2D array access time comparison - c++

Question

I have two ways of constructing a 2D array:
int arr[NUM_ROWS][NUM_COLS];
//...
tmp = arr[i][j]
and flattened array
int arr[NUM_ROWS*NUM_COLS];
//...
tmp = arr[i*NuM_COLS+j];
I am doing image processing so even a little improvement in access time is necessary. Which one is faster? I am thinking the first one since the second one needs calculation, but then the first one requires two addressing so I am not sure.

Answer 1

I don't think there is any performance difference. System will allocate same amount of contiguous memory in both cases. For calculate i*Numcols+j, either you would do it for 1D array declaration, or system would do it in 2D case. Only concern is ease of usage.

Answer 2

You should have trust into the capabilities of your compiler in optimizing standard code.
Also you should have trust into modern CPUs having fast numeric multiplication instructions.
Don't bother to use one or another!
I - decades ago - optimized some code greatly by using pointers instead of using 2d-array-calculation --> but this will a) only be useful if it is an option to store the pointer - e.g. in a loop and b) have low impact since i guess modern cpus should do 2d array access in a single cycle? Worth measuring! May be related to the array size.
In any case pointers using ptr++ or ptr += NuM_COLS will for sure be a little bit faster if applicable!

Answer 3

The first method will almost always be faster. IN GENERAL (because there are always corner cases) processor and memory architecture as well as compilers may have optimizations built in to aid with 2d arrays or other similar data structures. For example, GPUs are optimized for matrix (2d array) math.
So, again in general, I would allow the compiler and hardware to optimize your memory and address arithmetic if possible.
...also I agree with #Paul R, there are much bigger considerations when it comes to performance than your array allocation and address arithmetic.

Answer 4

There are two cases to consider: compile time definition and run-time definition of the array size. There is big difference in performance.
Static allocation, global or file scope, fixed size array:
The compiler knows the size of the array and tells the linker to allocate space in the data / memory section. This is the fastest method.
Example:
#define ROWS 5
#define COLUMNS 6
int array[ROWS][COLUMNS];
int buffer[ROWS * COLUMNS];
Run time allocation, function local scope, fixed size array:
The compiler knows the size of the array, and tells the code to allocate space in the local memory (a.k.a. stack) for the array. In general, this means adding a value to a stack register. Usually one or two instructions.
Example:
void my_function(void)
{
unsigned short my_array[ROWS][COLUMNS];
unsigned short buffer[ROWS * COLUMNS];
}
Run Time allocation, dynamic memory, fixed size array:
Again, the compiler has already calculated the amount of memory required for the array since it was declared with fixed size. The compiler emits code to call the memory allocation function with the required amount (usually passed as a parameter). A little slower because of the function call and the overhead required to find some dynamic memory (and maybe garbage collection).
Example:
void another_function(void)
{
unsigned char * array = new char [ROWS * COLS];
//...
delete[] array;
}
Run Time allocation, dynamic memory, variable size:
Regardless of the dimensions of the array, the compiler must emit code to calculate the amount of memory to allocate. This quantity is then passed to the memory allocation function. A little slower than above because of the code required to calculate the size.
Example:
int * create_board(unsigned int rows, unsigned int columns)
{
int * board = new int [rows * cols];
return board;
}

Answer 5

Since your goal is image processing then I would assume your images are too large for static arrays. The correct question you should be about dynamically allocated arrays
In C/C++ there are multiple ways you can allocate a dynamic 2D array How do I work with dynamic multi-dimensional arrays in C?. To make this work in both C/C++ we can use malloc with casting (for C++ only you can use new)
Method 1:
int** arr1 = (int**)malloc(NUM_ROWS * sizeof(int*));
for(int i=0; i<NUM_ROWS; i++)
arr[i] = (int*)malloc(NUM_COLS * sizeof(int));
Method 2:
int** arr2 = (int**)malloc(NUM_ROWS * sizeof(int*));
int* arrflat = (int*)malloc(NUM_ROWS * NUM_COLS * sizeof(int));
for (int i = 0; i < dimension1_max; i++)
arr2[i] = arrflat + (i*NUM_COLS);
Method 2 essentially creates a contiguous 2D array: i.e. arrflat[NUM_COLS*i+j] and arr2[i][j] should have identical performance. However, arrflat[NUM_COLS*i+j] and arr[i][j] from method 1 should not be expected to have identical performance since arr1 is not contiguous. Method 1, however, seems to be the method that is most commonly used for dynamic arrays.
In general, I use arrflat[NUM_COLS*i+j] so I don't have to think of how to allocated dynamic 2D arrays.