#include <errno.h>
#include <math.h>

#include "proj.h"
#include "proj_internal.h"

PROJ_HEAD(lagrng, "Lagrange") "\n\tMisc Sph\n\tW=";

#define TOL 1e-10

namespace { // anonymous namespace
struct pj_lagrng {
    double a1;
    double a2;
    double hrw;
    double hw;
    double rw;
    double w;
};
} // anonymous namespace

static PJ_XY lagrng_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */
    PJ_XY xy = {0.0, 0.0};
    struct pj_lagrng *Q = static_cast<struct pj_lagrng *>(P->opaque);
    double v, c;

    const double sin_phi = sin(lp.phi);
    if (fabs(fabs(sin_phi) - 1) < TOL) {
        xy.x = 0;
        xy.y = lp.phi < 0 ? -2. : 2.;
    } else {
        v = Q->a1 * pow((1. + sin_phi) / (1. - sin_phi), Q->hrw);
        lp.lam *= Q->rw;
        c = 0.5 * (v + 1. / v) + cos(lp.lam);
        if (c < TOL) {
            proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
            return xy;
        }
        xy.x = 2. * sin(lp.lam) / c;
        xy.y = (v - 1. / v) / c;
    }
    return xy;
}

static PJ_LP lagrng_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
    PJ_LP lp = {0.0, 0.0};
    struct pj_lagrng *Q = static_cast<struct pj_lagrng *>(P->opaque);
    double c, x2, y2p, y2m;

    if (fabs(fabs(xy.y) - 2.) < TOL) {
        lp.phi = xy.y < 0 ? -M_HALFPI : M_HALFPI;
        lp.lam = 0;
    } else {
        x2 = xy.x * xy.x;
        y2p = 2. + xy.y;
        y2m = 2. - xy.y;
        c = y2p * y2m - x2;
        if (fabs(c) < TOL) {
            proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
            return lp;
        }
        lp.phi = 2. * atan(pow((y2p * y2p + x2) / (Q->a2 * (y2m * y2m + x2)),
                               Q->hw)) -
                 M_HALFPI;
        lp.lam = Q->w * atan2(4. * xy.x, c);
    }
    return lp;
}

PJ *PJ_PROJECTION(lagrng) {
    double sin_phi1;
    struct pj_lagrng *Q =
        static_cast<struct pj_lagrng *>(calloc(1, sizeof(struct pj_lagrng)));
    if (nullptr == Q)
        return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);
    P->opaque = Q;

    if (pj_param(P->ctx, P->params, "tW").i)
        Q->w = pj_param(P->ctx, P->params, "dW").f;
    else
        Q->w = 2;
    if (Q->w <= 0) {
        proj_log_error(P, _("Invalid value for W: it should be > 0"));
        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);
    }
    Q->hw = 0.5 * Q->w;
    Q->rw = 1. / Q->w;
    Q->hrw = 0.5 * Q->rw;
    sin_phi1 = sin(pj_param(P->ctx, P->params, "rlat_1").f);
    if (fabs(fabs(sin_phi1) - 1.) < TOL) {
        proj_log_error(P,
                       _("Invalid value for lat_1: |lat_1| should be < 90°"));
        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);
    }

    Q->a1 = pow((1. - sin_phi1) / (1. + sin_phi1), Q->hrw);
    Q->a2 = Q->a1 * Q->a1;

    P->es = 0.;
    P->inv = lagrng_s_inverse;
    P->fwd = lagrng_s_forward;

    return P;
}