Thoughts on IEEE P754

David-Sarah Hopwood david.hopwood at
Fri Aug 22 12:54:13 PDT 2008

David-Sarah Hopwood wrote:
> One can argue about the merits or otherwise of scale preservation, but
> it's an intentional property of the P754 decimal floating point design.
> See section 2 of 
> <>
> for the arguments in favour (which I'm not sure I buy into fully).

Actually, I'm sure that I don't buy them. Waldemar's argument about
scale not implying precision is quite convincing. From the above paper:

# If the scale is not preserved, measurements and contracts may appear
# to be more vague (less precise) than intended, and information is
# lost. For example, the length of a beam might be specified as
# 1.200 meters; if this value is altered to 1.2 meters then a contractor
# could be entitled to provide a beam that is within 5 centimeters of
# that length, rather than measured to the nearest millimeter.
# Similarly, if the scale is altered by computation, it must be
# possible to detect that change (even if the value of the result
# is exact) so that incorrect changes to algorithms can be readily
# detected.

There are two arguments made here, and the first is simply wrong,
because it depends completely on scale being an indicator of
precision. The second argument (starting from "Similarly,") perhaps
has a little more merit, but there is a great risk that the
preservation of scale will lead people to incorrectly believe
that it indicates precision, and I think that outweighs any other
possible benefit.

David-Sarah Hopwood

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