| |
| .. _profile: |
| |
| ******************** |
| The Python Profilers |
| ******************** |
| |
| .. sectionauthor:: James Roskind |
| |
| |
| .. index:: single: InfoSeek Corporation |
| |
| Copyright © 1994, by InfoSeek Corporation, all rights reserved. |
| |
| Written by James Roskind. [#]_ |
| |
| 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. |
| |
| .. _profiler-introduction: |
| |
| Introduction to the profilers |
| ============================= |
| |
| .. index:: |
| single: deterministic profiling |
| single: profiling, deterministic |
| |
| 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 |
| :mod:`cProfile`, :mod:`profile` and :mod:`pstats`. This profiler |
| provides :dfn:`deterministic profiling` of Python programs. It also |
| provides a series of report generation tools to allow users to rapidly |
| examine the results of a profile operation. |
| |
| The Python standard library provides two different profilers: |
| |
| #. :mod:`cProfile` is recommended for most users; it's a C extension |
| with reasonable overhead |
| that makes it suitable for profiling long-running programs. |
| Based on :mod:`lsprof`, |
| contributed by Brett Rosen and Ted Czotter. |
| |
| #. :mod:`profile`, a pure Python module whose interface is imitated by |
| :mod:`cProfile`. Adds significant overhead to profiled programs. |
| If you're trying to extend |
| the profiler in some way, the task might be easier with this module. |
| Copyright © 1994, by InfoSeek Corporation. |
| |
| The :mod:`profile` and :mod:`cProfile` modules export the same interface, so |
| they are mostly interchangeable; :mod:`cProfile` has a much lower overhead but |
| is newer and might not be available on all systems. |
| :mod:`cProfile` is really a compatibility layer on top of the internal |
| <<<<<<< .working |
| :mod:`_lsprof` module. |
| ======= |
| :mod:`_lsprof` module. The :mod:`hotshot` module is reserved for specialized |
| usage. |
| >>>>>>> .merge-right.r62379 |
| |
| |
| .. _profile-instant: |
| |
| Instant User's 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 :func:`foo`, you would add |
| the following to your module:: |
| |
| import cProfile |
| cProfile.run('foo()') |
| |
| (Use :mod:`profile` instead of :mod:`cProfile` if the latter is not available on |
| your system.) |
| |
| The above action would cause :func:`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 :func:`run` function:: |
| |
| import cProfile |
| cProfile.run('foo()', 'fooprof') |
| |
| The file :file:`cProfile.py` can also be invoked as a script to profile another |
| script. For example:: |
| |
| python -m cProfile myscript.py |
| |
| :file:`cProfile.py` accepts two optional arguments on the command line:: |
| |
| cProfile.py [-o output_file] [-s sort_order] |
| |
| :option:`-s` only applies to standard output (:option:`-o` is not supplied). |
| Look in the :class:`Stats` documentation for valid sort values. |
| |
| When you wish to review the profile, you should use the methods in the |
| :mod:`pstats` module. Typically you would load the statistics data as follows:: |
| |
| import pstats |
| p = pstats.Stats('fooprof') |
| |
| The class :class:`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 ``p``. When you ran :func:`cProfile.run` above, what was printed was |
| the result of three method calls:: |
| |
| p.strip_dirs().sort_stats(-1).print_stats() |
| |
| 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. The third method printed out all the statistics. You |
| might try the following sort calls: |
| |
| .. (this is to comply with the semantics of the old profiler). |
| |
| :: |
| |
| p.sort_stats('name') |
| p.print_stats() |
| |
| 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:: |
| |
| p.sort_stats('cumulative').print_stats(10) |
| |
| 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:: |
| |
| p.sort_stats('time').print_stats(10) |
| |
| to sort according to time spent within each function, and then print the |
| statistics for the top ten functions. |
| |
| You might also try:: |
| |
| p.sort_stats('file').print_stats('__init__') |
| |
| This will sort all the statistics by file name, and then print out statistics |
| for only the class init methods (since they are spelled with ``__init__`` in |
| them). As one final example, you could try:: |
| |
| p.sort_stats('time', 'cum').print_stats(.5, 'init') |
| |
| 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: ``.5``) of its original size, then only |
| lines containing ``init`` are maintained, and that sub-sub-list is printed. |
| |
| If you wondered what functions called the above functions, you could now (``p`` |
| is still sorted according to the last criteria) do:: |
| |
| p.print_callers(.5, 'init') |
| |
| 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:: |
| |
| p.print_callees() |
| p.add('fooprof') |
| |
| Invoked as a script, the :mod:`pstats` module is a statistics browser for |
| reading and examining profile dumps. It has a simple line-oriented interface |
| (implemented using :mod:`cmd`) and interactive help. |
| |
| |
| .. _deterministic-profiling: |
| |
| What Is Deterministic Profiling? |
| ================================ |
| |
| :dfn:`Deterministic profiling` is meant to reflect the fact that all *function |
| call*, *function return*, and *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. |
| |
| |
| Reference Manual -- :mod:`profile` and :mod:`cProfile` |
| ====================================================== |
| |
| .. module:: cProfile |
| :synopsis: Python profiler |
| |
| |
| The primary entry point for the profiler is the global function |
| :func:`profile.run` (resp. :func:`cProfile.run`). It is typically used to create |
| any profile information. The reports are formatted and printed using methods of |
| the class :class:`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. |
| |
| |
| .. function:: run(command[, filename]) |
| |
| This function takes a single argument that can be passed to the :func:`exec` |
| function, and an optional file name. In all cases this routine attempts to |
| :func:`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:: |
| |
| 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) |
| ... |
| |
| The first 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: ``Ordered by: standard name``, indicates |
| that the text string in the far right column was used to sort the output. The |
| column headings include: |
| |
| ncalls |
| for the number of calls, |
| |
| tottime |
| for the total time spent in the given function (and excluding time made in calls |
| to sub-functions), |
| |
| percall |
| is the quotient of ``tottime`` divided by ``ncalls`` |
| |
| cumtime |
| is the total time spent in this and all subfunctions (from invocation till |
| exit). This figure is accurate *even* for recursive functions. |
| |
| percall |
| is the quotient of ``cumtime`` divided by primitive calls |
| |
| filename:lineno(function) |
| provides the respective data of each function |
| |
| When there are two numbers in the first column (for example, ``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. |
| |
| |
| .. function:: runctx(command, globals, locals[, filename]) |
| |
| This function is similar to :func:`run`, with added arguments to supply the |
| globals and locals dictionaries for the *command* string. |
| |
| Analysis of the profiler data is done using the :class:`Stats` class. |
| |
| .. note:: |
| |
| The :class:`Stats` class is defined in the :mod:`pstats` module. |
| |
| |
| .. module:: pstats |
| :synopsis: Statistics object for use with the profiler. |
| |
| |
| .. class:: Stats(filename[, stream=sys.stdout[, ...]]) |
| |
| This class constructor creates an instance of a "statistics object" from a |
| *filename* (or set of filenames). :class:`Stats` objects are manipulated by |
| methods, in order to print useful reports. You may specify an alternate output |
| stream by giving the keyword argument, ``stream``. |
| |
| The file selected by the above constructor must have been created by the |
| corresponding version of :mod:`profile` or :mod:`cProfile`. To be specific, |
| there is *no* file compatibility guaranteed with future versions of this |
| profiler, and there is no compatibility with files produced by other profilers. |
| 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 :class:`Stats` object, the :meth:`add` method can be used. |
| |
| .. (such as the old system profiler). |
| |
| |
| .. _profile-stats: |
| |
| The :class:`Stats` Class |
| ------------------------ |
| |
| :class:`Stats` objects have the following methods: |
| |
| |
| .. method:: Stats.strip_dirs() |
| |
| This method for the :class:`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 :meth:`strip_dirs` causes two function names to |
| be indistinguishable (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. |
| |
| |
| .. method:: Stats.add(filename[, ...]) |
| |
| This method of the :class:`Stats` class accumulates additional profiling |
| information into the current profiling object. Its arguments should refer to |
| filenames created by the corresponding version of :func:`profile.run` or |
| :func:`cProfile.run`. Statistics for identically named (re: file, line, name) |
| functions are automatically accumulated into single function statistics. |
| |
| |
| .. method:: Stats.dump_stats(filename) |
| |
| Save the data loaded into the :class:`Stats` object to a file named *filename*. |
| The file is created if it does not exist, and is overwritten if it already |
| exists. This is equivalent to the method of the same name on the |
| :class:`profile.Profile` and :class:`cProfile.Profile` classes. |
| |
| |
| .. method:: Stats.sort_stats(key[, ...]) |
| |
| This method modifies the :class:`Stats` object by sorting it according to the |
| supplied criteria. The argument is typically a string identifying the basis of |
| a sort (example: ``'time'`` or ``'name'``). |
| |
| When more than one key is provided, then additional keys are used as secondary |
| criteria when 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: |
| |
| +------------------+----------------------+ |
| | Valid Arg | Meaning | |
| +==================+======================+ |
| | ``'calls'`` | call count | |
| +------------------+----------------------+ |
| | ``'cumulative'`` | cumulative time | |
| +------------------+----------------------+ |
| | ``'file'`` | file name | |
| +------------------+----------------------+ |
| | ``'module'`` | file name | |
| +------------------+----------------------+ |
| | ``'pcalls'`` | primitive call count | |
| +------------------+----------------------+ |
| | ``'line'`` | line number | |
| +------------------+----------------------+ |
| | ``'name'`` | function name | |
| +------------------+----------------------+ |
| | ``'nfl'`` | name/file/line | |
| +------------------+----------------------+ |
| | ``'stdname'`` | standard name | |
| +------------------+----------------------+ |
| | ``'time'`` | internal time | |
| +------------------+----------------------+ |
| |
| 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 (alphabetical). The subtle distinction between ``'nfl'`` and |
| ``'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, ``'nfl'`` does a numeric compare of the line |
| numbers. In fact, ``sort_stats('nfl')`` is the same as ``sort_stats('name', |
| 'file', 'line')``. |
| |
| For backward-compatibility reasons, the numeric arguments ``-1``, ``0``, ``1``, |
| and ``2`` are permitted. They are interpreted as ``'stdname'``, ``'calls'``, |
| ``'time'``, and ``'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. |
| |
| .. For compatibility with the old profiler, |
| |
| |
| .. method:: Stats.reverse_order() |
| |
| This method for the :class:`Stats` class reverses the ordering of the basic list |
| within the object. Note that by default ascending vs descending order is |
| properly selected based on the sort key of choice. |
| |
| .. This method is provided primarily for compatibility with the old profiler. |
| |
| |
| .. method:: Stats.print_stats([restriction, ...]) |
| |
| This method for the :class:`Stats` class prints out a report as described in the |
| :func:`profile.run` definition. |
| |
| The order of the printing is based on the last :meth:`sort_stats` operation done |
| on the object (subject to caveats in :meth:`add` and :meth:`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; as of Python 1.5b1, this uses the Perl-style regular |
| expression syntax defined by the :mod:`re` module). If several restrictions are |
| provided, then they are applied sequentially. For example:: |
| |
| print_stats(.1, 'foo:') |
| |
| would first limit the printing to first 10% of list, and then only print |
| functions that were part of filename :file:`.\*foo:`. In contrast, the |
| command:: |
| |
| print_stats('foo:', .1) |
| |
| would limit the list to all functions having file names :file:`.\*foo:`, and |
| then proceed to only print the first 10% of them. |
| |
| |
| .. method:: Stats.print_callers([restriction, ...]) |
| |
| This method for the :class:`Stats` class prints a list of all functions that |
| called each function in the profiled database. The ordering is identical to |
| that provided by :meth:`print_stats`, and the definition of the restricting |
| argument is also identical. Each caller is reported on its own line. The |
| format differs slightly depending on the profiler that produced the stats: |
| |
| * With :mod:`profile`, a number is shown in parentheses after each caller to |
| show how many times this specific call was made. For convenience, a second |
| non-parenthesized number repeats the cumulative time spent in the function |
| at the right. |
| |
| * With :mod:`cProfile`, each caller is preceded by three numbers: the number of |
| times this specific call was made, and the total and cumulative times spent in |
| the current function while it was invoked by this specific caller. |
| |
| |
| .. method:: Stats.print_callees([restriction, ...]) |
| |
| This method for the :class:`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 :meth:`print_callers` method. |
| |
| |
| .. _profile-limits: |
| |
| Limitations |
| =========== |
| |
| One 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 |
| than the 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 *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 (less than one clock tick), but it *can* accumulate |
| and become very significant. |
| |
| The problem is more important with :mod:`profile` than with the lower-overhead |
| :mod:`cProfile`. For this reason, :mod:`profile` provides a means of |
| calibrating itself for a given platform so that this error can be |
| probabilistically (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 *not* be alarmed by negative numbers in |
| the profile. They should *only* appear if you have calibrated your profiler, |
| and the results are actually better than without calibration. |
| |
| |
| .. _profile-calibration: |
| |
| Calibration |
| =========== |
| |
| The profiler of the :mod:`profile` module subtracts a constant from each event |
| handling time to compensate for the overhead of calling the time function, and |
| socking away the results. By default, the constant is 0. The following |
| procedure can be used to obtain a better constant for a given platform (see |
| discussion in section Limitations above). :: |
| |
| import profile |
| pr = profile.Profile() |
| for i in range(5): |
| print(pr.calibrate(10000)) |
| |
| The method executes the number of Python calls given by the argument, directly |
| and again under the profiler, measuring the time for both. It then computes the |
| hidden overhead per profiler event, and returns that as a float. For example, |
| on an 800 MHz Pentium running Windows 2000, and using Python's time.clock() as |
| the timer, the magical number is about 12.5e-6. |
| |
| The object of this exercise is to get a fairly consistent result. If your |
| computer is *very* fast, or your timer function has poor resolution, you might |
| have to pass 100000, or even 1000000, to get consistent results. |
| |
| When you have a consistent answer, there are three ways you can use it: [#]_ :: |
| |
| import profile |
| |
| # 1. Apply computed bias to all Profile instances created hereafter. |
| profile.Profile.bias = your_computed_bias |
| |
| # 2. Apply computed bias to a specific Profile instance. |
| pr = profile.Profile() |
| pr.bias = your_computed_bias |
| |
| # 3. Specify computed bias in instance constructor. |
| pr = profile.Profile(bias=your_computed_bias) |
| |
| If you have a choice, you are better off choosing a smaller constant, and then |
| your results will "less often" show up as negative in profile statistics. |
| |
| |
| .. _profiler-extensions: |
| |
| Extensions --- Deriving Better Profilers |
| ======================================== |
| |
| The :class:`Profile` class of both modules, :mod:`profile` and :mod:`cProfile`, |
| were written so that derived classes could be developed to extend the profiler. |
| The details are not described here, as doing this successfully requires an |
| expert understanding of how the :class:`Profile` class works internally. Study |
| the source code of the module carefully if you want to pursue this. |
| |
| If all you want to do is change how current time is determined (for example, to |
| force use of wall-clock time or elapsed process time), pass the timing function |
| you want to the :class:`Profile` class constructor:: |
| |
| pr = profile.Profile(your_time_func) |
| |
| The resulting profiler will then call :func:`your_time_func`. |
| |
| :class:`profile.Profile` |
| :func:`your_time_func` should return a single number, or a list of numbers whose |
| sum is the current time (like what :func:`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 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. |
| (:func:`os.times` is *pretty* bad, as it returns a tuple of floating point |
| values). If you want to substitute a better timer in the cleanest fashion, |
| derive a class and hardwire a replacement dispatch method that best handles your |
| timer call, along with the appropriate calibration constant. |
| |
| :class:`cProfile.Profile` |
| :func:`your_time_func` should return a single number. If it returns plain |
| integers, you can also invoke the class constructor with a second argument |
| specifying the real duration of one unit of time. For example, if |
| :func:`your_integer_time_func` returns times measured in thousands of seconds, |
| you would constuct the :class:`Profile` instance as follows:: |
| |
| pr = profile.Profile(your_integer_time_func, 0.001) |
| |
| As the :mod:`cProfile.Profile` class cannot be calibrated, custom timer |
| functions should be used with care and should be as fast as possible. For the |
| best results with a custom timer, it might be necessary to hard-code it in the C |
| source of the internal :mod:`_lsprof` module. |
| |
| .. rubric:: Footnotes |
| |
| .. [#] Updated and converted to LaTeX by Guido van Rossum. Further updated by Armin |
| Rigo to integrate the documentation for the new :mod:`cProfile` module of Python |
| 2.5. |
| |
| .. [#] Prior to Python 2.2, it was necessary to edit the profiler source code to embed |
| the bias as a literal number. You still can, but that method is no longer |
| described, because no longer needed. |
| |