diff --git a/CMakeLists.txt b/CMakeLists.txt
index e7ab00feb..fba6f2a61 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -15,7 +15,6 @@ project(SDL2 C CXX)
 # !!! FIXME:  properly resolved.
 #cmake_policy(SET CMP0042 OLD)
 
-include(CheckFunctionExists)
 include(CheckLibraryExists)
 include(CheckIncludeFiles)
 include(CheckIncludeFile)
@@ -787,7 +786,8 @@ if(LIBC)
       check_include_file("${_HEADER}" ${_HAVE_H})
     endforeach()
 
-    check_include_files("dlfcn.h;stdint.h;stddef.h;inttypes.h;stdlib.h;strings.h;string.h;float.h" STDC_HEADERS)
+    set(STDC_HEADER_NAMES "dlfcn.h;stdint.h;stddef.h;inttypes.h;stdlib.h;stdio.h;strings.h;wchar.h;string.h;float.h")
+    check_include_files("${STDC_HEADER_NAMES}" STDC_HEADERS)
     check_type_size("size_t" SIZEOF_SIZE_T)
     check_symbol_exists(M_PI math.h HAVE_M_PI)
     # TODO: refine the mprotect check
@@ -801,14 +801,21 @@ if(LIBC)
             _uitoa _ultoa strtol strtoul _i64toa _ui64toa strtoll strtoull
             atoi atof strcmp strncmp _stricmp strcasecmp _strnicmp strncasecmp
             wcscmp wcsdup wcslcat wcslcpy wcslen wcsncmp wcsstr
-            sscanf vsscanf vsnprintf fopen64 fseeko fseeko64 sigaction setjmp
-            nanosleep sysconf sysctlbyname getauxval poll _Exit
+            sscanf vsscanf vsnprintf fopen64 fseeko fseeko64 _Exit
             )
       string(TOUPPER ${_FN} _UPPER)
       set(_HAVEVAR "HAVE_${_UPPER}")
-      check_function_exists("${_FN}" ${_HAVEVAR})
+      check_symbol_exists("${_FN}" "${STDC_HEADER_NAMES}" ${_HAVEVAR})
     endforeach()
 
+    check_symbol_exists(sigaction "signal.h" HAVE_SIGACTION)
+    check_symbol_exists(setjmp "setjmp.h" HAVE_SETJMP)
+    check_symbol_exists(nanosleep "time.h" HAVE_NANOSLEEP)
+    check_symbol_exists(sysconf "unistd.h" HAVE_SYSCONF)
+    check_symbol_exists(sysctlbyname "sys/types.h;sys/sysctl.h" HAVE_SYSCTLBYNAME)
+    check_symbol_exists(getauxval "sys/auxv.h" HAVE_GETAUXVAL)
+    check_symbol_exists(poll "poll.h" HAVE_POLL)
+
     check_library_exists(m pow "" HAVE_LIBM)
     if(HAVE_LIBM)
       set(CMAKE_REQUIRED_LIBRARIES m)
@@ -819,7 +826,7 @@ if(LIBC)
               asin asinf)
         string(TOUPPER ${_FN} _UPPER)
         set(_HAVEVAR "HAVE_${_UPPER}")
-        check_function_exists("${_FN}" ${_HAVEVAR})
+        check_symbol_exists("${_FN}" "math.h" ${_HAVEVAR})
       endforeach()
       set(CMAKE_REQUIRED_LIBRARIES)
       list(APPEND EXTRA_LIBS m)
@@ -833,7 +840,7 @@ if(LIBC)
 
     if(NOT APPLE)
       check_include_file(alloca.h HAVE_ALLOCA_H)
-      check_function_exists(alloca HAVE_ALLOCA)
+      check_symbol_exists(alloca "alloca.h" HAVE_ALLOCA)
     else()
       set(HAVE_ALLOCA_H 1)
       set(HAVE_ALLOCA 1)
diff --git a/cmake/sdlchecks.cmake b/cmake/sdlchecks.cmake
index 3b7f82138..3266e15f6 100644
--- a/cmake/sdlchecks.cmake
+++ b/cmake/sdlchecks.cmake
@@ -30,7 +30,7 @@ macro(FindLibraryAndSONAME _LIB)
 endmacro()
 
 macro(CheckDLOPEN)
-  check_function_exists(dlopen HAVE_DLOPEN)
+  check_symbol_exists(dlopen "dlfcn.h" HAVE_DLOPEN)
   if(NOT HAVE_DLOPEN)
     foreach(_LIBNAME dl tdl)
       check_library_exists("${_LIBNAME}" "dlopen" "" DLOPEN_LIB)
@@ -424,7 +424,7 @@ macro(CheckX11)
         set(X11_SHARED OFF)
       endif()
 
-      check_function_exists("shmat" HAVE_SHMAT)
+      check_symbol_exists(shmat "sys/shm.h" HAVE_SHMAT)
       if(NOT HAVE_SHMAT)
         check_library_exists(ipc shmat "" HAVE_SHMAT)
         if(HAVE_SHMAT)
@@ -476,7 +476,7 @@ macro(CheckX11)
         set(SDL_VIDEO_DRIVER_X11_SUPPORTS_GENERIC_EVENTS 1)
       endif()
 
-      check_function_exists(XkbKeycodeToKeysym SDL_VIDEO_DRIVER_X11_HAS_XKBKEYCODETOKEYSYM)
+      check_symbol_exists(XkbKeycodeToKeysym "X11/Xlib.h;X11/XKBlib.h" SDL_VIDEO_DRIVER_X11_HAS_XKBKEYCODETOKEYSYM)
 
       if(VIDEO_X11_XCURSOR AND HAVE_XCURSOR_H)
         set(HAVE_VIDEO_X11_XCURSOR TRUE)
@@ -899,12 +899,14 @@ macro(CheckPTHREAD)
         endif()
       endif()
 
-      check_c_source_compiles("
-          #include <pthread.h>
-          #include <pthread_np.h>
-          int main(int argc, char** argv) { return 0; }" HAVE_PTHREAD_NP_H)
-      check_function_exists(pthread_setname_np HAVE_PTHREAD_SETNAME_NP)
-      check_function_exists(pthread_set_name_np HAVE_PTHREAD_SET_NAME_NP)
+      check_include_files("pthread.h" HAVE_PTHREAD_H)
+      check_include_files("pthread_np.h" HAVE_PTHREAD_NP_H)
+      if (HAVE_PTHREAD_H)
+        check_symbol_exists(pthread_setname_np "pthread.h" HAVE_PTHREAD_SETNAME_NP)
+        if (HAVE_PTHREAD_NP_H)
+          check_symbol_exists(pthread_set_name_np "pthread.h;pthread_np.h" HAVE_PTHREAD_SET_NAME_NP)
+        endif()
+      endif()
 
       set(SOURCE_FILES ${SOURCE_FILES}
           ${SDL2_SOURCE_DIR}/src/thread/pthread/SDL_systhread.c