diff --git a/flang/include/flang/Common/Fortran-features.h b/flang/include/flang/Common/Fortran-features.h
index 9549e8bfbbef0..96c4de74cd6a8 100644
--- a/flang/include/flang/Common/Fortran-features.h
+++ b/flang/include/flang/Common/Fortran-features.h
@@ -71,7 +71,7 @@ ENUM_CLASS(UsageWarning, Portability, PointerToUndefinable,
     ZeroDoStep, UnusedForallIndex, OpenMPUsage, DataLength, IgnoredDirective,
     HomonymousSpecific, HomonymousResult, IgnoredIntrinsicFunctionType,
     PreviousScalarUse, RedeclaredInaccessibleComponent, ImplicitShared,
-    IndexVarRedefinition, IncompatibleImplicitInterfaces, BadTypeForTarget,
+    IndexVarRedefinition, IncompatibleImplicitInterfaces,
     VectorSubscriptFinalization, UndefinedFunctionResult, UselessIomsg,
     MismatchingDummyProcedure, SubscriptedEmptyArray, UnsignedLiteralTruncation,
     CompatibleDeclarationsFromDistinctModules)
diff --git a/flang/lib/Common/Fortran-features.cpp b/flang/lib/Common/Fortran-features.cpp
index 3565275915a31..bbf16a4f7ac67 100644
--- a/flang/lib/Common/Fortran-features.cpp
+++ b/flang/lib/Common/Fortran-features.cpp
@@ -79,7 +79,6 @@ LanguageFeatureControl::LanguageFeatureControl() {
   warnUsage_.set(UsageWarning::ImplicitShared);
   warnUsage_.set(UsageWarning::IndexVarRedefinition);
   warnUsage_.set(UsageWarning::IncompatibleImplicitInterfaces);
-  warnUsage_.set(UsageWarning::BadTypeForTarget);
   warnUsage_.set(UsageWarning::VectorSubscriptFinalization);
   warnUsage_.set(UsageWarning::UndefinedFunctionResult);
   warnUsage_.set(UsageWarning::UselessIomsg);
diff --git a/flang/lib/Semantics/expression.cpp b/flang/lib/Semantics/expression.cpp
index 3ec6f385ceb86..22f5f633d3b39 100644
--- a/flang/lib/Semantics/expression.cpp
+++ b/flang/lib/Semantics/expression.cpp
@@ -4079,8 +4079,7 @@ bool ExpressionAnalyzer::CheckIntrinsicKind(
     return true;
   } else if (foldingContext_.targetCharacteristics().CanSupportType(
                  category, kind)) {
-    Warn(common::UsageWarning::BadTypeForTarget,
-        "%s(KIND=%jd) is not an enabled type for this target"_warn_en_US,
+    Say("%s(KIND=%jd) is not an enabled type for this target"_err_en_US,
         ToUpperCase(EnumToString(category)), kind);
     return true;
   } else {
@@ -4102,20 +4101,7 @@ bool ExpressionAnalyzer::CheckIntrinsicSize(
       return false;
     }
   }
-  if (foldingContext_.targetCharacteristics().IsTypeEnabled(
-          category, kind)) { // C712, C714, C715, C727
-    return true;
-  } else if (foldingContext_.targetCharacteristics().CanSupportType(
-                 category, kind)) {
-    Warn(common::UsageWarning::BadTypeForTarget,
-        "%s*%jd is not an enabled type for this target"_warn_en_US,
-        ToUpperCase(EnumToString(category)), size);
-    return true;
-  } else {
-    Say("%s*%jd is not a supported type"_err_en_US,
-        ToUpperCase(EnumToString(category)), size);
-    return false;
-  }
+  return CheckIntrinsicKind(category, kind);
 }
 
 bool ExpressionAnalyzer::AddImpliedDo(parser::CharBlock name, int kind) {
diff --git a/flang/test/Evaluate/rewrite-out_of_range.F90 b/flang/test/Evaluate/rewrite-out_of_range.F90
index b5df610ff2fbb..9196bba591e63 100644
--- a/flang/test/Evaluate/rewrite-out_of_range.F90
+++ b/flang/test/Evaluate/rewrite-out_of_range.F90
@@ -1,5 +1,7 @@
 ! Tests rewriting of OUT_OF_RANGE()
-! RUN: %flang_fc1 -fdebug-unparse -cpp %s 2>&1 | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{,CHECK-X86-64%}
+! REQUIRES: target=x86-64{{.*}}
+! REQUIRES: system-linux
+! RUN: %flang_fc1 -fdebug-unparse -cpp %s 2>&1 | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{%if system-linux %{,CHECK-X86-64%}%}
 
 logical round
 
diff --git a/flang/test/Lower/HLFIR/convert-variable.f90 b/flang/test/Lower/HLFIR/convert-variable.f90
index 7acb1be578b93..07b91d0f34a07 100644
--- a/flang/test/Lower/HLFIR/convert-variable.f90
+++ b/flang/test/Lower/HLFIR/convert-variable.f90
@@ -1,5 +1,5 @@
 ! Test lowering of variables to fir.declare
-! RUN: bbc -emit-hlfir %s -o - | FileCheck %s
+! RUN: bbc -emit-hlfir %s -o - | FileCheck %s --check-prefixes=CHECK,%if flang-supports-f128-math %{F128%} %else %{F64%}
 
 subroutine scalar_numeric(x)
   integer :: x
@@ -68,13 +68,16 @@ subroutine scalar_numeric_attributes(x)
 ! CHECK:  %[[VAL_1:.*]] = hlfir.declare %[[VAL_0]] dummy_scope %{{[0-9]+}} {fortran_attrs = #fir.var_attrs<intent_in, optional, target>, uniq_name = "_QFscalar_numeric_attributesEx"} : (!fir.ref<i32>, !fir.dscope) -> (!fir.ref<i32>, !fir.ref<i32>)
 
 subroutine scalar_numeric_attributes_2(x)
-  real(16), value :: x(100)
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
+  real(rk), value :: x(100)
 end subroutine
 ! CHECK-LABEL: func.func @_QPscalar_numeric_attributes_2(
-! CHECK-SAME:    %[[VAL_0:.*]]: !fir.ref<!fir.array<100xf128>>
+! F128-SAME:    %[[VAL_0:.*]]: !fir.ref<!fir.array<100xf128>>
+! F64-SAME:    %[[VAL_0:.*]]: !fir.ref<!fir.array<100xf64>>
 ! CHECK:  %[[VAL_1:.*]] = arith.constant 100 : index
 ! CHECK:  %[[VAL_2:.*]] = fir.shape %[[VAL_1]] : (index) -> !fir.shape<1>
-! CHECK:  %[[VAL_3:.*]] = hlfir.declare %[[VAL_0]](%[[VAL_2]]) dummy_scope %{{[0-9]+}} {fortran_attrs = #fir.var_attrs<value>, uniq_name = "_QFscalar_numeric_attributes_2Ex"} : (!fir.ref<!fir.array<100xf128>>, !fir.shape<1>, !fir.dscope) -> (!fir.ref<!fir.array<100xf128>>, !fir.ref<!fir.array<100xf128>>)
+! F128:  %[[VAL_3:.*]] = hlfir.declare %[[VAL_0]](%[[VAL_2]]) dummy_scope %{{[0-9]+}} {fortran_attrs = #fir.var_attrs<value>, uniq_name = "_QFscalar_numeric_attributes_2Ex"} : (!fir.ref<!fir.array<100xf128>>, !fir.shape<1>, !fir.dscope) -> (!fir.ref<!fir.array<100xf128>>, !fir.ref<!fir.array<100xf128>>)
+! F64:  %[[VAL_3:.*]] = hlfir.declare %[[VAL_0]](%[[VAL_2]]) dummy_scope %{{[0-9]+}} {fortran_attrs = #fir.var_attrs<value>, uniq_name = "_QFscalar_numeric_attributes_2Ex"} : (!fir.ref<!fir.array<100xf64>>, !fir.shape<1>, !fir.dscope) -> (!fir.ref<!fir.array<100xf64>>, !fir.ref<!fir.array<100xf64>>)
 
 subroutine scalar_numeric_attributes_3(x)
   real, intent(in) :: x
diff --git a/flang/test/Lower/Intrinsics/abs.f90 b/flang/test/Lower/Intrinsics/abs.f90
index e5e4b79e9f79e..7150cb2d352fd 100644
--- a/flang/test/Lower/Intrinsics/abs.f90
+++ b/flang/test/Lower/Intrinsics/abs.f90
@@ -1,7 +1,7 @@
-! RUN: bbc -emit-fir -hlfir=false %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
+! RUN: bbc -emit-fir -hlfir=false %s -o - | FileCheck %s --check-prefixes=CHECK,CMPLX,CMPLX-PRECISE,%if flang-supports-f128-math %{F128%} %else %{F64%}
 ! RUN: bbc -emit-fir -hlfir=false --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: bbc --force-mlir-complex -emit-fir -hlfir=false %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
-! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s --check-prefixes=CHECK,CMPLX,CMPLX-PRECISE,%if flang-supports-f128-math %{F128%} %else %{F64%}
 ! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir -mllvm --force-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 ! RUN: %flang_fc1 -fapprox-func -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-APPROX"
@@ -85,13 +85,18 @@ subroutine abs_testd(a, b)
 end subroutine
 
 ! CHECK-LABEL: func @_QPabs_testr16(
-! CHECK-SAME:  %[[VAL_0:.*]]: !fir.ref<f128>{{.*}}, %[[VAL_1:.*]]: !fir.ref<f128>{{.*}}) {
+! F128-SAME:  %[[VAL_0:.*]]: !fir.ref<f128>{{.*}}, %[[VAL_1:.*]]: !fir.ref<f128>{{.*}}) {
+! F64-SAME:  %[[VAL_0:.*]]: !fir.ref<f64>{{.*}}, %[[VAL_1:.*]]: !fir.ref<f64>{{.*}}) {
 subroutine abs_testr16(a, b)
-! CHECK: %[[VAL_2:.*]] = fir.load %[[VAL_0]] : !fir.ref<f128>
-! CHECK: %[[VAL_3:.*]] = math.absf %[[VAL_2]] {{.*}}: f128
-! CHECK: fir.store %[[VAL_3]] to %[[VAL_1]] : !fir.ref<f128>
+! F128: %[[VAL_2:.*]] = fir.load %[[VAL_0]] : !fir.ref<f128>
+! F64: %[[VAL_2:.*]] = fir.load %[[VAL_0]] : !fir.ref<f64>
+! F128: %[[VAL_3:.*]] = math.absf %[[VAL_2]] {{.*}}: f128
+! F64: %[[VAL_3:.*]] = math.absf %[[VAL_2]] {{.*}}: f64
+! F128: fir.store %[[VAL_3]] to %[[VAL_1]] : !fir.ref<f128>
+! F64: fir.store %[[VAL_3]] to %[[VAL_1]] : !fir.ref<f64>
 ! CHECK: return
-  real(kind=16) :: a, b
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
+  real(kind=rk) :: a, b
   b = abs(a)
 end subroutine
 
diff --git a/flang/test/Lower/Intrinsics/exponent.f90 b/flang/test/Lower/Intrinsics/exponent.f90
index 32a3bda24b0bb..f5f0603ee13c8 100644
--- a/flang/test/Lower/Intrinsics/exponent.f90
+++ b/flang/test/Lower/Intrinsics/exponent.f90
@@ -7,7 +7,6 @@ subroutine exponent_test(i1, i2, x4, x8)
     integer :: i1, i2, i3
     real(kind = 4) :: x4
     real(kind = 8) :: x8
-    real(kind = 16) :: x16
 
     i1 = exponent(x4)
   ! CHECK: %[[temp0:.*]] = fir.load %{{.*}} : !fir.ref<f32>
diff --git a/flang/test/Lower/Intrinsics/fma_real16.f90 b/flang/test/Lower/Intrinsics/fma_real16.f90
index 62cf2fbcefbf1..ecc32635be9dc 100644
--- a/flang/test/Lower/Intrinsics/fma_real16.f90
+++ b/flang/test/Lower/Intrinsics/fma_real16.f90
@@ -1,3 +1,4 @@
+! REQUIRES: flang-supports-f128-math
 ! RUN: bbc -emit-fir %s -o - | FileCheck %s
 ! RUN: bbc --math-runtime=precise -emit-fir %s -o - | FileCheck %s
 ! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s
diff --git a/flang/test/Lower/Intrinsics/ieee_class_queries.f90 b/flang/test/Lower/Intrinsics/ieee_class_queries.f90
index 0123d8163b984..aae8071b6a8b5 100644
--- a/flang/test/Lower/Intrinsics/ieee_class_queries.f90
+++ b/flang/test/Lower/Intrinsics/ieee_class_queries.f90
@@ -1,5 +1,6 @@
 ! REQUIRES: flang-supports-f128-math
-! RUN: bbc -emit-fir -o - %s | FileCheck %s
+! REQUIRES: x86_64-registered-target
+! RUN: bbc -target x86_64-unknown-linux-gnu -emit-fir -o - %s | FileCheck %s
 
   ! CHECK-LABEL: func @_QQmain
   use ieee_arithmetic, only: ieee_is_finite, ieee_is_nan, ieee_is_negative, &
diff --git a/flang/test/Lower/Intrinsics/modulo.f90 b/flang/test/Lower/Intrinsics/modulo.f90
index 781ef8296a2b7..37c4cd1a94ca2 100644
--- a/flang/test/Lower/Intrinsics/modulo.f90
+++ b/flang/test/Lower/Intrinsics/modulo.f90
@@ -1,5 +1,5 @@
 ! RUN: bbc -emit-fir -hlfir=false %s -o - | FileCheck %s -check-prefixes=HONORINF,ALL
-! RUN: flang -fc1 -menable-no-infs -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s -check-prefixes=CHECK,ALL
+! RUN: flang -fc1 -menable-no-infs -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s -check-prefixes=CHECK,ALL,%if flang-supports-f128-math %{F128%} %else %{F64%}
 
 ! ALL-LABEL: func @_QPmodulo_testr(
 ! ALL-SAME: %[[arg0:.*]]: !fir.ref<f64>{{.*}}, %[[arg1:.*]]: !fir.ref<f64>{{.*}}, %[[arg2:.*]]: !fir.ref<f64>{{.*}}) {
@@ -39,9 +39,12 @@ subroutine modulo_testi(r, a, p)
 end subroutine
 
 ! CHECK-LABEL: func @_QPmodulo_testr16(
-! CHECK-SAME: %[[arg0:.*]]: !fir.ref<f128>{{.*}}, %[[arg1:.*]]: !fir.ref<f128>{{.*}}, %[[arg2:.*]]: !fir.ref<f128>{{.*}}) {
+! F128-SAME: %[[arg0:.*]]: !fir.ref<f128>{{.*}}, %[[arg1:.*]]: !fir.ref<f128>{{.*}}, %[[arg2:.*]]: !fir.ref<f128>{{.*}}) {
+! F64-SAME: %[[arg0:.*]]: !fir.ref<f64>{{.*}}, %[[arg1:.*]]: !fir.ref<f64>{{.*}}, %[[arg2:.*]]: !fir.ref<f64>{{.*}}) {
 subroutine modulo_testr16(r, a, p)
-  real(16) :: r, a, p
-  ! CHECK: fir.call @_FortranAModuloReal16({{.*}}){{.*}}: (f128, f128, !fir.ref<i8>, i32) -> f128
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
+  real(rk) :: r, a, p
+  !F128: fir.call @_FortranAModuloReal16({{.*}}){{.*}}: (f128, f128, !fir.ref<i8>, i32) -> f128
+  !F64: arith.remf %0, %1 fastmath<ninf,contract> : f64
   r = modulo(a, p)
 end subroutine
diff --git a/flang/test/Lower/Intrinsics/powi_real16.f90 b/flang/test/Lower/Intrinsics/powi_real16.f90
index 9e7d0f828b5cd..dc19b32742c0b 100644
--- a/flang/test/Lower/Intrinsics/powi_real16.f90
+++ b/flang/test/Lower/Intrinsics/powi_real16.f90
@@ -1,3 +1,4 @@
+! REQUIRES: flang-supports-f128-math
 ! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefix=CHECK-FAST
 ! RUN: bbc --math-runtime=precise -emit-fir %s -o - | FileCheck %s --check-prefix=CHECK-PRECISE
 ! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefix=CHECK-FAST
diff --git a/flang/test/Lower/Intrinsics/random_number_real16.f90 b/flang/test/Lower/Intrinsics/random_number_real16.f90
index 060574d5b3b3f..1597d9bd5397f 100644
--- a/flang/test/Lower/Intrinsics/random_number_real16.f90
+++ b/flang/test/Lower/Intrinsics/random_number_real16.f90
@@ -1,3 +1,4 @@
+! REQUIRES: flang-supports-f128-math
 ! RUN: bbc -emit-fir %s -o - | FileCheck %s
 ! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s
 
diff --git a/flang/test/Lower/Intrinsics/rrspacing.f90 b/flang/test/Lower/Intrinsics/rrspacing.f90
index 7125f6bf319b8..5cfd7c7befdc4 100644
--- a/flang/test/Lower/Intrinsics/rrspacing.f90
+++ b/flang/test/Lower/Intrinsics/rrspacing.f90
@@ -1,3 +1,4 @@
+! REQUIRES: flang-supports-f128-math
 ! RUN: bbc -emit-fir -hlfir=false %s -o - | FileCheck %s
 ! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s
 
diff --git a/flang/test/Lower/Intrinsics/sign.f90 b/flang/test/Lower/Intrinsics/sign.f90
index 218080f0d49b6..965bda3d5b834 100644
--- a/flang/test/Lower/Intrinsics/sign.f90
+++ b/flang/test/Lower/Intrinsics/sign.f90
@@ -1,4 +1,4 @@
-! RUN: bbc %s -o - | FileCheck %s
+! RUN: bbc %s -o - | FileCheck %s --check-prefixes=CHECK,%if flang-supports-f128-math %{F128%} %else %{F64%}
 
 ! CHECK-LABEL: sign_testi
 subroutine sign_testi(a, b, c)
@@ -22,8 +22,10 @@ subroutine sign_testr(a, b, c)
 
 ! CHECK-LABEL: sign_testr2
 subroutine sign_testr2(a, b, c)
-  real(KIND=16) a, b, c
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
+  real(KIND=rk) a, b, c
   ! CHECK-NOT: fir.call @{{.*}}fabs
-  ! CHECK: math.copysign{{.*}} : f128
+  ! F128: math.copysign{{.*}} : f128
+  ! F64: math.copysign{{.*}} : f64
   c = sign(a, b)
 end subroutine
diff --git a/flang/test/Lower/OpenMP/parallel-firstprivate-clause-scalar.f90 b/flang/test/Lower/OpenMP/parallel-firstprivate-clause-scalar.f90
index c9ed7ebe8bf93..017b2a3f2edd2 100644
--- a/flang/test/Lower/OpenMP/parallel-firstprivate-clause-scalar.f90
+++ b/flang/test/Lower/OpenMP/parallel-firstprivate-clause-scalar.f90
@@ -1,5 +1,6 @@
 ! This test checks lowering of `FIRSTPRIVATE` clause for scalar types.
 
+! REQUIRES: x86_64-registered-target
 ! REQUIRES: shell
 ! RUN: bbc -fopenmp -emit-hlfir %s -o - \
 ! RUN: | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{,CHECK-KIND10%}%if flang-supports-f128-math %{,CHECK-KIND16%}
diff --git a/flang/test/Lower/assignment.f90 b/flang/test/Lower/assignment.f90
index dde5110bdfa9a..defeec5b7edfe 100644
--- a/flang/test/Lower/assignment.f90
+++ b/flang/test/Lower/assignment.f90
@@ -1,4 +1,4 @@
-! RUN: %flang_fc1 %s -o "-" -emit-fir -cpp -flang-deprecated-no-hlfir | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{,CHECK-X86-64%}
+! RUN: %flang_fc1 %s -o "-" -emit-fir -cpp -flang-deprecated-no-hlfir | FileCheck %s --check-prefixes=CHECK,%if flang-supports-f128-math %{F128%} %else %{F64%}%if target=x86_64-unknown-linux{{.*}} %{,CHECK-X86-64%}
 
 subroutine sub1(a)
   integer :: a
@@ -261,27 +261,29 @@ real function divf(a, b)
 ! CHECK:         return %[[RET]] : complex<f32>
 
 subroutine real_constant()
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
   real(2) :: a
   real(4) :: b
   real(8) :: c
 #if __x86_64__
   real(10) :: d
 #endif
-  real(16) :: e
+  real(rk) :: e
   a = 2.0_2
   b = 4.0_4
   c = 8.0_8
 #if __x86_64__
   d = 10.0_10
 #endif
-  e = 16.0_16
+  e = 16.0_rk
 end
 
 ! CHECK: %[[A:.*]] = fir.alloca f16
 ! CHECK: %[[B:.*]] = fir.alloca f32
 ! CHECK: %[[C:.*]] = fir.alloca f64
 ! CHECK-X86-64: %[[D:.*]] = fir.alloca f80
-! CHECK: %[[E:.*]] = fir.alloca f128
+! F128: %[[E:.*]] = fir.alloca f128
+! F64: %[[E:.*]] = fir.alloca f64
 ! CHECK: %[[C2:.*]] = arith.constant 2.000000e+00 : f16
 ! CHECK: fir.store %[[C2]] to %[[A]] : !fir.ref<f16>
 ! CHECK: %[[C4:.*]] = arith.constant 4.000000e+00 : f32
@@ -290,8 +292,10 @@ subroutine real_constant()
 ! CHECK: fir.store %[[C8]] to %[[C]] : !fir.ref<f64>
 ! CHECK-X86-64: %[[C10:.*]] = arith.constant 1.000000e+01 : f80
 ! CHECK-X86-64: fir.store %[[C10]] to %[[D]] : !fir.ref<f80>
-! CHECK: %[[C16:.*]] = arith.constant 1.600000e+01 : f128
-! CHECK: fir.store %[[C16]] to %[[E]] : !fir.ref<f128>
+! F128: %[[C16:.*]] = arith.constant 1.600000e+01 : f128
+! F64: %[[C16:.*]] = arith.constant 1.600000e+01 : f64
+! F128: fir.store %[[C16]] to %[[E]] : !fir.ref<f128>
+! F64: fir.store %[[C16]] to %[[E]] : !fir.ref<f64>
 
 subroutine complex_constant()
   complex(4) :: a
diff --git a/flang/test/Lower/math-lowering/abs.f90 b/flang/test/Lower/math-lowering/abs.f90
index ead603c1d13e8..9d3b8b92cfdd6 100644
--- a/flang/test/Lower/math-lowering/abs.f90
+++ b/flang/test/Lower/math-lowering/abs.f90
@@ -1,9 +1,9 @@
-! RUN: bbc -emit-fir %s -o - --math-runtime=fast | FileCheck --check-prefixes=ALL,FAST %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=fast %s -o - | FileCheck --check-prefixes=ALL,FAST %s
-! RUN: bbc -emit-fir %s -o - --math-runtime=relaxed | FileCheck --check-prefixes=ALL,RELAXED %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=relaxed %s -o - | FileCheck --check-prefixes=ALL,RELAXED %s
-! RUN: bbc -emit-fir %s -o - --math-runtime=precise | FileCheck --check-prefixes=ALL,PRECISE %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=precise %s -o - | FileCheck --check-prefixes=ALL,PRECISE %s
+! RUN: bbc -emit-fir %s -o - --math-runtime=fast | FileCheck --check-prefixes=ALL,FAST-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
+! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=fast %s -o - | FileCheck --check-prefixes=ALL,FAST,FAST-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
+! RUN: bbc -emit-fir %s -o - --math-runtime=relaxed | FileCheck --check-prefixes=ALL,RELAXED,RELAXED-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
+! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=relaxed %s -o - | FileCheck --check-prefixes=ALL,RELAXED,RELAXED-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
+! RUN: bbc -emit-fir %s -o - --math-runtime=precise | FileCheck --check-prefixes=ALL,PRECISE,PRECISE-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
+! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=precise %s -o - | FileCheck --check-prefixes=ALL,PRECISE,PRECISE-%if flang-supports-f128-math %{F128%} %else %{F64%} %s
 
 function test_real4(x)
   real :: x, test_real4
@@ -26,13 +26,17 @@ function test_real8(x)
 ! PRECISE: {{%[A-Za-z0-9._]+}} = fir.call @fabs({{%[A-Za-z0-9._]+}}) {{.*}}: (f64) -> f64
 
 function test_real16(x)
-  real(16) :: x, test_real16
+  integer, parameter :: rk = merge(16, 8, selected_real_kind(33, 4931)==16)
+  real(rk) :: x, test_real16
   test_real16 = abs(x)
 end function
 ! ALL-LABEL: @_QPtest_real16
-! FAST: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f128
-! RELAXED: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f128
-! PRECISE: {{%[A-Za-z0-9._]+}} = fir.call @llvm.fabs.f128({{%[A-Za-z0-9._]+}}) {{.*}}: (f128) -> f128
+! FAST-F128: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f128
+! FAST-F64: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f64
+! RELAXED-F128: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f128
+! RELAXED-F64: {{%[A-Za-z0-9._]+}} = math.absf {{%[A-Za-z0-9._]+}} {{.*}}: f64
+! PRECISE-F128: {{%[A-Za-z0-9._]+}} = fir.call @llvm.fabs.f128({{%[A-Za-z0-9._]+}}) {{.*}}: (f128) -> f128
+! PRECISE-F64: {{%[A-Za-z0-9._]+}} = fir.call @fabs({{%[A-Za-z0-9._]+}}) {{.*}}: (f64) -> f64
 
 function test_complex4(c)
   complex(4) :: c, test_complex4
@@ -50,6 +54,6 @@ function test_complex8(c)
 
 ! PRECISE-DAG: func.func private @fabsf(f32) -> f32 attributes {fir.bindc_name = "fabsf", fir.runtime}
 ! PRECISE-DAG: func.func private @fabs(f64) -> f64 attributes {fir.bindc_name = "fabs", fir.runtime}
-! PRECISE-DAG: func.func private @llvm.fabs.f128(f128) -> f128 attributes {fir.bindc_name = "llvm.fabs.f128", fir.runtime}
+! PRECISE-F128-DAG: func.func private @llvm.fabs.f128(f128) -> f128 attributes {fir.bindc_name = "llvm.fabs.f128", fir.runtime}
 ! PRECISE-DAG: func.func private @cabsf(complex<f32>) -> f32 attributes {fir.bindc_name = "cabsf", fir.runtime}
 ! PRECISE-DAG: func.func private @cabs(complex<f64>) -> f64 attributes {fir.bindc_name = "cabs", fir.runtime}
diff --git a/flang/test/Lower/math-lowering/aint.f90 b/flang/test/Lower/math-lowering/aint.f90
index 103e152be15f6..6c7809f8ea1a3 100644
--- a/flang/test/Lower/math-lowering/aint.f90
+++ b/flang/test/Lower/math-lowering/aint.f90
@@ -1,9 +1,10 @@
-! RUN: bbc -emit-fir %s -o - --math-runtime=fast | FileCheck --check-prefixes=ALL %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=fast %s -o - | FileCheck --check-prefixes=ALL %s
-! RUN: bbc -emit-fir %s -o - --math-runtime=relaxed | FileCheck --check-prefixes=ALL %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=relaxed %s -o - | FileCheck --check-prefixes=ALL %s
-! RUN: bbc -emit-fir %s -o - --math-runtime=precise | FileCheck --check-prefixes=ALL %s
-! RUN: %flang_fc1 -emit-fir -mllvm -math-runtime=precise %s -o - | FileCheck --check-prefixes=ALL %s
+! REQUIRES: x86_64-registered-target
+! RUN: bbc -target x86_64-unknown-linux-gnu -emit-fir %s -o - --math-runtime=fast | FileCheck --check-prefixes=ALL %s
+! RUN: %flang_fc1 -target x86_64-unknown-linux-gnu -emit-fir -mllvm -math-runtime=fast %s -o - | FileCheck --check-prefixes=ALL %s
+! RUN: bbc -target x86_64-unknown-linux-gnu -emit-fir %s -o - --math-runtime=relaxed | FileCheck --check-prefixes=ALL %s
+! RUN: %flang_fc1 -target x86_64-unknown-linux-gnu -emit-fir -mllvm -math-runtime=relaxed %s -o - | FileCheck --check-prefixes=ALL %s
+! RUN: bbc -target x86_64-unknown-linux-gnu -emit-fir %s -o - --math-runtime=precise | FileCheck --check-prefixes=ALL %s
+! RUN: %flang_fc1 -target x86_64-unknown-linux-gnu -emit-fir -mllvm -math-runtime=precise %s -o - | FileCheck --check-prefixes=ALL %s
 
 function test_real4(x)
   real :: x, test_real4
diff --git a/flang/test/Lower/real-operations-1.f90 b/flang/test/Lower/real-operations-1.f90
index aeefc39ca2a0d..d155b7dc9570f 100644
--- a/flang/test/Lower/real-operations-1.f90
+++ b/flang/test/Lower/real-operations-1.f90
@@ -1,5 +1,4 @@
 ! RUN: bbc -emit-hlfir %s -o - | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{,CHECK-KIND10%}%if flang-supports-f128-math %{,CHECK-KIND16%}
-
 ! Test real add on real kinds.
 
 ! CHECK-LABEL: real2
diff --git a/flang/test/Semantics/kinds01.f90 b/flang/test/Semantics/kinds01.f90
index 5238a90719fe4..82c4d76da3710 100644
--- a/flang/test/Semantics/kinds01.f90
+++ b/flang/test/Semantics/kinds01.f90
@@ -1,3 +1,4 @@
+! REQUIRES: x86_64-registered-target
 ! RUN: %python %S/test_symbols.py %s %flang_fc1
  !DEF: /MainProgram1/jk1 ObjectEntity INTEGER(1)
  integer(kind=1) jk1
diff --git a/flang/test/Semantics/kinds02.f90 b/flang/test/Semantics/kinds02.f90
index 13dbb803de8e5..02b1e6c8c310a 100644
--- a/flang/test/Semantics/kinds02.f90
+++ b/flang/test/Semantics/kinds02.f90
@@ -1,3 +1,4 @@
+! REQUIRES: x86_64-registered-target
 ! RUN: %python %S/test_errors.py %s %flang_fc1
 ! C712 The value of scalar-int-constant-expr shall be nonnegative and 
 ! shall specify a representation method that exists on the processor.
diff --git a/flang/test/Semantics/resolve41.f90 b/flang/test/Semantics/resolve41.f90
index d2a991c0a52dc..4d0b3a3d31e55 100644
--- a/flang/test/Semantics/resolve41.f90
+++ b/flang/test/Semantics/resolve41.f90
@@ -21,7 +21,7 @@ module m
   integer :: ff = 2_f
   !ERROR: REAL(KIND=23) is not a supported type
   real(d/2) :: g
-  !ERROR: REAL*47 is not a supported type
+  !ERROR: REAL(KIND=47) is not a supported type
   real*47 :: h
   !ERROR: COMPLEX*47 is not a supported type
   complex*47 :: i