#define PJ_LIB__

#include <math.h>

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

PROJ_HEAD(eck4, "Eckert IV") "\n\tPCyl, Sph";

#define C_x .42223820031577120149
#define C_y 1.32650042817700232218
#define RC_y    .75386330736002178205
#define C_p 3.57079632679489661922
#define RC_p    .28004957675577868795
#define EPS 1e-7
#define NITER   6


static PJ_XY eck4_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forward */
    PJ_XY xy = {0.0,0.0};
    double p, V, s, c;
    int i;
    (void) P;

    p = C_p * sin(lp.phi);
    V = lp.phi * lp.phi;
    lp.phi *= 0.895168 + V * ( 0.0218849 + V * 0.00826809 );
    for (i = NITER; i ; --i) {
        c = cos(lp.phi);
        s = sin(lp.phi);
        lp.phi -= V = (lp.phi + s * (c + 2.) - p) /
            (1. + c * (c + 2.) - s * s);
        if (fabs(V) < EPS)
            break;
    }
    if (!i) {
        xy.x = C_x * lp.lam;
        xy.y = lp.phi < 0. ? -C_y : C_y;
    } else {
        xy.x = C_x * lp.lam * (1. + cos(lp.phi));
        xy.y = C_y * sin(lp.phi);
    }
    return xy;
}


static PJ_LP eck4_s_inverse (PJ_XY xy, PJ *P) {           /* Spheroidal, inverse */
    PJ_LP lp = {0.0,0.0};
    double c;

    lp.phi = aasin(P->ctx,xy.y * RC_y);
    lp.lam = xy.x / (C_x * (1. + (c = cos(lp.phi))));
    lp.phi = aasin(P->ctx,(lp.phi + sin(lp.phi) * (c + 2.)) * RC_p);
    return lp;
}


PJ *PROJECTION(eck4) {
    P->es = 0.0;
    P->inv = eck4_s_inverse;
    P->fwd = eck4_s_forward;

    return P;
}
