2 :mod:`random` --- Generate pseudo-random numbers
3 ================================================
6 :synopsis: Generate pseudo-random numbers with various common distributions.
9 This module implements pseudo-random number generators for various
12 For integers, uniform selection from a range. For sequences, uniform selection
13 of a random element, a function to generate a random permutation of a list
14 in-place, and a function for random sampling without replacement.
16 On the real line, there are functions to compute uniform, normal (Gaussian),
17 lognormal, negative exponential, gamma, and beta distributions. For generating
18 distributions of angles, the von Mises distribution is available.
20 Almost all module functions depend on the basic function :func:`random`, which
21 generates a random float uniformly in the semi-open range [0.0, 1.0). Python
22 uses the Mersenne Twister as the core generator. It produces 53-bit precision
23 floats and has a period of 2\*\*19937-1. The underlying implementation in C is
24 both fast and threadsafe. The Mersenne Twister is one of the most extensively
25 tested random number generators in existence. However, being completely
26 deterministic, it is not suitable for all purposes, and is completely unsuitable
27 for cryptographic purposes.
29 The functions supplied by this module are actually bound methods of a hidden
30 instance of the :class:`random.Random` class. You can instantiate your own
31 instances of :class:`Random` to get generators that don't share state. This is
32 especially useful for multi-threaded programs, creating a different instance of
33 :class:`Random` for each thread, and using the :meth:`jumpahead` method to make
34 it likely that the generated sequences seen by each thread don't overlap.
36 Class :class:`Random` can also be subclassed if you want to use a different
37 basic generator of your own devising: in that case, override the :meth:`random`,
38 :meth:`seed`, :meth:`getstate`, :meth:`setstate` and :meth:`jumpahead` methods.
39 Optionally, a new generator can supply a :meth:`getrandombits` method --- this
40 allows :meth:`randrange` to produce selections over an arbitrarily large range.
43 the :meth:`getrandombits` method.
45 As an example of subclassing, the :mod:`random` module provides the
46 :class:`WichmannHill` class that implements an alternative generator in pure
47 Python. The class provides a backward compatible way to reproduce results from
48 earlier versions of Python, which used the Wichmann-Hill algorithm as the core
49 generator. Note that this Wichmann-Hill generator can no longer be recommended:
50 its period is too short by contemporary standards, and the sequence generated is
51 known to fail some stringent randomness tests. See the references below for a
52 recent variant that repairs these flaws.
54 .. versionchanged:: 2.3
55 Substituted MersenneTwister for Wichmann-Hill.
57 Bookkeeping functions:
60 .. function:: seed([x])
62 Initialize the basic random number generator. Optional argument *x* can be any
63 :term:`hashable` object. If *x* is omitted or ``None``, current system time is used;
64 current system time is also used to initialize the generator when the module is
65 first imported. If randomness sources are provided by the operating system,
66 they are used instead of the system time (see the :func:`os.urandom` function
67 for details on availability).
69 .. versionchanged:: 2.4
70 formerly, operating system resources were not used.
72 If *x* is not ``None`` or an int or long, ``hash(x)`` is used instead. If *x* is
73 an int or long, *x* is used directly.
76 .. function:: getstate()
78 Return an object capturing the current internal state of the generator. This
79 object can be passed to :func:`setstate` to restore the state.
83 .. versionchanged:: 2.6
84 State values produced in Python 2.6 cannot be loaded into earlier versions.
87 .. function:: setstate(state)
89 *state* should have been obtained from a previous call to :func:`getstate`, and
90 :func:`setstate` restores the internal state of the generator to what it was at
91 the time :func:`setstate` was called.
96 .. function:: jumpahead(n)
98 Change the internal state to one different from and likely far away from the
99 current state. *n* is a non-negative integer which is used to scramble the
100 current state vector. This is most useful in multi-threaded programs, in
101 conjunction with multiple instances of the :class:`Random` class:
102 :meth:`setstate` or :meth:`seed` can be used to force all instances into the
103 same internal state, and then :meth:`jumpahead` can be used to force the
104 instances' states far apart.
106 .. versionadded:: 2.1
108 .. versionchanged:: 2.3
109 Instead of jumping to a specific state, *n* steps ahead, ``jumpahead(n)``
110 jumps to another state likely to be separated by many steps.
113 .. function:: getrandbits(k)
115 Returns a python :class:`long` int with *k* random bits. This method is supplied
116 with the MersenneTwister generator and some other generators may also provide it
117 as an optional part of the API. When available, :meth:`getrandbits` enables
118 :meth:`randrange` to handle arbitrarily large ranges.
120 .. versionadded:: 2.4
122 Functions for integers:
125 .. function:: randrange([start,] stop[, step])
127 Return a randomly selected element from ``range(start, stop, step)``. This is
128 equivalent to ``choice(range(start, stop, step))``, but doesn't actually build a
131 .. versionadded:: 1.5.2
134 .. function:: randint(a, b)
136 Return a random integer *N* such that ``a <= N <= b``.
138 Functions for sequences:
141 .. function:: choice(seq)
143 Return a random element from the non-empty sequence *seq*. If *seq* is empty,
144 raises :exc:`IndexError`.
147 .. function:: shuffle(x[, random])
149 Shuffle the sequence *x* in place. The optional argument *random* is a
150 0-argument function returning a random float in [0.0, 1.0); by default, this is
151 the function :func:`random`.
153 Note that for even rather small ``len(x)``, the total number of permutations of
154 *x* is larger than the period of most random number generators; this implies
155 that most permutations of a long sequence can never be generated.
158 .. function:: sample(population, k)
160 Return a *k* length list of unique elements chosen from the population sequence.
161 Used for random sampling without replacement.
163 .. versionadded:: 2.3
165 Returns a new list containing elements from the population while leaving the
166 original population unchanged. The resulting list is in selection order so that
167 all sub-slices will also be valid random samples. This allows raffle winners
168 (the sample) to be partitioned into grand prize and second place winners (the
171 Members of the population need not be :term:`hashable` or unique. If the population
172 contains repeats, then each occurrence is a possible selection in the sample.
174 To choose a sample from a range of integers, use an :func:`xrange` object as an
175 argument. This is especially fast and space efficient for sampling from a large
176 population: ``sample(xrange(10000000), 60)``.
178 The following functions generate specific real-valued distributions. Function
179 parameters are named after the corresponding variables in the distribution's
180 equation, as used in common mathematical practice; most of these equations can
181 be found in any statistics text.
184 .. function:: random()
186 Return the next random floating point number in the range [0.0, 1.0).
189 .. function:: uniform(a, b)
191 Return a random floating point number *N* such that ``a <= N < b``.
193 .. function:: triangular(low, high, mode)
195 Return a random floating point number *N* such that ``low <= N < high`` and
196 with the specified *mode* between those bounds. The *low* and *high* bounds
197 default to zero and one. The *mode* argument defaults to the midpoint
198 between the bounds, giving a symmetric distribution.
200 .. versionadded:: 2.6
203 .. function:: betavariate(alpha, beta)
205 Beta distribution. Conditions on the parameters are ``alpha > 0`` and ``beta >
206 0``. Returned values range between 0 and 1.
209 .. function:: expovariate(lambd)
211 Exponential distribution. *lambd* is 1.0 divided by the desired mean. (The
212 parameter would be called "lambda", but that is a reserved word in Python.)
213 Returned values range from 0 to positive infinity.
216 .. function:: gammavariate(alpha, beta)
218 Gamma distribution. (*Not* the gamma function!) Conditions on the parameters
219 are ``alpha > 0`` and ``beta > 0``.
222 .. function:: gauss(mu, sigma)
224 Gaussian distribution. *mu* is the mean, and *sigma* is the standard deviation.
225 This is slightly faster than the :func:`normalvariate` function defined below.
228 .. function:: lognormvariate(mu, sigma)
230 Log normal distribution. If you take the natural logarithm of this
231 distribution, you'll get a normal distribution with mean *mu* and standard
232 deviation *sigma*. *mu* can have any value, and *sigma* must be greater than
236 .. function:: normalvariate(mu, sigma)
238 Normal distribution. *mu* is the mean, and *sigma* is the standard deviation.
241 .. function:: vonmisesvariate(mu, kappa)
243 *mu* is the mean angle, expressed in radians between 0 and 2\*\ *pi*, and *kappa*
244 is the concentration parameter, which must be greater than or equal to zero. If
245 *kappa* is equal to zero, this distribution reduces to a uniform random angle
246 over the range 0 to 2\*\ *pi*.
249 .. function:: paretovariate(alpha)
251 Pareto distribution. *alpha* is the shape parameter.
254 .. function:: weibullvariate(alpha, beta)
256 Weibull distribution. *alpha* is the scale parameter and *beta* is the shape
260 Alternative Generators:
262 .. class:: WichmannHill([seed])
264 Class that implements the Wichmann-Hill algorithm as the core generator. Has all
265 of the same methods as :class:`Random` plus the :meth:`whseed` method described
266 below. Because this class is implemented in pure Python, it is not threadsafe
267 and may require locks between calls. The period of the generator is
268 6,953,607,871,644 which is small enough to require care that two independent
269 random sequences do not overlap.
272 .. function:: whseed([x])
274 This is obsolete, supplied for bit-level compatibility with versions of Python
275 prior to 2.1. See :func:`seed` for details. :func:`whseed` does not guarantee
276 that distinct integer arguments yield distinct internal states, and can yield no
277 more than about 2\*\*24 distinct internal states in all.
280 .. class:: SystemRandom([seed])
282 Class that uses the :func:`os.urandom` function for generating random numbers
283 from sources provided by the operating system. Not available on all systems.
284 Does not rely on software state and sequences are not reproducible. Accordingly,
285 the :meth:`seed` and :meth:`jumpahead` methods have no effect and are ignored.
286 The :meth:`getstate` and :meth:`setstate` methods raise
287 :exc:`NotImplementedError` if called.
289 .. versionadded:: 2.4
291 Examples of basic usage::
293 >>> random.random() # Random float x, 0.0 <= x < 1.0
295 >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0
297 >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included
299 >>> random.randrange(0, 101, 2) # Even integer from 0 to 100
301 >>> random.choice('abcdefghij') # Choose a random element
304 >>> items = [1, 2, 3, 4, 5, 6, 7]
305 >>> random.shuffle(items)
307 [7, 3, 2, 5, 6, 4, 1]
309 >>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements
316 M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally
317 equidistributed uniform pseudorandom number generator", ACM Transactions on
318 Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998.
320 Wichmann, B. A. & Hill, I. D., "Algorithm AS 183: An efficient and portable
321 pseudo-random number generator", Applied Statistics 31 (1982) 188-190.