(Thanks to Craig Burley for the important corrections and contributions 
  to this chapter)

 Arrays "internals"
 An array is an allocated area in memory, together with the information 
 needed to interpret it correctly. The information needed for that 
 consists of:

   1) The data type of the elements. All elements have
      the same data type, so it's natural to attribute
      the same data type to the array itself. In other
      words there is one data type per array, and it 
      applies to all elements.
   2) Number of dimensions 
   3) The start-index and end-index of each dimension
   4) Specification of the element order in memory 

 The compiler needs all this information in order to generate references 
 to array elements, or implement whole array operations. Since a FORTRAN 
 compiler compiles separately each procedure, this info must be available 
 in the called procedure, when passing an array to a procedure.

 Possible mechanisms for passing array configuration info are combinations 
 of the following: 

   1) Explicit declarations in the called procedure
   2) Using the procedure arguments or common block variables
   3) Ignoring some of the info, if possible
   4) A special data structure passed with the array itself

 In Fortran 90, when using assumed-shape arrays, part of this information 
 is passed explicitly with the help of a special data structure called 
 "dope vector" or "descriptor". In all other cases, the compiler uses info 
 inferred from the data declarations of the called procedure.

 The internal structure of arrays is imposed by the compiler consistently 
 interpreting the storage area as a sequence of specific elements.
 The interpretation is done by code the compiler inserts in the program,
 the code implements a formula that translates array indices to memory
 addresses. For example, a formula for a one-dimensional array may be
 similar to:

   Memory-address = 
       Base-address + Element-size * (Array-index - Start-index)

 The default start address in FORTRAN is of course 1.

 See the section on array storage order for a description of FORTRAN's 
 'column major' storage order and the implications on array processing
 loops and memory management.

 FORTRAN 77 array sizes are determined at the time of compilation, the 
 'outermost' declaration of the array allocates a chunk of memory, and 
 the size of that memory chunk can't be changed during runtime. 

 Passing arrays to subprograms
 Arrays declared at an 'outer' procedure (the calling procedure or 
 some procedure that called it) can be passed to another procedure 
 (the called procedure).

 Note that dimensional and data-type information is usually not 
 passed with variables (e.g. and arrays). As FORTRAN compiles 
 each procedure separately, the same storage area can be interpreted
 differently in each procedure without any warning.

 Most FORTRAN compilers pass arrays by passing the address of the 
 array, in this case all subprograms that use the array will then 
 work on the same (and only) copy.

 The FORTRAN standard allows array passing by another method called 
 copying in/out or copy/restore. This method is not popular on 
 uni-processor machines, copying the array on every procedure call, 
 will make large arrays get duplicated in memory again and again, 
 copying in/out only the array base address is done by many FORTRAN

 On distributed memory machines copying in/out is faster, it is more
 efficient to move the array in one piece over the network. This method 
 was also used in some of the early stack machine, like some of the 
 A series mainframes.

 If your compiler uses copying in/out, some non-standard tricks will
 not work, e.g. declaring arrays to have length 1 and having larger 
 array indices (that necessarily go out bounds).

 When the array is declared in the 'outermost' procedure, the compiler 
 allocates memory for it. When you pass the array with a CALL
 statement, the compiler actually passes the base-address of the same 
 array to the called procedure. When the called procedure operates on 
 the array it works on the same array - uses the same memory storage 
 area, the array is not 'copied' to another memory area (But, it might 
 be in some cases on some Fortran systems).

 In short, the memory used in an array is allocated in the 'topmost'
 declaration and reused when you pass the array to other procedures.

 Comparison of the various array (and string) types
 For further explanation see below. 

                   | Declaration syntax | Physical size in  | Logical size in
                   |                    | called routine    | called routine
  Constant         | INTEGER  ARR(10)   | Constant in all   | Same as the
  (created/passed) |                    | invocations       | physical size
  Adjustable       | INTEGER  ARR(N)    | The size it had   | Whatever value N
  (passed)         | N & ARR dummy args | in the caller     | had upon entry
  Assumed-size     | INTEGER  ARR(*)    | The size it had   | The compiler 
  (passed)         |                    | in the caller     | doesn't know it
  Automatic~       | INTEGER  ARR(N)    | Whatever value N  | Same as the
  (created)        | N a dummy arg      | had upon entry    | physical size
  Assumed-shape~~  | INTEGER ARR(:)     | Same bounds & size| Same as the
  (passed)         | ARR a dummy arg    | as in the caller  | physical size
  ~  Automatic arrays are supported in g77 and Fortran 90
  ~~ Assumed-shape arrays are supported in Fortran 90

  Constant string  | CHARACTER  ST*10   | constant in all   | same as the
  (created)        |                    | invocations       | physical size
  Passed-length    | CHARACTER  ST*(*)  | Whatever size it  | same as the
  string (passed)  |                    | had in the caller | physical size

 Redeclaration problem
 When you pass an array to a subprogram you really (in most compilers) 
 pass the memory address of the beginning of the array. 
 At the beginning of the called subprogram the compiler should have 
 also the dimensional information. 

 The dimensional information (with the memory element order) is 
 sufficient for the compiler to generate the code for the called 
 subprogram without knowing anything else about the calling subprogram.

 A parameter statement is the 'right' way to explicitly declare an 
 array size: 

     *                  MAXDATA
C     ------------------------------------------------------------------
     *                  MAXDATA = 1000)
C     ------------------------------------------------------------------
     *                  DATA(MAXDATA)

 Explicitly redeclaring the array size in the called subprogram is 
 not a good programming practice:

     1) In order to change the array size you have to hunt 
        for it in every subprogram that uses it. 

     2) Such a subprogram can't be reused in another program 
        without changing the parameter value, and so can't be 
        used effectively in a routine's library. 

     3) Reusing the subprogram in the same program may lead 
        to absurd situations, several copies of the same 
        subprogram with different parameters values will
        have to be kept.

 We see that explicit redeclarations are incompatible with good 
 programming practice. We need a way to pass the dimensional information 
 to the subprogram, thus making it more flexible, or give up some of the
 compiler dimension control. 

 So what we have to do is pass the array base-address and some extra
 variables containing the dimensional information to the subprogram,
 and tell the compiler to use all that when accessing the array.

 In FORTRAN you tell the compiler to perform this trick using the
 adjustable-size syntax or give up some dimension control with the 
 assumed-size syntax.

 Adjustable/ Assumed size arrays
 The adjustable size method allows you not only to pass the 'correct'
 dimensional information, but also to 'reconfigure' the array - tell 
 the compiler to treat the storage area of the original array as if 
 it belonged to an array with different dimensions.

 In the assumed size method, you pass the original array giving up 
 dimension control by the compiler. You can do this only with the size 
 of one 'bound', namely the last upper one. 

 The two special methods for passing arrays are very useful when you
 create general purpose routines. They can also be combined together,
 you can pass the 'last' dimension with the assumed-size syntax, and
 the other dimensions with the adjustable-size syntax.

 No such mechanism exists in standard C (some compilers had it 
 implemented, e.g. gcc's parameterized arrays), and you have to resort 
 to strange looking tricks (see the appendix on C pointers & arrays). 

 Example of adjustable and assumed size arrays
 In the following example we pass BOTH an array and the dimensional 
 information to a subroutine using 2 methods:

     1) Passing the array and the dimensional information 
        in the argument list. This is the usual ADJUSTABLE 

     2) Passing the array in the argument list as an
        ASSUMED SIZE ARRAY. The dimensional information
        except the upper bound of the last dimension is
        either implicit (lower bound = 1), passed with 
        the adjustable array method, or is constant. 

C     ==================================================================
C      Main program for both examples
C     ==================================================================
      INTEGER		N
      PARAMETER		(N = 10)
      REAL		Y(N)
C     ------------------------------------------------------------------
      Y(1) = 0.123456
      CALL A(N,Y)
      CALL B(Y)
C     ------------------------------------------------------------------

C     ==================================================================
C      Adjustable size array method
C     ==================================================================
      INTEGER		N
      REAL		Y(N)
C     ------------------------------------------------------------------
      WRITE (*,*) 
      WRITE (*,*) ' Adjustable array:   ', Y(1)
C     ------------------------------------------------------------------

C     ==================================================================
C      Assumed size method
C     ==================================================================
      REAL		Y(*)
C     ------------------------------------------------------------------
      WRITE (*,*) 
      WRITE (*,*) ' Assumed size array: ', Y(1)
C     ------------------------------------------------------------------

 Both routines will write the first element of the array Y.

 By the way, you can't write a all of an assumed size array using just 
 the array name, but you can do it with adjustable arrays and of course 
 with arrays whose dimensions are declared with constants.

 Internals of the assumed-size method
 In order to understand what really goes on in the assumed-size method, 
 let's look at the formula translating the indices of an array to memory

 To simplify the algebra let's take the case of a 2-dimensional array 
 with indices starting at 1 (The default). More dimensions and other 
 indices make the formula more complex, but doesn't change the result.

      INTEGER       i, j
      REAL          Array(M,N)

  Given a reference to Array(i,j), the address in memory of that
  element is calculated from the base address of Array as follows:

   Memory-address = Base-address  + 

                    Element-size  * (i - 1)  +

                    Element-size  * (j - 1)  *  M 

 Because FORTRAN uses the column-major scheme of storing arrays, 
 our formula doesn't involve N - the size of the last dimension!

 Similar results are found in the general case -- the UPPER-BOUND 
 OF THE LAST DIMENSION is not needed to calculate the offset of a 
 particular element of an array.  So, that upper bound can be left 
 unspecified (denoted as "*" in the code).  

 The upper-bound of the last dimension is needed only to determine 
 the maximum allowed value of the last index, and therefore the 
 size of the entire array.

 An array with an unspecified final upper bound is an "assumed array", 
 regardless of whether it is adjustable (whether the upper or lower 
 bound of any dimension is a non-constant expression) or constant.

 By the way, the maximal allowed number of dimensions in FORTRAN 77 
 is 7, a somewhat arbitrary limit, probably imposed to suit the 
 number of index registers in an old IBM mainframe.

 Problems of assumed-size arrays
 The implications of the above discussion are that the compiler doesn't 
 have to know the size of the last dimension in order to compute memory 
 addresses from array indices, so it can do without it, provided we don't 
 ask it to do something that requires this information, e.g. perform an 
 I/O operation on the whole array at once, which requires knowing the
 size of the array.

 The responsibility for keeping inside the bounds of the last dimension 
 of an assumed-size array is on the programmer, e.g. the bounds-checking
 compiler option wouldn't help you in this case and check out-of-bounds 
 references for you.

 Assumed-size arrays also can be a pain for specialized Fortran 
 implementations to handle, perhaps even impossible.  For example, 
 a compiler for a dual-machine configuration, where the boundary between 
 machines is normally the procedure, and arguments between procedures 
 are therefore copied as part of the call, must therefore know how much 
 information to copy for each argument, but cannot reliably determine 
 this for an assumed-size array.  

 A certain compiler for a two-processor machine that took this approach 
 simply skipped any such procedure, printed a diagnostic, and this meant 
 any procedure with an assumed-size array could not be called by code 
 that "lived" on the "other" processor.

 Assumed size arrays and character strings
 Passing a character variable (a string) to a procedure with the '*(*)' 
 syntax may seem at a first glance like using the assumed-size method, 
 but it is not, because, in this case, all code that calls the procedure
 is compiled to pass the actual length of any assumed-length string, 
 so the length is known to the procedure at run time.

      CHARACTER         string*80
      CALL SUB1(string)

      SUBROUTINE SUB1(string)
      CHARACTER         string*(*)

 In this example 'string' is NOT passed by the assumed-size method,
 and the I/O restriction on assumed-size arrays doesn't apply to it.

 You _can_ declare a dummy CHARACTER variable using the CHARACTER*(*) 
 syntax and then use it in I/O -- because the length is passed by the 
 caller at run time.  

 You can't use an assumed _array_ in I/O, so you can't, for example, 
 do "WRITE (10) CHA" given "CHARACTER*1 CHA(*)", even though, to some 
 people, that looks the same as if "CHARACTER*(*) CHA" was specified,
 in which case the WRITE would be valid.

 Internal mechanisms for passing the length of strings
 There are 4 methods (so it is said):

   1) An additional variable, hidden from the programmer
      after the end of the argument list. This is the 
      method used by most UNIX f77 compilers.

   2) Using a descriptor - a special data structure that
      holds the size of the string, the address it starts,
      and maybe some "identifying signature".

 For example, the Fixed-Length Descriptor used by DEC FORTRAN on VMS 
 is one of a large family of similar descriptors, it has the following
 structure (each "cell" is a byte long): 

    +------+------+ +------+ +------+ +------+------+------+------+
    |      |      | |  14  | |  1   | |      |      |      |      |
    +------+------+ +------+ +------+ +------+------+------+------+
       Length of      Data    Desc.    Address of first byte of
       string in      type    class    data storage (the string)
         bytes        code    code   
                                                ---?> Higher addresses

 When passing a string the address of the first byte (on the left) of 
 the descriptor is passed, and the called routine can access its fields.


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