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In this paper, time complexities of operation on &#8220;sets&#8221; and &#8220;ordered n-tuples&#8221; based on a hashing table search technique are presented as &#8220;Hashing LEMMAs&#8221; and are applied to formula manipulation. Unique normal forms for multivariate symbolic formulas resulting in <italic>O(1)</italic> time complexity for identity checks(More)
An economical, unbiased, overflow-free rounding scheme for multiplication of multiple-precision floating-point numbers is proposed. The new rounding scheme, which we call “the pseudorandom rounding,” saves multiplications of lower bits, and makes use of statistical properties of bits around the least significant bit of products in order to compensate for(More)
Recently, hashing as a method for fast pattern matching has been applied to many software systems (e.g. LEAP [ 11, SETL [7] , HLISP [3 ,a]), in which dashing is very heavily used at run-time. Therefore, the performance of these systems will be considerably improved L Jo speeding up the. hashing process. Though the performance of hashing has usually been(More)
This paper describes a new computer architecture, called a cyclic pipeline computer (CPC), which is especially suited for Josephson technologies. Since each Josephson logic device acts as a latch, it is possible to use high-pitch and shallow logic pipelining without any increase in delay time and cost which are required in case of pipeline registers in Si(More)