Editing Speedup (section)

==Additional details==
Let ''S'' be the speedup of execution of a task and ''s'' the speedup of execution of the part of the task that benefits from the improvement of the resources of an architecture. ''Linear speedup'' or ''ideal speedup'' is obtained when {{nowrap|1=''S'' = ''s''}}. When running a task with linear speedup, doubling the local speedup doubles the overall speedup. As this is ideal, it is considered very good [[scalability]].

''Efficiency'' is a metric of the utilization of the resources of the improved system defined as
: <math>\eta = \frac{S}{s}.</math>
Its value is typically between 0 and 1. Programs with linear speedup and programs running on a single processor have an efficiency of 1, while many difficult-to-parallelize programs have efficiency such as 1/ln(''s''){{citation needed|date=November 2010}} that approaches 0 as the number of processors {{nowrap|1=''A'' = ''s''}} increases.

In engineering contexts, efficiency curves are more often used for graphs than speedup curves, since
* all of the area in the graph is useful (whereas in speedup curves half of the space is wasted);
* it is easy to see how well the improvement of the system is working;
* there is no need to plot a "perfect speedup" curve.
In marketing contexts, speedup curves are more often used, largely because they go up and to the right and thus appear better to the less-informed.