What is the rationale for all comparisons returning false for IEEE754 NaN values?

Question

Why do comparisons of NaN values behave differently from all other values? That is, all comparisons with the operators ==, <=, >=, <, > where one or both values is NaN

Answer 1

While I agree that comparisons of NaN with any real number should be unordered, I think there is just cause for comparing NaN with itself. How, for example does one discover the difference between signaling NaNs and quiet NaNs? If we think of the signals as a set of Boolean values (i.e. a bit-vector) one might well ask whether the bit-vectors are the same or different and order the sets accordingly. For example, on decoding a maximum biased exponent, if the significand were left shifted so as to align the most significant bit of the significand on the most significant bit of the binary format, a negative value would be a quiet NaN and any positive value would be a signaling NaN. Zero of course is reserved for infinity and the comparison would be unordered. MSB alignment would allow for the direct comparison of signals even from different binary formats. Two NaNs with the same set of signals would therefore be equivalent and give meaning to equality.