A KISS pure Fortran Library to encode/decode, namely to map, multidimensional (integer) indexes into the Morton's index (Z-order)

• MORTIF is a pure Fortran (KISS) library for Morton's ordering;
• MORTIF is Fortran 2003+ standard compliant;
• MORTIF is OOP designed;
• MORTIF is a Free, Open Source Project.

| What is MORTIF? | Main features | Copyrights | Documentation | Install | References |

In mathematical analysis and computer science, Z-order, Morton order, or Morton code is a function which maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by G. M. Morton [1]. The z-value of a point in multidimensions is simply calculated by interleaving the binary representations of its coordinate values, see wikipedia.

Morton's code (Z-order) is a scheme to map multi-dimensional arrays onto to a linear one with a great deal of spatial locality.

MORTIF is a pure Fortran library to encode/decode multidimensional indexes to/from Morton's order. For the implementation details see [2] and [3].

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Here the main features are listed.

• User-friendly methods to encode/decode multidimensional indexes;
• Test Driven Developed (TDD);
• collaborative developed;
• well documented;
• free!

Any feature request is welcome.

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MORTIF is a Free and Open Source Software (FOSS), it is distributed under a very permissive multi-licensing system: selectable licenses are GPLv3, BSD2-Clause, BSD3-Clause and MIT, feel free to select the license that best matches your workflow.

Anyone is interest to use, to develop or to contribute to MORTIF is welcome.

More details can be found on wiki.

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Besides this README file the MORTIF documentation is contained into its own wiki. Detailed documentation of the API is contained into the GitHub Pages that can also be created locally by means of ford tool.

MORTIF is a damn simple library, it exposes only 4 (elemental) procedures:

• morton2D/demorton2D to encode/decode 2D indexes;
• morton3D/demorton3D to encode/decode 3D indexes.

The encoding procedure are function returning the 64 bits Morton's code, while the decoding procedures are subroutine returning 2 or 3 32 bits decoded indexes.

MORTIF assumes that that the Morton's code are stored into a 64 bits integer, thus the following limitations hold for encoding indexes:

• 2D indexes can have at most 32 significant bits, namely you can encode at most 2 2^32-1 indexes;
• 3D indexes can have at most 21 significant bits, namely you can encode at most 3 2^21-1 indexes.

All the procedures accept 32 bits indexes and 64 bits Morton's code, is up to the user to check to not overcome the limit of 2^21-1 for the 3D encoder, no check is performed (for not introduce computational overhead).

Encode a tuple of indexes is a simple as

use, intrinsic :: iso_fortran_env, only : int32
use mortif
print '(A,I20)', "Morton's code of {0,1,0}: ", morton3D(i=0_int32, j=1_int32, k=0_int32)
! output: Morton's code of {0,1,0}: 2

Similarly for 2D encoding.

Decode a Morton's code is a simple as

use, intrinsic :: iso_fortran_env, only : int32, int64
use mortif
integer(int32):: indexes(3) ! Indexes generated by decoding.
call demorton3D(code=2_int32, i=indexes(1), j=indexes(2), k=indexes(3))
print '(A,3(I11,1X))', "Decode indexes of Morton's code {2}: ", indexes
! output: Decode indexes of Morton's code {2}: 0, 1, 0

Similarly for 2D decoding.

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MORTIF is a Fortran library composed by several modules.

Before download and compile the library you must check the requirements.

To download and build the project two main ways are available:

• exploit the install script that can be downloaded here
• manually download and build:
  • download
  • build

MORTIF ships a bash script (downloadable from here) that is able to automatize the download and build steps. The script install.sh has the following usage:

→ ./install.sh
Install script of MORTIF
Usage:

install.sh --help|-?
    Print this usage output and exit

install.sh --download|-d <arg> [--verbose|-v]
    Download the project

    --download|-d [arg]  Download the project, arg=git|wget to download with git or wget respectively
    --verbose|-v         Output verbose mode activation

install.sh --build|-b <arg> [--verbose|-v]
    Build the project

    --build|-b [arg]  Build the project, arg=fobis|make|cmake to build with FoBiS.py, GNU Make or CMake respectively
    --verbose|-v      Output verbose mode activation

Examples:

install.sh --download git
install.sh --build make
install.sh --download wget --build cmake

The script does not cover all possibilities.

The script operation modes are 2 (collapsible into one-single-mode):

• download a new fresh-clone of the latest master-release by means of:
  • git;
  • wget (also curl is necessary);
• build a fresh-clone project as static-linked library by means of:
  • FoBiS.py;
  • GNU Make;
  • CMake;

you can mix any of the above combinations accordingly to the tools available.

Typical usages are:

# download and prepare the project by means of git and build with GNU Make
install.sh --dowload git --build make
# download and prepare the project by means of wget (curl) and build with CMake
install.sh --dowload wget --build cmake
# download and prepare the project by means of git and build with FoBiS.py
install.sh --dowload git --build fobis

To download all the available releases and utilities (fobos, license, readme, etc...), it can be convenient to clone whole the project:

git clone --recursive https://github.com/szaghi/MORTIF
cd MORTIF
git submodule update --init --recursive

Alternatively, you can directly download a release from GitHub server, see the ChangeLog.

The most easy way to compile MORTIF is to use FoBiS.py within the provided fobos file.

Consequently, it is strongly encouraged to install FoBiS.py.

| Build by means of FoBiS | Build by means of GNU Make | Build by means of CMake |

FoBiS.py is a KISS tool for automatic building of modern Fortran projects. Providing very few options, FoBiS.py is able to build almost automatically complex Fortran projects with cumbersome inter-modules dependency. This removes the necessity to write complex makefile. Moreover, providing a very simple options file (in the FoBiS.py nomenclature indicated as fobos file) FoBiS.py can substitute the (ab)use of makefile for other project stuffs (build documentations, make project archive, etc...). MORTIF is shipped with a fobos file that can build the library in both static and shared forms and also build the Test_Driver program. The provided fobos file has several building modes.

Typing:

FoBiS.py build -lmodes

the following message should be printed:

The fobos file defines the following modes:
 - "shared-gnu"
  - "static-gnu"
  - "test-driver-gnu"
  - "shared-gnu-debug"
  - "static-gnu-debug"
  - "test-driver-gnu-debug"
  - "shared-intel"
  - "static-intel"
  - "test-driver-intel"
  - "shared-intel-debug"
  - "static-intel-debug"
  - "test-driver-intel-debug"

The modes should be self-explicative: shared, static and test-driver are the modes for building (in release, optimized form) the shared and static versions of the library and the Test Driver program, respectively. The other 3 modes are the same, but in debug form instead of release one. -gnu use the GNU gfortran compiler while -intel the Intel one.

The shared or static directories are created accordingly to the form of the library built. The compiled objects and mod files are placed inside this directory, as well as the linked library.

FoBiS.py build -mode shared-gnu

FoBiS.py build -mode static-gnu

FoBiS.py build -mode shared-gnu-debug

FoBiS.py build -mode static-gnu-debug

The Test_Driver directory is created. The compiled objects and mod files are placed inside this directory, as well as the linked program.

FoBiS.py build -mode test-driver-gnu

FoBiS.py build -mode test-driver-gnu-debug

Typing:

FoBiS.py rule -ls

the following message should be printed:

The fobos file defines the following rules:
  - "makedoc" Rule for building documentation from source files
       Command => rm -rf doc/html/*
       Command => ford doc/main_page.md
       Command => cp -r doc/html/publish/* doc/html/
  - "deldoc" Rule for deleting documentation
       Command => rm -rf doc/html/*
  - "maketar" Rule for making tar archive of the project
       Command => tar -czf MORTIF.tar.gz *
  - "makecoverage" Rule for performing coverage analysis
       Command => FoBiS.py clean -mode test-driver-gnu
       Command => FoBiS.py build -mode test-driver-gnu -coverage
       Command => ./Test_Driver/Test_Driver
       Command => ./Test_Driver/Test_Driver -v
       Command => ./Test_Driver/Test_Driver -s 'Hello MORTIF' -i 2
       Command => ./Test_Driver/Test_Driver 33.0 -s 'Hello MORTIF' --integer_list 10 -3 87 -i 3 -r 64.123d0  --boolean --boolean_val .false.
  - "coverage-analysis" Rule for performing coverage analysis and saving reports in markdown
       Command => FoBiS.py clean -mode test-driver-gnu
       Command => FoBiS.py build -mode test-driver-gnu -coverage
       Command => ./Test_Driver/Test_Driver
       Command => ./Test_Driver/Test_Driver -v
       Command => ./Test_Driver/Test_Driver -s 'Hello MORTIF' -i 2
       Command => ./Test_Driver/Test_Driver 33.0 -s 'Hello MORTIF' --integer_list 10 -3 87 -i 3 -r 64.123d0  --boolean --boolean_val .false.
       Command => gcov -o Test_Driver/obj/ src/*
       Command => FoBiS.py rule -gcov_analyzer wiki/ Coverage-Analysis
       Command => rm -f *.gcov

The rules should be self-explicative.

Bad choice :-)

However, a makefile (generated by FoBiS.py...) to be used with a compatible GNU Make tool is provided.

It is convenient to clone the whole MORTIF repository and run a standard make:

git clone --recursive https://github.com/szaghi/MORTIF
cd MORTIF
make -j 1

This commands build all tests (executables are in exe/ directory). To build only the library (statically linked) type:

git clone --recursive https://github.com/szaghi/MORTIF
cd MORTIF
make -j 1 STATIC=yes

Bad choice :-)

However, a CMake setup (kindly developed by victorsndvg) is provided.

It is convenient to clone the whole MORTIF repository and run a standard CMake configure/build commands:

git clone --recursive https://github.com/szaghi/MORTIF $YOUR_MORTIF_PATH
mkdir build
cd build
cmake $YOUR_MORTIF_PATH
cmake --build .

If you want to run the tests suite type:

git clone --recursive https://github.com/szaghi/MORTIF $YOUR_MORTIF_PATH
mkdir build
cd build
cmake -DMORTIF_ENABLE_TESTS=ON $YOUR_MORTIF_PATH
cmake --build .
ctest

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[1] A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing, Morton G.M., technical report, IBM, 1966.

[2] On Spatial Orders and Location Codes, Stocco, LJ and Schrack, G, IEEE Transaction on Computers, vol 58, n 3, March 2009.

[3] Out-of-Core Construction of Sparse Voxel Octrees, J. Baert, A. Lagae and Ph. Dutré, Proceedings of the Fifth ACM SIGGRAPH/Eurographics conference on High-Performance Graphics, 2013.

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