diff --git a/src/common/bit_set.h b/src/common/bit_set.h
index 3059d0cb0..9c2e6b28c 100644
--- a/src/common/bit_set.h
+++ b/src/common/bit_set.h
@@ -121,22 +121,19 @@ public:
     class Iterator {
     public:
         Iterator(const Iterator& other) : m_val(other.m_val), m_bit(other.m_bit) {}
-        Iterator(IntTy val, int bit) : m_val(val), m_bit(bit) {}
+        Iterator(IntTy val) : m_val(val), m_bit(0) {}
         Iterator& operator=(Iterator other) {
             new (this) Iterator(other);
             return *this;
         }
         int operator*() {
-            return m_bit;
+            return m_bit + ComputeLsb();
         }
         Iterator& operator++() {
-            if (m_val == 0) {
-                m_bit = -1;
-            } else {
-                int bit = LeastSignificantSetBit(m_val);
-                m_val &= ~(1 << bit);
-                m_bit = bit;
-            }
+            int lsb = ComputeLsb();
+            m_val >>= lsb + 1;
+            m_bit += lsb + 1;
+            m_has_lsb = false;
             return *this;
         }
         Iterator operator++(int _) {
@@ -145,15 +142,24 @@ public:
             return other;
         }
         bool operator==(Iterator other) const {
-            return m_bit == other.m_bit;
+            return m_val == other.m_val;
         }
         bool operator!=(Iterator other) const {
-            return m_bit != other.m_bit;
+            return m_val != other.m_val;
         }
 
     private:
+        int ComputeLsb() {
+            if (!m_has_lsb) {
+                m_lsb = LeastSignificantSetBit(m_val);
+                m_has_lsb = true;
+            }
+            return m_lsb;
+        }
         IntTy m_val;
         int m_bit;
+        int m_lsb = -1;
+        bool m_has_lsb = false;
     };
 
     BitSet() : m_val(0) {}
@@ -221,11 +227,10 @@ public:
     }
 
     Iterator begin() const {
-        Iterator it(m_val, 0);
-        return ++it;
+        return Iterator(m_val);
     }
     Iterator end() const {
-        return Iterator(m_val, -1);
+        return Iterator(0);
     }
 
     IntTy m_val;