Index: benchmarks/algorithms.bench.cpp
===================================================================
--- benchmarks/algorithms.bench.cpp
+++ benchmarks/algorithms.bench.cpp
@@ -58,5 +58,84 @@
 BENCHMARK_CAPTURE(BM_Sort, single_element_strings,
     getDuplicateStringInputs)->Arg(TestNumInputs);
 
+template <typename GenInputs, typename Alg>
+void do_binary_search_benchmark(benchmark::State& st, GenInputs gen, Alg alg)
+{
+    using ValueType = typename decltype(gen(0))::value_type;
+    auto in = gen(st.range(0));
+    std::sort(in.begin(), in.end());
+
+    const auto every_10_percentile = [&]() -> std::vector<ValueType*>  {
+        size_t step = in.size() / 10;
+
+        if (step == 0) {
+            st.SkipWithError("Input doesn't contain enough elements");
+            return {};
+        }
+
+        std::vector<ValueType*> res;
+        for (size_t i = 0; i < in.size(); i += step)
+            res.push_back(&in[i]);
+
+        return res;
+    }();
+
+    for (auto _ : st)
+    {
+        for (auto* test : every_10_percentile)
+          benchmark::DoNotOptimize(alg(in.begin(), in.end(), *test));
+    }
+}
+
+template <typename GenInputs>
+void BM_LowerBound(benchmark::State& st, GenInputs gen)
+{
+    do_binary_search_benchmark(st, gen, [](auto f, auto l, const auto& v) {
+        return std::lower_bound(f, l, v);
+    });
+}
+
+void BM_LowerBoundSeanParent(benchmark::State& state) {
+  int a[1024];
+  std::iota(std::begin(a), std::end(a), 0);
+  // Code before the loop is not measured
+  for (auto _ : state) {
+    auto p = std::lower_bound(std::begin(a), std::end(a), 272291);
+    // Make sure the variable is not optimized away by compiler
+    benchmark::DoNotOptimize(p);
+
+  }
+}
+
+BENCHMARK_CAPTURE(BM_LowerBound, random_int32, getRandomIntegerInputs<int32_t>)
+    ->Arg(TestNumInputs)                    // Small int32_t vector
+    ->Arg(TestNumInputs * TestNumInputs);   // Big int32_t   vector
+
+BENCHMARK_CAPTURE(BM_LowerBound, random_int64, getRandomIntegerInputs<int64_t>)
+    ->Arg(TestNumInputs);  // Small int64_t vector. Should also represent pointers.
+
+BENCHMARK_CAPTURE(BM_LowerBound, random_strings, getRandomStringInputs)
+    ->Arg(TestNumInputs);  // Small string vector. What happens if the comparison is not very cheap.
+
+BENCHMARK(BM_LowerBoundSeanParent);
+
+template <typename GenInputs>
+void BM_EqualRange(benchmark::State& st, GenInputs gen)
+{
+    do_binary_search_benchmark(st, gen, [](auto f, auto l, const auto& v) {
+        return std::equal_range(f, l, v);
+    });
+}
+
+BENCHMARK_CAPTURE(BM_EqualRange, random_int32, getRandomIntegerInputs<int32_t>)
+    ->Arg(TestNumInputs)                    // Small int32_t vector
+    ->Arg(TestNumInputs * TestNumInputs);   // Big int32_t   vector
+
+BENCHMARK_CAPTURE(BM_EqualRange, random_int64, getRandomIntegerInputs<int64_t>)
+    ->Arg(TestNumInputs);  // Small int64_t vector. Should also represent pointers.
+
+BENCHMARK_CAPTURE(BM_EqualRange, random_strings, getRandomStringInputs)
+    ->Arg(TestNumInputs);  // Small string vector. What happens if the comparison is not very cheap.
+
 
 BENCHMARK_MAIN();
Index: include/algorithm
===================================================================
--- include/algorithm
+++ include/algorithm
@@ -750,6 +750,32 @@
     bool operator()(const _T1& __x, const _T2& __y) {return __p_(__y, __x);}
 };
 
+// Perform division by two quickly for positive integers (llvm.org/PR39129)
+
+template <typename _Integral>
+_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
+typename enable_if
+<
+    is_integral<_Integral>::value,
+    _Integral
+>::type
+__half_positive(_Integral __value)
+{
+    return static_cast<_Integral>(static_cast<typename make_unsigned<_Integral>::type>(__value) / 2);
+}
+
+template <typename _Tp>
+_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
+typename enable_if
+<
+    !is_integral<_Tp>::value,
+    _Tp
+>::type
+__half_positive(_Tp __value)
+{
+    return __value / 2;
+}
+
 #ifdef _LIBCPP_DEBUG
 
 template <class _Compare>
@@ -3202,7 +3228,7 @@
     difference_type __len = _VSTD::distance(__first, __last);
     while (__len != 0)
     {
-        difference_type __l2 = __len / 2;
+        difference_type __l2 = _VSTD::__half_positive(__len);
         _ForwardIterator __m = __first;
         _VSTD::advance(__m, __l2);
         if (__pred(*__m))
@@ -4069,7 +4095,7 @@
     difference_type __len = _VSTD::distance(__first, __last);
     while (__len != 0)
     {
-        difference_type __l2 = __len / 2;
+        difference_type __l2 = _VSTD::__half_positive(__len);
         _ForwardIterator __m = __first;
         _VSTD::advance(__m, __l2);
         if (__comp(*__m, __value_))
@@ -4111,7 +4137,7 @@
     difference_type __len = _VSTD::distance(__first, __last);
     while (__len != 0)
     {
-        difference_type __l2 = __len / 2;
+        difference_type __l2 = _VSTD::__half_positive(__len);
         _ForwardIterator __m = __first;
         _VSTD::advance(__m, __l2);
         if (__comp(__value_, *__m))
@@ -4153,7 +4179,7 @@
     difference_type __len = _VSTD::distance(__first, __last);
     while (__len != 0)
     {
-        difference_type __l2 = __len / 2;
+        difference_type __l2 = _VSTD::__half_positive(__len);
         _ForwardIterator __m = __first;
         _VSTD::advance(__m, __l2);
         if (__comp(*__m, __value_))