crcPlus CRC Generator User’s Guide

Table of Contents

CRC Generator Reference Model (crcplus)

Copyright © 2017  Mahlon R. Smith, The Software Samurai

This manual describes version 0.1.00 of ’crcplus’.

  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled 
  "GNU Free Documentation License".

'crcplus' is a fully-configurable reference design for implementing CRC
          (Cyclic Redundancy Check) error detection for any application
          where data corruption may be encountered in the data stream.

Introduction

A Brief Introduction to CRC

CRC (Cyclic Redundancy Check) algorithms are used to verify data integrity in streaming data which may be subject to data loss via single-bit or burst-error corruption.

A common use of CRC is in creating data packets for transport across a network. The Ethernet protocol creates “frames” i.e. packets which contain CRC error detection so that the receiver can discard a corrupted packet and request that the packet be sent again.

Another common use of CRC is for verification of audio and video data streams, whether from DVD media or from digital broadcast streams which represents our particular interest in CRC.

Additional applications of CRC can be found in the X.25 communications protocol, serial-ATA data transfer, Bluetooth, Bzip2 compression and in USB data tokens. For a more comprehensive list of CRC applications, see the Wikipedia article on “Cyclic Redundancy check”.

CRC should not be confused with “checksums” which are a simple sum of all data bytes in a byte stream. Checksums are mathematically vulnerable to accidental data validation where two or more data errors in the stream cancel each other out.

In contrast, CRC error detection uses a bit-shifting algorithm that renders accidental data validation virtually impossible (the odds of accidental validation being several millions to one).

In theory, CRC algorithms are based on polynomial division, traditionally polynomials based on powers of two(2), but other number bases are possible.

In practice, however, actual polynomial division would be impractical due to its calculation intensive nature. Happily, computer hardware is based on binary (base-2) architecture, making it possible to replace the actual polynomial with a binary divisor called (inappropriately) a “Generator Polynomial”.

This generator polynomial, referred to as a “poly” in Ross Williams’ original article, is used as a divisor in a specialized kind of binary division based on bit shifting (without carry-out). Please refer to Ross’s article for a very nice description of the mathematics behind this operation (see below).

A common misconception is that CRC is a form of encryption, which it is not. CRC is used to detect accidental errors in the data stream and is vulnerable to intentional manipulation of the data stream by black hats or by the morons who believe it is humorous to embed viruses and other malware into digital data.

In conclusion, a basic knowledge of CRC is a valuable tool for anyone who works with streaming data.

Introducing the Reference Model

A “Reference Model” is a reliable, easy-to-understand implementation of some algorithm or process which can be used to validate more sophisticated implementations.

A reference model is typically neither fast nor particularly elegant. The crcPlus model is no exception; instead, efficiency is sacrificed in the name of simple clarity and ease of integration into other applications.

The Basic CRC Algorithm

The algorithm used for the CRC Generator is adapted from a reference model written by Ross Williams (1993) which was written in C and is in the public domain. Ross’s original model can be found at:

"A Painless Guide To CRC Error Detection Algorithms,"
    <http://www.ross.net/crc/download/crc_v3.txt>

See also our C-language implementation of Ross’s reference model which was written as part of a student exercise (with extensive source code notes), and which is available as a separate download. (See Technical Support.)

The ‘crcPlus’ CRC Generator Implementation

‘crcPlus’ is a simple application, written in C++, which is used to validate the CRC algorithm and to demonstrate the use of the CRC Generator.

The ‘CRC_Gen’ class is a C++ header file which defines and implements the actual CRC Generator engine. The CRC Generator itself is very compact (less than 350 lines of code) which may be dropped into any application and provides a fully configurable environment for generating almost any flavour of CRC, using either a direct calculation algorithm or a hash table lookup algorithm.

Please see Operational Overview for detailed information on using the ‘crcPlus’ application.

Configuration Parameters

The CRC Generator is fully configurable. Configuration may be specified as a combination of command-line parameters used to invoke the ‘crcPlus’ application. These parameters, in turn, are used to create an instance (addressable object) of the CRC_Gen class.

• register width : The width of the (virtual) accumulator register in bits.
• poly : The Generator Polynomial i.e. the binary divisor used in CRC calculations.
• initial register value : The initial value of the register before CRC calculation begins.
• final XOR value : The bitmask used to perform a final Exclusive-OR on the calculated CRC value.
• the reflection flags : The two flags indicating whether the incomming data and the output value, respectively are to be reflected. ‘Reflection’ means reversing the order of bits within a data token, either the byte arriving in the data stream, or the contents of the accumulator register.

Each of these parameters is discussed in greater detail in Operational Overview.

Parameter syntax and range of valid arguments may be found in the chapter Invoking.

Direct Calculation versus Hash Table

The reference model CRC Generator code calculates the CRC directly using between 35 and 40 bitwise calculations for each byte of data in the stream. Obviously, this is very slow, but is extremely reliable for verification of CRC implementations in other projects. If your project has a limited data set or if speed is not a significant issue, then the reference model code can be used directly in your application.

If however, speed is an important issue, ‘crcplus’ can generate a hash table (lookup table) which embeds most of the run-time calculation into the table lookup, greatly reducing the processing overhead for large data sets.
Please see 'table' mode for additional information.

The next chapter discussses how to use the ‘crcPlus’ application to experiment with CRC generation.

Operational Overview

‘crcPlus’ is a simple console (command-line) application consisting of one C++ source module, one C++ header file and the CRC_Gen class definition header. See Building from Source, for information on compiling the application from source code.

Command-line Parameters

Invoke the application by opening a terminal window and typing:

crcplus MODE [OPTIONS]

• ‘MODE’ is the operational mode for the application and is a required parameter.
  
  
  • file : Specify a file to be scanned to create a CRC. external applications.
  • table : Create a hash table and write it to a file for use in another application
  • test : Validate the algorith used by the CRC Generator.
  
  
• ‘OPTIONS’ are one or more optional configuration parameters used to configure the CRC Generator.
  
  
  • regwidth

    All register widths between 8 bits and 32 bits (inclusive) are allowed. However, all but the most esoteric hardware is implemented with registers that are a multiple of 8 bits, and we cannot think of a reason why anyone would use fewer bits than the actual width of the register.

    • For instance, a 12-bit register may be specified, but it is likely that the actual hardware would use a 16-bit register for the calculations, leaving the top 4 bits of the register unused which would in turn reduce the robustness of the CRC in error detection.
    • Still, it was fun to implement the algorithm with an arbitrary register width, so please enjoy. :)
  • poly

    All polynomial values are allowed provided that the number of significant bits in the poly is less than or equal to the width of the register.

    • Note that for safety, any significant bits beyond the width of the register will be silently masked out to prevent register overflow.
  • reginit

    This parameter specifies the initial contents of the accumulator register before processing begins. This initial value may be any hexidecimal value provided that the number of significant bits is less than or equal to the width of the register.

    • Note that for safety, any significant bits beyond the width of the register will be silently masked out to prevent register overflow.
  • xorfinal

    This value is Exclusive-ORed with the final calculated CRC value. The final XOR value may be any hexidecimal value provided that the number of significant bits is less than or equal to the width of the register.

    • Note that for safety, any significant bits beyond the width of the register will be silently masked out to prevent register overflow.
  • reflectin
  • reflectout

    The two reflection flags may be specified in any combination.
    true / true
    true / false
    false / true
    false / false

    Our algorithm supports any combination of these flags because we were curious to see if it could be done. In the real world, however, these flags are generally either both set, or both reset to simplify the processing algorithm.

Please see Invoking for information on using these parameters.

Using ‘crcPlus’ Effectively

‘crcPlus’ is a reference model and a demonstration program for students and software designers who are planning to integrate CRC into their own projects.

For this reason, it is important to understand the use of each configuration parameter described in the previous section.

Although ‘crcPlus’ is very flexible in the use of these parameters, this should not be considered an invitation to insert strange and unorthodox parameter combinations into your own code.

Selecting a Generator Polynomial

This is especially true of the ‘poly’ parameter. While it is true that all poly values are accepted, research and experience show that certain poly values are much more effective (mathematically speaking) than others. It is recommended that you select a poly value which is already used in one or more commercial applications.

• For 32-bit CRC generation, one of the most common poly values is 04C11DB7h which is defined in CRC_Gen.hpp as ‘crcDFLT_POLY’.
• The 864CFBh 24-bit poly is used as part of PGP data encryption.
• For 16-bit CRC generation there are several choices such as 8005h used by USB (Universal Serial Bus) controllers, 1021h used by X.25 and Bluetooth, or C867h used across mobile phone networks.
• For a more comprehensive list of CRC applications, see the Wikipedia article on “Cyclic Redundancy check”.

Again, while any poly value will work, some polys are much better than others.

Register Width

When selecting a register width, the general rule would be that more register bits yeilds more robust error detection. If your CRC implementation will run on embedded controllers, you may be limited by the physical width of the registers on your target system. On such systems, it is recommended that the register width should be specified as the native width of the target CPU register (up to 32 bits), especially for systems with relatively low clock rates.

Initial Register Contents

The initial register value is to primarily a matter of preference. It is simply a known starting point for the calculations. The most common initial values are all bits set (FFFFFFFFh) or all bits reset 00000000h).

Keep in mind, however that an initial value of zero (0000h) will result in the register value remaining unchanged until a non-zero input byte arrives. This means that a sequence of zeros at the start of a data stream will, in effect, go unprocessed. While this is not an error, it does weaken the strength of the CRC.

Some CRC algorithms may use a non-standard initial value in an effort to make it more difficult for someone to intentionally corrupt the data stream. Although this will do little to protect the data from a determined black hat, it may deter the occasional weekend cracker.

Final Exclusive-OR

The use of a final XOR value, usually either 00000000h, or FFFFFFFFh will determine the way the CRC is validated at the receiving end of the data stream.

It should be obvious that if the final XOR value is zero, then the XOR operation need not be executed at all since performing an XOR against zero will not change the value. However, this is not the whole story.

As with the initial register value above, some algorithms may use a non-standard XOR value to deter the black hats.

Considerations for Reflection

The mathematical, physical and aesthetic reasoning behind using a reflected algorithm are beyond the scope of this document, but a few things should be kept in mind:

If a direct calculation method (no hash table) is used, then reflection of the input can have a significant impact on performance.

However, when a hash-table based calculation is used, then all the reflection is built into the table itself, negating most of the performance penalty for using bit reflection.

If you are one of those people i.e. the folks who dangerously over-clock their personal gaming systems, then the way the target hardware presents the data: whether in byte-sized chunks or serially (bit-by-bit), and whether the data are transported and stored as little-endian or big-endian may affect your decision on the use of bitwise reflection.

Technical Note: crcPlus creates color contrast in the operational reports written to stdout using ANSI escape sequences. If you redirect the output to a file or a text viewer, be sure your text reader supports ANSI color.

For instance, when using the ‘less’ utility to view data with ANSI color, use the ‘-R’ switch. Example:

crcplus --file='stream01.bin/0482D6E4h/T' --pair | less -R

Invoking

Summary of Options

Usage

    crcplus MODE [OPTIONS]

Operational Modes

crcplus --file=FILENAME[/EXPECTED_CRC[/TABLE_LOOKUP_FLAG]]

crcplus --file=’data_stream_01.bin’
crcplus --file=’data_stream_02.bin/0D48227Eh’
crcplus --file=’data_stream_03.bin/0E72144Eh/T’
crcplus --file=’data_stream_04.bin/0h/T’

crcplus --table[=FILENAME]

crcplus --table
crcplus --table=’CRC_Hash_Table16.hpp’ --regwidth=16 --poly=8005
crcplus --table=’CRC_Hash_Table32.hpp’ --reflectin=true --reflectout=true

The test has four(4) parts:
1) direct-calculation algorithm with a 16-bit configuration parameters
2) table-driven algorithm with a 16-bit configuration parameters
3) direct-calculation algorithm with a 32-bit configuration parameters
4) table-driven algorithm with a 32-bit configuration parameters

regwidth    16
poly        8005h
reginit     0000h
xorfinal    0000h
reflectin   true
reflectout  true

Expected CRC : BB3Dh

regwidth    32
poly        04C11DB7h
reginit     FFFFFFFFh
xorfinal    FFFFFFFFh
reflectin   true
reflectout  true

Expected CRC : CBF43926h

crcplus --test

Configuration Options

Configuration options may be specified in any order.

For options which require arguments, the option must be immediately followed by the EQUAL sign (’=’) which must be immediately followed by its argument.

If the argument string contains space characters, it must be enclosed in either single-quotes ( ' ) or double-quotes ( " ).

Examples:
   crcplus --file='data_stream_01.bin' --regwidth=32 --reflectin=true

   crcplus --file='data_stream_02.bin' --reginit=FFFFFFFFh --xorfinal=0h

   crcplus --table='Hash Table 4.h' --poly=8005h --xorfinal=0FFFFh

If an option is specified more than once (not recommended), then the last instance scanned will be used.

Default Configuration Options

All configuration options are optional, and if an option is not specified, then a default value for that option will be used. Default values for the configuration options are:

  regwidth: 32
      poly: 04C11DB7h
   reginit: FFFFFFFFh
  xorfinal: FFFFFFFFh
 reflectin: true
reflectout: true

crcplus MODE –regwidth=WIDTH [OPTIONS]

crcplus --file=’data_stream_01.bin’ --regwidth=32
crcplus --table --regwidth=16
crcplus --table=’HashTable16.h’ --regwidth=16 --poly=8005h

crcplus MODE --poly=POLY [OPTIONS]

crcplus --file=’data_stream_01.bin’ --poly=814141ABh
crcplus --file=’data_stream_02.bin’ --poly=8005h --regwidth=16 
crcplus --table --regwidth=24 --poly=864CFBh

crcplus MODE --reginit=HEX_VALUE [OPTIONS]

crcplus --file=’data_stream_01.bin’ --reginit=FFFFFFFFh
crcplus --file=’data_stream_02.bin’ --reginit=FFFFh --regwidth=16 
crcplus --table --regwidth=24 --reginit=A0A0A0h

crcplus MODE --reginit=HEX_VALUE [OPTIONS]

crcplus --file=’data_stream_01.bin’ --reginit=FFFFFFFFh
crcplus --file=’data_stream_02.bin’ --reginit=FFFFh --regwidth=16 
crcplus --table --regwidth=24 --reginit=A0A0A0h

Example:
                  B    (hex)
Incomming byte: 1011   (binary)
       Becomes: 1101   (binary)
                  D    (hex)

crcplus MODE --reflectin=[true | false] [OPTIONS]

crcplus --file=’data_stream_01.bin’ --reflectin=true
crcplus --file=’data_stream_02.bin’ --reflectin=false --reflectout=false 
crcplus --table --regwidth=16 --reflectin=true --reflectout=true

Example:
                    C    4    A    1  (hex)
Calculated value: 1100 0100 1010 0001 (binary)
         Becomes: 1000 0101 0010 0011 (binary)
                    8    5    2    3  (hex)

crcplus MODE --reflectout=[true | false] [OPTIONS]

crcplus --file=’data_stream_01.bin’ --reflectout=true
crcplus --file=’data_stream_02.bin’ --reflectout=false --reflectin=false 
crcplus --table --regwidth=16 --reflectout=true --reflectin=true

Other Options

crcplus --file=FILENAME --dump [OPTIONS]

crcplus --file=’data_stream_01.bin’ --dump
crcplus --file=’data_stream_02.bin’ --regwidth=16 --poly=8005h --dump 

crcplus --file=FILENAME --pair [OPTIONS]

crcplus --file=’data_stream_01.bin’ --pair
crcplus --file=’data_stream_02.bin’ --regwidth=16 --poly=8005h --pair 

1) The valid values will be reported as entered, but
2) the out-of-range parameters will be reported as they were 
   truncated to fit the register.

crcplus --file=FILENAME --verbose [OPTIONS]

crcplus --file=’data_stream_01.bin’ --verbose
crcplus --file=’data_stream_02.bin’ --regwidth=16 --verbose 

crcplus --help

crcplus --version

Building from Source

Tools

The crcPlus application is written in C++ and is built with the GNU C++ compiler and linker.

No additional link libraries or third-party tools are needed.

Compiling

crcPlus is compiled using the GNU/G++ compiler which is invoked through the 'gmake' (‘make’) utility. The compile and linking instructions are contained in the file named 'Makefile'.

Example:
      gmake             (build all modified components)

Build Options

No optional builds are currently defined.

Testing the Build

To test the build, invoke with a request for the crcPlus version number. You should get something similar to the following:

./crcplus --version

crcplus v:0.1.00 (c)2017      The Software Samurai (CRC_Gen v:0.1.00)
---------------------------------------------------------------------
License GPLv3: GNU GPL version 3 <http://gnu.org/licenses/gpl.html> 
This is free software: you are free to modify and/or redistribute it
under the terms set out in the license.
There is NO WARRANTY, to the extent permitted by law.

Installation

For the crcPlus application to be visible throughout your system, you will need to copy the 'crcplus' binary file to a directory on your execution path.

To see your execution path, type: echo $PATH.

[crcPlus]$ echo $PATH
/usr/local/bin:/usr/bin:/bin:/usr/local/sbin:
/usr/sbin:/home/sam/.local/bin:/home/sam/bin

The directories searched for binaries are separated by the colon ':' character. Generally, it is recommended that you choose the last entry in the list because that directory belong only to you.

EXAMPLE:  cp --preserve crcplus /home/sam/bin/.

Installing the Documentation

Documentation for crcPlus is provided in both Texinfo (info) format and HTML format.

To view the HTML-format documentation, navigate to:
crcPlus/Texinfo
then load the 'crcplus.html' document into your favorite browser. Note that the 'infodoc-styles.css' CSS style definition file must be in the same directory as the HTML document.

To view the Texinfo (info) documentation, navigate to:
crcPlus/Texinfo
then view the documentation using the following command:
info -f crcplus.info

Follow these steps to install the crcPlus documentation into the ’info’ database.

1. Note that installing the documentation is not necessary, but is recommended. Not only is it convenient to have the documentation always available, but it is a useful skill for when you begin installing documentation for your own applications!
2. Adding an ’info’ document to the info-reader database (or removing a document from the database) is easy, but it does require ’SUPERUSER’ (’root’) user privilege. If this makes you nervous, please make a backup copy of the 'dir' (info directory) file before modifying it.
3. Open a terminal window.
4. Navigate to the directory which contains the ’crcplus.info’ documentation.

   Example:
     cd ~/MySoftware/crcPlus/Texinfo
   
     (substitute your actual installation path)
   

5. Locate the master Info system directory file: 'dir'.
   For local users, this is typically:
   

   /usr/local/share/info/dir
   

   For global system users, this is typically:

   /usr/share/info/dir
   

6. Copy the document to the directory where you found the info ’dir’ file.

   Example:
   sudo cp --preserve=timestamps crcplus.info /usr/local/share/info/.
   
   (substitute the actual path to the directory containing the 'dir' file)
   Enter your password when prompted.
   

7. Navigate to the Info target directory.

   cd /usr/local/share/info
   

8. Verify that the document was copied correctly.

   ls -l crcplus.info
   

9. Add the menu entry.

   sudo install-info 
           --dir-file=dir --info-file=crcplus.info 
           --name=’CRC Generator’ --debug
   
   Note that this is a single command, typed all on one line 
   even though it may look strange as printed here.
   
   Enter your password when prompted.
   

10. Verify the install.

    Type the following command:
       info
    

    This will open the top-level menu of the Info system.
    Verify that your new entry is beautifully displayed and that the new Info document is accessible:

    First, press the forward-slash key ’/’ (search)
    Then, type: CRC Generator (and press ENTER)
    The highlight should now be on the menu entry.
    Press ENTER (RET) key again, and verify that the main page of the crcPlus documentation is displayed.
    Then, exit the Info system: ’q’ (quit).

11. If the menu item is not present OR if the new Info document is not accessible, then try the installation again.

    If you want to remove the menu entry, use the command:

    sudo install-info 
        --dir-file=dir --info-file=crcplus.info
        --name=’CRC Generator’ --remove --debug
        
    Again, this is a single command, typed all on one line.
    
    Enter your password when prompted.
    

Technical Support

Please Note: All trademarks and service marks mentioned in this
document are the entirely-too-proprietary property of their
respective owners, and this author makes no representation of
affiliation with or ownership of any of the damned things.

Contact Info

crcPlus (crcplus) binary, source code and associated Texinfo 
documentation were written and are maintained by:

                         Mahlon R. Smith,
                      The Software Samurai
                 Beijing University of Technology
                 on the web at: www.SoftwareSam.us 

For bugs, suggestions, periodic updates, or possible praise, 
please post a message to the author via website.

The author wishes to thank everyone for their intelligent, kind
and thoughtful responses.  (ranters I can live without)

By the same author

• NcDialog Application Programming Interface (API) library.
  The NcDialog API forms the basis for most of our other software projects. It provides the application developer with the tools to create dialog-based console applications, without the need to learn anything about the complexities of the underlying ‘ncurses’ C-language library.

  Console applications have always been the most efficient and easily-implemented of computer programs. What they lacked was a friendly and visually-pleasing user interface.

  With the NcDialog API, console applications can now be used and understood by experts and novice users alike.

• FileMangler (fmg), is a compact, fast and flexible tool for handling all your file management needs.

  FileMangler performs all basic file management tasks, as well as performing scheduled and ad-hoc file backup and synchronization activities.

  FileMangler runs in a console window, and thus provides access to many system tools not available to a GUI application. FileMangler also provides full support for accessing the local Trashcan.

  FileMangler is based on the NcDialog API, and thus will run in almost any GNU/Linux or UNIX terminal environment.

• Console Trashcan (ctrash) is a simple, console-based (command-line) utility for managing the contents of your local Trashcan. Send items to the trash, restore items from the trash, report the trashcan contents, and empty the trash. ’ctrash’ is designed as a safer, and more flexible alternative to the ’rm’ and ’rmdir’ commands.
  
  
• Infodoc, post-processing and CSS style for HTML documents created by the Texinfo (makeinfo) utility. If you write documentation using the Texinfo/makeinfo documentation engine, AND if you care at all about what your documentation looks like, then you really do need the ‘infodoc-styles.css‘ definition file and the ‘idpp’ HTML post-processor.

  The HTML version of this document was formatted using ‘idpp’ and is displayed using the ‘infodoc-styles.css‘ definition file. Many more examples are available on the author’s website.

• gString text internationalization tool.
  gString implements a C++ class that may be integraged into any application for smooth and painless text formatting, and for converting between UTF-8 and ‘wchar_t’ (wide) character encoding.

  The gString class is lightweight, consisting of one C++ source module and one header file. The gString class may be directly integrated into an application, or may built as a link library.
  The gString class is also embedded within the NcDialog API library (see above).

• Source Profiler (srcprof) is a source code analysis tool for determining the ‘maintainability’ of source code modules.

  ‘srcprof’ can be used to profile source code for high-level languages such as C, C++ and Java, as well as various assembly languages and scripting languages such as Python, Perl and Ruby. For a complete list of currently-supported source languages, please see the Source Profiler documentation.

  ’srcprof’ can be used both as a productivity-measurement tool and as a tool for testing source code quality based on an evaluation of its ‘maintainability’.

  Source Profiler is a console-based utility, which runs as either a pure, command-line utility, OR as a dialog application based on the NcDialog API.

• DVD Repair (dvdrep) is a utility for exploring the contents of a damaged DVD video disc and rescuing as much of the data as possible.

  ‘dvdrep’ can be used to rescue data from any non-encrypted DVD video source disc that is formatted using the Universal Disc Format (UDF) filesystem (as all commercially produced DVD movies are).

  ‘dvdrep’ takes a layered approach to the analysis of the source disc. A detailed log file is maintained for each step of the process in case manual intervention is needed at a later step.

  DVD Repair is based on the NcDialog API, and thus will run in almost any GNU/Linux or UNIX terminal environment.

• tbXClip clipboard access for console applications.
  Access to the system clipboard by console applications has traditionally been tedious, time-consuming and fragile.

  tbXClip utilizes the new XML interface to the X-server to provide simple, robust communication between the application and the system clipboard.

• Various other Linux utilities designed as academic exercises are also available for student use. For example: interprocess communication pipes, FIFOs, sockets, shared memory blocks, multi-threading, the ’Sleeping Barber’ problem and so on.
  These cannot be considered as production-worthy, but they demonstrate the concepts in simple terms.

Copyright Notice

The crcPlus binary and source code are released under
the GNU General Public License (GPL 3), and
the user documentation (this document) is released under
the GNU Free Documentation License (FDL 1.3):

Copyright © 2017  Mahlon R. Smith, The Software Samurai

This manual describes version 0.1.00 of ’crcplus’.

  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled 
  "GNU Free Documentation License".

GNU General Public License

Copyright © 2007 Free Software Foundation, Inc. http://fsf.org/

Everyone is permitted to copy and distribute verbatim copies of this
license document, but changing it is not allowed.

Preamble

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For the developers’ and authors’ protection, the GPL clearly explains that there is no warranty for this free software. For both users’ and authors’ sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions.

Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users’ freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users.

Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free.

The precise terms and conditions for copying, distribution and modification follow.

TERMS AND CONDITIONS

0. Definitions.

   “This License” refers to version 3 of the GNU General Public License.

   “Copyright” also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.

   “The Program” refers to any copyrightable work licensed under this License. Each licensee is addressed as “you”. “Licensees” and “recipients” may be individuals or organizations.

   To “modify” a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a “modified version” of the earlier work or a work “based on” the earlier work.

   A “covered work” means either the unmodified Program or a work based on the Program.

   To “propagate” a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well.

   To “convey” a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying.

   An interactive user interface displays “Appropriate Legal Notices” to the extent that it includes a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the interface presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.

1. Source Code.

   The “source code” for a work means the preferred form of the work for making modifications to it. “Object code” means any non-source form of a work.

   A “Standard Interface” means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language.

   The “System Libraries” of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A “Major Component”, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it.

   The “Corresponding Source” for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work.

   The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source.

   The Corresponding Source for a work in source code form is that same work.

2. Basic Permissions.

   All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law.

   You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you.

   Conveying under any other circumstances is permitted solely under the conditions stated below. Sublicensing is not allowed; section 10 makes it unnecessary.

3. Protecting Users’ Legal Rights From Anti-Circumvention Law.

   No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures.

   When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work’s users, your or third parties’ legal rights to forbid circumvention of technological measures.

4. Conveying Verbatim Copies.

   You may convey verbatim copies of the Program’s source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with section 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program.

   You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.

5. Conveying Modified Source Versions.

   You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions:

   1. The work must carry prominent notices stating that you modified it, and giving a relevant date.
   2. The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to “keep intact all notices”.
   3. You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 additional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it.
   4. If the work has interactive user interfaces, each must display Appropriate Legal Notices; however, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.

   A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an “aggregate” if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.

6. Conveying Non-Source Forms.

   You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways:

   1. Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.
   2. Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge.
   3. Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b.
   4. Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements.
   5. Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d.

   A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work.

   A “User Product” is either (1) a “consumer product”, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, “normally used” refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product.

   “Installation Information” for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made.

   If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM).

   The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network.

   Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.

7. Additional Terms.

   “Additional permissions” are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions.

   When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission.

   Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms:

   1. Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or
   2. Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or
   3. Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or
   4. Limiting the use for publicity purposes of names of licensors or authors of the material; or
   5. Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or
   6. Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors.

   All other non-permissive additional terms are considered “further restrictions” within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying.

   If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms.

   Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.

8. Termination.

   You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11).

   However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

   Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

   Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10.

9. Acceptance Not Required for Having Copies.

   You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.

10. Automatic Licensing of Downstream Recipients.

    Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License.

    An “entity transaction” is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts.

    You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.

11. Patents.

    A “contributor” is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s “contributor version”.

    A contributor’s “essential patent claims” are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, “control” includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.

    Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version.

    In the following three paragraphs, a “patent license” is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To “grant” such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.

    If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid.

    If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it.

    A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007.

    Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.

12. No Surrender of Others’ Freedom.

    If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.

13. Use with the GNU Affero General Public License.

    Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.

14. Revised Versions of this License.

    The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

    Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation.

    If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program.

    Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version.

15. Disclaimer of Warranty.

    THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

16. Limitation of Liability.

    IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

17. Interpretation of Sections 15 and 16.

    If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.

one line to give the program's name and a brief idea of what it does.
Copyright (C) year name of author

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see http://www.gnu.org/licenses/.

Also add information on how to contact you by electronic and paper mail.

If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:

program Copyright (C) year name of author
This program comes with ABSOLUTELY NO WARRANTY; for details type ‘show w’.
This is free software, and you are welcome to redistribute it
under certain conditions; type ‘show c’ for details.

The hypothetical commands ‘show w’ and ‘show c’ should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an “about box”.

You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyright disclaimer” for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see http://www.gnu.org/licenses/.

The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read http://www.gnu.org/philosophy/why-not-lgpl.html.

GNU Free Documentation License

Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
http://fsf.org/

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

0. PREAMBLE

   The purpose of this License is to make a manual, textbook, or other functional and useful document free in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

   This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

   We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

1. APPLICABILITY AND DEFINITIONS

   This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The “Document”, below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as “you”. You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

   A “Modified Version” of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

   A “Secondary Section” is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document’s overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

   The “Invariant Sections” are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

   The “Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

   A “Transparent” copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not “Transparent” is called “Opaque”.

   Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

   The “Title Page” means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, “Title Page” means the text near the most prominent appearance of the work’s title, preceding the beginning of the body of the text.

   The “publisher” means any person or entity that distributes copies of the Document to the public.

   A section “Entitled XYZ” means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” of such a section when you modify the Document means that it remains a section “Entitled XYZ” according to this definition.

   The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

2. VERBATIM COPYING

   You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

   You may also lend copies, under the same conditions stated above, and you may publicly display copies.

3. COPYING IN QUANTITY

   If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document’s license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

   If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

   If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

   It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

4. MODIFICATIONS

   You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

   1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
   2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
   3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
   4. Preserve all the copyright notices of the Document.
   5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
   6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
   7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document’s license notice.
   8. Include an unaltered copy of this License.
   9. Preserve the section Entitled “History”, Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled “History” in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
   10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the “History” section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
   11. For any section Entitled “Acknowledgements” or “Dedications”, Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
   12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
   13. Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
   14. Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
   15. Preserve any Warranty Disclaimers.

   If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version’s license notice. These titles must be distinct from any other section titles.

   You may add a section Entitled “Endorsements”, provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

   You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

   The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

5. COMBINING DOCUMENTS

   You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

   The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

   In the combination, you must combine any sections Entitled “History” in the various original documents, forming one section Entitled “History”; likewise combine any sections Entitled “Acknowledgements”, and any sections Entitled “Dedications”. You must delete all sections Entitled “Endorsements.”

6. COLLECTIONS OF DOCUMENTS

   You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

   You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKS

   A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an “aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation’s users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

   If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document’s Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATION

   Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

   If a section in the Document is Entitled “Acknowledgements”, “Dedications”, or “History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

9. TERMINATION

   You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.

   However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

   Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

   Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.

10. FUTURE REVISIONS OF THIS LICENSE

    The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

    Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Document.

11. RELICENSING

    “Massive Multiauthor Collaboration Site” (or “MMC Site”) means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A “Massive Multiauthor Collaboration” (or “MMC”) contained in the site means any set of copyrightable works thus published on the MMC site.

    “CC-BY-SA” means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.

    “Incorporate” means to publish or republish a Document, in whole or in part, as part of another Document.

    An MMC is “eligible for relicensing” if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.

    The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.

ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

  Copyright (C)  year  your name.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with…Texts.” line with this:

    with the Invariant Sections being list their titles, with
    the Front-Cover Texts being list, and with the Back-Cover Texts
    being list.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

Index