#ifndef lint
static const char SCCSID[]="@(#)x_nzmg.c	4.1	94/02/15	GIE	REL";
#endif
/* very loosely based upon DMA code by Bradford W. Drew */
#define PJ_LIB__
#include	<projects.h>
PROJ_HEAD(nzmg, "New Zealand Map Grid") "\n\tfixed Earth";
#define EPSLN 1e-10
#define SEC5_TO_RAD 0.4848136811095359935899141023
#define RAD_TO_SEC5 2.062648062470963551564733573
	static COMPLEX
bf[] = {
	.7557853228,	0.0,
	.249204646,		.003371507,
	-.001541739,	.041058560,
	-.10162907,		.01727609,
	-.26623489,		-.36249218,
	-.6870983,		-1.1651967 };
	static double
tphi[] = { 1.5627014243, .5185406398, -.03333098, -.1052906, -.0368594,
	.007317, .01220, .00394, -.0013 },
tpsi[] = { .6399175073, -.1358797613, .063294409, -.02526853, .0117879,
	-.0055161, .0026906, -.001333, .00067, -.00034 };
#define Nbf 5
#define Ntpsi 9
#define Ntphi 8
FORWARD(e_forward); /* ellipsoid */
	COMPLEX p;
	double *C;
	int i;

	lp.phi = (lp.phi - P->phi0) * RAD_TO_SEC5;
	for (p.r = *(C = tpsi + (i = Ntpsi)); i ; --i)
		p.r = *--C + lp.phi * p.r;
	p.r *= lp.phi;
	p.i = lp.lam;
	p = pj_zpoly1(p, bf, Nbf);
	xy.x = p.i;
	xy.y = p.r;
	return xy;
}
INVERSE(e_inverse); /* ellipsoid */
	int nn, i;
	COMPLEX p, f, fp, dp;
	double den, *C;

	p.r = xy.y;
	p.i = xy.x;
	for (nn = 20; nn ;--nn) {
		f = pj_zpolyd1(p, bf, Nbf, &fp);
		f.r -= xy.y;
		f.i -= xy.x;
		den = fp.r * fp.r + fp.i * fp.i;
		p.r += dp.r = -(f.r * fp.r + f.i * fp.i) / den;
		p.i += dp.i = -(f.i * fp.r - f.r * fp.i) / den;
		if ((fabs(dp.r) + fabs(dp.i)) <= EPSLN)
			break;
	}
	if (nn) {
		lp.lam = p.i;
		for (lp.phi = *(C = tphi + (i = Ntphi)); i ; --i)
			lp.phi = *--C + p.r * lp.phi;
		lp.phi = P->phi0 + p.r * lp.phi * SEC5_TO_RAD;
	} else
		lp.lam = lp.phi = HUGE_VAL;
	return lp;
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(nzmg)
	/* force to International major axis */
	P->ra = 1. / (P->a = 6378388.0);
	P->lam0 = DEG_TO_RAD * 173.;
	P->phi0 = DEG_TO_RAD * -41.;
	P->x0 = 2510000.;
	P->y0 = 6023150.;
	P->inv = e_inverse; P->fwd = e_forward;
ENDENTRY(P)