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Basic Blocks
Jingke Li
Portland State University
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Basic Blocks
A basic block is a sequence of consecutive (three-address) statements with no branch-in or branch-out statements.
- Only the first statement can be a label or target of a jump.
- Only the last statement can be a jump statement.
A basic block: (1) i := m- (2) j := n (3) t1 := 4*n (4) v := a[t1]
Not a basic block: (1) i := m- (2) j := n (3) t1 := 4n (4) v := a[t1] L1: (5) i := i+ (6) t2 := 4i (7) t3 := a[t2] (8) if t3<v goto L (9) j := j- (10) t4 := 4*j
Finding Basic Blocks
Algorithm:
- Find the “leaders” (the first statements of basic blocks).
- The first statement of the program, or
- The target of a conditional or unconditional branch statement, or
- The statement following a conditional or unconditional branch statement (this statement is an implicit target).
- For each leader, its basic block consists of the leader and all statements up to the next leader or the end of the program.
Example:
(1) a := 0 L1: (2) b := b+ (3) c := c+b (4) a := b* (5) if a<N goto L (6) return c
- Find leaders: (1), (2), and (6)
- Form basic blocks: B1: (1) B2: (2)--(5) B3: (6)
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Control Flow Graph
A graph representation of three-address code. Nodes — represent basic blocks Edges — represent (potential) flow of control
Example:
(1) a := 0 L1: (2) b := b+ (3) c := c+b (4) a := b* (5) if a<N goto L (6) return c
a := 0
b := a+ c := c+b a := b* a<N
return c
B
B
B
Control flow graph can be constructed by the basic block partition program.
Quicksort (cont.)
Basic Blocks:
B1: (1)--(4) B2: (5)--(8) B3: (9)--(12) B4: (13) B5: (14)--(22) B6: (23)--(30)
Control Flow Graph:
i := m- j := n t1 := 4n v := a[t1] i := i+ t2 := 4i t3 := a[t2] if t3<v goto B
j := j- t4 := 4*j t5 := a[t4] if t5>v goto B if i>=j goto B
t6 := 4i x := a[t6] t7 := 4i t8 := 4j t9 := a[t8] a[t7] := t t10 := 4j a[t10] := x goto B
t11 := 4i x := a[t11] t12 := 4i t13 := 4n t14 := a[t13] a[t12] := t t15 := 4n a[t15] := x
B
B
B
B B5 B
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Loops
Control flow graphs may contain “loops”. Loops are very important for optimization, because statements in a loop may be executed many times during the execution of the program.
What is a Loop?
Are there one or two loops in each of these CFGs?
1 2 3 4 5 6 1
2
3 4
5
Natural Loops
Given a “back edge” t → h, the natural loop of t → h is the subgraph
consisting of the set of nodes containing h and all the nodes that (1) are dominated by h and (2) from which t can be reached without passing through h, and the edge set connecting all the nodes in this node set.
Node h is the loop header, which is the unique entry node to the loop.
Dominance Relation — We say that node d dominates node i, if every possible execution path from CFG entry to i includes d. (e.g. You can’t execute i without executing d first.)
Observation: Node a dominates node b if and only if
- a = b, or
- (^) a is the unique immediate predecessor of b, or
- a dominates all the immediate predecessors of b.
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Back Edges
We call an edge t → h back edge if h dominates t.
Finding Back Edges:
- Find a spanning tree of the CFG (e.g. using a depth-first search algorithm).
- The edges that are not included in the spanning tree are candidates for back edges, check each of them against the dominance relation.
Traces
A trace is a sequence of statements that could be consecutively executed during the execution of the program. It can include conditional branches.
A program has many different, overlapping traces. We are only interested in the set of traces that exactly covers the program: each block must be in exactly one trace.
Reasons for forming traces:
- Jumps between blocks that belong to the same trace can be eliminated (e.g. by reversing the jump condition if it’s a conditional jump).
- This enables many optimizations to apply to a whole trace.
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Trace Examples
i := m- j := nt1 := 4n v := a[t1] i := i+ t2 := 4i t3 := a[t2]if t3<v goto B
j := j-1t4 := 4*j t5 := a[t4]if t5>v goto B
if i>=j goto B t6 := 4i x := a[t6]t7 := 4i t8 := 4jt9 := a[t8] a[t7] := t9t10 := 4j a[t10] := x goto B
t11 := 4ix := a[t11] t12 := 4i t13 := 4nt14 := a[t13] a[t12] := t14t15 := 4n a[t15] := x
B
B
B
B B5 B
- Overlapping traces: Trace 1 — statements from B1, B2, B3, B4, and B5. Trace 2 — statements from B1, B2, B3, B4, and B6.
- (^) Traces that exactly covers the program: Trace 1 — statements from B1, B2, B3, B4, and B5. Trace 2 — statements from B6.
- (^) Another set of traces that covers the program: Trace 1 — statements from B1. Trace 2 — statements from B2, B3, B4, and B5. Trace 3 — statements from B6.
