operations on the call graph. This one forms a cycle, and while not as
complex as removing an internal edge from an SCC, it involves
a reasonable amount of work to find all of the nodes newly connected in
a cycle.
Also somewhat alarming is the worst case complexity here: it might have
to walk roughly the entire SCC inverse DAG to insert a single edge. This
is carefully documented in the API (I hope).
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just connects an SCC to one of its descendants directly. Not much of an
impact. The last one is the hard one -- connecting an SCC to one of its
ancestors, and thereby forming a cycle such that we have to merge all
the SCCs participating in the cycle.
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of SCCs in the SCC DAG. Exercise them in the big graph test case. These
will be especially useful for establishing invariants in insertion
logic.
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edge entirely within an existing SCC. Shockingly, making the connected
component more connected is ... a total snooze fest. =]
Anyways, its wired up, and I even added a test case to make sure it
pretty much sorta works. =D
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bits), and discover that it's totally broken. Yay tests. Boo bug. Fix
the basic edge removal so that it works by nulling out the removed edges
rather than actually removing them. This leaves the indices valid in the
map from callee to index, and preserves some of the locality for
iterating over edges. The iterator is made bidirectional to reflect that
it now has to skip over null entries, and the skipping logic is layered
onto it.
As future work, I would like to track essentially the "load factor" of
the edge list, and when it falls below a threshold do a compaction.
An alternative I considered (and continue to consider) is storing the
callees in a doubly linked list where each element of the list is in
a set (which is essentially the classical linked-hash-table
datastructure). The problem with that approach is that either you need
to heap allocate the linked list nodes and use pointers to them, or use
a bucket hash table (with even *more* linked list pointer overhead!),
etc. It's pretty easy to get 5x overhead for values that are just
pointers. So far, I think punching holes in the vector, and periodic
compaction is likely to be much more efficient overall in the space/time
tradeoff.
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contract (and be much more useful). It now provides exactly the
post-order traversal a caller might need to perform on newly formed
SCCs.
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API requirements much more obvious.
The key here is that there are two totally different use cases for
mutating the graph. Prior to doing any SCC formation, it is very easy to
mutate the graph. There may be users that want to do small tweaks here,
and then use the already-built graph for their SCC-based operations.
This method remains on the graph itself and is documented carefully as
being cheap but unavailable once SCCs are formed.
Once SCCs are formed, and there is some in-flight DFS building them, we
have to be much more careful in how we mutate the graph. These mutation
operations are sunk onto the SCCs themselves, which both simplifies
things (the code was already there!) and helps make it obvious that
these interfaces are only applicable within that context. The other
primary constraint is that the edge being mutated is actually related to
the SCC on which we call the method. This helps make it obvious that you
cannot arbitrarily mutate some other SCC.
I've tried to write much more complete documentation for the interesting
mutation API -- intra-SCC edge removal. Currently one aspect of this
documentation is a lie (the result list of SCCs) but we also don't even
have tests for that API. =[ I'm going to add tests and fix it to match
the documentation next.
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them, just skip over any DFS-numbered nodes when finding the next root
of a DFS. This allows the entry set to just be a vector as we populate
it from a uniqued source. It also removes the possibility for a linear
scan of the entry set to actually do the removal which can make things
go quadratic if we get unlucky.
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the DFS stack for leaves in the call graph. As mentioned in my previous
commit, this is particularly interesting for graphs which have high fan
out but low connectivity resulting in many leaves. For such graphs, this
can remove a large % of the DFS stack traffic even though it doesn't
make the stack much smaller.
It's a bit easier to formulate this for the full algorithm because that
one stops completely for each SCC. For example, I was able to directly
eliminate the "Recurse" boolean used to continue an outer loop from the
inner loop.
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makes working through the worklist much cleaner, and makes it possible
to avoid the 'bool-to-continue-the-outer-loop' hack. Not a huge
difference, but I think this is approaching as polished as I can make
it.
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processed in the DFS out of the stack completely. Keep it exclusively in
a variable. Re-shuffle some code structure to make this easier. This can
have a very dramatic effect in some cases because call graphs tend to
look like a high fan-out spanning tree. As a consequence, there are
a large number of leaf nodes in the graph, and this technique causes
leaf nodes to never even go into the stack. While this only reduces the
max depth by 1, it may cause the total number of round trips through the
stack to drop by a lot.
Now, most of this isn't really relevant for the incremental version. =]
But I wanted to prototype it first here as this variant is in ways more
complex. As long as I can get the code factored well here, I'll next
make the primary walk look the same. There are several refactorings this
exposes I think.
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graph in any way because we don't track edges in the SCC graph, just
nodes. This also lets us add a nice assert about the invariant that
we're working on at least a certain number of nodes within the SCC.
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a helper function. Also factor the other two places where we did the
same thing into the helper function. =] Much cleaner this way. NFC.
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SCCMap to test for nodes that have been re-added to the root SCC rather
than a set vector. We already have done the SCCMap lookup, we juts need
to test it in two different ways. In turn, do most of the processing of
these nodes as they go into the root SCC rather than lazily. This
simplifies the final loop to just stitch the root SCC into its
children's parent sets. No functionlatiy changed.
However, this makes a few things painfully obvious, which was my intent.
=] There is tons of repeated code introduced here and elsewhere. I'm
splitting the refactoring of that code into helpers from this change so
its clear that this is the change which switches the datastructures used
around, and the other is a pure factoring & deduplication of code
change.
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remove the nodes in the SCC from the SCC map entirely prior to the DFS
walk. This allows the SCC map to represent both the state of
not-yet-re-added-to-an-SCC and added-back-to-this-SCC independently. The
first is being missing from the SCC map, the second is mapping back to
'this'. In a subsequent commit, I'm going to use this property to
simplify the new node list for this SCC.
In theory, I think this also makes the contract for orphaning a node
from the graph slightly less confusing. Now it is also orphaned from the
SCC graph. Still, this isn't quite right either, and so I'm not adding
test cases here. I'll add test cases for the behavior of orphaning nodes
when the code *actually* supports it. The change here is mostly
incidental, my goal is simplifying the algorithm.
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child from the worklist, wait until we actually need to pop another
element off of the worklist and skip over any that were already visited
by the DFS. This also enables swapping the nodes of the SCC into the
worklist. No functionality changed.
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thing, just mucking up the code. I feel bad that I even wrote this loop.
Very sorry. The diff is huge because of the indent change, but I promise
all this is doing is realizing that the outer two loops were actually
the exact same loops, and we didn't need two of them.
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factored into a more reasonable form, replace the tail call with
a simple outer-loop continuation. It's sad that C++ makes this so
awkward to write, but it seems more direct and clear than the tail call
at this point.
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condition into an obviously infinite loop with an assert about the
degenerate condition. No functionality changed.
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algorithm here: http://dl.acm.org/citation.cfm?id=177301.
The idea of isolating the roots has even more relevance when using the
stack not just to implement the DFS but also to implement the recursive
step. Because we use it for the recursive step, to isolate the roots we
need to maintain two stacks: one for our recursive DFS walk, and another
of the nodes that have been walked. The nice thing is that the latter
will be half the size. It also fixes a complete hack where we scanned
backwards over the stack to find the next potential-root to continue
processing. Now that is always the top of the DFS stack.
While this is a really nice improvement already (IMO) it further opens
the door for two important simplifications:
1) De-duplicating some of the code across the two different walks. I've
actually made the duplication a bit worse in some senses with this
patch because the two are starting to converge.
2) Dramatically simplifying the loop structures of both walks.
I wanted to do those separately as they'll be essentially *just* CFG
restructuring. This patch on the other hand actually uses different
datastructures to implement the algorithm itself.
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applied prior to pushing a node onto the DFSStack. This is the first
step toward avoiding the stack entirely for leaf nodes. It also
simplifies things a bit and I think is pointing the way toward factoring
some more of the shared logic out of the two implementations.
It is also making it more obvious how to restructure the loops
themselves to be a bit easier to read (although no different in terms of
functionality).
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a SmallPtrSet. Currently, there is no need for stable iteration in this
dimension, and I now thing there won't need to be going forward.
If this is ever re-introduced in any form, it needs to not be
a SetVector based solution because removal cannot be linear. There will
be many SCCs with large numbers of parents. When encountering these, the
incremental SCC update for intra-SCC edge removal was quadratic due to
linear removal (kind of).
I'm really hoping we can avoid having an ordering property here at all
though...
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than functions. So far, this access pattern is *much* more common. It
seems likely that any user of this interface is going to have nodes at
the point that they are querying the SCCs.
No functionality changed.
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values rather than an expensive dense map query to test whether children
have already been popped into an SCC. This matches the incremental SCC
building code. I've also included the assert that I put there but
updated both of their text.
No functionality changed here.
I still don't have any great ideas for sharing the code between the two
implementations, but I may try a brute-force approach to factoring it at
some point.
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This implements the core functionality necessary to remove an edge from
the call graph and correctly update both the basic graph and the SCC
structure. As part of that it has to run a tiny (in number of nodes)
Tarjan-style DFS walk of an SCC being mutated to compute newly formed
SCCs, etc.
This is *very rough* and a WIP. I have a bunch of FIXMEs for code
cleanup that will reduce the boilerplate in this change substantially.
I also have a bunch of simplifications to various parts of both
algorithms that I want to make, but first I'd like to have a more
holistic picture. Ideally, I'd also like more testing. I'll probably add
quite a few more unit tests as I go here to cover the various different
aspects and corner cases of removing edges from the graph.
Still, this is, so far, successfully updating the SCC graph in-place
without disrupting the identity established for the existing SCCs even
when we do challenging things like delete the critical edge that made an
SCC cycle at all and have to reform things as a tree of smaller SCCs.
Getting this to work is really critical for the new pass manager as it
is going to associate significant state with the SCC instance and needs
it to be stable. That is also the motivation behind the return of the
newly formed SCCs. Eventually, I'll wire this all the way up to the
public API so that the pass manager can use it to correctly re-enqueue
newly formed SCCs into a fresh postorder traversal.
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up the stack finishing the exploration of each entries children before
we're finished in addition to accounting for their low-links. Added
a unittest that really hammers home the need for this with interlocking
cycles that would each appear distinct otherwise and crash or compute
the wrong result. As part of this, nuke a stale fixme and bring the rest
of the implementation still more closely in line with the original
algorithm.
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resisted this for too long. Just with the basic testing here I was able
to exercise the analysis in more detail and sift out both type signature
bugs in the API and a bug in the DFS numbering. All of these are fixed
here as well.
The unittests will be much more important for the mutation support where
it is necessary to craft minimal mutations and then inspect the state of
the graph. There is just no way to do that with a standard FileCheck
test. However, unittesting these kinds of analyses is really quite easy,
especially as they're designed with the new pass manager where there is
essentially no infrastructure required to rig up the core logic and
exercise it at an API level.
As a minor aside about the DFS numbering bug, the DFS numbering used in
LCG is a bit unusual. Rather than numbering from 0, we number from 1,
and use 0 as the sentinel "unvisited" state. Other implementations often
use '-1' for this, but I find it easier to deal with 0 and it shouldn't
make any real difference provided someone doesn't write silly bugs like
forgetting to actually initialize the DFS numbering. Oops. ;]
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into a helper function. I plan to re-use it for doing incremental
DFS-based updates to the SCCs when we mutate the call graph.
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the Callee list. This is going to be quite important to prevent removal
from going quadratic. No functionality changed at this point, this is
one of the refactoring patches I've broken out of my initial work toward
mutation updates of the call graph.
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definition below all the header #include lines, lib/Analysis/...
edition.
This one has a bit extra as there were *other* #define's before #include
lines in addition to DEBUG_TYPE. I've sunk all of them as a block.
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Reality is that we're never going to copy one of these. Supporting this
was becoming a nightmare because nothing even causes it to compile most
of the time. Lots of subtle errors built up that wouldn't have been
caught by any "normal" testing.
Also, make the move assignment actually work rather than the bogus swap
implementation that would just infloop if used. As part of that, factor
out the graph pointer updates into a helper to share between move
construction and move assignment.
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LazyCallGraph. This is the start of the whole point of this different
abstraction, but it is just the initial bits. Here is a run-down of
what's going on here. I'm planning to incorporate some (or all) of this
into comments going forward, hopefully with better editing and wording.
=]
The crux of the problem with the traditional way of building SCCs is
that they are ephemeral. The new pass manager however really needs the
ability to associate analysis passes and results of analysis passes with
SCCs in order to expose these analysis passes to the SCC passes. Making
this work is kind-of the whole point of the new pass manager. =]
So, when we're building SCCs for the call graph, we actually want to
build persistent nodes that stick around and can be reasoned about
later. We'd also like the ability to walk the SCC graph in more complex
ways than just the traditional postorder traversal of the current CGSCC
walk. That means that in addition to being persistent, the SCCs need to
be connected into a useful graph structure.
However, we still want the SCCs to be formed lazily where possible.
These constraints are quite hard to satisfy with the SCC iterator. Also,
using that would bypass our ability to actually add data to the nodes of
the call graph to facilite implementing the Tarjan walk. So I've
re-implemented things in a more direct and embedded way. This
immediately makes it easy to get the persistence and connectivity
correct, and it also allows leveraging the existing nodes to simplify
the algorithm. I've worked somewhat to make this implementation more
closely follow the traditional paper's nomenclature and strategy,
although it is still a bit obtuse because it isn't recursive, using
an explicit stack and a tail call instead, and it is interruptable,
resuming each time we need another SCC.
The other tricky bit here, and what actually took almost all the time
and trials and errors I spent building this, is exactly *what* graph
structure to build for the SCCs. The naive thing to build is the call
graph in its newly acyclic form. I wrote about 4 versions of this which
did precisely this. Inevitably, when I experimented with them across
various use cases, they became incredibly awkward. It was all
implementable, but it felt like a complete wrong fit. Square peg, round
hole. There were two overriding aspects that pushed me in a different
direction:
1) We want to discover the SCC graph in a postorder fashion. That means
the root node will be the *last* node we find. Using the call-SCC DAG
as the graph structure of the SCCs results in an orphaned graph until
we discover a root.
2) We will eventually want to walk the SCC graph in parallel, exploring
distinct sub-graphs independently, and synchronizing at merge points.
This again is not helped by the call-SCC DAG structure.
The structure which, quite surprisingly, ended up being completely
natural to use is the *inverse* of the call-SCC DAG. We add the leaf
SCCs to the graph as "roots", and have edges to the caller SCCs. Once
I switched to building this structure, everything just fell into place
elegantly.
Aside from general cleanups (there are FIXMEs and too few comments
overall) that are still needed, the other missing piece of this is
support for iterating across levels of the SCC graph. These will become
useful for implementing #2, but they aren't an immediate priority.
Once SCCs are in good shape, I'll be working on adding mutation support
for incremental updates and adding the pass manager that this analysis
enables.
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graph. This simplifies the custom move constructor operation to one of
walking the graph and updating the 'up' pointers to point to the new
location of the graph. Switch the nodes from a reference to a pointer
for the 'up' edge to facilitate this.
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operand_values. The first provides a range view over operand Use
objects, and the second provides a range view over the Value*s being
used by those operands.
The naming is "STL-style" rather than "LLVM-style" because we have
historically named iterator methods STL-style, and range methods seem to
have far more in common with their iterator counterparts than with
"normal" APIs. Feel free to bikeshed on this one if you want, I'm happy
to change these around if people feel strongly.
I've switched code in SROA and LCG to exercise these mostly to ensure
they work correctly -- we don't really have an easy way to unittest this
and they're trivial.
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