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 -- To unsubscribe from this list: send the line "unsubscribe linux-wireless" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
