#define PJ_LIB__
#include <errno.h>
#include "proj.h"
#include "proj_internal.h"
#include <math.h>


namespace { // anonymous namespace
enum Type {
    EULER  = 0,
    MURD1  = 1,
    MURD2  = 2,
    MURD3  = 3,
    PCONIC = 4,
    TISSOT = 5,
    VITK1  = 6
};
} // anonymous namespace

namespace { // anonymous namespace
struct pj_opaque {
    double  n;
    double  rho_c;
    double  rho_0;
    double  sig;
    double  c1, c2;
    enum Type type;
};
} // anonymous namespace


#define EPS10   1.e-10
#define EPS 1e-10
#define LINE2 "\n\tConic, Sph\n\tlat_1= and lat_2="

PROJ_HEAD(euler, "Euler")                LINE2;
PROJ_HEAD(murd1, "Murdoch I")            LINE2;
PROJ_HEAD(murd2, "Murdoch II")           LINE2;
PROJ_HEAD(murd3, "Murdoch III")          LINE2;
PROJ_HEAD(pconic, "Perspective Conic")   LINE2;
PROJ_HEAD(tissot, "Tissot")              LINE2;
PROJ_HEAD(vitk1, "Vitkovsky I")          LINE2;



/* get common factors for simple conics */
static int phi12(PJ *P, double *del) {
    double p1, p2;
    int err = 0;

    if (!pj_param(P->ctx, P->params, "tlat_1").i ||
        !pj_param(P->ctx, P->params, "tlat_2").i) {
        err = -41;
    } else {
        p1 = pj_param(P->ctx, P->params, "rlat_1").f;
        p2 = pj_param(P->ctx, P->params, "rlat_2").f;
        *del = 0.5 * (p2 - p1);
        static_cast<struct pj_opaque*>(P->opaque)->sig = 0.5 * (p2 + p1);
        err = (fabs(*del) < EPS || fabs(static_cast<struct pj_opaque*>(P->opaque)->sig) < EPS) ? PJD_ERR_ABS_LAT1_EQ_ABS_LAT2 : 0;
    }
    return err;
}


static PJ_XY sconics_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forward */
    PJ_XY xy = {0.0, 0.0};
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    double rho;

    switch (Q->type) {
    case MURD2:
        rho = Q->rho_c + tan (Q->sig - lp.phi);
        break;
    case PCONIC:
        rho = Q->c2 * (Q->c1 - tan (lp.phi - Q->sig));
        break;
    default:
        rho = Q->rho_c - lp.phi;
        break;
    }

    xy.x = rho * sin ( lp.lam *= Q->n );
    xy.y = Q->rho_0 - rho * cos (lp.lam);
    return xy;
}


static PJ_LP sconics_s_inverse (PJ_XY xy, PJ *P) {  /* Spheroidal, (and ellipsoidal?) inverse */
    PJ_LP lp = {0.0, 0.0};
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    double rho;

    rho = hypot (xy.x,  xy.y = Q->rho_0 - xy.y);
    if (Q->n < 0.) {
        rho = - rho;
        xy.x = - xy.x;
        xy.y = - xy.y;
    }

    lp.lam = atan2 (xy.x, xy.y) / Q->n;

    switch (Q->type) {
    case PCONIC:
        lp.phi = atan (Q->c1 - rho / Q->c2) + Q->sig;
        break;
    case MURD2:
        lp.phi = Q->sig - atan(rho - Q->rho_c);
        break;
    default:
        lp.phi = Q->rho_c - rho;
    }
    return lp;
}


static PJ *setup(PJ *P, enum Type type) {
    double del, cs;
    int err;
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
    if (nullptr==Q)
        return pj_default_destructor (P, ENOMEM);
    P->opaque = Q;
    Q->type = type;

    err = phi12 (P, &del);
    if(err)
        return pj_default_destructor (P, err);

    switch (Q->type) {

    case TISSOT:
        Q->n = sin (Q->sig);
        cs = cos (del);
        Q->rho_c = Q->n / cs + cs / Q->n;
        Q->rho_0 = sqrt ((Q->rho_c - 2 * sin (P->phi0)) / Q->n);
        break;

    case MURD1:
        Q->rho_c = sin(del)/(del * tan(Q->sig)) + Q->sig;
        Q->rho_0 = Q->rho_c - P->phi0;
        Q->n = sin(Q->sig);
        break;

    case MURD2:
        Q->rho_c = (cs = sqrt (cos (del))) / tan (Q->sig);
        Q->rho_0 = Q->rho_c + tan (Q->sig - P->phi0);
        Q->n = sin (Q->sig) * cs;
        break;

    case MURD3:
        Q->rho_c = del / (tan(Q->sig) * tan(del)) + Q->sig;
        Q->rho_0 = Q->rho_c - P->phi0;
        Q->n = sin (Q->sig) * sin (del) * tan (del) / (del * del);
        break;

    case EULER:
        Q->n = sin (Q->sig) * sin (del) / del;
        del *= 0.5;
        Q->rho_c = del / (tan (del) * tan (Q->sig)) + Q->sig;
        Q->rho_0 = Q->rho_c - P->phi0;
        break;

    case PCONIC:
        Q->n = sin (Q->sig);
        Q->c2 = cos (del);
        Q->c1 = 1./tan (Q->sig);
        if (fabs (del = P->phi0 - Q->sig) - EPS10 >= M_HALFPI)
            return pj_default_destructor(P, PJD_ERR_LAT_0_HALF_PI_FROM_MEAN);

        Q->rho_0 = Q->c2 * (Q->c1 - tan (del));
        break;

    case VITK1:
        Q->n = (cs = tan (del)) * sin (Q->sig) / del;
        Q->rho_c = del / (cs * tan (Q->sig)) + Q->sig;
        Q->rho_0 = Q->rho_c - P->phi0;
        break;
    }

    P->inv = sconics_s_inverse;
    P->fwd = sconics_s_forward;
    P->es = 0;
    return (P);
}


PJ *PROJECTION(euler) {
    return setup(P, EULER);
}


PJ *PROJECTION(tissot) {
    return setup(P, TISSOT);
}


PJ *PROJECTION(murd1) {
    return setup(P, MURD1);
}


PJ *PROJECTION(murd2) {
    return setup(P, MURD2);
}


PJ *PROJECTION(murd3) {
    return setup(P, MURD3);
}


PJ *PROJECTION(pconic) {
    return setup(P, PCONIC);
}


PJ *PROJECTION(vitk1) {
    return setup(P, VITK1);
}

