A model of computation is defined over the algebraic numbers and over number fields. This model is non-uniform, and the cost of operations depends on the height of the operands and on the degree of the extension of the rational defined by those operands. A transfer theorem for the P 6 = NP Conjecture is proved, namely: P 6 = NP in this model over the real algebraic numbers if and only if P 6 = ...

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 x 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 x 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 x 80). Participants accomplished this est...

The present study investigated the neuroanatomical basis of different solution processes in single-digit multiplication by means of fMRI. Sixteen participants silently produced the solution of three distinct types of multiplication, i.e., problems involving zero (e.g., 3*0), small (e.g., 2*4), or large operands (e.g., 8*7). Zero and small problems are assumed to be solved by rule application an...

This paper describes a new accumulate-and-add multiplication algorithm. The method partitions one of the operands and re-combines the results of computations done with each of the partitions. The resulting design turns-out to be both compact and fast. When the operands’ bit-lengthm is 1024, the new algorithm requires only 0.194m+56 additions (on average), this is about half the number of additi...

On many of these technologies, two-qubit gates (or, if you prefer, two-operand instructions) can only have neighboring qubits as operands. When two operands that are not next to each are scheduled to be arguments to an instruction, they must be brought together by swapping qubit values (or variables) with their neighbors until the arguments are next to each other, and the algorithmically specif...

We design a systolic coprocessor for the addition of signed normalized rational numbers. This is the most complicated rational operation: it involves GCD, exact division, multiplication and addi-tion/subtraction. In particular, the implementation of GCD and exact division improve signiicantly (2 to 4 times) previously known solutions. In contrast to the traditional approach, all operations are ...

This paper proposes two parallelized radix-4 scalable Montgomery multiplier implementations. The designs do not require precomputed hard multiples of the operands, but instead uses Booth encoding to compute products. The designs use a novel method for propagating the sign bits for negative partial products. The first design right shifts operands to reduce critical path length when using Booth e...

OBJECTIVES Determining how individuals solve arithmetic problems is crucial for our understanding of human cognitive architecture. Elderly adults are supposed to use memory retrieval more often than younger ones. However, they might backup their retrieval by reconstructive strategies. In order to investigate this issue, we used the operand-recognition paradigm, which capitalizes on the fact tha...

Conventional microprocessor designs treat register operands as atomic units. In such designs, no portion of an operand may be consumed until the entire operand has been produced. In practice, logic circuits and arithmetic units that generate some portion of an operand in advance of the remaining portions are both feasible and desirable, and have been employed in several existing designs. In thi...