Package umontreal.ssj.rng

Streams of independent uniform random numbers. More...

Classes
class	AntitheticStream
	This container class allows the user to force any RandomStream to return antithetic variates. More...
class	BakerTransformedStream
	This container class permits one to apply the baker’s transformation to the output of any RandomStream. More...
class	BasicRandomStreamFactory
	Represents a basic random stream factory that can constructs new instances of a given RandomStream implementation via the newInstance method. More...
interface	CloneableRandomStream
	CloneableRandomStream extends RandomStream and Cloneable. More...
class	LFSR113
	Extends RandomStreamBase using a composite linear feedback shift register (LFSR) (or Tausworthe) RNG as defined in [144],. More...
class	LFSR258
	Extends RandomStreamBase using a 64-bit composite linear feedback shift register (LFSR) (or Tausworthe) RNG as defined in [144],. More...
class	MRG31k3p
	Extends the abstract class RandomStreamBase, thus implementing the. More...
class	MRG32k3a
	Extends the abstract class RandomStreamBase by using as a backbone (or main) generator the combined multiple recursive generator (CMRG) MRG32k3a proposed by L’Ecuyer [145] , implemented in 64-bit floating-point arithmetic. More...
class	MRG32k3aL
	The same generator as MRG32k3a, except here it is implemented with type long instead of double. More...
class	RandomPermutation
	Provides methods to randomly shuffle arrays or lists using a random stream. More...
interface	RandomStream
	This interface defines the basic structures to handle multiple streams of uniform (pseudo)random numbers and convenient tools to move around within and across these streams. More...
class	RandomStreamBase
	This class provides a convenient foundation on which RNGs can be built. More...
interface	RandomStreamFactory
	Represents a random stream factory capable of constructing instances of a given type of random stream by invoking the newInstance method each time a new random stream is needed, instead of invoking directly the specific constructor of the desired type. More...
class	RandomStreamInstantiationException
	This exception is thrown when a random stream factory cannot instantiate a stream on a call to its umontreal.ssj.rng.RandomStreamFactory.newInstance method. More...
class	RandomStreamManager
	Manages a list of random streams for more convenient synchronization. More...
class	RandomStreamWithCache
	This class represents a random stream whose uniforms are cached for more efficiency when using common random numbers. More...
class	TruncatedRandomStream
	Represents a container random stream generating numbers in an interval. More...
class	WELL512
	This class implements the RandomStream interface via inheritance from RandomStreamBase. More...

Detailed Description

Streams of independent uniform random numbers.

This package offers basic facilities for generating multiple streams and substreams of uniform random numbers over the interval \(U(0,1)\) or over a range of integer values. The design is based on the interface RandomStream and the package offers various implementations of this interface, with recurrence-based (sequential) random number generators. The interface specifies that each stream of random numbers is partitioned into multiple substreams and that methods are available to jump between the substreams, as discussed in [118], [116], [132], [138]. For examples of how to use these streams properly, see [154] and the InventoryCRN.java program in the tutorial examples.

Each implementation uses a specific backbone uniform random number generator (RNG), whose period length is typically partitioned into very long non-overlapping segments to provide the streams and substreams. A stream can generate uniform variates (real numbers) over the interval (0,1), uniform integers over a given range of values \(\{i,...,j\}\), and arrays of these.

The generators provided are all recommendable. They have been selected to be reasonably fast, to have a reasonably long period, good multivariate uniformity (based on theory), good statistical behavior, and the capacity to implement the interface effectively.
The LFSR113 generator produces sequences of bits that obey a linear recurrence, so they eventually fail statistical tests that measure the linear complexity of these binary sequences. But this can affect only very special types of applications.

The following tables give the approximate period length (period), the CPU time (in seconds) to generate \(10^9\) \(U(0,1)\) random numbers (gen. time), and the CPU time to jump ahead \(10^9\) times to the next substream (jump time). These timings were on a (old) 2100 MHz 32-bit AMD Athlon XP 2800+ computer running Linux, with the JDK 1.4.2.

RNG	period	gen. time	jump time
LFSR113	\(2^{113}\)	51	0.08
WELL512	\(2^{512}\)	55	372
WELL1024	\(2^{1024}\)	55	1450
MT19937	\(2^{19937}\)	56	60
WELL607	\(2^{607}\)	61	523
MRG31k3p	\(2^{185}\)	66	1.8
MRG32k3a	\(2^{191}\)	109	2.3

The following timings were made on a 2400 MHz 64-bit AMD Athlon 64 Processor 4000+ computer running Linux, with the JDK 1.5.0.

RNG	period	gen. time	jump time
LFSR113	\(2^{113}\)	31	0.08
WELL512	\(2^{512}\)	33	234
LFSR258	\(2^{258}\)	35	0.18
MRG31k3p	\(2^{185}\)	51	0.89
MRG32k3a	\(2^{191}\)	70	1.1

Other tools offered in this package are as follows: RandomStreamManager give tools to manage and synchronize several streams simultaneously, BasicRandomStreamFactory permits one to create random stream factories for a given type of stream, and AntitheticStream, BakerTransformedStream, and TruncatedRandomStream permit one to apply automatic transformations to the output of a given stream.

For further details about uniform RNGs, we refer the reader to [108], [151], [153], [154], [155], [140].