Java Expressions Library

Dr. Konstantin L. Metlov


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 Appendix.

Table of Contents

1. About this manual
2. JEL design goals
3. Features
4. How to use JEL.
5. Using libraries
Exporting static methods of classes to JEL namespace.
Exporting virtual methods of classes to JEL namespace.
Enabling the dot operator on objects.
Dynamic variables interface.
Objects down-casting.
6. Automatic unwrapping of objects to primitive types.
7. Error detection and reporting
8. Making things faster
9. Serialization of compiled expressions
10. Limitations of JEL
11. Summarizing remarks
A. GNU Free Documentation License

Chapter 1. About this manual

This manual is mostly examples-based. It starts with two simple step-by-step examples (showing how to deal with static and dynamic libraries), which should give enough information for basic JEL usage (but don't forget to read the rest of this manual to learn how to get the top performance from JEL). Additional information can be found in API documentation.

Chapter 2. JEL design goals

The main design goal was to create light weight expression compiler generating extremely fast code. The main emphasis is the code execution time and not the compilation time (it is nevertheless small). The other goal was to make JEL language to be very close to Java language with direct access to all built-in Java data types and functions.

Chapter 3. Features

  • Support for all Java data types (boolean, byte, char, short, long, int, float, double, arrays, references)

  • Octal (0456) and hexadecimal (0x1FFF) literals.

  • Support for all Java arithmetic operators: + (add),- (subtract), * (multiply), / (divide), % (remainder), & (bitwise and),| (bitwise or), ^ (bitwise xor),~ (bitwise complement), << (left shift), >> (right signed shift), >>> (right unsigned shift); on most of supported data types according to Java Language Specification (JLS)

  • Comparison operators (==,!=,<,>=,>,<=) as defined by Java Language Specification (JLS).

  • dot (".") operator on objects ("abc".length()==3).

  • dot (".") operator on objects ("abc".length()==3).

  • Boolean logical operators (&&,||,!) with lazy evaluation (i.e. in the expression false&&complexBooleanFunction() the function is never called).

  • Conditionals (true?2:3 = 2)

  • Direct access to methods and fields of Java objects.

  • Method overloading according to JLS.

  • Dynamic variables interface allowing to add variables to JEL namespace without supplying the class file defining them.

  • Automatic unwrapping of designated objects to Java primitive types.

  • Support for strings. Objects of class java.lang.String can be directly entered into expressions using double quotes, also the standard Java escape codes are parsed. Example : "a string\n\015".

  • String concatenation ("a"+2+(2>3)+object = "a2false"+object.toString()).

  • User definable string comparison using usual relational operators "<", "<=", ">", ">=", "==", "!=", which employs locale by default.

  • User-controllable object down-casting using "(" syntax. It is possible to assign names to classes in JEL expressions to be different from their real Java class names.

  • Constants folding, extended (by default, but can be controlled) to static methods (which are automatically called at compile time) and static fields (which are considered constants).

  • High performance of generated code.

Chapter 4. How to use JEL.

In this section a simple example of a program using JEL is given, and explained with references to more detailed sections of this manual. The example program evaluates the expression given on its command line (similar program exists in the distribution under the name ./samples/, let's follow it step by step.

    public static void main(String[] args) {
    // Assemble the expression
    StringBuffer expr_sb=new StringBuffer();
    for(int i=0;i<args.length;i++) {
      expr_sb.append(' ');
    String expr=expr_sb.toString();

This first part of the program is not related to JEL. It's purpose is to assemble the expression, possibly, containing spaces into the single line. This has to be done, because shells tend to tokenize parameters but we don't need it here.

    // Set up the library
    Class[] staticLib=new Class[1];
    try {
    } catch(ClassNotFoundException e) {
      // Can't be ;)) ...... in java ... ;)
    Library lib=new Library(staticLib,null,null,null,null);
    try {
    } catch (NoSuchMethodException e) {
      // Can't be also

This piece of code establishes the namespace for use in JEL compiled expressions. The gnu.jel.Library object maintains this namespace.

There can be two types of names in the Library : static and virtual (dynamic).

Methods and variables of the first class are assumed (by default) to be dependent only on their arguments i.e. not to save any information from call to call (they are "stateless")... Examples are mathematical functions like sin, cos, log, constants E, PI in java.lang.Math. For such methods (fields) it does not matter how many times (when) they will be called (their value will be taken) the result will always be the same provided arguments (if they are present) are the same. Stateless methods will be evaluated by JEL at compile time if their arguments are constants (known at compile time). To define set of static functions(fields) it is needed to pass the array of Class objects, defining those functions, as the first parameter of the library constructor (see example above). Note ONLY STATIC functions of the Classes, passed in the first argument of the gnu.jel.Library constructor will be defined in the namespace. By default all static functions are considered "stateless" by JEL.

However, some static functions still save their state (in static variables) in between calls. Thus they return different results, depending on when (how many times) they are is called even if their arguments are the same. If such function is evaluated at compile time, we have troubles, because it will be evaluated only once during expression lifetime and it's state dependence will be lost. Typical example of the static function, having a state is java.lang.Math.random. JEL has special mechanism, provided by gnu.jel.Library class to mark static functions as state dependent. (see the above example to find out how it was done for the java.lang.Math.random)

The virtual functions, which are explicitly state dependent, will be discussed later in this document. The example we currently consider does not use them. However, virtual functions are, actually, most important to JEL because expression, containing all stateless functions, is a constant, it will be completely evaluated at compile time, there is absolutely no sense to evaluate such expression repeatedly (this is what JEL was designed for). Still we shall continue with this simple example as the following code is mostly independent of whether we use virtual functions or not...

    // Compile
    CompiledExpression expr_c=null;
    try {
    } catch (CompilationException ce) {
      System.err.print("–––COMPILATION ERROR :");
      System.err.print("                       ");
      int column=ce.getColumn(); // Column, where error was found
      for(int i=0;i<column+23-1;i++) System.err.print(' ');

This chunk of code is for the expression compilation. The crucial line is the call to Evaluator.compile, it is the point, where expression gets transformed into Java bytecode, loaded into the Java Virtual Machine using JEL ClassLoader and returned to caller as an instance of the subclass of gnu.jel.CompiledExpression. Typical user of JEL is not required to know what magic is going on inside of Evaluator.compile(...). Other code in this chunk is for the error reporting and will be discussed in the specialized section Error detection and reporting below.

      if (expr_c !=null) {
      // Evaluate (Can do it now any number of times FAST !!!)
      Number result=null;
      try {
      } catch (Throwable e) {
	System.err.println("Exception emerged from JEL compiled"+
			   " code (IT'S OK) :");

This code does the evaluation of the expression. It is done by calling the evaluate method of the JEL compiled class, it is defined abstract in gnu.jel.CompiledExpression but is redefined in the class compiled by JEL. The argument of this method is discussed in the section on virtual functions below. If only static functions are present in the library it is safe to pass the null pointer as the argument to evaluate.

Result of the evaluate method is always an object. JEL converts primitive numeric types into instances of corresponding Java reflection classes (read the section Making things faster to find out how to avoid this conversion). For example, a value of primitive type long will be returned as an instance of java.lang.Long class (int maps to java.lang.Integer, float to java.lang.Float, etc.). If result is an arbitrary Java object it is returned as the reference to that object.


try ... catch

clause around the call to evaluate will be enforced by the Java compiler. It is required as errors can appear during evaluation. The general rule is: syntax, types incompatibility and function resolution errors will be reported at compile time (as thrown instance of gnu.jel.CompilationException), while the errors in the values of numbers will be reported at the execution time. For example expression "1/0" will generate no error at compile time (nevertheless it is the constant expression and its evaluation is attempted), but at the time of calling execute you will get a java.lang.ArithmeticError (division by zero) as it should be.

      // Print result
      if (result==null) 

This last piece of code will print the result. And is concluding our brief tour of the JEL usage.

Chapter 5. Using libraries

The namespace of JEL expressions is represented by gnu.jel.Library class. Its constructor:

Library(Class[] staticLib, Class[] dynamicLib,
Class[] dotClasses, DVMap  resolver,
Hashtable cnmap)

has five arguments. Their purposes are following:


enumerates classes whose static methods are exported to JEL namespace and become usable from within expressions. Such methods do not require this pointer supplied to them at execution time. More details


enumerates classes whose virtual methods are exported. These methods require the references to the corresponding classes (this pointers) supplied to the expression at run-time. This is done using the Class[]> argument of CompiledExpression's evaluate method. More details


controls access for the dot (".") operator on classes. More details


Dynamic variables interface. Allows to add new variables to the expressions names without supplying the class files defining them. More details


Maps the class names usable inside JEL expressions for non-primitive type casts into the Java classes More details

The details on usage of each of these arguments are given in a separate sections below.

The working example using all current functionality of JEL namespace is given in the examples/YourTestBed directory in the distribution. You'll want to check it after reading this section.

Exporting static methods of classes to JEL namespace.

The array of references to classes (java.lang.Class) whose public static methods and fields are to be exported should be passed as the first argument of the library constructor (staticLib). The public static fields and methods of all these classes are merged together into the JEL namespace. The non-public or non-static members of staticLib classes are ignored.

Methods overloading is supported and works also across classes (because the JEL namespace works similarly to the namespace defined in a single Java class). For example, if a class C1 contains the method public static C1.func(int) and a class C2 contains the method public static C2.func(double) and both these classes are passed as elements of the staticLib array. Then, the JEL expression "func(1)" calls C1.func(int) and the expression "func(1.0)" calls C2.func(double). It also means that methods and fields of all classes supplied to the Library are subject to the same constraints as members of a single Java class.

Moreover, because JEL allows to call methods with no arguments omitting the empty brackets (that is "func()" and "func" are equivalent) there should be no fields and methods with no arguments having the same names in all classes presented to the Library constructor.

To check whether the set of classes you gave to the library constructor satisfies all required constraints run your program against the debug version of JEL library (jel_g.jar). Then, potential problems will be reported to you on the standard output.

Exporting virtual methods of classes to JEL namespace.

The second argument of the library constructor (dynamicLib) works similarly to the first one. Except that only public virtual members are taken from the listed classes. These members are merged into the namespace created from classes from the staticLib. The rules for methods overloading are the same as for classes listed in the first argument of library constructor. Also, the overloading is working across the classes listed in both first and second arguments of the Library constructor.

The crucial difference in the handling of classes listed in the dynamicLib and the staticLib comes from the fact that virtual members of dynamicLib require this reference to the instance of the object of their defining class be supplied at run-time. Thus, if C1 contains the virtual method public func(double x) its invocation actually requires two arguments, one is x and the other is the reference to the instance of class C1.

References to the instances of classes of the dynamicLib array are supplied at the execution time to the argument of the evaluate(Object[] context) method of gnu.jel.CompiledExpression. The elements of the context array should be instances of classes listed in dynamicLib array at compile time and there should be one-to-one correspondence between them. For example, if


, the corresponding entry in the context array, context[0], must be a reference to the instance of com.mycompany.MyClass.

Formally, for every i, it should be possible to cast the object in the context[i] into the class, supplied in the dynamicLib[i] array of the Library constructor, otherwise ClassCastException will be thrown from evaluate.

Let's walk through the example, which calculates function of the single variable many times and uses virtual method calls. This example will consist of two classes : a user written class (providing access to the variable) and the main class compiling and evaluating expressions. First start with the variable provider:

public class VariableProvider {
  public double xvar;
  public double x() {return xvar;};

This class is trivial, it just defines the function, returning the value of the variable x.

In the main class (see the first JEL example for headers) the code, constructing the library will be replaced with:

    // Set up library
    Class[] staticLib=new Class[1];
    try {
    } catch(ClassNotFoundException e) {
      // Can't be ;)) ...... in java ... ;)

    Class[] dynamicLib=new Class[1];
    VariableProvider variables=new VariableProvider();
    Object[] context=new Object[1];
    Library lib=new Library(staticLib,dynamicLib,null,null,null);
    try {
    } catch (NoSuchMethodException e) {
      // Can't be also

Absent in the static example, the additional code creates the VariableProvider and assigns its reference to an element of context array (to be passed to the evaluate method of the compiled expression). Also, now the dynamicLib array as not null and contains the reference to the VariableProvider class.

The code for compilation is exactly the same as in the example for static functions, except we have additional function x and the variable xvar defined for use inside the compiled expressions. JEL has the special notation for the functions, having no arguments, namely, brackets in "x()" can be omitted to be "x". This allows to compile now ( with the above defined library) the expressions like "sin(x)", "exp(x*x)", "pow(sin(x),2)+pow(cos(x),2)"...

The code for evaluation of an expression having virtual functions is replaced with:

      if (expr_c !=null) {
        try {
           for(int i=0;i<100;i++) {
              variables.xvar=i;      // <- Value of the variable
                               //^^^^^^^^^^^^^^^ evaluating 100 times
        } catch (Throwable e) {
	   System.err.println("Exception emerged from JEL compiled"+
		              " code (IT'S OK) :");

Note the two major differences: 1. we have explicitly assigned the value to the variable; 2. the array of object references (consisting of one element in this example) is passed to the evaluate method. This piece of code will evaluate expressions for x=0..99 with step 1.

This concludes our dynamic library example. Try to modify the ./ sample yourself to allow compilation of virtual functions as described above.

Enabling the dot operator on objects.

The third argument of gnu.jel.Library constructor enumerates classes which are available for dot operator within the expression. If this parameter is null JEL would not allow to use the dot operator at all. If it is an array of the length zero (e.g. new Class[0]) JEL will open access to public methods of ALL objects encountered in the expression. From the security point of view allowing access to all objects can be dangerous, that is why there is a third case of non-zero length array explicitly enumerating classes allowing the dot operator on them.

Once the dot operator is allowed on a class, it is possible to call all its public methods using the syntax ".method(arg1,arg2,...)" in any context where this class appears in an expression.

Dynamic variables interface.

All methods of exporting names into JEL namespace described up to this point relied on the Java class files for actual description of methods names and parameters. However, sometimes it is required to add a new variable to JEL namespace at run-time.

One of the solutions would be to generate a new class file (e.g. using JEL) and supply it as a first or second argument of the library constructor. Unfortunately this can be quite cumbersome and time consuming.

The other solution can be to define a family of methods in JEL namespace

YYY getXXXProperty(String name)

for each possible variable types, where YYY is the class representing the property type and XXX is the name of the type. Then, supposing we have methods

  double getDoubleProperty(String name); // YYY=double XXX=Double
  String getStringProperty(String name); // YYY=java.lang.String XXX=String

in the JEL namespace (either static or dynamic), the variables with arbitrary names can be entered into expression using the syntax

getStringProperty("x") +

This way has two drawbacks: 1) user has to remember the type of the variable (to call the appropriate getXXX() method); 2) a lot to type.

Since the version 0.9.3 JEL provides the way to solve both these problems. To do that the fourth argument (resolver) of the library constructor is used. This argument supplies the reference to the subclass of gnu.jel.DVMap, and is used by JEL to resolve the dynamic variable names. The gnu.jel.DVMap has an abstract method

public String getTypeName(String  name)

which returns XXX (see above) for a given variable name, or null if no such variable is defined. Note that for resolver to work the family of methods

YYY getXXXProperty(String name)

must still be present in JEL namespace (e.g. as members of one of dynamicLib[] classes).

Then, supposing

resolver.getTypeName("x")=="String" &&

the expression "x+(y+1.0)" will be automatically converted by JEL into


and compiled. Thus, user does not have to remember the variable types, typing is reduced and the existence of variables can be checked at the compile time.

JEL also supports a hierarchical structure of variables. This means the dot (".") symbol can be present in the dynamic variable names. For example if

resolver.getTypeName("x")!=null && 
resolver.getTypeName("x.f1")=="String" && 

the expression "x.f1+(x.f2+1.0)" will be compiled by JEL as


and (combined with dot operator) the expression "x.f1.length()" will result in the length of the string getString("x1.f1").

Notice in the last example that if one wants to have defined the dynamic variable "x.y" the variable "x" must also be the dynamic variable (resolver.getTypeName("x")!=null).

If there is conflict between the dynamic variable name and other name in JEL namespace the dynamic variable has a priority.

Since JEL 0.9.9 it is possible to translate the names of dynamic variables from strings into the constants of Java primitive types. This is done using non-identity DVMap.translate method. The translation helps to improve performance in some cases.

Consider the following example. Suppose the underlying storage for dynamic variables is an array (or Vector), so that the value of the variable can be obtained by an integer index into that array (like numbered columns in a spreadsheet). Next, assume you still want to refer to the variables by names (e.g. you allowed user to assign names to the columns). Now, if the first column is named "x" and is of Double type, an expression "x", using dynamic variables interface with identity translation will be compiled into getDoubleProperty("x"). It means the translation of the string "x" into the column number 1 will have to be performed at run-time each time the expression is evaluated. Considering that Java strings are immutable, this may incur a substantial performance penalty.

The performance can be improved if the translate method of DVMap is overridden by the following:

public Object translate(String name) {
   if (name.equals("x")) return new Integer(1);
   return name;

This is already a non-identity translation. With such DVMap the expression "x" will be compiled by JEL into getDoubleProperty(1), note that it is getDoubleProperty(int) method, which is called. This way the mapping of the variable name into the variable index is performed at compile-time, while at run-time the index is readily available. By defining the appropriate translations the dynamic variable lookup can be split in a user-controlled way between the expression compilation and execution stages to achieve the best performance.

The translate method is allowed to return only instances of Java reflection classes wrapping the primitive types (java.lang.Integer, java.lang.Double, etc), or strings (otherwise an exception will emerge at compile-time). This is because only these types of objects can be stored in the Java class files directly. Also, it is responsibility of the caller to ensure that JEL namespace contains getXXXProperty methods with all the necessary argument types, corresponding to the translations defined in DVMap. For identity translations only getXXXProperty methods accepting strings are necessary.

Objects down-casting.

The cnmap argument of gnu.jel.Library constructor, allows to enable the non-primitive type casts in JEL compiled expressions. If cnmap!=null it must be java.util.Hashtable with java.lang.Class objects as elements and java.lang.String objects as keys. When the object cast "(non_primitive_type_name) var" is encountered in the expression, "the non_primitive_type_name" string is looked in the cnmap hashtable and the cast to the corresponding class is generated by JEL. The absence of the name in the hashtable produces the compile-time error. It is possible for keys in cnmap to contain "." (dot) symbols in them.

Chapter 6. Automatic unwrapping of objects to primitive types.

This problem appears mostly when one uses dynamic variables, but may also arise in other cases. Suppose a reference to the object of the class Weight (representing a weight of a certain item) appeared in the expression. It is clear that Weight is always represented by a floating point number (although it may have other properties, like units). If the class Weight has the method

public double getValue()

the value of weight can be accessed in expressions using syntax w.getValue(), supposing the variable w has type Weight.

To save typing (since version 0.9.3 of JEL) one may have the class Weight implement gnu.jel.reflect.Double interface. Then, the aforementioned getValue method will be called automatically by JEL (or object w will be "unwrapped" to primitive type). This unwrapping will be performed automatically when needed: one can have expressions "w+1.0" meaning "w.getValue()+1" and "w.getUnits()" both valid (in the second case w is not "unwrapped").

There are gnu.jel.reflect.* interfaces for all Java primitive types. To use the automatic unwrapping one just needs to make his classes to implement one of these interfaces.

There is a similar mechanism for strings (since version 0.9.6) and a corresponding empty interface gnu.jel.reflect.String to denote objects automatically convertible to java.lang.String by means of their .toString() method. For example, if x is of a class implementing gnu.jel.reflect.String interface the expression x+"a" will be compiled into x.toString()+"a" (otherwise this expression produces a error message). The objects automatically convertible to strings can also be supplied as arguments of methods requiring java.lang.String (usual method overloading rules apply). Still, in the current version of JEL it is impossible to cast methods of java.lang.String on such objects. That is x.substring(1) is a syntax error (unless x> itself has the .substring(int) method). This deficiency can be addressed in future.

Chapter 7. Error detection and reporting

Expressions are made by human, and making errors is the natural property of humans, consequently, JEL has to be aware of that.

There are two places, where errors can appear. First are the compilation errors, which are thrown in the form of gnu.jel.CompilationException by the gnu.jel.Evaluator.compile. These errors signal about syntax problems in the entered expressions, wrong function names, illegal types combinations, but NOT about illegal values of arguments of functions. The second source of errors is the compiled code itself, Throwables, thrown out of gnu.jel.CompiledExpression.evaluate are primarily due to the invalid values of function arguments.

Compilation errors are easy to process. Normally, you should surround compilation by the

   try {
      // ... compilation
   catch (CompilationException e) {
      // ... process and report the error

block. Caught gnu.jel.CompilationException can be interrogated, then, on the subject of WHERE error has occurred (getCol) and WHAT was the error (getMessage). This information should then be presented to user. It is wise to use information about error column to position the cursor automatically to the erroneous place in the expression.

Errors of the second type are appearing during the function evaluation and can not be so nicely dealt with by JEL. They depend on the actual library, supplied to the compiler. For example methods of java.lang.Math do not generate any checked exceptions at all (still, Errors are possible), but you may connect library, of functions throwing exceptions. As a general rule : exceptions thrown by functions from the library are thrown from evaluate method

Chapter 8. Making things faster

In the above text the result of the computation, returned by evaluate was always an object. While this is very flexible it is not very fast. Objects have to be allocated on heap and garbage collected. When the result of computation is the Java primitive type it can be desirable to retrieve it without creation of the object. This can be done (since the version 0.2 of JEL) with evaluateXX() family of calls (see gnu.jel.CompiledExpression. There is an evaluateXX() method for each Java primitive type, if you know what type expression has you can just call the corresponding method.

If you do not know the type of the compiled expression you can query it using getType. Be warned, that the call to wrong evaluateXX method will result in exception. Another tricky point is that JEL always selects smallest data type for constant representation. Namely, expression "1" has type byte and not int, thus in most cases you will have to query the type, and only then, call the proper evaluateXX method.

It is anyway possible to eliminate type checks at evaluation time completely. There is a version of compile method in gnu.jel.Evaluator, which allows to fix the type of the result. It directs the compiler to perform the widening conversion to the given type, before returning the result. For example: if you fix the type to be int (passing java.lang.Integer.TYPE as an argument to compile) all expressions (such as "1", "2+5", "2*2") will be evaluated by evaluate_int method of the compiled expression. Also, the attempt to evaluate "1+2L" will be rejected by compiler, asking to insert the explicit narrowing conversion (such as "(int)(1+2L)").

Chapter 9. Serialization of compiled expressions

There used to be a specialized serialization interface in JEL up to version 0.8.3. The need for such interface was dictated by the fact that JEL allowed to use constants of arbitrary reference types in expressions, which is not supported directly by the Java class file format. Starting with version 0.9 this feature was removed and now JEL generates ordinary Java class files.

To store compiled expressions into a file just grab their code with gnu.jel.Evaluator.compileBits. The code is returned as a byte array which is easy to save/restore. Then, the expression can be instantiated using gnu.jel.ImageLoader with the code

byte[] image; 
// ... code to read the JEL-generated class file into the "image" ...
CompiledExpression expression=(CompiledExpression)(ImageLoader.load(image)).newInstance();

or, alternatively, by compiling your source against generated class file. Note that in this version of JEL all generated classes have the name "dump" and are in the root package. If there will be such need in future the Evaluator interface can be extended to assign user-supplied names for new expressions.

Chapter 10. Limitations of JEL

There is one serious limitation, which should be mentioned. Actually it is not a JEL limitation but rather a limitation of the typical Java run-time

To load compiled expressions into the Java virtual machine memory JEL uses a custom java.lang.ClassLoader. While there is nothing wrong with that, setting up a classLoader is a privileged operation in Java. This means either JEL should run in a Java application (there are no security restrictions on Java applications), or , if JEL is distributed in some custom applet the applet should be signed.

Chapter 11. Summarizing remarks

I hope you found JEL useful. Don't hesitate to contact me if there are any problems with JEL, please, report BUGS, suggest tests, send me your patches,... There are still many improvements to be done.

Most current information about JEL should be available at

JEL is the "free software" and is distributed to you under terms of GNU General Public License. Find the precise terms of the license in the file ./COPYING in the root of this distribution.

Please, contact the author directly if you'd like JEL to be commercially licensed to you on a different terms.

Appendix A. GNU Free Documentation License

Version 1.3, 3 November 2008

Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.

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


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.


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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.


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.


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.


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.


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”.


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.


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.


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.


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.


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 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.


“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 © 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.