Squiggle.c

A self-contained C99 library that provides a subset of Squiggle's functionality in C. It should be fast, but at the margin, simplicity of implementation wins over speed.

Why C?

• Because it is fast
• Because I enjoy it
• Because C is honest
• Because it will last long
• Because it can fit in my head
• Because if you can implement something in C, you can implement it anywhere else
• Because it can be made faster if need be
  • e.g., with a multi-threading library like OpenMP, or by adding more algorithmic complexity
  • or more simply, by inlining the sampling functions (adding an inline directive before their function declaration)
• Because there are few abstractions between it and machine code (C => assembly => machine code with gcc, or C => machine code, with tcc), leading to fewer errors beyond the programmer's control.

Getting started

You can follow some example usage in the examples/ folder

1. In the first example, we define a small model, and draw one sample from it
2. In the second example, we define a small model, and return many samples
3. In the third example, we use a gcc extension—nested functions—to rewrite the code from point 2. in a more linear way.
4. In the fourth example, we define some simple cdfs, and we draw samples from those cdfs. We see that this approach is slower than using the built-in samplers, e.g., the normal sampler.
5. In the fifth example, we define the cdf for the beta distribution, and we draw samples from it.

Commentary

squiggle.c is short

squiggle.c is around 300 lines of C. The reader could just read it and grasp its contents.

Core strategy

This library provides some basic building blocks. The recommended strategy is to:

1. Define sampler functions, which take a seed, and return 1 sample
2. Compose those sampler functions to define your estimation model
3. At the end, call the last sampler function many times to generate many samples from your model

Cdf auxiliary functions

To help with the above core strategy, this library provides convenience functions, which take a cdf, and returns a sample from the distribution produced by that cdf.

This might make it easier to program models, at the cost of a 20x to 60x slowdown in the parts of the code that use it.

Nested functions and compilation with tcc.

GCC has an extension which allows a program to define a function inside another function. This makes squiggle.c code more linear and nicer to read, at the cost of becoming dependent on GCC and hence sacrificing portability and compilation times. Conversely, compiling with tcc (tiny c compiler) is almost instantaneous, and doesn't allow for nested functions.

Error propagation vs exiting on error

The process of taking a cdf and returning a sample might fail, e.g., it's a Newton method which might fail to converge because of cdf artifacts. The cdf itself might also fail, e.g., if a distribution only accepts a range of parameters, but is fed parameters outside that range.

This library provides two approaches:

1. Print the line and function in which the error occured, then exit on error
2. In situations where there might be an error, return a struct containing either the correct value or an error message:

struct box {
    int empty;
    float content;
    char* error_msg;
};

The first approach produces terser programs but might not scale. The second approach seems like it could lead to more robust programmes, but is more verbose.

Behaviour on error can be toggled by the EXIT_ON_ERROR variable. This library also provides a convenient macro, PROCESS_ERROR, to make error handling in either case much terser—see the usage in example 4 in the examples/ folder.

Related projects

• Squiggle
• SquigglePy
• Simple Squiggle
• time to botec

To do list

• Explain correlated samples
• Add tests in Stan?
• Have some more complicated & realistic example
• Add summarization functions: 90% ci (or all c.i.?)
• Systematize references
• Publish online
• Add efficient sampling from a beta distribution
  • https://dl.acm.org/doi/10.1145/358407.358414
  • https://link.springer.com/article/10.1007/bf02293108
  • https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution
  • 5cae51e794/numpy/random/src/distributions/distributions.c
• Support all distribution functions in https://www.squiggle-language.com/docs/Api/Dist
• Support all distribution functions in https://www.squiggle-language.com/docs/Api/Dist, and do so efficiently

Done

• Add example for only one sample
• Add example for many samples
• [ ] Add a custom preprocessor to allow simple nested functions that don't rely on local scope?
• Use gcc extension to define functions nested inside main.
• Chain various sample_mixture functions
• Add beta distribution
  • See https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution for a faster method.
• [-] Use OpenMP for acceleration
• Add function to get sample when given a cdf
• Don't have a single header file.
• Structure project a bit better
• Simplify PROCESS_ERROR macro
• Add README
  • Schema: a function which takes a sample and manipulates it,
  • and at the end, an array of samples.
  • Explain boxes
  • Explain nested functions
  • Explain exit on error
  • Explain individual examples
• Rename functions to something more self-explanatory, e.g,. sample_unit_normal.
• Add summarization functions: mean, std
• Add sampling from a gamma distribution
  • https://dl.acm.org/doi/pdf/10.1145/358407.358414