This module implements pseudo-random number generators for various distributions. For integers, uniform selection from a range. For sequences, uniform selection of a random element, and a function to generate a random permutation of a list in-place. On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distribution of angles, the circular uniform and von Mises distributions are available.
Almost all module functions depend on the basic function random(), which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the standard Wichmann-Hill generator, combining three pure multiplicative congruential generators of modulus 30269, 30307 and 30323. Its period (how many numbers it generates before repeating the sequence exactly) is 6,953,607,871,644. While of much higher quality than the rand() function supplied by most C libraries, the theoretical properties are much the same as for a single linear congruential generator of large modulus. It is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.
The functions in this module are not threadsafe: if you want to call these functions from multiple threads, you should explicitly serialize the calls. Else, because no critical sections are implemented internally, calls from different threads may see the same return values.
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 multi-threaded programs, creating a different instance of Random for each thread, and using the jumpahead() method to ensure that the generated sequences seen by each thread don't overlap (see example below).
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.
Here's one way to create threadsafe distinct and non-overlapping generators:
def create_generators(num, delta, firstseed=None): """Return list of num distinct generators. Each generator has its own unique segment of delta elements from Random.random()'s full period. Seed the first generator with optional arg firstseed (default is None, to seed from current time). """ from random import Random g = Random(firstseed) result = [g] for i in range(num - 1): laststate = g.getstate() g = Random() g.setstate(laststate) g.jumpahead(delta) result.append(g) return result gens = create_generators(10, 1000000)
That creates 10 distinct generators, which can be passed out to 10
distinct threads. The generators don't share state so can be called
safely in parallel. So long as no thread calls its
more than a million times (the second argument to
create_generators(), the sequences seen by each thread will
not overlap. The period of the underlying Wichmann-Hill generator
limits how far this technique can be pushed.
Just for fun, note that since we know the period, jumpahead() can also be used to ``move backward in time:''
>>> g = Random(42) # arbitrary >>> g.random() 0.25420336316883324 >>> g.jumpahead(6953607871644L - 1) # move *back* one >>> g.random() 0.25420336316883324
None, current system time is used; current system time is also used to initialize the generator when the module is first imported. If x is not
Noneor an int or long,
hash(x)is used instead. If x is an int or long, x is used directly. Distinct values between 0 and 27814431486575L inclusive are guaranteed to yield distinct internal states (this guarantee is specific to the default Wichmann-Hill generator, and may not apply to subclasses supplying their own basic generator).
Functions for integers:
range(start, stop, step). This is equivalent to
choice(range(start, stop, step)), but doesn't actually build a range object. New in version 1.5.2.
a <= N <= b.
Functions for sequences:
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.
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.
a <= N < b.
alpha > -1and
beta > -1. Returned values range between 0 and 1.
mean - arc/2and
mean + arc/2and are normalized to between 0 and pi.
(mean + arc * (random.random() - 0.5)) % math.pi.
alpha > 0and
beta > 0.
Wichmann, B. A. & Hill, I. D., ``Algorithm AS 183: An efficient and portable pseudo-random number generator'', Applied Statistics 31 (1982) 188-190.