The float and double floating-point data types have been present for a long time in the C (and C++) standard. While neither the C nor C++ standards do not enforce it, virtually all implementations comply to the IEEE 754—or try very hard to. In fact, I do not know as of today of an implementation that uses something very different. But the IEEE 754-type floats are aging. GPU started to add extensions such as short floats for evident reasons. Should we start considering adding new types on both ends of the spectrum?
The next step up, the quadruple precision float, is already part of the standard, but, as far as I know, not implemented anywhere. Intel x86 does have something in between for its internal float format on 80 bits, the so-called extended precision, but it’s not really standard as it is not sanctioned by the IEEE standards, and, generally speaking, and surprisingly enough, not really supported well by the instruction set. It’s sometimes supported by the long double C type. But, anyway, what’s in a floating point number?