"simplify" lecture notes

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# What every scientist should know about computer architecture
## Introduction
- [Puzzle](puzzle.ipynb)
- Question: how come that swapping dimensions in a for-loop makes out for a huge slowdown?
- Let students play around with the notebook and try to find the "bug"
- A more thorough [benchmark](benchmark_python/)
## A digression in CPU architecture and the memory hierarchy
- Go to [A Primer in CPU architecture](architecture/)
- Measure size and timings for the memory hierarchy on my machine with a low level [C benchmark](benchmark_low_level/)
## Analog programming
Two exercises to activate the body and the mind
Common goal of both exercises is to sort a deck of tarot cards by value
### First experiment: human sorting
Setup:
- 1 volunteer to keep the time spent sorting
- each person picks up a tarot card from the randomly shuffled deck on the table
- moving around and speaking is allowed until the tarot cards are displayed sorted on the table
### Second experiment: machine sorting
Setup:
- 2 volunteers to keep the time:
- one volunteer keeps the time spent *programming*
- one volunteer keeps the time spent *executing* the program
- 2 volunteers to be the *programmers*:
- can use the whiteboard
- can and should speak and think loudly and ask for help
- 2 volunteers to be two CPUs:
- only understand the instructions:
- **fetch** a value from a memory address into register `N` ➔ returns `0` if succeded else `1`
- **push** the value from register `N` to a memory address ➔ returns `0` if succeded else `1`
- **compare** var0 and var1 ➔ returns `0` if `var0 ≥ var1` else `1`
- 4 volunteers to be CPU registers:
- each register has a tag: `R1`, `R2`, `R3`, `R4`
- a value fetched from memory is kept in short-term memory by the registers
- the result value of an operation is stored in one register
- everyone else sits on their seats and represent RAM:
- they own a *value*, i.e. they hold on a tarot card
- they have an address based on their seating order: 0th seat, 1st seat, 2nd seat, 3rd seat, 4th seat, etc…
- when *fetched*, walk to the corresponding register and hand in their *value* (card)
- when *pushed*, walk to the corresponding register and fetch their new *value* (card)
- each RAM address comes and picks up a random tarot card as initialization step
## 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](numpy/)
## Back to the Python benchmark (third try)
- can we explain what is happening now? Yes, more or less ;-)
- quick fix for the [puzzle](puzzle.ipynb): try and add `order='F'` in the "bad" snippet and see that it "fixes" the bug ➔ why?
- the default memeory layout is also called row-major `== C_CONTIGUOUS`
- rule of thumb for multi-dimensional numpy arrays:
- the right-most index should be the inner-most loop in a series of nested loops over the dimensions of a multi-dimensional array
- the previous rule can be remembered as *the right-most index changes the faster* in a series of nested loops
- the logically contiguous data, for example the data points of a single time series, should be stored along the right-most dimension:
```python
x = np.zeros((n_series, lenght_of_one_series)) # ➔ good!
y = np.zeros((length_of_one_series, n_series)) # ➔ bad!
```
- … unless of course you plan to mostly loop *across* time series :)
- watch out when migrating code from MATLAB® or to `pandas.DataFrame` ➔ they store data in memory using the opposite convention, the column-major order!!!
## A final exercise to put it all together
- fork this repo to your account and clone your fork on the laptop
- create a branch `ex` and switch to it
- work on the [exercise](exercise.ipynb)
- push your solution to your fork and create a Pull Request to this repo
## Notes on the benchmarks
- 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
➔ 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):
> **Energy Efficient Turbo**
>
> When `Energy Efficient Turbo` is enabled, the CPUs optimal turbo
> frequency will be tuned dynamically based on CPU utilization. The actual
> turbo frequency the CPU is set to is proportionally adjusted based on the
> duration of the turbo request. Memory usage of the OS is also monitored.
> If the OS is using memory heavily and the CPU core performance is limited
> by the available memory resources, the turbo frequency will be reduced
> until more memory load dissipates, and more memory resources become
> available. The power/performance bias setting also influences energy
> efficient turbo. `Energy Efficient Turbo` is best used when attempting to
> maximize power consumption over performance.
## Concluding remarks
- how is all of this relevant for the users of a computing cluster?
- 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)
## Additional material if there's time left
- how does memory *allocation* to processes work at the OS level?
- virtual memory
- swap
- optimistic over-committing allocation policies
- the oom-killer watchdog
… the leture notes will be posted after the lecture …