#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(gall, "Gall (Gall Stereographic)") "\n\tCyl, Sph";

#define YF 1.70710678118654752440

#define XF 0.70710678118654752440

#define RYF 0.58578643762690495119

#define RXF 1.41421356237309504880

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

    PJ_XY xy = {0.0, 0.0};

    (void)P;

    xy.x = XF * lp.lam;

    xy.y = YF * tan(.5 * lp.phi);

    return xy;

}

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

    PJ_LP lp = {0.0, 0.0};

    (void)P;

    lp.lam = RXF * xy.x;

    lp.phi = 2. * atan(xy.y * RYF);

    return lp;

}

PJ *PJ_PROJECTION(gall) {

    P->es = 0.0;

    P->inv = gall_s_inverse;

    P->fwd = gall_s_forward;

    return P;

}