6 ms·

Why SSA?

222 points by transpute 1y ago

rdtsc 1y ago
I like the style of the blog but a minor nit I'd change is have a definition what SSA is right at the top. It discusses SSA for quite a while "SSA is a property of intermediate representations (IRs)", "it's frequently used" and only 10 paragraphs down actually defines what SSA is > SSA stands for “static single assignment”, and was developed in the 80s as a way to enhance the existing three-argument code (where every statement is in the form x = y op z) so that every program was circuit-like, using a very similar procedure to the one described above. I understand it's one of those "well if you don't know what it is, the post is not for you" but I think it's a nice article and could get people who are not familiar with the details interested in it > The reason this works so well is because we took a function with mutation, and converted it into a combinatorial circuit, a type of digital logic circuit that has no state, and which is very easy to analyze. That's an interesting insight, it made sense to me. I only dealt with SSA when decompiling bytecode or debugging compiler issues, and never knew why it was needed, but that sort of made it click.
- vidarh 1y ago
  This post is frankly one of the most convoluted discussions of SSA I've read. There's lots of info there, but I'd frankly suggest going back and look at a paper on implementing it. I think I first came across SSA in a paper adding it to Wirths Oberon compiler, and it was much more accessible. Edit: It was this paper by Brandis and Mössenböck: https://share.google/QNoV9G8yMBWQJqC82 https://share.google/QNoV9G8yMBWQJqC82
  - jhallenworld 1y ago
    Also I recommend Bob Morgan's book: https://turbo51.com/download/Building-an-Optimizing-Compile-Book-Preview.pdf https://turbo51.com/download/Building-an-Optimizing-Compile-...
    - Rochus 1y ago
      Indeed a great book; I even have a paper copy. The SSA book is also pretty good: https://web.archive.org/web/20201111210448/https://ssabook.gforge.inria.fr/latest/ https://web.archive.org/web/20201111210448/https://ssabook.g...
      - mananaysiempre 1y ago
        I’ve found the SSA book to be... unforgiving in its difficulty. Not in the sense that I thought it to be a bad book but rather in that I was getting the feeling that a dilettante in compilers like me wasn’t the target audience.
        Rochus 1y ago
        Like so many compiler books from academia.
        pbiggar 1y ago
        I was involved in making the book. It is very much a book for academics, and came out of an academic conference bringing together people working at the forefront of SSA-based research.
        mananaysiempre 1y ago
        I mean, once again, I’m not really complaining about the book. It’s fairly mathy, sure, but so what. I also actually welcome that it’s a coherent book rather than a bunch of papers in a trenchcoat or a menagerie of neat things people have thought of (*cough* Paxos variants). It’s rather that it’s a bit unusual in that it’s a coherent book whose prerequisites (on top of an old-timey compilers course, say) I don’t think actually exist in book form (I’d love to be proven wrong, as that’s likely what I need to read). The introductory part does make it self-contained in a sense, but it’s more like those grad-level maths books that include a definitions chapter or three: technically you don’t need to know any of that stuff beforehand, true, but in reality if it does more for you than just fill a few gaps and fix terminology, then you’re not going to have a good time with the rest. Again, just my experience, I don’t know if that’s what you were going for. If there was a criticism implied in my initial comment, it’s that I think that the kind of person that goes looking for literature recommendations in this thread isn’t going to have a good time with it, either; so at the very least they should know what they’re signing up for. But I don’t think you’re really disagreeing with that part?..
  - jchw 1y ago
    Honestly, I think it's just something you either like or don't. If all you were trying to do was understand SSA, I agree this blog post is probably inefficient at that particular task, but often blog posts are entertainment as much as education, so meandering through a bunch of different things along the way is part of the deal. Personally I thought there were a lot of pretty interesting insights that I haven't seen a lot of discussion about in other places, though I will admit I mostly learned about SSA from Wikipedia and from people yelling about compilers online.
  - Rochus 1y ago
    Thanks for the link. Looks like an interesting paper. Here is the original reference: https://dl.acm.org/doi/10.1145/197320.197331 https://dl.acm.org/doi/10.1145/197320.197331. And here is a better readable postscript version: https://web.archive.org/web/20170706013237/ftp://ftp.ssw.uni-linz.ac.at/pub/Papers/Moe94.ps.gz https://web.archive.org/web/20170706013237/ftp://ftp.ssw.uni...
  - anonymousDan 1y ago
    As someone who knows a bit about SSA, what do you make of LLVM's design decision not to use SSA for memory but only registers (i.e. it doesn't have memory SSA)? It has always confused me a bit as to why this was done.
    - vidarh 1y ago
      I don't really follow LLVM. I find it too big and convoluted for the stuff I'm doing.
- strbean 1y ago
  I learned a bit about SSA in a compiler course. Among many other things, it is crucial for register assignment. You want to know each distinct value that will exist, and the lifetimes of those values, in order to give each a register. Then, if have more distinct values existing at one time than you have registers, you have to push stuff to the stack.
  - tylerhou 1y ago
    It is not critical for register assignment -- in fact, SSA makes register assignment more difficult (see the swap problem; the lost copy problem). Lifetime analysis is important for register assignment, and SSA can make lifetime analysis easier, but plenty of non-SSA compilers (lower-tier JIT compilers often do not use SSA because SSA is heavyweight) are able to register allocate just fine without it.
    - tonfa 1y ago
      One nice thing is that it makes register assignment polynomial (the coloring of SSA variables graph is polynomial since it's not an arbitrary graph).
- tylerhou 1y ago
  Here's a concise explanation of SSA. Regular (imperative) code is hard to optimize because in general statements are not pure -- if a statement has side effects, then it might not preserve the behavior to optimize that statement by, for example: 1. Removing that statement (dead code elimination) 2. Deduplicating that statement (available expressions) 3. Reordering that statement with other statements (hoisting; loop-invariant code motion) 4. Duplicating that statement (can be useful to enable other optimizations) All of the above optimizations are very important in compilers, and they are much, much easier to implement if you don't have to worry about preserving side effects while manipulating the program. So the point of SSA is to translate a program into an equivalent program whose statements have as few side effects as possible. The result is often something that looks like a functional program. (See: https://www.cs.princeton.edu/~appel/papers/ssafun.pdf https://www.cs.princeton.edu/~appel/papers/ssafun.pdf, which is famous in the compilers community.) In fact, if you view basic blocks themselves as a function, phi nodes "declare" the arguments of the basic block, and branches correspond to tailcalling the next basic block with corresponding values. This has motivated basic block arguments in MLIR. The "combinatorial circuit" metaphor is slightly wrong, because most SSA implementations do need to consider state for loads and stores into arbitrary memory, or arbitrary function calls. Also, it's not easy to model a loop of arbitrary length as a (finite) combinatorial circuit. Given that the author works at an AI accelerator company, I can see why he leaned towards that metaphor, though.
  - deleted 1y ago
    [deleted]
  - rdtsc 1y ago
    Thank you. That’s a great explanation.
  - esrauch 1y ago
    > Given that the author works at an AI accelerator company I actually believe he works at Buf.build and his resume is stale, the author previously posted about their Go Protobuf parser hyperpb which is a Buf project. Maybe still "author recently worked at an AI accelerator company" though.
- DannyBee 1y ago
  The motivation and reason it works is also wrong anyway. Like i get it's a gentle intro, but i think there are ways to accomplish that without being egregiously history rewriting ;) Ken zadeck was my office mate for years, so this is my recollection, but it's also been a few decades, so sorry for any errors :) The reason of why it works is definitely wrong - they weren't even using rewriting forms of SSA, and didn't for a long time. Even the first "fully SSA" compiler (generally considered to be open64) did not rewrite the IR into SSA. The reason it works so well is because it enables you to perform effective per-variable dataflow. In fact, this is the only problem it solves - the ability to perform unrestricted per-variable dataflow quickly. This was obvious given the historical context at the time, but less obvious now that it is history :) In the simplest essence, SSA enables you to follow chains of dataflow for a variable very easily and simply, and that's probably what i would have said instead. It's true that for simple scalar programs, the variable name reuse that breaks these dataflow chains mostly occur at explicit mutation points, but this is not always correct depending on the compiler IR, and definitely not correct you extend it to memory, among other things. It's also not correct at all as you extend the thing SSA enables you to do (per-variable dataflow quickly) to other classes of problems (SSU, SSI, etc). History wise - this post also sort of implies SSA came out of nowhere and was some revolutionary thing nobody had ever thought about, just sort of developed in the 80's. In fact, it was a formalization of attempts at per-variable dataflow they had been working on for a while. I'd probably just say that as a gentle intro, but if you want the rest of history, here you go: Well before SSA, it was already known that lower bounds on bitvector dataflow (the dominant approach at the time of SSA) were not great. Over the years, it turned out they were much better than initially expected, but in the end, worse than anyone wanted as programs got bigger and bigger. N^2 or N^3 bitvector operations for most problems. Incrementality is basically impossible[2]. They were also hard to understand and debug because of dependencies between related variables, etc. Attempts at faster/better dataflow existed in two rough forms, neither of which are bound by the same lower bound: 1. Structured dataflow/Interval analysis algorithms/Elimination dataflow - reduce the CFG into various types of regions with a known system of equations, solve the equations, distribute the results to the regions. Only works well on reducible graphs Can be done incrementally with care. This was mostly studied in parallel to bitvectors, and was thought heavily about before it became known that there was a class of rapid dataflow problems (IE before the late 70's). Understanding the region equations well enough to debug them requires a very deep understanding of the basis of dataflow - lattices, etc. In that sense it was worse than bitvectors to understand for most people. Graph reducibility restrictions were annoying but tractable on forward graphs through node splitting and whatnot (studies showed 90+% of programs at the time had reducible flowgraphs already), but almost all backwards CFG's are not reducible, making backwards dataflow problems quite annoying. In the end, as iterative dataflow became provably faster/etc, and compilers became the province of more than just theory experts, this sort of died[3]. If you ever become a compiler theory nerd, it's actually really interesting to look at IMHO. 2. Per-variable dataflow approaches. This is basically "solve a dataflow problem for single variable or cluster of variables at a time instead of for all variables at once". There were not actually a ton of people who thought this would ever turn into a practical approach: a. The idea of solving reaching definitions (for example) one variable at a time seemed like it would be much slower than solving it for all variables at once. b. It was very non-obvious how to be able to effectively partition variables to be able to compute a problem on one variable (or a cluster of variables) at a time without it devolving into either bitvector-like time bounds or structured dataflow like math complexity. It was fairly obvious at the time that if you culd make it work, you could probably get much faster incremental dataflow solution. SSA came out of this approach. Kenny's thesis dealt with incremental dataflow and partitioned variable problems, and proved time bounds on various times of partitioned/clustered variable problems. You can even see the basis of SSA in how it thinks about things. Here, i'll quote from a few parts: " As the density of Def sites per variable increases, the average size of the affected area for each change will decrease...". His thesis is (amont other things) on a method for doing this that is typical for the time (IE not SSA): "The mechanism used to enhance performance is raising the density of Def sites for each variable. The most obvious way to increase the Use and Def density is to attempt a reduction on the program flow graph. This reduction would replace groups of nodes by a single new node. This new node would then be labeled with infcrmation that summarized the effects of execution through that group of nodes." This is because, as i mentioned, figuring out how to do it by partitioning the variables based on dominance relationships was not known - that is literally SSA, and also because Kenny wanted to finish his thesis before the heat death of the sun. In this sense, they were already aware that if they got "the right number of names" for a variable, the amount of dataflow computation needed for most problems (reaching defs, etc) would become very small, and that changes would be easy to handle. They knew fairly quickly that for the dataflow problems they wanted to solve, they needed each variable to have a single reaching definition (and reaching definitions was well known), etc. SSA was the incremental culmination of going from there to figuring out a clustering/partitioning of variables that was not based on formally structured control flow regions (which are all-variables things), but instead based on local dataflow for a variable with incorporation of the part of the CFG structure that could actually affect the local result for a given variable. It was approached systematically - understanding the properties they needed, figuring out algorithms that solved them, etc. Like a lot of things that turn out to be unexpectedly useful, take the world by storm, whatever, etc, history later seems to try to often represent them as a eureka moment. [1] Bitvectors are assumed to be fixed size, and thus constant cost, but feel free to add another factor of N here if you want. [2] This is not true in the sense that we knew how to recompute the result incrementally, and end up with a correct result, but doing so provably faster than solving the problem from scratch was not possible. [3] They actually saw somewhat of a resurgence in the world of GPUs and more general computation graphs because it all becomes heavily applicable again to solving. However, we almost always have eventually developed easier to understand (even if potentially slower theory-wise) global algorithms and use those instead, because we have the compute power to do it, and this tradeoff is IMHO worth it.
- paulmooreparks 1y ago
  Yes, this is a problem I see more and more often. Besides the fact that it's always a good habit to spell out an acrostic or abbreviation the first time it's used in an article, there's also the fact that this is, you know, the web, and it's very easy to make a link to a Wikipedia article or something that will explain the term, if you don't want to bother adding your own explanation.
- pbiggar 1y ago
  I don't think it really explains what it's for though. Here's my explanation (from my PhD thesis on compilers): Static single assignment (SSA) form provides an efficient intermediate representation for program analysis [Cytron et al., 1989, 1991]. It was introduced as a way of efficiently representing dataflow analyses. SSA uses a single key idea: that all variables in the program are renamed so that each variable is assigned a value at a single unique statement in the program. From this key idea, SSA is able to provide a number of advantages over other techniques of dataflow analyses: Factored use-def chain: With a def-use chain, dataflow results may be propagated directly from the assignment of a variable to all of its uses. However, a def-use chain requires an edge from each definition to each use, which may be expensive when a program has many definitions and uses of the same variable. In practice, this occurs in the presence of switch-statements. SSA factors the def-use chain over a φ-node, avoiding this pathological case. Flow-sensitivity: A flow-insensitive algorithm performed on an SSA form is much more precise than if SSA form were not used. The flow-insensitive problem of multiple definitions to the same variable is solved by the single assignment property. The allows a flow-insensitive algorithm to approach the precision of a flow-sensitive algorithm. Memory usage: Without SSA form, an analysis must store information for every variable at every program point. SSA form allows a sparse analysis, where an analysis must store information only for every assignment in the program. With a unique version per assignment, the memory usage of storing the results of an analysis can be considerably lower than using bit-vector or set-based approaches.
noelwelsh 1y ago
The shocking truth is that SSA is functional! That's right, the compiler for your favourite imperative language actually optimizes functional programs. See, for example, https://www.jantar.org/papers/chakravarty03perspective.pdf https://www.jantar.org/papers/chakravarty03perspective.pdf. In fact, SSA, continuation passing style, and ANF are basically the same thing.
- Chabsff 1y ago
  My experience with SSA is extremely limited, so that might be a stupid question. But does that remain true once memory enters the picture? The llvm tutorials I played with (admittedly a long time ago) made it seem like "just allocate everything and trust mem2reg" basically abstracted SSA pretty completely from a user pov.
  - PhilipRoman 1y ago
    If you're hell bent on functional style, you can represent memory writes as ((Address, Value, X) -> X), where X is a compile-time-only linear type representing the current memory state, which can be manipulated like any other SSA variable. It makes some things more elegant, like two reads of the same address naturally being the same value (as long as it's reading from the same memory state). Doesn't help at all with aliasing analysis or write reordering though so I don't think any serious compilers do this.
    - titzer 1y ago
      The sea-of-nodes representation renames memory as just another dependence edge in a somewhat analogous manner.
    - JonChesterfield 1y ago
      It helps _lots_ with aliasing analysis if you've got multiple instances of X representing disjoint areas of the address space. Could call them "heaps".
  - noelwelsh 1y ago
mbauman 1y ago
Forget compilers, SSA is an immensely valuable readability improvement for humans, too.
- MeetingsBrowser 1y ago
 Why have while (c < 10) { c *= 3; } when you could have %2 = alloca i32, align 4 %3 = alloca i32, align 4 store i32 %0, ptr %3, align 4 br label %4, !dbg !18 4: %5 = load i32, ptr %3, align 4, !dbg !19 %6 = icmp slt i32 %5, 10, !dbg !20 br i1 %6, label %7, label %10, !dbg !18 7: %8 = load i32, ptr %3, align 4, !dbg !21 %9 = mul nsw i32 %8, 3, !dbg !21 store i32 %9, ptr %3, align 4, !dbg !21 br label %4, !dbg !18
 - JonChesterfield 1y ago
 Try mem2reg on that to get rid of the loads and stores.
 - James_K 1y ago
 The second code snippet doesn't use SSA. It just translates the first loop into IR and mangles the variable names. Here is an SSA version of that in the Scheme language. (let loop ((c c)) (if (< c 10) (loop (* c 3)) c)) Notice that this is stateless and also returns the final value of “c” from the loop. People who use the below style have tended to find that it is much easier to reason about for more complicated looping structures.
 - MeetingsBrowser 1y ago
 I intended it to be mostly a joke. Many people equate LLVM IR with SSA. I might even argue that easy to read and easy to reason about are opposites. For the most part, languages like Python and Ruby can be very easy to read but difficult to understand precisely what actually happens at runtime. Things like LLVM IR are much more explicit, making it easier to reason about but extremely difficult to read. Maybe somewhere between is "pure" side effect free functional programs.
zachixer 1y ago
Every time I see a clean SSA explainer like this, I’m reminded that the “simplicity” of SSA only exists because we’ve decided mutation is evil. It’s not that SSA is simpler — it’s that we’ve engineered our entire optimization pipeline around pretending state doesn’t exist. It’s a brilliant illusion that works… until you hit aliasing, memory models, or concurrency, and suddenly the beautiful DAG collapses into a pile of phi nodes and load/store hell.
- vidarh 1y ago
  SSA is appealing because you can defer the load/store hell until after a bunch of optimizations, though, and a lot of those optimizations becomes a lot easier to reason about when you get to pretend state doesn't exist.
- achierius 1y ago
  You have it backwards. Modern compilers don't use SSA because it's "simpler", we use it because it enables very fast data-flow optimizations (constant prop, CSE, register allocation, etc.) that would otherwise require a lot of state. It doesn't "pretend state doesn't exist", it's actually exactly what makes it possible/practical for the compiler to handle changes in state. As some evidence to the second point: Haskell is a language that does enforce immutability, but it's compiler, GHC, does not use SSA for main IR -- it uses a "spineless tagless g-machine" graph representation that does, in fact, rely on that immutability. SSA only happens later once it's lowered to a mutating form. If your variables aren't mutated, then you don't even need to transform them to SSA! Of course, you're welcome to try something else, people certainly have -- take a look at how V8's move to Sea-of-Nodes has gone for them.
  - antonvs 1y ago
    > take a look at how V8's move to Sea-of-Nodes has gone for them. Are you implying it hasn't gone well? I thought it bought some performance at least. What are the major issues? Any sources I can follow up on?
    - kibwen 1y ago
KeplerBoy 1y ago
Smallest of nitpicks: the depicted multiplier is a 2 bit multiplier. A one bit multiplier is just an and gate.
pubby 1y ago
I like this article a lot but it doesn't answer the question of "Why SSA?". Sure, a graph representation is nice, but that isn't a unique property of SSA. You can have graph IRs that aren't SSA at all. And sure, SSA makes some optimizations easy, but it also makes other operations more difficult. When you consider that, plus the fact that going into and out of SSA is quite involved, it doesn't seem like SSA is worth the fuss. So why SSA? Well, it turns out compilers have sequencing issues. If you view compilation as a series of small code transformations, your representation goes from A -> B, then B -> C, then C -> D and so on. At least, that's how it works for non-optimizing compilers. For optimizing compilers however, passes want to loop. Whenever an optimization is found, previous passes should be run again with new inputs... if possible. The easiest way to ensure this is to make all optimizations input and output the same representation. So A -> B is no good. We want A -> A: a singular representation. So if we want a singular representation, let's pick a good one right? One that works reasonably well for most things. That's why SSA is useful: it's a decently good singular representation we can use for every pass.
- ebiederm 1y ago
  In the basic block with arguments variation there is no going in and out of SSA.
  - Findecanor 1y ago
    Phi-functions and block arguments are just different views of the same thing. Sometimes it is more convenient to use one or the other when thinking of a problem. If you lay out phi-functions and their parameters on a grid, you'd get a "phi-matrix" where phi-functions are rows and block arguments are the columns. If you don't do an out-of-SSA transform before register allocation, and effectively treat block parameters like function calls then you're pushing the complexity to the register allocator. An out-of-SSA transform before register allocation would coalesce not just registers but also variables in spill slots (thus avoiding memory-memory moves), it would reduce the complexity of parallel moves. A more advanced transform could also hoist moves out from before the hottest branch which could potentially lead to un-splitting previously split critical edges.
- 1y ago
ivanjermakov 1y ago
Static single assignment (SSA)
torginus 1y ago
SSA makes me think of a few interesting points: Considering it's a functional language (bar memory access bits), and most procedural languages can target this, we can say that a lot of procedural code can be compiled down to functional code - so procedural programming is syntactic sugar on top of a functional framework Also functional programmers have a couple of pet peeves - tail recursion to implement infinite recursion and loops being one. SSA uses a completely different paradigm - phi nodes - to achieve looping. Considering I don't particularly like tail recursion, as for example the naive recursive implementation of fibonacci is not tail recursive (and thus dangerous, a property that a functional program should never have), and trying to make it tail recursive looks very much like a transformation a compiler should do, which goes against the spirit of functional programming. I think functional programmers should think of other constructs to achieve infinite recursion or looping, considering I suspect there are infinitely many possible, I guess we could discover ones that are less inherently dangerous and easier to reason about as mere mortals.
- JonChesterfield 1y ago
  The transition from one basic block to another is to copy the live values to some common location, jump the instruction counter, then copy the values out of that location to give the results of the phi nodes. The transition from one function to another is to copy the arguments to some common location, jump the instruction counter, then copy the values our of that location to give the initial values of the parameters. These are the same thing, except that the branch in the first case is always at the end of the block. In the tail position. Your preferred looping construct of branching between basic blocks is _identically_ tail calls between functions, except that some of the block arguments are represented as phi nodes. This is because the blocks are functions.
  - torginus 1y ago
    I see your point - tail calls are identical to MLIR-style phi nodes, where not the branch source determines the value, but it's passed explicitly as a function argument. I still think that tail recursion is too low level a construct for functional programmers to interact with, but it's wrapped into something like a reduce operation, which allows to write an identical fibonacci impl, as you would in a procedural language.
ModernMech 1y ago
That minimap is wild, it duplicates the entire post but every word is surrounded by a span. I thought maybe it was like a bitmap or something but no: SSA is hugely popular, to the point that most compiler projects no longer bother with other IRs for optimization<a href="#fn:ghc" class="footnote" rel="footnote">7</a>.
unit149 1y ago
[dead]
anon291 1y ago
SSA is a representation of closed Cartesian categories that looks like normal code. Closed Cartesian categories model computation. You don't need SSA and modern compiler frameworks like MLIR make better choices that still mostly use SSA but have more sanity when it comes to basic block boundaries (treat them as having arguments, instead of phi nodes).
mhh__ 1y ago
https://lwn.net/Articles/84888/ https://lwn.net/Articles/84888/ bit of compiler history on GCC's move to SSA way back when
yencabulator 1y ago
I find basic block arguments much much more readable than phi functions. https://2pi.dk/2022/05/bb-arguments https://2pi.dk/2022/05/bb-arguments

222 points by transpute 1y ago

I like the style of the blog but a minor nit I'd change is have a definition what SSA is right at the top. It discusses SSA for quite a while "SSA is a property of intermediate representations (IRs)", "it's frequently used" and only 10 paragraphs down actually defines what SSA is > SSA stands for “static single assignment”, and was developed in the 80s as a way to enhance the existing three-argument code (where every statement is in the form x = y op z) so that every program was circuit-like, using a very similar procedure to the one described above. I understand it's one of those "well if you don't know what it is, the post is not for you" but I think it's a nice article and could get people who are not familiar with the details interested in it > The reason this works so well is because we took a function with mutation, and converted it into a combinatorial circuit, a type of digital logic circuit that has no state, and which is very easy to analyze. That's an interesting insight, it made sense to me. I only dealt with SSA when decompiling bytecode or debugging compiler issues, and never knew why it was needed, but that sort of made it click.

vidarh 1y ago
This post is frankly one of the most convoluted discussions of SSA I've read. There's lots of info there, but I'd frankly suggest going back and look at a paper on implementing it. I think I first came across SSA in a paper adding it to Wirths Oberon compiler, and it was much more accessible. Edit: It was this paper by Brandis and Mössenböck: https://share.google/QNoV9G8yMBWQJqC82 https://share.google/QNoV9G8yMBWQJqC82
- jhallenworld 1y ago
  Also I recommend Bob Morgan's book: https://turbo51.com/download/Building-an-Optimizing-Compile-Book-Preview.pdf https://turbo51.com/download/Building-an-Optimizing-Compile-...
  - Rochus 1y ago
    Indeed a great book; I even have a paper copy. The SSA book is also pretty good: https://web.archive.org/web/20201111210448/https://ssabook.gforge.inria.fr/latest/ https://web.archive.org/web/20201111210448/https://ssabook.g...
    - mananaysiempre 1y ago
      I’ve found the SSA book to be... unforgiving in its difficulty. Not in the sense that I thought it to be a bad book but rather in that I was getting the feeling that a dilettante in compilers like me wasn’t the target audience.
      - Rochus 1y ago
        Like so many compiler books from academia.
      - pbiggar 1y ago
        I was involved in making the book. It is very much a book for academics, and came out of an academic conference bringing together people working at the forefront of SSA-based research.
        mananaysiempre 1y ago
        I mean, once again, I’m not really complaining about the book. It’s fairly mathy, sure, but so what. I also actually welcome that it’s a coherent book rather than a bunch of papers in a trenchcoat or a menagerie of neat things people have thought of (*cough* Paxos variants). It’s rather that it’s a bit unusual in that it’s a coherent book whose prerequisites (on top of an old-timey compilers course, say) I don’t think actually exist in book form (I’d love to be proven wrong, as that’s likely what I need to read). The introductory part does make it self-contained in a sense, but it’s more like those grad-level maths books that include a definitions chapter or three: technically you don’t need to know any of that stuff beforehand, true, but in reality if it does more for you than just fill a few gaps and fix terminology, then you’re not going to have a good time with the rest. Again, just my experience, I don’t know if that’s what you were going for. If there was a criticism implied in my initial comment, it’s that I think that the kind of person that goes looking for literature recommendations in this thread isn’t going to have a good time with it, either; so at the very least they should know what they’re signing up for. But I don’t think you’re really disagreeing with that part?..
- jchw 1y ago
  Honestly, I think it's just something you either like or don't. If all you were trying to do was understand SSA, I agree this blog post is probably inefficient at that particular task, but often blog posts are entertainment as much as education, so meandering through a bunch of different things along the way is part of the deal. Personally I thought there were a lot of pretty interesting insights that I haven't seen a lot of discussion about in other places, though I will admit I mostly learned about SSA from Wikipedia and from people yelling about compilers online.
- Rochus 1y ago
  Thanks for the link. Looks like an interesting paper. Here is the original reference: https://dl.acm.org/doi/10.1145/197320.197331 https://dl.acm.org/doi/10.1145/197320.197331. And here is a better readable postscript version: https://web.archive.org/web/20170706013237/ftp://ftp.ssw.uni-linz.ac.at/pub/Papers/Moe94.ps.gz https://web.archive.org/web/20170706013237/ftp://ftp.ssw.uni...
- anonymousDan 1y ago
  As someone who knows a bit about SSA, what do you make of LLVM's design decision not to use SSA for memory but only registers (i.e. it doesn't have memory SSA)? It has always confused me a bit as to why this was done.
  - vidarh 1y ago
    I don't really follow LLVM. I find it too big and convoluted for the stuff I'm doing.
strbean 1y ago
I learned a bit about SSA in a compiler course. Among many other things, it is crucial for register assignment. You want to know each distinct value that will exist, and the lifetimes of those values, in order to give each a register. Then, if have more distinct values existing at one time than you have registers, you have to push stuff to the stack.
- tylerhou 1y ago
  It is not critical for register assignment -- in fact, SSA makes register assignment more difficult (see the swap problem; the lost copy problem). Lifetime analysis is important for register assignment, and SSA can make lifetime analysis easier, but plenty of non-SSA compilers (lower-tier JIT compilers often do not use SSA because SSA is heavyweight) are able to register allocate just fine without it.
  - tonfa 1y ago
    One nice thing is that it makes register assignment polynomial (the coloring of SSA variables graph is polynomial since it's not an arbitrary graph).
tylerhou 1y ago
Here's a concise explanation of SSA. Regular (imperative) code is hard to optimize because in general statements are not pure -- if a statement has side effects, then it might not preserve the behavior to optimize that statement by, for example: 1. Removing that statement (dead code elimination) 2. Deduplicating that statement (available expressions) 3. Reordering that statement with other statements (hoisting; loop-invariant code motion) 4. Duplicating that statement (can be useful to enable other optimizations) All of the above optimizations are very important in compilers, and they are much, much easier to implement if you don't have to worry about preserving side effects while manipulating the program. So the point of SSA is to translate a program into an equivalent program whose statements have as few side effects as possible. The result is often something that looks like a functional program. (See: https://www.cs.princeton.edu/~appel/papers/ssafun.pdf https://www.cs.princeton.edu/~appel/papers/ssafun.pdf, which is famous in the compilers community.) In fact, if you view basic blocks themselves as a function, phi nodes "declare" the arguments of the basic block, and branches correspond to tailcalling the next basic block with corresponding values. This has motivated basic block arguments in MLIR. The "combinatorial circuit" metaphor is slightly wrong, because most SSA implementations do need to consider state for loads and stores into arbitrary memory, or arbitrary function calls. Also, it's not easy to model a loop of arbitrary length as a (finite) combinatorial circuit. Given that the author works at an AI accelerator company, I can see why he leaned towards that metaphor, though.
- deleted 1y ago
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- rdtsc 1y ago
  Thank you. That’s a great explanation.
- esrauch 1y ago
  > Given that the author works at an AI accelerator company I actually believe he works at Buf.build and his resume is stale, the author previously posted about their Go Protobuf parser hyperpb which is a Buf project. Maybe still "author recently worked at an AI accelerator company" though.
DannyBee 1y ago
The motivation and reason it works is also wrong anyway. Like i get it's a gentle intro, but i think there are ways to accomplish that without being egregiously history rewriting ;) Ken zadeck was my office mate for years, so this is my recollection, but it's also been a few decades, so sorry for any errors :) The reason of why it works is definitely wrong - they weren't even using rewriting forms of SSA, and didn't for a long time. Even the first "fully SSA" compiler (generally considered to be open64) did not rewrite the IR into SSA. The reason it works so well is because it enables you to perform effective per-variable dataflow. In fact, this is the only problem it solves - the ability to perform unrestricted per-variable dataflow quickly. This was obvious given the historical context at the time, but less obvious now that it is history :) In the simplest essence, SSA enables you to follow chains of dataflow for a variable very easily and simply, and that's probably what i would have said instead. It's true that for simple scalar programs, the variable name reuse that breaks these dataflow chains mostly occur at explicit mutation points, but this is not always correct depending on the compiler IR, and definitely not correct you extend it to memory, among other things. It's also not correct at all as you extend the thing SSA enables you to do (per-variable dataflow quickly) to other classes of problems (SSU, SSI, etc). History wise - this post also sort of implies SSA came out of nowhere and was some revolutionary thing nobody had ever thought about, just sort of developed in the 80's. In fact, it was a formalization of attempts at per-variable dataflow they had been working on for a while. I'd probably just say that as a gentle intro, but if you want the rest of history, here you go: Well before SSA, it was already known that lower bounds on bitvector dataflow (the dominant approach at the time of SSA) were not great. Over the years, it turned out they were much better than initially expected, but in the end, worse than anyone wanted as programs got bigger and bigger. N^2 or N^3 bitvector operations for most problems. Incrementality is basically impossible[2]. They were also hard to understand and debug because of dependencies between related variables, etc. Attempts at faster/better dataflow existed in two rough forms, neither of which are bound by the same lower bound: 1. Structured dataflow/Interval analysis algorithms/Elimination dataflow - reduce the CFG into various types of regions with a known system of equations, solve the equations, distribute the results to the regions. Only works well on reducible graphs Can be done incrementally with care. This was mostly studied in parallel to bitvectors, and was thought heavily about before it became known that there was a class of rapid dataflow problems (IE before the late 70's). Understanding the region equations well enough to debug them requires a very deep understanding of the basis of dataflow - lattices, etc. In that sense it was worse than bitvectors to understand for most people. Graph reducibility restrictions were annoying but tractable on forward graphs through node splitting and whatnot (studies showed 90+% of programs at the time had reducible flowgraphs already), but almost all backwards CFG's are not reducible, making backwards dataflow problems quite annoying. In the end, as iterative dataflow became provably faster/etc, and compilers became the province of more than just theory experts, this sort of died[3]. If you ever become a compiler theory nerd, it's actually really interesting to look at IMHO. 2. Per-variable dataflow approaches. This is basically "solve a dataflow problem for single variable or cluster of variables at a time instead of for all variables at once". There were not actually a ton of people who thought this would ever turn into a practical approach: a. The idea of solving reaching definitions (for example) one variable at a time seemed like it would be much slower than solving it for all variables at once. b. It was very non-obvious how to be able to effectively partition variables to be able to compute a problem on one variable (or a cluster of variables) at a time without it devolving into either bitvector-like time bounds or structured dataflow like math complexity. It was fairly obvious at the time that if you culd make it work, you could probably get much faster incremental dataflow solution. SSA came out of this approach. Kenny's thesis dealt with incremental dataflow and partitioned variable problems, and proved time bounds on various times of partitioned/clustered variable problems. You can even see the basis of SSA in how it thinks about things. Here, i'll quote from a few parts: " As the density of Def sites per variable increases, the average size of the affected area for each change will decrease...". His thesis is (amont other things) on a method for doing this that is typical for the time (IE not SSA): "The mechanism used to enhance performance is raising the density of Def sites for each variable. The most obvious way to increase the Use and Def density is to attempt a reduction on the program flow graph. This reduction would replace groups of nodes by a single new node. This new node would then be labeled with infcrmation that summarized the effects of execution through that group of nodes." This is because, as i mentioned, figuring out how to do it by partitioning the variables based on dominance relationships was not known - that is literally SSA, and also because Kenny wanted to finish his thesis before the heat death of the sun. In this sense, they were already aware that if they got "the right number of names" for a variable, the amount of dataflow computation needed for most problems (reaching defs, etc) would become very small, and that changes would be easy to handle. They knew fairly quickly that for the dataflow problems they wanted to solve, they needed each variable to have a single reaching definition (and reaching definitions was well known), etc. SSA was the incremental culmination of going from there to figuring out a clustering/partitioning of variables that was not based on formally structured control flow regions (which are all-variables things), but instead based on local dataflow for a variable with incorporation of the part of the CFG structure that could actually affect the local result for a given variable. It was approached systematically - understanding the properties they needed, figuring out algorithms that solved them, etc. Like a lot of things that turn out to be unexpectedly useful, take the world by storm, whatever, etc, history later seems to try to often represent them as a eureka moment. [1] Bitvectors are assumed to be fixed size, and thus constant cost, but feel free to add another factor of N here if you want. [2] This is not true in the sense that we knew how to recompute the result incrementally, and end up with a correct result, but doing so provably faster than solving the problem from scratch was not possible. [3] They actually saw somewhat of a resurgence in the world of GPUs and more general computation graphs because it all becomes heavily applicable again to solving. However, we almost always have eventually developed easier to understand (even if potentially slower theory-wise) global algorithms and use those instead, because we have the compute power to do it, and this tradeoff is IMHO worth it.
paulmooreparks 1y ago
Yes, this is a problem I see more and more often. Besides the fact that it's always a good habit to spell out an acrostic or abbreviation the first time it's used in an article, there's also the fact that this is, you know, the web, and it's very easy to make a link to a Wikipedia article or something that will explain the term, if you don't want to bother adding your own explanation.
pbiggar 1y ago
I don't think it really explains what it's for though. Here's my explanation (from my PhD thesis on compilers): Static single assignment (SSA) form provides an efficient intermediate representation for program analysis [Cytron et al., 1989, 1991]. It was introduced as a way of efficiently representing dataflow analyses. SSA uses a single key idea: that all variables in the program are renamed so that each variable is assigned a value at a single unique statement in the program. From this key idea, SSA is able to provide a number of advantages over other techniques of dataflow analyses: Factored use-def chain: With a def-use chain, dataflow results may be propagated directly from the assignment of a variable to all of its uses. However, a def-use chain requires an edge from each definition to each use, which may be expensive when a program has many definitions and uses of the same variable. In practice, this occurs in the presence of switch-statements. SSA factors the def-use chain over a φ-node, avoiding this pathological case. Flow-sensitivity: A flow-insensitive algorithm performed on an SSA form is much more precise than if SSA form were not used. The flow-insensitive problem of multiple definitions to the same variable is solved by the single assignment property. The allows a flow-insensitive algorithm to approach the precision of a flow-sensitive algorithm. Memory usage: Without SSA form, an analysis must store information for every variable at every program point. SSA form allows a sparse analysis, where an analysis must store information only for every assignment in the program. With a unique version per assignment, the memory usage of storing the results of an analysis can be considerably lower than using bit-vector or set-based approaches.

noelwelsh 1y ago

The shocking truth is that SSA is functional! That's right, the compiler for your favourite imperative language actually optimizes functional programs. See, for example, https://www.jantar.org/papers/chakravarty03perspective.pdf https://www.jantar.org/papers/chakravarty03perspective.pdf. In fact, SSA, continuation passing style, and ANF are basically the same thing.

Chabsff 1y ago
My experience with SSA is extremely limited, so that might be a stupid question. But does that remain true once memory enters the picture? The llvm tutorials I played with (admittedly a long time ago) made it seem like "just allocate everything and trust mem2reg" basically abstracted SSA pretty completely from a user pov.
- PhilipRoman 1y ago
  If you're hell bent on functional style, you can represent memory writes as ((Address, Value, X) -> X), where X is a compile-time-only linear type representing the current memory state, which can be manipulated like any other SSA variable. It makes some things more elegant, like two reads of the same address naturally being the same value (as long as it's reading from the same memory state). Doesn't help at all with aliasing analysis or write reordering though so I don't think any serious compilers do this.
  - titzer 1y ago
    The sea-of-nodes representation renames memory as just another dependence edge in a somewhat analogous manner.
  - JonChesterfield 1y ago
    It helps _lots_ with aliasing analysis if you've got multiple instances of X representing disjoint areas of the address space. Could call them "heaps".
- noelwelsh 1y ago

mbauman 1y ago

Forget compilers, SSA is an immensely valuable readability improvement for humans, too.

MeetingsBrowser 1y ago
Why have while (c < 10) { c *= 3; } when you could have %2 = alloca i32, align 4 %3 = alloca i32, align 4 store i32 %0, ptr %3, align 4 br label %4, !dbg !18 4: %5 = load i32, ptr %3, align 4, !dbg !19 %6 = icmp slt i32 %5, 10, !dbg !20 br i1 %6, label %7, label %10, !dbg !18 7: %8 = load i32, ptr %3, align 4, !dbg !21 %9 = mul nsw i32 %8, 3, !dbg !21 store i32 %9, ptr %3, align 4, !dbg !21 br label %4, !dbg !18
- JonChesterfield 1y ago
 Try mem2reg on that to get rid of the loads and stores.
- James_K 1y ago
 The second code snippet doesn't use SSA. It just translates the first loop into IR and mangles the variable names. Here is an SSA version of that in the Scheme language. (let loop ((c c)) (if (< c 10) (loop (* c 3)) c)) Notice that this is stateless and also returns the final value of “c” from the loop. People who use the below style have tended to find that it is much easier to reason about for more complicated looping structures.
 - MeetingsBrowser 1y ago
 I intended it to be mostly a joke. Many people equate LLVM IR with SSA. I might even argue that easy to read and easy to reason about are opposites. For the most part, languages like Python and Ruby can be very easy to read but difficult to understand precisely what actually happens at runtime. Things like LLVM IR are much more explicit, making it easier to reason about but extremely difficult to read. Maybe somewhere between is "pure" side effect free functional programs.

zachixer 1y ago

Every time I see a clean SSA explainer like this, I’m reminded that the “simplicity” of SSA only exists because we’ve decided mutation is evil. It’s not that SSA is simpler — it’s that we’ve engineered our entire optimization pipeline around pretending state doesn’t exist. It’s a brilliant illusion that works… until you hit aliasing, memory models, or concurrency, and suddenly the beautiful DAG collapses into a pile of phi nodes and load/store hell.

vidarh 1y ago
SSA is appealing because you can defer the load/store hell until after a bunch of optimizations, though, and a lot of those optimizations becomes a lot easier to reason about when you get to pretend state doesn't exist.
achierius 1y ago
You have it backwards. Modern compilers don't use SSA because it's "simpler", we use it because it enables very fast data-flow optimizations (constant prop, CSE, register allocation, etc.) that would otherwise require a lot of state. It doesn't "pretend state doesn't exist", it's actually exactly what makes it possible/practical for the compiler to handle changes in state. As some evidence to the second point: Haskell is a language that does enforce immutability, but it's compiler, GHC, does not use SSA for main IR -- it uses a "spineless tagless g-machine" graph representation that does, in fact, rely on that immutability. SSA only happens later once it's lowered to a mutating form. If your variables aren't mutated, then you don't even need to transform them to SSA! Of course, you're welcome to try something else, people certainly have -- take a look at how V8's move to Sea-of-Nodes has gone for them.
- antonvs 1y ago
  > take a look at how V8's move to Sea-of-Nodes has gone for them. Are you implying it hasn't gone well? I thought it bought some performance at least. What are the major issues? Any sources I can follow up on?
  - kibwen 1y ago

KeplerBoy 1y ago

Smallest of nitpicks: the depicted multiplier is a 2 bit multiplier. A one bit multiplier is just an and gate.

pubby 1y ago

I like this article a lot but it doesn't answer the question of "Why SSA?". Sure, a graph representation is nice, but that isn't a unique property of SSA. You can have graph IRs that aren't SSA at all. And sure, SSA makes some optimizations easy, but it also makes other operations more difficult. When you consider that, plus the fact that going into and out of SSA is quite involved, it doesn't seem like SSA is worth the fuss. So why SSA? Well, it turns out compilers have sequencing issues. If you view compilation as a series of small code transformations, your representation goes from A -> B, then B -> C, then C -> D and so on. At least, that's how it works for non-optimizing compilers. For optimizing compilers however, passes want to loop. Whenever an optimization is found, previous passes should be run again with new inputs... if possible. The easiest way to ensure this is to make all optimizations input and output the same representation. So A -> B is no good. We want A -> A: a singular representation. So if we want a singular representation, let's pick a good one right? One that works reasonably well for most things. That's why SSA is useful: it's a decently good singular representation we can use for every pass.

ebiederm 1y ago
In the basic block with arguments variation there is no going in and out of SSA.
- Findecanor 1y ago
  Phi-functions and block arguments are just different views of the same thing. Sometimes it is more convenient to use one or the other when thinking of a problem. If you lay out phi-functions and their parameters on a grid, you'd get a "phi-matrix" where phi-functions are rows and block arguments are the columns. If you don't do an out-of-SSA transform before register allocation, and effectively treat block parameters like function calls then you're pushing the complexity to the register allocator. An out-of-SSA transform before register allocation would coalesce not just registers but also variables in spill slots (thus avoiding memory-memory moves), it would reduce the complexity of parallel moves. A more advanced transform could also hoist moves out from before the hottest branch which could potentially lead to un-splitting previously split critical edges.
1y ago

ivanjermakov 1y ago

Static single assignment (SSA)

torginus 1y ago

SSA makes me think of a few interesting points: Considering it's a functional language (bar memory access bits), and most procedural languages can target this, we can say that a lot of procedural code can be compiled down to functional code - so procedural programming is syntactic sugar on top of a functional framework Also functional programmers have a couple of pet peeves - tail recursion to implement infinite recursion and loops being one. SSA uses a completely different paradigm - phi nodes - to achieve looping. Considering I don't particularly like tail recursion, as for example the naive recursive implementation of fibonacci is not tail recursive (and thus dangerous, a property that a functional program should never have), and trying to make it tail recursive looks very much like a transformation a compiler should do, which goes against the spirit of functional programming. I think functional programmers should think of other constructs to achieve infinite recursion or looping, considering I suspect there are infinitely many possible, I guess we could discover ones that are less inherently dangerous and easier to reason about as mere mortals.

JonChesterfield 1y ago
The transition from one basic block to another is to copy the live values to some common location, jump the instruction counter, then copy the values out of that location to give the results of the phi nodes. The transition from one function to another is to copy the arguments to some common location, jump the instruction counter, then copy the values our of that location to give the initial values of the parameters. These are the same thing, except that the branch in the first case is always at the end of the block. In the tail position. Your preferred looping construct of branching between basic blocks is _identically_ tail calls between functions, except that some of the block arguments are represented as phi nodes. This is because the blocks are functions.
- torginus 1y ago
  I see your point - tail calls are identical to MLIR-style phi nodes, where not the branch source determines the value, but it's passed explicitly as a function argument. I still think that tail recursion is too low level a construct for functional programmers to interact with, but it's wrapped into something like a reduce operation, which allows to write an identical fibonacci impl, as you would in a procedural language.

ModernMech 1y ago

That minimap is wild, it duplicates the entire post but every word is surrounded by a span. I thought maybe it was like a bitmap or something but no: SSA is hugely popular, to the point that most compiler projects no longer bother with other IRs for optimization<a href="#fn:ghc" class="footnote" rel="footnote">7</a>.

unit149 1y ago

[dead]

anon291 1y ago

SSA is a representation of closed Cartesian categories that looks like normal code. Closed Cartesian categories model computation. You don't need SSA and modern compiler frameworks like MLIR make better choices that still mostly use SSA but have more sanity when it comes to basic block boundaries (treat them as having arguments, instead of phi nodes).

mhh__ 1y ago

https://lwn.net/Articles/84888/ https://lwn.net/Articles/84888/ bit of compiler history on GCC's move to SSA way back when

yencabulator 1y ago

I find basic block arguments much much more readable than phi functions. https://2pi.dk/2022/05/bb-arguments https://2pi.dk/2022/05/bb-arguments