Why Does My Program Slow Down Significantly When Processing 8192 Elements Due to Memory Access Patterns?

Memory Management Dilemma in Program with Slow Execution

When a program iterates over a specific number of elements, particularly 8192, it can exhibit a notable slowdown. This phenomenon stems from memory management, an intricate topic that warrants further exploration.

Code Overview

Consider the loop in question, which performs operations on a predefined matrix:

for (i = 1; i < SIZE - 1; i++) {
    for (j = 1; j < SIZE - 1; j++) {
        res[j][i] = 0;
        for (k = -1; k < 2; k++)
            for (l = -1; l < 2; l++)
                res[j][i] += img[j + l][i + k];
        res[j][i] /= 9;
    }
}

The program's performance discrepancy arises from the type of memory layout employed. When accessing arrays, modern processors prefer contiguous memory blocks for optimal efficiency. However, when loops iterate over elements in a non-linear fashion, as is the case in the provided code, the processor may encounter memory stalls as it attempts to access non-sequential data.

Super-Alignment and Cache Issues

The crux of the issue lies in "super-alignment," a phenomenon where the processor prefers to access memory blocks that are multiples of a particular size, often 16 or 32 bytes. In this case, the outer loop iterates over rows, while the inner loop iterates over columns. When SIZE is a multiple of 2048, the outer loop skips over large portions of memory between rows, causing the processor to incur delays while it waits for data.

Performance Comparison

The following execution times demonstrate the performance impact:

SIZE = 8191: 3.44 secs
SIZE = 8192: 7.20 secs
SIZE = 8193: 3.18 secs

Solution: Reordering Loops

The solution to this issue is to rearrange the loops such that the outer loop iterates over columns instead of rows. This ensures that the program accesses contiguous memory blocks, eliminating the non-sequential access that causes the slowdown.

The modified loop:

for (j = 1; j < SIZE - 1; j++) {
    for (i = 1; i < SIZE - 1; i++) {
        ... (same operations as before) ...
    }
}

By implementing this modification, the performance disparity disappears, as seen in the following execution times:

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

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