Source code:Lib/random.py

• Python Random Number Generator 3.6
• Random Key Generator Python

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1. The secrets module is used for generating cryptographically strong random numbers suitable for managing data such as passwords, account authentication, security tokens, and related secrets. In particularly, secrets should be used in preference to the default pseudo-random number generator in the random module, which is designed for modelling.
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This module implements pseudo-random number generators for variousdistributions.

For integers, uniform selection from a range. For sequences, uniform selectionof a random element, a function to generate a random permutation of a listin-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 generatingdistributions of angles, the von Mises distribution is available.

Almost all module functions depend on the basic function random(), whichgenerates a random float uniformly in the semi-open range [0.0, 1.0). Pythonuses the Mersenne Twister as the core generator. It produces 53-bit precisionfloats and has a period of 2**19937-1. The underlying implementation in C isboth fast and threadsafe. The Mersenne Twister is one of the most extensivelytested random number generators in existence. However, being completelydeterministic, it is not suitable for all purposes, and is completely unsuitablefor cryptographic purposes.

The functions supplied by this module are actually bound methods of a hiddeninstance of the random.Random class. You can instantiate your owninstances of Random to get generators that don’t share state. This isespecially useful for multi-threaded programs, creating a different instance ofRandom for each thread, and using the jumpahead() method to makeit likely that the generated sequences seen by each thread don’t overlap.

Class Random can also be subclassed if you want to use a differentbasic generator of your own devising: in that case, override the random(),seed(), getstate(), setstate() andjumpahead() methods. Optionally, a new generator can supply agetrandbits() method — thisallows randrange() to produce selections over an arbitrarily large range.

As an example of subclassing, the random module provides theWichmannHill class that implements an alternative generator in purePython. The class provides a backward compatible way to reproduce results fromearlier versions of Python, which used the Wichmann-Hill algorithm as the coregenerator. Note that this Wichmann-Hill generator can no longer be recommended:its period is too short by contemporary standards, and the sequence generated isknown to fail some stringent randomness tests. See the references below for arecent variant that repairs these flaws.

Changed in version 2.3: MersenneTwister replaced Wichmann-Hill as the default generator.

The random module also provides the SystemRandom class whichuses the system function os.urandom() to generate random numbersfrom sources provided by the operating system.

Warning

The pseudo-random generators of this module should not be used forsecurity purposes. Use os.urandom() or SystemRandom ifyou require a cryptographically secure pseudo-random number generator.

Bookkeeping functions:

Initialize internal state of the random number generator.

Python Random Number Generator 3.6

None or no argument seeds from current time or from an operatingsystem specific randomness source if available (see the os.urandom()function for details on availability).

If a is not None or an int or a long, thenhash(a) is used instead. Note that the hash values for some typesare nondeterministic when PYTHONHASHSEED is enabled.

Changed in version 2.4: formerly, operating system resources were not used.

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

Changed in version 2.6: State values produced in Python 2.6 cannot be loaded into earlier versions.

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

Change the internal state to one different from and likely far away from thecurrent state. n is a non-negative integer which is used to scramble thecurrent state vector. This is most useful in multi-threaded programs, inconjunction with multiple instances of the Random class:setstate() or seed() can be used to force all instances into thesame internal state, and then jumpahead() can be used to force theinstances’ 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.

Returns a python long int with k random bits. This method is suppliedwith the MersenneTwister generator and some other generators may also provide itas an optional part of the API. When available, getrandbits() enablesrandrange() to handle arbitrarily large ranges.

Functions for integers:

Return a randomly selected element from range(start,stop,step). This isequivalent to choice(range(start,stop,step)), but doesn’t actually build arange object.

New in version 1.5.2.

Return a random integer N such that a<=N<=b.

Functions for sequences:

Random Key Generator Python

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

Shuffle the sequence x in place. The optional argument random is a0-argument function returning a random float in [0.0, 1.0); by default, this isthe function random().

Note that for even rather small len(x), the total number of permutations ofx is larger than the period of most random number generators; this impliesthat most permutations of a long sequence can never be generated.

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 theoriginal population unchanged. The resulting list is in selection order so thatall sub-slices will also be valid random samples. This allows raffle winners(the sample) to be partitioned into grand prize and second place winners (thesubslices).

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Members of the population need not be hashable or unique. If the populationcontains 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 anargument. This is especially fast and space efficient for sampling from a largepopulation: sample(xrange(10000000),60).

The following functions generate specific real-valued distributions. Functionparameters are named after the corresponding variables in the distribution’sequation, as used in common mathematical practice; most of these equations canbe found in any statistics text.

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

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

The end-point value b may or may not be included in the rangedepending on floating-point rounding in the equation a+(b-a)*random().

Return a random floating point number N such that low<=N<=high andwith the specified mode between those bounds. The low and high boundsdefault to zero and one. The mode argument defaults to the midpointbetween the bounds, giving a symmetric distribution.

New in version 2.6.

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

Exponential distribution. lambd is 1.0 divided by the desiredmean. It should be nonzero. (The parameter would be called“lambda”, but that is a reserved word in Python.) Returned valuesrange from 0 to positive infinity if lambd is positive, and fromnegative infinity to 0 if lambd is negative.

Gamma distribution. (Not the gamma function!) Conditions on theparameters are alpha>0 and beta>0.

The probability distribution function is:

Gaussian distribution. mu is the mean, and sigma is the standarddeviation. This is slightly faster than the normalvariate() functiondefined below.

Log normal distribution. If you take the natural logarithm of thisdistribution, you’ll get a normal distribution with mean mu and standarddeviation sigma. mu can have any value, and sigma must be greater thanzero.

Normal distribution. mu is the mean, and sigma is the standard deviation.

mu is the mean angle, expressed in radians between 0 and 2*pi, and kappais the concentration parameter, which must be greater than or equal to zero. Ifkappa is equal to zero, this distribution reduces to a uniform random angleover the range 0 to 2*pi.

Pareto distribution. alpha is the shape parameter.

Weibull distribution. alpha is the scale parameter and beta is the shapeparameter.

Alternative Generators:

Class that implements the Wichmann-Hill algorithm as the core generator. Has allof the same methods as Random plus the whseed() method describedbelow. Because this class is implemented in pure Python, it is not threadsafeand may require locks between calls. The period of the generator is6,953,607,871,644 which is small enough to require care that two independentrandom sequences do not overlap.

This is obsolete, supplied for bit-level compatibility with versions of Pythonprior to 2.1. See seed() for details. whseed() does not guaranteethat distinct integer arguments yield distinct internal states, and can yield nomore than about 2**24 distinct internal states in all.

Class that uses the os.urandom() function for generating random numbersfrom sources provided by the operating system. Not available on all systems.Does not rely on software state and sequences are not reproducible. Accordingly,the seed() and jumpahead() methods have no effect and are ignored.The getstate() and setstate() methods raiseNotImplementedError if called.

New in version 2.4.

Examples of basic usage:

See also

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

Wichmann, B. A. & Hill, I. D., “Algorithm AS 183: An efficient and portablepseudo-random number generator”, Applied Statistics 31 (1982) 188-190.

Complementary-Multiply-with-Carry recipe for a compatible alternativerandom number generator with a long period and comparatively simple updateoperations.