Hints on using float128 (and __float128)

__float128 is the (optionally) compiler supplied hardware type, it's an C-ish extension to C++ and there is only minimal support for it in normal C++ (no IO streams or numeric_limits support, function names in libquadmath all have different names to the std:: ones etc.) So you can program type __float128 directly, but it's harder work.
Type float128 uses __float128 and makes it C++ and generic code friendly, with all the usual standard iostream, numeric_limits, complex in namspace std:: available, so strongly recommended for C++ use.

Make sure you declare variables with the correct type, here float128.
Make sure that if you pass a variable to a function then it is casted to float128.
Make sure you declare literals with the correct suffix - otherwise they'll be treated as type double with catastrophic loss of precision. So make sure they have a Q suffix for 128-bit floating-point literals.
All the std library functions, cmath functions, plus all the constants, and special functions from Boost.Math should then just work.
Make sure std lib functions are called unqualified so that the correct overload is found via Argument Dependent Lookup (ADL). So write sqrt(variable) and not std::sqrt(variable).
In general, try not to reinvent stuff - using constants from Boost.Math is probably less error prone than declaring your own, likewise the special functions etc.

Some examples of what can go horribly and silently wrong are at float128_example.cpp.

Boost C++ Libraries