Warnings are raised if the slowest timing is greater than 1e-6

It is often irritating when you do something like %timeit 3 and
a warning pops up. This assumes that any timing less than a
microsecond does not really matter

IPython/core/magics/execution.py

@@ -1,1329 +1,1332 b''
 # -*- coding: utf-8 -*-
 """Implementation of execution-related magic functions.
 """
 from __future__ import print_function
 #-----------------------------------------------------------------------------
 #  Copyright (c) 2012 The IPython Development Team.
 #
 #  Distributed under the terms of the Modified BSD License.
 #
 #  The full license is in the file COPYING.txt, distributed with this software.
 #-----------------------------------------------------------------------------
 
 #-----------------------------------------------------------------------------
 # Imports
 #-----------------------------------------------------------------------------
 
 # Stdlib
 import ast
 import bdb
 import os
 import sys
 import time
 from pdb import Restart
 
 # cProfile was added in Python2.5
 try:
     import cProfile as profile
     import pstats
 except ImportError:
     # profile isn't bundled by default in Debian for license reasons
     try:
         import profile, pstats
     except ImportError:
         profile = pstats = None
 
 # Our own packages
 from IPython.core import debugger, oinspect
 from IPython.core import magic_arguments
 from IPython.core import page
 from IPython.core.error import UsageError
 from IPython.core.macro import Macro
 from IPython.core.magic import (Magics, magics_class, line_magic, cell_magic,
                                 line_cell_magic, on_off, needs_local_scope)
 from IPython.testing.skipdoctest import skip_doctest
 from IPython.utils import py3compat
 from IPython.utils.py3compat import builtin_mod, iteritems, PY3
 from IPython.utils.contexts import preserve_keys
 from IPython.utils.io import capture_output
 from IPython.utils.ipstruct import Struct
 from IPython.utils.module_paths import find_mod
 from IPython.utils.path import get_py_filename, unquote_filename, shellglob
 from IPython.utils.timing import clock, clock2
 from IPython.utils.warn import warn, error
 
 if PY3:
     from io import StringIO
 else:
     from StringIO import StringIO
 
 #-----------------------------------------------------------------------------
 # Magic implementation classes
 #-----------------------------------------------------------------------------
 
 
 class TimeitResult(object):
     """
     Object returned by the timeit magic with info about the run.
 
     Contain the following attributes :
 
     loops: (int) number of loop done per measurement
     repeat: (int) number of time the mesurement has been repeated
     best: (float) best execusion time / number
     all_runs: (list of float) execusion time of each run (in s)
     compile_time: (float) time of statement compilation (s)
 
     """
 
     def __init__(self, loops, repeat, best, all_runs, compile_time, precision):
         self.loops = loops
         self.repeat = repeat
         self.best = best
         self.all_runs = all_runs
         self.compile_time = compile_time
         self._precision = precision
 
     def _repr_pretty_(self, p , cycle):
          unic =  u"%d loops, best of %d: %s per loop" % (self.loops, self.repeat,
                                             _format_time(self.best, self._precision))
          p.text(u'<TimeitResult : '+unic+u'>')
 
 
 class TimeitTemplateFiller(ast.NodeTransformer):
     """Fill in the AST template for timing execution.
 
     This is quite closely tied to the template definition, which is in
     :meth:`ExecutionMagics.timeit`.
     """
     def __init__(self, ast_setup, ast_stmt):
         self.ast_setup = ast_setup
         self.ast_stmt = ast_stmt
 
     def visit_FunctionDef(self, node):
         "Fill in the setup statement"
         self.generic_visit(node)
         if node.name == "inner":
             node.body[:1] = self.ast_setup.body
 
         return node
 
     def visit_For(self, node):
         "Fill in the statement to be timed"
         if getattr(getattr(node.body[0], 'value', None), 'id', None) == 'stmt':
             node.body = self.ast_stmt.body
         return node
 
 
 @magics_class
 class ExecutionMagics(Magics):
     """Magics related to code execution, debugging, profiling, etc.
 
     """
 
     def __init__(self, shell):
         super(ExecutionMagics, self).__init__(shell)
         if profile is None:
             self.prun = self.profile_missing_notice
         # Default execution function used to actually run user code.
         self.default_runner = None
 
     def profile_missing_notice(self, *args, **kwargs):
         error("""\
 The profile module could not be found. It has been removed from the standard
 python packages because of its non-free license. To use profiling, install the
 python-profiler package from non-free.""")
 
     @skip_doctest
     @line_cell_magic
     def prun(self, parameter_s='', cell=None):
 
         """Run a statement through the python code profiler.
 
         Usage, in line mode:
           %prun [options] statement
 
         Usage, in cell mode:
           %%prun [options] [statement]
           code...
           code...
 
         In cell mode, the additional code lines are appended to the (possibly
         empty) statement in the first line.  Cell mode allows you to easily
         profile multiline blocks without having to put them in a separate
         function.
 
         The given statement (which doesn't require quote marks) is run via the
         python profiler in a manner similar to the profile.run() function.
         Namespaces are internally managed to work correctly; profile.run
         cannot be used in IPython because it makes certain assumptions about
         namespaces which do not hold under IPython.
 
         Options:
 
         -l <limit>
           you can place restrictions on what or how much of the
           profile gets printed. The limit value can be:
 
              * A string: only information for function names containing this string
                is printed.
 
              * An integer: only these many lines are printed.
 
              * A float (between 0 and 1): this fraction of the report is printed
                (for example, use a limit of 0.4 to see the topmost 40% only).
 
           You can combine several limits with repeated use of the option. For
           example, ``-l __init__ -l 5`` will print only the topmost 5 lines of
           information about class constructors.
 
         -r
           return the pstats.Stats object generated by the profiling. This
           object has all the information about the profile in it, and you can
           later use it for further analysis or in other functions.
 
         -s <key>
           sort profile by given key. You can provide more than one key
           by using the option several times: '-s key1 -s key2 -s key3...'. The
           default sorting key is 'time'.
 
           The following is copied verbatim from the profile documentation
           referenced below:
 
           When more than one key is provided, additional keys are used as
           secondary criteria when the there is equality in all keys selected
           before them.
 
           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 (i.e., 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").
 
         -T <filename>
           save profile results as shown on screen to a text
           file. The profile is still shown on screen.
 
         -D <filename>
           save (via dump_stats) profile statistics to given
           filename. This data is in a format understood by the pstats module, and
           is generated by a call to the dump_stats() method of profile
           objects. The profile is still shown on screen.
 
         -q
           suppress output to the pager.  Best used with -T and/or -D above.
 
         If you want to run complete programs under the profiler's control, use
         ``%run -p [prof_opts] filename.py [args to program]`` where prof_opts
         contains profiler specific options as described here.
 
         You can read the complete documentation for the profile module with::
 
           In [1]: import profile; profile.help()
         """
         opts, arg_str = self.parse_options(parameter_s, 'D:l:rs:T:q',
                                            list_all=True, posix=False)
         if cell is not None:
             arg_str += '\n' + cell
         arg_str = self.shell.input_splitter.transform_cell(arg_str)
         return self._run_with_profiler(arg_str, opts, self.shell.user_ns)
 
     def _run_with_profiler(self, code, opts, namespace):
         """
         Run `code` with profiler.  Used by ``%prun`` and ``%run -p``.
 
         Parameters
         ----------
         code : str
             Code to be executed.
         opts : Struct
             Options parsed by `self.parse_options`.
         namespace : dict
             A dictionary for Python namespace (e.g., `self.shell.user_ns`).
 
         """
 
         # Fill default values for unspecified options:
         opts.merge(Struct(D=[''], l=[], s=['time'], T=['']))
 
         prof = profile.Profile()
         try:
             prof = prof.runctx(code, namespace, namespace)
             sys_exit = ''
         except SystemExit:
             sys_exit = """*** SystemExit exception caught in code being profiled."""
 
         stats = pstats.Stats(prof).strip_dirs().sort_stats(*opts.s)
 
         lims = opts.l
         if lims:
             lims = []  # rebuild lims with ints/floats/strings
             for lim in opts.l:
                 try:
                     lims.append(int(lim))
                 except ValueError:
                     try:
                         lims.append(float(lim))
                     except ValueError:
                         lims.append(lim)
 
         # Trap output.
         stdout_trap = StringIO()
         stats_stream = stats.stream
         try:
             stats.stream = stdout_trap
             stats.print_stats(*lims)
         finally:
             stats.stream = stats_stream
 
         output = stdout_trap.getvalue()
         output = output.rstrip()
 
         if 'q' not in opts:
             page.page(output)
         print(sys_exit, end=' ')
 
         dump_file = opts.D[0]
         text_file = opts.T[0]
         if dump_file:
             dump_file = unquote_filename(dump_file)
             prof.dump_stats(dump_file)
             print('\n*** Profile stats marshalled to file',\
                   repr(dump_file)+'.',sys_exit)
         if text_file:
             text_file = unquote_filename(text_file)
             pfile = open(text_file,'w')
             pfile.write(output)
             pfile.close()
             print('\n*** Profile printout saved to text file',\
                   repr(text_file)+'.',sys_exit)
 
         if 'r' in opts:
             return stats
         else:
             return None
 
     @line_magic
     def pdb(self, parameter_s=''):
         """Control the automatic calling of the pdb interactive debugger.
 
         Call as '%pdb on', '%pdb 1', '%pdb off' or '%pdb 0'. If called without
         argument it works as a toggle.
 
         When an exception is triggered, IPython can optionally call the
         interactive pdb debugger after the traceback printout. %pdb toggles
         this feature on and off.
 
         The initial state of this feature is set in your configuration
         file (the option is ``InteractiveShell.pdb``).
 
         If you want to just activate the debugger AFTER an exception has fired,
         without having to type '%pdb on' and rerunning your code, you can use
         the %debug magic."""
 
         par = parameter_s.strip().lower()
 
         if par:
             try:
                 new_pdb = {'off':0,'0':0,'on':1,'1':1}[par]
             except KeyError:
                 print ('Incorrect argument. Use on/1, off/0, '
                        'or nothing for a toggle.')
                 return
         else:
             # toggle
             new_pdb = not self.shell.call_pdb
 
         # set on the shell
         self.shell.call_pdb = new_pdb
         print('Automatic pdb calling has been turned',on_off(new_pdb))
 
     @skip_doctest
     @magic_arguments.magic_arguments()
     @magic_arguments.argument('--breakpoint', '-b', metavar='FILE:LINE',
         help="""
         Set break point at LINE in FILE.
         """
     )
     @magic_arguments.argument('statement', nargs='*',
         help="""
         Code to run in debugger.
         You can omit this in cell magic mode.
         """
     )
     @line_cell_magic
     def debug(self, line='', cell=None):
         """Activate the interactive debugger.
 
         This magic command support two ways of activating debugger.
         One is to activate debugger before executing code.  This way, you
         can set a break point, to step through the code from the point.
         You can use this mode by giving statements to execute and optionally
         a breakpoint.
 
         The other one is to activate debugger in post-mortem mode.  You can
         activate this mode simply running %debug without any argument.
         If an exception has just occurred, this lets you inspect its stack
         frames interactively.  Note that this will always work only on the last
         traceback that occurred, so you must call this quickly after an
         exception that you wish to inspect has fired, because if another one
         occurs, it clobbers the previous one.
 
         If you want IPython to automatically do this on every exception, see
         the %pdb magic for more details.
         """
         args = magic_arguments.parse_argstring(self.debug, line)
 
         if not (args.breakpoint or args.statement or cell):
             self._debug_post_mortem()
         else:
             code = "\n".join(args.statement)
             if cell:
                 code += "\n" + cell
             self._debug_exec(code, args.breakpoint)
 
     def _debug_post_mortem(self):
         self.shell.debugger(force=True)
 
     def _debug_exec(self, code, breakpoint):
         if breakpoint:
             (filename, bp_line) = breakpoint.split(':', 1)
             bp_line = int(bp_line)
         else:
             (filename, bp_line) = (None, None)
         self._run_with_debugger(code, self.shell.user_ns, filename, bp_line)
 
     @line_magic
     def tb(self, s):
         """Print the last traceback with the currently active exception mode.
 
         See %xmode for changing exception reporting modes."""
         self.shell.showtraceback()
 
     @skip_doctest
     @line_magic
     def run(self, parameter_s='', runner=None,
                   file_finder=get_py_filename):
         """Run the named file inside IPython as a program.
 
         Usage::
         
           %run [-n -i -e -G]
                [( -t [-N<N>] | -d [-b<N>] | -p [profile options] )]
                ( -m mod | file ) [args]
 
         Parameters after the filename are passed as command-line arguments to
         the program (put in sys.argv). Then, control returns to IPython's
         prompt.
 
         This is similar to running at a system prompt ``python file args``,
         but with the advantage of giving you IPython's tracebacks, and of
         loading all variables into your interactive namespace for further use
         (unless -p is used, see below).
 
         The file is executed in a namespace initially consisting only of
         ``__name__=='__main__'`` and sys.argv constructed as indicated. It thus
         sees its environment as if it were being run as a stand-alone program
         (except for sharing global objects such as previously imported
         modules). But after execution, the IPython interactive namespace gets
         updated with all variables defined in the program (except for __name__
         and sys.argv). This allows for very convenient loading of code for
         interactive work, while giving each program a 'clean sheet' to run in.
 
         Arguments are expanded using shell-like glob match.  Patterns
         '*', '?', '[seq]' and '[!seq]' can be used.  Additionally,
         tilde '~' will be expanded into user's home directory.  Unlike
         real shells, quotation does not suppress expansions.  Use
         *two* back slashes (e.g. ``\\\\*``) to suppress expansions.
         To completely disable these expansions, you can use -G flag.
 
         Options:
 
         -n
           __name__ is NOT set to '__main__', but to the running file's name
           without extension (as python does under import).  This allows running
           scripts and reloading the definitions in them without calling code
           protected by an ``if __name__ == "__main__"`` clause.
 
         -i
           run the file in IPython's namespace instead of an empty one. This
           is useful if you are experimenting with code written in a text editor
           which depends on variables defined interactively.
 
         -e
           ignore sys.exit() calls or SystemExit exceptions in the script
           being run.  This is particularly useful if IPython is being used to
           run unittests, which always exit with a sys.exit() call.  In such
           cases you are interested in the output of the test results, not in
           seeing a traceback of the unittest module.
 
         -t
           print timing information at the end of the run.  IPython will give
           you an estimated CPU time consumption for your script, which under
           Unix uses the resource module to avoid the wraparound problems of
           time.clock().  Under Unix, an estimate of time spent on system tasks
           is also given (for Windows platforms this is reported as 0.0).
 
         If -t is given, an additional ``-N<N>`` option can be given, where <N>
         must be an integer indicating how many times you want the script to
         run.  The final timing report will include total and per run results.
 
         For example (testing the script uniq_stable.py)::
 
             In [1]: run -t uniq_stable
 
             IPython CPU timings (estimated):
               User  :    0.19597 s.
               System:        0.0 s.
 
             In [2]: run -t -N5 uniq_stable
 
             IPython CPU timings (estimated):
             Total runs performed: 5
               Times :      Total       Per run
               User  :   0.910862 s,  0.1821724 s.
               System:        0.0 s,        0.0 s.
 
         -d
           run your program under the control of pdb, the Python debugger.
           This allows you to execute your program step by step, watch variables,
           etc.  Internally, what IPython does is similar to calling::
 
               pdb.run('execfile("YOURFILENAME")')
 
           with a breakpoint set on line 1 of your file.  You can change the line
           number for this automatic breakpoint to be <N> by using the -bN option
           (where N must be an integer). For example::
 
               %run -d -b40 myscript
 
           will set the first breakpoint at line 40 in myscript.py.  Note that
           the first breakpoint must be set on a line which actually does
           something (not a comment or docstring) for it to stop execution.
 
           Or you can specify a breakpoint in a different file::
 
               %run -d -b myotherfile.py:20 myscript
 
           When the pdb debugger starts, you will see a (Pdb) prompt.  You must
           first enter 'c' (without quotes) to start execution up to the first
           breakpoint.
 
           Entering 'help' gives information about the use of the debugger.  You
           can easily see pdb's full documentation with "import pdb;pdb.help()"
           at a prompt.
 
         -p
           run program under the control of the Python profiler module (which
           prints a detailed report of execution times, function calls, etc).
 
           You can pass other options after -p which affect the behavior of the
           profiler itself. See the docs for %prun for details.
 
           In this mode, the program's variables do NOT propagate back to the
           IPython interactive namespace (because they remain in the namespace
           where the profiler executes them).
 
           Internally this triggers a call to %prun, see its documentation for
           details on the options available specifically for profiling.
 
         There is one special usage for which the text above doesn't apply:
         if the filename ends with .ipy[nb], the file is run as ipython script,
         just as if the commands were written on IPython prompt.
 
         -m
           specify module name to load instead of script path. Similar to
           the -m option for the python interpreter. Use this option last if you
           want to combine with other %run options. Unlike the python interpreter
           only source modules are allowed no .pyc or .pyo files.
           For example::
 
               %run -m example
 
           will run the example module.
 
         -G
           disable shell-like glob expansion of arguments.
 
         """
 
         # get arguments and set sys.argv for program to be run.
         opts, arg_lst = self.parse_options(parameter_s,
                                            'nidtN:b:pD:l:rs:T:em:G',
                                            mode='list', list_all=1)
         if "m" in opts:
             modulename = opts["m"][0]
             modpath = find_mod(modulename)
             if modpath is None:
                 warn('%r is not a valid modulename on sys.path'%modulename)
                 return
             arg_lst = [modpath] + arg_lst
         try:
             filename = file_finder(arg_lst[0])
         except IndexError:
             warn('you must provide at least a filename.')
             print('\n%run:\n', oinspect.getdoc(self.run))
             return
         except IOError as e:
             try:
                 msg = str(e)
             except UnicodeError:
                 msg = e.message
             error(msg)
             return
 
         if filename.lower().endswith(('.ipy', '.ipynb')):
             with preserve_keys(self.shell.user_ns, '__file__'):
                 self.shell.user_ns['__file__'] = filename
                 self.shell.safe_execfile_ipy(filename)
             return
 
         # Control the response to exit() calls made by the script being run
         exit_ignore = 'e' in opts
 
         # Make sure that the running script gets a proper sys.argv as if it
         # were run from a system shell.
         save_argv = sys.argv # save it for later restoring
 
         if 'G' in opts:
             args = arg_lst[1:]
         else:
             # tilde and glob expansion
             args = shellglob(map(os.path.expanduser,  arg_lst[1:]))
 
         sys.argv = [filename] + args  # put in the proper filename
         # protect sys.argv from potential unicode strings on Python 2:
         if not py3compat.PY3:
             sys.argv = [ py3compat.cast_bytes(a) for a in sys.argv ]
 
         if 'i' in opts:
             # Run in user's interactive namespace
             prog_ns = self.shell.user_ns
             __name__save = self.shell.user_ns['__name__']
             prog_ns['__name__'] = '__main__'
             main_mod = self.shell.user_module
             
             # Since '%run foo' emulates 'python foo.py' at the cmd line, we must
             # set the __file__ global in the script's namespace
             # TK: Is this necessary in interactive mode?
             prog_ns['__file__'] = filename
         else:
             # Run in a fresh, empty namespace
             if 'n' in opts:
                 name = os.path.splitext(os.path.basename(filename))[0]
             else:
                 name = '__main__'
 
             # The shell MUST hold a reference to prog_ns so after %run
             # exits, the python deletion mechanism doesn't zero it out
             # (leaving dangling references). See interactiveshell for details
             main_mod = self.shell.new_main_mod(filename, name)
             prog_ns = main_mod.__dict__
 
         # pickle fix.  See interactiveshell for an explanation.  But we need to
         # make sure that, if we overwrite __main__, we replace it at the end
         main_mod_name = prog_ns['__name__']
 
         if main_mod_name == '__main__':
             restore_main = sys.modules['__main__']
         else:
             restore_main = False
 
         # This needs to be undone at the end to prevent holding references to
         # every single object ever created.
         sys.modules[main_mod_name] = main_mod
 
         if 'p' in opts or 'd' in opts:
             if 'm' in opts:
                 code = 'run_module(modulename, prog_ns)'
                 code_ns = {
                     'run_module': self.shell.safe_run_module,
                     'prog_ns': prog_ns,
                     'modulename': modulename,
                 }
             else:
                 if 'd' in opts:
                     # allow exceptions to raise in debug mode
                     code = 'execfile(filename, prog_ns, raise_exceptions=True)'
                 else:
                     code = 'execfile(filename, prog_ns)'
                 code_ns = {
                     'execfile': self.shell.safe_execfile,
                     'prog_ns': prog_ns,
                     'filename': get_py_filename(filename),
                 }
 
         try:
             stats = None
             with self.shell.readline_no_record:
                 if 'p' in opts:
                     stats = self._run_with_profiler(code, opts, code_ns)
                 else:
                     if 'd' in opts:
                         bp_file, bp_line = parse_breakpoint(
                             opts.get('b', ['1'])[0], filename)
                         self._run_with_debugger(
                             code, code_ns, filename, bp_line, bp_file)
                     else:
                         if 'm' in opts:
                             def run():
                                 self.shell.safe_run_module(modulename, prog_ns)
                         else:
                             if runner is None:
                                 runner = self.default_runner
                             if runner is None:
                                 runner = self.shell.safe_execfile
 
                             def run():
                                 runner(filename, prog_ns, prog_ns,
                                        exit_ignore=exit_ignore)
 
                         if 't' in opts:
                             # timed execution
                             try:
                                 nruns = int(opts['N'][0])
                                 if nruns < 1:
                                     error('Number of runs must be >=1')
                                     return
                             except (KeyError):
                                 nruns = 1
                             self._run_with_timing(run, nruns)
                         else:
                             # regular execution
                             run()
 
                 if 'i' in opts:
                     self.shell.user_ns['__name__'] = __name__save
                 else:
                     # update IPython interactive namespace
 
                     # Some forms of read errors on the file may mean the
                     # __name__ key was never set; using pop we don't have to
                     # worry about a possible KeyError.
                     prog_ns.pop('__name__', None)
 
                     with preserve_keys(self.shell.user_ns, '__file__'):
                         self.shell.user_ns.update(prog_ns)
         finally:
             # It's a bit of a mystery why, but __builtins__ can change from
             # being a module to becoming a dict missing some key data after
             # %run.  As best I can see, this is NOT something IPython is doing
             # at all, and similar problems have been reported before:
             # http://coding.derkeiler.com/Archive/Python/comp.lang.python/2004-10/0188.html
             # Since this seems to be done by the interpreter itself, the best
             # we can do is to at least restore __builtins__ for the user on
             # exit.
             self.shell.user_ns['__builtins__'] = builtin_mod
 
             # Ensure key global structures are restored
             sys.argv = save_argv
             if restore_main:
                 sys.modules['__main__'] = restore_main
             else:
                 # Remove from sys.modules the reference to main_mod we'd
                 # added.  Otherwise it will trap references to objects
                 # contained therein.
                 del sys.modules[main_mod_name]
 
         return stats
 
     def _run_with_debugger(self, code, code_ns, filename=None,
                            bp_line=None, bp_file=None):
         """
         Run `code` in debugger with a break point.
 
         Parameters
         ----------
         code : str
             Code to execute.
         code_ns : dict
             A namespace in which `code` is executed.
         filename : str
             `code` is ran as if it is in `filename`.
         bp_line : int, optional
             Line number of the break point.
         bp_file : str, optional
             Path to the file in which break point is specified.
             `filename` is used if not given.
 
         Raises
         ------
         UsageError
             If the break point given by `bp_line` is not valid.
 
         """
         deb = debugger.Pdb(self.shell.colors)
         # reset Breakpoint state, which is moronically kept
         # in a class
         bdb.Breakpoint.next = 1
         bdb.Breakpoint.bplist = {}
         bdb.Breakpoint.bpbynumber = [None]
         if bp_line is not None:
             # Set an initial breakpoint to stop execution
             maxtries = 10
             bp_file = bp_file or filename
             checkline = deb.checkline(bp_file, bp_line)
             if not checkline:
                 for bp in range(bp_line + 1, bp_line + maxtries + 1):
                     if deb.checkline(bp_file, bp):
                         break
                 else:
                     msg = ("\nI failed to find a valid line to set "
                            "a breakpoint\n"
                            "after trying up to line: %s.\n"
                            "Please set a valid breakpoint manually "
                            "with the -b option." % bp)
                     raise UsageError(msg)
             # if we find a good linenumber, set the breakpoint
             deb.do_break('%s:%s' % (bp_file, bp_line))
 
         if filename:
             # Mimic Pdb._runscript(...)
             deb._wait_for_mainpyfile = True
             deb.mainpyfile = deb.canonic(filename)
 
         # Start file run
         print("NOTE: Enter 'c' at the %s prompt to continue execution." % deb.prompt)
         try:
             if filename:
                 # save filename so it can be used by methods on the deb object
                 deb._exec_filename = filename
             while True:
                 try:
                     deb.run(code, code_ns)
                 except Restart:
                     print("Restarting")
                     if filename:
                         deb._wait_for_mainpyfile = True
                         deb.mainpyfile = deb.canonic(filename)
                     continue
                 else:
                     break
             
 
         except:
             etype, value, tb = sys.exc_info()
             # Skip three frames in the traceback: the %run one,
             # one inside bdb.py, and the command-line typed by the
             # user (run by exec in pdb itself).
             self.shell.InteractiveTB(etype, value, tb, tb_offset=3)
 
     @staticmethod
     def _run_with_timing(run, nruns):
         """
         Run function `run` and print timing information.
 
         Parameters
         ----------
         run : callable
             Any callable object which takes no argument.
         nruns : int
             Number of times to execute `run`.
 
         """
         twall0 = time.time()
         if nruns == 1:
             t0 = clock2()
             run()
             t1 = clock2()
             t_usr = t1[0] - t0[0]
             t_sys = t1[1] - t0[1]
             print("\nIPython CPU timings (estimated):")
             print("  User   : %10.2f s." % t_usr)
             print("  System : %10.2f s." % t_sys)
         else:
             runs = range(nruns)
             t0 = clock2()
             for nr in runs:
                 run()
             t1 = clock2()
             t_usr = t1[0] - t0[0]
             t_sys = t1[1] - t0[1]
             print("\nIPython CPU timings (estimated):")
             print("Total runs performed:", nruns)
             print("  Times  : %10s   %10s" % ('Total', 'Per run'))
             print("  User   : %10.2f s, %10.2f s." % (t_usr, t_usr / nruns))
             print("  System : %10.2f s, %10.2f s." % (t_sys, t_sys / nruns))
         twall1 = time.time()
         print("Wall time: %10.2f s." % (twall1 - twall0))
 
     @skip_doctest
     @line_cell_magic
     def timeit(self, line='', cell=None):
         """Time execution of a Python statement or expression
 
         Usage, in line mode:
           %timeit [-n<N> -r<R> [-t|-c] -q -p<P> -o] statement
         or in cell mode:
           %%timeit [-n<N> -r<R> [-t|-c] -q -p<P> -o] setup_code
           code
           code...
 
         Time execution of a Python statement or expression using the timeit
         module.  This function can be used both as a line and cell magic:
 
         - In line mode you can time a single-line statement (though multiple
           ones can be chained with using semicolons).
 
         - In cell mode, the statement in the first line is used as setup code
           (executed but not timed) and the body of the cell is timed.  The cell
           body has access to any variables created in the setup code.
 
         Options:
         -n<N>: execute the given statement <N> times in a loop. If this value
         is not given, a fitting value is chosen.
 
         -r<R>: repeat the loop iteration <R> times and take the best result.
         Default: 3
 
         -t: use time.time to measure the time, which is the default on Unix.
         This function measures wall time.
 
         -c: use time.clock to measure the time, which is the default on
         Windows and measures wall time. On Unix, resource.getrusage is used
         instead and returns the CPU user time.
 
         -p<P>: use a precision of <P> digits to display the timing result.
         Default: 3
 
         -q: Quiet, do not print result.
 
         -o: return a TimeitResult that can be stored in a variable to inspect
             the result in more details.
 
 
         Examples
         --------
         ::
 
           In [1]: %timeit pass
           10000000 loops, best of 3: 53.3 ns per loop
 
           In [2]: u = None
 
           In [3]: %timeit u is None
           10000000 loops, best of 3: 184 ns per loop
 
           In [4]: %timeit -r 4 u == None
           1000000 loops, best of 4: 242 ns per loop
 
           In [5]: import time
 
           In [6]: %timeit -n1 time.sleep(2)
           1 loops, best of 3: 2 s per loop
 
 
         The times reported by %timeit will be slightly higher than those
         reported by the timeit.py script when variables are accessed. This is
         due to the fact that %timeit executes the statement in the namespace
         of the shell, compared with timeit.py, which uses a single setup
         statement to import function or create variables. Generally, the bias
         does not matter as long as results from timeit.py are not mixed with
         those from %timeit."""
 
         import timeit
 
         opts, stmt = self.parse_options(line,'n:r:tcp:qo',
                                         posix=False, strict=False)
         if stmt == "" and cell is None:
             return
         
         timefunc = timeit.default_timer
         number = int(getattr(opts, "n", 0))
         repeat = int(getattr(opts, "r", timeit.default_repeat))
         precision = int(getattr(opts, "p", 3))
         quiet = 'q' in opts
         return_result = 'o' in opts
         if hasattr(opts, "t"):
             timefunc = time.time
         if hasattr(opts, "c"):
             timefunc = clock
 
         timer = timeit.Timer(timer=timefunc)
         # this code has tight coupling to the inner workings of timeit.Timer,
         # but is there a better way to achieve that the code stmt has access
         # to the shell namespace?
         transform  = self.shell.input_splitter.transform_cell
 
         if cell is None:
             # called as line magic
             ast_setup = self.shell.compile.ast_parse("pass")
             ast_stmt = self.shell.compile.ast_parse(transform(stmt))
         else:
             ast_setup = self.shell.compile.ast_parse(transform(stmt))
             ast_stmt = self.shell.compile.ast_parse(transform(cell))
 
         ast_setup = self.shell.transform_ast(ast_setup)
         ast_stmt = self.shell.transform_ast(ast_stmt)
 
         # This codestring is taken from timeit.template - we fill it in as an
         # AST, so that we can apply our AST transformations to the user code
         # without affecting the timing code.
         timeit_ast_template = ast.parse('def inner(_it, _timer):\n'
                                         '    setup\n'
                                         '    _t0 = _timer()\n'
                                         '    for _i in _it:\n'
                                         '        stmt\n'
                                         '    _t1 = _timer()\n'
                                         '    return _t1 - _t0\n')
 
         timeit_ast = TimeitTemplateFiller(ast_setup, ast_stmt).visit(timeit_ast_template)
         timeit_ast = ast.fix_missing_locations(timeit_ast)
 
         # Track compilation time so it can be reported if too long
         # Minimum time above which compilation time will be reported
         tc_min = 0.1
 
         t0 = clock()
         code = self.shell.compile(timeit_ast, "<magic-timeit>", "exec")
         tc = clock()-t0
 
         ns = {}
         exec(code, self.shell.user_ns, ns)
         timer.inner = ns["inner"]
 
         # This is used to check if there is a huge difference between the
         # best and worst timings.
         # Issue: https://github.com/ipython/ipython/issues/6471
         worst_tuning = 0
         if number == 0:
             # determine number so that 0.2 <= total time < 2.0
             number = 1
             for _ in range(1, 10):
                 time_number = timer.timeit(number)
                 worst_tuning = max(worst_tuning, time_number / number)
                 if time_number >= 0.2:
                     break
                 number *= 10
         all_runs = timer.repeat(repeat, number)
         best = min(all_runs) / number
         if not quiet :
             worst = max(all_runs) / number
             if worst_tuning:
                 worst = max(worst, worst_tuning)
             # Check best timing is greater than zero to avoid a
             # ZeroDivisionError.
-            if worst > 4 * best and best > 0:
+            # In cases where the slowest timing is lesser than a micosecond
+            # we assume that it does not really matter if the fastest
+            # timing is 4 times faster than the slowest timing or not.
+            if worst > 4 * best and best > 0 and worst > 1e-6:
                 print("The slowest run took %0.2f times longer than the "
                       "fastest. This could mean that an intermediate result "
                       "is being cached " % (worst / best))
             print(u"%d loops, best of %d: %s per loop" % (number, repeat,
                                                               _format_time(best, precision)))
             if tc > tc_min:
                 print("Compiler time: %.2f s" % tc)
         if return_result:
             return TimeitResult(number, repeat, best, all_runs, tc, precision)
 
     @skip_doctest
     @needs_local_scope
     @line_cell_magic
     def time(self,line='', cell=None, local_ns=None):
         """Time execution of a Python statement or expression.
 
         The CPU and wall clock times are printed, and the value of the
         expression (if any) is returned.  Note that under Win32, system time
         is always reported as 0, since it can not be measured.
         
         This function can be used both as a line and cell magic:
 
         - In line mode you can time a single-line statement (though multiple
           ones can be chained with using semicolons).
 
         - In cell mode, you can time the cell body (a directly 
           following statement raises an error).
 
         This function provides very basic timing functionality.  Use the timeit 
         magic for more controll over the measurement.
 
         Examples
         --------
         ::
 
           In [1]: %time 2**128
           CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
           Wall time: 0.00
           Out[1]: 340282366920938463463374607431768211456L
 
           In [2]: n = 1000000
 
           In [3]: %time sum(range(n))
           CPU times: user 1.20 s, sys: 0.05 s, total: 1.25 s
           Wall time: 1.37
           Out[3]: 499999500000L
 
           In [4]: %time print 'hello world'
           hello world
           CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
           Wall time: 0.00
 
           Note that the time needed by Python to compile the given expression
           will be reported if it is more than 0.1s.  In this example, the
           actual exponentiation is done by Python at compilation time, so while
           the expression can take a noticeable amount of time to compute, that
           time is purely due to the compilation:
 
           In [5]: %time 3**9999;
           CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
           Wall time: 0.00 s
 
           In [6]: %time 3**999999;
           CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
           Wall time: 0.00 s
           Compiler : 0.78 s
           """
 
         # fail immediately if the given expression can't be compiled
         
         if line and cell:
             raise UsageError("Can't use statement directly after '%%time'!")
         
         if cell:
             expr = self.shell.input_transformer_manager.transform_cell(cell)
         else:
             expr = self.shell.input_transformer_manager.transform_cell(line)
 
         # Minimum time above which parse time will be reported
         tp_min = 0.1
 
         t0 = clock()
         expr_ast = self.shell.compile.ast_parse(expr)
         tp = clock()-t0
 
         # Apply AST transformations
         expr_ast = self.shell.transform_ast(expr_ast)
 
         # Minimum time above which compilation time will be reported
         tc_min = 0.1
 
         if len(expr_ast.body)==1 and isinstance(expr_ast.body[0], ast.Expr):
             mode = 'eval'
             source = '<timed eval>'
             expr_ast = ast.Expression(expr_ast.body[0].value)
         else:
             mode = 'exec'
             source = '<timed exec>'
         t0 = clock()
         code = self.shell.compile(expr_ast, source, mode)
         tc = clock()-t0
 
         # skew measurement as little as possible
         glob = self.shell.user_ns
         wtime = time.time
         # time execution
         wall_st = wtime()
         if mode=='eval':
             st = clock2()
             out = eval(code, glob, local_ns)
             end = clock2()
         else:
             st = clock2()
             exec(code, glob, local_ns)
             end = clock2()
             out = None
         wall_end = wtime()
         # Compute actual times and report
         wall_time = wall_end-wall_st
         cpu_user = end[0]-st[0]
         cpu_sys = end[1]-st[1]
         cpu_tot = cpu_user+cpu_sys
         # On windows cpu_sys is always zero, so no new information to the next print 
         if sys.platform != 'win32':
             print("CPU times: user %s, sys: %s, total: %s" % \
                 (_format_time(cpu_user),_format_time(cpu_sys),_format_time(cpu_tot)))
         print("Wall time: %s" % _format_time(wall_time))
         if tc > tc_min:
             print("Compiler : %s" % _format_time(tc))
         if tp > tp_min:
             print("Parser   : %s" % _format_time(tp))
         return out
 
     @skip_doctest
     @line_magic
     def macro(self, parameter_s=''):
         """Define a macro for future re-execution. It accepts ranges of history,
         filenames or string objects.
 
         Usage:\\
           %macro [options] name n1-n2 n3-n4 ... n5 .. n6 ...
 
         Options:
 
           -r: use 'raw' input.  By default, the 'processed' history is used,
           so that magics are loaded in their transformed version to valid
           Python.  If this option is given, the raw input as typed at the
           command line is used instead.
           
           -q: quiet macro definition.  By default, a tag line is printed 
           to indicate the macro has been created, and then the contents of 
           the macro are printed.  If this option is given, then no printout
           is produced once the macro is created.
 
         This will define a global variable called `name` which is a string
         made of joining the slices and lines you specify (n1,n2,... numbers
         above) from your input history into a single string. This variable
         acts like an automatic function which re-executes those lines as if
         you had typed them. You just type 'name' at the prompt and the code
         executes.
 
         The syntax for indicating input ranges is described in %history.
 
         Note: as a 'hidden' feature, you can also use traditional python slice
         notation, where N:M means numbers N through M-1.
 
         For example, if your history contains (print using %hist -n )::
 
           44: x=1
           45: y=3
           46: z=x+y
           47: print x
           48: a=5
           49: print 'x',x,'y',y
 
         you can create a macro with lines 44 through 47 (included) and line 49
         called my_macro with::
 
           In [55]: %macro my_macro 44-47 49
 
         Now, typing `my_macro` (without quotes) will re-execute all this code
         in one pass.
 
         You don't need to give the line-numbers in order, and any given line
         number can appear multiple times. You can assemble macros with any
         lines from your input history in any order.
 
         The macro is a simple object which holds its value in an attribute,
         but IPython's display system checks for macros and executes them as
         code instead of printing them when you type their name.
 
         You can view a macro's contents by explicitly printing it with::
 
           print macro_name
 
         """
         opts,args = self.parse_options(parameter_s,'rq',mode='list')
         if not args:   # List existing macros
             return sorted(k for k,v in iteritems(self.shell.user_ns) if\
                                                         isinstance(v, Macro))
         if len(args) == 1:
             raise UsageError(
                 "%macro insufficient args; usage '%macro name n1-n2 n3-4...")
         name, codefrom = args[0], " ".join(args[1:])
 
         #print 'rng',ranges  # dbg
         try:
             lines = self.shell.find_user_code(codefrom, 'r' in opts)
         except (ValueError, TypeError) as e:
             print(e.args[0])
             return
         macro = Macro(lines)
         self.shell.define_macro(name, macro)
         if not ( 'q' in opts) : 
             print('Macro `%s` created. To execute, type its name (without quotes).' % name)
             print('=== Macro contents: ===')
             print(macro, end=' ')
 
     @magic_arguments.magic_arguments()
     @magic_arguments.argument('output', type=str, default='', nargs='?',
         help="""The name of the variable in which to store output.
         This is a utils.io.CapturedIO object with stdout/err attributes
         for the text of the captured output.
 
         CapturedOutput also has a show() method for displaying the output,
         and __call__ as well, so you can use that to quickly display the
         output.
 
         If unspecified, captured output is discarded.
         """
     )
     @magic_arguments.argument('--no-stderr', action="store_true",
         help="""Don't capture stderr."""
     )
     @magic_arguments.argument('--no-stdout', action="store_true",
         help="""Don't capture stdout."""
     )
     @magic_arguments.argument('--no-display', action="store_true",
         help="""Don't capture IPython's rich display."""
     )
     @cell_magic
     def capture(self, line, cell):
         """run the cell, capturing stdout, stderr, and IPython's rich display() calls."""
         args = magic_arguments.parse_argstring(self.capture, line)
         out = not args.no_stdout
         err = not args.no_stderr
         disp = not args.no_display
         with capture_output(out, err, disp) as io:
             self.shell.run_cell(cell)
         if args.output:
             self.shell.user_ns[args.output] = io
 
 def parse_breakpoint(text, current_file):
     '''Returns (file, line) for file:line and (current_file, line) for line'''
     colon = text.find(':')
     if colon == -1:
         return current_file, int(text)
     else:
         return text[:colon], int(text[colon+1:])
     
 def _format_time(timespan, precision=3):
     """Formats the timespan in a human readable form"""
     import math
     
     if timespan >= 60.0:
         # we have more than a minute, format that in a human readable form
         # Idea from http://snipplr.com/view/5713/
         parts = [("d", 60*60*24),("h", 60*60),("min", 60), ("s", 1)]
         time = []
         leftover = timespan
         for suffix, length in parts:
             value = int(leftover / length)
             if value > 0:
                 leftover = leftover % length
                 time.append(u'%s%s' % (str(value), suffix))
             if leftover < 1:
                 break
         return " ".join(time)
 
     
     # Unfortunately the unicode 'micro' symbol can cause problems in
     # certain terminals.  
     # See bug: https://bugs.launchpad.net/ipython/+bug/348466
     # Try to prevent crashes by being more secure than it needs to
     # E.g. eclipse is able to print a µ, but has no sys.stdout.encoding set.
     units = [u"s", u"ms",u'us',"ns"] # the save value   
     if hasattr(sys.stdout, 'encoding') and sys.stdout.encoding:
         try:
             u'\xb5'.encode(sys.stdout.encoding)
             units = [u"s", u"ms",u'\xb5s',"ns"]
         except:
             pass
     scaling = [1, 1e3, 1e6, 1e9]
         
     if timespan > 0.0:
         order = min(-int(math.floor(math.log10(timespan)) // 3), 3)
     else:
         order = 3
     return u"%.*g %s" % (precision, timespan * scaling[order], units[order])