What every scientist should know about computer architecture

Important: these are instructor notes, remove this file before showing the materials to the students. The notes can be added after the lecture, of course.

Introduction

• Puzzle (how swapping two nested for-loops makes out for a >27× slowdown
• Let students play around with the notebook and try to find the "bug"
• A more thorough benchmark using the same code is here

A digression in CPU architecture and the memory hierarchy

• Go to A Primer in CPU architecture

• The need for a hierarchical access to data for the CPU should be clear now ➔ the "starving" CPU problem

• Have a look at the historical evolution of speeds of different components in a computer:

  • the CPU clock rate
  • the memory (RAM) bandwidth, latency clock rate
  • the storage media access rates

• Measure size and timings for the memory hierarchy on my machine with a low level C benchmark

Back to the Python benchmark (second try)

• can we explain what is happening?
• it must have to do with the good (or bad) use of cache properties
• but how are numpy arrays laid out in memory?

Anatomy of a numpy array

• memory layout of numpy arrays

Back to the Python benchmark (third try)

• can we explain what is happening now? Yes, more or less ;-)
• quick fix for the puzzle: try and add order='F' in the "bad" snippet and see that is "fixes" the bug ➔ why?

Notes on the Python benchmark:

• while running it attached to the P-core (cpu0), the P-core was running under a constant load of 100% (almost completely user-time) and at a fixed frequency of 3.8 GHz, where the theoretical max would be 5.2 GHz
• while running it attached to the E-core (cpu10), the E-core was running under a constant load of 100% (almost completely user-time) and at a fixed requency of 2.5 GHz, where the theoretical max would be 3.9 GHz
• ... ➔ the CPU does not "starve" because it scales its speed down to match the memory throughput? Or I am misinterpreting this? This problem which at first sight should be perfectly memory-bound, becomes CPU-bound, or actually, exactly balanced? ;-)

Excerpts of parallel Python

• The dangers and joys of automatic parallelization (like in numpy linear algebra routines) and the use of clusters/schedulers (but also on your laptop)

Concluding remarks

• how is all of this relevant for the users of a computing cluster?