## Pointers to Functions

Up to this point we have been discussing pointers to data objects. C also permits the declaration of pointers to functions. Pointers to functions have a variety of uses and some of them will be discussed here.

Consider the following real problem. You want to write a function that is capable of sorting virtually any collection of data that can be stored in an array. This might be an array of strings, or integers, or floats, or even structures. The sorting algorithm can be the same for all. For example, it could be a simple bubble sort algorithm, or the more complex shell or quick sort algorithm. We’ll use a simple bubble sort for demonstration purposes.

Sedgewick  has described the bubble sort using C code by setting up a function which when passed a pointer to the array would sort it. If we call that function bubble(), a sort program is described by bubble_1.c, which follows:

```/*-------------------- bubble_1.c --------------------*/

/* Program bubble_1.c from PTRTUT10.HTM   6/13/97 */

#include <stdio.h>

int arr = { 3,6,1,2,3,8,4,1,7,2};

void bubble(int a[], int N);

int main(void)
{
int i;
putchar('\n');
for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
bubble(arr,10);
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
return 0;
}

void bubble(int a[], int N)
{
int i, j, t;
for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (a[j-1] > a[j])
{
t = a[j-1];
a[j-1] = a[j];
a[j] = t;
}
}
}
}

/*---------------------- end bubble_1.c -----------------------*/```

The bubble sort is one of the simpler sorts. The algorithm scans the array from the second to the last element comparing each element with the one which precedes it. If the one that precedes it is larger than the current element, the two are swapped so the larger one is closer to the end of the array. On the first pass, this results in the largest element ending up at the end of the array. The array is now limited to all elements except the last and the process repeated. This puts the next largest element at a point preceding the largest element. The process is repeated for a number of times equal to the number of elements minus 1. The end result is a sorted array.

Here our function is designed to sort an array of integers. Thus in line 1 we are comparing integers and in lines 2 through 4 we are using temporary integer storage to store integers. What we want to do now is see if we can convert this code so we can use any data type, i.e. not be restricted to integers.

At the same time we don’t want to have to analyze our algorithm and the code associated with it each time we use it. We start by removing the comparison from within the function bubble() so as to make it relatively easy to modify the comparison function without having to re-write portions related to the actual algorithm. This results in bubble_2.c:

```/*---------------------- bubble_2.c -------------------------*/

/* Program bubble_2.c from PTRTUT10.HTM   6/13/97 */

/* Separating the comparison function */

#include <stdio.h>

int arr = { 3,6,1,2,3,8,4,1,7,2};

void bubble(int a[], int N);
int compare(int m, int n);

int main(void)
{
int i;
putchar('\n');
for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
bubble(arr,10);
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
return 0;
}

void bubble(int a[], int N)

{
int i, j, t;
for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (compare(a[j-1], a[j]))
{
t = a[j-1];
a[j-1] = a[j];
a[j] = t;
}
}
}
}

int compare(int m, int n)
{
return (m > n);
}
/*--------------------- end of bubble_2.c -----------------------*/```

If our goal is to make our sort routine data type independent, one way of doing this is to use pointers to type void to point to the data instead of using the integer data type. As a start in that direction let’s modify a few things in the above so that pointers can be used. To begin with, we’ll stick with pointers to type integer.

```/*----------------------- bubble_3.c -------------------------*/

/* Program bubble_3.c from PTRTUT10.HTM    6/13/97 */

#include <stdio.h>

int arr = { 3,6,1,2,3,8,4,1,7,2};

void bubble(int *p, int N);
int compare(int *m, int *n);

int main(void)
{
int i;
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
bubble(arr,10);
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
return 0;
}

void bubble(int *p, int N)
{
int i, j, t;
for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (compare(&p[j-1], &p[j]))
{
t = p[j-1];
p[j-1] = p[j];
p[j] = t;
}
}
}
}

int compare(int *m, int *n)
{
return (*m > *n);
}

/*------------------ end of bubble3.c -------------------------*/```

Note the changes. We are now passing a pointer to an integer (or array of integers) to bubble(). And from within bubble we are passing pointers to the elements of the array that we want to compare to our comparison function. And, of course we are dereferencing these pointer in our compare() function in order to make the actual comparison. Our next step will be to convert the pointers in bubble() to pointers to type void so that that function will become more type insensitive. This is shown in bubble_4.

```/*------------------ bubble_4.c ----------------------------*/

/* Program bubble_4.c from PTRTUT10,HTM   6/13/97 */

#include <stdio.h>

int arr = { 3,6,1,2,3,8,4,1,7,2};

void bubble(int *p, int N);
int compare(void *m, void *n);

int main(void)
{
int i;
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
bubble(arr,10);
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
return 0;
}

void bubble(int *p, int N)
{
int i, j, t;
for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (compare((void *)&p[j-1], (void *)&p[j]))
{
t = p[j-1];
p[j-1] = p[j];
p[j] = t;
}
}
}
}

int compare(void *m, void *n)
{
int *m1, *n1;
m1 = (int *)m;
n1 = (int *)n;
return (*m1 > *n1);
}

/*------------------ end of bubble_4.c ---------------------*/```

Note that, in doing this, in compare() we had to introduce the casting of the void pointer types passed to the actual type being sorted. But, as we’ll see later that’s okay. And since what is being passed to bubble() is still a pointer to an array of integers, we had to cast these pointers to void pointers when we passed them as parameters in our call to compare().

We now address the problem of what we pass to bubble(). We want to make the first parameter of that function a void pointer also. But, that means that within bubble() we need to do something about the variable t, which is currently an integer. Also, where we use t = p[j-1]; the type of p[j-1] needs to be known in order to know how many bytes to copy to the variable t (or whatever we replace t with).

Currently, in bubble_4.c, knowledge within bubble() as to the type of the data being sorted (and hence the size of each individual element) is obtained from the fact that the first parameter is a pointer to type integer. If we are going to be able to use bubble() to sort any type of data, we need to make that pointer a pointer to type void. But, in doing so we are going to lose information concerning the size of individual elements within the array. So, in bubble_5.c we will add a separate parameter to handle this size information.

These changes, from bubble4.c to bubble5.c are, perhaps, a bit more extensive than those we have made in the past. So, compare the two modules carefully for differences.

```/*---------------------- bubble5.c ---------------------------*/

/* Program bubble_5.c from PTRTUT10.HTM    6/13/97 */

#include <stdio.h>
#include <string.h>

long arr = { 3,6,1,2,3,8,4,1,7,2};

void bubble(void *p, size_t width, int N);
int compare(void *m, void *n);

int main(void)
{
int i;
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%d ", arr[i]);
}
bubble(arr, sizeof(long), 10);
putchar('\n');

for (i = 0; i < 10; i++)
{
printf("%ld ", arr[i]);
}

return 0;
}

void bubble(void *p, size_t width, int N)
{
int i, j;
unsigned char buf;
unsigned char *bp = p;

for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (compare((void *)(bp + width*(j-1)),
(void *)(bp + j*width)))  /* 1 */
{
/*              t = p[j-1];   */
memcpy(buf, bp + width*(j-1), width);
/*              p[j-1] = p[j];   */
memcpy(bp + width*(j-1), bp + j*width , width);
/*              p[j] = t;   */
memcpy(bp + j*width, buf, width);
}
}
}
}

int compare(void *m, void *n)
{
long *m1, *n1;
m1 = (long *)m;
n1 = (long *)n;
return (*m1 > *n1);
}

/*--------------------- end of bubble5.c ---------------------*/```

Note that I have changed the data type of the array from int to long to illustrate the changes needed in the compare() function. Within bubble() I’ve done away with the variable t (which we would have had to change from type int to type long). I have added a buffer of size 4 unsigned characters, which is the size needed to hold a long (this will change again in future modifications to this code). The unsigned character pointer *bp is used to point to the base of the array to be sorted, i.e. to the first element of that array.

We also had to modify what we passed to compare(), and how we do the swapping of elements that the comparison indicates need swapping. Use of memcpy() and pointer notation instead of array notation work towards this reduction in type sensitivity.

Again, making a careful comparison of bubble5.c with bubble4.c can result in improved understanding of what is happening and why.

We move now to bubble6.c where we use the same function bubble() that we used in bubble5.c to sort strings instead of long integers. Of course we have to change the comparison function since the means by which strings are compared is different from that by which long integers are compared. And,in bubble6.c we have deleted the lines within bubble() that were commented out in bubble5.c.

```/*--------------------- bubble6.c ---------------------*/
/* Program bubble_6.c from PTRTUT10.HTM   6/13/97 */

#include <stdio.h>
#include <string.h>

#define MAX_BUF 256

char arr2 = {  "Mickey Mouse",

"Donald Duck",

"Minnie Mouse",

"Goofy",

"Ted Jensen" };

void bubble(void *p, int width, int N);
int compare(void *m, void *n);

int main(void)
{
int i;
putchar('\n');

for (i = 0; i < 5; i++)
{
printf("%s\n", arr2[i]);
}
bubble(arr2, 20, 5);
putchar('\n\n');

for (i = 0; i < 5; i++)
{
printf("%s\n", arr2[i]);
}
return 0;
}

void bubble(void *p, int width, int N)
{
int i, j, k;
unsigned char buf[MAX_BUF];
unsigned char *bp = p;

for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
k = compare((void *)(bp + width*(j-1)), (void *)(bp + j*width));
if (k > 0)
{
memcpy(buf, bp + width*(j-1), width);
memcpy(bp + width*(j-1), bp + j*width , width);
memcpy(bp + j*width, buf, width);
}
}
}
}

int compare(void *m, void *n)
{
char *m1 = m;
char *n1 = n;
return (strcmp(m1,n1));
}

/*------------------- end of bubble6.c ---------------------*/```

But, the fact that bubble() was unchanged from that used in bubble5.c indicates that that function is capable of sorting a wide variety of data types. What is left to do is to pass to bubble() the name of the comparison function we want to use so that it can be truly universal. Just as the name of an array is the address of the first element of the array in the data segment, the name of a function decays into the address of that function in the code segment. Thus we need to use a pointer to a function. In this case the comparison function.

Pointers to functions must match the functions pointed to in the number and types of the parameters and the type of the return value. In our case, we declare our function pointer as:

`   int (*fptr)(const void *p1, const void *p2);`

Note that were we to write:

`    int *fptr(const void *p1, const void *p2);`

we would have a function prototype for a function which returned a pointer to type int. That is because in C the parenthesis () operator have a higher precedence than the pointer * operator. By putting the parenthesis around the string (*fptr) we indicate that we are declaring a function pointer.

We now modify our declaration of bubble() by adding, as its 4th parameter, a function pointer of the proper type. It’s function prototype becomes:

```    void bubble(void *p, int width, int N,
int(*fptr)(const void *, const void *));```

When we call the bubble(), we insert the name of the comparison function that we want to use. bubble7.c illustrate how this approach permits the use of the same bubble() function for sorting different types of data.

```/*------------------- bubble7.c ------------------*/

/* Program bubble_7.c from PTRTUT10.HTM  6/10/97 */

#include <stdio.h>
#include <string.h>

#define MAX_BUF 256

long arr = { 3,6,1,2,3,8,4,1,7,2};
char arr2 = {  "Mickey Mouse",
"Donald Duck",
"Minnie Mouse",
"Goofy",
"Ted Jensen" };

void bubble(void *p, int width, int N,
int(*fptr)(const void *, const void *));
int compare_string(const void *m, const void *n);
int compare_long(const void *m, const void *n);

int main(void)
{
int i;
puts("\nBefore Sorting:\n");

for (i = 0; i < 10; i++)               /* show the long ints */
{
printf("%ld ",arr[i]);
}
puts("\n");

for (i = 0; i < 5; i++)                  /* show the strings */
{
printf("%s\n", arr2[i]);
}
bubble(arr, 4, 10, compare_long);          /* sort the longs */
bubble(arr2, 20, 5, compare_string);     /* sort the strings */
puts("\n\nAfter Sorting:\n");

for (i = 0; i < 10; i++)             /* show the sorted longs */
{
printf("%d ",arr[i]);
}
puts("\n");

for (i = 0; i < 5; i++)            /* show the sorted strings */
{
printf("%s\n", arr2[i]);
}
return 0;
}

void bubble(void *p, int width, int N,
int(*fptr)(const void *, const void *))
{
int i, j, k;
unsigned char buf[MAX_BUF];
unsigned char *bp = p;

for (i = N-1; i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
k = fptr((void *)(bp + width*(j-1)), (void *)(bp + j*width));
if (k > 0)
{
memcpy(buf, bp + width*(j-1), width);
memcpy(bp + width*(j-1), bp + j*width , width);
memcpy(bp + j*width, buf, width);
}
}
}
}

int compare_string(const void *m, const void *n)
{
char *m1 = (char *)m;
char *n1 = (char *)n;
return (strcmp(m1,n1));
}

int compare_long(const void *m, const void *n)
{
long *m1, *n1;
m1 = (long *)m;
n1 = (long *)n;
return (*m1 > *n1);
}

/*----------------- end of bubble7.c -----------------*/```

## Pointers and Dynamic Allocation of Memory

There are times when it is convenient to allocate memory at run time using malloc(), calloc(), or other allocation functions. Using this approach permits postponing the decision on the size of the memory block need to store an array, for example, until run time. Or it permits using a section of memory for the storage of an array of integers at one point in time, and then when that memory is no longer needed it can be freed up for other uses, such as the storage of an array of structures.

When memory is allocated, the allocating function (such as malloc(), calloc(), etc.) returns a pointer. The type of this pointer depends on whether you are using an older K&R compiler or the newer ANSI type compiler. With the older compiler the type of the returned pointer is char, with the ANSI compiler it is void.

If you are using an older compiler, and you want to allocate memory for an array of integers you will have to cast the char pointer returned to an integer pointer. For example, to allocate space for 10 integers we might write:

```    int *iptr;
iptr = (int *)malloc(10 * sizeof(int));
if (iptr == NULL)

{ .. ERROR ROUTINE GOES HERE .. }```

If you are using an ANSI compliant compiler, malloc() returns a void pointer and since a void pointer can be assigned to a pointer variable of any object type, the (int *) cast shown above is not needed. The array dimension can be determined at run time and is not needed at compile time. That is, the 10 above could be a variable read in from a data file or keyboard, or calculated based on some need, at run time.

Because of the equivalence between array and pointer notation, once iptr has been assigned as above, one can use the array notation. For example, one could write:

```    int k;
for (k = 0; k < 10; k++)
iptr[k] = 2;```

to set the values of all elements to 2.

Even with a reasonably good understanding of pointers and arrays, one place the newcomer to C is likely to stumble at first is in the dynamic allocation of multi-dimensional arrays. In general, we would like to be able to access elements of such arrays using array notation, not pointer notation, wherever possible. Depending on the application we may or may not know both dimensions at compile time. This leads to a variety of ways to go about our task.

As we have seen, when dynamically allocating a one dimensional array its dimension can be determined at run time. Now, when using dynamic allocation of higher order arrays, we never need to know the first dimension at compile time. Whether we need to know the higher dimensions depends on how we go about writing the code. Here I will discuss various methods of dynamically allocating room for 2 dimensional arrays of integers.

First we will consider cases where the 2nd dimension is known at compile time.

##### METHOD 1:

One way of dealing with the problem is through the use of the typedef keyword. To allocate a 2 dimensional array of integers recall that the following two notations result in the same object code being generated:

`    multi[row][col] = 1;     *(*(multi + row) + col) = 1;`

It is also true that the following two notations generate the same code:

`    multi[row]            *(multi + row)`

Since the one on the right must evaluate to a pointer, the array notation on the left must also evaluate to a pointer. In fact multi will return a pointer to the first integer in the first row, multi a pointer to the first integer of the second row, etc. Actually, multi[n] evaluates to a pointer to that array of integers that make up the n-th row of our 2 dimensional array. That is, multi can be thought of as an array of arrays and multi[n] as a pointer to the n-th array of this array of arrays. Here the word pointer is being used to represent an address value. While such usage is common in the literature, when reading such statements one must be careful to distinguish between the constant address of an array and a variable pointer which is a data object in itself.

Consider now:

```--------------- Program 9.1 --------------------------------

/* Program 9.1 from PTRTUT10.HTM  6/13/97 */

#include <stdio.h>
#include <stdlib.h>

#define COLS 5

typedef int RowArray[COLS];
RowArray *rptr;

int main(void)
{
int nrows = 10;
int row, col;
rptr = malloc(nrows * COLS * sizeof(int));
for (row = 0; row < nrows; row++)
{
for (col = 0; col < COLS; col++)
{
rptr[row][col] = 17;
}
}

return 0;
}
------------- End of Prog. 9.1 --------------------------------```

Here I have assumed an ANSI compiler so a cast on the void pointer returned by malloc() is not required. If you are using an older K&R compiler you will have to cast using:

`    rptr = (RowArray *)malloc(.... etc.`

Using this approach, rptr has all the characteristics of an array name name, (except that rptr is modifiable), and array notation may be used throughout the rest of the program. That also means that if you intend to write a function to modify the array contents, you must use COLS as a part of the formal parameter in that function, just as we did when discussing the passing of two dimensional arrays to a function.

##### METHOD 2:

In the METHOD 1 above, rptr turned out to be a pointer to type "one dimensional array of COLS integers". It turns out that there is syntax which can be used for this type without the need of typedef. If we write:

`    int (*xptr)[COLS];`

the variable xptr will have all the same characteristics as the variable rptr in METHOD 1 above, and we need not use the typedef keyword. Here xptr is a pointer to an array of integers and the size of that array is given by the #defined COLS. The parenthesis placement makes the pointer notation predominate, even though the array notation has higher precedence. i.e. had we written

`    int *xptr[COLS];`

we would have defined xptr as an array of pointers holding the number of pointers equal to that #defined by COLS. That is not the same thing at all. However, arrays of pointers have their use in the dynamic allocation of two dimensional arrays, as will be seen in the next 2 methods.

##### METHOD 3:

Consider the case where we do not know the number of elements in each row at compile time, i.e. both the number of rows and number of columns must be determined at run time. One way of doing this would be to create an array of pointers to type int and then allocate space for each row and point these pointers at each row. Consider:

```-------------- Program 9.2 ------------------------------------

/* Program 9.2 from PTRTUT10.HTM   6/13/97 */

#include <stdio.h>
#include <stdlib.h>

int main(void)
{
int nrows = 5;     /* Both nrows and ncols could be evaluated */
int ncols = 10;    /* or read in at run time */
int row;
int **rowptr;
rowptr = malloc(nrows * sizeof(int *));
if (rowptr == NULL)
{
puts("\nFailure to allocate room for row pointers.\n");
exit(0);
}

printf("\n\n\nIndex   Pointer(hex)   Pointer(dec)   Diff.(dec)");

for (row = 0; row < nrows; row++)
{
rowptr[row] = malloc(ncols * sizeof(int));
if (rowptr[row] == NULL)
{
printf("\nFailure to allocate for row[%d]\n",row);
exit(0);
}
printf("\n%d         %p         %d", row, rowptr[row], rowptr[row]);
if (row > 0)
printf("              %d",(int)(rowptr[row] - rowptr[row-1]));
}

return 0;
}

--------------- End 9.2 ------------------------------------```

In the above code rowptr is a pointer to pointer to type int. In this case it points to the first element of an array of pointers to type int. Consider the number of calls to malloc():

```    To get the array of pointers             1     call
To get space for the rows                5     calls
-----
Total                   6     calls```

If you choose to use this approach note that while you can use the array notation to access individual elements of the array, e.g. rowptr[row][col] = 17;, it does not mean that the data in the "two dimensional array" is contiguous in memory.

You can, however, use the array notation just as if it were a continuous block of memory. For example, you can write:

`    rowptr[row][col] = 176;`

just as if rowptr were the name of a two dimensional array created at compile time. Of course row and col must be within the bounds of the array you have created, just as with an array created at compile time.

If you want to have a contiguous block of memory dedicated to the storage of the elements in the array you can do it as follows:

##### METHOD 4:

In this method we allocate a block of memory to hold the whole array first. We then create an array of pointers to point to each row. Thus even though the array of pointers is being used, the actual array in memory is contiguous. The code looks like this:

```----------------- Program 9.3 -----------------------------------

/* Program 9.3 from PTRTUT10.HTM   6/13/97 */

#include <stdio.h>
#include <stdlib.h>

int main(void)
{
int **rptr;
int *aptr;
int *testptr;
int k;
int nrows = 5;     /* Both nrows and ncols could be evaluated */
int ncols = 8;    /* or read in at run time */
int row, col;

/* we now allocate the memory for the array */

aptr = malloc(nrows * ncols * sizeof(int));
if (aptr == NULL)
{
puts("\nFailure to allocate room for the array");
exit(0);
}

/* next we allocate room for the pointers to the rows */

rptr = malloc(nrows * sizeof(int *));
if (rptr == NULL)
{
puts("\nFailure to allocate room for pointers");
exit(0);
}

/* and now we 'point' the pointers */

for (k = 0; k < nrows; k++)
{
rptr[k] = aptr + (k * ncols);
}

/* Now we illustrate how the row pointers are incremented */
printf("\n\nIllustrating how row pointers are incremented");
printf("\n\nIndex   Pointer(hex)  Diff.(dec)");

for (row = 0; row < nrows; row++)
{
printf("\n%d         %p", row, rptr[row]);
if (row > 0)
printf("              %d",(rptr[row] - rptr[row-1]));
}
printf("\n\nAnd now we print out the array\n");
for (row = 0; row < nrows; row++)
{
for (col = 0; col < ncols; col++)
{
rptr[row][col] = row + col;
printf("%d ", rptr[row][col]);
}
putchar('\n');
}

puts("\n");

/* and here we illustrate that we are, in fact, dealing with
a 2 dimensional array in a contiguous block of memory. */
printf("And now we demonstrate that they are contiguous in memory\n");

testptr = aptr;
for (row = 0; row < nrows; row++)
{
for (col = 0; col < ncols; col++)
{
printf("%d ", *(testptr++));
}
putchar('\n');
}

return 0;
}

------------- End Program 9.3 -----------------```

Consider again, the number of calls to malloc()

```    To get room for the array itself      1      call
To get room for the array of ptrs     1      call
----
Total            2      calls```

Now, each call to malloc() creates additional space overhead since malloc() is generally implemented by the operating system forming a linked list which contains data concerning the size of the block. But, more importantly, with large arrays (several hundred rows) keeping track of what needs to be freed when the time comes can be more cumbersome. This, combined with the contiguousness of the data block that permits initialization to all zeroes using memset() would seem to make the second alternative the preferred one.

As a final example on multidimensional arrays we will illustrate the dynamic allocation of a three dimensional array. This example will illustrate one more thing to watch when doing this kind of allocation. For reasons cited above we will use the approach outlined in alternative two. Consider the following code:

```------------------- Program 9.4 -------------------------------------

/* Program 9.4 from PTRTUT10.HTM   6/13/97 */

#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>

int X_DIM=16;
int Y_DIM=5;
int Z_DIM=3;

int main(void)
{
char *space;
char ***Arr3D;
int y, z;
ptrdiff_t diff;

/* first we set aside space for the array itself */

space = malloc(X_DIM * Y_DIM * Z_DIM * sizeof(char));

/* next we allocate space of an array of pointers, each
to eventually point to the first element of a
2 dimensional array of pointers to pointers */

Arr3D = malloc(Z_DIM * sizeof(char **));

/* and for each of these we assign a pointer to a newly
allocated array of pointers to a row */

for (z = 0; z < Z_DIM; z++)
{
Arr3D[z] = malloc(Y_DIM * sizeof(char *));

/* and for each space in this array we put a pointer to
the first element of each row in the array space
originally allocated */

for (y = 0; y < Y_DIM; y++)
{
Arr3D[z][y] = space + (z*(X_DIM * Y_DIM) + y*X_DIM);
}
}

/* And, now we check each address in our 3D array to see if
the indexing of the Arr3d pointer leads through in a
continuous manner */

for (z = 0; z < Z_DIM; z++)
{
printf("Location of array %d is %p\n", z, *Arr3D[z]);
for ( y = 0; y < Y_DIM; y++)
{
printf("  Array %d and Row %d starts at %p", z, y, Arr3D[z][y]);
diff = Arr3D[z][y] - space;
printf("    diff = %d  ",diff);
printf(" z = %d  y = %d\n", z, y);
}
}
return 0;
}

------------------- End of Prog. 9.4 ----------------------------```

If you have followed this tutorial up to this point you should have no problem deciphering the above on the basis of the comments alone. There are a couple of points that should be made however. Let’s start with the line which reads:

`    Arr3D[z][y] = space + (z*(X_DIM * Y_DIM) + y*X_DIM);`

Note that here space is a character pointer, which is the same type as Arr3D[z][y]. It is important that when adding an integer, such as that obtained by evaluation of the expression (z*(X_DIM * Y_DIM) + y*X_DIM), to a pointer, the result is a new pointer value. And when assigning pointer values to pointer variables the data types of the value and variable must match.

## Pointers to Arrays

Pointers, of course, can be "pointed at" any type of data object, including arrays. While that was evident when we discussed program 3.1, it is important to expand on how we do this when it comes to multi-dimensional arrays.

To review, in Chapter 2 we stated that given an array of integers we could point an integer pointer at that array using:

```    int *ptr;
ptr = &my_array;       /* point our pointer at the first
integer in our array */```

As we stated there, the type of the pointer variable must match the type of the first element of the array.

In addition, we can use a pointer as a formal parameter of a function which is designed to manipulate an array. e.g.

Given:

```    int array = {'1', '5', '7'};
void a_func(int *p);```

Some programmers might prefer to write the function prototype as:

`   void a_func(int p[]);`

which would tend to inform others who might use this function that the function is designed to manipulate the elements of an array. Of course, in either case, what actually gets passed is the value of a pointer to the first element of the array, independent of which notation is used in the function prototype or definition. Note that if the array notation is used, there is no need to pass the actual dimension of the array since we are not passing the whole array, only the address to the first element.

We now turn to the problem of the 2 dimensional array. As stated in the last chapter, C interprets a 2 dimensional array as an array of one dimensional arrays. That being the case, the first element of a 2 dimensional array of integers is a one dimensional array of integers. And a pointer to a two dimensional array of integers must be a pointer to that data type. One way of accomplishing this is through the use of the keyword "typedef". typedef assigns a new name to a specified data type. For example:

`    typedef unsigned char byte;`

causes the name byte to mean type unsigned char. Hence

`    byte b;     would be an array of unsigned characters.`

Note that in the typedef declaration, the word byte has replaced that which would normally be the name of our unsigned char. That is, the rule for using typedef is that the new name for the data type is the name used in the definition of the data type. Thus in:

`    typedef int Array;`

Array becomes a data type for an array of 10 integers. i.e. Array my_arr; declares my_arr as an array of 10 integers and Array arr2d; makes arr2d an array of 5 arrays of 10 integers each.

Also note that Array *p1d; makes p1d a pointer to an array of 10 integers. Because *p1d points to the same type as arr2d, assigning the address of the two dimensional array arr2d to p1d, the pointer to a one dimensional array of 10 integers is acceptable. i.e. p1d = &arr2d; or p1d = arr2d; are both correct.

Since the data type we use for our pointer is an array of 10 integers we would expect that incrementing p1d by 1 would change its value by 10*sizeof(int), which it does. That is, sizeof(*p1d) is 20. You can prove this to yourself by writing and running a simple short program.

Now, while using typedef makes things clearer for the reader and easier on the programmer, it is not really necessary. What we need is a way of declaring a pointer like p1d without the need of the typedef keyword. It turns out that this can be done and that

`    int (*p1d);`

is the proper declaration, i.e. p1d here is a pointer to an array of 10 integers just as it was under the declaration using the Array type. Note that this is different from

`    int *p1d;`

which would make p1d the name of an array of 10 pointers to type int.

## More on Multi-Dimensional Arrays

In the previous chapter we noted that given

```    #define ROWS 5
#define COLS 10

int multi[ROWS][COLS];```

we can access individual elements of the array multi using either:

`    multi[row][col]`

or

`    *(*(multi + row) + col)`

To understand more fully what is going on, let us replace

`    *(multi + row)`

with X as in:

`    *(X + col)`

Now, from this we see that X is like a pointer since the expression is de-referenced and we know that col is an integer. Here the arithmetic being used is of a special kind called "pointer arithmetic" is being used. That means that, since we are talking about an integer array, the address pointed to by (i.e. value of) X + col + 1 must be greater than the address X + col by and amount equal to sizeof(int).

Since we know the memory layout for 2 dimensional arrays, we can determine that in the expression multi + row as used above, multi + row + 1 must increase by value an amount equal to that needed to "point to" the next row, which in this case would be an amount equal to COLS * sizeof(int).

That says that if the expression *(*(multi + row) + col) is to be evaluated correctly at run time, the compiler must generate code which takes into consideration the value of COLS, i.e. the 2nd dimension. Because of the equivalence of the two forms of expression, this is true whether we are using the pointer expression as here or the array expression multi[row][col].

Thus, to evaluate either expression, a total of 5 values must be known:

1. The address of the first element of the array, which is returned by the expression multi, i.e., the name of the array.
2. The size of the type of the elements of the array, in this case sizeof(int).
3. The 2nd dimension of the array
4. The specific index value for the first dimension, row in this case.
5. The specific index value for the second dimension, col in this case.

Given all of that, consider the problem of designing a function to manipulate the element values of a previously declared array. For example, one which would set all the elements of the array multi to the value 1.

```    void set_value(int m_array[][COLS])
{
int row, col;
for (row = 0; row < ROWS; row++)
{
for (col = 0; col < COLS; col++)
{
m_array[row][col] = 1;
}
}
}```

And to call this function we would then use:

`    set_value(multi);`

Now, within the function we have used the values #defined by ROWS and COLS that set the limits on the for loops. But, these #defines are just constants as far as the compiler is concerned, i.e. there is nothing to connect them to the array size within the function. row and col are local variables, of course. The formal parameter definition permits the compiler to determine the characteristics associated with the pointer value that will be passed at run time. We really don’t need the first dimension and, as will be seen later, there are occasions where we would prefer not to define it within the parameter definition, out of habit or consistency, I have not used it here. But, the second dimension must be used as has been shown in the expression for the parameter. The reason is that we need this in the evaluation of m_array[row][col] as has been described. While the parameter defines the data type (int in this case) and the automatic variables for row and column are defined in the for loops, only one value can be passed using a single parameter. In this case, that is the value of multi as noted in the call statement, i.e. the address of the first element, often referred to as a pointer to the array. Thus, the only way we have of informing the compiler of the 2nd dimension is by explicitly including it in the parameter definition.

In fact, in general all dimensions of higher order than one are needed when dealing with multi-dimensional arrays. That is if we are talking about 3 dimensional arrays, the 2nd and 3rd dimension must be specified in the parameter definition.