Class 41: Code Improvement (1)

Held: Thursday, 6 May 2004

Summary: Today we look at some of the issues involved in the improvement of program code, focusing primarily on intermediate code.

Related Pages:

• EBoard for morning.
• EBoard for afternoon.

Notes:

• That's right: Lab today is used for lecture.
• Custom course eval forms available this afternoon. Please fill one out by tomorrow.
• Tomorrow we meet at Dairy Barn.
• Time for your final questions on the project.
• You are now at the top of my grading heap.

Overview:

• Improvement basics.
• Analyzing basic blocks.
• Generating better assembly.
• Some common optimizations.

Introduction to Code Improvement

• Since the first compiler, one of the goals of compilation is to generate code nearly as good as that hand coded by a talented programmer.
• However, it is often better to generate less-good code on the first pass.
  • It may require less effort to generate that code.
  • An early optimization at one point may prevent optimizations at other points.
  • The original code may be more readable.
  • The original code may be easier to prove equivalent to the original program.
• While it is possible for a compiler to improve its code on the fly, as it generates code from portions of the annotated parse tree (or as it parses the program), it is often easier to improve the code in a separate pass.
• Traditionally, code improvement is called optimization, although the code it produces is often not optimal
  • Optimize implies optimal as in you can't be any better than this.
  • Few optimizations are guaranteed to produce unimprovable code because it may always be possible to choose a better algorithm (especially if you know more about the input data)
• Code improvement can typically be done at many stages in a program:
  • Source code
    • You can choose better algorithms.
    • You can identify slower parts of the program and recode them.
    • You can turn tail-recursion into iteration (if your compiler doesn't do it for you).
    • You can choose better data types _ ...
  • Intermediate code
    • Many of the transformations we'll talk about today.
  • Code generation
    • Select registers well
    • Select translations well
  • Target code
    • Peephole improvement (look at a few lines at a time)
• Algorithmic improvements are often among the most important. For some problems, the improvement in algorithms over the past thirty years outpaced the improvements in processors.
  • You were better off running the newer algorithm on older equipment than running the older algorithm on newer equipment.
• It's also worthwhile thinking about the data. For example, integer calculations are typically much faster than real calculations.
• It's also worth thinking about the arrangement of arrays. In most systems, one of the following two nested loops will run much faster for very large arrays. Can you tell why?

  for i := 1 to N do
    for j := 1 to N do
      B[i,j] := A[i,j];
  
  for j := 1 to N do
    for i := 1 to N do
      B[i,j] := A[i,j]
  

• These improvements can be broken down into local/peephole improvements (look at a small section of code and make it better) and more global improvements (reorder the flow of control, duplicate some code rather than do a procedure call, ...).
• Many optimizations (both local and global) require an understanding of control flow and data flow in the program.
  • So that's where we'll begin.

Flow Graphs

• In order to do most optimizations, it's important to get a sense of the control and data flow in a program. We do this by breaking the program up into so called basic blocks and edges between those basic blocks.
• A basic block is a sequence of consecutive statements in which control enters only at the top and leaves only at the end. That is, you're guaranteed to execute all the instructions in the block if you enter the block.
• How to build basic blocks:
  • Identify the possible starts of basic blocks (called leaders)
  • Anything between a leader and the next leader (not including the next leader) is a basic block.
• How to identify leaders:
  • The first statement is a leader
  • The target of a branch is a leader
  • Anything immediately following a branch is a leader

Simple Dataflow Analysis

• As we've seen in our discussion of register analysis, for each piece of code (e.g., statement, series of statements, block, and group of blocks), we might consider the variables that provide values that are used in the code (uses) and those variables that have values set by the code (defines).
• It's fairly easy to specify uses and defines for individual instructions (e.g., for ADD b c a, the instruction uses b and c and defines a).
• We should then consider how uses and defines might be defined for groups of statements. We might find that we have to define variants of uses and defines to deal with the interaction of types of use. In particular, what should we do about sequences of instructions?
• What about groups of blocks?
  • How should we define a group of blocks?
  • How should we find groups of blocks?
  • How should we define uses and defines for groups of blocks.

Code Generation, Revisited

• As I suggested earlier, many of the issues for building good programs require a careful understanding of the underlying assembly language.
• It also requires some understanding of how data are currently organized
• For example, if we've been using a three-parameter add (as I like to do), there are many ways to translate that to a two-parameter add, depending on what you already have in registers.
• Different but similar code can require different numbers of cycles. For example, given variables a, b, and c, all of which are stored in memory, how should we implement ADD b c -> a
  • We can put b in a register, add to that register, and move into a.
  • We can put b and c into registers, do register addition, and move the result into a.
  • Which is faster? It depends on the relative costs of the different kinds of move and add operations.
  • If any of the values are already in registers, we can eliminate one or more of the moves.
• We'll leave such careful consideration as a future topic.

Basic Transformations

• Once we've broken the program down into blocks and thought about the relationships between blocks, we can then do some simple transformations on the program.
• Common subexpression elimination Suppose we have a series of statements like

  ADD y z -> x
  ...
  ADD y z -> a
  

  and there are no changes to y and z in the ellided code. Then we can replace the latter operation with mov x a.
  • This kind of optimization is possible between blocks, but can be more difficult. Consider the case in which we have three identical assignments in three separate blocks, two of which lead to the third. If there are no other ways to enter the third block, we can use a copy rather than a computation.
  • In practice, we may even add a new variable and assign to it. Consider

      ADD a b -> c
      GOTO WHATEVER
      ADD a b -> d
      GOTO WHATEVER
    WHATEVER:
      ADD a b -> e
    

    In order to replace the final ADD by a MOVE, we need to add another variable and some extra work.

      ADD a b -> t
      MOVE t -> c
      GOTO WHATEVER
      ADD a b -> t
      MOVE t -> d
      GOTO WHATEVER
    WHATEVER:
      MOVE t -> e
    

• Copy propagation Whenever we have code for the form mov x y, we can use x in place of y in subsequent statements (until x or y is updated).
• Constant propagation. Whenever a container (memory location, register, or temporary) contains a known value, use that known value rather than the container,
• Dead-code elimination If no code reachable from a statement that defines x uses x, then we don't need to execute that statement, and can eliminate it.
  • Note that careful copy propagation may lead to dead code.
• Statement swapping (interchange) Given two subsequent statements, s1 and s2, if the intersection of uses(s1) and defines(s2) is empty and the intersection of uses(s2) defines(s1) is empty, then we can swap s1 and s2.
  • Why is this helpful? It can lead to other transofrmations.
• Algebraic transformations. We can rewrite some mathematical operations with more efficient code. For example, rather than multiplying by 2, we can add to itself or left shift one bit (depending on the underlying implementation of integers).
• Induction variables and reduction in strength: When two variables change together (as in the following code), use a simpler operation on the second.
  • From

      ADD $1 t -> t
      MUL t $4 -> u
    

  • To

      ADD $1 t -> t
      ADD $4 u -> u