Escape Analysis in PyPy's JIT

Running Example¶

For the purpose of this blog post, we are going to use a very simple object model, that just supports an integer and a float type. The objects support only two operations, add, which adds two objects (promoting ints to floats in a mixed addition) and is_positive, which returns whether the number is greater than zero. The implementation of add uses classical Smalltalk-like double-dispatching. These classes could be part of the implementation of a very simple interpreter written in RPython.

class Base(object):
    def add(self, other):
        """ add self to other """
        raise NotImplementedError("abstract base")
    def add__int(self, intother):
        """ add intother to self, where intother is a Python integer """
        raise NotImplementedError("abstract base")
    def add__float(self, floatother):
        """ add floatother to self, where floatother is a Python float """
        raise NotImplementedError("abstract base")
    def is_positive(self):
        """ returns whether self is positive """
        raise NotImplementedError("abstract base")

class BoxedInteger(Base):
    def __init__(self, intval):
        self.intval = intval
    def add(self, other):
        return other.add__int(self.intval)
    def add__int(self, intother):
        return BoxedInteger(intother + self.intval)
    def add__float(self, floatother):
        return BoxedFloat(floatother + float(self.intval))
    def is_positive(self):
        return self.intval > 0

class BoxedFloat(Base):
    def __init__(self, floatval):
        self.floatval = floatval
    def add(self, other):
        return other.add__float(self.floatval)
    def add__int(self, intother):
        return BoxedFloat(float(intother) + self.floatval)
    def add__float(self, floatother):
        return BoxedFloat(floatother + self.floatval)
    def is_positive(self):
        return self.floatval > 0.0

Using these classes to implement arithmetic shows the basic problem that a dynamic language implementation has. All the numbers are instances of either BoxedInteger or BoxedFloat, thus they consume space on the heap. Performing many arithmetic operations produces lots of garbage quickly, thus putting pressure on the garbage collector. Using double dispatching to implement the numeric tower needs two method calls per arithmetic operation, which is costly due to the method dispatch.

To understand the problems more directly, let us consider a simple function that uses the object model:

def f(y):
    res = BoxedInteger(0)
    while y.is_positive():
        res = res.add(y).add(BoxedInteger(-100))
        y = y.add(BoxedInteger(-1))
    return res

The loop iterates y times, and computes something in the process. To understand the reason why executing this function is slow, here is the trace that is produced by the tracing JIT when executing the function with y being a BoxedInteger:

# arguments to the trace: p0, p1
# inside f: res.add(y)
guard_class(p1, BoxedInteger)
    # inside BoxedInteger.add
    i2 = getfield_gc(p1, intval)
    guard_class(p0, BoxedInteger)
        # inside BoxedInteger.add__int
        i3 = getfield_gc(p0, intval)
        i4 = int_add(i2, i3)
        p5 = new(BoxedInteger)
            # inside BoxedInteger.__init__
            setfield_gc(p5, i4, intval)
# inside f: BoxedInteger(-100)
p6 = new(BoxedInteger)
    # inside BoxedInteger.__init__
    setfield_gc(p6, -100, intval)

# inside f: .add(BoxedInteger(-100))
guard_class(p5, BoxedInteger)
    # inside BoxedInteger.add
    i7 = getfield_gc(p5, intval)
    guard_class(p6, BoxedInteger)
        # inside BoxedInteger.add__int
        i8 = getfield_gc(p6, intval)
        i9 = int_add(i7, i8)
        p10 = new(BoxedInteger)
            # inside BoxedInteger.__init__
            setfield_gc(p10, i9, intval)

# inside f: BoxedInteger(-1)
p11 = new(BoxedInteger)
    # inside BoxedInteger.__init__
    setfield_gc(p11, -1, intval)

# inside f: y.add(BoxedInteger(-1))
guard_class(p0, BoxedInteger)
    # inside BoxedInteger.add
    i12 = getfield_gc(p0, intval)
    guard_class(p11, BoxedInteger)
        # inside BoxedInteger.add__int
        i13 = getfield_gc(p11, intval)
        i14 = int_add(i12, i13)
        p15 = new(BoxedInteger)
            # inside BoxedInteger.__init__
            setfield_gc(p15, i14, intval)

# inside f: y.is_positive()
guard_class(p15, BoxedInteger)
    # inside BoxedInteger.is_positive
    i16 = getfield_gc(p15, intval)
    i17 = int_gt(i16, 0)
# inside f
guard_true(i17)
jump(p15, p10)

(indentation corresponds to the stack level of the traced functions).

The trace is inefficient for a couple of reasons. One problem is that it checks repeatedly and redundantly for the class of the objects around, using a guard_class instruction. In addition, some new BoxedInteger instances are constructed using the new operation, only to be used once and then forgotten a bit later. In the next section, we will see how this can be improved upon, using escape analysis.

Virtual Objects¶

The main insight to improve the code shown in the last section is that some of the objects created in the trace using a new operation don't survive very long and are collected by the garbage collector soon after their allocation. Moreover, they are used only inside the loop, thus we can easily prove that nobody else in the program stores a reference to them. The idea for improving the code is thus to analyze which objects never escape the loop and may thus not be allocated at all.

This process is called escape analysis. The escape analysis of our tracing JIT works by using virtual objects: The trace is walked from beginning to end and whenever a new operation is seen, the operation is removed and a virtual object is constructed. The virtual object summarizes the shape of the object that is allocated at this position in the original trace, and is used by the escape analysis to improve the trace. The shape describes where the values that would be stored in the fields of the allocated objects come from. Whenever the optimizer sees a setfield that writes into a virtual object, that shape summary is thus updated and the operation can be removed. When the optimizer encounters a getfield from a virtual, the result is read from the virtual object, and the operation is also removed.

In the example from last section, the following operations would produce two virtual objects, and be completely removed from the optimized trace:

p5 = new(BoxedInteger)
setfield_gc(p5, i4, intval)
p6 = new(BoxedInteger)
setfield_gc(p6, -100, intval)

The virtual object stored in p5 would know that it is an BoxedInteger, and that the intval field contains i4, the one stored in p6 would know that its intval field contains the constant -100.

The following operations, that use p5 and p6 could then be optimized using that knowledge:

guard_class(p5, BoxedInteger)
i7 = getfield_gc(p5, intval)
# inside BoxedInteger.add
guard_class(p6, BoxedInteger)
# inside BoxedInteger.add__int
i8 = getfield_gc(p6, intval)
i9 = int_add(i7, i8)

The guard_class operations can be removed, because the classes of p5 and p6 are known to be BoxedInteger. The getfield_gc operations can be removed and i7 and i8 are just replaced by i4 and -100. Thus the only remaining operation in the optimized trace would be:

i9 = int_add(i4, -100)

The rest of the trace is optimized similarly.

So far we have only described what happens when virtual objects are used in operations that read and write their fields. When the virtual object is used in any other operation, it cannot stay virtual. For example, when a virtual object is stored in a globally accessible place, the object needs to actually be allocated, as it will live longer than one iteration of the loop.

This is what happens at the end of the trace above, when the jump operation is hit. The arguments of the jump are at this point virtual objects. Before the jump is emitted, they are forced. This means that the optimizers produces code that allocates a new object of the right type and sets its fields to the field values that the virtual object has. This means that instead of the jump, the following operations are emitted:

p15 = new(BoxedInteger)
setfield_gc(p15, i14, intval)
p10 = new(BoxedInteger)
setfield_gc(p10, i9, intval)
jump(p15, p10)

Note how the operations for creating these two instances has been moved down the trace. It looks like for these operations we actually didn't win much, because the objects are still allocated at the end. However, the optimization was still worthwhile even in this case, because some operations that have been performed on the forced virtual objects have been removed (some getfield_gc operations and guard_class operations).

The final optimized trace of the example looks like this:

# arguments to the trace: p0, p1
guard_class(p1, BoxedInteger)
i2 = getfield_gc(p1, intval)
guard_class(p0, BoxedInteger)
i3 = getfield_gc(p0, intval)
i4 = int_add(i2, i3)
i9 = int_add(i4, -100)

guard_class(p0, BoxedInteger)
i12 = getfield_gc(p0, intval)
i14 = int_add(i12, -1)

i17 = int_gt(i14, 0)
guard_true(i17)
p15 = new(BoxedInteger)
setfield_gc(p15, i14, intval)
p10 = new(BoxedInteger)
setfield_gc(p10, i9, intval)
jump(p15, p10)

The optimized trace contains only two allocations, instead of the original five, and only three guard_class operations, from the original seven.

Summary¶

In this blog post we described how simple escape analysis within the scope of one loop works. This optimizations reduces the allocation of many intermediate data structures that become garbage quickly in an interpreter. It also removes a lot of the type dispatching overhead. In a later post, we will explain how this optimization can be improved further.