FM / python2.7

/usr/lib64/python2.7

Name	Size	Mode	Actions
bsddb/	-	0755	rm
compiler/	-	0755	rm
config/	-	0755	rm
ctypes/	-	0755	rm
curses/	-	0755	rm
Demo/	-	0755	rm
distutils/	-	0755	rm
Doc/	-	0755	rm
email/	-	0755	rm
encodings/	-	0755	rm
ensurepip/	-	0755	rm
hotshot/	-	0755	rm
idlelib/	-	0755	rm
importlib/	-	0755	rm
json/	-	0755	rm
lib-dynload/	-	0755	rm
lib-tk/	-	0755	rm
lib2to3/	-	0755	rm
logging/	-	0755	rm
multiprocessing/	-	0755	rm
plat-linux2/	-	0755	rm
pydoc_data/	-	0755	rm
site-packages/	-	0755	rm
sqlite3/	-	0755	rm
test/	-	0755	rm
Tools/	-	0755	rm
unittest/	-	0755	rm
wsgiref/	-	0755	rm
xml/	-	0755	rm
abc.py	7145	0644	edit dl rm
abc.pyc	6143	0644	edit dl rm
abc.pyo	6087	0644	edit dl rm
aifc.py	34579	0644	edit dl rm
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aifc.pyo	30459	0644	edit dl rm
antigravity.py	60	0644	edit dl rm
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anydbm.py	2663	0644	edit dl rm
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argparse.py	89228	0644	edit dl rm
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argparse.pyo	64202	0644	edit dl rm
ast.py	11805	0644	edit dl rm
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asynchat.py	11581	0644	edit dl rm
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asyncore.py	20943	0644	edit dl rm
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atexit.py	1705	0644	edit dl rm
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audiodev.py	7597	0644	edit dl rm
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base64.py	11806	0755	edit dl rm
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BaseHTTPServer.py	22747	0644	edit dl rm
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Bastion.py	5744	0644	edit dl rm
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bdb.py	21714	0644	edit dl rm
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binhex.py	14698	0644	edit dl rm
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bisect.py	2595	0644	edit dl rm
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calendar.py	23384	0644	edit dl rm
calendar.pyc	27913	0644	edit dl rm
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cgi.py	36308	0755	edit dl rm
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cgi.pyo	33366	0644	edit dl rm
CGIHTTPServer.py	13089	0644	edit dl rm
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cgitb.py	12175	0644	edit dl rm
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chunk.py	5419	0644	edit dl rm
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cmd.py	15026	0644	edit dl rm
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code.py	10189	0644	edit dl rm
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codecs.py	36143	0644	edit dl rm
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codeop.py	5999	0644	edit dl rm
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collections.py	27798	0644	edit dl rm
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collections.pyo	26112	0644	edit dl rm
colorsys.py	3691	0644	edit dl rm
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commands.py	2545	0644	edit dl rm
commands.pyc	2469	0644	edit dl rm
commands.pyo	2469	0644	edit dl rm
compileall.py	7763	0644	edit dl rm
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ConfigParser.py	27746	0644	edit dl rm
ConfigParser.pyc	25213	0644	edit dl rm
ConfigParser.pyo	25213	0644	edit dl rm
contextlib.py	4424	0644	edit dl rm
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Cookie.py	26538	0644	edit dl rm
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cookielib.py	65486	0644	edit dl rm
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copy.py	11533	0644	edit dl rm
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copy_reg.py	6974	0644	edit dl rm
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cProfile.py	6573	0755	edit dl rm
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crypt.py	2292	0644	edit dl rm
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csv.py	16708	0644	edit dl rm
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dbhash.py	498	0644	edit dl rm
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decimal.py	221933	0644	edit dl rm
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difflib.py	82325	0644	edit dl rm
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dircache.py	1126	0644	edit dl rm
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dis.py	6499	0644	edit dl rm
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doctest.py	105095	0644	edit dl rm
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DocXMLRPCServer.py	10768	0644	edit dl rm
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dumbdbm.py	9141	0644	edit dl rm
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dummy_thread.py	4418	0644	edit dl rm
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dummy_threading.py	2804	0644	edit dl rm
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filecmp.py	9588	0644	edit dl rm
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fileinput.py	13746	0644	edit dl rm
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fnmatch.py	3315	0644	edit dl rm
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formatter.py	14911	0644	edit dl rm
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fpformat.py	4732	0644	edit dl rm
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fractions.py	22390	0644	edit dl rm
fractions.pyc	19711	0644	edit dl rm
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ftplib.py	38555	0644	edit dl rm
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functools.py	4806	0644	edit dl rm
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genericpath.py	3201	0644	edit dl rm
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getopt.py	7319	0644	edit dl rm
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getpass.py	5563	0644	edit dl rm
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gettext.py	22666	0644	edit dl rm
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glob.py	3114	0644	edit dl rm
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gzip.py	19028	0644	edit dl rm
gzip.pyc	15236	0644	edit dl rm
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hashlib.py	7841	0644	edit dl rm
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heapq.py	18295	0644	edit dl rm
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hmac.py	4588	0644	edit dl rm
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hmac.pyo	4542	0644	edit dl rm
htmlentitydefs.py	18056	0644	edit dl rm
htmlentitydefs.pyc	6367	0644	edit dl rm
htmlentitydefs.pyo	6367	0644	edit dl rm
htmllib.py	12869	0644	edit dl rm
htmllib.pyc	20309	0644	edit dl rm
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HTMLParser.py	17171	0644	edit dl rm
HTMLParser.pyc	13727	0644	edit dl rm
HTMLParser.pyo	13422	0644	edit dl rm
httplib.py	53306	0644	edit dl rm
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ihooks.py	18986	0644	edit dl rm
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imaplib.py	48366	0644	edit dl rm
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imghdr.py	3541	0644	edit dl rm
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imputil.py	25764	0644	edit dl rm
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inspect.py	43008	0644	edit dl rm
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io.py	3322	0644	edit dl rm
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keyword.py	1995	0755	edit dl rm
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linecache.py	4027	0644	edit dl rm
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locale.py	102834	0644	edit dl rm
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macpath.py	6289	0644	edit dl rm
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macurl2path.py	2731	0644	edit dl rm
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mailbox.py	81240	0644	edit dl rm
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mailcap.py	8404	0644	edit dl rm
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markupbase.py	14643	0644	edit dl rm
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md5.py	358	0644	edit dl rm
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mhlib.py	33434	0644	edit dl rm
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MimeWriter.py	6482	0644	edit dl rm
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mimify.py	15020	0755	edit dl rm
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modulefinder.py	24461	0644	edit dl rm
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multifile.py	4820	0644	edit dl rm
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mutex.py	1878	0644	edit dl rm
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netrc.py	5888	0644	edit dl rm
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new.py	610	0644	edit dl rm
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ntpath.py	19429	0644	edit dl rm
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nturl2path.py	2419	0644	edit dl rm
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numbers.py	10319	0644	edit dl rm
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opcode.py	5474	0644	edit dl rm
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pdb.doc	7914	0644	edit dl rm
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pickle.py	45489	0644	edit dl rm
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pickletools.py	74523	0644	edit dl rm
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pkgutil.py	20243	0644	edit dl rm
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platform.py	52801	0755	edit dl rm
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plistlib.py	15810	0644	edit dl rm
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profile.py	22781	0755	edit dl rm
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pydoc.py	95739	0755	edit dl rm
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py_compile.py	5936	0644	edit dl rm
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site.py	21296	0644	edit dl rm
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Edit: /usr/lib64/python2.7/random.py (32457B)

"""Random variable generators.

integers
    --------
           uniform within range

sequences
    ---------
           pick random element
           pick random sample
           generate random permutation

distributions on the real line:
    ------------------------------
           uniform
           triangular
           normal (Gaussian)
           lognormal
           negative exponential
           gamma
           beta
           pareto
           Weibull

distributions on the circle (angles 0 to 2pi)
    ---------------------------------------------
           circular uniform
           von Mises

General notes on the underlying Mersenne Twister core generator:

* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* Without a direct way to compute N steps forward, the semantics of
  jumpahead(n) are weakened to simply jump to another distant state and rely
  on the large period to avoid overlapping sequences.
* The random() method is implemented in C, executes in a single Python step,
  and is, therefore, threadsafe.

"""

from __future__ import division
from warnings import warn as _warn
from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType
from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from os import urandom as _urandom
from binascii import hexlify as _hexlify
import hashlib as _hashlib

__all__ = ["Random","seed","random","uniform","randint","choice","sample",
           "randrange","shuffle","normalvariate","lognormvariate",
           "expovariate","vonmisesvariate","gammavariate","triangular",
           "gauss","betavariate","paretovariate","weibullvariate",
           "getstate","setstate","jumpahead", "WichmannHill", "getrandbits",
           "SystemRandom"]

NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
TWOPI = 2.0*_pi
LOG4 = _log(4.0)
SG_MAGICCONST = 1.0 + _log(4.5)
BPF = 53        # Number of bits in a float
RECIP_BPF = 2**-BPF

# Translated by Guido van Rossum from C source provided by
# Adrian Baddeley.  Adapted by Raymond Hettinger for use with
# the Mersenne Twister  and os.urandom() core generators.

import _random

class Random(_random.Random):
    """Random number generator base class used by bound module functions.

Used to instantiate instances of Random to get generators that don't
    share state.  Especially useful for multi-threaded programs, creating
    a different instance of Random for each thread, and using the jumpahead()
    method to ensure that the generated sequences seen by each thread don't
    overlap.

Class Random can also be subclassed if you want to use a different basic
    generator of your own devising: in that case, override the following
    methods: random(), seed(), getstate(), setstate() and jumpahead().
    Optionally, implement a getrandbits() method so that randrange() can cover
    arbitrarily large ranges.

"""

VERSION = 3     # used by getstate/setstate

def __init__(self, x=None):
        """Initialize an instance.

Optional argument x controls seeding, as for Random.seed().
        """

self.seed(x)
        self.gauss_next = None

def seed(self, a=None):
        """Initialize internal state of the random number generator.

None or no argument seeds from current time or from an operating
        system specific randomness source if available.

If a is not None or is an int or long, hash(a) is used instead.
        Hash values for some types are nondeterministic when the
        PYTHONHASHSEED environment variable is enabled.
        """

if a is None:
            try:
                # Seed with enough bytes to span the 19937 bit
                # state space for the Mersenne Twister
                a = long(_hexlify(_urandom(2500)), 16)
            except NotImplementedError:
                import time
                a = long(time.time() * 256) # use fractional seconds

super(Random, self).seed(a)
        self.gauss_next = None

def getstate(self):
        """Return internal state; can be passed to setstate() later."""
        return self.VERSION, super(Random, self).getstate(), self.gauss_next

def setstate(self, state):
        """Restore internal state from object returned by getstate()."""
        version = state[0]
        if version == 3:
            version, internalstate, self.gauss_next = state
            super(Random, self).setstate(internalstate)
        elif version == 2:
            version, internalstate, self.gauss_next = state
            # In version 2, the state was saved as signed ints, which causes
            #   inconsistencies between 32/64-bit systems. The state is
            #   really unsigned 32-bit ints, so we convert negative ints from
            #   version 2 to positive longs for version 3.
            try:
                internalstate = tuple( long(x) % (2**32) for x in internalstate )
            except ValueError, e:
                raise TypeError, e
            super(Random, self).setstate(internalstate)
        else:
            raise ValueError("state with version %s passed to "
                             "Random.setstate() of version %s" %
                             (version, self.VERSION))

def jumpahead(self, n):
        """Change the internal state to one that is likely far away
        from the current state.  This method will not be in Py3.x,
        so it is better to simply reseed.
        """
        # The super.jumpahead() method uses shuffling to change state,
        # so it needs a large and "interesting" n to work with.  Here,
        # we use hashing to create a large n for the shuffle.
        s = repr(n) + repr(self.getstate())
        n = int(_hashlib.new('sha512', s).hexdigest(), 16)
        super(Random, self).jumpahead(n)

## ---- Methods below this point do not need to be overridden when
## ---- subclassing for the purpose of using a different core generator.

## -------------------- pickle support  -------------------

def __getstate__(self): # for pickle
        return self.getstate()

def __setstate__(self, state):  # for pickle
        self.setstate(state)

def __reduce__(self):
        return self.__class__, (), self.getstate()

## -------------------- integer methods  -------------------

def randrange(self, start, stop=None, step=1, _int=int, _maxwidth=1L<<BPF):
        """Choose a random item from range(start, stop[, step]).

This fixes the problem with randint() which includes the
        endpoint; in Python this is usually not what you want.

"""

# This code is a bit messy to make it fast for the
        # common case while still doing adequate error checking.
        istart = _int(start)
        if istart != start:
            raise ValueError, "non-integer arg 1 for randrange()"
        if stop is None:
            if istart > 0:
                if istart >= _maxwidth:
                    return self._randbelow(istart)
                return _int(self.random() * istart)
            raise ValueError, "empty range for randrange()"

# stop argument supplied.
        istop = _int(stop)
        if istop != stop:
            raise ValueError, "non-integer stop for randrange()"
        width = istop - istart
        if step == 1 and width > 0:
            # Note that
            #     int(istart + self.random()*width)
            # instead would be incorrect.  For example, consider istart
            # = -2 and istop = 0.  Then the guts would be in
            # -2.0 to 0.0 exclusive on both ends (ignoring that random()
            # might return 0.0), and because int() truncates toward 0, the
            # final result would be -1 or 0 (instead of -2 or -1).
            #     istart + int(self.random()*width)
            # would also be incorrect, for a subtler reason:  the RHS
            # can return a long, and then randrange() would also return
            # a long, but we're supposed to return an int (for backward
            # compatibility).

if width >= _maxwidth:
                return _int(istart + self._randbelow(width))
            return _int(istart + _int(self.random()*width))
        if step == 1:
            raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width)

# Non-unit step argument supplied.
        istep = _int(step)
        if istep != step:
            raise ValueError, "non-integer step for randrange()"
        if istep > 0:
            n = (width + istep - 1) // istep
        elif istep < 0:
            n = (width + istep + 1) // istep
        else:
            raise ValueError, "zero step for randrange()"

if n <= 0:
            raise ValueError, "empty range for randrange()"

if n >= _maxwidth:
            return istart + istep*self._randbelow(n)
        return istart + istep*_int(self.random() * n)

def randint(self, a, b):
        """Return random integer in range [a, b], including both end points.
        """

return self.randrange(a, b+1)

def _randbelow(self, n, _log=_log, _int=int, _maxwidth=1L<<BPF,
                   _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType):
        """Return a random int in the range [0,n)

Handles the case where n has more bits than returned
        by a single call to the underlying generator.
        """

try:
            getrandbits = self.getrandbits
        except AttributeError:
            pass
        else:
            # Only call self.getrandbits if the original random() builtin method
            # has not been overridden or if a new getrandbits() was supplied.
            # This assures that the two methods correspond.
            if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method:
                k = _int(1.00001 + _log(n-1, 2.0))   # 2**k > n-1 > 2**(k-2)
                r = getrandbits(k)
                while r >= n:
                    r = getrandbits(k)
                return r
        if n >= _maxwidth:
            _warn("Underlying random() generator does not supply \n"
                "enough bits to choose from a population range this large")
        return _int(self.random() * n)

## -------------------- sequence methods  -------------------

def choice(self, seq):
        """Choose a random element from a non-empty sequence."""
        return seq[int(self.random() * len(seq))]  # raises IndexError if seq is empty

def shuffle(self, x, random=None):
        """x, random=random.random -> shuffle list x in place; return None.

Optional arg random is a 0-argument function returning a random
        float in [0.0, 1.0); by default, the standard random.random.

"""

if random is None:
            random = self.random
        _int = int
        for i in reversed(xrange(1, len(x))):
            # pick an element in x[:i+1] with which to exchange x[i]
            j = _int(random() * (i+1))
            x[i], x[j] = x[j], x[i]

def sample(self, population, k):
        """Chooses k unique random elements from a population sequence.

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).

Members of the population need not be hashable or unique.  If the
        population contains repeats, then each occurrence is a possible
        selection in the sample.

To choose a sample in a range of integers, use xrange as an argument.
        This is especially fast and space efficient for sampling from a
        large population:   sample(xrange(10000000), 60)
        """

# Sampling without replacement entails tracking either potential
        # selections (the pool) in a list or previous selections in a set.

# When the number of selections is small compared to the
        # population, then tracking selections is efficient, requiring
        # only a small set and an occasional reselection.  For
        # a larger number of selections, the pool tracking method is
        # preferred since the list takes less space than the
        # set and it doesn't suffer from frequent reselections.

n = len(population)
        if not 0 <= k <= n:
            raise ValueError("sample larger than population")
        random = self.random
        _int = int
        result = [None] * k
        setsize = 21        # size of a small set minus size of an empty list
        if k > 5:
            setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
        if n <= setsize or hasattr(population, "keys"):
            # An n-length list is smaller than a k-length set, or this is a
            # mapping type so the other algorithm wouldn't work.
            pool = list(population)
            for i in xrange(k):         # invariant:  non-selected at [0,n-i)
                j = _int(random() * (n-i))
                result[i] = pool[j]
                pool[j] = pool[n-i-1]   # move non-selected item into vacancy
        else:
            try:
                selected = set()
                selected_add = selected.add
                for i in xrange(k):
                    j = _int(random() * n)
                    while j in selected:
                        j = _int(random() * n)
                    selected_add(j)
                    result[i] = population[j]
            except (TypeError, KeyError):   # handle (at least) sets
                if isinstance(population, list):
                    raise
                return self.sample(tuple(population), k)
        return result

## -------------------- real-valued distributions  -------------------

## -------------------- uniform distribution -------------------

def uniform(self, a, b):
        "Get a random number in the range [a, b) or [a, b] depending on rounding."
        return a + (b-a) * self.random()

## -------------------- triangular --------------------

def triangular(self, low=0.0, high=1.0, mode=None):
        """Triangular distribution.

Continuous distribution bounded by given lower and upper limits,
        and having a given mode value in-between.

http://en.wikipedia.org/wiki/Triangular_distribution

"""
        u = self.random()
        try:
            c = 0.5 if mode is None else (mode - low) / (high - low)
        except ZeroDivisionError:
            return low
        if u > c:
            u = 1.0 - u
            c = 1.0 - c
            low, high = high, low
        return low + (high - low) * (u * c) ** 0.5

## -------------------- normal distribution --------------------

def normalvariate(self, mu, sigma):
        """Normal distribution.

mu is the mean, and sigma is the standard deviation.

"""
        # mu = mean, sigma = standard deviation

# Uses Kinderman and Monahan method. Reference: Kinderman,
        # A.J. and Monahan, J.F., "Computer generation of random
        # variables using the ratio of uniform deviates", ACM Trans
        # Math Software, 3, (1977), pp257-260.

random = self.random
        while 1:
            u1 = random()
            u2 = 1.0 - random()
            z = NV_MAGICCONST*(u1-0.5)/u2
            zz = z*z/4.0
            if zz <= -_log(u2):
                break
        return mu + z*sigma

## -------------------- lognormal distribution --------------------

def lognormvariate(self, mu, sigma):
        """Log normal distribution.

If you take the natural logarithm of this distribution, you'll get a
        normal distribution with mean mu and standard deviation sigma.
        mu can have any value, and sigma must be greater than zero.

"""
        return _exp(self.normalvariate(mu, sigma))

## -------------------- exponential distribution --------------------

def expovariate(self, lambd):
        """Exponential distribution.

lambd 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 lambd is positive, and from negative
        infinity to 0 if lambd is negative.

"""
        # lambd: rate lambd = 1/mean
        # ('lambda' is a Python reserved word)

# we use 1-random() instead of random() to preclude the
        # possibility of taking the log of zero.
        return -_log(1.0 - self.random())/lambd

## -------------------- von Mises distribution --------------------

def vonmisesvariate(self, mu, kappa):
        """Circular data distribution.

mu is the mean angle, expressed in radians between 0 and 2*pi, and
        kappa is the concentration parameter, which must be greater than or
        equal to zero.  If kappa is equal to zero, this distribution reduces
        to a uniform random angle over the range 0 to 2*pi.

"""
        # mu:    mean angle (in radians between 0 and 2*pi)
        # kappa: concentration parameter kappa (>= 0)
        # if kappa = 0 generate uniform random angle

# Based upon an algorithm published in: Fisher, N.I.,
        # "Statistical Analysis of Circular Data", Cambridge
        # University Press, 1993.

# Thanks to Magnus Kessler for a correction to the
        # implementation of step 4.

random = self.random
        if kappa <= 1e-6:
            return TWOPI * random()

s = 0.5 / kappa
        r = s + _sqrt(1.0 + s * s)

while 1:
            u1 = random()
            z = _cos(_pi * u1)

d = z / (r + z)
            u2 = random()
            if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d):
                break

q = 1.0 / r
        f = (q + z) / (1.0 + q * z)
        u3 = random()
        if u3 > 0.5:
            theta = (mu + _acos(f)) % TWOPI
        else:
            theta = (mu - _acos(f)) % TWOPI

return theta

## -------------------- gamma distribution --------------------

def gammavariate(self, alpha, beta):
        """Gamma distribution.  Not the gamma function!

Conditions on the parameters are alpha > 0 and beta > 0.

The probability distribution function is:

x ** (alpha - 1) * math.exp(-x / beta)
          pdf(x) =  --------------------------------------
                      math.gamma(alpha) * beta ** alpha

"""

# alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2

# Warning: a few older sources define the gamma distribution in terms
        # of alpha > -1.0
        if alpha <= 0.0 or beta <= 0.0:
            raise ValueError, 'gammavariate: alpha and beta must be > 0.0'

random = self.random
        if alpha > 1.0:

# Uses R.C.H. Cheng, "The generation of Gamma
            # variables with non-integral shape parameters",
            # Applied Statistics, (1977), 26, No. 1, p71-74

ainv = _sqrt(2.0 * alpha - 1.0)
            bbb = alpha - LOG4
            ccc = alpha + ainv

while 1:
                u1 = random()
                if not 1e-7 < u1 < .9999999:
                    continue
                u2 = 1.0 - random()
                v = _log(u1/(1.0-u1))/ainv
                x = alpha*_exp(v)
                z = u1*u1*u2
                r = bbb+ccc*v-x
                if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
                    return x * beta

elif alpha == 1.0:
            # expovariate(1)
            u = random()
            while u <= 1e-7:
                u = random()
            return -_log(u) * beta

else:   # alpha is between 0 and 1 (exclusive)

# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle

while 1:
                u = random()
                b = (_e + alpha)/_e
                p = b*u
                if p <= 1.0:
                    x = p ** (1.0/alpha)
                else:
                    x = -_log((b-p)/alpha)
                u1 = random()
                if p > 1.0:
                    if u1 <= x ** (alpha - 1.0):
                        break
                elif u1 <= _exp(-x):
                    break
            return x * beta

## -------------------- Gauss (faster alternative) --------------------

def gauss(self, mu, sigma):
        """Gaussian distribution.

mu is the mean, and sigma is the standard deviation.  This is
        slightly faster than the normalvariate() function.

Not thread-safe without a lock around calls.

"""

# When x and y are two variables from [0, 1), uniformly
        # distributed, then
        #
        #    cos(2*pi*x)*sqrt(-2*log(1-y))
        #    sin(2*pi*x)*sqrt(-2*log(1-y))
        #
        # are two *independent* variables with normal distribution
        # (mu = 0, sigma = 1).
        # (Lambert Meertens)
        # (corrected version; bug discovered by Mike Miller, fixed by LM)

# Multithreading note: When two threads call this function
        # simultaneously, it is possible that they will receive the
        # same return value.  The window is very small though.  To
        # avoid this, you have to use a lock around all calls.  (I
        # didn't want to slow this down in the serial case by using a
        # lock here.)

random = self.random
        z = self.gauss_next
        self.gauss_next = None
        if z is None:
            x2pi = random() * TWOPI
            g2rad = _sqrt(-2.0 * _log(1.0 - random()))
            z = _cos(x2pi) * g2rad
            self.gauss_next = _sin(x2pi) * g2rad

return mu + z*sigma

## -------------------- beta --------------------
## See
## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html
## for Ivan Frohne's insightful analysis of why the original implementation:
##
##    def betavariate(self, alpha, beta):
##        # Discrete Event Simulation in C, pp 87-88.
##
##        y = self.expovariate(alpha)
##        z = self.expovariate(1.0/beta)
##        return z/(y+z)
##
## was dead wrong, and how it probably got that way.

def betavariate(self, alpha, beta):
        """Beta distribution.

Conditions on the parameters are alpha > 0 and beta > 0.
        Returned values range between 0 and 1.

"""

# This version due to Janne Sinkkonen, and matches all the std
        # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
        y = self.gammavariate(alpha, 1.)
        if y == 0:
            return 0.0
        else:
            return y / (y + self.gammavariate(beta, 1.))

## -------------------- Pareto --------------------

def paretovariate(self, alpha):
        """Pareto distribution.  alpha is the shape parameter."""
        # Jain, pg. 495

u = 1.0 - self.random()
        return 1.0 / pow(u, 1.0/alpha)

## -------------------- Weibull --------------------

def weibullvariate(self, alpha, beta):
        """Weibull distribution.

alpha is the scale parameter and beta is the shape parameter.

"""
        # Jain, pg. 499; bug fix courtesy Bill Arms

u = 1.0 - self.random()
        return alpha * pow(-_log(u), 1.0/beta)

## -------------------- Wichmann-Hill -------------------

class WichmannHill(Random):

VERSION = 1     # used by getstate/setstate

def seed(self, a=None):
        """Initialize internal state from hashable object.

None or no argument seeds from current time or from an operating
        system specific randomness source if available.

If a is not None or an int or long, hash(a) is used instead.

If a is an int or long, a is used directly.  Distinct values between
        0 and 27814431486575L inclusive are guaranteed to yield distinct
        internal states (this guarantee is specific to the default
        Wichmann-Hill generator).
        """

if a is None:
            try:
                a = long(_hexlify(_urandom(16)), 16)
            except NotImplementedError:
                import time
                a = long(time.time() * 256) # use fractional seconds

if not isinstance(a, (int, long)):
            a = hash(a)

a, x = divmod(a, 30268)
        a, y = divmod(a, 30306)
        a, z = divmod(a, 30322)
        self._seed = int(x)+1, int(y)+1, int(z)+1

self.gauss_next = None

def random(self):
        """Get the next random number in the range [0.0, 1.0)."""

# Wichman-Hill random number generator.
        #
        # Wichmann, B. A. & Hill, I. D. (1982)
        # Algorithm AS 183:
        # An efficient and portable pseudo-random number generator
        # Applied Statistics 31 (1982) 188-190
        #
        # see also:
        #        Correction to Algorithm AS 183
        #        Applied Statistics 33 (1984) 123
        #
        #        McLeod, A. I. (1985)
        #        A remark on Algorithm AS 183
        #        Applied Statistics 34 (1985),198-200

# This part is thread-unsafe:
        # BEGIN CRITICAL SECTION
        x, y, z = self._seed
        x = (171 * x) % 30269
        y = (172 * y) % 30307
        z = (170 * z) % 30323
        self._seed = x, y, z
        # END CRITICAL SECTION

# Note:  on a platform using IEEE-754 double arithmetic, this can
        # never return 0.0 (asserted by Tim; proof too long for a comment).
        return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0

def getstate(self):
        """Return internal state; can be passed to setstate() later."""
        return self.VERSION, self._seed, self.gauss_next

def setstate(self, state):
        """Restore internal state from object returned by getstate()."""
        version = state[0]
        if version == 1:
            version, self._seed, self.gauss_next = state
        else:
            raise ValueError("state with version %s passed to "
                             "Random.setstate() of version %s" %
                             (version, self.VERSION))

def jumpahead(self, n):
        """Act as if n calls to random() were made, but quickly.

n is an int, greater than or equal to 0.

Example use:  If you have 2 threads and know that each will
        consume no more than a million random numbers, create two Random
        objects r1 and r2, then do
            r2.setstate(r1.getstate())
            r2.jumpahead(1000000)
        Then r1 and r2 will use guaranteed-disjoint segments of the full
        period.
        """

if not n >= 0:
            raise ValueError("n must be >= 0")
        x, y, z = self._seed
        x = int(x * pow(171, n, 30269)) % 30269
        y = int(y * pow(172, n, 30307)) % 30307
        z = int(z * pow(170, n, 30323)) % 30323
        self._seed = x, y, z

def __whseed(self, x=0, y=0, z=0):
        """Set the Wichmann-Hill seed from (x, y, z).

These must be integers in the range [0, 256).
        """

if not type(x) == type(y) == type(z) == int:
            raise TypeError('seeds must be integers')
        if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
            raise ValueError('seeds must be in range(0, 256)')
        if 0 == x == y == z:
            # Initialize from current time
            import time
            t = long(time.time() * 256)
            t = int((t&0xffffff) ^ (t>>24))
            t, x = divmod(t, 256)
            t, y = divmod(t, 256)
            t, z = divmod(t, 256)
        # Zero is a poor seed, so substitute 1
        self._seed = (x or 1, y or 1, z or 1)

self.gauss_next = None

def whseed(self, a=None):
        """Seed from hashable object's hash code.

None or no argument seeds from current time.  It is not guaranteed
        that objects with distinct hash codes lead to distinct internal
        states.

This is obsolete, provided for compatibility with the seed routine
        used prior to Python 2.1.  Use the .seed() method instead.
        """

if a is None:
            self.__whseed()
            return
        a = hash(a)
        a, x = divmod(a, 256)
        a, y = divmod(a, 256)
        a, z = divmod(a, 256)
        x = (x + a) % 256 or 1
        y = (y + a) % 256 or 1
        z = (z + a) % 256 or 1
        self.__whseed(x, y, z)

## --------------- Operating System Random Source  ------------------

class SystemRandom(Random):
    """Alternate random number generator using sources provided
    by the operating system (such as /dev/urandom on Unix or
    CryptGenRandom on Windows).

Not available on all systems (see os.urandom() for details).
    """

def random(self):
        """Get the next random number in the range [0.0, 1.0)."""
        return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF

def getrandbits(self, k):
        """getrandbits(k) -> x.  Generates a long int with k random bits."""
        if k <= 0:
            raise ValueError('number of bits must be greater than zero')
        if k != int(k):
            raise TypeError('number of bits should be an integer')
        bytes = (k + 7) // 8                    # bits / 8 and rounded up
        x = long(_hexlify(_urandom(bytes)), 16)
        return x >> (bytes * 8 - k)             # trim excess bits

def _stub(self, *args, **kwds):
        "Stub method.  Not used for a system random number generator."
        return None
    seed = jumpahead = _stub

def _notimplemented(self, *args, **kwds):
        "Method should not be called for a system random number generator."
        raise NotImplementedError('System entropy source does not have state.')
    getstate = setstate = _notimplemented

## -------------------- test program --------------------

def _test_generator(n, func, args):
    import time
    print n, 'times', func.__name__
    total = 0.0
    sqsum = 0.0
    smallest = 1e10
    largest = -1e10
    t0 = time.time()
    for i in range(n):
        x = func(*args)
        total += x
        sqsum = sqsum + x*x
        smallest = min(x, smallest)
        largest = max(x, largest)
    t1 = time.time()
    print round(t1-t0, 3), 'sec,',
    avg = total/n
    stddev = _sqrt(sqsum/n - avg*avg)
    print 'avg %g, stddev %g, min %g, max %g' % \
              (avg, stddev, smallest, largest)

def _test(N=2000):
    _test_generator(N, random, ())
    _test_generator(N, normalvariate, (0.0, 1.0))
    _test_generator(N, lognormvariate, (0.0, 1.0))
    _test_generator(N, vonmisesvariate, (0.0, 1.0))
    _test_generator(N, gammavariate, (0.01, 1.0))
    _test_generator(N, gammavariate, (0.1, 1.0))
    _test_generator(N, gammavariate, (0.1, 2.0))
    _test_generator(N, gammavariate, (0.5, 1.0))
    _test_generator(N, gammavariate, (0.9, 1.0))
    _test_generator(N, gammavariate, (1.0, 1.0))
    _test_generator(N, gammavariate, (2.0, 1.0))
    _test_generator(N, gammavariate, (20.0, 1.0))
    _test_generator(N, gammavariate, (200.0, 1.0))
    _test_generator(N, gauss, (0.0, 1.0))
    _test_generator(N, betavariate, (3.0, 3.0))
    _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0))

# Create one instance, seeded from current time, and export its methods
# as module-level functions.  The functions share state across all uses
#(both in the user's code and in the Python libraries), but that's fine
# for most programs and is easier for the casual user than making them
# instantiate their own Random() instance.

_inst = Random()
seed = _inst.seed
random = _inst.random
uniform = _inst.uniform
triangular = _inst.triangular
randint = _inst.randint
choice = _inst.choice
randrange = _inst.randrange
sample = _inst.sample
shuffle = _inst.shuffle
normalvariate = _inst.normalvariate
lognormvariate = _inst.lognormvariate
expovariate = _inst.expovariate
vonmisesvariate = _inst.vonmisesvariate
gammavariate = _inst.gammavariate
gauss = _inst.gauss
betavariate = _inst.betavariate
paretovariate = _inst.paretovariate
weibullvariate = _inst.weibullvariate
getstate = _inst.getstate
setstate = _inst.setstate
jumpahead = _inst.jumpahead
getrandbits = _inst.getrandbits

if __name__ == '__main__':
    _test()

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