MORTon Indexer (Z-order) Fortran environment — a pure Fortran 2003+ library to encode and decode multidimensional integer indexes into Morton's Z-order.

• Encode two 32-bit indexes into a 64-bit Morton code with morton2D
• Encode three 32-bit indexes into a 64-bit Morton code with morton3D (up to 21 significant bits per axis)
• Decode Morton codes back to indexes with demorton2D / demorton3D
• All four procedures are elemental — apply directly to scalars or arrays
• Pure Fortran, no C extensions, single 194-line module

Documentation | API Reference

• Stefano Zaghi — @szaghi

Contributions are welcome — see the Contributing page.

This project is distributed under a multi-licensing system:

• FOSS projects: GPL v3
• Closed source / commercial: BSD 2-Clause, BSD 3-Clause, or MIT

Anyone interested in using, developing, or contributing to this project is welcome — pick the license that best fits your needs.

Encode a 3D index tuple and decode it back:

use, intrinsic :: iso_fortran_env, only : int32, int64
use mortif
implicit none
integer(int32) :: i, j, k
integer(int64) :: code

code = morton3D(i=0_int32, j=1_int32, k=0_int32)
print '(A,I20)', "Morton code of {0,1,0}: ", code   ! 2

call demorton3D(code=code, i=i, j=j, k=k)
print '(A,3(I0,1X))', "Decoded: ", i, j, k          ! 0 1 0

Elemental use on arrays:

use, intrinsic :: iso_fortran_env, only : int32, int64
use mortif
implicit none
integer(int32) :: ix(4) = [0, 1, 2, 3]
integer(int32) :: iy(4) = [0, 0, 1, 1]
integer(int64) :: codes(4)

codes = morton2D(i=ix, j=iy)   ! [0, 1, 4, 5]

git clone https://github.com/szaghi/MORTIF --recursive
cd MORTIF
FoBiS.py build -mode tests-gnu
./scripts/run_tests.sh

mkdir build && cd build
cmake -DMORTIF_ENABLE_TESTS=ON ..
cmake --build . && ctest