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Faster hilbert.Encode and hilbert.Decode #234

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49c601c
Hilbert encode/decode 35% and 53% faster respectively
matthinrichsen-wf Oct 17, 2025
9971cb5
Decode is now 65% faster
matthinrichsen-wf Oct 17, 2025
5b37112
Minor improvement to Encode and Decode now 71.7% faster
matthinrichsen-wf Oct 17, 2025
150f628
Updates the benchmark comment
matthinrichsen-wf Oct 17, 2025
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29 changes: 14 additions & 15 deletions numerics/hilbert/hilbert.go
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Original file line number Diff line number Diff line change
Expand Up @@ -26,8 +26,8 @@ This expects coordinates in the range [0, 0] to [MaxInt32, MaxInt32].
Using negative values for x and y will have undefinied behavior.

Benchmarks:
BenchmarkEncode-8 10000000 181 ns/op
BenchmarkDecode-8 10000000 191 ns/op
BenchmarkEncode-10 23791095 50.66 ns/op
BenchmarkDecode-10 32430058 36.99 ns/op
*/
package hilbert

Expand All @@ -44,29 +44,28 @@ func boolToInt(value bool) int32 {
return int32(0)
}

func rotate(n, rx, ry int32, x, y *int32) {
func rotate(n, rx, ry int32, x, y int32) (int32, int32) {
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@simeonsteward-wk simeonsteward-wk Oct 17, 2025

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🌵

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

if ry == 0 {
if rx == 1 {
*x = n - 1 - *x
*y = n - 1 - *y
x = n - 1 - x
y = n - 1 - y
}

t := *x
*x = *y
*y = t
x, y = y, x
}
return x, y
}

// Encode will encode the provided x and y coordinates into a Hilbert
// distance.
func Encode(x, y int32) int64 {
var rx, ry int32
var d int64
for s := int32(n / 2); s > 0; s /= 2 {
for s := int32(n >> 1); s > 0; s >>= 1 {
rx = boolToInt(x&s > 0)
ry = boolToInt(y&s > 0)
d += int64(int64(s) * int64(s) * int64(((3 * rx) ^ ry)))
rotate(s, rx, ry, &x, &y)
d += int64(int64(s) * int64(s) * int64(rx<<1|(rx^ry)))
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@joshprzybyszewski-wf joshprzybyszewski-wf Oct 17, 2025

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📖 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).

x, y = rotate(s, rx, ry, x, y)
}

return d
Expand All @@ -79,13 +78,13 @@ func Decode(h int64) (int32, int32) {
var x, y int32
t := h

for s := int64(1); s < int64(n); s *= 2 {
rx = 1 & (t / 2)
for s := int64(1); s < int64(n); s <<= 1 {
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@joshprzybyszewski-wf joshprzybyszewski-wf Oct 17, 2025

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🌵 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)
)

rx = 1 & (t >> 1)
ry = 1 & (t ^ rx)
rotate(int32(s), int32(rx), int32(ry), &x, &y)
x, y = rotate(int32(s), int32(rx), int32(ry), x, y)
x += int32(s * rx)
y += int32(s * ry)
Comment on lines 85 to 86
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@joshprzybyszewski-wf joshprzybyszewski-wf Oct 17, 2025 •
edited
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🔮 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)
}

t /= 4
t >>= 2
}

return x, y
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