mpc_complex_backend : Basic math operators + - * / are too greedy for real types.

[cosurgi]

Observe following example code where I lose 400 digits of precision without even a single warning from compiler:

#include <iostream>
#include <boost/core/demangle.hpp>
#include <boost/multiprecision/mpc.hpp>
#include <boost/multiprecision/mpfr.hpp>

template<typename T>
void print_name(T) {
	std::cout << boost::core::demangle(typeid(T).name()) << std::endl;
}

int main() {
	boost::multiprecision::number<boost::multiprecision::backends::mpfr_float_backend<500u>,  boost::multiprecision::et_off> a(1);
	boost::multiprecision::number<boost::multiprecision::backends::mpc_complex_backend<100u>, boost::multiprecision::et_off> b(1);

	// ERROR: 400 digits of precision are lost without even a warning from the compiler:
	auto c1 = a + b;
	auto c2 = b + a;

	auto c3 = a - b;
	auto c4 = b - a;

	auto c5 = a * b;
	auto c6 = b * a;

	auto c7 = a / b;
	auto c8 = b / a;

	print_name(c1);
	print_name(c2);
	print_name(c3);
	print_name(c4);
	print_name(c5);
	print_name(c6);
	print_name(c7);
	print_name(c8);
}

I suppose that such conversion could be allowed, but only explicitly when I really want to do it. Not by mistake like in such an arithmetic operation.

I encountered this problem when implementing a helper for upconverting precisions [1,2] which provides these four basic operations. My helper operators would create in example above an mpc_complex_500 type here. But they cannot, because the operators + - * / are already provided for this combination of types.

1. https://gitlab.com/yade-dev/trunk/-/blob/improveComplex/lib/high-precision/UpconversionOfBasicOperatorsHP.hpp

2. https://gitlab.com/yade-dev/trunk/-/blob/master/lib/high-precision/UpconversionOfBasicOperatorsHP.hpp - when 1. gets merged see 2.

[cosurgi]

BTW: it feels similar to boostorg/math#350

[jzmaddock]

That's a bug - all the machinery is in place to ensure that lossy conversions are always explicit, but somehow that one has escaped!

I'll look into it.

[cosurgi]

Thank you! :)