Time to BOTEC

About

This repository contains example of very simple code to manipulate samples in various programming languages, and tallies their speed and the complexity of their code. It implements this platonic estimate:

p_a = 0.8
p_b = 0.5
p_c = p_a * p_b

dists = [0, 1, 1 to 3, 2 to 10]
weights = [(1 - p_c), p_c/2, p_c/4, p_c/4 ]

result = mixture(dists, weights) # should be 1M samples
mean(result)

I don't particularly care about the speed of this particular example, but rather think that the speed in this simple exaxmple would be indicative of the speed when considering 100x or 1000x more complicated models. As of now, it may also be useful for checking the validity of simple estimations.

The title of this repository is a pun on two meanings of "time to": "how much time does it take to do x", and "let's do x". "BOTEC" stands for "back of the envelope calculation".

Current languages

• C
• Javascript (NodeJS)
• Squiggle
• R
• Python
• Nim

Comparison table

Language	Time	Lines of code
C (optimized, 16 threads)	5ms	249
Nim	68ms	84
C (naïve implementation)	292ms	149
Javascript (NodeJS)	732ms	69
Squiggle	1,536s	14
SquigglePy	1.602s	18
R	7,000s	49
Python (CPython)	16,641s	56

Time measurements taken with the time tool, using 1M samples.

Notes

Nim

I was really happy trying Nim, and as a result the Nim code is a bit more optimized and engineered:

1. It is using the fastest "danger" compilation mode.
2. It has some optimizations: I don't compute 1M samples for each dist, but instead pass functions around and compute the 1M samples at the end
3. I define the normal function from scratch, using the Box–Muller transform.
4. I also have a version in which I define the logarithm and sine functions themselves in nim to feed into the Box-Muller method. But it is much slower.

Without 1. and 2., the nim code takes 0m0.183s instead. But I don't think that these are unfair advantages: I liked trying out nim and therefore put in more love into the code, and this seems like it could be a recurring factor.

Ultimately, these optimizations were also incorporated into the C code as well.

Nim also has multithreading support, but I haven't bothered loooking into it yet.

C

The optimizations which make the final C code significantly faster than the naïve implementation are:

• To pass around pointers to functions, instead of large arrays. This is the same as in the nim implementation, but imho leads to more complex code
• To use the Box-Muller transform instead of using libraries, like in nim.
• To use multithreading support

The C code uses the -Ofast or -O3 compilation flags. Initially, without using those flags and without the algorithmic improvements, the code took ~0.4 seconds to run. So I was surprised that the Node and Squiggle code were comparable to the C code. It ended up being the case that the C code could be pushed to be ~100x faster, though :)

In fact, the C code ended up being so fast that I had to measure its time by running the code 100 times in a row and dividing that amount by 100, rather than by just running it once, because running it once was too fast for /bin/time. More sophisticated profiling tools exist that could e.g., account for how iddle a machine is when running the code, but I didn't think that was worth it at this point.

And still, there are some missing optimizations, like tweaking the code to take into account cache misses. I'm not exactly sure how that would go, though.

Once the code was at 6.6ms, there was a 0.6ms gain possible by using OMP better, and a 1ms gain by using a xorshift algorithm instead of rand_r from stdlib.

Although the above paragraphs were written in the first person, the C code was written together with Jorge Sierra, who translated the algorithmic improvements from nim to it and added the initial multithreading support.

NodeJS and Squiggle

Using bun instead of node is actually a bit slower. Also, both the NodeJS and the Squiggle code use stdlib in their innards, which has a bunch of interleaved functions that make the code slower. It's possible that not using that external library could make the code faster, but at the same time, the js approach does seem to be to use external libraries whenever possible.

I am not particularly sure that the Squiggle code is actually producing 1M samples, but also have no particular plan to debug this.

Python

For the Python code, it's possible that the lack of speed is more a function of me not being as familiar with Python. It's also very possible that the code would run faster with PyPy.

R

R has a warm place in my heart from back in the day, and it has predefined functions to do everything. It was particularly fast to write for me, though not particularly fast to run :) However, I do recall that R does have some multithreading support; it wasn't used.

Overall thoughts

Overall I don't think that this is a fair comparison of the languages intrinsically, because I'm just differentially good at them, because I've chosen to put more effort in ones than in others. But it is still useful to me personally, and perhaps mildly informative to others.

Languages I may add later

• Julia (TuringML)
• Rust
• Lisp
• Go
• Zig
• Forth
• OCaml
• Haskell
• CUDA
• [-] Stan => As far as I can tell, Stan is designed to generate samples from the posterior distribution given some data, not to create data by drawing samples from an arbitrary distribution.
  • Maybe still worth reversing the process?
• ... and suggestions welcome

Roadmap

The future of this project is uncertain. In most words, I simply forget about this repository.

Other similar projects

• Squigglepy: https://github.com/rethinkpriorities/squigglepy
• Simple Squiggle: https://github.com/quantified-uncertainty/simple-squiggle