diff --git a/flang/include/flang/Runtime/float128.h b/flang/include/flang/Common/float128.h
rename from flang/include/flang/Runtime/float128.h
rename to flang/include/flang/Common/float128.h
--- a/flang/include/flang/Runtime/float128.h
+++ b/flang/include/flang/Common/float128.h
@@ -1,4 +1,4 @@
-/*===-- flang/Runtime/float128.h ----------------------------------*- C -*-===
+/*===-- flang/Common/float128.h ----------------------------------*- C -*-===
  *
  * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
  * See https://llvm.org/LICENSE.txt for license information.
@@ -17,8 +17,8 @@
  * long double and __float128; prefer long double by testing for it first.
  */
 
-#ifndef FORTRAN_RUNTIME_FLOAT128_H_
-#define FORTRAN_RUNTIME_FLOAT128_H_
+#ifndef FORTRAN_COMMON_FLOAT128_H_
+#define FORTRAN_COMMON_FLOAT128_H_
 
 #ifdef __cplusplus
 /*
@@ -49,4 +49,4 @@
 #endif /* (defined(__FLOAT128__) || defined(__SIZEOF_FLOAT128__)) && \
           !defined(_LIBCPP_VERSION)  && !defined(__CUDA_ARCH__) */
 
-#endif /* FORTRAN_RUNTIME_FLOAT128_H_ */
+#endif /* FORTRAN_COMMON_FLOAT128_H_ */
diff --git a/flang/include/flang/Runtime/cpp-type.h b/flang/include/flang/Runtime/cpp-type.h
--- a/flang/include/flang/Runtime/cpp-type.h
+++ b/flang/include/flang/Runtime/cpp-type.h
@@ -12,8 +12,8 @@
 #define FORTRAN_RUNTIME_CPP_TYPE_H_
 
 #include "flang/Common/Fortran.h"
+#include "flang/Common/float128.h"
 #include "flang/Common/uint128.h"
-#include "flang/Runtime/float128.h"
 #include <cfloat>
 #include <complex>
 #include <cstdint>
diff --git a/flang/include/flang/Runtime/numeric.h b/flang/include/flang/Runtime/numeric.h
--- a/flang/include/flang/Runtime/numeric.h
+++ b/flang/include/flang/Runtime/numeric.h
@@ -12,6 +12,7 @@
 #ifndef FORTRAN_RUNTIME_NUMERIC_H_
 #define FORTRAN_RUNTIME_NUMERIC_H_
 
+#include "flang/Common/float128.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/entry-names.h"
 
diff --git a/flang/include/flang/Runtime/reduction.h b/flang/include/flang/Runtime/reduction.h
--- a/flang/include/flang/Runtime/reduction.h
+++ b/flang/include/flang/Runtime/reduction.h
@@ -11,10 +11,10 @@
 #ifndef FORTRAN_RUNTIME_REDUCTION_H_
 #define FORTRAN_RUNTIME_REDUCTION_H_
 
+#include "flang/Common/float128.h"
 #include "flang/Common/uint128.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/entry-names.h"
-#include "flang/Runtime/float128.h"
 #include <cfloat>
 #include <cinttypes>
 #include <complex>
diff --git a/flang/include/flang/Runtime/transformational.h b/flang/include/flang/Runtime/transformational.h
--- a/flang/include/flang/Runtime/transformational.h
+++ b/flang/include/flang/Runtime/transformational.h
@@ -17,9 +17,9 @@
 #ifndef FORTRAN_RUNTIME_TRANSFORMATIONAL_H_
 #define FORTRAN_RUNTIME_TRANSFORMATIONAL_H_
 
+#include "flang/Common/float128.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/entry-names.h"
-#include "flang/Runtime/float128.h"
 #include <cinttypes>
 
 namespace Fortran::runtime {
diff --git a/flang/lib/Evaluate/CMakeLists.txt b/flang/lib/Evaluate/CMakeLists.txt
--- a/flang/lib/Evaluate/CMakeLists.txt
+++ b/flang/lib/Evaluate/CMakeLists.txt
@@ -19,6 +19,12 @@
   endif()
 endif()
 
+check_include_file(quadmath.h FOUND_QUADMATH_HEADER)
+check_library_exists(quadmath sinq "" FOUND_QUADMATH_LIB)
+if(FOUND_QUADMATH_HEADER AND FOUND_QUADMATH_LIB)
+  add_compile_definitions(HAS_QUADMATHLIB)
+endif()
+
 add_flang_library(FortranEvaluate
   call.cpp
   characteristics.cpp
diff --git a/flang/lib/Evaluate/host.h b/flang/lib/Evaluate/host.h
--- a/flang/lib/Evaluate/host.h
+++ b/flang/lib/Evaluate/host.h
@@ -17,6 +17,10 @@
 // hardware type maps to Fortran intrinsic type T. Then HostType<T> can be used
 // to safely refer to this hardware type.
 
+#if HAS_QUADMATHLIB
+#include "quadmath.h"
+#include "flang/Common/float128.h"
+#endif
 #include "flang/Evaluate/type.h"
 #include <cfenv>
 #include <complex>
@@ -156,15 +160,20 @@
       long double, UnsupportedType>;
 };
 
-template <>
-struct HostTypeHelper<
-    Type<TypeCategory::Real, common::RealKindForPrecision(113)>> {
+#if HAS_QUADMATHLIB
+template <> struct HostTypeHelper<Type<TypeCategory::Real, 16>> {
+  // IEEE 754 128bits
+  using Type = __float128;
+};
+#else
+template <> struct HostTypeHelper<Type<TypeCategory::Real, 16>> {
   // IEEE 754 128bits
   using Type = std::conditional_t<sizeof(long double) == 16 &&
           std::numeric_limits<long double>::digits == 113 &&
           std::numeric_limits<long double>::max_exponent == 16384,
       long double, UnsupportedType>;
 };
+#endif
 
 template <int KIND> struct HostTypeHelper<Type<TypeCategory::Complex, KIND>> {
   using RealT = Fortran::evaluate::Type<TypeCategory::Real, KIND>;
@@ -172,6 +181,13 @@
       std::complex<HostType<RealT>>, UnsupportedType>;
 };
 
+#if HAS_QUADMATHLIB
+template <> struct HostTypeHelper<Type<TypeCategory::Complex, 16>> {
+  using RealT = Fortran::evaluate::Type<TypeCategory::Real, 16>;
+  using Type = __complex128;
+};
+#endif
+
 template <int KIND> struct HostTypeHelper<Type<TypeCategory::Logical, KIND>> {
   using Type = std::conditional_t<KIND <= 8, std::uint8_t, UnsupportedType>;
 };
diff --git a/flang/lib/Evaluate/intrinsics-library.cpp b/flang/lib/Evaluate/intrinsics-library.cpp
--- a/flang/lib/Evaluate/intrinsics-library.cpp
+++ b/flang/lib/Evaluate/intrinsics-library.cpp
@@ -20,6 +20,10 @@
 #include <cmath>
 #include <complex>
 #include <functional>
+#if HAS_QUADMATHLIB
+#include "quadmath.h"
+#include "flang/Common/float128.h"
+#endif
 #include <type_traits>
 
 namespace Fortran::evaluate {
@@ -313,6 +317,62 @@
 };
 #endif
 
+#if HAS_QUADMATHLIB
+template <> struct HostRuntimeLibrary<__float128, LibraryVersion::Libm> {
+  using F = FuncPointer<__float128, __float128>;
+  using F2 = FuncPointer<__float128, __float128, __float128>;
+  static constexpr HostRuntimeFunction table[]{
+      FolderFactory<F, F{::acosq}>::Create("acos"),
+      FolderFactory<F, F{::acoshq}>::Create("acosh"),
+      FolderFactory<F, F{::asinq}>::Create("asin"),
+      FolderFactory<F, F{::asinhq}>::Create("asinh"),
+      FolderFactory<F, F{::atanq}>::Create("atan"),
+      FolderFactory<F2, F2{::atan2q}>::Create("atan2"),
+      FolderFactory<F, F{::atanhq}>::Create("atanh"),
+      FolderFactory<F, F{::cosq}>::Create("cos"),
+      FolderFactory<F, F{::coshq}>::Create("cosh"),
+      FolderFactory<F, F{::erfq}>::Create("erf"),
+      FolderFactory<F, F{::erfcq}>::Create("erfc"),
+      FolderFactory<F, F{::expq}>::Create("exp"),
+      FolderFactory<F, F{::tgammaq}>::Create("gamma"),
+      FolderFactory<F, F{::logq}>::Create("log"),
+      FolderFactory<F, F{::log10q}>::Create("log10"),
+      FolderFactory<F, F{::lgammaq}>::Create("log_gamma"),
+      FolderFactory<F2, F2{::powq}>::Create("pow"),
+      FolderFactory<F, F{::sinq}>::Create("sin"),
+      FolderFactory<F, F{::sinhq}>::Create("sinh"),
+      FolderFactory<F, F{::tanq}>::Create("tan"),
+      FolderFactory<F, F{::tanhq}>::Create("tanh"),
+  };
+  static constexpr HostRuntimeMap map{table};
+  static_assert(map.Verify(), "map must be sorted");
+};
+template <> struct HostRuntimeLibrary<__complex128, LibraryVersion::Libm> {
+  using F = FuncPointer<__complex128, __complex128>;
+  using F2 = FuncPointer<__complex128, __complex128, __complex128>;
+  static constexpr HostRuntimeFunction table[]{
+      FolderFactory<F, F{::cacosq}>::Create("acos"),
+      FolderFactory<F, F{::cacoshq}>::Create("acosh"),
+      FolderFactory<F, F{::casinq}>::Create("asin"),
+      FolderFactory<F, F{::casinhq}>::Create("asinh"),
+      FolderFactory<F, F{::catanq}>::Create("atan"),
+      FolderFactory<F, F{::catanhq}>::Create("atanh"),
+      FolderFactory<F, F{::ccosq}>::Create("cos"),
+      FolderFactory<F, F{::ccoshq}>::Create("cosh"),
+      FolderFactory<F, F{::cexpq}>::Create("exp"),
+      FolderFactory<F, F{::clogq}>::Create("log"),
+      FolderFactory<F2, F2{::cpowq}>::Create("pow"),
+      FolderFactory<F, F{::csinq}>::Create("sin"),
+      FolderFactory<F, F{::csinhq}>::Create("sinh"),
+      FolderFactory<F, F{::csqrtq}>::Create("sqrt"),
+      FolderFactory<F, F{::ctanq}>::Create("tan"),
+      FolderFactory<F, F{::ctanhq}>::Create("tanh"),
+  };
+  static constexpr HostRuntimeMap map{table};
+  static_assert(map.Verify(), "map must be sorted");
+};
+#endif
+
 template <> struct HostRuntimeLibrary<double, LibraryVersion::LibmExtensions> {
   using F = FuncPointer<double, double>;
   using FN = FuncPointer<double, int, double>;
@@ -345,7 +405,7 @@
   static_assert(map.Verify(), "map must be sorted");
 };
 #endif // LDBL_MANT_DIG == 80 || LDBL_MANT_DIG == 113
-#endif
+#endif //_POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE >= 600
 
 /// Define pgmath description
 #if LINK_WITH_LIBPGMATH
@@ -455,6 +515,12 @@
             GetHostRuntimeMapHelper<long double, version>(resultType)}) {
       return map;
     }
+#if HAS_QUADMATHLIB
+    if (const auto *map{
+            GetHostRuntimeMapHelper<__float128, version>(resultType)}) {
+      return map;
+    }
+#endif
   }
   if (resultType.category() == TypeCategory::Complex) {
     if (const auto *map{GetHostRuntimeMapHelper<std::complex<float>, version>(
@@ -470,6 +536,12 @@
                 resultType)}) {
       return map;
     }
+#if HAS_QUADMATHLIB
+    if (const auto *map{
+            GetHostRuntimeMapHelper<__complex128, version>(resultType)}) {
+      return map;
+    }
+#endif
   }
   return nullptr;
 }
diff --git a/flang/lib/Frontend/CMakeLists.txt b/flang/lib/Frontend/CMakeLists.txt
--- a/flang/lib/Frontend/CMakeLists.txt
+++ b/flang/lib/Frontend/CMakeLists.txt
@@ -1,6 +1,12 @@
 get_property(dialect_libs GLOBAL PROPERTY MLIR_DIALECT_LIBS)
 get_property(extension_libs GLOBAL PROPERTY MLIR_EXTENSION_LIBS)
 
+check_include_file(quadmath.h FOUND_QUADMATH_HEADER)
+check_library_exists(quadmath sinq "" FOUND_QUADMATH_LIB)
+if(FOUND_QUADMATH_HEADER AND FOUND_QUADMATH_LIB)
+  set(QUADMATHLIB quadmath)
+endif()
+
 add_flang_library(flangFrontend
   CompilerInstance.cpp
   CompilerInvocation.cpp
@@ -42,6 +48,7 @@
   MLIRTargetLLVMIRImport
   ${dialect_libs}
   ${extension_libs}
+  ${QUADMATHLIB}
 
   LINK_COMPONENTS
   Passes
diff --git a/flang/runtime/dot-product.cpp b/flang/runtime/dot-product.cpp
--- a/flang/runtime/dot-product.cpp
+++ b/flang/runtime/dot-product.cpp
@@ -9,6 +9,7 @@
 #include "float.h"
 #include "terminator.h"
 #include "tools.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/descriptor.h"
 #include "flang/Runtime/reduction.h"
diff --git a/flang/runtime/extrema.cpp b/flang/runtime/extrema.cpp
--- a/flang/runtime/extrema.cpp
+++ b/flang/runtime/extrema.cpp
@@ -11,8 +11,8 @@
 // NORM2 using common infrastructure.
 
 #include "reduction-templates.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/character.h"
-#include "flang/Runtime/float128.h"
 #include "flang/Runtime/reduction.h"
 #include <algorithm>
 #include <cfloat>
diff --git a/flang/runtime/numeric.cpp b/flang/runtime/numeric.cpp
--- a/flang/runtime/numeric.cpp
+++ b/flang/runtime/numeric.cpp
@@ -8,7 +8,7 @@
 
 #include "flang/Runtime/numeric.h"
 #include "terminator.h"
-#include "flang/Runtime/float128.h"
+#include "flang/Common/float128.h"
 #include <cfloat>
 #include <climits>
 #include <cmath>
diff --git a/flang/runtime/product.cpp b/flang/runtime/product.cpp
--- a/flang/runtime/product.cpp
+++ b/flang/runtime/product.cpp
@@ -9,7 +9,7 @@
 // Implements PRODUCT for all required operand types and shapes.
 
 #include "reduction-templates.h"
-#include "flang/Runtime/float128.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/reduction.h"
 #include <cfloat>
 #include <cinttypes>
diff --git a/flang/runtime/random.cpp b/flang/runtime/random.cpp
--- a/flang/runtime/random.cpp
+++ b/flang/runtime/random.cpp
@@ -12,11 +12,11 @@
 #include "flang/Runtime/random.h"
 #include "lock.h"
 #include "terminator.h"
+#include "flang/Common/float128.h"
 #include "flang/Common/leading-zero-bit-count.h"
 #include "flang/Common/uint128.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/descriptor.h"
-#include "flang/Runtime/float128.h"
 #include <algorithm>
 #include <cmath>
 #include <cstdint>
diff --git a/flang/runtime/sum.cpp b/flang/runtime/sum.cpp
--- a/flang/runtime/sum.cpp
+++ b/flang/runtime/sum.cpp
@@ -13,7 +13,7 @@
 // (basically the same as manual "double-double").
 
 #include "reduction-templates.h"
-#include "flang/Runtime/float128.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/reduction.h"
 #include <cfloat>
 #include <cinttypes>
diff --git a/flang/runtime/transformational.cpp b/flang/runtime/transformational.cpp
--- a/flang/runtime/transformational.cpp
+++ b/flang/runtime/transformational.cpp
@@ -20,6 +20,7 @@
 #include "copy.h"
 #include "terminator.h"
 #include "tools.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/descriptor.h"
 
 namespace Fortran::runtime {
diff --git a/flang/tools/bbc/CMakeLists.txt b/flang/tools/bbc/CMakeLists.txt
--- a/flang/tools/bbc/CMakeLists.txt
+++ b/flang/tools/bbc/CMakeLists.txt
@@ -11,6 +11,13 @@
 llvm_update_compile_flags(bbc)
 get_property(dialect_libs GLOBAL PROPERTY MLIR_DIALECT_LIBS)
 get_property(extension_libs GLOBAL PROPERTY MLIR_EXTENSION_LIBS)
+
+check_include_file(quadmath.h FOUND_QUADMATH_HEADER)
+check_library_exists(quadmath sinq "" FOUND_QUADMATH_LIB)
+if(FOUND_QUADMATH_HEADER AND FOUND_QUADMATH_LIB)
+  set(QUADMATHLIB quadmath)
+endif()
+
 target_link_libraries(bbc PRIVATE
 FIRDialect
 FIRDialectSupport
@@ -28,4 +35,5 @@
 FortranEvaluate
 FortranSemantics
 FortranLower
+${QUADMATHLIB}
 )
diff --git a/flang/unittests/Evaluate/CMakeLists.txt b/flang/unittests/Evaluate/CMakeLists.txt
--- a/flang/unittests/Evaluate/CMakeLists.txt
+++ b/flang/unittests/Evaluate/CMakeLists.txt
@@ -8,8 +8,15 @@
 else()
   llvm_map_components_to_libnames(llvm_libs Support)
 endif()
+
+check_include_file(quadmath.h FOUND_QUADMATH_HEADER)
+check_library_exists(quadmath sinq "" FOUND_QUADMATH_LIB)
+if(FOUND_QUADMATH_HEADER AND FOUND_QUADMATH_LIB)
+  set(QUADMATHLIB quadmath)
+endif()
+
 target_link_libraries(FortranEvaluateTesting
-    ${llvm_libs})
+  ${llvm_libs} ${QUADMATHLIB})
 
 add_flang_nongtest_unittest(leading-zero-bit-count
   FortranEvaluateTesting
diff --git a/flang/unittests/Runtime/Numeric.cpp b/flang/unittests/Runtime/Numeric.cpp
--- a/flang/unittests/Runtime/Numeric.cpp
+++ b/flang/unittests/Runtime/Numeric.cpp
@@ -8,6 +8,7 @@
 
 #include "flang/Runtime/numeric.h"
 #include "gtest/gtest.h"
+#include "flang/Common/float128.h"
 #include <cmath>
 #include <limits>
 
diff --git a/flang/unittests/Runtime/Reduction.cpp b/flang/unittests/Runtime/Reduction.cpp
--- a/flang/unittests/Runtime/Reduction.cpp
+++ b/flang/unittests/Runtime/Reduction.cpp
@@ -9,6 +9,7 @@
 #include "flang/Runtime/reduction.h"
 #include "gtest/gtest.h"
 #include "tools.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/allocatable.h"
 #include "flang/Runtime/cpp-type.h"
 #include "flang/Runtime/descriptor.h"
diff --git a/flang/unittests/Runtime/Transformational.cpp b/flang/unittests/Runtime/Transformational.cpp
--- a/flang/unittests/Runtime/Transformational.cpp
+++ b/flang/unittests/Runtime/Transformational.cpp
@@ -9,6 +9,7 @@
 #include "flang/Runtime/transformational.h"
 #include "gtest/gtest.h"
 #include "tools.h"
+#include "flang/Common/float128.h"
 #include "flang/Runtime/type-code.h"
 #include <vector>