source: trunk/essentials/dev-lang/python/Lib/random.py

Last change on this file was 3225, checked in by bird, 18 years ago

Python 2.5
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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
29General 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
41from warnings import warn as _warn
42from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType
43from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
44from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
45from os import urandom as _urandom
46from 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
55NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
56TWOPI = 2.0*_pi
57LOG4 = _log(4.0)
58SG_MAGICCONST = 1.0 + _log(4.5)
59BPF = 53 # Number of bits in a float
60RECIP_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
67import _random
68
69class 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 + 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 > -1 and beta} > -1.
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
609class 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
759class 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
793def _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
815def _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()
839seed = _inst.seed
840random = _inst.random
841uniform = _inst.uniform
842randint = _inst.randint
843choice = _inst.choice
844randrange = _inst.randrange
845sample = _inst.sample
846shuffle = _inst.shuffle
847normalvariate = _inst.normalvariate
848lognormvariate = _inst.lognormvariate
849expovariate = _inst.expovariate
850vonmisesvariate = _inst.vonmisesvariate
851gammavariate = _inst.gammavariate
852gauss = _inst.gauss
853betavariate = _inst.betavariate
854paretovariate = _inst.paretovariate
855weibullvariate = _inst.weibullvariate
856getstate = _inst.getstate
857setstate = _inst.setstate
858jumpahead = _inst.jumpahead
859getrandbits = _inst.getrandbits
860
861if __name__ == '__main__':
862 _test()
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