H48: prototype for a new optimal solver and nissy backend

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

H48 is an experimental Rubik’s cube solver. The main goal is experimenting with various optimal solving methods and pruning tables, with nxopt and vcube as inspiration and benchmark reference.

In the future this project may evolve as a new “back-end” for the classic nissy.

Building

First run the configuration script to detect the system configuration. This is going to select a C compiler and architecture-specific optimizations.

$ ./configure.sh

These settings can be overridden, for example:

$ THREADS=3 CC=gcc ./configure.sh   # Use 3 threads and compile with gcc

All the configuration-time options are described in the configure.sh script.

Once the configuration is done, you can build with make

$ make

Running tests

This project includes a suite of “unit” test. They can be run with:

$ make test

To run only a subset of the tests, set the TEST variable to a regular expression that matches only the name of the tests you want to run:

$ TEST=coord make test

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.

See the test folder and test/test.sh for details.

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 must select it with the environment variable TOOL. For example the command:

TOOL=stats make tool

Will run the statstablesh48 tool.

To pass some arguments to a tool, use the TOOLARGS variable:

TOOL=gendata TOOLARGS="h48 0;2;20" make tool

Like for tests, the value of the TOOL variable can be any regular expression matching the name of the tool. Unlike tests, one and only one tool will be selected for each run. The content of the TOOLARGS variable is used directly as command line arguments for the chosen tool.

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 make debugtool.

Running commands manually

This project also includes a rudimentary shell that can be used to run commands manually. To build the shell use:

$ make shell

This will create an executable called run. Optionally, you can run some tests:

$ make shelltest

Then you can for example get a cube from a sequence of moves:

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

Or you can get a random cube

$ ./run randomcube
WDSQREVX=VBKYDUCJXWAb

If you don’t like this format, you can convert it:

$ ./run convert -fin B32 -fout H48 -cubestr "WDSQREVX=VBKYDUCJXWAb"
UL1 UB0 BL0 FR1 DF0 UR1 DB0 FL0 DR1 DL1 UF0 BR1 DFR2 DBR0 DFL2 UFR2 UBL2 UFL0 UBR2 DBL2

To solve a cube you can use:

$ ./run solve -solver "h48h0k4" -n 1 -M 4 -cube "JLQWSVUH=ZLCUABGIVTKH"
Found 0 solutions, searching at depth 0
Found 0 solutions, searching at depth 1
Found 0 solutions, searching at depth 2
Found 0 solutions, searching at depth 3
Solution found: F' U R
F' U R

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

Running commands from a Python shell

There is a work-in-progress python module available. To build it you need the Python development headers installed. You can check this from the output of ./configure.sh:

$ ./configure.sh
...
Python3 development libraries: version 3.12

Then to build the module:

$ make python

And to import it

$ python                                  # In the main folder
>>> import nissy_python_module as nissy   # In the python shell

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

>>> nissy.compose("NEORSQLH=ZFCYUAGLHTKB", "NEORSQLH=ZFCYUAGLHTKB")
'ASTUGFBH=DACXEZGBLIKF'

Some methods have a different signature in the Pythn module than in libnissy: for example solve() returns the solutions as a list of strings instead of writing them to a return parameter buffer. 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.

Please note: the support for the Python module is still rudimentary.

Cube formats

The cube is represented as a string in one of the following formats, all explained below:

• H48
• LST
• B32 (the default)

In all of the formats, the permutation of the center pieces is not stored. This means that the cube is assumed to be in a fixed orientation.

More formats will become available in the future.

Cube format: H48

In the H48 format, each edge is represented by two letters denoting the sides it belongs to and one number denoting its orientation (0 oriented, 1 mis-oriented). Similarly, each corner is represented by three letters and a number (0 oriented, 1 twisted clockwise, 2 twisted counter-clockwise).

The solved cube looks like this:

UF0 UB0 DB0 DF0 UR0 UL0 DL0 DR0 FR0 FL0 BL0 BR0 UFR0 UBL0 DFL0 DBR0 UFL0 UBR0 DFR0 DBL0

The cube after the move F looks like this:

FL1 UB0 DB0 FR1 UR0 UL0 DL0 DR0 UF1 DF1 BL0 BR0 UFL1 UBL0 DFR1 DBR0 DFL2 UBR0 UFR2 DBL0

Whitespace (including newlines) between pieces is ignored when reading the cube. A single whitespace character is added between pieces when writing.

You can find more examples of this format in the utils/cubes folder.

Cube format: LST

In the LST format, a cube is represented by a comma-separated list of integers. Each piece is represented by an (unsigned) 8-bit integer. The 4 least-significant bits determine which piece it is, the other 4 determine the 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

Corners are numbered as follows:

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

The orientation of the edges is with respect to F/B, the orientation of corners is with respect to U/D.

In this format, the solved cube looks like this:

0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

The cube after the move F looks like this:

36, 1, 38, 3, 66, 5, 64, 7, 25, 1, 2, 24, 4, 5, 6, 7, 16, 19, 10, 11

Cube format: B32

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). Edges and corners are separated by a single = character.

In this format, the solved cube looks like this:

ABCDEFGH=ABCDEFGHIJKL

The cube after the move F looks like this:

MBODSFQH=ZBCYEFGHQTKL

A cube in B32 format is always 21 characters long (22 if the terminating null character is included).