#fft #discrete-fourier #transform #fourier #discrete #quantum

nightly phastft

A high-performance, quantum-inspired, implementation of FFT in pure Rust

2 releases

0.1.1 Feb 13, 2024
0.1.0 Feb 12, 2024

#650 in Algorithms


811 lines

Build codecov unsafe forbidden


PhastFT is a high-performance, "quantum-inspired" Fast Fourier Transform (FFT) library written in pure Rust.


  • Simple implementation using a single, general-purpose FFT algorithm
  • Performance on par with other Rust FFT implementations
  • Zero unsafe code
  • Takes advantage of latest CPU features up to and including AVX-512, but performs well even without them
  • Optional parallelization of some steps to 2 threads (with even more planned)
  • 2x lower memory usage than RustFFT
  • Python bindings (via PyO3)


  • No runtime CPU feature detection (yet). Right now achieving the highest performance requires compiling with -C target-cpu=native or cargo multivers.
  • Requires nightly Rust compiler due to use of portable SIMD

Planned features

  • Runtime CPU feature detection
  • More multi-threading
  • More work on cache-optimal FFT

How is it so fast?

PhastFT is designed around the capabilities and limitations of modern hardware (that is, anything made in the last 10 years or so).

The two major bottlenecks in FFT are the CPU cycles and memory accesses.

We picked an efficient, general-purpose FFT algorithm. Our implementation can make use of latest CPU features such as AVX-512, but performs well even without them.

Our key insight for speeding up memory accesses is that FFT is equivalent to applying gates to all qubits in [0, n). This creates to oppurtunity to leverage the same memory access patterns as a high-performance quantum state simulator.

We also use the Cache-Optimal Bit Reveral Algorithm (COBRA) on large datasets and optionally run it on 2 parallel threads, accelerating it even further.

All of this combined results in a fast and efficient FFT implementation competitive with the performance of existing Rust FFT crates, including RustFFT, while using significantly less memory.



use phastft::planner::Direction;
use phastft::fft;

fn main() {
    let big_n = 1 << 10;
    let mut reals: Vec<f64> = (1..=big_n).map(|i| i as f64).collect();
    let mut imags: Vec<f64> = (1..=big_n).map(|i| i as f64).collect();
    fft(&mut reals, &mut imags, Direction::Forward);


Follow the instructions at https://rustup.rs/ to install Rust, then switch to the nightly channel with

rustup default nightly

Then you can install PhastFT itself:

pip install numpy
RUSTFLAGS='-Ctarget-cpu=native' pip install git+https://github.com/QuState/PhastFT#subdirectory=pybindings
import numpy as np
from pybindings import fft

sig_re = np.asarray(sig_re, dtype=np.float64)
sig_im = np.asarray(sig_im, dtype=np.float64)

fft(a_re, a_im)


PhastFT is benchmarked against several other FFT libraries. Scripts and instructions to reproduce benchmark results and plots are available here.

PhastFT vs. RustFFT vs. FFTW3 PhastFT vs. RustFFT vs. FFTW3

PhastFT vs. NumPy FFT vs. pyFFTW PhastFT vs. NumPy FFT vs. pyFFTW


Contributions to PhastFT are welcome! If you find any issues or have improvements to suggest, please open an issue or submit a pull request. Follow the contribution guidelines outlined in the CONTRIBUTING.md file.


PhastFT is licensed under MIT or Apache 2.0 license, at your option.

PhastFT vs RustFFT

RustFFT is another excellent FFT implementation in pure Rust. RustFFT and PhastFT make different trade-offs.

RustFFT made the choice to work on stable Rust compiler at the cost of unsafe code, while PhastFT contains no unsafe blocks but requires a nightly build of Rust compiler to access the Portable SIMD API.

RustFFT implements multiple FFT algorithms and tries to pick the best one depending on the workload, while PhastFT has a single FFT implementation and still achieves competitive performance.

PhastFT uses 2x less memory than RustFFT, which is important for processing large datasets.

What's with the name?

The name, PhastFT, is derived from the implementation of the Quantum Fourier Transform (QFT). Namely, the quantum circuit implementation of QFT consists of the Phase gates and Hadamard gates. Hence, PhastFT.

No runtime deps