source file: /System/Library/Frameworks/Python.framework/Versions/2.3/lib/python2.3/random.py
file stats: 343 lines, 81 executed: 23.6% covered
   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
  34.   semantics of jumpahead(n) are weakened to simply jump
  35.   to another distant state and rely on the large period
  36.   to avoid overlapping sequences.
  37. * The random() method is implemented in C, executes in
  38.   a single Python step, and is, therefore, threadsafe.
  39. 
  40. """
  41. from types import BuiltinMethodType as _BuiltinMethodType
  42. from math import log as _log, exp as _exp, pi as _pi, e as _e
  43. from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
  44. from math import floor as _floor
  45. 
  46. __all__ = ["Random","seed","random","uniform","randint","choice","sample",
  47.            "randrange","shuffle","normalvariate","lognormvariate",
  48.            "cunifvariate","expovariate","vonmisesvariate","gammavariate",
  49.            "stdgamma","gauss","betavariate","paretovariate","weibullvariate",
  50.            "getstate","setstate","jumpahead", "WichmannHill"]
  51. 
  52. NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
  53. TWOPI = 2.0*_pi
  54. LOG4 = _log(4.0)
  55. SG_MAGICCONST = 1.0 + _log(4.5)
  56. BPF = 53        # Number of bits in a float
  57. 
  58. # Translated by Guido van Rossum from C source provided by
  59. # Adrian Baddeley.  Adapted by Raymond Hettinger for use with
  60. # the Mersenne Twister core generator.
  61. 
  62. import _random
  63. 
  64. class Random(_random.Random):
  65.     """Random number generator base class used by bound module functions.
  66. 
  67.     Used to instantiate instances of Random to get generators that don't
  68.     share state.  Especially useful for multi-threaded programs, creating
  69.     a different instance of Random for each thread, and using the jumpahead()
  70.     method to ensure that the generated sequences seen by each thread don't
  71.     overlap.
  72. 
  73.     Class Random can also be subclassed if you want to use a different basic
  74.     generator of your own devising: in that case, override the following
  75.     methods:  random(), seed(), getstate(), setstate() and jumpahead().
  76. 
  77.     """
  78. 
  79.     VERSION = 2     # used by getstate/setstate
  80. 
  81.     def __init__(self, x=None):
  82.         """Initialize an instance.
  83. 
  84.         Optional argument x controls seeding, as for Random.seed().
  85.         """
  86. 
  87.         self.seed(x)
  88.         self.gauss_next = None
  89. 
  90.     def seed(self, a=None):
  91.         """Initialize internal state from hashable object.
  92. 
  93.         None or no argument seeds from current time.
  94. 
  95.         If a is not None or an int or long, hash(a) is used instead.
  96.         """
  97. 
  98.         if a is None:
  99.             import time
 100.             a = long(time.time() * 256) # use fractional seconds
 101.         super(Random, self).seed(a)
 102.         self.gauss_next = None
 103. 
 104.     def getstate(self):
 105.         """Return internal state; can be passed to setstate() later."""
 106.         return self.VERSION, super(Random, self).getstate(), self.gauss_next
 107. 
 108.     def setstate(self, state):
 109.         """Restore internal state from object returned by getstate()."""
 110.         version = state[0]
 111.         if version == 2:
 112.             version, internalstate, self.gauss_next = state
 113.             super(Random, self).setstate(internalstate)
 114.         else:
 115.             raise ValueError("state with version %s passed to "
 116.                              "Random.setstate() of version %s" %
 117.                              (version, self.VERSION))
 118. 
 119. ## ---- Methods below this point do not need to be overridden when
 120. ## ---- subclassing for the purpose of using a different core generator.
 121. 
 122. ## -------------------- pickle support  -------------------
 123. 
 124.     def __getstate__(self): # for pickle
 125.         return self.getstate()
 126. 
 127.     def __setstate__(self, state):  # for pickle
 128.         self.setstate(state)
 129. 
 130.     def __reduce__(self):
 131.         return self.__class__, (), self.getstate()
 132. 
 133. ## -------------------- integer methods  -------------------
 134. 
 135.     def randrange(self, start, stop=None, step=1, int=int, default=None,
 136.                   maxwidth=1L<<BPF, _BuiltinMethod=_BuiltinMethodType):
 137.         """Choose a random item from range(start, stop[, step]).
 138. 
 139.         This fixes the problem with randint() which includes the
 140.         endpoint; in Python this is usually not what you want.
 141.         Do not supply the 'int', 'default', and 'maxwidth' arguments.
 142.         """
 143. 
 144.         # This code is a bit messy to make it fast for the
 145.         # common case while still doing adequate error checking.
 146.         istart = int(start)
 147.         if istart != start:
 148.             raise ValueError, "non-integer arg 1 for randrange()"
 149.         if stop is default:
 150.             if istart > 0:
 151.                 if istart >= maxwidth and type(self.random) is _BuiltinMethod:
 152.                     return self._randbelow(istart)
 153.                 return int(self.random() * istart)
 154.             raise ValueError, "empty range for randrange()"
 155. 
 156.         # stop argument supplied.
 157.         istop = int(stop)
 158.         if istop != stop:
 159.             raise ValueError, "non-integer stop for randrange()"
 160.         width = istop - istart
 161.         if step == 1 and width > 0:
 162.             # Note that
 163.             #     int(istart + self.random()*(istop - istart))
 164.             # instead would be incorrect.  For example, consider istart
 165.             # = -2 and istop = 0.  Then the guts would be in
 166.             # -2.0 to 0.0 exclusive on both ends (ignoring that random()
 167.             # might return 0.0), and because int() truncates toward 0, the
 168.             # final result would be -1 or 0 (instead of -2 or -1).
 169.             #     istart + int(self.random()*(istop - istart))
 170.             # would also be incorrect, for a subtler reason:  the RHS
 171.             # can return a long, and then randrange() would also return
 172.             # a long, but we're supposed to return an int (for backward
 173.             # compatibility).
 174.             if width >= maxwidth and type(self.random) is _BuiltinMethod:
 175.                 return int(istart + self._randbelow(width))
 176.             return int(istart + int(self.random()*width))
 177.         if step == 1:
 178.             raise ValueError, "empty range for randrange()"
 179. 
 180.         # Non-unit step argument supplied.
 181.         istep = int(step)
 182.         if istep != step:
 183.             raise ValueError, "non-integer step for randrange()"
 184.         if istep > 0:
 185.             n = (width + istep - 1) / istep
 186.         elif istep < 0:
 187.             n = (width + istep + 1) / istep
 188.         else:
 189.             raise ValueError, "zero step for randrange()"
 190. 
 191.         if n <= 0:
 192.             raise ValueError, "empty range for randrange()"
 193. 
 194.         if n >= maxwidth and type(self.random) is _BuiltinMethod:
 195.             return istart + self._randbelow(n)
 196.         return istart + istep*int(self.random() * n)
 197. 
 198.     def randint(self, a, b):
 199.         """Return random integer in range [a, b], including both end points.
 200.         """
 201. 
 202.         return self.randrange(a, b+1)
 203. 
 204.     def _randbelow(self, n, bpf=BPF, maxwidth=1L<<BPF,
 205.                    long=long, _log=_log, int=int):
 206.         """Return a random int in the range [0,n)
 207. 
 208.         Handles the case where n has more bits than returned
 209.         by a single call to the underlying generator.
 210.         """
 211. 
 212.         # k is a sometimes over but never under estimate of the bits in n
 213.         k = int(1.00001 + _log(n-1, 2))     # 2**k > n-1 >= 2**(k-2)
 214. 
 215.         random = self.random
 216.         r = n
 217.         while r >= n:
 218.             # In Py2.4, this section becomes:  r = self.getrandbits(k)
 219.             r = long(random() * maxwidth)
 220.             bits = bpf
 221.             while bits < k:
 222.                 r = (r << bpf) | (long(random() * maxwidth))
 223.                 bits += bpf
 224.             r >>= (bits - k)
 225.         return r
 226. 
 227. ## -------------------- sequence methods  -------------------
 228. 
 229.     def choice(self, seq):
 230.         """Choose a random element from a non-empty sequence."""
 231.         return seq[int(self.random() * len(seq))]
 232. 
 233.     def shuffle(self, x, random=None, int=int):
 234.         """x, random=random.random -> shuffle list x in place; return None.
 235. 
 236.         Optional arg random is a 0-argument function returning a random
 237.         float in [0.0, 1.0); by default, the standard random.random.
 238. 
 239.         Note that for even rather small len(x), the total number of
 240.         permutations of x is larger than the period of most random number
 241.         generators; this implies that "most" permutations of a long
 242.         sequence can never be generated.
 243.         """
 244. 
 245.         if random is None:
 246.             random = self.random
 247.         for i in xrange(len(x)-1, 0, -1):
 248.             # pick an element in x[:i+1] with which to exchange x[i]
 249.             j = int(random() * (i+1))
 250.             x[i], x[j] = x[j], x[i]
 251. 
 252.     def sample(self, population, k):
 253.         """Chooses k unique random elements from a population sequence.
 254. 
 255.         Returns a new list containing elements from the population while
 256.         leaving the original population unchanged.  The resulting list is
 257.         in selection order so that all sub-slices will also be valid random
 258.         samples.  This allows raffle winners (the sample) to be partitioned
 259.         into grand prize and second place winners (the subslices).
 260. 
 261.         Members of the population need not be hashable or unique.  If the
 262.         population contains repeats, then each occurrence is a possible
 263.         selection in the sample.
 264. 
 265.         To choose a sample in a range of integers, use xrange as an argument.
 266.         This is especially fast and space efficient for sampling from a
 267.         large population:   sample(xrange(10000000), 60)
 268.         """
 269. 
 270.         # Sampling without replacement entails tracking either potential
 271.         # selections (the pool) in a list or previous selections in a
 272.         # dictionary.
 273. 
 274.         # When the number of selections is small compared to the population,
 275.         # then tracking selections is efficient, requiring only a small
 276.         # dictionary and an occasional reselection.  For a larger number of
 277.         # selections, the pool tracking method is preferred since the list takes
 278.         # less space than the dictionary and it doesn't suffer from frequent
 279.         # reselections.
 280. 
 281.         n = len(population)
 282.         if not 0 <= k <= n:
 283.             raise ValueError, "sample larger than population"
 284.         random = self.random
 285.         _int = int
 286.         result = [None] * k
 287.         if n < 6 * k:     # if n len list takes less space than a k len dict
 288.             pool = list(population)
 289.             for i in xrange(k):         # invariant:  non-selected at [0,n-i)
 290.                 j = _int(random() * (n-i))
 291.                 result[i] = pool[j]
 292.                 pool[j] = pool[n-i-1]   # move non-selected item into vacancy
 293.         else:
 294.             try:
 295.                 n > 0 and (population[0], population[n//2], population[n-1])
 296.             except (TypeError, KeyError):   # handle sets and dictionaries
 297.                 population = tuple(population)
 298.             selected = {}
 299.             for i in xrange(k):
 300.                 j = _int(random() * n)
 301.                 while j in selected:
 302.                     j = _int(random() * n)
 303.                 result[i] = selected[j] = population[j]
 304.         return result
 305. 
 306. ## -------------------- real-valued distributions  -------------------
 307. 
 308. ## -------------------- uniform distribution -------------------
 309. 
 310.     def uniform(self, a, b):
 311.         """Get a random number in the range [a, b)."""
 312.         return a + (b-a) * self.random()
 313. 
 314. ## -------------------- normal distribution --------------------
 315. 
 316.     def normalvariate(self, mu, sigma):
 317.         """Normal distribution.
 318. 
 319.         mu is the mean, and sigma is the standard deviation.
 320. 
 321.         """
 322.         # mu = mean, sigma = standard deviation
 323. 
 324.         # Uses Kinderman and Monahan method. Reference: Kinderman,
 325.         # A.J. and Monahan, J.F., "Computer generation of random
 326.         # variables using the ratio of uniform deviates", ACM Trans
 327.         # Math Software, 3, (1977), pp257-260.
 328. 
 329.         random = self.random
 330.         while True:
 331.             u1 = random()
 332.             u2 = 1.0 - random()
 333.             z = NV_MAGICCONST*(u1-0.5)/u2
 334.             zz = z*z/4.0
 335.             if zz <= -_log(u2):
 336.                 break
 337.         return mu + z*sigma
 338. 
 339. ## -------------------- lognormal distribution --------------------
 340. 
 341.     def lognormvariate(self, mu, sigma):
 342.         """Log normal distribution.
 343. 
 344.         If you take the natural logarithm of this distribution, you'll get a
 345.         normal distribution with mean mu and standard deviation sigma.
 346.         mu can have any value, and sigma must be greater than zero.
 347. 
 348.         """
 349.         return _exp(self.normalvariate(mu, sigma))
 350. 
 351. ## -------------------- circular uniform --------------------
 352. 
 353.     def cunifvariate(self, mean, arc):
 354.         """Circular uniform distribution.
 355. 
 356.         mean is the mean angle, and arc is the range of the distribution,
 357.         centered around the mean angle.  Both values must be expressed in
 358.         radians.  Returned values range between mean - arc/2 and
 359.         mean + arc/2 and are normalized to between 0 and pi.
 360. 
 361.         Deprecated in version 2.3.  Use:
 362.             (mean + arc * (Random.random() - 0.5)) % Math.pi
 363. 
 364.         """
 365.         # mean: mean angle (in radians between 0 and pi)
 366.         # arc:  range of distribution (in radians between 0 and pi)
 367.         import warnings
 368.         warnings.warn("The cunifvariate function is deprecated; Use (mean "
 369.                       "+ arc * (Random.random() - 0.5)) % Math.pi instead.",
 370.                       DeprecationWarning, 2)
 371. 
 372.         return (mean + arc * (self.random() - 0.5)) % _pi
 373. 
 374. ## -------------------- exponential distribution --------------------
 375. 
 376.     def expovariate(self, lambd):
 377.         """Exponential distribution.
 378. 
 379.         lambd is 1.0 divided by the desired mean.  (The parameter would be
 380.         called "lambda", but that is a reserved word in Python.)  Returned
 381.         values range from 0 to positive infinity.
 382. 
 383.         """
 384.         # lambd: rate lambd = 1/mean
 385.         # ('lambda' is a Python reserved word)
 386. 
 387.         random = self.random
 388.         u = random()
 389.         while u <= 1e-7:
 390.             u = random()
 391.         return -_log(u)/lambd
 392. 
 393. ## -------------------- von Mises distribution --------------------
 394. 
 395.     def vonmisesvariate(self, mu, kappa):
 396.         """Circular data distribution.
 397. 
 398.         mu is the mean angle, expressed in radians between 0 and 2*pi, and
 399.         kappa is the concentration parameter, which must be greater than or
 400.         equal to zero.  If kappa is equal to zero, this distribution reduces
 401.         to a uniform random angle over the range 0 to 2*pi.
 402. 
 403.         """
 404.         # mu:    mean angle (in radians between 0 and 2*pi)
 405.         # kappa: concentration parameter kappa (>= 0)
 406.         # if kappa = 0 generate uniform random angle
 407. 
 408.         # Based upon an algorithm published in: Fisher, N.I.,
 409.         # "Statistical Analysis of Circular Data", Cambridge
 410.         # University Press, 1993.
 411. 
 412.         # Thanks to Magnus Kessler for a correction to the
 413.         # implementation of step 4.
 414. 
 415.         random = self.random
 416.         if kappa <= 1e-6:
 417.             return TWOPI * random()
 418. 
 419.         a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
 420.         b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
 421.         r = (1.0 + b * b)/(2.0 * b)
 422. 
 423.         while True:
 424.             u1 = random()
 425. 
 426.             z = _cos(_pi * u1)
 427.             f = (1.0 + r * z)/(r + z)
 428.             c = kappa * (r - f)
 429. 
 430.             u2 = random()
 431. 
 432.             if not (u2 >= c * (2.0 - c) and u2 > c * _exp(1.0 - c)):
 433.                 break
 434. 
 435.         u3 = random()
 436.         if u3 > 0.5:
 437.             theta = (mu % TWOPI) + _acos(f)
 438.         else:
 439.             theta = (mu % TWOPI) - _acos(f)
 440. 
 441.         return theta
 442. 
 443. ## -------------------- gamma distribution --------------------
 444. 
 445.     def gammavariate(self, alpha, beta):
 446.         """Gamma distribution.  Not the gamma function!
 447. 
 448.         Conditions on the parameters are alpha > 0 and beta > 0.
 449. 
 450.         """
 451. 
 452.         # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2
 453. 
 454.         # Warning: a few older sources define the gamma distribution in terms
 455.         # of alpha > -1.0
 456.         if alpha <= 0.0 or beta <= 0.0:
 457.             raise ValueError, 'gammavariate: alpha and beta must be > 0.0'
 458. 
 459.         random = self.random
 460.         if alpha > 1.0:
 461. 
 462.             # Uses R.C.H. Cheng, "The generation of Gamma
 463.             # variables with non-integral shape parameters",
 464.             # Applied Statistics, (1977), 26, No. 1, p71-74
 465. 
 466.             ainv = _sqrt(2.0 * alpha - 1.0)
 467.             bbb = alpha - LOG4
 468.             ccc = alpha + ainv
 469. 
 470.             while True:
 471.                 u1 = random()
 472.                 if not 1e-7 < u1 < .9999999:
 473.                     continue
 474.                 u2 = 1.0 - random()
 475.                 v = _log(u1/(1.0-u1))/ainv
 476.                 x = alpha*_exp(v)
 477.                 z = u1*u1*u2
 478.                 r = bbb+ccc*v-x
 479.                 if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
 480.                     return x * beta
 481. 
 482.         elif alpha == 1.0:
 483.             # expovariate(1)
 484.             u = random()
 485.             while u <= 1e-7:
 486.                 u = random()
 487.             return -_log(u) * beta
 488. 
 489.         else:   # alpha is between 0 and 1 (exclusive)
 490. 
 491.             # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
 492. 
 493.             while True:
 494.                 u = random()
 495.                 b = (_e + alpha)/_e
 496.                 p = b*u
 497.                 if p <= 1.0:
 498.                     x = pow(p, 1.0/alpha)
 499.                 else:
 500.                     # p > 1
 501.                     x = -_log((b-p)/alpha)
 502.                 u1 = random()
 503.                 if not (((p <= 1.0) and (u1 > _exp(-x))) or
 504.                           ((p > 1)  and  (u1 > pow(x, alpha - 1.0)))):
 505.                     break
 506.             return x * beta
 507. 
 508. 
 509.     def stdgamma(self, alpha, ainv, bbb, ccc):
 510.         # This method was (and shall remain) undocumented.
 511.         # This method is deprecated
 512.         # for the following reasons:
 513.         # 1. Returns same as .gammavariate(alpha, 1.0)
 514.         # 2. Requires caller to provide 3 extra arguments
 515.         #    that are functions of alpha anyway
 516.         # 3. Can't be used for alpha < 0.5
 517. 
 518.         # ainv = sqrt(2 * alpha - 1)
 519.         # bbb = alpha - log(4)
 520.         # ccc = alpha + ainv
 521.         import warnings
 522.         warnings.warn("The stdgamma function is deprecated; "
 523.                       "use gammavariate() instead.",
 524.                       DeprecationWarning, 2)
 525.         return self.gammavariate(alpha, 1.0)
 526. 
 527. 
 528. 
 529. ## -------------------- Gauss (faster alternative) --------------------
 530. 
 531.     def gauss(self, mu, sigma):
 532.         """Gaussian distribution.
 533. 
 534.         mu is the mean, and sigma is the standard deviation.  This is
 535.         slightly faster than the normalvariate() function.
 536. 
 537.         Not thread-safe without a lock around calls.
 538. 
 539.         """
 540. 
 541.         # When x and y are two variables from [0, 1), uniformly
 542.         # distributed, then
 543.         #
 544.         #    cos(2*pi*x)*sqrt(-2*log(1-y))
 545.         #    sin(2*pi*x)*sqrt(-2*log(1-y))
 546.         #
 547.         # are two *independent* variables with normal distribution
 548.         # (mu = 0, sigma = 1).
 549.         # (Lambert Meertens)
 550.         # (corrected version; bug discovered by Mike Miller, fixed by LM)
 551. 
 552.         # Multithreading note: When two threads call this function
 553.         # simultaneously, it is possible that they will receive the
 554.         # same return value.  The window is very small though.  To
 555.         # avoid this, you have to use a lock around all calls.  (I
 556.         # didn't want to slow this down in the serial case by using a
 557.         # lock here.)
 558. 
 559.         random = self.random
 560.         z = self.gauss_next
 561.         self.gauss_next = None
 562.         if z is None:
 563.             x2pi = random() * TWOPI
 564.             g2rad = _sqrt(-2.0 * _log(1.0 - random()))
 565.             z = _cos(x2pi) * g2rad
 566.             self.gauss_next = _sin(x2pi) * g2rad
 567. 
 568.         return mu + z*sigma
 569. 
 570. ## -------------------- beta --------------------
 571. ## See
 572. ## http://sourceforge.net/bugs/?func=detailbug&bug_id=130030&group_id=5470
 573. ## for Ivan Frohne's insightful analysis of why the original implementation:
 574. ##
 575. ##    def betavariate(self, alpha, beta):
 576. ##        # Discrete Event Simulation in C, pp 87-88.
 577. ##
 578. ##        y = self.expovariate(alpha)
 579. ##        z = self.expovariate(1.0/beta)
 580. ##        return z/(y+z)
 581. ##
 582. ## was dead wrong, and how it probably got that way.
 583. 
 584.     def betavariate(self, alpha, beta):
 585.         """Beta distribution.
 586. 
 587.         Conditions on the parameters are alpha > -1 and beta} > -1.
 588.         Returned values range between 0 and 1.
 589. 
 590.         """
 591. 
 592.         # This version due to Janne Sinkkonen, and matches all the std
 593.         # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
 594.         y = self.gammavariate(alpha, 1.)
 595.         if y == 0:
 596.             return 0.0
 597.         else:
 598.             return y / (y + self.gammavariate(beta, 1.))
 599. 
 600. ## -------------------- Pareto --------------------
 601. 
 602.     def paretovariate(self, alpha):
 603.         """Pareto distribution.  alpha is the shape parameter."""
 604.         # Jain, pg. 495
 605. 
 606.         u = 1.0 - self.random()
 607.         return 1.0 / pow(u, 1.0/alpha)
 608. 
 609. ## -------------------- Weibull --------------------
 610. 
 611.     def weibullvariate(self, alpha, beta):
 612.         """Weibull distribution.
 613. 
 614.         alpha is the scale parameter and beta is the shape parameter.
 615. 
 616.         """
 617.         # Jain, pg. 499; bug fix courtesy Bill Arms
 618. 
 619.         u = 1.0 - self.random()
 620.         return alpha * pow(-_log(u), 1.0/beta)
 621. 
 622. ## -------------------- Wichmann-Hill -------------------
 623. 
 624. class WichmannHill(Random):
 625. 
 626.     VERSION = 1     # used by getstate/setstate
 627. 
 628.     def seed(self, a=None):
 629.         """Initialize internal state from hashable object.
 630. 
 631.         None or no argument seeds from current time.
 632. 
 633.         If a is not None or an int or long, hash(a) is used instead.
 634. 
 635.         If a is an int or long, a is used directly.  Distinct values between
 636.         0 and 27814431486575L inclusive are guaranteed to yield distinct
 637.         internal states (this guarantee is specific to the default
 638.         Wichmann-Hill generator).
 639.         """
 640. 
 641.         if a is None:
 642.             # Initialize from current time
 643.             import time
 644.             a = long(time.time() * 256)
 645. 
 646.         if not isinstance(a, (int, long)):
 647.             a = hash(a)
 648. 
 649.         a, x = divmod(a, 30268)
 650.         a, y = divmod(a, 30306)
 651.         a, z = divmod(a, 30322)
 652.         self._seed = int(x)+1, int(y)+1, int(z)+1
 653. 
 654.         self.gauss_next = None
 655. 
 656.     def random(self):
 657.         """Get the next random number in the range [0.0, 1.0)."""
 658. 
 659.         # Wichman-Hill random number generator.
 660.         #
 661.         # Wichmann, B. A. & Hill, I. D. (1982)
 662.         # Algorithm AS 183:
 663.         # An efficient and portable pseudo-random number generator
 664.         # Applied Statistics 31 (1982) 188-190
 665.         #
 666.         # see also:
 667.         #        Correction to Algorithm AS 183
 668.         #        Applied Statistics 33 (1984) 123
 669.         #
 670.         #        McLeod, A. I. (1985)
 671.         #        A remark on Algorithm AS 183
 672.         #        Applied Statistics 34 (1985),198-200
 673. 
 674.         # This part is thread-unsafe:
 675.         # BEGIN CRITICAL SECTION
 676.         x, y, z = self._seed
 677.         x = (171 * x) % 30269
 678.         y = (172 * y) % 30307
 679.         z = (170 * z) % 30323
 680.         self._seed = x, y, z
 681.         # END CRITICAL SECTION
 682. 
 683.         # Note:  on a platform using IEEE-754 double arithmetic, this can
 684.         # never return 0.0 (asserted by Tim; proof too long for a comment).
 685.         return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0
 686. 
 687.     def getstate(self):
 688.         """Return internal state; can be passed to setstate() later."""
 689.         return self.VERSION, self._seed, self.gauss_next
 690. 
 691.     def setstate(self, state):
 692.         """Restore internal state from object returned by getstate()."""
 693.         version = state[0]
 694.         if version == 1:
 695.             version, self._seed, self.gauss_next = state
 696.         else:
 697.             raise ValueError("state with version %s passed to "
 698.                              "Random.setstate() of version %s" %
 699.                              (version, self.VERSION))
 700. 
 701.     def jumpahead(self, n):
 702.         """Act as if n calls to random() were made, but quickly.
 703. 
 704.         n is an int, greater than or equal to 0.
 705. 
 706.         Example use:  If you have 2 threads and know that each will
 707.         consume no more than a million random numbers, create two Random
 708.         objects r1 and r2, then do
 709.             r2.setstate(r1.getstate())
 710.             r2.jumpahead(1000000)
 711.         Then r1 and r2 will use guaranteed-disjoint segments of the full
 712.         period.
 713.         """
 714. 
 715.         if not n >= 0:
 716.             raise ValueError("n must be >= 0")
 717.         x, y, z = self._seed
 718.         x = int(x * pow(171, n, 30269)) % 30269
 719.         y = int(y * pow(172, n, 30307)) % 30307
 720.         z = int(z * pow(170, n, 30323)) % 30323
 721.         self._seed = x, y, z
 722. 
 723.     def __whseed(self, x=0, y=0, z=0):
 724.         """Set the Wichmann-Hill seed from (x, y, z).
 725. 
 726.         These must be integers in the range [0, 256).
 727.         """
 728. 
 729.         if not type(x) == type(y) == type(z) == int:
 730.             raise TypeError('seeds must be integers')
 731.         if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256):
 732.             raise ValueError('seeds must be in range(0, 256)')
 733.         if 0 == x == y == z:
 734.             # Initialize from current time
 735.             import time
 736.             t = long(time.time() * 256)
 737.             t = int((t&0xffffff) ^ (t>>24))
 738.             t, x = divmod(t, 256)
 739.             t, y = divmod(t, 256)
 740.             t, z = divmod(t, 256)
 741.         # Zero is a poor seed, so substitute 1
 742.         self._seed = (x or 1, y or 1, z or 1)
 743. 
 744.         self.gauss_next = None
 745. 
 746.     def whseed(self, a=None):
 747.         """Seed from hashable object's hash code.
 748. 
 749.         None or no argument seeds from current time.  It is not guaranteed
 750.         that objects with distinct hash codes lead to distinct internal
 751.         states.
 752. 
 753.         This is obsolete, provided for compatibility with the seed routine
 754.         used prior to Python 2.1.  Use the .seed() method instead.
 755.         """
 756. 
 757.         if a is None:
 758.             self.__whseed()
 759.             return
 760.         a = hash(a)
 761.         a, x = divmod(a, 256)
 762.         a, y = divmod(a, 256)
 763.         a, z = divmod(a, 256)
 764.         x = (x + a) % 256 or 1
 765.         y = (y + a) % 256 or 1
 766.         z = (z + a) % 256 or 1
 767.         self.__whseed(x, y, z)
 768. 
 769. ## -------------------- test program --------------------
 770. 
 771. def _test_generator(n, funccall):
 772.     import time
 773.     print n, 'times', funccall
 774.     code = compile(funccall, funccall, 'eval')
 775.     total = 0.0
 776.     sqsum = 0.0
 777.     smallest = 1e10
 778.     largest = -1e10
 779.     t0 = time.time()
 780.     for i in range(n):
 781.         x = eval(code)
 782.         total += x
 783.         sqsum = sqsum + x*x
 784.         smallest = min(x, smallest)
 785.         largest = max(x, largest)
 786.     t1 = time.time()
 787.     print round(t1-t0, 3), 'sec,',
 788.     avg = total/n
 789.     stddev = _sqrt(sqsum/n - avg*avg)
 790.     print 'avg %g, stddev %g, min %g, max %g' % \
 791.               (avg, stddev, smallest, largest)
 792. 
 793. 
 794. def _test(N=2000):
 795.     _test_generator(N, 'random()')
 796.     _test_generator(N, 'normalvariate(0.0, 1.0)')
 797.     _test_generator(N, 'lognormvariate(0.0, 1.0)')
 798.     _test_generator(N, 'cunifvariate(0.0, 1.0)')
 799.     _test_generator(N, 'vonmisesvariate(0.0, 1.0)')
 800.     _test_generator(N, 'gammavariate(0.01, 1.0)')
 801.     _test_generator(N, 'gammavariate(0.1, 1.0)')
 802.     _test_generator(N, 'gammavariate(0.1, 2.0)')
 803.     _test_generator(N, 'gammavariate(0.5, 1.0)')
 804.     _test_generator(N, 'gammavariate(0.9, 1.0)')
 805.     _test_generator(N, 'gammavariate(1.0, 1.0)')
 806.     _test_generator(N, 'gammavariate(2.0, 1.0)')
 807.     _test_generator(N, 'gammavariate(20.0, 1.0)')
 808.     _test_generator(N, 'gammavariate(200.0, 1.0)')
 809.     _test_generator(N, 'gauss(0.0, 1.0)')
 810.     _test_generator(N, 'betavariate(3.0, 3.0)')
 811. 
 812. # Create one instance, seeded from current time, and export its methods
 813. # as module-level functions.  The functions share state across all uses
 814. #(both in the user's code and in the Python libraries), but that's fine
 815. # for most programs and is easier for the casual user than making them
 816. # instantiate their own Random() instance.
 817. 
 818. _inst = Random()
 819. seed = _inst.seed
 820. random = _inst.random
 821. uniform = _inst.uniform
 822. randint = _inst.randint
 823. choice = _inst.choice
 824. randrange = _inst.randrange
 825. sample = _inst.sample
 826. shuffle = _inst.shuffle
 827. normalvariate = _inst.normalvariate
 828. lognormvariate = _inst.lognormvariate
 829. cunifvariate = _inst.cunifvariate
 830. expovariate = _inst.expovariate
 831. vonmisesvariate = _inst.vonmisesvariate
 832. gammavariate = _inst.gammavariate
 833. stdgamma = _inst.stdgamma
 834. gauss = _inst.gauss
 835. betavariate = _inst.betavariate
 836. paretovariate = _inst.paretovariate
 837. weibullvariate = _inst.weibullvariate
 838. getstate = _inst.getstate
 839. setstate = _inst.setstate
 840. jumpahead = _inst.jumpahead
 841. 
 842. if __name__ == '__main__':
 843.     _test()