Amdahls Law was proposed in 1967 by Gene Amdahl for estimating the potential speedup of any program using parallel processors. The proposed serial percentage , although succinct and self-explanatory, is difficult to quantify. The speedup of the program is above bounded to 1/ , a seemingly pessimistic prediction. Hardware engineers at IBM built parallel machines without regarding Amdahls predictions. The machines were loaned to national laboratories for experimentation. In 1988, John Gustafson published a paper on CACM, entitled Reevaluation of Amdahls Law. In this paper, Gustafson reported simple time measures of running a parallel application using 1024 processors, both the parallel part and the sequential part. A new serial percentage was proposed using these measures. In Gustafsons proposal, the speedup seems to approach infinity if one scales P (number of processors) to infinity.

1. (4 pts) Let 10 seconds be the measured sequential running time, 40 seconds be the parallel running time using 10 processors for a parallel application. What would be the speedup prediction for 30 processors using Amdahls Law? What would be the prediction using Gustafsons Law? Please show all your steps.
2. (2 pts) Explain the projection differences, if any.
3. (3 pts) Using 100 processors, the sequential part is only 10 percent of the total 150 second running time of a parallel program. What would be the speedup prediction using Gustafsons Law? How would you predict for 200 processors using the Amdahls formula? Show all your steps.
4. (1 pt) Explain how to quantify Amdahls formula using Gustafsons formula. What is wrong if we take P->infinity using Gustafsons formula alone?