The actual motion? Re: Motion P1788/M0012.01:InnerAdditionAndSubtraction
(This is part of the discussion on Motion 12)
Nate (and P-1788),
On first reading of the paper for Motion 12, I understand
that the actual operations are specified in (1) and (2) on
page 1, with the directed rounding specified at the top
of page 2, and that the rest of the paper is essentially
"application" of this operation.
I'd like to say that, at least "inner subtraction" is useful
and simple. For example, I've been using it for 20 years or so.
(See my TOMS Algorithm 737, "INTLIB": the operation is implemented
as routine "CANCEL". Another name for it I know is "cancelminus".)
It can be viewed as recovering X after computing A = X+B, but doing it
in a mathematically rigorous way with appropriate directed rounding.
(The underlying assumption is different from subtracting B from A.
When merely subtracting B from A, we are assuming A and B are independent,
but when using CANCEL, we are assuming A was obtained by adding B to something.)
In fact, all "reverse" operations can be viewed as such a cancellation, although
things can become more complicated (if we let them) when the pre-image of
the operation we are trying to undo might not be a single interval.
I support including inner subtraction. (Otherwise, isn't inner addition an
instance of inner subtraction?)
Baker