1. Advanced Compiler Techniques
Control Flow Analysis &
Local Optimizations
LIU Xianhua
School of EECS, Peking University

2. Levels of Optimizations
Local
inside a basic block
Global (intraprocedural)
Across basic blocks
Whole procedure analysis
Interprocedural
Across procedures
Whole program analysis
“Advanced Compiler Techniques”

3. The Golden Rules of Optimization
Premature Optimization is Evil
Donald Knuth, premature optimization is the root of all evil
Optimization can introduce new, subtle bugs
Optimization usually makes code harder to understand and maintain
Get your code right first, then, if really needed, optimize it
Document optimizations carefully
Keep the non-optimized version handy, or even as a comment in your code
“Advanced Compiler Techniques”

4. The Golden Rules of Optimization
The 80/20 Rule
In general, 80% percent of a program’s execution time is spent executing 20% of the code
90%/10% for performance-hungry programs
Spend your time optimizing the important 10/20% of your program
Optimize the common case even at the cost of making the uncommon case slower
“Advanced Compiler Techniques”

5. The Golden Rules of Optimization
Good Algorithms Rule
The best and most important way of optimizing a program is using good algorithms
E.g. O(n*logn) rather than O(n2)
However, we still need lower level optimization to get more of our programs
In addition, asymptotic complexity is not always an appropriate metric of efficiency
Hidden constant may be misleading
E.g. a linear time algorithm than runs in 100*n+100 time is slower than a cubic time algorithm than runs in n3+10 time if the problem size is small
“Advanced Compiler Techniques”

6. General Optimization Techniques
Strength reduction
Use the fastest version of an operation
E.g.
x >> 2 instead of x / 4
x << 1 instead of x * 2
Common sub expression elimination
Eliminate redundant calculations
double x = d * (lim / max) * sx;
double y = d * (lim / max) * sy;
double depth = d * (lim / max);
double x = depth * sx;
double y = depth * sy;
“Advanced Compiler Techniques”

7. General Optimization Techniques
Code motion
Invariant expressions should be executed only once
E.g.
for (int i = 0; i < x.length; i++)
x[i] *= Math.PI * Math.cos(y);
double picosy = Math.PI * Math.cos(y);
x[i] *= picosy;
“Advanced Compiler Techniques”

8. General Optimization Techniques
Loop unrolling
The overhead of the loop control code can be reduced by executing more than one iteration in the body of the loop. E.g.
double picosy = Math.PI * Math.cos(y);
for (int i = 0; i < x.length; i++)
x[i] *= picosy;
for (int i = 0; i < x.length; i += 2) {
x[i+1] *= picosy; }
“Advanced Compiler Techniques”

9. Compiler Optimizations
Compilers try to generate good code
i.e. Fast
Code improvement is challenging
Many problems are NP-hard
Code improvement may slow down the compilation process
In some domains, such as just-in-time compilation, compilation speed is critical
“Advanced Compiler Techniques”

10. “Advanced Compiler Techniques”
Phases of Compilation
The first three phases are language-dependent
The last two are machine-dependent
The middle two dependent on neither the language nor the machine
“Advanced Compiler Techniques”

11. “Advanced Compiler Techniques”
Phases
“Advanced Compiler Techniques”

12. “Advanced Compiler Techniques”
Control Flow
Control transfer = branch (taken or fall-through)
Control flow
Branching behavior of an application
What sequences of instructions can be executed
Execution  Dynamic control flow
Direction of a particular instance of a branch
Predict, speculate, squash, etc.
Compiler  Static control flow
Not executing the program
Input not known, so what could happen
Control flow analysis
Determining properties of the program branch structure
Determining instruction execution properties
“Advanced Compiler Techniques”

13. “Advanced Compiler Techniques”
Basic Blocks
A basic block is a maximal sequence of consecutive three-address instructions with the following properties:
The flow of control can only enter the basic block thru the 1st instruction in the block. (no jumps into the middle of the block)
Control will leave the block without halting or branching, except possibly at the last instruction in the block.
Basic blocks become the nodes of a flow graph, with edges indicating the order.
“Advanced Compiler Techniques”

14. Examples for i from 1 to 10 do for j from 1 to 10 do a[i,j]=0.0
t1 = 10 * i
t2 = t1 + j
t3 = 8 * t2
t4 = t3 - 88
a[t4] = 0.0
j = j + 1
if j <= 10 goto (3)
i = i + 1
if i <= 10 goto (2)
t5 = i - 1
t6 = 88 * t5
a[t6] = 1.0
if i <= 10 goto (13)
for i from 1 to 10 do
for j from 1 to 10 do
a[i,j]=0.0
a[i,i]=1.0

15. Identifying Basic Blocks
Input: sequence of instructions instr(i)
Output: A list of basic blocks
Method:
Identify leaders: the first instruction of a basic block
Iterate: add subsequent instructions to basic block until we reach another leader
“Advanced Compiler Techniques”

16. “Advanced Compiler Techniques”
Identifying Leaders
Rules for finding leaders in code
First instr in the code is a leader
Any instr that is the target of a (conditional or unconditional) jump is a leader
Any instr that immediately follow a (conditional or unconditional) jump is a leader
“Advanced Compiler Techniques”

17. Basic Block Partition Algorithm
leaders = {1} // start of program
for i = 1 to |n| // all instructions
if instr(i) is a branch
leaders = leaders U targets of instr(i) U instr(i+1)
worklist = leaders
While worklist not empty
x = first instruction in worklist
worklist = worklist – {x}
block(x) = {x}
for i = x + 1; i <= |n| && i not in leaders; i++
block(x) = block(x) U {i}
“Advanced Compiler Techniques”

18. “Advanced Compiler Techniques”
Basic Block Example A
i = 1
j = 1
t1 = 10 * i
t2 = t1 + j
t3 = 8 * t2
t4 = t3 - 88
a[t4] = 0.0
j = j + 1
if j <= 10 goto (3)
i = i + 1
if i <= 10 goto (2)
t5 = i - 1
t6 = 88 * t5
a[t6] = 1.0
if i <= 10 goto (13) B C
Leaders
Basic Blocks D E F
“Advanced Compiler Techniques”

19. “Advanced Compiler Techniques”
Control-Flow Graphs
Control-flow graph:
Node: an instruction or sequence of instructions (a basic block)
Two instructions i, j in same basic block iff execution of i guarantees execution of j
Directed edge: potential flow of control
Distinguished start node Entry & Exit
First & last instruction in program
“Advanced Compiler Techniques”

20. “Advanced Compiler Techniques”
Control-Flow Edges
Basic blocks = nodes
Edges:
Add directed edge between P and S if:
Jump/branch from last statement of P to first statement of S, or
According to the initial order, S immediately follows P in program order and P does not end with unconditional branch (goto/return/call)
Definition of predecessor and successor
P is a predecessor of S
S is a successor of P
“Advanced Compiler Techniques”

21. Control-Flow Edge Algorithm
Input: block(i), sequence of basic blocks
Output: CFG where nodes are basic blocks
for i = 1 to the number of blocks
x = last instruction of block(i)
if instr(x) is a branch/jump
for each target y of instr(x),
create edge (i -> y)
if instr(x) is not unconditional branch,
create edge (i -> i+1)
“Advanced Compiler Techniques”

22. “Advanced Compiler Techniques”
Dominator
Defn: Dominator – Given a CFG(V, E, Entry, Exit), a node x dominates a node y, if every path from the Entry block to y contains x
In the reverse direction, node x post-dominates block y if every path from y to the exit has to pass through block x.
Some properties of dominators:
Reflexivity, transitivity, anti-symmetry
If x dominates z and y dominates z, then either x dominates y or y dominates x
Intuition
Given some BB, which blocks are guaranteed to have executed prior to executing the BB
“Advanced Compiler Techniques”

23. “Advanced Compiler Techniques”
Dominator Tree
It is said that a block x immediately dominates block y if x dominates y, and there is no intervening block P such that x dominates P and P dominates y.
In other words, x is the last dominator on all paths from entry to y.
Each block has a unique immediate dominator.
A dominator tree is a tree where each node's children are those nodes it immediately dominates. Because the immediate dominator is unique, it is a tree. The start node is the root of the tree.
{1} 1 1 2
{1,2} 4
{1,4} 2 4 3 5
{1,2,3} 3 5
{1,5}
“Advanced Compiler Techniques”

24. “Advanced Compiler Techniques”
Loops
Loops comes from
while, do-while, for, goto……
Many transformation depends on loops
Back edge: An edge is a back edge if its head dominates its tail.
Loop definition: A set of nodes L in a CFG is a loop if
There is a node called the loop entry: no other node in L has a predecessor outside L.
Every node in L has a nonempty path (within L) to the entry of L.
“Advanced Compiler Techniques”

25. “Advanced Compiler Techniques”
Example: Back Edges
{1} 1
CFG（Control Flow Graph） 2
{1,2} 4
{1,4} 3 5
{1}
{1,2,3} 1
{1,5} 2
{1,2} 4
{1,4}
DAG（Directed Acyclic Graph） 3 5
{1,2,3}
{1,5}
“Advanced Compiler Techniques”

26. “Advanced Compiler Techniques”
Loop Examples
{B3}
{B6}
{B2, B3, B4}
“Advanced Compiler Techniques”

27. “Advanced Compiler Techniques”
Identifying Loops
Motivation
majority of runtime
focus optimization on loop bodies!
remove redundant code, replace expensive operations ) speed up program
Finding loops:
easy…
i = 1; j = 1; k = 1;
A1: if i > 1000 goto L1;
A2: if j > 1000 goto L2;
A3: if k > 1000 goto L3;
do something
k = k + 1; goto A3;
L3: j = j + 1; goto A2;
L2: i = i + 1; goto A1;
L1: halt
for i = 1 to 1000
for j = 1 to 1000
for k = 1 to 1000
do something
or harder (GOTOs)
“Advanced Compiler Techniques”

28. Interval Analysis(T1/T2 Trans)
T1 Transformation
T2 Transformation
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29. Interval Analysis(T1/T2 Trans)4 3 5
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30. Interval Analysis(T1/T2 Trans)14 T1 23 5
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31. Interval Analysis(T1/T2 Trans)14 23 5
“Advanced Compiler Techniques”

32. Interval Analysis(T1/T2 Trans)
12345
12345
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33. “Advanced Compiler Techniques”
Structure Analysis
静态特征
特征描述 1
SS_No.
典型子结构唯一标识 2
Edge_No.
典型子结构中控制流边的唯一标识 3
I_last_of_head
该边首基本块最后一条指令的操作码 4
Br_direction
该边首基本块最后一条指令的跳转方向 5
I_pre_last
该边首基本块最后一条指令的前一条指令的操作码
“Advanced Compiler Techniques”

34. “Advanced Compiler Techniques”
Weighted CFG
Profiling – Run the application on 1 or more sample inputs, record some behavior
Control flow profiling
edge profile
block profile
Path profiling
Cache profiling
Memory dependence profiling
Annotate control flow profile onto a CFG  weighted CFG
Optimize more effectively with profile info!!
Optimize for the common case
Make educated guess
Entry 20
BB1 10 10
BB2
BB3 10 10
BB4 20
BB5
BB6 20
BB7 20
Exit
“Advanced Compiler Techniques”

35. “Advanced Compiler Techniques”
Local Optimization
Optimization of basic blocks
§8.5
“Advanced Compiler Techniques”

36. Transformations on basic blocks
eliminating local common sub-expressions
eliminating dead code
reordering statements that do not depend on one another
applying algebraic laws to reorder operands of three-address instructions
All of the above require symbolic execution of the basic block, to obtain def/use information
“Advanced Compiler Techniques”

37. Simple symbolic interpretation: next-use information
If x is computed in statement i, and is an operand of statement j, j > i, its value must be preserved (register or memory) until j.
If x is computed at k, k > i, the value computed at i has no further use, and be discarded (i.e. register reused)
Next-use information is annotated over statements and symbol table.
Computed on one backwards pass over statement.
“Advanced Compiler Techniques”

38. “Advanced Compiler Techniques”
Next-Use Information
Definitions
Statement i assigns a value to x;
Statement j has x as an operand;
Control can flow from i to j along a path with no intervening assignments to x;
Statement j uses the value of x computed at statement i.
i.e., x is live at statement i.
“Advanced Compiler Techniques”

39. “Advanced Compiler Techniques”
Computing next-use
Use symbol table to annotate status of variables
Each operand in a statement carries additional information:
Operand liveness (boolean)
Operand next use (later statement)
On exit from block, all temporaries are dead (no next-use)
“Advanced Compiler Techniques”

40. “Advanced Compiler Techniques”
Algorithm
INPUT: a basic block B
OUTPUT: at each statement i: x=y op z in B, create liveness and next-use for x, y, z
METHOD: for each statement in B (backward)
Retrieve liveness & next-use info from a table
Set x to “not live” and “no next-use”
Set y, z to “live” and the next uses of y,z to “i”
Note: step 2 & 3 cannot be interchanged.
E.g., x = x + y
“Advanced Compiler Techniques”

41. “Advanced Compiler Techniques”
Example
x = 1
y = 1
x = x + y
z = y
x = y + z
Exit:
x: live, 6
y: not live
z: not live 3:
x: live, 3
y: live, 3
z: not live, no 5:
x: not live, no
y: live, 5
z: live, 5 2:
x: live, 3
y: not live, no
z: not live, no
Exit:
x: live, 6
y: not live
z: not live 4:
x: not live, no
y: live, 4
z: not live, no 1:
x: not live, no
y: not live, no
z: not live, no
“Advanced Compiler Techniques”

42. Computing dependencies in BB: the DAG
Use directed acyclic graph (DAG) to recognize common subexpressions and remove redundant quadruples.
Intermediate code optimization:
basic block => DAG => improved block => assembly
Leaves are labeled with identifiers and constants.
Internal nodes are labeled with operators and identifiers
“Advanced Compiler Techniques”

43. DAG Representation of Basic Blocks
lec08-memoryorg
DAG Representation of Basic Blocks
December 29, 2018
Construct a DAG for a basic block
1. There is a node in the DAG for each of the initial values of the variables appearing in the basic block.
2. There is a node N associated with each statement s within the block. The children of N are those nodes corresponding to statements that are the last definitions, prior to s, of the operands used by s.
3. Node N is labeled by the operator applied at s, and also attached to N is the list of variables for which it is the last definition within the block.
4. Certain nodes are designated output nodes. These are the nodes whose variables are live on exit from the block; that is, their values may be used later, in another block of the flow graph.
“Advanced Compiler Techniques”

44. “Advanced Compiler Techniques”
DAG construction
Forward pass over basic block
For x = y op z;
Find node labeled y, or create one
Find node labeled z, or create one
Create new node for op, or find an existing one with descendants y, z (need hash scheme)
Add x to list of labels for new node
Remove label x from node on which it appeared
For x = y;
Add x to list of labels of node which currently holds y
a = b + c
b = a – d
c = b + c
d = a - d c b d + — a + d0 b0 c0
“Advanced Compiler Techniques”

45. Finding Local Common Subexpr.
Suppose b is not live on exit.
a = b + c
b = a – d
c = b + c
d = a - d c +
b, d - + a d0
a = b + c
d = a – d
c = d + c
a = b + c
d = a – d
b = d
c = d + c b0 c0
“Advanced Compiler Techniques”

46. “Advanced Compiler Techniques”
LCS: another example + - b0 c0 d0 a b e c
a = b + c
b = b – d
c = c + d
e = b + c
“Advanced Compiler Techniques”

47. “Advanced Compiler Techniques”
Dead Code Elimination
Delete any root that has no live variables attached
Repeated application of this transformation will remove all nodes from the DAG that correspond to dead code.
a = b + c
b = b – d
c = c + d
e = b + c + - b0 c0 d0 a b e c
On exit:
a, b live
c, e not live
a = b + c
b = b – d
“Advanced Compiler Techniques”

48. The Use of Algebraic Identities
Eliminate computations
Reduction in strength
Constant folding
2*3.14 = evaluated at compile time
Other algebraic transformations
x*y => y*x
x>y => x-y>0
a=b+c; e=c+d+b; => a=b+c; e=a+d;
“Advanced Compiler Techniques”

49. Representation of Array References
lec08-memoryorg
Representation of Array References
December 29, 2018
x = a[i]
a[j]=y
killed node
x = a[i]
a[j] = y
z = a[i]
z = x??
“Advanced Compiler Techniques”

50. Representation of Array References
lec08-memoryorg
Representation of Array References
December 29, 2018
b = a + 12
x = b[i]
b[j] = y
a is an array. b is a position in the array a.
x is killed by b[j]=y.
“Advanced Compiler Techniques”

51. Pointer Assign. & Proc. Calls
Problem of the following assignments
x = *p *q = y
we do not know what p or q point to.
x = *p is a use of every variable
*q = y is a possible assignment to every variable.
the operator =* must take all nodes that are currently associated with identifiers as arguments, which is relevant for dead-code elimination.
the *= operator kills all other nodes so far constructed in the DAG.
Global pointer analyses can be used to limit the set of variables
Procedure calls behave much like assignments through pointers.
Assume that a procedure uses and changes any data to which it has access.
If variable x is in the scope of a procedure P, a call to P both uses the node with attached variable x and kills that node.
“Advanced Compiler Techniques”

52. Reassembling BBs From DAG 's
b is not live on exit
b is live on exit
“Advanced Compiler Techniques”

53. Reassembling BBs From DAG 's
The rules of reassembling
The order of instructions must respect the order of nodes in the DAG
Assignments to an array must follow all previous assignments to, or evaluations from, the same array
Evaluations of array elements must follow any previous assignments to the same array
Any use of a variable must follow all previous procedure calls or indirect assignments through a pointer.
Any procedure call or indirect assignment through a pointer must follow all previous evaluations of any variable.
“Advanced Compiler Techniques”

54. Peephole Optimization
Dragon§8.7
Introduction to peephole
Common techniques
Algebraic identities
An example
“Advanced Compiler Techniques”

55. Peephole Optimization
Simple compiler do not perform machine-independent code improvement
They generates naive code
It is possible to take the target hole and optimize it
Sub-optimal sequences of instructions that match an optimization pattern are transformed into optimal sequences of instructions
This technique is known as peephole optimization
Peephole optimization usually works by sliding a window of several instructions (a peephole)
“Advanced Compiler Techniques”

56. Peephole Optimization
Goals:
- improve performance
- reduce memory footprint
- reduce code size
Method:
1. Exam short sequences of target instructions
2. Replacing the sequence by a more efficient one.
redundant-instruction elimination
algebraic simplifications
flow-of-control optimizations
use of machine idioms
“Advanced Compiler Techniques”

57. Peephole Optimization Common Techniques
“Advanced Compiler Techniques”

58. Peephole Optimization Common Techniques
“Advanced Compiler Techniques”

59. Peephole Optimization Common Techniques
“Advanced Compiler Techniques”

60. Peephole Optimization Common Techniques
“Advanced Compiler Techniques”

61. “Advanced Compiler Techniques”
Algebraic identities
Worth recognizing single instructions with a constant operand
Eliminate computations
A * 1 = A
A * 0 = 0
A / 1 = A
Reduce strenth
A * 2 = A + A
A/2 = A * 0.5
Constant folding
2 * 3.14 = 6.28
More delicate with floating-point
“Advanced Compiler Techniques”

62. “Advanced Compiler Techniques”
Is this ever helpful?
Why would anyone write X * 1?
Why bother to correct such obvious junk code?
In fact one might write
#define MAX_TASKS a = b * MAX_TASKS;
Also, seemingly redundant code can be produced by other optimizations.
This is an important effect.
“Advanced Compiler Techniques”

63. Replace Multiply by Shift
A := A * 4;
Can be replaced by 2-bit left shift (signed/unsigned)
But must worry about overflow if language does
A := A / 4;
If unsigned, can replace with shift right
But shift right arithmetic is a well-known problem
Language may allow it anyway (traditional C)
“Advanced Compiler Techniques”

64. The Right Shift problem
Arithmetic Right shift:
shift right and use sign bit to fill most significant bits
SAR
which is -3, not -2
in most languages -5/2 = -2
“Advanced Compiler Techniques”

65. Addition chains for multiplication
If multiply is very slow (or on a machine with no multiply instruction like the original SPARC), decomposing a constant operand into sum of powers of two can be effective:
X * = x * x*4 + x
two shifts, one subtract and one add, which may be faster than one multiply
Note similarity with efficient exponentiation method
“Advanced Compiler Techniques”

66. Flow-of-control optimizations
goto L1
. . .
L1: goto L2
goto L2
. . .
L1: goto L2
if a < b goto L1
. . .
L1: goto L2
if a < b goto L2
. . .
L1: goto L2
goto L1
. . .
L1: if a < b goto L2
L3:
if a < b goto L2
goto L3
. . .
L3:
“Advanced Compiler Techniques”

67. Peephole Opt: an Example
debug = 0
. . .
if(debug) {
print debugging information }
Source Code:
debug = 0
. . .
if debug = 1 goto L1
goto L2
L1: print debugging information
L2:
Intermediate
Code:
“Advanced Compiler Techniques”

68. Eliminate Jump after Jump
debug = 0
. . .
if debug = 1 goto L1
goto L2
L1: print debugging information
L2:
Before:
debug = 0
. . .
if debug  1 goto L2
print debugging information
L2:
After:
“Advanced Compiler Techniques”

69. “Advanced Compiler Techniques”
Constant Propagation
debug = 0
. . .
if debug  1 goto L2
print debugging information
L2:
Before:
debug = 0
. . .
if 0  1 goto L2
print debugging information
L2:
After:
“Advanced Compiler Techniques”

70. Unreachable Code (dead code elimination)
debug = 0
. . .
if 0  1 goto L2
print debugging information
L2:
Before:
debug = 0
. . .
After:
“Advanced Compiler Techniques”

71. Peephole Optimization Summary
Peephole optimization is very fast
Small overhead per instruction since they use a small, fixed-size window
It is often easier to generate naïve code and run peephole optimization than generating good code!
“Advanced Compiler Techniques”

72. “Advanced Compiler Techniques”
Summary
Introduction to optimization
Control Flow Analysis
Basic knowledge
Basic blocks
Control-flow graphs
Local Optimizations
Peephole optimizations
“Advanced Compiler Techniques”

73. “Advanced Compiler Techniques”
HW & Next Time
Homework
EX 8.4.1, 8.5.1, 8.5.2
Next Time: Dataflow analysis
Dragon§9.2
“Advanced Compiler Techniques”

74. If You Want to Get Started …
Go to
Download and install LLVM on your favorite Linux box
Read the installation instructions to help you
Will need gcc 4.x
Try to run it on a simple C program
“Advanced Compiler Techniques”