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Valgrind HOWTO

Deepak P.

Sandeep S.

24 August 2002
Revision History                                                             
Revision 1.1           2002-09-15            Revised by: tab                 
Converted to XML 4.1.2, added gfdl, reviewed, author revisions               
Revision 1.0           2002-08-24            Revised by: SS                  
Initial release                                                              

 This document is a guide to Valgrind, the malloc debugger. Valgrind 1.0.0 is

Table of Contents
1. Background
2. Introduction
    2.1. Purpose
    2.2. Acknowledgments
    2.3. Copyright and Distribution Policy
    2.4. Feedback and Corrections
3. Getting it Installed
    3.1. Getting Valgrind
    3.2. Installing
4. A Closer View
    4.1. Why Valgrind?
    4.2. Usage
    4.3. Limitations and Dependencies of Valgrind.
5. Let's Go Deeper
    5.1. How Valgrind Tracks Validity of Each Byte
    5.2. Cache Profiling
6. Concluding Remarks
7. References
A. GNU Free Documentation License
    A.12. How to use this License for your documents

1. Background

 Dynamic storage allocation plays an important role in C programming; it is
also the breeding ground of numerous hard-to-track-down bugs. Freeing an
allocated block twice, running off the edge of the malloc'ed buffer, and
failing to keep track of addresses of allocated blocks are common errors
which frustrate the programmer - debugging them is very difficult due to the
errors manifesting themselves as "mysterious behavior" at places far off from
the point where the programmer actually committed the blunder.

2. Introduction

2.1. Purpose

 Valgrind is an open-source tool for finding memory-management problems in
Linux-x86 executables. It detects memory leaks/corruption in the program
being run. It is being developed by [] Julian Seward.

2.2. Acknowledgments

 We express our sincere appreciation to Julian Seward for creating Valgrind.
Thanks to Mr.Pramode C.E and also friends at the Govt Engineering College,
Trichur for their advice and cooperation.

2.3. Copyright and Distribution Policy

 Copyright (C)2002 Deepak P, Sandeep S.

Permission is granted to copy, distribute and/or modify this document under
the terms of the GNU Free Documentation License, Version 1.1 or any later
version published by the Free Software Foundation; with no Invariant
Sections, with no Front-Cover Texts, and no Back-Cover Texts. A copy of the
license is included in Appendix A entitled "GNU Free Documentation License".

2.4. Feedback and Corrections

 Kindly forward feedback and criticism to []
Deepak.P or/and [] Sandeep.S. We shall be
indebted to anybody who points out errors and inaccuracies in this document;
we will rectify them as soon as we are informed.

3. Getting it Installed

3.1. Getting Valgrind

 Valgrind may be obtained from the following locations:

 1. []
 2. []

3.2. Installing

 Uncompress, compile and install it:
             #tar xvfz valgrind-1.0.0.tar.gz                                 
             #cd valgrind-1.0.0                                              
             #make install                                                   

 Add the path to your path variable. Now valgrind is ready to catch the bugs.

4. A Closer View

4.1. Why Valgrind?

 As said above, memory management is prone to errors that are too hard to
detect. Common errors may be listed as:


 1. Use of uninitialized memory
 2. Reading/writing memory after it has been freed
 3. Reading/writing off the end of malloc'd blocks
 4. Reading/writing inappropriate areas on the stack
 5. Memory leaks -- where pointers to malloc'd blocks are lost forever
 6. Mismatched use of malloc/new/new[] vs free/delete/delete[]
 7. Some misuses of the POSIX pthreads API

 These errors usually lead to crashes.

 This is a situation where we need Valgrind. Valgrind works directly with the
executables, with no need to recompile, relink or modify the program to be
checked. Valgrind decides whether the program should be modified to avoid
memory leak, and also points out the spots of "leak."

 Valgrind simulates every single instruction your program executes. For this
reason, Valgrind finds errors not only in your application but also in all
supporting dynamically-linked (.so-format) libraries, including the GNU C
library, the X client libraries, Qt if you work with KDE, and so on. That
often includes libraries, for example the GNU C library, which may contain
memory access violations.

4.2. Usage

4.2.1. Invoking Valgrind

 The checking may be performed by simply placing the word valgrind just
before the normal command used to invoke the program. For example:
#valgrind ps -ax                                                             

 Valgrind provides thousands of options. We deliberately avoid them, not to
make this article boring.

 The output contains the usual output of ps -ax also with the detailed report
by valgrind. Any error (memory related) is pointed out in the error report.

4.2.2. How to Identify the Error from the Error Report

 Consider the output of Valgrind for some test program:
   ==1353== Invalid read of size 4                                           
   ==1353==    at 0x80484F6: print (valg_eg.c:7)                             
   ==1353==    by 0x8048561: main (valg_eg.c:16)                             
   ==1353==    by 0x4026D177: __libc_start_main                              
(../sysdeps/generic/libc-start.c   :129)                                     
   ==1353==    by 0x80483F1: free@@GLIBC_2.0 (in /home/deepu/valg/a.out)     
   ==1353==    Address 0x40C9104C is 0 bytes after a block of size 40        
   ==1353==    at 0x40046824: malloc (vg_clientfuncs.c:100)                  
   ==1353==    by 0x8048524: main (valg_eg.c:12)                             
   ==1353==    by 0x4026D177: __libc_start_main                              
(../sysdeps/generic/libc-start.c   :129)                                     
   ==1353==    by 0x80483F1: free@@GLIBC_2.0 (in /home/deepu/valg/a.out)     

 Here, 1353 is the process ID. This part of the error report says that a read
error has occurred at line number 7, in the function print. The function
print is called by function main, and both are in the file valg_eg.c. The
function main is called by the function __libc_start_main at line number 129,
in ../sysdeps/generic/libc-start.c. The function __libc_start_main is called
by free@@GLIBC_2.0 in the file /home/deepu/valg/a.out. Similarly details of
calling malloc are also given.

4.2.3. Types of Errors with Examples

 Valgrind can only really detect two types of errors: use of illegal address
and use of undefined values. Nevertheless, this is enough to discover all
sorts of memory management problems in a program. Some common errors are
given below.
----------------------------------------------------------------------------- Use of uninitialized memory

 Sources of uninitialized data are:

��*�local variables that have not been initialized.
��*�The contents of malloc'd blocks, before writing something there.

 This is not a problem with calloc since it initializes each allocated bytes
with 0. The new operator in C++ is similar to malloc. Fields of the created
object will be uninitialized.

 Sample program:
#include <stdlib.h>                                                          
int main()                                                                   
        int p, t;                                                            
        if (p == 5)             /*Error occurs here*/                        
                t = p+1;                                                     
        return 0;                                                            

 Here the value of p is uninitialized, therefore p may contain some random
value (garbage), so an error may occur at the condition check. An
uninitialized variable will cause error in 2 situations:

��*�When it is used to determine the outcome of a conditional branch. Eg:'if
    (p == 5)' in the above program.
��*�When it is used to generate a memory address. Eg: In the above program
    let there be an integer array a[10], and if you write 'a[p] = 1', it will
    generate an error.

----------------------------------------------------------------------------- Illegal read/write

 Illegal read/write errors occurs when you try to read/write from/to an
address that is not in the address range of your program.

 Sample program:
#include <stdlib.h>                                                          
int main()                                                                   
        int *p, i, a;                                                        
        p = malloc(10*sizeof(int));                                          
        p[11] = 1;                /* invalid write error */                  
        a = p[11];                /* invalid read error */                   
        return 0;                                                            

 Here you are trying to read/write from/to address (p+sizeof(int)*11) which
is not allocated to the program.
----------------------------------------------------------------------------- Invalid free

 Valgrind keeps track of blocks allocated to your program with malloc/new. So
it can easily check whether argument to free/delete is valid or not.

 Sample program:
#include <stdlib.h>                                                          
int main()                                                                   
        int *p, i;                                                           
        p = malloc(10*sizeof(int));                                          
        for(i = 0;i < 10;i++)                                                
                p[i] = i;                                                    
        free(p);        /* Error: p has already been freed */                
        return 0;                                                            

 Valgrind checks the address, which is given as argument to free. If it is an
address that has already been freed you will be told that the free is
----------------------------------------------------------------------------- Mismatched Use of Functions

 In C++ you can allocate and free memory using more than one function, but
the following rules must be followed:

��*�If allocated with malloc, calloc, realloc, valloc or memalign, you must
    deallocate with free.
��*�If allocated with new[], you must deallocate with delete[].
��*�If allocated with new, you must deallocate with delete.

 Sample program:
#include <stdlib.h>                                                          
int main()                                                                   
        int *p, i;                                                           
        p = ( int* ) malloc(10*sizeof(int));                                 
        for(i = 0;i < 10;i++)                                                
                p[i] = i;                                                    
        delete(p);                /* Error: function mismatch */             
        return 0;                                                            

 Output by valgrind is:
             ==1066== ERROR SUMMARY: 1 errors from 1 contexts (suppressed:   
0 from 0)                                                                    
             ==1066== malloc/free: in use at exit: 0 bytes in 0 blocks.      
             ==1066== malloc/free: 1 allocs, 1 frees, 40 bytes allocated.    
             ==1066== For a detailed leak analysis,  rerun with:             
             ==1066== For counts of detected errors, rerun with: -v          

 >From the above "ERROR SUMMARY" it is clear that there is 0 bytes in 0
blocks in use at exit, which means that the malloc'd have been freed by
delete. Therefore this is not a problem in Linux, but this program may crash
on some other platform.
----------------------------------------------------------------------------- Errors Occur Due to Invalid System Call Parameter

 Valgrind checks all parameters to system calls.

 Sample program:

#include <stdlib.h>                                                          
#include <unistd.h>                                                          
int main()                                                                   
        int *p;                                                              
        p = malloc(10);                                                      
        read(0, p, 100);        /* Error: unaddressable bytes */             
        return 0;                                                            

             ==1045== Syscall param read(buf) contains unaddressable         
             ==1045==    at 0x4032AF44: __libc_read (in                      
             ==1045==    by 0x4026D177: __libc_start_main                    
             ==1045==    by 0x80483E1: read@@GLIBC_2.0 (in                   

 Here, buf = p contains the address of a 10 byte block. The read system call
tries to read 100 bytes from standard input and place it at p. But the bytes
after the first 10 are unaddressable.
----------------------------------------------------------------------------- Memory Leak Detection

 Consider the following program:

#include <stdlib.h>                                                          
int main()                                                                   
        int *p, i;                                                           
        p = malloc(5*sizeof(int));                                           
        for(i = 0;i < 5;i++)                                                 
                p[i] = i;                                                    
        return 0;                                                            

             ==1048== LEAK SUMMARY:                                          
             ==1048==    definitely lost: 20 bytes in 1 blocks.              
             ==1048==    possibly lost:   0 bytes in 0 blocks.               
             ==1048==    still reachable: 0 bytes in 0 blocks.               

 In the above program p contains the address of a 20-byte block. But it is
not freed anywhere in the program. So the pointer to this 20 byte block is
lost forever. This is known as memory leaking. We can get the leak summary by
using the Valgrind option --leak-check=yes.

4.2.4. How to Suppress Errors

 Valgrind detects numerous problems in many programs which come pre-installed
on your GNU/Linux system. You can't easily fix these, but you don't want to
see these errors (and yes, there are many!). So Valgrind reads a list of
errors to suppress at startup, from a suppression file ending in .supp.

 Suppression files may be modified. This is useful if part of your project
contains errors you can't or don't want to fix, yet you don't want to
continuously be reminded of them. The format of the file is as follows.

             Error name                                                      
             fun:function name, which contains the error to suppress         
        fun:function name, which calls the function specified above          

Error name can be any name.                                                  
             type=ValueN, if the error is an uninitialized value error.      
                 =AddrN, if it is an address error.(N=sizeof(data type))     
                 =Free, if it is a free error (eg:mismatched free)           
                 =Cond, if error is due to uninitialized CPU condition code. 
                 =Param, if it is an invalid system call parameter error.    

 You can then run the program with:
valgrind --suppressions=path/to/the/supp_file.supp testprog                  
The output will not contain the errors specified in the suppression file.

4.3. Limitations and Dependencies of Valgrind.

 No software is free from limitations. The same is the case of Valgrind,
however most programs work fine. The limitations are listed below.

 1. Program runs 25 to 50 times slower.
 2. Increased memory consumption.
 3. Highly optimized code (compiled with -O1, -O2 options ) may sometimes
    cheat Valgrind.
 4. Valgrind relies on dynamic linking mechanism.

 Valgrind is closely tied to details of the CPU, operating system and to a
less extent, compiler and basic C libraries. Presently Valgrind works only on
the Linux platform (kernels 2.2.X or 2.4.X) on x86s. Glibc 2.1.X or 2.2.X is
also required for Valgrind.

5. Let's Go Deeper

 Valgrind simulates an Intel x86 processor and runs our test program in this
synthetic processor. The two processors are not exactly same. Valgrind is
compiled into a shared object, A shell script valgrind sets the
LD_PRELOAD environment variable to point to This causes the .so
to be loaded as an extra library to any subsequently executed
dynamically-linked ELF binary, permitting the program to be debugged.

 The dynamic linker calls the initialization function of Valgrind. Then the
synthetic CPU takes control from the real CPU. In the memory there may be
some other .so files. The dynamic linker calls the initialization function of
all such .so files. Now the dynamic linker calls the main of the loaded
program. When main returns, the synthetic CPU calls the finalization function
of During the execution of the finalization function, summary of
all errors detected are printed and memory leaks are checked. Finalization
function exits giving back the control from the synthetic CPU to the real

5.1. How Valgrind Tracks Validity of Each Byte

 For every byte processed, the synthetic processor maintains 9 bits, 8 'V'
bits and 1 'A' bit. The 'V' bits indicate the validity of the 8 bits in the
byte and the 'A' bit indicates validity of the byte address. These
valid-value(V) bits are checked only in two situations:

 1. when data is used for address generation,
 2. when control flow decision is to be made.

 In any of these two situations, if the data is found to be undefined an
error report will be generated. But no error reports are generated while
copying or adding undefined data.

 However the case with floating-point data is different. During a
floating-point read instruction the 'V' bits corresponding to the data are
checked. Thus copying of uninitialized value will produce error in case of
floating-point numbers.

#include <stdlib.h>                                                          
int main()                                                                   
        int *p, *a;                                                          
        p = malloc(10*sizeof(int));                                          
        a = malloc(10*sizeof(int));                                          
        a[3] = p[3];                                                         
        return 0;                                                            
/*  produce no errors */                                                     

#include <stdlib.h>                                                          
int main()                                                                   
        float *p, *a;                                                        
        p = malloc(10*sizeof(float));                                        
        a = malloc(10*sizeof(float));                                        
        a[3] = p[3];                                                         
        return 0;                                                            
/* produces error */                                                         

 All bytes that are in memory but not in CPU have an associated valid-address
(A) bit, which indicates whether the corresponding memory location is
accessible by the program. When a program starts, the 'A' bits corresponding
to each global variables are set. When a call malloc, new or any other memory
allocating function is made, the 'A' bits corresponding to the allocated
bytes are set. Upon freeing the allocated block using free/new/new???? the
corresponding 'A' bits are cleared. While doing a system call the 'A' bits
are changed appropriately.

 When values are loaded from memory the 'A' bits corresponding to each bytes
are checked by Valgrind, and if the 'A' bit corresponding to a byte is set
then its 'V' bits is checked. If the 'V' bits are not set, an error will be
generated and the 'V' bits are set to indicate validity. This avoids long
chain of errors. If the 'A' bit corresponding to a loaded byte is 0 then its
'V' bits are forced to set, despite the value being invalid.

 Have a look on the following program. Run it.
#include <stdlib.h>                                                          
int main()                                                                   
        int *p, j;                                                           
        p = malloc(5*sizeof(int));                                           
        j = p[5];                                                            
        if (p[5] == 1)                                                       
                i = p[5]+1;                                                  
        return 0;                                                            

 Here two errors occur. Both of them are due to the accessing address
location p + sizeof(int)*5 which is not allocated to the program. During the
execution of j = p[5], since the address p + sizeof(int)*5 is invalid, the
'V' bits of 4 bytes starting at location p+sizeof(int)*5 are forced to set.
Therefore uninitialized value occurs neither during the execution of j = p[5]
nor during the execution of if(p[5]==1).

5.2. Cache Profiling

 Modern x86 machines use two levels of caching. These levels are L1 and L2,
in which L1 is a split cache that consists of Instruction cache(I1) and Data
cache(D1). L2 is a unified cache.

 The configuration of a cache means its size, associativity and number of
lines. If the data requested by the processor appears in the upper level it
is called a hit. If the data is not found in the upper level, the request is
called a miss. The lower level in the hierarchy is then accessed to retrieve
the block containing requested data. In modern machines L1 is first searched
for data/instruction requested by the processor. If it is a hit then that
data/instruction is copied to some register in the processor. Otherwise L2 is
searched. If it is a hit then data/instruction is copied to L1 and from there
it is copied to a register. If the request to L2 also is a miss then main
memory has to be accessed.

 Valgrind can simulate the cache, meaning it can display the things that
occur in the cache when a program is running. For this, first compile your
program with -g option as usual. Then use the shell script cachegrind instead
of valgrind.

 Sample output:

==7436== I1  refs:      12,841                                               
==7436== I1  misses:       238                                               
==7436== L2i misses:       237                                               
==7436== I1  miss rate:   1.85%                                              
==7436== L2i miss rate:   1.84%                                              
==7436== D   refs:       5,914  (4,626 rd + 1,288 wr)                        
==7436== D1  misses:       357  (  324 rd +    33 wr)                        
==7436== L2d misses:       352  (  319 rd +    33 wr)                        
==7436== D1  miss rate:    6.0% (  7.0%   +   2.5%  )                        
==7436== L2d miss rate:    5.9% (  6.8%   +   2.5%  )                        
==7436== L2 refs:          595  (  562 rd +    33 wr)                        
==7436== L2 misses:        589  (  556 rd +    33 wr)                        
==7436== L2 miss rate:     3.1% (  3.1%   +   2.5%  )                        

   L2i misses means the number of instruction misses that occur in L2        
   L2d misses means the number of data misses that occur in L2 cache.        
   Total number of data references = Number of reads + Number of writes.     
   Miss rate means fraction of misses that are not found in the upper        

  The shell script cachegrind also produces a file, cachegrind.out, that
contains line-by-line cache profiling information which is not humanly
understandable. A program vg_annotate can easily interpret this information.
If the shell script vg_annotate is used without any arguments it will read
the file cachegrind.out and produce an output which is humanly

 When C, C++ or assembly source programs are passed as input to vg_annotate
it displays the number of cache reads, writes, misses etc.
I1 cache:         16384 B, 32 B, 4-way associative                           
D1 cache:         16384 B, 32 B, 4-way associative                           
L2 cache:         262144 B, 32 B, 8-way associative                          
Command:          ./a.out                                                    
Events recorded:  Ir I1mr I2mr Dr D1mr D2mr Dw D1mw D2mw                     
Events shown:     Ir I1mr I2mr Dr D1mr D2mr Dw D1mw D2mw                     
Event sort order: Ir I1mr I2mr Dr D1mr D2mr Dw D1mw D2mw                     
Thresholds:       99 0 0 0 0 0 0 0 0                                         
Include dirs:                                                                
User annotated:   valg_flo.c                                                 
Auto-annotation:  off                                                        

 User-annotated source: valg_flo.c:
Ir I1mr I2mr Dr D1mr D2mr Dw D1mw D2mw                                       
 .   .   .   .   .    .   .   .    .   #include<stdlib.h>                    
 .   .   .   .   .    .   .   .    .   int main()                            
 3   1   1   .   .    .   1   0    0   {                                     
 .   .   .   .   .    .   .   .    .           float *p, *a;                 
 6   1   1   .   .    .   3   0    0           p = malloc(10*sizeof(float)); 
 6   0   0   .   .    .   3   0    0           a = malloc(10*sizeof(float)); 
 6   1   1   3   1    1   1   1    1           a[3] = p[3];                  
 4   0   0   1   0    0   1   0    0           free(a);                      
 4   0   0   1   0    0   1   0    0           free(p);                      
 2   0   0   2   0    0   .   .    .   }                                     


��*�Ir = Total instruction cache reads.
��*�I1mr = I1 cache read misses.
��*�I2mr = L2 cache instruction read misses.

6. Concluding Remarks

 This document has gone through the basics of Valgrind. Once you understand
the basic concept it is not difficult to make steps on your own.

 If you have found any glaring typos, or outdated info in this document,
please let us know.

7. References

 1. []
 2. The most valuable source of information is the source code itself.

A. GNU Free Documentation License

Version 1.1, March 2000

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Transparent copy of the Document, free of added material, which the general
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public-standard network protocols. 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:

 A. 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.
 B. 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 less than five).
 C. State on the Title page the name of the publisher of the Modified
    Version, as the publisher.
 D. Preserve all the copyright notices of the Document.
 E. Add an appropriate copyright notice for your modifications adjacent to
    the other copyright notices.
 F. 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.
 G. Preserve in that license notice the full lists of Invariant Sections and
    required Cover Texts given in the Document's license notice.
 H. Include an unaltered copy of this License.
 I. Preserve the section entitled "History", and 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
 J. 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.
 K. In any section entitled "Acknowledgements" or "Dedications", preserve the
    section's title, and preserve in the section all the substance and tone
    of each of the contributor acknowledgements and/or dedications given
 L. 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.
 M. Delete any section entitled "Endorsements". Such a section may not be
    included in the Modified Version.
 N. Do not retitle any existing section as "Endorsements" or to conflict in
    title with any Invariant Section.

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

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.

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, does not as a whole count as a Modified Version of the
Document, provided no compilation copyright is claimed for the compilation.
Such a compilation is called an "aggregate", and this License does not apply
to the other self-contained works thus compiled with the Document, on account
of their being thus compiled, if they 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 quarter of the entire
aggregate, the Document's Cover Texts may be placed on covers that surround
only the Document within the aggregate. Otherwise they must appear on covers
around 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 provided that you also include
the original English version of this License. In case of a disagreement
between the translation and the original English version of this License, the
original English version will prevail.


You may not copy, modify, sublicense, or distribute the Document except as
expressly provided for under this License. Any other attempt to copy, modify,
sublicense or distribute the Document is void, and will automatically
terminate your rights under this License. However, parties who have received
copies, or rights, from you under this License will not have their licenses
terminated so long as such parties remain in full compliance.


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://

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.

A.12. 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 1.1 or any later version published by the Free Software
    Foundation; with the Invariant Sections being LIST THEIR TITLES, with the
    Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. A
    copy of the license is included in the section entitled "GNU Free
    Documentation License".
If you have no Invariant Sections, write "with no Invariant Sections" instead
of saying which ones are invariant. If you have no Front-Cover Texts, write
"no Front-Cover Texts" instead of "Front-Cover Texts being LIST"; likewise
for Back-Cover Texts.

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

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