diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 0fde5c71e..e1b233d82 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -522,28 +522,24 @@ struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
 template<typename Scalar>
 struct random_default_impl<Scalar, false, true>
 {
-  typedef typename NumTraits<Scalar>::NonInteger NonInteger;
-
   static inline Scalar run(const Scalar& x, const Scalar& y)
   { 
     using std::max;
-    Scalar range = (max)(Scalar(0),Scalar(y-x));
-    Scalar offset = 0;
-    if(range<=RAND_MAX)
-    {
-      // rejection sampling
-      int divisor = RAND_MAX/(range+1);
+    using std::min;
+    typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX;
+    if(y<x)
+      return x;
+    std::size_t range = ScalarX(y)-ScalarX(x);
+    std::size_t offset = 0;
+    // rejection sampling
+    std::size_t divisor    = (range+RAND_MAX-1)/(range+1);
+    std::size_t multiplier = (range+RAND_MAX-1)/std::size_t(RAND_MAX);
 
-      do {
-        offset = Scalar(std::rand() / divisor);
-      } while (offset > range);
-    }
-    else
-    {
-      offset = std::rand() * range;
-    }
-    
-    return x + offset;
+    do {
+      offset = ( (std::size_t(std::rand()) * multiplier) / divisor );
+    } while (offset > range);
+
+    return Scalar(ScalarX(x) + offset);
   }
 
   static inline Scalar run()
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 1712b8718..734a0eb9b 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -139,6 +139,7 @@ endif(TEST_LIB)
 set_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT "Official")
 add_custom_target(BuildOfficial)
 
+ei_add_test(rand)
 ei_add_test(meta)
 ei_add_test(sizeof)
 ei_add_test(dynalloc)
diff --git a/test/rand.cpp b/test/rand.cpp
new file mode 100644
index 000000000..4e090cbad
--- /dev/null
+++ b/test/rand.cpp
@@ -0,0 +1,88 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename Scalar> Scalar check_in_range(Scalar x, Scalar y)
+{
+  Scalar r = internal::random<Scalar>(x,y);
+  VERIFY(r>=x);
+  if(y>=x)
+  {
+    VERIFY(r<=y);
+  }
+  return r;
+}
+
+template<typename Scalar> void check_all_in_range(Scalar x, Scalar y)
+{
+  Array<int,1,Dynamic> mask(y-x+1);
+  mask.fill(0);
+  long n = (y-x+1)*32;
+  for(long k=0; k<n; ++k)
+  {
+    mask( check_in_range(x,y)-x )++;
+  }
+  VERIFY( (mask>0).all() );
+}
+
+void test_rand()
+{
+  for(int i = 0; i < g_repeat*10; i++) {
+    CALL_SUBTEST(check_in_range<float>(10,11));
+    CALL_SUBTEST(check_in_range<float>(1.24234523,1.24234523));
+    CALL_SUBTEST(check_in_range<float>(-1,1));
+    CALL_SUBTEST(check_in_range<float>(-1432.2352,-1432.2352));
+    
+    CALL_SUBTEST(check_in_range<double>(10,11));
+    CALL_SUBTEST(check_in_range<double>(1.24234523,1.24234523));
+    CALL_SUBTEST(check_in_range<double>(-1,1));
+    CALL_SUBTEST(check_in_range<double>(-1432.2352,-1432.2352));
+    
+    
+    CALL_SUBTEST(check_in_range<int>(0,-1));
+    CALL_SUBTEST(check_in_range<short>(0,-1));
+    CALL_SUBTEST(check_in_range<long>(0,-1));
+    CALL_SUBTEST(check_in_range<int>(-673456,673456));
+    CALL_SUBTEST(check_in_range<short>(-24345,24345));
+    CALL_SUBTEST(check_in_range<long>(-6734565664234,6734565664234));
+  }
+  
+  char char_offset = (std::min)(g_repeat,64);
+  CALL_SUBTEST(check_all_in_range<char>(11,11));
+  CALL_SUBTEST(check_all_in_range<char>(11,11+char_offset));
+  CALL_SUBTEST(check_all_in_range<char>(-5,5));
+  CALL_SUBTEST(check_all_in_range<char>(-11-char_offset,-11));
+  CALL_SUBTEST(check_all_in_range<char>(-126,-126+char_offset));
+  CALL_SUBTEST(check_all_in_range<char>(126-char_offset,126));
+  CALL_SUBTEST(check_all_in_range<char>(-126,126));
+  
+  char short_offset = (std::min)(g_repeat,16000);
+  CALL_SUBTEST(check_all_in_range<short>(11,11));
+  CALL_SUBTEST(check_all_in_range<short>(11,11+short_offset));
+  CALL_SUBTEST(check_all_in_range<short>(-5,5));
+  CALL_SUBTEST(check_all_in_range<short>(-11-short_offset,-11));
+  CALL_SUBTEST(check_all_in_range<short>(-24345,-24345+short_offset));
+  CALL_SUBTEST(check_all_in_range<short>(24345,24345+short_offset));
+  
+    
+  CALL_SUBTEST(check_all_in_range<int>(11,11));
+  CALL_SUBTEST(check_all_in_range<int>(11,11+g_repeat));
+  CALL_SUBTEST(check_all_in_range<int>(-5,5));
+  CALL_SUBTEST(check_all_in_range<int>(-11-g_repeat,-11));
+  CALL_SUBTEST(check_all_in_range<int>(-673456,-673456+g_repeat));
+  CALL_SUBTEST(check_all_in_range<int>(673456,673456+g_repeat));
+  
+  CALL_SUBTEST(check_all_in_range<long>(11,11));
+  CALL_SUBTEST(check_all_in_range<long>(11,11+g_repeat));
+  CALL_SUBTEST(check_all_in_range<long>(-5,5));
+  CALL_SUBTEST(check_all_in_range<long>(-11-g_repeat,-11));
+  CALL_SUBTEST(check_all_in_range<long>(-6734565664234,-6734565664234+g_repeat));
+  CALL_SUBTEST(check_all_in_range<long>(6734565664234,6734565664234+g_repeat));
+}