faster virtualRebase in Solv

geometry2.cpp

@@ -331,6 +331,43 @@ void virtualRebase(cell*& base, T& at, const U& check) {
     return;
     }
 
+  if(geometry == gSol) {
+    /** the general algorithm sometimes makes much more iterations than needed... try to approximate the geodesic */
+    hyperpoint h = check(at);
+    auto step = [&] (int i) {
+      at = currentmap->adj(base, i) * at;
+      base = base->cmove(i);
+      h = check(at);
+      };
+
+    auto nw = vid.binary_width * log(2);
+    while(abs(h[0]) > 2) step(2);
+    while(h[0] < -0.5 * nw) step(0);
+    while(h[0] > +0.5 * nw) step(4);
+    while(abs(h[1]) > 2) {
+      step(6);
+      while(h[0] < -0.5 * nw) step(0);
+      while(h[0] > +0.5 * nw) step(4);
+      }
+    while(h[1] < -0.5 * nw) step(1);
+    while(h[1] > +0.5 * nw) step(5);
+    while(h[2] > 1) {
+      step(6);
+      while(h[0] < -0.5 * nw) step(0);
+      while(h[0] > +0.5 * nw) step(4);
+      while(h[1] < -0.5 * nw) step(1);
+      while(h[1] > +0.5 * nw) step(5);
+      }
+    while(h[2] < -1) {
+      step(2);
+      while(h[0] < -0.5 * nw) step(0);
+      while(h[0] > +0.5 * nw) step(4);
+      while(h[1] < -0.5 * nw) step(1);
+      while(h[1] > +0.5 * nw) step(5);
+      }
+    }
+  /* todo variants of sol */
+
   if(prod) {
     auto d = product_decompose(check(at)).first;
     while(d > cgi.plevel / 2)  {