Index: libcxx/include/__random/uniform_int_distribution.h
===================================================================
--- libcxx/include/__random/uniform_int_distribution.h
+++ libcxx/include/__random/uniform_int_distribution.h
@@ -237,8 +237,12 @@
         return __p.a();
     const size_t _Dt = numeric_limits<_UIntType>::digits;
     typedef __independent_bits_engine<_URNG, _UIntType> _Eng;
+    typedef typename _URNG::result_type _URNG_RT;
+    _URNG_RT _Rg = _URNG::max() - _URNG::min() + _URNG_RT(1);
     if (_Rp == 0)
         return static_cast<result_type>(_Eng(__g, _Dt)());
+    else if (_Rg != 0 && _Rg % _Rp == 0)
+        return static_cast<result_type>(__p.a() + (__g() / (_Rg / _Rp)));
     size_t __w = _Dt - __countl_zero(_Rp) - 1;
     if ((_Rp & (numeric_limits<_UIntType>::max() >> (_Dt - __w))) != 0)
         ++__w;
Index: libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/no_wasted_entropy.pass.cpp
===================================================================
--- /dev/null
+++ libcxx/test/std/numerics/rand/rand.dis/rand.dist.uni/rand.dist.uni.int/no_wasted_entropy.pass.cpp
@@ -0,0 +1,80 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// UNSUPPORTED: c++03
+
+// <random>
+
+// template<class _IntType = int>
+// class uniform_int_distribution
+
+// template<class _URNG> result_type operator()(_URNG& g);
+
+#include <random>
+#include <cassert>
+
+#include "test_macros.h"
+
+// Cycles through the range [0, 12) backwards.
+struct uniform_rbg {
+    using result_type = unsigned;
+
+    static constexpr unsigned min() noexcept { return 0; }
+    static constexpr unsigned max() noexcept { return 11; }
+
+    unsigned operator()() {
+        unsigned result = 11 - count;
+        count = (count + 1) % 12;
+        ++num_calls;
+        return result;
+    }
+
+    unsigned count = 0;
+    unsigned num_calls = 0;
+};
+
+// Returns numbers in the range [0, 24) which always have the lowest two bits set.
+struct non_uniform_rbg {
+    using result_type = unsigned;
+
+    static constexpr unsigned min() noexcept { return 0; }
+    static constexpr unsigned max() noexcept { return 23; }
+
+    unsigned operator()() {
+        // Bail out in case of an endless loop:
+        assert(num_calls <= 100);
+
+        unsigned result = count | 3;
+        count = (count + 1) % 24;
+        ++num_calls;
+        return result;
+    }
+
+    unsigned count = 0;
+    unsigned num_calls = 0;
+};
+
+int main() {
+    {
+        uniform_rbg urbg;
+        std::uniform_int_distribution<int> uni(0, 2);
+        int i = uni(urbg);
+        assert(0 <= i && i < 3);
+        assert(urbg.num_calls == 1);
+    }
+
+    {
+        non_uniform_rbg nurbg;
+        std::uniform_int_distribution<int> uni(0, 2);
+        int i = uni(nurbg);
+        assert(0 <= i && i < 3);
+        assert(nurbg.num_calls == 1);
+    }
+
+    return 0;
+}