I wrote: > Now have mentioned a simple example of error combination which I wanted > to use, namely 2^20 irrational numbers which should sum to an integer.
Not only is this simple, but IMO a realistic model of what "roundoff error" means in the context of Prime95. So I shall try to give an analysis which avoids "handwaving" arguments. Let us represent each number to 16 binary places of precision. The error is a real number uniformly distributed between -2^-17 and +2^-17. The variance (rms) of these errors is (2^-34)/3. (Think area under a parabola). The sum of the variances is (2^-14)/3 which equals the variance of the sum of the errors we seek. standard deviation is defined as SQR(variance) = (2^-7)/SQR(3) The chance of getting the wrong integer is negligable. Hope this clarifies where I'm coming from:-) David _________________________________________________________________ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
