embfft 0.2.0

Non-blocking FFT for embedded systems
Documentation 
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/* embfft | ifft.rs
 * Copyright (c) 2025 L. Sartory
 * SPDX-License-Identifier: MIT
 */

/******************************************************************************/

use crate::common::{Base, SineTable};

/******************************************************************************/

/// Decimation in time inverse fast Fourier transform
///
/// This structure contains a reference to the input / output data, as well as information related to the
/// internal state.
pub struct EmbIfft<'a, T, const N: usize> {
    data: &'a mut [(T, T); N],
    state: State,
    length: usize,
    step: usize,
    step_size: usize,
    top_idx: usize,
    bottom_idx: usize
}

/// Conversion state
#[derive(PartialEq)]
enum State {
    Reorder,
    Step1,
    Step2,
    Step3,
    Step4,
    Step5,
    Step6,
    Done
}

impl<'a, T, const N: usize> EmbIfft<'a, T, N> {
    /// Initializes a new IFFT conversion
    ///
    /// Use this function whenever a new conversion is required.
    pub fn new(data: &'a mut [(T, T); N]) -> Self {
        assert!(Base::<N>::IS_N_POW2);
        Self {
            data,
            state: State::Reorder,
            length: 1,
            step: 0,
            step_size: N / 4,
            top_idx: 0,
            bottom_idx: 0
        }
    }

    /// Checks if the conversion is complete
    ///
    /// Use this together with the [`EmbIfft::ifft_iterate()`] function.
    pub fn is_done(&self) -> bool {
        self.state == State::Done
    }
}

/******************************************************************************/

macro_rules! gen_ifft_iterate {
    ($self: ident, $T: ty, $N: expr) => {{
        let sine_table = &SineTable::<$T, $N>::SINE_TABLE;
        let top;
        let bottom;

        match $self.state {
            State::Reorder => {
                // Ensure the input order is reversed
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                if $self.bottom_idx > $self.top_idx {
                    $self.data[$self.top_idx] = bottom;
                    $self.data[$self.bottom_idx] = top;
                }
                if $self.top_idx < $N - 1 {
                    $self.bottom_idx = Base::<$N>::reverse_bits($self.top_idx + 1);
                    $self.top_idx += 1;
                } else {
                    $self.top_idx = 0;
                    $self.bottom_idx = 1;
                    $self.state = State::Step1;
                }
            },

            State::Step1 => {
                // Twiddle = 1 / N
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                $self.data[$self.top_idx].0 = (bottom.0 + top.0) * (1.0 / $N as $T);
                $self.data[$self.top_idx].1 = (bottom.1 + top.1) * (1.0 / $N as $T);
                $self.data[$self.bottom_idx].0 = (-bottom.0 + top.0) * (1.0 / $N as $T);
                $self.data[$self.bottom_idx].1 = (-bottom.1 + top.1) * (1.0 / $N as $T);
                if $self.bottom_idx < $N - 2 {
                    $self.top_idx += 2;
                    $self.bottom_idx += 2;
                } else {
                    $self.top_idx = 0;
                    $self.state = State::Step2;
                }
            },

            State::Step2 => {
                // Twiddle = 1
                $self.bottom_idx = $self.top_idx + ($self.length << 1);
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                $self.data[$self.top_idx].0 = bottom.0 + top.0;
                $self.data[$self.top_idx].1 = bottom.1 + top.1;
                $self.data[$self.bottom_idx].0 = top.0 - bottom.0;
                $self.data[$self.bottom_idx].1 = top.1 - bottom.1;
                $self.top_idx += 1;
                $self.bottom_idx += 1;
                $self.step = $self.step_size;
                if $self.step_size < $N / 4 {
                    $self.state = State::Step3;
                } else {
                    $self.state = State::Step4;
                }
            },

            State::Step3 => {
                // Twiddle = e^(+j * theta)
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                let temp = (
                    bottom.0 * sine_table[$N / 4 - $self.step] - bottom.1 * sine_table[$self.step],
                    bottom.1 * sine_table[$N / 4 - $self.step] + bottom.0 * sine_table[$self.step]
                );
                $self.data[$self.top_idx].0 = top.0 + temp.0;
                $self.data[$self.top_idx].1 = top.1 + temp.1;
                $self.data[$self.bottom_idx].0 = top.0 - temp.0;
                $self.data[$self.bottom_idx].1 = top.1 - temp.1;
                $self.top_idx += 1;
                $self.bottom_idx += 1;
                if $self.step < $N / 4 - $self.step_size {
                    $self.step += $self.step_size;
                } else {
                    $self.state = State::Step4;
                }
            },

            State::Step4 => {
                // Twiddle = +j
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                $self.data[$self.top_idx].0 = top.0 - bottom.1;
                $self.data[$self.top_idx].1 = top.1 + bottom.0;
                $self.data[$self.bottom_idx].0 = top.0 + bottom.1;
                $self.data[$self.bottom_idx].1 = top.1 - bottom.0;
                $self.top_idx += 1;
                $self.bottom_idx += 1;
                $self.step = $self.step_size;
                if $self.step_size < $N / 4 {
                    $self.state = State::Step5;
                } else {
                    $self.state = State::Step6;
                }
            },

            State::Step5 => {
                // Twiddle = +j * e^(+j * theta)
                top = $self.data[$self.top_idx];
                bottom = $self.data[$self.bottom_idx];
                let temp = (
                    -bottom.1 * sine_table[$N / 4 - $self.step] - bottom.0 * sine_table[$self.step],
                    bottom.0 * sine_table[$N / 4 - $self.step] - bottom.1 * sine_table[$self.step]
                );
                $self.data[$self.top_idx].0 = top.0 + temp.0;
                $self.data[$self.top_idx].1 = top.1 + temp.1;
                $self.data[$self.bottom_idx].0 = top.0 - temp.0;
                $self.data[$self.bottom_idx].1 = top.1 - temp.1;
                $self.top_idx += 1;
                $self.bottom_idx += 1;
                if $self.step < $N / 4 - $self.step_size {
                    $self.step += $self.step_size;
                } else {
                    $self.state = State::Step6;
                }
            },

            State::Step6 => {
                // Check if we need to loop
                if $self.bottom_idx < $N {
                    $self.top_idx = $self.bottom_idx;
                    $self.state = State::Step2;
                } else if $self.step_size > 1 {
                    $self.length <<= 1;
                    $self.step_size >>= 1;
                    $self.top_idx = 0;
                    $self.state = State::Step2;
                } else {
                    $self.state = State::Done;
                }
            },

            State::Done => {}
        }
    }};
}

/******************************************************************************/

impl<const N: usize> EmbIfft<'_, f32, N> {
    /// Non-blocking IFFT computation with f32 precision
    ///
    /// Use this together with the [`EmbIfft::is_done()`] function.
    /// For example:
    /// ```
    /// let mut data = [
    ///     (1.0f32, 1.0), (2.0, 2.0),
    ///     (3.0f32, 3.0), (4.0, 4.0),
    ///     (5.0f32, 5.0), (6.0, 6.0),
    ///     (7.0f32, 7.0), (8.0, 8.0)
    /// ];
    ///
    /// let mut ifft = embfft::EmbIfft::new(&mut data);
    /// while !ifft.is_done() {
    ///     ifft.ifft_iterate();
    ///     // Other actions can be performed here between two iterations
    /// }
    /// ```
    pub fn ifft_iterate(&mut self) {
        gen_ifft_iterate!(self, f32, N);
    }

    /// Blocking IFFT computation with f32 precision
    ///
    /// For example:
    /// ```
    /// let mut data = [
    ///     (1.0f32, 1.0), (2.0, 2.0),
    ///     (3.0f32, 3.0), (4.0, 4.0),
    ///     (5.0f32, 5.0), (6.0, 6.0),
    ///     (7.0f32, 7.0), (8.0, 8.0)
    /// ];
    /// embfft::EmbIfft::new(&mut data).ifft();
    /// ```
    pub fn ifft(&mut self) {
        while self.state != State::Done {
            gen_ifft_iterate!(self, f32, N);
        }
    }
}

impl<const N: usize> EmbIfft<'_, f64, N> {
    /// Non-blocking IFFT computation with f64 precision
    ///
    /// Use this together with the [`EmbIfft::is_done()`] function.
    /// For example:
    /// ```
    /// let mut data = [
    ///     (1.0f64, 1.0), (2.0, 2.0),
    ///     (3.0f64, 3.0), (4.0, 4.0),
    ///     (5.0f64, 5.0), (6.0, 6.0),
    ///     (7.0f64, 7.0), (8.0, 8.0)
    /// ];
    ///
    /// let mut ifft = embfft::EmbIfft::new(&mut data);
    /// while !ifft.is_done() {
    ///     ifft.ifft_iterate();
    ///     // Other actions can be performed here between two iterations
    /// }
    /// ```
    pub fn ifft_iterate(&mut self) {
        gen_ifft_iterate!(self, f64, N);
    }

    /// Blocking IFFT computation with f64 precision
    ///
    /// For example:
    /// ```
    /// let mut data = [
    ///     (1.0f64, 1.0), (2.0, 2.0),
    ///     (3.0f64, 3.0), (4.0, 4.0),
    ///     (5.0f64, 5.0), (6.0, 6.0),
    ///     (7.0f64, 7.0), (8.0, 8.0)
    /// ];
    /// embfft::EmbIfft::new(&mut data).ifft();
    /// ```
    pub fn ifft(&mut self) {
        while self.state != State::Done {
            gen_ifft_iterate!(self, f64, N);
        }
    }
}

/******************************************************************************/

#[cfg(test)]
mod tests {
    use super::*;
    use approx::assert_ulps_eq;

    #[test]
    fn test_ifft_f32() {
        let mut data: [(f32, f32); 64] = [
            ( 1.0, 0.0), ( 2.0, 0.0), ( 3.0, 0.0), ( 4.0, 0.0), ( 5.0, 0.0), ( 6.0, 0.0), ( 7.0, 0.0), ( 8.0, 0.0),
            ( 9.0, 0.0), (10.0, 0.0), (11.0, 0.0), (12.0, 0.0), (13.0, 0.0), (14.0, 0.0), (15.0, 0.0), (16.0, 0.0),
            (17.0, 0.0), (18.0, 0.0), (19.0, 0.0), (20.0, 0.0), (21.0, 0.0), (22.0, 0.0), (23.0, 0.0), (24.0, 0.0),
            (25.0, 0.0), (26.0, 0.0), (27.0, 0.0), (28.0, 0.0), (29.0, 0.0), (30.0, 0.0), (31.0, 0.0), (32.0, 0.0),
            (33.0, 0.0), (34.0, 0.0), (35.0, 0.0), (36.0, 0.0), (37.0, 0.0), (38.0, 0.0), (39.0, 0.0), (40.0, 0.0),
            (41.0, 0.0), (42.0, 0.0), (43.0, 0.0), (44.0, 0.0), (45.0, 0.0), (46.0, 0.0), (47.0, 0.0), (48.0, 0.0),
            (49.0, 0.0), (50.0, 0.0), (51.0, 0.0), (52.0, 0.0), (53.0, 0.0), (54.0, 0.0), (55.0, 0.0), (56.0, 0.0),
            (57.0, 0.0), (58.0, 0.0), (59.0, 0.0), (60.0, 0.0), (61.0, 0.0), (62.0, 0.0), (63.0, 0.0), (64.0, 0.0)
        ];

        let expected_data = [
            (32.500000000,  0.000000000), (-0.500000000, -10.177733812),
            (-0.500000000, -5.076585194), (-0.500000000,  -3.370726203),
            (-0.500000000, -2.513669746), (-0.500000000,  -1.996111892),
            (-0.500000000, -1.648279104), (-0.500000000,  -1.397406386),
            (-0.500000000, -1.207106781), (-0.500000000,  -1.057161179),
            (-0.500000000, -0.935434206), (-0.500000000,  -0.834199603),
            (-0.500000000, -0.748302881), (-0.500000000,  -0.674171957),
            (-0.500000000, -0.609251763), (-0.500000000,  -0.551664988),
            (-0.500000000, -0.500000000), (-0.500000000,  -0.453173585),
            (-0.500000000, -0.410339395), (-0.500000000,  -0.370825273),
            (-0.500000000, -0.334089319), (-0.500000000,  -0.299688467),
            (-0.500000000, -0.267255568), (-0.500000000,  -0.236482388),
            (-0.500000000, -0.207106781), (-0.500000000,  -0.178902861),
            (-0.500000000, -0.151673342), (-0.500000000,  -0.125243480),
            (-0.500000000, -0.099456184), (-0.500000000,  -0.074167994),
            (-0.500000000, -0.049245702), (-0.500000000,  -0.024563425),
            (-0.500000000,  0.000000000), (-0.500000000,   0.024563425),
            (-0.500000000,  0.049245702), (-0.500000000,   0.074167994),
            (-0.500000000,  0.099456184), (-0.500000000,   0.125243480),
            (-0.500000000,  0.151673342), (-0.500000000,   0.178902861),
            (-0.500000000,  0.207106781), (-0.500000000,   0.236482388),
            (-0.500000000,  0.267255568), (-0.500000000,   0.299688467),
            (-0.500000000,  0.334089319), (-0.500000000,   0.370825273),
            (-0.500000000,  0.410339395), (-0.500000000,   0.453173585),
            (-0.500000000,  0.500000000), (-0.500000000,   0.551664988),
            (-0.500000000,  0.609251763), (-0.500000000,   0.674171957),
            (-0.500000000,  0.748302881), (-0.500000000,   0.834199603),
            (-0.500000000,  0.935434206), (-0.500000000,   1.057161179),
            (-0.500000000,  1.207106781), (-0.500000000,   1.397406386),
            (-0.500000000,  1.648279104), (-0.500000000,   1.996111892),
            (-0.500000000,  2.513669746), (-0.500000000,   3.370726203),
            (-0.500000000,  5.076585194), (-0.500000000,  10.177733812)
        ];

        EmbIfft::new(&mut data).ifft();

        for (x, y) in core::iter::zip(data, expected_data) {
            assert_ulps_eq!(x.0, y.0, max_ulps=10);
            assert_ulps_eq!(x.1, y.1, max_ulps=10);
        }
    }

    #[test]
    fn test_ifft_f64() {
        let mut data: [(f64, f64); 64] = [
            ( 1.0, 0.0), ( 2.0, 0.0), ( 3.0, 0.0), ( 4.0, 0.0), ( 5.0, 0.0), ( 6.0, 0.0), ( 7.0, 0.0), ( 8.0, 0.0),
            ( 9.0, 0.0), (10.0, 0.0), (11.0, 0.0), (12.0, 0.0), (13.0, 0.0), (14.0, 0.0), (15.0, 0.0), (16.0, 0.0),
            (17.0, 0.0), (18.0, 0.0), (19.0, 0.0), (20.0, 0.0), (21.0, 0.0), (22.0, 0.0), (23.0, 0.0), (24.0, 0.0),
            (25.0, 0.0), (26.0, 0.0), (27.0, 0.0), (28.0, 0.0), (29.0, 0.0), (30.0, 0.0), (31.0, 0.0), (32.0, 0.0),
            (33.0, 0.0), (34.0, 0.0), (35.0, 0.0), (36.0, 0.0), (37.0, 0.0), (38.0, 0.0), (39.0, 0.0), (40.0, 0.0),
            (41.0, 0.0), (42.0, 0.0), (43.0, 0.0), (44.0, 0.0), (45.0, 0.0), (46.0, 0.0), (47.0, 0.0), (48.0, 0.0),
            (49.0, 0.0), (50.0, 0.0), (51.0, 0.0), (52.0, 0.0), (53.0, 0.0), (54.0, 0.0), (55.0, 0.0), (56.0, 0.0),
            (57.0, 0.0), (58.0, 0.0), (59.0, 0.0), (60.0, 0.0), (61.0, 0.0), (62.0, 0.0), (63.0, 0.0), (64.0, 0.0)
        ];

        let expected_data = [
            (32.500000000000000,  0.000000000000000), (-0.500000000000000, -10.177733812493605),
            (-0.500000000000000, -5.076585193804434), (-0.500000000000000,  -3.370726202707498),
            (-0.500000000000000, -2.513669746062925), (-0.500000000000000,  -1.996111891885044),
            (-0.500000000000000, -1.648279104469162), (-0.500000000000000,  -1.397406386245239),
            (-0.500000000000000, -1.207106781186548), (-0.500000000000000,  -1.057161178774320),
            (-0.500000000000000, -0.935434205894695), (-0.500000000000000,  -0.834199602791755),
            (-0.500000000000000, -0.748302881332745), (-0.500000000000000,  -0.674171956743360),
            (-0.500000000000000, -0.609251762793989), (-0.500000000000000,  -0.551664987866739),
            (-0.500000000000000, -0.500000000000000), (-0.500000000000000,  -0.453173584509572),
            (-0.500000000000000, -0.410339395414330), (-0.500000000000000,  -0.370825273136018),
            (-0.500000000000000, -0.334089318959649), (-0.500000000000000,  -0.299688466840962),
            (-0.500000000000000, -0.267255567975397), (-0.500000000000000,  -0.236482387945661),
            (-0.500000000000000, -0.207106781186548), (-0.500000000000000,  -0.178902860657261),
            (-0.500000000000000, -0.151673341803671), (-0.500000000000000,  -0.125243480095653),
            (-0.500000000000000, -0.099456183689830), (-0.500000000000000,  -0.074167993769174),
            (-0.500000000000000, -0.049245701678584), (-0.500000000000000,  -0.024563424884736),
            (-0.500000000000000,  0.000000000000000), (-0.500000000000000,   0.024563424884736),
            (-0.500000000000000,  0.049245701678584), (-0.500000000000000,   0.074167993769174),
            (-0.500000000000000,  0.099456183689830), (-0.500000000000000,   0.125243480095653),
            (-0.500000000000000,  0.151673341803671), (-0.500000000000000,   0.178902860657261),
            (-0.500000000000000,  0.207106781186548), (-0.500000000000000,   0.236482387945661),
            (-0.500000000000000,  0.267255567975397), (-0.500000000000000,   0.299688466840962),
            (-0.500000000000000,  0.334089318959649), (-0.500000000000000,   0.370825273136018),
            (-0.500000000000000,  0.410339395414330), (-0.500000000000000,   0.453173584509572),
            (-0.500000000000000,  0.500000000000000), (-0.500000000000000,   0.551664987866739),
            (-0.500000000000000,  0.609251762793989), (-0.500000000000000,   0.674171956743360),
            (-0.500000000000000,  0.748302881332745), (-0.500000000000000,   0.834199602791755),
            (-0.500000000000000,  0.935434205894695), (-0.500000000000000,   1.057161178774320),
            (-0.500000000000000,  1.207106781186548), (-0.500000000000000,   1.397406386245239),
            (-0.500000000000000,  1.648279104469162), (-0.500000000000000,   1.996111891885044),
            (-0.500000000000000,  2.513669746062925), (-0.500000000000000,   3.370726202707498),
            (-0.500000000000000,  5.076585193804434), (-0.500000000000000,  10.177733812493605)
        ];
        EmbIfft::new(&mut data).ifft();

        for (x, y) in core::iter::zip(data, expected_data) {
            assert_ulps_eq!(x.0, y.0, max_ulps=75);
            assert_ulps_eq!(x.1, y.1, max_ulps=75);
        }
    }
}