using for loop to install conda package

.CondaPkg/env/Lib/random.py

@@ -0,0 +1,904 @@
+"""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()