114 lines
6 KiB
Markdown
114 lines
6 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
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Common goal of both exercises is to sort a deck of tarot cards by value
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Before starting, make yourself acquainted with the meanining and the power of the tarot cards. Carefully read [this booklet](https://aspp.school/wiki/_media/tarot-runic.pdf)
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### First experiment: human sorting
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Setup:
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- 1 volunteer to keep the time spent sorting
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- each person picks up a tarot card from the randomly shuffled deck on the table
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- moving around and speaking is allowed until the tarot cards are displayed sorted on the table
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### Second experiment: machine sorting
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Setup:
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- 2 volunteers to keep the time:
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- one volunteer keeps the time spent *programming*
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- one volunteer keeps the time spent *executing* the program
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- 2 volunteers to be the *programmers*:
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- can use the whiteboard
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- can and should speak and think loudly and ask for help
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- 2 volunteers to be two CPUs:
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- only understand the instructions:
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- **fetch** a value from a memory address into register `N` ➔ returns `0` if succeded else `1`
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- **push** the value from register `N` to a memory address ➔ returns `0` if succeded else `1`
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- **compare** var0 and var1 ➔ returns `0` if `var0 ≥ var1` else `1`
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- 4 volunteers to be CPU registers:
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- each register has a tag: `R1`, `R2`, `R3`, `R4`
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- a value fetched from memory is kept in short-term memory by the registers
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- the result value of an operation is stored in one register
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- everyone else sits on their seats and represent RAM:
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- they own a *value*, i.e. they hold on a tarot card
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- they have an address based on their seating order: 0th seat, 1st seat, 2nd seat, 3rd seat, 4th seat, etc…
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- when *fetched*, walk to the corresponding register and hand in their *value* (card)
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- when *pushed*, walk to the corresponding register and fetch their new *value* (card)
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- each RAM address comes and picks up a random tarot card as initialization step
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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 also called row-major `== C_CONTIGUOUS`
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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® or to `pandas.DataFrame` ➔ they store data in memory using the opposite convention, the column-major order!!!
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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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- 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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