From 7065234c158d8a05018785fb4e6ee3dd18dcf766 Mon Sep 17 00:00:00 2001
From: Matt Wala <wala1@illinois.edu>
Date: Tue, 13 Dec 2016 18:57:11 -0600
Subject: [PATCH] find_idempotence(): Replace fixed point iteration with a
 check based on SCCs (closes #16).

---
 loopy/preprocess.py | 93 ++++++++++++++++++++++++++++++---------------
 1 file changed, 62 insertions(+), 31 deletions(-)

diff --git a/loopy/preprocess.py b/loopy/preprocess.py
index 6b5488a20..9a0a5b233 100644
--- a/loopy/preprocess.py
+++ b/loopy/preprocess.py
@@ -738,52 +738,83 @@ def find_idempotence(kernel):
             (insn.id, insn.read_dependency_names() & var_names)
             for insn in kernel.instructions)
 
-    non_idempotently_updated_vars = set()
-
-    # FIXME: This can be made more efficient by simply starting
-    # from all written variables and not even considering
-    # instructions as the start of the first pass.
+    dep_graph = {}
 
-    new_insns = []
     for insn in kernel.instructions:
-        all_my_var_writers = set()
-        for var in reads_map[insn.id]:
-            var_writers = writer_map.get(var, set())
-            all_my_var_writers |= var_writers
-
-        # {{{ find dependency loops, flag boostability
-
-        while True:
-            last_all_my_var_writers = all_my_var_writers
-
-            for writer_insn_id in last_all_my_var_writers:
-                for var in reads_map[writer_insn_id]:
-                    all_my_var_writers = \
-                            all_my_var_writers | writer_map.get(var, set())
+        dep_graph[insn.id] = set(writer_id
+                for var in reads_map[insn.id]
+                for writer_id in writer_map.get(var, set()))
+
+    # {{{ find SCCs of dep_graph
+
+    def dfs(graph, root_node=None, exclude=frozenset()):
+        postorder = []
+        visited = set()
+        have_root_node = root_node is not None
+        to_search = set([root_node] if have_root_node else graph.keys())
+
+        while to_search:
+            stack = [next(iter(to_search))]
+            visiting = set()
+
+            while stack:
+                top = stack[-1]
+                if top in visiting:
+                    visiting.discard(top)
+                    postorder.append(top)
+                    to_search.discard(top)
+                if top in visited:
+                    stack.pop()
+                else:
+                    visiting.add(top)
+                    visited.add(top)
+                    stack.extend(
+                            item for item in graph[top]
+                            if item not in visited and item not in exclude)
+
+        return postorder
+
+    inv_dep_graph = dict((insn.id, set()) for insn in kernel.instructions)
+    for key, vals in six.iteritems(dep_graph):
+        for val in vals:
+            inv_dep_graph[val].add(key)
+
+    postorder = dfs(inv_dep_graph)
+
+    sccs = {}
+    exclude = set()
+
+    for item in reversed(postorder):
+        if item in sccs:
+            continue
+        scc = dfs(dep_graph, root_node=item, exclude=exclude)
+        exclude.update(scc)
+        for scc_item in scc:
+            sccs[scc_item] = scc
 
-            if last_all_my_var_writers == all_my_var_writers:
-                break
+    # }}}
 
-        # }}}
+    non_idempotently_updated_vars = set()
 
-        boostable = insn.id not in all_my_var_writers
+    new_insns = []
+    for insn in kernel.instructions:
+        boostable = len(sccs[insn.id]) == 1 and insn.id not in dep_graph[insn.id]
 
         if not boostable:
             non_idempotently_updated_vars.update(
                     insn.assignee_var_names())
 
-        insn = insn.copy(boostable=boostable)
-
-        new_insns.append(insn)
+        new_insns.append(insn.copy(boostable=boostable))
 
     # {{{ remove boostability from isns that access non-idempotently updated vars
 
     new2_insns = []
     for insn in new_insns:
-        accessed_vars = insn.dependency_names()
-        boostable = insn.boostable and not bool(
-                non_idempotently_updated_vars & accessed_vars)
-        new2_insns.append(insn.copy(boostable=boostable))
+        if insn.boostable and bool(
+                non_idempotently_updated_vars & insn.dependency_names()):
+            new2_insns.append(insn.copy(boostable=False))
+        else:
+            new2_insns.append(insn)
 
     # }}}
 
-- 
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