--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,11 @@
 2011-06-25  Paul Eggert  <eggert@cs.ucla.edu>
 
+	nanosleep: simplify carrying
+	* lib/nanosleep.c (nanosleep): Use the requested tv_nsec for the
+	first call to the underyling nanosleep, not for the last one.
+	This doesn't fix any bugs, but it simplifies the computation of
+	the remaining delay.  Found while auditing integer overflow issues.
+
 	dup2: remove test for existence of fcntl
 	* m4/dup2.m4 (gl_FUNC_DUP2): Use "#ifdef FD_CLOEXEC", not
 	"#if HAVE_FCNTL", in the configure-time test program.

--- a/lib/nanosleep.c
+++ b/lib/nanosleep.c
@@ -65,7 +65,7 @@
     const time_t limit = 24 * 24 * 60 * 60;
     time_t seconds = requested_delay->tv_sec;
     struct timespec intermediate;
-    intermediate.tv_nsec = 0;
+    intermediate.tv_nsec = requested_delay->tv_nsec;
 
     while (limit < seconds)
       {
@@ -76,20 +76,12 @@
         if (result)
           {
             if (remaining_delay)
-              {
-                remaining_delay->tv_sec += seconds;
-                remaining_delay->tv_nsec += requested_delay->tv_nsec;
-                if (BILLION <= requested_delay->tv_nsec)
-                  {
-                    remaining_delay->tv_sec++;
-                    remaining_delay->tv_nsec -= BILLION;
-                  }
-              }
+              remaining_delay->tv_sec += seconds;
             return result;
           }
+        intermediate.tv_nsec = 0;
       }
     intermediate.tv_sec = seconds;
-    intermediate.tv_nsec = requested_delay->tv_nsec;
     return nanosleep (&intermediate, remaining_delay);
   }
 }