"""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(2.0) | |
TWOPI = 2.0*_pi | |
LOG4 = _log(4.0) | |
SG_MAGICCONST = 1.0 + _log(4.5) | |
BPF = 53 # Number of bits in a float | |
RECIP_BPF = 2**-BPF | |
# 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. | |
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 # 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): | |
"""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 | |
a = long(time.time() * 256) # use fractional seconds | |
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 | |
# 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( long(x) % (2**32) for x in internalstate ) | |
except ValueError, e: | |
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. | |
""" | |
# The super.jumpahead() method uses shuffling to change state, | |
# so it needs a large and "interesting" n to work with. Here, | |
# we use hashing to create a large n for the shuffle. | |
s = repr(n) + repr(self.getstate()) | |
n = int(_hashlib.new('sha512', s).hexdigest(), 16) | |
super(Random, self).jumpahead(n) | |
## ---- 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) | |
def __reduce__(self): | |
return self.__class__, (), self.getstate() | |
## -------------------- integer methods ------------------- | |
def randrange(self, start, stop=None, step=1, int=int, default=None, | |
maxwidth=1L<<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. | |
Do not supply the 'int', 'default', and 'maxwidth' 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: | |
if istart >= maxwidth: | |
return self._randbelow(istart) | |
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()" | |
width = istop - istart | |
if step == 1 and width > 0: | |
# Note that | |
# int(istart + self.random()*width) | |
# instead would be incorrect. For example, consider istart | |
# = -2 and istop = 0. Then the guts would be in | |
# -2.0 to 0.0 exclusive on both ends (ignoring that random() | |
# might return 0.0), and because int() truncates toward 0, the | |
# final result would be -1 or 0 (instead of -2 or -1). | |
# istart + int(self.random()*width) | |
# would also be incorrect, for a subtler reason: the RHS | |
# can return a long, and then randrange() would also return | |
# a long, but we're supposed to return an int (for backward | |
# compatibility). | |
if width >= maxwidth: | |
return int(istart + self._randbelow(width)) | |
return int(istart + int(self.random()*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()" | |
if n >= maxwidth: | |
return istart + istep*self._randbelow(n) | |
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) | |
def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<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 | |
else: | |
# Only call self.getrandbits if the original random() builtin method | |
# has not been overridden or if a new getrandbits() was supplied. | |
# This assures that the two methods correspond. | |
if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: | |
k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) | |
r = getrandbits(k) | |
while r >= n: | |
r = getrandbits(k) | |
return r | |
if n >= _maxwidth: | |
_warn("Underlying random() generator does not supply \n" | |
"enough bits to choose from a population range this large") | |
return int(self.random() * n) | |
## -------------------- sequence methods ------------------- | |
def choice(self, seq): | |
"""Choose a random element from a non-empty sequence.""" | |
return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty | |
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. | |
""" | |
if random is None: | |
random = self.random | |
for i in reversed(xrange(1, len(x))): | |
# 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): | |
"""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) | |
""" | |
# 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. | |
n = len(population) | |
if not 0 <= k <= n: | |
raise ValueError("sample larger than population") | |
random = self.random | |
_int = int | |
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 or hasattr(population, "keys"): | |
# An n-length list is smaller than a k-length set, or this is a | |
# mapping type so the other algorithm wouldn't work. | |
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] # move non-selected item into vacancy | |
else: | |
try: | |
selected = set() | |
selected_add = selected.add | |
for i in xrange(k): | |
j = _int(random() * n) | |
while j in selected: | |
j = _int(random() * n) | |
selected_add(j) | |
result[i] = population[j] | |
except (TypeError, KeyError): # handle (at least) sets | |
if isinstance(population, list): | |
raise | |
return self.sample(tuple(population), k) | |
return result | |
## -------------------- real-valued distributions ------------------- | |
## -------------------- uniform distribution ------------------- | |
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() | |
## -------------------- triangular -------------------- | |
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() | |
c = 0.5 if mode is None else (mode - low) / (high - low) | |
if u > c: | |
u = 1.0 - u | |
c = 1.0 - c | |
low, high = high, low | |
return low + (high - low) * (u * c) ** 0.5 | |
## -------------------- 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 1: | |
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 | |
## -------------------- 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)) | |
## -------------------- exponential distribution -------------------- | |
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) | |
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 1: | |
u1 = random() | |
z = _cos(_pi * u1) | |
f = (1.0 + r * z)/(r + z) | |
c = kappa * (r - f) | |
u2 = random() | |
if u2 < c * (2.0 - c) or 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. | |
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 < .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) | |
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 1: | |
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 | |
## -------------------- 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://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. | |
def betavariate(self, alpha, beta): | |
"""Beta distribution. | |
Conditions on the parameters are alpha > 0 and beta > 0. | |
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 = 1.0 - 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 = 1.0 - self.random() | |
return alpha * pow(-_log(u), 1.0/beta) | |
## -------------------- Wichmann-Hill ------------------- | |
class WichmannHill(Random): | |
VERSION = 1 # used by getstate/setstate | |
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) # use fractional seconds | |
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).""" | |
# 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) | |
## --------------- 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 (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 # bits / 8 and rounded up | |
x = long(_hexlify(_urandom(bytes)), 16) | |
return x >> (bytes * 8 - k) # trim excess bits | |
def _stub(self, *args, **kwds): | |
"Stub method. Not used for a system random number generator." | |
return None | |
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 | |
## -------------------- test program -------------------- | |
def _test_generator(n, func, args): | |
import time | |
print n, 'times', func.__name__ | |
total = 0.0 | |
sqsum = 0.0 | |
smallest = 1e10 | |
largest = -1e10 | |
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, (0.0, 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)) | |
# 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 | |
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() |