≤

The passage around this formula

Given a memory system built this way, the question for any specific piece of computation is simple to state and consequential to answer: for this kernel, is the bottleneck the arithmetic units or the memory system that feeds them? The quantity that answers it is arithmetic intensity , defined as the number of floating-point operations a kernel performs per byte it moves across the memory boundary that matters. Williams, Waterman and Patterson formalized the relationship between intensity and attainable performance as the roofline model: $P \;\le\; \min\!\left(P_{\max},\; I \cdot B\right), \qquad I = \frac{\text{FLOPs}}{\text{bytes moved}}$. with $P_{\max}$ the peak arithmetic rate of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the…

Read this part in the article →