The Finite Resolution Dynamics Software
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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... | |
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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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().
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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().
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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().
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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().
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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().
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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().