Decompiler Design - Control Flow Graph


Prev: Basic Blocks

Control Flow Graph

Now that we have a set of basic blocks to work with, it's much easier to implement a few more analyses and discover more about the structure of the program.

Because we've limited the construction of basic blocks to a single procedure, we'll be looking mostly at recovering statements at the procedure level. Analyzing the interaction between different procedures will be covered in the advanced section.

You may have noticed that in the basic block construction algorithm we saved the entry block into the procedure's data structure. Here's the relevant piece of code:

    current_address = current_procedure->entry_address
    block = get_block_at(current_address)
    current_procedure->entry_block = block
    workList.push = current_address
    while workList not empty
        current_address = workList.pop
        block = get_block_at(current_address)
Why didn't we simply enter the while loop and just use the first block in the blockList set?
That's because the blockList set will be sorted by each block's start address, and while most procedures' entry points will be the lowest address of the procedure, it's possible that the entry point is actually generated by the compiler in the middle or at the end of the procedure (for example in presence of call-tail optimizations), so after the sorting, the first entry in blockList would not be our entry block anymore.

Note that while there's only one entry block per each procedure (we don't consider languages with multiple entry points, like Fortran), there can be multiple blocks that exit the procedure, since there can be many instruction sequences that end with a RET instruction.

Knowing that we always enter the procedure from a specific block gives us a place where to start inspecting the code. From the entry block, we can visit all other blocks by following the succs list. This is called forward analysis, because it follows the execution flow.

Some analysis requires to visit the blocks in the opposite direction, that is from the exit point to the entry point. But, how do we do that when there are multiple exit blocks? The solution is to create a fake block, and make all blocks that end with a return instruction the fake exit block's predecessors (and automatically the fake exit block will become their only successor).
With this trick, we can implement the algorithms that require backward analysis, that is, that look at the code in the direction opposite to the code's execution.

Here's an example of a control flow graph for a simple procedure without loops:


If the procedure has some loops, there will be a link between the block at the bottom of the loop, and the block at the beginning of the loop. When we visit the different blocks we have to make sure that we don't endlessly analyze the blocks in the loop over and over again.
To do this, we add a visited field to each basic block, and we check that field as we visit the blocks.

There are many possible orders in which to visit each block, and some algorithm depend on the visiting order. Here's an example of a forward visiting algorithm that will visit each block as soon as possible (that's why it's called "depth-first traversal" algorithm):

    ForwardVisitBlocks(Block *block)
        block->visited = true;

        // do some work

        // visit all successors
	for each succ block in block->succs
        // do some work

        // to start visiting the blocks...
        for each block in blockList
            block->visited = false

We can add code to execute an algorithm to one of two places: before we visit the successor blocks, or after we visit them. In C++ we would probably implement a "visitor" pattern and provide a pointer to an object implementing a specific analysis as an argument to the visitor.

You may have noticed from the picture above that we can recognize "if-then-else" sequences by checking whether the predecessors and the successors of two blocks are the same. There are several similar configurations of basic blocks that can be used to convert code full of gotos into structured code.

However, some such structures require special handling: loops.

Finding loops

A control flow graph allows us to find loops. The algorithm to identify which block belongs to a loop depends on knowing the dominator block for each loop, so first we have to compute the set of dominators per each block.

Next: Loop analysis