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 triangular 17 normal (Gaussian) 18 lognormal 19 negative exponential 20 gamma 21 beta 22 pareto 23 Weibull 24 25 distributions on the circle (angles 0 to 2pi) 26 --------------------------------------------- 27 circular uniform 28 von Mises 29 30 General notes on the underlying Mersenne Twister core generator: 31 32 * The period is 2**19937-1. 33 * It is one of the most extensively tested generators in existence. 34 * Without a direct way to compute N steps forward, the semantics of 35 jumpahead(n) are weakened to simply jump to another distant state and rely 36 on the large period to avoid overlapping sequences. 37 * The random() method is implemented in C, executes in a single Python step, 38 and is, therefore, threadsafe. 39 40 """ 41 42 from __future__ import division 43 from warnings import warn as _warn 44 from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType 45 from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil 46 from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin 47 from os import urandom as _urandom 48 from binascii import hexlify as _hexlify 49 import hashlib as _hashlib 50 51 __all__ = ["Random","seed","random","uniform","randint","choice","sample", 52 "randrange","shuffle","normalvariate","lognormvariate", 53 "expovariate","vonmisesvariate","gammavariate","triangular", 54 "gauss","betavariate","paretovariate","weibullvariate", 55 "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", 56 "SystemRandom"] 57 58 NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) 59 TWOPI = 2.0*_pi 60 LOG4 = _log(4.0) 61 SG_MAGICCONST = 1.0 + _log(4.5) 62 BPF = 53 # Number of bits in a float 63 RECIP_BPF = 2**-BPF 64 65 66 # Translated by Guido van Rossum from C source provided by 67 # Adrian Baddeley. Adapted by Raymond Hettinger for use with 68 # the Mersenne Twister and os.urandom() core generators. 69 70 import _random 71 72 class Random(_random.Random): 73 """Random number generator base class used by bound module functions. 74 75 Used to instantiate instances of Random to get generators that don't 76 share state. Especially useful for multi-threaded programs, creating 77 a different instance of Random for each thread, and using the jumpahead() 78 method to ensure that the generated sequences seen by each thread don't 79 overlap. 80 81 Class Random can also be subclassed if you want to use a different basic 82 generator of your own devising: in that case, override the following 83 methods: random(), seed(), getstate(), setstate() and jumpahead(). 84 Optionally, implement a getrandbits() method so that randrange() can cover 85 arbitrarily large ranges. 86 87 """ 88 89 VERSION = 3 # used by getstate/setstate 90 91 def __init__(self, x=None): 92 """Initialize an instance. 93 94 Optional argument x controls seeding, as for Random.seed(). 95 """ 96 97 self.seed(x) 98 self.gauss_next = None 99 100 def seed(self, a=None): 101 """Initialize internal state from hashable object. 102 103 None or no argument seeds from current time or from an operating 104 system specific randomness source if available. 105 106 If a is not None or an int or long, hash(a) is used instead. 107 """ 108 109 if a is None: 110 try: 111 a = long(_hexlify(_urandom(16)), 16) 112 except NotImplementedError: 113 import time 114 a = long(time.time() * 256) # use fractional seconds 115 116 super(Random, self).seed(a) 117 self.gauss_next = None 118 119 def getstate(self): 120 """Return internal state; can be passed to setstate() later.""" 121 return self.VERSION, super(Random, self).getstate(), self.gauss_next 122 123 def setstate(self, state): 124 """Restore internal state from object returned by getstate().""" 125 version = state[0] 126 if version == 3: 127 version, internalstate, self.gauss_next = state 128 super(Random, self).setstate(internalstate) 129 elif version == 2: 130 version, internalstate, self.gauss_next = state 131 # In version 2, the state was saved as signed ints, which causes 132 # inconsistencies between 32/64-bit systems. The state is 133 # really unsigned 32-bit ints, so we convert negative ints from 134 # version 2 to positive longs for version 3. 135 try: 136 internalstate = tuple( long(x) % (2**32) for x in internalstate ) 137 except ValueError, e: 138 raise TypeError, e 139 super(Random, self).setstate(internalstate) 140 else: 141 raise ValueError("state with version %s passed to " 142 "Random.setstate() of version %s" % 143 (version, self.VERSION)) 144 145 def jumpahead(self, n): 146 """Change the internal state to one that is likely far away 147 from the current state. This method will not be in Py3.x, 148 so it is better to simply reseed. 149 """ 150 # The super.jumpahead() method uses shuffling to change state, 151 # so it needs a large and "interesting" n to work with. Here, 152 # we use hashing to create a large n for the shuffle. 153 s = repr(n) + repr(self.getstate()) 154 n = int(_hashlib.new('sha512', s).hexdigest(), 16) 155 super(Random, self).jumpahead(n) 156 157 ## ---- Methods below this point do not need to be overridden when 158 ## ---- subclassing for the purpose of using a different core generator. 159 160 ## -------------------- pickle support ------------------- 161 162 def __getstate__(self): # for pickle 163 return self.getstate() 164 165 def __setstate__(self, state): # for pickle 166 self.setstate(state) 167 168 def __reduce__(self): 169 return self.__class__, (), self.getstate() 170 171 ## -------------------- integer methods ------------------- 172 173 def randrange(self, start, stop=None, step=1, int=int, default=None, 174 maxwidth=1L<<BPF): 175 """Choose a random item from range(start, stop[, step]). 176 177 This fixes the problem with randint() which includes the 178 endpoint; in Python this is usually not what you want. 179 Do not supply the 'int', 'default', and 'maxwidth' arguments. 180 """ 181 182 # This code is a bit messy to make it fast for the 183 # common case while still doing adequate error checking. 184 istart = int(start) 185 if istart != start: 186 raise ValueError, "non-integer arg 1 for randrange()" 187 if stop is default: 188 if istart > 0: 189 if istart >= maxwidth: 190 return self._randbelow(istart) 191 return int(self.random() * istart) 192 raise ValueError, "empty range for randrange()" 193 194 # stop argument supplied. 195 istop = int(stop) 196 if istop != stop: 197 raise ValueError, "non-integer stop for randrange()" 198 width = istop - istart 199 if step == 1 and width > 0: 200 # Note that 201 # int(istart + self.random()*width) 202 # instead would be incorrect. For example, consider istart 203 # = -2 and istop = 0. Then the guts would be in 204 # -2.0 to 0.0 exclusive on both ends (ignoring that random() 205 # might return 0.0), and because int() truncates toward 0, the 206 # final result would be -1 or 0 (instead of -2 or -1). 207 # istart + int(self.random()*width) 208 # would also be incorrect, for a subtler reason: the RHS 209 # can return a long, and then randrange() would also return 210 # a long, but we're supposed to return an int (for backward 211 # compatibility). 212 213 if width >= maxwidth: 214 return int(istart + self._randbelow(width)) 215 return int(istart + int(self.random()*width)) 216 if step == 1: 217 raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) 218 219 # Non-unit step argument supplied. 220 istep = int(step) 221 if istep != step: 222 raise ValueError, "non-integer step for randrange()" 223 if istep > 0: 224 n = (width + istep - 1) // istep 225 elif istep < 0: 226 n = (width + istep + 1) // istep 227 else: 228 raise ValueError, "zero step for randrange()" 229 230 if n <= 0: 231 raise ValueError, "empty range for randrange()" 232 233 if n >= maxwidth: 234 return istart + istep*self._randbelow(n) 235 return istart + istep*int(self.random() * n) 236 237 def randint(self, a, b): 238 """Return random integer in range [a, b], including both end points. 239 """ 240 241 return self.randrange(a, b+1) 242 243 def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, 244 _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): 245 """Return a random int in the range [0,n) 246 247 Handles the case where n has more bits than returned 248 by a single call to the underlying generator. 249 """ 250 251 try: 252 getrandbits = self.getrandbits 253 except AttributeError: 254 pass 255 else: 256 # Only call self.getrandbits if the original random() builtin method 257 # has not been overridden or if a new getrandbits() was supplied. 258 # This assures that the two methods correspond. 259 if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: 260 k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) 261 r = getrandbits(k) 262 while r >= n: 263 r = getrandbits(k) 264 return r 265 if n >= _maxwidth: 266 _warn("Underlying random() generator does not supply \n" 267 "enough bits to choose from a population range this large") 268 return int(self.random() * n) 269 270 ## -------------------- sequence methods ------------------- 271 272 def choice(self, seq): 273 """Choose a random element from a non-empty sequence.""" 274 return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty 275 276 def shuffle(self, x, random=None, int=int): 277 """x, random=random.random -> shuffle list x in place; return None. 278 279 Optional arg random is a 0-argument function returning a random 280 float in [0.0, 1.0); by default, the standard random.random. 281 """ 282 283 if random is None: 284 random = self.random 285 for i in reversed(xrange(1, len(x))): 286 # pick an element in x[:i+1] with which to exchange x[i] 287 j = int(random() * (i+1)) 288 x[i], x[j] = x[j], x[i] 289 290 def sample(self, population, k): 291 """Chooses k unique random elements from a population sequence. 292 293 Returns a new list containing elements from the population while 294 leaving the original population unchanged. The resulting list is 295 in selection order so that all sub-slices will also be valid random 296 samples. This allows raffle winners (the sample) to be partitioned 297 into grand prize and second place winners (the subslices). 298 299 Members of the population need not be hashable or unique. If the 300 population contains repeats, then each occurrence is a possible 301 selection in the sample. 302 303 To choose a sample in a range of integers, use xrange as an argument. 304 This is especially fast and space efficient for sampling from a 305 large population: sample(xrange(10000000), 60) 306 """ 307 308 # Sampling without replacement entails tracking either potential 309 # selections (the pool) in a list or previous selections in a set. 310 311 # When the number of selections is small compared to the 312 # population, then tracking selections is efficient, requiring 313 # only a small set and an occasional reselection. For 314 # a larger number of selections, the pool tracking method is 315 # preferred since the list takes less space than the 316 # set and it doesn't suffer from frequent reselections. 317 318 n = len(population) 319 if not 0 <= k <= n: 320 raise ValueError("sample larger than population") 321 random = self.random 322 _int = int 323 result = [None] * k 324 setsize = 21 # size of a small set minus size of an empty list 325 if k > 5: 326 setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets 327 if n <= setsize or hasattr(population, "keys"): 328 # An n-length list is smaller than a k-length set, or this is a 329 # mapping type so the other algorithm wouldn't work. 330 pool = list(population) 331 for i in xrange(k): # invariant: non-selected at [0,n-i) 332 j = _int(random() * (n-i)) 333 result[i] = pool[j] 334 pool[j] = pool[n-i-1] # move non-selected item into vacancy 335 else: 336 try: 337 selected = set() 338 selected_add = selected.add 339 for i in xrange(k): 340 j = _int(random() * n) 341 while j in selected: 342 j = _int(random() * n) 343 selected_add(j) 344 result[i] = population[j] 345 except (TypeError, KeyError): # handle (at least) sets 346 if isinstance(population, list): 347 raise 348 return self.sample(tuple(population), k) 349 return result 350 351 ## -------------------- real-valued distributions ------------------- 352 353 ## -------------------- uniform distribution ------------------- 354 355 def uniform(self, a, b): 356 "Get a random number in the range [a, b) or [a, b] depending on rounding." 357 return a + (b-a) * self.random() 358 359 ## -------------------- triangular -------------------- 360 361 def triangular(self, low=0.0, high=1.0, mode=None): 362 """Triangular distribution. 363 364 Continuous distribution bounded by given lower and upper limits, 365 and having a given mode value in-between. 366 367 http://en.wikipedia.org/wiki/Triangular_distribution 368 369 """ 370 u = self.random() 371 c = 0.5 if mode is None else (mode - low) / (high - low) 372 if u > c: 373 u = 1.0 - u 374 c = 1.0 - c 375 low, high = high, low 376 return low + (high - low) * (u * c) ** 0.5 377 378 ## -------------------- normal distribution -------------------- 379 380 def normalvariate(self, mu, sigma): 381 """Normal distribution. 382 383 mu is the mean, and sigma is the standard deviation. 384 385 """ 386 # mu = mean, sigma = standard deviation 387 388 # Uses Kinderman and Monahan method. Reference: Kinderman, 389 # A.J. and Monahan, J.F., "Computer generation of random 390 # variables using the ratio of uniform deviates", ACM Trans 391 # Math Software, 3, (1977), pp257-260. 392 393 random = self.random 394 while 1: 395 u1 = random() 396 u2 = 1.0 - random() 397 z = NV_MAGICCONST*(u1-0.5)/u2 398 zz = z*z/4.0 399 if zz <= -_log(u2): 400 break 401 return mu + z*sigma 402 403 ## -------------------- lognormal distribution -------------------- 404 405 def lognormvariate(self, mu, sigma): 406 """Log normal distribution. 407 408 If you take the natural logarithm of this distribution, you'll get a 409 normal distribution with mean mu and standard deviation sigma. 410 mu can have any value, and sigma must be greater than zero. 411 412 """ 413 return _exp(self.normalvariate(mu, sigma)) 414 415 ## -------------------- exponential distribution -------------------- 416 417 def expovariate(self, lambd): 418 """Exponential distribution. 419 420 lambd is 1.0 divided by the desired mean. It should be 421 nonzero. (The parameter would be called "lambda", but that is 422 a reserved word in Python.) Returned values range from 0 to 423 positive infinity if lambd is positive, and from negative 424 infinity to 0 if lambd is negative. 425 426 """ 427 # lambd: rate lambd = 1/mean 428 # ('lambda' is a Python reserved word) 429 430 # we use 1-random() instead of random() to preclude the 431 # possibility of taking the log of zero. 432 return -_log(1.0 - self.random())/lambd 433 434 ## -------------------- von Mises distribution -------------------- 435 436 def vonmisesvariate(self, mu, kappa): 437 """Circular data distribution. 438 439 mu is the mean angle, expressed in radians between 0 and 2*pi, and 440 kappa is the concentration parameter, which must be greater than or 441 equal to zero. If kappa is equal to zero, this distribution reduces 442 to a uniform random angle over the range 0 to 2*pi. 443 444 """ 445 # mu: mean angle (in radians between 0 and 2*pi) 446 # kappa: concentration parameter kappa (>= 0) 447 # if kappa = 0 generate uniform random angle 448 449 # Based upon an algorithm published in: Fisher, N.I., 450 # "Statistical Analysis of Circular Data", Cambridge 451 # University Press, 1993. 452 453 # Thanks to Magnus Kessler for a correction to the 454 # implementation of step 4. 455 456 random = self.random 457 if kappa <= 1e-6: 458 return TWOPI * random() 459 460 s = 0.5 / kappa 461 r = s + _sqrt(1.0 + s * s) 462 463 while 1: 464 u1 = random() 465 z = _cos(_pi * u1) 466 467 d = z / (r + z) 468 u2 = random() 469 if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d): 470 break 471 472 q = 1.0 / r 473 f = (q + z) / (1.0 + q * z) 474 u3 = random() 475 if u3 > 0.5: 476 theta = (mu + _acos(f)) % TWOPI 477 else: 478 theta = (mu - _acos(f)) % TWOPI 479 480 return theta 481 482 ## -------------------- gamma distribution -------------------- 483 484 def gammavariate(self, alpha, beta): 485 """Gamma distribution. Not the gamma function! 486 487 Conditions on the parameters are alpha > 0 and beta > 0. 488 489 The probability distribution function is: 490 491 x ** (alpha - 1) * math.exp(-x / beta) 492 pdf(x) = -------------------------------------- 493 math.gamma(alpha) * beta ** alpha 494 495 """ 496 497 # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 498 499 # Warning: a few older sources define the gamma distribution in terms 500 # of alpha > -1.0 501 if alpha <= 0.0 or beta <= 0.0: 502 raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 503 504 random = self.random 505 if alpha > 1.0: 506 507 # Uses R.C.H. Cheng, "The generation of Gamma 508 # variables with non-integral shape parameters", 509 # Applied Statistics, (1977), 26, No. 1, p71-74 510 511 ainv = _sqrt(2.0 * alpha - 1.0) 512 bbb = alpha - LOG4 513 ccc = alpha + ainv 514 515 while 1: 516 u1 = random() 517 if not 1e-7 < u1 < .9999999: 518 continue 519 u2 = 1.0 - random() 520 v = _log(u1/(1.0-u1))/ainv 521 x = alpha*_exp(v) 522 z = u1*u1*u2 523 r = bbb+ccc*v-x 524 if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 525 return x * beta 526 527 elif alpha == 1.0: 528 # expovariate(1) 529 u = random() 530 while u <= 1e-7: 531 u = random() 532 return -_log(u) * beta 533 534 else: # alpha is between 0 and 1 (exclusive) 535 536 # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 537 538 while 1: 539 u = random() 540 b = (_e + alpha)/_e 541 p = b*u 542 if p <= 1.0: 543 x = p ** (1.0/alpha) 544 else: 545 x = -_log((b-p)/alpha) 546 u1 = random() 547 if p > 1.0: 548 if u1 <= x ** (alpha - 1.0): 549 break 550 elif u1 <= _exp(-x): 551 break 552 return x * beta 553 554 ## -------------------- Gauss (faster alternative) -------------------- 555 556 def gauss(self, mu, sigma): 557 """Gaussian distribution. 558 559 mu is the mean, and sigma is the standard deviation. This is 560 slightly faster than the normalvariate() function. 561 562 Not thread-safe without a lock around calls. 563 564 """ 565 566 # When x and y are two variables from [0, 1), uniformly 567 # distributed, then 568 # 569 # cos(2*pi*x)*sqrt(-2*log(1-y)) 570 # sin(2*pi*x)*sqrt(-2*log(1-y)) 571 # 572 # are two *independent* variables with normal distribution 573 # (mu = 0, sigma = 1). 574 # (Lambert Meertens) 575 # (corrected version; bug discovered by Mike Miller, fixed by LM) 576 577 # Multithreading note: When two threads call this function 578 # simultaneously, it is possible that they will receive the 579 # same return value. The window is very small though. To 580 # avoid this, you have to use a lock around all calls. (I 581 # didn't want to slow this down in the serial case by using a 582 # lock here.) 583 584 random = self.random 585 z = self.gauss_next 586 self.gauss_next = None 587 if z is None: 588 x2pi = random() * TWOPI 589 g2rad = _sqrt(-2.0 * _log(1.0 - random())) 590 z = _cos(x2pi) * g2rad 591 self.gauss_next = _sin(x2pi) * g2rad 592 593 return mu + z*sigma 594 595 ## -------------------- beta -------------------- 596 ## See 597 ## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html 598 ## for Ivan Frohne's insightful analysis of why the original implementation: 599 ## 600 ## def betavariate(self, alpha, beta): 601 ## # Discrete Event Simulation in C, pp 87-88. 602 ## 603 ## y = self.expovariate(alpha) 604 ## z = self.expovariate(1.0/beta) 605 ## return z/(y+z) 606 ## 607 ## was dead wrong, and how it probably got that way. 608 609 def betavariate(self, alpha, beta): 610 """Beta distribution. 611 612 Conditions on the parameters are alpha > 0 and beta > 0. 613 Returned values range between 0 and 1. 614 615 """ 616 617 # This version due to Janne Sinkkonen, and matches all the std 618 # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 619 y = self.gammavariate(alpha, 1.) 620 if y == 0: 621 return 0.0 622 else: 623 return y / (y + self.gammavariate(beta, 1.)) 624 625 ## -------------------- Pareto -------------------- 626 627 def paretovariate(self, alpha): 628 """Pareto distribution. alpha is the shape parameter.""" 629 # Jain, pg. 495 630 631 u = 1.0 - self.random() 632 return 1.0 / pow(u, 1.0/alpha) 633 634 ## -------------------- Weibull -------------------- 635 636 def weibullvariate(self, alpha, beta): 637 """Weibull distribution. 638 639 alpha is the scale parameter and beta is the shape parameter. 640 641 """ 642 # Jain, pg. 499; bug fix courtesy Bill Arms 643 644 u = 1.0 - self.random() 645 return alpha * pow(-_log(u), 1.0/beta) 646 647 ## -------------------- Wichmann-Hill ------------------- 648 649 class WichmannHill(Random): 650 651 VERSION = 1 # used by getstate/setstate 652 653 def seed(self, a=None): 654 """Initialize internal state from hashable object. 655 656 None or no argument seeds from current time or from an operating 657 system specific randomness source if available. 658 659 If a is not None or an int or long, hash(a) is used instead. 660 661 If a is an int or long, a is used directly. Distinct values between 662 0 and 27814431486575L inclusive are guaranteed to yield distinct 663 internal states (this guarantee is specific to the default 664 Wichmann-Hill generator). 665 """ 666 667 if a is None: 668 try: 669 a = long(_hexlify(_urandom(16)), 16) 670 except NotImplementedError: 671 import time 672 a = long(time.time() * 256) # use fractional seconds 673 674 if not isinstance(a, (int, long)): 675 a = hash(a) 676 677 a, x = divmod(a, 30268) 678 a, y = divmod(a, 30306) 679 a, z = divmod(a, 30322) 680 self._seed = int(x)+1, int(y)+1, int(z)+1 681 682 self.gauss_next = None 683 684 def random(self): 685 """Get the next random number in the range [0.0, 1.0).""" 686 687 # Wichman-Hill random number generator. 688 # 689 # Wichmann, B. A. & Hill, I. D. (1982) 690 # Algorithm AS 183: 691 # An efficient and portable pseudo-random number generator 692 # Applied Statistics 31 (1982) 188-190 693 # 694 # see also: 695 # Correction to Algorithm AS 183 696 # Applied Statistics 33 (1984) 123 697 # 698 # McLeod, A. I. (1985) 699 # A remark on Algorithm AS 183 700 # Applied Statistics 34 (1985),198-200 701 702 # This part is thread-unsafe: 703 # BEGIN CRITICAL SECTION 704 x, y, z = self._seed 705 x = (171 * x) % 30269 706 y = (172 * y) % 30307 707 z = (170 * z) % 30323 708 self._seed = x, y, z 709 # END CRITICAL SECTION 710 711 # Note: on a platform using IEEE-754 double arithmetic, this can 712 # never return 0.0 (asserted by Tim; proof too long for a comment). 713 return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 714 715 def getstate(self): 716 """Return internal state; can be passed to setstate() later.""" 717 return self.VERSION, self._seed, self.gauss_next 718 719 def setstate(self, state): 720 """Restore internal state from object returned by getstate().""" 721 version = state[0] 722 if version == 1: 723 version, self._seed, self.gauss_next = state 724 else: 725 raise ValueError("state with version %s passed to " 726 "Random.setstate() of version %s" % 727 (version, self.VERSION)) 728 729 def jumpahead(self, n): 730 """Act as if n calls to random() were made, but quickly. 731 732 n is an int, greater than or equal to 0. 733 734 Example use: If you have 2 threads and know that each will 735 consume no more than a million random numbers, create two Random 736 objects r1 and r2, then do 737 r2.setstate(r1.getstate()) 738 r2.jumpahead(1000000) 739 Then r1 and r2 will use guaranteed-disjoint segments of the full 740 period. 741 """ 742 743 if not n >= 0: 744 raise ValueError("n must be >= 0") 745 x, y, z = self._seed 746 x = int(x * pow(171, n, 30269)) % 30269 747 y = int(y * pow(172, n, 30307)) % 30307 748 z = int(z * pow(170, n, 30323)) % 30323 749 self._seed = x, y, z 750 751 def __whseed(self, x=0, y=0, z=0): 752 """Set the Wichmann-Hill seed from (x, y, z). 753 754 These must be integers in the range [0, 256). 755 """ 756 757 if not type(x) == type(y) == type(z) == int: 758 raise TypeError('seeds must be integers') 759 if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 760 raise ValueError('seeds must be in range(0, 256)') 761 if 0 == x == y == z: 762 # Initialize from current time 763 import time 764 t = long(time.time() * 256) 765 t = int((t&0xffffff) ^ (t>>24)) 766 t, x = divmod(t, 256) 767 t, y = divmod(t, 256) 768 t, z = divmod(t, 256) 769 # Zero is a poor seed, so substitute 1 770 self._seed = (x or 1, y or 1, z or 1) 771 772 self.gauss_next = None 773 774 def whseed(self, a=None): 775 """Seed from hashable object's hash code. 776 777 None or no argument seeds from current time. It is not guaranteed 778 that objects with distinct hash codes lead to distinct internal 779 states. 780 781 This is obsolete, provided for compatibility with the seed routine 782 used prior to Python 2.1. Use the .seed() method instead. 783 """ 784 785 if a is None: 786 self.__whseed() 787 return 788 a = hash(a) 789 a, x = divmod(a, 256) 790 a, y = divmod(a, 256) 791 a, z = divmod(a, 256) 792 x = (x + a) % 256 or 1 793 y = (y + a) % 256 or 1 794 z = (z + a) % 256 or 1 795 self.__whseed(x, y, z) 796 797 ## --------------- Operating System Random Source ------------------ 798 799 class SystemRandom(Random): 800 """Alternate random number generator using sources provided 801 by the operating system (such as /dev/urandom on Unix or 802 CryptGenRandom on Windows). 803 804 Not available on all systems (see os.urandom() for details). 805 """ 806 807 def random(self): 808 """Get the next random number in the range [0.0, 1.0).""" 809 return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 810 811 def getrandbits(self, k): 812 """getrandbits(k) -> x. Generates a long int with k random bits.""" 813 if k <= 0: 814 raise ValueError('number of bits must be greater than zero') 815 if k != int(k): 816 raise TypeError('number of bits should be an integer') 817 bytes = (k + 7) // 8 # bits / 8 and rounded up 818 x = long(_hexlify(_urandom(bytes)), 16) 819 return x >> (bytes * 8 - k) # trim excess bits 820 821 def _stub(self, *args, **kwds): 822 "Stub method. Not used for a system random number generator." 823 return None 824 seed = jumpahead = _stub 825 826 def _notimplemented(self, *args, **kwds): 827 "Method should not be called for a system random number generator." 828 raise NotImplementedError('System entropy source does not have state.') 829 getstate = setstate = _notimplemented 830 831 ## -------------------- test program -------------------- 832 833 def _test_generator(n, func, args): 834 import time 835 print n, 'times', func.__name__ 836 total = 0.0 837 sqsum = 0.0 838 smallest = 1e10 839 largest = -1e10 840 t0 = time.time() 841 for i in range(n): 842 x = func(*args) 843 total += x 844 sqsum = sqsum + x*x 845 smallest = min(x, smallest) 846 largest = max(x, largest) 847 t1 = time.time() 848 print round(t1-t0, 3), 'sec,', 849 avg = total/n 850 stddev = _sqrt(sqsum/n - avg*avg) 851 print 'avg %g, stddev %g, min %g, max %g' % \ 852 (avg, stddev, smallest, largest) 853 854 855 def _test(N=2000): 856 _test_generator(N, random, ()) 857 _test_generator(N, normalvariate, (0.0, 1.0)) 858 _test_generator(N, lognormvariate, (0.0, 1.0)) 859 _test_generator(N, vonmisesvariate, (0.0, 1.0)) 860 _test_generator(N, gammavariate, (0.01, 1.0)) 861 _test_generator(N, gammavariate, (0.1, 1.0)) 862 _test_generator(N, gammavariate, (0.1, 2.0)) 863 _test_generator(N, gammavariate, (0.5, 1.0)) 864 _test_generator(N, gammavariate, (0.9, 1.0)) 865 _test_generator(N, gammavariate, (1.0, 1.0)) 866 _test_generator(N, gammavariate, (2.0, 1.0)) 867 _test_generator(N, gammavariate, (20.0, 1.0)) 868 _test_generator(N, gammavariate, (200.0, 1.0)) 869 _test_generator(N, gauss, (0.0, 1.0)) 870 _test_generator(N, betavariate, (3.0, 3.0)) 871 _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) 872 873 # Create one instance, seeded from current time, and export its methods 874 # as module-level functions. The functions share state across all uses 875 #(both in the user's code and in the Python libraries), but that's fine 876 # for most programs and is easier for the casual user than making them 877 # instantiate their own Random() instance. 878 879 _inst = Random() 880 seed = _inst.seed 881 random = _inst.random 882 uniform = _inst.uniform 883 triangular = _inst.triangular 884 randint = _inst.randint 885 choice = _inst.choice 886 randrange = _inst.randrange 887 sample = _inst.sample 888 shuffle = _inst.shuffle 889 normalvariate = _inst.normalvariate 890 lognormvariate = _inst.lognormvariate 891 expovariate = _inst.expovariate 892 vonmisesvariate = _inst.vonmisesvariate 893 gammavariate = _inst.gammavariate 894 gauss = _inst.gauss 895 betavariate = _inst.betavariate 896 paretovariate = _inst.paretovariate 897 weibullvariate = _inst.weibullvariate 898 getstate = _inst.getstate 899 setstate = _inst.setstate 900 jumpahead = _inst.jumpahead 901 getrandbits = _inst.getrandbits 902 903 if __name__ == '__main__': 904 _test() 905
