Fast Hilbert

Fast Hilbert 2D curve computation using an efficient Lookup Table (LUT) and only considering the lowest order for a given input.

• Convert from discrete 2D space to 1D hilbert space and reverse
• Generalized for different unsigned integer input types (thanks DoubleHyphen PR#3)
• Speedup via lowest order computation (thanks DoubleHyphen PR#2)
• Very fast using an efficient 512 Byte LUT
• Only one additional dependency

Benchmarking the conversion from full 256x256 discrete 2D space to the 1D hilbert space, shows that fast_hilbert is about 12 times faster compared to the fastest 2D hilbert transformation libs written in rust. Benchmarked on a Intel i5-6400 CPU @ 2.70 GHz, 4 Cores with 8 GB RAM:

| Library | Time | Description | ------------------------------------------------------- |------------:| ----------------- | | fasthilbert | 0.2 ms | Optimized for fast computation in 2D discrete space using an efficient *LUT* | hilbert2d | 2.5 ms | Also allows other variants such as Moore and LIU | | hilbert_curve| 2.0 ms | Implements algorithm described on Wikipedia | | hilbert | 32.1 ms | Allows computation of higher dimensional Hilbert curves |

Especially for higher orders fast_hilbert outperforms other libraries by using only the next lowest relevant order instead of computing the hilbert curve bit per bit for the given input. See PR #2 and #9 for more details.

For example the computation of xy2h(1, 2, 64) is very fast to compute using fast_hilbert compared to a higher x,y pair such as xy2h(u32::MAX-1, u32::MAX-2, 64):

| Library | x=1, y=2, order=64 | x=u32::MAX-1, y=u32::MAX-2, order=64 | ----------------- | ------------------: | --------------------------------------: | | fasthilbert | 4 ns | 29 ns | | hilbert2d | 73 ns | 72 ns | | hilbert_curve | 67 ns | 49 ns | | hilbert | 690 ns | 680 ns |