#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

#define HLFPI2 2.46740110027233965467 /* (pi/2)^2 */

#define EPS 1e-10

namespace { // anonymous namespace

struct pj_bacon {

    int bacn;

    int ortl;

};

} // anonymous namespace

PROJ_HEAD(apian, "Apian Globular I") "\n\tMisc Sph, no inv";

PROJ_HEAD(ortel, "Ortelius Oval") "\n\tMisc Sph, no inv";

PROJ_HEAD(bacon, "Bacon Globular") "\n\tMisc Sph, no inv";

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

    PJ_XY xy = {0.0, 0.0};

    struct pj_bacon *Q = static_cast<struct pj_bacon *>(P->opaque);

    double ax, f;

    xy.y = Q->bacn ? M_HALFPI * sin(lp.phi) : lp.phi;

    ax = fabs(lp.lam);

    if (ax >= EPS) {

        if (Q->ortl && ax >= M_HALFPI)

            xy.x = sqrt(HLFPI2 - lp.phi * lp.phi + EPS) + ax - M_HALFPI;

        else {

            f = 0.5 * (HLFPI2 / ax + ax);

            xy.x = ax - f + sqrt(f * f - xy.y * xy.y);

        }

        if (lp.lam < 0.)

            xy.x = -xy.x;

    } else

        xy.x = 0.;

    return (xy);

}

PJ *PJ_PROJECTION(bacon) {

    struct pj_bacon *Q =

        static_cast<struct pj_bacon *>(calloc(1, sizeof(struct pj_bacon)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->bacn = 1;

    Q->ortl = 0;

    P->es = 0.;

    P->fwd = bacon_s_forward;

    return P;

}

PJ *PJ_PROJECTION(apian) {

    struct pj_bacon *Q =

        static_cast<struct pj_bacon *>(calloc(1, sizeof(struct pj_bacon)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->bacn = Q->ortl = 0;

    P->es = 0.;

    P->fwd = bacon_s_forward;

    return P;

}

PJ *PJ_PROJECTION(ortel) {

    struct pj_bacon *Q =

        static_cast<struct pj_bacon *>(calloc(1, sizeof(struct pj_bacon)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->bacn = 0;

    Q->ortl = 1;

    P->es = 0.;

    P->fwd = bacon_s_forward;

    return P;

}

#undef HLFPI2

#undef EPS