diff --git a/kll/include/kll_helper_impl.hpp b/kll/include/kll_helper_impl.hpp
index 31534d9a..56b5be69 100644
--- a/kll/include/kll_helper_impl.hpp
+++ b/kll/include/kll_helper_impl.hpp
@@ -39,8 +39,9 @@ uint8_t kll_helper::floor_of_log2_of_fraction(uint64_t numer, uint64_t denom) {
   if (denom > numer) { return 0; }
   uint8_t count = 0;
   while (true) {
+    // denom * 2 > numer, without overflowing denom
+    if (denom > (numer >> 1)) { return count; }
     denom <<= 1;
-    if (denom > numer) { return count; }
     count++;
   }
 }
diff --git a/kll/include/kll_sketch.hpp b/kll/include/kll_sketch.hpp
index d672c419..0133b899 100644
--- a/kll/include/kll_sketch.hpp
+++ b/kll/include/kll_sketch.hpp
@@ -237,6 +237,18 @@ class kll_sketch {
     template<typename FwdT>
     void update(FwdT&& item);
 
+    /**
+     * Updates this sketch with the given data item repeated the given number of times.
+     * The result is equivalent to calling update(item) weight times, at a cost that grows
+     * with the logarithm of the weight rather than with the weight itself.
+     * If cross-language portability is required, callers should ensure that
+     * the input string uses a compatible encoding (valid UTF-8).
+     * @param item from a stream of items
+     * @param weight number of times the item is repeated, must be positive
+     */
+    template<typename FwdT>
+    void update(FwdT&& item, uint64_t weight);
+
     /**
      * Merges another sketch into this one.
      * If sketches contain strings, callers are responsible for ensuring that
@@ -570,6 +582,9 @@ class kll_sketch {
         std::unique_ptr<T, items_deleter> items, uint32_t items_size, optional<T>&& min_item,
         optional<T>&& max_item, bool is_level_zero_sorted, const C& comparator);
 
+    // for weighted update
+    kll_sketch(uint16_t k, const T& item, uint64_t weight, const C& comparator, const A& allocator);
+
     // common update code
     inline void update_min_max(const T& item);
     inline uint32_t internal_update();
diff --git a/kll/include/kll_sketch_impl.hpp b/kll/include/kll_sketch_impl.hpp
index b12a39c8..fcc51d3a 100644
--- a/kll/include/kll_sketch_impl.hpp
+++ b/kll/include/kll_sketch_impl.hpp
@@ -186,6 +186,51 @@ void kll_sketch<T, C, A>::update(FwdT&& item) {
   reset_sorted_view();
 }
 
+template<typename T, typename C, typename A>
+template<typename FwdT>
+void kll_sketch<T, C, A>::update(FwdT&& item, uint64_t weight) {
+  if (weight == 0) throw std::invalid_argument("weight must be positive");
+  if (!check_update_item(item)) { return; }
+  if (weight < levels_[0]) { // fits into level zero without compaction
+    update_min_max(static_cast<const T&>(item));
+    for (uint64_t i = 1; i < weight; ++i) new (&items_[internal_update()]) T(static_cast<const T&>(item));
+    new (&items_[internal_update()]) T(std::forward<FwdT>(item));
+    reset_sorted_view();
+  } else {
+    merge(kll_sketch(k_, static_cast<const T&>(item), weight, comparator_, allocator_));
+  }
+}
+
+// An item at level h carries weight 2^h, so one copy of the item at each level
+// whose bit is set in the weight is an exact sketch of that many copies.
+// Level capacities are defined up to 61 levels, so bits above the top level
+// fold into weight >> 60 copies at level 60.
+template<typename T, typename C, typename A>
+kll_sketch<T, C, A>::kll_sketch(uint16_t k, const T& item, uint64_t weight, const C& comparator, const A& allocator):
+comparator_(comparator),
+allocator_(allocator),
+k_(k),
+m_(kll_constants::DEFAULT_M),
+min_k_(k),
+num_levels_(std::min<uint8_t>(64 - count_leading_zeros_in_u64(weight), 61)),
+is_level_zero_sorted_(true),
+n_(weight),
+levels_(num_levels_ + 1, 0, allocator),
+items_(nullptr),
+items_size_(0),
+min_item_(item),
+max_item_(item),
+sorted_view_(nullptr)
+{
+  for (uint8_t level = 0; level < num_levels_; ++level) {
+    const uint64_t count = level + 1 < num_levels_ ? (weight >> level) & 1 : weight >> level;
+    levels_[level + 1] = levels_[level] + static_cast<uint32_t>(count);
+  }
+  items_size_ = levels_[num_levels_];
+  items_ = allocator_.allocate(items_size_);
+  for (uint32_t i = 0; i < items_size_; ++i) new (&items_[i]) T(item);
+}
+
 template<typename T, typename C, typename A>
 void kll_sketch<T, C, A>::update_min_max(const T& item) {
   if (is_empty()) {
diff --git a/kll/test/kll_sketch_test.cpp b/kll/test/kll_sketch_test.cpp
index b8d0b031..d4aa396e 100644
--- a/kll/test/kll_sketch_test.cpp
+++ b/kll/test/kll_sketch_test.cpp
@@ -443,6 +443,9 @@ TEST_CASE("kll sketch", "[kll_sketch]") {
     REQUIRE(kll_helper::floor_of_log2_of_fraction(6, 2) == 1);
     REQUIRE(kll_helper::floor_of_log2_of_fraction(7, 2) == 1);
     REQUIRE(kll_helper::floor_of_log2_of_fraction(8, 2) == 2);
+    REQUIRE(kll_helper::floor_of_log2_of_fraction(1ULL << 63, 1) == 63);
+    REQUIRE(kll_helper::floor_of_log2_of_fraction(std::numeric_limits<uint64_t>::max(), 1) == 63);
+    REQUIRE(kll_helper::floor_of_log2_of_fraction(std::numeric_limits<uint64_t>::max(), 3) == 62);
   }
 
   SECTION("out of order split points, float") {
@@ -831,6 +834,123 @@ TEST_CASE("kll sketch", "[kll_sketch]") {
     REQUIRE(sb.get_n() == 3);
   }
 
+  SECTION("weighted update: zero weight") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    REQUIRE_THROWS_AS(sketch.update(1.0f, 0), std::invalid_argument);
+    REQUIRE(sketch.is_empty());
+  }
+
+  SECTION("weighted update: NaN") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    sketch.update(std::numeric_limits<float>::quiet_NaN(), 1000);
+    REQUIRE(sketch.is_empty());
+  }
+
+  SECTION("weighted update: same as repeated updates in exact mode") {
+    kll_float_sketch weighted(200, std::less<float>(), 0);
+    kll_float_sketch repeated(200, std::less<float>(), 0);
+    for (int i = 1; i <= 15; ++i) {
+      weighted.update(static_cast<float>(i), i);
+      for (int j = 0; j < i; ++j) repeated.update(static_cast<float>(i));
+    }
+    REQUIRE(weighted.get_n() == repeated.get_n());
+    REQUIRE(weighted.get_num_retained() == repeated.get_num_retained());
+    REQUIRE_FALSE(weighted.is_estimation_mode());
+    for (int i = 0; i <= 16; ++i) {
+      REQUIRE(weighted.get_rank(static_cast<float>(i)) == repeated.get_rank(static_cast<float>(i)));
+      REQUIRE(weighted.get_rank(static_cast<float>(i), false) == repeated.get_rank(static_cast<float>(i), false));
+    }
+  }
+
+  SECTION("weighted update: one item with large weight") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    const uint64_t weight = (1ULL << 40) + 12345;
+    sketch.update(7.0f, weight);
+    REQUIRE(sketch.get_n() == weight);
+    REQUIRE(sketch.get_num_retained() == 7); // number of bits set in the weight
+    REQUIRE(sketch.get_min_item() == 7.0f);
+    REQUIRE(sketch.get_max_item() == 7.0f);
+    REQUIRE(sketch.get_rank(7.0f) == 1);
+    REQUIRE(sketch.get_rank(7.0f, false) == 0);
+    REQUIRE(sketch.get_quantile(0.5) == 7.0f);
+
+    uint64_t total_weight = 0;
+    for (auto pair: sketch) total_weight += pair.second;
+    REQUIRE(total_weight == weight);
+  }
+
+  SECTION("weighted update: maximum weight") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    sketch.update(1.0f);
+    sketch.update(2.0f, std::numeric_limits<uint64_t>::max() - 1);
+    REQUIRE(sketch.get_n() == std::numeric_limits<uint64_t>::max());
+    REQUIRE(sketch.get_min_item() == 1.0f);
+    REQUIRE(sketch.get_max_item() == 2.0f);
+    REQUIRE(sketch.get_quantile(0.5) == 2.0f);
+
+    uint64_t total_weight = 0;
+    for (auto pair: sketch) total_weight += pair.second;
+    REQUIRE(total_weight == sketch.get_n());
+
+    auto bytes = sketch.serialize();
+    auto sketch2 = kll_float_sketch::deserialize(bytes.data(), bytes.size(), serde<float>(), std::less<float>(), 0);
+    REQUIRE(sketch2.get_n() == sketch.get_n());
+    REQUIRE(sketch2.get_num_retained() == sketch.get_num_retained());
+  }
+
+  SECTION("weighted update: large weights into a full sketch") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    for (int i = 0; i < 1000; ++i) sketch.update(static_cast<float>(i));
+    sketch.update(-1.0f, 1000);
+    sketch.update(2000.0f, 3000);
+    REQUIRE(sketch.get_n() == 5000);
+    REQUIRE(sketch.get_min_item() == -1.0f);
+    REQUIRE(sketch.get_max_item() == 2000.0f);
+    REQUIRE(sketch.get_rank(-1.0f) == Approx(0.2).margin(RANK_EPS_FOR_K_200));
+    REQUIRE(sketch.get_rank(2000.0f, false) == Approx(0.4).margin(RANK_EPS_FOR_K_200));
+  }
+
+  SECTION("weighted update: estimation mode") {
+    kll_float_sketch sketch(200, std::less<float>(), 0);
+    const int n = 10000;
+    std::vector<uint64_t> weights(n);
+    uint64_t total = 0;
+    for (int i = 0; i < n; ++i) {
+      weights[i] = static_cast<uint64_t>(i % 13) * 1000 + 1;
+      total += weights[i];
+      sketch.update(static_cast<float>(i), weights[i]);
+    }
+    REQUIRE(sketch.get_n() == total);
+    REQUIRE(sketch.is_estimation_mode());
+    REQUIRE(sketch.get_min_item() == 0);
+    REQUIRE(sketch.get_max_item() == n - 1);
+
+    uint64_t weight_below = 0;
+    for (int i = 0; i < n; ++i) {
+      const double true_rank = static_cast<double>(weight_below) / total;
+      REQUIRE(sketch.get_rank(static_cast<float>(i), false) == Approx(true_rank).margin(RANK_EPS_FOR_K_200));
+      weight_below += weights[i];
+    }
+
+    auto bytes = sketch.serialize();
+    auto sketch2 = kll_float_sketch::deserialize(bytes.data(), bytes.size(), serde<float>(), std::less<float>(), 0);
+    REQUIRE(sketch2.get_n() == sketch.get_n());
+    REQUIRE(sketch2.get_num_retained() == sketch.get_num_retained());
+    REQUIRE(sketch2.get_quantile(0.5) == sketch.get_quantile(0.5));
+  }
+
+  SECTION("weighted update: strings") {
+    kll_string_sketch sketch(200, std::less<std::string>(), 0);
+    sketch.update(std::string("b"), 3);
+    const std::string a("a");
+    sketch.update(a, 1000);
+    sketch.update(std::string("c"), 1ULL << 20);
+    REQUIRE(sketch.get_n() == 3 + 1000 + (1ULL << 20));
+    REQUIRE(sketch.get_min_item() == "a");
+    REQUIRE(sketch.get_max_item() == "c");
+    REQUIRE(sketch.get_rank("a") == Approx(1000.0 / sketch.get_n()).margin(RANK_EPS_FOR_K_200));
+  }
+
   // cleanup
   REQUIRE(test_allocator_total_bytes == 0);
 }