### Table 2 : Complexity of di erent implementations of circuits for division. Latency is measured in number of cycles needed. Throughput is number of cycles pr. computation. Throughput AT is calculated both for the size of registers equal to a full adder (static register), and half the area of a full adder (dynamic register). Parallel/serial SRT optimal for division as an isolated operation The traditional parallel/serial SRT shows the best AT for larger N - independent of the size of registers. However, this is for division as an isolated operation. Analyzing division as an isolated operation only is not especially interesting, as in general digital signal processing algorithms are dominated by multiplications and additions.

1994

"... In PAGE 20: ... This conversion is responsible for the major part of the latency for these implementations. The implementations in Table2 are: 1. Non-restoring division based on a binary ripple adder, parallel/serial architecture.... ..."

Cited by 3

### Table 3.1 Table 3.1 shows that the Karatsuba-Ofman+Non-restoring division is much better than Blakley with regard to the cost computed as the number of k x k-bit add and multiplications.

### Table 1 Subproblem division

"... In PAGE 14: ... The focus is on the technology component, in particular on models, algorithms and rulebases, but this approach allows us to investigate how technology affects other components and how other components influence the technology. Table1 illustrates this division. It states the explicit subproblem for each component pair and lists the papers forming this thesis that are dealing with each problem.... ..."

### Table 1 Subproblem division

"... In PAGE 17: ... 7 component, in particular on models, algorithms and rulebases, but this approach allows us to investigate how technology affects other components and how other components influence the technology. Table1 illustrates this division. It states the explicit subproblem for each component pair and lists the papers forming this thesis that are dealing with each problem.... ..."

### Table 2: Principal Direction Divisive Partitioning Algorithm Summary

1998

"... In PAGE 10: ... We remark that this scatter value is the only component of this algorithm that is based on a \distance quot; measure, and it would be just as easy to use other measures not based on a \distance quot; measure and appropriate for particular data sets. Having discussed all the components of our algorithm, we now summarize the overall algorithm in Table2 . At each pass through the main loop, we select a node based on our measure of \cohesiveness, quot; obtain the mean vector and principal direction for the documents associated with that node, and split the documents using the mean vector and principal direction into two children nodes.... In PAGE 11: ... In addition, typical values for snz in our examples range from :04 = 4% down to :0068 = :68%. The bulk of the cost in the algorithm of Table2 is the SVD computation in step 7. We have already mentioned that the main memory required for this step is space for ksvd m-vectors.... In PAGE 14: ... These are summarized in Table 3 [8]. We applied two algorithms to this data set, the divisive PDDP algorithm ( Table2 ), and an agglomerative algorithm [5]. The agglomerative algorithm is shown only for comparative purposes, and is brie y summarized as follows.... In PAGE 17: ...e joined. Further consolidation could occur using l = 2 or perhaps with larger values of k. This aspect deserves further investigation. 6 Extensions and Future Work The binary tree constructed by the PDDP algorithm of Table2 can be extended in several ways. In this section, we discuss several extensions that could be applied to this algorithm, including some preliminary experimental results validating some of them.... In PAGE 17: ... 6.1 Classi cation of New Documents The simplest extension to the PDDP algorithm of Table2 is to classify a new set of documents according to the clusters from an original document set by using the original binary PDDP... In PAGE 21: ... We selected the documents so that both document sets had representatives of every topic label. We used the method of Table2 on the rst half of the document set to construct a new PDDP tree with 16 leaf nodes, then we used the method of Table 8 to classify the remaining documents, so that we end up with a set of 16 clusters, each containing documents from both halves of the original document set. The resulting entropy of the combined result (i.... ..."

Cited by 64

### Table 3: Summary of subtractive division and square root algorithm definitions

"... In PAGE 19: ... The various techniques described above for quotient-digit selection, including redundant, truncated residuals, can be carried over to square root result-digit selection as well. Table3 summarizes the most important features of both the subtractive division and square root algorithms for easy reference and comparison. Table 3: Summary of subtractive division and square root algorithm definitions... In PAGE 28: ...ddition as well. This increases not only the amount of hardware required but also the latency of factor generation. For division, this delay is incurred only at the beginning of the operation since the divisor remains constant. In square root computation, the partial root value changes with each iteration (see Table3 ), requiring the generation of new factors every cycle. Higher degrees of redundancy increase the delay of factor generation, directly counteracting the... ..."

### Table 4. Computing 125/14 with the second division algorithm.

1994

"... In PAGE 11: ... A number X is declared positive if E Fa(X) E [0,255/512], negative if E F,(X) E [256/512,479/512], and indeterminate if E F,(X) E [480/512,511/512]. Table4 shows the intermediate values during execution of the division algorithm. Table 3.... ..."

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### Table 2. Running times for different region divisions

"... In PAGE 6: ...Table2 . As can be seen, when the view field is not divided, the running time is short, however the algorithm decides that every pair of cameras is connected.... ..."

### Table 2. Computing 125/14 with the first division algorithm.

1994

"... In PAGE 8: ... The correct quotient Q = 8 = (3,1,8,8) and remainder R = 13 = (3,6,4,2) are produced. Table2 shows the intermediate values during execution of the algorithm. Table 1.... ..."

Cited by 6