CS553 Colorado State University
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Control Flow
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10/15/09

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Loops are important (2)

    - the majority of execution time in programs is spent in loops
    
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Data-flow and Control-flow (3)

    Data-flow creates a partial ordering between the production of
    a value and its consumption.
    
    Control-flow creates a dependence between the execution of
    a guard expression and the statements being guarded.
    
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Control-flow in an AST (5)

    -> show an example AST and have students talk through the control flow
    
    In an AST control flow is implicit and in a control flow graph it is
    explicit.
    
    -> show the control flow graph for the same AST
    
    To make the control-flow explicit the intermediate representation
    has been lowered into something that is 3-address code like.
    
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Control-flow Analysis (6)

    After code has been lowered ...
    
        - create a control-flow graph
        - discover loops


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Loop Concepts (7)
        
    What is ...
        - a strongly connected component?
        - an edge source and target
        
    Today we will learn about ...
        - dominators
        - natural loops

    -> have students identify parts of loop in the While1.java 
    control-flow graph        
       

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Dominator approach to discovering loops (11)
    Note that dominators are also used to generate SSA representation.
    
    Back edges
        - back edge based on a depth first spanning tree is an edge that is not
        in the spanning tree and goes from a node to one of its ancestors
        - back edges for a natural loop has the additional constraint that the
        ancestor dominates the source node
   
    Natural loops are easier to optimize because they have a single entry point.
    For example loop invariant code motion needs a single loop header.

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Computing Dominators (12)
    
    - For the entry node s, we’ll initialize the Dom set to be the 
    set consisting of s

    - For all other nodes, set their Dom sets to be all nodes, 
    and we’ll prune these sets as we iterate
 
    - We then iterate until we reach a fixed point:
        D(n) is the set that consists of the node itself + all nodes 
        that dominate all of n’s predecessors.  This set will decrease 
        as we find that nodes do not dominate all predecessors
        
    --> Why do we init sets to N and not empty set?
    
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Reducibility (14, 15)
    
    --> Perform T1 and T2 transformations on example While1.java CFG.
    
    Recall that the depth of the CFG affects the complexity of data-flow 
    analysis.
    
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Induction Variables (18)

    Read why we want to do induction variable detection
    http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=546612
    Polaris paper
        -to recognize parallel loops, want to get rid of everything
         but loop index as having loop carried dependences
        -dependence analysis, array reference expressions need to be
         in terms of the loop index
    
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Example Induction Variables (19)
            
    3-address code
    --------------
    s = 0
    i = 0
    
    loop:
    if i>=N goto end
    t1 = i * 4
    t2 = a + t1
    t3 = M[t1]
    s = s + t3
    i = i + 1
    goto loop

    end:
    
    arithmetic progressions?
    i= 0, 1, 2, 3, ...
    t1 = 0, 4, 8, 12, ...
    t2 = a, a+4, a+8, a+12, ...
    t3 = nope, reading something from memory
    s = nope, depends on t3

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Induction Variable Identification (20)
   
    --> Which of the induction variables from the example were basic and 
    which were derived?

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Induction Variable Triples (21)

    --> What are the triples for the induction variables in the example?
    
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Example: Induction Variable Detection and Elimination (25-28)
    
    --> draw example on board and use algorithms to transform
    





    
    
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mstrout@cs.colostate.edu, 10/15/09