Consider processor x1 with 5 stage standard RISC pipeline with 2 GHz c...
Speedup Achieved using x2 and x1 Pipeline
To calculate the speedup achieved using the x2 and x1 pipelines, we need to consider the effects of control hazards and branch prediction on the overall performance of the processors.
Processor x1
- Processor x1 has a 5-stage standard RISC pipeline with a clock frequency of 2 GHz.
- It requires one clock cycle without any pipeline dependency.
- The program consists of 30% branch instructions, and control hazards result in 2 clock cycles.
Processor x2
- Processor x2 also has the same clock frequency of 2 GHz.
- It uses a branch prediction unit with 80% efficiency.
- If the prediction is correct, no stall is created.
- If the prediction is wrong, there is no effect on the number of stalls.
Calculating the Speedup
To calculate the speedup achieved by processor x2 compared to x1, we need to consider the number of stalls caused by control hazards in both cases.
Processor x1:
- For every branch instruction, there is a 30% chance of a control hazard, resulting in 2 clock cycles of stall.
- Therefore, the average number of stalls per branch instruction in x1 = 30% * 2 = 0.6 clock cycles per branch instruction.
Processor x2:
- Processor x2 uses branch prediction with 80% efficiency.
- This means that 80% of the time, the prediction will be correct and no stall will be created.
- For the remaining 20% of the time, the prediction will be wrong, but there will be no additional stalls.
- Therefore, the average number of stalls per branch instruction in x2 = 20% * 0 = 0 clock cycles per branch instruction.
Calculating the Speedup Ratio:
The speedup ratio can be calculated using the following formula:
Speedup Ratio = Execution Time of x1 / Execution Time of x2
In this case, we can assume that the execution time of a program is directly proportional to the number of clock cycles required.
Execution Time of x1:
- The execution time of x1 can be calculated by considering the number of instructions and the average number of stalls per branch instruction.
- Let's assume the program has 100 instructions.
- Since 30% of the instructions are branch instructions, the number of branch instructions = 30% of 100 = 30 instructions.
- The total number of clock cycles required by x1 = Number of instructions + (Number of branch instructions * Average number of stalls per branch instruction)
- = 100 + (30 * 0.6) = 100 + 18 = 118 clock cycles.
Execution Time of x2:
- The execution time of x2 can be calculated in the same way as x1, but with zero stalls due to branch prediction.
- The total number of clock cycles required by x2 = Number of instructions + (Number of branch instructions * Average number of stalls per branch instruction)
- = 100 + (30 * 0) = 100 clock cycles.
Calculating the Speedup Ratio:
- Speedup Ratio = Execution Time of x1 / Execution Time of x2
- = 118 / 100