Elements of Combinatorial Computing by Mark B. Wells

By Mark B. Wells

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Until W = { }: Wf)set(nbr(W)-l) - W "| W\ = 6" for counting 1-bits in W. ,L-i3/e w (1)? where L gives the number of bits to be searched (possibly the logical word length of the computer). Similarly, search for the /th 1-bit in a bit-pattern is illustrated by the program / = -l for k — 1 to j : if 3 i = / + i . / + 2 , . . L - i ( / e ^ ) : / = i otherwise: TAKE CARE OF NONEXISTENCE "/ is the position of the 7th 1-bit" These searches involve a common task, a scan of the bits of a word with interrup­ tion at each 1-bit found.

E. multiple-word) form. On a computer with inter­ rupt facilities, quantities could even vary in form during a calculation, the interrupt supervisor handling operations on the compound quantities. 3. Storage Allocation One of the chief advantages of using a programming language is that the compiler arranges for the exact allocation of code and data within the computer memory. Most languages, however, still require that the compiler be told how many memory locations will be needed for storage of each array.

1 (mod /i) - i, . . 6) for instance, where the details of the implementation are left unspecified. Such modular notation may be resolved in terms of simpler statements, but more efficient implementa­ tion probably involves computer design. The existence of "counters" in which counting (and possibly even addition) could be performed modulo a specified number n would be useful. For small n, a set of circular registers ("ring counters") in which positions of ones yield numerical values and in which counting corresponds to bit-shifting would be very efficient in this respect.

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