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This is ../../src/gprof/gprof.info, produced by makeinfo version 4.2
from ../../src/gprof/gprof.texi.

START-INFO-DIR-ENTRY
* gprof: (gprof).                Profiling your program's execution
END-INFO-DIR-ENTRY

   This file documents the gprof profiler of the GNU system.

   Copyright (C) 1988, 92, 97, 98, 99, 2000, 2001, 2003 Free Software
Foundation, Inc.

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

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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 document is distributed under the terms of the GNU Free
Documentation License.  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

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

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::.

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

   * You must run `gprof' to analyze the profile data.  *Note
     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 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 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 Annotated Source::.

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

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

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
     
      %         the percentage of the total running time of the

   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 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 will also need to
specify the `-g' option, instructing the compiler to insert debugging
symbols into the program that match program addresses to source code
lines.  *Note Line-by-line::.

   In addition to the `-pg' and `-g' options, older versions of GCC
required you to specify the `-a' option when compiling in order to
instrument it to perform basic-block counting.  Newer versions do not
require this option and will not accept it; basic-block counting is
always enabled when `-pg' is on.

   When basic-block counting is enabled, as the program runs it will
count how many times it executed each branch of each `if' statement,
each iteration of each `do' loop, etc.  This will enable `gprof' to
construct an annotated source code listing showing how many times each
line of code was executed.

   It also worth noting that GCC supports a different profiling method
which is enabled by the `-fprofile-arcs', `-ftest-coverage' and
`-fprofile-values' switches. These switches do not produce data which
is useful to `gprof' however, so they are not discussed further here.
There is also the `-finstrument-functions' switch which will cause GCC
to 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.

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

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 the 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.  There is currently no way to
tell the program to write the profile data under a different name, but
you can rename the file afterwards if you are concerned that it may be
overwritten.

   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]

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

`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' analyses 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

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

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::.

   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 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.

`-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 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 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 filesystem 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.

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

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.  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
     Sampling Error::.

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

`-n[SYMSPEC]'
`--time[=SYMSPEC]'
     The `-n' option causes `gprof', in its call graph analysis, to
     only propagate times for symbols matching SYMSPEC.

`-N[SYMSPEC]'
`--no-time[=SYMSPEC]'
     The `-n' option causes `gprof', in its call graph analysis, not to
     propagate times for symbols matching SYMSPEC.

`-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.

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

Miscellaneous Options
=====================

`-d[NUM]'
`--debug[=NUM]'
     The `-d NUM' option specifies debugging options.  If NUM is not
     specified, enable all debugging.  *Note 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.

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

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'.

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

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'.

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

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::.

* 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

\x1f
File: gprof.info,  Node: Flat Profile,  Next: Call Graph,  Up: Output

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 by 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 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.

\x1f
File: gprof.info,  Node: Call Graph,  Next: Line-by-line,  Prev: Flat Profile,  Up: Output

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 chapter.

     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 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'...

\x1f
File: gprof.info,  Node: Primary,  Next: Callers,  Up: Call Graph

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
     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]

\x1f
File: gprof.info,  Node: Callers,  Next: Subroutines,  Prev: Primary,  Up: Call Graph

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.

\x1f
File: gprof.info,  Node: Subroutines,  Next: Cycles,  Prev: Callers,  Up: Call Graph

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 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.

\x1f
File: gprof.info,  Node: Cycles,  Prev: Subroutines,  Up: Call Graph

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 `calls' 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 `calls' 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 `calls' 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.

\x1f
File: gprof.info,  Node: Line-by-line,  Next: Annotated Source,  Prev: Call Graph,  Up: Output

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.  The program usually
must be compiled with a `-g' option, in addition to `-pg', in order to
generate debugging symbols for tracking source code lines.

   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)

\x1f
File: gprof.info,  Node: Annotated Source,  Prev: Line-by-line,  Up: Output

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.

   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.  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'.  I also suggest use of the `-x' option, which ensures
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.

\x1f
File: gprof.info,  Node: Inaccuracy,  Next: How do I?,  Prev: Output,  Up: Top

Inaccuracy of `gprof' Output
****************************

* Menu:

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

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

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.

   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

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

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
nonce, the estimated figures are usually more useful than misleading.

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

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
     artifical 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?
     Compile your program with basic-block counting enabled, run it,
     then use the following pipeline:

          gprof -l -C OBJFILE | sort -k 3 -n -r

     This listing will show you the lines in your code executed most
     often, but not necessarily those that consumed the most time.

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).

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

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 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.

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

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

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

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.

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

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

   The old BSD-derived file format used for profile data does not
contain a magic cookie that allows 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.

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.

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.

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.

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

`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 starting address, ending
address, number of bins and sampling rate must match between the
various histograms, or a fatal error will result.  If everything
matches, just sum the additional histograms into the existing in-memory
array.

   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.

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

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

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

GNU Free Documentation License
******************************

   GNU Free Documentation License

   Version 1.1, March 2000

   Copyright (C) 2000  Free Software Foundation, Inc.    51 Franklin
Street, Fifth Floor, Boston, MA  02110-1301  USA

   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
written 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 that contains a
notice placed by the copyright holder saying it can be distributed
under the terms of this License.  The "Document", below, refers to any
such manual or work.  Any member of the public is a licensee, and is
addressed as "you".

   A "Modified Version" of the Document means any work containing the
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   A "Secondary Section" is a named appendix or a front-matter section
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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.

   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 "Transparent" copy of the Document means a machine-readable copy,
represented in a format whose specification is available to the general
public, whose contents can be viewed and edited directly and
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 has been designed to thwart or discourage subsequent
modification by readers is not Transparent.  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
designed for human modification.  Opaque formats include PostScript,
PDF, 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 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.

   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 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 publicly-accessible computer-network location containing a complete
Transparent copy of the Document, free of added material, which the
general network-using public has access to download anonymously at no
charge using public-standard network protocols.  If you use the latter
option, you must take reasonably prudent steps, when you begin
distribution of Opaque copies in quantity, to ensure that this
Transparent copy will remain thus accessible at the stated location
until at least one year after the last time you distribute an Opaque
copy (directly or through your agents or retailers) of that edition to
the public.

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

   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 less than five).  C.
State on the Title page the name of the publisher of the    Modified
Version, as the publisher.  D. Preserve all the copyright notices of
the Document.  E. Add an appropriate copyright notice for your
modifications    adjacent to the other copyright notices.  F. Include,
immediately after the copyright notices, a license notice    giving the
public permission to use the Modified Version under the    terms of
this License, in the form shown in the Addendum below.  G. Preserve in
that license notice the full lists of Invariant Sections    and
required Cover Texts given in the Document's license notice.  H.
Include an unaltered copy of this License.  I. Preserve the section
entitled "History", and its title, and add to    it an item stating at
least the title, year, new authors, and    publisher of the Modified
Version as given on the Title Page.  If    there is no section entitled
"History" in the Document, create one    stating the title, year,
authors, and publisher of the Document as    given on its Title Page,
then add an item describing the Modified    Version as stated in the
previous sentence.  J. Preserve the network location, if any, given in
the Document for    public access to a Transparent copy of the
Document, and likewise    the network locations given in the Document
for previous versions    it was based on.  These may be placed in the
"History" section.     You may omit a network location for a work that
was published at    least four years before the Document itself, or if
the original    publisher of the version it refers to gives permission.
K. In any section entitled "Acknowledgements" or "Dedications",
preserve the section's title, and preserve in the section all the
substance and tone of each of the contributor acknowledgements
and/or dedications given therein.  L. Preserve all the Invariant
Sections of the Document,    unaltered in their text and in their
titles.  Section numbers    or the equivalent are not considered part
of the section titles.  M. Delete any section entitled "Endorsements".
Such a section    may not be included in the Modified Version.  N. Do
not retitle any existing section as "Endorsements"    or to conflict in
title with any Invariant Section.

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

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

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

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

   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.

   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, does not as a whole count as a Modified Version of
the Document, provided no compilation copyright is claimed for the
compilation.  Such a compilation is called an "aggregate", and this
License does not apply to the other self-contained works thus compiled
with the Document, on account of their being thus compiled, if they are
not themselves derivative works of the Document.

   If the Cover Text requirement of section 3 is applicable to these
copies of the Document, then if the Document is less than one quarter
of the entire aggregate, the Document's Cover Texts may be placed on
covers that surround only the Document within the aggregate.  Otherwise
they must appear on covers around the whole aggregate.

   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 provided that you also include the original
English version of this License.  In case of a disagreement between the
translation and the original English version of this License, the
original English version will prevail.

   9. TERMINATION

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

   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.

   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 1.1
         or any later version published by the Free Software Foundation;
         with the Invariant Sections being LIST THEIR TITLES, with the
         Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.
         A copy of the license is included in the section entitled "GNU
         Free Documentation License".

   If you have no Invariant Sections, write "with no Invariant Sections"
instead of saying which ones are invariant.  If you have no Front-Cover
Texts, write "no Front-Cover Texts" instead of "Front-Cover Texts being
LIST"; likewise for Back-Cover Texts.

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