bug #1584: Improve random (avoid undefined behavior).

Eigen/src/Core/MathFunctions.h

@@ -617,20 +617,27 @@ struct random_default_impl<Scalar, false, true>
 {
   static inline Scalar run(const Scalar& x, const Scalar& y)
   {
-    typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX;
+    if (y <= x)
-    if(y<x)
       return x;
-    // the following difference might overflow on a 32 bits system,
+    // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself.
-    // but since y>=x the result converted to an unsigned long is still correct.
+    typedef typename make_unsigned<Scalar>::type ScalarU;
-    std::size_t range = ScalarX(y)-ScalarX(x);
+    // ScalarX is the widest of ScalarU and unsigned int.
-    std::size_t offset = 0;
+    // We'll deal only with ScalarX and unsigned int below thus avoiding signed
-    // rejection sampling
+    // types and arithmetic and signed overflows (which are undefined behavior).
-    std::size_t divisor = 1;
+    typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned>::type ScalarX;
-    std::size_t multiplier = 1;
+    // The following difference doesn't overflow, provided our integer types are two's
-    if(range<RAND_MAX) divisor = (std::size_t(RAND_MAX)+1)/(range+1);
+    // complement and have the same number of padding bits in signed and unsigned variants.
-    else               multiplier = 1 + range/(std::size_t(RAND_MAX)+1);
+    // This is the case in most modern implementations of C++.
+    ScalarX range = ScalarX(y) - ScalarX(x);
+    ScalarX offset = 0;
+    ScalarX divisor = 1;
+    ScalarX multiplier = 1;
+    const unsigned rand_max = RAND_MAX;
+    if (range <= rand_max) divisor = (rand_max + 1) / (range + 1);
+    else                   multiplier = 1 + range / (rand_max + 1);
+    // Rejection sampling.
     do {
-      offset = (std::size_t(std::rand()) * multiplier) / divisor;
+      offset = (unsigned(std::rand()) * multiplier) / divisor;
     } while (offset > range);
     return Scalar(ScalarX(x) + offset);
   }

Eigen/src/Core/util/Meta.h

@@ -97,17 +97,27 @@ template<> struct is_arithmetic<unsigned int>  { enum { value = true }; };
 template<> struct is_arithmetic<signed long>   { enum { value = true }; };
 template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
 
-template<typename T> struct is_integral        { enum { value = false }; };
+#if EIGEN_HAS_CXX11
-template<> struct is_integral<bool>            { enum { value = true }; };
+using std::make_unsigned;
-template<> struct is_integral<char>            { enum { value = true }; };
+#else
-template<> struct is_integral<signed char>     { enum { value = true }; };
+// TODO: Possibly improve this implementation of make_unsigned.
-template<> struct is_integral<unsigned char>   { enum { value = true }; };
+// It is currently used only by
-template<> struct is_integral<signed short>    { enum { value = true }; };
+// template<typename Scalar> struct random_default_impl<Scalar, false, true>.
-template<> struct is_integral<unsigned short>  { enum { value = true }; };
+template<typename> struct make_unsigned;
-template<> struct is_integral<signed int>      { enum { value = true }; };
+template<> struct make_unsigned<char>             { typedef unsigned char type; };
-template<> struct is_integral<unsigned int>    { enum { value = true }; };
+template<> struct make_unsigned<signed char>      { typedef unsigned char type; };
-template<> struct is_integral<signed long>     { enum { value = true }; };
+template<> struct make_unsigned<unsigned char>    { typedef unsigned char type; };
-template<> struct is_integral<unsigned long>   { enum { value = true }; };
+template<> struct make_unsigned<signed short>     { typedef unsigned short type; };
+template<> struct make_unsigned<unsigned short>   { typedef unsigned short type; };
+template<> struct make_unsigned<signed int>       { typedef unsigned int type; };
+template<> struct make_unsigned<unsigned int>     { typedef unsigned int type; };
+template<> struct make_unsigned<signed long>      { typedef unsigned long type; };
+template<> struct make_unsigned<unsigned long>    { typedef unsigned long type; };
+#if EIGEN_COMP_MSVC
+template<> struct make_unsigned<signed __int64>   { typedef unsigned __int64 type; };
+template<> struct make_unsigned<unsigned __int64> { typedef unsigned __int64 type; };
+#endif
+#endif
 
 template <typename T> struct add_const { typedef const T type; };
 template <typename T> struct add_const<T&> { typedef T& type; };