FORTRAN (formerly FORTRAN, derived from "Formula Translation" ) is a
general-purpose, imperative programming language that is especially
suited to numeric computation and scientific computing . Originally
* 1 Naming
* 2 History
* 2.1 FORTRAN
* 2.1.1 Fixed layout and punched cards
* 2.2 FORTRAN II
* 2.2.1 Simple FORTRAN II program
* 2.3 FORTRAN III
* 2.7 FORTRAN 77
* 2.7.1 Variants: Minnesota FORTRAN
* 2.8 Transition to ANSI Standard
* 2.9.1 Obsolescence and deletions * 2.9.2 "Hello world" example
* 2.10.1 Conditional compilation and varying length strings
* 6 Variants
* 6.4 Specific variants
* 6.4.1 FOR TRANSIT for the
* 6.5 Fortran-based languages
* 7 Code examples * 8 Humor * 9 See also * 10 References * 11 Further reading * 12 External links
The names of earlier versions of the language through FORTRAN 77 were
conventionally spelled in all-capitals (FORTRAN 77 was the last
version in which the use of lowercase letters in keywords was strictly
non-standard). The capitalization has been dropped in referring to
newer versions beginning with
An IBM 704 mainframe computer
In late 1953, John W. Backus submitted a proposal to his superiors at
A draft specification for The
While the community was skeptical that this new method could possibly
outperform hand-coding, it reduced the number of programming
statements necessary to operate a machine by a factor of 20, and
quickly gained acceptance.
John Backus said during a 1979 interview
with Think, the
The language was widely adopted by scientists for writing numerically intensive programs, which encouraged compiler writers to produce compilers that could generate faster and more efficient code. The inclusion of a complex number data type in the language made Fortran especially suited to technical applications such as electrical engineering.
By 1960, versions of FORTRAN were available for the
The development of FORTRAN paralleled the early evolution of compiler technology , and many advances in the theory and design of compilers were specifically motivated by the need to generate efficient code for FORTRAN programs.
The initial release of FORTRAN for the IBM 704 contained 32 statements , including:
* DIMENSION and EQUIVALENCE statements * Assignment statements * Three-way arithmetic IF statement, which passed control to one of three locations in the program depending on whether the result of the arithmetic statement was negative, zero, or positive * IF statements for checking exceptions (ACCUMULATOR OVERFLOW, QUOTIENT OVERFLOW, and DIVIDE CHECK); and IF statements for manipulating sense switches and sense lights * GO TO, computed GO TO, ASSIGN, and assigned GO TO * DO loops * Formatted I/O: FORMAT, READ, READ INPUT TAPE, WRITE, WRITE OUTPUT TAPE, PRINT, and PUNCH * Unformatted I/O: READ TAPE, READ DRUM, WRITE TAPE, and WRITE DRUM * Other I/O: END FILE, REWIND, and BACKSPACE * PAUSE, STOP, and CONTINUE * FREQUENCY statement (for providing optimization hints to the compiler).
The arithmetic IF statement was similar to a three-way branch
instruction on the
The fundamental unit of program is the basic block ; a basic block is a stretch of program which has one entry point and one exit point. The purpose of section 4 is to prepare for section 5 a table of predecessors (PRED table) which enumerates the basic blocks and lists for every basic block each of the basic blocks which can be its immediate predecessor in flow, together with the absolute frequency of each such basic block link. This table is obtained by running the program once in Monte-Carlo fashion, in which the outcome of conditional transfers arising out of IF-type statements and computed GO TO's is determined by a random number generator suitably weighted according to whatever FREQUENCY statements have been provided.
Many years later, the FREQUENCY statement had no effect on the code, and was treated as a comment statement, since the compilers no longer did this kind of compile-time simulation. A similar fate has befallen compiler hints in several other programming languages; for example C 's register keyword.
The first FORTRAN compiler reported diagnostic information by halting the program when an error was found and outputting an error code on its console. That code could be looked up by the programmer in an error messages table in the operator's manual, providing them with a brief description of the problem.
Fixed Layout And Punched Cards
FORTRAN code on a punched card , showing the specialized uses of columns 1–5, 6 and 73–80 Further information: Computer programming in the punched card era
Before the development of disk files, text editors and terminals,
programs were most often entered on a keypunch keyboard onto 80-column
punched cards , one line to a card. The resulting deck of cards would
be fed into a card reader to be compiled. Punched-card codes included
no lower-case letters or many special characters, and special versions
Reflecting punched-card input practice,
A letter "C" in column 1 caused the entire card to be treated as a comment and ignored by the compiler. Otherwise, the columns of the card were divided into four fields:
* 1 to 5 were the label field: a sequence of digits here was taken
as a label for use in DO or control statements such as GO TO and IF,
or to identify a FORMAT statement referred to in a WRITE or READ
statement. Leading zeros are ignored and 0 is not a valid label
* 6 was a continuation field: a character other than a blank or a
zero here caused the card to be taken as a continuation of the
statement on the prior card. The continuation cards were usually
numbered 1, 2, etc. and the starting card might therefore have zero in
its continuation column - which is not a continuation of its preceding
* 7 to 72 served as the statement field.
* 73 to 80 were ignored (the
Columns 73 to 80 could therefore be used for identification
information, such as punching a sequence number or text, which could
be used to re-order cards if a stack of cards was dropped; though in
practice this was reserved for stable, production programs. An
Within the statement field, whitespace characters (blanks) were ignored outside a text literal. This allowed omitting spaces between tokens for brevity or including spaces within identifiers for clarity. For example, AVG OF X was a valid identifier, equivalent to AVGOFX, and 101010DO101I=1,101 was a valid statement, equivalent to 10101 DO 101 I = 1, 101 because the zero in column 6 is treated as if it were a space (!), while 101010DO101I=1.101 was instead 10101 DO101I = 1.101, the assignment of 1.101 to a variable called DO101I. Note the slight visual difference between a comma and a period.
Hollerith strings , originally allowed only in FORMAT and DATA statements, were prefixed by a character count and the letter H (e.g., 26HTHIS IS ALPHANUMERIC DATA.), allowing blanks to be retained within the character string. Miscounts were a problem.
IBM's FORTRAN II appeared in 1958. The main enhancement was to support procedural programming by allowing user-written subroutines and functions which returned values, with parameters passed by reference . The COMMON statement provided a way for subroutines to access common (or global ) variables. Six new statements were introduced:
* SUBROUTINE, FUNCTION, and END * CALL and RETURN * COMMON
Over the next few years, FORTRAN II would also add support for the DOUBLE PRECISION and COMPLEX data types.
Early FORTRAN compilers supported no recursion in subroutines. Early
computer architectures supported no concept of a stack, and when they
did directly support subroutine calls, the return location was often
stored in one fixed location adjacent to the subroutine code (e.g. the
Simple FORTRAN II Program
This program, for Heron\'s formula , reads data on a tape reel containing three 5-digit integers A, B, and C as input. There are no "type" declarations available: variables whose name starts with I, J, K, L, M, or N are "fixed-point" (i.e. integers), otherwise floating-point. If A, B, and C cannot represent the sides of a triangle in plane geometry, then the program's execution will end with an error code of "STOP 1". Otherwise, an output line will be printed showing the input values for A, B, and C, followed by the computed AREA of the triangle as a floating-point number occupying ten spaces along the line of output and showing 2 digits after the decimal point, the .2 in F10.2 of the FORMAT statement with label 601.
C AREA OF A TRIANGLE WITH A STANDARD SQUARE ROOT FUNCTION C INPUT - TAPE READER UNIT 5, INTEGER INPUT C OUTPUT - LINE PRINTER UNIT 6, REAL OUTPUT C INPUT ERROR DISPLAY ERROR OUTPUT CODE 1 IN JOB CONTROL LISTING READ INPUT TAPE 5, 501, IA, IB, IC 501 FORMAT (3I5) C IA, IB, AND IC MAY NOT BE NEGATIVE OR ZERO C FURTHERMORE, THE SUM OF TWO SIDES OF A TRIANGLE C MUST BE GREATER THAN THE THIRD SIDE, SO WE CHECK FOR THAT, TOO IF (IA) 777, 777, 701 701 IF (IB) 777, 777, 702 702 IF (IC) 777, 777, 703 703 IF (IA+IB-IC) 777, 777, 704 704 IF (IA+IC-IB) 777, 777, 705 705 IF (IB+IC-IA) 777, 777, 799 777 STOP 1 C USING HERON'S FORMULA WE CALCULATE THE C AREA OF THE TRIANGLE 799 S = FLOATF (IA + IB + IC) / 2.0 AREA = SQRTF( S * (S - FLOATF(IA)) * (S - FLOATF(IB)) * + (S - FLOATF(IC))) WRITE OUTPUT TAPE 6, 601, IA, IB, IC, AREA 601 FORMAT (4H A= ,I5,5H B= ,I5,5H C= ,I5,8H AREA= ,F10.2, + 13H SQUARE UNITS) STOP END
A FORTRAN coding form, printed on paper and intended to be used by programmers to prepare programs for punching onto cards by keypunch operators. Now obsolete.
FORTRAN was provided for the
Starting in 1961, as a result of customer demands,
By 1965, FORTRAN IV was supposed to be compliant with the standard being developed by the American Standards Association X3.4.3 FORTRAN Working Group.
At about this time FORTRAN IV had started to become an important educational tool and implementations such as the University of Waterloo's WATFOR and WATFIV were created to simplify the complex compile and link processes of earlier compilers.
Perhaps the most significant development in the early history of
FORTRAN was the decision by the American Standards Association (now
American National Standards Institute
* Main program, SUBROUTINE, FUNCTION, and BLOCK DATA program units * INTEGER, REAL, DOUBLE PRECISION, COMPLEX, and LOGICAL data types * COMMON, DIMENSION, and EQUIVALENCE statements * DATA statement for specifying initial values * Intrinsic and EXTERNAL (e.g., library) functions * Assignment statement * GO TO, computed GO TO, assigned GO TO, and ASSIGN statements * Logical IF and arithmetic (three-way) IF statements * DO loop statement * READ, WRITE, BACKSPACE, REWIND, and ENDFILE statements for sequential I/O * FORMAT statement and assigned format * CALL, RETURN, PAUSE, and STOP statements * Hollerith constants in DATA and FORMAT statements, and as arguments to procedures * Identifiers of up to six characters in length * Comment lines * END line
FORTRAN-77 program with compiler output, written on a CDC 175 at
RWTH Aachen University , Germany, in 1987 4.3 BSD for the
Digital Equipment Corporation
After the release of the FORTRAN 66 standard, compiler vendors introduced several extensions to Standard Fortran, prompting ANSI committee X3J3 in 1969 to begin work on revising the 1966 standard, under sponsorship of CBEMA , the Computer Business Equipment Manufacturers Association (formerly BEMA). Final drafts of this revised standard circulated in 1977, leading to formal approval of the new FORTRAN standard in April 1978. The new standard, called FORTRAN 77 and officially denoted X3.9-1978, added a number of significant features to address many of the shortcomings of FORTRAN 66:
* Block IF and END IF statements, with optional ELSE and ELSE IF
clauses, to provide improved language support for structured
* DO loop extensions, including parameter expressions, negative
increments, and zero trip counts
* OPEN, CLOSE, and INQUIRE statements for improved I/O capability
* Direct-access file I/O
* IMPLICIT statement, to override implicit conventions that
undeclared variables are INTEGER if their name begins with I, J, K, L,
M, or N (and REAL otherwise)
* CHARACTER data type, replacing Hollerith strings with vastly
expanded facilities for character input and output and processing of
* PARAMETER statement for specifying constants
* SAVE statement for persistent local variables
* Generic names for intrinsic functions (e.g. SQRT also accepts
arguments of other types, such as COMPLEX or REAL*16 ).
* A set of intrinsics (LGE, LGT, LLE, LLT) for lexical comparison of
strings, based upon the
In this revision of the standard, a number of features were removed or altered in a manner that might invalidate formerly standard-conforming programs. (Removal was the only allowable alternative to X3J3 at that time, since the concept of "deprecation " was not yet available for ANSI standards.) While most of the 24 items in the conflict list (see Appendix A2 of X3.9-1978) addressed loopholes or pathological cases permitted by the prior standard but rarely used, a small number of specific capabilities were deliberately removed, such as:
* Hollerith constants and Hollerith data, such as GREET = 12HHELLO THERE! * Reading into an H edit (Hollerith field) descriptor in a FORMAT specification
* Overindexing of array bounds by subscripts
DIMENSION A(10,5) Y= A(11,1) * Transfer of control out of and back into the range of a DO loop (also known as "Extended Range")
Variants: Minnesota FORTRAN
Control Data Corporation
TRANSITION TO ANSI STANDARD FORTRAN
The development of a revised standard to succeed FORTRAN 77 would be repeatedly delayed as the standardization process struggled to keep up with rapid changes in computing and programming practice. In the meantime, as the "Standard FORTRAN" for nearly fifteen years, FORTRAN 77 would become the historically most important dialect.
An important practical extension to FORTRAN 77 was the release of
MIL-STD-1753 in 1978. This specification, developed by the U.S.
Department of Defense , standardized a number of features implemented
by most FORTRAN 77 compilers but not included in the ANSI FORTRAN 77
standard. These features would eventually be incorporated into the
* DO WHILE and END DO statements * INCLUDE statement * IMPLICIT NONE variant of the IMPLICIT statement * Bit manipulation intrinsic functions, based on similar functions included in Industrial Real-Time Fortran (ANSI/ISA S61.1 (1976))
The much delayed successor to FORTRAN 77, informally known as Fortran
90 (and prior to that,
* Free-form source input , also with lowercase
* Ability to operate on arrays (or array sections) as a whole, thus greatly simplifying math and engineering computations.
* whole, partial and masked array assignment statements and array expressions, such as X(1:N)=R(1:N)*COS(A(1:N)) * WHERE statement for selective array assignment * array-valued constants and expressions, * user-defined array-valued functions and array constructors.
* RECURSIVE procedures
* Modules , to group related procedures and data together, and make
them available to other program units, including the capability to
limit the accessibility to only specific parts of the module.
* A vastly improved argument-passing mechanism, allowing interfaces
to be checked at compile time
* User-written interfaces for generic procedures
* Derived (structured) data types
* New data type declaration syntax, to specify the data type and
other attributes of variables
Dynamic memory allocation
Obsolescence And Deletions
Unlike the prior revision,
A small set of features were identified as "obsolescent" and expected to be removed in a future standard.
OBSOLESCENT FEATURE EXAMPLE STATUS/FATE IN FORTRAN 95
IF (X) 10, 20, 30
Non-integer DO parameters or control variables
DO 9 X= 1.7, 1.6, -0.1 Deleted
Shared DO-loop termination or termination with a statement other than END DO or CONTINUE
DO 9 J= 1, 10 DO 9 K= 1, 10 9 L= J + K
Branching to END IF
from outside a block
66 GO TO 77 ; . . . IF (E) THEN ; . . . 77 END IF Deleted
CALL SUBR( X, Y *100, *200 )
PAUSE 600 Deleted
ASSIGN statement and assigned GO TO statement
100 . . . ASSIGN 100 TO H . . . GO TO H . . . Deleted
Assigned FORMAT specifiers
ASSIGN 606 TO F ... WRITE ( 6, F )... Deleted
H edit descriptors
606 FORMAT ( 9H1GOODBYE. ) Deleted
Computed GO TO statement
GO TO (10, 20, 30, 40), index (obsolete)
FOIL( X, Y )= X**2 + 2*X*Y + Y**2 (obsolete)
DATA statements among executable statements
X= 27.3 DATA A, B, C / 5.0, 12.0, 13.0 / . . . (obsolete)
CHARACTER* form of CHARACTER declaration
CHARACTER*8 STRING ! Use CHARACTER(8) (obsolete)
Assumed character length functions
CHARACTER*(*) STRING (obsolete)
Fixed form source code Column 1 contains C or * or ! for comments. Column 6 for continuation. (obsolete)
"Hello World" Example
program helloworld print *, "Hello world!" end program helloworld
Main article: Fortran 95 language features
* FORALL and nested WHERE constructs to aid vectorization * User-defined PURE and ELEMENTAL procedures * Default initialization of derived type components, including pointer initialization * Expanded the ability to use initialization expressions for data objects * Initialization of pointers to NULL() * Clearly defined that ALLOCATABLE arrays are automatically deallocated when they go out of scope.
A number of intrinsic functions were extended (for example a dim argument was added to the maxloc intrinsic).
* DO statements using REAL and DOUBLE PRECISION index variables * Branching to an END IF statement from outside its block * PAUSE statement * ASSIGN and assigned GO TO statement, and assigned format specifiers * H edit descriptor.
An important supplement to
Another important supplement to
Conditional Compilation And Varying Length Strings
In addition to the mandatory "Base language" (defined in ISO/IEC
1539-1 : 1997), the
* Varying length character strings (ISO/IEC 1539-2 : 2000) * Conditional compilation (ISO/IEC 1539-3 : 1998)
which, together, compose the multi-part International Standard (ISO/IEC 1539).
According to the standards developers, "the optional parts describe
self-contained features which have been requested by a substantial
body of users and/or implementors, but which are not deemed to be of
sufficient generality for them to be required in all
From that article, the major enhancements for this revision include:
* Derived type enhancements: parameterized derived types, improved
control of accessibility, improved structure constructors, and
Object-oriented programming support: type extension and
inheritance , polymorphism , dynamic type allocation, and type-bound
procedures, providing complete support for abstract data types
* Data manipulation enhancements: allocatable components
(incorporating TR 15581), deferred type parameters, VOLATILE attribute
, explicit type specification in array constructors and allocate
statements, pointer enhancements, extended initialization expressions,
and enhanced intrinsic procedures
* Input/output enhancements: asynchronous transfer, stream access,
user specified transfer operations for derived types, user specified
control of rounding during format conversions, named constants for
preconnected units, the FLUSH statement, regularization of keywords,
and access to error messages
* Procedure pointers
* Support for
An important supplement to
The most recent standard, ISO/IEC 1539-1:2010, informally known as
* Submodules – additional structuring facilities for modules; supersedes ISO/IEC TR 19767:2005 * Coarray Fortran – a parallel execution model * The DO CONCURRENT construct – for loop iterations with no interdependencies * The CONTIGUOUS attribute – to specify storage layout restrictions * The BLOCK construct – can contain declarations of objects with construct scope * Recursive allocatable components – as an alternative to recursive pointers in derived types
The Final Draft international Standard (FDIS) is available as document N1830.
An important supplement to
The next revision of the language (
FORTRAN AND SUPERCOMPUTERS
Although a 1968 journal article by the authors of
On the other hand, more modern code generally uses large program
libraries such as
Trilinos for linear algebra capabilities,
METIS for graph partitioning, deal.II or FEniCS for mesh and finite
element support, and other generic libraries. Since the late 1990s,
almost all of the most widely used support libraries have been written
in C and, more often,
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Portability was a problem in the early days because there was no agreed standard – not even IBM's reference manual – and computer companies vied to differentiate their offerings from others by providing incompatible features. Standards have improved portability. The 1966 standard provided a reference syntax and semantics, but vendors continued to provide incompatible extensions. Although careful programmers were coming to realize that use of incompatible extensions caused expensive portability problems, and were therefore using programs such as The PFORT Verifier, it was not until after the 1977 standard, when the National Bureau of Standards (now NIST ) published FIPS PUB 69, that processors purchased by the U.S. Government were required to diagnose extensions of the standard. Rather than offer two processors, essentially every compiler eventually had at least an option to diagnose extensions.
Incompatible extensions were not the only portability problem. For
numerical calculations, it is important to take account of the
characteristics of the arithmetic. This was addressed by Fox et al. in
the context of the 1966 standard by the PORT library. The ideas
therein became widely used, and were eventually incorporated into the
1990 standard by way of intrinsic inquiry functions. The widespread
(now almost universal) adoption of the
Access to the computing environment (e.g., the program's command line, environment variables, textual explanation of error conditions) remained a problem until it was addressed by the 2003 standard.
Large collections of library software that could be described as being loosely related to engineering and scientific calculations, such as graphics libraries, have been written in C, and therefore access to them presented a portability problem. This has been addressed by incorporation of C interoperability into the 2003 standard.
It is now possible (and relatively easy) to write an entirely portable program in Fortran, even without recourse to a preprocessor.
Univac also offered a compiler for the 1100 series known as Fortran
V. A spinoff of Univac
FORTRAN 6 or Visual
Vendors of high-performance scientific computers (e.g., Burroughs ,
Control Data Corporation
Object-Oriented Fortran was an object-oriented extension of Fortran, in which data items can be grouped into objects, which can be instantiated and executed in parallel. It was available for Sun, Iris, iPSC , and nCUBE, but is no longer supported.
Such machine-specific extensions have either disappeared over time or have had elements incorporated into the main standards. The major remaining extension is OpenMP , which is a cross-platform extension for shared memory programming. One new extension, Coarray Fortran , is intended to support parallel programming.
FOR TRANSIT For The
FOR TRANSIT was the name of a reduced version of the
IBM 704 FORTRAN
language, which was implemented for the
The FORTRAN system was designed for a more complex machine than the 650, and consequently some of the 32 statements found in the FORTRAN Programmer's Reference Manual are not acceptable to the FOR TRANSIT system. In addition, certain restrictions to the FORTRAN language have been added. However, none of these restrictions make a source program written for FOR TRANSIT incompatible with the FORTRAN system for the 704.
The permissible statements were:
* Arithmetic assignment statements, e.g., a = b * GO to n * GO TO (n1, n2, ..., nm), i * IF (a) n1, n2, n3 * PAUSE * STOP * DO n i = m1, m2 * CONTINUE * END * READ n, list * PUNCH n, list * DIMENSION V, V, V, ... * EQUIVALENCE (a,b,c), (d,c), ...
Up to ten subroutines could be used in one program.
FOR TRANSIT statements were limited to columns 7 through 56, only.
Punched cards were used for input and output on the
Two versions existed for the 650s with a 2000 word memory drum: FOR
TRANSIT I (S) and FOR TRANSIT II, the latter for machines equipped
with indexing registers and automatic floating point decimal
(bi-quinary ) arithmetic. Appendix A of the manual included wiring
diagrams for the
Prior to FORTRAN 77, a number of preprocessors were commonly used to
provide a friendlier language, with the advantage that the
preprocessed code could be compiled on any machine with a standard
FORTRAN compiler. These preprocessors would typically support
structured programming , variable names longer than six characters,
additional data types, conditional compilation , and even macro
capabilities. Popular preprocessors included FLECS , iftran , MORTRAN
, SFtran , S-
One of the earliest versions of FORTRAN, introduced in the 60's, was popularly used in colleges and universities. Developed, supported, and distributed by the University of Waterloo , WATFOR was based largely on FORTRAN IV. A WATFOR student could submit their batch FORTRAN job and, if there were no syntax errors, the program would move straight to execution. This simplification allowed students to concentrate on their program's syntax and semantics, or execution logic flow, rather than dealing with submission Job Control Language (JCL), the compile/link-edit/execution successive process(es), or other complexities of the mainframe/minicomputer environment. A down side to this simplified environment was that WATFOR was not a good choice for programmers needing the expanded abilities of their host processor(s), e.g., WATFOR typically had very limited access to I/O devices. WATFOR was succeeded by WATFIV and its later versions.
program; s=0 i=1,n; s=s+1; stop i; s='s' Stop
LRLTRAN was developed at the Lawrence Radiation Laboratory to provide support for vector arithmetic and dynamic storage, among other extensions to support systems programming. The distribution included the LTSS operating system .
The Fortran-95 Standard includes an optional Part 3 which defines an optional conditional compilation capability. This capability is often referred to as "CoCo".
The F programming language was designed to be a clean subset of
For more details on this topic, see Wikibooks:Fortran/Fortran examples.
The following program illustrates dynamic memory allocation and
array-based operations, two features introduced with
program average ! Read in some numbers and take the average ! As written, if there are no data points, an average of zero is returned ! While this may not be desired behavior, it keeps this example simple implicit none real, dimension(:), allocatable :: points integer :: number_of_points real :: average_points=0., positive_average=0., negative_average=0. write (*,*) "Input number of points to average:" read (*,*) number_of_points allocate (points(number_of_points)) write (*,*) "Enter the points to average:" read (*,*) points ! Take the average by summing points and dividing by number_of_points if (number_of_points > 0) average_points = sum(points) / number_of_points ! Now form average over positive and negative points only if (count(points > 0.) > 0) then positive_average = sum(points, points > 0.) / count(points > 0.) end if if (count(points 0) then negative_average = sum(points, points
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