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128-bit quadruple precision
The thing about IEEE 128-bit quadruple precision floats is that they only have hardware support in the POWER9, the IBM S/390 from the 1990s, and z/Architecture systems. We’re talking systems which cost at least $3000 and go up very quickly from there.
It *is* possible to change the default number type in luaconf.h (the #define LUA_NUMBER) to something else, such as IEEE binary128 or decimal128 float, as long as one’s C compiler supports the type. Of course, if using a type like that, it’s probably a good idea to change LUA_NUMBER_FMT to hold more digits (and make sure the buffers can hold the digits).
As it turns out, with mainstream processors, instead of having more widespread support for 80-bit floats, ARM processors -- read, most of the real-world processors out there in our smartphone-addicted age -- are instead increasing support for 16-bit float types. Armv8.1-M and ARMv8.2-A added 16-bit floats (1 sign bit, 5 exponent bits, 10 mantissa bits), ARMv8.6-A added support for another 16-bit float format, “BFloat16” (1 sign bit, 8 exponent bits, 7 mantissa bits).
Of course, someone *could* extend Lua to use GNU Multiple Precision Arithmetic Library or what not as the native number type, but Lua is not Python, and doing so would make Lua a lot larger and a lot slower. 64-bit floats, the default, is usually good enough, keeps Lua small (I like having a full Lua-5.1 derived interpreter which fits in 118,784 bytes) and when it’s not, there are solutions like https://github.com/LuaDist/mapm out there.