Features

Encoding

• Encode a pair of 32-bit integer indexes into a single 64-bit Morton code with morton2D
• Encode three 32-bit integer indexes into a single 64-bit Morton code with morton3D
• Optional b parameter to restrict the encoding to 2, 4, 8, 16, or 32 significant bits per axis
• Returns a standard integer(int64) Morton code — no custom types required

Decoding

• Decode a 64-bit Morton code back into two 32-bit indexes with demorton2D
• Decode a 64-bit Morton code back into three 32-bit indexes with demorton3D
• Fully symmetric with encoding — demorton* are the exact inverse of morton*

Elemental Interface

All four public procedures are declared elemental. This means they work on:

• Scalars (integer(int32) arguments)
• Conformable arrays with no extra code — pass arrays of indexes, receive arrays of codes

use mortif
use, intrinsic :: iso_fortran_env, only : int32, int64

integer(int32) :: ix(4) = [0, 1, 2, 3]
integer(int32) :: iy(4) = [0, 0, 1, 1]
integer(int64) :: codes(4)

! Encode an entire array of 2D points at once
codes = morton2D(i=ix, j=iy)

Encoding Limitations

Because Morton codes are stored in a 64-bit integer, the following bit limits apply:

Dimension	Max significant bits per axis	Max index value
2D	32	2³² − 1 ≈ 4.3 × 10⁹
3D	21	2²¹ − 1 = 2 097 151

WARNING

No range check is performed at runtime to avoid computational overhead. It is the caller's responsibility to stay within the 21-bit limit for 3D indexes.

Compiler Support

Compiler	Status
GNU gfortran ≥ 6.1	Supported
Intel Fortran ≥ 16.x	Supported
IBM XL Fortran	Not tested
g95	Not tested
NAG Fortran	Not tested
PGI / NVIDIA	Not tested

Design Principles

• Pure Fortran — no C extensions, no system calls, no external libraries beyond PENF
• Elemental — all procedures are declared elemental, enabling array-at-a-time use
• KISS — the entire library is a single 194-line Fortran module
• TDD — developed test-first; correctness tests cover encoding and round-trip decoding
• Free & Open Source — multi-licensed for both FOSS and commercial use