# fath [![crates.io](https://img.shields.io/crates/v/fath.svg)](https://crates.io/crates/fath)
### fa(st ma)th
### A math library written in Rust, built for speed.

Includes configurable-precision approximations and exact functions for both ints and floats. Uses cross-platform intrinsics and SIMD whenever possible.

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This library *heavily* relies on unsafe and nightly features to achieve the best performance. The primary use case for this library is in games or graphics development, where speed matters more than precision

When using SIMD functions in this package, compile with `lto="fat"` or `lto="thin"` and `opt-level=3` to ensure that auto-vectorization takes place. All SIMD functions have a feature cap at AVX2, and nothing in this library utilizes anything from AVX512. If certain functions vectorize on lower requirements, that's a bonus.

## Comparison to [sleef-rs](https://github.com/burrbull/sleef-rs)
Most of the functions in here are faster than equivalent functions in sleef, at the expense of safety.

Sleef's `sin_fast` and `cos_fast` are slightly less precise than fath's `sin_fast_approx::<3>`. The main performance detriment to sleef's is the branch that happens in it when it's outside the range of being within 350 ULPs. However, fath also includes additional optimizations for it. Sleef's `log2_u35` and `ln_u35` functions are its fastest implementations, and are much more accurate than fath's, being withing 3.5 ULPs. Fath is much less accurate, but achieves much better performance due to additional optimizations and less strict precision requirements.

"Cycles per Op" in this chart is calculated from the average cycles per 8-lane function iteration, divided by 8. This simulates a best-case scenario of maximum throughput.

![Benchmarks (Ryzen 5 5600x, lto= fat , opt-level=3, target-cpu=native)](https://github.com/burgerindividual/fath/assets/30326913/47ee1cba-daee-48c5-89dd-729d8c955bb7)

## Currently Implemented Functions
**Approximate `f32` Functions:**

Allows setting a variable precision level as a `const` generic.
* `sin` and `cos`
  * Does include wrapping with a range reduction, but will become less accurate as the input gets larger.
  * Includes equivalent functions without a range reduction
* `log` (`const` base and variable base)
  * This is based on a log base 2 approximation, and is scaled for other bases. The fastest version of this is `const` base 2.0.

**Exact Unsigned Integer Functions:**
* `ilog` with `const` base
  * Has multiple implementations depending on the base to achieve maximum performance. The fastest impl is for log base 2.
* `exp` with `const` coefficient
  * Similar to previous function, but calculates `COEFF^x` instead.

## Contributing
Any help on the library is greatly appreciated. If you'd like to contribute, just submit a PR and I'll respond to it as soon as I can.
For development, I'd recommend looking at the genertated assembly often. For development of individual functions, I would recommend using a tool like [Compiler Explorer](https://rust.godbolt.org/), and using something like llvm-mca (available in CE under "tools") often to get an idea of performance on different platforms.