1"""Random variable generators. 2 3 integers 4 -------- 5 uniform within range 6 7 sequences 8 --------- 9 pick random element 10 pick random sample 11 pick weighted random sample 12 generate random permutation 13 14 distributions on the real line: 15 ------------------------------ 16 uniform 17 triangular 18 normal (Gaussian) 19 lognormal 20 negative exponential 21 gamma 22 beta 23 pareto 24 Weibull 25 26 distributions on the circle (angles 0 to 2pi) 27 --------------------------------------------- 28 circular uniform 29 von Mises 30 31General notes on the underlying Mersenne Twister core generator: 32 33* The period is 2**19937-1. 34* It is one of the most extensively tested generators in existence. 35* The random() method is implemented in C, executes in a single Python step, 36 and is, therefore, threadsafe. 37 38""" 39 40from warnings import warn as _warn 41from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 42from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 43from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 44from os import urandom as _urandom 45from _collections_abc import Set as _Set, Sequence as _Sequence 46from hashlib import sha512 as _sha512 47import itertools as _itertools 48import bisect as _bisect 49 50__all__ = ["Random","seed","random","uniform","randint","choice","sample", 51 "randrange","shuffle","normalvariate","lognormvariate", 52 "expovariate","vonmisesvariate","gammavariate","triangular", 53 "gauss","betavariate","paretovariate","weibullvariate", 54 "getstate","setstate", "getrandbits", "choices", 55 "SystemRandom"] 56 57NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 58TWOPI = 2.0*_pi 59LOG4 = _log(4.0) 60SG_MAGICCONST = 1.0 + _log(4.5) 61BPF = 53 # Number of bits in a float 62RECIP_BPF = 2**-BPF 63 64 65# Translated by Guido van Rossum from C source provided by 66# Adrian Baddeley. Adapted by Raymond Hettinger for use with 67# the Mersenne Twister and os.urandom() core generators. 68 69import _random 70 71class Random(_random.Random): 72 """Random number generator base class used by bound module functions. 73 74 Used to instantiate instances of Random to get generators that don't 75 share state. 76 77 Class Random can also be subclassed if you want to use a different basic 78 generator of your own devising: in that case, override the following 79 methods: random(), seed(), getstate(), and setstate(). 80 Optionally, implement a getrandbits() method so that randrange() 81 can cover arbitrarily large ranges. 82 83 """ 84 85 VERSION = 3 # used by getstate/setstate 86 87 def __init__(self, x=None): 88 """Initialize an instance. 89 90 Optional argument x controls seeding, as for Random.seed(). 91 """ 92 93 self.seed(x) 94 self.gauss_next = None 95 96 def seed(self, a=None, version=2): 97 """Initialize internal state from hashable object. 98 99 None or no argument seeds from current time or from an operating 100 system specific randomness source if available. 101 102 If *a* is an int, all bits are used. 103 104 For version 2 (the default), all of the bits are used if *a* is a str, 105 bytes, or bytearray. For version 1 (provided for reproducing random 106 sequences from older versions of Python), the algorithm for str and 107 bytes generates a narrower range of seeds. 108 109 """ 110 111 if version == 1 and isinstance(a, (str, bytes)): 112 x = ord(a[0]) << 7 if a else 0 113 for c in a: 114 x = ((1000003 * x) ^ ord(c)) & 0xFFFFFFFFFFFFFFFF 115 x ^= len(a) 116 a = -2 if x == -1 else x 117 118 if version == 2 and isinstance(a, (str, bytes, bytearray)): 119 if isinstance(a, str): 120 a = a.encode() 121 a += _sha512(a).digest() 122 a = int.from_bytes(a, 'big') 123 124 super().seed(a) 125 self.gauss_next = None 126 127 def getstate(self): 128 """Return internal state; can be passed to setstate() later.""" 129 return self.VERSION, super().getstate(), self.gauss_next 130 131 def setstate(self, state): 132 """Restore internal state from object returned by getstate().""" 133 version = state[0] 134 if version == 3: 135 version, internalstate, self.gauss_next = state 136 super().setstate(internalstate) 137 elif version == 2: 138 version, internalstate, self.gauss_next = state 139 # In version 2, the state was saved as signed ints, which causes 140 # inconsistencies between 32/64-bit systems. The state is 141 # really unsigned 32-bit ints, so we convert negative ints from 142 # version 2 to positive longs for version 3. 143 try: 144 internalstate = tuple(x % (2**32) for x in internalstate) 145 except ValueError as e: 146 raise TypeError from e 147 super().setstate(internalstate) 148 else: 149 raise ValueError("state with version %s passed to " 150 "Random.setstate() of version %s" % 151 (version, self.VERSION)) 152 153## ---- Methods below this point do not need to be overridden when 154## ---- subclassing for the purpose of using a different core generator. 155 156## -------------------- pickle support ------------------- 157 158 # Issue 17489: Since __reduce__ was defined to fix #759889 this is no 159 # longer called; we leave it here because it has been here since random was 160 # rewritten back in 2001 and why risk breaking something. 161 def __getstate__(self): # for pickle 162 return self.getstate() 163 164 def __setstate__(self, state): # for pickle 165 self.setstate(state) 166 167 def __reduce__(self): 168 return self.__class__, (), self.getstate() 169 170## -------------------- integer methods ------------------- 171 172 def randrange(self, start, stop=None, step=1, _int=int): 173 """Choose a random item from range(start, stop[, step]). 174 175 This fixes the problem with randint() which includes the 176 endpoint; in Python this is usually not what you want. 177 178 """ 179 180 # This code is a bit messy to make it fast for the 181 # common case while still doing adequate error checking. 182 istart = _int(start) 183 if istart != start: 184 raise ValueError("non-integer arg 1 for randrange()") 185 if stop is None: 186 if istart > 0: 187 return self._randbelow(istart) 188 raise ValueError("empty range for randrange()") 189 190 # stop argument supplied. 191 istop = _int(stop) 192 if istop != stop: 193 raise ValueError("non-integer stop for randrange()") 194 width = istop - istart 195 if step == 1 and width > 0: 196 return istart + self._randbelow(width) 197 if step == 1: 198 raise ValueError("empty range for randrange() (%d,%d, %d)" % (istart, istop, width)) 199 200 # Non-unit step argument supplied. 201 istep = _int(step) 202 if istep != step: 203 raise ValueError("non-integer step for randrange()") 204 if istep > 0: 205 n = (width + istep - 1) // istep 206 elif istep < 0: 207 n = (width + istep + 1) // istep 208 else: 209 raise ValueError("zero step for randrange()") 210 211 if n <= 0: 212 raise ValueError("empty range for randrange()") 213 214 return istart + istep*self._randbelow(n) 215 216 def randint(self, a, b): 217 """Return random integer in range [a, b], including both end points. 218 """ 219 220 return self.randrange(a, b+1) 221 222 def _randbelow(self, n, int=int, maxsize=1<<BPF, type=type, 223 Method=_MethodType, BuiltinMethod=_BuiltinMethodType): 224 "Return a random int in the range [0,n). Raises ValueError if n==0." 225 226 random = self.random 227 getrandbits = self.getrandbits 228 # Only call self.getrandbits if the original random() builtin method 229 # has not been overridden or if a new getrandbits() was supplied. 230 if type(random) is BuiltinMethod or type(getrandbits) is Method: 231 k = n.bit_length() # don't use (n-1) here because n can be 1 232 r = getrandbits(k) # 0 <= r < 2**k 233 while r >= n: 234 r = getrandbits(k) 235 return r 236 # There's an overridden random() method but no new getrandbits() method, 237 # so we can only use random() from here. 238 if n >= maxsize: 239 _warn("Underlying random() generator does not supply \n" 240 "enough bits to choose from a population range this large.\n" 241 "To remove the range limitation, add a getrandbits() method.") 242 return int(random() * n) 243 rem = maxsize % n 244 limit = (maxsize - rem) / maxsize # int(limit * maxsize) % n == 0 245 r = random() 246 while r >= limit: 247 r = random() 248 return int(r*maxsize) % n 249 250## -------------------- sequence methods ------------------- 251 252 def choice(self, seq): 253 """Choose a random element from a non-empty sequence.""" 254 try: 255 i = self._randbelow(len(seq)) 256 except ValueError: 257 raise IndexError('Cannot choose from an empty sequence') from None 258 return seq[i] 259 260 def shuffle(self, x, random=None): 261 """Shuffle list x in place, and return None. 262 263 Optional argument random is a 0-argument function returning a 264 random float in [0.0, 1.0); if it is the default None, the 265 standard random.random will be used. 266 267 """ 268 269 if random is None: 270 randbelow = self._randbelow 271 for i in reversed(range(1, len(x))): 272 # pick an element in x[:i+1] with which to exchange x[i] 273 j = randbelow(i+1) 274 x[i], x[j] = x[j], x[i] 275 else: 276 _int = int 277 for i in reversed(range(1, len(x))): 278 # pick an element in x[:i+1] with which to exchange x[i] 279 j = _int(random() * (i+1)) 280 x[i], x[j] = x[j], x[i] 281 282 def sample(self, population, k): 283 """Chooses k unique random elements from a population sequence or set. 284 285 Returns a new list containing elements from the population while 286 leaving the original population unchanged. The resulting list is 287 in selection order so that all sub-slices will also be valid random 288 samples. This allows raffle winners (the sample) to be partitioned 289 into grand prize and second place winners (the subslices). 290 291 Members of the population need not be hashable or unique. If the 292 population contains repeats, then each occurrence is a possible 293 selection in the sample. 294 295 To choose a sample in a range of integers, use range as an argument. 296 This is especially fast and space efficient for sampling from a 297 large population: sample(range(10000000), 60) 298 """ 299 300 # Sampling without replacement entails tracking either potential 301 # selections (the pool) in a list or previous selections in a set. 302 303 # When the number of selections is small compared to the 304 # population, then tracking selections is efficient, requiring 305 # only a small set and an occasional reselection. For 306 # a larger number of selections, the pool tracking method is 307 # preferred since the list takes less space than the 308 # set and it doesn't suffer from frequent reselections. 309 310 if isinstance(population, _Set): 311 population = tuple(population) 312 if not isinstance(population, _Sequence): 313 raise TypeError("Population must be a sequence or set. For dicts, use list(d).") 314 randbelow = self._randbelow 315 n = len(population) 316 if not 0 <= k <= n: 317 raise ValueError("Sample larger than population or is negative") 318 result = [None] * k 319 setsize = 21 # size of a small set minus size of an empty list 320 if k > 5: 321 setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 322 if n <= setsize: 323 # An n-length list is smaller than a k-length set 324 pool = list(population) 325 for i in range(k): # invariant: non-selected at [0,n-i) 326 j = randbelow(n-i) 327 result[i] = pool[j] 328 pool[j] = pool[n-i-1] # move non-selected item into vacancy 329 else: 330 selected = set() 331 selected_add = selected.add 332 for i in range(k): 333 j = randbelow(n) 334 while j in selected: 335 j = randbelow(n) 336 selected_add(j) 337 result[i] = population[j] 338 return result 339 340 def choices(self, population, weights=None, *, cum_weights=None, k=1): 341 """Return a k sized list of population elements chosen with replacement. 342 343 If the relative weights or cumulative weights are not specified, 344 the selections are made with equal probability. 345 346 """ 347 random = self.random 348 if cum_weights is None: 349 if weights is None: 350 _int = int 351 total = len(population) 352 return [population[_int(random() * total)] for i in range(k)] 353 cum_weights = list(_itertools.accumulate(weights)) 354 elif weights is not None: 355 raise TypeError('Cannot specify both weights and cumulative weights') 356 if len(cum_weights) != len(population): 357 raise ValueError('The number of weights does not match the population') 358 bisect = _bisect.bisect 359 total = cum_weights[-1] 360 return [population[bisect(cum_weights, random() * total)] for i in range(k)] 361 362## -------------------- real-valued distributions ------------------- 363 364## -------------------- uniform distribution ------------------- 365 366 def uniform(self, a, b): 367 "Get a random number in the range [a, b) or [a, b] depending on rounding." 368 return a + (b-a) * self.random() 369 370## -------------------- triangular -------------------- 371 372 def triangular(self, low=0.0, high=1.0, mode=None): 373 """Triangular distribution. 374 375 Continuous distribution bounded by given lower and upper limits, 376 and having a given mode value in-between. 377 378 http://en.wikipedia.org/wiki/Triangular_distribution 379 380 """ 381 u = self.random() 382 try: 383 c = 0.5 if mode is None else (mode - low) / (high - low) 384 except ZeroDivisionError: 385 return low 386 if u > c: 387 u = 1.0 - u 388 c = 1.0 - c 389 low, high = high, low 390 return low + (high - low) * (u * c) ** 0.5 391 392## -------------------- normal distribution -------------------- 393 394 def normalvariate(self, mu, sigma): 395 """Normal distribution. 396 397 mu is the mean, and sigma is the standard deviation. 398 399 """ 400 # mu = mean, sigma = standard deviation 401 402 # Uses Kinderman and Monahan method. Reference: Kinderman, 403 # A.J. and Monahan, J.F., "Computer generation of random 404 # variables using the ratio of uniform deviates", ACM Trans 405 # Math Software, 3, (1977), pp257-260. 406 407 random = self.random 408 while 1: 409 u1 = random() 410 u2 = 1.0 - random() 411 z = NV_MAGICCONST*(u1-0.5)/u2 412 zz = z*z/4.0 413 if zz <= -_log(u2): 414 break 415 return mu + z*sigma 416 417## -------------------- lognormal distribution -------------------- 418 419 def lognormvariate(self, mu, sigma): 420 """Log normal distribution. 421 422 If you take the natural logarithm of this distribution, you'll get a 423 normal distribution with mean mu and standard deviation sigma. 424 mu can have any value, and sigma must be greater than zero. 425 426 """ 427 return _exp(self.normalvariate(mu, sigma)) 428 429## -------------------- exponential distribution -------------------- 430 431 def expovariate(self, lambd): 432 """Exponential distribution. 433 434 lambd is 1.0 divided by the desired mean. It should be 435 nonzero. (The parameter would be called "lambda", but that is 436 a reserved word in Python.) Returned values range from 0 to 437 positive infinity if lambd is positive, and from negative 438 infinity to 0 if lambd is negative. 439 440 """ 441 # lambd: rate lambd = 1/mean 442 # ('lambda' is a Python reserved word) 443 444 # we use 1-random() instead of random() to preclude the 445 # possibility of taking the log of zero. 446 return -_log(1.0 - self.random())/lambd 447 448## -------------------- von Mises distribution -------------------- 449 450 def vonmisesvariate(self, mu, kappa): 451 """Circular data distribution. 452 453 mu is the mean angle, expressed in radians between 0 and 2*pi, and 454 kappa is the concentration parameter, which must be greater than or 455 equal to zero. If kappa is equal to zero, this distribution reduces 456 to a uniform random angle over the range 0 to 2*pi. 457 458 """ 459 # mu: mean angle (in radians between 0 and 2*pi) 460 # kappa: concentration parameter kappa (>= 0) 461 # if kappa = 0 generate uniform random angle 462 463 # Based upon an algorithm published in: Fisher, N.I., 464 # "Statistical Analysis of Circular Data", Cambridge 465 # University Press, 1993. 466 467 # Thanks to Magnus Kessler for a correction to the 468 # implementation of step 4. 469 470 random = self.random 471 if kappa <= 1e-6: 472 return TWOPI * random() 473 474 s = 0.5 / kappa 475 r = s + _sqrt(1.0 + s * s) 476 477 while 1: 478 u1 = random() 479 z = _cos(_pi * u1) 480 481 d = z / (r + z) 482 u2 = random() 483 if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d): 484 break 485 486 q = 1.0 / r 487 f = (q + z) / (1.0 + q * z) 488 u3 = random() 489 if u3 > 0.5: 490 theta = (mu + _acos(f)) % TWOPI 491 else: 492 theta = (mu - _acos(f)) % TWOPI 493 494 return theta 495 496## -------------------- gamma distribution -------------------- 497 498 def gammavariate(self, alpha, beta): 499 """Gamma distribution. Not the gamma function! 500 501 Conditions on the parameters are alpha > 0 and beta > 0. 502 503 The probability distribution function is: 504 505 x ** (alpha - 1) * math.exp(-x / beta) 506 pdf(x) = -------------------------------------- 507 math.gamma(alpha) * beta ** alpha 508 509 """ 510 511 # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 512 513 # Warning: a few older sources define the gamma distribution in terms 514 # of alpha > -1.0 515 if alpha <= 0.0 or beta <= 0.0: 516 raise ValueError('gammavariate: alpha and beta must be > 0.0') 517 518 random = self.random 519 if alpha > 1.0: 520 521 # Uses R.C.H. Cheng, "The generation of Gamma 522 # variables with non-integral shape parameters", 523 # Applied Statistics, (1977), 26, No. 1, p71-74 524 525 ainv = _sqrt(2.0 * alpha - 1.0) 526 bbb = alpha - LOG4 527 ccc = alpha + ainv 528 529 while 1: 530 u1 = random() 531 if not 1e-7 < u1 < .9999999: 532 continue 533 u2 = 1.0 - random() 534 v = _log(u1/(1.0-u1))/ainv 535 x = alpha*_exp(v) 536 z = u1*u1*u2 537 r = bbb+ccc*v-x 538 if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 539 return x * beta 540 541 elif alpha == 1.0: 542 # expovariate(1) 543 u = random() 544 while u <= 1e-7: 545 u = random() 546 return -_log(u) * beta 547 548 else: # alpha is between 0 and 1 (exclusive) 549 550 # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 551 552 while 1: 553 u = random() 554 b = (_e + alpha)/_e 555 p = b*u 556 if p <= 1.0: 557 x = p ** (1.0/alpha) 558 else: 559 x = -_log((b-p)/alpha) 560 u1 = random() 561 if p > 1.0: 562 if u1 <= x ** (alpha - 1.0): 563 break 564 elif u1 <= _exp(-x): 565 break 566 return x * beta 567 568## -------------------- Gauss (faster alternative) -------------------- 569 570 def gauss(self, mu, sigma): 571 """Gaussian distribution. 572 573 mu is the mean, and sigma is the standard deviation. This is 574 slightly faster than the normalvariate() function. 575 576 Not thread-safe without a lock around calls. 577 578 """ 579 580 # When x and y are two variables from [0, 1), uniformly 581 # distributed, then 582 # 583 # cos(2*pi*x)*sqrt(-2*log(1-y)) 584 # sin(2*pi*x)*sqrt(-2*log(1-y)) 585 # 586 # are two *independent* variables with normal distribution 587 # (mu = 0, sigma = 1). 588 # (Lambert Meertens) 589 # (corrected version; bug discovered by Mike Miller, fixed by LM) 590 591 # Multithreading note: When two threads call this function 592 # simultaneously, it is possible that they will receive the 593 # same return value. The window is very small though. To 594 # avoid this, you have to use a lock around all calls. (I 595 # didn't want to slow this down in the serial case by using a 596 # lock here.) 597 598 random = self.random 599 z = self.gauss_next 600 self.gauss_next = None 601 if z is None: 602 x2pi = random() * TWOPI 603 g2rad = _sqrt(-2.0 * _log(1.0 - random())) 604 z = _cos(x2pi) * g2rad 605 self.gauss_next = _sin(x2pi) * g2rad 606 607 return mu + z*sigma 608 609## -------------------- beta -------------------- 610## See 611## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html 612## for Ivan Frohne's insightful analysis of why the original implementation: 613## 614## def betavariate(self, alpha, beta): 615## # Discrete Event Simulation in C, pp 87-88. 616## 617## y = self.expovariate(alpha) 618## z = self.expovariate(1.0/beta) 619## return z/(y+z) 620## 621## was dead wrong, and how it probably got that way. 622 623 def betavariate(self, alpha, beta): 624 """Beta distribution. 625 626 Conditions on the parameters are alpha > 0 and beta > 0. 627 Returned values range between 0 and 1. 628 629 """ 630 631 # This version due to Janne Sinkkonen, and matches all the std 632 # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 633 y = self.gammavariate(alpha, 1.0) 634 if y == 0: 635 return 0.0 636 else: 637 return y / (y + self.gammavariate(beta, 1.0)) 638 639## -------------------- Pareto -------------------- 640 641 def paretovariate(self, alpha): 642 """Pareto distribution. alpha is the shape parameter.""" 643 # Jain, pg. 495 644 645 u = 1.0 - self.random() 646 return 1.0 / u ** (1.0/alpha) 647 648## -------------------- Weibull -------------------- 649 650 def weibullvariate(self, alpha, beta): 651 """Weibull distribution. 652 653 alpha is the scale parameter and beta is the shape parameter. 654 655 """ 656 # Jain, pg. 499; bug fix courtesy Bill Arms 657 658 u = 1.0 - self.random() 659 return alpha * (-_log(u)) ** (1.0/beta) 660 661## --------------- Operating System Random Source ------------------ 662 663class SystemRandom(Random): 664 """Alternate random number generator using sources provided 665 by the operating system (such as /dev/urandom on Unix or 666 CryptGenRandom on Windows). 667 668 Not available on all systems (see os.urandom() for details). 669 """ 670 671 def random(self): 672 """Get the next random number in the range [0.0, 1.0).""" 673 return (int.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF 674 675 def getrandbits(self, k): 676 """getrandbits(k) -> x. Generates an int with k random bits.""" 677 if k <= 0: 678 raise ValueError('number of bits must be greater than zero') 679 if k != int(k): 680 raise TypeError('number of bits should be an integer') 681 numbytes = (k + 7) // 8 # bits / 8 and rounded up 682 x = int.from_bytes(_urandom(numbytes), 'big') 683 return x >> (numbytes * 8 - k) # trim excess bits 684 685 def seed(self, *args, **kwds): 686 "Stub method. Not used for a system random number generator." 687 return None 688 689 def _notimplemented(self, *args, **kwds): 690 "Method should not be called for a system random number generator." 691 raise NotImplementedError('System entropy source does not have state.') 692 getstate = setstate = _notimplemented 693 694## -------------------- test program -------------------- 695 696def _test_generator(n, func, args): 697 import time 698 print(n, 'times', func.__name__) 699 total = 0.0 700 sqsum = 0.0 701 smallest = 1e10 702 largest = -1e10 703 t0 = time.time() 704 for i in range(n): 705 x = func(*args) 706 total += x 707 sqsum = sqsum + x*x 708 smallest = min(x, smallest) 709 largest = max(x, largest) 710 t1 = time.time() 711 print(round(t1-t0, 3), 'sec,', end=' ') 712 avg = total/n 713 stddev = _sqrt(sqsum/n - avg*avg) 714 print('avg %g, stddev %g, min %g, max %g\n' % \ 715 (avg, stddev, smallest, largest)) 716 717 718def _test(N=2000): 719 _test_generator(N, random, ()) 720 _test_generator(N, normalvariate, (0.0, 1.0)) 721 _test_generator(N, lognormvariate, (0.0, 1.0)) 722 _test_generator(N, vonmisesvariate, (0.0, 1.0)) 723 _test_generator(N, gammavariate, (0.01, 1.0)) 724 _test_generator(N, gammavariate, (0.1, 1.0)) 725 _test_generator(N, gammavariate, (0.1, 2.0)) 726 _test_generator(N, gammavariate, (0.5, 1.0)) 727 _test_generator(N, gammavariate, (0.9, 1.0)) 728 _test_generator(N, gammavariate, (1.0, 1.0)) 729 _test_generator(N, gammavariate, (2.0, 1.0)) 730 _test_generator(N, gammavariate, (20.0, 1.0)) 731 _test_generator(N, gammavariate, (200.0, 1.0)) 732 _test_generator(N, gauss, (0.0, 1.0)) 733 _test_generator(N, betavariate, (3.0, 3.0)) 734 _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) 735 736# Create one instance, seeded from current time, and export its methods 737# as module-level functions. The functions share state across all uses 738#(both in the user's code and in the Python libraries), but that's fine 739# for most programs and is easier for the casual user than making them 740# instantiate their own Random() instance. 741 742_inst = Random() 743seed = _inst.seed 744random = _inst.random 745uniform = _inst.uniform 746triangular = _inst.triangular 747randint = _inst.randint 748choice = _inst.choice 749randrange = _inst.randrange 750sample = _inst.sample 751shuffle = _inst.shuffle 752choices = _inst.choices 753normalvariate = _inst.normalvariate 754lognormvariate = _inst.lognormvariate 755expovariate = _inst.expovariate 756vonmisesvariate = _inst.vonmisesvariate 757gammavariate = _inst.gammavariate 758gauss = _inst.gauss 759betavariate = _inst.betavariate 760paretovariate = _inst.paretovariate 761weibullvariate = _inst.weibullvariate 762getstate = _inst.getstate 763setstate = _inst.setstate 764getrandbits = _inst.getrandbits 765 766if __name__ == '__main__': 767 _test() 768