Fortran 2008 Overview

Table of Contents

• 1 Introduction
• 2 Overview of Fortran 2008
• 3 SPMD programming with coarrays [6.2]
  • 3.1 Overview
  • 3.2 Images
  • 3.3 Coarrays
  • 3.4 Declaring coarrays
  • 3.5 Accessing coarrays on other images
  • 3.6 Segments and synchronisation
  • 3.7 Allocating and deallocating coarrays
  • 3.8 Critical constructs
  • 3.9 Lock variables
  • 3.10 Atomic coarray accessing
  • 3.11 Normal termination of execution
  • 3.12 Error termination
  • 3.13 Fault tolerance
  • 3.14 Detailed syntax of coarray features
  • 3.15 Intrinsic procedures and coarrays
• 4 Data declaration [mostly 6.0]
• 5 Data usage and computation [mostly 5.3]
• 6 Execution control [mostly 6.0]
• 7 Intrinsic procedures and modules
  • 7.1 Additional mathematical intrinsic functions [mostly 5.3.1]
  • 7.2 Additional intrinsic functions for bit manipulation [mostly 5.3]
  • 7.3 Other new intrinsic procedures [mostly 5.3.1]
  • 7.4 Changes to existing intrinsic procedures [mostly 5.3.1]
  • 7.5 ISO_C_BINDING additions [6.2]
  • 7.6 ISO_FORTRAN_ENV additions
• 8 Input/output extensions [mostly 5.3]
• 9 Programs and procedures [mostly 5.3]
• 10 References

1 Introduction

This document describes those parts of the Fortran 2008 language which are not in Fortran 2003, and which are supported by the latest release of the NAG Fortran Compiler.

The compiler release in which a feature was made available is indicated by square brackets; for example, a feature marked as ‘[5.3]’ was first available in Release 5.3.

2 Overview of Fortran 2008

The new features of Fortran 2008 that are supported by the NAG Fortran Compiler can be grouped as follows:

• SPMD programming with coarrays;
• data declaration;
• data usage and computation;
• execution control;
• intrinsic procedures and modules;
• input/output extensions;
• programs and procedures.

3 SPMD programming with coarrays [6.2]

3.1 Overview

Release 6.2 of the NAG Fortran Compiler limits execution to a single image, i.e. there is no parallel execution. Coarray programs that require multiple images to operate correctly cannot be executed successfully in this release.

3.2 Images

3.3 Coarrays

A coarray has a “corank”, which is the number of “codimensions” it has. Each codimension has a lower “cobound” and an upper cobound, determining the “coshape”. The upper cobound of the last codimension is “*”; rather like an assumed-size array. The “cosubscripts” determine the image index of the reference, in the same way that the subscripts of an array determine the array element number. Again, like an assumed-size array, the image index must be less than or equal to the number of images.

A coarray can be a scalar or an array. It cannot have the POINTER attribute, but it can have pointer components.

As well as variables, coarray components are possible. In this case, the component must be an ALLOCATABLE coarray, and any variable with such a component must be a dummy argument or have the SAVE attribute.

3.4 Declaring coarrays

    REAL a[100,*]
    REAL,CODIMENSION[-10:10,-10:*] :: b
    CODIMENSION c[*]

An ALLOCATABLE coarray is declared with a deferred-coshape-spec, for example,

    REAL,ALLOCATABLE :: d[:,:,:,:]

3.5 Accessing coarrays on other images

    REAL,SAVE :: e[*]

    REAL,SAVE :: f[10,21:30,0:*]

When a coarray is an array, you cannot put the cosubscripts directly after the array name, but must use array section notation instead. For example, with

    REAL,SAVE :: g(10,10)[*]

Similarly, to access a single element of G, the cosubscripts follow the subscripts, e.g. g(i,j)[inum].

Finally, note that when a coarray is accessed, whether by its own image or remotely, the segment ordering rules (see next section) must be obeyed. This is to avoid nonsense answers from data races.

3.6 Segments and synchronisation

If a coarray is defined (assigned a value) in a segment on image I, another image J is only allowed to reference or define it in a segment that follows the segment on I.

The image control statements, and their synchronisation effects, are as follows.

SYNC ALL

synchronises with corresponding SYNC ALL statement executions on other images; the segment following the n^th execution of a SYNC ALL statement on one image follows all the segments that preceded the n^th execution of a SYNC ALL statement on every other image.

SYNC IMAGES (list)

synchronises with corresponding SYNC IMAGES statement executions on the images in list, which is an integer expression that may be scalar or a vector. Including the invoking image number in list has no effect. The segment following the n^th execution of a SYNC IMAGES statement on image I with the image number J in its list follows the segments on image J before its n^th execution of SYNC IMAGES with I in its list.

SYNC IMAGES (*)

is equivalent to SYNC IMAGES with every image no. in its list, e.g. SYNC IMAGES ([(i,i=1,NUM_IMAGES())]).

SYNC MEMORY

This only acts as a segment divider, without synchronising with any other image. It may be useful for user-defined orderings when some other mechanism has been used to synchronise.

ALLOCATE or DEALLOCATE

with a coarray object being allocated or deallocated. This synchronises all images, which must execute the same ALLOCATE or DEALLOCATE statement.

CRITICAL and END CRITICAL

Only one image can execute a CRITICAL construct at a time. The code inside a CRITICAL construct forms a segment, which follows the previous execution (on whatever image) of the CRITICAL construct.

LOCK and UNLOCK

The segment following a LOCK statements that locks a particular lock variable follows the UNLOCK statement that previously unlocked the variable.

END statement

An END BLOCK, END FUNCTION, or END SUBROUTINE statement that causes automatic deallocation of a local ALLOCATABLE coarray, synchronises with all images (which must execute the same END statement).

MOVE_ALLOC intrinsic

Execution of the intrinsic subroutine MOVE_ALLOC with coarray arguments synchronises all images, which must execute the same CALL statement.

Note that image control statements have side-effects, and therefore are not permitted in pure procedures or within DO CONCURRENT constructs.

3.7 Allocating and deallocating coarrays

    REAL,ALLOCATABLE :: x(:,:,:)[:,:]
    ...
    ALLOCATE(x(100,100,3)[1:10,*])

When allocating a coarray there is a synchronisation: all images must execute the same ALLOCATE statement, and all the bounds, type parameters, and cobounds of the coarray must be the same on all images.

Similarly, there is a synchronisation when a coarray is deallocated, whether by a DEALLOCATE statement or automatic deallocation by an END statement; every image must execute the same statement.

Note that the usual automatic reallocation of allocatable variables in an intrinsic assignment statement, e.g. when the expression is an array of a different shape, is not available for coarrays. An allocatable coarray variable being assigned to must already be allocated and be conformable with the expression; furthermore, if it has deferred type parameters they must have the same values, and if it is polymorphic it must have the same dynamic type.

3.8 Critical constructs

    CRITICAL
      ...do something
    END CRITICAL

As a construct, this may have a name, e.g.

    critsec: CRITICAL
      ...
    END CRITICAL critsec

3.9 Lock variables

Execution of the segment after a LOCK statement successfully locks the variable follows execution of the segment before the UNLOCK statement on the image that unlocked it. For example,

    INTEGER FUNCTION get_sequence_number()
      USE iso_fortran_env
      INTEGER :: number = 0
      TYPE(lock_type) lock[*]
      LOCK(lock[1])
      number = number + 1
      get_sequence_number = number
      UNLOCK(lock[1])
    END FUNCTION

Conditional locking is provided with the ACQUIRED_LOCK= specifier; if this specifier is present, the executing image only acquires the lock if it was previously unlocked. For example,

    LOGICAL gotit
    LOCK(lock[1],ACQUIRED_LOCK=gotit)
    IF (gotit) THEN
      ! We have the lock.
    ELSE
      ! We do not have the lock - some other image does.
    END IF

It is an error for an image to try to LOCK a variable that is already locked to that image, or to UNLOCK a variable that is already unlocked, or that is locked to another image. If the STAT= specifier is used, these errors will return the values STAT_LOCKED, STAT_UNLOCKED, or STAT_LOCKED_OTHER_IMAGE respectively (these named constants are provided by the intrinsic module ISO_FORTRAN_ENV).

3.10 Atomic coarray accessing

    MODULE stopping
      USE iso_fortran_env
      LOGICAL(atomic_logical_kind),PRIVATE :: stop_flag[*] = .FALSE.
    CONTAINS
      SUBROUTINE make_it_stop
        CALL atomic_define(stop_flag[1],.TRUE._atomic_logical_kind)
      END SUBROUTINE
      LOGICAL FUNCTION please_stop()
        CALL atomic_ref(please_stop,stop_flag[1])
      END FUNCTION
    END MODULE

Note that ordinary assignment and referencing should not be mixed with calls to the atomic subroutines, as ordinary assignment and referencing are always subject to the segment ordering rules.

3.11 Normal termination of execution

When normal termination has been initiated on all images, the program terminates.

3.12 Error termination

The ERROR STOP statement initiates error termination.

3.13 Fault tolerance

The FAIL IMAGE statement itself is not very useful when the number of images is equal to one, as it inevitably causes complete program failure.

3.14 Detailed syntax of coarray features

In a data object designator, a part (component or base object) that is a coarray can include an image selector: part-name [ ( section-subscript-list ) ] [ image-selector ]

left-bracket cosubscript-list [ , image-selector-spec ] right-bracket

STAT = scalar-int-variable
TEAM = team-value
TEAM_NUMBER = scalar-int-expression

CRITICAL construct:

[ construct-name : ] CRITICAL [ ( [ sync-stat-list ] ) ]
block
END CRITICAL [ construct-name ]

The block is not permitted to contain:

• a RETURN or STOP statement;
• an image control statement;
• a branch whose target is outside the construct.

FAIL IMAGE statement:

FAIL IMAGE

LOCK statement:

LOCK ( lock-variable [ , lock-stat-list ] )

ACQUIRED_LOCK = scalar-logical-variable
ERRMSG = scalar-default-character-variable
STAT = scalar-int-variable

SYNC ALL statement:

SYNC ALL [ ( [ sync-stat-list ] ) ]

SYNC IMAGES statement:

SYNC IMAGES ( image-set [ , sync-stat-list ] )

SYNC MEMORY statement:

SYNC MEMORY [ ( [ sync-stat-list ] ) ]

UNLOCK statement:

UNLOCK ( lock-variable [ , sync-stat-list ] )

Note:

• The variables in sync-stat-list or lock-stat-list are not permitted to be coindexed objects, nor may they depend on anything else in the statement.

3.15 Intrinsic procedures and coarrays

    SUBROUTINE ATOMIC_DEFINE(ATOM, VALUE, STAT)

ATOM

is INTENT(OUT) scalar INTEGER(ATOMIC_INT_KIND) or LOGICAL(ATOMIC_LOGICAL_KIND), and must be a coarray or a coindexed object.

VALUE

is scalar with the same type as ATOM.

STAT

(Optional) is scalar Integer and must have a decimal exponent range of at least four. It must not be coindexed.

    SUBROUTINE ATOMIC_REF(VALUE, ATOM, STAT)

VALUE

is INTENT(OUT) scalar with the same type as ATOM.

ATOM

is scalar INTEGER(ATOMIC_INT_KIND) or LOGICAL(ATOMIC_LOGICAL_KIND), and must be a coarray or a coindexed object.

STAT

(Optional) is scalar Integer and must have a decimal exponent range of at least four. It must not be coindexed.

    INTEGER FUNCTION IMAGE_INDEX(COARRAY, SUB)

COARRAY

a coarray of any type.

SUB

an integer vector whose size is equal to the corank of COARRAY.

    FUNCTION LCOBOUND(COARRAY, DIM , KIND)

COARRAY

coarray of any type and corank N;

DIM

(Optional) scalar Integer in the range 1 to N;

KIND

(Optional) scalar Integer constant expression;

Result

Integer or Integer(Kind=KIND).

    SUBROUTINE MOVE_ALLOC(FROM, TO, STAT, ERRMSG)  ! Revised

FROM

an allocatable variable of any type.

TO

an allocatable with the same declared type, type parameters, rank and corank, as FROM.

STAT

INTENT(OUT) scalar Integer with a decimal exponent range of at least four.

ERRMSG

INTENT(INOUT) scalar default character variable.

    INTEGER FUNCTION NUM_IMAGES()

    INTEGER FUNCTION THIS_IMAGE()

    FUNCTION THIS_IMAGE(COARRAY)

    INTEGER FUNCTION THIS_IMAGE(COARRAY, DIM)

COARRAY

is a coarray of any type.

DIM

is scalar Integer.

    FUNCTION UCOBOUND(COARRAY, DIM, KIND)

COARRAY

coarray of any type and corank N;

DIM

(Optional) scalar Integer in the range 1 to N;

KIND

(Optional) scalar Integer constant expression;

Result

Integer or Integer(Kind=KIND).

If DIM appears, the result is scalar, being the value of the upper cobound of that codimension of COARRAY. If DIM does not appear, the result is a vector of length N containing all the upper cobounds of COARRAY. The actual argument for DIM must not itself be an optional dummy argument.

Note that if COARRAY has corank N>1, and the number of images in the current execution is not an integer multiple of the coextents up to codimension N−1, the images do not make a full rectangular pattern. In this case, the value of the last upper cobound is the maximum value that a cosubscript can take for that codimension; e.g. with a coarray-spec of [1:3,1:*] and four images in the execution, the last upper cobound will be equal to 2 because the cosubscripts [1,2] are valid even though [2,2] and [2,3] are not.

4 Data declaration [mostly 6.0]

• The maximum rank of an array has been increased from 7 to 15. For example,

     REAL array(2,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
  

  declares a 15-dimensional array.
• [3.0] 64-bit integer support is required, that is, the result of SELECTED_INT_KIND(18) is a valid integer kind number.
• A named constant (PARAMETER) that is an array can assume its shape from its defining expression; this is called an implied-shape array. The syntax is that the upper bound of every dimension must be an asterisk, for example

     REAL,PARAMETER :: idmat3(*,*) = Reshape( [ 1,0,0,0,1,0,0,0,1 ], [ 3,3 ] )
     REAL,PARAMETER :: yeardata(2000:*) = [ 1,2,3,4,5,6,7,8,9 ]
  

  declares idmat3 to have the bounds (1:3,1:3), and yeardata to have the bounds (2000:2008).
• The TYPE keyword can be used to declare entities of intrinsic type, simply by putting the intrinsic type-spec within the parentheses. For example,

     TYPE(REAL) x
     TYPE(COMPLEX(KIND(0d0))) y
     TYPE(CHARACTER(LEN=80)) z
  

  is completely equivalent, apart from being more confusing, to

     REAL x
     COMPLEX(KIND(0d0)) y
     CHARACTER(LEN=80) z
  

• As a consequence of the preceding extension, it is no longer permitted to define a derived type that has the name DOUBLEPRECISION.
• [5.3] A type-bound procedure declaration statement may now declare multiple type-bound procedures. For example, instead of

        PROCEDURE,NOPASS :: a
        PROCEDURE,NOPASS :: b=>x
        PROCEDURE,NOPASS :: c
  

  the single statement

        PROCEDURE,NOPASS :: a, b=>x, c
  

  will suffice.

5 Data usage and computation [mostly 5.3]

• In a structure constructor, the value for an allocatable component may be omitted: this has the same effect as specifying NULL().
• [6.0] When allocating an array with the ALLOCATE statement, if SOURCE= or MOLD= is present and its expression is an array, the array can take its shape directly from the expression. This is a lot more concise than using SIZE or UBOUND, especially for a multi-dimensional array.

  For example,

     SUBROUTINE s(x,mask)
        REAL x(:,:,:)
        LOGICAL mask(:,:,:)
        REAL,ALLOCATABLE :: y(:,:,:)
        ALLOCATE(y,MOLD=x)
        WHERE (mask)
          y = 1/x
        ELSEWHERE
          y = HUGE(x)
        END WHERE
        ! ...
     END SUBROUTINE
  

• [6.2] An ALLOCATE statement with the SOURCE= clause is permitted to have more than one allocation. The source-expr is assigned to every variable allocated in the statement. For example,

     PROGRAM multi_alloc
        INTEGER,ALLOCATABLE :: x(:),y(:,:)
        ALLOCATE(x(3),y(2,4),SOURCE=42)
        PRINT *,x,y
     END PROGRAM
  

  will print the value “42” eleven times (the three elements of x and the eight elements of y). If the source-expr is an array, every allocation needs to have the same shape.
• [6.1] The real and imaginary parts of a COMPLEX object can be accessed using the complex part designators ‘%RE’ and ‘%IM’. For example, given

     COMPLEX,PARAMETER :: c = (1,2), ca(2) = [ (3,4),(5,6) ]
  

  the designators c%re and c%im have the values 1 and 2 respectively, and ca%re and ca%im are arrays with the values [ 3,5 ] and [ 4,6 ] respectively. In the case of variables, for example

     COMPLEX :: v, va(10)
  

  the real and imaginary parts can also be assigned to directly; the statement

     va%im = 0
  

  will set the imaginary part of each element of va to zero without affecting the real part.
• In an ALLOCATE statement for one or more variables, the MOLD= clause can be used to give the variable(s) the dynamic type and type parameters (and optionally shape) of an expression. The expression in MOLD= must be type-compatible with each allocate-object, and if the expression is a variable (e.g. MOLD=X), the variable need not be defined. Note that the MOLD= clause may appear even if the type, type parameters and shape of the variable(s) being allocated are not mutable. For example,

     CLASS(*),POINTER :: a,b,c
     ALLOCATE(a,b,c,MOLD=125)
  

  will allocate the unlimited polymorphic pointers A, B and C to be of type Integer (with default kind); unlike SOURCE=, the values of A, B and C will be undefined.
• [5.3.1] Assignment to a polymorphic allocatable variable is permitted. If the variable has different dynamic type or type parameters, or if an array, a different shape, it is first deallocated. If it is unallocated (or is deallocated by step 1), it is then allocated to have the correct type and shape. It is then assigned the value of the expression. Note that the operaton of this feature is similar to the way that ALLOCATE(variable,SOURCE=expr) works. For example, given

     CLASS(*),ALLOCATABLE :: x
  

  execution of the assignment statement

     x = 43
  

  will result in X having dynamic type Integer (with default kind) and value 43, regardless of whether X was previously unallocated or allocated with any other type (or kind).
• [6.1] Rank-remapping pointer assignment is now permitted when the target has rank greater than one, provided it is “simply contiguous” (a term which means that it must be easily seen at compile-time to be contiguous). For example, the pointer assignment in

     REAL,TARGET :: x(100,100)
     REAL,POINTER :: x1(:)
     x1(1:Size(x)) => x
  

  establishes X1 as a single-dimensional alias for the whole of X.

6 Execution control [mostly 6.0]

• [5.3] The BLOCK construct allows declarations of entities within executable code. For example,

    Do i=1,n
      Block
        Real tmp
        tmp = a(i)**3
        If (tmp>b(i)) b(i) = tmp
      End Block
    End Do
  

  Here the variable tmp has its scope limited to the BLOCK construct, so will not affect anything outside it. This is particularly useful when including code by INCLUDE or by macro preprocessing.

  All declarations are allowed within a BLOCK construct except for COMMON, EQUIVALENCE, IMPLICIT, INTENT, NAMELIST, OPTIONAL and VALUE; also, statement function definitions are not permitted.

  BLOCK constructs may be nested; like other constructs, branches into a BLOCK construct from outside are not permitted. A branch out of a BLOCK construct “completes” execution of the construct.

  Entities within a BLOCK construct that do not have the SAVE attribute (including implicitly via initialisation), will cease to exist when execution of the construct is completed. For example, an allocated ALLOCATABLE variable will be automatically deallocated, and a variable with a FINAL procedure will be finalised.

• The EXIT statement is no longer restricted to exiting from a DO construct; it can now be used to jump to the end of a named ASSOCIATE, BLOCK, IF, SELECT CASE or SELECT TYPE construct (i.e. any named construct except FORALL and WHERE). Note that an EXIT statement with no construct-name still exits from the innermost DO construct, disregarding any other named constructs it might be within.
• In a STOP statement, the stop-code may be any scalar constant expression of type integer or default character. (In the NAG Fortran Compiler this also applies to the PAUSE statement, but that statement is no longer standard Fortran.) Additionally, the STOP statement with an integer stop-code now returns that value as the process exit status (on most operating systems there are limits on the value that can be returned, so for the NAG Fortran Compiler this returns only the lower eight bits of the value).
• The ERROR STOP statement has been added. This is similar to the STOP statement, but causes error termination rather than normal termination. The syntax is identical to that of the STOP statement apart from the extra keyword ‘ERROR’ at the beginning. Also, the default process exit status is zero for normal termination, and non-zero for error termination.

  For example,

     IF (x<=0) ERROR STOP 'x must be positive'
  

• [6.1] The FORALL construct now has an optional type specifier in the initial statement of the construct, which can be used to specify the type (which must be INTEGER) and kind of the index variables. When this is specified, the existence or otherwise of any entity in the outer scope that has the same name as an index variable does not affect the index variable in any way. For example,

    Complex i(100)
    Real x(200)
    ...
    Forall (Integer :: i=1:Size(x)) x(i) = i
  

  Note that the FORALL construct is still not recommended for high performance, as the semantics imply evaluating the right-hand sides into array temps the size of the iteration space, and then assigning to the variables; this usually performs worse than ordinary DO loops.

• [6.1] The DO CONCURRENT construct is a DO loop with restrictions and semantics intended to allow efficient execution. The iterations of a DO CONCURRENT construct may be executed in any order, and possibly even in parallel. The loop index variables are local to the construct.

  The DO CONCURRENT header has similar syntax to the FORALL header, including the ability to explicitly specify the type and kind of the loop index variables, and including the scalar mask.

  The restrictions on the DO CONCURRENT construct are:

  • no branch is allowed from within the construct to outside of it (this includes the RETURN and STOP statements, but ERROR STOP is allowed);
  • the EXIT statement cannot be used to terminate the loop;
  • the CYCLE statement cannot refer to an outer loop;
  • there must be no dependencies between loop iterations, and if a variable is assigned to by any iteration, it is not allowed to be referenced by another iteration unless that iteration assigns it a value first;
  • all procedures referenced within the construct must be pure;
  • no image control statements can appear within the loop;
  • no reference to IEEE_GET_FLAG or IEEE_SET_HALTING_MODE is allowed.

  For example,

    Integer vsub(n)
    ...
    Do Concurrent (i=1:n)
      ! Safe because vsub has no duplicate values.
      x(vsub(i)) = i
    End Do
  

  The full syntax of the DO CONCURRENT statement is:

  [ do-construct-name : ] DO [ label ] [ , ] CONCURRENT forall-header

  where forall-header is

  ( [ integer-type-spec :: ] triplet-spec [ , triplet-spec ]... [ , mask-expr ] )

  where mask-expr is a scalar logical expression, and triplet-spec is

  name = expr : expr [ : expr ]

7 Intrinsic procedures and modules

7.1 Additional mathematical intrinsic functions [mostly 5.3.1]

• The elemental intrinsic functions ACOSH, ASINH and ATANH compute the inverse hyperbolic cosine, sine or tangent respectively. There is a single argument X, which may be of type Real or Complex; the result of the function has the same type and kind. When the argument is Complex, the imaginary part is expressed in radians and lies in the range 0≤im≤π for the ACOSH function, and −π/2≤im≤π/2 for the ASINH and ATANH functions.

  For example, ACOSH(1.543081), ASINH(1.175201) and ATANH(0.7615942) are all approximately equal to 1.0.

• [6.1] The new elemental intrinsic functions BESSEL_J0, BESSEL_Y0, BESSEL_J1 and BESSEL_Y1 compute the Bessel functions J₀, Y₀, J₁ and Y₁ respectively. These functions are solutions to Bessel's differential equation. The J functions are of the 1^st kind and the Y functions are of the 2^nd kind; the following subscript indicates the order (0 or 1). There is a single argument X, which must be of type Real; the result of the function has the same type and kind. For functions of the 2^nd kind (BESSEL_Y0 and BESSEL_Y1), the argument X must be positive. For example, BESSEL_J0(1.5) is approximately 0.5118276, BESSEL_Y0(1.5) is approximately 0.3824489, BESSEL_J1(1.5) is approximately 0.5579365 and BESSEL_Y1(1.5) is approximately -0.4123086.
• [6.1] The new intrinsic functions BESSEL_JN and BESSEL_YN compute the Bessel functions J_n and Y_n respectively. These functions come in two forms: an elemental form and a transformational form.

  The elemental form has two arguments: N, the order of the function to compute, and X, the argument of the Bessel function. BESSEL_JN(0,X) is identical to BESSEL_J0(X), etc..

  The transformational form has three scalar arguments: N1, N2 and X. The result is a vector of size MAX(N2-N1+1,0), containing approximations to the Bessel functions of orders N1 to N2 applied to X.

  For example, BESSEL_JN(5,7.5) is approximately 0.283474, BESSEL_YN(5,7.5) is approximately 0.175418, BESSEL_JN(3,5,7.5) is approximately [ -0.258061, 0.023825, 0.283474 ] and BESSEL_YN(3,5,7.5) is approximately [ 0.159708, 0.314180, 0.175418 ].

• [6.0] The elemental intrinsic functions ERF, ERFC and ERFC compute the error function, the complementary error function and the scaled complementary error function, respectively. The single argument X must be of type real.

  The error function is the integral of −t² from 0 to X, times 2/SQRT(π); this rapidly converges to 1. The complementary error function is 1 minus the error function, and fairly quickly converges to zero. The scaled complementary error function scales the value (of 1 minus the error function) by EXP(X**2); this also converges to zero but only very slowly.

• [6.0] The elemental intrinsic functions GAMMA and LOG_GAMMA compute the gamma function and the natural logarithm of the absolute value of the gamma function respectively. The single argument X must be of type real, and must not be zero or a negative integer.

  The gamma function is the extension of factorial from the integers to the reals; for positive integers, GAMMA(X) is equal to (X−1)!, i.e. factorial of X−1. This grows very rapidly and thus overflows for quite small X; LOG_GAMMA also diverges but much more slowly.

• The elemental intrinsic function HYPOT computes the “Euclidean distance function” (square root of the sum of squares) of its arguments X and Y without overflow or underflow for very large or small X or Y (unless the result itself overflows or underflows). The arguments must be of type Real with the same kind, and the result is of type Real with that kind. Note that HYPOT(X,Y) is semantically and numerically equal to ABS(CMPLX(X,Y,KIND(X))).

  For example, HYPOT(3e30,4e30) is approximately equal to 5e30.

• The array reduction intrinsic function NORM2(X,DIM) reduces Real arrays using the L₂-norm operation. This operates exactly the same as SUM and PRODUCT, except for the operation involved. The L₂ norm of an array is the square root of the sum of the squares of the elements. Note that unlike most of the other reduction functions, NORM2 does not have a MASK argument. The DIM argument is optional; an actual argument for DIM is not itself permitted to be an optional dummy argument.

  The calculation of the result value is done in such a way as to avoid intermediate overflow and underflow, except when the result itself is outside the maximum range. For example, NORM2([X,Y]) is approximately the same as HYPOT(X,Y).

7.2 Additional intrinsic functions for bit manipulation [mostly 5.3]

• The elemental intrinsic functions BGE, BGT, BLE and BLT perform bitwise (i.e. unsigned) comparisons. They each have two arguments, I and J, which must be of type Integer but may be of different kind. The result is default Logical.

  For example, BGE(INT(Z'FF',INT8),128) is true, while INT(Z'FF',INT8)>=128 is false.

• [5.3.1] The elemental intrinsic functions DSHIFTL and DSHIFTR perform double-width shifting. They each have three arguments, I, J and SHIFT which must be of type Integer, except that one of I or J may be a BOZ literal constant – it will be converted to the type and kind of the other I or J argument. I and J must have the same kind if they are both of type Integer. The result is of type Integer, with the same kind as I and J. The I and J arguments are effectively concatenated to form a single double-width value, which is shifted left or right by SHIFT positions; for DSHIFTL the result is the top half of the combined shift, and for DSHIFTR the result is the bottom half of the combined shift.

  For example, DSHIFTL(INT(B'11000101',1),B'11001001',2) has the value INT(B'00010111',1) (decimal value 23), whereas DSHIFTR(INT(B'11000101',1),B'11001001',2) has the value INT(B'01110010',1) (decimal value 114).

• The array reduction intrinsic functions IALL, IANY and IPARITY reduce arrays using bitwise operations. These are exactly the same as SUM and PRODUCT, except that instead of reducing the array by the + or * operation, they reduce it by the IAND, IOR and IEOR intrinsic functions respectively. That it, each element of the result is the bitwise-and, bitwise-or, or bitwise-exclusive-or of the reduced elements. If the number of reduced elements is zero, the result is zero for IANY and IPARITY, and NOT(zero) for IALL.
• The elemental intrinsic functions LEADZ and TRAILZ return the number of leading (most significant) and trailing (least significant) zero bits in the argument I, which must be of type Integer (of any kind). The result is default Integer.
• The elemental intrinsic functions MASKL and MASKR generate simple left-justified and right-justified bitmasks. The value of MASKL(I,KIND) is an integer with the specified kind that has its leftmost I bits set to one and the rest set to zero; I must be non-negative and less than or equal to the bitsize of the result. If KIND is omitted, the result is default integer. The value of MASKR is similar, but has its rightmost I bits set to one instead.
• [5.3.1] The elemental intrinsic function MERGE_BITS(I,J,MASK) merges the bits from Integer values I and J, taking the bit from I when the corresponding bit in MASK is 1, and taking the bit from J when it is zero. All arguments must be BOZ literal constants or of type Integer, and all the Integer arguments must have the same kind; at least one of I and J must be of type Integer, and the result has the same type and kind.

  Note that MERGE_BITS(I,J,MASK) is identical to IOR(IAND(I,MASK),IAND(J,NOT(MASK))).

  For example, MERGE_BITS(INT(B'00110011',1),B'11110000',B'10101010') is equal to INT(B'01110010') (decimal value 114).

• The array reduction intrinsic function PARITY reduces Logical arrays. It is exactly the same as ALL and ANY, except that instead of reducing the array by the .AND. or .OR. operation, it reduces it by the .NEQV. operation. That is, each element of the result is .TRUE. if an odd number of reduced elements is .TRUE..
• The elemental intrinsic function POPCNT(I) returns the number of bits in the Integer argument I that are set to 1. The elemental intrinsic function POPPAR(I) returns zero if the number of bits in I that are set to 1 are even, and one if it is odd. The result is default Integer.

7.3 Other new intrinsic procedures [mostly 5.3.1]

• The intrinsic subroutine EXECUTE_COMMAND_LINE passes a command line to the operating system's command processor for execution. It has five arguments, in order these are:
  CHARACTER(*),INTENT(IN) :: COMMAND — the command to be executed;
  LOGICAL,INTENT(IN),OPTIONAL :: WAIT — whether to wait for command completion (default true);
  INTEGER,INTENT(INOUT),OPTIONAL :: EXITSTAT — the result value of the command;
  INTEGER,INTENT(OUT),OPTIONAL :: CMDSTAT — see below;
  CHARACTER(*),INTENT(INOUT),OPTIONAL :: CMDMSG — the error message if CMDSTAT is non-zero.

  CMDSTAT values are zero for success, −1 if command line execution is not supported, −2 if WAIT is present and false but asynchronous execution is not supported, and a positive value to indicate some other error. If CMDSTAT is not present but would have been set non-zero, the program will be terminated. Note that Release 5.3.1 supports command line execution on all systems, and does not support asynchronous execution on any system.

  For example, CALL EXECUTE_COMMAND_LINE('echo Hello') will probably display ‘Hello’ in the console window.

• The intrinsic function STORAGE_SIZE(A,KIND) returns the size in bits of a scalar object with the same dynamic type and type parameters as A, when it is stored as an array element (i.e. including any padding). The KIND argument is optional; the result is type Integer with kind KIND if it is present, and default kind otherwise.

  If A is allocatable or a pointer, it does not have to be allocated unless it has a deferred type parameter (e.g. CHARACTER(:)) or is CLASS(*). If it is a polymorphic pointer, it must not have an undefined status.

  For example, STORAGE_SIZE(13_1) is equal to 8 (bits).

• [6.0] The intrinsic inquiry function IS_CONTIGUOUS has a single argument ARRAY, which can be an array of any type. The function returns true if ARRAY is stored contiguously, and false otherwise. Note that this question has no meaning for an array with no elements, or for an array expression since that is a value and not a variable.

7.4 Changes to existing intrinsic procedures [mostly 5.3.1]

• The intrinsic functions ACOS, ASIN, ATAN, COSH, SINH, TAN and TANH now accept arguments of type Complex. Note that the hyperbolic and non-hyperbolic versions of these functions and the new ACOSH, ASINH and ATANH functions are all related by simple algebraic identities, for example the new COSH(X) is identical to the old COS((0,1)*X) and the new SINH(X) is identical to the old (0,-1)*SIN((0,1)*X).
• The intrinsic function ATAN now has an extra form ATAN(Y,X), with exactly the same semantics as ATAN2(Y,X).
• [6.2] The intrinsic functions MAXVAL and MINVAL now have an additional optional argument BACK following the KIND argument. It is scalar and of type Logical; if present with the value .True., if there is more than one element that has the maximum value (for MAXVAL) or minimum value (for MINVAL), the array element index returned is for the last element with that value rather than the first.

  For example, the value of

         MAXVAL( [ 5,1,5 ], BACK=.TRUE.)
  

  is the array [ 3 ], rather than [ 1 ].
• The intrinsic function SELECTED_REAL_KIND now has a third argument RADIX; this specifies the desired radix of the Real kind requested. Note that the function IEEE_SELECTED_REAL_KIND in the intrinsic module IEEE_ARITHMETIC also has this new third argument, and will allow requesting IEEE decimal floating-point kinds if they become available in the future.

7.5 ISO_C_BINDING additions [6.2]

INTERFACE c_sizeof
  PURE INTEGER(c_size_t) FUNCTION c_sizeof...(x) ! Specific name not visible
    TYPE(*) :: x(..)
  END FUNCTION
END INTERFACE

The actual argument x must be interoperable. The result is the same as the C sizeof operator applied to the conceptually corresponding C entity; that is, the size of x in bytes. If x is an array, it is the size of the whole array, not just one element. Note that x cannot be an assumed-size array.

7.6 ISO_FORTRAN_ENV additions

• The additional scalar integer constants INT8, INT16, INT32, INT64, REAL32, REAL64 and REAL128 supply the kind type parameter values for integer and real kinds with the indicated bit sizes.
• The additional named array constants CHARACTER_KINDS, INTEGER_KINDS, LOGICAL_KINDS and REAL_KINDS list the available kind type parameter values for each type (in no particular order).

[6.1] The standard intrinsic module ISO_FORTRAN_ENV contains two new functions as follows.

• COMPILER_VERSION. This function is pure, has no arguments, and returns a scalar default character string that identifies the version of the compiler that was used to compile the source file. This function may be used in a constant expression, e.g. to initialise a variable or named constant with this information. For example,

    Module version_info
      Use Iso_Fortran_Env
      Character(Len(Compiler_Version())) :: compiler = Compiler_Version()
    End Module
    Program show_version_info
      Use version_info
      Print *,compiler
    End Program
  

  With release 6.1 of the NAG Fortran Compiler, this program will print something like

   NAG Fortran Compiler Release 6.1(Tozai) Build 6105
  

• COMPILER_OPTIONS. This function is pure, has no arguments, and returns a scalar default character string that identifies the options supplied to the compiler when the source file was compiled. This function may be used in a constant expression, e.g. to initialise a variable or named constant with this information. For example,

    Module options_info
      Use Iso_Fortran_Env
      Character(Len(Compiler_Options())) :: compiler = Compiler_Options()
    End Module
    Program show_options_info
      Use options_info
      Print *,compiler
    End Program
  

  If compiled with the options -C=array -C=pointer -O, this program will print something like

   -C=array -C=pointer -O
  

8 Input/output extensions [mostly 5.3]

• The NEWUNIT= specifier has been added to the OPEN statement; this allocates a new unit number that cannot clash with any other logical unit (the unit number will be a special negative value). For example,

        INTEGER unit
        OPEN(FILE='output.log',FORM='FORMATTED',NEWUNIT=unit)
        WRITE(unit,*) 'Logfile opened.'
  

  The NEWUNIT= specifier can only be used if either the FILE= specifier is also used, or if the STATUS= specifier is used with the value 'SCRATCH'.
• Recursive input/output is allowed on separate units. For example, in

     Write (*,Output_Unit) f(100)
  

  the function f is permitted to perform i/o on any unit except Output_Unit; for example, if the value 100 is out of range, it would be allowed to produce an error message with

     Write (*,Error_Unit) 'Error in F:',n,'is out of range'
  

• [6.0] A sub-format can be repeated an indefinite number of times by using an asterisk (*) as its repeat count. For example,

     SUBROUTINE s(x)
       LOGICAL x(:)
       PRINT 1,x
  1    FORMAT('x =',*(:,' ',L1))
     END SUBROUTINE
  

  will display the entire array x on a single line, no matter how many elements x has. An infinite repeat count is only allowed at the top level of the format specification, and must be the last format item.
• [6.0] The G0 and G0.d edit descriptors perform generalised editing with all leading and trailing blanks (except those within a character value itself) omitted. For example,

     PRINT 1,1.25,.True.,"Hi !",123456789
  1  FORMAT(*(G0,','))
  

  produces the output

  1.250000,T,Hi !,123456789,
  

9 Programs and procedures [mostly 5.3]

• An empty internal subprogram part, module subprogram part or type-bound procedure part is now permitted following a CONTAINS statement. In the case of the type-bound procedure part, an ineffectual PRIVATE statement may appear following the unnecessary CONTAINS statement.
• [6.0] An internal procedure can be passed as an actual argument or assigned to a procedure pointer. When the internal procedure is invoked via the dummy argument or procedure pointer, it can access the local variables of its host procedure. In the case of procedure pointer assignment, the pointer is only valid until the host procedure returns (since the local variables cease to exist at that point).

  For example,

    SUBROUTINE mysub(coeffs)
      REAL,INTENT(IN) :: coeffs(0:) ! Coefficients of polynomial.
      REAL integral
      integral = integrate(myfunc,0.0,1.0) ! Integrate from 0.0 to 1.0.
      PRINT *,'Integral =',integral
    CONTAINS
      REAL FUNCTION myfunc(x) RESULT(y)
        REAL,INTENT(IN) :: x
        INTEGER i
        y = coeffs(UBOUND(coeffs,1))
        DO i=UBOUND(coeffs,1)-1,0,-1
          y = y*x + coeffs(i)
        END DO
      END FUNCTION
    END SUBROUTINE
  

• The rules used for generic resolution and for checking that procedures in a generic are unambiguous have been extended. The extra rules are that
  • a dummy procedure is distinguishable from a dummy variable;
  • an ALLOCATABLE dummy variable is distinguishable from a POINTER dummy variable that does not have INTENT(IN).
• [6.0] A disassociated pointer, or an unallocated allocatable variable, may be passed as an actual argument to an optional nonallocatable nonpointer dummy argument. This is treated as if the actual argument were not present.
• [5.3.1] Impure elemental procedures can be defined using the IMPURE keyword. An impure elemental procedure has the restrictions that apply to elementality (e.g. all arguments must be scalar) but does not have any of the “pure” restrictions. This means that an impure elemental procedure may have side effects and can contain input/output and STOP statements. For example,

      Impure Elemental Integer Function checked_addition(a,b) Result(c)
        Integer,Intent(In) :: a,b
        If (a>0 .And. b>0) Then
          If (b>Huge(c)-a) Stop 'Positive Integer Overflow'
        Else If (a<0 .And. b<0) Then
          If ((a+Huge(c))+b<0) Stop 'Negative Integer Overflow'
        End If
        c = a + b
      End Function
  

  When an argument is an array, an impure elemental procedure is applied to each element in array element order (unlike a pure elemental procedure, which has no specified order). An impure elemental procedure cannot be referenced in a context that requires a procedure to be pure, e.g. within a FORALL construct.

  Impure elemental procedures are probably most useful for debugging (because i/o is allowed) and as final procedures.

• [6.0] If an argument of a pure procedure has the VALUE attribute it does not need any INTENT attribute. For example,

     PURE SUBROUTINE s(a,b)
       REAL,INTENT(OUT) :: a
       REAL,VALUE :: b
       a = b
     END SUBROUTINE
  

  Note however that the second argument of a defined assignment subroutine, and all arguments of a defined operator function, are still required to have the INTENT(IN) attribute even if they have the VALUE attribute.

• [5.3.1] The FUNCTION or SUBROUTINE keyword on the END statement for an internal or module subprogram is now optional (when the subprogram name does not appear). Previously these keywords were only optional for external subprograms.
• ENTRY statements are regarded as obsolescent.
• [1.0] A line in the program is no longer prohibited from beginning with a semi-colon.
• [6.2] The name of an external procedure with a binding label is now considered to be a local identifier only, and not a global identifier. That means that code like the following is now standard-conforming:

        SUBROUTINE sub() BIND(C,NAME='one')
          PRINT *,'one'
        END SUBROUTINE
        SUBROUTINE sub() BIND(C,NAME='two')
          PRINT *,'two'
        END SUBROUTINE
        PROGRAM test
          INTERFACE
            SUBROUTINE one() BIND(C)
            END SUBROUTINE
            SUBROUTINE two() BIND(C)
            END SUBROUTINE
          END INTERFACE
          CALL one
          CALL two
        END PROGRAM
  

• [6.2] An internal procedure is permitted to have the BIND(C) attribute, as long as it does not have a NAME= specifier. Such a procedure is interoperable with C, but does not have a binding label (as if it were specified with NAME='').
• [6.2] A dummy argument with the VALUE attribute is permitted to be an array, and is permitted to be of type CHARACTER with length non-constant and/or not equal to one. (It is still not permitted to have the ALLOCATABLE or POINTER attributes, and is not permitted to be a coarray.)

  The effect is that a copy is made of the actual argument, and the dummy argument is associated with the copy; any changes to the dummy argument do not affect the actual argument. For example,

         PROGRAM value_example_2008
           INTEGER :: a(3) = [ 1,2,3 ]
           CALL s('Hello?',a)
           PRINT '(7X,3I6)',a
         CONTAINS
           SUBROUTINE s(string,j)
             CHARACTER(*),VALUE :: string
             INTEGER,VALUE :: j(:)
             string(LEN(string):) = '!'
             j = j + 1
             PRINT '(7X,A,3I6)',string,j
           END SUBROUTINE
         END PROGRAM
  

  will produce the output

         Hello!     2     3     4
              1     2     3
  

10 References

The Fortran 2008 standard, IS 1539-1:2010(E), is available from ISO as well as from many national standards bodies. A number of books describing the new standard are available; the recommended reference book is “Modern Fortran Explained” by Metcalf, Reid & Cohen, Oxford University Press, 2011 (ISBN 978-0-19-960141-7).