FM / python3.11

/opt/alt/python311/lib64/python3.11

Name	Size	Mode	Actions
asyncio/	-	0755	rm
collections/	-	0755	rm
concurrent/	-	0755	rm
config-3.11-x86_64-linux-gnu/	-	0755	rm
ctypes/	-	0755	rm
curses/	-	0755	rm
dbm/	-	0755	rm
distutils/	-	0755	rm
email/	-	0755	rm
encodings/	-	0755	rm
ensurepip/	-	0755	rm
html/	-	0755	rm
http/	-	0755	rm
importlib/	-	0755	rm
json/	-	0755	rm
lib-dynload/	-	0755	rm
lib2to3/	-	0755	rm
logging/	-	0755	rm
multiprocessing/	-	0755	rm
pydoc_data/	-	0755	rm
re/	-	0755	rm
site-packages/	-	0755	rm
sqlite3/	-	0755	rm
tomllib/	-	0755	rm
unittest/	-	0755	rm
urllib/	-	0755	rm
venv/	-	0755	rm
wsgiref/	-	0755	rm
xml/	-	0755	rm
xmlrpc/	-	0755	rm
zoneinfo/	-	0755	rm
__phello__/	-	0755	rm
__pycache__/	-	0755	rm
abc.py	6538	0644	edit dl rm
aifc.py	34211	0644	edit dl rm
antigravity.py	500	0644	edit dl rm
argparse.py	100283	0644	edit dl rm
ast.py	61444	0644	edit dl rm
asynchat.py	11570	0644	edit dl rm
asyncore.py	20310	0644	edit dl rm
base64.py	21041	0755	edit dl rm
bdb.py	32463	0644	edit dl rm
bisect.py	3135	0644	edit dl rm
bz2.py	11847	0644	edit dl rm
calendar.py	24731	0644	edit dl rm
cgi.py	34432	0755	edit dl rm
cgitb.py	12421	0644	edit dl rm
chunk.py	5500	0644	edit dl rm
cmd.py	14873	0644	edit dl rm
code.py	10622	0644	edit dl rm
codecs.py	37150	0644	edit dl rm
codeop.py	5907	0644	edit dl rm
colorsys.py	4062	0644	edit dl rm
compileall.py	20252	0644	edit dl rm
configparser.py	55660	0644	edit dl rm
contextlib.py	27414	0644	edit dl rm
contextvars.py	129	0644	edit dl rm
copy.py	8681	0644	edit dl rm
copyreg.py	7677	0644	edit dl rm
cProfile.py	6359	0755	edit dl rm
crypt.py	3913	0644	edit dl rm
csv.py	16030	0644	edit dl rm
dataclasses.py	58472	0644	edit dl rm
datetime.py	91832	0644	edit dl rm
decimal.py	320	0644	edit dl rm
difflib.py	83308	0644	edit dl rm
dis.py	28906	0644	edit dl rm
doctest.py	106297	0644	edit dl rm
enum.py	79583	0644	edit dl rm
filecmp.py	10178	0644	edit dl rm
fileinput.py	15714	0644	edit dl rm
fnmatch.py	5999	0644	edit dl rm
fractions.py	28677	0644	edit dl rm
ftplib.py	35815	0644	edit dl rm
functools.py	38413	0644	edit dl rm
genericpath.py	4975	0644	edit dl rm
getopt.py	7489	0644	edit dl rm
getpass.py	5990	0644	edit dl rm
gettext.py	21320	0644	edit dl rm
glob.py	8732	0644	edit dl rm
graphlib.py	9656	0644	edit dl rm
gzip.py	24074	0644	edit dl rm
hashlib.py	11765	0644	edit dl rm
heapq.py	23024	0644	edit dl rm
hmac.py	7716	0644	edit dl rm
imaplib.py	55217	0644	edit dl rm
imghdr.py	3952	0644	edit dl rm
imp.py	10606	0644	edit dl rm
inspect.py	123419	0644	edit dl rm
io.py	4320	0644	edit dl rm
ipaddress.py	79124	0644	edit dl rm
keyword.py	1061	0644	edit dl rm
LICENSE.txt	13936	0644	edit dl rm
linecache.py	5649	0644	edit dl rm
locale.py	79095	0644	edit dl rm
lzma.py	13277	0644	edit dl rm
mailbox.py	78830	0644	edit dl rm
mailcap.py	9369	0644	edit dl rm
mimetypes.py	22962	0644	edit dl rm
modulefinder.py	23699	0644	edit dl rm
netrc.py	6929	0644	edit dl rm
nntplib.py	41087	0644	edit dl rm
ntpath.py	30222	0644	edit dl rm
nturl2path.py	2887	0644	edit dl rm
numbers.py	10348	0644	edit dl rm
opcode.py	10447	0644	edit dl rm
operator.py	10965	0644	edit dl rm
optparse.py	60369	0644	edit dl rm
os.py	39530	0644	edit dl rm
pathlib.py	48566	0644	edit dl rm
pdb.py	64186	0755	edit dl rm
pickle.py	65132	0644	edit dl rm
pickletools.py	93861	0644	edit dl rm
pipes.py	8978	0644	edit dl rm
pkgutil.py	24638	0644	edit dl rm
platform.py	42287	0755	edit dl rm
plistlib.py	28354	0644	edit dl rm
poplib.py	15198	0644	edit dl rm
posixpath.py	17013	0644	edit dl rm
pprint.py	24583	0644	edit dl rm
profile.py	22896	0755	edit dl rm
pstats.py	29356	0644	edit dl rm
pty.py	6317	0644	edit dl rm
pyclbr.py	11396	0644	edit dl rm
pydoc.py	112664	0755	edit dl rm
py_compile.py	7837	0644	edit dl rm
queue.py	11496	0644	edit dl rm
quopri.py	7281	0755	edit dl rm
random.py	32162	0644	edit dl rm
reprlib.py	5437	0644	edit dl rm
rlcompleter.py	7827	0644	edit dl rm
runpy.py	13159	0644	edit dl rm
sched.py	6351	0644	edit dl rm
secrets.py	2028	0644	edit dl rm
selectors.py	19671	0644	edit dl rm
shelve.py	8560	0644	edit dl rm
shlex.py	13501	0644	edit dl rm
shutil.py	56517	0644	edit dl rm
signal.py	2495	0644	edit dl rm
site.py	22987	0644	edit dl rm
smtpd.py	31175	0755	edit dl rm
smtplib.py	45431	0755	edit dl rm
sndhdr.py	7448	0644	edit dl rm
socket.py	37557	0644	edit dl rm
socketserver.py	27586	0644	edit dl rm
sre_compile.py	231	0644	edit dl rm
sre_constants.py	232	0644	edit dl rm
sre_parse.py	229	0644	edit dl rm
ssl.py	54305	0644	edit dl rm
stat.py	5485	0644	edit dl rm
statistics.py	47705	0644	edit dl rm
string.py	11786	0644	edit dl rm
stringprep.py	12917	0644	edit dl rm
struct.py	257	0644	edit dl rm
subprocess.py	88725	0644	edit dl rm
sunau.py	18480	0644	edit dl rm
symtable.py	10368	0644	edit dl rm
sysconfig.py	30315	0644	edit dl rm
tabnanny.py	11312	0755	edit dl rm
tarfile.py	107876	0755	edit dl rm
telnetlib.py	23301	0644	edit dl rm
tempfile.py	31873	0644	edit dl rm
textwrap.py	19718	0644	edit dl rm
this.py	1003	0644	edit dl rm
threading.py	58231	0644	edit dl rm
timeit.py	13532	0755	edit dl rm
token.py	2386	0644	edit dl rm
tokenize.py	26336	0644	edit dl rm
trace.py	29196	0755	edit dl rm
traceback.py	40547	0644	edit dl rm
tracemalloc.py	18047	0644	edit dl rm
tty.py	879	0644	edit dl rm
types.py	10067	0644	edit dl rm
typing.py	120951	0644	edit dl rm
uu.py	7341	0644	edit dl rm
uuid.py	27597	0644	edit dl rm
warnings.py	21110	0644	edit dl rm
wave.py	21818	0644	edit dl rm
weakref.py	21513	0644	edit dl rm
webbrowser.py	25149	0755	edit dl rm
xdrlib.py	5977	0644	edit dl rm
zipapp.py	7535	0644	edit dl rm
zipfile.py	93788	0644	edit dl rm
zipimport.py	30897	0644	edit dl rm
_aix_support.py	3389	0644	edit dl rm
_bootsubprocess.py	2675	0644	edit dl rm
_collections_abc.py	30193	0644	edit dl rm
_compat_pickle.py	8761	0644	edit dl rm
_compression.py	5681	0644	edit dl rm
_markupbase.py	14653	0644	edit dl rm
_osx_support.py	22023	0644	edit dl rm
_pydecimal.py	229202	0644	edit dl rm
_pyio.py	94193	0644	edit dl rm
_py_abc.py	6189	0644	edit dl rm
_sitebuiltins.py	3128	0644	edit dl rm
_strptime.py	25175	0644	edit dl rm
_sysconfigdata_d_linux_x86_64-linux-gnu.py	58878	0644	edit dl rm
_sysconfigdata__linux_x86_64-linux-gnu.py	59645	0644	edit dl rm
_threading_local.py	7220	0644	edit dl rm
_weakrefset.py	5893	0644	edit dl rm
__future__.py	5218	0644	edit dl rm
__hello__.py	227	0644	edit dl rm

Edit: /opt/alt/python311/lib64/python3.11/random.py (32162B)

"""Random variable generators.

bytes
    -----
           uniform bytes (values between 0 and 255)

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

sequences
    ---------
           pick random element
           pick random sample
           pick weighted 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.
* The random() method is implemented in C, executes in a single Python step,
  and is, therefore, threadsafe.

"""

# 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.

from warnings import warn as _warn
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 math import tau as TWOPI, floor as _floor, isfinite as _isfinite
from os import urandom as _urandom
from _collections_abc import Set as _Set, Sequence as _Sequence
from operator import index as _index
from itertools import accumulate as _accumulate, repeat as _repeat
from bisect import bisect as _bisect
import os as _os
import _random

try:
    # hashlib is pretty heavy to load, try lean internal module first
    from _sha512 import sha512 as _sha512
except ImportError:
    # fallback to official implementation
    from hashlib import sha512 as _sha512

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

NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0)
LOG4 = _log(4.0)
SG_MAGICCONST = 1.0 + _log(4.5)
BPF = 53        # Number of bits in a float
RECIP_BPF = 2 ** -BPF
_ONE = 1

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.

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(), and setstate().
    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, version=2):
        """Initialize internal state from a seed.

The only supported seed types are None, int, float,
        str, bytes, and bytearray.

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

If *a* is an int, all bits are used.

For version 2 (the default), all of the bits are used if *a* is a str,
        bytes, or bytearray.  For version 1 (provided for reproducing random
        sequences from older versions of Python), the algorithm for str and
        bytes generates a narrower range of seeds.

"""

if version == 1 and isinstance(a, (str, bytes)):
            a = a.decode('latin-1') if isinstance(a, bytes) else a
            x = ord(a[0]) << 7 if a else 0
            for c in map(ord, a):
                x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF
            x ^= len(a)
            a = -2 if x == -1 else x

elif version == 2 and isinstance(a, (str, bytes, bytearray)):
            if isinstance(a, str):
                a = a.encode()
            a = int.from_bytes(a + _sha512(a).digest())

elif not isinstance(a, (type(None), int, float, str, bytes, bytearray)):
            raise TypeError('The only supported seed types are: None,\n'
                            'int, float, str, bytes, and bytearray.')

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

def getstate(self):
        """Return internal state; can be passed to setstate() later."""
        return self.VERSION, super().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().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(x % (2 ** 32) for x in internalstate)
            except ValueError as e:
                raise TypeError from e
            super().setstate(internalstate)
        else:
            raise ValueError("state with version %s passed to "
                             "Random.setstate() of version %s" %
                             (version, self.VERSION))

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

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

# Issue 17489: Since __reduce__ was defined to fix #759889 this is no
    # longer called; we leave it here because it has been here since random was
    # rewritten back in 2001 and why risk breaking something.
    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()

## ---- internal support method for evenly distributed integers ----

def __init_subclass__(cls, /, **kwargs):
        """Control how subclasses generate random integers.

The algorithm a subclass can use depends on the random() and/or
        getrandbits() implementation available to it and determines
        whether it can generate random integers from arbitrarily large
        ranges.
        """

for c in cls.__mro__:
            if '_randbelow' in c.__dict__:
                # just inherit it
                break
            if 'getrandbits' in c.__dict__:
                cls._randbelow = cls._randbelow_with_getrandbits
                break
            if 'random' in c.__dict__:
                cls._randbelow = cls._randbelow_without_getrandbits
                break

def _randbelow_with_getrandbits(self, n):
        "Return a random int in the range [0,n).  Defined for n > 0."

getrandbits = self.getrandbits
        k = n.bit_length()  # don't use (n-1) here because n can be 1
        r = getrandbits(k)  # 0 <= r < 2**k
        while r >= n:
            r = getrandbits(k)
        return r

def _randbelow_without_getrandbits(self, n, maxsize=1<<BPF):
        """Return a random int in the range [0,n).  Defined for n > 0.

The implementation does not use getrandbits, but only random.
        """

random = self.random
        if n >= maxsize:
            _warn("Underlying random() generator does not supply \n"
                "enough bits to choose from a population range this large.\n"
                "To remove the range limitation, add a getrandbits() method.")
            return _floor(random() * n)
        rem = maxsize % n
        limit = (maxsize - rem) / maxsize   # int(limit * maxsize) % n == 0
        r = random()
        while r >= limit:
            r = random()
        return _floor(r * maxsize) % n

_randbelow = _randbelow_with_getrandbits

## --------------------------------------------------------
    ## ---- Methods below this point generate custom distributions
    ## ---- based on the methods defined above.  They do not
    ## ---- directly touch the underlying generator and only
    ## ---- access randomness through the methods:  random(),
    ## ---- getrandbits(), or _randbelow().

## -------------------- bytes methods ---------------------

def randbytes(self, n):
        """Generate n random bytes."""
        return self.getrandbits(n * 8).to_bytes(n, 'little')

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

def randrange(self, start, stop=None, step=_ONE):
        """Choose a random item from range(stop) or range(start, stop[, step]).

Roughly equivalent to ``choice(range(start, stop, step))`` but
        supports arbitrarily large ranges and is optimized for common cases.

"""

# This code is a bit messy to make it fast for the
        # common case while still doing adequate error checking.
        try:
            istart = _index(start)
        except TypeError:
            istart = int(start)
            if istart != start:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer arg 1 for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        if stop is None:
            # We don't check for "step != 1" because it hasn't been
            # type checked and converted to an integer yet.
            if step is not _ONE:
                raise TypeError('Missing a non-None stop argument')
            if istart > 0:
                return self._randbelow(istart)
            raise ValueError("empty range for randrange()")

# stop argument supplied.
        try:
            istop = _index(stop)
        except TypeError:
            istop = int(stop)
            if istop != stop:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer stop for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        width = istop - istart
        try:
            istep = _index(step)
        except TypeError:
            istep = int(step)
            if istep != step:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer step for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        # Fast path.
        if istep == 1:
            if width > 0:
                return istart + self._randbelow(width)
            raise ValueError("empty range for randrange() (%d, %d, %d)" % (istart, istop, width))

# Non-unit step argument supplied.
        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()")
        return istart + istep * self._randbelow(n)

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

return self.randrange(a, b+1)

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

def choice(self, seq):
        """Choose a random element from a non-empty sequence."""

# As an accommodation for NumPy, we don't use "if not seq"
        # because bool(numpy.array()) raises a ValueError.
        if not len(seq):
            raise IndexError('Cannot choose from an empty sequence')
        return seq[self._randbelow(len(seq))]

def shuffle(self, x):
        """Shuffle list x in place, and return None."""

randbelow = self._randbelow
        for i in reversed(range(1, len(x))):
            # pick an element in x[:i+1] with which to exchange x[i]
            j = randbelow(i + 1)
            x[i], x[j] = x[j], x[i]

def sample(self, population, k, *, counts=None):
        """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.

Repeated elements can be specified one at a time or with the optional
        counts parameter.  For example:

sample(['red', 'blue'], counts=[4, 2], k=5)

is equivalent to:

sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)

To choose a sample from a range of integers, use range() for the
        population argument.  This is especially fast and space efficient
        for sampling from a large population:

sample(range(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.

# The number of calls to _randbelow() is kept at or near k, the
        # theoretical minimum.  This is important because running time
        # is dominated by _randbelow() and because it extracts the
        # least entropy from the underlying random number generators.

# Memory requirements are kept to the smaller of a k-length
        # set or an n-length list.

# There are other sampling algorithms that do not require
        # auxiliary memory, but they were rejected because they made
        # too many calls to _randbelow(), making them slower and
        # causing them to eat more entropy than necessary.

if not isinstance(population, _Sequence):
            raise TypeError("Population must be a sequence.  "
                            "For dicts or sets, use sorted(d).")
        n = len(population)
        if counts is not None:
            cum_counts = list(_accumulate(counts))
            if len(cum_counts) != n:
                raise ValueError('The number of counts does not match the population')
            total = cum_counts.pop()
            if not isinstance(total, int):
                raise TypeError('Counts must be integers')
            if total <= 0:
                raise ValueError('Total of counts must be greater than zero')
            selections = self.sample(range(total), k=k)
            bisect = _bisect
            return [population[bisect(cum_counts, s)] for s in selections]
        randbelow = self._randbelow
        if not 0 <= k <= n:
            raise ValueError("Sample larger than population or is negative")
        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:
            # An n-length list is smaller than a k-length set.
            # Invariant:  non-selected at pool[0 : n-i]
            pool = list(population)
            for i in range(k):
                j = randbelow(n - i)
                result[i] = pool[j]
                pool[j] = pool[n - i - 1]  # move non-selected item into vacancy
        else:
            selected = set()
            selected_add = selected.add
            for i in range(k):
                j = randbelow(n)
                while j in selected:
                    j = randbelow(n)
                selected_add(j)
                result[i] = population[j]
        return result

def choices(self, population, weights=None, *, cum_weights=None, k=1):
        """Return a k sized list of population elements chosen with replacement.

If the relative weights or cumulative weights are not specified,
        the selections are made with equal probability.

"""
        random = self.random
        n = len(population)
        if cum_weights is None:
            if weights is None:
                floor = _floor
                n += 0.0    # convert to float for a small speed improvement
                return [population[floor(random() * n)] for i in _repeat(None, k)]
            try:
                cum_weights = list(_accumulate(weights))
            except TypeError:
                if not isinstance(weights, int):
                    raise
                k = weights
                raise TypeError(
                    f'The number of choices must be a keyword argument: {k=}'
                ) from None
        elif weights is not None:
            raise TypeError('Cannot specify both weights and cumulative weights')
        if len(cum_weights) != n:
            raise ValueError('The number of weights does not match the population')
        total = cum_weights[-1] + 0.0   # convert to float
        if total <= 0.0:
            raise ValueError('Total of weights must be greater than zero')
        if not _isfinite(total):
            raise ValueError('Total of weights must be finite')
        bisect = _bisect
        hi = n - 1
        return [population[bisect(cum_weights, random() * total, 0, hi)]
                for i in _repeat(None, k)]

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

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()

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) * _sqrt(u * c)

def normalvariate(self, mu=0.0, sigma=1.0):
        """Normal distribution.

mu is the mean, and sigma is the 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 True:
            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

def gauss(self, mu=0.0, sigma=1.0):
        """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

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))

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

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.

"""
        # 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 True:
            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

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 True:
                u1 = random()
                if not 1e-7 < u1 < 0.9999999:
                    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/beta)
            return -_log(1.0 - random()) * beta

else:
            # alpha is between 0 and 1 (exclusive)
            # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
            while True:
                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

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

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

"""
        ## 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.

# 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, 1.0)
        if y:
            return y / (y + self.gammavariate(beta, 1.0))
        return 0.0

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

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

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 * (-_log(u)) ** (1.0 / beta)

## ------------------------------------------------------------------
## --------------- 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 <= X < 1.0."""
        return (int.from_bytes(_urandom(7)) >> 3) * RECIP_BPF

def getrandbits(self, k):
        """getrandbits(k) -> x.  Generates an int with k random bits."""
        if k < 0:
            raise ValueError('number of bits must be non-negative')
        numbytes = (k + 7) // 8                       # bits / 8 and rounded up
        x = int.from_bytes(_urandom(numbytes))
        return x >> (numbytes * 8 - k)                # trim excess bits

def randbytes(self, n):
        """Generate n random bytes."""
        # os.urandom(n) fails with ValueError for n < 0
        # and returns an empty bytes string for n == 0.
        return _urandom(n)

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

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

# ----------------------------------------------------------------------
# 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
choices = _inst.choices
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
getrandbits = _inst.getrandbits
randbytes = _inst.randbytes

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

def _test_generator(n, func, args):
    from statistics import stdev, fmean as mean
    from time import perf_counter

t0 = perf_counter()
    data = [func(*args) for i in _repeat(None, n)]
    t1 = perf_counter()

xbar = mean(data)
    sigma = stdev(data, xbar)
    low = min(data)
    high = max(data)

print(f'{t1 - t0:.3f} sec, {n} times {func.__name__}')
    print('avg %g, stddev %g, min %g, max %g\n' % (xbar, sigma, low, high))

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))

## ------------------------------------------------------
## ------------------ fork support  ---------------------

if hasattr(_os, "fork"):
    _os.register_at_fork(after_in_child=_inst.seed)

if __name__ == '__main__':
    _test()

cmd: