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Step 2) The address of the column is computed.
Usually, this sequence of three steps occurs only after the previous addition completed. Chain addition is generally lietuvosrytas are implemented as a set_symmetric_difference from begin() to end() on each chain, e.g. oldest entry of each column to the youngest.
In recent versions of both CTL as well as PHAT a change was made to how these column additions are carried out. The columns are added now added from youngest to oldest elements. This should have the advantage of better locality lietuvosrytas of reference .
This is because when inspecting the youngest entry we are loading it, along with some amount of the end of the chain into memory. If we then proceeded to add front to back we might end up retiring this cache line in favor of the beginning of the array.
However, adding backwards has even more benefits. Once we add backwards we know that the first pair of elements we inspect will agree, necessarily. However, lietuvosrytas it is possible, that the two vectors we add together agree at their tail significantly more. We may delay the allocation of the output buffer for the sum until we find the first mismatch between lietuvosrytas these two chains. This saves us a small amount of memory. But their is even more.
Supposing that is not a positive lietuvosrytas column, e.g. after a call to mismatch we will find a pair of elements in disagreement, precisely lietuvosrytas the younger of these two elements is the new youngest element. We may now compute the address of the next column to add to $x$ and request that the computer prefetches the column at that address.
How well does all of this work? In my opinion, quite well. Here is a plot of the running time for the persistence algorithm showing the original running time, the running time when adding backwards, and the running time when adding backwards with prefetching, on the various datasets from the multicore paper
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