Valgrind HOWTO
Deepak P.
<pdeepak16@vsnl.com>
              Â
Sandeep S.
<sandeep_gect@yahoo.com>
               Â
24 August 2002
Revision History
Revision 1.1 2002-09-15 tab
Converted to XML 4.1.2, added gfdl, reviewed, author revisions
Revision 1.0 2002-08-24 SS
Initial release
Abstract
This document is a guide to Valgrind, the malloc debugger. Valgrind 1.0.0 is
described.
-------------------------------------------------------------------------------
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
1._PREAMBLE
2._APPLICABILITY_AND_DEFINITIONS
3._VERBATIM_COPYING
4._COPYING_IN_QUANTITY
5._MODIFICATIONS
6._COMBINING_DOCUMENTS
7._COLLECTIONS_OF_DOCUMENTS
8._AGGREGATION_WITH_INDEPENDENT_WORKS
9._TRANSLATION
10._TERMINATION
11._FUTURE_REVISIONS_OF_THIS_LICENSE
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,_GNU_Free_Documentation_License 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. http://developer.kde.org/~sewardj/
2. http://freshmeat.net/projects/valgrind/
3.2. Installing
Uncompress, compile and install it:
#tar xvfz valgrind-1.0.0.tar.gz
#cd valgrind-1.0.0
#./configure
#make
#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.â€
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
alloc'd
==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.
4.2.3.1. 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.
4.2.3.2. 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 */
free(p);
return 0;
}
Here you are trying to read/write from/to address (p+sizeof(int)*11) which is
not allocated to the program.
4.2.3.3. 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);
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 invalid.
4.2.3.4. 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:
--leak-check=yes
==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.
4.2.3.5. 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 */
free(p);
return 0;
}
==1045== Syscall param read(buf) contains unaddressable
byte(s)
==1045== at 0x4032AF44: __libc_read (in
/lib/i686/libc-2.2.2.so)
==1045== by 0x4026D177: __libc_start_main
(../sysdeps/generic/libc-start.c:129)
==1045== by 0x80483E1: read@@GLIBC_2.0 (in
/home/deepu/valg/a.out)
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.
4.2.3.6. 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
Type
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, valgrind.so. A shell script valgrind sets the
LD_PRELOAD environment variable to point to valgrind.so. 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
valgrind.so. 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 one.
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];
free(a);
free(p);
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];
free(a);
free(p);
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;
free(p);
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==
==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==
==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
cache.
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
level.
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 understandable.
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. http://developer.kde.org/~sewardj/docs/
2. The most valuable source of information is the source code itself.
A. GNU Free Documentation License
Version 1.1, March 2000
Copyright (C) 2000 Free Software Foundation, Inc. 59 Temple Place,
Suite 330, Boston, MA 02111-1307 USA Everyone is permitted to copy
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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.
5. 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:
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
sentence.
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 therein.
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 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.
6. 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.
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."
7. 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.
8. 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, 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.
9. 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 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.
10. TERMINATION
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.
11. 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.
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
software.