Abstract
The problem of evaluating arithmetic expressions on a machine with N ≥ 1 general purpose registers is considered. It is initially assumed that no algebraic laws apply to the operators and operands in the expression. An algorithm for evaluation of expressions under this assumption is proposed, and it is shown to take the shortest possible number of instructions. It is then assumed that certain operators are commutative or both commutative and associative. In this case a procedure is given for finding an expression equivalent to a given one and having the shortest possible evaluation sequence. It is then shown that the algorithms presented here also minimize the number of storage references in the evaluation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 715-728 |
| Number of pages | 14 |
| Journal | Journal of the ACM (JACM) |
| Volume | 17 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1 1970 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Information Systems
- Hardware and Architecture
- Artificial Intelligence
Cite this
The Generation of Optimal Code for Arithmetic Expressions. / Sethi, Ravi; Ullman, J. D.
In: Journal of the ACM (JACM), Vol. 17, No. 4, 01.10.1970, p. 715-728.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The Generation of Optimal Code for Arithmetic Expressions
AU - Sethi, Ravi
AU - Ullman, J. D.
PY - 1970/10/1
Y1 - 1970/10/1
N2 - The problem of evaluating arithmetic expressions on a machine with N ≥ 1 general purpose registers is considered. It is initially assumed that no algebraic laws apply to the operators and operands in the expression. An algorithm for evaluation of expressions under this assumption is proposed, and it is shown to take the shortest possible number of instructions. It is then assumed that certain operators are commutative or both commutative and associative. In this case a procedure is given for finding an expression equivalent to a given one and having the shortest possible evaluation sequence. It is then shown that the algorithms presented here also minimize the number of storage references in the evaluation.
AB - The problem of evaluating arithmetic expressions on a machine with N ≥ 1 general purpose registers is considered. It is initially assumed that no algebraic laws apply to the operators and operands in the expression. An algorithm for evaluation of expressions under this assumption is proposed, and it is shown to take the shortest possible number of instructions. It is then assumed that certain operators are commutative or both commutative and associative. In this case a procedure is given for finding an expression equivalent to a given one and having the shortest possible evaluation sequence. It is then shown that the algorithms presented here also minimize the number of storage references in the evaluation.
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UR - http://www.scopus.com/inward/citedby.url?scp=0014855855&partnerID=8YFLogxK
U2 - 10.1145/321607.321620
DO - 10.1145/321607.321620
M3 - Article
AN - SCOPUS:0014855855
VL - 17
SP - 715
EP - 728
JO - Journal of the ACM
JF - Journal of the ACM
SN - 0004-5411
IS - 4
ER -