[libcxx] Speeding up partition_point/lower_bound/upper_bound

This is a re-application of r345525, which had been reverted by fear of
a regression.

Reviewed as https://reviews.llvm.org/D53994.
Thanks to Denis Yaroshevskiy for the patch.

git-svn-id: https://llvm.org/svn/llvm-project/libcxx/trunk@349358 91177308-0d34-0410-b5e6-96231b3b80d8

test/libcxx/algorithms/half_positive.pass.cpp

@@ -0,0 +1,56 @@
+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// __half_positive divides an integer number by 2 as unsigned number for known types.
+// It can be an important optimization for lower bound, for example.
+
+#include <algorithm>
+#include <cassert>
+#include <limits>
+#include <type_traits>
+
+#include "test_macros.h"
+#include "user_defined_integral.hpp"
+
+namespace {
+
+template <class IntType, class UnderlyingType = IntType>
+TEST_CONSTEXPR bool test(IntType max_v = IntType(std::numeric_limits<UnderlyingType>::max())) {
+    return std::__half_positive(max_v) == max_v / 2;
+}
+
+}  // namespace
+
+int main()
+{
+    {
+        assert(test<char>());
+        assert(test<int>());
+        assert(test<long>());
+        assert((test<UserDefinedIntegral<int>, int>()));
+        assert(test<size_t>());
+#if !defined(_LIBCPP_HAS_NO_INT128)
+        assert(test<__int128_t>());
+#endif  // !defined(_LIBCPP_HAS_NO_INT128)
+    }
+
+#if TEST_STD_VER >= 11
+    {
+        static_assert(test<char>(), "");
+        static_assert(test<int>(), "");
+        static_assert(test<long>(), "");
+        static_assert(test<size_t>(), "");
+#if !defined(_LIBCPP_HAS_NO_INT128)
+        static_assert(test<__int128_t>(), "");
+#endif  // !defined(_LIBCPP_HAS_NO_INT128)
+    }
+#endif // TEST_STD_VER >= 11
+}