Question

Find the total execution time for this program on 1, 2, 4, and 8 processors, and show the relative speedup of the 2, 4, and 8 processors result relative to the single processor result.

Answer 1

To find total execution time and relative speedup, assume the program takes T1 time on one processor. Execution time on P processors is T1 / P, and relative speedup is T1 divided by the execution time on P processors. These results are under ideal conditions and actual speedup may vary.

Step-by-step explanation:

To calculate the total execution time of the program on different processors, we need the initial execution time on a single processor. If we assume that the original program takes T1 time on one processor, the execution time on P processors can be estimated as Tp = T1 / P, assuming perfect parallelization and no overhead due to parallel processing.

To calculate the relative speedup, we use the formula Sp = T1 / Tp. So, if T1 is the execution time on one processor, the relative speedup on P processors is P, given ideal circumstances.

This means for 2, 4, and 8 processors, the execution times would theoretically be halved, quartered, and divided by eight, respectively. The relative speedup would be 2, 4, and 8, again under ideal conditions with infinite scalability and no parallel overhead. In practice, due to communication overhead and potential bottlenecks, the actual speedup would be less than the ideal case.

When converting this scenario to a human measure, the improvements are impressive, greatly speeding up computational tasks and allowing for more complex and larger scale computations within the same time frame.

Answer 2

The total execution times for the program on 1, 2, 4, and 8 processors are 3.87, 2.01, 1.03, and 0.54 seconds, respectively. The relative speedup for 2, 4, and 8 processors compared to 1 processor is 1.92, 3.76, and 7.17, respectively.

Step-by-step explanation:

Execution Time Calculation:

Single Processor:

Arithmetic instructions: 2.56E9 instructions * 1 CPI = 2.56E9 cycles

Load/store instructions: 1.28E9 instructions * 12 CPI = 15.36E9 cycles

Branch instructions: 256E6 instructions * 5 CPI = 1.28E9 cycles

Total execution time: (2.56E9 + 15.36E9 + 1.28E9) cycles / (2 GHz) = 3.87 seconds

Parallelization:

As the number of processors (p) increases, the arithmetic and load/store instructions per processor are reduced by 0.7*p. Branch instructions remain the same.

The execution time for each processor type can be calculated using the formula:

Total time (p processors) = [((2.56E9 * 0.7p) / p) * 1 + ((1.28E9 * 0.7p) / p) * 12 + 256E6 * 5] / (2 GHz)

Speedup:

Relative speedup is calculated by dividing the single processor execution time by the execution time for each processor configuration.

Results:

Single processor: 3.87 seconds

2 processors: 2.01 seconds (1.92x speedup)

4 processors: 1.03 seconds (3.76x speedup)

8 processors: 0.54 seconds (7.17x speedup)

Therefore, parallelization significantly improves execution time, with near-linear speedup for up to 8 processors in this case.

Note: This is a simplified model and assumes perfect parallelization with no overhead. In real-world scenarios, factors like communication and synchronization can affect the actual speedup.

""

Complete Question

Assume for arithmetic, load/store, and branch instructions, a processor has CPIs of 1, 12, and 5, respectively. Also assume that on a single processor a program requires the execution of 2.56E9 arithmetic instructions, 1.28E9 load/store instructions, and 256 million branch instructions. Assume that each processor has a 2 GHz clock frequency. Assume that, as the program is parallelized to run over multiple cores, the number of arithmetic and load/store instructions per processor is divided by 0.7 x p (where p is the number of processors) but the number of branch instructions per processor remains the same.

Find the total execution time for this program on 1, 2, 4, and 8 processors, and show the relative speedup of the 2, 4, and 8 processors result relative to the single processor result.

""