From help-octave-request at bevo dot che dot wisc dot edu  Wed Sep 22 14:05:17 1999
Subject: Re: max() and min() of nan/inf
From: "Joao Cardoso" <jcardoso at inescn dot pt>
To: <olli dot saarela at kcl dot fi>, <help-octave@bevo.che.wisc.edu>
Date: Tue, 21 Sep 1999 23:51:00 +0100


----- Original Message -----
From: Olli Saarela <olli dot saarela at kcl dot fi>
To: Joao Cardoso <jcardoso at inescn dot pt>; <help-octave@bevo.che.wisc.edu>
Sent: Tuesday, September 21, 1999 7:00 AM
Subject: Re: max() and min() of nan/inf


> Hello,
>
> > Is this a correct behaviour?
> >
> > max() or min() return nan is a nan is one of its arguments? max() or
> > min() considering +/-Inf looks OK.
>
> Yes, it is correct. Of course this is a matter of definition (defined in
> the IEEE Standard 754), but the following example tries to give some
> rationale:
...
> A NaN value (Not a Number) is not a real number. It doesn't have a
> magnitude which could be compared. The min and max functions return the
> smallest and the largest number of the set of numbers given.

Yes. As NaN are not numbers, min/max should return the maximum/minimum
numbers in the set, not nans.

> When the
> set contains a NaN,

min/max should either return an error or return the min/max *number* in the
set

> the numbers don't any more have a minimum or a
> maximum value. Hence, the value NaN is returned, indicating that there
> is no number equal to the minimum or maximum value of the set.

sorry. There are there numbers and not numbers.

>
> > arithmetic or comparition operations
> > are of course not defined on nans...
>
> But they are defined. Any arithmethic operation with a NaN operand is
> defined to evaluate to NaN. Any comparison with a NaN operand is defined
> to evaluate to FALSE (except the ~= operation to TRUE).
>
> For example:
>   Is NaN bigger than 3? No.   (NaN > 3) --> FALSE
>   Is NaN smaller than 3? No.  (NaN < 3) --> FALSE
>   Is NaN equal to 3? No.      (NaN == 3) --> FALSE

using your example,  max(Nan,3), if evaluated as

3>nan -> F => max:=nan

but if evaluated as:

nan>3 -> F  => max:=3

so it is not enough to define that comparition operations on NaNs always
return false, the order of evaluation also seems to be important, and that
is certainly not defined in any standard.

Octave has the same behaviour as matlab, in this respect.

Thanks,
Joao

>
> For more complete description, please see:
>
http://www.lpthe.jussieu.fr/DOC_HTML/WorkShop/common-tools/numerical_comp_gu
ide/goldberg1.ps
>
>
> Best regards,
> Olli
> --
> Olli Saarela                       KCL Development Oy
> Olli dot Saarela at kcl dot fi                tel. +358-9-4371538 (office)
> Tekniikantie 2, Espoo-Otaniemi     fax. +358-9-464305
> P.O. Box 70, FIN-02151 Espoo, Finland



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