Value Numbering

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Value Numbering

• Presented by
• Ben Graver
• Wayne Eggert

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Overview

• Value numbering is an optimization that assigns
  numbers to expressions in such a way that two
  expressions are assigned the same number if the
  compiler can prove they are equal.
• Used by GCC when it does a CSE pass
• Originally developed by Balke in 1967

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Problems With Basic CSE

• Expressions that look identical only produce the
  same results if none of the values of variables
  referenced by the two expressions change between
  their evaluations.
• Even if we only looked for examples of identical
  expressions, we would need to find an efficient
  way to look for matching subtrees.
• Expressions that don't look identical may produce
  identical results, as in the following example
• Example - CSE fails, but Value Numbering works
• a ? b c
• d ? b
• e ? d c
• Notice a e have the same value but are not
  lexically identical.

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Value Numbering Setup

• Based on the form of a lookup table.
• The table will associate expressions with their
  "value numbers".
• For each expression we encounter as we traverse
  the subtrees of a basic block we envoke the
  following algorithm ..

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Value Numbering Algorithm

• Look the expression up in our table.
• If the expression is not in out table, we will
  assign it the next unused value number and enter
  the expression/number pair in the table.
• If an expression is already in the table, we will
  associate it with its already assigned value
  number.

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Efficiency of Table Lookups

• Tables can be partitioned into two parts.
• 1 Value numbers and descriptors for simple
  variables which are stored in a new field.
• 2 The hash table used for all expressions
  except references to simple variables.

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Accounting for Assignments

• Value numbers are assigned to variables used in
  expressions when they are first encountered.
• For each assignment encountered, a new value
  number is assigned to the variable so that when
  the variable is referenced in subsequent
  expressions we will recognize the variable may
  produce distinct values from earlier,
  syntactically identical expressions.

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Accounting for Assignments Cont.

• Brand new value numbers are not given to the
  targets of assignments. Instead, when processing
  the assignment
• x E
• E's value number is assigned to x since future
  references to x will produce the same value as E.
  

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Processing An Expression

• To process an expression, we
• Process its sub-expressions (receiving their
  value numbers as return values).
• Build the appropriate key based on the expression
  type and the value numbers of its
  sub-expressions.
• Look the key up in the hash table, and
• make a new table entry associating the key with
  the next value number if no match is found, or
• recognize that we have found a CSE if a match is
  found (and then return the associated value
  number).

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Summary

• Value Numbering looks for equations that have
  value equivalence as opposed to matching
  lexical patterns as in CSE.

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fin.
Value Numbering CSE What a Team!