The engine of Nissy, including the H48 optimal solver

Warning: this library is work in progress, breaking changes can happen without notice.

This repository contains the core functionality for future versions of nissy.

H48 is an experimental Rubik’s cube solver. It is heavily inspired by nxopt and vcube, but it uses a different set of pruning tables that were developed independently.

Building

This project is mainly developed on UNIX systems (Linux, MacOS, BSD…), but it is also possible to build it on Windows, with some limitations.

UNIX (Linux, MaxOS, BSD…)

To build nissy simply run

$ ./build.sh

For a list of options and targets for the build system run ./build.sh help. Some compiler settings can be overridden using environment variables, as explained in the comments at the beginning of the build script. For example, the command:

$ export NISSY_BUILD_THREADS=3
$ CC=gcc ./build.sh

is going to configure nissy to use at most 3 threads, and build it with gcc. Se the comments in ./build.sh for more details.

Windows

It is possible to build this project on Windows using build.bat. The Clang compiler must be installed, and the command prompt must be correctly configured to run it.

We suggest installing Clang via the Visual Studio Istaller, selecting the “C++ development” pack, as well as the “clang” and “Windows SDK 11” components. It is advised to use “x64 Native Tools Command Prompt for VS 2022” instead of a regular command prompt to run the build script.

The build.bat script has the same syntax as the build.sh script, but not all options are available. For example

> build.bat shell

can be used to build the basic shell, while

> build.bat test

Builds and runs the unit tests. See build.bat help for a list of all available options.

Not: At the moment certain optimizations, such as multithreading and advanced CPU instructions, are not supported on Windows. Work is ongoing to improve Windows support.

Running tests

This project includes a suite of “unit” test. You can run them with:

$ ./build.sh test

For running the tests for the WebAssembly build with nodejs you can use:

$ ./build.sh webtest

To run only a subset of the tests, you can pass as argument a regular expression that matches only the name of the tests you want to run:

$ ./buld test coord

Each subfolder of the test folder contains a test. A test can consist of multiple test cases (.in files). Running a test means compiling and running the corresponding test against each test case. When a test case is run, the .in file is read a the output of the program is compared to the corresponding .out filei using diff(1). If the two differ, the difference is printed out and no other test is run.

The results of the last test case run is saved in test/last.out (standard output, the results compared with the .out files) and test/last.err (standard error).

Tests are always run in debug mode: this means that optimizations are disabled and some extra logging is enabled.

More comprehensive tests (integration tests) can be performed with tools.

Running “tools”

In the tools folder there are some small programs that test various functionality of the H48 library. They work similarly to test, but they are not run in debug mode by default.

To run a tool you can use:

$ ./build.sh tool TOOLNAME PARAMETERS...

Where TOOLNAME is the name of one of the tools, or a regular expression that matches one, and PARAMETERS... is a tool-specific list of parameters.

For example:

$ :./build.sh tool gendata h48h2k2

Will run a tool that generates the data table for the H48 solver with parameters h=2 and `k=2.

Each tool run is automatically timed, so these tools can be used as benchmark. The output as well as the time of the run are saved to a file in the tools/results folder.

To build and run a tool in debug mode, use ./build.sh -d tool.

The solvetest tools

The tools denoted with solvetest can be used to test that the various solvers produce the correct solutions. They can be run individually as all other tools, or all together with

$ ./build.sh solvetest   # Use -d for debug mode (very slow for some solvers)

If one of the solvetests fails, subsequent tests are going to be skipped.

Command-line interface

The shell folder contains the code for a rudimentary shell that can be used to run commands manually. The user experience in not amazing, as the commands require quite verbose options.

To build the shell run:

$ ./build.sh shell

This will create an executable called run. Then you can for example get a cube from a sequence of moves:

$ ./run frommoves -moves "R' U' F"
JLQWSVUH=ZLCUABGIVTKH=A

The cube format is meant to be easy to copy-paste and read for the software, but not necessarily intuitive for the user. See below for a detaileed description.

You can also get a random cube

$ ./run randomcube
WDSQREVX=VBKYDUCJXWAb=A

To solve a cube you can use:

$ ./run solve -solver h48h0k4 -n 1 -M 4 -cube "JLQWSVUH=ZLCUABGIVTKH=A"
F' U' R

Or alternatively:

$ ./run solve_scramble -solver h48h0k4 -n 1 -M 4 -moves "R' U' F"
F' U' R

For a full list of available command, use ./run help.

Using this software as a library

This tool has been developed as a library, so it can be easily included in other programs. For this reason, some bindings for languages other than C are available.

The API is documented in the public header file src/nissy.h.

C

To use this in a C project, simly include src/nissy.h. The tools in the tools/ folder are a good example for how to use this.

NOTE: this project is developed using the C11 standard. If you are using an older version of C, you can write your own header file.

C++

The cpp folder contains a C++ header nissy.h (C++20 standard) and an implementation file nissy.cpp. This interface wraps the calls to the C functions in an object-oriented C++ interface for more convenient use.

The cpp/examples folder contains some examples for how to use this interface. You can build them and run them with the build tool, for example:

./build.sh cpp cpp/examples/solve_h48h3k2.cpp

NOTE: If you prefer to use a C-style API, you’ll have to write your own header, similar to the extern "C" {} block at the top of cpp/nissy.cpp. The C header src/nissy.h cannot be compiled as C++, as it uses features of C that are not compatible with it.

Python

The python folder contains a Python module. The API provided by this module follows the C API quite closely, except its functions sometimes return strings instead of writing to char * buffers.

To build the Python module you need the Python development headers installed. You can check this from the output of ./build.sh config:

$ ./build.sh config
...
Python bindings: version 3.13

Then to build the module:

$ ./build.sh python

And to import it

$ python           # In the main folder or in the python subfolder
>>> import nissy   # In the python shell

From here you can call the library functions directly, for example:

>>> nissy.applymoves('ABCDEFGH=ABCDEFGHIJKL=A', "R U R' U'")
'WFCDERQH=AECDIFGHBJKL=A'

The python/examples folder contains some examples, that you can run for example with:

$ python python/examples/solve.py

You can access the documentation for the Python module from within a Python interpreter with help(nissy). Cross-check this documentation with the comments in nissy.h for more details.

NOTE: Support for the Python module is still rudimentary.

JavaScript (and WebAssembly)

Bindings for JavaScript via a WebAssembly build (using emscripten) are work in progress. The JavaScript module can be built with

$ ./build.sh web

An example web app running nissy can be found in the web/http folder. You can run a web server in that folder to check it out, but you need to set some extra headers to make it work. For example, if you are using darkhttpd you can start the server with the following command:

$ darkhttpd web/http/ \
  --header 'Cross-Origin-Opener-Policy: same-origin' \
  --header 'Cross-Origin-Embedder-Policy: require-corp' \
  --mimetypes web/http/mime

The command above can also be run with the web/http/start-server.sh script.

Cube format

This format is a “base 32” encoding of the cube. It is not meant to be human-readable, but it is compact while still being plain text. Each piece, including the orientation value, is encoded as a number from 0 to 31, and this number is then converted to an uppercase letter (0-26) or to a lowercase letter (27-31).

The format looks like this:

cccccccc=eeeeeeeeeeee=r

Where the first 8 characters represent the corner, the 12 characters after the first 12 represent the edges and the last character represents the orientation of the cube with respect to the base orientation.

Edges are numbered as follows (see also constants.h):

UF=0 UB=1 DB=2 DF=3 UR=4 UL=5 DL=6 DR=7 FR=8 FL=9 BL=10 BR=11

If the edge is misoriented with respect to the F/B axis, the value is increased by 16.

Corners are numbered as follows:

UFR=0 UBL=1 DFL=2 DBR=3 UFL=4 UBR=5 DFR=6 DBL=7

If the corner is twisted clockwise with respect to the U/D axis orientation, the value is increased by 8. If it is twisted counter-clowsie, the value is increased by 16.

The orientations of the cube are numbered as follows, where e.g. “RB” means that the R face in on top and the B face is on front:

UF=0  UR=1  UB=2  UL=3
DF=4  DR=5  DB=6  DL=7
RF=8  RD=9  RB=10 RU=11
LF=12 LD=13 LB=14 LU=15
FD=16 FR=17 FU=18 FL=19
BD=20 BR=21 BU=22 BL=23

In this format, the solved cube looks like this:

ABCDEFGH=ABCDEFGHIJKL=A

The cube after the move Fw looks like this:

ANCPETGR=AbaDEFGHIJRS=L

A cube in B32 format is always 23 characters long (24 if the terminating null character is included).