143 lines
3.9 KiB
C++
143 lines
3.9 KiB
C++
/// @ref gtx_fast_trigonometry
|
|
|
|
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
|