#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

namespace { // anonymous namespace

struct pj_putp6 {

    double C_x, C_y, A, B, D;

};

} // anonymous namespace

PROJ_HEAD(putp6, "Putnins P6") "\n\tPCyl, Sph";

PROJ_HEAD(putp6p, "Putnins P6'") "\n\tPCyl, Sph";

#define EPS 1e-10

#define NITER 10

#define CON_POLE 1.732050807568877 /* sqrt(3) */

static PJ_XY putp6_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */

    PJ_XY xy = {0.0, 0.0};

    struct pj_putp6 *Q = static_cast<struct pj_putp6 *>(P->opaque);

    int i;

    const double p = Q->B * sin(lp.phi);

    lp.phi *= 1.10265779;

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

        const double r = sqrt(1. + lp.phi * lp.phi);

        const double V =

            ((Q->A - r) * lp.phi - log(lp.phi + r) - p) / (Q->A - 2. * r);

        lp.phi -= V;

        if (fabs(V) < EPS)

            break;

    }

    double sqrt_1_plus_phi2;

    if (!i) {

        // Note: it seems this case is rarely reached as from experimenting,

        // i seems to be >= 6

        lp.phi = p < 0. ? -CON_POLE : CON_POLE;

        // the formula of the else case would also work, but this makes

        // some cppcheck versions happier.

        sqrt_1_plus_phi2 = 2;

    } else {

        sqrt_1_plus_phi2 = sqrt(1. + lp.phi * lp.phi);

    }

    xy.x = Q->C_x * lp.lam * (Q->D - sqrt_1_plus_phi2);

    xy.y = Q->C_y * lp.phi;

    return xy;

}

static PJ_LP putp6_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */

    PJ_LP lp = {0.0, 0.0};

    struct pj_putp6 *Q = static_cast<struct pj_putp6 *>(P->opaque);

    double r;

    lp.phi = xy.y / Q->C_y;

    r = sqrt(1. + lp.phi * lp.phi);

    lp.lam = xy.x / (Q->C_x * (Q->D - r));

    lp.phi = aasin(P->ctx, ((Q->A - r) * lp.phi - log(lp.phi + r)) / Q->B);

    return lp;

}

PJ *PJ_PROJECTION(putp6) {

    struct pj_putp6 *Q =

        static_cast<struct pj_putp6 *>(calloc(1, sizeof(struct pj_putp6)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->C_x = 1.01346;

    Q->C_y = 0.91910;

    Q->A = 4.;

    Q->B = 2.1471437182129378784;

    Q->D = 2.;

    P->es = 0.;

    P->inv = putp6_s_inverse;

    P->fwd = putp6_s_forward;

    return P;

}

PJ *PJ_PROJECTION(putp6p) {

    struct pj_putp6 *Q =

        static_cast<struct pj_putp6 *>(calloc(1, sizeof(struct pj_putp6)));

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->C_x = 0.44329;

    Q->C_y = 0.80404;

    Q->A = 6.;

    Q->B = 5.61125;

    Q->D = 3.;

    P->es = 0.;

    P->inv = putp6_s_inverse;

    P->fwd = putp6_s_forward;

    return P;

}

#undef EPS

#undef NITER

#undef CON_POLE