### Table 4.2: Characteristics of the 1327-loop benchmark suite for sched- ules with unlimited schedule length. The data most relevant to the computational complexity of the optimal stage scheduling algorithm is the number of operations that belong to some nontrivial underlying cycle, the number of register edges, and the initiation interval. Table 4.2 indicates that, in this regard, the 1327-loop benchmark contains a wide range of loops, including loops with up to 158 operations in underlying cycles, 220 register edges, and 138

### Table 3: Global optimization of the intensity of radiation. Intensity of Radiation errors computed after independent model optimization (1st stage) and after simultaneous model optimization (2nd stage). Italics indicate the column used for training at each stage.

"... In PAGE 15: ... As we have previously pointed out, automatically built models cannot compete in accuracy with carefully crafted models, but offer a good compromise for applications for which there is no readily available physical knowledge or its implementation cost is too expensive. In Table3 we present the results of this optimization scheme, on the previously discussed i- NN-10 model. The first stage consists on the optimization of parameter functions with a cost function similar to C, as described in Section 3; the results obtained are the same as those of Table 1.... In PAGE 20: ... Table 2: Model Complexity and Mean Validation Error. Table3 : Global optimization of the intensity of radiation. Intensity of Radiation errors compu- ted after independent model optimization (1st stage) and after simultaneous model optimiza- tion (2nd stage).... ..."

### Table 2: Complexity of the different stages.

### Table 1: Complexity of a general 16-bit multiplier with digit-size four (excluding partial product generation and CPA stage).

"... In PAGE 3: ... It can be seen that if h is large, no CSA stages must be used as the reduction tree has reduced the par- tial products in the output digit to at most two bits. Table1 shows metrics of a general 16-bit coefficient multiplier with digit-size four using different architectures and maximal criti- cal path lengths. For h = 1 the multiplier without pre-accumulation yields the implementation with the lowest number of registers.... ..."

### Table 2: Complexity of a fixed multiplier with digit-size four and coefficient 1839 (excluding CPA stage). No pre-accumulation is used.

"... In PAGE 3: ... Again, note that the registers includes the pipeline registers.A fixed coefficient multiplier with coefficient 1839 and digit-size four was also designed and the metrics of the different implementa- tions are shown in Table2 . No pre-accumulation could be used as the number of partial products for any significance level was small- er than three.... ..."

### Table 4. Design result of optimization 1-stage 2-stage Item

"... In PAGE 6: ... 67 Carrier Ring gear Planet pinion Sun gear Carrier Ring gear Planet pinion Sun gear (a) Old model (b) New model Fig.2 Model of 2-stage gear trains of escalator Table4 shows design results that are obtained at 8664th generation, and from this, we can easily notice optimum values of integer and discrete variables are found adequately satisfying constraints. In this design results, the correction of solution according to the types of variables after design is not needed.... ..."

### Table 1: Complexity results for the different instances of the mapping problem.

2007

"... In PAGE 13: ... 4.1 Summary We summarize in Table1 all the new complexity results. In Table 1, the upper part refers to Homogeneous platforms while the lower part refers to Heterogeneous ones.... In PAGE 13: ...1 Summary We summarize in Table 1 all the new complexity results. In Table1 , the upper part refers to Homogeneous platforms while the lower part refers to Heterogeneous ones. The second column corresponds to the model without data-parallel stages, while the third column corresponds to the model with data-parallel stages (replication is allowed in both models).... In PAGE 30: ...there is no chance to find an optimal mapping when adding the complexity of communications. We have succeeded to establish the complexity of all the problems exposed in Table1 , sometimes distinguishing whether the application is fully regular or not. Some results are surprising: for instance consider the bi-criteria optimization problem on a pipeline application mapped onto a Heterogeneous platform.... ..."

### Table II. Level of Staging Optimizations for Experiments

2004

Cited by 7

### Table 1: Memory and Computation Requirements Algorithm Stages Levels Memory Complexity

"... In PAGE 2: ...Six different codebook structures were used. The codebooks are listed in Table1 , along with the number of tree levels, the size of the codebook in bytes, and the computational complexity for quantization as compared to that of six-stage RVQ. The label used in subsequent plots is also listed.... ..."