Introduction
Local Variables
- Doubles
- Test Yourself #1
Global Variables
Non-Local Variables
- Static Scoping
- Dynamic Scoping
  - Deep Access
    - Test Yourself #5
  - Shallow Access
    - Test Yourself #6

In this set of notes we will consider how three different kinds of variables: local, global, and non-local, are accessed at runtime. For the purposes of this discussion, we will define these three categories as follows:

Local variables: variables that are declared in the method that accesses them.
Global variables: variables that are not declared in any method, but are accessible in all methods. For example, the public static fields of a Java class can be used in any method; variables can be declared at the file level in a C or C++ program, and used in any function; variables can be declared in the outermost scope of a Pascal program and can be used in any procedure or function.
Non-local variables: we will use this term for two situations:
1. In languages that allow sub-programs to be nested, it refers to variables that are declared in one sub-program and used in a nested sub-program. This is allowed, for example, in Pascal.
2. In languages with dynamic scope, it refers to variables that are used in a method without being declared there (so the use corresponds to the declaration in the "most recently called, still active" method).

Our discussion will include information specific to the last programming assignment (the code generator); i.e., how to generate MIPS code to access these three kinds of variables.

Local Variables

Local variables and parameters are stored in the activation record of the method in which they are declared. They are accessed at runtime using an offset relative to the frame pointer (FP). Since we're assuming that "up" in the stack means a lower address, these offsets will be (i) positive numbers for parameters, and (ii) negative numbers for local variables of the procedure. For example, given this code:

        void P(int x) {
          int a, b;
	  ...
	}

and assuming that activation records do not include an access link field or space for saved registers, P's activation records will be organized as follows:

           _______________ 
          |               |   <--- Stack Pointer
          |_______________|                
       b: |               |
          |_______________|
       a: |               |   // locals have negative offsets relative to the frame pointer
          |_______________|
          | Control Link  |
          |_______________|
          | Return Addr   |   <--- Frame Pointer
          |_______________|
       x: |               |   // parameters have positive offsets relative to the frame pointer
          |_______________|

We will assume that each address and each integer takes up 4 bytes. Our memory-organization invariant will be that (i) the stack pointer points to the next 4-byte slot to use, and (ii) the frame pointer points to the 4-byte slot that holds the return address. (This invariant is only one possible convention that one could choose. For instance, you could choose to have the stack pointer point to the last item pushed -- i.e., the slot for b in the example above -- and you could have the frame pointer point to the control link. It is necessary to pick some convention and stick to it.)

For the example above, here are the offsets for each of P's parameters and locals:

x: offset +4
a: offset -8
b: offset -12

The following MIPS code loads the values of a and b into registers t1 and t2, respectively:

lw $t1, -8($fp)   # load a
lw $t2, -12($fp)  # load b

To be able to generate this code at compile time (e.g., to process a statement like x = a + b), the offset of each local variable must be known by the compiler. Therefore, the offset of each local variable from the Frame Pointer should be stored as an attribute of the variable in the symbol table. This can be done as follows:

Keep track of the current offset in a global variable (e.g., a static ASTnode field) or in the symboltable (i.e., add a new field to the SymTab class, with methods to set and get the field's value).
When the symbol-table-building code starts processing a method, set the current offset to +4.
For each parameter: add the name to the symboltable as usual, but also include the value of the current offset as an attribute, and then update the current offset by adding the size of the parameter (in bytes), which will depend on the parameter's type.
After processing all of the parameters, set the offset to -4 (to leave room for the control link).
For each local variable, subtract from the current offset the size of the local (in bytes), and then add the name of the local to the symboltable with the current offset as an attribute.

Note that the "current offset" is not reset at the start of a nested block, and thus each variable declared (somewhere) in a method M has its own, unique offset in the AR for M.

Note as well that the formal parameters are traversed in left-to-right order, and are given successively greater and greater positive offsets (with respect to the callee's frame pointer). Thus, we must arrange for the caller to evaluate the actuals from right to left, so that the resulting values are pushed on the stack in an order that is consistent with the numbering scheme given above.

Doubles

For MIPS code, each double variable requires 8 bytes. For example, given this code:

        void P(double x) {
          double a, b;
	  ...
	}

variable x will be stored in the bytes at offsets +4 to +11 from the frame pointer, and the offset that should be stored in x's symboltable entry (and used to access x at runtime) is +4. Here are the offsets for all of P's locals:

x: offset +4
a: offset -12
b: offset -20

Pairs of floating-point registers with consecutive numbers (e.g., {$f0,$f1}, {$f2,$f3}) must be used for double-valued computations at runtime, and there are special opcodes for operations on double values. Note that the instructions only refer to the even-numbered register of each pair (although both the even-numbered and the next-higher register both participate in the computation). For instance, the following MIPS code loads the values of a and b into the register pairs {$f0,$f1} and {$f2,$f3}, respectively:

l.d $f0, -12($fp)  # load a
l.d $f2, -20($fp)  # load b

TEST YOURSELF #1

Assume that both an address and an integer require 4 bytes of storage, and that a double requires 8 bytes. Also assume that each activation record includes parameters, a return address, a control link, and space for local variables as illustrated above. What are the offsets (in bytes) for each of the parameters and local variables in the following functions?

void P1(int x, int y) {
   int a, b, c;
   ...
   while (...) {
      double a, w;
   }
}

void P2() {
   int x, y;
   ...
   if (...) {
      double a;
      ...
   }
   else {
      int b, c;
      ...
   }
}

solution

Global Variables

As noted above, global variables are stored in the static data area. Using MIPS code, each global is stored in space labeled with the name of the variable, and the variable is accessed at runtime using its name. (Since we will be using the SPIM simulator, and since SPIM has some reserved words that can also be used as Simple variable names, you will need to add an underscore to global variable names to prevent clashes with SPIM reserved words.)

For example, if the source code includes:

       // global variables
       int g;
       double d;

The following code would be generated to reserve space in the static data area for variables g and d:

                .data          # put the following in the static data area
		.align 2       # align on a word boundary
        _g:     .space 4       # set aside 4 bytes
	        .data
		.align 2
        _d:     .space 8

And the following code would be generated to load the value of variable g into register t0, and to load the value of variable d into register f0:

                lw    $t0, _g       # load contents of g into t0
		l.d   $f0, _dd      # load contents of dd into f0

Non-Local Variables

Recall that we are using the term "non-local variable" to refer to two situations:

In statically-scoped languages that allow nested sub-programs, a variable can be declared in one sub-program and accessed in another, nested sub-program. Such variables are "non-local" in the nested sub-program that accesses them. These variables are stored in the activation record of the sub-program that declares them. When they are used as non-local variables, that activation record is found at runtime either using access links or a display (discussed below).
In dynamically-scoped languages, a variable can be declared in one method, and accessed in a called method. The variable is non-local in the method that accesses it. Two different approaches to supporting the use of non-local variables in dynamically-scoped languages are discussed below.

Note that in languages (like C and C++) that permit the same name to be used in nested blocks within a method, we might also use the term "non-local variable" to refer to a use of a variable in one block that was declared in an enclosing block. However, this is not an interesting case in terms of runtime access. All of a method's variables (regardless of which block they are declared in) are stored in the method's activation record, and are accessed using offsets from the frame pointer, as discussed above.

Static Scoping

First, let's consider an example (Pascal) program that includes accesses to non-local variables (the nesting levels of the procedures are given for later reference):

   + program MAIN;
   | var x: integer;
   |
   |	+ procedure P;
   |   (2)  write(x);
   |    +
   |   
   |	+ procedure Q;
   |    | var y: integer = x;
   |    |
   |	|    + procedure R;
   |	|    |   x = x + 1;
   |    |    |   y = y + x;
  (1)  (2)  (3)  if y<6 call R;
   |	|    |   call P
   |    |    +
   |    |     
   |	|    call R;
   |	|    call P;
   |    |    if x < 5 call Q;
   |    +
   |    
   |    x = 2;
   |    call Q;
   +

solution

TEST YOURSELF #2

Trace the execution of this program, drawing the activation records for the main program and for each called procedure (include only local variables and control links in the activation records). Each time a non-local variable is accessed, determine which activation record it is stored in. Notice that the relative nesting levels of the variable's declaration and its use does not tell you how far down the stack to look for the activation record that contains the non-local variable. In fact, this number changes for different calls (e.g., due to recursion).

solution

Method #1: Access Links

The idea behind the use of access links is as follows:

Add a new field to each AR -- the access link field.
If P is (lexically) nested inside Q, then at runtime, P's AR's access link will point to the access link field in the AR of the most recent activation of Q.
Therefore, at runtime, access links will form a chain corresponding to the nesting of sub-programs. For each use of a non-local x:
- At compile time, use the "Level Number" attribute of x and the "Current Level Number" (of the sub-program that is accessing x) to determine how many links of the chain to follow at runtime.
- If P at level i uses variable x, declared at level j, follow i-j links, then use x's "Offset" attribute to find x's storage space inside the AR.

We will put the access-link field as the first field in the AR (proper)—that is, register FP points to the access-link field. Thus, the layout of an AR with one parameter and two locals is as follows:

           _______________ 
          |               |   <--- Stack Pointer
          |_______________|                
  local2: |               |
          |_______________|
  local1: |               |   // locals have negative offsets relative to the frame pointer
          |_______________|
          | Control Link  |
          |_______________|
          | Return Addr   |
          |_______________|
          | Access Link   |   <--- Frame Pointer
          |_______________|
  param1: |               |   // parameters have positive offsets relative to the frame pointer
          |_______________|

A good way of thinking about the ARs is in terms of linked lists: each AR is an element that can participate in two kinds of lists:

A list that is linked via the control-link fields (i.e., the saved FP values)
A list that is linked via the access-link fields

The control-link list is the ``primary list,'' because it consists of the ARs of the pending calls that have not yet completed (in the order that they need to complete). The access links provide another linked list (on typically a subset of the ARs). Note that with ordinary objects you can have exactly the same situation: each object can have multiple fields that serve to link the same set (or a subset) of objects in different linked lists.

Returning to the example program given earlier, here's a snapshot of the runtime stack after the first call from R to P (where we show only the access links and the local variables in the ARs):

			____________
	          P	|          |------------+   <-- FP
			+==========+            |
	          R	|          |----------+ |
			+==========+          | |
                  R    	|          |------+   | |
			+==========+      |   | |
		      y:|    9     |      |   | |
		  Q     +----------|      |   | |
	          	|          |--+ <-+ <-+ |
			+==========+  |         |
		      x:|    4     |  |         |
		MAIN	|----------|  |         |
		        |   null   |<-+      <--+
			|__________|

To access the value of x from procedure R, access links must be followed. The number of links that must be followed is:

So the code for y = x in procedure R would be as shown below (Note: we assume that because we have access links, FP always points to the access-link field.) We also assume that both variable x and variable y are at offset -12 in their respective ARs. Because the access link is at offset 0 with respect to FP, the return address is at offset -4, and the control link is at -8. Because x and y are the first local variables in their respective program/procedure, they are each at offset -12 in their respective ARs.)

        move $t0, FP     // no links followed yet; t0 holds ptr to R's access link field
        lw $t0, ($t0)     // 1 link: t0 holds ptr to Q's AR's access link field
 +->    lw $t0, ($t0)     // 2 links: t0 holds ptr to main's AR's access link field
 |      lw $t0, -12($t0)  // t0 holds value of x
 |      sw $t0, -12(FP)  // y = x
 |
This code would be repeated if we needed to follow more links.

How to set up access links:

The link is set up by the calling procedure.
How to set up the link depends on the relative nesting levels of the calling and called procedures.

There are two cases:
Case 1: The calling procedure's level is less than the called procedure's level (i.e., the called procedure is nested directly inside the calling procedure, because if it's not, it's invisible and it can't be called). In this case, the called procedure's access link should point to the access link field of the calling procedure's AR. This case occurs in the example when Q calls R.

In this case, the calling procedure sets up the called procedure's access link by pushing the value of the FP just before the call, since the FP points to its access link. For example, when Q is calling R, here is a picture of the stack just after R's access link has been set up by Q:

                                             <-- SP
			|----------|        
			|	   |------+
			|==========|      |     
		      y:|          |      |     
		  Q     |----------|      |     
                        |          |--+ <-+  <-- FP
                        |==========|  |
		      x:|          |  |        
		MAIN	|----------|  |        
			|   null   |<-+
			|__________|

Case 2: The calling procedure's level is greater than or equal to the called procedure's level. In this case, the called procedure's access link should point to an AR that is already on the stack. The value for the new access link is found by starting with the value of the calling procedure's access link field (which is pointed to by the FP), and following X-Y access links, where:

The following code loads the value of the calling procedure's access link field into register t0:

lw    $t0, 0(FP)

If X == Y (i.e., no links should be followed to find the value of the new access link), then the value of t0 should simply be pushed onto the stack. If X is greater than Y, then the code:

lw    $t0, 0($t0)

should be generated X - Y times, before pushing the value of t0.

To illustrate this situation, consider two cases from the example code: R calls P, and Q calls itself. Recall that the nesting structure of the example program is:

      +--
      |
      |   +--
      |   |
      |  P|
      |   |
      |   +--
      |
MAIN  |   +--
      |   |
      |   |     +--
      |   |	|
      |  Q|    R|
      |   |	|
      |   |	+--
      |   |
      |   +--
      |
      +--

When R is about to call P, the stack looks like this:

			+==========+            
	          R	|          |----------+ 
			+==========+          | 
                  R    	|          |------+   | 
			+==========+      |   | 
		      y:|    9     |      |   | 
		  Q     +----------|      |   | 
	          	|          |--+ <-+ <-+ 
			+==========+  |         
		      x:|    4     |  |         
		MAIN	|----------|  |         
		        |   null   |<-+      
			|__________|

Since P is nested inside MAIN, P's access link should point to MAIN's AR (i.e., the bottom AR on the stack). R's nesting level is 3 and P's nesting level is 2. Therefore, we start with the value of R's access link (the pointer to Q's AR) and follow one link. This retrieves the values of Q's access link, which is (as desired) a pointer to MAIN's AR. This is the value that will be pushed onto the stack (copied into P's AR as its access link).

When Q is about to call itself, the stack looks like this:

			|==========|      
		      y:|          |           
		  Q     |----------|           
	          	|          |--+        
			|==========|  |    
		      x:|          |  |   
		MAIN	|----------|  |   
		        |   null   |<-+
			|__________|

The access link in the new AR for Q should be the same as the access link in the current AR for Q; namely, it should be a pointer to the AR for MAIN. This value is found by starting with the value of Q's access link (a pointer to MAIN's AR) and following zero links (because X = Y = 1).

TEST YOURSELF #3

Trace the execution of the example program again. Each time a procedure is called, determine which case applies in terms of how to set up the called procedure's access link. Then use the appropriate algorithm to find the value of the new access link, and draw the new AR with its access link.

Each time a non-local variable x is accessed, make sure that you find its activation record by following i - j access links (where i is the nesting level of the procedure that uses x and j is the nesting level of the procedure that declares x).

solution

Access Links: Summary

To use an access link:

Follow i - j links to find the AR with space for non-local x, where i is the nesting level of the procedure that uses x and j is the nesting level of the procedure that declares x. To set up an access link:

case #1: Calling procedure's level is less than called procedure's level: Push the value of the FP to be the access link field of the called procedure's AR.
case #2: Calling procedure's level is greater than or equal to the called procedure's level: Find the value to push by starting with the value of the calling procedure's access links, then following X-Y links, where X = calling procedure's level, and Y = called procedure's level.

Method #2: The Display

The motivation for using a display is to avoid the runtime overhead of following multiple access links to find the activation record that contains a non-local variable. The idea is to maintain a global "array" called the display. Ideally, the display is actually implemented using registers (one for each array element) rather than an actual array; however, it can also be implemented using an array in the static data area.

The size of the display is the maximum nesting depth of a procedure in the program (which is known at compile time). The display is used as follows:

When procedure P at nesting level k is executing, DISPLAY[0],...DISPLAY[k-2] hold pointers to the ARs of the most recent activations of the k-1 procedures that lexically enclose P. DISPLAY[k-1] holds a pointer to P's AR.
To access a non-local variable declared at level x, use DISPLAY[x-1] to get to the AR that holds x, then use the usual offset to get x itself.

To illustrate this, refer back to our running example program, outlined below:

      +--
      |int x;
      |
      |   +--
      |   |
      |  P|...x...
      |   |
      |   +--
      |
MAIN  |   +--
      |   | int y;
      |	  |
      |   |     +--
      |   |	|...x...y...
      |  Q|    R|call R
      |   |	|call P
      |   |	+--
      |   |
      |   | call R
      |   | call P
      |   | if (...) call Q
      |   +--
      |
      | call Q
      +--

Below are two pictures comparing the use of access links with the use of a display. Both show the same moment at runtime.

        USING ACCESS LINKS                  USING A DISPLAY


         ____________                          ----------
   P     |          |------------+	   P   |        |<--+
         |==========|            |	       |========|   |   +--+
   R     |          |----------+ |	   R   |        |<------|  | [2]
         |==========|          | |             |========|   |   +--+
       y:|          |          | |           y:|        |   +---|  | [1]
   Q     |----------|          | |         Q   |--------|       +--+
         |          |------+ <-+ |             |        |   +---|  | [0]
         |==========|      |     |             |========|   |   +--+
       x:|          |      |     |           x:|        |   | DISPLAY
 MAIN    |----------|      |     |       MAIN  |--------|   |
         |   null   |    <-+  <--+             |        |<--+
         |__________|                          ----------

	    STACK                                STACK

To maintain the display, a new field (called the "save-display" field) is added to each activation record. The display is maintained as follows:

When a procedure at nesting level k is called:
- The current value of DISPLAY[k-1] is saved in the "save-display" field of the new AR.
- DISPLAY[k-1] is set to point to (the save-display field of) the new AR.
When the procedure returns, DISPLAY[k-1] is restored using the value saved in the "save-display" field (of the returning procedure).

This process is illustrate below, showing how the display and the save-display fields are updated when R calls P (only the local variable and save-display fields of the ARs are shown).

        Before R calls P:               
        ----------------

              ________                  ____________
          [2] |      |--\            R  |          |
              |______|   -------------->|          |
          [1] |      |--\               |==========|
              |______|   \            y:|          |
          [0] |      |--\ \          Q  |----------|
              |______|   \ ------------>|          |
                          \             |==========|
                           \          x:|          |
                            \     MAIN  |----------|
                             ---------->|          |  
                                        |==========|


        After R calls P:                
        ---------------

                        
              ________                 
          [2] |      |--\               ------------
              |______|   \          P   |          |---+
          [1] |      |----\------------>|          |   |
              |______|     \            |==========|   |
          [0] |      |--\   \       R   |          |   |  
              |______|   \   ---------->|          |   |
                          \             |==========|   |
                           \          x:|          |   |
                            \       Q   |----------|   |
                             \          |          |<--+
                              \         |==========|
                               \      y:|          |
                                \  MAIN |----------|
                                 ------>|          |
				        |----------|

TEST YOURSELF #4

Trace the execution of the running example program, assuming that a display is used instead of access links. Each time a non-local variable x is accessed, make sure that you understand how to find its AR using the display.

Comparison: Access Links vs The Display

Access links can require more time (at runtime) to access non-locals (especially when the non-local is many nesting levels away).
It can also require more time to set up a new access link when a procedure is called (if the nesting level of the called procedure is much smaller than the nesting level of the calling procedure).
Displays require more space (at runtime).
If the compiler is flexible enough to implement the display using registers if enough are available, or using space in the static data area, then the compiler code itself may be rather complicated (and error-prone).
In practice, sub-programs usually are not very deeply nested, so the runtime considerations may not be very important.

Dynamic Scoping

Recall that under dynamic scoping, a use of a non-local variable corresponds to the declaration in the "most recently called, still active" method. So the question of which non-local variable to use can't be determined at compile time. It can only be determined at run-time. There are two ways to implement access to non-locals under dynamic scope: "deep access" and "shallow access", described below.

Deep Access

Using this approach, given a use of a non-local variable, control links are used to search back in the stack for the most recent AR that contains space for that variable. Note that this requires that it be possible to tell which variables are stored in each AR; this is more natural for languages that are interpreted rather than being compiled (which was indeed the case for languages that used dynamic scope). Note also that the number of control links that must be followed cannot be determined at compile time; in fact, a different number of links may be followed at different times during execution, as illustrated by the following example program:

void P() { write x; }

void Q() {
  x = x + 1;
  if (x < 23) Q();
  else P();
}

void R() {
  int x = 20;
  Q();
  P():
}

void main() {
  int x = 10;
  R();
  P();
}

TEST YOURSELF #5

Trace the execution of the program given above. Note that method P includes a use of non-local variable x. How many control links must be followed to find the AR with space for x each time P is called?

Shallow Access

Using this approach, space is allocated (in registers or in the static data area) for every variable name that is in the program (i.e., one space for variable x even if there are several declarations of x in different methods). For every reference to x, the generated code refers to the same location.

When a method is called, it saves, in its own AR, the current values of all of the variables that it declares itself (i.e., if it declares x and y, then it saves the values of x and y that are currently in the space for x and y). It restores those values when it finishes.

Note that this means that when a method accesses a non-local variable x, the value of x from the most-recently-called, still-active method is stored in the (single) location for x. There is no need to go searching down the stack!

TEST YOURSELF #6

Question 1: Trace the execution of the program given above again, this time assuming that shallow access is used.

Question 2: What are the advantages and disadvantages of shallow access compared with deep access? (Consider both time and space requirements.)