tile_id: more improvements

cpp/pmtiles.hpp

@@ -323,7 +323,7 @@ uint64_t decode_varint(const char **data, const char *end) {
 
 void rotate(int64_t n, int64_t &x, int64_t &y, int64_t rx, int64_t ry) {
 	if (ry == 0) {
-		if (rx == 1) {
+		if (rx != 0) {
 			x = n - 1 - x;
 			y = n - 1 - y;
 		}
@@ -404,13 +404,13 @@ inline zxy tileid_to_zxy(uint64_t tileid) {
 	uint64_t pos = tileid - acc;
 	int64_t x = 0, y = 0;
 	for (uint8_t a = 0; a < z; a++) {
-        uint64_t rx = (pos / 2) & 1;
-        uint64_t ry = (pos ^ rx) & 1;
         uint64_t s = 1 << a;
+        uint64_t rx = s & (pos / 2);
+        uint64_t ry = s & (pos ^ rx);
 		rotate(s, x, y, rx, ry);
-        pos /= 4;
-        x += s * rx;
-        y += s * ry;
+        pos >>= 1;
+        x += rx;
+        y += ry;
 	}
 	return zxy(z, static_cast<int>(x), static_cast<int>(y));
 }
@@ -424,12 +424,13 @@ inline uint64_t zxy_to_tileid(uint8_t z, uint32_t x, uint32_t y) {
 	}
 	uint64_t acc = ((1LL << (z * 2U)) - 1) / 3;
 	int64_t tx = x, ty = y;
-	for (int32_t a = z - 1; a >= 0; a--) {
-		int64_t rx = (tx >> a) & 1;
-		int64_t ry = (ty >> a) & 1;
-		int64_t s = 1LL << a;
+	int a = z - 1;
+	for (int64_t s = 1LL << a; s > 0; s >>= 1) {
+		int64_t rx = s & tx;
+		int64_t ry = s & ty;
 		rotate(s, tx, ty, rx, ry);
-		acc += s * s * ((3 * rx) ^ ry);
+		acc += ((3 * rx) ^ ry) << a;
+		a--;
 	}
 	return acc;
 }

js/src/index.ts

@@ -62,17 +62,16 @@ function rotate(
   rx: number,
   ry: number
 ): [number, number] {
-  let [tx, ty] = [x, y];
   if (ry === 0) {
-    if (rx === 1) {
-      tx = n - 1 - tx;
-      ty = n - 1 - ty;
+    if (rx !== 0) {
+      x = n - 1 - x;
+      y = n - 1 - y;
     }
-    const t = tx;
-    tx = ty;
-    tx = t;
+    const t = x;
+    x = y;
+    y = t;
   }
-  return [tx, ty];
+  return [x, y];
 }
 
 /**
@@ -82,40 +81,50 @@ export function zxyToTileId(z: number, x: number, y: number): number {
   if (z > 26) {
     throw new Error("Tile zoom level exceeds max safe number limit (26)");
   }
-  if (x > 2 ** z - 1 || y > 2 ** z - 1) {
+  if (x >= 1 << z || y >= 1 << z) {
     throw new Error("tile x/y outside zoom level bounds");
   }
-  let [tx, ty] = [x, y];
-  let acc = (4 ** z - 1) / 3;
-  for (let a = z - 1; a >= 0; a--) {
-    const rx = (tx >> a) & 1;
-    const ry = (ty >> a) & 1;
-    const s = 2 ** a;
-    [tx, ty] = rotate(s, tx, ty, rx, ry);
-    acc += s * s * ((3 * rx) ^ ry);
+  let acc = ((1 << z) * (1 << z) - 1) / 3;
+  let a = z - 1;
+  for (let s = 1 << a; s > 0; s >>= 1) {
+    const rx = x & s;
+    const ry = y & s;
+    acc += ((3 * rx) ^ ry) * (1 << a);
+    [x, y] = rotate(s, x, y, rx, ry);
+    a--;
   }
   return acc;
 }
 
+function tileIdToZ(i: number): number {
+  let c = 3 * i + 1;
+  if (c < 0x100000000) {
+    return 31 - Math.clz32(c);
+  } else {
+    return 63 - Math.clz32(c / 0x100000000);
+  }
+}
+
 /**
  * Convert a Hilbert TileID to Z,X,Y.
  */
 export function tileIdToZxy(i: number): [number, number, number] {
-  const z = Math.floor(Math.log2(3 * i + 1)) >> 1;
+  const z = tileIdToZ(i) >> 1;
   if (z > 26)
     throw new Error("Tile zoom level exceeds max safe number limit (26)");
-  const acc = (4 ** z - 1) / 3;
-  let pos = i - acc;
+  const acc = ((1 << z) * (1 << z) - 1) / 3;
+
+  let t = i - acc;
   let x = 0;
   let y = 0;
-  for (let a = 0; a < z; a++) {
-    const rx = (pos >> 1) & 1;
-    const ry = (pos ^ rx) & 1;
-    const s = 2 ** a;
+  let n = 1 << z;
+  for (let s = 1; s < n; s <<= 1) {
+    const rx = s & (t / 2);
+    const ry = s & (t ^ rx);
     [x, y] = rotate(s, x, y, rx, ry);
-    pos = Math.floor(pos / 4);
-    x += s * rx;
-    y += s * ry;
+    t = t / 2;
+    x += rx;
+    y += ry;
   }
   return [z, x, y];
 }

python/pmtiles/tile.py

@@ -18,7 +18,7 @@ def __str__(self):
 
 def rotate(n, x, y, rx, ry):
     if ry == 0:
-        if rx == 1:
+        if rx != 0:
             x = n - 1 - x
             y = n - 1 - y
         x, y = y, x
@@ -32,12 +32,14 @@ def zxy_to_tileid(z, x, y):
         raise ValueError("tile x/y outside zoom level bounds")
 
     acc = ((1 << (z * 2)) - 1) // 3
-    for a in reversed(range(0, z)):
-        rx = (x >> a) & 1
-        ry = (y >> a) & 1
+    a = z - 1
+    while a >= 0:
         s = 1 << a
+        rx = s & x
+        ry = s & y
+        acc += ((3 * rx) ^ ry) << a
         (x, y) = rotate(s, x, y, rx, ry)
-        acc += s * s * ((3 * rx) ^ ry)
+        a -= 1
     return acc
 
 
@@ -49,14 +51,16 @@ def tileid_to_zxy(tile_id):
     pos = tile_id - acc
     x = 0
     y = 0
-    for a in range(0, z):
-        rx = (pos // 2) & 1
-        ry = (pos ^ rx) & 1
-        s = 1 << a
+    s = 1
+    n = 1 << z
+    while s < n:
+        rx = (pos // 2) & s
+        ry = (pos ^ rx) & s
         (x, y) = rotate(s, x, y, rx, ry)
-        pos //= 4
-        x += s * rx
-        y += s * ry
+        x += rx
+        y += ry
+        pos >>= 1
+        s <<= 1
     return (z, x, y)