expansion is now computed exactly and for most geometries

bigstuff.cpp

@@ -1268,7 +1268,7 @@ void moreBigStuff(cell *c) {
         }
       if(d == 1) {
         // roughly as many knights as table cells
-        if(hrand(PURE ? 2618 : 1720) < 1000) 
+        if(hrand(1000000) < 1000000 / expansion.get_growth())
           c->monst = moKnight;
         if(!eubinary) for(int i=0; i<S7; i++) generateAlts(c->master->move(i));
         for(int i=0; i<c->type; i++) 

compileunits.h

@@ -33,6 +33,7 @@
 #include "archimedean.cpp"
 #include "language.cpp"
 #include "cell.cpp"
+#include "expansion.cpp"
 #include "goldberg.cpp"
 #include "irregular.cpp"
 #include "pattern2.cpp"

game.cpp

@@ -6931,44 +6931,6 @@ void roundTableMessage(cell *c2) {
     }
   }
 
-long long circlesize[100], disksize[100];
-ld circlesizeD[10000];
-int lastsize;
-
-bool sizes_known() {
-  return euclid || (geometry == gNormal && STDVAR);
-  }
-
-void computeSizes() {
-  lastsize = PURE ? 44 : 76;
-
-  circlesize[0] = 1;
-  
-  if(euclid) {
-    for(int i=1; i<100; i++) circlesize[i] = 6 * i;
-    }
-  
-  else if(BITRUNCATED) {
-    circlesize[1] = 1*7;
-    circlesize[2] = 2*7;
-    circlesize[3] = 4*7;
-    circlesize[4] = 7*7;
-    for(int i=5; i<100; i++) 
-      circlesize[i] = circlesize[i-1] + circlesize[i-2] + circlesize[i-3] - circlesize[i-4];
-    }
-  else {
-    // actually these are each second Fibonacci number
-    circlesize[1] = 1*7;
-    circlesize[2] = 3*7;
-    for(int i=3; i<100; i++) 
-      circlesize[i] = 3*circlesize[i-1] - circlesize[i-2];
-    }
-    
-  disksize[0] = 0;
-  for(int i=1; i<100; i++) 
-    disksize[i] = disksize[i-1] + circlesize[i-1];
-  }
-
 void knightFlavorMessage(cell *c2) {
 
   if(!euclid && !c2->master->alt) {
@@ -6981,8 +6943,6 @@ void knightFlavorMessage(cell *c2) {
     return;
     }
 
-  computeSizes();
-
   bool grailfound = grailWasFound(c2);
   int rad = roundTableRadius(c2);
   bool tooeasy = (rad < newRoundTableRadius());
@@ -7016,14 +6976,11 @@ void knightFlavorMessage(cell *c2) {
   else if(msgid == 7 && items[itSpice] < 10 && !peace::on) {
     addMessage(XLAT("\"Train in the Desert first!\""));
     }
-  else if(msgid == 8 && sizes_known()) {
-    if(rad <= lastsize)
-      addMessage(XLAT("\"Our Table seats %1 Knights!\"", llts(circlesize[rad])));
-    else
-      addMessage(XLAT("\"By now, you should have your own formula, you know?\""));
+  else if(msgid == 8 && sizes_known() && !tactic::on) {
+    addMessage(XLAT("\"Our Table seats %1 Knights!\"", expansion.get_descendants(rad).get_str(100)));
     }
-  else if(msgid == 9 && rad <= lastsize && sizes_known()) {
-      addMessage(XLAT("\"There are %1 floor tiles inside our Table!\"", llts(disksize[rad])));
+  else if(msgid == 9 && sizes_known() && !tactic::on) {
+    addMessage(XLAT("\"There are %1 floor tiles inside our Table!\"", expansion.get_descendants(rad-1, expansion.diskid).get_str(100)));
     }
   else if(msgid == 10 && !items[itPirate] && !items[itWhirlpool] && !peace::on) {
     addMessage(XLAT("\"Have you tried to take a boat and go into the Ocean? Try it!\""));

hud.cpp

@@ -346,46 +346,8 @@ bool nofps = false;
 void drawStats() {
   if(nohud || stereo::mode == stereo::sLR) return;
   if(callhandlers(false, hooks_prestats)) return;
-  if(viewdists && sidescreen) {
-    distcolors[0] = forecolor;
-    dialog::init("");
-    int qty[64];
-    vector<cell*>& ac = currentmap->allcells();
-    for(int i=0; i<64; i++) qty[i] = 0;
-    for(int i=0; i<isize(ac); i++) {
-      int d = celldistance(ac[i], cwt.at);
-      if(d >= 0 && d < 64) qty[d]++;
-      }
-
-    if(geometry == gNormal && BITRUNCATED)
-      for(int i=8; i<=15; i++) 
-        qty[i] = qty[i-1] + qty[i-2] + qty[i-3] - qty[i-4];
-
-    if(geometry == gNormal && PURE)
-      for(int i=6; i<=15; i++) 
-        qty[i] = 3*qty[i-1] - qty[i-2];
-
-    if(geometry == gEuclid)
-      for(int i=8; i<=15; i++) qty[i] = 6*i;
-    for(int i=0; i<64; i++) if(qty[i])
-      dialog::addInfo(its(qty[i]), distcolors[i&7]);
-
-    if(geometry == gNormal && BITRUNCATED) {
-      dialog::addBreak(200);
-      dialog::addHelp("a(d+4) = a(d+3) + a(d+2) + a(d+1) - a(d)");
-      dialog::addInfo("a(d) ~ 1.72208ᵈ", forecolor);
-      }
-    if(geometry == gNormal && PURE) {
-      dialog::addBreak(200);
-      dialog::addHelp("a(d+2) = 3a(d+1) - a(d+2)");
-      dialog::addInfo("a(d) ~ 2.61803ᵈ", forecolor);
-      }
-    if(geometry == gEuclid) {
-      dialog::addBreak(300);
-      dialog::addInfo("a(d) = 6d", forecolor);
-      }
-    dialog::display();
-    }
+  if(viewdists && sidescreen) 
+    expansion.view_distances_dialog();
   if(sidescreen) return;
 
   {

hyper.h

@@ -4106,5 +4106,69 @@ namespace anims {
 extern int animation_lcm;
 extern ld animation_factor;
 ld parseld(const string& s);
+pair<int, int> vec_to_pair(int vec);
+
+struct bignum {
+  static const int BASE = 1000000000;
+  static const long long BASE2 = BASE * (long long)BASE;
+  vector<int> digits;
+  bignum() {}
+  bignum(int i) : digits() { digits.push_back(i); }
+  void be(int i) { digits.resize(1); digits[0] = i; }
+  bignum& operator +=(const bignum& b);
+  string get_str(int max_length);
+  ld approx() {
+    if(digits.empty()) return 0;
+    return digits.back() * pow(BASE, isize(digits) - 1);
+    }
+  
+  int approx_int() {
+    if(isize(digits) > 1) return BASE;
+    if(digits.empty()) return 0;
+    return digits[0];
+    }
+  
+  long long approx_ll() {
+    if(isize(digits) > 2) return BASE2;
+    if(digits.empty()) return 0;
+    if(isize(digits) == 1) return digits[0];
+    return digits[0] + digits[1] * (long long) BASE;
+    }
+  };
+
+struct expansion_analyzer {
+  vector<int> gettype(cell *c);
+  int N;
+  vector<cell*> samples;  
+  map<vector<int>, int> codeid;  
+  vector<vector<int> > children;  
+  int rootid, diskid;
+  int coefficients_known;
+  vector<int> coef;
+  int valid_from, tested_to;
+  ld growth;
+  
+  int sample_id(cell *c);
+  void preliminary_grouping();
+  void reduce_grouping();
+  vector<vector<bignum>> descendants;
+  bignum& get_descendants(int level);
+  bignum& get_descendants(int level, int type);
+  void find_coefficients();
+  void reset();
+  
+  expansion_analyzer() { reset(); }
+
+  string approximate_descendants(int d, int max_length);
+  void view_distances_dialog();
+  ld get_growth();
+
+  private:
+  bool verify(int id);
+  int valid(int v, int step);
+  };
+
+extern expansion_analyzer expansion;
+
 }
 

quit.cpp

@@ -31,25 +31,6 @@ void noaction() {}
 
 function<void()> cancel = noaction;
 
-string circlesizestr(int r) {
-  computeSizes();
-  string s;
-  int last = lastsize;
-  if(r <= last)
-    return llts(circlesize[r]);
-  else {
-    double d = log(circlesize[last]) + (log(circlesize[last]) - log(circlesize[last-1]))*(r-last);
-    int dlost = 0;
-    while(d > 10 * log(10)) d -= log(10), dlost++;
-    char buf[300]; sprintf(buf, "%.0f", exp(d)); 
-    string ss = XLAT("about ") + buf;
-    while(dlost % 9) dlost--, ss += '0';
-    for(int r = 0; r < 50 && dlost; r++) dlost -= 9, ss += " 000000000";
-    if(dlost) ss += XLAT(" (%1 more digits)", its(dlost));
-    return ss;
-    }
-  }
-
 hint hints[] = {
 
   {
@@ -246,13 +227,13 @@ hint hints[] = {
     0,
     []() { return !canmove && sizes_known() && celldist(cwt.at) >= 50; },
     []() {
-      int c = celldist(cwt.at);
-      string s = circlesizestr(c);
+      int d = celldist(cwt.at);
+      string s = expansion.approximate_descendants(d, 10000);
       dialog::addHelp(XLAT(
         "You are %1 cells away from the starting point, or "
         "the place where you used an Orb of Safety last time. "
         "There are %2 such cells.\n",
-        its(c), s
+        its(d), s
         ));
       dialog::addBreak(50);
       dialog::addItem(XLAT("expansion"), 'z');

system.cpp

@@ -1267,6 +1267,7 @@ void start_game() {
   game_active = true;
   if(need_reset_geometry) resetGeometry(), need_reset_geometry = false;
   initcells();
+  expansion.reset();
 
   if(randomPatternsMode) {
     for(int i=0; i<landtypes; i++) {