Comment by Sharlin
2 days ago
Because IEEE 754 creators wanted to signal non-trapping error conditions for mathematically undefined operations, and they had a plenty of bit patterns to spare. Apparently back in the 70s and 80s in many cases it was preferable for a computation to go through and produce NaNs rather than trapping instantly when executing an undefined operation. I'm not quite sure what the reasoning was exactly.
In early FP machines the floating point processor could not take a trap at a faulting instruction precisely: it could only go bad things. Furthermore for programmers and hardware it can be very expensive. Rather than go through a loop and filter NaN out of results it becomes trap every time and resume and is a pain.
It avoids traps which are really inconvenient.