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Issue: EXPT-ZERO-ZERO (Version 1)
- To: KMP@stony-brook.scrc.symbolics.com
- Subject: Issue: EXPT-ZERO-ZERO (Version 1)
- From: Guy Steele <gls@Think.COM>
- Date: Tue, 28 Feb 89 12:44:34 EST
- Cc: CL-Cleanup@sail.stanford.edu, Cyphers@jasper.scrc.symbolics.com
- In-reply-to: Kent M Pitman's message of Mon, 27 Feb 89 19:37 EST <890227193717.1.KMP@BOBOLINK.SCRC.Symbolics.COM>
For what it is worth, W. Kahan of Berkeley recommends that
(expt 0.0 0) => 1.0 but (expt 0.0 0.0) => error.
I believe that the rationale is that in the case of an underflow,
(expt 0.0 0) => 1 saves you when what you were trying to do was
raise some very tiny but non-zero number to an integer power that
turned out to be zero (as in evaluating a polynomial?).
However, in the case of (expt x 0.0) the case is much less clear,
and if underflow is involved in the exponent there is more likely
to be some nuemrical instability.
I realize that this is a bit of a handwave, and I have probably
exceeded the limits of my own competence.
To summarize: yes, there is an essential singularity in the expt
function at (0, 0), but it is nevertheless convenient to define
the result to be 1, at least when the exponent is a rational zero.