93 lines
4.8 KiB
Markdown
93 lines
4.8 KiB
Markdown
# What every scientist should know about computer architecture
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## Introduction
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- [Puzzle](puzzle.ipynb)
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- Question: how come that swapping dimensions in a for-loop makes out for a huge slowdown?
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- Let students play around with the notebook and try to find the "bug"
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- A more thorough [benchmark](benchmark_python/)
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## A digression in CPU architecture and the memory hierarchy
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- Go to [A Primer in CPU architecture](architecture/)
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- Measure size and timings for the memory hierarchy on my machine with a low level [C benchmark](benchmark_low_level/)
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## Analog programming
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- [Two exercises to activate the body and the mind](analog_programming.md)
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## Back to the Python benchmark (second try)
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- can we explain what is happening?
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- it must have to do with the good (or bad) use of cache properties
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- but how are numpy arrays laid out in memory?
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## Anatomy of a numpy array
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- [memory layout of numpy arrays](numpy/)
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## Back to the Python benchmark (third try)
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- can we explain what is happening now? Yes, more or less ;-)
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- quick fix for the [puzzle](puzzle.ipynb): try and add `order='F'` in the "bad" snippet and see that it "fixes" the bug ➔ why?
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- the default memeory layout is called "C-contiguous" or "row-major":
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```python
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np.zeros((2,2)).flags.c_contiguous == True
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np.zeros((2,2)).flags.f_contiguous == False
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```
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- note that for one-dimensional arrays it makes no difference:
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```python
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np.zeros(2).flags.c_contiguous == True
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np.zeros(2).flags.f_contiguous == True
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```
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- rule of thumb for multi-dimensional numpy arrays:
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- the right-most index should be the inner-most loop in a series of nested loops over the dimensions of a multi-dimensional array
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- the previous rule can be remembered as *the right-most index changes the faster* in a series of nested loops
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- the logically contiguous data, for example the data points of a single time series, should be stored along the right-most dimension:
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```python
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x = np.zeros((n_series, lenght_of_one_series)) # ➔ good!
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y = np.zeros((length_of_one_series, n_series)) # ➔ bad!
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```
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- … unless of course you plan to mostly loop *across* time series :)
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- watch out when migrating code from MATLAB® : it stores data in memory using the opposite convention, the column-major order!
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- **DANGER**: watch out when working with [`pandas.DataFrame`](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html):
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➔ the data are stored in memory using different conventions depending on how the `DataFrame` was initialized! Be sure to
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check the `DataFrame.values.flags` attribute!
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## A final exercise to put it all together
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- fork this repo to your account and clone your fork on the laptop
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- create a branch `ex` and switch to it
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- work on the [exercise](exercise.ipynb)
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- push your solution to your fork and create a Pull Request to this repo
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## Notes on the benchmarks
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- while running the benchmarks attached to one core on my laptop, the 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
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➔ 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? From the [Intel documentation](https://lenovopress.lenovo.com/lp1836-tuning-uefi-settings-4th-gen-intel-xeon-scalable-processor):
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> **Energy Efficient Turbo**
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>
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> When `Energy Efficient Turbo` is enabled, the CPU’s optimal turbo
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> frequency will be tuned dynamically based on CPU utilization. The actual
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> turbo frequency the CPU is set to is proportionally adjusted based on the
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> duration of the turbo request. Memory usage of the OS is also monitored.
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> If the OS is using memory heavily and the CPU core performance is limited
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> by the available memory resources, the turbo frequency will be reduced
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> until more memory load dissipates, and more memory resources become
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> available. The power/performance bias setting also influences energy
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> efficient turbo. `Energy Efficient Turbo` is best used when attempting to
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> maximize power consumption over performance.
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## Concluding remarks
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- how is all of this relevant for the users of a computing cluster?
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- Never trust benchmarks! See for example [Producing Wrong Data Without Doing Anything Obviously Wrong!](https://users.cs.northwestern.edu/~robby/courses/322-2013-spring/mytkowicz-wrong-data.pdf)
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## Additional material if there's time left
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- [Excerpts of parallel Python](parallel)
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- how does memory *allocation* to processes work at the OS level?
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- virtual memory
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- swap
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- optimistic over-committing allocation policies
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- the oom-killer watchdog
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