I understand your words, and I have previously studied the help reference you gave. What I don't understand is why they are correct (or not). Possibly my problem is that I can't find a precise definition of "adjusted price", and what its significance should be. My best guess is that the price is "adjusted" to reflect the "total return" of a stock purchased some time in the past. Then we have to define "total return", which I would say is the capital gain reflected in the current price versus the purchase price, plus the sum of all cash dividends received in the meantime. A stock split (dividend) does not directly contribute to either of these, it just makes them a bit harder to compute. This algorithm must be strictly additive - there is no number (that applies to more than one date) which you can multiply a closing price by to get an adjusted close.
IF those definitions are correct, I stand by my computational objections - the adjusted price SHOULD be the current price minus the sum of cash dividends paid. At MOST, the rounding error could be 1 cent in the stock prices (current and date being computed) plus 1 cent for each dividend payment due to rounding/truncation. Most of these could be easily avoided, so there should not be any large systematic errors in the computation.
If those definitions are not correct, PLEASE tell me what the definitions actually are, because the algorithm you cite with fractions mathematically assumes that there is some multiplying factor that can be computed on the "ex" date that can be used to compute some other day's adjusted price. I do believe that this is what is happening, but I do not see a definition of "adjustment" that makes this a meaningful number. Cash dividend checks are additive in nature, and are totally independent of the closing price on ANY particular date.
The trouble is, that there are discrepencies much larger than potential rounding errors.
(apparantly this is too long for a "comment" to the previous comment)