Performance Impact When Looping Over 8192 Elements
Certain matrix operations exhibit performance anomalies when the matrix size, particularly the number of rows, is a multiple of 2048 (e.g., 8192). This phenomenon, referred to as super-alignment, arises due to specific memory management practices in modern CPUs.
The provided code snippet demonstrates this issue, where a matrix res[][] is computed from a matrix img[][]. The performance for different matrix sizes, specifically 8191, 8192, and 8193, reveals a significant slowdown when the matrix size is 8192.
Super-Alignment Effects
The performance variations stem from the non-uniform access to memory caused by the nested loops iterating column-wise over the matrix img[][]. This non-sequential access pattern results in performance penalties on modern CPUs, which operate more efficiently with sequential memory access.
Resolution: Interchanging Outer Loops
The solution lies in reordering the nested loops, prioritizing row-wise iteration over column-wise iteration. By doing so, memory access becomes sequential, significantly improving performance:
for(j=1;j<size-1 for code to compute res><p><strong>Performance Results</strong></p> <p>The following performance results demonstrate the improvement achieved by interchanging the outer loops:</p> <table> <thead><tr> <th>Matrix Size</th> <th>Original Code (s)</th> <th>Interchanged Loops (s)</th> </tr></thead> <tbody> <tr> <td>8191</td> <td>1.499</td> <td>0.376</td> </tr> <tr> <td>8192</td> <td>2.122</td> <td>0.357</td> </tr> <tr> <td>8193</td> <td>1.582</td> <td>0.351</td> </tr> </tbody> </table> <p>This optimization drastically reduces the performance gap for matrices with dimensions that are multiples of 2048, resulting in consistent performance across different matrix sizes.</p></size-1>
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