Morton Code Decoder

It supports the complete 64-bit Morton range, so each decoded coordinate may use all 32 unsigned bits. The operation is exact, deterministic, and useful when inspecting spatial indexes, debugging encoders, reading compact tile identifiers, or verifying database and graphics code without writing a one-off bit manipulation script.

How Morton decoding recovers two coordinates

A two-dimensional Morton code stores two coordinate bit streams inside one integer. Starting at the least significant end, bit position zero belongs to x, bit position one belongs to y, position two returns to x, and the pattern continues. Decoding therefore does not approximate, divide, or infer a location. It extracts every even-positioned bit into the corresponding position of x and every odd-positioned bit into y. For example, a coordinate bit found at Morton position six becomes bit three of x, while a bit at position seven becomes bit three of y. This capability applies that rule across all 64 available code bits, producing two unsigned 32-bit coordinates. The returned code is also normalized as a decimal string, which makes leading-zero inputs unambiguous and preserves the exact original numeric value. This convention is the common two-dimensional layout in which x occupies even bit positions. If an upstream system interleaves y first instead, swap the two returned coordinates or adjust that encoder's convention before comparing results.

Entering large codes without losing precision

Send the Morton index in the code field as an unsigned base-ten integer string, such as "39" or "18446744073709551615". A string is important for large values because ordinary JSON numbers and JavaScript numbers cannot exactly represent every integer across the full unsigned 64-bit range. The decoder parses the string with exact integer arithmetic and never converts the combined Morton code to a floating-point number. Signs, decimal points, exponential notation, whitespace, commas, hexadecimal prefixes, and values above 2^64 minus one are rejected instead of being silently rounded or reinterpreted. Small safe integer values are accepted defensively by the implementation, but the published contract uses a string so the same request remains exact in every SDK and transport. The resulting x and y values never exceed 4,294,967,295, which is within the exact integer range of JSON numbers, so coordinates are returned as convenient numeric fields. A code of zero decodes to x zero and y zero, and the maximum 64-bit code decodes to the maximum value on both axes.

Using the result to test spatial systems

Morton ordering appears in spatial databases, quadtrees, tile stores, voxel and texture layouts, cache-friendly arrays, and graphics pipelines. During debugging, decode a suspicious index and compare the returned point with the coordinate pair that entered your encoder. A correct round trip should reproduce both coordinates exactly under the same x-first bit convention. Boundary tests are especially valuable: try zero, values where only one Morton bit is set, coordinate powers of two, and the maximum supported code. Single-bit cases reveal swapped axes or off-by-one shifts immediately because only one output bit should appear. This decoder deliberately returns coordinates rather than geographic longitude and latitude; Morton coding is a bit layout and does not define a projection, scale, signed-number representation, or coordinate reference system. If your application offsets signed coordinates, quantizes floating-point positions, or projects geographic locations before encoding, reverse those application-specific steps after decoding. The API performs one bounded pass with no network access, randomness, stored state, or hidden platform-dependent integer operations, making it suitable for repeatable tests and automated validation.