# The FFT Butterfly

*Module of the free GPU.js GPGPU course · 6 tasks*

Split the sum by parity and the transform collapses from n² terms to log₂n passes of a two-line butterfly — the same multi-pass gather every ladder in this course uses.

## Tasks

1. [Where the Saving Comes From](https://gpu.rocks/learn/fft-butterfly-d4375da7/1.md)
2. [The Butterfly: One Thread, One Output](https://gpu.rocks/learn/fft-butterfly-d4375da7/2.md)
3. [Put the Input in the Right Order](https://gpu.rocks/learn/fft-butterfly-d4375da7/3.md)
4. [Drive log₂n Passes](https://gpu.rocks/learn/fft-butterfly-d4375da7/4.md)
5. [Same Answer, Two Centuries Apart](https://gpu.rocks/learn/fft-butterfly-d4375da7/5.md)
6. [Run It Backwards for Free](https://gpu.rocks/learn/fft-butterfly-d4375da7/6.md)

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Interactive version: https://gpu.rocks/learn/fft-butterfly-d4375da7