diff --git a/flang/runtime/time-intrinsic.cpp b/flang/runtime/time-intrinsic.cpp
--- a/flang/runtime/time-intrinsic.cpp
+++ b/flang/runtime/time-intrinsic.cpp
@@ -12,14 +12,29 @@
 
 #include <ctime>
 
-namespace Fortran::runtime {
-extern "C" {
-
 // CPU_TIME (Fortran 2018 16.9.57)
-double RTNAME(CpuTime)() {
-  // This is part of the c++ standard, so it should at least exist everywhere.
-  // It probably does not have the best resolution, so we prefer other
-  // platform-specific alternatives if they exist.
+// We can use std::clock() from the <ctime> header as a fallback implementation
+// that should be available everywhere. This may not provide the best resolution
+// and is particularly troublesome on (some?) POSIX systems where CLOCKS_PER_SEC
+// is defined as 10^6 regardless of the actual precision of std::clock().
+// Therefore, we will usually prefer platform-specific alternatives when they
+// are available.
+//
+// We can use SFINAE to choose a platform-specific alternative. To do so, we
+// introduce a helper function template, whose overload set will contain only
+// implementations relying on interfaces which are actually available. Each
+// overload will have a dummy parameter whose type indicates whether or not it
+// should be preferred. Any other parameters required for SFINAE should have
+// default values provided.
+namespace {
+// Types for the dummy parameter indicating the priority of a given overload.
+// We will invoke our helper with an integer literal argument, so the overload
+// with the highest priority should have the type int.
+using fallback_implementation = double;
+using preferred_implementation = int;
+
+// This is the fallback implementation, which should work everywhere.
+template <typename Unused = void> double getCpuTime(fallback_implementation) {
   std::clock_t timestamp{std::clock()};
   if (timestamp != std::clock_t{-1}) {
     return static_cast<double>(timestamp) / CLOCKS_PER_SEC;
@@ -28,5 +43,36 @@
   // Return some negative value to represent failure.
   return -1.0;
 }
+
+// POSIX implementation using clock_gettime. This is only enabled if
+// clock_gettime is available.
+template <typename T = int, typename U = struct timespec>
+double getCpuTime(preferred_implementation,
+    // We need some dummy parameters to pass to decltype(clock_gettime).
+    T ClockId = 0, U *Timespec = nullptr,
+    decltype(clock_gettime(ClockId, Timespec)) *Enabled = nullptr) {
+#if defined CLOCK_THREAD_CPUTIME_ID
+#define CLOCKID CLOCK_THREAD_CPUTIME_ID
+#elif defined CLOCK_PROCESS_CPUTIME_ID
+#define CLOCKID CLOCK_PROCESS_CPUTIME_ID
+#elif defined CLOCK_MONOTONIC
+#define CLOCKID CLOCK_MONOTONIC
+#else
+#define CLOCKID CLOCK_REALTIME
+#endif
+  struct timespec tspec;
+  if (clock_gettime(CLOCKID, &tspec) == 0) {
+    return tspec.tv_nsec * 1.0e-9 + tspec.tv_sec;
+  }
+
+  // Return some negative value to represent failure.
+  return -1.0;
+}
+} // anonymous namespace
+
+namespace Fortran::runtime {
+extern "C" {
+
+double RTNAME(CpuTime)() { return getCpuTime(0); }
 } // extern "C"
 } // namespace Fortran::runtime