#define PJ_LIB__

#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 *PROJECTION(vandg4) {
    P->es = 0.;
    P->fwd = vandg4_s_forward;

    return P;
}
