Package umontreal.iro.lecuyer.rng

This package offers the basic facilities for generating uniform random numbers.

See: Description

Interface Summary

Interface	Description
CloneableRandomStream	CloneableRandomStream extends RandomStream and Cloneable.
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.
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.

Class Summary

Class	Description
AntitheticStream	This container class allows the user to force any RandomStream to return antithetic variates.
BakerTransformedStream	This container class permits one to apply the baker's transformation to the output of any RandomStream.
BasicRandomStreamFactory	Represents a basic random stream factory that can constructs new instances of a given RandomStream implementation via the newInstance method.
F2NL607	Implements the RandomStream interface by using as a backbone generator the combination of the WELL607 proposed in (and implemented in WELL607) with a nonlinear generator.
GenF2w32	Implements the RandomStream interface via inheritance from RandomStreamBase.
LFSR113	Extends RandomStreamBase using a composite linear feedback shift register (LFSR) (or Tausworthe) RNG as defined in.
LFSR258	Extends RandomStreamBase using a 64-bit composite linear feedback shift register (LFSR) (or Tausworthe) RNG as defined in.
MRG31k3p	Extends the abstract class RandomStreamBase, thus implementing the RandomStream interface indirectly.
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, implemented in 64-bit floating-point arithmetic.
MRG32k3aL	The same generator as MRG32k3a, except here it is implemented with type long instead of double.
MT19937	Implements the RandomStream interface via inheritance from RandomStreamBase.
RandMrg	Deprecated
RandomPermutation	Provides methods to randomly shuffle arrays or lists using a random stream.
RandomStreamBase	This class provides a convenient foundation on which RNGs can be built.
RandomStreamManager	Manages a list of random streams for more convenient synchronization.
RandomStreamWithCache	This class represents a random stream whose uniforms are cached for more efficiency when using common random numbers.
RandRijndael	Implements a RNG using the Rijndael block cipher algorithm (AES) with key and block lengths of 128 bits.
TruncatedRandomStream	Represents a container random stream generating numbers in an interval (a, b) instead of in (0, 1), where 0 <= a < b <= 1, by using the contained stream.
WELL1024	Implements the RandomStream interface via inheritance from RandomStreamBase.
WELL512	This class implements the RandomStream interface via inheritance from RandomStreamBase.
WELL607	This class implements the RandomStream interface via inheritance from RandomStreamBase.

Exception Summary

Exception	Description
RandomStreamInstantiationException	This exception is thrown when a random stream factory cannot instantiate a stream on a call to its newInstance method.

Package umontreal.iro.lecuyer.rng Description

This package offers the basic facilities for generating uniform random numbers. It provides an interface called umontreal.iro.lecuyer.rngRandomStream and some implementations of that interface. 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[#!rLEC91a!#,#!rLEC97d!#,#!rLEC02a!#]. For an example of how to use these streams properly, see InventoryCRN in the set of example programs.

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 here have various speeds and period lengths. umontreal.iro.lecuyer.rngMRG32k3a is the one that has been most extensively tested, but it is not among the fastest. The umontreal.iro.lecuyer.rngLFSR113, umontreal.iro.lecuyer.rngGenF2w32, umontreal.iro.lecuyer.rngMT19937, and the WELL generators produce sequences of bits that obey a linear recurrence, so they eventually fail statistical tests that measure the linear complexity of these bits sequences. But this can affect only very special types of applications.

For each generator, the following tables give the approximate period length (period), the CPU time (in seconds) to generate 10⁹ U(0, 1) random numbers (gen. time), and the CPU time to jump ahead 10⁶ times to the next substream (jump time). The following timings are on a 2100 MHz 32-bit AMD Athlon XP 2800+ computer running Linux, with the JDK 1.4.2.

RNG	period	gen. time	jump time
LFSR113	2113	51	0.08
WELL512	2512	55	372
WELL1024	21024	55	1450
MT19937	219937	56	60
WELL607	2607	61	523
GenF2w32	2800	62	937
MRG31k3p	2185	66	1.8
MRG32k3a	2191	109	2.3
F2NL607	2637	125	523
RandRijndael	2130	260	0.9

The following timings are 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	2113	31	0.08
WELL607	2607	33	329
WELL512	2512	33	234
WELL1024	21024	34	917
LFSR258	2258	35	0.18
MT19937	219937	36	46
GenF2w32	2800	43	556
MRG31k3p	2185	51	0.89
F2NL607	2637	65	329
MRG32k3a	2191	70	1.1
RandRijndael	2130	127	0.6

Other tools included in this package permit one to manage and synchronize several streams simultaneously (umontreal.iro.lecuyer.rngRandomStreamManager), to create random stream factories for a given type of stream (umontreal.iro.lecuyer.rngBasicRandomStreamFactory), and to apply automatic transformations to the output of a given stream (umontreal.iro.lecuyer.rngAntitheticStream and umontreal.iro.lecuyer.rngBakerTransformedStream).

For further details about uniform RNGs, we refer the reader to[#!rKNU98a!#,#!rLEC01d!#,#!rLEC04b!#].

Should add an example somewhere.