Fortran Explained

Fortran
Paradigm:multi-paradigm

procedural, imperative, structured, object-oriented

Year:1957
Designer:John Backus
Developer:John Backus & IBM
Latest Release Version:Fortran 2003
Latest Release Date:2003
Typing:strong, static
Implementations:Absoft, GFortran, G95, Intel, Lahey/Fujitsu, Open Watcom, Pathscale, PGI, Silverfrost, Sun, XL Fortran, Visual Fortran, others
Influenced:ALGOL 58, BASIC, PL/I, C

Fortran (previously FORTRAN[1]) is a general-purpose,[2] procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. Originally developed by IBM in the 1950s for scientific and engineering applications, Fortran came to dominate this area of programming early on and has been in continual use for over half a century in computationally intensive areas such as numerical weather prediction, finite element analysis, computational fluid dynamics (CFD), computational physics, and computational chemistry. It is one of the most popular languages in the area of High-performance computing and programs to benchmark and rank the world's fastest supercomputers are written in Fortran[4] .

Fortran (a blend word derived from The IBM Mathematical Formula Translating System) encompasses a lineage of versions, each of which evolved to add extensions to the language while usually retaining compatibility with previous versions. Successive versions have added support for processing of character-based data (FORTRAN 77), array programming, module-based programming and object-based programming (Fortran 90 / 95), and object-oriented and generic programming (Fortran 2003).

History

In late 1953, John W. Backus submitted a proposal to his superiors at IBM to develop a more efficient alternative to assembly language for programming their IBM 704 mainframe computer. Backus' historic FORTRAN team consisted of programmers Richard Goldberg, Sheldon F. Best, Harlan Herrick, Peter Sheridan, Roy Nutt, Robert Nelson, Irving Ziller, Lois Haibt and David Sayre.[5]

A draft specification for The IBM Mathematical Formula Translating System was completed by mid-1954. The first manual for FORTRAN appeared in October 1956, with the first FORTRAN compiler delivered in April 1957. This was an optimizing compiler, because customers were reluctant to use a high-level programming language unless its compiler could generate code whose performance was comparable to that of hand-coded assembly language.

While the community was skeptical that this new method could possibly out-perform hand-coding, it reduced the amount of programming statements necessary to operate a machine by a factor of 20, and quickly gained acceptance. Said creator John Backus during a 1979 interview with Think, the IBM employee magazine, "Much of my work has come from being lazy. I didn't like writing programs, and so, when I was working on the IBM 701 (an early computer), writing programs for computing missile trajectories, I started work on a programming system to make it easier to write programs."[6]

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 IBM 709, 650, 1620, and 7090 computers. Significantly, the increasing popularity of FORTRAN spurred competing computer manufacturers to provide FORTRAN compilers for their machines, so that by 1963 over 40 FORTRAN compilers existed. For these reasons, FORTRAN is considered to be the first widely used programming language supported across a variety of computer architectures.

The development of FORTRAN paralleled the early evolution of compiler technology; indeed many advances in the theory and design of compilers were specifically motivated by the need to generate efficient code for FORTRAN programs.

FORTRAN

The initial release of FORTRAN for the IBM 704 contained 32 statements, including:

FORTRAN II

IBM's FORTRAN II appeared in 1958. The main enhancement was to support procedural programming by allowing user-written subroutines and functions. Six new statements were introduced:

Over the next few years, FORTRAN II would also add support for the DOUBLE PRECISION and COMPLEX data types.

Simple Fortran II program

This program, for Heron's formula, has one data card input, with simple zero-data edit check. If one of the input values is zero or negative, then the program will end with an error code of "STOP 1" in the job control card listing following the execution of the program. Normal output will be one line printed with A, B, C, and AREA on the "report" page following the compilation with no specific units are stated; and with a normal "STOP" in the job card listing.

C AREA OF A TRIANGLE WITH A STANDARD SQUARE ROOT FUNCTION 
C INPUT - CARD 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
C FURTHERMORE, THE SUM OF TWO SIDES OF A TRIANGLE
C IS 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 = SQRT(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

FORTRAN III

IBM also developed a FORTRAN III in 1958 that allowed for inline assembler code among other features; however, this version was never released as a product. Like the 704 FORTRAN and FORTRAN II, FORTRAN III included machine-dependent features that made code written in it unportable from machine to machine. Early versions of FORTRAN provided by other vendors suffered from the same disadvantage.

FORTRAN IV

Starting in 1961, as a result of customer demands, IBM began development of a FORTRAN IV that removed the machine-dependent features of FORTRAN II (such as READ INPUT TAPE), while adding new features such as a LOGICAL data type, logical Boolean expressions and the logical IF statement as an alternative to the arithmetic IF statement. FORTRAN IV was eventually released in 1962, first for the IBM 7030 ("Stretch") computer, followed by versions for the IBM 7090 and IBM 7094.

By 1965, Fortran IV was supposed to be the "standard" and in compliance with American Standards Association X3.4.3 FORTRAN Working Group.[9]

FORTRAN 66

Perhaps the most significant development in the early history of FORTRAN was the decision by the American Standards Association (now ANSI) to form a committee to develop an "American Standard Fortran." The resulting two standards, approved in March 1966, defined two languages, FORTRAN (based on FORTRAN IV, which had served as a de facto standard), and Basic FORTRAN (based on FORTRAN II, but stripped of its machine-dependent features). The FORTRAN defined by the first standard became known as FORTRAN 66 (although many continued to refer to it as FORTRAN IV, the language upon which the standard was largely based). FORTRAN 66 effectively became the first "industry-standard" version of FORTRAN. FORTRAN 66 included:

FORTRAN 77

After the release of the FORTRAN 66 standard, compiler vendors introduced a number of extensions to "Standard Fortran", prompting ANSI in 1969 to begin work on revising the 1966 standard. Final drafts of this revised standard circulated in 1977, leading to formal approval of the new FORTRAN standard in April 1978. The new standard, known as FORTRAN 77, added a number of significant features to address many of the shortcomings of FORTRAN 66:

(ASCII functions were demanded by the U. S. Department of Defense, in their conditional approval vote.)

In this revision of the standard, a number of features were removed or altered in a manner that might invalidate previously 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 previous standard but rarely used, a small number of specific capabilities were deliberately removed, such as:

GREET = 12HHELLO THERE!

DIMENSION A(10,5)

Y= A(11,1)

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 Fortran 90 standard.

The IEEE 1003.9 POSIX Standard, released in 1991, provided a simple means for Fortran-77 programmers to issue POSIX system calls. Over 100 calls were defined in the document — allowing access to POSIX-compatible process control, signal handling, file system control, device control, procedure pointing, and stream I/O in a portable manner.

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.

Control Data Corporation computers had another version of FORTRAN 77, called Minnesota FORTRAN, with variations in output constructs, special uses of COMMONs and DATA statements, optimizations code levels for compiling, and detailed error listings, extensive warning messages, and debugs.[10]

Fortran 90

The much delayed successor to FORTRAN 77, informally known as Fortran 90, was finally released as an ISO standard in 1991 and an ANSI Standard in 1992. This major revision added many new features to reflect the significant changes in programming practice that had evolved since the 1978 standard:

Obsolescence & deletions

Unlike the previous revision, Fortran 90 did not delete any features.(Appendix B.1 says, "The list of deleted features in this standard is empty.")Any standard-conforming FORTRAN 77 program is also standard-conforming under Fortran 90, and either standard should be usable to define its behavior.

A small set of features were identified as "obsolescent"and expected to be removed in a future standard.

Obsolescent featureExampleStatus / 95
Arithmetic IF-statement     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
Alternate return    CALL SUBR(X, Y *100, *200)
PAUSE statement    PAUSE 600 Deleted
ASSIGN statement
  and assigned GO TO statement
100  . . .     ASSIGN 100 TO H
    . . .
    GO TO H . . .
Deleted
Assigned FORMAT specifiers    ASSIGN F TO 606Deleted
H edit descriptors606 FORMAT (9H1GOODBYE.) Deleted
Computed GO TO statement    GO TO (10, 20, 30, 40), index(Obso.)
Statement functions    FOIL(X, Y)= X**2 + 2*X*Y + Y**2(Obso.)
DATA statements
  among executable statements
    X= 27.3
    DATA A, B, C / 5.0, 12.0. 13.0 /    . . .
(Obso.)
CHARACTER* form of CHARACTER declaration    CHARACTER*8 STRING  !Use CHARACTER(8) (Obso.)
Assumed character length functions
Fixed form source code
  • Column 1 contains * or!or C for comments.
    C       Column 6 for continuation.

Fortran 95

Fortran 95 was a minor revision, mostly to resolve some outstanding issues from the Fortran 90 standard. Nevertheless, Fortran 95 also added a number of extensions, notably from the High Performance Fortran specification:

A number of intrinsic functions were extended (for example a dim argument was added to the maxloc intrinsic).

Several features noted in Fortran 90 to be deprecated were removed from Fortran 95:

An important supplement to Fortran 95 was the ISO technical report TR-15581: Enhanced Data Type Facilities, informally known as the Allocatable TR. This specification defined enhanced use of ALLOCATABLE arrays, prior to the availability of fully Fortran 2003-compliant Fortran compilers. Such uses include ALLOCATABLE arrays as derived type components, in procedure dummy argument lists, and as function return values. (ALLOCATABLE arrays are preferable to POINTER-based arrays because ALLOCATABLE arrays are guaranteed by Fortran 95 to be deallocated automatically when they go out of scope, eliminating the possibility of memory leakage. In addition, aliasing is not an issue for optimization of array references, allowing compilers to generate faster code than in the case of pointers.)

Another important supplement to Fortran 95 was the ISO technical report TR-15580: Floating-point exception handling, informally known as the IEEE TR. This specification defined support for IEEE floating-point arithmetic and floating point exception handling.

Conditional compilation and varying length strings

In addition to the mandatory "Base language"(defined in ISO/IEC 1539-1 : 1997),the Fortran 95 language also includes two optional modules:

which, together, comprise 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 standard-conforming Fortran compilers." Nevertheless, if a standard-conforming Fortran does provide such options, then they "must be provided in accordance with the description of those facilities in the appropriate Part of the Standard."

Fortran 2003

The most recent standard, Fortran 2003, is a major revision introducing many new features. A comprehensive summary of the new features of Fortran 2003 is available at the Fortran Working Group (WG5) official Web site.[11]

From that article, the major enhancements for this revision include:

An important supplement to Fortran 2003 was the ISO technical report TR-19767: Enhanced module facilities in Fortran. This report provided submodules, which make Fortran modules more similar to Modula-2 modules. They are similar to Ada private child subunits. This allows the specification and implementation of a module to be expressed in separate program units, which improves packaging of large libraries, allows preservation of trade secrets while publishing definitive interfaces, and prevents compilation cascades.

Fortran 2008

Efforts are underway to develop a revision to Fortran 2003, tentatively called Fortran 2008. As with Fortran 95, this is intended to be a minor upgrade, incorporating clarifications and corrections to Fortran 2003, as well as introducing a select few new capabilities. As of February 2007, the proposed new capabilities included[12]

In August 2007, the BIT data type was removed. In February 2008, Coarrays were scaled back: Parallel I/O and teams were removed.

The complete original work plan is available at http://j3-fortran.org/doc/year/07/07-010.html.

The legacy of FORTRAN

Since Fortran has been in use for more than fifty years, there is a vast body of Fortran in daily use throughout the scientific and engineering communities. It is the primary language for some of the most intensive supercomputing tasks, such as weather and climate modeling, computational fluid dynamics, computational chemistry, computational economics, and computational physics. Even today, half a century later, many of the floating-point benchmarks to gauge the performance of new computer processors are still written in Fortran (e.g., CFP2006, the floating-point component of the SPEC CPU2006 benchmarks).

Language features

The Fortran language features described are intended to be a fairly comprehensive overview of the Fortran language; full details may be found in any of several Fortran textbooks. Only those features widely used in new programs are described, as few of the historic features are used in modern programs. Still, most have been retained in the language to maintain backward compatibility.

Portability

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 IEEE 754 standard for binary floating-point arithmetic has essentially removed this problem.

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.

Variants of Fortran

Fortran 5

Fortran 5 was a programming language marketed by Data General Corp in the late 1970s and early 80s, for the Nova, Eclipse, and MV line of computers. It had an optimizing compiler that was quite good for minicomputers of its time. The language most closely resembles Fortran 66. The name is a pun on the earlier Fortran IV.

Specific variants

Vendors of high-performance scientific computers (e.g., Burroughs, CDC, Cray, Honeywell, IBM, Texas Instruments, and UNIVAC) added extensions to Fortran to take advantage of special hardware features such as instruction cache, CPU pipelines, and vector arrays. For example, one of IBM's FORTRAN compilers (H Extended IUP) had a level of optimization which reordered the machine language instructions to keep multiple internal arithmetic units busy simultaneously. Another example is CFD, a special variant of Fortran designed specifically for the ILLIAC IV supercomputer, running at NASA's Ames Research Center.IBM Research Labs also developed an extended FORTRAN-based language called "VECTRAN"for processing of vectors and matricies.

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 IBM 650

"FOR TRANSIT" was the name of a reduced version of the IBM 704 FORTRAN language, which was implemented for the IBM 650, using a translator program developed at Carnegie [13] in the late 1950s.The following comment appears in the IBM Reference Manual ("FOR TRANSIT Automatic Coding System" C28-4038, Copyright 1957, 1959 by IBM):

The FORTRAN system was designed for a more complexmachine than the 650, and consequently some of the 32 statements found in the FORTRAN Programmer's Reference Manual are notacceptable to the FOR TRANSIT system. In addition, certainrestrictions 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 thru 56, only.Punched cards were used for input and output on the IBM 650. Three passes were required to translate source code to the "IT" language, then to compile the IT statements into SOAP assembly language, and finally to produce the object program, which could then be loaded into the machine to run the program (using punched cards for data input, and outputting results onto punched cards.)

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 IBM 533 control panel.

Fortran-based languages

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. Popular preprocessors included FLECS, MORTRAN, Ratfor, and Ratfiv. (Ratfor and Ratfiv, for example, implemented a remarkably C-like language, outputting preprocessed code in standard FORTRAN 66.[14])

The Fortran-95 Standard includes an optional Part 3 which defines an optional conditional compilation capability. This capability is often referred to as "CoCo".

Many Fortran compilers have integrated subsets of the C preprocessor into their systems.

SIMSCRIPT is an application specific Fortran preprocessor for modeling and simulating large discrete systems.

F (programming language) was designed to be a clean subset of Fortran 95 that attempted to remove the redundant, unstructured, and deprecated features of Fortran, such as the EQUIVALENCE statement. F retains the array features added in Fortran 90, and removes control statements that were obsoleted by structured programming constructs added both Fortran 77 and Fortran 90. F is described by its creators as "a compiled, structured, array programming language especially well suited to education and scientific computing." Web site: F Programming Language Homepage).

Code examples

The sample programs can be compiled and run with any standard Fortran compiler (see the end of this article for lists of compilers). Most modern Fortran compilers expect a file with a .f or .for extension (for FORTRAN 66 or FORTRAN 77 fixed-form source, although the FORTRAN 66 dialect may have to be selected specifically with a command-line option) or .f90/.f95 extension (for Fortran 90/95 free-form source, respectively).

FORTRAN quotations

For a programming language with a half-century legacy, FORTRAN not surprisingly has accumulated its share of jokes and folklore.

Letter O considered harmful

During the same Fortran Standards Committee meeting at which the name "FORTRAN 77" was chosen, a technical proposal was somehow smuggled into the official distribution, bearing the title, "Letter O considered harmful".This deceptively simple proposal purported to address the confusion that sometimes arises between the letter "O" and the numeral zero, by eliminating the letter from allowable variable names.However, the method proposed was to eliminate the letter from the character set entirely (thereby retaining 48 as the number of lexical characters, which the colon had increased to 49).

Among the "PRO" arguments was the assertion that this would also promote structured programming, by making it impossible to use the notorious GO TO statement as before. (Troublesome FORMAT statements would be eliminated, as well.)

The sole "CON" argument conceded that "this might invalidate some existing programs" but noted that most of these "probably were non-conforming, anyway".[15] [16]

See also

References

Textbooks

"Core" language standards

Related standards

Further reading

External links

History

Standards

Tutorials

References

Code repositories

Open source compilers

Non-open source compilers

Integrated Development Environment

Graphical libraries/GUI

Testing Frameworks

Miscellaneous

Notes and References

  1. The names of earlier versions of the language through FORTRAN 77 were conventionally spelled in all-caps (FORTRAN 77 was the version in which the use of lowercase letters in keywords was strictly nonstandard). The capitalization has been dropped in referring to newer versions beginning with Fortran 90. The official language standards now refer to the language as "Fortran." Because the capitalisation (or lack thereof) of the word FORTRAN was never 100% consistent in actual usage, and because many hold impassioned beliefs on the issue, this article, rather than attempt to be normative, adopts the convention of using the all-caps FORTRAN in referring to versions of FORTRAN through FORTRAN 77 and the title-caps Fortran in referring to versions of Fortran from Fortran 90 onward. This convention is reflected in the capitalization of FORTRAN in the ANSI X3.9-1966 (FORTRAN 66) and ANSI X3.9-1978 (FORTRAN 77) standards and the title caps Fortran in the ANSI X3.198-1992 (Fortran 90) standard.
  2. Since FORTRAN 77, which introduced the CHARACTER data type.
  3. Since FORTRAN II (1958).
  4. http://en.wikipedia.org/wiki/LINPACK and http://www.top500.org/project/linpack
  5. http://www.softwarepreservation.org/projects/FORTRAN/index.html#By_FORTRAN_project_members
  6. http://www.msnbc.msn.com/id/17704662/ Fortran creator John Backus dies - Gadgets - MSNBC.com
  7. Note: It is commonly believed that this statement corresponded to a three-way branch instruction on the IBM 704. This is not true, the 704 branch instructions all contained only one destination address (e.g., TZE — Transfer AC Zero, TNZ — Transfer AC Not Zero, TPL — Transfer AC Plus, TMI — Transfer AC Minus). The machine (and its successors in the 700/7000 series) did have a three-way skip instruction (CAS — Compare AC with Storage), which was probably the origin of this belief, but using this instruction to implement the IF would consume 4 instruction words, require the constant Zero in a word of storage, and take 3 machine cycles to execute; using the Transfer instructions to implement the IF could be done in 1 to 3 instruction words, required no constants in storage, and take 1 to 3 machine cycles to execute. An optimizing compiler like FORTRAN would most likely select the more compact and usually faster Transfers instead of the Compare (use of Transfers also allowed the FREQUENCY statement to optimize IFs, which could not be done using the Compare). Also the Compare considered -0 and +0 to be different values while the Transfer Zero and Transfer Not Zero considered them to be the same.
  8. The FREQUENCY statement in FORTRAN was used originally and optionally to give branch probabilities for the three branch cases of the Arithmetic IF statement to bias the way code was generated and order of the basic blocks of code generated, in the global optimisation sense, were arranged in memory for optimality. The first FORTRAN compiler used this weighting to do a Monte Carlo simulation of the run-time generated code at compile time. It was very sophisticated for its time. This technique is documented in the original article in 1957 on the first FORTRAN compiler implementation by J. Backus, et al. 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.

    Below is a part of the 1957 paper, "The FORTRAN Automatic Coding System" by Backus, et al., with this snippet on the FREQUENCY statement and its use in a compile-time Monte Carlo simulation of the run-time to optimise the code generated. Quoting …

    The fundamental unit of program is the basic block; a basic block is a stretch of program which has a single entry point and a single 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 an actual "execution" of the program 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.

  9. Book: McCracken, Daniel D.. A Guide to FORTRAN IV Programming. John Wiley & Sons, Inc., New York. 1965(3rd printing 1968). LCCCN 65-26848. Preface p. v
  10. http://www.chilton-computing.org.uk/acd/literature/reports/p008.htm Chilton Computing with FORTRAN
  11. http://www.nag.co.uk/sc22wg5/ Fortran Working Group (WG5)
  12. A full list is in the report available at .
  13. "Internal Translator (IT) A Compiler for the IBM 650", by A. J. Perlis, J. W. Smith, and H. R. Van Zoeren, Computation Center,Carnegie Institute of Technology
  14. This is not altogether surprising, as Brian Kernighan, one of the co-creators of Ratfor, is also co-author of The C Programming Language.
  15. X3J3 post-meeting distribution for meeting held at Brookhaven National Laboratory in November 1976.
  16. "The obliteration of O", Computer Weekly, March 3, 1977