#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(nell_h, "Nell-Hammer") "\n\tPCyl, Sph";

#define NITER 9

#define EPS 1e-7

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

    PJ_XY xy = {0.0, 0.0};

    (void)P;

    xy.x = 0.5 * lp.lam * (1. + cos(lp.phi));

    xy.y = 2.0 * (lp.phi - tan(0.5 * lp.phi));

    return xy;

}

static PJ_LP nell_h_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */

    PJ_LP lp = {0.0, 0.0};

    int i;

    (void)P;

    const double p = 0.5 * xy.y;

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

        const double c = cos(0.5 * lp.phi);

        const double V = (lp.phi - tan(lp.phi / 2) - p) / (1. - 0.5 / (c * c));

        lp.phi -= V;

        if (fabs(V) < EPS)

            break;

    }

    if (!i) {

        lp.phi = p < 0. ? -M_HALFPI : M_HALFPI;

        lp.lam = 2. * xy.x;

    } else

        lp.lam = 2. * xy.x / (1. + cos(lp.phi));

    return lp;

}

PJ *PJ_PROJECTION(nell_h) {

    P->es = 0.;

    P->inv = nell_h_s_inverse;

    P->fwd = nell_h_s_forward;

    return P;

}

#undef NITER

#undef EPS