Code-generation for machines with multiregister operations

ABSTRACT

Previous work on optimal code generation has usually assumed that the underlying machine has identical registers and that all operands fit in a single register or memory location. This paper considers the more realistic problem of generating optimal code for expressions involving single and double length operands, using several models of register-pair machines permitting both single and double word instructions. With register-pair machines a new phenomenom arises that is not present in optimal code generation for single register machines: In an optimal evaluation of an expression it may be necessary to oscillate back and forth between evaluating subexpressions of the expression.A linear-time optimal code generation algorithm is derived for a register-pair machine in which all registers are interchangeable. The algorithm is based on showing that for this model there is an optimal evaluation sequence with limited oscillation between the sub-trees dominated by the children of a given node. For other machine models including the familiar even-odd register-pair machine, optimal evaluation sequences can always require unlimited oscillation.

REFERENCES

• 1: A. V. Aho , S. C. Johnson, Optimal Code Generation for Expression Trees, Journal of the ACM (JACM), v.23 n.3, p.488-501, July 1976 [doi>10.1145/321958.321970]
• 2: A. V. Aho , S. C. Johnson , J. D. Ullman, Code Generation for Expressions with Common Subexpressions, Journal of the ACM (JACM), v.24 n.1, p.146-160, Jan. 1977 [doi>10.1145/321992.322001]
• 3: {AU} A. V. Aho and J. D. Ullman, "Optimization of Straight Line Code," SIAM J. Computing 1,1 (1972), 1-19.
• 4: James C. Beatty, An axiomatic approach to code optimization for expressions, Journal of the ACM (JACM), v.19 n.4, p.613-640, Oct. 1972 [doi>10.1145/321724.321728]
• 5: J. L. Bruno , T. Lassagne, The Generation of Optimal Code for Stack Machines, Journal of the ACM (JACM), v.22 n.3, p.382-396, July 1975 [doi>10.1145/321892.321901]
• 6: John Bruno , Ravi Sethi, Code Generation for a One-Register Machine, Journal of the ACM (JACM), v.23 n.3, p.502-510, July 1976 [doi>10.1145/321958.321971]
• 7: A. P. Ershov, On programming of arithmetic operations, Communications of the ACM, v.1 n.8, p.3-6, Aug. 1958 [doi>10.1145/368892.368907]
• 8: Ikuo Nakata, On compiling algorithms for arithmetic expressions, Communications of the ACM, v.10 n.8, p.492-494, Aug. 1967 [doi>10.1145/363534.363549]
• 9: R. R. Redziejowski, On arithmetic expressions and trees, Communications of the ACM, v.12 n.2, p.81-84, Feb. 1969 [doi>10.1145/362848.362859]
• 10: {RKL} D. M. Ritchie, B. W. Kernighan, and M. E. Lesk, "The C Programming Language," CSTR #31, Bell Laboratories, Murray Hill, N. J., 1975.
• 11: Ravi Sethi , J. D. Ullman, The Generation of Optimal Code for Arithmetic Expressions, Journal of the ACM (JACM), v.17 n.4, p.715-728, Oct. 1970 [doi>10.1145/321607.321620]
• 12: William Allan Wulf , Richard K. Johnsson , Charles B. Weinstock , Steven O. Hobbs , Charles M. Geschke, The Design of an Optimizing Compiler, Elsevier Science Inc., New York, NY, 1975