Re: fixed point vs floating point

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Robin says

<<Rubbish.  If evaluation of this expression fails, it
is because of exceeding the capacity of the fixed-point
multiplier.  It has -- incidentally -- nothing to do
with the division.

The above is the WRONG way to compute an expression
using fixed-point facilities.

You would write it x = (y * V1) / V3;
>>

No that's quite wrong, the fixed point expressions

   y * (V1 / V3)

and

   (y * V1) / V3

are quite different expressions (to substitute one for the other, for
example in the computation of interest in a bond, would not only be
an error, but might actually be a violation of the law, since the
details of such calculations are often contained in the bond instruments
and mandated).

These two expressions give quite different values, it is wrong to say
that one is right and one is wrong. Which one is right depends on the
problem at hand, and the intermediate precision required in both cases
must be carefully controlled.

I can easily see how the fixed-point facilities in PL/1 would seduce
PL/1 enthusiasts into such errors. It is one of the reasons that the
fixed-point design in PL/1 is generally considered a failure. Please
note I am talking a very specific language design point here. I quite
realize that most language designers consider the whole of PL/1 a
dismal failure, but I don't go that far, PL/1 is not nearly as bad
as its reputation, but it did make a number of serious mistakes,
and the fixed-point design was one of them.