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+
+<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
+<h1 class="settitle" align="center">GNU gprof</h1>
+
+
+
+
+
+<a name="SEC_Contents"></a>
+<h2 class="contents-heading">Table of Contents</h2>
+
+<div class="contents">
+
+<ul class="no-bullet">
+ <li><a name="toc-Introduction-to-Profiling" href="#Introduction">1 Introduction to Profiling</a></li>
+ <li><a name="toc-Compiling-a-Program-for-Profiling" href="#Compiling">2 Compiling a Program for Profiling</a></li>
+ <li><a name="toc-Executing-the-Program" href="#Executing">3 Executing the Program</a></li>
+ <li><a name="toc-gprof-Command-Summary" href="#Invoking">4 <code>gprof</code> Command Summary</a>
+ <ul class="no-bullet">
+ <li><a name="toc-Output-Options-1" href="#Output-Options">4.1 Output Options</a></li>
+ <li><a name="toc-Analysis-Options-1" href="#Analysis-Options">4.2 Analysis Options</a></li>
+ <li><a name="toc-Miscellaneous-Options-1" href="#Miscellaneous-Options">4.3 Miscellaneous Options</a></li>
+ <li><a name="toc-Deprecated-Options-1" href="#Deprecated-Options">4.4 Deprecated Options</a></li>
+ <li><a name="toc-Symspecs-1" href="#Symspecs">4.5 Symspecs</a></li>
+ </ul></li>
+ <li><a name="toc-Interpreting-gprof_0027s-Output" href="#Output">5 Interpreting <code>gprof</code>&rsquo;s Output</a>
+ <ul class="no-bullet">
+ <li><a name="toc-The-Flat-Profile" href="#Flat-Profile">5.1 The Flat Profile</a></li>
+ <li><a name="toc-The-Call-Graph" href="#Call-Graph">5.2 The Call Graph</a>
+ <ul class="no-bullet">
+ <li><a name="toc-The-Primary-Line" href="#Primary">5.2.1 The Primary Line</a></li>
+ <li><a name="toc-Lines-for-a-Function_0027s-Callers" href="#Callers">5.2.2 Lines for a Function&rsquo;s Callers</a></li>
+ <li><a name="toc-Lines-for-a-Function_0027s-Subroutines" href="#Subroutines">5.2.3 Lines for a Function&rsquo;s Subroutines</a></li>
+ <li><a name="toc-How-Mutually-Recursive-Functions-Are-Described" href="#Cycles">5.2.4 How Mutually Recursive Functions Are Described</a></li>
+ </ul></li>
+ <li><a name="toc-Line_002dby_002dline-Profiling" href="#Line_002dby_002dline">5.3 Line-by-line Profiling</a></li>
+ <li><a name="toc-The-Annotated-Source-Listing" href="#Annotated-Source">5.4 The Annotated Source Listing</a></li>
+ </ul></li>
+ <li><a name="toc-Inaccuracy-of-gprof-Output" href="#Inaccuracy">6 Inaccuracy of <code>gprof</code> Output</a>
+ <ul class="no-bullet">
+ <li><a name="toc-Statistical-Sampling-Error" href="#Sampling-Error">6.1 Statistical Sampling Error</a></li>
+ <li><a name="toc-Estimating-children-Times" href="#Assumptions">6.2 Estimating <code>children</code> Times</a></li>
+ </ul></li>
+ <li><a name="toc-Answers-to-Common-Questions" href="#How-do-I_003f">7 Answers to Common Questions</a></li>
+ <li><a name="toc-Incompatibilities-with-Unix-gprof" href="#Incompatibilities">8 Incompatibilities with Unix <code>gprof</code></a></li>
+ <li><a name="toc-Details-of-Profiling" href="#Details">9 Details of Profiling</a>
+ <ul class="no-bullet">
+ <li><a name="toc-Implementation-of-Profiling" href="#Implementation">9.1 Implementation of Profiling</a></li>
+ <li><a name="toc-Profiling-Data-File-Format" href="#File-Format">9.2 Profiling Data File Format</a>
+ <ul class="no-bullet">
+ <li><a name="toc-Histogram-Records" href="#Histogram-Records">9.2.1 Histogram Records</a></li>
+ <li><a name="toc-Call_002dGraph-Records" href="#Call_002dGraph-Records">9.2.2 Call-Graph Records</a></li>
+ <li><a name="toc-Basic_002dBlock-Execution-Count-Records" href="#Basic_002dBlock-Execution-Count-Records">9.2.3 Basic-Block Execution Count Records</a></li>
+ </ul></li>
+ <li><a name="toc-gprof_0027s-Internal-Operation" href="#Internals">9.3 <code>gprof</code>&rsquo;s Internal Operation</a></li>
+ <li><a name="toc-Debugging-gprof" href="#Debugging">9.4 Debugging <code>gprof</code></a></li>
+ </ul></li>
+ <li><a name="toc-GNU-Free-Documentation-License-1" href="#GNU-Free-Documentation-License">Appendix A GNU Free Documentation License</a></li>
+</ul>
+</div>
+
+
+<a name="Top"></a>
+<div class="header">
+<p>
+Next: <a href="#Introduction" accesskey="n" rel="next">Introduction</a>, Up: <a href="dir.html#Top" accesskey="u" rel="up">(dir)</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Profiling-a-Program_003a-Where-Does-It-Spend-Its-Time_003f"></a>
+<h1 class="top">Profiling a Program: Where Does It Spend Its Time?</h1>
+
+<p>This manual describes the <small>GNU</small> profiler, <code>gprof</code>, 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. <small>GNU</small> <code>gprof</code> was written by Jay Fenlason.
+</p>
+<p>This manual is for <code>gprof</code>
+(Arm GNU Toolchain 13.2.rel1 (Build arm-13.7))
+version 2.41.0.
+</p>
+<p>This document is distributed under the terms of the GNU Free
+Documentation License version 1.3. A copy of the license is included
+in the section entitled &ldquo;GNU Free Documentation License&rdquo;.
+</p>
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Introduction" accesskey="1">Introduction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">What profiling means, and why it is useful.
+</td></tr>
+<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
+</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Compiling" accesskey="2">Compiling</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">How to compile your program for profiling.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Executing" accesskey="3">Executing</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Executing your program to generate profile data
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Invoking" accesskey="4">Invoking</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">How to run <code>gprof</code>, and its options
+</td></tr>
+<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
+</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Output" accesskey="5">Output</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Interpreting <code>gprof</code>&rsquo;s output
+</td></tr>
+<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
+</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Inaccuracy" accesskey="6">Inaccuracy</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Potential problems you should be aware of
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#How-do-I_003f" accesskey="7">How do I?</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Answers to common questions
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Incompatibilities" accesskey="8">Incompatibilities</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">(between <small>GNU</small> <code>gprof</code> and Unix <code>gprof</code>.)
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Details" accesskey="9">Details</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Details of how profiling is done
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">GNU Free Documentation License
+</td></tr>
+</table>
+
+<hr>
+<a name="Introduction"></a>
+<div class="header">
+<p>
+Next: <a href="#Compiling" accesskey="n" rel="next">Compiling</a>, Previous: <a href="#Top" accesskey="p" rel="previous">Top</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Introduction-to-Profiling"></a>
+<h2 class="chapter">1 Introduction to Profiling</h2>
+
+
+<p>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.
+</p>
+<p>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&rsquo;t use some feature of your program while it is being profiled, no
+profile information will be generated for that feature.
+</p>
+<p>Profiling has several steps:
+</p>
+<ul>
+<li> You must compile and link your program with profiling enabled.
+See <a href="#Compiling">Compiling a Program for Profiling</a>.
+
+</li><li> You must execute your program to generate a profile data file.
+See <a href="#Executing">Executing the Program</a>.
+
+</li><li> You must run <code>gprof</code> to analyze the profile data.
+See <a href="#Invoking"><code>gprof</code> Command Summary</a>.
+</li></ul>
+
+<p>The next three chapters explain these steps in greater detail.
+</p>
+
+<p>Several forms of output are available from the analysis.
+</p>
+<p>The <em>flat profile</em> 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.
+See <a href="#Flat-Profile">The Flat Profile</a>.
+</p>
+<p>The <em>call graph</em> 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. See <a href="#Call-Graph">The Call Graph</a>.
+</p>
+<p>The <em>annotated source</em> listing is a copy of the program&rsquo;s
+source code, labeled with the number of times each line of the
+program was executed. See <a href="#Annotated-Source">The Annotated Source
+Listing</a>.
+</p>
+<p>To better understand how profiling works, you may wish to read
+a description of its implementation.
+See <a href="#Implementation">Implementation of Profiling</a>.
+</p>
+<hr>
+<a name="Compiling"></a>
+<div class="header">
+<p>
+Next: <a href="#Executing" accesskey="n" rel="next">Executing</a>, Previous: <a href="#Introduction" accesskey="p" rel="previous">Introduction</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Compiling-a-Program-for-Profiling"></a>
+<h2 class="chapter">2 Compiling a Program for Profiling</h2>
+
+<p>The first step in generating profile information for your program is
+to compile and link it with profiling enabled.
+</p>
+<p>To compile a source file for profiling, specify the &lsquo;<samp>-pg</samp>&rsquo; option when
+you run the compiler. (This is in addition to the options you normally
+use.)
+</p>
+<p>To link the program for profiling, if you use a compiler such as <code>cc</code>
+to do the linking, simply specify &lsquo;<samp>-pg</samp>&rsquo; in addition to your usual
+options. The same option, &lsquo;<samp>-pg</samp>&rsquo;, alters either compilation or linking
+to do what is necessary for profiling. Here are examples:
+</p>
+<div class="example">
+<pre class="example">cc -g -c myprog.c utils.c -pg
+cc -o myprog myprog.o utils.o -pg
+</pre></div>
+
+<p>The &lsquo;<samp>-pg</samp>&rsquo; option also works with a command that both compiles and links:
+</p>
+<div class="example">
+<pre class="example">cc -o myprog myprog.c utils.c -g -pg
+</pre></div>
+
+<p>Note: The &lsquo;<samp>-pg</samp>&rsquo; 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 <code>gprof</code> you will get an error
+message like this:
+</p>
+<div class="example">
+<pre class="example">gprof: gmon.out file is missing call-graph data
+</pre></div>
+
+<p>If you add the &lsquo;<samp>-Q</samp>&rsquo; switch to suppress the printing of the call
+graph data you will still be able to see the time samples:
+</p>
+<div class="example">
+<pre class="example">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
+</pre></div>
+
+<p>If you run the linker <code>ld</code> directly instead of through a compiler
+such as <code>cc</code>, you may have to specify a profiling startup file
+<samp>gcrt0.o</samp> as the first input file instead of the usual startup
+file <samp>crt0.o</samp>. In addition, you would probably want to
+specify the profiling C library, <samp>libc_p.a</samp>, by writing
+&lsquo;<samp>-lc_p</samp>&rsquo; instead of the usual &lsquo;<samp>-lc</samp>&rsquo;. This is not absolutely
+necessary, but doing this gives you number-of-calls information for
+standard library functions such as <code>read</code> and <code>open</code>. For
+example:
+</p>
+<div class="example">
+<pre class="example">ld -o myprog /lib/gcrt0.o myprog.o utils.o -lc_p
+</pre></div>
+
+<p>If you are running the program on a system which supports shared
+libraries you may run into problems with the profiling support code in
+a shared library being called before that library has been fully
+initialised. This is usually detected by the program encountering a
+segmentation fault as soon as it is run. The solution is to link
+against a static version of the library containing the profiling
+support code, which for <code>gcc</code> users can be done via the
+&lsquo;<samp>-static</samp>&rsquo; or &lsquo;<samp>-static-libgcc</samp>&rsquo; command-line option. For
+example:
+</p>
+<div class="example">
+<pre class="example">gcc -g -pg -static-libgcc myprog.c utils.c -o myprog
+</pre></div>
+
+<p>If you compile only some of the modules of the program with &lsquo;<samp>-pg</samp>&rsquo;, you
+can still profile the program, but you won&rsquo;t get complete information about
+the modules that were compiled without &lsquo;<samp>-pg</samp>&rsquo;. 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 <code>calls</code> field for
+the functions will be blank), but will greatly reduce the usefulness of the
+call graph.
+</p>
+<p>If you wish to perform line-by-line profiling you should use the
+<code>gcov</code> tool instead of <code>gprof</code>. See that tool&rsquo;s manual or
+info pages for more details of how to do this.
+</p>
+<p>Note, older versions of <code>gcc</code> produce line-by-line profiling
+information that works with <code>gprof</code> rather than <code>gcov</code> so
+there is still support for displaying this kind of information in
+<code>gprof</code>. See <a href="#Line_002dby_002dline">Line-by-line Profiling</a>.
+</p>
+<p>It also worth noting that <code>gcc</code> implements a
+&lsquo;<samp>-finstrument-functions</samp>&rsquo; command-line option which will insert
+calls to special user supplied instrumentation routines at the entry
+and exit of every function in their program. This can be used to
+implement an alternative profiling scheme.
+</p>
+<hr>
+<a name="Executing"></a>
+<div class="header">
+<p>
+Next: <a href="#Invoking" accesskey="n" rel="next">Invoking</a>, Previous: <a href="#Compiling" accesskey="p" rel="previous">Compiling</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Executing-the-Program"></a>
+<h2 class="chapter">3 Executing the Program</h2>
+
+<p>Once the program is compiled for profiling, you must run it in order to
+generate the information that <code>gprof</code> needs. Simply run the program
+as usual, using the normal arguments, file names, etc. The program should
+run normally, producing the same output as usual. It will, however, run
+somewhat slower than normal because of the time spent collecting and
+writing the profile data.
+</p>
+<p>The way you run the program&mdash;the arguments and input that you give
+it&mdash;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.
+</p>
+<p>Your program will write the profile data into a file called <samp>gmon.out</samp>
+just before exiting. If there is already a file called <samp>gmon.out</samp>,
+its contents are overwritten. You can rename the file afterwards if you
+are concerned that it may be overwritten. If your system libc allows you
+may be able to write the profile data under a different name. Set the
+GMON_OUT_PREFIX environment variable; this name will be appended with
+the PID of the running program.
+</p>
+<p>In order to write the <samp>gmon.out</samp> file properly, your program must exit
+normally: by returning from <code>main</code> or by calling <code>exit</code>. Calling
+the low-level function <code>_exit</code> does not write the profile data, and
+neither does abnormal termination due to an unhandled signal.
+</p>
+<p>The <samp>gmon.out</samp> file is written in the program&rsquo;s <em>current working
+directory</em> at the time it exits. This means that if your program calls
+<code>chdir</code>, the <samp>gmon.out</samp> file will be left in the last directory
+your program <code>chdir</code>&rsquo;d to. If you don&rsquo;t have permission to write in
+this directory, the file is not written, and you will get an error message.
+</p>
+<p>Older versions of the <small>GNU</small> profiling library may also write a file
+called <samp>bb.out</samp>. This file, if present, contains an human-readable
+listing of the basic-block execution counts. Unfortunately, the
+appearance of a human-readable <samp>bb.out</samp> means the basic-block
+counts didn&rsquo;t get written into <samp>gmon.out</samp>.
+The Perl script <code>bbconv.pl</code>, included with the <code>gprof</code>
+source distribution, will convert a <samp>bb.out</samp> file into
+a format readable by <code>gprof</code>. Invoke it like this:
+</p>
+<div class="smallexample">
+<pre class="smallexample">bbconv.pl &lt; bb.out &gt; <var>bh-data</var>
+</pre></div>
+
+<p>This translates the information in <samp>bb.out</samp> into a form that
+<code>gprof</code> can understand. But you still need to tell <code>gprof</code>
+about the existence of this translated information. To do that, include
+<var>bb-data</var> on the <code>gprof</code> command line, <em>along with
+<samp>gmon.out</samp></em>, like this:
+</p>
+<div class="smallexample">
+<pre class="smallexample">gprof <var>options</var> <var>executable-file</var> gmon.out <var>bb-data</var> [<var>yet-more-profile-data-files</var>&hellip;] [&gt; <var>outfile</var>]
+</pre></div>
+
+<hr>
+<a name="Invoking"></a>
+<div class="header">
+<p>
+Next: <a href="#Output" accesskey="n" rel="next">Output</a>, Previous: <a href="#Executing" accesskey="p" rel="previous">Executing</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="gprof-Command-Summary"></a>
+<h2 class="chapter">4 <code>gprof</code> Command Summary</h2>
+
+<p>After you have a profile data file <samp>gmon.out</samp>, you can run <code>gprof</code>
+to interpret the information in it. The <code>gprof</code> program prints a
+flat profile and a call graph on standard output. Typically you would
+redirect the output of <code>gprof</code> into a file with &lsquo;<samp>&gt;</samp>&rsquo;.
+</p>
+<p>You run <code>gprof</code> like this:
+</p>
+<div class="smallexample">
+<pre class="smallexample">gprof <var>options</var> [<var>executable-file</var> [<var>profile-data-files</var>&hellip;]] [&gt; <var>outfile</var>]
+</pre></div>
+
+<p>Here square-brackets indicate optional arguments.
+</p>
+<p>If you omit the executable file name, the file <samp>a.out</samp> is used. If
+you give no profile data file name, the file <samp>gmon.out</samp> 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.
+</p>
+<p>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.
+</p>
+<p>The order of these options does not matter.
+</p>
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Output-Options" accesskey="1">Output Options</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Controlling <code>gprof</code>&rsquo;s output style
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Analysis-Options" accesskey="2">Analysis Options</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Controlling how <code>gprof</code> analyzes its data
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Miscellaneous-Options" accesskey="3">Miscellaneous Options</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Deprecated-Options" accesskey="4">Deprecated Options</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Options you no longer need to use, but which
+ have been retained for compatibility
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Symspecs" accesskey="5">Symspecs</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Specifying functions to include or exclude
+</td></tr>
+</table>
+
+<hr>
+<a name="Output-Options"></a>
+<div class="header">
+<p>
+Next: <a href="#Analysis-Options" accesskey="n" rel="next">Analysis Options</a>, Up: <a href="#Invoking" accesskey="u" rel="up">Invoking</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Output-Options-1"></a>
+<h3 class="section">4.1 Output Options</h3>
+
+<p>These options specify which of several output formats
+<code>gprof</code> should produce.
+</p>
+<p>Many of these options take an optional <em>symspec</em> 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. See <a href="#Symspecs">Symspecs</a>.
+</p>
+<p>Specifying any of these options overrides the default (&lsquo;<samp>-p -q</samp>&rsquo;),
+which prints a flat profile and call graph analysis
+for all functions.
+</p>
+<dl compact="compact">
+<dt><code>-A[<var>symspec</var>]</code></dt>
+<dt><code>--annotated-source[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-A</samp>&rsquo; option causes <code>gprof</code> to print annotated source code.
+If <var>symspec</var> is specified, print output only for matching symbols.
+See <a href="#Annotated-Source">The Annotated Source Listing</a>.
+</p>
+</dd>
+<dt><code>-b</code></dt>
+<dt><code>--brief</code></dt>
+<dd><p>If the &lsquo;<samp>-b</samp>&rsquo; option is given, <code>gprof</code> doesn&rsquo;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.
+</p>
+</dd>
+<dt><code>-B</code></dt>
+<dd><p>The &lsquo;<samp>-B</samp>&rsquo; option causes <code>gprof</code> to print the call graph analysis.
+</p>
+</dd>
+<dt><code>-C[<var>symspec</var>]</code></dt>
+<dt><code>--exec-counts[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-C</samp>&rsquo; option causes <code>gprof</code> to
+print a tally of functions and the number of times each was called.
+If <var>symspec</var> is specified, print tally only for matching symbols.
+</p>
+<p>If the profile data file contains basic-block count records, specifying
+the &lsquo;<samp>-l</samp>&rsquo; option, along with &lsquo;<samp>-C</samp>&rsquo;, will cause basic-block
+execution counts to be tallied and displayed.
+</p>
+</dd>
+<dt><code>-i</code></dt>
+<dt><code>--file-info</code></dt>
+<dd><p>The &lsquo;<samp>-i</samp>&rsquo; option causes <code>gprof</code> 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.
+</p>
+</dd>
+<dt><code>-I <var>dirs</var></code></dt>
+<dt><code>--directory-path=<var>dirs</var></code></dt>
+<dd><p>The &lsquo;<samp>-I</samp>&rsquo; option specifies a list of search directories in
+which to find source files. Environment variable <var>GPROF_PATH</var>
+can also be used to convey this information.
+Used mostly for annotated source output.
+</p>
+</dd>
+<dt><code>-J[<var>symspec</var>]</code></dt>
+<dt><code>--no-annotated-source[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-J</samp>&rsquo; option causes <code>gprof</code> not to
+print annotated source code.
+If <var>symspec</var> is specified, <code>gprof</code> prints annotated source,
+but excludes matching symbols.
+</p>
+</dd>
+<dt><code>-L</code></dt>
+<dt><code>--print-path</code></dt>
+<dd><p>Normally, source filenames are printed with the path
+component suppressed. The &lsquo;<samp>-L</samp>&rsquo; option causes <code>gprof</code>
+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>
+</dd>
+<dt><code>-p[<var>symspec</var>]</code></dt>
+<dt><code>--flat-profile[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-p</samp>&rsquo; option causes <code>gprof</code> to print a flat profile.
+If <var>symspec</var> is specified, print flat profile only for matching symbols.
+See <a href="#Flat-Profile">The Flat Profile</a>.
+</p>
+</dd>
+<dt><code>-P[<var>symspec</var>]</code></dt>
+<dt><code>--no-flat-profile[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-P</samp>&rsquo; option causes <code>gprof</code> to suppress printing a flat profile.
+If <var>symspec</var> is specified, <code>gprof</code> prints a flat profile,
+but excludes matching symbols.
+</p>
+</dd>
+<dt><code>-q[<var>symspec</var>]</code></dt>
+<dt><code>--graph[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-q</samp>&rsquo; option causes <code>gprof</code> to print the call graph analysis.
+If <var>symspec</var> is specified, print call graph only for matching symbols
+and their children.
+See <a href="#Call-Graph">The Call Graph</a>.
+</p>
+</dd>
+<dt><code>-Q[<var>symspec</var>]</code></dt>
+<dt><code>--no-graph[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-Q</samp>&rsquo; option causes <code>gprof</code> to suppress printing the
+call graph.
+If <var>symspec</var> is specified, <code>gprof</code> prints a call graph,
+but excludes matching symbols.
+</p>
+</dd>
+<dt><code>-t</code></dt>
+<dt><code>--table-length=<var>num</var></code></dt>
+<dd><p>The &lsquo;<samp>-t</samp>&rsquo; option causes the <var>num</var> most active source lines in
+each source file to be listed when source annotation is enabled. The
+default is 10.
+</p>
+</dd>
+<dt><code>-y</code></dt>
+<dt><code>--separate-files</code></dt>
+<dd><p>This option affects annotated source output only.
+Normally, <code>gprof</code> prints annotated source files
+to standard-output. If this option is specified,
+annotated source for a file named <samp>path/<var>filename</var></samp>
+is generated in the file <samp><var>filename</var>-ann</samp>. If the underlying
+file system would truncate <samp><var>filename</var>-ann</samp> so that it
+overwrites the original <samp><var>filename</var></samp>, <code>gprof</code> generates
+annotated source in the file <samp><var>filename</var>.ann</samp> instead (if the
+original file name has an extension, that extension is <em>replaced</em>
+with <samp>.ann</samp>).
+</p>
+</dd>
+<dt><code>-Z[<var>symspec</var>]</code></dt>
+<dt><code>--no-exec-counts[=<var>symspec</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-Z</samp>&rsquo; option causes <code>gprof</code> not to
+print a tally of functions and the number of times each was called.
+If <var>symspec</var> is specified, print tally, but exclude matching symbols.
+</p>
+</dd>
+<dt><code>-r</code></dt>
+<dt><code>--function-ordering</code></dt>
+<dd><p>The &lsquo;<samp>--function-ordering</samp>&rsquo; option causes <code>gprof</code> 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.
+</p>
+<p>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.
+</p>
+</dd>
+<dt><code>-R <var>map_file</var></code></dt>
+<dt><code>--file-ordering <var>map_file</var></code></dt>
+<dd><p>The &lsquo;<samp>--file-ordering</samp>&rsquo; option causes <code>gprof</code> 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.
+</p>
+<p>Use of the &lsquo;<samp>-a</samp>&rsquo; argument is highly recommended with this option.
+</p>
+<p>The <var>map_file</var> 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 <code>nm</code>.
+</p>
+<div class="smallexample">
+<pre class="smallexample">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
+&hellip;
+
+</pre></div>
+
+<p>To create a <var>map_file</var> with <small>GNU</small> <code>nm</code>, type a command like
+<kbd>nm --extern-only --defined-only -v --print-file-name program-name</kbd>.
+</p>
+</dd>
+<dt><code>-T</code></dt>
+<dt><code>--traditional</code></dt>
+<dd><p>The &lsquo;<samp>-T</samp>&rsquo; option causes <code>gprof</code> to print its output in
+&ldquo;traditional&rdquo; BSD style.
+</p>
+</dd>
+<dt><code>-w <var>width</var></code></dt>
+<dt><code>--width=<var>width</var></code></dt>
+<dd><p>Sets width of output lines to <var>width</var>.
+Currently only used when printing the function index at the bottom
+of the call graph.
+</p>
+</dd>
+<dt><code>-x</code></dt>
+<dt><code>--all-lines</code></dt>
+<dd><p>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 <code>tcov</code>&rsquo;s &lsquo;<samp>-a</samp>&rsquo;.
+</p>
+</dd>
+<dt><code>--demangle[=<var>style</var>]</code></dt>
+<dt><code>--no-demangle</code></dt>
+<dd><p>These options control whether C++ symbol names should be demangled when
+printing output. The default is to demangle symbols. The
+<code>--no-demangle</code> 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.
+</p></dd>
+</dl>
+
+<hr>
+<a name="Analysis-Options"></a>
+<div class="header">
+<p>
+Next: <a href="#Miscellaneous-Options" accesskey="n" rel="next">Miscellaneous Options</a>, Previous: <a href="#Output-Options" accesskey="p" rel="previous">Output Options</a>, Up: <a href="#Invoking" accesskey="u" rel="up">Invoking</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Analysis-Options-1"></a>
+<h3 class="section">4.2 Analysis Options</h3>
+
+<dl compact="compact">
+<dt><code>-a</code></dt>
+<dt><code>--no-static</code></dt>
+<dd><p>The &lsquo;<samp>-a</samp>&rsquo; option causes <code>gprof</code> 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.
+</p>
+</dd>
+<dt><code>-c</code></dt>
+<dt><code>--static-call-graph</code></dt>
+<dd><p>The &lsquo;<samp>-c</samp>&rsquo; 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 <em>not</em> found
+by this option.
+Parents or children identified via this heuristic
+are indicated in the call graph with call counts of &lsquo;<samp>0</samp>&rsquo;.
+</p>
+</dd>
+<dt><code>-D</code></dt>
+<dt><code>--ignore-non-functions</code></dt>
+<dd><p>The &lsquo;<samp>-D</samp>&rsquo; option causes <code>gprof</code> 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).
+</p>
+</dd>
+<dt><code>-k <var>from</var>/<var>to</var></code></dt>
+<dd><p>The &lsquo;<samp>-k</samp>&rsquo; option allows you to delete from the call graph any arcs from
+symbols matching symspec <var>from</var> to those matching symspec <var>to</var>.
+</p>
+</dd>
+<dt><code>-l</code></dt>
+<dt><code>--line</code></dt>
+<dd><p>The &lsquo;<samp>-l</samp>&rsquo; option enables line-by-line profiling, which causes
+histogram hits to be charged to individual source code lines,
+instead of functions. This feature only works with programs compiled
+by older versions of the <code>gcc</code> compiler. Newer versions of
+<code>gcc</code> are designed to work with the <code>gcov</code> tool instead.
+</p>
+<p>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 <code>gprof</code>, and magnifies statistical
+inaccuracies.
+See <a href="#Sampling-Error">Statistical Sampling Error</a>.
+</p>
+</dd>
+<dt><code>--inline-file-names</code></dt>
+<dd><p>This option causes <code>gprof</code> to print the source file after each
+symbol in both the flat profile and the call graph. The full path to the
+file is printed if used with the &lsquo;<samp>-L</samp>&rsquo; option.
+</p>
+</dd>
+<dt><code>-m <var>num</var></code></dt>
+<dt><code>--min-count=<var>num</var></code></dt>
+<dd><p>This option affects execution count output only.
+Symbols that are executed less than <var>num</var> times are suppressed.
+</p>
+</dd>
+<dt><code>-n<var>symspec</var></code></dt>
+<dt><code>--time=<var>symspec</var></code></dt>
+<dd><p>The &lsquo;<samp>-n</samp>&rsquo; option causes <code>gprof</code>, in its call graph analysis,
+to only propagate times for symbols matching <var>symspec</var>.
+</p>
+</dd>
+<dt><code>-N<var>symspec</var></code></dt>
+<dt><code>--no-time=<var>symspec</var></code></dt>
+<dd><p>The &lsquo;<samp>-n</samp>&rsquo; option causes <code>gprof</code>, in its call graph analysis,
+not to propagate times for symbols matching <var>symspec</var>.
+</p>
+</dd>
+<dt><code>-S<var>filename</var></code></dt>
+<dt><code>--external-symbol-table=<var>filename</var></code></dt>
+<dd><p>The &lsquo;<samp>-S</samp>&rsquo; option causes <code>gprof</code> to read an external symbol table
+file, such as <samp>/proc/kallsyms</samp>, rather than read the symbol table
+from the given object file (the default is <code>a.out</code>). This is useful
+for profiling kernel modules.
+</p>
+</dd>
+<dt><code>-z</code></dt>
+<dt><code>--display-unused-functions</code></dt>
+<dd><p>If you give the &lsquo;<samp>-z</samp>&rsquo; option, <code>gprof</code> 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
+&lsquo;<samp>-c</samp>&rsquo; option for discovering which routines were never called.
+</p>
+</dd>
+</dl>
+
+<hr>
+<a name="Miscellaneous-Options"></a>
+<div class="header">
+<p>
+Next: <a href="#Deprecated-Options" accesskey="n" rel="next">Deprecated Options</a>, Previous: <a href="#Analysis-Options" accesskey="p" rel="previous">Analysis Options</a>, Up: <a href="#Invoking" accesskey="u" rel="up">Invoking</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Miscellaneous-Options-1"></a>
+<h3 class="section">4.3 Miscellaneous Options</h3>
+
+<dl compact="compact">
+<dt><code>-d[<var>num</var>]</code></dt>
+<dt><code>--debug[=<var>num</var>]</code></dt>
+<dd><p>The &lsquo;<samp>-d <var>num</var></samp>&rsquo; option specifies debugging options.
+If <var>num</var> is not specified, enable all debugging.
+See <a href="#Debugging">Debugging <code>gprof</code></a>.
+</p>
+</dd>
+<dt><code>-h</code></dt>
+<dt><code>--help</code></dt>
+<dd><p>The &lsquo;<samp>-h</samp>&rsquo; option prints command line usage.
+</p>
+</dd>
+<dt><code>-O<var>name</var></code></dt>
+<dt><code>--file-format=<var>name</var></code></dt>
+<dd><p>Selects the format of the profile data files. Recognized formats are
+&lsquo;<samp>auto</samp>&rsquo; (the default), &lsquo;<samp>bsd</samp>&rsquo;, &lsquo;<samp>4.4bsd</samp>&rsquo;, &lsquo;<samp>magic</samp>&rsquo;, and
+&lsquo;<samp>prof</samp>&rsquo; (not yet supported).
+</p>
+</dd>
+<dt><code>-s</code></dt>
+<dt><code>--sum</code></dt>
+<dd><p>The &lsquo;<samp>-s</samp>&rsquo; option causes <code>gprof</code> to summarize the information
+in the profile data files it read in, and write out a profile data
+file called <samp>gmon.sum</samp>, which contains all the information from
+the profile data files that <code>gprof</code> read in. The file <samp>gmon.sum</samp>
+may be one of the specified input files; the effect of this is to
+merge the data in the other input files into <samp>gmon.sum</samp>.
+</p>
+<p>Eventually you can run <code>gprof</code> again without &lsquo;<samp>-s</samp>&rsquo; to analyze the
+cumulative data in the file <samp>gmon.sum</samp>.
+</p>
+</dd>
+<dt><code>-v</code></dt>
+<dt><code>--version</code></dt>
+<dd><p>The &lsquo;<samp>-v</samp>&rsquo; flag causes <code>gprof</code> to print the current version
+number, and then exit.
+</p>
+</dd>
+</dl>
+
+<hr>
+<a name="Deprecated-Options"></a>
+<div class="header">
+<p>
+Next: <a href="#Symspecs" accesskey="n" rel="next">Symspecs</a>, Previous: <a href="#Miscellaneous-Options" accesskey="p" rel="previous">Miscellaneous Options</a>, Up: <a href="#Invoking" accesskey="u" rel="up">Invoking</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Deprecated-Options-1"></a>
+<h3 class="section">4.4 Deprecated Options</h3>
+
+<p>These options have been replaced with newer versions that use symspecs.
+</p>
+<dl compact="compact">
+<dt><code>-e <var>function_name</var></code></dt>
+<dd><p>The &lsquo;<samp>-e <var>function</var></samp>&rsquo; option tells <code>gprof</code> to not print
+information about the function <var>function_name</var> (and its
+children&hellip;) 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 &lsquo;<samp>[not printed]</samp>&rsquo;. More than one &lsquo;<samp>-e</samp>&rsquo; option may be
+given; only one <var>function_name</var> may be indicated with each &lsquo;<samp>-e</samp>&rsquo;
+option.
+</p>
+</dd>
+<dt><code>-E <var>function_name</var></code></dt>
+<dd><p>The <code>-E <var>function</var></code> option works like the <code>-e</code> 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 &lsquo;<samp>-E</samp>&rsquo; option may be given; only one
+<var>function_name</var> may be indicated with each &lsquo;<samp>-E</samp>&rsquo; option.
+</p>
+</dd>
+<dt><code>-f <var>function_name</var></code></dt>
+<dd><p>The &lsquo;<samp>-f <var>function</var></samp>&rsquo; option causes <code>gprof</code> to limit the
+call graph to the function <var>function_name</var> and its children (and
+their children&hellip;). More than one &lsquo;<samp>-f</samp>&rsquo; option may be given;
+only one <var>function_name</var> may be indicated with each &lsquo;<samp>-f</samp>&rsquo;
+option.
+</p>
+</dd>
+<dt><code>-F <var>function_name</var></code></dt>
+<dd><p>The &lsquo;<samp>-F <var>function</var></samp>&rsquo; option works like the <code>-f</code> option, but
+only time spent in the function and its children (and their
+children&hellip;) will be used to determine total-time and
+percentages-of-time for the call graph. More than one &lsquo;<samp>-F</samp>&rsquo; option
+may be given; only one <var>function_name</var> may be indicated with each
+&lsquo;<samp>-F</samp>&rsquo; option. The &lsquo;<samp>-F</samp>&rsquo; option overrides the &lsquo;<samp>-E</samp>&rsquo; option.
+</p>
+</dd>
+</dl>
+
+
+<p>Note that only one function can be specified with each <code>-e</code>,
+<code>-E</code>, <code>-f</code> or <code>-F</code> option. To specify more than one
+function, use multiple options. For example, this command:
+</p>
+<div class="example">
+<pre class="example">gprof -e boring -f foo -f bar myprogram &gt; gprof.output
+</pre></div>
+
+<p>lists in the call graph all functions that were reached from either
+<code>foo</code> or <code>bar</code> and were not reachable from <code>boring</code>.
+</p>
+<hr>
+<a name="Symspecs"></a>
+<div class="header">
+<p>
+Previous: <a href="#Deprecated-Options" accesskey="p" rel="previous">Deprecated Options</a>, Up: <a href="#Invoking" accesskey="u" rel="up">Invoking</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Symspecs-1"></a>
+<h3 class="section">4.5 Symspecs</h3>
+
+<p>Many of the output options allow functions to be included or excluded
+using <em>symspecs</em> (symbol specifications), which observe the
+following syntax:
+</p>
+<div class="example">
+<pre class="example"> filename_containing_a_dot
+| funcname_not_containing_a_dot
+| linenumber
+| ( [ any_filename ] `:' ( any_funcname | linenumber ) )
+</pre></div>
+
+<p>Here are some sample symspecs:
+</p>
+<dl compact="compact">
+<dt>&lsquo;<samp>main.c</samp>&rsquo;</dt>
+<dd><p>Selects everything in file <samp>main.c</samp>&mdash;the
+dot in the string tells <code>gprof</code> 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, &lsquo;<samp>odd:</samp>&rsquo; is
+interpreted as the file named <samp>odd</samp>.
+</p>
+</dd>
+<dt>&lsquo;<samp>main</samp>&rsquo;</dt>
+<dd><p>Selects all functions named &lsquo;<samp>main</samp>&rsquo;.
+</p>
+<p>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.
+</p>
+<p>Sometimes, function names contain dots. In such cases, it is necessary
+to add a leading colon to the name. For example, &lsquo;<samp>:.mul</samp>&rsquo; selects
+function &lsquo;<samp>.mul</samp>&rsquo;.
+</p>
+<p>In some object file formats, symbols have a leading underscore.
+<code>gprof</code> will normally not print these underscores. When you name a
+symbol in a symspec, you should type it exactly as <code>gprof</code> prints
+it in its output. For example, if the compiler produces a symbol
+&lsquo;<samp>_main</samp>&rsquo; from your <code>main</code> function, <code>gprof</code> still prints
+it as &lsquo;<samp>main</samp>&rsquo; in its output, so you should use &lsquo;<samp>main</samp>&rsquo; in
+symspecs.
+</p>
+</dd>
+<dt>&lsquo;<samp>main.c:main</samp>&rsquo;</dt>
+<dd><p>Selects function &lsquo;<samp>main</samp>&rsquo; in file <samp>main.c</samp>.
+</p>
+</dd>
+<dt>&lsquo;<samp>main.c:134</samp>&rsquo;</dt>
+<dd><p>Selects line 134 in file <samp>main.c</samp>.
+</p></dd>
+</dl>
+
+<hr>
+<a name="Output"></a>
+<div class="header">
+<p>
+Next: <a href="#Inaccuracy" accesskey="n" rel="next">Inaccuracy</a>, Previous: <a href="#Invoking" accesskey="p" rel="previous">Invoking</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Interpreting-gprof_0027s-Output"></a>
+<h2 class="chapter">5 Interpreting <code>gprof</code>&rsquo;s Output</h2>
+
+<p><code>gprof</code> 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.
+See <a href="#Output-Options">Output Options</a>.
+</p>
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Flat-Profile" accesskey="1">Flat Profile</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The flat profile shows how much time was spent
+ executing directly in each function.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Call-Graph" accesskey="2">Call Graph</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The call graph shows which functions called which
+ others, and how much time each function used
+ when its subroutine calls are included.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Line_002dby_002dline" accesskey="3">Line-by-line</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top"><code>gprof</code> can analyze individual source code lines
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Annotated-Source" accesskey="4">Annotated Source</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The annotated source listing displays source code
+ labeled with execution counts
+</td></tr>
+</table>
+
+
+<hr>
+<a name="Flat-Profile"></a>
+<div class="header">
+<p>
+Next: <a href="#Call-Graph" accesskey="n" rel="next">Call Graph</a>, Up: <a href="#Output" accesskey="u" rel="up">Output</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="The-Flat-Profile"></a>
+<h3 class="section">5.1 The Flat Profile</h3>
+<a name="index-flat-profile"></a>
+
+<p>The <em>flat profile</em> shows the total amount of time your program
+spent executing each function. Unless the &lsquo;<samp>-z</samp>&rsquo; 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&rsquo;t run long enough to show up on the program
+counter histogram, it will be indistinguishable from a function that
+was never called.
+</p>
+<p>This is part of a flat profile for a small program:
+</p>
+<div class="smallexample">
+<pre class="smallexample">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
+&hellip;
+</pre></div>
+
+<p>The functions are sorted first by decreasing run-time spent in them,
+then by decreasing number of calls, then alphabetically by name. The
+functions &lsquo;<samp>mcount</samp>&rsquo; and &lsquo;<samp>profil</samp>&rsquo; 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.
+</p>
+<p>Just before the column headers, a statement appears indicating
+how much time each sample counted as.
+This <em>sampling period</em> 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&rsquo;s total execution time was 0.06
+seconds, as indicated by the &lsquo;<samp>cumulative seconds</samp>&rsquo; 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 &lsquo;<samp>open</samp>&rsquo; function, as indicated by the
+&lsquo;<samp>self seconds</samp>&rsquo; field. Each of the other four samples
+occurred one each in &lsquo;<samp>offtime</samp>&rsquo;, &lsquo;<samp>memccpy</samp>&rsquo;, &lsquo;<samp>write</samp>&rsquo;,
+and &lsquo;<samp>mcount</samp>&rsquo;.
+Since only six samples were taken, none of these values can
+be regarded as particularly reliable.
+In another run,
+the &lsquo;<samp>self seconds</samp>&rsquo; field for
+&lsquo;<samp>mcount</samp>&rsquo; might well be &lsquo;<samp>0.00</samp>&rsquo; or &lsquo;<samp>0.02</samp>&rsquo;.
+See <a href="#Sampling-Error">Statistical Sampling Error</a>,
+for a complete discussion.
+</p>
+<p>The remaining functions in the listing (those whose
+&lsquo;<samp>self seconds</samp>&rsquo; field is &lsquo;<samp>0.00</samp>&rsquo;) didn&rsquo;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 &lsquo;<samp>calls</samp>&rsquo; field.
+Clearly some time was spent executing these functions,
+but the paucity of histogram samples prevents any
+determination of how much time each took.
+</p>
+<p>Here is what the fields in each line mean:
+</p>
+<dl compact="compact">
+<dt><code>% time</code></dt>
+<dd><p>This is the percentage of the total execution time your program spent
+in this function. These should all add up to 100%.
+</p>
+</dd>
+<dt><code>cumulative seconds</code></dt>
+<dd><p>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.
+</p>
+</dd>
+<dt><code>self seconds</code></dt>
+<dd><p>This is the number of seconds accounted for by this function alone.
+The flat profile listing is sorted first by this number.
+</p>
+</dd>
+<dt><code>calls</code></dt>
+<dd><p>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 <em>calls</em> field is blank.
+</p>
+</dd>
+<dt><code>self ms/call</code></dt>
+<dd><p>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.
+</p>
+</dd>
+<dt><code>total ms/call</code></dt>
+<dd><p>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.
+</p>
+</dd>
+<dt><code>name</code></dt>
+<dd><p>This is the name of the function. The flat profile is sorted by this
+field alphabetically after the <em>self seconds</em> and <em>calls</em>
+fields are sorted.
+</p></dd>
+</dl>
+
+<hr>
+<a name="Call-Graph"></a>
+<div class="header">
+<p>
+Next: <a href="#Line_002dby_002dline" accesskey="n" rel="next">Line-by-line</a>, Previous: <a href="#Flat-Profile" accesskey="p" rel="previous">Flat Profile</a>, Up: <a href="#Output" accesskey="u" rel="up">Output</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="The-Call-Graph"></a>
+<h3 class="section">5.2 The Call Graph</h3>
+<a name="index-call-graph"></a>
+
+<p>The <em>call graph</em> 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.
+</p>
+<p>Here is a sample call from a small program. This call came from the
+same <code>gprof</code> run as the flat profile example in the previous
+section.
+</p>
+<div class="smallexample">
+<pre class="smallexample">granularity: each sample hit covers 2 byte(s) for 20.00% of 0.05 seconds
+
+index % time self children called name
+ &lt;spontaneous&gt;
+[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 &lt;cycle 1&gt; [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 &lt;cycle 2 as a whole&gt; [4]
+ 0.01 0.02 244+260 offtime &lt;cycle 2&gt; [7]
+ 0.00 0.00 236+1 tzset &lt;cycle 2&gt; [26]
+-----------------------------------------------
+</pre></div>
+
+<p>The lines full of dashes divide this table into <em>entries</em>, one for each
+function. Each entry has one or more lines.
+</p>
+<p>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
+<em>children</em> when we speak of the call graph).
+</p>
+<p>The entries are sorted by time spent in the function and its subroutines.
+</p>
+<p>The internal profiling function <code>mcount</code> (see <a href="#Flat-Profile">The
+Flat Profile</a>) is never mentioned in the call graph.
+</p>
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Primary" accesskey="1">Primary</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Details of the primary line&rsquo;s contents.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Callers" accesskey="2">Callers</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Details of caller-lines&rsquo; contents.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Subroutines" accesskey="3">Subroutines</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Details of subroutine-lines&rsquo; contents.
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Cycles" accesskey="4">Cycles</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">When there are cycles of recursion,
+ such as <code>a</code> calls <code>b</code> calls <code>a</code>&hellip;
+</td></tr>
+</table>
+
+<hr>
+<a name="Primary"></a>
+<div class="header">
+<p>
+Next: <a href="#Callers" accesskey="n" rel="next">Callers</a>, Up: <a href="#Call-Graph" accesskey="u" rel="up">Call Graph</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="The-Primary-Line"></a>
+<h4 class="subsection">5.2.1 The Primary Line</h4>
+
+<p>The <em>primary line</em> 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.
+</p>
+<p>For reference, we repeat the primary line from the entry for function
+<code>report</code> in our main example, together with the heading line that
+shows the names of the fields:
+</p>
+<div class="smallexample">
+<pre class="smallexample">index % time self children called name
+&hellip;
+[3] 100.0 0.00 0.05 1 report [3]
+</pre></div>
+
+<p>Here is what the fields in the primary line mean:
+</p>
+<dl compact="compact">
+<dt><code>index</code></dt>
+<dd><p>Entries are numbered with consecutive integers. Each function
+therefore has an index number, which appears at the beginning of its
+primary line.
+</p>
+<p>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.
+</p>
+</dd>
+<dt><code>% time</code></dt>
+<dd><p>This is the percentage of the total time that was spent in this
+function, including time spent in subroutines called from this
+function.
+</p>
+<p>The time spent in this function is counted again for the callers of
+this function. Therefore, adding up these percentages is meaningless.
+</p>
+</dd>
+<dt><code>self</code></dt>
+<dd><p>This is the total amount of time spent in this function. This
+should be identical to the number printed in the <code>seconds</code> field
+for this function in the flat profile.
+</p>
+</dd>
+<dt><code>children</code></dt>
+<dd><p>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 <code>self</code>
+and <code>children</code> entries of the children listed directly below this
+function.
+</p>
+</dd>
+<dt><code>called</code></dt>
+<dd><p>This is the number of times the function was called.
+</p>
+<p>If the function called itself recursively, there are two numbers,
+separated by a &lsquo;<samp>+</samp>&rsquo;. The first number counts non-recursive calls,
+and the second counts recursive calls.
+</p>
+<p>In the example above, the function <code>report</code> was called once from
+<code>main</code>.
+</p>
+</dd>
+<dt><code>name</code></dt>
+<dd><p>This is the name of the current function. The index number is
+repeated after it.
+</p>
+<p>If the function is part of a cycle of recursion, the cycle number is
+printed between the function&rsquo;s name and the index number
+(see <a href="#Cycles">How Mutually Recursive Functions Are Described</a>).
+For example, if function <code>gnurr</code> is part of
+cycle number one, and has index number twelve, its primary line would
+be end like this:
+</p>
+<div class="example">
+<pre class="example">gnurr &lt;cycle 1&gt; [12]
+</pre></div>
+</dd>
+</dl>
+
+<hr>
+<a name="Callers"></a>
+<div class="header">
+<p>
+Next: <a href="#Subroutines" accesskey="n" rel="next">Subroutines</a>, Previous: <a href="#Primary" accesskey="p" rel="previous">Primary</a>, Up: <a href="#Call-Graph" accesskey="u" rel="up">Call Graph</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Lines-for-a-Function_0027s-Callers"></a>
+<h4 class="subsection">5.2.2 Lines for a Function&rsquo;s Callers</h4>
+
+<p>A function&rsquo;s entry has a line for each function it was called by.
+These lines&rsquo; fields correspond to the fields of the primary line, but
+their meanings are different because of the difference in context.
+</p>
+<p>For reference, we repeat two lines from the entry for the function
+<code>report</code>, the primary line and one caller-line preceding it, together
+with the heading line that shows the names of the fields:
+</p>
+<div class="smallexample">
+<pre class="smallexample">index % time self children called name
+&hellip;
+ 0.00 0.05 1/1 main [2]
+[3] 100.0 0.00 0.05 1 report [3]
+</pre></div>
+
+<p>Here are the meanings of the fields in the caller-line for <code>report</code>
+called from <code>main</code>:
+</p>
+<dl compact="compact">
+<dt><code>self</code></dt>
+<dd><p>An estimate of the amount of time spent in <code>report</code> itself when it was
+called from <code>main</code>.
+</p>
+</dd>
+<dt><code>children</code></dt>
+<dd><p>An estimate of the amount of time spent in subroutines of <code>report</code>
+when <code>report</code> was called from <code>main</code>.
+</p>
+<p>The sum of the <code>self</code> and <code>children</code> fields is an estimate
+of the amount of time spent within calls to <code>report</code> from <code>main</code>.
+</p>
+</dd>
+<dt><code>called</code></dt>
+<dd><p>Two numbers: the number of times <code>report</code> was called from <code>main</code>,
+followed by the total number of non-recursive calls to <code>report</code> from
+all its callers.
+</p>
+</dd>
+<dt><code>name and index number</code></dt>
+<dd><p>The name of the caller of <code>report</code> to which this line applies,
+followed by the caller&rsquo;s index number.
+</p>
+<p>Not all functions have entries in the call graph; some
+options to <code>gprof</code> 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.
+</p>
+<p>If the caller is part of a recursion cycle, the cycle number is
+printed between the name and the index number.
+</p></dd>
+</dl>
+
+<p>If the identity of the callers of a function cannot be determined, a
+dummy caller-line is printed which has &lsquo;<samp>&lt;spontaneous&gt;</samp>&rsquo; as the
+&ldquo;caller&rsquo;s name&rdquo; and all other fields blank. This can happen for
+signal handlers.
+</p>
+<hr>
+<a name="Subroutines"></a>
+<div class="header">
+<p>
+Next: <a href="#Cycles" accesskey="n" rel="next">Cycles</a>, Previous: <a href="#Callers" accesskey="p" rel="previous">Callers</a>, Up: <a href="#Call-Graph" accesskey="u" rel="up">Call Graph</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Lines-for-a-Function_0027s-Subroutines"></a>
+<h4 class="subsection">5.2.3 Lines for a Function&rsquo;s Subroutines</h4>
+
+<p>A function&rsquo;s entry has a line for each of its subroutines&mdash;in other
+words, a line for each other function that it called. These lines&rsquo;
+fields correspond to the fields of the primary line, but their meanings
+are different because of the difference in context.
+</p>
+<p>For reference, we repeat two lines from the entry for the function
+<code>main</code>, the primary line and a line for a subroutine, together
+with the heading line that shows the names of the fields:
+</p>
+<div class="smallexample">
+<pre class="smallexample">index % time self children called name
+&hellip;
+[2] 100.0 0.00 0.05 1 main [2]
+ 0.00 0.05 1/1 report [3]
+</pre></div>
+
+<p>Here are the meanings of the fields in the subroutine-line for <code>main</code>
+calling <code>report</code>:
+</p>
+<dl compact="compact">
+<dt><code>self</code></dt>
+<dd><p>An estimate of the amount of time spent directly within <code>report</code>
+when <code>report</code> was called from <code>main</code>.
+</p>
+</dd>
+<dt><code>children</code></dt>
+<dd><p>An estimate of the amount of time spent in subroutines of <code>report</code>
+when <code>report</code> was called from <code>main</code>.
+</p>
+<p>The sum of the <code>self</code> and <code>children</code> fields is an estimate
+of the total time spent in calls to <code>report</code> from <code>main</code>.
+</p>
+</dd>
+<dt><code>called</code></dt>
+<dd><p>Two numbers, the number of calls to <code>report</code> from <code>main</code>
+followed by the total number of non-recursive calls to <code>report</code>.
+This ratio is used to determine how much of <code>report</code>&rsquo;s <code>self</code>
+and <code>children</code> time gets credited to <code>main</code>.
+See <a href="#Assumptions">Estimating <code>children</code> Times</a>.
+</p>
+</dd>
+<dt><code>name</code></dt>
+<dd><p>The name of the subroutine of <code>main</code> to which this line applies,
+followed by the subroutine&rsquo;s index number.
+</p>
+<p>If the caller is part of a recursion cycle, the cycle number is
+printed between the name and the index number.
+</p></dd>
+</dl>
+
+<hr>
+<a name="Cycles"></a>
+<div class="header">
+<p>
+Previous: <a href="#Subroutines" accesskey="p" rel="previous">Subroutines</a>, Up: <a href="#Call-Graph" accesskey="u" rel="up">Call Graph</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="How-Mutually-Recursive-Functions-Are-Described"></a>
+<h4 class="subsection">5.2.4 How Mutually Recursive Functions Are Described</h4>
+<a name="index-cycle"></a>
+<a name="index-recursion-cycle"></a>
+
+<p>The graph may be complicated by the presence of <em>cycles of
+recursion</em> 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 <code>a</code> calls <code>b</code>,
+and <code>b</code> calls <code>a</code>, then <code>a</code> and <code>b</code> form a cycle.
+</p>
+<p>Whenever there are call paths both ways between a pair of functions, they
+belong to the same cycle. If <code>a</code> and <code>b</code> call each other and
+<code>b</code> and <code>c</code> call each other, all three make one cycle. Note that
+even if <code>b</code> only calls <code>a</code> if it was not called from <code>a</code>,
+<code>gprof</code> cannot determine this, so <code>a</code> and <code>b</code> are still
+considered a cycle.
+</p>
+<p>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 &lsquo;<samp>&lt;cycle <var>number</var>&gt;</samp>&rsquo;.
+</p>
+<p>The reason cycles matter is that they make the time values in the call
+graph paradoxical. The &ldquo;time spent in children&rdquo; of <code>a</code> should
+include the time spent in its subroutine <code>b</code> and in <code>b</code>&rsquo;s
+subroutines&mdash;but one of <code>b</code>&rsquo;s subroutines is <code>a</code>! How much of
+<code>a</code>&rsquo;s time should be included in the children of <code>a</code>, when
+<code>a</code> is indirectly recursive?
+</p>
+<p>The way <code>gprof</code> 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
+&ldquo;subroutines&rdquo; of the cycle are the individual functions of the cycle, and
+all other functions that were called directly by them. The &ldquo;callers&rdquo; of
+the cycle are the functions, outside the cycle, that called functions in
+the cycle.
+</p>
+<p>Here is an example portion of a call graph which shows a cycle containing
+functions <code>a</code> and <code>b</code>. The cycle was entered by a call to
+<code>a</code> from <code>main</code>; both <code>a</code> and <code>b</code> called <code>c</code>.
+</p>
+<div class="smallexample">
+<pre class="smallexample">index % time self children called name
+----------------------------------------
+ 1.77 0 1/1 main [2]
+[3] 91.71 1.77 0 1+5 &lt;cycle 1 as a whole&gt; [3]
+ 1.02 0 3 b &lt;cycle 1&gt; [4]
+ 0.75 0 2 a &lt;cycle 1&gt; [5]
+----------------------------------------
+ 3 a &lt;cycle 1&gt; [5]
+[4] 52.85 1.02 0 0 b &lt;cycle 1&gt; [4]
+ 2 a &lt;cycle 1&gt; [5]
+ 0 0 3/6 c [6]
+----------------------------------------
+ 1.77 0 1/1 main [2]
+ 2 b &lt;cycle 1&gt; [4]
+[5] 38.86 0.75 0 1 a &lt;cycle 1&gt; [5]
+ 3 b &lt;cycle 1&gt; [4]
+ 0 0 3/6 c [6]
+----------------------------------------
+</pre></div>
+
+<p>(The entire call graph for this program contains in addition an entry for
+<code>main</code>, which calls <code>a</code>, and an entry for <code>c</code>, with callers
+<code>a</code> and <code>b</code>.)
+</p>
+<div class="smallexample">
+<pre class="smallexample">index % time self children called name
+ &lt;spontaneous&gt;
+[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 &lt;cycle 1&gt; [5]
+----------------------------------------
+ 1.77 0 1/1 main [2]
+[3] 91.71 1.77 0 1+5 &lt;cycle 1 as a whole&gt; [3]
+ 1.02 0 3 b &lt;cycle 1&gt; [4]
+ 0.75 0 2 a &lt;cycle 1&gt; [5]
+ 0 0 6/6 c [6]
+----------------------------------------
+ 3 a &lt;cycle 1&gt; [5]
+[4] 52.85 1.02 0 0 b &lt;cycle 1&gt; [4]
+ 2 a &lt;cycle 1&gt; [5]
+ 0 0 3/6 c [6]
+----------------------------------------
+ 1.77 0 1/1 main [2]
+ 2 b &lt;cycle 1&gt; [4]
+[5] 38.86 0.75 0 1 a &lt;cycle 1&gt; [5]
+ 3 b &lt;cycle 1&gt; [4]
+ 0 0 3/6 c [6]
+----------------------------------------
+ 0 0 3/6 b &lt;cycle 1&gt; [4]
+ 0 0 3/6 a &lt;cycle 1&gt; [5]
+[6] 0.00 0 0 6 c [6]
+----------------------------------------
+</pre></div>
+
+<p>The <code>self</code> field of the cycle&rsquo;s primary line is the total time
+spent in all the functions of the cycle. It equals the sum of the
+<code>self</code> fields for the individual functions in the cycle, found
+in the entry in the subroutine lines for these functions.
+</p>
+<p>The <code>children</code> fields of the cycle&rsquo;s primary line and subroutine lines
+count only subroutines outside the cycle. Even though <code>a</code> calls
+<code>b</code>, the time spent in those calls to <code>b</code> is not counted in
+<code>a</code>&rsquo;s <code>children</code> time. Thus, we do not encounter the problem of
+what to do when the time in those calls to <code>b</code> includes indirect
+recursive calls back to <code>a</code>.
+</p>
+<p>The <code>children</code> field of a caller-line in the cycle&rsquo;s entry estimates
+the amount of time spent <em>in the whole cycle</em>, and its other
+subroutines, on the times when that caller called a function in the cycle.
+</p>
+<p>The <code>called</code> 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.
+</p>
+<p>The <code>called</code> field of a subroutine-line for a cycle member in the
+cycle&rsquo;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&rsquo;s
+<code>called</code> field.
+</p>
+<p>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 <code>self</code> and <code>children</code> fields in these
+lines are blank because of the difficulty of defining meanings for them
+when recursion is going on.
+</p>
+<hr>
+<a name="Line_002dby_002dline"></a>
+<div class="header">
+<p>
+Next: <a href="#Annotated-Source" accesskey="n" rel="next">Annotated Source</a>, Previous: <a href="#Call-Graph" accesskey="p" rel="previous">Call Graph</a>, Up: <a href="#Output" accesskey="u" rel="up">Output</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Line_002dby_002dline-Profiling"></a>
+<h3 class="section">5.3 Line-by-line Profiling</h3>
+
+<p><code>gprof</code>&rsquo;s &lsquo;<samp>-l</samp>&rsquo; option causes the program to perform
+<em>line-by-line</em> profiling. In this mode, histogram
+samples are assigned not to functions, but to individual
+lines of source code. This only works with programs compiled with
+older versions of the <code>gcc</code> compiler. Newer versions of <code>gcc</code>
+use a different program - <code>gcov</code> - to display line-by-line
+profiling information.
+</p>
+<p>With the older versions of <code>gcc</code> the program usually has to be
+compiled with a &lsquo;<samp>-g</samp>&rsquo; option, in addition to &lsquo;<samp>-pg</samp>&rsquo;, in order
+to generate debugging symbols for tracking source code lines.
+Note, in much older versions of <code>gcc</code> the program had to be
+compiled with the &lsquo;<samp>-a</samp>&rsquo; command-line option as well.
+</p>
+<p>The flat profile is the most useful output table
+in line-by-line mode.
+The call graph isn&rsquo;t as useful as normal, since
+the current version of <code>gprof</code> 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.
+</p>
+<p>Here is a section of <code>gprof</code>&rsquo;s output, without line-by-line profiling.
+Note that <code>ct_init</code> accounted for four histogram hits, and
+13327 calls to <code>init_block</code>.
+</p>
+<div class="smallexample">
+<pre class="smallexample">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
+
+</pre></div>
+
+<p>Now let&rsquo;s look at some of <code>gprof</code>&rsquo;s output from the same program run,
+this time with line-by-line profiling enabled. Note that <code>ct_init</code>&rsquo;s
+four histogram hits are broken down into four lines of source code&mdash;one hit
+occurred on each of lines 349, 351, 382 and 385. In the call graph,
+note how
+<code>ct_init</code>&rsquo;s 13327 calls to <code>init_block</code> are broken down
+into one call from line 396, 3071 calls from line 384, 3730 calls
+from line 385, and 6525 calls from 387.
+</p>
+<div class="smallexample">
+<pre class="smallexample">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)
+
+</pre></div>
+
+
+<hr>
+<a name="Annotated-Source"></a>
+<div class="header">
+<p>
+Previous: <a href="#Line_002dby_002dline" accesskey="p" rel="previous">Line-by-line</a>, Up: <a href="#Output" accesskey="u" rel="up">Output</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="The-Annotated-Source-Listing"></a>
+<h3 class="section">5.4 The Annotated Source Listing</h3>
+
+<p><code>gprof</code>&rsquo;s &lsquo;<samp>-A</samp>&rsquo; option triggers an annotated source listing,
+which lists the program&rsquo;s source code, each function labeled with the
+number of times it was called. You may also need to specify the
+&lsquo;<samp>-I</samp>&rsquo; option, if <code>gprof</code> can&rsquo;t find the source code files.
+</p>
+<p>With older versions of <code>gcc</code> compiling with &lsquo;<samp>gcc &hellip; -g
+-pg -a</samp>&rsquo; augments your program with basic-block counting code, in
+addition to function counting code. This enables <code>gprof</code> to
+determine how many times each line of code was executed. With newer
+versions of <code>gcc</code> support for displaying basic-block counts is
+provided by the <code>gcov</code> program.
+</p>
+<p>For example, consider the following function, taken from gzip,
+with line numbers added:
+</p>
+<div class="smallexample">
+<pre class="smallexample"> 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 }
+
+</pre></div>
+
+<p><code>updcrc</code> has at least five basic-blocks.
+One is the function itself. The
+<code>if</code> statement on line 9 generates two more basic-blocks, one
+for each branch of the <code>if</code>. A fourth basic-block results from
+the <code>if</code> on line 13, and the contents of the <code>do</code> loop form
+the fifth basic-block. The compiler may also generate additional
+basic-blocks to handle various special cases.
+</p>
+<p>A program augmented for basic-block counting can be analyzed with
+&lsquo;<samp>gprof -l -A</samp>&rsquo;.
+The &lsquo;<samp>-x</samp>&rsquo; option is also helpful,
+to ensure that each line of code is labeled at least once.
+Here is <code>updcrc</code>&rsquo;s
+annotated source listing for a sample <code>gzip</code> run:
+</p>
+<div class="smallexample">
+<pre class="smallexample"> ulg updcrc(s, n)
+ uch *s;
+ unsigned n;
+ 2 -&gt;{
+ register ulg c;
+
+ static ulg crc = (ulg)0xffffffffL;
+
+ 2 -&gt; if (s == NULL) {
+ 1 -&gt; c = 0xffffffffL;
+ 1 -&gt; } else {
+ 1 -&gt; c = crc;
+ 1 -&gt; if (n) do {
+ 26312 -&gt; c = crc_32_tab[...];
+26312,1,26311 -&gt; } while (--n);
+ }
+ 2 -&gt; crc = c;
+ 2 -&gt; return c ^ 0xffffffffL;
+ 2 -&gt;}
+</pre></div>
+
+<p>In this example, the function was called twice, passing once through
+each branch of the <code>if</code> statement. The body of the <code>do</code>
+loop was executed a total of 26312 times. Note how the <code>while</code>
+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.
+</p>
+<hr>
+<a name="Inaccuracy"></a>
+<div class="header">
+<p>
+Next: <a href="#How-do-I_003f" accesskey="n" rel="next">How do I?</a>, Previous: <a href="#Output" accesskey="p" rel="previous">Output</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Inaccuracy-of-gprof-Output"></a>
+<h2 class="chapter">6 Inaccuracy of <code>gprof</code> Output</h2>
+
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Sampling-Error" accesskey="1">Sampling Error</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Statistical margins of error
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Assumptions" accesskey="2">Assumptions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Estimating children times
+</td></tr>
+</table>
+
+<hr>
+<a name="Sampling-Error"></a>
+<div class="header">
+<p>
+Next: <a href="#Assumptions" accesskey="n" rel="next">Assumptions</a>, Up: <a href="#Inaccuracy" accesskey="u" rel="up">Inaccuracy</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Statistical-Sampling-Error"></a>
+<h3 class="section">6.1 Statistical Sampling Error</h3>
+
+<p>The run-time figures that <code>gprof</code> 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.
+</p>
+<p>By contrast, the number-of-calls and basic-block figures are derived
+by counting, not sampling. They are completely accurate and will not
+vary from run to run if your program is deterministic and single
+threaded. In multi-threaded applications, or single threaded
+applications that link with multi-threaded libraries, the counts are
+only deterministic if the counting function is thread-safe. (Note:
+beware that the mcount counting function in glibc is <em>not</em>
+thread-safe). See <a href="#Implementation">Implementation of Profiling</a>.
+</p>
+<p>The <em>sampling period</em> 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.
+</p>
+<p>The actual amount of error can be predicted.
+For <var>n</var> samples, the <em>expected</em> error
+is the square-root of <var>n</var>. For example,
+if the sampling period is 0.01 seconds and <code>foo</code>&rsquo;s run-time is 1 second,
+<var>n</var> is 100 samples (1 second/0.01 seconds), sqrt(<var>n</var>) is 10 samples, so
+the expected error in <code>foo</code>&rsquo;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 <code>bar</code>&rsquo;s run-time is
+100 seconds, <var>n</var> is 10000 samples, sqrt(<var>n</var>) is 100 samples, so
+the expected error in <code>bar</code>&rsquo;s run-time is 1 second,
+or one percent of the observed value.
+It is likely to
+vary this much <em>on the average</em> from one profiling run to the next.
+(<em>Sometimes</em> it will vary more.)
+</p>
+<p>This does not mean that a small run-time figure is devoid of information.
+If the program&rsquo;s <em>total</em> 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&rsquo;s time. Usually this means it is not worth optimizing.
+</p>
+<p>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 &lsquo;<samp>-s</samp>&rsquo; option of <code>gprof</code>. Here is how:
+</p>
+<ol>
+<li> Run your program once.
+
+</li><li> Issue the command &lsquo;<samp>mv gmon.out gmon.sum</samp>&rsquo;.
+
+</li><li> Run your program again, the same as before.
+
+</li><li> Merge the new data in <samp>gmon.out</samp> into <samp>gmon.sum</samp> with this command:
+
+<div class="example">
+<pre class="example">gprof -s <var>executable-file</var> gmon.out gmon.sum
+</pre></div>
+
+</li><li> Repeat the last two steps as often as you wish.
+
+</li><li> Analyze the cumulative data using this command:
+
+<div class="example">
+<pre class="example">gprof <var>executable-file</var> gmon.sum &gt; <var>output-file</var>
+</pre></div>
+</li></ol>
+
+<hr>
+<a name="Assumptions"></a>
+<div class="header">
+<p>
+Previous: <a href="#Sampling-Error" accesskey="p" rel="previous">Sampling Error</a>, Up: <a href="#Inaccuracy" accesskey="u" rel="up">Inaccuracy</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Estimating-children-Times"></a>
+<h3 class="section">6.2 Estimating <code>children</code> Times</h3>
+
+<p>Some of the figures in the call graph are estimates&mdash;for example, the
+<code>children</code> time values and all the time figures in caller and
+subroutine lines.
+</p>
+<p>There is no direct information about these measurements in the profile
+data itself. Instead, <code>gprof</code> estimates them by making an assumption
+about your program that might or might not be true.
+</p>
+<p>The assumption made is that the average time spent in each call to any
+function <code>foo</code> is not correlated with who called <code>foo</code>. If
+<code>foo</code> used 5 seconds in all, and 2/5 of the calls to <code>foo</code> came
+from <code>a</code>, then <code>foo</code> contributes 2 seconds to <code>a</code>&rsquo;s
+<code>children</code> time, by assumption.
+</p>
+<p>This assumption is usually true enough, but for some programs it is far
+from true. Suppose that <code>foo</code> returns very quickly when its argument
+is zero; suppose that <code>a</code> always passes zero as an argument, while
+other callers of <code>foo</code> pass other arguments. In this program, all the
+time spent in <code>foo</code> is in the calls from callers other than <code>a</code>.
+But <code>gprof</code> has no way of knowing this; it will blindly and
+incorrectly charge 2 seconds of time in <code>foo</code> to the children of
+<code>a</code>.
+</p>
+<p>We hope some day to put more complete data into <samp>gmon.out</samp>, so that
+this assumption is no longer needed, if we can figure out how. For the
+novice, the estimated figures are usually more useful than misleading.
+</p>
+<hr>
+<a name="How-do-I_003f"></a>
+<div class="header">
+<p>
+Next: <a href="#Incompatibilities" accesskey="n" rel="next">Incompatibilities</a>, Previous: <a href="#Inaccuracy" accesskey="p" rel="previous">Inaccuracy</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Answers-to-Common-Questions"></a>
+<h2 class="chapter">7 Answers to Common Questions</h2>
+
+<dl compact="compact">
+<dt>How can I get more exact information about hot spots in my program?</dt>
+<dd>
+<p>Looking at the per-line call counts only tells part of the story.
+Because <code>gprof</code> can only report call times and counts by function,
+the best way to get finer-grained information on where the program
+is spending its time is to re-factor large functions into sequences
+of calls to smaller ones. Beware however that this can introduce
+artificial hot spots since compiling with &lsquo;<samp>-pg</samp>&rsquo; adds a significant
+overhead to function calls. An alternative solution is to use a
+non-intrusive profiler, e.g. oprofile.
+</p>
+</dd>
+<dt>How do I find which lines in my program were executed the most times?</dt>
+<dd>
+<p>Use the <code>gcov</code> program.
+</p>
+</dd>
+<dt>How do I find which lines in my program called a particular function?</dt>
+<dd>
+<p>Use &lsquo;<samp>gprof -l</samp>&rsquo; and lookup the function in the call graph.
+The callers will be broken down by function and line number.
+</p>
+</dd>
+<dt>How do I analyze a program that runs for less than a second?</dt>
+<dd>
+<p>Try using a shell script like this one:
+</p>
+<div class="example">
+<pre class="example">for i in `seq 1 100`; do
+ fastprog
+ mv gmon.out gmon.out.$i
+done
+
+gprof -s fastprog gmon.out.*
+
+gprof fastprog gmon.sum
+</pre></div>
+
+<p>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).
+</p>
+</dd>
+</dl>
+
+<hr>
+<a name="Incompatibilities"></a>
+<div class="header">
+<p>
+Next: <a href="#Details" accesskey="n" rel="next">Details</a>, Previous: <a href="#How-do-I_003f" accesskey="p" rel="previous">How do I?</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Incompatibilities-with-Unix-gprof"></a>
+<h2 class="chapter">8 Incompatibilities with Unix <code>gprof</code></h2>
+
+<p><small>GNU</small> <code>gprof</code> and Berkeley Unix <code>gprof</code> use the same data
+file <samp>gmon.out</samp>, and provide essentially the same information. But
+there are a few differences.
+</p>
+<ul>
+<li> <small>GNU</small> <code>gprof</code> uses a new, generalized file format with support
+for basic-block execution counts and non-realtime histograms. A magic
+cookie and version number allows <code>gprof</code> to easily identify
+new style files. Old BSD-style files can still be read.
+See <a href="#File-Format">Profiling Data File Format</a>.
+
+</li><li> For a recursive function, Unix <code>gprof</code> lists the function as a
+parent and as a child, with a <code>calls</code> field that lists the number
+of recursive calls. <small>GNU</small> <code>gprof</code> omits these lines and puts
+the number of recursive calls in the primary line.
+
+</li><li> When a function is suppressed from the call graph with &lsquo;<samp>-e</samp>&rsquo;, <small>GNU</small>
+<code>gprof</code> still lists it as a subroutine of functions that call it.
+
+</li><li> <small>GNU</small> <code>gprof</code> accepts the &lsquo;<samp>-k</samp>&rsquo; with its argument
+in the form &lsquo;<samp>from/to</samp>&rsquo;, instead of &lsquo;<samp>from to</samp>&rsquo;.
+
+</li><li> In the annotated source listing,
+if there are multiple basic blocks on the same line,
+<small>GNU</small> <code>gprof</code> prints all of their counts, separated by commas.
+
+
+</li><li> The blurbs, field widths, and output formats are different. <small>GNU</small>
+<code>gprof</code> prints blurbs after the tables, so that you can see the
+tables without skipping the blurbs.
+</li></ul>
+
+<hr>
+<a name="Details"></a>
+<div class="header">
+<p>
+Next: <a href="#GNU-Free-Documentation-License" accesskey="n" rel="next">GNU Free Documentation License</a>, Previous: <a href="#Incompatibilities" accesskey="p" rel="previous">Incompatibilities</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Details-of-Profiling"></a>
+<h2 class="chapter">9 Details of Profiling</h2>
+
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">&bull; <a href="#Implementation" accesskey="1">Implementation</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">How a program collects profiling information
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#File-Format" accesskey="2">File Format</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Format of &lsquo;<samp>gmon.out</samp>&rsquo; files
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Internals" accesskey="3">Internals</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top"><code>gprof</code>&rsquo;s internal operation
+</td></tr>
+<tr><td align="left" valign="top">&bull; <a href="#Debugging" accesskey="4">Debugging</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Using <code>gprof</code>&rsquo;s &lsquo;<samp>-d</samp>&rsquo; option
+</td></tr>
+</table>
+
+<hr>
+<a name="Implementation"></a>
+<div class="header">
+<p>
+Next: <a href="#File-Format" accesskey="n" rel="next">File Format</a>, Up: <a href="#Details" accesskey="u" rel="up">Details</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Implementation-of-Profiling"></a>
+<h3 class="section">9.1 Implementation of Profiling</h3>
+
+<p>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 &lsquo;<samp>-pg</samp>&rsquo; option,
+which causes every function to call <code>mcount</code>
+(or <code>_mcount</code>, or <code>__mcount</code>, depending on the OS and compiler)
+as one of its first operations.
+</p>
+<p>The <code>mcount</code> 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&rsquo;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, <code>mcount</code>
+itself is typically a short assembly-language stub routine
+that extracts the required
+information, and then calls <code>__mcount_internal</code>
+(a normal C function) with two arguments&mdash;<code>frompc</code> and <code>selfpc</code>.
+<code>__mcount_internal</code> is responsible for maintaining
+the in-memory call graph, which records <code>frompc</code>, <code>selfpc</code>,
+and the number of times each of these call arcs was traversed.
+</p>
+<p>GCC Version 2 provides a magical function (<code>__builtin_return_address</code>),
+which allows a generic <code>mcount</code> 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 <code>mcount</code> is used for performance reasons.
+</p>
+<p>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 &lsquo;<samp>-pg</samp>&rsquo;. If you
+link your program with &lsquo;<samp>gcc &hellip; -pg</samp>&rsquo;, it automatically uses the
+profiling version of the library.
+</p>
+<p>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.
+</p>
+<p>This is done is one of two ways. Most UNIX-like operating systems
+provide a <code>profil()</code> system call, which registers a memory
+array with the kernel, along with a scale
+factor that determines how the program&rsquo;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.
+</p>
+<p>However, some operating systems, most notably Linux 2.0 (and earlier),
+do not provide a <code>profil()</code> system call. On such a system,
+arrangements are made for the kernel to periodically deliver
+a signal to the process (typically via <code>setitimer()</code>),
+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.
+</p>
+<p>A special startup routine allocates memory for the histogram and
+either calls <code>profil()</code> or sets up
+a clock signal handler.
+This routine (<code>monstartup</code>) can be invoked in several ways.
+On Linux systems, a special profiling startup file <code>gcrt0.o</code>,
+which invokes <code>monstartup</code> before <code>main</code>,
+is used instead of the default <code>crt0.o</code>.
+Use of this special startup file is one of the effects
+of using &lsquo;<samp>gcc &hellip; -pg</samp>&rsquo; to link.
+On SPARC systems, no special startup files are used.
+Rather, the <code>mcount</code> routine, when it is invoked for
+the first time (typically when <code>main</code> is called),
+calls <code>monstartup</code>.
+</p>
+<p>If the compiler&rsquo;s &lsquo;<samp>-a</samp>&rsquo; 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 <code>if</code> 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.
+</p>
+<p>The profiling library also includes a function (<code>mcleanup</code>) which is
+typically registered using <code>atexit()</code> to be called as the
+program exits, and is responsible for writing the file <samp>gmon.out</samp>.
+Profiling is turned off, various headers are output, and the histogram
+is written, followed by the call-graph arcs and the basic-block counts.
+</p>
+<p>The output from <code>gprof</code> 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&rsquo;s run time.
+Therefore, the
+time measurements in <code>gprof</code> 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 <code>gprof</code> 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&rsquo;t directly affect the output you get.
+</p>
+<hr>
+<a name="File-Format"></a>
+<div class="header">
+<p>
+Next: <a href="#Internals" accesskey="n" rel="next">Internals</a>, Previous: <a href="#Implementation" accesskey="p" rel="previous">Implementation</a>, Up: <a href="#Details" accesskey="u" rel="up">Details</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Profiling-Data-File-Format"></a>
+<h3 class="section">9.2 Profiling Data File Format</h3>
+
+<p>The old BSD-derived file format used for profile data does not contain a
+magic cookie that allows one to check whether a data file really is a
+<code>gprof</code> file. Furthermore, it does not provide a version number, thus
+rendering changes to the file format almost impossible. <small>GNU</small> <code>gprof</code>
+uses a new file format that provides these features. For backward
+compatibility, <small>GNU</small> <code>gprof</code> 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.
+</p>
+<p>The new file format is defined in header file <samp>gmon_out.h</samp>. 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. <small>GNU</small> <code>gprof</code> adapts automatically
+to the byte-order in use.
+</p>
+<p>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, <small>GNU</small> <code>gprof</code> 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.
+</p>
+<a name="Histogram-Records"></a>
+<h4 class="subsection">9.2.1 Histogram Records</h4>
+
+<p>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
+&ldquo;seconds&rdquo; and the abbreviation as &ldquo;s&rdquo;. This feature is useful for
+architectures that support performance monitor hardware (which,
+fortunately, is becoming increasingly common). For example, under DEC
+OSF/1, the &ldquo;uprofile&rdquo; 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 &ldquo;i-cache misses&rdquo; and the abbreviation
+could be set to &ldquo;1&rdquo; (because it is simply a count, not a physical
+dimension). Also, the profiling rate would have to be set to 1 in
+this case.
+</p>
+<p>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.
+</p>
+
+<a name="Call_002dGraph-Records"></a>
+<h4 class="subsection">9.2.2 Call-Graph Records</h4>
+
+<p>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&rsquo;s function and the second must be
+within the callee&rsquo;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.
+</p>
+<a name="Basic_002dBlock-Execution-Count-Records"></a>
+<h4 class="subsection">9.2.3 Basic-Block Execution Count Records</h4>
+
+<p>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.
+</p>
+<hr>
+<a name="Internals"></a>
+<div class="header">
+<p>
+Next: <a href="#Debugging" accesskey="n" rel="next">Debugging</a>, Previous: <a href="#File-Format" accesskey="p" rel="previous">File Format</a>, Up: <a href="#Details" accesskey="u" rel="up">Details</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="gprof_0027s-Internal-Operation"></a>
+<h3 class="section">9.3 <code>gprof</code>&rsquo;s Internal Operation</h3>
+
+<p>Like most programs, <code>gprof</code> begins by processing its options.
+During this stage, it may building its symspec list
+(<code>sym_ids.c:sym_id_add</code>), if
+options are specified which use symspecs.
+<code>gprof</code> maintains a single linked list of symspecs,
+which will eventually get turned into 12 symbol tables,
+organized into six include/exclude pairs&mdash;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).
+</p>
+<p>After option processing, <code>gprof</code> finishes
+building the symspec list by adding all the symspecs in
+<code>default_excluded_list</code> 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.
+</p>
+<p>Next, the BFD library is called to open the object file,
+verify that it is an object file,
+and read its symbol table (<code>core.c:core_init</code>),
+using <code>bfd_canonicalize_symtab</code> after mallocing
+an appropriately sized array of symbols. At this point,
+function mappings are read (if the &lsquo;<samp>--file-ordering</samp>&rsquo; option
+has been specified), and the core text space is read into
+memory (if the &lsquo;<samp>-c</samp>&rsquo; option was given).
+</p>
+<p><code>gprof</code>&rsquo;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 (&lsquo;<samp>-l</samp>&rsquo; 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&mdash;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 <code>Sym</code> is created of
+the appropriate length.
+Finally, <code>symtab.c:symtab_finalize</code>
+is called to sort the symbol table and remove duplicate entries
+(entries with the same memory address).
+</p>
+<p>The symbol table must be a contiguous array for two reasons.
+First, the <code>qsort</code> library function (which sorts an array)
+will be used to sort the symbol table.
+Also, the symbol lookup routine (<code>symtab.c:sym_lookup</code>),
+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 <code>is_func</code> flag.
+Line number symbols have no special flags set.
+Additionally, a symbol can have an <code>is_static</code> flag
+to indicate that it is a local symbol.
+</p>
+<p>With the symbol table read, the symspecs can now be translated
+into Syms (<code>sym_ids.c:sym_id_parse</code>). Remember that a single
+symspec can match multiple symbols.
+An array of symbol tables
+(<code>syms</code>) 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, <code>gprof</code> simply uses its
+standard symbol lookup routine on the appropriate table
+in the <code>syms</code> array.
+</p>
+<p>Now the profile data file(s) themselves are read
+(<code>gmon_io.c:gmon_out_read</code>),
+first by checking for a new-style &lsquo;<samp>gmon.out</samp>&rsquo; header,
+then assuming this is an old-style BSD &lsquo;<samp>gmon.out</samp>&rsquo;
+if the magic number test failed.
+</p>
+<p>New-style histogram records are read by <code>hist.c:hist_read_rec</code>.
+For the first histogram record, allocate a memory array to hold
+all the bins, and read them in.
+When multiple profile data files (or files with multiple histogram
+records) are read, the memory ranges of each pair of histogram records
+must be either equal, or non-overlapping. For each pair of histogram
+records, the resolution (memory region size divided by the number of
+bins) must be the same. The time unit must be the same for all
+histogram records. If the above containts are met, all histograms
+for the same memory range are merged.
+</p>
+<p>As each call graph record is read (<code>call_graph.c:cg_read_rec</code>),
+the parent and child addresses
+are matched to symbol table entries, and a call graph arc is
+created by <code>cg_arcs.c:arc_add</code>, 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&rsquo;s child arcs, and of the child&rsquo;s
+parent arcs.
+Both the child&rsquo;s call count and the arc&rsquo;s call count are
+incremented by the record&rsquo;s call count.
+</p>
+<p>Basic-block records are read (<code>basic_blocks.c:bb_read_rec</code>),
+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&rsquo;s
+bb_addr and bb_calls arrays. Again, if multiple basic-block
+records are present for the same address, the call counts
+are cumulative.
+</p>
+<p>A gmon.sum file is dumped, if requested (<code>gmon_io.c:gmon_out_write</code>).
+</p>
+<p>If histograms were present in the data files, assign them to symbols
+(<code>hist.c:hist_assign_samples</code>) 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.
+</p>
+<p>If call graph data is present, <code>cg_arcs.c:cg_assemble</code> is called.
+First, if &lsquo;<samp>-c</samp>&rsquo; was specified, a machine-dependent
+routine (<code>find_call</code>) scans through each symbol&rsquo;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 (<code>cg_dfn.c:cg_dfn</code>), 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&rsquo;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.
+</p>
+<p>Finally, print the various outputs the user requested, which is now fairly
+straightforward. The call graph (<code>cg_print.c:cg_print</code>) and
+flat profile (<code>hist.c:hist_print</code>) are regurgitations of values
+already computed. The annotated source listing
+(<code>basic_blocks.c:print_annotated_source</code>) uses basic-block
+information, if present, to label each line of code with call counts,
+otherwise only the function call counts are presented.
+</p>
+<p>The function ordering code is marginally well documented
+in the source code itself (<code>cg_print.c</code>). 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.
+</p>
+<hr>
+<a name="Debugging"></a>
+<div class="header">
+<p>
+Previous: <a href="#Internals" accesskey="p" rel="previous">Internals</a>, Up: <a href="#Details" accesskey="u" rel="up">Details</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="Debugging-gprof"></a>
+<h3 class="section">9.4 Debugging <code>gprof</code></h3>
+
+<p>If <code>gprof</code> was compiled with debugging enabled,
+the &lsquo;<samp>-d</samp>&rsquo; 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:
+</p>
+<dl compact="compact">
+<dt>2 - Topological sort</dt>
+<dd><p>Monitor depth-first numbering of symbols during call graph analysis
+</p></dd>
+<dt>4 - Cycles</dt>
+<dd><p>Shows symbols as they are identified as cycle heads
+</p></dd>
+<dt>16 - Tallying</dt>
+<dd><p>As the call graph arcs are read, show each arc and how
+the total calls to each function are tallied
+</p></dd>
+<dt>32 - Call graph arc sorting</dt>
+<dd><p>Details sorting individual parents/children within each call graph entry
+</p></dd>
+<dt>64 - Reading histogram and call graph records</dt>
+<dd><p>Shows address ranges of histograms as they are read, and each
+call graph arc
+</p></dd>
+<dt>128 - Symbol table</dt>
+<dd><p>Reading, classifying, and sorting the symbol table from the object file.
+For line-by-line profiling (&lsquo;<samp>-l</samp>&rsquo; option), also shows line numbers
+being assigned to memory addresses.
+</p></dd>
+<dt>256 - Static call graph</dt>
+<dd><p>Trace operation of &lsquo;<samp>-c</samp>&rsquo; option
+</p></dd>
+<dt>512 - Symbol table and arc table lookups</dt>
+<dd><p>Detail operation of lookup routines
+</p></dd>
+<dt>1024 - Call graph propagation</dt>
+<dd><p>Shows how function times are propagated along the call graph
+</p></dd>
+<dt>2048 - Basic-blocks</dt>
+<dd><p>Shows basic-block records as they are read from profile data
+(only meaningful with &lsquo;<samp>-l</samp>&rsquo; option)
+</p></dd>
+<dt>4096 - Symspecs</dt>
+<dd><p>Shows symspec-to-symbol pattern matching operation
+</p></dd>
+<dt>8192 - Annotate source</dt>
+<dd><p>Tracks operation of &lsquo;<samp>-A</samp>&rsquo; option
+</p></dd>
+</dl>
+
+<hr>
+<a name="GNU-Free-Documentation-License"></a>
+<div class="header">
+<p>
+Previous: <a href="#Details" accesskey="p" rel="previous">Details</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>]</p>
+</div>
+<a name="GNU-Free-Documentation-License-1"></a>
+<h2 class="appendix">Appendix A GNU Free Documentation License</h2>
+<div align="center">Version 1.3, 3 November 2008
+</div>
+
+<div class="display">
+<pre class="display">Copyright &copy; 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
+<a href="http://fsf.org/">http://fsf.org/</a>
+
+Everyone is permitted to copy and distribute verbatim copies
+of this license document, but changing it is not allowed.
+</pre></div>
+
+<ol>
+<li> PREAMBLE
+
+<p>The purpose of this License is to make a manual, textbook, or other
+functional and useful document <em>free</em> 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.
+</p>
+<p>This License is a kind of &ldquo;copyleft&rdquo;, 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.
+</p>
+<p>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.
+</p>
+</li><li> APPLICABILITY AND DEFINITIONS
+
+<p>This License applies to any manual or other work, in any medium, that
+contains a notice placed by the copyright holder saying it can be
+distributed under the terms of this License. Such a notice grants a
+world-wide, royalty-free license, unlimited in duration, to use that
+work under the conditions stated herein. The &ldquo;Document&rdquo;, below,
+refers to any such manual or work. Any member of the public is a
+licensee, and is addressed as &ldquo;you&rdquo;. You accept the license if you
+copy, modify or distribute the work in a way requiring permission
+under copyright law.
+</p>
+<p>A &ldquo;Modified Version&rdquo; of the Document means any work containing the
+Document or a portion of it, either copied verbatim, or with
+modifications and/or translated into another language.
+</p>
+<p>A &ldquo;Secondary Section&rdquo; is a named appendix or a front-matter section
+of the Document that deals exclusively with the relationship of the
+publishers or authors of the Document to the Document&rsquo;s overall
+subject (or to related matters) and contains nothing that could fall
+directly within that overall subject. (Thus, if the Document is in
+part a textbook of mathematics, a Secondary Section may not explain
+any mathematics.) The relationship could be a matter of historical
+connection with the subject or with related matters, or of legal,
+commercial, philosophical, ethical or political position regarding
+them.
+</p>
+<p>The &ldquo;Invariant Sections&rdquo; are certain Secondary Sections whose titles
+are designated, as being those of Invariant Sections, in the notice
+that says that the Document is released under this License. If a
+section does not fit the above definition of Secondary then it is not
+allowed to be designated as Invariant. The Document may contain zero
+Invariant Sections. If the Document does not identify any Invariant
+Sections then there are none.
+</p>
+<p>The &ldquo;Cover Texts&rdquo; are certain short passages of text that are listed,
+as Front-Cover Texts or Back-Cover Texts, in the notice that says that
+the Document is released under this License. A Front-Cover Text may
+be at most 5 words, and a Back-Cover Text may be at most 25 words.
+</p>
+<p>A &ldquo;Transparent&rdquo; copy of the Document means a machine-readable copy,
+represented in a format whose specification is available to the
+general public, that is suitable for revising the document
+straightforwardly with generic text editors or (for images composed of
+pixels) generic paint programs or (for drawings) some widely available
+drawing editor, and that is suitable for input to text formatters or
+for automatic translation to a variety of formats suitable for input
+to text formatters. A copy made in an otherwise Transparent file
+format whose markup, or absence of markup, has been arranged to thwart
+or discourage subsequent modification by readers is not Transparent.
+An image format is not Transparent if used for any substantial amount
+of text. A copy that is not &ldquo;Transparent&rdquo; is called &ldquo;Opaque&rdquo;.
+</p>
+<p>Examples of suitable formats for Transparent copies include plain
+<small>ASCII</small> without markup, Texinfo input format, LaTeX input
+format, <acronym>SGML</acronym> or <acronym>XML</acronym> using a publicly available
+<acronym>DTD</acronym>, and standard-conforming simple <acronym>HTML</acronym>,
+PostScript or <acronym>PDF</acronym> designed for human modification. Examples
+of transparent image formats include <acronym>PNG</acronym>, <acronym>XCF</acronym> and
+<acronym>JPG</acronym>. Opaque formats include proprietary formats that can be
+read and edited only by proprietary word processors, <acronym>SGML</acronym> or
+<acronym>XML</acronym> for which the <acronym>DTD</acronym> and/or processing tools are
+not generally available, and the machine-generated <acronym>HTML</acronym>,
+PostScript or <acronym>PDF</acronym> produced by some word processors for
+output purposes only.
+</p>
+<p>The &ldquo;Title Page&rdquo; 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, &ldquo;Title Page&rdquo; means
+the text near the most prominent appearance of the work&rsquo;s title,
+preceding the beginning of the body of the text.
+</p>
+<p>The &ldquo;publisher&rdquo; means any person or entity that distributes copies
+of the Document to the public.
+</p>
+<p>A section &ldquo;Entitled XYZ&rdquo; means a named subunit of the Document whose
+title either is precisely XYZ or contains XYZ in parentheses following
+text that translates XYZ in another language. (Here XYZ stands for a
+specific section name mentioned below, such as &ldquo;Acknowledgements&rdquo;,
+&ldquo;Dedications&rdquo;, &ldquo;Endorsements&rdquo;, or &ldquo;History&rdquo;.) To &ldquo;Preserve the Title&rdquo;
+of such a section when you modify the Document means that it remains a
+section &ldquo;Entitled XYZ&rdquo; according to this definition.
+</p>
+<p>The Document may include Warranty Disclaimers next to the notice which
+states that this License applies to the Document. These Warranty
+Disclaimers are considered to be included by reference in this
+License, but only as regards disclaiming warranties: any other
+implication that these Warranty Disclaimers may have is void and has
+no effect on the meaning of this License.
+</p>
+</li><li> VERBATIM COPYING
+
+<p>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.
+</p>
+<p>You may also lend copies, under the same conditions stated above, and
+you may publicly display copies.
+</p>
+</li><li> COPYING IN QUANTITY
+
+<p>If you publish printed copies (or copies in media that commonly have
+printed covers) of the Document, numbering more than 100, and the
+Document&rsquo;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.
+</p>
+<p>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.
+</p>
+<p>If you publish or distribute Opaque copies of the Document numbering
+more than 100, you must either include a machine-readable Transparent
+copy along with each Opaque copy, or state in or with each Opaque copy
+a computer-network location from which the general network-using
+public has access to download using public-standard network protocols
+a complete Transparent copy of the Document, free of added material.
+If you use the latter option, you must take reasonably prudent steps,
+when you begin distribution of Opaque copies in quantity, to ensure
+that this Transparent copy will remain thus accessible at the stated
+location until at least one year after the last time you distribute an
+Opaque copy (directly or through your agents or retailers) of that
+edition to the public.
+</p>
+<p>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.
+</p>
+</li><li> MODIFICATIONS
+
+<p>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:
+</p>
+<ol>
+<li> 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.
+
+</li><li> List on the Title Page, as authors, one or more persons or entities
+responsible for authorship of the modifications in the Modified
+Version, together with at least five of the principal authors of the
+Document (all of its principal authors, if it has fewer than five),
+unless they release you from this requirement.
+
+</li><li> State on the Title page the name of the publisher of the
+Modified Version, as the publisher.
+
+</li><li> Preserve all the copyright notices of the Document.
+
+</li><li> Add an appropriate copyright notice for your modifications
+adjacent to the other copyright notices.
+
+</li><li> 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.
+
+</li><li> Preserve in that license notice the full lists of Invariant Sections
+and required Cover Texts given in the Document&rsquo;s license notice.
+
+</li><li> Include an unaltered copy of this License.
+
+</li><li> Preserve the section Entitled &ldquo;History&rdquo;, Preserve its Title, and add
+to it an item stating at least the title, year, new authors, and
+publisher of the Modified Version as given on the Title Page. If
+there is no section Entitled &ldquo;History&rdquo; 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.
+
+</li><li> 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 &ldquo;History&rdquo; 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.
+
+</li><li> For any section Entitled &ldquo;Acknowledgements&rdquo; or &ldquo;Dedications&rdquo;, Preserve
+the Title of the section, and preserve in the section all the
+substance and tone of each of the contributor acknowledgements and/or
+dedications given therein.
+
+</li><li> 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.
+
+</li><li> Delete any section Entitled &ldquo;Endorsements&rdquo;. Such a section
+may not be included in the Modified Version.
+
+</li><li> Do not retitle any existing section to be Entitled &ldquo;Endorsements&rdquo; or
+to conflict in title with any Invariant Section.
+
+</li><li> Preserve any Warranty Disclaimers.
+</li></ol>
+
+<p>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&rsquo;s license notice.
+These titles must be distinct from any other section titles.
+</p>
+<p>You may add a section Entitled &ldquo;Endorsements&rdquo;, provided it contains
+nothing but endorsements of your Modified Version by various
+parties&mdash;for example, statements of peer review or that the text has
+been approved by an organization as the authoritative definition of a
+standard.
+</p>
+<p>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.
+</p>
+<p>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.
+</p>
+</li><li> COMBINING DOCUMENTS
+
+<p>You may combine the Document with other documents released under this
+License, under the terms defined in section 4 above for modified
+versions, provided that you include in the combination all of the
+Invariant Sections of all of the original documents, unmodified, and
+list them all as Invariant Sections of your combined work in its
+license notice, and that you preserve all their Warranty Disclaimers.
+</p>
+<p>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.
+</p>
+<p>In the combination, you must combine any sections Entitled &ldquo;History&rdquo;
+in the various original documents, forming one section Entitled
+&ldquo;History&rdquo;; likewise combine any sections Entitled &ldquo;Acknowledgements&rdquo;,
+and any sections Entitled &ldquo;Dedications&rdquo;. You must delete all
+sections Entitled &ldquo;Endorsements.&rdquo;
+</p>
+</li><li> COLLECTIONS OF DOCUMENTS
+
+<p>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.
+</p>
+<p>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.
+</p>
+</li><li> AGGREGATION WITH INDEPENDENT WORKS
+
+<p>A compilation of the Document or its derivatives with other separate
+and independent documents or works, in or on a volume of a storage or
+distribution medium, is called an &ldquo;aggregate&rdquo; if the copyright
+resulting from the compilation is not used to limit the legal rights
+of the compilation&rsquo;s users beyond what the individual works permit.
+When the Document is included in an aggregate, this License does not
+apply to the other works in the aggregate which are not themselves
+derivative works of the Document.
+</p>
+<p>If the Cover Text requirement of section 3 is applicable to these
+copies of the Document, then if the Document is less than one half of
+the entire aggregate, the Document&rsquo;s Cover Texts may be placed on
+covers that bracket the Document within the aggregate, or the
+electronic equivalent of covers if the Document is in electronic form.
+Otherwise they must appear on printed covers that bracket the whole
+aggregate.
+</p>
+</li><li> TRANSLATION
+
+<p>Translation is considered a kind of modification, so you may
+distribute translations of the Document under the terms of section 4.
+Replacing Invariant Sections with translations requires special
+permission from their copyright holders, but you may include
+translations of some or all Invariant Sections in addition to the
+original versions of these Invariant Sections. You may include a
+translation of this License, and all the license notices in the
+Document, and any Warranty Disclaimers, provided that you also include
+the original English version of this License and the original versions
+of those notices and disclaimers. In case of a disagreement between
+the translation and the original version of this License or a notice
+or disclaimer, the original version will prevail.
+</p>
+<p>If a section in the Document is Entitled &ldquo;Acknowledgements&rdquo;,
+&ldquo;Dedications&rdquo;, or &ldquo;History&rdquo;, the requirement (section 4) to Preserve
+its Title (section 1) will typically require changing the actual
+title.
+</p>
+</li><li> TERMINATION
+
+<p>You may not copy, modify, sublicense, or distribute the Document
+except as expressly provided under this License. Any attempt
+otherwise to copy, modify, sublicense, or distribute it is void, and
+will automatically terminate your rights under this License.
+</p>
+<p>However, if you cease all violation of this License, then your license
+from a particular copyright holder is reinstated (a) provisionally,
+unless and until the copyright holder explicitly and finally
+terminates your license, and (b) permanently, if the copyright holder
+fails to notify you of the violation by some reasonable means prior to
+60 days after the cessation.
+</p>
+<p>Moreover, your license from a particular copyright holder is
+reinstated permanently if the copyright holder notifies you of the
+violation by some reasonable means, this is the first time you have
+received notice of violation of this License (for any work) from that
+copyright holder, and you cure the violation prior to 30 days after
+your receipt of the notice.
+</p>
+<p>Termination of your rights under this section does not terminate the
+licenses of parties who have received copies or rights from you under
+this License. If your rights have been terminated and not permanently
+reinstated, receipt of a copy of some or all of the same material does
+not give you any rights to use it.
+</p>
+</li><li> FUTURE REVISIONS OF THIS LICENSE
+
+<p>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
+<a href="http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</a>.
+</p>
+<p>Each version of the License is given a distinguishing version number.
+If the Document specifies that a particular numbered version of this
+License &ldquo;or any later version&rdquo; applies to it, you have the option of
+following the terms and conditions either of that specified version or
+of any later version that has been published (not as a draft) by the
+Free Software Foundation. If the Document does not specify a version
+number of this License, you may choose any version ever published (not
+as a draft) by the Free Software Foundation. If the Document
+specifies that a proxy can decide which future versions of this
+License can be used, that proxy&rsquo;s public statement of acceptance of a
+version permanently authorizes you to choose that version for the
+Document.
+</p>
+</li><li> RELICENSING
+
+<p>&ldquo;Massive Multiauthor Collaboration Site&rdquo; (or &ldquo;MMC Site&rdquo;) means any
+World Wide Web server that publishes copyrightable works and also
+provides prominent facilities for anybody to edit those works. A
+public wiki that anybody can edit is an example of such a server. A
+&ldquo;Massive Multiauthor Collaboration&rdquo; (or &ldquo;MMC&rdquo;) contained in the
+site means any set of copyrightable works thus published on the MMC
+site.
+</p>
+<p>&ldquo;CC-BY-SA&rdquo; means the Creative Commons Attribution-Share Alike 3.0
+license published by Creative Commons Corporation, a not-for-profit
+corporation with a principal place of business in San Francisco,
+California, as well as future copyleft versions of that license
+published by that same organization.
+</p>
+<p>&ldquo;Incorporate&rdquo; means to publish or republish a Document, in whole or
+in part, as part of another Document.
+</p>
+<p>An MMC is &ldquo;eligible for relicensing&rdquo; if it is licensed under this
+License, and if all works that were first published under this License
+somewhere other than this MMC, and subsequently incorporated in whole
+or in part into the MMC, (1) had no cover texts or invariant sections,
+and (2) were thus incorporated prior to November 1, 2008.
+</p>
+<p>The operator of an MMC Site may republish an MMC contained in the site
+under CC-BY-SA on the same site at any time before August 1, 2009,
+provided the MMC is eligible for relicensing.
+</p>
+</li></ol>
+
+<a name="ADDENDUM_003a-How-to-use-this-License-for-your-documents"></a>
+<h3 class="heading">ADDENDUM: How to use this License for your documents</h3>
+
+<p>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:
+</p>
+<div class="smallexample">
+<pre class="smallexample"> Copyright (C) <var>year</var> <var>your name</var>.
+ Permission is granted to copy, distribute and/or modify this document
+ under the terms of the GNU Free Documentation License, Version 1.3
+ or any later version published by the Free Software Foundation;
+ with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
+ Texts. A copy of the license is included in the section entitled ``GNU
+ Free Documentation License''.
+</pre></div>
+
+<p>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
+replace the &ldquo;with&hellip;Texts.&rdquo; line with this:
+</p>
+<div class="smallexample">
+<pre class="smallexample"> with the Invariant Sections being <var>list their titles</var>, with
+ the Front-Cover Texts being <var>list</var>, and with the Back-Cover Texts
+ being <var>list</var>.
+</pre></div>
+
+<p>If you have Invariant Sections without Cover Texts, or some other
+combination of the three, merge those two alternatives to suit the
+situation.
+</p>
+<p>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.
+</p>
+
+
+<hr>
+
+
+
+</body>
+</html>