sva-engine 0.7.15

// Concern: proves a named waveform is a function of its fundamental's phase, delayed or modulated whole | Non-concern: a written sum's own series (refs.rs) | IO: (a composition) -> samples

use std::f64::consts::TAU;

use crate::fixtures::graph_of;
use sva_engine::{RenderConfig, Tier, render};

const HALF_LSB: f64 = 1.0 / (1u64 << 24) as f64;

fn plane(files: &[(&str, &str)], root: &str, secs: f64) -> Vec<f64> {
    let g = graph_of(root, files);
    let held = render(
        &g,
        root,
        RenderConfig::seconds(44_100, secs),
        &Tier::default(),
    )
    .expect("a waveform renders");
    let id = held.id(root).expect("the root");
    held.output(id).expect("its samples").plane(0).to_vec()
}

fn peak(samples: &[f64]) -> f64 {
    samples.iter().fold(0.0f64, |held, s| held.max(s.abs()))
}

/// `pi/10` at 441 Hz delays the wave by exactly five steps at 44.1 kHz.
#[test]
fn a_constant_phase_delays_the_whole_wave() {
    for name in ["saw", "square", "triangle"] {
        let plain = plane(&[("plain", &format!("{name}(441)\n"))], "plain", 0.06);
        let phased = plane(
            &[("phased", &format!("{name}(441, pi/10)\n"))],
            "phased",
            0.05,
        );
        for (i, s) in phased.iter().enumerate() {
            let want = plain[i + 5];
            assert!(
                (s - want).abs() <= HALF_LSB,
                "{name} sample {i}: {s} against the plain wave's {want}"
            );
        }
    }
}

#[test]
fn a_quarter_turn_keeps_the_saw_s_peak() {
    let plain = plane(&[("plain", "saw(100)\n")], "plain", 0.05);
    let turned = plane(&[("turned", "saw(100, pi/2)\n")], "turned", 0.05);
    let (a, b) = (peak(&plain), peak(&turned));
    assert!(
        (a - b).abs() < 0.02 * a,
        "a delayed saw peaks as a saw: {b} against {a}"
    );
}

const VIBRATO: &str = "0.3*sin(2*pi*5*t)";

/// A moving phase is the plain wave read at a moving time, every harmonic under the band kept.
#[test]
fn a_moving_phase_is_the_plain_wave_read_at_a_moving_time() {
    let files = [
        ("plain", "saw(220)\n".to_string()),
        ("warped", format!("@plain(t + {VIBRATO}/(2*pi*220))\n")),
        ("vibrato", format!("saw(220, {VIBRATO})\n")),
    ];
    let files: Vec<(&str, &str)> = files.iter().map(|(k, v)| (*k, v.as_str())).collect();
    let warped = plane(&files, "warped", 0.05);
    let vibrato = plane(&files, "vibrato", 0.05);
    for (i, (s, want)) in vibrato.iter().zip(&warped).enumerate() {
        assert!(
            (s - want).abs() <= HALF_LSB,
            "sample {i}: {s} against the warped read's {want}"
        );
    }
}

/// The share of a signal's energy in DFT bins above `hz`.
fn share_above(samples: &[f64], hz: f64, rate: f64) -> f64 {
    let n = samples.len();
    let bin = |k: usize| {
        let (mut re, mut im) = (0.0, 0.0);
        for (i, s) in samples.iter().enumerate() {
            let w = TAU * (k * i % n) as f64 / n as f64;
            re += s * w.cos();
            im -= s * w.sin();
        }
        re * re + im * im
    };
    let total: f64 = samples.iter().map(|s| s * s).sum::<f64>() * n as f64 / 2.0;
    let from = (hz / rate * n as f64).ceil() as usize;
    (from..n / 2).map(bin).sum::<f64>() / total
}

/// The plain saw's harmonics from 15 kHz to the ceiling hold about 0.2% of its energy.
#[test]
fn a_vibrato_saw_keeps_its_harmonics_up_to_the_ceiling() {
    let files = [
        ("plain", "saw(220)\n".to_string()),
        ("vibrato", format!("saw(220, {VIBRATO})\n")),
    ];
    let files: Vec<(&str, &str)> = files.iter().map(|(k, v)| (*k, v.as_str())).collect();
    let [plain, vibrato] = ["plain", "vibrato"]
        .map(|root| share_above(&plane(&files, root, 0.1)[..4096], 15_000.0, 44_100.0));
    assert!(
        (vibrato / plain - 1.0).abs() < 0.2 && plain > 1e-3,
        "energy above 15 kHz: {vibrato} against the plain saw's {plain}"
    );
}