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converted docs for Jim Roskind's profiler

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File Doc/Makefile

 	libmd5.tex libmimetools.tex libmm.tex libmods.tex libmpz.tex \
 libnntplib.tex \
 libobjs.tex libos.tex \
-libpanel.tex libposix.tex libposixfile.tex libppath.tex libpickle.tex \
-	libpwd.tex \
+libpanel.tex libpickle.tex libposix.tex libposixfile.tex \
+	libppath.tex libprofile.tex libpwd.tex \
 librand.tex libregex.tex libregsub.tex \
 	librfc822.tex librgbimg.tex librotor.tex \
 libselect.tex libsgi.tex libsgmllib.tex \
 \input{libtypes2}		% types is already taken :-(
 \input{libtempfile}
 \input{libtraceback}
-\input{libpdb}
+
+\input{libpdb}			% The Python Debugger
+
+\input{libprofile}		% The Python Profiler
 
 \input{libunix}			% UNIX ONLY
 \input{libdbm}

File Doc/lib/lib.tex

 \input{libtypes2}		% types is already taken :-(
 \input{libtempfile}
 \input{libtraceback}
-\input{libpdb}
+
+\input{libpdb}			% The Python Debugger
+
+\input{libprofile}		% The Python Profiler
 
 \input{libunix}			% UNIX ONLY
 \input{libdbm}

File Doc/lib/libprofile.tex

+\chapter{The Python Profiler}
+\stmodindex{profile}
+\stmodindex{pstats}
+
+Copyright 1994, by InfoSeek Corporation, all rights reserved.
+
+Written by James Roskind%
+\footnote{
+Updated and converted to LaTeX by Guido van Rossum.  The references to
+the old profiler are left in the text, although it no longer exists.
+}
+
+Permission to use, copy, modify, and distribute this Python software
+and its associated documentation for any purpose (subject to the
+restriction in the following sentence) without fee is hereby granted,
+provided that the above copyright notice appears in all copies, and
+that both that copyright notice and this permission notice appear in
+supporting documentation, and that the name of InfoSeek not be used in
+advertising or publicity pertaining to distribution of the software
+without specific, written prior permission.  This permission is
+explicitly restricted to the copying and modification of the software
+to remain in Python, compiled Python, or other languages (such as C)
+wherein the modified or derived code is exclusively imported into a
+Python module.
+
+INFOSEEK CORPORATION DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
+SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
+FITNESS. IN NO EVENT SHALL INFOSEEK CORPORATION BE LIABLE FOR ANY
+SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
+RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF
+CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
+CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+
+
+The profiler was written after only programming in Python for 3 weeks.
+As a result, it is probably clumsy code, but I don't know for sure yet
+'cause I'm a beginner :-).  I did work hard to make the code run fast,
+so that profiling would be a reasonable thing to do.  I tried not to
+repeat code fragments, but I'm sure I did some stuff in really awkward
+ways at times.  Please send suggestions for improvements to:
+\code{jar@infoseek.com}.  I won't promise \emph{any} support.  ...but
+I'd appreciate the feedback.
+
+
+\section{Introduction}
+
+A \dfn{profiler} is a program that describes the run time performance
+of a program, providing a variety of statistics.  This documentation
+describes the profiler functionality provided in the modules
+\code{profile} and \code{pstats.}  This profiler provides
+\dfn{deterministic profiling} of any Python programs.  It also
+provides a series of report generation tools to allow users to rapidly
+examine the results of a profile operation.
+
+
+\section{How Is This Profiler Different From The Old Profiler?}
+
+The big changes from old profiling module are that you get more
+information, and you pay less CPU time.  It's not a trade-off, it's a
+trade-up.
+
+To be specific:
+
+\begin{description}
+
+\item[Bugs removed:]
+Local stack frame is no longer molested, execution time is now charged
+to correct functions.
+
+\item[Accuracy increased:]
+Profiler execution time is no longer charged to user's code,
+calibration for platform is supported, file reads are not done \emph{by}
+profiler \emph{during} profiling (and charged to user's code!).
+
+\item[Speed increased:]
+Overhead CPU cost was reduced by more than a factor of two (perhaps a
+factor of five), lightweight profiler module is all that must be
+loaded, and the report generating module (\code{pstats}) is not needed
+during profiling.
+
+\item[Recursive functions support:]
+Cumulative times in recursive functions are correctly calculated;
+recursive entries are counted.
+
+\item[Large growth in report generating UI:]
+Distinct profiles runs can be added together forming a comprehensive
+report; functions that import statistics take arbitrary lists of
+files; sorting criteria is now based on keywords (instead of 4 integer
+options); reports shows what functions were profiled as well as what
+profile file was referenced; output format has been improved.
+
+\end{description}
+
+
+\section{Instant Users Manual}
+
+This section is provided for users that ``don't want to read the
+manual.'' It provides a very brief overview, and allows a user to
+rapidly perform profiling on an existing application.
+
+To profile an application with a main entry point of \samp{foo()}, you
+would add the following to your module:
+
+\begin{verbatim}
+    import profile
+    profile.run("foo()")
+\end{verbatim}
+
+The above action would cause \samp{foo()} to be run, and a series of
+informative lines (the profile) to be printed.  The above approach is
+most useful when working with the interpreter.  If you would like to
+save the results of a profile into a file for later examination, you
+can supply a file name as the second argument to the \code{run()}
+function:
+
+\begin{verbatim}
+    import profile
+    profile.run("foo()", 'fooprof')
+\end{verbatim}
+
+When you wish to review the profile, you should use the methods in the
+\code{pstats} module.  Typically you would load the statistics data as
+follows:
+
+\begin{verbatim}
+    import pstats
+    p = pstats.Stats('fooprof')
+\end{verbatim}
+
+The class \code{Stats} (the above code just created an instance of
+this class) has a variety of methods for manipulating and printing the
+data that was just read into \samp{p}.  When you ran
+\code{profile.run()} above, what was printed was the result of three
+method calls:
+
+\begin{verbatim}
+    p.strip_dirs().sort_stats(-1).print_stats()
+\end{verbatim}
+
+The first method removed the extraneous path from all the module
+names. The second method sorted all the entries according to the
+standard module/line/name string that is printed (this is to comply
+with the semantics of the old profiler).  The third method printed out
+all the statistics.  You might try the following sort calls:
+
+\begin{verbatim}
+    p.sort_stats('name')
+    p.print_stats()
+\end{verbatim}
+
+The first call will actually sort the list by function name, and the
+second call will print out the statistics.  The following are some
+interesting calls to experiment with:
+
+\begin{verbatim}
+    p.sort_stats('cumulative').print_stats(10)
+\end{verbatim}
+
+This sorts the profile by cumulative time in a function, and then only
+prints the ten most significant lines.  If you want to understand what
+algorithms are taking time, the above line is what you would use.
+
+If you were looking to see what functions were looping a lot, and
+taking a lot of time, you would do:
+
+\begin{verbatim}
+    p.sort_stats('time').print_stats(10)
+\end{verbatim}
+
+to sort according to time spent within each function, and then print
+the statistics for the top ten functions.
+
+You might also try:
+
+\begin{verbatim}
+    p.sort_stats('file').print_stats('__init__')
+\end{verbatim}
+
+This will sort all the statistics by file name, and then print out
+statistics for only the class init methods ('cause they are spelled
+with \code{__init__} in them).  As one final example, you could try:
+
+\begin{verbatim}
+    p.sort_stats('time', 'cum').print_stats(.5, 'init')
+\end{verbatim}
+
+This line sorts statistics with a primary key of time, and a secondary
+key of cumulative time, and then prints out some of the statistics.
+To be specific, the list is first culled down to 50\% (re: \samp{.5})
+of its original size, then only lines containing \code{init} are
+maintained, and that sub-sub-list is printed.
+
+If you wondered what functions called the above functions, you could
+now (\samp{p} is still sorted according to the last criteria) do:
+
+\begin{verbatim}
+    p.print_callers(.5, 'init')
+\end{verbatim}
+
+and you would get a list of callers for each of the listed functions. 
+
+If you want more functionality, you're going to have to read the
+manual, or guess what the following functions do:
+
+\begin{verbatim}
+    p.print_callees()
+    p.add('fooprof')
+\end{verbatim}
+
+
+\section{What Is Deterministic Profiling?}
+
+\dfn{Deterministic profiling} is meant to reflect the fact that all
+\dfn{function call}, \dfn{function return}, and \dfn{exception} events
+are monitored, and precise timings are made for the intervals between
+these events (during which time the user's code is executing).  In
+contrast, \dfn{statistical profiling} (which is not done by this
+module) randomly samples the effective instruction pointer, and
+deduces where time is being spent.  The latter technique traditionally
+involves less overhead (as the code does not need to be instrumented),
+but provides only relative indications of where time is being spent.
+
+In Python, since there is an interpreter active during execution, the
+presence of instrumented code is not required to do deterministic
+profiling.  Python automatically provides a \dfn{hook} (optional
+callback) for each event.  In addition, the interpreted nature of
+Python tends to add so much overhead to execution, that deterministic
+profiling tends to only add small processing overhead in typical
+applications.  The result is that deterministic profiling is not that
+expensive, yet provides extensive run time statistics about the
+execution of a Python program.
+
+Call count statistics can be used to identify bugs in code (surprising
+counts), and to identify possible inline-expansion points (high call
+counts).  Internal time statistics can be used to identify ``hot
+loops'' that should be carefully optimized.  Cumulative time
+statistics should be used to identify high level errors in the
+selection of algorithms.  Note that the unusual handling of cumulative
+times in this profiler allows statistics for recursive implementations
+of algorithms to be directly compared to iterative implementations.
+
+
+\section{Reference Manual}
+
+\renewcommand{\indexsubitem}{}
+
+The primary entry point for the profiler is the global function
+\code{profile.run()}.  It is typically used to create any profile
+information.  The reports are formatted and printed using methods of
+the class \code{pstats.Stats}.  The following is a description of all
+of these standard entry points and functions.  For a more in-depth
+view of some of the code, consider reading the later section on
+Profiler Extensions, which includes discussion of how to derive
+``better'' profilers from the classes presented, or reading the source
+code for these modules.
+
+\begin{funcdesc}{profile.run}{string\optional{\, filename}}
+
+This function takes a single argument that has can be passed to the
+\code{exec} statement, and an optional file name.  In all cases this
+routine attempts to \code{exec} its first argument, and gather profiling
+statistics from the execution. If no file name is present, then this
+function automatically prints a simple profiling report, sorted by the
+standard name string (file/line/function-name) that is presented in
+each line.  The following is a typical output from such a call:
+
+\begin{verbatim}
+         main()
+         2706 function calls (2004 primitive calls) in 4.504 CPU seconds
+
+   Ordered by: standard name
+
+   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
+        2    0.006    0.003    0.953    0.477 pobject.py:75(save_objects)
+     43/3    0.533    0.012    0.749    0.250 pobject.py:99(evaluate)
+    ...
+\end{verbatim}
+
+The first line indicates that this profile was generated by the call:\\
+\code{profile.run('main()')}, and hence the exec'ed string is
+\code{'main()'}.  The second line indicates that 2706 calls were
+monitored.  Of those calls, 2004 were \dfn{primitive}.  We define
+\dfn{primitive} to mean that the call was not induced via recursion.
+The next line: \code{Ordered by:\ standard name}, indicates that
+the text string in the far right column was used to sort the output.
+The column headings include:
+
+\begin{description}
+
+\item[ncalls ]
+for the number of calls, 
+
+\item[tottime ]
+for the total time spent in the given function (and excluding time
+made in calls to sub-functions),
+
+\item[percall ]
+is the quotient of \code{tottime} divided by \code{ncalls}
+
+\item[cumtime ]
+is the total time spent in this and all subfunctions (i.e., from
+invocation till exit). This figure is accurate \emph{even} for recursive
+functions.
+
+\item[percall ]
+is the quotient of \code{cumtime} divided by primitive calls
+
+\item[filename:lineno(function) ]
+provides the respective data of each function
+
+\end{description}
+
+When there are two numbers in the first column (e.g.: \samp{43/3}),
+then the latter is the number of primitive calls, and the former is
+the actual number of calls.  Note that when the function does not
+recurse, these two values are the same, and only the single figure is
+printed.
+\end{funcdesc}
+
+\begin{funcdesc}{pstats.Stats}{filename\optional{\, ...}}
+This class constructor creates an instance of a ``statistics object''
+from a \var{filename} (or set of filenames).  \code{Stats} objects are
+manipulated by methods, in order to print useful reports.
+
+The file selected by the above constructor must have been created by
+the corresponding version of \code{profile}.  To be specific, there is
+\emph{NO} file compatibility guaranteed with future versions of this
+profiler, and there is no compatibility with files produced by other
+profilers (e.g., the old system profiler).
+
+If several files are provided, all the statistics for identical
+functions will be coalesced, so that an overall view of several
+processes can be considered in a single report.  If additional files
+need to be combined with data in an existing \code{Stats} object, the
+\code{add()} method can be used.
+\end{funcdesc}
+
+
+\subsection{Methods Of The \sectcode{Stats} Class}
+
+\renewcommand{\indexsubitem}{(Stats method)}
+
+\begin{funcdesc}{strip_dirs}{}
+This method for the code{Stats} class removes all leading path information
+from file names.  It is very useful in reducing the size of the
+printout to fit within (close to) 80 columns.  This method modifies
+the object, and the stripped information is lost.  After performing a
+strip operation, the object is considered to have its entries in a
+``random'' order, as it was just after object initialization and
+loading.  If \code{strip_dirs()} causes two function names to be
+indistinguishable (i.e., they are on the same line of the same
+filename, and have the same function name), then the statistics for
+these two entries are accumulated into a single entry.
+\end{funcdesc}
+
+
+\begin{funcdesc}{add}{filename\optional{\, ...}}
+This method of the code{Stats} class accumulates additional profiling
+information into the current profiling object.  Its arguments should
+refer to filenames created by the corresponding version of
+\code{profile.run()}.  Statistics for identically named (re: file,
+line, name) functions are automatically accumulated into single
+function statistics.
+\end{funcdesc}
+
+\begin{funcdesc}{sort_stats}{key\optional{\, ...}}
+This method modifies the code{Stats} object by sorting it according to the
+supplied criteria.  The argument is typically a string identifying the
+basis of a sort (example: \code{"time"} or \code{"name"}).
+
+When more than one key is provided, then additional keys are used as
+secondary criteria when the there is equality in all keys selected
+before them.  For example, sort_stats('name', 'file') will sort all
+the entries according to their function name, and resolve all ties
+(identical function names) by sorting by file name.
+
+Abbreviations can be used for any key names, as long as the
+abbreviation is unambiguous.  The following are the keys currently
+defined: 
+
+\begin{tableii}{|l|l|}{code}{Valid Arg}{Meaning}
+\lineii{"calls"}{call count}
+\lineii{"cumulative"}{cumulative time}
+\lineii{"file"}{file name}
+\lineii{"module"}{file name}
+\lineii{"pcalls"}{primitive call count}
+\lineii{"line"}{line number}
+\lineii{"name"}{function name}
+\lineii{"nfl"}{name/file/line}
+\lineii{"stdname"}{standard name}
+\lineii{"time"}{internal time}
+\end{tableii}
+
+Note that all sorts on statistics are in descending order (placing
+most time consuming items first), where as name, file, and line number
+searches are in ascending order (i.e., alphabetical). The subtle
+distinction between \code{"nfl"} and \code{"stdname"} is that the
+standard name is a sort of the name as printed, which means that the
+embedded line numbers get compared in an odd way.  For example, lines
+3, 20, and 40 would (if the file names were the same) appear in the
+string order 20, 3 and 40.  In contrast, \code{"nfl"} does a numeric
+compare of the line numbers.  In fact, \code{sort_stats("nfl")} is the
+same as \code{sort_stats("name", "file", "line")}.
+
+For compatibility with the old profiler, the numeric arguments
+\samp{-1}, \samp{0}, \samp{1}, and \samp{2} are permitted.  They are
+interpreted as \code{"stdname"}, \code{"calls"}, \code{"time"}, and
+\code{"cumulative"} respectively.  If this old style format (numeric)
+is used, only one sort key (the numeric key) will be used, and
+additional arguments will be silently ignored.
+\end{funcdesc}
+
+
+\begin{funcdesc}{reverse_order}{}
+This method for the code{Stats} class reverses the ordering of the basic
+list within the object.  This method is provided primarily for
+compatibility with the old profiler.  Its utility is questionable
+now that ascending vs descending order is properly selected based on
+the sort key of choice.
+\end{funcdesc}
+
+\begin{funcdesc}{print_stats}{restriction\optional{\, ...}}
+This method for the code{Stats} class prints out a report as described
+in the \code{profile.run()} definition.
+
+The order of the printing is based on the last \code{sort_stats()}
+operation done on the object (subject to caveats in \code{add()} and
+\code{strip_dirs())}.
+
+The arguments provided (if any) can be used to limit the list down to
+the significant entries.  Initially, the list is taken to be the
+complete set of profiled functions.  Each restriction is either an
+integer (to select a count of lines), or a decimal fraction between
+0.0 and 1.0 inclusive (to select a percentage of lines), or a regular
+expression (to pattern match the standard name that is printed).  If
+several restrictions are provided, then they are applied sequentially.
+For example:
+
+\begin{verbatim}
+    print_stats(.1, "foo:")
+\end{verbatim}
+
+would first limit the printing to first 10\% of list, and then only
+print functions that were part of filename \samp{.*foo:}.  In
+contrast, the command:
+
+\begin{verbatim}
+    print_stats("foo:", .1)
+\end{verbatim}
+
+would limit the list to all functions having file names \samp{.*foo:},
+and then proceed to only print the first 10\% of them.
+\end{funcdesc}
+
+
+\begin{funcdesc}{print_callers}{restrictions\optional{\, ...}}
+This method for the code{Stats} class prints a list of all functions
+that called each function in the profiled database.  The ordering is
+identical to that provided by \code{print_stats()}, and the definition
+of the restricting argument is also identical.  For convenience, a
+number is shown in parentheses after each caller to show how many
+times this specific call was made.  A second non-parenthesized number
+is the cumulative time spent in the function at the right.
+\end{funcdesc}
+
+\begin{funcdesc}{print_callees}{restrictions\optional{\, ...}}
+This method for the code{Stats} class prints a list of all function
+that were called by the indicated function.  Aside from this reversal
+of direction of calls (re: called vs was called by), the arguments and
+ordering are identical to the \code{print_callers()} method.
+\end{funcdesc}
+
+\begin{funcdesc}{ignore}{}
+This method of the code{Stats} class is used to dispose of the value
+returned by earlier methods.  All standard methods in this class
+return the instance that is being processed, so that the commands can
+be strung together.  For example:
+
+\begin{verbatim}
+pstats.Stats('foofile').strip_dirs().sort_stats('cum').print_stats().ignore()
+\end{verbatim}
+
+would perform all the indicated functions, but it would not return
+the final reference to the code{Stats} instance.%
+\footnote{
+This was once necessary, when Python would print any unused expression
+result that was not \code{None}.  The method is still defined for
+backward compatibility.
+}
+\end{funcdesc}
+
+
+\section{Limitations}
+
+There are two fundamental limitations on this profiler.  The first is
+that it relies on the Python interpreter to dispatch \dfn{call},
+\dfn{return}, and \dfn{exception} events.  Compiled C code does not
+get interpreted, and hence is ``invisible'' to the profiler.  All time
+spent in C code (including builtin functions) will be charged to the
+Python function that was invoked the C code.  If the C code calls out
+to some native Python code, then those calls will be profiled
+properly.
+
+The second limitation has to do with accuracy of timing information.
+There is a fundamental problem with deterministic profilers involving
+accuracy.  The most obvious restriction is that the underlying ``clock''
+is only ticking at a rate (typically) of about .001 seconds.  Hence no
+measurements will be more accurate that that underlying clock.  If
+enough measurements are taken, then the ``error'' will tend to average
+out. Unfortunately, removing this first error induces a second source
+of error...
+
+The second problem is that it ``takes a while'' from when an event is
+dispatched until the profiler's call to get the time actually
+\emph{gets} the state of the clock.  Similarly, there is a certain lag
+when exiting the profiler event handler from the time that the clock's
+value was obtained (and then squirreled away), until the user's code
+is once again executing.  As a result, functions that are called many
+times, or call many functions, will typically accumulate this error.
+The error that accumulates in this fashion is typically less than the
+accuracy of the clock (i.e., less than one clock tick), but it
+\emph{can} accumulate and become very significant.  This profiler
+provides a means of calibrating itself for a given platform so that
+this error can be probabilistically (i.e., on the average) removed.
+After the profiler is calibrated, it will be more accurate (in a least
+square sense), but it will sometimes produce negative numbers (when
+call counts are exceptionally low, and the gods of probability work
+against you :-). )  Do \emph{NOT} be alarmed by negative numbers in
+the profile.  They should \emph{only} appear if you have calibrated
+your profiler, and the results are actually better than without
+calibration.
+
+
+\section{Calibration}
+
+The profiler class has a hard coded constant that is added to each
+event handling time to compensate for the overhead of calling the time
+function, and socking away the results.  The following procedure can
+be used to obtain this constant for a given platform (see discussion
+in section Limitations above).
+
+\begin{verbatim}
+    import profile
+    pr = profile.Profile()
+    pr.calibrate(100)
+    pr.calibrate(100)
+    pr.calibrate(100)
+\end{verbatim}
+
+The argument to calibrate() is the number of times to try to do the
+sample calls to get the CPU times.  If your computer is \emph{very}
+fast, you might have to do:
+
+\begin{verbatim}
+    pr.calibrate(1000)
+\end{verbatim}
+
+or even:
+
+\begin{verbatim}
+    pr.calibrate(10000)
+\end{verbatim}
+
+The object of this exercise is to get a fairly consistent result.
+When you have a consistent answer, you are ready to use that number in
+the source code.  For a Sun Sparcstation 1000 running Solaris 2.3, the
+magical number is about .00053.  If you have a choice, you are better
+off with a smaller constant, and your results will ``less often'' show
+up as negative in profile statistics.
+
+The following shows how the trace_dispatch() method in the Profile
+class should be modified to install the calibration constant on a Sun
+Sparcstation 1000:
+
+\begin{verbatim}
+    def trace_dispatch(self, frame, event, arg):
+        t = self.timer()
+        t = t[0] + t[1] - self.t - .00053 # Calibration constant
+
+        if self.dispatch[event](frame,t):
+            t = self.timer()
+            self.t = t[0] + t[1]
+        else:
+            r = self.timer()
+            self.t = r[0] + r[1] - t # put back unrecorded delta
+        return
+\end{verbatim}
+
+Note that if there is no calibration constant, then the line
+containing the callibration constant should simply say:
+
+\begin{verbatim}
+        t = t[0] + t[1] - self.t  # no calibration constant
+\end{verbatim}
+
+You can also achieve the same results using a derived class (and the
+profiler will actually run equally fast!!), but the above method is
+the simplest to use.  I could have made the profiler ``self
+calibrating'', but it would have made the initialization of the
+profiler class slower, and would have required some \emph{very} fancy
+coding, or else the use of a variable where the constant \samp{.00053}
+was placed in the code shown.  This is a \strong{VERY} critical
+performance section, and there is no reason to use a variable lookup
+at this point, when a constant can be used.
+
+
+\section{Extensions: Deriving Better Profilers}
+
+The \code{Profile} class of module \code{profile} was written so that
+derived classes could be developed to extend the profiler.  Rather
+than describing all the details of such an effort, I'll just present
+the following two examples of derived classes that can be used to do
+profiling.  If the reader is an avid Python programmer, then it should
+be possible to use these as a model and create similar (and perchance
+better) profile classes.
+
+If all you want to do is change how the timer is called, or which
+timer function is used, then the basic class has an option for that in
+the constructor for the class.  Consider passing the name of a
+function to call into the constructor:
+
+\begin{verbatim}
+    pr = profile.Profile(your_time_func)
+\end{verbatim}
+
+The resulting profiler will call \code{your_time_func()} instead of
+\code{os.times()}.  The function should return either a single number
+or a list of numbers (like what \code{os.times()} returns).  If the
+function returns a single time number, or the list of returned numbers
+has length 2, then you will get an especially fast version of the
+dispatch routine.
+
+Be warned that you \emph{should} calibrate the profiler class for the
+timer function that you choose.  For most machines, a timer that
+returns a lone integer value will provide the best results in terms of
+low overhead during profiling.  (os.times is \emph{pretty} bad, 'cause
+it returns a tuple of floating point values, so all arithmetic is
+floating point in the profiler!).  If you want to substitute a
+better timer in the cleanest fashion, you should derive a class, and
+simply put in the replacement dispatch method that better handles your
+timer call, along with the appropriate calibration constant :-).
+
+
+\subsection{OldProfile Class}
+
+The following derived profiler simulates the old style profiler,
+providing errant results on recursive functions. The reason for the
+usefulness of this profiler is that it runs faster (i.e., less
+overhead) than the old profiler.  It still creates all the caller
+stats, and is quite useful when there is \emph{no} recursion in the
+user's code.  It is also a lot more accurate than the old profiler, as
+it does not charge all its overhead time to the user's code.
+
+\begin{verbatim}
+class OldProfile(Profile):
+
+    def trace_dispatch_exception(self, frame, t):
+        rt, rtt, rct, rfn, rframe, rcur = self.cur
+        if rcur and not rframe is frame:
+            return self.trace_dispatch_return(rframe, t)
+        return 0
+
+    def trace_dispatch_call(self, frame, t):
+        fn = `frame.f_code`
+        
+        self.cur = (t, 0, 0, fn, frame, self.cur)
+        if self.timings.has_key(fn):
+            tt, ct, callers = self.timings[fn]
+            self.timings[fn] = tt, ct, callers
+        else:
+            self.timings[fn] = 0, 0, {}
+        return 1
+
+    def trace_dispatch_return(self, frame, t):
+        rt, rtt, rct, rfn, frame, rcur = self.cur
+        rtt = rtt + t
+        sft = rtt + rct
+
+        pt, ptt, pct, pfn, pframe, pcur = rcur
+        self.cur = pt, ptt+rt, pct+sft, pfn, pframe, pcur
+
+        tt, ct, callers = self.timings[rfn]
+        if callers.has_key(pfn):
+            callers[pfn] = callers[pfn] + 1
+        else:
+            callers[pfn] = 1
+        self.timings[rfn] = tt+rtt, ct + sft, callers
+
+        return 1
+
+
+    def snapshot_stats(self):
+        self.stats = {}
+        for func in self.timings.keys():
+            tt, ct, callers = self.timings[func]
+            nor_func = self.func_normalize(func)
+            nor_callers = {}
+            nc = 0
+            for func_caller in callers.keys():
+                nor_callers[self.func_normalize(func_caller)]=\
+                      callers[func_caller]
+                nc = nc + callers[func_caller]
+            self.stats[nor_func] = nc, nc, tt, ct, nor_callers
+\end{verbatim}
+        
+
+\subsection{HotProfile Class}
+
+This profiler is the fastest derived profile example.  It does not
+calculate caller-callee relationships, and does not calculate
+cumulative time under a function.  It only calculates time spent in a
+function, so it runs very quickly (re: very low overhead).  In truth,
+the basic profiler is so fast, that is probably not worth the savings
+to give up the data, but this class still provides a nice example.
+
+\begin{verbatim}
+class HotProfile(Profile):
+
+    def trace_dispatch_exception(self, frame, t):
+        rt, rtt, rfn, rframe, rcur = self.cur
+        if rcur and not rframe is frame:
+            return self.trace_dispatch_return(rframe, t)
+        return 0
+
+    def trace_dispatch_call(self, frame, t):
+        self.cur = (t, 0, frame, self.cur)
+        return 1
+
+    def trace_dispatch_return(self, frame, t):
+        rt, rtt, frame, rcur = self.cur
+
+        rfn = `frame.f_code`
+
+        pt, ptt, pframe, pcur = rcur
+        self.cur = pt, ptt+rt, pframe, pcur
+
+        if self.timings.has_key(rfn):
+            nc, tt = self.timings[rfn]
+            self.timings[rfn] = nc + 1, rt + rtt + tt
+        else:
+            self.timings[rfn] =      1, rt + rtt
+
+        return 1
+
+
+    def snapshot_stats(self):
+        self.stats = {}
+        for func in self.timings.keys():
+            nc, tt = self.timings[func]
+            nor_func = self.func_normalize(func)
+            self.stats[nor_func] = nc, nc, tt, 0, {}
+\end{verbatim}

File Doc/libprofile.tex

+\chapter{The Python Profiler}
+\stmodindex{profile}
+\stmodindex{pstats}
+
+Copyright 1994, by InfoSeek Corporation, all rights reserved.
+
+Written by James Roskind%
+\footnote{
+Updated and converted to LaTeX by Guido van Rossum.  The references to
+the old profiler are left in the text, although it no longer exists.
+}
+
+Permission to use, copy, modify, and distribute this Python software
+and its associated documentation for any purpose (subject to the
+restriction in the following sentence) without fee is hereby granted,
+provided that the above copyright notice appears in all copies, and
+that both that copyright notice and this permission notice appear in
+supporting documentation, and that the name of InfoSeek not be used in
+advertising or publicity pertaining to distribution of the software
+without specific, written prior permission.  This permission is
+explicitly restricted to the copying and modification of the software
+to remain in Python, compiled Python, or other languages (such as C)
+wherein the modified or derived code is exclusively imported into a
+Python module.
+
+INFOSEEK CORPORATION DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
+SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
+FITNESS. IN NO EVENT SHALL INFOSEEK CORPORATION BE LIABLE FOR ANY
+SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
+RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF
+CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
+CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+
+
+The profiler was written after only programming in Python for 3 weeks.
+As a result, it is probably clumsy code, but I don't know for sure yet
+'cause I'm a beginner :-).  I did work hard to make the code run fast,
+so that profiling would be a reasonable thing to do.  I tried not to
+repeat code fragments, but I'm sure I did some stuff in really awkward
+ways at times.  Please send suggestions for improvements to:
+\code{jar@infoseek.com}.  I won't promise \emph{any} support.  ...but
+I'd appreciate the feedback.
+
+
+\section{Introduction}
+
+A \dfn{profiler} is a program that describes the run time performance
+of a program, providing a variety of statistics.  This documentation
+describes the profiler functionality provided in the modules
+\code{profile} and \code{pstats.}  This profiler provides
+\dfn{deterministic profiling} of any Python programs.  It also
+provides a series of report generation tools to allow users to rapidly
+examine the results of a profile operation.
+
+
+\section{How Is This Profiler Different From The Old Profiler?}
+
+The big changes from old profiling module are that you get more
+information, and you pay less CPU time.  It's not a trade-off, it's a
+trade-up.
+
+To be specific:
+
+\begin{description}
+
+\item[Bugs removed:]
+Local stack frame is no longer molested, execution time is now charged
+to correct functions.
+
+\item[Accuracy increased:]
+Profiler execution time is no longer charged to user's code,
+calibration for platform is supported, file reads are not done \emph{by}
+profiler \emph{during} profiling (and charged to user's code!).
+
+\item[Speed increased:]
+Overhead CPU cost was reduced by more than a factor of two (perhaps a
+factor of five), lightweight profiler module is all that must be
+loaded, and the report generating module (\code{pstats}) is not needed
+during profiling.
+
+\item[Recursive functions support:]
+Cumulative times in recursive functions are correctly calculated;
+recursive entries are counted.
+
+\item[Large growth in report generating UI:]
+Distinct profiles runs can be added together forming a comprehensive
+report; functions that import statistics take arbitrary lists of
+files; sorting criteria is now based on keywords (instead of 4 integer
+options); reports shows what functions were profiled as well as what
+profile file was referenced; output format has been improved.
+
+\end{description}
+
+
+\section{Instant Users Manual}
+
+This section is provided for users that ``don't want to read the
+manual.'' It provides a very brief overview, and allows a user to
+rapidly perform profiling on an existing application.
+
+To profile an application with a main entry point of \samp{foo()}, you
+would add the following to your module:
+
+\begin{verbatim}
+    import profile
+    profile.run("foo()")
+\end{verbatim}
+
+The above action would cause \samp{foo()} to be run, and a series of
+informative lines (the profile) to be printed.  The above approach is
+most useful when working with the interpreter.  If you would like to
+save the results of a profile into a file for later examination, you
+can supply a file name as the second argument to the \code{run()}
+function:
+
+\begin{verbatim}
+    import profile
+    profile.run("foo()", 'fooprof')
+\end{verbatim}
+
+When you wish to review the profile, you should use the methods in the
+\code{pstats} module.  Typically you would load the statistics data as
+follows:
+
+\begin{verbatim}
+    import pstats
+    p = pstats.Stats('fooprof')
+\end{verbatim}
+
+The class \code{Stats} (the above code just created an instance of
+this class) has a variety of methods for manipulating and printing the
+data that was just read into \samp{p}.  When you ran
+\code{profile.run()} above, what was printed was the result of three
+method calls:
+
+\begin{verbatim}
+    p.strip_dirs().sort_stats(-1).print_stats()
+\end{verbatim}
+
+The first method removed the extraneous path from all the module
+names. The second method sorted all the entries according to the
+standard module/line/name string that is printed (this is to comply
+with the semantics of the old profiler).  The third method printed out
+all the statistics.  You might try the following sort calls:
+
+\begin{verbatim}
+    p.sort_stats('name')
+    p.print_stats()
+\end{verbatim}
+
+The first call will actually sort the list by function name, and the
+second call will print out the statistics.  The following are some
+interesting calls to experiment with:
+
+\begin{verbatim}
+    p.sort_stats('cumulative').print_stats(10)
+\end{verbatim}
+
+This sorts the profile by cumulative time in a function, and then only
+prints the ten most significant lines.  If you want to understand what
+algorithms are taking time, the above line is what you would use.
+
+If you were looking to see what functions were looping a lot, and
+taking a lot of time, you would do:
+
+\begin{verbatim}
+    p.sort_stats('time').print_stats(10)
+\end{verbatim}
+
+to sort according to time spent within each function, and then print
+the statistics for the top ten functions.
+
+You might also try:
+
+\begin{verbatim}
+    p.sort_stats('file').print_stats('__init__')
+\end{verbatim}
+
+This will sort all the statistics by file name, and then print out
+statistics for only the class init methods ('cause they are spelled
+with \code{__init__} in them).  As one final example, you could try:
+
+\begin{verbatim}
+    p.sort_stats('time', 'cum').print_stats(.5, 'init')
+\end{verbatim}
+
+This line sorts statistics with a primary key of time, and a secondary
+key of cumulative time, and then prints out some of the statistics.
+To be specific, the list is first culled down to 50\% (re: \samp{.5})
+of its original size, then only lines containing \code{init} are
+maintained, and that sub-sub-list is printed.
+
+If you wondered what functions called the above functions, you could
+now (\samp{p} is still sorted according to the last criteria) do:
+
+\begin{verbatim}
+    p.print_callers(.5, 'init')
+\end{verbatim}
+
+and you would get a list of callers for each of the listed functions. 
+
+If you want more functionality, you're going to have to read the
+manual, or guess what the following functions do:
+
+\begin{verbatim}
+    p.print_callees()
+    p.add('fooprof')
+\end{verbatim}
+
+
+\section{What Is Deterministic Profiling?}
+
+\dfn{Deterministic profiling} is meant to reflect the fact that all
+\dfn{function call}, \dfn{function return}, and \dfn{exception} events
+are monitored, and precise timings are made for the intervals between
+these events (during which time the user's code is executing).  In
+contrast, \dfn{statistical profiling} (which is not done by this
+module) randomly samples the effective instruction pointer, and
+deduces where time is being spent.  The latter technique traditionally
+involves less overhead (as the code does not need to be instrumented),
+but provides only relative indications of where time is being spent.
+
+In Python, since there is an interpreter active during execution, the
+presence of instrumented code is not required to do deterministic
+profiling.  Python automatically provides a \dfn{hook} (optional
+callback) for each event.  In addition, the interpreted nature of
+Python tends to add so much overhead to execution, that deterministic
+profiling tends to only add small processing overhead in typical
+applications.  The result is that deterministic profiling is not that
+expensive, yet provides extensive run time statistics about the
+execution of a Python program.
+
+Call count statistics can be used to identify bugs in code (surprising
+counts), and to identify possible inline-expansion points (high call
+counts).  Internal time statistics can be used to identify ``hot
+loops'' that should be carefully optimized.  Cumulative time
+statistics should be used to identify high level errors in the
+selection of algorithms.  Note that the unusual handling of cumulative
+times in this profiler allows statistics for recursive implementations
+of algorithms to be directly compared to iterative implementations.
+
+
+\section{Reference Manual}
+
+\renewcommand{\indexsubitem}{}
+
+The primary entry point for the profiler is the global function
+\code{profile.run()}.  It is typically used to create any profile
+information.  The reports are formatted and printed using methods of
+the class \code{pstats.Stats}.  The following is a description of all
+of these standard entry points and functions.  For a more in-depth
+view of some of the code, consider reading the later section on
+Profiler Extensions, which includes discussion of how to derive
+``better'' profilers from the classes presented, or reading the source
+code for these modules.
+
+\begin{funcdesc}{profile.run}{string\optional{\, filename}}
+
+This function takes a single argument that has can be passed to the
+\code{exec} statement, and an optional file name.  In all cases this
+routine attempts to \code{exec} its first argument, and gather profiling
+statistics from the execution. If no file name is present, then this
+function automatically prints a simple profiling report, sorted by the
+standard name string (file/line/function-name) that is presented in
+each line.  The following is a typical output from such a call:
+
+\begin{verbatim}
+         main()
+         2706 function calls (2004 primitive calls) in 4.504 CPU seconds
+
+   Ordered by: standard name
+
+   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
+        2    0.006    0.003    0.953    0.477 pobject.py:75(save_objects)
+     43/3    0.533    0.012    0.749    0.250 pobject.py:99(evaluate)
+    ...
+\end{verbatim}
+
+The first line indicates that this profile was generated by the call:\\
+\code{profile.run('main()')}, and hence the exec'ed string is
+\code{'main()'}.  The second line indicates that 2706 calls were
+monitored.  Of those calls, 2004 were \dfn{primitive}.  We define
+\dfn{primitive} to mean that the call was not induced via recursion.
+The next line: \code{Ordered by:\ standard name}, indicates that
+the text string in the far right column was used to sort the output.
+The column headings include:
+
+\begin{description}
+
+\item[ncalls ]
+for the number of calls, 
+
+\item[tottime ]
+for the total time spent in the given function (and excluding time
+made in calls to sub-functions),
+
+\item[percall ]
+is the quotient of \code{tottime} divided by \code{ncalls}
+
+\item[cumtime ]
+is the total time spent in this and all subfunctions (i.e., from
+invocation till exit). This figure is accurate \emph{even} for recursive
+functions.
+
+\item[percall ]
+is the quotient of \code{cumtime} divided by primitive calls
+
+\item[filename:lineno(function) ]
+provides the respective data of each function
+
+\end{description}
+
+When there are two numbers in the first column (e.g.: \samp{43/3}),
+then the latter is the number of primitive calls, and the former is
+the actual number of calls.  Note that when the function does not
+recurse, these two values are the same, and only the single figure is
+printed.
+\end{funcdesc}
+
+\begin{funcdesc}{pstats.Stats}{filename\optional{\, ...}}
+This class constructor creates an instance of a ``statistics object''
+from a \var{filename} (or set of filenames).  \code{Stats} objects are
+manipulated by methods, in order to print useful reports.
+
+The file selected by the above constructor must have been created by
+the corresponding version of \code{profile}.  To be specific, there is
+\emph{NO} file compatibility guaranteed with future versions of this
+profiler, and there is no compatibility with files produced by other
+profilers (e.g., the old system profiler).
+
+If several files are provided, all the statistics for identical
+functions will be coalesced, so that an overall view of several
+processes can be considered in a single report.  If additional files
+need to be combined with data in an existing \code{Stats} object, the
+\code{add()} method can be used.
+\end{funcdesc}
+
+
+\subsection{Methods Of The \sectcode{Stats} Class}
+
+\renewcommand{\indexsubitem}{(Stats method)}
+
+\begin{funcdesc}{strip_dirs}{}
+This method for the code{Stats} class removes all leading path information
+from file names.  It is very useful in reducing the size of the
+printout to fit within (close to) 80 columns.  This method modifies
+the object, and the stripped information is lost.  After performing a
+strip operation, the object is considered to have its entries in a
+``random'' order, as it was just after object initialization and
+loading.  If \code{strip_dirs()} causes two function names to be
+indistinguishable (i.e., they are on the same line of the same
+filename, and have the same function name), then the statistics for
+these two entries are accumulated into a single entry.
+\end{funcdesc}
+
+
+\begin{funcdesc}{add}{filename\optional{\, ...}}
+This method of the code{Stats} class accumulates additional profiling
+information into the current profiling object.  Its arguments should
+refer to filenames created by the corresponding version of
+\code{profile.run()}.  Statistics for identically named (re: file,
+line, name) functions are automatically accumulated into single
+function statistics.
+\end{funcdesc}
+
+\begin{funcdesc}{sort_stats}{key\optional{\, ...}}
+This method modifies the code{Stats} object by sorting it according to the
+supplied criteria.  The argument is typically a string identifying the
+basis of a sort (example: \code{"time"} or \code{"name"}).
+
+When more than one key is provided, then additional keys are used as
+secondary criteria when the there is equality in all keys selected
+before them.  For example, sort_stats('name', 'file') will sort all
+the entries according to their function name, and resolve all ties
+(identical function names) by sorting by file name.
+
+Abbreviations can be used for any key names, as long as the
+abbreviation is unambiguous.  The following are the keys currently
+defined: 
+
+\begin{tableii}{|l|l|}{code}{Valid Arg}{Meaning}
+\lineii{"calls"}{call count}
+\lineii{"cumulative"}{cumulative time}
+\lineii{"file"}{file name}
+\lineii{"module"}{file name}
+\lineii{"pcalls"}{primitive call count}
+\lineii{"line"}{line number}
+\lineii{"name"}{function name}
+\lineii{"nfl"}{name/file/line}
+\lineii{"stdname"}{standard name}
+\lineii{"time"}{internal time}
+\end{tableii}
+
+Note that all sorts on statistics are in descending order (placing
+most time consuming items first), where as name, file, and line number
+searches are in ascending order (i.e., alphabetical). The subtle
+distinction between \code{"nfl"} and \code{"stdname"} is that the
+standard name is a sort of the name as printed, which means that the
+embedded line numbers get compared in an odd way.  For example, lines
+3, 20, and 40 would (if the file names were the same) appear in the
+string order 20, 3 and 40.  In contrast, \code{"nfl"} does a numeric
+compare of the line numbers.  In fact, \code{sort_stats("nfl")} is the
+same as \code{sort_stats("name", "file", "line")}.
+
+For compatibility with the old profiler, the numeric arguments
+\samp{-1}, \samp{0}, \samp{1}, and \samp{2} are permitted.  They are
+interpreted as \code{"stdname"}, \code{"calls"}, \code{"time"}, and
+\code{"cumulative"} respectively.  If this old style format (numeric)
+is used, only one sort key (the numeric key) will be used, and
+additional arguments will be silently ignored.
+\end{funcdesc}
+
+
+\begin{funcdesc}{reverse_order}{}
+This method for the code{Stats} class reverses the ordering of the basic
+list within the object.  This method is provided primarily for
+compatibility with the old profiler.  Its utility is questionable
+now that ascending vs descending order is properly selected based on
+the sort key of choice.
+\end{funcdesc}
+
+\begin{funcdesc}{print_stats}{restriction\optional{\, ...}}
+This method for the code{Stats} class prints out a report as described
+in the \code{profile.run()} definition.
+
+The order of the printing is based on the last \code{sort_stats()}
+operation done on the object (subject to caveats in \code{add()} and
+\code{strip_dirs())}.
+
+The arguments provided (if any) can be used to limit the list down to
+the significant entries.  Initially, the list is taken to be the
+complete set of profiled functions.  Each restriction is either an
+integer (to select a count of lines), or a decimal fraction between
+0.0 and 1.0 inclusive (to select a percentage of lines), or a regular
+expression (to pattern match the standard name that is printed).  If
+several restrictions are provided, then they are applied sequentially.
+For example:
+
+\begin{verbatim}
+    print_stats(.1, "foo:")
+\end{verbatim}
+
+would first limit the printing to first 10\% of list, and then only
+print functions that were part of filename \samp{.*foo:}.  In
+contrast, the command:
+
+\begin{verbatim}
+    print_stats("foo:", .1)
+\end{verbatim}
+
+would limit the list to all functions having file names \samp{.*foo:},
+and then proceed to only print the first 10\% of them.
+\end{funcdesc}
+
+
+\begin{funcdesc}{print_callers}{restrictions\optional{\, ...}}
+This method for the code{Stats} class prints a list of all functions
+that called each function in the profiled database.  The ordering is
+identical to that provided by \code{print_stats()}, and the definition
+of the restricting argument is also identical.  For convenience, a
+number is shown in parentheses after each caller to show how many
+times this specific call was made.  A second non-parenthesized number
+is the cumulative time spent in the function at the right.
+\end{funcdesc}
+
+\begin{funcdesc}{print_callees}{restrictions\optional{\, ...}}
+This method for the code{Stats} class prints a list of all function
+that were called by the indicated function.  Aside from this reversal
+of direction of calls (re: called vs was called by), the arguments and
+ordering are identical to the \code{print_callers()} method.
+\end{funcdesc}
+
+\begin{funcdesc}{ignore}{}
+This method of the code{Stats} class is used to dispose of the value
+returned by earlier methods.  All standard methods in this class
+return the instance that is being processed, so that the commands can
+be strung together.  For example:
+
+\begin{verbatim}
+pstats.Stats('foofile').strip_dirs().sort_stats('cum').print_stats().ignore()
+\end{verbatim}
+
+would perform all the indicated functions, but it would not return
+the final reference to the code{Stats} instance.%
+\footnote{
+This was once necessary, when Python would print any unused expression
+result that was not \code{None}.  The method is still defined for
+backward compatibility.
+}
+\end{funcdesc}
+
+
+\section{Limitations}
+
+There are two fundamental limitations on this profiler.  The first is
+that it relies on the Python interpreter to dispatch \dfn{call},
+\dfn{return}, and \dfn{exception} events.  Compiled C code does not
+get interpreted, and hence is ``invisible'' to the profiler.  All time
+spent in C code (including builtin functions) will be charged to the
+Python function that was invoked the C code.  If the C code calls out
+to some native Python code, then those calls will be profiled
+properly.
+
+The second limitation has to do with accuracy of timing information.
+There is a fundamental problem with deterministic profilers involving
+accuracy.  The most obvious restriction is that the underlying ``clock''
+is only ticking at a rate (typically) of about .001 seconds.  Hence no
+measurements will be more accurate that that underlying clock.  If
+enough measurements are taken, then the ``error'' will tend to average
+out. Unfortunately, removing this first error induces a second source
+of error...
+
+The second problem is that it ``takes a while'' from when an event is
+dispatched until the profiler's call to get the time actually
+\emph{gets} the state of the clock.  Similarly, there is a certain lag
+when exiting the profiler event handler from the time that the clock's
+value was obtained (and then squirreled away), until the user's code
+is once again executing.  As a result, functions that are called many
+times, or call many functions, will typically accumulate this error.
+The error that accumulates in this fashion is typically less than the
+accuracy of the clock (i.e., less than one clock tick), but it
+\emph{can} accumulate and become very significant.  This profiler
+provides a means of calibrating itself for a given platform so that
+this error can be probabilistically (i.e., on the average) removed.
+After the profiler is calibrated, it will be more accurate (in a least
+square sense), but it will sometimes produce negative numbers (when
+call counts are exceptionally low, and the gods of probability work
+against you :-). )  Do \emph{NOT} be alarmed by negative numbers in
+the profile.  They should \emph{only} appear if you have calibrated
+your profiler, and the results are actually better than without
+calibration.
+
+
+\section{Calibration}
+
+The profiler class has a hard coded constant that is added to each
+event handling time to compensate for the overhead of calling the time
+function, and socking away the results.  The following procedure can
+be used to obtain this constant for a given platform (see discussion
+in section Limitations above).
+
+\begin{verbatim}
+    import profile
+    pr = profile.Profile()
+    pr.calibrate(100)
+    pr.calibrate(100)
+    pr.calibrate(100)
+\end{verbatim}
+
+The argument to calibrate() is the number of times to try to do the
+sample calls to get the CPU times.  If your computer is \emph{very}
+fast, you might have to do:
+
+\begin{verbatim}
+    pr.calibrate(1000)
+\end{verbatim}
+
+or even:
+
+\begin{verbatim}
+    pr.calibrate(10000)
+\end{verbatim}
+
+The object of this exercise is to get a fairly consistent result.
+When you have a consistent answer, you are ready to use that number in
+the source code.  For a Sun Sparcstation 1000 running Solaris 2.3, the
+magical number is about .00053.  If you have a choice, you are better
+off with a smaller constant, and your results will ``less often'' show
+up as negative in profile statistics.
+
+The following shows how the trace_dispatch() method in the Profile
+class should be modified to install the calibration constant on a Sun
+Sparcstation 1000:
+
+\begin{verbatim}
+    def trace_dispatch(self, frame, event, arg):
+        t = self.timer()
+        t = t[0] + t[1] - self.t - .00053 # Calibration constant
+
+        if self.dispatch[event](frame,t):
+            t = self.timer()
+            self.t = t[0] + t[1]
+        else:
+            r = self.timer()
+            self.t = r[0] + r[1] - t # put back unrecorded delta
+        return
+\end{verbatim}
+
+Note that if there is no calibration constant, then the line
+containing the callibration constant should simply say:
+
+\begin{verbatim}
+        t = t[0] + t[1] - self.t  # no calibration constant
+\end{verbatim}
+
+You can also achieve the same results using a derived class (and the
+profiler will actually run equally fast!!), but the above method is
+the simplest to use.  I could have made the profiler ``self
+calibrating'', but it would have made the initialization of the
+profiler class slower, and would have required some \emph{very} fancy
+coding, or else the use of a variable where the constant \samp{.00053}
+was placed in the code shown.  This is a \strong{VERY} critical
+performance section, and there is no reason to use a variable lookup
+at this point, when a constant can be used.
+
+
+\section{Extensions: Deriving Better Profilers}
+
+The \code{Profile} class of module \code{profile} was written so that
+derived classes could be developed to extend the profiler.  Rather
+than describing all the details of such an effort, I'll just present
+the following two examples of derived classes that can be used to do
+profiling.  If the reader is an avid Python programmer, then it should
+be possible to use these as a model and create similar (and perchance
+better) profile classes.
+
+If all you want to do is change how the timer is called, or which
+timer function is used, then the basic class has an option for that in
+the constructor for the class.  Consider passing the name of a
+function to call into the constructor:
+
+\begin{verbatim}
+    pr = profile.Profile(your_time_func)
+\end{verbatim}
+
+The resulting profiler will call \code{your_time_func()} instead of
+\code{os.times()}.  The function should return either a single number
+or a list of numbers (like what \code{os.times()} returns).  If the
+function returns a single time number, or the list of returned numbers
+has length 2, then you will get an especially fast version of the
+dispatch routine.
+
+Be warned that you \emph{should} calibrate the profiler class for the
+timer function that you choose.  For most machines, a timer that
+returns a lone integer value will provide the best results in terms of
+low overhead during profiling.  (os.times is \emph{pretty} bad, 'cause
+it returns a tuple of floating point values, so all arithmetic is
+floating point in the profiler!).  If you want to substitute a
+better timer in the cleanest fashion, you should derive a class, and
+simply put in the replacement dispatch method that better handles your
+timer call, along with the appropriate calibration constant :-).
+
+
+\subsection{OldProfile Class}
+
+The following derived profiler simulates the old style profiler,
+providing errant results on recursive functions. The reason for the
+usefulness of this profiler is that it runs faster (i.e., less
+overhead) than the old profiler.  It still creates all the caller
+stats, and is quite useful when there is \emph{no} recursion in the
+user's code.  It is also a lot more accurate than the old profiler, as
+it does not charge all its overhead time to the user's code.
+
+\begin{verbatim}
+class OldProfile(Profile):
+
+    def trace_dispatch_exception(self, frame, t):
+        rt, rtt, rct, rfn, rframe, rcur = self.cur
+        if rcur and not rframe is frame:
+            return self.trace_dispatch_return(rframe, t)
+        return 0
+
+    def trace_dispatch_call(self, frame, t):
+        fn = `frame.f_code`
+        
+        self.cur = (t, 0, 0, fn, frame, self.cur)
+        if self.timings.has_key(fn):
+            tt, ct, callers = self.timings[fn]
+            self.timings[fn] = tt, ct, callers
+        else:
+            self.timings[fn] = 0, 0, {}
+        return 1
+
+    def trace_dispatch_return(self, frame, t):
+        rt, rtt, rct, rfn, frame, rcur = self.cur
+        rtt = rtt + t
+        sft = rtt + rct
+
+        pt, ptt, pct, pfn, pframe, pcur = rcur
+        self.cur = pt, ptt+rt, pct+sft, pfn, pframe, pcur
+
+        tt, ct, callers = self.timings[rfn]
+        if callers.has_key(pfn):
+            callers[pfn] = callers[pfn] + 1
+        else:
+            callers[pfn] = 1
+        self.timings[rfn] = tt+rtt, ct + sft, callers
+
+        return 1
+
+
+    def snapshot_stats(self):
+        self.stats = {}
+        for func in self.timings.keys():
+            tt, ct, callers = self.timings[func]
+            nor_func = self.func_normalize(func)
+            nor_callers = {}
+            nc = 0
+            for func_caller in callers.keys():
+                nor_callers[self.func_normalize(func_caller)]=\
+                      callers[func_caller]
+                nc = nc + callers[func_caller]
+            self.stats[nor_func] = nc, nc, tt, ct, nor_callers
+\end{verbatim}
+        
+
+\subsection{HotProfile Class}
+
+This profiler is the fastest derived profile example.  It does not
+calculate caller-callee relationships, and does not calculate
+cumulative time under a function.  It only calculates time spent in a
+function, so it runs very quickly (re: very low overhead).  In truth,
+the basic profiler is so fast, that is probably not worth the savings
+to give up the data, but this class still provides a nice example.
+
+\begin{verbatim}
+class HotProfile(Profile):
+
+    def trace_dispatch_exception(self, frame, t):
+        rt, rtt, rfn, rframe, rcur = self.cur
+        if rcur and not rframe is frame:
+            return self.trace_dispatch_return(rframe, t)
+        return 0
+
+    def trace_dispatch_call(self, frame, t):
+        self.cur = (t, 0, frame, self.cur)
+        return 1
+
+    def trace_dispatch_return(self, frame, t):
+        rt, rtt, frame, rcur = self.cur
+
+        rfn = `frame.f_code`
+
+        pt, ptt, pframe, pcur = rcur
+        self.cur = pt, ptt+rt, pframe, pcur
+
+        if self.timings.has_key(rfn):
+            nc, tt = self.timings[rfn]
+            self.timings[rfn] = nc + 1, rt + rtt + tt
+        else:
+            self.timings[rfn] =      1, rt + rtt
+
+        return 1
+
+
+    def snapshot_stats(self):
+        self.stats = {}
+        for func in self.timings.keys():
+            nc, tt = self.timings[func]
+            nor_func = self.func_normalize(func)
+            self.stats[nor_func] = nc, nc, tt, 0, {}
+\end{verbatim}