Module random
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Source Code for Module random

  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             generate random permutation 
 12   
 13      distributions on the real line: 
 14      ------------------------------ 
 15             uniform 
 16             normal (Gaussian) 
 17             lognormal 
 18             negative exponential 
 19             gamma 
 20             beta 
 21             pareto 
 22             Weibull 
 23   
 24      distributions on the circle (angles 0 to 2pi) 
 25      --------------------------------------------- 
 26             circular uniform 
 27             von Mises 
 28   
 29  General notes on the underlying Mersenne Twister core generator: 
 30   
 31  * The period is 2**19937-1. 
 32  * It is one of the most extensively tested generators in existence. 
 33  * Without a direct way to compute N steps forward, the semantics of 
 34    jumpahead(n) are weakened to simply jump to another distant state and rely 
 35    on the large period to avoid overlapping sequences. 
 36  * The random() method is implemented in C, executes in a single Python step, 
 37    and is, therefore, threadsafe. 
 38   
 39  """ 
 40   
 41  from warnings import warn as _warn 
 42  from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 
 43  from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 
 44  from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 
 45  from os import urandom as _urandom 
 46  from binascii import hexlify as _hexlify 
 47   
 48  __all__ = ["Random","seed","random","uniform","randint","choice","sample", 
 49             "randrange","shuffle","normalvariate","lognormvariate", 
 50             "expovariate","vonmisesvariate","gammavariate", 
 51             "gauss","betavariate","paretovariate","weibullvariate", 
 52             "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 
 53             "SystemRandom"] 
 54   
 55  NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 
 56  TWOPI = 2.0*_pi 
 57  LOG4 = _log(4.0) 
 58  SG_MAGICCONST = 1.0 + _log(4.5) 
 59  BPF = 53        # Number of bits in a float 
 60  RECIP_BPF = 2**-BPF 
 61   
 62   
 63  # Translated by Guido van Rossum from C source provided by 
 64  # Adrian Baddeley.  Adapted by Raymond Hettinger for use with 
 65  # the Mersenne Twister  and os.urandom() core generators. 
 66   
 67  import _random 
 68   
69 -class Random(_random.Random):
70 """Random number generator base class used by bound module functions. 71 72 Used to instantiate instances of Random to get generators that don't 73 share state. Especially useful for multi-threaded programs, creating 74 a different instance of Random for each thread, and using the jumpahead() 75 method to ensure that the generated sequences seen by each thread don't 76 overlap. 77 78 Class Random can also be subclassed if you want to use a different basic 79 generator of your own devising: in that case, override the following 80 methods: random(), seed(), getstate(), setstate() and jumpahead(). 81 Optionally, implement a getrandombits() method so that randrange() 82 can cover arbitrarily large ranges. 83 84 """ 85 86 VERSION = 2 # used by getstate/setstate 87
88 - def __init__(self, x=None):
89 """Initialize an instance. 90 91 Optional argument x controls seeding, as for Random.seed(). 92 """ 93 94 self.seed(x) 95 self.gauss_next = None
96
97 - def seed(self, a=None):
98 """Initialize internal state from hashable object. 99 100 None or no argument seeds from current time or from an operating 101 system specific randomness source if available. 102 103 If a is not None or an int or long, hash(a) is used instead. 104 """ 105 106 if a is None: 107 try: 108 a = long(_hexlify(_urandom(16)), 16) 109 except NotImplementedError: 110 import time 111 a = long(time.time() * 256) # use fractional seconds 112 113 super(Random, self).seed(a) 114 self.gauss_next = None
115
116 - def getstate(self):
117 """Return internal state; can be passed to setstate() later.""" 118 return self.VERSION, super(Random, self).getstate(), self.gauss_next
119
120 - def setstate(self, state):
121 """Restore internal state from object returned by getstate().""" 122 version = state[0] 123 if version == 2: 124 version, internalstate, self.gauss_next = state 125 super(Random, self).setstate(internalstate) 126 else: 127 raise ValueError("state with version %s passed to " 128 "Random.setstate() of version %s" % 129 (version, self.VERSION))
130 131 ## ---- Methods below this point do not need to be overridden when 132 ## ---- subclassing for the purpose of using a different core generator. 133 134 ## -------------------- pickle support ------------------- 135
136 - def __getstate__(self): # for pickle
137 return self.getstate()
138
139 - def __setstate__(self, state): # for pickle
140 self.setstate(state) 141
142 - def __reduce__(self):
143 return self.__class__, (), self.getstate()
144 145 ## -------------------- integer methods ------------------- 146
147 - def randrange(self, start, stop=None, step=1, int=int, default=None, 148 maxwidth=1L<<BPF):
149 """Choose a random item from range(start, stop[, step]). 150 151 This fixes the problem with randint() which includes the 152 endpoint; in Python this is usually not what you want. 153 Do not supply the 'int', 'default', and 'maxwidth' arguments. 154 """ 155 156 # This code is a bit messy to make it fast for the 157 # common case while still doing adequate error checking. 158 istart = int(start) 159 if istart != start: 160 raise ValueError, "non-integer arg 1 for randrange()" 161 if stop is default: 162 if istart > 0: 163 if istart >= maxwidth: 164 return self._randbelow(istart) 165 return int(self.random() * istart) 166 raise ValueError, "empty range for randrange()" 167 168 # stop argument supplied. 169 istop = int(stop) 170 if istop != stop: 171 raise ValueError, "non-integer stop for randrange()" 172 width = istop - istart 173 if step == 1 and width > 0: 174 # Note that 175 # int(istart + self.random()*width) 176 # instead would be incorrect. For example, consider istart 177 # = -2 and istop = 0. Then the guts would be in 178 # -2.0 to 0.0 exclusive on both ends (ignoring that random() 179 # might return 0.0), and because int() truncates toward 0, the 180 # final result would be -1 or 0 (instead of -2 or -1). 181 # istart + int(self.random()*width) 182 # would also be incorrect, for a subtler reason: the RHS 183 # can return a long, and then randrange() would also return 184 # a long, but we're supposed to return an int (for backward 185 # compatibility). 186 187 if width >= maxwidth: 188 return int(istart + self._randbelow(width)) 189 return int(istart + int(self.random()*width)) 190 if step == 1: 191 raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 192 193 # Non-unit step argument supplied. 194 istep = int(step) 195 if istep != step: 196 raise ValueError, "non-integer step for randrange()" 197 if istep > 0: 198 n = (width + istep - 1) // istep 199 elif istep < 0: 200 n = (width + istep + 1) // istep 201 else: 202 raise ValueError, "zero step for randrange()" 203 204 if n <= 0: 205 raise ValueError, "empty range for randrange()" 206 207 if n >= maxwidth: 208 return istart + istep*self._randbelow(n) 209 return istart + istep*int(self.random() * n)
210
211 - def randint(self, a, b):
212 """Return random integer in range [a, b], including both end points. 213 """ 214 215 return self.randrange(a, b+1)
216
217 - def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, 218 _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType):
219 """Return a random int in the range [0,n) 220 221 Handles the case where n has more bits than returned 222 by a single call to the underlying generator. 223 """ 224 225 try: 226 getrandbits = self.getrandbits 227 except AttributeError: 228 pass 229 else: 230 # Only call self.getrandbits if the original random() builtin method 231 # has not been overridden or if a new getrandbits() was supplied. 232 # This assures that the two methods correspond. 233 if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 234 k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 235 r = getrandbits(k) 236 while r >= n: 237 r = getrandbits(k) 238 return r 239 if n >= _maxwidth: 240 _warn("Underlying random() generator does not supply \n" 241 "enough bits to choose from a population range this large") 242 return int(self.random() * n)
243 244 ## -------------------- sequence methods ------------------- 245
246 - def choice(self, seq):
247 """Choose a random element from a non-empty sequence.""" 248 return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty
249
250 - def shuffle(self, x, random=None, int=int):
251 """x, random=random.random -> shuffle list x in place; return None. 252 253 Optional arg random is a 0-argument function returning a random 254 float in [0.0, 1.0); by default, the standard random.random. 255 """ 256 257 if random is None: 258 random = self.random 259 for i in reversed(xrange(1, len(x))): 260 # pick an element in x[:i+1] with which to exchange x[i] 261 j = int(random() * (i+1)) 262 x[i], x[j] = x[j], x[i]
263
264 - def sample(self, population, k):
265 """Chooses k unique random elements from a population sequence. 266 267 Returns a new list containing elements from the population while 268 leaving the original population unchanged. The resulting list is 269 in selection order so that all sub-slices will also be valid random 270 samples. This allows raffle winners (the sample) to be partitioned 271 into grand prize and second place winners (the subslices). 272 273 Members of the population need not be hashable or unique. If the 274 population contains repeats, then each occurrence is a possible 275 selection in the sample. 276 277 To choose a sample in a range of integers, use xrange as an argument. 278 This is especially fast and space efficient for sampling from a 279 large population: sample(xrange(10000000), 60) 280 """ 281 282 # XXX Although the documentation says `population` is "a sequence", 283 # XXX attempts are made to cater to any iterable with a __len__ 284 # XXX method. This has had mixed success. Examples from both 285 # XXX sides: sets work fine, and should become officially supported; 286 # XXX dicts are much harder, and have failed in various subtle 287 # XXX ways across attempts. Support for mapping types should probably 288 # XXX be dropped (and users should pass mapping.keys() or .values() 289 # XXX explicitly). 290 291 # Sampling without replacement entails tracking either potential 292 # selections (the pool) in a list or previous selections in a set. 293 294 # When the number of selections is small compared to the 295 # population, then tracking selections is efficient, requiring 296 # only a small set and an occasional reselection. For 297 # a larger number of selections, the pool tracking method is 298 # preferred since the list takes less space than the 299 # set and it doesn't suffer from frequent reselections. 300 301 n = len(population) 302 if not 0 <= k <= n: 303 raise ValueError, "sample larger than population" 304 random = self.random 305 _int = int 306 result = [None] * k 307 setsize = 21 # size of a small set minus size of an empty list 308 if k > 5: 309 setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 310 if n <= setsize or hasattr(population, "keys"): 311 # An n-length list is smaller than a k-length set, or this is a 312 # mapping type so the other algorithm wouldn't work. 313 pool = list(population) 314 for i in xrange(k): # invariant: non-selected at [0,n-i) 315 j = _int(random() * (n-i)) 316 result[i] = pool[j] 317 pool[j] = pool[n-i-1] # move non-selected item into vacancy 318 else: 319 try: 320 selected = set() 321 selected_add = selected.add 322 for i in xrange(k): 323 j = _int(random() * n) 324 while j in selected: 325 j = _int(random() * n) 326 selected_add(j) 327 result[i] = population[j] 328 except (TypeError, KeyError): # handle (at least) sets 329 if isinstance(population, list): 330 raise 331 return self.sample(tuple(population), k) 332 return result
333 334 ## -------------------- real-valued distributions ------------------- 335 336 ## -------------------- uniform distribution ------------------- 337
338 - def uniform(self, a, b):
339 """Get a random number in the range [a, b).""" 340 return a + (b-a) * self.random()
341 342 ## -------------------- normal distribution -------------------- 343
344 - def normalvariate(self, mu, sigma):
345 """Normal distribution. 346 347 mu is the mean, and sigma is the standard deviation. 348 349 """ 350 # mu = mean, sigma = standard deviation 351 352 # Uses Kinderman and Monahan method. Reference: Kinderman, 353 # A.J. and Monahan, J.F., "Computer generation of random 354 # variables using the ratio of uniform deviates", ACM Trans 355 # Math Software, 3, (1977), pp257-260. 356 357 random = self.random 358 while 1: 359 u1 = random() 360 u2 = 1.0 - random() 361 z = NV_MAGICCONST*(u1-0.5)/u2 362 zz = z*z/4.0 363 if zz <= -_log(u2): 364 break 365 return mu + z*sigma
366 367 ## -------------------- lognormal distribution -------------------- 368
369 - def lognormvariate(self, mu, sigma):
370 """Log normal distribution. 371 372 If you take the natural logarithm of this distribution, you'll get a 373 normal distribution with mean mu and standard deviation sigma. 374 mu can have any value, and sigma must be greater than zero. 375 376 """ 377 return _exp(self.normalvariate(mu, sigma))
378 379 ## -------------------- exponential distribution -------------------- 380
381 - def expovariate(self, lambd):
382 """Exponential distribution. 383 384 lambd is 1.0 divided by the desired mean. (The parameter would be 385 called "lambda", but that is a reserved word in Python.) Returned 386 values range from 0 to positive infinity. 387 388 """ 389 # lambd: rate lambd = 1/mean 390 # ('lambda' is a Python reserved word) 391 392 random = self.random 393 u = random() 394 while u <= 1e-7: 395 u = random() 396 return -_log(u)/lambd
397 398 ## -------------------- von Mises distribution -------------------- 399
400 - def vonmisesvariate(self, mu, kappa):
401 """Circular data distribution. 402 403 mu is the mean angle, expressed in radians between 0 and 2*pi, and 404 kappa is the concentration parameter, which must be greater than or 405 equal to zero. If kappa is equal to zero, this distribution reduces 406 to a uniform random angle over the range 0 to 2*pi. 407 408 """ 409 # mu: mean angle (in radians between 0 and 2*pi) 410 # kappa: concentration parameter kappa (>= 0) 411 # if kappa = 0 generate uniform random angle 412 413 # Based upon an algorithm published in: Fisher, N.I., 414 # "Statistical Analysis of Circular Data", Cambridge 415 # University Press, 1993. 416 417 # Thanks to Magnus Kessler for a correction to the 418 # implementation of step 4. 419 420 random = self.random 421 if kappa <= 1e-6: 422 return TWOPI * random() 423 424 a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) 425 b = (a - _sqrt(2.0 * a))/(2.0 * kappa) 426 r = (1.0 + b * b)/(2.0 * b) 427 428 while 1: 429 u1 = random() 430 431 z = _cos(_pi * u1) 432 f = (1.0 + r * z)/(r + z) 433 c = kappa * (r - f) 434 435 u2 = random() 436 437 if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): 438 break 439 440 u3 = random() 441 if u3 > 0.5: 442 theta = (mu % TWOPI) + _acos(f) 443 else: 444 theta = (mu % TWOPI) - _acos(f) 445 446 return theta
447 448 ## -------------------- gamma distribution -------------------- 449
450 - def gammavariate(self, alpha, beta):
451 """Gamma distribution. Not the gamma function! 452 453 Conditions on the parameters are alpha > 0 and beta > 0. 454 455 """ 456 457 # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 458 459 # Warning: a few older sources define the gamma distribution in terms 460 # of alpha > -1.0 461 if alpha <= 0.0 or beta <= 0.0: 462 raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 463 464 random = self.random 465 if alpha > 1.0: 466 467 # Uses R.C.H. Cheng, "The generation of Gamma 468 # variables with non-integral shape parameters", 469 # Applied Statistics, (1977), 26, No. 1, p71-74 470 471 ainv = _sqrt(2.0 * alpha - 1.0) 472 bbb = alpha - LOG4 473 ccc = alpha + ainv 474 475 while 1: 476 u1 = random() 477 if not 1e-7 < u1 < .9999999: 478 continue 479 u2 = 1.0 - random() 480 v = _log(u1/(1.0-u1))/ainv 481 x = alpha*_exp(v) 482 z = u1*u1*u2 483 r = bbb+ccc*v-x 484 if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 485 return x * beta 486 487 elif alpha == 1.0: 488 # expovariate(1) 489 u = random() 490 while u <= 1e-7: 491 u = random() 492 return -_log(u) * beta 493 494 else: # alpha is between 0 and 1 (exclusive) 495 496 # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 497 498 while 1: 499 u = random() 500 b = (_e + alpha)/_e 501 p = b*u 502 if p <= 1.0: 503 x = p ** (1.0/alpha) 504 else: 505 x = -_log((b-p)/alpha) 506 u1 = random() 507 if p > 1.0: 508 if u1 <= x ** (alpha - 1.0): 509 break 510 elif u1 <= _exp(-x): 511 break 512 return x * beta
513 514 ## -------------------- Gauss (faster alternative) -------------------- 515
516 - def gauss(self, mu, sigma):
517 """Gaussian distribution. 518 519 mu is the mean, and sigma is the standard deviation. This is 520 slightly faster than the normalvariate() function. 521 522 Not thread-safe without a lock around calls. 523 524 """ 525 526 # When x and y are two variables from [0, 1), uniformly 527 # distributed, then 528 # 529 # cos(2*pi*x)*sqrt(-2*log(1-y)) 530 # sin(2*pi*x)*sqrt(-2*log(1-y)) 531 # 532 # are two *independent* variables with normal distribution 533 # (mu = 0, sigma = 1). 534 # (Lambert Meertens) 535 # (corrected version; bug discovered by Mike Miller, fixed by LM) 536 537 # Multithreading note: When two threads call this function 538 # simultaneously, it is possible that they will receive the 539 # same return value. The window is very small though. To 540 # avoid this, you have to use a lock around all calls. (I 541 # didn't want to slow this down in the serial case by using a 542 # lock here.) 543 544 random = self.random 545 z = self.gauss_next 546 self.gauss_next = None 547 if z is None: 548 x2pi = random() * TWOPI 549 g2rad = _sqrt(-2.0 * _log(1.0 - random())) 550 z = _cos(x2pi) * g2rad 551 self.gauss_next = _sin(x2pi) * g2rad 552 553 return mu + z*sigma
554 555 ## -------------------- beta -------------------- 556 ## See 557 ## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470 558 ## for Ivan Frohne's insightful analysis of why the original implementation: 559 ## 560 ## def betavariate(self, alpha, beta): 561 ## # Discrete Event Simulation in C, pp 87-88. 562 ## 563 ## y = self.expovariate(alpha) 564 ## z = self.expovariate(1.0/beta) 565 ## return z/(y+z) 566 ## 567 ## was dead wrong, and how it probably got that way. 568
569 - def betavariate(self, alpha, beta):
570 """Beta distribution. 571 572 Conditions on the parameters are alpha > 0 and beta > 0. 573 Returned values range between 0 and 1. 574 575 """ 576 577 # This version due to Janne Sinkkonen, and matches all the std 578 # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 579 y = self.gammavariate(alpha, 1.) 580 if y == 0: 581 return 0.0 582 else: 583 return y / (y + self.gammavariate(beta, 1.))
584 585 ## -------------------- Pareto -------------------- 586
587 - def paretovariate(self, alpha):
588 """Pareto distribution. alpha is the shape parameter.""" 589 # Jain, pg. 495 590 591 u = 1.0 - self.random() 592 return 1.0 / pow(u, 1.0/alpha)
593 594 ## -------------------- Weibull -------------------- 595
596 - def weibullvariate(self, alpha, beta):
597 """Weibull distribution. 598 599 alpha is the scale parameter and beta is the shape parameter. 600 601 """ 602 # Jain, pg. 499; bug fix courtesy Bill Arms 603 604 u = 1.0 - self.random() 605 return alpha * pow(-_log(u), 1.0/beta)
606 607 ## -------------------- Wichmann-Hill ------------------- 608
609 -class WichmannHill(Random):
610 611 VERSION = 1 # used by getstate/setstate 612
613 - def seed(self, a=None):
614 """Initialize internal state from hashable object. 615 616 None or no argument seeds from current time or from an operating 617 system specific randomness source if available. 618 619 If a is not None or an int or long, hash(a) is used instead. 620 621 If a is an int or long, a is used directly. Distinct values between 622 0 and 27814431486575L inclusive are guaranteed to yield distinct 623 internal states (this guarantee is specific to the default 624 Wichmann-Hill generator). 625 """ 626 627 if a is None: 628 try: 629 a = long(_hexlify(_urandom(16)), 16) 630 except NotImplementedError: 631 import time 632 a = long(time.time() * 256) # use fractional seconds 633 634 if not isinstance(a, (int, long)): 635 a = hash(a) 636 637 a, x = divmod(a, 30268) 638 a, y = divmod(a, 30306) 639 a, z = divmod(a, 30322) 640 self._seed = int(x)+1, int(y)+1, int(z)+1 641 642 self.gauss_next = None
643
644 - def random(self):
645 """Get the next random number in the range [0.0, 1.0).""" 646 647 # Wichman-Hill random number generator. 648 # 649 # Wichmann, B. A. & Hill, I. D. (1982) 650 # Algorithm AS 183: 651 # An efficient and portable pseudo-random number generator 652 # Applied Statistics 31 (1982) 188-190 653 # 654 # see also: 655 # Correction to Algorithm AS 183 656 # Applied Statistics 33 (1984) 123 657 # 658 # McLeod, A. I. (1985) 659 # A remark on Algorithm AS 183 660 # Applied Statistics 34 (1985),198-200 661 662 # This part is thread-unsafe: 663 # BEGIN CRITICAL SECTION 664 x, y, z = self._seed 665 x = (171 * x) % 30269 666 y = (172 * y) % 30307 667 z = (170 * z) % 30323 668 self._seed = x, y, z 669 # END CRITICAL SECTION 670 671 # Note: on a platform using IEEE-754 double arithmetic, this can 672 # never return 0.0 (asserted by Tim; proof too long for a comment). 673 return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
674
675 - def getstate(self):
676 """Return internal state; can be passed to setstate() later.""" 677 return self.VERSION, self._seed, self.gauss_next
678
679 - def setstate(self, state):
680 """Restore internal state from object returned by getstate().""" 681 version = state[0] 682 if version == 1: 683 version, self._seed, self.gauss_next = state 684 else: 685 raise ValueError("state with version %s passed to " 686 "Random.setstate() of version %s" % 687 (version, self.VERSION))
688
689 - def jumpahead(self, n):
690 """Act as if n calls to random() were made, but quickly. 691 692 n is an int, greater than or equal to 0. 693 694 Example use: If you have 2 threads and know that each will 695 consume no more than a million random numbers, create two Random 696 objects r1 and r2, then do 697 r2.setstate(r1.getstate()) 698 r2.jumpahead(1000000) 699 Then r1 and r2 will use guaranteed-disjoint segments of the full 700 period. 701 """ 702 703 if not n >= 0: 704 raise ValueError("n must be >= 0") 705 x, y, z = self._seed 706 x = int(x * pow(171, n, 30269)) % 30269 707 y = int(y * pow(172, n, 30307)) % 30307 708 z = int(z * pow(170, n, 30323)) % 30323 709 self._seed = x, y, z
710
711 - def __whseed(self, x=0, y=0, z=0):
712 """Set the Wichmann-Hill seed from (x, y, z). 713 714 These must be integers in the range [0, 256). 715 """ 716 717 if not type(x) == type(y) == type(z) == int: 718 raise TypeError('seeds must be integers') 719 if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 720 raise ValueError('seeds must be in range(0, 256)') 721 if 0 == x == y == z: 722 # Initialize from current time 723 import time 724 t = long(time.time() * 256) 725 t = int((t&0xffffff) ^ (t>>24)) 726 t, x = divmod(t, 256) 727 t, y = divmod(t, 256) 728 t, z = divmod(t, 256) 729 # Zero is a poor seed, so substitute 1 730 self._seed = (x or 1, y or 1, z or 1) 731 732 self.gauss_next = None
733
734 - def whseed(self, a=None):
735 """Seed from hashable object's hash code. 736 737 None or no argument seeds from current time. It is not guaranteed 738 that objects with distinct hash codes lead to distinct internal 739 states. 740 741 This is obsolete, provided for compatibility with the seed routine 742 used prior to Python 2.1. Use the .seed() method instead. 743 """ 744 745 if a is None: 746 self.__whseed() 747 return 748 a = hash(a) 749 a, x = divmod(a, 256) 750 a, y = divmod(a, 256) 751 a, z = divmod(a, 256) 752 x = (x + a) % 256 or 1 753 y = (y + a) % 256 or 1 754 z = (z + a) % 256 or 1 755 self.__whseed(x, y, z)
756 757 ## --------------- Operating System Random Source ------------------ 758
759 -class SystemRandom(Random):
760 """Alternate random number generator using sources provided 761 by the operating system (such as /dev/urandom on Unix or 762 CryptGenRandom on Windows). 763 764 Not available on all systems (see os.urandom() for details). 765 """ 766
767 - def random(self):
768 """Get the next random number in the range [0.0, 1.0).""" 769 return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF
770
771 - def getrandbits(self, k):
772 """getrandbits(k) -> x. Generates a long int with k random bits.""" 773 if k <= 0: 774 raise ValueError('number of bits must be greater than zero') 775 if k != int(k): 776 raise TypeError('number of bits should be an integer') 777 bytes = (k + 7) // 8 # bits / 8 and rounded up 778 x = long(_hexlify(_urandom(bytes)), 16) 779 return x >> (bytes * 8 - k) # trim excess bits
780
781 - def _stub(self, *args, **kwds):
782 "Stub method. Not used for a system random number generator." 783 return None
784 seed = jumpahead = _stub 785
786 - def _notimplemented(self, *args, **kwds):
787 "Method should not be called for a system random number generator." 788 raise NotImplementedError('System entropy source does not have state.')
789 getstate = setstate = _notimplemented
790 791 ## -------------------- test program -------------------- 792
793 -def _test_generator(n, func, args):
794 import time 795 print n, 'times', func.__name__ 796 total = 0.0 797 sqsum = 0.0 798 smallest = 1e10 799 largest = -1e10 800 t0 = time.time() 801 for i in range(n): 802 x = func(*args) 803 total += x 804 sqsum = sqsum + x*x 805 smallest = min(x, smallest) 806 largest = max(x, largest) 807 t1 = time.time() 808 print round(t1-t0, 3), 'sec,', 809 avg = total/n 810 stddev = _sqrt(sqsum/n - avg*avg) 811 print 'avg %g, stddev %g, min %g, max %g' % \ 812 (avg, stddev, smallest, largest)
813 814
815 -def _test(N=2000):
816 _test_generator(N, random, ()) 817 _test_generator(N, normalvariate, (0.0, 1.0)) 818 _test_generator(N, lognormvariate, (0.0, 1.0)) 819 _test_generator(N, vonmisesvariate, (0.0, 1.0)) 820 _test_generator(N, gammavariate, (0.01, 1.0)) 821 _test_generator(N, gammavariate, (0.1, 1.0)) 822 _test_generator(N, gammavariate, (0.1, 2.0)) 823 _test_generator(N, gammavariate, (0.5, 1.0)) 824 _test_generator(N, gammavariate, (0.9, 1.0)) 825 _test_generator(N, gammavariate, (1.0, 1.0)) 826 _test_generator(N, gammavariate, (2.0, 1.0)) 827 _test_generator(N, gammavariate, (20.0, 1.0)) 828 _test_generator(N, gammavariate, (200.0, 1.0)) 829 _test_generator(N, gauss, (0.0, 1.0)) 830 _test_generator(N, betavariate, (3.0, 3.0))
831 832 # Create one instance, seeded from current time, and export its methods 833 # as module-level functions. The functions share state across all uses 834 #(both in the user's code and in the Python libraries), but that's fine 835 # for most programs and is easier for the casual user than making them 836 # instantiate their own Random() instance. 837 838 _inst = Random() 839 seed = _inst.seed 840 random = _inst.random 841 uniform = _inst.uniform 842 randint = _inst.randint 843 choice = _inst.choice 844 randrange = _inst.randrange 845 sample = _inst.sample 846 shuffle = _inst.shuffle 847 normalvariate = _inst.normalvariate 848 lognormvariate = _inst.lognormvariate 849 expovariate = _inst.expovariate 850 vonmisesvariate = _inst.vonmisesvariate 851 gammavariate = _inst.gammavariate 852 gauss = _inst.gauss 853 betavariate = _inst.betavariate 854 paretovariate = _inst.paretovariate 855 weibullvariate = _inst.weibullvariate 856 getstate = _inst.getstate 857 setstate = _inst.setstate 858 jumpahead = _inst.jumpahead 859 getrandbits = _inst.getrandbits 860 861 if __name__ == '__main__': 862 _test() 863