MergeFunctions pass, how it works

Introduction

Sometimes code contains equal functions, or functions that does exactly the samething even though they are non-equal on the IR level (e.g.: multiplication on 2and ‘shl 1’). It could happen due to several reasons: mainly, the usage oftemplates and automatic code generators. Though, sometimes the user itself couldwrite the same thing twice :-)

The main purpose of this pass is to recognize such functions and merge them.

This document is the extension to pass comments and describes the pass logic. Itdescribes the algorithm that is used in order to compare functions andexplains how we could combine equal functions correctly to keep the modulevalid.

Material is brought in a top-down form, so the reader could start to learn passfrom high level ideas and end with low-level algorithm details, thus preparinghim or her for reading the sources.

The main goal is to describe the algorithm and logic here and the concept. Ifyou don’t want to read the source code, but want to understand passalgorithms, this document is good for you. The author tries not to repeat thesource-code and covers only common cases to avoid the cases of needing toupdate this document after any minor code changes.

What should I know to be able to follow along with this document?

The reader should be familiar with common compile-engineering principles andLLVM code fundamentals. In this article, we assume the reader is familiar withSingle Static Assignmentconcept and has an understanding ofIR structure.

We will use terms such as“module”,“function”,“basic block”,“user”,“value”,“instruction”.

As a good starting point, the Kaleidoscope tutorial can be used:

LLVM Tutorial: Table of Contents

It’s especially important to understand chapter 3 of tutorial:

Kaleidoscope Tutorial

The reader should also know how passes work in LLVM. They could use thisarticle as a reference and start point here:

Writing an LLVM Pass

What else? Well perhaps the reader should also have some experience in LLVM passdebugging and bug-fixing.

Narrative structure

The article consists of three parts. The first part explains pass functionalityon the top-level. The second part describes the comparison procedure itself.The third part describes the merging process.

In every part, the author tries to put the contents in the top-down form.The top-level methods will first be described followed by the terminal ones atthe end, in the tail of each part. If the reader sees the reference to themethod that wasn’t described yet, they will find its description a bit below.

Basics

How to do it?

Do we need to merge functions? The obvious answer is: Yes, that is quite apossible case. We usually do have duplicates and it would be good to get ridof them. But how do we detect duplicates? This is the idea: we split functionsinto smaller bricks or parts and compare the “bricks” amount. If equal,we compare the “bricks” themselves, and then do our conclusions about functionsthemselves.

What could the difference be? For example, on a machine with 64-bit pointers(let’s assume we have only one address space), one function stores a 64-bitinteger, while another one stores a pointer. If the target is the machinementioned above, and if functions are identical, except the parameter type (wecould consider it as a part of function type), then we can treat a uint64_tand a void* as equal.

This is just an example; more possible details are described a bit below.

As another example, the reader may imagine two more functions. The firstfunction performs a multiplication on 2, while the second one performs anarithmetic right shift on 1.

Possible solutions

Let’s briefly consider possible options about how and what we have to implementin order to create full-featured functions merging, and also what it wouldmean for us.

Equal function detection obviously supposes that a “detector” method to beimplemented and latter should answer the question “whether functions are equal”.This “detector” method consists of tiny “sub-detectors”, which each answersexactly the same question, but for function parts.

As the second step, we should merge equal functions. So it should be a “merger”method. “Merger” accepts two functions F1 and F2, and produces _F1F2_function, the result of merging.

Having such routines in our hands, we can process a whole module, and merge allequal functions.

In this case, we have to compare every function with every another function. Asthe reader may notice, this way seems to be quite expensive. Of course we couldintroduce hashing and other helpers, but it is still just an optimization, andthus the level of O(N*N) complexity.

Can we reach another level? Could we introduce logarithmical search, or randomaccess lookup? The answer is: “yes”.

Random-access

How it could this be done? Just convert each function to a number, and gatherall of them in a special hash-table. Functions with equal hashes are equal.Good hashing means, that every function part must be taken into account. Thatmeans we have to convert every function part into some number, and then add itinto the hash. The lookup-up time would be small, but such a approach adds somedelay due to the hashing routine.

Logarithmical search

We could introduce total ordering among the functions set, once ordered wecould then implement a logarithmical search. Lookup time still depends on N,but adds a little of delay (log(N)).

Present state

Both of the approaches (random-access and logarithmical) have been implementedand tested and both give a very good improvement. What was mostsurprising is that logarithmical search was faster; sometimes by up to 15%. Thehashing method needs some extra CPU time, which is the main reason why it worksslower; in most cases, total “hashing” time is greater than total“logarithmical-search” time.

So, preference has been granted to the “logarithmical search”.

Though in the case of need, logarithmical-search (read “total-ordering”) couldbe used as a milestone on our way to the random-access implementation.

Every comparison is based either on the numbers or on the flags comparison. Inthe random-access approach, we could use the same comparison algorithm.During comparison, we exit once we find the difference, but here we might haveto scan the whole function body every time (note, it could be slower). Like in“total-ordering”, we will track every number and flag, but instead ofcomparison, we should get the numbers sequence and then create the hash number.So, once again, total-ordering could be considered as a milestone for evenfaster (in theory) random-access approach.

MergeFunctions, main fields and runOnModule

There are two main important fields in the class:

FnTree – the set of all unique functions. It keeps items that couldn’t bemerged with each other. It is defined as:

std::set<FunctionNode> FnTree;

Here FunctionNode is a wrapper for llvm::Function class, withimplemented “<” operator among the functions set (below we explain how it worksexactly; this is a key point in fast functions comparison).

Deferred – merging process can affect bodies of functions that are inFnTree already. Obviously, such functions should be rechecked again. In thiscase, we remove them from FnTree, and mark them to be rescanned, namelyput them into Deferred list.

runOnModule

The algorithm is pretty simple:

• Put all module’s functions into the worklist.

1. Scan worklist’s functions twice: first enumerate only strong functions andthen only weak ones:

2.1. Loop body: take a function from worklist (call it FCur) and try toinsert it into FnTree: check whether FCur is equal to one of functionsin FnTree. If there is an equal function in FnTree(call it FExists): merge function FCur with FExists. Otherwise addthe function from the worklist to FnTree.

1. Once the worklist scanning and merging operations are complete, check theDeferred list. If it is not empty: refill the worklist contents withDeferred list and redo step 2, if the Deferred list is empty, then exitfrom method.

Comparison and logarithmical search

Let’s recall our task: for every function F from module M, we have to findequal functions F` in the shortest time possible , and merge them into asingle function.

Defining total ordering among the functions set allows us to organizefunctions into a binary tree. The lookup procedure complexity would beestimated as O(log(N)) in this case. But how do we define total-ordering?

We have to introduce a single rule applicable to every pair of functions, andfollowing this rule, then evaluate which of them is greater. What kind of rulecould it be? Let’s declare it as the “compare” method that returns one of 3possible values:

-1, left is less than right,

0, left and right are equal,

1, left is greater than right.

Of course it means, that we have to maintainstrict and non-strict order relation 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).

As mentioned before, the comparison routine consists of“sub-comparison-routines”, with each of them also consisting of“sub-comparison-routines”, and so on. Finally, it ends up with primitivecomparison.

Below, we will use the following operations:

• cmpNumbers(number1, number2) is a method that returns -1 if left is lessthan right; 0, if left and right are equal; and 1 otherwise.
• cmpFlags(flag1, flag2) is a hypothetical method that compares two flags.The logic is the same as in cmpNumbers, where true is 1, andfalse is 0.The rest of the article is based on MergeFunctions.cpp source code(found in <llvm_dir>/lib/Transforms/IPO/MergeFunctions.cpp). We would liketo ask reader to keep this file open, so we could use it as a referencefor further explanations.

Now, we’re ready to proceed to the next chapter and see how it works.

Functions comparison

At first, let’s define how exactly we compare complex objects.

Complex object comparison (function, basic-block, etc) is mostly based on itssub-object comparison results. It is similar to the next “tree” objectscomparison:

• For two trees T1 and T2 we perform depth-first-traversal and havetwo sequences as a product: “T1Items” and “T2Items”.
• We then compare chains “T1Items” and “T2Items” inthe most-significant-item-first order. The result of items comparisonwould be the result of T1 and T2 comparison itself.

FunctionComparator::compare(void)

A brief look at the source code tells us that the comparison starts in the“int FunctionComparator::compare(void)” method.

1. The first parts to be compared are the function’s attributes and someproperties that is outside the “attributes” term, but still could make thefunction different without changing its body. This part of the comparison isusually done within simple cmpNumbers or cmpFlags operations (e.g.cmpFlags(F1->hasGC(), F2->hasGC())). Below is a full list of function’sproperties to be compared on this stage:

• Attributes (those are returned by Function::getAttributes()method).
• GC, for equivalence, RHS and LHS should be both either withoutGC or with the same one.
• Section, just like a GC: RHS and LHS should be defined in thesame section.
• Variable arguments. LHS and RHS should be both either with orwithout var-args.
• Calling convention should be the same.

1. Function type. Checked by FunctionComparator::cmpType(Type, Type)method. It checks return type and parameters type; the method itself will bedescribed later.

2. Associate function formal parameters with each other. Then comparing functionbodies, if we see the usage of LHS’s i-th argument in LHS’s body, then,we want to see usage of RHS’s i-th argument at the same place in RHS’sbody, otherwise functions are different. On this stage we grant the preferenceto those we met later in function body (value we met first would be less).This is done by “FunctionComparator::cmpValues(const Value, const Value)”method (will be described a bit later).

• Function body comparison. As it written in method comments:“We do a CFG-ordered walk since the actual ordering of the blocks in the linkedlist is immaterial. Our walk starts at the entry block for both functions, thentakes each block from each terminator in order. As an artifact, this also meansthat unreachable blocks are ignored.”

So, using this walk we get BBs from left and right in the same order, andcompare them by “FunctionComparator::compare(const BasicBlock, constBasicBlock)” method.

We also associate BBs with each other, like we did it with function formalarguments (see cmpValues method below).

FunctionComparator::cmpType

Consider how type comparison works.

1. Coerce pointer to integer. If left type is a pointer, try to coerce it to theinteger type. It could be done if its address space is 0, or if address spacesare ignored at all. Do the same thing for the right type.

2. If left and right types are equal, return 0. Otherwise we need to givepreference to one of them. So proceed to the next step.

3. If types are of different kind (different type IDs). Return result of typeIDs comparison, treating them as numbers (use cmpNumbers operation).

4. If types are vectors or integers, return result of their pointers comparison,comparing them as numbers.

• Check whether type ID belongs to the next group (call it equivalent-group):

  • Void
  • Float
  • Double
  • X86_FP80
  • FP128
  • PPC_FP128
  • Label
  • Metadata.If ID belongs to group above, return 0. Since it’s enough to see thattypes has the same TypeID. No additional information is required.

1. Left and right are pointers. Return result of address space comparison(numbers comparison).

2. Complex types (structures, arrays, etc.). Follow complex objects comparisontechnique (see the very first paragraph of this chapter). Both left andright are to be expanded and their element types will be checked the sameway. If we get -1 or 1 on some stage, return it. Otherwise return 0.

3. Steps 1-6 describe all the possible cases, if we passed steps 1-6 and didn’tget any conclusions, then invoke llvm_unreachable, since it’s quite anunexpectable case.

cmpValues(const Value, const Value)

Method that compares local values.

This method gives us an answer to a very curious question: whether we couldtreat local values as equal, and which value is greater otherwise. It’sbetter to start from example:

Consider the situation when we’re looking at the same place in leftfunction “FL” and in right function “FR”. Every part of left place isequal to the corresponding part of right place, and (!) both parts useValue instances, for example:

instr0 i32 %LV   ; left side, function FL
instr0 i32 %RV   ; right side, function FR

So, now our conclusion depends on Value instances comparison.

The main purpose of this method is to determine relation between such values.

What can we expect from equal functions? At the same place, in functions“FL” and “FR” we expect to see equal values, or values defined atthe same place in “FL” and “FR”.

Consider a small example here:

define void %f(i32 %pf0, i32 %pf1) {
  instr0 i32 %pf0 instr1 i32 %pf1 instr2 i32 123
}

define void %g(i32 %pg0, i32 %pg1) {
  instr0 i32 %pg0 instr1 i32 %pg0 instr2 i32 123
}

In this example, pf0 is associated with pg0, pf1 is associated withpg1, and we also declare that pf0 < pf1, and thus pg0 < pf1.

Instructions with opcode “instr0” would be equal, since their types andopcodes are equal, and values are associated.

Instructions with opcode “instr1” from f is greater than instructionswith opcode “instr1” from g; here we have equal types and opcodes, but“pf1 is greater than “pg0”.

Instructions with opcode “instr2” are equal, because their opcodes andtypes are equal, and the same constant is used as a value.

What we associate in cmpValues?

• Function arguments. i-th argument from left function associated withi-th argument from right function.
• BasicBlock instances. In basic-block enumeration loop we associate i-thBasicBlock from the left function with i-th BasicBlock from the rightfunction.
• Instructions.
• Instruction operands. Note, we can meet Value here we have never seenbefore. In this case it is not a function argument, nor BasicBlock, norInstruction. It is a global value. It is a constant, since it’s the onlysupposed global here. The method also compares: Constants that are of thesame type and if right constant can be losslessly bit-casted to the leftone, then we also compare them.

How to implement cmpValues?

Association is a case of equality for us. We just treat such values as equal,but, in general, we need to implement antisymmetric relation. As mentionedabove, to understand what is less, we can use order in which wemeet values. If both values have the same order in a function (met at the sametime), we then treat values as associated. Otherwise – it depends on who wasfirst.

Every time we run the top-level compare method, we initialize two identicalmaps (one for the left side, another one for the right side):

map<Value, int> sn_mapL, sn_mapR;

The key of the map is the Value itself, the value – is its order (call itserial number).

To add value V we need to perform the next procedure:

sn_map.insert(std::make_pair(V, sn_map.size()));

For the first Value, map will return 0, for the second Value map willreturn 1, and so on.

We can then check whether left and right values met at the same time witha simple comparison:

cmpNumbers(sn_mapL[Left], sn_mapR[Right]);

Of course, we can combine insertion and comparison:

std::pair<iterator, bool>
  LeftRes = sn_mapL.insert(std::make_pair(Left, sn_mapL.size())), RightRes
  = sn_mapR.insert(std::make_pair(Right, sn_mapR.size()));
return cmpNumbers(LeftRes.first->second, RightRes.first->second);

Let’s look, how whole method could be implemented.

1. We have to start with the bad news. Consider function self andcross-referencing cases:

// self-reference unsigned fact0(unsigned n) { return n > 1 ? n
* fact0(n-1) : 1; } unsigned fact1(unsigned n) { return n > 1 ? n *
fact1(n-1) : 1; }
 
// cross-reference unsigned ping(unsigned n) { return n!= 0 ? pong(n-1) : 0;
} unsigned pong(unsigned n) { return n!= 0 ? ping(n-1) : 0; }

This comparison has been implemented in initial MergeFunctions passversion. But, unfortunately, it is not transitive. And this is the only casewe can’t convert to less-equal-greater comparison. It is a seldom case, 4-5functions of 10000 (checked in test-suite), and, we hope, the reader wouldforgive us for such a sacrifice in order to get the O(log(N)) pass time.

1. If left/right Value is a constant, we have to compare them. Return 0 if itis the same constant, or use cmpConstants method otherwise.

2. If left/right is InlineAsm instance. Return result of Value pointerscomparison.

3. Explicit association of L (left value) and R (right value). We need tofind out whether values met at the same time, and thus are associated. Or weneed to put the rule: when we treat L < R. Now it is easy: we just returnthe result of numbers comparison:

std::pair<iterator, bool>
  LeftRes = sn_mapL.insert(std::make_pair(Left, sn_mapL.size())),
  RightRes = sn_mapR.insert(std::make_pair(Right, sn_mapR.size()));
if (LeftRes.first->second == RightRes.first->second) return 0;
if (LeftRes.first->second < RightRes.first->second) return -1;
return 1;

Now when cmpValues returns 0, we can proceed the comparison procedure.Otherwise, if we get (-1 or 1), we need to pass this result to the top level,and finish comparison procedure.

cmpConstants

Performs constants comparison as follows:

1. Compare constant types using cmpType method. If the result is -1 or 1,goto step 2, otherwise proceed to step 3.

2. If types are different, we still can check whether constants could belosslessly bitcasted to each other. The further explanation is modification ofcanLosslesslyBitCastTo method.

2.1 Check whether constants are of the first class types(isFirstClassType check):

2.1.1. If both constants are not of the first class type: return resultof cmpType.

2.1.2. Otherwise, if left type is not of the first class, return -1. Ifright type is not of the first class, return 1.

2.1.3. If both types are of the first class type, proceed to the next step(2.1.3.1).

2.1.3.1. If types are vectors, compare their bitwidth using thecmpNumbers. If result is not 0, return it.

2.1.3.2. Different types, but not a vectors:

• if both of them are pointers, good for us, we can proceed to step 3.
• if one of types is pointer, return result of isPointer flagscomparison (cmpFlags operation).
• otherwise we have no methods to prove bitcastability, and thus returnresult of types comparison (-1 or 1).

Steps below are for the case when types are equal, or case when constants arebitcastable:

1. One of constants is a “null” value. Return the result ofcmpFlags(L->isNullValue, R->isNullValue) comparison.

• Compare value IDs, and return result if it is not 0:

if (int Res = cmpNumbers(L->getValueID(), R->getValueID()))
  return Res;

1. Compare the contents of constants. The comparison depends on the kind ofconstants, but on this stage it is just a lexicographical comparison. Just seehow it was described in the beginning of “Functions comparison” paragraph.Mathematically, it is equal to the next case: we encode left constant and rightconstant (with similar way bitcode-writer does). Then compare left codesequence and right code sequence.

compare(const BasicBlock, const BasicBlock)

Compares two BasicBlock instances.

It enumerates instructions from left BB and right BB.

1. It assigns serial numbers to the left and right instructions, usingcmpValues method.

2. If one of left or right is GEP (GetElementPtr), then treat GEP asgreater than other instructions. If both instructions are GEPs use cmpGEPmethod for comparison. If result is -1 or 1, pass it to the top-levelcomparison (return it).

3.1. Compare operations. Call cmpOperation method. If result is -1 or1, return it.

3.2. Compare number of operands, if result is -1 or 1, return it.

3.3. Compare operands themselves, use cmpValues method. Return resultif it is -1 or 1.

3.4. Compare type of operands, using cmpType method. Return result ifit is -1 or 1.

3.5. Proceed to the next instruction.

• We can finish instruction enumeration in 3 cases:

4.1. We reached the end of both left and right basic-blocks. We didn’texit on steps 1-3, so contents are equal, return 0.

4.2. We have reached the end of the left basic-block. Return -1.

4.3. Return 1 (we reached the end of the right basic block).

cmpGEP

Compares two GEPs (getelementptr instructions).

It differs from regular operations comparison with the only thing: possibilityto use accumulateConstantOffset method.

So, if we get constant offset for both left and right GEPs, then compare it asnumbers, and return comparison result.

Otherwise treat it like a regular operation (see previous paragraph).

cmpOperation

Compares instruction opcodes and some important operation properties.

• Compare opcodes, if it differs return the result.
• Compare number of operands. If it differs – return the result.

1. Compare operation types, use cmpType. All the same – if types aredifferent, return result.

2. Compare subclassOptionalData, get it with getRawSubclassOptionalDatamethod, and compare it like a numbers.

• Compare operand types.

1. For some particular instructions, check equivalence (relation in our case) ofsome significant attributes. For example, we have to compare alignment forload instructions.

O(log(N))

Methods described above implement order relationship. And latter, could be usedfor nodes comparison in a binary tree. So we can organize functions set intothe binary tree and reduce the cost of lookup procedure fromO(N*N) to O(log(N)).

Merging process, mergeTwoFunctions

Once MergeFunctions detected that current function (G) is equal to one thatwere analyzed before (function F) it calls mergeTwoFunctions(Function,Function).

Operation affects FnTree contents with next way: F will stay inFnTree. G being equal to F will not be added to FnTree. Calls ofG would be replaced with something else. It changes bodies of callers. So,functions that calls G would be put into Deferred set and removed fromFnTree, and analyzed again.

The approach is next:

1. Most wished case: when we can use alias and both of F and G are weak. Wemake both of them with aliases to the third strong function H. Actually H_is _F. See below how it’s made (but it’s better to look straight into thesource code). Well, this is a case when we can just replace G with F_everywhere, we use replaceAllUsesWith operation here (_RAUW).

2. F could not be overridden, while G could. It would be good to do thenext: after merging the places where overridable function were used, still useoverridable stub. So try to make G alias to F, or create overridable tailcall wrapper around F and replace G with that call.

3. Neither F nor G could be overridden. We can’t use RAUW. We can justchange the callers: call F instead of G. That’s whatreplaceDirectCallers does.

Below is a detailed body description.

If “F” may be overridden

As follows from mayBeOverridden comments: “whether the definition of thisglobal may be replaced by something non-equivalent at link time”. If so, that’sok: we can use alias to F instead of G or change call instructions itself.

HasGlobalAliases, removeUsers

First consider the case when we have global aliases of one function name toanother. Our purpose is make both of them with aliases to the third strongfunction. Though if we keep F alive and without major changes we can leave itin FnTree. Try to combine these two goals.

Do stub replacement of F itself with an alias to F.

1. Create stub function H, with the same name and attributes like functionF. It takes maximum alignment of F and G.

2. Replace all uses of function F with uses of function H. It is the twosteps procedure instead. First of all, we must take into account, all functionsfrom whom F is called would be changed: since we change the call argument(from F to H). If so we must to review these caller functions again afterthis procedure. We remove callers from FnTree, method with nameremoveUsers(F) does that (don’t confuse with replaceAllUsesWith):

2.1. Inside removeUsers(Value*V) we go through the all values that use value V (or F in our context).If value is instruction, we go to function that holds this instruction andmark it as to-be-analyzed-again (put to Deferred set), we also removecaller from FnTree.

2.2. Now we can do the replacement: call F->replaceAllUsesWith(H).

1. H (that now “officially” plays F’s role) is replaced with alias to F.Do the same with G: replace it with alias to F. So finally everywhere F_was used, we use _H and it is alias to F, and everywhere G was used wealso have alias to F.

• Set F linkage to private. Make it strong :-)

No global aliases, replaceDirectCallers

If global aliases are not supported. We call replaceDirectCallers. Justgo through all calls of G and replace it with calls of F. If you look intothe method you will see that it scans all uses of G too, and if use is callee(if user is call instruction and G is used as what to be called), we replaceit with use of F.

If “F” could not be overridden, fix it!

We call writeThunkOrAlias(Function F, Function G). Here we try to replaceG with alias to F first. The next conditions are essential:

• target should support global aliases,
• the address itself of G should be not significant, not named and notreferenced anywhere,
• function should come with external, local or weak linkage.

Otherwise we write thunk: some wrapper that has G’s interface and calls F,so G could be replaced with this wrapper.

writeAlias

As follows from llvm reference:

“Aliases act as second name for the aliasee value”. So we just want to createa second name for F and use it instead of G:

• create global alias itself (GA),

• adjust alignment of F so it must be maximum of current and G’s alignment;

• replace uses of G:

3.1. first mark all callers of G as to-be-analyzed-again, usingremoveUsers method (see chapter above),

3.2. call G->replaceAllUsesWith(GA).

• Get rid of G.

writeThunk

As it written in method comments:

“Replace G with a simple tail call to bitcast(F). Also replace direct uses of Gwith bitcast(F). Deletes G.”

In general it does the same as usual when we want to replace callee, except thefirst point:

1. We generate tail call wrapper around F, but with interface that allows useit instead of G.

• “As-usual”: removeUsers and replaceAllUsesWith then.
• Get rid of G.