Doxygen Reference Manual for RNG Library

Reference Manual
Generated by Doxygen 1.6.3
Sun Dec 4 13:06:32 2011

Contents
1

1

1.1
2

Namespace Index

1

Namespace List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.1
3

Class Index

3

Class Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

3.1
4

Class Index

5

Class List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

4.1
5

File Index

7

File List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

5.1

RNG Namespace Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

5.1.1

Detailed Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

5.1.2

Function Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

5.1.2.1
6

Namespace Documentation

9

swap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Class Documentation

11

6.1

RNG::BoxMuller Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

6.1.1


13

6.1.2

Constructor & Destructor Documentation . . . . . . . . . . . . . . . . . . . . . .

14

6.1.2.1

BoxMuller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

6.1.2.2

BoxMuller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

Member Function Documentation . . . . . . . . . . . . . . . . . . . . . . . . . .

14

6.1.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

RNG::Distribution Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

6.2.1


18

6.2.2


18

6.2.2.1

18

6.1.3

6.2

Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ii

CONTENTS
6.2.2.2

Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18


18

6.2.3.1

Bernoulli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

6.2.3.2

Binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

6.2.3.3

Chisquare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

6.2.3.4

Equilikely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

6.2.3.5

Erlang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

6.2.3.6

Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

6.2.3.7

Geometric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

6.2.3.8

Lognormal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

6.2.3.9

Normal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

6.2.3.10 Pascal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

6.2.3.11 Poisson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

6.2.3.12 Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

6.2.3.13 Uniform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

RNG::MersenneTwisterDouble Class Reference . . . . . . . . . . . . . . . . . . . . . . .

25

6.3.1


26

6.3.2


27

6.3.2.1

MersenneTwisterDouble . . . . . . . . . . . . . . . . . . . . . . . . . .

27

6.3.2.2


27

6.3.2.3


27

6.3.2.4

∼MersenneTwisterDouble . . . . . . . . . . . . . . . . . . . . . . . . .

27


27

6.3.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

RNG::MersenneTwisterDouble53 Class Reference . . . . . . . . . . . . . . . . . . . . .

29

6.4.1


30

6.4.2


31

6.4.2.1

MersenneTwisterDouble53 . . . . . . . . . . . . . . . . . . . . . . . .

31

6.4.2.2


31

6.4.2.3


31

6.4.2.4

∼MersenneTwisterDouble53 . . . . . . . . . . . . . . . . . . . . . . .

31


31

6.4.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

RNG::MersenneTwisterDoubleClosed Class Reference . . . . . . . . . . . . . . . . . . .

33

6.5.1


34

6.5.2


35

6.2.3

6.3

6.3.3

6.4

6.4.3

6.5

Generated on Sun Dec 4 13:06:32 2011 by Doxygen

CONTENTS

iii
6.5.2.1

MersenneTwisterDoubleClosed . . . . . . . . . . . . . . . . . . . . . .

35

6.5.2.2


35

6.5.2.3


35

6.5.2.4

∼MersenneTwisterDoubleClosed . . . . . . . . . . . . . . . . . . . . .

35


35

6.5.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

RNG::MersenneTwisterDoubleOpened Class Reference . . . . . . . . . . . . . . . . . . .

37

6.6.1


38

6.6.2


39

6.6.2.1

MersenneTwisterDoubleOpened . . . . . . . . . . . . . . . . . . . . .

39

6.6.2.2


39

6.6.2.3


39

6.6.2.4

∼MersenneTwisterDoubleOpened . . . . . . . . . . . . . . . . . . . .

39


39

6.6.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

RNG::MersenneTwisterInt32 Class Reference . . . . . . . . . . . . . . . . . . . . . . . .

41

6.7.1


41

6.7.2


42

6.7.2.1

MersenneTwisterInt32 . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

6.7.2.2


42

6.7.2.3


42

6.7.2.4

∼MersenneTwisterInt32 . . . . . . . . . . . . . . . . . . . . . . . . . .

42


42

6.7.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

6.7.3.2

rand_int32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

6.7.3.3

Seed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

6.7.3.4

Seed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

RNG::R250Base Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

6.8.1


46

6.8.2


46

6.8.2.1

R250Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

6.8.2.2

R250Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46


46

6.8.3.1

myrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

6.8.3.2

mysrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

6.8.3.3

r250_init . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

6.5.3

6.6

6.6.3

6.7

6.7.3

6.8

6.8.3


iv

CONTENTS
6.8.4

Member Data Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

6.8.4.1

r250_buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

6.8.4.2

r250_index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

6.8.4.3

seed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

RNG::R250Double Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

6.9.1


50

6.9.2


51

6.9.2.1

R250Double . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

6.9.2.2

R250Double . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51


51

6.9.3.1

operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

6.10 RNG::R250Int Class Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

6.10.1 Detailed Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

6.10.2 Constructor & Destructor Documentation . . . . . . . . . . . . . . . . . . . . . .

54

6.10.2.1 R250Int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

6.10.2.2 R250Int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

6.10.3 Member Function Documentation . . . . . . . . . . . . . . . . . . . . . . . . . .

54

6.10.3.1 operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

6.10.3.2 operator() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

6.11 RNG::RandomNumberGenerator Class Reference . . . . . . . . . . . . . . . . . . . . . .

56

6.11.1 Detailed Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.2 Constructor & Destructor Documentation . . . . . . . . . . . . . . . . . . . . . .

57

6.11.2.1 RandomNumberGenerator . . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.2.2 RandomNumberGenerator . . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.2.3 ∼RandomNumberGenerator . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.3 Member Function Documentation . . . . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.3.1 ClockRandomSeed . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

6.11.3.2 GetDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

6.11.3.3 GetDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

6.11.3.4 GetDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

6.11.3.5 GetInt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

6.11.3.6 GetInt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

6.11.3.7 GetInt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

6.11.3.8 InitSeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

6.11.3.9 Random . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

6.11.3.10 Seed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

6.9

6.9.3


CONTENTS
7

v

File Documentation

63

7.1

RandomNumberGenerator.cxx File Reference . . . . . . . . . . . . . . . . . . . . . . . .

63

7.2

RandomNumberGenerator.cxx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

7.3

RandomNumberGenerator.h File Reference . . . . . . . . . . . . . . . . . . . . . . . . .

72

7.4

RandomNumberGenerator.h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

7.5

Sys-LibraryRandom.cpp File Reference . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

7.5.1

Function Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

7.5.1.1

main . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Sys-LibraryRandom.cpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

7.6


Chapter 1

Namespace Index
1.1

Namespace List

Here is a list of all namespaces with brief descriptions:
RNG

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Chapter 2

Class Index
2.1

Class Hierarchy

This inheritance list is sorted roughly, but not completely, alphabetically:
RNG::MersenneTwisterInt32 . . . . . . .
RNG::MersenneTwisterDouble . . . .
RNG::MersenneTwisterDouble53 . .
RNG::MersenneTwisterDoubleClosed
RNG::MersenneTwisterDoubleOpened
RNG::R250Base . . . . . . . . . . . . .
RNG::R250Double . . . . . . . . . .
RNG::R250Int . . . . . . . . . . . . .
RNG::RandomNumberGenerator . . . . .
RNG::BoxMuller . . . . . . . . . . .
RNG::Distribution . . . . . . . . . . .

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41
25
29
33
37
45
49
52
56
11
16

Chapter 3

Class Index
3.1

Class List

Here are the classes, structs, unions and interfaces with brief descriptions:
RNG::BoxMuller . . . . . . . . . . .
RNG::Distribution . . . . . . . . . .
RNG::MersenneTwisterDouble . . .
RNG::MersenneTwisterDouble53 . .
RNG::MersenneTwisterInt32 . . . . .
RNG::R250Base . . . . . . . . . . .
RNG::R250Double . . . . . . . . . .
RNG::R250Int . . . . . . . . . . . .
RNG::RandomNumberGenerator . .

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11
16
25
29
33
37
41
45
49
52
56

6

Class Index


Chapter 4

File Index
4.1

File List

Here is a list of all ﬁles with brief descriptions:
RandomNumberGenerator.cxx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RandomNumberGenerator.h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sys-LibraryRandom.cpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63
72
78

8

File Index


Chapter 5

5.1

RNG Namespace Reference

Classes
•
•
•
•
•
•
•
•
•
•
•

class RandomNumberGenerator
class MersenneTwisterInt32
class MersenneTwisterDouble
class MersenneTwisterDoubleClosed
class MersenneTwisterDoubleOpened
class MersenneTwisterDouble53
class R250Base
class R250Int
class R250Double
class BoxMuller
class Distribution

Functions
• template<typename T >
void swap (T &a, T &b)

5.1.1

Detailed Description

Namespace RandomNumberGenerator
RNG - RandomNumberGenerator Namespace para os algoritmos de geracao de numeros pseudo-aleatórios
em suas diversas implementacoes.

5.1.2

Function Documentation

5.1.2.1

template<typename T > void RNG::swap (T & a, T & b) [inline]

Deﬁnition at line 686 of ﬁle RandomNumberGenerator.h.

10
00686 { T temp(a);

a = b;

b = temp; };

Here is the caller graph for this function:
RNG::Distribution::Equilikely
RNG::swap
RNG::Distribution::Uniform


Chapter 6

Class Documentation
6.1

RNG::BoxMuller Class Reference

#include <RandomNumberGenerator.h>

12

Class Documentation

Inheritance diagram for RNG::BoxMuller:

RNG::RandomNumberGenerator
- _seed
+ RandomNumberGenerator()
+ InitSeed()
+ ClockRandomSeed()
+ Seed()
+ GetInt()
+ GetInt()
+ GetInt()
+ GetDouble()
+ Random()
+ GetDouble()
+ GetDouble()
+ ~RandomNumberGenerator()

RNG::BoxMuller

+ BoxMuller()
+ BoxMuller()
+ operator()()


6.1 RNG::BoxMuller Class Reference

13

Collaboration diagram for RNG::BoxMuller:

- _seed
+ InitSeed()
+ ClockRandomSeed()
+ Seed()
+ GetInt()
+ GetInt()
+ GetInt()
+ GetDouble()
+ Random()
+ GetDouble()
+ GetDouble()

RNG::BoxMuller

+ BoxMuller()
+ BoxMuller()
+ operator()()

Public Member Functions
• BoxMuller ()
• BoxMuller (unsigned long seed)
• double operator() (double Mean, double StandardDev)

6.1.1


Classe para geração de números pseudo-aleatórios que tem como principal algoritmo a distribuição BoxMuller ou Forma Polar da Transformação Box-Muller, caracterizado como um método simples de geração
de números aleatórios em distribução normal através de números aleatórios uniformemente distrbuídos,
ou seja, o algoritmo converte sequências de distribuição uniforme U(0,1) em sequências com distribuição
gaussiana N(0,1).

14

Class Documentation

6.1.2

Constructor & Destructor Documentation

6.1.2.1

RNG::BoxMuller::BoxMuller () [inline]

Método construtor da classe de geracao de numeros aleatórios
00542 : RandomNumberGenerator() {};

6.1.2.2

RNG::BoxMuller::BoxMuller (unsigned long seed) [inline]

Método construtor que recebe uma semente inicial
00547 : RandomNumberGenerator(seed) {};

6.1.3

Member Function Documentation

6.1.3.1

double RNG::BoxMuller::operator() (double Mean, double StandardDev)

Overload do operador () fazendo com que o objeto criado tenha um aspecto de objeto-função. Esse método
retorna números pseudo-aleatório reais distribuídos dentro intervalo compreendido entre 0 e 1. Parâmetros
: Mean - Média , StandardDev - Desvio Padrão
Classe para geração de números pseudo-aleatórios que tem como principal algoritmo a distribuição BoxMuller ou Forma Polar da Transformação Box-Muller, caracterizado como um método simples de geração
de números aleatórios em distribução normal através de números aleatórios uniformemente distrbuídos,
ou seja, o algoritmo converte sequências de distribuição uniforme U(0,1) em sequências com distribuição
gaussiana N(0,1). Overload do operador () fazendo com que o objeto criado tenha um aspecto de objetofunção. Esse método retorna números pseudo-aleatório reais distribuídos dentro intervalo compreendido
entre 0 e 1.
Deﬁnition at line 448 of ﬁle RandomNumberGenerator.cxx.
00454 {
00455
float x1, x2, w, y1;
00456
static float y2;
00457
static bool use_last = false;
00458
00459
//Verifica se o valor usado deve ser o da última chamada
00460
if (use_last)
00461
{
00462
y1 = y2;
00463
use_last = false;
00464
}
00465
else
00466
{
00467
00468
//Calculo da localização do número dentro do intervalo passado
00469
do
00470
{
00471
x1 = 2.0 * GetDouble() - 1.0;
00472
x2 = 2.0 * GetDouble() - 1.0;
00473
w = x1 * x1 + x2 * x2;
00474
}
00475
while ( w >= 1.0 );

6.1 RNG::BoxMuller Class Reference
00476
00477
00478
00479
00480

w = sqrt( (-2.0 * log( w ) ) / w );
y1 = x1 * w;
y2 = x2 * w;
use_last = true;

The documentation for this class was generated from the following ﬁles:
• RandomNumberGenerator.h
• RandomNumberGenerator.cxx


15

16

6.2

Class Documentation

RNG::Distribution Class Reference

Inheritance diagram for RNG::Distribution:

- _seed
+ InitSeed()
+ ClockRandomSeed()
+ Seed()
+ GetInt()
+ GetInt()
+ GetInt()
+ GetDouble()
+ Random()
+ GetDouble()
+ GetDouble()

RNG::Distribution

+ Distribution()
+ Distribution()
+ Bernoulli()
+ Binomial()
+ Equilikely()
+ Geometric()
+ Pascal()
+ Poisson()
+ Uniform()
+ Exponential()
+ Erlang()
+ Normal()
+ Lognormal()
+ Chisquare()
+ Student()


6.2 RNG::Distribution Class Reference

17

Collaboration diagram for RNG::Distribution:
- _seed
+ InitSeed()
+ ClockRandomSeed()
+ Seed()
+ GetInt()
+ GetInt()
+ GetInt()
+ GetDouble()
+ Random()
+ GetDouble()
+ GetDouble()

RNG::Distribution

+ Distribution()
+ Distribution()
+ Bernoulli()
+ Binomial()
+ Equilikely()
+ Geometric()
+ Pascal()
+ Poisson()
+ Uniform()
+ Exponential()
+ Erlang()
+ Normal()
+ Lognormal()
+ Chisquare()
+ Student()

•
•
•
•
•
•
•
•
•
•
•
•
•

Distribution ()
Distribution (unsigned long seed)
long Bernoulli (double probability=0.5)
long Binomial (unsigned long limit_experiment, double probability=0.5)
long Equilikely (long a, long b)
unsigned long Geometric (double probability=0.5)
long Pascal (unsigned long limit_experiment, double probability=0.5)
long Poisson (double mean)
double Uniform (double a, double b)
double Exponential (double mean=0.5)
double Erlang (long limit_experiment, double base)
double Normal (double Mean, double StandarDev)
double Lognormal (double a, double b)


18

Class Documentation
• double Chisquare (unsigned long limit_experiment)
• double Student (unsigned long limit_experiment)

6.2.1


Classe para geração de números pseudo-aleatórios que possui em seu núcleo um gerador com distribuição
uniforme - no caso especíﬁco dessa classe usaremos a ancestral RandomNumberGenerator para gerar essa
distribuição uniforme e a partir desse ’motor’ iremos gerar os demais tipos de distribuição. Com isso
teremos para a classe Distribuition 6 distribuições discretas :
Generator Range (x) Mean Variance
Bernoulli(p) x = 0,1 p p∗(1-p) Binomial(n, p) x = 0,...,n n∗p n∗p∗(1-p) Equilikely(a, b) x = a,...,b (a+b)/2
((b-a+1)∗(b-a+1)-1)/12 Geometric(p) x = 0,... p/(1-p) p/((1-p)∗(1-p)) Pascal(n, p) x = 0,... n∗p/(1-p)
n∗p/((1-p)∗(1-p)) Poisson(m) x = 0,... m m
E sete distribuições contínuas :
Uniform(a, b) a < x < b (a + b)/2 (b - a)∗(b - a)/12 Exponential(m) x > 0 m m∗m Erlang(n, b) x > 0 n∗b
n∗b∗b Normal(m, s) all x m s∗s Lognormal(a, b) x > 0 (ver abaixo) Chisquare(n) x > 0 n 2∗n Student(n)
all x 0 (n > 1) n/(n - 2) (n > 2)
Para a Lognormal(a, b), sua média e sua variância serão dadas por:
mean = exp(a + 0.5∗b∗b) variance = (exp(b∗b) - 1) ∗ exp(2∗a + b∗b)

6.2.2


6.2.2.1

RNG::Distribution::Distribution () [inline]

00597 : RandomNumberGenerator() {};

6.2.2.2

RNG::Distribution::Distribution (unsigned long seed) [inline]

00602 : RandomNumberGenerator(seed) {};

6.2.3


6.2.3.1

long RNG::Distribution::Bernoulli (double probability = 0.5)

Método que retorna 1 com probabilidade p ou 0 com probabilidade (1-p). Para isso p deverá estar compreendido no intervalo aberto 0.0 e 1.0 - (0.0, 1.0) Adotamos aqui 0.5 como 50% de chance do número
randômico ser maior ou menor que o número internamente escolhido pelo método.


19

Classe para geração de números pseudo-aleatórios que possui em seu núcleo um gerador com distribuição
uniforme - no caso especíﬁco dessa classe usaremos a ancestral RandomNumberGenerator para gerar essa
distribuição uniforme e a partir desse ’motor’ iremos gerar os demais tipos de distribuição. Com isso
Método que retorna 1 com probabilidade p ou 0 com probabilidade (1-p). Para isso ’p’ deverá estar compreendido no intervalo aberto 0.0 e 1.0 - (0.0, 1.0)
Here is the call graph for this function:
RNG::Distribution::Bernoulli

RNG::RandomNumberGenerator::Random

RNG::RandomNumberGenerator::GetDouble


6.2.3.2

RNG::Distribution::Binomial

long RNG::Distribution::Binomial (unsigned long limit_experiment, double probability =
0.5)

Método que retorna um inteiro distribuído de forma binomial entre 0 e limit Nota : use limit > 0 e 0.0 <
probabilidade < 1.0
00507
: use limit > 0 e 0.0 < probabilidade < 1.0
00508 */
00509 long Distribution::Binomial (unsigned long limit_experiment, double probability)


6.2.3.3




double RNG::Distribution::Chisquare (unsigned long limit_experiment)

Método que retorna um número real com distribuição Chi-square. Nota: use limit_experiment > 0
00633
: use limit_experiment > 0
00634 **/
00635 double Distribution::Chisquare(unsigned long limit_experiment)
00636 {
00637
unsigned long
i;
00638
double z, x = 0.0;
00639
00640
for (i = 0; i < limit_experiment; i++)
00641
{
00642
z = Normal(0.0, 1.0);

20

Class Documentation

RNG::Distribution::Chisquare

RNG::Distribution::Normal




6.2.3.4

RNG::Distribution::Student

long RNG::Distribution::Equilikely (long a, long b)

Método que retorna um inteiro eqüitativamente distribuído compreendido no intervalo semi-aberto (a,b].


RNG::swap

6.2.3.5

double RNG::Distribution::Erlang (long limit_experiment, double base)

Método que retorna um número real positivo com distribuição de Erlang. Nota: use limit_experiment > 0
e base > 0.0
00585
: use limit_experiment > 0 e base > 0.0
00586 **/
00587 double Distribution::Erlang(long limit_experiment, double base)
00588 {

RNG::Distribution::Erlang

6.2.3.6

RNG::Distribution::Exponential



double RNG::Distribution::Exponential (double mean = 0.5)

Método que retorna um número real positivo exponencialmente distribuído. Nota: use mean > 0.0
00576

: use mean > 0.0


21




RNG::Distribution::Poisson

6.2.3.7

unsigned long RNG::Distribution::Geometric (double probability = 0.5)

Método que retorna um inteiro não negativo geometricamente distribuído. Nota: use 0.0 < p < 1.0
00528

: use 0.0 < p < 1.0

RNG::Distribution::Geometric




6.2.3.8

RNG::Distribution::Pascal

double RNG::Distribution::Lognormal (double a, double b)

Método que retorna um número real com distribuição lognormal. Nota: use b > 0.0
00624

: use b > 0.0

RNG::Distribution::Lognormal





22

Class Documentation

6.2.3.9

double RNG::Distribution::Normal (double Mean, double StandarDev)

Método que retorna um número real com distribuição normal (gaussiana). Nota: use StandardDev > 0.0
00597
: use StandardDev > 0.0
00598 **/
00599 double Distribution::Normal(double Mean, double StandarDev)
00600 {
00601
const double p0 = 0.322232431088;
const double q0 = 0.099348462606;
00602
const double p1 = 1.0;
const double q1 = 0.588581570495;
00603
const double p2 = 0.342242088547;
const double q2 = 0.531103462366;
00604
const double p3 = 0.204231210245e-1; const double q3 = 0.103537752850;
00605
const double p4 = 0.453642210148e-4; const double q4 = 0.385607006340e-2;
00606
double u, t, p, q, z;
00607
00608
u
= Random();
00609
00610
if (u < 0.5) t = sqrt(-2.0 * log(u));
00611
else t = sqrt(-2.0 * log(1.0 - u));
00612
00613
p
= p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)));
00614
q
= q0 + t * (q1 + t * (q2 + t * (q3 + t * q4)));
00615






6.2.3.10

long RNG::Distribution::Pascal (unsigned long limit_experiment, double probability =
0.5)

Método que retorna um inteiro não negativo com distribuição de Pascal. Nota: use n > 0 e 0.0 < p < 1.0
00537
: use n > 0 e 0.0 < p < 1.0
00538 **/
00539 long Distribution::Pascal(unsigned long limit_experiment, double probability)






6.2.3.11

23

long RNG::Distribution::Poisson (double mean)

Método que retorna um inteiro não negativo com distribuição de Poisson. Nota: use mean > 0
00548
: use mean > 0
00549 **/
00550 long Distribution::Poisson(double mean)
00551 {
00552
double t = 0.0;
00553
long
x = 0;
00554
00555
while (t < mean)
00556
{
00557
t += Exponential(1.0);


6.2.3.12




double RNG::Distribution::Student (unsigned long limit_experiment)

Método que retorna um número real com distribuição Student-t. Nota: use limit_experiment > 0
00651

: use limit_experiment > 0


6.2.3.13




double RNG::Distribution::Uniform (double a, double b)

Método que retorna um número real uniformemente distribuído entre a e b. Nota: use a < b.
00566
00567

: use a < b.
**/



RNG::swap


24

Class Documentation


6.3 RNG::MersenneTwisterDouble Class Reference

6.3

RNG::MersenneTwisterDouble Class Reference

Inheritance diagram for RNG::MersenneTwisterDouble:

RNG::MersenneTwisterInt32
-n
-m
- state
-p
- init
+ MersenneTwisterInt32()
+ Seed()
+ Seed()
+ operator()()
+ ~MersenneTwisterInt32()
# rand_int32()
- twiddle()
- gen_state()
- MersenneTwisterInt32()
- operator=()

RNG::MersenneTwisterDouble

+ MersenneTwisterDouble()
+ operator()()
+ ~MersenneTwisterDouble()
- MersenneTwisterDouble()
- operator=()


25

26

Class Documentation

Collaboration diagram for RNG::MersenneTwisterDouble:
-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ operator()()
- operator=()

•
•
•
•
•

6.3.1

MersenneTwisterDouble ()
MersenneTwisterDouble (unsigned long seed)
MersenneTwisterDouble (const unsigned long ∗seed, int size)
double operator() ()
∼MersenneTwisterDouble ()


Classe para geração de números pseudo-aleatórios que tem como principal algoritmo o ’Mersenne Twister
Pseudo-random Number Generator’ que possui periodicidade de 2∧ 19937-1. A classe abaixo retorna
números em ponto ﬂutuante no intervalo semi-aberto [0,1).

6.3 RNG::MersenneTwisterDouble Class Reference

6.3.2


6.3.2.1

27

RNG::MersenneTwisterDouble::MersenneTwisterDouble () [inline]

Método construtor da classe de geracao de numeros aleatorios
00210 : MersenneTwisterInt32() {};

6.3.2.2

RNG::MersenneTwisterDouble::MersenneTwisterDouble (unsigned long seed)
[inline]

Método construtor que recebe um chave de 32 bits como semente
00215 : MersenneTwisterInt32(seed) {};

6.3.2.3

RNG::MersenneTwisterDouble::MersenneTwisterDouble (const unsigned long ∗ seed, int
size) [inline]

Método construtor que recebe um array inteiro de 32 bits e o tamanho do array como semente de geração
de números
00222

: MersenneTwisterInt32(seed, size) {};

6.3.2.4

RNG::MersenneTwisterDouble::∼MersenneTwisterDouble () [inline]

Método destrutor da classe responsável por desalocar qualquer recurso previamente alocado retornando o
mesmo ao sistema .
00235 {};

6.3.3


6.3.3.1

double RNG::MersenneTwisterDouble::operator() () [inline]

Overload do operador () fazendo com que o objeto criado tenha um aspecto de objeto-função.
Reimplemented from RNG::MersenneTwisterInt32.
00229

{ return static_cast<double>(rand_int32()) * (1. / 4294967296.); } // divisão p
or 2^32


28

Class Documentation

RNG::MersenneTwisterDouble::operator()

RNG::MersenneTwisterInt32::rand_int32

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


6.4 RNG::MersenneTwisterDouble53 Class Reference

6.4

RNG::MersenneTwisterDouble53 Class Reference

Inheritance diagram for RNG::MersenneTwisterDouble53:

-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()

RNG::MersenneTwisterDouble53

+ MersenneTwisterDouble53()
+ operator()()
+ ~MersenneTwisterDouble53()
- MersenneTwisterDouble53()
- operator=()


29

30

Class Documentation

Collaboration diagram for RNG::MersenneTwisterDouble53:
-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ operator()()
- operator=()

•
•
•
•
•

6.4.1

MersenneTwisterDouble53 ()
MersenneTwisterDouble53 (unsigned long seed)
MersenneTwisterDouble53 (const unsigned long ∗seed, int size)
∼MersenneTwisterDouble53 ()


números em ponto ﬂutuante com uma resolução de até 53 bits no intervalo semi-aberto [0,1) .

6.4 RNG::MersenneTwisterDouble53 Class Reference

6.4.2


6.4.2.1

31

RNG::MersenneTwisterDouble53::MersenneTwisterDouble53 () [inline]


6.4.2.2

RNG::MersenneTwisterDouble53::MersenneTwisterDouble53 (unsigned long seed)
[inline]

Método construtor que recebe uma chave de 32 bits como semente
00381 : MersenneTwisterInt32(seed) {};

6.4.2.3

RNG::MersenneTwisterDouble53::MersenneTwisterDouble53 (const unsigned long ∗ seed,
int size) [inline]

de números
00388


6.4.2.4

RNG::MersenneTwisterDouble53::∼MersenneTwisterDouble53 () [inline]

mesmo ao sistema .
00404 {};

6.4.3


6.4.3.1

double RNG::MersenneTwisterDouble53::operator() () [inline]

00395
00396
00397

{
return (static_cast<double>(rand_int32() >> 5) * 67108864. +
static_cast<double>(rand_int32() >> 6)) * (1. / 9007199254740992.
);

00398

}


32

Class Documentation

RNG::MersenneTwisterDouble53::operator()




6.5 RNG::MersenneTwisterDoubleClosed Class Reference

6.5

RNG::MersenneTwisterDoubleClosed Class Reference

Inheritance diagram for RNG::MersenneTwisterDoubleClosed:

-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ MersenneTwisterDoubleClosed()
+ operator()()
+ ~MersenneTwisterDoubleClosed()
- MersenneTwisterDoubleClosed()
- operator=()


33

34

Class Documentation

Collaboration diagram for RNG::MersenneTwisterDoubleClosed:
-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ operator()()
- operator=()

•
•
•
•
•

6.5.1

MersenneTwisterDoubleClosed ()
MersenneTwisterDoubleClosed (unsigned long seed)
MersenneTwisterDoubleClosed (const unsigned long ∗seed, int size)
∼MersenneTwisterDoubleClosed ()


números em ponto ﬂutuante no intervalo fechado [0,1].

6.5 RNG::MersenneTwisterDoubleClosed Class Reference

6.5.2


6.5.2.1

35

RNG::MersenneTwisterDoubleClosed::MersenneTwisterDoubleClosed () [inline]


6.5.2.2

RNG::MersenneTwisterDoubleClosed::MersenneTwisterDoubleClosed (unsigned long
seed) [inline]

00270

: MersenneTwisterInt32(seed) {};

6.5.2.3

RNG::MersenneTwisterDoubleClosed::MersenneTwisterDoubleClosed (const unsigned
long ∗ seed, int size) [inline]

de números
00277


6.5.2.4

RNG::MersenneTwisterDoubleClosed::∼MersenneTwisterDoubleClosed () [inline]

mesmo ao sistema .
00290 {};

6.5.3


6.5.3.1

double RNG::MersenneTwisterDoubleClosed::operator() () [inline]

00284

{ return static_cast<double>(rand_int32()) * (1. / 4294967295.); } // divisão p
or 2^32 - 1


36

Class Documentation

RNG::MersenneTwisterDoubleClosed::operator()




6.6 RNG::MersenneTwisterDoubleOpened Class Reference

6.6

RNG::MersenneTwisterDoubleOpened Class Reference

Inheritance diagram for RNG::MersenneTwisterDoubleOpened:

-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ MersenneTwisterDoubleOpened()
+ operator()()
+ ~MersenneTwisterDoubleOpened()
- MersenneTwisterDoubleOpened()
- operator=()


37

38

Class Documentation

Collaboration diagram for RNG::MersenneTwisterDoubleOpened:
-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()


+ operator()()
- operator=()

•
•
•
•
•

6.6.1

MersenneTwisterDoubleOpened ()
MersenneTwisterDoubleOpened (unsigned long seed)
MersenneTwisterDoubleOpened (const unsigned long ∗seed, int size)
∼MersenneTwisterDoubleOpened ()


números em ponto ﬂutuante no intervalo aberto (0,1).

6.6 RNG::MersenneTwisterDoubleOpened Class Reference

39

6.6.2


6.6.2.1

RNG::MersenneTwisterDoubleOpened::MersenneTwisterDoubleOpened () [inline]


6.6.2.2

RNG::MersenneTwisterDoubleOpened::MersenneTwisterDoubleOpened (unsigned long
seed) [inline]

00326

: MersenneTwisterInt32(seed) {};

6.6.2.3

RNG::MersenneTwisterDoubleOpened::MersenneTwisterDoubleOpened (const unsigned
long ∗ seed, int size) [inline]

de números
00333


6.6.2.4

RNG::MersenneTwisterDoubleOpened::∼MersenneTwisterDoubleOpened () [inline]

mesmo ao sistema .
00346 {};

6.6.3


6.6.3.1

double RNG::MersenneTwisterDoubleOpened::operator() () [inline]

00340

{ return (static_cast<double>(rand_int32()) + .5) * (1. / 4294967296.); } // di
visão por 2^32


40

Class Documentation

RNG::MersenneTwisterDoubleOpened::operator()




6.7 RNG::MersenneTwisterInt32 Class Reference

6.7

41

RNG::MersenneTwisterInt32 Class Reference

Inheritance diagram for RNG::MersenneTwisterInt32:
-n
-m
- state
-p
- init
+ Seed()
+ Seed()
+ operator()()
# rand_int32()
- twiddle()
- gen_state()
- operator=()





+ operator()()
- operator=()

+ operator()()
- operator=()

+ operator()()
- operator=()

+ operator()()
- operator=()

•
•
•
•
•
•
•

MersenneTwisterInt32 ()
MersenneTwisterInt32 (unsigned long seed)
MersenneTwisterInt32 (const unsigned long ∗array, int size)
void Seed (unsigned long seed)
void Seed (const unsigned long ∗array, int size)
unsigned long operator() ()
virtual ∼MersenneTwisterInt32 ()

Protected Member Functions
• unsigned long rand_int32 ()

6.7.1


Pseudo-Random Number Generator’ que possui periodicidade de 2∧ 19937-1. A classe abaixo gera número
pseudo-aleatórios em formato inteiro sem sinal.

42

Class Documentation

6.7.2


6.7.2.1

RNG::MersenneTwisterInt32::MersenneTwisterInt32 ()

6.7.2.2

RNG::MersenneTwisterInt32::MersenneTwisterInt32 (unsigned long seed)

00169 { if (!init) Seed(5489UL); init = true; };
00170

RNG::MersenneTwisterInt32::MersenneTwisterInt32

6.7.2.3

RNG::MersenneTwisterInt32::Seed

RNG::MersenneTwisterInt32::MersenneTwisterInt32 (const unsigned long ∗ array, int
size)

Método construtor que recebe um array inteiro de 32 bits e o tamanho do array como semente de geração de
números. Um bom exemplo para uso com esse método seria : unsigned long init_seed[4]={0x123, 0x234,
0x345, 0x456}, length=4; MersenneTwisterInt32 mt(init_seed, length);
de números

6.7.2.4


RNG::MersenneTwisterInt32::∼MersenneTwisterInt32 () [virtual]

mesmo ao sistema .
Metodo destrutor da classe

6.7.3


6.7.3.1

unsigned long RNG::MersenneTwisterInt32::operator() () [inline]


6.7 RNG::MersenneTwisterInt32 Class Reference

43

Reimplemented
in
RNG::MersenneTwisterDouble,
RNG::MersenneTwisterDoubleClosed,
RNG::MersenneTwisterDoubleOpened, and RNG::MersenneTwisterDouble53.
00186 { return rand_int32(); }

RNG::MersenneTwisterInt32::operator()

6.7.3.2


unsigned long RNG::MersenneTwisterInt32::rand_int32 () [protected]

Método que gera um inteiro randômico de 32 bits
00253 {
00254
//Caso seja necessario um novo estado para o vetor de estados
00255
if (p == n) gen_state();
00256
00257
//O método gen_state() é dividido para ser inline, porque ele só é
00258
//chamado uma vez a cada 624 chamadas de outro modo ele se tornaria muito
00259
//grande para ser implementado como método inline.
00260
unsigned long x = state[p++];

RNG::MersenneTwisterDouble53::operator()

RNG::MersenneTwisterDoubleOpened::operator()


RNG::MersenneTwisterDoubleClosed::operator()

RNG::MersenneTwisterDouble::operator()

RNG::MersenneTwisterInt32::operator()

6.7.3.3

void RNG::MersenneTwisterInt32::Seed (const unsigned long ∗ array, int size)

Geração de semente através de um array de inteiros de 32 bits
00211 {
00212
Seed(19650218UL);
00213
int i = 1, j = 0;
00214
00215
for (int k = ((n > size) ? n : size); k; --k)
00216
{
00217
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1664525UL))
00218
+ array[j] + j; // non linear

44

Class Documentation

00219
00220
00221
00222
00223
00224
00225
00226
00227
00228
00229
00230
00231
00232
00233
00234

6.7.3.4

state[i] &= 0xFFFFFFFFUL; // Para máquinas com mais de 32 bits
++j; j %= size;
if ((++i) == n) { state[0] = state[n - 1]; i = 1; }
}
for (int k = n - 1; k; --k)
{
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30))
* 1566083941UL)) - i;
}
// O estado zero recebe 1 - assumindo um inicio de array não-nulo

void RNG::MersenneTwisterInt32::Seed (unsigned long seed)

Geração de semente através de um inteiro de 32 bits
00192 {
00193
// Para máquinas com mais de 32 bits
00194
state[0] = seed & 0xFFFFFFFFUL;
00195
00196
// Looping que obtem a nova semente para geração de números
00197
for (int i = 1; i < n; ++i)
00198
{
00199
state[i] = 1812433253UL * (state[i - 1] ^ (state[i - 1] >> 30)) + i;
00200





6.8 RNG::R250Base Class Reference

6.8

45

RNG::R250Base Class Reference

Inheritance diagram for RNG::R250Base:

RNG::R250Base
+ r250_index
+ r250_buffer
+ seed
+ R250Base()
+ R250Base()
+ r250_init()
+ myrand()
+ mysrand()

RNG::R250Double

+ R250Double()
+ R250Double()
+ operator()()

• R250Base ()
• R250Base (unsigned long seed)
• void r250_init (unsigned long seed)

Static Public Member Functions
• static unsigned myrand ()
• static void mysrand (unsigned newseed)

Static Public Attributes
• static int r250_index = 0

RNG::R250Int

+ R250Int()
+ R250Int()
+ operator()()
+ operator()()

46

Class Documentation
• static unsigned int r250_buffer [250]
• static unsigned long seed = 1

6.8.1


Classe para geração de números pseudo-aleatórios que tem como principal algoritmo o ’R250’ que possui
periodicidade de 2∧ 250-1. A classe abaixo serve como base para as demais classes que usarão o algoritmo
R250.

6.8.2


6.8.2.1

RNG::R250Base::R250Base () [inline]

00435 {};

6.8.2.2

RNG::R250Base::R250Base (unsigned long seed) [inline]

Método construtor que recebe uma chave como semente
00440 { r250_init(seed); }

RNG::R250Base::R250Base

RNG::R250Base::r250_init

6.8.3


6.8.3.1

unsigned RNG::R250Base::myrand () [inline, static]

Método que retorna um número pseudo aleatório no intervalo entre 0 e 32768 Produzindo a seguinte sequencia de números randômicos : 346, 130, 10982, 1090... (9996 numbers skipped) ...23369, 2020, 5703,
12762, 10828, 16252, 28648, 27041, 23444, 6604...
Método que retorna um número pseudo-aleatório no intervalo entre 0 e 32768.
6.8.3.2

void RNG::R250Base::mysrand (unsigned newseed) [inline, static]

Inicializa a semente de geração rândomica usando o método de congruência linear
Inicializa a semente de geração usando o método de congruência linear

6.8 RNG::R250Base Class Reference
6.8.3.3

47

void RNG::R250Base::r250_init (unsigned long seed)

Inicializa o gerador de números aleatórios.
00329 {
00330
int
j, k;
00331
unsigned int mask;
00332
unsigned int msb;
00333
00334
mysrand(seed);
00335
r250_index = 0;
00336
00337
for (j = 0; j < 250; j++)
/* Fill the r250 buffer with 15-bit values */
00338
r250_buffer[j] = myrand();
00339
00340
for (j = 0; j < 250; j++)
/* Set some of the MS bits to 1 */
00341
if (myrand() > 16384) r250_buffer[j] |= 0x8000;
00342
00343
msb = 0x8000;
/* To turn on the diagonal bit
*/
00344
mask = 0xffff;
/* To turn off the leftmost bits */
00345
00346
for (j = 0; j < 16; j++)
00347
{
00348
k = 11 * j + 3;
/* Select a word to operate on
*/
00349
r250_buffer[k] &= mask;
/* Turn off bits left of the diagonal */

RNG::R250Base::r250_init

RNG::R250Base::R250Base

6.8.4

Member Data Documentation

6.8.4.1

unsigned int RNG::R250Base::r250_buffer [static]

Initial value:
{
15301,57764,10921,56345,19316,43154,54727,49252,32360,49582,
26124,25833,34404,11030,26232,13965,16051,63635,55860,5184,
15931,39782,16845,11371,38624,10328,9139,1684,48668,59388,
13297,1364,56028,15687,63279,27771,5277,44628,31973,46977,
16327,23408,36065,52272,33610,61549,58364,3472,21367,56357,
56345,54035,7712,55884,39774,10241,50164,47995,1718,46887,
47892,6010,29575,54972,30458,21966,54449,10387,4492,644,
57031,41607,61820,54588,40849,54052,59875,43128,50370,44691,
286,12071,3574,61384,15592,45677,9711,23022,35256,45493,
48913,146,9053,5881,36635,43280,53464,8529,34344,64955,
38266,12730,101,16208,12607,58921,22036,8221,31337,11984,
20290,26734,19552,48,31940,43448,34762,53344,60664,12809,
57318,17436,44730,19375,30,17425,14117,5416,23853,55783,
57995,32074,26526,2192,11447,11,53446,35152,64610,64883,
26899,25357,7667,3577,39414,51161,4,58427,57342,58557,
53233,1066,29237,36808,19370,17493,37568,3,61468,38876,
17586,64937,21716,56472,58160,44955,55221,63880,1,32200,
62066,22911,24090,10438,40783,36364,14999,2489,43284,9898,
39612,9245,593,34857,41054,30162,65497,53340,27209,45417,
37497,4612,58397,52910,56313,62716,22377,40310,15190,34471,
64005,18090,11326,50839,62901,59284,5580,15231,9467,13161,

48

Class Documentation
58500,7259,317,50968,2962,23006,32280,6994,18751,5148,
52739,49370,51892,18552,52264,54031,2804,17360,1919,19639,
2323,9448,43821,11022,45500,31509,49180,35598,38883,19754,
987,11521,55494,38056,20664,2629,50986,31009,54043,59743
}

6.8.4.2

int RNG::R250Base::r250_index = 0 [static]

6.8.4.3

unsigned long RNG::R250Base::seed = 1 [static]



6.9 RNG::R250Double Class Reference

6.9

RNG::R250Double Class Reference

Inheritance diagram for RNG::R250Double:

RNG::R250Base
+ r250_index
+ r250_buffer
+ seed
+ R250Base()
+ R250Base()
+ r250_init()
+ myrand()
+ mysrand()

RNG::R250Double

+ R250Double()
+ R250Double()
+ operator()()


49

50

Class Documentation

Collaboration diagram for RNG::R250Double:

RNG::R250Base
+ r250_index
+ r250_buffer
+ seed
+ R250Base()
+ R250Base()
+ r250_init()
+ myrand()
+ mysrand()

RNG::R250Double

+ R250Double()
+ R250Double()
+ operator()()

• R250Double ()
• R250Double (unsigned long seed)
• double operator() ()

6.9.1


periodicidade de 2∧ 250-1. A classe abaixo retorna um número pseudo-aleatório real de precisão dupla no
intervalo compreendido entre 0 e 1.

6.9 RNG::R250Double Class Reference

6.9.2


6.9.2.1

51

RNG::R250Double::R250Double () [inline]

00512 : R250Base() {};

6.9.2.2

RNG::R250Double::R250Double (unsigned long seed) [inline]

00517 : R250Base(seed) {};

6.9.3


6.9.3.1

double RNG::R250Double::operator() ()

retorna números pseudo-aleatório reais distribuídos dentro intervalo compreendido entre 0 e 1.
00420 {
00421
register int
j;
00422
register unsigned int new_rand;
00423
00424
// Verifica limites de salto - Wrap pointer around
00425
if (r250_index >= 147) j = r250_index - 147;
00426
else j = r250_index + 103;
00427
00428
new_rand = r250_buffer[r250_index] ^= r250_buffer[j];
00429
00430
//Incrementa o ponteiro para o próximo salto dentro do vetor de sementes



52

6.10

Class Documentation

RNG::R250Int Class Reference

Inheritance diagram for RNG::R250Int:

RNG::R250Base
+ r250_index
+ r250_buffer
+ seed
+ R250Base()
+ R250Base()
+ r250_init()
+ myrand()
+ mysrand()

RNG::R250Int

+ R250Int()
+ R250Int()
+ operator()()
+ operator()()


6.10 RNG::R250Int Class Reference

53

Collaboration diagram for RNG::R250Int:

RNG::R250Base
+ r250_index
+ r250_buffer
+ seed
+ R250Base()
+ R250Base()
+ r250_init()
+ myrand()
+ mysrand()

RNG::R250Int

+ R250Int()
+ R250Int()
+ operator()()
+ operator()()

•
•
•
•

R250Int ()
R250Int (unsigned long seed)
unsigned int operator() ()
unsigned int operator() (unsigned int maximum_limit)

6.10.1


periodicidade de 2∧ 250-1. A classe abaixo retorna um número pseudo-aleatório inteiro sem sinal uniformemente distribuído no intervalo compreendido entre 0 e 65535.

54

Class Documentation

6.10.2


6.10.2.1

RNG::R250Int::R250Int () [inline]

00476 : R250Base() {};

6.10.2.2

RNG::R250Int::R250Int (unsigned long seed) [inline]

00481 : R250Base(seed) {};

6.10.3


6.10.3.1

unsigned int RNG::R250Int::operator() (unsigned int maximum_limit)

Overload do operador () fazendo com que o objeto criado tenha um aspecto de objeto-função. Retorna um
determinado número k inteiro sem sinal uniformmente distribuído dentro do intervalo compreendido entre
0 e maximum_limit.
Overload do operador () fazendo com que o objeto criado tenha um aspecto de objeto-função. Retorna um
determinado número k inteiro sem sinal uniformmente distribuído dentro do intervalo compreendido entre
0 e limit.
00385 {
00386
register int
j;
00387
register unsigned int new_rand, limit;
00388
unsigned int n = maximum_limit;
00389
00390
// LImitede geração de números
00391
limit = (65535U/n)*n;
00392
00393
do
00394
{
00395
//Usando o operador que retorna numeros entre 0 e 65535
00396
new_rand = operator ()();
00397
00398
00399
00400
00401
00402
00403
00404
00405
if (r250_index >= 249) r250_index = 0;
00406
else r250_index++;
00407


6.10 RNG::R250Int Class Reference
6.10.3.2

55

unsigned int RNG::R250Int::operator() ()

retorna números pseudo-aleatório inteiros sem sinal uniformemente distribuídos dentro intervalo compreendido entre 0 e 65535.
00362 {
00363
register int
j;
00364
00365
00366
00367
00368
00369
00370
00371
00372



56

Class Documentation

6.11

RNG::RandomNumberGenerator Class Reference

Inheritance diagram for RNG::RandomNumberGenerator:
- _seed
+ InitSeed()
+ ClockRandomSeed()
+ Seed()
+ GetInt()
+ GetInt()
+ GetInt()
+ GetDouble()
+ Random()
+ GetDouble()
+ GetDouble()

RNG::Distribution

RNG::BoxMuller

+ BoxMuller()
+ BoxMuller()
+ operator()()

+ Distribution()
+ Distribution()
+ Bernoulli()
+ Binomial()
+ Equilikely()
+ Geometric()
+ Pascal()
+ Poisson()
+ Uniform()
+ Exponential()
+ Erlang()
+ Normal()
+ Lognormal()
+ Chisquare()
+ Student()

•
•
•
•
•
•
•
•
•

RandomNumberGenerator ()
RandomNumberGenerator (unsigned long seed)
void InitSeed (unsigned int seed=0)
unsigned int ClockRandomSeed (unsigned int myseed=0)
unsigned int Seed (void)
unsigned int GetInt (void)
unsigned int GetInt (unsigned int maximum_limit)
unsigned int GetInt (unsigned int minimum_limit, unsigned int maximum_limit)
double GetDouble (void)

6.11 RNG::RandomNumberGenerator Class Reference
•
•
•
•

57

double Random (void)
double GetDouble (double maximum_limit)
double GetDouble (double minimum_limit, double maximum_limit)
virtual ∼RandomNumberGenerator ()

6.11.1


Classe para geracao de numeros pseudo-aleatorios que tem como principal algoritmo o ’Linear Congruential Generator’ [ou Gerador de Congruência Linear] da funcao rand() existente na biblioteca padrão.

6.11.2


6.11.2.1

RNG::RandomNumberGenerator::RandomNumberGenerator ()

Construtor da classe de geração de números aleatórios
6.11.2.2

RNG::RandomNumberGenerator::RandomNumberGenerator (unsigned long seed)
[inline]

Método construtor que recebe como parâmetro uma semente incial
00042 { InitSeed(seed); };

RNG::RandomNumberGenerator::RandomNumberGenerator

6.11.2.3

RNG::RandomNumberGenerator::InitSeed

RNG::RandomNumberGenerator::∼RandomNumberGenerator () [virtual]

mesmo ao sistema .
Metodo destrutor da classe

6.11.3


6.11.3.1

unsigned int RNG::RandomNumberGenerator::ClockRandomSeed (unsigned int myseed
= 0)

Método que retorna uma semente aleatória para geração de números baseada no clock/relógio interno local.

58

Class Documentation

Método que retorna uma semente aleatoria baseada no clock interno
00039 {
00040
/*Estrutura responsavel pelo armazenamento do horario local*/
00041
/*utilizado na geracao da semente randômica*/
00042
struct tm myTM;
00043
double divisor = 1;
00044
00045
//Semente baseada no tempo é sugerida se a fornecida for nula
00046
if (myseed == 0) return (time(0)*rand());
00047
00048
/*Caso a semente inicial fornecida seja nula então usaremos a estrutura de*/
00049
/*tempo local para geração da semente*/
00050
mktime(&myTM);
00051
00052
/*Se a semente fornecida não for nula entao uma semente baseada no algoritmo
00053
*de divisao abaixo é fornecida*/
00054
if ((myseed%2) == 0)
00055
{
00056
divisor = myseed + 0.13579;
00057
return (unsigned int)((myTM.tm_min*rand()*time(0))/divisor);
00058
}
00059
else

RNG::RandomNumberGenerator::ClockRandomSeed

6.11.3.2

main

double RNG::RandomNumberGenerator::GetDouble (double minimum_limit, double
maximum_limit)

Método que retorna um número pseudo-aleatório em ponto ﬂutuante entre minimum_limit e maximum_limit
Método que retorna um número entre minimum_limit e maximum_limit ...
00122 {
00123
//Criando alias para melhorar a legibilidade do programa
00124
double min = minimum_limit;
00125
double max = maximum_limit;
00126
00127
//Verificando se os limites estão corretamente colocados

6.11.3.3

double RNG::RandomNumberGenerator::GetDouble (double maximum_limit)

Método que retorna um número pseudo-aleatório em ponto ﬂutuante entre 0.0 e maximum_limit
Método que retorna um número entre 0 e maximum_limit ...

6.11.3.4

59

double RNG::RandomNumberGenerator::GetDouble (void)

Método que retorna um número pseudo-aleatório em ponto ﬂutuante entre 0 e 0.99999 ...
Método que retorna um número entre 0 e 0.99999 ...










main



6.11.3.5

unsigned int RNG::RandomNumberGenerator::GetInt (unsigned int minimum_limit,
unsigned int maximum_limit)

Método que retorna um número pseudo-aleatóro em formato inteiro sem sinal entre minimum_limit e
maximum_limit
Metodo que retorna um número entre minimum_limit e maximum_limit
00089 {
00090
00091
int min = minimum_limit;
00092
int max = maximum_limit;
00093
00094

6.11.3.6

unsigned int RNG::RandomNumberGenerator::GetInt (unsigned int maximum_limit)

Método que retorna um número pseudo-aleatório em formato inteiro sem sinal entre 0 e maximum_limit
Metodo que retorna um número entre 0 e maximum_limit
00074
00075

6.11.3.7

{ return rand(); }

unsigned int RNG::RandomNumberGenerator::GetInt (void)

Metodo que retorna um numero pseudo-aleatorio em formato inteiro sem sinal entre 0 e 32767.
Metodo que retorna um número gerado pseudo-aleatoriamente

60

Class Documentation

00069 { return _seed;

6.11.3.8

}

void RNG::RandomNumberGenerator::InitSeed (unsigned int seed = 0)

Metodo que executa atribuicao inicial na semente interna de geracao de numeros aleatorios. Caso essa
semente nao seja modiﬁcada entre a geracao de sequencias numericas entao os mesmos numero serao
retornados.
Método que inicia a semente de geração de número aleatórios
00024
00025

{ _seed = time(0); }

main
RNG::RandomNumberGenerator::InitSeed
RNG::RandomNumberGenerator::RandomNumberGenerator

6.11.3.9

double RNG::RandomNumberGenerator::Random (void) [inline]

Apenas um alias para o método GetDouble. Dessa forma podemos interpretar o método como um gerador
de números pseudo-aleatórios que retorna elementos uniformemente distribuídos no intervalo aberto (0.0 ,
1.0)
00092 { return GetDouble(); }

















6.11.3.10

unsigned int RNG::RandomNumberGenerator::Seed (void)

Método que retorna a semente de geração de numeros aleatorios armazenada na variavel de estado.
Método que retorna o valor da semente armazenada na variavel de estado


61

62

Class Documentation


Chapter 7

File Documentation
7.1

RandomNumberGenerator.cxx File Reference

#include "RandomNumberGenerator.h"
#include <ctime>
#include <cmath>
#include <cstdlib>
Include dependency graph for RandomNumberGenerator.cxx:
RandomNumberGenerator.cxx

ctime

cmath

cstdlib

This graph shows which ﬁles directly or indirectly include this ﬁle:

Namespaces
• namespace RNG

64

7.2
00001
00002
00003
00004
00005
00006
00007
00008
00009
00013
00014
00015
00016
00017
00018
00019
00020
00024
00025
00029
00030
00031
00032
00033
00034
00038
00039
00040
00041
00042
00043
00044
00045
00046
00047
00048
00049
00050
00051
00052
00053
00054
00055
00056
00057
00058
00059
00060
00061
00062
00063
00064
00065
00069
00070
00074
00075
00079
00080
00081
00082
00083
00087
00088

File Documentation

/*
* RandomNumberGenerator.cxx
*
* Created on: 21/10/2009
Author: Michel Alves dos Santos
*
*/
#include "RandomNumberGenerator.h"
namespace RNG
{
//----------------------------------------------------------------------------//
// Implementação dos métodos da classe RandomNumberGenerator baseada na função
// rand() da biblioteca padrão que usa o método Linear Congruential Generator
//----------------------------------------------------------------------------//
RandomNumberGenerator::RandomNumberGenerator() { _seed = time(0); }
void RandomNumberGenerator::InitSeed(unsigned int seed)
{
_seed = (seed)?(seed):((unsigned)(time(NULL)));
srand( _seed );
}
unsigned int RandomNumberGenerator::ClockRandomSeed(unsigned int myseed)
{
/*Estrutura responsavel pelo armazenamento do horario local*/
/*utilizado na geracao da semente randômica*/
struct tm myTM;
double divisor = 1;
//Semente baseada no tempo é sugerida se a fornecida for nula
if (myseed == 0) return (time(0)*rand());
/*Caso a semente inicial fornecida seja nula então usaremos a estrutura de*/
/*tempo local para geração da semente*/
mktime(&myTM);
/*Se a semente fornecida não for nula entao uma semente baseada no algoritmo
*de divisao abaixo é fornecida*/
if ((myseed%2) == 0)
{
return (unsigned int)((myTM.tm_min*rand()*time(0))/divisor);
}
else
{
return (unsigned int)((myTM.tm_min*rand()*time(0))/(divisor/2));
}
}
unsigned int RandomNumberGenerator::Seed(void)

{ return _seed;

}

unsigned int RandomNumberGenerator::GetInt(void){ return rand(); }
unsigned int RNG::RandomNumberGenerator::GetInt(unsigned int maximum_limit)
{
return (int)(maximum_limit*rand()/(RAND_MAX + 1.0));
}
unsigned int RNG::RandomNumberGenerator::GetInt(unsigned int minimum_limit,
unsigned int maximum_limi
t)

7.2 RandomNumberGenerator.cxx
00089
00090
00091
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65

{
int min = minimum_limit;
int max = maximum_limit;
if (min > max) RNG::swap(min,max);
//Retornando um número gerado dentro dos limites impostos
return (int)((max - min + 1)*rand()/(RAND_MAX + 1.0)) + min;
}
double RNG::RandomNumberGenerator::GetDouble(void)
{
return rand()/(double(RAND_MAX) + 1);
}
double RNG::RandomNumberGenerator::GetDouble(double maximum_limit)
{
return this->GetDouble()*maximum_limit;
}
double RNG::RandomNumberGenerator::GetDouble(double minimum_limit,
double maximum_limit)
{
double min = minimum_limit;
double max = maximum_limit;
if (min > max) RNG::swap(min,max);
//Retornando um número gerado dentro dos limites impostos
return GetDouble()*(max - min) + min;
}
RandomNumberGenerator::~RandomNumberGenerator() {}
//----------------------------------------------------------------------------//
// Classe para geração de números pseudo-aleatórios que tem como principal
// algoritmo o ’Mersenne Twister Pseudo-random Number Generator’ que possui
// periodicidade de 2^19937-1.
//----------------------------------------------------------------------------//
// Inicializando os membros estáticos privados
unsigned long MersenneTwisterInt32::state[n] = {0x0UL};
int
MersenneTwisterInt32::p = 0;
bool
MersenneTwisterInt32::init = false;
inline void MersenneTwisterInt32::gen_state()
{
for (int i = 0; i < (n - m); ++i)
state[i] = state[i + m] ^ twiddle(state[i], state[i + 1]);
for (int i = n - m; i < (n - 1); ++i)
state[i] = state[i + m - n] ^ twiddle(state[i], state[i + 1]);
state[n - 1] = state[m - 1] ^ twiddle(state[n - 1], state[0]);
p = 0; // reinicia a posicao
}
MersenneTwisterInt32::MersenneTwisterInt32()
{ if (!init) Seed(5489UL); init = true; };
MersenneTwisterInt32::MersenneTwisterInt32(unsigned long
{
Seed(seed); init = true;


seed)

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File Documentation
}
MersenneTwisterInt32::MersenneTwisterInt32(const unsigned long *array, int size)
{
Seed(array, size); init = true;
}
void MersenneTwisterInt32::Seed(unsigned long
{
// Para máquinas com mais de 32 bits
state[0] = seed & 0xFFFFFFFFUL;

seed)

// Looping que obtem a nova semente para geração de números
for (int i = 1; i < n; ++i)
{
state[i] = 1812433253UL * (state[i - 1] ^ (state[i - 1] >> 30)) + i;
}
// Força gen_state() a ser chamada para um novo número aleatório
p = n;
}
void MersenneTwisterInt32::Seed(const unsigned long* array, int size)
{
Seed(19650218UL);
int i = 1, j = 0;
for (int k = ((n > size) ? n : size); k; --k)
{
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1664525UL))
+ array[j] + j; // non linear
++j; j %= size;
}
for (int k = n - 1; k; --k)
{
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30))
* 1566083941UL)) - i;
}
// O estado zero recebe 1 - assumindo um inicio de array não-nulo
state[0] = 0x80000000UL;
// Força gen_state() a ser chamada para um novo número aleatório
p = n;
}

unsigned long MersenneTwisterInt32::twiddle(unsigned long u, unsigned long v)
{
return (((u & 0x80000000UL) | (v & 0x7FFFFFFFUL)) >> 1)^ ((v & 1UL) ? 0x9908B0D
FUL : 0x0UL);
00247 }
00248
00252 unsigned long MersenneTwisterInt32::rand_int32()
00253 {
00254
//Caso seja necessario um novo estado para o vetor de estados
00255
if (p == n) gen_state();
00256
00257
//O método gen_state() é dividido para ser inline, porque ele só é
00258
//chamado uma vez a cada 624 chamadas de outro modo ele se tornaria muito


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67

//grande para ser implementado como método inline.
unsigned long x = state[p++];
x ^= (x >> 11);
x ^= (x << 7) & 0x9D2C5680UL;
x ^= (x << 15) & 0xEFC60000UL;
return x ^ (x >> 18);
}
MersenneTwisterInt32::~MersenneTwisterInt32(){};
//----------------------------------------------------------------------------//
// Classes para geração de números pseudo-aleatórios que tem como principal
// algoritmo o ’R250’ que possui periodicidade de 2^250-1.
//----------------------------------------------------------------------------//
// Inicializando os membros estáticos da classe
int
R250Base::r250_index
= 0;
unsigned long R250Base::seed
= 1;
unsigned int R250Base::r250_buffer[250] = {
15301,57764,10921,56345,19316,43154,54727,49252,32360,49582,
26124,25833,34404,11030,26232,13965,16051,63635,55860,5184,
15931,39782,16845,11371,38624,10328,9139,1684,48668,59388,
13297,1364,56028,15687,63279,27771,5277,44628,31973,46977,
16327,23408,36065,52272,33610,61549,58364,3472,21367,56357,
56345,54035,7712,55884,39774,10241,50164,47995,1718,46887,
47892,6010,29575,54972,30458,21966,54449,10387,4492,644,
57031,41607,61820,54588,40849,54052,59875,43128,50370,44691,
286,12071,3574,61384,15592,45677,9711,23022,35256,45493,
48913,146,9053,5881,36635,43280,53464,8529,34344,64955,
38266,12730,101,16208,12607,58921,22036,8221,31337,11984,
20290,26734,19552,48,31940,43448,34762,53344,60664,12809,
57318,17436,44730,19375,30,17425,14117,5416,23853,55783,
57995,32074,26526,2192,11447,11,53446,35152,64610,64883,
26899,25357,7667,3577,39414,51161,4,58427,57342,58557,
53233,1066,29237,36808,19370,17493,37568,3,61468,38876,
17586,64937,21716,56472,58160,44955,55221,63880,1,32200,
62066,22911,24090,10438,40783,36364,14999,2489,43284,9898,
39612,9245,593,34857,41054,30162,65497,53340,27209,45417,
37497,4612,58397,52910,56313,62716,22377,40310,15190,34471,
64005,18090,11326,50839,62901,59284,5580,15231,9467,13161,
58500,7259,317,50968,2962,23006,32280,6994,18751,5148,
52739,49370,51892,18552,52264,54031,2804,17360,1919,19639,
2323,9448,43821,11022,45500,31509,49180,35598,38883,19754,
987,11521,55494,38056,20664,2629,50986,31009,54043,59743
};
inline unsigned R250Base::myrand()
{
seed = seed*0x015a4e35L + 1;
return (seed>>16)&0x7fff;
}
inline void R250Base::mysrand(unsigned newseed)
{
seed = newseed;
}
void R250Base::r250_init(unsigned long seed)
{
int
j, k;
unsigned int mask;
unsigned int msb;
mysrand(seed);
r250_index = 0;
for (j = 0; j < 250; j++)


/* Fill the r250 buffer with 15-bit values */

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File Documentation
r250_buffer[j] = myrand();
for (j = 0; j < 250; j++)
/* Set some of the MS bits to 1 */
if (myrand() > 16384) r250_buffer[j] |= 0x8000;
msb = 0x8000;
mask = 0xffff;

/* To turn on the diagonal bit
*/
/* To turn off the leftmost bits */

for (j = 0; j < 16; j++)
{
k = 11 * j + 3;
r250_buffer[k] &= mask;
r250_buffer[k] |= msb;
mask >>= 1;
msb >>= 1;
}

/* Select a word to operate on
*/
/* Turn off bits left of the diagonal */
/* Turn on the diagonal bit
*/

}
unsigned int R250Int::operator ()()
{
register int
j;
if (r250_index >= 249) r250_index = 0;
else r250_index++;
return new_rand;
}
unsigned int R250Int::operator ()(unsigned int maximum_limit)
{
register int
j;
register unsigned int new_rand, limit;
unsigned int n = maximum_limit;
// LImitede geração de números
limit = (65535U/n)*n;
do
{
//Usando o operador que retorna numeros entre 0 e 65535
new_rand = operator ()();
if (r250_index >= 249) r250_index = 0;
else r250_index++;
} while(new_rand >= limit);
// Retorno da função ...
return new_rand%n;
}
double R250Double::operator ()()


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{
register int
j;
if (r250_index >= 249) r250_index = 0;
else r250_index++;
return new_rand / 65536.;

// Retorna um numero entre [0.0 até 1.0)

}
//----------------------------------------------------------------------------//
//----------------------------------------------------------------------------//
double BoxMuller::operator ()(double Mean, double StandardDev)
{
float x1, x2, w, y1;
static float y2;
static bool use_last = false;
//Verifica se o valor usado deve ser o da última chamada
if (use_last)
{
y1 = y2;
use_last = false;
}
else
{
//Calculo da localização do número dentro do intervalo passado
do
{
x1 = 2.0 * GetDouble() - 1.0;
x2 = 2.0 * GetDouble() - 1.0;
w = x1 * x1 + x2 * x2;
}
while ( w >= 1.0 );
w = sqrt( (-2.0 * log( w ) ) / w );
y1 = x1 * w;
y2 = x2 * w;
use_last = true;
}
//Retorno do número transformado ...
return( Mean + y1 * StandardDev );
}
//----------------------------------------------------------------------------//
//----------------------------------------------------------------------------//
long Distribution::Bernoulli(double probability)
{
return ((Random() < (1.0 - probability)) ? 0 : 1);
}
long Distribution::Binomial (unsigned long limit_experiment, double probability)
{
unsigned long i, x = 0;
for (i = 0; i < limit_experiment; i++) x += Bernoulli(probability);
return (x);


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File Documentation
}
long Distribution::Equilikely (long a, long b)
{
if (a > b) swap(a,b); // Verificando se o intervalo foi fornecido corretamente
return (a + (long)((b - a + 1) * Random()));
}
unsigned long Distribution::Geometric(double probability)
{
return ((long) (log(1.0 - Random()) / log(probability)));
}
long Distribution::Pascal(unsigned long limit_experiment, double probability)
{
unsigned long i, x = 0;
for (i = 0; i < limit_experiment; i++) x += Geometric(probability);
return (x);
}
long Distribution::Poisson(double mean)
{
double t = 0.0;
long
x = 0;
while (t < mean)
{
t += Exponential(1.0);
x++;
}
return (x - 1);
}
double Distribution::Uniform(double a, double b)
{
if (a > b) swap(a,b);
return (a + (b - a) * Random());
}
double Distribution::Exponential(double mean)
{
return (-mean * log(1.0 - Random()));
}
double Distribution::Erlang(long limit_experiment, double base)
{
long
i;
double x = 0.0;
for (i = 0; i < limit_experiment; i++) x += Exponential(base);
return (x);
}
double Distribution::Normal(double Mean, double StandarDev)
{
const double p0 = 0.322232431088;
const double q0 = 0.099348462606;
const double p1 = 1.0;
const double q1 = 0.588581570495;
const double p2 = 0.342242088547;
const double q2 = 0.531103462366;
const double p3 = 0.204231210245e-1; const double q3 = 0.103537752850;
const double p4 = 0.453642210148e-4; const double q4 = 0.385607006340e-2;
double u, t, p, q, z;
u

= Random();

if (u < 0.5) t = sqrt(-2.0 * log(u));
else t = sqrt(-2.0 * log(1.0 - u));


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p
q

= p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)));
= q0 + t * (q1 + t * (q2 + t * (q3 + t * q4)));

if (u < 0.5) z = (p / q) - t;
else
z = t - (p / q);
return (Mean + StandarDev * z);
}
double Distribution::Lognormal(double a, double b)
{
return (exp(a + b * Normal(0.0, 1.0)));
}
double Distribution::Chisquare(unsigned long limit_experiment)
{
unsigned long
i;
double z, x = 0.0;
for (i = 0; i < limit_experiment; i++)
{
z = Normal(0.0, 1.0);
x += z * z;
}
return (x);
}
double Distribution::Student(unsigned long limit_experiment)
{
return (Normal(0.0, 1.0)/sqrt(Chisquare(limit_experiment)/limit_experiment));
}
}; //Fim do namespace RNG


71

72

File Documentation

7.3

RandomNumberGenerator.h File Reference

#include <ctime>
#include <cmath>
#include <cstdlib>
Include dependency graph for RandomNumberGenerator.h:
RandomNumberGenerator.h

ctime

cmath

cstdlib

This graph shows which ﬁles directly or indirectly include this ﬁle:

Sys-LibraryRandom.cpp

Classes
•
•
•
•
•
•
•
•
•
•
•

class RNG::RandomNumberGenerator
class RNG::MersenneTwisterInt32
class RNG::MersenneTwisterDouble
class RNG::MersenneTwisterDoubleClosed
class RNG::MersenneTwisterDoubleOpened
class RNG::MersenneTwisterDouble53
class RNG::R250Base
class RNG::R250Int
class RNG::R250Double
class RNG::BoxMuller
class RNG::Distribution

Namespaces
• namespace RNG

Functions
• template<typename T >
void RNG::swap (T &a, T &b)


7.4 RandomNumberGenerator.h

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73

/*
* RandomNumberGenerator.h
*
* Created on: 21/10/2009
Author: Michel Alves dos Santos
*
*/
#ifndef RANDOMNUMBERGENERATOR_H_
#define RANDOMNUMBERGENERATOR_H_
#include <ctime>
#include <cmath>
#include <cstdlib>
namespace RNG
{
class RandomNumberGenerator
{
unsigned int _seed; /*Armazena a semente de geração de números aleatórios*/
public:
RandomNumberGenerator();
RandomNumberGenerator(unsigned long seed) { InitSeed(seed); };
void InitSeed(unsigned int seed = 0);
unsigned int ClockRandomSeed(unsigned int myseed = 0);
unsigned int Seed(void);
unsigned int GetInt(void);
unsigned int GetInt(unsigned int maximum_limit);
unsigned int GetInt(unsigned int minimum_limit, unsigned int maximum_limit);
double GetDouble(void);
double Random(void) { return GetDouble(); }
double GetDouble(double maximum_limit);
double GetDouble(double minimum_limit, double maximum_limit);
virtual ~RandomNumberGenerator();
};

class MersenneTwisterInt32
{
static const int n = 624, m = 397;
static unsigned long state[n];
static int p;
static bool init;

//
//
//
//

constantes em tempo de compilacao
Estado do vetor
posição dentro do vetor de estados
true se a função init foi invocada

unsigned long twiddle(unsigned long u, unsigned long v);
void gen_state();
MersenneTwisterInt32(const MersenneTwisterInt32&); // Construtor de cópia
void operator=(const MersenneTwisterInt32&);
// Operador de atribuição
protected:


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