Path: utzoo!utgpu!water!watmath!clyde!ima!bbn!rochester!quiroz
From: quiroz@cs.rochester.edu (Cesar Quiroz)
Newsgroups: comp.lang.c
Subject: Re: pow again
Summary: Argh!
Message-ID: <5856@sol.ARPA>
Date: 13 Jan 88 22:03:27 GMT
References: <629@PT.CS.CMU.EDU> <5825@sol.ARPA> <7071@brl-smoke.ARPA>
Reply-To: quiroz@ROCHESTER.UUCP (Cesar Quiroz)
Organization: U of Rochester, CS Dept, Rochester, NY
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From article <7071@brl-smoke.ARPA> (gwyn@brl-smoke.ARPA (Doug Gwyn )):
:In article <5825@sol.ARPA>, quiroz@cs.rochester.edu (Cesar Quiroz) writes:
:>       There is no such thing as a unique, universally accepted
:>       definition for the exponentiation.
:
:I don't buy this.
:
Neither do I!  I found myself arguing against my own position (this
bad habit of posting when late and lacking sleep).

The confusion came about this way:  Somebody (I think E. Wyatt)
argued that expt(-2,3) could be chosen to be either -8 real or
-8 + 0i complex (which happens to  project into a real, of
course).  My article tried to defend the point that there is no such
choice, the universally accepted *definition* for exponentiation is
the complex one.

The problem is that the *implementation* of some special cases
(those with rational exponents) can be made very efficient, by
ignoring that it doesn't generalize into a continuous function in
any sensible way.  Same goes for sqrt, where the NonNegative->Real
definition can be made very efficient (by a Newton-Raphson
iteration, for instance) while exponentiation to the 0.5 (or
negative arguments for the common sqrt) might involve more expensive
stuff.  Catering for efficiency in such special cases I find
defensible (so the power functions you posted are desirable in the
library).

The noise about sqrt reduces to this: There are no negative numbers
for which we might want to define a real square root, so setting
EDOM or signalling a matherr for all the negatives is good enough.
With pow, some negative integer exponents produce complex numbers
that can be identified with reals, and so there are people who find
useful to believe that -2^3 = -8, although they don't know how to
define things like -2^3.1.  Catering to this sloppiness, even if it
happens to argue for the same library functions, is what I found
indefensible.

-- 
Cesar Augusto  Quiroz Gonzalez
Department of Computer Science     ...allegra!rochester!quiroz
University of Rochester            or
Rochester,  NY 14627               quiroz@cs.rochester.edu