By the way, a 128-bit floating point number is called a "double double" in C, and a "quadruple" in other languages.
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I was wrong about "double double" in C, that is only a 107 bit significant" which is different than an IEEE 754 quadruple. So when you get into 128-but floating point numbers, you will run into divergent primitives across languages, which is a liability that is not present in the "safer" 64-bit floating point.