Date:         Mon, 3 Mar 1997 14:47:40 -0500
Reply-To:     "Zuckier, Gerald" <Zuckier@CHIME.ORG>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         "Zuckier, Gerald" <Zuckier@CHIME.ORG>
Subject:      Re: Negative Cubic Roots
Content-Type: text/plain; charset="us-ascii"

Oops, that last one got away from me. Sorry. Anyway, didn't this come up
on SAS-L a few months ago, or something similar? In general, a number
raised to the 1/x will have x roots, equally spaced rotationally around
the real and imaginary number axes. The easy thing to do is just require
the operand to be a positive real number and throw away all the roots
except the one that also falls on the positive real number axis, but
that's not really correct. If you know you are going to use an odd root
(1/3, 1/5, etc.) you can kluge around it slightly by separating the sign
and the absolute value, i.e.
>cuberoot = sign(cube)*(abs(cube)) ** (1/3);
You still are only getting one root, so it's not really correct, but at
least it won't crash and will give you an answer. That's probably what
most people are looking for, most of the time, rather than some complex
root.
 
>----------
>From:  Mark Covello[SMTP:Mark.Covello@BARRA.COM]
>Sent:  Monday, March 03, 1997 11:13 AM
>To:    Multiple recipients of list SAS-L
>Subject:       Negative Cubic Roots
>
>---------------------- Information from the mail header
>-----------------------
>Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
>Poster:       Mark Covello <Mark.Covello@BARRA.COM>
>Organization: Barra
>Subject:      Negative Cubic Roots
>------------------------------------------------------------------------
>-------
>
>I was surprised by the following this weekend:
>
>
>145  DATA _NULL_;
>146  cube = -27;
>147  cuberoot = cube ** (1/3);
>148  PUT _ALL_;
>149  RUN;
>
>NOTE: Invalid argument(s) to the exponential
>operator "**" at line 147 column 17.
>CUBE=-27 CUBEROOT=. _ERROR_=1 _N_=1
>CUBE=-27 CUBEROOT=. _ERROR_=1 _N_=1
>NOTE: Mathematical operations could not be
>performed at the following places. The results of
>the operations have been set to
>      missing values.
>
>I checked the SAS language reference to see if it
>mentioned that negative numbers could not be raised
>to fractional exponents, but found nothing.
>
>I tried the same thing on my WIN3.1 version of
>MS Excel and got an error as well.  Today I tried
>it on the NT version of Excel and it resolved to
>-3.
>
>Can someone explain to me the algorithm that
>creates this error.
>
>Does Microsoft overwrite the error for
>specific values of the exponent?
>
>
>I would also be interested to know how most
>people handle this in their code. something like:
>
>  IF cube < 0 THEN mult  = -1;
>  else mult = 1;
>  cuberoot = mult * ((mult*cube) ** (1/3));
>
>???
>
>I was really amazed that I don't remember ever
>running into this (seemingly basic) problem before.
>
>
>Thanks for your input,
>
>Mark
>
>
>
>
>--
>***************************************************
>*****
>Mark S. Covello
>Programming Consultant
>current assigment:
>    Barra
>    Berkeley, California
>
>The views expressed in this post do not necessarily
>represent the views of Barra.
>
>"If one (member of Congress) had been there when
> the deity was on the point of saying,
>        'Let there be light,'
> we never would have had it."
>
>                               Mark Twain
>
>***************************************************
>*****
>