/// @ref gtx_fast_trigonometry /// @file glm/gtx/fast_trigonometry.inl namespace glm{ namespace detail { template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> taylorCos(vecType<T, P> const & x) { return static_cast<T>(1) - (x * x) / 2.f + (x * x * x * x) / 24.f - (x * x * x * x * x * x) / 720.f + (x * x * x * x * x * x * x * x) / 40320.f; } template <typename T> GLM_FUNC_QUALIFIER T cos_52s(T x) { T const xx(x * x); return (T(0.9999932946) + xx * (T(-0.4999124376) + xx * (T(0.0414877472) + xx * T(-0.0012712095)))); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> cos_52s(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(cos_52s, x); } }//namespace detail // wrapAngle template <typename T> GLM_FUNC_QUALIFIER T wrapAngle(T angle) { return abs<T>(mod<T>(angle, two_pi<T>())); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> wrapAngle(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(wrapAngle, x); } // cos template <typename T> GLM_FUNC_QUALIFIER T fastCos(T x) { T const angle(wrapAngle<T>(x)); if(angle < half_pi<T>()) return detail::cos_52s(angle); if(angle < pi<T>()) return -detail::cos_52s(pi<T>() - angle); if(angle < (T(3) * half_pi<T>())) return -detail::cos_52s(angle - pi<T>()); return detail::cos_52s(two_pi<T>() - angle); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastCos(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastCos, x); } // sin template <typename T> GLM_FUNC_QUALIFIER T fastSin(T x) { return fastCos<T>(half_pi<T>() - x); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastSin(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastSin, x); } // tan template <typename T> GLM_FUNC_QUALIFIER T fastTan(T x) { return x + (x * x * x * T(0.3333333333)) + (x * x * x * x * x * T(0.1333333333333)) + (x * x * x * x * x * x * x * T(0.0539682539)); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastTan(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastTan, x); } // asin template <typename T> GLM_FUNC_QUALIFIER T fastAsin(T x) { return x + (x * x * x * T(0.166666667)) + (x * x * x * x * x * T(0.075)) + (x * x * x * x * x * x * x * T(0.0446428571)) + (x * x * x * x * x * x * x * x * x * T(0.0303819444));// + (x * x * x * x * x * x * x * x * x * x * x * T(0.022372159)); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastAsin(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastAsin, x); } // acos template <typename T> GLM_FUNC_QUALIFIER T fastAcos(T x) { return T(1.5707963267948966192313216916398) - fastAsin(x); //(PI / 2) } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastAcos(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastAcos, x); } // atan template <typename T> GLM_FUNC_QUALIFIER T fastAtan(T y, T x) { T sgn = sign(y) * sign(x); return abs(fastAtan(y / x)) * sgn; } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastAtan(vecType<T, P> const & y, vecType<T, P> const & x) { return detail::functor2<T, P, vecType>::call(fastAtan, y, x); } template <typename T> GLM_FUNC_QUALIFIER T fastAtan(T x) { return x - (x * x * x * T(0.333333333333)) + (x * x * x * x * x * T(0.2)) - (x * x * x * x * x * x * x * T(0.1428571429)) + (x * x * x * x * x * x * x * x * x * T(0.111111111111)) - (x * x * x * x * x * x * x * x * x * x * x * T(0.0909090909)); } template <typename T, precision P, template <typename, precision> class vecType> GLM_FUNC_QUALIFIER vecType<T, P> fastAtan(vecType<T, P> const & x) { return detail::functor1<T, T, P, vecType>::call(fastAtan, x); } }//namespace glm