Infinite precision random numbers. More...

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

Public Member Functions
	RandomNumber (int n=0)
int	Integer () const
template<class Random >
unsigned	Digit (Random &r, unsigned k)
unsigned	RawDigit (unsigned k) const
void	AddInteger (int k)
void	SetInteger (int k)
void	Init (int n=0)
template<class Random >
bool	LessThan (Random &r, RandomNumber &t)
void	Negate ()
size_t	Size () const
template<typename RealType , typename Random >
RealType	Fraction (Random &r)
template<typename RealType , class Random >
RealType	Value (Random &r)
std::pair< double, double >	Range () const
Private Member Functions
template<class Random >
void	ExpandTo (Random &r, size_t k)
Static Private Member Functions
static int	highest_bit_idx (unsigned x)
Private Attributes
int	_n
std::vector< unsigned >	_f
Static Private Attributes
static const int	w = std::numeric_limits<unsigned>::digits
Related Functions
(Note that these are not member functions.)
template<int bits>
std::ostream &	operator<< (std::ostream &os, const RandomNumber< bits > &n)

Detailed Description

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 sum_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 vRandomNumber is able to represent all numbers in the symmetric open interval (-2³¹, 2³¹). In this implementation b must be less than 4 or a multiple of 4. (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.)

Constructor & Destructor Documentation

RandomLib::RandomNumber::RandomNumber ( int n = 0 ) [inline]

Constructor sets number to n + (0,1).

Definition at line 49 of file RandomNumber.hpp.

Member Function Documentation

int RandomLib::RandomNumber::Integer ( ) const [inline]

Return integer part of RandomNumber.

Definition at line 53 of file RandomNumber.hpp.

References _n.

Referenced by Value(), and Range().

template<class Random >

unsigned RandomLib::RandomNumber::Digit	(	Random &	r,
		unsigned	k
	)		`[inline]`

Return digit number k, generating it if necesary.

Definition at line 57 of file RandomNumber.hpp.

References ExpandTo(), and _f.

Referenced by LessThan(), Fraction(), and Value().

unsigned RandomLib::RandomNumber::RawDigit ( unsigned k ) const [inline]

Return digit number k, without generating new digits.

Definition at line 64 of file RandomNumber.hpp.

References _f.

Referenced by Fraction(), Value(), and Range().

void RandomLib::RandomNumber::AddInteger ( int k ) [inline]

Add integer k to RandomNumber

Definition at line 70 of file RandomNumber.hpp.

References _n.

void RandomLib::RandomNumber::SetInteger ( int k ) [inline]

Set integer part of RandomNumber k

Definition at line 74 of file RandomNumber.hpp.

References _n.

Referenced by RandomLib::ExactExponential::operator()().

void RandomLib::RandomNumber::Init ( int n = 0 ) [inline]

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

Definition at line 78 of file RandomNumber.hpp.

References STATIC_ASSERT, w, _n, and _f.

Referenced by RandomLib::ExactExponential::operator()(), RandomLib::ExactExponential::ExpFraction(), and RandomLib::ExactPower::operator()().

template<class Random >

bool RandomLib::RandomNumber::LessThan	(	Random &	r,
		RandomNumber &	t
	)		`[inline]`

Compare two RandomNumbers, *this < t

Definition at line 87 of file RandomNumber.hpp.

References _n, and Digit().

Referenced by RandomLib::ExactExponential::ExpFraction(), and RandomLib::ExactPower::operator()().

void RandomLib::RandomNumber::Negate ( ) [inline]

Change sign of a RandomNumber

Definition at line 106 of file RandomNumber.hpp.

References w, Size(), _f, and _n.

Referenced by Value().

size_t RandomLib::RandomNumber::Size ( ) const [inline]

Return the number of digits in fraction

Definition at line 116 of file RandomNumber.hpp.

References _f.

Referenced by Negate(), and Range().

template<typename RealType , typename Random >

RealType RandomLib::RandomNumber::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.

Definition at line 126 of file RandomNumber.hpp.

References STATIC_ASSERT, Digit(), and RawDigit().

template<typename RealType , class Random >

RealType RandomLib::RandomNumber::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.

Definition at line 150 of file RandomNumber.hpp.

References STATIC_ASSERT, Integer(), Negate(), highest_bit_idx(), Digit(), and RawDigit().

std::pair<double, double> RandomLib::RandomNumber::Range ( ) const [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.

Definition at line 206 of file RandomNumber.hpp.

References Integer(), Size(), and RawDigit().

template<class Random >

void RandomLib::RandomNumber::ExpandTo	(	Random &	r,
		size_t	k
	)		`[inline, private]`

Fill RandomNumber to k digits.

Definition at line 229 of file RandomNumber.hpp.

References _f.

Referenced by Digit().

static int RandomLib::RandomNumber::highest_bit_idx ( unsigned x ) [inline, static, private]

Return index [0..32] of highest bit set. Return 0 if x = 0, 32 is if x = ~0. (From Algorithms for programmers by Joerg Arndt.)

Definition at line 241 of file RandomNumber.hpp.

Referenced by Value().

Friends And Related Function Documentation

template<int bits>

std::ostream & operator<<	(	std::ostream &	os,
		const RandomNumber< bits > &	n
	)		`[related]`

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 265 of file RandomNumber.hpp.