#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(fouc_s, "Foucaut Sinusoidal") "\n\tPCyl, Sph";

#define MAX_ITER 10

#define LOOP_TOL 1e-7

namespace { // anonymous namespace

struct pj_fouc_s_data {

    double n, n1;

};

} // anonymous namespace

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

    PJ_XY xy = {0.0, 0.0};

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

    double t;

    t = cos(lp.phi);

    xy.x = lp.lam * t / (Q->n + Q->n1 * t);

    xy.y = Q->n * lp.phi + Q->n1 * sin(lp.phi);

    return xy;

}

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

    PJ_LP lp = {0.0, 0.0};

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

    int i;

    if (Q->n != 0.0) {

        lp.phi = xy.y;

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

            const double V = (Q->n * lp.phi + Q->n1 * sin(lp.phi) - xy.y) /

                             (Q->n + Q->n1 * cos(lp.phi));

            lp.phi -= V;

            if (fabs(V) < LOOP_TOL)

                break;

        }

        if (!i)

            lp.phi = xy.y < 0. ? -M_HALFPI : M_HALFPI;

    } else

        lp.phi = aasin(P->ctx, xy.y);

    const double V = cos(lp.phi);

    lp.lam = xy.x * (Q->n + Q->n1 * V) / V;

    return lp;

}

PJ *PJ_PROJECTION(fouc_s) {

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

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

    if (nullptr == Q)

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

    P->opaque = Q;

    Q->n = pj_param(P->ctx, P->params, "dn").f;

    if (Q->n < 0. || Q->n > 1.) {

        proj_log_error(P,

                       _("Invalid value for n: it should be in [0,1] range."));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    Q->n1 = 1. - Q->n;

    P->es = 0;

    P->inv = fouc_s_s_inverse;

    P->fwd = fouc_s_s_forward;

    return P;

}

#undef MAX_ITER

#undef LOOP_TOL