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Nie sankcjonuje ( bóg powoływać gdyż jest lubią grzebać się oczach decompress and adjusts the prediction inverse proportion to the count. The count is incremented up to a maximum value. At this point, the model switches from stationary to adaptive. and LIMIT are tunable parameters. The best values depend on the data. A large LIMIT works best for stationary data. A smaller LIMIT works better for mixed data types. On stationary sources, the compressed size is typically larger by 1 LIMIT. The choice of is less critical because it only has a large effect when the data size is small With 1, a series of zero bits would result the prediction sequence 1, 1, 1, 1, 1. With 0, the sequence would be 1, 1, 1, 1, 1. Cleary and Teahan measured the actual probabilities English text and found a sequence near 1, 1, 1, 1... for zeros and 1, 19, 39, 59... for consecutive ones. This would fit around 0 to 0. A real implementation would use integer arithmetic to represent fixed point numbers, and use a lookup table to compute 1 update and orders 0 through 2 on the 14 file Calgary corpus concatenated into a single data stream Using a higher order model can improve compression at the cost of memory. However, direct lookup tables are not practical for orders higher than about 2. The order 2 model ZPAQ uses 134 MB memory. The higher orders have no effect on π because the digits are independent pi Calgary corpus LIMIT order-0 order-0 order-1 order-2 455 1,853,408 1,855 435 1,081,334 1,621 425 1,809,306 1,660 420 1,890,304 1,029 417 1,784,315 1,612 416 1,478,335 1,717 415 1,658,357 1,790 415 1,035,379 1,800 415 1,280,399 1,737 Indirect Models. indirect context model answers the question of how to map a sequence of bits to a prediction for the next bit. Suppose you are given a sequence like 0000000001 and asked to predict what bit is next. If we assume that the source is stationary, then the answer is 0 because 1 out of 10 bits is a 1. If we assume a nonstationary source then the answer is higher because we give preference to newer history. How do we decide? indirect model learns the answer by observing what happened after similar sequences appeared. The model uses two tables. The first table maps a context to a bit history, a state representing a past sequence of bits. The second table maps the history to a prediction, just like a direct context model. Indirect models were introduced paq6 2004 A bit history be written the form which means that there have been n 0 zeros, n 1 ones, and that the last bit was LB For example, the sequence 00101 would result the state The initial state is meaning there is no last bit. paq6 and its derivatives a bit history is stored as 1 byte, which limits the number of states to 256. The state diagram below shows the allowed states ZPAQ with n 0 on the horizontal axis and n 1 on the vertical axis. Two dots represents two states for LB=0 and LB=1. A single represents a single state where LB can take only one value because the state is reachable with either a 0 or 1 but not both. general, update with a 0 moves to the right and update with a 1 moves up. The initial state is marked with a 0 the lower left corner. The diagram is symmetric about the diagonal. There are a total of 219 states. n 1 47 23 21 19 17 15 13 11 9 7 5 3 1 0 15 48 n 0 There are some exceptions to the update rule. Since it is not possible to go off the end of the diagram, the general rule is to move back to the nearest allowed state the direction of the lower left corner There is another rule intended to make the model somewhat nonstationary, and that is when one of the counts is large and the other is incremented, then the larger count is reduced. The specific rule from the ZPAQ standard is that if the larger count is 6 or 7 it is decremented, and if it is larger than 7 then it is reduced to 7. This rule is applied first, prior to moving