# MaxMath MaxMath is the most powerful and extensive SIMD math library available to Unity developers. Built on top of Unity.Mathematics and utilizing Unity.Burst, it introduces the following key features: - **Support For All Primitive Data Types:** MaxMath adds support for `(s)byte`, `(u)short`, and `(u)long` vectors and matrices. These data types come with optimized overloads for all functions in Unity.Mathematics. Additionally, specialized `Random8/16/32/64/128` types are available for efficient pseudo-random number generation. - **Wider Vectors With Full Hardware Support:** Vector types are expanded to 256 bits, enabling types like `byte32`, `short16`, `int8`, and `float8`. This allows you to leverage the full potential of SIMD computation. - **Many Additional Functions:** MaxMath includes a massive library of mathematical functions not found in Unity.Mathematics, with about five times as many highly optimized functions at your disposal. Each function is fully documented with XML annotations. A full list is provided further below. - **Exotic Data Types:** MaxMath introduces data types such as `(U)Int128` (scalar only), 128-bit `quadruple` precision floats (scalar only), and 8-bit `quarter` precision floats (in both scalar and vector forms). Additionally, `Divider` offers highly optimized integer division operations, extending and outperforming specialized libraries like libdivide. - **Written Entirely With Hardware Intrinsics:** MaxMath guarantees optimal performance by utilizing specialized CPU instructions for both ARM and x86 ISAs, while abstracting these complexities away from the user entirely. - **Extends The Burst Compiler:** MaxMath integrates deeply with Unity.Burst and LLVM, leveraging `Unity.Burst.CompilerServices.Constant.IsConstantExpression()` to include code typically only found in optimizing compilers. This functionality allows MaxMath to choose more optimized code paths at compile time, and users can influence this behavior via the optional `Promise` enum parameter available in many functions. - **Easy To Use:** MaxMath is just as easy to use as Unity.Mathematics. It supports features like `implicit` and `explicit` type conversions, making it seamless for you to use if you expect typical C# behavior of primitive types. - **Extensive Test Coverage:** MaxMath is backed by 250,000 lines of unit tests for its 400,000 lines of code, as well as `DEBUG` only runtime checks where appropriate, together ensuring it is _production ready_. # How To Use This Library ![alt text](https://camo.githubusercontent.com/d5c3d640c54517187280e5a64a6d87f0a77a2dcf73914797fc354a730cb5da9e/68747470733a2f2f692e696d6775722e636f6d2f30427072314d6f2e706e67) ## New Types ### Integer

(S)Byte

![alt text](https://camo.githubusercontent.com/7fcfd87ea7ebccaca03884eb5948b9e3cdc57719ac7093545d99a5775fdae263/68747470733a2f2f692e696d6775722e636f6d2f4c77785a6966692e706e67)

(U)Short

![alt text](https://camo.githubusercontent.com/ac1d3423a537677505361209feea869b0cd4d090e52cbcbec9dddad6f11c1230/68747470733a2f2f692e696d6775722e636f6d2f7945356f3352482e706e67)

(U)Int

![alt text](https://camo.githubusercontent.com/6250be15702e20bcb15447392cb24468bf4401def10a86de4622e6852dd367bd/68747470733a2f2f692e696d6775722e636f6d2f584e7a4b3569532e706e67)

(U)Long

![alt text](https://camo.githubusercontent.com/87a38a557dbbbcbfd6a4b1199cf983a7b64e6f1c0a15272d7bc8618370ff1542/68747470733a2f2f692e696d6775722e636f6d2f443057556672552e706e67)

### Floating Point

Float

![alt text](https://camo.githubusercontent.com/fa8a53d5cd8ce6a5f9f8c13df65b5e813a0a55430f25db7ee3e5d44eb3bb2393/68747470733a2f2f692e696d6775722e636f6d2f346c53754566552e706e67)

Half

![alt text](https://camo.githubusercontent.com/8b469b69a95e2331c001db330787049fb049badabafe00e825aa767823993ea2/68747470733a2f2f692e696d6775722e636f6d2f566b306a5143682e706e67)

Quarter (8-bit 1.3.4.-3 IEEE 754 floating point)

![alt text](https://camo.githubusercontent.com/031da7359d3c65a914bd9c2ce442a7830373814b223e51ca810760d50e4d416f/68747470733a2f2f692e696d6775722e636f6d2f7952627950474b2e706e67)

### Random Number Generators

XOR-Shift

![alt text](https://camo.githubusercontent.com/33a2f988961cb5c3f725dca89b651603f5867e7ba4efbda6f2af0895eeb7eecc/68747470733a2f2f692e696d6775722e636f6d2f32745962786b302e706e67)

## New Functions

Miscellaneous

![alt text](https://camo.githubusercontent.com/13df934445ea51aedf21dabea5fca5cabe8469a75233bbc823b4da79f6b5876a/68747470733a2f2f692e696d6775722e636f6d2f41684c4b7641622e706e67)

Arithmetic

![alt text](https://camo.githubusercontent.com/cc45e5fc1a427a5685334029e5aa3d83d53c59f3026008c3852a8ae82252a15f/68747470733a2f2f692e696d6775722e636f6d2f59553264536a352e706e67) ![alt text](https://camo.githubusercontent.com/ee83e0a9977e45ccb83cfb3431844ccafd46a80dfc8d19f9cd67176d35ca36fd/68747470733a2f2f692e696d6775722e636f6d2f723166343456612e706e67) ![alt text](https://camo.githubusercontent.com/75c2421129e8434515db9d9c09e8c48eb034ee4e7851f6e5857d77d8824c03b7/68747470733a2f2f692e696d6775722e636f6d2f4a5562594c364a2e706e67) ![alt text](https://camo.githubusercontent.com/6ed3e65ab9a693cd11b55cd5bc03ed50f762c0d3ac4b8d0e7063de4ad414678c/68747470733a2f2f692e696d6775722e636f6d2f4b4476484331312e706e67) ![alt text](https://camo.githubusercontent.com/4e82debfaaa93e86606a2ba2dfa45d97e7074dbfe9410752eb2d745b985fdfe1/68747470733a2f2f692e696d6775722e636f6d2f576f44617849552e706e67) ![alt text](https://camo.githubusercontent.com/00a3cfe7dbed8772040e9e22eb10d21324859d07b982628bbb3a628fad521c48/68747470733a2f2f692e696d6775722e636f6d2f33584a597571772e706e67)

Bitwise Operations

![alt text](https://camo.githubusercontent.com/58692d5bd72c813840eaa952962c6d62d2add49d245bb9ffc58567d2fc694a2b/68747470733a2f2f692e696d6775722e636f6d2f46446e6a6430462e706e67) ![alt text](https://camo.githubusercontent.com/30a1e3f64fa42750505dedbb04bf5e727be82e363a5571a5f936fd67636977ef/68747470733a2f2f692e696d6775722e636f6d2f7a304d746e55732e706e67) ![alt text](https://camo.githubusercontent.com/059005d6900cb0c6faab93d8fc3d112a704530ace8b5c42dc1d9f6a2283a786d/68747470733a2f2f692e696d6775722e636f6d2f6b6e61433071342e706e67) ![alt text](https://camo.githubusercontent.com/d3f78cc36fd31c7e9e166725ab50faee6e0e946235ebf6afd4e45c9707c0d81c/68747470733a2f2f692e696d6775722e636f6d2f517750354157752e706e67)

Vector Operations

![alt text](https://camo.githubusercontent.com/1f3c055cf535eeba9bff520a93289e1ca1ef241d2773316e4a87f157a2d5d213/68747470733a2f2f692e696d6775722e636f6d2f7547336b3552652e706e67) ![alt text](https://camo.githubusercontent.com/ad8dace8f291ee65c2df1ed105cbe323077dd113b59ff69156391a78d8c62324/68747470733a2f2f692e696d6775722e636f6d2f744749686763722e706e67) ![alt text](https://camo.githubusercontent.com/0d869252083c3d76a49b12322b1036b2f54f47e82a22827c6826466618139721/68747470733a2f2f692e696d6775722e636f6d2f556555766c69692e706e67) ![alt text](https://camo.githubusercontent.com/27effd65ff8380af296391a3afd4b1dad20bdf886d5f4f091774c0563949063e/68747470733a2f2f692e696d6775722e636f6d2f70475537364c752e706e67)

Interpolation and Geometry

![alt text](https://camo.githubusercontent.com/d2d7f998b4455e7aa47503e4a895115a2f8b3e6e6357878d1e9804bcd9f2b3e6/68747470733a2f2f692e696d6775722e636f6d2f53367a665a354f2e706e67) ![alt text](https://camo.githubusercontent.com/cc70826cfd2ccdc59c2b5c834f72fbfcb9b11188cedafa16f449990649486eba/68747470733a2f2f692e696d6775722e636f6d2f367478525151652e706e67) ![alt text](https://camo.githubusercontent.com/7c9920c28b5a7debb018c2b7a518fd7ee59c03a7ac48219b8126721afcccedb3/68747470733a2f2f692e696d6775722e636f6d2f4e3070677070582e706e67)

Type Conversion

![alt text](https://camo.githubusercontent.com/b1697dd7548b12fd651db1e9f0c02081335a795f45cb241c50aa5df0f3707b3b/68747470733a2f2f692e696d6775722e636f6d2f713175457062322e706e67)

# What Kind Of Performance To Expect ![alt text](https://camo.githubusercontent.com/c2b5501205402160985de4babbe0500fdf8f1e8cbb290fded7e53b32346e4ec3/68747470733a2f2f692e696d6775722e636f6d2f426937396e34512e6a7067) ### Highlights - Division and modulo operations of (s)byte and (u)short vectors _by_ _other_ _vectors_ are implemented as either a long division algorithm ((s)byte32, (s)byte16 and (s)byte8 if not compiling for Avx2) or reciprocal multiplication after converting the vectors to float vectors (up to (s)byte8, all (u)short vectors) - it is very fast and, of course, 100% accurate! - This library uses Wojciech Mula's SIMD population count algorithm. You can count the amount of set bits of a contiguous block of memory very efficiently using either the (s)byte32 (Avx2) or (s)byte16 (Ssse3) type ### Notes - It is recommended, just like with Unity.Mathematics, to use vector types that use up an entire SIMD register (128 and 256 bits, respectively). LLVM has a very hard time optimizing code which does not follow this recommendation # How To Install This Library Disclaimer: I firmly believe in open source - being able to copy/modify/understand other people's code is great :) I also want people to be able to step through code with a debugger. For these reasons I usually don't distribute DLLs. - Download the package and unzip it into your "LocalPackages" folder, which is located at the root folder of your Unity project (where your "Assets" folder resides at). - Start up Unity. Usually Unity detects new packages and will generate .meta files for you. - In case that doesn't work, open up the package manager from within Unity and click on the '+' symbol at the upper left corner of the window, further clicking on "Add package from disk..." - "Add package from git URL" should also work. ![alt text](https://camo.githubusercontent.com/e9c0d959d554e43c7c2f48315b712cf51c351d78555695cce434bef640dbc6bd/68747470733a2f2f692e696d6775722e636f6d2f516371463936652e706e67) - Locate the library's "package.json" file - DONE!