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2to3.html
49.27
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__builtin__.html
10.26
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__future__.html
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__main__.html
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_winreg.html
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abc.html
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aepack.html
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aetools.html
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aetypes.html
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aifc.html
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al.html
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allos.html
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anydbm.html
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archiving.html
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argparse.html
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array.html
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ast.html
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asynchat.html
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asyncore.html
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atexit.html
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audioop.html
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autogil.html
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base64.html
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basehttpserver.html
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bastion.html
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bdb.html
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binascii.html
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binhex.html
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bisect.html
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bsddb.html
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bz2.html
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calendar.html
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carbon.html
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cd.html
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cgi.html
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cgihttpserver.html
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cgitb.html
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chunk.html
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cmath.html
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cmd.html
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code.html
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codecs.html
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codeop.html
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collections.html
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colorpicker.html
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colorsys.html
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commands.html
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compileall.html
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compiler.html
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configparser.html
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constants.html
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contextlib.html
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cookie.html
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cookielib.html
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copy.html
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copy_reg.html
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crypt.html
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crypto.html
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csv.html
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ctypes.html
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curses.ascii.html
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curses.html
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curses.panel.html
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custominterp.html
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datatypes.html
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datetime.html
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dbhash.html
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dbm.html
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debug.html
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decimal.html
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development.html
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difflib.html
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dircache.html
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dis.html
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distutils.html
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dl.html
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doctest.html
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docxmlrpcserver.html
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dumbdbm.html
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dummy_thread.html
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dummy_threading.html
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easydialogs.html
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email-examples.html
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email.charset.html
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email.encoders.html
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email.errors.html
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email.generator.html
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email.header.html
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email.html
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email.iterators.html
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email.message.html
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email.mime.html
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email.parser.html
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email.util.html
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errno.html
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exceptions.html
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fcntl.html
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filecmp.html
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fileformats.html
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fileinput.html
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filesys.html
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fl.html
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fm.html
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fnmatch.html
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formatter.html
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fpectl.html
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fpformat.html
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fractions.html
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framework.html
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frameworks.html
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ftplib.html
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functions.html
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functools.html
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future_builtins.html
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gc.html
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gdbm.html
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gensuitemodule.html
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getopt.html
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getpass.html
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gettext.html
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gl.html
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glob.html
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grp.html
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gzip.html
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hashlib.html
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heapq.html
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hmac.html
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hotshot.html
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htmllib.html
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htmlparser.html
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httplib.html
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i18n.html
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ic.html
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idle.html
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imageop.html
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imaplib.html
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imgfile.html
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imghdr.html
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imp.html
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importlib.html
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imputil.html
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index.html
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inspect.html
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internet.html
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intro.html
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io.html
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ipc.html
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itertools.html
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jpeg.html
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json.html
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keyword.html
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language.html
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linecache.html
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locale.html
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logging.config.html
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logging.handlers.html
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logging.html
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mac.html
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macos.html
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macosa.html
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macostools.html
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macpath.html
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mailbox.html
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mailcap.html
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markup.html
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marshal.html
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math.html
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md5.html
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mhlib.html
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mimetools.html
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mimewriter.html
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mimify.html
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miniaeframe.html
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misc.html
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mm.html
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mmap.html
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modulefinder.html
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modules.html
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msilib.html
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msvcrt.html
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multifile.html
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multiprocessing.html
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mutex.html
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netdata.html
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netrc.html
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new.html
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nis.html
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nntplib.html
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numbers.html
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numeric.html
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operator.html
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os.html
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os.path.html
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ossaudiodev.html
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othergui.html
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parser.html
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pdb.html
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persistence.html
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pickle.html
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pickletools.html
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pipes.html
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pkgutil.html
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platform.html
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plistlib.html
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poplib.html
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posix.html
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pprint.html
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profile.html
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pty.html
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pwd.html
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py_compile.html
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pyclbr.html
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pydoc.html
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pyexpat.html
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python.html
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queue.html
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quopri.html
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random.html
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re.html
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readline.html
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repr.html
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resource.html
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restricted.html
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rexec.html
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rfc822.html
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rlcompleter.html
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robotparser.html
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runpy.html
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sched.html
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scrolledtext.html
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select.html
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sets.html
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sgi.html
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sgmllib.html
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sha.html
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shelve.html
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shlex.html
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shutil.html
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signal.html
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simplehttpserver.html
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site.html
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smtpd.html
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smtplib.html
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sndhdr.html
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socket.html
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socketserver.html
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someos.html
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spwd.html
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sqlite3.html
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ssl.html
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stat.html
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statvfs.html
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stdtypes.html
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string.html
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stringio.html
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stringprep.html
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strings.html
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struct.html
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subprocess.html
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sun.html
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sunaudio.html
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symbol.html
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symtable.html
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sys.html
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sysconfig.html
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syslog.html
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tarfile.html
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tempfile.html
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test.html
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threading.html
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time.html
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timeit.html
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tix.html
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tk.html
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tkinter.html
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token.html
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tokenize.html
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trace.html
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traceback.html
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ttk.html
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tty.html
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turtle.html
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types.html
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undoc.html
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unittest.html
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unix.html
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urllib.html
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urllib2.html
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urlparse.html
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user.html
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userdict.html
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uu.html
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uuid.html
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warnings.html
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wave.html
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weakref.html
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webbrowser.html
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whichdb.html
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windows.html
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xdrlib.html
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xml.dom.html
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xml.etree.elementtree.html
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xml.html
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xml.sax.handler.html
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xml.sax.html
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xml.sax.reader.html
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xml.sax.utils.html
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xmlrpclib.html
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zipfile.html
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zipimport.html
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zlib.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>9.6. random — Generate pseudo-random numbers — Python 2.7.5 documentation</title> <link rel="stylesheet" href="../_static/default.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../', VERSION: '2.7.5', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: true }; </script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 2.7.5 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="top" title="Python 2.7.5 documentation" href="../index.html" /> <link rel="up" title="9. 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Numeric and Mathematical Modules</a> »</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="module-random"> <span id="random-generate-pseudo-random-numbers"></span><h1>9.6. <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-mod docutils literal"><span class="pre">random</span></tt></a> — Generate pseudo-random numbers<a class="headerlink" href="#module-random" title="Permalink to this headline">¶</a></h1> <p><strong>Source code:</strong> <a class="reference external" href="http://hg.python.org/cpython/file/2.7/Lib/random.py">Lib/random.py</a></p> <hr class="docutils" /> <p>This module implements pseudo-random number generators for various distributions.</p> <p>For integers, uniform selection from a range. For sequences, uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.</p> <p>On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.</p> <p>Almost all module functions depend on the basic function <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-func docutils literal"><span class="pre">random()</span></tt></a>, which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne Twister is one of the most extensively tested random number generators in existence. However, being completely deterministic, it is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.</p> <p>The functions supplied by this module are actually bound methods of a hidden instance of the <tt class="xref py py-class docutils literal"><span class="pre">random.Random</span></tt> class. You can instantiate your own instances of <tt class="xref py py-class docutils literal"><span class="pre">Random</span></tt> to get generators that don’t share state. This is especially useful for multi-threaded programs, creating a different instance of <tt class="xref py py-class docutils literal"><span class="pre">Random</span></tt> for each thread, and using the <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><tt class="xref py py-meth docutils literal"><span class="pre">jumpahead()</span></tt></a> method to make it likely that the generated sequences seen by each thread don’t overlap.</p> <p>Class <tt class="xref py py-class docutils literal"><span class="pre">Random</span></tt> can also be subclassed if you want to use a different basic generator of your own devising: in that case, override the <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-meth docutils literal"><span class="pre">random()</span></tt></a>, <a class="reference internal" href="#random.seed" title="random.seed"><tt class="xref py py-meth docutils literal"><span class="pre">seed()</span></tt></a>, <a class="reference internal" href="#random.getstate" title="random.getstate"><tt class="xref py py-meth docutils literal"><span class="pre">getstate()</span></tt></a>, <a class="reference internal" href="#random.setstate" title="random.setstate"><tt class="xref py py-meth docutils literal"><span class="pre">setstate()</span></tt></a> and <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><tt class="xref py py-meth docutils literal"><span class="pre">jumpahead()</span></tt></a> methods. Optionally, a new generator can supply a <a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><tt class="xref py py-meth docutils literal"><span class="pre">getrandbits()</span></tt></a> method — this allows <a class="reference internal" href="#random.randrange" title="random.randrange"><tt class="xref py py-meth docutils literal"><span class="pre">randrange()</span></tt></a> to produce selections over an arbitrarily large range.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.4: </span>the <a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><tt class="xref py py-meth docutils literal"><span class="pre">getrandbits()</span></tt></a> method.</p> <p>As an example of subclassing, the <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-mod docutils literal"><span class="pre">random</span></tt></a> module provides the <a class="reference internal" href="#random.WichmannHill" title="random.WichmannHill"><tt class="xref py py-class docutils literal"><span class="pre">WichmannHill</span></tt></a> class that implements an alternative generator in pure Python. The class provides a backward compatible way to reproduce results from earlier versions of Python, which used the Wichmann-Hill algorithm as the core generator. Note that this Wichmann-Hill generator can no longer be recommended: its period is too short by contemporary standards, and the sequence generated is known to fail some stringent randomness tests. See the references below for a recent variant that repairs these flaws.</p> <p class="versionchanged"> <span class="versionmodified">Changed in version 2.3: </span>MersenneTwister replaced Wichmann-Hill as the default generator.</p> <p>The <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-mod docutils literal"><span class="pre">random</span></tt></a> module also provides the <a class="reference internal" href="#random.SystemRandom" title="random.SystemRandom"><tt class="xref py py-class docutils literal"><span class="pre">SystemRandom</span></tt></a> class which uses the system function <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><tt class="xref py py-func docutils literal"><span class="pre">os.urandom()</span></tt></a> to generate random numbers from sources provided by the operating system.</p> <p>Bookkeeping functions:</p> <dl class="function"> <dt id="random.seed"> <tt class="descclassname">random.</tt><tt class="descname">seed</tt><big>(</big><span class="optional">[</span><em>x</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#random.seed" title="Permalink to this definition">¶</a></dt> <dd><p>Initialize the basic random number generator. Optional argument <em>x</em> can be any <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a> object. If <em>x</em> is omitted or <tt class="docutils literal"><span class="pre">None</span></tt>, current system time is used; current system time is also used to initialize the generator when the module is first imported. If randomness sources are provided by the operating system, they are used instead of the system time (see the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><tt class="xref py py-func docutils literal"><span class="pre">os.urandom()</span></tt></a> function for details on availability).</p> <p class="versionchanged"> <span class="versionmodified">Changed in version 2.4: </span>formerly, operating system resources were not used.</p> </dd></dl> <dl class="function"> <dt id="random.getstate"> <tt class="descclassname">random.</tt><tt class="descname">getstate</tt><big>(</big><big>)</big><a class="headerlink" href="#random.getstate" title="Permalink to this definition">¶</a></dt> <dd><p>Return an object capturing the current internal state of the generator. This object can be passed to <a class="reference internal" href="#random.setstate" title="random.setstate"><tt class="xref py py-func docutils literal"><span class="pre">setstate()</span></tt></a> to restore the state.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.1.</span></p> <p class="versionchanged"> <span class="versionmodified">Changed in version 2.6: </span>State values produced in Python 2.6 cannot be loaded into earlier versions.</p> </dd></dl> <dl class="function"> <dt id="random.setstate"> <tt class="descclassname">random.</tt><tt class="descname">setstate</tt><big>(</big><em>state</em><big>)</big><a class="headerlink" href="#random.setstate" title="Permalink to this definition">¶</a></dt> <dd><p><em>state</em> should have been obtained from a previous call to <a class="reference internal" href="#random.getstate" title="random.getstate"><tt class="xref py py-func docutils literal"><span class="pre">getstate()</span></tt></a>, and <a class="reference internal" href="#random.setstate" title="random.setstate"><tt class="xref py py-func docutils literal"><span class="pre">setstate()</span></tt></a> restores the internal state of the generator to what it was at the time <a class="reference internal" href="#random.getstate" title="random.getstate"><tt class="xref py py-func docutils literal"><span class="pre">getstate()</span></tt></a> was called.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.1.</span></p> </dd></dl> <dl class="function"> <dt id="random.jumpahead"> <tt class="descclassname">random.</tt><tt class="descname">jumpahead</tt><big>(</big><em>n</em><big>)</big><a class="headerlink" href="#random.jumpahead" title="Permalink to this definition">¶</a></dt> <dd><p>Change the internal state to one different from and likely far away from the current state. <em>n</em> is a non-negative integer which is used to scramble the current state vector. This is most useful in multi-threaded programs, in conjunction with multiple instances of the <tt class="xref py py-class docutils literal"><span class="pre">Random</span></tt> class: <a class="reference internal" href="#random.setstate" title="random.setstate"><tt class="xref py py-meth docutils literal"><span class="pre">setstate()</span></tt></a> or <a class="reference internal" href="#random.seed" title="random.seed"><tt class="xref py py-meth docutils literal"><span class="pre">seed()</span></tt></a> can be used to force all instances into the same internal state, and then <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><tt class="xref py py-meth docutils literal"><span class="pre">jumpahead()</span></tt></a> can be used to force the instances’ states far apart.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.1.</span></p> <p class="versionchanged"> <span class="versionmodified">Changed in version 2.3: </span>Instead of jumping to a specific state, <em>n</em> steps ahead, <tt class="docutils literal"><span class="pre">jumpahead(n)</span></tt> jumps to another state likely to be separated by many steps.</p> </dd></dl> <dl class="function"> <dt id="random.getrandbits"> <tt class="descclassname">random.</tt><tt class="descname">getrandbits</tt><big>(</big><em>k</em><big>)</big><a class="headerlink" href="#random.getrandbits" title="Permalink to this definition">¶</a></dt> <dd><p>Returns a python <a class="reference internal" href="functions.html#long" title="long"><tt class="xref py py-class docutils literal"><span class="pre">long</span></tt></a> int with <em>k</em> random bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available, <a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><tt class="xref py py-meth docutils literal"><span class="pre">getrandbits()</span></tt></a> enables <a class="reference internal" href="#random.randrange" title="random.randrange"><tt class="xref py py-meth docutils literal"><span class="pre">randrange()</span></tt></a> to handle arbitrarily large ranges.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.4.</span></p> </dd></dl> <p>Functions for integers:</p> <dl class="function"> <dt id="random.randrange"> <tt class="descclassname">random.</tt><tt class="descname">randrange</tt><big>(</big><em>stop</em><big>)</big><a class="headerlink" href="#random.randrange" title="Permalink to this definition">¶</a></dt> <dt> <tt class="descclassname">random.</tt><tt class="descname">randrange</tt><big>(</big><em>start</em>, <em>stop</em><span class="optional">[</span>, <em>step</em><span class="optional">]</span><big>)</big></dt> <dd><p>Return a randomly selected element from <tt class="docutils literal"><span class="pre">range(start,</span> <span class="pre">stop,</span> <span class="pre">step)</span></tt>. This is equivalent to <tt class="docutils literal"><span class="pre">choice(range(start,</span> <span class="pre">stop,</span> <span class="pre">step))</span></tt>, but doesn’t actually build a range object.</p> <p class="versionadded"> <span class="versionmodified">New in version 1.5.2.</span></p> </dd></dl> <dl class="function"> <dt id="random.randint"> <tt class="descclassname">random.</tt><tt class="descname">randint</tt><big>(</big><em>a</em>, <em>b</em><big>)</big><a class="headerlink" href="#random.randint" title="Permalink to this definition">¶</a></dt> <dd><p>Return a random integer <em>N</em> such that <tt class="docutils literal"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">b</span></tt>.</p> </dd></dl> <p>Functions for sequences:</p> <dl class="function"> <dt id="random.choice"> <tt class="descclassname">random.</tt><tt class="descname">choice</tt><big>(</big><em>seq</em><big>)</big><a class="headerlink" href="#random.choice" title="Permalink to this definition">¶</a></dt> <dd><p>Return a random element from the non-empty sequence <em>seq</em>. If <em>seq</em> is empty, raises <a class="reference internal" href="exceptions.html#exceptions.IndexError" title="exceptions.IndexError"><tt class="xref py py-exc docutils literal"><span class="pre">IndexError</span></tt></a>.</p> </dd></dl> <dl class="function"> <dt id="random.shuffle"> <tt class="descclassname">random.</tt><tt class="descname">shuffle</tt><big>(</big><em>x</em><span class="optional">[</span>, <em>random</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#random.shuffle" title="Permalink to this definition">¶</a></dt> <dd><p>Shuffle the sequence <em>x</em> in place. The optional argument <em>random</em> is a 0-argument function returning a random float in [0.0, 1.0); by default, this is the function <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><tt class="xref py py-func docutils literal"><span class="pre">random()</span></tt></a>.</p> <p>Note that for even rather small <tt class="docutils literal"><span class="pre">len(x)</span></tt>, the total number of permutations of <em>x</em> is larger than the period of most random number generators; this implies that most permutations of a long sequence can never be generated.</p> </dd></dl> <dl class="function"> <dt id="random.sample"> <tt class="descclassname">random.</tt><tt class="descname">sample</tt><big>(</big><em>population</em>, <em>k</em><big>)</big><a class="headerlink" href="#random.sample" title="Permalink to this definition">¶</a></dt> <dd><p>Return a <em>k</em> length list of unique elements chosen from the population sequence. Used for random sampling without replacement.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.3.</span></p> <p>Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).</p> <p>Members of the population need not be <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a> or unique. If the population contains repeats, then each occurrence is a possible selection in the sample.</p> <p>To choose a sample from a range of integers, use an <a class="reference internal" href="functions.html#xrange" title="xrange"><tt class="xref py py-func docutils literal"><span class="pre">xrange()</span></tt></a> object as an argument. This is especially fast and space efficient for sampling from a large population: <tt class="docutils literal"><span class="pre">sample(xrange(10000000),</span> <span class="pre">60)</span></tt>.</p> </dd></dl> <p>The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.</p> <dl class="function"> <dt id="random.random"> <tt class="descclassname">random.</tt><tt class="descname">random</tt><big>(</big><big>)</big><a class="headerlink" href="#random.random" title="Permalink to this definition">¶</a></dt> <dd><p>Return the next random floating point number in the range [0.0, 1.0).</p> </dd></dl> <dl class="function"> <dt id="random.uniform"> <tt class="descclassname">random.</tt><tt class="descname">uniform</tt><big>(</big><em>a</em>, <em>b</em><big>)</big><a class="headerlink" href="#random.uniform" title="Permalink to this definition">¶</a></dt> <dd><p>Return a random floating point number <em>N</em> such that <tt class="docutils literal"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">b</span></tt> for <tt class="docutils literal"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">b</span></tt> and <tt class="docutils literal"><span class="pre">b</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">a</span></tt> for <tt class="docutils literal"><span class="pre">b</span> <span class="pre"><</span> <span class="pre">a</span></tt>.</p> <p>The end-point value <tt class="docutils literal"><span class="pre">b</span></tt> may or may not be included in the range depending on floating-point rounding in the equation <tt class="docutils literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">(b-a)</span> <span class="pre">*</span> <span class="pre">random()</span></tt>.</p> </dd></dl> <dl class="function"> <dt id="random.triangular"> <tt class="descclassname">random.</tt><tt class="descname">triangular</tt><big>(</big><em>low</em>, <em>high</em>, <em>mode</em><big>)</big><a class="headerlink" href="#random.triangular" title="Permalink to this definition">¶</a></dt> <dd><p>Return a random floating point number <em>N</em> such that <tt class="docutils literal"><span class="pre">low</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">high</span></tt> and with the specified <em>mode</em> between those bounds. The <em>low</em> and <em>high</em> bounds default to zero and one. The <em>mode</em> argument defaults to the midpoint between the bounds, giving a symmetric distribution.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.6.</span></p> </dd></dl> <dl class="function"> <dt id="random.betavariate"> <tt class="descclassname">random.</tt><tt class="descname">betavariate</tt><big>(</big><em>alpha</em>, <em>beta</em><big>)</big><a class="headerlink" href="#random.betavariate" title="Permalink to this definition">¶</a></dt> <dd><p>Beta distribution. Conditions on the parameters are <tt class="docutils literal"><span class="pre">alpha</span> <span class="pre">></span> <span class="pre">0</span></tt> and <tt class="docutils literal"><span class="pre">beta</span> <span class="pre">></span> <span class="pre">0</span></tt>. Returned values range between 0 and 1.</p> </dd></dl> <dl class="function"> <dt id="random.expovariate"> <tt class="descclassname">random.</tt><tt class="descname">expovariate</tt><big>(</big><em>lambd</em><big>)</big><a class="headerlink" href="#random.expovariate" title="Permalink to this definition">¶</a></dt> <dd><p>Exponential distribution. <em>lambd</em> is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called “lambda”, but that is a reserved word in Python.) Returned values range from 0 to positive infinity if <em>lambd</em> is positive, and from negative infinity to 0 if <em>lambd</em> is negative.</p> </dd></dl> <dl class="function"> <dt id="random.gammavariate"> <tt class="descclassname">random.</tt><tt class="descname">gammavariate</tt><big>(</big><em>alpha</em>, <em>beta</em><big>)</big><a class="headerlink" href="#random.gammavariate" title="Permalink to this definition">¶</a></dt> <dd><p>Gamma distribution. (<em>Not</em> the gamma function!) Conditions on the parameters are <tt class="docutils literal"><span class="pre">alpha</span> <span class="pre">></span> <span class="pre">0</span></tt> and <tt class="docutils literal"><span class="pre">beta</span> <span class="pre">></span> <span class="pre">0</span></tt>.</p> <p>The probability distribution function is:</p> <div class="highlight-python"><pre> x ** (alpha - 1) * math.exp(-x / beta) pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha</pre> </div> </dd></dl> <dl class="function"> <dt id="random.gauss"> <tt class="descclassname">random.</tt><tt class="descname">gauss</tt><big>(</big><em>mu</em>, <em>sigma</em><big>)</big><a class="headerlink" href="#random.gauss" title="Permalink to this definition">¶</a></dt> <dd><p>Gaussian distribution. <em>mu</em> is the mean, and <em>sigma</em> is the standard deviation. This is slightly faster than the <a class="reference internal" href="#random.normalvariate" title="random.normalvariate"><tt class="xref py py-func docutils literal"><span class="pre">normalvariate()</span></tt></a> function defined below.</p> </dd></dl> <dl class="function"> <dt id="random.lognormvariate"> <tt class="descclassname">random.</tt><tt class="descname">lognormvariate</tt><big>(</big><em>mu</em>, <em>sigma</em><big>)</big><a class="headerlink" href="#random.lognormvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean <em>mu</em> and standard deviation <em>sigma</em>. <em>mu</em> can have any value, and <em>sigma</em> must be greater than zero.</p> </dd></dl> <dl class="function"> <dt id="random.normalvariate"> <tt class="descclassname">random.</tt><tt class="descname">normalvariate</tt><big>(</big><em>mu</em>, <em>sigma</em><big>)</big><a class="headerlink" href="#random.normalvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Normal distribution. <em>mu</em> is the mean, and <em>sigma</em> is the standard deviation.</p> </dd></dl> <dl class="function"> <dt id="random.vonmisesvariate"> <tt class="descclassname">random.</tt><tt class="descname">vonmisesvariate</tt><big>(</big><em>mu</em>, <em>kappa</em><big>)</big><a class="headerlink" href="#random.vonmisesvariate" title="Permalink to this definition">¶</a></dt> <dd><p><em>mu</em> is the mean angle, expressed in radians between 0 and 2*<em>pi</em>, and <em>kappa</em> is the concentration parameter, which must be greater than or equal to zero. If <em>kappa</em> is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*<em>pi</em>.</p> </dd></dl> <dl class="function"> <dt id="random.paretovariate"> <tt class="descclassname">random.</tt><tt class="descname">paretovariate</tt><big>(</big><em>alpha</em><big>)</big><a class="headerlink" href="#random.paretovariate" title="Permalink to this definition">¶</a></dt> <dd><p>Pareto distribution. <em>alpha</em> is the shape parameter.</p> </dd></dl> <dl class="function"> <dt id="random.weibullvariate"> <tt class="descclassname">random.</tt><tt class="descname">weibullvariate</tt><big>(</big><em>alpha</em>, <em>beta</em><big>)</big><a class="headerlink" href="#random.weibullvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Weibull distribution. <em>alpha</em> is the scale parameter and <em>beta</em> is the shape parameter.</p> </dd></dl> <p>Alternative Generators:</p> <dl class="class"> <dt id="random.WichmannHill"> <em class="property">class </em><tt class="descclassname">random.</tt><tt class="descname">WichmannHill</tt><big>(</big><span class="optional">[</span><em>seed</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#random.WichmannHill" title="Permalink to this definition">¶</a></dt> <dd><p>Class that implements the Wichmann-Hill algorithm as the core generator. Has all of the same methods as <tt class="xref py py-class docutils literal"><span class="pre">Random</span></tt> plus the <a class="reference internal" href="#random.whseed" title="random.whseed"><tt class="xref py py-meth docutils literal"><span class="pre">whseed()</span></tt></a> method described below. Because this class is implemented in pure Python, it is not threadsafe and may require locks between calls. The period of the generator is 6,953,607,871,644 which is small enough to require care that two independent random sequences do not overlap.</p> </dd></dl> <dl class="function"> <dt id="random.whseed"> <tt class="descclassname">random.</tt><tt class="descname">whseed</tt><big>(</big><span class="optional">[</span><em>x</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#random.whseed" title="Permalink to this definition">¶</a></dt> <dd><p>This is obsolete, supplied for bit-level compatibility with versions of Python prior to 2.1. See <a class="reference internal" href="#random.seed" title="random.seed"><tt class="xref py py-func docutils literal"><span class="pre">seed()</span></tt></a> for details. <a class="reference internal" href="#random.whseed" title="random.whseed"><tt class="xref py py-func docutils literal"><span class="pre">whseed()</span></tt></a> does not guarantee that distinct integer arguments yield distinct internal states, and can yield no more than about 2**24 distinct internal states in all.</p> </dd></dl> <dl class="class"> <dt id="random.SystemRandom"> <em class="property">class </em><tt class="descclassname">random.</tt><tt class="descname">SystemRandom</tt><big>(</big><span class="optional">[</span><em>seed</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#random.SystemRandom" title="Permalink to this definition">¶</a></dt> <dd><p>Class that uses the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><tt class="xref py py-func docutils literal"><span class="pre">os.urandom()</span></tt></a> function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state and sequences are not reproducible. Accordingly, the <a class="reference internal" href="#random.seed" title="random.seed"><tt class="xref py py-meth docutils literal"><span class="pre">seed()</span></tt></a> and <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><tt class="xref py py-meth docutils literal"><span class="pre">jumpahead()</span></tt></a> methods have no effect and are ignored. The <a class="reference internal" href="#random.getstate" title="random.getstate"><tt class="xref py py-meth docutils literal"><span class="pre">getstate()</span></tt></a> and <a class="reference internal" href="#random.setstate" title="random.setstate"><tt class="xref py py-meth docutils literal"><span class="pre">setstate()</span></tt></a> methods raise <a class="reference internal" href="exceptions.html#exceptions.NotImplementedError" title="exceptions.NotImplementedError"><tt class="xref py py-exc docutils literal"><span class="pre">NotImplementedError</span></tt></a> if called.</p> <p class="versionadded"> <span class="versionmodified">New in version 2.4.</span></p> </dd></dl> <p>Examples of basic usage:</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="c"># Random float x, 0.0 <= x < 1.0</span> <span class="go">0.37444887175646646</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="c"># Random float x, 1.0 <= x < 10.0</span> <span class="go">1.1800146073117523</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="c"># Integer from 1 to 10, endpoints included</span> <span class="go">7</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">101</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c"># Even integer from 0 to 100</span> <span class="go">26</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="s">'abcdefghij'</span><span class="p">)</span> <span class="c"># Choose a random element</span> <span class="go">'c'</span> <span class="gp">>>> </span><span class="n">items</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">]</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">items</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">items</span> <span class="go">[7, 3, 2, 5, 6, 4, 1]</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="c"># Choose 3 elements</span> <span class="go">[4, 1, 5]</span> </pre></div> </div> <div class="admonition-see-also admonition seealso"> <p class="first admonition-title">See also</p> <p>M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998.</p> <p>Wichmann, B. A. & Hill, I. D., “Algorithm AS 183: An efficient and portable pseudo-random number generator”, Applied Statistics 31 (1982) 188-190.</p> <p class="last"><a class="reference external" href="http://code.activestate.com/recipes/576707/">Complementary-Multiply-with-Carry recipe</a> for a compatible alternative random number generator with a long period and comparatively simple update operations.</p> </div> </div> </div> </div> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="fractions.html" title="previous chapter">9.5. <tt class="docutils literal"><span class="pre">fractions</span></tt> — Rational numbers</a></p> <h4>Next topic</h4> <p class="topless"><a href="itertools.html" title="next chapter">9.7. <tt class="docutils literal"><span class="pre">itertools</span></tt> — Functions creating iterators for efficient looping</a></p> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li><a href="../_sources/library/random.txt" rel="nofollow">Show Source</a></li> </ul> <div id="searchbox" style="display: none"> <h3>Quick search</h3> <form class="search" action="../search.html" method="get"> <input type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> <p class="searchtip" style="font-size: 90%"> Enter search terms or a module, class or function name. </p> </div> <script type="text/javascript">$('#searchbox').show(0);</script> </div> </div> <div class="clearer"></div> </div> <div class="related"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="itertools.html" title="9.7. itertools — Functions creating iterators for efficient looping" >next</a> |</li> <li class="right" > <a href="fractions.html" title="9.5. fractions — Rational numbers" >previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="http://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.5 documentation</a> » </li> <li><a href="index.html" >The Python Standard Library</a> »</li> <li><a href="numeric.html" >9. 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