250 lines
8.4 KiB
Text
250 lines
8.4 KiB
Text
.NH 2
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Implementation
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.PP
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.NH 3
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The value number method
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.PP
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To determine whether two expressions have the same result,
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there must be some way to determine whether their operands have
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the same values.
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We use a system of \fIvalue numbers\fP
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.[
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kennedy data flow analysis
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.]
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in which each distinct value of whatever type,
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created or used within the working window,
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receives a unique identifying number, its value number.
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Two items have the same value number if and only if,
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based only upon information from the instructions in the window,
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their values are provably identical.
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For example, after processing the statement
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.DS
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a := 4;
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.DE
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the variable a and the constant 4 have the same value number.
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.PP
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The value number of the result of an expression depends only
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on the kind of operator and the value number(s) of the operand(s).
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The expressions need not be textually equal, as shown in Fig. 7.5.
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.DS
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.TS
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l l.
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a := c; (1)
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use(a * b); (2)
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d := b; (3)
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use(c * d); (4)
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.TE
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Fig. 7.5 Different expressions with the same value number
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.DE
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At line (1) a receives the same value number as c.
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At line (2) d receives the same value number as b.
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At line (4) the expression "c * d" receives the same value number
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as the expression "a * b" at line (2),
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because the value numbers of their left and right operands are the same,
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and the operator (*) is the same.
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.PP
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As another example of the value number method, consider Fig. 7.6.
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.DS
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.TS
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l l.
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use(a * b); (1)
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a := 123; (2)
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use(a * b); (3)
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.TE
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Fig. 7.6 Identical expressions with the different value numbers
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.DE
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Although textually the expressions "a * b" in line 1 and line 3 are equal,
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a will have different value numbers at line 3 and line 1.
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The two expressions will not mistakenly be recognized as equivalent.
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.NH 3
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Entities
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.PP
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The Value Number Method distinguishes between operators and operands.
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The value numbers of operands are stored in a table,
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called the \fIsymbol table\fR.
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The value number of a subexpression depends on the
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(root) operator of the expression and on the value numbers
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of its operands.
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A table of "available expressions" is used to do this mapping.
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.PP
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CS recognizes the following kinds of EM operands, called \fIentities\fR:
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.DS
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- constant
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- local variable
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- external variable
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- indirectly accessed entity
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- offsetted entity
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- address of local variable
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- address of external variable
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- address of offsetted entity
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- address of local base
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- address of argument base
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- array element
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- procedure identifier
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- floating zero
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- local base
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- heap pointer
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- ignore mask
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.DE
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.LP
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Whenever a new entity is encountered in the working window,
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it is entered in the symbol table and given a brand new value number.
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Most entities have attributes (e.g. the offset in
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the current stackframe for local variables),
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which are also stored in the symbol table.
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.PP
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An entity is called static if its value cannot be changed
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(e.g. a constant or an address).
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.NH 3
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Parsing expressions
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.PP
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Common subexpressions are recognized by simulating the behaviour
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of the EM machine.
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The EM code is parsed from left to right;
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as EM is postfix code, this is a bottom up parse.
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At any point the current state of the EM runtime stack is
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reflected by a simulated "fake stack",
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containing descriptions of the parsed operands and expressions.
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A descriptor consists of:
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.DS
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(1) the value number of the operand or expression
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(2) the size of the operand or expression
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(3) a pointer to the first line of EM-code
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that constitutes the operand or expression
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.DE
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Note that operands may consist of several EM instructions.
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Whenever an operator is encountered, the
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descriptors of its operands are on top of the fake stack.
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The operator and the value numbers of the operands
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are used as indices in the table of available expressions,
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to determine the value number of the expression.
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.PP
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During the parsing process,
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we keep track of the first line of each expression;
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we need this information when we decide to eliminate the expression.
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.NH 3
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Updating entities
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.PP
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An entity is assigned a value number when it is
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used for the first time
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in the working window.
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If the entity is used as left hand side of an assignment,
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it gets the value number of the right hand side.
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Sometimes the effects of an instruction on an entity cannot
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be determined exactly;
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the current value and value number of the entity may become
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inconsistent.
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Hence the current value number must be forgotten.
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This is achieved by giving the entity a new value number
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that was not used before.
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The entity is said to be \fIkilled\fR.
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.PP
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As information is lost when an entity is killed,
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CS tries to save as many entities as possible.
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In case of an indirect assignment through a pointer,
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some analysis is done to see which variables cannot be altered.
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For a procedure call, the interprocedural information contained
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in the procedure table is used to restrict the set of entities that may
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be changed by the call.
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Local variables for which the front end generated
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a register message can never be changed by an indirect assignment
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or a procedure call.
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.NH 3
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Changing the EM text
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.PP
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When a new expression comes available,
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it is checked whether its result is saved in a local
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that may go in a register.
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The last line of the expression must be followed
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by a STL or SDL instruction
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(depending on the size of the result)
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and a register message must be present for
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this local.
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If there is such a local,
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it is recorded in the available expressions table.
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Each time a new occurrence of this expression
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is found,
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the value number of the local is compared against
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the value number of the result.
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If they are different the local cannot be used and is forgotten.
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.PP
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The available expressions are linked in a list.
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New expressions are linked at the head of the list.
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In this way expressions that are contained within other
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expressions appear later in the list,
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because EM-expressions are postfix.
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The elimination process walks through the list,
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starting at the head, to find the largest expressions first.
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If an expression is eliminated,
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any expression later on in the list, contained in the former expression,
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is removed from the list,
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as expressions can only be eliminated once.
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.PP
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A STL or SDL is emitted after the first occurrence of the expression,
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unless there was an existing local variable that could hold the result.
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.NH 3
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Desirability analysis
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.PP
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Although the global optimizer works on EM code,
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the goal is to improve the quality of the object code.
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Therefore some machine-dependent information is needed
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to decide whether it is desirable to
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eliminate a given expression.
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Because it is impossible for the CS phase to know
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exactly what code will be generated,
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some heuristics are used.
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CS essentially looks for some special cases
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that should not be eliminated.
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These special cases can be turned on or off for a given machine,
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as indicated in a machine descriptor file.
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.PP
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Some operators can sometimes be translated
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into an addressing mode for the machine at hand.
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Such an operator is only eliminated
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if its operand is itself expensive,
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i.e. it is not just a simple load.
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The machine descriptor file contains a set of such operators.
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.PP
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Eliminating the loading of the Local Base or
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the Argument Base by the LXL resp. LXA instruction
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is only beneficial if the difference in lexical levels
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exceeds a certain threshold.
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The machine descriptor file contains this threshold.
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.PP
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Replacing a SAR or a LAR by an AAR followed by a LOI
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may possibly increase the size of the object code.
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We assume that this is only possible when the
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size of the array element is greater than some limit.
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.PP
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There are back ends that can very efficiently translate
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the index computing instruction sequence LOC SLI ADS.
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If this is the case,
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the SLI instruction between a LOC
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and an ADS is not eliminated.
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.PP
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To handle unforseen cases, the descriptor file may also contain
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a set of operators that should never be eliminated.
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.NH 3
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The algorithm
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.PP
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After these preparatory explanations,
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the algorithm itself is easy to understand.
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For each instruction within the current window,
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the following steps are performed in the given order :
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.IP 1.
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Check if this instruction defines an entity.
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If so, the set of entities is updated accordingly.
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.IP 2.
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Kill all entities that might be affected by this instruction.
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.IP 3.
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Simulate the instruction on the fake-stack.
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If this instruction is an operator,
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update the list of available expressions accordingly.
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.PP
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The result of this process is
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a list of available expressions plus the information
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needed to eliminate them.
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Expressions that are desirable to eliminate are eliminated.
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Next, the window is shifted and the process is repeated.
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