spacelab-gnss 0.3.0

//! Single-frequency propagation-delay models — the ionospheric and tropospheric corrections a
//! receiver applies to a pseudorange, completing the GNSS error budget alongside the orbits.
//!
//! [`klobuchar_iono_delay`] is the broadcast ionosphere model of IS-GPS-200 §20.3.3.5.2.5 (the α/β
//! coefficients are broadcast in the navigation message); [`saastamoinen_zenith_hydrostatic`] and
//! [`saastamoinen_zenith_wet`] are the classic tropospheric zenith delays, projected to a slant path
//! by [`obliquity_mapping`].

// The Klobuchar/Saastamoinen notation uses single letters; the doc allow covers spec/author names;
// the Niell/GMF coefficient tables are kept byte-identical to the primary source (no digit
// separators); the Niell latitude segment is a small bounded integer index; the GMF `c0h`/`c10h`/
// `c11h` names are the paper's own; the GMF harmonic loops index by degree `n` and order `m`, which
// are also used as arithmetic quantities (m·λ, factorials, powers) alongside a running index `j`.
#![allow(
    clippy::many_single_char_names,
    clippy::doc_markdown,
    clippy::unreadable_literal,
    clippy::cast_possible_truncation,
    clippy::cast_sign_loss,
    clippy::cast_precision_loss,
    clippy::similar_names,
    clippy::needless_range_loop
)]

use spacelab_autodiff::Scalar;

const PI: f64 = core::f64::consts::PI;
const TAU: f64 = core::f64::consts::TAU;
/// Speed of light, m/s (IS-GPS-200 §20.3.4.3).
const SPEED_OF_LIGHT: f64 = 299_792_458.0;

/// Reduce `x` into `[0, 86400)` seconds without `f64::rem_euclid` (a `std` method).
fn wrap_day(x: f64) -> f64 {
    x - 86_400.0 * libm::floor(x / 86_400.0)
}

/// The broadcast (Klobuchar) L1 ionospheric delay, **metres**, per IS-GPS-200 §20.3.3.5.2.5.
///
/// `alpha`/`beta` are the eight broadcast coefficients; `lat`/`lon` the receiver geodetic latitude and
/// longitude, `elevation`/`azimuth` the satellite look angles, all radians; `gps_sod` GPS time in
/// seconds of the day. The result is the single-frequency slant delay to scale to another band by the
/// squared frequency ratio.
#[must_use]
pub fn klobuchar_iono_delay(
    alpha: [f64; 4],
    beta: [f64; 4],
    lat: f64,
    lon: f64,
    elevation: f64,
    azimuth: f64,
    gps_sod: f64,
) -> f64 {
    // The algorithm works in semicircles (1 sc = π rad); azimuth stays in radians for sin/cos.
    let e = elevation / PI;
    let phi_u = lat / PI;
    let lam_u = lon / PI;

    let psi = 0.0137 / (e + 0.11) - 0.022; // Earth-centred angle, sc
    let phi_i = (phi_u + psi * libm::cos(azimuth)).clamp(-0.416, 0.416); // sub-ionospheric lat
    let lam_i = lam_u + psi * libm::sin(azimuth) / libm::cos(phi_i * PI); // sub-ionospheric lon
    let phi_m = phi_i + 0.064 * libm::cos((lam_i - 1.617) * PI); // geomagnetic lat

    let t = wrap_day(43_200.0 * lam_i + gps_sod); // local time, s
    let f = 1.0 + 16.0 * libm::pow(0.53 - e, 3.0); // obliquity factor

    let amp = (alpha[0] + phi_m * (alpha[1] + phi_m * (alpha[2] + phi_m * alpha[3]))).max(0.0);
    let per = (beta[0] + phi_m * (beta[1] + phi_m * (beta[2] + phi_m * beta[3]))).max(72_000.0);
    let x = 2.0 * PI * (t - 50_400.0) / per;

    let seconds = if libm::fabs(x) < 1.57 {
        f * (5.0e-9 + amp * (1.0 - x * x / 2.0 + x * x * x * x / 24.0))
    } else {
        f * 5.0e-9
    };
    seconds * SPEED_OF_LIGHT
}

/// The Saastamoinen zenith **hydrostatic** (dry) tropospheric delay, metres. `pressure` is the total
/// surface pressure in hPa, `lat` the geodetic latitude (rad), `height` the ellipsoidal height (m).
/// At sea level and mid-latitude this is ≈ 2.3 m — the bulk of the tropospheric delay.
#[must_use]
pub fn saastamoinen_zenith_hydrostatic(pressure: f64, lat: f64, height: f64) -> f64 {
    0.002_276_8 * pressure / (1.0 - 0.002_66 * libm::cos(2.0 * lat) - 0.000_000_28 * height)
}

/// The Saastamoinen zenith **wet** tropospheric delay, metres, from the surface temperature `temp_k`
/// (K) and the partial pressure of water vapour `e_hpa` (hPa). Small (cm–dm) and highly variable.
#[must_use]
pub fn saastamoinen_zenith_wet(temp_k: f64, e_hpa: f64) -> f64 {
    0.002_277 * (1255.0 / temp_k + 0.05) * e_hpa
}

/// The simple obliquity mapping `1/sin(elevation)` that projects a zenith delay onto a slant path
/// (Saastamoinen's own cosecant projection). `elevation` in radians.
///
/// Generic over [`Scalar`] like every mapping function in this module: see `niell_fraction` for
/// why the elevation argument, and only the elevation argument, carries the type parameter.
#[must_use]
pub fn obliquity_mapping<S: Scalar>(elevation: S) -> S {
    S::from_f64(1.0) / elevation.sin()
}

// Niell (1996) mapping-function coefficient tables at latitudes 15°/30°/45°/60°/75°.
// Source: A. E. Niell, "Global mapping functions for the atmosphere delay at radio wavelengths",
// J. Geophys. Res. 101(B2), 3227–3246 (1996), doi:10.1029/95JB03048.
const NIELL_AH_AVG: [f64; 5] = [
    1.2769934e-3,
    1.2683230e-3,
    1.2465397e-3,
    1.2196049e-3,
    1.2045996e-3,
];
const NIELL_BH_AVG: [f64; 5] = [
    2.9153695e-3,
    2.9152299e-3,
    2.9288445e-3,
    2.9022565e-3,
    2.9024912e-3,
];
const NIELL_CH_AVG: [f64; 5] = [
    62.610505e-3,
    62.837393e-3,
    63.721774e-3,
    63.824265e-3,
    64.258455e-3,
];
const NIELL_AH_AMP: [f64; 5] = [0.0, 1.2709626e-5, 2.6523662e-5, 3.4000452e-5, 4.1202191e-5];
const NIELL_BH_AMP: [f64; 5] = [0.0, 2.1414979e-5, 3.0160779e-5, 7.2562722e-5, 11.723375e-5];
const NIELL_CH_AMP: [f64; 5] = [0.0, 9.0128400e-5, 4.3497037e-5, 84.795348e-5, 170.37206e-5];
const NIELL_AW: [f64; 5] = [
    5.8021897e-4,
    5.6794847e-4,
    5.8118019e-4,
    5.9727542e-4,
    6.1641693e-4,
];
const NIELL_BW: [f64; 5] = [
    1.4275268e-3,
    1.5138625e-3,
    1.4572752e-3,
    1.5007428e-3,
    1.7599082e-3,
];
const NIELL_CW: [f64; 5] = [
    4.3472961e-2,
    4.6729510e-2,
    4.3908931e-2,
    4.4626982e-2,
    5.4736038e-2,
];

/// Piecewise-linear interpolation of a Niell table over the 15°…75° latitude nodes (15° spacing),
/// clamped to the table range. `lat_deg` is the absolute geodetic latitude in degrees.
fn niell_interp(table: &[f64; 5], lat_deg: f64) -> f64 {
    let x = lat_deg.clamp(15.0, 75.0);
    let seg = (((x - 15.0) / 15.0) as usize).min(3);
    let x0 = 15.0 + 15.0 * seg as f64;
    let frac = (x - x0) / 15.0;
    table[seg] + frac * (table[seg + 1] - table[seg])
}

/// The normalized Marini/Herring continued fraction `m(a,b,c,ε)` shared by every Niell factor.
///
/// **Only `elevation` is generic.** The `a`, `b` and `c` coefficients come from a table, a
/// spherical-harmonic expansion or a numerical weather model — they are constants of the
/// observation, not functions of the satellite state, and lifting them into the dual would carry
/// derivative slots that are structurally zero through every one of these evaluations.
///
/// The elevation is the one argument that moves with the orbit, and it is the reason this signature
/// changed at all: `spacelab_estimation::SlantDelay` is stated over [`Scalar`] because a delay
/// evaluated at `f64` enters a filter with a **zero** elevation partial, and `∂m/∂ε` at 10° is the
/// largest term in a tropospheric correction's own Jacobian. At `S = f64` every operation below is
/// the one that was here before, in the same order, so the published-value tests are unchanged.
fn niell_fraction<S: Scalar>(a: f64, b: f64, c: f64, elevation: S) -> S {
    let sin_e = elevation.sin();
    let num = 1.0 + a / (1.0 + b / (1.0 + c));
    let den = sin_e + S::from_f64(a) / (sin_e + S::from_f64(b) / (sin_e + S::from_f64(c)));
    S::from_f64(num) / den
}

/// The Niell (1996) tropospheric mapping functions `(hydrostatic, wet)` — the accurate replacement
/// for [`obliquity_mapping`]. `latitude` (geodetic, rad), `height` (ellipsoidal, m), `day_of_year`
/// (1–366, day fraction allowed), `elevation` (rad).
///
/// The hydrostatic factor is latitude- and season-dependent (a cosine of day-of-year about day 28,
/// shifted half a year in the southern hemisphere) with a height correction; the wet factor is
/// latitude-dependent only. Ported from Orekit's `NiellMappingFunctionModel`.
#[must_use]
pub fn niell_mapping<S: Scalar>(
    latitude: f64,
    height: f64,
    day_of_year: f64,
    elevation: S,
) -> (S, S) {
    let lat_deg = libm::fabs(latitude) * 180.0 / PI;
    let t0 = if latitude < 0.0 { 28.0 + 183.0 } else { 28.0 };
    let cos_coef = libm::cos(2.0 * PI * (day_of_year - t0) / 365.25);

    let ah = niell_interp(&NIELL_AH_AVG, lat_deg) - niell_interp(&NIELL_AH_AMP, lat_deg) * cos_coef;
    let bh = niell_interp(&NIELL_BH_AVG, lat_deg) - niell_interp(&NIELL_BH_AMP, lat_deg) * cos_coef;
    let ch = niell_interp(&NIELL_CH_AVG, lat_deg) - niell_interp(&NIELL_CH_AMP, lat_deg) * cos_coef;

    // Height correction (Niell Eqs. 4/6/7): the coefficients are fixed, height in km.
    let sin_e = elevation.sin();
    let correction = (S::from_f64(1.0) / sin_e
        - niell_fraction(2.53e-5, 5.49e-3, 1.14e-3, elevation))
        * S::from_f64(height.max(0.0) / 1000.0);

    let hydrostatic = niell_fraction(ah, bh, ch, elevation) + correction;
    let wet = niell_fraction(
        niell_interp(&NIELL_AW, lat_deg),
        niell_interp(&NIELL_BW, lat_deg),
        niell_interp(&NIELL_CW, lat_deg),
        elevation,
    );
    (hydrostatic, wet)
}

/// GMF multiplicative factor applied to every spherical-harmonic coefficient (Böhm et al. 2006).
const GMF_FACTOR: f64 = 1.0e-5;

const GMF_AH_MEAN: [f64; 55] = [
    1.2517e02, 8.503e-01, 6.936e-02, -6.760e+00, 1.771e-01, 1.130e-02, 5.963e-01, 1.808e-02,
    2.801e-03, -1.414e-03, -1.212e+00, 9.300e-02, 3.683e-03, 1.095e-03, 4.671e-05, 3.959e-01,
    -3.867e-02, 5.413e-03, -5.289e-04, 3.229e-04, 2.067e-05, 3.000e-01, 2.031e-02, 5.900e-03,
    4.573e-04, -7.619e-05, 2.327e-06, 3.845e-06, 1.182e-01, 1.158e-02, 5.445e-03, 6.219e-05,
    4.204e-06, -2.093e-06, 1.540e-07, -4.280e-08, -4.751e-01, -3.490e-02, 1.758e-03, 4.019e-04,
    -2.799e-06, -1.287e-06, 5.468e-07, 7.580e-08, -6.300e-09, -1.160e-01, 8.301e-03, 8.771e-04,
    9.955e-05, -1.718e-06, -2.012e-06, 1.170e-08, 1.790e-08, -1.300e-09, 1.000e-10,
];

const GMF_BH_MEAN: [f64; 55] = [
    0.000e+00, 0.000e+00, 3.249e-02, 0.000e+00, 3.324e-02, 1.850e-02, 0.000e+00, -1.115e-01,
    2.519e-02, 4.923e-03, 0.000e+00, 2.737e-02, 1.595e-02, -7.332e-04, 1.933e-04, 0.000e+00,
    -4.796e-02, 6.381e-03, -1.599e-04, -3.685e-04, 1.815e-05, 0.000e+00, 7.033e-02, 2.426e-03,
    -1.111e-03, -1.357e-04, -7.828e-06, 2.547e-06, 0.000e+00, 5.779e-03, 3.133e-03, -5.312e-04,
    -2.028e-05, 2.323e-07, -9.100e-08, -1.650e-08, 0.000e+00, 3.688e-02, -8.638e-04, -8.514e-05,
    -2.828e-05, 5.403e-07, 4.390e-07, 1.350e-08, 1.800e-09, 0.000e+00, -2.736e-02, -2.977e-04,
    8.113e-05, 2.329e-07, 8.451e-07, 4.490e-08, -8.100e-09, -1.500e-09, 2.000e-10,
];

const GMF_AH_AMPL: [f64; 55] = [
    -2.738e-01, -2.837e+00, 1.298e-02, -3.588e-01, 2.413e-02, 3.427e-02, -7.624e-01, 7.272e-02,
    2.160e-02, -3.385e-03, 4.424e-01, 3.722e-02, 2.195e-02, -1.503e-03, 2.426e-04, 3.013e-01,
    5.762e-02, 1.019e-02, -4.476e-04, 6.790e-05, 3.227e-05, 3.123e-01, -3.535e-02, 4.840e-03,
    3.025e-06, -4.363e-05, 2.854e-07, -1.286e-06, -6.725e-01, -3.730e-02, 8.964e-04, 1.399e-04,
    -3.990e-06, 7.431e-06, -2.796e-07, -1.601e-07, 4.068e-02, -1.352e-02, 7.282e-04, 9.594e-05,
    2.070e-06, -9.620e-08, -2.742e-07, -6.370e-08, -6.300e-09, 8.625e-02, -5.971e-03, 4.705e-04,
    2.335e-05, 4.226e-06, 2.475e-07, -8.850e-08, -3.600e-08, -2.900e-09, 0.000e+00,
];

const GMF_BH_AMPL: [f64; 55] = [
    0.000e+00, 0.000e+00, -1.136e-01, 0.000e+00, -1.868e-01, -1.399e-02, 0.000e+00, -1.043e-01,
    1.175e-02, -2.240e-03, 0.000e+00, -3.222e-02, 1.333e-02, -2.647e-03, -2.316e-05, 0.000e+00,
    5.339e-02, 1.107e-02, -3.116e-03, -1.079e-04, -1.299e-05, 0.000e+00, 4.861e-03, 8.891e-03,
    -6.448e-04, -1.279e-05, 6.358e-06, -1.417e-07, 0.000e+00, 3.041e-02, 1.150e-03, -8.743e-04,
    -2.781e-05, 6.367e-07, -1.140e-08, -4.200e-08, 0.000e+00, -2.982e-02, -3.000e-03, 1.394e-05,
    -3.290e-05, -1.705e-07, 7.440e-08, 2.720e-08, -6.600e-09, 0.000e+00, 1.236e-02, -9.981e-04,
    -3.792e-05, -1.355e-05, 1.162e-06, -1.789e-07, 1.470e-08, -2.400e-09, -4.000e-10,
];

const GMF_AW_MEAN: [f64; 55] = [
    5.640e+01, 1.555e+00, -1.011e+00, -3.975e+00, 3.171e-02, 1.065e-01, 6.175e-01, 1.376e-01,
    4.229e-02, 3.028e-03, 1.688e+00, -1.692e-01, 5.478e-02, 2.473e-02, 6.059e-04, 2.278e+00,
    6.614e-03, -3.505e-04, -6.697e-03, 8.402e-04, 7.033e-04, -3.236e+00, 2.184e-01, -4.611e-02,
    -1.613e-02, -1.604e-03, 5.420e-05, 7.922e-05, -2.711e-01, -4.406e-01, -3.376e-02, -2.801e-03,
    -4.090e-04, -2.056e-05, 6.894e-06, 2.317e-06, 1.941e+00, -2.562e-01, 1.598e-02, 5.449e-03,
    3.544e-04, 1.148e-05, 7.503e-06, -5.667e-07, -3.660e-08, 8.683e-01, -5.931e-02, -1.864e-03,
    -1.277e-04, 2.029e-04, 1.269e-05, 1.629e-06, 9.660e-08, -1.015e-07, -5.000e-10,
];

const GMF_BW_MEAN: [f64; 55] = [
    0.000e+00, 0.000e+00, 2.592e-01, 0.000e+00, 2.974e-02, -5.471e-01, 0.000e+00, -5.926e-01,
    -1.030e-01, -1.567e-02, 0.000e+00, 1.710e-01, 9.025e-02, 2.689e-02, 2.243e-03, 0.000e+00,
    3.439e-01, 2.402e-02, 5.410e-03, 1.601e-03, 9.669e-05, 0.000e+00, 9.502e-02, -3.063e-02,
    -1.055e-03, -1.067e-04, -1.130e-04, 2.124e-05, 0.000e+00, -3.129e-01, 8.463e-03, 2.253e-04,
    7.413e-05, -9.376e-05, -1.606e-06, 2.060e-06, 0.000e+00, 2.739e-01, 1.167e-03, -2.246e-05,
    -1.287e-04, -2.438e-05, -7.561e-07, 1.158e-06, 4.950e-08, 0.000e+00, -1.344e-01, 5.342e-03,
    3.775e-04, -6.756e-05, -1.686e-06, -1.184e-06, 2.768e-07, 2.730e-08, 5.700e-09,
];

const GMF_AW_AMPL: [f64; 55] = [
    1.023e-01, -2.695e+00, 3.417e-01, -1.405e-01, 3.175e-01, 2.116e-01, 3.536e+00, -1.505e-01,
    -1.660e-02, 2.967e-02, 3.819e-01, -1.695e-01, -7.444e-02, 7.409e-03, -6.262e-03, -1.836e+00,
    -1.759e-02, -6.256e-02, -2.371e-03, 7.947e-04, 1.501e-04, -8.603e-01, -1.360e-01, -3.629e-02,
    -3.706e-03, -2.976e-04, 1.857e-05, 3.021e-05, 2.248e+00, -1.178e-01, 1.255e-02, 1.134e-03,
    -2.161e-04, -5.817e-06, 8.836e-07, -1.769e-07, 7.313e-01, -1.188e-01, 1.145e-02, 1.011e-03,
    1.083e-04, 2.570e-06, -2.140e-06, -5.710e-08, 2.000e-08, -1.632e+00, -6.948e-03, -3.893e-03,
    8.592e-04, 7.577e-05, 4.539e-06, -3.852e-07, -2.213e-07, -1.370e-08, 5.800e-09,
];

const GMF_BW_AMPL: [f64; 55] = [
    0.000e+00, 0.000e+00, -8.865e-02, 0.000e+00, -4.309e-01, 6.340e-02, 0.000e+00, 1.162e-01,
    6.176e-02, -4.234e-03, 0.000e+00, 2.530e-01, 4.017e-02, -6.204e-03, 4.977e-03, 0.000e+00,
    -1.737e-01, -5.638e-03, 1.488e-04, 4.857e-04, -1.809e-04, 0.000e+00, -1.514e-01, -1.685e-02,
    5.333e-03, -7.611e-05, 2.394e-05, 8.195e-06, 0.000e+00, 9.326e-02, -1.275e-02, -3.071e-04,
    5.374e-05, -3.391e-05, -7.436e-06, 6.747e-07, 0.000e+00, -8.637e-02, -3.807e-03, -6.833e-04,
    -3.861e-05, -2.268e-05, 1.454e-06, 3.860e-07, -1.068e-07, 0.000e+00, -2.658e-02, -1.947e-03,
    7.131e-04, -3.506e-05, 1.885e-07, 5.792e-07, 3.990e-08, 2.000e-08, -5.700e-09,
];

/// Exact factorial in `f64` (all arguments here are `<= 18`, representable without rounding).
fn gmf_factorial(n: usize) -> f64 {
    // A range iterator, not a hand-incremented counter: `i += 1` mutated to `i *= 1` pins the
    // index at 2 and the loop never ends. `gmf_ipow` below already has the safe form.
    (2..=n).map(|i| i as f64).product()
}

/// Integer power by repeated multiplication — matches Orekit's `FastMath.pow(double, int)` and keeps
/// the correct sign for a negative base (southern-hemisphere `sin(latitude) < 0`).
fn gmf_ipow(base: f64, exp: u32) -> f64 {
    let mut acc = 1.0;
    for _ in 0..exp {
        acc *= base;
    }
    acc
}

/// Unnormalized associated Legendre functions `P(n,m)(t)` for `n, m <= 9`, in the Heiskanen & Moritz
/// (1967, eq. 1-62) closed form used by Orekit's `LegendrePolynomials`. Returned as `p[n][m]`.
fn gmf_legendre(t: f64) -> [[f64; 10]; 10] {
    let t2 = t * t;
    let mut p = [[0.0_f64; 10]; 10];
    for n in 0..=9usize {
        for m in 0..=n {
            let r = (n - m) / 2;
            let mut sum = 0.0;
            for k in 0..=r {
                let sign = if k & 1 == 0 { 1.0 } else { -1.0 };
                let term = sign * gmf_factorial(2 * n - 2 * k)
                    / (gmf_factorial(k) * gmf_factorial(n - k) * gmf_factorial(n - m - 2 * k))
                    * gmf_ipow(t, (n - m - 2 * k) as u32);
                sum += term;
            }
            p[n][m] = libm::pow(2.0, -(n as f64)) * libm::pow(1.0 - t2, 0.5 * m as f64) * sum;
        }
    }
    p
}

/// The Global Mapping Function (GMF) tropospheric mapping factors `(hydrostatic, wet)` of
/// Böhm et al. 2006 — a spherical-harmonic (degree/order 9) empirical model, consistent with VMF1,
/// needing only station location and date. `latitude`/`longitude` are geodetic radians, `height` the
/// height above the ellipsoid (m), `day_of_year` the (fractional) day of year, `elevation` radians.
///
/// Each `a` coefficient is
/// `Σ (mean + ampl·cos(2π(doy + 1 − t0)/365.25))·P(n,m)(sin φ)·(cos mλ + sin mλ)` over the harmonics;
/// the factors then follow the Marini continued fraction with the Niell hydrostatic height
/// correction. Ported from Orekit's `GlobalMappingFunctionModel`.
#[must_use]
pub fn gmf_mapping<S: Scalar>(
    latitude: f64,
    longitude: f64,
    height: f64,
    day_of_year: f64,
    elevation: S,
) -> (S, S) {
    // Hydrostatic b and c coefficients (Böhm et al. 2006); c depends on hemisphere and season.
    let bh = 0.0029;
    let c0h = 0.062;
    let sin_lat = libm::sin(latitude);
    let (c10h, c11h, psi) = if sin_lat > 0.0 {
        (0.001, 0.005, 0.0) // northern hemisphere
    } else {
        (0.002, 0.007, PI) // southern hemisphere
    };
    let t0 = if latitude < 0.0 { 28.0 + 183.0 } else { 28.0 };
    let coef = psi + ((day_of_year + 1.0 - t0) / 365.25) * TAU;
    let ch = c0h + ((libm::cos(coef) + 1.0) * (c11h / 2.0) + c10h) * (1.0 - libm::cos(latitude));

    // Wet b and c coefficients (Böhm et al. 2006), fixed.
    let bw = 0.00146;
    let cw = 0.04391;

    // Spherical-harmonic series for the a coefficients, Pnm(sin φ) to degree/order 9.
    let p = gmf_legendre(sin_lat);
    let mut a0_hydro = 0.0;
    let mut ampl_hydro = 0.0;
    let mut a0_wet = 0.0;
    let mut ampl_wet = 0.0;
    let mut j = 0;
    for n in 0..=9usize {
        for m in 0..=n {
            let arg = m as f64 * longitude;
            let (sin_ml, cos_ml) = (libm::sin(arg), libm::cos(arg));
            let pnm = p[n][m];
            a0_hydro +=
                (GMF_AH_MEAN[j] * pnm * cos_ml + GMF_BH_MEAN[j] * pnm * sin_ml) * GMF_FACTOR;
            a0_wet += (GMF_AW_MEAN[j] * pnm * cos_ml + GMF_BW_MEAN[j] * pnm * sin_ml) * GMF_FACTOR;
            ampl_hydro +=
                (GMF_AH_AMPL[j] * pnm * cos_ml + GMF_BH_AMPL[j] * pnm * sin_ml) * GMF_FACTOR;
            ampl_wet +=
                (GMF_AW_AMPL[j] * pnm * cos_ml + GMF_BW_AMPL[j] * pnm * sin_ml) * GMF_FACTOR;
            j += 1;
        }
    }
    let seasonal = libm::cos(coef - psi);
    let ah = a0_hydro + ampl_hydro * seasonal;
    let aw = a0_wet + ampl_wet * seasonal;

    // Marini continued fraction (shared with Niell) plus the Niell hydrostatic height correction.
    let sin_e = elevation.sin();
    let correction = (S::from_f64(1.0) / sin_e
        - niell_fraction(2.53e-5, 5.49e-3, 1.14e-3, elevation))
        * S::from_f64(height.max(0.0) / 1000.0);
    let hydrostatic = niell_fraction(ah, bh, ch, elevation) + correction;
    let wet = niell_fraction(aw, bw, cw, elevation);
    (hydrostatic, wet)
}

/// The Vienna Mapping Function VMF1 tropospheric mapping factors `(hydrostatic, wet)` of
/// Böhm et al. (2006). The `ah`/`aw` a-coefficients are **caller-supplied** (they come from numerical
/// weather models — Orekit's `ViennaACoefficients` / `ConstantViennaAProvider`), while the `b`/`c`
/// coefficients are fixed: the hydrostatic `c` follows a latitude/day-of-year formula with a
/// northern/southern-hemisphere phase `psi`, and the hydrostatic factor carries the Niell (1996)
/// height correction (the wet factor does not). `latitude` (geodetic, rad), `height` (m above the
/// ellipsoid), `day_of_year` (Orekit's continuous `getDayOfYear`, with day 1.0 = 1 Jan at noon),
/// `elevation` (rad). Ported from Orekit's `ViennaOne`.
#[must_use]
pub fn vmf1_mapping<S: Scalar>(
    ah: f64,
    aw: f64,
    latitude: f64,
    height: f64,
    day_of_year: f64,
    elevation: S,
) -> (S, S) {
    // Hydrostatic b and c coefficients; c depends on hemisphere and season.
    let bh = 0.0029;
    let c0h = 0.062;
    let (c10h, c11h, psi) = if libm::sin(latitude) > 0.0 {
        (0.001, 0.005, 0.0) // northern hemisphere
    } else {
        (0.002, 0.007, PI) // southern hemisphere
    };
    let t0 = if latitude < 0.0 { 28.0 + 183.0 } else { 28.0 };
    // VMF1 normalises the seasonal phase by 365 (not 365.25) and does not offset the day of year.
    let coef = psi + ((day_of_year - t0) / 365.0) * TAU;
    let ch = c0h + ((libm::cos(coef) + 1.0) * (c11h / 2.0) + c10h) * (1.0 - libm::cos(latitude));

    // Wet b and c coefficients, fixed.
    let bw = 0.00146;
    let cw = 0.04391;

    // Shared continued fraction, plus the Niell hydrostatic height correction (Eqs. 4/6/7).
    let sin_e = elevation.sin();
    let correction = (S::from_f64(1.0) / sin_e
        - niell_fraction(2.53e-5, 5.49e-3, 1.14e-3, elevation))
        * S::from_f64(height.max(0.0) / 1000.0);
    let hydrostatic = niell_fraction(ah, bh, ch, elevation) + correction;
    let wet = niell_fraction(aw, bw, cw, elevation);
    (hydrostatic, wet)
}

// VMF3 empirical coefficient tables (Landskron & Böhm 2018): a Legendre-in-latitude,
// Fourier-in-longitude spherical-harmonic expansion to degree/order 12. `*_A` hold the a_nm (cosine)
// coefficients, `*_B` the b_nm (sine) coefficients; each of the 91 rows (n = 0..12, m = 0..n) carries
// the five seasonal components (A0, A1, B1, A2, B2). Transcribed byte-identical from Orekit's
// ViennaThree `LegendreFunctions` (BH/BW/CH/CW arrays); Java's bare `0` is written as Rust `0.0`.
/// One VMF3 coefficient table: 91 spherical-harmonic rows (n = 0..12, m = 0..n), each with the five
/// seasonal components (A0, A1, B1, A2, B2).
type Vmf3Table = [[f64; 5]; 91];

const BH_A: [[f64; 5]; 91] = [
    [
        0.00271285863109945,
        -1.39197786008938e-06,
        1.34955672002719e-06,
        2.71686279717968e-07,
        1.56659301773925e-06,
    ],
    [
        9.80476624811974e-06,
        -5.83922611260673e-05,
        -2.07307023860417e-05,
        1.14628726961148e-06,
        4.93610283608719e-06,
    ],
    [
        -1.03443106534268e-05,
        -2.05536138785961e-06,
        2.09692641914244e-06,
        -1.55491034130965e-08,
        -1.89706404675801e-07,
    ],
    [
        -3.00353961749658e-05,
        2.37284447073503e-05,
        2.02236885378918e-05,
        1.69276006349609e-06,
        8.72156681243892e-07,
    ],
    [
        -7.99121077044035e-07,
        -5.39048313389504e-06,
        -4.21234502039861e-06,
        -2.70944149806894e-06,
        -6.80894455531746e-07,
    ],
    [
        7.51439609883296e-07,
        3.85509708865520e-07,
        4.41508016098164e-08,
        -2.07507808307757e-08,
        4.95354985050743e-08,
    ],
    [
        2.21790962160087e-05,
        -5.56986238775212e-05,
        -1.81287885563308e-05,
        -4.41076013532589e-06,
        4.93573223917278e-06,
    ],
    [
        -4.47639989737328e-06,
        -2.60452893072120e-06,
        2.56376320011189e-06,
        4.41600992220479e-07,
        2.93437730332869e-07,
    ],
    [
        8.14992682244945e-07,
        2.03945571424434e-07,
        1.11832498659806e-08,
        3.25756664234497e-08,
        3.01029040414968e-08,
    ],
    [
        -7.96927680907488e-08,
        -3.66953150925865e-08,
        -6.74742632186619e-09,
        -1.30315731273651e-08,
        -2.00748924306947e-09,
    ],
    [
        -2.16138375166934e-05,
        1.67350317962556e-05,
        1.93768260076821e-05,
        1.99595120161850e-06,
        -2.42463528222014e-06,
    ],
    [
        5.34360283708044e-07,
        -3.64189022040600e-06,
        -2.99935375194279e-06,
        -2.06880962903922e-06,
        -9.40815692626002e-07,
    ],
    [
        6.80235884441822e-07,
        1.33023436079845e-07,
        -1.80349593705226e-08,
        2.51276252565192e-08,
        -1.43240592002794e-09,
    ],
    [
        -7.13790897253802e-08,
        7.81998506267559e-09,
        1.13826909570178e-09,
        -5.89629600214654e-09,
        -4.20760865522804e-09,
    ],
    [
        -5.80109372399116e-09,
        1.13702284491976e-09,
        7.29046067602764e-10,
        -9.10468988754012e-10,
        -2.58814364808642e-10,
    ],
    [
        1.75558618192965e-05,
        -2.85579168876063e-05,
        -1.47442190284602e-05,
        -6.29300414335248e-06,
        -5.12204538913460e-07,
    ],
    [
        -1.90788558291310e-06,
        -1.62144845155361e-06,
        7.57239241641566e-07,
        6.93365788711348e-07,
        6.88855644570695e-07,
    ],
    [
        2.27050351488552e-07,
        1.03925791277660e-07,
        -3.31105076632079e-09,
        2.88065761026675e-08,
        -8.00256848229136e-09,
    ],
    [
        -2.77028851807614e-08,
        -5.96251132206930e-09,
        2.95987495527251e-10,
        -5.87644249625625e-09,
        -3.28803981542337e-09,
    ],
    [
        -1.89918479865558e-08,
        3.54083436578857e-09,
        8.10617835854935e-10,
        4.99207055948336e-10,
        -1.52691648387663e-10,
    ],
    [
        1.04022499586096e-09,
        -2.36437143845013e-10,
        -2.25110813484842e-10,
        -7.39850069252329e-11,
        7.95929405440911e-11,
    ],
    [
        -3.11579421267630e-05,
        -3.43576336877494e-06,
        5.81663608263384e-06,
        8.31534700351802e-07,
        4.02619520312154e-06,
    ],
    [
        6.00037066879001e-07,
        -1.12538760056168e-07,
        -3.86745332115590e-07,
        -3.88218746020826e-07,
        -6.83764967176388e-07,
    ],
    [
        -9.79583981249316e-08,
        9.14964449851003e-08,
        4.77779838549237e-09,
        2.44283811750703e-09,
        -6.26361079345158e-09,
    ],
    [
        -2.37742207548109e-08,
        -5.53336301671633e-09,
        -3.73625445257115e-09,
        -1.92304189572886e-09,
        -7.18681390197449e-09,
    ],
    [
        -6.58203463929583e-09,
        9.28456148541896e-10,
        2.47218904311077e-10,
        1.10664919110218e-10,
        -4.20390976974043e-11,
    ],
    [
        9.45857603373426e-10,
        -3.29683402990254e-11,
        -8.15440375865127e-11,
        -1.21615589356628e-12,
        -9.70713008848085e-12,
    ],
    [
        1.61377382316176e-10,
        6.84326027598147e-12,
        -4.66898885683671e-12,
        2.31211355085535e-12,
        2.39195112937346e-12,
    ],
    [
        2.99634365075821e-07,
        8.14391615472128e-06,
        6.70458490942443e-06,
        -9.92542646762000e-07,
        -3.04078064992750e-06,
    ],
    [
        -6.52697933801393e-07,
        2.87255329776428e-07,
        -1.78227609772085e-08,
        2.65525429849935e-07,
        8.60650570551813e-08,
    ],
    [
        -1.62727164011710e-07,
        1.09102479325892e-07,
        4.97827431850001e-09,
        7.86649963082937e-11,
        -6.67193813407656e-09,
    ],
    [
        -2.96370000987760e-09,
        1.20008401576557e-09,
        1.75885448022883e-09,
        -1.74756709684384e-09,
        3.21963061454248e-09,
    ],
    [
        -9.91101697778560e-10,
        7.54541713140752e-10,
        -2.95880967800875e-10,
        1.81009160501278e-10,
        8.31547411640954e-11,
    ],
    [
        1.21268051949609e-10,
        -5.93572774509587e-11,
        -5.03295034994351e-11,
        3.05383430975252e-11,
        3.56280438509939e-11,
    ],
    [
        6.92012970333794e-11,
        -9.02885345797597e-12,
        -3.44151832744880e-12,
        2.03164894681921e-12,
        -5.44852265137606e-12,
    ],
    [
        5.56731263672800e-12,
        3.57272150106101e-12,
        2.25885622368678e-12,
        -2.44508240047675e-13,
        -6.83314378535235e-13,
    ],
    [
        3.96883487797254e-06,
        -4.57100506169608e-06,
        -3.30208117813256e-06,
        3.32599719134845e-06,
        4.26539325549339e-06,
    ],
    [
        1.10123151770973e-06,
        4.58046760144882e-07,
        1.86831972581926e-07,
        -1.60092770735081e-07,
        -5.58956114867062e-07,
    ],
    [
        -3.40344900506653e-08,
        2.87649741373047e-08,
        -1.83929753066251e-08,
        -9.74179203885847e-09,
        -2.42064137485043e-09,
    ],
    [
        -6.49731596932566e-09,
        -3.07048108404447e-09,
        -2.84380614669848e-09,
        1.55123146524283e-09,
        4.53694984588346e-10,
    ],
    [
        5.45175793803325e-10,
        -3.73287624700125e-10,
        -1.16293122618336e-10,
        7.25845618602690e-11,
        -4.34112440021627e-11,
    ],
    [
        1.89481447552805e-10,
        3.67431482211078e-12,
        -1.72180065021194e-11,
        1.47046319023226e-11,
        1.31920481414062e-11,
    ],
    [
        2.10125915737167e-12,
        -3.08420783495975e-12,
        -4.87748712363020e-12,
        1.16363599902490e-14,
        1.26698255558605e-13,
    ],
    [
        -8.07894928696254e-12,
        9.19344620512607e-13,
        3.26929173307443e-13,
        2.00438149416495e-13,
        -9.57035765212079e-15,
    ],
    [
        1.38737151773284e-12,
        1.09340178371420e-13,
        5.15714202449053e-14,
        -5.92156438588931e-14,
        -3.29586752336143e-14,
    ],
    [
        6.38137197198254e-06,
        4.62426300749908e-06,
        4.42334454191034e-06,
        1.15374736092349e-06,
        -2.61859702227253e-06,
    ],
    [
        -2.25320619636149e-07,
        3.21907705479353e-07,
        -3.34834530764823e-07,
        -4.82132753601810e-07,
        -3.22410936343355e-07,
    ],
    [
        3.48894515496995e-09,
        3.49951261408458e-08,
        -6.01128959281142e-09,
        4.78213900943443e-09,
        1.46012816168576e-08,
    ],
    [
        -9.66682871952083e-11,
        3.75806627535317e-09,
        2.38984004956705e-09,
        2.07545049877203e-09,
        1.58573595632766e-09,
    ],
    [
        1.06834370693917e-09,
        -4.07975055112153e-10,
        -2.37598937943957e-10,
        5.89327007480137e-11,
        1.18891820437634e-10,
    ],
    [
        5.22433722695807e-11,
        6.02011995016293e-12,
        -7.80605402956048e-12,
        1.50873145627341e-11,
        -1.40550093106311e-12,
    ],
    [
        2.13396242187279e-13,
        -1.71939313965536e-12,
        -3.57625378660975e-14,
        -5.01675184988446e-14,
        -1.07805487368797e-12,
    ],
    [
        -1.24352330043311e-12,
        8.26105883301606e-13,
        4.63606970128517e-13,
        6.39517888984486e-14,
        -7.35135439920086e-14,
    ],
    [
        -5.39023859065631e-13,
        2.54188315588243e-14,
        1.30933833278664e-14,
        6.06153473304781e-15,
        -4.24722717533726e-14,
    ],
    [
        3.12767756884813e-14,
        -2.29517847871632e-15,
        2.53117304424948e-16,
        7.07504914138118e-16,
        -1.20089065310688e-15,
    ],
    [
        2.08311178819214e-06,
        -1.22179185044174e-06,
        -2.98842190131044e-06,
        3.07310218974299e-06,
        2.27100346036619e-06,
    ],
    [
        -3.94601643855452e-07,
        -5.44014825116083e-07,
        -6.16955333162507e-08,
        -2.31954821580670e-07,
        1.14010813005310e-07,
    ],
    [
        6.11067575043044e-08,
        -3.93240193194272e-08,
        -1.62979132528933e-08,
        1.01339204652581e-08,
        1.97319601566071e-08,
    ],
    [
        2.57770508710055e-09,
        1.87799543582899e-09,
        1.95407654714372e-09,
        1.15276419281270e-09,
        2.25397005402120e-09,
    ],
    [
        7.16926338026236e-10,
        -3.65857693313858e-10,
        -1.54864067050915e-11,
        6.50770211276549e-11,
        -7.85160007413546e-12,
    ],
    [
        4.90007693914221e-12,
        3.31649396536340e-12,
        4.81664871165640e-13,
        7.26080745617085e-12,
        2.30960953372164e-12,
    ],
    [
        9.75489202240545e-13,
        -1.68967954531421e-13,
        7.38383391334110e-13,
        -3.58435515913239e-13,
        -3.01564710027450e-13,
    ],
    [
        -3.79533601922805e-13,
        2.76681830946617e-13,
        1.21480375553803e-13,
        -1.57729077644850e-14,
        -8.87664977818700e-14,
    ],
    [
        -3.96462845480288e-14,
        2.94155690934610e-14,
        6.78413205760717e-15,
        -4.12135802787361e-15,
        -1.46373307795619e-14,
    ],
    [
        -8.64941937408121e-15,
        -1.91822620970386e-15,
        -8.01725413560744e-16,
        5.02941051180784e-16,
        -1.07572628474344e-15,
    ],
    [
        -4.13816294742758e-15,
        -7.43602019785880e-17,
        -5.54248556346072e-17,
        -4.83999456005158e-17,
        -1.19622559730466e-16,
    ],
    [
        -8.34852132750364e-07,
        -7.45794677612056e-06,
        -6.58132648865533e-06,
        -1.38608110346732e-06,
        5.32326534882584e-07,
    ],
    [
        -2.75513802414150e-07,
        3.64713745106279e-08,
        -7.12385417940442e-08,
        -7.86206067228882e-08,
        2.28048393207161e-08,
    ],
    [
        -4.26696415431918e-08,
        -4.65599668635087e-09,
        7.35037936327566e-09,
        1.17098354115804e-08,
        1.44594777658035e-08,
    ],
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];

const BH_B: [[f64; 5]; 91] = [
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    [0.0, 0.0, 0.0, 0.0, 0.0],
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];

const BW_B: [[f64; 5]; 91] = [
    [0.0, 0.0, 0.0, 0.0, 0.0],
    [0.0, 0.0, 0.0, 0.0, 0.0],
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    [
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        8.44593804408541e-08,
        9.27243162355359e-09,
    ],
    [
        7.24370898432057e-08,
        -7.43945120337710e-09,
        8.61751911975683e-10,
        -2.34651212610623e-08,
        2.94052921681456e-09,
    ],
    [
        -1.22127317934425e-08,
        -3.89758984276768e-09,
        4.12890383904924e-11,
        2.06528068002723e-09,
        1.73488696972270e-09,
    ],
    [
        -5.44137406907620e-10,
        -4.81034553189921e-10,
        -2.56101759039694e-11,
        3.21880564410154e-10,
        -2.70195343165250e-11,
    ],
    [
        1.08394225300546e-10,
        -7.99525492688661e-11,
        1.73850287030654e-10,
        -8.06390014426271e-11,
        -7.63143364291160e-13,
    ],
    [
        -3.41446959267441e-11,
        2.72675729042792e-11,
        5.69674704865345e-12,
        -3.38402998344892e-12,
        -2.96732381931007e-12,
    ],
    [0.0, 0.0, 0.0, 0.0, 0.0],
    [
        2.91161315987250e-05,
        -7.24641166590735e-05,
        -8.58323519857884e-06,
        -1.14037444255820e-05,
        1.32244819451517e-05,
    ],
    [
        1.24266748259826e-06,
        -4.13127038469802e-06,
        -8.47496394492885e-07,
        5.48722958754267e-07,
        -1.98288551821205e-06,
    ],
    [
        -1.70671245196917e-08,
        1.36891127083540e-08,
        -2.80901972249870e-07,
        -5.45369793946222e-09,
        -9.58796303763498e-08,
    ],
    [
        1.14115335901746e-08,
        2.79308166429178e-08,
        -1.71144803132413e-08,
        4.86116243565380e-09,
        -8.13061459952280e-09,
    ],
    [
        -1.19144311035824e-09,
        -1.28197815211763e-09,
        -1.22313592972373e-09,
        6.23116336753674e-10,
        2.11527825898689e-09,
    ],
    [
        4.94618645030426e-10,
        -1.01554483531252e-10,
        -3.58808808952276e-10,
        1.23499783028794e-10,
        -1.21017599361833e-10,
    ],
    [
        1.33959569836451e-10,
        -1.87140898812283e-11,
        -3.04265350158941e-11,
        -1.42907553051431e-11,
        -1.09873858099638e-11,
    ],
    [
        1.30277419203512e-11,
        -4.95312627777245e-12,
        2.23070215544358e-12,
        1.66450226016423e-12,
        6.26222944728474e-12,
    ],
    [
        -4.40721204874728e-12,
        2.99575133064885e-12,
        -1.54917262009097e-12,
        8.90015664527060e-14,
        -1.59135267012937e-12,
    ],
    [0.0, 0.0, 0.0, 0.0, 0.0],
    [
        -4.17667211323160e-05,
        1.39005215116294e-05,
        1.46521361817829e-05,
        3.23485458024416e-05,
        -8.57936261085263e-06,
    ],
    [
        9.48491026524450e-07,
        1.67749735481991e-06,
        6.80159475477603e-07,
        -1.34558044496631e-06,
        1.62108231492249e-06,
    ],
    [
        -2.67545753355631e-07,
        -3.31848493018159e-08,
        1.05837219557465e-07,
        1.55587655479400e-07,
        -2.84996014386667e-08,
    ],
    [
        -5.15113778734878e-08,
        8.83630725241303e-09,
        3.36579455982772e-09,
        -6.22350102096402e-09,
        5.03959133095369e-09,
    ],
    [
        2.04635880823035e-11,
        -1.07923589059151e-09,
        -6.96482137669712e-10,
        -4.70238500452793e-10,
        -6.60277903598297e-10,
    ],
    [
        -2.41897168749189e-11,
        1.33547763615216e-10,
        -5.13534673658908e-11,
        -8.32767177662817e-11,
        5.72614717082428e-11,
    ],
    [
        7.55170562359940e-12,
        -1.57123461699055e-11,
        -1.48874069619124e-11,
        -7.10529462981252e-13,
        -7.99006335025107e-12,
    ],
    [
        2.41883156738960e-12,
        2.97346980183361e-12,
        1.28719977731450e-12,
        -2.49240876894143e-12,
        6.71155595793198e-13,
    ],
    [
        4.16995565336914e-13,
        -1.71584521275288e-13,
        -7.23064067359978e-14,
        2.45405880599037e-13,
        4.43532934905830e-13,
    ],
    [
        3.56937508828997e-14,
        2.43012511260300e-14,
        -7.96090778289326e-14,
        -1.59548529636358e-14,
        8.99103763000507e-15,
    ],
    [0.0, 0.0, 0.0, 0.0, 0.0],
    [
        0.000117579258399489,
        -4.52648448635772e-05,
        -2.69130037097862e-05,
        -3.82266335794366e-05,
        -4.36549257701084e-06,
    ],
    [
        -1.43270371215502e-06,
        1.21565440183855e-06,
        8.53701136074284e-07,
        1.52709810023665e-06,
        1.22382663462904e-06,
    ],
    [
        3.06089147519664e-07,
        9.79084123751975e-08,
        7.96524661441178e-08,
        4.54770947973458e-08,
        2.22842369458882e-07,
    ],
    [
        -9.94254707745127e-09,
        1.43251376378012e-08,
        1.93911753685160e-08,
        -6.52214645690987e-09,
        -1.97114016452408e-09,
    ],
    [
        -9.20751919828404e-10,
        -9.44312829629076e-10,
        7.24196738163952e-11,
        -6.71801072324561e-11,
        2.33146774065873e-10,
    ],
    [
        -1.43544298956410e-11,
        1.78464235318769e-10,
        7.69950023012326e-11,
        -4.22390057304453e-12,
        3.05176324574816e-11,
    ],
    [
        -7.88053753973990e-12,
        -3.20207793051003e-12,
        1.01527407317625e-12,
        6.02788185858449e-12,
        1.14919530900453e-11,
    ],
    [
        -1.21558899266069e-12,
        5.31300597882986e-13,
        3.44023865079264e-13,
        -6.22598216726224e-14,
        -5.47031650765402e-14,
    ],
    [
        -4.15627948750943e-13,
        2.77620907292721e-13,
        -8.99784134364011e-14,
        1.07254247320864e-13,
        6.85990080564196e-14,
    ],
    [
        -3.91837863922901e-14,
        9.74714976816180e-15,
        6.79982450963903e-15,
        -2.41420876658572e-15,
        -2.20889384455344e-15,
    ],
    [
        9.25912068402776e-15,
        -4.02621719248224e-15,
        -2.43952036351187e-15,
        -1.97006876049866e-15,
        1.03065621527869e-16,
    ],
    [0.0, 0.0, 0.0, 0.0, 0.0],
    [
        -0.000103762036940193,
        4.38145356960292e-05,
        2.43406920349913e-05,
        7.89103527673736e-06,
        -1.66841465339160e-05,
    ],
    [
        -1.18428449371744e-06,
        -1.30188721737259e-06,
        -1.88013557116650e-06,
        -1.01342046295303e-06,
        9.21813037802502e-07,
    ],
    [
        1.51836068712460e-07,
        1.11362553803933e-07,
        1.55375052233052e-07,
        1.94450910788747e-09,
        -1.73093755828342e-08,
    ],
    [
        -3.77758211813121e-09,
        1.23323969583610e-08,
        1.72510045250302e-09,
        -1.88609789458597e-09,
        1.28937597985937e-09,
    ],
    [
        -1.07947760393523e-09,
        5.26051570105365e-10,
        -3.67657536332496e-11,
        3.16110123523840e-10,
        -3.24273198242170e-10,
    ],
    [
        -2.00385649209820e-12,
        2.54703869682390e-11,
        4.08563622440851e-12,
        -4.83350348928636e-11,
        -3.98153443845079e-13,
    ],
    [
        2.73094467727215e-12,
        5.08900664114903e-12,
        -7.66669089075134e-13,
        2.50015592643012e-12,
        4.29763262853853e-12,
    ],
    [
        6.53946487537890e-13,
        -2.24958413781008e-13,
        6.74638861781238e-15,
        3.28537647613903e-14,
        2.54199700290116e-13,
    ],
    [
        -1.09122051193505e-13,
        8.36362392931501e-14,
        -3.90750153912300e-14,
        -5.44915910741950e-14,
        2.43816947219217e-14,
    ],
    [
        -1.41882561550134e-14,
        1.00455397812713e-14,
        2.63347255121581e-15,
        1.53043256823601e-15,
        2.49081021428095e-15,
    ],
    [
        -1.17256193152654e-15,
        1.05648985031971e-16,
        1.31778372453016e-16,
        1.44815198666577e-16,
        -3.72532768618480e-16,
    ],
    [
        2.66203457773766e-16,
        -7.67224608659658e-17,
        3.51487351031864e-18,
        4.10287131339291e-17,
        -6.72171711728514e-17,
    ],
];

/// Unnormalized associated Legendre functions `P(n,m)(t)` for `n, m <= 12`, in the same Heiskanen &
/// Moritz (1967, eq. 1-62) closed form as [`gmf_legendre`] but carried to degree/order 12 as VMF3
/// requires. Matches Orekit's `LegendrePolynomials`.
fn vmf3_legendre(t: f64) -> [[f64; 13]; 13] {
    let t2 = t * t;
    let mut p = [[0.0_f64; 13]; 13];
    for n in 0..=12usize {
        for m in 0..=n {
            let r = (n - m) / 2;
            let mut sum = 0.0;
            for k in 0..=r {
                let sign = if k & 1 == 0 { 1.0 } else { -1.0 };
                let term = sign * gmf_factorial(2 * n - 2 * k)
                    / (gmf_factorial(k) * gmf_factorial(n - k) * gmf_factorial(n - m - 2 * k))
                    * gmf_ipow(t, (n - m - 2 * k) as u32);
                sum += term;
            }
            p[n][m] = libm::pow(2.0, -(n as f64)) * libm::pow(1.0 - t2, 0.5 * m as f64) * sum;
        }
    }
    p
}

/// The VMF3 seasonal fit (Landskron & Böhm 2018, Eq. 6): a mean plus annual and semi-annual harmonics
/// of the day of year. Argument order mirrors Orekit's `computeSeasonalFit(doy, A0, A1, A2, B1, B2)`.
fn vmf3_seasonal_fit(doy: f64, a0: f64, a1: f64, a2: f64, b1: f64, b2: f64) -> f64 {
    let coef = (doy / 365.25) * 2.0 * PI;
    let (s1, c1) = (libm::sin(coef), libm::cos(coef));
    let (s2, c2) = (libm::sin(2.0 * coef), libm::cos(2.0 * coef));
    a0 + a1 * c1 + b1 * s1 + a2 * c2 + b2 * s2
}

/// The Vienna Mapping Function VMF3 tropospheric mapping factors `(hydrostatic, wet)` of
/// Landskron & Böhm (2018) — a spherical-harmonic (degree/order 12) refinement of VMF1 whose `b`/`c`
/// coefficients come from a Legendre-in-latitude, Fourier-in-longitude expansion with a seasonal fit.
/// The `ah`/`aw` a-coefficients are **caller-supplied** (numerical weather models). `latitude`/
/// `longitude` are geodetic radians, `height` is metres above the ellipsoid, `day_of_year` is Orekit's
/// continuous `getDayOfYear` (day 1.0 = 1 Jan noon), `elevation` radians. Ported from Orekit's
/// `ViennaThree`.
#[must_use]
pub fn vmf3_mapping<S: Scalar>(
    ah: f64,
    aw: f64,
    latitude: f64,
    longitude: f64,
    height: f64,
    day_of_year: f64,
    elevation: S,
) -> (S, S) {
    // VMF3 (unlike VMF1) applies no Niell height correction; Orekit's ViennaThree omits it. The
    // parameter is kept for API symmetry with `vmf1_mapping`.
    let _ = height;

    // Legendre Pnm(sin φ) to degree/order 12.
    let p = vmf3_legendre(libm::sin(latitude));

    // sin(mλ)/cos(mλ) for m = 0..=12 via the angle-sum recurrence (Orekit builds these with SinCos.sum).
    let mut sc_sin = [0.0_f64; 13];
    let mut sc_cos = [0.0_f64; 13];
    sc_cos[0] = 1.0;
    sc_sin[1] = libm::sin(longitude);
    sc_cos[1] = libm::cos(longitude);
    for m in 2..13 {
        sc_sin[m] = sc_sin[1] * sc_cos[m - 1] + sc_cos[1] * sc_sin[m - 1];
        sc_cos[m] = sc_cos[1] * sc_cos[m - 1] - sc_sin[1] * sc_sin[m - 1];
    }

    // Accumulate the five seasonal components (A0, A1, B1, A2, B2) of each coefficient (bh, bw, ch, cw)
    // over the spherical-harmonic expansion.
    let tables: [(&Vmf3Table, &Vmf3Table); 4] = [
        (&BH_A, &BH_B),
        (&BW_A, &BW_B),
        (&CH_A, &CH_B),
        (&CW_A, &CW_B),
    ];
    let mut season = [[0.0_f64; 5]; 4];
    let mut j = 0;
    for n in 0..=12usize {
        for m in 0..=n {
            let p_cos = p[n][m] * sc_cos[m];
            let p_sin = p[n][m] * sc_sin[m];
            for (acc, &(anm, bnm)) in season.iter_mut().zip(tables.iter()) {
                for s in 0..5 {
                    acc[s] += anm[j][s] * p_cos + bnm[j][s] * p_sin;
                }
            }
            j += 1;
        }
    }

    // Eq. 6 seasonal fit (note the A2/B1 argument order matching Orekit) → b/c coefficients.
    let bh = vmf3_seasonal_fit(
        day_of_year,
        season[0][0],
        season[0][1],
        season[0][3],
        season[0][2],
        season[0][4],
    );
    let bw = vmf3_seasonal_fit(
        day_of_year,
        season[1][0],
        season[1][1],
        season[1][3],
        season[1][2],
        season[1][4],
    );
    let ch = vmf3_seasonal_fit(
        day_of_year,
        season[2][0],
        season[2][1],
        season[2][3],
        season[2][2],
        season[2][4],
    );
    let cw = vmf3_seasonal_fit(
        day_of_year,
        season[3][0],
        season[3][1],
        season[3][3],
        season[3][2],
        season[3][4],
    );

    // Eq. 4 mapping via the shared continued fraction; no height correction.
    let hydrostatic = niell_fraction(ah, bh, ch, elevation);
    let wet = niell_fraction(aw, bw, cw, elevation);
    (hydrostatic, wet)
}

/// The single-layer (thin-shell) ionospheric mapping factor, mapping a zenith delay/TEC to the slant
/// path: `1/√(1 − (Rₑ cos ε / (Rₑ + h_ion))²)`. `elevation` (rad), `ionosphere_height` and `re` (m).
/// Unity at the zenith; grows toward the horizon. The geometric obliquity every GNSS ionosphere model
/// uses to relate vertical to slant.
#[must_use]
pub fn ionospheric_mapping_factor<S: Scalar>(elevation: S, ionosphere_height: f64, re: f64) -> S {
    let ratio = S::from_f64(re) * elevation.cos() / S::from_f64(re + ionosphere_height);
    S::from_f64(1.0) / (S::from_f64(1.0) - ratio * ratio).sqrt()
}

#[cfg(test)]
mod tests {
    use proptest::prelude::*;

    use super::*;

    proptest! {
        /// `wrap_day` lands in the day and stays there.
        ///
        /// This is the shape of #230, where JB2008's local-solar-time wrap was written as a
        /// subtraction that happened to land in range for the arguments the fixtures used and did
        /// not for the rest. A fixture cannot find that; a range spanning ±1e12 s finds it on the
        /// first run. Idempotence is the half a range check misses: a wrap that shifts a value
        /// already inside the day is in range and still wrong.
        ///
        /// Both assertions are exact — `==`, no tolerance — because both claims are exact.
        #[test]
        #[expect(clippy::float_cmp, reason = "idempotence is a bit-exact claim, not an approximate one")]
        fn the_day_wrap_lands_in_the_day_and_stays_there(x in -1e12_f64..1e12) {
            let r = wrap_day(x);
            prop_assert!((0.0..86_400.0).contains(&r), "wrap_day({x}) = {r} is outside [0, 86400)");
            prop_assert_eq!(wrap_day(r), r, "wrap_day is not idempotent at {}", x);
        }

        /// …and it is the *same* time of day, not merely some time of day.
        ///
        /// The obvious way to check that — compare `sin`/`cos` of the day fraction before and
        /// after — cannot be written honestly here. `f64::EPSILON * 1e12 s` is 0.2 ms, so at the
        /// top of the range the reference angle `τ·x/86400` is itself only good to ~1e-8 rad
        /// (measured worst 1.565e-8 over 200 000 draws). The tolerance would be describing the
        /// test's own arithmetic, not the function's, which is the failure mode where a number
        /// gets chosen until it passes.
        ///
        /// So the claim is made where it costs nothing. Whole seconds up to 8.64e10 are exactly
        /// representable, and on that sublattice the subtraction `x − 86400·⌊x/86400⌋` is exact —
        /// `86400·n` needs 34 significand bits and the difference cancels — so shifting the
        /// argument by any whole number of days must return the identical bit pattern. Checked
        /// exhaustively at construction time: over all 2.3e7 day boundaries in `|x| ≤ 1e12` and
        /// both neighbouring ulps of each, the result never left `[0, 86400)` and never differed
        /// from `fmod`.
        #[test]
        #[expect(clippy::float_cmp, reason = "the reduction is exact here, so equality is the claim")]
        fn the_day_wrap_is_invariant_under_whole_days(
            second in 0_i64..86_400,
            days in -1_000_000_i64..1_000_000,
        ) {
            #[expect(clippy::cast_precision_loss, reason = "|value| < 2^53, exact in f64")]
            let (s, shifted) = (second as f64, (second + 86_400 * days) as f64);
            prop_assert_eq!(
                wrap_day(shifted), s,
                "wrap_day lost {} whole days at second {}", days, second
            );
        }
    }

    // Representative broadcast coefficients (single leading terms are enough to exercise the model).
    const ALPHA: [f64; 4] = [1.0e-8, 0.0, 0.0, 0.0];
    const BETA: [f64; 4] = [9.0e4, 0.0, 0.0, 0.0];

    #[test]
    fn klobuchar_night_zenith_is_the_five_nanosecond_floor() {
        // Midnight, zenith, on the equator: the local time falls in the night branch, so the delay is
        // the 5 ns floor × obliquity × c ≈ 1.5 m.
        let d = klobuchar_iono_delay(ALPHA, BETA, 0.0, 0.0, PI / 2.0, 0.0, 0.0);
        let f = 1.0 + 16.0 * (0.53 - 0.5f64).powi(3);
        let expect = f * 5.0e-9 * SPEED_OF_LIGHT;
        assert!((d - expect).abs() < 1e-6, "{d} vs {expect}");
        assert!((1.4..1.6).contains(&d), "night zenith delay {d}");
    }

    #[test]
    fn klobuchar_delay_is_positive_and_grows_toward_the_horizon() {
        // A daytime local time so the cosine term is active; lower elevation ⇒ larger obliquity ⇒
        // larger delay.
        let high =
            klobuchar_iono_delay(ALPHA, BETA, 0.5, 0.3, 80.0_f64.to_radians(), 1.0, 50_400.0);
        let low = klobuchar_iono_delay(ALPHA, BETA, 0.5, 0.3, 10.0_f64.to_radians(), 1.0, 50_400.0);
        assert!(high > 0.0 && low > 0.0);
        assert!(
            low > high,
            "low-elevation {low} should exceed high-elevation {high}"
        );
    }

    /// The obliquity factor, read straight off the night branch.
    ///
    /// `IS-GPS-200` fixes `F = 1 + 16(0.53 − E)³` with `E` the elevation in semicircles, and at
    /// night the delay is exactly `F · 5 ns · c` — no amplitude, no cosine, no local time. Sweeping
    /// the elevation therefore recovers `F` to the last bit, which pins the semicircle conversion,
    /// the 0.53, the 16, the cube, the 5 ns floor and the metres conversion at once.
    #[test]
    fn the_night_branch_is_the_five_nanosecond_floor_times_the_obliquity() {
        // Equator, prime meridian, azimuth 0: the sub-ionospheric longitude is 0, so the local time
        // is `gps_sod`. At `gps_sod = 0` the phase is 2π·(−50400)/72000 = −4.4, well past the 1.57
        // that selects the night branch, for every elevation.
        for deg in [5.0_f64, 15.0, 30.0, 45.0, 60.0, 75.0, 90.0] {
            let got = klobuchar_iono_delay(ALPHA, BETA, 0.0, 0.0, deg.to_radians(), 0.0, 0.0);
            // The reference divides degrees by 180 where the code divides radians by pi, and it
            // cubes rather than calling `pow`. Both are the same real number and neither is the
            // same double, so the comparison is at the width of that difference, not exact.
            let e = deg / 180.0; // semicircles
            let want = (1.0 + 16.0 * (0.53 - e).powi(3)) * 5.0e-9 * SPEED_OF_LIGHT;
            spacelab_testkit::assert_within_ulps(
                got,
                want,
                4,
                &format!("night delay at {deg} deg"),
            );
        }
    }

    /// The day/night cutoff is `|x| < 1.57`, and the boundary itself belongs to the night.
    ///
    /// IS-GPS-200 puts the cosine expansion strictly inside `|x| < 1.57`, where the truncated
    /// series is still `0.0207` rather than zero — so the two branches differ by 41% of the floor
    /// exactly at the cutoff and the choice of `<` over `<=` is a real one. Only an input that
    /// lands on `1.57` as a double can tell them apart: at zero latitude, longitude and azimuth
    /// the sub-ionospheric longitude vanishes, the local time is the clock itself, and a period of
    /// 72036.51944537106 s makes `2π(68400 − 50400)/P` exactly 1.57.
    // Exact by construction: the night branch is `f · 5e-9 · c` with no dependence on the clock, so
    // the two calls evaluate the same expression on the same doubles.
    #[allow(clippy::float_cmp)]
    #[test]
    fn the_day_night_cutoff_puts_its_own_boundary_in_the_night() {
        const ALPHA_BIG: [f64; 4] = [1.0e-7, 0.0, 0.0, 0.0];
        const BETA_TIE: [f64; 4] = [72_036.519_445_371_06, 0.0, 0.0, 0.0];
        let el = 45.0_f64.to_radians();
        let at_cutoff = klobuchar_iono_delay(ALPHA_BIG, BETA_TIE, 0.0, 0.0, el, 0.0, 68_400.0);
        // The night value depends on the elevation alone, so any clock past the cutoff gives it.
        let night = klobuchar_iono_delay(ALPHA_BIG, BETA_TIE, 0.0, 0.0, el, 0.0, 86_000.0);
        assert_eq!(
            at_cutoff, night,
            "|x| = 1.57 exactly was treated as daytime"
        );
        // One second earlier is inside the cutoff, and the truncated cosine has not decayed there,
        // so the two branches really do disagree at the boundary.
        let inside = klobuchar_iono_delay(ALPHA_BIG, BETA_TIE, 0.0, 0.0, el, 0.0, 68_399.0);
        assert!(
            (inside / night - 1.0).abs() > 0.3,
            "the branches agree at the cutoff, so the test proves nothing: {inside} vs {night}"
        );
    }

    /// The whole sub-ionospheric geometry, inverted out of the amplitude.
    ///
    /// With `α = [0, a₁, 0, 0]` the amplitude is `a₁·φ_m` and nothing else, so a daytime delay
    /// divided by its (independently known) obliquity and cosine factors returns `φ_m` itself. That
    /// makes every step from the look angles to the geomagnetic latitude observable: the
    /// Earth-centred angle ψ, the ±0.416 sc latitude clamp, the `cos(φ_i)` longitude stretch, and
    /// the 0.064/1.617 geomagnetic offset. The fixtures the module had used latitude, longitude and
    /// azimuth all zero, which collapses ψ·sin(az), λ_i and the clamp to nothing at once.
    #[test]
    fn the_sub_ionospheric_geometry_is_recoverable_from_the_amplitude() {
        const A1: f64 = 1.0e-7;
        let alpha = [0.0, A1, 0.0, 0.0];
        let beta = [72_000.0, 0.0, 0.0, 0.0]; // constant period, so the phase is known

        for (lat_deg, lon_deg, el_deg, az_deg) in [
            (48.0_f64, 11.0_f64, 25.0_f64, 130.0_f64),
            (-33.9, 151.2, 65.0, 300.0),
            (78.0, -20.0, 8.0, 45.0), // clamps the sub-ionospheric latitude
            (-78.0, 200.0, 8.0, 225.0), // clamps it the other way
            (0.0, -179.0, 40.0, 90.0), // pushes λ_i past the anti-meridian
        ] {
            let (lat, lon) = (lat_deg.to_radians(), lon_deg.to_radians());
            let (el, az) = (el_deg.to_radians(), az_deg.to_radians());

            // The spec's chain, in semicircles, written from IS-GPS-200 §20.3.3.5.2.5.
            let e = el_deg / 180.0;
            let psi = 0.0137 / (e + 0.11) - 0.022;
            let phi_i = (lat_deg / 180.0 + psi * az.cos()).clamp(-0.416, 0.416);
            let lam_i = lon_deg / 180.0 + psi * az.sin() / (phi_i * PI).cos();
            let phi_m = phi_i + 0.064 * ((lam_i - 1.617) * PI).cos();
            let f = 1.0 + 16.0 * (0.53 - e).powi(3);

            // Pick the clock so local time lands mid-afternoon: at gps_sod = 0 the western cases
            // fall in the night branch, where the amplitude cancels out and the test proves nothing.
            let shift = 43_200.0 * lam_i;
            let wrap = |x: f64| x - 86_400.0 * (x / 86_400.0).floor();
            let sod = wrap(56_400.0 - shift);
            let t = wrap(shift + sod);
            let x = TAU * (t - 50_400.0) / 72_000.0;
            assert!(x.abs() < 1.57, "case needs the daytime branch, x = {x}");
            let cosine = 1.0 - x * x / 2.0 + x * x * x * x / 24.0;

            let got = klobuchar_iono_delay(alpha, beta, lat, lon, el, az, sod);
            let want = f * (5.0e-9 + (A1 * phi_m).max(0.0) * cosine) * SPEED_OF_LIGHT;
            let rel = (got - want).abs() / want;
            assert!(
                rel < 1e-13,
                "lat {lat_deg} lon {lon_deg} el {el_deg} az {az_deg}: \
                 {got:.15e} vs {want:.15e} (phi_m {phi_m:.6}, rel {rel:.2e})"
            );
        }
    }

    /// The broadcast amplitude and period are the cubics the message carries.
    ///
    /// `A = Σ αₙ φ_mⁿ` and `P = Σ βₙ φ_mⁿ` are evaluated by Horner, and the fixture that used only
    /// α₀/β₀ could not see a single one of the nested multiplications. Sampling four geomagnetic
    /// latitudes and solving the 4×4 Vandermonde returns the broadcast coefficients themselves.
    #[test]
    fn the_amplitude_and_period_are_the_broadcast_cubics_in_the_geomagnetic_latitude() {
        let alpha = [2.0e-8, 6.0e-8, -4.0e-8, 9.0e-8];
        let beta = [90_000.0, 30_000.0, -20_000.0, 40_000.0];

        // Latitude is the only free variable; azimuth 0 keeps λ_i at 0, so the local time is
        // `gps_sod` and the geomagnetic latitude is an affine function of the geodetic one.
        let el_deg = 30.0_f64;
        let e = el_deg / 180.0;
        let psi = 0.0137 / (e + 0.11) - 0.022;
        let f = 1.0 + 16.0 * (0.53 - e).powi(3);
        let offset = 0.064 * ((0.0 - 1.617) * PI).cos();

        let sample = |lat_deg: f64, sod: f64| {
            let phi_m = (lat_deg / 180.0 + psi).clamp(-0.416, 0.416) + offset;
            let d = klobuchar_iono_delay(
                alpha,
                beta,
                lat_deg.to_radians(),
                0.0,
                el_deg.to_radians(),
                0.0,
                sod,
            );
            (phi_m, d / (f * SPEED_OF_LIGHT) - 5.0e-9)
        };

        // At the 14:00 peak the cosine factor is exactly 1, so the residual *is* the amplitude,
        // whatever the period happens to be.
        for lat_deg in [-40.0_f64, -10.0, 20.0, 50.0] {
            let (phi_m, amp) = sample(lat_deg, 50_400.0);
            let want =
                alpha[0] + phi_m * (alpha[1] + phi_m * (alpha[2] + phi_m * alpha[3])).max(0.0);
            let want = want.max(0.0);
            assert!(
                (amp - want).abs() <= 1e-13 * want.abs().max(1e-9),
                "lat {lat_deg}: amplitude {amp:.15e} vs {want:.15e}"
            );
        }

        // Then hold the latitude and move the clock: the residual over the amplitude is the
        // four-term cosine of `2π(t − 50400)/P`, which determines `P`.
        for lat_deg in [-40.0_f64, 20.0] {
            let (phi_m, amp) = sample(lat_deg, 50_400.0);
            let per =
                (beta[0] + phi_m * (beta[1] + phi_m * (beta[2] + phi_m * beta[3]))).max(72_000.0);
            for sod in [40_000.0_f64, 46_000.0, 55_000.0, 61_000.0] {
                let (_, got) = sample(lat_deg, sod);
                let x = TAU * (sod - 50_400.0) / per;
                assert!(x.abs() < 1.57, "case needs the daytime branch, x = {x}");
                let want = amp * (1.0 - x * x / 2.0 + x * x * x * x / 24.0);
                assert!(
                    (got - want).abs() <= 1e-12 * want.abs(),
                    "lat {lat_deg} sod {sod}: {got:.15e} vs {want:.15e} (period {per})"
                );
            }
        }
    }

    /// Local time is the sub-ionospheric longitude plus GPS time of day, wrapped into one day.
    ///
    /// `wrap_day` exists for the two ways `43200·λ_i + t_GPS` leaves `[0, 86400)`: λ_i is up to a
    /// semicircle either side, so the sum runs over `[−43200, 129600)`. Both ends are reached here,
    /// and the delay at a wrapped time must equal the delay at the unwrapped one.
    #[test]
    fn the_local_time_wraps_the_day_around_the_sub_ionospheric_longitude() {
        let alpha = [3.0e-8, 0.0, 0.0, 0.0];
        let beta = [72_000.0, 0.0, 0.0, 0.0];
        let (el, az) = (60.0_f64.to_radians(), 0.0);

        for (lon_deg, sod) in [
            (-170.0_f64, 1_000.0_f64),
            (170.0, 85_000.0),
            (0.0, 50_400.0),
        ] {
            let d = klobuchar_iono_delay(alpha, beta, 0.0, lon_deg.to_radians(), el, az, sod);
            let raw = 43_200.0 * (lon_deg / 180.0) + sod;
            let t = raw - 86_400.0 * (raw / 86_400.0).floor();
            assert!(
                (0.0..86_400.0).contains(&t),
                "the fixture must exercise a wrap: raw {raw}"
            );
            let e = 60.0_f64 / 180.0;
            let f = 1.0 + 16.0 * (0.53 - e).powi(3);
            let x = TAU * (t - 50_400.0) / 72_000.0;
            let inner = if x.abs() < 1.57 {
                5.0e-9 + 3.0e-8 * (1.0 - x * x / 2.0 + x * x * x * x / 24.0)
            } else {
                5.0e-9
            };
            let want = f * inner * SPEED_OF_LIGHT;
            assert!(
                (d - want).abs() <= 1e-12 * want,
                "lon {lon_deg} sod {sod}: {d:.15e} vs {want:.15e} (t {t})"
            );
        }
    }

    #[test]
    fn saastamoinen_hydrostatic_is_about_two_point_three_metres_at_sea_level() {
        let zhd = saastamoinen_zenith_hydrostatic(1013.25, 45.0_f64.to_radians(), 0.0);
        assert!((2.28..2.32).contains(&zhd), "ZHD {zhd}");
    }

    #[test]
    fn saastamoinen_wet_is_a_small_positive_delay() {
        let zwd = saastamoinen_zenith_wet(288.0, 10.0);
        assert!((0.05..0.20).contains(&zwd), "ZWD {zwd}");
    }

    /// The zenith hydrostatic delay returns the three constants of Davis et al. (1985) Eq. A11.
    ///
    /// The range check above stands at 1013.25 hPa, 45° and sea level — the one point that
    /// annihilates both correction terms at once, since `cos 2φ` is zero there and the height is
    /// zero, so the denominator collapses to 1 and no mutation of it is visible. Sampling at the
    /// two latitudes where `cos 2φ` is exactly ±1 and once well off the ellipsoid instead inverts
    /// the model: `1/δ` is affine in the denominator, so three samples separate the three
    /// published constants and pin each of them.
    #[test]
    fn the_hydrostatic_delay_returns_the_three_published_constants() {
        const P: f64 = 900.0;
        const H: f64 = 2_500.0;
        let equator = saastamoinen_zenith_hydrostatic(P, 0.0, 0.0); // denominator 1 − a
        let pole = saastamoinen_zenith_hydrostatic(P, PI / 2.0, 0.0); // denominator 1 + a
        let raised = saastamoinen_zenith_hydrostatic(P, 0.0, H); // denominator 1 − a − b·H

        let a = (1.0 / pole - 1.0 / equator) / (1.0 / pole + 1.0 / equator);
        let k = 2.0 / (P * (1.0 / equator + 1.0 / pole));
        let b = (1.0 / equator - 1.0 / raised) * k * P / H;

        // The differences cancel about eight bits, so the recovery is good to ~1e-13 relative.
        for (got, want, what) in [
            (k, 0.002_276_8, "pressure scale factor"),
            (a, 0.002_66, "latitude coefficient"),
            (b, 0.000_000_28, "height coefficient"),
        ] {
            assert!(
                (got / want - 1.0).abs() < 1e-11,
                "{what}: recovered {got:.17e}, published {want:.17e}"
            );
        }
    }

    /// The zenith wet delay returns the two constants of its published form.
    ///
    /// `δ = k (1255/T + c) e` is affine in `1/T`, so two temperatures at one vapour pressure give
    /// the slope `k·1255·e` and the intercept `k·c·e`. Their ratio is `1255/c = 25100`, which no
    /// scaling of the delay can fake and which changes sign if the two terms are subtracted rather
    /// than added — the range check above admits both.
    #[test]
    fn the_wet_delay_returns_its_two_published_constants() {
        const E_HPA: f64 = 12.0;
        let (t1, t2) = (250.0_f64, 310.0_f64);
        let (d1, d2) = (
            saastamoinen_zenith_wet(t1, E_HPA),
            saastamoinen_zenith_wet(t2, E_HPA),
        );
        let slope = (d1 - d2) / (1.0 / t1 - 1.0 / t2);
        let intercept = d1 - slope / t1;

        assert!(
            (slope / intercept / 25_100.0 - 1.0).abs() < 1e-11,
            "1255/0.05 recovered as {:.17e}",
            slope / intercept
        );
        let k = slope / (1255.0 * E_HPA);
        assert!(
            (k / 0.002_277 - 1.0).abs() < 1e-11,
            "the scale factor recovered as {k:.17e}"
        );
    }

    #[test]
    fn obliquity_mapping_is_one_at_zenith_and_grows_at_low_elevation() {
        assert!((obliquity_mapping(PI / 2.0) - 1.0).abs() < 1e-12);
        assert!(obliquity_mapping(10.0_f64.to_radians()) > 5.0);
    }

    #[test]
    fn niell_matches_the_orekit_reference_values() {
        // Orekit NiellMappingFunctionModelTest: 48° lat, 68 m, 1994-01-01 (DOY 1), 5° elevation
        // → hydrostatic 10.156, wet 10.748.
        let (hydro, wet) = niell_mapping(48.0_f64.to_radians(), 68.0, 1.0, 5.0_f64.to_radians());
        assert!((hydro - 10.156).abs() < 2e-3, "hydrostatic {hydro}");
        assert!((wet - 10.748).abs() < 2e-3, "wet {wet}");
    }

    /// The southern hemisphere is the northern one, 183 days later.
    ///
    /// `t0` is 28 in the north and `28 + 183` in the south, and the latitude enters the
    /// coefficient tables only through its absolute value, so a southern site on day `d` must land
    /// on exactly the same doubles as its northern mirror on day `d − 183`. The single 48° N
    /// reference point cannot reach the southern branch at all, nor see the 183 that defines it.
    #[test]
    fn the_southern_niell_season_is_the_northern_one_shifted_by_183_days() {
        for lat_deg in [8.0_f64, 33.0, 62.0, 81.0] {
            let lat = lat_deg.to_radians();
            for doy in [1.0_f64, 97.5, 200.0, 364.0] {
                for el_deg in [5.0_f64, 25.0, 70.0] {
                    let el = el_deg.to_radians();
                    assert_eq!(
                        niell_mapping(-lat, 300.0, doy, el),
                        niell_mapping(lat, 300.0, doy - 183.0, el),
                        "lat {lat_deg}, day {doy}, elevation {el_deg}"
                    );
                }
            }
        }
    }

    /// Every Niell coefficient is affine in `cos 2π(d − t0)/365.25`.
    ///
    /// `a, b, c` are each `avg − amp·cos`, so the quarter-phase day, where the cosine passes
    /// through zero, carries the annual mean and must sit midway between the two solstitial
    /// values up to the curvature of the continued fraction — measured at `1.1e-5` relative.
    /// Dividing by the cosine instead of multiplying leaves both solstices untouched, since
    /// `amp·(±1) = amp/(±1)`, but sends the quarter-phase day to `avg ∓ amp/1e-17`: the two such
    /// mutants move the mapping factor by 13% and 2.6%, and nothing else here sees them.
    #[test]
    fn the_niell_season_is_affine_in_the_cosine_of_the_day() {
        let el = 5.0_f64.to_radians();
        for lat_deg in [-71.0_f64, -22.0, 39.0, 66.0] {
            let lat = lat_deg.to_radians();
            let t0 = if lat_deg < 0.0 { 28.0 + 183.0 } else { 28.0 };
            let m = |doy: f64| niell_mapping(lat, 0.0, doy, el);
            let (winter, summer, mean) = (m(t0), m(t0 + 365.25 / 2.0), m(t0 + 365.25 / 4.0));
            for (mid, lo, hi, what) in [
                (mean.0, winter.0, summer.0, "hydrostatic"),
                (mean.1, winter.1, summer.1, "wet"),
            ] {
                let midpoint = f64::midpoint(lo, hi);
                assert!(
                    (mid / midpoint - 1.0).abs() < 1e-4,
                    "{what} at {lat_deg}°: quarter phase {mid} against the solstitial mean \
                     {midpoint} ({lo}, {hi})"
                );
            }
        }
    }

    /// At a table-node latitude and zero height the hydrostatic factor is the bare continued
    /// fraction of `(ah, bh, ch)`, so the single seasonal factor that produced all three can be
    /// bisected back out of the public mapping and compared with the day it was asked for. That
    /// pins the *sign* of the season, which no magnitude check above can: flipping the `ch` season
    /// alone moves the 75° factor by 4.4e-4 relative, inside the 2e-3 the quoted 10.156 allows,
    /// but moves the recovered phase from 1.000000000000 to 0.867.
    ///
    /// The subtraction is independently the right direction. A ray-trace of an exponential
    /// atmosphere -- `m = ∫exp(−z(s)/H) ds / H` with `z(s)` the spherical slant geometry and no
    /// bending -- gives 10.269 at `H` = 7 km against 10.081 at 8.5 km for 5° elevation, so the
    /// factor is largest when the atmosphere is most compressed. Day 28 is northern midwinter and
    /// is where `cos` is +1, and `m` rises with the recovered phase, so that is where this puts it.
    #[test]
    fn the_niell_hydrostatic_season_is_subtracted_at_the_table_nodes() {
        let el = 5.0_f64.to_radians();
        // Node 0 (15°) has zero amplitude in all three coefficients: no season to recover.
        for (node, lat_deg) in [(1_usize, 30.0_f64), (2, 45.0), (3, 60.0), (4, 75.0)] {
            for hemisphere in [1.0_f64, -1.0] {
                let lat = (hemisphere * lat_deg).to_radians();
                let t0 = if hemisphere < 0.0 { 28.0 + 183.0 } else { 28.0 };
                for doy in [28.0_f64, 120.0, 210.0, 300.0] {
                    let want = niell_mapping(lat, 0.0, doy, el).0;
                    // Every coefficient falls as the phase rises and the fraction falls with each
                    // of them, so `m` is monotone increasing in it -- checked over [−4, 4].
                    let (mut lo, mut hi) = (-4.0_f64, 4.0);
                    for _ in 0..100 {
                        let k = f64::midpoint(lo, hi);
                        let m = niell_fraction(
                            NIELL_AH_AVG[node] - NIELL_AH_AMP[node] * k,
                            NIELL_BH_AVG[node] - NIELL_BH_AMP[node] * k,
                            NIELL_CH_AVG[node] - NIELL_CH_AMP[node] * k,
                            el,
                        );
                        if m < want { lo = k } else { hi = k }
                    }
                    let phase = f64::midpoint(lo, hi);
                    let expect = libm::cos(2.0 * PI * (doy - t0) / 365.25);
                    assert!(
                        (phase - expect).abs() < 1e-9,
                        "{lat_deg}° day {doy}: recovered phase {phase} against cos {expect}"
                    );
                }
            }
        }
    }

    #[test]
    fn niell_is_near_unity_at_the_zenith() {
        // At the zenith the continued fraction is 1 and the height correction vanishes (1/sin − 1 → 0).
        let (hydro, wet) = niell_mapping(45.0_f64.to_radians(), 0.0, 100.0, PI / 2.0);
        assert!(
            (hydro - 1.0).abs() < 1e-6 && (wet - 1.0).abs() < 1e-6,
            "{hydro} {wet}"
        );
    }

    #[test]
    fn ionospheric_mapping_is_one_at_zenith_and_grows_toward_the_horizon() {
        let (re, h) = (6_378_137.0, 350_000.0); // 350 km single-layer height
        assert!((ionospheric_mapping_factor(PI / 2.0, h, re) - 1.0).abs() < 1e-12);
        let low = ionospheric_mapping_factor(10.0_f64.to_radians(), h, re);
        let high = ionospheric_mapping_factor(60.0_f64.to_radians(), h, re);
        assert!(low > high && high > 1.0, "low {low} high {high}");
        assert!((2.0..4.0).contains(&low), "10° factor {low}"); // ~3 at low elevation
    }

    #[test]
    fn gmf_matches_the_orekit_reference_values() {
        // Orekit GlobalMappingFunctionModelTest (NRAO, Green Bank, WV): MJD 55055 (12 Aug 2009) at
        // 43200 s UTC → hydrostatic 3.425246, wet 3.449589 (IERS Conventions 2010 reference).
        let latitude = 0.6708665767;
        let longitude = -1.393397187;
        let height = 844.715;
        let elevation = 0.5 * PI - 1.278564131;
        // Orekit's AbsoluteDate.getDayOfYear(utc): day 1.0 falls on 1 January at noon, so noon of the
        // 224th day of 2009 is 224.0 (NOT 224.5); durationFrom() also crosses the 2008-12-31 leap
        // second, adding 1 s = 1/86400 day (negligible at this tolerance).
        let day_of_year = (224.0 * 86_400.0 + 1.0) / 86_400.0;
        let (hydro, wet) = gmf_mapping(latitude, longitude, height, day_of_year, elevation);
        assert!((hydro - 3.425246).abs() < 2e-6, "hydrostatic {hydro}");
        assert!((wet - 3.449589).abs() < 2e-6, "wet {wet}");
    }

    /// GMF and VMF1 are affine in the cosine of the seasonal phase, on both hemispheres. (G3)
    ///
    /// GMF's `a` coefficients are `mean + ampl·cos u` and both models' hydrostatic `c` is
    /// `c0h + [(cos u + 1)·c11h/2 + c10h]·(1 − cos φ)`, so every coefficient is affine in the same
    /// `u = cos(2π(d − t0)/T)`. The quarter-phase day, where that cosine vanishes, must therefore
    /// sit midway between the two extremes up to the curvature of the continued fraction. Each
    /// model is checked against one Orekit point on one day at one northern latitude, which fixes
    /// neither the period, nor the phase normalisation, nor the southern branch.
    /// GMF's equator belongs to the northern hemisphere.
    ///
    /// `t0` is chosen by `latitude < 0.0`, so the equator and a site an inch north of it differ in
    /// nothing else: the spherical-harmonic `a` coefficients are continuous in `sin φ` and the `c`
    /// coefficient's whole latitude term is multiplied by `1 − cos φ`, which is exactly zero
    /// there. What is left is the seasonal phase, and half a year of it is not a rounding.
    ///
    /// The neighbour is the smallest positive double, so the `a` series sees a `sin φ` that differs
    /// from zero by `1e-308` and the two calls can only disagree through `t0` — bar the couple of
    /// ulps that reducing `cos(coef − ψ)` costs when `ψ` is `π` rather than `0`.
    #[test]
    fn the_gmf_equator_belongs_to_the_northern_hemisphere() {
        let el = 12.0_f64.to_radians();
        for doy in [1.0_f64, 88.0, 205.0, 331.0] {
            let equator = gmf_mapping(0.0, 0.3, 400.0, doy, el);
            let north = gmf_mapping(f64::MIN_POSITIVE, 0.3, 400.0, doy, el);
            assert!(
                (equator.0 / north.0 - 1.0).abs() < 1e-14
                    && (equator.1 / north.1 - 1.0).abs() < 1e-14,
                "day {doy}: the equator {equator:?} does not continue the northern side {north:?}"
            );
        }
    }

    #[test]
    fn the_gmf_and_vmf1_seasons_are_affine_in_the_cosine_of_the_day() {
        let el = 7.0_f64.to_radians();
        let midway = |(mid, lo, hi): (f64, f64, f64), what: &str, at: f64| {
            let midpoint = f64::midpoint(lo, hi);
            // The floor is the continued fraction's own curvature, measured at 1.24e-5 over these
            // cases; a mutant that quadruples the seasonal swing of `c` quadruples it squared.
            assert!(
                (mid / midpoint - 1.0).abs() < 3e-5,
                "{what} at {at} deg: quarter phase {mid} against the extremal mean {midpoint} \
                 ({lo}, {hi})"
            );
        };
        for lat_deg in [-64.0_f64, -19.0, 24.0, 57.0] {
            let lat = lat_deg.to_radians();
            let t0 = if lat_deg < 0.0 { 28.0 + 183.0 } else { 28.0 };

            // GMF: period 365.25, and the day is offset by one before the phase is taken.
            let g = |doy: f64| gmf_mapping(lat, 0.7, 600.0, doy, el);
            let (peak, trough, mean) = (
                g(t0 - 1.0),
                g(t0 - 1.0 + 365.25 / 2.0),
                g(t0 - 1.0 + 365.25 / 4.0),
            );
            midway((mean.0, peak.0, trough.0), "GMF hydrostatic", lat_deg);
            midway((mean.1, peak.1, trough.1), "GMF wet", lat_deg);

            // VMF1: period 365, no day offset, and the `a` coefficients are caller-supplied, so
            // only the hydrostatic `c` carries the season.
            let v = |doy: f64| vmf1_mapping(0.001_276_83, 0.000_609_55, lat, 600.0, doy, el);
            let (peak, trough, mean) = (v(t0), v(t0 + 365.0 / 2.0), v(t0 + 365.0 / 4.0));
            midway((mean.0, peak.0, trough.0), "VMF1 hydrostatic", lat_deg);
        }
    }

    #[test]
    fn vmf1_matches_the_orekit_reference_values() {
        // Orekit ViennaOneMappingFunctionTest (NRAO, Green Bank, WV): ah=0.00127683, aw=0.00060955;
        // lat 38°, lon 280°, h 824.17 m; MJD 55055 at 0h UTC → hydrostatic 3.425088, wet 3.448300.
        // getDayOfYear(utc): 2009-08-12 is DOY 224 at noon, so midnight is 223.5; durationFrom() also
        // crosses the 2008-12-31 leap second, adding 1 s = 1/86400 day.
        let day_of_year = (223.5 * 86_400.0 + 1.0) / 86_400.0;
        let elevation = 0.5 * PI - 1.278564131;
        let (hydro, wet) = vmf1_mapping(
            0.00127683,
            0.00060955,
            38.0_f64.to_radians(),
            824.17,
            day_of_year,
            elevation,
        );
        assert!((hydro - 3.425088).abs() < 2e-6, "hydrostatic {hydro}");
        assert!((wet - 3.448300).abs() < 2e-6, "wet {wet}");
    }

    /// The three published VMF1 hydrostatic `c` constants, recovered by inverting the model.
    ///
    /// VMF1 takes its `a` coefficients from the caller and its height correction vanishes at
    /// `h = 0`, so `ch` is the single unknown left in the Marini fraction and bisection recovers it
    /// outright -- the fraction is strictly decreasing in `ch` at low elevation (measured
    /// `d(m)/m = -0.143 dc` at 5 degrees). What is asserted is Boehm et al. (2006) `c0h = 0.062`,
    /// `c10h = 0.001` north and `0.002` south, `c11h = 0.005` and `0.007`, with no restatement of
    /// the seasonal formula. Recovery is good to about thirteen significant digits.
    ///
    /// The inversion calls [`niell_fraction`] itself, which cancels exactly on both sides and so
    /// says nothing about the fraction; the published reference values above are what pin that.
    #[test]
    fn the_vmf1_hydrostatic_c_recovers_its_three_published_constants() {
        const AH: f64 = 0.001_276_83;
        const AW: f64 = 0.000_609_55;
        let el = 5.0_f64.to_radians();
        let recover_ch = |lat: f64, day: f64| {
            let want = vmf1_mapping(AH, AW, lat, 0.0, day, el).0;
            let (mut lo, mut hi) = (0.03_f64, 0.12_f64);
            for _ in 0..100 {
                let mid = f64::midpoint(lo, hi);
                if niell_fraction(AH, 0.0029, mid, el) > want {
                    lo = mid;
                } else {
                    hi = mid;
                }
            }
            f64::midpoint(lo, hi)
        };
        // VMF1 takes the phase straight from the day, so the extrema sit on t0 and half a period
        // away; in the south `psi = PI` swaps which of the two is the peak.
        for lat_deg in [-70.0_f64, -31.0, 18.0, 47.0] {
            let north = lat_deg > 0.0;
            let (t0, c10h, c11h) = if north {
                (28.0, 0.001, 0.005)
            } else {
                (28.0 + 183.0, 0.002, 0.007)
            };
            let half = 365.0 / 2.0;
            let (peak, trough) = if north {
                (t0, t0 + half)
            } else {
                (t0 - half, t0)
            };
            let lat = lat_deg.to_radians();
            let k = 1.0 - libm::cos(lat);
            let (cp, ct) = (recover_ch(lat, peak), recover_ch(lat, trough));
            for (got, want, what) in [
                ((ct - 0.062) / k, c10h, "c10h"),
                ((cp - ct) / k, c11h, "c11h"),
            ] {
                assert!(
                    (got / want - 1.0).abs() < 1e-9,
                    "{what} at {lat_deg} deg: {got} against the published {want} \
                     (c recovered as {cp} on day {peak} and {ct} on day {trough})"
                );
            }
            // The season has one peak a year, not many: a single day past it the coefficient has
            // already fallen. Nothing above sees the length of the year, because both solstices sit
            // on a half-integer number of turns and that survives dropping the 365 -- the drop is
            // `c11h/2 (1 - cos(TAU/365))` per unit `k`, 3.7e-7 north and 5.2e-7 south.
            let day_after = (cp - recover_ch(lat, peak + 1.0)) / k;
            assert!(
                day_after > 2e-7,
                "at {lat_deg} deg the day after the peak is not below it: {day_after} per unit k"
            );
            // The whole seasonal term is multiplied by `1 - cos(latitude)`, so the equator keeps the
            // mean value on every day of the year.
            let equator = recover_ch(0.0, peak);
            assert!(
                (equator - 0.062).abs() < 1e-11,
                "c0h recovered as {equator} on day {peak}"
            );
        }
    }

    /// The three published GMF hydrostatic `c` constants, recovered by inverting the model.
    ///
    /// At `h = 0` the height correction vanishes and the hydrostatic factor is the Marini fraction
    /// `m(ah, bh, ch, e)` alone, with `bh` a fixed constant. Solving that fraction for `ah` at an
    /// assumed `ch` gives `ah = (1 - m sin e) / (m Q - P)` with `P = 1/(1 + bh/(1 + ch))` and
    /// `Q = 1/(sin e + bh/(sin e + ch))`, so the `ch` at which two elevations agree on `ah` is the
    /// one the model used -- the residual is monotone in `ch` over the whole plausible range.
    /// Neither the degree-9 spherical-harmonic series behind `ah` nor the seasonal formula for `ch`
    /// is restated here: both are measured out of the model, and what is asserted is Boehm et al.
    /// (2006) `c0h = 0.062`, `c10h = 0.001` north and `0.002` south, `c11h = 0.005` and `0.007`.
    /// Recovery is good to about thirteen significant digits.
    #[test]
    fn the_gmf_hydrostatic_c_recovers_its_three_published_constants() {
        const BH: f64 = 0.0029;
        let (e1, e2) = (4.0_f64.to_radians(), 20.0_f64.to_radians());
        let ah_at = |m: f64, ch: f64, e: f64| {
            let se = libm::sin(e);
            (1.0 - m * se) / (m / (se + BH / (se + ch)) - 1.0 / (1.0 + BH / (1.0 + ch)))
        };
        let recover_ch = |lat: f64, day: f64| {
            let m = |e: f64| gmf_mapping(lat, 0.7, 0.0, day, e).0;
            let (m1, m2) = (m(e1), m(e2));
            let (mut lo, mut hi) = (0.03_f64, 0.12_f64);
            for _ in 0..100 {
                let mid = f64::midpoint(lo, hi);
                if ah_at(m1, mid, e1) - ah_at(m2, mid, e2) > 0.0 {
                    lo = mid;
                } else {
                    hi = mid;
                }
            }
            f64::midpoint(lo, hi)
        };
        // GMF offsets the day by one before taking the phase, so the extrema sit at t0 - 1 and half
        // a period away; in the south `psi = PI` swaps which of the two is the peak.
        for lat_deg in [-70.0_f64, -31.0, 18.0, 47.0] {
            let north = lat_deg > 0.0;
            let (t0, c10h, c11h) = if north {
                (28.0, 0.001, 0.005)
            } else {
                (28.0 + 183.0, 0.002, 0.007)
            };
            let half = 365.25 / 2.0;
            let (peak, trough) = if north {
                (t0 - 1.0, t0 - 1.0 + half)
            } else {
                (t0 - 1.0 - half, t0 - 1.0)
            };
            let lat = lat_deg.to_radians();
            let k = 1.0 - libm::cos(lat);
            let (cp, ct) = (recover_ch(lat, peak), recover_ch(lat, trough));
            for (got, want, what) in [
                ((ct - 0.062) / k, c10h, "c10h"),
                ((cp - ct) / k, c11h, "c11h"),
            ] {
                assert!(
                    (got / want - 1.0).abs() < 1e-9,
                    "{what} at {lat_deg} deg: {got} against the published {want} \
                     (c recovered as {cp} on day {peak} and {ct} on day {trough})"
                );
            }
            // The whole seasonal term is multiplied by `1 - cos(latitude)`, so the equator keeps the
            // mean value on every day of the year.
            let equator = recover_ch(0.0, peak);
            assert!(
                (equator - 0.062).abs() < 1e-11,
                "c0h recovered as {equator} on day {peak}"
            );
        }
    }

    #[test]
    fn vmf3_matches_the_orekit_reference_values() {
        // Orekit ViennaThreeMappingFunctionTest: ah=0.00123462, aw=0.00047101; lat 37.5°, lon 277.5°,
        // h 824.0 m; 2018-11-25 12:00:00 UTC → DOY 329.0 (noon, no leap second crossed in 2018).
        let day_of_year = 329.0;
        let ah = 0.00123462;
        let aw = 0.00047101;
        let lat = 37.5_f64.to_radians();
        let lon = 277.5_f64.to_radians();
        let h = 824.0;

        // Elevation 38° → hydrostatic 1.621024, wet 1.623023.
        let (hydro, wet) = vmf3_mapping(ah, aw, lat, lon, h, day_of_year, 38.0_f64.to_radians());
        assert!((hydro - 1.621024).abs() < 2e-6, "38° hydrostatic {hydro}");
        assert!((wet - 1.623023).abs() < 2e-6, "38° wet {wet}");

        // Elevation 5° → hydrostatic 10.132802, wet 10.879154.
        let (hydro, wet) = vmf3_mapping(ah, aw, lat, lon, h, day_of_year, 5.0_f64.to_radians());
        assert!((hydro - 10.132802).abs() < 2e-6, "5° hydrostatic {hydro}");
        assert!((wet - 10.879154).abs() < 2e-6, "5° wet {wet}");

        // Elevation 85° → hydrostatic 1.003810, wet 1.003816.
        let (hydro, wet) = vmf3_mapping(ah, aw, lat, lon, h, day_of_year, 85.0_f64.to_radians());
        assert!((hydro - 1.003810).abs() < 2e-6, "85° hydrostatic {hydro}");
        assert!((wet - 1.003816).abs() < 2e-6, "85° wet {wet}");
    }

    /// The Niell, GMF and VMF3 coefficient tables, sealed.
    ///
    /// The mapping factors these tables drive are smooth functions of a few thousand harmonic
    /// coefficients, and the accuracy assertions above hold them to ~1e-6 — far above what a single
    /// flipped sign at degree 11 moves the answer by. `cargo mutants` makes that concrete: 426 of
    /// the module's survivors are `delete -` on a table entry, and not one existing test can see
    /// any of them. What a test *can* see is that the bytes are no longer the ones that were
    /// transcribed. The constant comes from `derivations/table_seals.py`, which reads the same file
    /// with Python's float parser, so the two sides are independent parses of the same text rather
    /// than one checked against itself.
    #[test]
    fn the_mapping_coefficient_tables_are_the_ones_that_were_transcribed() {
        let niell = [
            NIELL_AH_AVG,
            NIELL_BH_AVG,
            NIELL_CH_AVG,
            NIELL_AH_AMP,
            NIELL_BH_AMP,
            NIELL_CH_AMP,
            NIELL_AW,
            NIELL_BW,
            NIELL_CW,
        ];
        let gmf = [
            GMF_AH_MEAN,
            GMF_BH_MEAN,
            GMF_AH_AMPL,
            GMF_BH_AMPL,
            GMF_AW_MEAN,
            GMF_BW_MEAN,
            GMF_AW_AMPL,
            GMF_BW_AMPL,
        ];
        let vmf3: [&Vmf3Table; 8] = [&BH_A, &BW_A, &CH_A, &CW_A, &BH_B, &BW_B, &CH_B, &CW_B];
        let flat: Vec<f64> = niell
            .iter()
            .flatten()
            .chain(gmf.iter().flatten())
            .chain(vmf3.iter().copied().flatten().flatten())
            .copied()
            .collect();
        assert_eq!(flat.len(), 9 * 5 + 8 * 55 + 8 * 91 * 5, "table sizes moved");
        let seal = spacelab_testkit::fnv1a_f64(flat);
        assert_eq!(
            seal, 0xa6ba_046e_48bd_170b,
            "Niell/GMF/VMF3 coefficients moved"
        );
    }
}