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So we defined abs(NaN), sounds like a feature to me ;-)

You made a good point. But one might argue that -nan should become nan after an abs operation. I don't know enough about this topic to determine whether such an argument has merit though.

It's not -NaN vs NaN. There are a bunch of NaN types, which are not related like that. It could (according to the spec) change "NaN: Attempt to arcsin value greater than 1" to "NaN: Zero divided by Zero operation"

Too late to edit now, but the floating point standard actually specifies that this is what abs should do.