[LLVMdev] MergeFunctions: reduce complexity to O(log(N))
Stepan Dyatkovskiy
stpworld at narod.ru
Thu Feb 27 08:23:58 PST 2014
Hi Nick,
I tried to rework changes as you requested. One of patches (0004 with
extra assertions) has been removed.
> + bool isEquivalentType(Type *Ty1, Type *Ty2) const {
> + return cmpType(Ty1, Ty2) == 0;
> + }
>
> Why do we still need isEquivalentType? Can we nuke this?
Yup. After applying all the patches isEquivalentType will be totally
replaced with cmpType. All isEqXXXX and friends will be removed in 0011
(old 0012). No traces left.
Old function wasn't removed in 0001 just for keeping patches without
extra noise like:
- something that uses isEquivalentType
+ something that uses cmpType
The point is, that "something" that uses isEquivalentType, will be also
replaced with one of next patches in this series.
>
> +static int cmpNumbers(uint64_t L, uint64_t R) {
> + if (L < R) return -1;
> + if (L > R) return 1;
> + return 0;
> +}
>
> At a high level, you don't actually need a <=> operator to use a sort. A
> strict ordering ( < operator) is sufficient. (Note that for mergefunc, a
> strict weak ordering is not sufficient, it must be a total ordering.)
That could be done with int FunctionComparator::compare(). We can
replace it with bool FunctionComparator::less(). Though for all other
cmp methods need at least 2 bits of information as result:
1. Whether things are equal.
2. Whether left less than right.
As for FunctionComparator::compare(), conversion into less() will
increase time of sanity check (patch #0010).
Sanity check is just a sweet bonus. It checks that ordering implemented
properly (checks order relation properties).
Turning compare() into less() mean, that we'll have to run comparison
two times: L.less(R) and R.less(L). But may be sanity check is not a
thing to be published at all.
>
> Consider hoisting this inside the FunctionComparator class? That class
> should have a bunch of implementations of comparisons between various
> different things, which can pass down to other methods in the same class.
In new patch series attached to this post, I have moved all static
methods into FunctionComparator.
> + // Replacement for type::canLosslesslyBitCastTo, that
> + // establish order relation on this kind of properties.
> + int checkForLosslessBitcast(const Type *L, const Type *R);
>
> Type:: not type:: . Please make this comment more descriptive.
Done.
[new comment]
Replacement for Type::canLosslesslyBitCastTo, that
establish order relation on this kind of properties
Returns 0, if L and R types could be converted to each other without
reinterpretation of bits.
Otherwise method returns -1 or 1, defining total ordering between
types in context of lossless bitcastability trait.
E.g.: if L is less than R (result is -1), than every type that could be
losslessly bitcasted to L is less than R.
[/new comment]
>
> + /// Replacement for C1 == getBitCast(C2, C1Ty)
> + /// Its more controllable, and supposed to be simpler and more
> predictionable.
> + /// As very important advantage: it allows to introduce order
relation on
> + /// constants set, and thus use it as trait in refinement routines.
>
> "Its" --> "It's". "predictionable" --> "predictable". And how is it more
> predictable? I think this comment would be better if it described the
> function instead of making comparisons between it and other functions.
> Something like, "Compare constants under a system where pointer to X and
> pointer to Y are considered equal" or whatever is actually true here.
Done.
[new comment]
Replacement for C1 == getBitCast(C2, C1Ty)
Parses constants contents, assuming that types are losslessly
bitcasted between each other. So actually it ignores types and only
compares bits from L and R.
Returns 0, if L and R has equivalent content.
-1 or 1 if values are different. Maintaining total ordering requires
two values that indicates non-equivalence (L less R, L greater R).
[/new comment]
>
> +enum ConstantType {
> I'm not sure that this buys you much. All the "isa" tests can be broken
> down into a switch on getValueID() with the one exception of
isNullValue().
Done.
> + assert(
> + C1->getType()->canLosslesslyBitCastTo(C2->getType()) &&
> + "Pass is healthless. checkForLosslessBitcast should be twin of "
> + "canLosslesslyBitCastTo method, except the case when the last
one "
> + "returns false, the first one should return -1 or 1");
...
> I think we can skip the asserts here. They aren't detecting a specific
> bug, they're checking whether the new code does a certain task relative
> to the old code. Drop the old code, your new code is the new sheriff in
> town.
Asserts has been removed.
>
> + DenseMap<const Value*, int> sn_map1, sn_map2;
>
> What is sn short for ("seen")? Why are there two of these?
Serial number :-)
>
> + std::pair<DenseMap<const Value *, int>::iterator, bool>
> + LeftSN = sn_map1.insert(std::make_pair(V1, sn_map1.size())),
> + RightSN = sn_map2.insert(std::make_pair(V2, sn_map2.size()));
>
> So I think I get it, this is easy to reason about. You number each value
> going down both functions. But I think you can eliminate one of these
> maps because you know that if the left and right were ever different
> then we terminate the comparison immediately. You can at least share one
> map with both V1 and V2, but I think you can reduce the number of map
> insertions.
Not sure. Consider that in left you have:
%A = alloca i32
%B = alloca i32
store i32 1, i32* %A
And in right:
%A = alloca i32
%B = alloca i32
store i32 1, i32* %B
When we meet 'store' instruction we need to check in which order %A was
allocated at left and in which order %B was allocated at right.
So for each value in function we have to assign serial number. Then
comparing to local values from different functions we can just check
their serial numbers.
Though, may be I missed something? May be there is another way to
determine "who was first".
> High-level question, are attributes ordered? Your comparison is ordered.
> So if I have function F with string attributes "sse2", "gc=hemisphere"
> and another function G with string attributes "gc=hemisphere", "sse2"
> then they would be considered different. I don't think that's right.
I didn't check it. But if it is not ordered, we could order it
lexicographically.
>
> + int cmpOperation(const Instruction *I1, const Instruction *I2) const;
> +
> bool isEquivalentOperation(const Instruction *I1,
> - const Instruction *I2) const;
> + const Instruction *I2) const {
> + return cmpOperation(I1, I2) == 0;
> + }
>
> Hopefully this patch series ultimately eliminates calls of
> isEquivalentOperation?
Of course. Just like isEquivalentType.
> By the way, this is an interesting one. Should "add x, y" and "add nsw
> x, y" be equal or not?
Yeah. Those are interesting questions. We could even treat 'mul a, 2'
and 'shl a,1' as equal in some cases. I think it's matter of time and
further optimization.
Please find first reworked patches in attachment.
-Stepan
Nick Lewycky wrote:
> /// Compare two Types, treating all pointer types as equal.
> - bool isEquivalentType(Type *Ty1, Type *Ty2) const;
> + int cmpType(Type *Ty1, Type *Ty2) const;
> +
> + /// Compare two Types, treating all pointer types as equal.
> + bool isEquivalentType(Type *Ty1, Type *Ty2) const {
> + return cmpType(Ty1, Ty2) == 0;
> + }
>
> Why do we still need isEquivalentType? Can we nuke this?
>
> +static int cmpNumbers(uint64_t L, uint64_t R) {
> + if (L < R) return -1;
> + if (L > R) return 1;
> + return 0;
> +}
>
> At a high level, you don't actually need a <=> operator to use a sort. A
> strict ordering ( < operator) is sufficient. (Note that for mergefunc, a
> strict weak ordering is not sufficient, it must be a total ordering.)
>
> Consider hoisting this inside the FunctionComparator class? That class
> should have a bunch of implementations of comparisons between various
> different things, which can pass down to other methods in the same class.
>
> + // Replacement for type::canLosslesslyBitCastTo, that
> + // establish order relation on this kind of properties.
> + int checkForLosslessBitcast(const Type *L, const Type *R);
>
> Type:: not type:: . Please make this comment more descriptive.
>
> + /// Replacement for C1 == getBitCast(C2, C1Ty)
> + /// Its more controllable, and supposed to be simpler and more
> predictionable.
> + /// As very important advantage: it allows to introduce order relation on
> + /// constants set, and thus use it as trait in refinement routines.
>
> "Its" --> "It's". "predictionable" --> "predictable". And how is it more
> predictable? I think this comment would be better if it described the
> function instead of making comparisons between it and other functions.
> Something like, "Compare constants under a system where pointer to X and
> pointer to Y are considered equal" or whatever is actually true here.
>
> +enum ConstantType {
>
> I'm not sure that this buys you much. All the "isa" tests can be broken
> down into a switch on getValueID() with the one exception of isNullValue().
>
> + // Check whether C2 and C1 has equal bit patterns.
> + if (checkForLosslessBitcast(C1->getType(), C2->getType()) != 0)
> + return false;
> +
> + assert(
> + C1->getType()->canLosslesslyBitCastTo(C2->getType()) &&
> + "Pass is healthless. checkForLosslessBitcast should be twin of "
> + "canLosslesslyBitCastTo method, except the case when the last one "
> + "returns false, the first one should return -1 or 1");
> +
> + // Compare constant contents
> + if (cmpConstants(C1, C2) != 0)
> + return false;
> +
> + assert(
> + C1 ==
> + ConstantExpr::getBitCast(const_cast<Constant*>(C2), C1->getType()) &&
> + "Pass is healthless. cmpConstants should detect *subset* of "
> + "equivalent constants that could be detected by "
> + "getBitCast method. So whereas cmpConstants returns 0 "
> + "getBitCast also must return true. And wheres getBitCast "
> + "returns false, cmpConstants also must return -1 or 1.");
>
> I think we can skip the asserts here. They aren't detecting a specific
> bug, they're checking whether the new code does a certain task relative
> to the old code. Drop the old code, your new code is the new sheriff in
> town.
>
> + DenseMap<const Value*, int> sn_map1, sn_map2;
>
> What is sn short for ("seen")? Why are there two of these?
>
> + std::pair<DenseMap<const Value *, int>::iterator, bool>
> + LeftSN = sn_map1.insert(std::make_pair(V1, sn_map1.size())),
> + RightSN = sn_map2.insert(std::make_pair(V2, sn_map2.size()));
>
> So I think I get it, this is easy to reason about. You number each value
> going down both functions. But I think you can eliminate one of these
> maps because you know that if the left and right were ever different
> then we terminate the comparison immediately. You can at least share one
> map with both V1 and V2, but I think you can reduce the number of map
> insertions.
>
> +// Mostly cloned from BitcodeWriter, but simplified a bit.
>
> Missing indent.
>
> +static int cmpAttrs(const AttributeSet L, const AttributeSet R) {
>
> High-level question, are attributes ordered? Your comparison is ordered.
> So if I have function F with string attributes "sse2", "gc=hemisphere"
> and another function G with string attributes "gc=hemisphere", "sse2"
> then they would be considered different. I don't think that's right.
>
> + int cmpOperation(const Instruction *I1, const Instruction *I2) const;
> +
> bool isEquivalentOperation(const Instruction *I1,
> - const Instruction *I2) const;
> + const Instruction *I2) const {
> + return cmpOperation(I1, I2) == 0;
> + }
>
> Hopefully this patch series ultimately eliminates calls of
> isEquivalentOperation?
>
> + if (int Res = cmpNumbers(I1->getRawSubclassOptionalData(),
> + I2->getRawSubclassOptionalData()))
>
> By the way, this is an interesting one. Should "add x, y" and "add nsw
> x, y" be equal or not? Depends whether the backend uses it, and whether
> we're going to do more optimization afterwards (ie., this is the compile
> step of an LTO build). Nothing for you to change here, just want you to
> be aware that this is a point where we might want to have a flag and
> make mergefunc behave differently in different compile strategies.
>
> (I stopped before getting to 0008.)
>
> Nick
>
>
> On 3 February 2014 11:11, Stepan Dyatkovskiy <stpworld at narod.ru
> <mailto:stpworld at narod.ru>> wrote:
>
> Hi all,
>
> Previous patch has been split onto series of small changes.
> On each stage (after each patch) MergeFunctions pass is compilable
> and stable.
>
> Please find patches in attachment for review.
>
> To apply all patches at once, use "apply-patches.sh" script as follows:
> 0. Place "apply-patches.sh" in same directory with patches.
> 1. cd <llvm-sources-dir>
> 2. "bash <path-to-patches-dir>/apply-__patches.sh"
>
> -Stepan
>
> Stepan Dyatkovskiy wrote:
>
> Hi Nick,
> About partition refinement.
>
>
> It looks like patch proposed here allows to apply your idea with
> painless way (as series of small changes actually).
>
> If I got it right, you would like to introduce the next
> partition-refinement.
>
> Initial partition P consists of only one functions class X0 (whole
> module, single bucket). Suppose S is subset of X0, so S represents
> functions with some trait that is absent in rest part of X0.
>
> Then refinement looks like below:
>
> P`=refine(P, S):
> X`[0] = intersection(X[0], S)
> X`[1] = difference(X[0], S) // X0 without S0
>
> so P`={X`[0], X`[1]}
>
> And actually X`[0] and X`[1] are classes of functions that
> differs with
> trait defined by S.
>
> Then (suppose, we need to introduce new trait, so it would be S`):
>
> P``=refine(P`, S`), so each X`` could be defined like below:
> for each X`[i] in P`:
> X``[i*2] = intersection(X`[i], S`)
> X``[i*2+1] = difference(X`[i], S`)
>
> and so on, until all the traits are over.
>
> Finally we got the classes (set of Xs) that consists of equivalent
> functions. So, we can merge functions inside the class bounds.
>
> Am I right?
>
> Patch, that was proposed here could be represented as such partition
> refinement then:
>
> On each refinement stage, you need to introduce S somehow, the
> algorithm
> that answers the question: "what sort of difference we want to
> check in
> this bucket?"
>
> In existing implementation we check traits already, but pair-wise
> (attributes, calling convention, number of arguments, number of
> basic
> blocks, etc.). How to to use the same traits in partition
> refinement?
>
> Consider next example. Suppose we want to split some bucket X:
>
> 0. Take some trait from *pair-wise* comparison. For example:
> number of
> arguments.
> 1. Take some function from bucket X, let it be F1. Let F1 has N1
> number
> of arguments.
> 2. Then S are functions with number of arguments *less* than N1.
> 3. Do refinement by S. As result we got X`[0] and X`[1].
> 4. If both of X`[0] and X`[1] are not empty, then repeat #1-#3
> for them.
> 5. If some of X`[0] of X`[1] is empty set, then all functions in
> X are
> the same in context of trait S. We need another trait, go to #0. And
> repeat #0-#5 for all X` buckets we have.
>
> Finally we got the groups of equivalent functions. And actually
> these
> groups would be organized in binary tree.
> Most of stuff is implemented in std::map. I showed it as #0-#5
> just to
> put it into context of your idea. The only problem was to
> introduce way
> of how to define order-relation (or how to define S). But this
> problem
> has been solved.
> And on output we got groups of equal functions.
>
> Fix me if I'm wrong. But it looks like every advantage given by
> partition refinement is present here.
>
> As I said in beginning, it is way of how to commit things you
> proposed
> with minimum of changes. We will use old comparison routines,
> only thing
> we need to change is return type (from bool to -1,0,1).
> In this way, partition refinement could be committed as series
> of small
> changes: one comparison routine per commit.
>
> Every change in MergeFunctions from now could be well checked by
> this
> builder:
> Now we have special builder for MergeFunctions. It runs
> test-suite with
> forced MergeFunctions pass:
> http://lab.llvm.org:8011/__builders/clang-mergefunc-x86___64-freeBSD9.2
> <http://lab.llvm.org:8011/builders/clang-mergefunc-x86_64-freeBSD9.2>
> Currently, MergeFunctions pass is stable, builder is green and
> passes
> all test-suite programs.
>
> -Stepan.
>
> Stepan Dyatkovskiy wrote:
>
> Hi all,
> Please find the updated patch in attachment:
> * Added some comments.
> * Fixed some typos.
>
> -Stepan
>
> Nick Lewycky wrote:
>
> On 30 January 2014 01:27, Stepan Dyatkovskiy
> <stpworld at narod.ru <mailto:stpworld at narod.ru>
> <mailto:stpworld at narod.ru <mailto:stpworld at narod.ru>>>
> wrote:
>
> Hello Sean and Tobias,
>
> Sean,
> Thank you. Could you describe Nick's ideas in few
> words or give me
> links to your discussion, so I could adapt my ideas
> to it.
>
>
> Sorry I haven't had time to write it up. The essential
> idea is that we
> use partition-refinement to determine the differences
> between a group of
> functions instead of using pair-wise comparison.
>
> Imagine you want to compare long sequences of numbers.
> You can grab a
> pair of sequences and run down them until they differ or
> you reach the
> end, and move on to another pair of sequences. With
> partition refinement
> you start with the first number in all the sequences and
> bucket them.
> Say, three 1's, two 2's, and an 8. You've just formed 3
> buckets. For
> each bucket (with more than 1 member), do it again with
> the next number
> in the sequence. This gets you an equivalence comparison
> at less than
> the complexity of pairwise comparisons. (The buckets are
> partitions, and
> you're refining them as you read more data. Partition
> refinement is the
> dual of union-find, which we use quite heavily in the
> compiler.)
>
> I haven't figured out how this stacks up against
> Stepan's sorting with
> <=> comparison. I can probably do that, I just haven't
> spent the time
> thinking about it.
>
> I also haven't thought through how to integrate it with
> "near miss"
> comparison. My current leading idea is that you do the
> same thing, but
> make a record of what makes two buckets similar. (Note
> that the wrong
> solution is to store a per-function-pair list of
> similarities/differences.)
>
> Nick
>
> Tobias,
> Your patch fails on several modules in my benchmark
> (73 of ~1800
> tests). I have sent one as attachment.
>
> See statistics files for more details, all the .ll
> files you could
> simply find in test-suite object directory (after
> "make TEST=nightly
> report").
> I have attached script that launches benchmark.
> Example of usage
> (you need Linux OS):
> bash test-scipt.sh report.txt opt-no-patch
> opt-with-patch
>
> Some numbers.
>
> Total number of functions: 52715
>
> Below, by default, I have excluded modules where
> your patch fails.
>
> Functions merged
> Original version: 1113
> Order relation patch: 1112
> Similar merging patch: 541
>
> Functions merged (including failed tests)
> Original version: 8398
> Order relation patch: 8395
>
> Summary files size
> Initial: 163595634
> bytes.
> After merging with order relation patch: 163147731
> bytes.
> After similar merging patch: 162491905
> bytes.
>
> Summary files size (including failed tests)
> Initial: 250242266 bytes.
> Original version: 247168198 bytes.
> Order relation: 247175650 bytes.
>
> Time. I measured with "time" utility, and used
> "real (wall clock)
> time used by the process".
>
> Summary time spent
> With existing version: 28.05 secs.
> With order relation patch: 28.19 secs.
> Similar merging patch: 28.61 secs.
>
> Summary time spent (including failed tests)
> With existing version: 41.74 secs.
> With order relation patch: 36.35 secs.
>
> -Stepan
>
> Sean Silva wrote:
>
>
>
>
> On Tue, Jan 28, 2014 at 2:47 PM, Tobias von Koch
> <tobias.von.koch at gmail.com
> <mailto:tobias.von.koch at gmail.com>
> <mailto:tobias.von.koch at gmail.__com
> <mailto:tobias.von.koch at gmail.com>>
> <mailto:tobias.von.koch at gmail.
> <mailto:tobias.von.koch at gmail.>____com
> <mailto:tobias.von.koch at gmail.__com
> <mailto:tobias.von.koch at gmail.com>>>> wrote:
>
> Hi Stepan,
>
> Sorry for the delay. It's great that you
> are working on
> MergeFunctions as well and I agree, we
> should definitely
> try to
> combine our efforts to improve MergeFunctions.
>
> Just to give you some context, the pass
> (with the similar
> function
> merging patch) is already being used in a
> production
> setting. From
> my point of view, it would be better if we
> focus on
> improving its
> capability of merging functions at this
> stage rather
> than on
> reduction of compilation time.
>
> I'll give a brief overview of how our
> similar function
> merging
> algorithm works (you can also watch the
> presentation from
> the US
> LLVM conference to hear me explain it
> using an animation).
>
> 1. Hash all functions into buckets
>
> In each bucket, separately:
>
> 2. Compare functions pair-wise and
> determine a
> similarity metric for each pair (%age
> of equivalent
> instructions)
>
> 3. Merge identical functions (with
> similarity = 100%),
> update call
> sites for those functions.
>
> 4. If the updates of call sites have
> touched other
> functions,
> go back to step 2 and re-compare
> *only* those
> functions to all
> others in their buckets.
>
> Finally,
>
> 5. Form groups of similar functions for
> merging:
> a) Pick most similar pair (A,B)
> b) Find all functions C that are also
> similar to B but
> are not
> more similar to some other function D.
> c) Merge A with B and all the C's.
> Repeat until there are no more
> functions to merge.
>
> As you can see, we need to compute a
> similarity measure for
> each
> pair of functions in a bucket. If I
> understand correctly,
> your patch
> reduces compile-time by avoiding
> comparisons of functions
> that
> cannot be identical. That's exactly what
> you want to do if
> you only
> want to merge identical functions.
> However, because we also
> need to
> determine whether functions are merely
> *similar*, I can't
> see how
> your idea could be applied in that case.
>
>
> Yeah, the existing pass only tries to merge
> identical functions
> (identical in machine code). I'm wondering if
> the "similar"
> function
> merging would be better as a separate pass (I'm
> genuinely
> wondering; I
> have no clue). I would wait for Nick's feedback.
>
> -- Sean Silva
>
>
> Looking at your statistics, I see that you
> are considering
> a very
> large number of functions. I don't know
> which benchmarks
> you are
> using, but I doubt that many of these are
> worth merging.
> For
> instance, you rarely gain a code size
> benefit from merging
> functions
> with just a few instructions. Our patch
> takes care of this
> using
> thresholds. It's worth looking at actual
> code size
> reductions,
> rather than just numbers of functions
> merged/ compilation
> time spent
> comparing functions. It turns out that the
> number of
> functions in
> each bucket is really quite small once you
> apply some
> heuristics
> (and could still be further reduced!).
>
> Given your experience with MergeFunctions,
> it would be
> really great
> if you could review our patch and also try
> it out on your
> benchmarks.
>
> Tobias
>
>
> On 24/01/2014 19:11, Stepan Dyatkovskiy wrote:
>
> Hi Tobias.
>
> So, what do you think?
>
> If it means to much extra-job for your
> team, may be I
> can help you
> somehow? I really would like to.
>
> -Stepan
>
> Stepan Dyatkovskiy wrote:
>
> Hi Tobias,
>
> I can't really see a way to
> combine our
> approach with
> your patch. What
> are your thoughts?
>
>
> I think it is possible. Even more
> - we need to
> combine our
> efforts, in
> order to bring this pass into real
> live.
> I'have read your presentation
> file, and
> unfortunately read
> your patch
> only a little.
> How exactly you scan functions on
> 2nd stage?
> Could you
> explain the
> algorithm in few words, how you
> compare workflow?
> Is it
> possible to
> scan binary tree instead of hash
> table? ...OK.
>
> That's how I see the modification.
> Now its
> important to
> explain idea,
> so consider the simplest case: you
> need to catch
> two
> functions that
> are differs with single
> instruction somewhere.
>
> 1. Imagine, that IR *module*
> contents is
> represented as
> binary tree:
> Each line (trace) from root to
> terminal node is a
> function.
> Each node - is function's
> primitive (instruction
> opcode, for
> example).
> Down - is direction to terminal
> nodes, up - is
> direction to
> the root.
>
> 2. Now you are standing on some
> node. And you
> have two
> directions
> down-left and down-right.
>
> 3. If you are able to find two
> equal sub-traces
> down (at
> left and at
> right), then the only difference
> lies in this node.
> Then we
> catch that
> case.
>
> 4. Even more, if two subtrees at
> left and at
> right are
> equal, than you
> catch at once all the cases that
> are represented by
> these
> subtrees.
>
> I still didn't look at you patch
> carefully. Sorry..
> But I
> hope that
> helps, and I'll try look at it in
> nearest time and
> perhaps
> its not the
> best solution I gave in this post.
>
> -Stepan
>
> 22.01.2014, 20:53, "Tobias von Koch"
> <tobias.von.koch at gmail.com
> <mailto:tobias.von.koch at gmail.com>
> <mailto:tobias.von.koch at gmail.__com
> <mailto:tobias.von.koch at gmail.com>>
> <mailto:tobias.von.koch at gmail.
> <mailto:tobias.von.koch at gmail.>____com
> <mailto:tobias.von.koch at gmail.__com
> <mailto:tobias.von.koch at gmail.com>>>>:
>
>
> Hi Stepan,
>
> As you've seen we have
> recently implemented a
> significant enhancement to
> the MergeFunctions pass that
> also allows
> merging of
> functions that are
> only similar but not identical
>
> (http://llvm-reviews.__chandle____rc.com/D2591
> <http://chandle__rc.com/D2591>
> <http://chandlerc.com/D2591>
>
> <http://llvm-reviews.__chandle__rc.com/D2591
> <http://chandlerc.com/D2591>
> <http://llvm-reviews.__chandlerc.com/D2591
> <http://llvm-reviews.chandlerc.com/D2591>>>).
>
>
> Our patch also changes the way
> that functions
> are
> compared quite
> significantly. This is
> necessary because we
> need to
> compare all
> functions in a bucket in order
> to get a
> similarity
> measure for each
> pair, so we can then decide
> which 'groups' of
> functions
> to merge.
>
> I can't really see a way to
> combine our
> approach with
> your patch. What
> are your thoughts?
>
> Another way to improve the
> performance of
> MergeFunctions
> might be to
> make the hash function better.
> I've already
> added the
> size of the first
> BB to it, and perhaps there
> are other factors
> we could
> try... if we
> don't have to compare
> functions in the first
> place
> (because they're in
> different buckets) then that's
> obviously a much
> bigger win.
>
> Thanks,
> Tobias
>
> On 17/01/2014 20:25, Stepan
> Dyatkovskiy wrote:
>
> Hi all,
>
> I propose simple
> improvement for
> MergeFunctions
> pass, that reduced
> its
> complexity from O(N^2)
> to O(log(N)),
> where N is
> number of
> functions in
> module.
>
> The idea, is to replace
> the result of
> comparison
> from "bool" to
> "-1,0,1". In another
> words: define order
> relation
> on functions set.
> To be sure, that
> functions could be
> comparable
> that way, we have to
> prove that order
> relation is possible
> on all
> comparison stage.
>
> The last one is
> possible, if for each
> comparison
> stage we
> implement has
> next properties:
> * reflexivity (a <= a,
> a == a, a >= a),
> * antisymmetry (if a <=
> b and b <= a
> then a == b),
> * transitivity (a <= b
> and b <= c, then
> a <= c)
> * asymmetry (if a < b,
> then a > b or a
> == b).
>
> Once we have defined
> order relation we
> can store
> all the functions in
> binary tree and perform
> lookup in
> O(log(N)) time.
>
> This post has two
> attachments:
> 1. The patch, that has
> implementation of
> this idea.
> 2. The MergeFunctions
> pass detailed
> description,
> with explanation how
> order relation could be
> possible.
>
> Hope it helps to make
> things better!
>
> -Stepan.
>
>
>
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