Re: FW: Transcendental function tables: comments welcome!

[Nick Maclaren <nmm1@xxxxxxxxxxxxx>]

"Fred J. Tydeman" <tydeman@xxxxxxxxx> wrote:
> If one takes what is in the IEEE 754 and the drafts as a guide, in the 
> first instance, NaN's are the return value appropriate for a domain 
> error, ...

Agreed.  Whether they mean "absolutely any value, including infinity",
"the result of an erroneous calculation" (e.g. sqrt(-1)) or a true
"not a number" (e.g. float("purple")) is less clear.  But that isn't
critical, as those categories have similar propagation characteristics.

> ...  The only exception to this principle that I can see 
> are the min/maxNum and min/maxNumMag functions, which treat NaN as an 
> uninitialised value to be ignored.  I had the impression this caused 
> much angst and argument in the committee a few years ago.

I wasn't involved at the time, but am completely baffled why 40 years
of prior art was completely ignored.  I tried raising this in C99,
and merely got flamed.  In particular, "missing value" indicators go
back to the 1960s, and were first used (as far as I know) in Rothamsted
software.  SPSS was the first package to make them available to the
masses.  They have the following properties:

    1) They propagate as error indicators (i.e. max(miss,1.0) = miss)
in normal calculations.

    2) They propagate as missing values (i.e. max(miss,1.0) = 1.0) ONLY
in reduction operations.

    3) They are superseded by error indicators in ANY operation, if
the arithmetic supports both.

For example, if X = (1.0,miss,2.0), Y = (miss,2.0,3.0) and
Z = (NaN,2.0,3.0), then X+Y = (miss,miss,5.0), Y+Z = (NaN.4.0,6.0),
sum(X) = 3.0 and sum(Z) = NaN.

It is claimed by some people that it is a great efficiency advantage
in statistics if max(NaN,1.0) = 1.0.  This is nonsense, as I can
witness (and statistical packages were my 'area' for some years).
The primary reduction operations which need missing value handling
are IN THIS ORDER:

    Counting (i.e. the number of non-missing values)
    Summation
    Variance (i.e. sum(x^2)-sum(x)^2/count(x))
    Maximum/minimum
    Product

Counting is not in IEEE 754, and it is unclear whether reduction or
normal operations are more important, anyway.

> The idea the NaN represents any number is not really supported by the 
> standard.  What happens if you attempt to ascii to binary conversion of 
> "purple".  It belongs more to an interval arithmetic approach, which 
> still needs NaN to deal with examples such as sqrt(-1).

Agreed.


Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email:  nmm1@xxxxxxxxx
Tel.:  +44 1223 334761    Fax:  +44 1223 334679