C Versus FORTRAN conventions

Language conventions

For any external procedure or function you can specify whether the DLL procedure or function to which the execution is relayed, is written in C-like languages (such as C and C++) or FORTRAN (see also Declaration of External Procedures and Functions). For FORTRAN code AIMMS will make sure that

  • scalar values are always passed by reference (i.e. as a pointer), and

  • multidimensional arrays are ordered in a FORTRAN-compatible manner.

By default, AIMMS will use C conventions when passing arguments to the DLL procedure or function.

Strings excluded

AIMMS will not directly translate strings into FORTRAN format, because most FORTRAN compilers use their own particular string representation. Thus, if you want to pass strings to a FORTRAN subroutine, you should write your own C interface which converts C strings into the format appropriate for your FORTRAN compiler.

Array dimensions and ordering

When a multidimensional parameter (or parameter slice) is specified as a array argument to an external procedure, AIMMS passes an array of the specified type which is constructed as follows. If the actual argument has \(n\) remaining (i.e. non-sliced) dimensions of cardinality \(N_1,\dots,N_n\), respectively, then the associated values are passed as a (one-dimensional) array of length \(N_1\cdots N_n\). The value associated with the tuple \((i_1,\dots,i_n)\) is mapped onto the element

\[i_n + N_n\bigl( i_{n-1} + N_{n-1}\bigl( \cdots \bigl( i_2 + N_2 i_1\bigr) \cdots \bigr)\bigr)\]

for running indices \(i_j=0,\dots,N_j-1\) (C-style programming). For Pascal-like languages (with indices running from \(1,\dots,N\)) all running indices in this formula must be decreased by 1, and the final result increased by 1. This ordering is compatible with the C declaration of e.g. the multidimensional array

double arr[\(N_1\)][\(N_2\)]…[\(N_n\)];

Multidimensional example in C

The C function ComputeAverage defined below computes the average of a 2-dimensional parameter a(i,j) passed as an argument in AIMMS.

DLL_EXPORT(void) ComputeAverage( double *a, int card_i, int card_j, double *average )
{ int i, j;
  double sum_a = 0.0;

#define __A(i,j)    a[j + i*card_j]

  for ( i = 0; i < card_i; i++ )
    for ( j = 0; j < card_j; j++ )
      sum_a += __A(i,j);

  *average = sum_a / (card_i*card_j);

Within your AIMMS model, you can call this procedure via an external procedure declaration ExternalAverage defined as follows.

ExternalProcedure ExternalAverage {
    Arguments     : (x,res);
    DLLName       : "Userfunc.dll";
    BodyCall      : ComputeAverage(double array: x, card: i, card: j, double scalar: res);

where the argument x and res are declared as

Parameter x {
    IndexDomain   : (i,j);
    Property      : Input;
Parameter res {
    Property      : Output;

FORTRAN array ordering

When you specify the FORTRAN language convention for an external procedure, AIMMS will order the array passed to the external procedure such that the tuple \((i_1,\dots,i_n)\) is mapped onto the element

\[i_1 + N_1\bigl( i_{2} - 1 + N_{2}\bigl( \cdots \bigl( i_{n-1} -1 + N_{n-1} \bigl(i_n-1\bigr)\bigr) \cdots \bigr)\bigr)\]

for running indices \(i_j=1,\dots,N_j\). This is compatible with the default storage of multidimensional arrays in FORTRAN, and allows you to access such array arguments using the ordinary multidimensional notation.


Consider a parameter a(i,j), where the index i is associated with the set {1, 2} and j with the set {1, 2, 3}. When this parameter is passed as a array argument to an external procedure, the resulting array (as a one-dimensional array with 6 elements) is ordered as follows in the C convention (default).

\[\begin{split}\begin{array}{|l|c|c|c|c|c|c|} \hline \mathbf{Element\:\#} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \mathbf{Value} & \mathtt{a(1,1)} & \mathtt{a(1,2)} & \mathtt{a(1,3)} & \mathtt{a(2,1)} & \mathtt{a(2,2)} & \mathtt{a(2,3)} \\ \hline \end{array}\end{split}\]

With the FORTRAN language convention, the ordering is changed as follows.

\[\begin{split}\begin{array}{|l|c|c|c|c|c|c|} \hline \mathbf{Element\:\#} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \mathbf{Value} & \mathtt{a(1,1)} & \mathtt{a(2,1)} & \mathtt{a(1,2)} & \mathtt{a(2,2)} & \mathtt{a(1,3)} & \mathtt{a(2,3)} \\ \hline \end{array}\end{split}\]