[eigen] Custom complex type

[Pavel Holoborodko <pavel@xxxxxxxxxxxxxxx>]

Hello, 

Eigen's magicians, please advise on how to implement custom complex type for smooth integration with Eigen..

I plan to create multi-precision C++ complex scalar class based on MPC: http://www.multiprecision.org/index.php?prog=mpc. 

MPC is cousin of MPFR from the same authors - http://mpfr.org. 

There are two possible ways to proceed:

(1).  Add template specialization for std::complex<mpfr::mpreal>.

(2).  Create own scalar class something like mpcomplex based on low-level MPC.

Second option seems attractive from optimization point of view - minimum overhead, no conversion mpreal <-> MPC low level stuff is required.

There is only one problem - will it be possible to integrate such complex type with Eigen?

Documentation on NumTraits says:

"An enum value IsComplex. It is equal to 1 if T is a std::complex type, and to 0 otherwise."

Does it mean that only std::complex<T> custom complex types are supported in Eigen?

If yes, do I need to provide something besides NumTraits<std::complex<mpreal> > specialization?

Thanks in advance, 

Pavel.