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System.Random

Portability | portable
Stability | stable
Maintainer | libraries@haskell.org

Contents

The `RandomGen` class, and the `StdGen` generator
The `Random` class
The global random number generator
References

Description
Random numbers.
Synopsis

class RandomGen g where

next :: g -> (Int, g)
split :: g -> (g, g)
genRange :: g -> (Int, Int)

data StdGen
mkStdGen :: Int -> StdGen
class Random a where

randomR :: RandomGen g => (a, a) -> g -> (a, g)
random :: RandomGen g => g -> (a, g)
randomRs :: RandomGen g => (a, a) -> g -> [a]
randoms :: RandomGen g => g -> [a]
randomRIO :: (a, a) -> IO a
randomIO :: IO a

getStdRandom :: (StdGen -> (a, StdGen)) -> IO a
getStdGen :: IO StdGen
setStdGen :: StdGen -> IO ()
newStdGen :: IO StdGen

Documentation

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 class `Random` provides a way to extract particular values 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#LEcuyer] for 32-bit computers, transliterated by Lennart Augustsson. It has a period of roughly 2.30584e18.

The `RandomGen` class, and the `StdGen` generator
class RandomGen g where

The class `RandomGen` provides a common interface to random number generators.
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#Burton, System.Random#Hellekalek] 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` is not strict.

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`.

Instances

RandomGen StdGen

data StdGen

The System.Random library provides one instance of `RandomGen`, the abstract data type `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#Park, System.Random#Carta]. 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

RandomGen StdGen
Read StdGen
Show 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. Programmers may, of course, supply their own instances of `RandomGen`.
The `Random` class
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#globalrng).
randomIO :: IO a
A variant of `random` that uses the global random number generator (see System.Random#globalrng).

Instances

Random Bool
Random Char
Random Double
Random Float
Random Int
Random Integer

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.
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.

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