Re: [Boost-users] Multiprecison: converting a complex class to a number<> backend

On 28/06/2016 20:49, Daniel Brake wrote:

Hi Boost,

I have implemented my own complex class wrapping around Boost.Multiprecision number<>, particularly mpfr_float. Now, I'd like to take the class I've written, and extend/convert it into a backend suitable for use in number<>. While I've read the documentation describing the requirements for a backend http://www.boost.org/doc/libs/1_61_0/libs/multiprecision/doc/html/boost_mult..., and think I understand what I need to do, I have found 0 examples in the wild.

My current setup has a pair of files mpfr_complex.hpp, mpfr_complex.cpp describing something like (just what you'd expect, really)

--------- class complex{ mpfr_float real_, imag_;

public: // the *= family of operators, getters, setters, // some factory functions, etc };

//the free operators defined down here, along with pow, exp, etc. --------------

I think what I'd like to write is a new complex_backend.hpp file which implements the required functions for the complex wrapper around mpfr_float. In this file, I believe I implement the family of functions such as eval_multiply(b, a) in terms of the operators for my complex class. Is this right?

Yes.

In a related vein, with et_on for mpfr_float, I've started adding templated overloads for the complex operators and math function accepting expressions of reals, and I think this is going to get out of hand, so using number<> would conceivably save me a ton of time writing my own functions. It will also save me a ton of errors for hand-writing the expression templates for complexes, which appear to be ready to go from Boost.Multiprecision once I get a backend implemented.

Again, my goal is expression templates for complexes with real and imaginary fields consisting of mpfr_floats, leveraging the number<> template, with et_on, and my own backend. Do you have any advice? Any references to any other custom backends?

I suggest you take a look at rational_adaptor which does more or less exactly this but for rational types - if you basically just gut the function implementations from that file, search and replace the class names, and then fill in the blanks you should be 95% there. This is actually something that's been on our TODO list for far too long, ideally this should be part of the library - fancy helping out - or at least being a testing guinea pig? I quickly mocked up an example (attached) of how I think this should look if we were to add it to the library, basically: template<class Backend> struct complex_adaptor{ /* details */ }; Then complex number typedefs that mirror each floating point typedef: typedef number > complex_cpp_bin_float_quad; // etc As noted in the attached example, we really need another number category for complex types, and while mixed arithmetic with (real) scalars will just work, if you wanted an imaginary type as well, that would involve a whole lot more work, as class number does not currently support return a type different from either argument type in the binary operators (for real + imaginary for example). And finally... there is this: https://code.google.com/archive/p/cpp-imaginary-numbers/ which takes a different view of things (but loses multiprecision's expression templates). HTH, John. PS, one final note: ideally this would be handled by std::complex, but sadly that class can not be instantiated on any type other than float/double/long double with invoking undefined behaviour.