Affects Version/s: 1.2
Fix Version/s: 2.0
Here are some suggestions on improving the speed and computational-efficiency of FastFourierTransformer.
1. Store roots of unity as a double array of arrays instead of Complex array.
No need for all the functionality that comes with class Complex when all that is required are the values of the roots of unity.
2. Keep track of the largest set of roots of unity calculated so far, and adopt Singleton pattern.
Subsequent requests for smaller sets of roots of unity can be derived from the largest set – no need to recalculate the roots of unity from scratch.
3. When computing the nth roots of unity, need only compute n/4 roots instead of all n roots.
Since the roots of unity lie along a circle of unity radius, trigonometric relations can be leveraged to reduce the number of roots that need to be computed from n to n/4.
4. Execute transform algorithm on double primitives instead of on class Complex.
New instances of Complex are instantiated each time a simple arithmetic operation is performed on the Complex variables. Much time is lost to object creation and initialisation.