diff --git a/Include/pytime.h b/Include/pytime.h
index 7a14456d3f5..d46b17c6293 100644
--- a/Include/pytime.h
+++ b/Include/pytime.h
@@ -41,13 +41,6 @@ PyAPI_FUNC(int) _PyTime_gettimeofday_info(
     _PyTime_timeval *tp,
     _Py_clock_info_t *info);
 
-#define _PyTime_ADD_SECONDS(tv, interval) \
-do { \
-    tv.tv_usec += (long) (((long) interval - interval) * 1000000); \
-    tv.tv_sec += (time_t) interval + (time_t) (tv.tv_usec / 1000000); \
-    tv.tv_usec %= 1000000; \
-} while (0)
-
 #define _PyTime_INTERVAL(tv_start, tv_end) \
     ((tv_end.tv_sec - tv_start.tv_sec) + \
      (tv_end.tv_usec - tv_start.tv_usec) * 0.000001)
@@ -109,6 +102,11 @@ PyAPI_FUNC(int) _PyTime_monotonic_info(
     _PyTime_timeval *tp,
     _Py_clock_info_t *info);
 
+/* Add interval seconds to tv */
+PyAPI_FUNC(void)
+_PyTime_AddDouble(_PyTime_timeval *tv, double interval,
+                  _PyTime_round_t round);
+
 /* Initialize time.
    Return 0 on success, raise an exception and return -1 on error. */
 PyAPI_FUNC(int) _PyTime_Init(void);
diff --git a/Lib/test/eintrdata/eintr_tester.py b/Lib/test/eintrdata/eintr_tester.py
index 400dd21191e..64db2e55dc3 100644
--- a/Lib/test/eintrdata/eintr_tester.py
+++ b/Lib/test/eintrdata/eintr_tester.py
@@ -258,13 +258,10 @@ class TimeEINTRTest(EINTRBaseTest):
 
     def test_sleep(self):
         t0 = time.monotonic()
-        # time.sleep() may retry when interrupted by a signal
-        time.sleep(2)
+        time.sleep(self.sleep_time)
         signal.alarm(0)
         dt = time.monotonic() - t0
-        # Tolerate a difference 100 ms: on Windows, time.monotonic() has
-        # a resolution of 15.6 ms or greater
-        self.assertGreaterEqual(dt, 1.9)
+        self.assertGreaterEqual(dt, self.sleep_time)
 
 
 def test_main():
diff --git a/Modules/socketmodule.c b/Modules/socketmodule.c
index 057430b7040..480ee5ab4ec 100644
--- a/Modules/socketmodule.c
+++ b/Modules/socketmodule.c
@@ -687,7 +687,7 @@ internal_select(PySocketSockObject *s, int writing)
         if (has_timeout) { \
             _PyTime_monotonic(&now); \
             deadline = now; \
-            _PyTime_ADD_SECONDS(deadline, s->sock_timeout); \
+            _PyTime_AddDouble(&deadline, s->sock_timeout, _PyTime_ROUND_UP); \
         } \
         while (1) { \
             errno = 0; \
diff --git a/Modules/timemodule.c b/Modules/timemodule.c
index 179c33fb922..204626e8f76 100644
--- a/Modules/timemodule.c
+++ b/Modules/timemodule.c
@@ -1399,14 +1399,14 @@ floatsleep(double secs)
 #endif
 
     _PyTime_monotonic(&deadline);
-    _PyTime_ADD_SECONDS(deadline, secs);
+    _PyTime_AddDouble(&deadline, secs, _PyTime_ROUND_UP);
 
     do {
 #ifndef MS_WINDOWS
         frac = fmod(secs, 1.0);
         secs = floor(secs);
         timeout.tv_sec = (long)secs;
-        timeout.tv_usec = (long)(frac*1000000.0);
+        timeout.tv_usec = (long)(frac*1e6);
 
         Py_BEGIN_ALLOW_THREADS
         err = select(0, (fd_set *)0, (fd_set *)0, (fd_set *)0, &timeout);
diff --git a/Python/pytime.c b/Python/pytime.c
index cdaa22ec669..894008db8b7 100644
--- a/Python/pytime.c
+++ b/Python/pytime.c
@@ -367,6 +367,23 @@ _PyTime_ObjectToTimeval(PyObject *obj, time_t *sec, long *usec,
     return _PyTime_ObjectToDenominator(obj, sec, usec, 1e6, round);
 }
 
+void
+_PyTime_AddDouble(_PyTime_timeval *tv, double interval, _PyTime_round_t round)
+{
+    _PyTime_timeval tv2;
+    double frac;
+
+    frac = fmod(interval, 1.0);
+    interval = floor(interval);
+    tv2.tv_sec = (long)interval;
+    tv2.tv_usec = (long)(frac*1e6);
+
+    tv->tv_sec += tv2.tv_sec;
+    tv->tv_usec += tv2.tv_usec;
+    tv->tv_sec += (time_t)(tv->tv_usec / 1000000);
+    tv->tv_usec %= 1000000;
+}
+
 int
 _PyTime_Init(void)
 {