Why is My Loop Slow When Processing 8192 Elements?

Why Performance Drops When Looping Over 8192 Elements

When looping over 8192 elements, the program encounters a significant slowdown. This is attributed to a memory alignment issue, exacerbated by an inefficient loop structure.

Memory Alignment

Modern processors utilize cache hierarchies to improve data access speed. Aligned memory accesses, where data is stored at addresses that are multiples of the cache line size, allow for faster data retrieval. However, in this case, the SIZE parameter is defined as 8192, which is not a multiple of the cache line size (typically 64 bytes). This misalignment can slow down memory access operations.

Loop Ordering

Compounding the memory alignment issue is the ordering of the loops. The original code iterates over the matrix column-wise, resulting in non-sequential memory accesses. This forces the processor to perform slower, random retrievals of data from memory.

Solution

There are two possible solutions:

1. Align the memory: Redefine SIZE to a multiple of the cache line size (e.g., 8192 64).
2. Interchange loop ordering: Instead of column-wise iteration, iterate over the matrix row-wise. This aligns memory accesses with the cache line organization, allowing for faster and more efficient data retrieval.

By interchanging the loop ordering in the code, the performance bottleneck is eliminated.

Example

The following code illustrates the fix:

for(j=1;j<SIZE-1;j++) {
    for(i=1;i<SIZE-1;i++) {
        res[j][i]=0;
        res[j][i] += img[j-1][i-1];
        ...
    }
}

Performance Comparison

After applying the fix, the performance improves significantly:

Original Code:

SIZE = 8191: 1.499 seconds
SIZE = 8192: 2.122 seconds
SIZE = 8193: 1.582 seconds

Fixed Code:

SIZE = 8191: 0.376 seconds
SIZE = 8192: 0.357 seconds
SIZE = 8193: 0.351 seconds

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