Infinite precision random numbers. More...

#include <RandomLib/RandomNumber.hpp>

Public Member Functions
	RandomNumber () throw ()

void	swap (RandomNumber &t) throw ()

void	Init () throw ()

int	Sign () const throw ()

void	Negate () throw ()

int	Floor () const throw ()

int	Ceiling () const throw ()

unsigned	UInteger () const throw ()

void	AddInteger (int k) throw ()

template<class Random >
bool	LessThan (Random &r, RandomNumber &t)

template<class Random >
bool	GreaterPair (Random &r, RandomNumber &u, RandomNumber &v)

template<class Random , typename IntType >
bool	LessThan (Random &r, IntType p, IntType q)

template<class Random , typename IntType >
bool	LessThan (Random &r, IntType p0, IntType c, IntType q, UniformInteger< IntType, bits > &j)

template<class Random >
unsigned	Digit (Random &r, unsigned k)

template<class Random >
void	AddDigit (Random &r)

const unsigned &	RawDigit (unsigned k) const throw ()

unsigned &	RawDigit (unsigned k) throw ()

void	Clear ()

unsigned	Size () const throw ()

template<typename RealType , typename Random >
RealType	Fraction (Random &r)

template<typename RealType , class Random >
RealType	Value (Random &r)

std::pair< double, double >	Range () const throw ()

Static Public Member Functions
template<class Random >
static unsigned	RandomDigit (Random &r) throw ()

Static Public Attributes
static const unsigned	mask

Related Functions
(Note that these are not member functions.)
template<int bits>
std::ostream &	operator<< (std::ostream &os, const RandomNumber< bits > &n)

Detailed Description

template<int bits = 1>
class RandomLib::RandomNumber< bits >

Infinite precision random numbers.

Implement infinite precision random numbers. Integer part is non-random. Fraction part consists of any some number of digits in base 2^b. If m digits have been generated then the fraction is uniformly distributed in the open interval ∑_k=1^m f_k−1/2^kb + (0,1)/2^mb. When a RandomNumber is first constructed the integer part is zero and m = 0, and the number represents (0,1). A RandomNumber is able to represent all numbers in the symmetric open interval (−2³¹, 2³¹). In this implementation, b must one of 1, 2, 3, 4, 8, 12, 16, 20, 24, 28, or 32. (This restriction allows printing in hexadecimal and can easily be relaxed. There's also no essential reason why the base should be a power of 2.)

Template Parameters

bits	the number of bits in each digit.

Definition at line 41 of file RandomNumber.hpp.

Constructor & Destructor Documentation

template<int bits = 1>

RandomLib::RandomNumber< bits >::RandomNumber	(	)
throw	(
	)

inline

Constructor sets number to a random number uniformly distributed in (0,1).

Definition at line 47 of file RandomNumber.hpp.

Member Function Documentation

template<int bits = 1>

void RandomLib::RandomNumber< bits >::swap	(	RandomNumber< bits > &	t	)
throw	(
	)

inline

Swap with another RandomNumber. This is a fast way of doing an assignment.

Parameters

[in,out] t the RandomNumber to swap with.

Definition at line 54 of file RandomNumber.hpp.

References std::swap().

template<int bits = 1>

void RandomLib::RandomNumber< bits >::Init	(	)
throw	(
	)

inline

Return to initial state, uniformly distributed in (0,1).

Definition at line 64 of file RandomNumber.hpp.

References STATIC_ASSERT.

Referenced by coverage32(), and coverage64().

template<int bits = 1>

int RandomLib::RandomNumber< bits >::Sign	(	)	const
throw	(
	)

inline

Returns: the sign of the RandomNumber (± 1).

Definition at line 74 of file RandomNumber.hpp.

Referenced by coverage32(), coverage64(), and RandomLib::RandomNumber< bits >::operator<<().

template<int bits = 1>

void RandomLib::RandomNumber< bits >::Negate	(	)
throw	(
	)

inline

Change the sign of the RandomNumber.

Definition at line 78 of file RandomNumber.hpp.

Referenced by coverage32(), and coverage64().

template<int bits = 1>

int RandomLib::RandomNumber< bits >::Floor	(	)	const
throw	(
	)

inline

Returns: the floor of the RandomNumber.

Definition at line 82 of file RandomNumber.hpp.

Referenced by RandomLib::RandomNumber< bits >::AddInteger(), coverage32(), and coverage64().

template<int bits = 1>

int RandomLib::RandomNumber< bits >::Ceiling	(	)	const
throw	(
	)

inline

Returns: the ceiling of the RandomNumber.

Definition at line 86 of file RandomNumber.hpp.

Referenced by coverage32(), and coverage64().

template<int bits = 1>

unsigned RandomLib::RandomNumber< bits >::UInteger	(	)	const
throw	(
	)

inline

Returns: the unsigned integer component of the RandomNumber.

Definition at line 90 of file RandomNumber.hpp.

Referenced by RandomLib::RandomNumber< bits >::operator<<().

template<int bits = 1>

void RandomLib::RandomNumber< bits >::AddInteger	(	int	k	)
throw	(
	)

inline

Add integer k to the RandomNumber.

Parameters

[in] k the integer to add.

Definition at line 96 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Floor(), RandomLib::RandomNumber< bits >::mask, and RandomLib::RandomNumber< bits >::Size().

Referenced by coverage32(), and coverage64().

template<int bits = 1>

template<class Random >

bool RandomLib::RandomNumber< bits >::LessThan	(	Random &	r,
		RandomNumber< bits > &	t
	)

inline

Compare with another RandomNumber, *this < t

Template Parameters

Random the type of the random generator.

Parameters

[in,out]	r	a random generator.
[in,out]	t	a RandomNumber to compare.

Returns: true if *this < t.

Definition at line 112 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit().

Referenced by coverage32(), and coverage64().

template<int bits = 1>

template<class Random >

bool RandomLib::RandomNumber< bits >::GreaterPair	(	Random &	r,
		RandomNumber< bits > &	u,
		RandomNumber< bits > &	v
	)

inline

Compare RandomNumber with two others, *this > max(u, v)

Template Parameters

Random the type of the random generator.

Parameters

[in,out]	r	a random generator.
[in,out]	u	first RandomNumber to compare.
[in,out]	v	second RandomNumber to compare.

Returns: true if *this > max(u, v).

Definition at line 133 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit().

template<int bits = 1>

template<class Random , typename IntType >

bool RandomLib::RandomNumber< bits >::LessThan	(	Random &	r,
		IntType	p,
		IntType	q
	)

inline

Compare with a fraction, *this < p/q

Template Parameters

Random the type of the random generator.

Parameters

[in,out]	r	a random generator.
[in]	p	the numerator of the fraction.
[in]	q	the denominator of the fraction (require q > 0).

Returns: true if *this < p/q.

Definition at line 187 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit().

template<int bits = 1>

template<class Random , typename IntType >

bool RandomLib::RandomNumber< bits >::LessThan	(	Random &	r,
		IntType	p0,
		IntType	c,
		IntType	q,
		UniformInteger< IntType, bits > &	j
	)

inline

Compare with a paritally sampled fraction

Template Parameters

Random the type of the random generator.

Parameters

[in,out]	r	a random generator.
[in]	p0	the starting point for the numerator.
[in]	c	the stride for the fraction (require c > 0).
[in]	q	the denominator of the fraction (require q > 0).
[in,out]	j	the increment for the numerator.

Returns: true if *this < (p₀ + cj)/q.

Definition at line 208 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit(), and RandomLib::UniformInteger< IntType, bits >::GreaterThanEqual().

template<int bits = 1>

template<class Random >

unsigned RandomLib::RandomNumber< bits >::Digit	(	Random &	r,
		unsigned	k
	)

inline

Template Parameters

Random the type of the random generator.

Parameters

[in,out]	r	a random generator.
[in]	k	the index of a digit of the fraction

Returns: digit number k, generating it if necessary.

Definition at line 224 of file RandomNumber.hpp.

Referenced by coverage32(), coverage64(), RandomLib::RandomNumber< bits >::Fraction(), RandomLib::RandomNumber< bits >::GreaterPair(), RandomLib::RandomNumber< bits >::LessThan(), and RandomLib::RandomNumber< bits >::Value().

template<int bits = 1>

template<class Random >

void RandomLib::RandomNumber< bits >::AddDigit ( Random & r )

inline

Add one digit to the fraction.

Template Parameters

Random the type of the random generator.

Parameters

[in,out] r a random generator.

Definition at line 234 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::RandomDigit().

template<int bits = 1>

const unsigned& RandomLib::RandomNumber< bits >::RawDigit	(	unsigned	k	)	const
throw	(
	)

inline

Parameters

[in] k the index of a digit of the fraction

Returns: a const reference to digit number k, without generating new digits.

Exceptions

std::out_of_range if the digit hasn't been generated.

Definition at line 242 of file RandomNumber.hpp.

Referenced by coverage32(), coverage64(), RandomLib::RandomNumber< bits >::Fraction(), RandomLib::RandomNumber< bits >::operator<<(), RandomLib::RandomNumber< bits >::Range(), and RandomLib::RandomNumber< bits >::Value().

template<int bits = 1>

unsigned& RandomLib::RandomNumber< bits >::RawDigit	(	unsigned	k	)
throw	(
	)

inline

Parameters

[in] k the index of a digit of the fraction

Returns: a non-const reference to digit number k, without generating new digits.

Exceptions

std::out_of_range if the digit hasn't been generated.

Definition at line 250 of file RandomNumber.hpp.

template<int bits = 1>

void RandomLib::RandomNumber< bits >::Clear ( )

inline

Return to initial state, uniformly distributed in n + (0,1). This is similar to Init but also returns the memory used by the object to the system. Normally Init should be used.

Definition at line 257 of file RandomNumber.hpp.

template<int bits = 1>

unsigned RandomLib::RandomNumber< bits >::Size	(	)	const
throw	(
	)

inline

Returns: the number of digits in fraction

Definition at line 266 of file RandomNumber.hpp.

Referenced by RandomLib::RandomNumber< bits >::AddInteger(), coverage32(), coverage64(), RandomLib::RandomNumber< bits >::operator<<(), and RandomLib::RandomNumber< bits >::Range().

template<int bits = 1>

template<typename RealType , typename Random >

RealType RandomLib::RandomNumber< bits >::Fraction ( Random & r )

inline

Return the fraction part of the RandomNumber as a floating point number of type RealType rounded to the nearest multiple of 1/2^p, where p = std::numeric_limits<RealType>::digits, and, if necessary, creating additional digits of the number.

Template Parameters

RealType	the floating point type to convert to.
Random	the type of the random generator.

Parameters

[in,out] r a random generator for generating the necessary digits.

Returns: the fraction of the RandomNumber rounded to a RealType.

Definition at line 279 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit(), RandomLib::RandomNumber< bits >::RawDigit(), and STATIC_ASSERT.

Referenced by coverage32(), and coverage64().

template<int bits = 1>

template<typename RealType , class Random >

RealType RandomLib::RandomNumber< bits >::Value ( Random & r )

inline

Return the value of the RandomNumber rounded to nearest floating point number of type RealType and, if necessary, creating additional digits of the number.

Template Parameters

RealType	the floating point type to convert to.
Random	the type of the random generator.

Parameters

[in,out] r a random generator for generating the necessary digits.

Returns: the value of the RandomNumber rounded to a RealType.

Definition at line 308 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::Digit(), RandomLib::RandomNumber< bits >::RawDigit(), and STATIC_ASSERT.

Referenced by coverage32(), coverage64(), and main().

template<int bits = 1>

std::pair<double, double> RandomLib::RandomNumber< bits >::Range	(	)	const
throw	(
	)

inline

Return the range of possible values for the RandomNumber as pair of doubles. This doesn't create any additional digits of the result and doesn't try to control roundoff.

Returns: a pair denoting the range with first being the lower limit and second being the upper limit.

Definition at line 360 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::RawDigit(), and RandomLib::RandomNumber< bits >::Size().

Referenced by coverage32(), coverage64(), and main().

template<int bits = 1>

template<class Random >

static unsigned RandomLib::RandomNumber< bits >::RandomDigit	(	Random &	r	)
throw	(
	)

inlinestatic

Template Parameters

Random the type of the random generator.

Parameters

[in,out] r a random generator.

Returns: a random digit in [0, 2^bits).

Definition at line 376 of file RandomNumber.hpp.

Referenced by RandomLib::RandomNumber< bits >::AddDigit().

Friends And Related Function Documentation

template<int bits>

std::ostream & operator<<	(	std::ostream &	os,
		const RandomNumber< bits > &	n
	)

Print a RandomNumber. Format is n.dddd... where the base for printing is 2^max(4,b). The ... represents an infinite sequence of ungenerated random digits (uniformly distributed). Thus with b = 1, 0.0... = (0,1/2), 0.00... = (0,1/4), 0.11... = (3/4,1), etc.

Definition at line 437 of file RandomNumber.hpp.

References RandomLib::RandomNumber< bits >::RawDigit(), RandomLib::RandomNumber< bits >::Sign(), RandomLib::RandomNumber< bits >::Size(), and RandomLib::RandomNumber< bits >::UInteger().