Analysis
Your program can achieve a maximum speedup of 1.00x with 4 processors.
Calculate the theoretical speedup of parallel computing systems using Amdahl's Law. Understand the limits of parallelization in your programs.
Amdahl's Law, named after computer architect Gene Amdahl, is a formula used to find the maximum expected improvement to an overall system when only part of the system is improved.
It's particularly useful in parallel computing to calculate the theoretical speedup when using multiple processors.
Where:
| Variable | Description | Range |
|---|---|---|
| S | Theoretical Speedup | S ≥ 1 |
| P | Parallel portion of the program (decimal) | 0 ≤ P ≤ 1 |
| N | Number of processors/cores | N ≥ 1 |
| 1 - P | Serial portion of the program | 0 ≤ (1-P) ≤ 1 |
Parallel Portion (P): 0.85 (85% can be parallelized)
Typical Processors: 8 cores
Maximum Speedup: 4.7x (Amdahl's Law limitation)
Even with perfect parallelization of encoding algorithms, file I/O remains serial.
Parallel Portion (P): 0.95 (95% can be parallelized)
Typical Processors: 32 cores
Maximum Speedup: 12.3x
Sequencing individual segments can be parallelized, but assembly remains serial.
Parallel Portion (P): 0.70 (70% can be parallelized)
Typical Processors: 6 cores
Maximum Speedup: 2.3x
Physics calculations can be distributed, but game state synchronization is serial.
Adding more processors provides less benefit as P approaches 1. Even with P=0.95, infinite processors only give 20x speedup.
A program with just 10% serial code (P=0.9) can never achieve more than 10x speedup, regardless of processor count.
Adding processors beyond a certain point yields minimal improvements. Focus on reducing serial portions first.
Improving the serial portion (1-P) has a much greater impact than adding more processors when P is already high.