Tested on x86_64-pc-linux-gnu, does this look OK for trunk/backports?
Also available in PR form at https://forge.sourceware.org/gcc/gcc-TEST/pulls/8

-- >8 --

Views are required to have a amortized O(1) begin(), but our drop_view's
const begin overload is O(n) for non-common ranges.  This patch
reimplements it so that it's O(1) even in that case.  See also LWG 4009.

        PR libstdc++/112641

libstdc++-v3/ChangeLog:

        * include/std/ranges (drop_view::begin const): Reimplement
        so that it's O(1) instead of O(n) even in the non-common
        range case.
        * testsuite/std/ranges/adaptors/drop.cc (test10): New test.
---
 libstdc++-v3/include/std/ranges                    |  4 ++--
 libstdc++-v3/testsuite/std/ranges/adaptors/drop.cc | 12 ++++++++++++
 2 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/libstdc++-v3/include/std/ranges b/libstdc++-v3/include/std/ranges
index cebe10683f9..743429dbcea 100644
--- a/libstdc++-v3/include/std/ranges
+++ b/libstdc++-v3/include/std/ranges
@@ -2664,8 +2664,8 @@ namespace views::__adaptor
       begin() const
        requires random_access_range<const _Vp> && sized_range<const _Vp>
       {
-       return ranges::next(ranges::begin(_M_base), _M_count,
-                           ranges::end(_M_base));
+       return ranges::begin(_M_base) + ranges::min(ranges::distance(_M_base),
+                                                   _M_count);
       }
 
       constexpr auto
diff --git a/libstdc++-v3/testsuite/std/ranges/adaptors/drop.cc 
b/libstdc++-v3/testsuite/std/ranges/adaptors/drop.cc
index c9987c61e3c..0bd5bebb785 100644
--- a/libstdc++-v3/testsuite/std/ranges/adaptors/drop.cc
+++ b/libstdc++-v3/testsuite/std/ranges/adaptors/drop.cc
@@ -274,6 +274,17 @@ test09()
   static_assert(!requires { views::all | drop; });
 }
 
+constexpr bool
+test10()
+{
+  // PR libstdc++/112641 - drop_view::begin const may have O(n) complexity
+  const auto s = ranges::subrange(views::iota(size_t(1)), size_t(-1));
+  const auto r = ranges::drop_view(s, s.size() - 1);
+  const auto b = r.begin(); // time out
+  VERIFY( *b == size_t(-1) );
+  return true;
+}
+
 int
 main()
 {
@@ -286,4 +297,5 @@ main()
   test07();
   test08();
   test09();
+  static_assert(test10());
 }
-- 
2.47.0.118.gfd3785337b

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