abacus: bignum: optimize div_mod

src/bignum/bignum.cc

@@ -139,27 +139,28 @@ std::pair<digits_type, digits_type> do_div_mod(digits_type const& lhs,
         throw std::invalid_argument("attempt to divide by zero");
     }
 
-    digits_type quotient;
-    digits_type remainder = lhs;
-
-    while (!do_less_than(remainder, rhs)) {
-        // TODO: use `do_halve` to back down after calculate highest multiple
     digits_type multiple = rhs;
     digits_type rank;
     rank.push_back(1);
 
-        digits_type prev_multiple = multiple;
-        digits_type prev_rank = rank;
-
-        while (!do_less_than(remainder, multiple)) {
-            prev_multiple = multiple;
-            prev_rank = rank;
+    while (!do_less_than(lhs, multiple)) {
         multiple = do_addition(multiple, multiple);
         rank = do_addition(rank, rank);
     }
 
-        quotient = do_addition(quotient, prev_rank);
-        remainder = do_substraction(remainder, prev_multiple);
+    digits_type quotient;
+    digits_type remainder = lhs;
+
+    while (!do_less_than(remainder, rhs)) {
+        while (do_less_than(remainder, multiple)) {
+            multiple = do_halve(multiple);
+            rank = do_halve(rank);
+        }
+
+        assert(!do_less_than(multiple, rhs));
+
+        quotient = do_addition(quotient, rank);
+        remainder = do_substraction(remainder, multiple);
     }
 
     return std::make_pair(quotient, remainder);