will be

'SHAKE

'

where the last ve characters are blanks.

7 CHARACTER HANDLING AND LOGIC

51

7.5 Character Intrinsic Functions

The four main character intrinsic functions are described in this section. There another four functions provided to compare character strings with each other using the ASCII collating sequence: these are described in section 7.6.
CHAR

These two functions perform integer to character conversion and vice-versa using the internal code of the machine. Although most computers now use the ASCII character code, it is by no means universal, so these functions can only be used in a very limited way in portable software. CHAR(I) returns the character at position I in the code table. For example, on a machine using ASCII code, CHAR(74) = 'J', since "J" is the character number 74 in the ASCII code table. ICHAR(STRING) returns the integer position in the code table of the rst character of the argument STRING.For example, on a machine using ASCII code, ICHAR('JOHN') = 74 ) ICHAR('john') = 106 )
INDEX INDEX is a search function; it takes two character arguments and returns an integer INDEX(S1, S2) searches for the character-string S2 in another string S1, which is usually If S2 is presentin S1 the function returns the character position at which it nds starts. is no match (or S1 is shorter than S2) then it returns the value zero. For example: CHARACTER*20 SPELL SPELL = 'ABRACADABRA' K = INDEX(SPELL, 'RA')

and

ICHAR

result. longer. If there

Here K will be set to 3 because this is the position of the rst occurrence of the string 'RA'. To nd the second occurrence it is necessary to restart the search at the next character in the main string, for example: This will return the value 7 because the rst occurrence of 'RA' in the substring 'ACADABRA' is at position 7. To nd its position in the parent string the oset, K,must be added, making 10. The INDEX function is often useful when manipulating character information. Suppose, for example, wehave an string NAME containing the a person's surname and initials, e.g. The name can be reformatted to put the initials before the surname and omit the comma like this:
CHARACTER NAME*25, PERSON*25 *... KCOMMA = INDEX(NAME, ',') KSPACE = INDEX(NAME, ' ') PERSON = NAME(KCOMMA+1:KSPACE-1) // NAME(1:KCOMMA-1) Mozart,W.A L = INDEX(SPELL(K+1:), 'RA')

Then PERSON will contain the string 'W.A.Mozart' (with blanks appended to the length of 25). Note that a separate variable, PERSON, was necessary because of the rule about overlapping strings in assignments.

7 CHARACTER HANDLING AND LOGIC
LEN

52

The LEN function takes a character argument and returns its length as an integer. The argument may be a local character variable or array element but this will just return a constant. LEN is more useful in procedures where character dummy arguments (and character function names) mayhave their length passed over from the calling unit, so that the length may be dierent on each procedure call. The length returned by LEN is that declared for the item. Sometimes it is more useful to nd the length excluding trailing blanks. The next function does just that, using LEN in the process.
INTEGER FUNCTION LENGTH(STRING) *Returns length of string ignoring trailing blanks CHARACTER*(*) STRING DO 15, I = LEN(STRING), 1, -1 IF(STRING(I:I) .NE. ' ') GO TO 20 15 CONTINUE 20 LENGTH = I END

7.6 Relational Expressions

A relational expression compares the values of two arithmetic expressions or two character expressions: the result is a logical value, either true or false. Relational expressions are commonly used in IF statements, as in this example:
IF(SENSOR .GT. UPPER) THEN CALL COOL ELSE IF(SENSOR .LT. LOWER) THEN CALL HEAT END IF

The relational operators have forms such as .GT. and .LT. because the Fortran character set does not include the usual characters . and <. Relational expressions are most commonly used in IF statements, but any logical variable or array element may be used to store a logical value for use later on.
CHARACTER*10 OPTION LOGICAL EXIT EXIT = OPTION .EQ. 'FINISH' *... IF(EXIT) STOP 'Finish requested'

Logical expressions are covered in more detail in the next section.

General Forms of Relational Expression
arithmetic-exprn rel-op arithmetic-exprn or character-exprn rel-op character-exprn In either case the resulting expression has the logical type. The relational operator rel-op can be any of the following:

7 CHARACTER HANDLING AND LOGIC
.EQ. .GE. .GT. .LE. .LT. .NE.

53

equal to greater than or equal to greater than less than or equal to less than not equal to

Note that these operators need a decimal point at either end to distinguish them from symbolic names.

Arithmetic Comparisons
When the two arithmetic values of diering data type are compared, a conversion is automatically applied to one of them (as in arithmetic expressions) to bring it to the type of the other. The direction of conversion is always: integer =) real =) complex or double precision. When comparing integer expressions, there is a considerable dierence between the .LE. and .LT. operators, and similarly between .GE. and .GT., so that you should consider carefully what action is required in the limiting case before selecting the appropriate operator. In comparisons involving the other arithmetic types you should remember that the value of anumber may not be stored exactly. This means that it is unwise to rely on tests involving the .EQ. and .NE. operators except in special cases, for example if one of the values has previously been set to zero or some other small integer. There are two restrictions on complex values: rstly they cannot be compared at all to ones of double precision type. Secondly they cannot use relational operators other than .EQ. and .NE. because there is no simple linear ordering of complex numbers.

Character comparisons
A character value can only be compared to another character value; if they do not have the same length then the shorter one is padded out with blanks to the length of the other before the comparison takes place. Tests for equality (or inequality) do not depend on the character code, the two strings are just compared character bycharacter until a dierence is found. Comparisons using the other operators (.GE., .GT., .LE., and .LT.) do, however, depend on the local character code. The two expressions are compared one character position at a time until a dierence is found: the result then depends on the relative positions of the two characters in the local collating sequence, i.e. the order in which the characters appear in the character code table. The Fortran Standard species that the collating sequence used by all systems must have the following basic properties: all the upper-case letters are in order, A < B < C etc. all digits are in order, 0 < 1 < 2 etc. all digits precede all letters or vice-versa, the blank (space) character precedes letters and digits. It does not, however, specify whether letters precede digits or follow them. As a result, if strings of mixed text are sorted using relational operators the results may be machine dependent. For example, the expression

7 CHARACTER HANDLING AND LOGIC
'APPLE' .LT. 'APRICOT'

54

is always true because at the two strings rst dier at the third character position, and the letter 'P' precedes 'R' in all Fortran collating sequences. However: will havea value true if your system uses EBCDIC but false if it uses ASCII, because the digits follow letters in the former and precede them in the latter. In order to allow character comparisons to be made in a truly portable way, Fortran has provided four additional intrinsic functions. These perform character comparisons using the ASCII collating sequence no matter what the native character code of the machine. These functions are: LGE(S1, S2) greater than or equal to LGT(S1, S2) greater than LLE(S1, S2) less than or equal to LLT(S1, S2) less than. They take two character arguments (of any length) and return a logical value. Thus the expression: will always have the value false. Character comparisons are case-sensitive on machines which have lower-case letters in their character set. It is advisable to convert both arguments to the same case beforehand.
LGT('A1', 'AONE') 'A1' .GT. 'AONE'

Guidelines

Systems which supports both upper and lower-case characters are usually case-sensitive: before testing for the presence of particular keywords or commands it is usually best to convert the an input string to a standard case, usually upper-case. Unfortunately there are no standard intrinsic functions to do this, though many systems provide them as an extension. In character sorting operations where the strings contain mixtures of letters, digits, or other symbols, you should use the intrinsic functions to make the program portable. In other character comparisons, however, the relational operator notation is probably preferable because it has a more familiar form and may be slightly more ecient.

7.7 Logical Expressions

Logical expressions can be used in logical assignment statements, but are most commonly encountered in IF statements where there is a compound condition, for example:
$ IF(AGE .GE. 60 .OR. (STATUS .EQ. 'WIDOW' .AND. NCHILD .GT. 0) THEN

This combines the values of three relational expressions, two of them comparing arithmetic values, the other character values. The logical operators such as .AND. and .OR. also need decimal points at either end to distinguish them from symbolic names. The .OR. operator performs an inclusive or, the exclusive or operator is called .NEQV..

Rules
A logical expression can haveany of the following forms:

7 CHARACTER HANDLING AND LOGIC

55

logical-term .NOT. logical-term logical-expression logical-operator logical-term
Where: logical-term can be any of the following: logical constant (literal or named), logical variable, logical array element, logical function reference, logical expression enclosed in parentheses, relational expression. and the logical operator can be any of the following: .AND. logical and .OR. logical inclusive or .EQV. logical equivalence .NEQV. logical non-equivalence (i.e. exclusive or). Note that the rules of logical expressions only allow two successive operators to occur if the second of them is the unary operator .NOT. which negates the value of its operand. The eects of the four binary logical operators are shown in the table below for the four possible combinations of operands, x and y. x false true false true y x .AND. y x .OR. y x .EQV. y x .NEQV. y false false false true false false false true false true true false true false true true true true true false

Note that a logical expression can have operands which are complete relational expressions, and these can in turn contain arithmetic expressions. The complete order of precedence of the operators in a general expression is as follows: 1. arithmetical operators (in the order dened in section 6.1 above). 2. relational operators 3. .NOT. 4. .AND. 5. .OR. 6. .EQV. and .NEQV.

8 CONTROL STATEMENTS

56

If the operators .EQV. and .NEQV. are used at the same level in an expression they are evaluated from left to right. These rules reduce the need for parentheses in logical expressions, thus: would have exactly the same meaning if all the parentheses had been omitted. AFortran system is not required to evaluate every term in a logical expression completely if its value can be determined more simply. In the above example, if X had been greater than A then it would not be necessary to compare Y and B for the expression would have been true in either case. This improves eciency but means that functions with side-eects should not be used.
(X .GT. A) .OR. (Y .GT. B)

Guidelines
Complicated logical and relational expressions can be hard to read especially if they extend on to several successive lines. It helps to line up similar conditions on successive lines, and to use parentheses.

7.8 Logical Assignment Statements

A logical assignment statement has the form: logical-var = logical-expression Where the logical-var can be a logical variable or array element. Logical variables and array elements are mainly used to store the values of relational expressions until some later point where they are used in IF statements.

8 Control Statements
Executable statements are normally executed in sequence except as specied by control statements. The END= and ERR= keywords of input/output statements can also aect the execution sequence.

8.1 Control Structures
Branches
The best way to select alternative paths through a program is to use the block-IF structure: this may comprise a single block to be executed when a specied condition is true or several blocks to cover several eventualities. Where the IF-block would only contain one statementit is possible to use an abbreviated form called (for historical reasons) the logical-IF statement. There is also a computed GO TO statement which can produce a multi-way branch similar to the \case" statements of other languages.

Loops
Another fundamental requirement is that of repetition. If the number of cycles is known in advance then the DO statement should be used. This also controls a block of statements known as the DO-loop. A CONTINUE statement usually marks the end of a DO-loop. Fortran has no direct equivalent of the \do while" and \repeat until" forms available in some program languages for loops of an indenite number of iterations, but they can be constructed using simple GO TO and IF statements.

8 CONTROL STATEMENTS

57

Other Control Statements
The STOP statement can be used to terminate execution. Other statements which aect execution sequence are described in other sections: the END statementwas covered in section 4.7; procedure calls including the CALL and RETURN statements are described in section 9.

8.2

IF

The simplest form of IF-block looks like this:
IF(N .NE. 0) THEN AVERAG = SUM / N AVGSQ = SUMSQ / N END IF

-Blocks

The statements in the block are only executed if the condition is true. In this example the statements in the block are not executed if N is zero in order to avoid division by zero. The IF-block can also contain an ELSE statement to handle the alternative:
IF(B**2 .GE. 4.0 * A * C) THEN WRITE(UNIT=*,FMT=*)'Real roots' ELSE WRITE(UNIT=*,FMT=*)'No real roots' END IF

Since the IF statement contains a logical expression its value can only be true or false, thus one or other of these blocks will always be executed. If there are several alternative conditions to be tested, they can be specied with ELSE IF statements:
IF(OPTION .EQ. 'PRINT') THEN CALL OUTPUT(ARRAY) ELSE IF(OPTION .EQ. 'READ') THEN CALL INPUT(ARRAY) ELSE IF(OPTION .EQ. 'QUIT') THEN CLOSE(UNIT=OUT) STOP 'end of program' ELSE WRITE(UNIT=*,FMT=*)'Incorrect reply, try again...' END IF

There can be any number of ELSE IF blocks but in each case one, and only one, will be executed each time. Without an ELSE block on the end an nothing would have happened when an invalid option was selected.

Block-IF General Rules
The general form of the block-if structure is as follows:
IF( logical-expression ) THEN a block of statements ELSE IF( logical-expression ) THEN

8 CONTROL STATEMENTS
another block of statements ELSE a final block of statements END IF

58

The IF THEN, ELSE IF, and ELSE statements eachgovern one block of statements. There can be any number of ELSE IF statements. The ELSE statement (together with its block) is also optional, and there can be at most one of these. The rst block of statements is executed only if the rst expression is true. Each block after an ELSE IF is executed only if none of the preceding blocks have been executed and the attached ELSE IF expression is true. If there is an ELSE block it is executed only if none of the preceding blocks has been executed. After a block has been executed control is transferred to the statement following the END IF statement at the end of the structure (unless the block ends with some statement which transfers control elsewhere). Any block can contain a complete block-IF structure properly nested within it, or a complete DO-loop, or any other executable statements (except END). It is illegal to transfer control into any block from outside it, but there is no restriction on transferring control out of a block. The rules for logical expressions are covered in section 7.7.

Guidelines
The indentation scheme shown in the examples above indenting each block by a few characters relative to the mended. It makes the structure of the block immediately to match each IF with an END IF. An indenting scheme nested within others. For example:
IF(POWER .GT. LIMIT) THEN IF(.NOT. WARNED) THEN CALL SET('WARNING') WARNED = .TRUE. ELSE CALL SET('ALARM') END IF END IF

is not mandatory but the practice of rest of the program is strongly recomapparent and reduces the risk of failing is especially useful when IF-blocks are

The limited width of the statement eld can be a problem when IF-blocks are nested to a very great depth: but this tends to mean that the program unit is getting too complicated and that it will usually be benecial to divide it into subroutines. If you accidentally omit an END IF statement the compiler will ag the error but will not know where you forgot to put it. In such cases the compiler may get confused and generate a large number of other error messages. When an IF-block which is executed frequently contains a large number of ELSE IF statements it will be slightly more ecient to put the most-likely conditions near the top of the list as when they occur the tests lower down in the list will not need to be executed.

8.3

DO

The DO statement controls a block of statements which are executed repeatedly, once for each value of a variable called the loop-control variable. The number of iterations depends on the

-Loops

8 CONTROL STATEMENTS

59

parameters of the DO statement at the heads of the loop. The rst item after the keyword \DO" is the label which is attached to the last statement of the loop. For example:
*Sum the squares of the first N elements of the array X SUM = 0.0 DO 15, I = 1,N SUM = SUM + X(I)**2 15 CONTINUE

If we had wanted only to sum alternate elements of the arraywe could have used a statement like: and then the value of I in successive loops would have been 1, 3, 5, etc. The nal value would be N if N were odd, or only to N-1 if N were even. If the third parameter is omitted the step-size is one; if it is negative then the steps go downwards. For example
100 DO 100,I = 5,1,-1 WRITE(UNIT=*,FMT=*) I**2 CONTINUE DO 15,I = 1,N,2

will produce 5 records containing the values 25, 16, 9, 4, and 1 respectively. Loops can be nested to any reasonable depth. Thus the following statements will set the two dimensional array FIELD to zero.
REAL FIELD(NX, NY) DO 50, IY = 1,NY DO 40, IX = 1.NX FIELD(IX,IY) = 0.0 CONTINUE CONTINUE DO

40 50

General Form of
The
DO DO DO

Statement

statement has two forms: label , variable = start , limit, step label , variable = start , limit In the second form the step size is implicitly one. The label marks the nal statement of the loop. It must be attached to an executable statement further on in the program unit. The rules permit this statementto be any executable statement except another control statement, but it strongly recommended that you use the CONTINUE statement here. CONTINUE has no other function except to act as a dummy placemarker. The comma after the label is optional but, as noted in section 1.4, is a useful precaution. The variable which follows is known as the loop control variable or loop index; it must be a variable (not an array element) but mayhaveinteger, real, or double precision type. The start, limit, and step values may be expressions of any form of integer, real, or double precision type. If the step value is present it must not be zero, of omitted it is taken as one. The number of iterations is computed before the start of the rst one, using the formula: iterations = MAX(INT(0, (limit - start + step) / step)) Note that if the limit value is less than start the iteration count is zero unless step is negative.

8 CONTROL STATEMENTS

60

A zero iteration count is permitted but means that the contents of the loop will not be executed at all and control is transferred to the rst statement after the end of the loop. The loop control variable does not necessarily reach the limiting value, especially if the step-size is larger than one. Statements within the loop are permitted to alter the value of the expressions used for start, limit, or step but this has no eect on the iteration count which is xed before the rst iteration starts. The loop control variable may be used in expressions but a new value must not be assigned to it within the loop. DO-loops may contain other DO-loops completely nested within them provided that a dierent loop control variable is used in each one. Although it is permissible for two dierent loops to terminate on the same statement, this can be very confusing. It is much better to use a separate CONTINUE statement at the end of each loop. Similarly complete IF-blocks may be nested within DO-loops, and vice-versa. Other control statements may be used to transfer control out of the range of a DO-loop but it is illegal to try to jump into a loop from outside it. If you exit from a loop prematurely in this way the loop control variable keeps its currentvalue and may be used outside to determine how many loops were actually executed. After the normal termination of a DO-loop the loop control variable has the value it had on the last iteration plus one extra increment of the step value. Thus with:
1000 DO 1000, NUMBER = 1,100,3 CONTINUE

On the last iteration NUMBER would be 99, and on exit from the loop NUMBER would be 102. This provision can be useful in the event of exit from a loop because of some error:
PARAMETER (MAXVAL = 100) REAL X(MAXVAL) DO 15, I = 1,MAXVAL READ(UNIT=*, FMT=*, END=90) X(I) CONTINUE NVALS = I - 1

15 90

The action of the statement labelled 90 is to set NVALS to the number of values actually read from the le whether there was a premature exit because the end-of-le was detected or it reached the end of the array space at MAXVAL.

Guidelines
If you a loop-control variable of anytype other than integer there is a risk that rounding errors will accumulate as it is incremented repeatedly. In addition, if the expressions for the start, limit, and step values are not of integer type the number of iterations may not be what you expect because the formula uses the INT function (not NINT). None of these problems can occur if integer quantities are used throughout the DO statement.

8.4 Logical-IF Statement

The logical-IF statement is best regarded as a special case of the IF-block when it only contains one statement. Thus:

8 CONTROL STATEMENTS
IF(E .NE. 0.0) THEN RECIPE = 1.0 / E END IF

61

can be replaced by a single logical-IF statement:
IF(E .NE. 0.0) RECIPE = 1.0 / E

The general form of the logical-IF statement is: IF( logical-expression ) statement The statement is executed only if the logical expression has a true value. Any executable statement can follow except DO, IF, ELSE IF, ELSE, END IF,or END.

8.5 Unconditional

GO TO

The unconditional GO TO statement simply produces a transfer of control to a labelled executable statement elsewhere in the program unit. Its general form is: GO TO label Note that control must not be transferred into an IF-blockora DO-loop from outside it.

Statement

Guidelines
The unconditional GO TO statement makes it possible to construct programs with a very undisciplined structure; such programs are usually hard to understand and to maintain. Good programmers use GO TO statements and labels very sparingly. Unfortunately it is not always possible to avoid them entirely in Fortran because of a lack of alternative control structures. The next example nds the highest common factor of twointegers M and N using a Euclid's algorithm. It can be expressed roughly: while (M N) subtract the smaller of M and N from the other repeat until they are equal.
PROGRAM EUCLID WRITE(UNIT=*, FMT=*) 'Enter two integers' READ(UNIT=*, FMT=*) M, N IF(M .NE. N) THEN IF(M .GT. N) THEN M=M-N ELSE N=N-M END IF GO TO 10 END IF WRITE(UNIT=*, FMT=*)'Highest common factor = ', M END

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8.6 Computed

GO TO

The computed GO TO statement is an alternative to the block-IF when a large number of options are required and they can be selected by the value of an integer expression. The general form of the statement is: GO TO( label1, label2, ... labelN ), integer-expression The comma after the right parenthesis is optional.

Statement

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The expression is evaluated; if its value is one then control is transferred to the statement attached to the rst label in the list; if it is two control goes to the second label, and so on. If the value of the expression is less than one or higher than N (where there are N labels in the list) then the statement has no eect and execution continues with the next statement in sequence. The same label may be present more than once in the list. The computed GO TO suers from many of the same drawbacks as the unconditional GO TO, since if its branches are used without restraint they can become impenetrable thickets. The best way is to follow the computed GO TO statement with the sections of code in order, all except the last terminated with its own unconditional GO TO to transfer control to the end of the whole structure. Any computed GO TO structure could be replaced by an IF-block with a suitable number of ELSE IF clauses. If there are a very large number of cases then this would be a little less ecient; this has to be balanced against the increased clarity of the IF structure compared to the label-ridden GO TO. An example of the use of the computed GO TO is given here in a subroutine which computes the number of days in a month, given the month number MONTH between 1 and 12, and the four-digit year number in YEAR. Note that each section of code except the last is terminated with a GO TO statement to escape from the structure.
SUBROUTINE CALEND(YEAR, MONTH, DAYS) INTEGER YEAR, MONTH, DAYS GO TO(310,280,310,300,310,300,310,310,300,310,300,310)MONTH * Jan Feb Mar Apr May Jun Jly Aug Sep Oct Nov Dec STOP 'Impossible month number' *February: has 29 days in leap year, 28 otherwise. 280 IF(MOD(YEAR,400) .EQ. 0 .OR. (MOD(YEAR,100) .NE. 0 $ .AND. MOD(YEAR,4) .EQ. 0)) THEN DAYS = 29 ELSE DAYS = 28 END IF GO TO 1000 * Short months 300 DAYS = 30 GO TO 1000 * Long months 310 DAYS = 31 * return the value of DAYS 1000 END

8.7

STOP

The STOP statement simply terminates the execution of the program and returns control to the operating system. Its general form is: STOP ' character constant ' The character constant (whichmust be a literal and not named constant) is optional: if present its value is \made available" to the user; usually it the message appears on your terminal. For compatibility with Fortran66 it is possible to use a string of one to ve decimal digits instead of the character constant.

Statement

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Ideally a program should only return control to the operating system from one point, the end of the main program, where the END statement does all that is necessary. In practice, even in the best-planned programs, situations can arise which makeitpointless to continue. If these are detected in the main program there is always the option of jumping to the END statement, but within procedures there maybeno choice but to use a STOP statement.

9 Procedures
Any set of computations can be encapsulated in a procedure. The main purpose of a procedure is to allow the same set of operations to be invoked at dierent points in a program. Procedures also make it possible to use the same code in several dierent programs. It is good practice to split a large program into sections whenever it becomes too large to be handled conveniently in one piece. The optimum size of a program unit is quite small, probably no more than 100 lines. Four dierent forms of procedure can be used in Fortran programs: Intrinsic functions Statement functions External functions (also known as function subprograms) Subroutines. Intrinsic functions are provided automatically by the Fortran system, whereas the other three forms of procedure are user-written. Statement functions, which are dened with the statement function statement, can be only be used in the program unit in which they were dened and are sub ject to other special restrictions. External functions and subroutines are two alternative forms of external procedure: each is specied as a separate program unit and can be used (with only a few restrictions) anywhere else in the program.

9.1 Intrinsic Functions

Intrinsic functions havea number of unique properties. The data type of eachintrinsic function is known to the Fortran system and is not sub ject to the normal rules. IMPLICIT and type statements alone have no eect on them. Some intrinsic functions have generic names: when these are used the compiler selects the appropriate specic function according to the data type of the arguments. A few intrinsic functions such as MAX, MIN, and CMPLX, are allowed to have a variable number of arguments, but all of the arguments must have the same data type. User-written procedures cannot have optional arguments or generic type. Although intrinsic functions can be used in any program unit, their names are not global, nor are they reserved words. It is, however, best to avoid choosing a name for a variable or array which is identical to that of an intrinsic function. It may cause confusion and in the long run it may make it more dicult to enhance the program. A name clash is more serious if it involves an external function or subroutine, for in this case the external procedure name must be specied in an EXTERNAL statement to resolve the ambiguity. By this means it is possible to substitute an external function of your own for one of the intrinsic functions. The Fortran Standard species a fairly extensive set of intrinsic functions whichmust always be available but it does not prevent the provision of additional ones. Many systems provide additional intrinsic functions which, for example, obtain the current date and time, generate

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pseudo-random numbers, or evaluate Gaussian probability. The main drawback in using nonstandard functions is that you mayhave to nd a substitute if your program is moved to another system which does not have the same extensions. The standard intrinsic functions for the arithmetic types are described in detail in section 6.2; those used with character-strings are covered in section 7.5. A complete alphabetical list is provided in the appendix.

9.2 StatementFunctions

Statement functions can be dened within any executable program unit by means of statement function statements. They can only be used, however, within the same program unit. Although statement functions have limited uses, they are unjustly neglected by many programmers. The statement function statement resembles an ordinary assignment statement. For example: The function FAHR converts a temperature in degrees Celsius to its equivalent in Fahrenheit. Thus FAHR(20.0) would return a value 68.0 approximately. A statement function can have any number of dummy arguments (such as CELS above) all of whichmust appear in the expression on the right-hand side; this expression may also include constants, variables, or array elements used elsewhere in the program. When the function is called the currentvalues of these items will be used. For example:
REAL M1, M2, G, R NEWTON(M1, M2, R) = G * M1 * M2 / R**2 FAHR(CELS) = 32.0 + 1.8 * CELS

A reference to the function in an assignment statement such as: will return a value depending on the values of the actual arguments X, Y, and DIST, and that of the variable G at the time the function is referenced. Denitions of statement functions can also include references to intrinsic functions, external functions, or previously dened statement functions:
PARAMETER (PI SIND(THETA) = COSD(THETA) = TAND(THETA) = = 3.14159265, DTOR = PI/180.0) SIN(THETA * DTOR) COS(THETA * DTOR) SIND(THETA) / COSD(THETA) FORCE = NEWTON(X, Y, DIST)

These denitions allow trigonometry on angles specied in degrees rather than radians. The scope of each dummy argument name (such as THETA above) is that of the statement alone; these names can be used elsewhere in the program unit as variables of the same data type with no eect whatever on the evaluation of the function. Statement functions can haveany data type; the name and arguments follow the normal type rules. They can be useful in character handling, for example:
LOGICAL MATH, DIGIT, DORM CHARACTER C*1 DIGIT(C) = LGE(C, '0') .AND. LLE(C, '9') MATH(C) = INDEX('+-*/', C) .NE. 0 DORM(C) = DIGIT(C) .OR. MATH(C)

These three functions each return a logical value when presented with a single character argument: DIGIT tests to see whether the character is a digit, MATH whether it is an operator symbol,

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and DORM will test for either condition. Note the use of the lexical comparison functions LGE and LLE in the denition of DIGIT which make it completely independent of the local character code.

StatementFunction Rules
Statement function statements must appear after any the specication statements but before all executable statements in the program unit. They maybe intermixed with DATA and FORMAT statements. The general form is: function ( dummy1, dummy2, ... dummyN ) = expression The function may have any data type; the expression will normally have the same data type but if both have an arithmetic type then the normal conversion rules for arithmetic assignment statements apply. The name of the function must be distinct from all other symbolic names in the program unit. It may appear in type statements but not in other specication statements. (There is one exception: a common block is permitted to have the same name as a statement function but since common block names always appear between slashes there is little risk of confusion). If the function has character type its length must be an integer constant expression. The dummy arguments are simply symbolic names. A name may not appear more than once in the same list. These names may be used elsewhere in the program unit as variables of the same data type. The expression must contain the dummy arguments as operands. The operands may also include: literal constants, named constants, variables, and array elements; these will have their values at the time the function is executed and must then be dened. references to intrinsic and external functions, references to statement functions dened earlier in the same program unit, complete expressions enclosed in parentheses. Note that character substrings are not permitted. The variables and array elements used in the expression must be dened at the time that the function reference is executed.

Guidelines
Although statement functions have a limited role to play in programs because they can only be dened in a single statement, references to statement functions they may be executed more eciently than references to external functions; many modern compilers expand statement function references to in-line code when it is advantageous to do so. If the same statement function is needed in more than one program unit it would is possible to use an INCLUDE facility to provide the same denition each time, but it will usually be better to use an external function instead.

9.3 External Procedures

There are two forms of external procedure, both of which take the form of a complete program unit.

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FUNCTION statement. They are executed whenever the corresponding function is used as an operand in an expression. Subroutines, which are specied by a program unit starting with a SUBROUTINE statement. They are executed in response to a CALL statement. In either form the last statement of the program unit must be an END statement. Any other statements (except PROGRAM or BLOCK DATA statements) may be used within the program unit. There are two statements provided especially for use in external procedures. The SAVE statement ensures that the values of local variables and arrays are preserved after the procedure returns control to the calling unit: these values will then be available if the procedure is executed subsequently. The RETURN statementmay be used to terminate the execution of the procedure and cause an immediate return to the control of the calling unit. Execution of the END statement at the end of the procedure has exactly the same eect. Both of these are described in full later in the section. Most Fortran systems also allow external procedures to be specied in languages other than Fortran: they can be called in the same wayasFortran procedures but their internal operations are, of course, beyond the scope of this book. It is best to think of the subroutine as the more general form of procedure; the external function should be regarded as a special case for use when you only need to return a single value to the calling unit. Here is a simple example of a procedure which converts a time of day in hours, minutes, and seconds into a count of seconds since midnight. Since only one value needs to be returned, the procedure can have the form of an external function. (In fact this is such a simple example that it would have been possible to dene it as a statement function.) *TSECS converts hours, minutes, seconds to total seconds. REAL FUNCTION TSECS(NHOURS, MINS, SECS) INTEGER NHOURS, MINS REAL SECS TIME = ((NHOURS * 60) + MINS) * 60 + SECS END

External functions, which are specied by a program unit starting with a

Thus if we use a function reference like TSECS(12,30,0.0) in an expression elsewhere in the program it will convert the time to seconds since midnight (about 45000.0 seconds in this case). The items in parentheses after the function name : are known as the actual arguments of the function; these values are transferred to the corresponding dummy arguments of the procedure before it is executed. In this example the argument list is used only to transfer information into the function from outside, the function name itself returns the required value to the calling program. In subroutines, however, there is no function name to return information but the arguments can be used for transfers in either direction, or both. The rules permit them to be used in this more general way in functions, but it is a practice best avoided. The next example performs the inverse conversion to the TSECS function. Since it has to return three values to the calling program unit the functional form is no longer appropriate, and a subroutine will be used instead.
(NHOURS, MINS, SECS) (12,30,0.0)

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*Subroutine HMS converts TIME in seconds into hours, mins,secs. SUBROUTINE HMS(TIME, NHOURS, MINS, SECS) REAL TIME, SECS INTEGER NHOURS, MINS NHOURS = INT(TIME / 3600.0) SECS = TIME - 3600.0 * NHOURS MINS = INT(SECS / 60.0) SECS = TIME - 60.0 * MINS END

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In this case the subroutine could be executed by using a statement such as:
CALL HMS(45000.0, NHRS, MINS, SECS) WRITE(UNIT=*, FMT=*) NHRS, MINS, SECS

Here the rst argument transfers information into the subroutine, the other three are used to return the values which it calculates. You do not have to specify whether a particular argument is to transfer information in or out (or in both directions), but there are rules about the form of actual argument that you can use in each case. These are explained in full below.

Procedure Independence
Each program unit has its own independent set of symbolic names and labels. Type statements and IMPLICIT statements may be used to specify their data types. External procedures can themselves call any other procedures and these may call others in turn, but procedure are not allowed to call themselves either directly or indirectly; that is recursive calling is not permitted in Fortran.

Information Transfer
Information can be transferred to and from an external procedure byany of three methods. An argument list: as shown in the two examples above. This is the preferred method of interfacing as it is the most exible and modular. It is described in detail in the remainder of this section. Common blocks: these are lists of variables or arrays which are stored in areas of areas of memory shared between two or more program units. They are useful in special circumstances when procedures have to be coupled closely together, but are otherwise less satisfactory. Common blocks are covered in detail in section 12. External les: interfacing via external les is neither convenient nor ecient but it is mentioned here to point out that external les are global. Once a le has been opened in any program unit it can be accessed anywhere in the program provided that the appropriate I/O unit numberisavailable. A unit number can be passed into a procedure as an integer argument.

Procedure Execution
It is not necessary to know how the Fortran system actually transfers information from one procedure to another to make use of the system, but the rules governing the process are somewhat

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complicated and it may be easier to understand them if you appreciate the basis on which they have been formulated. The rules in the Fortran Standard are based on the assumption that the address of an actual argument is transferred in each case: this may or may not be true in practice but the properties will be the same as if it is. This means that when you reference a dummyvariable or assign a new value to one you are likely to be using the memory location occupied by the actual argument. By this means even large arrays can be transferred eciently to procedures. A slight modication of this system is needed for items of character type so that the length of the item can be transferred as well as its address. When a function reference or CALL statement is executed any expressions in the argument list are evaluated; the addresses of the arguments are then passed to the procedure. When it returns control this automatically makes updated values available to the corresponding items in the actual argument list.

Functions with Side-eects

The rules of Fortran allow functions to have side-eects, that is to alter their actual arguments or to change other variables within common blocks. Functions with side-eects cannot be used in expressions where any of the other operands of the expression would be aected, nor can they be used in subscript or substring references when any other expression used in the same references would be aected. This rule ensures that the value of an expression cannot depend arbitrarily on the way in which the computer chooses to evaluate it. There are also restrictions on functions which make use of input/output statements even on internal les: these cannot be used in expressions in other I/O statements. This is to avoid the I/O system being used recursively. By far the best course is to use the subroutine form for any procedure with side-eects.

9.4 Arguments of External Procedures

Arguments can pass information into a procedure or out from it, or in both directions. This just depends on the way that the dummy argument is used within the procedure. Although any argument order is permitted, it is common practice to put input arguments rst, then those that pass information both ways, and then arguments which just return information from the procedure. The rules for argument association are the same for both forms of external procedure. The list of dummy arguments (sometimes called formal arguments) of an external procedure is specied in its FUNCTION or SUBROUTINE statement. There can be any number of arguments, including none at all. If there are no arguments then the parentheses can be omitted in the CALL and SUBROUTINE statement but not in a FUNCTION statement or function reference. The dummy argument list is simply a list of symbolic names which can representany mixture of variables arrays procedures. A name cannot, of course, appear twice in the same dummy argument list. Dummy variables, arrays, and procedures are distinguished only by the way that they are used within the procedure. The dimension bounds of a dummy arrays must be specied in a

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subsequenttype or DIMENSION statement; dummy procedures must appear in a CALL or EXTERNAL statement or be used in a function reference; anything else is, by elimination, a dummy argument variable. Dummy argument variables and arrays can be used in executable statements in just the same way as local items of the same form, but they cannot appear in SAVE, COMMON, DATA, or EQUIVALENCE statements.

Argument Association

The actual arguments of the function reference or CALL statement become associated with the corresponding dummy arguments of the FUNCTION or SUBROUTINE statement. The main rules are as follows: There must be the same number of actual and dummy arguments; they are associated solely by their position in the two lists. Optional arguments are not permitted in Fortran77. If the dummy argument is a variable, array, or procedure used as a function then the corresponding actual argumentmust have the same data type. If the dummy argument is an array then its array bounds must not be larger than those of the corresponding actual argument. Alternatively the dimension bounds of a dummy array can be passed in by means of other procedure arguments to form an adjustable. This option and the assumed-size array are both described in section 9.6. If the dummy argumentisa character item then its length must not be greater than that of the corresponding actual argument. Alternatively there is a passed-length option for character arguments: see section 9.5. Because program units are compiled independently, it is dicult for the compiler to check for mismatches in actual and dummy argument lists. Although mismatches could, in principle, be detected by the linker, this rarely seems to happen in practice. Errors, particularly mismatches of data type or array bounds, are especially easy to make but hard to detect. Sometimes the only indication is that the program produces the wrong answer. This shows how important it is to check procedure interfaces.

Duplicate Arguments
The same actual argument cannot be used more than once in a procedure call if the corresponding dummy arguments are assigned new values. For example, with:
SUBROUTINE FUNNY(X, Y) X = 2.0 Y = 3.0 END

A call such as:

would be illegal because the system would try to assign both 2.0 and 3.0 to the variable A. A similar restriction applies to variables which are returned via a common block and also through the procedure argument list.

CALL FUNNY(A, A)

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9.5 Variables as Dummy Arguments

If the dummy argument of a procedure is a variable and it has a value assigned to it within the procedure, then the corresponding actual argument can be: avariable, an array element, or acharacter substring. If, however, the dummyvariable preserves its initial value throughout the execution then the actual argument can be any of these three forms above or alternatively: an expression of any form (including a constant). The reason for this restrictions is easy to see by considering the ways of calling the subroutine SILLY in the next example:
SUBROUTINE SILLY(N, M) N=N+M END

If it is called with a statement such as:
NUMBER = 10 CALL SILLY(NUMBER, 5)

then the value of NUMBER will be updated to 15 as a result of the call. But it is illegal to call the function with a constant as the rst argument, thus:
CALL SILLY(10, 7)

because on exit the subroutine will attempt to return the value of 17 to the actual argument which was specied as the constant ten. The eects of committing such an error are systemdependent. Some systems detect the attempt to over-write a constant and issue an error message; others ignore the attempt and allow the program to continue; but some systems will actually go ahead and over-write the constant with a new value, so that if you use the constant 10 in some subsequent statement in the program you may get a value of 17. Since this can havevery puzzling eects and be hard to diagnose, it is importantto avoid doing this inadvertently. If you make use of procedures written by other people you maybe worried about unintentional eects of this sort. In principle it should be possible to prevent a procedure altering a constant argumentby turning each one into an expression, for example like this: or
CALL SILLY(+10, +5)

Although either of these forms should protect the constants, it is still against the rules of Fortran for the procedure to attempt to alter the values of the corresponding dummy arguments. You will have to judge whether it is better to break the rules of the language than to risk corrupting a constant.

CALL SILLY((10), (5))

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71 these are evaluated before the procedure starts operands of the expression this has no eect The same rule applies to array subscript and the procedure call consists of:

Expressions, Subscripts, and Substrings
If the actual argument contains expressions then to execute; even if the procedure later modies on the value passed to the dummy argument. character substring expressions. For example, if

and the procedure assigns a new value to the second argument, N, during its execution, it has no eect on the other arguments which all use the original value of N. The updated value of N will, of course, be passed back to the calling unit.

CALL SUB( ARRAY(N), N, SIN(4.0*N), TEXT(1:N) )

Passed-length Character Arguments
Acharacter dummy argument will have its length set automatically to that of the corresponding actual argument if the special length specication of *(*) is used. To illustrate this, here is a procedure to count the number of vowels in a character string. It uses the intrinsic function LEN to determine the length of its dummy argument, and the INDEX function to see whether each character in turn is in the set "AEIOU" or not.
INTEGER FUNCTION VOWELS(STRING) CHARACTER*(*) STRING VOWELS = 0 DO 25, K = 1,LEN(STRING) IF( INDEX('AEIOU', STRING(K:K)) .NE. 0) THEN VOWELS = VOWELS + 1 END IF CONTINUE END

25

Note that the function has a data type which is not the default for its initial letter so that it will usually be necessary to specify its name in a INTEGER statement in each program unit which references the function. This passed-length mechanism is recommended not only for general-purpose software where the actual argument lengths are unknown, but in all cases unless there is a good reason to specify a dummy argument of xed length. There is one restriction on dummy arguments with passed length: they cannot be operands of the concatenation operator (//) except in assignment statements. Note that the same form of length specication \*(*)" can be used for named character constants but with a completely dierent meaning: named constants are not sub ject to this restriction.

9.6 Arrays as Arguments

If the dummy argument of a procedure is an array then the actual argument can be either: an array name (without subscripts) an array element. The rst form transfers the entire array; the second form, which just transfers a section starting at the specied element, is described in more detail further on.

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The simplest, and most common, requirement is to make the entire contents of an array available in a procedure. If the actual argument arrays are always going to be the same size then the dummy arrays in the procedure can use xed bounds. For example:
SUBROUTINE DOT(X, Y, Z) *Computes the dot product of arrays X and Y of 100 elements * producing array Z of the same size. REAL X(100), Y(100), Z(100) DO 15, I = 1,100 Z(I) = X(I) * Y(I) 15 CONTINUE END

This procedure could be used within a program unit like this:
PROGRAM PROD REAL A(100), B(100), C(100) READ(UNIT=*,FMT=*)A,B CALL DOT(A, B, C) WRITE(UNIT=*,FMT=*)C END

This is perfectly legitimate, if in exible, since it will not work on arrays of any other size.

Adjustable Arrays
A more satisfactory solution is to generalise the procedure so that it can b of any size. This is done by using an adjustable arrays declaration. Here each dimension bound expression may include integer variables which are also procedure (or members of a common block). The following example shows done:
SUBROUTINE DOTPRO(NPTS, X, Y, Z) REAL X(NPTS), Y(NPTS), Z(NPTS) DO 15, I = 1,NPTS * etc.

e used on arrays the operands in arguments of the how this may be

In this case the calling sequence would be something like: An adjustable array declaration is permitted only for arrays which are dummy arguments, since the actual array space has in this case already been allocated in the calling unit or at some higher level. The method can be extended in the obvious wayto cover multi-dimensional arrays and those with upper and lower bounds, for example:
SUBROUTINE MULTI(MAP, K1, L1, K2, L2, TRACE) DOUBLE PRECISION MAP(K1:L1, K2:L2) REAL TRACE(L1-K1+1) CALL DOTPRO(100, A, B, C)

The adjustable array mechanism can, of course, be used for arrays of any data type; an adjustable array can also be passed as an actual argument of a procedure with, if necessary, the array bounds passed on in parallel.

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Each array bound of a dummy argument array may be an integer expression involving not only constants but also integer variables passed in to the procedure either as arguments or by means of a common block. The extent of each dimension of the arraymust not be less than one and must not be greater than the extent of the corresponding dimension of the actual argument array. If any integer variable (or named constant) used in an array-bound expression has a name which does not imply integer type then the INTEGER statement which species its type must precede its use in a dimension-bound expression.

Assumed-size Arrays
There may be circumstances in which it is impracticable to use either xed declarations in a procedure because the actual size of the array is unknown starts executing. In this case an assumed-size array is a viable alternative. permitted for dummy argument arrays of procedures, but here the array is, to be of unknown or indenite size. For example:
REAL FUNCTION ADDTWO(TABLE, ANGLE) REAL TABLE(*) N = MAX(1, NINT(SIN(ANGLE) * 500.0)) ADDTWO = TABLE(N) + TABLE(N+1) END

or adjustable array when the procedure These are also only eectively, declared

Here the procedure only knows that array TABLE is one-dimensional with a lower-bound of one: that is all it needs to know to access the appropriate elements N and N+1. In executing the procedure it is our responsibility to ensure that the value of ANGLE will never result in an array subscript which is out of range. This is always a danger with assumed-size arrays. Because the compiler does not haveany information about the upper-bound of an assumed-size array it cannot use any array-bound checking code even if it is normally able to do this. An assumed-size array can only have the upper-bound of its last dimension specied by an asterisk, all the other bounds (if any) must conform to the normal rules (or be adjustable using integer arguments). An assumed size dummy argument array is specied with an asterisk as the upper bound of its last (or only) dimension. All the other dimension bounds, if any, must conform to normal rules for local arrays or adjustable arrays. There is one important restriction on assumed size arrays: they cannot be used without subscripts in I/O statements, for example in the input list of a READ statement or the output list of a WRITE statement. This is because the compiler has no information about the total size of the array when compiling the procedure.

Array Sections
The rules of Fortran require that the extent of an array (in each dimension if it is multidimensional) must be at least as large in the actual argument as in the dummy argument, but they do not require actual agreement of both lower and upper bounds. For example:
PROGRAM CONFUS REAL X(-1:50), Y(10:1000) READ(UNIT=*,FMT=*) X, Y CALL OUTPUT(X)

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CALL OUTPUT(Y) END SUBROUTINE OUTPUT(ARRAY) REAL ARRAY(50) WRITE(UNIT=*,FMT=*) ARRAY END

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The eect of this program will be to output the elements X(-1) to X(48) since X(48) corresponds to ARRAY(50), and then output Y(10) to Y(59) also. The subroutine will work similarly on a slice through a two-dimensional array:
PROGRAM TWODIM REAL D(100,20) * ... NSLICE = 15 CALL OUTPUT(D(1,NSLICE))

In this example the slice of the array from elements D(1,15) to D(50,15) will be written to the output le. In order to work out what is going to happen you need to know that Fortran arrays are stored with the rst subscript most rapidly varying, and that the argument association operates as if the address of the specied element were transferred to the base address of the dummy argument array. The use of an array element as an actual argument when the dummy argument is a complete arrayis a very misleading notation and the transfer of array sections should be avoided if at all possible.

Character Arrays
When a dummy argument isacharacter array the passed-length mechanism can be used in the same way as for a character variable. Every element of the dummy array has the length that was passed in from the actual argument. For example, a subroutine designed to sort an arrayofcharacter strings into ascending order might start with specication statements like these:
SUBROUTINE SORT(NELS, NAMES) INTEGER NELS CHARACTER NAMES(NELS)*(*)

Alternatively the actual argument can be a character variable or substring. In such cases it usually makes more sense not to use the passed-length mechanism. For example an actual argument declared: could be passed to a subroutine which declared it as an array of four 20-character elements:
SUBROUTINE SPLIT(LINE) CHARACTER LINE(4)*20 CHARACTER*80 LINE

Although this is valid Fortran, it is not a very satisfactory programming technique to use a procedure call to alter the shape of an item so radically.

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9.7 Procedures as Arguments

Fortran allows one procedure to be used as the actual argument of another procedure. This provides a powerful facility, though one that most programmers use only rarely. Procedures are normally used to carry out a given set of operations on dierent sets of data; but sometimes you want to carry out the same set of operations on dierent functional forms. Examples include: nding the gradient of a function, integrating the area under a curve, or simply plotting a graph. If the curve is specied as a set of data points then you can simply pass over an array, but if it is specied by means of some algorithm then the procedure which evaluates it can itself be an actual argument. In the next example, the subroutine GRAPH plots a graph of a function MYFUNC between specied limits, with its argument range divided somewhat arbitrarily into 101 points. For simplicity it assumes the existence of a subroutine PLOT which moves the pen to position (X,Y). Some other subroutines would, in practice, almost certainly be required.
SUBROUTINE GRAPH(MYFUNC, XMIN, XMAX) *Plots functional form of MYFUNC(X) with X in range XMIN:XMAX. REAL MYFUNC, XMIN, XMAX XDELTA = (XMAX - XMIN) / 100.0 DO 25, I = 0,100 X = XMIN + I * XDELTA Y = MYFUNC(X) CALL PLOT(X, Y) 25 CONTINUE END

The procedure GRAPH can then be used to plot a function simply by providing its name them as the rst argument of the call. The only other requirement is that the name of each function used as an actual argument in this waymust be specied in an INTRINSIC or EXTERNAL statement, as appropriate. Thus:
PROGRAM CURVES INTRINSIC SIN, TAN EXTERNAL MESSY CALL GRAPH(SIN, 0.0, 3.14159) CALL GRAPH(TAN, 0.0, 0.5) CALL GRAPH(MESSY, 0.1, 0.9) END REAL FUNCTION MESSY(X) MESSY = COS(0.1*X) + 0.02 * SIN(SQRT(X)) END

This will rst plot a graph of the sine function, then of the tangent function with a dierent range, and nally produce another plot of the external function called MESSY. These functions must, of course, have the same procedure interface themselves and must be called correctly in the GRAPH procedure. It is possible to pass either a function or a subroutine as an actual argument in this way: the only dierence is that a CALL statement is used instead of a function reference to execute the dummy procedure. It is possible to pass a procedure through more than one level of procedure call in the same way. Continuing the last example, another level could be introduced like this:

9 PROCEDURES
PROGRAM CURVE2 EXTERNAL MESSY INTRINSIC SIN, TAN CALL GRAPH2(PRETTY) CALL GRAPH2(TAN) END SUBROUTINE GRAPH2(PROC) EXTERNAL PROC CALL GRAPH(PROC, 0.1, 0.7) END

76

Thus the procedure GRAPH2 sets limits to each plot and passes the procedure name on to GRAPH. The symbolic name PROC must be declared in an EXTERNAL statement as it is a dummy procedure: an EXTERNAL statement is required whether the actual procedure at the top level is intrinsic or external. The syntax of the INTRINSIC and EXTERNAL statements is given in section 9.12 below. The name of an intrinsic function used as an actual argument must be a specic name and not a generic one. This is the only circumstance in whichyou still have to use specic names for intrinsic functions. A full list of specic names is given in the appendix. A few of the most basic intrinsic functions which are often expanded to in-line code (those for type conversion, lexical comparison, as well as MIN and MAX) cannot be passed as actual arguments.

9.8 Subroutine and Call Statements

It is convenient to describe these two statements together as they have to be closely matched in use. The general form of the SUBROUTINE statement is: SUBROUTINE name ( dummy1, dummy2, ... dummyN ) or SUBROUTINE name The second form just indicates that if there are no arguments then the parentheses are optional. The symbolic name of the subroutine becomes a global name; it must not be used at all within the program unit and must not be used for any other global item within the entire executable program. The dummy arguments are also simply symbolic names. The way in which these are interpreted is covered in the next section. The CALL statement has similar general forms: CALL name ( arg1, arg2, ... argN ) or CALL name Again, if there are no arguments the parentheses are optional. The name must be that of a subroutine (or dummy subroutine). Each arg is an actual argument which can be a variable, array, substring, array element or any form of expression. The permitted forms, which depend on the form of the corresponding dummy argument and how it is used within the subroutine, are fully described in the preceding sections.

9.9

RETURN

The

RETURN RETURN

statement just consists of the keyword

Statement

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Its eect is to stop the procedure executing and to return control, and where appropriate argument and function values, to the calling program unit. The execution of the END statement at the end of the program unit has the exactly the same eect, so that RETURN is super uous in procedures which have only one entry and one exit point (as all well-designed procedures should). It is, however, sometimes convenient to use RETURN for an emergency exit. Here is a somewhat simple-minded example just to illustrate the point:
REAL *Computes REAL IF(X FUNCTION HYPOT(X, Y) the hypotenuse of a right-angled triangle. X, Y .LE. 0.0 .OR. Y .LE. 0.0) THEN WRITE(UNIT=*,FMT=*)'Warning: impossible values' HYPOT = 0.0 RETURN END IF HYPOT = SQRT(X**2 + Y**2) END

This function could be used in another program unit like this:
X = HYPOT(12.0, 5.0) Y = HYPOT(0.0, 5.0)

whichwould assign to X the value of 13.0000 approximately, while the second function call would cause a warning message to be issued and would return a value of zero to Y. In the external function shown above it would have been perfectly possible to avoid having two exits points by an alternative ending to the procedure, such as:
IF(X .LE. 0.0 .OR. Y .LE. 0.0) THEN WRITE(UNIT=*,FMT=*)'Warning: impossible values' HYPOT = 0.0 ELSE HYPOT = SQRT(X**2 + Y**2) END IF END

In more realistic cases, however, the just one statement and it might then were to be used than with almost all possibility for emergency exits is to placed on the END statement.

main part of the calculation would be much longer than be easier to understand the working if a RETURN statement of the procedure contained within an ELSE-block. A third use an unconditional GO TO statement to jump to a label

9.10
The is:

FUNCTION

FUNCTION

statementmust be the rst statementof every external function. Its general form

Statement

type FUNCTION( dummy1, dummy2, ... dummyN ) The type specication is optional: if it is omitted then the type of the result is determined by the usual rules. The function name mayhave its type specied bya type or IMPLICIT statement which appears later in the program unit. If the function is of type character then the length may be specied by a literal constant (but not a named constant) or may be given in the form

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CHARACTER*(*)

78

in which case the length will be passed in as the length declared for the function name in the calling program unit. There may be any number of dummy arguments including none, but the parentheses must still be present. Dummy arguments may, as described in section 9.4, be variables, arrays, or procedures. The function name may be used as a variable within the function subprogram unit; a value must be assigned to this variable before the procedure returns control to the calling unit. If the function name used the passed-length option then the corresponding variable cannot be used as an operand of the concatenation operator except in an assignment statement. The passed-length option is less useful for character functions than for arguments because the length is inevitably the same for all references from the same program unit. For example:
PROGRAM FLEX CHARACTER CODE*8, CLASS*6, TITLE*16 CLASS = CODE('SECRET') TITLE = CODE('ORDER OF BATTLE') END CHARACTER*(*) FUNCTION CODE(WORD) CHARACTER WORD*(*), BUFFER*80 DO 15, K = 1,LEN(WORD) BUFFER(K:K) = CHAR(ICHAR(WORD(K:K) + 1) CONTINUE CODE = BUFFER END

15

Unfortunately, although this function can take in an argumentof any length up to 80 characters long and encode it, it can only return a result of exactly 8 characters long when called from the program FLEX, so that it will not produce the desired result when provided with the longer character string. This limitation could be overcome with the use of a subroutine with a second passed-length argument to handle the returned value. Functions without arguments do not have a wide range of uses but applications for them do occur up from time to time, for example when generating random numbers or reading values from an input le. For example:
PROGRAM COPY REAL NEXT DO 10,I = 1,100 WRITE(UNIT=*,FMT=*) NEXT() CONTINUE END REAL FUNCTION NEXT() READ(UNIT=*,FMT=*) NEXT END

10

The parentheses are needed on the function call to distinguish it from a variable. The function statement itself also has to have the empty pair of parentheses, presumably to match the call.

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9.11
SAVE

SAVE

is a specication statement which can be used to ensure that variables and arrays used within a procedure preserve their values between successive calls to the procedure. Under normal circumstances local items will become \undened" as soon as the procedure returns control to the calling unit. It is often useful to store the values of certain items used on one call to avoid doing extra work on the next. For example:
SUBROUTINE EXTRA(MILES) INTEGER MILES, LAST SAVE LAST DATA LAST /0/ WRITE(UNIT=*, FMT=*) MILES - LAST, ' more miles.' LAST = MILES END

Statement

This subroutine simply saves the value of the argument MILES each time and subtracts it from the next one, so that it can print out the incremental value. The value of LAST had to be given an initial value using a DATA statement in order to prevent its use with an undened value on the initial call. Local variables and arrays and complete named common blocks can be saved using SAVE statements, but not variables and arrays which are dummy arguments or which appear within common blocks. Items which are initially dened with a DATA statement but which are never updated with a new value do not need to be saved. The SAVE statement has two alternative forms: SAVE item, item, ... item Where each item can be a local variable or (unsubscripted) array, or the name of a common block enclosed in slashes. The second form, with no list of items, saves all the allowable items in the program unit. This form should not be used in any program unit which uses a common block unless all common blocks used in that program unit are also used in the main program or saved in every program unit in which it appears. The SAVE statement can be used in the main program unit (so that it could be packaged with other specications in an INCLUDE le) but has no eect. Many current Fortran systems have a simple static storage allocation scheme in which all variables are saved whether SAVE is used or not. But on small computers which make use of disc overlays, or large ones with virtual memory systems, this may not be so. You should always take care to use the SAVE statementanywhere that its use is indicated to makeyour programs safe and portable. Even where it is at present strictly redundant it still indicates to the reader that the procedure works by retaining information from one call to the next, and this is valuable in itself.
SAVE

9.12

EXTERNAL

The EXTERNAL statement is used to name external procedures which are required in order to run a given program unit. It may specify the name of any external function or subroutine. It is required in three rather dierent circumstances: whenever an external procedure or dummy procedure is used as the actual argument of another procedure call;

and

INTRINSIC

Statements

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program. This specialised use is covered further in section 12.4. The INTRINSIC statement is used to declare a name to be that of an intrinsic function. It is normally necessary only when that function is to be used as the actual argument of another procedure call, but may also be advisable when calling a non-standard intrinsic function to removeanyambiguity which might arise if an external function of the same name also existed. The general form of the two statements is the same: EXTERNAL ename, ename, ... ename INTRINSIC iname, iname, ... iname Where ename can be the name of an external function or subroutine or a dummy procedure; iname must be specic name of an intrinsic function. For example, to use the real and double precision versions of the trigonometric functions as actual arguments we need: When the function name SIN is used as an actual argument it refers to the specic real sine function; in other contexts it still has its usual generic property. The use of procedures as actual arguments is covered in detail in section 9.7; a list of specic names of intrinsic functions is given in the appendix.
INTRINSIC SIN, COS, TAN, DCOS, DSIN, DTAN

to call any procedure which has a name duplicating an intrinsic function; to ensure that a named block data subprogram is linked into the complete executable

10 Input/Output Facilities
The I/O system of Fortran is relatively powerful, exible, and well-dened. Programs can be portable and device-independent even if they make extensive use of input/output facilities: this is dicult if not impossible in many other high-level languages. The eects of the hardware and operating system cannot, of course, be ignored entirely but they usually only aect fairly minor matters such as the forms of le-name and the maximum record length that can be used. The READ and WRITE statements are most common and generally look like this:
READ(UNIT=*, FMT=*) NUMBER WRITE(UNIT=13, ERR=999) NUMBER, ARRAY(1), ARRAY(N)

The pair of parentheses after the word READ or WRITE encloses the control-list: a list of items which species where and how the data transfer takes place. The items in this list are usually specied with keywords. The list of data items to be read or written follow the control-list. Other input/output statements have a similar form except that they only have a control-list. There are the le-handling statements OPEN, CLOSE, and INQUIRE, as well as the REWIND and BACKSPACE statements which alter the currently active position within a le. Before covering the these statements in detail, it is necessary to explain some of the concepts and terminology involved.

10.1 Files, I/O Units, and Records

In Fortran the term le is used for anything that can be handled with a READ or WRITE statement: the term covers not just data les stored on disc or tape and also peripheral devices such as printers or terminals. Strictly these should all be called external les, to distinguish them from internal les. An internal le is nothing more than a character variable or array which is used as a temporary le while the program is running. Internal les can be used with READ and WRITE statements in

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order to process character information under the control of a format specication. They cannot be used by other I/O statements. Before an external le can be used it must be connected to an I/O unit. I/O units are integers which maybe chosen freely from zero up to a system-dependent limit (usually at least 99). Except in OPEN and INQUIRE statements, les can only be referred to via their unit numbers. The OPEN statement connects a named le to a numbered unit. It usually species whether the le already exists or whether a new one is to be created, for example:
OPEN(UNIT=1, FILE='B:INPUT.DAT', STATUS='OLD') OPEN(UNIT=9, FILE='PRINTOUT', STATUS='NEW')

For simplicity most of the examples in this section show an actual integer as the unit identier, but it helps to make software more modular and adaptable if a named constantora variable is used instead. I/O units are a global resource. A le can be opened in any program unit; once it is open I/O operations can be performed on it in any program unit provided that the same unit number is used. The unit number can be held in an integer variable and passed to the procedure as an argument. The connection between a le and a unit, once established, persists until: the program terminates normally (at a STOP statementorthe END of the main program); another OPEN statement connects a dierent le to the same unit; or a CLOSE statement is executed on that unit. Although all les are closed when the program exits, it is good practice to close them explicitly as soon as I/O operations on them are completed. If the program terminates abnormally, for example because an error occurs or it is aborted by the user, any les which are open, especially output les, may be left with incomplete or corrupted records. The INQUIRE statement can be used to obtain information about the current properties of external les and I/O units. INQUIRE is particularly useful when writing library procedures which may have to run in a variety of dierent program environments. You can nd out, for example, which unit numbers are free for use or whether a particular le exists and if so what its characteristics are.

Records
A le consists of a sequence of records. In a text le a record corresponds to a line of text; in other cases a record has no physical basis, it is just a convenient collection of values chosen to suit the application. There is no need for a record to correspond to a disc sector or a tape block. READ and WRITE statements always start work at the beginning of a record and always transfer a whole number of records. The rules of Fortran set no upper limit to the length of a record but, in practice, each operating system may do so. This may be dierent for dierent forms of record.

Formatted and Unformatted Records
External les come in twovarieties according to whether their records are formatted or unformatted. Formatted records store data in character-coded form, i.e. as lines of text. This makes them suitable for a wide range of applications since, depending on their contents, they maybe

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legible to humans as well as computers. The main complication for the programmer is that each WRITE or READ statementmust specify how each value is to be converted from internal to external form or vice-versa. This is usually done with a format specication. Unformatted records store data in the internal code of the computer so that no format conversions are involved. This has a several advantages for les of numbers, especially oatingpoint numbers. Unformatted data transfers are simpler to program, faster in execution, and free from rounding errors. Furthermore the resulting data les, sometimes called binary les, are usually much smaller. A real number would, for example, have to be turned into a string of 10 or even 15 characters to preserve its precision on a formatted record, but on an unformatted record a real number typically occupies only 4 bytes i.e. the same as 4 characters. The drawback is that unformatted les are highly system-specic. They are usually illegible to humans and to other brands of computer and sometimes incompatible with les produced by other programming languages on the same machine. Unformatted les should only be used for information to be written and read byFortran programs running on the same type of computer.

Sequential and Direct Access
All peripheral devices allow les to be processed sequentially: you start at the beginning of the le and work through each record in turn. One important advantage of sequential les is that dierent records can have dierent lengths; the minimum record length is zero but the maximum is system-dependent. Sequential les behave as if there were a pointer attached to the le which always indicates the next record to be transferred. On devices such as terminals and printers you can only read or write in strict sequential order, but when a le is stored on disc or tape it is possible to use the REWIND statement to reset this pointer to the start of the le, allowing it to be read in again or re-written. On suitable les the BACKSPACE statement can be used to move the pointer back by one record so that the last record can be read again or over-written. One unfortunate omission from the Fortran Standard is that the position of the record pointer is not dened when an existing sequential le is opened. Most Fortran systems behave sensibly and make sure that they start at the beginning of the le, but there are a few rogue systems around which make it advisable, in portable software, to use REWIND after the OPEN statement. Another problem is how append new records to an existing sequential le. Some systems provide (as an extension) an \append" option in the OPEN statement, but the best method using Standard Fortran is to open the le and read records one at a time until the end-of-le condition is encountered; then use BACKSPACE to move the pointer back and clear the end-of-le condition. New records can then be added in the usual way. The alternative access method is direct-access which allows records to be read and written in any order. Most systems only permit this for les stored on random-access devices such as discs; it is sometimes also permitted on tapes. All records in a direct-access le must be the same length so that the system can compute the location of a record from its record number. The record length has to be chosen when the le is created and (on most systems) is then xed for the life of the le. In Fortran, direct-access records are numbered from one upwards; each READ or WRITE statement species the record number at which the transfer starts. Records may be written to a direct-access le in any order. Any record can be read provided that it exists, i.e. it has been written at some time since the le was created. Once a record has been written there is no way of deleting it, but its contents can be updated, i.e. replaced, at any time. A few primitive operating systems require the maximum length of a direct-access le to be

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specied when the le is created; this is not necessary in systems which comply fully with the Fortran Standard.

10.2 External Files

Formatted and unformatted records cannot be mixed on the same le and on most systems les designed for sequential-access are quite distinct from those created for direct-access: thus there are four dierenttypes of external le. There is no special support in Standard Fortran for any other types of le such as indexed-sequential les or name-list les.

Formatted Sequential Files

These are often just called text les. Terminals and printers should always be treated as formatted sequential les. Data les of this type can be created in a variety of ways, for example by direct entry from the keyboard, or by using a text editor. Some Fortran systems do not allow records to be longer than a normal line of text, for example 132 characters. Unless a text le is pre-connected it must be opened with an OPEN statement, but the FORM= and ACCESS= keywords are not needed as the default values are suitable: All data transfers must be carried out under format control. There are two options with les of this type: you can either provide your own format specication or use list-directed formatting. The attraction of list-directed I/O is that the Fortran system does the work, providing simple data transfers with little programming eort. They are specied by having an asterisk as the format identier:
WRITE(UNIT=*, FMT=*)'Enter velocity: ' READ(UNIT=*, FMT=*, END=999) SPEED OPEN(UNIT=4, FILE='REPORT', STATUS='NEW')

List-directed input is quite convenient when reading numbers from a terminal since it allows virtually \free-format" data entry. It may also be useful when reading data les where the layout is not regular enough to be handled by a format specication. List-directed output is satisfactory when used just to output a character string (as in the example above), but it produces less pleasing results when used to output numerical values since you havenocontrol over the positioning of items on the line, the eld-width, or the number of decimal digits displayed. Thus:
WRITE(UNIT=LP, FMT=*)' Box of',N,' costs ',PRICE

will produce a record something like this:
Box of 12 costs

List-directed output is best avoided except to write simple messages and for diagnostic output during program development. The rules for list-directed formatting are covered in detail in section 10.10. The alternative is to provide a format specication: this provides complete control over the data transfer. The previous example can be modied to use a format specication like this:
55 WRITE(UNIT=LP, FMT=55)'Box of',N,' costs ',PRICE FORMAT(1X, A, I3, A, F6.2)

9.5000000

and will produce a record like this: Box of 12 costs 9.50

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The format specication is provided in this case bya FORMAT statement: its label is the format identier in the WRITE statement. Other ways of providing format specications are described in section 10.6. One unusual feature of input under control of a format specication is that each line of text will appear to be padded out on the right with an indenite number of blanks irrespective of the actual length of the data record. This means that, among other things, it is not possible to distinguish between an empty record and one lled with blanks. If numbers are read from an empty record they will simply be zero.

Unformatted Sequential Files
Unformatted sequential les are often used as to transfer data from one program to another. They are also suitable for scratch les, i.e. those used temporarily during program execution. The only limit on the length of unformatted records is that set by the operating system; most systems allow records to contain a few thousand data items at least. The OPEN statementmust specify the le format, but the default access method is \sequential". Each READ or WRITE statement transfers one unformatted record. For example, these statements open an existing unformatted le and read two records from it:
OPEN(UNIT=15, FILE='BIN', STATUS='OLD', FORM='UNFORMATTED') READ(15) HEIGHT, LENGTH, WIDTH READ(15) ARRAYP, ARRAYQ BACKSPACE

and

REWIND

statements may generally be used on all unformatted sequential les.

Unformatted Direct-access Files
Since direct-access les are readable only by machine, it seems sensible to use unformatted records to maximise eciency. The OPEN statement must specify ACCESS='DIRECT' and also specify the record length. Unfortunately the units used to measure the length of a record are not standardised: some systems measure them in bytes, others in numerical storage units, i.e. the number of real or integer variables a record can hold (see section 5.1). This is a minor obstacle to portability and means that you may need to know how many bytes your machine uses for eachnumerical storage unit, although this is just about the only place in Fortran where this is necessary. Most systems will allow you to open an existing le only if the record length is the same as that used when the le was created. Each READ and WRITE statement transfers exactly one record and must specify the number of that record: an integer value from one upwards. The record length must not be greater than that declared in the OPEN statement; if an output record is not completely lled the remainder is undened. To illustrate how direct-access les can be used, here is a complete program which allows a very simple data-base, such as a set of stock records, to be examined. Assuming that the record length is measured in numerical storage units of 4 bytes, the required record length in this case can be computed as follows: NAME 1 CHARACTER*10 variable 10 chars=10bytes. STOCK 1 INTEGER variable 1 unit = 4 bytes PRICE 1 REAL variable 1 unit = 4 bytes

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The total record length is 18 bytes or 5 numerical storage units (rounding up to the next integer).
PROGRAM DBASE1 INTEGER STOCK, NERR REAL PRICE CHARACTER NAME*10 *Assume record length in storage units holding 4 chars each. OPEN(UNIT=1, FILE='STOCKS', STATUS='OLD', $ ACCESS='DIRECT', RECL=5) 100 CONTINUE *Ask user for part number which will be used as record number. WRITE(UNIT=*,FMT=*)'Enter part number (or zero to quit):' READ(UNIT=*,FMT=*) NPART IF(NPART .LE. 0) STOP READ(UNIT=1, REC=NPART, IOSTAT=NERR) NAME, STOCK, PRICE IF(NERR .NE. 0) THEN WRITE(UNIT=*,FMT=*)'Unknown part number, re-enter' GO TO 100 END IF WRITE(*,115)STOCK, NAME, PRICE 115 FORMAT(1X,'Stock is',I4, 1X, A,' at ', F8.2, ' each') GO TO 100 END

The typical output record of the program will be of the form: This program could be extended fairly easily to allow the contents of the record to be updated as the stockchanges.
Stock is 123 widgets at 556.89 each

Formatted Direct-access Files
Formatted direct-access les are slightly more portable than the unformatted form because their record length is always measured in characters. Otherwise there is little to be said for them. The OPEN statementmust specify both ACCESS='DIRECT' and FORM='FORMATTED' and each READ and WRITE statementmust contain both format and record-number identiers. List-directed transfers are not permitted. If the format specication requires more than one record to be used, these additional records follow on sequentially from that specied by REC=. It is an error to try to read beyond the end of a record, but an incompletely lled record will be padded out with blanks.

10.3 Internal Files

An internal le is an area of central memory which can be used as if it were a formatted sequential le. It exists, of course, only while the program is executing. Internal les are used for a variety of purposes, particularly to carry out data conversions to and from character data type. Some earlier versions of Fortran included ENCODE and DECODE statements: the internal le READ (which replaces DECODE) and internal le WRITE (which replaces ENCODE) are simpler, more exible, and entirely portable.

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An internal le can only be used with READ and WRITE statements and an explicit format specication is required: list-directed transfers are not permitted. The unit must havecharacter data type but it can be a variable, array element, substring, or a complete array. If it is a complete array then each array element constitutes a record; in all other cases the le only consists of one record. Data transfers always start at the beginning of the internal le, that is an implicit rewind is performed each time. The record length is the length of the character item. It is illegal to try to transfer more characters than the internal le contains, but if a record of too few characters is written it will be padded out with blanks. The END= and IOSTAT= mechanisms can be used to detect the end-of-le. An internal le WRITE is typically used to convert a numerical value to a character string by using a suitable format specication, for example:
CHARACTER*8 CVAL RVALUE = 98.6 WRITE(CVAL, '(SP, F7.2)') RVALUE

The WRITE statement will ll the character variable CVAL with the characters ' +98.60 ' (note that there is one blank at each end of the number, the rst because the number is right-justied in the eld of 7 characters, the second because the record is padded out to the declared length of8characters). Once a number has been turned into a character-string it can be processed further in the various ways described in section 7. This makes it possible, for example, to write numbers left-justied in a eld, or mark negativenumbers with \DR" (as in bank statements) in or even use a pair of parentheses (as in balance-sheets). With suitable arithmetic you can even output values in other number-bases such as octal or hexadecimal. Even more elaborate conversions maybe achieved by rst writing a suitable format specication intoacharacter string and then using that format to carry out the desired conversion. Internal le READ statements can be used to decode a character string containing a numerical value. One obvious application is to handle the user input to a command-driven program. Suppose the command line consists of a word followed, optionally, by a number (in integer or real format), with at least one blank separating the two. Thus the input commands might be something like:
UP 4 RIGHT 123.45

A simple way to deal with this is to read the whole line into a character variable and then use the INDEX function to locate the rst blank. The preceding characters constitute the command word, those following can be converted to a real number using an internal le READ.For example:
CHARACTER CLINE*80 *... 100 WRITE(UNIT=*,FMT=*)'Enter command: ' READ(*, '(A)', IOSTAT=KODE) CLINE IF(KODE .NE. 0) STOP K = INDEX(CLINE, ' ') *The command word is now in CLINE(1:K-1); Assume the * number is in the next 20 characters: read it into RVALUE READ(CLINE(K+1:), '(BN,F20.0)', IOSTAT=KODE) RVALUE

10 INPUT/OUTPUT FACILITIES
IF(KODE .NE. 0) THEN WRITE(UNIT=*,FMT=*)'Error in number: try again' GO TO 100 END IF

87

Note that the edit descriptor BN is needed to ensure that any trailing blanks will be ignored; the F20.0 will then handle any real or integer constantanywhere in the next 20 characters. A eld of blanks will be converted into zero.

10.4 Pre-Connected Files
Terminal Input/Output
Many programs are interactive and need to access the user's terminal. Although the terminal is a le which can be connected with an OPEN statement, its name is system-dependent. Fortran solves the problem by providing two special les usually called the standard input le and the standard output le. These les are pre-connected, i.e. no OPEN statement is needed (or permitted). They are both formatted sequential les and, on interactive systems, handle input and output to the terminal. You can READ and WRITE from these les simply by having an asterisk \*" as the unit identier. These les make terminal I/O simple and portable; examples of their use can be found throughout this book. When a program is run in batch mode most systems arrange for standard output to be diverted to a log le or to the system printer. There may be some similar arrangement for the standard input le. The asterisk notation has one slight drawback: the unit numbers is often specied by an integer variable so that the source of input or destination of output can be switched from one le to another merely be altering the value of this integer. This cannot be done with the standard input or output les.

Other Pre-connected Files
In order to retain compatibility with Fortran66, many systems provide other pre-connected les. It used to be customary to have unit 5 connected to the card-reader, and unit 6 to the line printer. Other units were usually connected to disc les with appropriate names: thus unit 39 might be connected to a le called FTN039.DAT or even TAPE39. These pre-connections are completely obsolete and should be ignored: an OPEN statement can supersede a pre-connection on anynumbered unit. Unfortunately these obsolete pre-connections can have unexpected side eects. If you forget to open an output le you may nd that your program will run without error but that the results will be hidden on a le with one of these special names.

10.5 Error and End-Of-File Conditions

Errors in most executable statements can be prevented by taking sucient care in writing the program, but in I/O statements errors can be caused by events beyond the control of the programmer: for example through trying to open a le which no longer exists, writing to a disc which is full, or reading a data le which has been created with the wrong format. Since I/O statements are so vulnerable, Fortran provides an error-handling mechanism for them. There are actually two dierentways of handling errors whichmay be used independently or in combination.

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Firstly,you can include in the I/O control list an item of the form:
IOSTAT=integer-variable

88

When the statement has executed the integer variable (or array element) will be assigned a value representing the I/O status. If the statement has completed successfully this variable is set to zero, otherwise it is set to some other value, a positive number if an error has occurred, or a negative value if the end of an input le was detected. Since the value of this status code is system-dependent, in portable software the most you can do is to compare it to zero and, possibly, report the actual error code to the user. Thus:
100 WRITE(UNIT=*, FMT=*)'Enter name of input file: ' READ(UNIT=*, FMT=*) FNAME OPEN(UNIT=INPUT, FILE=FNAME, STATUS='OLD', IOSTAT=KODE) IF(KODE .NE. 0) THEN WRITE(UNIT=*,FMT=*)FNAME, ' cannot be opened' GO TO 100 END IF

This simple error-handling scheme makes the program just a little more user-friendly: if the le cannot be opened, perhaps because it does not exist, the program asks for another le-name. The second method is to include an item of the form which causes control to be transferred to the statement attached to that label in the event of an error. This must, of course, be an executable statement and in the same program unit. For example:
READ(UNIT=IN, FMT=*, ERR=999) VOLTS, AMPS WATTS = VOLTS * AMPS * rest of program in here . . . . . and finally STOP 999 WRITE(UNIT=*,FMT=*)'Error reading VOLTS or AMPS' END ERR=label

This method has its uses but is open to the same ob jections as the GO TO statement: it often leads to badly-structured programs with lots of arbitrary jumps. By using both IOSTAT= and ERR= in the same statement it is possible to nd out the actual error number and jump to the error-handling code. The presence of either keyword in an I/O statement will allow the program to continue after an I/O error; on most systems it also prevents an error message being issued. The ERR= and IOSTAT= items can be used in all I/O statements. Professional programmers should make extensive use of these error-handling mechanisms to enhance the robustness and user-friendliness of their software. There is one fairly common mistake which does not count as an errors for this purpose: if you write a number to a formatted record using a eld width too narrowtocontain it, the eld will simply be lled with asterisks. If an error occurs in a data transfer statement then the position of the le becomes indeterminate. It may be quite dicult to locate the oending record if an error is detected when transferring a large array or using a large number of records.

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End-of-le Detection
A READ statement which tries to read a record beyond the end of a sequential or internal le will trigger the end-of-le condition. If an item of the form: IOSTAT=integer-variable is included in its control-list then the status value will be returned as some negativenumber. If it includes an item of the form: END=label then control is transferred to the labelled statement when the end-of-le condition is detected. The END= keyword may only be used in READ statements, but it is can be used in the presence of both ERR= and IOSTAT= keywords. End-of-le detection is very useful when reading a le of unknown length, but some caution is necessary. If you read several records at a time from a formatted le there is no easy way of knowing exactly where the end-of-le condition occurred. The data list items beyond that point will have their values unaltered. Note also that there is no concept of end-of-le on direct-access les: it is simply an error to read a record which does not exist, whether it is beyond the \end" of the le or not. Most systems provide some method for signalling end-of-le on terminal input: those based on the ASCII code often use the character ETX which is usually produced by pressing control/Z on the keyboard (or EOT which is control/D). After an end-of-le condition has been raised in this wayit may persist, preventing further terminal input to that program. Formally, the Fortran Standard only requires Fortran systems to detect the end-of-le condition on external les if there is a special \end-le" record on the end. The END FILE statement is provided specically to write such a record. In practice, however, virtually all Fortran systems respond perfectly well when you try to read the rst non-existent record, so that the END FILE statement is eectively obsolete and is not recommended for general use.

10.6 Format Specications

Every READ or WRITE statement which uses a formatted external le or an internal le must include a format identier. This mayhaveany of the following forms: FMT=* This species a list-directed transfer (and is only permitted for external sequential les). Detailed rules are given in section 10.10 below. FMT=label The label must be attached to a FORMAT statement in the same program unit which provides the format specication. FMT=char-exp The value of the character expression is a complete format specication. FMT=char-array The elements of the character array contain the format specication, whichmay occupyasmany elements of the array as are necessary. Note that the characters FMT= may be omitted if it is the second item in the I/O control list and if the unit identier with UNIT= omitted comes rst. A format specication consists a pair of parentheses enclosing a list of items called edit descriptors. Any blanks before the left parenthesis will be ignored and (except in a FORMAT statement) all characters after the matching right parenthesis are ignored. In most cases the format can be chosen when the program is written and the simplest option is to use a character constant: Alternatively you can use a
915 WRITE(UNIT=LP, FMT='(1X,A,F10.5)') 'Frequency =', HERTZ FORMAT statement: WRITE(UNIT=LP, FMT=915) 'Frequency =', HERTZ FORMAT(1X, A, F10.5)

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This allows the same format to be used by more than one data-transfer statement. The FORMAT statementmay also be the neater form if the specication is long and complicated, or if characterconstant descriptors are involved, since the enclosing apostrophes have to be doubled up if the whole format is part of another character constant. It is also possible to compute a format specication at run-time by using a suitable character expression. By this means you could, for example, arrange to read the format specication of a data le from the rst record of the le. The program fragment below shows how to output a real number in xed-point format (F10.2) when it is small, changing to exponential format (E18.6) when it is larger. A threshold of a million has been chosen here.
CHARACTER F1*(*), F2*12, F3*(*) *Items F1, F2, F3 hold the three parts of a format specification. *F1 and F3 are constants, F2 is a variable. PARAMETER (F1 = '(1X,''Peak size ='',') PARAMETER (F3 = ')') *... calculation of PEAK assumed to be in here IF(PEAK .LT. 1.0E6) THEN F2 = 'F10.2' ELSE F2 = 'E18.6' END IF WRITE(UNIT=*, FMT=F1//F2//F3) PEAK

Note that the apostrophes surrounding the character constant 'Peak size =' have been doubled in the PARAMETER statement because they are inside another character constant. Here are two examples of output records, with blanks shown explicitly:
Peak size = Peak size = FORMAT 12345.67 0.987654E+08

statement

The FORMAT statement is classed as non-executable and can, in principle, go almost anywhere in the program unit. A FORMAT statement can, of course, be continued so its maximum length is 20 lines. The same FORMAT statement can be used by more than one data transfer statement and, unless it contains character constant descriptors, used for both input and output. Since it is very easy to make a mistake in matching the items in a data transfer list with the edit descriptors in the format specication, it makes sense to put the FORMAT statement as close as possible to the READ and WRITE statements which use it.

10.7 Format Edit Descriptors

There are twotypes of edit descriptor: data descriptors and control descriptors. A data descriptor must be provided for each data item transferred by a READ or WRITE statement; the descriptors permitted depend on the data type of the item. The data descriptors all start with a letter indicating the data type followed by an unsigned integer denoting the eld width, for example: I5 denotes an integer eld 5 characters wide, F9.2 denotes a oating-point eld 9 character wide with 2 digits after the decimal point. Full details of all the data descriptors are given in the next section.

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The control descriptors are used for a variety of purposes, such as tabbing to specic columns, producing or skipping records, and controlling the transfer of subsequentnumerical data. They are described fully in section 10.9. Note that only literal constants are permitted within format specications, not named constants or variables.

10.8 Format Data Descriptors

A, E, F, G, I, L

A data descriptor must be provided for each data item present (or implied) in a data transfer list. Real, double precision, and complex items may use any of the E, F, or G descriptors but in all other cases the data type must match. Two oating-point descriptors are needed for each complex value. Data type Data descriptors Integer Iw, Iw.m Real, Double Precision, or Complex Ew.d, Ew.dEe, Logical Lw Character A, Aw
Fw.d, Gw.d, Gw.dEe

The letters w, m, d, and e used with these data descriptors represent unsigned integer constants; w and e must be greater than zero.
w m d e

is is is is

the the the the

total eld minimum number of number of

width. number of digits produced on output. digits after the decimal point. digits used for the exponent.

Any data descriptor can be preceded by a repeat-count (also an unsigned integer), thus: 3F6.0 is equivalent to F6.0,F6.0,F6.0 This facility is particularly useful when handling arrays.

General Rules for Numeric Input/Output
Numbers are always converted using the decimal number base: there is no provision in Standard Fortran for transfers in other number bases such as octal or hexadecimal. More complicated conversions such as these can be performed with the aid of internal les. On output number are generally right-justied in the specied eld; leading blanks are supplied where necessary. Negative values are always preceded by a minus sign (for which space must be allowed in the eld); zero is always unsigned; the SP and SS descriptors control whether positive numbers are to be preceded by a plus sign or not. A number which is too large to t into its eld will appear instead as a set of w asterisks. On input numbers should be right-justied in each eld. All forms of constant permitted in aFortran program can safely be used in an input eld of the corresponding type, as long there are no embedded or trailing blanks. Leading blanks are always ignored; a eld whichisentirely blank will be read as zero. The treatment of embedded and trailing blanks can be controlled with the BN and BZ descriptors. The rules here are another relic of very early Fortran systems. When reading a le which has been connected by means of an OPEN statement (provided it does not contain BLANK='ZERO') all embedded and trailing blanks in numeric input elds are treated as nulls, i.e. they are ignored. In all other cases, such as input from the standard pre-connected le or from an internal le, embedded and trailing blanks are treated as zeros.

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These defaults can be altered with the BN and BZ control descriptors. It is hard to imagine any circumstances in which it is desirable to interpret embedded blanks as zeros; the default settings are particularly ill-chosen since numbers entered by a user at a terminal are often left-justied and may appear to be padded out with zeros. Errors from this source can be avoided by using BN at the beginning of all input format specications.

Integer Data (Iw,

Iw.m

)

An integer value written with Iw appears right-justied in a eld of w characters with leading blanks. Iw.m is similar but ensures that at least m digits will appear even if leading zeros are necessary. This is useful, for instance, to output the times in hours and minutes:
NHOURS = 8 MINUTE = 6 WRITE(UNIT=*, FMT='(I4.2, I2.2)') NHOURS, MINUTE

The output record (with blanks shown explicitly) is:
0806

On input Iw and Iw.m are identical. Note that an integer eld must not contain a decimal point, exponent, or any punctuation characters such as commas.

Floating Point Data (Ew.d,

Ew.dEe, Fw.d, Gw.d, Gw.dEe

Data of any of the oating-pointtypes (Real, Double Precision, and Complex) may be transferred using any of the descriptors E, F, or G. For each complex number two descriptors must be provided, one for each component; these components may be separated, if required, by control descriptors. On output numbers are rounded to the specied number of digits. All oatingpoint data transfers are aected by the setting of the scale-factor; this is initially zero but can be altered by the P control descriptor, as explained in the section 10.9. Output using Fw.d produces a xed-point value in a eld of w characters with exactly d digits after the decimal point. The decimal point is present even if w is zero, so that if a sign is produced there is only space for, at most, w-2 digits before the decimal point. If it is really important to suppress the decimal pointin numbers with no fractional part one way is to use a format specication of the form (F15.0,TL1)... so that the next eld starts one place to the left and over-writes the decimal point. Another wayistocopy the numberto aninteger variable and write it with an I descriptor, but note the limited range of integers on most systems. F format is especially convenient in tabular layouts since the decimal points will line up in successive records, but it is not suitable for very large or small numbers. Output with Ew.d produces a number in exponential or \scientic" notation. The mantissa will be between 0.1 and 1 (if the scale-factor is zero). The form Ew.dEe species that there should be exactly e digits in the exponent. This form must be used if the exponent will have more than three digits (although this problem does not arise on machines on which the number range is too small). E format can be used to handle numbers of any magnitude. The disadvantage is that exceptionally large or small values do not stand out very well in the resulting columns of gures. Gw.d is the general-purpose descriptor: if the value is greater than 0.1 but not too large to t it the eld it will be written using a xed-point format with d digits in total and with 4 blanks at the end of the eld; otherwise it is equivalent to Ew.d format. The form Gw.dEe allows you

)

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to specify the length of the exponent; if a xed-point format is chosen there are e+2 blanks at the end. The next example shows the dierent properties of these three formats on output:
X = 123.456789 Y = 0.09876543 WRITE(UNIT=*, FMT='(E12.5, F12.5, G12.5)') X,X,X, Y,Y,Y

produces two records (with t representing the blank):
0.12346E+03 0.98766E-01 123.45679 123.46 0.09877 0.98766E-01

On input all the E, F, and G descriptors have identical eects: if the input eld contains an explicit decimal point it always takes precedence, otherwise the last d digits are taken as the decimal fraction. If an exponent is used it may be preceded by E or D (but the exponent letter is optional if the exponent is signed). If the input eld provides more digits than the internal storage can utilise, the extra precision is ignored. It is usually best to use (Fw.0) which will cope with all common oating-point or even integer forms.

Logical Data (Lw)
When a logical value is written with Lw the eld will contain the letter T or F preceded by (w-1) blanks. On input the eld must contain the letter T or F; the letter may be preceded by a decimal point and any number of blanks. Characters after the T or F are ignored. Thus the forms .TRUE. and .FALSE. are acceptable.

Character Data (A and Aw)
If the A descriptor is used without an explicit eld-width then the length of the character item in the data-transfer list determines it. This is generally what is required but note that the position of the remaining items in the record will change if the length of the character item is altered. If is important to use xed column layouts the form Aw may be preferred: it always uses a eld w characters wide. On output if the actual length len is less than w the value is right-justied in the eld and preceded by (w-len) blanks; otherwise only the rst w characters are output, the rest are ignored. On input if the length len is less than w then the right-most len characters are used, otherwise w characters will be read into the character variable with (len-w) blanks appended.

10.9 Format Control Descriptors

Control descriptors do not correspond to any item in the data-transfer list: they are obeyed when the format scan reaches that point in the list. A format specication consisting of nothing but control descriptors is valid only if the READ or WRITE statement has an empty data-transfer list.

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Control Function Control Descriptor Skip to next record / Move to specied column position Tn, TLn, TRn, nX Output a character constant 'any char string' Stop format scan if data list empty : Control + before positive numbers SP, SS, S Treat blanks as nulls/zeros BN, BZ Set scale factor for numeric transfers kP

94

Here n and k are integer constants, k mayhave a sign but n must be non-zero and unsigned. The control descriptors such as SP, BN, kP aect all numbers transferred subsequently. The settings are unaected by forced reversion but the system defaults are restored at the start of the next READ or WRITE operation. Any list of edit descriptors may be enclosed in parentheses and preceded byaninteger constant as a repetition count, e.g. is equivalent to
2(I2.2, '-'),I2.2

These sub-lists can be nested to any reasonable depth, but the presence of internal pairs of parentheses can have special eects when forced reversion takes place, as explained later. Commas may be omitted between items in the following special cases: either side of a slash (/) or colon (:) descriptor, and after a scale-factor (kP) if it immediately precedes a D, E, F, or G descriptor.

I2.2, '-', I2.2, '-', I2.2

Record Control (/)
The slash descriptor (/) starts a new record on output or skips to a new record on input, ignoring anything left on the current record. On a text le a record normally corresponds to a line of text. Note that a formatted transfer always process at least one record: if the format contains N slashes then a total of (N+1) records are processed. With N consecutive slashes in an output format there will be (N-1) blank lines; on input then (N-1) lines will be ignored. Note that if a formatted sequential le is sent to a printer the rst character of every record may be used for carriage-control (see section 10.11). It is good practice to put 1X at the beginning of every format specication and after every slash to ensure single line spacing. Here, for example, there is a blank line after the column headings.
95 WRITE(UNIT=LP, FMT=95) (NYEAR(I), POP(I), I=1,NYEARS) FORMAT(1X,'Year Population', //, 100(1X, I4, F12.0, /)) TLn, TRn, nX

Column Position Control (Tn,

)

These descriptors cause subsequentvalues to be transferred starting at a dierent column position in the record. They can, for instance, be used to set up a table with headings positioned over each column. In all these descriptors the value of n must be 1 or more. Columns are numbered from 1 on the left (but remember that column 1 may be used for carriage-control if the output is sent to a printer).

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Tn TRn TLn nX

95

causes subsequent output to start at column n. causes a shift to the rightby n columns. causes a shift to the left by n columns (but it will not move the position to the left of column 1). is exactly equivalent to TRn.

On input TLn can be used to re-read the same eld again, possibly using a dierent data descriptor. On output these descriptors do not necessarily haveany direct eect on the record: they do not cause any existing characters to be replaced by blanks, but when the record is complete any column positions embedded in the record which are still unset will be replaced by blanks. Thus:
9000 WRITE(UNIT=LP, FMT=9000) FORMAT('A', TR1000, TL950, 'Z')

will cause a record of 52 characters to be output, middle 50 of them blanks.

Character Constant Output ('string')
The character constant descriptor can only be used with WRITE statements: the character string is simply copied to the output record. As in all character constants an apostrophe can be represented in the string bytwo successive apostrophes, and blanks are signicant.

Sign Control (

SP, SS, S

)

After SP has been used, positive numbers will be written with a leading + sign; after SS has been used the + sign is suppressed. The S descriptor restores the initial default which is systemdependent. These descriptors have no eect on numerical input. The initial default is restored at the start of every new formatted transfer.

Blank Control (BN, BZ)
After BN is used all embedded and trailing blanks in numerical input elds are treated as nulls, i.e. ignored. After BZ they are treated as zeros. These descriptors have no eect on numerical output. The initial default, which depends on the BLANK= item in the OPEN statement, is restored at the start of every new formatted transfer.

Scale Factor Control (kP)
The scale factor can be used to introduce a scaling by any power of 10 between internal and external values when E, F, or G descriptors are used. In principle this could be useful when dealing with data which are too large, or too small, for the exponent range of the oating-point data types of the machine, but in other diculties usually make this impracticable. The scale factor can result in particularly insidious errors when used with F descriptors and should be avoided by all sensible programmers. The rules are as follows. The initial scale factor in each formatted transfer is zero. It the descriptor kP is used, where k is a small (optionally signed) integer, then it is set to k. It aects all subsequent oating point values transferred by the statement. On input there is no eect if the input eld contains an explicit exponent, otherwise internal-value = external-value /10 On output the eect depends on the descriptor used. With E descriptors the decimal point is
k

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moved k places to the right and the exponent reduced by k so the eective value is unaltered. With F descriptors there is always a scaling: external-value =em internal-value * 10 With G descriptors the scale-factor is ignored if the value is in the range for F-type output, otherwise it has the same eects as with E descriptors.
k

Scan Control (:) and Forced Reversion
The list of edit descriptors is scanned from left to right (apart from the eect of parentheses) starting at the beginning of the list whenever a new data transfer statement is executed. The action of the I/O system depends jointly on the next edit descriptor and the next item in datatransfer list. If a data descriptor comes next then the next data item is transferred if one exists, otherwise the format scan comes to an end. If a colon descriptor (:) comes next and the datatransfer list is empty the format scan ends, otherwise the descriptor has no eect. If any other control descriptor comes next then it is obeyed whether or not the data-transfer list is empty. If the format list is exhausted when there are still more items in the data-transfer list then forced reversion occurs: the le is positioned at the beginning of the next record and the format list is scanned again, starting at the left-parenthesis matching the last preceding rightparenthesis. If this is preceded by a repeat-count then this count is re-used. If there is no preceding right-parenthesis then the whole format is re-used. Forced reversion has no eect upon the settings for scale-factor, sign, or blank control. Forced reversion can be useful when reading or writing an array contained on a sequence of records since it is not necessary to know how many records there are in total, but when producing printed output it is easy to forget that a carriage-control character is required for each record, even those produced by forced reversion.

10.10 List-Directed Formatting
List-directed Output

List-directed output uses a format chosen by the system according to the data type of the item. The exact layout is system-dependent, but the general rules are as follows. Each WRITE statement starts a new record; additional records are produced when necessary. Each record starts with a single blank to provide carriage-control on printing. Arithmetic data types are converted to decimal values with the number of digits appropriate for the internal precision; integer values will not have a decimal point, the system may choose xed-point or exponential (scientic) form for oating-point values depending on their magnitude. Complex values are enclosed in parentheses with a comma separating the two parts. Logical values are output as a single letter, either T or F. Character values are output without enclosing apostrophes; if a character string is too long for one record it may be continued on the next. Except for character values, each item is followed by at least one blank or a comma (or both) to separate it from the next value.

List-directed Input
The rules for List-directed input eectively allow free-format entry for numerical data. Each READ statement starts with a new record and reads as many records as are necessary to satisfy its data-transfer list. The input records must contain a suitable sequence of values and separators.

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The values may be given in any form which would be acceptable in a Fortran program for a constant of the corresponding type, except that embedded blanks are only permitted in character values. When reading a real or double-precision value an integer constant will be accepted; when reading a logical value only the letter T or F is required (a preceding dot and any following characters will be ignored). Note that a character constant must be enclosed in apostrophes and a complex constant must be enclosed in parentheses with a comma between the two components. If a character constant is too long to t on one record it may be continued on to the next; the two parts of a complex constantmay also be given on two records. The separator between successive values must be one or more blanks, or a comma, or both. A new record may start at any point at which a blank would be permitted. If several successive items are to have the same value a repetition factor can be used: this has the form n*constant where n is an unsigned integer. Blanks are not allowed either side of the asterisk. Two successive commas representanull value: the corresponding variable in the READ statement has its value unchanged. It is also possible to use the form n* to representaset ofnnull values. A slash (/) may be used instead of an item separator; it has the eect of completing the current READ without further input; all remaining items in its data transfer list are unchanged in value. List-directed output les are generally compatible with list-directed input, unless they contain character items, which will not have the enclosing apostrophes which are required on input.

10.11 Carriage-Control and Printing

Although a format specication allows complete control over the layout of each line of text, it does not include anywayofcontrolling pagination. The only way to do this is by using a unique and extraordinary mechanism dating back to the earliest days of Fortran. Even if you are not concerned with pagination you still need to know about the carriage-control convention since it is liable to aect every text le you produce. Whenever formatted output is sent to a \printer", the rst character of every record is removed and used to control the vertical spacing. This carriage-control character must be one of the four listed in the the table below. Character Vertical spacing before printing blank Advance to next line 0 Advance two lines 1 Advance to top of next page + No advance, i.e. print on same line An empty record is treated as if it started with a single blank. For example, these statements start a new page with a page number at the top and a title on the third line:
55 WRITE(LP, 55) NUMBER, 'Report and Accounts' FORMAT('1PAGE', I4, /, '0', A)

This carriage-control convention is an absurd relic which causes a multitude of problems in practice. Firstly, systems dier on what they call a \printer": it mayormay not apply to visual display terminals or to text initially saved on a disc le and later printed out. Some operating systems have a special le type for Fortran formatted output which is treated dierently by

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printers (and terminals). Others have been known to chop o the rst character of all les sent to the system printer so that special utilities are needed to print ordinary text. To be on the safe side you should always provide an explicit carriage-control character at the start of each format specication and after each slash. Special care is needed in formats which use forced reversion. Normal single spacing is obtained with a blank, conveniently produced by the 1X edit descriptor. If you forget and accidentally printa number at the start of each record with a leading digit 1 then each record will start a new page. The eect of + as a carriage-control character would be more useful if its eects were more predictable. Some devices over-print the previous record (allowing the formation of composite characters like ), others append to it, and some (including many visual display terminals) erase what was there before. In portable software there is no alternative but to ignore the + case altogether. Standard Fortran can only use the four carriage-control characters listed in the table but many systems use other symbols for special formatting purposes, such as setting vertical spacing, changing fonts, and so on. One extension which is widely available is the use of the currency symbol $ to suppress carriage-return at the end of the line. This can be useful when producing terminal prompts as it allows the reply to be entered on the same line. There is, unfortunately, no way of doing this in Standard Fortran. The rules for list-directed output ensure that the lines are single-spaced by requiring at least one blank at the start of every record.

10.12 Input/Output Statements and Keywords

The I/O statements fall into three groups: The data transfer statements READ and WRITE. The le connection statements OPEN, CLOSE, and INQUIRE. The le positioning statements REWIND and BACKSPACE. All these statements have a similar general form (except that only the READ and WRITE statements can have a data-transfer list): READ( control-list ) input-list WRITE( control-list ) output-list The items in each list are separated by commas. Those in the control list are usually specied by keywords, in which case the order does not matter, although it is conventional to have the unit identier rst. For compatibility with Fortran66, if the unit identier does come rst then the keyword UNIT= may be omitted. Furthermore, when this keyword is omitted in READ and WRITE statements and the format identier is second its keyword may also be omitted. Thus these two statements are exactly equivalent:
READ(UNIT=1, FMT=*, ERR=999) AMPS, VOLTS, HERTZ READ(1, *, ERR=999) AMPS, VOLTS, HERTZ

Use of this abbreviated form is a matter of taste: for the sake of clarity the keywords will all be shown in other examples. Many of the keywords in the control-list can takea character expression as an argument: in such cases any trailing blanks in the value will be ignored. This makes it easy to use character variables to specify le names and characteristics.

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There is one general restriction on expressions used in all I/O statements: they must not call external functions which themselves execute further I/O statements. This restriction avoids the possibility of recursive calls to the I/O system.

10.13

OPEN

The OPEN statement is used to connect a le to an I/O unit and describe its characteristics. It can open an existing le or create a new one. If the unit is already connected to another le then this is closed before the new connection is made, so that it is impossible to connect two les simultaneously to the same unit. It is an error to try to connect more than one unit simultaneously to the same le. In the special case in which the unit and le are already connected to each other, the OPEN statementmay be used to alter the properties of the connection, although in practice only the BLANK= (and sometimes RECL=)values can be changed in this way. The Fortran Standard does not specify the le position when an existing sequential le is opened. Although most operating systems behave sensibly, in portable software a REWIND statement should be used to ensure that the le is rewound before you read it. The general form of the OPEN statement is just: OPEN( control-list ) The control-list can contain any of the following items in any order: UNIT=integer-expression species the I/O unit number which must be zero or above; the upper limit is system-dependent, typically 99 or 255. The unit identier must always be given, there is no default value. STATUS=character-expression describes or species the le status. The value must be one of: 'OLD' The le must exist. 'NEW' The le must not already exist, a new le is created. 'SCRATCH' An unnamed temporary le is created; it is deleted automatically when the program exits. 'UNKNOWN' The eect is system-dependent, but usually means that an old le will be used if one exists, otherwise a new le will be created. The default value is 'UNKNOWN', but it is unwise to omit the STATUS keyword because the eect of 'UNKNOWN' is so ill-dened. FILE=character-expression species the le-name (but any trailing blanks will be ignored). The forms of le-name acceptable are system-dependent: a complete le-specication on some operating systems may include the device, user-name, directory path, le-type, version number etc. and may require various punctuation marks to separate these. In portable software, where the name has to be acceptable to a variety of operating systems, short and simple names should be used. Alternatively the FILE= identier may be a character variable (or array element) so that the user can choose a le-name at run-time. There is no default for the le-name so one should be specied in all cases unless STATUS='SCRATCH' in which case the le must not be named. ACCESS=character-expression species the le access method. The value may be either: 'SEQUENTIAL' a sequential le: this is the default. 'DIRECT' a direct-access le: in this case the RECL= keyword is also needed. FORM=character-expression species the record format. The value may be either:

Statement

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'FORMATTED' 'UNFORMATTED'

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the default for a sequential le. the default for a direct-access le. RECL=integer-expression species the record length. This must be given for a direct-access le but not otherwise. The record-length is measured in characters for a formatted le, but is in system-dependent units (often numeric storage units) for an unformatted le. BLANK=character-expression species how embedded and trailing blanks in numerical input elds of formatted les are to be treated (in the absence of explicit format descriptors BN or BZ). The value may be either: 'NULL' blanks treated as nulls, i.e. ignored: the default. 'ZERO' blanks treated as zeros. The default value is likely to be the sensible choice in all cases. IOSTAT=integer-variable (or array element) returns the I/O status code after execution of the OPEN statement. This will be zero if no error has occurred, otherwise it will return a system-dependent positive value. ERR=label transfers control to the labelled executable statement in the same program unit in the event of an error.

10.14

CLOSE

The CLOSE statement is used to close a le and break its connection to a unit. The unit and the le (if it still exists) are then free for re-use in anyway. If the specied unit is not connected to a le the statement has no eect. The general form of the statement is: CLOSE( control-list ) where the control-list may contain the following items: UNIT=integer-expression species the unit number to close (the same as in the OPEN statement). STATUS=character-expression species the status of the le after closure. The expression must have a value of either: 'KEEP' for the le to be preserved, or 'DELETE' for the le to be deleted after closure. The default is STATUS='KEEP' except for les opened with STATUS='SCRATCH': such les are always deleted after closure and STATUS='KEEP' is not permitted. IOSTAT=integer-variable and ERR=label are both permitted, as in the OPEN statement (but not much can go wrong with a CLOSE statement).

Statement

10.15
The

INQUIRE

The rst form, an inquire by unit, returns information about the unit and, if it is connected to a le, about the le as well. If it is not connected to a le then most of the arguments will be undened or return a value of 'UNKNOWN' as appropriate. The second form, inquire by le, can always be used to nd out whether a named le exists, i.e. can be opened by a Fortran program. Any trailing blanks in the character expression are

INQUIRE statement can be used in two slightly dierent forms: INQUIRE(UNIT= integer-expression, inquire-list ) INQUIRE(FILE= em character-expression, inquire-list )

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ignored, and the forms of le-name acceptable are, as in the OPEN statement, system-dependent. If the le exists and is connected to a unit then much more information can be obtained. The inquire-list may contain any of the items below. Note that all of them (except for ERR=label) return information by assigning a value to a named variable (or array element). The normal rules of assignment statements apply, so that so that character items mayhaveany reasonable length will return a value which is padded out with blanks to its declared length if necessary.
IOSTAT=integer-variable

and ERR=label can both be used in the same wayas in OPEN or CLOSE; note that they detect errors during the execution of the INQUIRE statement itself, and do not re ect the state of the le or unit which is the sub ject of the inquiry. EXIST=logical-variable sets the variable (or array-element) to .TRUE. if the specied unit or le exists, or .FALSE. if it does not. A unit exists if it has a number in the permitted range. A le exists if it can be used in an OPEN statement. A le may appear not to exist merely because the operating system prevents its use, for example because a password is needed or because some other user has already opened it. OPENED=logical-variable sets the variable to .TRUE. if the specied unit (or le) is currently connected to a le (or unit) in the program. NUMBER=integer-variable returns the unit number of a le which is connected to the variable; otherwise it becomes undened. NAME=character-variable returns the le-name to the variable if the le has a name; if not it becomes undened. In the case of an inquire by le the name may not be the same as that specied using FILE= (because a device-name or directory path mayhave been added) but the name returned will always be suitable for use in an OPEN statement. ACCESS=character-variable returns the record access-method, either 'SEQUENTIAL' or 'DIRECT' if the le is connected; if it is not connected the variable becomes undened. SEQUENTIAL=character-variable returns 'YES' if the le can be opened for sequential access, 'NO' if it cannot, and 'UNKNOWN' otherwise. DIRECT=character-variable returns 'YES' if the le can be opened for direct access, 'NO' if it cannot, and 'UNKNOWN' otherwise. FORM=character-variable returns 'FORMATTED' if the le is connected for formatted access, 'UNFORMATTED' if it is connected for unformatted access, or becomes undened if there is no connection. FORMATTED=character-variable returns 'YES' if formatted access is permitted, 'NO' if it is not, or 'UNKNOWN' otherwise. UNFORMATTED=character-variable returns 'YES' if unformatted access is permitted, 'NO' if it is not, or 'UNKNOWN' otherwise. RECL=integer-variable returns the record length if the le is connected for direct-access but becomes undened otherwise. Note that the units are characters for formatted les, but are system-dependent for unformatted les.

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returns a number which is one higher than the last record read or written if the le is connected for direct access. If it is connected for direct access but no records have been transferred, the variable returns one. If the le is not connected for direct access the variable becomes undened. BLANK=character-variable returns 'NULL' or 'BLANK' if the le is connected for formatted access according to the way embedded and trailing blanks are to be treated. In other cases it becomes undened.

10.16

READ

The READ statement reads information from one or more records on a le into a list of variables, array elements, etc. The WRITE statement writes information from a list of items which may include variables, arrays, and expressions and produces one or more records on a le. Each READ or WRITE statement can only transfer one record on an unformatted le but on formatted les, including internal les, more than one record may be transferred, depending on the contents of the format specication. The two statements have the same general form: READ( control-list ) data-list WRITE( control-list ) data-list The control-list must contain a unit identier; the other items may be optional depending on the type of le. The data-list is also optional: if it is absent the statement transfers one record (or possibly more under the control of a format specication).

and

WRITE

Statements

Unit Identier
This mayhaveany of the following forms: UNIT= integer-expression The value of the expression must be zero or greater and must refer to avalid I/O unit. UNIT=* For the standard pre-connected input or output le. UNIT=internal-le The internal-le maybe a variable, array-element, substring, or arrayof type character, see section 10.3. Note that the keyword UNIT= is optional if the unit identier is the rst item in the control list.

Format Identier

A format identier must be provided when using a formatted (or internal) le but not otherwise. It mayhaveany of the following forms: FMT=label The label of a FORMAT statement in the same program unit. FMT=format The format maybe a character expression or character array containing a complete format specication (section 10.6). FMT=* For list-directed formatting (section 10.10). Note that the keyword FMT= is also optional if the format identier is the second item in the control list and the rst item is a unit identier specied without its keyword.

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Record Number
A record number identier must be provided for direct-access les but not otherwise. It has the form: REC=integer-expression The record number must be greater than zero; for READ it must refer to a record which exists.

Error and End-of-le Identiers
These may be provided in any combination, but or internal le. See 10.5 for more information.
END=label ERR=label IOSTAT=integer-variable END=

label is only valid when reading a sequential

The data list of a READ statementmay contain variables, array-elements, character-substrings, or complete arrays of any data type. An array-name without subscripts represents all the elements of the array; this is not permitted for assumed-size dummy arguments in procedures (because the array size is indeterminate). The list may also contain implied DO-loops (explained below). The data list of a WRITE statementmay contain any of the items permitted in a READ statement and in addition expressions of any data type. As in all I/O statements, expressions must not themselves involve the execution of other I/O statements.

Implied DO-loops

The simplest and most ecient way to read or write all the elements of an array is to put its name, unsubscripted, in the data-transfer list. In the case of a multi-dimensional array the elements will be transferred in the normal storage sequence, with the rst subscript varying most rapidly. An implied-DO loop allows the elements to be transferred selectively or in some non-standard order. The rules for an implied-DO are similar to that of an ordinary DO-loop but the loop forms a single item in the data-transfer list and is enclosed by a pair of parentheses rather than by DO and CONTINUE statements. For example:
15 READ(UNIT=*, FMT=*) (ARRAY(I), I= IMIN, IMAX) WRITE(UNIT=*, FMT=15) (M, X(M), Y(M), M=1,101,5) FORMAT(1X, I6, 2F12.3)

Amulti-dimensional array can be printed out in a transposed form. The next example outputs an array X(100,5) but with 5 elements across and 100 lines vertically:
5 WRITE(UNIT=*, FMT=5) (I,I=1,5), $ ((L,X(L,I),I=1,5),L=1,100) FORMAT(1X,'LINE', 5I10, 100(/,1X,I4, 5F10.2))

The rst loop writes headings for the ve columns, then the double loop writes a line-number for each line followed byve array elements. Note that the parentheses have to be matched and that a comma is needed after the inner right-parenthesis since the inner loop is just an item in the list contained in the outer loop.

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The implied DO-loop has the general form: ( data-list, loop-variable = start, limit, step ) where the rules for the start, limit, and step values are exactly as in an ordinary DO statement. The loop-variable (normally an integer) may be used within the data-list and this list may, in turn, include further complete implied-DO lists. If an error or end-of-le condition occurs in an implied DO-loop then the loop-control variable will be undened on exit; this means that an explicit DO-loop is required to read an indenite list of data records and exit with knowledge of how many items were actually input.

10.17

REWIND

These le-positioning statements may only be used on external sequential les; most systems will restrict them to les stored on suitable peripheral devices such as discs or tapes. REWIND repositions a le to the beginning of information so that the next READ statement will read the rst record; if a WRITE statement is used after REWIND all existing records on the le are destroyed. REWIND has no eect if the le is already rewound. If a REWIND statement is used on a unit which is connected but does not exist (e.g. a pre-connected output le) it creates the le. BACKSPACE moves the le position back by one record so that the record can be re-read or over-written. There is no eect if the le is already positioned at the beginning of information but it is an error to back-space a le which does not exist. It is also illegal to back-space over records written by list-directed formatting (because the number of records produced each time is system-dependent). A few operating systems nd it dicult to implement the BACKSPACE statement directly and actually manage it only by rewinding the le and spacing forward to the appropriate record. It is sometimes possible to avoid backspacing a le by allocating buers within the program and, for a formatted le, using an internal le READ and WRITE statements. These statements have similar general forms: REWIND( control-list ) BACKSPACE( control-list ) where the control-list may contain:
UNIT=integer-expression IOSTAT=integer-variable ERR=label

and

BACKSPACE

Statements

The unit identier is compulsory, the others optional. If only the unit identier is used then (for compatibility with Fortran66) an abbreviated form of the statement is permitted: REWIND integer-expression BACKSPACE integer-expression where the integer expression identies the unit number.

11

DATA

Statement

The DATA statement is used to specify initial values for variables and array elements. The DATA statement is non-executable, but in a main program unit it has the same eect as a set of assignment statements at the very beginning of the program. Thus in a main program a DATA statement like this:
DATA LINES/625/, FREQ/50.0/, NAME/'PAL'/

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could replace several assignment statements:
LINES = 625 FREQ = 50.0 NAME = 'PAL'

This is more convenient, especially when initialising arrays, and ecient, since the work is done when the program is loaded. In a procedure, however, these two methods are not equivalent, especially in the case of items which are modied as the procedure executes. A DATA statement only sets the values once at the start of execution, whereas assignment statements will do so every time the procedure is called. It is important to distinguish between the DATA and PARAMETER statements. The DATA statement merely species an initial value for a variable (or array) which may be altered during the course of execution. The PARAMETER statement species values for constants which cannot be changed without recompiling the program. If, however, you need an array of constants, for which there is no direct support in Fortran, you should use an ordinary array with a DATA statement to initialise its elements (and take care not to corrupt the contents afterwards).

11.1 Dened and Undened Values

The value of eachvariable and array element is undened at the start of execution unless it has been initialised with a DATA statement. An undened value may only be used in executable statements in ways which cause it to become dened. An item can become dened by its use in any of the following ways: on the left-hand side of an assignment statement, as the control variable of a DO statement, in the input list of a READ statement, as the internal le identier of a WRITE statement, as the I/O status identier in an I/O statement, in an INQUIRE statement except as le or unit number, in a procedure call provided that the corresponding dummy argument is dened before the procedure returns control. An undened variable must not be used in any other way. Errors caused by the inadvertent use of undened values are easy to make and sometimes havevery obscure eects. It is important, therefore, to identify every item which needs to be initialised and provide a suitable set of DATA statements. Modern operating systems often clear the area of memory into which they load a program to prevent unauthorized access to the data used in the preceding job. A few operating systems preset their memory to a bit-pattern which corresponds to an illegal numerical value: this is a very helpful diagnostic facility since whenever an undened variable is used in an expression it generates an error at run time. Other systems merely set their memory to zero: this makes it more dicult to trackdown the use of undened variables and they may only come to light when a program is transported to another system. To rely on undened variables and arrays having an initial value of zero is to leave the program completely at the mercy of changes to the operating system.

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11.2 Initialising Variables

The simplest form of the DATA statement consists of a list of the variable names each followed by a constant enclosed in a pair of slashes:
DOUBLE PRECISION EPOCH LOGICAL OPENED CHARACTER INFILE*20 DATA EPOCH/1950.0D0/, OPENED/.TRUE./, INFILE/'B:OBS.DAT'/

Note that DATA statements must follow all specication statements. An alternative form is to give a complete list of names can be given rst and followed by a separate list of constants:
DATA EPOCH, OPENED, INFILE / 1950.0D0, .TRUE., 'B:OBS.DAT'/ DATA

When there are many items to be initialised it is a matter of taste whether to use several statements or to use one with many continuation lines. It is, of course, illegal to have the same name appearing twice. Character variables can be initialised in sections using the substring notation if this is more convenient:
CHARACTER*52 LETTER DATA LETTER(1:26)/'ABCDEFGHIJKLMNOPQRSTUVWXYZ'/, $ LETTER(27:) /'abcdefghijklmnopqrstuvwxyz'/

If the length of the character constant diers from that of the variable then the string is truncated or padded with blanks as in an assignment statement. The type conversion rules of assignment statements also apply to arithmetic items in DATA statements.

11.3 Initialising Arrays

There are several ways of using DATA statements to initialise arrays, all of them simpler and more ecient than the equivalent set of DO-loops. Perhaps the most common requirementis to initialise all the elements of an array: in this case the array name can appear without subscripts. If several of the elements are to have the same initial value a repeat count can be precede any constant:
REAL FLUX(1000) DATA FLUX / 512*0.0, 488*-1.0 /

The total number of constants must equal the number of array elements. The constants correspond to the elements in the array in the normal storage sequence, that is with the rst subscript varying most rapidly. Named constants are permitted, but not constant expressions. The repeat count may be a literal or named integer constant. To initialise a multi-dimensional array with parameterised array bounds it is necessary to dene another integer constant to hold the total number of elements:
PARAMETER (NX = 800, NY = 360, NTOTAL = NX * NY) DOUBLE PRECISION SCREEN(NX,NY), ZERO PARAMETER (ZERO = 0.0D0) DATA SCREEN / NTOTAL * ZERO /

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If only a few array elements are to be initialised they can be listed individually:
REAL SPARSE(50,50) DATA SPARSE(1,1), SPARSE(50,50) / 1.0, 99.99999 /

The third, and most complicated, option is to use an implied-DO loop. This operates in much the same way as an implied-DO in an I/O statement:
INTEGER ODD(10) DATA (ODD(I),I=1,10,2)/ 5 * 43/ DATA (ODD(I),I=2,10,2)/ 5 * 0 /

This example has initialised all the odd numbered elements to one value and all the even numbered elements to another. Note that the loop control variable (I in this example) has a scope which does not extend outside the section of the DATA statement in which it is used. Any integer variable may be used as a loop control index in a DATA statement without eects elsewhere; the value of I itself is not dened by these statements. When initialising part of a multi-dimensional array it may occasionally be useful to nest DO-loops like this:
DOUBLE PRECISION FIELD(5,5) DATA ((FIELD(I,J),I=1,J), J=1,5) / 15 * -1.0D0 /

This species initial values only for the upper triangle of the square array FIELD.

11.4

DATA

In procedures, DATA statements perform a role for which assignment statements are no substitute. It is quite often necessary to arrange for some action to be carried out at the start of the rst call but not subsequently, such as opening a le or initialising a variable or array which accumulates information during subsequent calls. If information is preserved in a local variable or array from one invocation to another a SAVE statement (described in section 9.11) is also needed. Indeed, in general any ob ject initialised in a DATA statement in a procedure also needs to be named in a SAVE statement unless its value is never altered. In the next example the procedure opens a data le on its rst call, using a logical variable OPENED to remember the state of the le.
SUBROUTINE LOOKUP(INDEX, RECORD) INTEGER INDEX REAL RECORD LOGICAL OPENED SAVE OPENED DATA OPENED / .FALSE. / *On first call OPENED is false so open the file. IF(.NOT. OPENED) THEN OPEN(UNIT=57, FILE='HIDDEN.DAT', STATUS='OLD', $ ACCESS='DIRECT', RECL=100) OPENED = .TRUE. END IF READ(UNIT=57, REC=INDEX) RECORD END

Statements in Procedures

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Here, for simplicity, the I/O unit number is a literal constant. The procedure would be more modular if the unit number were also an argument of the procedure or if it contained some code, using the INQUIRE statement, to determine for itself a suitable unused unit number. There is, of course, no corresponding way to determine which is the last call to the procedure so that the le can be closed, but this is not strictly necessary as the Fortran system closes all les automatically when the program exits. Note that DATA statements cannot be used to initialise variables or arrays which are dummy arguments of a procedure, nor the variable which has the same name as the function.

11.5 General Rules

The general form of the DATA statement is: DATA nlist / clist /, nlist / clist /, ... Where nlist is a list of variable names, array names, substring names, and implied-DO lists, and clist is a list of items which may be literal or named constants or either of these preceded by a repeat-count and an asterisk. The repeat-count can also be an unsigned integer constant or named constant. The comma which precedes each list of names except the rst is optional. An implied-DO list has the general form: ( d list, intvar = start, limit, step ) Where em dlist is a list of implied-DO lists and array elements; intvar is an integer variable called the loop-control variable; start, limit, and step are integer expressions in which all the operands must be integer constants or loop-control variables of outer implied-DO lists. DATA statements cannot be used to initialise items in the blank common block; items in named common blocks can only be initialised within a BLOCK DATA program unit (see section 12.4). The DATA statements in each program unit must follow all specication statements but they can be interspersed with executable statements and statement function statements. It is, however, best to follow the usual practice of putting all DATA statements before any of the executable statements.

12 Common Blocks
A common block is a list of variables and arrays stored in a named area whichmay be accessed directly in more than one program unit. Common blocks are mainly used to transfer information from one program unit to another; they can be used in as an alternative to argument-list transfers or in addition to them. Common blocks are sometimes used to t large programs into small computers by arranging for several program units to share a common pool of memory. This is not a recommended programming practice and is likely to become redundant with the spread of virtual-memory operating systems. The name of a common block is an external name which must be dierent from all other global names, such as those of procedures, in the executable program. The variables and arrays stored with the block cannot be initialised in the normal way, but only in a BLOCK DATA program unit which was invented especially for this purpose.

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12.1 Using Common Blocks

In most cases the best way to pass information from one program unit to another is to use the procedure argument list mechanism. This preserves the modularity and independence of procedures as much as possible. Argument lists are, however, less satisfactory in a group of procedures forming a package which have to share a large amount of information with each other. Procedure argument lists then tend to be come long, cumbersome, and even inecient. If this package of procedures is intended for general use it is quite importantto keep the external interface as uncomplicated as possible. This can be achieved by using the procedure argument lists only for import of information from and export to the rest of the program, and handling the communications between one procedure in the package and another with common blocks. The user is then free to ignore the internal workings of the package. For example, in a simple package to handle a pen-plotter you may want to provide simple procedure calls such as: CALL PLOPEN Initialise the plotting device CALL SCALE(F) Set the scaling factor to F. CALL MOVE(X,Y) Move the pen to position (X,Y) CALL DRAW(X,Y) Draw a line from the last pen position to (X,Y). These procedures clearly have to pass information from one to another about the currentpen position, scaling factor, etc. A suitable common block denition might look like this:
COMMON /PLOT/ OPENED, ORIGIN(2), PSCALE, NUMPEN LOGICAL OPENED INTEGER NUMPEN REAL PSCALE, ORIGIN SAVE /PLOT/

These specication statements would be needed in each procedure in the package.

Common Block Names
A program unit can access the contents of any common block by quoting its name in a COMMON statement. Common block names are always enclosed in a pair of slashes and can only be used in COMMON and SAVE statements. The common block itself has no data type and has a global name which must be distinct from the names of all program units. The name should also be distinct from all local names in each program units which access the block. Each program unit can make use of anynumber of dierent common blocks. There is also a special blank or un-named common block with unique properties which are covered in section 12.2 below. The variables and arrays within a common block do not have any global status: they are associated with items in blocks bearing the same name in other program units only by their position within the block. Thus, if in one program unit species:
COMMON /OBTUSE/ X(3)

and in another:
COMMON /OBTUSE/ A, B, C

then, assuming the data types are the same, X(1) corresponds to A, X(2) to B, and X(3) to C. The COMMON statements here are eectively setting up dierent names or aliases for the same

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set of memory locations. The data types do not have to match provided the overall length is the same, but it is generally only possible to transfer information from one program unit to another if the corresponding items have the same data type. If they do not, when one item becomes dened all names for the same location which have a dierent data type become undened. There is one minor exception to this rule: information may be transferred from a complex variable (or array element) to two variables of type real (or vice-versa) since these are directly associated with its real and imaginary parts. Usually it is necessary to arrange for corresponding items to have identical data types; it also minimises confusion if the same symbolic names are used as well. The simplest waytoachieve this is to use an INCLUDE statement, if your system provides one. The include-le should contain not only the COMMON statement but also all the associated type and SAVE statements which are necessary. It is, of course, still necessary to recompile every program unit which accesses the common block whenever its denition is altered signicantly.

Declaring Arrays
The bounds of an array can be declared in the COMMON statement itself, or in a separate type or DIMENSION statement, but only in one of them. Thus:
COMMON /DEMO/ ARRAY(5000) DOUBLE PRECISION ARRAY

is exactly equivalent to:
COMMON /DEMO/ ARRAY DOUBLE PRECISION ARRAY(5000)

or even:
COMMON /DEMO/ ARRAY DOUBLE PRECISION ARRAY DIMENSION ARRAY(5000)

but the verbosity of the third form has little to recommend it.

Data Types
The normal data type rules apply to variables and arrays in each common block. A type statement is not required if the initial letter rule would have the required eect, but type statements are advisable, especially if the implied-type rules are anywhere aected by IMPLICIT statements. Type statements may precede or follow the COMMON statement. Similarly the lengths of character items should be specied in a separate type statement: these cannot be specied in the COMMON statement.

Storage Units
The length of each common block is measured in storage units, as described in section 5.1. In summary, integer, real, and logical items occupy one numeric storage unit each; complex and double precision items occupy two each. To maximise portability, character storage units are considered incommensurate with numerical storage units. For this reason character and non-character items cannot be mixed in the same common block.

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In practice this often means that two common blocks are needed to hold a particular data structure: one for the character items and one for all the others. If, in the rst example, it had been necessary for the plotting package to store a plot title this would have to appear in a separate common block such as:
COMMON /PLOTC/ TITLE CHARACTER TITLE*40 SAVE /PLOTC/

It is good practice to use related names for the blocks to indicate that the character and non-character items are used in conjunction. The length of a named common block must be the same in each program unit in which it appears. Obviously the easiest way to ensure this is to make the common block contents identical in each program unit. Note, however, that there is no requirement for data types to match, or for them to be listed in any particular order, provided the items are not used for information transfer, and provided the total length of the block is the same in each case. Thus these common blocks are both 2000 numerical storage units in length:
COMMON /SAME/ G(1000) DOUBLE PRECISION G COMMON /SAME/ A, B, C, R(1997) REAL A, R LOGICAL B INTEGER C

Items in a common block are stored in consecutive memory locations. Unfortunately there a few computer systems which require double precision and complex items to be stored in evennumbered storage locations: these may nd it hard to cope with blocks which contain a mixture of data types. Machines with this defect can nearly always be placated by arranging for all double precision and complex items to come at the beginning of each block.
SAVE

Items in common blocks may become undened when a procedure returns control to the calling unit just like local variables and arrays. This will not, however, occur in the case of the blank common block nor in any common block which is also declared in a program unit which is higher up the currentchain of procedure calls. Since the main program unit is always at the top of the chain any common block declared in the main program can never become undened in this way. In all other cases it is prudent to use SAVE statements. The individual items in common blocks cannot be specied in a SAVE statement, only the common block name itself. Thus:
SAVE /SAME/, /DEMO/

Statements and Common Blocks

If a common block is saved in any program unit then it must be saved in all of them. The SAVE statement ought therefore to be included with the COMMON and associated type statements if INCLUDE statements are used. If the program is later modied so that the common block is also declared in the main program this will bring a SAVE statementinto the main program unit, but although it then has no eect, it does no harm.

12 COMMON BLOCKS

112 common block nor, in a function, are also some restrictions on the calls because of the possibility of this:

Restrictions
The dummy arguments of a procedure cannot be members of a can the variable which has same name as the function. There use of common block items as actual arguments of procedure multiple denition. For example, if a procedure is dened like
SUBROUTINE SILLY(ARG) COMMON /BLOCK/ COM

And the same common block is also used in the calling unit, with a common block item as the actual argument, such as:
PROGRAM DUMMY COMMON /BLOCK/ VALUE *... CALL SILLY(VALUE)

Then both ARG and COM within the subroutine SILLY are associated with the same item, VALUE, and it is therefore illegal to assign a new value to either of them.

12.2 Blank Common Blocks

Common blocks are sometimes also used to reduce the total amount of memory used by a program by arranging for several program units to share the same set of memory locations. This is a dicult and risky procedure which should not be attempted unless all else fails. Most Fortran systems operate a storage allocation system which is completely static: each program unit has a separate allocation of memory for its local variables and arrays. If several procedures each need to use large arrays internally the total amount of memory occupied by the program may be rather large. If a set of procedures can be identied which are invoked in sequence, rather than one calling another, it may be feasible to reduce the total memory allocation by arranging for them to share a storage area. Each will use the same common block for their internal array space. Named common blocks are required to have the same length in each program unit: if they are used it is necessary to work out which one needs the most storage and pad out all the others to same length. An alternative is to the use the special blank (or un-named) common block which has the useful property that it mayhave a dierent length in dierent program units. In one program unit, for example, you could specify:
COMMON // DUMMY(10000)

and in another
COMPLEX SERIES(512,512), SLICE(512), EXPECT(1024) COMMON // SERIES, SLICE, EXPECT

The blank common block has two other special properties. Firstly it cannot be initialised by a DATA statementeven within a BLOCK DATA program unit (but this is not a serious limitation for a block used just for scratch storage). Secondly items within the blank common block never become undened as a result of a procedure exit. For this reason the blank common block cannot be specied in a SAVE statement.

12 COMMON BLOCKS

113

12.3

COMMON

A program unit may contain anynumber of COMMON statements, each of which can dene contents for anynumber of dierent common blocks. COMMON statements are specication statements and have a general form: COMMON / name/ list-of-items , / name / list-of-items ... Each name is dened as a common block name, which has global scope. The Fortran Standard allows it to use the same name as an intrinsic function, a local variable, or local array but not that of a named constant or an intrinsic function. Each list of items can contain names of variables and arrays. The array name may be followed by a dimension specication provided that each array is only dimensioned once in each program unit. The comma shown before the second and subsequent block-name is optional. The name of the blank common block is normally specied as two consecutive slashes (ignoring any intervening blanks) but if it is the rst block in the statement then the pair of slashes may be omitted. The contents of a common block are a concatenation of the all the denitions for it in the program unit. Thus:
COMMON /ONE/ A, B, C, /TWO/ ALPHA, BETA, GAMMA COMMON /TWO/ DELTA

Statement

denes two blocks, /ONE/ contains three items while /TWO/ contains four of them. In procedures, variables which are dummy arguments or which are the same as the function name cannot appear in common blocks.

12.4

BLOCK DATA

The block data program unit is a special form of program unit which is required only if it is necessary to specify initial values for variables and arrays in named common blocks. The program unit starts with a BLOCK DATA statement, ends with an END statement, and contains only specication and DATA statements. Comment lines are also permitted. The block data program unit is not executable and it is not a procedure. The next example initialises the items in the common block for the plotting package used in section 12.1, so that the initial pen position is at the origin, the scaling factor starts at one, and so on. Thus a suitable program unit would be:
BLOCK DATA SETPLT *SETPLT initialises the values used in the plotting package. COMMON /PLOT/ OPENED, ORIGIN(2), PSCALE, NUMPEN LOGICAL OPENED INTEGER NUMPEN REAL PSCALE, ORIGIN SAVE /PLOT/ DATA OPENED/.FALSE./, ORIGIN/2*0.0/, PSCALE/1.0/ DATA NUMPEN/-1/ END

Program Units

A block data unit can specify initial values for anynumber of named common blocks (blank common cannot be initialised). Each common block must be complete but it is not necessary to specify initial values for all of the items within it. There can be more than one block data program unit, but a given common block cannot appear in more than one of them.

13 OBSOLETE AND DEPRECATED FEATURES

114

For compatibility with Fortran66 it is also possible to have one un-named block data program unit in a program.

Linking Block Data Program Units
If, when linking a program, one of the modules containing a procedure is accidentally omitted the linker is almost certain to produce an error message. But, unless additional precautions are taken, this will not occur if a block data subprogram unit is omitted. The program may even appear to work without it, but is likely to produce the wrong answer. There is a simple way to guard against this possibility: the name of the block data unit should be specied in an EXTERNAL statement in at least some of the program units in which the common block is used. There is no harm in declaring it in all of them. This ensures that a linktime reference will be generated if any of these other program units are used. There is a slight snag to this technique if an INCLUDE statement is used to bring the common block denition into each program unit including the block data unit. In order to avoid a self-reference, the include-le should not contain the EXTERNAL statement. Despite this slight complication, this is a simple and valuable precaution. It also makes is possible to hold block data units on ob ject libraries and retrieve them automatically when they are required, just like all other types of subprogram unit.

13 Obsolete and Deprecated Features
None of the features covered here should be used in new software: some of them are completely obsolete, others have practical defects which make them unsuitable for use in well-structured software. These brief descriptions are provided only for the benet of programmers who have to understand and update programs designed in earlier years.

13.1 Storage of Character Strings in Non-character Items

Before the advent of the character data type it was possible to store text in arithmetic variables and arrays, although only very limited manipulation was possible. The number of characters which could be stored in each item was entirely system-dependent. One side-eect is that many systems still allow the A format descriptor to match input/output items of arithmetic types; this sometimes allows mismatches between data-transfer lists and format descriptors to pass undetected.

13.2 Arithmetic

IF

This is an executable statement with the form: IF( arithmetic-expression ) label1, label2, label3 It generally provides a three-way branch (but two of the labels may be identical for a two-way branch). The expression maybeaninteger, real, or double-precision value: control is transferred to the statement attached to label1 if its value is negative, label2 if zero, or label3, if positive.

Statement

13.3

ASSIGN

These two executable statements are normally used together. The ASSIGN statement assigns a statement label value to an integer variable. When this has been done the variable no longer has an arithmetic value. If the label is attached to an executable statement the variable can only be

and assigned

GO TO

Statements

13 OBSOLETE AND DEPRECATED FEATURES

115

used in an assigned GO TO statement; if attached to a FORMAT statement the variable can only be used in a READ or WRITE statement. The general forms of these statements are: ASSIGN label TO integer-variable GO TO integer-variable ,(label, label, ... label) In the assigned GO TO statement the comma and the entire parenthesised list of labels is optional. Assigned GO TO can be used to provide a linkage to and from a section of a program unit acting as an internal subroutine, but is not a very convenient or satisfactory way of doing this.

13.4

PAUSE

is an executable statement which halts the program in suchaway that execution can be resumed in some wayby the user (or on some systems by the computer operator). The general forms of the statement are identical to those of STOP, for example:
PAUSE PAUSE 'NOW MOUNT THE NEXT TAPE'

Statement

or
PAUSE PAUSE 54321 WRITE

can be replaced by one system-dependent.

and one

READ

statement: this is more exible and less

13.5 Alternate

RETURN

The alternate RETURN mechanism can be used in subroutines (but not external functions) to arrange a transfer of control to some labelled statement on completion of a CALL statement. In order to use it the arguments of the CALL statementmust include a list of labels, each preceded by an asterisk. These labels are attached to points in the calling program unit at which execution may resume after the CALL statement is executed. For example:
CALL BAD(X, Y, Z, *150, *220, *390)

The corresponding subroutine statement will have asterisks as dummy arguments for each label specication:
SUBROUTINE BAD(A, B, C, *, *, *)

The return point depends on the value of an integer expression given in the Thus:
RETURN 2

RETURN

statement.

will cause execution to be resumed at the statement attached to the second label argument, 220 in this case. If the value of the integer expression in the RETURN statement is not in the range 1 to n (where there are n label arguments) or a plain RETURN statement is executed, then execution resumes at the statement after the CALL in the usual way. The mechanism can be used for error-handling but is not very exible as information cannot be passed through more than one procedure level. It is better to use an integer argument to return a status value and use that with an IF (or even a computed GO TO statement) in the calling program.

13 OBSOLETE AND DEPRECATED FEATURES

116

13.6

ENTRY

ENTRY

statements can be used to specify additional entry points in external functions and subroutines. ENTRY is a non-executable statement which has the same form as a SUBROUTINE statement. An ENTRY statementmay be used at any point in a procedure but all specication statements relating to its dummy arguments must appear in the appropriate place with the other specication statements. If the main entry pointis a SUBROUTINE statement than all alternativeentry points can be called in the same way as subroutines; if it is a FUNCTION statement than all alternative entry point names can be used as functions. If the main entry point is a character function then all the alternative entry points must also have that type. Alternative entry points may have dierent lists of dummy arguments; it is up to the user to ensure that all those returning information to the calling program are properly dened before exit. The rules for the ENTRY statement are necessarily complicated so it is easy to make mistakes. It is generally better, or at least less unsatisfactory, to use a set of separate procedures which share information using common blocks.

Statement

13.7

EQUIVALENCE

EQUIVALENCE

is a specication statement which causes two or more items (variables or arrays) to be associated with each other, i.e. to correspond to the same area of memory. Character items can only be associated with other character items; otherwise the data types do not have to match. As with common blocks, however, transfer of information is only permitted via associated items if their data types match. A special exception is made for a complex item which is associated with two real ones. EQUIVALENCE statements can be used fairly safely to provide a simple variable name as an alias for a particular array element or to associate a character variable with an array of the same length. For example:
CHARACTER STRING*80, ARRAY(80)*1 EQUIVALENCE (STRING, ARRAY)

Statement

This slightly simplies access to a single character in the string as the form ARRAY(K) can be used instead of STRING(K:K). The general form of the statement is: EQUIVALENCE (v, v,... v),(v, v,... v),... where each v is a variable, array, array element, or substring. Dummy arguments of procedures (and variables which are external function names) cannot appear. An array name without subscripts refers to the rst element of the array. It is illegal to associate two or more elements of the same array, directly or indirectly, ordoanything which con icts with the storage sequence rules. Variables and arrays in common blocks can appear in EQUIVALENCE statements but this has the eect of bringing all the associated items into the block. They can be used to extend the contents of the blockupwards, sub ject to the rules for common block length, but not downwards. Although the EQUIVALENCE statementdoes have a few legitimate uses it is usually encountered in programs where the rules of Fortran are broken to obtain some special eect. Programs which do this are rarely portable.

13.8 Specic Names of Intrinsic Functions

Specic names should be used instead of the generic name of an intrinsic function only if the name is to be the actual argument of a procedure call; the name then must also be declared

13 OBSOLETE AND DEPRECATED FEATURES

117

in an INTRINSIC statement. The following intrinsic functions cannot be used in this way, and their specic names are therefore completely obsolete. Obsolete specic name IFIX, IDINT FLOAT, SNGL MAX0, AMAX1, DMAX1 AMAX0, MAX1 MIN0, AMIN1, DMIN1 AMIN0, MIN1
*

Preferred generic form INT REAL MAX MAX * MIN MIN *

the functions AMAX0, MAX1, AMIN0, and MIN1 whichhave a data type dierent from that of their arguments can only be replaced by appropriate type conversion functions in addition to MAX or MIN.

13.9

PRINT

The PRINT statement can produce formatted or list-directed output on the standard pre-connected output le. Thus these two statements have exactly the same eect:
PRINT fmt, data-list WRITE(*, fmt) data-list

Statement and simplied

READ

The PRINT statement is limited in its functionality and misleading, since there is no necessity for its output to appear in printed form. In a similar way there is a simplied form of READ statement, so these have the same eect:
READ fmt, data-list READ(*, fmt) data-list

13.10
The

END FILE

END FILE

statement has the same general forms as REWIND and

Statement

BACKSPACE

:

END FILE(UNIT=unit, ERR=label, IOSTAT=int-var) END FILE unit

It appends a special \end-le" record to a sequential le which is designed to trigger the end-of-le detection mechanism on subsequent input. No further records can be written to the le after this end-le record, i.e. the next operation must be CLOSE, REWIND, or BACKSPACE. The statement seems to be super uous on almost all current systems since they can detect the end of an input le without its aid. The Fortran Standard requires that the end-le record be treated as a physical record, so that after an end-of-le condition has been detected an explicit BACKSPACE operation is required before any new data records are appended. This notion is somewhat articial and not all systems implement it correctly. This is one of the few cases where a deliberate departure from the Fortran Standard can enhance portability.

13.11 Obsolete Format Descriptors

The data descriptor Dw.d is exactly equivalent to Ew.d on input; on output it is similar except that the exponent will use the letter D instead of E. Real and double precision data items can be read equally well by D, E, F, or G descriptors.

14 APPENDIX A { LIST OF INTRINSIC FUNCTIONS
The format signed integer statement the to be doubled

118

descriptor nHstring is exactly equivalent to 'string' (where n is an unconstant giving the length of the string). When used with a formatted WRITE string is copied to the output record. The nH form does not require apostrophes within the string but does require an accurate character count.

14 Appendix A { List of Intrinsic Functions
This table shows the number of arguments for each function and what data types are permitted. The data type codes are: I = Integer, R = Real, D = Double precision, X = Complex, C = Character, L = Logical, * means the result has the same data type as the argument(s). Note that if there is more than one argument in such cases they must all have the same data type.

14 APPENDIX A { LIST OF INTRINSIC FUNCTIONS
R = ABS(X) * = ACOS(RD) R = AIMAG(X) * = ANINT(RD) * = ATAN2(RD,RD)

119

C X X * D *

= = = = = =

CHAR(I) CMPLX(IRDX,IRD) CONJG(X) COS(RDX) DBLE(IRDX) DIM(IRD,IRD)

D = DPROD(R,R) * = EXP(RDX) I = ICHAR(C) I = INDEX(C,C) I = INT(IRDX) I = LEN(C) L = LGE(C,C) L = LGT(C,C) L = LLE(C,C) L = LLT(C,C) * * * * * = = = = = LOG(RDX) LOG10(RD) MAX(IRD,IRD,...) MIN(IRD,IRD,...) MOD(IRD,IRD)

R = REAL(IRDX) * = SIGN(IRD,IRD) * = SQRT(RDX) * = TAN(RD)

Takes the modulus of a complex number (i.e. the square-root of the sum of the squares of the two components). Arc-cosine; the result is in the range 0 to + Extracts the imaginary component of a complex number. Use REAL to extract the real component. Rounds to the nearest whole number. Arc-tangentof arg1/arg2 resolved into the correct quadrant, the result is in the range to + . It is an error to have both arguments zero. Returns Nth character in local character code table. Converts to complex, second arg optional. Computes the complex conjugate of a complex number. Cosine of the angle in radians. Converts to double precision. Returns the positive dierence of arg1 and arg2 , i.e. if arg1 > arg2 it returns (arg1 arg2), otherwise zero. Computes the double precision product of two real values. Returns the exponential, i.e. e to the power of the argument. This is the inverse of the natural logarithm. Returns position of rst character of the string in the local character code table. Searches rst string and returns position of second string within it starting at 1, otherwise zero. Converts to integer by truncation. Returns length of the argumentin characters. Lexical comparison using ASCII collating sequence: returns true if arg1 >= arg2. Lexical comparison using ASCII collating sequence: returns true if arg1 >arg2 . Lexical comparison using ASCII collating sequence: returns true if arg1 <= arg2. Lexical comparison using ASCII collating sequence: returns true if arg1

15 APPENDIX B { SPECIFIC NAMES OF GENERIC FUNCTIONS

120

15 AppendixB{Specic Names of Generic Functions
Specic names are still needed when the function name is used as the actual argument of another procedure. The specic name must then also be declared in an INTRINSIC statement. This table lists all the specic names which are still useful in Fortran77 in these rare circumstances. The other functions either do not have generic names or cannot be passed as actual arguments. Generic Specic names Name INTEGER REAL DOUBLE PRECISION COMPLEX ABS IABS ABS DABS CABS ACOS ACOS DACOS AINT AINT DINT ANINT ANINT DNINT ASIN ASIN DASIN ATAN ATAN DATAN ATAN2 ATAN2 DATAN2 COS COS DCOS CCOS COSH COSH DCOSH DIM IDIM DIM DDIM EXP EXP DEXP CEXP LOG ALOG DLOG CLOG LOG10 ALOG10 DLOG10 MOD MOD AMOD DMOD NINT NINT IDNINT SIGN ISIGN SIGN DSIGN SIN SIN DSIN CSIN SINH SINH DSINH SQRT SQRT DSQRT CSQRT TAN TAN DTAN TANH TANH DTANH

Index

Adjustable arrays 72 Arguments of procedures 69 Arithmetic expressions 41 Arithmetic IF statement 114 Arithmetic operators 41 Arrays 38 Array elements 39 Arrays, adjustable 72 Arrays as arguments 71 Arrays, assumed-size 73 Arrays, character 74 Arrays, declaring size of 38 Arrays, initialising 106 ASCII collating sequence 51 ASSIGN statement 114 Assigned GO TO statement 114 Assignment, character 50 Assignment statements 47 Assumed-size arrays 73 BACKSPACE statement 104 Bit-wise logical operations 44 Blank characters 22 BLOCK DATA program units 113 CALL statement76 Carriage-control 97 Character arrays 74 Character collating sequence 53 Character constants 33 Character data type 30 Character expressions 50 Character functions 51 Character handling 48 Character set, Fortran 21 CHARACTER statement34 Characters, non-standard 22 CLOSE statement 100 Column control in formats 94 Comment lines 23 Common blocks 108 COMMON statement 113 Comparisons, arithmetic 53 Comparisons, character 53 Compiling 18 Complex constants 33 Complex data type 30 121

Computed GO TO statement61 Constant expressions 44 Constants, named 36 Constants 32 Continuation lines 23 Currency symbol 22 DATA statement 104 Data type conversions 43 Data type defaults 34 Data types, non-standard 31 Data types 28 DIMENSION statement38 Direct access les 82, 84 DO WHILE loops 7 DO-loops 58 Double precision constants 33 Double precision data type 30 ELSE and ELSE IF statements 57 END DO statement7 END FILE statement 117 End-of-le condition 89 ENTRY statement 116 EQUIVALENCE statement 116 Errors, I/O 87 Errors 21 Execution sequence 26 Expressions, arithmetic 40 Expressions, logical 54 Expressions, relational 52 Extensions 7 External les 83 External procedures 65 EXTERNAL statement79 Files, external 81 Files, internal 80 Files 80 Format data descriptors 91 Format specication 89 FORMAT statement90 Formats, character 93 Formats, oating-point 92 Formats, integer 92 Formats, logical 93 Fortran90 6 FUNCTION statement77

INDEX
Functions, external 68 Functions, intrinsic 45 Functions, statement64 Functions, type conversion 46 Global names 27 GO TO statement61 IF-blocks 57 IMPLICIT NONE statement7 IMPLICIT statement35 Implied DO-loops in I/O 103 INCLUDE statement7,18 Initialising variables 106 Input/output facilities 80 INQUIRE statement 81, 100 Integer constants 32 Integer data type 29 Integer division 43 Internal les 80, 85 Intrinsic function names 27, 116 Intrinsic functions 45, 63, 118 INTRINSIC statement79 I/O units 81 Labels 24 Linking 19 List-directed input 96 List-directed I/O 83 List-directed output 96 Logical constants 33 Logical data type 30 Logical expressions 54 Logical-IF statement60 Loops 56 Named constants 36 Names, scope of 27 Names, symbolic 26 Ob ject libraries 19 OPEN statement 81, 99 Operators, logical 55 PARAMETER statement37 PAUSE statement 115 Pre-connected les 87 PRINT statement 117 Printing and carriage-control 97 Procedures as arguments 75 Procedures, external 65 Procedures 25, 63 PROGRAM statement28 Program units 25

122 READ statement 80, 102 Real constants 32 Real data type 29 Record control in formats 94 Records 81 Relational expressions 52 Reserved words 27 RETURN, alternate 115 RETURN statement76 REWIND statement 104 SAVE statement and common blocks 111 SAVE statement79 Scale factors in formats 95 Sequential access les 82 Source Code 17 Statement functions 64 Statement labels 24 Statementlayout 23 Statement order 25 STOP statement 57, 62 Storage sequence 40 Storage units 31 SUBROUTINE statement76 Substrings, character 49 Symbolic names 26 Termainal I/O 87 Text les 83 Trigonometric functions 45 Type conversion 46 Type statements 34 Undened values 44 Variables 38 WRITE statement 80, 102