rustfft 0.0.2

A mixed-radix FFT library written in pure Rust
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//! These are the unrolled butterflies for specific FFT lengths. They are mostly
//! translations of the butterfly functions from KissFFT, copyright Mark Borgerding.

use num::{Complex, Zero};

pub fn butterfly_2(data: &mut [Complex<f32>], stride: usize,
                   twiddles: &[Complex<f32>], num_ffts: usize) {
    let mut idx_1 = 0usize;
    let mut idx_2 = num_ffts;
    let mut twiddle_idx = 0usize;
    // TODO speed: use pointers instead of pointer offsets?
    for _ in 0..num_ffts {
        unsafe {
            let twiddle = twiddles.get_unchecked(twiddle_idx);
            let temp = data.get_unchecked(idx_2) * twiddle;
            *data.get_unchecked_mut(idx_2) = data.get_unchecked(idx_1) - temp;
            *data.get_unchecked_mut(idx_1) = data.get_unchecked(idx_1) + temp;
        }
        twiddle_idx += stride;
        idx_1 += 1;
        idx_2 += 1;
    }
}

pub fn butterfly_3(data: &mut [Complex<f32>], stride: usize,
                   twiddles: &[Complex<f32>], num_ffts: usize) {
    let mut idx = 0usize;
    let mut tw_idx_1 = 0usize;
    let mut tw_idx_2 = 0usize;
    let mut scratch: [Complex<f32>; 5] = [Zero::zero(); 5];
    for _ in 0..num_ffts {
        unsafe {
            scratch[1] = data.get_unchecked(idx + 1 * num_ffts) * twiddles[tw_idx_1];
            scratch[2] = data.get_unchecked(idx + 2 * num_ffts) * twiddles[tw_idx_2];
            scratch[3] = scratch[1] + scratch[2];
            scratch[0] = scratch[1] - scratch[2];

            data.get_unchecked_mut(idx + num_ffts).re = data.get_unchecked(idx).re
                                                        - scratch[3].re / 2.0;
            data.get_unchecked_mut(idx + num_ffts).im = data.get_unchecked(idx).im
                                                        - scratch[3].im / 2.0;

            scratch[0].re = scratch[0].re * twiddles[stride * num_ffts].im;
            scratch[0].im = scratch[0].im * twiddles[stride * num_ffts].im;

            *data.get_unchecked_mut(idx) = data.get_unchecked(idx) + scratch[3];
            data.get_unchecked_mut(idx + 2 * num_ffts).re = data.get_unchecked(idx + num_ffts).re
                                                            + scratch[0].im;
            data.get_unchecked_mut(idx + 2 * num_ffts).im = data.get_unchecked(idx + num_ffts).im
                                                            - scratch[0].re;
            data.get_unchecked_mut(idx + num_ffts).re = data.get_unchecked(idx + num_ffts).re
                                                        - scratch[0].im;
            data.get_unchecked_mut(idx + num_ffts).im = data.get_unchecked(idx + num_ffts).im
                                                        + scratch[0].re;

            tw_idx_1 += 1 * stride;
            tw_idx_2 += 2 * stride;
            idx += 1;
        }
    }
}

pub fn butterfly_4(data: &mut [Complex<f32>], stride: usize,
                   twiddles: &[Complex<f32>], num_ffts: usize) {
    let mut idx = 0usize;
    let mut tw_idx_1 = 0usize;
    let mut tw_idx_2 = 0usize;
    let mut tw_idx_3 = 0usize;
    let mut scratch: [Complex<f32>; 6] = [Zero::zero(); 6];
    //TODO does using get_unchecked on scratch help with speed?
    for _ in 0..num_ffts {
        unsafe {
            scratch[0] = data.get_unchecked(idx + 1 * num_ffts) * twiddles[tw_idx_1];
            scratch[1] = data.get_unchecked(idx + 2 * num_ffts) * twiddles[tw_idx_2];
            scratch[2] = data.get_unchecked(idx + 3 * num_ffts) * twiddles[tw_idx_3];
            scratch[5] = data.get_unchecked(idx) - scratch[1];
            *data.get_unchecked_mut(idx) = data.get_unchecked(idx) + scratch[1];
            scratch[3] = scratch[0] + scratch[2];
            scratch[4] = scratch[0] - scratch[2];
            *data.get_unchecked_mut(idx + 2 * num_ffts) = data.get_unchecked(idx) - scratch[3];
            *data.get_unchecked_mut(idx) = data.get_unchecked(idx) + scratch[3];
            data.get_unchecked_mut(idx + num_ffts).re = scratch[5].re + scratch[4].im;
            data.get_unchecked_mut(idx + num_ffts).im = scratch[5].im - scratch[4].re;
            data.get_unchecked_mut(idx + 3 * num_ffts).re = scratch[5].re - scratch[4].im;
            data.get_unchecked_mut(idx + 3 * num_ffts).im = scratch[5].im + scratch[4].re;

            tw_idx_1 += 1 * stride;
            tw_idx_2 += 2 * stride;
            tw_idx_3 += 3 * stride;
            idx += 1;
        }
    }
}

pub fn butterfly_5(data: &mut [Complex<f32>], stride: usize,
                   twiddles: &[Complex<f32>], num_ffts: usize) {
    let mut idx_0 = 0 * num_ffts;
    let mut idx_1 = 1 * num_ffts;
    let mut idx_2 = 2 * num_ffts;
    let mut idx_3 = 3 * num_ffts;
    let mut idx_4 = 4 * num_ffts;
    let mut scratch: [Complex<f32>; 13] = [Zero::zero(); 13];
    let ya = twiddles[stride * num_ffts];
    let yb = twiddles[stride * 2 * num_ffts];
    for i in 0..num_ffts {
        unsafe {
            scratch[0] = *data.get_unchecked(idx_0);
            scratch[1] = data.get_unchecked(idx_1) * twiddles[1 * i * stride];
            scratch[2] = data.get_unchecked(idx_2) * twiddles[2 * i * stride];
            scratch[3] = data.get_unchecked(idx_3) * twiddles[3 * i * stride];
            scratch[4] = data.get_unchecked(idx_4) * twiddles[4 * i * stride];

            scratch[7] = scratch[1] + scratch[4];
            scratch[10] = scratch[1] - scratch[4];
            scratch[8] = scratch[2] + scratch[3];
            scratch[9] = scratch[2] - scratch[3];

            data.get_unchecked_mut(idx_0).re += scratch[7].re + scratch[8].re;
            data.get_unchecked_mut(idx_0).im += scratch[7].im + scratch[8].im;

            scratch[5].re = scratch[0].re + scratch[7].re * ya.re + scratch[8].re * yb.re;
            scratch[5].im = scratch[0].im + scratch[7].im * ya.re + scratch[8].im * yb.re;

            scratch[6].re = scratch[10].im * ya.im + scratch[9].im * yb.im;
            scratch[6].im = -1.0 * scratch[10].re * ya.im - scratch[9].re * yb.im;

            *data.get_unchecked_mut(idx_1) = scratch[5] - scratch[6];
            *data.get_unchecked_mut(idx_4) = scratch[5] + scratch[6];

            scratch[11].re = scratch[0].re + scratch[7].re * yb.re + scratch[8].re * ya.re;
            scratch[11].im = scratch[0].im + scratch[7].im * yb.re + scratch[8].im * ya.re;
            scratch[12].re = -1.0 * scratch[10].im * yb.im + scratch[9].im * ya.im;
            scratch[12].im = scratch[10].re * yb.im - scratch[9].re * ya.im;

            *data.get_unchecked_mut(idx_2) = scratch[11] + scratch[12];
            *data.get_unchecked_mut(idx_3) = scratch[11] - scratch[12];

            idx_0 += 1;
            idx_1 += 1;
            idx_2 += 1;
            idx_3 += 1;
            idx_4 += 1;
        }
    }
}

#[cfg(test)]
mod benches {
    use std::f32;
    use std::iter::repeat;
    use test::Bencher;
    use num::{Complex, Zero};
    use super::{butterfly_2, butterfly_3, butterfly_4, butterfly_5};

    fn set_up_bench(butterfly_len: usize, stride: usize, num_ffts: usize) -> (Vec<Complex<f32>>, Vec<Complex<f32>>) {
        let len = butterfly_len * stride * num_ffts;
        let twiddles: Vec<Complex<f32>> = (0..len)
            .map(|i| -1. * (i as f32) * f32::consts::PI_2 / (len as f32))
            .map(|phase| Complex::from_polar(&1., &phase))
            .collect();

        let data: Vec<Complex<f32>> = repeat(Zero::zero()).take(len).collect();
        (data, twiddles)
    }

    #[bench]
    fn bench_butterfly_2(b: &mut Bencher) {
        let stride = 4usize;
        let num_ffts = 1000usize;
        let (mut data, twiddles) = set_up_bench(2, stride, num_ffts);

        b.iter(|| butterfly_2(&mut data, stride, &twiddles, num_ffts));
    }

    #[bench]
    fn bench_butterfly_3(b: &mut Bencher) {
        let stride = 4usize;
        let num_ffts = 1000usize;
        let (mut data, twiddles) = set_up_bench(3, stride, num_ffts);

        b.iter(|| butterfly_3(&mut data, stride, &twiddles, num_ffts));
    }

    #[bench]
    fn bench_butterfly_4(b: &mut Bencher) {
        let stride = 4usize;
        let num_ffts = 1000usize;
        let (mut data, twiddles) = set_up_bench(4, stride, num_ffts);

        b.iter(|| butterfly_4(&mut data, stride, &twiddles, num_ffts));
    }

    #[bench]
    fn bench_butterfly_5(b: &mut Bencher) {
        let stride = 4usize;
        let num_ffts = 1000usize;
        let (mut data, twiddles) = set_up_bench(5, stride, num_ffts);

        b.iter(|| butterfly_5(&mut data, stride, &twiddles, num_ffts));
    }
}