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I think NaNs should cause ARITHMETIC-ERROR, since "what's one man's NaN is
another man's number."

To put it another way, TYPE-ERROR is generally a sign of a program error
and the cases in which it is signalled should usually not vary from
implementation to implementation; however, which cases signal
ARITHMETIC-ERROR can vary depending on the implementation's floating number

Should we define specific conditions to correspond to the IEEE conditions
as subtypes of ARITHMETIC-ERROR?

I think that it is important to bring this issue to the X3J13 meeting, even
if it isn't quite ready for vote. 

If there's a new draft soon, we can have it available for discussion there,
and maybe get an "endorse in principle".