  `On Sat November 20 2010 08:01:55 Peter Zijlstra wrote:> On Fri, 2010-11-19 at 17:28 -0500, Bob Copeland wrote:> > On Fri, Nov 19, 2010 at 06:07:05PM +0900, Bruno Randolf wrote:> > > Hmm, maybe I suck in mathemathics, but I don't see a way to do that> > > given the formula:> > > > > > (((internal * (weight - 1)) + (val * factor)) / weight> > > > I was thinking something along the lines of:> > > > round = (1 << n) - 1;> > (((internal * (weight - 1) + round) >> n) + val) * ((1 << n) / weight)> > > > where (1 << n) is the factor and ((1 << n) / weight) can be precomputed.> > If you think about it, this is just reciprocal multiplication in fixed-> > point math with n bits of decimal resolution.> > > > The problem is the shift of the older terms introduces roundoff error,> > but there are some tricks you can do to maintain bounded error, e.g.> > shifting by some smaller factor of n and scaling other terms -- in the> > limit you reinvent floating point and then it's slower than division :)> > Sure, x/y := x/z * z/y, and by picking z := 2^n, we can pre-compute z/y> and write x/z using a shift. The problem however is always range vs> granularity, you chose to first /z and then *z/y, this avoids some> overflow issues but truncates the lower n bits of x.> > If you first *z/y and then /z you keep your low bits but risk loosing> the top bits to an overflow.> > I guess the question is do we really need weights outside of 2^n? If> not, you can use the weight := 2^n version. If you do, you get to pick> either of the previously mentioned options.> > Sadly gcc doesn't sanely support a u128 type, which would be very useful> to avoid some of these overflow issues (like we used to use u64 mults> for u32 fixed points mults).Thank you all for your help and sorry for following up so late!I think we don't really need weights outside of 2^n and i'm going to post a patch based on Peter Zijlstra's formula. Thanks again! Would it make sense to have the factor 2^n too, so we can bitshift there too?bruno`   