is_heap doesn't seem like a particularly useful operation though, generally a heap is intentionally constructed as such via push_heap/pop_heap
mananaysiempre 40 minutes ago [-]
Indeed that part seems more like an artist’s study than an attempt at actual usefulness, but that’s okay when figuring out if anything at all in the neighbourhood of what you’re trying to do with SIMD is even possible. As far as constructing heaps, don’t forget about (linear-time) heapify, which can be significantly faster if you have a bunch of elements and want to construct a heap with all of them in it. (This doesn’t get you a linear-time heap sort because you’ll still pay the full linearithmic price for the subsequent pop_heaps.)
simonask 42 minutes ago [-]
I think it's fairly useful. It means that you can convert a contiguous array to a heap with a fast O(n) read-only check instead of O(n log n) writes, so if you know that's the common case, you can detect it up front and only revert to normal binary heap insertion if it returns false.
madars 9 minutes ago [-]
By the way, you can also construct heap in linear time - instead of doing n consecutive insertions, at least half of which require log n work, you can apply sift-down operations from bottom up, beginning with the last non-leaf node and working backwards to the root.
That way, roughly half the nodes are leaves (requiring no work), a quarter are at the second-to-last level (requiring at most 1 comparison/swap), an eighth at the third-to-last level (requiring at most 2 comparisons/swaps), and so on. Summing up 1 n/4 + 2 n/8 + ... gets you O(n) total complexity.
That way, roughly half the nodes are leaves (requiring no work), a quarter are at the second-to-last level (requiring at most 1 comparison/swap), an eighth at the third-to-last level (requiring at most 2 comparisons/swaps), and so on. Summing up 1 n/4 + 2 n/8 + ... gets you O(n) total complexity.
See https://en.wikipedia.org/wiki/Heapsort?useskin=monobook#Vari...