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As per page 89 of the text book, where examples of calculating Safe Endurance are given, contingency fuel is removed as part of that calculation along with start up/taxy, final and holding reserve fuel.
Contingency fuel is considered as extra 'trip fuel'. It is applied simply by multiplying the trip fuel by 1.1. That increases the trip fuel by 10%. Contingency fuel accounts for unexpected events such as diversions around bad weather or bush fires or unexpected headwinds. Contingency fuel may or may not be used during a particular flight, its carried 'just in case'. It is not treated like start-up and taxi fuel which you know will be used on every flight.
