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Diffstat (limited to 'lib/python2.7/random.py')
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diff --git a/lib/python2.7/random.py b/lib/python2.7/random.py new file mode 100644 index 0000000..af04ab2 --- /dev/null +++ b/lib/python2.7/random.py @@ -0,0 +1,904 @@ +"""Random variable generators. + + integers + -------- + uniform within range + + sequences + --------- + pick random element + pick random sample + generate random permutation + + distributions on the real line: + ------------------------------ + uniform + triangular + normal (Gaussian) + lognormal + negative exponential + gamma + beta + pareto + Weibull + + distributions on the circle (angles 0 to 2pi) + --------------------------------------------- + circular uniform + von Mises + +General notes on the underlying Mersenne Twister core generator: + +* The period is 2**19937-1. +* It is one of the most extensively tested generators in existence. +* Without a direct way to compute N steps forward, the semantics of + jumpahead(n) are weakened to simply jump to another distant state and rely + on the large period to avoid overlapping sequences. +* The random() method is implemented in C, executes in a single Python step, + and is, therefore, threadsafe. + +""" + +from __future__ import division +from warnings import warn as _warn +from types import MethodType as _MethodType, BuiltinMethodType as _BuiltinMethodType +from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil +from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin +from os import urandom as _urandom +from binascii import hexlify as _hexlify +import hashlib as _hashlib + +__all__ = ["Random","seed","random","uniform","randint","choice","sample", + "randrange","shuffle","normalvariate","lognormvariate", + "expovariate","vonmisesvariate","gammavariate","triangular", + "gauss","betavariate","paretovariate","weibullvariate", + "getstate","setstate","jumpahead", "WichmannHill", "getrandbits", + "SystemRandom"] + +NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0) +TWOPI = 2.0*_pi +LOG4 = _log(4.0) +SG_MAGICCONST = 1.0 + _log(4.5) +BPF = 53 # Number of bits in a float +RECIP_BPF = 2**-BPF + + +# Translated by Guido van Rossum from C source provided by +# Adrian Baddeley. Adapted by Raymond Hettinger for use with +# the Mersenne Twister and os.urandom() core generators. + +import _random + +class Random(_random.Random): + """Random number generator base class used by bound module functions. + + Used to instantiate instances of Random to get generators that don't + share state. Especially useful for multi-threaded programs, creating + a different instance of Random for each thread, and using the jumpahead() + method to ensure that the generated sequences seen by each thread don't + overlap. + + Class Random can also be subclassed if you want to use a different basic + generator of your own devising: in that case, override the following + methods: random(), seed(), getstate(), setstate() and jumpahead(). + Optionally, implement a getrandbits() method so that randrange() can cover + arbitrarily large ranges. + + """ + + VERSION = 3 # used by getstate/setstate + + def __init__(self, x=None): + """Initialize an instance. + + Optional argument x controls seeding, as for Random.seed(). + """ + + self.seed(x) + self.gauss_next = None + + def seed(self, a=None): + """Initialize internal state from hashable object. + + None or no argument seeds from current time or from an operating + system specific randomness source if available. + + If a is not None or an int or long, hash(a) is used instead. + """ + + if a is None: + try: + a = long(_hexlify(_urandom(16)), 16) + except NotImplementedError: + import time + a = long(time.time() * 256) # use fractional seconds + + super(Random, self).seed(a) + self.gauss_next = None + + def getstate(self): + """Return internal state; can be passed to setstate() later.""" + return self.VERSION, super(Random, self).getstate(), self.gauss_next + + def setstate(self, state): + """Restore internal state from object returned by getstate().""" + version = state[0] + if version == 3: + version, internalstate, self.gauss_next = state + super(Random, self).setstate(internalstate) + elif version == 2: + version, internalstate, self.gauss_next = state + # In version 2, the state was saved as signed ints, which causes + # inconsistencies between 32/64-bit systems. The state is + # really unsigned 32-bit ints, so we convert negative ints from + # version 2 to positive longs for version 3. + try: + internalstate = tuple( long(x) % (2**32) for x in internalstate ) + except ValueError, e: + raise TypeError, e + super(Random, self).setstate(internalstate) + else: + raise ValueError("state with version %s passed to " + "Random.setstate() of version %s" % + (version, self.VERSION)) + + def jumpahead(self, n): + """Change the internal state to one that is likely far away + from the current state. This method will not be in Py3.x, + so it is better to simply reseed. + """ + # The super.jumpahead() method uses shuffling to change state, + # so it needs a large and "interesting" n to work with. Here, + # we use hashing to create a large n for the shuffle. + s = repr(n) + repr(self.getstate()) + n = int(_hashlib.new('sha512', s).hexdigest(), 16) + super(Random, self).jumpahead(n) + +## ---- Methods below this point do not need to be overridden when +## ---- subclassing for the purpose of using a different core generator. + +## -------------------- pickle support ------------------- + + def __getstate__(self): # for pickle + return self.getstate() + + def __setstate__(self, state): # for pickle + self.setstate(state) + + def __reduce__(self): + return self.__class__, (), self.getstate() + +## -------------------- integer methods ------------------- + + def randrange(self, start, stop=None, step=1, int=int, default=None, + maxwidth=1L<<BPF): + """Choose a random item from range(start, stop[, step]). + + This fixes the problem with randint() which includes the + endpoint; in Python this is usually not what you want. + Do not supply the 'int', 'default', and 'maxwidth' arguments. + """ + + # This code is a bit messy to make it fast for the + # common case while still doing adequate error checking. + istart = int(start) + if istart != start: + raise ValueError, "non-integer arg 1 for randrange()" + if stop is default: + if istart > 0: + if istart >= maxwidth: + return self._randbelow(istart) + return int(self.random() * istart) + raise ValueError, "empty range for randrange()" + + # stop argument supplied. + istop = int(stop) + if istop != stop: + raise ValueError, "non-integer stop for randrange()" + width = istop - istart + if step == 1 and width > 0: + # Note that + # int(istart + self.random()*width) + # instead would be incorrect. For example, consider istart + # = -2 and istop = 0. Then the guts would be in + # -2.0 to 0.0 exclusive on both ends (ignoring that random() + # might return 0.0), and because int() truncates toward 0, the + # final result would be -1 or 0 (instead of -2 or -1). + # istart + int(self.random()*width) + # would also be incorrect, for a subtler reason: the RHS + # can return a long, and then randrange() would also return + # a long, but we're supposed to return an int (for backward + # compatibility). + + if width >= maxwidth: + return int(istart + self._randbelow(width)) + return int(istart + int(self.random()*width)) + if step == 1: + raise ValueError, "empty range for randrange() (%d,%d, %d)" % (istart, istop, width) + + # Non-unit step argument supplied. + istep = int(step) + if istep != step: + raise ValueError, "non-integer step for randrange()" + if istep > 0: + n = (width + istep - 1) // istep + elif istep < 0: + n = (width + istep + 1) // istep + else: + raise ValueError, "zero step for randrange()" + + if n <= 0: + raise ValueError, "empty range for randrange()" + + if n >= maxwidth: + return istart + istep*self._randbelow(n) + return istart + istep*int(self.random() * n) + + def randint(self, a, b): + """Return random integer in range [a, b], including both end points. + """ + + return self.randrange(a, b+1) + + def _randbelow(self, n, _log=_log, int=int, _maxwidth=1L<<BPF, + _Method=_MethodType, _BuiltinMethod=_BuiltinMethodType): + """Return a random int in the range [0,n) + + Handles the case where n has more bits than returned + by a single call to the underlying generator. + """ + + try: + getrandbits = self.getrandbits + except AttributeError: + pass + else: + # Only call self.getrandbits if the original random() builtin method + # has not been overridden or if a new getrandbits() was supplied. + # This assures that the two methods correspond. + if type(self.random) is _BuiltinMethod or type(getrandbits) is _Method: + k = int(1.00001 + _log(n-1, 2.0)) # 2**k > n-1 > 2**(k-2) + r = getrandbits(k) + while r >= n: + r = getrandbits(k) + return r + if n >= _maxwidth: + _warn("Underlying random() generator does not supply \n" + "enough bits to choose from a population range this large") + return int(self.random() * n) + +## -------------------- sequence methods ------------------- + + def choice(self, seq): + """Choose a random element from a non-empty sequence.""" + return seq[int(self.random() * len(seq))] # raises IndexError if seq is empty + + def shuffle(self, x, random=None, int=int): + """x, random=random.random -> shuffle list x in place; return None. + + Optional arg random is a 0-argument function returning a random + float in [0.0, 1.0); by default, the standard random.random. + """ + + if random is None: + random = self.random + for i in reversed(xrange(1, len(x))): + # pick an element in x[:i+1] with which to exchange x[i] + j = int(random() * (i+1)) + x[i], x[j] = x[j], x[i] + + def sample(self, population, k): + """Chooses k unique random elements from a population sequence. + + Returns a new list containing elements from the population while + leaving the original population unchanged. The resulting list is + in selection order so that all sub-slices will also be valid random + samples. This allows raffle winners (the sample) to be partitioned + into grand prize and second place winners (the subslices). + + Members of the population need not be hashable or unique. If the + population contains repeats, then each occurrence is a possible + selection in the sample. + + To choose a sample in a range of integers, use xrange as an argument. + This is especially fast and space efficient for sampling from a + large population: sample(xrange(10000000), 60) + """ + + # Sampling without replacement entails tracking either potential + # selections (the pool) in a list or previous selections in a set. + + # When the number of selections is small compared to the + # population, then tracking selections is efficient, requiring + # only a small set and an occasional reselection. For + # a larger number of selections, the pool tracking method is + # preferred since the list takes less space than the + # set and it doesn't suffer from frequent reselections. + + n = len(population) + if not 0 <= k <= n: + raise ValueError("sample larger than population") + random = self.random + _int = int + result = [None] * k + setsize = 21 # size of a small set minus size of an empty list + if k > 5: + setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets + if n <= setsize or hasattr(population, "keys"): + # An n-length list is smaller than a k-length set, or this is a + # mapping type so the other algorithm wouldn't work. + pool = list(population) + for i in xrange(k): # invariant: non-selected at [0,n-i) + j = _int(random() * (n-i)) + result[i] = pool[j] + pool[j] = pool[n-i-1] # move non-selected item into vacancy + else: + try: + selected = set() + selected_add = selected.add + for i in xrange(k): + j = _int(random() * n) + while j in selected: + j = _int(random() * n) + selected_add(j) + result[i] = population[j] + except (TypeError, KeyError): # handle (at least) sets + if isinstance(population, list): + raise + return self.sample(tuple(population), k) + return result + +## -------------------- real-valued distributions ------------------- + +## -------------------- uniform distribution ------------------- + + def uniform(self, a, b): + "Get a random number in the range [a, b) or [a, b] depending on rounding." + return a + (b-a) * self.random() + +## -------------------- triangular -------------------- + + def triangular(self, low=0.0, high=1.0, mode=None): + """Triangular distribution. + + Continuous distribution bounded by given lower and upper limits, + and having a given mode value in-between. + + http://en.wikipedia.org/wiki/Triangular_distribution + + """ + u = self.random() + c = 0.5 if mode is None else (mode - low) / (high - low) + if u > c: + u = 1.0 - u + c = 1.0 - c + low, high = high, low + return low + (high - low) * (u * c) ** 0.5 + +## -------------------- normal distribution -------------------- + + def normalvariate(self, mu, sigma): + """Normal distribution. + + mu is the mean, and sigma is the standard deviation. + + """ + # mu = mean, sigma = standard deviation + + # Uses Kinderman and Monahan method. Reference: Kinderman, + # A.J. and Monahan, J.F., "Computer generation of random + # variables using the ratio of uniform deviates", ACM Trans + # Math Software, 3, (1977), pp257-260. + + random = self.random + while 1: + u1 = random() + u2 = 1.0 - random() + z = NV_MAGICCONST*(u1-0.5)/u2 + zz = z*z/4.0 + if zz <= -_log(u2): + break + return mu + z*sigma + +## -------------------- lognormal distribution -------------------- + + def lognormvariate(self, mu, sigma): + """Log normal distribution. + + If you take the natural logarithm of this distribution, you'll get a + normal distribution with mean mu and standard deviation sigma. + mu can have any value, and sigma must be greater than zero. + + """ + return _exp(self.normalvariate(mu, sigma)) + +## -------------------- exponential distribution -------------------- + + def expovariate(self, lambd): + """Exponential distribution. + + lambd is 1.0 divided by the desired mean. It should be + nonzero. (The parameter would be called "lambda", but that is + a reserved word in Python.) Returned values range from 0 to + positive infinity if lambd is positive, and from negative + infinity to 0 if lambd is negative. + + """ + # lambd: rate lambd = 1/mean + # ('lambda' is a Python reserved word) + + # we use 1-random() instead of random() to preclude the + # possibility of taking the log of zero. + return -_log(1.0 - self.random())/lambd + +## -------------------- von Mises distribution -------------------- + + def vonmisesvariate(self, mu, kappa): + """Circular data distribution. + + mu is the mean angle, expressed in radians between 0 and 2*pi, and + kappa is the concentration parameter, which must be greater than or + equal to zero. If kappa is equal to zero, this distribution reduces + to a uniform random angle over the range 0 to 2*pi. + + """ + # mu: mean angle (in radians between 0 and 2*pi) + # kappa: concentration parameter kappa (>= 0) + # if kappa = 0 generate uniform random angle + + # Based upon an algorithm published in: Fisher, N.I., + # "Statistical Analysis of Circular Data", Cambridge + # University Press, 1993. + + # Thanks to Magnus Kessler for a correction to the + # implementation of step 4. + + random = self.random + if kappa <= 1e-6: + return TWOPI * random() + + s = 0.5 / kappa + r = s + _sqrt(1.0 + s * s) + + while 1: + u1 = random() + z = _cos(_pi * u1) + + d = z / (r + z) + u2 = random() + if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d): + break + + q = 1.0 / r + f = (q + z) / (1.0 + q * z) + u3 = random() + if u3 > 0.5: + theta = (mu + _acos(f)) % TWOPI + else: + theta = (mu - _acos(f)) % TWOPI + + return theta + +## -------------------- gamma distribution -------------------- + + def gammavariate(self, alpha, beta): + """Gamma distribution. Not the gamma function! + + Conditions on the parameters are alpha > 0 and beta > 0. + + The probability distribution function is: + + x ** (alpha - 1) * math.exp(-x / beta) + pdf(x) = -------------------------------------- + math.gamma(alpha) * beta ** alpha + + """ + + # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2 + + # Warning: a few older sources define the gamma distribution in terms + # of alpha > -1.0 + if alpha <= 0.0 or beta <= 0.0: + raise ValueError, 'gammavariate: alpha and beta must be > 0.0' + + random = self.random + if alpha > 1.0: + + # Uses R.C.H. Cheng, "The generation of Gamma + # variables with non-integral shape parameters", + # Applied Statistics, (1977), 26, No. 1, p71-74 + + ainv = _sqrt(2.0 * alpha - 1.0) + bbb = alpha - LOG4 + ccc = alpha + ainv + + while 1: + u1 = random() + if not 1e-7 < u1 < .9999999: + continue + u2 = 1.0 - random() + v = _log(u1/(1.0-u1))/ainv + x = alpha*_exp(v) + z = u1*u1*u2 + r = bbb+ccc*v-x + if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z): + return x * beta + + elif alpha == 1.0: + # expovariate(1) + u = random() + while u <= 1e-7: + u = random() + return -_log(u) * beta + + else: # alpha is between 0 and 1 (exclusive) + + # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle + + while 1: + u = random() + b = (_e + alpha)/_e + p = b*u + if p <= 1.0: + x = p ** (1.0/alpha) + else: + x = -_log((b-p)/alpha) + u1 = random() + if p > 1.0: + if u1 <= x ** (alpha - 1.0): + break + elif u1 <= _exp(-x): + break + return x * beta + +## -------------------- Gauss (faster alternative) -------------------- + + def gauss(self, mu, sigma): + """Gaussian distribution. + + mu is the mean, and sigma is the standard deviation. This is + slightly faster than the normalvariate() function. + + Not thread-safe without a lock around calls. + + """ + + # When x and y are two variables from [0, 1), uniformly + # distributed, then + # + # cos(2*pi*x)*sqrt(-2*log(1-y)) + # sin(2*pi*x)*sqrt(-2*log(1-y)) + # + # are two *independent* variables with normal distribution + # (mu = 0, sigma = 1). + # (Lambert Meertens) + # (corrected version; bug discovered by Mike Miller, fixed by LM) + + # Multithreading note: When two threads call this function + # simultaneously, it is possible that they will receive the + # same return value. The window is very small though. To + # avoid this, you have to use a lock around all calls. (I + # didn't want to slow this down in the serial case by using a + # lock here.) + + random = self.random + z = self.gauss_next + self.gauss_next = None + if z is None: + x2pi = random() * TWOPI + g2rad = _sqrt(-2.0 * _log(1.0 - random())) + z = _cos(x2pi) * g2rad + self.gauss_next = _sin(x2pi) * g2rad + + return mu + z*sigma + +## -------------------- beta -------------------- +## See +## http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html +## for Ivan Frohne's insightful analysis of why the original implementation: +## +## def betavariate(self, alpha, beta): +## # Discrete Event Simulation in C, pp 87-88. +## +## y = self.expovariate(alpha) +## z = self.expovariate(1.0/beta) +## return z/(y+z) +## +## was dead wrong, and how it probably got that way. + + def betavariate(self, alpha, beta): + """Beta distribution. + + Conditions on the parameters are alpha > 0 and beta > 0. + Returned values range between 0 and 1. + + """ + + # This version due to Janne Sinkkonen, and matches all the std + # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution"). + y = self.gammavariate(alpha, 1.) + if y == 0: + return 0.0 + else: + return y / (y + self.gammavariate(beta, 1.)) + +## -------------------- Pareto -------------------- + + def paretovariate(self, alpha): + """Pareto distribution. alpha is the shape parameter.""" + # Jain, pg. 495 + + u = 1.0 - self.random() + return 1.0 / pow(u, 1.0/alpha) + +## -------------------- Weibull -------------------- + + def weibullvariate(self, alpha, beta): + """Weibull distribution. + + alpha is the scale parameter and beta is the shape parameter. + + """ + # Jain, pg. 499; bug fix courtesy Bill Arms + + u = 1.0 - self.random() + return alpha * pow(-_log(u), 1.0/beta) + +## -------------------- Wichmann-Hill ------------------- + +class WichmannHill(Random): + + VERSION = 1 # used by getstate/setstate + + def seed(self, a=None): + """Initialize internal state from hashable object. + + None or no argument seeds from current time or from an operating + system specific randomness source if available. + + If a is not None or an int or long, hash(a) is used instead. + + If a is an int or long, a is used directly. Distinct values between + 0 and 27814431486575L inclusive are guaranteed to yield distinct + internal states (this guarantee is specific to the default + Wichmann-Hill generator). + """ + + if a is None: + try: + a = long(_hexlify(_urandom(16)), 16) + except NotImplementedError: + import time + a = long(time.time() * 256) # use fractional seconds + + if not isinstance(a, (int, long)): + a = hash(a) + + a, x = divmod(a, 30268) + a, y = divmod(a, 30306) + a, z = divmod(a, 30322) + self._seed = int(x)+1, int(y)+1, int(z)+1 + + self.gauss_next = None + + def random(self): + """Get the next random number in the range [0.0, 1.0).""" + + # Wichman-Hill random number generator. + # + # Wichmann, B. A. & Hill, I. D. (1982) + # Algorithm AS 183: + # An efficient and portable pseudo-random number generator + # Applied Statistics 31 (1982) 188-190 + # + # see also: + # Correction to Algorithm AS 183 + # Applied Statistics 33 (1984) 123 + # + # McLeod, A. I. (1985) + # A remark on Algorithm AS 183 + # Applied Statistics 34 (1985),198-200 + + # This part is thread-unsafe: + # BEGIN CRITICAL SECTION + x, y, z = self._seed + x = (171 * x) % 30269 + y = (172 * y) % 30307 + z = (170 * z) % 30323 + self._seed = x, y, z + # END CRITICAL SECTION + + # Note: on a platform using IEEE-754 double arithmetic, this can + # never return 0.0 (asserted by Tim; proof too long for a comment). + return (x/30269.0 + y/30307.0 + z/30323.0) % 1.0 + + def getstate(self): + """Return internal state; can be passed to setstate() later.""" + return self.VERSION, self._seed, self.gauss_next + + def setstate(self, state): + """Restore internal state from object returned by getstate().""" + version = state[0] + if version == 1: + version, self._seed, self.gauss_next = state + else: + raise ValueError("state with version %s passed to " + "Random.setstate() of version %s" % + (version, self.VERSION)) + + def jumpahead(self, n): + """Act as if n calls to random() were made, but quickly. + + n is an int, greater than or equal to 0. + + Example use: If you have 2 threads and know that each will + consume no more than a million random numbers, create two Random + objects r1 and r2, then do + r2.setstate(r1.getstate()) + r2.jumpahead(1000000) + Then r1 and r2 will use guaranteed-disjoint segments of the full + period. + """ + + if not n >= 0: + raise ValueError("n must be >= 0") + x, y, z = self._seed + x = int(x * pow(171, n, 30269)) % 30269 + y = int(y * pow(172, n, 30307)) % 30307 + z = int(z * pow(170, n, 30323)) % 30323 + self._seed = x, y, z + + def __whseed(self, x=0, y=0, z=0): + """Set the Wichmann-Hill seed from (x, y, z). + + These must be integers in the range [0, 256). + """ + + if not type(x) == type(y) == type(z) == int: + raise TypeError('seeds must be integers') + if not (0 <= x < 256 and 0 <= y < 256 and 0 <= z < 256): + raise ValueError('seeds must be in range(0, 256)') + if 0 == x == y == z: + # Initialize from current time + import time + t = long(time.time() * 256) + t = int((t&0xffffff) ^ (t>>24)) + t, x = divmod(t, 256) + t, y = divmod(t, 256) + t, z = divmod(t, 256) + # Zero is a poor seed, so substitute 1 + self._seed = (x or 1, y or 1, z or 1) + + self.gauss_next = None + + def whseed(self, a=None): + """Seed from hashable object's hash code. + + None or no argument seeds from current time. It is not guaranteed + that objects with distinct hash codes lead to distinct internal + states. + + This is obsolete, provided for compatibility with the seed routine + used prior to Python 2.1. Use the .seed() method instead. + """ + + if a is None: + self.__whseed() + return + a = hash(a) + a, x = divmod(a, 256) + a, y = divmod(a, 256) + a, z = divmod(a, 256) + x = (x + a) % 256 or 1 + y = (y + a) % 256 or 1 + z = (z + a) % 256 or 1 + self.__whseed(x, y, z) + +## --------------- Operating System Random Source ------------------ + +class SystemRandom(Random): + """Alternate random number generator using sources provided + by the operating system (such as /dev/urandom on Unix or + CryptGenRandom on Windows). + + Not available on all systems (see os.urandom() for details). + """ + + def random(self): + """Get the next random number in the range [0.0, 1.0).""" + return (long(_hexlify(_urandom(7)), 16) >> 3) * RECIP_BPF + + def getrandbits(self, k): + """getrandbits(k) -> x. Generates a long int with k random bits.""" + if k <= 0: + raise ValueError('number of bits must be greater than zero') + if k != int(k): + raise TypeError('number of bits should be an integer') + bytes = (k + 7) // 8 # bits / 8 and rounded up + x = long(_hexlify(_urandom(bytes)), 16) + return x >> (bytes * 8 - k) # trim excess bits + + def _stub(self, *args, **kwds): + "Stub method. Not used for a system random number generator." + return None + seed = jumpahead = _stub + + def _notimplemented(self, *args, **kwds): + "Method should not be called for a system random number generator." + raise NotImplementedError('System entropy source does not have state.') + getstate = setstate = _notimplemented + +## -------------------- test program -------------------- + +def _test_generator(n, func, args): + import time + print n, 'times', func.__name__ + total = 0.0 + sqsum = 0.0 + smallest = 1e10 + largest = -1e10 + t0 = time.time() + for i in range(n): + x = func(*args) + total += x + sqsum = sqsum + x*x + smallest = min(x, smallest) + largest = max(x, largest) + t1 = time.time() + print round(t1-t0, 3), 'sec,', + avg = total/n + stddev = _sqrt(sqsum/n - avg*avg) + print 'avg %g, stddev %g, min %g, max %g' % \ + (avg, stddev, smallest, largest) + + +def _test(N=2000): + _test_generator(N, random, ()) + _test_generator(N, normalvariate, (0.0, 1.0)) + _test_generator(N, lognormvariate, (0.0, 1.0)) + _test_generator(N, vonmisesvariate, (0.0, 1.0)) + _test_generator(N, gammavariate, (0.01, 1.0)) + _test_generator(N, gammavariate, (0.1, 1.0)) + _test_generator(N, gammavariate, (0.1, 2.0)) + _test_generator(N, gammavariate, (0.5, 1.0)) + _test_generator(N, gammavariate, (0.9, 1.0)) + _test_generator(N, gammavariate, (1.0, 1.0)) + _test_generator(N, gammavariate, (2.0, 1.0)) + _test_generator(N, gammavariate, (20.0, 1.0)) + _test_generator(N, gammavariate, (200.0, 1.0)) + _test_generator(N, gauss, (0.0, 1.0)) + _test_generator(N, betavariate, (3.0, 3.0)) + _test_generator(N, triangular, (0.0, 1.0, 1.0/3.0)) + +# Create one instance, seeded from current time, and export its methods +# as module-level functions. The functions share state across all uses +#(both in the user's code and in the Python libraries), but that's fine +# for most programs and is easier for the casual user than making them +# instantiate their own Random() instance. + +_inst = Random() +seed = _inst.seed +random = _inst.random +uniform = _inst.uniform +triangular = _inst.triangular +randint = _inst.randint +choice = _inst.choice +randrange = _inst.randrange +sample = _inst.sample +shuffle = _inst.shuffle +normalvariate = _inst.normalvariate +lognormvariate = _inst.lognormvariate +expovariate = _inst.expovariate +vonmisesvariate = _inst.vonmisesvariate +gammavariate = _inst.gammavariate +gauss = _inst.gauss +betavariate = _inst.betavariate +paretovariate = _inst.paretovariate +weibullvariate = _inst.weibullvariate +getstate = _inst.getstate +setstate = _inst.setstate +jumpahead = _inst.jumpahead +getrandbits = _inst.getrandbits + +if __name__ == '__main__': + _test() |