Packages

  • package root

    The Scala compiler and reflection APIs.

    The Scala compiler and reflection APIs.

    Definition Classes
    root
  • package scala
    Definition Classes
    root
  • package tools
    Definition Classes
    scala
  • package nsc
    Definition Classes
    tools
  • package backend
    Definition Classes
    nsc
  • package jvm
    Definition Classes
    backend
  • package analysis

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

    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 (fixpoint).
    • 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 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 * #loc2 * 106 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.

    Definition Classes
    jvm
  • AliasSet
  • AliasingAnalyzer
  • AliasingAsmAnalyzerMarker
  • AliasingFrame
  • AsmAnalyzer
  • BackendUtils
  • BasicAliasingAnalyzer
  • BasicAnalyzer
  • ExceptionProducer
  • InitialProducer
  • InitialProducerSourceInterpreter
  • InstructionStackEffect
  • IntIterator
  • NonLubbingTypeFlowAnalyzer
  • NonLubbingTypeFlowInterpreter
  • NotNullValue
  • NullValue
  • NullnessAnalyzer
  • NullnessAnalyzerImpl
  • NullnessFrame
  • NullnessInterpreter
  • NullnessValue
  • ParameterProducer
  • ProdConsAnalyzer
  • TypeFlowInterpreter
  • UninitializedLocalProducer
  • UnknownValue1
  • UnknownValue2

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

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.

Source
AliasingAnalyzer.scala
Linear Supertypes
Frame[V], AnyRef, Any
Known Subclasses
NullnessFrame
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. AliasingFrame
  2. Frame
  3. AnyRef
  4. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new AliasingFrame(src: Frame[_ <: V])
  2. new AliasingFrame(nLocals: Int, nStack: Int)

Value Members

  1. val aliases: Array[AliasSet]

    For every value the set of values that are aliases of it.

    For every value the set of values that are aliases of it.

    Invariants:

    • If aliases(i) == null then i has no aliases. This is equivalent to having aliases(i) == SingletonSet(i).
    • If aliases(i) != null then aliases(i) contains i.
    • If aliases(i) contains j then aliases(i) eq aliases(j), i.e., they are references to the same (mutable) AliasSet.
  2. def aliasesOf(entry: Int): AliasSet

    The set of aliased values for a given entry in the values array.

  3. def clearStack(): Unit

    When entering an exception handler, all values are dropped from the stack (and the exception value is pushed).

    When entering an exception handler, all values are dropped from the stack (and the exception value is pushed). The ASM analyzer invokes firstHandlerInstructionFrame.clearStack(). To ensure consistent aliasing sets, we need to remove the dropped values from aliasing sets.

    Definition Classes
    AliasingFrame → Frame
  4. def execute(insn: AbstractInsnNode, interpreter: asm.tree.analysis.Interpreter[V]): Unit
    Definition Classes
    AliasingFrame → Frame
  5. def getLocal(index: Int): V
    Definition Classes
    Frame
  6. def getLocals(): Int
    Definition Classes
    Frame
  7. def getMaxStackSize(): Int
    Definition Classes
    Frame
  8. def getStack(index: Int): V
    Definition Classes
    Frame
  9. def getStackSize(): Int
    Definition Classes
    Frame
  10. def init(src: Frame[_ <: V]): Frame[V]
    Definition Classes
    AliasingFrame → Frame
  11. def initJumpTarget(opcode: Int, target: LabelNode): Unit
    Definition Classes
    Frame
  12. def merge(other: Frame[_ <: V], interpreter: asm.tree.analysis.Interpreter[V]): Boolean

    Merge the AliasingFrame other into this AliasingFrame.

    Merge the AliasingFrame other into this AliasingFrame.

    Aliases that are common in both frames are kept. Example:

    var x, y = null if (...) { x = a y = a // (x, y, a) are aliases } else { x = a y = b // (x, a) and (y, b) } [...] // (x, a) -- merge of ((x, y, a)) and ((x, a), (y, b))

    Definition Classes
    AliasingFrame → Frame
  13. def merge(frame: Frame[_ <: V], localsUsed: Array[Boolean]): Boolean
    Definition Classes
    Frame
  14. def pop(): V
    Definition Classes
    Frame
  15. def push(value: V): Unit
    Definition Classes
    Frame
  16. def setLocal(index: Int, value: V): Unit
    Definition Classes
    Frame
  17. def setReturn(v: V): Unit
    Definition Classes
    Frame
  18. def setStack(index: Int, value: V): Unit
    Definition Classes
    Frame
  19. def toString(): String
    Definition Classes
    AliasingFrame → Frame → AnyRef → Any