Question

In: Computer Science

Assume for arithmetic, load/store, and branch instructions, a processor has CPIs of 1, 12, and 5,...

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 processor result relative to the single processor result.

Expert Solution

We know, clock cycles = Number of instructions * CPI

There are different types of instructions so the total clock cycles would be the sum of all the various clock cycle

So, number clock cycles for one processor:

Clock cycles = ((2.56 * 10⁹ * 1) + (1.28 * 10⁹ * 12) + (256 * 10⁶ * 5)) = 1.92 * 10¹⁰

Execution time = Clock cycles / Clock speed.

Clock Speed = 2 GHz = 2 * 10⁹ Hz [As we know, 1 GHz = 10⁹ Hz]

So, execution time for one processor = ((1.92 * 10¹⁰) / (2 * 10⁹)) = 9.6 seconds

The clock cycles for p processors:

According to the question, the arithmetic and load store instructions get divided by 0.7p.

So, Clock cycles = (2.56 * 10⁹ * 1) / 0.7p + (1.28 * 10⁹ * 12) / 0.7p + 256 * 10⁶ * 5

or, Clock cycles = (2.56 * 10¹⁰) / p + 1.28 * 10⁹

The execution time for p processors:

Execution time = Clock cycles / Clock speed.

= ((2.56 * 10¹⁰) / p + 1.28 * 10⁹) / (2 * 10⁹)

= 12.8 / p + 0.64

The execution time for p = 2.

Execution time = 12.8 / 2 + 0.64 = 7.04

Speedup (compared to single processor) = 9.6 / 7.04 = 1.36

Let's find execution time for p = 4.

Execution time = 12.8 / 4 + 0.64 = 3.84

Speedup (compared to single processor) = 9.6 / 3.84 = 2.5

Let's find execution time for p = 8.

Execution time = 12.8 / 8 + 0.64 = 2.24

Speedup (compared to single processor) = 9.6 / 2.24 = 4.29

Please comment in case of any doubt.
Please upvote if this helps.

venereology answered 1 year ago

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