[libcxx-commits] [libcxx] [libc++] Introduce one-sided binary search for lower_bound on non-random iterators, and use that to improve the average complexity of set_intersection. (PR #75230)

[Iuri Chaer via libcxx-commits]

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@@ -46,6 +48,43 @@ _Iter __lower_bound(_Iter __first, _Sent __last, const _Type& __value, _Comp& __
   return __first;
 }
 
+// One-sided binary search, aka meta binary search, has been in the public domain for decades, and has the general
+// advantage of being Ω(1) rather than the classic algorithm's Ω(log(n)), with the downside of executing at most
+// 2*(log(n)-1) comparisons vs the classic algorithm's exact log(n). There are two scenarios in which it really shines:
+// the first one is when operating over non-random iterators, because the classic algorithm requires knowing the
+// container's size upfront, which adds Ω(n) iterator increments to the complexity. The second one is when you're
+// traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm
+// would yield Ω(n*log(n)) comparisons and, for non-random iterators, Ω(n^2) iterator increments, whereas the one-sided
+// version will yield O(n) operations on both counts, with a Ω(log(n)) bound on the number of comparisons.
+template <class _AlgPolicy, class _Iter, class _Sent, class _Type, class _Proj, class _Comp>
+_LIBCPP_NODISCARD_EXT _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Iter
+__lower_bound_onesided(_Iter __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {
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ichaer wrote:

I left `__lower_bound_onesided()` here even after removing all references to it from this file because it looked like it would be happier (and easier to find and maintain) with its family. I don't feel strongly about it, though.

https://github.com/llvm/llvm-project/pull/75230