Extending well-known functions

There are large numbers of questions that have to be resolved in a fixed way, subject to debate on what is the most useful computational result.

Natural extensions don't always exist: compromises must be made. Their consequences must be traced through the design so as to formulate as coherent a system as possible.

Example. What is the max of (0,NaN)?

Sample desirable axioms:

• max(x,y) must be the same as max(y,x).
• These comparisons return FALSE:

   max(x,y) < y
   max(x,y) < x

This means that max(NaN,x) could be either NaN or x, a non-NaN. Tough choice.

How best to identify values of complex functions on branch cuts?

(Need clear definitions for elementary function defaults). There are uses for signed zero allowing us to distinguish, for example, x+0i from x-0i. (WK paper on Branch Cuts for Complex Elem. Funs, 1987)