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 random = self.random 431 u = random() 432 while u <= 1e-7: 433 u = random() 434 return -_log(u)/lambd 435 436 ## -------------------- von Mises distribution -------------------- 437 438 def vonmisesvariate(self, mu, kappa): 439 """Circular data distribution. 440 441 mu is the mean angle, expressed in radians between 0 and 2*pi, and 442 kappa is the concentration parameter, which must be greater than or 443 equal to zero. If kappa is equal to zero, this distribution reduces 444 to a uniform random angle over the range 0 to 2*pi. 445 446 """ 447 # mu: mean angle (in radians between 0 and 2*pi) 448 # kappa: concentration parameter kappa (>= 0) 449 # if kappa = 0 generate uniform random angle 450 451 # Based upon an algorithm published in: Fisher, N.I., 452 # "Statistical Analysis of Circular Data", Cambridge 453 # University Press, 1993. 454 455 # Thanks to Magnus Kessler for a correction to the 456 # implementation of step 4. 457 458 random = self.random 459 if kappa <= 1e-6: 460 return TWOPI * random() 461 462 a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa) 463 b = (a - _sqrt(2.0 * a))/(2.0 * kappa) 464 r = (1.0 + b * b)/(2.0 * b) 465 466 while 1: 467 u1 = random() 468 469 z = _cos(_pi * u1) 470 f = (1.0 + r * z)/(r + z) 471 c = kappa * (r - f) 472 473 u2 = random() 474 475 if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c): 476 break 477 478 u3 = random() 479 if u3 > 0.5: 480 theta = (mu % TWOPI) + _acos(f) 481 else: 482 theta = (mu % TWOPI) - _acos(f) 483 484 return theta 485 486 ## -------------------- gamma distribution -------------------- 487 488 def gammavariate(self, alpha, beta): 489 """Gamma distribution. Not the gamma function! 490 491 Conditions on the parameters are alpha > 0 and beta > 0. 492 493 The probability distribution function is: 494 495 x ** (alpha - 1) * math.exp(-x / beta) 496 pdf(x) = -------------------------------------- 497 math.gamma(alpha) * beta ** alpha 498 499 """ 500 501 # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 502 503 # Warning: a few older sources define the gamma distribution in terms 504 # of alpha > -1.0 505 if alpha <= 0.0 or beta <= 0.0: 506 raise ValueError, 'gammavariate: alpha and beta must be > 0.0' 507 508 random = self.random 509 if alpha > 1.0: 510 511 # Uses R.C.H. Cheng, "The generation of Gamma 512 # variables with non-integral shape parameters", 513 # Applied Statistics, (1977), 26, No. 1, p71-74 514 515 ainv = _sqrt(2.0 * alpha - 1.0) 516 bbb = alpha - LOG4 517 ccc = alpha + ainv 518 519 while 1: 520 u1 = random() 521 if not 1e-7 < u1 < .9999999: 522 continue 523 u2 = 1.0 - random() 524 v = _log(u1/(1.0-u1))/ainv 525 x = alpha*_exp(v) 526 z = u1*u1*u2 527 r = bbb+ccc*v-x 528 if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): 529 return x * beta 530 531 elif alpha == 1.0: 532 # expovariate(1) 533 u = random() 534 while u <= 1e-7: 535 u = random() 536 return -_log(u) * beta 537 538 else: # alpha is between 0 and 1 (exclusive) 539 540 # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle 541 542 while 1: 543 u = random() 544 b = (_e + alpha)/_e 545 p = b*u 546 if p <= 1.0: 547 x = p ** (1.0/alpha) 548 else: 549 x = -_log((b-p)/alpha) 550 u1 = random() 551 if p > 1.0: 552 if u1 <= x ** (alpha - 1.0): 553 break 554 elif u1 <= _exp(-x): 555 break 556 return x * beta 557 558 ## -------------------- Gauss (faster alternative) -------------------- 559 560 def gauss(self, mu, sigma): 561 """Gaussian distribution. 562 563 mu is the mean, and sigma is the standard deviation. This is 564 slightly faster than the normalvariate() function. 565 566 Not thread-safe without a lock around calls. 567 568 """ 569 570 # When x and y are two variables from [0, 1), uniformly 571 # distributed, then 572 # 573 # cos(2*pi*x)*sqrt(-2*log(1-y)) 574 # sin(2*pi*x)*sqrt(-2*log(1-y)) 575 # 576 # are two *independent* variables with normal distribution 577 # (mu = 0, sigma = 1). 578 # (Lambert Meertens) 579 # (corrected version; bug discovered by Mike Miller, fixed by LM) 580 581 # Multithreading note: When two threads call this function 582 # simultaneously, it is possible that they will receive the 583 # same return value. The window is very small though. To 584 # avoid this, you have to use a lock around all calls. (I 585 # didn't want to slow this down in the serial case by using a 586 # lock here.) 587 588 random = self.random 589 z = self.gauss_next 590 self.gauss_next = None 591 if z is None: 592 x2pi = random() * TWOPI 593 g2rad = _sqrt(-2.0 * _log(1.0 - random())) 594 z = _cos(x2pi) * g2rad 595 self.gauss_next = _sin(x2pi) * g2rad 596 597 return mu + z*sigma 598 599 ## -------------------- beta -------------------- 600 ## See 601 ## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html 602 ## for Ivan Frohne's insightful analysis of why the original implementation: 603 ## 604 ## def betavariate(self, alpha, beta): 605 ## # Discrete Event Simulation in C, pp 87-88. 606 ## 607 ## y = self.expovariate(alpha) 608 ## z = self.expovariate(1.0/beta) 609 ## return z/(y+z) 610 ## 611 ## was dead wrong, and how it probably got that way. 612 613 def betavariate(self, alpha, beta): 614 """Beta distribution. 615 616 Conditions on the parameters are alpha > 0 and beta > 0. 617 Returned values range between 0 and 1. 618 619 """ 620 621 # This version due to Janne Sinkkonen, and matches all the std 622 # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). 623 y = self.gammavariate(alpha, 1.) 624 if y == 0: 625 return 0.0 626 else: 627 return y / (y + self.gammavariate(beta, 1.)) 628 629 ## -------------------- Pareto -------------------- 630 631 def paretovariate(self, alpha): 632 """Pareto distribution. alpha is the shape parameter.""" 633 # Jain, pg. 495 634 635 u = 1.0 - self.random() 636 return 1.0 / pow(u, 1.0/alpha) 637 638 ## -------------------- Weibull -------------------- 639 640 def weibullvariate(self, alpha, beta): 641 """Weibull distribution. 642 643 alpha is the scale parameter and beta is the shape parameter. 644 645 """ 646 # Jain, pg. 499; bug fix courtesy Bill Arms 647 648 u = 1.0 - self.random() 649 return alpha * pow(-_log(u), 1.0/beta) 650 651 ## -------------------- Wichmann-Hill ------------------- 652 653 class WichmannHill(Random): 654 655 VERSION = 1 # used by getstate/setstate 656 657 def seed(self, a=None): 658 """Initialize internal state from hashable object. 659 660 None or no argument seeds from current time or from an operating 661 system specific randomness source if available. 662 663 If a is not None or an int or long, hash(a) is used instead. 664 665 If a is an int or long, a is used directly. Distinct values between 666 0 and 27814431486575L inclusive are guaranteed to yield distinct 667 internal states (this guarantee is specific to the default 668 Wichmann-Hill generator). 669 """ 670 671 if a is None: 672 try: 673 a = long(_hexlify(_urandom(16)), 16) 674 except NotImplementedError: 675 import time 676 a = long(time.time() * 256) # use fractional seconds 677 678 if not isinstance(a, (int, long)): 679 a = hash(a) 680 681 a, x = divmod(a, 30268) 682 a, y = divmod(a, 30306) 683 a, z = divmod(a, 30322) 684 self._seed = int(x)+1, int(y)+1, int(z)+1 685 686 self.gauss_next = None 687 688 def random(self): 689 """Get the next random number in the range [0.0, 1.0).""" 690 691 # Wichman-Hill random number generator. 692 # 693 # Wichmann, B. A. & Hill, I. D. (1982) 694 # Algorithm AS 183: 695 # An efficient and portable pseudo-random number generator 696 # Applied Statistics 31 (1982) 188-190 697 # 698 # see also: 699 # Correction to Algorithm AS 183 700 # Applied Statistics 33 (1984) 123 701 # 702 # McLeod, A. I. (1985) 703 # A remark on Algorithm AS 183 704 # Applied Statistics 34 (1985),198-200 705 706 # This part is thread-unsafe: 707 # BEGIN CRITICAL SECTION 708 x, y, z = self._seed 709 x = (171 * x) % 30269 710 y = (172 * y) % 30307 711 z = (170 * z) % 30323 712 self._seed = x, y, z 713 # END CRITICAL SECTION 714 715 # Note: on a platform using IEEE-754 double arithmetic, this can 716 # never return 0.0 (asserted by Tim; proof too long for a comment). 717 return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 718 719 def getstate(self): 720 """Return internal state; can be passed to setstate() later.""" 721 return self.VERSION, self._seed, self.gauss_next 722 723 def setstate(self, state): 724 """Restore internal state from object returned by getstate().""" 725 version = state[0] 726 if version == 1: 727 version, self._seed, self.gauss_next = state 728 else: 729 raise ValueError("state with version %s passed to " 730 "Random.setstate() of version %s" % 731 (version, self.VERSION)) 732 733 def jumpahead(self, n): 734 """Act as if n calls to random() were made, but quickly. 735 736 n is an int, greater than or equal to 0. 737 738 Example use: If you have 2 threads and know that each will 739 consume no more than a million random numbers, create two Random 740 objects r1 and r2, then do 741 r2.setstate(r1.getstate()) 742 r2.jumpahead(1000000) 743 Then r1 and r2 will use guaranteed-disjoint segments of the full 744 period. 745 """ 746 747 if not n >= 0: 748 raise ValueError("n must be >= 0") 749 x, y, z = self._seed 750 x = int(x * pow(171, n, 30269)) % 30269 751 y = int(y * pow(172, n, 30307)) % 30307 752 z = int(z * pow(170, n, 30323)) % 30323 753 self._seed = x, y, z 754 755 def __whseed(self, x=0, y=0, z=0): 756 """Set the Wichmann-Hill seed from (x, y, z). 757 758 These must be integers in the range [0, 256). 759 """ 760 761 if not type(x) == type(y) == type(z) == int: 762 raise TypeError('seeds must be integers') 763 if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): 764 raise ValueError('seeds must be in range(0, 256)') 765 if 0 == x == y == z: 766 # Initialize from current time 767 import time 768 t = long(time.time() * 256) 769 t = int((t&0xffffff) ^ (t>>24)) 770 t, x = divmod(t, 256) 771 t, y = divmod(t, 256) 772 t, z = divmod(t, 256) 773 # Zero is a poor seed, so substitute 1 774 self._seed = (x or 1, y or 1, z or 1) 775 776 self.gauss_next = None 777 778 def whseed(self, a=None): 779 """Seed from hashable object's hash code. 780 781 None or no argument seeds from current time. It is not guaranteed 782 that objects with distinct hash codes lead to distinct internal 783 states. 784 785 This is obsolete, provided for compatibility with the seed routine 786 used prior to Python 2.1. Use the .seed() method instead. 787 """ 788 789 if a is None: 790 self.__whseed() 791 return 792 a = hash(a) 793 a, x = divmod(a, 256) 794 a, y = divmod(a, 256) 795 a, z = divmod(a, 256) 796 x = (x + a) % 256 or 1 797 y = (y + a) % 256 or 1 798 z = (z + a) % 256 or 1 799 self.__whseed(x, y, z) 800 801 ## --------------- Operating System Random Source ------------------ 802 803 class SystemRandom(Random): 804 """Alternate random number generator using sources provided 805 by the operating system (such as /dev/urandom on Unix or 806 CryptGenRandom on Windows). 807 808 Not available on all systems (see os.urandom() for details). 809 """ 810 811 def random(self): 812 """Get the next random number in the range [0.0, 1.0).""" 813 return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF 814 815 def getrandbits(self, k): 816 """getrandbits(k) -> x. Generates a long int with k random bits.""" 817 if k <= 0: 818 raise ValueError('number of bits must be greater than zero') 819 if k != int(k): 820 raise TypeError('number of bits should be an integer') 821 bytes = (k + 7) // 8 # bits / 8 and rounded up 822 x = long(_hexlify(_urandom(bytes)), 16) 823 return x >> (bytes * 8 - k) # trim excess bits 824 825 def _stub(self, *args, **kwds): 826 "Stub method. Not used for a system random number generator." 827 return None 828 seed = jumpahead = _stub 829 830 def _notimplemented(self, *args, **kwds): 831 "Method should not be called for a system random number generator." 832 raise NotImplementedError('System entropy source does not have state.') 833 getstate = setstate = _notimplemented 834 835 ## -------------------- test program -------------------- 836 837 def _test_generator(n, func, args): 838 import time 839 print n, 'times', func.__name__ 840 total = 0.0 841 sqsum = 0.0 842 smallest = 1e10 843 largest = -1e10 844 t0 = time.time() 845 for i in range(n): 846 x = func(*args) 847 total += x 848 sqsum = sqsum + x*x 849 smallest = min(x, smallest) 850 largest = max(x, largest) 851 t1 = time.time() 852 print round(t1-t0, 3), 'sec,', 853 avg = total/n 854 stddev = _sqrt(sqsum/n - avg*avg) 855 print 'avg %g, stddev %g, min %g, max %g' % \ 856 (avg, stddev, smallest, largest) 857 858 859 def _test(N=2000): 860 _test_generator(N, random, ()) 861 _test_generator(N, normalvariate, (0.0, 1.0)) 862 _test_generator(N, lognormvariate, (0.0, 1.0)) 863 _test_generator(N, vonmisesvariate, (0.0, 1.0)) 864 _test_generator(N, gammavariate, (0.01, 1.0)) 865 _test_generator(N, gammavariate, (0.1, 1.0)) 866 _test_generator(N, gammavariate, (0.1, 2.0)) 867 _test_generator(N, gammavariate, (0.5, 1.0)) 868 _test_generator(N, gammavariate, (0.9, 1.0)) 869 _test_generator(N, gammavariate, (1.0, 1.0)) 870 _test_generator(N, gammavariate, (2.0, 1.0)) 871 _test_generator(N, gammavariate, (20.0, 1.0)) 872 _test_generator(N, gammavariate, (200.0, 1.0)) 873 _test_generator(N, gauss, (0.0, 1.0)) 874 _test_generator(N, betavariate, (3.0, 3.0)) 875 _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) 876 877 # Create one instance, seeded from current time, and export its methods 878 # as module-level functions. The functions share state across all uses 879 #(both in the user's code and in the Python libraries), but that's fine 880 # for most programs and is easier for the casual user than making them 881 # instantiate their own Random() instance. 882 883 _inst = Random() 884 seed = _inst.seed 885 random = _inst.random 886 uniform = _inst.uniform 887 triangular = _inst.triangular 888 randint = _inst.randint 889 choice = _inst.choice 890 randrange = _inst.randrange 891 sample = _inst.sample 892 shuffle = _inst.shuffle 893 normalvariate = _inst.normalvariate 894 lognormvariate = _inst.lognormvariate 895 expovariate = _inst.expovariate 896 vonmisesvariate = _inst.vonmisesvariate 897 gammavariate = _inst.gammavariate 898 gauss = _inst.gauss 899 betavariate = _inst.betavariate 900 paretovariate = _inst.paretovariate 901 weibullvariate = _inst.weibullvariate 902 getstate = _inst.getstate 903 setstate = _inst.setstate 904 jumpahead = _inst.jumpahead 905 getrandbits = _inst.getrandbits 906 907 if __name__ == '__main__': 908 _test() 909
