Why is Loop Order Crucial for Efficient Processing of an 8192x8192 Matrix?

Slow Looping Over 8192 Elements: Understanding the Performance Penalty

The provided code processes a matrix, img, by calculating the average of the nine surrounding cells for each non-border element and stores the result in the matrix res. When the matrix size is 8192x8192, the program exhibits a significant performance drop.

This slow down is attributed to memory management issues related to super-alignment. The compiler aligns data structures in memory to improve performance, and in this case, the matrix layout can cause inefficient memory access.

To resolve this issue, the order of the loops in the averaging operation should be interchanged. Instead of iterating column-wise, the loop should iterate row-wise.

Here is the modified code:

By changing the loop order, sequential memory access is maintained, eliminating the performance penalty associated with non-sequential access.

Performance Comparison:

The interchanged looping structure improves performance significantly:

Original Code:

• 8191: 1.499 seconds
• 8192: 2.122 seconds
• 8193: 1.582 seconds

Interchanged Loops:

• 8191: 0.376 seconds
• 8192: 0.357 seconds
• 8193: 0.351 seconds

This modification ensures efficient memory management and resolves the slow performance when looping over 8192 elements.

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