9.6. random
— Generate pseudorandom numbers¶
Source code: Lib/random.py
This module implements pseudorandom number generators for various distributions.
For integers, uniform selection from a range. For sequences, uniform selection of a random element, a function to generate a random permutation of a list inplace, and a function for random sampling without replacement.
On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.
Almost all module functions depend on the basic function random()
, which
generates a random float uniformly in the semiopen range [0.0, 1.0). Python
uses the Mersenne Twister as the core generator. It produces 53bit precision
floats and has a period of 2**199371. The underlying implementation in C is
both fast and threadsafe. The Mersenne Twister is one of the most extensively
tested random number generators in existence. However, being completely
deterministic, it is not suitable for all purposes, and is completely unsuitable
for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden
instance of the random.Random
class. You can instantiate your own
instances of Random
to get generators that don’t share state. This is
especially useful for multithreaded programs, creating a different instance of
Random
for each thread, and using the jumpahead()
method to make
it likely 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 random()
,
seed()
, getstate()
, setstate()
and
jumpahead()
methods. Optionally, a new generator can supply a
getrandbits()
method — this
allows randrange()
to produce selections over an arbitrarily large range.
New in version 2.4: the getrandbits()
method.
As an example of subclassing, the random
module provides the
WichmannHill
class that implements an alternative generator in pure
Python. The class provides a backward compatible way to reproduce results from
earlier versions of Python, which used the WichmannHill algorithm as the core
generator. Note that this WichmannHill generator can no longer be recommended:
its period is too short by contemporary standards, and the sequence generated is
known to fail some stringent randomness tests. See the references below for a
recent variant that repairs these flaws.
Changed in version 2.3: MersenneTwister replaced WichmannHill as the default generator.
The random
module also provides the SystemRandom
class which
uses the system function os.urandom()
to generate random numbers
from sources provided by the operating system.
Warning
The pseudorandom generators of this module should not be used for
security purposes. Use os.urandom()
or SystemRandom
if
you require a cryptographically secure pseudorandom number generator.
Bookkeeping functions:

random.
seed
(a=None)¶ Initialize internal state of the random number generator.
None
or no argument seeds from current time or from an operating system specific randomness source if available (see theos.urandom()
function for details on availability).If a is not
None
or anint
or along
, thenhash(a)
is used instead. Note that the hash values for some types are nondeterministic whenPYTHONHASHSEED
is enabled.Changed in version 2.4: formerly, operating system resources were not used.

random.
getstate
()¶ Return an object capturing the current internal state of the generator. This object can be passed to
setstate()
to restore the state.New in version 2.1.
Changed in version 2.6: State values produced in Python 2.6 cannot be loaded into earlier versions.

random.
setstate
(state)¶ state should have been obtained from a previous call to
getstate()
, andsetstate()
restores the internal state of the generator to what it was at the timegetstate()
was called.New in version 2.1.

random.
jumpahead
(n)¶ Change the internal state to one different from and likely far away from the current state. n is a nonnegative integer which is used to scramble the current state vector. This is most useful in multithreaded programs, in conjunction with multiple instances of the
Random
class:setstate()
orseed()
can be used to force all instances into the same internal state, and thenjumpahead()
can be used to force the instances’ states far apart.New in version 2.1.
Changed in version 2.3: Instead of jumping to a specific state, n steps ahead,
jumpahead(n)
jumps to another state likely to be separated by many steps.

random.
getrandbits
(k)¶ Returns a python
long
int with k random bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available,getrandbits()
enablesrandrange()
to handle arbitrarily large ranges.New in version 2.4.
Functions for integers:

random.
randrange
(stop)¶ 
random.
randrange
(start, stop[, step]) Return a randomly selected element from
range(start, stop, step)
. This is equivalent tochoice(range(start, stop, step))
, but doesn’t actually build a range object.New in version 1.5.2.

random.
randint
(a, b)¶ Return a random integer N such that
a <= N <= b
.
Functions for sequences:

random.
choice
(seq)¶ Return a random element from the nonempty sequence seq. If seq is empty, raises
IndexError
.

random.
shuffle
(x[, random])¶ Shuffle the sequence x in place. The optional argument random is a 0argument function returning a random float in [0.0, 1.0); by default, this is the function
random()
.Note that for even rather small
len(x)
, the total number of permutations of x is larger than the period of most random number generators; this implies that most permutations of a long sequence can never be generated.

random.
sample
(population, k)¶ Return a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.
New in version 2.3.
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 subslices 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 from a range of integers, use an
xrange()
object as an argument. This is especially fast and space efficient for sampling from a large population:sample(xrange(10000000), 60)
.
The following functions generate specific realvalued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.

random.
random
()¶ Return the next random floating point number in the range [0.0, 1.0).

random.
uniform
(a, b)¶ Return a random floating point number N such that
a <= N <= b
fora <= b
andb <= N <= a
forb < a
.The endpoint value
b
may or may not be included in the range depending on floatingpoint rounding in the equationa + (ba) * random()
.

random.
triangular
(low, high, mode)¶ Return a random floating point number N such that
low <= N <= high
and with the specified mode between those bounds. The low and high bounds default to zero and one. The mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.New in version 2.6.

random.
betavariate
(alpha, beta)¶ Beta distribution. Conditions on the parameters are
alpha > 0
andbeta > 0
. Returned values range between 0 and 1.

random.
expovariate
(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.

random.
gammavariate
(alpha, beta)¶ Gamma distribution. (Not the gamma function!) Conditions on the parameters are
alpha > 0
andbeta > 0
.The probability distribution function is:
x ** (alpha  1) * math.exp(x / beta) pdf(x) =  math.gamma(alpha) * beta ** alpha

random.
gauss
(mu, sigma)¶ Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the
normalvariate()
function defined below.

random.
lognormvariate
(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.

random.
normalvariate
(mu, sigma)¶ Normal distribution. mu is the mean, and sigma is the standard deviation.

random.
vonmisesvariate
(mu, kappa)¶ 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.

random.
paretovariate
(alpha)¶ Pareto distribution. alpha is the shape parameter.

random.
weibullvariate
(alpha, beta)¶ Weibull distribution. alpha is the scale parameter and beta is the shape parameter.
Alternative Generators:

class
random.
WichmannHill
([seed])¶ Class that implements the WichmannHill algorithm as the core generator. Has all of the same methods as
Random
plus thewhseed()
method described below. Because this class is implemented in pure Python, it is not threadsafe and may require locks between calls. The period of the generator is 6,953,607,871,644 which is small enough to require care that two independent random sequences do not overlap.

random.
whseed
([x])¶ This is obsolete, supplied for bitlevel compatibility with versions of Python prior to 2.1. See
seed()
for details.whseed()
does not guarantee that distinct integer arguments yield distinct internal states, and can yield no more than about 2**24 distinct internal states in all.

class
random.
SystemRandom
([seed])¶ Class that uses the
os.urandom()
function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state and sequences are not reproducible. Accordingly, theseed()
andjumpahead()
methods have no effect and are ignored. Thegetstate()
andsetstate()
methods raiseNotImplementedError
if called.New in version 2.4.
Examples of basic usage:
>>> random.random() # Random float x, 0.0 <= x < 1.0
0.37444887175646646
>>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0
1.1800146073117523
>>> random.randint(1, 10) # Integer from 1 to 10, endpoints included
7
>>> random.randrange(0, 101, 2) # Even integer from 0 to 100
26
>>> random.choice('abcdefghij') # Choose a random element
'c'
>>> items = [1, 2, 3, 4, 5, 6, 7]
>>> random.shuffle(items)
>>> items
[7, 3, 2, 5, 6, 4, 1]
>>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements
[4, 1, 5]
See also
M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.
Wichmann, B. A. & Hill, I. D., “Algorithm AS 183: An efficient and portable pseudorandom number generator”, Applied Statistics 31 (1982) 188190.
ComplementaryMultiplywithCarry recipe for a compatible alternative random number generator with a long period and comparatively simple update operations.