This is gprof.info, produced by makeinfo version 7.1 from gprof.texi.

This file documents the gprof profiler of the GNU system.

   Copyright © 1988-2024 Free Software Foundation, Inc.

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under the terms of the GNU Free Documentation License, Version 1.3 or
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INFO-DIR-SECTION Software development
START-INFO-DIR-ENTRY
* gprof: (gprof).                Profiling your program's execution
END-INFO-DIR-ENTRY


File: gprof.info,  Node: Top,  Next: Introduction,  Up: (dir)

Profiling a Program: Where Does It Spend Its Time?
**************************************************

This manual describes the GNU profiler, ‘gprof’, and how you can use it
to determine which parts of a program are taking most of the execution
time.  We assume that you know how to write, compile, and execute
programs.  GNU ‘gprof’ was written by Jay Fenlason.

   This manual is for ‘gprof’ (GNU Binutils) version 2.43.

   This document is distributed under the terms of the GNU Free
Documentation License version 1.3.  A copy of the license is included in
the section entitled "GNU Free Documentation License".

* Menu:

* Introduction::        What profiling means, and why it is useful.

* Compiling::           How to compile your program for profiling.
* Executing::           Executing your program to generate profile data
* Invoking::            How to run ‘gprof’, and its options

* Output::              Interpreting ‘gprof’'s output

* Inaccuracy::          Potential problems you should be aware of
* How do I?::           Answers to common questions
* Incompatibilities::   (between GNU ‘gprof’ and Unix ‘gprof’.)
* Details::             Details of how profiling is done
* GNU Free Documentation License::  GNU Free Documentation License


File: gprof.info,  Node: Introduction,  Next: Compiling,  Prev: Top,  Up: Top

1 Introduction to Profiling
***************************

Profiling allows you to learn where your program spent its time and
which functions called which other functions while it was executing.
This information can show you which pieces of your program are slower
than you expected, and might be candidates for rewriting to make your
program execute faster.  It can also tell you which functions are being
called more or less often than you expected.  This may help you spot
bugs that had otherwise been unnoticed.

   Since the profiler uses information collected during the actual
execution of your program, it can be used on programs that are too large
or too complex to analyze by reading the source.  However, how your
program is run will affect the information that shows up in the profile
data.  If you don't use some feature of your program while it is being
profiled, no profile information will be generated for that feature.

   Profiling has several steps:

   • You must compile and link your program with profiling enabled.
     *Note Compiling a Program for Profiling: Compiling.

   • You must execute your program to generate a profile data file.
     *Note Executing the Program: Executing.

   • You must run ‘gprof’ to analyze the profile data.  *Note ‘gprof’
     Command Summary: Invoking.

   The next three chapters explain these steps in greater detail.

   Several forms of output are available from the analysis.

   The “flat profile” shows how much time your program spent in each
function, and how many times that function was called.  If you simply
want to know which functions burn most of the cycles, it is stated
concisely here.  *Note The Flat Profile: Flat Profile.

   The “call graph” shows, for each function, which functions called it,
which other functions it called, and how many times.  There is also an
estimate of how much time was spent in the subroutines of each function.
This can suggest places where you might try to eliminate function calls
that use a lot of time.  *Note The Call Graph: Call Graph.

   The “annotated source” listing is a copy of the program's source
code, labeled with the number of times each line of the program was
executed.  *Note The Annotated Source Listing: Annotated Source.

   To better understand how profiling works, you may wish to read a
description of its implementation.  *Note Implementation of Profiling:
Implementation.


File: gprof.info,  Node: Compiling,  Next: Executing,  Prev: Introduction,  Up: Top

2 Compiling a Program for Profiling
***********************************

The first step in generating profile information for your program is to
compile and link it with profiling enabled.

   To compile a source file for profiling, specify the ‘-pg’ option when
you run the compiler.  (This is in addition to the options you normally
use.)

   To link the program for profiling, if you use a compiler such as ‘cc’
to do the linking, simply specify ‘-pg’ in addition to your usual
options.  The same option, ‘-pg’, alters either compilation or linking
to do what is necessary for profiling.  Here are examples:

     cc -g -c myprog.c utils.c -pg
     cc -o myprog myprog.o utils.o -pg

   The ‘-pg’ option also works with a command that both compiles and
links:

     cc -o myprog myprog.c utils.c -g -pg

   Note: The ‘-pg’ option must be part of your compilation options as
well as your link options.  If it is not then no call-graph data will be
gathered and when you run ‘gprof’ you will get an error message like
this:

     gprof: gmon.out file is missing call-graph data

   If you add the ‘-Q’ switch to suppress the printing of the call graph
data you will still be able to see the time samples:

     Flat profile:

     Each sample counts as 0.01 seconds.
       %   cumulative   self              self     total
      time   seconds   seconds    calls  Ts/call  Ts/call  name
      44.12      0.07     0.07                             zazLoop
      35.29      0.14     0.06                             main
      20.59      0.17     0.04                             bazMillion

   If you run the linker ‘ld’ directly instead of through a compiler
such as ‘cc’, you may have to specify a profiling startup file ‘gcrt0.o’
as the first input file instead of the usual startup file ‘crt0.o’.  In
addition, you would probably want to specify the profiling C library,
‘libc_p.a’, by writing ‘-lc_p’ instead of the usual ‘-lc’.  This is not
absolutely necessary, but doing this gives you number-of-calls
information for standard library functions such as ‘read’ and ‘open’.
For example:

     ld -o myprog /lib/gcrt0.o myprog.o utils.o -lc_p

   If you are running the program on a system which supports shared
libraries you may run into problems with the profiling support code in a
shared library being called before that library has been fully
initialised.  This is usually detected by the program encountering a
segmentation fault as soon as it is run.  The solution is to link
against a static version of the library containing the profiling support
code, which for ‘gcc’ users can be done via the ‘-static’ or
‘-static-libgcc’ command-line option.  For example:

     gcc -g -pg -static-libgcc myprog.c utils.c -o myprog

   If you compile only some of the modules of the program with ‘-pg’,
you can still profile the program, but you won't get complete
information about the modules that were compiled without ‘-pg’.  The
only information you get for the functions in those modules is the total
time spent in them; there is no record of how many times they were
called, or from where.  This will not affect the flat profile (except
that the ‘calls’ field for the functions will be blank), but will
greatly reduce the usefulness of the call graph.

   If you wish to perform line-by-line profiling you should use the
‘gcov’ tool instead of ‘gprof’.  See that tool's manual or info pages
for more details of how to do this.

   Note, older versions of ‘gcc’ produce line-by-line profiling
information that works with ‘gprof’ rather than ‘gcov’ so there is still
support for displaying this kind of information in ‘gprof’.  *Note
Line-by-line Profiling: Line-by-line.

   It also worth noting that ‘gcc’ implements a ‘-finstrument-functions’
command-line option which will insert calls to special user supplied
instrumentation routines at the entry and exit of every function in
their program.  This can be used to implement an alternative profiling
scheme.


File: gprof.info,  Node: Executing,  Next: Invoking,  Prev: Compiling,  Up: Top

3 Executing the Program
***********************

Once the program is compiled for profiling, you must run it in order to
generate the information that ‘gprof’ needs.  Simply run the program as
usual, using the normal arguments, file names, etc.  The program should
run normally, producing the same output as usual.  It will, however, run
somewhat slower than normal because of the time spent collecting and
writing the profile data.

   The way you run the program--the arguments and input that you give
it--may have a dramatic effect on what the profile information shows.
The profile data will describe the parts of the program that were
activated for the particular input you use.  For example, if the first
command you give to your program is to quit, the profile data will show
the time used in initialization and in cleanup, but not much else.

   Your program will write the profile data into a file called
‘gmon.out’ just before exiting.  If there is already a file called
‘gmon.out’, its contents are overwritten.  You can rename the file
afterwards if you are concerned that it may be overwritten.  If your
system libc allows you may be able to write the profile data under a
different name.  Set the GMON_OUT_PREFIX environment variable; this name
will be appended with the PID of the running program.

   In order to write the ‘gmon.out’ file properly, your program must
exit normally: by returning from ‘main’ or by calling ‘exit’.  Calling
the low-level function ‘_exit’ does not write the profile data, and
neither does abnormal termination due to an unhandled signal.

   The ‘gmon.out’ file is written in the program's _current working
directory_ at the time it exits.  This means that if your program calls
‘chdir’, the ‘gmon.out’ file will be left in the last directory your
program ‘chdir’'d to.  If you don't have permission to write in this
directory, the file is not written, and you will get an error message.

   Older versions of the GNU profiling library may also write a file
called ‘bb.out’.  This file, if present, contains an human-readable
listing of the basic-block execution counts.  Unfortunately, the
appearance of a human-readable ‘bb.out’ means the basic-block counts
didn't get written into ‘gmon.out’.  The Perl script ‘bbconv.pl’,
included with the ‘gprof’ source distribution, will convert a ‘bb.out’
file into a format readable by ‘gprof’.  Invoke it like this:

     bbconv.pl < bb.out > BH-DATA

   This translates the information in ‘bb.out’ into a form that ‘gprof’
can understand.  But you still need to tell ‘gprof’ about the existence
of this translated information.  To do that, include BB-DATA on the
‘gprof’ command line, _along with ‘gmon.out’_, like this:

     gprof OPTIONS EXECUTABLE-FILE gmon.out BB-DATA [YET-MORE-PROFILE-DATA-FILES...] [> OUTFILE]


File: gprof.info,  Node: Invoking,  Next: Output,  Prev: Executing,  Up: Top

4 ‘gprof’ Command Summary
*************************

After you have a profile data file ‘gmon.out’, you can run ‘gprof’ to
interpret the information in it.  The ‘gprof’ program prints a flat
profile and a call graph on standard output.  Typically you would
redirect the output of ‘gprof’ into a file with ‘>’.

   You run ‘gprof’ like this:

     gprof OPTIONS [EXECUTABLE-FILE [PROFILE-DATA-FILES...]] [> OUTFILE]

Here square-brackets indicate optional arguments.

   If you omit the executable file name, the file ‘a.out’ is used.  If
you give no profile data file name, the file ‘gmon.out’ is used.  If any
file is not in the proper format, or if the profile data file does not
appear to belong to the executable file, an error message is printed.

   You can give more than one profile data file by entering all their
names after the executable file name; then the statistics in all the
data files are summed together.

   The order of these options does not matter.

* Menu:

* Output Options::      Controlling ‘gprof’'s output style
* Analysis Options::    Controlling how ‘gprof’ analyzes its data
* Miscellaneous Options::
* Deprecated Options::  Options you no longer need to use, but which
                            have been retained for compatibility
* Symspecs::            Specifying functions to include or exclude


File: gprof.info,  Node: Output Options,  Next: Analysis Options,  Up: Invoking

4.1 Output Options
==================

These options specify which of several output formats ‘gprof’ should
produce.

   Many of these options take an optional “symspec” to specify functions
to be included or excluded.  These options can be specified multiple
times, with different symspecs, to include or exclude sets of symbols.
*Note Symspecs: Symspecs.

   Specifying any of these options overrides the default (‘-p -q’),
which prints a flat profile and call graph analysis for all functions.

‘-A[SYMSPEC]’
‘--annotated-source[=SYMSPEC]’
     The ‘-A’ option causes ‘gprof’ to print annotated source code.  If
     SYMSPEC is specified, print output only for matching symbols.
     *Note The Annotated Source Listing: Annotated Source.

‘-b’
‘--brief’
     If the ‘-b’ option is given, ‘gprof’ doesn't print the verbose
     blurbs that try to explain the meaning of all of the fields in the
     tables.  This is useful if you intend to print out the output, or
     are tired of seeing the blurbs.

‘-B’
     The ‘-B’ option causes ‘gprof’ to print the call graph analysis.

‘-C[SYMSPEC]’
‘--exec-counts[=SYMSPEC]’
     The ‘-C’ option causes ‘gprof’ to print a tally of functions and
     the number of times each was called.  If SYMSPEC is specified,
     print tally only for matching symbols.

     If the profile data file contains basic-block count records,
     specifying the ‘-l’ option, along with ‘-C’, will cause basic-block
     execution counts to be tallied and displayed.

‘-i’
‘--file-info’
     The ‘-i’ option causes ‘gprof’ to display summary information about
     the profile data file(s) and then exit.  The number of histogram,
     call graph, and basic-block count records is displayed.

‘-I DIRS’
‘--directory-path=DIRS’
     The ‘-I’ option specifies a list of search directories in which to
     find source files.  Environment variable GPROF_PATH can also be
     used to convey this information.  Used mostly for annotated source
     output.

‘-J[SYMSPEC]’
‘--no-annotated-source[=SYMSPEC]’
     The ‘-J’ option causes ‘gprof’ not to print annotated source code.
     If SYMSPEC is specified, ‘gprof’ prints annotated source, but
     excludes matching symbols.

‘-L’
‘--print-path’
     Normally, source filenames are printed with the path component
     suppressed.  The ‘-L’ option causes ‘gprof’ to print the full
     pathname of source filenames, which is determined from symbolic
     debugging information in the image file and is relative to the
     directory in which the compiler was invoked.

‘-p[SYMSPEC]’
‘--flat-profile[=SYMSPEC]’
     The ‘-p’ option causes ‘gprof’ to print a flat profile.  If SYMSPEC
     is specified, print flat profile only for matching symbols.  *Note
     The Flat Profile: Flat Profile.

‘-P[SYMSPEC]’
‘--no-flat-profile[=SYMSPEC]’
     The ‘-P’ option causes ‘gprof’ to suppress printing a flat profile.
     If SYMSPEC is specified, ‘gprof’ prints a flat profile, but
     excludes matching symbols.

‘-q[SYMSPEC]’
‘--graph[=SYMSPEC]’
     The ‘-q’ option causes ‘gprof’ to print the call graph analysis.
     If SYMSPEC is specified, print call graph only for matching symbols
     and their children.  *Note The Call Graph: Call Graph.

‘-Q[SYMSPEC]’
‘--no-graph[=SYMSPEC]’
     The ‘-Q’ option causes ‘gprof’ to suppress printing the call graph.
     If SYMSPEC is specified, ‘gprof’ prints a call graph, but excludes
     matching symbols.

‘-t’
‘--table-length=NUM’
     The ‘-t’ option causes the NUM most active source lines in each
     source file to be listed when source annotation is enabled.  The
     default is 10.

‘-y’
‘--separate-files’
     This option affects annotated source output only.  Normally,
     ‘gprof’ prints annotated source files to standard-output.  If this
     option is specified, annotated source for a file named
     ‘path/FILENAME’ is generated in the file ‘FILENAME-ann’.  If the
     underlying file system would truncate ‘FILENAME-ann’ so that it
     overwrites the original ‘FILENAME’, ‘gprof’ generates annotated
     source in the file ‘FILENAME.ann’ instead (if the original file
     name has an extension, that extension is _replaced_ with ‘.ann’).

‘-Z[SYMSPEC]’
‘--no-exec-counts[=SYMSPEC]’
     The ‘-Z’ option causes ‘gprof’ not to print a tally of functions
     and the number of times each was called.  If SYMSPEC is specified,
     print tally, but exclude matching symbols.

‘-r’
‘--function-ordering’
     The ‘--function-ordering’ option causes ‘gprof’ to print a
     suggested function ordering for the program based on profiling
     data.  This option suggests an ordering which may improve paging,
     tlb and cache behavior for the program on systems which support
     arbitrary ordering of functions in an executable.

     The exact details of how to force the linker to place functions in
     a particular order is system dependent and out of the scope of this
     manual.

‘-R MAP_FILE’
‘--file-ordering MAP_FILE’
     The ‘--file-ordering’ option causes ‘gprof’ to print a suggested .o
     link line ordering for the program based on profiling data.  This
     option suggests an ordering which may improve paging, tlb and cache
     behavior for the program on systems which do not support arbitrary
     ordering of functions in an executable.

     Use of the ‘-a’ argument is highly recommended with this option.

     The MAP_FILE argument is a pathname to a file which provides
     function name to object file mappings.  The format of the file is
     similar to the output of the program ‘nm’.

          c-parse.o:00000000 T yyparse
          c-parse.o:00000004 C yyerrflag
          c-lang.o:00000000 T maybe_objc_method_name
          c-lang.o:00000000 T print_lang_statistics
          c-lang.o:00000000 T recognize_objc_keyword
          c-decl.o:00000000 T print_lang_identifier
          c-decl.o:00000000 T print_lang_type
          ...


     To create a MAP_FILE with GNU ‘nm’, type a command like ‘nm
     --extern-only --defined-only -v --print-file-name program-name’.

‘-T’
‘--traditional’
     The ‘-T’ option causes ‘gprof’ to print its output in "traditional"
     BSD style.

‘-w WIDTH’
‘--width=WIDTH’
     Sets width of output lines to WIDTH.  Currently only used when
     printing the function index at the bottom of the call graph.

‘-x’
‘--all-lines’
     This option affects annotated source output only.  By default, only
     the lines at the beginning of a basic-block are annotated.  If this
     option is specified, every line in a basic-block is annotated by
     repeating the annotation for the first line.  This behavior is
     similar to ‘tcov’'s ‘-a’.

‘--demangle[=STYLE]’
‘--no-demangle’
     These options control whether C++ symbol names should be demangled
     when printing output.  The default is to demangle symbols.  The
     ‘--no-demangle’ option may be used to turn off demangling.
     Different compilers have different mangling styles.  The optional
     demangling style argument can be used to choose an appropriate
     demangling style for your compiler.


File: gprof.info,  Node: Analysis Options,  Next: Miscellaneous Options,  Prev: Output Options,  Up: Invoking

4.2 Analysis Options
====================

‘-a’
‘--no-static’
     The ‘-a’ option causes ‘gprof’ to suppress the printing of
     statically declared (private) functions.  (These are functions
     whose names are not listed as global, and which are not visible
     outside the file/function/block where they were defined.)  Time
     spent in these functions, calls to/from them, etc., will all be
     attributed to the function that was loaded directly before it in
     the executable file.  This option affects both the flat profile and
     the call graph.

‘-c’
‘--static-call-graph’
     The ‘-c’ option causes the call graph of the program to be
     augmented by a heuristic which examines the text space of the
     object file and identifies function calls in the binary machine
     code.  Since normal call graph records are only generated when
     functions are entered, this option identifies children that could
     have been called, but never were.  Calls to functions that were not
     compiled with profiling enabled are also identified, but only if
     symbol table entries are present for them.  Calls to dynamic
     library routines are typically _not_ found by this option.  Parents
     or children identified via this heuristic are indicated in the call
     graph with call counts of ‘0’.

‘-D’
‘--ignore-non-functions’
     The ‘-D’ option causes ‘gprof’ to ignore symbols which are not
     known to be functions.  This option will give more accurate profile
     data on systems where it is supported (Solaris and HPUX for
     example).

‘-k FROM/TO’
     The ‘-k’ option allows you to delete from the call graph any arcs
     from symbols matching symspec FROM to those matching symspec TO.

‘-l’
‘--line’
     The ‘-l’ option enables line-by-line profiling, which causes
     histogram hits to be charged to individual source code lines,
     instead of functions.  This feature only works with programs
     compiled by older versions of the ‘gcc’ compiler.  Newer versions
     of ‘gcc’ are designed to work with the ‘gcov’ tool instead.

     If the program was compiled with basic-block counting enabled, this
     option will also identify how many times each line of code was
     executed.  While line-by-line profiling can help isolate where in a
     large function a program is spending its time, it also
     significantly increases the running time of ‘gprof’, and magnifies
     statistical inaccuracies.  *Note Statistical Sampling Error:
     Sampling Error.

‘--inline-file-names’
     This option causes ‘gprof’ to print the source file after each
     symbol in both the flat profile and the call graph.  The full path
     to the file is printed if used with the ‘-L’ option.

‘-m NUM’
‘--min-count=NUM’
     This option affects execution count output only.  Symbols that are
     executed less than NUM times are suppressed.

‘-nSYMSPEC’
‘--time=SYMSPEC’
     The ‘-n’ option causes ‘gprof’, in its call graph analysis, to only
     propagate times for symbols matching SYMSPEC.

‘-NSYMSPEC’
‘--no-time=SYMSPEC’
     The ‘-n’ option causes ‘gprof’, in its call graph analysis, not to
     propagate times for symbols matching SYMSPEC.

‘-SFILENAME’
‘--external-symbol-table=FILENAME’
     The ‘-S’ option causes ‘gprof’ to read an external symbol table
     file, such as ‘/proc/kallsyms’, rather than read the symbol table
     from the given object file (the default is ‘a.out’).  This is
     useful for profiling kernel modules.

‘-z’
‘--display-unused-functions’
     If you give the ‘-z’ option, ‘gprof’ will mention all functions in
     the flat profile, even those that were never called, and that had
     no time spent in them.  This is useful in conjunction with the ‘-c’
     option for discovering which routines were never called.


File: gprof.info,  Node: Miscellaneous Options,  Next: Deprecated Options,  Prev: Analysis Options,  Up: Invoking

4.3 Miscellaneous Options
=========================

‘-d[NUM]’
‘--debug[=NUM]’
     The ‘-d NUM’ option specifies debugging options.  If NUM is not
     specified, enable all debugging.  *Note Debugging ‘gprof’:
     Debugging.

‘-h’
‘--help’
     The ‘-h’ option prints command line usage.

‘-ONAME’
‘--file-format=NAME’
     Selects the format of the profile data files.  Recognized formats
     are ‘auto’ (the default), ‘bsd’, ‘4.4bsd’, ‘magic’, and ‘prof’ (not
     yet supported).

‘-s’
‘--sum’
     The ‘-s’ option causes ‘gprof’ to summarize the information in the
     profile data files it read in, and write out a profile data file
     called ‘gmon.sum’, which contains all the information from the
     profile data files that ‘gprof’ read in.  The file ‘gmon.sum’ may
     be one of the specified input files; the effect of this is to merge
     the data in the other input files into ‘gmon.sum’.

     Eventually you can run ‘gprof’ again without ‘-s’ to analyze the
     cumulative data in the file ‘gmon.sum’.

‘-v’
‘--version’
     The ‘-v’ flag causes ‘gprof’ to print the current version number,
     and then exit.


File: gprof.info,  Node: Deprecated Options,  Next: Symspecs,  Prev: Miscellaneous Options,  Up: Invoking

4.4 Deprecated Options
======================

These options have been replaced with newer versions that use symspecs.

‘-e FUNCTION_NAME’
     The ‘-e FUNCTION’ option tells ‘gprof’ to not print information
     about the function FUNCTION_NAME (and its children...) in the call
     graph.  The function will still be listed as a child of any
     functions that call it, but its index number will be shown as ‘[not
     printed]’.  More than one ‘-e’ option may be given; only one
     FUNCTION_NAME may be indicated with each ‘-e’ option.

‘-E FUNCTION_NAME’
     The ‘-E FUNCTION’ option works like the ‘-e’ option, but time spent
     in the function (and children who were not called from anywhere
     else), will not be used to compute the percentages-of-time for the
     call graph.  More than one ‘-E’ option may be given; only one
     FUNCTION_NAME may be indicated with each ‘-E’ option.

‘-f FUNCTION_NAME’
     The ‘-f FUNCTION’ option causes ‘gprof’ to limit the call graph to
     the function FUNCTION_NAME and its children (and their
     children...).  More than one ‘-f’ option may be given; only one
     FUNCTION_NAME may be indicated with each ‘-f’ option.

‘-F FUNCTION_NAME’
     The ‘-F FUNCTION’ option works like the ‘-f’ option, but only time
     spent in the function and its children (and their children...) will
     be used to determine total-time and percentages-of-time for the
     call graph.  More than one ‘-F’ option may be given; only one
     FUNCTION_NAME may be indicated with each ‘-F’ option.  The ‘-F’
     option overrides the ‘-E’ option.

   Note that only one function can be specified with each ‘-e’, ‘-E’,
‘-f’ or ‘-F’ option.  To specify more than one function, use multiple
options.  For example, this command:

     gprof -e boring -f foo -f bar myprogram > gprof.output

lists in the call graph all functions that were reached from either
‘foo’ or ‘bar’ and were not reachable from ‘boring’.


File: gprof.info,  Node: Symspecs,  Prev: Deprecated Options,  Up: Invoking

4.5 Symspecs
============

Many of the output options allow functions to be included or excluded
using “symspecs” (symbol specifications), which observe the following
syntax:

       filename_containing_a_dot
     | funcname_not_containing_a_dot
     | linenumber
     | ( [ any_filename ] `:' ( any_funcname | linenumber ) )

   Here are some sample symspecs:

‘main.c’
     Selects everything in file ‘main.c’--the dot in the string tells
     ‘gprof’ to interpret the string as a filename, rather than as a
     function name.  To select a file whose name does not contain a dot,
     a trailing colon should be specified.  For example, ‘odd:’ is
     interpreted as the file named ‘odd’.

‘main’
     Selects all functions named ‘main’.

     Note that there may be multiple instances of the same function name
     because some of the definitions may be local (i.e., static).
     Unless a function name is unique in a program, you must use the
     colon notation explained below to specify a function from a
     specific source file.

     Sometimes, function names contain dots.  In such cases, it is
     necessary to add a leading colon to the name.  For example, ‘:.mul’
     selects function ‘.mul’.

     In some object file formats, symbols have a leading underscore.
     ‘gprof’ will normally not print these underscores.  When you name a
     symbol in a symspec, you should type it exactly as ‘gprof’ prints
     it in its output.  For example, if the compiler produces a symbol
     ‘_main’ from your ‘main’ function, ‘gprof’ still prints it as
     ‘main’ in its output, so you should use ‘main’ in symspecs.

‘main.c:main’
     Selects function ‘main’ in file ‘main.c’.

‘main.c:134’
     Selects line 134 in file ‘main.c’.


File: gprof.info,  Node: Output,  Next: Inaccuracy,  Prev: Invoking,  Up: Top

5 Interpreting ‘gprof’'s Output
*******************************

‘gprof’ can produce several different output styles, the most important
of which are described below.  The simplest output styles (file
information, execution count, and function and file ordering) are not
described here, but are documented with the respective options that
trigger them.  *Note Output Options: Output Options.

* Menu:

* Flat Profile::        The flat profile shows how much time was spent
                            executing directly in each function.
* Call Graph::          The call graph shows which functions called which
                            others, and how much time each function used
                            when its subroutine calls are included.
* Line-by-line::        ‘gprof’ can analyze individual source code lines
* Annotated Source::    The annotated source listing displays source code
                            labeled with execution counts


File: gprof.info,  Node: Flat Profile,  Next: Call Graph,  Up: Output

5.1 The Flat Profile
====================

The “flat profile” shows the total amount of time your program spent
executing each function.  Unless the ‘-z’ option is given, functions
with no apparent time spent in them, and no apparent calls to them, are
not mentioned.  Note that if a function was not compiled for profiling,
and didn't run long enough to show up on the program counter histogram,
it will be indistinguishable from a function that was never called.

   This is part of a flat profile for a small program:

     Flat profile:

     Each sample counts as 0.01 seconds.
       %   cumulative   self              self     total
      time   seconds   seconds    calls  ms/call  ms/call  name
      33.34      0.02     0.02     7208     0.00     0.00  open
      16.67      0.03     0.01      244     0.04     0.12  offtime
      16.67      0.04     0.01        8     1.25     1.25  memccpy
      16.67      0.05     0.01        7     1.43     1.43  write
      16.67      0.06     0.01                             mcount
       0.00      0.06     0.00      236     0.00     0.00  tzset
       0.00      0.06     0.00      192     0.00     0.00  tolower
       0.00      0.06     0.00       47     0.00     0.00  strlen
       0.00      0.06     0.00       45     0.00     0.00  strchr
       0.00      0.06     0.00        1     0.00    50.00  main
       0.00      0.06     0.00        1     0.00     0.00  memcpy
       0.00      0.06     0.00        1     0.00    10.11  print
       0.00      0.06     0.00        1     0.00     0.00  profil
       0.00      0.06     0.00        1     0.00    50.00  report
     ...

The functions are sorted first by decreasing run-time spent in them,
then by decreasing number of calls, then alphabetically by name.  The
functions ‘mcount’ and ‘profil’ are part of the profiling apparatus and
appear in every flat profile; their time gives a measure of the amount
of overhead due to profiling.

   Just before the column headers, a statement appears indicating how
much time each sample counted as.  This “sampling period” estimates the
margin of error in each of the time figures.  A time figure that is not
much larger than this is not reliable.  In this example, each sample
counted as 0.01 seconds, suggesting a 100 Hz sampling rate.  The
program's total execution time was 0.06 seconds, as indicated by the
‘cumulative seconds’ field.  Since each sample counted for 0.01 seconds,
this means only six samples were taken during the run.  Two of the
samples occurred while the program was in the ‘open’ function, as
indicated by the ‘self seconds’ field.  Each of the other four samples
occurred one each in ‘offtime’, ‘memccpy’, ‘write’, and ‘mcount’.  Since
only six samples were taken, none of these values can be regarded as
particularly reliable.  In another run, the ‘self seconds’ field for
‘mcount’ might well be ‘0.00’ or ‘0.02’.  *Note Statistical Sampling
Error: Sampling Error, for a complete discussion.

   The remaining functions in the listing (those whose ‘self seconds’
field is ‘0.00’) didn't appear in the histogram samples at all.
However, the call graph indicated that they were called, so therefore
they are listed, sorted in decreasing order by the ‘calls’ field.
Clearly some time was spent executing these functions, but the paucity
of histogram samples prevents any determination of how much time each
took.

   Here is what the fields in each line mean:

‘% time’
     This is the percentage of the total execution time your program
     spent in this function.  These should all add up to 100%.

‘cumulative seconds’
     This is the cumulative total number of seconds the computer spent
     executing this functions, plus the time spent in all the functions
     above this one in this table.

‘self seconds’
     This is the number of seconds accounted for by this function alone.
     The flat profile listing is sorted first by this number.

‘calls’
     This is the total number of times the function was called.  If the
     function was never called, or the number of times it was called
     cannot be determined (probably because the function was not
     compiled with profiling enabled), the “calls” field is blank.

‘self ms/call’
     This represents the average number of milliseconds spent in this
     function per call, if this function is profiled.  Otherwise, this
     field is blank for this function.

‘total ms/call’
     This represents the average number of milliseconds spent in this
     function and its descendants per call, if this function is
     profiled.  Otherwise, this field is blank for this function.  This
     is the only field in the flat profile that uses call graph
     analysis.

‘name’
     This is the name of the function.  The flat profile is sorted by
     this field alphabetically after the “self seconds” and “calls”
     fields are sorted.


File: gprof.info,  Node: Call Graph,  Next: Line-by-line,  Prev: Flat Profile,  Up: Output

5.2 The Call Graph
==================

The “call graph” shows how much time was spent in each function and its
children.  From this information, you can find functions that, while
they themselves may not have used much time, called other functions that
did use unusual amounts of time.

   Here is a sample call from a small program.  This call came from the
same ‘gprof’ run as the flat profile example in the previous section.

     granularity: each sample hit covers 2 byte(s) for 20.00% of 0.05 seconds

     index % time    self  children    called     name
                                                      <spontaneous>
     [1]    100.0    0.00    0.05                 start [1]
                     0.00    0.05       1/1           main [2]
                     0.00    0.00       1/2           on_exit [28]
                     0.00    0.00       1/1           exit [59]
     -----------------------------------------------
                     0.00    0.05       1/1           start [1]
     [2]    100.0    0.00    0.05       1         main [2]
                     0.00    0.05       1/1           report [3]
     -----------------------------------------------
                     0.00    0.05       1/1           main [2]
     [3]    100.0    0.00    0.05       1         report [3]
                     0.00    0.03       8/8           timelocal [6]
                     0.00    0.01       1/1           print [9]
                     0.00    0.01       9/9           fgets [12]
                     0.00    0.00      12/34          strncmp <cycle 1> [40]
                     0.00    0.00       8/8           lookup [20]
                     0.00    0.00       1/1           fopen [21]
                     0.00    0.00       8/8           chewtime [24]
                     0.00    0.00       8/16          skipspace [44]
     -----------------------------------------------
     [4]     59.8    0.01        0.02       8+472     <cycle 2 as a whole> [4]
                     0.01        0.02     244+260         offtime <cycle 2> [7]
                     0.00        0.00     236+1           tzset <cycle 2> [26]
     -----------------------------------------------

   The lines full of dashes divide this table into “entries”, one for
each function.  Each entry has one or more lines.

   In each entry, the primary line is the one that starts with an index
number in square brackets.  The end of this line says which function the
entry is for.  The preceding lines in the entry describe the callers of
this function and the following lines describe its subroutines (also
called “children” when we speak of the call graph).

   The entries are sorted by time spent in the function and its
subroutines.

   The internal profiling function ‘mcount’ (*note The Flat Profile:
Flat Profile.) is never mentioned in the call graph.

* Menu:

* Primary::       Details of the primary line's contents.
* Callers::       Details of caller-lines' contents.
* Subroutines::   Details of subroutine-lines' contents.
* Cycles::        When there are cycles of recursion,
                   such as ‘a’ calls ‘b’ calls ‘a’...


File: gprof.info,  Node: Primary,  Next: Callers,  Up: Call Graph

5.2.1 The Primary Line
----------------------

The “primary line” in a call graph entry is the line that describes the
function which the entry is about and gives the overall statistics for
this function.

   For reference, we repeat the primary line from the entry for function
‘report’ in our main example, together with the heading line that shows
the names of the fields:

     index  % time    self  children called     name
     ...
     [3]    100.0    0.00    0.05       1         report [3]

   Here is what the fields in the primary line mean:

‘index’
     Entries are numbered with consecutive integers.  Each function
     therefore has an index number, which appears at the beginning of
     its primary line.

     Each cross-reference to a function, as a caller or subroutine of
     another, gives its index number as well as its name.  The index
     number guides you if you wish to look for the entry for that
     function.

‘% time’
     This is the percentage of the total time that was spent in this
     function, including time spent in subroutines called from this
     function.

     The time spent in this function is counted again for the callers of
     this function.  Therefore, adding up these percentages is
     meaningless.

‘self’
     This is the total amount of time spent in this function.  This
     should be identical to the number printed in the ‘seconds’ field
     for this function in the flat profile.

‘children’
     This is the total amount of time spent in the subroutine calls made
     by this function.  This should be equal to the sum of all the
     ‘self’ and ‘children’ entries of the children listed directly below
     this function.

‘called’
     This is the number of times the function was called.

     If the function called itself recursively, there are two numbers,
     separated by a ‘+’.  The first number counts non-recursive calls,
     and the second counts recursive calls.

     In the example above, the function ‘report’ was called once from
     ‘main’.

‘name’
     This is the name of the current function.  The index number is
     repeated after it.

     If the function is part of a cycle of recursion, the cycle number
     is printed between the function's name and the index number (*note
     How Mutually Recursive Functions Are Described: Cycles.).  For
     example, if function ‘gnurr’ is part of cycle number one, and has
     index number twelve, its primary line would be end like this:

          gnurr <cycle 1> [12]


File: gprof.info,  Node: Callers,  Next: Subroutines,  Prev: Primary,  Up: Call Graph

5.2.2 Lines for a Function's Callers
------------------------------------

A function's entry has a line for each function it was called by.  These
lines' fields correspond to the fields of the primary line, but their
meanings are different because of the difference in context.

   For reference, we repeat two lines from the entry for the function
‘report’, the primary line and one caller-line preceding it, together
with the heading line that shows the names of the fields:

     index  % time    self  children called     name
     ...
                     0.00    0.05       1/1           main [2]
     [3]    100.0    0.00    0.05       1         report [3]

   Here are the meanings of the fields in the caller-line for ‘report’
called from ‘main’:

‘self’
     An estimate of the amount of time spent in ‘report’ itself when it
     was called from ‘main’.

‘children’
     An estimate of the amount of time spent in subroutines of ‘report’
     when ‘report’ was called from ‘main’.

     The sum of the ‘self’ and ‘children’ fields is an estimate of the
     amount of time spent within calls to ‘report’ from ‘main’.

‘called’
     Two numbers: the number of times ‘report’ was called from ‘main’,
     followed by the total number of non-recursive calls to ‘report’
     from all its callers.

‘name and index number’
     The name of the caller of ‘report’ to which this line applies,
     followed by the caller's index number.

     Not all functions have entries in the call graph; some options to
     ‘gprof’ request the omission of certain functions.  When a caller
     has no entry of its own, it still has caller-lines in the entries
     of the functions it calls.

     If the caller is part of a recursion cycle, the cycle number is
     printed between the name and the index number.

   If the identity of the callers of a function cannot be determined, a
dummy caller-line is printed which has ‘<spontaneous>’ as the "caller's
name" and all other fields blank.  This can happen for signal handlers.


File: gprof.info,  Node: Subroutines,  Next: Cycles,  Prev: Callers,  Up: Call Graph

5.2.3 Lines for a Function's Subroutines
----------------------------------------

A function's entry has a line for each of its subroutines--in other
words, a line for each other function that it called.  These lines'
fields correspond to the fields of the primary line, but their meanings
are different because of the difference in context.

   For reference, we repeat two lines from the entry for the function
‘main’, the primary line and a line for a subroutine, together with the
heading line that shows the names of the fields:

     index  % time    self  children called     name
     ...
     [2]    100.0    0.00    0.05       1         main [2]
                     0.00    0.05       1/1           report [3]

   Here are the meanings of the fields in the subroutine-line for ‘main’
calling ‘report’:

‘self’
     An estimate of the amount of time spent directly within ‘report’
     when ‘report’ was called from ‘main’.

‘children’
     An estimate of the amount of time spent in subroutines of ‘report’
     when ‘report’ was called from ‘main’.

     The sum of the ‘self’ and ‘children’ fields is an estimate of the
     total time spent in calls to ‘report’ from ‘main’.

‘called’
     Two numbers, the number of calls to ‘report’ from ‘main’ followed
     by the total number of non-recursive calls to ‘report’.  This ratio
     is used to determine how much of ‘report’'s ‘self’ and ‘children’
     time gets credited to ‘main’.  *Note Estimating ‘children’ Times:
     Assumptions.

‘name’
     The name of the subroutine of ‘main’ to which this line applies,
     followed by the subroutine's index number.

     If the caller is part of a recursion cycle, the cycle number is
     printed between the name and the index number.


File: gprof.info,  Node: Cycles,  Prev: Subroutines,  Up: Call Graph

5.2.4 How Mutually Recursive Functions Are Described
----------------------------------------------------

The graph may be complicated by the presence of “cycles of recursion” in
the call graph.  A cycle exists if a function calls another function
that (directly or indirectly) calls (or appears to call) the original
function.  For example: if ‘a’ calls ‘b’, and ‘b’ calls ‘a’, then ‘a’
and ‘b’ form a cycle.

   Whenever there are call paths both ways between a pair of functions,
they belong to the same cycle.  If ‘a’ and ‘b’ call each other and ‘b’
and ‘c’ call each other, all three make one cycle.  Note that even if
‘b’ only calls ‘a’ if it was not called from ‘a’, ‘gprof’ cannot
determine this, so ‘a’ and ‘b’ are still considered a cycle.

   The cycles are numbered with consecutive integers.  When a function
belongs to a cycle, each time the function name appears in the call
graph it is followed by ‘<cycle NUMBER>’.

   The reason cycles matter is that they make the time values in the
call graph paradoxical.  The "time spent in children" of ‘a’ should
include the time spent in its subroutine ‘b’ and in ‘b’'s
subroutines--but one of ‘b’'s subroutines is ‘a’!  How much of ‘a’'s
time should be included in the children of ‘a’, when ‘a’ is indirectly
recursive?

   The way ‘gprof’ resolves this paradox is by creating a single entry
for the cycle as a whole.  The primary line of this entry describes the
total time spent directly in the functions of the cycle.  The
"subroutines" of the cycle are the individual functions of the cycle,
and all other functions that were called directly by them.  The
"callers" of the cycle are the functions, outside the cycle, that called
functions in the cycle.

   Here is an example portion of a call graph which shows a cycle
containing functions ‘a’ and ‘b’.  The cycle was entered by a call to
‘a’ from ‘main’; both ‘a’ and ‘b’ called ‘c’.

     index  % time    self  children called     name
     ----------------------------------------
                      1.77        0    1/1        main [2]
     [3]     91.71    1.77        0    1+5    <cycle 1 as a whole> [3]
                      1.02        0    3          b <cycle 1> [4]
                      0.75        0    2          a <cycle 1> [5]
     ----------------------------------------
                                       3          a <cycle 1> [5]
     [4]     52.85    1.02        0    0      b <cycle 1> [4]
                                       2          a <cycle 1> [5]
                         0        0    3/6        c [6]
     ----------------------------------------
                      1.77        0    1/1        main [2]
                                       2          b <cycle 1> [4]
     [5]     38.86    0.75        0    1      a <cycle 1> [5]
                                       3          b <cycle 1> [4]
                         0        0    3/6        c [6]
     ----------------------------------------

(The entire call graph for this program contains in addition an entry
for ‘main’, which calls ‘a’, and an entry for ‘c’, with callers ‘a’ and
‘b’.)

     index  % time    self  children called     name
                                                  <spontaneous>
     [1]    100.00       0     1.93    0      start [1]
                      0.16     1.77    1/1        main [2]
     ----------------------------------------
                      0.16     1.77    1/1        start [1]
     [2]    100.00    0.16     1.77    1      main [2]
                      1.77        0    1/1        a <cycle 1> [5]
     ----------------------------------------
                      1.77        0    1/1        main [2]
     [3]     91.71    1.77        0    1+5    <cycle 1 as a whole> [3]
                      1.02        0    3          b <cycle 1> [4]
                      0.75        0    2          a <cycle 1> [5]
                         0        0    6/6        c [6]
     ----------------------------------------
                                       3          a <cycle 1> [5]
     [4]     52.85    1.02        0    0      b <cycle 1> [4]
                                       2          a <cycle 1> [5]
                         0        0    3/6        c [6]
     ----------------------------------------
                      1.77        0    1/1        main [2]
                                       2          b <cycle 1> [4]
     [5]     38.86    0.75        0    1      a <cycle 1> [5]
                                       3          b <cycle 1> [4]
                         0        0    3/6        c [6]
     ----------------------------------------
                         0        0    3/6        b <cycle 1> [4]
                         0        0    3/6        a <cycle 1> [5]
     [6]      0.00       0        0    6      c [6]
     ----------------------------------------

   The ‘self’ field of the cycle's primary line is the total time spent
in all the functions of the cycle.  It equals the sum of the ‘self’
fields for the individual functions in the cycle, found in the entry in
the subroutine lines for these functions.

   The ‘children’ fields of the cycle's primary line and subroutine
lines count only subroutines outside the cycle.  Even though ‘a’ calls
‘b’, the time spent in those calls to ‘b’ is not counted in ‘a’'s
‘children’ time.  Thus, we do not encounter the problem of what to do
when the time in those calls to ‘b’ includes indirect recursive calls
back to ‘a’.

   The ‘children’ field of a caller-line in the cycle's entry estimates
the amount of time spent _in the whole cycle_, and its other
subroutines, on the times when that caller called a function in the
cycle.

   The ‘called’ field in the primary line for the cycle has two numbers:
first, the number of times functions in the cycle were called by
functions outside the cycle; second, the number of times they were
called by functions in the cycle (including times when a function in the
cycle calls itself).  This is a generalization of the usual split into
non-recursive and recursive calls.

   The ‘called’ field of a subroutine-line for a cycle member in the
cycle's entry says how many time that function was called from functions
in the cycle.  The total of all these is the second number in the
primary line's ‘called’ field.

   In the individual entry for a function in a cycle, the other
functions in the same cycle can appear as subroutines and as callers.
These lines show how many times each function in the cycle called or was
called from each other function in the cycle.  The ‘self’ and ‘children’
fields in these lines are blank because of the difficulty of defining
meanings for them when recursion is going on.


File: gprof.info,  Node: Line-by-line,  Next: Annotated Source,  Prev: Call Graph,  Up: Output

5.3 Line-by-line Profiling
==========================

‘gprof’'s ‘-l’ option causes the program to perform “line-by-line”
profiling.  In this mode, histogram samples are assigned not to
functions, but to individual lines of source code.  This only works with
programs compiled with older versions of the ‘gcc’ compiler.  Newer
versions of ‘gcc’ use a different program - ‘gcov’ - to display
line-by-line profiling information.

   With the older versions of ‘gcc’ the program usually has to be
compiled with a ‘-g’ option, in addition to ‘-pg’, in order to generate
debugging symbols for tracking source code lines.  Note, in much older
versions of ‘gcc’ the program had to be compiled with the ‘-a’
command-line option as well.

   The flat profile is the most useful output table in line-by-line
mode.  The call graph isn't as useful as normal, since the current
version of ‘gprof’ does not propagate call graph arcs from source code
lines to the enclosing function.  The call graph does, however, show
each line of code that called each function, along with a count.

   Here is a section of ‘gprof’'s output, without line-by-line
profiling.  Note that ‘ct_init’ accounted for four histogram hits, and
13327 calls to ‘init_block’.

     Flat profile:

     Each sample counts as 0.01 seconds.
       %   cumulative   self              self     total
      time   seconds   seconds    calls  us/call  us/call  name
      30.77      0.13     0.04     6335     6.31     6.31  ct_init


     		     Call graph (explanation follows)


     granularity: each sample hit covers 4 byte(s) for 7.69% of 0.13 seconds

     index % time    self  children    called     name

                     0.00    0.00       1/13496       name_too_long
                     0.00    0.00      40/13496       deflate
                     0.00    0.00     128/13496       deflate_fast
                     0.00    0.00   13327/13496       ct_init
     [7]      0.0    0.00    0.00   13496         init_block


   Now let's look at some of ‘gprof’'s output from the same program run,
this time with line-by-line profiling enabled.  Note that ‘ct_init’'s
four histogram hits are broken down into four lines of source code--one
hit occurred on each of lines 349, 351, 382 and 385.  In the call graph,
note how ‘ct_init’'s 13327 calls to ‘init_block’ are broken down into
one call from line 396, 3071 calls from line 384, 3730 calls from line
385, and 6525 calls from 387.

     Flat profile:

     Each sample counts as 0.01 seconds.
       %   cumulative   self
      time   seconds   seconds    calls  name
       7.69      0.10     0.01           ct_init (trees.c:349)
       7.69      0.11     0.01           ct_init (trees.c:351)
       7.69      0.12     0.01           ct_init (trees.c:382)
       7.69      0.13     0.01           ct_init (trees.c:385)


     		     Call graph (explanation follows)


     granularity: each sample hit covers 4 byte(s) for 7.69% of 0.13 seconds

       % time    self  children    called     name

                 0.00    0.00       1/13496       name_too_long (gzip.c:1440)
                 0.00    0.00       1/13496       deflate (deflate.c:763)
                 0.00    0.00       1/13496       ct_init (trees.c:396)
                 0.00    0.00       2/13496       deflate (deflate.c:727)
                 0.00    0.00       4/13496       deflate (deflate.c:686)
                 0.00    0.00       5/13496       deflate (deflate.c:675)
                 0.00    0.00      12/13496       deflate (deflate.c:679)
                 0.00    0.00      16/13496       deflate (deflate.c:730)
                 0.00    0.00     128/13496       deflate_fast (deflate.c:654)
                 0.00    0.00    3071/13496       ct_init (trees.c:384)
                 0.00    0.00    3730/13496       ct_init (trees.c:385)
                 0.00    0.00    6525/13496       ct_init (trees.c:387)
     [6]  0.0    0.00    0.00   13496         init_block (trees.c:408)



File: gprof.info,  Node: Annotated Source,  Prev: Line-by-line,  Up: Output

5.4 The Annotated Source Listing
================================

‘gprof’'s ‘-A’ option triggers an annotated source listing, which lists
the program's source code, each function labeled with the number of
times it was called.  You may also need to specify the ‘-I’ option, if
‘gprof’ can't find the source code files.

   With older versions of ‘gcc’ compiling with ‘gcc ... -g -pg -a’
augments your program with basic-block counting code, in addition to
function counting code.  This enables ‘gprof’ to determine how many
times each line of code was executed.  With newer versions of ‘gcc’
support for displaying basic-block counts is provided by the ‘gcov’
program.

   For example, consider the following function, taken from gzip, with
line numbers added:

      1 ulg updcrc(s, n)
      2     uch *s;
      3     unsigned n;
      4 {
      5     register ulg c;
      6
      7     static ulg crc = (ulg)0xffffffffL;
      8
      9     if (s == NULL) {
     10         c = 0xffffffffL;
     11     } else {
     12         c = crc;
     13         if (n) do {
     14             c = crc_32_tab[...];
     15         } while (--n);
     16     }
     17     crc = c;
     18     return c ^ 0xffffffffL;
     19 }


   ‘updcrc’ has at least five basic-blocks.  One is the function itself.
The ‘if’ statement on line 9 generates two more basic-blocks, one for
each branch of the ‘if’.  A fourth basic-block results from the ‘if’ on
line 13, and the contents of the ‘do’ loop form the fifth basic-block.
The compiler may also generate additional basic-blocks to handle various
special cases.

   A program augmented for basic-block counting can be analyzed with
‘gprof -l -A’.  The ‘-x’ option is also helpful, to ensure that each
line of code is labeled at least once.  Here is ‘updcrc’'s annotated
source listing for a sample ‘gzip’ run:

                     ulg updcrc(s, n)
                         uch *s;
                         unsigned n;
                 2 ->{
                         register ulg c;

                         static ulg crc = (ulg)0xffffffffL;

                 2 ->    if (s == NULL) {
                 1 ->        c = 0xffffffffL;
                 1 ->    } else {
                 1 ->        c = crc;
                 1 ->        if (n) do {
             26312 ->            c = crc_32_tab[...];
     26312,1,26311 ->        } while (--n);
                         }
                 2 ->    crc = c;
                 2 ->    return c ^ 0xffffffffL;
                 2 ->}

   In this example, the function was called twice, passing once through
each branch of the ‘if’ statement.  The body of the ‘do’ loop was
executed a total of 26312 times.  Note how the ‘while’ statement is
annotated.  It began execution 26312 times, once for each iteration
through the loop.  One of those times (the last time) it exited, while
it branched back to the beginning of the loop 26311 times.


File: gprof.info,  Node: Inaccuracy,  Next: How do I?,  Prev: Output,  Up: Top

6 Inaccuracy of ‘gprof’ Output
******************************

* Menu:

* Sampling Error::      Statistical margins of error
* Assumptions::         Estimating children times


File: gprof.info,  Node: Sampling Error,  Next: Assumptions,  Up: Inaccuracy

6.1 Statistical Sampling Error
==============================

The run-time figures that ‘gprof’ gives you are based on a sampling
process, so they are subject to statistical inaccuracy.  If a function
runs only a small amount of time, so that on the average the sampling
process ought to catch that function in the act only once, there is a
pretty good chance it will actually find that function zero times, or
twice.

   By contrast, the number-of-calls and basic-block figures are derived
by counting, not sampling.  They are completely accurate and will not
vary from run to run if your program is deterministic and single
threaded.  In multi-threaded applications, or single threaded
applications that link with multi-threaded libraries, the counts are
only deterministic if the counting function is thread-safe.  (Note:
beware that the mcount counting function in glibc is _not_ thread-safe).
*Note Implementation of Profiling: Implementation.

   The “sampling period” that is printed at the beginning of the flat
profile says how often samples are taken.  The rule of thumb is that a
run-time figure is accurate if it is considerably bigger than the
sampling period.

   The actual amount of error can be predicted.  For N samples, the
_expected_ error is the square-root of N.  For example, if the sampling
period is 0.01 seconds and ‘foo’'s run-time is 1 second, N is 100
samples (1 second/0.01 seconds), sqrt(N) is 10 samples, so the expected
error in ‘foo’'s run-time is 0.1 seconds (10*0.01 seconds), or ten
percent of the observed value.  Again, if the sampling period is 0.01
seconds and ‘bar’'s run-time is 100 seconds, N is 10000 samples, sqrt(N)
is 100 samples, so the expected error in ‘bar’'s run-time is 1 second,
or one percent of the observed value.  It is likely to vary this much
_on the average_ from one profiling run to the next.  (_Sometimes_ it
will vary more.)

   This does not mean that a small run-time figure is devoid of
information.  If the program's _total_ run-time is large, a small
run-time for one function does tell you that that function used an
insignificant fraction of the whole program's time.  Usually this means
it is not worth optimizing.

   One way to get more accuracy is to give your program more (but
similar) input data so it will take longer.  Another way is to combine
the data from several runs, using the ‘-s’ option of ‘gprof’.  Here is
how:

  1. Run your program once.

  2. Issue the command ‘mv gmon.out gmon.sum’.

  3. Run your program again, the same as before.

  4. Merge the new data in ‘gmon.out’ into ‘gmon.sum’ with this command:

          gprof -s EXECUTABLE-FILE gmon.out gmon.sum

  5. Repeat the last two steps as often as you wish.

  6. Analyze the cumulative data using this command:

          gprof EXECUTABLE-FILE gmon.sum > OUTPUT-FILE


File: gprof.info,  Node: Assumptions,  Prev: Sampling Error,  Up: Inaccuracy

6.2 Estimating ‘children’ Times
===============================

Some of the figures in the call graph are estimates--for example, the
‘children’ time values and all the time figures in caller and subroutine
lines.

   There is no direct information about these measurements in the
profile data itself.  Instead, ‘gprof’ estimates them by making an
assumption about your program that might or might not be true.

   The assumption made is that the average time spent in each call to
any function ‘foo’ is not correlated with who called ‘foo’.  If ‘foo’
used 5 seconds in all, and 2/5 of the calls to ‘foo’ came from ‘a’, then
‘foo’ contributes 2 seconds to ‘a’'s ‘children’ time, by assumption.

   This assumption is usually true enough, but for some programs it is
far from true.  Suppose that ‘foo’ returns very quickly when its
argument is zero; suppose that ‘a’ always passes zero as an argument,
while other callers of ‘foo’ pass other arguments.  In this program, all
the time spent in ‘foo’ is in the calls from callers other than ‘a’.
But ‘gprof’ has no way of knowing this; it will blindly and incorrectly
charge 2 seconds of time in ‘foo’ to the children of ‘a’.

   We hope some day to put more complete data into ‘gmon.out’, so that
this assumption is no longer needed, if we can figure out how.  For the
novice, the estimated figures are usually more useful than misleading.


File: gprof.info,  Node: How do I?,  Next: Incompatibilities,  Prev: Inaccuracy,  Up: Top

7 Answers to Common Questions
*****************************

How can I get more exact information about hot spots in my program?

     Looking at the per-line call counts only tells part of the story.
     Because ‘gprof’ can only report call times and counts by function,
     the best way to get finer-grained information on where the program
     is spending its time is to re-factor large functions into sequences
     of calls to smaller ones.  Beware however that this can introduce
     artificial hot spots since compiling with ‘-pg’ adds a significant
     overhead to function calls.  An alternative solution is to use a
     non-intrusive profiler, e.g. oprofile.

How do I find which lines in my program were executed the most times?

     Use the ‘gcov’ program.

How do I find which lines in my program called a particular function?

     Use ‘gprof -l’ and lookup the function in the call graph.  The
     callers will be broken down by function and line number.

How do I analyze a program that runs for less than a second?

     Try using a shell script like this one:

          for i in `seq 1 100`; do
            fastprog
            mv gmon.out gmon.out.$i
          done

          gprof -s fastprog gmon.out.*

          gprof fastprog gmon.sum

     If your program is completely deterministic, all the call counts
     will be simple multiples of 100 (i.e., a function called once in
     each run will appear with a call count of 100).


File: gprof.info,  Node: Incompatibilities,  Next: Details,  Prev: How do I?,  Up: Top

8 Incompatibilities with Unix ‘gprof’
*************************************

GNU ‘gprof’ and Berkeley Unix ‘gprof’ use the same data file ‘gmon.out’,
and provide essentially the same information.  But there are a few
differences.

   • GNU ‘gprof’ uses a new, generalized file format with support for
     basic-block execution counts and non-realtime histograms.  A magic
     cookie and version number allows ‘gprof’ to easily identify new
     style files.  Old BSD-style files can still be read.  *Note
     Profiling Data File Format: File Format.

   • For a recursive function, Unix ‘gprof’ lists the function as a
     parent and as a child, with a ‘calls’ field that lists the number
     of recursive calls.  GNU ‘gprof’ omits these lines and puts the
     number of recursive calls in the primary line.

   • When a function is suppressed from the call graph with ‘-e’, GNU
     ‘gprof’ still lists it as a subroutine of functions that call it.

   • GNU ‘gprof’ accepts the ‘-k’ with its argument in the form
     ‘from/to’, instead of ‘from to’.

   • In the annotated source listing, if there are multiple basic blocks
     on the same line, GNU ‘gprof’ prints all of their counts, separated
     by commas.

   • The blurbs, field widths, and output formats are different.  GNU
     ‘gprof’ prints blurbs after the tables, so that you can see the
     tables without skipping the blurbs.


File: gprof.info,  Node: Details,  Next: GNU Free Documentation License,  Prev: Incompatibilities,  Up: Top

9 Details of Profiling
**********************

* Menu:

* Implementation::      How a program collects profiling information
* File Format::         Format of ‘gmon.out’ files
* Internals::           ‘gprof’'s internal operation
* Debugging::           Using ‘gprof’'s ‘-d’ option


File: gprof.info,  Node: Implementation,  Next: File Format,  Up: Details

9.1 Implementation of Profiling
===============================

Profiling works by changing how every function in your program is
compiled so that when it is called, it will stash away some information
about where it was called from.  From this, the profiler can figure out
what function called it, and can count how many times it was called.
This change is made by the compiler when your program is compiled with
the ‘-pg’ option, which causes every function to call ‘mcount’ (or
‘_mcount’, or ‘__mcount’, depending on the OS and compiler) as one of
its first operations.

   The ‘mcount’ routine, included in the profiling library, is
responsible for recording in an in-memory call graph table both its
parent routine (the child) and its parent's parent.  This is typically
done by examining the stack frame to find both the address of the child,
and the return address in the original parent.  Since this is a very
machine-dependent operation, ‘mcount’ itself is typically a short
assembly-language stub routine that extracts the required information,
and then calls ‘__mcount_internal’ (a normal C function) with two
arguments--‘frompc’ and ‘selfpc’.  ‘__mcount_internal’ is responsible
for maintaining the in-memory call graph, which records ‘frompc’,
‘selfpc’, and the number of times each of these call arcs was traversed.

   GCC Version 2 provides a magical function
(‘__builtin_return_address’), which allows a generic ‘mcount’ function
to extract the required information from the stack frame.  However, on
some architectures, most notably the SPARC, using this builtin can be
very computationally expensive, and an assembly language version of
‘mcount’ is used for performance reasons.

   Number-of-calls information for library routines is collected by
using a special version of the C library.  The programs in it are the
same as in the usual C library, but they were compiled with ‘-pg’.  If
you link your program with ‘gcc ... -pg’, it automatically uses the
profiling version of the library.

   Profiling also involves watching your program as it runs, and keeping
a histogram of where the program counter happens to be every now and
then.  Typically the program counter is looked at around 100 times per
second of run time, but the exact frequency may vary from system to
system.

   This is done is one of two ways.  Most UNIX-like operating systems
provide a ‘profil()’ system call, which registers a memory array with
the kernel, along with a scale factor that determines how the program's
address space maps into the array.  Typical scaling values cause every 2
to 8 bytes of address space to map into a single array slot.  On every
tick of the system clock (assuming the profiled program is running), the
value of the program counter is examined and the corresponding slot in
the memory array is incremented.  Since this is done in the kernel,
which had to interrupt the process anyway to handle the clock interrupt,
very little additional system overhead is required.

   However, some operating systems, most notably Linux 2.0 (and
earlier), do not provide a ‘profil()’ system call.  On such a system,
arrangements are made for the kernel to periodically deliver a signal to
the process (typically via ‘setitimer()’), which then performs the same
operation of examining the program counter and incrementing a slot in
the memory array.  Since this method requires a signal to be delivered
to user space every time a sample is taken, it uses considerably more
overhead than kernel-based profiling.  Also, due to the added delay
required to deliver the signal, this method is less accurate as well.

   A special startup routine allocates memory for the histogram and
either calls ‘profil()’ or sets up a clock signal handler.  This routine
(‘monstartup’) can be invoked in several ways.  On Linux systems, a
special profiling startup file ‘gcrt0.o’, which invokes ‘monstartup’
before ‘main’, is used instead of the default ‘crt0.o’.  Use of this
special startup file is one of the effects of using ‘gcc ... -pg’ to
link.  On SPARC systems, no special startup files are used.  Rather, the
‘mcount’ routine, when it is invoked for the first time (typically when
‘main’ is called), calls ‘monstartup’.

   If the compiler's ‘-a’ option was used, basic-block counting is also
enabled.  Each object file is then compiled with a static array of
counts, initially zero.  In the executable code, every time a new
basic-block begins (i.e., when an ‘if’ statement appears), an extra
instruction is inserted to increment the corresponding count in the
array.  At compile time, a paired array was constructed that recorded
the starting address of each basic-block.  Taken together, the two
arrays record the starting address of every basic-block, along with the
number of times it was executed.

   The profiling library also includes a function (‘mcleanup’) which is
typically registered using ‘atexit()’ to be called as the program exits,
and is responsible for writing the file ‘gmon.out’.  Profiling is turned
off, various headers are output, and the histogram is written, followed
by the call-graph arcs and the basic-block counts.

   The output from ‘gprof’ gives no indication of parts of your program
that are limited by I/O or swapping bandwidth.  This is because samples
of the program counter are taken at fixed intervals of the program's run
time.  Therefore, the time measurements in ‘gprof’ output say nothing
about time that your program was not running.  For example, a part of
the program that creates so much data that it cannot all fit in physical
memory at once may run very slowly due to thrashing, but ‘gprof’ will
say it uses little time.  On the other hand, sampling by run time has
the advantage that the amount of load due to other users won't directly
affect the output you get.


File: gprof.info,  Node: File Format,  Next: Internals,  Prev: Implementation,  Up: Details

9.2 Profiling Data File Format
==============================

The old BSD-derived file format used for profile data does not contain a
magic cookie that allows one to check whether a data file really is a
‘gprof’ file.  Furthermore, it does not provide a version number, thus
rendering changes to the file format almost impossible.  GNU ‘gprof’
uses a new file format that provides these features.  For backward
compatibility, GNU ‘gprof’ continues to support the old BSD-derived
format, but not all features are supported with it.  For example,
basic-block execution counts cannot be accommodated by the old file
format.

   The new file format is defined in header file ‘gmon_out.h’.  It
consists of a header containing the magic cookie and a version number,
as well as some spare bytes available for future extensions.  All data
in a profile data file is in the native format of the target for which
the profile was collected.  GNU ‘gprof’ adapts automatically to the
byte-order in use.

   In the new file format, the header is followed by a sequence of
records.  Currently, there are three different record types: histogram
records, call-graph arc records, and basic-block execution count
records.  Each file can contain any number of each record type.  When
reading a file, GNU ‘gprof’ will ensure records of the same type are
compatible with each other and compute the union of all records.  For
example, for basic-block execution counts, the union is simply the sum
of all execution counts for each basic-block.

9.2.1 Histogram Records
-----------------------

Histogram records consist of a header that is followed by an array of
bins.  The header contains the text-segment range that the histogram
spans, the size of the histogram in bytes (unlike in the old BSD format,
this does not include the size of the header), the rate of the profiling
clock, and the physical dimension that the bin counts represent after
being scaled by the profiling clock rate.  The physical dimension is
specified in two parts: a long name of up to 15 characters and a single
character abbreviation.  For example, a histogram representing real-time
would specify the long name as "seconds" and the abbreviation as "s".
This feature is useful for architectures that support performance
monitor hardware (which, fortunately, is becoming increasingly common).
For example, under DEC OSF/1, the "uprofile" command can be used to
produce a histogram of, say, instruction cache misses.  In this case,
the dimension in the histogram header could be set to "i-cache misses"
and the abbreviation could be set to "1" (because it is simply a count,
not a physical dimension).  Also, the profiling rate would have to be
set to 1 in this case.

   Histogram bins are 16-bit numbers and each bin represent an equal
amount of text-space.  For example, if the text-segment is one thousand
bytes long and if there are ten bins in the histogram, each bin
represents one hundred bytes.

9.2.2 Call-Graph Records
------------------------

Call-graph records have a format that is identical to the one used in
the BSD-derived file format.  It consists of an arc in the call graph
and a count indicating the number of times the arc was traversed during
program execution.  Arcs are specified by a pair of addresses: the first
must be within caller's function and the second must be within the
callee's function.  When performing profiling at the function level,
these addresses can point anywhere within the respective function.
However, when profiling at the line-level, it is better if the addresses
are as close to the call-site/entry-point as possible.  This will ensure
that the line-level call-graph is able to identify exactly which line of
source code performed calls to a function.

9.2.3 Basic-Block Execution Count Records
-----------------------------------------

Basic-block execution count records consist of a header followed by a
sequence of address/count pairs.  The header simply specifies the length
of the sequence.  In an address/count pair, the address identifies a
basic-block and the count specifies the number of times that basic-block
was executed.  Any address within the basic-address can be used.


File: gprof.info,  Node: Internals,  Next: Debugging,  Prev: File Format,  Up: Details

9.3 ‘gprof’'s Internal Operation
================================

Like most programs, ‘gprof’ begins by processing its options.  During
this stage, it may building its symspec list (‘sym_ids.c:sym_id_add’),
if options are specified which use symspecs.  ‘gprof’ maintains a single
linked list of symspecs, which will eventually get turned into 12 symbol
tables, organized into six include/exclude pairs--one pair each for the
flat profile (INCL_FLAT/EXCL_FLAT), the call graph arcs
(INCL_ARCS/EXCL_ARCS), printing in the call graph
(INCL_GRAPH/EXCL_GRAPH), timing propagation in the call graph
(INCL_TIME/EXCL_TIME), the annotated source listing
(INCL_ANNO/EXCL_ANNO), and the execution count listing
(INCL_EXEC/EXCL_EXEC).

   After option processing, ‘gprof’ finishes building the symspec list
by adding all the symspecs in ‘default_excluded_list’ to the exclude
lists EXCL_TIME and EXCL_GRAPH, and if line-by-line profiling is
specified, EXCL_FLAT as well.  These default excludes are not added to
EXCL_ANNO, EXCL_ARCS, and EXCL_EXEC.

   Next, the BFD library is called to open the object file, verify that
it is an object file, and read its symbol table (‘core.c:core_init’),
using ‘bfd_canonicalize_symtab’ after mallocing an appropriately sized
array of symbols.  At this point, function mappings are read (if the
‘--file-ordering’ option has been specified), and the core text space is
read into memory (if the ‘-c’ option was given).

   ‘gprof’'s own symbol table, an array of Sym structures, is now built.
This is done in one of two ways, by one of two routines, depending on
whether line-by-line profiling (‘-l’ option) has been enabled.  For
normal profiling, the BFD canonical symbol table is scanned.  For
line-by-line profiling, every text space address is examined, and a new
symbol table entry gets created every time the line number changes.  In
either case, two passes are made through the symbol table--one to count
the size of the symbol table required, and the other to actually read
the symbols.  In between the two passes, a single array of type ‘Sym’ is
created of the appropriate length.  Finally, ‘symtab.c:symtab_finalize’
is called to sort the symbol table and remove duplicate entries (entries
with the same memory address).

   The symbol table must be a contiguous array for two reasons.  First,
the ‘qsort’ library function (which sorts an array) will be used to sort
the symbol table.  Also, the symbol lookup routine
(‘symtab.c:sym_lookup’), which finds symbols based on memory address,
uses a binary search algorithm which requires the symbol table to be a
sorted array.  Function symbols are indicated with an ‘is_func’ flag.
Line number symbols have no special flags set.  Additionally, a symbol
can have an ‘is_static’ flag to indicate that it is a local symbol.

   With the symbol table read, the symspecs can now be translated into
Syms (‘sym_ids.c:sym_id_parse’).  Remember that a single symspec can
match multiple symbols.  An array of symbol tables (‘syms’) is created,
each entry of which is a symbol table of Syms to be included or excluded
from a particular listing.  The master symbol table and the symspecs are
examined by nested loops, and every symbol that matches a symspec is
inserted into the appropriate syms table.  This is done twice, once to
count the size of each required symbol table, and again to build the
tables, which have been malloced between passes.  From now on, to
determine whether a symbol is on an include or exclude symspec list,
‘gprof’ simply uses its standard symbol lookup routine on the
appropriate table in the ‘syms’ array.

   Now the profile data file(s) themselves are read
(‘gmon_io.c:gmon_out_read’), first by checking for a new-style
‘gmon.out’ header, then assuming this is an old-style BSD ‘gmon.out’ if
the magic number test failed.

   New-style histogram records are read by ‘hist.c:hist_read_rec’.  For
the first histogram record, allocate a memory array to hold all the
bins, and read them in.  When multiple profile data files (or files with
multiple histogram records) are read, the memory ranges of each pair of
histogram records must be either equal, or non-overlapping.  For each
pair of histogram records, the resolution (memory region size divided by
the number of bins) must be the same.  The time unit must be the same
for all histogram records.  If the above containts are met, all
histograms for the same memory range are merged.

   As each call graph record is read (‘call_graph.c:cg_read_rec’), the
parent and child addresses are matched to symbol table entries, and a
call graph arc is created by ‘cg_arcs.c:arc_add’, unless the arc fails a
symspec check against INCL_ARCS/EXCL_ARCS. As each arc is added, a
linked list is maintained of the parent's child arcs, and of the child's
parent arcs.  Both the child's call count and the arc's call count are
incremented by the record's call count.

   Basic-block records are read (‘basic_blocks.c:bb_read_rec’), but only
if line-by-line profiling has been selected.  Each basic-block address
is matched to a corresponding line symbol in the symbol table, and an
entry made in the symbol's bb_addr and bb_calls arrays.  Again, if
multiple basic-block records are present for the same address, the call
counts are cumulative.

   A gmon.sum file is dumped, if requested (‘gmon_io.c:gmon_out_write’).

   If histograms were present in the data files, assign them to symbols
(‘hist.c:hist_assign_samples’) by iterating over all the sample bins and
assigning them to symbols.  Since the symbol table is sorted in order of
ascending memory addresses, we can simple follow along in the symbol
table as we make our pass over the sample bins.  This step includes a
symspec check against INCL_FLAT/EXCL_FLAT. Depending on the histogram
scale factor, a sample bin may span multiple symbols, in which case a
fraction of the sample count is allocated to each symbol, proportional
to the degree of overlap.  This effect is rare for normal profiling, but
overlaps are more common during line-by-line profiling, and can cause
each of two adjacent lines to be credited with half a hit, for example.

   If call graph data is present, ‘cg_arcs.c:cg_assemble’ is called.
First, if ‘-c’ was specified, a machine-dependent routine (‘find_call’)
scans through each symbol's machine code, looking for subroutine call
instructions, and adding them to the call graph with a zero call count.
A topological sort is performed by depth-first numbering all the symbols
(‘cg_dfn.c:cg_dfn’), so that children are always numbered less than
their parents, then making a array of pointers into the symbol table and
sorting it into numerical order, which is reverse topological order
(children appear before parents).  Cycles are also detected at this
point, all members of which are assigned the same topological number.
Two passes are now made through this sorted array of symbol pointers.
The first pass, from end to beginning (parents to children), computes
the fraction of child time to propagate to each parent and a print flag.
The print flag reflects symspec handling of INCL_GRAPH/EXCL_GRAPH, with
a parent's include or exclude (print or no print) property being
propagated to its children, unless they themselves explicitly appear in
INCL_GRAPH or EXCL_GRAPH. A second pass, from beginning to end (children
to parents) actually propagates the timings along the call graph,
subject to a check against INCL_TIME/EXCL_TIME. With the print flag,
fractions, and timings now stored in the symbol structures, the
topological sort array is now discarded, and a new array of pointers is
assembled, this time sorted by propagated time.

   Finally, print the various outputs the user requested, which is now
fairly straightforward.  The call graph (‘cg_print.c:cg_print’) and flat
profile (‘hist.c:hist_print’) are regurgitations of values already
computed.  The annotated source listing
(‘basic_blocks.c:print_annotated_source’) uses basic-block information,
if present, to label each line of code with call counts, otherwise only
the function call counts are presented.

   The function ordering code is marginally well documented in the
source code itself (‘cg_print.c’).  Basically, the functions with the
most use and the most parents are placed first, followed by other
functions with the most use, followed by lower use functions, followed
by unused functions at the end.


File: gprof.info,  Node: Debugging,  Prev: Internals,  Up: Details

9.4 Debugging ‘gprof’
=====================

If ‘gprof’ was compiled with debugging enabled, the ‘-d’ option triggers
debugging output (to stdout) which can be helpful in understanding its
operation.  The debugging number specified is interpreted as a sum of
the following options:

2 - Topological sort
     Monitor depth-first numbering of symbols during call graph analysis
4 - Cycles
     Shows symbols as they are identified as cycle heads
16 - Tallying
     As the call graph arcs are read, show each arc and how the total
     calls to each function are tallied
32 - Call graph arc sorting
     Details sorting individual parents/children within each call graph
     entry
64 - Reading histogram and call graph records
     Shows address ranges of histograms as they are read, and each call
     graph arc
128 - Symbol table
     Reading, classifying, and sorting the symbol table from the object
     file.  For line-by-line profiling (‘-l’ option), also shows line
     numbers being assigned to memory addresses.
256 - Static call graph
     Trace operation of ‘-c’ option
512 - Symbol table and arc table lookups
     Detail operation of lookup routines
1024 - Call graph propagation
     Shows how function times are propagated along the call graph
2048 - Basic-blocks
     Shows basic-block records as they are read from profile data (only
     meaningful with ‘-l’ option)
4096 - Symspecs
     Shows symspec-to-symbol pattern matching operation
8192 - Annotate source
     Tracks operation of ‘-A’ option


File: gprof.info,  Node: GNU Free Documentation License,  Prev: Details,  Up: Top

Appendix A GNU Free Documentation License
*****************************************

                     Version 1.3, 3 November 2008

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

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

  0. PREAMBLE

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

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

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

  1. APPLICABILITY AND DEFINITIONS

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

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

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

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

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

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

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

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

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

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

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

  2. VERBATIM COPYING

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

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

  3. COPYING IN QUANTITY

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

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

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

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

  4. MODIFICATIONS

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

       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 fewer than five), unless they release you
          from this requirement.

       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", 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.

       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. 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.

       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 to be Entitled
          "Endorsements" or to conflict in title with any Invariant
          Section.

       O. Preserve any Warranty Disclaimers.

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

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

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

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

  5. COMBINING DOCUMENTS

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

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

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

  6. COLLECTIONS OF DOCUMENTS

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

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

  7. AGGREGATION WITH INDEPENDENT WORKS

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

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

  8. TRANSLATION

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

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

  9. TERMINATION

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

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

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

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

  10. FUTURE REVISIONS OF THIS LICENSE

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

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

  11. RELICENSING

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

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

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

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

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

ADDENDUM: How to use this License for your documents
====================================================

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

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

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

         with the Invariant Sections being LIST THEIR TITLES, with
         the Front-Cover Texts being LIST, and with the Back-Cover Texts
         being LIST.

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

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



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