sofars 0.6.0

Pure Rust implementation of the IAU SOFA library
Documentation 
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use crate::consts::{D2PI, DAS2R, DJ00, DJM};
use crate::vm::anpm;

///  Approximate heliocentric position and velocity of a nominated
///  planet:  Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or
///  Neptune (but not the Earth itself).
///
///  This function is part of the International Astronomical Union's
///  SOFA (Standards of Fundamental Astronomy) software collection.
///
///  Status:  support function.
///
///  n.b. Not IAU-endorsed and without canonical status.
///
///  Given:
///     date1  double       TDB date part A (Note 1)
///     date2  double       TDB date part B (Note 1)
///     np     int          planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
///                             5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
///
///  Returned:
///     pv     [[f64; 3]; 2] planet p,v (heliocentric, J2000.0, au,au/d)
///
///  Returned (function value):
///            int          status: -1 = illegal NP (outside 1-8)
///                                  0 = OK
///                                 +1 = warning: year outside 1000-3000
///                                 +2 = warning: failed to converge
///
pub fn plan94(date1: f64, date2: f64, np: i32) -> Result<([[f64; 3]; 2], i32), i32> {
    /* Gaussian constant */
    const GK: f64 = 0.017202098950;

    /* Sin and cos of J2000.0 mean obliquity (IAU 1976) */
    const SINEPS: f64 = 0.3977771559319137;
    const COSEPS: f64 = 0.9174820620691818;

    /* Maximum number of iterations allowed to solve Kepler's equation */
    const KMAX: i32 = 10;

    /* Planetary inverse masses */
    const AMAS: [f64; 8] = [
        6023600.0, /* Mercury */
        408523.5,  /* Venus   */
        328900.5,  /* EMB     */
        3098710.0, /* Mars    */
        1047.355,  /* Jupiter */
        3498.5,    /* Saturn  */
        22869.0,   /* Uranus  */
        19314.0,   /* Neptune */
    ];

    /* Mean semi-major axis (au) */
    const A_COEFFS: [[f64; 3]; 8] = [
        [0.3870983098, 0.0, 0.0],
        [0.7233298200, 0.0, 0.0],
        [1.0000010178, 0.0, 0.0],
        [1.5236793419, 3e-10, 0.0],
        [5.2026032092, 19132e-10, -39e-10],
        [9.5549091915, -0.0000213896, 444e-10],
        [19.2184460618, -3716e-10, 979e-10],
        [30.1103868694, -16635e-10, 686e-10],
    ];

    /* Mean longitude (degree and arcsecond) */
    const DLM_COEFFS: [[f64; 3]; 8] = [
        [252.25090552, 5381016286.88982, -1.92789],
        [181.97980085, 2106641364.33548, 0.59381],
        [100.46645683, 1295977422.83429, -2.04411],
        [355.43299958, 689050774.93988, 0.94264],
        [34.35151874, 109256603.77991, -30.60378],
        [50.07744430, 43996098.55732, 75.61614],
        [314.05500511,   15424811.93933,  -1.75083],
        [304.34866548,    7865503.20744,   0.21103]
    ];

    /* Eccentricity */
    const E_COEFFS: [[f64; 3]; 8] = [
        [0.2056317526, 0.0002040653, -28349e-10],
        [0.0067719164, -0.0004776521, 98127e-10],
        [0.0167086342, -0.0004203654, -0.0000126734],
        [0.0934006477, 0.0009048438, -80641e-10],
        [0.0484979255, 0.0016322542, -0.0000471366],
        [0.0555481426, -0.0034664062, -0.0000643639],
        [0.0463812221, -0.0002729293, 0.0000078913],
        [0.0094557470, 0.0000603263, 0.0],
    ];

    /* Longitude of the perihelion (degree and arcsecond) */
    const PI_COEFFS: [[f64; 3]; 8] = [
        [77.45611904, 5719.11590, -4.83016],
        [131.56370300, 175.48640, -498.48184],
        [102.93734808, 11612.35290, 53.27577],
        [336.06023395, 15980.45908, -62.32800],
        [14.33120687, 7758.75163, 259.95938],
        [93.05723748, 20395.49439, 190.25952],
        [173.00529106, 3215.56238, -34.09288],
        [48.12027554, 1050.71912, 27.39717],
    ];

    /* Inclination (degree and arcsecond) */
    const DINC_COEFFS: [[f64; 3]; 8] = [
        [7.00498625, -214.25629, 0.28977],
        [3.39466189, -30.84437, -11.67836],
        [0.0, 469.97289, -3.35053],
        [1.84972648, -293.31722, -8.11830],
        [1.30326698, -71.55890, 11.95297],
        [2.48887878, 91.85195, -17.66225],
        [0.77319689, -60.72723, 1.25759],
        [1.76995259, 8.12333, 0.08135],
    ];

    /* Longitude of the ascending node (degree and arcsecond) */
    const OMEGA_COEFFS: [[f64; 3]; 8] = [
        [48.33089304, -4515.21727, -31.79892],
        [76.67992019, -10008.48154, -51.32614],
        [174.87317577, -8679.27034, 15.34191],
        [49.55809321, -10620.90088, -230.57416],
        [100.46440702,   6362.03561,  326.52178],
        [113.66550252,  -9240.19942,  -66.23743],
        [74.00595701,   2669.15033,  145.93964],
        [131.78405702,   -221.94322,   -0.78728]
    ];

    const KP: [[f64; 9]; 8] = [
        [69613.0, 75645.0, 88306.0, 59899.0, 15746.0, 71087.0, 142173.0, 3086.0, 0.0],
        [21863.0, 32794.0, 26934.0, 10931.0, 26250.0, 43725.0, 53867.0, 28939.0, 0.0],
        [16002.0, 21863.0, 32004.0, 10931.0, 14529.0, 16368.0, 15318.0, 32794.0, 0.0],
        [6345.0, 7818.0, 15636.0, 7077.0, 8184.0, 14163.0, 1107.0, 4872.0, 0.0],
        [1760.0, 1454.0, 1167.0, 880.0, 287.0, 2640.0, 19.0, 2047.0, 1454.0],
        [574.0, 0.0, 880.0, 287.0, 19.0, 1760.0, 1167.0, 306.0, 574.0],
        [204.0, 0.0, 177.0, 1265.0, 4.0, 385.0, 200.0, 208.0, 204.0],
        [0.0, 102.0, 106.0, 4.0, 98.0, 1367.0, 487.0, 204.0, 0.0],
    ];

    const CA: [[f64; 9]; 8] = [
        [4.0, -13.0, 11.0, -9.0, -9.0, -3.0, -1.0, 4.0, 0.0],
        [-156.0, 59.0, -42.0, 6.0, 19.0, -20.0, -10.0, -12.0, 0.0],
        [64.0, -152.0, 62.0, -8.0, 32.0, -41.0, 19.0, -11.0, 0.0],
        [124.0, 621.0, -145.0, 208.0, 54.0, -57.0, 30.0, 15.0, 0.0],
        [-23437.0, -2634.0, 6601.0, 6259.0, -1507.0, -1821.0, 2620.0, -2115.0, -1489.0],
        [62911.0, -119919.0, 79336.0, 17814.0, -24241.0, 12068.0, 8306.0, -4893.0, 8902.0],
        [389061.0, -262125.0, -44088.0, 8387.0, -22976.0, -2093.0, -615.0, -9720.0, 6633.0],
        [-412235.0, -157046.0, -31430.0, 37817.0, -9740.0, -13.0, -7449.0, 9644.0, 0.0],
    ];

    const SA: [[f64; 9]; 8] = [
        [-29.0, -1.0, 9.0, 6.0, -6.0, 5.0, 4.0, 0.0, 0.0],
        [-48.0, -125.0, -26.0, -37.0, 18.0, -13.0, -20.0, -2.0, 0.0],
        [-150.0, -46.0, 68.0, 54.0, 14.0, 24.0, -28.0, 22.0, 0.0],
        [-621.0, 532.0, -694.0, -20.0, 192.0, -94.0, 71.0, -73.0, 0.0],
        [-14614.0, -19828.0, -5869.0, 1881.0, -4372.0, -2255.0, 782.0, 930.0, 913.0],
        [139737.0, 0.0, 24667.0, 51123.0, -5102.0, 7429.0, -4095.0, -1976.0, -9566.0],
        [-138081.0, 0.0, 37205.0, -49039.0, -41901.0, -33872.0, -27037.0, -12474.0, 18797.0],
        [0.0, 28492.0, 133236.0, 69654.0, 52322.0, -49577.0, -26430.0, -3593.0, 0.0],
    ];

    const KQ: [[f64; 10]; 8] = [
        [3086.0, 15746.0, 69613.0, 59899.0, 75645.0, 88306.0, 12661.0, 2658.0, 0.0, 0.0],
        [21863.0, 32794.0, 10931.0, 73.0, 4387.0, 26934.0, 1473.0, 2157.0, 0.0, 0.0],
        [10.0, 16002.0, 21863.0, 10931.0, 1473.0, 32004.0, 4387.0, 73.0, 0.0, 0.0],
        [10.0, 6345.0, 7818.0, 1107.0, 15636.0, 7077.0, 8184.0, 532.0, 10.0, 0.0],
        [19.0, 1760.0, 1454.0, 287.0, 1167.0, 880.0, 574.0, 2640.0, 19.0, 1454.0],
        [19.0, 574.0, 287.0, 306.0, 1760.0, 12.0, 31.0, 38.0, 19.0, 574.0],
        [4.0, 204.0, 177.0, 8.0, 31.0, 200.0, 1265.0, 102.0, 4.0, 204.0],
        [4.0, 102.0, 106.0, 8.0, 98.0, 1367.0, 487.0, 204.0, 4.0, 102.0],
    ];

    const CL: [[f64; 10]; 8] = [
        [21.0, -95.0, -157.0, 41.0, -5.0, 42.0, 23.0, 30.0, 0.0, 0.0],
        [-160.0, -313.0, -235.0, 60.0, -74.0, -76.0, -27.0, 34.0, 0.0, 0.0],
        [-325.0, -322.0, -79.0, 232.0, -52.0, 97.0, 55.0, -41.0, 0.0, 0.0],
        [2268.0, -979.0, 802.0, 602.0, -668.0, -33.0, 345.0, 201.0, -55.0, 0.0],
        [7610.0, -4997.0, -7689.0, -5841.0, -2617.0, 1115.0, -748.0, -607.0, 6074.0, 354.0],
        [-18549.0, 30125.0, 20012.0, -730.0, 824.0, 23.0, 1289.0, -352.0, -14767.0, -2062.0],
        [-135245.0, -14594.0, 4197.0, -4030.0, -5630.0, -2898.0, 2540.0, -306.0, 2939.0, 1986.0],
        [89948.0, 2103.0, 8963.0, 2695.0, 3682.0, 1648.0, 866.0, -154.0, -1963.0, -283.0],
    ];

    const SL: [[f64; 10]; 8] = [
        [-342.0, 136.0, -23.0, 62.0, 66.0, -52.0, -33.0, 17.0, 0.0, 0.0],
        [524.0, -149.0, -35.0, 117.0, 151.0, 122.0, -71.0, -62.0, 0.0, 0.0],
        [-105.0, -137.0, 258.0, 35.0, -116.0, -88.0, -112.0, -80.0, 0.0, 0.0],
        [854.0, -205.0, -936.0, -240.0, 140.0, -341.0, -97.0, -232.0, 536.0, 0.0],
        [-56980.0, 8016.0, 1012.0, 1448.0, -3024.0, -3710.0, 318.0, 503.0, 3767.0, 577.0],
        [138606.0, -13478.0, -4964.0, 1441.0, -1319.0, -1482.0, 427.0, 1236.0, -9167.0, -1918.0],
        [71234.0, -41116.0, 5334.0, -4935.0, -1848.0, 66.0, 434.0, -1748.0, 3780.0, -701.0],
        [-47645.0, 11647.0, 2166.0, 3194.0, 679.0, 0.0, -244.0, -419.0, -2531.0, 48.0],
    ];

    let mut jstat;
    let mut pv = [[0.0; 3]; 2];

    /* Validate the planet number. */
    if (np < 1) || (np > 8) {
        return Err(-1);
    }

    /* Decrement the planet number to start at zero. */
    let p_idx = (np - 1) as usize;

    /* Time: Julian millennia since J2000.0. */
    let t = ((date1 - DJ00) + date2) / DJM;

    /* OK status unless remote date. */
    jstat = if t.abs() <= 1.0 { 0 } else { 1 };

    /* Compute the mean elements. */
    let mut da = A_COEFFS[p_idx][0] + (A_COEFFS[p_idx][1] + A_COEFFS[p_idx][2] * t) * t;
    let mut dl = (3600.0 * DLM_COEFFS[p_idx][0] + (DLM_COEFFS[p_idx][1] + DLM_COEFFS[p_idx][2] * t) * t) * DAS2R;
    let de = E_COEFFS[p_idx][0] + (E_COEFFS[p_idx][1] + E_COEFFS[p_idx][2] * t) * t;
    let dp = anpm((3600.0 * PI_COEFFS[p_idx][0] + (PI_COEFFS[p_idx][1] + PI_COEFFS[p_idx][2] * t) * t) * DAS2R);
    let di = (3600.0 * DINC_COEFFS[p_idx][0] + (DINC_COEFFS[p_idx][1] + DINC_COEFFS[p_idx][2] * t) * t) * DAS2R;
    let dom = anpm((3600.0 * OMEGA_COEFFS[p_idx][0] + (OMEGA_COEFFS[p_idx][1] + OMEGA_COEFFS[p_idx][2] * t) * t) * DAS2R);

    /* Apply the trigonometric terms. */
    let dmu = 0.35953620 * t;
    for k in 0..8 {
        let arga = KP[p_idx][k] * dmu;
        let argl = KQ[p_idx][k] * dmu;
        da += (CA[p_idx][k] * arga.cos() + SA[p_idx][k] * arga.sin()) * 1e-7;
        dl += (CL[p_idx][k] * argl.cos() + SL[p_idx][k] * argl.sin()) * 1e-7;
    }
    let arga = KP[p_idx][8] * dmu;
    da += t * (CA[p_idx][8] * arga.cos() + SA[p_idx][8] * arga.sin()) * 1e-7;
    for k in 8..10 {
        let argl = KQ[p_idx][k] * dmu;
        dl += t * (CL[p_idx][k] * argl.cos() + SL[p_idx][k] * argl.sin()) * 1e-7;
    }
    dl = dl.rem_euclid(D2PI);

    /* Iterative soln. of Kepler's equation to get eccentric anomaly. */
    let am = dl - dp;
    let mut ae = am + de * am.sin();
    let mut k = 0;
    let mut dae: f64 = 1.0;
    while k < KMAX && dae.abs() > 1e-12 {
        dae = (am - ae + de * ae.sin()) / (1.0 - de * ae.cos());
        ae += dae;
        k += 1;
        if k == KMAX - 1 {
            jstat = 2;
        }
    }

    /* True anomaly. */
    let ae2 = ae / 2.0;
    let at = 2.0 * (((1.0 + de) / (1.0 - de)).sqrt() * ae2.sin()).atan2(ae2.cos());

    /* Distance (au) and speed (radians per day). */
    let r = da * (1.0 - de * ae.cos());
    let v = GK * ((1.0 + 1.0 / AMAS[p_idx]) / (da * da * da)).sqrt();

    let si2 = (di / 2.0).sin();
    let xq = si2 * dom.cos();
    let xp = si2 * dom.sin();
    let tl = at + dp;
    let xsw = tl.sin();
    let xcw = tl.cos();
    let xm2 = 2.0 * (xp * xcw - xq * xsw);
    let xf = da / (1.0 - de * de).sqrt();
    let ci2 = (di / 2.0).cos();
    let xms = (de * dp.sin() + xsw) * xf;
    let xmc = (de * dp.cos() + xcw) * xf;
    let xpxq2 = 2.0 * xp * xq;

    /* Position (J2000.0 ecliptic x,y,z in au). */
    let x = r * (xcw - xm2 * xp);
    let y = r * (xsw + xm2 * xq);
    let z = r * (-xm2 * ci2);

    /* Rotate to equatorial. */
    pv[0][0] = x;
    pv[0][1] = y * COSEPS - z * SINEPS;
    pv[0][2] = y * SINEPS + z * COSEPS;

    /* Velocity (J2000.0 ecliptic xdot,ydot,zdot in au/d). */
    let vx = v * ((-1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc);
    let vy = v * ((1.0 - 2.0 * xq * xq) * xmc - xpxq2 * xms);
    let vz = v * (2.0 * ci2 * (xp * xms + xq * xmc));

    /* Rotate to equatorial. */
    pv[1][0] = vx;
    pv[1][1] = vy * COSEPS - vz * SINEPS;
    pv[1][2] = vy * SINEPS + vz * COSEPS;

    Ok((pv, jstat))
}