...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
There is no log
or sqrt
provided for quaternions in this implementation,
and pow
is likewise restricted
to integral powers of the exponent. There are several reasons to this: on the
one hand, the equivalent of analytic continuation for quaternions ("branch
cuts") remains to be investigated thoroughly (by me, at any rate...),
and we wish to avoid the nonsense introduced in the standard by exponentiations
of complexes by complexes (which is well defined, but not in the standard...).
Talking of nonsense, saying that pow(0,0)
is "implementation
defined" is just plain brain-dead...
We do, however provide several transcendentals, chief among which is the exponential. This author claims the complete proof of the "closed formula" as his own, as well as its independent invention (there are claims to prior invention of the formula, such as one by Professor Shoemake, and it is possible that the formula had been known a couple of centuries back, but in absence of bibliographical reference, the matter is pending, awaiting further investigation; on the other hand, the definition and existence of the exponential on the quaternions, is of course a fact known for a very long time). Basically, any converging power series with real coefficients which allows for a closed formula in C can be transposed to H. More transcendentals of this type could be added in a further revision upon request. It should be noted that it is these functions which force the dependency upon the boost/math/special_functions/sinc.hpp and the boost/math/special_functions/sinhc.hpp headers.
template<typename T> quaternion<T> exp(quaternion<T> const & q);
Computes the exponential of the quaternion.
template<typename T> quaternion<T> cos(quaternion<T> const & q);
Computes the cosine of the quaternion
template<typename T> quaternion<T> sin(quaternion<T> const & q);
Computes the sine of the quaternion.
template<typename T> quaternion<T> tan(quaternion<T> const & q);
Computes the tangent of the quaternion.
template<typename T> quaternion<T> cosh(quaternion<T> const & q);
Computes the hyperbolic cosine of the quaternion.
template<typename T> quaternion<T> sinh(quaternion<T> const & q);
Computes the hyperbolic sine of the quaternion.
template<typename T> quaternion<T> tanh(quaternion<T> const & q);
Computes the hyperbolic tangent of the quaternion.
template<typename T> quaternion<T> pow(quaternion<T> const & q, int n);
Computes the n-th power of the quaternion q.