source: git/src/netbits.c @ e3f7ea7

/* netbits.c
 * Miscellaneous primitive network routines for Survex
 * Copyright (C) 1992-2025 Olly Betts
 *
 * 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 St, Fifth Floor, Boston, MA  02110-1301  USA
 */

#include <config.h>

#if 0
# define DEBUG_INVALID 1
#endif

#include "debug.h"
#include "cavern.h"
#include "filename.h"
#include "message.h"
#include "netbits.h"
#include "datain.h" /* for compile_error */
#include "validate.h" /* for compile_error */
#include <math.h>

#define THRESHOLD (REAL_EPSILON * 1000) /* 100 was too small */

node *stn_iter = NULL; /* for FOR_EACH_STN */

static struct {
   prefix * to_name;
   prefix * fr_name;
   linkfor * leg;
   int n;
} last_leg = { NULL, NULL, NULL, 0 };

void clear_last_leg(void) {
   last_leg.to_name = NULL;
}

static char freeleg(node **stnptr);

#ifdef NO_COVARIANCES
static void check_var(const var *v) {
   bool bad = false;

   for (int i = 0; i < 3; i++) {
      if (isnan(v[i])
         printf("*** NaN!!!\n"), bad = true;
   }
   if (bad) print_var(v);
   return;
}
#else
#define V(A,B) ((*v)[A][B])
static void check_var(const var *v) {
   bool bad = false;
   bool ok = false;
#if DEBUG_INVALID
   real det = 0.0;
#endif

   for (int i = 0; i < 3; i++) {
      for (int j = 0; j < 3; j++) {
         if (isnan(V(i, j)))
            printf("*** NaN!!!\n"), bad = true, ok = true;
         if (V(i, j) != 0.0) ok = true;
      }
   }
   if (!ok) return; /* ignore all-zero matrices */

#if DEBUG_INVALID
   for (int i = 0; i < 3; i++) {
      det += V(i, 0) * (V((i + 1) % 3, 1) * V((i + 2) % 3, 2) -
                        V((i + 1) % 3, 2) * V((i + 2) % 3, 1));
   }

   if (fabs(det) < THRESHOLD)
      printf("*** Singular!!!\n"), bad = true;
#endif

#if 0
   /* don't check this - it isn't always the case! */
   if (fabs(V(0,1) - V(1,0)) > THRESHOLD ||
       fabs(V(0,2) - V(2,0)) > THRESHOLD ||
       fabs(V(1,2) - V(2,1)) > THRESHOLD)
      printf("*** Not symmetric!!!\n"), bad = true;
   if (V(0,0) <= 0.0 || V(1,1) <= 0.0 || V(2,2) <= 0.0)
      printf("*** Not positive definite (diag <= 0)!!!\n"), bad = true;
   if (sqrd(V(0,1)) >= V(0,0)*V(1,1) || sqrd(V(0,2)) >= V(0,0)*V(2,2) ||
       sqrd(V(1,0)) >= V(0,0)*V(1,1) || sqrd(V(2,0)) >= V(0,0)*V(2,2) ||
       sqrd(V(1,2)) >= V(2,2)*V(1,1) || sqrd(V(2,1)) >= V(2,2)*V(1,1))
      printf("*** Not positive definite (off diag^2 >= diag product)!!!\n"), bad = true;
#endif
   if (bad) print_var(*v);
}

#define SN(V,A,B) ((*(V))[(A)==(B)?(A):2+(A)+(B)])
#define S(A,B) SN(v,A,B)

static void check_svar(const svar *v) {
   bool bad = false;
   bool ok = false;
#if DEBUG_INVALID
   real det = 0.0;
#endif

   for (int i = 0; i < 6; i++) {
      if (isnan((*v)[i]))
         printf("*** NaN!!!\n"), bad = true, ok = true;
      if ((*v)[i] != 0.0) ok = true;
   }
   if (!ok) return; /* ignore all-zero matrices */

#if DEBUG_INVALID
   for (int i = 0; i < 3; i++) {
      det += S(i, 0) * (S((i + 1) % 3, 1) * S((i + 2) % 3, 2) -
                        S((i + 1) % 3, 2) * S((i + 2) % 3, 1));
   }

   if (fabs(det) < THRESHOLD)
      printf("*** Singular!!!\n"), bad = true;
#endif

#if 0
   /* don't check this - it isn't always the case! */
   if ((*v)[0] <= 0.0 || (*v)[1] <= 0.0 || (*v)[2] <= 0.0)
      printf("*** Not positive definite (diag <= 0)!!!\n"), bad = true;
   if (sqrd((*v)[3]) >= (*v)[0]*(*v)[1] ||
       sqrd((*v)[4]) >= (*v)[0]*(*v)[2] ||
       sqrd((*v)[5]) >= (*v)[1]*(*v)[2])
      printf("*** Not positive definite (off diag^2 >= diag product)!!!\n"), bad = true;
#endif
   if (bad) print_svar(*v);
}
#endif

static void check_d(const delta *d) {
   bool bad = false;

   for (int i = 0; i < 3; i++) {
      if (isnan((*d)[i]))
         printf("*** NaN!!!\n"), bad = true;
   }

   if (bad) printf("(%4.2f,%4.2f,%4.2f)\n", (*d)[0], (*d)[1], (*d)[2]);
}

/* insert at head of double-linked list */
void
add_stn_to_list(node **list, node *stn) {
   SVX_ASSERT(list);
   SVX_ASSERT(stn);
   SVX_ASSERT(stn_iter != stn); /* if it does, we're still on a list... */
#if 0
   printf("add_stn_to_list(%p, [%p] ", list, stn);
   if (stn->name) print_prefix(stn->name);
   printf(")\n");
#endif
   stn->next = *list;
   stn->prev = NULL;
   if (*list) (*list)->prev = stn;
   *list = stn;
}

/* remove from double-linked list */
void
remove_stn_from_list(node **list, node *stn) {
   SVX_ASSERT(list);
   SVX_ASSERT(stn);
#if 0
   printf("remove_stn_from_list(%p, [%p] ", list, stn);
   if (stn->name) print_prefix(stn->name);
   printf(")\n");
#endif
#if DEBUG_INVALID
     {
        /* Go back to the head of the list stn is actually on and
         * check it's the same as the list we were asked to remove
         * it from.
         */
        validate();
        node *find_head = stn;
        while (find_head->prev) {
            find_head = find_head->prev;
        }
        SVX_ASSERT(find_head == *list);
     }
#endif
   /* adjust the iterator if it points to the element we're deleting */
   if (stn_iter == stn) stn_iter = stn_iter->next;
   /* need a special case if we're removing the list head */
   if (stn->prev == NULL) {
      *list = stn->next;
      if (*list) (*list)->prev = NULL;
   } else {
      stn->prev->next = stn->next;
      if (stn->next) stn->next->prev = stn->prev;
   }
}

/* Create (uses osmalloc) a forward leg containing the data in leg, or
 * the reversed data in the reverse of leg, if leg doesn't hold data
 */
linkfor *
copy_link(linkfor *leg)
{
   linkfor *legOut = osnew(linkfor);
   if (data_here(leg)) {
      for (int d = 2; d >= 0; d--) legOut->d[d] = leg->d[d];
   } else {
      leg = reverse_leg(leg);
      SVX_ASSERT(data_here(leg));
      for (int d = 2; d >= 0; d--) legOut->d[d] = -leg->d[d];
   }
#if 1
# ifndef NO_COVARIANCES
   check_svar(&(leg->v));
   for (int i = 0; i < 6; i++) legOut->v[i] = leg->v[i];
# else
   for (int d = 2; d >= 0; d--) legOut->v[d] = leg->v[d];
# endif
#else
   memcpy(legOut->v, leg->v, sizeof(svar));
#endif
   legOut->meta = pcs->meta;
   if (pcs->meta) ++pcs->meta->ref_count;
   return legOut;
}

/* Adds to the forward leg “leg”, the data in leg2, or the reversed data
 * in the reverse of leg2, if leg2 doesn't hold data
 */
linkfor *
addto_link(linkfor *leg, const linkfor *leg2)
{
   if (data_here(leg2)) {
      adddd(&leg->d, &leg->d, &((linkfor *)leg2)->d);
   } else {
      leg2 = reverse_leg(leg2);
      SVX_ASSERT(data_here(leg2));
      subdd(&leg->d, &leg->d, &((linkfor *)leg2)->d);
   }
   addss(&leg->v, &leg->v, &((linkfor *)leg2)->v);
   return leg;
}

static linkfor *
addleg_(node *fr, node *to,
        real dx, real dy, real dz,
        real vx, real vy, real vz,
#ifndef NO_COVARIANCES
        real cyz, real czx, real cxy,
#endif
        int leg_flags)
{
   /* we have been asked to add a leg with the same node at both ends
    * - this should be trapped by the caller */
   SVX_ASSERT(fr->name != to->name);

   linkfor *leg = osnew(linkfor);
   linkfor *leg2 = (linkfor*)osnew(linkcommon);

   int i = freeleg(&fr);
   int j = freeleg(&to);

   leg->l.to = to;
   leg2->l.to = fr;
   leg->d[0] = dx;
   leg->d[1] = dy;
   leg->d[2] = dz;
#ifndef NO_COVARIANCES
   leg->v[0] = vx;
   leg->v[1] = vy;
   leg->v[2] = vz;
   leg->v[3] = cxy;
   leg->v[4] = czx;
   leg->v[5] = cyz;
   check_svar(&(leg->v));
#else
   leg->v[0] = vx;
   leg->v[1] = vy;
   leg->v[2] = vz;
#endif
   leg2->l.reverse = i;
   leg->l.reverse = j | FLAG_DATAHERE | leg_flags;

   leg->l.flags = pcs->flags | (pcs->recorded_style << FLAGS_STYLE_BIT0);
   leg->meta = pcs->meta;
   if (pcs->meta) ++pcs->meta->ref_count;

   fr->leg[i] = leg;
   to->leg[j] = leg2;

   return leg;
}

/* Add a leg between names *fr_name and *to_name
 * If either is a three node, then it is split into two
 * and the data structure adjusted as necessary.
 */
void
addlegbyname(prefix *fr_name, prefix *to_name, bool fToFirst,
             real dx, real dy, real dz,
             real vx, real vy, real vz
#ifndef NO_COVARIANCES
             , real cyz, real czx, real cxy
#endif
             )
{
   if (to_name == fr_name) {
      int type = pcs->from_equals_to_is_only_a_warning ? DIAG_WARN : DIAG_ERR;
      /* TRANSLATORS: Here a "survey leg" is a set of measurements between two
       * "survey stations".
       *
       * %s is replaced by the name of the station. */
      compile_diagnostic(type, /*Survey leg with same station (“%s”) at both ends - typing error?*/50,
                         sprint_prefix(to_name));
      return;
   }
   node *to, *fr;
   if (fToFirst) {
      to = StnFromPfx(to_name);
      fr = StnFromPfx(fr_name);
   } else {
      fr = StnFromPfx(fr_name);
      to = StnFromPfx(to_name);
   }
   if (last_leg.to_name) {
      if (last_leg.to_name == to_name && last_leg.fr_name == fr_name) {
         /* FIXME: Not the right way to average... */
         linkfor * leg = last_leg.leg;
         int n = last_leg.n++;
         leg->d[0] = (leg->d[0] * n + dx) / (n + 1);
         leg->d[1] = (leg->d[1] * n + dy) / (n + 1);
         leg->d[2] = (leg->d[2] * n + dz) / (n + 1);
#ifndef NO_COVARIANCES
         leg->v[0] = (leg->v[0] * n + vx) / (n + 1);
         leg->v[1] = (leg->v[1] * n + vy) / (n + 1);
         leg->v[2] = (leg->v[2] * n + vz) / (n + 1);
         leg->v[3] = (leg->v[3] * n + cxy) / (n + 1);
         leg->v[4] = (leg->v[4] * n + czx) / (n + 1);
         leg->v[5] = (leg->v[5] * n + cyz) / (n + 1);
         check_svar(&(leg->v));
#else
         leg->v[0] = (leg->v[0] * n + vx) / (n + 1);
         leg->v[1] = (leg->v[1] * n + vy) / (n + 1);
         leg->v[2] = (leg->v[2] * n + vz) / (n + 1);
#endif
         return;
      }
   }
   cLegs++;

   /* Suppress "unused fixed point" warnings for these stations. */
   fr_name->sflags &= ~BIT(SFLAGS_UNUSED_FIXED_POINT);
   to_name->sflags &= ~BIT(SFLAGS_UNUSED_FIXED_POINT);

   last_leg.to_name = to_name;
   last_leg.fr_name = fr_name;
   last_leg.n = 1;
   last_leg.leg = addleg_(fr, to, dx, dy, dz, vx, vy, vz,
#ifndef NO_COVARIANCES
                          cyz, czx, cxy,
#endif
                          0);
}

/* helper function for replace_pfx */
static void
replace_pfx_(node *stn, node *from, pos *pos_with, bool move_to_fixedlist)
{
   SVX_ASSERT(!fixed(stn));
   if (move_to_fixedlist) {
      SVX_ASSERT(pos_fixed(pos_with));
      SVX_ASSERT(!fixed(stn));
      remove_stn_from_list(&stnlist, stn);
      add_stn_to_list(&fixedlist, stn);
   }
   stn->name->pos = pos_with;
   for (int d = 0; d < 3; d++) {
      linkfor *leg = stn->leg[d];
      if (!leg) break;
      node *to = leg->l.to;
      if (to == from) continue;

      if (fZeros(data_here(leg) ? &leg->v : &reverse_leg(leg)->v))
         replace_pfx_(to, stn, pos_with, move_to_fixedlist);
   }
}

/* We used to iterate over the whole station list (inefficient) - now we
 * just look at any neighbouring nodes to see if they are equated */
static void
replace_pfx(const prefix *pfx_replace, const prefix *pfx_with,
            bool move_to_fixedlist)
{
   SVX_ASSERT(pfx_replace);
   SVX_ASSERT(pfx_with);
   pos *pos_replace = pfx_replace->pos;
   SVX_ASSERT(pos_replace != pfx_with->pos);

   replace_pfx_(pfx_replace->stn, NULL, pfx_with->pos, move_to_fixedlist);

#if DEBUG_INVALID
   for (node *stn = stnlist; stn; stn = stn->next) {
      SVX_ASSERT(stn->name->pos != pos_replace);
   }
   for (node *stn = fixedlist; stn; stn = stn->next) {
      SVX_ASSERT(stn->name->pos != pos_replace);
   }
#endif

   /* free the (now-unused) old pos */
   osfree(pos_replace);
}

// Add equating leg between existing stations whose names are name1 and name2.
void
process_equate(prefix *name1, prefix *name2)
{
   clear_last_leg();
   if (name1 == name2) {
      /* catch something like *equate "fred fred" */
      /* TRANSLATORS: Here "station" is a survey station, not a train station.
       */
      compile_diagnostic(DIAG_WARN, /*Station “%s” equated to itself*/13,
                         sprint_prefix(name1));
      return;
   }
   node *stn1 = StnFromPfx(name1);
   node *stn2 = StnFromPfx(name2);
   /* equate nodes if not already equated */
   if (name1->pos != name2->pos) {
      if (pfx_fixed(name1)) {
         bool name2_fixed = pfx_fixed(name2);
         if (name2_fixed) {
            /* both are fixed, but let them off iff their coordinates match */
            char *s = osstrdup(sprint_prefix(name1));
            for (int d = 2; d >= 0; d--) {
               if (name1->pos->p[d] != name2->pos->p[d]) {
                  compile_diagnostic(DIAG_ERR, /*Tried to equate two non-equal fixed stations: “%s” and “%s”*/52,
                                     s, sprint_prefix(name2));
                  osfree(s);
                  return;
               }
            }
            /* TRANSLATORS: "equal" as in:
             *
             * *fix a 1 2 3
             * *fix b 1 2 3
             * *equate a b */
            compile_diagnostic(DIAG_WARN, /*Equating two equal fixed points: “%s” and “%s”*/53,
                               s, sprint_prefix(name2));
            osfree(s);
         }

         /* name1 is fixed, so replace all refs to name2's pos with name1's */
         replace_pfx(name2, name1, !name2_fixed);
      } else {
         /* name1 isn't fixed, so replace all refs to its pos with name2's */
         replace_pfx(name1, name2, pfx_fixed(name2));
      }

      /* Suppress "unused fixed point" warnings for these stations. */
      name1->sflags &= ~BIT(SFLAGS_UNUSED_FIXED_POINT);
      name2->sflags &= ~BIT(SFLAGS_UNUSED_FIXED_POINT);

      /* count equates as legs for now... */
      cLegs++;
      addleg_(stn1, stn2,
              (real)0.0, (real)0.0, (real)0.0,
              (real)0.0, (real)0.0, (real)0.0,
#ifndef NO_COVARIANCES
              (real)0.0, (real)0.0, (real)0.0,
#endif
              FLAG_FAKE);
   }
}

/* Add a 'fake' leg (not counted or treated as a use of a fixed point) between
 * existing stations *fr and *to (which *must* be different).
 *
 * If either node is a three node, then it is split into two
 * and the data structure adjusted as necessary.
 */
void
addfakeleg(node *fr, node *to,
           real dx, real dy, real dz,
           real vx, real vy, real vz
#ifndef NO_COVARIANCES
           , real cyz, real czx, real cxy
#endif
           )
{
   clear_last_leg();
   addleg_(fr, to, dx, dy, dz, vx, vy, vz,
#ifndef NO_COVARIANCES
           cyz, czx, cxy,
#endif
           FLAG_FAKE);
}

static char
freeleg(node **stnptr)
{
   node *stn = *stnptr;

   if (stn->leg[0] == NULL) return 0; /* leg[0] unused */
   if (stn->leg[1] == NULL) return 1; /* leg[1] unused */
   if (stn->leg[2] == NULL) return 2; /* leg[2] unused */

   /* All legs used, so split node in two */
   node *newstn = osnew(node);
   linkfor *leg = osnew(linkfor);
   linkfor *leg2 = (linkfor*)osnew(linkcommon);

   *stnptr = newstn;

   add_stn_to_list(fixed(stn) ? &fixedlist : &stnlist, newstn);
   newstn->name = stn->name;

   leg->l.to = newstn;
   leg->d[0] = leg->d[1] = leg->d[2] = (real)0.0;

#ifndef NO_COVARIANCES
   for (int i = 0; i < 6; i++) leg->v[i] = (real)0.0;
#else
   leg->v[0] = leg->v[1] = leg->v[2] = (real)0.0;
#endif
   leg->l.reverse = 1 | FLAG_DATAHERE | FLAG_FAKE;
   leg->l.flags = pcs->flags | (pcs->recorded_style << FLAGS_STYLE_BIT0);

   leg2->l.to = stn;
   leg2->l.reverse = 0;

   // NB this preserves pos->stn->leg[0] pointing to the "real" fixed point
   // for stations fixed with error estimates.
   newstn->leg[0] = stn->leg[0];
   // Update the reverse leg.
   reverse_leg(newstn->leg[0])->l.to = newstn;
   newstn->leg[1] = leg2;

   stn->leg[0] = leg;

   newstn->leg[2] = NULL; /* needed as newstn->leg[dirn]==NULL indicates unused */

   return 2; /* leg[2] unused */
}

node *
StnFromPfx(prefix *name)
{
   if (name->stn != NULL) return name->stn;
   node *stn = osnew(node);
   stn->name = name;
   bool fixed = false;
   if (name->pos == NULL) {
      name->pos = osnew(pos);
      unfix(stn);
   } else {
      fixed = pfx_fixed(name);
   }
   stn->leg[0] = stn->leg[1] = stn->leg[2] = NULL;
   add_stn_to_list(fixed ? &fixedlist : &stnlist, stn);
   name->stn = stn;
   // Don't re-count a station which already exists from before a `*solve`.
   // After we solve we delete and NULL-out its `node*`, but set SFLAGS_SOLVED.
   if (!TSTBIT(name->sflags, SFLAGS_SOLVED)) cStns++;
   return stn;
}

extern void
fprint_prefix(FILE *fh, const prefix *ptr)
{
   SVX_ASSERT(ptr);
   if (TSTBIT(ptr->sflags, SFLAGS_ANON)) {
      /* We release the stations, so ptr->stn is NULL late on, so we can't
       * use that to print "anonymous station surveyed from somesurvey.12"
       * here.  FIXME */
      fputs("anonymous station", fh);
      /* FIXME: if ident is set, show it? */
      return;
   }
   if (ptr->up != NULL) {
      fprint_prefix(fh, ptr->up);
      if (ptr->up->up != NULL) fputc(output_separator, fh);
      SVX_ASSERT(prefix_ident(ptr));
      fputs(prefix_ident(ptr), fh);
   }
}

static char *buffer = NULL;
static OSSIZE_T buffer_len = 256;

static OSSIZE_T
sprint_prefix_(const prefix *ptr)
{
   OSSIZE_T len = 1;
   if (ptr->up != NULL) {
      const char *ident = prefix_ident(ptr);
      SVX_ASSERT(ident);
      len = sprint_prefix_(ptr->up);
      OSSIZE_T end = len - 1;
      if (ptr->up->up != NULL) len++;
      len += strlen(ident);
      if (len > buffer_len) {
         buffer = osrealloc(buffer, len);
         buffer_len = len;
      }
      char *p = buffer + end;
      if (ptr->up->up != NULL) *p++ = output_separator;
      strcpy(p, ident);
   }
   return len;
}

extern char *
sprint_prefix(const prefix *ptr)
{
   SVX_ASSERT(ptr);
   if (!buffer) buffer = osmalloc(buffer_len);
   if (TSTBIT(ptr->sflags, SFLAGS_ANON)) {
      /* We release the stations, so ptr->stn is NULL late on, so we can't
       * use that to print "anonymous station surveyed from somesurvey.12"
       * here.  FIXME */
      strcpy(buffer, "anonymous station");
      /* FIXME: if ident is set, show it? */
      return buffer;
   }
   *buffer = '\0';
   sprint_prefix_(ptr);
   return buffer;
}

/* r = ab ; r,a,b are variance matrices */
void
mulss(var *r, const svar *a, const svar *b)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*a)[0] * (*b)[0];
   (*r)[1] = (*a)[1] * (*b)[1];
   (*r)[2] = (*a)[2] * (*b)[2];
#else
#if 0
   SVX_ASSERT((const var *)r != a);
   SVX_ASSERT((const var *)r != b);
#endif

   check_svar(a);
   check_svar(b);

   for (int i = 0; i < 3; i++) {
      for (int j = 0; j < 3; j++) {
         real tot = 0;
         for (int k = 0; k < 3; k++) {
            tot += SN(a,i,k) * SN(b,k,j);
         }
         (*r)[i][j] = tot;
      }
   }
   check_var(r);
#endif
}

#ifndef NO_COVARIANCES
/* r = ab ; r,a,b are variance matrices */
void
smulvs(svar *r, const var *a, const svar *b)
{
#if 0
   SVX_ASSERT((const var *)r != a);
#endif
   SVX_ASSERT((const svar *)r != b);

   check_var(a);
   check_svar(b);

   (*r)[3]=(*r)[4]=(*r)[5]=-999;
   for (int i = 0; i < 3; i++) {
      for (int j = 0; j < 3; j++) {
         real tot = 0;
         for (int k = 0; k < 3; k++) {
            tot += (*a)[i][k] * SN(b,k,j);
         }
         if (i <= j)
            SN(r,i,j) = tot;
         else if (fabs(SN(r,j,i) - tot) > THRESHOLD) {
            printf("not sym - %d,%d = %f, %d,%d was %f\n",
                   i,j,tot,j,i,SN(r,j,i));
            BUG("smulvs didn't produce a sym mx\n");
         }
      }
   }
   check_svar(r);
}
#endif

/* r = vb ; r,b delta vectors; a variance matrix */
void
mulsd(delta *r, const svar *v, const delta *b)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*v)[0] * (*b)[0];
   (*r)[1] = (*v)[1] * (*b)[1];
   (*r)[2] = (*v)[2] * (*b)[2];
#else
   SVX_ASSERT((const delta*)r != b);
   check_svar(v);
   check_d(b);

   for (int i = 0; i < 3; i++) {
      real tot = 0;
      for (int j = 0; j < 3; j++) tot += S(i,j) * (*b)[j];
      (*r)[i] = tot;
   }
   check_d(r);
#endif
}

/* r = ca ; r,a variance matrices; c real scaling factor  */
void
mulsc(svar *r, const svar *a, real c)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*a)[0] * c;
   (*r)[1] = (*a)[1] * c;
   (*r)[2] = (*a)[2] * c;
#else
   check_svar(a);
   for (int i = 0; i < 6; i++) (*r)[i] = (*a)[i] * c;
   check_svar(r);
#endif
}

/* r = a + b ; r,a,b delta vectors */
void
adddd(delta *r, const delta *a, const delta *b)
{
   check_d(a);
   check_d(b);
   (*r)[0] = (*a)[0] + (*b)[0];
   (*r)[1] = (*a)[1] + (*b)[1];
   (*r)[2] = (*a)[2] + (*b)[2];
   check_d(r);
}

/* r = a - b ; r,a,b delta vectors */
void
subdd(delta *r, const delta *a, const delta *b) {
   check_d(a);
   check_d(b);
   (*r)[0] = (*a)[0] - (*b)[0];
   (*r)[1] = (*a)[1] - (*b)[1];
   (*r)[2] = (*a)[2] - (*b)[2];
   check_d(r);
}

/* r = a + b ; r,a,b variance matrices */
void
addss(svar *r, const svar *a, const svar *b)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*a)[0] + (*b)[0];
   (*r)[1] = (*a)[1] + (*b)[1];
   (*r)[2] = (*a)[2] + (*b)[2];
#else
   check_svar(a);
   check_svar(b);
   for (int i = 0; i < 6; i++) (*r)[i] = (*a)[i] + (*b)[i];
   check_svar(r);
#endif
}

/* r = a - b ; r,a,b variance matrices */
void
subss(svar *r, const svar *a, const svar *b)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*a)[0] - (*b)[0];
   (*r)[1] = (*a)[1] - (*b)[1];
   (*r)[2] = (*a)[2] - (*b)[2];
#else
   check_svar(a);
   check_svar(b);
   for (int i = 0; i < 6; i++) (*r)[i] = (*a)[i] - (*b)[i];
   check_svar(r);
#endif
}

/* inv = v^-1 ; inv,v variance matrices */
extern int
invert_svar(svar *inv, const svar *v)
{
#ifdef NO_COVARIANCES
   for (int i = 0; i < 3; i++) {
      if ((*v)[i] == 0.0) return 0; /* matrix is singular */
      (*inv)[i] = 1.0 / (*v)[i];
   }
#else
#if 0
   SVX_ASSERT((const var *)inv != v);
#endif

   check_svar(v);
   /* a d e
    * d b f
    * e f c
    */
   real a = (*v)[0], b = (*v)[1], c = (*v)[2];
   real d = (*v)[3], e = (*v)[4], f = (*v)[5];
   real bcff = b * c - f * f;
   real efcd = e * f - c * d;
   real dfbe = d * f - b * e;
   real det = a * bcff + d * efcd + e * dfbe;

   if (det == 0.0) {
      /* printf("det=%.20f\n", det); */
      return 0; /* matrix is singular */
   }

   det = 1 / det;

   (*inv)[0] = det * bcff;
   (*inv)[1] = det * (c * a - e * e);
   (*inv)[2] = det * (a * b - d * d);
   (*inv)[3] = det * efcd;
   (*inv)[4] = det * dfbe;
   (*inv)[5] = det * (e * d - a * f);

#if 0
   /* This test fires very occasionally, and there's not much point in
    * it anyhow - the matrix inversion algorithm is simple enough that
    * we can be confident it's correctly implemented, so we might as
    * well save the cycles and not perform this check.
    */
     { /* check that original * inverse = identity matrix */
        int i;
        var p;
        real D = 0;
        mulss(&p, v, inv);
        for (i = 0; i < 3; i++) {
           int j;
           for (j = 0; j < 3; j++) D += fabs(p[i][j] - (real)(i==j));
        }
        if (D > THRESHOLD) {
           printf("original * inverse=\n");
           print_svar(*v);
           printf("*\n");
           print_svar(*inv);
           printf("=\n");
           print_var(p);
           BUG("matrix didn't invert");
        }
        check_svar(inv);
     }
#endif
#endif
   return 1;
}

/* r = (b^-1)a ; r,a delta vectors; b variance matrix */
#ifndef NO_COVARIANCES
void
divds(delta *r, const delta *a, const svar *b)
{
#ifdef NO_COVARIANCES
   /* variance-only version */
   (*r)[0] = (*a)[0] / (*b)[0];
   (*r)[1] = (*a)[1] / (*b)[1];
   (*r)[2] = (*a)[2] / (*b)[2];
#else
   svar b_inv;
   if (!invert_svar(&b_inv, b)) {
      print_svar(*b);
      BUG("covariance matrix is singular");
   }
   mulsd(r, &b_inv, a);
#endif
}
#endif

bool
fZeros(const svar *v) {
#ifdef NO_COVARIANCES
   /* variance-only version */
   return ((*v)[0] == 0.0 && (*v)[1] == 0.0 && (*v)[2] == 0.0);
#else
   check_svar(v);
   for (int i = 0; i < 6; i++) if ((*v)[i] != 0.0) return false;

   return true;
#endif
}