#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(somerc, "Swiss. Obl. Mercator") "\n\tCyl, Ell\n\tFor CH1903";

namespace { // anonymous namespace

struct pj_somerc {

    double K, c, hlf_e, kR, cosp0, sinp0;

};

} // anonymous namespace

#define EPS 1.e-10

#define NITER 6

static PJ_XY somerc_e_forward(PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */

    PJ_XY xy = {0.0, 0.0};

    double phip, lamp, phipp, lampp, sp, cp;

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

    sp = P->e * sin(lp.phi);

    phip = 2. * atan(exp(Q->c * (log(tan(M_FORTPI + 0.5 * lp.phi)) -

                                 Q->hlf_e * log((1. + sp) / (1. - sp))) +

                         Q->K)) -

           M_HALFPI;

    lamp = Q->c * lp.lam;

    cp = cos(phip);

    phipp = aasin(P->ctx, Q->cosp0 * sin(phip) - Q->sinp0 * cp * cos(lamp));

    lampp = aasin(P->ctx, cp * sin(lamp) / cos(phipp));

    xy.x = Q->kR * lampp;

    xy.y = Q->kR * log(tan(M_FORTPI + 0.5 * phipp));

    return xy;

}

static PJ_LP somerc_e_inverse(PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */

    PJ_LP lp = {0.0, 0.0};

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

    double phip, lamp, phipp, lampp, cp, esp, con, delp;

    int i;

    phipp = 2. * (atan(exp(xy.y / Q->kR)) - M_FORTPI);

    lampp = xy.x / Q->kR;

    cp = cos(phipp);

    phip = aasin(P->ctx, Q->cosp0 * sin(phipp) + Q->sinp0 * cp * cos(lampp));

    lamp = aasin(P->ctx, cp * sin(lampp) / cos(phip));

    con = (Q->K - log(tan(M_FORTPI + 0.5 * phip))) / Q->c;

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

        esp = P->e * sin(phip);

        delp = (con + log(tan(M_FORTPI + 0.5 * phip)) -

                Q->hlf_e * log((1. + esp) / (1. - esp))) *

               (1. - esp * esp) * cos(phip) * P->rone_es;

        phip -= delp;

        if (fabs(delp) < EPS)

            break;

    }

    if (i) {

        lp.phi = phip;

        lp.lam = lamp / Q->c;

    } else {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return lp;

    }

    return (lp);

}

PJ *PJ_PROJECTION(somerc) {

    double cp, phip0, sp;

    struct pj_somerc *Q =

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

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->hlf_e = 0.5 * P->e;

    cp = cos(P->phi0);

    cp *= cp;

    Q->c = sqrt(1 + P->es * cp * cp * P->rone_es);

    sp = sin(P->phi0);

    Q->sinp0 = sp / Q->c;

    phip0 = aasin(P->ctx, Q->sinp0);

    Q->cosp0 = cos(phip0);

    sp *= P->e;

    Q->K = log(tan(M_FORTPI + 0.5 * phip0)) -

           Q->c * (log(tan(M_FORTPI + 0.5 * P->phi0)) -

                   Q->hlf_e * log((1. + sp) / (1. - sp)));

    Q->kR = P->k0 * sqrt(P->one_es) / (1. - sp * sp);

    P->inv = somerc_e_inverse;

    P->fwd = somerc_e_forward;

    return P;

}

#undef EPS

#undef NITER