Math Utility

Number rounding and other common utility functions. More...

Collaboration diagram for Math Utility:

Classes
class	Vector< T, N >
	Algebraic vector. More...

Functions
template<class S, class T, int N>
Vector< T, N >	operator* (S a, const Vector< T, N > &b)
	Multiply a scalar with a vector.

Fast Fourier Transform (FFT)
template<template< class > class Vector, class Complex>
void	fft (Vector< Complex > *vf, const Vector< Complex > &vt)
	Translate vt from time domain to vf in frequency domain.
template<template< class > class Vector, class Complex>
void	fft (Vector< Complex > *v)
	Translate v in-place from time domain to frequency domain.
template<template< class > class Vector, class Complex>
void	ift (Vector< Complex > *vf, const Vector< Complex > &vt)
	Translate vf from frequency domain to vt in time domain.
template<template< class > class Vector, class Complex>
void	ift (Vector< Complex > *v)
	Translate v in-place from frequency domain to time domain.

Rounding Functions
double	roundNearestOrOut (double x)
	Round x towards nearest integral number or if ambigious towards +-infinity.
double	roundNearestOrIn (double x)
	Round x towards nearest integral number or if ambigious towards zero.
double	roundNearestOrIn (double x, double y)
	Round x towards the nearest multiple of y or if ambiguous towards zero.
double	roundNearestOrOut (double x, double y)
	Round x towards the nearest multiple of y or if ambiguous towards +-infinity.
double	roundOut (double x)
	Round x towards next integral number towards +-infinity.
double	roundIn (double x)
	Round x towards next integral number towards zero.
double	roundUp (double x)
	Round x towards the next integral number towards +infinity.
double	roundDown (double x)
	Round x towards the next integral number towards -infinity.
template<class G, class X>
X	downToNext (G g, X x)
	Round x down to the next multiple of a whole number g.
template<class G, class X>
X	upToNext (G g, X x)
	Round x up to the next multiple of a whole number g.
template<int B>
int	ilog (int n)
	Rounded up logarithm of n to base B.

Utility Functions
template<class T>
int	sign (T x)
	Return sign of x -1 if x < 0, +1 if x >= 0)
template<class T>
int	sgn (T x)
	Return signum of x (-1 if x < 0, +1 if x > 0, 0 if x == 0)
template<class T>
T	bound (T min, T x, T max)
	Limit x to the range [min, max].

Detailed Description

Number rounding and other common utility functions.

Function Documentation

fft() [1/2]

template<template< class > class Vector, class Complex>

void fft	(	Vector< Complex > *	vf,
		const Vector< Complex > &	vt )

Translate vt from time domain to vf in frequency domain.

fft() [2/2]

template<template< class > class Vector, class Complex>

void fft

(

Vector< Complex > *

v

)

Translate v in-place from time domain to frequency domain.

ift() [1/2]

template<template< class > class Vector, class Complex>

void ift	(	Vector< Complex > *	vf,
		const Vector< Complex > &	vt )

Translate vf from frequency domain to vt in time domain.

ift() [2/2]

template<template< class > class Vector, class Complex>

void ift

(

Vector< Complex > *

v

)

Translate v in-place from frequency domain to time domain.

roundNearestOrOut() [1/2]

double roundNearestOrOut

(

double

x

)

Round x towards nearest integral number or if ambigious towards +-infinity.

sign()

template<class T>

int sign

(

T

x

)

Return sign of x -1 if x < 0, +1 if x >= 0)

operator*()

template<class S, class T, int N>

Vector< T, N > operator*	(	S	a,
		const Vector< T, N > &	b )

Multiply a scalar with a vector.

roundNearestOrIn() [1/2]

double roundNearestOrIn

(

double

x

)

Round x towards nearest integral number or if ambigious towards zero.

roundNearestOrIn() [2/2]

double roundNearestOrIn	(	double	x,
		double	y )

Round x towards the nearest multiple of y or if ambiguous towards zero.

roundNearestOrOut() [2/2]

double roundNearestOrOut	(	double	x,
		double	y )

Round x towards the nearest multiple of y or if ambiguous towards +-infinity.

roundOut()

double roundOut

(

double

x

)

Round x towards next integral number towards +-infinity.

roundIn()

double roundIn

(

double

x

)

Round x towards next integral number towards zero.

roundUp()

double roundUp

(

double

x

)

Round x towards the next integral number towards +infinity.

roundDown()

double roundDown

(

double

x

)

Round x towards the next integral number towards -infinity.

downToNext()

template<class G, class X>

X downToNext	(	G	g,
		X	x )

Round x down to the next multiple of a whole number g.

upToNext()

template<class G, class X>

X upToNext	(	G	g,
		X	x )

Round x up to the next multiple of a whole number g.

ilog()

template<int B>

int ilog

(

int

n

)

Rounded up logarithm of n to base B.

sgn()

template<class T>

int sgn

(

T

x

)

Return signum of x (-1 if x < 0, +1 if x > 0, 0 if x == 0)

bound()

template<class T>

T bound	(	T	min,
		T	x,
		T	max )

Limit x to the range [min, max].