android / platform / prebuilts / python / darwin-x86 / 2.7.5 / refs/tags/android-n-mr1-preview-2 / . / lib / python2.7 / random.py

"""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) | |

# we use 1-random() instead of random() to preclude the | |

# possibility of taking the log of zero. | |

return -_log(1.0 - self.random())/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() | |

s = 0.5 / kappa | |

r = s + _sqrt(1.0 + s * s) | |

while 1: | |

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 | |

## -------------------- 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() |