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10.5 Static Single Assignment

Most of the tree optimizers rely on the data flow information provided by the Static Single Assignment (SSA) form. We implement the SSA form as described in R. Cytron, J. Ferrante, B. Rosen, M. Wegman, and K. Zadeck. Efficiently Computing Static Single Assignment Form and the Control Dependence Graph. ACM Transactions on Programming Languages and Systems, 13(4):451-490, October 1991.

The SSA form is based on the premise that program variables are assigned in exactly one location in the program. Multiple assignments to the same variable create new versions of that variable. Naturally, actual programs are seldom in SSA form initially because variables tend to be assigned multiple times. The compiler modifies the program representation so that every time a variable is assigned in the code, a new version of the variable is created. Different versions of the same variable are distinguished by subscripting the variable name with its version number. Variables used in the right-hand side of expressions are renamed so that their version number matches that of the most recent assignment.

We represent variable versions using SSA_NAME nodes. The renaming process in tree-ssa.c wraps every real and virtual operand with an SSA_NAME node which contains the version number and the statement that created the SSA_NAME. Only definitions and virtual definitions may create new SSA_NAME nodes.

Sometimes, flow of control makes it impossible to determine what is the most recent version of a variable. In these cases, the compiler inserts an artificial definition for that variable called PHI function or PHI node. This new definition merges all the incoming versions of the variable to create a new name for it. For instance,

     if (...)
       a_1 = 5;
     else if (...)
       a_2 = 2;
       a_3 = 13;
     # a_4 = PHI <a_1, a_2, a_3>
     return a_4;

Since it is not possible to determine which of the three branches will be taken at runtime, we don't know which of a_1, a_2 or a_3 to use at the return statement. So, the SSA renamer creates a new version a_4 which is assigned the result of “merging” a_1, a_2 and a_3. Hence, PHI nodes mean “one of these operands. I don't know which”.

The following macros can be used to examine PHI nodes

— Macro: PHI_RESULT (phi)

Returns the SSA_NAME created by PHI node phi (i.e., phi's LHS).

— Macro: PHI_NUM_ARGS (phi)

Returns the number of arguments in phi. This number is exactly the number of incoming edges to the basic block holding phi.

— Macro: PHI_ARG_ELT (phi, i)

Returns a tuple representing the ith argument of phi. Each element of this tuple contains an SSA_NAME var and the incoming edge through which var flows.

— Macro: PHI_ARG_EDGE (phi, i)

Returns the incoming edge for the ith argument of phi.

— Macro: PHI_ARG_DEF (phi, i)

Returns the SSA_NAME for the ith argument of phi.

10.5.1 Preserving the SSA form

Some optimization passes make changes to the function that invalidate the SSA property. This can happen when a pass has added new symbols or changed the program so that variables that were previously aliased aren't anymore. Whenever something like this happens, the affected symbols must be renamed into SSA form again. Transformations that emit new code or replicate existing statements will also need to update the SSA form.

Since GCC implements two different SSA forms for register and virtual variables, keeping the SSA form up to date depends on whether you are updating register or virtual names. In both cases, the general idea behind incremental SSA updates is similar: when new SSA names are created, they typically are meant to replace other existing names in the program.

For instance, given the following code:

          1	L0:
          2	x_1 = PHI (0, x_5)
          3	if (x_1 < 10)
          4	  if (x_1 > 7)
          5	    y_2 = 0
          6	  else
          7	    y_3 = x_1 + x_7
          8	  endif
          9	  x_5 = x_1 + 1
          10   goto L0;
          11	endif

Suppose that we insert new names x_10 and x_11 (lines 4 and 8).

          1	L0:
          2	x_1 = PHI (0, x_5)
          3	if (x_1 < 10)
          4	  x_10 = ...
          5	  if (x_1 > 7)
          6	    y_2 = 0
          7	  else
          8	    x_11 = ...
          9	    y_3 = x_1 + x_7
          10	  endif
          11	  x_5 = x_1 + 1
          12	  goto L0;
          13	endif

We want to replace all the uses of x_1 with the new definitions of x_10 and x_11. Note that the only uses that should be replaced are those at lines 5, 9 and 11. Also, the use of x_7 at line 9 should not be replaced (this is why we cannot just mark symbol x for renaming).

Additionally, we may need to insert a PHI node at line 11 because that is a merge point for x_10 and x_11. So the use of x_1 at line 11 will be replaced with the new PHI node. The insertion of PHI nodes is optional. They are not strictly necessary to preserve the SSA form, and depending on what the caller inserted, they may not even be useful for the optimizers.

Updating the SSA form is a two step process. First, the pass has to identify which names need to be updated and/or which symbols need to be renamed into SSA form for the first time. When new names are introduced to replace existing names in the program, the mapping between the old and the new names are registered by calling register_new_name_mapping (note that if your pass creates new code by duplicating basic blocks, the call to tree_duplicate_bb will set up the necessary mappings automatically). On the other hand, if your pass exposes a new symbol that should be put in SSA form for the first time, the new symbol should be registered with mark_sym_for_renaming.

After the replacement mappings have been registered and new symbols marked for renaming, a call to update_ssa makes the registered changes. This can be done with an explicit call or by creating TODO flags in the tree_opt_pass structure for your pass. There are several TODO flags that control the behavior of update_ssa:

10.5.2 Examining SSA_NAME nodes

The following macros can be used to examine SSA_NAME nodes

— Macro: SSA_NAME_DEF_STMT (var)

Returns the statement s that creates the SSA_NAME var. If s is an empty statement (i.e., IS_EMPTY_STMT (s) returns true), it means that the first reference to this variable is a USE or a VUSE.

— Macro: SSA_NAME_VERSION (var)

Returns the version number of the SSA_NAME object var.

10.5.3 Walking use-def chains

— Tree SSA function: void walk_use_def_chains (var, fn, data)

Walks use-def chains starting at the SSA_NAME node var. Calls function fn at each reaching definition found. Function FN takes three arguments: var, its defining statement (def_stmt) and a generic pointer to whatever state information that fn may want to maintain (data). Function fn is able to stop the walk by returning true, otherwise in order to continue the walk, fn should return false.

Note, that if def_stmt is a PHI node, the semantics are slightly different. For each argument arg of the PHI node, this function will:

  1. Walk the use-def chains for arg.
  2. Call FN (arg, phi, data).

Note how the first argument to fn is no longer the original variable var, but the PHI argument currently being examined. If fn wants to get at var, it should call PHI_RESULT (phi).

10.5.4 Walking the dominator tree

— Tree SSA function: void walk_dominator_tree (walk_data, bb)

This function walks the dominator tree for the current CFG calling a set of callback functions defined in struct dom_walk_data in domwalk.h. The call back functions you need to define give you hooks to execute custom code at various points during traversal:

  1. Once to initialize any local data needed while processing bb and its children. This local data is pushed into an internal stack which is automatically pushed and popped as the walker traverses the dominator tree.
  2. Once before traversing all the statements in the bb.
  3. Once for every statement inside bb.
  4. Once after traversing all the statements and before recursing into bb's dominator children.
  5. It then recurses into all the dominator children of bb.
  6. After recursing into all the dominator children of bb it can, optionally, traverse every statement in bb again (i.e., repeating steps 2 and 3).
  7. Once after walking the statements in bb and bb's dominator children. At this stage, the block local data stack is popped.