#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(mbt_fps, "McBryde-Thomas Flat-Pole Sine (No. 2)") "\n\tCyl, Sph";

#define MAX_ITER 10

#define LOOP_TOL 1e-7

#define C1 0.45503

#define C2 1.36509

#define C3 1.41546

#define C_x 0.22248

#define C_y 1.44492

#define C1_2 0.33333333333333333333333333

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

    PJ_XY xy = {0.0, 0.0};

    (void)P;

    const double k = C3 * sin(lp.phi);

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

        const double t = lp.phi / C2;

        const double V =

            (C1 * sin(t) + sin(lp.phi) - k) / (C1_2 * cos(t) + cos(lp.phi));

        lp.phi -= V;

        if (fabs(V) < LOOP_TOL)

            break;

    }

    const double t = lp.phi / C2;

    xy.x = C_x * lp.lam * (1. + 3. * cos(lp.phi) / cos(t));

    xy.y = C_y * sin(t);

    return xy;

}

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

    PJ_LP lp = {0.0, 0.0};

    const double t = aasin(P->ctx, xy.y / C_y);

    lp.phi = C2 * t;

    lp.lam = xy.x / (C_x * (1. + 3. * cos(lp.phi) / cos(t)));

    lp.phi = aasin(P->ctx, (C1 * sin(t) + sin(lp.phi)) / C3);

    return (lp);

}

PJ *PJ_PROJECTION(mbt_fps) {

    P->es = 0;

    P->inv = mbt_fps_s_inverse;

    P->fwd = mbt_fps_s_forward;

    return P;

}

#undef MAX_ITER

#undef LOOP_TOL

#undef C1

#undef C2

#undef C3

#undef C_x

#undef C_y

#undef C1_2