//! S2-3 pre-flight (host): the flag + cylinder body at ny 62 — the mask
//! builds, its cut geometry closes, the counts and the build time (the
//! moving body's per-step host rebuild cost) are recorded.
use rtx_cfd::solvers::incompressible::embedded3::{Body, Boundaries, Grid, Mask, Side};

const H: f64 = 0.41;
const FLAG_X0: f64 = 0.6;
const FLAG_LEN: f64 = 0.35;
const FLAG_HALF: f64 = 0.01;
const FLAG_SPAN: f64 = 0.2;
const AMP: f64 = 0.084;
const BETA_L: f64 = 1.875_104_069;

fn mode(s: f64) -> f64 {
    let b = BETA_L;
    let sigma = (b.sinh() - b.sin()) / (b.cosh() + b.cos());
    let phi = |s: f64| (b * s).cosh() - (b * s).cos() - sigma * ((b * s).sinh() - (b * s).sin());
    phi(s) / phi(1.0)
}

fn flag_2d(x: f64, y: f64, phase: f64) -> f64 {
    let n = 40;
    let mut best = f64::INFINITY;
    let point = |m: usize| {
        let s = m as f64 / n as f64;
        (FLAG_X0 + s * FLAG_LEN, 0.2 + AMP * mode(s) * phase)
    };
    for m in 0..n {
        let (ax, ay) = point(m);
        let (bx, by) = point(m + 1);
        let (ex, ey) = (bx - ax, by - ay);
        let u = (((x - ax) * ex + (y - ay) * ey) / (ex * ex + ey * ey)).clamp(0.0, 1.0);
        let d = ((x - ax - u * ex).powi(2) + (y - ay - u * ey).powi(2)).sqrt();
        best = best.min(d);
    }
    best - FLAG_HALF
}

fn flag_3d(x: f64, y: f64, z: f64, phase: f64, r: f64) -> f64 {
    let d2 = flag_2d(x, y, phase);
    let q1 = d2 + r;
    let q2 = (z - 0.5 * H).abs() - 0.5 * FLAG_SPAN + r;
    (q1.max(0.0).powi(2) + q2.max(0.0).powi(2)).sqrt() + q1.max(q2).min(0.0) - r
}

#[test]
fn flag_body_builds_at_ny_62() {
    let ny = 62;
    let h = H / ny as f64;
    let nx = (2.5 / h).round() as usize;
    let g = Grid::cubic(nx, ny, ny, h);
    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
    for phase in [0.0, 1.0] {
        let body = Body::from_sdf(move |x, y, z, _t| cyl(x, y).min(flag_3d(x, y, z, phase, h)));
        let b = Boundaries {
            x1: Side::PressureOutlet,
            ..Boundaries::default()
        };
        let start = std::time::Instant::now();
        let mask = Mask::build_cut(&body, g, 0.0, b).expect("mask");
        let build = start.elapsed().as_secs_f64();
        let cut = mask.cut().unwrap();
        let (area, closure) = cut.wall_area_and_closure();
        let solid = g.cells() - mask.fluid_cells();
        println!(
            "  phase {phase}: {} cells, {} fluid, {solid} solid, {} merged; wall area {area:.4} m² (cylinder 0.129 + flag ~0.156), closure {:.2e}; build {build:.2} s",
            g.cells(),
            mask.fluid_cells(),
            mask.merged_cells(),
            (closure[0].powi(2) + closure[1].powi(2) + closure[2].powi(2)).sqrt()
        );
        assert!(solid > 1000 && mask.fluid_cells() > g.cells() / 2);
        assert!((closure[0].powi(2) + closure[1].powi(2) + closure[2].powi(2)).sqrt() < 1e-9);
    }
}

/// Where the per-step host rebuild's time goes at ny 62 (S2-2b's target).
#[test]
#[ignore = "profile: the rebuild's parts at ny 62 (seconds)"]
fn rebuild_profile_at_ny_62() {
    use rtx_cfd::solvers::incompressible::embedded3::CutGeometry;
    let ny = 62;
    let h = H / ny as f64;
    let nx = (2.5 / h).round() as usize;
    let g = Grid::cubic(nx, ny, ny, h);
    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
    let body = Body::from_sdf(move |x, y, z, _t| cyl(x, y).min(flag_3d(x, y, z, 0.3, h)));
    let b = Boundaries {
        x1: Side::PressureOutlet,
        ..Boundaries::default()
    };
    let t0 = std::time::Instant::now();
    let _cut = CutGeometry::build(&body, g, 0.0);
    let t_cut = t0.elapsed().as_secs_f64();
    let t1 = std::time::Instant::now();
    let nodes = (nx + 1) * (ny + 1) * (ny + 1);
    let mut acc = 0.0;
    for n in 0..nodes {
        let (k, j, i) = (
            n / ((nx + 1) * (ny + 1)),
            (n / (nx + 1)) % (ny + 1),
            n % (nx + 1),
        );
        acc += body.phi(i as f64 * h, j as f64 * h, k as f64 * h, 0.0);
    }
    let t_phi = t1.elapsed().as_secs_f64();
    let t2 = std::time::Instant::now();
    let mask = Mask::build_cut(&body, g, 0.0, b).expect("mask");
    let t_mask = t2.elapsed().as_secs_f64();
    let t3 = std::time::Instant::now();
    let (_table, _) = mask.wall_flux_table(&body, 0.0);
    let t_flux = t3.elapsed().as_secs_f64();
    println!(
        "  ny 62 rebuild parts: cut geometry {t_cut:.2} s (of which φ at {nodes} nodes {t_phi:.2} s), whole mask build {t_mask:.2} s, wall-flux table {t_flux:.2} s (Σφ {acc:.1})"
    );
}

/// The narrow band is invisible to the solution: the moving circle
/// marched with and without `max_surface_speed` gives bit-identical
/// fields; the flag body's rebuild time at ny 62 with the band recorded.
#[test]
fn narrow_band_is_bit_identical_and_fast() {
    use rtx_cfd::solvers::incompressible::ConvectionScheme;
    use rtx_cfd::solvers::incompressible::embedded3::{
        CutGeometry, Field, Fluid, Parameters, Solver, WallScheme,
    };
    let n = 76;
    let h = 1.0 / n as f64;
    let dt = 3.24e-4;
    let run = |band: bool| {
        let mut solver = Solver::new(
            Fluid {
                density: 1000.0,
                viscosity: 1.0,
                reference_velocity: 1.0,
                reference_length: 0.1,
            },
            Parameters {
                corrector_steps: 2,
                tolerance: 1e-8,
                convection_scheme: ConvectionScheme::Upwind,
                wall_scheme: WallScheme::CutCell,
                boundaries: Boundaries {
                    z0: Side::Periodic,
                    z1: Side::Periodic,
                    ..Boundaries::default()
                },
                max_surface_speed: band.then_some(1.0),
                ..Parameters::default()
            },
        );
        solver.set_boundary_velocity(|_, _, _, _| (0.0, 0.0, 0.0));
        let yc = |t: f64| 0.5 + 0.08 * (t / 0.08).sin();
        let vc = |t: f64| (t / 0.08).cos();
        solver.set_moving_body(
            Body::from_sdf(move |x, y, _z, t| {
                ((x - 0.5_f64).powi(2) + (y - yc(t)).powi(2)).sqrt() - 0.05
            })
            .with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0)),
        );
        let g = Grid::cubic(n, n, 4, h);
        let mut f = Field::new(g);
        solver.initialize(&mut f);
        let start = std::time::Instant::now();
        for _ in 0..40 {
            solver.advance(&mut f, dt);
        }
        (f, start.elapsed().as_secs_f64())
    };
    let (full, t_full) = run(false);
    let (band, t_band) = run(true);
    let same = full.u == band.u && full.v == band.v && full.w == band.w && full.p == band.p;
    println!(
        "  moving circle 76²×4, 40 steps: full {t_full:.2} s, band {t_band:.2} s; fields bit-identical: {same}"
    );
    assert!(same, "the narrow band changed the solution");
    // The flag body at ny 62: a full build, then a banded rebuild after a small motion.
    let ny = 62;
    let hh = H / ny as f64;
    let nx = (2.5 / hh).round() as usize;
    let g = Grid::cubic(nx, ny, ny, hh);
    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
    let body = Body::from_sdf(move |x, y, z, t| cyl(x, y).min(flag_3d(x, y, z, t, hh)));
    let t0 = std::time::Instant::now();
    let prev = CutGeometry::build(&body, g, 0.3);
    let t_prev = t0.elapsed().as_secs_f64();
    let t1 = std::time::Instant::now();
    let next = CutGeometry::build_from(&body, g, 0.31, Some((&prev, 3.0 * hh, 1.0e-3)));
    let t_next = t1.elapsed().as_secs_f64();
    let exact = CutGeometry::build(&body, g, 0.31);
    let vol_same = next.vol == exact.vol
        && next.a_u == exact.a_u
        && next.a_v == exact.a_v
        && next.a_w == exact.a_w;
    println!(
        "  flag ny 62: full build {t_prev:.2} s, banded rebuild {t_next:.2} s; volumes and apertures identical to a full build: {vol_same}"
    );
    assert!(vol_same);
}

/// The per-step operator cost at ny 62 (host side of the device CG's
/// rebuild: the problem, the fine level, the components, the hierarchy
/// export) — S2-2b-ii's target.
#[test]
#[ignore = "profile: the operator export at ny 62 (seconds)"]
fn operator_export_profile_at_ny_62() {
    use rtx_cfd::solvers::incompressible::embedded3::poisson::export::export_hierarchy;
    use rtx_cfd::solvers::incompressible::embedded3::{
        Field, Fluid, Parameters, Solver, WallScheme,
    };
    use rtx_cfd::solvers::incompressible::{ConvectionScheme, MultigridParameters};
    let ny = 62;
    let h = H / ny as f64;
    let nx = (2.5 / h).round() as usize;
    let g = Grid::cubic(nx, ny, ny, h);
    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
    let body = Body::from_sdf(move |x, y, z, _t| cyl(x, y).min(flag_3d(x, y, z, 0.3, h)));
    let mut solver = Solver::new(
        Fluid {
            density: 1000.0,
            viscosity: 1.0,
            reference_velocity: 1.0,
            reference_length: 0.1,
        },
        Parameters {
            wall_scheme: WallScheme::CutCell,
            convection_scheme: ConvectionScheme::TvdVanAlbada,
            boundaries: Boundaries {
                x1: Side::PressureOutlet,
                ..Boundaries::default()
            },
            ..Parameters::default()
        },
    );
    solver.set_body(body);
    let mut f = Field::new(g);
    let t0 = std::time::Instant::now();
    solver.initialize(&mut f);
    let t_init = t0.elapsed().as_secs_f64();
    let t1 = std::time::Instant::now();
    let problem = solver.poisson_operator(g, 1e-3);
    let t_op = t1.elapsed().as_secs_f64();
    let t2 = std::time::Instant::now();
    let levels = export_hierarchy(&problem, &MultigridParameters::default());
    let t_exp = t2.elapsed().as_secs_f64();
    println!(
        "  ny 62 operator: initialize (mask + impose) {t_init:.2} s, poisson_operator {t_op:.2} s, export_hierarchy {t_exp:.2} s ({} levels, {} links)",
        levels.len(),
        problem.links.len()
    );
}

/// The residual clause's remedy, measured on the moving circle (host):
/// the worst mass residual over 100 steps with two correctors at the
/// 1e-2 inner stop against three correctors at 1e-3.
#[test]
#[ignore = "residual study on the moving circle (host, a minute)"]
fn moving_circle_residual_remedy() {
    use rtx_cfd::solvers::incompressible::ConvectionScheme;
    use rtx_cfd::solvers::incompressible::embedded3::{
        Field, Fluid, Parameters, Solver, WallScheme,
    };
    let n = 152;
    let h = 1.0 / n as f64;
    let dt = 3.24e-4;
    for (correctors, inner) in [(2usize, 1e-2), (3, 1e-3), (4, 1e-4)] {
        let mut solver = Solver::new(
            Fluid {
                density: 1000.0,
                viscosity: 1.0,
                reference_velocity: 1.0,
                reference_length: 0.1,
            },
            Parameters {
                corrector_steps: correctors,
                tolerance: 1e-8,
                inner_stop_factor: inner,
                convection_scheme: ConvectionScheme::Upwind,
                wall_scheme: WallScheme::CutCell,
                boundaries: Boundaries {
                    z0: Side::Periodic,
                    z1: Side::Periodic,
                    ..Boundaries::default()
                },
                max_surface_speed: Some(1.0),
                ..Parameters::default()
            },
        );
        solver.set_boundary_velocity(|_, _, _, _| (0.0, 0.0, 0.0));
        let yc = |t: f64| 0.5 + 0.08 * (t / 0.08).sin();
        let vc = |t: f64| (t / 0.08).cos();
        solver.set_moving_body(
            Body::from_sdf(move |x, y, _z, t| {
                ((x - 0.5_f64).powi(2) + (y - yc(t)).powi(2)).sqrt() - 0.05
            })
            .with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0)),
        );
        let g = Grid::cubic(n, n, 4, h);
        let mut f = Field::new(g);
        solver.initialize(&mut f);
        let (mut worst, mut sum_cg, mut sum_corr) = (0.0_f64, 0usize, 0usize);
        let start = std::time::Instant::now();
        for _ in 0..100 {
            let r = solver.advance(&mut f, dt);
            worst = worst.max(r.final_residual);
            sum_cg += r.poisson_iterations;
            sum_corr += r.corrector_steps_performed;
        }
        println!(
            "  correctors {correctors} inner {inner:.0e}: worst residual {worst:.2e}, CG {:.1}/step, correctors {:.2}/step, {:.2} s",
            sum_cg as f64 / 100.0,
            sum_corr as f64 / 100.0,
            start.elapsed().as_secs_f64()
        );
    }
}