multi: remove MULTI_TIMEOUT_INACCURACY

With the recently added timeout "reminder" functionality, there's no
reason left for us to execute timeout code before the time is
ripe. Simplifies the handling too.

This will make the *TIMEOUT and *CONNECTTIMEOUT options more accurate
again, which probably is most important when the *_MS versions are used.

In multi_socket, make sure to update 'now' after having handled activity
on a socket.
diff --git a/lib/connect.c b/lib/connect.c
index f04cce7..0816af2 100644
--- a/lib/connect.c
+++ b/lib/connect.c
@@ -1104,8 +1104,7 @@
   conn->tempaddr[1] = NULL;
   conn->tempsock[0] = CURL_SOCKET_BAD;
   conn->tempsock[1] = CURL_SOCKET_BAD;
-  Curl_expire(conn->data,
-              HAPPY_EYEBALLS_TIMEOUT + (MULTI_TIMEOUT_INACCURACY/1000));
+  Curl_expire(conn->data, HAPPY_EYEBALLS_TIMEOUT);
 
   /* Max time for the next connection attempt */
   conn->timeoutms_per_addr =
diff --git a/lib/multi.c b/lib/multi.c
index 3af460d..cab3030 100644
--- a/lib/multi.c
+++ b/lib/multi.c
@@ -2231,6 +2231,8 @@
 
       data = NULL; /* set data to NULL again to avoid calling
                       multi_runsingle() in case there's no need to */
+      now = Curl_tvnow(); /* get a newer time since the multi_runsingle() loop
+                             may have taken some time */
     }
   }
   else {
@@ -2241,30 +2243,6 @@
     memset(&multi->timer_lastcall, 0, sizeof(multi->timer_lastcall));
   }
 
-  /* Compensate for bad precision timers that might've triggered too early.
-
-     This precaution was added in commit 2c72732ebf3da5e as a result of bad
-     resolution in the windows function use(d).
-
-     The problematic case here is when using the multi_socket API and libcurl
-     has told the application about a timeout, and that timeout is what fires
-     off a bit early. As we don't have any IDs associated with the timeout we
-     can't tell which timeout that fired off but we only have the times to use
-     to check what to do. If it fires off too early, we don't run the correct
-     actions and we don't tell the application again about the same timeout as
-     was already first in the queue...
-
-     Originally we made the timeouts run 40 milliseconds early on all systems,
-     but now we have an #ifdef setup to provide a decent precaution inaccuracy
-     margin.
-  */
-
-  now.tv_usec += MULTI_TIMEOUT_INACCURACY;
-  if(now.tv_usec >= 1000000) {
-    now.tv_sec++;
-    now.tv_usec -= 1000000;
-  }
-
   /*
    * The loop following here will go on as long as there are expire-times left
    * to process in the splay and 'data' will be re-assigned for every expired
diff --git a/lib/multiif.h b/lib/multiif.h
index 15163da..1cbd310 100644
--- a/lib/multiif.h
+++ b/lib/multiif.h
@@ -7,7 +7,7 @@
  *                            | (__| |_| |  _ <| |___
  *                             \___|\___/|_| \_\_____|
  *
- * Copyright (C) 1998 - 2013, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2014, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -22,16 +22,6 @@
  *
  ***************************************************************************/
 
-/* See multi_socket() for the explanation of this constant. Counted in number
-   of microseconds. */
-#ifdef WIN32
-#define MULTI_TIMEOUT_INACCURACY 40000
-#else
-#define MULTI_TIMEOUT_INACCURACY 3000
-#endif
-
-#define MULTI_TIMEOUT_INACCURACY_MS (MULTI_TIMEOUT_INACCURACY / 1000)
-
 /*
  * Prototypes for library-wide functions provided by multi.c
  */
diff --git a/lib/transfer.c b/lib/transfer.c
index 7861174..3408a84 100644
--- a/lib/transfer.c
+++ b/lib/transfer.c
@@ -5,7 +5,7 @@
  *                            | (__| |_| |  _ <| |___
  *                             \___|\___/|_| \_\_____|
  *
- * Copyright (C) 1998 - 2013, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2014, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -1320,11 +1320,10 @@
     Curl_pgrsStartNow(data);
 
     if(data->set.timeout)
-      Curl_expire(data, data->set.timeout + MULTI_TIMEOUT_INACCURACY_MS);
+      Curl_expire(data, data->set.timeout);
 
     if(data->set.connecttimeout)
-      Curl_expire(data, data->set.connecttimeout +
-                  MULTI_TIMEOUT_INACCURACY_MS);
+      Curl_expire(data, data->set.connecttimeout);
 
     /* In case the handle is re-used and an authentication method was picked
        in the session we need to make sure we only use the one(s) we now
@@ -1970,8 +1969,7 @@
 
         /* Set a timeout for the multi interface. Add the inaccuracy margin so
            that we don't fire slightly too early and get denied to run. */
-        Curl_expire(data, CURL_TIMEOUT_EXPECT_100 +
-                    MULTI_TIMEOUT_INACCURACY / 1000);
+        Curl_expire(data, CURL_TIMEOUT_EXPECT_100);
       }
       else {
         if(data->state.expect100header)