On 09/16/2016 12:44 AM, Bill Woodger wrote:
> I had been wondering why there were not "rules of algebra" explanations for 
> the floating-point variants of MULTIPLY. So I looked:
> "The sign of the product, if the product is numeric, is the exclusive or of 
> the operand signs. This includes the sign of a zero or infinite product."
> In mathematics, is there a problem with infinity having a sign? Drifting OT 
> again...
Mathematically, discussing both +∞  and -∞ make sense, and they derive
naturally in a number of contexts; such  as from considering the limit
of  (1/x) as x→0 from the right (x>0) versus as x→0 from the left (x<0),
or from just trying to describe both upper and lower bounds for real or
natural numbers.

Obviously the description of floating-point multiply given above needs
some liberal interpretation as well.  The hardware obviously cannot
produce an "infinite product". Since there is a fixed maximum magnitude
positive or negative that can be represented in each of the various
number representations used on any computer, the maximum product that
could be attempted would be the square of that magnitude.  As a 
practical matter, any result that overflows that maximum magnitude may
be regarded as infinity by the architecture, or it might just produce a
garbaged value and an overflow indication.  Some architectures have
reserved values that stand for +∞  and -∞ so that once one of these
values is produced in a chain of computations, subsequent calculations
based on those values also convey that the results have lost meaning.
    Joel C. Ewing

Joel C. Ewing,    Bentonville, AR       jcew...@acm.org 

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