#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(vandg4, "van der Grinten IV") "\n\tMisc Sph, no inv";

#define TOL 1e-10

static PJ_XY vandg4_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */

    PJ_XY xy = {0.0, 0.0};

    double x1, t, bt, ct, ft, bt2, ct2, dt, dt2;

    (void)P;

    if (fabs(lp.phi) < TOL) {

        xy.x = lp.lam;

        xy.y = 0.;

    } else if (fabs(lp.lam) < TOL || fabs(fabs(lp.phi) - M_HALFPI) < TOL) {

        xy.x = 0.;

        xy.y = lp.phi;

    } else {

        bt = fabs(M_TWO_D_PI * lp.phi);

        bt2 = bt * bt;

        ct = 0.5 * (bt * (8. - bt * (2. + bt2)) - 5.) / (bt2 * (bt - 1.));

        ct2 = ct * ct;

        dt = M_TWO_D_PI * lp.lam;

        dt = dt + 1. / dt;

        dt = sqrt(dt * dt - 4.);

        if ((fabs(lp.lam) - M_HALFPI) < 0.)

            dt = -dt;

        dt2 = dt * dt;

        x1 = bt + ct;

        x1 *= x1;

        t = bt + 3. * ct;

        ft = x1 * (bt2 + ct2 * dt2 - 1.) +

             (1. - bt2) *

                 (bt2 * (t * t + 4. * ct2) + ct2 * (12. * bt * ct + 4. * ct2));

        x1 = (dt * (x1 + ct2 - 1.) + 2. * sqrt(ft)) / (4. * x1 + dt2);

        xy.x = M_HALFPI * x1;

        xy.y = M_HALFPI * sqrt(1. + dt * fabs(x1) - x1 * x1);

        if (lp.lam < 0.)

            xy.x = -xy.x;

        if (lp.phi < 0.)

            xy.y = -xy.y;

    }

    return xy;

}

PJ *PJ_PROJECTION(vandg4) {

    P->es = 0.;

    P->fwd = vandg4_s_forward;

    return P;

}