| """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() |