Created
March 22, 2020 10:24
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Calculating sine function using taylor series.
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| #include <iostream> | |
| #include <boost/math/constants/constants.hpp> | |
| #include <boost/multiprecision/cpp_bin_float.hpp> | |
| #include <boost/multiprecision/number.hpp> | |
| #include <numeric> | |
| using namespace boost::multiprecision; | |
| typedef cpp_bin_float_50 num; | |
| using namespace boost::math::constants; | |
| num eval_sin(const num& val) | |
| { | |
| num EPS = std::numeric_limits<num>::epsilon(); | |
| const num PI = boost::math::constants::pi<num>(); | |
| const num PI_2 = boost::math::constants::half_pi<num>(); | |
| num x = val; | |
| bool negate_result = false; | |
| if (x.sign() < 0) | |
| { | |
| negate_result = true; | |
| x = -x; | |
| } | |
| while (x > PI) | |
| { | |
| x -= PI; | |
| negate_result = !negate_result; | |
| } | |
| if (x > PI_2) | |
| { | |
| x = PI - x; | |
| } | |
| const num MINUS_ONE = -1.0; | |
| const num ONE = 1.0; | |
| const num TWO = 2.0; | |
| num result = 0; | |
| num multiplier = ONE; | |
| num seq = x; | |
| do | |
| { | |
| result += seq; | |
| seq = (MINUS_ONE * seq * x * x) / ((multiplier + ONE) * (multiplier + TWO)); | |
| multiplier = multiplier + TWO; | |
| } while (abs(seq) > EPS); | |
| if (negate_result) | |
| { | |
| result = -result; | |
| } | |
| return result; | |
| } | |
| int main() | |
| { | |
| // PI / 2 | |
| num t1(boost::math::constants::half_pi<num>()); | |
| std::cout << "Calculated: " << std::setprecision(std::numeric_limits<num>::digits10) << eval_sin(t1) << std::endl; | |
| std::cout << "Library Code: " << std::setprecision(std::numeric_limits<num>::digits10) << sin(t1) << std::endl; | |
| // PI / 3 | |
| num t2(boost::math::constants::third_pi<num>()); | |
| std::cout << "Calculated: " << std::setprecision(std::numeric_limits<num>::digits10) << eval_sin(t2) << std::endl; | |
| std::cout << "Library Code: " << std::setprecision(std::numeric_limits<num>::digits10) << sin(t2) << std::endl; | |
| // 2 | |
| num t3(2); | |
| std::cout << "Calculated: " << std::setprecision(std::numeric_limits<num>::digits10) << eval_sin(t3) << std::endl; | |
| std::cout << "Library Code: " << std::setprecision(std::numeric_limits<num>::digits10) << sin(t3) << std::endl; | |
| // PI + 2 | |
| num t4(boost::math::constants::pi<num>() + 2); | |
| std::cout << "Calculated: " << std::setprecision(std::numeric_limits<num>::digits10) << eval_sin(t4) << std::endl; | |
| std::cout << "Library Code: " << std::setprecision(std::numeric_limits<num>::digits10) << sin(t4) << std::endl; | |
| } |
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