On Mon, Jun 12, 2017 at 06:16:06PM +0000, Stefan Koch via Digitalmars-d-learn wrote: > On Monday, 12 June 2017 at 06:15:07 UTC, Biotronic wrote: [...] > > On a multi-core system we can do better: > > > > auto nums = iota(10_000_000.0f); > > auto sum = taskPool.reduce!"a + b"(nums); > > > > Given arbitrary parallelism (yeah, right!), this will be O(log(N)). > > For real-world systems, it might give a speed-up for large arrays, > > but won't reduce the big-O complexity. Of course, there will also be > > overhead to such a solution, so there is a limit to how much one'd > > actually benefit from it. > > > > -- > > Biotronic > > Biotronic how do you arrive at O(log(N)) ?? > And which logarithm ?
His stated presupposition is arbitrary parallelism, which I assume means arbitrary number of CPUs or cores that can run in parallel, so then you can divide the array of N elements into N/2 pairs, sum each pair in parallel, which gives you N/2 subtotals after one iteration, then you recursively repeat this on the subtotals until you're left with the final total. The complexity would be O(log_2(N)) iterations, assuming that the constant factor hidden by the big-O covers the overhead of managing the parallel summing operations across the arbitrary number of cores. You can also get logarithms of a different base if you divided the initial array, say, into triplets or j-tuplets, for some constant j. Then you'd get O(log_j(N)). (Of course, with a slightly larger constant factor, assuming that each CPU core only has binary summation instructions. But if your instruction set has multiple-summation instructions you may be able to get a higher j at little or no additional cost. Assuming you can produce a machine with an unlimited number of cores in the first place.) Of course, his comment "yeah, right!" indicates that he's aware that this is an unrealistic scenario. :-) T -- Notwithstanding the eloquent discontent that you have just respectfully expressed at length against my verbal capabilities, I am afraid that I must unfortunately bring it to your attention that I am, in fact, NOT verbose.
