Roofline: Why L1 L2 DRAM’s slope is the same? Why doesn’t the line go through the origin?

Roofline plots are conventionally shown on a log-log scale. On a log-log scale, straight lines of the same slope have the same *power* relationship (e.g. y = C·x^a → log(y) = log(C) + a·log(x)).

Your lines have the same slope because they have the same, linear scaling: a memory bandwidth-bound kernel will take (size)/(bandwidth) seconds to run, giving FLOPs proportional to the reciprocal (bandwidth)/(size). Higher-bandwidth memories (L1 > L2 > DRAM) shift upwards on the plot.

The lines also *do* pass through the origin, but on a log-log plot the origin is infinitely far away to the bottom left.

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