fast_trigonometry.inl

 
 
namespace glm{
namespace detail
{
    template<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> taylorCos(vec<L, T, Q> const& x)
    {
        return static_cast<T>(1)
            - (x * x) * (1.f / 2.f)
            + ((x * x) * (x * x)) * (1.f / 24.f)
            - (((x * x) * (x * x)) * (x * x)) * (1.f / 720.f)
            + (((x * x) * (x * x)) * ((x * x) * (x * x))) * (1.f / 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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> cos_52s(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> wrapAngle(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastCos(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::call(fastCos, x);
    }
 
    // sin
    template<typename T>
    GLM_FUNC_QUALIFIER T fastSin(T x)
    {
        return fastCos<T>(half_pi<T>() - x);
    }
 
    template<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastSin(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastTan(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastAsin(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::call(fastAsin, x);
    }
 
    // acos
    template<typename T>
    GLM_FUNC_QUALIFIER T fastAcos(T x)
    {
        return T(1.5707963267948966192313216916398) - fastAsin(x); //(PI / 2)
    }
 
    template<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastAcos(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastAtan(vec<L, T, Q> const& y, vec<L, T, Q> const& x)
    {
        return detail::functor2<vec, L, T, Q>::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<length_t L, typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<L, T, Q> fastAtan(vec<L, T, Q> const& x)
    {
        return detail::functor1<vec, L, T, T, Q>::call(fastAtan, x);
    }
}//namespace glm