Issue: EXPT-ZERO-ZERO (Version 1)

[Kent M Pitman <KMP@STONY-BROOK.SCRC.Symbolics.COM>]

Issue:        EXPT-ZERO-ZERO
Forum:        Cleanup
References:   EXPT (pp203-204)
Category:     CHANGE
Edit history: 27-Feb-89, Version 1 by Scott Cyphers (Cyphers@Symbolics.COM),
              27-Feb-89, Version 2 by Pitman (signals->is an error, misc edits)
Status:       For Internal Discussion

Problem Description:

 (expt 0 0) is mathematically undefined, but CLtL defines it as 
 being 1 in most cases.

Proposal (EXPT-ZERO-ZERO:MAKE-UNDEFINED):

 Make (expt 0 0) an error for zeros of all types.
 That is, it has ``undefined effect.''

Test Case:

 (EXPT 0 0) => 1                ;according to CLtL
 (EXPT 0 0) is undefined        ;proposed

Rationale:

                                       0
 For some examples of the behavior of 0 , consider:
 
           X
 1)  Lim  0  = 0
     X->0
 
 
               ln k
 2)   Y(X) = --------
             c + ln X
   
      Lim  Y(X) = 0
      X->0 
   
    but
   
              Y(X)
      Lim    X      = k
      x->0   

Current Practice:

 Symbolics Genera returns 1 for the test case.

Cost to Implementors:

 Technically, there is no cost to implementors because this would become
 an ``is an error'' situation, and all implementations that already conform
 would continue to conform.

 In practice, most implementations would want to detect the error in
 high safety situations. In most cases, this is a straightforward change
 to one or two functions, and including perhaps some compiler optimizers.
 If any implementations have microcoded this operation, the change may
 be more complicated.

Cost to Users:

 Even though some implementations might not change, users would not be
 able to depend on this feature in portable code.  Given the mathematical
 questionableness of the behavior, however, some of the affected users
 may treat a trend toward error detection as a `bug fix.'

Cost of Non-Adoption:

 Some mathematical errors will not be detected because CL supplies a
 value which is not always appropriate.

Benefits:

 In implementations which choose to reliably signal an error in this case,
 condition handling can be used to customize the behavior of (expt 0 0)
 in a manner appropriate to the application.

Aesthetics:

 Cleaner mathematically.

Discussion:

 We'd really prefer one of ``must signal'' or ``should signal,'' but
 since non-integer 0 powers are already ``is an error'' this is most
 consistent.

 Cyphers, Pitman, and several other Lisp developers at Symbolics think
 this is a good idea.