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What happens if I define LONGDOUBLE_TYPE as double?
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Unless it has changed in recent years (as IEEE-754 evolves with time), 80 bit extended precision has never been an "official" IEEE standard. Yes, it is compatible with IEEE guidelines, but it isn't a blessed rigidly standardized format like 32 bit single precision floating point and 64 bit double precision floating point. And "long double" is only required to be as precise as "double" ...

It would certainly be nice if "long double" supported more precision than "double" but none of the standards require that to be true.