#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

#include <math.h>

PROJ_HEAD(bipc, "Bipolar conic of western hemisphere") "\n\tConic Sph";

#define EPS 1e-10

#define EPS10 1e-10

#define ONEEPS 1.000000001

#define NITER 10

#define lamB -.34894976726250681539

#define n .63055844881274687180

#define F 1.89724742567461030582

#define Azab .81650043674686363166

#define Azba 1.82261843856185925133

#define T 1.27246578267089012270

#define rhoc 1.20709121521568721927

#define cAzc .69691523038678375519

#define sAzc .71715351331143607555

#define C45 .70710678118654752469

#define S45 .70710678118654752410

#define C20 .93969262078590838411

#define S20 -.34202014332566873287

#define R110 1.91986217719376253360

#define R104 1.81514242207410275904

namespace { // anonymous namespace

struct pj_bipc_data {

    int noskew;

};

} // anonymous namespace

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

    PJ_XY xy = {0.0, 0.0};

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

    double cphi, sphi, tphi, t, al, Az, z, Av, cdlam, sdlam, r;

    int tag;

    cphi = cos(lp.phi);

    sphi = sin(lp.phi);

    cdlam = cos(sdlam = lamB - lp.lam);

    sdlam = sin(sdlam);

    if (fabs(fabs(lp.phi) - M_HALFPI) < EPS10) {

        Az = lp.phi < 0. ? M_PI : 0.;

        tphi = HUGE_VAL;

    } else {

        tphi = sphi / cphi;

        Az = atan2(sdlam, C45 * (tphi - cdlam));

    }

    if ((tag = (Az > Azba))) {

        sdlam = lp.lam + R110;

        cdlam = cos(sdlam);

        sdlam = sin(sdlam);

        z = S20 * sphi + C20 * cphi * cdlam;

        if (fabs(z) > 1.) {

            if (fabs(z) > ONEEPS) {

                proj_errno_set(

                    P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

                return xy;

            } else

                z = z < 0. ? -1. : 1.;

        } else

            z = acos(z);

        if (tphi != HUGE_VAL)

            Az = atan2(sdlam, (C20 * tphi - S20 * cdlam));

        Av = Azab;

        xy.y = rhoc;

    } else {

        z = S45 * (sphi + cphi * cdlam);

        if (fabs(z) > 1.) {

            if (fabs(z) > ONEEPS) {

                proj_errno_set(

                    P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

                return xy;

            } else

                z = z < 0. ? -1. : 1.;

        } else

            z = acos(z);

        Av = Azba;

        xy.y = -rhoc;

    }

    if (z < 0.) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return xy;

    }

    t = pow(tan(.5 * z), n);

    r = F * t;

    if ((al = .5 * (R104 - z)) < 0.) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return xy;

    }

    al = (t + pow(al, n)) / T;

    if (fabs(al) > 1.) {

        if (fabs(al) > ONEEPS) {

            proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

            return xy;

        } else

            al = al < 0. ? -1. : 1.;

    } else

        al = acos(al);

    t = n * (Av - Az);

    if (fabs(t) < al)

        r /= cos(al + (tag ? t : -t));

    xy.x = r * sin(t);

    xy.y += (tag ? -r : r) * cos(t);

    if (Q->noskew) {

        t = xy.x;

        xy.x = -xy.x * cAzc - xy.y * sAzc;

        xy.y = -xy.y * cAzc + t * sAzc;

    }

    return (xy);

}

static PJ_LP bipc_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */

    PJ_LP lp = {0.0, 0.0};

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

    double t, r, rp, rl, al, z = 0.0, fAz, Az, s, c, Av;

    int neg, i;

    if (Q->noskew) {

        t = xy.x;

        xy.x = -xy.x * cAzc + xy.y * sAzc;

        xy.y = -xy.y * cAzc - t * sAzc;

    }

    if ((neg = (xy.x < 0.))) {

        xy.y = rhoc - xy.y;

        s = S20;

        c = C20;

        Av = Azab;

    } else {

        xy.y += rhoc;

        s = S45;

        c = C45;

        Av = Azba;

    }

    r = hypot(xy.x, xy.y);

    rl = rp = r;

    Az = atan2(xy.x, xy.y);

    fAz = fabs(Az);

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

        z = 2. * atan(pow(r / F, 1 / n));

        al = acos((pow(tan(.5 * z), n) + pow(tan(.5 * (R104 - z)), n)) / T);

        if (fAz < al)

            r = rp * cos(al + (neg ? Az : -Az));

        if (fabs(rl - r) < EPS)

            break;

        rl = r;

    }

    if (!i) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return lp;

    }

    Az = Av - Az / n;

    lp.phi = asin(s * cos(z) + c * sin(z) * cos(Az));

    lp.lam = atan2(sin(Az), c / tan(z) - s * cos(Az));

    if (neg)

        lp.lam -= R110;

    else

        lp.lam = lamB - lp.lam;

    return (lp);

}

PJ *PJ_PROJECTION(bipc) {

    struct pj_bipc_data *Q = static_cast<struct pj_bipc_data *>(

        calloc(1, sizeof(struct pj_bipc_data)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->noskew = pj_param(P->ctx, P->params, "bns").i;

    P->inv = bipc_s_inverse;

    P->fwd = bipc_s_forward;

    P->es = 0.;

    return P;

}

#undef EPS

#undef EPS10

#undef ONEEPS

#undef NITER

#undef lamB

#undef n

#undef F

#undef Azab

#undef Azba

#undef T

#undef rhoc

#undef cAzc

#undef sAzc

#undef C45

#undef S45

#undef C20

#undef S20

#undef R110

#undef R104