## Line Chart: Mstencil/s vs. Input Length ### Overview The image is a line chart comparing the performance (Mstencil/s) of different stencil configurations (2x3, 2x2, 1x3, 1x2, 1x1) against varying input lengths. A horizontal dashed line represents the "Compute peak". ### Components/Axes * **X-axis:** Input length, ranging from 0 to 400. * **Y-axis:** Mstencil/s, ranging from 0 to 70. * **Legend:** Located on the right side of the chart. * Compute peak (dashed black line) * 2x3 (solid black line) * 2x2 (solid green line) * 1x3 (solid purple line) * 1x2 (solid cyan line) * 1x1 (solid red line) ### Detailed Analysis * **Compute peak:** A horizontal dashed black line at approximately 63 Mstencil/s. * **2x3 (Black Line):** Starts at approximately 42 Mstencil/s at input length 20, rises to a peak of approximately 53 Mstencil/s around input length 70, and then fluctuates between 40 and 45 Mstencil/s for the remaining input lengths. * **2x2 (Green Line):** Starts at approximately 34 Mstencil/s at input length 20, rises to a peak of approximately 44 Mstencil/s around input length 70, and then fluctuates between 38 and 42 Mstencil/s for the remaining input lengths. * **1x3 (Purple Line):** Starts at approximately 25 Mstencil/s at input length 20, rises to a peak of approximately 34 Mstencil/s around input length 60, and then fluctuates between 27 and 30 Mstencil/s for the remaining input lengths. * **1x2 (Cyan Line):** Starts at approximately 18 Mstencil/s at input length 20, rises to a peak of approximately 24 Mstencil/s around input length 60, and then fluctuates between 22 and 24 Mstencil/s for the remaining input lengths. * **1x1 (Red Line):** Starts at approximately 10 Mstencil/s at input length 20, rises to approximately 12 Mstencil/s around input length 50, and then remains relatively constant at approximately 12 Mstencil/s for the remaining input lengths. ### Key Observations * The "Compute peak" represents an upper bound on performance. * The 2x3 stencil configuration consistently achieves the highest Mstencil/s performance among the tested configurations. * The 1x1 stencil configuration has the lowest Mstencil/s performance. * All stencil configurations show an initial increase in performance with increasing input length, followed by a relatively stable performance after an input length of approximately 70. * The performance of the 2x3, 2x2, 1x3, and 1x2 configurations fluctuates slightly with increasing input length after the initial rise. ### Interpretation The chart illustrates the performance of different stencil configurations as a function of input length. The 2x3 configuration consistently outperforms the others, suggesting it is the most efficient for this particular task. The initial increase in performance for all configurations likely reflects the benefits of larger input sizes in amortizing overhead costs. The subsequent stabilization suggests that performance becomes limited by other factors, such as memory bandwidth or computational complexity, beyond a certain input length. The "Compute peak" line indicates the theoretical maximum performance, which none of the configurations reach, suggesting there is room for further optimization. The fluctuations in performance after the initial rise could be due to variations in memory access patterns or other system-level effects.

## Line Chart: Performance Scaling of Stencil Configurations ### Overview This image is a line chart illustrating the performance (measured in Mstencil/s) of various stencil configurations (2x3, 2x2, 1x3, 1x2, 1x1) against varying input lengths. It also includes a reference line for the theoretical "Compute peak." The chart demonstrates that performance is highly dependent on the configuration size and exhibits periodic oscillations as the input length increases. ### Components/Axes * **X-Axis:** Labeled "Input length," ranging from 0 to 400 in increments of 50. * **Y-Axis:** Labeled "Mstencil/s," ranging from 0 to 70 in increments of 10. * **Legend:** Located in the bottom-right quadrant of the chart area. * **Compute peak:** Dashed black line. * **2x3:** Solid black line. * **2x2:** Solid green line. * **1x3:** Solid magenta (purple) line. * **1x2:** Solid cyan (light blue) line. * **1x1:** Solid red line. ### Detailed Analysis #### Trend Verification * **Compute peak (Dashed):** A perfectly horizontal line at approximately 63 Mstencil/s. * **2x3 (Black):** Starts at ~42, rises to a peak of ~53 at input length 60, then drops and enters a periodic oscillation pattern between ~40 and ~45 Mstencil/s. * **2x2 (Green):** Starts at ~34, rises to a peak of ~44 at input length 60, then enters a periodic oscillation pattern between ~37 and ~41 Mstencil/s. * **1x3 (Magenta):** Starts at ~26, rises to a peak of ~35 at input length 60, then enters a periodic oscillation pattern between ~27 and ~30 Mstencil/s. * **1x2 (Cyan):** Starts at ~18, rises to a peak of ~24 at input length 60, then enters a periodic oscillation pattern between ~22 and ~24 Mstencil/s. * **1x1 (Red):** Starts at ~10, rises rapidly to ~12 by input length 40, and remains nearly flat at ~12.5 Mstencil/s for the remainder of the range. #### Data Points (Approximate) | Input Length | 2x3 (Black) | 2x2 (Green) | 1x3 (Magenta) | 1x2 (Cyan) | 1x1 (Red) | | :--- | :--- | :--- | :--- | :--- | :--- | | **~10** | ~42 | ~34 | ~26 | ~18 | ~10 | | **~60 (Peak)** | ~53 | ~44 | ~35 | ~24 | ~12 | | **~110 (Trough)**| ~40 | ~37 | ~28 | ~22 | ~12.5 | | **~130 (Peak)** | ~45 | ~41 | ~30 | ~23 | ~12.5 | | **~150 (Trough)**| ~41 | ~38 | ~27 | ~22 | ~12.5 | | **~180 (Peak)** | ~45 | ~40 | ~30 | ~23 | ~12.5 | | **~200 (Trough)**| ~42 | ~38 | ~27 | ~22 | ~12.5 | | **~240 (Peak)** | ~45 | ~40 | ~30 | ~23 | ~12.5 | | **~250 (Trough)**| ~42 | ~38 | ~28 | ~22 | ~12.5 | | **~310 (Peak)** | ~45 | ~40 | ~30 | ~23 | ~12.5 | ### Key Observations 1. **Universal "Hump":** All configurations except 1x1 exhibit a significant performance spike at an input length of approximately 60. 2. **Periodic Oscillations:** After the initial rise, the 2x3, 2x2, 1x3, and 1x2 lines show a consistent "sawtooth" pattern. This suggests that performance is sensitive to specific input length alignments, likely related to cache line boundaries or vectorization block sizes. 3. **Configuration Scaling:** There is a clear correlation between the configuration size and throughput. The 2x3 configuration consistently outperforms the 2x2, which outperforms the 1x3, and so on. 4. **1x1 Anomaly:** The 1x1 configuration is the only one that does not exhibit the periodic oscillation pattern, suggesting it is likely limited by overhead or memory latency rather than the compute-bound factors affecting the larger configurations. ### Interpretation The data suggests that the stencil computation is highly sensitive to input length, likely due to memory alignment or cache utilization. The periodic oscillations indicate that as the input length increases, the efficiency of the computation fluctuates based on how well the data fits into the processor's cache or vector registers. The "Compute peak" line serves as a theoretical ceiling that none of the configurations reach, indicating that the system is likely memory-bandwidth bound or limited by instruction overhead rather than raw compute throughput. The 1x1 configuration is likely too small to trigger the specific optimization patterns (or cache-related penalties) seen in the larger configurations, resulting in a stable, low-performance baseline. The "hump" at input length 60 likely represents an optimal data size where the cache utilization is maximized before the periodic overheads begin to dominate.

## Line Graph: Mstencil/s vs Input Length ### Overview The image is a line graph comparing the performance of different computational configurations (e.g., 2x3, 2x2, 1x3, etc.) in terms of "Mstencil/s" (measured on the y-axis) against "Input length" (x-axis). A dashed horizontal line labeled "Compute peak" at ~60 Mstencil/s serves as a reference. The graph includes five data series with distinct colors and labels, showing varying performance trends across input lengths. --- ### Components/Axes - **X-axis (Input length)**: Ranges from 0 to 400, with increments of 50. Labeled "Input length." - **Y-axis (Mstencil/s)**: Ranges from 0 to 70, with increments of 10. Labeled "Mstencil/s." - **Legend**: Located in the bottom-right corner, with the following mappings: - **Black dashed line**: "Compute peak" (~60 Mstencil/s). - **Black solid line**: "2x3" (highest performance). - **Green solid line**: "2x2" (moderate performance). - **Purple solid line**: "1x3" (lower performance). - **Cyan solid line**: "1x2" (lower performance). - **Red solid line**: "1x1" (lowest performance). --- ### Detailed Analysis 1. **Black solid line (2x3)**: - Starts at ~42 Mstencil/s at input length 0. - Peaks at ~52 Mstencil/s around input length 50. - Fluctuates between ~40–50 Mstencil/s for input lengths 100–400. - **Trend**: Highest performance, with a sharp initial rise and gradual stabilization. 2. **Green solid line (2x2)**: - Starts at ~34 Mstencil/s at input length 0. - Peaks at ~42 Mstencil/s around input length 50. - Stabilizes between ~38–40 Mstencil/s for input lengths 100–400. - **Trend**: Moderate performance, with a peak followed by steady values. 3. **Purple solid line (1x3)**: - Starts at ~28 Mstencil/s at input length 0. - Peaks at ~34 Mstencil/s around input length 50. - Fluctuates between ~28–30 Mstencil/s for input lengths 100–400. - **Trend**: Lower performance, with a peak and gradual decline. 4. **Cyan solid line (1x2)**: - Starts at ~19 Mstencil/s at input length 0. - Peaks at ~23 Mstencil/s around input length 50. - Stabilizes between ~22–23 Mstencil/s for input lengths 100–400. - **Trend**: Lower performance, with a peak and steady values. 5. **Red solid line (1x1)**: - Remains flat at ~10 Mstencil/s across all input lengths. - **Trend**: Constant, lowest performance. 6. **Dashed line (Compute peak)**: - Horizontal line at ~60 Mstencil/s, above all data series. - **Trend**: Theoretical maximum, not achieved by any configuration. --- ### Key Observations - The **2x3 configuration** consistently outperforms others, with the highest Mstencil/s values. - The **1x1 configuration** is the baseline, showing no improvement with input length. - All configurations except the 1x1 show a peak around input length 50, followed by stabilization. - The **Compute peak** (~60 Mstencil/s) is unattainable by any configuration, suggesting a theoretical limit. --- ### Interpretation The data demonstrates that larger computational configurations (e.g., 2x3) achieve higher performance, but with variability. The 1x1 configuration serves as a baseline, while the Compute peak represents an idealized target. The fluctuations in performance (e.g., 2x3's peaks and troughs) may indicate sensitivity to input length or resource allocation. The absence of any configuration reaching the Compute peak suggests potential bottlenecks or inefficiencies in the system. This graph highlights the trade-off between configuration complexity and performance, with diminishing returns as input length increases.