86 lines
2.4 KiB
Text
86 lines
2.4 KiB
Text
.NH 2
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Specification of the Common Subexpression Elimination phase
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.PP
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In this section we will describe
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the window
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through which CS examines the code,
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the expressions recognized by CS,
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and finally the changes made to the code.
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.NH 3
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The working window
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.PP
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The CS algorithm is applied to the
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largest sequence of textually adjacent basic blocks
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B1,..,Bn, for which
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.DS
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PRED(Bj) = {Bj-1}, j = 2,..,n.
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.DE
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Intuitively, this window consists of straight line code,
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with only one entry point (at the beginning); it may
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contain jumps, which should all have their targets outside the window.
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This is illustrated in Fig. 7.2.
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.DS
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x := a * b; (1)
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if x < 10 then (2)
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y := a * b; (3)
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Fig. 7.2 The working window of CS
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.DE
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Line (2) can only be executed after line (1).
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Likewise, line (3) can only be executed after
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line (2).
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Both a and b have the same values at line (1) and at line (3).
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.PP
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Larger windows were avoided.
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In Fig. 7.3, the value of a at line (4) may have been obtained
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at more than one point.
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.DS
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x := a * b; (1)
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if x < 10 then (2)
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a := 100; (3)
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y := a * b; (4)
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Fig. 7.3 Several working windows
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.DE
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.NH 3
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Recognized expressions.
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.PP
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The computations eliminated by CS need not be normal expressions
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(like "a * b"),
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but can even consist of a single operand that is expensive to access,
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such as an array element or a record field.
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If an array element is used,
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its address is computed implicitly.
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CS is able to eliminate either the element itself or its
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address, whichever one is most profitable.
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A variable of a textually enclosing procedure may also be
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expensive to access, depending on the lexical level difference.
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.NH 3
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Transformations
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.PP
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CS creates a new temporary local variable (TMP)
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for every eliminated expression,
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unless it is able to use an existing local variable.
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It emits code to initialize this variable with the
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result of the expression.
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Most recurrences of the expression
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can simply be replaced by a reference to TMP.
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If the address of an array element is recognized as
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a common subexpression,
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references to the element itself are replaced by
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indirect references through TMP (see Fig. 7.4).
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.DS
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.TS
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l l l.
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x := A[i]; TMP := &A[i];
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. . . --> x := *TMP;
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A[i] := y; . . .
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*TMP := y;
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.TE
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Fig. 7.4 Elimination of an array address computation
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.DE
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Here, '&' is the 'address of' operator,
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and unary '*' is the indirection operator.
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(Note that EM actually has different instructions to do
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a use-indirect or an assign-indirect.)
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