Mapping Python to LLVM

Firstly, thank you to everyone who engaged with, tried out, or gave feedback on Codon over the past few weeks! This is the first in a series of blog posts that describe how Codon works internally, various design decisions, performance considerations, and so on.

At a high level, the Codon compiler works in these steps:

  1. Parse source code into an abstract syntax tree (AST).
  2. Perform type checking on the AST using a modified Hindley-Milner-like algorithm.
  3. Convert the typed AST to an intermediate representation called CIR.
  4. Perform numerous analyses, transformations and optimizations on the CIR.
  5. Convert from CIR to LLVM IR.
  6. Run the LLVM optimization pipeline, among other things.

This post will mainly focus on the LLVM IR generation, and how we map various Python constructs to LLVM IR. Sometimes this is very straightforward, while other times it can be very tricky to get right, as we’ll see below.

(This post assumes a basic familiarity with LLVM and code generation. See Eli Bendersky’s excellent blog posts for an informal introduction or refresher, or this great tutorial.)

Getting started: Python types to LLVM types

One of the first things we need to consider is how to convert from Python types to LLVM IR types. Some of the conversions are quite easy:

  • int can become an LLVM i64 (note that this deviates from Python’s arbitrary- width integers, but it turns out 64 bits are more than enough for most applications)
  • float can become an LLVM double
  • bool can become an LLVM i8 (we could use i1 in theory, but i8 is compatible with C/C++)

What about tuples? We can convert tuple types to structs containing the tuple’s element types. For example, the type of (42, 3.14, True) becomes the LLVM structure type {i64, double, i8}. Since tuples are immutable, we can pass these structs by value, and in many cases tuples can be completely optimized out by LLVM’s optimization passes.

What about user-defined classes? We can actually do something very similar to what we did for tuples, except instead of passing by value, we dynamically allocate and pass by pointer, which allows mutations to be handled correctly. For example, consider:

				
					class C:
        a: int
        b: float
        c: bool
				
			

When we instantiate C(), under the hood we’ll dynamically allocate memory to store the contents of the same {i64, double, i8}, and return a pointer to that memory as the result of instantiation (after calling C.__init__()).

There are a few other LLVM types that we expose through Codon, like Ptr[T] to represent a pointer to an object of type T. Most of the other Python types, though, can be constructed from these building blocks. For example, the built-in collection types like listdict and set are all implemented within Codon as classes; some other built-in types are implemented as named tuples, and so on.

Operators

Now that we know how to do type conversions, we need to think about how to actually do operations on those types. For example, how do we add two ints as in 2 + 2? Python implements various operators like +-* etc. through its magic method interface. For example, a + b (typically) becomes a.__add__(b)a - b becomes a.__sub__(b) and so on.

It turns out we can do the same in Codon, and in fact, all operators are defined by magic methods within Codon’s standard library. For example, list.__add__ might look like:

				
					class List:
        ...

        def __add__(self, other):
            result = copy(self)
            result.extend(other)
            return result
				
			

Magic methods are convenient because they allow all operators to be implemented in standard library code, rather than having some be hard-coded in the compiler. But, you may ask, what about operators of primitive types, like int.__add__? That’s where Codon’s inline LLVM IR functionality comes into play: primitive operators are all implemented using inline LLVM IR (via the @llvm decorator):

				
					class int:
        ...

        @llvm
        def __add__(self, other: int) -> int:
            %tmp = add i64 %self, %other
            ret i64 %tmp

        @llvm
        def __add__(self, other: float) -> float:
            %tmp1 = sitofp i64 %self to double
            %tmp2 = fadd double %tmp1, %other
            ret double %tmp2
				
			

Note that Codon supports method overloading: the compiler will choose the correct __add__ based on the right-hand side’s type. Now, actually figuring out which magic methods need to be called for a given expression is a complex task in itself and is handled by the type checker, which we’ll discuss in detail in a future blog post. For now, we’ll assume we have all of this information at our disposal, which is indeed the case by the time we’re generating LLVM IR.

Control flow

At this point, we more or less know how to generate code for expressions, so the natural next step is higher-level control flow like ifwhilefor etc. Unlike (most) expressions, control flow constructs require us to generate multiple basic blocks—blocks of straight-line code without any branches, themselves linked together by branches or conditional branches. The basic block is a fundamental concept in LLVM (and compilers in general), and acts as the substrate for LLVM IR.

The compiler itself maintains a pointer to the “current” basic block, 𝐵. Different control flow constructs require us to generate a number of basic blocks and link them together in various ways. Let’s look at an example:

				
					if condition:
    true_branch
else:
    false_branch
				
			

Compilation would roughly proceed as follows (remember, we always generate code in the current basic block

𝐵

):

    1. Create four new basic blocks:
𝐵cond

𝐵true

𝐵false
 

and 

𝐵exit

.

2. Generate a branch to 

𝐵cond

3. Set

𝐵←𝐵cond

and generate code

𝐶

for condition, then generate a conditional branch to

𝐵body

and

𝐵exit

based on

𝐶.

4. Set

𝐵←𝐵body

and generate code for body, then add a branch to

𝐵cond

5. Set

𝐵←𝐵exit

As a diagram…

Let’s look at one other example:

				
					while condition:
     body
				
			
Here’s how compilation would go:
  1. Create three new basic blocks:

𝐵cond

,

𝐵body

and

𝐵exit

2. Generate a branch to

𝐵cond

.

3. Set

𝐵←𝐵cond

and generate code

𝐶

for condition, then generate a conditional branch to

𝐵body

and

𝐵exit

based on

𝐶

.

4. Set

𝐵←𝐵body

and generate code for body, then add a branch to

𝐵cond

.

5. Set

𝐵←𝐵exit

.

Again as a diagram…
What about break and continue? These turn out to be very straightforward when thinking in terms of basic blocks: break simply becomes a branch to

𝐵exit

and continue becomes a branch to

𝐵cond

. Other control flow constructs (like elif) work in an analogous way, and in fact can be constructed using just ifelse and while. There is one particular statement that requires special care, however, as we’ll see next.

try-exceptfinally

  While most of Python’s control flow constructs are relatively easy to compile, tryexceptfinally is quite possibly one of the most difficult and nuanced things to get right when it comes to mapping Python to LLVM IR, on a number of different levels. Exception handling itself is actually not too difficult, as we can use the Itanium C++ ABI for zero-cost exceptions along with LLVM’s exception handling instructions: (landingpadresumeinvoke) and appropriate personality function. We won’t go into too much detail since this is all very similar to what C++ does. Just know that there is some additional bookkeeping required for knowing when we’re inside a try block, which requires us to call functions with the LLVM invoke instruction (rather than the usual call) and to specify a basic block to branch to if an exception occurs (i.e. the basic block corresponding to except). The real difficulty with tryexceptfinally comes from the finally. It turns out finally has certain semantics that many programmers might not even be aware of. For example, take a look at this code:-
				
					def foo():
        try:
            return 1
        finally:
            return 2
				
			

What does foo() return? If you’re not familiar with finally semantics, you might be inclined to say 1, but the correct answer is 2finally blocks are always executed, which makes sense as they will typically be performing some cleanup action that shouldn’t be skipped.

This has some important implications for compilation: namely, branches always need to be aware of enclosing tryfinally blocks. Let’s take another concrete example; remember when I said break and continue are straightforward? That turns out to not be entirely true in the presence of finally:

				
					def bar():
        for i in range(10):
            print(i)
            try:
                if i == 5:
                    break
            finally:
                continue
				
			

What does bar() print? Well, when i == 5, we’ll reach the break statement, but the break needs to actually branch to the finally block, otherwise the finally block would we skipped over. Now, the finally itself has a continue, which overrides the previous break and resumes the loop. So, in the end, all the integers 09 are printed.

To actually generate correct code for tryexceptfinally, we need a couple different ingredients:

  • Firstly, we need to maintain a stack of enclosing tryexceptfinally blocks, since if we reach a returnbreak or continue, we need to know whether we really need to branch to some finally block.

  • Next, we need to set up a state machine for each series of nested tryexceptfinally blocks, since once we do reach the finally, we need to know how we got there in order to determine what action we need to take next. For instance, if we got there via a return, we need to actually execute that return statement at the end of the block; or perhaps we got there by catching an exception that needs to be delegated to a parent tryexceptfinally.

At the end of the day, we need to construct a state machine with the following states:

  • NORMAL: We reached the finally through normal execution of the code. Nothing special needs to be done; we can just branch to the next block normally.

  • THROWN: We’ve thrown an exception and are executing the finally before propagating the exception out of the function. The exception object itself will be stored in a pre-defined place that we can access from the finally block.

  • CAUGHT: We’ve caught an exception and are reaching the finally through some except block. Again nothing special needs to be done here; we can just branch to the next block normally.

  • RETURN: We’ve reached the finally after encountering an enclosed return statement. After executing the finally, we need to execute the return. The return value itself will be stored in a pre-defined place that we can access from the finally block.

  • BREAK: We’ve reached the finally after encountering a break. We need to actually execute the break after executing the finally block.

  • CONTINUE: We’ve reached the finally after encountering a continue. We need to actually execute the continue after executing the finally block.

Importantly, these actions are recursive, so when we say “execute the return after executing the finally block”, that may entail branching to another enclosing finally block and repeating the same action.

Let’s look at a real example of what this state machine looks like. Here’s a function:

				
					def baz():
        for i in range(5):
            try:
                try:
                    if i == 3:
                        return i
                finally:
                    if i > 2:
                        break
            finally:
                if i < 4:
                    continue
        return i
				
			

And here are the various transitions between the states for different conditions throughout the loop:

The internal state machine will transition between the states based on these conditions until the loop terminates, signified by reaching the end state.

Variables and functions

LLVM IR uses static single assignment form, or SSA, which effectively means LLVM IR variables must be assigned exactly once. As a result, we can’t map Python variables directly to LLVM IR variables. Instead, we map each Python variable to a stack-allocated piece of memory:

				
					x = 42
				
			

becomes:

				
					%x = alloca i64, align 8
store i64 42, i64* %x, align 8
				
			

alloca is an LLVM IR instruction that allocates space on the current stack frame; alloca i64 allocates space for a 64-bit integer. Treating variables this way is standard practice when compiling to LLVM IR, and C/C++ compilers will do the same (e.g. long x = 42 produces this exact code with Clang). Notice also that alloca actually returns a pointer, so when we dereference a variable (by e.g. using x in a later expression), the compiler inserts an implicit dereference of the underlying alloca pointer. In C, we can avoid this dereference via the address-of operator &, as in &x; Codon actually supports this via the __ptr__ built-in: __ptr__(x) returns the address of x. This is often useful when interfacing with C functions that take a pointer as an argument.

Many variables are implicitly introduced by the parser and/or type checker. For example:

				
					a, b = b, a
				
			

… a common Python idiom for swapping the values of two variables, will implicitly be transformed into

				
					tmp = (b, a)
a = tmp[0]
b = tmp[1]
				
			

thus introducing the new variable tmp. We’ll discuss these types of front-end transformations in much more detail in a subsequent blog post.

As for functions: we can actually map Python functions directly to LLVM functions:

				
					def foo(a: int, b: int):
        return a + b
				
			

becomes:

				
					define i64 @foo(i64 %0, i64 %1) {
  %a = alloca i64, align 8
  %b = alloca i64, align 8
  store i64 %0, i64* %a, align 8
  store i64 %1, i64* %b, align 8
  %a0 = load i64, i64* %a, align 8
  %b0 = load i64, i64* %b, align 8
  %ans = add nsw i64 %a0, %b0
  ret i64 %ans
}
				
			

Notice that we allocate space for the arguments via alloca, since they should be treated like normal variables inside the function. The only complication to this otherwise fairly straightforward conversion is generators, which we’ll talk about next.

Generators

Generators are one of the hallmarks of the Python language, and are used extensively in the standard library. For example, many of the built-in functions operate on or return generators:

				
					map(lambda x: x + 1, [1, 2, 3])  # generator giving 2, 3, 4
reversed('abc')                  # generator giving 'c', 'b', 'a'
zip('abc', [1, 2, 3])            # generator giving ('a', 1), ('b', 2), ('c', 3)
				
			

Generators can be defined by using yield:

				
					def squares(n):
        for i in range(1, n + 1):
            yield i * i
				
			

list(squares(5)) gives all the square numbers up to 52[1, 4, 9, 16, 25].

Since generators are so fundamental in Python, we need a way to handle them efficiently in LLVM. Fortunately, LLVM supports coroutines, which we can use as the foundation for implementing generators. (Note that C++20 also adds support for coroutines.)

You can learn about all the intricacies of LLVM coroutines in the docs. Briefly, though, coroutines are like functions that allow suspension and resumption (much like what happens with Python’s yield). Coroutines maintain their state (i.e. local variables, position in the function, yielded value) in what’s called a coroutine frame. Coroutines in LLVM are indeed also like normal functions, but delineate their resume/suspend points with special intrinsics and “return” a handle to their coroutine frames. Here are some of the more important LLVM intrinsics we’ll use when generating code for coroutines:

  • @llvm.coro.id: Gives us a token that can identify the coroutine, which we’ll pass to many of the other intrinsics.
  • @llvm.coro.size.i64: Tells us the size of the coroutine frame for dynamic allocation.
  • @llvm.coro.begin: Gives us a “handle” to the coroutine frame.
  • @llvm.coro.suspend: Marks a suspension point.
  • @llvm.coro.end: Marks the end of the coroutine and destroys the coroutine frame.

These intrinsics are all used within the coroutine function itself, but how do we actually call and manipulate the coroutine externally? Well, there are intrinsics for that as well:

  • @llvm.coro.resume: Resumes a coroutine given a coroutine handle.
  • @llvm.coro.done: Checks if a coroutine is at its final suspend point.
  • @llvm.coro.promise: Returns a pointer to the coroutine promise: a region of memory that stores values “yielded” from the coroutine.
  • @llvm.coro.destroy: Destroys a finished coroutine.

With these primitives in hand, we can implement all we need to support generators:

  • Functions with yield will be converted to LLVM coroutines.
  • We can generate code for yield statements by storing the yielded value in the coroutine promise, then calling @llvm.coro.suspend.
  • We can implement Python’s next() built-in by calling @llvm.coro.done to see if the given generator is finished, then calling @llvm.coro.resume to resume it and finally @llvm.coro.promise to obtain the generated value.
  • We can implement for x in generator by repeatedly calling @llvm.coro.resume/@llvm.coro.promise until @llvm.coro.done tells us to stop.

Let’s look at an example:

				
					for i in range(3):
        print(i)
				
			

Here’s the (simplified) LLVM IR we’ll generate for this snippet:

				
					entry:
  %g = call i8* @range(i64 3)
  br label %for

for:
  call void @llvm.coro.resume(i8* %g)
  %done = call i1 @llvm.coro.done(i8* %g)
  br i1 %done, label %exit, label %body

body:
  %p1 = call i8* @llvm.coro.promise(i8* %g, i32 8, i1 false)
  %p2 = bitcast i8* %p1 to i64*
  %i = load i64, i64* %p2
  call void @print(i32 %i)
  br label %for

exit:
  call void @llvm.coro.destroy(i8* %g)
				
			

Just to recap…

  • The call to @range gives us a handle (with type i8*) to the range generator.
  • We resume the generator with @llvm.coro.resume (note that all coroutines will be initially suspended to match Python’s generator semantics).
  • If @llvm.coro.done tells us the generator is done, we exit the loop and call @llvm.coro.destroy to destroy it.
  • Otherwise, in the body of the loop, we obtain the next value for i by calling @llvm.coro.promise (the other arguments are simply the alignment of the promise (i32 8) and whether we want to obtain a promise given a handle or vice versa (i1 false)).

At this point you might be asking yourself: isn’t that a lot of code to just loop over 0, 1, 2 and print each value? That’s where LLVM’s coroutine optimization passes come in: it turns out coroutines are particularly amenable to compiler optimizations that can typically eliminate all of the coroutine overhead entirely. Specifically, by far the most common case when dealing with generators in Python is for them to be created and destroyed in the same function, in which case the coroutine passes can inline them, elide heap allocation for the frame and so on. Here’s the result of running the coroutine passes on our example above:

				
					  call void @print(i64 0)
  call void @print(i64 1)
  call void @print(i64 2)
				
			

We were able to get rid of everything coroutine-related! By default, LLVM’s coroutine passes rely on an analysis of @llvm.coro.destroy calls. Codon’s LLVM fork instead relies on an escape analysis of the coroutine handle, which we found to be much better at determining which coroutines can be optimized.

Program structure

We have most of the key ingredients at this point, but what about the overarching program structure? Python doesn’t have an explicit main() function as an entry point like C does. LLVM, on the other hand, does, so we need to reconcile that difference.

The way we handle this in Codon is by putting everything at the top level into its own implicit function:

				
					a = 42
print(a * 2)
				
			

becomes:

				
					a = 0
def main():
    global a
    a = 42
    print(a * 2)
				
			

This also allows us to do some setup and initialization as well, such as initializing the runtime/GC, setting up sys.argv, etc.

This approach usually works fairly seamlessly, but there is one subtle case that needs special care: exporting Codon functions in a shared library. For example, consider the following:

				
					def bar() -> int:
    ... # some complex operation

M = bar()

def foo(n: int) -> int:
    return n + M
				
			

and assume we want to generate a shared library libfoo.so from Codon that exposes the foo function. If we do so naively, the global variable M will actually not be initialized: we need to run the implicit main() we created in order to initialize M. We solve this by running main() as a global constructor if we’re compiling to a shared object.

Optimizations

Now is a good time to talk about optimizations. LLVM has an extensive repertoire of IR passes for doing various things. These include many of the standard compiler optimizations like constant folding, dead code elimination, loop invariant code motion, etc. These passes are grouped into standard pipelines, like the “O0” pipeline or the “O3” pipeline, which correspond to the -O0 and -O3 flags on a C/C++ compiler like Clang.

Codon uses these default optimization pipelines, but also adds a few of its own LLVM passes. One example is AllocationRemover, which 1) removes unused heap (GC) allocations and 2) demotes small heap allocations to the stack (i.e. to an alloca instruction). This turns out to be useful when instantiating classes; for example creating an instance of a class C that never escapes its enclosing function can actually be done purely on the stack:

				
					def foo():
        c = C('hello')  # codegen'd as dynamic allocation; demoted to alloca
        ...  # C never escapes foo
				
			

The same goes for the built-in collection types like lists or dictionaries:

				
					a = [1, 2, 3]
print(a[0] + a[1] + a[2])  # optimized to 6; no allocations take place
				
			

Codon uses a couple other custom LLVM passes, but the vast majority of its custom optimizations are performed in its own IR, which we’ll discuss in a future post.

Examples

To conclude this post, I want to showcase a few neat examples that illustrate many of these pieces coming together, combined with LLVM’s optimization passes. I’ve simplified the naming in the LLVM IR outputs for clarity.

User-defined generator with loop

				
					def squares(n):
    for i in range(1, n + 1):
        yield i**2

x = 0
for s in squares(1000):
    x += s

print(x)
				
			

This gets optimized away entirely, and the final answer 333833500 is printed directly:

				
					%answer = call { i64, i8* } @int_to_str(i64 333833500)
				
			

Tail recursion elimination

				
					from sys import argv
N = int(argv[1])

def collatz(n):
    if n == 1:
        return 0
    else:
        return 1 + collatz(3*n + 1 if n % 2 else n // 2)

print(collatz(N))
				
			

The recursion is eliminated and replaced with a loop:

				
					collatz_entry:
  %tmp1 = icmp eq i64 %N, 1
  br i1 %tmp1, label %collatz_exit, label %if.false

if.false:
  %tmp2 = phi i64 [ %tmp7, %ternary.exit ], [ %N, %collatz_entry ]
  %accumulator = phi i64 [ %tmp8, %ternary.exit ], [ 0, %collatz_entry ]
  %tmp3 = and i64 %tmp2, 1
  %not1 = icmp eq i64 %tmp3, 0
  br i1 %not1, label %ternary.false, label %ternary.true

ternary.true:
  %tmp4 = mul i64 %tmp2, 3
  %tmp5 = add i64 %tmp4, 1
  br label %ternary.exit

ternary.false:
  %tmp6 = sdiv i64 %tmp2, 2
  br label %ternary.exit

ternary.exit:
  %tmp7 = phi i64 [ %tmp5, %ternary.true ], [ %tmp6, %ternary.false ]
  %tmp8 = add i64 %accumulator, 1
  %not2 = icmp eq i64 %tmp7, 1
  br i1 %not2, label %collatz_exit, label %if.false

collatz_exit:
  %answer = phi i64 [ 0, %collatz_entry ], [ %tmp8, %ternary.exit ]
				
			

List of tuples

				
					from sys import argv
from random import random
from math import hypot

# Random points in quadrant
points = [(random(), random()) for _ in range(10_000_000)]

# How many points are inside/outside of quarter-circle?
inside, outside = 0, 0
for x, y in points:
    if hypot(x, y) < 1:
        inside += 1
    else:
        outside += 1

# Estimate pi using the ratio
pi = 4 * inside / (inside + outside)
print(pi)
				
			

Tuples are eliminated, and the inside and outside variables are converted to LLVM IR SSA variables:

				
					for.body:
  %idx = phi i64 [ %idx_add, %for.body ], [ 0, %for.cleanup ]
  %inside = phi i64 [ %inside_add, %for.body ], [ 0, %for.cleanup ]
  %outside = phi i64 [ %outside_add, %for.body ], [ 0, %for.cleanup ]
  %p1 = getelementptr { double, double }, ptr %points, i64 %idx
  %x = load double, ptr %p1, align 8
  %p2 = getelementptr { double, double }, ptr %points, i64 %idx, i32 1
  %y = load double, ptr %p2, align 8
  %h = tail call double @hypot(double %x, double %y)
  %tmp1 = fcmp uge double %h, 1.000000e+00
  %tmp2 = zext i1 %tmp1 to i64
  %outside_add = add i64 %outside, %tmp2
  %tmp3 = xor i1 %tmp1, true
  %tmp4 = zext i1 %tmp3 to i64
  %inside_add = add i64 %inside, %tmp4
  %idx_add = add nuw nsw i64 %idx, 1
  %exitcond = icmp eq i64 %idx, %N
  br i1 %exitcond, label %for.exit, label %for.body
				
			

Conclusion

I hope this post helped shed some light on the various methods we can employ to compile Python code to LLVM. You can view the LLVM IR output of your own code with codon build -llvm (remember to add the -release flag to enable optimizations).

There are many things we took for granted here, like how we determine the data types to begin with, or how we put the source code in a format that’s suitable for code generation. These, among other things, will be topics of future posts in this series. Stay tuned!

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