python3标准库random模块

傷城~ 2022-05-11 06:12 486阅读 0赞

# 1.random模块源代码 #

"""Random variable generators.
    随机变量生成器
    
        integers
        --------
               uniform within range
    
        sequences
        ---------
               pick random element          # 选择随机元素
               pick random sample           # 选择随机样本
               pick weighted random sample  # 随机抽样
               generate random permutation  # 产生随机序列
    
        distributions on the real line:
    包含的重要分布
        ------------------------------
               uniform              # 均匀分布
               triangular           # 三角形分布
               normal (Gaussian)    # 正态分布
               lognormal            # 对数正态分布
               negative exponential # 负指数分布（指数分布）
               gamma                # gamma分布
               beta                 # β分布
               pareto               # 帕累托函数
               Weibull              # 韦布尔函数
    
        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.
    * The random() method is implemented in C, executes in a single Python step,
      and is, therefore, threadsafe.
    
    """
    
    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 _collections_abc import Set as _Set, Sequence as _Sequence
    from hashlib import sha512 as _sha512
    import itertools as _itertools
    import bisect as _bisect
    
    __all__ = ["Random","seed","random","uniform","randint","choice","sample",
               "randrange","shuffle","normalvariate","lognormvariate",
               "expovariate","vonmisesvariate","gammavariate","triangular",
               "gauss","betavariate","paretovariate","weibullvariate",
               "getstate","setstate", "getrandbits", "choices",
               "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.
    随机数生成器基类用于绑定模块函数
        Used to instantiate instances of Random to get generators that don't
        share state.
    
        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(), and setstate().
        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, version=2):
            """Initialize internal state from hashable object.
            随机数种子生成器。生成的随机数与seed中整数值相同
            None or no argument seeds from current time or from an operating
            system specific randomness source if available.
    
            If *a* is an int, all bits are used.
    
            For version 2 (the default), all of the bits are used if *a* is a str,
            bytes, or bytearray.  For version 1 (provided for reproducing random
            sequences from older versions of Python), the algorithm for str and
            bytes generates a narrower range of seeds.
    
            """
    
            if version == 1 and isinstance(a, (str, bytes)):
                a = a.decode('latin-1') if isinstance(a, bytes) else a
                x = ord(a[0]) << 7 if a else 0
                for c in map(ord, a):
                    x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF
                x ^= len(a)
                a = -2 if x == -1 else x
    
            if version == 2 and isinstance(a, (str, bytes, bytearray)):
                if isinstance(a, str):
                    a = a.encode()
                a += _sha512(a).digest()
                a = int.from_bytes(a, 'big')
    
            super().seed(a)
            self.gauss_next = None
    
        def getstate(self):
            """Return internal state; can be passed to setstate() later."""
            return self.VERSION, super().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().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(x % (2**32) for x in internalstate)
                except ValueError as e:
                    raise TypeError from e
                super().setstate(internalstate)
            else:
                raise ValueError("state with version %s passed to "
                                 "Random.setstate() of version %s" %
                                 (version, self.VERSION))
    
    ## ---- Methods below this point do not need to be overridden when
    ## ---- subclassing for the purpose of using a different core generator.
    
    ## -------------------- pickle support  -------------------
    
        # Issue 17489: Since __reduce__ was defined to fix #759889 this is no
        # longer called; we leave it here because it has been here since random was
        # rewritten back in 2001 and why risk breaking something.
        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):
            """Choose a random item from range(start, stop[, step]).
            从[a, b)内按照制定的step选择元素组成一个集合，并从集合中随机选择一个数
            This fixes the problem with randint() which includes the
            endpoint; in Python this is usually not what you want.
    
            """
    
            # 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 None:
                if istart > 0:
                    return self._randbelow(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:
                return istart + self._randbelow(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()")
    
            return istart + istep*self._randbelow(n)
    
        def randint(self, a, b):
            """Return random integer in range [a, b], including both end points.
            """
            [a, b]中随机选择一个整数
    
            return self.randrange(a, b+1)
    
        def _randbelow(self, n, int=int, maxsize=1<<BPF, type=type,
                       Method=_MethodType, BuiltinMethod=_BuiltinMethodType):
            "Return a random int in the range [0,n).  Raises ValueError if n==0."
    
            random = self.random
            getrandbits = self.getrandbits
            # Only call self.getrandbits if the original random() builtin method
            # has not been overridden or if a new getrandbits() was supplied.
            if type(random) is BuiltinMethod or type(getrandbits) is Method:
                k = n.bit_length()  # don't use (n-1) here because n can be 1
                r = getrandbits(k)          # 0 <= r < 2**k
                while r >= n:
                    r = getrandbits(k)
                return r
            # There's an overridden random() method but no new getrandbits() method,
            # so we can only use random() from here.
            if n >= maxsize:
                _warn("Underlying random() generator does not supply \n"
                    "enough bits to choose from a population range this large.\n"
                    "To remove the range limitation, add a getrandbits() method.")
                return int(random() * n)
            rem = maxsize % n
            limit = (maxsize - rem) / maxsize   # int(limit * maxsize) % n == 0
            r = random()
            while r >= limit:
                r = random()
            return int(r*maxsize) % n
    
    ## -------------------- sequence methods  -------------------
    
        def choice(self, seq):
            """Choose a random element from a non-empty sequence."""
            从非空序列中选择一个元素（list,tuple,字符串）
            try:
                i = self._randbelow(len(seq))
            except ValueError:
                raise IndexError('Cannot choose from an empty sequence') from None
            return seq[i]
    
        def shuffle(self, x, random=None):
            """Shuffle list x in place, and return None.
            打乱list顺序,并不生成新列表
    
            Optional argument random is a 0-argument function returning a
            random float in [0.0, 1.0); if it is the default None, the
            standard random.random will be used.
    
            """
    
            if random is None:
                randbelow = self._randbelow
                for i in reversed(range(1, len(x))):
                    # pick an element in x[:i+1] with which to exchange x[i]
                    j = randbelow(i+1)
                    x[i], x[j] = x[j], x[i]
            else:
                _int = int
                for i in reversed(range(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 or set.
            从列表、元组或集合中随机抽取k个样本，输出列表
    
            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 range as an argument.
            This is especially fast and space efficient for sampling from a
            large population:   sample(range(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.
    
            if isinstance(population, _Set):
                population = tuple(population)
            if not isinstance(population, _Sequence):
                raise TypeError("Population must be a sequence or set.  For dicts, use list(d).")
            randbelow = self._randbelow
            n = len(population)
            if not 0 <= k <= n:
                raise ValueError("Sample larger than population or is negative")
            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:
                # An n-length list is smaller than a k-length set
                pool = list(population)
                for i in range(k):         # invariant:  non-selected at [0,n-i)
                    j = randbelow(n-i)
                    result[i] = pool[j]
                    pool[j] = pool[n-i-1]   # move non-selected item into vacancy
            else:
                selected = set()
                selected_add = selected.add
                for i in range(k):
                    j = randbelow(n)
                    while j in selected:
                        j = randbelow(n)
                    selected_add(j)
                    result[i] = population[j]
            return result
    
        def choices(self, population, weights=None, *, cum_weights=None, k=1):
            """Return a k sized list of population elements chosen with replacement.
            与choice相比，能够设计权重和选随机数的个数
            If the relative weights or cumulative weights are not specified,
            the selections are made with equal probability.
    
            """
            random = self.random
            if cum_weights is None:
                if weights is None:
                    _int = int
                    total = len(population)
                    return [population[_int(random() * total)] for i in range(k)]
                cum_weights = list(_itertools.accumulate(weights))
            elif weights is not None:
                raise TypeError('Cannot specify both weights and cumulative weights')
            if len(cum_weights) != len(population):
                raise ValueError('The number of weights does not match the population')
            bisect = _bisect.bisect
            total = cum_weights[-1]
            return [population[bisect(cum_weights, random() * total)] for i in range(k)]
    
    ## -------------------- 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."
            根据四舍五入在[a, b]或[a, b)内选择一个随机数
            return a + (b-a) * self.random()
    
    ## -------------------- triangular --------------------
    
        def triangular(self, low=0.0, high=1.0, mode=None):
            """Triangular distribution.
            三角形分布随机数
            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()
            try:
                c = 0.5 if mode is None else (mode - low) / (high - low)
            except ZeroDivisionError:
                return 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.
            生成正态分布随机数
    
            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.
            对数正态分布随机数
            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.
            指数分布随机数
            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.
            循环数据分布。mu:平均角度，位于0~2Pi之间； kappa:浓度参数>=0,如果=0， 该分布会成为0~2Pi之间的随机角度
    
            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!
            伽马分布。并不是伽马函数。
            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.
            高斯分布随机数。效率高于normalvariate()
    
            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.
            β分布
    
            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, 1.0)
            if y == 0:
                return 0.0
            else:
                return y / (y + self.gammavariate(beta, 1.0))
    
    ## -------------------- Pareto --------------------
    
        def paretovariate(self, alpha):
            """Pareto distribution.  alpha is the shape parameter."""
            帕累托分布
            # Jain, pg. 495
    
            u = 1.0 - self.random()
            return 1.0 / u ** (1.0/alpha)
    
    ## -------------------- Weibull --------------------
    
        def weibullvariate(self, alpha, beta):
            """Weibull distribution.
            韦布尔分布
    
            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 * (-_log(u)) ** (1.0/beta)
    
    ## --------------- Operating System Random Source  ------------------
    操作系统随机源
    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).
         使用操作系统提供的源替代随机数生成器。其并不能再所有操作系统中使用。
        """
    
        def random(self):
            """Get the next random number in the range [0.0, 1.0)."""
            return (int.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF
    
        def getrandbits(self, k):
            """getrandbits(k) -> x.  Generates an 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')
            numbytes = (k + 7) // 8                       # bits / 8 and rounded up
            x = int.from_bytes(_urandom(numbytes), 'big')
            return x >> (numbytes * 8 - k)                # trim excess bits
    
        def seed(self, *args, **kwds):
            "Stub method.  Not used for a system random number generator."
            return None
    
        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 --------------------
    测试程序
    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,', end=' ')
        avg = total/n
        stddev = _sqrt(sqsum/n - avg*avg)
        print('avg %g, stddev %g, min %g, max %g\n' % \
                  (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.
    
    此处的目的是为了简化操作，将Random类的方法的地址赋值给了对应的名称，调用方式变得简单； random.Random.random() == random.random()
    _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
    choices = _inst.choices
    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
    getrandbits = _inst.getrandbits
    
    if __name__ == '__main__':
        _test()

# 2.random模块的常见用法 #

# ! /usr/bin/env python
    # coding:utf-8
    # python interpreter:3.6.2
    # author: admin_maxin
    import random
    
    # random.random()用于生成一个0到1的随机符点数: 0 <= n < 1.0
    print(random.random())
    
    # random.randint()的函数原型为：random.randint(a, b)，用于生成一个指定范围内的整数。
    print(random.randint(1, 7))
    
    # 其中参数a是下限，参数b是上限，生成的随机数n: a <= n <= b
    print(random.randrange(1, 10))
    # random.randrange的函数原型为：random.randrange([start], stop[, step])，
    # 从指定范围内，按指定基数递增的集合中 获取一个随机数。如：random.randrange(10, 100, 2)，
    # 结果相当于从[10, 12, 14, 16, ... 96, 98]序列中获取一个随机数。
    # random.randrange(10, 100, 2)在结果上与 random.choice(range(10, 100, 2) 等效。
    
    # random.choice从序列中获取一个随机元素。
    # 其函数原型为：random.choice(sequence)。参数sequence表示一个有序类型。
    # 这里要说明一下：sequence在python不是一种特定的类型，而是泛指一系列的类型。
    # list, tuple, 字符串都属于sequence。
    print(random.choice('liukuni'))
    
    # 下面是使用choice的一些例子：
    print(random.choice("学习Python"))
    print(random.choice(["JGood", "is", "a", "handsome", "boy"]))
    print(random.choice(("Tuple", "List", "Dict")))
    
    # random.sample的函数原型为：random.sample(sequence, k)，从指定序列中随机获取指定长度的片断。sample函数不会修改原有序列。
    print(random.sample([1, 2, 3, 4, 5], 3))

# 3.random模块的实际应用 #

> 简单的6位验证码实现

import random
    
    
    checkcode = ""
    for i in range(6):
        current = random.randrange(0, 6)
        if current == i:
            tmp = chr(random.randint(65, 90))
        else:
            tmp = random.randint(0, 9)
        checkcode += str(tmp)
    
    print(checkcode)