Why is Looping Over 8192 Elements So Much Slower Than 8191 or 8193?
Dec 11, 2024 am 08:56 AMPerformance 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;j++) { for(i=1;i<SIZE-1;i++) { // Code to compute res[j][i] } }
Performance Results
The following performance results demonstrate the improvement achieved by interchanging the outer loops:
Matrix Size | Original Code (s) | Interchanged Loops (s) |
---|---|---|
8191 | 1.499 | 0.376 |
8192 | 2.122 | 0.357 |
8193 | 1.582 | 0.351 |
This optimization drastically reduces the performance gap for matrices with dimensions that are multiples of 2048, resulting in consistent performance across different matrix sizes.
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