Class 38: Additional Improvement Techniques

Held Wednesday, December 4, 2002

Summary

Today we continue our study of optimization with an extended example.

Notes

• I now have one parser in hand. Can I expect the others soon?
• Upcoming schedule:
  • Friday: Final distributed; More optimization
  • Monday: Nathan presents on type inference
  • Wednesday: Garbage collection
  • Friday: Wrapup
• Due dates:
  • Parser: Monday, 9 December 2002 (final deadline)
  • Translator: Friday, 20 December 2002
  • Final: Friday, 20 December 2002
• I will also assign a short essay on your project experience. I expect you to take it much more seriously than you took the previous essay.

Overview

• Improvement, reviewed
• Loop optimization
• An example

Loop Optimizations

• We typically want to spend the most effort where it will make the most difference.
  • The typical observation is that 10% of the code does 90% of the work.
  • At the source level, we can profile the code to figure out where most of the work goes on and then carefully recode that section.
  • At the intermediate level, we can identify loops and optimize there.
• How do we identify loops? By looking at the flow graph.
• What optimizations are available?
• Code movement: If we can get statements out of loops, we're much better off.
• Induction variables and reduction in strength not all operations are the same (for example, multiplication may take more time than addition). At times, we can trade one for the other by observing when two variables change in lockstep.
• Consider the following sample code

  LOOP:
    add t1, $1, t1
    mul t1, $4, t2
    ...
  

• We call t1 and t2 induction variables because they change in relation to the loop and because a proof of the loop's termination will typically involve inducation on one of these variables
• Some simple analysis tells us that at every step of the loop, t1 is incremented by 1 which means that t2 is incremented by 4.
• If t1 is never used again, we can replace the code with

  LOOP:
    add t2, $4, t2
    ...
  

• Even if t1 is used again, the add is still cheaper than the multiply.

A Longer Example

• Let's look at a slightly longer program and consider how to optimize it.
• Consider the code fragment

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

• Assumptions for translation:
  • Integers take four bytes
  • Each dimension of the array is indexed from 1..n.
  • The array is stored in row-major order. That is, if n is 3, we have the following elements in sequence A[1,1], A[1,2], A[1,3], A[2,1], A[2,2], A[2,3], A[3,1], A[3,2], A[3,3].
• Given those assumptions, and knowledge that the representation of A begins at some position (which we'll also call A), where if A[x,y]?
  • base of A + offset n*4*(x-1) + 4*(y-1)
• The code will look something like the following

   
    MOV   $1, i
  NEXT_OUTER:
    JEQ   i, n     -> END_OUTER
    MOV   $1       -> j
  NEXT_INNER:
    JEQ   j,   n   -> END_INNER
    ISUB  i,   $1  -> t1
    IMUL  t1,  $4  -> t2
    IMUL  t2,  n   -> t3
    ISUB  j,   $1  -> t4
    IMUL  t4,  $4  -> t5
    IADD  t3,  t5  -> t6
    MOV   offset(A,t6) -> t7
    ISUB  j,   $1  -> t8
    IMUL  t8,  $4  -> t9
    IMUL  t9,  n   -> t10
    ISUB  i,   $1  -> t11
    IMUL  t11, $4  -> t12
    IADD  t10, t12 -> t13
    IMOV  t7 -> offset(B,t13)
    IADD  j, $1 -> j
    JUMP  NEXT_INNER
  END_INNER:
    IADD  i, $1    -> i
    JUMP  NEXT_OUTER
  END_OUTER:
    ...
  

• We'll start by breaking the code into basic blocks.
• We'll continue by identifying and eliminating common subexpressions.
• We'll continue by propagating copies.
• We'll conclude by identifying induction variables and reducing the strength of some operations.