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https://github.com/13rac1/fastmath
Golang 8/16 bit math functions for when speed matters more than precision
https://github.com/13rac1/fastmath
fastled fastled-library go golang golang-library math tinygo wasm webassembly
Last synced: 2 months ago
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Golang 8/16 bit math functions for when speed matters more than precision
- Host: GitHub
- URL: https://github.com/13rac1/fastmath
- Owner: 13rac1
- License: mit
- Created: 2019-08-08T07:52:29.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2021-03-06T21:40:53.000Z (almost 4 years ago)
- Last Synced: 2024-08-03T23:27:34.173Z (4 months ago)
- Topics: fastled, fastled-library, go, golang, golang-library, math, tinygo, wasm, webassembly
- Language: Go
- Homepage: https://pkg.go.dev/github.com/13rac1/fastmath
- Size: 16.6 KB
- Stars: 13
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-golang-repositories - fastmath
README
# FastMath for Go
> "I can make things very fast if they don’t have to be correct." — Russ Cox
8 and 16 bit math functions for when speed matters more than precision.
Potential use cases include LED displays, 2D/3D graphics, and games.
* Designed for use with [TinyGo][tinygo] and/or [WebAssembly][go-wasm].
* Based on the [FastLED][fastled] [lib8tion][lib8ation-src] library.
[tinygo]:https://tinygo.org/
[go-wasm]:https://github.com/golang/go/wiki/WebAssembly
[fastled]:http://fastled.io/
[lib8ation-src]:https://raw.githubusercontent.com/FastLED/FastLED/dcbf3993/lib8tion/trig8.h
## Functions
* `Sin8()` / `Sin16()`
* `Cos8()` / `Cos16()`
* `Random8()` / `Random16()`
* `Random8Limit()` / `Random16Limit()`
* `Random8Range()` / `Random16Range()`
* `Random16SetSeed()` / `Random16GetSeed()` / `Random16AddEntropy()`
* `Scale8()` / `Scale8Video()`
* `NScale8x3()` / `NScale8x3Video()` - Scale three 8 bit integers at the same time.
* `Scale16()` / `Scale16By8()`
* `QAdd8()` / `QSub8()` / `QMul8()` - Saturating non-overflowing math functions.
* `Abs8()`
* `Sqrt16()`
Note: Functionality already well handled by the Go runtime has not be re-implemented.
## Approximation Error
Computer-based math functions have an error delta verses the pure mathematical
results. The Golang Standard Library's math functions are precise up to 64 bit
floats. The math functions provided by this library sacrifice additional
precision for speed by working with small integers.
* `Sin8()` - Max Error: 1.63%, Average Error: 0.78%
* `Sin16()` - Max Error: 0.34%, Average Error: 0.19%
## Benchmarks
Run on a Intel(R) Core(TM) i7-7600U CPU @ 2.80GHz.
```bash
BenchmarkStdLibFallbackSqrt-4 20000000 50.7 ns/op
BenchmarkStdLibDefaultSqrt-4 2000000000 0.30 ns/op
BenchmarkSqrt16-4 200000000 9.12 ns/op
BenchmarkStdLibRandom8-4 50000000 25.6 ns/op
BenchmarkRandom8-4 1000000000 2.12 ns/op
BenchmarkStdLibSin8-4 50000000 20.8 ns/op
BenchmarkSin8-4 300000000 4.07 ns/op
BenchmarkStdLibSin16-4 50000000 20.0 ns/op
BenchmarkSin16-4 2000000000 0.94 ns/op
```
`Random8()`, `Sin8()` and `Sin16()` are significantly faster than using the
equivalent Go Standard Library's Math package functions.
`Sqrt16()` is compared against both the default compiled `math.Sqrt()` and a
copy of the fallback Standard Library `sqrt()` function. The default version is
optimized by the Go compiler into a single instruction on the AMD64
architecture, so the fallback version is used for a fair comparison.
## TODO
* Should `Sin8()` be a lookup table? Why is it 4ns/op vs `Sin16()`@0.9ns/op?
* Add ARM assembly implementations from upstream, benchmark difference.
## License
Licensed MIT
© 2019 Brad Erickson
Based on FastLED MIT-licensed code:
© 2013 FastLED
Parts of test-only BSD code:
© 2009 The Go Authors