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To: Ali Chen who wrote (74161)	3/11/2002 1:32:47 AM
From: pgerassi	Read Replies (1) \| Respond to of 275872

Dear Ali: Fallen into another trap I see. Noise is the combination of all of the other factors you neglect to consider. Call the product of all of those error terms X. The correct answer is the one found by experimentation over many runs under carefully controlled conditions. These conditions attempt to minimize X. But when you attempt to project something from a base you add in many more terms some of which can be very large. In essence what you are doing is projecting what happens at 3GHz from a base only 200MHz wide where it is no less than 800MHz away. You assume linear interpolation (great when the data point desired is within the base (standard use) in most cases but terrible when the data point desired is far outside the base) when there is no proof that this is correct and much evidence that it is not. Let us look at the equation from an error range point of view. First you have the two samples that you use as base call them p1 and p2 where the x coordinate is the clock frequency and the y coordinate the SPECint score. Y3 at a sample is equal to the average of all trials at this speed +/- a value equal to standard deviation of all those trials. The last is what many rank amateurs forget to do. The standard linear interpolation is target y = (y2 - y1)(x3 - x2)/(x2 - x1) + y2. Now add in those standard deviation terms that newbies miss and you get y3 + std(y3) = (y2 + c2 * std(y2) - (y1 + c1 * std(y1))(x3 - x1)/(x2 - x1) + y1 + c1 * std(y1) + X (those non linear terms we are not considering). C2 and c1 are terms that are moved from -inf to + inf via normal distribution curve to get the many results to obtain the std. dev. of the projection. Now lets us assume that the std. dev. is constant wrt to the average result say 1%. By going through the motions we see that with x1 = 2000, x2 = 2200 and x3 = 3000, we see that std(y3) is 1.4% * 5 + 1% or 7%. And that's assuming that linear interpolation is correct. If we take that the upper acceptable bound of the std. dev. is half the expected increase or 25%, the highest std. dev. of the samples must be no less than 4.7%. For serious scientific work, the 3 sigma standard is the minimum allowed. And then the minimum std. dev. is more like 0.33%. No way is the std. dev. of those SPECint scores anywhere near that! Just look how far off the projections are from 1.5 and 1.6 to 2.0 for the 0.18u P4. They are definitly non linear and appear to have serious 2nd and 3rd order coefficients. Thus your methods fail using historical numbers where the results are known now. Heck your picks have numbers from as little as one month prior having nearly 1% lower performance on the supposed exact system with the same supposedly exact same software. Some of the tests show 6% differences in speed between the two samples taken a month apart. Just looking at SPECint_rates, show that less than 50% of clock speedups show in performance gains and the percentages are shrinking. And that yields less than 20% for a 50% clock speed up from 2.0. Pete