Re: Saturated Math

["Robert I. Eachus" <rieachus@attbi.com>]

Robert A Duff wrote:

> It seems to me that a saturating arithmetic ought to "stick" at
> infinity.  If you say "X + 1000", and that returns the max, then
> subtracting 1 from it should return the max, not max-1.  Others have
> said otherwise, and I wonder why.

All this discussion has convinced me is that any attempt to add 
saturating integer types to Ada is definitely a bad thing.  If a user 
implements the type of saturating arithmetic he needs, that is 
relatively safe.  At least he or she will know what happens and where. 
But adding a predefined saturating type to Ada would be like giving a 
loaded gun to a baby.  For every problem it solved, a dozen others would 
be papered over and hidden.

A case might be made for adding optional NaN values to fixed-point 
types, especially decimal types. As for floating point, I think GNAT 
allows users to "take advantage" of the saturating modes of IEEE 
floating point.  The idea makes my skin crawl slightly, but that is 
normal when I see floating point.

Seriously, there are many cases where error analysis for floating point 
code gives reasonable results. The creepy feeling comes when either the 
analysis obviously hasn't been done or the territory is full of land 
mines. So the real problem is that cases where the error analysis is 
tough get pushed into floating point, when using integer arithmetic or 
fixed point is probably impossible anyway.

The latitude and longitude discussion we just had was a good example. 
It takes about a minute to work out the worst case error for 32-bit 
fixed point.  The suitability of (24-bit) floating-point will depend on 
the accuracy you need and where you are.  (Degrees of longitude get 
smaller as you approach the poles, so the worst case is just above 32.0 
degrees of latitude or below -32.0 degrees. (Assuming decimal degrees.) 
  Degrees of latitude are the same size everywhere--modulo the Earth's 
deviation from spherical.  So the worst case in floating point, will be 
latitudes greater that 64.0 degrees or less than -64.0 degrees.

If I felt that people who used 32-bit floating point latitudes and 
longitudes had done that analysis, I'd sleep a lot more comfortably. 
Especially on overseas flights that might cross that magic 64 degree 
line. (Just below the Artic circle, or above the Antartic circle.)