diff --git a/README.md b/README.md index 90d7228..35f4a1c 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,110 @@ # What every scientist should know about computer architecture - … the leture notes will be posted after the lecture … + +## 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 CPU’s 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