analysis

Summary on the ASM analyzer framework --------------------------------------

Value

Abstract, needs to be implemented for each analysis.
Represents the desired information about local variables and stack values, for example:
- Is this value known to be null / not null?
- What are the instructions that could potentially have produced this value?

Interpreter

Abstract, needs to be implemented for each analysis. Sometimes one can subclass an existing interpreter, e.g., SourceInterpreter or BasicInterpreter.
Multiple abstract methods that receive an instruction and the instruction's input values, and return a value representing the result of that instruction.
- Note: due to control flow, the interpreter can be invoked multiple times for the same instruction, until reaching a fixed point.
Abstract merge function that computes the least upper bound of two values. Used by Frame.merge (see below).

Frame

Can be used directly for many analyses, no subclass required.
Every frame has an array of values: one for each local variable and for each stack slot.
- A top index stores the index of the current stack top
- NOTE: for a size-2 local variable at index i, the local variable at i+1 is set to an empty value. However, for a size-2 value at index i on the stack, the value at i+1 holds the next stack value. IMPORTANT: this is only the case in ASM's analysis framework, not in bytecode. See comment below.
Defines the execute(instruction) method.
- executing mutates the state of the frame according to the effect of the instruction
  - pop consumed values from the stack
  - pass them to the interpreter together with the instruction
  - if applicable, push the resulting value on the stack
Defines the merge(otherFrame) method
- called by the analyzer when multiple control flow paths lead to an instruction
  - the frame at the branching instruction is merged into the current frame of the instruction (held by the analyzer)
  - mutates the values of the current frame, merges all values using interpreter.merge.

Analyzer

Stores a frame for each instruction
merge function takes an instruction and a frame, merges the existing frame for that instr (from the frames array) with the new frame passed as argument. if the frame changed, puts the instruction on the work queue (fixpiont).
initial frame: initialized for first instr by calling interpreter.new[...]Value for each slot (locals and params), stored in frames[firstInstr] by calling merge
work queue of instructions (queue array, top index for next instruction to analyze)
analyze(method): simulate control flow. while work queue non-empty:
- copy the state of frames[instr] into a local frame current
- call current.execute(instr, interpreter), mutating the current frame
- if it's a branching instruction
  - for all potential destination instructions
    - merge the destination instruction frame with the current frame (this enqueues the destination instr if its frame changed)
  - invoke newControlFlowEdge (see below)
the analyzer also tracks active exception handlers at each instruction
the empty method newControlFlowEdge can be overridden to track control flow if required

MaxLocals and MaxStack ----------------------

At the JVM level, long and double values occupy two slots, both as local variables and on the stack, as specified in the JVM spec 2.6.2: "At any point in time, an operand stack has an associated depth, where a value of type long or double contributes two units to the depth and a value of any other type contributes one unit."

For example, a method class A { def f(a: Long, b: Long) = a + b } has MAXSTACK=4 in the classfile. This value is computed by the ClassWriter / MethodWriter when generating the classfile (we always pass COMPUTE_MAXS to the ClassWriter).

For running an ASM Analyzer, long and double values occupy two local variable slots, but only a single slot on the call stack, as shown by the following snippet:

import scala.tools.nsc.backend.jvm._ import scala.tools.nsc.backend.jvm.opt.BytecodeUtils._ import scala.collection.convert.decorateAsScala._ import scala.tools.asm.tree.analysis._

val cn = AsmUtils.readClass("/Users/luc/scala/scala/sandbox/A.class") val m = cn.methods.iterator.asScala.find(_.name == "f").head

// the value is read from the classfile, so it's 4 println(s"maxLocals: ${m.maxLocals}, maxStack: ${m.maxStack}") // maxLocals: 5, maxStack: 4

// we can safely set it to 2 for running the analyzer. m.maxStack = 2

val a = new Analyzer(new BasicInterpreter) a.analyze(cn.name, m) val addInsn = m.instructions.iterator.asScala.find(_.getOpcode == 97).get // LADD Opcode val addFrame = a.frameAt(addInsn, m)

addFrame.getStackSize // 2: the two long values only take one slot each addFrame.getLocals // 5: this takes one slot, the two long parameters take 2 slots each

While running the optimizer, we need to make sure that the maxStack value of a method is large enough for running an ASM analyzer. We don't need to worry if the value is incorrect in the JVM perspective: the value will be re-computed and overwritten in the ClassWriter.

Lessons learnt while benchmarking the alias tracking analysis -------------------------------------------------------------

Profiling

Use YourKit for finding hotspots (cpu profiling). when it comes to drilling down into the details of a hotspot, don't pay too much attention to the percentages / time counts.
Should also try other profilers.
Use timers. When a method showed up as a hotspot, i added a timer around that method, and a second one within the method to measure specific parts. The timers slow things down, but the relative numbers show what parts of a method are slow.

ASM analyzer insights

The time for running an analysis depends on the number of locals and the number of instructions. Reducing the number of locals helps speeding up the analysis: there are less values to merge when merging to frames. See also https://github.com/scala/scala-dev/issues/47
The common hot spot of an ASM analysis is Frame.merge, for example in producers / consumers.
For nullness analysis the time is spent as follows
- 20% merging nullness values. this is as expected: for example, the same absolute amount of time is spent in merging BasicValues when running a BasicInterpreter.
- 50% merging alias sets. i tried to optimize what i could out of this.
- 20% is spent creating new frames from existing ones, see comment on AliasingFrame.init.
The implementation of Frame.merge (the main hot spot) contains a megamorphic callsite to interpreter.merge. This can be observed easily by running a test program that either runs a BasicValue analysis only, versus a program that first runs a nullness analysis and then a BasicValue. In an example, the time for the BasicValue analysis goes from 519ms to 1963ms, a 3.8x slowdown.
I added counters to the Frame.merge methods for nullness and BasicValue analysis. In the examples I benchmarked, the number of merge invocations was always exactly the same. It would probably be possible to come up with an example where alias set merging forces additional analysis rounds until reaching the fixpoint, but I did not observe such cases.

To benchmark an analysis, instead of benchmarking analysis while it runs in the compiler backend, one can easily run it from a separate program (or the repl). The bytecode to analyze can simply be parsed from a classfile. See example at the end of this comment.

Nullness Analysis in Miguel's Optimizer ---------------------------------------

Miguel implemented alias tracking for nullness analysis differently [1]. Remember that every frame has an array of values. Miguel's idea was to represent aliasing using reference equality in the values array: if two entries in the array point to the same value object, the two entries are aliases in the frame of the given instruction.

While this idea seems elegant at first sight, Miguel's implementation does not merge frames correctly when it comes to aliasing. Assume in frame 1, values (a, b, c) are aliases, while in frame 2 (a, b) are aliases. When merging the second into the first, we have to make sure that c is removed as an alias of (a, b).

It would be possible to implement correct alias set merging in Miguel's approach. However, frame merging is the main hot spot of analysis. The computational complexity of implementing alias set merging by traversing the values array and comparing references is too high. The concrete alias set representation that is used in the current implementation (see class AliasingFrame) makes alias set merging more efficient.

[1] https://github.com/scala-opt/scala/blob/opt/rebase/src/compiler/scala/tools/nsc/backend/bcode/NullnessPropagator.java

Complexity and scaling of analysis ----------------------------------

The time complexity of a data flow analysis depends on:

The size of the method. The complexity factor is linear (assuming the number of locals and branching instructions remains constant). The main analysis loop runs through all instructions of a method once. Instructions are only re-enqueued if a control flow merge changes the frame at some instruction.
The branching instructions. When a second (third, ..) control flow edge arrives at an instruction, the existing frame at the instruction is merged with the one computed on the new branch. If the merge function changes the existing frame, the instruction is enqueued for another analysis. This results in a merge operation for the successors of the instruction.
The number of local variables. The hot spot of analysis is frame merging. The merge function iterates through the values in the frame (locals and stack values) and merges them.

I measured the running time of an analysis for two examples:

Keep the number of locals and branching instructions constant, increase the number of instructions. The running time grows linearly with the method size.
Increase the size and number of locals in a method. The method size and number of locals grow in the same pace. Here, the running time increase is polynomial. It looks like the complexity is be #instructions * #locals^2 (see below).

I measured nullness analysis (which tracks aliases) and a SimpleValue analysis. Nullness runs roughly 5x slower (because of alias tracking) at every problem size - this factor doesn't change.

The numbers below are for nullness. Note that the the last column is constant, i.e., the running time is proportional to #ins * #loc^2. Therefore we use this factor when limiting the maximal method size for running an analysis.

#insns #locals time (ms) time / #ins * #loc^{2 * 10}6 1305 156 34 1.07 2610 311 165 0.65 3915 466 490 0.57 5220 621 1200 0.59 6525 776 2220 0.56 7830 931 3830 0.56 9135 1086 6570 0.60 10440 1241 9700 0.60 11745 1396 13800 0.60

As a second experiment, nullness analysis was run with varying #insns but constant #locals. The last column shows linear complexity with respect to the method size (linearOffset = 2279):

#insns #locals time (ms) (time + linearOffset) / #insns 5220 621 1090 0.645 6224 621 1690 0.637 7226 621 2280 0.630 8228 621 2870 0.625 9230 621 3530 0.629 10232 621 4130 0.626 11234 621 4770 0.627 12236 621 5520 0.637 13238 621 6170 0.638

When running a BasicValue analysis, the complexity observation is the same (time is proportional to #ins * #loc^2).

Measuring analysis execution time ---------------------------------

See code below.

Source: package.scala

Linear Supertypes

AnyRef, Any

Content Hierarchy

Type Members

class AliasSet extends AnyRef

An efficient mutable bit set.
class AliasingAnalyzer[V <: Value] extends Analyzer[V]

An analyzer that uses AliasingFrames instead of bare Frames.
An analyzer that uses AliasingFrames instead of bare Frames. This can be used when an analysis needs to track aliases, but doesn't require a more specific Frame subclass.
class AliasingFrame[V <: Value] extends Frame[V]

A subclass of Frame that tracks aliasing of values stored in local variables and on the stack.
A subclass of Frame that tracks aliasing of values stored in local variables and on the stack.
Note: an analysis tracking aliases is roughly 5x slower than a usual analysis (assuming a simple value domain with a fast merge function). For example, nullness analysis is roughly 5x slower than a BasicValue analysis.
See the doc of package object analysis for some notes on the performance of alias analysis.
class BackendUtils[BT <: BTypes] extends AnyRef

This component hosts tools and utilities used in the backend that require access to a BTypes instance.
This component hosts tools and utilities used in the backend that require access to a BTypes instance.
One example is the AsmAnalyzer class, which runs computeMaxLocalsMaxStack on the methodNode to be analyzed. This method in turn lives inside the BTypes assembly because it queries the per-run cache maxLocalsMaxStackComputed defined in there.
case class ExceptionProducer[V <: Value](handlerFrame: Frame[V]) extends InitialProducer with Product with Serializable
abstract class InitialProducer extends AbstractInsnNode

A class for pseudo-instructions representing the initial producers of local values that have no producer instruction in the method:
A class for pseudo-instructions representing the initial producers of local values that have no producer instruction in the method:
- parameters, including this
- uninitialized local variables
- exception values in handlers
The ASM built-in SourceValue analysis yields an empty producers set for such values. This leads to ambiguities. Example (in Java one can re-assign parameter):
void foo(int a) { if (a == 0) a = 1; return a; }
In the first frame of the method, the SoruceValue for parameter a gives an empty set of producer instructions.
In the frame of the IRETURN instruction, the SoruceValue for parameter a lists a single producer instruction: the ISTORE 1. This makes it look as if there was a single producer for a, where in fact it might still hold the parameter's initial value.
class InitialProducerSourceInterpreter extends SourceInterpreter
abstract class IntIterator extends Iterator[Int]

An iterator over Int (required to prevent boxing the result of next).
class NullnessAnalyzer extends Analyzer[NullnessValue]

This class is required to override the newFrame methods, which makes makes sure the analyzer uses NullnessFrames.
class NullnessFrame extends AliasingFrame[NullnessValue]
final class NullnessInterpreter extends Interpreter[NullnessValue]
sealed abstract class NullnessValue extends Value

Represents the nullness state for a local variable or stack value.
Represents the nullness state for a local variable or stack value.
Note that nullness of primitive values is not tracked, it will be always unknown.
case class ParameterProducer(local: Int) extends InitialProducer with Product with Serializable
trait ProdConsAnalyzerImpl extends AnyRef

This class provides additional queries over ASM's built-in SourceValue analysis.
This class provides additional queries over ASM's built-in SourceValue analysis.
The analysis computes for each value in a frame a set of source instructions, which are the potential producers. Most instructions produce either nothing or a stack value. For example, a LOAD instruction is the producer of the value pushed onto the stack. The exception are STORE instructions, which produce a new value for a local variable slot, so they are used as producers for the value they stored.
Note that pseudo-instructions are used as initial producers for parameters and local variables. See the documentation on class InitialProducer.
This class implements the following queries over the data computed by the SourceValue analysis:
- producersForValueAt(insn, slot)
- consumersOfValueAt(insn, slot)
- producersForInputsOf(insn)
- consumersOfOutputsFrom(insn)
- initialProducersForValueAt(insn, slot)
- ultimateConsumersOfValueAt(insn, slot)
- initialProducersForInputsOf(insn)
- ultimateConsumersOfOutputsFrom(insn)
The following operations are considered as copying operations:
- xLOAD, xSTORE
- DUP, DUP2, DUP_X1, DUP_X2, DUP2_X1, DUP2_X2
- SWAP
- CHECKCAST
If ever needed, we could introduce a mode where primitive conversions (l2i) are considered as copying operations.
Note on performance: thee data flow analysis (SourceValue / SourceInterpreter, provided by ASM) is roughly 2-3x slower than a simple analysis (like BasicValue). The reason is that the merge function (merging producer sets) is more complex than merging simple basic values. See also the doc comment in the package object analysis.
case class UninitializedLocalProducer(local: Int) extends InitialProducer with Product with Serializable

Value Members

object AliasSet
object AliasingFrame
object InstructionStackEffect
object NotNullValue extends NullnessValue
object NullValue extends NullnessValue
object NullnessValue
object UnknownValue1 extends NullnessValue
object UnknownValue2 extends NullnessValue

package analysis

Type Members

class AliasSet extends AnyRef

class AliasingAnalyzer[V <: Value] extends Analyzer[V]

class AliasingFrame[V <: Value] extends Frame[V]

class BackendUtils[BT <: BTypes] extends AnyRef

case class ExceptionProducer[V <: Value](handlerFrame: Frame[V]) extends InitialProducer with Product with Serializable

abstract class InitialProducer extends AbstractInsnNode

class InitialProducerSourceInterpreter extends SourceInterpreter

abstract class IntIterator extends Iterator[Int]

class NullnessAnalyzer extends Analyzer[NullnessValue]

class NullnessFrame extends AliasingFrame[NullnessValue]

final class NullnessInterpreter extends Interpreter[NullnessValue]

sealed abstract class NullnessValue extends Value

case class ParameterProducer(local: Int) extends InitialProducer with Product with Serializable

trait ProdConsAnalyzerImpl extends AnyRef

case class UninitializedLocalProducer(local: Int) extends InitialProducer with Product with Serializable

Value Members

object AliasSet

object AliasingFrame

object InstructionStackEffect

object NotNullValue extends NullnessValue

object NullValue extends NullnessValue

object NullnessValue

object UnknownValue1 extends NullnessValue

object UnknownValue2 extends NullnessValue

Inherited from AnyRef

Inherited from Any

Ungrouped