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# Source Generated with Decompyle++
# File: in.pyc (Python 2.7)
'''Random variable generators.
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
triangular
normal (Gaussian)
lognormal
negative exponential
gamma
beta
pareto
Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
General notes on the underlying Mersenne Twister core generator:
* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* Without a direct way to compute N steps forward, the semantics of
jumpahead(n) are weakened to simply jump to another distant state and rely
on the large period to avoid overlapping sequences.
* The random() method is implemented in C, executes in a single Python step,
and is, therefore, threadsafe.
'''
from __future__ import division
from warnings import warn as _warn
from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType
from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from os import urandom as _urandom
from binascii import hexlify as _hexlify
import hashlib as _hashlib
__all__ = [
'Random',
'seed',
'random',
'uniform',
'randint',
'choice',
'sample',
'randrange',
'shuffle',
'normalvariate',
'lognormvariate',
'expovariate',
'vonmisesvariate',
'gammavariate',
'triangular',
'gauss',
'betavariate',
'paretovariate',
'weibullvariate',
'getstate',
'setstate',
'jumpahead',
'WichmannHill',
'getrandbits',
'SystemRandom']
NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2)
TWOPI = 2 * _pi
LOG4 = _log(4)
SG_MAGICCONST = 1 + _log(4.5)
BPF = 53
RECIP_BPF = 2 ** (-BPF)
import _random
class Random(_random.Random):
"""Random number generator base class used by bound module functions.
Used to instantiate instances of Random to get generators that don't
share state. Especially useful for multi-threaded programs, creating
a different instance of Random for each thread, and using the jumpahead()
method to ensure that the generated sequences seen by each thread don't
overlap.
Class Random can also be subclassed if you want to use a different basic
generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), setstate() and jumpahead().
Optionally, implement a getrandbits() method so that randrange() can cover
arbitrarily large ranges.
"""
VERSION = 3
def __init__(self, x = None):
'''Initialize an instance.
Optional argument x controls seeding, as for Random.seed().
'''
self.seed(x)
self.gauss_next = None
def seed(self, a = None):
'''Initialize internal state from hashable object.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If a is not None or an int or long, hash(a) is used instead.
'''
if a is None:
try:
a = long(_hexlify(_urandom(16)), 16)
except NotImplementedError:
import time as time
a = long(time.time() * 256)
super(Random, self).seed(a)
self.gauss_next = None
def getstate(self):
'''Return internal state; can be passed to setstate() later.'''
return (self.VERSION, super(Random, self).getstate(), self.gauss_next)
def setstate(self, state):
'''Restore internal state from object returned by getstate().'''
version = state[0]
if version == 3:
(version, internalstate, self.gauss_next) = state
super(Random, self).setstate(internalstate)
elif version == 2:
(version, internalstate, self.gauss_next) = state
try:
internalstate = tuple((lambda .0: pass)(internalstate))
except ValueError:
e = None
raise TypeError, e
super(Random, self).setstate(internalstate)
else:
raise ValueError('state with version %s passed to Random.setstate() of version %s' % (version, self.VERSION))
def jumpahead(self, n):
'''Change the internal state to one that is likely far away
from the current state. This method will not be in Py3.x,
so it is better to simply reseed.
'''
s = repr(n) + repr(self.getstate())
n = int(_hashlib.new('sha512', s).hexdigest(), 16)
super(Random, self).jumpahead(n)
def __getstate__(self):
return self.getstate()
def __setstate__(self, state):
self.setstate(state)
def __reduce__(self):
return (self.__class__, (), self.getstate())
def randrange(self, start, stop = None, step = 1, _int = int, _maxwidth = 0x1L << BPF):
'''Choose a random item from range(start, stop[, step]).
This fixes the problem with randint() which includes the
endpoint; in Python this is usually not what you want.
'''
istart = _int(start)
if istart != start:
raise ValueError, 'non-integer arg 1 for randrange()'
if stop is None:
if istart > 0:
if istart >= _maxwidth:
return self._randbelow(istart)
return None(self.random() * istart)
raise None, 'empty range for randrange()'
istop = _int(stop)
if istop != stop:
raise ValueError, 'non-integer stop for randrange()'
width = istop - istart
if step == 1 and width > 0:
if width >= _maxwidth:
return _int(istart + self._randbelow(width))
return None(istart + _int(self.random() * width))
if None == 1:
raise ValueError, 'empty range for randrange() (%d,%d, %d)' % (istart, istop, width)
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 None <= 0:
raise ValueError, 'empty range for randrange()'
if n >= _maxwidth:
return istart + istep * self._randbelow(n)
return None + istep * _int(self.random() * n)
def randint(self, a, b):
'''Return random integer in range [a, b], including both end points.
'''
return self.randrange(a, b + 1)
def _randbelow(self, n, _log = _log, _int = int, _maxwidth = 0x1L << BPF, _Method = _MethodType, _BuiltinMethod = _BuiltinMethodType):
'''Return a random int in the range [0,n)
Handles the case where n has more bits than returned
by a single call to the underlying generator.
'''
try:
getrandbits = self.getrandbits
except AttributeError:
pass
if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method:
k = _int(1.00001 + _log(n - 1, 2))
r = getrandbits(k)
while r >= n:
r = getrandbits(k)
return r
if None >= _maxwidth:
_warn('Underlying random() generator does not supply \nenough bits to choose from a population range this large')
return _int(self.random() * n)
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):
'''x, random=random.random -> shuffle list x in place; return None.
Optional arg random is a 0-argument function returning a random
float in [0.0, 1.0); by default, the standard random.random.
'''
if random is None:
random = self.random
_int = int
for i in reversed(xrange(1, len(x))):
j = _int(random() * (i + 1))
x[i] = x[j]
x[j] = x[i]
def sample(self, population, k):
'''Chooses k unique random elements from a population sequence.
Returns a new list containing elements from the population while
leaving the original population unchanged. The resulting list is
in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
To choose a sample in a range of integers, use xrange as an argument.
This is especially fast and space efficient for sampling from a
large population: sample(xrange(10000000), 60)
'''
n = len(population)
if k <= k:
pass
elif not k <= n:
raise ValueError('sample larger than population')
random = self.random
_int = int
result = [
None] * k
setsize = 21
if k > 5:
setsize += 4 ** _ceil(_log(k * 3, 4))
return result
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, high = 1, 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()
c = 0.5 if mode is None else (mode - low) / (high - low)
if u > c:
u = 1 - u
c = 1 - c
low = high
high = low
return low + (high - low) * (u * c) ** 0.5
def normalvariate(self, mu, sigma):
'''Normal distribution.
mu is the mean, and sigma is the standard deviation.
'''
random = self.random
while None:
u1 = random()
u2 = 1 - random()
z = NV_MAGICCONST * (u1 - 0.5) / u2
zz = z * z / 4
if zz <= -_log(u2):
break
continue
continue
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.
'''
return -_log(1 - 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.
'''
random = self.random
if kappa <= 1e-06:
return TWOPI * random()
s = None / kappa
r = s + _sqrt(1 + s * s)
while None:
u1 = random()
z = _cos(_pi * u1)
d = z / (r + z)
u2 = random()
if not u2 < 1 - d * d:
if u2 <= (1 - d) * _exp(d):
break
continue
continue
q = 1 / r
f = (q + z) / (1 + 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
'''
if alpha <= 0 or beta <= 0:
raise ValueError, 'gammavariate: alpha and beta must be > 0.0'
random = self.random
if alpha > 1:
ainv = _sqrt(2 * alpha - 1)
bbb = alpha - LOG4
ccc = alpha + ainv
while None:
u1 = random()
if u1 < u1:
pass
elif not u1 < 1:
continue
u2 = 1 - random()
v = _log(u1 / (1 - u1)) / ainv
x = alpha * _exp(v)
z = u1 * u1 * u2
r = bbb + ccc * v - x
while None:
u = random()
b = (_e + alpha) / _e
p = b * u
u1 = random()
if p > 1 or u1 <= x ** (alpha - 1):
break
if u1 <= _exp(-x):
break
continue
continue
return x * beta
return None if p <= 1 else 1e-07 if not r + SG_MAGICCONST - 4.5 * z >= 0 else u1 < 1
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.
'''
random = self.random
z = self.gauss_next
self.gauss_next = None
if z is None:
x2pi = random() * TWOPI
g2rad = _sqrt(-2 * _log(1 - random()))
z = _cos(x2pi) * g2rad
self.gauss_next = _sin(x2pi) * g2rad
return mu + z * sigma
def betavariate(self, alpha, beta):
'''Beta distribution.
Conditions on the parameters are alpha > 0 and beta > 0.
Returned values range between 0 and 1.
'''
y = self.gammavariate(alpha, 1)
if y == 0:
return 0
return None / (y + self.gammavariate(beta, 1))
def paretovariate(self, alpha):
'''Pareto distribution. alpha is the shape parameter.'''
u = 1 - self.random()
return 1 / pow(u, 1 / alpha)
def weibullvariate(self, alpha, beta):
'''Weibull distribution.
alpha is the scale parameter and beta is the shape parameter.
'''
u = 1 - self.random()
return alpha * pow(-_log(u), 1 / beta)
class WichmannHill(Random):
VERSION = 1
def seed(self, a = None):
'''Initialize internal state from hashable object.
None or no argument seeds from current time or from an operating
system specific randomness source if available.
If a is not None or an int or long, hash(a) is used instead.
If a is an int or long, a is used directly. Distinct values between
0 and 27814431486575L inclusive are guaranteed to yield distinct
internal states (this guarantee is specific to the default
Wichmann-Hill generator).
'''
if a is None:
try:
a = long(_hexlify(_urandom(16)), 16)
except NotImplementedError:
import time
a = long(time.time() * 256)
if not isinstance(a, (int, long)):
a = hash(a)
(a, x) = divmod(a, 30268)
(a, y) = divmod(a, 30306)
(a, z) = divmod(a, 30322)
self._seed = (int(x) + 1, int(y) + 1, int(z) + 1)
self.gauss_next = None
def random(self):
'''Get the next random number in the range [0.0, 1.0).'''
(x, y, z) = self._seed
x = 171 * x % 30269
y = 172 * y % 30307
z = 170 * z % 30323
self._seed = (x, y, z)
return (x / 30269 + y / 30307 + z / 30323) % 1
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 type(y) == type(y) and type(z) == type(z):
pass
elif not type(z) == int:
raise TypeError('seeds must be integers')
self._seed = (type(z) == int, x < 256 if x <= x else y < 256 if y <= y else 1, 1 if not y else 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._WichmannHill__whseed()
return None
a = None(a)
(a, x) = divmod(a, 256)
(a, y) = divmod(a, 256)
(a, z) = divmod(a, 256)
if not (x + a) % 256:
pass
x = 1
if not (y + a) % 256:
pass
y = 1
if not (z + a) % 256:
pass
z = 1
self._WichmannHill__whseed(x, y, z)
class SystemRandom(Random):
'''Alternate random number generator using sources provided
by the operating system (such as /dev/urandom on Unix or
CryptGenRandom on Windows).
Not available on all systems (see os.urandom() for details).
'''
def random(self):
'''Get the next random number in the range [0.0, 1.0).'''
return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF
def getrandbits(self, k):
'''getrandbits(k) -> x. Generates a long int with k random bits.'''
if k <= 0:
raise ValueError('number of bits must be greater than zero')
if k != int(k):
raise TypeError('number of bits should be an integer')
bytes = (k + 7) // 8
x = long(_hexlify(_urandom(bytes)), 16)
return x >> bytes * 8 - k
def _stub(self, *args, **kwds):
'''Stub method. Not used for a system random number generator.'''
pass
seed = jumpahead = _stub
def _notimplemented(self, *args, **kwds):
'''Method should not be called for a system random number generator.'''
raise NotImplementedError('System entropy source does not have state.')
getstate = setstate = _notimplemented
def _test_generator(n, func, args):
import time
print n, 'times', func.__name__
total = 0
sqsum = 0
smallest = 1e+10
largest = -1e+10
t0 = time.time()
for i in range(n):
x = func(*args)
total += x
sqsum = sqsum + x * x
smallest = min(x, smallest)
largest = max(x, largest)
t1 = time.time()
print round(t1 - t0, 3), 'sec,',
avg = total / n
stddev = _sqrt(sqsum / n - avg * avg)
print 'avg %g, stddev %g, min %g, max %g' % (avg, stddev, smallest, largest)
def _test(N = 2000):
_test_generator(N, random, ())
_test_generator(N, normalvariate, (0, 1))
_test_generator(N, lognormvariate, (0, 1))
_test_generator(N, vonmisesvariate, (0, 1))
_test_generator(N, gammavariate, (0.01, 1))
_test_generator(N, gammavariate, (0.1, 1))
_test_generator(N, gammavariate, (0.1, 2))
_test_generator(N, gammavariate, (0.5, 1))
_test_generator(N, gammavariate, (0.9, 1))
_test_generator(N, gammavariate, (1, 1))
_test_generator(N, gammavariate, (2, 1))
_test_generator(N, gammavariate, (20, 1))
_test_generator(N, gammavariate, (200, 1))
_test_generator(N, gauss, (0, 1))
_test_generator(N, betavariate, (3, 3))
_test_generator(N, triangular, (0, 1, 0.333333))
_inst = Random()
seed = _inst.seed
random = _inst.random
uniform = _inst.uniform
triangular = _inst.triangular
randint = _inst.randint
choice = _inst.choice
randrange = _inst.randrange
sample = _inst.sample
shuffle = _inst.shuffle
normalvariate = _inst.normalvariate
lognormvariate = _inst.lognormvariate
expovariate = _inst.expovariate
vonmisesvariate = _inst.vonmisesvariate
gammavariate = _inst.gammavariate
gauss = _inst.gauss
betavariate = _inst.betavariate
paretovariate = _inst.paretovariate
weibullvariate = _inst.weibullvariate
getstate = _inst.getstate
setstate = _inst.setstate
jumpahead = _inst.jumpahead
getrandbits = _inst.getrandbits
if __name__ == '__main__':
_test()