System.Random

This library deals with the common task of pseudo-random number generation. The library makes it possible to generate repeatable results, by starting with a specified initial random number generator, or to get different results on each run by using the system-initialised generator or by supplying a seed from some other source.

The library is split into two layers:

• A core random number generator provides a supply of bits. The class RandomGen provides a common interface to such generators. The library provides one instance of RandomGen, the abstract data type StdGen. Programmers may, of course, supply their own instances of RandomGen.
• The class Random provides a way to extract values of a particular type from a random number generator. For example, the Float instance of Random allows one to generate random values of type Float.

This implementation uses the Portable Combined Generator of L'Ecuyer [System.Random] for 32-bit computers, transliterated by Lennart Augustsson. It has a period of roughly 2.30584e18.

Random number generators

class RandomGen g where

The class RandomGen provides a common interface to random number generators.

Minimal complete definition: next and split.

Methods

next :: g -> (Int, g)

The next operation returns an Int that is uniformly distributed in the range returned by genRange (including both end points), and a new generator.

split :: g -> (g, g)

The split operation allows one to obtain two distinct random number generators. This is very useful in functional programs (for example, when passing a random number generator down to recursive calls), but very little work has been done on statistically robust implementations of split ([System.Random, System.Random] are the only examples we know of).

genRange :: g -> (Int, Int)

The genRange operation yields the range of values returned by the generator.

It is required that:

• If (a,b) = genRange g, then a < b.
• genRange always returns a pair of defined Ints.

The second condition ensures that genRange cannot examine its argument, and hence the value it returns can be determined only by the instance of RandomGen. That in turn allows an implementation to make a single call to genRange to establish a generator's range, without being concerned that the generator returned by (say) next might have a different range to the generator passed to next.

The default definition spans the full range of Int.

Instances

RandomGen StdGen

Standard random number generators

data StdGen

The StdGen instance of RandomGen has a genRange of at least 30 bits.

The result of repeatedly using next should be at least as statistically robust as the Minimal Standard Random Number Generator described by [System.Random, System.Random]. Until more is known about implementations of split, all we require is that split deliver generators that are (a) not identical and (b) independently robust in the sense just given.

The Show and Read instances of StdGen provide a primitive way to save the state of a random number generator. It is required that read (show g) == g.

In addition, read may be used to map an arbitrary string (not necessarily one produced by show) onto a value of type StdGen. In general, the read instance of StdGen has the following properties:

• It guarantees to succeed on any string.
• It guarantees to consume only a finite portion of the string.
• Different argument strings are likely to result in different results.

Instances

Read StdGen

Show StdGen

RandomGen StdGen

mkStdGen :: Int -> StdGen

The function mkStdGen provides an alternative way of producing an initial generator, by mapping an Int into a generator. Again, distinct arguments should be likely to produce distinct generators.

The global random number generator

There is a single, implicit, global random number generator of type StdGen, held in some global variable maintained by the IO monad. It is initialised automatically in some system-dependent fashion, for example, by using the time of day, or Linux's kernel random number generator. To get deterministic behaviour, use setStdGen.

getStdRandom :: (StdGen -> (a, StdGen)) -> IO a

Uses the supplied function to get a value from the current global random generator, and updates the global generator with the new generator returned by the function. For example, rollDice gets a random integer between 1 and 6:

  rollDice :: IO Int
  rollDice = getStdRandom (randomR (1,6))

getStdGen :: IO StdGen

Gets the global random number generator.

setStdGen :: StdGen -> IO ()

Sets the global random number generator.

newStdGen :: IO StdGen

Applies split to the current global random generator, updates it with one of the results, and returns the other.

Random values of various types

class Random a where

With a source of random number supply in hand, the Random class allows the programmer to extract random values of a variety of types.

Minimal complete definition: randomR and random.

Methods

randomR :: RandomGen g => (a, a) -> g -> (a, g)

Takes a range (lo,hi) and a random number generator g, and returns a random value uniformly distributed in the closed interval [lo,hi], together with a new generator. It is unspecified what happens if lo>hi. For continuous types there is no requirement that the values lo and hi are ever produced, but they may be, depending on the implementation and the interval.

random :: RandomGen g => g -> (a, g)

The same as randomR, but using a default range determined by the type:

• For bounded types (instances of Bounded, such as Char), the range is normally the whole type.
• For fractional types, the range is normally the semi-closed interval [0,1).
• For Integer, the range is (arbitrarily) the range of Int.

randomRs :: RandomGen g => (a, a) -> g -> [a]

Plural variant of randomR, producing an infinite list of random values instead of returning a new generator.

randoms :: RandomGen g => g -> [a]

Plural variant of random, producing an infinite list of random values instead of returning a new generator.

randomRIO :: (a, a) -> IO a

A variant of randomR that uses the global random number generator (see System.Random).

randomIO :: IO a

A variant of random that uses the global random number generator (see System.Random).

Instances

Random Bool

Random Char

Random Double

Random Float

Random Int

Random Integer

References

1. FW Burton and RL Page, Distributed random number generation, Journal of Functional Programming, 2(2):203-212, April 1992.
2. SK Park, and KW Miller, /Random number generators - good ones are hard to find/, Comm ACM 31(10), Oct 1988, pp1192-1201.
3. DG Carta, /Two fast implementations of the minimal standard random number generator/, Comm ACM, 33(1), Jan 1990, pp87-88.
4. P Hellekalek, Don\'t trust parallel Monte Carlo, Department of Mathematics, University of Salzburg, http://random.mat.sbg.ac.at/~peter/pads98.ps, 1998.
5. Pierre L'Ecuyer, /Efficient and portable combined random number generators/, Comm ACM, 31(6), Jun 1988, pp742-749.

The Web site http://random.mat.sbg.ac.at/ is a great source of information.