Messages in this thread | | | Date | Wed, 12 Sep 2012 17:38:21 -0400 | From | Nick Bowler <> | Subject | Re: [PATCH v2] lib: gcd: prevent possible div by 0 |
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On 2012-09-12 12:36 -0700, Andrew Morton wrote: > On Wed, 12 Sep 2012 21:20:30 +0200 > Davidlohr Bueso <dave@gnu.org> wrote: > > On Wed, 2012-09-12 at 12:10 -0700, Andrew Morton wrote: > > > On Mon, 10 Sep 2012 16:35:19 +0200 > > > Davidlohr Bueso <dave@gnu.org> wrote: > > > > > > > Account for all properties when a and/or b are 0: > > > > gcd(0, 0) = 0 > > > > gcd(a, 0) = a > > > > gcd(0, b) = b [...] > I'm scratching my head a bit at the patch though. What does gcd(0, 13) > mean? That 0 can be divided by 13 zero times, which is an integer > result? I wonder why any non-buggy code would do that....
The number-theoretical definition of gcd(a, b) on the integers, leaving aside the case where a and b are both 0, are defined as the greatest integer which divides both a and b.
An integer x divides y if there exists an integer M such that x*M equals y.
Observe that all integers divide zero (since we can set M to 0, and x*0 = 0 for any x). So it's easy to see that the result of gcd(x, 0) and gcd(0, x) must be |x|.
The case of gcd(0, 0) is tricky. Clearly, as all integers divide zero, none of these can be the greatest one. So this is normally treated as a special case, defined to be 0 by convention, as this makes the use of gcd "nicer" in other areas of mathematics.
Cheers, -- Nick Bowler, Elliptic Technologies (http://www.elliptictech.com/)
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