The Finite Resolution Dynamics Software: tOpenSine< NumType, nTerms > Class Template Reference

The Finite Resolution Dynamics Software

Computes the sine function using the expansion into the Taylor series at pi/2. More...

#include <opensine.h>

Static Public Member Functions
static int	compute (const NumType &xLeft, const NumType &xRight, NumType &yLeft, NumType &yRight)
	Computes the sine function in the open interval arithmetic. More...

Static Private Member Functions
static void	computeTaylorTerms (const NumType &x, NumType lower_x2k, NumType upper_x2k, int n)
	Computes the provided number of terms in the expansion of sin(pi+x) in the Taylor series at pi. More...

static NumType	lowerBoundTaylor (const NumType &x)
	Returns a lower bound for the sine function. More...

static NumType	upperBoundTaylor (const NumType &x)
	Returns an upper bound for the sine function. More...

static int	shifted1pi (const NumType &xLeft, const NumType &xRight, NumType &yLeft, NumType &yRight)
	Computes the sine function in the open interval arithmetic with the arguments shifted so that xLeft is in [0,pi]. More...

static int	shifted2pi (const NumType &xLeft, const NumType &xRight, NumType &yLeft, NumType &yRight)
	Computes the sine function in the open interval arithmetic with the arguments shifted so that xLeft is in [0,2pi]. More...

Detailed Description

template<class NumType, int nTerms>
class tOpenSine< NumType, nTerms >

Computes the sine function using the expansion into the Taylor series at pi/2.

Definition at line 51 of file opensine.h.

Member Function Documentation

◆ compute()

template<class NumType , int nTerms>

int tOpenSine< NumType, nTerms >::compute	(	const NumType &	xLeft,
		const NumType &	xRight,
		NumType &	yLeft,
		NumType &	yRight
	)

inlinestatic

Computes the sine function in the open interval arithmetic.

Definition at line 202 of file opensine.h.

References tOpenSine< NumType, nTerms >::shifted1pi(), and tOpenSine< NumType, nTerms >::shifted2pi().

Referenced by tOpenSine< NumType, nTerms >::upperBoundTaylor().

◆ computeTaylorTerms()

template<class NumType , int nTerms>

void tOpenSine< NumType, nTerms >::computeTaylorTerms	(	const NumType &	x,
		NumType *	lower_x2k,
		NumType *	upper_x2k,
		int	n
	)

inlinestaticprivate

Computes the provided number of terms in the expansion of sin(pi+x) in the Taylor series at pi.

Definition at line 88 of file opensine.h.

Referenced by tOpenSine< NumType, nTerms >::lowerBoundTaylor(), and tOpenSine< NumType, nTerms >::upperBoundTaylor().

◆ lowerBoundTaylor()

template<class NumType , int nTerms>

NumType tOpenSine< NumType, nTerms >::lowerBoundTaylor ( const NumType & x )

inlinestaticprivate

Returns a lower bound for the sine function.

The argument must be in the interval (0,pi).

Definition at line 139 of file opensine.h.

References tOpenSine< NumType, nTerms >::computeTaylorTerms().

Referenced by tOpenSine< NumType, nTerms >::shifted1pi().

◆ shifted1pi()

template<class NumType , int nTerms>

int tOpenSine< NumType, nTerms >::shifted1pi	(	const NumType &	xLeft,
		const NumType &	xRight,
		NumType &	yLeft,
		NumType &	yRight
	)

inlinestaticprivate

Computes the sine function in the open interval arithmetic with the arguments shifted so that xLeft is in [0,pi].

Definition at line 258 of file opensine.h.

References tOpenSine< NumType, nTerms >::lowerBoundTaylor(), tOpenSine< NumType, nTerms >::shifted2pi(), and tOpenSine< NumType, nTerms >::upperBoundTaylor().

Referenced by tOpenSine< NumType, nTerms >::compute(), and tOpenSine< NumType, nTerms >::shifted2pi().

◆ shifted2pi()

template<class NumType , int nTerms>

int tOpenSine< NumType, nTerms >::shifted2pi	(	const NumType &	xLeft,
		const NumType &	xRight,
		NumType &	yLeft,
		NumType &	yRight
	)

inlinestaticprivate

Computes the sine function in the open interval arithmetic with the arguments shifted so that xLeft is in [0,2pi].

Definition at line 402 of file opensine.h.

References tOpenSine< NumType, nTerms >::shifted1pi().

Referenced by tOpenSine< NumType, nTerms >::compute(), and tOpenSine< NumType, nTerms >::shifted1pi().

◆ upperBoundTaylor()

template<class NumType , int nTerms>

NumType tOpenSine< NumType, nTerms >::upperBoundTaylor ( const NumType & x )

inlinestaticprivate

Returns an upper bound for the sine function.

The argument must be in the interval (0,pi).

Definition at line 169 of file opensine.h.

References tOpenSine< NumType, nTerms >::compute(), and tOpenSine< NumType, nTerms >::computeTaylorTerms().

Referenced by tOpenSine< NumType, nTerms >::shifted1pi().

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

opensine.h