RandomLib::MixerMT1 Class Reference

The modified MT19937 mixing functionality. More...

#include <RandomLib-2010-01/RandomMixer.hpp>

List of all members.

Public Types
typedef RandomType	mixer_t
Static Public Member Functions
static void	SeedToState (const std::vector< RandomSeed::seed_type > &seed, mixer_type state[], unsigned n) throw ()
static std::string	Name () throw ()
Static Public Attributes
static const unsigned	version = 0x4d784d56UL + (mixer_t::width == 64)
Private Types
typedef mixer_t::type	mixer_type
Private Attributes
static const mixer_type	b = mixer_t::width == 32 ? 1812433253ULL : 6364136223846793005ULL
static const mixer_type	c = mixer_t::width == 32 ? 1664525ULL : 3935559000370003845ULL
static const mixer_type	d = mixer_t::width == 32 ? 1566083941ULL : 2862933555777941757ULL
Static Private Attributes
static const mixer_type	mask = mixer_t::mask
static const mixer_type	a = 5489ULL

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Detailed Description

The modified MT19937 mixing functionality.

MixerMT0 has two defects

• The zeroth word of the state is set to a constant (independent of the seed). This is a relatively minor defect which halves the accessible state space for MT19937 (but the resulting state space is still huge). (Actually, for the 64-bit version, it reduces the accessible states by 2³³. On the other hand the 64-bit has better mixing properies.)
• Close seeds, for example, [1] and [1,0], result in the same state. This is a potentially serious flaw which might result is identical random number sequences being generated instead of independent sequences.

MixerMT1 fixes these defects in a straightforward manner. The resulting algorithm was included in one of the proposals for Random Number Generation for C++0X, see Brown, et al., http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2079.pdf

The template parameter RandomType switches between the 32-bit and 64-bit versions.

MixerMT1 still has a weakness in that it doesn't thoroughly mix the state. This is illustrated by an example given to me by Makoto Matsumoto: Consider a seed of length N and suppose we consider all W^N/2 values for the first half of the seed (here W = 2^width). MixerMT1 has a bottleneck in the way that the state is initialized which results in the second half of the state only taking on W² possible values. MixerSFMT mixes the seed into the state much more thoroughly.

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Member Typedef Documentation

typedef RandomType RandomLib::MixerMT1::mixer_t

The RandomType controlling the output of MixerMT1::SeedToState

Definition at line 135 of file RandomMixer.hpp.

typedef mixer_t::type RandomLib::MixerMT1::mixer_type [private]

The unsigned type corresponding to mixer_t.

Definition at line 146 of file RandomMixer.hpp.

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Member Function Documentation

void RandomLib::MixerMT1::SeedToState	(	const std::vector< RandomSeed::seed_type > &	seed,
		mixer_type	state[],
		unsigned	n
	)		throw () [static]

Mix the seed vector, seed, into the state array, state, of size n.

Definition at line 566 of file Random.cpp.

static std::string RandomLib::MixerMT1::Name

(

)

throw () [inline, static]

Return the name of this class.

Definition at line 161 of file RandomMixer.hpp.

References RandomLib::RandomType::width.

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Member Data Documentation

const unsigned RandomLib::MixerMT1::version = 0x4d784d56UL + (mixer_t::width == 64) [static]

A version number which should be unique to this RandomMixer. This prevents RandomEngine::Load from loading a saved generator with a different RandomMixer. Here the version is "MxMV" or "MxMW".

Definition at line 141 of file RandomMixer.hpp.

const mixer_type RandomLib::MixerMT1::mask = mixer_t::mask [static, private]

The mask for mixter_t.

Definition at line 150 of file RandomMixer.hpp.

const mixer_type RandomLib::MixerMT1::a = 5489ULL [static, private]

Definition at line 166 of file RandomMixer.hpp.

const mixer_type RandomLib::MixerMT1::b = mixer_t::width == 32 ? 1812433253ULL : 6364136223846793005ULL [private]

Definition at line 167 of file RandomMixer.hpp.

const mixer_type RandomLib::MixerMT1::c = mixer_t::width == 32 ? 1664525ULL : 3935559000370003845ULL [private]

Definition at line 168 of file RandomMixer.hpp.

const mixer_type RandomLib::MixerMT1::d = mixer_t::width == 32 ? 1566083941ULL : 2862933555777941757ULL [private]

Definition at line 169 of file RandomMixer.hpp.

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The documentation for this class was generated from the following files:

• RandomMixer.hpp
• Random.cpp