ROOT::Math::MixMaxEngine< N, SkipNumber > Class Template Reference

template<int N, int SkipNumber>
class ROOT::Math::MixMaxEngine< N, SkipNumber >

MixMaxEngine is a wrapper class for the MIXMAX Random number generator.

MIXMAX is a matrix-recursive random number generator introduced by G. Savvidy.

The real implementation of the generator, written in C, is in the mixmax.h and mixmax.cxx files. This generator code is available also at hepforge: http://mixmax.hepforge.org The MIXMAX code has been created and developed by Konstantin Savvidy and it is released under GNU Lesser General Public License v3.

This wrapper class provides 3 different variants of MIXMAX according to the template para extra parameter N. The extra parameter, SkipNumber, is used to perform additional iterations of the generator before returning the random numbers. For example, when SkipNumber = 2, the generator will have two extra iterations that will be discarder.

• MIXMAX with N = 240. This is a new version of the generator (version 2.0beta) described in the 2016 paper (3rd reference), with special number \(s=487013230256099140\), \(m=2^{51}+1\) and having a period of \(10^{4389}\).
• MIXMAX with N = 17, from the 2.0 beta version with \(s=0\) and \(m=2^{36}+1\). The period of the generator is \(10^{294}\).
• MIXMAX with N = 256 from the 1.0 version. The period is (for SkipNumber=0) \(10^{4682}\). For this generator we recommend in ROOT using a default value of `SkipNumber=2, while for the previous two generators skipping is not needed.

This table describes the properties of the MIXMAX generators. MIXMAX is a genuine 61 bit generator on the Galois field GF[p], where \(p=2^{61}-1\) is the Mersenne prime number. The MIXMAX generators with these parameters pass all of the BigCrush tests in the TestU01 suite

Dimension	Entropy	Decorrelation Time	Iteration Time	Relaxation Time	Period q
N	\(~h(T)\)	\(\tau_0 = {1\over h(T) 2N }\)	t	\(\tau ={1\over h(T) \ln {1\over \delta v_0}}\)	\(\log_{10} (q)\)
256	194	0.000012	1	95.00	4682 (full period is not confirmed)
8	220	0.00028	1	1.54	129
17	374	0.000079	1	1.92	294
240	8679	0.00000024	1	1.17	4389

The entropy \(h(T)\), decorrelation time \(\tau_0\) decorrelation time, relaxation time \(\tau\) and period of the MIXMAX generator, expressed in units of the iteration time \(t\), which is normalised to 1. Clearly \(\tau_0~ < t ~< \tau\).

The References for MIXMAX are:

• G.K.Savvidy and N.G.Ter-Arutyunian, On the Monte Carlo simulation of physical systems, J.Comput.Phys. 97, 566 (1991); Preprint EPI-865-16-86, Yerevan, Jan. 1986
• K.Savvidy, The MIXMAX random number generator, Computer Physics Communications 196 (2015), pp 161–165 http://dx.doi.org/10.1016/j.cpc.2015.06.003
• K.Savvidy and G.Savvidy, Spectrum and Entropy of C-systems MIXMAX Random Number Generator, Chaos, Solitons & Fractals, Volume 91, (2016) pp. 33–38 http://dx.doi.org/10.1016/j.chaos.2016.05.003

Definition at line 102 of file MixMaxEngine.h.

Public Types
typedef TRandomEngine	BaseType
typedef uint64_t	Result_t
typedef uint64_t	StateInt_t

Public Member Functions
	MixMaxEngine (uint64_t seed=1)
	~MixMaxEngine () override
Result_t	IntRndm ()
	generate a 64 bit integer number
double	operator() ()
	generate a double random number (faster interface)
double	Rndm () override
void	RndmArray (int n, double *array)
	generate an array of random numbers
void	SetSeed (Result_t seed)
	set the generator seed
Public Member Functions inherited from ROOT::Math::TRandomEngine
virtual	~TRandomEngine ()

Static Public Member Functions
static uint64_t	MaxInt ()
	maximum integer that can be generated. For MIXMAX is 2^61-1
static uint64_t	MinInt ()
	minimum integer that can be generated. For MIXMAX is 0
static const char *	Name ()
	get name of the generator
static int	Size ()
	Get the size of the generator.

Protected Member Functions
int	Counter () const
	Get the counter (between 0 and Size-1)
void	GetState (std::vector< StateInt_t > &state) const
	get the state of the generator
void	SetState (const std::vector< StateInt_t > &state)
	set the full initial generator state

Private Member Functions
double	Rndm_impl ()
	implementation function to generate the random number

Private Attributes
MixMaxEngineImpl< N > *	fRng
	mixmax internal engine class

#include <Math/MixMaxEngine.h>

Inheritance diagram for ROOT::Math::MixMaxEngine< N, SkipNumber >:

Member Typedef Documentation

BaseType

template<int N, int SkipNumber>

typedef TRandomEngine ROOT::Math::MixMaxEngine< N, SkipNumber >::BaseType

Definition at line 106 of file MixMaxEngine.h.

Result_t

template<int N, int SkipNumber>

typedef uint64_t ROOT::Math::MixMaxEngine< N, SkipNumber >::Result_t

Definition at line 114 of file MixMaxEngine.h.

StateInt_t

template<int N, int SkipNumber>

typedef uint64_t ROOT::Math::MixMaxEngine< N, SkipNumber >::StateInt_t

Definition at line 110 of file MixMaxEngine.h.

Constructor & Destructor Documentation

MixMaxEngine()

template<int N, int S>

ROOT::Math::MixMaxEngine< N, S >::MixMaxEngine

(

uint64_t

seed = 1

)

Definition at line 35 of file MixMaxEngine.icc.

~MixMaxEngine()

template<int N, int S>

ROOT::Math::MixMaxEngine< N, S >::~MixMaxEngine

override

Definition at line 42 of file MixMaxEngine.icc.

Member Function Documentation

Counter()

template<int N, int S>

int ROOT::Math::MixMaxEngine< N, S >::Counter

protected

Get the counter (between 0 and Size-1)

Definition at line 152 of file MixMaxEngine.icc.

GetState()

template<int N, int S>

void ROOT::Math::MixMaxEngine< N, S >::GetState ( std::vector< StateInt_t > &  state ) const

protected

get the state of the generator

Definition at line 141 of file MixMaxEngine.icc.

IntRndm()

template<int N, int S>

uint64_t ROOT::Math::MixMaxEngine< N, S >::IntRndm

generate a 64 bit integer number

Definition at line 103 of file MixMaxEngine.icc.

MaxInt()

template<int N, int S>

uint64_t ROOT::Math::MixMaxEngine< N, S >::MaxInt

static

maximum integer that can be generated. For MIXMAX is 2^61-1

Definition at line 111 of file MixMaxEngine.icc.

MinInt()

template<int N, int S>

uint64_t ROOT::Math::MixMaxEngine< N, S >::MinInt

static

minimum integer that can be generated. For MIXMAX is 0

Definition at line 117 of file MixMaxEngine.icc.

Name()

template<int N, int S>

const char * ROOT::Math::MixMaxEngine< N, S >::Name

static

get name of the generator

Definition at line 157 of file MixMaxEngine.icc.

operator()()

template<int N, int SkipNumber>

double ROOT::Math::MixMaxEngine< N, SkipNumber >::operator() ( )

inline

generate a double random number (faster interface)

Definition at line 138 of file MixMaxEngine.h.

Rndm()

template<int N, int SkipNumber>

double ROOT::Math::MixMaxEngine< N, SkipNumber >::Rndm ( )

inlineoverridevirtual

Implements ROOT::Math::TRandomEngine.

Definition at line 135 of file MixMaxEngine.h.

Rndm_impl()

template<int N, int S>

double ROOT::Math::MixMaxEngine< N, S >::Rndm_impl

private

implementation function to generate the random number

Definition at line 92 of file MixMaxEngine.icc.

RndmArray()

template<int N, int S>

void ROOT::Math::MixMaxEngine< N, S >::RndmArray	(	int	n,
		double *	array
	)

generate an array of random numbers

Definition at line 123 of file MixMaxEngine.icc.

SetSeed()

template<int N, int S>

void ROOT::Math::MixMaxEngine< N, S >::SetSeed

(

Result_t

seed

)

set the generator seed

Definition at line 53 of file MixMaxEngine.icc.

SetState()

template<int N, int S>

void ROOT::Math::MixMaxEngine< N, S >::SetState ( const std::vector< StateInt_t > &  state )

protected

set the full initial generator state

Definition at line 130 of file MixMaxEngine.icc.

Size()

template<int N, int S>

int ROOT::Math::MixMaxEngine< N, S >::Size

static

Get the size of the generator.

Definition at line 147 of file MixMaxEngine.icc.

Member Data Documentation

fRng

template<int N, int SkipNumber>

MixMaxEngineImpl<N>* ROOT::Math::MixMaxEngine< N, SkipNumber >::fRng

private

mixmax internal engine class

Definition at line 170 of file MixMaxEngine.h.