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#include "scalar_constants.hpp"
namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> exp(qua<T, Q> const& q)
{
vec<3, T, Q> u(q.x, q.y, q.z);
T const Angle = glm::length(u);
if (Angle < epsilon<T>())
return qua<T, Q>();
vec<3, T, Q> const v(u / Angle);
return qua<T, Q>(cos(Angle), sin(Angle) * v);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> log(qua<T, Q> const& q)
{
vec<3, T, Q> u(q.x, q.y, q.z);
T Vec3Len = length(u);
if (Vec3Len < epsilon<T>())
{
if(q.w > static_cast<T>(0))
return qua<T, Q>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
else if(q.w < static_cast<T>(0))
return qua<T, Q>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
else
return qua<T, Q>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
}
else
{
T t = atan(Vec3Len, T(q.w)) / Vec3Len;
T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
return qua<T, Q>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> pow(qua<T, Q> const& x, T y)
{
//Raising to the power of 0 should yield 1
//Needed to prevent a division by 0 error later on
if(y > -epsilon<T>() && y < epsilon<T>())
return qua<T, Q>(1,0,0,0);
//To deal with non-unit quaternions
T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
T Angle;
if(abs(x.w / magnitude) > cos_one_over_two<T>())
{
//Scalar component is close to 1; using it to recover angle would lose precision
//Instead, we use the non-scalar components since sin() is accurate around 0
//Prevent a division by 0 error later on
T VectorMagnitude = x.x * x.x + x.y * x.y + x.z * x.z;
if (glm::abs(VectorMagnitude - static_cast<T>(0)) < glm::epsilon<T>()) {
//Equivalent to raising a real number to a power
return qua<T, Q>(pow(x.w, y), 0, 0, 0);
}
Angle = asin(sqrt(VectorMagnitude) / magnitude);
}
else
{
//Scalar component is small, shouldn't cause loss of precision
Angle = acos(x.w / magnitude);
}
T NewAngle = Angle * y;
T Div = sin(NewAngle) / sin(Angle);
T Mag = pow(magnitude, y - static_cast<T>(1));
return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> sqrt(qua<T, Q> const& x)
{
return pow(x, static_cast<T>(0.5));
}
}//namespace glm
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