#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(wink2, "Winkel II") "\n\tPCyl, Sph\n\tlat_1=";

namespace { // anonymous namespace

struct pj_wink2_data {

    double cosphi1;

};

} // anonymous namespace

#define MAX_ITER 10

#define LOOP_TOL 1e-7

static PJ_XY wink2_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */

    PJ_XY xy = {0.0, 0.0};

    int i;

    xy.y = lp.phi * M_TWO_D_PI;

    const double k = M_PI * sin(lp.phi);

    lp.phi *= 1.8;

    for (i = MAX_ITER; i; --i) {

        const double V = (lp.phi + sin(lp.phi) - k) / (1. + cos(lp.phi));

        lp.phi -= V;

        if (fabs(V) < LOOP_TOL)

            break;

    }

    if (!i)

        lp.phi = (lp.phi < 0.) ? -M_HALFPI : M_HALFPI;

    else

        lp.phi *= 0.5;

    xy.x =

        0.5 * lp.lam *

        (cos(lp.phi) + static_cast<struct pj_wink2_data *>(P->opaque)->cosphi1);

    xy.y = M_FORTPI * (sin(lp.phi) + xy.y);

    return xy;

}

static PJ_LP wink2_s_inverse(PJ_XY xy, PJ *P) {

    PJ_LP lpInit;

    lpInit.phi = xy.y;

    lpInit.lam = xy.x;

    constexpr double deltaXYTolerance = 1e-10;

    return pj_generic_inverse_2d(xy, P, lpInit, deltaXYTolerance);

}

PJ *PJ_PROJECTION(wink2) {

    struct pj_wink2_data *Q = static_cast<struct pj_wink2_data *>(

        calloc(1, sizeof(struct pj_wink2_data)));

    if (nullptr == Q)

        return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);

    P->opaque = Q;

    static_cast<struct pj_wink2_data *>(P->opaque)->cosphi1 =

        cos(pj_param(P->ctx, P->params, "rlat_1").f);

    P->es = 0.;

    P->fwd = wink2_s_forward;

    P->inv = wink2_s_inverse;

    return P;

}

#undef MAX_ITER

#undef LOOP_TOL