MORTIFMorton Indexer (Z-order)

A pure Fortran 2003+ library to encode and decode multidimensional integer indexes into Morton's Z-order.

Guide

API Reference

View on GitHub

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2D Encoding & Decoding

Map a pair of 32-bit integer indexes to a single 64-bit Morton code and back with morton2D / demorton2D.

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3D Encoding & Decoding

Map three integer indexes to a 64-bit Morton code with morton3D / demorton3D. Supports up to 21 significant bits per axis.

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Elemental Procedures

All four public procedures are elemental — apply them to scalars or entire arrays with no extra code.

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Multi Build System

Build with FoBiS.py, GNU Make, or CMake. A fobos file covers all modes for GNU gfortran and Intel Fortran.

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Pure Fortran / TDD

No C extensions, no external dependencies beyond PENF. Developed test-first with a correctness test suite.

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Free & Open Source

Multi-licensed — GPLv3 for FOSS projects, BSD 2/3-Clause or MIT for commercial use. Fortran 2003+ standard compliant.

Quick start

Encode a 3D index tuple and decode it back:

fortran

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

integer(int32) :: i, j, k
integer(int64) :: code

! Encode
code = morton3D(i=1_int32, j=2_int32, k=3_int32)
print '(A,I20)', "Morton code of {1,2,3}: ", code

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

fortran

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

integer(int64) :: code

! 2D example
code = morton2D(i=0_int32, j=1_int32)
print '(A,I20)', "Morton code of {0,1}: ", code   ! 2

Authors

Stefano Zaghi — @szaghi

Contributions are welcome — see the Contributing page.

Copyrights

MORTIF is distributed under a multi-licensing system:

Use case	License
FOSS projects	GPL v3
Closed source / commercial	BSD 2-Clause
Closed source / commercial	BSD 3-Clause
Closed source / commercial	MIT

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