Model
The roofline model
Left of the ridge point, performance = intensity × bandwidth: only moving fewer bytes helps.
- Performance
- achievable performance (FLOPs per second)
- Arithmetic intensity
- FLOPs done per byte loaded from DRAM
- Memory bandwidth
- DRAM bandwidth, ~50–200 GB/s per socket
- Compute peak
- the flat compute roof: peak FLOPs per second of the cores
How it behaves
One input on the horizontal axis, the others held fixed.
Data table
| Arithmetic intensity I (FLOP/byte) | Performance (FLOP/s) |
|---|---|
| 0.01 | 1B |
| 0.011 | 1.12B |
| 0.013 | 1.26B |
| 0.014 | 1.41B |
| 0.016 | 1.58B |
| 0.018 | 1.78B |
| 0.02 | 2B |
| 0.022 | 2.24B |
| 0.025 | 2.51B |
| 0.028 | 2.82B |
| 0.032 | 3.16B |
| 0.036 | 3.55B |
| 0.04 | 3.98B |
| 0.045 | 4.47B |
| 0.05 | 5.01B |
| 0.056 | 5.62B |
| 0.063 | 6.31B |
| 0.071 | 7.08B |
| 0.079 | 7.94B |
| 0.089 | 8.91B |
| 0.1 | 10B |
| 0.112 | 11.2B |
| 0.126 | 12.6B |
| 0.141 | 14.1B |
| 0.158 | 15.8B |
| 0.178 | 17.8B |
| 0.2 | 20B |
| 0.224 | 22.4B |
| 0.251 | 25.1B |
| 0.282 | 28.2B |
| 0.316 | 31.6B |
| 0.355 | 35.5B |
| 0.398 | 39.8B |
| 0.447 | 44.7B |
| 0.501 | 50.1B |
| 0.562 | 56.2B |
| 0.631 | 63.1B |
| 0.708 | 70.8B |
| 0.794 | 79.4B |
| 0.891 | 89.1B |
| 1 | 100B |
| 1.12 | 112B |
| 1.26 | 126B |
| 1.41 | 141B |
| 1.58 | 158B |
| 1.78 | 178B |
| 2 | 200B |
| 2.24 | 224B |
| 2.51 | 251B |
| 2.82 | 282B |
| 3.16 | 316B |
| 3.55 | 355B |
| 3.98 | 398B |
| 4.47 | 447B |
| 5.01 | 501B |
| 5.62 | 562B |
| 6.31 | 631B |
| 7.08 | 708B |
| 7.94 | 794B |
| 8.91 | 891B |
| 10 | 1,000B |
| 11.2 | 1,000B |
| 12.6 | 1,000B |
| 14.1 | 1,000B |
| 15.8 | 1,000B |
| 17.8 | 1,000B |
| 20 | 1,000B |
| 22.4 | 1,000B |
| 25.1 | 1,000B |
| 28.2 | 1,000B |
| 31.6 | 1,000B |
| 35.5 | 1,000B |
| 39.8 | 1,000B |
| 44.7 | 1,000B |
| 50.1 | 1,000B |
| 56.2 | 1,000B |
| 63.1 | 1,000B |
| 70.8 | 1,000B |
| 79.4 | 1,000B |
| 89.1 | 1,000B |
| 100 | 1,000B |
Where it appears
Each mechanism states it in its own names. The general symbol each name stands for is shown with it.
- Physical Substrate & Performance Laws
Why do trade-offs exist at all?