MemorySSA

Introduction

MemorySSA is an analysis that allows us to cheaply reason about the interactions between various memory operations. Its goal is to replace MemoryDependenceAnalysis for most (if not all) use-cases. This is because, unless you’re very careful, use of MemoryDependenceAnalysis can easily result in quadratic-time algorithms in LLVM. Additionally, MemorySSA doesn’t have as many arbitrary limits as MemoryDependenceAnalysis, so you should get better results, too. One common use of MemorySSA is to quickly find out that something definitely cannot happen (for example, reason that a hoist out of a loop can’t happen).

At a high level, one of the goals of MemorySSA is to provide an SSA based form for memory, complete with def-use and use-def chains, which enables users to quickly find may-def and may-uses of memory operations. It can also be thought of as a way to cheaply give versions to the complete state of memory, and associate memory operations with those versions.

This document goes over how MemorySSA is structured, and some basic intuition on how MemorySSA works.

A paper on MemorySSA (with notes about how it’s implemented in GCC) can be found here. Though, it’s relatively out-of-date; the paper references multiple memory partitions, but GCC eventually swapped to just using one, like we now have in LLVM. Like GCC’s, LLVM’s MemorySSA is intraprocedural.

MemorySSA Structure

MemorySSA is a virtual IR. After it’s built, MemorySSA will contain a structure that maps Instructions to MemoryAccesses, which are MemorySSA’s parallel to LLVM Instructions.

Each MemoryAccess can be one of three types:

• MemoryDef

• MemoryPhi

• MemoryUse

MemoryDefs are operations which may either modify memory, or which introduce some kind of ordering constraints. Examples of MemoryDefs include stores, function calls, loads with acquire (or higher) ordering, volatile operations, memory fences, etc. A MemoryDef always introduces a new version of the entire memory and is linked with a single MemoryDef/MemoryPhi which is the version of memory that the new version is based on. This implies that there is a single Def chain that connects all the Defs, either directly or indireclty. For example in:

b = MemoryDef(a)
c = MemoryDef(b)
d = MemoryDef(c)

d is connected directly with c and indirectly with b. This means that d potentially clobbers (see below) c or b or both. This in turn implies that without the use of The walker, initially every MemoryDef clobbers every other MemoryDef.

MemoryPhis are PhiNodes, but for memory operations. If at any point we have two (or more) MemoryDefs that could flow into a BasicBlock, the block’s top MemoryAccess will be a MemoryPhi. As in LLVM IR, MemoryPhis don’t correspond to any concrete operation. As such, BasicBlocks are mapped to MemoryPhis inside MemorySSA, whereas Instructions are mapped to MemoryUses and MemoryDefs.

Note also that in SSA, Phi nodes merge must-reach definitions (that is, definitions that must be new versions of variables). In MemorySSA, PHI nodes merge may-reach definitions (that is, until disambiguated, the versions that reach a phi node may or may not clobber a given variable).

MemoryUses are operations which use but don’t modify memory. An example of a MemoryUse is a load, or a readonly function call.

Every function that exists has a special MemoryDef called liveOnEntry. It dominates every MemoryAccess in the function that MemorySSA is being run on, and implies that we’ve hit the top of the function. It’s the only MemoryDef that maps to no Instruction in LLVM IR. Use of liveOnEntry implies that the memory being used is either undefined or defined before the function begins.

An example of all of this overlaid on LLVM IR (obtained by running opt -passes='print<memoryssa>' -disable-output on an .ll file) is below. When viewing this example, it may be helpful to view it in terms of clobbers. The operands of a given MemoryAccess are all (potential) clobbers of said MemoryAccess, and the value produced by a MemoryAccess can act as a clobber for other MemoryAccesses.

If a MemoryAccess is a clobber of another, it means that these two MemoryAccesses may access the same memory. For example, x = MemoryDef(y) means that x potentially modifies memory that y modifies/constrains (or has modified / constrained). In the same manner, a = MemoryPhi({BB1,b},{BB2,c}) means that anyone that uses a is accessing memory potentially modified / constrained by either b or c (or both). And finally, MemoryUse(x) means that this use accesses memory that x has modified / constrained (as an example, think that if x = MemoryDef(...) and MemoryUse(x) are in the same loop, the use can’t be hoisted outside alone).

Another useful way of looking at it is in terms of memory versions. In that view, operands of a given MemoryAccess are the version of the entire memory before the operation, and if the access produces a value (i.e. MemoryDef/MemoryPhi), the value is the new version of the memory after the operation.

define void @foo() {
entry:
  %p1 = alloca i8
  %p2 = alloca i8
  %p3 = alloca i8
  ; 1 = MemoryDef(liveOnEntry)
  store i8 0, i8* %p3
  br label %while.cond

while.cond:
  ; 6 = MemoryPhi({entry,1},{if.end,4})
  br i1 undef, label %if.then, label %if.else

if.then:
  ; 2 = MemoryDef(6)
  store i8 0, i8* %p1
  br label %if.end

if.else:
  ; 3 = MemoryDef(6)
  store i8 1, i8* %p2
  br label %if.end

if.end:
  ; 5 = MemoryPhi({if.then,2},{if.else,3})
  ; MemoryUse(5)
  %1 = load i8, i8* %p1
  ; 4 = MemoryDef(5)
  store i8 2, i8* %p2
  ; MemoryUse(1)
  %2 = load i8, i8* %p3
  br label %while.cond
}

The MemorySSA IR is shown in comments that precede the instructions they map to (if such an instruction exists). For example, 1 = MemoryDef(liveOnEntry) is a MemoryAccess (specifically, a MemoryDef), and it describes the LLVM instruction store i8 0, i8* %p3. Other places in MemorySSA refer to this particular MemoryDef as 1 (much like how one can refer to load i8, i8* %p1 in LLVM with %1). Again, MemoryPhis don’t correspond to any LLVM Instruction, so the line directly below a MemoryPhi isn’t special.

Going from the top down:

• 6 = MemoryPhi({entry,1},{if.end,4}) notes that, when entering while.cond, the reaching definition for it is either 1 or 4. This MemoryPhi is referred to in the textual IR by the number 6.

• 2 = MemoryDef(6) notes that store i8 0, i8* %p1 is a definition, and its reaching definition before it is 6, or the MemoryPhi after while.cond. (See the Build-time use optimization and Precision sections below for why this MemoryDef isn’t linked to a separate, disambiguated MemoryPhi.)

• 3 = MemoryDef(6) notes that store i8 0, i8* %p2 is a definition; its reaching definition is also 6.

• 5 = MemoryPhi({if.then,2},{if.else,3}) notes that the clobber before this block could either be 2 or 3.

• MemoryUse(5) notes that load i8, i8* %p1 is a use of memory, and that it’s clobbered by 5.

• 4 = MemoryDef(5) notes that store i8 2, i8* %p2 is a definition; it’s reaching definition is 5.

• MemoryUse(1) notes that load i8, i8* %p3 is just a user of memory, and the last thing that could clobber this use is above while.cond (e.g. the store to %p3). In memory versioning parlance, it really only depends on the memory version 1, and is unaffected by the new memory versions generated since then.

As an aside, MemoryAccess is a Value mostly for convenience; it’s not meant to interact with LLVM IR.

Design of MemorySSA

MemorySSA is an analysis that can be built for any arbitrary function. When it’s built, it does a pass over the function’s IR in order to build up its mapping of MemoryAccesses. You can then query MemorySSA for things like the dominance relation between MemoryAccesses, and get the MemoryAccess for any given Instruction .

When MemorySSA is done building, it also hands you a MemorySSAWalker that you can use (see below).

The walker

A structure that helps MemorySSA do its job is the MemorySSAWalker, or the walker, for short. The goal of the walker is to provide answers to clobber queries beyond what’s represented directly by MemoryAccesses. For example, given:

define void @foo() {
  %a = alloca i8
  %b = alloca i8

  ; 1 = MemoryDef(liveOnEntry)
  store i8 0, i8* %a
  ; 2 = MemoryDef(1)
  store i8 0, i8* %b
}

The store to %a is clearly not a clobber for the store to %b. It would be the walker’s goal to figure this out, and return liveOnEntry when queried for the clobber of MemoryAccess 2.

By default, MemorySSA provides a walker that can optimize MemoryDefs and MemoryUses by consulting whatever alias analysis stack you happen to be using. Walkers were built to be flexible, though, so it’s entirely reasonable (and expected) to create more specialized walkers (e.g. one that specifically queries GlobalsAA, one that always stops at MemoryPhi nodes, etc).

Locating clobbers yourself

If you choose to make your own walker, you can find the clobber for a MemoryAccess by walking every MemoryDef that dominates said MemoryAccess. The structure of MemoryDefs makes this relatively simple; they ultimately form a linked list of every clobber that dominates the MemoryAccess that you’re trying to optimize. In other words, the definingAccess of a MemoryDef is always the nearest dominating MemoryDef or MemoryPhi of said MemoryDef.

Build-time use optimization

MemorySSA will optimize some MemoryAccesses at build-time. Specifically, we optimize the operand of every MemoryUse to point to the actual clobber of said MemoryUse. This can be seen in the above example; the second MemoryUse in if.end has an operand of 1, which is a MemoryDef from the entry block. This is done to make walking, value numbering, etc, faster and easier.

It is not possible to optimize MemoryDef in the same way, as we restrict MemorySSA to one memory variable and, thus, one Phi node per block.

Invalidation and updating

Because MemorySSA keeps track of LLVM IR, it needs to be updated whenever the IR is updated. “Update”, in this case, includes the addition, deletion, and motion of Instructions. The update API is being made on an as-needed basis. If you’d like examples, GVNHoist is a user of MemorySSAs update API.

Phi placement

MemorySSA only places MemoryPhis where they’re actually needed. That is, it is a pruned SSA form, like LLVM’s SSA form. For example, consider:

define void @foo() {
entry:
  %p1 = alloca i8
  %p2 = alloca i8
  %p3 = alloca i8
  ; 1 = MemoryDef(liveOnEntry)
  store i8 0, i8* %p3
  br label %while.cond

while.cond:
  ; 3 = MemoryPhi({%0,1},{if.end,2})
  br i1 undef, label %if.then, label %if.else

if.then:
  br label %if.end

if.else:
  br label %if.end

if.end:
  ; MemoryUse(1)
  %1 = load i8, i8* %p1
  ; 2 = MemoryDef(3)
  store i8 2, i8* %p2
  ; MemoryUse(1)
  %2 = load i8, i8* %p3
  br label %while.cond
}

Because we removed the stores from if.then and if.else, a MemoryPhi for if.end would be pointless, so we don’t place one. So, if you need to place a MemoryDef in if.then or if.else, you’ll need to also create a MemoryPhi for if.end.

If it turns out that this is a large burden, we can just place MemoryPhis everywhere. Because we have Walkers that are capable of optimizing above said phis, doing so shouldn’t prohibit optimizations.

Non-Goals

MemorySSA is meant to reason about the relation between memory operations, and enable quicker querying. It isn’t meant to be the single source of truth for all potential memory-related optimizations. Specifically, care must be taken when trying to use MemorySSA to reason about atomic or volatile operations, as in:

define i8 @foo(i8* %a) {
entry:
  br i1 undef, label %if.then, label %if.end

if.then:
  ; 1 = MemoryDef(liveOnEntry)
  %0 = load volatile i8, i8* %a
  br label %if.end

if.end:
  %av = phi i8 [0, %entry], [%0, %if.then]
  ret i8 %av
}

Going solely by MemorySSA’s analysis, hoisting the load to entry may seem legal. Because it’s a volatile load, though, it’s not.

Design tradeoffs

Precision

MemorySSA in LLVM deliberately trades off precision for speed. Let us think about memory variables as if they were disjoint partitions of the memory (that is, if you have one variable, as above, it represents the entire memory, and if you have multiple variables, each one represents some disjoint portion of the memory)

First, because alias analysis results conflict with each other, and each result may be what an analysis wants (IE TBAA may say no-alias, and something else may say must-alias), it is not possible to partition the memory the way every optimization wants. Second, some alias analysis results are not transitive (IE A noalias B, and B noalias C, does not mean A noalias C), so it is not possible to come up with a precise partitioning in all cases without variables to represent every pair of possible aliases. Thus, partitioning precisely may require introducing at least N^2 new virtual variables, phi nodes, etc.

Each of these variables may be clobbered at multiple def sites.

To give an example, if you were to split up struct fields into individual variables, all aliasing operations that may-def multiple struct fields, will may-def more than one of them. This is pretty common (calls, copies, field stores, etc).

Experience with SSA forms for memory in other compilers has shown that it is simply not possible to do this precisely, and in fact, doing it precisely is not worth it, because now all the optimizations have to walk tons and tons of virtual variables and phi nodes.

So we partition. At the point at which you partition, again, experience has shown us there is no point in partitioning to more than one variable. It simply generates more IR, and optimizations still have to query something to disambiguate further anyway.

As a result, LLVM partitions to one variable.

Use Optimization

Unlike other partitioned forms, LLVM’s MemorySSA does make one useful guarantee - all loads are optimized to point at the thing that actually clobbers them. This gives some nice properties. For example, for a given store, you can find all loads actually clobbered by that store by walking the immediate uses of the store.