PDP Chapter 3: Quantitative Principles of Computer Design

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Questions and Answers

What does Amdahl's Law primarily help to determine in computer systems?

The cost-effectiveness of a hardware upgrade

The total number of operating units in a system

The energy consumption of a system

The overall performance gain from improvements (correct)

In the context of Amdahl's Law, what limits the performance improvement of a computer system?

The amount of memory available in the system

The speed of the input-output operations

The total operational costs of the enhancements

The fraction of time the enhanced mode can be used (correct)

When calculating execution times, which of the following represents the execution time before any enhancements?

Execution time non-enhanced (correct)

Execution time before enhanced

Execution time enhanced

Execution time new-enhanced

Which formula correctly represents the definition of execution time after an enhancement according to Amdahl's Law?

Execution time new = Execution time old-enhanced + Execution time enhanced Signup and view all the answers

What is the key factor that remains constant when comparing execution times before and after enhancements?

Execution time non-enhanced Signup and view all the answers

What is Amdahl’s Law primarily used for in computer science?

To calculate the overall performance speedup for a system based on its components. Signup and view all the answers

Using Amdahl's Law, if a processor spends 40% of its time on computation, what fraction remains for other operations?

0.6 Signup and view all the answers

In the web serving application example, what does a speedup factor of 10 signify?

The new processor executes computations 10 times faster than the original. Signup and view all the answers

If a system demonstrates a theoretical maximum speedup of approximately 1.67, what does this imply?

Performance limitations exist due to a significant portion of non-parallel work. Signup and view all the answers

Which factor does NOT influence the parallel runtime of a program?

The amount of random memory access. Signup and view all the answers

What does wall clock time measure in a parallel computing context?

The elapsed time from the start to the finish of the overall process. Signup and view all the answers

In the context of a parallel processing system, which element is emphasized as critical to performance?

The combination of both algorithm and platform. Signup and view all the answers

Which of the following statements about performance metrics is false?

Parallel runtime is independent of the machine's communication parameters. Signup and view all the answers

What is the formula for calculating the speedup achieved after enhancement according to Amdahl's Law?

$rac{Execution time_{old} - Execution time_{enhanced}}{Execution time_{new} - Execution time_{enhanced}}$ Signup and view all the answers

Which of the following parameters is NOT required when applying Amdahl's Law?

The total execution time of the original program Signup and view all the answers

How is the overall speedup calculated when a fraction of the program is enhanced?

$Speedup_{overall} = rac{Execution time_{old}}{(1 - Fraction_{enhanced}) + rac{Execution time_{old}}{Speedup_{enhanced}}}$ Signup and view all the answers

What does the 'Fraction enhanced' signify in Amdahl’s Law?

The portion of the program that benefits from the enhancement Signup and view all the answers

In Amdahl’s Law, what is implied if the speedup of the enhanced portion is very high?

Even with a high enhancement, overall speedup may be limited Signup and view all the answers

If the execution time of the old program is 100 seconds, and the enhanced part's execution time is reduced to 20 seconds with a speedup factor of 5, what is the fraction enhanced if the total execution time for the new program is 80 seconds?

0.75 Signup and view all the answers

Which component contributes to the overall execution time in the Amdahl's Law formula?

The execution times of both enhanced and non-enhanced parts Signup and view all the answers

What is the implication of a 'Fraction enhanced' value of zero in Amdahl's Law?

There is no part of the program that can be enhanced Signup and view all the answers

Study Notes

Amdahl’s Law

Amdahl’s Law calculates overall performance gains from speed enhancements in computer systems.
Performance improvement is limited by the fraction of time the improved function can be utilized.
Enhancements, like a faster floating-point unit, only reduce execution time for specific operations.

Execution Time Calculations

Old Execution Time Formula:
- Execution time old = Execution time non-enhanced + Execution time old-enhanced
New Execution Time Formula:
- Execution time new = Execution time non-enhanced + Execution time new-enhanced
Execution time for non-enhanced components remains fixed, while enhanced execution time is reduced.

Fraction Enhanced and Speedup

Fraction enhanced is calculated as:
- Fraction enhanced = Execution time old-enhanced / Execution time old
Speedup after enhancement is given by:
- Speedup enhanced = Execution time old-enhanced / Execution time new-enhanced

Required Factors for Amdahl’s Law

Determine the computation time fraction that can leverage the enhancement.
Identify the speed improvement achievable by the enhanced execution mode for the entire program.
Overall speedup formula:
- Speedup overall = Execution time old / [ (1 - Fraction enhanced) + (Speedup enhanced)]

Example Calculation

For a Web server, enhancing the processor results in a 10x speed increase for computation, with the original processor busy 40% of the time.
Fraction enhanced = 0.4, Speedup enhanced = 10.
Overall speedup can be approximated:
- Speedup overall ≈ 1.56; theoretical maximum ≈ 1.67.

Analytical Modeling Basics

Sequential algorithms are evaluated by their runtime, typically as a function of input size.
Parallel runtime depends on input size, number of processors, and communication parameters.
Performance of a parallel system is influenced by both the algorithm and the underlying platform.

Performance Measures

Wall clock time refers to the total time from the initiation of the first processor to the completion of the last processor in a parallel setup.

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Description

Explore the impact of Amdahl’s Law on the performance of computer systems with this quiz. Understand how improvements in specific parts of a system can influence overall efficiency. Test your knowledge on quantitative principles related to computer design.