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<h1>Control Flow Analysis for Java Methods</h1>

<p class="hint">
  Implementing a coverage tool that supports statement (C0) as well as branch
  coverage coverage (C1) requires detailed analysis of the internal control flow
  of Java methods. Due to the architecture of JaCoCo this analysis happens on
  the bytecode of compiled class files. This document describes JaCoCo's
  strategies for inserting probes into the control flow at runtime and analyzing
  the actual code coverage. Marc R. Hoffmann, November 2011
</p>

<h2>Control Flow Graphs for Java Bytecode</h2>

<p>
  As an starting point we take the following example method that contains a
  single branching point:
</p>

<pre class="source lang-java linenums">
public static void example() {
    a();
    if (cond()) {
        b();
    } else {
        c();
    }
    d();
}
</pre>

<p>
  A Java compiler will create the following bytecode from this example method.
  Java bytecode is a linear sequence of instructions. Control flow is
  implemented with <i>jump</i> instructions like the conditional
  <code>IFEQ</code> or the unconditional <code>GOTO</code> opcode. The jump
  targets are technically relative offsets to the target instruction. For better
  readability we use symbolic labels (<code>L1</code>, <code>L2</code>) instead
  (also the ASM API uses such symbolic labels):
</p>

<pre class="source linenums">
public static example()V
      INVOKESTATIC a()V
      INVOKESTATIC cond()Z
      IFEQ L1
      INVOKESTATIC b()V
      GOTO L2
  L1: INVOKESTATIC c()V
  L2: INVOKESTATIC d()V
      RETURN
</pre>

<p>
  The possible control flow in the bytecode above can be represented by a graph.
  The nodes are byte code instruction, the edged of the graph represent the
  possible control flow between the instructions. The control flow of the
  example is shown in the left box of this diagram:
</p>

<img src="resources/flow-example.png" alt="Bytecode Control Flow"/>


<h3>Flow Edges</h3>

<p>
  The control flow graph of a Java method defined by Java byte code may have
  the following Edges. Each edge connects a source instruction with a target
  instruction. In some cases the source instruction or the target instruction
  does not exist (virtual edges for method entry and exit) or cannot be
  exactly specified (exception handlers).
</p>

<table class="coverage">
  <thead>
    <tr>
      <td>Type</td>
      <td>Source</td>
      <td>Target</td>
      <td>Remarks</td>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>ENTRY</td>
      <td>-</td>
      <td>First instruction in method</td>
      <td></td>
    </tr>
    <tr>
      <td>SEQUENCE</td>
      <td>Instruction, except <code>GOTO</code>, <code>xRETURN</code>,
        <code>THROW</code>, <code>TABLESWITCH</code> and <code>LOOKUPSWITCH</code></td>
      <td>Subsequent instruction</td>
      <td></td>
    </tr>
    <tr>
      <td>JUMP</td>
      <td><code>GOTO</code>, <code>IFx</code>, <code>TABLESWITCH</code> or
        <code>LOOKUPSWITCH</code>  instruction</td>
      <td>Target instruction</td>
      <td><code>TABLESWITCH</code> and <code>LOOKUPSWITCH</code> will define
        multiple edges.</td>
    </tr>
    <tr>
      <td>EXHANDLER</td>
      <td>Any instruction in handler scope</td>
      <td>Target instruction</td>
      <td></td>
    </tr>
    <tr>
      <td>EXIT</td>
      <td><code>xRETURN</code> or <code>THROW</code> instruction</td>
      <td>-</td>
      <td></td>
    </tr>
    <tr>
      <td>EXEXIT</td>
      <td>Any instruction</td>
      <td>-</td>
      <td>Unhandled exception.</td>
    </tr>
  </tbody>
</table>

<p>
  The current JaCoCo implementation ignores edges caused by implicit exceptions
  and the the method entry. This means we consider SEQUENCE, JUMP, EXIT.
</p>


<h2>Probe Insertion Strategy</h2>

<p>
  Probes are additional instructions that can be inserted between existing
  instructions. They do not change the behavior of the method but record the
  fact that they have been executed. One can think probes are placed on edges of
  the control flow graph. Theoretically we could insert a probe at every edge of
  the control flow graph. As a probe implementation itself requires multiple
  bytecode instructions this would increase the size of the class files several
  times and significantly slow down execution speed of the instrumented classes.
  Fortunately this is not required, in fact we only need a few probes per method
  depending on the control flow of the method. For example a method without any
  branches requires a single probe only. The reason for this is that starting
  from a certain probe we can back-trace the execution path and typically get
  coverage information for multiple instructions.
</p>

<p>
  If a probe has been executed we know that the corresponding edge has been
  visited. From this edge we can conclude to other preceding nodes and edges:
</p>

<ul>
  <li>If a edge has been visited, we know that the source node of the this edge
      has been executed.</li>
  <li>If a node has been executed and the node is the target of only one edge
      we know that this edge has been visited.</li>
</ul>

<p>
  Recursively applying these rules allows to determine the execution status of
  all instructions of a method &ndash; given that we have probes at the right
  positions. Therefore JaCoCo inserts probes
</p>

<ul>
  <li>at every method exit (return or throws) and</li>
  <li>at every edge where the target instruction is the target of more than one
      edge.</li>
</ul>

<p>
  We recall that a probe is simply a small sequence of additional instructions
  that needs to be inserted at a control flow edge. The following table
  illustrates how this extra instructions are added in case of different edge
  types.
</p>

<table class="coverage">
  <thead>
    <tr>
      <td>Type</td>
      <td>Before</td>
      <td>After</td>
      <td>Remarks</td>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>SEQUENCE</td>
      <td><img src="resources/flow-sequence.png" alt="Sequence"/></td>
      <td><img src="resources/flow-sequence-probe.png" alt="Sequence with Probe"/></td>
      <td>
        In case of a simple sequence the probe is simply inserted between the
        two instructions.
      </td>
    </tr>
    <tr>
      <td>JUMP (unconditional)</td>
      <td><img src="resources/flow-goto.png" alt="Unconditional Jump"/></td>
      <td><img src="resources/flow-goto-probe.png" alt="Unconditional Jump with Probe"/></td>
      <td>
        As an unconditional jump is executed in any case, we can also insert the
        probe just before the GOTO instruction.
      </td>
    </tr>
    <tr>
      <td>JUMP (conditional)</td>
      <td><img src="resources/flow-cond.png" alt="Conditional Jump"/></td>
      <td><img src="resources/flow-cond-probe.png" alt="Conditional Jump with Probe"/></td>
      <td>
        Adding a probe to an conditional jump is little bit more tricky. We
        invert the semantic of the opcode and add the probe right after the
        conditional jump. With a subsequent <code>GOTO</code> instruction we
        jump to the original target. Note that this approach will not introduce
        a backward jump, which would cause trouble with the Java verifier if we
        have an uninitialized object on the stack.
      </td>
    </tr>
    <tr>
      <td>EXIT</td>
      <td><img src="resources/flow-exit.png" alt="Exit"/></td>
      <td><img src="resources/flow-exit-probe.png" alt="Exit with Probe"/></td>
      <td>
        As is is the nature of RETURN and THROW statements to actually leave the
        method we add the probe right before these statements.
      </td>
    </tr>
  </tbody>
</table>

<p>
  Now let's see how this rules apply to the example snippet above. We see that
  <code>INVOKE d()</code> instruction is the only node with more than one
  incoming edge. So we need to place probes on those edges and another probe on
  the only exit node. The result is shown the the right box of the diagram
  above.
</p>

<h2>Additional Probes Between Lines</h2>

<p>
  The probe insertion strategy described so far does not consider implicit
  exceptions thrown for example from invoked methods. If the control flow
  between two probes is interrupted by a exception not explicitly created with
  a <code>throw</code> statement all instruction in between are considered as
  not covered. This leads to unexpected results especially when the the block of
  instructions spans multiple lines of source code.
</p>

<p>
  Therefore JaCoCo adds an additional probe between the instructions of two
  lines whenever the subsequent line contains at least one method invocation.
  This limits the effect of implicit exceptions from method invocations to
  single lines of source. The approach only works for class files compiled with
  debug information (line numbers) and does not consider implicit exceptions
  from other instructions than method invocations (e.g.
  <code>NullPointerException</code> or <code>ArrayIndexOutOfBoundsException</code>).
</p>

<h2>Probe Implementation</h2>

<p>
  Code coverage analysis is a runtime metric that provides execution details
  of the software under test. This requires detailed recording about the
  instructions (instruction coverage) that have been executed. For branch
  coverage also the outcome of decisions has to be recorded. In any case
  execution data is collected by so called probes:
</p>

<p class="hint">
  A <b>probe</b> is a sequence of bytecode instructions that can be inserted
  into a Java method. When the probe is executed, this fact is recorded and can
  be reported by the coverage runtime. The probe must not change the behavior
  of the original code.
</p>

<p>
  The only purpose of the probe is to record that it has been executed at least
  once. The probe does not record the number of times it has been called or
  collect any timing information. The latter is out of scope for code coverage
  analysis and more in the objective of a performance analysis tool. Typically
  multiple probes needs to be inserted into each method, therefore probes needs
  to be identified. Also the probe implementation and the storage mechanism it
  depends on needs to be thread safe as multi-threaded execution is a common
  scenario for java applications (albeit not for plain unit tests). Probes must
  not have any side effects on the original code of the method. Also they should
  add minimal overhead.
</p>

<p>
  So to summarize the requirements for execution probes:
</p>

<ul>
  <li>Record execution</li>
  <li>Identification for different probes</li>
  <li>Thread safe</li>
  <li>No side effects on application code</li>
  <li>Minimal runtime overhead</li>
</ul>

<p>
  JaCoCo implements probes with a <code>boolean[]</code> array instance per
  class. Each probe corresponds to a entry in this array. Whenever the probe is
  executed the entry is set to <code>true</code> with the following four
  bytecode instructions:
</p>

<pre class="source">
ALOAD    probearray
xPUSH    probeid
ICONST_1
BASTORE
</pre>

<p>
  Note that this probe code is thread safe and does not modify the operand stack
  or modify local variables. It does also not leave the
  method through an external call. The only prerequisite is that the probe array
  is available as a local variable. For this at the beginning of each method
  additional instrumentation code needs to be added to obtain the array instance
  associated with the belonging class. To avoid code duplication the
  initialization is delegated to a static private method
  <code>$jacocoinit()</code> which is added to every non-interface class.
</p>

<p>
  The size of the probe code above depends on the position of the probe array
  variable and the value of the probe identifier as different opcodes can be
  used. As calculated in the table below the overhead per probe ranges between 4
  and 7 bytes of additional bytecode:
</p>

<table class="coverage">
  <thead>
    <tr>
      <td>Possible Opcodes</td>
      <td>Min. Size [bytes]</td>
      <td>Max. Size [bytes]</td>
    </tr>
  </thead>
  <tfoot>
    <tr>
      <td>Total:</td>
      <td>4</td>
      <td>7</td>
    </tr>
  </tfoot>
  <tbody>
    <tr>
      <td><code>ALOAD_x</code>, <code>ALOAD</code> <sup>1</sup></td>
      <td>1</td>
      <td>2</td>
    </tr>
    <tr>
      <td><code>ICONST_x</code>, <code>BIPUSH</code>, <code>SIPUSH</code>, <code>LDC</code>, <code>LDC_W</code> <sup>2</sup></td>
      <td>1</td>
      <td>3</td>
    </tr>
    <tr>
      <td><code>ICONST_1</code></td>
      <td>1</td>
      <td>1</td>
    </tr>
    <tr>
      <td><code>BASTORE</code></td>
      <td>1</td>
      <td>1</td>
    </tr>
  </tbody>
</table>

<p>
  <sup>1</sup> The probe array is the first variable after the arguments.
  If the method arguments do not consume more that 3 slots the 1-byte opcode can
  be used.<br/>
  <sup>2</sup> 1-byte opcodes for ids 0 to 5, 2-byte opcode for ids up to 127,
  3-byte opcode for ids up to 32767. Ids values of 32768 or more require an
  additional constant pool entry. For normal class files it is very unlikely to
  require more than 32,000 probes.
</p>

<h2>Performance</h2>

<p>
  The control flow analysis and probe insertion strategy described in this
  document allows to efficiently record instruction and branch coverage. In
  total classes instrumented with JaCoCo increase their size by about 30%. Due
  to the fact that probe execution does not require any method calls, only local
  instructions, the observed execution time overhead for instrumented
  applications typically is less than 10%.
</p>

<h2>References</h2>

<ul>
  <li><a href="http://asm.objectweb.org/">ASM byte code library</a> by Eric Bruneton at al.</li>
  <li><a href="http://andrei.gmxhome.de/bytecode/index.html">Bytecode Outline Plug-In</a> by Andrei Loskutov</li>
  <li><a href="http://en.wikipedia.org/wiki/Glossary_of_graph_theory">Wikipedia: Glossary of Graph Theory</a></li>
</ul>

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