What is rocFFT?

What is rocFFT?#

Introduction#

The rocFFT library is an implementation of the discrete Fast Fourier Transform (FFT) written in HIP for GPU devices. The code is open and hosted here: ROCmSoftwarePlatform/rocFFT

The rocFFT library provides a fast and accurate platform for calculating discrete FFTs. It supports the following features:

  • Half (FP16), single, and double precision floating point formats

  • 1D, 2D, and 3D transforms

  • Computation of transforms in batches

  • Real and complex FFTs

  • Arbitrary lengths, with optimizations for combinations of powers of 2, 3, 5, 7, 11, 13, and 17

FFT Computation#

The FFT is an implementation of the Discrete Fourier Transform (DFT) that makes use of symmetries in the DFT definition to reduce the mathematical complexity from \(O(N^2)\) to \(O(N \log N)\).

What is computed by the library? Here are the formulas:

For a 1D complex DFT:

\({\tilde{x}}_j = \sum_{k=0}^{n-1}x_k\exp\left({\pm i}{{2\pi jk}\over{n}}\right)\hbox{ for } j=0,1,\ldots,n-1\)

Where, \(x_k\) are the complex data to be transformed, \(\tilde{x}_j\) are the transformed data, and the sign \(\pm\) determines the direction of the transform: \(-\) for forward and \(+\) for backward.

For a 2D complex DFT:

\({\tilde{x}}_{jk} = \sum_{q=0}^{m-1}\sum_{r=0}^{n-1}x_{rq}\exp\left({\pm i} {{2\pi jr}\over{n}}\right)\exp\left({\pm i}{{2\pi kq}\over{m}}\right)\)

For \(j=0,1,\ldots,n-1\hbox{ and } k=0,1,\ldots,m-1\), where, \(x_{rq}\) are the complex data to be transformed, \(\tilde{x}_{jk}\) are the transformed data, and the sign \(\pm\) determines the direction of the transform.

For a 3D complex DFT:

\(\tilde{x}_{jkl} = \sum_{s=0}^{p-1}\sum_{q=0}^{m-1}\sum_{r=0}^{n-1}x_{rqs}\exp\left({\pm i} {{2\pi jr}\over{n}}\right)\exp\left({\pm i}{{2\pi kq}\over{m}}\right)\exp\left({\pm i}{{2\pi ls}\over{p}}\right)\)

For \(j=0,1,\ldots,n-1\hbox{ and } k=0,1,\ldots,m-1\hbox{ and } l=0,1,\ldots,p-1\), where \(x_{rqs}\) are the complex data to be transformed, \(\tilde{x}_{jkl}\) are the transformed data, and the sign \(\pm\) determines the direction of the transform.

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