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From "Daniel Kuan (JIRA)" <>
Subject [jira] Created: (MATH-216) Faster and more computationally-efficient Fast Fourier Transform implementation
Date Fri, 11 Jul 2008 18:52:31 GMT
Faster and more computationally-efficient Fast Fourier Transform implementation

                 Key: MATH-216
             Project: Commons Math
          Issue Type: Improvement
    Affects Versions: 1.2
            Reporter: Daniel Kuan
            Priority: Minor

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.

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.

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