Common series to compile-time calculation of sine and cosine functions. More...
#include <pseudometafunc.h>
Static Public Member Functions | |
| static long double | value () |
Detailed Description
template<unsigned M, unsigned N, unsigned B, unsigned A>
struct MF::SinCosSeries< M, N, B, A >
- Template Parameters
-
M is the starting counter of members in the series (2 for Sin function and 1 for Cos function) N is the number of last member in the series A numerator B denominator
Using theory of Taylor series sine and cosine functions can be defined as infinite series, which are valid for all real numbers x:
![\[ \sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ... = x(1 - \frac{x^2}{2\cdot 3}(1 - \frac{x^2}{4\cdot 5}(1 - \frac{x^2}{6\cdot 7}(1 - ... )))) \approx x S(x,M,N), \quad M=2 , \]](form_0.png)
![\[ \cos(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n)!} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + ... = 1 - \frac{x^2}{1\cdot 2}(1 - \frac{x^2}{3\cdot 4}(1 - \frac{x^2}{5\cdot 6}(1 - ... ))) \approx S(x,M,N), \quad M=1 . \]](form_1.png)
Both series contain common series S :
![\[ S(x,M,N) = 1 - \frac{x^2}{M(M+1)}(1 - \frac{x^2}{(M+2)(M+3)}(1 - ... \frac{x^2}{N(N+1)})) \]](form_2.png)
which can be parametrized by the starting denominator coefficient M and parameter N as the stopping criterium M = N. This template class implements the common series S for the argument 
.
The documentation for this struct was generated from the following file: