diff --git a/Lib/random.py b/Lib/random.py index 75f70d5d699..02a56c6935b 100644 --- a/Lib/random.py +++ b/Lib/random.py @@ -39,7 +39,7 @@ General notes on the underlying Mersenne Twister core generator: 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 sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin, tau as TWOPI 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 @@ -54,19 +54,38 @@ except ImportError: from hashlib import sha512 as _sha512 -__all__ = ["Random","seed","random","uniform","randint","choice","sample", - "randrange","shuffle","normalvariate","lognormvariate", - "expovariate","vonmisesvariate","gammavariate","triangular", - "gauss","betavariate","paretovariate","weibullvariate", - "getstate","setstate", "getrandbits", "choices", - "SystemRandom"] +__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) -TWOPI = 2.0*_pi +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 +RECIP_BPF = 2 ** -BPF # Translated by Guido van Rossum from C source provided by @@ -75,6 +94,7 @@ RECIP_BPF = 2**-BPF import _random + class Random(_random.Random): """Random number generator base class used by bound module functions. @@ -180,7 +200,7 @@ class Random(_random.Random): # 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) + internalstate = tuple(x % (2 ** 32) for x in internalstate) except ValueError as e: raise TypeError from e super().setstate(internalstate) @@ -189,21 +209,21 @@ class Random(_random.Random): "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. + ## ---- Methods below this point do not need to be overridden when + ## ---- subclassing for the purpose of using a different core generator. -## -------------------- bytes methods --------------------- + ## -------------------- bytes methods --------------------- def randbytes(self, n): """Generate n random bytes.""" return self.getrandbits(n * 8).to_bytes(n, 'little') -## -------------------- pickle support ------------------- + ## -------------------- 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 + def __getstate__(self): # for pickle return self.getstate() def __setstate__(self, state): # for pickle @@ -212,7 +232,7 @@ class Random(_random.Random): def __reduce__(self): return self.__class__, (), self.getstate() -## -------------------- integer methods ------------------- + ## -------------------- integer methods ------------------- def randrange(self, start, stop=None, step=1, _int=int): """Choose a random item from range(start, stop[, step]). @@ -256,7 +276,7 @@ class Random(_random.Random): if n <= 0: raise ValueError("empty range for randrange()") - return istart + istep*self._randbelow(n) + return istart + istep * self._randbelow(n) def randint(self, a, b): """Return random integer in range [a, b], including both end points. @@ -271,7 +291,7 @@ class Random(_random.Random): 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 + r = getrandbits(k) # 0 <= r < 2**k while r >= n: r = getrandbits(k) return r @@ -295,15 +315,16 @@ class Random(_random.Random): r = random() while r >= limit: r = random() - return int(r*maxsize) % n + return int(r * maxsize) % n _randbelow = _randbelow_with_getrandbits -## -------------------- sequence methods ------------------- + ## -------------------- sequence methods ------------------- def choice(self, seq): """Choose a random element from a non-empty sequence.""" - return seq[self._randbelow(len(seq))] # raises IndexError if seq is empty + # 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. @@ -318,7 +339,7 @@ class Random(_random.Random): 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) + j = randbelow(i + 1) x[i], x[j] = x[j], x[i] else: _warn('The *random* parameter to shuffle() has been deprecated\n' @@ -328,7 +349,7 @@ class Random(_random.Random): _int = int 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)) + j = _int(random() * (i + 1)) x[i], x[j] = x[j], x[i] def sample(self, population, k, *, counts=None): @@ -410,14 +431,15 @@ class Random(_random.Random): 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 + 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 + # 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): # invariant: non-selected at [0,n-i) - j = randbelow(n-i) + 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 + pool[j] = pool[n - i - 1] # move non-selected item into vacancy else: selected = set() selected_add = selected.add @@ -456,15 +478,15 @@ class Random(_random.Random): return [population[bisect(cum_weights, random() * total, 0, hi)] for i in _repeat(None, k)] -## -------------------- real-valued distributions ------------------- + ## -------------------- real-valued distributions ------------------- -## -------------------- uniform distribution ------------------- + ## -------------------- 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() + return a + (b - a) * self.random() -## -------------------- triangular -------------------- + ## -------------------- triangular -------------------- def triangular(self, low=0.0, high=1.0, mode=None): """Triangular distribution. @@ -486,7 +508,7 @@ class Random(_random.Random): low, high = high, low return low + (high - low) * _sqrt(u * c) -## -------------------- normal distribution -------------------- + ## -------------------- normal distribution -------------------- def normalvariate(self, mu, sigma): """Normal distribution. @@ -502,16 +524,16 @@ class Random(_random.Random): # Math Software, 3, (1977), pp257-260. random = self.random - while 1: + while True: u1 = random() u2 = 1.0 - random() - z = NV_MAGICCONST*(u1-0.5)/u2 - zz = z*z/4.0 + z = NV_MAGICCONST * (u1 - 0.5) / u2 + zz = z * z / 4.0 if zz <= -_log(u2): break - return mu + z*sigma + return mu + z * sigma -## -------------------- lognormal distribution -------------------- + ## -------------------- lognormal distribution -------------------- def lognormvariate(self, mu, sigma): """Log normal distribution. @@ -523,7 +545,7 @@ class Random(_random.Random): """ return _exp(self.normalvariate(mu, sigma)) -## -------------------- exponential distribution -------------------- + ## -------------------- exponential distribution -------------------- def expovariate(self, lambd): """Exponential distribution. @@ -540,9 +562,9 @@ class Random(_random.Random): # we use 1-random() instead of random() to preclude the # possibility of taking the log of zero. - return -_log(1.0 - self.random())/lambd + return -_log(1.0 - self.random()) / lambd -## -------------------- von Mises distribution -------------------- + ## -------------------- von Mises distribution -------------------- def vonmisesvariate(self, mu, kappa): """Circular data distribution. @@ -571,7 +593,7 @@ class Random(_random.Random): s = 0.5 / kappa r = s + _sqrt(1.0 + s * s) - while 1: + while True: u1 = random() z = _cos(_pi * u1) @@ -590,7 +612,7 @@ class Random(_random.Random): return theta -## -------------------- gamma distribution -------------------- + ## -------------------- gamma distribution -------------------- def gammavariate(self, alpha, beta): """Gamma distribution. Not the gamma function! @@ -625,32 +647,31 @@ class Random(_random.Random): while 1: u1 = random() - if not 1e-7 < u1 < .9999999: + 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): + 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) - + else: + # alpha is between 0 and 1 (exclusive) # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle - - while 1: + while True: u = random() - b = (_e + alpha)/_e - p = b*u + b = (_e + alpha) / _e + p = b * u if p <= 1.0: - x = p ** (1.0/alpha) + x = p ** (1.0 / alpha) else: - x = -_log((b-p)/alpha) + x = -_log((b - p) / alpha) u1 = random() if p > 1.0: if u1 <= x ** (alpha - 1.0): @@ -659,7 +680,7 @@ class Random(_random.Random): break return x * beta -## -------------------- Gauss (faster alternative) -------------------- + ## -------------------- Gauss (faster alternative) -------------------- def gauss(self, mu, sigma): """Gaussian distribution. @@ -698,21 +719,21 @@ class Random(_random.Random): z = _cos(x2pi) * g2rad self.gauss_next = _sin(x2pi) * g2rad - return mu + z*sigma + 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. + ## -------------------- 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. @@ -725,21 +746,20 @@ class Random(_random.Random): # 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 == 0: - return 0.0 - else: + if y: return y / (y + self.gammavariate(beta, 1.0)) + return 0.0 -## -------------------- Pareto -------------------- + ## -------------------- Pareto -------------------- def paretovariate(self, alpha): """Pareto distribution. alpha is the shape parameter.""" # Jain, pg. 495 u = 1.0 - self.random() - return 1.0 / u ** (1.0/alpha) + return 1.0 / u ** (1.0 / alpha) -## -------------------- Weibull -------------------- + ## -------------------- Weibull -------------------- def weibullvariate(self, alpha, beta): """Weibull distribution. @@ -750,7 +770,8 @@ class Random(_random.Random): # Jain, pg. 499; bug fix courtesy Bill Arms u = 1.0 - self.random() - return alpha * (-_log(u)) ** (1.0/beta) + return alpha * (-_log(u)) ** (1.0 / beta) + ## --------------- Operating System Random Source ------------------ @@ -789,6 +810,7 @@ class SystemRandom(Random): raise NotImplementedError('System entropy source does not have state.') getstate = setstate = _notimplemented + ## -------------------- test program -------------------- def _test_generator(n, func, args): @@ -806,11 +828,10 @@ def _test_generator(n, func, args): smallest = min(x, smallest) largest = max(x, largest) t1 = time.perf_counter() - 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\n' % \ - (avg, stddev, smallest, largest)) + 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\n' % (avg, stddev, smallest, largest)) def _test(N=2000): @@ -829,11 +850,11 @@ def _test(N=2000): _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)) + _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 +# (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.