| """Random variable generators. |
| |
| integers |
| -------- |
| uniform within range |
| |
| sequences |
| --------- |
| pick random element |
| pick random sample |
| generate random permutation |
| |
| distributions on the real line: |
| ------------------------------ |
| uniform |
| normal (Gaussian) |
| lognormal |
| negative exponential |
| gamma |
| beta |
| 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 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 |
| |
| __all__ = ["Random","seed","random","uniform","randint","choice","sample", |
| "randrange","shuffle","normalvariate","lognormvariate", |
| "expovariate","vonmisesvariate","gammavariate", |
| "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 getrandombits() 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 = int(_hexlify(_urandom(16)), 16) |
| except NotImplementedError: |
| import time |
| a = int(time.time() * 256) # use fractional seconds |
| |
| super().seed(a) |
| self.gauss_next = None |
| |
| def getstate(self): |
| """Return internal state; can be passed to setstate() later.""" |
| return self.VERSION, super().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().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( x % (2**32) for x in internalstate ) |
| except ValueError as e: |
| raise TypeError from e |
| super(Random, self).setstate(internalstate) |
| else: |
| raise ValueError("state with version %s passed to " |
| "Random.setstate() of version %s" % |
| (version, self.VERSION)) |
| |
| ## ---- 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=1<<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=1<<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(range(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 range as an argument. |
| This is especially fast and space efficient for sampling from a |
| large population: sample(range(10000000), 60) |
| """ |
| |
| # XXX Although the documentation says `population` is "a sequence", |
| # XXX attempts are made to cater to any iterable with a __len__ |
| # XXX method. This has had mixed success. Examples from both |
| # XXX sides: sets work fine, and should become officially supported; |
| # XXX dicts are much harder, and have failed in various subtle |
| # XXX ways across attempts. Support for mapping types should probably |
| # XXX be dropped (and users should pass mapping.keys() or .values() |
| # XXX explicitly). |
| |
| # 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 range(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 range(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).""" |
| return a + (b-a) * self.random() |
| |
| ## -------------------- normal distribution -------------------- |
| |
| def normalvariate(self, mu, sigma): |
| """Normal distribution. |
| |
| mu is the mean, and sigma is the standard deviation. |
| |
| """ |
| # mu = mean, sigma = standard deviation |
| |
| # Uses Kinderman and Monahan method. Reference: Kinderman, |
| # A.J. and Monahan, J.F., "Computer generation of random |
| # variables using the ratio of uniform deviates", ACM Trans |
| # Math Software, 3, (1977), pp257-260. |
| |
| random = self.random |
| while 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. (The parameter would be |
| called "lambda", but that is a reserved word in Python.) Returned |
| values range from 0 to positive infinity. |
| |
| """ |
| # lambd: rate lambd = 1/mean |
| # ('lambda' is a Python reserved word) |
| |
| random = self.random |
| u = random() |
| while u <= 1e-7: |
| u = random() |
| return -_log(u)/lambd |
| |
| ## -------------------- von Mises distribution -------------------- |
| |
| def vonmisesvariate(self, mu, kappa): |
| """Circular data distribution. |
| |
| mu is the mean angle, expressed in radians between 0 and 2*pi, and |
| kappa is the concentration parameter, which must be greater than or |
| equal to zero. If kappa is equal to zero, this distribution reduces |
| to a uniform random angle over the range 0 to 2*pi. |
| |
| """ |
| # mu: mean angle (in radians between 0 and 2*pi) |
| # kappa: concentration parameter kappa (>= 0) |
| # if kappa = 0 generate uniform random angle |
| |
| # Based upon an algorithm published in: Fisher, N.I., |
| # "Statistical Analysis of Circular Data", Cambridge |
| # University Press, 1993. |
| |
| # Thanks to Magnus Kessler for a correction to the |
| # implementation of step 4. |
| |
| random = self.random |
| if kappa <= 1e-6: |
| return TWOPI * random() |
| |
| a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) |
| b = (a - _sqrt(2.0 * a))/(2.0 * kappa) |
| r = (1.0 + b * b)/(2.0 * b) |
| |
| while 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. |
| |
| """ |
| |
| # 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://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 |
| ## for Ivan Frohne's insightful analysis of why the original implementation: |
| ## |
| ## def betavariate(self, alpha, beta): |
| ## # Discrete Event Simulation in C, pp 87-88. |
| ## |
| ## y = self.expovariate(alpha) |
| ## z = self.expovariate(1.0/beta) |
| ## return z/(y+z) |
| ## |
| ## was dead wrong, and how it probably got that way. |
| |
| def betavariate(self, alpha, beta): |
| """Beta distribution. |
| |
| Conditions on the parameters are alpha > 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 = int(_hexlify(_urandom(16)), 16) |
| except NotImplementedError: |
| import time |
| a = int(time.time() * 256) # use fractional seconds |
| |
| if not isinstance(a, int): |
| 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 = int(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 (int(_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 = int(_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,', end=' ') |
| 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)) |
| |
| # 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 |
| 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() |