#define PJ_LIB__
#include <errno.h>
#include "proj.h"
#include "proj_internal.h"
#include <math.h>

PROJ_HEAD(lcc, "Lambert Conformal Conic")
    "\n\tConic, Sph&Ell\n\tlat_1= and lat_2= or lat_0, k_0=";

#define EPS10 1.e-10

namespace { // anonymous namespace
struct pj_opaque {
    double phi1;
    double phi2;
    double n;
    double rho0;
    double c;
};
} // anonymous namespace


static PJ_XY lcc_e_forward (PJ_LP lp, PJ *P) {          /* Ellipsoidal, forward */
    PJ_XY xy = {0., 0.};
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    double rho;

    if (fabs(fabs(lp.phi) - M_HALFPI) < EPS10) {
        if ((lp.phi * Q->n) <= 0.) {
            proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
            return xy;
        }
        rho = 0.;
    } else {
        rho = Q->c * (P->es != 0. ?
                      pow(pj_tsfn(lp.phi, sin(lp.phi), P->e), Q->n) :
                      pow(tan(M_FORTPI + .5 * lp.phi), -Q->n));
    }
    lp.lam *= Q->n;
    xy.x = P->k0 * (rho * sin(lp.lam));
    xy.y = P->k0 * (Q->rho0 - rho * cos(lp.lam));
    return xy;
}


static PJ_LP lcc_e_inverse (PJ_XY xy, PJ *P) {          /* Ellipsoidal, inverse */
    PJ_LP lp = {0., 0.};
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    double rho;

    xy.x /= P->k0;
    xy.y /= P->k0;

    xy.y = Q->rho0 - xy.y;
    rho = hypot(xy.x, xy.y);
    if (rho != 0.) {
        if (Q->n < 0.) {
            rho = -rho;
            xy.x = -xy.x;
            xy.y = -xy.y;
        }
        if (P->es != 0.) {
            lp.phi = pj_phi2(P->ctx, pow(rho / Q->c, 1./Q->n), P->e);
            if (lp.phi == HUGE_VAL) {
                proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
                return lp;
            }

        } else
            lp.phi = 2. * atan(pow(Q->c / rho, 1./Q->n)) - M_HALFPI;
        lp.lam = atan2(xy.x, xy.y) / Q->n;
    } else {
        lp.lam = 0.;
        lp.phi = Q->n > 0. ? M_HALFPI : -M_HALFPI;
    }
    return lp;
}


PJ *PROJECTION(lcc) {
    double cosphi, sinphi;
    int secant;
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc(1, sizeof (struct pj_opaque)));

    if (nullptr == Q)
        return pj_default_destructor(P, ENOMEM);
    P->opaque = Q;

    Q->phi1 = pj_param(P->ctx, P->params, "rlat_1").f;
    if (pj_param(P->ctx, P->params, "tlat_2").i)
        Q->phi2 = pj_param(P->ctx, P->params, "rlat_2").f;
    else {
        Q->phi2 = Q->phi1;
        if (!pj_param(P->ctx, P->params, "tlat_0").i)
            P->phi0 = Q->phi1;
    }
    if (fabs(Q->phi1) > M_HALFPI || fabs(Q->phi2) > M_HALFPI)
        return pj_default_destructor(P, PJD_ERR_LAT_LARGER_THAN_90);
    if (fabs(Q->phi1 + Q->phi2) < EPS10)
        return pj_default_destructor(P, PJD_ERR_CONIC_LAT_EQUAL);

    Q->n = sinphi = sin(Q->phi1);
    cosphi = cos(Q->phi1);
    secant = fabs(Q->phi1 - Q->phi2) >= EPS10;
    if (P->es != 0.) {
        double ml1, m1;

        m1 = pj_msfn(sinphi, cosphi, P->es);
        ml1 = pj_tsfn(Q->phi1, sinphi, P->e);
        if( ml1 == 0 ) {
            return pj_default_destructor(P, PJD_ERR_LAT_1_OR_2_ZERO_OR_90);
        }
        if (secant) { /* secant cone */
            sinphi = sin(Q->phi2);
            Q->n = log(m1 / pj_msfn(sinphi, cos(Q->phi2), P->es));
            if (Q->n == 0) {
                // Not quite, but es is very close to 1...
                return pj_default_destructor(P, PJD_ERR_INVALID_ECCENTRICITY);
            }
            const double ml2 = pj_tsfn(Q->phi2, sinphi, P->e);
            if( ml2 == 0 ) {
                return pj_default_destructor(P, PJD_ERR_LAT_1_OR_2_ZERO_OR_90);
            }
            const double denom = log(ml1 / ml2);
            if( denom == 0 ) {
                // Not quite, but es is very close to 1...
                return pj_default_destructor(P, PJD_ERR_INVALID_ECCENTRICITY);
            }
            Q->n /= denom;
        }
        Q->rho0 = m1 * pow(ml1, -Q->n) / Q->n;
        Q->c = Q->rho0;
        Q->rho0 *= (fabs(fabs(P->phi0) - M_HALFPI) < EPS10) ? 0. :
            pow(pj_tsfn(P->phi0, sin(P->phi0), P->e), Q->n);
    } else {
        if( fabs(cosphi) < EPS10 || fabs(cos(Q->phi2)) < EPS10 ) {
            return pj_default_destructor(P, PJD_ERR_LAT_1_OR_2_ZERO_OR_90);
        }
        if (secant)
            Q->n = log(cosphi / cos(Q->phi2)) /
               log(tan(M_FORTPI + .5 * Q->phi2) /
               tan(M_FORTPI + .5 * Q->phi1));
        if( Q->n == 0 ) {
            // Likely reason is that phi1 / phi2 are too close to zero.
            // Can be reproduced with +proj=lcc +a=1 +lat_2=.0000001
            return pj_default_destructor(P, PJD_ERR_CONIC_LAT_EQUAL);
        }
        Q->c = cosphi * pow(tan(M_FORTPI + .5 * Q->phi1), Q->n) / Q->n;
        Q->rho0 = (fabs(fabs(P->phi0) - M_HALFPI) < EPS10) ? 0. :
            Q->c * pow(tan(M_FORTPI + .5 * P->phi0), -Q->n);
    }

    P->inv = lcc_e_inverse;
    P->fwd = lcc_e_forward;

    return P;
}