How data layout in RAM memory?

Question

I have a basic architecture based question. How does multi dimensional arrays layout in memory? Is this correct that data layout linearly in memory? Is so, is it correct that in row major order data store based on row orders (first row store, then second row ...) and in column major data stores based on columns?

Thanks

Answer 1

Each array is stored in sequence, naturally. It makes no sense to spread data all over the place.

Example in C:

int matrix[10][10];
matrix[9][1] = 1234;
printf("%d\n", matrix[9][1]); // prints 1234
printf("%d\n", ((int*)matrix)[9 * 10 + 1]); // prints 1234

Of course there is nothing enforcing you to organize data this way, if you want to make a mess you can do it.

For example, if instead of using an array of arrays you decide to dynamically allocate your matrix:

int **matrix;
matrix = malloc(10 * sizeof(int*));
for (int i = 0; i < 10; ++i)
    matrix[i] = malloc(10 * sizeof(int));

The above example is most likely still stored in sequence, but certainly not in a contiguous manner, because there are 11 different memory blocks allocated and the memory manager is free to allocate them wherever it makes sense to it.

Answer 2

The representation of an array depends upon the programming language. Most languages (the C abortion and its progeny being notable exceptions) represent arrays using a descriptor. The descriptor specifies the number of dimensions the upper and lower bounds of each dimension, and where the data is located.

Usually, the all the data for the array is stored contiguously. Even when stored contiguously the ordering depends upon the language. In some languages [0, 0, 0] is stored next to [1, 0, 0] (Column Major—eg FORTRAN)). In others [0, 0, 0] is next to [0, 0, 1] (and [0, 0, 0] and [1, 0, 0] are apart—row major—eg, Pascal). Some languages, such as Ada, leave the ordering up to the compiler implementation.