Update prebuilt Clang to r416183b from Android.
https://android.googlesource.com/platform/prebuilts/clang/host/
linux-x86/+/06a71ddac05c22edb2d10b590e1769b3f8619bef
clang 12.0.5 (based on r416183b) from build 7284624.
Change-Id: I277a316abcf47307562d8b748b84870f31a72866
Signed-off-by: Olivier Deprez <olivier.deprez@arm.com>
diff --git a/linux-x64/clang/python3/lib/python3.9/random.py b/linux-x64/clang/python3/lib/python3.9/random.py
new file mode 100644
index 0000000..a6454f5
--- /dev/null
+++ b/linux-x64/clang/python3/lib/python3.9/random.py
@@ -0,0 +1,887 @@
+"""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
+from os import urandom as _urandom
+from _collections_abc import Set as _Set, Sequence as _Sequence
+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",
+ "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
+
+
+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 += _sha512(a).digest()
+ a = int.from_bytes(a, 'big')
+
+ elif not isinstance(a, (type(None), int, float, str, bytes, bytearray)):
+ _warn('Seeding based on hashing is deprecated\n'
+ 'since Python 3.9 and will be removed in a subsequent '
+ 'version. The only \n'
+ 'supported seed types are: None, '
+ 'int, float, str, bytes, and bytearray.',
+ DeprecationWarning, 2)
+
+ 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). Returns 0 if n==0."
+
+ if not n:
+ return 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). Returns 0 if 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)
+ if n == 0:
+ return 0
+ 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=1):
+ """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:
+ return self._randbelow(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:
+ return istart + self._randbelow(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()")
+
+ 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."""
+ # raises IndexError if seq is empty
+ return seq[self._randbelow(len(seq))]
+
+ def shuffle(self, x, random=None):
+ """Shuffle list x in place, and return None.
+
+ Optional argument random is a 0-argument function returning a
+ random float in [0.0, 1.0); if it is the default None, the
+ standard random.random will be used.
+
+ """
+
+ if random is 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]
+ else:
+ _warn('The *random* parameter to shuffle() has been deprecated\n'
+ 'since Python 3.9 and will be removed in a subsequent '
+ 'version.',
+ DeprecationWarning, 2)
+ floor = _floor
+ for i in reversed(range(1, len(x))):
+ # pick an element in x[:i+1] with which to exchange x[i]
+ j = floor(random() * (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 or set.
+
+ 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 isinstance(population, _Set):
+ _warn('Sampling from a set deprecated\n'
+ 'since Python 3.9 and will be removed in a subsequent version.',
+ DeprecationWarning, 2)
+ population = tuple(population)
+ 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 = 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)]
+ cum_weights = list(_accumulate(weights))
+ 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')
+ 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, sigma):
+ """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, 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
+
+ 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 1:
+ 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 1.0 / 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, 1.0)."""
+ return (int.from_bytes(_urandom(7), 'big') >> 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), 'big')
+ 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 range(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()