random — Generate pseudo-random numbers

Source code: Lib/random.py

This module implements pseudo-random number generators for various distributions.

For integers, there is uniform selection from a range. For sequences, there is uniform selection of a random element, a function to generate a random permutation of a list in-place, 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 half-open range 0.0 <= X < 1.0. Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. 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.

Class Random can also be subclassed if you want to use a different basic generator of your own devising: see the documentation on that class for more details.

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 pseudo-random generators of this module should not be used for security purposes. For security or cryptographic uses, see the secrets module.

See also

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.

Complementary-Multiply-with-Carry recipe for a compatible alternative random number generator with a long period and comparatively simple update operations.

Note

The global random number generator and instances of Random are thread-safe. However, in the free-threaded build, concurrent calls to the global generator or to the same instance of Random may encounter contention and poor performance. Consider using separate instances of Random per thread instead.

Bookkeeping functions

random.seed(a=None, version=2)

Initialize the random number generator.

If a is omitted or None, the current system time is used. If randomness sources are provided by the operating system, they are used instead of the system time (see the os.urandom() function for details on availability).

If a is an int, its absolute value is used directly.

With version 2 (the default), a str, bytes, or bytearray object gets converted to an int and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versions of Python), the algorithm for str and bytes generates a narrower range of seeds.

Changed in version 3.2: Moved to the version 2 scheme which uses all of the bits in a string seed.

Changed in version 3.11: The seed must be one of the following types: None, int, float, str, bytes, or bytearray.

random.getstate()

Return an object capturing the current internal state of the generator. This object can be passed to setstate() to restore the state.

random.setstate(state)

state should have been obtained from a previous call to getstate(), and setstate() restores the internal state of the generator to what it was at the time getstate() was called.

Functions for bytes

random.randbytes(n)

Generate n random bytes.

This method should not be used for generating security tokens. Use secrets.token_bytes() instead.

Added in version 3.9.

Functions for integers

random.randrange(stop)
random.randrange(start, stop[, step])

Return a randomly selected element from range(start, stop, step).

This is roughly equivalent to choice(range(start, stop, step)) but supports arbitrarily large ranges and is optimized for common cases.

The positional argument pattern matches the range() function.

Keyword arguments should not be used because they can be interpreted in unexpected ways. For example randrange(start=100) is interpreted as randrange(0, 100, 1).

Changed in version 3.2: randrange() is more sophisticated about producing equally distributed values. Formerly it used a style like int(random()*n) which could produce slightly uneven distributions.

Changed in version 3.12: Automatic conversion of non-integer types is no longer supported. Calls such as randrange(10.0) and randrange(Fraction(10, 1)) now raise a TypeError.

random.randint(a, b)

Return a random integer N such that a <= N <= b. Alias for randrange(a, b+1).

random.getrandbits(k)

Returns a non-negative Python integer with k random bits. This method is supplied with the Mersenne Twister generator and some other generators may also provide it as an optional part of the API. When available, getrandbits() enables randrange() to handle arbitrarily large ranges.

Changed in version 3.9: This method now accepts zero for k.

Functions for sequences

random.choice(seq)

Return a random element from the non-empty sequence seq. If seq is empty, raises IndexError.

random.choices(population, weights=None, *, cum_weights=None, k=1)

Return a k sized list of elements chosen from the population with replacement. If the population is empty, raises IndexError.

If a weights sequence is specified, selections are made according to the relative weights. Alternatively, if a cum_weights sequence is given, the selections are made according to the cumulative weights (perhaps computed using itertools.accumulate()). For example, the relative weights [10, 5, 30, 5] are equivalent to the cumulative weights [10, 15, 45, 50]. Internally, the relative weights are converted to cumulative weights before making selections, so supplying the cumulative weights saves work.

If neither weights nor cum_weights are specified, selections are made with equal probability. If a weights sequence is supplied, it must be the same length as the population sequence. It is a TypeError to specify both weights and cum_weights.

The weights or cum_weights can use any numeric type that interoperates with the float values returned by random() (that includes integers, floats, and fractions but excludes decimals). Weights are assumed to be non-negative and finite. A ValueError is raised if all weights are zero.

For a given seed, the choices() function with equal weighting typically produces a different sequence than repeated calls to choice(). The algorithm used by choices() uses floating-point arithmetic for internal consistency and speed. The algorithm used by choice() defaults to integer arithmetic with repeated selections to avoid small biases from round-off error.

Added in version 3.6.

Changed in version 3.9: Raises a ValueError if all weights are zero.

random.shuffle(x)

Shuffle the sequence x in place.

To shuffle an immutable sequence and return a new shuffled list, use sample(x, k=len(x)) instead.

Note that even for small len(x), the total number of permutations of x can quickly grow larger than the period of most random number generators. This implies that most permutations of a long sequence can never be generated. For example, a sequence of length 2080 is the largest that can fit within the period of the Mersenne Twister random number generator.

Changed in version 3.11: Removed the optional parameter random.

random.sample(population, k, *, counts=None)

Return a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.

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.

Repeated elements can be specified one at a time or with the optional keyword-only counts parameter. For example, sample(['red', 'blue'], counts=[4, 2], k=5) is equivalent to sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5).

To choose a sample from a range of integers, use a range() object as an argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), k=60).

If the sample size is larger than the population size, a ValueError is raised.

Changed in version 3.9: Added the counts parameter.

Changed in version 3.11: The population must be a sequence. Automatic conversion of sets to lists is no longer supported.

Discrete distributions

The following function generates a discrete distribution.

random.binomialvariate(n=1, p=0.5)

Binomial distribution. Return the number of successes for n independent trials with the probability of success in each trial being p:

Mathematically equivalent to:

sum(random() < p for i in range(n))

The number of trials n should be a non-negative integer. The probability of success p should be between 0.0 <= p <= 1.0. The result is an integer in the range 0 <= X <= n.

Added in version 3.12.

Real-valued distributions

The following functions generate specific real-valued 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 <= X < 1.0

random.uniform(a, b)

Return a random floating-point number N such that a <= N <= b for a <= b and b <= N <= a for b < a.

The end-point value b may or may not be included in the range depending on floating-point rounding in the expression a + (b-a) * 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.

random.betavariate(alpha, beta)

Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1.

random.expovariate(lambd=1.0)

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.