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I don't quite understand the bandwidth factor in roofline models described in Wikipedia (like the pic and its caption shown below):

  1. why the intersection between the β x I and axises could be changed? Why could there be performance while operation intensity is zero?
  2. When changing bandwidth ceilings, why the slope of the β x I does not change?

enter image description here

An example of a Roofline model with added bandwidth ceilings. In this model, the two additional ceilings represent the absence of software prefetching and NUMA organization of memory. -- Wikipedia

Peter Cordes
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gasoon
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  • This question seems to be more appropriate for https://cs.stackexchange.com/ – Marat Aug 29 '22 at 18:58
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    The x and y axes are log scales. Zero FLOPs/byte is infinitely far to the left, and not part of the area shown. This model is a simplification, probably only close to accurate in the range near the ALU throughput roof-line. It's not trying to show you the limit as each FLOP requires huge numbers of loads (or ALU work other than FLOPs, e.g. bitwise stuff or integer stuff), where practical effects might come into play. – Peter Cordes Aug 29 '22 at 19:14

1 Answers1

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The axes in this graph are logarithmic. So the zero intensity case is not actually on the graph. Also, because of that logarithmic scale, any factor degradation, for instance from lack of prefetching, is a constant displacement.

Victor Eijkhout
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