EscapeAnalysis

Compiler.EscapeAnalysis is a compiler utility module that aims to analyze escape information of [Julia's SSA-form IR](@ref Julia-SSA-form-IR) a.k.a. IRCode.

This escape analysis aims to:

• leverage Julia's high-level semantics, especially reason about escapes and aliasing via inter-procedural calls
• be versatile enough to be used for various optimizations including alias-aware SROA, early finalize insertion, copy-free ImmutableArray construction, stack allocation of mutable objects, and so on.
• achieve a simple implementation based on a fully backward data-flow analysis implementation as well as a new lattice design that combines orthogonal lattice properties

Try it out!

You can give a try to the escape analysis by loading the EAUtils.jl utility script that defines the convenience entries code_escapes and @code_escapes for testing and debugging purposes:

# InteractiveUtils.@activate Compiler # to use the stdlib version of the Compiler

let JULIA_DIR = normpath(Sys.BINDIR, Base.DATAROOTDIR, "julia")
    include(normpath(JULIA_DIR, "Compiler", "test", "EAUtils.jl"))
    using .EAUtils
end

mutable struct SafeRef{T}
    x::T
end
Base.getindex(x::SafeRef) = x.x;
Base.setindex!(x::SafeRef, v) = x.x = v;
Base.isassigned(x::SafeRef) = true;
get′(x) = isassigned(x) ? x[] : throw(x);

result = code_escapes((Base.RefValue{String},String,String,)) do r1, s2, s3
    r2 = Ref(s2)
    r3 = SafeRef(s3)
    try
        s1 = get′(r1)
        ret = sizeof(s1)
    catch err
        global GV = err # `r1` may escape
    end
    s2 = get′(r2)       # `r2` doesn't escape
    s3 = get′(r3)       # `r3` doesn't escape
    return s2, s3, s4
end

The symbols on the side of each call argument and SSA statements represent the following meaning:

• ◌ (plain): this value is not analyzed because escape information of it won't be used anyway (when the object is isbitstype for example)
• ✓ (green or cyan): this value never escapes (has_no_escape(result.state[x]) holds), colored blue if it has arg escape also (has_arg_escape(result.state[x]) holds)
• ↑ (blue or yellow): this value can escape to the caller via return (has_return_escape(result.state[x]) holds), colored yellow if it has unhandled thrown escape also (has_thrown_escape(result.state[x]) holds)
• X (red): this value can escape to somewhere the escape analysis can't reason about like escapes to a global memory (has_all_escape(result.state[x]) holds)
• * (bold): this value's escape state is between the ReturnEscape and AllEscape in the partial order of [EscapeInfo](@ref Base.Compiler.EscapeAnalysis.EscapeInfo), colored yellow if it has unhandled thrown escape also (has_thrown_escape(result.state[x]) holds)
• ′: this value has additional object field / array element information in its AliasInfo property

Escape information of each call argument and SSA value can be inspected programmatically as like:

result.state[Core.Argument(3)] # get EscapeInfo of `s2`

result.state[Core.SSAValue(3)] # get EscapeInfo of `r3`

Analysis Design

Lattice Design

EscapeAnalysis is implemented as a data-flow analysis that works on a lattice of [x::EscapeInfo](@ref Base.Compiler.EscapeAnalysis.EscapeInfo), which is composed of the following properties:

• x.Analyzed::Bool: not formally part of the lattice, only indicates x has not been analyzed or not
• x.ReturnEscape::BitSet: records SSA statements where x can escape to the caller via return
• x.ThrownEscape::BitSet: records SSA statements where x can be thrown as exception (used for the [exception handling](@ref EA-Exception-Handling) described below)
• x.AliasInfo: maintains all possible values that can be aliased to fields or array elements of x (used for the [alias analysis](@ref EA-Alias-Analysis) described below)
• x.ArgEscape::Int (not implemented yet): indicates it will escape to the caller through setfield! on argument(s)

These attributes can be combined to create a partial lattice that has a finite height, given the invariant that an input program has a finite number of statements, which is assured by Julia's semantics. The clever part of this lattice design is that it enables a simpler implementation of lattice operations by allowing them to handle each lattice property separately¹.

Backward Escape Propagation

This escape analysis implementation is based on the data-flow algorithm described in the paper². The analysis works on the lattice of EscapeInfo and transitions lattice elements from the bottom to the top until every lattice element gets converged to a fixed point by maintaining a (conceptual) working set that contains program counters corresponding to remaining SSA statements to be analyzed. The analysis manages a single global state that tracks EscapeInfo of each argument and SSA statement, but also note that some flow-sensitivity is encoded as program counters recorded in EscapeInfo's ReturnEscape property, which can be combined with domination analysis later to reason about flow-sensitivity if necessary.

One distinctive design of this escape analysis is that it is fully backward, i.e. escape information flows from usages to definitions. For example, in the code snippet below, EA first analyzes the statement return %1 and imposes ReturnEscape on %1 (corresponding to obj), and then it analyzes %1 = %new(Base.RefValue{Base.RefValue{String}, _2})) and propagates the ReturnEscape imposed on %1 to the call argument _2 (corresponding to s):

code_escapes((Base.RefValue{String},)) do s
    obj = Ref(s)
    return obj
end

The key observation here is that this backward analysis allows escape information to flow naturally along the use-def chain rather than control-flow³. As a result this scheme enables a simple implementation of escape analysis, e.g. PhiNode for example can be handled simply by propagating escape information imposed on a PhiNode to its predecessor values:

code_escapes((Bool, Base.RefValue{String}, Base.RefValue{String})) do cnd, s, t
    if cnd
        obj = Ref(s)
    else
        obj = Ref(t)
    end
    return obj
end

[Alias Analysis](@id EA-Alias-Analysis)

EscapeAnalysis implements a backward field analysis in order to reason about escapes imposed on object fields with certain accuracy, and x::EscapeInfo's x.AliasInfo property exists for this purpose. It records all possible values that can be aliased to fields of x at "usage" sites, and then the escape information of that recorded values are propagated to the actual field values later at "definition" sites. More specifically, the analysis records a value that may be aliased to a field of object by analyzing getfield call, and then it propagates its escape information to the field when analyzing %new(...) expression or setfield! call⁴.

code_escapes((String,)) do s
    obj = SafeRef("init")
    obj[] = s
    v = obj[]
    return v
end

In the example above, ReturnEscape imposed on %3 (corresponding to v) is not directly propagated to %1 (corresponding to obj) but rather that ReturnEscape is only propagated to _2 (corresponding to s). Here %3 is recorded in %1's AliasInfo property as it can be aliased to the first field of %1, and then when analyzing Base.setfield!(%1, :x, _2)::String, that escape information is propagated to _2 but not to %1.

So EscapeAnalysis tracks which IR elements can be aliased across a getfield-%new/setfield! chain in order to analyze escapes of object fields, but actually this alias analysis needs to be generalized to handle other IR elements as well. This is because in Julia IR the same object is sometimes represented by different IR elements and so we should make sure that those different IR elements that actually can represent the same object share the same escape information. IR elements that return the same object as their operand(s), such as PiNode and typeassert, can cause that IR-level aliasing and thus requires escape information imposed on any of such aliased values to be shared between them. More interestingly, it is also needed for correctly reasoning about mutations on PhiNode. Let's consider the following example:

code_escapes((Bool, String,)) do cond, x
    if cond
        ϕ2 = ϕ1 = SafeRef("foo")
    else
        ϕ2 = ϕ1 = SafeRef("bar")
    end
    ϕ2[] = x
    y = ϕ1[]
    return y
end

ϕ1 = %5 and ϕ2 = %6 are aliased and thus ReturnEscape imposed on %8 = Base.getfield(%6, :x)::String (corresponding to y = ϕ1[]) needs to be propagated to Base.setfield!(%5, :x, _3)::String (corresponding to ϕ2[] = x). In order for such escape information to be propagated correctly, the analysis should recognize that the predecessors of ϕ1 and ϕ2 can be aliased as well and equalize their escape information.

One interesting property of such aliasing information is that it is not known at "usage" site but can only be derived at "definition" site (as aliasing is conceptually equivalent to assignment), and thus it doesn't naturally fit in a backward analysis. In order to efficiently propagate escape information between related values, EscapeAnalysis.jl uses an approach inspired by the escape analysis algorithm explained in an old JVM paper⁵. That is, in addition to managing escape lattice elements, the analysis also maintains an "equi"-alias set, a disjoint set of aliased arguments and SSA statements. The alias set manages values that can be aliased to each other and allows escape information imposed on any of such aliased values to be equalized between them.

[Array Analysis](@id EA-Array-Analysis)

The alias analysis for object fields described above can also be generalized to analyze array operations. EscapeAnalysis implements handlings for various primitive array operations so that it can propagate escapes via arrayref-arrayset use-def chain and does not escape allocated arrays too conservatively:

code_escapes((String,)) do s
    ary = Any[]
    push!(ary, SafeRef(s))
    return ary[1], length(ary)
end

In the above example EscapeAnalysis understands that %20 and %2 (corresponding to the allocated object SafeRef(s)) are aliased via the arrayset-arrayref chain and imposes ReturnEscape on them, but not impose it on the allocated array %1 (corresponding to ary). EscapeAnalysis still imposes ThrownEscape on ary since it also needs to account for potential escapes via BoundsError, but also note that such unhandled ThrownEscape can often be ignored when optimizing the ary allocation.

Furthermore, in cases when array index information as well as array dimensions can be known precisely, EscapeAnalysis is able to even reason about "per-element" aliasing via arrayref-arrayset chain, as EscapeAnalysis does "per-field" alias analysis for objects:

code_escapes((String,String)) do s, t
    ary = Vector{Any}(undef, 2)
    ary[1] = SafeRef(s)
    ary[2] = SafeRef(t)
    return ary[1], length(ary)
end

Note that ReturnEscape is only imposed on %2 (corresponding to SafeRef(s)) but not on %4 (corresponding to SafeRef(t)). This is because the allocated array's dimension and indices involved with all arrayref/arrayset operations are available as constant information and EscapeAnalysis can understand that %6 is aliased to %2 but never be aliased to %4. In this kind of case, the succeeding optimization passes will be able to replace Base.arrayref(true, %1, 1)::Any with %2 (a.k.a. "load-forwarding") and eventually eliminate the allocation of array %1 entirely (a.k.a. "scalar-replacement").

When compared to object field analysis, where an access to object field can be analyzed trivially using type information derived by inference, array dimension isn't encoded as type information and so we need an additional analysis to derive that information. EscapeAnalysis at this moment first does an additional simple linear scan to analyze dimensions of allocated arrays before firing up the main analysis routine so that the succeeding escape analysis can precisely analyze operations on those arrays.

However, such precise "per-element" alias analysis is often hard. Essentially, the main difficulty inherit to array is that array dimension and index are often non-constant:

• loop often produces loop-variant, non-constant array indices
• (specific to vectors) array resizing changes array dimension and invalidates its constant-ness

Let's discuss those difficulties with concrete examples.

In the following example, EscapeAnalysis fails the precise alias analysis since the index at the Base.arrayset(false, %4, %8, %6)::Vector{Any} is not (trivially) constant. Especially Any[nothing, nothing] forms a loop and calls that arrayset operation in a loop, where %6 is represented as a ϕ-node value (whose value is control-flow dependent). As a result, ReturnEscape ends up imposed on both %23 (corresponding to SafeRef(s)) and %25 (corresponding to SafeRef(t)), although ideally we want it to be imposed only on %23 but not on %25:

code_escapes((String,String)) do s, t
    ary = Any[nothing, nothing]
    ary[1] = SafeRef(s)
    ary[2] = SafeRef(t)
    return ary[1], length(ary)
end

The next example illustrates how vector resizing makes precise alias analysis hard. The essential difficulty is that the dimension of allocated array %1 is first initialized as 0, but it changes by the two :jl_array_grow_end calls afterwards. EscapeAnalysis currently simply gives up precise alias analysis whenever it encounters any array resizing operations and so ReturnEscape is imposed on both %2 (corresponding to SafeRef(s)) and %20 (corresponding to SafeRef(t)):

code_escapes((String,String)) do s, t
    ary = Any[]
    push!(ary, SafeRef(s))
    push!(ary, SafeRef(t))
    ary[1], length(ary)
end

In order to address these difficulties, we need inference to be aware of array dimensions and propagate array dimensions in a flow-sensitive way⁶, as well as come up with nice representation of loop-variant values.

EscapeAnalysis at this moment quickly switches to the more imprecise analysis that doesn't track precise index information in cases when array dimensions or indices are trivially non constant. The switch can naturally be implemented as a lattice join operation of EscapeInfo.AliasInfo property in the data-flow analysis framework.

[Exception Handling](@id EA-Exception-Handling)

It would be also worth noting how EscapeAnalysis handles possible escapes via exceptions. Naively it seems enough to propagate escape information imposed on :the_exception object to all values that may be thrown in a corresponding try block. But there are actually several other ways to access to the exception object in Julia, such as Base.current_exceptions and rethrow. For example, escape analysis needs to account for potential escape of r in the example below:

const GR = Ref{Any}();
@noinline function rethrow_escape!()
    try
        rethrow()
    catch err
        GR[] = err
    end
end;
get′(x) = isassigned(x) ? x[] : throw(x);

code_escapes() do
    r = Ref{String}()
    local t
    try
        t = get′(r)
    catch err
        t = typeof(err)   # `err` (which `r` aliases to) doesn't escape here
        rethrow_escape!() # but `r` escapes here
    end
    return t
end

It requires a global analysis in order to correctly reason about all possible escapes via existing exception interfaces. For now we always propagate the topmost escape information to all potentially thrown objects conservatively, since such an additional analysis might not be worthwhile to do given that exception handling and error path usually don't need to be very performance sensitive, and also optimizations of error paths might be very ineffective anyway since they are often even "unoptimized" intentionally for latency reasons.

x::EscapeInfo's x.ThrownEscape property records SSA statements where x can be thrown as an exception. Using this information EscapeAnalysis can propagate possible escapes via exceptions limitedly to only those may be thrown in each try region:

result = code_escapes((String,String)) do s1, s2
    r1 = Ref(s1)
    r2 = Ref(s2)
    local ret
    try
        s1 = get′(r1)
        ret = sizeof(s1)
    catch err
        global GV = err # will definitely escape `r1`
    end
    s2 = get′(r2)       # still `r2` doesn't escape fully
    return s2
end

Analysis Usage

analyze_escapes is the entry point to analyze escape information of SSA-IR elements.

Most optimizations like SROA (sroa_pass!) are more effective when applied to an optimized source that the inlining pass (ssa_inlining_pass!) has simplified by resolving inter-procedural calls and expanding callee sources. Accordingly, analyze_escapes is also able to analyze post-inlining IR and collect escape information that is useful for certain memory-related optimizations.

However, since certain optimization passes like inlining can change control flows and eliminate dead code, they can break the inter-procedural validity of escape information. In particularity, in order to collect inter-procedurally valid escape information, we need to analyze a pre-inlining IR.

Because of this reason, analyze_escapes can analyze IRCode at any Julia-level optimization stage, and especially, it is supposed to be used at the following two stages:

• IPO EA: analyze pre-inlining IR to generate IPO-valid escape information cache
• Local EA: analyze post-inlining IR to collect locally-valid escape information

Escape information derived by IPO EA is transformed to the ArgEscapeCache data structure and cached globally. By passing an appropriate get_escape_cache callback to analyze_escapes, the escape analysis can improve analysis accuracy by utilizing cached inter-procedural information of non-inlined callees that has been derived by previous IPO EA. More interestingly, it is also valid to use IPO EA escape information for type inference, e.g., inference accuracy can be improved by forming Const/PartialStruct/MustAlias of mutable object.

Base.Compiler.EscapeAnalysis.analyze_escapes
Base.Compiler.EscapeAnalysis.EscapeState
Base.Compiler.EscapeAnalysis.EscapeInfo