Sometimes code contains equal functions, or functions that does exactly the same thing even though they are non-equal on the IR level (e.g.: multiplication on 2 and 'shl 1'). It could happen due to several reasons: mainly, the usage of templates and automatic code generators. Though, sometimes user itself could write the same thing twice :-)
The main purpose of this pass is to recognize such functions and merge them.
Document is the extension to pass comments and describes the pass logic. It describes algorithm that is used in order to compare functions, it also explains how we could combine equal functions correctly, keeping module valid.
Material is brought in top-down form, so reader could start learn pass from ideas and end up with low-level algorithm details, thus preparing him for reading the sources.
So main goal is do describe algorithm and logic here; the concept. This document is good for you, if you don't want to read the source code, but want to understand pass algorithms. Author tried not to repeat the source-code and cover only common cases, and thus avoid cases when after minor code changes we need to update this document.
Reader should be familiar with common compile-engineering principles and LLVM code fundamentals. In this article we suppose reader is familiar with Single Static Assingment concepts. Understanding of IR structure is also important.
We will use such terms as "module", "function", "basic block", "user", "value", "instruction".
As a good start point, Kaleidoscope tutorial could be used:
Especially it's important to understand chapter 3 of tutorial:
Reader also should know how passes work in LLVM, they could use next article as a reference and start point here:
What else? Well perhaps reader also should have some experience in LLVM pass debugging and bug-fixing.
Main purpose is to provide reader with comfortable form of algorithms description, namely the human reading text. Since it could be hard to understand algorithm straight from the source code: pass uses some principles that have to be explained first.
Author wishes to everybody to avoid case, when you read code from top to bottom again and again, and yet you don't understand why we implemented it that way.
We hope that after this article reader could easily debug and improve MergeFunctions pass and thus help LLVM project.
Article consists of three parts. First part explains pass functionality on the top-level. Second part describes the comparison procedure itself. The third part describes the merging process.
In every part author also tried to put the contents into the top-down form. First, the top-level methods will be described, while the terminal ones will be at the end, in the tail of each part. If reader will see the reference to the method that wasn't described yet, they will find its description a bit below.
Do we need to merge functions? Obvious thing is: yes that's a quite possible case, since usually we do have duplicates. And it would be good to get rid of them. But how to detect such a duplicates? The idea is next: we split functions onto small bricks (parts), then we compare "bricks" amount, and if it equal, compare "bricks" themselves, and then do our conclusions about functions themselves.
What the difference it could be? For example, on machine with 64-bit pointers
(let's assume we have only one address space), one function stores 64-bit
integer, while another one stores a pointer. So if the target is a machine
mentioned above, and if functions are identical, except the parameter type (we
could consider it as a part of function type), then we can treat uint64_t
and``void*`` as equal.
It was just an example; possible details are described a bit below.
As another example reader may imagine two more functions. First function performs multiplication on 2, while the second one performs arithmetic right shift on 1.
Let's briefly consider possible options about how and what we have to implement in order to create full-featured functions merging, and also what it would meant for us.
Equal functions detection, obviously supposes "detector" method to be implemented, latter should answer the question "whether functions are equal". This "detector" method consists of tiny "sub-detectors", each of them answers exactly 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 a routines in our hands, we can process whole module, and merge all equal functions.
In this case, we have to compare every function with every another function. As reader could notice, this way seems to be quite expensive. Of course we could introduce hashing and other helpers, but it is still just an optimization, and thus the level of O(N*N) complexity.
Can we reach another level? Could we introduce logarithmical search, or random access lookup? The answer is: "yes".
How it could be done? Just convert each function to number, and gather all of them in special hash-table. Functions with equal hash are equal. Good hashing means, that every function part must be taken into account. That means we have to convert every function part into some number, and then add it into hash. Lookup-up time would be small, but such approach adds some delay due to hashing routine.
We could introduce total ordering among the functions set, once we had it we could then implement a logarithmical search. Lookup time still depends on N, but adds a little of delay (log(N)).
Both of approaches (random-access and logarithmical) has been implemented and tested. And both of them gave a very good improvement. And what was most surprising, logarithmical search was faster; sometimes up to 15%. Hashing needs some extra CPU time, and it is the main reason why it works slower; in most of cases total "hashing" time was 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") could be used as a milestone on our way to the random-access implementation.
Every comparison is based either on the numbers or on flags comparison. In random-access approach we could use the same comparison algorithm. During comparison we exit once we find the difference, but here we might have to scan whole function body every time (note, it could be slower). Like in "total-ordering", we will track every numbers and flags, but instead of comparison, we should get numbers sequence and then create the hash number. So, once again, total-ordering could be considered as a milestone for even faster (in theory) random-access approach.
There are two most important fields in class:
FnTree – the set of all unique functions. It keeps items that couldn't be
merged with each other. It is defined as:
std::set<FunctionNode> FnTree;
Here FunctionNode is a wrapper for llvm::Function class, with
implemented “<” operator among the functions set (below we explain how it works
exactly; this is a key point in fast functions comparison).
Deferred – merging process can affect bodies of functions that are in
FnTree already. Obviously such functions should be rechecked again. In this
case we remove them from FnTree, and mark them as to be rescanned, namely
put them into Deferred list.
The algorithm is pretty simple:
- Put all module's functions into the worklist.
2. Scan worklist's functions twice: first enumerate only strong functions and then only weak ones:
2.1. Loop body: take function from worklist (call it FCur) and try to insert it into FnTree: check whether FCur is equal to one of functions in FnTree. If there is equal function in FnTree (call it FExists): merge function FCur with FExists. Otherwise add function from worklist to FnTree.
3. Once worklist scanning and merging operations is complete, check Deferred list. If it is not empty: refill worklist contents with Deferred list and do step 2 again, if Deferred is empty, then exit from method.
Let's recall our task: for every function F from module M, we have to find equal functions F` in shortest time, and merge them into the single function.
Defining total ordering among the functions set allows to organize functions into the binary tree. The lookup procedure complexity would be estimated as O(log(N)) in this case. But how to define total-ordering?
We have to introduce a single rule applicable to every pair of functions, and following this rule then evaluate which of them is greater. What kind of rule it could be? Let's declare it as "compare" method, that returns one of 3 possible 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 maintain strict and non-strict order relation properties:
- reflexivity (
a <= a,a == a,a >= a), - antisymmetry (if
a <= bandb <= athena == b), - transitivity (
a <= bandb <= c, thena <= c) - asymmetry (if
a < b, thena > bora == b).
As it was mentioned before, comparison routine consists of "sub-comparison-routines", each of them also consists "sub-comparison-routines", and so on, finally it ends up with a primitives comparison.
Below, we will use the next operations:
cmpNumbers(number1, number2)is method that returns -1 if left is less than right; 0, if left and right are equal; and 1 otherwise.cmpFlags(flag1, flag2)is hypothetical method that compares two flags. The logic is the same as incmpNumbers, wheretrueis 1, andfalseis 0.
The rest of article is based on MergeFunctions.cpp source code (<llvm_dir>/lib/Transforms/IPO/MergeFunctions.cpp). We would like to ask reader to keep this file open nearby, so we could use it as a reference for further explanations.
Now we're ready to proceed to the next chapter and see how it works.
At first, let's define how exactly we compare complex objects.
Complex objects comparison (function, basic-block, etc) is mostly based on its sub-objects comparison results. So it is similar to the next "tree" objects comparison:
- For two trees T1 and T2 we perform depth-first-traversal and have two sequences as a product: "T1Items" and "T2Items".
- Then compare chains "T1Items" and "T2Items" in most-significant-item-first order. Result of items comparison would be the result of T1 and T2 comparison itself.
Brief look at the source code tells us, that comparison starts in
“int FunctionComparator::compare(void)” method.
1. First parts to be compared are function's attributes and some properties that
outsides “attributes” term, but still could make function different without
changing its body. This part of comparison is usually done within simple
cmpNumbers or cmpFlags operations (e.g.
cmpFlags(F1->hasGC(), F2->hasGC())). Below is full list of function's
properties to be compared on this stage:
- Attributes (those are returned by
Function::getAttributes()method).- GC, for equivalence, RHS and LHS should be both either without GC or with the same one.
- Section, just like a GC: RHS and LHS should be defined in the same section.
- Variable arguments. LHS and RHS should be both either with or without var-args.
- Calling convention should be the same.
2. Function type. Checked by FunctionComparator::cmpType(Type*, Type*)
method. It checks return type and parameters type; the method itself will be
described later.
3. Associate function formal parameters with each other. Then comparing function
bodies, 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's
body, otherwise functions are different. On this stage we grant the preference
to 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 linked list is immaterial. Our walk starts at the entry block for both functions, then takes each block from each terminator in order. As an artifact, this also means that unreachable blocks are ignored.”
So, using this walk we get BBs from left and right in the same order, and
compare them by “FunctionComparator::compare(const BasicBlock*, const
BasicBlock*)” method.
We also associate BBs with each other, like we did it with function formal
arguments (see cmpValues method below).
Consider how types comparison works.
1. Coerce pointer to integer. If left type is a pointer, try to coerce it to the integer type. It could be done if its address space is 0, or if address spaces are 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 give preference to one of them. So proceed to the next step.
3. If types are of different kind (different type IDs). Return result of type
IDs comparison, treating them as a 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 that types has the same
TypeID. No additional information is required.
6. Left and right are pointers. Return result of address space comparison (numbers comparison).
7. Complex types (structures, arrays, etc.). Follow complex objects comparison technique (see the very first paragraph of this chapter). Both left and right are to be expanded and their element types will be checked the same way. If we get -1 or 1 on some stage, return it. Otherwise return 0.
8. Steps 1-6 describe all the possible cases, if we passed steps 1-6 and didn't
get any conclusions, then invoke llvm_unreachable, since it's quite
unexpectable case.
Method that compares local values.
This method gives us an answer on a very curious quesion: whether we could treat local values as equal, and which value is greater otherwise. It's better to start from example:
Consider situation when we're looking at the same place in left function "FL" and in right function "FR". And every part of left place is equal to the corresponding part of right place, and (!) both parts use Value 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.
Main purpose of this method is to determine relation between such values.
What we expect from equal functions? At the same place, in functions "FL" and "FR" we expect to see equal values, or values defined at the same place in "FL" and "FR".
Consider 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 with pg1, and we also declare that pf0 < pf1, and thus pg0 < pf1.
Instructions with opcode "instr0" would be equal, since their types and opcodes are equal, and values are associated.
Instruction with opcode "instr1" from f is greater than instruction with opcode "instr1" from g; here we have equal types and opcodes, but "pf1 is greater than "pg0".
And instructions with opcode "instr2" are equal, because their opcodes and types are equal, and the same constant is used as a value.
- Function arguments. i-th argument from left function associated with i-th argument from right function.
- BasicBlock instances. In basic-block enumeration loop we associate i-th BasicBlock from the left function with i-th BasicBlock from the right function.
- Instructions.
- Instruction operands. Note, we can meet Value here we have never seen before. In this case it is not a function argument, nor BasicBlock, nor Instruction. It is global value. It is constant, since its the only supposed global here. Method also compares:
- Constants that are of the same type.
- If right constant could be losslessly bit-casted to the left one, then we also compare them.
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 it was mentioned above, to understand what is less, we can use order in which we meet values. If both of values has the same order in function (met at the same time), then treat values as associated. Otherwise – it depends on who was first.
Every time we run top-level compare method, we initialize two identical maps (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 it serial 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 second Value map will return 1, and so on.
Then we can check whether left and right values met at the same time with 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 from the bad news. Consider function self and cross-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 pass version. But, unfortunately, it is not transitive. And this is the only case we can't convert to less-equal-greater comparison. It is a seldom case, 4-5 functions of 10000 (checked on test-suite), and, we hope, reader would forgive us for such a sacrifice in order to get the O(log(N)) pass time.
2. If left/right Value is a constant, we have to compare them. Return 0 if it
is the same constant, or use cmpConstants method otherwise.
3. If left/right is InlineAsm instance. Return result of Value pointers comparison.
4. Explicit association of L (left value) and R (right value). We need to find out whether values met at the same time, and thus are associated. Or we need to put the rule: when we treat L < R. Now it is easy: just return 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 comparison procedure. Otherwise, if we get (-1 or 1), we need to pass this result to the top level, and finish comparison procedure.
Performs constants comparison as follows:
1. Compare constant types using cmpType method. If 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 be
losslessly bitcasted to each other. The further explanation is modification of
canLosslesslyBitCastTo method.
2.1 Check whether constants are of the first class types (
isFirstClassTypecheck):2.1.1. If both constants are not of the first class type: return result of
cmpType.2.1.2. Otherwise, if left type is not of the first class, return -1. If right 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 the cmpNumbers. 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 flags comparison (cmpFlags operation).
- otherwise we have no methods to prove bitcastability, and thus return result of types comparison (-1 or 1).
Steps below are for the case when types are equal, or case when constants are bitcastable:
3. One of constants is a "null" value. Return the result of
cmpFlags(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;5. Compare the contents of constants. The comparison depends on kind of constants, but on this stage it is just a lexicographical comparison. Just see how it was described in the beginning of "Functions comparison" paragraph. Mathematically it is equal to the next case: we encode left constant and right constant (with similar way bitcode-writer does). Then compare left code sequence and right code sequence.
Compares two BasicBlock instances.
It enumerates instructions from left BB and right BB.
1. It assigns serial numbers to the left and right instructions, using
cmpValues method.
2. If one of left or right is GEP (GetElementPtr), then treat GEP as
greater than other instructions, if both instructions are GEPs use cmpGEP
method for comparison. If result is -1 or 1, pass it to the top-level
comparison (return it).
3.1. Compare operations. Call
cmpOperationmethod. If result is -1 or 1, return it.3.2. Compare number of operands, if result is -1 or 1, return it.
3.3. Compare operands themselves, use
cmpValuesmethod. Return result if it is -1 or 1.3.4. Compare type of operands, using
cmpTypemethod. Return result if it 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't exit on steps 1-3, so contents is equal, return 0.
4.2. We have reached the end of the left basic-block. Return -1.
4.3. Return 1 (the end of the right basic block).
Compares two GEPs (getelementptr instructions).
It differs from regular operations comparison with the only thing: possibility
to use accumulateConstantOffset method.
So, if we get constant offset for both left and right GEPs, then compare it as numbers, and return comparison result.
Otherwise treat it like a regular operation (see previous paragraph).
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.
3. Compare operation types, use cmpType. All the same – if types are different, return result.
4. Compare subclassOptionalData, get it with getRawSubclassOptionalData
method, and compare it like a numbers.
- Compare operand types.
6. For some particular instructions check equivalence (relation in our case) of
some significant attributes. For example we have to compare alignment for
load instructions.
Methods described above implement order relationship. And latter, could be used for nodes comparison in a binary tree. So we can organize functions set into the binary tree and reduce the cost of lookup procedure from O(N*N) to O(log(N)).
Once MergeFunctions detected that current function (G) is equal to one that
were analyzed before (function F) it calls mergeTwoFunctions(Function*,
Function*).
Operation affects FnTree contents with next way: F will stay in
FnTree. G being equal to F will not be added to FnTree. Calls of
G would be replaced with something else. It changes bodies of callers. So,
functions that calls G would be put into Deferred set and removed from
FnTree, and analyzed again.
The approach is next:
1. Most wished case: when we can use alias and both of F and G are weak. We
make 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 the
source 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 the next: after merging the places where overridable function were used, still use overridable stub. So try to make G alias to F, or create overridable tail call wrapper around F and replace G with that call.
3. Neither F nor G could be overridden. We can't use RAUW. We can just
change the callers: call F instead of G. That's what
replaceDirectCallers does.
Below is detailed body description.
As follows from mayBeOverridden comments: “whether the definition of this
global may be replaced by something non-equivalent at link time”. If so, that's
ok: we can use alias to F instead of G or change call instructions itself.
First consider the case when we have global aliases of one function name to
another. Our purpose is make both of them with aliases to the third strong
function. Though if we keep F alive and without major changes we can leave it
in 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 function F. It takes maximum alignment of F and G.
2. Replace all uses of function F with uses of function H. It is the two
steps procedure instead. First of all, we must take into account, all functions
from 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 after
this procedure. We remove callers from FnTree, method with name
removeUsers(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 and mark it as to-be-analyzed-again (put toDeferredset), we also remove caller fromFnTree.2.2. Now we can do the replacement: call
F->replaceAllUsesWith(H).
3. 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 we also have alias to F.
- Set F linkage to private. Make it strong :-)
If global aliases are not supported. We call replaceDirectCallers then. Just
go through all calls of G and replace it with calls of F. If you look into
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 replace it
with use of F.
We call writeThunkOrAlias(Function *F, Function *G). Here we try to replace
G with alias to F first. Next conditions are essential:
- target should support global aliases,
- the address itself of G should be not significant, not named and not referenced 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 create 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, using
removeUsersmethod (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 G with bitcast(F). Deletes G.”
In general it does the same as usual when we want to replace callee, except the first point:
1. We generate tail call wrapper around F, but with interface that allows use it instead of G.
- “As-usual”:
removeUsersandreplaceAllUsesWiththen. - Get rid of G.
We have described how to detect equal functions, and how to merge them, and in first chapter we have described how it works all-together. Author hopes, reader have some picture from now, and it helps him improve and debug this pass.
Reader is welcomed to send us any questions and proposals ;-)