#include <math.h>

#include "proj.h"
#include "proj_internal.h"

PROJ_HEAD(putp2, "Putnins P2") "\n\tPCyl, Sph";

#define C_x 1.89490
#define C_y 1.71848
#define C_p 0.6141848493043784
#define EPS 1e-10
#define NITER 10
#define PI_DIV_3 1.0471975511965977

static PJ_XY putp2_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */
    PJ_XY xy = {0.0, 0.0};
    int i;
    (void)P;

    const double p = C_p * sin(lp.phi);
    const double phi_pow_2 = lp.phi * lp.phi;
    lp.phi *= 0.615709 + phi_pow_2 * (0.00909953 + phi_pow_2 * 0.0046292);
    for (i = NITER; i; --i) {
        const double c = cos(lp.phi);
        const double s = sin(lp.phi);
        const double V =
            (lp.phi + s * (c - 1.) - p) / (1. + c * (c - 1.) - s * s);
        lp.phi -= V;
        if (fabs(V) < EPS)
            break;
    }
    if (!i)
        lp.phi = lp.phi < 0 ? -PI_DIV_3 : PI_DIV_3;
    xy.x = C_x * lp.lam * (cos(lp.phi) - 0.5);
    xy.y = C_y * sin(lp.phi);

    return xy;
}

static PJ_LP putp2_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
    PJ_LP lp = {0.0, 0.0};

    lp.phi = aasin(P->ctx, xy.y / C_y);
    const double c = cos(lp.phi);
    lp.lam = xy.x / (C_x * (c - 0.5));
    lp.phi = aasin(P->ctx, (lp.phi + sin(lp.phi) * (c - 1.)) / C_p);

    return lp;
}

PJ *PJ_PROJECTION(putp2) {
    P->es = 0.;
    P->inv = putp2_s_inverse;
    P->fwd = putp2_s_forward;

    return P;
}

#undef C_x
#undef C_y
#undef C_p
#undef EPS
#undef NITER
#undef PI_DIV_3