Faster hilbert.Encode and hilbert.Decode

[matthinrichsen-wf]

Description

Encode/Decode can be improved.

This PR makes the following changes:

• all divisions which are powers of two converted to bit shift
• removes pointer dereferencing
• prefers bitwise operators where we can

Results:

goos: darwin
goarch: arm64
pkg: github.com/Workiva/go-datastructures/numerics/hilbert
cpu: Apple M1 Max
          │  master.txt  │               pr4.txt               │
          │    sec/op    │   sec/op     vs base                │
Encode-10    78.71n ± 0%   50.64n ± 0%  -35.66% (p=0.000 n=30)
Decode-10   131.80n ± 1%   37.30n ± 0%  -71.70% (p=0.000 n=30)
geomean      101.9n        43.46n       -57.33%

          │  master.txt  │               pr4.txt               │
          │     B/op     │    B/op     vs base                 │
Encode-10   0.000 ± 0%     0.000 ± 0%       ~ (p=1.000 n=30) ¹
Decode-10   0.000 ± 0%     0.000 ± 0%       ~ (p=1.000 n=30) ¹
geomean                ²               +0.00%                ²
¹ all samples are equal
² summaries must be >0 to compute geomean

          │  master.txt  │               pr4.txt               │
          │  allocs/op   │ allocs/op   vs base                 │
Encode-10   0.000 ± 0%     0.000 ± 0%       ~ (p=1.000 n=30) ¹
Decode-10   0.000 ± 0%     0.000 ± 0%       ~ (p=1.000 n=30) ¹
geomean                ²               +0.00%                ²
¹ all samples are equal
² summaries must be >0 to compute geomean

[simeonsteward-wk]

🌵

Suggested change

	func rotate(n, rx, ry int32, x, y int32) (int32, int32) {
	func rotate(n, rx, ry, x, y int32) (int32, int32) {

[joshprzybyszewski-wf]

🔮 I don't know definitively, but aren't rx and ry only ever zero or one? Aren't they essentially bools? Isn't it always true that rx != ry? I'm not sure. But if so, would a

if rx {
	x += int32(s)
} else {
	y += int32(s)
}

be faster than a multiplication?

Or maybe they're not mutually exclusive: is a bool check still faster than a mult?

if rx {
	x += int32(s)
}
if ry {
	y += int32(s)
}

[joshprzybyszewski-wf]

📖 There's a lot magic bitwise stuff happening in this file (there was before!). Especially since this is OSS, perhaps we could add comments to the code describing the intent of what's happening (and why we're doing it the obscure way, not the clear way).

[joshprzybyszewski-wf]

🌵 I wonder what the impact is to cast n to int64 on every iteration. Could we just have a sister const at the top of the file?

const (
	n = int32(1 << 31)
	n_64 = int64(n)
)