#ifndef lint
static const char SCCSID[]="@(#)PJ_glabsgm.c	4.5	07/09/24	???	???";
#endif
#define PROJ_PARMS__ \
	double lamc;\
	double phic;\
	double c;\
	double n1;\
	double n2;

#define PJ_LIB__
# include	<projects.h>
PROJ_HEAD(glabsgm, "Gauss Laborde (Sphere Geometric Mean)")
	"\n\tCyl, Sph&Ell\n\tlat_0= lon_0= k_0=";
FORWARD(s_forward); /* spheroid */
	double L, Ls, sinLs1, Ls1;
	L= P->n1*lp.lam;
        Ls= P->c+P->n1*log(pj_tsfn(-1.0*lp.phi,-1.0*sin(lp.phi),P->e));
        sinLs1= sin(L)/cosh(Ls);
        Ls1= log(pj_tsfn(-1.0*asin(sinLs1),0.0,0.0));
        xy.x= P->n2*P->ra*Ls1;
        xy.y= P->n2*P->ra*atan(sinh(Ls)/cos(L));
	return (xy);
}
INVERSE(s_inverse); /* spheroid */
	double L, LC, sinC;
	L= atan(sinh(xy.x*P->a/P->n2)/cos(xy.y*P->a/P->n2));
        sinC= sin(xy.y*P->a/P->n2)/cosh(xy.x*P->a/P->n2);
        LC= log(pj_tsfn(-1.0*asin(sinC),0.0,0.0));
        lp.lam= L/P->n1;
        lp.phi= -1.0*pj_phi2(exp((LC-P->c)/P->n1),P->e);
	return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(glabsgm)
        P->n1= sqrt(1.0+P->es*pow(cos(P->phi0),4.0)/(1.0-P->es));
        P->phic= asin(sin(P->phi0)/P->n1);
        P->c=       log(pj_tsfn(-1.0*P->phic,0.0,0.0))
             -P->n1*log(pj_tsfn(-1.0*P->phi0,-1.0*sin(P->phi0),P->e));
        P->n2= P->k0*P->a*sqrt(1.0-P->es)/(1.0-P->es*sin(P->phi0)*sin(P->phi0));
        P->y0-= P->n2*P->phic;
	P->inv= s_inverse;
	P->fwd= s_forward;
ENDENTRY(P)