This rewrites ranges::minmax and ranges::minmax_element so that it
performs at most 3*N/2 many comparisons, as required by the standard.
In passing, this also fixes PR100387 by avoiding a premature std::move
in ranges::minmax and in std::shift_right.

Tested on x86_64-pc-linux-gnu, does this look OK for trunk and perhaps
10/11?

libstdc++-v3/ChangeLog:

        PR libstdc++/100387
        * include/bits/ranges_algo.h (__minmax_fn::operator()): Rewrite
        to limit comparison complexity to 3*N/2.  Avoid premature std::move.
        (__minmax_element_fn::operator()): Likewise.
        (shift_right): Avoid premature std::move of __result.
        * testsuite/25_algorithms/minmax/constrained.cc (test04, test05):
        New tests.
        * testsuite/25_algorithms/minmax_element/constrained.cc (test02):
        Likewise.
---
 libstdc++-v3/include/bits/ranges_algo.h       | 87 ++++++++++++++-----
 .../25_algorithms/minmax/constrained.cc       | 31 +++++++
 .../minmax_element/constrained.cc             | 19 ++++
 3 files changed, 113 insertions(+), 24 deletions(-)

diff --git a/libstdc++-v3/include/bits/ranges_algo.h 
b/libstdc++-v3/include/bits/ranges_algo.h
index cda3042c11f..bbd29127e89 100644
--- a/libstdc++-v3/include/bits/ranges_algo.h
+++ b/libstdc++-v3/include/bits/ranges_algo.h
@@ -3291,18 +3291,39 @@ namespace ranges
        auto __first = ranges::begin(__r);
        auto __last = ranges::end(__r);
        __glibcxx_assert(__first != __last);
+       auto __comp_proj = __detail::__make_comp_proj(__comp, __proj);
        minmax_result<range_value_t<_Range>> __result = {*__first, *__first};
        while (++__first != __last)
          {
-           auto __tmp = *__first;
-           if (std::__invoke(__comp,
-                             std::__invoke(__proj, __tmp),
-                             std::__invoke(__proj, __result.min)))
-             __result.min = std::move(__tmp);
-           if (!(bool)std::__invoke(__comp,
-                                    std::__invoke(__proj, __tmp),
-                                    std::__invoke(__proj, __result.max)))
-             __result.max = std::move(__tmp);
+           // Process two elements at a time so that we perform at most
+           // 3*N/2 many comparisons in total (each of the N/2 iterations
+           // of this loop performs three comparisions).
+           auto __val1 = *__first;
+           if (++__first == __last)
+             {
+               // N is odd; in this final iteration, we perform a just one
+               // comparison, for a total of 3*(N-1)/2 + 1 < 3*N/2 comparisons.
+               if (__comp_proj(__val1, __result.min))
+                 __result.min = std::move(__val1);
+               else if (!__comp_proj(__val1, __result.max))
+                 __result.max = std::move(__val1);
+               break;
+             }
+           auto __val2 = *__first;
+           if (!__comp_proj(__val2, __val1))
+             {
+               if (__comp_proj(__val1, __result.min))
+                 __result.min = std::move(__val1);
+               if (!__comp_proj(__val2, __result.max))
+                 __result.max = std::move(__val2);
+             }
+           else
+             {
+               if (__comp_proj(__val2, __result.min))
+                 __result.min = std::move(__val2);
+               if (!__comp_proj(__val1, __result.max))
+                 __result.max = std::move(__val1);
+             }
          }
        return __result;
       }
@@ -3408,21 +3429,40 @@ namespace ranges
       operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
       {
-       if (__first == __last)
-         return {__first, __first};
-
+       auto __comp_proj = __detail::__make_comp_proj(__comp, __proj);
        minmax_element_result<_Iter> __result = {__first, __first};
-       auto __i = __first;
-       while (++__i != __last)
+       if (__first == __last)
+         return __result;
+       while (++__first != __last)
          {
-           if (std::__invoke(__comp,
-                             std::__invoke(__proj, *__i),
-                             std::__invoke(__proj, *__result.min)))
-             __result.min = __i;
-           if (!(bool)std::__invoke(__comp,
-                                    std::__invoke(__proj, *__i),
-                                    std::__invoke(__proj, *__result.max)))
-             __result.max = __i;
+           // Process two elements at a time so that we perform at most
+           // 3*N/2 many comparisons in total (each of the N/2 iterations
+           // of this loop performs three comparisions).
+           auto __prev = __first;
+           if (++__first == __last)
+             {
+               // N is odd; in this final iteration, we perform a just one
+               // comparison, for a total of 3*(N-1)/2 + 1 < 3*N/2 comparisons.
+               if (__comp_proj(*__prev, *__result.min))
+                 __result.min = __prev;
+               else if (!__comp_proj(*__prev, *__result.max))
+                 __result.max = __prev;
+               break;
+             }
+           if (!__comp_proj(*__first, *__prev))
+             {
+               if (__comp_proj(*__prev, *__result.min))
+                 __result.min = __prev;
+               if (!__comp_proj(*__first, *__result.max))
+                 __result.max = __first;
+             }
+           else
+             {
+               if (__comp_proj(*__first, *__result.min))
+                 __result.min = __first;
+               if (!__comp_proj(*__prev, *__result.max))
+                 __result.max = __prev;
+             }
          }
        return __result;
       }
@@ -3749,8 +3789,7 @@ namespace ranges
                  // i.e. we are shifting out at least half of the range.  In
                  // this case we can safely perform the shift with a single
                  // move.
-                 std::move(std::move(__first), std::move(__dest_head),
-                           std::move(__result));
+                 std::move(std::move(__first), std::move(__dest_head), 
__result);
                  return __result;
                }
              ++__dest_head;
diff --git a/libstdc++-v3/testsuite/25_algorithms/minmax/constrained.cc 
b/libstdc++-v3/testsuite/25_algorithms/minmax/constrained.cc
index 786922414b5..2373c15a9d2 100644
--- a/libstdc++-v3/testsuite/25_algorithms/minmax/constrained.cc
+++ b/libstdc++-v3/testsuite/25_algorithms/minmax/constrained.cc
@@ -19,6 +19,8 @@
 // { dg-do run { target c++2a } }
 
 #include <algorithm>
+#include <string>
+#include <vector>
 #include <testsuite_hooks.h>
 #include <testsuite_iterators.h>
 
@@ -89,10 +91,39 @@ test03()
          == res_t(1,4) );
 }
 
+void
+test04()
+{
+  // Verify we perform most 3*N/2 applications of the comparison predicate.
+  static int counter;
+  struct counted_less
+  { bool operator()(int a, int b) { ++counter; return a < b; } };
+
+  ranges::minmax({1,2,3,4,5,6,7,8,9,10}, counted_less{});
+  VERIFY( counter <= 15 );
+
+  counter = 0;
+  ranges::minmax({10,9,8,7,6,5,4,3,2,1}, counted_less{});
+  VERIFY( counter <= 15 );
+}
+
+void
+test05()
+{
+  // PR libstdc++/100387
+  std::vector<std::string> v{"b", "a"};
+  auto [min, max] = ranges::minmax(v, [](const auto& a, const auto& b) {
+    return a.size() == b.size() ? a.front() < b.front() : a.size() > b.size();
+  });
+  VERIFY( min == "a" && max == "b" );
+}
+
 int
 main()
 {
   test01();
   test02();
   test03();
+  test04();
+  test05();
 }
diff --git a/libstdc++-v3/testsuite/25_algorithms/minmax_element/constrained.cc 
b/libstdc++-v3/testsuite/25_algorithms/minmax_element/constrained.cc
index 3b11c0dd96c..89044181530 100644
--- a/libstdc++-v3/testsuite/25_algorithms/minmax_element/constrained.cc
+++ b/libstdc++-v3/testsuite/25_algorithms/minmax_element/constrained.cc
@@ -61,8 +61,27 @@ test01()
   static_assert(ranges::minmax_element(y, y+3, {}, &X::i).max->j == 3);
 }
 
+void
+test02()
+{
+  // Verify we perform most 3*N/2 applications of the comparison predicate.
+  static int counter;
+  struct counted_less
+  { bool operator()(int a, int b) { ++counter; return a < b; } };
+
+  int x[] = {1,2,3,4,5,6,7,8,9,10};
+  ranges::minmax(x, counted_less{});
+  VERIFY( counter <= 15 );
+
+  ranges::reverse(x);
+  counter = 0;
+  ranges::minmax(x, counted_less{});
+  VERIFY( counter <= 15 );
+}
+
 int
 main()
 {
   test01();
+  test02();
 }
-- 
2.31.1.442.g7e39198978

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