miscell.cpp

/* miscell.cpp: misc. astronomy-related functions

Copyright (C) 2010, Project Pluto

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.    */

#define __USE_MINGW_ANSI_STDIO 1
         /* above causes MinGW to use "real" long doubles */

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>
#include <string.h>
#include <ctype.h>
#include "watdefs.h"
#include "stringex.h"
#include "afuncs.h"
#include "date.h"

#ifdef __WATCOMC__
#define floorl floor
#define sinl sin
#endif

static const double pi = 3.1415926535897932384626433832795028841971693993751058209749445923;
static const long double j2000 = 2451545.0;

/* It's embarrassingly common to find out that,  after roundoff errors,
   you're attempting to take the arccosine or arcsine of +/- 1.0000001,
   resulting in a math exception.  Use of acose( ) and asine( ) lets you
   slip around such difficulties.

      There are two reasons to be careful about this.  First,  if a for-real
   error results in arg=78,  acose( ) (for example) will silently truncate it
   to 1 and return 0.  Second,  if you're sometimes getting 1+(1e-14),  you're
   probably also sometimes getting 1-(1e-14).  In this range,  the precision
   of the acos and asin functions is horrible,  and deformed values will be
   returned silently.  It's better,  in such cases,  to give some thought as
   to a better way to get the answer you want.  Look,  for example,  in
   'dist_pa.cpp' where asin is used in one domain and acos in the other,
   avoiding areas where bad values would be generated.
*/

double DLL_FUNC acose( const double arg)
{
   if( arg >= 1.)
      return( 0.);
   if( arg <= -1.)
      return( pi);
   return( acos( arg));
}

double DLL_FUNC asine( const double arg)
{
   if( arg >= 1.)
      return( pi / 2);
   if( arg <= -1.)
      return( -pi / 2.);
   return( asin( arg));
}

void DLL_FUNC set_identity_matrix( double DLLPTR *matrix)
{
   int i;

   for( i = 0; i < 9; i++)
      matrix[i] = ((i & 3) ? 0. : 1.);
}

          /* Inverting an orthonormal matrix happens to be an unusually   */
          /* simple job:  swap rows and columns,  and you're in business. */
          /* This really ought to be just called 'transpose_matrix'.      */

#define SWAP( A, B, TEMP)  { TEMP = A;  A = B;  B = TEMP; }

void DLL_FUNC invert_orthonormal_matrix( double DLLPTR *matrix)
{
   double temp;

   SWAP( matrix[1], matrix[3], temp);
   SWAP( matrix[2], matrix[6], temp);
   SWAP( matrix[5], matrix[7], temp);
}

/* Variable star designations follow a rather ugly scheme,  for historical
reasons.  The first 334 are labelled in the following order:

 R  S  T  U  V  W  X  Y  Z RR RS RT RU RV RW RX RY RZ SS ST SU SV SW SX
SY SZ TT TU TV TW TX TY TZ UU UV UW UX UY UZ VV VW VX VY VZ WW WX WY WZ
XX XY XZ YY YZ ZZ AA AB AC AD AE AF AG AH AI AK AL AM AN AO AP AQ AR AS
AT AU AV AW AX AY AZ BB BC BD BE BF BG BH BI BK BL BM BN BO BP BQ BR BS
BT BU BV BW BX BY BZ CC CD CE CF CG CH CI CK CL CM CN CO CP CQ CR CS CT
CU CV CW CX CY CZ DD DE DF DG DH DI DK DL DM DN DO DP DQ DR DS DT DU DV
DW DX DY DZ EE EF EG EH EI EK EL EM EN EO EP EQ ER ES ET EU EV EW EX EY
EZ FF FG FH FI FK FL FM FN FO FP FQ FR FS FT FU FV FW FX FY FZ GG GH GI
GK GL GM GN GO GP GQ GR GS GT GU GV GW GX GY GZ HH HI HK HL HM HN HO HP
HQ HR HS HT HU HV HW HX HY HZ II IK IL IM IN IO IP IQ IR IS IT IU IV IW
IX IY IZ KK KL KM KN KO KP KQ KR KS KT KU KV KW KX KY KZ LL LM LN LO LP
LQ LR LS LT LU LV LW LX LY LZ MM MN MO MP MQ MR MS MT MU MV MW MX MY MZ
NN NO NP NQ NR NS NT NU NV NW NX NY NZ OO OP OQ OR OS OT OU OV OW OX OY
OZ PP PQ PR PS PT PU PV PW PX PY PZ QQ QR QS QT QU QV QW QX QY QZ

   The first one found in a constellation is 'R (constellation name)';
followed by 'S', 'T',  ... 'Z'.  That allows up to nine variables per
constellation;  the tenth gets labelled 'RR',  followed by 'RS', 'RT',
'RU',... 'RZ';  then 'SS', 'ST', 'SU'... 'SZ', 'TT'... 'TZ',  and so on,
up to 'ZZ'.  This allows a further 9+8+7+6+5+4+3+2+1=45 stars to be
labelled. The letters are always 'R' through 'Z',  and the second letter
is never alphabetically before the first.

   Following this,  we cycle the first letter back to 'A'.  This
gives 'AA', 'AB', 'AC', ... 'AZ';  'BB', 'BC', 'BD', ... 'BZ';  and,
eventually,  'QQ', 'QR', ... 'QZ'.  For some reason,  'J' is always
skipped.

   Following this lunacy for 334 variable stars,  they are simply labelled
"V335",  "V336",  etc.

*/

void DLL_FUNC make_var_desig( char DLLPTR *buff, int var_no)
{
   int i, curr_no = 10;

   if( var_no < 10)
      {
      *buff++ = (char)('R' + var_no - 1);
      *buff = '\0';
      }
   else if( var_no > 334)
      {
      *buff++ = 'V';
      for( i = 1000; i; i /= 10)
         if( var_no >= i)
            *buff++ = (char)( (var_no / i) % 10 + '0');
      *buff = '\0';
      }
   else     /* two-letter abbr */
      {
      buff[2] = '\0';
      for( i = 'R'; i <= 'Z' && curr_no + ('Z' - i) < var_no; i++)
         curr_no += 'Z' - i + 1;
               /* gotta get weird to allow for fact that J isn't used */
      if( i > 'Z')                    /* in variable star designators */
         for( i = 'A'; i < 'Q' && curr_no + ('Y' - i) < var_no; i++)
            curr_no += 'Z' - i;
      buff[0] = (char)i;
      buff[1] = (char)(i + var_no - curr_no);
               /* more weirdness due to missing J:  bump up letters J-Q */
      if( buff[0] < 'R' && buff[0] >= 'J')
         buff[0]++;
      if( buff[0] < 'R' && buff[1] >= 'J')
         buff[1]++;
      }
}

void DLL_FUNC rotate_vector( double DLLPTR *v, const double angle,
                                          const int axis)
{
   const double sin_ang = sin( angle), cos_ang = cos( angle);
   const int a = (axis + 1) % 3, b = (axis + 2) % 3;
   const double temp = v[a] * cos_ang - v[b] * sin_ang;

   v[b] = v[b] * cos_ang + v[a] * sin_ang;
   v[a] = temp;
}

void DLL_FUNC pre_spin_matrix( double *v1, double *v2, const double angle)
{
   const double sin_ang = sin( angle);
   const double cos_ang = cos( angle);
   int i;

   for( i = 3; i; i--)
      {
      const double tval = *v1 * cos_ang - *v2 * sin_ang;

      *v2 = *v2 * cos_ang + *v1 * sin_ang;
      *v1 = tval;
      v1 += 3;
      v2 += 3;
      }
}

void DLL_FUNC spin_matrix( double *v1, double *v2, const double angle)
{
   const double sin_ang = sin( angle);
   const double cos_ang = cos( angle);
   int i;

   for( i = 3; i; i--)
      {
      const double tval = *v1 * cos_ang - *v2 * sin_ang;

      *v2 = *v2 * cos_ang + *v1 * sin_ang;
      *v1++ = tval;
      v2++;
      }
}

/* See above for a discussion of the variable star designation scheme. */

int DLL_FUNC decipher_var_desig( const char DLLPTR *desig)
{
   int len, first,  second, rval = -2;

   first = toupper( desig[0]);
   second = toupper( desig[1]);
   for( len = 0; desig[len] && desig[len] != ' '; len++)
      ;
   switch( len)
      {
      case 1:
         if( first >= 'R' && first <= 'Z')
            rval = first - 'R';
         if( desig[0] >= 'A' && desig[0] <= 'Q')
            rval = 9200 + desig[0] - 'A';
         if( (desig[0] >= 'a' && desig[0] <= 'q') || desig[0] == 'u')
            rval = 9100 + desig[0] - 'a';
         break;
      case 2:
         if( second >= first && second <= 'Z')
            {
            if( first >= 'R')  /* RR...ZZ */
               {
               first -= 'R';
               second -= 'R';
               rval = first * 8 - first * (first - 1) / 2 + 9 + second;
               }
            else if( first != 'J' && second != 'J' && first >= 'A')
               {                  /* AA...QQ */
               first -= 'A';
               if( first > 8) first--;
               second -= 'A';
               if( second > 8) second--;
               rval = first * 24 - first * (first - 1) / 2 + 9 + 45 + second;
               }
            }
         break;
      default:
         if( first == 'V')
            rval = atoi( desig + 1) - 1;
         break;
      }
   rval++;
   return( rval);
}

/* Used in showing the decimal part of a time unit,  in the following
full_ctimel( ) function.  Just using sprintf and friends can lead to
problems with .999999... being rendered as 1.  */

static void show_remainder( char *buff, long double remainder, unsigned precision)
{
   *buff++ = '.';
   assert( remainder >= 0. && remainder < 1.);
   while( precision--)
      {
      unsigned digit;

      remainder *= 10.;
      digit = (unsigned)remainder;
      *buff++ = (char)( '0' + digit);
      assert( digit <= 9);
      remainder -= (double)digit;
      }
   *buff++ = '\0';
}

static void remove_char( char *buff, const char removed)
{
   size_t i, j;

   for( i = j = 0; buff[i]; i++)
      if( buff[i] != removed)
         buff[j++] = buff[i];
   buff[j] = '\0';
}

/* The following is analogous to the C ctime( ) function,  except that it
   handles dates previous to 1970 (at least back to -5.5 million years
   and forward to 5.5 million years) and allows for other calendars
   (Gregorian, Julian,  Hebrew,  etc.;  see 'date.cpp' for details).
   Also,  greater control over the output format is provided. */

void DLL_FUNC full_ctimel( char *buff, long double t2k, const int format)
{
   const int precision = (format >> 4) & 0xf, calendar = format & 0xf;
   const int output_format = (format & FULL_CTIME_FORMAT_MASK);
   char *ibuff = buff;   /* keep track of the start of the output */
   int day, month;
   long units, i;
   const int leading_zeroes = (format & FULL_CTIME_LEADING_ZEROES);
   long year, int_t2k, day_of_week;
   long double add_on = 1.;
   long double remains;
   const size_t max_buff_size = 80;
   char *leading_digit_ptr;

   if( output_format == FULL_CTIME_FORMAT_SECONDS)
      units = seconds_per_day;
   else if( output_format == FULL_CTIME_FORMAT_HH_MM)
      units = minutes_per_day;
   else if( output_format == FULL_CTIME_FORMAT_HH)
      units = hours_per_day;
   else                   /* output in days */
      units = 1;
   for( i = precision; i; i--)
      add_on /= 10.;
   if( format & FULL_CTIME_ROUNDING)
      add_on *= 0.5 / (double)units;
   else
      add_on *= 0.05 / seconds_per_day;
   t2k += add_on;

   if( output_format == FULL_CTIME_FORMAT_YEAR)
      {
      char tbuff[40];

#ifdef _WIN32
      snprintf( tbuff, sizeof( tbuff), "%21.16Lf", t2k / 365.25 + 2000.);
#else
      snprintf_err( tbuff, sizeof( tbuff), "%21.16Lf", t2k / 365.25 + 2000.);
#endif
      tbuff[precision + 5] = '\0';
      if( !precision)
         tbuff[4] = '\0';
      strlcpy_err( buff, tbuff, max_buff_size);
      if( leading_zeroes)
         while( *buff == ' ')
            *buff++ = '0';
      return;
      }
   if( output_format == FULL_CTIME_FORMAT_JD
                     || output_format == FULL_CTIME_FORMAT_MJD)
      {
      char format_str[10];

      snprintf_err( format_str, sizeof( format_str), "JD %%.%dLf", precision);
      if( output_format == FULL_CTIME_FORMAT_MJD)
         {
         *buff++ = 'M';
         t2k += j2000 - 2400000.5;
         }
      else
         t2k += j2000;
      snprintf_err( buff, max_buff_size, format_str, t2k);
      if( leading_zeroes)
         while( *buff == ' ')
            *buff++ = '0';
      return;
      }

   t2k += .5;
   int_t2k = (long)floorl( t2k);
   day_of_week = (int_t2k + 6) % 7;
   if( day_of_week < 0)    /* keep 0 <= day_of_week < 7: */
      day_of_week += 7;
   if( format & FULL_CTIME_DAY_OF_WEEK_FIRST)
      snprintf_err( buff, max_buff_size, "%s ",
                     set_day_of_week_name( (int)day_of_week, NULL));
   else
      *buff = '\0';

   day_to_dmy( int_t2k + 2451545, &day, &month, &year, calendar);

   remains = t2k - (long double)int_t2k;
          /* i.e.,  fractional part of day */
   if( !(format & FULL_CTIME_TIME_ONLY))     /* we want the date: */
      {
      char month_str[25];
      char year_str[20];
      char day_str[15];

      if( format & FULL_CTIME_MONTHS_AS_DIGITS)
         snprintf_err( month_str, sizeof( month_str), (leading_zeroes ? "%02d" : "%2d"), month);
      else
         strlcpy_err( month_str, set_month_name( month, NULL), sizeof( month_str));

      if( format & FULL_CTIME_TWO_DIGIT_YEAR)
         snprintf_err( year_str, sizeof( year_str), "%02d", abs( (int)year % 100));
      else
         snprintf_err( year_str, sizeof( year_str), (leading_zeroes ? "%04ld" : "%4ld"), year);

      if( format & FULL_CTIME_YEAR_FIRST)
         if( !(format & FULL_CTIME_NO_YEAR))
            snprintf_append( buff, max_buff_size, "%s ", year_str);

      snprintf_err( day_str, sizeof( day_str), (leading_zeroes ? "%02d" : "%2d"), day);
      if( output_format == FULL_CTIME_FORMAT_DAY && precision)
         show_remainder( day_str + 2, remains, (unsigned)precision);

      if( format & FULL_CTIME_DAY_OF_YEAR)
         {
         const int day_of_year = int_t2k + 2451545 - dmy_to_day( 0, 1, year, calendar);

         snprintf_append( buff, max_buff_size, "%03d%s", day_of_year, day_str + 2);
         }
      else if( format & FULL_CTIME_MONTH_DAY)
         snprintf_append( buff, max_buff_size, "%s %s", month_str, day_str);
      else
         snprintf_append( buff, max_buff_size, "%s %s", day_str, month_str);

      if( !(format & FULL_CTIME_YEAR_FIRST))       /* year comes at end */
         if( !(format & FULL_CTIME_NO_YEAR))
            snprintf_append( buff, max_buff_size, " %s", year_str);
      if( output_format != FULL_CTIME_FORMAT_DAY)
         strlcat_err( buff, " ", max_buff_size);
      }

   remains *= (double)units;
   i = (long)remains;
   if( i == units)   /* keep things from rounding up incorrectly */
      i--;
   leading_digit_ptr = buff + strlen( buff);
   switch( output_format)
      {
      case FULL_CTIME_FORMAT_SECONDS:
         snprintf_append( buff, max_buff_size, "%2ld:%02ld:%02ld", i / 3600L, (i / 60) % 60L,
                           i % 60L);
         break;
      case FULL_CTIME_FORMAT_HH_MM:
         snprintf_append( buff, max_buff_size, "%2ld:%02ld", i / 60L, i % 60L);
         break;
      case FULL_CTIME_FORMAT_HH:
         snprintf_append( buff, max_buff_size, "%2ld", i);
         break;
      }
   if( output_format != FULL_CTIME_FORMAT_DAY)
      {
      if( leading_zeroes && *leading_digit_ptr == ' ')
         *leading_digit_ptr = '0';
      if( precision)
         show_remainder( buff + strlen( buff), remains - (double)i,
                                                      (unsigned)precision);
      }
   if( format & FULL_CTIME_DAY_OF_WEEK_LAST)
      snprintf_append( buff, max_buff_size, " %s",
                     set_day_of_week_name( (int)day_of_week, NULL));
   if( format & FULL_CTIME_NO_SPACES)
      remove_char( ibuff, ' ');
   if( format & FULL_CTIME_NO_COLONS)
      remove_char( ibuff, ':');
}

void DLL_FUNC full_ctime( char *buff, double jd, const int format)
{
   full_ctimel( buff, (long double)jd - j2000, format);
}

void DLL_FUNC polar3_to_cartesian( double *vect, const double lon, const double lat)
{
   double clat = cos( lat);

   *vect++ = cos( lon) * clat;
   *vect++ = sin( lon) * clat;
   *vect   = sin( lat);
}

double DLL_FUNC vector3_length( const double *vect)
{
   return( sqrt( vect[0] * vect[0] + vect[1] * vect[1] + vect[2] * vect[2]));
}

double DLL_FUNC dot_product( const double *a, const double *b)
{
   return( a[0] * b[0] + a[1] * b[1] + a[2] * b[2]);
}

double DLL_FUNC normalize_vect3( double *vect)
{
   const double d2 = vect[0] * vect[0] + vect[1] * vect[1]
                                       + vect[2] * vect[2];
   const double d = sqrt( d2);
   if( d)
      {
      vect[0] /= d;
      vect[1] /= d;
      vect[2] /= d;
      }
   return( d);
}

/* Greenwich sidereal time from UT.  Based on Meeus' _Astronomical
   Algorithms_,  pp 87-88 (2nd edition).  Note that UT0 should be
   used,  the version that reflects the earth's current rotational
   state.  (UTC comes close,  but leap seconds are inserted so that
   each second can be equal in length,  rather than "stretching" each
   second as the earth slows down.  The difference is kept within one
   second,  and can be ignored for many purposes.)   */

double DLL_FUNC green_sidereal_time( double jd_ut)
{
   double t_cen, rval, base_t;

   jd_ut -= 2451545.0;        /* set relative to 2000.0 */
   t_cen = jd_ut / 36525.;    /* convert to julian centuries */
   base_t = floor( jd_ut);
   jd_ut -= base_t;
   rval = 280.46061837 + 360.98564736629 * jd_ut + .98564736629 * base_t +
           t_cen * t_cen * (3.87933e-4 - t_cen / 38710000.);

         /* See p 84,  in Meeus:  the following should get apparent */
         /* Greenwich sidereal time: */
   return( rval * pi / 180.);
}

void DLL_FUNC vector_cross_product( double *xprod, const double *a, const double *b)
{
   xprod[0] = a[1] * b[2] - a[2] * b[1];
   xprod[1] = a[2] * b[0] - a[0] * b[2];
   xprod[2] = a[0] * b[1] - a[1] * b[0];
}