_LETTERS TO THE EDITOR_
from T. Graham Freeman, Australian Defence Force Academy


Example 1: Simplest algorithm for array multiplication

for i = 1 to m
  for j = 1 to p
    C(i,j) = 0
    for k = 1 to n
       C(i,j) = C(i,j) + A(i,k)*B(k,j);

Example 2: C/C++ function using macros to simplify
array references.

void matmul(int m, int n, int p, 
   float *a, float *b, float *c)
   /* "a" is m rows by n cols,
      "b" is n rows by p cols, and
      "c" is m rows by p cols */
{
#define A(I,J) (*(a+(I)*n+(J)))
#define B(I,J) (*(b+(I)*p+(J)))
#define C(I,J) (*(c+(I)*p+(J)))
   int i, j, k;
   for (i=0; i<m; ++i)  {
      for (j=0; j<p; ++j)  {
      C(i,j) = 0;
      for (k=0; k<n; ++k)  {     
         C(i,j) += A(i,k)*B(k,j);
     }
   }
 }
#undef A
#undef B
#undef C
}



Example 3: Main program to call the function in Example 2.

void matmul(int m, int n, int p,
    float *a, float *b, float *c);
main()
{
    float aa[6][4],
          bb[4][7],
          cc[6][7];
     /* read numbers into aa and bb */   
    matmul(6,4,7,aa,bb,cc);   
    /* matmul(6,4,7,
         (float*)aa,(float*)bb,(float*)cc);      
         will press the warning messages */   
  /* print cc */
}