[Cfp-interest 1979] Re: remquo( )

[Paul Zimmermann]

       Hi David,

is there any interest in defining (q,r) for y=0?
Another solution is to say that division by 0 is undefined,
and thus that (q,r) can be any value.

Paul

> Date: Wed, 14 Apr 2021 15:43:08 -0700 (PDT)
> From: David Hough CFP  <pcfp at oakapple.net>
> 
> The general property of
> 
> x mod y -> (q,r)
> 
> is that x = q*y + r, exactly;  the difference between mod and remainder
> is how q is rounded to an integral value.
> 
> So if q is integral and y is 0, then q is irrelevant and r is x.
> 
> So which q?   inf or NaN messes up the property.
> 
> Offhand I'd say q could be zero.
> 
> But looking at limiting cases of x mod y as y approaches 0, q gets bigger
> and bigger and r gets smaller and smaller.    q does not approach 0 and r
> does not approach x.    So from that point of view, q should be inf and
> r should be zero, both signed appropriately, but that means q*y should
> approach inf*0 which is indeterminate in general but should be defined to
> be x here!    In exact cases when x is an integral multiple of y, then
> r is 0, and q*y is indeed exactly x.