diff --git a/include/time.h b/include/time.h
index eaec898fac..8c261abcf4 100644
--- a/include/time.h
+++ b/include/time.h
@@ -50,13 +50,13 @@ extern void __tzset_parse_tz (const char *tz) attribute_hidden;
 extern void __tz_compute (__time64_t timer, struct tm *tm, int use_localtime)
   __THROW attribute_hidden;
 
-/* Subroutine of `mktime'.  Return the `time_t' representation of TP and
-   normalize TP, given that a `struct tm *' maps to a `time_t' as performed
+/* Subroutine of `mktime'.  Return the `__time64_t' representation of TP and
+   normalize TP, given that a `struct tm *' maps to a `__time64_t' as performed
    by FUNC.  Keep track of next guess for time_t offset in *OFFSET.  */
-extern time_t __mktime_internal (struct tm *__tp,
-				 struct tm *(*__func) (const time_t *,
-						       struct tm *),
-				 time_t *__offset) attribute_hidden;
+extern __time64_t __mktime_internal (struct tm *__tp,
+				     struct tm *(*__func) (const __time64_t *,
+							   struct tm *),
+				     __time64_t *__offset) attribute_hidden;
 
 /* nis/nis_print.c needs ctime, so even if ctime is not declared here,
    we define __ctime64 as ctime so that nis/nis_print.c can get linked
diff --git a/time/mktime.c b/time/mktime.c
index 5f038a212f..18837c87cd 100644
--- a/time/mktime.c
+++ b/time/mktime.c
@@ -1,4 +1,4 @@
-/* Convert a 'struct tm' to a time_t value.
+/* Convert a 'struct tm' to a __time64_t value.
    Copyright (C) 1993-2018 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Paul Eggert <eggert@twinsun.com>.
@@ -35,6 +35,7 @@
 #include <time.h>
 
 #include <limits.h>
+#include <errno.h>
 
 #include <string.h>		/* For the real memcpy prototype.  */
 
@@ -92,50 +93,36 @@ verify (long_int_is_wide_enough, INT_MAX == INT_MAX * (long_int) 2 / 2);
 #define SHR(a, b)                                               \
   ((-1 >> 1 == -1                                               \
     && (long_int) -1 >> 1 == -1                                 \
-    && ((time_t) -1 >> 1 == -1 || ! TYPE_SIGNED (time_t)))      \
+    && (__time64_t) -1 >> 1 == -1)                              \
    ? (a) >> (b)                                                 \
    : (a) / (1 << (b)) - ((a) % (1 << (b)) < 0))
 
 /* The extra casts in the following macros work around compiler bugs,
    e.g., in Cray C 5.0.3.0.  */
 
-/* True if the arithmetic type T is an integer type.  bool counts as
-   an integer.  */
-#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
-
 /* True if negative values of the signed integer type T use two's
    complement, or if T is an unsigned integer type.  */
 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
 
-/* True if the arithmetic type T is signed.  */
-#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
-
 /* The maximum and minimum values for the integer type T.  These
    macros have undefined behavior if T is signed and has padding bits.
    If this is a problem for you, please let us know how to fix it for
    your host.  */
-#define TYPE_MINIMUM(t) \
-  ((t) (! TYPE_SIGNED (t) \
-	? (t) 0 \
-	: ~ TYPE_MAXIMUM (t)))
-#define TYPE_MAXIMUM(t) \
-  ((t) (! TYPE_SIGNED (t) \
-	? (t) -1 \
-	: ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
-
-#ifndef TIME_T_MIN
-# define TIME_T_MIN TYPE_MINIMUM (time_t)
+#define TYPE_MINIMUM(t) (~ TYPE_MAXIMUM (t))
+#define TYPE_MAXIMUM(t) ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)
+
+#ifndef TIME64_T_MIN
+# define TIME64_T_MIN TYPE_MINIMUM (__time64_t)
 #endif
-#ifndef TIME_T_MAX
-# define TIME_T_MAX TYPE_MAXIMUM (time_t)
+#ifndef TIME64_T_MAX
+# define TIME64_T_MAX TYPE_MAXIMUM (__time64_t)
 #endif
-#define TIME_T_MIDPOINT (SHR (TIME_T_MIN + TIME_T_MAX, 1) + 1)
+#define TIME_T_MIDPOINT (SHR (TIME64_T_MIN + TIME64_T_MAX, 1) + 1)
 
-verify (time_t_is_integer, TYPE_IS_INTEGER (time_t));
 verify (twos_complement_arithmetic,
 	(TYPE_TWOS_COMPLEMENT (int)
 	 && TYPE_TWOS_COMPLEMENT (long_int)
-	 && TYPE_TWOS_COMPLEMENT (time_t)));
+	 && TYPE_TWOS_COMPLEMENT (__time64_t)));
 
 #define EPOCH_YEAR 1970
 #define TM_YEAR_BASE 1900
@@ -196,7 +183,7 @@ isdst_differ (int a, int b)
    The result may overflow.  It is the caller's responsibility to
    detect overflow.  */
 
-static time_t
+static __time64_t
 ydhms_diff (long_int year1, long_int yday1, int hour1, int min1, int sec1,
 	    int year0, int yday0, int hour0, int min0, int sec0)
 {
@@ -212,80 +199,73 @@ ydhms_diff (long_int year1, long_int yday1, int hour1, int min1, int sec1,
   int b400 = SHR (b100, 2);
   int intervening_leap_days = (a4 - b4) - (a100 - b100) + (a400 - b400);
 
-  /* Compute the desired time in time_t precision.  Overflow might
+  /* Compute the desired time in __time64_t precision.  Overflow might
      occur here.  */
-  time_t tyear1 = year1;
-  time_t years = tyear1 - year0;
-  time_t days = 365 * years + yday1 - yday0 + intervening_leap_days;
-  time_t hours = 24 * days + hour1 - hour0;
-  time_t minutes = 60 * hours + min1 - min0;
-  time_t seconds = 60 * minutes + sec1 - sec0;
+  __time64_t tyear1 = year1;
+  __time64_t years = tyear1 - year0;
+  __time64_t days = 365 * years + yday1 - yday0 + intervening_leap_days;
+  __time64_t hours = 24 * days + hour1 - hour0;
+  __time64_t minutes = 60 * hours + min1 - min0;
+  __time64_t seconds = 60 * minutes + sec1 - sec0;
   return seconds;
 }
 
 /* Return the average of A and B, even if A + B would overflow.  */
-static time_t
-time_t_avg (time_t a, time_t b)
+static __time64_t
+time_t_avg (__time64_t a, __time64_t b)
 {
   return SHR (a, 1) + SHR (b, 1) + (a & b & 1);
 }
 
-/* Return 1 if A + B does not overflow.  If time_t is unsigned and if
-   B's top bit is set, assume that the sum represents A - -B, and
-   return 1 if the subtraction does not wrap around.  */
+/* Return 1 if A + B does not overflow.  */
 static int
-time_t_add_ok (time_t a, time_t b)
+time_t_add_ok (__time64_t a, __time64_t b)
 {
-  if (! TYPE_SIGNED (time_t))
-    {
-      time_t sum = a + b;
-      return (sum < a) == (TIME_T_MIDPOINT <= b);
-    }
-  else if (WRAPV)
+  if (WRAPV)
     {
-      time_t sum = a + b;
+      __time64_t sum = a + b;
       return (sum < a) == (b < 0);
     }
   else
     {
-      time_t avg = time_t_avg (a, b);
-      return TIME_T_MIN / 2 <= avg && avg <= TIME_T_MAX / 2;
+      __time64_t avg = time_t_avg (a, b);
+      return TIME64_T_MIN / 2 <= avg && avg <= TIME64_T_MAX / 2;
     }
 }
 
 /* Return 1 if A + B does not overflow.  */
 static int
-time_t_int_add_ok (time_t a, int b)
+time_t_int_add_ok (__time64_t a, int b)
 {
-  verify (int_no_wider_than_time_t, INT_MAX <= TIME_T_MAX);
+  verify (int_no_wider_than_time_t, INT_MAX <= TIME64_T_MAX);
   if (WRAPV)
     {
-      time_t sum = a + b;
+      __time64_t sum = a + b;
       return (sum < a) == (b < 0);
     }
   else
     {
       int a_odd = a & 1;
-      time_t avg = SHR (a, 1) + (SHR (b, 1) + (a_odd & b));
-      return TIME_T_MIN / 2 <= avg && avg <= TIME_T_MAX / 2;
+      __time64_t avg = SHR (a, 1) + (SHR (b, 1) + (a_odd & b));
+      return TIME64_T_MIN / 2 <= avg && avg <= TIME64_T_MAX / 2;
     }
 }
 
-/* Return a time_t value corresponding to (YEAR-YDAY HOUR:MIN:SEC),
+/* Return a __time64_t value corresponding to (YEAR-YDAY HOUR:MIN:SEC),
    assuming that *T corresponds to *TP and that no clock adjustments
    occurred between *TP and the desired time.
    If TP is null, return a value not equal to *T; this avoids false matches.
    If overflow occurs, yield the minimal or maximal value, except do not
    yield a value equal to *T.  */
-static time_t
+static __time64_t
 guess_time_tm (long_int year, long_int yday, int hour, int min, int sec,
-	       const time_t *t, const struct tm *tp)
+	       const __time64_t *t, const struct tm *tp)
 {
   if (tp)
     {
-      time_t d = ydhms_diff (year, yday, hour, min, sec,
-			     tp->tm_year, tp->tm_yday,
-			     tp->tm_hour, tp->tm_min, tp->tm_sec);
+      __time64_t d = ydhms_diff (year, yday, hour, min, sec,
+				 tp->tm_year, tp->tm_yday,
+				 tp->tm_hour, tp->tm_min, tp->tm_sec);
       if (time_t_add_ok (*t, d))
 	return *t + d;
     }
@@ -296,30 +276,30 @@ guess_time_tm (long_int year, long_int yday, int hour, int min, int sec,
      match; and don't oscillate between two values, as that would
      confuse the spring-forward gap detector.  */
   return (*t < TIME_T_MIDPOINT
-	  ? (*t <= TIME_T_MIN + 1 ? *t + 1 : TIME_T_MIN)
-	  : (TIME_T_MAX - 1 <= *t ? *t - 1 : TIME_T_MAX));
+	  ? (*t <= TIME64_T_MIN + 1 ? *t + 1 : TIME64_T_MIN)
+	  : (TIME64_T_MAX - 1 <= *t ? *t - 1 : TIME64_T_MAX));
 }
 
 /* Use CONVERT to convert *T to a broken down time in *TP.
    If *T is out of range for conversion, adjust it so that
    it is the nearest in-range value and then convert that.  */
 static struct tm *
-ranged_convert (struct tm *(*convert) (const time_t *, struct tm *),
-		time_t *t, struct tm *tp)
+ranged_convert (struct tm *(*convert) (const __time64_t *, struct tm *),
+		__time64_t *t, struct tm *tp)
 {
   struct tm *r = convert (t, tp);
 
   if (!r && *t)
     {
-      time_t bad = *t;
-      time_t ok = 0;
+      __time64_t bad = *t;
+      __time64_t ok = 0;
 
-      /* BAD is a known unconvertible time_t, and OK is a known good one.
+      /* BAD is a known unconvertible __time64_t, and OK is a known good one.
 	 Use binary search to narrow the range between BAD and OK until
 	 they differ by 1.  */
       while (bad != ok + (bad < 0 ? -1 : 1))
 	{
-	  time_t mid = *t = time_t_avg (ok, bad);
+	  __time64_t mid = *t = time_t_avg (ok, bad);
 	  r = convert (t, tp);
 	  if (r)
 	    ok = mid;
@@ -340,18 +320,18 @@ ranged_convert (struct tm *(*convert) (const time_t *, struct tm *),
 }
 
 
-/* Convert *TP to a time_t value, inverting
+/* Convert *TP to a __time64_t value, inverting
    the monotonic and mostly-unit-linear conversion function CONVERT.
    Use *OFFSET to keep track of a guess at the offset of the result,
    compared to what the result would be for UTC without leap seconds.
    If *OFFSET's guess is correct, only one CONVERT call is needed.
    This function is external because it is used also by timegm.c.  */
-time_t
+__time64_t
 __mktime_internal (struct tm *tp,
-		   struct tm *(*convert) (const time_t *, struct tm *),
-		   time_t *offset)
+		   struct tm *(*convert) (const __time64_t *, struct tm *),
+		   __time64_t *offset)
 {
-  time_t t, gt, t0, t1, t2;
+  __time64_t t, gt, t0, t1, t2;
   struct tm tm;
 
   /* The maximum number of probes (calls to CONVERT) should be enough
@@ -382,7 +362,7 @@ __mktime_internal (struct tm *tp,
 
   /* The other values need not be in range:
      the remaining code handles minor overflows correctly,
-     assuming int and time_t arithmetic wraps around.
+     assuming int and __time64_t arithmetic wraps around.
      Major overflows are caught at the end.  */
 
   /* Calculate day of year from year, month, and day of month.
@@ -393,7 +373,7 @@ __mktime_internal (struct tm *tp,
   long_int lmday = mday;
   long_int yday = mon_yday + lmday;
 
-  time_t guessed_offset = *offset;
+  __time64_t guessed_offset = *offset;
 
   int sec_requested = sec;
 
@@ -413,12 +393,12 @@ __mktime_internal (struct tm *tp,
   t0 = ydhms_diff (year, yday, hour, min, sec,
 		   EPOCH_YEAR - TM_YEAR_BASE, 0, 0, 0, - guessed_offset);
 
-  if (TIME_T_MAX / INT_MAX / 366 / 24 / 60 / 60 < 3)
+  if (TIME64_T_MAX / INT_MAX / 366 / 24 / 60 / 60 < 3)
     {
-      /* time_t isn't large enough to rule out overflows, so check
-	 for major overflows.  A gross check suffices, since if t0
-	 has overflowed, it is off by a multiple of TIME_T_MAX -
-	 TIME_T_MIN + 1.  So ignore any component of the difference
+      /* __time64_t is large enough to rule out overflows, but check
+	 for major overflows anyway.  A gross check suffices, since if t0
+	 has overflowed, it is off by a multiple of TIME64_T_MAX -
+	 TIME64_T_MIN + 1.  So ignore any component of the difference
 	 that is bounded by a small value.  */
 
       /* Approximate log base 2 of the number of time units per
@@ -447,20 +427,21 @@ __mktime_internal (struct tm *tp,
       int diff = approx_biennia - approx_requested_biennia;
       int approx_abs_diff = diff < 0 ? -1 - diff : diff;
 
-      /* IRIX 4.0.5 cc miscalculates TIME_T_MIN / 3: it erroneously
+      /* IRIX 4.0.5 cc miscalculates 32-bit TIME_T_MIN / 3: it erroneously
 	 gives a positive value of 715827882.  Setting a variable
-	 first then doing math on it seems to work.
-	 (ghazi@caip.rutgers.edu) */
-      time_t time_t_max = TIME_T_MAX;
-      time_t time_t_min = TIME_T_MIN;
-      time_t overflow_threshold =
+	 first then doing math on it seems to work (ghazi@caip.rutgers.edu).
+	 Do this with 64-bit TIME64_T_MIN too just in case.
+	 */
+      __time64_t time_t_max = TIME64_T_MAX;
+      __time64_t time_t_min = TIME64_T_MIN;
+      __time64_t overflow_threshold =
 	(time_t_max / 3 - time_t_min / 3) >> ALOG2_SECONDS_PER_BIENNIUM;
 
       if (overflow_threshold < approx_abs_diff)
 	{
 	  /* Overflow occurred.  Try repairing it; this might work if
 	     the time zone offset is enough to undo the overflow.  */
-	  time_t repaired_t0 = -1 - t0;
+	  __time64_t repaired_t0 = -1 - t0;
 	  approx_biennia = SHR (repaired_t0, ALOG2_SECONDS_PER_BIENNIUM);
 	  diff = approx_biennia - approx_requested_biennia;
 	  approx_abs_diff = diff < 0 ? -1 - diff : diff;
@@ -533,7 +514,7 @@ __mktime_internal (struct tm *tp,
 	for (direction = -1; direction <= 1; direction += 2)
 	  if (time_t_int_add_ok (t, delta * direction))
 	    {
-	      time_t ot = t + delta * direction;
+	      __time64_t ot = t + delta * direction;
 	      struct tm otm;
 	      ranged_convert (convert, &ot, &otm);
 	      if (! isdst_differ (isdst, otm.tm_isdst))
@@ -575,11 +556,11 @@ __mktime_internal (struct tm *tp,
    offset in seconds.  'int' should be good enough for GNU code.  We
    can't fix this unilaterally though, as other modules invoke
    __mktime_internal.  */
-static time_t localtime_offset;
+static __time64_t localtime_offset;
 
-/* Convert *TP to a time_t value.  */
-time_t
-mktime (struct tm *tp)
+/* Convert *TP to a __time64_t value.  */
+__time64_t
+__mktime64 (struct tm *tp)
 {
 #ifdef _LIBC
   /* POSIX.1 8.1.1 requires that whenever mktime() is called, the
@@ -588,7 +569,22 @@ mktime (struct tm *tp)
   __tzset ();
 #endif
 
-  return __mktime_internal (tp, __localtime_r, &localtime_offset);
+  return __mktime_internal (tp, __localtime64_r, &localtime_offset);
+}
+
+#ifdef weak_alias
+weak_alias (__mktime64, __timelocal64)
+#endif
+
+/* The 32-bit-time wrapper.  */
+time_t
+mktime (struct tm *tp)
+{
+  __time64_t t64 = __mktime64 (tp);
+  if (fits_in_time_t (t64))
+    return (time_t) t64;
+  __set_errno (EOVERFLOW);
+  return -1;
 }
 
 #ifdef weak_alias
diff --git a/time/timegm.c b/time/timegm.c
index fb720e2d7d..b36fef2320 100644
--- a/time/timegm.c
+++ b/time/timegm.c
@@ -33,15 +33,27 @@
 # include <time_r.h>
 # undef __gmtime_r
 # define __gmtime_r gmtime_r
-time_t __mktime_internal (struct tm *,
-			  struct tm * (*) (time_t const *, struct tm *),
-			  time_t *);
+time64_t __mktime_internal (struct tm *,
+			  struct tm * (*) (__time64_t const *, struct tm *),
+			  __time64_t *);
 #endif
+# include <limits.h>
+# include <errno.h>
+
+__time64_t
+__timegm64 (struct tm *tmp)
+{
+  static __time64_t gmtime_offset;
+  tmp->tm_isdst = 0;
+  return __mktime_internal (tmp, __gmtime64_r, &gmtime_offset);
+}
 
 time_t
 timegm (struct tm *tmp)
 {
-  static time_t gmtime_offset;
-  tmp->tm_isdst = 0;
-  return __mktime_internal (tmp, __gmtime_r, &gmtime_offset);
+  __time64_t t64 = __timegm64(tmp);
+  if (fits_in_time_t (t64))
+    return (time_t) t64;
+  __set_errno (EOVERFLOW);
+  return -1;
 }
