SolSystem.cxx Source File

00001 // SolSystem.cpp: implementation of the SolSystem class.
00002 //
00004 #include "SolSystem.h"
00005 #include <iostream>
00006 #include <cmath>
00007 #include <string>
00008 #include "vsop87_data.h"
00009 #include "chap95_data.h"
00010 //#include "CTimeClass.h"
00011 
00012 
00013 #define A2000 2451545.00000000
00014 
00015 #define Conv_Rad 0.017453292
00016 #define Conv_Grad 57.29578122
00017 #define Conv_Ora_Rad 0.261799387
00018 
00019 #define SPD             (24.0*3600.0)   /* seconds per day */
00020 #define MJD0    2415020.0
00021 #define J2000   (2451545.0 - MJD0) 
00022 #define MAU             (1.4959787e11)  /* m / au */
00023 #define ERAD    (6.37816e6)     /* earth equitorial radius, m */
00024 #define SIDRATE .9972695677
00025 
00026 
00027 
00028 extern "C" {void precess (double mjd1, double mjd2, double *ra, double *dec);
00029 void range (double *v, double r);
00030 int Conv_GST_UT(double jd,double gst,double *tu);
00031 int Sun_Pos(double jd,double *ra,double *decs,double *lon,double *r);
00032 int Conv_lb_ad(double jd,double l,double b,double *ra,double *dec);
00033 void riset (double ra, double dec, double lat, double dis, double *lstr,double * lsts,
00034            double *azr, double *azs, int *status);
00035 int vsop87 (double mjd, int obj, double prec, double *ret);
00036 void sunpos (double mjd, double *lsn, double *rsn, double *bsn);
00037 
00038 void cal_mjd (int mn, double dy, int yr, double *mjd);
00039 double mjd_day(double jd);
00040 void rnd_second (double *t);
00041 void year_mjd (double y, double *mjd);
00042 void mjd_year (double mjd, double *yr);
00043 void mjd_dpm (double mjd, int *ndays);
00044 int mjd_dow (double mjd,int *dow);
00045 void mjd_cal (double mjd, int *mn, double dy, int *yr);
00046 
00047 void cartsph (double x,double  y,double  z,double *l, double *b, double *r);
00048 void sphcart (double l, double b, double r, double *x, double *y, double *z);
00049 void zero_mem (void *loc, unsigned len);
00050 
00051 void reduce_elements (double mjd0, double mjd, double inc0, double ap0, double om0, double *inc, double *ap, double *om);
00052 void obliquity (double mjd, double *eps);
00053 void anomaly (double ma, double s, double *nu, double *ea);
00054 void comet (double mjd, double ep, double inc, double ap, double qp, double om, double *lpd, double *psi, double *rp, double *rho, double *lam, double *bet);
00055 int chap95 (double mjd, int obj, double prec, double *ret);
00056 void moon (double mjd, double *lam, double *bet, double *rho,
00057     double *msp, double *mdp);
00058 void nut_eq (double mjd, double *ra, double *dec);
00059 void nutation (double mjd, double *deps, double *dpsi);
00060 void ta_par (double tha, double tdec, double phi, double ht, double *rho, double *aha, double *adec);
00061 void refract (double pr,double tr, double ta,double *aa);
00062 void ab_eq (double mjd, double lsn, double *ra, double *dec);
00063 void ab_ecl (double mjd, double lsn, double *lam, double *bet);
00064 void unrefract (double pr, double tr, double aa, double *ta);
00065 
00066 void eq_ecl (double mjd, double ra, double dec, double *lat, double *lng);
00067 void ecl_eq (double mjd, double lat, double lng, double *ra, double *dec);
00068 
00069 void aa_hadec (double lat, double alt,double  az, double *ha, double *dec);
00070 void hadec_aa (double lat, double ha, double dec, double *alt, double *az);
00071 
00072 void solve_sphere (double A, double b, double cc, double sc, double *cap, double *Bp);
00073 double deltat(double mjd);
00074 double mm_mjed (double mjd);
00075 double Tempo_Siderale(double J_D,double Ora_Un_Dec);
00076 void now_lst(double mdj,double lng, double *lstp);
00077 void plans (double mjd, int p, double *lpd0, double *psi0, double *rp0, double *rho0, double *lam, double *bet, double *dia, double *mag);
00078 }
00079 #define TMACC   (10./3600./24.0)        /* convergence accuracy, days */
00080 
00081 
00082 /*static void SolSystem::elongation (double lam, double bet, double lsn, double *el);
00083 static void SolSystem::ephi_pos(double mdj,int obj,double lng,double lat,double elev, double hlong, double hlat,double bet, double lam, double *rho, double *ra1, double *dec1);
00084 static int SolSystem::ephi_moon(double jd,double lng, double lat,double elev, double *ra, double *dec, double *phase, double *dist);
00085 static void SolSystem::deflect (double mjd1, double lpd, double psi, double lsn, double rsn, double rho, double *ra,double *dec);
00086 static int SolSystem::ephi_sun(double *ra, double *dec, double *dist);
00087 static void SolSystem::ephi_planet(double jd,int obj,double lng, double lat,double elev, double *ra, double *dec, double *phase, double *dist);
00088 static int SolSystem::find_transit (double mjd, double lat,double lng, double dt, double dis, double *alt, double *mjdt);
00089 static int SolSystem::find_0alt (double mjd, double lat,double lng,  double dt, double dis, double *az, double *mjdt);
00090 
00091 */
00092 
00093 
00095 // Construction/Destruction
00097 
00098 SolSystem::SolSystem()
00099 {
00100         LOCSET=-1;      
00101         dis=9.89e-3;
00102         lat=degrad(43.);
00103         lng=0.0;
00104         elev=0.0;
00105         GG=A2000;
00106         Obj=8;
00107 }
00108 
00109 SolSystem::~SolSystem()
00110 {
00111         LOCSET=-1;
00112 }
00113 
00114 void SolSystem::RiseSet()
00115 {
00116         ephi_riset ();
00117 
00118 }
00119 
00120 void SolSystem::RiseSet(double diso)
00121 {
00122         dis=degrad(diso);
00123         ephi_riset ();
00124 
00125 }
00126 
00127 
00128 void SolSystem::CalculatePos(double jd, int obo)
00129 {
00130         if(LOCSET){
00131                 GG=jd;
00132                 if(obo>=0 && obo<=9)
00133                 {
00134                         Obj=obo;
00135                 switch(Obj){
00136                 case 8: ephi_sun();
00137                         break;
00138                 case 9:ephi_moon();
00139                         break;
00140                 default:
00141                         ephi_planet();
00142                 break;
00143                 }       
00144                 }
00145         }
00146 }
00147 
00148 void SolSystem::CalculatePos(double JD)
00149 {
00150         if(LOCSET){
00151                 //Obj=obo;
00152                 SetJD(JD);
00153                 switch(Obj){
00154                 case 8: ephi_sun();
00155                         break;
00156                 case 9:ephi_moon();
00157                         break;
00158                 default:
00159                                 ephi_planet();
00160                 break;
00161                 }       
00162         }
00163 }
00164 
00165 void SolSystem::SetLocation(double lati, double loni, double eleva)
00166 {
00167         lat=degrad(lati);
00168         lng=degrad(loni);
00169         elev=eleva;
00170         
00171         LOCSET=1;
00172 }
00173 void SolSystem::SetJD(double jd)
00174 {
00175         GG=jd;
00176 }
00177 
00178 void SolSystem::SetObj(int nob)
00179 {       
00180         if(nob>=0 && nob<=9)
00181                 Obj=nob;
00182 }
00183 
00184 void SolSystem::elongation (double lam, double bet, double lsn, double *el)
00185 {
00186         *el = acos(cos(bet)*cos(lam-lsn));
00187         if (lam>lsn+PI || (lam>lsn-PI && lam<lsn)) *el = - *el;
00188 }
00189 
00190 void SolSystem::deflect (double mjd1, double lpd, double psi, double lsn, double rsn, double rho, double *ra,double *dec)
00191 /* double mjd1;          epoch 
00192 double lpd, psi;heliocentric ecliptical long / lat 
00193 double rsn, lsn;         distance and longitude of sun 
00194 double rho;             geocentric distance 
00195 double *ra, *dec;        geocentric equatoreal */
00196 {
00197         double hra, hdec;       /* object heliocentric equatoreal */
00198         double el;              /* HELIOCENTRIC elongation object--earth */
00199         double g1, g2;          /* relativistic weights */
00200         double u[3];            /* object geocentric cartesian */
00201         double q[3];            /* object heliocentric cartesian unit vect */
00202         double e[3];            /* earth heliocentric cartesian unit vect */
00203         double qe, uq, eu;      /* scalar products */
00204         int i;                  /* counter */
00205 
00206 #define G       1.32712438e20   /* heliocentric grav const; in m^3*s^-2 */
00207 #define c       299792458.0     /* speed of light in m/s */
00208 
00209         elongation(lpd, psi, lsn-PI, &el);
00210         el = fabs(el);
00211         /* only continue if object is within about 10 deg around the sun
00212          * and not obscured by the sun's disc (radius 0.25 deg)
00213          *
00214          * precise geocentric deflection is:  g1 * tan(el/2)
00215          *      radially outwards from sun;  the vector munching below
00216          *      just applys this component-wise
00217          *      Note:   el = HELIOCENTRIC elongation.
00218          *              g1 is always about 0.004 arc seconds
00219          *              g2 varies from 0 (highest contribution) to 2
00220          */
00221         if (el<degrad(170) || el>degrad(179.75)) return;
00222 
00223         /* get cartesian vectors */
00224         sphcart(*ra, *dec, rho, u, u+1, u+2);
00225 
00226         ecl_eq(mjd1, psi, lpd, &hra, &hdec);
00227         sphcart(hra, hdec, 1.0, q, q+1, q+2);
00228 
00229         ecl_eq(mjd1, 0.0, lsn-PI, &hra, &hdec);
00230         sphcart(hra, hdec, 1.0, e, e+1, e+2);
00231 
00232         /* evaluate scalar products */
00233         qe = uq = eu = 0.0;
00234         for(i=0; i<=2; ++i) {
00235             qe += q[i]*e[i];
00236             uq += u[i]*q[i];
00237             eu += e[i]*u[i];
00238         }
00239 
00240         g1 = 2*G/(c*c*MAU)/rsn;
00241         g2 = 1 + qe;
00242 
00243         /* now deflect geocentric vector */
00244         g1 /= g2;
00245         for(i=0; i<=2; ++i)
00246             u[i] += g1*(uq*e[i] - eu*q[i]);
00247         
00248         /* back to spherical */
00249         cartsph(u[0], u[1], u[2], ra, dec, &rho);       /* rho thrown away */
00250 #undef G
00251 #undef c
00252 }
00253 
00254 
00255 int SolSystem::ephi_sun()
00256 {
00257         double lsn, rsn;        /* true geoc lng of sun; dist from sn to earth*/
00258         double bsn;             /* true latitude beta of sun */
00259         double dhlong;
00260         double mjd, mjed;
00261         double ra,dec;
00262 
00263         mjd=GG-MJD0;
00264         mjed=mm_mjed(mjd);
00265 
00266 
00267         sunpos (mjed, &lsn, &rsn, &bsn);/* sun's true coordinates; mean ecl. */
00268 
00269         Sdist = 0.0;
00270         Elong = 0.0;
00271         Phase = 100.0;
00272         Mag= -26.8;     /* TODO */
00273         dhlong = lsn-PI;        /* geo- to helio- centric */
00274         range (&dhlong, 2*PI);
00275         Hlong = dhlong;
00276         Hlat = -bsn;
00277         ephi_pos(mjd,SUN,bsn, lsn, &rsn, &ra,&dec);
00278         /* fill sun's ra/dec, alt/az in op */
00279         //cir_pos (np, bsn, lsn, &rsn, op);
00280         Edist = rsn;
00281         Size = raddeg(4.65242e-3/rsn)*3600*2;
00282         HRa=radhr(ra);
00283         DDec=raddeg(dec);
00284         Ra=ra;
00285         Dec=dec;
00286         return (0);
00287 }
00288 
00289 
00290 
00291 
00292 int SolSystem::ephi_moon()
00293 
00294 {
00295         double lsn, rsn;        /* true geoc lng of sun; dist from sn to earth*/
00296         double lam;             /* geocentric ecliptic longitude */
00297         double bet;             /* geocentric ecliptic latitude */
00298         double edistau;         /* earth-moon dist, in au */
00299         double el;              /* elongation, rads east */
00300         double ms;              /* sun's mean anomaly */
00301         double md;              /* moon's mean anomaly */
00302         double i;
00303         double mjd, mjed;
00304         double  ra,dec;
00305 
00306         mjd=GG-MJD0;
00307         mjed=mm_mjed(mjd);
00308 
00309         moon (mjed, &lam, &bet, &edistau, &ms, &md);    /* mean ecliptic & EOD*/
00310         sunpos (mjed, &lsn, &rsn, NULL);                /* mean ecliptic & EOD*/
00311 
00312         //op->s_hlong = lam;                    /* save geo in helio fields */
00313         //op->s_hlat = bet;
00314         Hlong=lam;
00315         Hlat=bet;
00316         /* find angular separation from sun */
00317         elongation (lam, bet, lsn, &el);
00318         Elong = raddeg(el);             /* want degrees */
00319 
00320         /* solve triangle of earth, sun, and elongation for moon-sun dist */
00321         Sdist= sqrt (edistau*edistau + rsn*rsn - 2.0*edistau*rsn*cos(el));
00322                 //*dist= sqrt (edistau*edistau + rsn*rsn - 2.0*edistau*rsn*cos(el));
00323 
00324 
00325         /* TODO: improve mag; this is based on a flat moon model. */
00326         //set_smag (op, -12.7 + 2.5*(log10(PI) - log10(PI/2*(1+1.e-6-cos(el)))));
00327 
00328         /* find phase -- allow for projection effects */
00329         i = 0.1468*sin(el)*(1 - 0.0549*sin(md))/(1 - 0.0167*sin(ms));
00330         //op->s_phase = (1+cos(PI-el-degrad(i)))/2*100;
00331 
00332                 Phase = (1+cos(PI-el-degrad(i)))/2*100;
00333 
00334         /* fill moon's ra/dec, alt/az in op and update for topo dist */
00335         //cir_pos (np, bet, lam, &edistau, op);
00336         ephi_pos(mjd,MOON,bet, lam, &edistau, &ra,&dec);
00337         //op->s_edist = edistau;
00338         HRa=radhr(ra);
00339         DDec=raddeg(dec);
00340         Ra=ra;
00341         Dec=dec;
00342         Edist=edistau;
00343         //Size = 3600*2.0*raddeg(asin(MRAD/MAU/edistau));
00344                                                 /* moon angular dia, seconds */
00345 
00346         return (0);
00347 }
00348 
00349 void SolSystem::ephi_planet()
00350 {
00351         double el;              /* elongation */
00352         double f;               /* fractional phase from earth */
00353         double mjd, mjed;
00354 
00355 
00356         double lsn, rsn;        /* true geoc lng of sun; dist from sn to earth*/
00357         double lpd, psi;        /* heliocentric ecliptic long and lat */
00358         double rp;              /* dist from sun */
00359         double rho;             /* dist from earth */
00360         double lam, bet;        /* geocentric ecliptic long and lat */
00361         double dia, mag;        /* angular diameter at 1 AU and magnitude */
00362         double ra, dec;
00363         mjd=GG-MJD0;
00364         mjed=mm_mjed(mjd);
00365         /* compute elongation and phase */
00366         sunpos (mjed, &lsn, &rsn, 0);
00367 
00368         /* find helio long/lat; sun/planet and earth/plant dist; ecliptic
00369          * long/lat; diameter and mag.
00370          */
00371         plans(mjed, Obj, &lpd, &psi, &rp, &rho, &lam, &bet, &dia, &mag);
00372         Size=dia;
00373         Mag=mag;
00374 
00375         elongation (lam, bet, lsn, &el);
00376         Elong=el = raddeg(el);
00377         //op->s_elong = el;
00378          f = 0.25 * ((rp+rho)*(rp+ rho) - rsn*rsn)/(rp*rho);
00379         Phase= f*100.0; /* percent */
00380 
00381         /* set heliocentric long/lat; mean ecliptic and EOD */
00382         Hlong = lpd;
00383         Hlat = psi;
00384 
00385         /* fill solar sys body's ra/dec, alt/az in op */
00386         //cir_pos (np, bet, lam, rho, op);        /* updates rho */
00387         ephi_pos(mjd,Obj,bet, lam, &rho, &ra,&dec);
00388         HRa=radhr(ra);
00389         DDec=raddeg(dec);
00390         Ra=ra;
00391         Dec=dec;
00392         /* set earth/planet and sun/planet distance */
00393         Edist = rho;
00394         //op->s_sdist = rp;
00395 }
00396 
00397 
00398 
00399 void SolSystem::ephi_pos(double mjd,int obj, double bet, double lam, double *rho, double *ra1, double *dec1)
00400 //cir_pos (np, bet, lam, rho, op)
00401 //Now *np;
00402 //double bet, lam;/* geo lat/long (mean ecliptic of date) */
00403 //double *rho;  /* in: geocentric dist in AU; out: geo- or topocentic dist */
00404 //Obj *op;      /* object to set s_ra/dec as per epoch */
00405 {
00406         double ra, dec;         /* apparent ra/dec, corrected for nut/ab */
00407         double tra, tdec;       /* astrometric ra/dec, no nut/ab */
00408         double lsn, rsn;        /* solar geocentric (mean ecliptic of date) */
00409         double ha_in, ha_out;   /* local hour angle before/after parallax */
00410         double dec_out;         /* declination after parallax */
00411         double dra, ddec;       /* parallax correction */
00412         double alt, az;         /* current alt, az */
00413         double lst;             /* local sidereal time */
00414         double rho_topo;        /* topocentric distance in earth radii */
00415         double temp_ra,temp_dec;
00416         double mjed;
00417         
00418         /* convert to equatoreal [mean equator, with mean obliquity] */
00419         ecl_eq (mjd, bet, lam, &ra, &dec);
00420         tra = ra;       /* keep mean coordinates */
00421         tdec = dec;
00422 
00423         /* get sun position */
00424         mjed=mm_mjed(mjd);
00425         sunpos(mjed, &lsn, &rsn, NULL);
00426 
00427         /* allow for relativistic light bending near the sun.
00428          * (avoid calling deflect() for the sun itself).
00429          */
00430         //if (!is_planet(op,SUN) && !is_planet(op,MOON))
00431                  if((obj!=SUN)&&(obj!=MOON))
00432         deflect (mjd, Hlong, Hlat, lsn, rsn, *rho, &ra, &dec);
00433 
00434         /* correct ra/dec to form geocentric apparent */
00435         nut_eq (mjd, &ra, &dec);
00436         //if (!is_planet(op,MOON))
00437         if(obj!=MOON)
00438                 ab_eq (mjd, lsn, &ra, &dec);
00439         GRa = raddeg(ra);
00440         GDec = raddeg(dec);
00441         temp_ra = ra;   /* keep geocentric apparent  coordinates */
00442         temp_dec = dec;
00443         //cout<<"NNNNNNNNN  "<<radhr(ra)<<"   "<<raddeg(dec)<<endl;
00444         //printang(radhr(ra));
00445         //printang(raddeg(dec));
00446         /* find parallax correction for equatoreal coords */
00447 /* inserire last..
00448         now_lst (np, &lst);
00449 */
00450         now_lst(mjd,lng,&lst);
00451         ha_in = hrrad(lst) - ra;
00452         rho_topo = *rho * MAU/ERAD;             /* convert to earth radii */
00453         double dd=(elev/1000.)/ERAD;
00454         ta_par (ha_in, dec, lat, dd, &rho_topo, &ha_out, &dec_out);
00455 
00456         /* transform into alt/az and apply refraction */
00457         ha_in = hrrad(lst) - ra;
00458         hadec_aa (lat, ha_out, dec_out, &alt, &az);
00459         //refract (pressure, temp, alt, &alt);
00460 
00461         Alt = alt;
00462         Az = az;
00463 
00464         /* Get parallax differences and apply to apparent or astrometric place
00465          * as needed.  For the astrometric place, rotating the CORRECTIONS
00466          * back from the nutated equator to the mean equator will be
00467          * neglected.  This is an effect of about 0.1" at moon distance.
00468          * We currently don't have an inverse nutation rotation.
00469          */
00470 //      if (pref_get(PREF_EQUATORIAL) == PREF_GEO) {
00471             /* no topo corrections to eq. coords */
00472 //          dra = ddec = 0.0;
00473 //      } else {
00474             dra = ha_in - ha_out;       /* ra sign is opposite of ha */
00475             ddec = dec_out - dec;
00476             *rho = rho_topo * ERAD/MAU; /* return topocentric distance in AU */
00477 //      }
00478 
00479         /* fill in ra/dec fields */
00480 //      if (epoch == EOD) {             /* apparent geo/topocentric */
00481             ra = ra + dra;
00482             dec = dec + ddec;
00483 //      } else {                        /* astrometric geo/topocent */
00484 //          ra = tra + dra;
00485 //          dec = tdec + ddec;
00486 //          precess (mjd, epoch, &ra, &dec);
00487 //      }
00488         range(&ra, 2*PI);
00489         //op->s_ra = ra;
00490         //op->s_dec = dec;
00491         *ra1=ra;
00492         *dec1=dec;
00493         //printang(radhr(ra));
00494 }
00495 
00496 /* find where and when an object, op, will rise and set and
00497  *   it's transit circumstances. all times are utc mjd, angles rads e of n.
00498  * dis is the angle down from an ideal horizon, in rads (see riset()).
00499  * N.B. dis should NOT include refraction, we do that here.
00500  */
00501 void SolSystem::ephi_riset ()
00502 {
00503         double mjdn;    /* mjd of local noon */
00504         double lstn;    /* lst at local noon */
00505         double lr, ls;  /* lst rise/set times */
00506         double ar, as;  /* az of rise/set */
00507         double ran;     /* RA at noon */
00508         int rss;        /* temp status */
00509         
00510         double mjd=GG-MJD0;
00511         /* assume no problems initially */
00512         Flags = 0;
00513 
00514         /* start the iteration at local noon */
00515         mjdn = mjd_day(mjd)+0.5;
00516         now_lst (mjdn,lng, &lstn);
00517         //ephi_sun(2451690.0,lng,lat,.0, &ra1, &dec1, &ls1);
00518         SetJD(mjdn+MJD0);
00519         //cout<<Obj<<endl;
00520         switch(Obj){
00521                 case 8: ephi_sun();
00522                         break;
00523                 case 9: ephi_moon();
00524                         break;
00525                 default:
00526                            ephi_planet();
00527                 break;
00528                 }       
00529         ran=Ra;
00530         //cout<<"MMMM "<<lstn<<"  "<<mjd_hr(mjdn)<<endl;
00531         //printang(ra1);
00532         /* first approximation is to find rise/set times of a fixed object
00533          * at the current epoch in its position at local noon.
00534          * N.B. add typical refraction for initial go/no-go test. if it
00535          *   passes, real code does refraction rigorously.
00536          */
00537         riset (Ra,Dec, lat, dis+0.01, &lr, &ls, &ar, &as, &rss);
00538         switch (rss) {
00539         case  0:  break;
00540         case  1: Flags = RS_NEVERUP; RiseTu=0.0; RiseAz=0.0;return;
00541         case -1: Flags = RS_CIRCUMPOLAR; goto dotransit;
00542         default: Flags = RS_ERROR; RiseTu=0.0; RiseAz=0.0;return;
00543         }
00544 
00545         /* iterate to find better rise time */
00546 
00547         double mjdt;
00548         switch (find_0alt (mjdn,(lr - lstn)/SIDRATE, dis, &ar, &mjdt)) {
00549         case 0: /* ok */
00550             RiseTu = mjd_hr(mjdt);
00551             RiseAz = raddeg(ar);
00552             break;
00553         case -1: /* obj_cir error */
00554             Flags |= RS_RISERR;
00555                 RiseTu=0.0; RiseAz=0.0;
00556             break;
00557         case -2: /* converged but not today */ /* FALLTHRU */
00558         case -3: /* probably never up */
00559             Flags |= RS_NORISE;
00560                 RiseTu=0.0; RiseAz=0.0;
00561             break;
00562         }
00563 
00564         /* iterate to find better set time */
00565         switch (find_0alt (mjdn, (ls - lstn)/SIDRATE, dis, &ar, &mjdt)) {
00566         case 0: /* ok */
00567             SetTu =  mjd_hr(mjdt);
00568             SetAz = raddeg(ar);
00569             break;
00570         case -1: /* obj_cir error */
00571             Flags |= RS_SETERR;
00572                 SetTu=-1.0; SetAz=0.0;
00573             break;
00574         case -2: /* converged but not today */ /* FALLTHRU */
00575         case -3: /* probably circumpolar */
00576             Flags |= RS_NOSET;
00577                 SetTu=-1.0; SetAz=0.0;
00578             break;
00579         }
00580 
00581         /* can try transit even if rise or set failed */
00582     dotransit:
00583         switch (find_transit (mjdn,(radhr(ran) - lstn)/SIDRATE, dis, &as, &mjdt)) {
00584         case 0: /* ok */
00585             TranTu = mjd_hr(mjdt);
00586             TranAlt = raddeg(as);
00587             break;
00588         case -1: /* did not converge */
00589             Flags |= RS_TRANSERR;
00590                 TranTu=-1.0;TranAlt=0.0;
00591             break;
00592         case -2: /* converged but not today */
00593             Flags |= RS_NOTRANS;
00594                 TranTu=-1.0;TranAlt=0.0;
00595             break;
00596         }
00597 }
00598 
00599 int SolSystem::find_0alt (double mjd, double dt, double dis, double *az, double *mjdt)
00600 {
00601 #define MAXPASSES       20              /* max iterations to try */
00602 #define FIRSTSTEP       (1.0/60.0/24.0) /* first time step, days */
00603 
00604         double a0 = 0, alt=0;
00605         double mjdn = mjd;
00606         int npasses;
00607         /* insure initial guess is today -- if not, move by 24 hours */
00608         if (dt < -12.0)
00609             dt += 24.0;
00610         if (dt > 12.0)
00611             dt -= 24.0;
00612         //cout<<"DT="<<dt<<endl;
00613         /* convert dt to days for remainder of algorithm */
00614         dt /= 24.0;
00615 
00616         /* use secant method to look for s_alt + dis == 0 */
00617         
00618         npasses = 0;
00619         do {
00620             double a1,lst,ha;
00621                 
00622             mjd += dt;
00623                 *mjdt=mjd;
00624                 //now_lst (mjd,lng, &lst);
00625                 SetJD(mjd+MJD0);
00626                 switch(Obj){
00627                 case 8: ephi_sun();
00628                         break;
00629                 case 9:ephi_moon();
00630                         break;
00631                 default:
00632                                 ephi_planet();
00633                 break;
00634                 }       
00635                 now_lst (mjd,lng, &lst);
00636                 //printang(lst);
00637                 ha= hrrad(lst) - Ra;
00638                 
00639             hadec_aa (lat, ha, Dec, &alt, az);
00640                 //cout<<"MMMM "<<raddeg(*az)<<" ALT= "<<mjd_hr(mjd)<<endl;
00641             a1 = alt;
00642                 
00643             dt = (npasses == 0) ? FIRSTSTEP : (dis+a1)*dt/(a0-a1);
00644             a0 = a1;
00645 
00646         } while (++npasses < MAXPASSES && fabs(dt) > TMACC);
00647 
00648         /* return codes */
00649         if (npasses == MAXPASSES)
00650             return (-3);
00651         
00652         return (fabs(mjdn-mjd) < .5 ? 0 : -2);
00653 
00654 #undef  MAXPASSES
00655 #undef  FIRSTSTEP
00656 }
00657 
00658 /* find when the given object transits. start the search when LST matches the
00659  *   object's RA at noon.
00660  * if ok, return 0 with np and op set to the transit conditions; if can't
00661  *   converge return -1; if converges ok but not today return -2.
00662  * N.B. we assume np is passed set to local noon.
00663  */
00664 int SolSystem::find_transit (double mjd, double dt, double dis, double *alt, double *mjdt)
00665 {
00666 #define MAXLOOPS        10
00667 #define MAXERR          (0.25/60.)              /* hours */
00668         double mjdn = mjd;
00669         double lst,az;
00670         int i;
00671 
00672         /* insure initial guess is today -- if not, move by 24 hours */
00673         if (dt < -12.0)
00674             dt += 24.0;
00675         if (dt > 12.0)
00676             dt -= 24.0;
00677 
00678         i = 0;
00679         double ha;
00680         do {
00681             mjd += dt/24.0;
00682                 SetJD(mjd+MJD0);
00683                 switch(Obj){
00684                 case 8: ephi_sun();
00685                         break;
00686                 case 9:ephi_moon();
00687                         break;
00688                 default:
00689                           ephi_planet();
00690                 break;
00691                 }       
00692             now_lst (mjd,lng, &lst);
00693                 ha= hrrad(lst) - Ra;
00694                 hadec_aa (lat, ha, Dec, alt, &az);
00695             dt = (radhr(Ra) - lst);
00696             if (dt < -12.0)
00697                 dt += 24.0;
00698             if (dt > 12.0)
00699                 dt -= 24.0;
00700         } while (++i < MAXLOOPS && fabs(dt) > MAXERR);
00701 
00702         /* return codes */
00703         if (i == MAXLOOPS)
00704             return (-1);
00705         *mjdt=mjd;
00706         return (fabs(mjd - mjdn) < 0.5 ? 0 : -2);
00707 
00708 #undef  MAXLOOPS
00709 #undef  MAXERR
00710 }
00711 
00712 
00713 
00714 
00715 /*
00716 *****************************************************************************************
00717                                 R O U T I N E S ASTRO
00718 
00719 *****************************************************************************************
00720 */
00721 
00722 
00723 double Tempo_Siderale(double J_D,double Ora_Un_Dec)
00724 {
00725         double M,T,T1,Tempo_Siderale_0,Tempo_Siderale_Ora,Tempo_Siderale_Loc;
00726 
00727         T = ((J_D) - A2000) / 36525.;
00728         T1 = (24110.54841 + 8640184.812866 * T + 0.0093103 * T * T)/86400.0;
00729         Tempo_Siderale_0 = modf(T1,&M) * 24.;
00730         Tempo_Siderale_Ora = Tempo_Siderale_0 + Ora_Un_Dec * 1.00273790935;
00731         if (Tempo_Siderale_Ora < 0.) Tempo_Siderale_Ora = Tempo_Siderale_Ora + 24.;
00732         if (Tempo_Siderale_Ora >= 24.) Tempo_Siderale_Ora = Tempo_Siderale_Ora - 24.;
00733         Tempo_Siderale_Loc = Tempo_Siderale_Ora;
00734         if (Tempo_Siderale_Loc < 0.) Tempo_Siderale_Loc = Tempo_Siderale_Loc + 24.;
00735         if (Tempo_Siderale_Loc >= 24.) Tempo_Siderale_Loc = Tempo_Siderale_Loc - 24.;
00736         return Tempo_Siderale_Loc;
00737 }   /* Calcolo_Tempo_Siderale */
00738 
00739 
00740 
00741 
00742 
00743 
00744 
00745 void now_lst(double mjd,double lng, double *lstp)
00746 //now_lst (np, lstp)
00747 //Now *np;
00748 //double *lstp;
00749 {
00750         static double last_mjd = -23243, last_lng = 121212, last_lst;
00751         double eps, lst, deps, dpsi;
00752 
00753         if (last_mjd == mjd && last_lng == lng) {
00754             *lstp = last_lst;
00755             return;
00756         }
00757 
00758         //utc_gst (mjd_day(mjd), mjd_hr(mjd), &lst);
00759         lst=Tempo_Siderale(mjd_day(mjd)+MJD0,mjd_hr(mjd));
00760         lst += radhr(lng);
00761 
00762         obliquity(mjd, &eps);
00763         nutation(mjd, &deps, &dpsi);
00764         lst += radhr(dpsi*cos(eps+deps));
00765 
00766         range (&lst, 24.0);
00767 
00768         last_mjd = mjd;
00769         last_lng = lng;
00770         *lstp = last_lst = lst;
00771 }
00773 double mm_mjed (double mjd)
00774 {
00775         return (mjd + deltat(mjd)/86400.0);
00776 }
00777 
00778 
00779 int Conv_GST_UT(double jd,double gst,double *tu)
00780 /* GST deve essere il tempo siderale medio di greenwich;*/
00781 {
00782         double t,t0;
00783         t=(jd-A2000)/36525.;
00784         t0=fmod(6.697374558 + 2400.051336 * t + 0.000025862 * t * t,24.);
00785         if(t0<0.)t0+=24.;
00786         *tu=fmod((gst-t0),24.);
00787         if(*tu<0.)*tu+=24.;
00788         (*tu)=(*tu)*0.9972695663;
00789         return 0;
00790 }
00791 
00792 int Sun_Pos(double jd,double *ra,double *decs,double *lon,double *r)
00793 {
00794         double TW=2.*PI,t,m,tl,tl0,m1;
00795         t=jd-A2000;
00796         tl=4.8949504+0.017202792*t; /*Long media sole*/
00797         while(tl<0.)tl+=TW;
00798         tl0= 6.240040768+.01720197*t; /*Anomalia media sole*/
00799         while(tl0<0.)tl0+=TW;
00800         m=tl+0.033423055*sin(tl0)+0.000349065*sin(2.*tl0); /*Oss.Long sole*/
00801         m1=fmod(m,TW);
00802         *r=1.00014-0.01671*cos(tl0)-0.00014*cos(2.*tl0);
00803         *lon=(m1 -9.93e-5)/Conv_Rad;
00804         Conv_lb_ad(jd,*lon,0.,ra,decs);
00805         return 0;
00806 }
00807 
00808 int Conv_lb_ad(double jd,double l,double b,double *ra,double *dec)
00809         /*l,b,in gradi ridotti tra 0-360 per l
00810    ritorna ra, dec in ore , gradi decimali*/
00811 {
00812         double e,ras,a,c1;
00813 
00814         e=0.409087723-0.069813e-9*(jd-A2000);/*obliquita eclittica*/
00815         a=cos(e)*sin(l*Conv_Rad)-tan(b*Conv_Rad)*sin(e);
00816         c1=cos(l*Conv_Rad);
00817         ras=atan(a/c1);
00818         if(l>90.)ras+=PI;
00819         if(l>270.)ras+=PI;
00820         *ra=(ras/Conv_Ora_Rad);
00821         a=sin(e)*sin(l*Conv_Rad)*cos(b*Conv_Rad);
00822         c1=sin(b*Conv_Rad)*cos(e) ;
00823         *dec=asin( a + c1 )/Conv_Rad;
00824         return 0;
00825 }
00826 
00827 void riset (double ra, double dec, double lat, double dis, double *lstr,double * lsts,
00828            double *azr, double *azs, int *status)
00829 {
00830 #define EPS     (1e-9)  /* math rounding fudge - always the way, eh? */
00831         double h;               /* hour angle */
00832         double cos_h;           /* cos h */
00833         double z;               /* zenith angle */
00834         double zmin, zmax;      /* Minimum and maximum zenith angles */
00835         double xaz, yaz;        /* components of az */
00836         int shemi;              /* flag for southern hemisphere reflection */
00837 
00838         /* reflect lat and dec if in southern hemisphere, then az back later */
00839         if ((shemi= (lat < 0.)) != 0) {
00840             lat = -lat;
00841             dec = -dec;
00842         }
00843 
00844         /* establish zenith angle, and its extrema */
00845         z = (PI/2.) + dis;
00846         zmin = fabs (dec - lat);
00847         zmax = PI - fabs(dec + lat);
00848 
00849         /* first consider special cases.
00850          * these also avoid any boundary problems in subsequent computations.
00851          */
00852         if (zmax <= z + EPS) {
00853             *status = -1;       /* never sets */
00854             return;
00855         }
00856         if (zmin >= z - EPS) {
00857             *status = 1;        /* never rises */
00858             return;
00859         }
00860 
00861         /* compute rising hour angle -- beware found off */
00862         cos_h = (cos(z)-sin(lat)*sin(dec))/(cos(lat)*cos(dec));
00863         if (cos_h >= 1.)
00864             h =  0.;
00865         else if (cos_h <= -1.)
00866             h = PI;
00867         else
00868             h = acos (cos_h);
00869 
00870         /* compute setting azimuth -- beware found off */
00871         xaz = sin(dec)*cos(lat)-cos(dec)*cos(h)*sin(lat);
00872         yaz = -1.*cos(dec)*sin(h);
00873         if (xaz == 0.) {
00874             if (yaz > 0)
00875                 *azs = PI/2;
00876             else
00877                 *azs = -PI/2;
00878         } else
00879             *azs = atan2 (yaz, xaz);
00880 
00881         /* reflect az back if southern */
00882         if (shemi)
00883             *azs = PI - *azs;
00884         range(azs, 2.*PI);
00885 
00886         /* rising is just the opposite side */
00887         *azr = 2.*PI - *azs;
00888         range(azr, 2.*PI);
00889 
00890         /* rise and set are just ha either side of ra */
00891         *lstr = radhr(ra-h);
00892         range(lstr,24.0);
00893         *lsts = radhr(ra+h);
00894         range(lsts,24.0);
00895 
00896         /* OK */
00897         *status = 0;
00898 }
00899 
00900 void range (double *v, double r)
00901 {
00902         *v -= r*floor(*v/r);
00903 }
00904 
00905 
00906 #define VSOP_ASCALE     1e8     /* amplitude factor as stored */
00907 
00908 /* coding flags */
00909 #define VSOP_SPHERICAL  1       /* version in data.c uses spherical coords */
00910 #define VSOP_GETRATE    0       /* calculate time derivatives of coordinates */
00911 
00912 #define VSOP_A1000      365250.0        /* days per millenium */
00913 #define VSOP_MAXALPHA   5               /* max degree of time */
00914 
00915 
00916 /******************************************************************
00917  * adapted from BdL FORTRAN Code; stern
00918  *
00919  *    Reference : Bureau des Longitudes - PBGF9502
00920  *
00921  *    Object :  calculate a VSOP87 position for a given time.
00922  *
00923  *    Input :
00924  *
00925  *    mjd      modified julian date, counted from J1900.0
00926  *             time scale : dynamical time TDB.
00927  *
00928  *    obj       object number as in astro.h, NB: not for pluto
00929  *
00930  *    prec     relative precision
00931  *
00932  *             if prec is equal to 0 then the precision is the precision
00933  *                p0 of the complete solution VSOP87.
00934  *                Mercury    p0 =  0.6 10**-8
00935  *                Venus      p0 =  2.5 10**-8
00936  *                Earth      p0 =  2.5 10**-8
00937  *                Mars       p0 = 10.0 10**-8
00938  *                Jupiter    p0 = 35.0 10**-8
00939  *                Saturn     p0 = 70.0 10**-8
00940  *                Uranus     p0 =  8.0 10**-8
00941  *                Neptune    p0 = 42.0 10**-8
00942  *
00943  *             if prec is not equal to 0, let us say in between p0 and
00944  *             10**-3, the precision is :
00945  *                for the positions :
00946  *                - prec*a0 au for the distances.
00947  *                - prec rad for the other variables.
00948  *                for the velocities :
00949  *                - prec*a0 au/day for the distances.
00950  *                - prec rad/day for the other variables.
00951  *                  a0 is the semi-major axis of the body.
00952  *
00953  *    Output :
00954  *
00955  *    ret[6]     array of the results (double).
00956  *
00957  *             for spherical coordinates :
00958  *                 1: longitude (rd)
00959  *                 2: latitude (rd)
00960  *                 3: radius (au)
00961  *              #if VSOP_GETRATE:
00962  *                 4: longitude velocity (rad/day)
00963  *                 5: latitude velocity (rad/day)
00964  *                 6: radius velocity (au/day)
00965  *
00966  *    return:     error index (int)
00967  *                 0: no error.
00968  *                 2: object out of range [MERCURY .. NEPTUNE, SUN]
00969  *                 3: precision out of range [0.0 .. 1e-3]
00970  ******************************************************************/
00971 int vsop87 (double mjd, int obj, double prec, double *ret)
00972 {
00973     static double (*vx_map[])[3] = {            /* data tables */
00974                 vx_mercury, vx_venus, vx_mars, vx_jupiter,
00975                 vx_saturn, vx_uranus, vx_neptune, 0, vx_earth,
00976         };
00977     static int (*vn_map[])[3] = {               /* indexes */
00978                 vn_mercury, vn_venus, vn_mars, vn_jupiter,
00979                 vn_saturn, vn_uranus, vn_neptune, 0, vn_earth,
00980         };
00981     static double a0[] = {      /* semimajor axes; for precision ctrl only */
00982             0.39, 0.72, 1.5, 5.2, 9.6, 19.2, 30.1, 39.5, 1.0,
00983         };
00984     double (*vx_obj)[3] = vx_map[obj];          /* VSOP87 data and indexes */
00985     int (*vn_obj)[3] = vn_map[obj];
00986 
00987     double t[VSOP_MAXALPHA+1];                  /* powers of time */
00988     double t_abs[VSOP_MAXALPHA+1];              /* powers of abs(time) */
00989     double q;                                   /* aux for precision control */
00990     int i, cooidx, alpha;                       /* misc indexes */
00991 
00992     if (obj == PLUTO || obj > SUN)
00993         return (2);
00994 
00995     if (prec < 0.0 || prec > 1e-3)
00996         return(3);
00997 
00998     /* zero result array */
00999     for (i = 0; i < 6; ++i) ret[i] = 0.0;
01000 
01001     /* time and its powers */
01002     t[0] = 1.0;
01003     t[1] = (mjd - J2000)/VSOP_A1000;
01004     for (i = 2; i <= VSOP_MAXALPHA; ++i) t[i] = t[i-1] * t[1];
01005     t_abs[0] = 1.0;
01006     for (i = 1; i <= VSOP_MAXALPHA; ++i) t_abs[i] = fabs(t[i]);
01007 
01008     /* precision control */
01009     q = -log10(prec + 1e-35) - 2;       /* decades below 1e-2 */
01010     q = VSOP_ASCALE * prec / 10.0 / q;  /* reduce threshold progressively
01011                                          * for higher precision */
01012 
01013     /* do the term summation; first the spatial dimensions */
01014     for (cooidx = 0; cooidx < 3; ++cooidx) {
01015 
01016         /* then the powers of time */
01017         for (alpha = 0; vn_obj[alpha+1][cooidx] ; ++alpha) {
01018             double p, term, termdot;
01019 
01020             /* precision threshold */
01021             p = q/(t_abs[alpha] + alpha * t_abs[alpha-1] * 1e-4 + 1e-35);
01022 #if VSOP_SPHERICAL
01023             if (cooidx == 2)    /* scale by semimajor axis for radius */
01024 #endif
01025                 p *= a0[obj];
01026 
01027             term = termdot = 0.0;
01028             for (i = vn_obj[alpha][cooidx]; i < vn_obj[alpha+1][cooidx]; ++i) {
01029                 double a, b, c, arg;
01030 
01031                 a = vx_obj[i][0];
01032                 if (a < p) continue;    /* ignore small terms */
01033 
01034                 b = vx_obj[i][1];
01035                 c = vx_obj[i][2];
01036 
01037                 arg = b + c * t[1];
01038                 term += a * cos(arg);
01039 #if VSOP_GETRATE
01040                 termdot += -c * a * sin(arg);
01041 #endif
01042             }
01043 
01044             ret[cooidx] += t[alpha] * term;
01045 #if VSOP_GETRATE
01046             ret[cooidx + 3] += t[alpha] * termdot +
01047                     ((alpha > 0) ? alpha * t[alpha - 1] * term : 0.0);
01048 #endif
01049         } /* alpha */
01050     } /* cooidx */
01051 
01052     for (i = 0; i < 6; ++i) ret[i] /= VSOP_ASCALE;
01053 
01054 #if VSOP_SPHERICAL
01055     /* reduce longitude to 0..2pi */
01056     ret[0] -= floor(ret[0]/(2.*PI)) * (2.*PI);
01057 #endif
01058 
01059 #if VSOP_GETRATE
01060     /* convert millenium rate to day rate */
01061     for (i = 3; i < 6; ++i) ret[i] /= VSOP_A1000;
01062 #endif
01063 
01064 #if VSOP_SPHERICAL
01065     /* reduction from dynamical equinox of VSOP87 to FK5;
01066      */
01067     if (prec < 5e-7) {          /* 5e-7 rad = 0.1 arc seconds */
01068         double L1, c1, s1;
01069         L1 = ret[0] - degrad(13.97 * t[1] - 0.031 * t[2]);
01070         c1 = cos(L1); s1 = sin(L1);
01071         ret[0] += degrad(-0.09033 + 0.03916 * (c1 + s1) * tan(ret[1]))/3600.0;
01072         ret[1] += degrad(0.03916 * (c1 - s1))/3600.0;
01073     }
01074 #endif
01075 
01076     return (0);
01077 }
01078 
01079 void sunpos (double mjd, double *lsn, double *rsn, double *bsn)
01080 {
01081         static double last_mjd = -3691, last_lsn, last_rsn, last_bsn;
01082         double ret[6];
01083 
01084         if (mjd == last_mjd) {
01085             *lsn = last_lsn;
01086             *rsn = last_rsn;
01087             if (bsn) *bsn = last_bsn;
01088             return;
01089         }
01090 
01091         vsop87(mjd, SUN, 0.0, ret);     /* full precision earth pos */
01092 
01093         *lsn = ret[0] - PI;             /* revert to sun pos */
01094         range (lsn, 2*PI);              /* normalise */
01095 
01096         last_lsn = *lsn;                /* memorise */
01097         last_rsn = *rsn = ret[2];
01098         last_bsn = -ret[1];
01099         last_mjd = mjd;
01100 
01101         if (bsn) *bsn = last_bsn;       /* assign only if non-NULL pointer */
01102 
01103 }
01104 
01105 
01106 
01107 #define DCOS(x)         cos(degrad(x))
01108 #define DSIN(x)         sin(degrad(x))
01109 #define DASIN(x)        raddeg(asin(x))
01110 #define DATAN2(y,x)     raddeg(atan2((y),(x)))
01111 
01112 static void precess_hiprec (double mjd1, double mjd2, double *ra,
01113     double *dec);
01114 
01115 /* corrects ra and dec, both in radians, for precession from epoch 1 to epoch 2.
01116  * the epochs are given by their modified JDs, mjd1 and mjd2, respectively.
01117  * N.B. ra and dec are modifed IN PLACE.
01118  */
01119 void precess (double mjd1, double mjd2, double *ra, double *dec)
01120 /*mjd1, mjd2;   initial and final epoch modified JDs 
01121 double *ra, *dec;       / ra/dec for mjd1 in, for mjd2 out */
01122 {
01123         precess_hiprec (mjd1, mjd2, ra, dec);
01124 }
01125 
01126 /*
01127  * Copyright (c) 1990 by Craig Counterman. All rights reserved.
01128  *
01129  * This software may be redistributed freely, not sold.
01130  * This copyright notice and disclaimer of warranty must remain
01131  *    unchanged. 
01132  *
01133  * No representation is made about the suitability of this
01134  * software for any purpose.  It is provided "as is" without express or
01135  * implied warranty, to the extent permitted by applicable law.
01136  *
01137  * Rigorous precession. From Astronomical Ephemeris 1989, p. B18
01138  *
01139  * 96-06-20 Hayo Hase <hase@wettzell.ifag.de>: theta_a corrected
01140  */
01141 static void precess_hiprec (double mjd1, double mjd2, double *ra, double *dec)
01142 /*double mjd1, mjd2;     initial and final epoch modified JDs 
01143 ra, *dec;       ra/dec for mjd1 in, for mjd2 out */
01144 {
01145         static double last_mjd1 = -213.432, last_from;
01146         static double last_mjd2 = -213.432, last_to;
01147         double zeta_A, z_A, theta_A;
01148         double T;
01149         double A, B, C;
01150         double alpha, delta;
01151         double alpha_in, delta_in;
01152         double from_equinox, to_equinox;
01153         double alpha2000, delta2000;
01154 
01155         /* convert mjds to years;
01156          * avoid the remarkably expensive calls to mjd_year()
01157          */
01158         if (last_mjd1 == mjd1)
01159             from_equinox = last_from;
01160         else {
01161             mjd_year (mjd1, &from_equinox);
01162             last_mjd1 = mjd1;
01163             last_from = from_equinox;
01164         }
01165         if (last_mjd2 == mjd2)
01166             to_equinox = last_to;
01167         else {
01168             mjd_year (mjd2, &to_equinox);
01169             last_mjd2 = mjd2;
01170             last_to = to_equinox;
01171         }
01172 
01173         /* convert coords in rads to degs */
01174         alpha_in = raddeg(*ra);
01175         delta_in = raddeg(*dec);
01176 
01177         /* precession progresses about 1 arc second in .047 years */
01178         /* From from_equinox to 2000.0 */
01179         if (fabs (from_equinox-2000.0) > .02) {
01180             T = (from_equinox - 2000.0)/100.0;
01181             zeta_A  = 0.6406161* T + 0.0000839* T*T + 0.0000050* T*T*T;
01182             z_A     = 0.6406161* T + 0.0003041* T*T + 0.0000051* T*T*T;
01183             theta_A = 0.5567530* T - 0.0001185* T*T - 0.0000116* T*T*T;
01184 
01185             A = DSIN(alpha_in - z_A) * DCOS(delta_in);
01186             B = DCOS(alpha_in - z_A) * DCOS(theta_A) * DCOS(delta_in)
01187               + DSIN(theta_A) * DSIN(delta_in);
01188             C = -DCOS(alpha_in - z_A) * DSIN(theta_A) * DCOS(delta_in)
01189               + DCOS(theta_A) * DSIN(delta_in);
01190 
01191             alpha2000 = DATAN2(A,B) - zeta_A;
01192             range (&alpha2000, 360.0);
01193             delta2000 = DASIN(C);
01194         } else {
01195             /* should get the same answer, but this could improve accruacy */
01196             alpha2000 = alpha_in;
01197             delta2000 = delta_in;
01198         };
01199 
01200 
01201         /* From 2000.0 to to_equinox */
01202         if (fabs (to_equinox - 2000.0) > .02) {
01203             T = (to_equinox - 2000.0)/100.0;
01204             zeta_A  = 0.6406161* T + 0.0000839* T*T + 0.0000050* T*T*T;
01205             z_A     = 0.6406161* T + 0.0003041* T*T + 0.0000051* T*T*T;
01206             theta_A = 0.5567530* T - 0.0001185* T*T - 0.0000116* T*T*T;
01207 
01208             A = DSIN(alpha2000 + zeta_A) * DCOS(delta2000);
01209             B = DCOS(alpha2000 + zeta_A) * DCOS(theta_A) * DCOS(delta2000)
01210               - DSIN(theta_A) * DSIN(delta2000);
01211             C = DCOS(alpha2000 + zeta_A) * DSIN(theta_A) * DCOS(delta2000)
01212               + DCOS(theta_A) * DSIN(delta2000);
01213 
01214             alpha = DATAN2(A,B) + z_A;
01215             range(&alpha, 360.0);
01216             delta = DASIN(C);
01217         } else {
01218             /* should get the same answer, but this could improve accruacy */
01219             alpha = alpha2000;
01220             delta = delta2000;
01221         };
01222 
01223         *ra = degrad(alpha);
01224         *dec = degrad(delta);
01225 }
01226 
01227 void cal_mjd (int mn, double dy, int yr, double *mjd)
01228 {
01229         static double last_mjd, last_dy;
01230         static int last_mn, last_yr;
01231         int b, d, m, y;
01232         long c;
01233 
01234         if (mn == last_mn && yr == last_yr && dy == last_dy) {
01235             *mjd = last_mjd;
01236             return;
01237         }
01238 
01239         m = mn;
01240         y = (yr < 0) ? yr + 1 : yr;
01241         if (mn < 3) {
01242             m += 12;
01243             y -= 1;
01244         }
01245 
01246         if (yr < 1582 || (yr == 1582 && (mn < 10 || (mn == 10 && dy < 15))))
01247             b = 0;
01248         else {
01249             int a;
01250             a = y/100;
01251             b = 2 - a + a/4;
01252         }
01253 
01254         if (y < 0)
01255             c = (long)((365.25*y) - 0.75) - 694025L;
01256         else
01257             c = (long)(365.25*y) - 694025L;
01258 
01259         d = (int)30.6001*(m+1);
01260 
01261         *mjd = b + c + d + dy - 0.5;
01262 
01263         last_mn = mn;
01264         last_dy = dy;
01265         last_yr = yr;
01266         last_mjd = *mjd;
01267 }
01268 
01269 
01270 /* given the modified Julian date (number of days elapsed since 1900 jan 0.5,),
01271  * mjd, return the calendar date in months, *mn, days, *dy, and years, *yr.
01272  */
01273 
01274 void mjd_cal (double mjd, int *mn, double *dy, int *yr)
01275 {
01276         static double last_mjd, last_dy;
01277         static int last_mn, last_yr;
01278         double d, f;
01279         double i, a, b, ce, g;
01280 
01281         /* we get called with 0 quite a bit from unused epoch fields.
01282          * 0 is noon the last day of 1899.
01283          */
01284         if (mjd == 0.0) {
01285             *mn = 12;
01286             *dy = 31.5;
01287             *yr = 1899;
01288             return;
01289         }
01290 
01291         if (mjd == last_mjd) {
01292             *mn = last_mn;
01293             *yr = last_yr;
01294             *dy = last_dy;
01295             return;
01296         }
01297 
01298         d = mjd + 0.5;
01299         i = floor(d);
01300         f = d-i;
01301         if (f == 1) {
01302             f = 0;
01303             i += 1;
01304         }
01305 
01306         if (i > -115860.0) {
01307             a = floor((i/36524.25)+.99835726)+14;
01308             i += 1 + a - floor(a/4.0);
01309         }
01310 
01311         b = floor((i/365.25)+.802601);
01312         ce = i - floor((365.25*b)+.750001)+416;
01313         g = floor(ce/30.6001);
01314         *mn = (int)(g - 1);
01315         *dy = ce - floor(30.6001*g)+f;
01316         *yr = (int)(b + 1899);
01317 
01318         if (g > 13.5)
01319             *mn = (int)(g - 13);
01320         if (*mn < 2.5)
01321             *yr = (int)(b + 1900);
01322         if (*yr < 1)
01323             *yr -= 1;
01324 
01325         last_mn = *mn;
01326         last_dy = *dy;
01327         last_yr = *yr;
01328         last_mjd = mjd;
01329 }
01330 
01331 /* given an mjd, set *dow to 0..6 according to which day of the week it falls
01332  * on (0=sunday).
01333  * return 0 if ok else -1 if can't figure it out.
01334  */
01335 
01336 int mjd_dow (double mjd,int *dow)
01337 
01338 {
01339         /* cal_mjd() uses Gregorian dates on or after Oct 15, 1582.
01340          * (Pope Gregory XIII dropped 10 days, Oct 5..14, and improved the leap-
01341          * year algorithm). however, Great Britian and the colonies did not
01342          * adopt it until Sept 14, 1752 (they dropped 11 days, Sept 3-13,
01343          * due to additional accumulated error). leap years before 1752 thus
01344          * can not easily be accounted for from the cal_mjd() number...
01345          */
01346         if (mjd < -53798.5) {
01347             /* pre sept 14, 1752 too hard to correct |:-S */
01348             return (-1);
01349         }
01350         *dow = ((long)floor(mjd-.5) + 1) % 7;/* 1/1/1900 (mjd 0.5) is a Monday*/
01351         if (*dow < 0)
01352             *dow += 7;
01353         return (0);
01354 }
01355 
01356 /* given a mjd, return the the number of days in the month.  */
01357 
01358 void mjd_dpm (double mjd, int *ndays)
01359 {
01360         static short dpm[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
01361         int m, y;
01362         double d;
01363 
01364         mjd_cal (mjd, &m, &d, &y);
01365         *ndays = (m==2 && ((y%4==0 && y%100!=0)||y%400==0)) ? 29 : dpm[m-1];
01366 }
01367 
01368 /* given a mjd, return the year as a double. */
01369 
01370 void mjd_year (double mjd, double *yr)
01371 {
01372         static double last_mjd, last_yr;
01373         int m, y;
01374         double d;
01375         double e0, e1;  /* mjd of start of this year, start of next year */
01376 
01377         if (mjd == last_mjd) {
01378             *yr = last_yr;
01379             return;
01380         }
01381 
01382         mjd_cal (mjd, &m, &d, &y);
01383         if (y == -1) y = -2;
01384         cal_mjd (1, 1.0, y, &e0);
01385         cal_mjd (1, 1.0, y+1, &e1);
01386         *yr = y + (mjd - e0)/(e1 - e0);
01387 
01388         last_mjd = mjd;
01389         last_yr = *yr;
01390 }
01391 
01392 /* given a decimal year, return mjd */
01393 
01394 void year_mjd (double y, double *mjd)
01395 {
01396         double e0, e1;  /* mjd of start of this year, start of next year */
01397         int yf =(int) floor (y);
01398         if (yf == -1) yf = -2;
01399 
01400         cal_mjd (1, 1.0, yf, &e0);
01401         cal_mjd (1, 1.0, yf+1, &e1);
01402         *mjd = e0 + (y - yf)*(e1-e0);
01403 }
01404 
01405 /* round a time in days, *t, to the nearest second, IN PLACE. */
01406 
01407 void rnd_second (double *t)
01408 {
01409         *t = floor(*t*SPD+0.5)/SPD;
01410 }
01411         
01412 /* given an mjd, truncate it to the beginning of the whole day */
01413 
01414 double mjd_day(double jd)
01415 
01416 {
01417         return (floor(jd-0.5)+0.5);
01418 }
01419 
01420 /* given an mjd, return the number of hours past midnight of the whole day */
01421 double mjd_hr(double jd)
01422 {
01423         return ((jd-mjd_day(jd))*24.0);
01424 }
01425 
01426 void sphcart (double l, double b, double r, double *x, double *y, double *z)
01427 {
01428         double rcb = r * cos(b);
01429 
01430         *x = rcb * cos(l);
01431         *y = rcb * sin(l);
01432         *z = r * sin(b);
01433 }
01434 
01435 /* transformation from cartesian to spherical coordinates */
01436 void cartsph (double x,double  y,double  z,double *l, double *b, double *r)
01437 /*double x, y, z;       source: rectangular coordinates 
01438 double *l, *b, *r;      result: spherical coordinates */
01439 {
01440         double rho = x*x + y*y;
01441 
01442         if (rho > 1e-35) {      /* standard case: off axis */
01443             *l = atan2(y, x);
01444             range (l, 2*PI);
01445             *b = atan2(z, sqrt(rho));
01446             *r = sqrt(rho + z*z);
01447         } else {                /* degenerate case; avoid math error */
01448             *l = 0.0;
01449             if (z == 0.0)
01450                 *b = 0.0;
01451             else
01452                 *b = (z > 0.0) ? PI/2. : -PI/2.;
01453             *r = fabs(z);
01454         }
01455 }
01456 
01457 /* convert those orbital elements that change from epoch mjd0 to epoch mjd.
01458  */
01459 void reduce_elements (double mjd0, double mjd, double inc0, double ap0, double om0, double *inc, double *ap, double *om)
01460 /*double mjd0;  initial epoch
01461 double mjd;     desired epoch 
01462 double inc0;     initial inclination, rads 
01463 double ap0;     initial argument of perihelion, as an mjd 
01464 double om0;      initial long of ascending node, rads 
01465 double *inc;    desired inclination, rads 
01466 double *ap;     desired epoch of perihelion, as an mjd 
01467 double *om;     desired long of ascending node, rads */
01468 {
01469         double t0, t1;
01470         double tt, tt2, t02, tt3;
01471         double eta, th, th0;
01472         double a, b;
01473         double dap;
01474         double cinc, sinc;
01475         double ot, sot, cot, ot1;
01476         double seta, ceta;
01477 
01478         if (fabs(mjd - mjd0) < 1e-5) {
01479             /* sin(eta) blows for inc < 10 degrees -- anyway, no need */
01480             *inc = inc0;
01481             *ap = ap0;
01482             *om = om0;
01483             return;
01484         }
01485 
01486         t0 = mjd0/365250.0;
01487         t1 = mjd/365250.0;
01488 
01489         tt = t1-t0;
01490         tt2 = tt*tt;
01491         t02 = t0*t0;
01492         tt3 = tt*tt2;
01493         eta = (471.07-6.75*t0+.57*t02)*tt+(.57*t0-3.37)*tt2+.05*tt3;
01494         th0 = 32869.0*t0+56*t02-(8694+55*t0)*tt+3*tt2;
01495         eta = degrad(eta/3600.0);
01496         th0 = degrad((th0/3600.0)+173.950833);
01497         th = (50256.41+222.29*t0+.26*t02)*tt+(111.15+.26*t0)*tt2+.1*tt3;
01498         th = th0+degrad(th/3600.0);
01499         cinc = cos(inc0);
01500         sinc = sin(inc0);
01501         ot = om0-th0;
01502         sot = sin(ot);
01503         cot = cos(ot);
01504         seta = sin(eta);
01505         ceta = cos(eta);
01506         a = sinc*sot;
01507         b = ceta*sinc*cot-seta*cinc;
01508         ot1 = atan(a/b);
01509         if (b<0) ot1 += PI;
01510         b = sinc*ceta-cinc*seta*cot;
01511         a = -1*seta*sot;
01512         dap = atan(a/b);
01513         if (b<0) dap += PI;
01514 
01515         *ap = ap0+dap;
01516         range (ap, 2*PI);
01517         *om = ot1+th;
01518         range (om, 2*PI);
01519 
01520         if (inc0<.175)
01521             *inc = asin(a/sin(dap));
01522         else
01523             *inc = 1.570796327-asin((cinc*ceta)+(sinc*seta*cot));
01524 }
01525 
01526 /* given a modified Julian date, mjd, and a set of heliocentric parabolic
01527  * orbital elements referred to the epoch of date (mjd):
01528  *   ep:   epoch of perihelion,
01529  *   inc:  inclination,
01530  *   ap:   argument of perihelion (equals the longitude of perihelion minus the
01531  *         longitude of ascending node)
01532  *   qp:   perihelion distance,
01533  *   om:   longitude of ascending node;
01534  * find:
01535  *   lpd:  heliocentric longitude, 
01536  *   psi:  heliocentric latitude,
01537  *   rp:   distance from the sun to the planet, 
01538  *   rho:  distance from the Earth to the planet,
01539  *   lam:  geocentric ecliptic longitude, 
01540  *   bet:  geocentric ecliptic latitude,
01541  *         none are corrected for light time, ie, they are the true values for
01542  *         the given instant.
01543  *
01544  * all angles are in radians, all distances in AU.
01545  * mutual perturbation corrections with other solar system objects are not
01546  * applied. corrections for nutation and abberation must be made by the caller.
01547  * The RA and DEC calculated from the fully-corrected ecliptic coordinates are
01548  * then the apparent geocentric coordinates. Further corrections can be made,
01549  * if required, for atmospheric refraction and geocentric parallax.
01550  */
01551 void comet (double mjd, double ep, double inc, double ap, double qp, double om, double *lpd, double *psi, double *rp, double *rho, double *lam, double *bet)
01552 {
01553         double w, s, s2;
01554         double l, sl, cl, y;
01555         double spsi, cpsi;
01556         double rd, lsn, rsn;
01557         double lg, re, ll;
01558         double cll, sll;
01559         double nu;
01560 
01561 #define ERRLMT  0.0001
01562         w = ((mjd-ep)*3.649116e-02)/(qp*sqrt(qp));
01563         s = w/3;
01564         for (;;) {
01565             double d;
01566             s2 = s*s;
01567             d = (s2+3)*s-w;
01568             if (fabs(d) <= ERRLMT)
01569                 break;
01570             s = ((2*s*s2)+w)/(3*(s2+1));
01571         }
01572 
01573         nu = 2*atan(s);
01574         *rp = qp*(1+s2);
01575         l = nu+ap;
01576         sl = sin(l);
01577         cl = cos(l);
01578         spsi = sl*sin(inc);
01579         *psi = asin(spsi);
01580         y = sl*cos(inc);
01581         *lpd = atan(y/cl)+om;
01582         cpsi = cos(*psi);
01583         if (cl<0) *lpd += PI;
01584         range (lpd, 2*PI);
01585         rd = *rp * cpsi;
01586         sunpos (mjd, &lsn, &rsn, 0);
01587         lg = lsn+PI;
01588         re = rsn;
01589         ll = *lpd - lg;
01590         cll = cos(ll);
01591         sll = sin(ll);
01592         *rho = sqrt((re * re)+(*rp * *rp)-(2*re*rd*cll));
01593         if (rd<re) 
01594             *lam = atan((-1*rd*sll)/(re-(rd*cll)))+lg+PI;
01595         else
01596             *lam = atan((re*sll)/(rd-(re*cll)))+*lpd;
01597         range (lam, 2*PI);
01598         *bet = atan((rd*spsi*sin(*lam-*lpd))/(cpsi*re*sll));
01599 }
01600 
01601 void obliquity (double mjd, double *eps)
01602 {
01603         static double lastmjd = -16347, lasteps;
01604 
01605         if (mjd != lastmjd) {
01606             double t = (mjd - J2000)/36525.;    /* centuries from J2000 */
01607             lasteps = degrad(23.4392911 +       /* 23^ 26' 21".448 */
01608                             t * (-46.8150 +
01609                             t * ( -0.00059 +
01610                             t * (  0.001813 )))/3600.0);
01611             lastmjd = mjd;
01612         }
01613         *eps = lasteps;
01614 }
01615 
01616 static void pluto_ell (double mjd, double *ret);
01617 static void chap_trans (double mjd, double *ret);
01618 static void planpos (double mjd, int obj, double prec, double *ret);
01619 
01620 
01621 static void chap_trans (double mjd, double *ret)
01622 /*double mjd;    destination epoch 
01623 double *ret;    vector to be transformed _IN PLACE_ */
01624 {
01625         double ra, dec, r, eps;
01626         double sr, cr, sd, cd, se, ce;
01627 
01628         cartsph(ret[0], ret[1], ret[2], &ra, &dec, &r);
01629         precess(J2000, mjd, &ra, &dec);
01630         obliquity(mjd, &eps);
01631         sr = sin(ra); cr = cos(ra);
01632         sd = sin(dec); cd = cos(dec);
01633         se = sin(eps); ce = cos(eps);
01634         ret[0] = atan2( sr * ce + sd/cd * se, cr);      /* long */
01635         ret[1] = asin( sd * ce - cd * se * sr);         /* lat */
01636         ret[2] = r;                                     /* radius */
01637 }
01638 
01639 /* low precision ecliptic coordinates of Pluto from mean orbit.
01640  * Only for sake of completeness outside available perturbation theories.
01641  */
01642 static void pluto_ell (double mjd, double *ret)
01643 /*double mjd epoch 
01644 double *ret;    ecliptic coordinates {l,b,r} at equinox of date */
01645 {
01646         /* mean orbital elements of Pluto.
01647          * The origin of these is somewhat obscure.
01648          */
01649         double  a = 39.543,                     /* semimajor axis, au */
01650                 e = 0.2490,                     /* excentricity */
01651                 inc0 = 17.140,                  /* inclination, deg */
01652                 Om0 = 110.307,                  /* long asc node, deg */
01653                 omeg0 = 113.768,                /* arg of perihel, deg */
01654                 mjdp = 2448045.539 - MJD0,      /* epoch of perihel */
01655                 mjdeq = J2000,                  /* equinox of elements */
01656                 n = 144.9600/36525.;            /* daily motion, deg */
01657 
01658         double inc, Om, omeg;   /* orbital elements at epoch of date */
01659         double ma, ea, nu;      /* mean, excentric and true anomaly */
01660         double lo, slo, clo;    /* longitude in orbit from asc node */
01661 
01662         reduce_elements(mjdeq, mjd, degrad(inc0), degrad(omeg0), degrad(Om0),
01663                                 &inc, &omeg, &Om);
01664         ma = degrad((mjd - mjdp) * n);
01665         anomaly(ma, e, &nu, &ea);
01666         ret[2] = a * (1.0 - e*cos(ea));                 /* r */
01667         lo = omeg + nu;
01668         slo = sin(lo);
01669         clo = cos(lo);
01670         ret[1] = asin(slo * sin(inc));                  /* b */
01671         ret[0] = atan2(slo * cos(inc), clo) + Om;       /* l */
01672 }
01673 
01674 /*************************************************************/
01675 
01676 /* geometric heliocentric position of planet, mean ecliptic of date
01677  * (not corrected for light-time)
01678  */
01679 static void planpos (double mjd, int obj, double prec, double *ret)
01680 {
01681         if (mjd >= CHAP_BEGIN && mjd <= CHAP_END) {
01682             if (obj >= JUPITER) {               /* prefer Chapront */
01683                 chap95(mjd, obj, prec, ret);
01684                 chap_trans (mjd, ret);
01685             } else {                            /* VSOP for inner planets */
01686                 vsop87(mjd, obj, prec, ret);
01687             }
01688         } else {                                /* outside Chapront time: */
01689             if (obj != PLUTO) {                 /* VSOP for all but Pluto */
01690                 vsop87(mjd, obj, prec, ret);
01691             } else {                            /* Pluto mean elliptic orbit */
01692                 pluto_ell(mjd, ret);
01693             }
01694         }
01695 }
01696 
01697 /*************************************************************/
01698 
01699 /* visual elements of planets
01700  * [planet][0] = angular size at 1 AU
01701  * [planet][1] = magnitude at 1 AU from sun and earth and 0 deg phase angle
01702  */
01703 static double vis_elements[8][2] = {
01704         /* Mercury */   { 6.74, -0.42, },
01705         /* Venus */     { 16.92, -4.34, },
01706         /* Mars */      { 9.36, -1.20, },
01707         /* Jupiter */   { 196.74, -9.4, },
01708         /* Saturn */    { 165.6, -8.88, },
01709         /* Uranus */    { 65.8, -7.19, },
01710         /* Neptune */   { 62.2, -6.87, },
01711         /* Pluto */     { 8.2, -1.0, }
01712 };
01713 
01714 /* given a modified Julian date, mjd, and a planet, p, find:
01715  *   lpd0: heliocentric longitude, 
01716  *   psi0: heliocentric latitude,
01717  *   rp0:  distance from the sun to the planet, 
01718  *   rho0: distance from the Earth to the planet,
01719  *         none corrected for light time, ie, they are the true values for the
01720  *         given instant.
01721  *   lam:  geocentric ecliptic longitude, 
01722  *   bet:  geocentric ecliptic latitude,
01723  *         each corrected for light time, ie, they are the apparent values as
01724  *         seen from the center of the Earth for the given instant.
01725  *   dia:  angular diameter in arcsec at 1 AU, 
01726  *   mag:  visual magnitude when 1 AU from sun and earth at 0 phase angle.
01727  *
01728  * all angles are in radians, all distances in AU.
01729  *
01730  * corrections for nutation and abberation must be made by the caller. The RA 
01731  *   and DEC calculated from the fully-corrected ecliptic coordinates are then
01732  *   the apparent geocentric coordinates. Further corrections can be made, if
01733  *   required, for atmospheric refraction and geocentric parallax.
01734  */
01735 void plans (double mjd, int p, double *lpd0, double *psi0, double *rp0, double *rho0, double *lam, double *bet, double *dia, double *mag)
01736 {
01737         static double lastmjd = -10000;
01738         static double lsn, bsn, rsn;    /* geometric geocentric coords of sun */
01739         static double xsn, ysn, zsn;
01740         double lp, bp, rp;              /* heliocentric coords of planet */
01741         double xp, yp, zp, rho;         /* rect. coords and geocentric dist. */
01742         double dt;                      /* light time */
01743         int pass;
01744 
01745         /* get sun cartesian; needed only once at mjd */
01746         if (mjd != lastmjd) {
01747             sunpos (mjd, &lsn, &rsn, &bsn);
01748             sphcart (lsn, bsn, rsn, &xsn, &ysn, &zsn);
01749             lastmjd = mjd;
01750         }
01751 
01752         /* first find the true position of the planet at mjd.
01753          * then repeat a second time for a slightly different time based
01754          * on the position found in the first pass to account for light-travel
01755          * time.
01756          */
01757         dt = 0.0;
01758         for (pass = 0; pass < 2; pass++) {
01759             double ret[6];
01760 
01761             /* get spherical coordinates of planet from precision routines,
01762              * retarded for light time in second pass;
01763              * alternative option:  vsop allows calculating rates.
01764              */
01765             planpos(mjd - dt, p, 0.0, ret);
01766 
01767             lp = ret[0];
01768             bp = ret[1];
01769             rp = ret[2];
01770 
01771             sphcart (lp, bp, rp, &xp, &yp, &zp);
01772             cartsph (xp + xsn, yp + ysn, zp + zsn, lam, bet, &rho);
01773 
01774             if (pass == 0) {
01775                 /* save heliocentric coordinates at first pass since, being
01776                  * true, they are NOT to be corrected for light-travel time.
01777                  */
01778                 *lpd0 = lp;
01779                 range (lpd0, 2.*PI);
01780                 *psi0 = bp;
01781                 *rp0 = rp;
01782                 *rho0 = rho;
01783             }
01784 
01785             /* when we view a planet we see it in the position it occupied
01786              * dt days ago, where rho is the distance between it and earth,
01787              * in AU. use this as the new time for the next pass.
01788              */
01789             dt = rho * 5.7755183e-3;
01790         }
01791 
01792         *dia = vis_elements[p][0];
01793         *mag = vis_elements[p][1];
01794 }
01795 
01796 
01797 #define TWOPI           (2*PI)
01798 #define STOPERR         (1e-8)
01799 
01800 /* given the mean anomaly, ma, and the eccentricity, s, of elliptical motion,
01801  * find the true anomaly, *nu, and the eccentric anomaly, *ea.
01802  * all angles in radians.
01803  */
01804 void anomaly (double ma, double s, double *nu, double *ea)
01805 {
01806         double m, fea, corr;
01807 
01808         if (s < 1.0) {
01809             /* elliptical */
01810             double dla;
01811 
01812             m = ma-TWOPI*(long)(ma/TWOPI);
01813             if (m > PI) m -= TWOPI;
01814             if (m < -PI) m += TWOPI;
01815             fea = m;
01816 
01817             for (;;) {
01818                 dla = fea-(s*sin(fea))-m;
01819                 if (fabs(dla)<STOPERR)
01820                     break;
01821                 /* avoid runnaway corrections for e>.97 and M near 0*/
01822                 corr = 1-(s*cos(fea));
01823                 if (corr < .1) corr = .1;
01824                 dla /= corr;
01825                 fea -= dla;
01826             }
01827             *nu = 2*atan(sqrt((1+s)/(1-s))*tan(fea/2));
01828         } else {
01829             /* hyperbolic */
01830             double fea1;
01831 
01832             m = fabs(ma);
01833             fea = m / (s-1.);
01834             fea1 = pow(6*m/(s*s),1./3.);
01835             /* whichever is smaller is the better initial guess */
01836             if (fea1 < fea) fea = fea1;
01837 
01838             corr = 1;
01839             while (fabs(corr) > STOPERR) {
01840                 corr = (m - s * sinh(fea) + fea) / (s*cosh(fea) - 1);
01841                 fea += corr;
01842             }
01843             if (ma < 0.) fea = -fea;
01844             *nu = 2*atan(sqrt((s+1)/(s-1))*tanh(fea/2));
01845         }
01846         *ea = fea;
01847 }
01848 
01849 
01850 
01851 /* heliocentric rectangular equatorial coordinates of Jupiter to Pluto;
01852  * from Chapront's expansion of DE200/extension of DE200;  mean equator J2000.0
01853  *
01854  * calculation time (milliseconds) on an HP 715/75, Jupiter to Pluto:
01855  * (each coordinate component counted as 1 term,
01856  * secular terms included for JD 2448908.5 = 1992 Oct 13.0)
01857  *
01858  *      prec    terms   rates   no rates
01859  *      0.0     2256    5.1     4.6
01860  *
01861  *      1e-7    792     2.6     2.4     --> nominal precision rel. to DE200
01862  *      1e-6    535     2.1     2.0
01863  *      1e-5    350     1.8     1.6
01864  *      1e-4    199     1.5     1.4
01865  *      1e-3    96      1.2     1.1
01866  *
01867  *      no drop 2256    4.5     3.9     (code without test criterion)
01868  */
01869 
01870 
01871 #define CHAP_MAXTPOW    2       /* NB: valid for all 5 outer planets */
01872 
01873 /* chap95()
01874  *
01875  * input:
01876  *      mjd     modified JD; days from J1900.0 = 2415020.0
01877  *
01878  *      prec    precision level, in radians.
01879  *              if (prec = 0.0), you get the full precision, namely
01880  *              a deviation of not more than 0.02 arc seconds (1e-7 rad)
01881  *              from the JPL DE200 integration, on which this expansion
01882  *              is based.
01883  *
01884  *      obj     object number as in astro.h (jupiter=3, saturn=4, ...)
01885  *
01886  * output:
01887  *      ret[6]  cartesian components of position and velocity
01888  *
01889  * return:
01890  *      0       Ok
01891  *      1       time out of range [CHAP_BEGIN .. CHAP_END]
01892  *      2       object out of range [JUPITER .. PLUTO]
01893  *      3       precision out of range [0.0 .. 1e-3]
01894  */
01895 int chap95 (double mjd, int obj, double prec, double *ret)
01896 {
01897         static double a0[] = {          /* semimajor axes for precision ctrl */
01898             0.39, 0.72, 1.5, 5.2, 9.6, 19.2, 30.1, 39.5, 1.0
01899         };
01900         double sum[CHAP_MAXTPOW+1][6];  /* [T^0, ..][X,Y,Z,X',Y',Z'] */
01901         double T, t;                    /* time in centuries and years */
01902         double ca, sa, Nu;              /* aux vars for terms */
01903         double precT[CHAP_MAXTPOW+1];   /* T-augmented precision threshold */
01904         chap95_rec *rec;                /* term coeffs */
01905         int cooidx;
01906 
01907         /* check parameters */
01908         if (mjd < CHAP_BEGIN || mjd > CHAP_END)
01909                 return (1);
01910 
01911         if (obj < JUPITER || obj > PLUTO)
01912                 return (2);
01913 
01914         if (prec < 0.0 || prec > 1e-3)
01915                 return (3);
01916 
01917         /* init the sums */
01918         zero_mem ((void *)sum, sizeof(sum));
01919 
01920         T = (mjd - J2000)/36525.0;      /* centuries since J2000.0 */
01921 
01922         /* modify precision treshold for
01923          * a) term storing scale
01924          * b) convert radians to au
01925          * c) account for skipped terms (more terms needed for better prec)
01926          *    threshold empirically established similar to VSOP; stern
01927          * d) augment for secular terms
01928          */
01929         precT[0] = prec * CHAP_SCALE                            /* a) */
01930                         * a0[obj]                               /* b) */
01931                         / (10. * (-log10(prec + 1e-35) - 2));   /* c) */
01932         t = 1./(fabs(T) + 1e-35);                               /* d) */
01933         precT[1] = precT[0]*t;
01934         precT[2] = precT[1]*t;
01935 
01936         t = T * 100.0;          /* YEARS since J2000.0 */
01937 
01938         ca = sa = Nu = 0.;      /* shut up compiler warning 'uninitialised' */
01939 
01940         switch (obj) {          /* set initial term record pointer */
01941             case JUPITER:       rec = chap95_jupiter;   break;
01942             case SATURN:        rec = chap95_saturn;    break;
01943             case URANUS:        rec = chap95_uranus;    break;
01944             case NEPTUNE:       rec = chap95_neptune;   break;
01945             case PLUTO:         rec = chap95_pluto;     break;
01946             default:
01947                 return (2);     /* wrong object: severe internal trouble */
01948         }
01949 
01950         /* do the term summation into sum[T^n] slots */
01951         for (; rec->n >= 0; ++rec) {
01952             double *amp;
01953 
01954             /* NOTE:  The formula
01955              * X = SUM[i=1,Records] T**n_i*(CX_i*cos(Nu_k*t)+SX_i*sin(Nu_k*t))
01956              * could be rewritten as  SUM( ... A sin (B + C*t) )
01957              * "saving" trigonometric calls.  However, e.g. for Pluto,
01958              * there are only 65 distinct angles NU_k (130 trig calls).
01959              * With that manipulation, EVERY arg_i would be different for X,
01960              * Y and Z, which is 3*96 terms.  Hence, the formulation as
01961              * given is good (optimal?).
01962              */
01963 
01964             for (cooidx = 0, amp = rec->amp; cooidx < 3; ++cooidx) {
01965                 double C, S, term, termdot;
01966                 short n;                /* fast access */
01967 
01968                 C = *amp++;
01969                 S = *amp++;
01970                 n = rec->n;
01971 
01972                 /* drop term if too small
01973                  * this is quite expensive:  17% of loop time
01974                  */
01975                 if (fabs(C) + fabs(S) < precT[n])
01976                         continue;
01977 
01978                 if (n == 0 && cooidx == 0) {    /* new Nu only here */
01979                     double arg;
01980 
01981                     Nu = rec->Nu;
01982                     arg = Nu * t;
01983                     arg -= floor(arg/(2.*PI))*(2.*PI);
01984                     ca = cos(arg);      /* blast it - even for Nu = 0.0 */
01985                     sa = sin(arg);
01986                 }
01987 
01988                 term = C * ca + S * sa;
01989                 sum[n][cooidx] += term;
01990 #if CHAP_GETRATE
01991                 termdot = (-C * sa + S * ca) * Nu;
01992                 sum[n][cooidx+3] += termdot;
01993                 if (n > 0) sum[n - 1][cooidx+3] += n/100.0 * term;
01994 #endif
01995             } /* cooidx */
01996         } /* records */
01997 
01998         /* apply powers of time and sum up */
01999         for (cooidx = 0; cooidx < 6; ++cooidx) {
02000             ret[cooidx] = (sum[0][cooidx] +
02001                         T * (sum[1][cooidx] +
02002                         T * (sum[2][cooidx] )) )/CHAP_SCALE;
02003         }
02004 
02005         /* TEST: if the MAIN terms are dropped, get angular residue
02006         ret[0] = sqrt(ret[0]*ret[0] + ret[1]*ret[1] + ret[2]*ret[2])/a0[obj];
02007         */
02008 
02009 #if CHAP_GETRATE
02010         for (cooidx = 3; cooidx < 6; ++cooidx) {
02011             ret[cooidx] /= 365.25;      /* yearly to daily rate */
02012         }
02013 #endif
02014 
02015     return (0);
02016 }
02017 
02018 void zero_mem (void *loc, unsigned len)
02019 {
02020         (void) memset (loc, 0, len);
02021 }
02022 
02023 
02024 #define CHAR short
02025 
02026 #define NARGS 18
02027  
02028 struct plantbl {
02029   char max_harmonic[NARGS];
02030   char max_power_of_t;
02031   CHAR *arg_tbl;
02032   long *lon_tbl;
02033   long *lat_tbl;
02034   long *rad_tbl;
02035   double distance;
02036   double timescale;
02037   double trunclvl;
02038 };
02039 
02040 static double mods3600 (double x);
02041 static void mean_elements (double JED);
02042 static int sscc (int k, double arg, int n);
02043 static int g2plan (double J, struct plantbl *plan, double *pobj, int flag);
02044 static double g1plan (double J, struct plantbl *plan);
02045 static int gecmoon (double J, struct plantbl *lrtab,
02046         struct plantbl *lattab, double *pobj);
02047 
02048 /* time points */
02049 #define MOSHIER_J2000 (2451545.0)
02050 
02051 #define MOSHIER_BEGIN (1221000.5 - MJD0) /* directly from above */
02052 #define MOSHIER_END   (2798525.5 - MJD0) /* 2950.0; from libration table */
02053 
02054 
02055 static double Args[NARGS];
02056 static double LP_equinox;
02057 static double NF_arcsec;
02058 static double Ea_arcsec;
02059 static double pA_precession;
02060 
02061 
02062 /* This storage ought to be allocated dynamically.  */
02063 double ss[NARGS][30];
02064 double cc[NARGS][30];
02065 
02066 /* Time, in units of 10,000 Julian years from JED 2451545.0.  */
02067 static double T;
02068 
02069 /* Conversion factors between degrees and radians */
02070 #define DTR 1.7453292519943295769e-2
02071 #define RTD 5.7295779513082320877e1
02072 #define RTS 2.0626480624709635516e5     /* arc seconds per radian */
02073 #define STR 4.8481368110953599359e-6    /* radians per arc second */
02074 #define AUKM 1.4959787e8
02075 
02076 
02077 static long lrtabl[] = {
02078     175667,     66453,      5249,       -42,
02079      20057,       403,     -2360,      6148,
02080      -7644,     24646,     -1273,      9127,
02081      -1395,      1958,
02082        232,      -289,
02083        -97,       553,        69,       130,
02084        -80,         6,
02085        129,      -868,        26,       -89,
02086       1042,      1172,       194,      -112,
02087     -47433,   -241666,    224626,   -103752,
02088      63419,    127606,
02089       2294,      -691,     -1827,     -1254,
02090         -1,      -119,
02091       1057,       324,
02092        505,      -195,       254,      -641,
02093        -36,      1008,     -1082,        -3,
02094        -87,       122,
02095        161,        11,
02096          2,      -106,
02097         29,      -123,
02098        -32,        41,
02099       -524,       -35,
02100        133,      -595,
02101        225,       837,      -108,      -191,
02102      -2294,       841,      -340,      -394,
02103       -351,     -1039,       238,      -108,
02104        -66,        21,
02105       1405,       869,       520,      2776,
02106       -174,        71,
02107        425,       652,     -1260,       -80,
02108        249,        77,
02109       -192,       -17,
02110        -97,       134,
02111         -7,       -54,
02112       -802,     -7436,     -2824,     70869,
02113        -35,      2481,
02114       1865,      1749,     -2166,      2415,
02115         33,      -183,
02116       -835,       283,
02117         27,       -45,
02118         56,       235,
02119          2,       718,
02120      -1206,       275,       -87,      -158,
02121         -7,     -2534,         0,     10774,
02122          1,      -324,
02123       -208,       821,
02124        281,      1340,      -797,       440,
02125        224,        72,
02126        -65,        -5,
02127         -7,       -44,
02128        -48,        66,
02129       -151,       -40,
02130        -41,       -45,
02131         76,      -108,
02132        -18,      1202,         0,     -2501,
02133       1438,      -595,       900,      3040,
02134      -3435,        -5,
02135       -100,       -26,
02136          0,    -13714,
02137       -183,        68,
02138        453,       -83,
02139       -228,       325,
02140         97,        13,
02141          2,       105,
02142        -61,       257,
02143          0,        57,
02144         88,       -11,
02145         -1,     -8220,
02146          0,       275,
02147        -43,       -10,
02148       -199,       105,
02149          1,     -5849,         2,     24887,
02150       -128,        48,
02151        712,       970,     -1407,       845,
02152       -266,       378,
02153        311,      1526,     -1751,        27,
02154          0,   -185858,
02155        133,      6383,
02156       -108,        25,
02157         -7,      1944,
02158          5,       390,
02159        -11,        31,
02160        277,      -384,       158,        72,
02161        -81,       -41,       -13,      -111,
02162      -2332,    -65804,      -698,    505812,
02163         34,   1676716,       -72,  -6664384,
02164        154,       -57,        52,        95,
02165         -4,        -5,
02166         -7,        37,
02167        -63,       -32,
02168          4,      3349,         1,    -14370,
02169         16,       -83,
02170          0,      -401,
02171         13,      3013,
02172         48,       -20,
02173          0,       250,
02174         51,       -79,
02175         -7,      -146,
02176        148,         9,
02177          0,       -64,
02178        -17,       -59,
02179        -67,      -492,
02180         -2,   2116601,
02181        -12,     -1848,
02182          8,      -436,
02183         -6,       324,         0,     -1363,
02184       -163,         9,
02185          0,       -74,
02186         63,      8167,       -29,     37587,
02187        -22,    -74501,
02188        -71,       497,
02189         -1,    551747,
02190        -87,       -22,
02191          0,       -51,
02192         -1,      -463,
02193          0,      -444,
02194          3,        89,
02195         15,       -84,
02196        -36,     -6829,        -5,    -21663,
02197          0,     86058,
02198          0,      -298,
02199         -2,       751,        -2,     -1015,
02200          0,        69,
02201          1,     -4989,         0,     21458,
02202          0,      -330,
02203          0,        -7,
02204          0,      -226,
02205          0,     -1407,         0,      2942,
02206          0,        66,
02207          0,       667,
02208          0,      -155,
02209          0,       105,
02210          0,      -107,
02211          0,       -74,
02212          0,       -52,
02213          0,        91,
02214          0,        59,
02215          0,       235,
02216         -1,     -1819,         0,      2470,
02217         71,        13,
02218          0,      1026,
02219         14,       -54,
02220          0,      -174,
02221       -121,       -19,
02222          0,      -200,
02223          0,      3008,
02224        -16,     -8043,       -10,    -37136,
02225         -3,     73724,
02226       -157,        -5,
02227          0,      -854,
02228          8,       147,
02229        -13,      -893,
02230          0,     11869,
02231        -23,      -172,
02232         89,        14,
02233         -1,       872,         0,     -3744,
02234         11,      1606,
02235          0,      -559,
02236         -1,     -2530,
02237          0,       454,
02238          0,      -193,
02239        -60,       -10,
02240        -82,       -13,
02241        -75,         6,
02242         36,        81,
02243        354,   -162836,       148,   -516569,
02244          4,   2054441,
02245          4,       -94,
02246         39,        38,
02247         61,       -30,
02248          2,       121,
02249        -11,       590,
02250         62,      2108,
02251          0,    -12242,
02252       -476,       -42,
02253        -84,       113,
02254       -394,       236,
02255          0,       276,
02256        -49,        31,
02257          0,        86,
02258          1,     -1313,
02259          1,        69,
02260        -60,        88,
02261        -46,        18,
02262          0,    -63818,
02263         14,       -93,
02264        113,       547,      -618,        17,
02265         -7,     12290,        -1,    -25679,
02266          0,        92,
02267       -115,        50,
02268        -48,       233,
02269          4,      1311,         1,     -5567,
02270          3,      1251,
02271         29,       548,
02272       -244,       257,
02273         -2,      1825,
02274         42,       637,
02275        -46,        68,
02276        -62,         8,
02277          3,       110,
02278        445,      -100,      -316,      -202,
02279       2925,      -621,       763,      1495,
02280       -169,      -184,        20,       -76,
02281       -475,      -138,         8,      -141,
02282       -197,      1351,     -1284,       422,
02283       -129,      1879,      -102,      8382,
02284         -9,  45864958,
02285       -215,      1350,     -1285,       422,
02286       -481,      -136,         8,      -140,
02287         40,       -53,
02288       2622,      -543,       700,      1406,
02289        402,       -95,      -318,      -194,
02290        122,        13,
02291        -30,       147,
02292       -121,      -902,
02293         61,       -23,
02294        -63,         7,
02295         69,       479,
02296       -224,       228,
02297         -7,       500,
02298          0,      -429,
02299        -42,       193,
02300        -92,        37,
02301         67,         5,
02302       -350,       -31,
02303          0,        67,
02304        -55,        -5,
02305          0,        47,
02306        -36,        53,
02307          5,       561,
02308          0,      -126,
02309          0,       871,
02310        -52,         4,
02311       -201,    116922,       -22,    371352,
02312        -12,  -1473285,
02313          0,        87,
02314       -164,        84,
02315         -3,       422,
02316         30,      1434,
02317        -26,        38,
02318          2,  -1249943,
02319       -404,       -34,
02320        -57,        79,
02321          5,       509,
02322          1,       131,
02323       -344,       168,
02324        112,     22540,        30,     71218,
02325         18,   -283983,
02326          0,      -851,
02327          0,     -1538,
02328          0,      1360,
02329        -12,        51,
02330        -48,        68,
02331         88,       -20,
02332          1,        63,
02333          0,      -568,
02334        303,        25,
02335          0,      -122,
02336         87,       586,      -606,       -14,
02337          0,      -100,
02338        -85,         8,
02339       -165,        54,
02340        -45,       140,
02341          0,       -54,
02342          4,      -831,         1,      3495,
02343         31,       116,
02344        -46,       -11,
02345       -371,       190,
02346       -507,       399,
02347         -2,        57,
02348        -60,        36,
02349       -198,     -1174,      -613,      4988,
02350        -87,        -4,
02351        141,       560,      -276,       187,
02352       1876,      1379,       778,      4386,
02353         24,       -15,
02354        167,      -774,
02355        -71,        -9,
02356        -62,        90,
02357         98,       580,      -663,        -7,
02358         34,      -112,
02359         57,        15,
02360       -355,      -214,
02361      -3240,    -13605,     12229,     -5723,
02362       3496,      7063,
02363         33,       -51,
02364       1908,      1160,      -226,       715,
02365        964,      1170,     -1264,       623,
02366      14071,      5280,      5614,      3026,
02367        488,      1576,        -2, 226395859,
02368        824,      1106,     -1287,       617,
02369       1917,      1156,      -214,       718,
02370         90,       -97,
02371      12078,     -2366,      3282,      6668,
02372       -219,      9179,       593,      2015,
02373       -282,      -186,
02374         57,        25,
02375         31,      -102,
02376        -77,        -4,
02377       -268,      -341,        -7,       -45,
02378         -3,        74,
02379         15,      -615,
02380        -88,        -7,
02381        234,      -353,
02382          1,      -119,
02383       -163,     -1159,      -601,      4969,
02384         22,       -58,
02385        -17,    -11434,
02386         17,        54,
02387        348,       348,      -460,       434,
02388       -371,       175,
02389        -11,      -204,
02390          4,     -6440,
02391         -5,       -53,
02392         -4,    -14388,       -37,    -45231,
02393         -7,    179562,
02394        -44,       136,
02395       -160,        49,
02396       -101,        81,
02397         -1,      -188,
02398          0,         2,
02399         -4,     12124,       -11,    -25217,
02400         71,       543,      -557,       -14,
02401        -75,       526,
02402          0,    395274,
02403       -233,       -16,
02404         93,       -20,
02405        -43,        61,
02406          0,     -1275,
02407          0,      -824,
02408          1,      -415,         0,      1762,
02409       -261,       131,
02410        -45,        64,
02411       -297,       -25,
02412          0,    -17533,
02413         -6,       -56,
02414         21,      1100,
02415          1,       327,
02416          1,        66,
02417         23,      -217,
02418        -83,        -7,
02419         83,     86847,        49,    275754,
02420         -4,  -1093857,
02421        -46,         2,
02422          0,       -24,
02423          0,      -419,
02424          0,     -5833,
02425          1,       506,
02426          0,      -827,
02427         -1,      -377,
02428        -11,       -78,
02429          0,    131945,
02430         -2,      -334,
02431          1,       -75,
02432          0,       -72,
02433          0,      -213,
02434         -6,      5564,        -2,    -11618,
02435          0,      1790,
02436          0,      -131,
02437          0,         6,
02438          0,       -76,
02439          0,      -130,
02440          0,     -1115,         0,      4783,
02441          0,      -195,
02442          0,      -627,
02443          0,       -55,
02444          0,       -83,
02445          0,       163,
02446          0,       -54,
02447          0,        82,
02448          0,       149,
02449          0,      -754,         0,      1578,
02450          0,       138,
02451          0,        68,
02452          2,     -2506,         0,      3399,
02453          0,      -125,
02454         86,        16,
02455          0,     -6350,         0,     27316,
02456         18,       -63,
02457          0,      -169,
02458         -1,        46,
02459       -136,       -21,
02460          0,      -239,
02461        -30,     -8788,       -15,    -40549,
02462         -4,     80514,
02463        -46,        -8,
02464       -168,        -6,
02465         -1,       536,         0,     -2314,
02466          9,       148,
02467        -13,      -842,
02468         -1,    307713,
02469        -23,      -175,
02470         95,        15,
02471          0,      -297,
02472         11,      1341,
02473          0,      -106,
02474          0,         5,
02475         -4,        68,
02476       -114,        10,
02477         32,        75,
02478        159,   -130487,        98,   -413967,
02479          2,   1647339,
02480         -4,       -85,
02481        100,       -46,
02482          2,        95,
02483        -11,       461,
02484         51,      1647,
02485          0,    -32090,
02486       -375,       -33,
02487        -65,        86,
02488       -300,       180,
02489          0,       836,         0,     -3576,
02490          0,      -222,
02491          0,      -993,
02492        -41,        60,
02493          0,     -4537,
02494       -431,       -34,
02495          2,       927,         0,     -1931,
02496        -79,        33,
02497        -31,       144,
02498         -1,       284,         0,     -1207,
02499          0,        88,
02500        -11,       315,
02501       -178,       177,
02502         -1,       144,
02503        -58,       986,
02504         11,        86,
02505       -228,      -110,
02506       2636,      -494,       718,      1474,
02507         28,       -35,
02508        -24,       782,      -797,       277,
02509       2142,     -1231,       856,      1853,
02510         74,     10797,         0,  23699298,
02511        -21,       786,      -796,       277,
02512         27,       -34,
02513       2615,      -494,       712,      1461,
02514       -226,      -109,
02515        -11,       663,
02516          0,      -123,
02517       -169,       157,
02518        -54,       266,
02519          0,       -76,
02520          1,      -634,         0,      2738,
02521        -25,       106,
02522        -63,        24,
02523          0,      -372,
02524       -221,       -24,
02525          0,     -5356,
02526          0,      -219,
02527          0,        91,
02528        -28,      7684,        -6,     24391,
02529         -1,    -96795,
02530        -77,        43,
02531          2,        95,
02532        -47,        -3,
02533          0,    -84530,
02534          2,       310,
02535          1,        88,
02536        111,     19331,        32,     61306,
02537          4,   -243595,
02538          0,       770,
02539          0,      -103,
02540          0,       160,
02541          0,       356,
02542          0,       236,
02543        -41,       354,
02544         39,       303,
02545         12,       -56,
02546        873,      -143,       238,       482,
02547        -28,        35,
02548        -93,        31,
02549         -3,   7690211,
02550        -91,        33,
02551        -34,        43,
02552        824,      -130,       226,       450,
02553        -39,       341,
02554         -1,      -687,
02555          0,      -303,
02556         11,     -2935,         1,     12618,
02557        121,       924,         9,     -1836,
02558       -268,     -1144,      -678,      3685,
02559        -69,      -261,
02560          0,  -4115951,
02561        -69,      -261,
02562          5,      -151,
02563          0,       -88,
02564          0,        91,
02565          0,       187,
02566          0,     -1281,
02567          1,        77,
02568          1,      6059,         3,     19238,
02569          0,    -76305,
02570          0,       -90,
02571          0,      -238,
02572          0,      -962,         0,      4133,
02573          0,        96,
02574          0,      9483,
02575          0,        85,
02576          0,      -688,
02577          0,     -5607,
02578          0,        55,
02579          0,      -752,
02580          0,        71,
02581          0,       303,
02582          0,      -288,
02583          0,        57,
02584          0,        45,
02585          0,       189,
02586          0,       401,
02587          0,     -1474,         0,      3087,
02588          0,       -71,
02589          0,      2925,
02590          0,       -75,
02591          0,       359,
02592          0,        55,
02593          1,    -10155,         0,     43735,
02594          0,      -572,
02595          0,       -49,
02596          0,      -660,
02597          0,     -3591,         0,      7516,
02598          0,       668,
02599         -1,       -53,
02600         -2,    384259,
02601          0,      -163,
02602          0,       -93,
02603          1,       112,
02604        -95,    -11528,       -22,    -36505,
02605         -1,    145308,
02606          5,       145,
02607          0,      4047,
02608          1,      1483,         0,     -6352,
02609          0,       991,         0,     -4262,
02610          0,       -93,
02611          0,      -334,
02612          0,      -160,
02613          0,      -153,
02614        -10,       127,
02615         51,       185,
02616        -77,        18,
02617         56,      1217,         6,   1919574,
02618        -74,        17,
02619         50,       180,
02620         -5,        93,
02621          0,      -104,
02622          0,       -58,
02623         -3,      -353,        -1,      1499,
02624          0,      -229,
02625        -15,        86,
02626          0,    -93657,
02627          0,      1561,         0,     -6693,
02628          0,     -5839,
02629          1,      6791,         0,    -29143,
02630          1,      -701,         0,      3015,
02631          0,      2543,
02632          0,       693,
02633         -1,    361233,
02634          0,       -50,
02635          0,       946,
02636         -1,      -140,
02637        -70,       407,
02638          0,   -450995,
02639          0,      -368,
02640          0,        54,
02641          0,      -802,
02642          0,       -96,
02643          0,      1274,         0,     -5459,
02644          0,      -614,         0,      2633,
02645          0,       685,
02646          0,      -915,
02647          0,       -85,
02648          0,        88,
02649          0,       106,
02650          0,       928,
02651          0,      -726,         0,      1523,
02652          0,      5715,
02653          0,     -4338,         0,     18706,
02654          0,      -135,
02655          0,      -132,
02656          0,      -158,
02657          0,       -98,
02658          0,       680,
02659         -1,    138968,
02660          0,      -192,
02661          0,     -1698,
02662          0,     -2734,         0,     11769,
02663          0,         4,
02664          0,       673,         0,     -2891,
02665          0,       889,         0,     -3821,
02666          0,       121,
02667         -1,    143783,
02668          0,       231,
02669         -9,        51,
02670          0,    -57413,
02671          0,      -483,
02672          0,      -407,
02673          0,       676,         0,     -2902,
02674          0,       531,
02675          0,       445,
02676          0,       672,
02677          0,     19336,
02678          0,        70,
02679          0,    -39976,
02680          0,       -68,
02681          0,      4203,
02682          0,      -406,
02683          0,       446,
02684          0,      -108,
02685          0,        79,
02686          0,        84,
02687          0,       734,
02688          0,       255,
02689          0,      3944,
02690          0,      -655,         0,      2825,
02691          0,      -109,
02692          0,      -234,
02693          0,        57,
02694          0,     19773,
02695          0,     -2013,
02696          0,       958,
02697          0,      -521,
02698          0,      -757,
02699          0,     10594,
02700          0,     -9901,
02701          0,       199,
02702          0,      -275,
02703          0,        64,
02704          0,        54,
02705          0,       165,
02706          0,      1110,
02707          0,     -3286,
02708          0,       909,
02709          0,        54,
02710          0,        87,
02711          0,       258,
02712          0,      1261,
02713          0,       -51,
02714          0,       336,
02715          0,      -114,
02716          0,      2185,
02717          0,      -850,
02718          0,        75,
02719          0,       -69,
02720          0,      -103,
02721          0,       776,
02722          0,     -1238,
02723          0,       137,
02724          0,        67,
02725          0,      -260,
02726          0,       130,
02727          0,        49,
02728          0,       228,
02729          0,       215,
02730          0,      -178,
02731          0,        57,
02732          0,      -133,
02733 };
02734 static long lrtabb[] = {-1};
02735 static long lrtabr[] = {
02736      -5422,     -2120,      1077,       772,
02737         39,        75,         3,        10,
02738       -468,      -326,      -113,       -78,
02739         -4,        -2,
02740          1,         3,
02741         29,        24,         4,         2,
02742          1,         0,
02743         -9,         7,        -2,         0,
02744        -32,       -13,        -3,        -3,
02745        233,       126,        89,        77,
02746        -33,        16,
02747          3,        -3,         0,        -1,
02748          2,         0,
02749          0,         1,
02750          4,         9,         1,         1,
02751         16,        -1,         0,        18,
02752          3,         2,
02753          0,         0,
02754          0,         0,
02755          0,         0,
02756          0,         0,
02757          0,        -1,
02758        -22,        -5,
02759         10,         3,         1,         1,
02760        -15,         7,        -2,         1,
02761         -8,       -11,        -1,        -2,
02762         -1,         1,
02763         46,       -58,       126,       -23,
02764          4,         8,
02765         35,         8,        10,       -17,
02766          0,         0,
02767          0,         0,
02768        -10,        -7,
02769          0,         0,
02770        -23,         3,       151,        10,
02771       -327,         0,
02772          4,        -5,         6,         5,
02773          1,         0,
02774         -1,        -3,
02775          0,         0,
02776          0,         1,
02777       -185,         0,
02778         -3,       -24,        -5,        -2,
02779      -1062,         3,      4560,         0,
02780         -3,         0,
02781          4,         1,
02782          8,        -1,         2,         4,
02783          0,         1,
02784          0,        -1,
02785          0,         0,
02786         -1,         0,
02787          0,         1,
02788          0,         0,
02789         -1,        -1,
02790        277,         3,      -583,         1,
02791         -1,         4,       -32,         7,
02792          0,       -34,
02793          1,        -1,
02794     -23685,         0,
02795         -1,        -2,
02796         -1,        -7,
02797         -5,        -4,
02798          0,         2,
02799         -2,         0,
02800         -5,        -1,
02801         35,         0,
02802          0,         2,
02803        202,         0,
02804        180,         0,
02805          0,        -1,
02806         -3,        -6,
02807       -193,         0,       770,        -1,
02808         -2,        -4,
02809        -32,        23,       -28,       -46,
02810        -13,        -9,
02811        -54,        10,        -1,       -61,
02812     -44895,         0,
02813       -230,         5,
02814         -1,        -4,
02815        -71,         0,
02816        -15,         0,
02817          1,         0,
02818         15,        11,        -3,         6,
02819          2,        -3,         4,        -1,
02820       2576,      -138,    -19881,       -47,
02821     -65906,        -1,    261925,        -4,
02822         -2,        -7,         4,        -2,
02823          0,         0,
02824         -1,         0,
02825          1,        -3,
02826        172,        -2,      -727,         0,
02827          4,         1,
02828        324,         0,
02829       -139,         1,
02830          1,         3,
02831       -276,         0,
02832          5,         3,
02833          9,         0,
02834         -1,        10,
02835        -37,         0,
02836          5,        -1,
02837         76,       -10,
02838    1318810,         1,
02839         12,        -1,
02840        -38,         1,
02841       -141,         0,       611,         0,
02842          0,       -11,
02843          4,         0,
02844       -627,         2,     -2882,        -3,
02845       5711,        -2,
02846        -48,        -7,
02847      55294,         0,
02848          2,        -7,
02849         31,         0,
02850         34,         0,
02851       -259,         0,
02852        -55,         2,
02853          6,         3,
02854      -4273,        20,    -13554,         3,
02855      53878,         0,
02856        -46,         0,
02857        -85,         0,       114,         0,
02858        -45,         0,
02859       -818,         0,      3520,         0,
02860         34,         0,
02861       -157,         0,
02862         29,         0,
02863       -878,         0,      1838,         0,
02864       -428,         0,
02865        161,         0,
02866         24,         0,
02867         65,         0,
02868         19,         0,
02869         15,         0,
02870         12,         0,
02871        -26,         0,
02872        -14,         0,
02873       -149,         0,
02874        584,         0,      -793,         0,
02875          4,       -23,
02876       -238,         0,
02877        -18,        -5,
02878         45,         0,
02879         -7,        42,
02880         79,         0,
02881      -1723,         0,
02882       2895,        -6,     13362,        -4,
02883     -26525,        -1,
02884         -2,        57,
02885        291,         0,
02886         52,        -3,
02887       -327,         5,
02888      -2755,         0,
02889        -63,         9,
02890          5,       -33,
02891       -261,        -1,      1122,         0,
02892        621,        -4,
02893       -227,         0,
02894       1077,         0,
02895       -167,         0,
02896         85,         0,
02897         -4,        23,
02898         -5,        32,
02899          3,        30,
02900        -32,        14,
02901      64607,       141,    204958,        59,
02902    -815115,         2,
02903        -37,        -1,
02904         15,       -15,
02905         12,        24,
02906         48,        -1,
02907        235,         4,
02908        843,       -25,
02909       4621,         0,
02910        -17,       191,
02911         45,        34,
02912         95,       159,
02913       -132,         0,
02914         13,        20,
02915         32,         0,
02916       -540,         0,
02917         29,         0,
02918         37,        25,
02919          8,        19,
02920      22127,         0,
02921        -35,        -5,
02922        232,       -48,         7,       262,
02923       5428,         3,    -11342,         1,
02924        -45,         0,
02925        -21,       -49,
02926       -100,       -21,
02927       -626,         1,      2665,         0,
02928        532,        -2,
02929        235,       -12,
02930       -111,      -105,
02931        774,         1,
02932       -283,        17,
02933         29,        20,
02934          3,        27,
02935         47,        -2,
02936        -43,      -192,       -87,       136,
02937       -269,     -1264,       646,      -330,
02938        -79,        73,       -33,        -9,
02939         60,      -205,        61,         4,
02940       -584,       -85,      -182,      -555,
02941       -780,       -57,     -3488,       -45,
02942  -19818328,        -4,
02943        583,        93,       182,       555,
02944        -59,       208,       -60,        -4,
02945         23,        17,
02946        235,      1133,      -608,       302,
02947         41,       174,        84,      -137,
02948          6,       -53,
02949         63,        13,
02950       -392,        52,
02951        -10,       -27,
02952         -3,       -27,
02953        199,       -31,
02954         99,        97,
02955       -218,        -3,
02956        209,         0,
02957         84,        18,
02958         16,        40,
02959          2,       -30,
02960         14,      -154,
02961         30,         0,
02962         -2,        24,
02963       -108,         0,
02964        -24,       -16,
02965        262,        -2,
02966         55,         0,
02967       -304,         0,
02968          2,        25,
02969      55112,        95,    175036,        11,
02970    -694477,         5,
02971         41,         0,
02972        -38,       -76,
02973        199,         1,
02974        679,       -14,
02975        -17,       -12,
02976     582619,         1,
02977        -16,       191,
02978         38,        27,
02979       -234,         2,
02980        -60,         0,
02981         80,       163,
02982     -10296,        48,    -32526,        13,
02983     129703,         8,
02984      -1366,         0,
02985       -741,         0,
02986       -646,         0,
02987         25,         6,
02988         33,        23,
02989         10,        43,
02990        -31,         0,
02991         -6,         0,
02992        -12,       147,
02993         59,         0,
02994        287,       -42,        -7,       297,
02995        -59,         0,
02996         -4,       -42,
02997        -27,       -81,
02998        -69,       -22,
02999         27,         0,
03000       -423,        -2,      1779,        -1,
03001        -57,        15,
03002          5,       -23,
03003         94,       182,
03004       -197,      -250,
03005         24,         1,
03006        -18,       -30,
03007        581,       -98,     -2473,      -303,
03008         -2,        43,
03009       -277,        70,       -92,      -136,
03010       -681,       925,     -2165,       384,
03011         -8,       -12,
03012        382,        82,
03013         -4,        35,
03014        -45,       -31,
03015       -286,        48,         3,      -328,
03016        -55,       -17,
03017          8,       -28,
03018       -106,       175,
03019      -6735,      1601,     -2832,     -6052,
03020       3495,     -1730,
03021        -25,       -17,
03022       -574,       944,      -354,      -112,
03023       -579,       476,      -308,      -625,
03024      -2411,      7074,     -1529,      2828,
03025      -1335,       247,-112000844,        -1,
03026        545,      -409,       305,       637,
03027        572,      -950,       356,       106,
03028         48,        44,
03029       1170,      5974,     -3298,      1624,
03030      -4538,      -106,      -996,       294,
03031         92,      -139,
03032        -12,        28,
03033         50,        16,
03034          2,       -38,
03035        169,      -133,        22,        -3,
03036         38,         1,
03037        305,         7,
03038          4,       -44,
03039        175,       116,
03040         59,         1,
03041       -573,        81,      2453,       297,
03042         29,        11,
03043       5674,        -8,
03044        -27,         9,
03045        173,      -173,       215,       228,
03046        -87,      -184,
03047        102,        -5,
03048       3206,         2,
03049        -53,         2,
03050       7159,        -7,     22505,       -19,
03051     -89344,        -3,
03052         67,        22,
03053         24,        79,
03054        -40,       -50,
03055         94,         0,
03056        186,         0,
03057      -6063,         0,     12612,        -5,
03058       -271,        35,         7,      -278,
03059       -479,       -74,
03060     426754,         0,
03061          8,      -116,
03062        -10,       -47,
03063        -31,       -22,
03064        645,         0,
03065        426,         0,
03066       -213,         0,       903,         0,
03067        -67,      -133,
03068        -33,       -23,
03069         13,      -152,
03070      -9316,         0,
03071         29,        -3,
03072       -564,        11,
03073       -167,         0,
03074        -34,         0,
03075        114,        12,
03076          4,       -44,
03077     -44561,        42,   -141493,        25,
03078     561256,        -2,
03079         -1,       -24,
03080       -261,         0,
03081        211,         0,
03082      -4263,         0,
03083       -262,         1,
03084       1842,         0,
03085        202,         0,
03086         41,        -6,
03087      77165,         0,
03088        176,        -1,
03089         39,         1,
03090        -24,         0,
03091        118,         0,
03092      -2991,        -4,      6245,        -1,
03093      46886,         0,
03094        -75,         0,
03095       -100,         0,
03096         40,         0,
03097         75,         0,
03098       -618,         0,      2652,         0,
03099        112,         0,
03100       1780,         0,
03101         30,         0,
03102         49,         0,
03103         86,         0,
03104         33,         0,
03105        -30,         0,
03106        -95,         0,
03107        277,         0,      -580,         0,
03108        -35,         0,
03109       -319,         0,
03110       1622,         1,     -2201,         0,
03111         79,         0,
03112         10,       -57,
03113       2363,         0,    -10162,         0,
03114        -41,       -12,
03115         62,         0,
03116         30,         1,
03117        -14,        89,
03118      -2721,         0,
03119       5780,       -19,     26674,       -10,
03120     -52964,        -2,
03121         -5,        30,
03122         -4,       111,
03123       -317,        -1,      1369,         0,
03124         93,        -6,
03125       -564,         9,
03126    -115913,         0,
03127       -113,        15,
03128         10,       -62,
03129         99,         0,
03130        891,        -7,
03131         36,         0,
03132        108,         0,
03133        -42,        -2,
03134          7,        75,
03135        -50,        21,
03136      86822,       104,    275441,        65,
03137   -1096109,         1,
03138        -56,         3,
03139         31,        66,
03140         63,        -1,
03141        307,         7,
03142       1097,       -34,
03143      17453,         0,
03144        -22,       250,
03145         57,        43,
03146        120,       200,
03147       -297,         0,      1269,         0,
03148        166,         0,
03149       -662,         0,
03150         40,        28,
03151       1521,         0,
03152        -23,       288,
03153        351,        -2,      -729,         0,
03154        -22,       -52,
03155        -96,       -21,
03156       -139,        -1,       589,         0,
03157         35,         0,
03158        210,         7,
03159       -118,      -119,
03160         62,         0,
03161       -583,       -26,
03162        -42,         5,
03163        -73,       152,
03164       -330,     -1759,       983,      -479,
03165        -23,       -19,
03166       -522,       -15,      -185,      -533,
03167        739,      1559,     -1300,       614,
03168      -7332,        52, -15836758,         0,
03169        524,        16,       185,       532,
03170         23,        18,
03171        330,      1751,      -978,       476,
03172         73,      -151,
03173        519,        18,
03174         38,         0,
03175        105,       113,
03176       -178,       -37,
03177         26,         0,
03178        262,         1,     -1139,         0,
03179         71,        17,
03180         16,        42,
03181        151,         0,
03182         16,      -148,
03183       4147,         0,
03184        149,         0,
03185        -30,         0,
03186       2980,         9,      9454,         2,
03187     -37519,         0,
03188        -28,       -49,
03189         37,        -1,
03190          2,       -31,
03191      33870,         0,
03192       -208,         1,
03193        -59,         1,
03194     -13105,        68,    -41564,        21,
03195     165148,         3,
03196      -1022,         0,
03197        -40,         0,
03198       -132,         0,
03199       -228,         0,
03200         95,         0,
03201       -138,       -16,
03202       -126,        16,
03203         24,         5,
03204        -57,      -346,       191,       -94,
03205        -14,       -11,
03206        -12,       -37,
03207   -3053364,        -1,
03208         13,        36,
03209         17,        13,
03210         51,       327,      -179,        90,
03211        138,        16,
03212        233,         0,
03213         62,         0,
03214       1164,         0,     -5000,         0,
03215       -407,       117,       770,         9,
03216         -4,         1,        21,         2,
03217          1,         0,
03218     -16869,         0,
03219         -1,         0,
03220          1,         0,
03221         35,         0,
03222        -78,         0,
03223         78,         0,
03224       -533,         0,
03225        -31,         1,
03226      -2448,        -6,     -7768,        -1,
03227      30812,         0,
03228         37,         0,
03229       -227,         0,
03230        197,         0,      -846,         0,
03231        -77,         0,
03232       4171,         0,
03233        -67,         0,
03234        287,         0,
03235       2532,         0,
03236        -19,         0,
03237        -40,         0,
03238        -56,         0,
03239        128,         0,
03240         83,         0,
03241        -45,         0,
03242        -36,         0,
03243        -92,         0,
03244       -134,         0,
03245        714,         0,     -1495,         0,
03246         32,         0,
03247       -981,         0,
03248         15,         0,
03249       -166,         0,
03250        -59,         0,
03251       4923,         0,    -21203,         0,
03252        246,         0,
03253         15,         0,
03254        104,         0,
03255       1683,         0,     -3523,         0,
03256       -865,         0,
03257        -25,         1,
03258    -186329,        -1,
03259         10,         0,
03260         50,         0,
03261         53,         0,
03262       5455,       -45,     17271,       -10,
03263     -68747,         0,
03264         69,        -2,
03265      -7604,         0,
03266       -724,         1,      3101,         0,
03267        -46,         0,       200,         0,
03268        -44,         0,
03269         97,         0,
03270        -53,         0,
03271         62,         0,
03272        -54,        -4,
03273         88,       -24,
03274         -9,       -36,
03275       -581,        27,   -914711,         3,
03276          8,        35,
03277        -86,        24,
03278         51,         3,
03279         48,         0,
03280         26,         0,
03281        133,         1,      -577,         0,
03282        105,         0,
03283         -3,        -1,
03284       3194,         0,
03285        528,         0,     -2263,         0,
03286       2028,         0,
03287      -3266,         1,     14016,         0,
03288         10,         0,       -41,         0,
03289       -100,         0,
03290        -32,         0,
03291    -124348,         0,
03292         16,         0,
03293       -325,         0,
03294         50,        -1,
03295          1,         0,
03296       -553,         0,
03297          0,         0,
03298          0,         0,
03299          2,         0,
03300        -34,         0,
03301       -444,         0,      1902,         0,
03302          9,         0,       -37,         0,
03303        254,         0,
03304        156,         0,
03305         -2,         0,
03306        -35,         0,
03307        -48,         0,
03308       -368,         0,
03309        327,         0,      -686,         0,
03310      -2263,         0,
03311       1952,         0,     -8418,         0,
03312        -13,         0,
03313         52,         0,
03314          9,         0,
03315         21,         0,
03316       -261,         0,
03317     -62404,         0,
03318          0,         0,
03319         79,         0,
03320       1056,         0,     -4547,         0,
03321       -351,         0,
03322       -305,         0,      1310,         0,
03323         -1,         0,         6,         0,
03324          0,         0,
03325     -55953,         0,
03326        -80,         0,
03327          0,         0,
03328        168,         0,
03329       -147,         0,
03330        127,         0,
03331       -265,         0,      1138,         0,
03332         -1,         0,
03333         -9,         0,
03334         -8,         0,
03335      -5984,         0,
03336        -22,         0,
03337         -5,         0,
03338          0,         0,
03339          0,         0,
03340        127,         0,
03341         -2,         0,
03342         10,         0,
03343        -31,         0,
03344        -29,         0,
03345       -286,         0,
03346        -98,         0,
03347      -1535,         0,
03348        252,         0,     -1087,         0,
03349         43,         0,
03350          4,         0,
03351        -19,         0,
03352      -7620,         0,
03353         29,         0,
03354       -322,         0,
03355        203,         0,
03356          0,         0,
03357      -3587,         0,
03358         10,         0,
03359          0,         0,
03360         94,         0,
03361          0,         0,
03362         -1,         0,
03363         -1,         0,
03364       -315,         0,
03365          1,         0,
03366          0,         0,
03367          0,         0,
03368        -30,         0,
03369        -94,         0,
03370       -460,         0,
03371          1,         0,
03372       -114,         0,
03373          0,         0,
03374       -746,         0,
03375          4,         0,
03376        -23,         0,
03377         24,         0,
03378          0,         0,
03379       -237,         0,
03380          1,         0,
03381          0,         0,
03382        -18,         0,
03383          0,         0,
03384          0,         0,
03385        -16,         0,
03386        -76,         0,
03387        -67,         0,
03388          0,         0,
03389        -16,         0,
03390          0,         0,
03391 };
03392 static CHAR lrargs[] = {
03393   0,  3,
03394   3,  4,  3, -8,  4,  3,  5,  1,
03395   2,  2,  5, -5,  6,  2,
03396   5, -1, 10,  2, 13, -1, 11,  3,  3, -7,  4,  0,
03397   3,  1, 13, -1, 11,  2,  5,  1,
03398   2,  4,  5,-10,  6,  0,
03399   4,  2, 10, -2, 13, 14,  3,-23,  4,  1,
03400   3,  3,  2, -7,  3,  4,  4,  1,
03401   3, -1, 13, 18,  2,-16,  3,  2,
03402   2,  8,  2,-13,  3,  1,
03403   5,  2, 10, -2, 13,  2,  3, -3,  5,  1,  6,  0,
03404   3, -1, 13, 26,  2,-29,  3,  0,
03405   3,  1, 10, -1, 11,  2,  4,  1,
03406   4,  1, 10, -1, 13,  3,  2, -4,  3,  1,
03407   4,  1, 10, -1, 13,  3,  3, -4,  4,  0,
03408   3, -1, 10, 15,  2,-12,  3,  0,
03409   4,  2, 10, -3, 13, 24,  2,-24,  3,  0,
03410   3, -1, 10, 23,  2,-25,  3,  0,
03411   4,  1, 10, -1, 11,  1,  3,  1,  6,  0,
03412   4,  2, 10, -2, 11,  5,  2, -6,  3,  0,
03413   4,  2, 10, -2, 13,  6,  2, -8,  3,  0,
03414   4, -2, 10,  1, 13, 12,  2, -8,  3,  1,
03415   5, -1, 10,  1, 13, -1, 11, 20,  2,-20,  3,  1,
03416   4, -2, 10,  1, 13,  3,  1, -1,  3,  1,
03417   5,  2, 10, -2, 13,  2,  3, -5,  5,  5,  6,  0,
03418   4,  2, 10, -2, 13,  2,  3, -3,  5,  1,
03419   4,  2, 10, -2, 13,  6,  3, -8,  4,  0,
03420   4, -2, 10,  1, 13, 20,  2,-21,  3,  1,
03421   4,  1, 10, -1, 11,  1,  3,  1,  5,  0,
03422   1,  1,  6,  0,
03423   4,  2, 10, -2, 13,  5,  3, -6,  4,  0,
03424   3,  3,  2, -5,  3,  2,  5,  0,
03425   2, -1, 11,  1, 14,  1,
03426   4,  2, 10, -2, 13,  2,  3, -2,  5,  0,
03427   2,  1,  3, -2,  4,  1,
03428   4,  1, 10, -1, 11,  5,  2, -7,  3,  0,
03429   1,  1,  5,  0,
03430   2,  7,  3,-13,  4,  0,
03431   4, -2, 10,  1, 13, 15,  2,-13,  3,  0,
03432   4,  2, 10, -2, 13,  3,  2, -3,  3,  0,
03433   2, -2, 11,  2, 14,  1,
03434   3,  1, 10,  1, 12, -1, 13,  1,
03435   3, -1, 13, 21,  2,-21,  3,  0,
03436   2,  3,  2, -5,  3,  0,
03437   2,  2,  3, -4,  4,  1,
03438   2,  5,  2, -8,  3,  0,
03439   3, -1, 13, 23,  2,-24,  3,  0,
03440   2,  6,  3,-11,  4,  0,
03441   1,  2,  5,  0,
03442   2,  3,  3, -6,  4,  0,
03443   2,  5,  3, -9,  4,  0,
03444   4,  1, 10, -1, 11,  1,  3, -2,  5,  0,
03445   3,  2, 10,  2, 12, -2, 13,  1,
03446   2,  2,  2, -3,  3,  2,
03447   2,  4,  3, -7,  4,  0,
03448   2,  2, 13, -2, 11,  0,
03449   2,  3,  3, -5,  4,  0,
03450   2,  1,  2, -2,  3,  0,
03451   2,  2,  3, -3,  4,  0,
03452   4,  1, 10, -1, 11,  4,  2, -5,  3,  0,
03453   2,  1,  3, -1,  4,  0,
03454   2,  4,  2, -6,  3,  0,
03455   4,  2, 10, -2, 13,  2,  2, -2,  3,  0,
03456   3,  1, 10, -1, 11,  1,  2,  0,
03457   2,  1,  2, -1,  3,  0,
03458   3,  1, 12,  2, 13, -2, 11,  0,
03459   2,  5,  3, -8,  4,  0,
03460   2,  1,  3, -3,  5,  0,
03461   3,  2, 10,  1, 12, -2, 13,  1,
03462   2,  4,  3, -6,  4,  0,
03463   2,  1,  3, -2,  5,  1,
03464   2,  3,  3, -4,  4,  0,
03465   2,  3,  2, -4,  3,  1,
03466   2,  1, 10, -1, 13,  0,
03467   2,  1,  3, -1,  5,  0,
03468   2,  1,  3, -2,  6,  0,
03469   2,  2,  3, -2,  4,  0,
03470   2,  1,  3, -1,  6,  0,
03471   2,  8,  2,-14,  3,  0,
03472   3,  1,  3,  2,  5, -5,  6,  1,
03473   3,  5,  3, -8,  4,  3,  5,  1,
03474   1,  1, 12,  3,
03475   3,  3,  3, -8,  4,  3,  5,  1,
03476   3,  1,  3, -2,  5,  5,  6,  0,
03477   2,  8,  2,-12,  3,  0,
03478   2,  1,  3,  1,  5,  0,
03479   3,  2, 10,  1, 12, -2, 11,  1,
03480   2,  5,  2, -7,  3,  0,
03481   3,  1, 10,  1, 13, -2, 11,  0,
03482   2,  2,  2, -2,  3,  0,
03483   2,  5,  3, -7,  4,  0,
03484   3,  1, 12, -2, 13,  2, 11,  0,
03485   2,  4,  3, -5,  4,  0,
03486   2,  3,  3, -3,  4,  0,
03487   1,  1,  2,  0,
03488   3,  3, 10,  1, 12, -3, 13,  0,
03489   2,  2,  3, -4,  5,  0,
03490   2,  2,  3, -3,  5,  0,
03491   2,  2, 10, -2, 13,  0,
03492   2,  2,  3, -2,  5,  0,
03493   2,  3,  2, -3,  3,  0,
03494   3,  1, 10, -1, 12, -1, 13,  1,
03495   2,  2,  3, -1,  5,  0,
03496   2,  2,  3, -2,  6,  0,
03497   1,  2, 12,  2,
03498   3, -2, 10,  1, 11,  1, 14,  0,
03499   2,  2, 10, -2, 11,  0,
03500   2,  2,  2, -1,  3,  0,
03501   4, -2, 10,  2, 13,  1,  2, -1,  3,  0,
03502   2,  4,  2, -4,  3,  0,
03503   2,  3, 10, -3, 13,  0,
03504   4, -2, 10,  2, 13,  1,  3, -1,  5,  0,
03505   2,  3,  3, -3,  5,  0,
03506   3,  2, 10, -1, 12, -2, 13,  2,
03507   3,  3, 10, -1, 13, -2, 11,  0,
03508   1,  3, 12,  1,
03509   4, -2, 10,  2, 13,  2,  2, -2,  3,  0,
03510   3,  2, 10, -1, 12, -2, 11,  1,
03511   2,  5,  2, -5,  3,  0,
03512   2,  4, 10, -4, 13,  0,
03513   2,  6,  2, -6,  3,  0,
03514   3,  2, 10, -2, 12, -2, 13,  1,
03515   3,  4, 10, -2, 13, -2, 11,  0,
03516   3,  2, 10, -2, 12, -2, 11,  0,
03517   2,  7,  2, -7,  3,  0,
03518   3,  2, 10, -3, 12, -2, 13,  0,
03519   2,  8,  2, -8,  3,  0,
03520   2,  9,  2, -9,  3,  0,
03521   2, 10,  2,-10,  3,  0,
03522   3,  2, 10, -4, 12, -1, 13,  0,
03523   3,  4, 10, -2, 12, -3, 13,  0,
03524   4,  4, 10, -1, 12, -1, 13, -2, 11,  0,
03525   3,  2, 10, -3, 12, -1, 13,  1,
03526   4, -2, 10,  1, 13,  3,  3, -2,  5,  0,
03527   3,  4, 10, -1, 12, -3, 13,  0,
03528   4, -2, 10,  1, 13,  3,  3, -3,  5,  0,
03529   4,  2, 10, -2, 12,  1, 13, -2, 11,  0,
03530   4, -2, 10,  1, 13,  2,  2, -1,  3,  0,
03531   3,  3, 10, -1, 12, -2, 11,  0,
03532   3,  4, 10, -1, 13, -2, 11,  0,
03533   3,  2, 10, -2, 12, -1, 13,  2,
03534   4, -2, 10,  1, 13,  2,  3, -1,  5,  0,
03535   3,  3, 10, -1, 12, -2, 13,  0,
03536   4, -2, 10,  1, 13,  3,  2, -3,  3,  0,
03537   4, -2, 10,  1, 13,  2,  3, -2,  5,  0,
03538   2,  4, 10, -3, 13,  0,
03539   4, -2, 10,  1, 13,  2,  3, -3,  5,  0,
03540   3, -2, 10,  1, 13,  1,  2,  0,
03541   4,  2, 10, -1, 12,  1, 13, -2, 11,  1,
03542   4, -2, 10,  1, 13,  2,  2, -2,  3,  0,
03543   2,  3, 12, -1, 13,  0,
03544   2,  3, 10, -2, 11,  0,
03545   2,  1, 10, -2, 12,  0,
03546   4,  4, 10,  1, 12, -1, 13, -2, 11,  0,
03547   3, -1, 13,  3,  2, -2,  3,  0,
03548   3, -1, 13,  3,  3, -2,  5,  0,
03549   3, -2, 10, 18,  2,-15,  3,  0,
03550   5,  2, 10, -1, 13,  3,  3, -8,  4,  3,  5,  0,
03551   3,  2, 10, -1, 12, -1, 13,  2,
03552   5, -2, 10,  1, 13,  5,  3, -8,  4,  3,  5,  0,
03553   5, -2, 10,  1, 13,  1,  3,  2,  5, -5,  6,  0,
03554   4,  2, 10, -2, 13, 18,  2,-17,  3,  0,
03555   4, -2, 10,  1, 13,  1,  3, -1,  6,  0,
03556   4, -2, 10,  1, 13,  2,  3, -2,  4,  0,
03557   4, -2, 10,  1, 13,  1,  3, -1,  5,  0,
03558   2,  3, 10, -2, 13,  0,
03559   4, -2, 10,  1, 13,  3,  2, -4,  3,  0,
03560   4, -2, 10,  1, 13,  3,  3, -4,  4,  0,
03561   4, -2, 10,  1, 13,  1,  3, -2,  5,  0,
03562   3,  4, 10,  1, 12, -3, 13,  0,
03563   4, -2, 10,  1, 13,  1,  3, -3,  5,  0,
03564   3, -1, 13,  4,  2, -4,  3,  0,
03565   4, -2, 10,  1, 13,  1,  2, -1,  3,  0,
03566   4, -2, 10,  1, 13,  1,  3, -1,  4,  0,
03567   4, -2, 10,  1, 13,  2,  3, -3,  4,  0,
03568   4, -2, 10,  1, 13,  3,  3, -5,  4,  0,
03569   3,  2, 10,  1, 13, -2, 11,  0,
03570   4, -2, 10, -1, 13,  1, 11,  1, 14,  0,
03571   4, -2, 10,  1, 13,  2,  2, -3,  3,  1,
03572   2,  2, 12, -1, 13,  1,
03573   3,  3, 10,  1, 12, -2, 11,  0,
03574   4,  2, 10, -1, 13,  2,  3, -4,  4,  0,
03575   4,  2, 10, -1, 13,  3,  2, -5,  3,  0,
03576   2,  1, 10, -1, 12,  1,
03577   3, -1, 13,  3,  2, -3,  3,  0,
03578   3, -2, 10,  1, 13,  1,  5,  0,
03579   4,  2, 10, -1, 13,  1,  3, -2,  4,  0,
03580   3, -1, 13,  2,  3, -2,  5,  0,
03581   4,  2, 10, -1, 13, -1, 11,  1, 14,  0,
03582   3, -1, 13,  5,  3, -6,  4,  0,
03583   3, -2, 10,  1, 13,  1,  6,  0,
03584   3, -1, 10,  1,  3, -1,  5,  0,
03585   4, -2, 10,  1, 13,  8,  2,-13,  3,  1,
03586   3, -2, 10, 18,  2,-16,  3,  1,
03587   5, -2, 10,  1, 13,  3,  2, -7,  3,  4,  4,  1,
03588   4,  2, 10, -1, 13,  2,  5, -5,  6,  1,
03589   5,  2, 10, -1, 13,  4,  3, -8,  4,  3,  5,  1,
03590   2,  2, 10, -1, 13,  2,
03591   5, -2, 10,  1, 13,  4,  3, -8,  4,  3,  5,  1,
03592   4, -2, 10,  1, 13,  2,  5, -5,  6,  1,
03593   5,  2, 10, -1, 13,  3,  2, -7,  3,  4,  4,  0,
03594   4,  2, 10, -2, 13, 18,  2,-16,  3,  1,
03595   4,  2, 10, -1, 13,  8,  2,-13,  3,  1,
03596   3, -1, 10,  3,  2, -4,  3,  0,
03597   3, -1, 13,  6,  2, -8,  3,  0,
03598   3, -1, 13,  2,  3, -3,  5,  0,
03599   3, -1, 13,  6,  3, -8,  4,  0,
03600   3,  2, 10, -1, 13,  1,  6,  0,
03601   4, -2, 10,  1, 13, -1, 11,  1, 14,  0,
03602   4, -2, 10,  1, 13,  1,  3, -2,  4,  0,
03603   3,  2, 10, -1, 13,  1,  5,  0,
03604   3,  3, 10,  1, 12, -2, 13,  0,
03605   4, -2, 10,  1, 13,  3,  2, -5,  3,  0,
03606   4, -2, 10,  1, 13,  2,  3, -4,  4,  0,
03607   2, -1, 13,  1,  2,  0,
03608   4,  2, 10, -1, 13,  2,  2, -3,  3,  0,
03609   3, -1, 10,  1,  2, -1,  3,  0,
03610   3, -1, 13,  4,  2, -5,  3,  0,
03611   3,  2, 10, -3, 13,  2, 11,  0,
03612   4,  2, 10, -1, 13,  2,  3, -3,  4,  0,
03613   3, -1, 13,  2,  2, -2,  3,  0,
03614   4,  2, 10, -1, 13,  1,  2, -1,  3,  0,
03615   4,  2, 10,  1, 12,  1, 13, -2, 11,  0,
03616   3, -2, 13, 18,  2,-15,  3,  0,
03617   2,  1, 12, -1, 13,  2,
03618   3, -1, 13,  1,  3, -1,  6,  0,
03619   4,  2, 10, -1, 13,  1,  3, -2,  5,  0,
03620   3, -1, 13,  2,  3, -2,  4,  0,
03621   3, -1, 13,  1,  3, -1,  5,  0,
03622   4,  2, 10, -1, 13,  3,  3, -4,  4,  0,
03623   1,  1, 10,  0,
03624   3, -1, 13,  3,  2, -4,  3,  0,
03625   3, -1, 13,  3,  3, -4,  4,  0,
03626   4,  2, 10, -1, 13,  1,  3, -1,  5,  0,
03627   4,  2, 10, -1, 13,  2,  3, -2,  4,  0,
03628   3, -1, 13,  1,  3, -2,  5,  0,
03629   3,  2, 10,  1, 12, -1, 13,  2,
03630   3,  1, 12,  1, 13, -2, 11,  0,
03631   3, -1, 13,  1,  2, -1,  3,  0,
03632   4,  2, 10, -1, 13,  2,  2, -2,  3,  0,
03633   3, -1, 13,  4,  2, -6,  3,  0,
03634   3, -1, 13,  2,  3, -3,  4,  0,
03635   3,  1, 13,  1,  2, -2,  3,  0,
03636   4,  2, 10, -1, 13,  3,  3, -3,  4,  0,
03637   2,  3, 13, -2, 11,  0,
03638   4,  2, 10, -1, 13,  4,  2, -5,  3,  0,
03639   3,  1, 10,  1,  2, -1,  3,  0,
03640   3, -1, 13,  2,  2, -3,  3,  1,
03641   3,  2, 10,  2, 12, -3, 13,  0,
03642   3,  2, 10, -1, 13,  1,  2,  0,
03643   3,  1, 13,  2,  3, -4,  4,  0,
03644   3,  1, 13,  3,  2, -5,  3,  0,
03645   2, 21,  2,-21,  3,  0,
03646   3,  1, 10,  1, 12, -2, 13,  1,
03647   4,  2, 10, -1, 13,  2,  3, -4,  5,  0,
03648   4,  2, 10, -1, 13,  7,  3,-10,  4,  0,
03649   2, -1, 13,  1,  5,  0,
03650   3,  1, 13,  1,  3, -2,  4,  0,
03651   4,  2, 10, -3, 13,  2,  3, -2,  5,  0,
03652   3,  1, 10,  1,  3, -2,  5,  0,
03653   3,  1, 13, -1, 11,  1, 14,  1,
03654   2, -1, 13,  1,  6,  0,
03655   4,  2, 10, -1, 13,  6,  3, -8,  4,  1,
03656   4,  2, 10, -1, 13,  2,  3, -3,  5,  1,
03657   3, -1, 13,  8,  3,-15,  4,  0,
03658   4,  2, 10, -1, 13,  6,  2, -8,  3,  0,
03659   5,  2, 10, -1, 13, -2, 11,  5,  2, -6,  3,  0,
03660   3,  1, 10,  3,  3, -4,  4,  0,
03661   3,  1, 10,  3,  2, -4,  3,  1,
03662   4,  1, 10, -1, 13, -1, 11,  2,  4,  0,
03663   3, -2, 13, 26,  2,-29,  3,  0,
03664   3, -1, 13,  8,  2,-13,  3,  0,
03665   3, -2, 13, 18,  2,-16,  3,  2,
03666   4, -1, 13,  3,  2, -7,  3,  4,  4,  0,
03667   3,  1, 13,  2,  5, -5,  6,  1,
03668   4,  1, 13,  4,  3, -8,  4,  3,  5,  1,
03669   1,  1, 13,  3,
03670   4, -1, 13,  4,  3, -8,  4,  3,  5,  1,
03671   3, -1, 13,  2,  5, -5,  6,  1,
03672   4,  1, 13,  3,  2, -7,  3,  4,  4,  0,
03673   2, 18,  2,-16,  3,  1,
03674   3,  1, 13,  8,  2,-13,  3,  2,
03675   2, 26,  2,-29,  3,  0,
03676   4,  1, 10,  1, 13, -1, 11,  2,  4,  0,
03677   5,  2, 10,  1, 13, -2, 11,  5,  2, -6,  3,  0,
03678   3,  1, 13,  8,  3,-15,  4,  1,
03679   4,  2, 10, -3, 13,  2,  3, -3,  5,  0,
03680   3,  1, 10,  1,  3, -1,  5,  0,
03681   2,  1, 13,  1,  6,  0,
03682   4,  2, 10, -1, 13,  5,  3, -6,  4,  0,
03683   3,  1, 10,  2,  3, -2,  4,  0,
03684   3, -1, 13, -1, 11,  1, 14,  1,
03685   4,  2, 10, -1, 13,  2,  3, -5,  6,  0,
03686   4,  2, 10, -1, 13,  2,  3, -2,  5,  0,
03687   5,  2, 10, -1, 13,  2,  3, -4,  5,  5,  6,  0,
03688   3, -1, 13,  1,  3, -2,  4,  1,
03689   2,  1, 13,  1,  5,  0,
03690   4,  2, 10, -1, 13,  4,  3, -4,  4,  0,
03691   4,  2, 10, -1, 13,  3,  2, -3,  3,  0,
03692   4,  2, 10,  2, 12, -1, 13, -2, 11,  0,
03693   2,  1, 10,  1, 12,  2,
03694   3, -1, 13,  3,  2, -5,  3,  0,
03695   3, -1, 13,  2,  3, -4,  4,  0,
03696   4,  2, 10, -1, 13,  2,  3, -1,  5,  0,
03697   4,  2, 10, -1, 13,  2,  3, -2,  6,  0,
03698   3,  1, 10,  1, 12, -2, 11,  0,
03699   3,  2, 10,  2, 12, -1, 13,  1,
03700   3,  1, 13,  2,  2, -3,  3,  1,
03701   3, -1, 13,  1, 11,  1, 14,  0,
03702   2,  1, 13, -2, 11,  0,
03703   4,  2, 10, -1, 13,  5,  2, -6,  3,  0,
03704   3, -1, 13,  1,  2, -2,  3,  0,
03705   3,  1, 13,  2,  3, -3,  4,  0,
03706   3,  1, 13,  1,  2, -1,  3,  0,
03707   4,  2, 10, -1, 13,  4,  2, -4,  3,  0,
03708   3,  2, 10,  1, 12, -3, 13,  1,
03709   3,  1, 13,  1,  3, -2,  5,  0,
03710   3,  1, 13,  3,  3, -4,  4,  0,
03711   3,  1, 13,  3,  2, -4,  3,  0,
03712   2,  1, 10, -2, 13,  0,
03713   4,  2, 10, -1, 13,  3,  3, -4,  5,  0,
03714   3,  1, 13,  1,  3, -1,  5,  0,
03715   3,  1, 13,  2,  3, -2,  4,  0,
03716   3,  1, 13,  1,  3, -1,  6,  0,
03717   4,  2, 10, -1, 13,  3,  3, -3,  5,  0,
03718   4,  2, 10, -1, 13,  6,  2, -7,  3,  0,
03719   2,  1, 12,  1, 13,  2,
03720   4,  2, 10, -1, 13,  3,  3, -2,  5,  0,
03721   4,  2, 10,  1, 12, -1, 13, -2, 11,  0,
03722   2,  1, 10,  2, 12,  0,
03723   2,  1, 10, -2, 11,  0,
03724   3,  1, 13,  2,  2, -2,  3,  0,
03725   3,  1, 12, -1, 13,  2, 11,  0,
03726   4,  2, 10, -1, 13,  5,  2, -5,  3,  0,
03727   3,  1, 13,  2,  3, -3,  5,  0,
03728   2,  2, 10, -3, 13,  0,
03729   3,  1, 13,  2,  3, -2,  5,  0,
03730   3,  1, 13,  3,  2, -3,  3,  0,
03731   3,  1, 10, -1, 12, -2, 13,  0,
03732   4,  2, 10, -1, 13,  6,  2, -6,  3,  0,
03733   2,  2, 12,  1, 13,  1,
03734   3,  2, 10, -1, 13, -2, 11,  0,
03735   3,  1, 10, -1, 12, -2, 11,  0,
03736   3,  2, 10,  1, 13, -4, 11,  0,
03737   3,  1, 13,  4,  2, -4,  3,  0,
03738   4,  2, 10, -1, 13,  7,  2, -7,  3,  0,
03739   3,  2, 10, -1, 12, -3, 13,  1,
03740   2,  3, 12,  1, 13,  0,
03741   4,  2, 10, -1, 12, -1, 13, -2, 11,  0,
03742   3,  1, 13,  5,  2, -5,  3,  0,
03743   4,  2, 10, -1, 13,  8,  2, -8,  3,  0,
03744   3,  2, 10, -2, 12, -3, 13,  0,
03745   4,  2, 10, -1, 13,  9,  2, -9,  3,  0,
03746   3,  4, 10, -3, 12, -2, 13,  0,
03747   2,  2, 10, -4, 12,  0,
03748   3,  4, 10, -2, 12, -2, 13,  1,
03749   2,  6, 10, -4, 13,  0,
03750   3,  4, 10, -1, 12, -2, 11,  0,
03751   2,  2, 10, -3, 12,  1,
03752   3,  3, 10, -2, 12, -1, 13,  0,
03753   3, -2, 10,  3,  3, -2,  5,  0,
03754   3,  4, 10, -1, 12, -2, 13,  1,
03755   3, -2, 10,  3,  3, -3,  5,  0,
03756   2,  5, 10, -3, 13,  0,
03757   3, -2, 10,  4,  2, -4,  3,  0,
03758   3, -2, 10,  2,  2, -1,  3,  0,
03759   2,  4, 10, -2, 11,  0,
03760   2,  2, 10, -2, 12,  2,
03761   3, -2, 10,  3,  3, -2,  4,  0,
03762   3, -2, 10,  2,  3, -1,  5,  0,
03763   3,  3, 10, -1, 12, -1, 13,  1,
03764   3, -2, 10,  3,  2, -3,  3,  0,
03765   3, -2, 10,  2,  3, -2,  5,  0,
03766   2,  4, 10, -2, 13,  0,
03767   3, -2, 10,  2,  3, -3,  5,  0,
03768   2, -2, 10,  1,  2,  0,
03769   4,  2, 10, -1, 12,  2, 13, -2, 11,  0,
03770   3, -2, 10,  2,  2, -2,  3,  0,
03771   3,  3, 10,  1, 13, -2, 11,  0,
03772   3,  4, 10,  1, 12, -2, 11,  0,
03773   4,  2, 10, -1, 12, -1, 11,  1, 14,  0,
03774   4, -2, 10, -1, 13, 18,  2,-15,  3,  0,
03775   4,  2, 10,  3,  3, -8,  4,  3,  5,  0,
03776   2,  2, 10, -1, 12,  2,
03777   4, -2, 10,  5,  3, -8,  4,  3,  5,  0,
03778   4,  2, 10, -1, 13, 18,  2,-17,  3,  0,
03779   3, -2, 10,  1,  3, -1,  6,  0,
03780   3, -2, 10,  2,  3, -2,  4,  0,
03781   3, -2, 10,  1,  3, -1,  5,  0,
03782   2,  3, 10, -1, 13,  0,
03783   3, -2, 10,  3,  2, -4,  3,  0,
03784   3, -2, 10,  3,  3, -4,  4,  0,
03785   3, -2, 10,  1,  3, -2,  5,  0,
03786   3,  4, 10,  1, 12, -2, 13,  1,
03787   4,  2, 10, -1, 12, -2, 13,  2, 11,  0,
03788   3, -2, 10,  1,  2, -1,  3,  0,
03789   3, -2, 10,  2,  3, -3,  4,  0,
03790   3,  2, 10,  2, 13, -2, 11,  0,
03791   3, -2, 10,  2,  2, -3,  3,  0,
03792   2,  2, 12, -2, 13,  1,
03793   3,  2, 10,  2,  3, -4,  4,  0,
03794   3,  2, 10,  3,  2, -5,  3,  0,
03795   3,  1, 10, -1, 12,  1, 13,  1,
03796   3, -2, 13,  3,  2, -3,  3,  0,
03797   2, -2, 10,  1,  5,  0,
03798   3,  2, 10,  1,  3, -2,  4,  0,
03799   3, -2, 13,  2,  3, -2,  5,  0,
03800   3,  2, 10, -1, 11,  1, 14,  0,
03801   4,  4, 10, -2, 13,  2,  3, -3,  5,  0,
03802   3, -2, 10,  8,  2,-13,  3,  0,
03803   4, -2, 10, -1, 13, 18,  2,-16,  3,  1,
03804   4, -2, 10,  3,  2, -7,  3,  4,  4,  0,
03805   4,  2, 10,  4,  3, -8,  4,  3,  5,  1,
03806   1,  2, 10,  3,
03807   4, -2, 10,  4,  3, -8,  4,  3,  5,  1,
03808   4,  2, 10,  3,  2, -7,  3,  4,  4,  0,
03809   4,  2, 10, -1, 13, 18,  2,-16,  3,  1,
03810   3,  2, 10,  8,  2,-13,  3,  0,
03811   3, -2, 10, -1, 11,  1, 14,  0,
03812   4,  4, 10, -2, 13,  2,  3, -2,  5,  0,
03813   3, -2, 10,  1,  3, -2,  4,  0,
03814   2,  2, 10,  1,  5,  0,
03815   4,  4, 10, -2, 13,  3,  2, -3,  3,  0,
03816   3,  3, 10,  1, 12, -1, 13,  1,
03817   3, -2, 10,  3,  2, -5,  3,  0,
03818   3, -2, 10,  2,  3, -4,  4,  0,
03819   3,  4, 10,  2, 12, -2, 13,  0,
03820   3,  2, 10,  2,  2, -3,  3,  0,
03821   3,  2, 10, -2, 13,  2, 11,  0,
03822   3,  2, 10,  1,  2, -1,  3,  0,
03823   4,  2, 10,  1, 12,  2, 13, -2, 11,  0,
03824   2,  1, 12, -2, 13,  2,
03825   3,  2, 10,  1,  3, -2,  5,  0,
03826   3, -2, 13,  1,  3, -1,  5,  0,
03827   3,  2, 10,  3,  2, -4,  3,  0,
03828   2,  1, 10,  1, 13,  0,
03829   3,  2, 10,  1,  3, -1,  5,  0,
03830   3,  2, 10,  2,  3, -2,  4,  0,
03831   2,  2, 10,  1, 12,  2,
03832   2,  1, 12, -2, 11,  0,
03833   3, -2, 13,  1,  2, -1,  3,  0,
03834   3,  1, 10, -1, 13,  2, 11,  0,
03835   3,  2, 10,  2,  2, -2,  3,  0,
03836   3,  1, 10,  1, 12, -3, 13,  0,
03837   3,  2, 13, -1, 11,  1, 14,  0,
03838   3,  2, 10,  2,  3, -3,  5,  0,
03839   3,  2, 10,  6,  2, -8,  3,  0,
03840   3, -3, 13, 18,  2,-16,  3,  1,
03841   3,  2, 13,  2,  5, -5,  6,  0,
03842   4,  2, 13,  4,  3, -8,  4,  3,  5,  0,
03843   1,  2, 13,  0,
03844   4, -2, 13,  4,  3, -8,  4,  3,  5,  0,
03845   3, -2, 13,  2,  5, -5,  6,  0,
03846   3,  1, 13, 18,  2,-16,  3,  1,
03847   3, -2, 13, -1, 11,  1, 14,  0,
03848   3,  2, 10,  2,  3, -2,  5,  0,
03849   3,  2, 10,  3,  2, -3,  3,  0,
03850   3,  1, 10,  1, 12,  1, 13,  1,
03851   2,  2, 10,  2, 12,  1,
03852   2,  1, 11,  1, 14,  1,
03853   4, -1, 13, -2, 11, 18,  2,-16,  3,  0,
03854   1,  2, 11,  0,
03855   4, -1, 13,  2, 11, 18,  2,-16,  3,  0,
03856   2, -3, 11,  1, 14,  0,
03857   3,  2, 13,  1,  2, -1,  3,  0,
03858   3,  2, 10,  4,  2, -4,  3,  0,
03859   3,  2, 10,  1, 12, -4, 13,  0,
03860   2,  1, 10, -3, 13,  0,
03861   3,  2, 13,  1,  3, -1,  5,  0,
03862   2,  1, 12,  2, 13,  2,
03863   3,  1, 10,  2, 12,  1, 13,  0,
03864   3,  1, 10, -1, 13, -2, 11,  0,
03865   2,  1, 12,  2, 11,  1,
03866   3,  2, 10,  5,  2, -5,  3,  0,
03867   2,  2, 10, -4, 13,  0,
03868   3,  2, 10,  6,  2, -6,  3,  0,
03869   2,  2, 12,  2, 13,  0,
03870   3,  2, 10, -2, 13, -2, 11,  0,
03871   2,  2, 12,  2, 11,  0,
03872   2,  2, 10, -4, 11,  0,
03873   3,  2, 10,  7,  2, -7,  3,  0,
03874   3,  2, 10, -1, 12, -4, 13,  0,
03875   4,  2, 10, -1, 12, -2, 13, -2, 11,  0,
03876   3,  2, 10,  8,  2, -8,  3,  0,
03877   3,  2, 10,  9,  2, -9,  3,  0,
03878   3,  4, 10, -3, 12, -1, 13,  0,
03879   3,  6, 10, -1, 12, -3, 13,  0,
03880   3,  4, 10, -2, 12, -1, 13,  1,
03881   3,  5, 10, -1, 12, -2, 13,  0,
03882   2,  6, 10, -3, 13,  0,
03883   4,  4, 10, -1, 12,  1, 13, -2, 11,  0,
03884   3,  2, 10, -3, 12,  1, 13,  0,
03885   2,  3, 10, -2, 12,  0,
03886   3,  4, 10, -1, 12, -1, 13,  1,
03887   2,  5, 10, -2, 13,  0,
03888   3,  6, 10,  1, 12, -3, 13,  0,
03889   3,  4, 10,  1, 13, -2, 11,  0,
03890   3,  2, 10, -2, 12,  1, 13,  1,
03891   2,  3, 10, -1, 12,  0,
03892   4, -2, 10, -1, 13,  2,  3, -2,  5,  0,
03893   2,  4, 10, -1, 13,  0,
03894   4,  2, 10, -2, 12, -1, 13,  2, 11,  0,
03895   3,  4, 10, -3, 13,  2, 11,  0,
03896   4, -2, 10, -1, 13,  2,  2, -2,  3,  0,
03897   3,  2, 10, -1, 12,  1, 13,  2,
03898   4, -2, 10, -1, 13,  1,  3, -1,  5,  0,
03899   1,  3, 10,  0,
03900   3,  4, 10,  1, 12, -1, 13,  1,
03901   4,  2, 10, -1, 12, -1, 13,  2, 11,  1,
03902   4, -2, 10, -1, 13,  1,  2, -1,  3,  0,
03903   3,  2, 10,  3, 13, -2, 11,  0,
03904   2,  2, 12, -3, 13,  0,
03905   3,  1, 10, -1, 12,  2, 13,  0,
03906   4,  2, 10,  1, 13, -1, 11,  1, 14,  0,
03907   4, -2, 10, -2, 13, 18,  2,-16,  3,  0,
03908   5,  2, 10,  1, 13,  4,  3, -8,  4,  3,  5,  0,
03909   2,  2, 10,  1, 13,  1,
03910   5, -2, 10, -1, 13,  4,  3, -8,  4,  3,  5,  0,
03911   3,  2, 10, 18,  2,-16,  3,  0,
03912   4, -2, 10, -1, 13, -1, 11,  1, 14,  0,
03913   4,  4, 10, -1, 13,  2,  3, -2,  5,  0,
03914   4,  4, 10, -1, 13,  3,  2, -3,  3,  0,
03915   2,  3, 10,  1, 12,  1,
03916   3,  4, 10,  2, 12, -1, 13,  0,
03917   4,  2, 10, -1, 13,  1, 11,  1, 14,  0,
03918   3,  2, 10, -1, 13,  2, 11,  0,
03919   2,  1, 12, -3, 13,  1,
03920   2,  1, 10,  2, 13,  0,
03921   3,  2, 10,  1, 12,  1, 13,  1,
03922   3,  1, 12, -1, 13, -2, 11,  1,
03923   2,  1, 10,  2, 11,  0,
03924   4,  2, 10,  1, 12, -1, 13,  2, 11,  0,
03925   1,  3, 13,  0,
03926   4,  2, 10,  1, 13,  2,  3, -2,  5,  0,
03927   3,  1, 10,  1, 12,  2, 13,  0,
03928   3,  2, 10,  2, 12,  1, 13,  0,
03929   3,  1, 13,  1, 11,  1, 14,  0,
03930   2,  1, 13,  2, 11,  0,
03931   3,  1, 10,  1, 12,  2, 11,  0,
03932   4,  2, 10,  2, 12, -1, 13,  2, 11,  0,
03933   2,  1, 13, -4, 11,  0,
03934   2,  1, 10, -4, 13,  0,
03935   2,  1, 12,  3, 13,  1,
03936   3,  1, 12,  1, 13,  2, 11,  1,
03937   2,  2, 10, -5, 13,  0,
03938   3,  2, 10, -3, 13, -2, 11,  0,
03939   3,  2, 10, -1, 13, -4, 11,  0,
03940   3,  6, 10, -2, 12, -2, 13,  0,
03941   2,  4, 10, -3, 12,  0,
03942   3,  6, 10, -1, 12, -2, 13,  0,
03943   2,  4, 10, -2, 12,  1,
03944   2,  6, 10, -2, 13,  0,
03945   2,  4, 10, -1, 12,  1,
03946   2,  5, 10, -1, 13,  0,
03947   3,  6, 10,  1, 12, -2, 13,  0,
03948   4,  4, 10, -1, 12, -2, 13,  2, 11,  0,
03949   3,  4, 10,  2, 13, -2, 11,  0,
03950   3,  2, 10, -2, 12,  2, 13,  0,
03951   1,  4, 10,  0,
03952   3,  2, 10, -2, 12,  2, 11,  0,
03953   3,  4, 10, -2, 13,  2, 11,  0,
03954   3,  2, 10, -1, 12,  2, 13,  1,
03955   2,  3, 10,  1, 13,  0,
03956   2,  4, 10,  1, 12,  1,
03957   3,  2, 10, -1, 12,  2, 11,  1,
03958   3,  3, 10, -1, 13,  2, 11,  0,
03959   2,  2, 10,  2, 13,  0,
03960   3,  3, 10,  1, 12,  1, 13,  0,
03961   3,  2, 10,  1, 11,  1, 14,  0,
03962   2,  2, 10,  2, 11,  0,
03963   2,  1, 12, -4, 13,  0,
03964   2,  1, 10,  3, 13,  0,
03965   3,  2, 10,  1, 12,  2, 13,  1,
03966   3,  1, 12, -2, 13, -2, 11,  0,
03967   3,  1, 10,  1, 13,  2, 11,  0,
03968   3,  2, 10,  1, 12,  2, 11,  0,
03969   1,  4, 13,  0,
03970   3,  1, 10,  1, 12,  3, 13,  0,
03971   2,  2, 13,  2, 11,  0,
03972   4,  1, 10,  1, 12,  1, 13,  2, 11,  0,
03973   1,  4, 11,  0,
03974   2,  1, 12,  4, 13,  0,
03975   3,  1, 12,  2, 13,  2, 11,  0,
03976   3,  2, 10, -4, 13, -2, 11,  0,
03977   3,  6, 10, -2, 12, -1, 13,  0,
03978   2,  8, 10, -3, 13,  0,
03979   3,  6, 10, -1, 12, -1, 13,  0,
03980   3,  4, 10, -2, 12,  1, 13,  0,
03981   2,  6, 10, -1, 13,  0,
03982   3,  4, 10, -1, 12,  1, 13,  1,
03983   3,  6, 10,  1, 12, -1, 13,  0,
03984   4,  4, 10, -1, 12, -1, 13,  2, 11,  0,
03985   3,  2, 10, -2, 12,  3, 13,  0,
03986   2,  4, 10,  1, 13,  0,
03987   3,  4, 10, -1, 13,  2, 11,  0,
03988   3,  2, 10, -1, 12,  3, 13,  0,
03989   3,  4, 10,  1, 12,  1, 13,  0,
03990   4,  2, 10, -1, 12,  1, 13,  2, 11,  0,
03991   2,  2, 10,  3, 13,  0,
03992   3,  2, 10,  1, 13,  2, 11,  0,
03993   3,  2, 10, -1, 13,  4, 11,  0,
03994   3,  2, 10,  1, 12,  3, 13,  0,
03995   3,  1, 12, -3, 13, -2, 11,  0,
03996   3,  1, 10,  2, 13,  2, 11,  0,
03997   4,  2, 10,  1, 12,  1, 13,  2, 11,  0,
03998   1,  5, 13,  0,
03999   2,  3, 13,  2, 11,  0,
04000   2,  1, 13,  4, 11,  0,
04001   3,  1, 12,  3, 13,  2, 11,  0,
04002   2,  8, 10, -2, 13,  0,
04003   2,  6, 10, -1, 12,  0,
04004   1,  6, 10,  0,
04005   3,  6, 10, -2, 13,  2, 11,  0,
04006   3,  4, 10, -1, 12,  2, 13,  0,
04007   3,  4, 10, -1, 12,  2, 11,  0,
04008   2,  4, 10,  2, 13,  0,
04009   2,  4, 10,  2, 11,  0,
04010   3,  2, 10, -1, 12,  4, 13,  0,
04011   3,  4, 10,  1, 12,  2, 13,  0,
04012   4,  2, 10, -1, 12,  2, 13,  2, 11,  0,
04013   2,  2, 10,  4, 13,  0,
04014   3,  2, 10,  2, 13,  2, 11,  0,
04015   2,  2, 10,  4, 11,  0,
04016   1,  6, 13,  0,
04017   2,  4, 13,  2, 11,  0,
04018   2,  2, 13,  4, 11,  0,
04019   3,  6, 10, -1, 12,  1, 13,  0,
04020   2,  6, 10,  1, 13,  0,
04021   2,  4, 10,  3, 13,  0,
04022   3,  4, 10,  1, 13,  2, 11,  0,
04023   2,  2, 10,  5, 13,  0,
04024   3,  2, 10,  3, 13,  2, 11,  0,
04025  -1
04026 };
04027 
04028 static long btabr[] = {-1};
04029 static long btabb[] = {-1};
04030 static long btabl[] = {
04031         -3,        -4,
04032          4,     -1856,         0,      8043,
04033         -9,     -1082,
04034         -1,      -310,
04035         -1,      -522,
04036       -330,     -1449,      -853,      4656,
04037        -66,         7,
04038         -1,   9996928,
04039        -66,         6,
04040         23,       183,
04041          0,       173,
04042          0,       -56,
04043          0,        50,
04044          0,      -785,
04045          1,        51,
04046          0,       -60,
04047          1,     11843,         0,    -50754,
04048          0,      1834,         1,     -7910,
04049          0,    -48060,
04050          1,        56,
04051          0,     13141,        -1,    -56318,
04052          0,      2541,
04053         -1,      -649,
04054       -133,       778,
04055        -46,         8,
04056          1,   1665737,
04057        -47,         7,
04058          0,        65,
04059          0,        45,
04060          0,      -138,
04061          0,     -1005,
04062          0,     -2911,
04063          0,       -47,
04064          0,        96,
04065          0,      -394,
04066          2,        76,
04067          2,    -17302,         0,     74337,
04068          0,      -101,
04069          0,        58,
04070          0,      -171,
04071          0,       -77,
04072          0,     -1283,         0,      2686,
04073          0,       -55,
04074          0,        99,
04075          0,        55,
04076          0,       397,
04077          0,       540,
04078          0,       626,
04079         -1,     -5188,         0,     10857,
04080          0,      -216,
04081         -2,      -123,
04082          0,      6337,
04083          2,       224,
04084       -152,    -23472,       -29,    -74336,         0,    295775,
04085        -20,       149,
04086         -2,        84,
04087          9,       304,
04088          0,     -3051,
04089        -70,        -6,
04090        -57,        34,
04091          0,      -638,
04092          0,      -201,
04093        -73,         9,
04094          0,      -100,
04095       -101,        -8,
04096          0,       -57,
04097          0,      -207,
04098         -3,        80,
04099        -45,        45,
04100         -5,       102,
04101        -59,       -23,
04102         52,       201,
04103        -48,       233,      -220,        71,
04104          4,      2810,         0,   6236541,
04105        -61,       218,      -216,        67,
04106         51,       201,
04107        -59,       -23,
04108       -144,      -837,      -457,      3029,
04109        -45,        42,
04110        -15,        73,
04111         -6,      -169,
04112          0,       135,
04113        -64,        -7,
04114          0,    -16245,
04115          0,       -81,
04116        -74,       -10,
04117          0,       702,         0,     -3013,
04118          0,     -5889,
04119          1,       141,
04120         58,      9598,        12,     30443,         1,   -120946,
04121         -1,       -84,
04122         -2,     11246,        -1,    -48391,
04123          0,      1393,
04124          0,       200,
04125       -136,       -17,
04126          0,       558,
04127        -64,        -8,
04128          0,       -71,
04129          0,    317577,
04130        -28,       183,
04131          1,       219,
04132          0,       421,
04133          0,      -133,
04134        501,      -139,
04135          3,       354,
04136       -101,       -13,
04137         74,         7,
04138        144,       -84,
04139         59,        -2,
04140          1,        64,
04141      -2931,     12559,     -4641,      2638,      -303,     -2058,
04142        -13,      -100,      -123,       -79,
04143     -19214,      6084,      1494,     26993,     15213,    -82219,
04144         42,        52,        48,      -101,
04145        -53,        -4,
04146          4,        47,
04147         58,      -131,
04148         46,        14,
04149        -21,        -6,
04150      -1311,     -8791,     10198,     -4185,      2815,      5640,
04151        167,       422,      -229,        83,
04152       3140,        39,      1221,       120,        96,       -30,
04153         -1, 184612405,
04154        187,       416,      -226,        81,
04155      -1985,    -10083,      9983,     -4464,      2807,      5643,
04156        -21,        -9,
04157        113,      -367,
04158        120,       580,      -667,        27,
04159          8,        66,
04160        -56,        -6,
04161        337,        95,
04162        -87,      3303,
04163         -1,        65,
04164         68,      -374,
04165          0,      -574,
04166         15,       -94,
04167          0,       -53,
04168          0,     -1303,
04169          0,      -236,
04170        283,        36,
04171         -1,       -54,
04172        269,       -35,
04173          0,       -83,
04174          0,       -52,
04175          0,       730,         0,     -3129,
04176          0,       813,
04177          0,     -4299,
04178          1,        59,
04179         -6,      5130,         1,     16239,        -1,    -64603,
04180          0,       -80,
04181         91,        12,
04182          0,      -561,
04183        133,       -17,
04184          0,       250,
04185        -12,        71,
04186          0,    155664,
04187         82,       -11,
04188          0,       106,
04189          0,      -604,
04190          0,     21862,
04191         55,        -7,
04192          0,     -1514,         0,      6501,
04193          0,       906,
04194          0,       -68,
04195          0,       241,
04196          0,       366,
04197          0,        70,
04198          0,     -1382,         0,      5957,
04199          0,       113,
04200          0,       -51,
04201          0,       -55,
04202          0,       731,
04203          0,      -264,
04204          0,     65788,
04205          1,     -1504,         0,      3147,
04206          0,       217,
04207          0,     -4105,         0,     17658,
04208          1,        69,
04209          0,     -3518,
04210          0,     -1767,
04211        -43,     -7044,       -10,    -22304,         0,     88685,
04212          3,        91,
04213          0,      -485,
04214          0,       -57,
04215         -1,    333548,
04216        -24,       172,
04217         11,       544,         1,     -1132,
04218          0,       353,
04219          0,      -188,
04220          0,        53,
04221          0,        77,
04222        158,      -887,
04223         35,       131,
04224        -54,        13,
04225          0,   1994821,
04226        -53,        14,
04227         36,       125,
04228          2,        56,
04229          0,      -243,
04230          0,      -364,
04231         -2,      1916,         0,     -8227,
04232          0,     15700,        -1,    -67308,
04233          1,        66,
04234          0,    -53686,
04235          1,      3058,         1,    -13177,
04236          0,       -72,
04237          0,       -72,
04238          0,        61,
04239          0,     15812,
04240          0,       165,
04241          8,       -96,
04242        318,      1341,       803,     -4252,
04243         24,       193,
04244       1137,      -226,       310,       622,
04245        -56,        30,
04246         -3,  10101666,
04247        -56,        30,
04248       1096,      -225,       300,       600,
04249        -31,       409,
04250         -1,      -507,
04251          0,      -287,
04252          0,     -1869,         0,      8026,
04253          1,       544,        -1,     -1133,
04254          0,     27984,
04255          0,       -62,
04256          0,      -249,
04257          0,       187,
04258          0,     -1096,
04259          1,        53,
04260          2,     12388,         0,    -53107,
04261          0,      -322,
04262          0,       -94,
04263          0,     15157,
04264          0,      -582,
04265          0,      3291,
04266          0,       565,
04267          0,       106,
04268          0,       112,
04269          0,       306,
04270          0,       809,
04271          0,       130,
04272          0,      -961,         0,      4149,
04273          0,       174,
04274          0,      -105,
04275          0,      2196,
04276          0,        59,
04277          0,     36737,
04278         -1,     -1832,         0,      3835,
04279          0,      -139,
04280          0,     24138,
04281          0,      1325,
04282          1,        64,
04283          0,      -361,
04284          0,     -1162,
04285        -44,     -6320,       -10,    -20003,         0,     79588,
04286          2,        80,
04287          0,     -2059,
04288          0,      -304,
04289          0,     21460,
04290          0,      -166,
04291          0,       -87,
04292         89,      -493,
04293         32,       114,
04294         34,       510,         1,   1172616,
04295         31,       113,
04296         -1,        57,
04297          0,       214,
04298          0,      -656,
04299          0,      -646,
04300          0,      1850,         0,     -7931,
04301          0,     -6674,
04302          0,      2944,         0,    -12641,
04303          0,       916,
04304         45,      -255,
04305         16,        60,
04306         -1,    619116,
04307         16,        57,
04308          0,       -58,
04309          0,      1045,
04310          0,      -156,
04311        -15,        88,
04312          0,    -62964,
04313          0,      -126,
04314          0,      1490,         0,     -6387,
04315          0,       119,
04316          0,      1338,
04317          0,       -56,
04318          0,       204,
04319          0,       153,
04320          0,       940,
04321          0,       251,
04322          0,       312,
04323          0,       584,
04324          0,      -786,         0,      3388,
04325          0,       -52,
04326          0,      4733,
04327          0,       618,
04328          0,     29982,
04329          0,       101,
04330          0,      -174,
04331          0,     -2637,         0,     11345,
04332          0,      -284,
04333          0,      -524,
04334          0,      -121,
04335          0,      1464,
04336         11,       -60,
04337         -1,    151205,
04338          0,       139,
04339          0,     -2448,
04340          0,       -51,
04341          0,      -768,
04342          0,      -638,
04343          0,       552,         0,     -2370,
04344          0,        70,
04345          0,        64,
04346          0,        57,
04347          0,     39840,
04348          0,       104,
04349          0,    -10194,
04350          0,      -635,
04351          0,        69,
04352          0,       113,
04353          0,        67,
04354          0,        96,
04355          0,       367,
04356          0,       134,
04357          0,       596,
04358          0,        63,
04359          0,      1622,
04360          0,       483,
04361          0,        72,
04362          0,     11917,
04363          0,       -63,
04364          0,      1273,
04365          0,       -66,
04366          0,      -262,
04367          0,       -97,
04368          0,       103,
04369          0,     15196,
04370          0,     -1445,
04371          0,       -66,
04372          0,       -55,
04373          0,      -323,
04374          0,      2632,
04375          0,     -1179,
04376          0,        59,
04377          0,       -56,
04378          0,        78,
04379          0,        65,
04380          0,       422,
04381          0,       309,
04382          0,      2125,
04383          0,       -66,
04384          0,       124,
04385          0,       -57,
04386          0,      1379,
04387          0,      -304,
04388          0,       177,
04389          0,      -118,
04390          0,       146,
04391          0,       283,
04392          0,       119,
04393 };
04394 static CHAR bargs[] = {
04395   0,  1,
04396   3,  1, 10,  1, 12, -1, 11,  1,
04397   4,  2, 10,  2, 12, -1, 13, -1, 11,  0,
04398   5,  2, 10, -1, 13, -1, 11,  3,  2, -3,  3,  0,
04399   5,  2, 10, -1, 13, -1, 11,  2,  3, -2,  5,  0,
04400   2, -1, 13,  1, 14,  1,
04401   5, -1, 13,  1, 11,  4,  3, -8,  4,  3,  5,  0,
04402   2,  1, 13, -1, 11,  0,
04403   5,  1, 13, -1, 11,  4,  3, -8,  4,  3,  5,  0,
04404   5,  2, 10, -1, 13, -1, 11,  2,  3, -3,  5,  0,
04405   4,  1, 10,  1, 12, -2, 13,  1, 11,  0,
04406   4,  1, 13, -1, 11,  1,  2, -1,  3,  0,
04407   5,  2, 10, -1, 13, -1, 11,  2,  2, -2,  3,  0,
04408   3,  1, 10, -2, 13,  1, 11,  0,
04409   4,  1, 13, -1, 11,  1,  3, -1,  5,  0,
04410   4, -1, 13,  1, 11,  1,  2, -1,  3,  0,
04411   3,  1, 12,  1, 13, -1, 11,  1,
04412   4,  2, 10,  1, 12, -1, 13, -1, 11,  1,
04413   2,  1, 10, -1, 11,  0,
04414   4, -1, 13,  1, 11,  1,  3, -1,  5,  0,
04415   3,  1, 12, -1, 13,  1, 11,  1,
04416   3,  2, 10, -3, 13,  1, 11,  0,
04417   3,  2, 12,  1, 13, -1, 11,  0,
04418   3, -2, 10,  1, 13,  1, 14,  0,
04419   6, -2, 10,  1, 13,  1, 11,  4,  3, -8,  4,  3,  5,  0,
04420   3,  2, 10, -1, 13, -1, 11,  0,
04421   6,  2, 10, -1, 13, -1, 11,  4,  3, -8,  4,  3,  5,  0,
04422   4, -1, 13,  1, 11,  2,  3, -2,  5,  0,
04423   4, -1, 13,  1, 11,  3,  2, -3,  3,  0,
04424   3,  1, 10, -1, 12, -1, 11,  0,
04425   3,  2, 12, -1, 13,  1, 11,  0,
04426   3,  2, 10,  1, 13, -3, 11,  0,
04427   5, -2, 10,  1, 13,  1, 11,  1,  2, -1,  3,  0,
04428   4,  2, 10, -1, 12, -3, 13,  1, 11,  0,
04429   3,  3, 10, -2, 13, -1, 11,  0,
04430   5, -2, 10,  1, 13,  1, 11,  1,  3, -1,  5,  0,
04431   4,  2, 10, -1, 12, -1, 13, -1, 11,  1,
04432   2,  3, 10, -3, 11,  0,
04433   5, -2, 10,  1, 13,  1, 11,  2,  2, -2,  3,  0,
04434   4,  2, 10, -1, 12,  1, 13, -3, 11,  0,
04435   3,  4, 10, -3, 13, -1, 11,  0,
04436   4,  2, 10, -2, 12, -1, 13, -1, 11,  1,
04437   3,  4, 10, -1, 13, -3, 11,  0,
04438   4,  2, 10, -3, 12, -1, 13, -1, 11,  0,
04439   3,  4, 10, -1, 12, -3, 11,  0,
04440   3,  2, 10, -3, 12, -1, 11,  0,
04441   4,  4, 10, -1, 12, -2, 13, -1, 11,  0,
04442   2,  4, 10, -3, 11,  0,
04443   3,  2, 10, -2, 12, -1, 11,  1,
04444   4,  3, 10, -1, 12, -1, 13, -1, 11,  0,
04445   4, -2, 10,  1, 11,  2,  3, -2,  5,  0,
04446   3,  4, 10, -2, 13, -1, 11,  0,
04447   4, -2, 10,  1, 11,  2,  2, -2,  3,  0,
04448   3,  2, 10, -1, 12, -1, 11,  2,
04449   3, -2, 10,  1, 12,  1, 14,  0,
04450   4, -2, 10,  1, 11,  2,  3, -2,  4,  0,
04451   4, -2, 10,  1, 11,  1,  3, -1,  5,  0,
04452   3,  3, 10, -1, 13, -1, 11,  0,
04453   4, -2, 10,  1, 11,  3,  2, -4,  3,  0,
04454   4, -2, 10,  1, 11,  1,  3, -2,  5,  0,
04455   4,  2, 10, -1, 12, -2, 13,  1, 11,  0,
04456   4, -2, 10,  1, 11,  1,  2, -1,  3,  0,
04457   2, -1, 10,  1,  2,  0,
04458   3,  2, 10,  2, 13, -3, 11,  0,
04459   4, -2, 10,  1, 11,  2,  2, -3,  3,  0,
04460   3,  2, 12, -2, 13,  1, 11,  0,
04461   4,  1, 10, -1, 12,  1, 13, -1, 11,  0,
04462   3, -2, 10,  1, 11,  1,  5,  0,
04463   4,  2, 10, -1, 11,  1,  3, -2,  4,  0,
04464   3,  2, 10, -2, 11,  1, 14,  0,
04465   4, -2, 10,  1, 11,  8,  2,-13,  3,  0,
04466   5, -2, 10, -1, 13,  1, 11, 18,  2,-16,  3,  0,
04467   5,  2, 10, -1, 11,  4,  3, -8,  4,  3,  5,  1,
04468   2,  2, 10, -1, 11,  1,
04469   5, -2, 10,  1, 11,  4,  3, -8,  4,  3,  5,  1,
04470   5,  2, 10, -1, 13, -1, 11, 18,  2,-16,  3,  0,
04471   4,  2, 10, -1, 11,  8,  2,-13,  3,  0,
04472   2, -2, 10,  1, 14,  1,
04473   4, -2, 10,  1, 11,  1,  3, -2,  4,  0,
04474   3,  2, 10, -1, 11,  1,  5,  0,
04475   2,  2, 12, -1, 11,  0,
04476   4,  3, 10,  1, 12, -1, 13, -1, 11,  0,
04477   4,  2, 10, -1, 11,  2,  2, -3,  3,  0,
04478   3,  2, 10, -2, 13,  1, 11,  0,
04479   4,  2, 10, -1, 11,  1,  2, -1,  3,  0,
04480   3,  1, 10,  1,  2, -2,  3,  0,
04481   3,  1, 12, -2, 13,  1, 11,  1,
04482   3,  1, 10,  1, 13, -1, 11,  0,
04483   4,  2, 10, -1, 11,  1,  3, -1,  5,  0,
04484   3,  2, 10,  1, 12, -1, 11,  2,
04485   3, -2, 10, -1, 12,  1, 14,  0,
04486   2,  1, 12, -1, 11,  1,
04487   3,  1, 10, -1, 13,  1, 11,  0,
04488   4,  2, 10, -1, 11,  2,  2, -2,  3,  0,
04489   3,  1, 10,  2,  2, -3,  3,  0,
04490   4,  2, 10,  1, 12, -2, 13,  1, 11,  0,
04491   3, -1, 10,  1,  2, -2,  3,  0,
04492   3, -1, 11,  1,  2, -1,  3,  0,
04493   2,  2, 13, -1, 11,  0,
04494   2, -2, 13,  1, 14,  0,
04495   4,  2, 10, -1, 11,  2,  3, -2,  5,  0,
04496   4,  2, 10, -1, 11,  3,  2, -3,  3,  0,
04497   4,  2, 10,  2, 12, -2, 13, -1, 11,  0,
04498   3,  1, 10,  1,  3, -2,  5,  0,
04499   4,  1, 10,  1, 12,  1, 13, -1, 11,  0,
04500   3,  1, 10,  3,  2, -4,  3,  0,
04501   3,  1, 10,  1,  3, -1,  5,  0,
04502   3,  1, 10,  1,  3, -2,  6,  0,
04503   3,  1, 10,  2,  3, -2,  4,  0,
04504   4,  1, 10,  1, 12, -1, 13, -1, 11,  0,
04505   3,  2, 10,  2, 12, -1, 11,  2,
04506   4,  1, 10,  1,  3,  2,  5, -5,  6,  1,
04507   1,  1, 14,  2,
04508   3,  1, 10,  8,  2,-12,  3,  1,
04509   5, -2, 10,  1, 13, -1, 11, 20,  2,-21,  3,  0,
04510   5,  2, 10, -2, 13,  1, 11,  2,  3, -3,  5,  0,
04511   3,  1, 10,  1,  3,  1,  6,  0,
04512   4, -1, 13, -1, 11, 26,  2,-29,  3,  0,
04513   3, -1, 11,  8,  2,-13,  3,  0,
04514   4, -1, 13, -1, 11, 18,  2,-16,  3,  2,
04515   4, -1, 13,  1, 11, 10,  2, -3,  3,  1,
04516   1,  1, 11,  3,
04517   4, -1, 13, -1, 11, 10,  2, -3,  3,  1,
04518   4, -1, 13,  1, 11, 18,  2,-16,  3,  2,
04519   3,  1, 11,  8,  2,-13,  3,  0,
04520   2,  1, 10,  2,  4,  0,
04521   4,  2, 10, -1, 11,  5,  2, -6,  3,  1,
04522   5,  2, 10, -2, 13, -1, 11,  2,  3, -3,  5,  0,
04523   5, -2, 10,  1, 13,  1, 11, 20,  2,-21,  3,  0,
04524   3,  1, 10,  1,  3,  1,  5,  0,
04525   2, -2, 11,  1, 14,  0,
04526   5,  2, 10, -2, 13,  1, 11,  2,  3, -2,  5,  0,
04527   3,  1, 10,  5,  2, -7,  3,  0,
04528   4,  1, 10,  1, 12, -1, 13,  1, 11,  0,
04529   3,  1, 10,  2,  2, -2,  3,  0,
04530   4,  2, 10,  2, 12, -2, 13,  1, 11,  0,
04531   2,  2, 13, -3, 11,  0,
04532   4,  2, 10, -1, 11,  4,  2, -4,  3,  0,
04533   3,  1, 10,  4,  2, -5,  3,  0,
04534   3,  1, 10, -3, 13,  1, 11,  0,
04535   2,  1, 10,  1,  2,  0,
04536   3,  1, 11,  1,  2, -1,  3,  0,
04537   4,  2, 10, -1, 11,  3,  3, -3,  5,  0,
04538   3,  1, 12,  2, 13, -1, 11,  1,
04539   4,  2, 10,  1, 12, -2, 13, -1, 11,  0,
04540   3,  1, 10, -1, 13, -1, 11,  0,
04541   3,  1, 11,  1,  3, -1,  5,  0,
04542   2,  1, 12,  1, 11,  2,
04543   4,  2, 10, -1, 11,  5,  2, -5,  3,  0,
04544   3,  1, 10,  5,  2, -6,  3,  0,
04545   3,  2, 10,  1, 12, -3, 11,  0,
04546   3,  1, 10,  2,  2, -1,  3,  0,
04547   3,  2, 10, -4, 13,  1, 11,  0,
04548   3, -2, 10,  2, 13,  1, 14,  0,
04549   3,  2, 10, -2, 13, -1, 11,  0,
04550   3,  1, 10,  3,  2, -2,  3,  0,
04551   4,  1, 10, -1, 12, -1, 13, -1, 11,  0,
04552   2,  2, 12,  1, 11,  0,
04553   2,  2, 10, -3, 11,  0,
04554   3,  1, 10,  4,  2, -3,  3,  0,
04555   4,  2, 10, -1, 12, -2, 13, -1, 11,  1,
04556   3,  2, 10, -1, 12, -3, 11,  0,
04557   3,  4, 10, -4, 13, -1, 11,  0,
04558   4,  2, 10, -2, 12, -2, 13, -1, 11,  0,
04559   4,  4, 10, -2, 12, -1, 13, -1, 11,  0,
04560   3,  6, 10, -3, 13, -1, 11,  0,
04561   4,  4, 10, -1, 12, -1, 13, -1, 11,  1,
04562   4,  2, 10, -3, 12, -1, 13,  1, 11,  0,
04563   3,  5, 10, -2, 13, -1, 11,  0,
04564   3,  4, 10,  1, 13, -3, 11,  0,
04565   4,  2, 10, -2, 12,  1, 13, -1, 11,  0,
04566   3,  3, 10, -1, 12, -1, 11,  0,
04567   3,  4, 10, -1, 13, -1, 11,  0,
04568   4,  2, 10, -2, 12, -1, 13,  1, 11,  1,
04569   3,  4, 10, -3, 13,  1, 11,  0,
04570   4,  2, 10, -1, 12,  1, 13, -1, 11,  1,
04571   5, -2, 10,  1, 13, -1, 11,  2,  2, -2,  3,  0,
04572   2,  3, 10, -1, 11,  0,
04573   4,  4, 10,  1, 12, -1, 13, -1, 11,  0,
04574   4,  2, 10, -1, 12, -1, 13,  1, 11,  2,
04575   5, -2, 10,  1, 13, -1, 11,  1,  3, -1,  5,  0,
04576   3,  3, 10, -2, 13,  1, 11,  0,
04577   5, -2, 10,  1, 13, -1, 11,  1,  2, -1,  3,  0,
04578   3,  2, 10,  1, 13, -1, 11,  0,
04579   3, -2, 10, -1, 13,  1, 14,  0,
04580   3,  2, 12, -1, 13, -1, 11,  1,
04581   3,  3, 10,  1, 12, -1, 11,  0,
04582   3,  1, 10, -1, 12,  1, 11,  0,
04583   4, -1, 13, -1, 11,  3,  2, -3,  3,  0,
04584   4, -1, 13, -1, 11,  2,  3, -2,  5,  0,
04585   3,  2, 10, -1, 13,  1, 14,  0,
04586   4, -2, 10, -1, 11, 18,  2,-16,  3,  0,
04587   6,  2, 10, -1, 13,  1, 11,  4,  3, -8,  4,  3,  5,  0,
04588   3,  2, 10, -1, 13,  1, 11,  0,
04589   6, -2, 10,  1, 13, -1, 11,  4,  3, -8,  4,  3,  5,  0,
04590   5,  2, 10, -2, 13,  1, 11, 18,  2,-16,  3,  0,
04591   4, -2, 10,  1, 13, -2, 11,  1, 14,  0,
04592   3,  1, 12, -3, 13,  1, 11,  0,
04593   3,  1, 10,  2, 13, -1, 11,  0,
04594   4,  2, 10,  1, 12,  1, 13, -1, 11,  1,
04595   3,  1, 12, -1, 13, -1, 11,  1,
04596   4, -1, 13, -1, 11,  1,  3, -1,  5,  0,
04597   2,  1, 10,  1, 11,  0,
04598   4,  2, 10,  1, 12, -1, 13,  1, 11,  1,
04599   3,  1, 12,  1, 13, -3, 11,  0,
04600   4, -1, 13, -1, 11,  1,  2, -1,  3,  0,
04601   5,  2, 10, -1, 13,  1, 11,  2,  2, -2,  3,  0,
04602   2,  3, 13, -1, 11,  0,
04603   4,  1, 10,  1, 12, -2, 13, -1, 11,  0,
04604   4,  2, 10,  2, 12,  1, 13, -1, 11,  0,
04605   2,  1, 13,  1, 14,  1,
04606   5,  2, 10, -1, 13,  1, 11,  2,  3, -3,  5,  0,
04607   4, -2, 13, -1, 11, 18,  2,-16,  3,  1,
04608   5,  1, 13,  1, 11,  4,  3, -8,  4,  3,  5,  0,
04609   2,  1, 13,  1, 11,  0,
04610   5, -1, 13, -1, 11,  4,  3, -8,  4,  3,  5,  0,
04611   3,  1, 11, 18,  2,-16,  3,  1,
04612   3, -1, 13, -2, 11,  1, 14,  0,
04613   5,  2, 10, -1, 13,  1, 11,  2,  3, -2,  5,  0,
04614   5,  2, 10, -1, 13,  1, 11,  3,  2, -3,  3,  0,
04615   3,  1, 10,  1, 12,  1, 11,  1,
04616   4,  2, 10,  2, 12, -1, 13,  1, 11,  1,
04617   2,  1, 13, -3, 11,  0,
04618   4,  1, 13,  1, 11,  1,  2, -1,  3,  0,
04619   3,  1, 12,  3, 13, -1, 11,  0,
04620   4,  2, 10,  1, 12, -3, 13, -1, 11,  0,
04621   3,  1, 10, -2, 13, -1, 11,  0,
04622   4,  1, 13,  1, 11,  1,  3, -1,  5,  0,
04623   3,  1, 12,  1, 13,  1, 11,  1,
04624   2,  1, 10, -3, 11,  0,
04625   3,  1, 12, -1, 13,  3, 11,  0,
04626   3,  2, 10, -3, 13, -1, 11,  0,
04627   3,  2, 12,  1, 13,  1, 11,  0,
04628   3,  2, 10, -1, 13, -3, 11,  0,
04629   4,  2, 10, -1, 12, -3, 13, -1, 11,  0,
04630   4,  2, 10, -1, 12, -1, 13, -3, 11,  0,
04631   4,  6, 10, -1, 12, -2, 13, -1, 11,  0,
04632   3,  4, 10, -2, 12, -1, 11,  0,
04633   3,  6, 10, -2, 13, -1, 11,  0,
04634   4,  4, 10, -2, 12, -2, 13,  1, 11,  0,
04635   3,  4, 10, -1, 12, -1, 11,  1,
04636   3,  2, 10, -3, 12,  1, 11,  0,
04637   3,  5, 10, -1, 13, -1, 11,  0,
04638   4,  4, 10, -1, 12, -2, 13,  1, 11,  0,
04639   4,  2, 10, -2, 12,  2, 13, -1, 11,  0,
04640   2,  4, 10, -1, 11,  0,
04641   3,  2, 10, -2, 12,  1, 11,  1,
04642   4,  3, 10, -1, 12, -1, 13,  1, 11,  0,
04643   3,  4, 10, -2, 13,  1, 11,  0,
04644   4,  2, 10, -1, 12,  2, 13, -1, 11,  0,
04645   4, -2, 10, -1, 11,  2,  2, -2,  3,  0,
04646   3,  3, 10,  1, 13, -1, 11,  0,
04647   3,  4, 10,  1, 12, -1, 11,  0,
04648   3,  2, 10, -1, 12,  1, 11,  2,
04649   4, -2, 10, -1, 11,  1,  3, -1,  5,  0,
04650   3,  3, 10, -1, 13,  1, 11,  0,
04651   4,  4, 10,  1, 12, -2, 13,  1, 11,  0,
04652   3,  2, 10,  2, 13, -1, 11,  0,
04653   3,  2, 12, -2, 13, -1, 11,  0,
04654   4,  1, 10, -1, 12,  1, 13,  1, 11,  0,
04655   2,  2, 10,  1, 14,  0,
04656   5, -2, 10, -1, 13, -1, 11, 18,  2,-16,  3,  0,
04657   2,  2, 10,  1, 11,  1,
04658   5,  2, 10, -1, 13,  1, 11, 18,  2,-16,  3,  0,
04659   3, -2, 10, -2, 11,  1, 14,  0,
04660   4,  3, 10,  1, 12, -1, 13,  1, 11,  0,
04661   3,  2, 10, -2, 13,  3, 11,  0,
04662   4,  2, 10,  1, 12,  2, 13, -1, 11,  0,
04663   3,  1, 12, -2, 13, -1, 11,  1,
04664   3,  1, 10,  1, 13,  1, 11,  0,
04665   3,  2, 10,  1, 12,  1, 11,  1,
04666   2,  4, 13, -1, 11,  0,
04667   2,  2, 13,  1, 14,  0,
04668   4, -3, 13, -1, 11, 18,  2,-16,  3,  0,
04669   2,  2, 13,  1, 11,  0,
04670   4,  1, 13,  1, 11, 18,  2,-16,  3,  0,
04671   4,  2, 10,  1, 11,  2,  3, -2,  5,  0,
04672   4,  1, 10,  1, 12,  1, 13,  1, 11,  0,
04673   3,  2, 10,  2, 12,  1, 11,  0,
04674   2,  2, 11,  1, 14,  0,
04675   1,  3, 11,  0,
04676   3,  1, 10, -3, 13, -1, 11,  0,
04677   3,  1, 12,  2, 13,  1, 11,  1,
04678   2,  1, 12,  3, 11,  0,
04679   3,  2, 10, -4, 13, -1, 11,  0,
04680   3,  2, 12,  2, 13,  1, 11,  0,
04681   3,  2, 10, -2, 13, -3, 11,  0,
04682   4,  6, 10, -1, 12, -1, 13, -1, 11,  0,
04683   3,  6, 10, -1, 13, -1, 11,  0,
04684   4,  4, 10, -2, 12, -1, 13,  1, 11,  0,
04685   3,  6, 10, -3, 13,  1, 11,  0,
04686   4,  4, 10, -1, 12,  1, 13, -1, 11,  0,
04687   4,  4, 10, -1, 12, -1, 13,  1, 11,  1,
04688   3,  5, 10, -2, 13,  1, 11,  0,
04689   3,  4, 10,  1, 13, -1, 11,  0,
04690   4,  2, 10, -2, 12,  1, 13,  1, 11,  0,
04691   3,  4, 10, -1, 13,  1, 11,  0,
04692   4,  2, 10, -1, 12,  3, 13, -1, 11,  0,
04693   4,  4, 10,  1, 12,  1, 13, -1, 11,  0,
04694   4,  2, 10, -1, 12,  1, 13,  1, 11,  1,
04695   2,  3, 10,  1, 11,  0,
04696   4,  4, 10,  1, 12, -1, 13,  1, 11,  0,
04697   4,  2, 10, -1, 12, -1, 13,  3, 11,  0,
04698   3,  2, 10,  3, 13, -1, 11,  0,
04699   3,  2, 10,  1, 13,  1, 14,  0,
04700   3,  2, 10,  1, 13,  1, 11,  0,
04701   3,  3, 10,  1, 12,  1, 11,  0,
04702   3,  2, 10, -1, 13,  3, 11,  0,
04703   4,  2, 10,  1, 12,  3, 13, -1, 11,  0,
04704   3,  1, 12, -3, 13, -1, 11,  0,
04705   3,  1, 10,  2, 13,  1, 11,  0,
04706   4,  2, 10,  1, 12,  1, 13,  1, 11,  1,
04707   3,  1, 12, -1, 13, -3, 11,  0,
04708   2,  1, 10,  3, 11,  0,
04709   2,  5, 13, -1, 11,  0,
04710   2,  3, 13,  1, 11,  0,
04711   4,  1, 10,  1, 12,  2, 13,  1, 11,  0,
04712   2,  1, 13,  3, 11,  0,
04713   3,  1, 12,  3, 13,  1, 11,  0,
04714   3,  1, 12,  1, 13,  3, 11,  0,
04715   3,  2, 10, -5, 13, -1, 11,  0,
04716   3,  6, 10, -1, 12, -1, 11,  0,
04717   4,  6, 10, -1, 12, -2, 13,  1, 11,  0,
04718   2,  6, 10, -1, 11,  0,
04719   3,  4, 10, -2, 12,  1, 11,  0,
04720   3,  6, 10, -2, 13,  1, 11,  0,
04721   4,  4, 10, -1, 12,  2, 13, -1, 11,  0,
04722   3,  4, 10, -1, 12,  1, 11,  0,
04723   3,  4, 10,  2, 13, -1, 11,  0,
04724   4,  2, 10, -2, 12,  2, 13,  1, 11,  0,
04725   2,  4, 10,  1, 11,  0,
04726   3,  4, 10, -2, 13,  3, 11,  0,
04727   4,  2, 10, -1, 12,  2, 13,  1, 11,  0,
04728   3,  3, 10,  1, 13,  1, 11,  0,
04729   3,  4, 10,  1, 12,  1, 11,  0,
04730   3,  2, 10, -1, 12,  3, 11,  0,
04731   3,  2, 10,  4, 13, -1, 11,  0,
04732   3,  2, 10,  2, 13,  1, 11,  0,
04733   2,  2, 10,  3, 11,  0,
04734   3,  1, 12, -4, 13, -1, 11,  0,
04735   3,  1, 10,  3, 13,  1, 11,  0,
04736   4,  2, 10,  1, 12,  2, 13,  1, 11,  0,
04737   2,  4, 13,  1, 11,  0,
04738   2,  2, 13,  3, 11,  0,
04739   1,  5, 11,  0,
04740   3,  1, 12,  4, 13,  1, 11,  0,
04741   4,  6, 10, -1, 12, -1, 13,  1, 11,  0,
04742   3,  6, 10,  1, 13, -1, 11,  0,
04743   3,  6, 10, -1, 13,  1, 11,  0,
04744   4,  4, 10, -1, 12,  1, 13,  1, 11,  0,
04745   3,  4, 10,  1, 13,  1, 11,  0,
04746   3,  4, 10, -1, 13,  3, 11,  0,
04747   4,  2, 10, -1, 12,  3, 13,  1, 11,  0,
04748   4,  4, 10,  1, 12,  1, 13,  1, 11,  0,
04749   3,  2, 10,  3, 13,  1, 11,  0,
04750   3,  2, 10,  1, 13,  3, 11,  0,
04751   2,  5, 13,  1, 11,  0,
04752   2,  3, 13,  3, 11,  0,
04753   2,  6, 10,  1, 11,  0,
04754   3,  4, 10,  2, 13,  1, 11,  0,
04755   3,  2, 10,  4, 13,  1, 11,  0,
04756  -1
04757 };
04758 struct plantbl moonlr = {
04759   {  3, 26, 29, 23,  5, 10,  0,  0,  0,  8,  4,  4,  6,  2,  0,  0,  0,  0,},
04760  3,
04761  lrargs,
04762  lrtabl,
04763  lrtabb,
04764  lrtabr,
04765  2.5735686895300000e-03,
04766  3.6525000000000000e+06,
04767  1.0000000000000000e-04,
04768 };
04769 
04770 struct plantbl moonlat = {
04771   {  0, 26, 29,  8,  3,  5,  0,  0,  0,  6,  5,  3,  5,  1,  0,  0,  0,  0,},
04772  3,
04773  bargs,
04774  btabl,
04775  btabb,
04776  btabr,
04777  0.0000000000000000e+00,
04778  3.6525000000000000e+06,
04779  1.0000000000000000e-04,
04780 };
04781 
04782 
04783 /* Reduce arc seconds modulo 360 degrees
04784    answer in arc seconds  */
04785 static double mods3600(double x)
04786 {
04787   double y;
04788   y = x - 1296000. * floor( x/1296000.);
04789   return(y);
04790 }
04791 
04792 
04793 /* Time argument is Julian ephemeris date.  */
04794 
04795 static void mean_elements (double JED)
04796 {
04797   double x, T, T2;
04798 
04799   /* Time variables.  T is in Julian centuries.  */
04800   T = (JED - MOSHIER_J2000) / 36525.0;
04801   T2 = T*T;
04802 
04803   /* Mean longitudes of planets (Simon et al, 1994)
04804      .047" subtracted from constant term for offset to DE403 origin. */
04805 
04806   /* Mercury */
04807   x = mods3600( 538101628.6889819 * T + 908103.213 );
04808   x += (6.39e-6 * T
04809          - 0.0192789) * T2;
04810   Args[0] = x;
04811 
04812   /* Venus */
04813   x = mods3600( 210664136.4335482 * T + 655127.236 );
04814   x += (-6.27e-6  * T
04815          + 0.0059381) * T2;
04816   Args[1] = x;
04817 
04818   /* Earth  */
04819   x = mods3600( 129597742.283429 * T + 361679.198 );
04820   x += (-5.23e-6 * T
04821          - 2.04411e-2 ) * T2;
04822   Ea_arcsec = x;
04823   Args[2] = x;
04824 
04825   /* Mars */
04826   x = mods3600(  68905077.493988 * T +  1279558.751 );
04827   x += (-1.043e-5 * T
04828          + 0.0094264) * T2;
04829   Args[3] = x;
04830 
04831   /* Jupiter */
04832   x = mods3600( 10925660.377991 * T + 123665.420 );
04833   x += ((((-3.4e-10 * T
04834             + 5.91e-8) * T
04835            + 4.667e-6) * T
04836           + 5.706e-5) * T
04837          - 3.060378e-1)*T2;
04838   Args[4] = x;
04839 
04840    /* Saturn */
04841   x = mods3600( 4399609.855372 * T + 180278.752 );
04842   x += (((( 8.3e-10 * T
04843           - 1.452e-7) * T
04844           - 1.1484e-5) * T
04845            - 1.6618e-4) * T
04846          + 7.561614E-1)*T2;
04847   Args[5] = x;
04848 
04849   /* Uranus */
04850   x = mods3600( 1542481.193933 * T + 1130597.971 )
04851        + (0.00002156*T - 0.0175083)*T2;
04852   Args[6] = x;
04853 
04854   /* Neptune */
04855   x = mods3600( 786550.320744 * T + 1095655.149 )
04856        + (-0.00000895*T + 0.0021103)*T2;
04857   Args[7] = x;
04858 
04859   /* Copied from cmoon.c, DE404 version.  */
04860   /* Mean elongation of moon = D */
04861   x = mods3600( 1.6029616009939659e+09 * T + 1.0722612202445078e+06 );
04862   x += (((((-3.207663637426e-013 * T
04863                + 2.555243317839e-011) * T
04864               + 2.560078201452e-009) * T
04865              - 3.702060118571e-005) * T
04866             + 6.9492746836058421e-03) * T /* D, t^3 */
04867            - 6.7352202374457519e+00) * T2; /* D, t^2 */
04868   Args[9] = x;
04869 
04870   /* Mean distance of moon from its ascending node = F */
04871   x = mods3600( 1.7395272628437717e+09 * T + 3.3577951412884740e+05 );
04872   x += ((((( 4.474984866301e-013 * T
04873                + 4.189032191814e-011) * T
04874                - 2.790392351314e-009) * T
04875               - 2.165750777942e-006) * T
04876               - 7.5311878482337989e-04) * T /* F, t^3 */
04877              - 1.3117809789650071e+01) * T2; /* F, t^2 */
04878   NF_arcsec = x;
04879   Args[10] = x;
04880 
04881 /* Mean anomaly of sun = l' (J. Laskar) */
04882   x = mods3600(1.2959658102304320e+08 * T + 1.2871027407441526e+06);
04883   x += ((((((((
04884                1.62e-20 * T
04885                - 1.0390e-17 ) * T
04886               - 3.83508e-15 ) * T
04887              + 4.237343e-13 ) * T
04888             + 8.8555011e-11 ) * T
04889            - 4.77258489e-8 ) * T
04890           - 1.1297037031e-5 ) * T
04891          + 8.7473717367324703e-05) * T
04892         - 5.5281306421783094e-01) * T2;
04893   Args[11] = x;
04894 
04895   /* Mean anomaly of moon = l */
04896   x = mods3600( 1.7179159228846793e+09 * T + 4.8586817465825332e+05 );
04897   x += (((((-1.755312760154e-012) * T
04898                 + 3.452144225877e-011 * T
04899                 - 2.506365935364e-008) * T
04900                - 2.536291235258e-004) * T
04901               + 5.2099641302735818e-02) * T /* l, t^3 */
04902              + 3.1501359071894147e+01) * T2; /* l, t^2 */
04903   Args[12] = x;
04904 
04905   /* Mean longitude of moon, re mean ecliptic and equinox of date = L  */
04906   x = mods3600( 1.7325643720442266e+09 * T + 7.8593980921052420e+05);
04907   x += ((((( 7.200592540556e-014 * T
04908              + 2.235210987108e-010) * T
04909             - 1.024222633731e-008) * T
04910            - 6.073960534117e-005) * T
04911          + 6.9017248528380490e-03) * T /* L, t^3 */
04912         - 5.6550460027471399e+00) * T2; /* L, t^2 */
04913   LP_equinox = x;
04914   Args[13] = x;
04915 
04916   /* Precession of the equinox  */
04917  x = ((((((((( -8.66e-20*T - 4.759e-17)*T
04918            + 2.424e-15)*T
04919            + 1.3095e-12)*T
04920            + 1.7451e-10)*T
04921            - 1.8055e-8)*T
04922            - 0.0000235316)*T
04923            + 0.000076)*T
04924            + 1.105414)*T
04925            + 5028.791959)*T;
04926   /* Moon's longitude re fixed J2000 equinox.  */
04927  /*
04928    Args[13] -= x;
04929  */
04930    pA_precession = x;
04931 
04932   /*  OM = LP - NF; */
04933 
04934   /* Free librations.  */
04935   /*  LB 2.891725 years, psi amplitude 1.8" */
04936   Args[14] = mods3600( 4.48175409e7 * T + 8.060457e5 );
04937 
04938   /* 24.2 years */
04939   Args[15] = mods3600(  5.36486787e6 * T - 391702.8 );
04940 
04941 #if 0
04942   /* 27.34907 days */
04943   Args[16] = mods3600( 1.7308227257e9 * T - 4.443583e5 );
04944 #endif
04945   /* LA 74.7 years. */
04946 Args[17] = mods3600( 1.73573e6 * T );
04947 }
04948 
04949 
04950 /* Prepare lookup table of sin and cos ( i*Lj )
04951  * for required multiple angles
04952  */
04953 static int  sscc (int k, double arg, int n)
04954 {
04955   double cu, su, cv, sv, s;
04956   int i;
04957 
04958   s = STR * arg;
04959   su = sin (s);
04960   cu = cos (s);
04961   ss[k][0] = su;                /* sin(L) */
04962   cc[k][0] = cu;                /* cos(L) */
04963   sv = 2.0 * su * cu;
04964   cv = cu * cu - su * su;
04965   ss[k][1] = sv;                /* sin(2L) */
04966   cc[k][1] = cv;
04967   for (i = 2; i < n; i++)
04968     {
04969       s = su * cv + cu * sv;
04970       cv = cu * cv - su * sv;
04971       sv = s;
04972       ss[k][i] = sv;            /* sin( i+1 L ) */
04973       cc[k][i] = cv;
04974     }
04975   return (0);
04976 }
04977 
04978 /* Generic program to accumulate sum of trigonometric series
04979    in two variables (e.g., longitude, radius)
04980    of the same list of arguments.  */
04981 static int  g2plan (double J, struct plantbl *plan, double pobj[], int flag)
04982 {
04983   int i, j, k, m, k1, ip, np, nt;
04984   /* On some systems such as Silicon Graphics, char is unsigned
04985      by default.  */
04986   CHAR *p;
04987   long *pl, *pr;
04988   double su, cu, sv, cv;
04989   double t, sl, sr;
04990 
04991   mean_elements (J);
04992   /* For librations, moon's longitude is sidereal.  */
04993   if (flag)
04994     Args[13] -= pA_precession;
04995 
04996   T = (J - MOSHIER_J2000) / plan->timescale;
04997   /* Calculate sin( i*MM ), etc. for needed multiple angles.  */
04998   for (i = 0; i < NARGS; i++)
04999     {
05000       if ((j = plan->max_harmonic[i]) > 0)
05001         {
05002           sscc (i, Args[i], j);
05003         }
05004     }
05005 
05006   /* Point to start of table of arguments. */
05007   p = plan->arg_tbl;
05008   /* Point to tabulated cosine and sine amplitudes.  */
05009   pl = plan->lon_tbl;
05010   pr = plan->rad_tbl;
05011   sl = 0.0;
05012   sr = 0.0;
05013 
05014   for (;;)
05015     {
05016       /* argument of sine and cosine */
05017       /* Number of periodic arguments. */
05018       np = *p++;
05019       if (np < 0)
05020         break;
05021       if (np == 0)
05022         {                       /* It is a polynomial term.  */
05023           nt = *p++;
05024           /* Longitude polynomial. */
05025           cu = *pl++;
05026           for (ip = 0; ip < nt; ip++)
05027             {
05028               cu = cu * T + *pl++;
05029             }
05030           /*      sl +=  mods3600 (cu); */
05031           sl += cu;
05032           /* Radius polynomial. */
05033           cu = *pr++;
05034           for (ip = 0; ip < nt; ip++)
05035             {
05036               cu = cu * T + *pr++;
05037             }
05038           sr += cu;
05039           continue;
05040         }
05041       k1 = 0;
05042       cv = 0.0;
05043       sv = 0.0;
05044       for (ip = 0; ip < np; ip++)
05045         {
05046           /* What harmonic.  */
05047           j = *p++;
05048           /* Which planet.  */
05049           m = *p++ - 1;
05050           if (j)
05051             {
05052               k = abs (j);
05053               k -= 1;
05054               su = ss[m][k];    /* sin(k*angle) */
05055               if (j < 0)
05056                 su = -su;
05057               cu = cc[m][k];
05058               if (k1 == 0)
05059                 {               /* set first angle */
05060                   sv = su;
05061                   cv = cu;
05062                   k1 = 1;
05063                 }
05064               else
05065                 {               /* combine angles */
05066                   t = su * cv + cu * sv;
05067                   cv = cu * cv - su * sv;
05068                   sv = t;
05069                 }
05070             }
05071         }
05072       /* Highest power of T.  */
05073       nt = *p++;
05074       /* Longitude. */
05075       cu = *pl++;
05076       su = *pl++;
05077       for (ip = 0; ip < nt; ip++)
05078         {
05079           cu = cu * T + *pl++;
05080           su = su * T + *pl++;
05081         }
05082       sl += cu * cv + su * sv;
05083       /* Radius. */
05084       cu = *pr++;
05085       su = *pr++;
05086       for (ip = 0; ip < nt; ip++)
05087         {
05088           cu = cu * T + *pr++;
05089           su = su * T + *pr++;
05090         }
05091       sr += cu * cv + su * sv;
05092     }
05093   t = plan->trunclvl;
05094   pobj[0] = t * sl;
05095   pobj[2] = t * sr;
05096   return (0);
05097 }
05098 
05099 
05100 
05101 /* Generic program to accumulate sum of trigonometric series
05102    in one variable.  */
05103 
05104 static double g1plan (double J, struct plantbl *plan)
05105 {
05106   int i, j, k, m, k1, ip, np, nt;
05107   /* On some systems such as Silicon Graphics, char is unsigned
05108      by default.  */
05109   CHAR *p;
05110   long *pl;
05111   double su, cu, sv, cv;
05112   double t, sl;
05113 
05114   T = (J - MOSHIER_J2000) / plan->timescale;
05115   mean_elements (J);
05116   /* Calculate sin( i*MM ), etc. for needed multiple angles.  */
05117   for (i = 0; i < NARGS; i++)
05118     {
05119       if ((j = plan->max_harmonic[i]) > 0)
05120         {
05121           sscc (i, Args[i], j);
05122         }
05123     }
05124 
05125   /* Point to start of table of arguments. */
05126   p = plan->arg_tbl;
05127   /* Point to tabulated cosine and sine amplitudes.  */
05128   pl = plan->lon_tbl;
05129   sl = 0.0;
05130 
05131   for (;;)
05132     {
05133       /* argument of sine and cosine */
05134       /* Number of periodic arguments. */
05135       np = *p++;
05136       if (np < 0)
05137         break;
05138       if (np == 0)
05139         {                       /* It is a polynomial term.  */
05140           nt = *p++;
05141           cu = *pl++;
05142           for (ip = 0; ip < nt; ip++)
05143             {
05144               cu = cu * T + *pl++;
05145             }
05146           /*      sl +=  mods3600 (cu); */
05147           sl += cu;
05148           continue;
05149         }
05150       k1 = 0;
05151       cv = 0.0;
05152       sv = 0.0;
05153       for (ip = 0; ip < np; ip++)
05154         {
05155           /* What harmonic.  */
05156           j = *p++;
05157           /* Which planet.  */
05158           m = *p++ - 1;
05159           if (j)
05160             {
05161               k = abs (j);
05162               k -= 1;
05163               su = ss[m][k];    /* sin(k*angle) */
05164               if (j < 0)
05165                 su = -su;
05166               cu = cc[m][k];
05167               if (k1 == 0)
05168                 {               /* set first angle */
05169                   sv = su;
05170                   cv = cu;
05171                   k1 = 1;
05172                 }
05173               else
05174                 {               /* combine angles */
05175                   t = su * cv + cu * sv;
05176                   cv = cu * cv - su * sv;
05177                   sv = t;
05178                 }
05179             }
05180         }
05181       /* Highest power of T.  */
05182       nt = *p++;
05183       /* Cosine and sine coefficients.  */
05184       cu = *pl++;
05185       su = *pl++;
05186       for (ip = 0; ip < nt; ip++)
05187         {
05188           cu = cu * T + *pl++;
05189           su = su * T + *pl++;
05190         }
05191       sl += cu * cv + su * sv;
05192     }
05193   return (plan->trunclvl * sl);
05194 }
05195 
05196 
05197 /* geocentric moon, mean ecliptic and equinox of date
05198  * J is Julian Epemeris Date
05199  * output in pobj[]:
05200  * pobj[0]:  l in rad
05201  * pobj[1]:  b in rad
05202  * pobj[2]:  r in au
05203  */
05204 static int  gecmoon (double J, struct plantbl *lrtab, struct plantbl *lattab,  double pobj[])
05205 {
05206   double x;
05207 
05208   g2plan (J, lrtab, pobj, 0);
05209   x = pobj[0];
05210   x += LP_equinox;
05211   if (x < -6.45e5)
05212     x += 1.296e6;
05213   if (x > 6.45e5)
05214     x -= 1.296e6;
05215   pobj[0] = STR * x;
05216   x = g1plan (J, lattab);
05217   pobj[1] = STR * x;
05218   pobj[2] = (STR * pobj[2] + 1.0) * lrtab->distance;
05219   return 0;
05220 }
05221 
05222 /*********** end stephen moshier's moon code ****************/
05223 
05224 static void moon_fast (double mjd, double *lam, double *bet,
05225         double *hp, double *msp, double *mdp);
05226 
05227 /* previous version (elwood):
05228  *
05229  * given the mjd, find the geocentric ecliptic longitude, lam, and latitude,
05230  *   bet, and horizontal parallax, hp for the moon. also return the sun's
05231  *   mean anomaly, *msp, and the moon's mean anomaly, *mdp.
05232  * N.B. series for long and lat are good to about 10 and 3 arcseconds. however,
05233  *   math errors cause up to 100 and 30 arcseconds error, even if use double.
05234  *   why?? suspect highly sensitive nature of difference used to get m1..6.
05235  * N.B. still need to correct for nutation. then for topocentric location
05236  *   further correct for parallax and refraction.
05237  */
05238 static void moon_fast (double mjd, double *lam, double *bet,
05239         double *hp, double *msp, double *mdp)
05240 {
05241         double t, t2;
05242         double ld;
05243         double ms;
05244         double md;
05245         double de;
05246         double f;
05247         double n;
05248         double a, sa, sn, b, sb, c, sc, e, e2, l, g, w1, w2;
05249         double m1, m2, m3, m4, m5, m6;
05250 
05251         t = mjd/36525.;
05252         t2 = t*t;
05253 
05254         m1 = mjd/27.32158213;
05255         m1 = 360.0*(m1-(long)m1);
05256         m2 = mjd/365.2596407;
05257         m2 = 360.0*(m2-(long)m2);
05258         m3 = mjd/27.55455094;
05259         m3 = 360.0*(m3-(long)m3);
05260         m4 = mjd/29.53058868;
05261         m4 = 360.0*(m4-(long)m4);
05262         m5 = mjd/27.21222039;
05263         m5 = 360.0*(m5-(long)m5);
05264         m6 = mjd/6798.363307;
05265         m6 = 360.0*(m6-(long)m6);
05266 
05267         ld = 270.434164+m1-(.001133-.0000019*t)*t2;
05268         ms = 358.475833+m2-(.00015+.0000033*t)*t2;
05269         md = 296.104608+m3+(.009192+.0000144*t)*t2;
05270         de = 350.737486+m4-(.001436-.0000019*t)*t2;
05271         f = 11.250889+m5-(.003211+.0000003*t)*t2;
05272         n = 259.183275-m6+(.002078+.000022*t)*t2;
05273 
05274         a = degrad(51.2+20.2*t);
05275         sa = sin(a);
05276         sn = sin(degrad(n));
05277         b = 346.56+(132.87-.0091731*t)*t;
05278         sb = .003964*sin(degrad(b));
05279         c = degrad(n+275.05-2.3*t);
05280         sc = sin(c);
05281         ld = ld+.000233*sa+sb+.001964*sn;
05282         ms = ms-.001778*sa;
05283         md = md+.000817*sa+sb+.002541*sn;
05284         f = f+sb-.024691*sn-.004328*sc;
05285         de = de+.002011*sa+sb+.001964*sn;
05286         e = 1-(.002495+7.52e-06*t)*t;
05287         e2 = e*e;
05288 
05289         ld = degrad(ld);
05290         ms = degrad(ms);
05291         n = degrad(n);
05292         de = degrad(de);
05293         f = degrad(f);
05294         md = degrad(md);
05295 
05296         l = 6.28875*sin(md)+1.27402*sin(2*de-md)+.658309*sin(2*de)+
05297             .213616*sin(2*md)-e*.185596*sin(ms)-.114336*sin(2*f)+
05298             .058793*sin(2*(de-md))+.057212*e*sin(2*de-ms-md)+
05299             .05332*sin(2*de+md)+.045874*e*sin(2*de-ms)+.041024*e*sin(md-ms);
05300         l = l-.034718*sin(de)-e*.030465*sin(ms+md)+.015326*sin(2*(de-f))-
05301             .012528*sin(2*f+md)-.01098*sin(2*f-md)+.010674*sin(4*de-md)+
05302             .010034*sin(3*md)+.008548*sin(4*de-2*md)-e*.00791*sin(ms-md+2*de)-
05303             e*.006783*sin(2*de+ms);
05304         l = l+.005162*sin(md-de)+e*.005*sin(ms+de)+.003862*sin(4*de)+
05305             e*.004049*sin(md-ms+2*de)+.003996*sin(2*(md+de))+
05306             .003665*sin(2*de-3*md)+e*.002695*sin(2*md-ms)+
05307             .002602*sin(md-2*(f+de))+e*.002396*sin(2*(de-md)-ms)-
05308             .002349*sin(md+de);
05309         l = l+e2*.002249*sin(2*(de-ms))-e*.002125*sin(2*md+ms)-
05310             e2*.002079*sin(2*ms)+e2*.002059*sin(2*(de-ms)-md)-
05311             .001773*sin(md+2*(de-f))-.001595*sin(2*(f+de))+
05312             e*.00122*sin(4*de-ms-md)-.00111*sin(2*(md+f))+.000892*sin(md-3*de);
05313         l = l-e*.000811*sin(ms+md+2*de)+e*.000761*sin(4*de-ms-2*md)+
05314              e2*.000704*sin(md-2*(ms+de))+e*.000693*sin(ms-2*(md-de))+
05315              e*.000598*sin(2*(de-f)-ms)+.00055*sin(md+4*de)+.000538*sin(4*md)+
05316              e*.000521*sin(4*de-ms)+.000486*sin(2*md-de);
05317         l = l+e2*.000717*sin(md-2*ms);
05318         *lam = ld+degrad(l);
05319         range (lam, 2*PI);
05320 
05321         g = 5.12819*sin(f)+.280606*sin(md+f)+.277693*sin(md-f)+
05322             .173238*sin(2*de-f)+.055413*sin(2*de+f-md)+.046272*sin(2*de-f-md)+
05323             .032573*sin(2*de+f)+.017198*sin(2*md+f)+.009267*sin(2*de+md-f)+
05324             .008823*sin(2*md-f)+e*.008247*sin(2*de-ms-f);
05325         g = g+.004323*sin(2*(de-md)-f)+.0042*sin(2*de+f+md)+
05326             e*.003372*sin(f-ms-2*de)+e*.002472*sin(2*de+f-ms-md)+
05327             e*.002222*sin(2*de+f-ms)+e*.002072*sin(2*de-f-ms-md)+
05328             e*.001877*sin(f-ms+md)+.001828*sin(4*de-f-md)-e*.001803*sin(f+ms)-
05329             .00175*sin(3*f);
05330         g = g+e*.00157*sin(md-ms-f)-.001487*sin(f+de)-e*.001481*sin(f+ms+md)+
05331              e*.001417*sin(f-ms-md)+e*.00135*sin(f-ms)+.00133*sin(f-de)+
05332              .001106*sin(f+3*md)+.00102*sin(4*de-f)+.000833*sin(f+4*de-md)+
05333              .000781*sin(md-3*f)+.00067*sin(f+4*de-2*md);
05334         g = g+.000606*sin(2*de-3*f)+.000597*sin(2*(de+md)-f)+
05335             e*.000492*sin(2*de+md-ms-f)+.00045*sin(2*(md-de)-f)+
05336             .000439*sin(3*md-f)+.000423*sin(f+2*(de+md))+
05337             .000422*sin(2*de-f-3*md)-e*.000367*sin(ms+f+2*de-md)-
05338             e*.000353*sin(ms+f+2*de)+.000331*sin(f+4*de);
05339         g = g+e*.000317*sin(2*de+f-ms+md)+e2*.000306*sin(2*(de-ms)-f)-
05340             .000283*sin(md+3*f);
05341         w1 = .0004664*cos(n);
05342         w2 = .0000754*cos(c);
05343         *bet = degrad(g)*(1-w1-w2);
05344 
05345         *hp = .950724+.051818*cos(md)+.009531*cos(2*de-md)+.007843*cos(2*de)+
05346               .002824*cos(2*md)+.000857*cos(2*de+md)+e*.000533*cos(2*de-ms)+
05347               e*.000401*cos(2*de-md-ms)+e*.00032*cos(md-ms)-.000271*cos(de)-
05348               e*.000264*cos(ms+md)-.000198*cos(2*f-md);
05349         *hp = *hp+.000173*cos(3*md)+.000167*cos(4*de-md)-e*.000111*cos(ms)+
05350              .000103*cos(4*de-2*md)-.000084*cos(2*md-2*de)-
05351              e*.000083*cos(2*de+ms)+.000079*cos(2*de+2*md)+.000072*cos(4*de)+
05352              e*.000064*cos(2*de-ms+md)-e*.000063*cos(2*de+ms-md)+
05353              e*.000041*cos(ms+de);
05354         *hp = *hp+e*.000035*cos(2*md-ms)-.000033*cos(3*md-2*de)-
05355              .00003*cos(md+de)-.000029*cos(2*(f-de))-e*.000029*cos(2*md+ms)+
05356              e2*.000026*cos(2*(de-ms))-.000023*cos(2*(f-de)+md)+
05357              e*.000019*cos(4*de-ms-md);
05358         *hp = degrad(*hp);
05359 
05360         *msp = ms;
05361         *mdp = md;
05362 }
05363 
05364 
05365 #define EarthRadius 6378.16             /* Kilometers           */
05366 
05367 /* moon() - front end rountine to get moon position; stern
05368  *
05369  * given the mjd, find the geocentric ecliptic longitude, lam, and latitude,
05370  *   bet, and geocentric distance, rho in a.u. for the moon.  also return
05371  *   the sun's mean anomaly, *msp, and the moon's mean anomaly, *mdp.
05372  *
05373  * now uses Stephen Moshier's expansion and code.
05374  *
05375  * TODO: - clarify lunar aberration for apparent places
05376  * 
05377  * still need to correct for nutation. then for topocentric location
05378  *   further correct for parallax and refraction.
05379  * NB:  Do NOT correct for aberration - the geocentric moon frame moves
05380  *      along with the earth.
05381  */
05382 
05383  void moon (double mjd, double *lam, double *bet, double *rho, double *msp, double *mdp)
05384 {
05385         double pobj[3], dt;
05386         double hp;
05387 
05388         if (mjd >= MOSHIER_BEGIN && mjd <= MOSHIER_END) {
05389                 /* retard for light time */
05390                 moon_fast (mjd, lam, bet, &hp, msp, mdp);
05391                 *rho = EarthRadius/AUKM/sin(hp);
05392                 dt = *rho * 5.7755183e-3;       /* speed of light in a.u/day */
05393                 gecmoon(mjd + MJD0 - dt, &moonlr, &moonlat, pobj);
05394 
05395                 *lam = pobj[0];
05396                 range (lam, 2*PI);
05397                 *bet = pobj[1];
05398                 *rho = pobj[2];
05399                 *msp = STR * Args[11];  /* don't need range correction here */
05400                 *mdp = STR * Args[12];
05401         } else {
05402                 moon_fast (mjd, lam, bet, &hp, msp, mdp);
05403                 *rho = EarthRadius/AUKM/sin(hp);
05404 
05405         }
05406 }
05407 
05408 #define NUT_SCALE       1e4
05409 #define NUT_SERIES      106
05410 #define NUT_MAXMUL      4
05411 #define SECPERCIRC      (3600.*360.)
05412 
05413 /* Delaunay arguments, in arc seconds; they differ slightly from ELP82B */
05414 static double delaunay[5][4] = {
05415     {485866.733,  1717915922.633, 31.310,  0.064}, /* M', moon mean anom */
05416     {1287099.804, 129596581.224,  -0.577, -0.012}, /* M, sun mean anom */
05417     {335778.877,  1739527263.137, -13.257, 0.011}, /* F, moon arg lat */
05418     {1072261.307, 1602961601.328, -6.891,  0.019}, /* D, elong moon sun */
05419     {450160.280,  -6962890.539,   7.455,   0.008}, /* Om, moon l asc node */
05420 };
05421 
05422 /* multipliers for Delaunay arguments */
05423 static short multarg[NUT_SERIES][5] = {
05424         /* bounds:  -2..3, -2..2, -2/0/2/4, -4..4, 0..2 */
05425     {0, 0, 0, 0, 1},
05426     {0, 0, 0, 0, 2},
05427     {-2, 0, 2, 0, 1},
05428     {2, 0, -2, 0, 0},
05429     {-2, 0, 2, 0, 2},
05430     {1, -1, 0, -1, 0},
05431     {0, -2, 2, -2, 1},
05432     {2, 0, -2, 0, 1},
05433     {0, 0, 2, -2, 2},
05434     {0, 1, 0, 0, 0},
05435     {0, 1, 2, -2, 2},
05436     {0, -1, 2, -2, 2},
05437     {0, 0, 2, -2, 1},
05438     {2, 0, 0, -2, 0},
05439     {0, 0, 2, -2, 0},
05440     {0, 2, 0, 0, 0},
05441     {0, 1, 0, 0, 1},
05442     {0, 2, 2, -2, 2},
05443     {0, -1, 0, 0, 1},
05444     {-2, 0, 0, 2, 1},
05445     {0, -1, 2, -2, 1},
05446     {2, 0, 0, -2, 1},
05447     {0, 1, 2, -2, 1},
05448     {1, 0, 0, -1, 0},
05449     {2, 1, 0, -2, 0},
05450     {0, 0, -2, 2, 1},
05451     {0, 1, -2, 2, 0},
05452     {0, 1, 0, 0, 2},
05453     {-1, 0, 0, 1, 1},
05454     {0, 1, 2, -2, 0},
05455     {0, 0, 2, 0, 2},
05456     {1, 0, 0, 0, 0},
05457     {0, 0, 2, 0, 1},
05458     {1, 0, 2, 0, 2},
05459     {1, 0, 0, -2, 0},
05460     {-1, 0, 2, 0, 2},
05461     {0, 0, 0, 2, 0},
05462     {1, 0, 0, 0, 1},
05463     {-1, 0, 0, 0, 1},
05464     {-1, 0, 2, 2, 2},
05465     {1, 0, 2, 0, 1},
05466     {0, 0, 2, 2, 2},
05467     {2, 0, 0, 0, 0},
05468     {1, 0, 2, -2, 2},
05469     {2, 0, 2, 0, 2},
05470     {0, 0, 2, 0, 0},
05471     {-1, 0, 2, 0, 1},
05472     {-1, 0, 0, 2, 1},
05473     {1, 0, 0, -2, 1},
05474     {-1, 0, 2, 2, 1},
05475     {1, 1, 0, -2, 0},
05476     {0, 1, 2, 0, 2},
05477     {0, -1, 2, 0, 2},
05478     {1, 0, 2, 2, 2},
05479     {1, 0, 0, 2, 0},
05480     {2, 0, 2, -2, 2},
05481     {0, 0, 0, 2, 1},
05482     {0, 0, 2, 2, 1},
05483     {1, 0, 2, -2, 1},
05484     {0, 0, 0, -2, 1},
05485     {1, -1, 0, 0, 0},
05486     {2, 0, 2, 0, 1},
05487     {0, 1, 0, -2, 0},
05488     {1, 0, -2, 0, 0},
05489     {0, 0, 0, 1, 0},
05490     {1, 1, 0, 0, 0},
05491     {1, 0, 2, 0, 0},
05492     {1, -1, 2, 0, 2},
05493     {-1, -1, 2, 2, 2},
05494     {-2, 0, 0, 0, 1},
05495     {3, 0, 2, 0, 2},
05496     {0, -1, 2, 2, 2},
05497     {1, 1, 2, 0, 2},
05498     {-1, 0, 2, -2, 1},
05499     {2, 0, 0, 0, 1},
05500     {1, 0, 0, 0, 2},
05501     {3, 0, 0, 0, 0},
05502     {0, 0, 2, 1, 2},
05503     {-1, 0, 0, 0, 2},
05504     {1, 0, 0, -4, 0},
05505     {-2, 0, 2, 2, 2},
05506     {-1, 0, 2, 4, 2},
05507     {2, 0, 0, -4, 0},
05508     {1, 1, 2, -2, 2},
05509     {1, 0, 2, 2, 1},
05510     {-2, 0, 2, 4, 2},
05511     {-1, 0, 4, 0, 2},
05512     {1, -1, 0, -2, 0},
05513     {2, 0, 2, -2, 1},
05514     {2, 0, 2, 2, 2},
05515     {1, 0, 0, 2, 1},
05516     {0, 0, 4, -2, 2},
05517     {3, 0, 2, -2, 2},
05518     {1, 0, 2, -2, 0},
05519     {0, 1, 2, 0, 1},
05520     {-1, -1, 0, 2, 1},
05521     {0, 0, -2, 0, 1},
05522     {0, 0, 2, -1, 2},
05523     {0, 1, 0, 2, 0},
05524     {1, 0, -2, -2, 0},
05525     {0, -1, 2, 0, 1},
05526     {1, 1, 0, -2, 1},
05527     {1, 0, -2, 2, 0},
05528     {2, 0, 0, 2, 0},
05529     {0, 0, 2, 4, 2},
05530     {0, 1, 0, 1, 0}
05531 };
05532 
05533 /* amplitudes which  have secular terms; in 1/NUT_SCALE arc seconds
05534  * {index, constant dPSI, T/10 in dPSI, constant in dEPS, T/10 in dEPS}
05535  */
05536 static long ampsecul[][5] = {
05537     {0  ,-171996 ,-1742 ,92025 ,89},
05538     {1  ,2062    ,2     ,-895  ,5},
05539     {8  ,-13187  ,-16   ,5736  ,-31},
05540     {9  ,1426    ,-34   ,54    ,-1},
05541     {10 ,-517    ,12    ,224   ,-6},
05542     {11 ,217     ,-5    ,-95   ,3},
05543     {12 ,129     ,1     ,-70   ,0},
05544     {15 ,17      ,-1    ,0     ,0},
05545     {17 ,-16     ,1     ,7     ,0},
05546     {30 ,-2274   ,-2    ,977   ,-5},
05547     {31 ,712     ,1     ,-7    ,0},
05548     {32 ,-386    ,-4    ,200   ,0},
05549     {33 ,-301    ,0     ,129   ,-1},
05550     {37 ,63      ,1     ,-33   ,0},
05551     {38 ,-58     ,-1    ,32    ,0},
05552     /* termination */  { -1, }
05553 };
05554 
05555 /* amplitudes which only have constant terms; same unit as above
05556  * {dPSI, dEPS}
05557  * indexes which are already in ampsecul[][] are zeroed
05558  */
05559 static short ampconst[NUT_SERIES][2] = {
05560     {0,0},
05561     {0,0},
05562     {46,-24},
05563     {11,0},
05564     {-3,1},
05565     {-3,0},
05566     {-2,1},
05567     {1,0},
05568     {0,0},
05569     {0,0},
05570     {0,0},
05571     {0,0},
05572     {0,0},
05573     {48,1},
05574     {-22,0},
05575     {0,0},
05576     {-15,9},
05577     {0,0},
05578     {-12,6},
05579     {-6,3},
05580     {-5,3},
05581     {4,-2},
05582     {4,-2},
05583     {-4,0},
05584     {1,0},
05585     {1,0},
05586     {-1,0},
05587     {1,0},
05588     {1,0},
05589     {-1,0},
05590     {0,0},
05591     {0,0},
05592     {0,0},
05593     {0,0},
05594     {-158,-1},
05595     {123,-53},
05596     {63,-2},
05597     {0,0},
05598     {0,0},
05599     {-59,26},
05600     {-51,27},
05601     {-38,16},
05602     {29,-1},
05603     {29,-12},
05604     {-31,13},
05605     {26,-1},
05606     {21,-10},
05607     {16,-8},
05608     {-13,7},
05609     {-10,5},
05610     {-7,0},
05611     {7,-3},
05612     {-7,3},
05613     {-8,3},
05614     {6,0},
05615     {6,-3},
05616     {-6,3},
05617     {-7,3},
05618     {6,-3},
05619     {-5,3},
05620     {5,0},
05621     {-5,3},
05622     {-4,0},
05623     {4,0},
05624     {-4,0},
05625     {-3,0},
05626     {3,0},
05627     {-3,1},
05628     {-3,1},
05629     {-2,1},
05630     {-3,1},
05631     {-3,1},
05632     {2,-1},
05633     {-2,1},
05634     {2,-1},
05635     {-2,1},
05636     {2,0},
05637     {2,-1},
05638     {1,-1},
05639     {-1,0},
05640     {1,-1},
05641     {-2,1},
05642     {-1,0},
05643     {1,-1},
05644     {-1,1},
05645     {-1,1},
05646     {1,0},
05647     {1,0},
05648     {1,-1},
05649     {-1,0},
05650     {-1,0},
05651     {1,0},
05652     {1,0},
05653     {-1,0},
05654     {1,0},
05655     {1,0},
05656     {-1,0},
05657     {-1,0},
05658     {-1,0},
05659     {-1,0},
05660     {-1,0},
05661     {-1,0},
05662     {-1,0},
05663     {1,0},
05664     {-1,0},
05665     {1,0}
05666 };
05667 
05668 /* given the modified JD, mjd, find the nutation in obliquity, *deps, and
05669  * the nutation in longitude, *dpsi, each in radians.
05670  */
05671 void nutation (double mjd, double *deps, double *dpsi)
05672 /*double mjd;
05673 double *deps;    on input:  precision parameter in arc seconds 
05674 double *dpsi;*/
05675 {
05676         static double lastmjd = -10000, lastdeps, lastdpsi;
05677         double T, T2, T3, T10;                  /* jul cent since J2000 */
05678         double prec;                            /* series precis in arc sec */
05679         int i, isecul;                          /* index in term table */
05680         static double delcache[5][2*NUT_MAXMUL+1];
05681                         /* cache for multiples of delaunay args
05682                          * [M',M,F,D,Om][-min*x, .. , 0, .., max*x]
05683                          * make static to have unfilled fields cleared on init
05684                          */
05685 
05686         if (mjd == lastmjd) {
05687             *deps = lastdeps;
05688             *dpsi = lastdpsi;
05689             return;
05690         }
05691 
05692         prec = 0.0;
05693 
05694 #if 0   /* this is if deps should contain a precision value */
05695         prec =* deps;
05696         if (prec < 0.0 || prec > 1.0)   /* accept only sane value */
05697                 prec = 1.0;
05698 #endif
05699 
05700         /* augment for abundance of small terms */
05701         prec *= NUT_SCALE/10;
05702 
05703         T = (mjd - J2000)/36525.;
05704         T2 = T * T;
05705         T3 = T2 * T;
05706         T10 = T/10.;
05707 
05708         /* calculate delaunay args and place in cache */
05709         for (i = 0; i < 5; ++i) {
05710             double x;
05711             short j;
05712 
05713             x = delaunay[i][0] +
05714                 delaunay[i][1] * T +
05715                 delaunay[i][2] * T2 +
05716                 delaunay[i][3] * T3;
05717 
05718             /* convert to radians */
05719             x /= SECPERCIRC;
05720             x -= floor(x);
05721             x *= 2.*PI;
05722 
05723             /* fill cache table */
05724             for (j = 0; j <= 2*NUT_MAXMUL; ++j)
05725                 delcache[i][j] = (j - NUT_MAXMUL) * x;
05726         }
05727 
05728         /* find dpsi and deps */
05729         lastdpsi = lastdeps = 0.;
05730         for (i = isecul = 0; i < NUT_SERIES ; ++i) {
05731             double arg = 0., ampsin, ampcos;
05732             short j;
05733 
05734             if (ampconst[i][0] || ampconst[i][1]) {
05735                 /* take non-secular terms from simple array */
05736                 ampsin = ampconst[i][0];
05737                 ampcos = ampconst[i][1];
05738             } else {
05739                 /* secular terms from different array */
05740                 ampsin = ampsecul[isecul][1] + ampsecul[isecul][2] * T10;
05741                 ampcos = ampsecul[isecul][3] + ampsecul[isecul][4] * T10;
05742                 ++isecul;
05743             }
05744 
05745             for (j = 0; j < 5; ++j)
05746                 arg += delcache[j][NUT_MAXMUL + multarg[i][j]];
05747 
05748             if (fabs(ampsin) >= prec)
05749                 lastdpsi += ampsin * sin(arg);
05750 
05751             if (fabs(ampcos) >= prec)
05752                 lastdeps += ampcos * cos(arg);
05753 
05754         }
05755 
05756         /* convert to radians.
05757          */
05758         lastdpsi = degrad(lastdpsi/3600./NUT_SCALE);
05759         lastdeps = degrad(lastdeps/3600./NUT_SCALE);
05760 
05761         lastmjd = mjd;
05762         *deps = lastdeps;
05763         *dpsi = lastdpsi;
05764 }
05765 
05766 /* given the modified JD, mjd, correct, IN PLACE, the right ascension *ra
05767  * and declination *dec (both in radians) for nutation.
05768  */
05769 void nut_eq (double mjd, double *ra, double *dec)
05770 {
05771         static double lastmjd = -10000;
05772         static double a[3][3];          /* rotation matrix */
05773         double xold, yold, zold, x, y, z;
05774 
05775         if (mjd != lastmjd) {
05776             double epsilon, dpsi, deps;
05777             double se, ce, sp, cp, sede, cede;
05778 
05779             obliquity(mjd, &epsilon);
05780             nutation(mjd, &deps, &dpsi);
05781 
05782             /* the rotation matrix a applies the nutation correction to
05783              * a vector of equatoreal coordinates Xeq to Xeq' by 3 subsequent
05784              * rotations:  R1 - from equatoreal to ecliptic system by
05785              * rotation of angle epsilon about x, R2 - rotate ecliptic
05786              * system by -dpsi about its z, R3 - from ecliptic to equatoreal
05787              * by rotation of angle -(epsilon + deps)
05788              *
05789              *  Xeq' = A * Xeq = R3 * R2 * R1 * Xeq
05790              * 
05791              *          [ 1       0          0    ]
05792              * R1 =     [ 0   cos(eps)   sin(eps) ]
05793              *          [ 0  - sin(eps)  cos(eps) ]
05794              * 
05795              *          [ cos(dpsi)  - sin(dpsi)  0 ]
05796              * R2 =     [ sin(dpsi)   cos(dpsi)   0 ]
05797              *          [      0           0      1 ]
05798              * 
05799              *          [ 1         0                 0         ]
05800              * R3 =     [ 0  cos(eps + deps)  - sin(eps + deps) ]
05801              *          [ 0  sin(eps + deps)   cos(eps + deps)  ]
05802              * 
05803              * for efficiency, here is a explicitely:
05804              */
05805             
05806             se = sin(epsilon);
05807             ce = cos(epsilon);
05808             sp = sin(dpsi);
05809             cp = cos(dpsi);
05810             sede = sin(epsilon + deps);
05811             cede = cos(epsilon + deps);
05812 
05813             a[0][0] = cp;
05814             a[0][1] = -sp*ce;
05815             a[0][2] = -sp*se;
05816 
05817             a[1][0] = cede*sp;
05818             a[1][1] = cede*cp*ce+sede*se;
05819             a[1][2] = cede*cp*se-sede*ce;
05820 
05821             a[2][0] = sede*sp;
05822             a[2][1] = sede*cp*ce-cede*se;
05823             a[2][2] = sede*cp*se+cede*ce;
05824 
05825             lastmjd = mjd;
05826         }
05827 
05828         sphcart(*ra, *dec, 1.0, &xold, &yold, &zold);
05829         x = a[0][0] * xold + a[0][1] * yold + a[0][2] * zold;
05830         y = a[1][0] * xold + a[1][1] * yold + a[1][2] * zold;
05831         z = a[2][0] * xold + a[2][1] * yold + a[2][2] * zold;
05832         cartsph(x, y, z, ra, dec, &zold);       /* radius should be 1.0 */
05833         if (*ra < 0.) *ra += 2.*PI;             /* make positive for display */
05834 }
05835 
05836 void ta_par (double tha, double tdec, double phi, double ht, double *rho, double *aha, double *adec)
05837 {
05838         static double last_phi = 1000.0, last_ht = -1000.0, xobs, zobs;
05839         double x, y, z; /* obj cartesian coord, in Earth radii */
05840 
05841         /* avoid calcs involving the same phi and ht */
05842         if (phi != last_phi || ht != last_ht) {
05843             double cphi, sphi, robs, e2 = (2 - 1/298.257)/298.257;
05844             cphi = cos(phi);
05845             sphi = sin(phi);
05846             robs = 1/sqrt(1 - e2 * sphi * sphi);
05847 
05848             /* observer coordinates: x to meridian, y east, z north */
05849             xobs = (robs + ht) * cphi;
05850             zobs = (robs*(1-e2) + ht) * sphi;
05851             last_phi  =  phi;
05852             last_ht  =  ht;
05853         }
05854 
05855         sphcart(-tha, tdec, *rho, &x, &y, &z);
05856         cartsph(x - xobs, y, z - zobs, aha, adec, rho);
05857         *aha *= -1;
05858         range (aha, 2*PI);
05859 }
05860 
05861 static void elongation (double lam, double bet, double lsn, double *el);
05862 static void unrefractLT15 (double pr, double tr, double aa, double *ta);
05863 static void unrefractGE15 (double pr, double tr, double aa, double *ta);
05864 
05865 void unrefract (double pr, double tr, double aa, double *ta)
05866 {
05867 #define LTLIM   14.5
05868 #define GELIM   15.5
05869 
05870         double aadeg = raddeg(aa);
05871 
05872         if (aadeg < LTLIM)
05873             unrefractLT15 (pr, tr, aa, ta);
05874         else if (aadeg >= GELIM)
05875             unrefractGE15 (pr, tr, aa, ta);
05876         else {
05877             /* smooth blend -- important for inverse */
05878             double taLT, taGE, p;
05879 
05880             unrefractLT15 (pr, tr, aa, &taLT);
05881             unrefractGE15 (pr, tr, aa, &taGE);
05882             p = (aadeg - LTLIM)/(GELIM - LTLIM);
05883             *ta = taLT + (taGE - taLT)*p;
05884         }
05885             
05886 }
05887 
05888 static void unrefractGE15 (double pr, double tr, double aa, double *ta)
05889 {
05890         double r;
05891         
05892         r = 7.888888e-5*pr/((273+tr)*tan(aa));
05893         *ta  =  aa - r;
05894 }
05895 
05896 static void unrefractLT15 (double pr, double tr, double aa, double *ta)
05897 {
05898         double aadeg = raddeg(aa);
05899         double r, a, b;
05900 
05901         a = ((2e-5*aadeg+1.96e-2)*aadeg+1.594e-1)*pr;
05902         b = (273+tr)*((8.45e-2*aadeg+5.05e-1)*aadeg+1);
05903         r = degrad(a/b);
05904 
05905         *ta  =  aa - r;
05906 }
05907 
05908 /* correct the true altitude, ta, for refraction to the apparent altitude, aa,
05909  * each in radians, given the local atmospheric pressure, pr, in mbars, and
05910  * the temperature, tr, in degrees C.
05911  */
05912 /* correct the true altitude, ta, for refraction to the apparent altitude, aa,
05913  * each in radians, given the local atmospheric pressure, pr, in mbars, and
05914  * the temperature, tr, in degrees C.
05915  */
05916 void refract (double pr,double tr, double ta,double *aa)
05917 {
05918 #define MAXRERR degrad(0.1/3600.)       /* desired accuracy, rads */
05919 
05920         double d, t, t0, a;
05921 
05922         /* first guess of error is to go backwards.
05923          * make use that we know delta-apparent is always < delta-true.
05924          */
05925         unrefract (pr, tr, ta, &t);
05926         d = 0.8*(ta - t);
05927         t0 = t;
05928         a = ta;
05929 
05930         /* use secant method to discover a value that unrefracts to ta.
05931          * max=7 ave=2.4 loops in hundreds of test cases.
05932          */
05933         do {
05934             a += d;
05935             unrefract (pr, tr, a, &t);
05936             d *= -(ta - t)/(t0 - t);
05937             t0 = t;
05938         } while (fabs(ta-t) > MAXRERR);
05939 
05940         *aa = a;
05941 
05942 #undef  MAXRERR
05943 }
05944 
05945 #define ABERR_CONST     (20.49552/3600./180.*PI)  /* aberr const in rad */
05946 #define AB_ECL_EOD      0
05947 #define AB_EQ_EOD       1
05948 
05949 static void ab_aux (double mjd, double *x, double *y, double lsn,int mode);
05950 
05951 /* apply aberration correction to ecliptical coordinates *lam and *bet
05952  * (in radians) for a given time mjd and handily supplied longitude of sun,
05953  * lsn (in radians)
05954  */
05955 
05956 void ab_ecl (double mjd, double lsn, double *lam, double *bet)
05957 {
05958         ab_aux(mjd, lam, bet, lsn, AB_ECL_EOD);
05959 }
05960 
05961 /* apply aberration correction to equatoreal coordinates *ra and *dec
05962  * (in radians) for a given time mjd and handily supplied longitude of sun,
05963  * lsn (in radians)
05964  */
05965 void ab_eq (double mjd, double lsn, double *ra, double *dec)
05966 {
05967         ab_aux(mjd, ra, dec, lsn, AB_EQ_EOD);
05968 }
05969 
05970 /* because the e-terms are secular, keep the real transformation for both
05971  * coordinate systems in here with the secular variables cached.
05972  * mode == AB_ECL_EOD:  x = lam, y = bet        (ecliptical)
05973  * mode == AB_EQ_EOD:   x = ra,  y = dec        (equatoreal)
05974  */
05975 static void ab_aux (double mjd, double *x, double *y, double lsn, int mode)
05976 {
05977         static double lastmjd = -10000;
05978         static double eexc;     /* earth orbit excentricity */
05979         static double leperi;   /* ... and longitude of perihelion */
05980         static char dirty = 1;  /* flag for cached trig terms */
05981 
05982         if (mjd != lastmjd) {
05983             double T;           /* centuries since J2000 */
05984 
05985             T = (mjd - J2000)/36525.;
05986             eexc = 0.016708617 - (42.037e-6 + 0.1236e-6 * T) * T;
05987             leperi = degrad(102.93735 + (0.71953 + 0.00046 * T) * T);
05988             lastmjd = mjd;
05989             dirty = 1;
05990         }
05991 
05992         switch (mode) {
05993         case AB_ECL_EOD:                /* ecliptical coords */
05994             {
05995                 double *lam = x, *bet = y;
05996                 double dlsun, dlperi;
05997 
05998                 dlsun = lsn - *lam;
05999                 dlperi = leperi - *lam;
06000 
06001                 /* valid only for *bet != +-PI/2 */
06002                 *lam -= ABERR_CONST/cos(*bet) * (cos(dlsun) -
06003                                 eexc*cos(dlperi));
06004                 *bet -= ABERR_CONST*sin(*bet) * (sin(dlsun) -
06005                                 eexc*sin(dlperi));
06006             }
06007             break;
06008 
06009         case AB_EQ_EOD:                 /* equatoreal coords */
06010             {
06011                 double *ra = x, *dec = y;
06012                 double sr, cr, sd, cd, sls, cls;/* trig values coords */
06013                 static double cp, sp, ce, se;   /* .. and perihel/eclipic */
06014                 double dra, ddec;               /* changes in ra and dec */
06015 
06016                 if (dirty) {
06017                     double eps;
06018 
06019                     cp = cos(leperi);
06020                     sp = sin(leperi);
06021                     obliquity(mjd, &eps);
06022                     se = sin(eps);
06023                     ce = cos(eps);
06024                     dirty = 0;
06025                 }
06026 
06027                 sr = sin(*ra);
06028                 cr = cos(*ra);
06029                 sd = sin(*dec);
06030                 cd = cos(*dec);
06031                 sls = sin(lsn);
06032                 cls = cos(lsn);
06033 
06034                 dra = ABERR_CONST/cd * ( -(cr * cls * ce + sr * sls) +
06035                             eexc * (cr * cp * ce + sr * sp));
06036 
06037                 ddec = se/ce * cd - sr * sd;    /* tmp use */
06038                 ddec = ABERR_CONST * ( -(cls * ce * ddec + cr * sd * sls) +
06039                             eexc * (cp * ce * ddec + cr * sd * sp) );
06040                 
06041                 *ra += dra;
06042                 range (ra, 2*PI);
06043                 *dec += ddec;
06044             }
06045             break;
06046 
06047         default:
06048             //printf ("ab_aux: bad mode: %d\n", mode);
06049             //exit (1);
06050             break;
06051 
06052         } /* switch (mode) */
06053 }
06054 
06055 
06056 
06057 
06058 
06059 
06060 static void ecleq_aux (int sw, double mjd, double x, double y,
06061     double *p, double *q);
06062 
06063 #define EQtoECL 1
06064 #define ECLtoEQ (-1)
06065 
06066 
06067 /* given the modified Julian date, mjd, and an equitorial ra and dec, each in
06068  * radians, find the corresponding geocentric ecliptic latitude, *lat, and
06069  * longititude, *lng, also each in radians.
06070  * correction for the effect on the angle of the obliquity due to nutation is
06071  * not included.
06072  */
06073 void eq_ecl (double mjd, double ra, double dec, double *lat, double *lng)
06074 {
06075         ecleq_aux (EQtoECL, mjd, ra, dec, lng, lat);
06076 }
06077 
06078 /* given the modified Julian date, mjd, and a geocentric ecliptic latitude,
06079  * *lat, and longititude, *lng, each in radians, find the corresponding
06080  * equitorial ra and dec, also each in radians.
06081  * correction for the effect on the angle of the obliquity due to nutation is
06082  * not included.
06083  */
06084 void ecl_eq (double mjd, double lat, double lng, double *ra, double *dec)
06085 {
06086         ecleq_aux (ECLtoEQ, mjd, lng, lat, ra, dec);
06087 }
06088 
06089 static void ecleq_aux (int sw, double mjd, double x, double y, double *p,double *q)
06090 /*
06091 int sw;          +1 for eq to ecliptic, -1 for vv. 
06092 double mjd;
06093 double x, y;             sw==1: x==ra, y==dec.  sw==-1: x==lng, y==lat. 
06094 double *p, *q;           sw==1: p==lng, q==lat. sw==-1: p==ra, q==dec. */
06095 {
06096         static double lastmjd = -10000; /* last mjd calculated */
06097         static double seps, ceps;       /* sin and cos of mean obliquity */
06098         double sx, cx, sy, cy, ty;
06099 
06100         if (mjd != lastmjd) {
06101             double eps;
06102             obliquity (mjd, &eps);              /* mean obliquity for date */
06103             seps = sin(eps);
06104             ceps = cos(eps);
06105             lastmjd = mjd;
06106         }
06107 
06108         sy = sin(y);
06109         cy = cos(y);                            /* always non-negative */
06110         if (fabs(cy)<1e-20) cy = 1e-20;         /* insure > 0 */
06111         ty = sy/cy;
06112         cx = cos(x);
06113         sx = sin(x);
06114         *q = asin((sy*ceps)-(cy*seps*sx*sw));
06115         *p = atan(((sx*ceps)+(ty*seps*sw))/cx);
06116         if (cx<0) *p += PI;             /* account for atan quad ambiguity */
06117         range (p, 2*PI);
06118 }
06119 
06120 double geoc_lat (double phi);
06121 static void aaha_aux (double lat, double x, double y, double *p, double *q);
06122 
06123 /* given geographical latitude (n+, radians), lat, altitude (up+, radians),
06124  * alt, and azimuth (angle round to the east from north+, radians),
06125  * return hour angle (radians), ha, and declination (radians), dec.
06126  */
06127 void aa_hadec (double lat, double alt,double  az, double *ha, double *dec)
06128 {
06129         aaha_aux (lat, az, alt, ha, dec);
06130         if (*ha > PI)
06131             *ha -= 2*PI;
06132 }
06133 
06134 /* given geographical (n+, radians), lat, hour angle (radians), ha, and
06135  * declination (radians), dec, return altitude (up+, radians), alt, and
06136  * azimuth (angle round to the east from north+, radians),
06137  */
06138 void hadec_aa (double lat, double ha, double dec, double *alt, double *az)
06139 {
06140         aaha_aux (lat, ha, dec, az, alt);
06141 }
06142 
06143 #ifdef NEED_GEOC
06144 /* given a geographic (surface-normal) latitude, phi, return the geocentric
06145  * latitude, psi.
06146  */
06147 double geoc_lat (double phi)
06148 {
06149 #define MAXLAT  degrad(89.9999) /* avoid tan() greater than this */
06150         return (fabs(phi)>MAXLAT ? phi : atan(tan(phi)/1.00674));
06151 }
06152 #endif
06153 
06154 /* the actual formula is the same for both transformation directions so
06155  * do it here once for each way.
06156  * N.B. all arguments are in radians.
06157  */
06158 static void aaha_aux (double lat, double x, double y, double *p, double *q)
06159 /*double lat;
06160 double x, y;
06161 double *p, *q;*/
06162 {
06163         static double last_lat = -3434, slat, clat;
06164         double cap, B;
06165 
06166         if (lat != last_lat) {
06167             slat = sin(lat);
06168             clat = cos(lat);
06169             last_lat = lat;
06170         }
06171 
06172         solve_sphere (-x, PI/2-y, slat, clat, &cap, &B);
06173         *p = B;
06174         *q = PI/2 - acos(cap);
06175 }
06176 
06177 /* solve a spherical triangle:
06178  *           A
06179  *          /  \
06180  *         /    \
06181  *      c /      \ b
06182  *       /        \
06183  *      /          \
06184  *    B ____________ C
06185  *           a
06186  *
06187  * given A, b, c find B and a in range 0..B..2PI and 0..a..PI, respectively..
06188  * cap and Bp may be NULL if not interested in either one.
06189  * N.B. we pass in cos(c) and sin(c) because in many problems one of the sides
06190  *   remains constant for many values of A and b.
06191  */
06192 void solve_sphere (double A, double b, double cc, double sc, double *cap, double *Bp)
06193 {
06194         double cb = cos(b), sb = sin(b);
06195         double cA = cos(A);
06196         double ca;
06197         double B;
06198 
06199         ca = cb*cc + sb*sc*cA;
06200         if (ca >  1.0) ca =  1.0;
06201         if (ca < -1.0) ca = -1.0;
06202         if (cap)
06203             *cap = ca;
06204 
06205         if (!Bp)
06206             return;
06207 
06208         if (cc > .99999) {
06209             /* as c approaches 0, B approaches pi - A */
06210             B = PI - A;
06211         } else if (cc < -.99999) {
06212             /* as c approaches PI, B approaches A */
06213             B = A;
06214         } else {
06215             /* compute cB and sB and remove common factor of sa from quotient.
06216              * be careful where B causes atan to blow.
06217              */
06218             double sA = sin(A);
06219             double x, y;
06220 
06221             y = sA*sb*sc;
06222             x = cb - ca*cc;
06223         
06224             if (fabs(x) < 1e-5)
06225                 B = y < 0 ? 3*PI/2 : PI/2;
06226             else
06227                 B = atan2 (y, x);
06228         }
06229 
06230         *Bp = B;
06231         range (Bp, 2*PI);
06232 }
06233 
06234 
06235 #define TABSTART 1620.0
06236 #define TABEND 2004.0
06237 #define TABSIZ 385
06238 
06239 /* Note, Stephenson and Morrison's table starts at the year 1630.
06240  * The Chapronts' table does not agree with the Almanac prior to 1630.
06241  * The actual accuracy decreases rapidly prior to 1780.
06242  */
06243 static short dt[TABSIZ] = {
06244     /* 1620.0 thru 1659.0 */
06245     12400, 11900, 11500, 11000, 10600, 10200, 9800, 9500, 9100, 8800,
06246     8500, 8200, 7900, 7700, 7400, 7200, 7000, 6700, 6500, 6300,
06247     6200, 6000, 5800, 5700, 5500, 5400, 5300, 5100, 5000, 4900,
06248     4800, 4700, 4600, 4500, 4400, 4300, 4200, 4100, 4000, 3800,
06249     /* 1660.0 thru 1699.0 */
06250     3700, 3600, 3500, 3400, 3300, 3200, 3100, 3000, 2800, 2700,
06251     2600, 2500, 2400, 2300, 2200, 2100, 2000, 1900, 1800, 1700,
06252     1600, 1500, 1400, 1400, 1300, 1200, 1200, 1100, 1100, 1000,
06253     1000, 1000, 900, 900, 900, 900, 900, 900, 900, 900,
06254     /* 1700.0 thru 1739.0 */
06255     900, 900, 900, 900, 900, 900, 900, 900, 1000, 1000,
06256     1000, 1000, 1000, 1000, 1000, 1000, 1000, 1100, 1100, 1100,
06257     1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100,
06258     1100, 1100, 1100, 1100, 1200, 1200, 1200, 1200, 1200, 1200,
06259     /* 1740.0 thru 1779.0 */
06260     1200, 1200, 1200, 1200, 1300, 1300, 1300, 1300, 1300, 1300,
06261     1300, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1500, 1500,
06262     1500, 1500, 1500, 1500, 1500, 1600, 1600, 1600, 1600, 1600,
06263     1600, 1600, 1600, 1600, 1600, 1700, 1700, 1700, 1700, 1700,
06264     /* 1780.0 thru 1799.0 */
06265     1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700,
06266     1700, 1700, 1600, 1600, 1600, 1600, 1500, 1500, 1400, 1400,
06267     /* 1800.0 thru 1819.0 */
06268     1370, 1340, 1310, 1290, 1270, 1260, 1250, 1250, 1250, 1250,
06269     1250, 1250, 1250, 1250, 1250, 1250, 1250, 1240, 1230, 1220,
06270     /* 1820.0 thru 1859.0 */
06271     1200, 1170, 1140, 1110, 1060, 1020, 960, 910, 860, 800,
06272     750, 700, 660, 630, 600, 580, 570, 560, 560, 560,
06273     570, 580, 590, 610, 620, 630, 650, 660, 680, 690,
06274     710, 720, 730, 740, 750, 760, 770, 770, 780, 780,
06275     /* 1860.0 thru 1899.0 */
06276     788, 782, 754, 697, 640, 602, 541, 410, 292, 182,
06277     161, 10, -102, -128, -269, -324, -364, -454, -471, -511,
06278     -540, -542, -520, -546, -546, -579, -563, -564, -580, -566,
06279     -587, -601, -619, -664, -644, -647, -609, -576, -466, -374,
06280     /* 1900.0 thru 1939.0 */
06281     -272, -154, -2, 124, 264, 386, 537, 614, 775, 913,
06282     1046, 1153, 1336, 1465, 1601, 1720, 1824, 1906, 2025, 2095,
06283     2116, 2225, 2241, 2303, 2349, 2362, 2386, 2449, 2434, 2408,
06284     2402, 2400, 2387, 2395, 2386, 2393, 2373, 2392, 2396, 2402,
06285     /* 1940.0 thru 1979.0 */
06286      2433, 2483, 2530, 2570, 2624, 2677, 2728, 2778, 2825, 2871,
06287      2915, 2957, 2997, 3036, 3072, 3107, 3135, 3168, 3218, 3268,
06288      3315, 3359, 3400, 3447, 3503, 3573, 3654, 3743, 3829, 3920,
06289      4018, 4117, 4223, 4337, 4449, 4548, 4646, 4752, 4853, 4959,
06290     /* 1980.0 thru 1995.0 */
06291      5054, 5138, 5217, 5296, 5379, 5434, 5487, 5532, 5582, 5630,
06292      5686, 5757, 5831, 5912, 5998, 6078,
06293     /* new USNO data (stern) */
06294      6163, 6230,
06295     /* new USNO extrapolation (stern), 2000.0 to 2004.0 */
06296      6296, 6420,
06297      6510, 6600, 6700, 6800, 6900  /* 7000, 7100, 7200, 7300, 7400, */
06298 
06299     /* Extrapolated values (USNO) (original Moshier)
06300      6183, 6280, 6377, 6475,
06301      6572, 6667, 6765, 6861, 6957
06302      */
06303 };
06304 
06305 
06306 /* calculate  DeltaT = ET - UT in seconds.  Describes the irregularities
06307  * of the Earth rotation rate in the ET time scale.
06308  */
06309 double deltat(double mjd)
06310 {
06311         double Y;
06312         double p, B;
06313         int d[6];
06314         int i, iy, k;
06315         static double ans;
06316         static double lastmjd = -10000;
06317 
06318         if (mjd == lastmjd) {
06319             return(ans);
06320         }
06321         lastmjd = mjd;
06322 
06323         Y = 2000.0 + (mjd - J2000)/365.25;
06324 
06325         if( Y > TABEND ) {
06326             /* linear interpolation from table end; stern */
06327             B = Y - TABEND;
06328             ans = dt[TABSIZ-1] + B * (dt[TABSIZ-1]  - dt[TABSIZ-2]);
06329             ans *= 0.01;
06330             return(ans);
06331         }
06332 
06333         if( Y < TABSTART ) {
06334             if( Y >= 948.0 ) {
06335                 /* Stephenson and Morrison, stated domain is 948 to 1600:
06336                  * 25.5(centuries from 1800)^2 - 1.9159(centuries from 1955)^2
06337                  */
06338                 B = 0.01*(Y - 2000.0);
06339                 ans = (23.58 * B + 100.3)*B + 101.6;
06340             } else {
06341                 /* Borkowski */
06342                 B = 0.01*(Y - 2000.0)  +  3.75;
06343                 ans = 35.0 * B * B  +  40.;
06344             }
06345             return(ans);
06346         }
06347 
06348         /* Besselian interpolation from tabulated values.
06349          * See AA page K11.
06350          */
06351 
06352         /* Index into the table.
06353          */
06354         double a=Y;
06355         p = floor(a);
06356         iy =(int)( p - TABSTART);
06357         /* Zeroth order estimate is value at start of year
06358          */
06359         ans = dt[iy];
06360         k = iy + 1;
06361         if( k >= TABSIZ )
06362             goto done; /* No data, can't go on. */
06363 
06364         /* The fraction of tabulation interval
06365          */
06366         p = Y - p;
06367 
06368         /* First order interpolated value
06369          */
06370         ans += p*(dt[k] - dt[iy]);
06371         if( (iy-1 < 0) || (iy+2 >= TABSIZ) )
06372             goto done; /* can't do second differences */
06373 
06374         /* Make table of first differences
06375          */
06376         k = iy - 2;
06377         for( i=0; i<5; i++ ) {
06378             if( (k < 0) || (k+1 >= TABSIZ) )
06379                 d[i] = 0;
06380             else d[i] = dt[k+1] - dt[k];
06381                 k += 1;
06382         }
06383 
06384         /* Compute second differences
06385          */
06386         for( i=0; i<4; i++ )
06387             d[i] = d[i+1] - d[i];
06388         B = 0.25*p*(p-1.0);
06389         ans += B*(d[1] + d[2]);
06390         if( iy+2 >= TABSIZ )
06391             goto done;
06392 
06393         /* Compute third differences
06394          */
06395         for( i=0; i<3; i++ )
06396             d[i] = d[i+1] - d[i];
06397         B = 2.0*B/3.0;
06398         ans += (p-0.5)*B*d[1];
06399         if( (iy-2 < 0) || (iy+3 > TABSIZ) )
06400             goto done;
06401 
06402         /* Compute fourth differences
06403          */
06404         for( i=0; i<2; i++ )
06405             d[i] = d[i+1] - d[i];
06406         B = 0.125*B*(p+1.0)*(p-2.0);
06407         ans += B*(d[0] + d[1]);
06408 
06409         done:
06410         /* Astronomical Almanac table is corrected by adding the expression
06411          *     -0.000091 (ndot + 26)(year-1955)^2  seconds
06412          * to entries prior to 1955 (AA page K8), where ndot is the secular
06413          * tidal term in the mean motion of the Moon.
06414          *
06415          * Entries after 1955 are referred to atomic time standards and
06416          * are not affected by errors in Lunar or planetary theory.
06417          */
06418         ans *= 0.01;
06419         if( Y < 1955.0 ) {
06420             B = (Y - 1955.0);
06421             ans += -0.000091 * (-25.8 + 26.0) * B * B;
06422         }
06423         return( ans );
06424 }
06425 
06426 
06427 /* given a Now at noon and a dt from noon, in hours, for a first approximation
06428  * to a rise or set event, refine the event by searching for when alt+dis = 0.
06429  * return 0: if find one within 12 hours of noon with np and op set to the
06430  *    better time and circumstances;
06431  * return -1: if error from obj_cir;
06432  * return -2: if converges but not today;
06433  * return -3: if does not converge at all (probably circumpolar or never up);
06434  */
06435 
06436 
06437 
06438 
06439 
06440 
06441 
06442