Index: flang/runtime/CMakeLists.txt
===================================================================
--- flang/runtime/CMakeLists.txt
+++ flang/runtime/CMakeLists.txt
@@ -62,6 +62,38 @@
   message(FATAL_ERROR "None of strerror, strerror_r, strerror_s found.")
 endif()
 
+include(CheckCXXCompilerFlag)
+check_cxx_compiler_flag(-fext-numeric-literals SUPPORTS_FEXT_NUMERIC_LITERALS)
+check_cxx_compiler_flag(-Wno-error=pedantic SUPPORTS_W_NO_ERROR_PEDANTIC)
+if (SUPPORTS_FEXT_NUMERIC_LITERALS AND SUPPORTS_W_NO_ERROR_PEDANTIC)
+  set(CMAKE_REQUIRED_FLAGS
+    "${CMAKE_REQUIRED_FLAGS} -Wno-error=pedantic -fext-numeric-literals")
+  check_cxx_source_compiles(
+    "#include <quadmath.h>
+     int main() {
+       __float128 x = FLT128_MAX;
+       return 0;
+     }
+    "
+    HAVE_QUADMATH_H)
+
+  # Even with -fext-numeric-literals, GCC -Wpedantic warns about
+  # non-standard suffix on floating constant expanded from FLT128_MAX.
+  # Neither __extension__ nor 'GCC diagnostic ignored "-Wpedantic"' work,
+  # so usage of FLT128_MAX will cause warnings with -Wpedantic.
+  # -Werror will turn this warning into an error, so we have to
+  # override it with -Wno-error=pedantic both here and for the files
+  # that use FLT128_MAX (e.g. extrema.cpp).
+  # Also see: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87274
+  if (HAVE_QUADMATH_H)
+    set(files_with_quadmath extrema.cpp)
+    set_source_files_properties(${files_with_quadmath}
+      PROPERTIES COMPILE_OPTIONS "-Wno-error=pedantic;-fext-numeric-literals")
+    set_source_files_properties(${files_with_quadmath}
+      PROPERTIES COMPILE_DEFINITIONS "HAVE_QUADMATH_H")
+  endif()
+endif()
+
 configure_file(config.h.cmake config.h)
 # include_directories is used here instead of target_include_directories
 # because add_flang_library creates multiple objects (STATIC/SHARED, OBJECT)
Index: flang/runtime/extrema.cpp
===================================================================
--- flang/runtime/extrema.cpp
+++ flang/runtime/extrema.cpp
@@ -19,6 +19,9 @@
 #include <cinttypes>
 #include <cmath>
 #include <optional>
+#if HAVE_QUADMATH_H
+#include <quadmath.h>
+#endif // HAVE_QUADMATH_H
 
 namespace Fortran::runtime {
 
@@ -301,7 +304,8 @@
 
 // MAXVAL and MINVAL
 
-template <TypeCategory CAT, int KIND, bool IS_MAXVAL> struct MaxOrMinIdentity {
+template <TypeCategory CAT, int KIND, bool IS_MAXVAL, typename Enable = void>
+struct MaxOrMinIdentity {
   using Type = CppTypeFor<CAT, KIND>;
   static constexpr Type Value() {
     return IS_MAXVAL ? std::numeric_limits<Type>::lowest()
@@ -318,6 +322,23 @@
   }
 };
 
+#if HAVE_QUADMATH_H
+// std::numeric_limits<> may not support __float128,
+// so use macros defined in quadmath.h (if available).
+//
+// Note that HAVE_QUADMATH_H implies that __float128 is available,
+// but it does not necessarily mean that __float128 is used for REAL(16).
+// This specialization must engage only when
+// CppTypeFor<TypeCategory::Real, 16> is __float128.
+template <bool IS_MAXVAL>
+struct MaxOrMinIdentity<TypeCategory::Real, 16, IS_MAXVAL,
+    typename std::enable_if_t<
+        std::is_same_v<CppTypeFor<TypeCategory::Real, 16>, __float128>>> {
+  using Type = CppTypeFor<TypeCategory::Real, 16>;
+  static constexpr Type Value() { return IS_MAXVAL ? -FLT128_MAX : FLT128_MAX; }
+};
+#endif // HAVE_QUADMATH_H
+
 template <TypeCategory CAT, int KIND, bool IS_MAXVAL>
 class NumericExtremumAccumulator {
 public:
Index: flang/unittests/Runtime/Reduction.cpp
===================================================================
--- flang/unittests/Runtime/Reduction.cpp
+++ flang/unittests/Runtime/Reduction.cpp
@@ -616,3 +616,20 @@
   EXPECT_FALSE(RTNAME(DotProductLogical)(
       *logicalVector2, *logicalVector1, __FILE__, __LINE__));
 }
+
+#if LDBL_MANT_DIG == 113 || HAS_FLOAT128
+TEST(Reductions, ExtremaReal16) {
+  // The identity value for Min/Maxval for REAL(16) was mistakenly
+  // set to 0.0.
+  using ElemType = CppTypeFor<TypeCategory::Real, 16>;
+  std::vector<int> shape{3};
+  //   1.0  2.0  3.0
+  std::vector<ElemType> rawMinData{1.0, 2.0, 3.0};
+  auto minArray{MakeArray<TypeCategory::Real, 16>(shape, rawMinData)};
+  EXPECT_EQ(RTNAME(MinvalReal16)(*minArray, __FILE__, __LINE__), 1.0);
+  //   -1.0  -2.0  -3.0
+  std::vector<ElemType> rawMaxData{-1.0, -2.0, -3.0};
+  auto maxArray{MakeArray<TypeCategory::Real, 16>(shape, rawMaxData)};
+  EXPECT_EQ(RTNAME(MaxvalReal16)(*maxArray, __FILE__, __LINE__), -1.0);
+}
+#endif // LDBL_MANT_DIG == 113 || HAS_FLOAT128