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diff --git a/m4/sleep.m4 b/m4/sleep.m4
index 2c9d75cd..b789ac57 100644
--- a/m4/sleep.m4
+++ b/m4/sleep.m4
@@ -1,5 +1,5 @@
-# sleep.m4 serial 1
-dnl Copyright (C) 2007 Free Software Foundation, Inc.
+# sleep.m4 serial 7
+dnl Copyright (C) 2007-2015 Free Software Foundation, Inc.
 dnl This file is free software; the Free Software Foundation
 dnl gives unlimited permission to copy and/or distribute it,
 dnl with or without modifications, as long as this notice is preserved.
@@ -7,13 +7,56 @@ dnl with or without modifications, as long as this notice is preserved.
 AC_DEFUN([gl_FUNC_SLEEP],
 [
   AC_REQUIRE([gl_UNISTD_H_DEFAULTS])
+  AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
+  dnl We expect to see the declaration of sleep() in a header file.
+  dnl Older versions of mingw have a sleep() function that is an alias to
+  dnl _sleep() in MSVCRT. It has a different signature than POSIX sleep():
+  dnl it takes the number of milliseconds as argument and returns void.
+  dnl mingw does not declare this function.
+  AC_CHECK_DECLS([sleep], , , [[#include <unistd.h>]])
   AC_CHECK_FUNCS_ONCE([sleep])
-  if test $ac_cv_func_sleep = no; then
+  if test $ac_cv_have_decl_sleep != yes; then
     HAVE_SLEEP=0
-    AC_LIBOBJ([sleep])
-    gl_PREREQ_SLEEP
+  else
+    dnl Cygwin 1.5.x has a bug where sleep can't exceed 49.7 days.
+    AC_CACHE_CHECK([for working sleep], [gl_cv_func_sleep_works],
+      [AC_RUN_IFELSE([AC_LANG_PROGRAM([[
+#include <errno.h>
+#include <unistd.h>
+#include <signal.h>
+static void
+handle_alarm (int sig)
+{
+  if (sig != SIGALRM)
+    _exit (2);
+}
+]], [[
+    /* Failure to compile this test due to missing alarm is okay,
+       since all such platforms (mingw) also lack sleep.  */
+    unsigned int pentecost = 50 * 24 * 60 * 60; /* 50 days.  */
+    unsigned int remaining;
+    signal (SIGALRM, handle_alarm);
+    alarm (1);
+    remaining = sleep (pentecost);
+    if (remaining > pentecost)
+      return 3;
+    if (remaining <= pentecost - 10)
+      return 4;
+    return 0;
+    ]])],
+      [gl_cv_func_sleep_works=yes], [gl_cv_func_sleep_works=no],
+      [case "$host_os" in
+                 # Guess yes on glibc systems.
+         *-gnu*) gl_cv_func_sleep_works="guessing yes" ;;
+                 # If we don't know, assume the worst.
+         *)      gl_cv_func_sleep_works="guessing no" ;;
+       esac
+      ])])
+    case "$gl_cv_func_sleep_works" in
+      *yes) ;;
+      *)
+        REPLACE_SLEEP=1
+        ;;
+    esac
   fi
 ])
-
-# Prerequisites of lib/sleep.c.
-AC_DEFUN([gl_PREREQ_SLEEP], [:])