bass-foundry/plugins/braze/core/tests/dsp.rs

// Sample indices address several signals at once.
#![allow(clippy::needless_range_loop)]
use braze_core::{cycles, envelope, Engine, Rate, Settings};
use common_dsp::Saw;
use std::f32::consts::TAU;

const RATE: f32 = 48000.;
const TEMPO: f64 = 120.;

fn engine(s: Settings) -> (Engine, usize) {
    let mut e = Engine::new(RATE, 2).unwrap();
    e.set_settings(s).unwrap();
    e.set_transport(Some(TEMPO), Some(0.));
    let l = e.latency_samples() as usize;
    (e, l)
}
fn seconds(t: f32) -> usize {
    (t * RATE) as usize
}
fn render(e: &mut Engine, x: &[f32]) -> Vec<[f32; 2]> {
    x.iter().map(|&s| e.process_sample([s, s])).collect()
}
/// A saw at `hz` from 0.05 s on, with a 1 ms fade-in.
fn saw(hz: f32, total: f32) -> Vec<f32> {
    let mut osc = Saw::new(RATE, hz);
    (0..seconds(total))
        .map(|i| {
            let start = seconds(0.05);
            if i < start {
                return 0.;
            }
            0.5 * osc.sample() * ((i - start) as f32 / seconds(0.001) as f32).min(1.)
        })
        .collect()
}
/// Amplitude of harmonic `n` of `hz` over one period centred on sample `at`.
fn harmonic(x: &[f32], at: usize, hz: f32, n: u32) -> f32 {
    let half = (RATE / hz / 2.).round() as usize;
    let w = TAU * hz * n as f32 / RATE;
    let (mut re, mut im) = (0f32, 0f32);
    for i in at - half..at + half {
        re += x[i] * (w * i as f32).cos();
        im -= x[i] * (w * i as f32).sin();
    }
    2. * (re * re + im * im).sqrt() / (2 * half) as f32
}
/// Beat position (quarter notes) of output sample `i`.
fn beats(i: usize, latency: usize) -> f64 {
    (i as f64 - latency as f64) / RATE as f64 * TEMPO / 60.
}

/// Harmonics 1–4 of A1 at falling levels, a periodic note the tracker reads exactly.
fn partials(t: f64) -> f64 {
    (1..=4)
        .map(|n| 0.4 / n as f64 * (std::f64::consts::TAU * 55. * n as f64 * t).sin())
        .sum()
}

#[test]
fn every_harmonic_beats_on_the_tempo_grid() {
    for (harmonic, rate) in [(1, Rate::Eighth), (2, Rate::Sixteenth), (3, Rate::Quarter)] {
        let s = Settings {
            harmonic,
            rate,
            depth: 100.,
            snap: true,
            low_cut: 0.,
            ..Settings::default()
        };
        let (mut e, l) = engine(s);
        let x: Vec<f32> = (0..seconds(1.5))
            .map(|i| partials(i as f64 / RATE as f64) as f32)
            .collect();
        let y = render(&mut e, &x);
        let mut worst = 0f32;
        for i in seconds(0.5)..seconds(1.4) {
            // Cycles of the chosen harmonic, from the grid alone: peaks on every multiple
            // of `rate`. The copy lags the bass by (0.5 − frac(u)) periods.
            let u = beats(i, l) / rate.quarters() / harmonic as f64 + 0.5;
            let t = (i - l) as f64 / RATE as f64;
            let lag = (0.5 - u.fract()) / 55.;
            let ideal = (partials(t) + partials(t - lag)) / 2f64.sqrt();
            worst = worst.max((y[i][0] - ideal as f32).abs());
        }
        assert!(worst < 3e-3, "harmonic {harmonic}, {rate:?}: {worst}");
    }
}

#[test]
fn envelope_peaks_on_the_grid_and_harmonic_n_beats_n_over_k_as_fast() {
    let s = Settings {
        harmonic: 2,
        ..Settings::default()
    };
    // At cycle 0 every harmonic peaks: twice the bass, less the loudness correction.
    for n in 1..=8 {
        assert!((envelope(&s, n, 0., 1.) - 2f32.sqrt()).abs() < 1e-5);
    }
    // Harmonic 2 nulls half a cycle later; harmonic 1, beating half as fast, a cycle later.
    assert!(envelope(&s, 2, 0.5, 1.) < 1e-5);
    assert!(envelope(&s, 1, 1., 1.) < 1e-5);
    assert!(envelope(&s, 4, 0.25, 1.) < 1e-5);
}

#[test]
fn the_copy_is_seamless_across_its_jumps() {
    // A pure sine at exactly A1: the ideal copy is a smooth sine whose phase follows the beat.
    let s = Settings {
        harmonic: 1,
        rate: Rate::Sixteenth,
        depth: 100.,
        snap: true,
        low_cut: 0.,
        ..Settings::default()
    };
    let (mut e, l) = engine(s);
    let x: Vec<f32> = (0..seconds(1.5))
        .map(|i| 0.5 * (TAU * 55. * i as f32 / RATE).sin())
        .collect();
    let y = render(&mut e, &x);
    let mut worst = 0f32;
    for i in seconds(0.5)..seconds(1.4) {
        let u = cycles(&s, beats(i, l), 0) + 0.5;
        let dry = x[i - l];
        let phase = TAU as f64 * (55. * (i - l) as f64 / RATE as f64 + u.fract());
        let copy = -0.5 * phase.sin() as f32;
        let ideal = (dry + copy) / 2f32.sqrt();
        worst = worst.max((y[i][0] - ideal).abs());
    }
    assert!(worst < 2e-3, "{worst}");
}

#[test]
fn depth_zero_is_the_delayed_input() {
    let (mut e, l) = engine(Settings {
        depth: 0.,
        low_cut: 0.,
        ..Settings::default()
    });
    let x = saw(55., 0.6);
    let y = render(&mut e, &x);
    for i in l..x.len() {
        assert_eq!(y[i][0], x[i - l]);
    }
}

#[test]
fn width_moves_the_right_channel_half_a_cycle() {
    let s = Settings {
        harmonic: 1,
        width: 100.,
        depth: 100.,
        rate: Rate::Quarter,
        low_cut: 0.,
        ..Settings::default()
    };
    let (mut e, l) = engine(s);
    let x = saw(55., 1.5);
    let y = render(&mut e, &x);
    let left: Vec<f32> = y.iter().map(|v| v[0]).collect();
    let right: Vec<f32> = y.iter().map(|v| v[1]).collect();
    // On the beat the left fundamental peaks and the right one nulls; half a beat later
    // they swap.
    for (beat, loud, quiet) in [
        (1., &left, &right),
        (1.5, &right, &left),
        (2., &left, &right),
    ] {
        let at = l + (beat / (TEMPO / 60.) * RATE as f64) as usize;
        let (a, b) = (harmonic(loud, at, 55., 1), harmonic(quiet, at, 55., 1));
        assert!(20. * (a / b).log10() > 20., "beat {beat}: {a} vs {b}");
    }
}

#[test]
fn note_changes_and_transport_jumps_do_not_click() {
    let s = Settings {
        depth: 100.,
        ..Settings::default()
    };
    let (mut e, _) = engine(s);
    // Phase-continuous sine from A1 to D2, no gap.
    let mut phase = 0f32;
    let x: Vec<f32> = (0..seconds(1.2))
        .map(|i| {
            let hz = if i < seconds(0.6) { 55. } else { 73.42 };
            phase = (phase + hz / RATE).fract();
            0.5 * (TAU * phase).sin()
        })
        .collect();
    let mut y = Vec::new();
    for (i, &v) in x.iter().enumerate() {
        if i == seconds(0.9) {
            // A locate to another bar.
            e.set_transport(Some(TEMPO), Some(37.3));
        }
        y.push(e.process_sample([v, v])[0]);
    }
    // Two sines of peak 0.5 at up to 79 Hz move at most this much per sample (after the
    // loudness correction), plus some room for the fades.
    let bound = 2. * 0.5 * TAU * 79. / RATE / 2f32.sqrt() * 1.5;
    for i in seconds(0.2)..y.len() - 1 {
        assert!(
            (y[i + 1] - y[i]).abs() < bound,
            "{i}: {}",
            (y[i + 1] - y[i]).abs()
        );
    }
}

#[test]
fn low_cut_keeps_the_sub_steady_and_the_beat_on_the_grid() {
    let s = Settings {
        harmonic: 1,
        depth: 100.,
        rate: Rate::Half,
        low_cut: 150.,
        ..Settings::default()
    };
    let (mut e, l) = engine(s);
    let x = saw(55., 2.4);
    let y: Vec<f32> = render(&mut e, &x).iter().map(|v| v[0]).collect();
    // One cycle (a half note, 1 s at 120 BPM): the fundamental, under the cut, does not beat.
    let sub: Vec<f32> = (0..50)
        .map(|k| harmonic(&y, seconds(1.) + k * seconds(0.02), 55., 1))
        .collect();
    let (lo, hi) = sub
        .iter()
        .fold((f32::MAX, 0f32), |(a, b), &v| (a.min(v), b.max(v)));
    // Without the cut it would null fully; what remains is leakage of the beating
    // harmonics into the one-period window.
    assert!(20. * (hi / lo).log10() < 1.5, "{lo} .. {hi}");
    // And it keeps its level: the loudness correction for the copy applies above the cut.
    let dry = harmonic(&x, seconds(1.) - l, 55., 1);
    let mean = sub.iter().sum::<f32>() / sub.len() as f32;
    assert!((20. * (mean / dry).log10()).abs() < 0.5, "{mean} vs {dry}");
    // Harmonic 6 (330 Hz) beats 6 times per cycle: it peaks on the grid, the high-pass's
    // phase is matched on the bass, and nulls 1/12 cycle later.
    for beat in [2., 4.] {
        let peak = l + (beat / (TEMPO / 60.) * RATE as f64) as usize;
        let null = peak + (RATE / 12.) as usize;
        let (a, b) = (harmonic(&y, peak, 55., 6), harmonic(&y, null, 55., 6));
        assert!(20. * (a / b).log10() > 15., "beat {beat}: {a} vs {b}");
    }
}

#[test]
fn the_ratio_follows_the_note() {
    let (mut e, _) = engine(Settings {
        harmonic: 1,
        ..Settings::default()
    });
    for hz in [55., 110.] {
        let x = saw(hz, 0.5);
        render(&mut e, &x);
        let f = e.take_analyzer();
        // An eighth at 120 BPM beats 4 times per second: r = 1 + 4 / f0.
        assert!((f.ratio - (1. + 4. / hz)).abs() < 2e-3, "{hz}: {}", f.ratio);
    }
}

#[test]
fn settings_are_validated_and_serialise() {
    let mut e = Engine::new(RATE, 1).unwrap();
    assert!(e
        .set_settings(Settings {
            harmonic: 0,
            ..Settings::default()
        })
        .is_err());
    let json = serde_json::to_string(&Settings::default()).unwrap();
    assert_eq!(
        serde_json::from_str::<Settings>(&json).unwrap(),
        Settings::default()
    );
    assert!(Engine::new(1000., 2).is_err());
    assert!(Engine::new(48000., 3).is_err());
}