Question

I imagine we all agree that it is considered idiomatic C to access a true multidimensional array by dereferencing a (possibly offset) pointer to its first element in a one-dimensional fashion, e.g.:

void clearBottomRightElement(int *array, int M, int N)
{
    array[M*N-1] = 0;  // Pretend the array is one-dimensional
}


int mtx[5][3];
...
clearBottomRightElement(&mtx[0][0], 5, 3);

However, the language-lawyer in me needs convincing that this is actually well-defined C! In particular:

1. Does the standard guarantee that the compiler won’t put padding in-between e.g. mtx[0][2] and mtx[1][0]?

2. Normally, indexing off the end of an array (other than one-past the end) is undefined (C99, 6.5.6/8). So the following is clearly undefined:

   struct {
       int row[3];           // The object in question is an int[3]
       int other[10];
   } foo;
   int *p = &foo.row[7];     // ERROR: A crude attempt to get &foo.other[4];
   

   So by the same rule, one would expect the following to be undefined:

   int mtx[5][3];
   int (*row)[3] = &mtx[0];  // The object in question is still an int[3]
   int *p = &(*row)[7];      // Why is this any better?
   

   So why should this be defined?

   int mtx[5][3];
   int *p = &(&mtx[0][0])[7];
   

So what part of the C standard explicitly permits this? (Let’s assume c99 for the sake of discussion.)

EDIT

Note that I have no doubt that this works fine in all compilers. What I’m querying is whether this is explicitly permitted by the standard.

Answer 1

The only obstacle to the kind of access you want to do is that objects of type int [5][3] and int [15] are not allowed to alias one another. Thus if the compiler is aware that a pointer of type int * points into one of the int [3] arrays of the former, it could impose array bounds restrictions that would prevent accessing anything outside that int [3] array.

You might be able to get around this issue by putting everything inside a union that contains both the int [5][3] array and the int [15] array, but I’m really unclear on whether the union hacks people use for type-punning are actually well-defined. This case might be slightly less problematic since you would not be type-punning individual cells, only the array logic, but I’m still not sure.

One special case that should be noted: if your type were unsigned char (or any char type), accessing the multi-dimensional array as a one-dimensional array would be perfectly well-defined. This is because the one-dimensional array of unsigned char that overlaps it is explicitly defined by the standard as the “representation” of the object, and is inherently allowed to alias it.