diff --git a/clang/lib/Headers/__clang_hip_cmath.h b/clang/lib/Headers/__clang_hip_cmath.h
--- a/clang/lib/Headers/__clang_hip_cmath.h
+++ b/clang/lib/Headers/__clang_hip_cmath.h
@@ -52,8 +52,46 @@
 __DEVICE__ float frexp(float __arg, int *__exp) {
   return ::frexpf(__arg, __exp);
 }
+
+#if defined(__OPENMP_AMDGCN__)
+// For OpenMP we work around some old system headers that have non-conforming
+// `isinf(float)` and `isnan(float)` implementations that return an `int`. We do
+// this by providing two versions of these functions, differing only in the
+// return type. To avoid conflicting definitions we disable implicit base
+// function generation. That means we will end up with two specializations, one
+// per type, but only one has a base function defined by the system header.
+#pragma omp begin declare variant match(                                       \
+    implementation = {extension(disable_implicit_base)})
+
+// FIXME: We lack an extension to customize the mangling of the variants, e.g.,
+//        add a suffix. This means we would clash with the names of the variants
+//        (note that we do not create implicit base functions here). To avoid
+//        this clash we add a new trait to some of them that is always true
+//        (this is LLVM after all ;)). It will only influence the mangled name
+//        of the variants inside the inner region and avoid the clash.
+#pragma omp begin declare variant match(implementation = {vendor(llvm)})
+
+__DEVICE__ int isinf(float __x) { return ::__isinff(__x); }
+__DEVICE__ int isinf(double __x) { return ::__isinf(__x); }
+__DEVICE__ int isfinite(float __x) { return ::__finitef(__x); }
+__DEVICE__ int isfinite(double __x) { return ::__finite(__x); }
+__DEVICE__ int isnan(float __x) { return ::__isnanf(__x); }
+__DEVICE__ int isnan(double __x) { return ::__isnan(__x); }
+
+#pragma omp end declare variant
+#endif // defined(__OPENMP_AMDGCN__)
+
+__DEVICE__ bool isinf(float __x) { return ::__isinff(__x); }
+__DEVICE__ bool isinf(double __x) { return ::__isinf(__x); }
 __DEVICE__ bool isfinite(float __x) { return ::__finitef(__x); }
 __DEVICE__ bool isfinite(double __x) { return ::__finite(__x); }
+__DEVICE__ bool isnan(float __x) { return ::__isnanf(__x); }
+__DEVICE__ bool isnan(double __x) { return ::__isnan(__x); }
+
+#if defined(__OPENMP_AMDGCN__)
+#pragma omp end declare variant
+#endif // defined(__OPENMP_AMDGCN__)
+
 __DEVICE__ bool isgreater(float __x, float __y) {
   return __builtin_isgreater(__x, __y);
 }
@@ -66,8 +104,6 @@
 __DEVICE__ bool isgreaterequal(double __x, double __y) {
   return __builtin_isgreaterequal(__x, __y);
 }
-__DEVICE__ bool isinf(float __x) { return ::__isinff(__x); }
-__DEVICE__ bool isinf(double __x) { return ::__isinf(__x); }
 __DEVICE__ bool isless(float __x, float __y) {
   return __builtin_isless(__x, __y);
 }
@@ -86,8 +122,6 @@
 __DEVICE__ bool islessgreater(double __x, double __y) {
   return __builtin_islessgreater(__x, __y);
 }
-__DEVICE__ bool isnan(float __x) { return ::__isnanf(__x); }
-__DEVICE__ bool isnan(double __x) { return ::__isnan(__x); }
 __DEVICE__ bool isnormal(float __x) { return __builtin_isnormal(__x); }
 __DEVICE__ bool isnormal(double __x) { return __builtin_isnormal(__x); }
 __DEVICE__ bool isunordered(float __x, float __y) {
diff --git a/clang/test/Headers/hip-header.hip b/clang/test/Headers/hip-header.hip
--- a/clang/test/Headers/hip-header.hip
+++ b/clang/test/Headers/hip-header.hip
@@ -8,6 +8,20 @@
 // RUN: %clang_cc1 -include __clang_hip_runtime_wrapper.h \
 // RUN:   -internal-isystem %S/../../lib/Headers/cuda_wrappers \
 // RUN:   -internal-isystem %S/Inputs/include \
+// RUN:   -include cmath \
+// RUN:   -triple amdgcn-amd-amdhsa -aux-triple x86_64-unknown-unknown \
+// RUN:   -target-cpu gfx906 -emit-llvm %s -fcuda-is-device -o - \
+// RUN:   -D__HIPCC_RTC__ | FileCheck %s  -check-prefixes=AMD_BOOL_RETURN
+// RUN: %clang_cc1 -include __clang_hip_runtime_wrapper.h \
+// RUN:   -internal-isystem %S/../../lib/Headers/cuda_wrappers \
+// RUN:   -internal-isystem %S/Inputs/include \
+// RUN:   -include cmath \
+// RUN:   -triple amdgcn-amd-amdhsa -aux-triple x86_64-unknown-unknown \
+// RUN:   -target-cpu gfx906 -emit-llvm %s -fcuda-is-device -o - \
+// RUN:   -D__HIPCC_RTC__ -DUSE_ISNAN_WITH_INT_RETURN | FileCheck %s -check-prefixes=AMD_INT_RETURN
+// RUN: %clang_cc1 -include __clang_hip_runtime_wrapper.h \
+// RUN:   -internal-isystem %S/../../lib/Headers/cuda_wrappers \
+// RUN:   -internal-isystem %S/Inputs/include \
 // RUN:   -triple amdgcn-amd-amdhsa -aux-triple x86_64-unknown-unknown \
 // RUN:   -target-cpu gfx906 -emit-llvm %s -fcuda-is-device -o - \
 // RUN:   -D__HIPCC_RTC__ -std=c++14 | FileCheck -check-prefixes=CHECK,CXX14 %s
@@ -84,3 +98,20 @@
 __device__ float test_max() {
   return max(5, 6.0);
 }
+
+// CHECK-LABEL: define{{.*}}@_Z10test_isnanv
+__device__ double test_isnan() {
+  double r = 0;
+  double d = 5.0;
+  float f = 5.0;
+
+  // AMD_INT_RETURN: call i32 @__ocml_isnan_f32(float
+  // AMD_BOOL_RETURN: call i32 @__ocml_isnan_f32(float
+  r += isnan(f);
+
+  // AMD_INT_RETURN: call i32 @__ocml_isnan_f64(double
+  // AMD_BOOL_RETURN: call i32 @__ocml_isnan_f64(double
+  r += isnan(d);
+
+  return r ;
+}
diff --git a/clang/test/Headers/openmp_device_math_isnan.cpp b/clang/test/Headers/openmp_device_math_isnan.cpp
--- a/clang/test/Headers/openmp_device_math_isnan.cpp
+++ b/clang/test/Headers/openmp_device_math_isnan.cpp
@@ -1,11 +1,19 @@
 // RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-ppc-host.bc
+// RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm-bc %s -o %t-ppc-host.bc
 // RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple nvptx64-nvidia-cuda -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - | FileCheck %s --check-prefix=BOOL_RETURN
+// RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple amdgcn-amd-amdhsa -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - | FileCheck %s --check-prefix=AMD_BOOL_RETURN
 // RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-ppc-host.bc -ffast-math -ffp-contract=fast
+// RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm-bc %s -o %t-ppc-host.bc -ffast-math -ffp-contract=fast
 // RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple nvptx64-nvidia-cuda -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -ffast-math -ffp-contract=fast | FileCheck %s --check-prefix=BOOL_RETURN
+// RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple amdgcn-amd-amdhsa -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -ffast-math -ffp-contract=fast | FileCheck %s --check-prefix=AMD_BOOL_RETURN
 // RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-ppc-host.bc -DUSE_ISNAN_WITH_INT_RETURN
+// RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm-bc %s -o %t-ppc-host.bc -DUSE_ISNAN_WITH_INT_RETURN
 // RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple nvptx64-nvidia-cuda -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -DUSE_ISNAN_WITH_INT_RETURN | FileCheck %s --check-prefix=INT_RETURN
+// RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple amdgcn-amd-amdhsa -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -DUSE_ISNAN_WITH_INT_RETURN | FileCheck %s --check-prefix=AMD_INT_RETURN
 // RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-ppc-host.bc -ffast-math -ffp-contract=fast -DUSE_ISNAN_WITH_INT_RETURN
+// RUN: %clang_cc1 -x c++ -internal-isystem %S/Inputs/include -fopenmp -triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm-bc %s -o %t-ppc-host.bc -ffast-math -ffp-contract=fast -DUSE_ISNAN_WITH_INT_RETURN
 // RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple nvptx64-nvidia-cuda -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -ffast-math -ffp-contract=fast -DUSE_ISNAN_WITH_INT_RETURN | FileCheck %s --check-prefix=INT_RETURN
+// RUN: %clang_cc1 -x c++ -include __clang_openmp_device_functions.h -internal-isystem %S/../../lib/Headers/openmp_wrappers -internal-isystem %S/Inputs/include -fopenmp -triple amdgcn-amd-amdhsa -aux-triple powerpc64le-unknown-unknown -fopenmp-targets=amdgcn-amd-amdhsa -emit-llvm %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-ppc-host.bc -o - -ffast-math -ffp-contract=fast -DUSE_ISNAN_WITH_INT_RETURN | FileCheck %s --check-prefix=AMD_INT_RETURN
 // expected-no-diagnostics
 
 #include <cmath>
@@ -13,10 +21,14 @@
 double math(float f, double d) {
   double r = 0;
   // INT_RETURN: call i32 @__nv_isnanf(float
+  // AMD_INT_RETURN: call i32 @_{{.*}}isnanf(float
   // BOOL_RETURN: call i32 @__nv_isnanf(float
+  // AMD_BOOL_RETURN: call zeroext i1 @_{{.*}}isnanf(float
   r += std::isnan(f);
   // INT_RETURN: call i32 @__nv_isnand(double
+  // AMD_INT_RETURN: call i32 @_{{.*}}isnand(double
   // BOOL_RETURN: call i32 @__nv_isnand(double
+  // AMD_BOOL_RETURN: call zeroext i1 @_{{.*}}isnand(double
   r += std::isnan(d);
   return r;
 }