Opening your learning space
Starting the app …
Opening your learning space
Starting the app …
Amdahl’s law bounds total speedup by the fraction of program work that remains serial.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
SN dimensionless; P is a fraction from 0 to 1; N is the number of processors
| Symbol | Meaning | Unit |
|---|---|---|
| Speedup over one processing unit | dimensionless | |
| Fraction of the program that can be parallelized | dimensionless | |
| Number of equally fast processing units | count |
S_N=\frac{1}{(1-P)+P/N}The model assumes fraction P is ideally parallelized over N units while 1−P remains serial. Communication, synchronization and load imbalance are omitted, so real speedup is usually lower. As N tends to infinity, S approaches 1/(1−P). The fraction must refer to execution time or work, not simply a share of source-code lines.
The model assumes fraction P is ideally parallelized over N units while 1−P remains serial. Communication, synchronization and load imbalance are omitted, so real speedup is usually lower. As N tends to infinity, S approaches 1/(1−P). The fraction must refer to execution time or work, not simply a share of source-code lines.
Amdahl’s law bounds total speedup by the fraction of program work that remains serial.
Serial fraction from speedup
Assume ideal parallel execution and N≥1.
Use the example for Amdahl’s law (parallel speedup) to explain which inputs determine the requested output.
The example connects concrete inputs to its result.
Amdahl’s law bounds total speedup by the fraction of program work that remains serial.
The relation applies only under its stated assumptions.
Applying the relation to a different case without checking its stated assumptions.
Check the validity range before substituting values: The model assumes fraction P is ideally parallelized over N units while 1−P remains serial. Communication, synchronization and load imbalance are omitted, so real speedup is usually lower. As N.
Formula cluster
Amdahl’s law bounds total speedup by the fraction of program work that remains serial.
For P=0.8 and N=4, S4=1/(0.2+0.8/4)=2.5. Four processors therefore yield only 2.5× speedup in the idealized model.
Estimate the value of added processor cores and prioritize serial bottlenecks.
Here is how to work through a typical Amdahl’s law (parallel speedup) (Sₙ = 1/((1−P)+P/N)) task step by step:
Task
Use the example for Amdahl’s law (parallel speedup) to explain which inputs determine the requested output.
Solution path
The example connects concrete inputs to its result.
Amdahl’s law bounds total speedup by the fraction of program work that remains serial.
The relation applies only under its stated assumptions.
Amdahl’s law estimates how much a program can speed up on N parallel units when only fraction P is parallelizable. The remaining 1−P stays serial and sets an upper bound. The formula describes a runtime ratio, not an improvement to every operation. Even a small serial fraction can dominate when many processors are used. Amdahl’s model assumes fixed work, no parallelization overhead and equal processing units. It is a theoretical bound; real synchronization and communication costs make performance worse. Treat P as a measured runtime fraction, not as a share of parallelizable source-code lines. Consider input size when comparing.
The denominator is (1−0.8)+0.8/4=0.2+0.2=0.4. Thus S4=1/0.4=2.5. Four units do not provide fourfold speedup because one fifth of the runtime remains serial. Check that P is entered as a fraction from zero to one, not the percentage 80. Amdahl’s model assumes fixed work, no parallelization overhead and equal processing units. It is a theoretical bound; real synchronization and communication costs make performance worse. Treat P as a measured runtime fraction, not as a share of parallelizable source-code lines. Consider input size when comparing.
As N tends to infinity, P/N approaches zero, leaving Smax=1/(1−P). For P=0.8 the limit is five, even with infinitely many ideal processors. This shows why optimizing serial work can matter more than adding cores. If P=1, the simple model predicts unbounded speedup, which real systems cannot reach because of overhead. Amdahl’s model assumes fixed work, no parallelization overhead and equal processing units. It is a theoretical bound; real synchronization and communication costs make performance worse. Treat P as a measured runtime fraction, not as a share of parallelizable source-code lines. Consider input size when comparing.
P is the fraction of original execution time that can actually run in parallel on the system considered. Do not estimate it from lines of code; short and long computations have different weight. Measure representative runs and separate serial work, synchronization and communication. The measured fraction may change with input size or architecture. Amdahl’s model assumes fixed work, no parallelization overhead and equal processing units. It is a theoretical bound; real synchronization and communication costs make performance worse. Treat P as a measured runtime fraction, not as a share of parallelizable source-code lines. Consider input size when comparing.
The equation omits communication, synchronization, load imbalance, memory bandwidth and startup costs. These consume time without adding parallel work. On small problems, parallelization overhead can erase the gain. Use Amdahl’s result as an ideal upper bound and measure the implementation with identical inputs and timing methods. Amdahl’s model assumes fixed work, no parallelization overhead and equal processing units. It is a theoretical bound; real synchronization and communication costs make performance worse. Treat P as a measured runtime fraction, not as a share of parallelizable source-code lines. Consider input size when comparing.
Quanta exam set
Curated exam set for "Amdahl’s law (parallel speedup)":
Question (front)
Which formula describes Amdahl’s law (parallel speedup)?
Answer in your set
Question (front)
How do you rearrange Amdahl’s law (parallel speedup) for Serial fraction from speedup?
Answer in your set
Question (front)
Which common mistake happens with Amdahl’s law (parallel speedup)?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
Create a curated FSRS exam set for Sₙ = 1/((1−P)+P/N): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential