| """Random variable generators. |
| |
| bytes |
| ----- |
| uniform bytes (values between 0 and 255) |
| |
| integers |
| -------- |
| uniform within range |
| |
| sequences |
| --------- |
| pick random element |
| pick random sample |
| pick weighted 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. |
| * The random() method is implemented in C, executes in a single Python step, |
| and is, therefore, threadsafe. |
| |
| """ |
| |
| # 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. |
| |
| from warnings import warn as _warn |
| 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 math import tau as TWOPI, floor as _floor, isfinite as _isfinite |
| from os import urandom as _urandom |
| from _collections_abc import Set as _Set, Sequence as _Sequence |
| from itertools import accumulate as _accumulate, repeat as _repeat |
| from bisect import bisect as _bisect |
| import os as _os |
| import _random |
| |
| try: |
| # hashlib is pretty heavy to load, try lean internal module first |
| from _sha512 import sha512 as _sha512 |
| except ImportError: |
| # fallback to official implementation |
| from hashlib import sha512 as _sha512 |
| |
| __all__ = [ |
| "Random", |
| "SystemRandom", |
| "betavariate", |
| "choice", |
| "choices", |
| "expovariate", |
| "gammavariate", |
| "gauss", |
| "getrandbits", |
| "getstate", |
| "lognormvariate", |
| "normalvariate", |
| "paretovariate", |
| "randint", |
| "random", |
| "randrange", |
| "sample", |
| "seed", |
| "setstate", |
| "shuffle", |
| "triangular", |
| "uniform", |
| "vonmisesvariate", |
| "weibullvariate", |
| ] |
| |
| NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0) |
| LOG4 = _log(4.0) |
| SG_MAGICCONST = 1.0 + _log(4.5) |
| BPF = 53 # Number of bits in a float |
| RECIP_BPF = 2 ** -BPF |
| |
| |
| 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. |
| |
| 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(), and setstate(). |
| 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, version=2): |
| """Initialize internal state from a seed. |
| |
| The only supported seed types are None, int, float, |
| str, bytes, and bytearray. |
| |
| None or no argument seeds from current time or from an operating |
| system specific randomness source if available. |
| |
| If *a* is an int, all bits are used. |
| |
| For version 2 (the default), all of the bits are used if *a* is a str, |
| bytes, or bytearray. For version 1 (provided for reproducing random |
| sequences from older versions of Python), the algorithm for str and |
| bytes generates a narrower range of seeds. |
| |
| """ |
| |
| if version == 1 and isinstance(a, (str, bytes)): |
| a = a.decode('latin-1') if isinstance(a, bytes) else a |
| x = ord(a[0]) << 7 if a else 0 |
| for c in map(ord, a): |
| x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF |
| x ^= len(a) |
| a = -2 if x == -1 else x |
| |
| elif version == 2 and isinstance(a, (str, bytes, bytearray)): |
| if isinstance(a, str): |
| a = a.encode() |
| a += _sha512(a).digest() |
| a = int.from_bytes(a, 'big') |
| |
| elif not isinstance(a, (type(None), int, float, str, bytes, bytearray)): |
| _warn('Seeding based on hashing is deprecated\n' |
| 'since Python 3.9 and will be removed in a subsequent ' |
| 'version. The only \n' |
| 'supported seed types are: None, ' |
| 'int, float, str, bytes, and bytearray.', |
| DeprecationWarning, 2) |
| |
| 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().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 or extended |
| ## ---- when subclassing for the purpose of using a different core generator. |
| |
| |
| ## -------------------- pickle support ------------------- |
| |
| # Issue 17489: Since __reduce__ was defined to fix #759889 this is no |
| # longer called; we leave it here because it has been here since random was |
| # rewritten back in 2001 and why risk breaking something. |
| 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() |
| |
| |
| ## ---- internal support method for evenly distributed integers ---- |
| |
| def __init_subclass__(cls, /, **kwargs): |
| """Control how subclasses generate random integers. |
| |
| The algorithm a subclass can use depends on the random() and/or |
| getrandbits() implementation available to it and determines |
| whether it can generate random integers from arbitrarily large |
| ranges. |
| """ |
| |
| for c in cls.__mro__: |
| if '_randbelow' in c.__dict__: |
| # just inherit it |
| break |
| if 'getrandbits' in c.__dict__: |
| cls._randbelow = cls._randbelow_with_getrandbits |
| break |
| if 'random' in c.__dict__: |
| cls._randbelow = cls._randbelow_without_getrandbits |
| break |
| |
| def _randbelow_with_getrandbits(self, n): |
| "Return a random int in the range [0,n). Returns 0 if n==0." |
| |
| if not n: |
| return 0 |
| getrandbits = self.getrandbits |
| k = n.bit_length() # don't use (n-1) here because n can be 1 |
| r = getrandbits(k) # 0 <= r < 2**k |
| while r >= n: |
| r = getrandbits(k) |
| return r |
| |
| def _randbelow_without_getrandbits(self, n, maxsize=1<<BPF): |
| """Return a random int in the range [0,n). Returns 0 if n==0. |
| |
| The implementation does not use getrandbits, but only random. |
| """ |
| |
| random = self.random |
| if n >= maxsize: |
| _warn("Underlying random() generator does not supply \n" |
| "enough bits to choose from a population range this large.\n" |
| "To remove the range limitation, add a getrandbits() method.") |
| return _floor(random() * n) |
| if n == 0: |
| return 0 |
| rem = maxsize % n |
| limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0 |
| r = random() |
| while r >= limit: |
| r = random() |
| return _floor(r * maxsize) % n |
| |
| _randbelow = _randbelow_with_getrandbits |
| |
| |
| ## -------------------------------------------------------- |
| ## ---- Methods below this point generate custom distributions |
| ## ---- based on the methods defined above. They do not |
| ## ---- directly touch the underlying generator and only |
| ## ---- access randomness through the methods: random(), |
| ## ---- getrandbits(), or _randbelow(). |
| |
| |
| ## -------------------- bytes methods --------------------- |
| |
| def randbytes(self, n): |
| """Generate n random bytes.""" |
| return self.getrandbits(n * 8).to_bytes(n, 'little') |
| |
| |
| ## -------------------- integer methods ------------------- |
| |
| def randrange(self, start, stop=None, step=1): |
| """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. |
| |
| """ |
| |
| # 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 None: |
| if istart > 0: |
| return self._randbelow(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: |
| return istart + self._randbelow(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()") |
| |
| return istart + istep * self._randbelow(n) |
| |
| def randint(self, a, b): |
| """Return random integer in range [a, b], including both end points. |
| """ |
| |
| return self.randrange(a, b+1) |
| |
| |
| ## -------------------- sequence methods ------------------- |
| |
| def choice(self, seq): |
| """Choose a random element from a non-empty sequence.""" |
| # raises IndexError if seq is empty |
| return seq[self._randbelow(len(seq))] |
| |
| def shuffle(self, x, random=None): |
| """Shuffle list x in place, and return None. |
| |
| Optional argument random is a 0-argument function returning a |
| random float in [0.0, 1.0); if it is the default None, the |
| standard random.random will be used. |
| |
| """ |
| |
| if random is None: |
| randbelow = self._randbelow |
| for i in reversed(range(1, len(x))): |
| # pick an element in x[:i+1] with which to exchange x[i] |
| j = randbelow(i + 1) |
| x[i], x[j] = x[j], x[i] |
| else: |
| _warn('The *random* parameter to shuffle() has been deprecated\n' |
| 'since Python 3.9 and will be removed in a subsequent ' |
| 'version.', |
| DeprecationWarning, 2) |
| floor = _floor |
| for i in reversed(range(1, len(x))): |
| # pick an element in x[:i+1] with which to exchange x[i] |
| j = floor(random() * (i + 1)) |
| x[i], x[j] = x[j], x[i] |
| |
| def sample(self, population, k, *, counts=None): |
| """Chooses k unique random elements from a population sequence or set. |
| |
| 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. |
| |
| Repeated elements can be specified one at a time or with the optional |
| counts parameter. For example: |
| |
| sample(['red', 'blue'], counts=[4, 2], k=5) |
| |
| is equivalent to: |
| |
| sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5) |
| |
| To choose a sample from a range of integers, use range() for the |
| population argument. This is especially fast and space efficient |
| for sampling from a large population: |
| |
| sample(range(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. |
| |
| # The number of calls to _randbelow() is kept at or near k, the |
| # theoretical minimum. This is important because running time |
| # is dominated by _randbelow() and because it extracts the |
| # least entropy from the underlying random number generators. |
| |
| # Memory requirements are kept to the smaller of a k-length |
| # set or an n-length list. |
| |
| # There are other sampling algorithms that do not require |
| # auxiliary memory, but they were rejected because they made |
| # too many calls to _randbelow(), making them slower and |
| # causing them to eat more entropy than necessary. |
| |
| if isinstance(population, _Set): |
| _warn('Sampling from a set deprecated\n' |
| 'since Python 3.9 and will be removed in a subsequent version.', |
| DeprecationWarning, 2) |
| population = tuple(population) |
| if not isinstance(population, _Sequence): |
| raise TypeError("Population must be a sequence. For dicts or sets, use sorted(d).") |
| n = len(population) |
| if counts is not None: |
| cum_counts = list(_accumulate(counts)) |
| if len(cum_counts) != n: |
| raise ValueError('The number of counts does not match the population') |
| total = cum_counts.pop() |
| if not isinstance(total, int): |
| raise TypeError('Counts must be integers') |
| if total <= 0: |
| raise ValueError('Total of counts must be greater than zero') |
| selections = sample(range(total), k=k) |
| bisect = _bisect |
| return [population[bisect(cum_counts, s)] for s in selections] |
| randbelow = self._randbelow |
| if not 0 <= k <= n: |
| raise ValueError("Sample larger than population or is negative") |
| 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: |
| # An n-length list is smaller than a k-length set. |
| # Invariant: non-selected at pool[0 : n-i] |
| pool = list(population) |
| for i in range(k): |
| j = randbelow(n - i) |
| result[i] = pool[j] |
| pool[j] = pool[n - i - 1] # move non-selected item into vacancy |
| else: |
| selected = set() |
| selected_add = selected.add |
| for i in range(k): |
| j = randbelow(n) |
| while j in selected: |
| j = randbelow(n) |
| selected_add(j) |
| result[i] = population[j] |
| return result |
| |
| def choices(self, population, weights=None, *, cum_weights=None, k=1): |
| """Return a k sized list of population elements chosen with replacement. |
| |
| If the relative weights or cumulative weights are not specified, |
| the selections are made with equal probability. |
| |
| """ |
| random = self.random |
| n = len(population) |
| if cum_weights is None: |
| if weights is None: |
| floor = _floor |
| n += 0.0 # convert to float for a small speed improvement |
| return [population[floor(random() * n)] for i in _repeat(None, k)] |
| cum_weights = list(_accumulate(weights)) |
| elif weights is not None: |
| raise TypeError('Cannot specify both weights and cumulative weights') |
| if len(cum_weights) != n: |
| raise ValueError('The number of weights does not match the population') |
| total = cum_weights[-1] + 0.0 # convert to float |
| if total <= 0.0: |
| raise ValueError('Total of weights must be greater than zero') |
| if not _isfinite(total): |
| raise ValueError('Total of weights must be finite') |
| bisect = _bisect |
| hi = n - 1 |
| return [population[bisect(cum_weights, random() * total, 0, hi)] |
| for i in _repeat(None, k)] |
| |
| |
| ## -------------------- real-valued distributions ------------------- |
| |
| def uniform(self, a, b): |
| "Get a random number in the range [a, b) or [a, b] depending on rounding." |
| return a + (b - a) * self.random() |
| |
| def triangular(self, low=0.0, 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() |
| try: |
| c = 0.5 if mode is None else (mode - low) / (high - low) |
| except ZeroDivisionError: |
| return low |
| if u > c: |
| u = 1.0 - u |
| c = 1.0 - c |
| low, high = high, low |
| return low + (high - low) * _sqrt(u * c) |
| |
| def normalvariate(self, mu, sigma): |
| """Normal distribution. |
| |
| mu is the mean, and sigma is the 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 True: |
| 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 |
| |
| 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 |
| |
| def lognormvariate(self, mu, sigma): |
| """Log normal distribution. |
| |
| If you take the natural logarithm of this distribution, you'll get a |
| normal distribution with mean mu and standard deviation sigma. |
| mu can have any value, and sigma must be greater than zero. |
| |
| """ |
| return _exp(self.normalvariate(mu, sigma)) |
| |
| def expovariate(self, lambd): |
| """Exponential distribution. |
| |
| lambd is 1.0 divided by the desired mean. It should be |
| nonzero. (The parameter would be called "lambda", but that is |
| a reserved word in Python.) Returned values range from 0 to |
| positive infinity if lambd is positive, and from negative |
| infinity to 0 if lambd is negative. |
| |
| """ |
| # 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 |
| |
| 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. |
| |
| """ |
| # 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 True: |
| 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 |
| |
| 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 True: |
| u1 = random() |
| if not 1e-7 < u1 < 0.9999999: |
| 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/beta) |
| return -_log(1.0 - random()) * beta |
| |
| else: |
| # alpha is between 0 and 1 (exclusive) |
| # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle |
| while True: |
| 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 |
| |
| def betavariate(self, alpha, beta): |
| """Beta distribution. |
| |
| Conditions on the parameters are alpha > 0 and beta > 0. |
| Returned values range between 0 and 1. |
| |
| """ |
| ## 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. |
| |
| # 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, 1.0) |
| if y: |
| return y / (y + self.gammavariate(beta, 1.0)) |
| return 0.0 |
| |
| def paretovariate(self, alpha): |
| """Pareto distribution. alpha is the shape parameter.""" |
| # Jain, pg. 495 |
| |
| u = 1.0 - self.random() |
| return u ** (-1.0 / alpha) |
| |
| 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 * (-_log(u)) ** (1.0 / beta) |
| |
| |
| ## ------------------------------------------------------------------ |
| ## --------------- 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.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF |
| |
| def getrandbits(self, k): |
| """getrandbits(k) -> x. Generates an int with k random bits.""" |
| if k < 0: |
| raise ValueError('number of bits must be non-negative') |
| numbytes = (k + 7) // 8 # bits / 8 and rounded up |
| x = int.from_bytes(_urandom(numbytes), 'big') |
| return x >> (numbytes * 8 - k) # trim excess bits |
| |
| def randbytes(self, n): |
| """Generate n random bytes.""" |
| # os.urandom(n) fails with ValueError for n < 0 |
| # and returns an empty bytes string for n == 0. |
| return _urandom(n) |
| |
| def seed(self, *args, **kwds): |
| "Stub method. Not used for a system random number generator." |
| return None |
| |
| 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 |
| |
| |
| # ---------------------------------------------------------------------- |
| # 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 |
| choices = _inst.choices |
| 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 |
| getrandbits = _inst.getrandbits |
| randbytes = _inst.randbytes |
| |
| |
| ## ------------------------------------------------------ |
| ## ----------------- test program ----------------------- |
| |
| def _test_generator(n, func, args): |
| from statistics import stdev, fmean as mean |
| from time import perf_counter |
| |
| t0 = perf_counter() |
| data = [func(*args) for i in range(n)] |
| t1 = perf_counter() |
| |
| xbar = mean(data) |
| sigma = stdev(data, xbar) |
| low = min(data) |
| high = max(data) |
| |
| print(f'{t1 - t0:.3f} sec, {n} times {func.__name__}') |
| print('avg %g, stddev %g, min %g, max %g\n' % (xbar, sigma, low, high)) |
| |
| |
| 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)) |
| |
| |
| ## ------------------------------------------------------ |
| ## ------------------ fork support --------------------- |
| |
| if hasattr(_os, "fork"): |
| _os.register_at_fork(after_in_child=_inst.seed) |
| |
| |
| if __name__ == '__main__': |
| _test() |