#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