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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  It is no longer maintained and may be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.  If several files are provided, all the statistics for identical
337   functions will be coalesced, so that an overall view of several processes can
338   be considered in a single report.  If additional files need to be combined
339   with data in an existing :class:`~pstats.Stats` object, the
340   :meth:`~pstats.Stats.add` method can be used.
341
342   Instead of reading the profile data from a file, a :class:`cProfile.Profile`
343   or :class:`profile.Profile` object can be used as the profile data source.
344
345   :class:`Stats` objects have the following methods:
346
347   .. method:: strip_dirs()
348
349      This method for the :class:`Stats` class removes all leading path
350      information from file names.  It is very useful in reducing the size of
351      the printout to fit within (close to) 80 columns.  This method modifies
352      the object, and the stripped information is lost.  After performing a
353      strip operation, the object is considered to have its entries in a
354      "random" order, as it was just after object initialization and loading.
355      If :meth:`~pstats.Stats.strip_dirs` causes two function names to be
356      indistinguishable (they are on the same line of the same filename, and
357      have the same function name), then the statistics for these two entries
358      are accumulated into a single entry.
359
360
361   .. method:: add(*filenames)
362
363      This method of the :class:`Stats` class accumulates additional profiling
364      information into the current profiling object.  Its arguments should refer
365      to filenames created by the corresponding version of :func:`profile.run`
366      or :func:`cProfile.run`. Statistics for identically named (re: file, line,
367      name) functions are automatically accumulated into single function
368      statistics.
369
370
371   .. method:: dump_stats(filename)
372
373      Save the data loaded into the :class:`Stats` object to a file named
374      *filename*.  The file is created if it does not exist, and is overwritten
375      if it already exists.  This is equivalent to the method of the same name
376      on the :class:`profile.Profile` and :class:`cProfile.Profile` classes.
377
378   .. versionadded:: 2.3
379
380
381   .. method:: sort_stats(*keys)
382
383      This method modifies the :class:`Stats` object by sorting it according to
384      the supplied criteria.  The argument is typically a string identifying the
385      basis of a sort (example: ``'time'`` or ``'name'``).
386
387      When more than one key is provided, then additional keys are used as
388      secondary criteria when there is equality in all keys selected before
389      them.  For example, ``sort_stats('name', 'file')`` will sort all the
390      entries according to their function name, and resolve all ties (identical
391      function names) by sorting by file name.
392
393      Abbreviations can be used for any key names, as long as the abbreviation
394      is unambiguous.  The following are the keys currently defined:
395
396      +------------------+----------------------+
397      | Valid Arg        | Meaning              |
398      +==================+======================+
399      | ``'calls'``      | call count           |
400      +------------------+----------------------+
401      | ``'cumulative'`` | cumulative time      |
402      +------------------+----------------------+
403      | ``'cumtime'``    | cumulative time      |
404      +------------------+----------------------+
405      | ``'file'``       | file name            |
406      +------------------+----------------------+
407      | ``'filename'``   | file name            |
408      +------------------+----------------------+
409      | ``'module'``     | file name            |
410      +------------------+----------------------+
411      | ``'ncalls'``     | call count           |
412      +------------------+----------------------+
413      | ``'pcalls'``     | primitive call count |
414      +------------------+----------------------+
415      | ``'line'``       | line number          |
416      +------------------+----------------------+
417      | ``'name'``       | function name        |
418      +------------------+----------------------+
419      | ``'nfl'``        | name/file/line       |
420      +------------------+----------------------+
421      | ``'stdname'``    | standard name        |
422      +------------------+----------------------+
423      | ``'time'``       | internal time        |
424      +------------------+----------------------+
425      | ``'tottime'``    | internal time        |
426      +------------------+----------------------+
427
428      Note that all sorts on statistics are in descending order (placing most
429      time consuming items first), where as name, file, and line number searches
430      are in ascending order (alphabetical). The subtle distinction between
431      ``'nfl'`` and ``'stdname'`` is that the standard name is a sort of the
432      name as printed, which means that the embedded line numbers get compared
433      in an odd way.  For example, lines 3, 20, and 40 would (if the file names
434      were the same) appear in the string order 20, 3 and 40.  In contrast,
435      ``'nfl'`` does a numeric compare of the line numbers.  In fact,
436      ``sort_stats('nfl')`` is the same as ``sort_stats('name', 'file',
437      'line')``.
438
439      For backward-compatibility reasons, the numeric arguments ``-1``, ``0``,
440      ``1``, and ``2`` are permitted.  They are interpreted as ``'stdname'``,
441      ``'calls'``, ``'time'``, and ``'cumulative'`` respectively.  If this old
442      style format (numeric) is used, only one sort key (the numeric key) will
443      be used, and additional arguments will be silently ignored.
444
445      .. For compatibility with the old profiler.
446
447
448   .. method:: reverse_order()
449
450      This method for the :class:`Stats` class reverses the ordering of the
451      basic list within the object.  Note that by default ascending vs
452      descending order is properly selected based on the sort key of choice.
453
454      .. This method is provided primarily for compatibility with the old
455         profiler.
456
457
458   .. method:: print_stats(*restrictions)
459
460      This method for the :class:`Stats` class prints out a report as described
461      in the :func:`profile.run` definition.
462
463      The order of the printing is based on the last
464      :meth:`~pstats.Stats.sort_stats` operation done on the object (subject to
465      caveats in :meth:`~pstats.Stats.add` and
466      :meth:`~pstats.Stats.strip_dirs`).
467
468      The arguments provided (if any) can be used to limit the list down to the
469      significant entries.  Initially, the list is taken to be the complete set
470      of profiled functions.  Each restriction is either an integer (to select a
471      count of lines), or a decimal fraction between 0.0 and 1.0 inclusive (to
472      select a percentage of lines), or a regular expression (to pattern match
473      the standard name that is printed.  If several restrictions are provided,
474      then they are applied sequentially.  For example::
475
476         print_stats(.1, 'foo:')
477
478      would first limit the printing to first 10% of list, and then only print
479      functions that were part of filename :file:`.\*foo:`.  In contrast, the
480      command::
481
482         print_stats('foo:', .1)
483
484      would limit the list to all functions having file names :file:`.\*foo:`,
485      and then proceed to only print the first 10% of them.
486
487
488   .. method:: print_callers(*restrictions)
489
490      This method for the :class:`Stats` class prints a list of all functions
491      that called each function in the profiled database.  The ordering is
492      identical to that provided by :meth:`~pstats.Stats.print_stats`, and the
493      definition of the restricting argument is also identical.  Each caller is
494      reported on its own line.  The format differs slightly depending on the
495      profiler that produced the stats:
496
497      * With :mod:`profile`, a number is shown in parentheses after each caller
498        to show how many times this specific call was made.  For convenience, a
499        second non-parenthesized number repeats the cumulative time spent in the
500        function at the right.
501
502      * With :mod:`cProfile`, each caller is preceded by three numbers: the
503        number of times this specific call was made, and the total and
504        cumulative times spent in the current function while it was invoked by
505        this specific caller.
506
507
508   .. method:: print_callees(*restrictions)
509
510      This method for the :class:`Stats` class prints a list of all function
511      that were called by the indicated function.  Aside from this reversal of
512      direction of calls (re: called vs was called by), the arguments and
513      ordering are identical to the :meth:`~pstats.Stats.print_callers` method.
514
515
516.. _deterministic-profiling:
517
518What Is Deterministic Profiling?
519================================
520
521:dfn:`Deterministic profiling` is meant to reflect the fact that all *function
522call*, *function return*, and *exception* events are monitored, and precise
523timings are made for the intervals between these events (during which time the
524user's code is executing).  In contrast, :dfn:`statistical profiling` (which is
525not done by this module) randomly samples the effective instruction pointer, and
526deduces where time is being spent.  The latter technique traditionally involves
527less overhead (as the code does not need to be instrumented), but provides only
528relative indications of where time is being spent.
529
530In Python, since there is an interpreter active during execution, the presence
531of instrumented code is not required to do deterministic profiling.  Python
532automatically provides a :dfn:`hook` (optional callback) for each event.  In
533addition, the interpreted nature of Python tends to add so much overhead to
534execution, that deterministic profiling tends to only add small processing
535overhead in typical applications.  The result is that deterministic profiling is
536not that expensive, yet provides extensive run time statistics about the
537execution of a Python program.
538
539Call count statistics can be used to identify bugs in code (surprising counts),
540and to identify possible inline-expansion points (high call counts).  Internal
541time statistics can be used to identify "hot loops" that should be carefully
542optimized.  Cumulative time statistics should be used to identify high level
543errors in the selection of algorithms.  Note that the unusual handling of
544cumulative times in this profiler allows statistics for recursive
545implementations of algorithms to be directly compared to iterative
546implementations.
547
548
549.. _profile-limitations:
550
551Limitations
552===========
553
554One limitation has to do with accuracy of timing information. There is a
555fundamental problem with deterministic profilers involving accuracy.  The most
556obvious restriction is that the underlying "clock" is only ticking at a rate
557(typically) of about .001 seconds.  Hence no measurements will be more accurate
558than the underlying clock.  If enough measurements are taken, then the "error"
559will tend to average out. Unfortunately, removing this first error induces a
560second source of error.
561
562The second problem is that it "takes a while" from when an event is dispatched
563until the profiler's call to get the time actually *gets* the state of the
564clock.  Similarly, there is a certain lag when exiting the profiler event
565handler from the time that the clock's value was obtained (and then squirreled
566away), until the user's code is once again executing.  As a result, functions
567that are called many times, or call many functions, will typically accumulate
568this error. The error that accumulates in this fashion is typically less than
569the accuracy of the clock (less than one clock tick), but it *can* accumulate
570and become very significant.
571
572The problem is more important with :mod:`profile` than with the lower-overhead
573:mod:`cProfile`.  For this reason, :mod:`profile` provides a means of
574calibrating itself for a given platform so that this error can be
575probabilistically (on the average) removed. After the profiler is calibrated, it
576will be more accurate (in a least square sense), but it will sometimes produce
577negative numbers (when call counts are exceptionally low, and the gods of
578probability work against you :-). )  Do *not* be alarmed by negative numbers in
579the profile.  They should *only* appear if you have calibrated your profiler,
580and the results are actually better than without calibration.
581
582
583.. _profile-calibration:
584
585Calibration
586===========
587
588The profiler of the :mod:`profile` module subtracts a constant from each event
589handling time to compensate for the overhead of calling the time function, and
590socking away the results.  By default, the constant is 0. The following
591procedure can be used to obtain a better constant for a given platform (see
592:ref:`profile-limitations`). ::
593
594   import profile
595   pr = profile.Profile()
596   for i in range(5):
597       print pr.calibrate(10000)
598
599The method executes the number of Python calls given by the argument, directly
600and again under the profiler, measuring the time for both. It then computes the
601hidden overhead per profiler event, and returns that as a float.  For example,
602on a 1.8Ghz Intel Core i5 running Mac OS X, and using Python's time.clock() as
603the timer, the magical number is about 4.04e-6.
604
605The object of this exercise is to get a fairly consistent result. If your
606computer is *very* fast, or your timer function has poor resolution, you might
607have to pass 100000, or even 1000000, to get consistent results.
608
609When you have a consistent answer, there are three ways you can use it: [#]_ ::
610
611   import profile
612
613   # 1. Apply computed bias to all Profile instances created hereafter.
614   profile.Profile.bias = your_computed_bias
615
616   # 2. Apply computed bias to a specific Profile instance.
617   pr = profile.Profile()
618   pr.bias = your_computed_bias
619
620   # 3. Specify computed bias in instance constructor.
621   pr = profile.Profile(bias=your_computed_bias)
622
623If you have a choice, you are better off choosing a smaller constant, and then
624your results will "less often" show up as negative in profile statistics.
625
626.. _profile-timers:
627
628Using a custom timer
629====================
630
631If you want to change how current time is determined (for example, to force use
632of wall-clock time or elapsed process time), pass the timing function you want
633to the :class:`Profile` class constructor::
634
635    pr = profile.Profile(your_time_func)
636
637The resulting profiler will then call ``your_time_func``. Depending on whether
638you are using :class:`profile.Profile` or :class:`cProfile.Profile`,
639``your_time_func``'s return value will be interpreted differently:
640
641:class:`profile.Profile`
642   ``your_time_func`` should return a single number, or a list of numbers whose
643   sum is the current time (like what :func:`os.times` returns).  If the
644   function returns a single time number, or the list of returned numbers has
645   length 2, then you will get an especially fast version of the dispatch
646   routine.
647
648   Be warned that you should calibrate the profiler class for the timer function
649   that you choose (see :ref:`profile-calibration`).  For most machines, a timer
650   that returns a lone integer value will provide the best results in terms of
651   low overhead during profiling.  (:func:`os.times` is *pretty* bad, as it
652   returns a tuple of floating point values).  If you want to substitute a
653   better timer in the cleanest fashion, derive a class and hardwire a
654   replacement dispatch method that best handles your timer call, along with the
655   appropriate calibration constant.
656
657:class:`cProfile.Profile`
658   ``your_time_func`` should return a single number.  If it returns integers,
659   you can also invoke the class constructor with a second argument specifying
660   the real duration of one unit of time.  For example, if
661   ``your_integer_time_func`` returns times measured in thousands of seconds,
662   you would construct the :class:`Profile` instance as follows::
663
664      pr = cProfile.Profile(your_integer_time_func, 0.001)
665
666   As the :class:`cProfile.Profile` class cannot be calibrated, custom timer
667   functions should be used with care and should be as fast as possible.  For
668   the best results with a custom timer, it might be necessary to hard-code it
669   in the C source of the internal :mod:`_lsprof` module.
670
671
672.. rubric:: Footnotes
673
674.. [#] Prior to Python 2.2, it was necessary to edit the profiler source code to
675   embed the bias as a literal number.  You still can, but that method is no longer
676   described, because no longer needed.
677