1.. _profile:
2
3********************
4The Python Profilers
5********************
6
7**Source code:** :source:`Lib/profile.py` and :source:`Lib/pstats.py`
8
9--------------
10
11.. _profiler-introduction:
12
13Introduction to the profilers
14=============================
15
16.. index::
17   single: deterministic profiling
18   single: profiling, deterministic
19
20:mod:`cProfile` and :mod:`profile` provide :dfn:`deterministic profiling` of
21Python programs. A :dfn:`profile` is a set of statistics that describes how
22often and for how long various parts of the program executed. These statistics
23can be formatted into reports via the :mod:`pstats` module.
24
25The Python standard library provides three different implementations of the same
26profiling interface:
27
281. :mod:`cProfile` is recommended for most users; it's a C extension with
29   reasonable overhead that makes it suitable for profiling long-running
30   programs.  Based on :mod:`lsprof`, contributed by Brett Rosen and Ted
31   Czotter.
32
33   .. versionadded:: 2.5
34
352. :mod:`profile`, a pure Python module whose interface is imitated by
36   :mod:`cProfile`, but which adds significant overhead to profiled programs.
37   If you're trying to extend the profiler in some way, the task might be easier
38   with this module.  Originally designed and written by Jim Roskind.
39
40   .. versionchanged:: 2.4
41      Now also reports the time spent in calls to built-in functions
42      and methods.
43
443. :mod:`hotshot` was an experimental C module that focused on minimizing
45   the overhead of profiling, at the expense of longer data
46   post-processing times.  It is no longer maintained and may be
47   dropped in a future version of Python.
48
49
50   .. versionchanged:: 2.5
51      The results should be more meaningful than in the past: the timing core
52      contained a critical bug.
53
54The :mod:`profile` and :mod:`cProfile` modules export the same interface, so
55they are mostly interchangeable; :mod:`cProfile` has a much lower overhead but
56is newer and might not be available on all systems.
57:mod:`cProfile` is really a compatibility layer on top of the internal
58:mod:`_lsprof` module.  The :mod:`hotshot` module is reserved for specialized
59usage.
60
61.. note::
62
63   The profiler modules are designed to provide an execution profile for a given
64   program, not for benchmarking purposes (for that, there is :mod:`timeit` for
65   reasonably accurate results).  This particularly applies to benchmarking
66   Python code against C code: the profilers introduce overhead for Python code,
67   but not for C-level functions, and so the C code would seem faster than any
68   Python one.
69
70
71.. _profile-instant:
72
73Instant User's Manual
74=====================
75
76This section is provided for users that "don't want to read the manual." It
77provides a very brief overview, and allows a user to rapidly perform profiling
78on an existing application.
79
80To profile a function that takes a single argument, you can do::
81
82   import cProfile
83   import re
84   cProfile.run('re.compile("foo|bar")')
85
86(Use :mod:`profile` instead of :mod:`cProfile` if the latter is not available on
87your system.)
88
89The above action would run :func:`re.compile` and print profile results like
90the following::
91
92         197 function calls (192 primitive calls) in 0.002 seconds
93
94   Ordered by: standard name
95
96   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
97        1    0.000    0.000    0.001    0.001 <string>:1(<module>)
98        1    0.000    0.000    0.001    0.001 re.py:212(compile)
99        1    0.000    0.000    0.001    0.001 re.py:268(_compile)
100        1    0.000    0.000    0.000    0.000 sre_compile.py:172(_compile_charset)
101        1    0.000    0.000    0.000    0.000 sre_compile.py:201(_optimize_charset)
102        4    0.000    0.000    0.000    0.000 sre_compile.py:25(_identityfunction)
103      3/1    0.000    0.000    0.000    0.000 sre_compile.py:33(_compile)
104
105The first line indicates that 197 calls were monitored.  Of those calls, 192
106were :dfn:`primitive`, meaning that the call was not induced via recursion. The
107next line: ``Ordered by: standard name``, indicates that the text string in the
108far right column was used to sort the output. The column headings include:
109
110ncalls
111   for the number of calls,
112
113tottime
114    for the total time spent in the given function (and excluding time made in
115    calls to sub-functions)
116
117percall
118   is the quotient of ``tottime`` divided by ``ncalls``
119
120cumtime
121   is the cumulative time spent in this and all subfunctions (from invocation
122   till exit). This figure is accurate *even* for recursive functions.
123
124percall
125   is the quotient of ``cumtime`` divided by primitive calls
126
127filename:lineno(function)
128   provides the respective data of each function
129
130When there are two numbers in the first column (for example ``3/1``), it means
131that the function recursed.  The second value is the number of primitive calls
132and the former is the total number of calls.  Note that when the function does
133not recurse, these two values are the same, and only the single figure is
134printed.
135
136Instead of printing the output at the end of the profile run, you can save the
137results to a file by specifying a filename to the :func:`run` function::
138
139   import cProfile
140   import re
141   cProfile.run('re.compile("foo|bar")', 'restats')
142
143The :class:`pstats.Stats` class reads profile results from a file and formats
144them in various ways.
145
146The file :mod:`cProfile` can also be invoked as a script to profile another
147script.  For example::
148
149   python -m cProfile [-o output_file] [-s sort_order] myscript.py
150
151``-o`` writes the profile results to a file instead of to stdout
152
153``-s`` specifies one of the :func:`~pstats.Stats.sort_stats` sort values to sort
154the output by. This only applies when ``-o`` is not supplied.
155
156The :mod:`pstats` module's :class:`~pstats.Stats` class has a variety of methods
157for manipulating and printing the data saved into a profile results file::
158
159   import pstats
160   p = pstats.Stats('restats')
161   p.strip_dirs().sort_stats(-1).print_stats()
162
163The :meth:`~pstats.Stats.strip_dirs` method removed the extraneous path from all
164the module names. The :meth:`~pstats.Stats.sort_stats` method sorted all the
165entries according to the standard module/line/name string that is printed. The
166:meth:`~pstats.Stats.print_stats` method printed out all the statistics.  You
167might try the following sort calls::
168
169   p.sort_stats('name')
170   p.print_stats()
171
172The first call will actually sort the list by function name, and the second call
173will print out the statistics.  The following are some interesting calls to
174experiment with::
175
176   p.sort_stats('cumulative').print_stats(10)
177
178This sorts the profile by cumulative time in a function, and then only prints
179the ten most significant lines.  If you want to understand what algorithms are
180taking time, the above line is what you would use.
181
182If you were looking to see what functions were looping a lot, and taking a lot
183of time, you would do::
184
185   p.sort_stats('time').print_stats(10)
186
187to sort according to time spent within each function, and then print the
188statistics for the top ten functions.
189
190You might also try::
191
192   p.sort_stats('file').print_stats('__init__')
193
194This will sort all the statistics by file name, and then print out statistics
195for only the class init methods (since they are spelled with ``__init__`` in
196them).  As one final example, you could try::
197
198   p.sort_stats('time', 'cum').print_stats(.5, 'init')
199
200This line sorts statistics with a primary key of time, and a secondary key of
201cumulative time, and then prints out some of the statistics. To be specific, the
202list is first culled down to 50% (re: ``.5``) of its original size, then only
203lines containing ``init`` are maintained, and that sub-sub-list is printed.
204
205If you wondered what functions called the above functions, you could now (``p``
206is still sorted according to the last criteria) do::
207
208   p.print_callers(.5, 'init')
209
210and you would get a list of callers for each of the listed functions.
211
212If you want more functionality, you're going to have to read the manual, or
213guess what the following functions do::
214
215   p.print_callees()
216   p.add('restats')
217
218Invoked as a script, the :mod:`pstats` module is a statistics browser for
219reading and examining profile dumps.  It has a simple line-oriented interface
220(implemented using :mod:`cmd`) and interactive help.
221
222:mod:`profile` and :mod:`cProfile` Module Reference
223=======================================================
224
225.. module:: cProfile
226.. module:: profile
227   :synopsis: Python source profiler.
228
229Both the :mod:`profile` and :mod:`cProfile` modules provide the following
230functions:
231
232.. function:: run(command, filename=None, sort=-1)
233
234   This function takes a single argument that can be passed to the :func:`exec`
235   function, and an optional file name.  In all cases this routine executes::
236
237      exec(command, __main__.__dict__, __main__.__dict__)
238
239   and gathers profiling statistics from the execution. If no file name is
240   present, then this function automatically creates a :class:`~pstats.Stats`
241   instance and prints a simple profiling report. If the sort value is specified
242   it is passed to this :class:`~pstats.Stats` instance to control how the
243   results are sorted.
244
245.. function:: runctx(command, globals, locals, filename=None)
246
247   This function is similar to :func:`run`, with added arguments to supply the
248   globals and locals dictionaries for the *command* string. This routine
249   executes::
250
251      exec(command, globals, locals)
252
253   and gathers profiling statistics as in the :func:`run` function above.
254
255.. class:: Profile(timer=None, timeunit=0.0, subcalls=True, builtins=True)
256
257   This class is normally only used if more precise control over profiling is
258   needed than what the :func:`cProfile.run` function provides.
259
260   A custom timer can be supplied for measuring how long code takes to run via
261   the *timer* argument. This must be a function that returns a single number
262   representing the current time. If the number is an integer, the *timeunit*
263   specifies a multiplier that specifies the duration of each unit of time. For
264   example, if the timer returns times measured in thousands of seconds, the
265   time unit would be ``.001``.
266
267   Directly using the :class:`Profile` class allows formatting profile results
268   without writing the profile data to a file::
269
270      import cProfile, pstats, StringIO
271      pr = cProfile.Profile()
272      pr.enable()
273      # ... do something ...
274      pr.disable()
275      s = StringIO.StringIO()
276      sortby = 'cumulative'
277      ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
278      ps.print_stats()
279      print s.getvalue()
280
281   .. method:: enable()
282
283      Start collecting profiling data.
284
285   .. method:: disable()
286
287      Stop collecting profiling data.
288
289   .. method:: create_stats()
290
291      Stop collecting profiling data and record the results internally
292      as the current profile.
293
294   .. method:: print_stats(sort=-1)
295
296      Create a :class:`~pstats.Stats` object based on the current
297      profile and print the results to stdout.
298
299   .. method:: dump_stats(filename)
300
301      Write the results of the current profile to *filename*.
302
303   .. method:: run(cmd)
304
305      Profile the cmd via :func:`exec`.
306
307   .. method:: runctx(cmd, globals, locals)
308
309      Profile the cmd via :func:`exec` with the specified global and
310      local environment.
311
312   .. method:: runcall(func, *args, **kwargs)
313
314      Profile ``func(*args, **kwargs)``
315
316.. _profile-stats:
317
318The :class:`Stats` Class
319========================
320
321Analysis of the profiler data is done using the :class:`~pstats.Stats` class.
322
323.. module:: pstats
324   :synopsis: Statistics object for use with the profiler.
325
326.. class:: Stats(*filenames or profile, stream=sys.stdout)
327
328   This class constructor creates an instance of a "statistics object" from a
329   *filename* (or list of filenames) or from a :class:`Profile` instance. Output
330   will be printed to the stream specified by *stream*.
331
332   The file selected by the above constructor must have been created by the
333   corresponding version of :mod:`profile` or :mod:`cProfile`.  To be specific,
334   there is *no* file compatibility guaranteed with future versions of this
335   profiler, and there is no compatibility with files produced by other
336   profilers, or the same profiler run on a different operating system.  If
337   several files are provided, all the statistics for identical functions will
338   be coalesced, so that an overall view of several processes can be considered
339   in a single report.  If additional files need to be combined with data in an
340   existing :class:`~pstats.Stats` object, the :meth:`~pstats.Stats.add` method
341   can be used.
342
343   Instead of reading the profile data from a file, a :class:`cProfile.Profile`
344   or :class:`profile.Profile` object can be used as the profile data source.
345
346   :class:`Stats` objects have the following methods:
347
348   .. method:: strip_dirs()
349
350      This method for the :class:`Stats` class removes all leading path
351      information from file names.  It is very useful in reducing the size of
352      the printout to fit within (close to) 80 columns.  This method modifies
353      the object, and the stripped information is lost.  After performing a
354      strip operation, the object is considered to have its entries in a
355      "random" order, as it was just after object initialization and loading.
356      If :meth:`~pstats.Stats.strip_dirs` causes two function names to be
357      indistinguishable (they are on the same line of the same filename, and
358      have the same function name), then the statistics for these two entries
359      are accumulated into a single entry.
360
361
362   .. method:: add(*filenames)
363
364      This method of the :class:`Stats` class accumulates additional profiling
365      information into the current profiling object.  Its arguments should refer
366      to filenames created by the corresponding version of :func:`profile.run`
367      or :func:`cProfile.run`. Statistics for identically named (re: file, line,
368      name) functions are automatically accumulated into single function
369      statistics.
370
371
372   .. method:: dump_stats(filename)
373
374      Save the data loaded into the :class:`Stats` object to a file named
375      *filename*.  The file is created if it does not exist, and is overwritten
376      if it already exists.  This is equivalent to the method of the same name
377      on the :class:`profile.Profile` and :class:`cProfile.Profile` classes.
378
379   .. versionadded:: 2.3
380
381
382   .. method:: sort_stats(*keys)
383
384      This method modifies the :class:`Stats` object by sorting it according to
385      the supplied criteria.  The argument is typically a string identifying the
386      basis of a sort (example: ``'time'`` or ``'name'``).
387
388      When more than one key is provided, then additional keys are used as
389      secondary criteria when there is equality in all keys selected before
390      them.  For example, ``sort_stats('name', 'file')`` will sort all the
391      entries according to their function name, and resolve all ties (identical
392      function names) by sorting by file name.
393
394      Abbreviations can be used for any key names, as long as the abbreviation
395      is unambiguous.  The following are the keys currently defined:
396
397      +------------------+----------------------+
398      | Valid Arg        | Meaning              |
399      +==================+======================+
400      | ``'calls'``      | call count           |
401      +------------------+----------------------+
402      | ``'cumulative'`` | cumulative time      |
403      +------------------+----------------------+
404      | ``'cumtime'``    | cumulative time      |
405      +------------------+----------------------+
406      | ``'file'``       | file name            |
407      +------------------+----------------------+
408      | ``'filename'``   | file name            |
409      +------------------+----------------------+
410      | ``'module'``     | file name            |
411      +------------------+----------------------+
412      | ``'ncalls'``     | call count           |
413      +------------------+----------------------+
414      | ``'pcalls'``     | primitive call count |
415      +------------------+----------------------+
416      | ``'line'``       | line number          |
417      +------------------+----------------------+
418      | ``'name'``       | function name        |
419      +------------------+----------------------+
420      | ``'nfl'``        | name/file/line       |
421      +------------------+----------------------+
422      | ``'stdname'``    | standard name        |
423      +------------------+----------------------+
424      | ``'time'``       | internal time        |
425      +------------------+----------------------+
426      | ``'tottime'``    | internal time        |
427      +------------------+----------------------+
428
429      Note that all sorts on statistics are in descending order (placing most
430      time consuming items first), where as name, file, and line number searches
431      are in ascending order (alphabetical). The subtle distinction between
432      ``'nfl'`` and ``'stdname'`` is that the standard name is a sort of the
433      name as printed, which means that the embedded line numbers get compared
434      in an odd way.  For example, lines 3, 20, and 40 would (if the file names
435      were the same) appear in the string order 20, 3 and 40.  In contrast,
436      ``'nfl'`` does a numeric compare of the line numbers.  In fact,
437      ``sort_stats('nfl')`` is the same as ``sort_stats('name', 'file',
438      'line')``.
439
440      For backward-compatibility reasons, the numeric arguments ``-1``, ``0``,
441      ``1``, and ``2`` are permitted.  They are interpreted as ``'stdname'``,
442      ``'calls'``, ``'time'``, and ``'cumulative'`` respectively.  If this old
443      style format (numeric) is used, only one sort key (the numeric key) will
444      be used, and additional arguments will be silently ignored.
445
446      .. For compatibility with the old profiler.
447
448
449   .. method:: reverse_order()
450
451      This method for the :class:`Stats` class reverses the ordering of the
452      basic list within the object.  Note that by default ascending vs
453      descending order is properly selected based on the sort key of choice.
454
455      .. This method is provided primarily for compatibility with the old
456         profiler.
457
458
459   .. method:: print_stats(*restrictions)
460
461      This method for the :class:`Stats` class prints out a report as described
462      in the :func:`profile.run` definition.
463
464      The order of the printing is based on the last
465      :meth:`~pstats.Stats.sort_stats` operation done on the object (subject to
466      caveats in :meth:`~pstats.Stats.add` and
467      :meth:`~pstats.Stats.strip_dirs`).
468
469      The arguments provided (if any) can be used to limit the list down to the
470      significant entries.  Initially, the list is taken to be the complete set
471      of profiled functions.  Each restriction is either an integer (to select a
472      count of lines), or a decimal fraction between 0.0 and 1.0 inclusive (to
473      select a percentage of lines), or a regular expression (to pattern match
474      the standard name that is printed.  If several restrictions are provided,
475      then they are applied sequentially.  For example::
476
477         print_stats(.1, 'foo:')
478
479      would first limit the printing to first 10% of list, and then only print
480      functions that were part of filename :file:`.\*foo:`.  In contrast, the
481      command::
482
483         print_stats('foo:', .1)
484
485      would limit the list to all functions having file names :file:`.\*foo:`,
486      and then proceed to only print the first 10% of them.
487
488
489   .. method:: print_callers(*restrictions)
490
491      This method for the :class:`Stats` class prints a list of all functions
492      that called each function in the profiled database.  The ordering is
493      identical to that provided by :meth:`~pstats.Stats.print_stats`, and the
494      definition of the restricting argument is also identical.  Each caller is
495      reported on its own line.  The format differs slightly depending on the
496      profiler that produced the stats:
497
498      * With :mod:`profile`, a number is shown in parentheses after each caller
499        to show how many times this specific call was made.  For convenience, a
500        second non-parenthesized number repeats the cumulative time spent in the
501        function at the right.
502
503      * With :mod:`cProfile`, each caller is preceded by three numbers: the
504        number of times this specific call was made, and the total and
505        cumulative times spent in the current function while it was invoked by
506        this specific caller.
507
508
509   .. method:: print_callees(*restrictions)
510
511      This method for the :class:`Stats` class prints a list of all function
512      that were called by the indicated function.  Aside from this reversal of
513      direction of calls (re: called vs was called by), the arguments and
514      ordering are identical to the :meth:`~pstats.Stats.print_callers` method.
515
516
517.. _deterministic-profiling:
518
519What Is Deterministic Profiling?
520================================
521
522:dfn:`Deterministic profiling` is meant to reflect the fact that all *function
523call*, *function return*, and *exception* events are monitored, and precise
524timings are made for the intervals between these events (during which time the
525user's code is executing).  In contrast, :dfn:`statistical profiling` (which is
526not done by this module) randomly samples the effective instruction pointer, and
527deduces where time is being spent.  The latter technique traditionally involves
528less overhead (as the code does not need to be instrumented), but provides only
529relative indications of where time is being spent.
530
531In Python, since there is an interpreter active during execution, the presence
532of instrumented code is not required to do deterministic profiling.  Python
533automatically provides a :dfn:`hook` (optional callback) for each event.  In
534addition, the interpreted nature of Python tends to add so much overhead to
535execution, that deterministic profiling tends to only add small processing
536overhead in typical applications.  The result is that deterministic profiling is
537not that expensive, yet provides extensive run time statistics about the
538execution of a Python program.
539
540Call count statistics can be used to identify bugs in code (surprising counts),
541and to identify possible inline-expansion points (high call counts).  Internal
542time statistics can be used to identify "hot loops" that should be carefully
543optimized.  Cumulative time statistics should be used to identify high level
544errors in the selection of algorithms.  Note that the unusual handling of
545cumulative times in this profiler allows statistics for recursive
546implementations of algorithms to be directly compared to iterative
547implementations.
548
549
550.. _profile-limitations:
551
552Limitations
553===========
554
555One limitation has to do with accuracy of timing information. There is a
556fundamental problem with deterministic profilers involving accuracy.  The most
557obvious restriction is that the underlying "clock" is only ticking at a rate
558(typically) of about .001 seconds.  Hence no measurements will be more accurate
559than the underlying clock.  If enough measurements are taken, then the "error"
560will tend to average out. Unfortunately, removing this first error induces a
561second source of error.
562
563The second problem is that it "takes a while" from when an event is dispatched
564until the profiler's call to get the time actually *gets* the state of the
565clock.  Similarly, there is a certain lag when exiting the profiler event
566handler from the time that the clock's value was obtained (and then squirreled
567away), until the user's code is once again executing.  As a result, functions
568that are called many times, or call many functions, will typically accumulate
569this error. The error that accumulates in this fashion is typically less than
570the accuracy of the clock (less than one clock tick), but it *can* accumulate
571and become very significant.
572
573The problem is more important with :mod:`profile` than with the lower-overhead
574:mod:`cProfile`.  For this reason, :mod:`profile` provides a means of
575calibrating itself for a given platform so that this error can be
576probabilistically (on the average) removed. After the profiler is calibrated, it
577will be more accurate (in a least square sense), but it will sometimes produce
578negative numbers (when call counts are exceptionally low, and the gods of
579probability work against you :-). )  Do *not* be alarmed by negative numbers in
580the profile.  They should *only* appear if you have calibrated your profiler,
581and the results are actually better than without calibration.
582
583
584.. _profile-calibration:
585
586Calibration
587===========
588
589The profiler of the :mod:`profile` module subtracts a constant from each event
590handling time to compensate for the overhead of calling the time function, and
591socking away the results.  By default, the constant is 0. The following
592procedure can be used to obtain a better constant for a given platform (see
593:ref:`profile-limitations`). ::
594
595   import profile
596   pr = profile.Profile()
597   for i in range(5):
598       print pr.calibrate(10000)
599
600The method executes the number of Python calls given by the argument, directly
601and again under the profiler, measuring the time for both. It then computes the
602hidden overhead per profiler event, and returns that as a float.  For example,
603on a 1.8Ghz Intel Core i5 running Mac OS X, and using Python's time.clock() as
604the timer, the magical number is about 4.04e-6.
605
606The object of this exercise is to get a fairly consistent result. If your
607computer is *very* fast, or your timer function has poor resolution, you might
608have to pass 100000, or even 1000000, to get consistent results.
609
610When you have a consistent answer, there are three ways you can use it: [#]_ ::
611
612   import profile
613
614   # 1. Apply computed bias to all Profile instances created hereafter.
615   profile.Profile.bias = your_computed_bias
616
617   # 2. Apply computed bias to a specific Profile instance.
618   pr = profile.Profile()
619   pr.bias = your_computed_bias
620
621   # 3. Specify computed bias in instance constructor.
622   pr = profile.Profile(bias=your_computed_bias)
623
624If you have a choice, you are better off choosing a smaller constant, and then
625your results will "less often" show up as negative in profile statistics.
626
627.. _profile-timers:
628
629Using a custom timer
630====================
631
632If you want to change how current time is determined (for example, to force use
633of wall-clock time or elapsed process time), pass the timing function you want
634to the :class:`Profile` class constructor::
635
636    pr = profile.Profile(your_time_func)
637
638The resulting profiler will then call ``your_time_func``. Depending on whether
639you are using :class:`profile.Profile` or :class:`cProfile.Profile`,
640``your_time_func``'s return value will be interpreted differently:
641
642:class:`profile.Profile`
643   ``your_time_func`` should return a single number, or a list of numbers whose
644   sum is the current time (like what :func:`os.times` returns).  If the
645   function returns a single time number, or the list of returned numbers has
646   length 2, then you will get an especially fast version of the dispatch
647   routine.
648
649   Be warned that you should calibrate the profiler class for the timer function
650   that you choose (see :ref:`profile-calibration`).  For most machines, a timer
651   that returns a lone integer value will provide the best results in terms of
652   low overhead during profiling.  (:func:`os.times` is *pretty* bad, as it
653   returns a tuple of floating point values).  If you want to substitute a
654   better timer in the cleanest fashion, derive a class and hardwire a
655   replacement dispatch method that best handles your timer call, along with the
656   appropriate calibration constant.
657
658:class:`cProfile.Profile`
659   ``your_time_func`` should return a single number.  If it returns integers,
660   you can also invoke the class constructor with a second argument specifying
661   the real duration of one unit of time.  For example, if
662   ``your_integer_time_func`` returns times measured in thousands of seconds,
663   you would construct the :class:`Profile` instance as follows::
664
665      pr = cProfile.Profile(your_integer_time_func, 0.001)
666
667   As the :class:`cProfile.Profile` class cannot be calibrated, custom timer
668   functions should be used with care and should be as fast as possible.  For
669   the best results with a custom timer, it might be necessary to hard-code it
670   in the C source of the internal :mod:`_lsprof` module.
671
672
673.. rubric:: Footnotes
674
675.. [#] Prior to Python 2.2, it was necessary to edit the profiler source code to
676   embed the bias as a literal number.  You still can, but that method is no longer
677   described, because no longer needed.
678