Taylor Series based Sin() implementation using templates C++ -

i working on implementation of sin() function based on taylor series using templates. code far goes follows:

template<unsigned i> struct factorial{     enum{       value = * factorial<i -1>::value     }; }; template<> struct factorial<0> {     enum{ value = 1}; }; template<unsigned pow> inline double power(double const& value){     return value * power<pow-1>(value); } template<> inline double power<1>(double const& value){     return value; } template <unsigned term> inline double taylor_sine_term(double const& x) {     return (power<term>(-1) / factorial<(2*term)+1>::value) * power<(2*term)+1>(x); } 

the issue having creating function use taylor_sine_term function expand series n number of terms.the function functionally equivalent following.

template<unsigned terms> inline double taylor_sine(double const& x){     return taylor_sine_term<1>(x)+taylor_sine_term<2>(x) + ... + taylor_sine_term<terms>(x); } 

basically need figure out way generate sequence of integer constants can used term number template parameter in taylor_sine_term function n number of terms , sum them together. result expand full taylor series n number of terms. problem don't know start.

any appreciated, thanks.

same way wrote other ones: recursive case , base case:

template<unsigned terms> inline double taylor_sine(double const& x) {     return taylor_sine_term<terms>(x) + // current term            taylor_sine<terms-1>(x);     // rest of terms }  template <> inline double taylor_sine<0>(const double& x) {     return taylor_sine_term<0>(x); } 

alternatively, use index sequence trick of them:

template <unsigned terms> inline double taylor_sine(double const& x) {     return taylor_sine(x, std::make_index_sequence<terms+1>{}); }  template <unsigned terms, size_t... is> inline double taylor_sine(const double& x, std::index_sequence<is...> ) {     double res = 0.0;     (double t : {taylor_sine_term<is>(x)...}) {         res += t;     }     return res;      /* or in c++17     return (taylor_sine_term<is>(x) + ...);     */ } 

note should change base case on power power<0>.