[libcxx-commits] [libcxx] [libc++] Introduce one-sided binary search for set_intersection so that it can be completed in sub-linear time for a large class of inputs. (PR #75230)

[Louis Dionne via libcxx-commits]

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@@ -46,6 +48,52 @@ __lower_bound(_Iter __first, _Sent __last, const _Type& __value, _Comp& __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 \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at
+// most 2*log(n) 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 \Omega(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 \Omega(n*log(n)) comparisons and, for non-random iterators, \Omega(n^2) iterator increments, whereas the
+// one-sided version will yield O(n) operations on both counts, with a \Omega(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) {
+  // static_assert(std::is_base_of<std::forward_iterator_tag, typename _IterOps<_AlgPolicy>::template
+  // __iterator_category<_Iter>>::value,
+  //       "lower_bound() is a multipass algorithm and requires forward iterator or better");
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ldionne wrote:

Let's remove this. If we wanted to enforce iterator requirements strictly, we'd do something like `_LIBCPP_REQUIRE_CPP17_FORWARD_ITERATOR` but we'd do it in the user-facing function (`std::set_intersection` itself).

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