remove unneeded limit register

bericht.tex

@@ -52,8 +52,8 @@
 \begin{lstlisting}
 typedef uint32_t u32;
 void heron_sqrt(u32 *mem) {
-  int i;
-  for (i = 1; i <= mem[0]; i++){
+  int i = mem[0];
+  while (i > 0) {
     u32 s = mem[i];
     if (s > 1) {
       // x_0 = (s + 1) / 2
@@ -71,6 +71,7 @@ void heron_sqrt(u32 *mem) {
       }
       mem[i] = x;
     }
+    i--;
   }
 }
 \end{lstlisting}

graph.dot

@@ -2,19 +2,17 @@
 digraph heron {
   //node [shape=circle,regular=1,style=filled,fillcolor=white];
   edge [arrowhead=odot];
-  graph [overlap=false];
-
+  graph [overlap=scale];
   subgraph {
     edge [weight=3];
-    C0 -> C1 -> C2 -> C3 -> C4 -> C5 -> C6 -> C7 -> C8 -> C9
+    C0 -> C1 -> C2 -> C3 -> C4 -> C5 -> C6 -> C7 -> C8 -> C9 [minlen=3.5];
   }
 
-
   // variables & constants
   mem_0         [label="mem[0]"];
   mem_i         [label="mem[i]"];
-  mem_i2        [label="mem[i]"];
-  i             [              ];
+  mem_i2        [label="mem[i]",shape="box"];
+  i             [label="i"];
   1             [              ];
   "1a"          [label="1"     ];
   "1b"          [label="1"     ];
@@ -23,30 +21,32 @@ digraph heron {
   Finish        [label="Finish"];
 
   // operands
-  s_shift_1       [label=">>",];
-  i_lte_mem_0     [label=">=",];
+  s_shift_1 [label=">>",];
+  i_lt_0   [label=">",];
 
   // i <= mem[0]
-  mem_0 -> i_lte_mem_0;
-  i -> i_lte_mem_0;
-  { rank=same; C1; i_lte_mem_0; }
-  { rank=same; C0; i; mem_0;}
+  mem_0 -> i:n [label="C0",style=dotted];
+
+  0 -> i_lt_0;
+  i -> i_lt_0;
+  { rank=same; C0; i}
+  { rank=same; C1; i_lt_0; }
 
   // if (i <= mem[0]) ->
-  i_lte_mem_0 -> mem_s_gte_1  [style=dotted, arrowhead=normal,label="True",lhead=cluster_i_lte_mem_0];
+  i_lt_0 -> mem_s_gte_1  [style=dotted, arrowhead=normal,label="True"];
   // else
-  i_lte_mem_0 -> Finish  [style=dotted, arrowhead=normal,label="False",lhead=cluster_i_lte_mem_0];
+  i_lt_0 -> Finish  [style=dotted, arrowhead=normal,label="False"];
   { rank=same; C9; Finish;}
 
-  subgraph i_lte_mem_0 {
+  subgraph i_lt_0 {
     mem_s_gte_1     [label=">"];
 
     s_div_x         [label="/",];
     new_x           [label="+",];
     s_div_x_shift_1 [label=">>",];
     x_shift_1       [label=">>",];
-    old_x_lte_new_x [label="¹>=",];
-    inc_i           [label="+",];
+    old_x_lte_new_x [label=">=",];
+    dec_i           [label="-",];
 
     // (s > 1)
     mem_i -> mem_s_gte_1;
@@ -56,16 +56,17 @@ digraph heron {
     // if (s > 1)
     mem_s_gte_1 -> s_shift_1 [style=dotted,arrowhead=normal,label="True"];
     // else
-    mem_s_gte_1 -> inc_i [style=dotted,arrowhead=normal,label="False"];
+    mem_s_gte_1 -> dec_i [style=dotted,arrowhead=normal,label="False"];
 
     subgraph if_mem_i_gte_1 {
       // x = s >> 1
       mem_i -> s_shift_1;
       1 -> s_shift_1;
-      s_shift_1 -> x;
+      s_shift_1 -> x [style=dotted,arrowhead=normal,label="C2->C3"];
       { rank=same; C3; s_shift_1; x}
 
       // (x >> 1)
+      x [shape="box"];
       x -> x_shift_1;
       "1a" -> x_shift_1;
       // (s/x)
@@ -86,20 +87,20 @@ digraph heron {
       // (old_x <= X)
       x -> old_x_lte_new_x;
       new_x -> old_x_lte_new_x;
-      new_x -> x [style=dotted,label="if(¹)"];
+      new_x -> x [style=dotted,label="C7->C3"];
 
       { rank=same; C7; old_x_lte_new_x;}
 
       // if (old_x <= X)
-      old_x_lte_new_x -> inc_i [style=dotted,arrowhead=normal,label="True"];
+      old_x_lte_new_x -> dec_i [style=dotted,arrowhead=normal,label="True"];
       // else
+      old_x_lte_new_x -> x [style=dotted,arrowhead=normal,label="False"];
 
-
-      "1c" -> inc_i;
-      i -> inc_i:ne;
-      inc_i:s -> i:s;
-      new_x -> mem_i2 [label="if(¹)", style=dotted];
-      { rank=same; C8; inc_i; mem_i2};
+      "1c" -> dec_i;
+      i -> dec_i:ne;
+      dec_i:s -> i:s;
+      new_x -> mem_i2 [label="C7->C8", style=dotted];
+      { rank=same; C8; dec_i; mem_i2};
     }
   }
 }

sqrt.c

@@ -7,8 +7,8 @@
 typedef uint32_t u32;
 
 void heron_sqrt(u32 *mem) {
-  int i;
-  for (i = 1; i <= mem[0]; i++){
+  int i = mem[0];
+  while (i > 0) {
     u32 s = mem[i];
     if (s > 1) {
       // x_0 = (s + 1) / 2
@@ -26,6 +26,7 @@ void heron_sqrt(u32 *mem) {
       }
       mem[i] = x;
     }
+    i--;
   }
 }