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cpython/Lib/random.py
Raymond Hettinger 311f419628 Improve comments. Clarify docs. 
Replace "type(0)" with "int".
Replace "while 1" with "while True"
2002-11-18 09:01:24 +00:00

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"""Random variable generators.
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
normal (Gaussian)
lognormal
negative exponential
gamma
beta
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
Translated from anonymously contributed C/C++ source.
Multi-threading note: the random number generator used here is not thread-
safe; it is possible that two calls return the same random value. However,
you can instantiate a different instance of Random() in each thread to get
generators that don't share state, then use .setstate() and .jumpahead() to
move the generators to disjoint segments of the full period. For example,
def create_generators(num, delta, firstseed=None):
""\"Return list of num distinct generators.
Each generator has its own unique segment of delta elements from
Random.random()'s full period.
Seed the first generator with optional arg firstseed (default is
None, to seed from current time).
""\"
from random import Random
g = Random(firstseed)
result = [g]
for i in range(num - 1):
laststate = g.getstate()
g = Random()
g.setstate(laststate)
g.jumpahead(delta)
result.append(g)
return result
gens = create_generators(10, 1000000)
That creates 10 distinct generators, which can be passed out to 10 distinct
threads. The generators don't share state so can be called safely in
parallel. So long as no thread calls its g.random() more than a million
times (the second argument to create_generators), the sequences seen by
each thread will not overlap.
The period of the underlying Wichmann-Hill generator is 6,953,607,871,644,
and that limits how far this technique can be pushed.
Just for fun, note that since we know the period, .jumpahead() can also be
used to "move backward in time":
>>> g = Random(42) # arbitrary
>>> g.random()
0.25420336316883324
>>> g.jumpahead(6953607871644L - 1) # move *back* one
>>> g.random()
0.25420336316883324
"""
# XXX The docstring sucks.
from math import log as _log, exp as _exp, pi as _pi, e as _e
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from math import floor as _floor
__all__ = ["Random","seed","random","uniform","randint","choice","sample",
"randrange","shuffle","normalvariate","lognormvariate",
"cunifvariate","expovariate","vonmisesvariate","gammavariate",
"stdgamma","gauss","betavariate","paretovariate","weibullvariate",
"getstate","setstate","jumpahead","whseed"]
def _verify(name, computed, expected):
if abs(computed - expected) > 1e-7:
raise ValueError(
"computed value for %s deviates too much "
"(computed %g, expected %g)" % (name, computed, expected))
NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
_verify('NV_MAGICCONST', NV_MAGICCONST, 1.71552776992141)
TWOPI = 2.0*_pi
_verify('TWOPI', TWOPI, 6.28318530718)
LOG4 = _log(4.0)
_verify('LOG4', LOG4, 1.38629436111989)
SG_MAGICCONST = 1.0 + _log(4.5)
_verify('SG_MAGICCONST', SG_MAGICCONST, 2.50407739677627)
del _verify
# Translated by Guido van Rossum from C source provided by
# Adrian Baddeley.
class Random:
"""Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state. Especially useful for multi-threaded programs, creating
a different instance of Random for each thread, and using the jumpahead()
method to ensure that the generated sequences seen by each thread don't
overlap.
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), setstate() and jumpahead().
"""
VERSION = 1 # used by getstate/setstate
def __init__(self, x=None):
"""Initialize an instance.
Optional argument x controls seeding, as for Random.seed().
"""
self.seed(x)
## -------------------- core generator -------------------
# Specific to Wichmann-Hill generator. Subclasses wishing to use a
# different core generator should override the seed(), random(),
# getstate(), setstate() and jumpahead() methods.
def seed(self, a=None):
"""Initialize internal state from hashable object.
None or no argument seeds from current time.
If a is not None or an int or long, hash(a) is used instead.
If a is an int or long, a is used directly. Distinct values between
0 and 27814431486575L inclusive are guaranteed to yield distinct
internal states (this guarantee is specific to the default
Wichmann-Hill generator).
"""
if a is None:
# Initialize from current time
import time
a = long(time.time() * 256)
if type(a) not in (type(3), type(3L)):
a = hash(a)
a, x = divmod(a, 30268)
a, y = divmod(a, 30306)
a, z = divmod(a, 30322)
self._seed = int(x)+1, int(y)+1, int(z)+1
self.gauss_next = None
def random(self):
"""Get the next random number in the range [0.0, 1.0)."""
# Wichman-Hill random number generator.
#
# Wichmann, B. A. & Hill, I. D. (1982)
# Algorithm AS 183:
# An efficient and portable pseudo-random number generator
# Applied Statistics 31 (1982) 188-190
#
# see also:
# Correction to Algorithm AS 183
# Applied Statistics 33 (1984) 123
#
# McLeod, A. I. (1985)
# A remark on Algorithm AS 183
# Applied Statistics 34 (1985),198-200
# This part is thread-unsafe:
# BEGIN CRITICAL SECTION
x, y, z = self._seed
x = (171 * x) % 30269
y = (172 * y) % 30307
z = (170 * z) % 30323
self._seed = x, y, z
# END CRITICAL SECTION
# Note: on a platform using IEEE-754 double arithmetic, this can
# never return 0.0 (asserted by Tim; proof too long for a comment).
return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
def getstate(self):
"""Return internal state; can be passed to setstate() later."""
return self.VERSION, self._seed, self.gauss_next
def setstate(self, state):
"""Restore internal state from object returned by getstate()."""
version = state[0]
if version == 1:
version, self._seed, self.gauss_next = state
else:
raise ValueError("state with version %s passed to "
"Random.setstate() of version %s" %
(version, self.VERSION))
def jumpahead(self, n):
"""Act as if n calls to random() were made, but quickly.
n is an int, greater than or equal to 0.
Example use: If you have 2 threads and know that each will
consume no more than a million random numbers, create two Random
objects r1 and r2, then do
r2.setstate(r1.getstate())
r2.jumpahead(1000000)
Then r1 and r2 will use guaranteed-disjoint segments of the full
period.
"""
if not n >= 0:
raise ValueError("n must be >= 0")
x, y, z = self._seed
x = int(x * pow(171, n, 30269)) % 30269
y = int(y * pow(172, n, 30307)) % 30307
z = int(z * pow(170, n, 30323)) % 30323
self._seed = x, y, z
def __whseed(self, x=0, y=0, z=0):
"""Set the Wichmann-Hill seed from (x, y, z).
These must be integers in the range [0, 256).
"""
if not type(x) == type(y) == type(z) == int:
raise TypeError('seeds must be integers')
if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
raise ValueError('seeds must be in range(0, 256)')
if 0 == x == y == z:
# Initialize from current time
import time
t = long(time.time() * 256)
t = int((t&0xffffff) ^ (t>>24))
t, x = divmod(t, 256)
t, y = divmod(t, 256)
t, z = divmod(t, 256)
# Zero is a poor seed, so substitute 1
self._seed = (x or 1, y or 1, z or 1)
self.gauss_next = None
def whseed(self, a=None):
"""Seed from hashable object's hash code.
None or no argument seeds from current time. It is not guaranteed
that objects with distinct hash codes lead to distinct internal
states.
This is obsolete, provided for compatibility with the seed routine
used prior to Python 2.1. Use the .seed() method instead.
"""
if a is None:
self.__whseed()
return
a = hash(a)
a, x = divmod(a, 256)
a, y = divmod(a, 256)
a, z = divmod(a, 256)
x = (x + a) % 256 or 1
y = (y + a) % 256 or 1
z = (z + a) % 256 or 1
self.__whseed(x, y, z)
## ---- Methods below this point do not need to be overridden when
## ---- subclassing for the purpose of using a different core generator.
## -------------------- pickle support -------------------
def __getstate__(self): # for pickle
return self.getstate()
def __setstate__(self, state): # for pickle
self.setstate(state)
## -------------------- integer methods -------------------
def randrange(self, start, stop=None, step=1, int=int, default=None):
"""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.
Do not supply the 'int' and 'default' arguments.
"""
# 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 default:
if istart > 0:
return int(self.random() * istart)
raise ValueError, "empty range for randrange()"
# stop argument supplied.
istop = int(stop)
if istop != stop:
raise ValueError, "non-integer stop for randrange()"
if step == 1 and istart < istop:
try:
return istart + int(self.random()*(istop - istart))
except OverflowError:
# This can happen if istop-istart > sys.maxint + 1, and
# multiplying by random() doesn't reduce it to something
# <= sys.maxint. We know that the overall result fits
# in an int, and can still do it correctly via math.floor().
# But that adds another function call, so for speed we
# avoided that whenever possible.
return int(istart + _floor(self.random()*(istop - istart)))
if step == 1:
raise ValueError, "empty range for randrange()"
# Non-unit step argument supplied.
istep = int(step)
if istep != step:
raise ValueError, "non-integer step for randrange()"
if istep > 0:
n = (istop - istart + istep - 1) / istep
elif istep < 0:
n = (istop - istart + istep + 1) / istep
else:
raise ValueError, "zero step for randrange()"
if n <= 0:
raise ValueError, "empty range for randrange()"
return istart + istep*int(self.random() * n)
def randint(self, a, b):
"""Return random integer in range [a, b], including both end points.
"""
return self.randrange(a, b+1)
## -------------------- sequence methods -------------------
def choice(self, seq):
"""Choose a random element from a non-empty sequence."""
return seq[int(self.random() * len(seq))]
def shuffle(self, x, random=None, int=int):
"""x, random=random.random -> shuffle list x in place; return None.
Optional arg random is a 0-argument function returning a random
float in [0.0, 1.0); by default, the standard random.random.
Note that for even rather small len(x), the total number of
permutations of x is larger than the period of most random number
generators; this implies that "most" permutations of a long
sequence can never be generated.
"""
if random is None:
random = self.random
for i in xrange(len(x)-1, 0, -1):
# pick an element in x[:i+1] with which to exchange x[i]
j = int(random() * (i+1))
x[i], x[j] = x[j], x[i]
def sample(self, population, k, random=None, int=int):
"""Chooses k unique random elements from a population sequence.
Returns a new list containing elements from the population while
leaving the original population unchanged. The resulting list is
in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
To choose a sample in a range of integers, use xrange as an argument.
This is especially fast and space efficient for sampling from a
large population: sample(xrange(10000000), 60)
Optional arg random is a 0-argument function returning a random
float in [0.0, 1.0); by default, the standard random.random.
"""
# Sampling without replacement entails tracking either potential
# selections (the pool) or previous selections.
# Pools are stored in lists which provide __getitem__ for selection
# and provide a way to remove selections. But each list.remove()
# rebuilds the entire list, so it is better to rearrange the list,
# placing non-selected elements at the head of the list. Tracking
# the selection pool is only space efficient with small populations.
# Previous selections are stored in dictionaries which provide
# __contains__ for detecting repeat selections. Discarding repeats
# is efficient unless most of the population has already been chosen.
# So, tracking selections is fast only with small sample sizes.
n = len(population)
if not 0 <= k <= n:
raise ValueError, "sample larger than population"
if random is None:
random = self.random
result = [None] * k
if n < 6 * k: # if n len list takes less space than a k len dict
pool = list(population)
for i in xrange(k): # invariant: non-selected at [0,n-i)
j = int(random() * (n-i))
result[i] = pool[j]
pool[j] = pool[n-i-1]
else:
selected = {}
for i in xrange(k):
j = int(random() * n)
while j in selected:
j = int(random() * n)
result[i] = selected[j] = population[j]
return result
## -------------------- real-valued distributions -------------------
## -------------------- uniform distribution -------------------
def uniform(self, a, b):
"""Get a random number in the range [a, b)."""
return a + (b-a) * self.random()
## -------------------- normal distribution --------------------
def normalvariate(self, mu, sigma):
"""Normal distribution.
mu is the mean, and sigma is the standard deviation.
"""
# mu = mean, sigma = standard deviation
# Uses Kinderman and Monahan method. Reference: Kinderman,
# A.J. and Monahan, J.F., "Computer generation of random
# variables using the ratio of uniform deviates", ACM Trans
# Math Software, 3, (1977), pp257-260.
random = self.random
while True:
u1 = random()
u2 = random()
z = NV_MAGICCONST*(u1-0.5)/u2
zz = z*z/4.0
if zz <= -_log(u2):
break
return mu + z*sigma
## -------------------- lognormal distribution --------------------
def lognormvariate(self, mu, sigma):
"""Log normal distribution.
If you take the natural logarithm of this distribution, you'll get a
normal distribution with mean mu and standard deviation sigma.
mu can have any value, and sigma must be greater than zero.
"""
return _exp(self.normalvariate(mu, sigma))
## -------------------- circular uniform --------------------
def cunifvariate(self, mean, arc):
"""Circular uniform distribution.
mean is the mean angle, and arc is the range of the distribution,
centered around the mean angle. Both values must be expressed in
radians. Returned values range between mean - arc/2 and
mean + arc/2 and are normalized to between 0 and pi.
Deprecated in version 2.3. Use:
(mean + arc * (Random.random() - 0.5)) % Math.pi
"""
# mean: mean angle (in radians between 0 and pi)
# arc: range of distribution (in radians between 0 and pi)
import warnings
warnings.warn("The cunifvariate function is deprecated; Use (mean "
"+ arc * (Random.random() - 0.5)) % Math.pi instead",
DeprecationWarning)
return (mean + arc * (self.random() - 0.5)) % _pi
## -------------------- exponential distribution --------------------
def expovariate(self, lambd):
"""Exponential distribution.
lambd is 1.0 divided by the desired mean. (The parameter would be
called "lambda", but that is a reserved word in Python.) Returned
values range from 0 to positive infinity.
"""
# lambd: rate lambd = 1/mean
# ('lambda' is a Python reserved word)
random = self.random
u = random()
while u <= 1e-7:
u = random()
return -_log(u)/lambd
## -------------------- von Mises distribution --------------------
def vonmisesvariate(self, mu, kappa):
"""Circular data distribution.
mu is the mean angle, expressed in radians between 0 and 2*pi, and
kappa is the concentration parameter, which must be greater than or
equal to zero. If kappa is equal to zero, this distribution reduces
to a uniform random angle over the range 0 to 2*pi.
"""
# mu: mean angle (in radians between 0 and 2*pi)
# kappa: concentration parameter kappa (>= 0)
# if kappa = 0 generate uniform random angle
# Based upon an algorithm published in: Fisher, N.I.,
# "Statistical Analysis of Circular Data", Cambridge
# University Press, 1993.
# Thanks to Magnus Kessler for a correction to the
# implementation of step 4.
random = self.random
if kappa <= 1e-6:
return TWOPI * random()
a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
r = (1.0 + b * b)/(2.0 * b)
while True:
u1 = random()
z = _cos(_pi * u1)
f = (1.0 + r * z)/(r + z)
c = kappa * (r - f)
u2 = random()
if not (u2 >= c * (2.0 - c) and u2 > c * _exp(1.0 - c)):
break
u3 = random()
if u3 > 0.5:
theta = (mu % TWOPI) + _acos(f)
else:
theta = (mu % TWOPI) - _acos(f)
return theta
## -------------------- gamma distribution --------------------
def gammavariate(self, alpha, beta):
"""Gamma distribution. Not the gamma function!
Conditions on the parameters are alpha > 0 and beta > 0.
"""
# 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()
u2 = random()
v = _log(u1/(1.0-u1))/ainv
x = alpha*_exp(v)
z = u1*u1*u2
r = bbb+ccc*v-x
if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
return x * beta
elif alpha == 1.0:
# expovariate(1)
u = random()
while u <= 1e-7:
u = random()
return -_log(u) * beta
else: # alpha is between 0 and 1 (exclusive)
# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
while True:
u = random()
b = (_e + alpha)/_e
p = b*u
if p <= 1.0:
x = pow(p, 1.0/alpha)
else:
# p > 1
x = -_log((b-p)/alpha)
u1 = random()
if not (((p <= 1.0) and (u1 > _exp(-x))) or
((p > 1) and (u1 > pow(x, alpha - 1.0)))):
break
return x * beta
def stdgamma(self, alpha, ainv, bbb, ccc):
# This method was (and shall remain) undocumented.
# This method is deprecated
# for the following reasons:
# 1. Returns same as .gammavariate(alpha, 1.0)
# 2. Requires caller to provide 3 extra arguments
# that are functions of alpha anyway
# 3. Can't be used for alpha < 0.5
# ainv = sqrt(2 * alpha - 1)
# bbb = alpha - log(4)
# ccc = alpha + ainv
import warnings
warnings.warn("The stdgamma function is deprecated; "
"use gammavariate() instead",
DeprecationWarning)
return self.gammavariate(alpha, 1.0)
## -------------------- Gauss (faster alternative) --------------------
def gauss(self, mu, sigma):
"""Gaussian distribution.
mu is the mean, and sigma is the standard deviation. This is
slightly faster than the normalvariate() function.
Not thread-safe without a lock around calls.
"""
# When x and y are two variables from [0, 1), uniformly
# distributed, then
#
# cos(2*pi*x)*sqrt(-2*log(1-y))
# sin(2*pi*x)*sqrt(-2*log(1-y))
#
# are two *independent* variables with normal distribution
# (mu = 0, sigma = 1).
# (Lambert Meertens)
# (corrected version; bug discovered by Mike Miller, fixed by LM)
# Multithreading note: When two threads call this function
# simultaneously, it is possible that they will receive the
# same return value. The window is very small though. To
# avoid this, you have to use a lock around all calls. (I
# didn't want to slow this down in the serial case by using a
# lock here.)
random = self.random
z = self.gauss_next
self.gauss_next = None
if z is None:
x2pi = random() * TWOPI
g2rad = _sqrt(-2.0 * _log(1.0 - random()))
z = _cos(x2pi) * g2rad
self.gauss_next = _sin(x2pi) * g2rad
return mu + z*sigma
## -------------------- beta --------------------
## See
## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470
## for Ivan Frohne's insightful analysis of why the original implementation:
##
## def betavariate(self, alpha, beta):
## # Discrete Event Simulation in C, pp 87-88.
##
## y = self.expovariate(alpha)
## z = self.expovariate(1.0/beta)
## return z/(y+z)
##
## was dead wrong, and how it probably got that way.
def betavariate(self, alpha, beta):
"""Beta distribution.
Conditions on the parameters are alpha > -1 and beta} > -1.
Returned values range between 0 and 1.
"""
# This version due to Janne Sinkkonen, and matches all the std
# texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
y = self.gammavariate(alpha, 1.)
if y == 0:
return 0.0
else:
return y / (y + self.gammavariate(beta, 1.))
## -------------------- Pareto --------------------
def paretovariate(self, alpha):
"""Pareto distribution. alpha is the shape parameter."""
# Jain, pg. 495
u = self.random()
return 1.0 / pow(u, 1.0/alpha)
## -------------------- Weibull --------------------
def weibullvariate(self, alpha, beta):
"""Weibull distribution.
alpha is the scale parameter and beta is the shape parameter.
"""
# Jain, pg. 499; bug fix courtesy Bill Arms
u = self.random()
return alpha * pow(-_log(u), 1.0/beta)
## -------------------- test program --------------------
def _test_generator(n, funccall):
import time
print n, 'times', funccall
code = compile(funccall, funccall, 'eval')
sum = 0.0
sqsum = 0.0
smallest = 1e10
largest = -1e10
t0 = time.time()
for i in range(n):
x = eval(code)
sum = sum + x
sqsum = sqsum + x*x
smallest = min(x, smallest)
largest = max(x, largest)
t1 = time.time()
print round(t1-t0, 3), 'sec,',
avg = sum/n
stddev = _sqrt(sqsum/n - avg*avg)
print 'avg %g, stddev %g, min %g, max %g' % \
(avg, stddev, smallest, largest)
def _test_sample(n):
# For the entire allowable range of 0 <= k <= n, validate that
# the sample is of the correct length and contains only unique items
population = xrange(n)
for k in xrange(n+1):
s = sample(population, k)
assert len(dict([(elem,True) for elem in s])) == len(s) == k
assert None not in s
def _sample_generator(n, k):
# Return a fixed element from the sample. Validates random ordering.
return sample(xrange(n), k)[k//2]
def _test(N=2000):
print 'TWOPI =', TWOPI
print 'LOG4 =', LOG4
print 'NV_MAGICCONST =', NV_MAGICCONST
print 'SG_MAGICCONST =', SG_MAGICCONST
_test_generator(N, 'random()')
_test_generator(N, 'normalvariate(0.0, 1.0)')
_test_generator(N, 'lognormvariate(0.0, 1.0)')
_test_generator(N, 'cunifvariate(0.0, 1.0)')
_test_generator(N, 'expovariate(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, 'paretovariate(1.0)')
_test_generator(N, 'weibullvariate(1.0, 1.0)')
_test_generator(N, '_sample_generator(50, 5)') # expected s.d.: 14.4
_test_generator(N, '_sample_generator(50, 45)') # expected s.d.: 14.4
_test_sample(500)
# Test jumpahead.
s = getstate()
jumpahead(N)
r1 = random()
# now do it the slow way
setstate(s)
for i in range(N):
random()
r2 = random()
if r1 != r2:
raise ValueError("jumpahead test failed " + `(N, r1, r2)`)
# Create one instance, seeded from current time, and export its methods
# as module-level functions. The functions are not threadsafe, and state
# is shared 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
randint = _inst.randint
choice = _inst.choice
randrange = _inst.randrange
sample = _inst.sample
shuffle = _inst.shuffle
normalvariate = _inst.normalvariate
lognormvariate = _inst.lognormvariate
cunifvariate = _inst.cunifvariate
expovariate = _inst.expovariate
vonmisesvariate = _inst.vonmisesvariate
gammavariate = _inst.gammavariate
stdgamma = _inst.stdgamma
gauss = _inst.gauss
betavariate = _inst.betavariate
paretovariate = _inst.paretovariate
weibullvariate = _inst.weibullvariate
getstate = _inst.getstate
setstate = _inst.setstate
jumpahead = _inst.jumpahead
whseed = _inst.whseed
if __name__ == '__main__':
_test()
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