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/// Delta-sigma modulator
///
/// * MASH-(1)^K architecture
/// * `0 <= K <= 8` (`K=0` is valid but the output will be the constant quantized 0)
/// * The output range is `1 - (1 << K - 1)..=(1 << K - 1)`.
/// * Given constant input `x0`, the average output is `x0/(1 << 32)`.
/// * The noise goes up as `K * 20 dB/decade`.
///
/// ```
/// # use idsp::Dsm;
/// let mut d = Dsm::<3>::default();
/// let x = 0x87654321;
/// let n = 1 << 20;
/// let y = (0..n).map(|_| d.update(x) as f32).sum::<f32>() / n as f32;
/// let m = x as f32 / (1u64 << 32) as f32;
/// assert!((y / m - 1.0).abs() < (1.0 / n as f32).sqrt(), "{y} != {m}");
/// ```
#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd)]
pub struct Dsm<const K: usize> {
    a: [u32; K],
    c: [i8; K],
}

impl<const K: usize> Default for Dsm<K> {
    fn default() -> Self {
        Self {
            a: [0; K],
            c: [0; K],
        }
    }
}

impl<const K: usize> Dsm<K> {
    /// Ingest input sample, emit new output.
    ///
    /// # Arguments
    /// * `x`: New input sample
    ///
    /// # Returns
    /// New output
    pub fn update(&mut self, x: u32) -> i8 {
        let mut d = 0i8;
        let mut c = false;
        self.a.iter_mut().fold(x, |x, a| {
            (*a, c) = a.overflowing_add(x);
            d = (d << 1) | c as i8;
            *a
        });
        self.c.iter_mut().take(K - 1).fold(d & 1, |mut y, c| {
            d >>= 1;
            (y, *c) = ((d & 1) + y - *c, y);
            y
        })
    }
}