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Questions and Answers
What is one primary reason for implementing parallel algorithms in computing?
What is one primary reason for implementing parallel algorithms in computing?
What is meant by 'real-time computation' in the context of parallel programming?
What is meant by 'real-time computation' in the context of parallel programming?
Which of the following best describes the ideal outcome of program parallelization?
Which of the following best describes the ideal outcome of program parallelization?
Which of the following factors is considered when evaluating the effectiveness of parallel algorithms?
Which of the following factors is considered when evaluating the effectiveness of parallel algorithms?
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What is suggested as a future requirement in computing based on the discussion of parallel programming?
What is suggested as a future requirement in computing based on the discussion of parallel programming?
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How many floating point operations must be performed for a 7-day weather forecast using the described simulation method?
How many floating point operations must be performed for a 7-day weather forecast using the described simulation method?
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What is the maximum average distance, r, between the CPU and memory for a certain calculation to fit within one second?
What is the maximum average distance, r, between the CPU and memory for a certain calculation to fit within one second?
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Which of the following is NOT listed as a Grand Challenge problem?
Which of the following is NOT listed as a Grand Challenge problem?
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What is the time taken on a 1 GFLOP machine to complete the required computations for the weather prediction simulation?
What is the time taken on a 1 GFLOP machine to complete the required computations for the weather prediction simulation?
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How many memory moves per second are required to calculate an array of one trillion elements in one second?
How many memory moves per second are required to calculate an array of one trillion elements in one second?
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What is a significant factor that limits the effectiveness of parallel computing?
What is a significant factor that limits the effectiveness of parallel computing?
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Which factor is NOT considered an important consideration in parallel computing?
Which factor is NOT considered an important consideration in parallel computing?
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Why can bad parallel programs underperform compared to sequential programs?
Why can bad parallel programs underperform compared to sequential programs?
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What does scalability in parallel computing primarily allow for?
What does scalability in parallel computing primarily allow for?
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Which of the following statements is true regarding the Collatz conjecture?
Which of the following statements is true regarding the Collatz conjecture?
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What does Gustafson's law fundamentally focus on in relation to speedup?
What does Gustafson's law fundamentally focus on in relation to speedup?
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Which of the following best describes loop-carried dependence?
Which of the following best describes loop-carried dependence?
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What is indicated by the variable 'a(N)' in the context of Gustafson's law?
What is indicated by the variable 'a(N)' in the context of Gustafson's law?
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In the context of parallelism, what approach can increase speed when facing loop-carried dependencies?
In the context of parallelism, what approach can increase speed when facing loop-carried dependencies?
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Which iteration method exhibits no loop-carried dependencies?
Which iteration method exhibits no loop-carried dependencies?
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What possible consequence arises from rewriting an algorithm to eliminate dependencies?
What possible consequence arises from rewriting an algorithm to eliminate dependencies?
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To ensure proper execution in parallelizable loops, which action is NOT recommended?
To ensure proper execution in parallelizable loops, which action is NOT recommended?
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What does the variable 'b(N)' represent in the analysis of speedup?
What does the variable 'b(N)' represent in the analysis of speedup?
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What is the purpose of the variable dxi in the loops?
What is the purpose of the variable dxi in the loops?
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Which of the following best describes the impact of data dependencies on parallelization?
Which of the following best describes the impact of data dependencies on parallelization?
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In which scenario is parallelization most likely restricted?
In which scenario is parallelization most likely restricted?
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Which loop would operate more efficiently on a sequential machine?
Which loop would operate more efficiently on a sequential machine?
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What does Δ represent in the context of CPU idle time?
What does Δ represent in the context of CPU idle time?
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What is the main limitation to speedup in parallel computing, as discussed?
What is the main limitation to speedup in parallel computing, as discussed?
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Which factor is most essential for optimizing the performance of parallel tasks?
Which factor is most essential for optimizing the performance of parallel tasks?
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What does Amdahl's law suggest about parallel computing?
What does Amdahl's law suggest about parallel computing?
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What is the term for the gap in performance between CPUs and memory?
What is the term for the gap in performance between CPUs and memory?
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What is essential for achieving high performance in computing?
What is essential for achieving high performance in computing?
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What can lead to cache misses during program execution?
What can lead to cache misses during program execution?
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What should be prioritized when evaluating the performance overhead of code?
What should be prioritized when evaluating the performance overhead of code?
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What aspect of sequential execution has the greatest concern for optimal performance?
What aspect of sequential execution has the greatest concern for optimal performance?
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Which statement is true regarding the utilization of hardware in computing?
Which statement is true regarding the utilization of hardware in computing?
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What is an important aspect of using compiler optimizations effectively?
What is an important aspect of using compiler optimizations effectively?
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Study Notes
Introduction
- Introduction to the topic of parallel computing
Books
- HPC: "Software Optimization for High Performance Computing: Creating Faster Applications" by K.R. Wadleigh and I.L. Crawford, Hewlett-Packard professional books, Prentice Hall.
- OPT: "The Software Optimization Cookbook" (2nd ed.) by R. Gerber, A. Bik, K. Smith, and X. Tian, Intel Press.
- PP2: "Parallel Programming: Techniques and Applications using Networked Workstations and Parallel Computers" (2nd ed.) by B. Wilkinson and M. Allen, Prentice Hall.
- PSC: "Parallel Scientific Computing in C++ and MPI" by G. Karniadakis and R. Kirby II, Cambridge University Press.
- SPC: "Scientific Parallel Computing" by L.R. Scott, T. Clark, and B. Bagheri, Princeton University Press.
- SRC: "Sourcebook of Parallel Programming" by J. Dongara, I. Foster, G. Fox, W. Gropp, K. Kennedy, L. Torczon, and A. White (eds), Morgan Kaufmann.
Introduction
- Why parallel computing?
- Why not parallel computing?
- Benefit depends on speedup, efficiency, and scalability of parallel algorithms
- What are the limitations to parallel speedup?
- The future of computing
- Lessons learned
- Further reading
Why Parallel?
- It's not always obvious that a parallel algorithm has benefits, must consider wanting to do things faster (same work in less time), or bigger (more work in same time).
- Both these reasons can produce better results, which is the meaningful outcome of parallelization.
Faster, Bigger!
- Increased demand for computational power to improve speed or accuracy of solutions to real-world problems (faster computations and/or bigger simulations)
- Computations must be completed in acceptable time (real-time computation)
Faster, Bigger!
- Illustrative example: weather prediction simulation should not take longer than the event itself.
- Atmosphere of Earth divided into 5 x 108 cubes, each 1 x 1 x 1 mile, stacked 10 miles high.
- 200 floating-point operations per cube to complete one time step.
- 104 time steps for a 7-day forecast.
- 1015 floating-point operations needed.
- This takes 106 seconds (10 days) on a 1 GFLOP machine
Grand Challenge Problems
- "Grand Challenge" problems cannot be solved in reasonable time with today's computers.
- Examples:
- Applied Fluid Dynamics
- Meso- to Macro-Scale Environmental Modeling
- Ecosystem Simulations
- Biomedical Imaging and Biomechanics
- Molecular Biology
- Molecular Design and Process Optimization
- Fundamental Computational Sciences
- Nuclear power and weapons simulations
Physical Limits
- Which tasks are too big for one CPU?
- Calculation example:
for (i =0; i < ONE TRILLION; i++){ z[i] = x[i] + y[i]; } - 3 x 1012 memory moves per second required.
- Data travels at speed of light (3 x 108 m/s)
- Distance between CPU and memory (r) must satisfy 3 x 1012 r = 3 x 108 × 1 giving r = 10-4 meters.
- Memory cell size: 2 x 10-4 m / (√3 x 106) = 10-10 m
CPU Energy Consumption & Heat Dissipation
- Increased power requirements of newer chips will lead to CPUs hotter than the surface of the sun by 2010 (Intel CTO)
- Parallelism can help to conserve energy.
Important Factors
- Physical limitations: speed of light, CPU heat dissipation
- Economic factors: cheaper components to achieve comparable levels of aggregate performance
- Scalability: subdividing data over CPUs to match algorithms and resources for increased performance
- Memory: increase aggregate memory bandwidth with processing power at a reasonable cost
And Why Not Parallel?
- Bad parallel programs can be worse than sequential counterparts.
- Slower: due to communication overhead.
- Scalability: some parallel algorithms are only faster when problem size is large.
- Need to understand the problem and use common sense.
- Not all problems are amenable to parallelism.
- Course will focus on non-parallel optimizations for sequential programs to get better performance
And Why Not Parallel?
- Some algorithms are inherently sequential (Collatz conjecture example).
Speedup
- Definition: speedup of an algorithm using P processors (Sp = ts / tp).
- ts = execution time of best sequential algorithm.
- tp = execution time of the parallel algorithm.
- Perfect or ideal speedup if Sp = P.
- Linear speedup if Sp ≈ P.
- Superlinear speedup if Sp >P for some P.
Relative Speedup
- Definition: The relative speedup (S1p = t1/tp).
- t1 = execution time of the parallel algorithm on one processor.
- Similarly, Skp = tk/tp .
- k < P.
- Used when k is the smallest number of processors on which the problem runs efficiently
An Example
- Parallel search by partitioning the search space into P chunks.
- Worst case for sequential search (item in last chunk): Sp → ∞ as ∆t tends to zero.
- Best case for sequential search (item in first chunk) : Sp = 1.
Effects that can Cause Superlinear Speedup
- Cache effects: Data is partitioned, distributed over P processors, individual data items (much) smaller, may fit in processor's data cache.
- Algorithm with linear speedup: extra reduction in cache misses may lead to superlinear speedup.
Efficiency
- Definition: Efficiency of an algorithm using P processors (Ep = Sp / P).
- Efficiency estimates how well-utilized the processors are, compared to effort lost in idling and communication/synchronization.
- Ideal (or perfect) speedup means 100% efficiency (Ep = 1).
Scalability
- Speedup describes how parallel algorithm's performance changes with increasing P.
- Scalability concerns efficiency of the algorithm with changing problem size (N) by choosing P dependent on N.
- Definition: algorithm is scalable if there is minimal efficiency ε > 0 such that for any problem size N, there's a processor # (P(N)) that tends to infinity as N tends to infinity; where efficiency EP(N) ≥ ε > 0
Amdahl's Law
- Several factors limit speedup:
- Processors may be idle.
- Extra computations in parallel version.
- Overhead in communication and synchronization.
- Consider fraction (f) of sequential computation that cannot be divided into concurrent tasks.
Amdahl's Law
- Amdahl's law states that speedup given P processors is Sp = ts / (f * ts + (1-f)*ts/P) = P / (1+(P-1)f)
- Maximum speedup is limited by f-1 as P → ∞
Gustafson's Law
- Amdahl's law based on fixed workload/problem size per processor.
- Gustafson's law defines scaled speedup by keeping parallel execution time constant.
- SP,N = P + (1 - P)α(N)
Limitations to Speedup: Data Dependences
- Collatz iteration loop has a loop-carried dependence (n's value carried over to next iteration).
- Loops with loop-carried dependences cannot be parallelized.
Limitations to Speedup: Data Dependences
- Example: Gauss-Seidel and Jacobi iteration loops.
- Jacobi iteration doesn't exhibit loop-carried dependences, allowing partitioning and distribution to processors.
-Three simple example loops to initialize a finite difference matrix.
- Which loop(s) can be parallelized?
- Which loop likely runs more efficiently on a sequential machine?
Limitations to Speedup: Data Dependences
- Presence of dependences between events in two or more tasks limits parallelization strategies for conserving energy.
Efficient Parallel Execution
- Trying to construct parallel version of an algorithm is not the "end-all" for high performance computing.
- Amdahl's law: maximum speedup is bounded by f-1 as P → ∞.
- Efficient parallel execution is important to optimize non-parallel fraction (f) and parallel tasks.
- Improving sequential execution, I/O, communication and synchronization reduces the sequential fraction.
Limitations to Speedup: Memory Locality
- Memory hierarchy forms barrier to performance when locality is poor.
- Temporal locality: same memory location repeatedly accessed.
- Spatial locality: consecutive memory locations accessed (or "sufficiently near").
- Memory wall: growing disparity of speed between CPU and external memory.
Efficient Sequential Execution
- Memory effects are primary concern for optimal sequential execution.
- Store-load dependences: data flow through memory
- Cache misses, TLB misses, page faults.
- CPU resource effects: limited floating point units, unpredictable branching.
- Compiler optimizations helpful for efficient sequential execution.
Lessons Learned from the Past
- Parallel computing can transform science and engineering by solving societal challenges.
- Redesigning an application, rather than just porting, may be necessary.
- Hardware underutilization can stem from poor software and algorithms.
- Portability of software is an issue.
- Parallelism isn't everything, good commercial software is rare.
Any questions?
- Open question for clarifying any remaining points.
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Description
This quiz introduces the fundamental concepts of parallel computing, discussing its significance and potential benefits. You will explore why parallel computing is essential and the challenges associated with it, as well as the insights provided by various key texts in the field.
