tOpenSine< NumType, nTerms > Class Template Reference

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

#include <opensine.h>

List of all members.

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.
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.
static NumType	lowerBoundTaylor (const NumType &x)
	Returns a lower bound for the sine function.
static NumType	upperBoundTaylor (const NumType &x)
	Returns an upper bound for the sine function.
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].
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].

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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.

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Member Function Documentation

template<class NumType, int nTerms>

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

Computes the sine function in the open interval arithmetic.

Definition at line 202 of file opensine.h.

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

template<class NumType, int nTerms>

void tOpenSine< NumType, nTerms >::computeTaylorTerms	(	const NumType &	x,
		NumType *	lower_x2k,
		NumType *	upper_x2k,
		int	n
	)			[inline, static, private]

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().

template<class NumType, int nTerms>

NumType tOpenSine< NumType, nTerms >::lowerBoundTaylor

(

const NumType &

x

)

[inline, static, private]

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().

template<class NumType, int nTerms>

NumType tOpenSine< NumType, nTerms >::upperBoundTaylor

(

const NumType &

x

)

[inline, static, private]

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 >::computeTaylorTerms().

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

template<class NumType, int nTerms>

int tOpenSine< NumType, nTerms >::shifted1pi	(	const NumType &	xLeft,
		const NumType &	xRight,
		NumType &	yLeft,
		NumType &	yRight
	)			[inline, static, private]

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

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

template<class NumType, int nTerms>

int tOpenSine< NumType, nTerms >::shifted2pi	(	const NumType &	xLeft,
		const NumType &	xRight,
		NumType &	yLeft,
		NumType &	yRight
	)			[inline, static, private]

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().

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

• opensine.h

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