source: git/src/network.c

/* network.c
 * Survex network reduction - find patterns and apply network reductions
 * Copyright (C) 1991-2002,2005,2024 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
 */

#if 0
#define DEBUG_INVALID 1
#define VALIDATE 1
#define DUMP_NETWORK 1
#endif

#include <config.h>

#include "validate.h"
#include "debug.h"
#include "cavern.h"
#include "message.h"
#include "netbits.h"
#include "network.h"
#include "osalloc.h"
#include "out.h"

typedef struct reduction {
   struct reduction *next;
   enum {
       TYPE_PARALLEL,
       TYPE_LOLLIPOP,
       TYPE_DELTASTAR,
   } type;
   linkfor* join[];
} reduction;

#define allocate_reduction(N) osmalloc(sizeof(reduction) + (N) * sizeof(linkfor*))

// Head of linked list of reductions.
static reduction *reduction_stack;

/* can be altered by -z<letters> on command line */
unsigned long optimize = BITA('l') | BITA('p') | BITA('d');
/* Lollipops, Parallel legs, Iterate mx, Delta* */

extern void
remove_subnets(void)
{
   node *stn, *stn2, *stn3, *stn4;
   int dirn, dirn2, dirn3, dirn4;
   reduction *trav;
   linkfor *newleg, *newleg2;
   bool fMore = true;

   reduction_stack = NULL;

   out_current_action(msg(/*Simplifying network*/129));

   while (fMore) {
      fMore = false;
      if (optimize & BITA('l')) {
#if PRINT_NETBITS
         printf("replacing lollipops\n");
#endif
         /* NB can have non-fixed 0 nodes */
         FOR_EACH_STN(stn, stnlist) {
            if (three_node(stn)) {
               dirn = -1;
               if (stn->leg[1]->l.to == stn) dirn++;
               if (stn->leg[0]->l.to == stn) dirn += 2;
               if (dirn < 0) continue;

               stn2 = stn->leg[dirn]->l.to;
               if (fixed(stn2)) {
                   /*    _
                    *   ( )
                    *    * stn
                    *    |
                    *    * stn2 (fixed)
                    *    : (may have other connections)
                    *
                    * The leg forming the "stick" of the lollipop is
                    * articulating so we can just fix stn with coordinates
                    * calculated by adding or subtracting the leg's vector.
                    */
                   linkfor *leg = stn->leg[dirn];
                   linkfor *rev_leg = reverse_leg(leg);
                   leg->l.reverse |= FLAG_ARTICULATION;
                   rev_leg->l.reverse |= FLAG_ARTICULATION;
                   if (data_here(leg)) {
                       subdd(&POSD(stn), &POSD(stn2), &leg->d);
                   } else {
                       adddd(&POSD(stn), &POSD(stn2), &rev_leg->d);
                   }
                   remove_stn_from_list(&stnlist, stn);
                   add_stn_to_list(&fixedlist, stn);
                   continue;
               }

               SVX_ASSERT(three_node(stn2));

               /*        _
                *       ( )
                *        * stn
                *        |
                *        * stn2
                *       / \
                * stn4 *   * stn3  -->  stn4 *---* stn3
                *      :   :                 :   :
                */
               dirn2 = reverse_leg_dirn(stn->leg[dirn]);
               dirn2 = (dirn2 + 1) % 3;
               stn3 = stn2->leg[dirn2]->l.to;
               if (stn2 == stn3) continue; /* dumb-bell - leave alone */

               dirn3 = reverse_leg_dirn(stn2->leg[dirn2]);

               trav = allocate_reduction(2);
               trav->type = TYPE_LOLLIPOP;

               newleg2 = (linkfor*)osnew(linkcommon);

               newleg = copy_link(stn3->leg[dirn3]);

               dirn2 = (dirn2 + 1) % 3;
               stn4 = stn2->leg[dirn2]->l.to;
               dirn4 = reverse_leg_dirn(stn2->leg[dirn2]);
#if 0
               printf("Lollipop found with stn...stn4 = \n");
               print_prefix(stn->name); putnl();
               print_prefix(stn2->name); putnl();
               print_prefix(stn3->name); putnl();
               print_prefix(stn4->name); putnl();
#endif

               addto_link(newleg, stn2->leg[dirn2]);

               /* remove stn and stn2 */
               remove_stn_from_list(&stnlist, stn);
               remove_stn_from_list(&stnlist, stn2);

               /* stack lollipop and replace with a leg between stn3 and stn4 */
               trav->join[0] = stn3->leg[dirn3];
               newleg->l.to = stn4;
               newleg->l.reverse = dirn4 | FLAG_DATAHERE | FLAG_REPLACEMENTLEG;

               trav->join[1] = stn4->leg[dirn4];
               newleg2->l.to = stn3;
               newleg2->l.reverse = dirn3 | FLAG_REPLACEMENTLEG;

               stn3->leg[dirn3] = newleg;
               stn4->leg[dirn4] = newleg2;

               trav->next = reduction_stack;
#if PRINT_NETBITS
               printf("remove lollipop\n");
#endif
               reduction_stack = trav;
               fMore = true;
            }
         }
      }

      if (optimize & BITA('p')) {
#if PRINT_NETBITS
         printf("replacing parallel legs\n");
#endif
         FOR_EACH_STN(stn, stnlist) {
            /*
             *  :            :
             *  * stn3       * stn3
             *  |            |
             *  * stn        |
             * ( )      -->  |
             *  * stn2       |
             *  |            |
             *  * stn4       * stn4
             *  :            :
             */
            if (three_node(stn)) {
               stn2 = stn->leg[0]->l.to;
               if (stn2 == stn->leg[1]->l.to) {
                  dirn = 2;
               } else if (stn2 == stn->leg[2]->l.to) {
                  dirn = 1;
               } else {
                  if (stn->leg[1]->l.to != stn->leg[2]->l.to) continue;
                  stn2 = stn->leg[1]->l.to;
                  dirn = 0;
               }

               /* stn == stn2 => lollipop */
               if (stn == stn2 || fixed(stn2)) continue;

               SVX_ASSERT(three_node(stn2));

               stn3 = stn->leg[dirn]->l.to;
               /* 3 parallel legs (=> nothing else) so leave */
               if (stn3 == stn2) continue;

               dirn3 = reverse_leg_dirn(stn->leg[dirn]);
               dirn2 = (0 + 1 + 2 - reverse_leg_dirn(stn->leg[(dirn + 1) % 3])
                        - reverse_leg_dirn(stn->leg[(dirn + 2) % 3]));

               stn4 = stn2->leg[dirn2]->l.to;
               dirn4 = reverse_leg_dirn(stn2->leg[dirn2]);

               trav = allocate_reduction(2);
               trav->type = TYPE_PARALLEL;

               newleg = copy_link(stn->leg[(dirn + 1) % 3]);
               /* use newleg2 for scratch */
               newleg2 = copy_link(stn->leg[(dirn + 2) % 3]);
                 {
#ifdef NO_COVARIANCES
                    vars sum;
                    var prod;
                    delta temp, temp2;
                    addss(&sum, &newleg->v, &newleg2->v);
                    SVX_ASSERT2(!fZeros(&sum), "loop of zero variance found");
                    mulss(&prod, &newleg->v, &newleg2->v);
                    mulsd(&temp, &newleg2->v, &newleg->d);
                    mulsd(&temp2, &newleg->v, &newleg2->d);
                    adddd(&temp, &temp, &temp2);
                    divds(&newleg->d, &temp, &sum);
                    sdivvs(&newleg->v, &prod, &sum);
#else
                    svar inv1, inv2, sum;
                    delta temp, temp2;
                    /* if leg one is an equate, we can just ignore leg two
                     * whatever it is */
                    if (invert_svar(&inv1, &newleg->v)) {
                       if (invert_svar(&inv2, &newleg2->v)) {
                          addss(&sum, &inv1, &inv2);
                          if (!invert_svar(&newleg->v, &sum)) {
                             BUG("matrix singular in parallel legs replacement");
                          }

                          mulsd(&temp, &inv1, &newleg->d);
                          mulsd(&temp2, &inv2, &newleg2->d);
                          adddd(&temp, &temp, &temp2);
                          mulsd(&newleg->d, &newleg->v, &temp);
                       } else {
                          /* leg two is an equate, so just ignore leg 1 */
                          linkfor *tmpleg;
                          tmpleg = newleg;
                          newleg = newleg2;
                          newleg2 = tmpleg;
                       }
                    }
#endif
                 }
               free(newleg2);
               newleg2 = (linkfor*)osnew(linkcommon);

               addto_link(newleg, stn2->leg[dirn2]);
               addto_link(newleg, stn3->leg[dirn3]);

#if 0
               printf("Parallel found with stn...stn4 = \n");
               (dump_node)(stn); (dump_node)(stn2); (dump_node)(stn3); (dump_node)(stn4);
               printf("dirns = %d %d %d %d\n", dirn, dirn2, dirn3, dirn4);
#endif
               SVX_ASSERT2(stn3->leg[dirn3]->l.to == stn, "stn3 end of || doesn't recip");
               SVX_ASSERT2(stn4->leg[dirn4]->l.to == stn2, "stn4 end of || doesn't recip");
               SVX_ASSERT2(stn->leg[(dirn+1)%3]->l.to == stn2 && stn->leg[(dirn + 2) % 3]->l.to == stn2, "|| legs aren't");

               /* remove stn and stn2 (already discarded triple parallel) */
               /* so stn!=stn4 <=> stn2!=stn3 */
               remove_stn_from_list(&stnlist, stn);
               remove_stn_from_list(&stnlist, stn2);

               /* stack parallel and replace with a leg between stn3 and stn4 */
               trav->join[0] = stn3->leg[dirn3];
               newleg->l.to = stn4;
               newleg->l.reverse = dirn4 | FLAG_DATAHERE | FLAG_REPLACEMENTLEG;

               trav->join[1] = stn4->leg[dirn4];
               newleg2->l.to = stn3;
               newleg2->l.reverse = dirn3 | FLAG_REPLACEMENTLEG;

               stn3->leg[dirn3] = newleg;
               stn4->leg[dirn4] = newleg2;

               trav->next = reduction_stack;
#if PRINT_NETBITS
               printf("remove parallel\n");
#endif
               reduction_stack = trav;
               fMore = true;
            }
         }
      }

      if (optimize & BITA('d')) {
         node *stn5, *stn6;
         int dirn5, dirn6;
         linkfor *legAB, *legBC, *legCA;
#if PRINT_NETBITS
         printf("replacing deltas with stars\n");
#endif
         FOR_EACH_STN(stn, stnlist) {
            /*    printf("*");*/
            /*
             *          :                     :
             *          * stn5                * stn5
             *          |                     |
             *          * stn2                |
             *         / \        -->         O stnZ
             *        |   |                  / \
             *    stn *---* stn3            /   \
             *       /     \               /     \
             * stn4 *       * stn6   stn4 *       * stn6
             *      :       :             :       :
             */
            if (three_node(stn)) {
               for (int dirn12 = 0; dirn12 <= 2; dirn12++) {
                  stn2 = stn->leg[dirn12]->l.to;
                  if (stn2 == stn || fixed(stn2)) continue;
                  SVX_ASSERT(three_node(stn2));
                  int dirn13 = (dirn12 + 1) % 3;
                  stn3 = stn->leg[dirn13]->l.to;
                  if (stn3 == stn || stn3 == stn2 || fixed(stn3)) continue;
                  SVX_ASSERT(three_node(stn3));
                  int dirn23 = reverse_leg_dirn(stn->leg[dirn12]);
                  dirn23 = (dirn23 + 1) % 3;
                  if (stn2->leg[dirn23]->l.to != stn3) {
                      dirn23 = (dirn23 + 1) % 3;
                      if (stn2->leg[dirn23]->l.to != stn3) {
                          continue;
                      }
                  }
                  legAB = copy_link(stn->leg[dirn12]);
                  legBC = copy_link(stn2->leg[dirn23]);
                  legCA = copy_link(stn3->leg[reverse_leg_dirn(stn->leg[dirn13])]);
                  dirn = (0 + 1 + 2) - dirn12 - dirn13;
                  dirn2 = (0 + 1 + 2) - dirn23 - reverse_leg_dirn(stn->leg[dirn12]);
                  dirn3 = (0 + 1 + 2) - reverse_leg_dirn(stn->leg[dirn13]) - reverse_leg_dirn(stn2->leg[dirn23]);
                  stn4 = stn->leg[dirn]->l.to;
                  stn5 = stn2->leg[dirn2]->l.to;
                  stn6 = stn3->leg[dirn3]->l.to;
                  if (stn4 == stn2 || stn4 == stn3 || stn5 == stn3) continue;
                  dirn4 = reverse_leg_dirn(stn->leg[dirn]);
                  dirn5 = reverse_leg_dirn(stn2->leg[dirn2]);
                  dirn6 = reverse_leg_dirn(stn3->leg[dirn3]);
#if 0
                  printf("delta-star, stn ... stn6 are:\n");
                  (dump_node)(stn);
                  (dump_node)(stn2);
                  (dump_node)(stn3);
                  (dump_node)(stn4);
                  (dump_node)(stn5);
                  (dump_node)(stn6);
#endif
                  SVX_ASSERT(stn4->leg[dirn4]->l.to == stn);
                  SVX_ASSERT(stn5->leg[dirn5]->l.to == stn2);
                  SVX_ASSERT(stn6->leg[dirn6]->l.to == stn3);

                  trav = allocate_reduction(3);
                  trav->type = TYPE_DELTASTAR;
                  {
                    linkfor *legAZ, *legBZ, *legCZ;
                    node *stnZ;
                    prefix *nameZ;
                    svar invAB, invBC, invCA, tmp, sum, inv;
                    var vtmp;
                    svar sumAZBZ, sumBZCZ, sumCZAZ;
                    delta temp, temp2;

                    /* FIXME: ought to handle cases when some legs are
                     * equates, but handle as a special case maybe? */
                    if (!invert_svar(&invAB, &legAB->v)) break;
                    if (!invert_svar(&invBC, &legBC->v)) break;
                    if (!invert_svar(&invCA, &legCA->v)) break;

                    addss(&sum, &legBC->v, &legCA->v);
                    addss(&tmp, &sum, &legAB->v);
                    if (!invert_svar(&inv, &tmp)) {
                       /* impossible - loop of zero variance */
                       BUG("loop of zero variance found");
                    }

                    legAZ = osnew(linkfor);
                    legBZ = osnew(linkfor);
                    legCZ = osnew(linkfor);

                    /* AZBZ */
                    /* done above: addvv(&sum, &legBC->v, &legCA->v); */
                    mulss(&vtmp, &sum, &inv);
                    smulvs(&sumAZBZ, &vtmp, &legAB->v);

                    adddd(&temp, &legBC->d, &legCA->d);
                    divds(&temp2, &temp, &sum);
                    mulsd(&temp, &invAB, &legAB->d);
                    subdd(&temp, &temp2, &temp);
                    mulsd(&legBZ->d, &sumAZBZ, &temp);

                    /* leg vectors after transform are determined up to
                     * a constant addition, so arbitrarily fix AZ = 0 */
                    legAZ->d[2] = legAZ->d[1] = legAZ->d[0] = 0;

                    /* BZCZ */
                    addss(&sum, &legCA->v, &legAB->v);
                    mulss(&vtmp, &sum, &inv);
                    smulvs(&sumBZCZ, &vtmp, &legBC->v);

                    /* CZAZ */
                    addss(&sum, &legAB->v, &legBC->v);
                    mulss(&vtmp, &sum, &inv);
                    smulvs(&sumCZAZ, &vtmp, &legCA->v);

                    adddd(&temp, &legAB->d, &legBC->d);
                    divds(&temp2, &temp, &sum);
                    mulsd(&temp, &invCA, &legCA->d);
                    /* NB: swapped arguments to negate answer for legCZ->d */
                    subdd(&temp, &temp, &temp2);
                    mulsd(&legCZ->d, &sumCZAZ, &temp);

                    free(legAB);
                    free(legBC);
                    free(legCA);

                    /* Now add two, subtract third, and scale by 0.5 */
                    addss(&sum, &sumAZBZ, &sumCZAZ);
                    subss(&sum, &sum, &sumBZCZ);
                    mulsc(&legAZ->v, &sum, 0.5);

                    addss(&sum, &sumBZCZ, &sumAZBZ);
                    subss(&sum, &sum, &sumCZAZ);
                    mulsc(&legBZ->v, &sum, 0.5);

                    addss(&sum, &sumCZAZ, &sumBZCZ);
                    subss(&sum, &sum, &sumAZBZ);
                    mulsc(&legCZ->v, &sum, 0.5);

                    nameZ = osnew(prefix);
                    nameZ->pos = osnew(pos);
                    nameZ->ident.p = NULL;
                    stnZ = osnew(node);
                    stnZ->name = nameZ;
                    nameZ->stn = stnZ;
                    nameZ->up = NULL;
                    nameZ->min_export = nameZ->max_export = 0;
                    nameZ->sflags = 0;
                    unfix(stnZ);
                    add_stn_to_list(&stnlist, stnZ);
                    legAZ->l.to = stnZ;
                    legAZ->l.reverse = 0 | FLAG_DATAHERE | FLAG_REPLACEMENTLEG;
                    legBZ->l.to = stnZ;
                    legBZ->l.reverse = 1 | FLAG_DATAHERE | FLAG_REPLACEMENTLEG;
                    legCZ->l.to = stnZ;
                    legCZ->l.reverse = 2 | FLAG_DATAHERE | FLAG_REPLACEMENTLEG;
                    stnZ->leg[0] = (linkfor*)osnew(linkcommon);
                    stnZ->leg[1] = (linkfor*)osnew(linkcommon);
                    stnZ->leg[2] = (linkfor*)osnew(linkcommon);
                    stnZ->leg[0]->l.to = stn4;
                    stnZ->leg[0]->l.reverse = dirn4;
                    stnZ->leg[1]->l.to = stn5;
                    stnZ->leg[1]->l.reverse = dirn5;
                    stnZ->leg[2]->l.to = stn6;
                    stnZ->leg[2]->l.reverse = dirn6;
                    addto_link(legAZ, stn4->leg[dirn4]);
                    addto_link(legBZ, stn5->leg[dirn5]);
                    addto_link(legCZ, stn6->leg[dirn6]);
                    /* stack stuff */
                    trav->join[0] = stn4->leg[dirn4];
                    trav->join[1] = stn5->leg[dirn5];
                    trav->join[2] = stn6->leg[dirn6];
                    trav->next = reduction_stack;
#if PRINT_NETBITS
                    printf("remove delta*\n");
#endif
                    reduction_stack = trav;
                    fMore = true;

                    remove_stn_from_list(&stnlist, stn);
                    remove_stn_from_list(&stnlist, stn2);
                    remove_stn_from_list(&stnlist, stn3);
                    stn4->leg[dirn4] = legAZ;
                    stn5->leg[dirn5] = legBZ;
                    stn6->leg[dirn6] = legCZ;
                  }
                  break;
               }
            }
         }
      }

   }
}

extern void
replace_subnets(void)
{
   node *stn2, *stn3, *stn4;
   int dirn2, dirn3, dirn4;

   /* help to catch bad accesses */
   stn2 = stn3 = stn4 = NULL;
   dirn2 = dirn3 = dirn4 = 0;

   out_current_action(msg(/*Calculating network*/130));

   while (reduction_stack != NULL) {
      /*  printf("replace_subnets() type %d\n", reduction_stack->type);*/

#if PRINT_NETBITS
      printf("replace_subnets\n");
      if (reduction_stack->type == TYPE_LOLLIPOP) printf("islollipop\n");
      if (reduction_stack->type == TYPE_PARALLEL) printf("isparallel\n");
      if (reduction_stack->type == TYPE_DELTASTAR) printf("isdelta*\n");
#endif

      if (reduction_stack->type != TYPE_DELTASTAR) {
         linkfor *leg;
         leg = reduction_stack->join[0]; leg = reverse_leg(leg);
         stn3 = leg->l.to; dirn3 = reverse_leg_dirn(leg);
         leg = reduction_stack->join[1]; leg = reverse_leg(leg);
         stn4 = leg->l.to; dirn4 = reverse_leg_dirn(leg);

         if (!fixed(stn3) || !fixed(stn4)) {
             SVX_ASSERT(!fixed(stn3) && !fixed(stn4));
             goto skip;
         }
         SVX_ASSERT(data_here(stn3->leg[dirn3]));
      }

      if (reduction_stack->type == TYPE_LOLLIPOP) {
         node *stn;
         delta e;
         linkfor *leg;
         int zero;

         leg = stn3->leg[dirn3];
         stn2 = reduction_stack->join[0]->l.to;
         dirn2 = reverse_leg_dirn(reduction_stack->join[0]);

         zero = fZeros(&leg->v);
         if (!zero) {
            delta tmp;
            subdd(&e, &POSD(stn4), &POSD(stn3));
            subdd(&tmp, &e, &leg->d);
            divds(&e, &tmp, &leg->v);
         }
         if (data_here(reduction_stack->join[0])) {
            adddd(&POSD(stn2), &POSD(stn3), &reduction_stack->join[0]->d);
            if (!zero) {
               delta tmp;
               mulsd(&tmp, &reduction_stack->join[0]->v, &e);
               adddd(&POSD(stn2), &POSD(stn2), &tmp);
            }
         } else {
            subdd(&POSD(stn2), &POSD(stn3), &stn2->leg[dirn2]->d);
            if (!zero) {
               delta tmp;
               mulsd(&tmp, &stn2->leg[dirn2]->v, &e);
               adddd(&POSD(stn2), &POSD(stn2), &tmp);
            }
         }
         dirn2 = (dirn2 + 2) % 3; /* point back at stn again */
         stn = stn2->leg[dirn2]->l.to;
#if 0
         printf("Replacing lollipop with stn...stn4 = \n");
         print_prefix(stn->name); putnl();
         print_prefix(stn2->name); putnl();
         print_prefix(stn3->name); putnl();
         print_prefix(stn4->name); putnl();
#endif
         if (data_here(stn2->leg[dirn2]))
            adddd(&POSD(stn), &POSD(stn2), &stn2->leg[dirn2]->d);
         else
            subdd(&POSD(stn), &POSD(stn2), &reverse_leg(stn2->leg[dirn2])->d);

         /* The "stick" of the lollipop is a new articulation. */
         stn2->leg[dirn2]->l.reverse |= FLAG_ARTICULATION;
         reverse_leg(stn2->leg[dirn2])->l.reverse |= FLAG_ARTICULATION;

         add_stn_to_list(&fixedlist, stn);
         add_stn_to_list(&fixedlist, stn2);

         free(stn3->leg[dirn3]);
         stn3->leg[dirn3] = reduction_stack->join[0];
         free(stn4->leg[dirn4]);
         stn4->leg[dirn4] = reduction_stack->join[1];
      } else if (reduction_stack->type == TYPE_PARALLEL) {
         /* parallel legs */
         node *stn;
         delta e, e2;
         linkfor *leg;
         int dirn;

         stn = reduction_stack->join[0]->l.to;
         stn2 = reduction_stack->join[1]->l.to;

         dirn = reverse_leg_dirn(reduction_stack->join[0]);
         dirn2 = reverse_leg_dirn(reduction_stack->join[1]);

         leg = stn3->leg[dirn3];

         if (leg->l.reverse & FLAG_ARTICULATION) {
            reduction_stack->join[0]->l.reverse |= FLAG_ARTICULATION;
            stn->leg[dirn]->l.reverse |= FLAG_ARTICULATION;
            reduction_stack->join[1]->l.reverse |= FLAG_ARTICULATION;
            stn2->leg[dirn2]->l.reverse |= FLAG_ARTICULATION;
         }

         if (fZeros(&leg->v))
            e[0] = e[1] = e[2] = 0.0;
         else {
            delta tmp;
            subdd(&e, &POSD(stn4), &POSD(stn3));
            subdd(&tmp, &e, &leg->d);
            divds(&e, &tmp, &leg->v);
         }

         if (data_here(reduction_stack->join[0])) {
            leg = reduction_stack->join[0];
            adddd(&POSD(stn), &POSD(stn3), &leg->d);
         } else {
            leg = stn->leg[dirn];
            subdd(&POSD(stn), &POSD(stn3), &leg->d);
         }
         mulsd(&e2, &leg->v, &e);
         adddd(&POSD(stn), &POSD(stn), &e2);

         if (data_here(reduction_stack->join[1])) {
            leg = reduction_stack->join[1];
            adddd(&POSD(stn2), &POSD(stn4), &leg->d);
         } else {
            leg = stn2->leg[dirn2];
            subdd(&POSD(stn2), &POSD(stn4), &leg->d);
         }
         mulsd(&e2, &leg->v, &e);
         subdd(&POSD(stn2), &POSD(stn2), &e2);
#if 0
         printf("Replacing parallel with stn...stn4 = \n");
         print_prefix(stn->name); putnl();
         print_prefix(stn2->name); putnl();
         print_prefix(stn3->name); putnl();
         print_prefix(stn4->name); putnl();
#endif

         add_stn_to_list(&fixedlist, stn);
         add_stn_to_list(&fixedlist, stn2);

         free(stn3->leg[dirn3]);
         stn3->leg[dirn3] = reduction_stack->join[0];
         free(stn4->leg[dirn4]);
         stn4->leg[dirn4] = reduction_stack->join[1];
      } else if (reduction_stack->type == TYPE_DELTASTAR) {
         node *stnZ;
         node *stn[3];
         int dirn[3];
         int i;
         linkfor *leg;

         /* work out ends as we don't bother stacking them */
         leg = reverse_leg(reduction_stack->join[0]);
         stn[0] = leg->l.to;
         dirn[0] = reverse_leg_dirn(leg);
         stnZ = stn[0]->leg[dirn[0]]->l.to;
         if (!fixed(stnZ)) {
            SVX_ASSERT(!fixed(stn[0]));
            goto skip;
         }
         stn[1] = stnZ->leg[1]->l.to;
         dirn[1] = reverse_leg_dirn(stnZ->leg[1]);
         stn[2] = stnZ->leg[2]->l.to;
         dirn[2] = reverse_leg_dirn(stnZ->leg[2]);
         /*print_prefix(stnZ->name);printf(" %p\n",(void*)stnZ);*/

         for (i = 0; i < 3; i++) {
            SVX_ASSERT2(fixed(stn[i]), "stn not fixed for D*");

            leg = stn[i]->leg[dirn[i]];

            SVX_ASSERT2(data_here(leg), "data not on leg for D*");
            SVX_ASSERT2(leg->l.to == stnZ, "bad sub-network for D*");

            stn2 = reduction_stack->join[i]->l.to;

            if (data_here(reduction_stack->join[i])) {
               adddd(&POSD(stn2), &POSD(stn[i]), &reduction_stack->join[i]->d);
            } else {
               subdd(&POSD(stn2), &POSD(stn[i]), &reverse_leg(reduction_stack->join[i])->d);
            }

            if (!fZeros(&leg->v)) {
               delta e, tmp;
               subdd(&e, &POSD(stnZ), &POSD(stn[i]));
               subdd(&e, &e, &leg->d);
               divds(&tmp, &e, &leg->v);
               if (data_here(reduction_stack->join[i])) {
                  mulsd(&e, &reduction_stack->join[i]->v, &tmp);
               } else {
                  mulsd(&e, &reverse_leg(reduction_stack->join[i])->v, &tmp);
               }
               adddd(&POSD(stn2), &POSD(stn2), &e);
            }
            add_stn_to_list(&fixedlist, stn2);
            free(leg);
            stn[i]->leg[dirn[i]] = reduction_stack->join[i];
            /* transfer the articulation status of the radial legs */
            if (stnZ->leg[i]->l.reverse & FLAG_ARTICULATION) {
               reduction_stack->join[i]->l.reverse |= FLAG_ARTICULATION;
               reverse_leg(reduction_stack->join[i])->l.reverse |= FLAG_ARTICULATION;
            }
            free(stnZ->leg[i]);
            stnZ->leg[i] = NULL;
         }
/*printf("---%f %f %f\n",POS(stnZ, 0), POS(stnZ, 1), POS(stnZ, 2));*/
         remove_stn_from_list(&fixedlist, stnZ);
         free(stnZ->name);
         free(stnZ);
      } else {
         BUG("reduction_stack has unknown type");
      }

skip:;
      reduction *ptrOld = reduction_stack;
      reduction_stack = reduction_stack->next;
      free(ptrOld);
   }
}