Hi!

I want to thank all of you on this topic for helping point out the wider
meaning of Kahan's statement. After getting some sleep I now realize the
"Eureka!" that I missed in the wider sense, along with every other language
(that I know about) that uses rectangular mapping of the complex plane. I
need to stop working all night into the red-eye zone so that these things
become a bit more apparent on first glimpse...

Indeed a rectangular representation *IS* insufficient and something which
also encodes the Riemann sheet is needed to properly handle all
possibilities.

Will I fix NML in this regard? Probably not... simply because letter-perfect
complex arithmetic is so rarely needed in practice. But I might play around
with a limited class of compelx numbers that do things correctly. I wouldn't
want to hose down the performance of my FFT's and such.

- DM

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