abacus: bignum: optimize div_mod

src/bignum/bignum.cc

@@ -30,6 +30,35 @@ void trim_leading_zeros(digits_type& num) {
     num.erase(it.base(), num.end());
 }
 
+// More optimised than full-on div_mod
+digits_type do_halve(digits_type num) {
+    assert(num.size() != 0);
+
+    int carry = 0;
+    for (auto i = num.rbegin(); i != num.rend(); ++i) {
+        auto const was_odd = (*i % 2) == 1;
+        *i /= 2;
+        *i += carry;
+        if (was_odd) {
+            carry = BASE / 2;
+        } else {
+            carry = 0;
+        }
+    }
+
+    trim_leading_zeros(num);
+
+    return num;
+}
+
+bool is_odd(digits_type const& num) {
+    if (num.size() == 0) {
+        return false;
+    }
+
+    return (num.front() % 2) == 1;
+}
+
 digits_type do_addition(digits_type const& lhs, digits_type const& rhs) {
     int carry = 0;
     digits_type res;
@@ -110,59 +139,33 @@ std::pair<digits_type, digits_type> do_div_mod(digits_type const& lhs,
         throw std::invalid_argument("attempt to divide by zero");
     }
 
+    digits_type multiple = rhs;
+    digits_type rank;
+    rank.push_back(1);
+
+    while (!do_less_than(lhs, multiple)) {
+        multiple = do_addition(multiple, multiple);
+        rank = do_addition(rank, rank);
+    }
+
     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;
-            multiple = do_addition(multiple, multiple);
-            rank = do_addition(rank, rank);
+        while (do_less_than(remainder, multiple)) {
+            multiple = do_halve(multiple);
+            rank = do_halve(rank);
         }
 
-        quotient = do_addition(quotient, prev_rank);
-        remainder = do_substraction(remainder, prev_multiple);
+        assert(!do_less_than(multiple, rhs));
+
+        quotient = do_addition(quotient, rank);
+        remainder = do_substraction(remainder, multiple);
     }
 
     return std::make_pair(quotient, remainder);
 }
 
-// More optimised than full-on div_mod
-digits_type do_halve(digits_type num) {
-    assert(num.size() != 0);
-
-    int carry = 0;
-    for (auto i = num.rbegin(); i != num.rend(); ++i) {
-        auto const was_odd = (*i % 2) == 1;
-        *i /= 2;
-        *i += carry;
-        if (was_odd) {
-            carry = BASE / 2;
-        }
-    }
-
-    trim_leading_zeros(num);
-
-    return num;
-}
-
-bool is_odd(digits_type const& num) {
-    if (num.size() == 0) {
-        return false;
-    }
-
-    return (num.front() % 2) == 1;
-}
-
 digits_type do_pow(digits_type lhs, digits_type rhs) {
     assert(rhs.size() != 0);