OPTIMIZING THE JAVA VIRTUAL MACHINE INSTRUCTION SET BY ...

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because of the presence of the intervening transfers of control. Many optimizations
are possible. They are discussed in Section 7.7. The codelet for a multicode that has
been optimized in this manner will be expressed as:
x 1 x 2 x 3 ...x n → (7.5)
The difference in performance between the optimized multicode and the original
sequence of bytecodes is expressed as:
∆ x1 x 2 x 3 ...x n→ = Cost(x 1 → x 2 → x 3 → ... → x n →) − Cost(x 1 x 2 x 3 ...x n →) (7.6)
Because the cost of a transfer of control is non-zero, the following relationship
exists between a bytecode sequence, its equivalent unoptimized multicode and its
equivalent optimized multicode:
Cost(x 1 x 2 x 3 ...x n →) ≤ Cost(x 1 /x 2 /.../x n →) < Cost(x 1 → x 2 → ... → x n →)
(7.7)
The first relational operator is expressed as a less than or equal because there is no
guarantee that additional optimization opportunities will be possible. Consequently,
it is possible that the performance of x 1 x 2 x 3 ...x n → will be identical to x 1 / x 2 / x 3 / ...
/ x n →. However, because a transfer of control has a non-zero cost, it is known that
the cost of x 1 / x 2 / x 3 / ... / x n → will be strictly less than the cost of x 1 →x 2 →x 3 →...
→x n → since n is known to be greater than 1 from the definition of a multicode. Based
on the relationships in Equation 7.7 it is also known that the relationship between
the changes in performance is:
∆ x1 x 2 x 3 ...x n→ ≥ ∆ x1 /x 2 /x 3 /.../x n→ (7.8)
The impact a multicode has on application performance is not solely related to
the difference in performance between the the bytecode sequence and the multicode.
The number of times that the bytecode sequence will be executed is also a critical
factor, and will be denoted by:
N x1 →x 2 →x 3 →...→x n→ (7.9)
There may be occurrences of the bytecode sequence that are executed but are not