Ways to generate SSA
36 comments
·February 11, 2025pizlonator
ebiederm
I guess that depends on what you mean by equivalence between CPS and SSA.
My prefered form is basic blocks with arguments. Where the final jump has parameters it passes to it's destination blocks.
That form has a 1-1 equivalence with SSA and I find it much easier to reason about. Every SSA algorithm I have looked at so far works just fine on the representation. Plus there is none of the annoying transforming into and out of SSA.
If you omit the mucking about with return closures in CPS what is left is basic blocks with arguments.
To see basic blocks with arguments as a form of SSA just see every basic block argument as a phi function, and the callers parameters that feed into that argument as the other end of the sources of the phi function.
Just from your description I think your pizlo special SSA is actually a form of basic blocks with arguments. What I don't see from your description is why Upsilon and phi aren't combined into a single notion (What I would call an incoming block parameter).
tylerhou
Nit: the correspondence between phi-SSA and basic block arguments is not one to one. With block arguments, you can jump to the same block with different arguments depending on a condition. You can’t do that in SSA without adding new blocks.
pizlonator
Pizlo form is not basic block with arguments, because basic blocks don't have arguments in Pizlo form.
I don't think basic block with arguments is CPS because CPS, in practice, involves return closures.
ebiederm
What is Upsilon? It sounds like something that figures out the value coming into a block, which I would call a basic block argument.
How does Upsilon know which values from other basic blocks it could receive? That information is critical for transformations like constant propagation, and register allocation.
zozbot234
Isn't it supposed to be ANF ("A-normal form") rather than full CPS? That looks a bit closer to what you're talking about re: basic blocks w/ arguments.
zzo38computer
> My prefered form is basic blocks with arguments. Where the final jump has parameters it passes to it's destination blocks.
This was my idea too; I also think this is better.
herobird
Have you had experience implementing SSA via sea-of-nodes representation? Could it be that in this case dominance frontier is no longer important and one could use the simpler SSA construction algorithms that do not require dominance frontiers?
k4st
The Pizlo special approach sounds a bit like converting out of SSA form via compensating `alloca`s in LLVM. E.g. one `alloca` per SSA variable, with a `store` into the `alloca` in the source block, and the `phi` replaced by a `load`.
If this is the case, this is an approach I've taken in the past to unify how LLVM-based taint tracking instrumentation of "normal" `alloca`s and phi nodes works, e.g.: https://github.com/lifting-bits/vmill/blob/master/tools/Tain...
pizlonator
It's not, because the Phi's in Pizlo form introduce a Static Single Use variable, which makes them easy to analyze.
Allocas have no requirement that there's a static single use. They are quite hard to analyze.
fuhsnn
>Phi just loads the value out of its shadow variable and assigns it to its implicit variable.
Isn't this similar to block arguments? These shadow variables would have been block parameters, just unordered and maybe not explicitly collected in a set.
tekknolagi
Please write up your "Pizlo special" on Phi nodes
pizlonator
Sure.
Let's first define a syntax for SSA and some terminology. Here's an example SSA node:
A = Add(B, C)
X = Sub(A, 1)
Here's an example function:
int foo(int a, int b)
{
int x;
if (a)
x = b + 1
else
x = b * 2
return x + 42;
}
root:
A = GetArgument(0)
B = GetArgument(1)
Branch(A, then, else)
then:
X1 = Add(B, 1)
Upsilon(X1, ^X)
Jump(return)
else:
X2 = Mul(B, 2)
Upsilon(X2, ^X)
Jump(return)
return:
X = Phi()
R = Add(X, 42)
Return(R)
- Every SSA node has an implicit variable, as mentioned above.
- Every Phi node has a shadow variable in addition to the implicit variable.
Let's say that given a Phi like "X = Phi()", the implicit variable is called "X", and the shadow variable is called "^X".
Therefore, the semantics of an upsilon like "Upsilon(X1, ^X)" is just "set ^X = X1". And the semantics of a Phi like "X = Phi()" is just "set X = ^X".
In other words, you can think of Upsilon as being a side effect (a store to a shadow variable). And you can think of Phi as being a side effect (a load from a shadow variable). You can model them that way in your effect analysis to block reordering Upsilons and Phis.
But also, the shadow variables of Phis in Pizlo form are "Static Single Use" (SSU) variables. This falls out naturally from the fact that the only syntax for loading a shadow variable is the Phi itself. So you can think of Pizlo form as "SSA-SSU form".
The main benefit of this form is that basic blocks - and all CFG data structures - have zero knowledge about SSA. There are no basic block arguments. There's no requirement that Phis appear at the tops of blocks. In fact, this is a valid program in Pizlo form (albeit suboptimal):
M = Stuff(...)
Upsilon(M, ^N)
N = Phi()
MoreStuff(N)
In any Pizlo-form compiler, you'll want to have a Phi simplification pass, which you can implement either by running Cytron or by running any other SSA converter. The simplest is just to just fixpoint the rule that if you have a Phi that has Upsilons that only use the Phi or exactly one other value, then replace the Phi with that other value.
pizlonator
I posted this to a gist, so it's a bit easier to find/cite: https://gist.github.com/pizlonator/79b0aa601912ff1a0eb1cb925...
tekknolagi
Mind if I quote you on this in the post?
UncleEntity
> CPS isn’t really anything like SSA.
Though with CPS you can do fun stuff like copy-and-patch compilation and the fancified musttail interpreter thing (which I'm not sure even has a proper name). Admittedly the two are so similar that the second one could (probably) be converted into the first one without too much trouble. From what I understand, IANAL &etc.
swid
I worked on compilers at Fortify which does static code analysis, and it's always surprised me SSA does not come up more in context about how to write clean, maintainable, and secure code.
SSA makes auditing code for dataflow issues much easier - both for people and programs. If you learn how to transform your code to SSA, you might find yourself choosing to write code this way so that you know, exactly, where that input to whatever sensitive string you are building came from. You can more easily trace the lifetime of that input and see what transformations it has been through already.
I feel like I am the only person in the world talking about SSA outside of compilers! It is useful for humans as well, and we all want to write readable and secure code.
pbiggar
I'll add my own way of constructing SSA, which is mostly untested but worked fine in my compiler: https://paulbiggar.com/research/fit-2009.pdf
burjui
I've used the 2013 algorithm, it's fast, simple enough and easy to implement in Rust.
null
RossBencina
This looks helpful. I would love to find a simple method of generating SSA that can deal with goto statements.
A paper that was suggested to me (not mentioned in the linked blog post) is:
"Practical Improvements to the Construction and Destruction of Static Single Assignment Form", by Preston Briggs, Keith D. Cooper, Timothy J. Harvey, I. Taylor Simpson all at Rice University SOFTWARE—PRACTICE AND EXPERIENCE, VOL. 28(8), 1–28 (July 1998)
rayiner
That one is pretty easy to implement. The Cooper & Torczon book describes the algorithm well and has worked examples. https://shop.elsevier.com/books/engineering-a-compiler/coope...
Note also if you’re dealing with weird control flow you might get oddities in translating out of SSA form: https://www.tjhsst.edu/~rlatimer/papers/sreedharTranslatingO.... Sreedhar’s algorithm for translating out of SSA form is relatively easy to implement.
This is probably useless to you unless you know Common Lisp, but I put together a couple of toy implementations of these algorithms years ago to help myself learn them. There’s a couple of nits the papers gloss over that are noted in comments. You’ll need to compute liveness and dominance frontiers. Examples for those are in the project too. https://github.com/rayiner/portfolio/blob/master/ssa_analysi...
https://github.com/rayiner/portfolio/blob/master/ssa_analysi...
barrkel
Gotos are edges in a graph of basic blocks - runs of code with only one entry and one exit. Once you have your code in the form of basic blocks, there's lots of resources. See e.g. https://www.cs.cmu.edu/~fp/courses/15411-f13/lectures/06-ssa...
ufo
I presume their question is about "simple" techniqyes. With goto, the most famous one needs to compute dominance frontiers.
rayiner
Simple as in low time complexity? Computing dominance frontiers is pretty easy: https://www.cs.tufts.edu/~nr/cs257/archive/keith-cooper/dom1...
tekknolagi
What source language are you working with that has go-to?
swiftcoder
Doesn't every language with break-to-label (i.e. break out of multiple nested loops) effectively have goto, from an implementation standpoint?
tekknolagi
Yes but that is not what makes irreducible control flow graphs, I think. You'll still have structured control flow
RossBencina
ISO C
kldx
Can anyone suggest simple to implement algorithms for SSA destruction? I find Cytron's destruction easy (paired with copy propagation), but the more recent ones are difficult to implement directly from the papers.
UncleEntity
I don't remember the exact details[0] but the AIs were saying Destination Driven Code Generation is a good (and simple) algorithm for lowering to SSA form. Something about it naturally produces a CFG or the dominance frontier or IDK, I filed it away as something to look into later.
It does make sense because it can produce reasonably efficient machine code directly from an AST so it is doing a lot of work a naive SSA lowering algorithm leaves for later stages.
[0] leave this as an exercise for the reader, we aren't on speaking terms lately.
theodorethomas
FORTRAN (IBM, 1956) introduced the "Computed GOTO".
SSA (IBM, 1988) introduced the "Computed COMEFROM".
Pro tips from an SSA hacker.
- Ignore the SSA conversion algorithms that don’t use dominance frontiers. Also ignore the dominator tree generation algorithms that aren’t Langauer-Trajan. Reason: you’ll want to have a dominator tree (ie immediate dominators) anyway for a bunch of SSA optimizations. So, you’ll want Langauer-Tarjan. And if you have that, then using dominance frontiers to generate SSA is just easier.
- CPS isn’t really anything like SSA. Don’t believe that hype. Any claim in PL of two languages or forms being equivalent is not falsifiable because any two Turing complete languages are going to have some transformation between them, so really these papers are just saying “hey look I invented a translation that we all knew was going to be possible and I like my translation for aesthetic reasons”. Working with CPS is nothing like working with SSA.
- The best way I know of representing Phi in your SSA IR is a Pizlo special. I haven’t written it up except by implementing it (JavaScriptCore uses Pizlo SSA). Here’s the idea. Phi takes no arguments (no block arguments and no value arguments). Each Phi has a shadow variable (in addition to the implicit SSA variable it assigns to). Phi just loads the value out of its shadow variable and assigns it to its implicit variable. Then I have a second instruction called Upsilon that takes two args: an input variable and a Phi. It loads the input variable’s implicit value (just as any SSA use would) and stores it to the Phi’s shadow variable. The result of using this IR is that you have zero coupling between your CFG and the SSA graph. It makes CFG transforms much much easier to write. It also means much less special casing of Phi, in practice.