### Table 1. Annotations required to enable parallelization of Java Grande Forum bench- marks

### Table 1: Comparing the precision of results and simulation times of the standard Monte Carlo method with the new approach of tracing one ray for all wavelengths

"... In PAGE 63: ... In the second simulation, the number of rays has been increased 5 times. The corresponding results are in Table1 . The average variances are about three times lower as compared to the simulation with less rays.... In PAGE 63: ... Thus in the following two simulations, the previous two experiments were repeated, with the number of triangles increased to 150 and their area set to 1. The results, shown in Table1 , support the observation about the effect of the direct light, because the difference in rel #16 #1B R=FR (for the two methods) is reduced. Nevertheless, the value rel #16 #1B R=FR for the new method is still below the one produced by the original method and the values of deviations for red and far red light are again comparable.... In PAGE 63: ... In the last two simulations, the number of triangles was further increased to 200, and their area to 2. As illustrated in Table1 , the difference in rel #16 #1B R=FR is further reduced and the values of rel #16 #1B R and rel #16 #1B FR for the new method are higher that the ones for the old method, especially for red light where the difference is about 35#25. These results are caused by the fact that the size and the number of triangles is very high considering the size of the cube in which they are placed (10#02 10 #02 10)andmost triangles receive only reflected or transmitted light.... ..."

### Table 1: Preprocessing times for the 3D grid using three different method; 1) GPU acceleration and occlusion queries to only compute the ambient occlusion in each cell, 2) GPU acceleration computing occlusion cones, and 3) ray tracing with 256 rays per cell with Monte Carlo sampling

2006

"... In PAGE 15: ... For all our scenes, a grid resolution of 323 was used. Table1 shows the run-times. For comparison purposes, we have also included one very large model of 1M triangles.... ..."

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### Table 4: The elapsed time (sec.) Euler Molecular Monte Carlo Ray Tracer Search

2004

"... In PAGE 9: ... This advice was woven at all the method calls (caller-side) included in benchmark programs, which are taken from the sequential benchmarks of the Java Grande forum5. Table4 lists the results. Original represents the execu- tion time of the benchmark programs without the before advice.... ..."

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### Table 5.2: Number of rays cast in gures 5.24(a) (global Monte Carlo), (b) and (c) (local Monte Carlo). The global rays stands here as the average of global lines intersecting the scene. (1) An average of 9.7 bounces per ray. (2) An average of 2.0 bounces per ray. Global ( gure 5.24(a)) local rays(1) global rays total rays

### Table 5.3: Number of rays cast in gures 5.27(a) (global Monte Carlo) and (b) and (c) (local Monte Carlo). The global rays stands here as the average of global lines intersecting the scene. (1) An average of 11.9 rays per path. (2) An average of 2.1 rays per path. Global ( gure5.27(a)) local rays global rays total rays

### Table 1 presents high level benchmarks for several JGF applications: Monte Carlo (size B), Ray Tracer (size B) and SOR (size C).

"... In PAGE 7: ... Table1 . Annotations (AN) versus JGF multithreaded benchmarks (MT) execution time In Monte Carlo and RayTracer benchmarks the framework presents an overhead less than 5%.... ..."

### Table 4. Monte Carlo method

"... In PAGE 5: ...4615 0.4342 7175 430 500 Table4 . contains results obtained by standard Monte Carlo method with 10 million points, presented in [2].... ..."

### Table 2. Monte Carlo Statistics

"... In PAGE 9: ...nclination is between 44.7 and 45.3 degrees. Table2 summarizes some statistics from the Monte Carlo simulation. 44.... ..."

### Table 2. Monte Carlo Uncertainties

2004

"... In PAGE 5: ... In the reference case, delivery, atmospheric and aerodynamic uncertainties were based on state of the art navigation, current knowledge of Neptune atmosphere and computational fluid dynamics analyses respectively. Table2 lists the uncertainties and dis- tribution types used in the Monte Carlo reference case. In the first sensitivity case study, the magnitudes of the high frequency random density perturbations were reduced by 50%.... ..."

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