Enter the proportion of the program that cannot be parallelized (1 – p) and the number of processors used (n) into the calculator to determine the overall speedup achieved by parallel processing; this calculator can also evaluate any of the variables given the others are known.

## Amdahl’S Law Formula

The following formula is used to calculate the speedup achieved by using parallel processing according to Amdahl’s Law:

Speedup = {1}/({(1 - p) + {p}/{n}})

Variables:

• Speedup is the overall speedup achieved by parallel processing
• p is the proportion of the program that can be parallelized (between 0 and 1)
• n is the number of processors used

To calculate the speedup, subtract the proportion of the program that cannot be parallelized (1 – p) from 1. Divide the result by the sum of the proportion of the program that can be parallelized (p) divided by the number of processors used (n).

## What is Amdahl’S Law?

Amdahl’s Law, named after computer architect Gene Amdahl, is a formula used to find the maximum improvement possible by enhancing a particular part of a system. In the context of parallel computing, it is used to predict the theoretical maximum speedup for program processing using multiple processors. The law states that the speedup of a program using a parallel algorithm is limited by the time needed for the sequential fraction of the program. In other words, if a program needs 20 hours to complete in sequential mode (i.e., with one processor) and a particular part of the program which takes one hour to execute cannot be parallelized, while the remaining 19 hours (95%) of execution time can be parallelized, then regardless of how many processors are devoted to a parallelized execution of this program, the minimum execution time cannot be less than that critical one hour. Hence, the speedup is limited by the non-parallelizable section of the process.

## How to Calculate Amdahl’S Law?

The following steps outline how to calculate Amdahl’s Law:

1. First, determine the speedup factor (S).
2. Next, determine the proportion of the program that can be parallelized (P).
3. Next, calculate the speedup of the parallel portion (Sp) using the formula Sp = 1 / (1 – P).
4. Next, calculate the speedup of the non-parallel portion (Sn) using the formula Sn = 1.
5. Finally, calculate the overall speedup (So) using the formula So = S = 1 / ((1 – P) + (P / S)).

Example Problem :

Use the following variables as an example problem to test your knowledge.

speedup factor (S) = 4

proportion of the program that can be parallelized (P) = 0.6