From 2fb92ecc2d9aa1220fc65a7c016f7d07c47d09e4 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Mon, 6 Oct 2025 21:13:03 +0200
Subject: [PATCH] arbiquotient

---
 arbiquotient.cpp | 413 +++++++++++++++++++++++++++++++++++++++++++++++
 geom-exp.cpp     |  18 ++-
 history.cpp      |   2 +-
 hyper.cpp        |   1 +
 4 files changed, 429 insertions(+), 5 deletions(-)
 create mode 100644 arbiquotient.cpp

diff --git a/arbiquotient.cpp b/arbiquotient.cpp
new file mode 100644
index 00000000..72f37928
--- /dev/null
+++ b/arbiquotient.cpp
@@ -0,0 +1,413 @@
+#include "hyper.h"
+#include <iostream>
+#include <fstream>
+#include <thread>
+
+namespace hr {
+
+EX namespace arbiquotient {
+
+map<cell*, cellwalker> aqs;
+
+int next_id;
+
+struct aqdata {
+  cell *where;
+  bool closed;
+  cellwalker parent;
+  int size;
+  int id;
+  aqdata(cell *c) : where(c), parent(c) { id = next_id++; size = 1; closed = false; }
+  };
+
+/* the stack of known unifications */
+vector<pair<cellwalker, cellwalker>> unifications;
+
+vector<aqdata*> allaq;
+
+map<cell*, aqdata> aq;
+
+struct hr_precision_error : hr_exception { hr_precision_error() : hr_exception("precision error") {} };
+
+struct aq_overflow : hr_exception { aq_overflow(): hr_exception("autoquotient overflow") {} };
+struct aq_unsupported : hr_exception { aq_unsupported(): hr_exception("unsupported orbifold") {} };
+
+cellwalker rezero(cellwalker cw, cellwalker base) {
+  if(base.mirrored) cw += wmirror; cw -= base.spin;
+  return cw;
+  }
+
+cellwalker dezero(cellwalker cw, cellwalker base) {
+  cw += base.spin; if(base.mirrored) cw += wmirror; 
+  return cw;
+  }
+
+cellwalker ufind(cellwalker cw) {
+  auto& d = aq.at(cw.at);
+  if(d.where != cw.at) throw hr_exception("where incorrect");
+  if(d.parent == cw.at) return cw;
+  auto f = ufind(d.parent);
+  if(f.at != d.parent.at)
+    d.parent = f;
+  return dezero(f, cw);
+  }
+
+void enlist(cell *c) {
+  aq.emplace(c, c);
+  aqdata& ref = aq.at(c);
+  allaq.push_back(&ref);
+  }
+
+void default_list() {
+  cellwalker cw0 = currentmap->gamestart();
+  aqs.clear();
+  auto cw1 = cw0; for(int i=0; i<10; i++) cw1 = cw1 + wstep + 2;
+  auto cw2 = cw0+1; for(int i=0; i<10; i++) cw2 = cw2 + wstep + 2; cw2 = cw2 - 1;
+  aqs[cw1.at] = cw1;
+  aqs[cw2.at] = cw2;
+  }
+
+void clear_all() {
+  unifications = {}; next_id = 0; aq.clear(); allaq.clear();
+  }
+
+bool apply_uni() {
+  while(unifications.size()) {
+    auto cwp = unifications.back();
+    auto cw1 = cwp.first, cw2 = cwp.second;
+    unifications.pop_back();
+    cw1 = ufind(cw1);
+    cw2 = ufind(cw2);
+    if(cw1.at == cw2.at) {
+      if(cw1 != cw2) return false;
+      continue;
+      }
+    auto d1 = &aq.at(cw1.at);
+    auto d2 = &aq.at(cw2.at);
+    if(d1->id > d2->id) { swap(cw1, cw2); swap(d1, d2); }
+    d1->size += d2->size;
+    d2->parent = rezero(cw1, cw2);
+    if(cw2.at->item == itGold) cw2.at->item = itRuby;
+    for(int i=0; i<cw1.at->type; i++) {
+      auto m1 = cw1 + i + wstep;
+      auto m2 = cw2 + i + wstep;
+      if(aq.count(m1.at) && aq.count(m2.at))
+        unifications.emplace_back(m1, m2);
+      }
+    }
+  return true;
+  }
+
+vector<int> quotient_output(int dir) {
+  vector<int> output;
+  int next_offset = 0;
+  map<cell*, pair<int, cellwalker>> offsets;
+  vector<cell*> listorder;
+  auto assign_id = [&] (cellwalker cw) {
+    if(!offsets.count(cw.at)) {
+      auto& sh = arb::current.shapes[shvid(cw.at)];
+      while(cw.spin % sh.cycle_length) cw--;
+      offsets[cw.at] = { next_offset, cw };
+      listorder.push_back(cw.at);
+      next_offset += cw.at->type;
+      }
+    // auto [ofs, cw1] = offsets[cw.at];
+    auto &tmp = offsets[cw.at];
+    auto ofs = tmp.first;
+    auto cw1 = tmp.second;
+    return ofs + gmod(cw.spin - cw1.spin, cw.at->type);
+    };
+  assign_id(cellwalker(currentmap->gamestart(), dir));
+  for(int i=0; i<isize(listorder); i++) {
+    cell *c = listorder[i];
+    // auto [ofs, cw] = offsets[c];
+    auto cw = offsets[c].second;
+    for(int j=0; j<c->type; j++)
+      output.push_back(assign_id(ufind(cw + j + wstep)));
+    }
+  return output;
+  }
+
+set<buckethash_t> seen_outputs;
+
+struct qdata {
+  string name;
+  vector<int> connections;
+  };
+
+vector<qdata> all_found;
+
+void create() {
+  clear_all();
+
+  cellwalker cw0 = currentmap->gamestart();
+
+  enlist(cw0.at);
+
+  int loop_id = 0;
+
+  while(true) {
+
+    if(!apply_uni()) throw aq_unsupported();
+
+    if(loop_id == isize(allaq)) break;
+
+    cell *c = allaq[loop_id++]->where;
+    cellwalker cw(c);
+    auto cw1 = ufind(cw);
+    if(cw1 != cw) continue;
+    c->item = itGold;
+
+    for(int i=0; i<cw.at->type; i++) {
+      cellwalker cw2 = cw + i + wstep;
+      if(!aq.count(cw2.at)) {
+        enlist(cw2.at);
+        if(aqs.count(cw2.at)) unifications.emplace_back(cw0, aqs[cw2.at]);
+        }
+      else {
+        auto cw3 = ufind(cw2);
+        auto cw4 = cw3 + wstep - i;
+        if(aq.count(cw4.at)) unifications.emplace_back(cw4, cw);
+        }
+      }
+
+    if(next_id > 10000) throw aq_overflow();
+    }
+
+  /* vector<cell*> masters;
+  for(auto& data: aq) if(data.first == data.second.parent.at) masters.push_back(data.first);
+
+  println(hlog, "masters size = ", isize(masters)); */
+
+  }
+
+int aq_max = 100;
+bool running = false;
+bool displaying = false;
+
+set<buckethash_t> seen_hashes;
+
+void recurse() {
+  if(!running) return;
+  if(displaying) {
+    int tick = SDL_GetTicks();
+    if(tick > history::lastprogress + history::progress_each) {
+      history::lastprogress = tick;
+      mainloopiter();
+      }
+    }
+  vector<cell*> active;
+  int numopen = 0;
+  vector<cellwalker> backup;
+  buckethash_t hash = 0;
+  for(auto p: allaq) {
+    auto ref = ufind(p->where);
+    hashmix(hash, aq.at(ref.at).id);
+    hashmix(hash, ref.spin);
+    backup.push_back(p->parent);
+    if(p->parent.at == p->where) {
+      active.push_back(p->where);
+      if(!p->closed) numopen++;
+      }
+    }
+  if(seen_hashes.count(hash)) return;
+  seen_hashes.insert(hash);
+  
+  cellwalker cw0 = currentmap->gamestart();
+
+  println(hlog, "active ", isize(active), " numopen = ", numopen, " actives = ", active);
+  if(numopen == 0) {
+    println(hlog, "closed found!");
+    int shid = shvid(cw0.at);
+    vector<int> bqo = {999};
+    int cl = arb::current.shapes[shid].cycle_length;
+    for(int i=0; i<cw0.at->type; i+=cl) {
+      auto qo = quotient_output(i);
+      if(qo < bqo) bqo = qo;
+      }
+
+    buckethash_t vhash = 0;
+    for(auto i: bqo) hashmix(vhash, i);
+    if(seen_outputs.count(vhash)) return;
+    seen_outputs.insert(vhash);
+    println(hlog, "[", isize(all_found), "] ", bqo);
+    all_found.push_back(qdata{format("%016lX", (long) vhash), bqo});
+    if(!(cgflags & qCLOSED)) return;
+    }
+  indenter ind(2);
+
+  int shid = shvid(cw0.at);
+  int cl = arb::current.shapes[shid].cycle_length;
+
+  for(auto li: active) if(li != cw0.at) {
+    if(shvid(li) != shid) continue;
+    for(int ro=0; ro<cw0.at->type; ro+=cl) {
+      unifications.emplace_back(cw0, cellwalker(li, ro));
+      bool b = apply_uni();
+      if(b) recurse();
+      else unifications.clear();
+      }
+    auto backup_iterator = backup.begin();
+    for(auto p: allaq) p->parent = *(backup_iterator++);
+    }
+  }
+
+void auto_create(int num) {
+  clear_all();
+  seen_hashes.clear();
+  seen_outputs.clear();
+
+  cellwalker cw0 = currentmap->gamestart();
+  enlist(cw0.at);
+
+  int id = 0;
+  while(id < num) {
+    auto aqd = allaq[id++];
+    cell *c = aqd->where;
+    forCellCM(c1, c) if(!aq.count(c1)) enlist(c1);
+    aqd->closed = true;
+    }
+
+  println(hlog, "calling recurse");
+  indenter ind(2);
+  recurse();
+
+  println(hlog, "solutions found: ", isize(all_found));
+  }
+
+vector<int> quotient_data;
+
+void enable_by_id(int id) {
+  if(id >= isize(all_found)) throw hr_exception("not that many AQ quotients known");
+  stop_game();
+  cgflags |= qANYQ | qCLOSED;
+  quotient_data = all_found[id].connections;
+  start_game();
+  }
+
+struct hrmap_autoquotient : hrmap {
+
+  vector<pair<heptagon*, int>> connections;
+
+  pair<heptagon*, int> get_conn(int id, int shape) {
+    if(id >= isize(connections)) {
+      int t = arb::current.shapes[shape].size();
+      heptagon *h = init_heptagon(t);
+      h->zebraval = shape;
+      for(int i=0; i<t; i++) connections.emplace_back(h, i);
+      h->c7 = newCell(t, h);
+      }
+    if(id >= isize(connections)) throw hr_exception("illegal values in autoquotient");
+    return connections[id];
+    }
+
+  hrmap_autoquotient() {
+    get_conn(0, 0);
+    for(int i=0; i<isize(connections); i++) {
+      auto co = connections[i];
+      auto co2 = get_conn(quotient_data[i], arb::current.shapes[co.first->zebraval].connections[co.second].sid);
+      println(hlog, "connectng ", co, " to ", co2);
+      co.first->c.connect(co.second, co2.first, co2.second, 0);
+      }
+    println(hlog, "connections created");
+    }
+
+  heptagon *getOrigin() override { 
+    return connections[0].first;
+    }
+
+  transmatrix adj(heptagon *h, int dir) override {
+    return arb::get_adj(arb::current_or_slided(), h->zebraval, dir, h->move(dir)->zebraval, h->c.spin(dir), false);
+    }
+
+  int shvid(cell *c) override {
+    return c->master->zebraval;
+    }
+
+  hyperpoint get_corner(cell *c, int cid, ld cf) override {
+    auto& sh = arb::current_or_slided().shapes[c->master->zebraval];
+    int id = gmod(cid, c->type);
+    if(sh.angles[gmod(id-1, c->type)] <= 0) return sh.vertices[id];
+    return normalize(C0 + (sh.vertices[id] - C0) * 3 / cf);
+    }
+  };
+
+void show_auto_dialog() {
+  cmode = sm::SIDE | sm::DIALOG_STRICT_X;
+  gamescreen();
+  dialog::init(XLAT("auto-generate quotients"));
+  add_edit(aq_max);
+  dialog::addBoolItem(XLAT("running"), running, 'r');
+  dialog::add_action([] { 
+    println(hlog, "action");
+    if(!running) {
+      running = true;
+      displaying = true;
+      all_found.clear();
+      auto_create(aq_max);
+      }
+    running = false;
+    });
+  dialog::addSelItem(XLAT("quotients found"), its(isize(all_found)), 'n');
+  if(running) dialog::addBreak(100);
+  else dialog::addBack();
+  dialog::display();
+  // todo actually prevent backing
+  }
+
+EX void show_dialog() {
+  cmode = sm::SIDE | sm::DIALOG_STRICT_X;
+  gamescreen();
+  dialog::init(XLAT("arbitrary quotients"));
+
+  dialog::start_list(2000, 2000, 'A');
+  
+  for(auto& q: all_found) {
+    dialog::addBoolItem(q.name, q.connections == quotient_data, dialog::list_fake_key++);
+    dialog::add_action([q] {
+      stop_game();
+      cgflags |= qANYQ | qCLOSED;
+      quotient_data = q.connections;
+      ginf[geometry].quotient_name = q.name;
+      start_game();
+      });
+    }
+  dialog::end_list();
+
+  dialog::addItem("auto-generate", 'g');
+  dialog::add_action_push(show_auto_dialog);
+  if(cgflags & qANYQ) {
+    dialog::addItem("disable", 'd');
+    dialog::add_action([] {
+      stop_game();
+      cgflags &=~ qANYQ;
+      if(!sphere) cgflags &=~ qCLOSED;
+      quotient_data = {};
+      start_game();
+      });
+    }
+  else dialog::addBreak(100);
+  dialog::addBack();
+  dialog::display();
+  }
+
+auto aqhook =
+  arg::add3("-aq-test", [] { try { default_list(); create(); } catch(aq_overflow&) { println(hlog, "AQ overflow"); } })
++ arg::add3("-aq-auto", [] { displaying = false; running = true; arg::shift(); auto_create(arg::argi()); })
++ arg::add3("-aq-enable", [] { arg::shift(); enable_by_id(arg::argi()); })
++ arg::add3("-d:aq", [] { arg::launch_dialog(show_dialog); })
++ addHook(hooks_configfile, 100, [] {
+    param_i(aq_max, "aq_max")
+    -> editable(1, 500, 10, "limit on the quotient size", "", 'm');
+    })
++ addHook(hooks_newmap, 0, [] {
+    if(geometry == gArbitrary && quotient) {
+      return (hrmap*) new hrmap_autoquotient;
+      }
+    return (hrmap*) nullptr;
+    });
+
+
+}
+
+}
\ No newline at end of file
diff --git a/geom-exp.cpp b/geom-exp.cpp
index 43759e9b..6d4512b1 100644
--- a/geom-exp.cpp
+++ b/geom-exp.cpp
@@ -633,6 +633,8 @@ EX void select_quotient() {
     pushScreen(product::show_config);
   else if(mtwisted)
     hybrid::configure_period();
+  else if(arb::in())
+    pushScreen(arbiquotient::show_dialog);
   else {
     vector<eGeometry> choices;
     for(int i=0; i<isize(ginf); i++) if(same_tiling(eGeometry(i))) choices.push_back(eGeometry(i));
@@ -818,7 +820,12 @@ EX geometry_data compute_geometry_data() {
     case gMacbeath:
       gd.euler = -12;
       break;
-    
+
+    case gArbitrary:
+      gd.worldsize = isize(currentmap->allcells());
+      gd.euler = UNKNOWN;
+      break;
+
     default: 
       gd.worldsize = isize(currentmap->allcells());
       println(hlog, "warning: Euler characteristics unknown, worldsize = ", gd.worldsize);
@@ -851,6 +858,8 @@ EX geometry_data compute_geometry_data() {
   if(gd.euler < 0 && !closed_manifold)
     gd.worldsize = -gd.worldsize;
 
+  if(arb::in()) gd.worldsize = isize(currentmap->allcells());
+
   auto& spf = gd.spf;
   spf = its(ts);
   if(0) ;
@@ -952,6 +961,7 @@ EX geometry_data compute_geometry_data() {
 
   if(WDIM == 3) gd.euler = 0;
   gd.demigenus = 2 - gd.euler;
+  if(gd.euler == UNKNOWN) gd.demigenus = UNKNOWN;
 
   return gd;
   }
@@ -1179,12 +1189,12 @@ EX void showEuclideanMenu() {
   add_size_action();
 
   if(closed_manifold) {
-    dialog::addSelItem(XLAT("Euler characteristics"), its(gd.euler), 0);
+    dialog::addSelItem(XLAT("Euler characteristics"), gd.euler == UNKNOWN ? "?" : its(gd.euler), 0);
     if(WDIM == 3) ;
     else if(nonorientable)
-      dialog::addSelItem(XLAT("demigenus"), its(gd.demigenus), 0);
+      dialog::addSelItem(XLAT("demigenus"), gd.demigenus == UNKNOWN ? "?" : its(gd.demigenus), 0);
     else
-      dialog::addSelItem(XLAT("genus"), its(gd.demigenus/2), 0);
+      dialog::addSelItem(XLAT("genus"), gd.demigenus == UNKNOWN ? "?" : its(gd.demigenus/2), 0);
     }
   else dialog::addBreak(200);
   
diff --git a/history.cpp b/history.cpp
index 1230c589..d046f7b5 100644
--- a/history.cpp
+++ b/history.cpp
@@ -194,7 +194,7 @@ EX namespace history {
 
   void handleKeyC(int sym, int uni);
   
-  int lastprogress;
+  EX int lastprogress;
   
   EX void progress_screen() {
     gamescreen();
diff --git a/hyper.cpp b/hyper.cpp
index 0b8e2a57..a9c080da 100644
--- a/hyper.cpp
+++ b/hyper.cpp
@@ -134,6 +134,7 @@
 #include "intra.cpp"
 #include "crossbow.cpp"
 #include "fundamental.cpp"
+#include "arbiquotient.cpp"
 
 #if CAP_ROGUEVIZ
 #include "rogueviz/rogueviz-all.cpp"