[PATCH 2/3] s6-rc-update.c: rewrite O(n^2) loop as O(n) complexity

[Adam Joseph <adam@westernsemico.com>]

Prior to this commit, s6-rc-update had a loop with the following
comment:

  This part runs in O(oldn*newn). There are no syscalls in the loop,
  so it should still be negligible unless you have 10k services.

The loop does the following:

   for each old service which was already up
     for each new service
       if the old service converts to the new service,
         set some new service flags based on old service flags

The loop is O(n^2) due to the nested iteration.  We can rewrite this
with a single iteration by making use of the invimage[] array, which
maps from new services to old services:

   for each new service
     if *ANY* old service converts to the new service,
       set some new service flags based on that old service's flags

This takes advantage of the fact that invimage is an injective
(partial) function.

Signed-off-by: Adam Joseph <adam@westernsemico.com>
---
 src/s6-rc/s6-rc-update.c | 15 ++++++---------
 1 file changed, 6 insertions(+), 9 deletions(-)

diff --git a/src/s6-rc/s6-rc-update.c b/src/s6-rc/s6-rc-update.c
index c1074de..e0726a2 100644
--- a/src/s6-rc/s6-rc-update.c
+++ b/src/s6-rc/s6-rc-update.c
@@ -257,20 +257,17 @@ static void compute_transitions (char const *convfile, unsigned char *oldstate,
    /*
       Convert the old state to the new state: if an old service is up,
       the new service will be either up or wanted up.
-      This part runs in O(oldn*newn). There are no syscalls in the loop,
-      so it should still be negligible unless you have 10k services.
    */
 
-    i = oldn ;
+    i = newn;
     while (i--)
-      if (oldstate[i] & OLDSTATE_WAS_UP) {
-        unsigned int j = newn ;
-        while (j--)
-          if (bitarray_peek(conversion_table + i * newm, j))
-            newstate[j] |=
-              (oldstate[i] & OLDSTATE_WANT_DOWN_OR_RESTART)
+      if (newstate[i] & NEWSTATE_IS_CONVERSION_TARGET) {
+        if (oldstate[invimage[i]] & OLDSTATE_WAS_UP) {
+            newstate[i] |=
+              (oldstate[invimage[i]] & OLDSTATE_WANT_DOWN_OR_RESTART)
               ? NEWSTATE_INCLUDE_IN_UP_TRANSITION
               : (NEWSTATE_WAS_UP | NEWSTATE_WANT_UP_AFTER_CLOSURE) ;
+        }
       }
 
 
-- 
2.41.0