diff --git a/sysdeps/mach/gettimeofday.c b/sysdeps/mach/clock_gettime.c
similarity index 67%
rename from sysdeps/mach/gettimeofday.c
rename to sysdeps/mach/clock_gettime.c
index 8d0dfbb7dc..0fe0619aa5 100644
--- a/sysdeps/mach/gettimeofday.c
+++ b/sysdeps/mach/clock_gettime.c
@@ -16,28 +16,31 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <errno.h>
-#include <stddef.h>
-#include <sys/time.h>
+#include <time.h>
 #include <mach.h>
 
-/* Get the current time of day and timezone information,
-   putting it into *TV and *TZ.  If TZ is NULL, *TZ is not filled.
+/* Get the current time of day, putting it into *TS.
    Returns 0 on success, -1 on errors.  */
 int
-__gettimeofday (struct timeval *tv, struct timezone *tz)
+__clock_gettime (clockid_t clock_id, struct timespec *ts)
 {
   kern_return_t err;
+  time_value_t tv;
 
-  if (tz != NULL)
-    *tz = (struct timezone){0, 0}; /* XXX */
+  if (clock_id != CLOCK_REALTIME)
+    {
+      errno = EINVAL;
+      return -1;
+    }
 
-  if (err = __host_get_time (__mach_host_self (), (time_value_t *) tv))
+  if (err = __host_get_time (__mach_host_self (), &tv))
     {
       errno = err;
       return -1;
     }
+
+  TIME_VALUE_TO_TIMESPEC (&tv, ts);
   return 0;
 }
-libc_hidden_def (__gettimeofday)
-weak_alias (__gettimeofday, gettimeofday)
-libc_hidden_weak (gettimeofday)
+weak_alias (__clock_gettime, clock_gettime)
+libc_hidden_def (__clock_gettime)
diff --git a/sysdeps/mach/hurd/settimeofday.c b/sysdeps/mach/hurd/clock_settime.c
similarity index 71%
rename from sysdeps/mach/hurd/settimeofday.c
rename to sysdeps/mach/hurd/clock_settime.c
index bd0ffd64ac..a642b82b3e 100644
--- a/sysdeps/mach/hurd/settimeofday.c
+++ b/sysdeps/mach/hurd/clock_settime.c
@@ -16,37 +16,32 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <errno.h>
+#include <time.h>
 #include <sys/time.h>
 #include <hurd.h>
 #include <hurd/port.h>
 
-/* Set the current time of day and timezone information.
+/* Set the current time of day.
    This call is restricted to the super-user.  */
 int
-__settimeofday (const struct timeval *tv, const struct timezone *tz)
+__clock_settime (clockid_t clock_id, const struct timespec *ts)
 {
   error_t err;
   mach_port_t hostpriv;
+  time_value_t tv;
 
-  if (tz != NULL)
-    {
-      errno = ENOSYS;
-      return -1;
-    }
+  if (clock_id != CLOCK_REALTIME)
+    return __hurd_fail (EINVAL);
 
   err = __get_privileged_ports (&hostpriv, NULL);
   if (err)
     return __hurd_fail (EPERM);
 
-  /* `time_value_t' and `struct timeval' are in fact identical with the
-     names changed.  */
-  err = __host_set_time (hostpriv, *(time_value_t *) tv);
+  TIMESPEC_TO_TIME_VALUE (&tv, ts);
+  err = __host_set_time (hostpriv, tv);
   __mach_port_deallocate (__mach_task_self (), hostpriv);
 
-  if (err)
-    return __hurd_fail (err);
-
-  return 0;
+  return __hurd_fail (err);
 }
-
-weak_alias (__settimeofday, settimeofday)
+libc_hidden_def (__clock_settime)
+weak_alias (__clock_settime, clock_settime)
diff --git a/sysdeps/unix/clock_gettime.c b/sysdeps/unix/clock_gettime.c
deleted file mode 100644
index 10a6c96d9d..0000000000
--- a/sysdeps/unix/clock_gettime.c
+++ /dev/null
@@ -1,64 +0,0 @@
-/* clock_gettime -- Get the current time from a POSIX clockid_t.  Unix version.
-   Copyright (C) 1999-2019 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-
-   The GNU C Library is free software; you can redistribute it and/or
-   modify it under the terms of the GNU Lesser General Public
-   License as published by the Free Software Foundation; either
-   version 2.1 of the License, or (at your option) any later version.
-
-   The GNU C Library is distributed in the hope that it will be useful,
-   but WITHOUT ANY WARRANTY; without even the implied warranty of
-   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-   Lesser General Public License for more details.
-
-   You should have received a copy of the GNU Lesser General Public
-   License along with the GNU C Library; if not, see
-   <http://www.gnu.org/licenses/>.  */
-
-#include <errno.h>
-#include <stdint.h>
-#include <time.h>
-#include <sys/time.h>
-#include <libc-internal.h>
-#include <ldsodefs.h>
-
-
-static inline int
-realtime_gettime (struct timespec *tp)
-{
-  struct timeval tv;
-  int retval = __gettimeofday (&tv, NULL);
-  if (retval == 0)
-    /* Convert into `timespec'.  */
-    TIMEVAL_TO_TIMESPEC (&tv, tp);
-  return retval;
-}
-
-
-/* Get current value of CLOCK and store it in TP.  */
-int
-__clock_gettime (clockid_t clock_id, struct timespec *tp)
-{
-  int retval = -1;
-
-  switch (clock_id)
-    {
-    case CLOCK_REALTIME:
-      {
-	struct timeval tv;
-	retval = __gettimeofday (&tv, NULL);
-	if (retval == 0)
-	  TIMEVAL_TO_TIMESPEC (&tv, tp);
-      }
-      break;
-
-    default:
-      __set_errno (EINVAL);
-      break;
-    }
-
-  return retval;
-}
-weak_alias (__clock_gettime, clock_gettime)
-libc_hidden_def (__clock_gettime)
diff --git a/sysdeps/unix/clock_settime.c b/sysdeps/unix/clock_settime.c
deleted file mode 100644
index 109a1ad872..0000000000
--- a/sysdeps/unix/clock_settime.c
+++ /dev/null
@@ -1,54 +0,0 @@
-/* Copyright (C) 1999-2019 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-
-   The GNU C Library is free software; you can redistribute it and/or
-   modify it under the terms of the GNU Lesser General Public
-   License as published by the Free Software Foundation; either
-   version 2.1 of the License, or (at your option) any later version.
-
-   The GNU C Library is distributed in the hope that it will be useful,
-   but WITHOUT ANY WARRANTY; without even the implied warranty of
-   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-   Lesser General Public License for more details.
-
-   You should have received a copy of the GNU Lesser General Public
-   License along with the GNU C Library; if not, see
-   <http://www.gnu.org/licenses/>.  */
-
-#include <errno.h>
-#include <time.h>
-#include <sys/time.h>
-#include <ldsodefs.h>
-
-
-/* Set CLOCK to value TP.  */
-int
-__clock_settime (clockid_t clock_id, const struct timespec *tp)
-{
-  int retval = -1;
-
-  /* Make sure the time cvalue is OK.  */
-  if (tp->tv_nsec < 0 || tp->tv_nsec >= 1000000000)
-    {
-      __set_errno (EINVAL);
-      return -1;
-    }
-
-  switch (clock_id)
-    {
-    case CLOCK_REALTIME:
-      {
-	struct timeval tv;
-	TIMESPEC_TO_TIMEVAL (&tv, tp);
-	retval = __settimeofday (&tv, NULL);
-      }
-      break;
-
-    default:
-      __set_errno (EINVAL);
-      break;
-    }
-
-  return retval;
-}
-weak_alias (__clock_settime, clock_settime)
