The most common source of "super-linear scaling" is that L1 and L2 caches increase for each additional hardware thread you put on a task.Dann Corbit wrote: ↑Wed Jan 08, 2020 6:29 pm Doesn't this indicate that the reductions are flawed? Otherwise, where does the Elo increase come from?
If a fatter tree is better then maybe the reductions are incorrect or too extreme.
On the other hand, it seems possible that the small extra randomness introduced by the thread local storage might indicate a.phenomenon where k threads in n time are actually superior to one thread in k"n time, which is really interesting. But it's clearly not enough to compensate for SMP loss. I guess the next question is, can this effect be enhanced?
Lets take the AMD Threadripper 3970x (32-core) as an example. 1x thread will only have 512kB of L2 cache. But max out the system with 64-threads, and they will effectively be searching across 16MBs of L2 cache.
EDIT: Here's a good discussion on superlinear speedups: https://www.drdobbs.com/cpp/going-super ... 542?pgno=1
In particular, page 2:There are two main ways to enter that rarefied realm:
* Do disproportionately less work.
* Harness disproportionately more resources.
But something interesting happens when the distribution of solutions is not uniform, because then averages no longer apply the same way. To illustrate what happens when matches are clustered, consider Figure 4: We still have M matches in the collection, as before, but let's assume that they are distributed, not evenly throughout, but with higher probability in some regions.
For simple sequential search, this is no big news: It fares neither better nor worse, and on average still takes as long to find a match as it would if the matches were distributed uniformly throughout the collection. Even if the sequential algorithm writer knows in advance that matches tend to be clustered, it's hard to see how to take advantage of that without also knowing in advance where the clusters are.
For the simple parallel search, on the other hand, clustering is great news, because a parallel search directly takes advantage of any locality there may be in the matches. Consider: Any clustering effect means that some subrange workers will end up discovering that they are impoverished, having relatively fewer matches, or none at all, in their assigned search areas. But other workers will enjoy a correspondingly higher number of matches in their areas, which means—and this is the important part—they will have a higher probability of finding a match each time they test an element, which in turn means that on average they will need to visit fewer elements to find a match. Like Forty-Niners panning and digging for nonuniformly distributed gold in California (near Sutter's Mill; no relation), many workers will find little or nothing, while a lucky few, or just one, will hit the Motherlode. And "just one" is all it takes; any clustering at all is immediately helpful because the time to perform the total search is the minimum of the workers' runtimes—we're done as soon as any worker finds a match.
[Superlinear Speedup from clustered results] isn't limited to simple array-like collections. Many kinds of collections naturally enjoy clustered matches. For example, when we traverse a tree or graph using depth-first search, the parallel version of the algorithm typically has each parallel worker searching a localized subtree, and in many problem domains the solutions tend to be clustered in subtrees. When that happens, one worker will have a disproportionately better chance of being assigned an area with more matches, and we can expect superlinear improvement. Example applications range from searching game trees (for example, a bad move at one node in the tree can cause the entire subtree below it containing subsequent moves to have no good solutions), to CAD and VLSI circuit layout algorithms (see [2]).