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 ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN